diff --git a/.gitignore b/.gitignore new file mode 100644 index 000000000..bb4c651eb --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +lectures/_build \ No newline at end of file diff --git a/lectures/_build/.doctrees/environment.pickle b/lectures/_build/.doctrees/environment.pickle deleted file mode 100644 index 2e4564c17..000000000 Binary files a/lectures/_build/.doctrees/environment.pickle and /dev/null differ diff --git a/lectures/_build/.doctrees/geom_series.doctree b/lectures/_build/.doctrees/geom_series.doctree deleted file mode 100644 index b72b106da..000000000 Binary files a/lectures/_build/.doctrees/geom_series.doctree and /dev/null differ diff --git a/lectures/_build/.doctrees/glue_cache.json b/lectures/_build/.doctrees/glue_cache.json deleted file mode 100644 index 9e26dfeeb..000000000 --- a/lectures/_build/.doctrees/glue_cache.json +++ /dev/null @@ -1 +0,0 @@ -{} \ No newline at end of file diff --git a/lectures/_build/.doctrees/intro.doctree b/lectures/_build/.doctrees/intro.doctree deleted file mode 100644 index 733ace9d7..000000000 Binary files a/lectures/_build/.doctrees/intro.doctree and /dev/null differ diff --git a/lectures/_build/.doctrees/scalar_dynam.doctree b/lectures/_build/.doctrees/scalar_dynam.doctree deleted file mode 100644 index 3d572b7f5..000000000 Binary files a/lectures/_build/.doctrees/scalar_dynam.doctree and /dev/null differ diff --git a/lectures/_build/.doctrees/schelling.doctree b/lectures/_build/.doctrees/schelling.doctree deleted file mode 100644 index b343afd91..000000000 Binary files a/lectures/_build/.doctrees/schelling.doctree and /dev/null differ diff --git a/lectures/_build/.doctrees/short_path.doctree b/lectures/_build/.doctrees/short_path.doctree deleted file mode 100644 index 21fe1aab8..000000000 Binary files a/lectures/_build/.doctrees/short_path.doctree and /dev/null differ diff --git a/lectures/_build/.doctrees/status.doctree b/lectures/_build/.doctrees/status.doctree deleted file mode 100644 index 288572522..000000000 Binary files a/lectures/_build/.doctrees/status.doctree and /dev/null differ diff --git a/lectures/_build/.doctrees/troubleshooting.doctree b/lectures/_build/.doctrees/troubleshooting.doctree deleted file mode 100644 index 6f9364080..000000000 Binary files a/lectures/_build/.doctrees/troubleshooting.doctree and /dev/null differ diff --git a/lectures/_build/.doctrees/zreferences.doctree b/lectures/_build/.doctrees/zreferences.doctree deleted file mode 100644 index 8c81bc5e6..000000000 Binary files a/lectures/_build/.doctrees/zreferences.doctree and /dev/null differ diff --git a/lectures/_build/.jupyter_cache/executed/170074b5d9d4045ef1d2e1b41f5a7037/base.ipynb b/lectures/_build/.jupyter_cache/executed/170074b5d9d4045ef1d2e1b41f5a7037/base.ipynb deleted file mode 100644 index 8319aa317..000000000 --- a/lectures/_build/.jupyter_cache/executed/170074b5d9d4045ef1d2e1b41f5a7037/base.ipynb +++ /dev/null @@ -1,492 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "dbe8981c", - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "plt.rcParams[\"figure.figsize\"] = (11, 5) #set default figure size\n", - "import numpy as np\n", - "import sympy as sym\n", - "from sympy import init_printing, latex\n", - "from matplotlib import cm\n", - "from mpl_toolkits.mplot3d import Axes3D" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "f2100093", - "metadata": {}, - "outputs": [], - "source": [ - "# True present value of a finite lease\n", - "def finite_lease_pv_true(T, g, r, x_0):\n", - " G = (1 + g)\n", - " R = (1 + r)\n", - " return (x_0 * (1 - G**(T + 1) * R**(-T - 1))) / (1 - G * R**(-1))\n", - "# First approximation for our finite lease\n", - "\n", - "def finite_lease_pv_approx_1(T, g, r, x_0):\n", - " p = x_0 * (T + 1) + x_0 * r * g * (T + 1) / (r - g)\n", - " return p\n", - "\n", - "# Second approximation for our finite lease\n", - "def finite_lease_pv_approx_2(T, g, r, x_0):\n", - " return (x_0 * (T + 1))\n", - "\n", - "# Infinite lease\n", - "def infinite_lease(g, r, x_0):\n", - " G = (1 + g)\n", - " R = (1 + r)\n", - " return x_0 / (1 - G * R**(-1))" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "a792020d", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "def plot_function(axes, x_vals, func, args):\n", - " axes.plot(x_vals, func(*args), label=func.__name__)\n", - "\n", - "T_max = 50\n", - "\n", - "T = np.arange(0, T_max+1)\n", - "g = 0.02\n", - "r = 0.03\n", - "x_0 = 1\n", - "\n", - "our_args = (T, g, r, x_0)\n", - "funcs = [finite_lease_pv_true,\n", - " finite_lease_pv_approx_1,\n", - " finite_lease_pv_approx_2]\n", - " ## the three functions we want to compare\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Finite Lease Present Value $T$ Periods Ahead')\n", - "for f in funcs:\n", - " plot_function(ax, T, f, our_args)\n", - "ax.legend()\n", - "ax.set_xlabel('$T$ Periods Ahead')\n", - "ax.set_ylabel('Present Value, $p_0$')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "957e0eb4", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Convergence of infinite and finite\n", - "T_max = 1000\n", - "T = np.arange(0, T_max+1)\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Infinite and Finite Lease Present Value $T$ Periods Ahead')\n", - "f_1 = finite_lease_pv_true(T, g, r, x_0)\n", - "f_2 = np.full(T_max+1, infinite_lease(g, r, x_0))\n", - "ax.plot(T, f_1, label='T-period lease PV')\n", - "ax.plot(T, f_2, '--', label='Infinite lease PV')\n", - "ax.set_xlabel('$T$ Periods Ahead')\n", - "ax.set_ylabel('Present Value, $p_0$')\n", - "ax.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "d1003ceb", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# First view\n", - "# Changing r and g\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Value of lease of length $T$')\n", - "ax.set_ylabel('Present Value, $p_0$')\n", - "ax.set_xlabel('$T$ periods ahead')\n", - "T_max = 10\n", - "T=np.arange(0, T_max+1)\n", - "\n", - "rs, gs = (0.9, 0.5, 0.4001, 0.4), (0.4, 0.4, 0.4, 0.5),\n", - "comparisons = ('$\\gg$', '$>$', r'$\\approx$', '$<$')\n", - "for r, g, comp in zip(rs, gs, comparisons):\n", - " ax.plot(finite_lease_pv_true(T, g, r, x_0), label=f'r(={r}) {comp} g(={g})')\n", - "\n", - "ax.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "0b4e8184", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Second view\n", - "fig = plt.figure()\n", - "T = 3\n", - "ax = plt.subplot(projection='3d')\n", - "r = np.arange(0.01, 0.99, 0.005)\n", - "g = np.arange(0.011, 0.991, 0.005)\n", - "\n", - "rr, gg = np.meshgrid(r, g)\n", - "z = finite_lease_pv_true(T, gg, rr, x_0)\n", - "\n", - "# Removes points where undefined\n", - "same = (rr == gg)\n", - "z[same] = np.nan\n", - "surf = ax.plot_surface(rr, gg, z, cmap=cm.coolwarm,\n", - " antialiased=True, clim=(0, 15))\n", - "fig.colorbar(surf, shrink=0.5, aspect=5)\n", - "ax.set_xlabel('$r$')\n", - "ax.set_ylabel('$g$')\n", - "ax.set_zlabel('Present Value, $p_0$')\n", - "ax.view_init(20, 10)\n", - "ax.set_title('Three Period Lease PV with Varying $g$ and $r$')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "1bc6d81f", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Our formula is:\n" - ] - }, - { - "data": { - "text/latex": [ - "$\\displaystyle \\frac{x_{0}}{- \\frac{g + 1}{r + 1} + 1}$" - ], - "text/plain": [ - " x₀ \n", - "───────────\n", - " g + 1 \n", - "- ───── + 1\n", - " r + 1 " - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Creates algebraic symbols that can be used in an algebraic expression\n", - "g, r, x0 = sym.symbols('g, r, x0')\n", - "G = (1 + g)\n", - "R = (1 + r)\n", - "p0 = x0 / (1 - G * R**(-1))\n", - "init_printing(use_latex='mathjax')\n", - "print('Our formula is:')\n", - "p0" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "aad09aba", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "dp0 / dg is:\n" - ] - }, - { - "data": { - "text/latex": [ - "$\\displaystyle \\frac{x_{0}}{\\left(r + 1\\right) \\left(- \\frac{g + 1}{r + 1} + 1\\right)^{2}}$" - ], - "text/plain": [ - " x₀ \n", - "──────────────────────\n", - " 2\n", - " ⎛ g + 1 ⎞ \n", - "(r + 1)⋅⎜- ───── + 1⎟ \n", - " ⎝ r + 1 ⎠ " - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "print('dp0 / dg is:')\n", - "dp_dg = sym.diff(p0, g)\n", - "dp_dg" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "505e6b2d", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "dp0 / dr is:\n" - ] - }, - { - "data": { - "text/latex": [ - "$\\displaystyle - \\frac{x_{0} \\left(g + 1\\right)}{\\left(r + 1\\right)^{2} \\left(- \\frac{g + 1}{r + 1} + 1\\right)^{2}}$" - ], - "text/plain": [ - " -x₀⋅(g + 1) \n", - "───────────────────────\n", - " 2\n", - " 2 ⎛ g + 1 ⎞ \n", - "(r + 1) ⋅⎜- ───── + 1⎟ \n", - " ⎝ r + 1 ⎠ " - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "print('dp0 / dr is:')\n", - "dp_dr = sym.diff(p0, r)\n", - "dp_dr" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "3794600b", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Function that calculates a path of y\n", - "def calculate_y(i, b, g, T, y_init):\n", - " y = np.zeros(T+1)\n", - " y[0] = i + b * y_init + g\n", - " for t in range(1, T+1):\n", - " y[t] = b * y[t-1] + i + g\n", - " return y\n", - "\n", - "# Initial values\n", - "i_0 = 0.3\n", - "g_0 = 0.3\n", - "# 2/3 of income goes towards consumption\n", - "b = 2/3\n", - "y_init = 0\n", - "T = 100\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Path of Aggregate Output Over Time')\n", - "ax.set_xlabel('$t$')\n", - "ax.set_ylabel('$y_t$')\n", - "ax.plot(np.arange(0, T+1), calculate_y(i_0, b, g_0, T, y_init))\n", - "# Output predicted by geometric series\n", - "ax.hlines(i_0 / (1 - b) + g_0 / (1 - b), xmin=-1, xmax=101, linestyles='--')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "005825a5", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "bs = (1/3, 2/3, 5/6, 0.9)\n", - "\n", - "fig,ax = plt.subplots()\n", - "ax.set_title('Changing Consumption as a Fraction of Income')\n", - "ax.set_ylabel('$y_t$')\n", - "ax.set_xlabel('$t$')\n", - "x = np.arange(0, T+1)\n", - "for b in bs:\n", - " y = calculate_y(i_0, b, g_0, T, y_init)\n", - " ax.plot(x, y, label=r'$b=$'+f\"{b:.2f}\")\n", - "ax.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "7ffa8394", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 10))\n", - "fig.subplots_adjust(hspace=0.3)\n", - "\n", - "x = np.arange(0, T+1)\n", - "values = [0.3, 0.4]\n", - "\n", - "for i in values:\n", - " y = calculate_y(i, b, g_0, T, y_init)\n", - " ax1.plot(x, y, label=f\"i={i}\")\n", - "for g in values:\n", - " y = calculate_y(i_0, b, g, T, y_init)\n", - " ax2.plot(x, y, label=f\"g={g}\")\n", - "\n", - "axes = ax1, ax2\n", - "param_labels = \"Investment\", \"Government Spending\"\n", - "for ax, param in zip(axes, param_labels):\n", - " ax.set_title(f'An Increase in {param} on Output')\n", - " ax.legend(loc =\"lower right\")\n", - " ax.set_ylabel('$y_t$')\n", - " ax.set_xlabel('$t$')\n", - "plt.show()" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 51, - 60, - 655, - 676, - 682, - 707, - 716, - 730, - 739, - 756, - 768, - 791, - 806, - 817, - 823, - 827, - 842, - 867, - 876, - 889, - 896, - 918 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/.jupyter_cache/executed/2bb907f4829d3669796ae565b04f49a3/base.ipynb b/lectures/_build/.jupyter_cache/executed/2bb907f4829d3669796ae565b04f49a3/base.ipynb deleted file mode 100644 index 60b85a79b..000000000 --- a/lectures/_build/.jupyter_cache/executed/2bb907f4829d3669796ae565b04f49a3/base.ipynb +++ /dev/null @@ -1,386 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "99bf1576", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "d7b3fa8e", - "metadata": {}, - "outputs": [], - "source": [ - "from numpy import inf\n", - "\n", - "Q = np.array([[inf, 1, 5, 3, inf, inf, inf],\n", - " [inf, inf, inf, 9, 6, inf, inf],\n", - " [inf, inf, inf, inf, inf, 2, inf],\n", - " [inf, inf, inf, inf, inf, 4, 8],\n", - " [inf, inf, inf, inf, inf, inf, 4],\n", - " [inf, inf, inf, inf, inf, inf, 1],\n", - " [inf, inf, inf, inf, inf, inf, 0]])" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "b67652e5", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The cost-to-go function is [ 8 10 3 5 4 1 0]\n" - ] - } - ], - "source": [ - "nodes = range(7) # Nodes = 0, 1, ..., 6\n", - "J = np.zeros_like(nodes, dtype=int) # Initial guess\n", - "next_J = np.empty_like(nodes, dtype=int) # Stores updated guess\n", - "\n", - "max_iter = 500\n", - "i = 0\n", - "\n", - "while i < max_iter:\n", - " for v in nodes:\n", - " # minimize Q[v, w] + J[w] over all choices of w\n", - " lowest_cost = inf\n", - " for w in nodes:\n", - " cost = Q[v, w] + J[w]\n", - " if cost < lowest_cost:\n", - " lowest_cost = cost\n", - " next_J[v] = lowest_cost\n", - " if np.equal(next_J, J).all():\n", - " break\n", - " else:\n", - " J[:] = next_J # Copy contents of next_J to J\n", - " i += 1\n", - "\n", - "print(\"The cost-to-go function is\", J)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "8a4eac05", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Writing graph.txt\n" - ] - } - ], - "source": [ - "%%file graph.txt\n", - "node0, node1 0.04, node8 11.11, node14 72.21\n", - "node1, node46 1247.25, node6 20.59, node13 64.94\n", - "node2, node66 54.18, node31 166.80, node45 1561.45\n", - "node3, node20 133.65, node6 2.06, node11 42.43\n", - "node4, node75 3706.67, node5 0.73, node7 1.02\n", - "node5, node45 1382.97, node7 3.33, node11 34.54\n", - "node6, node31 63.17, node9 0.72, node10 13.10\n", - "node7, node50 478.14, node9 3.15, node10 5.85\n", - "node8, node69 577.91, node11 7.45, node12 3.18\n", - "node9, node70 2454.28, node13 4.42, node20 16.53\n", - "node10, node89 5352.79, node12 1.87, node16 25.16\n", - "node11, node94 4961.32, node18 37.55, node20 65.08\n", - "node12, node84 3914.62, node24 34.32, node28 170.04\n", - "node13, node60 2135.95, node38 236.33, node40 475.33\n", - "node14, node67 1878.96, node16 2.70, node24 38.65\n", - "node15, node91 3597.11, node17 1.01, node18 2.57\n", - "node16, node36 392.92, node19 3.49, node38 278.71\n", - "node17, node76 783.29, node22 24.78, node23 26.45\n", - "node18, node91 3363.17, node23 16.23, node28 55.84\n", - "node19, node26 20.09, node20 0.24, node28 70.54\n", - "node20, node98 3523.33, node24 9.81, node33 145.80\n", - "node21, node56 626.04, node28 36.65, node31 27.06\n", - "node22, node72 1447.22, node39 136.32, node40 124.22\n", - "node23, node52 336.73, node26 2.66, node33 22.37\n", - "node24, node66 875.19, node26 1.80, node28 14.25\n", - "node25, node70 1343.63, node32 36.58, node35 45.55\n", - "node26, node47 135.78, node27 0.01, node42 122.00\n", - "node27, node65 480.55, node35 48.10, node43 246.24\n", - "node28, node82 2538.18, node34 21.79, node36 15.52\n", - "node29, node64 635.52, node32 4.22, node33 12.61\n", - "node30, node98 2616.03, node33 5.61, node35 13.95\n", - "node31, node98 3350.98, node36 20.44, node44 125.88\n", - "node32, node97 2613.92, node34 3.33, node35 1.46\n", - "node33, node81 1854.73, node41 3.23, node47 111.54\n", - "node34, node73 1075.38, node42 51.52, node48 129.45\n", - "node35, node52 17.57, node41 2.09, node50 78.81\n", - "node36, node71 1171.60, node54 101.08, node57 260.46\n", - "node37, node75 269.97, node38 0.36, node46 80.49\n", - "node38, node93 2767.85, node40 1.79, node42 8.78\n", - "node39, node50 39.88, node40 0.95, node41 1.34\n", - "node40, node75 548.68, node47 28.57, node54 53.46\n", - "node41, node53 18.23, node46 0.28, node54 162.24\n", - "node42, node59 141.86, node47 10.08, node72 437.49\n", - "node43, node98 2984.83, node54 95.06, node60 116.23\n", - "node44, node91 807.39, node46 1.56, node47 2.14\n", - "node45, node58 79.93, node47 3.68, node49 15.51\n", - "node46, node52 22.68, node57 27.50, node67 65.48\n", - "node47, node50 2.82, node56 49.31, node61 172.64\n", - "node48, node99 2564.12, node59 34.52, node60 66.44\n", - "node49, node78 53.79, node50 0.51, node56 10.89\n", - "node50, node85 251.76, node53 1.38, node55 20.10\n", - "node51, node98 2110.67, node59 23.67, node60 73.79\n", - "node52, node94 1471.80, node64 102.41, node66 123.03\n", - "node53, node72 22.85, node56 4.33, node67 88.35\n", - "node54, node88 967.59, node59 24.30, node73 238.61\n", - "node55, node84 86.09, node57 2.13, node64 60.80\n", - "node56, node76 197.03, node57 0.02, node61 11.06\n", - "node57, node86 701.09, node58 0.46, node60 7.01\n", - "node58, node83 556.70, node64 29.85, node65 34.32\n", - "node59, node90 820.66, node60 0.72, node71 0.67\n", - "node60, node76 48.03, node65 4.76, node67 1.63\n", - "node61, node98 1057.59, node63 0.95, node64 4.88\n", - "node62, node91 132.23, node64 2.94, node76 38.43\n", - "node63, node66 4.43, node72 70.08, node75 56.34\n", - "node64, node80 47.73, node65 0.30, node76 11.98\n", - "node65, node94 594.93, node66 0.64, node73 33.23\n", - "node66, node98 395.63, node68 2.66, node73 37.53\n", - "node67, node82 153.53, node68 0.09, node70 0.98\n", - "node68, node94 232.10, node70 3.35, node71 1.66\n", - "node69, node99 247.80, node70 0.06, node73 8.99\n", - "node70, node76 27.18, node72 1.50, node73 8.37\n", - "node71, node89 104.50, node74 8.86, node91 284.64\n", - "node72, node76 15.32, node84 102.77, node92 133.06\n", - "node73, node83 52.22, node76 1.40, node90 243.00\n", - "node74, node81 1.07, node76 0.52, node78 8.08\n", - "node75, node92 68.53, node76 0.81, node77 1.19\n", - "node76, node85 13.18, node77 0.45, node78 2.36\n", - "node77, node80 8.94, node78 0.98, node86 64.32\n", - "node78, node98 355.90, node81 2.59\n", - "node79, node81 0.09, node85 1.45, node91 22.35\n", - "node80, node92 121.87, node88 28.78, node98 264.34\n", - "node81, node94 99.78, node89 39.52, node92 99.89\n", - "node82, node91 47.44, node88 28.05, node93 11.99\n", - "node83, node94 114.95, node86 8.75, node88 5.78\n", - "node84, node89 19.14, node94 30.41, node98 121.05\n", - "node85, node97 94.51, node87 2.66, node89 4.90\n", - "node86, node97 85.09\n", - "node87, node88 0.21, node91 11.14, node92 21.23\n", - "node88, node93 1.31, node91 6.83, node98 6.12\n", - "node89, node97 36.97, node99 82.12\n", - "node90, node96 23.53, node94 10.47, node99 50.99\n", - "node91, node97 22.17\n", - "node92, node96 10.83, node97 11.24, node99 34.68\n", - "node93, node94 0.19, node97 6.71, node99 32.77\n", - "node94, node98 5.91, node96 2.03\n", - "node95, node98 6.17, node99 0.27\n", - "node96, node98 3.32, node97 0.43, node99 5.87\n", - "node97, node98 0.30\n", - "node98, node99 0.33\n", - "node99," - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "5d57bcc7", - "metadata": {}, - "outputs": [], - "source": [ - "num_nodes = 100\n", - "destination_node = 99\n", - "\n", - "def map_graph_to_distance_matrix(in_file):\n", - "\n", - " # First let's set of the distance matrix Q with inf everywhere\n", - " Q = np.full((num_nodes, num_nodes), np.inf)\n", - "\n", - " # Now we read in the data and modify Q\n", - " with open(in_file) as infile:\n", - " for line in infile:\n", - " elements = line.split(',')\n", - " node = elements.pop(0)\n", - " node = int(node[4:]) # convert node description to integer\n", - " if node != destination_node:\n", - " for element in elements:\n", - " destination, cost = element.split()\n", - " destination = int(destination[4:])\n", - " Q[node, destination] = float(cost)\n", - " Q[destination_node, destination_node] = 0\n", - " return Q" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "9f115617", - "metadata": {}, - "outputs": [], - "source": [ - "def bellman(J, Q):\n", - " num_nodes = Q.shape[0]\n", - " next_J = np.empty_like(J)\n", - " for v in range(num_nodes):\n", - " next_J[v] = np.min(Q[v, :] + J)\n", - " return next_J\n", - "\n", - "\n", - "def compute_cost_to_go(Q):\n", - " num_nodes = Q.shape[0]\n", - " J = np.zeros(num_nodes) # Initial guess\n", - " max_iter = 500\n", - " i = 0\n", - "\n", - " while i < max_iter:\n", - " next_J = bellman(J, Q)\n", - " if np.allclose(next_J, J):\n", - " break\n", - " else:\n", - " J[:] = next_J # Copy contents of next_J to J\n", - " i += 1\n", - "\n", - " return(J)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "50a572a7", - "metadata": {}, - "outputs": [], - "source": [ - "def print_best_path(J, Q):\n", - " sum_costs = 0\n", - " current_node = 0\n", - " while current_node != destination_node:\n", - " print(current_node)\n", - " # Move to the next node and increment costs\n", - " next_node = np.argmin(Q[current_node, :] + J)\n", - " sum_costs += Q[current_node, next_node]\n", - " current_node = next_node\n", - "\n", - " print(destination_node)\n", - " print('Cost: ', sum_costs)" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "69240f46", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0\n", - "8\n", - "11\n", - "18\n", - "23\n", - "33\n", - "41\n", - "53\n", - "56\n", - "57\n", - "60\n", - "67\n", - "70\n", - "73\n", - "76\n", - "85\n", - "87\n", - "88\n", - "93\n", - "94\n", - "96\n", - "97\n", - "98\n", - "99\n", - "Cost: 160.55000000000007\n" - ] - } - ], - "source": [ - "Q = map_graph_to_distance_matrix('graph.txt')\n", - "J = compute_cost_to_go(Q)\n", - "print_best_path(J, Q)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "f0a315c3", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "160.55" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "J[0]" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 51, - 53, - 202, - 212, - 223, - 247, - 279, - 381, - 392, - 414, - 425, - 449, - 457, - 470, - 474, - 478, - 482, - 484 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/.jupyter_cache/executed/7876e0c772fb532967c6522d8316a28c/base.ipynb b/lectures/_build/.jupyter_cache/executed/7876e0c772fb532967c6522d8316a28c/base.ipynb deleted file mode 100644 index 6b463705e..000000000 --- a/lectures/_build/.jupyter_cache/executed/7876e0c772fb532967c6522d8316a28c/base.ipynb +++ /dev/null @@ -1,573 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "84fd71b1", - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "plt.rcParams[\"figure.figsize\"] = (11, 5) #set default figure size\n", - "import numpy as np" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "f6a375dd", - "metadata": { - "tags": [ - "output_scroll" - ] - }, - "outputs": [], - "source": [ - "def subplots(fs):\n", - " \"Custom subplots with axes throught the origin\"\n", - " fig, ax = plt.subplots(figsize=fs)\n", - "\n", - " # Set the axes through the origin\n", - " for spine in ['left', 'bottom']:\n", - " ax.spines[spine].set_position('zero')\n", - " ax.spines[spine].set_color('green')\n", - " for spine in ['right', 'top']:\n", - " ax.spines[spine].set_color('none')\n", - "\n", - " return fig, ax\n", - "\n", - "\n", - "def plot45(g, xmin, xmax, x0, num_arrows=6, var='x'):\n", - "\n", - " xgrid = np.linspace(xmin, xmax, 200)\n", - "\n", - " fig, ax = subplots((6.5, 6))\n", - " ax.set_xlim(xmin, xmax)\n", - " ax.set_ylim(xmin, xmax)\n", - "\n", - " hw = (xmax - xmin) * 0.01\n", - " hl = 2 * hw\n", - " arrow_args = dict(fc=\"k\", ec=\"k\", head_width=hw,\n", - " length_includes_head=True, lw=1,\n", - " alpha=0.6, head_length=hl)\n", - "\n", - " ax.plot(xgrid, g(xgrid), 'b-', lw=2, alpha=0.6, label='g')\n", - " ax.plot(xgrid, xgrid, 'k-', lw=1, alpha=0.7, label='45')\n", - "\n", - " x = x0\n", - " xticks = [xmin]\n", - " xtick_labels = [xmin]\n", - "\n", - " for i in range(num_arrows):\n", - " if i == 0:\n", - " ax.arrow(x, 0.0, 0.0, g(x), **arrow_args) # x, y, dx, dy\n", - " else:\n", - " ax.arrow(x, x, 0.0, g(x) - x, **arrow_args)\n", - " ax.plot((x, x), (0, x), 'k', ls='dotted')\n", - "\n", - " ax.arrow(x, g(x), g(x) - x, 0, **arrow_args)\n", - " xticks.append(x)\n", - " xtick_labels.append(r'${}_{}$'.format(var, str(i)))\n", - "\n", - " x = g(x)\n", - " xticks.append(x)\n", - " xtick_labels.append(r'${}_{}$'.format(var, str(i+1)))\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n", - "\n", - " xticks.append(xmax)\n", - " xtick_labels.append(xmax)\n", - " ax.set_xticks(xticks)\n", - " ax.set_yticks(xticks)\n", - " ax.set_xticklabels(xtick_labels)\n", - " ax.set_yticklabels(xtick_labels)\n", - "\n", - " bbox = (0., 1.04, 1., .104)\n", - " legend_args = {'bbox_to_anchor': bbox, 'loc': 'upper right'}\n", - "\n", - " ax.legend(ncol=2, frameon=False, **legend_args, fontsize=14)\n", - " plt.show()\n", - "\n", - "def ts_plot(g, xmin, xmax, x0, ts_length=6, var='x'):\n", - " fig, ax = subplots((7, 5.5))\n", - " ax.set_ylim(xmin, xmax)\n", - " ax.set_xlabel(r'$t$', fontsize=14)\n", - " ax.set_ylabel(r'${}_t$'.format(var), fontsize=14)\n", - " x = np.empty(ts_length)\n", - " x[0] = x0\n", - " for t in range(ts_length-1):\n", - " x[t+1] = g(x[t])\n", - " ax.plot(range(ts_length),\n", - " x,\n", - " 'bo-',\n", - " alpha=0.6,\n", - " lw=2,\n", - " label=r'${}_t$'.format(var))\n", - " ax.legend(loc='best', fontsize=14)\n", - " ax.set_xticks(range(ts_length))\n", - " plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "fe89c161", - "metadata": {}, - "outputs": [], - "source": [ - "A, s, alpha, delta = 2, 0.3, 0.3, 0.4" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "47377f76", - "metadata": {}, - "outputs": [], - "source": [ - "def g(k):\n", - " return A * s * k**alpha + (1 - delta) * k" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "3a504d01", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "xmin, xmax = 0, 4 # Suitable plotting region.\n", - "\n", - "plot45(g, xmin, xmax, 0, num_arrows=0)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "30615bc7", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "k0 = 0.25\n", - "\n", - "plot45(g, xmin, xmax, k0, num_arrows=5, var='k')" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "4e28af8a", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, k0, var='k')" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "e9756e69", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, k0, ts_length=20, var='k')" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "cdcfa4d2", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "k0 = 2.95\n", - "\n", - "plot45(g, xmin, xmax, k0, num_arrows=5, var='k')" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "0648ae5a", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, k0, var='k')" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "929a2fe0", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "xmin, xmax = 0, 1\n", - "g = lambda x: 4 * x * (1 - x)\n", - "\n", - "x0 = 0.3\n", - "plot45(g, xmin, xmax, x0, num_arrows=0)" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "d8d1522a", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plot45(g, xmin, xmax, x0, num_arrows=6)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "4d110e5c", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=6)" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "483858bc", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=20)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "5cf2ab06", - "metadata": {}, - "outputs": [], - "source": [ - "a, b = 0.5, 1\n", - "xmin, xmax = -1, 3\n", - "g = lambda x: a * x + b" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "bd257fbd", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "x0 = -0.5\n", - "plot45(g, xmin, xmax, x0, num_arrows=5)" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "83b69fc8", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=10)" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "ff6de5c0", - "metadata": {}, - "outputs": [], - "source": [ - "a, b = -0.5, 1\n", - "xmin, xmax = -1, 3\n", - "g = lambda x: a * x + b" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "23b1b504", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAhcAAAIjCAYAAACwMjnzAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAABuyElEQVR4nO3deVwU9f8H8NcCcgoooniAFyKICt5532hqHn3TMvMo86j82aGpqNyIXGXaqWlWHllZmld55m14o+J9I+LBISw3LDu/P6ZdIC8Wdnd2l9fz8djHAxnYeU+pvJz5zGtkgiAIICIiItISM6kHICIiItPCcEFERERaxXBBREREWsVwQURERFrFcEFERERaxXBBREREWsVwQURERFrFcEFERERaxXBBREREWsVwQURERFrFcEFERERaxXBBREREWsVwQURERFrFcEFERERaxXBBREREWsVwQURERFrFcEFERERaxXBBREREWsVwQUREZABiYmIgk8kgk8kQFxf32PaQkBD19v++rK2tJZj46SykHoCIiKiqu3jxIoKCgmBnZ4ecnJxnfu2ECRPQuHHjMp+zsDCsH+eGNQ0REVEVU1xcjAkTJsDX1xfNmzfHmjVrnvn1b775Jnr37q2f4SqIl0WIiEyQQqFAZGQk3N3dYW1tjWbNmiEyMhI3btyATCbDm2++KfWI9K/o6GicOXMGK1euhLm5udTjaAXPXBARmaCJEydi9erVcHd3x7Rp01BQUIDFixfjn3/+kXo0KiUhIQGhoaEICAhAy5Yty/U9Bw8exLFjx2Bubg4vLy/0798fVlZWOp5UMwwXREQmZs+ePVi9ejU6dOiAAwcOwMbGBgAQEBCAtm3bSjwdqSgUCrz55pto0aIF/P39y/19QUFBZX5dr149/Pjjj/Dz89P2iBXGcEFEVcrChUBmptRTPJujIzBvXsW/X3XNPjAwUB0sAKBu3br44IMPMHfu3MqOqHMFBQVISkqSeoxncnV1rdQZg4ULF+LMmTM4evQoqlWr9tyvb9OmDX788Uf06tULLi4uSEpKws8//4yFCxdi2LBhiIuLg6+vb4Xn0SaGCyKqUjIzgYwMqafQrTNnzgAAunbt+ti2J33OECUlJeHDDz+UeoxnWrx4Mdzd3Sv0vWfOnMGCBQvw8ccfo127duX6nhEjRpT5dbNmzRAQEAAXFxdMmTIFCxYswPr16ys0j7YxXBBRleLoKPUEz1fZGeVyOczMzFCrVq3Htrm4uFTuzfXE1dUVixcvlnqMZ3J1da3w906YMAHu7u4ICQmp9BwTJkzAe++9h8OHD1f6vbSF4YKIqpTKXG4wFg4ODlAqlUhLS4Ozs3OZbQ8ePJBoKs1YWVlV+KyAMVCdXXpa+VWXLl0AABs3bnzsjMV/WVpawt7eHrm5uVqdsTIYLoiITIyvry9Onz6NI0eOYNiwYWW2HTlyRKKpqLS33377iZ8/cOAArl69imHDhqF27dqPlWU9ydWrV/Ho0SODWW8BMFwQEZmcN954Az/88APCw8MxYMAA9b+O79+/jyVLlkg8HQHAihUrnvj5N998E1evXsXcuXPRuXNn9eezsrJw8+ZN+Pj4lPn6R48eqYPK66+/rruBNcRwQURkYvr374833ngDa9euRevWrTF8+HAUFBTg119/xQsvvIAtW7bAzIwdisYkLS0Nvr6+6NChA1q3bo06derg7t27+Ouvv5CWlgY/Pz989NFHUo+pxnBBRGSCfvjhB3h5eWHlypX44osv4Orqig8//BD9+vXDli1b4ODgIPWIpAEnJydMmzYNcXFx2LJlCzIyMmBnZ4fWrVtj7NixmDRpkkG1e8oEQRCkHoKIiPRjxYoVmDx5Mr7++mu8++67Uo9DJorhgojIBN2/fx8uLi6QyWTqz929exfdunVDUlISbt68CTc3NwknJFPGyyJERCYoKioK27ZtQ48ePVCnTh0kJiZi69atyMrKQkhICIMF6RTDBRGRCXrxxRdx4cIFbNu2DY8ePYK1tTV8fHzw3nvvYcyYMVKPRyaOl0WIiIhIq3gvEhEREWkVwwURERFpFcMFERERaRXDBREREWkVwwURERFpFcMFERERaRXDBREREWkVwwURERFpFcMFERERaRXDBREREWkVwwURERFpFcMFERERaRXDBREREWkVwwURERFpFcMFERERaRXDBREREWkVwwURERFpFcMFERERaRXDBREREWkVwwURERFpFcMFERERaRXDBREREWkVwwURERFpFcMFERERaRXDRRX0zTffwMfHBw4ODnBwcECXLl3w119/ST0WERGZCJkgCILUQ5B+bdmyBebm5mjWrBkA4Mcff0RsbCxOnz6Nli1bSjwdEREZO4YLAgA4OTkhNjYWb7/9ttSjEBGRkbOQegCSVnFxMdavX4+cnBx06dJF6nGIiMgEMFxUUefOnUOXLl2Qn5+P6tWrY+PGjfD29n7q1xcUFKCgoED9a0EQUCgrhLO9M2QymT5GJiIiI8EFnVWUp6cn4uPjERcXh3fffRcTJkzAhQsXnvr1kZGRcHR0VL9quNRAnc/qIKswS49TExGRLgmCgJ9++glDhw7FihUrKvw+XHNBAID+/fvD3d0dy5Yte+L2/565kBfI4fa1GzL9M+Fg5aCvMYmISEeUSiWWLVuGP//8ExMmTMArr7xS4TPTvCxCAMS0Wjo8/JeVlRWsrKxKPvH0LyUiIiOjUCiwaNEiHDp0CNOnT8eAAQMq9X4MF1XQvHnzMGjQILi5uSErKws///wz9u3bh+3bt0s9GhER6Vl+fj4iIiKQkJAAf39/dO3atdLvyXBRBT148ADjxo3DvXv34OjoCB8fH2zfvh1+fn5Sj0ZERHokl8sRGhqKO3fuIDQ0FD4+Plp5X4aLKui7776TegQiIpJYamoqAgMDkZWVhcjISLi7u2vtvRkuiIiIqpikpCQEBgbCzMwM0dHRaNCggVbfn7eiEhERVSFXrlzB7NmzYWtri5iYGK0HC4DhgoiIqMqIj4/H/Pnz4erqiqioKNSqVUsn++FlESIioirg0KFD+PTTT9GmTRv4+/uXrRfQMoYLIiIiE/fnn39i6dKl6N27N95//31YWOj2xz/DBRERkYkSBAE///wzfvrpJwwfPhxvv/22Xp4HxXBBRERkggRBwLfffoutW7di3LhxGDVqlN4eNMlwQUREZGIUCgU+++wzHDx4ENOmTcOLL76o1/0zXBAREZmQ/Px8LFy4EOfOndNanbemGC6IiIhMRFZWFkJDQ3H79m2t1nlriuGCiIjIBKSmpiIoKAhyuRyRkZFo1qyZZLMwXBARERk5Xdd5a4oNnUREREbs6tWrOq/z1hTDBRERkZGKj4/HvHnz0KBBA53WeWuKl0WIiIiMkKrO29fXF/7+/rC2tpZ6JDWGCyIiIiPz119/4ZtvvkHPnj3x4Ycf6rzOW1OGNQ0RERE9lSAI+OWXX7B27VoMHToUkydP1lvrpiYYLoiIiIxA6TrvsWPH4tVXXzXIYAEwXBARERk8qeu8NcVwQUREZMDy8/MRGRmJs2fPYs6cOejWrZvUIz0XwwUREZGBKl3nHRISAl9fX6lHKheGCyIiIgOkqvPOzMzEwoUL4eHhIfVI5cZwQUREZGDu3r2LwMBAADCY1k1NsKGTiIjIgKjqvK2trY0yWAAMF0RERAZDVeddr149REdHw9nZWeqRKoSXRYiIiAzA4cOH8cknn8DHxwdz5841qDpvTTFcEBERSWz79u34+uuv0aNHD3z00UcGV+etKeOenoiIyIgJgoBff/0Va9asMeg6b00xXBAREUlAEAQsX74cW7ZswRtvvIHXXnvNJIIFwHBBRESkdwqFAkuWLMH+/fvx7rvvYvDgwVKPpFUMF0RERHqUn5+PqKgonDlzBrNnz0b37t2lHknrGC6IiIj0JCsrC2FhYbh16xaCg4PRpk0bqUfSCYYLIiIiPUhLS0NQUBAePXpkdHXemmK4ICIi0jFVnbcgCIiJiYGrq6vUI+kUGzqJiIh06Nq1a+o679jYWJMPFgDDBRERkc6cPXsWc+fONfo6b03xsggREZEOHDlyBLGxsWjdujXmzZtn1HXemmK4ICIi0rIdO3bgq6++Mpk6b01VraMlIiLSIUEQsH79eqxevRpDhgzB1KlTTaZ1UxMMF0RERFogCAJWrFiBzZs3Y8yYMRg9enSVDBYAwwUREVGlKRQKfP7559i3b59J1nlriuGCiIioEgoKChAVFYX4+HiTrfPWFMMFERFRBWVlZSE8PBw3b9406TpvTTFcEBERVUBaWhqCg4ORnp6OiIgING/eXOqRDAbDBRERkYaSk5MRGBgIpVKJ6OhouLm5ST2SQWFDJxERkQauX7+O2bNnw9LSErGxsQwWT8BwQUREVE6qOm8XF5cqVeetKV4WISIiKgdVnXerVq0wf/78KlXnrSmGCyIioudQ1Xl3794dM2bMqHJ13prifx0iIqKnEAQBv/32G1atWoXBgwdj6tSpMDPjioLnYbggIiJ6AkEQ8N1332HTpk1Vvs5bUwwXRERE/1G6zvudd97BkCFDpB7JqDBcEBERlVJQUIDo6GicPn0aH3/8MXr27Cn1SEaH4YKIiOhf2dnZCAsLw40bNxAUFIS2bdtKPZJRYrggIiICkJ6ejqCgIHWdt6enp9QjGS2GCyIiqvJY561dvJ+GiIiqtBs3bmD27NmoVq0aYmJiGCy0gOGCiIiqrHPnzsHf3x916tRBTEwMateuLfVIJoGXRYiIqEqKi4tDTEwMWrZsiXnz5sHGxkbqkUwGwwUREVU5u3btwhdffIFu3bphxowZqFatmtQjmRSGCyIiqjIEQcDvv/+OH3/8EYMGDcI777zDOm8dYLggIqIqQRAEfP/999i4cSNGjx6NMWPGsM5bRxguiIjI5CkUCnzxxRfYu3cvpk6dipdeeknqkUwawwUREZk0VZ33qVOnWOetJwwXRERksnJychAWFobr168jKCgI7dq1k3qkKoHhgoiITFJ6ejqCg4ORlpbGOm89Y7ggIiKTc+/ePQQGBkKhULDOWwK8/4aIiEyKqs7bwsKCdd4SYbggIiKTkZCQgLlz56J27dqIjo5GnTp1pB6pSuJlESIiMgmqOm9vb2/Mnz+fdd4SYrggIiKjp6rz7tq1K2bOnMk6b4kxXBARkVH7/fff8cMPP7DO24AwXBARkVFinbfhYrggIiKjU1xcjC+++AJ79uzBlClTMHToUKlHolIYLoiIyKgUFhYiOjoaJ0+exMcff4xevXpJPRL9B8MFEREZjZycHISHh+Pq1asIDAxE+/btpR6JnoDhgoiIjIKqzjs1NRURERHw8vKSeiR6CoYLIiIyePfu3UNQUBCKiooQHR2Nhg0bSj0SPQPv1yEiIoOmqvM2NzdHTEwMg4URYLggIiKDparzdnZ2Zp23EeFlESIiMkhHjx5FTEwMvLy8EBAQwDpvI8JwQUREBmfPnj34/PPP0blzZ3z88ces8zYyDBdERGRQNmzYgO+//x4vvvgi3n33XdZ5GyGGCyIiMgiCIOCHH37Ahg0b8Oqrr2Ls2LGs8zZSDBdERCS50nXekydPxrBhw6QeiSqB4YKIiCRVWFiImJgYnDhxAjNnzkTv3r2lHokqieGCiIgkk5OTgwULFuDKlSus8zYhDBdERCSJR48eITg4GA8fPsSCBQvQokULqUciLWG4ICIivbt//z6CgoJQUFCA6OhoNGrUSOqRSIt4fw8REenVrVu3MHv2bMhkMsTGxjJYmCCGCyIi0pvz58/D398fTk5OiImJYZ23ieJlESIi0otjx44hOjoaXl5emD9/PmxtbaUeiXSE4YKIiHSudJ33zJkzYWlpKfVIpEMMF0REpFMbN27EypUrMXDgQLz33nus864CGC6IiEgnBEHAjz/+iN9//5113lUMwwUREWldcXExvvrqK+zatQuTJk3C8OHDpR6J9IjhgoiItKqwsBCxsbE4duwYZsyYgT59+kg9EukZwwUREWlN6TrvgIAAdOzYUeqRSAIMF0REpBUZGRkIDg7GgwcPWOddxTFcEBFRpZWu846KikLjxo2lHokkxPuBiIioUlR13gAQGxvLYEEMF0REVHEXLlyAv78/atasidjYWNZ5EwBeFiEiogo6fvw4oqKi4OnpiYCAANZ5kxrDBRERaezvv//GkiVL8MILL+Djjz9mnTeVwXBBREQa+eOPP/Ddd9/Bz88P06ZNg7m5udQjkYFhuCAionIRBAGrVq3Cb7/9hpEjR2L8+PGs86YnYrggIqLnKl3n/fbbb2PEiBFSj0QGjOGCiIieqXSd90cffYS+fftKPRIZOIYLIiJ6qtzcXCxYsACXL19mnTeVG8MFERE9Uek67/DwcHh7e0s9EhkJhgsiInrMgwcPEBgYyDpvqhA2dBIRURml67xjYmIYLEhjDBdERKR28eJF+Pv7o0aNGoiJiYGLi4vUI5ER4mURIiICUFLn3bx5cwQEBMDOzk7qkchIMVwQERH27t2LxYsXo1OnTpg1axbrvKlSGC6IiKq4TZs2YcWKFazzJq1huCAiqqIEQcDq1auxfv161nmTVjFcEBFVQUqlEl9//TV27NiBiRMn4uWXX5Z6JDIhDBdERFVMYWEhPv30U8TFxeHDDz9Ev379pB6JTAzDBRFRFZKbm4uIiAhcunQJ8+fPR6dOnaQeiUwQwwURURWRmZmJ4OBg3L9/H2FhYWjZsqXUI5GJYrggIqoCHj58iICAAOTn5yMyMhJNmjSReiQyYWzoJCIycbdv38asWbMAiHXeDBakawwXREQm7OLFi5gzZw4cHR0RHR2NunXrSj0SVQG8LEJEZKJOnDiByMhI1nmT3jFcEBGZoH379mHx4sXo0KEDZs+ezTpv0iuGCyIiE7N582YsX74c/fv3x//93/+xzpv0juGCiMhECIKANWvW4Ndff8X//vc/vPnmm6zzJkkwXBARmQClUolvvvkG27dvx1tvvYX//e9/Uo9EVRjDBRGRkSsqKsInn3yCuLg4fPDBB+jfv7/UI1EVx3BBRGTE8vLysGDBAly6dAnz5s3DCy+8IPVIRAwXRETGKjMzEyEhIUhOTkZoaChatWol9UhEABguiIiM0sOHDxEUFIScnBxERUWxdZMMChs6iYiMTGJiImbNmoXi4mLWeZNBYrggIjIily5dwpw5c+Dg4IDo6GjUq1dP6pGIHsNwQURkJE6ePImAgAA0atQIUVFRcHJyknokoifimgsiIiOgqvNu37495syZwzpvMmgMF0REBm7Lli349ttv0a9fP0yfPp113mTwGC6IiAyUIAhYu3YtfvnlF7z88st46623WOdNRoHhgojIALHOm4wZwwURkYEpKirCp59+iiNHjrDOm4wSwwURkQHJy8tDREQELly4gPnz57POm4wSwwURkYHIzMxEaGgo7t69i7CwMNZ5k9FiuCAiMgCqOu/s7GxERkaiadOmUo9EVGEMF0REEktMTERQUBAsLCwQGxvL1k0yemzoJCKS0OXLlzFnzhzY29sjJiaGwYJMAsMFEZFETp48ifnz56Nhw4as8yaTwssiREQSOHDgABYtWoR27dphzpw5sLKyknokIq1huCAi0rOtW7fi22+/RZ8+fTB9+nRYWPCvYjIt/B1NRKQngiDgp59+ws8//8w6bzJpDBdERHqgVCqxbNky/Pnnn5gwYQJeeeUVBgsyWQwXREQ6VlRUhEWLFuHw4cN4//334efnJ/VIRDrFcEFEpEN5eXlYuHAhzp8/j3nz5qFz585Sj0SkcwwXREQ6IpfLERISgqSkJISGhqJ169ZSj0SkFwwXREQ6kJKSgsDAQGRnZyMqKop13lSlMFwQEWnZnTt3EBQUBDMzM8TExKB+/fpSj0SkV2zoJCLSIlWdt52dHWJjYxksqEpiuCAi0pJTp05h/vz5cHV1ZZ03VWm8LEJEpAUHDhzAZ599hrZt27LOm6o8hgsiokratm0bli1bht69e+P9999nnTdVefwTQERUQYIgYN26dVi3bh1GjBiBiRMnsnWTCAwXREQVwjpvoqdjuCAi0pBCocCiRYtw6NAhTJ8+HQMGDJB6JCKDwnBBRKSB/Px8REREICEhAf7+/ujatavUIxEZHIYLIqJyksvlCA0NxZ07dxAaGgofHx+pRyIySFrpudi6FcjJ0cY7EREZppSUFMyZMwcPHjxAZGQkgwXRM2jlzMWWLcD27UD37kD//oCzszbelYjIMLDOm0gzWrssUlQE7N0L7NsHtG8PDBgANGqkrXcnIpLGlStXEBISAicnJ4SFhbF1k6gctBIu+vYFDh0CCgsBQQBOnBBfnp7AwIGAtzfAO7SIyNjEx8cjIiICTZo0QVBQEKpXry71SERGQSYIgqCNN8rJAfbvB/7+G8jKKrutQQPxTEbHjoC5uTb2RlKTF8jhGOWITP9MOFg5SD0OkdYdOnQIn376Kdq0aQN/f3/WeRNpQGvhQqWoCIiLA3buBB4+LLutZk2gXz+gRw/A2lqbeyV9Y7ggU/bnn39i6dKlrPMmqiCthwsVpRI4c0YMGTdulN1mYwP07CkGDUdHXeyddI3hgkyRIAj4+eef8dNPP2H48OF4++232bpJVAE6CxcqggBcvy6GjDNnym6zsABeeAHw8wPq1dPlFKRtDBdkagRBwLJly7Bt2zaMGzcOo0aNYrAgqiCdh4vS7t0Ddu0Cjh4FFIqy23x8xHUZzZpx8acxYLggU1K6zvu9997Diy++KPVIREZNr+FCJTNTXPi5fz+Ql1d2W9OmYsjw9QXMtFLxRbrAcEGmIj8/HwsXLsS5c+cwa9Ys1nkTaYEk4UIlP1+8hXX3buDRo7Lb6tQRL5d06QJUqybNfPR0DBdkCrKyshAaGorbt28jMDCQrZtEWiJpuFApLhZ7MXbsAO7eLbvN3h7o0wfo3Ruws5NkPHoChgsydqmpqQgKCoJcLkdISAiaNWsm9UhEJsMgwoWKIAAXLoiLPy9dKrvN0hLo1k08m1GrljTzUQmGCzJmSUlJCAwMhJmZGcLCwtCgQQOpRyIyKQYVLkpLTBRDxokTYuhQMTMrqRdv2FC6+ao6hgsyVlevXkVwcDBq1qyJsLAw1OK/Voi0zmDDhUpqqrgm4/BhsV68NC8vMWSwXlz/GC7IGKnqvBs3boygoCDY29tLPRKRSTL4cKGSkyM+FG3v3sfrxV1dxZDRoQPrxfWF4YKMjarO29fXF/7+/rBmTTCRzhhNuFApKgL++Ufsy3hSvXj//uKj3/n3hm4xXJAxUdV59+rVCx988AHrvIl0zOjChYqqXnzHDuDmzbLbbG2BXr3Ep7U68OeeTjBckDEQBAG//PIL1q5di2HDhmHSpEls3STSA6MNFyqCAFy7Ji7+PHu27DZVvfiAAUDdutLMZ6oYLsjQCYKAb7/9Flu3bmWdN5GeGX24KE1VLx4XJ3ZnlObrCwwcCLi7SzObqWG4IEOmUCjw2Wef4eDBg6zzJpKASYULlYwMsV78wIGn14u3acM7TCqD4YIMVX5+PiIjI3H27Fl8/PHH6Natm9QjEVU5JhkuVPLzgYMHgT17Hq8Xd3ERC7k6d2a9eEUwXJAhKl3nHRAQAF9fX6lHIqqSTDpcqCgUJfXiyclltzk4iPXivXqxXlwTDBdkaFR13pmZmQgJCYGHh4fUIxFVWVUiXKgIAnD+vLj48/LlstusrMRbWPv1Y714eTBckCG5e/cuAgMDAQDh4eGs8yaSWJUKF6Xdvi2GjJMnH68X79BBXJfh5ibdfIaO4YIMxdWrVxESEgJHR0eEh4ezzpvIAFTZcKGSmireYXL4sFjQVVqLFmLIaNGCiz//i+GCDIGqzrtRo0YIDg5mnTeRgajy4UIlO7ukXjw7u+w21os/juGCpHb48GF88sknrPMmMkBmUg9gKKpXB156CYiMBMaMAWrXLtmWlASsXAkEBIh3nhQUSDenJqZPnw6ZTIYTJ06oP+fp6QkbGxskJiZKOBlRCaVSiQsXLkAul5f7e7Zv347o6Gh07doVAQEBDBZEBoZnLp5CqQTi48U7TG7dKrvNWOrFlUol7Ozs4OHhgbNnz6JPnz44ePAg4uLi0KFDh0q9N89ckLb89ddfWLJkCaytrdG4cWO0bt0aHh4ecHd3R/369cu0agqCgF9//RVr1qzB0KFDMXnyZLZuEhkgPr3nKczMgHbtgLZtgatXxcWf586J23Jzgb/+AnbsKEbr1tno2bMQdeoYZkZ77733sGjRIvTu3RsHDhzA999/j4YNG+Lhw4fw8fHBgwcPULduXZw5c0aj980qFB9Nm5KSgnzLfF2MTlVESkoKsrKyYGtri4SEBJw4cQIymQz29vaoU6cOfH190bx5czRt2hR///03tm/fjjfeeAOvvfYagwWRgeKZCw0kJ4uLP48eFevFDxw4gNzcHFhbW6NmzTuoX/8cHBxSpB7zMWvWrEFxcTE6duwIb29v9efPnz+PwsJCXLt2DaNGjXrmexQWFqKo1IrXIrMibPLehNdvvQ5LwVJns1PVcPbsWXTs2FH96+LiYmRmZiI5ORkZGRmoXr06UlJSUFhYiG+//RaDBw+WcFoieh6eudBA/frAhAnA8OHApk1Z2L49DYAN6tWrB6Ae0tM7wdw8C61a3YWra7pB3GGydetWFP/7oJWuXbvCx8dHva1nz57YuXMnEhMT0bNnz2e+T3R0NK5cuVLyCSsA3kC3bt1gY2aji9Gpijhx4gQsLS1RWFgIuVwOuVyOvLw8yGQyODg4oHHjxkhOTkZycjLs7Oye+3uViKTHcFEBNWoA7u5n4Or6FYDuaNu2D3JzrdTbk5M7orhYvMPkhRekqxdfu3YtNm7ciKlTp2LDhg347bffsHjx4jJfI5fLcejQIUycOPGZ7zVy5MgyC+6yCrPgvdob48aN45oLqpQaNWrg7NmzuHnzJhwcHODp6QlfX180a9YMdevWxXfffYfCwkKMHDkS5ubmqF69utQjE9FzMFxUUEJCAhSKLNjY7MOrrw4B0BE7d5bUiz94AKxeDWzaJC787NVLXAiqL4cOHcL48ePh5+eHpUuXonv37hg3bhzWrFmDsWPHavx+Dg4OcCi1elVeUP6V/UTP4ufnBzMzM7i6usLd3R01a9YEAKSlpSEoKAgZGRlYuHAhvvnmG6SlpUk8LRGVB29FrQClUonjx4+jRo0aKCoqwuXL59GlCxAUBEyfDjRvXvK1cjnwxx+Avz/w669Aerru57t+/Tr69euH5s2bY+fOnQCAsWPHom7duvjwww91PwCRBuzt7TFixAh06NBBHSzu3r2LWbNmITc3F9HR0WjSpAkePHiAtLQ0KBQKiScmoufhmYsKSExMRHJyMmrWrKkOGhMmTIBMJkOrVkCrVuLtqzt3AqdOifXiBQViR8bevUDHjuIlE1dX3czn7u6OgieUcdy7d083OyTSomvXriE4OBiOjo4ICwuDs7MzHj58iJ9++gkAkJ6ejjp16kg8JRE9C8NFBVy4cAFZWVlwdXVFcXExbt++jfv37/+7sFPUuDEwZQqQkgLs3l1SL65UinebHD0KeHuLIcPLS5p6cWdnZ6Snp0MQBJibm2PlypWYMGGC/gch+tfZs2cRHh7OOm8iI8dwUQFnzpyBTCaDmZkZHB0dcf/+fVy4cKFMuFCpXRt4/XWx/VNVL56TI267cEF8ubkBAwcC7duL/Rr6kpqaqr+dET3HkSNHEBsbi9atW2PevHllWjfr1KmDjz76CGlpaTxrQWQEuOZCQ/n5+Th9+jRq1KgBADD/92Ej51QNW09hbw8MHQpERYlhw9m5ZNudO8CKFWK9+N9/G0+9OJG2bN++HVFRUejatSuCgoJY501k5HjmQkOJiYnIysqCXC7HnTt3IJPJUK1aNZw7dw6CIDy3MdDSEujdG+jZEzh9WqwXv31b3JaWBvzyC7Bli/g1ffoYdr04UWUJgoD169dj9erVeOmllzBlyhS2bhKZADZ0akgQBGzbtg25ubnYtm0brK2t0a9fPzRr1gzt2rWrwPuJ9eI7dgAJCWW3WVgAXboAfn6Ai4uWDkBL+GwRqixBELBixQps3rz5uXXecrkcTZs2Va9xcmDqJjJoDBeVMGHCBFhbW2PZsmVaeb/kZPEOk2PHxHpxFZkMaNNGXPzZtKlWdlVpDBdUGQqFAp9//jn27duHd95557l13g8fPoTLvwn7wYMHXHdBZOB4WcSA1K8PvPmmWC/+99/AgQNAfr54duP0afHVrJkYMnx8pLnDhKiyCgoKEBUVhfj4eMyePRvdu3d/7vfY2tqiQYMGKCoqgq0+2+iIqEIYLgxQzZrAK68AgweLAePvv4GMDHHbtWviq27dknpxC/5fJCORlZWF8PBw3Lx5E8HBwWjTpk25vq969ep49dVXkZaWxvpvIiPAH0sGzMZGvEW1Xz/xUsnOnYCqB+v+fWDVKrH9s18/cYEo/0FHhiwtLQ3BwcFIT09HREQEmpeusiUik8JwYQQsLICuXcXFnQkJ4uLPq1fFbXI5sHEj8OefQI8eYtBwcpJ2XqL/unv3LoKCgqBUKhEdHQ03NzeNvl+pVCIzMxPZ2dlQKpUw02chDBFpjOHCiMhkQOvW4uvWLTFknD5dUi++e7d4CUXX9eJEmrh27RpCQkJgb2+P8PBwOJcueSmn1NRUrFy5Uv0xF3QSGTaGCyPVuDEwdSrw8KEYKo4cebxevGVLMWR4enLxJ0nj7NmzWLBgAdzc3NQBg4hMH8OFkatTBxgzRmz//G+9+Pnz4qthQzFk6LtenKq2Z9V5a8rZ2RnTpk3Do0ePKnTmg4j0i+HCRKjqxQcMEM9i7N4NqB4dkpgo1otv3CgWcnXtClhZSTsvmbYdO3bgq6++Qvfu3TFjxgxYVPKWJjMzM1haWsLCwoLrLYiMAMOFibGyEmvDe/USH/e+c2fZevGffy5bL86z1KRNgiDgt99+w6pVqzB48GBMnTqVYYCoCmK4MFFmZkCHDuKlkCtXxMWf58+L23JygG3bxOChqhfn+jiqLEEQ8N1332HTpk0YM2YMRo8erbXnhGRnZ+Onn36CQqFAdnY2uy6IDBzDhYmTycQFnZ6eQFISsGuX2JmhVIoLQA8cAA4eFOvFBw4EmjSRemIyRv+t8x4yZIhW3z83NxcPHjxQf8xwQWTYGC6qEFdX4K23gBEjgD17xGBRUFC2XtzDQ1y30bo17zCh8ikoKEB0dDROnz6Njz/+GD179tT6PmxtbeHi4gKFQsH6byIjwHBRBdWsCYwcKdaLHzwoLv6Uy8VtV6+Kr3r1xMslrBenZ8nOzkZYWBhu3ryJoKAgtG3bVif7qV69OsaMGcP6byIjwR8bVZitbUm9+NGj4iUTVb34vXtivfimTeL2Hj1YL05lpaenIygoCOnp6ViwYAE8PT2lHomIDATDBcHCAujWTbxF9dw5caGnql48MxPYsKFsvXjNmtLOS9JLTk5GYGBgheu8NaVUKlFYWAiFQsH6byIjIBMEQZB6CGM1YcIEWFtbY9myZVKPonU3boghIz5eXJOhYmYGdOoEdOktR4tVjsj0z4SDlYNkc5L+3bhxA0FBQahevTrCw8NRu3Ztne/z4cOHcHFxAQA8ePCA9d9EBo5nLuiJmjYF3nlHrBfftUss5lIoxLtM4uKAA0cB1BPPcLRrycWfVcW5c+cQHh4OV1dXhISEwMGBwZKIHsdwQc9Upw7wxhti++fevWLFeG5uyfYvvwQ8/q0Xb9eO9eKm7J9//kFsbCxatmyJefPmwcbGRm/7dnZ2xsSJE5GRkcH6byIjwHBB5eLgAAwfDrz4ongWY+uukm23bwPLlwPOzkD//qwXN0U7d+7El19+iW7dumHGjBmoVq2aXvdvZmYGR0dHKBQKrrcgMgL8U0oaUdWLBwaKvy79WPfUVLFefO5csWI8K0uaGUl7VHXeX3zxBQYNGoRZs2bpPVgQkfHhmQuqENU/Hj/+GLh3S1z8WbpefOtWsXK8a1fxbAbX3xkfQRCwcuVK/PHHH3j99dfx+uuva63OW1PZ2dn49ddfUVRUxPpvIiPAcEGVIpMBXl7iKylJDBnHj5fUi+/fLzaBtm0rdmo0biz1xFQeCoUCX3zxBfbu3YupU6fipZdeknSe3Nxc3L17V/0xwwWRYWO4IK1xdQUmTiypFz94sKRe/NQp8eXhIYaMVq14h4mhUtV5nzp1Smd13pqytrZGrVq1UFxcDGtra6nHIaLnYLggrXNyAkaNAoYMEc9a7Nnz5HrxAQPEzgzWixuOnJwchIWF4fr16wgKCkK7du2kHgkA4ODggPHjxyMtLY23vxIZAf61TjpjayveXdK/v1gvvmMH8O+DLXHvHvDjj2K9eN++QM+egB7vbKQnSE9PR3BwMNLS0hAREcE6byKqMIYL0rnS9eJnz4rrMq5dE7dlZJTUi/fsKQYN1ovr37179xAYGAiFQqGXOm8iMm2s/64EU67/fh55gRyOURWv/35avbi5uXipZMAAoH597c1LTydFnbemWP9NZFx45oIkoaoXf/BArBf/5x+xXry4WPz4n3/ERZ8DB4qLQLn4UzcSEhIQHh6OBg0aIDg4GI6OjlKPREQmgOGCJOXiAowdCwwb9ni9eEKC+GrUSAwZbduyXlyb4uLiEBMTA29vb8yfP1+vdd6acnJywpgxY5CZmQknJyepxyGi52C4IINQul780CHxDpO0NHHb7dvAt9+K9eJ+fuLaDUtLaec1drt27cIXX3yBrl27YubMmQbfumlhYQEXFxdYWFjAgrcXERk8/iklg2JlBfTrJ1aMnzwp3mFy5464LTUVWLdOrBbv0wfo3Rtgl5Lmfv/9d/zwww8YNGgQ3nnnHT6rg4i0juGCDJKZGdCxI9ChA3DpkhgyLl4Ut2VniwFj+3bxLpT+/QEDXINocARBwPfff4+NGzdi9OjRGDNmjGR13prKzs7GH3/8gcLCQtZ/ExkBhgsyaDIZ0KKF+LpzR1z8WbpefN8+sWK8XTvxDhPWiz9ZcXExvvjiC+zZswdTpkzB0KFDpR5JI7m5ubh586b6Y4YLIsPGcEFGw81NrBcfPlxck3HoUEm9+MmT4qt5c3HxZ8uWvMNEpbCwEFFRUeo67169ekk9ksasra3h6OgIpVLJ+m8iI8BwQUanVi3g1VeBl14Sz1r8/XdJvfiVK+Krfn3xTEbHjlW7Xrx0nXdgYCDat28v9UgV4uDggIkTJ7L+m8hIVOG/dsnY2doCgwaJay7i4sRLJqp68eRk4IcfgD/+EBeI9uwJVLV/8KrqvFNTU7FgwQJ4eXlJPRIRVRFcJm7Cpk+fDplMhhMnTqg/5+npCRsbGyQmJko4mXZVqwb06AGEhgLvvgu4u5dsy8gAfv8dmDNHrBnPyJBqysq5dOkSoqKi8PvvvyM+Ph5ZWVnP/Pp79+5hzpw5yMrKQnR0NIMFEekV678rwdDrv5VKJezs7ODh4YGzZ8+iT58+OHjwIOLi4tChQ4dKvXdl67917fp1sV78zJnH68VfeEHsyzCmevHvv/8en3/+Oezs7GBpaQkHBwe4u7ujdevWcHd3R7NmzVC3bl3IZDLcuHEDwcHBsLOzQ1hYmElUZbP+m8i48LKICTMzM8OsWbMQHh6OAQMGYP/+/di4cSM6dOiA5ORkeHh4QKlUQhAEvPrqq1i1atVT30sul0OuWtgAIKvw2f9ylpq7u3gW40n14rt25SA2Nh6Ojolwc7sAB4eHRrH408zMDC1btkR+fj7kcjni4+Nx9OhRmJmZwd7eHi4uLrC3t0dCQgJ8fHwQEhLCOm8ikgTPXFSCoZ+5ULG1tUVeXh4WL16MDz74AIB4B4FcLoezszNSU1NRr149XLhwAR4eHk98j969e2P//v0ln7ACMBcGe+biv+RyceHn/v3A9u0HcP/+fdSpI5ZjVK+eivr1E+DklAiZzHD/OJw8eRJdu3YFACgUCmRlZalDn1KpRHFxMRISElCrVi1cvHgR9vb2Ek+sPQqFAq+99hrkcjn++usvtnQSGTj+CTVxERERyMvLA4AywcHS0hLOzs4AgMzMTAiCAKVS+dT32bx582NnLrxXe+toau1zcABGjAB69szFyZN7oVC0ROfOnWFtrXqexijUrl1SL25obdjff/89Lly4gGvXrqGgoABmZmZwcHBA/fr1MWjQIOTk5ODvv/9Gq1at4OXlZVLBAhDrvxs1aoS0tDQGCyIjwD+lJmzt2rUICAjA1KlTsWHDBkyZMgVJSUnq7bdv34aXlxfy8/MxatQoeHp6PvW9HBwcytwCKC+QP/VrDdmtW5dgYbEfdevuRdeuzfDwYRuo/pOkpAA//SS2f/buLVaM29lJOq5agwYN4OrqiiZNmqB169Zo1qwZ3N3dUbduXWzcuBHff/89Xn75ZZw5cwYFBQVSj0tEVRzDhYk6dOgQxo8fDz8/PyxduhTdu3fHuHHjsGbNGowdOxYA0KhRI+Tl5SEhIQFdu3ZFQkICWrVqJfHkunXhwgUUFhYCAJTKfxAQ0AYXL4qLP1X14llZJfXi3buLt7r+e5JHMgMGDED37t1ha2ur/lzpOu/XXnsNL7/8Mnx8fFBcXIzc3NwyX2vscnNzsXXrVhQWFprcsRGZIt6KaoKuX7+Ofv36oXnz5ti5cycAYOzYsahbty4+/PDDx76+VatWcHNzw8qVK/U8qX4JgoDjx4/DysoK1atXx/HjxyEISnh7Ax9+CAQEiKVbqud4FRWJj4EPCACWLxefziql0j9Qi4uLsWTJEmzcuBFTpkzB2LFjkZOTgxs3buD27dvIzs6WcFLty87OxtWrV03y2IhMEc9cmCB3d/cnnhq/d++e+uOEhATUqFEDrq6uSEpKwvXr19WLBU1VSkoKbty4gZo1a6JatWpITk7G7du30aRJEwBivfikScDLL4v14gcPAoWF4q2sJ06IL09PsV7c21u6evHCwkLExMTgxIkTmDlzJnr37g1AXEejCiCWJvZMektLS1SvXh1KpdLkjo3IFDFcVFHx8fGYPHmy+tcvv/wyRo4cKeFEunfx4kVkZGSgefPmMDc3x507d3Dx4kV1uFBR1YsPGVJSL67qrLp8WXw1aFBSL25urr9jyMnJwYIFC3DlypXH6rxr1KiBsWPHIj8/HzVq1NDfUHpQo0YNTJ48GWlpaSZ3bESmiJdFqqixY8ciLy9P/Vq3bp3UI+lcQkICBEGAhYUFZDIZzMzMcObMmad+vZ0dMHgwEBkJjB0LlO5tunsX+P57YP58sUcjP1/38z969Ahz587FzZs3sWDBAqN9TggRmT6euaAqobi4GMeOHYNMJkNqaioEQYC5uTlOnTqF/Pz8Zz5pU1Uv3q2b2Pi5cydw44a47dEj4LffgG3bxOeX9O0L6OIf1vfu3UNQUBAKCwsRHR2NRo0aaX8nRERawjMXJmzdunWwtrbG3bt31Z+bNGkSfHx8kJmZKeFk+qdQKODo6IiaNWuiqKgIBQUFsLe3R82aNaFQKMr1HmZmQNu24nNKZs8GfH1LtuXlATt2APPmAatWAaWWtzwmIyPjmZ0i/3Xz5k3Mnj0bZmZmiI2NfWqwSE1NxfLly7Fq1SqkpqaW+/2NQWpqKhYvXmySx0ZkinjmwoSNHj0aUVFRiIyMxJdffonQ0FDs2LEDcXFxVa4W2srKCrGxsSgoKMDMmTNRVFSEzz//HJaWls88a/E07u7Ae++JIWLXLuDo0ZJ68cOHxZePj7guo1mzksWf58+fR3BwMGxtbeHj4wNPT080a9YMTZo0eeIc58+fR3h4OOrWrYvQ0NBn/n9TVbmrPjYlpnxsRKaI4cKEyWQyREREYOTIkahfvz6WLFmCgwcPokGDBgDE1kNVr0WHDh2wYsUKKcfVOSsrK1hZWal/XboUrKLq1QPGjweGDy+pF/+3EBVnz4qvJk3EO0x8fYG0tDTcv38fDg4O2LRpEwRBgLW1NWrUqAFPT0+0atUK7u7ucHd3x7Vr1xATEwMvLy/Mnz//ud0ONWrUQN++fVFUVGRyix5r1KiBQYMGITs72+SOjcgUMVyYuJdeegne3t4IDQ3Fzp070bJlS/W2GjVqID4+vlzvU1BQUOb2VmNt6NQVR0fxFtZBg4BDh4Ddu8X1GEVFRVi+fD+WLweqV89FvXoJKCoC3NzcAIjdG3l5eZDL5Thw4AD++usvODg4oKioCAqFAiNGjMDMmTPLdfulpaUlmjVrhvz8fJO7XdPS0hJeXl5IS0szuWMjMkVcc2HiduzYgUuXLqG4uFj9yOqKiIyMhKOjo/ql+uFIZVlbi42eERHAxImAlVUKsrOz/w0LTrh9uzuSkt7D7dutkJWlREpKCpKTk5GWlgaZTIb69evD3NwcmZmZ6N+/P+bMmcMfpkRkdBguTNipU6cwatQoLFu2DAMHDkRgYGCZ7XK5HO3bt0f37t3LPvH0CebOnYvMzEz1686dO7oc3eiZmwMvvAB06bIHNWuuRsuW5ujevTs8PDxQXGyH+PiGOHBgMJKSusPTsxsmT56MhQsXws/PD9bW1ujatSuaNWuG4uLicu8zNzcX+/fvx5EjR5Cbm6vDo9O/3Nxc7Ny50ySPjcgU8bKIibp16xaGDBkCf39/jBs3Dt7e3ujYsSNOnjyp7ke4desW6tevj4SEBAwZMgTnzp176jqE/65XAJ+N9VyCIODkyROwsroGO7tvMWNGD2zf7oBHj5rBxsb234fBvQSlshoKCoqxZ89XOHFiN8aPH4/Ro0dj+fLlePXVV1GtHI9oPXv2LE6fPo3Lly8DANavXw9XV1f07dsXMqmqRLUoOzsb58+fV3/MZ4sQGTaGCxOUnp6OQYMGYdiwYZg3bx4AoH379hg6dCjmz5+P7du3AwDq168PQHy2iLe3N65cuYIOHTpINrepUdWNN2zYEOnp6cjNvYQPPmiLN95oid27xTtKCgsBhaIQy5fHICXlOAYPngEPjy4YPHgwAMC8HPWfgiBg0aJFOH/+vPpx5F9//TVq166NJk2aoGnTpjo9Tn2wtLSEjY0N67+JjATDhQlycnLCRdUjPkvZtGmT+uNHjx7B1tYWVlZWSEpKwoULF0zih5AhuXDhAjIzM9G8eXNcunQJ58+fR9u2beHsDIweDQwdCmzfnoOYmAVITb2Ctm0DUFzcEcuWAZ07b8OAAWKB1/PIZDK0aNEC169fx8SJEwEAycnJsLOzU98ZZOxq1KiBd955h/XfREaCay6qqIsXL6JDhw7w9fXFSy+9hCVLlsDJyUnqsUzKuXPnoFQqYW5uDisrK5w4caLM9qKiDBw4MA+NGt1EaOgCtGrVUb0tKQlYuVKsF9+9+/n14j4+PhAEQd0BkZmZiXbt2pW9lEVEpCc8c1FFde3aFefOnZN6DJNVXFyM48ePw97eHgBQs2ZNXL9+HSkpKahduzbu37+PoKAgFBQUICYmCo0bN4ZSKdaL79gB3Lwpvs+jR8D69cDWrUCvXmK9+JN6tLy9vWFvb4+srCzY29tDEAT4+Pjo8YiJiEowXBDpwI0bN/DgwQPUqlULAODo6IgrV67gwoULaNSoEYKCgmBtbY3Y2FjU+feJaKp68ebNc9GypS9yc4GhQ8/AwsIWeXnA9u3iWYwXXhCbP+vWLdlfw4YNUatWLfz0008AgL59+8Lb21vvx60rqampWLJkCQRBwKeffgpnZ2epRyKiZ2C4INKBy5cv49GjR8jNzUVqaiqcnZ2RlZWFPXv24MqVK3BxcUFYWNhT6rwF3L59DQAwb56Aw4eBuDixWlyhKKkX9/UVmz/d3cV1F76+vli7di0AwMXFxaS6SJRKpfqSD+u/iQwfw4UJmz59Or788kscP35cfReIp6cnEhMTcfnyZTRs2FDiCU1Xhw4dMHr0aGRlZeHatWuwtraGnZ0d/vnnH3Ts2BEBAQHq2ykfPXqE69evIyMjA3369IG1tTUOHToEAGjc2Bru7sCwYWK9+IEDJfXiZ86Ir6ZNxTMZ7dp1QLNmzaBQKNCtWzeTuAVVRVVtnpOTwwWdREaA4cKELVmyBCtWrMDEiRNx9uxZ9OnTB9evX0dcXByDhY7VrVsXM2bMwK1btxAcHIx69erhzJkz6N27N0aPHo2jR4/i2rVrOHv2LG7fvg25XA5LS0s4OjqiY8eO6NatW5n3q1ED+N//gMGDgYMHgT17xPUYgPj496VLAXv7znBxGQkgDm3atNH3IeuUpaUlfH19Wf9NZCQYLkyYmZkZZs2ahfDwcAwYMAD79+/Hxo0by3RZpKamom7dumjTps1jdzOUJpfLIZeXPE8kqzBLp7ObkitXruDw4cNo1aoVLl68iOnTpyMrKwuCIMDGxgYODg5o1KgRbt68id27d+P27dvPfc+2bWW4fr0mzpxxQXq6jfrzd+70gplZByQltUZODmBnp8sjIyJ6MoYLExcWFoZPPvkEu3btwuLFizF8+PAy24cPH4569eo9932GDRtWtiLcCsBcLQ9rYgRBwKZNmxAfHw8bGxvcunULhYWFqFOnDtzc3FC9enX1pQulUoni4mJcvnwZFy9eRGJiIgBxoaaZ2dPvGLe2Bmxt6yM5uTUyMpyQnr4M1apVw44dQ3DoENCtm/isk3/XlRqt/Px87N+/H3l5ecjPz3/i4+mJyHAwXJi4iIgI5P17kd7Dw6PMtl27duHWrVsYNGjQc5+Ounnz5sfOXHivNp27EbStuLgYX331FbZu3Yr8/Hzk5+cjMjISSUlJuHjxIlJSUpCYmAiZTIbq1aujevXqMDc3x7Bhw9CsWTP4+voCAM6cOVPuquuEhAy8/PIfAIDCwi9hYWGNv/8G9u0D2rcXF38a6xpPuVyOU6dOqT9muCAybAwXJmzt2rUICAjA1KlTsWHDBkyZMgVJSUnq7ePHj8cPP/yA9evXP/e9xOdglDx3hI9cf7rCwkLExsbi2LFjmDZtGo4fPw4AGDVqFJycnFBQUICbN2/i+vXruHLlCuLj45GSkgIHBwc0bdoUHh4e6NWrFwAxENrY2Dxrd2pOTulwdHSEIAC9elkgPh4oKgKUSuD4cfHVooW4+LNFC8CY1ntaWFjA0tISgiCoK86JyHDxT6mJOnToEMaPHw8/Pz8sXboU3bt3x7hx47BmzRqMHTsW8+bNg6urKwYOHFiucEHlk5ubiwULFuDy5csICAhAx44dkZGRUeZrrKys4OXlBS8vLwwZMgRKpRLJycnIyMhAy5YtIZPJsG/fPo337eTkVGZf2dniWYu9e8WPAeDiRfHl6iqGjA4dxCe4GjonJydMmzYNaWlpbJIlMgKs/zZB169fR79+/dC8eXPs3LkTADB27FjUrVsXH374IQBg7969OH36NCwsLLBy5UqcPHkSffv2lXBq45eRkYG5c+fixo0bCA8PR8eOHZ//TRAX3rq6uqJVq1ZavX20enXgpZeAyEhgzBigdu2Sbap68YAA8c6TAj7lloi0iGcuTJC7uzsKnvDT4t69e+qP//nnH/XHkyZNQnx8PP7++2+9zGeKHjx4gMDAQBQUFCAqSqzzNhSWlmJ1eI8eQHy8WC9+65a4LT0d+PXXsvXipa5+ERFVCM9cEFXSrVu3MHv2bABATExMmWCRnp4OGxsb2NjYID09vVzvl5eXhzZt2qBNmzbqxbjl8bx9mZkB7doB/v7Axx8DrVuXbMvNBf76C5g7F1izBnjwoNy71Yv09HR8/vnnWLt2bbn/OxKRdHjmgrBixQqpRzBaFy5cQFhYGFxcXBAaGvpYe6RCoUD+v480VSgU5XpPpVKJM2fOqD8ur/LuSyYDPDzEV3IysGsXcPRoSb34wYPAoUOAj09JvbjUFAoFiouL1R8TkWFjuCCqoOPHjyMqKgrNmzdHQEAA7J7QWFWjRg1ERkaqPy4Pa2tr9VoZTW65rMi+6tcHJkwAhg8X68X37xcf7y4IJfXi7u7i4k9fX+nuMKlRowa6deuG3Nxc1n8TGQGGC6IK2Lt3LxYvXoxOnTph1qxZT62ktrS0hL+/v0bvbW5uDj8/P41nqsi+VFT14oMGldSLq248uX4d+OYbwMUF8PMDOncGqlWr0G4qzNLSEp06dWL9N5GRYLgg0tCmTZuwYsUK+Pn5Ydq0aTA3hns5y8nGRjxL0bev2Iuxc6d46QQQ12GsWQNs3ixu79ULKGe/FxFVMQwXROUkCAJWr16N9evXY+TIkRg/fvxzbx3Nz89HVFQUAMDf379clzkUCgV27NgBABg4cGC5S6Mqsq+nsbAAunQRz1KcPy/eYXLlirhNLgf++ENcANq9O9Cvn+7rxfPz83HkyBHWfxMZCZkgCILUQxirCRMmwNraGsuWLZN6FL2TF8jhGOWITP9MOFgZ172LkydPRlFREX744Ydyf49SqcTXX3+NHTt2YOLEiXj55ZfL9X0PHz6Ei4sLAPF21Tp16jz3e3JyclC9enUAQHZ29hPXcmhrX5q4dUs8k3HqlLgmQ8XMTCzjGjBAd/Xiuj42ItIunrkgeo7CwkJ8+umniIuLw4cffoh+/fqV+3stLCzUzwYp7xkIMzMz9ZNrn/XQMm3sSxONGwNTpgApKcDu3cDhwyX14seOia8WLcQ7TLy8tLv408LCAhYWFqz/JjIS/FNK9Ay5ubmIiIjApUuXMH/+fHTq1Emj73dyckJOTo5G32NjY6N+Homu91URtWsDr78ODB0q1ov//Teg2q2qXtzNTQwZ7duLZzYqy8nJCdOnT2f9N5GRYLggeorMzEwEBwfj/v37CA8Ph7c3nwJbmqpefMAA4MgRsS8jNVXcducOsGIFsHGjuCaje3fAyqpi+5HL5bh//746OF25cgWWlpYG1YJKRGUxXBA9wcOHDxEQEKBeJMkfZE9naQn07g307AmcPi2uy1DVi6elldSL9+4N9Omjeb14bGws4uLiAIiLXadNmwY7OztERUXBy8tLm4dCRFrC+m+i/7h9+zZmzZoF4PE6b02lp6erH1evSf13t27d0K1bN43rvzXdlzaZmYmXQfz9gZkzgVatSrbl5gJ//lmxenHV01737duHQ4cOwcLCAoWFhepFr0RkeHjmgqiUixcvIjQ0FHXq1EFoaChq1qxZqfdTKBTIyspSf1weSqUSR44cUX+sy33pgkwGNG8uvpKTxTMZx449Xi/epo14SaVp02e/X+vWrWFmZqY+pry8PHh5eaFBgwa6PxgiqhCGC6J/nThxApGRkc+s89aUg4ODujXToZzXA6ysrLBx40b1x7rcl67Vrw+8+WZJvfiBAyX14qdPiy93d3Hxp4/Pk+8wadGiBWrUqAFPT0/Y2NigsLAQHTt21Orj6YlIuxguiCDWeS9ZsgQdOnTA7NmztVYxbW1trX7eR3lZWFhgxIgRetmXvtSsCbzyCjB4sBgw/v67bL34118DdeuKZzJeeEEs8VKpX78+mjRpAqVSCVdXV9y4cQMtW7aU5DiIqHy45oKqvE2bNmHRokXo06cP5s6dy2dX6JCNjXiWIiJCfGBavXol2+7fB1atEtdl/PWXuE4DAGQyGTp16oS8vDxkZGSgZs2aaNGihTQHQETlwnBhwqZPnw6ZTIYTJ06oP6c6tZyYmCjhZIZBVee9YsUKvPLKK3j//ffVzwlRKpW4ffs2CgoKKrWPwsJCLF68GIsXL0ZhYWG5vqe4uBj79u3Dvn371I8Z19W+pGJhAXTtCgQHA//3f+L6DBVVvbi/P7B+PZCeDnh4eOD+/fuIj4+Hh4cHHB0dJZudiJ6P9d+VYOj130qlEnZ2dvDw8MDZs2fRp08fHDx4EHFxceoGyIoy9vrvwsJCdOrUCdu3b8fEiRPx4osv4saNG7h27RouX76Ms2fPIi0tDX379lXfOVIRplT/rWu3bonPMDl9+vF68YYNb2PevMYAgOXLl2PSpEmSzEhE5cM1FybMzMwMs2bNQnh4OAYMGID9+/dj48aN6NChA44ePYqBAwciLy8PZmZmePfdd7Fo0SKpR9YLpVKJ+Ph43Lx5E926dcPRo0exZs0aZGZmIj8/HzKZDPb29pDL5UhLS0Ou6vx8BeTn56svs+Tn55frvfLy8tSn/fPy8sq9cLEi+zIkdeoA48aJl0327jXH0aNmKCoStyUkWEImqwZAgI1NawiCduvFiUi7eOaiEgz9zIWKra0t8vLysHjxYnzwwQcAgPj4eFy+fBmvvfYazp8/Dx8fH9y7d++p/9qVy+WQy+XqX2cVZsF7tbfRnbnIy8tD9+7dcenSJXh6ekIQBJiZmaFBgwZwdHSEjY2N+of5iRMn0Lx5c43u2CDtKSqyxv37Xrh/3wsKhRWys3OgVCoxZMgQNGlijgEDtFcvTkTaxTMXJi4iIkJdxOTh4aH+fJs2bdCmTRsAQMuWLWFpaYmbN28+NVwMGzYM+/fvL/mEFYC5uppaNzIzMxESEgI3Nze89tprkMlkOHfuHFJSUvDo0SOkp6fDxsZGXUTl4OAAKysr1n5LyNe3EArFedy+3QDXrjVCnTreMDc3R2JiSb24n5+4foMZkMhwMFyYsLVr1yIgIABTp07Fhg0bMGXKFCQlJT32datWrYIgCHjhhRee+l6bN29+4pkLY/Hw4UMEBQUhJycHn332GZo0aQJAvERy9+5dXLt2DdeuXcOZM2eQmJiImzdvIjs7Gw0aNMDs2bMlnp4A8emrp06JpVy3b4ufS0sDfv4Z2LIF6NUL6NsXsLeXdk4iYrgwWYcOHcL48ePh5+eHpUuXonv37hg3bhzWrFmDsWPHqr/u6tWrmDx5Mj7//PNnvp/qX/Iq8gL5M77asCQmJiIwMBCWlpaYO3euejHr1atX4eTkBDc3N7i5uaFPnz4AgEePHuH69eu4du2a+uxORaWnp6vPGKn29zx5eXkYNmwYADHU2djY6GxfxqL0sV25chWpqU7YuRNISBC35+SI9eK7dgFduohnM4xsPSuRSeGai0ow1DUX169fh7e3N5o2bYqLFy+qP1+vXj0UFRUh9d9HV8rlcri5ueH111/H0qVLNdqHsdwtcvHiRYSFhaF27doICQmBQqHQ6x0VvFtEO552bHfvltSLl25Kl8nEevGBA4F/T1IRkR7xzIUJcnd3f2I/w71799QfK5VKtG7dGm3bttU4WBiLkydPYuHChfDw8EBgYCDs7OyQn5+Pd999F4B+KrIdHBw03p+VlRXWrFmj/liX+zIWTzu2Bg2At94CRowA9uwR2z8LCsrWi3t4iM2frVvzDhMifeGZi0ow1DMX5fH1119j2rRpsLa2Vn9uzZo1eOWVV8r1/YZ+5mLfvn1YvHix1uu8ybDl5ooPRtuzB8jMLLutXj3xcsl/68WJSPsYLirBmMNFZRlyuNiyZQu+/fZb9OvXD9OnT1e3blLVoVCIl0p27gRKnbADADg6Av36AT16ALa20sxHZOqY38lkCIKAtWvX4pdffsHLL7+Mt95667ECqsLCQqxbtw4A8Prrr+v8jEZF9ldcXIxTp04BANq1a1fucKTvY9MnTY9NVS/epQtw7pwYMq5eFbdlZgIbNogLQLt3B/r3Fx+sRkTawzMXlcAzF4Zz5kKpVOKbb77B9u3b8dZbb+F///vfE79O34seuaBTO7RxbDduiCEjPv7xevFOncR1GQ0aaGlgoiqOZy7I6BUVFeHTTz/FkSNH8MEHH6B///5P/VozMzP1mQAzPVQ7VmR/MpkMjRo1Un+sy30ZC20cW9OmwDvvAA8firesHjkiXj5RKoG4OPHVsqV4h0nz5lz8SVQZDBdk1PLy8rBgwQJcvHgR8+fPf2YRGAA4OztDoVDoabqK7c/W1ha3bt3Sy76MhTaPrU4d4I03gGHDgL17gX37xJ4MADh/Xnw1aiSeyWjXjvXiRBXBcEFGS1XnnZycjLCwMLRq1UrqkciI2NuLAWPgQPEsxq5dYuMnIDaALl8OODuLazJYL06kGYYLMkql67wjIyPRtGlTqUciI2VlBfTpI9aHnzwprstITBS3paaW1Iv36QP07s16caLy4Ak/MjqJiYmYPXs2FAoFYmJiNAoWGRkZqFevHurVq4eMjAzdDVmJ/eXn52PEiBEYMWIE8vPzdbovY6GPYzMzAzp2BObNAz76SFx/oZKTA2zdCsydC/z0k7hug4iejmcuyKhcvnwZISEhcHZ2RmhoqMbPzygsLMT9+/fVH+taRfZXXFyMTZs2qT/W5b6MhT6PTSYDvLzEV1KSeCbj+HFx4WdREbB/v9gE2rateEmlcWOdjkNklBguyGicPHkSkZGRcHd3R1BQULlv0SytevXqGDdunPpjXavI/iwtLfHtt9+qP9blvoyFVMfm6gpMnFhSL37wYEm9+KlT4ov14kSPY89FJbDnQn89FwcOHMCiRYvQrl07zJkzR6NnbhBpS26ueNZizx5A/p8HA9erJ4aMTp1YL07EPwJk8LZs2YLly5ejT58+mD59Oiz4NzdJxNYWePFF8Q6So0fFSyb/Xq3BvXvAjz8CmzYBffsCPXsCNjbSzkskFf4tTQZLEAT89NNP+Pnnn59a560phUKBbdu2AQCGDBmi86BSkf0plUpcvHgRANCiRYtyl0bp+9j0ydCOzcIC6NZNvEX17FkxZFy7Jm7LyCipF+/ZUwwarBenqoaXRSqBl0V0d1lEqVRi6dKl+Ouvv/Dmm2+W+2mtz8P6b+NkDMf2rHrxF14QL5nUry/ZeER6ZTr/tCGTUVRUhEWLFuHw4cN4//334efnp9X3r+zZD33sz9nZWW/7MhaGfmyqevEHD8RCrn/+KakX/+cf8dWqlXiHiYcHF3+SaWO4IIOSl5eHhQsX4vz585g3bx46d+6s1fevU6cOlEqlVt9T2/uzs7NDSkqKXvZlLIzp2FxcgLFjy9aL5+aK2xISxFejRmLIaNuW9eJkmhguyGDI5XKEhIQgKSkJoaGhaN26tdQjEVWYgwMwfLi4APTwYWD37rL14t9+K9aL+/mJazc0uOuYyOAxXJBBSElJQWBgILKzsxEVFcU6bzIZVlbios7evcV68R07gDt3xG2pqcC6dcDmzawXJ9PCE3IkuTt37mD27NkoKirSuM5bUxkZGWjcuDEaN26st/pvTfeXn5+PN954A2+88YbG9d/6PDZ9MoVjU9WLz58PfPgh4O1dsq10vfi6dUAFrooRGRSeuSBJXb58GaGhoahVq1aF6rw1VVhYiNu3b6s/1rWK7K+4uBg//fQTAKibOnW1L2NhSscmkwEtWoivO3fExZ+l68X37RMrxtu1E+8wYb04GSOGC5LMqVOnsHDhQjRt2hRBQUF6q+MeMWKE+mND3J+lpSU+++wz9ce63JexMNVjc3MT68WHDxdbPw8dKqkXP3lSfDVvLi7+bNmSd5iQ8WDPRSWw56LiPRcHDhzAZ599hrZt27LOm+hfubniWYu//368Xrx+ffFMRseOrBcnw8ffoqR327Ztw7Jly1jnTfQftrbAoEFl68UfPBC3JScDP/wA/PEH0K+f2P5pbS3ltERPx7/VSW8EQcC6deuwbt06jBgxAhMnTtR7MZJCoUBcXBwAoHPnznqp/9Z0f0qlEomJiQCAhg0balT/rc9j0ydTPrYnqVYN6N5drBg/e1a8w+T6dXFbRgbw++/Atm1Ar17inSg1akg5LdHjTPtPKBkMpVKJZcuW4c8//8SECRPwyiuvSNK4mJ6ejh49egDQT410RfaXl5eHJk2aANCs/lvfx6ZPpnxszyKTAb6+4uv6dfFMxpkz4pqM/HwxdOzeLdaL+/mxXpwMB8MF6ZxCocCiRYtw6NAhTJ8+HQMGDJB6JINna2sr9QhkYNzdgXfffbxevLgYOHJEfLVuLa7LYL04SY3hgnQqPz8fEREROH/+PObOnYsuXbpIOk+dOnWgzzXMFdmfnZ0dcnJy9LIvY2HKx6ap0vXif/8tLgBV1YufOye+GjcW7zBp04b14iQNhgvSGdZ5E+mOgwMwYkTZevH0dHHbrVvAsmVA7dol9eLVqkk5LVU1DBekEykpKQgKCkJWVhYiIyPh7u4u9UhEJsnaWrx7pHdv4MQJcV1GUpK4LSUF+OmnsvXiJlQTQgaMJ8xI61R13oWFhYiJiTGoYCGXy+Hl5QUvLy/I/1skYCD7KygowOTJkzF58mQUFBTodF/GwpSPTVvMzcWFnQEBYr14ixYl27KzgS1bAH9/sV48NVWyMamK4JkL0qorV64gJCQETk5OCAsL03mdt6by8/Nx+fJl9ccODpoXgOl6fwqFAitWrAAALF68uNwFY/o+Nn0y5WPTtv/Wi+/cKZ7R+G+9ePv24uLPRo2knphMEcMFaU18fDwiIiLQpEkTvdV5a8rW1hb9+/dXf2yI+6tWrRoWLFig/liX+zIWpnxsuuTmBrz9trg2Y88e4OBBoLBQvJX1xAnx5ekphgzWi5M2sf67Elj/XVL/fejQIXz66ado06YN/P39WedNZIByckrqxbOyym5r0EAMGR06sF6cKo+/hajS/vzzTyxduhS9e/fG+++/b/LtiUTGys4OGDxYvIMkLk7sy1DVi9+9C3z/fUm9eI8erBeniuNPAaqUX3/9FZt+3YThw4fj7bfflqR1UxNKpVJ97d7T07Pc1dr63J8gCEj9d8Wds7Nzuf+b6vvY9MmUj00K1aqJ4aFbN7Hxc+dO4MYNcdujR8Bvv4n14j17sl6cKobhgipEdTXtt99+w9vj38bIkSMNPlgAQGpqKry9vQHop0a6IvvLzc1Vf50m9d/6PjZ9MuVjk5KZGdC2rfi6fl2sEz9zRtyWl1e2XnzAAKBePWnnJeNR6XAhCAKyCrOe/4UmqFBWCCtLK8gLqtatcQqFAp988QkAYOzbYzFw4ECj+T2QVZgFWJV8bF2g2/O+FdlfTkGO+nvkBXIUWxTrbF/GwpSPzVDUdgXGvg30vw/s3Ssu9lQoACiBff+Ir5YtxUsmTZty8WdVYm9pr/E/Hiu9oDNFnoI6n/FfEURERKbo4UcPUduhtkbfU+lwkZmZiRouNXDnzp0qd++5XC6Hm5tblTn2rKwsREVF4c6dO5j20TQM2DEAdz66Awcr4zr2u3fvwtvbGxcuXECDBg0Mcn8V/b2l72PTJ1M+NkOWny8+JG3fPvFx76XVri02f3bqxHpxU6T6eyjjQQYcHR01+t5KXxaRyWRAAeBg5WB0P2QqzQpV5thTU1MRERQBuVyOTyI+QR23OsAO4zx2uaUcKBBP9elj9grtr4K/t/R9bPpkysdmyBysgOEvAi/5PV4vnvkQ+OMXYM+fJfXi5VwiRMbg37+HKrKejgs66bmSkpIQGBgIMzMzREdHo0GDBlVunQlRVaeqF+/UCbhwQQwZly6J27KyxOeXbN8u3oHSvz/g7CztvCQthgt6JlWdd82aNREWFoZatWpJPRIRSUgmExd2tmwJJCaW1IsLgtj+uXeveAmlQwfxDpOGDaWemKRQ6XBhZWWF4ODgKtnIaOrHXrrOOzAwEPb29lKPpBUODg7o1auX3tbJVGR/Ff29pe9j0ydTPjZj1bAhMGmSWC++e7f46HdVvfjx4+LLy0sMGd7evMPE2FTmZxzrv+mJVHXevr6+mDt37mO/uf5b/01E9Kx6cVdXsRm0Y0fxEguZNoYLeoyqzrtXr1744IMPnljnzXBBRE9TVCTeYbJrF/DwYdltNWuKazK6d2e9uCljuCA1QRDwyy+/YO3atRg2bBgmTZr01FXCDBdE9DxKpdj4uWMHcPNm2W02NkCvXmK9uIZ3OZIRYLggAGKw+Pbbb7F161aMGzcOo0aNeubtRwwXRFReggBcuyYu/jx7tuw2C4uSevG6daWZj7SP4YKgUCjw2Wef4eDBg3jvvffw4osvPvd7GC6IqCLu3RMvlxw9+m+9eCm+vmLIcHfn4k9jV+lHC27YsAEDBw5UP70xPj5eC2MZnnXr1sHa2hp3795Vf27SpEnw8fFBZmamhJNVTn5+PsLDw3HkyBHMmTOnXMHCmEyfPh0ymQwnTpxQf87T0xM2NjZITEw0iP1V9PeWvo9Nn0z52Kq6evWA8eOBiAhg4EDx8ojKmTNAbCwQEwOcPi1eViH9+uabb+Dj4wMHBwc4ODigS5cu+OuvvzR/I6GSVq1aJYSGhgrLly8XAAinT5+u7FsaJKVSKfj4+AjTpk0TBEEQQkJCBFdXVyEpKUniySpOLpcLM2fOFEaOHCnEx8dr9L2Z+ZkCQiBk5mfqaDrtKC4uFqytrYXWrVsLgiAIvXv3FszNzYXjx48bzP4q+ntL38emT6Z8bFRWXp4g7NolCHPmCMKUKWVfAQGCsH+/IBQWSj1l1bF582Zh27ZtwuXLl4XLly8L8+bNE6pVqyYkJCRo9D6VDhcqN2/eNOlwIQiCsGXLFsHKykqIiIgQatasWeY/9pYtW4TmzZsLzZo1E5YvXy7hlOWTkpIivPvuu8KYMWOEK1euaPz9xhIuBEEQAgMDBQCCn5+fIJPJhD/++EMQBEGIi4sTHB0dBUtLS8Ha2lr46KOPdLo/lZSUFMHc3Fxo3769+nPP+r1lbm4u+Pr6Cr6+vsLbb79drn3dvXtXsLW1FaytrQUrKyth3LhxWjk2fXrWf8d69eoJMplMaNCggYQTkjYVFQnCP/8IQkjI4yFj5kxB2LZNELKzpZ6yaqpZs6awYsUKjb6H4UJDbdu2FSwtLYV9+/apP1dUVCR4eHgISUlJglwuF5o1ayakpaVJOOWzJSUlCW+99Zbw1ltvVfjMizGFC0EQBBsbGwGAsHjxYvXnTp8+Lfz888+CIAhCQkKCYGZmJjx48EBn+1Pp2rWr4OrqWiZcCMKTf28JgiDUqlVL430VFBQIKSkpgiCIYcbCwqJCIVJqT/vv+OmnnwoBAQEMFyZIqRSEhARBWLTo8ZAxfbog/PyzIKSmSj1l1aBQKIR169YJlpaWwvnz5zX63kqvuahKduzYgUuXLqG4uBguLi7qzx87dgwtW7ZEgwYNYG9vj8GDB2PHjh0STvp0V69exezZs2FtbY3Y2Ngq8XTJiIgI5OXlAQA8PDzUn2/Tpg1ee+01AEDLli1haWmJm/+9X06L+wOAXbt24datWxg4cGCZzz/t91ZF92VpaQnnfx/ukJmZCUEQoDSyC9jP+u84Y8YMVtGbKFW9+EcfAfPmiTXiqsWdBQViQVdAALBiBXDnjrSzmqpz586hevXqsLKywjvvvIONGzfC29tbo/fQKFysXbsW1atXV78OHjyo0c6M2alTpzBq1CgsW7YMAwcORGBgoHpbcnJymR/Srq6uZRbnGYr4+HjMmzcP9erVQ3R0dJX4y3nt2rUICAjA1KlTUbt2bUyZMuWJX7dq1SoIgoAXXnhBp/sbP348Vq5cWeZzz/q9BYiPPW7fvj26d++O/fv3l3tft2/fho2NDZo1a4b//e9/8PT0rNSx6VN5/7+RaWvUCJg8GViwQHzqquqx7kqlWC2+YAGweLH4IDXe96g9np6eiI+PR1xcHN59911MmDABFy5c0OxNNDnNIZfLhatXr6pfubm56m2mfFnk5s2bQt26dYWIiAhBEAThxIkTgkwmE06cOCEIgiD8+uuv6sV4giAIMTExwieffCLJrE9z6NAhYcSIEUJwcLCQl5dX6fczhssiBw8eFMzMzAQ/Pz9BEARh9erVAgBh9erVZb7uypUrgqWlpbB06VKd7m/u3LlChw4dBEEQhLffflto3779c39vCYK4fkIQBOHcuXNCw4YNhczMzHIfm+r77O3thXPnzlXq+PSlvMf22Wef8bJIFZOVJQhbtgjCjBmPXzIJCxOEuDhBUCikntL09OvXT5gyZYpG38M1F8+RlpYmeHl5PfYfdtiwYcLAgQMFQRCEw4cPCyNGjFBve//994W1a9fqdc5n+fPPP4WhQ4cKMTExQlFRkVbe09DDxbVr1wRLS0vBy8urzOfr1q1bZg1DZmam4ODgIEydOlXn++vcubNgbm4umJubCzKZTAAg2NraPvP31n+9+OKLwsaNG8t1bKV5e3trbcGqLpX3/5sgMFxUZYWF4l0k8+c/HjL8/QVh925ByM+XekrT0bdvX2HChAkafU+lS7TS09ORmJiI5ORkDBkyBD///DM8PT1Rt25d1K0idWsKhQItWrTAvn374ODggHbt2iEuLk7yyw5CqTrvoUOHYvLkyc9s3dSEKZRoKZVKNGnSBE2aNMG+ffv0uu9JkyYhPj6+TI/Dkzx69Ai2trawsrJCUlISunXrhtOnT8PJyemZ35eQkIAaNWrA1dUVSUlJaNasGdasWYORI0dq8zAktXjxYnzyySdISkqSehSSiFIJxMeL9eK3bpXdZmtbUi/OB+mW37x58zBo0CC4ubkhKysLP//8M6KiorB9+3b4+fmV+30q/cj1zZs346233lL/evTo0QCA4OBghISEVPbtjYKFhQU+/fRT9OnTB0qlErNnzzaIYLF8+XJs2bIFY8eOxauvvqq1YGEqli5disTERDx8+BA2/zb5rFmzBq+88orEk5W4ePEipk6dCjMzM8hkMixZsuS5wQIQ19dMnjxZ/euXX37ZpIKFs7Mz0tPTIQgCzM3NsXLlSkyYMEHqsUjPzMyAdu2Atm3FevEdO4Bz58RtubnAX3+JbaCdO4vNnxqsla6yHjx4gHHjxuHevXtwdHSEj4+PxsECYP23SVIoFFi8eDEOHDiAd999F4MGDdL6PkzhzAURmZ7k5JJ68eLiks/LZICPj9gK6u4u3XxVBcOFicnPz0dUVBTOnDmDmTNnonv37jrZD8MFERmyjAzxttX9+4H8/LLb3N3FMxm+vnyGia4wXJiQrKwshIWF4datW5g/fz7atGmjs30xXBCRMcjPBw4cAPbsEQNHaS4ugJ+feNlEdZsraQfDhYlIS0tDUFAQMjIyEBIS8ljpkLYxXBCRMVEoxG6MnTvFSyelOTiICz979RIXglLlMVyYgLt37yIwMBCCICA8PByurq463yfDBREZI0EAzp8XF39euVJ2m5UV0L070K8fUAU6BnWK4cLIXb16FSEhIXB0dERYWJi68lnXGC6IyNjduiWeyTh1qmzDp5mZWDs+YADg5ibZeEaN4cKInTlzBgsWLECjRo0QHBwMe3t7ve2b4YKITEVKCrB7N3D4MFBUVHZbixbiHSZeXlz8qQmGCyN1+PBhfPLJJ/Dx8cHcuXNhbW2t1/0zXBCRqcnOBvbtA/buFT8uzc1NPJPRoYN4ZoOejeHCCG3fvh1ff/01evTogY8++ggWFpXuQtMYwwURmarCQuDIEbEvIzW17LZatcQ1Gd27i2s06MkYLoyIIAhYv349Vq9ejZdeeglTpkyRrHWT4YKITJ1SCZw+La7LeFK9eO/e4tNaWS/+OIYLIyEIAlasWIHNmzfjjTfewGuvvSZpnTfDBRFVFYIAXL0q3mGSkFB2m4UF0KWL2JfBevESDBdGQKFQ4PPPP8e+ffvwzjvvYPDgwVKPxHBBRFVScrJ4JuPYscfrxX19xcWfTZtKN5+hYLgwcPqq89YUwwURVWUZGWLr54EDT64XHzhQfJZJVb3DhOHCgOmzzltTDBdEREBeHnDw4JPrxevWFS+XvPBC1asXZ7gwUKo670ePHiE0NFTndd6aYrggIiqhUIiXSnbuBO7dK7utKtaLM1wYoLt37yIoKAhKpVJvdd6aYrggInqcIIiLPnfufHK9eI8e4q2sTk7SzKcvDBcG5tq1awgJCYGDg4Ne67w1xXBBRPRst26Jd5icPv14vXjHjmIplwH+21ErGC4MyNmzZ7FgwQK4ubkhJCREr3XemmK4ICIqn4cPxXrxI0cerxf39hYXf3p6mtbiT4YLA3HkyBHExsaidevWmDdvnt7rvDXFcEFEpJmsrJJ68Zycstvc3MSQ0b69adSLM1wYgB07duCrr75C9+7dMWPGDEnqvDXFcEFEVDHPqxfv3x/o1s2468UZLiQkCAJ+++03rFq1CkOGDMGUKVNgZiSRleGCiKhylErxce87dwK3b5fdZmcn3l3Sty9gwFfIn4rhQiKCIOC7777Dpk2bMGbMGIwePVrSOm9NMVwQEWmHIIh3luzc+Xi9eLVqJfXidepIM19FMFxIwBDrvDXFcEFEpH1375bUiyuVJZ+XyYA2bcQ7TIyhXpzhQs8KCgoQHR2N06dPY8aMGejRo4fUI1UIwwURke48eiS2fh48+Hi9uIeHGDJatzbcO0wYLvQoOzsbYWFhuHnzJubNm4e2bdtKPVKFMVwQEelebm5JvXhmZtlt9eqV1Isb2n0ADBd6kp6ejqCgIKSnpyM4OBienp5Sj1QpDBdERPrzrHpxR0dx4WfPnoZTL85woQfJyckIDAyEUqlEWFgY3NzcpB6p0hguiIj0TxCAc+fEkHH1atltqnrx/v2BmjWlmU+F4ULHrl+/juDgYFSvXh3h4eGoXbu21CNpBcMFEZG0bt4UQ8aT6sU7dRLXZTRoIM1sDBc6pKrzdnV1VT8vxFQwXBARGYaHD8VCriNHxMsnpbVsKYYMfdeLM1zoyD///IOYmBi0atUK8+fPN/g6b00xXBARGZasLLFafN++x+vFGzUSQ0a7dvqpF2e40IGdO3fiyy+/RLdu3TBjxgxUq1ZN6pG0juGCiMgwFRSU1IunpZXd5uwsrsno2lW39eIMF1okCAJ+//13/Pjjjxg8eDCmTp1qNHXemmK4ICIybKp68R07gMTEstvs7IA+fYDevXVTL85woSWCIGDlypX4448/8Prrr+P11183qjpvTTFcEBEZB0EALl8WF3+eP192m67qxU3zn9V6plAosHjxYmzatAlTp07FmDFjDCJYrFu3DtbW1rh79676c5MmTYKPjw8y/9vGQkREJkkmA7y8gPffBwIDgc6dS9ZdFBUBBw4AQUHAsmXiHSha2SfPXFSOqs771KlTmDFjBnr27Cn1SGqCIKBNmzbo0aMHvvzyS4SGhmLFihWIi4tDg0ren8QzF0RExuvRI2D3brH9s6Cg7DZt1IsbWGGoccnOzkZ4eDiuX7+OoKAgtGvXTuqRypDJZIiIiMDIkSNRv359LFmyBAcPHlQHi61bt2LmzJlQKpWYM2cOJk2aJPHERESkDzVrAqNGAUOGiGcu9uwB5HJx29Wr4qtePSAkpGLvzzMXFaSq8U5LSzP4Ou927drh/Pnz2LlzJ3r16gVAvJTj7e2NvXv3wsHBAe3atcPRo0fh5OT0xPcoKChAQal4Ky+Qw+1rN565ICIyAQoFcPSouC7j/v2Szy9bVrH345qLCrh37x5mzZqF7OxsREdHG3Sw2LFjBy5duoTi4mK4uLioP3/s2DG0bNkSDRo0gL29PQYPHowdO3Y89X0iIyPh6OiofplChTkREYksLIBu3cQzFe+9BzRrVrn3Y7jQ0I0bNzBr1ixUq1YNMTExBv1D9tSpUxg1ahSWLVuGgQMHIjAwUL0tOTm5zLoLV1fXMgs//2vu3LnIzMxUv+7cuaPT2YmISP9kMsDXF5g1C5gzp+LvwzUXGkhISEB4eDgaNGiA4OBgODo6Sj3SU926dQtDhgyBv78/xo0bB29vb3Ts2BEnT55E+/bt8aSrYc+6w8XKygpWpRtXCp76pUREZAKaNq349/LMRTnFxcUhKCgIHh4eiIiIMOhgkZ6ejkGDBmHYsGGYN28eAKB9+/YYOnQo5s+fDwBo0KBBmTMVSUlJqFevniTzEhGRaeGCznLYtWsXvvjiC3Tt2hUzZ840iTpvhUKBFi1aYN++feoFnXFxcahVq1a5vp+3ohIR0dPwssgzCIKADRs24IcffsCgQYPwzjvvmEydt4WFBT799FP06dMHSqUSs2fPLnewICIiehaeuXgKQRDw/fffY+PGjRg9erTBtG4aCp65ICKip+GZiydQKBT48ssvsWfPHkyZMgVDhw6VeiQiIiKjwXDxH4WFhYiKisKpU6cwa9Ysg6rzJiIiMgYMF6Xk5OQgLCwM169fR2BgINq3by/1SEREREaH4eJfqjrv1NRULFiwAF5eXlKPREREZJQYLiDWeQcFBaGoqAjR0dFo2LCh1CMREREZLdO4r7ISbty4gdmzZ8Pc3BwxMTEMFkRERJVUpcNFQkIC5s6di9q1ayM6Ohp16tSReiQiIiKjV2Uvixw9ehTR0dHw9vbG/PnzYWNjI/VIREREJqFKhovdu3fj888/N6k6byIiIkNR5cLFhg0b8P333+PFF1/Eu+++azJ13kRERIaiyoSL0nXer732Gt544w3WeRMREelAlQgXxcXF+OKLL1jnTUREpAcmHy4KCwsRExODEydOYObMmejdu7fUIxEREZk0kw4XOTk5CA8Px9WrV1nnTUREpCcmGy4ePXqE4OBgpKSkICIignXeREREemKS4UJV511YWMg6byIiIj0zufswb968idmzZ8PMzAyxsbEMFkRERHpmUuHi/PnzmDt3LmrVqoWYmBjWeRMREUnAZC6LHDt2DNHR0fDy8sL8+fNha2sr9UhERERVkkmEiz179uDzzz9H586dMXPmTFhaWko9EhERUZVl9OFi48aNWLlyJQYOHIj33nuPdd5EREQSM9pwIQgCfvjhB2zYsAGvvvoqxo4dyzpvIiIiA2CU4aK4uBhffvkldu/ejcmTJ2PYsGFSj0RERET/MrpwUbrOe8aMGejTp4/UIxEREVEpRhUucnJysGDBAly5cgUBAQHo0KGD1CMRERHRfxhNuMjIyEBwcDAePHiABQsWoEWLFlKPRERERE9gFOHi/v37CAoKQkFBAaKiotC4cWOpRyIiIqKnMPj7Nm/duoXZs2cDAGJjYxksiIiIDJxBh4vz58/D398fTk5OiI2NZZ03ERGRETDYyyKs8yYiIjJOBhkuWOdNRERkvAwuXKjqvAcMGIBp06axzpuIiMjIGEy4EAQBq1atwm+//YZRo0Zh3LhxrPMmIiIyQgYRLoqLi/HVV19h165dmDRpEoYPHy71SERERFRBkoeLwsJCxMbG4tixY/joo4/Qt29fqUciIiKiSpA0XPy3zrtjx45SjkNERERaIFm4KF3nHR4eDm9vb6lGISIiIi2SJFw8ePAAgYGBrPMmIiIyQXq/z7N0nXdMTAyDBRERkYnRa7i4cOEC/P39UaNGDcTExMDFxUWfuyciIiI90NtlkePHjyMqKgrNmzdHQEAA7Ozs9LVrIiIi0iO9hIu9e/di8eLF6NSpE2bNmsU6byIiIhOm83CxadMmrFixAn5+fpg2bRrMzc11vUsiIiKSkM7ChSAIWL16NdavX4+RI0di/PjxrPMmIiKqAnQSLoqLi/H1119j586dePvttzFixAhd7IaIiIgMkNbDRWFhIT755BMcPXqUdd5ERERVkFZvRc3NzUVoaChOnjyJ+fPnM1gYqA0bNmDgwIFwdnaGTCZDfHy81CMREZEJ0Vq4yMzMxLx583D9+nWEh4ejU6dO2npr0rKcnBx069YNUVFRUo9CREQmSCuXRR4+fIiAgADk5+ezztsIjBs3DoDYlkpERKRtWgkXs2bNgpWVFWJiYlC3bl1tvCUREREZKa2EC0dHR4SGhqJmzZraeDsyQAUFBSgoKFD/Wl4gl3AaIiIyZFpZc/H5558zWBiotWvXonr16urXwYMHK/Q+kZGRcHR0VL/c3Ny0PCkREZkKmSAIgtRDkO5kZWXhwYMH6l83aNAANjY2AMQ1F02aNMHp06fRpk2bZ77Pf89cCIKAQlkhnO2dWY5GRERl6O3BZSQNe3t72NvbV/p9rKysYGVlpYWJiIjI1DFcVEHp6elITExEcnIyAODy5csAgLp163JBLhERVZpWS7TIOGzevBlt27bFkCFDAACjR49G27ZtsXTpUoknIyIiU8A1F0RERKRVPHNBREREWsVwQURERFrFcEFERERaxXBBREREWsVwQURERFrFcEFERERaxXBBREREWsVwQURERFrFcEFERERaxXBBREREWsVwQURERFrFcEFERERa9f9AVop0hKO+OAAAAABJRU5ErkJggg==\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "x0 = -0.5\n", - "plot45(g, xmin, xmax, x0, num_arrows=5)" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "9ad45f31", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=10)" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 39, - 44, - 218, - 304, - 309, - 311, - 315, - 318, - 322, - 326, - 361, - 365, - 370, - 372, - 376, - 378, - 383, - 387, - 391, - 393, - 408, - 414, - 418, - 420, - 426, - 428, - 432, - 434, - 466, - 470, - 474, - 477, - 482, - 484, - 490, - 494, - 498, - 501, - 506, - 508 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/.jupyter_cache/executed/8fe1ed5b58896d77284919eb2433f9d1/base.ipynb b/lectures/_build/.jupyter_cache/executed/8fe1ed5b58896d77284919eb2433f9d1/base.ipynb deleted file mode 100644 index e3b14cbb5..000000000 --- a/lectures/_build/.jupyter_cache/executed/8fe1ed5b58896d77284919eb2433f9d1/base.ipynb +++ /dev/null @@ -1,226 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "7739073e", - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "plt.rcParams[\"figure.figsize\"] = (11, 5) #set default figure size\n", - "from random import uniform, seed\n", - "from math import sqrt" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "202b187a", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 1\n" - ] - }, - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAp8AAAKoCAYAAAAxl5QdAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAAEAAElEQVR4nOz9eXgc5Znuj99V1XtL3a1d1m55k2xjA5ZZw2KTYCAYkklCDuQkkwwkYZIZkoHJmTD5npNfMjlDTmaSYZgEJuEww0lCnJAFBhwDccAGggHbgBdsyZtk7ZK1dZfUe1fV7w9ZspZu9VZ7P5/rykUsdUslqep972e7X0aSJAkEQRAEQRAEoQKs1hdAEARBEARBFA4kPgmCIAiCIAjVIPFJEARBEARBqAaJT4IgCIIgCEI1SHwSBEEQBEEQqkHikyAIgiAIglANEp8EQRAEQRCEapD4JAiCIAiCIFSDxCdBEARBEAShGiQ+CYIgznPkyBF87nOfw/Lly+FwOFBUVIRLL70U3/ve9zA+Pq7I97z++utx/fXXy/o1z507h89+9rMoLy+Hy+XClVdeiZdfflnW70EQBJErFq0vgCAIQg88/vjj+NKXvoQ1a9bga1/7GtauXYt4PI6DBw/i3//93/Hmm2/imWee0foy0xKNRnHDDTfA7/fjX//1X1FZWYkf/ehHuOmmm/DHP/4R1113ndaXSBBEgcPQ2e4EQRQ6b775Jq655hp86EMfwrPPPgu73T7v87FYDC+++CJuu+022b/3TNZz7969sny9Rx99FF/+8pexb98+XHnllQCARCKBjRs3oqioCG+//bYs34cgCCJXqOxOEETB84//+I9gGAY/+clPFglPALDZbLPC8+6770ZpaSlCodCi123duhXr1q2b/bcoivi3f/s3XHzxxXA6nfD5fLjiiivw3HPPLXk9sVgM3/nOd9DS0gK73Y6Kigp87nOfw8jISNqf5ZlnnsGaNWtmhScAWCwW/Pf//t+xf/9+9Pf3p/0aBEEQSkLikyCIgkYQBLzyyivYtGkT6uvr077+K1/5CiYmJvCLX/xi3sePHz+OPXv24Mtf/vLsxz772c/iK1/5CjZv3oxf/epX+OUvf4nbbrsNZ8+eTfn1RVHE7bffju9+97u466678Pvf/x7f/e53sXv3blx//fUIh8NLXt/777+PDRs2LPr4zMeOHTuW9mckCIJQEur5JAiioBkdHUUoFMLy5cszev2GDRtw3XXX4Uc/+hHuueee2Y//8Ic/hMfjwWc+8xkAwOuvv46f/exn+MY3voHvfOc7s6+76aablvz6Tz/9NF588UX89re/xZ/92Z/Nfnzjxo3YvHkznnzySfzlX/5lyvePjY2htLR00cdnPjY2NpbRz0kQBKEUlPkkCILIkq985Ss4dOgQ3njjDQAAz/P42c9+hj//8z9HUVERAOCFF14AgHmZ0EzYuXMnfD4ftm/fjkQiMfu/iy++GNXV1Rn1hjIMk9PnCIIg1IDEJ0EQBc2MHVFXV1fG77n99tvR1NSEH/3oRwCAJ598EsFgcJ7QHBkZAcdxqK6uzup6hoeH4ff7YbPZYLVa5/1vaGgIo6OjS76/rKwsaXZzxioqWVaUIAhCTajsThBEQcNxHG644Qa88MIL6OvrQ11dXdr3sCyLL3/5y/j7v/97fP/738ejjz6KG264AWvWrJl9TUVFBQRBwNDQEJYtW5bx9ZSXl6OsrAwvvvhi0s8XFxcv+f6LLroIR48eXfTxmY+tX78+42shCIJQAsp8EgRR8Dz44IOQJAmf//znEYvFFn0+Ho/j+eefn/exe+65BzabDZ/61Kdw4sQJ/NVf/dW8z998880AgMceeyyra7n11lsxNjYGQRDQ1ta26H9zBW4yPvrRj6Kjo2OepVIikcDPf/5zXH755aipqcnqegiCIOSGfD4JgiBwwWS+paUFf/mXf4l169YhHo/jvffew09+8hOsX79+kcn8l770JTz22GNobGxEZ2cnWHZ+PP+Zz3wGP//5z/H5z38et956K+x2O9577z24XC789V//NYDFPp+CIGD79u14++238ZWvfAWXXXYZrFYr+vr6sGfPHtx+++346Ec/mvLniEaj2LRpE3iex3e/+11UVlbi0UcfxfPPP08m8wRB6AISnwRBEOc5fPgw/uVf/gV79uzB0NAQrFYrVq9eje3bt+Ov/uqvUFFRMe/1r776Kq6//np897vfxd/93d8t+nqiKOKRRx7BE088gZMnT8LpdGLt2rX4+7//e9x6660AkpvMJxIJ/Ou//it+9rOf4cSJE7BYLKirq8N1112Hv/3bv8XKlSuX/DmGh4fxP/7H/8DOnTsRCoVw8cUX4x/+4R/wwQ9+ML9fEEEQhAyQ+CQIgsiRBx54AI899hh6e3tRVlam9eUQBEEYAho4IgiCyJK33noLJ0+exKOPPoovfvGLJDwJgiCygDKfBEEQWcIwDFwuF2655Rb853/+56y3J0EQBJEeynwSBEFkCcXsBEEQuUNWSwRBEARBEIRqkPgkCIIgCIIgVIPEJ0EQBEEQBKEahuj5FEURAwMDKC4uBsMwWl8OQRAEQRAEsQBJkjA5OYmamppFh27MxRDic2BgAPX19VpfBkEQBEEQBJGG3t5e1NXVpfy8IcRncXExAOBYby+KPR6Nr4YgCIIgCIJYyCTPY119/axuS4UhxOdMqb3Y44GHxCdBEARBEIRuSdciSQNHBEEQBEEQhGqQ+CQIgiAIgiBUg8QnQRAEQRAEoRokPgmCIAiCIAjVIPFJEARBEARBqAaJT4IgCIIgCEI1SHwSBEEQBEEQqkHikyAIgiAIglANEp8EQRAEQRCEapD4JAiCIAiCIFSDxCdBEARBEAShGiQ+CYIgCIIgCNUg8UkQBEEQBEGoBolPgiAIgiAIQjVIfBIEQRAEQRCqQeKTIAiCIAiCUA0SnwRBEARBEIRqkPgkCIIgCIIgVIPEJ0EQBEEQBKEaWYvP1157Ddu3b0dNTQ0YhsGzzz6b9j2vvvoqNm3aBIfDgebmZvz7v/97LteqP4Q4uN4DsB14Atwbj0z/t/cAIMS1vjKCIAiCIAhdYsn2DcFgEBs3bsTnPvc5fOxjH0v7+q6uLtxyyy34/Oc/j5///Od444038KUvfQkVFRUZvV+vsENHETvwOPrHTqNdiIBnWHgkEa3HfouqspWwbf4CxOr1Wl8mQRAEQRCErmAkSZJyfjPD4JlnnsFHPvKRlK/5u7/7Ozz33HNob2+f/di9996Lw4cP480338zo+/A8D6/Xi55AAB6PJ9fLlQ126Cj4vd/FnvAwDnhrwVsds5/zxCPYHOjHFmcVPNd/HWL1RRpeKaEJQhzcwCFwQ0cgxILgbG4I1Rsg1FwMcFatr44gCIIgFIHneTR4vQik0WtZZz6z5c0338SNN94472Pbtm3DE088gXg8DqvVYJuxEEfswOPYEx7GK2XNkBhm3qd5qwOvlDUDY524+cDjsNzyfRIcyTCpQKOMOEEQBEEsjeLic2hoCFVVVfM+VlVVhUQigdHRUSxbtmzRe6LRKKLR6Oy/eZ5X+jIzhhs4hP6x0zjgrV0kPGeQGAYHvLW4dOw0GgYPQ6hrU/kq9Y1ZBdpSGfHX4hFsHj2OLXsfoow4QRAEUdCoMu3OLBBpM5X+hR+f4aGHHoLX6539X319veLXmCnc0JFpwTRHWCSDtzrQLkTADR5W6cqMwYxAe2H0OH7sqcDOylV4rWIFdlauwo89FXhh9Dj4vQ+BHTqq9aVmx4KM+ML7YyYjvic8jNiBx2kojSAIgihYFM98VldXY2hoaN7Hzp07B4vFgrKysqTvefDBB3H//ffP/pvned0IUCEWBM9kptl5hoUQCyp8RQbCxC0LlBEniPyICyLa+wPoGOARjcVgt9nQUuNBa60XVo5cAQnzUcj3vOLi88orr8Tzzz8/72N/+MMf0NbWlrLf0263w263K31pOcHZ3PBIYkav9UjidC+jwtdkFBQVaBr3kGabEV9O4pMgZjkxwGPn/g6E/b1osnbDawmDTzjxXEcjdvvqsf3yFqxepv2waa4UssggkmP2ez4dWYvPqakpnD59evbfXV1dOHToEEpLS9HQ0IAHH3wQ/f39+OlPfwpgerL9hz/8Ie6//358/vOfx5tvvoknnngCO3bskO+nUBGhegNaj/0Wr8WXFhqeeAStnAPCso0qXp2+UUqg6aGHlDLiBJEbJwZ4/PrVA2hlDmJbcz/KHRf6/UcjZ/HSQC2e3juJT1y3GWtqjLcZF7rIIBZj9ns+E7IWnwcPHsSWLVtm/z1THv/zP/9zPPnkkxgcHERPT8/s55cvX45du3bhb/7mb/CjH/0INTU1eOSRRwzr8SnUXIyqspXYPHo8aekYABhJwuZAP6rK15L4nIMSAk0vQz6UESeI7IkLInbu70ArcxB3Lu8Eu2A5LXdEcefyTuzoAnbuL0bz9jZDZQpJZBALMfs9nylZ/0TXX389JEla9L8nn3wSAPDkk09i7969895z3XXX4d1330U0GkVXVxfuvfdeOa5dGzgrbJu/gC3OKmwd64QnHpn3aU88gq1jndjirIJt8xcM07OoBrkItCXR0ZCPUL0BrZxj0f2wEMqIE8QF2vsDCPt7sa2mf9EmPAPLANtq+hEO9KK9P6DuBebBQpExV3gCF0RGK3MQO/d3IC5ktjYSxsbM93w2KN7zaUbE6vXwXP913HzgcVy6sNTLOVBVvtawdkFKInfLgp6GfCgjXsAk6zeuXAsA4M4dN5WPrdx0DPBosnYvEmYLKXdE0WjpRscAjw0NJSpdXX7Miozm9CLj4a5etPevkuVno/5SfWPmez4bSHzmiFh9ESy3fB8Ng4enexNnNphlGyEs2wiRNphFyC3QdDXkM5MR3/sQMNa55MlXts1fkOf+MKlRv5FI2m8cm0LL1CiKweCEuwx99iJT+NgqQTQWg9cSzui1XksYgZhxLMq0EBnUX6p/zHzPZwOJz3zgrBDq2mYFDfXwpUFmgaa3IR81M+J6GLIqdJL1GzPhccQGuhGWgrgUFlwaDaCrtAG9rhJDHDSgdtbMbrOBTzgzem0g4YTdZpygSm2RQf2lxsDM93w2kPgkVEVOgabHIR81MuJ6GbIqaJJ51koihJF2DAgh9Dt9OAYJiUgIm0dOYaChTfc+tlpkzVpqPHiuoxGjkbNLZghHI3Z0Jxpxm4FEk5oig4ZYjIOZ7/lsIPFJqI5cAk23tldKZsRNbNRvJJL1GzOhMYQjPEZsboABJDB4yW7HJREejaEJdLrLdHvQgFZZs9ZaL3b76vHSQG1S0QQAogS8NFALp7cerbVe2b630qgpMrTqLyWyx8z3fDaQ+CS0QQaBVohDPnoasjIacpaUk/UbM6Ex+CUBMZab/dgYy+GkFEHDefEJZNCDrHIvr5ZZMyvHYvvlLXh67yR2dE2Lo/nC146XBmrRLrXhjstbDJWtU1Nk0BCLccj3njfLQBmJT8K4aDHkozG6GrIyEHKXlJP1G0tiArEkr/UzQM0Cm69UPcha9PJqnTVbvcyDT1y3GTv3F+Phrl40Wqb/PoGEE92JRji99bjDgIMyagprGmIxFrne82YaKCPxSRiaQrO90tuQlRFQoqScrN+YYS2wJXmtTwLiCwKfZD3IWvXy6iFrtqbGg+btbWjvX4WOAR6BWBx2mxW3GTCjM5esRUaOWW8aYjEe2d7zZhsoI/FJGJ5Csr3S45CVnlGqpJys31hylcE30YVB8ULpvUwUsJqx4rDrglhL2oOsYS+vXrJmVo7FhoYS05WDMxUZ+WS98+0vNUsp12hkes+bcaCMxCehHkr2shWI7ZVuh6x0ilIl5WT9xpKrDE6HBxWRCfTbPWAgYVs0CsZRiu7z4jNVD7KWvbyUNVOedCIj36x3a60XL3nr8LvOKmwtPQZJEsGxLHxuG3wuG1iWSdlfmkkpd3llEYlTDdG6NUYJSHwSqkC+lPJQiENW+aBYSTlFvzFX0YqagUMoCfunfT6tRdhXsRoCwy7Zg6xlLy9Zv2iMDFnvzuEpBEICDg81IMgPYYvvKIq4KLr9xeizu1HkrcKbE8sX9ZdmUsr9jxcmwNmL4YwPGr7P0KjooTVGbkh8EopDvpR5kCRbbGm4ClumRgpmyCoflCwpp+o39jpKsSYBFAM4YfeiOTiGi6dGluxB1rKXl6xftCXfrPeMgLyEO4iPrefx6kATfhdYhkZrP1xsGN1jJTh2thXVdS349JYNs0Ixk1LuLZUd6H1/AqcmmvG1TcdQ7YrMft6IfYZGRS+tMXJC4pNQFvKlzJmU2WLOgWpnKW51VeNSfsT0Q1b5oHRJOWW/cdU6AMAHho9l1IOsZS+vme2OjEA+We9kArKtfAzH/V4c99ciKrBo8IhggiHEHFYsryya/XrpSrmiKKF31I8bvd0I8R4MRxzzxKcR+wyNihlbY0h8EopCvpS5kTZbHOjHFmcFmi75cyyPTZl6yCofVCkpL9FvLDRcsehjydC6l9esdkdGIJ+sd3t/AMGJXtSWTuFXXY2ICgzsnIRWH4+PN/XAykoApu/vh7tq0d6/erYcm66U6w/FIESD2OA7h/fC/Tjur8XGUv+81xitz9ComLE1hsQnoShm9qVUbEJ0qWyxJGIyNom9YgzM0CHcEhqH9Yb/37T4IcG5CKOUlLXq5V14D9dUVsJeU41oYhMCiYQp7I70Tj5Z71fbhzEwNoFXppxosvXBw4XACy78bqQOL9rL8ZHlw2jx8kl7AdOVcv3BGIrZSTg4AV5LEFNC8r+/kfoMjYpR1rFsIPFJKIpSvWxaW4MoafabKlvMhMchjLQjHOHhlwT8RhTRNOxHzYv/A56aS6jUngTDlJQ1ODAh1T18PN4IJw2SqEauWe8TAzyOnjyBzfb38Ona/Si3Tc2+djRWhBfHNmLHyRbcuQpo8fGLegHTlXIFUYSNTQAAAgk3XFxqgWyUPkOjYph1LAtIfBKKokQvm9anPCht9pv06MbwOGIDhzAghDBic8/6SL4ZCqKBZRCjoa2UGKWkrOaBCWYzrDYyuWS9Z3o9NzkOYZvz3XnCEwDKbVO4q3offjEEPHu2FQ9smFzUC5iulMuxLOKiBaOxInTHa/ExXyDlz2CUPkMjY5R1LFNIfBKKIncvm9abphpmv4uyxZIIYaQdA0II/XYPMOd7+hmgBqChrTQY5QQdNQ5MMKNhtaHJIevd3jOBsL8Xn6wbwORoMSLCdHl8Liwj4aayw/hBfzP2natY1AuYrpTrc9vQNVGMN0ea4LLbsTaF+DRSn6HRMco6lgkkPglFkbOXTQ+bphpmvwuzxUxoDOEIjxGbe57wBC4c3UhDW+kxzAk6Ch+YYEbDaqOTbdZ7ZliouUTC+5Nu9AbdWOnhFy4PKLdNodHaj2d7NqK8bn4vYLpSboItxsuTl6EjVIuvbeycHV6ad90G6zM0A4ZZx9JA4tMMKHlyUL7I2Mumh01TDbPfhdliJjQGv3ThyMYZFh7daMShLUJ9zGhYbQayyXrPDAuxLIPGSh86B+I4zQP17uC8DGhE4BCNCxgQ6/G5JL2A6Uq50ZIquJxhvDvOo8IRNXyfIaEfSHwaHCOcHCRXL5seNk01zH4XZYvFBGILXsNIi49uBOQ3ICfMhxkNq01DhlnvucNCXpcNzcsq0D1ixVE+iCJ2EjY2gZhowZRYjBGpBptbmlP2AqYr5XYOT2Hnfq8p+gwJ/UDi08AY6eQgOXrZ9LBpqmL2uyBb/I4kwTbn02WigG3RKC6zuGaPbpxBbgNywnyY0bC60Fg4LOR127DeWQF/yAt/MIaYOH22e7GlGDFhLW5urVzy6y1VyjVTnyGhH0h8GhUjnhyUZy+bHjZNtcx+52aLNw28i0NxASekSRSBxWrGCsZRin0Vq9Hn8s2+RykDcsJcmNGwutBINizEsgxKi+woLbIDmO7H3NHVDJevIe9+TLP0GRL6gUIWg8INHMJwhicHDY+dBjd4WOUrlJ+WGg/OxhsxGrEv+bqZTbNFgU2ztdYL5/lFX1zcfw9Avib8mWxx/c3/jO1VG3GL1YvK0pU4XHcJ/quhbZ7wnB3aKltJ4pNYEjXvYUIZZoaF2qU27OhqXrQmjkbs2NHVjHapDdupH5PQIZT5NChmPjkoFXo45UF1s1/OCqHhCrC3fB+1ex/CyfAwRm3u+aV2BQzICfNiRsPqQkQO30etD+sgChdGkqQUsa9+4HkeXq8XPYEAPB4qAQEA98Yj+PWJ5/BaxYq0r7125Aw+seY2CFffp8KVKcvJQR5P7z3v87nUpnn9ZsWN5nfu70A4kHzRV8Lofma4bDjZ0JZOhssI46DFPUzIz3wBOd2PmYmAXHhYh+f8YR1n6YQrIg94nkeD14tAGr1G4tOg2A48gV1HnsLOylVpX3vruVO4ZcOnENt8twpXNh8lImu9bJq5Lvp5IcTBDR4Gl2RoS/OeXsJwaHIPE5oz77COJYJ4OuGKyBYSnyaH6z2Anpe/iR97KtKeHPRFfgQNH/y26mV3JSNr2jQJgiCyJy6IeOT5g2iK7FmyfWlHVzPOOrbgPjrhSvfoqX0iU/FJPZ8GRc6Tg5RA6WMwafqSIAgie/RwWAchHwuTPN7zSZ7nOhqxW8ftEyQ+jYqMJwfJjR6OwSQIgiAWo4fDOgh5UDrJoyQkPg2MXCcHyQ1F1gRBmBo9H2mcBj0c1kHkj9GTPCQ+DY4cJwfJDUXWBJEFBhYyhYgRjjReCj0c1kHkj9GTPCQ+zUCeJwfJDUXWBJEZRhcyhYaRjjROBZ1wZQ6MnuQh8UnIjmKRNWWIzAP9LU0hZGbQ07StYhjxSOMk6OGwDiJ/jJ7kIfFJyI4SkTVliJRDbeFAf0uoJ2RUEPmppm13ttei3RbGjdVBlDsEwwcY3MAh9Gd4pPGlY6fRoNNT5eiEK3Ng9PYJEp+E7MgdWZspQ6Q31LbpoL/lNGoIGTVEfqppW4afwPiZTpwYCePZPjtsXg+qrKyhAwwzHWksx9GcmVIQWXENMHr7BIlPQnZkjaxNUurSI6rbdNDfchalhYwaIj/VtC3DT2D81FG8Eg/hgM+O90JFmIyXYH1NBV5LRA0bYAixIHgmM7HEMyyEWFDhK8qduCAimhBQU1mJXsaO90PNKHVY0FBRjNvqvLIJQ6N6UBoBo7dPkPhUmUKJAuWKrM1S6tIbWth00N/yAooKGZVEftJpW1FEqPsUXomHsMfthMQwqHMHcZQPYiLoBVtk3ACDs7nhkcSMXuuRxOk2A4WvKRcWCsIWSxi86MTZiUYMSPXYtLxUNuFpVA9KI2D09gkSnypSaFHgmhoPmre3ob1/FToGeATOH4N5WxZi20ylLj2hhU0H/S0voKSQUUvkJ5u2ZQLjGAryOOi0z35vByegmJ2EPxRDWZE9t++tgwE1oXoDWo/9Fq/Fl76HPfEIWjmH6qfKZYJagtDoHpRGQc32Cbkh8akShRoF5nsMpplKXXpCC5sO+lteQEkho5bITzZty/B+tEtx8Jxt3sdtbAIx8YLYzuZ7p+tdZTfdg/cT9YpXkzQ70lgm4a2mIDS6B6WRkCPJowUkPpfCgA+92TBLqUtvLGXTIYoS/KEY/MEYBFFELDSBweEA4oKY131Jf8sLKClk1BL5yaZtBSEOPonYiIkWsOz8a8rke6frXV3ffwSrTv8d3nXfCLtbUraapMGRxnIOjakpCI3uQWk08k3yaAGJzxQY9aE3G2YodemRVDYdgWAM3SN+CNEgitlJ2NgEAsE6tHd24pHnI3lt5vS3nIOCQkYtkZ9s2pbjrPBI818XEThMisVodM3Phqb93ml6V3viLF4Nu/HZ2Gnc5X4KJSsuAc4LXKWqSWoeaSz30JiagtDoHpSE8pD4TIKRH3qzoVmpy+QkEw6BYAydgyPwYQT1niAcnIDRWBEiXCnubXwHfaETeW3m9Lecj1JCRi2Rn2zaVvL40DpoxeuCAJ7jIElAX9ANi82NEvcF8ZnJ916qd1WUJPSc88PHjKK7RII/MoFSfgKSrwyAstUkVY40VmBoTE1BaHQPSkJ5qLa7kAUP/cLFe+ah3xMeRuzA44CQ/gGNxmLwZPHQRykKvMBMhshZha1jnfDEI/M+7YlHsHWsczZDZJTJWa1prfXCeV44iNJ0qb17xA8fRrDSw8PBCRAlBi+ObYTLbsdVlSO4c3knWpmD2Lm/A3Ehs8zaPOhvuYhZIfPBb+OWDZ/CJ9bchls2fAoNH/w2LLd8P6cM2qzID/SDkaSkr5kV+WUrcxafM9O27VIbdnQ1YzRih+QtRbXbg7ZwFNEEizOTHkygAo2VPrDnBVSm33up3tWJYAyJWBB17iAmLRzapTiYwMS818xUk8KBXrT3B3L6GVNf3PSRxrHNd0O4+r7p/9a1yXbPcgOHMJzh0Njw2Glwg4fTfk01BWFLjQdn440YjdiXfN2MB2WLieYciMygzOcClJgUpSgwP9QsdRUKC206Lvd2QogGUe8JggEwGivCi2Mb0R5rwZ2rh2Blp0VMvq0hevxbam5/dl7IzKwjefe55lPSz7LPPdm0baPFheXRN9EaimHIWY4V1RXwni+5Z9NOsFTvqj8UQzE7CQc3/dviGUBMkggwajVJiaExNU3Jje5BSSgPic8FGP2hNyuqlLoKjLnC4dVTdWgSi3EmWoNAwo3ueC1cdjvuXD2EFi8/+56Fm3kuwk1Pf0uz2p/lIvJz7XNfOG3bHYsjtuzD+MTob3F7tAcdU93gg9kHGEv1roqiCBubmP23RwJYzopkr9ZTT2Gmz4sSQ2NqCkKje1ASykPicwFGf+hNjdwZImJWOPzL7x0Y753ElLMcLk7Ex3wBrPUFZjOec5nZzPMSbjr4W5rd/iwbkZ9vn/viaduVgLAF3OBhNOcYYCzVu8qyLGLi9PblEQS0MlZI3uSZTb1Uk7J5XpIJb04S0RgcR0PYD4sQR4Kzosfpg1cUMhoaU1sQGtmDklAeEp8LUGJSlKJAQs9YORZNlV7EJkP47KqutK8PJJzwhwVDC7eCsT/LROQrdSJSngHGUgNqPpcN3f5iRBM82iIhVLtLIXkWi0+9VJOyDXQWCu/60AQ2j5yCGOFxSorDzwA+CbgUHC5iLJBsRRldh9qC0KgelITykPhcgFKTohQFEnomm9aQs/EGBM+NYrPVuMKN7M8uoNtjT5foXS1x2xC2WLFpIoEtHhdcjashLfAR1Us1KZdAB3OE9ylnCa4Yeh/7EyG8ZLdjjD3vGiAB68N+fAQObG1/Fp6qtRm5r6gtCI3oQUkoD4nPBShpB0NRIKFXsmkNCVuq4IoPYVujcYUb2Z9dQM/Hni7Vu9rktGBcvAj7HI0oCrowOOpEVGBg5yQsc4bREyrCSWhfTco10LFt/gK27PnfWNu3Hy9IMexwumf3I5sooCIWhNNahL3LNoIJjWSVlSZBSGgNic+FKHyKBT30hB7JpjVkWUUlSkYPGFq46dUEW4vJe70fe7pU7+oLIxV46tWjsA33odVxCiWWKQwkirArsgoxRx3++9a1mlWTZv6WT71xFrGAH7sHqtHq47HO50/aS73weRGr18O39jb4+w/gLCQ0RCYRA2AD4GM4OB0l4CpaITpLccDqVjcrTRB5QuIzCXq0gyEIpcm0NeTtU8NZ+dbqZdJ4Lnq0P9Nq8t4Qx54m6R89McBjf8cBbK96H1f4usAmJiGIIjh2EqJlCm/5/Xj7mBMN5W7V+47n/i2rwh0o4XoQDnD43UgdXrSX4yPLh+e5SMyw8HlhYyF0lNRDcJegPjQGSUyAYS2QXGXT/zsfNGiRlSb0jeYWcmkg8ZkCPdnBEIRaZNIacqh7QnfCLVv0Zn+m5eS9EY89nd9H2XW+nF087zXNpV3Y0cWo3ne88G/JB0Yh8l1o8fpn/XN3nGzBnauAFt98AbrweZnOSnOQ3BWQ3BUAgOTHBmiTlSb0iREs5Eh8LoUO7GCIAiZLw2+5SNcaojfhlgt6sj/TevLeiMee6nVgLNnfkk1MT+ZHhEmU26ZwV/U+/GIIePZsKx7YMDlbgk/2vBgiK03oCqNYyGmfeyUIYhHs0FEkdj2Anpe/iV1HnsKvTzyHXUeeQs/L30Ri1wNgh97X7NoWHs2ZDL1MGqci2dGQcxmN2LGjqxntUhu2KzywMiukatILqYyOihTi4HoPwHbgCXBvPDL9394DqY8CNuCxp7kMjKlBsr+lz2UDZ3ejN+iGBIBlJNxUdhihaBTH/dPPRqrnRajegFbOsehvshA9ZaUJ7VgY/Cx8PmYC2byOSZYJynwSukHvPSpqka/ht9KYxbdWL/Znck7e53pKkdH63PU6MJbsb8myDBorfegciOM0D9S7gyi3TaHR2o/j/lrUusIpnxcjZqUJ7dBrRSAZJD4JXWCEHhVVUMrwW2b0ItzyRQ/2Z3IJqXyDFiP1uetxYAxI/bf0umxoXlaB7hErjvJBFLGTiCUSODBchWPRNamfFxncVyioLxyMZCFH4pPQHKP0qKiBbg2/k6AH4SYHqXpc44KIIz0TuW/aGfbsyiKk5ApaZvrcl20EN3AIGDoCdO+DbfCwKv3GmaLXvuOl/pZetw3rnRXwh7zwB2OY4BthL7sUt13dtOQ9lU9W+livHz/bewzDoyPwsWNwW+Lw2ER0tFdhd0kBBfUFgl4rAskg8UloitbDFnpDz4bfyTCrb22+mfhsyt9yCCk5g5ZcS/dLIXf2TU8DY3NJ97dkWQalRXaIFg9C42vwqaubMnp2cslKv3R4AD/d/TYqxC5cX9yJMusUeMGFs5E62CxROCd6CyaoLxT0WhFIBolPQlOM1KOiBno3/C4EjvX58eRLb2Gl+DY+5OtCuSMGn9sGn8uG8Vj6THy25W85hJRcQYsS/cZKtNTote9YUVGchfvKsT4/fvHHfbjOthefrnsbFbap2c/N2D0dD7WgBO8XRFBfKOi1IpAMEp+EphipR0UNyFpFW471+vG93/4JlzCv4uayP8GeSCDOW9DtL0af3Y3GSt/Smfgcyt9Wzpq3kJIlaFGg31jJlho99h3rQRTHBRFP7T2CSyxv496GV+GyJOZ9fq7dU0dkHWJ+8wf1SdHIyk5J9FoRSAaJT0JTjNSjogZGNPw2CycGePzflw6gJHYSn13+OuqcFyyNIsIkeoNudA7E0bysImUmPtfyd75CSo6gRe5+YzVaavTYd6y1KG7vDyA43osbvO8tEp4zzNg9He9vhiM+bPqgfiFKtJYoRTYtK3oIfjKFxCehKUbqUVEDslbRhhmh5Ih04SLv6XnCEwAcnICVHh6neaB7xIr1Ddakmfh8yt/5CCk5gpa01y6JYEJjmAqNoYMfxsq3HkPs8ntTZorUaqnRY9+xlqK4Y4BHo/UsKu1L+8HO2D21x0oRNXlQPxe9W9nNJZeWFa2Dn0wh8UnISraDBUbqUVEFGaxViOyZEUorigLwJEJJX8Ng2qPxKB+EP+RNmonPt/ydq5CSI2hZ6tqZ8DiEkXaEIzz8koAz8TiO9b4J+9RgykxRobfUaCWKp6tJEcTF9Nu71xLEVNRq+qB+FoNY2QH5tazosSKwEBKfhGzkEqUZqUdFLYxm+G0GZoSSm4uDD7hSvs7BCShiJ+EPxpJm4jXr2ZUhaEl17Ux4HLGBQxgQQhixuRFjOTBSEEe8y/CupyJlpigai6GIC+PQeAna/R5EBQZ2TkKrj8c6n3/2WEmgMFpq1MJusyHEFWNSnD7S08GlvsPG4kUISGVoMXtQfx6jWNnJ0bKix4rAXEh8ErKQa5RmpB4VNTGS4Xc6jGByPdN7vNo7id+N1GE0VoTyORPCc7GxCQxHbEkz8Vr27OYbtCS9dkmEMNKOASGEfrsHYIAyUcBqxorDrpIlM0X+sIA3+qrQPsKgydYHDxcCL7jwu5E6vGgvx0eWD6PFO33sZSG01KhFS40H/9XRjEm2HL3BAFZ6eCSTWSOxIrw7uQJVyyoKIqgHjGNlVwguMCQ+ibzJN0ozSo+K6mRhrZIRGkx3GuXkqpne43W+XrxoL8eLYxtxV/U+sMziw+sjggVvTi2Hs2JxJl7rnt18gpZk186ExhCO8BixuQFm+tq3RaNgHKXodk1vdskyRScGePT0nUWL9QQ+Wz1/eGvG6mfHyRbcuWp6fSiIlhqVmK4mNeAUvw5ujp890nNuBjSUsOBnfZdjlG3CN7as000QqDRGsbIrhJYVEp9E3sgRpRmhR8XIaDHdqYeTqzLNus70HgdiZ/GR5cPYcbIFvxgCbio7PC8D2hf24pmxD6C/6HJ8PlkmXg89u1kGLXN/R0XcTVgd6UWw/yTer2xAKDQGvyQgxnIoEwVsi0ZxmcWFfRWrIczZxOdmiiLLLsXO/R243HUI64tOIxyXIDkxm32ba/XzzNlW1BYnCqalRg3mVpOkOLCaOwY/P4oidnI6ax/14pXAJXgvcTk+e+MVWFvn0/qSVcMoVnaF4AJD4pPIG7miNL33qBgVLaY79XByVTZZ14W9x3euAp4924of9Dej0doPryWIQMKN/fxKTNhW4es3XZEyY2uknt2Fv6OEJYxO+yo0j7ejqasTfpxDTzwORgpiNWMF4yjFvorV6HP5Fn2tmUzRTDB6U/MArKIPnQPxRdk3lpFwve997Olahx72Uvzl9YXTUqMGc6tJXf41qBS7YBF4BBJOnI03oqisAX+35SKsrfVpfamqYhQru0JwgSHxSeRNIURphkWj6U6te5ayzbom6z1+YMMpHPd7cdxfi6GIFWciXrCly/H1mzan3bSN0LO75O8o1Ih3u5Zj1XgnlltPo720FoddJeh2lczLeM5lJlM0Pxi1oXlZBbpHrDjKB2ezbzHRgimxGDWOSbjrG/JvvTChYXi+LKwmRWNx1Nms+GABV5O0bovJlEJwgSHxaUZUXogLIUozKlpNd2rZs5Rr1nV5ZRE2rlmDFw4Ce4dr0WzvRbUrhjjrwBDTiPK6LHtU5e7ZlZG0vyNXHB9cC/zxeDOsY34c9NZiypb6GZ+bKYp2zg9GvW4b1jsr4A954Q/GEBNFcCyLRrcNa6wcJp1cXj+LkQzD1YaqSQvQQ1tMBhSCCwyJT5OhxUJcCFGaUdFqulPLbHguWVe7hZstP1/u6saUhUHXVCUOhUpgd5fh9stW4MYNNabJFmX6O7p0uYjjYyVYf64Hb9euzihTZO8bWBSMsiyD0iI7Sovs8z4+OZhfMGokw3BCHxihLaYQXGBIfJoIrRbiQojS9EAulkVaTXdqmQ3PNuv6avswAuP9KUr004v8ex0JrKzyKDYYpTYZ/45ccYyWrsUl0ZNwZ5gpUi0YNZBhuCxQa4FsqNYWk8ffzOwuMCQ+zYKGC3EhRGlak6tlkVbTnVpmw7PJuhZxYfypsxc3lryr2WCUFmTzO0q4PThT9XncLL6YUaZIrWDUKIbhcqBZa4GZBa/CbTFy/M3M7AJD4lOnZJvl0nohNnuUpiX5WBZpNd2pZTY8m6zryckSOOLnsK3GvGbOycg6M122DpbNH8ooU6RWMGoUw/B80aqipZteWgMKYDn/Zmbt2yXxqUNyyXLpYSE2c5SmFflaFmk13allNjybrGtHsAZXeE6a2sw5GTllpjkrIssuRbu4YjooDsdg77OhRZxa9HyrEYwaxTA8LzSqaOmll1Y3AjgbCq0dJEdIfOqMXLNcelmIzRqlaUXelkUaTndqlQ3PJutqsRWjypXZsJOZbMJyyUxnGxQrHYwaxTA8HzSpaOlEPOlFAGeL1lVIo0DiU0fkk+UqhIW4EJHDskjL6U4tsuHZZF03rqjD1Gjh2YRlm5nuHJ7KKShWMhg1imF4PmhR0dKFeNKJAM4FPVQhjQCJTx2RT5ZLjoU4l2lqQlnksizS0vRci2x4plnXSFzAc68Upk1Ypr+j5ZVFeOT5g5qeVpUMoxiG54MWFS09iCddCOAc0UsVUu+Q+MwCpcVZPlmufBfiXKepCWWR1bJIx6bnSpBJ1jUuiAVtE5bJ7+hIz4Smp1WlxCCG4fmgRUVLD+JJDwI4V6gKmRkkPjNEDXGWV5Yrj4U4n2lqQlnIwD8/0mVdySYs/e9Iy9Oq0mEEw/B80KK1QA/iSQ8COFcKoR1EDkh8ZoBa4izfLFcuC3G+09SEspCBv/KQTdjSaHlaVSZo1lKiggWQFq0FehBPehDAuVII7SByQOIzDWqKMzmyXNkuxHlPUxOKQpk5dSCbsNRoeVpVxqjcUqKaBZAGrQV6EE96EMA5UwDtIHJA4jMNaooz2bJcWSzEei6pEdNQZk4dyCYsOdT6MR+1LYBUby3QgXjSgwDOB7O3g8gBic80qCnOtMhy6b2kRkxDmTlCK6j1Yw4aWQCp3VqguXjSgQDOFy0dRowAic80qC3O1M5yGaKkRgCgzByhDdT6cQFNLYBUbi3QWjxpLoDloMAcRrKBxGcatBBnama5qKRGEEQ6qPVjGiNbAOWExuJJawFMKAeJzzRoJc7UynLpraRGRvcEoU+o9WO+BRAniWgMjqMh7IdFiCPBWdHj9KHbXQqBYXVnASQXqq/RlD00JSQ+06A3cSY3eiqpkdE9QciAghZAemv9UFsIzVgA1YcmsHnkFMQIj1NSHH4G8EnABsaKix0e7K9YrTsLIDmgNZqQC0aSJEnri0gHz/Pwer3oCQTg8ah/Y58c5PH03vM+n0uJs+s3G/bBm11UAslLakovKvO8VJf4HReC0T1lf4lcmbEAGk7WIyenBZAOWCiEPOeF0Nl4I5wKCSGu9wCGX/hbdE4NYZ8YwUt2O8ZYbvbzZaKAbdEormIdaC6qRtUt3zd22X0OtEYTmcDzPBq8XgTS6DUSnxmitThTg/miZ7qkpoboiQsiHnn+IJoie5bMLu/oasZZxxbcZ2Kjey02VEJ51AgolrIAmjsdLJcFkJZoJoRiIcR+ci12TPbg0aJSSEkWK0aU8KWpcdxV3ADrF14DbC75vr9G0BpNZEqm4pPK7hlSCP1OWpXUyOh+Gjrm1JyoUqrUyAJIC7Q8lY0bPoYRmwsd9mLUxCYxYnMjNifzaRMFVMSC6LAXY8TmRv2546bIfNIaTcgNic8s0Fu/k1kgo3s65tSsqBVQaGoBpDJaCiFu6AjaOQsidZeifqQd5REefklADIANgI/h4HSUIFLRiuOTY2gy8O95Loqt0SocUUroExKfhOaQ0T1lFsyImgFFIVkAaRmszky7S85SsPVXoig0huLQGCQxAYa1QHKVTf+PYcFPTZhm2l2JNVq1I0oJXULi02CYcRiFjO4p+2tG1Awo5loApcPoFkBaBqsz0+4AAIaF5K6A5K4AACwcnjDTtLvca7TaR5QS+oPEp4Ewq80FGd1T9teMyBVQZBJwzhNFaTC6KNIyWBWqN6D12G/xWnzpLLMnHkEr59DdmeO5EBdEWFgGL5xrRiQuoMwRR6uPxzqfH1Z2vuTOaI0uoP5kIjUkPg2CGYdRZjbVY30B9IY9eOpEGT7V3IVStw3sglSRkb1UM4Gyv+ZDjoAi04CzkESRlsGqUHMxqspWYvPo8aTCCQAYScLmQD+qytfK/3tWuUdy5v4L+XvQajkOdnIA4SiL343U4UV7OT6yfBgtXh5A5mt0IfUnE6kh8WkAzDiMsnBT3eSU8M65aoTfn8JV5f3YWGuH12UDUBhnR1P213zkG1BkF3BqLIpURNODPzgrbJu/gC17HwLGOpe0tLJt/oKsxz+q3SO58P6zipPoHBiBDyNwWt/FXv967DjZgjtXTe9Bma7RhdSfTKSGxKcBMNswSqpNtaPGg1+eqcFT/TV4ecSP5lIOMa6oIM6ONvtJWoVIPgFFLgGnXSNRpDZan8omVq+H5/qv4+YDj+PSZGb+5WtlF4Jq90gmv/9saF5Wge4RK/yRIC5xHsNIxI6HjlyC2vISuH2ZrdGF1J9MpIbEpwEw0zDKUptqi4/HNy6ZxPsTXvz0zArsnlqJGy5uxm11XkMPVGWC1hsqIT/5BBS5BZzqiyKtWL3Mg09ctxk79xfj4a7kB38oGayK1RfBcsv30TB4eDozN1MCX7YRwrKN8op7DXokU91/XrcN650V8Ie88AdjuNwexNFBJ9av24ztl9ZltC4VUn8ykRoSnwbATMMo6TZVKyvhkjI/6t3v4+GuMqyr8+pWSMuN1hsqIS/5BBS5BpyqiiK5ybKfUfODPzgrhLq22ZKwUgJJix7Jpe4/lmVQWmRHaZEdzQAOx4aREKSMf9+F1J9MpIbEpwEw0zCKmbK4SqD5hkrISq4BRV4Bp0qiSE5y7WcshIM/tOiRVDLhofnQFqELchKfjz76KP7pn/4Jg4ODWLduHR5++GFcc801KV//1FNP4Xvf+x5OnToFr9eLm266Cf/8z/+MsrKynC+8kDDTMIqZsrhKUQgbaiGRS0AxL+AURTCBcTC8H4IQB8dZIXl8kLylAMvqPuBMB3k+Lo0WPZKKJjw0HNoi9EPW4vNXv/oVvvrVr+LRRx/F1VdfjR//+Me4+eabcfz4cTQ0NCx6/Z/+9Cd85jOfwb/8y79g+/bt6O/vx7333ot77rkHzzzzjCw/hNkx0zCKmbK4BJEp2QYUMwGnf+Rd2IeOYSjIo12Kg2cAjwS0DlpR7fYgumyd7gPOJSHPx7Ro0SOZV8Ijg/YJLYa2CH2Rtfj8wQ9+gLvvvhv33HMPAODhhx/GSy+9hMceewwPPfTQote/9dZbaGpqwn333QcAWL58Ob74xS/ie9/7Xp6XXjiYaRjFTFlcglCK1lovjthj6G7vwCnrON5x2cFzttnPvy4I2DQ1jlXHO9BUG9N1wLkU5PmYHi16JHNNeGTTPmHo/mQib7ISn7FYDO+88w6+/vWvz/v4jTfeiH379iV9z1VXXYVvfOMb2LVrF26++WacO3cOv/nNb/DhD3845feJRqOIRi8IE57ns7lMU2KWYRQzZXEJQimsEHAT8yp+JUjYzVWhFiE45uSzzsGG/yv68CFBwH9jX4MVHweg36AzFeT5mB4teiRzSXjk1D5hwP5kQh6yEp+jo6MQBAFVVVXzPl5VVYWhoaGk77nqqqvw1FNP4ZOf/CQikQgSiQRuu+02/Nu//VvK7/PQQw/hW9/6VjaXVhCYYRjFTFlcglAKbuAQopEenKxbDX48gnE+iGJ2EjY2gZhowaRYDIvNjVOVDkTC3eAMKsrI8zEDNOqRzCrhQe0TRJbkNHDELLixJEla9LEZjh8/jvvuuw//63/9L2zbtg2Dg4P42te+hnvvvRdPPPFE0vc8+OCDuP/++2f/zfM86uvrc7lU02GGYRSzZHEJQilmMoJMWT3WFxdjIuiFPxRDTBTBsiwaXTaUuG0Aw6D93LBhM4Lk+ZgZWvVIZprwoPYJIluyEp/l5eXgOG5RlvPcuXOLsqEzPPTQQ7j66qvxta99DQCwYcMGuN1uXHPNNfjOd76DZcuWLXqP3W6H3W7P5tIIg2GGLC5BKMXcjCDLMCgrsqOsKPmaaOSMIHk+Zo5WPZKZJDyofYLIlqzEp81mw6ZNm7B792589KMfnf347t27cfvttyd9TygUgsUy/9twHAdgOmNKFC5myOIShBIUSkaQPB+zRKc9ktQ+QWRL1uml+++/H//3//5f/Md//Afa29vxN3/zN+jp6cG9994LYLpk/pnPfGb29du3b8fvfvc7PPbYY+js7MQbb7yB++67D5dddhlqamrk+0kIQi2EOLjeA7AdeALcG49M/7f3ACAUnicpoQxC9Qa0cg544pElX2f4jOBMP6OzClvHOhf9vJ54BFvHOmf7GalPUJ/kEiwRhU3WPZ+f/OQnMTY2hm9/+9sYHBzE+vXrsWvXLjQ2NgIABgcH0dPTM/v6z372s5icnMQPf/hDPPDAA/D5fNi6dSv+z//5P/L9FAShErmexEIQ2VBIGUHyfDQ+1D5BZAsjGaD2zfM8vF4vegIBeDw0hGJosjy/WU8sZSUyd+K0UE9iIeSFHXof/N6HMrjfHjSHMBPi4AYPT0/uL+hn1PvaUPAIcSR2PYAX0gRLW8c6cXP5Wpp2NzE8z6PB60UgjV4j8UmoxkzWcDhZdkPvWUNaXAkNMPQzQxQUBRcsEUkh8UnoCqNnDbneA+h5+Zv4sacibVnpi/wIGj74bZrmBBAXRLT3B9AxwCMai8Fus6GFHA2ygzKChEGgYInIVHzm5PNJEFlhAgNishLJnhMDPHbu70DY34sm67SXK59w4rmORuz21WM7eblmhk4nnAliIdGKdei46P/DaMfbKJ14H9WIobKsFBUtl4OpvYSOzCRmIfFJKI4ZDIjJSiQ7Tgzw+PWrB9DKHMS25oWnWJ3FSwO1eHrvJD5x3WasqSEBShBGZ2GwOWkRwSeKcXagBs4QsN0axuplJD6JaUh8EopjhqxhofguykFcELFzfwdamYO4c3kn2AXxRrkjijuXd2JHF7BzfzGat7dRCZ4gDAwFm0S2kPgksibbPj4zZA11aSWiU+eA9v4Awv5ebGvuXyQ8Z2AZYFtNPx7u6kV7/yo6aIAgDAoFm0QukPgksiKXPj4zZA315ruoZ7/RjgEeTdbuedmPZJQ7omi0dKNjgDeW+NSp6CcILaBgk8gFEp9GRYMNMNfSii6zhtkycxLL3oeAsc4lJ/Ztm7+gaGP9Us4Br8Uj2Dx6HFv2PqSZc0A0FoPXEs7otV5LGIGYcU6G0rPoJwgtMH2wSSgCiU8DosUGmE9pRW9Zw1zRxUksBnAOsNts4BPOjF4bSDhhtxkjW6h30U+YE73blZk52CSUg8SnwdBqA8yrtKKjrGG+iNUXwXLL99EweHh6MGqB76LS124E54CWGg+e62jEaOTsktmQ0Ygd3YlG3GaEAQQDiH7CfBjBrsyswSahLCQ+56L3Xi4NN8B8Syu6yBrKhYa+i0ZwDmit9WK3rx4vDdQmzZIDgCgBLw3UwumtR2utV9XrywUjiH7CXBhlgtyUweZc9K4LDAqJz/MYoZdLyw1QjtKK1llDM2AE5wArx2L75S14eu8kdnRNZ8Pnb5x2vDRQi3apDXdc3qKL0mE6jCD6CfNgpAlyMwabMxhBFxgVEp8wTi+XlhugbKUVOq0lL4ziHLB6mQefuG4zdu4vxsNdvWi0TJcMAwknuhONcHrrcYcOSoaZYgTRT5gHI02QmzHYBIyjC4wKiU8D9XJpuQEaqrRi4jKJkZwD1tR40Ly9De39q9AxwCMQi8Nus+I2HQ1LZIpRRD9hDow2QW62YNNIusCoFLz4NFIvl5YboFFKK2YvkxjNOcDKsdjQUGJ4axUjiX7C+BhxgtxUwaaBdIFRMc7doBDZlrK5wcMqXdlihOoNaOUc8MQjS75OiQ1wprTSLrVhR1czRiP2eZ8fjdixo6sZ7VIbtmtUWpkpk7wwehw/9lRgZ+UqvFaxAjsrV+HHngq8MHoc/N6HwA4dVf3aZGPGOcBZha1jnYvuBU88gq1jnbPOARSNy8Os6A/0g5GkpK+ZFf1lK0l8Enlh1AnymWDzjisa8elrV+KOKxqxoaHEUMITMJYuMCoFn/k0Ui+X1lkvXZdWCqhMYirnAKOgU7swvXtAErlhqDYnE2IkXWBUCl58GqqXSwcboF5LK4VWJiHnAPXRm+g3ggckkRtGaXMyK4bSBQal4MWn0Xq59LAB6rGPL9syScPAIRwRV+gnY5TLkBQ5B6iOXkS/UTwgidww6wS5UTCaLjAiJD4NNsAB6GcD1BPZlEmG4yJePXQCe22v6CJjZPYhKSOTuqx9Kawaif55HpCNp8Hx42CG/RCEODjOigqPD3c2hrGjW3sPSCJ3dN3mZHKMqAuMRsGLTz2UsnOCsl7zyLRM4g/FEA/w8Hl68NXmqLoZoyTZTcnqxkTHf2FPeIS85HSGXsvaMx6QH644iujxYxgK8miX4uAZwCMBrYNWVLs9+PCyMP55ZKWmHpBEfui1zcn0GFUXGAhGklKMbuoInufh9XrREwjA41FmsZ/JPg0nK2VT9kn3cL0H0PPyN/FjT0XKMokoSRjo6sf/Fz2Lyze2gikpS/IaYEdXM846tuA+GTNGye4vryigzd+HV5HA3vpNEF2Lr4eRJGwd68TN5WsNPSRlNOaVtZcoeWpR1n76rW4UH/8Rro8+j1fiIRx02sFz3OznPYKAtnAUW60u7LFvx9TaL+OOKxpVvUZVMLGfL6EPSBdkD8/zaPB6EUij1yjzeR4qZRubTMok/qkotoT6sabMCcabPBOkxKkhqU7KaJ4ahX3iLJ5FBM7Bw7DVXAzJWTrvvWYakjIKej/aMB4JYTX/Jl5hQ9jjdi52duA47HE7gWAILdE38Vbkc6pdm1pQqwqhBqQLlIPE51yolG1cMiiTbBg5gystNpQ2L4fEphYLsp4asoQFVEPYj3YIeN/pQ22UR/1IO9j6K4EFvat0Xri66P1ow9rIKfijfhwstS/p7HDQaUf1uB81kdMAWlW7PqWhYw8JVSFdoAgkPgnTkM4JgHeuwIjPB8mztEk/IN+pIUtZQFmEOPwMAAYYsblRHuFRFBqD5K5Y9HXIS0499H604Vq2G78XGZyDDY4ltsJzsOGoyOAW9qxq16Y4BeTnSxBmhsSnGlBvkmosVSb5ZY8P0a7nAJxI+3XkOjVkKQuoBGeF73zHdYzl4JcEFKcQn+Qlpx56P9qw0iVgyuJAX5DBimIeyZKfkgT0Bd1osUioconQfWN/hhSany9BmBUSnwpDvUkakKJMskacwHMn1T01ZCkLqB6nDxsYK8pEAWMshxgASUwseh15yamLLEcbKhhw2uzFaCpyYiJajDOTQJ07CAd3ISyJCBz6gm5MoALLi3hY7UWI5fUd9UO2fr7UqkIQ+oTEp4JQb5K+0OLUkKUsoLrdpbjY4cG2yDh2OJywAWBYy7wsFXnJqU++RxsqHXAK1RtwqdONSzzFODpuxVE+iGJ2EjY2gZhowaRYDIvNjUtLHbgkLprqvjH1sYdUISMKCBKfSkG9SbpDi1NDljopQ2BY7K9YjasGj8ASnsJZMBDm2C2p7SVH54RPk0+QokbAOePs8MHR40DDcoyHvPCHYoiJIliWRaPLhlKXFTeMd5kuaDHrsYdUISMKDRKfCkG9SfpE7VND0llA9bl8eKt6PW7vexd2sOgIToAP8aqfF65XQ3UtyDlIUSvgnOvsMN41LXKLimc/7YlHsHm8y5QG2GY89pAqZEQhQuJTIag3Sb+oempIBhZQq8ITqKq9DL61H0FzbEp1Lzk6J3wxuQQpagac6ZwdFA1aNCwPm+7YQ6qQUbtBgULiUyH03ptU6CVWK8diQ0OJKhY5mQqFxByhoFapUO+G6lqSbZCidsApmwF2Fpu/5uVhkx17WOgVMs3vJ0IzSHwqhJ57kwxdYjVolKzXkzL0bqiuNdkEKZoEnHkaYGez+eulPKxW1leNAL2QK2R6uZ/MgBGTSSQ+FUKvvUlGLrEaPkrW4UkZejdUNxJ6DjiTkdXmX9Giq/Kw0sGcWgG63itkikHtBrJh1GQSiU+F0GNvkpFLrBQlK4PeDdWNhF4DzqRkufnbN9ypv/KwQsGcmgG60QIWuSj0dgO5MHQySesLMC0zvUnOKmwd64QnfuFIR1GSIPgDuKjrOFaE3Njr2I4j/VOIC5ktQrkyW2KtSV9iDQd60d4fUPR6MmbBRrlwY5/ZKPeEhxE78DggkEDKFFkM1QkAcwLOQD8YKfmZQrMBZ9lKTcUnN3AIwxlu/sNjp2E58UJW5WFu8LASl604CwP0hRWBmQC9lTmInfs78l6zheoNaOUc8/aHZOgiYJGRbNsNjHo/KYna96rcUOZzAXL2TiTrTRqOixAmg1ghAKW2Ioz4mjB07ije6ucVT5EbtcRKUbJy5GuoTmBeH7LVWoQbImEw/Yexv3I1eJtr9mVLDcOo3bOV7ebfPN5ZEOVhtXug9VghU4OCbTeQEaP365P4nIMSvRNze5OcHW/j8IkOVBSdw6o6Ft6KIoCNADihSorcqCXWQm7KVxotTn0yE8n6kOsh4JrgOC7uegsnikoRsBUvOQxzYoDHrrffR9nwn3CRcAhOZgphqQiHDl2Ml6s+gA9fsV72gDTbzR+Q1C8PazBcqHqAbrLp/Uwp1HYDOTFqMmkGEp/nUbR3grMisuxS/OdBEU1lU9i2PKZJv6VRS6wUJSuHFqc+mYWl+pA90SCuHziBS4ISxiyrEPE0I9a8CdKGqyHa7LOvOzHA408vPY1b/T+FnRnAaSaGbgbwSMD18f2Int2J1/x/DmnbJ2QNSLPd/FG6Aq2RCdX6WbUaLtQiQNfUs1UjDNUfrVOMmkyagcQn1BnE0UOK3KglVoqSlUXtU59MwRIDO/5QDEfOBfFqzIfPJHpx/dT7OGZvROzgQTQe2oOLaotRXV6GaOV6vPPGKXxg7N9xwjqCd1x28Jx79ut4BAGbQt34wNhjOPCqC813fFI28Z/t5p9ouQVVUb8q5WEthwu1CtD1asWmFIXabiAnRk0mzUDiE+oIQz2kyDMtse7qr8UUW41jfQEcPjuquWcYRcnKo+qpTyYgVR+yPxRD5+AISjCCOm8QfRBRMtmDT07+P/TG4ngzyuK9sWKs8BRhDWPF9aM9OOUIY2+Re/HEOcdhb5ETCX4Mq/t/gY7eG3BRU6Us15/15l+7CTZbkfLlYY0teDQN0HVoxaYYBdpuICdGTSbNQOIT6ghDPaTIMymx/r8zK7BvrAFNnj4IXW/rwjOMomR1UPPUJ6OTrA9ZlCT0nPOjBCNYUcyDYQBPTEQgPIm3EmEcKPEhUMzhzKQFzyVKsYIJYKs4gpUJC2rjdvQlyUxIDIPDRVbUj5/FaMfbQNN2mX6A7Dd/NcrDWg8XUg+0ehRiu4GcGP1eJfEJdYShXlLkS5VYD081YWRKxC2Vx3F707B+PMMoSiZ0RrI+5IlgDIlYEHWeIBgG4CQJmyen8KoUx/tWGySOAwOgzh3EUT6IgMRjByPiBimOzZNTGCz1QUgiuHiOwxlEsHLiGACZxCdy2/yVLg9rPVxIPdDqUmjtBnJi9HuVxCfUEYZ6SpEnK7FaLBbYOnuw3bMPdzX36M6A3nRRskGPCc0ak/6cyfqQ/aEYitlJOLjpgmljLA4hEccbrAQvy82+zsEJKGYnIcQSiDAMXuKAixNxNMTi6LLbkn6/cXCwYenKTC7ktPkrWB7Ww3Ah9UDLSCbPfyG1G8iMke9VEp9QRxjqLUW+sMR6pGcCZ06O4KaGAd16hpklSjb8MaEZYuafM1kfsiiKsLGJ2dfUx+I4IyXAMCykORPuAGBjE+A4K7gYh3OMhFOSkFJ8RgQODpFFZVmpMj+MjjZ/vQwXUg90/pj5+dcTRr1XSXxCHWGo9xS5JgNRuWTFdLRR5kKhHBOay8+pttF6PiTrQ2ZZFjHxwpJqEUWIoginww4sEJ8x0QKLywtftBeDcQF+RkRNEtElSUBw0o4WqxMVLZcr/nNpjZ6GC03VA61yBaJQ1jm9YMR7lcQn1BOGek6Rqz0QVZBRcYpJXlGSMBGM4UwojneFMozw3bj1lR+i5OOPwLpAtBiCHCaWTwyHZT/gQVGS9CH7XDZ0+4sRESZRiRhWxBOwMBzai7zAnF9BROAwKRajrKQSrlgpKqZG4JA4hBcsxxGBQ/+UCx+KC1jVdBGY2ktU/iHVh4YL5Uf1tVZjx4KCxWAtTiQ+z6OWMNRrilzNgahCjYqTTfL6QzH0nPMjEQuimJ2EjU3glQSwpudd9P36l7hk60f1JboyINuJZenoPvy6PaHMAQ8KsrAP+bgQRocYROV4DNc6BdQWlcATDeFNjgN//j2SBPQF3bDY3PC5HeBq1uHi7oO4LBzCM5FKdEgcbGwCMdECa8KBbQjho1UrUHHdlw3TVpIXNFwoK1qstVo7FhQiRkzmkPicg1rCUI8pctUGogo4Kl44yTvPE9ITnB1UAYCpQBjr+F14em+d7kRXOrKZWD4uhGE7+Ee0FhUpdsCDkizsQ24bG8M7XaM45YiguDGB6q430RYcxx63E2HRgr6gGxOowIpKH1iGARwluNZTjYsdcZRYivFuNIIJyYYSBrik2IKmZZfDcbn+Ng4lMd1woVZotNZq7VhQaBg1mUPicwF6FIZqoNZAVCFHxXMneZN5Qs4lzInY5BvECeagLkXXUmQzsTwUE1EXG8S21S7dDrqlZU4fcgmA+gEeO/d34LXeXlzKFGN17I8YDAWxk6vApMOHFZU+eF22C1k8bzMc134NLWIC6ww8SCcnZhku1JJM1loWEs5ZnIh1vQ7HS38PtqIl71KtHhwLCgYDJ3NIfBIA1Ot7LeSoeO4k70JPyIV4JICzWLGtSseiKwXZTCzbogn4rCGUO7glX6fkyV9yM7+C0oZTY9fh2sHf4NpEL7qtfkwGJ+GZSp7FM+ognSIYfLhQa9KttfWhCWweOQUxwmNXfBKW0y+gaPCdvEu1enEsKASMnMwh8UnMokbfayFHxXMnec+E4vM8IefiEQS0MlZI3hJDia4ZsplYXgkrwu4SAImUr5tBqZO/lGB+BaURED4EbvAw1ps8i5eNY4GR3A2MyFJrbX1oAlcOHsX+RAgv2e2wwYpmlxdS5aq8S7V6ciwwO0ZO5pD4JOahdN9rIUfFcyd53xXK5nlCzsBIEtrCUVS7SyF5psWmkUQXkN3EcnFRM05YmgCcTvt1lTz5S3EKIIt34ny7QSaOBdm8lsiNVGstJ4nYPHIK+xMh7HA4ITEMGgEwrAUS8i/VkmOBehg5mUPik1iEkn2vBR0Vz5nkHeG78coC7ekRBLSFo9hqdcHVuBoSO72oGE50ZTGxPNRyDzoPDWI00qv5yV9E7pwY4PHrVw9k5FgAIOPXGmnQTm+kWmsbg+MQIzxestshMQxsogAfw0Fylc2+Jq9SLTkWqIaRkzkkPglVKfSoeGaS99ZXfog1Pe9iKhBGmBPhkYBWxopqd+m08PT4ABhXdGU6sWyvWAvn2YO6OfmLyJ64IGLn/g60MgfTOhY893YRICGj1xpt0E5vpFprG8J+nJLiGGNtgARUxIJwOkrmiU8gv1KtIRwLDOaLmQwjJ3NIfGaDCW5WzaGoGGL1RSj5+CPo+/UvsY7fhU2+QXCW6R5PyVMym/E0uujKZGLZCuQ+6EbPoy5o7w8g7O/Ftub+tI4F/7v9LCKiFX+5Lv1rjTZopztSrLUWIQ4/A9hEARWxIGo4F7iKVkhJyrf5lGr17FhgRF/MZBg5mUPiM0PMcrNqyYUBg2IUFd+FNVO/xZpzvei2JjDJcPqKihXGarPjkq0fxdN763CCOYhtVfo6blU2Muh1zGXQjZ5H/ZDN0byVUif645XqHuNbwCTLQC4L+RGJR9DKAE5HybTwdJYmfX/epVod9job1RczKQZO5pD4zABT3awasXDAIGEJ46CjFfFgC5qkSWypLUZVWZkuomK10PNxq2qTzaAbPY/6IpujeYvYICzIbHjOaIN2emVhBlI614GSM7txtLQWAU9N0ownoM9Sbd4Y2BczFYZocUgCic90mPBmVZulhxGmM3w/mtiET2wovAEDvR63qgUZDbop/DyS/U/2ZHM075ToRgKZ/T0MN2inZ+ZmIIU4KndF0TZ6HK+AgZTk5Xot1QL5PaNG9sVcCj23OKSCxGcazHqzqkU2wwimHDDIoC+xUE/VygUln0ey/8mNbI7mPcc0Q7BaMRqxk7uBVhi4VJvvM2pkX8y06LDFYSlIfKZB85vV4EMV2QwjmG3AgPoS5Uep5zEbq6BCy86nI5ujeUsrm4Dz/5/cDbRDlVKtzHuXHM+okX0xzQaJzzRoebOaQbxkM4xgpgEDI/UlGqnUrMTzWPDZ+TzJ6mjeK1oBAE/vnVL0GF8iPUqWauXeu+R6Ro3si2k2SHymQaub1UjiZSmyGUYwzYCBgfqEjVZqVuJ5LOTsvFxkOzxHg3Y6QYFSrRJ7l1zPqJF9Mc0Gic80aHKzGki8pCObYQSzDBgYpU/YiKVmJZ7HQs3Oy002w3M0aGdSFNq75HpGjeyLaTZIfKZBi5vVKOIlE7IZRjDLgIHmfcIZYNRSc7LnUZQkTARj8IdiEEURHMPgrvggKmo2ZPQ8FmR2XiGyGZ6jQTvzodTeJdszms2w1aV/AcbA8xZ6h8RnOjSYDDSCeMmUbIYRzDJgYISmdsOWmhc8j3+0VeD98QgSsSCK2UlUIYKro2GsZKvxdOgqXHYujNXLln4mCzE7T6TGSD3QeiObvasjEUbz8f8CN7ffNIW4k/MZzWTYyrF8CyLv/geGDTxvoXdIfGaA2iauuhQvOU4uZjWMYJIBAyM0tRu51DzzPF6591GU9hzCVdIYWHsMZYyIVsaK6goPosvq0BnoxmO/fxvN9Q3wOdmUIqIQs/NEcozWA603Mt276kMTaJjoQVfwWRwvqkgr7mR7RufsY4xvOZrtPjQDSLhKwNk9EJZthMRw8L/+z4aft9A7JD4zRE0TV72Jl3wnFwvtJB8jNLWrVmpWyCosWrEOP7N/GpsqrPhs0TFIQhwsZ4XkLYHkKUE370P/JAfJfxTh8Juor+AwJSQXEYWYnScWo6seaD1Y7OVwDZnsXfWhCVw5eBRvJSZxxlcFf+Wq2c+lEndyPKMp9zHOcWEfq1iDxK4HTDFvoXdIfGaDSiauehIvcycX3/bUoDvGzvbWlQlx3NJ3BB8O/iO81z+4ZBRYSAMGRmhqV6PUrKRVWHt/AMHAIC5dAUiOlQCAmS2vw+/BjlNVaLV14HPL38dgxIPGyhqUFtmTiohCzM4T89FTD7QeLPZyvYZ0excnidg8cgrvxqdwxGqHu7h63udTibt8n9FMJ/B9rbeaZt5C75D4VIMsI0jdiJc5k4u/c9aheyAw21tnYxMYEy14TCjCxNQZ3PHqoyj7+CNpS/AFMWBggBNElC41K20VlqptIC4yePbstPC8q3ofWEbCZIyBPxhDaZE9pYjQY3aeeg/VQy890Hqw2MvnGtLtXY3BcUiRAN5FAkXOMkiuskXfP5W4y/kZzWIC/yPvPIl2KWaKeQu9Q+JTYXKKIJOJF4sNTGgMTGgMxfEINkeD2FLcANumv1BMvMxMLv7RVoEzQ6MowQjqPEE4uAs534gwibcn7djQfQiNR/eh7uLrFLkWo6F2n3C2KFpqVsEqLFXbwDG/D6FoDDfVHgbLTJ9abWMTiIkXSoGpRISesvPUe6guuuiB1oPFXr7XkCbwXjM1guH4FJxOL7iKVkgp+kNTibuZZ/Rozwq82n4Oh8aCYBgRtRXFuK61EssrixZ9rWwm8Lf0vodJe2YVIToBKT9IfCpIPhHkXPGyafAQjgd6MJqIwCoJWMFYUWJxIOwIwv7Of8DGKiNiuKEjOCaEcXTSjhKMYEUxj4XProMTYPeG0Dc6icTBP6LqomsoK3MeNfuEs0XJUrMaVmGp2gba/R402fpQbpua/VhMtIBj519/KhGhh+y8rnoPCwQ92G3pwWJPjmtYKvC+IuTHS1YXbDUXQ3KWLnktqcRd5/AU9hw+g7C/F5dYu+GxhMFPOLHr1UbsSRKYZTOBPwwJnujUkq+bIeN5Cz307+oQEp9KIUMUK1ZfBNuln0PZH76BOrsH8NRgyurEa64SdDu9KJocwuauV7Cl522UtnwYidU3y3pDC7EghmMiErEg6jzBRcJzBoYBWHsMYnAQ7f0B85fVs0GlPuFcUKrUrIZVWKq2gajAwMOFZv8dEThMicVodNsWfQ09enbqqfewkNCD3ZYeLPbkuoZUgTfj74G357W0whNILu5yCcyycY8ZsLnRGgviVZnmLfTQv6tXSHwqhCxRrBBH7N3/xB8QwytNV8x+HSY8DqHvbQxEePxUTGAkcQ5b330Slp59qCpfLdsNzdncsEYTKGZj80rtyShjRHgtIV1Z8iiCyaJYJUrNaliFpWobsHMSeMEFAJAA9Abd4Oxu+FyLxacePTv10ntYaOjBbksPFnuyXkOSwJvrPYDW/gM5DdPmGphl4x4TszpRbfNgc6A/73kLPfTv6hkKmRUi2wiSGzy8+GsMHMLwAgHLhMcRGziE3sgE2m0OnHV58XSRD2cZBi9arXhh9Dj4vQ+BHTqa988gVG/AKlhRhciSr/MIAloZKyLuEkR1lkmSE3boKBK7HkDPy9/EriNP4dcnnsOuI0+h5+VvIrHrAbBD72t9iTkxU2q+44pGfPralbjjikZsaCjJOaOWi1VYtsy0DbRLbdjR1YzRiB0A0OrjcTZWh76wF6d5D/yoQGOlD+yCnWpGRLTorGydS+8hkT+ttV44zwczopT8NUrbbanx3Gh9DbMDSYF+MFLyX/SsuCtbOU/czQZmNekDs3CgF+39genvWb0BrZwDnniafSweQYvFCXvb3djirMLWsc5F7/HEI9g61jk7LJoy4bCg8rlQB8xUPveEhxE78DggmHffTAWJT4WQI4JcJGAlEcJIOwaEEPrtHsRYDgAwxnI4KcVRFgvJekMLNRejuGg5ro6Gl1wo2sJRVLs96LI06S6TJBczUewLo8fxY08FdlauwmsVK7CzchV+7KmQVfQbnWwW+3yswmbaBs46tuDhruvw+Kk1aPcXoztaiScHrkGAq0FzTQW8C7KeevbsjMZi8GTRe2jmYE9NUgUzM4xG7NjR1Yx2qQ3bFbLbUuu50fQaZgaSchB3uQZm2Qre+Po/m+5ZLV+LL/IjuPXcKVw7cga3njuFL/IjuLl8LTzXP7hkdTFZ4mghM5XP4bHTSZNPZofK7gqRk1H8gpIu07sf9lgInCRCYFgwoTGEIzxGbG5gwf3sZ4AaIS5vQzpnBdv2eWz8QxfK+G4cLrKC57gL1y0IaAtHsdXqQnTZOnSNNJvz9Bc9TKEaCDWtwha2DUzF4lhfIqCnrw7vi2WoYwcAGMezUw+9h4WK1nZberDYU+MacnUCyXkoLAfru3yHRfXQv6t3SHwqRLZG8ZKtCIldD8xrTPZODqIyNI7bhSj2V6zGQGgMfkmYzXjOxScB8fMPhJw3dONFV+Ct9i/i8qHHcHm4H+1SBDwDeCRMH2XoLoWjYTV+MXaRLjNJcqCHKVRDobLPabIJ9RMDy7Bzf6luPDszRbHeQ5P1KiuFpnZbevAHVukachF3+QRmOQnePIZF9dC/q3dIfCpENhFkjasaE+3PYk94ZN7Dzrg84Hr3oyk8iqsGI3jL5sSZJN+rTBSwmrHisOvC5ivXDW3lWFx2/Yfx6z2l+ED097jecQIuJjx7lOGIrRq/G6rXbSZJDiiKzR6tfU715NmZDUr4r9LEbXZoabel9XOj6jVkKe5yDswyOM/d7Edk6xESn0qRaQTpqIAIYE94ZJFIlVxliLl8eCU8DiERxOZ4BPsxv2eFkSRsi0bBOErRPUd8ynlDr17mwceuvxI795fgtcD5TBITRmBEmUyS3k52oSg2N7T2OdWDZ2e2yO2/ShO3xkPr50Yv17CQXAKzjM5zV0DI6+mIbL1C4lNBMokgHQ1Xofu9nyYv6TIsuIpWLBs4hMPxKWwSRVzCAH3idOm9TBSwLRrFZRYX9lWshnBeIClxQ6uVSdLjyS4UxeaBjn1O9YpsvYd59irrLQgsKPTw3OjhGuaQbWBmHzmmWeClh/5dvUPiU2HSRZDsuz9dsqQrOUthq7kY3Eg7+MAIPg4WZVN+SBYHVjNWMI5S7KtYjT6XD4CyN7TSmaR0BsIv9tfg8V3jaKhrgs/JqbYZUhRLqI0cwV4+vcp6DAIJIuPArNKJ2C4Nh0T10L+rc0h8qsESEWQmJV3JWQq2/kpEuSNY66hCU/AcTgkhvFHaiOOe6nkZT6Pe0OkMhK3CJNazb6NvagzHjq7BtrphBAV1NkOKYgktyDnYO9/jZnv739Hh78KUGATjKoPkKgOSrDULe5XpeM8CxgCDaZkEZlzvAc2HRPXQv6tnSHxqTMYlXYZFsdUNad3tsNZfhpUHHkfx2Gk0jpwxxQ291MkugWAMnYMj8GEEn60ZxKNDJVjr47GxtEedzZCiWMIgzO1xi0ycxZnIGHoTPHwTXXA6POAqWpMebTjTq0zHexoHudsijDSYli4w08uQqB57Z/UCiU8FyGZRyKWka8YbOpWBsChK6B7xw4cRrPTwYAA0Wvtx3F+LjaV+1TZDimIXQz2B+mLhcNGlYhRMYgrdTjcGRQEVkQnUDByCrebiRQJ0pleZjvc0BnK3RZhtME1XQ6I6653VCyQ+ZSbbRSHnkq7Jbui5BsJxkcExvw/tfg/GQwKCk8W4oSyKhDgFKyvCawliSriwsKi1GZpR9OcK9QTqjCTDRT1OHzYwVpSJAsZYDv12DxDlUT/SDrb+ytkS/NzAtqMv+1NkSHyqi+xtESY8RIOGRPUPiU8ZyWlRoJIugAsGwh1+D549W4VQNIYmWx+8wiQYicPzw+vx8tha/Fn1uwgk3HBx8xcW1TZDk4n+XKCeQP2RbLio212Kix0ebIuMY4fDCYlhMGJzozzCoyg0BsldsSiwjXaeze0UGR1ixsy8Em0RZjxEg4ZE9Q+JT5nIZ1Ggku60gfBPDzXh9DhwseM4bqo9jHLbFAKhGNgEjyhceHHiMvxH31WYZEpxT9Pwoq+h983QDFBPoD5J1uMmMCz2V6zGVYNHgEgIL9ntGGM5+CUBxaExFNuKFwW2Zjne06yZeSXaIvTSHyknNCSqf0h8ykS+i0Khl3RXVRdjJGLDarYTd1bvA8dMm+kzDANRYlFh43FXxcs41+9BZ6QJqzynFn0NPW+GZoF6AvVJqh63PpcPby67CJtHTuGSCI+TUgRSIo4V/DBaWPeiwFax4z1VxMyZ+VS98QvJphKkq/5IuaCKou4h8SkTsiwKBVzSPTU0iTpXEBfZh9E5WYx6dxAOToDNwmEqakVQAAaiJdhQdBY9WINTvAcbS/2z79fzZmgmlNj8iPxZqset11WCgYY2NIYm0BCawIbAINbVXYnYFX+5KLBV4nhPNTF7Zn5ub3w6Mq0EmbU/kiqK+obEp0wosSgUEh0DPFrd/bi0pgjdIzU4ygdRxE7CyiQQiBYjGLKi2A60lY3ijNA9O+0O6HszTIaRe9HoPtcn6XrcBIZFp7sMozY3NrP2aeGZpHQq9/GeamP2zLwSbRFm7o8s9IqiniHxKRNm6ZXSihlR43XbsN5ZAX/IC38whrgowmKXwExNwW0dhYMT5k27630zXIjRe9HoPtcncva4yXa8pwaYPTOvRFuE6fsjC7iiqGdIfMqEGXqltGSuqGFZBqVFdpQW2Wc/Hwi60D1iw1E+iJNT5RiP+vD4qTW63wznYoZeNLrPdYrMPW5yHO+pBWbPzCvSFkH9kYQGkPiUCaP3SmlNOlEzkxHtnKjE2YlLUFe/AfZKj+43wxnM0otG97l+kbvHLefjPTXE7Jl5pdoiqD+SUBsSnzIw08Nnd3rxfPdFODhagtvre3F11Qis7PTUttHKw2qTiagBw+DtQDMaG1bhvg+vM9Tv0Cy9aEbvCdQ9eZ6tXeg9blpk5uXs4c7kaynVFlHo9w6hLowkSZLWF5EOnufh9XrREwjA49FXGW9hD59VmEJ3ADgVrARrsWBTeQBOKzO7KOi9p09LTg7yeHrv+bL0UqLm+s2G+x0+/VY3Ymd+i3tWnUj72sdPrYF9xcdwxxWNKlxZbsze94Hkmx/d59kzc7b2cLLMU6qztfMUq1qTTmxlK+zigohHnj+IpsieJTPzO7qacdaxBfflWWFYuP57zvdwn403wpllD3e2X2v+72a6LcIog4uEeeF5Hg1eLwJp9BqJzzyY18M3RyyJooTOCQa/76vBO5FLcNHq1biutYoWhQwwq6j52Wun4B18Gncs70n72qe7GhBY9kl8+tqVKlxZ7tDmJx9Lna09t+du7tnaOYlVHZFObF3UXIejnX1ZCzu1gthU6//C75NJD7ecX4sgtITEp8KoHWEXEmYUNWbLfBIyIsSR2PUAXpg7bSyJYEJjYEJjkMQEWIbDllgUN9VshuXWfwE70pG1WNUT6cTW/zuzAm+OVOGm6jP4SNNw1mJM6SBWzvWf9hLCTGQqPqnnM0fM0sOnR4w46JAOmhInUrHwbG0mPA5hpB3hCA+/JCAGwAZgr8Tg4lPjaDryNCJ9b2NPeDipNQ5vdeCVsmZgrBM3H3gcllu+r6sSfLrhO68thlg8jmsdf0KbvR+ltgoAF16UyXCe0tP6cq7/tJekxsieyMTSkPjMEbP7yRHyQlPiS1PIm8zcs7WZ8DhiA4cwIIQwYnMjxnKzrxsUBeyb9KP+te9j2FmEA+XLk3oyAoDEMDjgrcWlY6fRoLOzuNOJrWN+H8LRGD637CAGIx74Q955tmtAZmJMySBWzvWf9pLkGN0TmVgaEp85YnY/OUJeaEo8NYW+ycyerS2JEEbaMSCE0G/3zE32AQBiLIdumwNjkTEcj42Dr16z5NflrQ60C5HpyWUdic90Yqvd70GTrQ91zgAmYwz8wdgi8QloK8bkXP9pL1mMGTyRiaXJaYd79NFHsXz5cjgcDmzatAmvv/76kq+PRqP4xje+gcbGRtjtdqxYsQL/8R//kdMF6wWz+8kR8jNjkXLWsQUPd12Hx0+twdNdDXj81Bo83HUdzjq2GHKSPx9mNpmmyB58tflV3LPqBO5Y3oN7Vp3AV5tfRVNkD57eewAnBnitL1UxZs7WZkJjCEd4jNjci4TnDD4JGLc6MZaIgAmNpf3aPMNCiAVlvuL8iMZi8CwhtqICAw8XAgDY2AQEMfW5415LGFENxJic6z/tJfNZ2JaxMEiZabtoZQ5i5/4OxIXMzqUn9EXW4vNXv/oVvvrVr+Ib3/gG3nvvPVxzzTW4+eab0dOTeor3jjvuwMsvv4wnnngCJ06cwI4dO9DS0pLXhWtNS40HZ+ONGI0sjsjnMtPD10LRGYHpXrT7trfhti1bYV/xMQSWfRL2FR/DbVu24r7tbQUlPGmTmUao3oBWzgHv5NB0j+ecUvtcykQBqxkrhpxeWCBmJD49kgjO5pb7kvMindiycxJ4wQUAiIkWcGzqbUorMSbn+k97yXxm2zJq0vfAhgO9aO8PqHuBhCxkLT5/8IMf4O6778Y999yD1tZWPPzww6ivr8djjz2W9PUvvvgiXn31VezatQsf/OAH0dTUhMsuuwxXXXVV3hevJa21XjjP9/CJKfwCCrmHj0jNTC/aHVc04tPXrsQdVzRiQ0NJQZXaAdpkZpg5W7stOIF4CvMRRpKwLRoF4/DgsK8WK2FBcTyy5Nf1xCNo5Ry6O4s7ndhq9fE4G6tDX9iLKbEYPrct6eu0FGNyrv+0l8wnlx5YwnhktdvFYjG88847uPHGG+d9/MYbb8S+ffuSvue5555DW1sbvve976G2tharV6/G3/7t3yIczqzHRa/M9PC1S23Y0dW8aCEdjdixo6sZ7VIbthdYDx9BZAJtMuc5f7b2VnspPpZIoEwU5n26TBRwZySMyywu7K9YjU53GUosDmyOBsEsIVY3B/pRVbZSd+Izndha5/PDabfh6cE2MDY3fK7F4lNrMSbn+k97yQXigoiu4QA6/C48eaoJOzobcWi8BHExeXSac9uFEAfXewC2A0+Ae+OR6f/2HgAE8/fT6oWsBo5GR0chCAKqqqrmfbyqqgpDQ0NJ39PZ2Yk//elPcDgceOaZZzA6OoovfelLGB8fT9n3GY1GEY1e2JB4Xp+bjlLHnBFEIUCDFhcQq9fDe+Vf47Y//k8sj8TRjgj8zHSP52rGCsZRin0Vq9Hn8sETj8DtrccWmxvSWOeSPp+2zV/Q3bGI6YbvAjEb7FYLXvN/AO7oGdTFUvt8ajmcJ+f6T3vJhcHDgZ5TaBJPoSg8Bl5w4XcjdXjRXo6PLB9Gi3e+Fsil7WLmcIb+hYczHPutIQ5nMAs5TbszC+w9JEla9LEZRFEEwzB46qmn4PVOR6g/+MEP8PGPfxw/+tGP4HQu7v156KGH8K1vfSuXS1Mdpf3kCEIJ9GBtRIMW84lf9DG4e/4EduAgKq0u1IgJxDkrDrtK0O0qgcCwsxlN37KNsF36Odz87n/i0mQnHJWv1fUmmlZsldTjM5vqcLSzedHnz8YbELZUYVlFJd4+NYxD3ROa2XLJuf4X8l4yd7r9k6s6MTnahYs8A3BwAkZjRXhxbCN2nGzBnauAFt+0AM3FE3mpk8Rei0ewefQ4tux9SLeHM5iJrMRneXk5OI5blOU8d+7comzoDMuWLUNtbe2s8ASA1tZWSJKEvr4+rFq1atF7HnzwQdx///2z/+Z5HvX19dlcqqqY0RSdMC96sTYi4/0FcFbYLrsXG/Y+hD3hYbxdsnzpjGb1eliq16Nh8PC0ndLM2e7LNkJYtlF3Gc+FZCK2tqyrnvd5f1hA8NwoXPEhlIwemD1yU0tbLjnX/0LcSxYOHkKS8P6kG71BN1Z6eJTbpnBX9T78Ygh49mwrHtgwCY6Rsm+7EOKIHXjcsIczmI2sxKfNZsOmTZuwe/dufPSjH539+O7du3H77bcnfc/VV1+NX//615iamkJRUREA4OTJk2BZFnV1dUnfY7fbYbcvPflHEET26Mk/j4z3FyNWr4fn+q/j5gOPZ5bR5KwQ6tpmfTyFJb62Xsgm6z5XjM3cu5utB7GtkbwfzcKiQwcYBo2VPnQOxHGaB+rdQTg4ATeVHcYP+pux71wF+kJFWbddLDxJLBl6PpzBbGRddr///vvx6U9/Gm1tbbjyyivxk5/8BD09Pbj33nsBTGct+/v78dOf/hQAcNddd+Ef/uEf8LnPfQ7f+ta3MDo6iq997Wv4i7/4i6Qld4IglCHdsYaZHFsoJ2S8nxyx+iJYbvm+YTOaS5Fr1l1v9y4hH8kGD70uG5qXVaB7xIqjfBBF7CRsbAIOYRz/3vkBrG+qWboHVoiDGzgEbujI7PPDTHSjXQjPqyYkQ6+HM5iNrMXnJz/5SYyNjeHb3/42BgcHsX79euzatQuNjY0AgMHBwXmen0VFRdi9ezf++q//Gm1tbSgrK8Mdd9yB73znO/L9FGYnyYMkVG+AUHMxlQWIjNHjGdI0aJECA2Y005FP1l2P9y4hD6kGD71uG9Y7K+APeeEPxhATRXjdTrRWNuO+W9enDC6SDRR5RQEf8A9gMu4HE/ODsXsgucogucoAZvHX0ePhDGYjp4GjL33pS/jSl76U9HNPPvnkoo+1tLRg9+7duXyrgocm8wi50OsZ0oU8aFEo5Ju51Ou9S+TPUoOHLMugtMg+e7zq3qkSNFWlXhOSDRTVhyaweeQUhmM8ovEgzoydhN1WBB9nh9PhAVfRCslZOu/rzBzOYIagT6/Q2e46hibzCDnRs7VRIQ5aFBL5Zi71fO8S+SHb4GGSgaL60ASuHDyK/YkQnnPYca0Ug1+KICzFYbd6UBGZQM3AIdhqLp4VoHo9nMFsUEpBryx4kBb2qcxM5u0JDyN24HEyxyXSQtZGhFbke6AA3bvmRa4TnriBQxieM1DESSI2j5zC/kQIOxxO7LM5EOWsuBEWiPEYYmIC/XYPBoQQhJF2QBJ1fTiD2aDMp06hyTyVKKB+WrI2IrQi38yl4vduAa0DemRNQw12vrkW5wJhXFveg+UlInwuG1iWyXjwkBs6Mt2adj5R0xgchxjh8ZLdDolhkADwnLMIdwQF2BJh7I2FMWp1YMTmRnmERw0/gLZ4VLeHM5gNEp86ZeGDlAqazMudQuunJWsjQisWZS5FEUxgHAzvhyDEwXFWSB4fJG9p0sylkvduoa0DemKu+8Fq+xCOB5bheMCHGusIvHYBVmcZhtnmjAYPhVgQ/JzhoYawH6ekOMbYC8eznrBY8bTbi/82KeJyQcLJUBB+BmiOhXHVxAAqmq6hv7dKkPjUKQsfpKWgybzsKcR+WrI2IrRibuayIjaEUPcpDAV5tEtx8AzgkYDWQSt89hLE2HXYuCBzqdS9W4jrgF5I5n4QFxkc93uxf6QMRyZ8GJ1qxMeuXodtG2vS/k05mxseSZz9t0WIw58kSDlhseJndjuuLqpBvd2LGiGOppAfDSs+iPi2f6SMp0qQ+NQpCx+kpaDJvCwp4JMuDGdtROVQUzCTuTzQacHl4aPYEw/hoNMOnruQlXotIaBxYhKX2l7Cem4LgPnDZ7LfuwW8DmhNKvcDKythY6kfG0v9ECVgR9cETvSUYNvGmgtvTrUmVK5FK+fAa/HpimGCs8KXpIfUJgooZi3oLGnAGXcFAODWc6dwSUUL/X1VhMSnThGqN6D12G9nH6RU0GRe9hR6P61RrI2oHGoerByL29pWYOLX3fhVTMQ7JUWwcxeC64jA4XTIgz22cnzZFcRF7z4Btnqx2JPz3i2YdUCHAVyu7gdLrgklzahxlmJzoB+vlDWjx+nDBsaKMlHAGMtNf1EJqIgF4XSUTHt8gvZQrSDxKQcKPNxCzcWoKluJzaPHk0blAC5M5pWvpQcnC6ifVv/WRlQONR8tUic6XJP4PbsS5ybjKD5/ak1MtGBSLIbF5kZzpQ/vW0VcvYTYk+veLYR1QK8BXC7uBxfb+pZeE8Y7sJV14kOMExjrxDueZWAdHmyLjGOHwwmrJKIiFkQN55r29mRY2kM1hMRnnij2cHNW2DZ/AVv2PgSMdS562DzxCDYH+mkyLweon1bnUDnUlHBDR9BtSaBmeROcwRj8oelTa1iWRaPLhhK3DSzDgAdUEXtmXwf0HMBl634wGQllvCbc4qrGzc5GXDreiX7OjlsECWWT4zhssSHmKpk1lac9VFtIfOaB0g+3WL0enuu/jpsPPI5LF4pbzoGq8rVUeswB6qfVNwVTDi0wZsQeyzAoK7Kj7PypNclQQ+yZeh3QeQCXrW9rfeTUPA/PZMyuCfwIGq78KzSwFiwfPAxp7DRWDryLG+IhHLdYwE9NwDM5RnuoxpD4zBWVHm6x+iJYbvk+GgYPT2cCZsr6yzZCWLaRorUcoH5afVMI5dBCRG9iz8zrgN4DuGx9W7ex3TiSzZowfAyxzXfP/kysEEf94GE00R6qG0h8ZsOc3k7xXAdCXa/jXEkdWEgQsPgBl+3h5qwQ6tpm32+Y6FunUD+tvjF7ObRQ0ZvYM/M6oPcALlvf1kpXb35rAu2hukMfY60GgB06isSuB9Dz8jex68hT+M2ZF7Ar2I8Vw8dxe89B1IX8Sd8383Bzg4fVvWAiNTP9tM4qbB3rhCcemfdpTzyCrWOds71A1E+oLrlkyAj9Myv2Av1gpOTnKKp6vKGJ1wG9B3Azvq3tUht+2dmIwDAPtvs0pM52sN2nERjm8cvORrRLbdh+eQts9mJaE0wGZT4zIFlvJzMcRWdsAjE7h22RcVw1eARvLrsIva7FE5iUndEf1E+rX/SWISNkQodDlGZdB/TW4pCM1cs8+Mx6N0b3HMHB7tPoxiRCrAiXyKIRATS5JGzeegPql3kgJGhNMBskPtORoreTYS2wARhkOexwOIFICJtHTmGgoQ3CgojTcM3qBQL102aABh6BZi6HFjo5iT2F70EzrgNGCODYoaMoPfZvOFQ0gt0lK3E2xkI8737QZBPxofgIVr//CNjyr9OaYEJIfKYhVeO25CqDb6ILg6KAGMvhJbsdl0R4NIYm0Okum30dRWI6h3qBUqKZR2AGGbI2fx8uZUqx17Edg2+chd1mQ4vOTPKJ5GQj9lS7B022Dmgq1jIJFuYkdfaUrwDHMFix4MvskTxg5gzsyp01jwsi2vsD6BjgEY3FaA1RGUaSUjTf6Aie5+H1etETCMDjUffYP9uBJ7DryFPYWblq/ickEWLvm+iNTKDf7gEY4POhICrKVmFvxUoA0w/31rFO3Fy+lrwICcWRczFdykZs7kKvpEfgjPAYXiA8GgULJqOleM9+BexuER5LGHzCibPxRjh99diup+NBlUaHp9fIhR7uQSPDDr0Pfu9DGfz+HpQtiEz1zLZyjnnBAtd7AD0vfxM/9lSkzcx+kR9Bwwe/DaGuLeOvn44TAzx27u9A2N+LJmt3Ya8hMsPzPBq8XgTS6DUSn2ng3ngEvz7xHF6rWBiXAUx4HLGBQxgQQhixuXF7NIK13ibsrm5V7OEmiGTIupgKcSR2PYAX0mRNVAmshDi4wcPgzmfIRsIcnu9hUeycwI21Q/NsWkYjdrw0UIt2qQ2fuG4z1tSYe/OQayPWJXq6Bw2MmvdINsGCpXd/8qROEm49dwq3bPgUYpvvnv7AgjVhbtY8k3vgxACPX796AK3MQWyr6S/oNUQJMhWfVHZPw1KN25KzFLaai1E/0o7yCI/mWBhNIT9uPXfK0M3qhLGYt5g2L1xMz+KlgVo8vXcy48VUVx6Bc8qhcUHEfz5/EE2uPfhvy7sX2bOUO6K4c3kndnQBO/cXo3l7m2nLZ3o+vUYOdHUPGhjV+lmz9L1mSpbnPo2fR4tEXBCxc38HWpmDSS2eCmkN0Rr6raZBqN6AVs6xyIZjBslZCrb+StRUXYSriutw8aptuGXDp9DwwW/Dcsv3SXgSirJwMV1o2DyzmLYyB7FzfwfiQvoJ2Gw9AtWyEWvvDyDs78W2mv6kvoAAwDLAtpp+hAO9aO8PqHJdqrNgo1/4d5rZ6PeEhxE78DggxDW60NzR6z1oSM6LtdjmuyFcfd8F83UZM8XcwKGMTyAaHjsNS9iviXUSrSH6gcRnGjLypgODtngUFU3XIL7tHxV5uAkiGUospnr1COwY4NFk7V7yRBRgWnA3WrrRMcCrcl1qk+1Gb0Rhptd7kEhOtsECzpf+UyV1ZpB7YNf0a4gQB9d7ALYDT4B745Hp//Ye0GUASmX3dOjQm44gZshlMd3QsNiLdi569QiMxmLwWsIZvdZrCSMQ09+CKwd6P71GDhbdg5IIJjQGJjQGSUyAYS2QXGWQXGVkZacDsg0WEs5STabxzbyGaOZOkiMkPjPArEbEhPFRYjHVq0eg3WYDn3Bm9NpAwgm7zZyBoJZZQbXsaebeg5OJEISRdoQjPPySgBgAGwDfRBeqbG6stVeSlZ3GZB2wOjyaJHXMuoYYsQecxGeGmNGImDA+SiymejV0bqnx4LmORoxGzi6Z6R2N2NGdaMRtJp1U1SozvdBRwXveUeG5jkbsltmeZvYeHDiAl0Ij6BfDGLG5EWO52dcMCQl8YGoMJQkOEsMt8dUIpVkYsHKSiMbgOBrCfliEOBKcFT1OH8ZtrtmAVYukjinXkCyHvfTiDEHicw5po3qTGRET5zGwV6Iii6lOW01aa73Y7avHSwO1SSdVAUCUgJcGauH01qO11qvKdamNFplpuR0V0sJZYdv0F7j+zCsYj/A44/bNE55looBtsSgarSXYLdqx6vcP4/31/xNr6srMbxKuw/VqbsB6ylmCttHTECM8Tklx+BnAJwEbGQvqwKCm/srZe1LtpI4Z1xCjOkOQ+DyPmlE9oR+M1iezEKUWUz22mlg5Ftsvb8HTeyexowtLevTdcXmLaQWI2plprexpGCGOqKsMa1gWX48FcVKKzAqZ5RKHKcGFn3HliHJRfM1/AL72R/HcyavxkrcOrY21CMUE051co9v16nzA+qEXH0RL99t4iZXwe4cTY6wNAGATBayOTOI2kUN1JIDikY4L5V8VkzpmXEOM2gNO4hMaRPWELjBin8xClFxM9dhqsnqZB5+4bjN27i/Gw129aLRMB4qBhBPdiUY4vfW4w+yBosqZ6VlHheb0jgoPd/WivX9V2qG2TOCGjuAQx+GFpsvRGJpAQ2gCNUIcvMDgmSkJg9YIlhX54eMEjE0GcbvnMNYVh/CbM+X45Yk1uLScx8piv2mSCHpfr8SKNbA6vWjnOBxBAkXRIGw435/LcHC6yvBaeQu4kD+r8q/cfcZmW0OM6gxR8OKTTGcLFIP2ySRD0cVUh60ma2o8aN7ehvb+VegY4BGIxWG3WXGbSbJbmaBmZloJR4VMmNlUBYZFp7sMne4yiJKE97tHUGwZwIriScw8tjwDBMMRBOJ9+JjvPSyznEO/uAYfbeyFlZWMn0QwwHrFDRxCf3gcB5d/AO54EEVJnAlEhsUBqzvj8q9SFUkzrSF6dSdJR8GLT62iekJbjNonkwozLaaZYOVYbGgoKehnUa3MtFb2NMk21YlgDIlYEHWeIOY+th4R8Ifi8HlGsNLLo8z5Hn7Q34Tjfi82lvoNn0Qwwno1W/61uQCbC5K7Yvq6Frwu0/Kv0hVJs6whenUnSYdxnj6FML3pLJEUM56gMrOY3nFFIz597UrccUUjNjSUGGqTJbJEhdNrtLKnSXa6nD8UQzE7CQd3IXfjEQSskjhMcRbUu4NgAJTbptBo7cdx/4UeZyOfXGOE9UrO8q8SJ7eZlYwOwpnpAS9bSeJTL0RjMXiyiOqjOjGdjQsijvRM4Om3uvGz107h6be6caRnoqAfwmzIdqGMR6fo900UJC01HpyNN2I0Yl/ydTOOCi0ylbSTbaqiKMLGJmZfw0gS2sJReK1uME5xnij1WoKICvOfcaMmEYzQ15dL+TcVdAxmFsz0gDursHWsc9GpUZ54BFvHOmd7wPXSPlbwZXcjms7SZH7+ZLNQ2qIx7O0YxeunX6HfN1FwaGZPk2SwimVZxMTpbcsjCGgLR7HV6sJkSQOs0si8twcSbri4xc94Lq0Bapnrp8IIfX1yln+16jPWC9neb3p0J0lHwYtPo5nO0mS+PGS6UEo8j5LJOISKAL7a/Cr9vomCQ0t7moWb6jvRKXRGwmhFGBs4DtXuUrgaV2MizEHkJy5cU6wI3fFafMy3OCOWbRJBD8G+Efr65LQA06rPWOsgA8j9ftOjO8lSFLz4NJLpLE3my0cmC6UkimgZ6ESl1Y51LWGw3OISHv2+iUJAS3uauZtqw8AhvHroBHxCD5qaBTDeEkgsCx8bRbe/GBFhEjZWxItjG+Gy27F2gfjMNomgl2Bfr6eOzUNGCzAtKpJ6CDLyvt906E6SioIXn0YynaXJfBnJYKFcO9yNlZIT9WvqFgnPGej3rTE6PO3FrGjqqHB+U0VdGyrreTy99wBOTBzENuf0eu1z2dBnd+OIvxInYs3oiLXgztVDsLIXBjCyTSLoKtjX6aljC5Gr/Kt2RVIPQYau7jcVKHjxCRjHdLbQ+2DkJt1CGbQ240x5BXzl/iW/Dv2+tUG3p72YGD3Y06Rar4dDq7B/pAQ2TsTn15xFi/fCUFEuSQS9BftG6euTo/yrZkVSL6JPb/eb0pD4PI8RfBK16oMxM0stlD897Ubx8O8A+NN+Hfp9q4veT3shlCXZeu21WXH7Rg7tZ/uxc6wMRwP5JRH0GOwbpq8vz/KvmhVJvYg+Pd5vSkLicw56iOqXwoiT+YYgxUJp7eum37ceMcBpL4TypFqvt22sQXv/6ryTCLoN9g3U15cPalUkMxF9cZFBX8iFiYAfP33tFC5bWSX7IJJu7zeFIPFpIIw2mW906PetT4xw2guhHXIlESjY1x41KpLpRF+H34Nnz1YhFI2hUXofzlAXYmdKZR9EKrT7jcSngTDSZL4ZoN+3ymQ4PJTtaS/pjvEjiGRQ8KkPlK5ILiX6Ovwe7DhVhVZbB26qPYyRsAWcZzmaq0ZkH0QqtPuNxKeBMNJkvhmg37d6ZDM8ZITTXjJFD76CRHIo+CwMUom+uMjg2bPTwvOu6n2IiSy6xBo0um0A5B9EKrT7jcSnwTDKZL5ZoN+38mQ7PGSE014yQQ++gkRqKPgsDFKJvmN+H0LRGG6qPQyGkdAbdIOzu+Fz2WbfK+cgUqHdb4wkpTiJXkfwPA+v14ueQAAejwkWYxm8CednTKb7YChjohz0+1YIIY7ErgfwQhrz7K1jnbi5fC0st3wf3MAh9Lz8TfzYU5H2tJcv8iNo+OC3dVd2n+cruMQmQydnac9skBBIHnxSkGB8Tg5Oe8fOfR53dDYiHOjDZ6pfQ2/QDT8q0FxTAe8c8TnD46fWwL7iY7jjisa8r8Xo9xvP82jwehFIo9co86kycnkT6n0y32zQ71sZchoeMsJpL0ugF1/BQifTlgcj2PAR+ZGswnV8zIVmpg9H+RpwdjeaK31JhScg7/R5odxvJD5VhLwJdQydlKMJuQ4PGeG0l1ToxVdQl6j0HGbb8kDBp/lZKPpi4giCwQk01obgc9nApnpYIf/0eSHcbyQ+1YK8CXULnZSjHbkODxnltJdkFJqZdKao9Rzq4ShFQp/MFX0tNR4890o3RMsgWNb80+dqQ+JTJcibUJ9QNlpb8hkeMsxpLwsoNDPpTFDrOaSWByJTCm36XG3oqVKJbMuL3OBhla6sgFmQjV74t5nJRu8JDyN24HFAML8IUBuhegNaOQc88ciSr/PEI2jlHIv7N8+f9hLbfDeEq++b/m9dm66rBoVmJp0WFZ/D2ZaHmvQtD+FAL9r7Azl/L8LYzEyft0tt2NHVjNGIfd7nRyN27OhqRrvUhu0mmD5XG8p8qoSZvAnNAmWjtcfow0O5UGhm0ulQ8zmklocCQMa+YbLaUw4SnyphFm/CXNCrkXbBn5SjhyErzmro4aFcoHLefNR8Dqnlwdwo0TdcKNPnakPiUyWE6g1oPfZbvBZfepFNWV40KHo20i7kbLSehqyMPDyUC4VmJp0ONZ9DankwL0r2DRfC9LnakPhUiUIsL+p9qrRQs9F6HLIy6vBQrlA57wJqPofU8mBSyE3GcJD4VIsCKy/OnSr9eGMX2gM+7B6oRlRgYOcktPp4fLyxC7/p1m6qtCCz0XpepM8PD82UVM0g9JeCynnTqPkcUsuDOaH+ff22t6WCxKeKFFJ5cWaqtLmcx78cXYlQNIYmWx88XAhTCQcODnAYYQL4QNEeeEd60ffeJJZfcq2q0WghZqNpkdYXVM5T9zmklgdzUuj9+3pub0sFiU+VSVpetDogcQ4wiQiEM6/A1vu24U/X6Rjg4UoM4cXuErTaOnBT7WGU26aAUBzBc1PoEUTsizvwbsgJH9ONsn3HkBi8SF3xXWDZaIAWaUKHqPwcUsuD+Sjk/n29t7elgsSnFswpL7JDRxE68DiGdTD4ISehSBRnAxy2ejpwV/U+sIwEhOIYHQjglUQcBx0A74rjdMiF/lgFVll9uFOTXsPCyUYDhb1Iy43Rylx6Ru3nsJBaHgrhPi3U/n0jH5pA4lND9Dj4IRcTIQGSEMFNZYenhacoIXhuCq8k4tjrmC7tMgDqHWPoj5ZiSLJq1mtYSMMuhbpIy40Ry1x6R+3nsBBaHrS6T9UWvAXZv485hyY0pz804eGuXrT3r9LN/U7iUyv0PPghEzXWERRx5z31QnEMRuM4aMe8n9XCCHCx06/RtNewQIZdCnWRlhOjlrkMQYE8h2qg1X2qheAtxP59wNiHJugj/1qAcAOHMJzh4Mfw2GnDHbdZ4uLgtQvoDbohAWBCcbSLAibnhGcSgGDcAhsnwW6ZvhXpeFFlmV2kA/1gJCnpa2YX6bKVplmk5WJhmWvhoj9T5mplDmLn/g7EhcyyzMTSxAURR3om8PRb3fjZa6fw9FvdONIzQb/fFGh1n84I3qbIHny1+VXcs+oE7ljeg3tWncBXm19FU2QPnt57ACcGeFm+3ywzfcPOKmwd61x0XK8nHsHWsc7ZvmGjJXJSEY3F4Mni0ISojg5NoMynRph98MPlsCPuLIMfFTjNAw2JIPg5GjshMQjGLYjCCdbigGVOKYZ6DRWkAIes5MTIZS6jQi0O2aPofZriZLRI1QZN+w8LrX8fMPahCSQ+NcLsgx/TZs7N8JaewSRvxVAsAksiBD7OQJBYxCUrWM4Km82JcMiDSpdt9r3Ua6gshbhIy4WRy1xGxHQtDiodaavUfbrUyWgWWz18U63Y1qJdYFZI/fuAsQ9NIPGpEWYf/Jgxc37TvxyfbBQRtgloPe3HKywLnuNQbOFgtbDonCyGxeZGiXtafFKvoTpovUgbdQKXzgZXDyNP8iZDzSNtlbhP0w3INvUew1Wx91ARa4LkSC0qFQ/MCqhv2MiHJpD4lIMcolmzD37MNXP+VTewrdqG5SW92Bocxx6HHWHRgs5JNyZQgRWVPrAMY8qGcF2j0SJt5DKqkctcRsNMLQ5yOJtkE7DJfp9mMCD7O2ct2Mh7aOk+Bee6NoBNHQhQYCYPRj40gcRnnuQazRbCdN48M+fuXlzKuLE69kcMhoLYyVVg0uHDikofvC4b9RoWCEYvoxq5zGU0TNPiIIOzSbYBm9z3aSYnozEchz9avNgWHEczPwHJV5by6ykWmKnU1qAnjHpoAonPPMgrmi2QwY/5Zs5tODV2Ha4d/A2uTfSi2+rHZHASninqNSwEzFBGNXKZSxEU3OzN0uKQ75G2uQRsct+nmQzI+lw2dPtLcEQYwYpAavGpVGCmZluD3jDioQkkPnNFhmi2UAY/5ps5NwLCh8ANHsb6AmgIJy5ghjJqpmWu42IbLmmowTMHeg3V05oNSm/2ZmlxyMfZJNeATe5ybCYDsiVuG/ptbnSH7BAScSR7xJUKzMx8YEumGO3QBBKfOZJvNDuD1oMfmlBADeHEBcxSRk1X5opaqyBJLA4dedtwPa2ZosZmb5YWh3ycTfIJ2OQsx2YyIMsyDBorfbCddeMd/zI0Rezq9B8WwIEtZoTEZ47I6tNJYowoAMxSRgVSl7kutnF4t6MD67h3sK1enz2teTsNqLTZm6XFIR9nk3wDNrnKsZkOyNZbRVxdUo533bfg2a4iVfoP5UoEEepC4jNHzO7TSWSOUW2D1MYsZdQZFpa54oKIR54/iHXsO7rtaZXDaUCtzV7pSV61ntt8nE3kCNjkKMdmMyC7fNlaNG37b2gfCqnSf2j2A1vMConPHDG7TyeRGUa2DVIbs5RRU6H3nla5nAbU3OyVmuRV87nNx9lENwFbtgOyNjs2NNhVub8pEWRMSHzmiBl8Oiljlx9Gtw1SG7OUUVOh555WOZ0G1N7s5Z7kVf25zcPZRE8Bm14HZCkRZExIfOaI0X06KWOXH2awDVIbIxsiZ4Kee1rlzMpqsdlnVTpewv4pDk6T5zZX4aa3gE2PA7KaJ4IK0FtUDkh85oqBfTopY5cBaRYUvZdY9YpRDZEzQTcl0iTImZXVfLNfgnT2T931/w1h/6Amz20uwm1RwFbdi4roIBjeD0GIIyw58afIGpywX4yPqxWw6WxAVstEUCF7i+YLic880LoMkUvZnDJ26clkQekYKNZtiVXvGNEQORMyLZEOhRx4d7IJDeMh/Oy1U6q0u8iZldVr1ScT+6fVff+ETfZV2j23OQi3mYDtwKvncPzgn8AJZ3EGEYyDg120ocUaxBfqYqhkaiGiAIWORokg8hbNDxKfeaJVGSLXsjll7JYm0wWlqPguJHRaYjUCRjNETkdcEJEQRPREy/HtQ+txReUo1vp4rPP5YWWl2dcd93vw/aOrkJACKB/fBe9kRJV2F1mzsnqs+mRo/zR85hi2REcBsWXJs8cBfT23rWw3apjn8Xv3JHZxqzHGWMGyLHwuG87YRFzOny5ooaN6Ioi8RfOGxKccqFyGyKdsruehCM3JYkFZM/VbHHS0ZvRljWAbROTO3EBws60T0dg59A4JODpcCa+zHB9ZPowWL483z5Xj8fY6rLZ34o41fjSXXBClSre7yD24onXVZyGZ2j+95q7GpRMnwaQ5exzQ0XN7fl3aGz6Ht2tXo5RhUDrn01MACR2omwgib9H8IfFpMPItm+t5KEJrsllQ1pzrRTzYgtEFp3gsxKi2QURmJAsEA8EYukf8GAt24tBkPf7pUCuafBIOTZThcvf7+PzaYZS4bfO+jtLtLkoMruhp+CRT+yepuBhHxhhcPDYJ1xLiU0/PLQmdLFApEUTeovljzOaqAma2bF6TvmweDvSivT8w73N6HorQmmwWlG5rAk3cJF4aqIUoLX5NXGTw7lgJ/veR9egO+nCsL4AjPROIC5lNCRP6Z2EgOBOEeN02rG+owMZGH7Y3jWG95xzeD69EnQf47LrAIuE5w1LPbb7MDK60S23Y0dWM0Yh93udHI3bs6GpGu9SG7dkMrpzf7GOb74Zw9X3T/61rUz3zlqn9U4nbhkmLAx3jrqTPLaA/u69shQ43eFilKytcyFs0fyjzaTDyLZvryTdOb2SzoEwyHLbUFuNHE5sW2QZ1+D345ZkaDE1KqLL14eKyIcS7DuO5k2RjZSaW6p9mWQalRXaUFtnxad842g+NoowLoNIVW/JrKtnukqnTwPLKIhzpmTCU/2+m9k8sw2B5kQMDWIX2rjJD2H2R0NEf5C2aPyQ+tSZLj7B8y+Z6843TE9kuKFVlZfjEhvmbeSgm4Z2RIqy1n8Zdtf3YWGuH1zWd6SIbK2OQqYtENoFgk7Ub47HSJV83g5LtLumcBjqHp/DI8weXHmSsdOrO1zAb+6dLnEWQLv4wfnXWaQi7LxI6+kPPdmNGgcSnhuTiEZZv2dzsRt/5kMuCMnczP9YXwLuHT2FTyT58qnkEpe4isHPUvZFsrAr19KtsXCSyDQR7Q5kJM6XbXVI5DWQyyPj6i0dQ6jyIaKRHV76G2do/WS66CvddxBnC7ouEjv7Qq92YkSDxmSFyb8a5eoTJUTY3i9G33H+TXBeUmc0cAM6c5PGp5jGUO+yL3gsYw8bKFKdf5XDqSLYuEtkEggnOA79YptsBtUwGGe8qewdHDnfi1xKH/uY1mLJd+Nk19zXMwf7JChjC7ouEjg7J4n5jN92DI/1TBRfIp4PEZwbIvhnn4REmV9nc6EbfigikPP0LzWBjZYbTr3KpKOTiIpFNIHiOXY6q8grdtruk9f8VRUR6TqGd8+OXwko0xFiUzZmb0oOvod7sn2RDj76qREb320DTp/Dj/RGE/a8YN5BXCBKfaVBiM87HOkPOsrlRjb6VFEj5bGBGt7Eyw+lXuVYUcjl8IZtA0OVrwMfaVuN3r0d02e6SLnBiAuMYCvI4XGRF0dQU/KEYyormZ/f1YPejJ/snOTGtsDY4S91v7ViOp18/ZOhAXklIfC6BUptxvh5hZimb54IaAinXDczoNlaGP/0qj4pCrlnrbALB1cs84HT63M4ETqIowR+KwR+MQRBFcCwLn9uGssAE2qU4eM4GG5tATEw+AOO32PFOaArj+/bgULVXmxKjzs4elwux+iJI2/4JsSNvoKrzHVREebB2D2LNmyBtuBqiLXmrD6EwSe63uCDi+ecPGjqQVxoSn0ug1GYsh3WG0cvmuaKaQMphAzO6jZXR2wbyqSjkmrXONhDU63Nrt9kwHLLh/Z4RCNEgitlJ2NgE4qIF3f5iRCb9mDhvjBkTLWCTHE3pD8XQc86P5ikejeLb8EoxKjHKyIVWowk0WTl4bA7wcQ5n35+As+8w/X51hOEDeRUg8bkESm3GcllnGLVsng96FkhGt7EyettAPhWFfLLW2QpKPT63TiuH3SMluJoNYIPvHBzchRUnIkxicjIGazQOPspgUixGo2u+Ub4/FEPn4AhKMIJWhx9XVk3g8sYeAFRilAMz9GIXEnrep/QCic8lUGozztY6I1p1EY4azPRZKfQskIxuY2X0toF8Kgr5Zq31KCgzJS6I6Ojuh40TcSLWjDZ2aN7nHZwAe6mA9ZMSfh6wgHO7553SJEoSes75UYIRXOKawIYIB8l74fdgphKjFhZkZujFLjT0vE/pBRKfS6DUZpyNdYbduQoPv5NAMEDTcoD+BZKR+3H10DaQz+aeT0XB6FnrfGjvDyDK9+Hza87ihe4W/GIIuKnsMMptU7OvGebKEBDKcUksgp12oGtkCj6XDSVuGyaCMSRiQdQXT2FzJIpqdykkz3wRboYSo1YWZFTCNR5636f0AInPJVBsM87QOmMzU4r/CrehAa9TqeU8ehBI6dBrX186tBZg+W7u+ZhxGz1rnQ8zJcIrKsfgs8Xx7NlW/KC/GY3WfngtQZwKVeMdfjnWMl24ybIL5eGjeFUsQbe/BP02N1iLDQ2YwM2RKWy1uuBqXA0pSU+oEUuMM8HQq+3n8E7HGSzj+nB7fS+urhqBlZ3ugVV6LaYSrvEwwj6lNSQ+l0DJzTiddUZF6Vo8HboKPqabSi1z0FogZYoRy7BaCjA5etryNeM2ctY6H+aWCFt8PB7YMInjfi+O+2txZsqFU1Ebbip7F39W+R6iPNA8Zcet0jiOCCPoDtkhxR241CKizVc6LTw9vpTfy0glxplgKOTvgX3yOK5lB+Cwsnilpw5vDa/ER5YPo8XLK74WUwnXeBhln9ISEp9LoPRmvJSlz6FEA87ufR1fpVLLPAo5Q6UGWggw2XraZDDjNmrWOh8WlgitrISNpX6s9QXw/SMrcaPvfdxVvQ8sI6Hd5gPX2IgVjgRWBCYgJOJ4bbgce6PrcEXrMCRLisXqPEYpMc4Nhi6v6sQk14WLPANwcAJGY0V4cWwjdpxswZ2rpgW7kmsxlXCNB+1T6SHxmQbFN+MUlj7tb3VTqSUFhZqhUgu1BZicPW1ymHEbMWudD6lKhMf8PoSiMdxUexgsIyEicJgSi9FY5IBUZIfkKwMDoNYHnDxci32jwHXV51J+H6OUGBcGQ2fPTaKYnZx1ACi3TeGu6n34xRDw7NlWPLBhElZWUmwtphKuMdFsn8rhaGEtIPGZAVpkQ6jUsjSFmKFSEzUFmNw9bWY95UYpUpUI2/0eNNn6UG6bggSgN+gGZ3fDt8BmqblEwkrXOTzbU49rqs4ZvsS4MBgSRBE2NjHvNSwj4aayw/hBfzOO+73YWOoHoMxaTCVc46L2PpXL0cJaQeIzQ9TOhlCpJT2FlqEyK4oEWiY95UYJUpUIowIDDxdCRODQG3TDjwo0V/rALlA/LMugqQTYNV6PHV0Thi8xLgyGOJZFXFy8VZbbptBo7cdxf+2s+FRiLaYS7hIYIMun1j6V69HCWkHiU6dQqYUoFCjQ0p5kJcITfhdK42U4aq8BZ3ejudIH74Ks5wwxtgiXrW5AYnwYbx3uRTkzCruFQa+lAQctl8PuW26YVpiFwZDPbZs+5UmYnGe+DwBeSxBTwrTYU3ItplajxRgpy6c4eRwtrBUkPnUKlVqIQoECLX2wsERYPMyju7sYxeVTaC6RFmU8ZxiN2BELMvg48wjisR68wwVxJi6iOC6glRvD3eVBVFz2ZbAGEUYLgyGfy4Y+uxu9QTdWenjM/S0EEm64OFGVtZhajS5gtCyf0uRztLBWkPjUKWYutSw0EndYGLTZurFS7ALiIV2WTgjl0HWgZYCynpzMLRHGBRGPPB/G24E+NJd2Jn29KAEHOi24NPgHvG2J4aCvDnz5BSHQEY9gc+AMtrz2fwwjBBYGQyzLoLHSh86BOE7zQL07ODv13h2vxQ2uMHZ0NauyFqtVwtXiJKeMMWCWT2nyOVpYK0h86hhNSi0Kb7YLjcSbEt0oHzuMgdgUXuNYWIpdqLKyhVk6KVD0GmgVelkvk7/LH/qrUTfxDk65wnizfLUphECyYMjrsqF5WQW6R6w4ygfhYibxh4lL0R2txEvjJXD7zFP21uokp0wxYpZPafI5WlgrSHzqHDVLLUpvtguNxCtiQxg/dRSvWEL4k8uF4xEPJiJFaC6pQINVLLjSSSGjt542KutNk+7vssoyiRL3XuwsbzSNEEglur1uG9Y7K9A5UYnf99XgHVyCiy5ag+taK/WREZQBOQ57UBojZvmUJp+jhbWCxKcBUKPUovRmu8hIXBIROnUKr8RD2ON2QmKAFVYeZyaBnnNWeBorDJcxIfJDNz1tVNabJS6IiCYE1FRWopex4/1QM0odFjRUFOO2Oi8uGfotXjqaMJ0QSBsMVdTjb02S6ZxBtsMeFMaIWT6lyedoYa3ISXw++uij+Kd/+icMDg5i3bp1ePjhh3HNNdekfd8bb7yB6667DuvXr8ehQ4dy+daEEqiw2S70zmP84xgK8jjotM9+P4YB6txBHOWDmAh6UVZkN1TGxGxo0felB/ssKutNs7D82mIJgxedODvRiAGpHpuWlwLxkGmFgG6CIZWQ87AHJTFilk9p8j1aWAuyFp+/+tWv8NWvfhWPPvoorr76avz4xz/GzTffjOPHj6OhoSHl+wKBAD7zmc/ghhtuwPDwcF4XTciLGpvtQu88hvejXYqD5+Zbtzg4AcXsJPyhGMqK7IbLmJgFvfd9KQmV9TIvv36pgjO1ENBDMKQWch/2oBRGzPIpjgxHC6tN1uLzBz/4Ae6++27cc889AICHH34YL730Eh577DE89NBDKd/3xS9+EXfddRc4jsOzzz6b8wUT8qPGZrvQO08Q4uBTRNc2NoGYeGFDM1rGxOgYoe9LSQq9rJdN+XX3cBWuZu0kBExANoc9+Lgp2Efehe3AH1V3gTBilk8N5DhaWE2yEp+xWAzvvPMOvv71r8/7+I033oh9+/alfN9//ud/4syZM/j5z3+O73znO7ldKaEYamy2C73zOM4Kj5T8tTHRApa9cD1GzJgYFaP0fSlJoZf1sim/PtLZhOvtDdgcOENCwOBketgDw09gxcAJRC17sOsco74LhAGzfGphpKOFsxKfo6OjEAQBVVVV8z5eVVWFoaGhpO85deoUvv71r+P111+HxZLZt4tGo4hGL2RbeJ7P5jKJLFFjs13onSd5fGgdtOJ1QQDPcbOviwgcJsViNJ4/SYUyJupilL4vJSn0sl6q8qsoSvCHYvAHYxBEERzLokzswaGyj2HLxP8jIWBwMjnsgeEnMHjiOPbELOioaAHnu+C5q6YLhNGyfKpikKOFcxo4YhZEt5IkLfoYAAiCgLvuugvf+ta3sHr16oy//kMPPYRvfetbuVwakQNqbLaLvPO8pah2e9AWHD8/7c5AkoC+oBsWmxslbhtlTDRA9b4vHZq4F3pZL1n5NRCMoXvEDyEaRDE7CRubQFy0ID5ZhV+f2YS11/41bu76BQkBA5P2sAdRRLD7FJ6ZiuN3rpVY553fcqO2C4SRsnzEYrISn+Xl5eA4blGW89y5c4uyoQAwOTmJgwcP4r333sNf/dVfAQBEUYQkSbBYLPjDH/6ArVu3Lnrfgw8+iPvvv3/23zzPo76+PptLJbJAjc02mXdeReNqbD11BAiG8CfbeZ9PVGBFpQ++RNQ4GRMdCqhcyabvy2sJIxCL5/y9dGviXuBlvYXl10Awhs7BEfgwgnpPcN755sV8HBXCafy/oytwxzXfRCu6SAgYlHSHCgRGptA+FsN/WRvRUFUCNsk+oboLhEGyfMRishKfNpsNmzZtwu7du/HRj3509uO7d+/G7bffvuj1Ho8HR48enfexRx99FK+88gp+85vfYPny5Um/j91uh91uz+bSiHxYYrMVJQlSgMcl431YYSnDXsd2VPZP5WQ1ksw7r8lVjeaxI/CFptDKieCKp1A1FTJMxkS3AipHMu37AoBAwgm7LTdRoXcT90Iu680tv5baIuge8cOHkUXnmo/GitCfqMFnVp7B8cAEnj9YjOXb22AlIWBYlvI3XTbeiX7GjZLaWnjPt0WJkoSJYAz+UAyiKIJlWfhcNhwXwqZ0gSDkI+uy+/33349Pf/rTaGtrw5VXXomf/OQn6Onpwb333gtgOmvZ39+Pn/70p2BZFuvXz1+cKysr4XA4Fn2c0JZkm+1wXIQwGcQKASi1FWHE14Shc0fxVj+fs93OQu+8s7E4hlYBbbYeXCt2Xjjb3QAZE70LqFzIpO8LmD5asTvRiNtymXY3iIl7oZb15pZft1W0Q4gGUe8JzhOeosTgxbGNcNntWF8SQL07bNoe4EIjlb/pBu8OBM61zwpPfyiGnnN+JGIXWjFiogXd/mJ0iEG0jY3B8HeCiapaeiNr8fnJT34SY2Nj+Pa3v43BwUGsX78eu3btQmNjIwBgcHAQPT09sl8ooTxzN1tnx9s4fKIDFUXnsKqOhbeiCGAjAE7kbbeT3DtvJQRMt2AYImNiEAGVLWn7vgCIEvDSQC2c3nq01noXvyANhjJxL8Cy3tzy62hnBFdZ++aV2kdjRXhxbCPaYy24c/UQrKykufcjIS/J1mjbgQp4h6ctSvyh6VaMEoygbkErRkSYROV4DO90jaJ+gDesHZvZqlp6g5EkKYXhjX7geR5erxc9gQA8HmPeyEYiLoh45PmDaIrsWVKA7OhqxlnHFtxnQruddHC9B9Dz8jfxY09F2iGtL/IjaPjgtw1Tgjo5yOPpved9PmsW+nza8dJALdqlNtxx/eacjOZtB57AriNPYWflqrSvvfXcKdyy4VOIbb476+9D5MeJAR4/+K+34Zw8is2eM/Bagggk3OiO18Jlt+Mjy4fQ4r3gRPJ0VwMCyz6JT1+7UsOrJpRiZs17rLgc+wYmUSwMYEUxj4Xxo0cQ8IWwgFPFH8aBkv9uyP1hqarW3J5vI1W11ILneTR4vQik0Wt0truRUKkEQHY76THzKThpz7X21uOOPE44KnQTd6OwpsaD6zeuQu+xU3AV12JKYOHiRHzMF8BaXwBWdn7eIp8eYCIPVNoXZgZT1/cdwetRK+q8wUXCk5EktIWjqHaXoni5iNe6Dbg/mLSqpTdIfGpINmdnq1kCMMoxa1oyK6AkEUxoDExoDJKYAMNaILnKILnKgPMCy4gCSslzrQvdxN1IrKvz4szJKnyopkO5HmAiZ1QtDZ8fTL2k73/iM4l29EEEjwsezR5BQFs4iq1WF1yNq+F0xQ25PxiqLcjAkPjUiGzOzlZ7sEVNux2jwtnc8MSmIPa+iXCEh18SEANgA+Cb6ILT4QFX0QrJWWpYAaXUudaFbuKuR1IFwquqi+FUuAeYyA0tBh7F6vU403APrj/1XbjCA2iXIuAZwCMBrYwV1e5SuBpXQ/L4AOS3P2STnJETM1e19ASJTw3I6uzsKqfqJQC17HZ0TZpSlmhzYTU/iCkmhpOOYsTYCxmAQVFARWQCNQOHUF7ZSgJqAYVu4q43lgqEnb56bGiux9vH2pJ6P87rAb68xXC9fYZFw9LwVNl6vD1xG+6ufBsrAhMQhThYzgrJWwLJUwJpztHIue4P2SRn5CbjtiBJxGQ8CObMK+BoEj5rSHyqTLZnZ6++RMKwyiUAVex2dEzaUtalf4FI9xuIsxZshIRjCxaqGMuh3+4BEwlg28BRVK36MAmouRS4ibueyCQQfvtYGzb//9t78/A46ivf+1tVvalb6m7tqyVbtmzJK7ZljGHYfA2OzZLJBpPkyWSBCTzJDGHInTswmXcIufcNN5khIcwbEsJlkjv3ggMESMBjYjwgG4fNMngDS7Zsrda+9aKWequu9w+pZS2t7q7uquqq6vN5njw8kUpWtarqV9/fOd9zztoGfNwhjweYEE8mU8PT74daDFt6UOQsBADEMtGk+n4QFZyR4d2TjC2ImRoDP9wCs2cEZwOTODU5SJXwIiHxqTBii3mGz/UpngJQot2OWkkmlXXzG/+AkdAEDpVvwLbhcxD8kzhoNmN0TvSzUOCxU+CwQxCQs/xahEhAzSObm7irBTEb4Y878vCtvVvQNiC9B5gQTyZTw2m/H+JklULgRAVnamWopE9kC2KmxhDsO4mp0ATshhz8R+katNumRbhW+ztnAhKfCiO2mGdo1KN4ZXCiMWu6TbUlmcqq63wfPQEPWsvWwGcwYdtwGzb7PTgv+OFiAKcArGaMYHKK0MGZURmcyNAHUjfZ2sRdLYjdCLcN1MniASbEk8mOEem8HxJllbqW/QWmXP0Z7bQS1xYkRMAPt6A/7MP1jBERixNd1su/nyrhk4fEp8KILeYJhM3g/EFcHPLOG1+WbzMtmq0rZWGL3O121EiyqaxLJhtGfUNgJkfRYytGX3UjaibHUT05jgo+hBBnxClrPrqs+bhmpENzle6KkoVN3NUCdbXQLpnuGJHK+yGZrNLqS/+Mrea6zN6TcWxBzOQoTJMu7ASHLUYb3i1eDX7BJoAq4ZODxKfCiCnmafM6ccHPYPvEJBzGNvgMmB1f1muyoabEOTvqTI7KYDnb7aiRZFNZEyYrDJhusSTYisEzLNpthbOpl7lotdKd0D/U1UK7qKFjhKj3Q5JZpcGLn+DGwAgQqQfY+O8XOe/JpWxBTm8fSsI8xvLK8G7xalyyOmP+PFXCJ4bEp8IkW8zz3lARToza8amSDmwxAl8MDKHJlgOBYeDnvbjks+Fifwi15cXIzzHKVhksV7sdNZJsKqs7x4nrYMCZkB/uOMdRqyBCzVBXC+2ilo4Ryb4fks0qvW0rw5bx82A84xCcizfzc5H7noxlCzL0HMOh8Qv4Q+WGRRHPhWixv7OSkPhUmGTM2gGewf86V4Mrc8/ha/VDMPpWYmebD/BN4niOGeCAlXkeXPQCEwMCPpvnx43WMqoMTpNkU1ldtgLkGyzYFvDhTUGgVkGEJklqIxyJwD08gfKxdmx07IOpuZjayaiBuanhkYs4brLAG5yYHXSRZ8pFYzD594LcPTWTzSoJeXk4PcrgilEvrHHEp2KdVhbYgrjmZxA83ZdQeAKU9UoEiU+FScas/UzbKgR5Fp9fNQIDx0CwO1FQtwF7u9qwxeeZbey7W5hCrj+CuuItsN/wN1QZnCbJprJs4SBsjmW40WSDQK2CCI2SaCPMeMbh62pDy2gQvYwN7qEWOAYFaieTCjMV3ug/hf6hEQxOcujPWQl34UasqSpMSeRFytbDuf5z+NThH2LdUCtORIIYZRgUCgI2syYsyy1Hzva/QTjBNVKip2ayWaV8mwlegwWtY1ZcUQvVdVpRg91BL5D4zACJzNrd4SJcWXwMtfmXZycL9nzkrGtErWd8XmPf33s24cjyb+ELZasy+In0gZhUlrN8E0xbvo49H/2aWgURmiTeRpjxjKP/3Fm8MhHCH4w1yK+snPWXUzsZcUQrvNv6WvGux4XxcBAlzBTWsRyWGUrwbu6f41DJ1aJFHjtwBq6PX8Jhqx2DznIUBidROVPw2GSyojToww1nXoS9cOWS10ipnprJZpVYhsGKXAv6UIeWjkLVdVpRi91BDzCCIAiJD8ssHo8HDocD3W437Hb9VFfPT3VMm7XrK+z4qH0YBYMv4o4V3Qn/jRc6quEuvxNfuY7EZ7LESzGZh8/Cc/jRmBWZcyOa9hsemhaWfAhc/ylwMVoFUVqS0AKzkS/39EbYyU1gZd9baAq68LJ1OapL82eFZxRGELBztB17itZSO5k4RCu8D7h68dykCQLrRpXNBwvHz85Cv4bLwwnbzXjHfEvyIo8PIXzgu3g9gQiKd41CfARPvHYcy/1Ncft17uuoRaflRtyXRk9NrqcZ3W8+jKfsxQkjhvd4hiFc8fd4vjNn9p5cWEkv54SjRLADH4t7R2QZHo8H1Q4H3An0GkU+M8hSZu3WPs90IUAkAsY9BsbjAs+HwHFGCHYnBEfBbCUgFQKII5kUU72Y5ufUKojQOAurls3DHyFgaEJrcT3WOeyLWroB1E4mKWYqvN+aHMBTQSdy2X6szPMg+uf0cByabDmAz4s9fBPGUZR043QpJhyJ7fOaTk9NsRFDw4arcd8GTpWdVmhAhjSQ+FQh9RV2NJ9mMH7qBFyBcbQIIXgYwC4ADf1GlNnssNasxrCpVJfjLeVCVIqJmp9nF3GmrmRDVG/uRtjU/J84MMSAc8b301E7mfhEBeIhYzFCoTFU2X1YqLkEhsHxHDO2+Dy4peQM/nlsTVIiT4oJR4r2eU1hpK4RUG2nFRqQkT4kPlXIeq4bvO8N/DboRVc+B6/hcsrrKM+j0TeGG9tOozlnD3Kc+hpvmSxiqzPFjBKMRh9AEc2sINHUlWyLYmRyeo6eiArETt6JPNYLCxd7FfFwHFoEP271DyUt8qS4RpL0eRWxadNdxJCyXmlB4lNt8CFEPnoGbdYp/Aar4JwcmfUIAdML1euWXAyNh7HO343bd63UXbP3RKRSnalkikkysjwapwTJTF3JtsKaucUhEUHAuC8I12Qw5oQ1aiezNFGBGOEjMLHhuMd6GCDCh5JunC7FhKN0+7ymsmmjiCERhcSnyoimaj4ursGKEIvuIRPOeHzIY70wsWEEIwZ4I3kYsBhxbY4Ha9ABHvGb8eqJVKsztTZKUDXROD0L4CSnrmTbnOZoO5nXPB58POZHODh//YlOWNtYYKF2MnGICkSWZRGMxH/V2gWA5YxwB5Pz8EvR8ifZgSexemqmtWmjiCEBEp+qY66Xx2kE7DXFGPc54JoMIjgTeaiZiTx0Dl/A2izyW6WSOo9GhbU0SlAt0TjVCGCZkKJoQ4/wFVfAbKnG6q5mdJk4VNon56WM/bwXvRNW1F3iYa65ksTnEkQF4nIuglORPPj52Kl3O8+jgTFi3FKCrsnkPPxStPxJZuBJzJ6atGkjJCC78rUaYKGXh2UYFOaasbIkD3VlDqwsyUNhrhksw2Sd32o2dV6ROHU+5e5BS+/l4ZeaGSW4YGFfGNWILuxNU4MINj8N8PKI5KgAfn3kLJ6yF2N/SR3eLl6J/SV1eMpejNdHpltSsQNnZPn9SiC2aIPrP6XQmWWWEDj8UbgBuzgGd7ODKEFw3vdLEMTd7CB2cQz+KFyPELgMnam6iQrEm0LDMBqtuOSzYWFjQ0YQ0DgVQKnNjv+Y2JB84/RoAU9OKXaOtsMe8s/7tj3kx87R9tkCnljiL9rntUVoxL6OWoz4zfO+P+I3Y19HLVqERtw2p6cm13cSgws2bRFBwOhEABeHvGgbcOPC8ATeMBRhYKQta54bQhwU+VQZUnh59Eo6qfN0UkxKooponNSRDZWm7qmwJjYtvW50Boz4fEM9Vg/w2DpnqppdABoYI8pyCxAor8eLw0a09Loz749WIzMCcefhR+EP9eI5nwMXvYjZ5/MwtxNnsV1U43QpCngSDTzJcSzDHQs89As3ba7JILqHXIvsGacieXgrMo7bzn2A/CzIGBDiIPGpMmh819KkkzpPOcUkNQmEmBQtVNJFSgGs5tQ9bfRiE93kOYttQOHiqWqCI3964hrLomY88/7oRahosxMViJ9tfhqb+1vxnjuCsREDSpkQ1rIGmAyVeCnn03A5r14k8pL799Mv4FnY5zVRT825mzbXZBDt/cPIxzCq7L5F9gz/WAgnW1tR0eBJa0ISoT9IfKoMGt+1NOmkzuONEgSUGduWjBBTQzROKgGsFu/qUtBGLzbzNnksC8FZCME5XdS4UKpn2h+9EDVudqICsb7/FOr7TqJ/eBSDPhb9OavgLtyAbSnOdp9FggKepQaexPx1M5u2iCCge8iFfAzPa54fxcLxWGWeQjE7hP3HWpNqnk9kDyQ+1UYKzXizhXRT56mkmKQiWSFWWLwm49E4SQSwBooSltrozW0vJPA8PjvVC2PxOvhLNiAbnjbN+KMXoOrNzoxARFUjSgCUANBq467opu0Pbg/CQV/M5vnATCEVa0RBFYvfj6mkfR2hGkh8qhDdNeOVCClS52JTTJIgQojtHYqggTVlNBonRTpaFd7VRMTY6HWH2Fn/WjXGsSvsxnbWidcmGuA6cCqjM6WVQiv+6HloYLOjF6Kbts3tH6GDCces4I8WUpXZCpBTnIsaTwJ7hoqsEoQykPhUKdSMdzFSpc7FpJikQJQQcw+iMicf29y9GbNdSJGOVoN3NRnmbvTq+1vxzvgIgvChxhTARo5DmdMOa80KLDO142BfIGYPWb2hGn+0CDSx2dELM5u2q7q/B9bfgi5+evhJlGgh1U6jFdaa1RBYNq49Q41WCUJ+SHyqGWrGu4hMps5TRZQQiwRRW7wWNw63Zsx2IYXvWA3e1WSJlG2AsPuf8dGLv0UjfwBbnf3gDJcLawSWRRGW7iGrN9TgjxaLVjY7eiFSth59dd/G9o8fxe6p7sXdEGwF08LT7gSwtD1D1VYJQlZIfBKaIyOp8zQQK8TCFkdmbRcS+I61VkneMjCJtlAubllXCsbiXFRYA2Rm/GqIj6Cl143WPg8CwSDMJhPqFbjPtbbJ09JmRy+U1G/DK7334rtFv8et/qFF3RAEdvp6LGnPIKtEVkPiUw7IvyI7SqfO0yEVIRbMsO0iXd+x1irJ1Th+9VyfB/uPtWLK1YPlxmnx5wnn4NXWGhxyLpPdf6qlTZ7WNjt6oKHSgUP5K7Dfd8WsPWPhFYhnzyCrRHZD4lNiyL9CLCRlIZZh20U6vmOttQxT2/jVc30evHikGQ3MceyuXZj27sTBvkpF/Kda2eRpbbOjB9K1Z5BVIrsh8Skh5F8hYqE1ITaPVAWwxlqGqam9UIiPYP+xVjQwx2MW/BRZssd/miyafsY0TDr2DLJKZDckPqWC/CvEUqhEiCntH4ydugccAS/WhsMoseTDWlyPcGhqekZ9Bp8HNbUXaul1Y8rVg921vTErzQER/tNssQCp5BnLRlK1Z5BVIrsh8SkR5F8h4pHp3q1z/YM1hk4YIhPomzTh6AdViORUYE/jGuzeVCG5CJ2buq899zqC7U3whcJoMZjwPgvkdTahoee9jFtS1NReSCr/abZZgDL9jGUzqdgzyCqR3ZD4lAjyrxCJyFTv1rn+wR1lHZjwDIIP+JCX58WE1Ywm1wb89o0r8V7LSnx153rpi1g4IwSDGaPDrWgysGiu2qg6S4qa2gtJ4T/NVgsQ9UfWDmSVyG5IfEoE+VeIpFC4iGiuf3BvSSs6B4bhxDCW2X2zk0m25A+hqC+AwwNT+G3TJO684cr4RSxiU7kasaSopb1Q2v5Tjfy9UyEp6wj1R9YGZJXIakh8SgT5Vwg1EvUP3rT8EnqGXHBiGKvsHsyVIywj4LbiE2gLLodtyo/9x+xLFrGkksrVkiVFDe2F0vWfaunvLYZMt54ipIesEtkLiU+JIP8KoUai/kFDxAs+4MMyuw+x5EiRaQI1xl5ETDXocscuYkk1las1S0qm2wul6z/V2t87GdTSeoqQHrJKZCckPiUiFf9KpqaXENlD1D/o8gWRx3pnU+2xcBh8mGAjqGFjFLGkkcrViiVFLc9juv5Trfy9k4VaT2UBZJWYJlu6U4DEp3SI9K+0DE5RComQnah/kI9EYGLDcY91h22wchFYmcVFLOmkcrVgSVFbSjcd/6kW/t5ikLT1FEGolGzrTkHiU0KS9a+0RKophUQoQtQ/uDn8MRyRpR/3kWAuukKV+JzTjWOjpYuKWNJJ5ardkqLWlG6q/lO1/73FosbRpwQhJdnYnYLEp8Qk8q8EwGH/a8cphaQwakmpKk3UP/ihayW2spfg5xen3iMCgz+OboLVbEapxR+ziCWdVK6aW6qoPaWbUv9EFf+9U0Fto08JQlJ03J0iHiQ+5SCOf6Wle5xSSAqjtpSqkkT9g883eeEanwIjvItthf2zRUcjwVz8cXQTWoL1+Iu6Abw5UBG7iCWdVK6KW6roMqWr4r93Kqhp9CkxQxZ5E8UiNtCh1+4UiSDxqTCUQlIWtaZUlWR1uR133LAN//ewGT+9tBzrxltQYx3HZCQHXaFKWM1m7KkZxUdjRUsXsaSZylVrS5Wkn0fTFK4MvQPm/XZwPWbVv2zV+vdOBTWNPiWyz5sohlQCHXrsTpEMJD4VhlJIyqH2lKqSrKmw45/uvBoHTy3Hq811ODExiiLDOGpzPbCZBOwf3Rq3iEWKVK4aW6ok8zwynnFMdrWhdCyAM14H2iZsmnjZqvHvnQqyjD6lyF1KZKM3MVlSDXTorTtFspD4VBhKISmHLlOqaWDkWNy6pQq7N1XMSQsl2URdqlSuylqqJHoeGc84xtrO4K3QJPZxJXDbV2BlcR4AjbxsM/X3llDcST36NOXIXbYL1iz1JsZkwb0AoxUn2wxYy/bhL1Z0iQp06K07RbKQ+FQYSiEpB1kcYpNqE3U9pXKjxH0eIxFMdrXhrdAkXrfkojuUjxqrafbbWfWyFcGS4u7jF1FmccJasg5hi0OUeJNq9GmqkTtKNWevN3Ehse4Fzh9ElWcSW/IBzrsSgt25+OeWCHTorTtFspD4VJiEKaRIBIJrDJ0dBtzAvofNA+MAsyl7dtcSQhYH6dFLKjdKvOeRcY9hwOdBs8WMnslcGEw25NtM834+G162ScOHYDzzEtzv/SveCozhuC0f7rwyCNZCMH4XDg9+jCsGTmJL9zvociwDb7SIEm9pjz5NMXJHqeZpstWbOJel7oWLQ144jG34YmAIO9t8KKjbAMG+eHMfK9Cht+4UyULiU2HipZAYzzjGLrbjnHsKJwQzTI5BHDzzERrOvpw1u2spIYvDDFKnC1WWOk+H+M+jC6d5HicmizCOYqwscYKN8WLQ88s2WdiBMwgeewru8wfxasiNlwwGGN0eOD2XYDWYEQoH0Ykwjtjy8LlgEFvCU9hfsQ5vh4OixFs6o09TityVb6JU8wzZ6k2cJc7mJRKJwGcAmmw5gG8Se7vakLOuEWAX/70WBTp01p0iWUh8ZoBYKaTl4S4UDnWiiQ+jKWc58spK4JhJ8WXT7lpKyOJA6cJkWCqlWz08gha/E97cCqwscc4+j7HQ5cs2SaLRoDOui+CFMJ7LdWKU5QAA/XwYq72DGBN49OeVQuAMOGhmsNnvQc3kONpthYqJt1QidxAESjXPkK3exCjxNi8syyIYMUBgGBzPMWOLz4NazzgEZ+GifydWoEOPlqZEkPjMEHNTSOcujaLwzH/H+yYTPihuQEWueV6EJZt211IiS5WsClmqr9x6rhsTR3+c9enCZIiV0uUYE1aww1hfVRwz4jkXPb5sk2JONChitGIIPEbZy/eZJRKGD0AnI8Dod4GxlWKU5XBe8KN6RnwqJd5SidxRqvky2epNjBLvXnBaTehy5cHPewEOaBH8WOleLD7jBTr0ZmlKBInPDBJNIW1mLqD7/DA6i1eiYImHOlt211IidZWsGlmqr9z+lkqEva/ggnkA75Wvzup0YbIsTOlyPTeg4M0mfBgOZOXLNhnmRoOuHO2Aa4FGzw0H4UIEbs6I/HAQhrAfMFrgYoAK/nLqUQnxllLkLttTzXPIVm9ilHj3Qr7NhF6TDZd8NqzM88DDABF+fg1BUoEOHVmaEkHiUwXQ7lo+pKqSVSPx+sq5B5vRMnwGz4Ur4ZwKwRkjZUwbmvhk+8s2GeauXWHOCKcw//uMEEEQQIRhEUAYxrAfgtECpwCEFmx25BZvqUTuuP5TWZ1qngdnhGnLN3DzG/+Aus73cclkw4TJiu4cJ7psBbCFg7r0JkaJt3lhGQY1JU5c7A/hohfYLUyB5YyIHi1VoENPY6JJfKoA2l3LS9pVsiokUQP9fP8QRk1eCHCje8gGe03s1LESGxrNLphZWggghrlrV3eOExsZIwoj/KznU2BYRLc9EQCCIKAwwmM1Y8Qp6/yiIbnFW0qbCUHI6lTzXNiBMwh+9G8YCU2gJ+DBqG8IBkRwHQzIN1hgcyyDs3yT7ryJURJtXhxWE2rLizExICDXH8HvPZvg7yiULNChtzHRJD5VQLYbuZUgnSpZNZKogT7Ph+BlgaocH854fBj3OVCYa475b8m5odH6gpmNhQBimLt2ddkKcIXFjt3+Meyz5EBgGEwYTCgIsDALEbAAWAC7AwEwlgJ0zRGfioi3FDYTFP2eZl6LoaIV8JStATM5CmZyFGdCfmwL+HCjyQbTlq/r9llI5l7IzzHis3l+1BVvwZHl34I/DEkCHXocE03iUwVku5GbEE+iBvocZ4RdACwcjzzWC9dkcEnxKdeGRi8LZrYVAohh4dp1rHg1ru4/DfgncdBsxpjBgkLOhGreD0ZgcGuExTazFe8WrwY/EzFVUryJ3kxQ9HvJFkOCrRiCrRhuAG8KAoTRduz56NcwlK3Xp3882XvBWgb7DX+DL5StkuTX6nVMNIlPFUC7a0IsiRroC3YnGvqNOMrzMLFhBCOxI+tybWh0t2BmUSGAGBauXZesTrxXvgHbhtuw2e/BecEPP2PGCj6AZTBgylKIP5WtxSWrE0BmxJvYzUS2R79pstFlMnEv6HVMNIlPNUC7a0IkiRroC44ClNnsaPSNoZnnwMZodiznhkavCyaxgBhrV481H33VjaiZHMca7xCW+0ZRn1MGwV6GXoHHFRPDqPWNZla8idxMZHP0mwpi56P0vaDXMdEkPlVCtu+uCXEkbKDPsrDWrMY15z5B56Qfrab5kU+5NzR6XTCJxcRdu4y5KF15BZht34RQvEbb4i1Lo99UEBsDBe8FvY6JJvGpIrJ5d02II5kG+nyeEydsN2NHpA+fDrvROjSk2IZGrwsmEZtk165sFG9ahwpiM4tex0ST+FQbWbq7JsSRdAN9cyPu3HUFatCBWgU3NHpdMIk40NqlS6ggNrPodUw0iU+C0CjJNtCvK7eDR6GiokCvCyZBpAwfAtd3EtzA6cubwLKN4CuuUHV1OBXEZha9jokm8UkQGkatDfT1umASRCqwA2cQbH4avQs9sZ+8hNLCVer281NBbEbR65hoRhAEIfFhmcXj8cDhcKDb7YbdThESgtAC5/s9eOHwTJ/PeAvmDdtU3WheL2h20pTGmdegPY5ws9/wICJlGzJ4pvGJCujBWAWxahfQOmB2YIc7dpZLLQM7PB4Pqh0OuBPoNRKfBEHIhlYWTL2zcNKUfWbSVGeoBjkamDSlWfgQwge+i9cTpKx3jrZjT9FaGPY+puoUPPgQuP5T4GL4x1V93jph/gZyOsultg0kiU+CIFSBFhZMPTNv0lScCLTaJ01pEa6nGd1vPoyn7MUJi3Xu8QyjetcPdN0jk9A/yYpP8nwSBCErRo7Fxup86uOZAXQ3aUpjZEWDdo0WUhGZhcQnQRCETqFJUwoSQ4QJQ63wJvnjWmzQrulCKiKjkPgkCILQKTRpShmWEmFrfWPYEvDgYm7x7Dz7pdBag/Z4hVRvh/zYNnIWNx5+VPWFVERmIPFJEAShU2jSlPzEE2FH3ZewoWcA1/WexNHKTeixxhb2mmvQzocQbH4aTVODMQupPEYL3iqsBUbbsaf5afUXUhGKQ+KTIAh9Ql40mjQlNwlEmNtegaN5ndjiHcaVQ23oq2kEv2BOuhYbtHN9J9E7egHNjsqYFfwAIDAMmh2V2DJ6AdVa9LISskLikyAI3UFetGlo0pS8JBRhDAu2ZC1agx/hCt8g1noGcMZRMfttrTZoz4pCKkJWSHwSBKEryIt2GZo0JS/JiDAhpwD+qi0Y7mrGF8cuoSbgm9+gvWit5jZDfHD6MySDFgupCPkh8UkQhH4gL9o89DqaTy0kK8KEnAJ4CmvhKGvE3uI1ixq0ayXiGYUz2WAXIkkdq7VCKkIZSHwShEhoTKF6IS/aYlaX2/GF67dh/7E8PN4Re9LUHTThKCXEiTCAKV6D4La7AEDTYowv24iGT17C26H4UV/NFVIRikHiUymo+EEXLBxT6JgZU/hqaw0O0ZhC2Ukk/MmLFps1FXbU3taIlt46tPZ54J6ZNHU7bZrSIltFGF9xBUoLV2FbgrGhWiukIpSDxKcCUPGDPpg3prB2YfqyEwf7KvHCYS+NKZSJZIR/A3nRloQmTUmPrkVYgoCJads3cePhR4HR9kXeaq0WUhHKQeJTZqj4QR/QmMLMkqzw/1YxR140Qjl0KsKSDZjYb3gQe5qfxpaFx2m0kIpQDhKfckLFD7qBxhRmDjHC/9BgKa5hzVmXBiXiILPlSW8iTGzAxLD3MVT3n5q2sGi8kIpQDhKfMkLFD/opzqExhZlDjPB/on05bjBXY5v7ov7SoIRolLI86UaEpRgw4asaZ99dlEkgkoHEp4xke/GDnopzaExh5hAj/JcZe3Gm+PO4cfQ3ukqDEuJR3PKkAxFGARNCKUh8pkoSqZxsbsSrt+IcGlOYOcQK/37zCl2lQYkUIMtTSmR7wIRQDhKfKZBsKidbG/HqsTiHxhRmjlSEf6RslT7SoERKUAQvNbI5YEIoC4lPkYhJ5WRrDzg9FufQmMLMMSv8J9tRHOgH43GB50PgOCMEuxOCowBg2cXCXwdpUCI1KIKXGtkaMCGUh8SnGMSmcnb/z9kecEcKlqN6chzVUy4Y+BDCnBHdOU50W/N1V/ygx+IcGlOYORoqHThtDqL/xGl4uF60CiF4mOmJMQ39RpRZ85CTX4LOoXzcwL6HzQPjALOJBjhkMRTBS41sDZgQykPiUwQJUzlCBJgcxYfhSWxtP4wVh/8nDNVX46aRi1jb1oR+IYIW8HAxgFMAtoDDLQyLyqgHTScvSr0W59CYwsxgHv4EuwKv4KWgD81GJ2x5AVi46XjL0Sk/rhjsQWN/HzoMxfDkD+LgmY/QcPZlGuCQxVAELzV03TSfUBUkPkUQL5XDTI2BH27BlN+DSwKPo8EQplpegaXzMAo8A+jlg3iVFdDFCAgCMDHAOSGC62BEGQMAgtIfRzb0XJxDYwoVZibb0CyM4XjNBnQPuxH2+JDHepEbmYDF78M7vIBdLIstORwOV9SBZ1ga4JDlUAQvRXTaNJ9QHyQ+RbBUKoeZGkOw7yT6+EkMm2wIshy64UOu1Yn3/MOoC7lQZylARf4yRCJBCJEwGNYA3lqIppwCMGOduqq4jFWcE4kIcE0G4fIFwUci4FgWEUMeOkPV+LTGinNoTKFyzM02OIxmrLcWY9zngNvnh2XsIwyyLAatRXiLA7YHfaiZHEe7rZCqmbMciuCljt6a5hPqhMSnCGKmcoQI+OEW9PGT6DXbgZk1zikA4XAAg0Efjtgc+FxwCo0TI+itbkSEYefFOfVWcbmwOMc7GUTXsAt8YDpiZWLDCPAGvDz6Z2gTLDAsVZVEZD0Lsw0sw6Aw14wixoMJtx8TOXaYWQ5jAM4LflTPiE+AqpmzGorgpYVumuYTqoXEpwhipXKYyVFM+T0YNtlmhWdhhMdqxojTiMAl8AhwBhw0M9js98xGZuait4rLucU5/3YujJXCSSw39mGZ3QcLx2MkmIs/jq6Diy3HVbkX8PLRHHAa6fdJKMuS2YbJUbgEHkGWm/2aiwEq+Pn+Yb09W0TyUAQvTahbBCEjJD5FECuVs/AlyAgCdgcCYCwF6DKYEJz52VGWWxSZmYveKi5Xl9vxmWu34ke/m0J+0Ior7SVwTPrgDtvQFaqE1WzG1+r7sdruwb6OgGb6fRLKslThiBAJzz5bUZwCEIoRkdHbs0UkD0XwCEKdkPgUQ4xUjnfOS7AwwmN3IIArDVa8W7waEd8ATHN+PFZkJooeKy75iIBVjgB2F46hb7ISEzwLKxfB55xurHW6YWSnzQda6vdJKMtShSMMa5j3bEWzDaesi+8fPT5bhAgogkcQqoPEp0gWpnLO+cbRGQqBF3xYzRjBWArwbvFqXLI6wQghOMc70B+ZjowuFZnRa8Vla58HtaYuXF82FPc4LfX7JJRlqcIRwVo4+2yFGPZytmGB+NTrs0UQBKFlSHzOJYl57cD8VE7t2Vcx2vJ7vGN14lReCbqs+eBnPGqCtRA5FjuK/ePwG20xIzN6rrjUa79PQkGWKByJPlurJ0exiTFim8GGd4tXzz57gL6fLYIgCC1D4nOGZOe1zxJN5ZRvgiXgQnDkLDqsBfNbejAsuOIGVPaewDafC2Zb2bzIjN4rLvXc7zNVQnwELb1utPZ5EAgGYTaZUE89QuOyVOGIg7OhTphAiOFwqHgNLlmdsz+j92eLIAhCy5D4hLh57YuaVSdo6ZFnsGKbtRg3MBYELPnYM3wxayouY/X7jMWimdw65VyfB/uPtWLK1YPlxunpSJ5wDl5trcEh5zLcRtORlmSpwpGIyQZ/159w21g7Vg21Zc2zpVdoc0YQ2QEjCILqR+t4PB44HA50u92w2yV+OfMhhA98F68naEa8c7Qde4rWLtmsOho5HYzV0qNwFUxbvwEmEgYXo+JSr82vQ3wET7x2HMv9TfjiinbEaucZEYB9HbXotNyI+3Rc7X6uz4MXjzSjgTkedy78F3Tccko2YcGHwPWfyqpnS48s3JzZZzZnnaEa5NDmjCA0gcfjQbXDAXcCvZb14pPraUb3mw/jKXtxwjFs93iGUb3rB0v3C6SX4CLO93vwwuHEouuz125FOCLoMuJBIpyEhVZRKhJJmzOC0AfJis+sT7vHm9c+l6SaVVNLj0WsLrfjC9dvw/5jeXi8owc1hul0szucg65wDXIcy3BlbRVeP35et+noll43plw92F3bG1N4AgDL6Lfl1DxhUbtQWHTiYF8lXjjsJWGhMpSyiYT4CPYfa0UDczzm5qzIEsAXV7RjXweoHzBB6ISsF59LTVCJBTWrTo01FXbU3taIlt46tPZ54A6GYDYZcXuFHRzL4JWjH+pamLT2ebDc2BXX9wros+UUCQttouSGIds3ZxklyQ4vBCE1WS8+l5qgEos8gUe/j8Hh97t0lxqWGyPHYmN1/ryXRjQdrXdhks0tp0hYaA+lNwzZvDnLJKI7vBCEhGjvTS4xfNlGNHAW2EP+uMcJHg/yxkN4vWMKwYsvwdH/AoIXX8Krb72FJ147jvP9HoXOWD/MCpOKxMJkyt2Dll63sicoEdnccioVYUFkFqWfy0AwCLuIzVlAR5uzTBHt8PL6yFk8ZS/G/pI6vF28EvtL6vCUvRivj5yF5/CjYAfOZPpUCZ2Skvh88sknsWLFClgsFmzduhVHjx5d8tiXX34ZN910E4qLi2G327Fjxw4cPHgw5ROWmtkJKu5eMEvUXrl9Aay+dB6FHIvPrenG3XXncMeK6f/eX3sEy/1NeOFwM87Ri1MU2SJM6ivs6AzVYMRvjntctOVUvUbtBbEgYaE9lH4us3lzlhH4EILNT6NpahBvFdYuqnfwGC14q7AWTVODCDY/DSwxElrqc+J6mmFqfgbcO09M/7enWZnfTWQE0Wn3559/Hvfffz+efPJJXHPNNXjqqaewZ88enD17FtXV1YuOf/vtt3HTTTfhhz/8IZxOJ37961/jtttuwwcffIDNmzdL8iHSIkGfztzgFNb0nMNOjsH69eVgrPMfhkymhrXeEy9b0tENlQ4cci7Dwb7KuNXuB/sqkeNYhoZKh/InOQcp7ysSFtpD6eeS+gErC9d3Er2jF9DsqIzZWhAABIZBs6MSW0YvoDpeka0EUPo/OxEtPn/yk5/grrvuwt133w0AePzxx3Hw4EH84he/wKOPPrro+Mcff3ze///hD3+IP/zhD3jttdfUIT6x9AQVuxBBdYiDiylBzVoHGIct5s9nwrOmh4bl2SJMjByL27bX44XDXuzrQNxWMndsr8/cxoEP4dLpd3DxwzcR8fWjzjCJKVs+Og3L8WprbUr3FQkL7aH0c6m1zZnWkbTDS5qkNeCF0DSixGcwGMSHH36IBx98cN7Xb775Zrz77rtJ/RuRSARerxcFBQVLHhMIBBAIXH5ReTzyp1uXmqBycLQE/SOtuK7oQtyfV9IMr5fWNdkkTOa2nHqivQON4Q+wLNyNQFjAiFCOcEEp7rz+CtRlaMPADpzB0OGfo6v7JAaEMbDmIIRwBA0eI3bY7AiUr8N/eDaIvq9IWGgPpZ9LzWzOFqLRSnHVdHhZkP5fGIWNpv8x2o49zU8vOeBFK2g9Uyk1osTnyMgIeJ5HaWnpvK+XlpZiYGAgqX/jscceg8/nwx133LHkMY8++igeeeQRMacmDTH6dF56uw0O4+mkflyJ1LCeWtdkmzBZU2FH3TYzho+8hT7PeZzg/fCyHMqMw7gmeBFlJz4Ca1A+xcQOnIH78KN4seciPjCEUeDgwDDTka+jPI9G3xh2dn2IL60K4rlRcfeVZoVFFpOJ5zKZfsB3qCibo+VUsZgOL3YhMi2q5TgPlaX/5UQPmUqpSanVErPgRhEEYdHXYrFv3z58//vfxx/+8AeUlJQsedxDDz2EBx54YPb/ezweLFu2LJVTTRu1pYb11Lom24QJO3AGE0d/jGOBQTRXVc+mmFoAfJipFNNM9OE/xvvwW8aO9Xn9mPsoezgOTbYcwDeJvd1t2L2yBI93ibuvtCYssp1MPZfx+gGrKTqk9VQxX7YRDZ+8hLdD8VPv9pAfDZxlekKfDKgp/S8nYjOV2RIhFSU+i4qKwHHcoijn0NDQomjoQp5//nncddddePHFF7Fr1664x5rNZpjN8SuDlUJtqWG99cTLGmESJ8UUEQR0BBic5Isx2N+J6/b/FIFd/xP1y4pkX2yi0YcDXCFyuT5YuMUxDoFhcDzHjC0+D2qDA6jmuvDmxwOiFketCAtimkw9l7H6AasKHaSKZzu8jJyN+RkAgBEEbHP3orRorWziUzXpfxkRm6kMN67GH3U87W8uosSnyWTC1q1bcejQIXzmM5+Z/fqhQ4fw6U9/esmf27dvH77xjW9g3759uOWWW1I/2wygttSwHivEs0GYLJVick0G0T3kQjjoQx7rxbvwY8toM84c/A3eKL1B9sUmGn0YZewwseElj/NwHFoEPyqGhzHhGcLJoRYUl3aKWhxVLyyIeWTDcykWXaSKE3R4sYf82ObuxY05pdP2AZnEs1rS/3IiJlP5/ZZL+M3BMVxlO6XpWo5kEZ12f+CBB/CVr3wFjY2N2LFjB371q1+hu7sb9957L4DplHlvby/+/d//HcC08PzLv/xL/OxnP8NVV101GzXNycmBw6F+D5/aUsNqswFIhd6FSawUk2syiPb+YeRjGFV232zU0eX14Sv2N/GKX5B9sYlGH1iWRTASfzkYjwgYGXchGA5hV/EF3F13cfZ7elwcF6HRApN00PtzKRa9pIrjdXhp4CwoLVoru29VLel/OUk2U+kwBeH1jmGL4wy+uKJP07UcySJafN55550YHR3FD37wA/T392P9+vU4cOAAampqAAD9/f3o7u6ePf6pp55COBzGt7/9bXz729+e/fpXv/pV/OY3v0n/EyiAmlLDarMBEMmxMMUUEQR0D7mQj2GszPPM91kygJWZUmSxiUYfnFYTulx58PPe2Kl3ATAHw4AhgkmuEHuKR+d9X4+L41y0XGBCSIeeUsVLdXjhyzeBL98kW8QzilrS/3KSbKbyE5cT1ogHO5wdYJnYlkOt1HIkS0oFR9/61rfwrW99K+b3FgrKw4cPp/IrVIdaUlBqswEQybEwxTTuCyIc9KHK7sPCNdcuACxnBBRYbKLRhxpTBL0mGy75bIvEMABYAiGsFhicwWpYzWasdS4eqai3xTGK1gtMCOnQXao4RocXJX+3GtL/cpJsprLFZccyUy+KLEEAS9e7aKWWIxlSEp/ZihpSUGqzARDJsTDF5JoMIo9dHGW08zwaGCMEx/Q9JvdiE40+bB85i77iKlwYCOGiF6iyXbYBMIKATb4g/EI5PmCuxJ0rBmBkY4+iVd3imG6qXAcFJoR0ZEOqWEnUkP6Xk2QzlaN+I0xMBE6bKeG/qZVajkSQ+NQgarIBEEszt2VGyJ+LbeFSrB3swHsVdYhEIosKfBhBQONUAGW2Agj2y8JN1sVmbvRh6hL+s7gYZ8aMOOOZLoAqhR9XB6ZQxdfgj8b/gjvXjKDeEX/og1oWRylS5booMCGSI4mNSjakipUm0+l/0YjY0Cabqbw44UA+OwWnNbFNQ0u1HPEg8alR1GIDIGKzsKmw3TCFi2wJVnk7MH7+NPpzyuGbU+Bj53k0TgWw02iFtWY1BPby9ZN7sVkYfThrncKAIQJTgMUqOJFXtBnHnX+OUv8F1Dv6E/57algcpUqV66XAhIhP0huVLEgVZ4RMpv9FIHZDm2ym0m9ZAXfEgbHgSNbUcpD41DBqsAEQi4nXVNg1XAXH+W6s8/bjfMQPBzOFQiaCBsaIMlvBtPC0O2ePV2qxSRR98PdO4NW3QtoodJMwVa6nAhMiNmI3KnpPFROxSXVDm0ym8q/+bDVeP34eB/s6s6aWg8QnoVq0OOkhUVNhZ7EN9oI16GuxwDrMocHYhW0lHsCRD8GePy/iqfhiEyf6oKVCNylT5borMCHmk+JGRXOpYjFkYUuxhKS5oU0mU2ngsquWg8QnoUq0Ogs3qabCHIutqxi8Eb4azewtOMd/hN2WXhSx6l1stFToJmWqXFcFJiQqFpHWRkUNqWKJrym1FIuNFBvaRJnKbKvlIPFJqA6xs3DVhJjxp/W2S3AVbULnlEMTi41WFkcpU+WpFpioLWpPoiI2yW5UfAYTBidHsOr9XyBYvkkVwl3qa0otxZZGKe93NtVykPgkVIXYWbhqa2Yudvwpcjj8xS7tLDZaWBxTTZUvJRjXb70bN779o6QLTNQWtSdRsTTJbFSWTY5j23AbWO8g9ge9cHu6Mi7cJb+m1FIsLkp6v7OlloPEJ6EqxMzCVWMz81TGn2ptsVH7+aaSKk8kGO9Y/zfY0/FcwgIT1UXtSVTEJdFGZdnkOHb0n8Gx8CQ+4QTk2UsQKV4JIIPCXYZrSi3F4kPeb+nJfJiCIOYgJm0dbWauJuor7OgM1WDEv/SUCuByVXi9ymwDemA2Ve7uBSPEboY/myovXIUWrMCLR5qx3N+E+2uP4O66c7hjRTfurjuH+2uPYLm/Cf/7jA/tmx9G9a4fYO/GL+MLa27H3o1fRvWuH8Cw9zFEytYvitovvIejUfsG5jj2H2tFiE/uZZYOXN9JDCYpKgZHL4DrPyX7OakJvmwjGjgL7CH/ou9xQgTbhttwLDyJl0wmgDNCsBbOfj8q8pqmBhFsfhrgleltK8c1FZtWpvskNprwfqsEEp+EqggEg7CLSFsHVNDMfC4NlQ7kzFSFR2LrHtVUheuWaC/GnFLsHG1f9MKwh/zYOdqOG3NKwW69G68dv5iUYHzt+EX4y7cguO0u8NfcN/3fqsbZqNJs1L4icdR+yt2Dlt7FI0qlJptERYiP4HT3OF54vwv/5+02vPB+F053j8cV+fE2KjW+MUT8Hhw0mVEUmkSOxT5PfAKZEe5yXFPdtBTjQ+B6mmFqfgbcO09M/7enOe2NgdgNLYnPxFDanVAFUb/dx70TKHUB7VYvnDYTnFYT2CXe5GpoZr4QVVWFZ3F1c7K9GE8GKzHleksSm0cqUXu5rQu6ERUJSNlnG6dpfPWUC+2RICyhCCo4K7jiBggx/pZKDxiQ45rqIa0sa1EdDReQHBKfRMaZ++IoDA2ix5uD0dEhuF0sLpltqClxwmGdP/NW6WbmYqqX1VAVTtXNyY3ta32/SzLBKLbYTIkRpHoQFYlI12e71EZlg7sfzXwIy2xF08Izp2DJc1BSuMtxTbXeUkyJojoaLiAtJD6lIoujTOmw8MXhMAXx2OlVuBhajs86P0DvpBXtfSHUlhfDYZsWoEqnrUVFVWbugw0Dp7GmyIshK4ezkVXoN63AsmAHdrNdKLH2wHTpDPiwPPcHVTfPIUEvxqUEYyjC4BOXEy0uOwI8AzMnwBNgYPMHl/xVqRSbyY3WRUUipOqOEWujYuo/hc7hM2ArN8WMeM5FSeEuxzXV9Mx6BYvqdD1cQGFIfEoARZlSY6kXx5+vGMS+8/V4eRjYXXgK8A+ja9iI9TnFGAtaFG1mLiaq0sB2xbwPruB5XB30YdhkxWnOIO/9QdXNooglGFtddvy+sxSTgSCWmy7Bzk3Cw1vR6l6NSLgbV68pjRm1rq+w49XWGlWNINW0qEgCSbtjLNioBHuaUf/mwzgSDqpKuMtyTTWcVla8Ul8NwwV0AInPNKEoU+os9eKod3jwxTrg950N+GlvLSoNffAGjWiaqMAwV6tYM3MxUZXmI0OoYF7D4amheffBsslx2HtPoSUwjlZzHvxVW8BanKjxjYGfGMbExTdRd+kjmK7+NsLrP5+2EKSWKeJYKBhbXXbsaytFg6kVn6o8hSLTBADAz3NYYepDG+PDC4cRM4WryhGkcooKFWR75PTZqla4y3RNtZpWVqoBPCEtJD7TgaJMaRHvxVHv9OC7G70463LgrKsCJwZLYc7Zgi9fs1yxZuZJR1XKenD2+J/wHzYvPqhcPXsfRFu1vBvxY19uASqCXlzdfwrbWSsiAS/ahBBOM0DN1DCuPvT/oKzzHZi235vW4k4LsTjmCsbP13Tg953TwvNLZe+CZaarWgUAPT4bCm0Mrl3Whee7DDFTuKoqNpvDXFGxeaQNH0350B+KwB7hUc/loLKoDtbrvi16Go4asj2y+mxVHA2USyiqIa0sdjpYthTV6Q0Sn2lAUab0SPTiMLICNhW4sKnABY4R4C7PU7SxebJRleJAPzi+Ewe41SiYcx/MtmoxmyGwDPJZE7Z7R3DCaMEfrbkYZac9rCazBcf8k7ihrxk3HB5PK0pOC7E45grGx8/mwD01iU8tOzUrPP08hx6fDS4Uo7bECQPHxE3hqqHYLBaRsg1o3/wwThzZj0JvM67iBmAyA5eM1Xg9sB3mY37ctt2T1HmpKdsjt89WzdFA2YRiBtPKqXQtyIaiOj1C4jMNKMqUHmos0JhLslEVxuPCRfgxyhgxtx62esqFNiGEUdYEgyBgT2AK70eCeJk1IcJys8cFWQ5djIAmkxnC1GBaUXJaiMUTFYyPvWbAisgbGJ4ywB3IRTBiwEQkD5zZhto5HRcSpXDVOIL0XJ8HLx49iQZuAFddwaLIMt2vcjN82OF/Bwf7OpObvKSybI8SPls1RAOXREf+w1S7Fui9qE6vkPhMA4oypYcaCzTmkqw45vkQxsCBZeffCwY+BNfMu3ldOAQzH8JrrIBY0jAIICLwaUfJaSFOjTUVdly9phzmbhM4+woEIxFwLIuaJXrNJkrhqmkEqVQV4YD6sj2K+Wx1JPLUSDr3qGq9uUuhAq+0GqAJR2mQSpSJuIzapwElOypzSsiBOTItUuYS5oxwznyuhnAIbQKPMQZgYiyOJgAMa0h70gxN4kgdq8UMnstDbWke6sodqC3NQ0GuOeaQAzUOOFgKKScvqW1iUtQ20SI0Yl9H7aJndcRvxr6OWrQIjbhtez0AiJ6CRMhPWveoiIlmpm3fzKjAYwfOIHzgu+h+82EcOP0sXjz3Kg6cfhbdbz6M8IHvgh34OGPnpjQU+UwDijKlh1oLNKIkG1X5k38N6o0+XDRFMDHne905TmxkjCiM8DALEQxBgBkMBMP8e8UU4eFkuNnRfWlFyVVcJKF21B6JTxUpK8LVmO1J1mcrCMATrx0XPwWJkJ1071E1e3OjqMkrrQZIfKaB5sL9KkStBRpA8uL4nPkKfLMqiO2eC/Pugy5bAa6w2LHbP4YAGBQJEXBGEzBXfApAcdCHHEv+rPhM14uphYVYjaiyVZIESFkRrlZPcSKfbfvgRFpTkAh5keIeVbU3V2VeaTVA4jMdKMokCWos0IiSjDj+/PZ6lDCVi+4DnmFxrHg1rus9ifGpUVhhwAGTHaMz644pwqM46Js3N1qqKLmqF2KVovZIfKpIWdin5mzPUj5bKT2vhDxIdo+q1JurNq+0GiDxuQCxPcYoyiQNairQWEgy4jiCpe+D2twyOIy5mJwaw5f8PrwUDsLIMHAyHHIs+bNzoyWPkqt0IVYzao7Ep4qUdgItZnsknYJEyIJeLS9RqDPOYkh8ziGVHmMARZmygWTEcdz7oGQtilpew+fefQL5gTEct+XDnVcGwVo4G/GkKLk6UHMkPhUktRNoMNsj5xQkQhr0anmJokavdKYh8TlDqj3GZqEo0zTZ3kYizn0Q2nQnckvX4lPNT2Pz6AW0+FzwTHooSq5C1ByJF4vUdgKtZXtknYJESIJeLS9R1OqVziQkPkGeIKlQy8g9NUNRciITSG0n0NJ9rPZhFsQ0erC8LGXb21CyHg2cRZVe6UxB4hPkCZICaiMhAoqSExlAcjuBRu7jTPsJxdYRZDNatrzEs+296SjHVyzV2Oa+oBmvtNyQ+AR5gtKG2kgQhCbQk50gWTLpJ0y1jiCb0eI9moxt7w9T23ALM6YZr7TckPgEeYLShdpIEAShVjLlJ0y7joDQBGJse/8pfAZ3WN/DlnH1e6XlhsQnyBOULtRGgiAINaO0n5DqCLIHcba9VTi34x9xhaFb9V5puSHxicx7grSOHG0kyCdFEISUKOknpDqC7EGsba9loBEbrlK/V1puSHxC/z3G5EbqNhLkkyIIQg6U8hNSHUH2kI5tL5uDLCQ+of8eY3Ij5cg98kkRBKF1qI4ge0jVtpftQRYSnzPoocdYppBq5B75pAiCkBOlIk1UR5A9pGLboyALic95aLnHWEaRaOQe+aQIQvuoNZWoZKSJ6giyB7G2vbqyPDx54KOsD7KQ+FyAFnuMqQEpRu6RT4pIi2wf7aoC1JpKVDrSRHUE2YNY217bgJeCLCDxSUhIuiP3yCdFpAqNds08ak0lZsLOQ3UE2YUY294L73dRkAUkPgmpSWPkHvmkNIZKIo002jXzqNmvnSk7D9URZBfJ2vYoyDINiU9CNZBPSjuoJtJIo11VgZr92pm081AdQXaRjG2PgizTkPgk0kaqAgPySWkDNUUaabSrOlCzXzvTkSaqIyDmQkGWaUh8EmkhZYEB+aQ0gMoijTTaVR1kWuDFgyJNhJpIK8iiEquTFJD4JFJGjgID8kmpG7VFGuUY7UqIR80CjyJNhJpINciiGquTRJD4JFJCzgID8kmpF7VFGqUe7UqkhpoFHtl5CLUhNsiiJquTVJD4JFJC7gID8kmpE7VFGqUc7UqkjpoFXrp2HrU2zU8GLZ+73kk6yKIyq5NUkPgkUkLKAgO5FkhaeKVHbZFGqUa7Eumhdr92qnYetTbNTwYtn3u2kEyQRW1WJ6kg8ZkhtC6MpCowkGuBpIVXHqSMNEryDEg02pVIH7X7tcXaedTaND8ZtHzuqkBFhT1qszpJBYnPDKAHYSRFgYFcCyQtvPIhVaRRymdg7mjXzSNt+GjKh/5QBPYIj3ouB5VFdbBe921NmfG1itr92snaedTcND8RWj53NaC2wh61WZ2kgsSnwuhFGKVbYCDXAkkLr8xIEGmU4xmIlG1A++aHceLIfhR6m3EVNwCTGbhkrMbrge0wH/Pjtu0e1W/q9IAe/NpSe9qVzHSpueG/2lFjYY/arE5SQW9dBVkojBaKtqgwamCOY/+xVoT45G64TNBQ6UDOTIFBRIh9TLwCg9kFsiLxAjnl7kFLrzup85Lr3yUuMxtpLFqLezzDuHWoDdcNX8StQ224xzOMPUVrYb/hoZjRAbmegXN9Hrxw9CQM3ACuuoLF9isLsXlLIW7b4MN9K9/Bcn8TXjjcjHN9Hkn+BoS+ScXTvhTn+jx44rXjePWttxC8+BIc/S8gePElvPrWW3jiteM43y/tPSnluWcVCwp7Fqa5o4U9TVODCDY/DfDK9KrlyzaigbPAHvLHPU5rRZUU+VQQPe1I0y0wkGsiiponreiJSNkGGPY+hur+U9Meo6gvqnwT+PJNS3or5XgGKNpNSI2UnnalM11qbvivZtRa2KPXokoSnwqiN2GUToGBXAskLbwKwhnBVzXOLsDJpHrkeAb0tKkj1IEUnvZMbYrU3PBfzai2sEenRZUkPhVEj8Io1QIDuRZIWnjVjRzPgN42dUTmkaJpfqY2RWpu+K9m1FzYM7eocsvCQijOgtKitTThiFgavQqjVAoM5FogaeFVN3I8A3rc1BGZRYqm+ZnaFKm54b+aUXthT6pWJ7VCxicFqa+wozNUgxG/Oe5xUWFUr2NhlG7BktL/LiENcjwDet3UEZkj6mlvERqxr6N20f064jdjX0ctWoRG3LZE0/xAMAi7iE1RQKJNkRTnno1oorBnxuoU3HYX+Gvum/5vVaMmJhothCKfCkI70svINRFF7ZNWsh05ngGKdhNykG7T/ExuitTe8F+N6LWwR60wgiAsER9SDx6PBw6HA91uN+x2bT8s5/s9eOHwTPVjPGF0w7asWBhmm427Yy+QaU84kvjfFY2KJmWoBamfgRAfwROvHcdyf1NcQbuvoxadlhtxH1W7EyKY36Nz2tOeTI/O093jePWtt3B/7ZGEm6LHO67H7TfulNyLnOq5ZyvswMfwHH40Zp/PuYU9S7WSI6b1WrXDAXcCvUbiMwOoRhipBLkWyEwvvNFJGYOxDOIZmJShJqR+BmhTR6gN2hRpE1q304PEp8rJtDAi5CXepIz5O2jlJmWoDamfAdrUEWqDNkUahQ+B6z8FLkZhT7ZmrJKFxCdBiEHK9DgfQvjAd/F6Au/QztF27ClaC8Pex5Rf0CT6vEqODRR/PrSpIzIPbYqIbILEJ0EkidRpFq6nGd1vPoyn7MVxGxbbQ37c4xlG9a4fKNOseAapPu/sS9XVg+XGLtgNU/CEc9AZqkGOk16qBBGFNkVEtpCs+KRqdyKriZcefzvkx7aRs7jx8KOi0uOqnZQB6T5vJsYGqgoqJCNEkEovZILQMyQ+U4VePtqHDyHY/DSapgZjpsc9RgveKqwFRtuxp/nppNPjqp2UIdHn1dIsdTlsAdHIce/CyPEnL1FBAkEQRBKQ+EwBevnoA67vJHpHL6DZURnTlwkAAsOg2VGJLaMXUJ1khFKtkzKk+rxamaW+0BbgmLEFvNpag0Mp2gLkiJTrEbV5gQmCUBckPkVCLx/9IFd6nC/biIZPXsLbofj/ttKTMqT6vFqYpS6LLUCmSLnekEP0EwShL0h8ikFLLx+yBSRErvS4WidlSPV51T5LXS5bgFyRcj2R9V5ggiCSgsSnCLTy8iFbQHLIlh7njDBt+yZuPPwoMNoet8+nads3EVFoMyDV51X7LHW5bAFqLiRTA1ryAhMahAIquoLEpwi08PIhW0DyyJkej5Sth/2GB7Gn+WlsidXSqGit4psAqT6v2mepy2ULUG0hmUqYFf3Le8C5RsB4XOD5EDjOCMHuhOAoAMuyGfcCE9qDAir6g8SnCJZ6+UQEAeO+IFyTQUQiEbAsi/4gj1BgQuETDMH/wa+wf7wXzxnLwY8GwLIhOK0m5NtM6rIFpIqEu1+50+ORsg0w7H0M1f2npjciCyZlKBXxjCLV522odOCQcxkO9lXGHRt4sK8SOY5laKh0SP1R4iKXLUCthWRqobXPg62RD2C7+A7afR60CCF4GMAuAA39RpTZ7LDWrEaR3ZkxLzChPSigok9IfIog1svHNRlE95AL4aAPeawXJjaMYMQA3u/D4dYRlK/0KGauv3T6HfS0ncBvBSN4Q+fsuXS58tBrsqGmxAmH1ZRxW0CqSL77VSI9zhnBVzXO/p0zKkYk+rxGjsVt2+vxwmEv9nUg/tjA7fWKp1blsgWotZBMLeSOfoxVY2/igGkMx3PM8HCm2e8d5Xk0+saws+00Cuo2ZMQLrAiUGpYWLdVZEKIg8SmChS8f12QQ7f3DyMcwquw+WLhpaWHneexkBHRybrxwuFkRc/25Pg963j+AUX4IlQWm2XMBAD/vxSWfDRf7Q6gtLwas2vOkybX7VWN6XE6k+ryry+34wvXbsP9YHh7viD028A45q5rjvOTlsgWotZBMFfAhrOr/Hd4O+9CSn7NYJHAcmmw5gG8Se7va4DVvU9wLHD1PseIw2bZRlBqWHq3UWRDiIfEpgrkvn/8sWIHuIRfyMYyVeR5EnwtGENA4FcCyvAKsqp/CcNdx2c31UaP/nsh5TFj8sHDcvO9bOB4r8zy46AW6h4yw1xRry5Mm8+5XbelxuZHq866psKP2tka09Nahtc8D98zYwNsr7Kgry0PbgBcvvN8leZ/HRC/59VvvlscWoNJCMjXA9Z2EEL6E17hyVEaG521+owgMg+M5ZmzwTiAcFrBBYS9wKuIw2bZRlBqWBy3UWSQD9b1dDIlPMcx5+fj62tDlZ1Dp9M0KTzvPo3EqgJ1GK6w1qyFwypjro0b/+oIpDAzFPoZhgCqbD2c8Poz7HJrypCmy+1VTelwGYi9+K9GwZQuMHJvy5401NvBcnwdPHvhIlj6PSb3k3/4R7lj/N/jfZxoltwXMixyPnMfg1BjMIT8skTDKOTOsxfVgr/07/US4kowUcgOn0WUMw2NxQvBNztuQz8XNcngvwGN5rldRL3Aq4jDZtlF3XHsFak9QalgO9FDkR31vY0PiUyTRl8+W/T/F6kgzXJOey6Z6xogyW8G08LQ7ASjTaDta3WsryEXDsBFHeR6eBdFPYDoCmsd6wXi9aDBpx5Oml91vplBy8ZO1z6OYCHjHc7jj2ofx2nHpbQGRsg0wbfk6yt7+MRjvAFqEELwch06jEfX+cZR+9G8wcdpPsYqJFPJBHyYYDjUlTlzsD+Gid3qzO9/+w+GSz4ZqhHFzVZ5yEZ8UMichcEm3jTpxpAfWYJt2U8Mq9qlqvciP+t4uDYnPFIiUbUDzqr/DCsP/h1ttrYjwIbCcEYIjH4I9HwI7f1GV21wfre4VHAUos9nR6BtDk22x7woAzEwI1/kGUFq+VTPiUw+730yh5OInd59HsRHwBnRgxRK2gHRnu3uO/gua/MNorto0b1N0RCcpVrGRwqhIcFhNqC0vRveQEWc884swvZE8cCYbKnOGcMnDYP/bbYqkH1PJnJyOrEy6V+z7p3rwIeeDp0h7m2O1+1S1XOSXqb63Wknxk/hMEaPFinbjSkRqwgCAeHszuRttz1b3siysNauxs+004JucqTi9HAG18zz2+idwrWOZpjxpWt/9ZgqlFz+5Z76nEgE3VjUusgWkRTZU36bwGeeKBFgtsNcUY9zngGsyiOBM+7lClgXrGUfFVBAD3n44hBcUST+mct+08sVJ94otYkZwMZTc+qSmzbEWfKpaLvKLrof/ZXkfTo/no8VlR4BnYOYENDg9WOd0wcgKklrztJTiV48M1hj1FXZ0hmow4jfHPS5aUVsvY0h97rkIdicK6jZgr60A35zicYvXh2snfLjF68PXfQI2GurA7dCWJ40v24gGzgJ7yB/3ODXufjPJrBisSCwGp9w9aOl1p/X7UmnuLgY1RMC5vpMYTDKKNjh6AVz/KcnPQW5S+YyzIsHdC0YQwDIMCnPNWFmSh7oyBwpzzRhzjeNW/wVsKRBw2zov7ljRjbvrzuH+2iNY7m/CC4ebcU7kPZEMqdw3gWAQ9iR7xZoNDPIiyW13o5vjjLNgg7FQmEc3GE1Tgwg2Pw3wGWqLFa2zyCnFztH2Re8Ae8iPnaPts0V+atrotfZ5YA0P4Dfnl+HlNjum3JeQO3UOU+5LeLnNjsdOr0Kr257yeriQaJZrub8J99cewd115xR7xlKBxGeKNFQ6kDNTURsRYh+jVKPtheci2PORs64RtfWbcWtFHf6iZDluqahDp2MP3ln5EGo2XCXbucjBwhdbLGZ3v4WrSHzOILcYXIiYF7bDMIWASCtKKhFwqREbRdOk+EzlM8YRCRFBwMTAEL4WvIA77SwKalcCc6xJ0Qh8A3Mc+4+1IsQnd42T/jwp3DdiesX2GKo1tznW0iZqtsivaC3u8Qzj1qE2XDd8EbcOteEezzD2FK2F/YaHVBdQ6Rnx4uI4g+VMKx6ofAXfrGzCX5R9gG9WNuGBylewnGnFvvOlaHXZU1oP57Iwy7VwzZf7GUsFSruniJoabS91LoKzEIKz8PK5WBpxx1XrVeX7SApqcZMSck36WQq5Z74HStZjWYjDWP8IRhkjWJadnd7FznmByvmSV0P0VW5S/YxL9ZA1+IMonJrCloI8FNSunC3GnEs6doyEnycF32B9JPlesccN23FXkQ/b3Bc1kxrWWhGn1trhhfgI2vsGsd7cgi+VvQuWmR80KTJN4Etl7+K5AeD3nQ1wWhlY07DmyW15kgMSn2mQ8UbbKj0XOci2ZvBSILcYXIicM9/P9Xlw4CMeV09YsCPYgmfZAgQFDj2CBTkWC1ZX5CPfZpb9JZ8N/uN0PmMskXCyN4ABcz/y13kXFWPORa7OIKn4BhvAJd0r1uxcgeIrv40b3/6RZjbHmtxEaagdXkuvG3ZhGFfk9SAYYWP2vWUZAZ8qPIUf9axCV2Q1vp6GNS+VLBeJT40Tr9G20tVlajoXOdDa7jfTyCkGYyHXzPeolynf/zFaTGtxZbAPJr4H7xiNGBDMGJm048TFKVxZ7sCnmXFZX/Jarr5NlrQ/4wKRcPLtNjiEFwA2sYCRpTNICpkTIyAqs8WW2zW1OVZsE6XiNk5y0trnwVpbLwpNDHp8NqyyexArIFlomoBDGEYvsyMta57SWS4pIPEpAbEabdO5yISGdr+ZRi4xuBRyWFGiXqZ8/8dwT4ZQmTOKTYUhNI4HcEtgAi0RHqPmfgQCeSjtLcamVY2w3/DXsr3ktVx9myxSf0alI/CxSCVzIjabpKXNsRKbKLW3cZKTQDAIh9GPmhIn2vtCuOABlsXoe9vjs8HAsaivLEwrOBTrGQtFGHzici6qsh8L5aSV4pcKEp8EoVMy4UuW2v7R0uuGb7wHIX8Ea02tl/1TeU6smgyhbjIEPhIBDwb/170OPwvfiYeL10K2pTUb/McSf0alI/BLkYo4FJ1N0sjmWO5NlBbaOMlJVAxG+952DU/3vc2d0/d2IpIHzmyDObcEJUV5af2+hc9Yq8uO33eWYjIQxHLTJdi5SXh4K54frMb5QAW+uHbxEBqlIfFJEDomE15gKe0frX0eWMKDCIen8KnSU5eN+ywD5Jog5JrAYrptxxpDL46O96Gl1y1r5D8b/MdSfkalI/BxSUEc6jKbJOcmKht64SZgnhi0AetziuGadMDlm+57y7EsamwmhNk8DHbVYruElqfNBSN4vq0UDaZWfKryFIpMEwAAAUDzaDn+c+JqnGgtRl2ZPaNTlUh8EoTOyYQXWKoXdiAYhCfIYq3p0uwiuhSlZjeWG5Ux02spxZoqUn1GNXUGIS4j1yYqlYlSapn4JBWLNlwsg4JcMwpyL/cFjwjAvo4qSS1Pv23y4K0z7bgh9/i8Kvtoip8xWvFXa3txYPC4pFOVUoHEJ0FkAVqN3phNJvjCRtjNkwmPDUYMaffLE4VGUqxpIdFn1Hs3Dq0ixyZKa22c5CBTlqfNa+qxv68HVaYhnPM4FqX4a0uccFhNqmi5ROKTIAjVUl9hx+uRQoyGcuMe5+c5TETyEObsyFOBmT5riVPdvKbCjtq9m3DptBcT7e3gA35wZhP+bI0TVRs3wWiKPy2OkAmJN1GabOMkA5nYcE2FePxZ2Rg2VTjh8lnnpfidVhPYGc+LGloukfgkCEK1NFQ6UFpUjBP9tRgOfoDiGKl3AUCPzwYvW4QhdgV2ZNDHlM0kqm62rLgR4Y4mmEYvYDD6/WAEBR83gen/A1iN+2SJabKhF26yKG15ilbZL0zxxyLTLZdIfBIEoVqMHIu/vHEd/t/fDuH/XNqOe6uPwGoIz34/6mUaE4rRxq+D1Vktb8EKEZNE1c039R3HhnN/xNG8QjQXr8666udsIht64YpBScuTGtqaJQuJT4IgVM3aKie+evNVePYQj8muHOx0nECp2T3rZfKyRWjj16HDeBUVrGSCBNXNPoMJCE7iDyEXPgoZwRhM876fDdXP2USsNk4RQcC4LwjXZBCRSAQcw+BLoX4UV2ycLz6ztCm9VKilrVkykPgkCEL13LyxHJUFu/Ds4VL8r7ErsNw47Z8Kc3YMsStgdVZTwUqGSFTdXOMbAx/w4mVrHkoCXuROjkKwFc87Ru/Vz1nFgjZO/2kqxsdjfoSDPuSxXpTCj2sCU1jFluGFyatx5dAUVpcbs7opvVSoqq1ZAkh8EgShCdZVOfHIF69BS+96tPZ5EAiGkGcyYodOxsdqlUTVzdVTLrQJIfQbbDCF/MiLIT4BfVc/ZxvRNk47Dj+Jgu6TuFoYBWsOopCJoIExoqzYjkB5Fbo8XXjhcDP+cr0NBZ/8a9Y2pZcKLbU1I/FJ6JoQH0FLr3tGrARhNplQT2JFs2i1ZZTUqOm+TlTdbOBDcM1EYIIAhEh4yWP1XP2cbQSK1+H/mL+CrcVGfC33Ewh8CCxnhODIh2DPRw7L4ouF7fhtO4+RptM4mTuMpqKVWdmUXkq00taMxCehW871ebD/WCumXD2zaVpPOAevttbgkHMZblPBA0gQYlHbfZ2oujnMGeGcGUxlAsCwBghLHKv36udsoqXXDZ+7H1tWAoJlFQBg4V3CMsAtuWdwvOsCDuWvApelTemlJhODRcRC4pPQJef6PHjxSDMamOPYXbsw9dCJg32VeOGwF1+4fltGR4wRhBjUeF8nqm7uznFiI2NEeTgIJ8NBsBbG/Heypfo5W2jt82C5sQtFpikw42NgPC7wfAgcZ4Rgd0JwFAAsi3z/ELrgRWeQxco4/x7ZMsSh9iwRiU8tQ5WBMQnxEew/1ooG5nhM03WRJYAvrmjHvg5kfMQYQSSLWu/rWNXNc+myFWCzOQ+fnejDR3nFMcUnIwjY5u5FadFaEp86IRAMYnm4C1OfHMeAz4MWIQQPA9gFoKHfiDKbHdaa1eD5ECbZCCKRxL1ByZahH0h8SoiSPiyqDFyall43plw92F3bG7PaD5hO96hhxJhWUJPHMFtR7X29oLp5YcGILRwETFZ82uhEgdGO5nBw3vftIT+2uXtxY07p9LqVxRtnPVHu70DR0Hs4YB7D8RwzPNzlFltHeR6NvjHsbDuNwlwnrBEWLJt4HYlry6BgjKYg8SkRSvqwEjV0zvbKwNl0T5w+Z4A6RoxpAbV5DLMVNd/X0ermPc1PY8vCDTFnQWlFIywrbsSejqbY3y9am9UbZt3Bh7Bh5CX8LhxEiyMXZm5+VNPDcWiy5QC+Sexys1gu5GK5KX7kM54tg4Ix2oPEpwQo6sNK0NCZKgNnRowZppI6NtMjxtSOGj2G2Yok97WM0aFI2QYY9j6G6v5T07686L9fvgl8+SaEOSMMDbcu+X2KeOoHru8kQoFuNFkrEZocwco8DxbWEgkMg2aLGZUuoMRcjJtCw2gS7DF7xcazZVAwRpuQ+EwTpX1YiRo6A1QZqKURY2pGrR7DbCXd+1qR6BBnBF/VOLvmLEqPJvo+oQu4gdNojQSQV1aDi/0MLnqBKpsPFu7yFffzHC5M2rFcCOHzK7ehbKodTAzbRlxbBgVjNEtKb4onn3wSK1asgMViwdatW3H06NG4xx85cgRbt26FxWJBbW0tfvnLX6Z0smpk1odVkdiHNeXuQUuvO63fl6ihc5RoZSDXfyqt36dF6ivs6AzVYMRvjntcdMRYPUXsYqL0vU3EJ537Ohoden3kLJ6yF2N/SR3eLl6J/SV1eMpejNdHzsJz+FGwA2fk/hhEFhDt/eqwmlBbXgwvV4Ezngq0up1o9+ai1e3EGU8FvFwFjA47HEXF07aNorW4xzOMW4facN3wRdw61IZ7PMPYU7QW9hseWrQ54vpOYjDJYMzg6IWsfB+qFdHi8/nnn8f999+P733vezhx4gSuvfZa7NmzB93d3TGP7+jowN69e3HttdfixIkT+Id/+Afcd999eOmll9I+eTWQig8rHRI1dJ5LtlYGNlQ6kDMzYiyyRENBtYwYUzNK39tEfFK+rxdEhxZuXKPRoaapQQSbnwZ4sqEQ6TG396vTasL6mmLUVFSAta9A0LoSrH0FaioqsL6mGKVGFpzJdtm2sesH2Lvxy/jCmtuxd+OXUb3rBzDsfSxmVJ6CMdpFtPj8yU9+grvuugt33303Ghoa8Pjjj2PZsmX4xS9+EfP4X/7yl6iursbjjz+OhoYG3H333fjGN76Bf/mXf0n75NVAIBiEXYQPK5CmvzBRQ+e5RCsDs43oiLEWoRH7OmoXRYpG/Gbs66hFi9CI2zI8YkzNKH1vE/FJ9b6m6BChNHzZRjRwFthDfgAAyzAozDVjZUke6socWFmSh8JcM5zhwPwiohlbRnDbXeCvuW/6v1WNS6bKKRijXUR5PoPBID788EM8+OCD875+880349133435M++99x5uvvnmeV/bvXs3nnnmGYRCIRiN2vZfKO0vTNTQOUq2N2zWyogxNUPeWfWRyn0tNjpETbyJdEnU+xWQprdrKsEY8hmrA1Hic2RkBDzPo7S0dN7XS0tLMTAwEPNnBgYGYh4fDocxMjKC8vLyRT8TCAQQCFxO9Xk86k3n1VfY8WprDUb8nXHTk1Ef1u1p+guVeqj1gBZGjKkZpe9tIjnE3tcUHSIUJ0HvV6l6u1IwRrukVO3OLBA8giAs+lqi42N9Pcqjjz6KRx55JJVTU5yGSgcOzfiwYlUEAxL7CxV6qPWC2keMqRnF720iacTc1xQdIjJBwt6vEvR2pWCMdhElPouKisBx3KIo59DQ0KLoZpSysrKYxxsMBhQWxp7x+9BDD+GBBx6Y/f8ejwfLli0Tc6qKEfVhvXDYi30d05W/83shmnGwrxItQiPukMhfqMRDTRCZuLcJ6aHoEJEpEvV+TTs4QsEYzSJKfJpMJmzduhWHDh3CZz7zmdmvHzp0CJ/+9Kdj/syOHTvw2muvzfvaG2+8gcbGxiX9nmazGWZz/HYiaiIT/kLZH2qCAHln9QBFh4iMInNvVwrGaBNGiObAk+T555/HV77yFfzyl7/Ejh078Ktf/QpPP/00PvnkE9TU1OChhx5Cb28v/v3f/x3AdKul9evX45577sFf/dVf4b333sO9996Lffv24XOf+1xSv9Pj8cDhcKDb7Ybdrt6X3Pz519M+LJp/TegBure1DTvwMTyHH405BWZudChWL0WC0AR8CFz/KXAxgjHUWF45PB4Pqh0OuBPoNdHiE5huMv/jH/8Y/f39WL9+PX7605/iuuuuAwB87WtfQ2dnJw4fPjx7/JEjR/C3f/u3+OSTT1BRUYG///u/x7333ivqw2hBfBIEQaiV6ISjwVjRIZp/TRCEBMgqPpWGxCdBEIQEUHSIIAgZSVZ80mx3giCIbIFmqxMEoQLIrEUQBEEQBEEoBolPgiAIgiAIQjFIfBIEQRAEQRCKQeKTIAiCIAiCUAwSnwRBEARBEIRikPgkCIIgCIIgFIPEJ0EQBEEQBKEYJD4JgiAIgiAIxSDxSRAEQRAEQSgGiU+CIAiCIAhCMUh8EgRBEARBEIpB4pMgCIIgCIJQDBKfBEEQBEEQhGKQ+CQIgiAIgiAUg8QnQRAEQRAEoRgkPgmCIAiCIAjFIPFJEARBEARBKAaJT4IgCIIgCEIxSHwSBEEQBEEQimHI9AkkgyAIAACvx5PhMyEIgiAIgiBiEdVpUd22FJoQn16vFwCwbtmyDJ8JQRAEQRAEEQ+v1wuHw7Hk9xkhkTxVAZFIBH19fcjLywPDMLL9Ho/Hg2XLlqGnpwd2u12230PIB11DfUDXUfvQNdQ+dA21j9LXUBAEeL1eVFRUgGWXdnZqIvLJsiyqqqoU+312u50eNI1D11Af0HXUPnQNtQ9dQ+2j5DWMF/GMQgVHBEEQBEEQhGKQ+CQIgiAIgiAUg8TnHMxmMx5++GGYzeZMnwqRInQN9QFdR+1D11D70DXUPmq9hpooOCIIgiAIgiD0AUU+CYIgCIIgCMUg8UkQBEEQBEEoBolPgiAIgiAIQjFIfBIEQRAEQRCKkXXi88knn8SKFStgsViwdetWHD16NO7xR44cwdatW2GxWFBbW4tf/vKXCp0psRRiruHLL7+Mm266CcXFxbDb7dixYwcOHjyo4NkSsRD7HEZ55513YDAYcMUVV8h7gkRCxF7DQCCA733ve6ipqYHZbMbKlSvxb//2bwqdLbEUYq/js88+i02bNsFqtaK8vBxf//rXMTo6qtDZEnN5++23cdttt6GiogIMw+D3v/99wp9RjaYRsojf/va3gtFoFJ5++mnh7Nmzwne+8x3BZrMJXV1dMY9vb28XrFar8J3vfEc4e/as8PTTTwtGo1H43e9+p/CZE1HEXsPvfOc7wo9+9CPh2LFjwvnz54WHHnpIMBqNwkcffaTwmRNRxF7DKC6XT+lnXwAABgFJREFUS6itrRVuvvlmYdOmTcqcLBGTVK7h7bffLmzfvl04dOiQ0NHRIXzwwQfCO++8o+BZEwsRex2PHj0qsCwr/OxnPxPa29uFo0ePCuvWrRP+/M//XOEzJwRBEA4cOCB873vfE1566SUBgPDKK6/EPV5NmiarxOeVV14p3HvvvfO+Vl9fLzz44IMxj/9v/+2/CfX19fO+ds899whXXXWVbOdIxEfsNYzF2rVrhUceeUTqUyOSJNVreOeddwr/+I//KDz88MMkPjOM2Gv4+uuvCw6HQxgdHVXi9IgkEXsd//mf/1mora2d97UnnnhCqKqqku0cieRIRnyqSdNkTdo9GAziww8/xM033zzv6zfffDPefffdmD/z3nvvLTp+9+7dOH78OEKhkGznSsQmlWu4kEgkAq/Xi4KCAjlOkUhAqtfw17/+NS5evIiHH35Y7lMkEpDKNXz11VfR2NiIH//4x6isrMTq1avxX//rf8XU1JQSp0zEIJXrePXVV+PSpUs4cOAABEHA4OAgfve73+GWW25R4pSJNFGTpjEo+tsyyMjICHieR2lp6byvl5aWYmBgIObPDAwMxDw+HA5jZGQE5eXlsp0vsZhUruFCHnvsMfh8Ptxxxx1ynCKRgFSuYVtbGx588EEcPXoUBkPWLFmqJZVr2N7ejj/96U+wWCx45ZVXMDIygm9961sYGxsj32eGSOU6Xn311Xj22Wdx5513wu/3IxwO4/bbb8e//uu/KnHKRJqoSdNkTeQzCsMw8/6/IAiLvpbo+FhfJ5RD7DWMsm/fPnz/+9/H888/j5KSErlOj0iCZK8hz/P40pe+hEceeQSrV69W6vSIJBDzHEYiETAMg2effRZXXnkl9u7di5/85Cf4zW9+Q9HPDCPmOp49exb33Xcf/umf/gkffvgh/vjHP6KjowP33nuvEqdKSIBaNE3WhBGKiorAcdyiHd3Q0NCinUCUsrKymMcbDAYUFhbKdq5EbFK5hlGef/553HXXXXjxxRexa9cuOU+TiIPYa+j1enH8+HGcOHECf/3Xfw1gWsgIggCDwYA33ngDO3fuVOTciWlSeQ7Ly8tRWVkJh8Mx+7WGhgYIgoBLly6hrq5O1nMmFpPKdXz00UdxzTXX4O/+7u8AABs3boTNZsO1116L//E//gdlA1WOmjRN1kQ+TSYTtm7dikOHDs37+qFDh3D11VfH/JkdO3YsOv6NN95AY2MjjEajbOdKxCaVawhMRzy/9rWv4bnnniNvUoYRew3tdjvOnDmDkydPzv7v3nvvxZo1a3Dy5Els375dqVMnZkjlObzmmmvQ19eHiYmJ2a+dP38eLMuiqqpK1vMlYpPKdZycnATLzpcNHMcBuBxBI9SLqjSN4iVOGSTaVuKZZ54Rzp49K9x///2CzWYTOjs7BUEQhAcffFD4yle+Mnt8tC3B3/7t3wpnz54VnnnmGWq1lGHEXsPnnntOMBgMws9//nOhv79/9n8ulytTHyHrEXsNF0LV7plH7DX0er1CVVWV8PnPf1745JNPhCNHjgh1dXXC3XffnamPQAjir+Ovf/1rwWAwCE8++aRw8eJF4U9/+pPQ2NgoXHnllZn6CFmN1+sVTpw4IZw4cUIAIPzkJz8RTpw4MdsqS82aJqvEpyAIws9//nOhpqZGMJlMwpYtW4QjR47Mfu+rX/2qcP311887/vDhw8LmzZsFk8kkLF++XPjFL36h8BkTCxFzDa+//noBwKL/ffWrX1X+xIlZxD6HcyHxqQ7EXsOWlhZh165dQk5OjlBVVSU88MADwuTkpMJnTSxE7HV84oknhLVr1wo5OTlCeXm58OUvf1m4dOmSwmdNCIIgNDU1xX2/qVnTMIJAsXKCIAiCIAhCGbLG80kQBEEQBEFkHhKfBEEQBEEQhGKQ+CQIgiAIgiAUg8QnQRAEQRAEoRgkPgmCIAiCIAjFIPFJEARBEARBKAaJT4IgCIIgCEIxSHwSBEEQBEEQikHikyAIgiAIglAMEp8EQRAEQRCEYpD4JAiCIAiCIBSDxCdBEARBEAShGP8/1FbkJ7QmixcAAAAASUVORK5CYII=\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 2\n" - ] - }, - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAp8AAAKoCAYAAAAxl5QdAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAAEAAElEQVR4nOy9eXgchZXu/VZVd/UmdbfU2qzVFl4k29jGlgBDCBgmbAmQlSTMTSYJZEIyM0lumDyTTJ5750sm35BJJhluZgKTcMnwJSFOyMYQAjgesIFgwDbgBVvygvZdaqm7pd6qu6q+P2TJWrql3mrt83sePwlSd6ukrq56zznvOYeRZVkGQRAEQRAEQagAq/UBEARBEARBEMUDiU+CIAiCIAhCNUh8EgRBEARBEKpB4pMgCIIgCIJQDRKfBEEQBEEQhGqQ+CQIgiAIgiBUg8QnQRAEQRAEoRokPgmCIAiCIAjVIPFJEARBEARBqAaJT4IgiAucOHECn/zkJ7Fu3TrY7XaUlJRg586d+Pa3v43JyUlFfuZ1112H6667rmCvNzAwgC9+8Yu49tpr4fV6wTAMHn300YK9PkEQRL6Q+CQIggDw8MMPY9euXThy5Ai+/OUv49lnn8Xvfvc7fOhDH8J//Md/4O6779b6EDPi/PnzeOyxx8DzPG699VatD4cgCGIZFq0PgCAIQmteeeUVfPazn8W73vUuPPHEE7DZbPPfe9e73oX77rsPzz77rIZHmDnvfOc7MT4+DgA4evQo9u7dq/EREQRBLIYynwRBFD3/9E//BIZh8KMf/WiR8JyD53ncfvvtAIC7774b5eXliEQiyx53/fXXY8uWLfP/LUkS/u3f/g07duyAw+GA1+vFlVdeiSeffHLF4xEEAd/85jfR0tICm82GyspKfPKTn5wXlSvBsnRZJwhC39BViiCIokYURTz//PPYtWsXGhoaVn38F77wBUxNTeHnP//5oq+fPn0aBw4cwF/91V/Nf+0Tn/gEvvCFL6C9vR2//OUv8Ytf/AK33347enp60r6+JEm444478K1vfQt33XUX/vCHP+Bb3/oW9u/fj+uuuw7RaDTn35UgCEIPUNmdIIiiZmJiApFIBOvWrcvo8du2bcO1116LH/zgB7jnnnvmv/7v//7vcLvd+PjHPw4AeOmll/DTn/4UX/va1/DNb35z/nE333zziq//+OOP49lnn8VvfvMbvP/975//+vbt29He3o5HH30Un/3sZ7P5FQmCIHQFZT4JgiCy5Atf+AKOHTuGl19+GQAQCoXw05/+FH/xF3+BkpISAMAzzzwDAIsyoZnw1FNPwev14rbbbkMymZz/t2PHDtTU1ODgwYMF/V0IgiDUhsQnQRBFTUVFBZxOJ7q7uzN+zh133IG1a9fiBz/4AQDg0UcfRTgcXiQ0x8fHwXEcampqsjqe0dFRBAIB8DwPq9W66N/IyAgmJiayej2CIAi9QWV3giCKGo7jcMMNN+CZZ57BwMAA6uvrV30Oy7L4q7/6K/z93/89vvvd7+LBBx/EDTfcgE2bNs0/prKyEqIoYmRkBGvWrMn4eCoqKuDz+dJ215eWlmb8WgRBEHqEMp8EQRQ9X/3qVyHLMj796U9DEIRl308kEvj973+/6Gv33HMPeJ7Hn//5n+PMmTP467/+60Xfv+WWWwAADz30UFbH8p73vAd+vx+iKKKtrW3Zv4UClyAIwohQ5pMgiKJn9+7deOihh/C5z30Ou3btwmc/+1ls2bIFiUQCb775Jn70ox9h69atuO222+af4/V68fGPfxwPPfQQmpqaFn0PAK655hp87GMfwze/+U2Mjo7iPe95D2w2G9588004nU78zd/8Tcpj+chHPoLHHnsMt956K77whS/g8ssvh9VqxcDAAA4cOIA77rgD73vf+1b8fX79618DALq6ugDMzvuc86J+8IMfzPnvRBAEUQgYWZZlrQ+CIAhCDxw/fhz/+q//igMHDmBkZARWqxUbN27Ebbfdhr/+679GZWXlose/8MILuO666/Ctb30Lf/d3f7fs9SRJwve//3088sgjOHv2LBwOBzZv3oy///u/x3ve8x4AmF+tubCRKJlM4v/8n/+Dn/70pzhz5gwsFgvq6+tx7bXX4m//9m+xfv36FX8PhmHSfo8u+QRBaA2JT4IgiBy577778NBDD6G/vx8+n0/rwyEIgjAEVHYnCILIkldffRVnz57Fgw8+iM985jMkPAmCILKAMp8EQRBZwjAMnE4nbr31Vvznf/7nvJ+SIAiCWB3KfBIEQWQJxewEQRC5Q6OWCIIgCIIgCNUg8UkQBEEQBEGoBolPgiAIgiAIQjUM4fmUJAlDQ0MoLS1dcX4dQRAEQRAEoQ2yLGN6ehq1tbVg2fT5TUOIz6GhITQ0NGh9GARBEARBEMQq9Pf3o76+Pu33DSE+S0tLAQCn+vtR6nZrfDQEQRAEQRDEUqZDIWxpaJjXbekwhPicK7WXut1wk/gkCIIgCILQLatZJKnhiCAIgiAIglANEp8EQRAEQRCEapD4JAiCIAiCIFSDxCdBEARBEAShGiQ+CYIgCIIgCNUg8UkQBEEQBEGoBolPgiAIgiAIQjVIfBIEQRAEQRCqQeKTIAiCIAiCUA0SnwRBEARBEIRqkPgkCIIgCIIgVIPEJ0EQBEEQBKEaJD4JgiAIgiAI1SDxSRAEQRAEQagGiU+CIAiCIAhCNUh8EgRBEARBEKpB4pMgCIIgCIJQDRKfBEEQBEEQhGqQ+CQIgiAIgiBUI2vx+eKLL+K2225DbW0tGIbBE088sepzXnjhBezatQt2ux3Nzc34j//4j1yOVZ+ICXD9R8AfeQTcy9+f/d/+I4CY0PrICIIgCIIgdIcl2yeEw2Fs374dn/zkJ/GBD3xg1cd3d3fj1ltvxac//Wn87Gc/w8svv4zPfe5zqKyszOj5eoYdOQnhyMMY9J9HhxhDiGHhliW0nvoNqn3rwbf/JaSarVofJkEQBEEQhG5gZFmWc34yw+B3v/sd3vve96Z9zN/93d/hySefREdHx/zX7r33Xhw/fhyvvPJKRj8nFArB4/GgLxiE2+3O9XALCjtyEqGD38KB6CiOeOoQstrnv+dOxNAeHMQeRzXc130FUs2lGh4poQliAtzQMXAjJyAKYXC8C2LNNoi1OwDOqvXRFTf03hAEQShCKBRCo8eD4Cp6LevMZ7a88soruPHGGxd97aabbsIjjzyCRCIBq9WAF3sxAeHIwzgQHcXzvmbIDLPo2yGrHc/7mgF/F2458jAst36XbmqpMKkIoIy4fqH3hiAIQnsUF58jIyOorq5e9LXq6mokk0lMTExgzZo1y54Tj8cRj8fn/zsUCil9mFnBDR3DoP88jnjqlgnPOWSGwRFPHXb6z6Nx+DjE+jaVj1LfmFUErJQRfzERQ/vEaew5eD9lxDWA3huCIAh9oEq3O7NEoM1V+pd+fY77778fHo9n/l9DQ4Pix5gN3MiJWcG04OaVipDVjg4xBm74uEpHZgzmRMAzE6fxQ3clnqragBcrL8FTVRvwQ3clnpk4jdDB+8GOnNT6ULNjSUZ86fkxlxE/EB2FcORhakpTE3pvCIIgdIPi4rOmpgYjIyOLvjY2NgaLxQKfz5fyOV/96lcRDAbn//X39yt9mFkhCmGEmMz+dCGGhSiEFT4iA2FiEcANHcNohhnxUf95CkpUhN4b/ZMQJZzom8Ljr/bipy+ew+Ov9uJE3xQSoqT1oRGEIhTzOa942X337t34/e9/v+hrf/zjH9HW1pbW72mz2WCz2ZQ+tJzheBfccmYnh1uWZr2MCh+TUVDUsqCxhzTbjPg6smOoBr03+ubMUAhPHe5ENNCPtdZeeCxRhJIOPNnZhP3eBtx2RQs2rtFHs2kuJEQJHYNBdA6FEBcE2HgeLbVutNZ5YOVo3HYxYvZzfjWyFp8zMzM4f/78/H93d3fj2LFjKC8vR2NjI7761a9icHAQP/nJTwDMdrb/+7//O770pS/h05/+NF555RU88sgj2Lt3b+F+C5URa7ah9dRv8GJi5ZuZOxFDK2eHuGa7ikenb5QSAXrwkFJGXL/Qe6NfzgyF8KsXjqCVOYqbmgdRYb/o95+I9WDfUB0ePziND13bjk21xrsZF7vIIJZj9nM+E7IWn0ePHsWePXvm//tLX/oSAOAv/uIv8Oijj2J4eBh9fX3z31+3bh2efvpp/M//+T/xgx/8ALW1tfj+979v6BmfYu0OVPvWo33idMpudwBgZBntwUFUV2wm8bkAJUSAXhpJKCOuX+i90ScJUcJThzvRyhzFR9d1gV1yKa2wx/HRdV3Y2w08dbgUzbe1GSpTSCKDWIrZz/lMyfo3uu666yDL8rJ/jz76KADg0UcfxcGDBxc959prr8Ubb7yBeDyO7u5u3HvvvYU4du3grODb/xJ7HNW43t8FdyK26NvuRAzX+7uwx1ENvv0vDT02qNDkIgJWREceUrFmG1o5+7LzYSmUEVcfem/0ScdgENFAP26qHVx2E56DZYCbagcRDfajYzCo7gHmwVKRsVB4AhdFRitzFE8d7iwKn99CitXvaOZzPhsU93yaFalmK9zXfQW3HHkYO5eWejk7qis2G3ZckJIU2rKgp7FXlBHXL4q+N6m8xlWbAQDc2GlTzbAtNJ1DIay19i4TZkupsMfRZOlF51AI2xrLVDq6/JgXGc2ri4wHuvvRMbihIL+bEfylxWxFMPM5nw0kPvNAqrkUllu/i8bh47PexLmbzJrtENdsh0Q3mWUUWgToqpFkLiN+8H7A37Xi5iu+/S8Lc36YdFB/wVHovUnpNRZm0DIzgVIwOOPyYcBWYooZtkoQFwR4LNGMHuuxRBEUjDP9QguRYQRRV+xWBDOf89lA4jNfOCvE+rZ5QUM+sVUosAjQWyOJmhlxPTRZGYlCvzepvMZMdBLCUC+ichg7YcHOeBDd5Y3od5bRIPsU2HgeoaQjo8cGkw7YeOMEVGqLDCOIOvI7mvuczwYSn4TqFFIE6LGRRI2MuF6arIxGwd6bVCt2ZQnieAeGxAgGHV6cgoxkLIL28XMYamyjtbspaKl148nOJkzEelbMEE7EbOhNNuF2A2XC1BQZRhF1WlkR9ISZz/lsIPFJaEKhRIBux14pmRFPJXwWQCJnFQrw3qTyGjMRP6KxEMZ5F8AAMhjss9lwWSyEpsgUulw+Wru7hNY6D/Z7G7BvqC6laAIASQb2DdXB4WlAa51H/YPMETVFhlFEHfkdzX3OZwOJT0I7CiACirHJR09NVsVKKq8xE/EjIIsQWG7+a36Ww1k5hsYL4hPIwH9cRD5eK8fitita8PjBaeztnhVHi8vFNuwbqkOH3IY7r2gxVAlWTZFhFFFHfsf8z3kjNJRlAolPwtho0eSjMbpqsipSUnmNZSkJIcVjAwxQu2TEVzr/cTH6eDeuceND17bjqcOleKC7H02W2UaZYNKB3mQTHJ4G3KmDRplsUVNYG0XUkd9xllzPeSM0lGUKiU/C8BTb2Cu9NVkVI6m8xgxrAZ/isV4ZSCwJelL5j4vZx7up1o3m29rQMbgBnUMhBIUEbLwVtxswo7MQtYS1UUQd+R0vku05b4SGsmwg8UmYgmIae6XHJqtiI5XXWHb64J3qxrB0sfTuk0RsZKw47rxY4kzpPyYfL6wci22NZabz+KkhrPMVdWqVcsnvuJhMz3mjNJRlA4lPQl2U8rOle9012013k9Ztk1URkcprLDt9cNjdqIxNYdDmBgMZN8XjYOzl6L0gPtP5j8nHa26UFtatdR7s89Tjt13VuL78FGRZAsey8Lp4eJ08WJZJK+oyKeWuqyopiDg1s8dXSYzSUJYNJD4J1VDKz1ZsPrlibLLSlDSBDbvrU9jz4ncWeY25ylbUDh1DWTQwO+fTWoJDlRshMuyK/mPy8RL50DU6g2BExPGRRoRDI9jjPYkSLo7eQCkGbC6UeKrxytS6ZaIuk1Luj5+ZAmcrhSMxXBCfoVk9vkpilIaybCDxSaiCUn420/vk0gmfnZ/Cnpe+UzRNVlqxWmDj3fpB3NJ9YJHX2GMvx6YkUArgjM2D5rAfO2bGV/Qfk4+XyJU5AXkZdxQf2BrCC0Nr8dvgGjRZB+Fko+j1l+FUTytq6lvwsT3b5kVdJqXcW6s60f/WFM5NNePLu06hxhmb/34+PkMje3y16DY3SkNZNpD4JJRHKT+byX1yqwqfSz+IW7oOFEWTlRZkFNiE/XBf87dolMXFXuPqLQCAd4yeysh/TD5eIhdSCci2Cj9OBzw4HahDXGTR6JbAhCMQ7FasqyqZf+5qpVxJktE/EcCNnl5EQm6MxuyLxGe+PkMjeny16jY3SkNZNpD4JBRHKT+bmX1yeQkfEzZZqU6awIaTJTSFJ9EYDYBNChiYPomWF78NfOCRlPNqxcYrl30t5Y8jHy+RA3MC8oa1QzgxVYaOgBtxkYGNk9HqDWGLNwArK2MiZsMD3XXoGNw4L/ZWK+UGIgLEeBjbvGN4MzqI04E6bC8PLHqM0XyG+aBlt7kZpwToN7dNmIZs/Wzc8HFNX1dzlgifpb9fyMLjgL0UB8eOI/H0feAG35htrrrysxDa754VQSQ884IbOobRJYFNQ2QKd/QdxbbBYxj3n8PpUC8OxabQ1fsixN/cDXbkrZx/3ryPNzgIRpZTPmbex+tbT+KTADArIJ3JETx6tgG/PedGNDiAkugZRIMD+O05N757Yj06g+5FXsA54oIA9wql3EBYQCk7DTsnwmMJIy6mlgupXttsLM0wLxWAc1ngVuYonjrciYSYWRUjU1rrPHBcmBIgpb48GG5KAGU+CcVRys9mVp/cShldJjoJcbwD4VgI/yUmUB+ehPj6I6jp8JmyuUorlgY2DZEp7B4+icPJCPbZbPCzFyd6vhIO4I7xk7guH29xES5LIPKnf2IaXVMM3uXtxM11x1HBz8x/b0IowbP+7dh7tgUf3bDcC7haKVeUJPBsEgAQTLrg5NILKqP4DHNF625zM04JIPFJKI5Sfjaz+uTSZXSZ6CSEoWMYEiMY510QWBeORMKotJfgv9yVxm+u0hELAxtOltA+fg6HkxHstTuWBQRjLIvnHW7I0dG8vMXFtiyByI+EKKFraBRbbR24q+YQWGZxSqyCn8FdNYfw8xHgiZ5WeJ0MnAu8gKuVcjmWRUKyYEIoQW+iDh/wBtMei1F8hrmih25zs00JIPFJKI5Sfjaz+uRSZnRlCeJ4B4bECAZtbuCC/plb3Wj05iq9sTCwaQpPQoqFsM9mS+kt5gGAsxbEW1xMyxKI/OgYDMItj2NHaT8EiYWdWx5as4yMm33H8c/969ErbcQnF3gBVxv47nXx6J4qxSvja+G02bA5jfg0ks8wV/TSbW7kKQFLIfFJKI5ScynNOu8y5erGiB/RWAjjvGteeAKLVzcatblKjywMbBqjAZyTE4tK7XPwkggvw0F2+go3g5OzQqxvS9nARBBzdA6FsNk1CB/PoD/swnp3CKkqwj5+Bh55HIPM7kVewNVKuUm2FM9NX47OSB2+vL0LVna52dBoPsNc0VO3uRGnBKSCxKeZUGp7UL4o5WczqU8uVUaXifgRkC+ubQRSr26kIeSFYWFgwyYFBFLd1WWgUgjDYS+D7PQBMJa3mDA2cUGAxxpDU5UXXUMJnA8BDa7wogxoTOTQH3bBwrFoqfMty4ytVsqNl1XD6YjijckQKu1xw/sMc8WM3eZaQ+LTJOh9y49SfjYz+uRSrm6UkhAWPIaRl69unIMEUAFYENgMTJ/E6JIWU14SUSmEUcs5wVW2Qr5gkzCSt5gwNnPZOI+TR/OaSvSOW3EyFEYJOw2eTUKQLJiRSsHZXLCVVKGqojTl66xWyu0ancFThz2m8BnmCu2kLzwkPk2AUbb8KOVnM51PLkVGd4a1YK7o65NE3BSP43KLc35140JIABWGucCm5cA/ge99Ea+EAxhjWfAAvAwHh71sVng6ygEYz1usFVpsiDEji7JxLmCroxKBiAeBsABBmt3t3uTikWRLMdrbjCtWyMatVMo1k88wV8zYba41jCynGSqnI0KhEDweD/qCQbjd5o6wskZMIPn0fXhmFd/j9f4u3FKxmRpRDMRcNnvUfx6d0XGMB/oR5SxoZm1g7G4crtyIAad30XPciRg+ExpH4599g8ruhUKIQPzN3Xhm/CSed7gBzgrZ6ZsttV8Q/vQZy4ylG2LcFzbE9CSa4FBwQ4wZSYgSvv/7o1gbO7BiNm5vdzN67Hvw+Sw3EBHLmT9/g6mzwHT+zuq1Ro8HwVX0GmU+DY6Zt/wUO4syukNvIHH8F+iITmB/5Qb0uMqXZTyN2FxlCHgnrHu+husO3g85RXXBqN5itdFyQ4wZoWyc+lAWuHCQ+DQ42W75oUYUg7Gg85ltvAr1B+/H2ugoxm0lJIBUxIzeYjVJtYN8IfnuCS9WCjH7kWwQ2WGWbnOtIfFpcMy65YdYDgkgbTGdt1hFtN4QY2byycYttUF4Ltggnuxswn6yQRAKQuLT4Jh1yw+RGhJAGkMzOHNCDxtizEwu2TiyQRBaQuLT4Jh1yw+xAiSACIOR14YYvc4vNjBGtEGQPSA9RvzbkPg0OGbd8kMQhHnIdUOM3ucXGxWj2SDIHpAeo/5tSHwaHZNu+SEIwjzksiHGKPOLjYiRbBBkD0iPkf82JD5NQLE0ohixtEAQRA4bYmqcEPY9jAPR0ZQVnZDVjud9zYC/C7cceZhmq2ZJXjYIFTGiPUAtjP63IfFpEszeiGLU0gJBZITJfY3ZzqS0j55AH80vVoxcbRBqYzR7gJoY/W9D4tNMmLQRxcilBYJYjWLxNWYzk5I7QvOLlSQXG4QWGMkeoDZG/9uQ+CR0zbLSgiyBmZoEEwpAFBOo4qy4yzuIvVOiLksLBLESxeZrzHQmJc0vVpasbRB1HvUPEsaxB2iB0f82JD4JXbOwtMBNTyHSew4j4RA65ARCDOCWgVbGiltsvfj5jFN3pQWCSIuYgHBEBV+jliX9FD+bq9mGbXU7Vvyc0vxiZTHKak6j2AO0wOh/GxKfhK6ZKy1UCiOYPHcSzyciOOqwIcTx8495SRTRFh3H7vjPMdS5GWi8UcMjJojM4IaOYVBhX6OWJf18fjbNL1aeQqzmzIR8GkWNYg/QAqP/bUh8EromLgjwcjOI9J7D84kIDrgcyzNEHIcDLgfGowFc0fNzQNxjiiYNwtxwI8r6GgtS0s8xa5rvz6b5xcqTECXEkyJqq6rQz9jwVqQZ5XYLGitLcXu9pyBTRPJtFDWKPUALjP63IfGpATQyKHNsPA/7TAAjkRCOOmwrZoj+2+LB9lgfOGo+IAyAor7GApT0c85cFsJOYMD5xUa6ri8VhS2WKEKSAz1TTRiSG7BrXXlBhGe+jaJGsQdogdH/NiQ+VYZGBmVHS60bY4cFnBDFRaX2pcREDn0oQ78lhitIfBIGQElfY74l/Xwyl4WyEyyaXzxxFp0xP6YTUZRKSWzmHKiqaIH1nV/WxSQAI13X1ZgeUsgZlGrZA4yIkf82JD5VhEYGZU9rnQchmx2nAzbIMpDqXibLwEDYBQvvQsIuUucrYQiU9DXmVdLPM3NZSDuBVHMp+J2fRN1L30bZ9ChGRAlRlscQx0OKTaH69R+DxT14K9mgWcbRSNd1tQaTF3oGZaZTEooRo/5tSHyqhNG3EWiFlWOxZf06nDvqwtvTVtS7wrBzF/M/MZHDQNiFKVTikiovPDNB6nwtAEYqIRoVJX2N+ZT0881cFtJOwI6cROilf8GB6DiO1G9DwGLDVFhAICLAE4/imnNHsb3jLE56boKjRFY942i067pag8mVmEFp5VhsayyjaSYpMOLfhsSnShh9G4GWVGy8HO84/1/4Q8yKkyEPStlp8GwSgmTBtFQKC+/CJVVeNFgl6nwtAEYqIRoaBX2N+ZT0881cFsxOsCQDOxVNoG9wHEkhjFJ2GkE5gb0xCdHkJN4hPYmKtTvRUjYDQL2Mo9Gu62oNJjf6DEpCeUh8qoTRtxFoiVi7A+tqW/Dx8VP4tb0eU9EKCJIElmXR5ORR5uLBAWj3d1Hna54YqYRoBuZ9jYd/iKuHjmMqHkBclmBjWJTZvHDXbgd/+b1Z+xrzKennm7kslJ1gYQZ2KppA1/A4yjCOencYNlbE1EwMaxxhjLESrGEBf+rYAWx2o8UbUi3jaLTrulqi0OgzKAnlofqZSsQFAe4sPvRxigQvciFDdL2zBh+KD+KyMis21HhwSVUpfCU2eJNxXO/vms8Q0Zil3FhaQlx6Q527obcyR/HU4U4kxMyyW0QGyECMkdEDCWcgoQcSYowMyLm93HxJPzgIRk79IvMlfd/6RQIwl8xloX72QriRE+hMRuGLT6O97xTuiXXiU8wwNiejEBMiJDEBlzWJhEXEpHUSO3EMT/TUICHNpiDnMo7RYD86BoMZ/T7ZYrTrulqisKXWjZ5EEyZithUfNzeDsoUC2aKDMp8qQZFgfizqfF06+oWzo7pis2l2YGuF0UqIhUJLf+uirvLKSxZlCl9IxNA+2Znbes08Svpi1WZsTgj408hJBBkGDGuB7PRBdvqABRnRtJnLAtkJZP95NE71QZrswVvxCEa4OOIRYGuEQyvD4WWLjBAzK25DDHCdow9PxOM4HfBge3kAgPIZR6Nd19UaTG70GZSE8pD4VAmjbyPQA1LNpbDc+l00Dh+f9ZnNDb1esx3imu26mPVnZHItIRq5OUlTf6vC6zVzCdjYkZOIH38MrplRXJII4jcWC6wMA+9UNxx2N7jKVsiO8lUbofINFtmRkwh2v4hXk9P4IVeCcQ7w8rN/H58k4gYhieuSwBtWBgMWBm4ZcFsTaJIHcTpQNy8+AWU9hdle199dU4oTfVOafVbUEoVGn0FJKA+JT5WgSLBAcFaI9W3zDQ7U1V44cvGDGbk5SWt/qxrrNbMJ2BZmYQfXbMG28TO4LhnBPpsNwwAqY1OoHTqGiqpWtMUjq2Yucw4WL4jy55HES1YbQpIMjrloA/CzDH5ukcEkRFwR5TDtlNHKWiA7rfBIYcyIi4WMkhnHbK7rcWs1/vuNc4iHBjT7rKgpCo08g5JQHhKfKkGRIKF3si0hBqKiYZuT9DAiR+n1mhd/UAYBW4osbNjCo338HC6LhXBWTiDAcGiKBHHVUAdqNtwE/ooMGqFyCBbnRPnhqo2wj4RRG5pAj7z4b8+wDP7AytiVlPCuKIs1LivgtCIYcMHJXRSqSleSMr2uH4nsQBJR7GBf1vyzoqYoTDeD8t01pZBlGcd6p/DauVFDVUuIwkDiU0VW+9DbSuuxY20dfSAJTcimhNiTaER4bALtVmPMN1yKHvytiq7XzJJUWdh+ZxmGGtvQFJlCY2QKtWICFgBOSYbtsv8BUSF/9bwo553gKlvREHsdYiSIsATMJTU5lsE0w2JElPBhWOGqKsFEshS9iTp8wDvbXKRWJWnV67q7HhZRRDv3km4+K2oOJl86g9LI1RKicJD4VJl0H/rtPIfO3kEcO/EafSAJTcimhBi1VMOZGMFNTcZsTtLDiBwl12tmfSxpsrAiw6LL5UOXy3fxsWPncOvoKYiNVypyLAtFuewoh7N+J6q73wQjTCLGJZAAYAXgZRgwjAVRmwcn4xvxi76rMC5V4eQUg6k4j75ICc5CnUrSSmIuKUp4+oWDuKlBX58VLQaTa211IfQDiU8NSBUJ0geS0JpsrCFrKqtQNnHEMPMNl6KHIdhKrtfM+lj0lIVdIsoZpw/Wte/A6EAXKsQh1FpjsHKAzNtgn5HwXLQdT/W2ocY6gTb7EPpGHdgX2wDBXo//cf1m1YL2dGLu8Vd7NQ909IAerC6EfiDxqTH0gST0RKZ+sNfOjWY131BvG0z0MCJHyfWa2aKnLGwqUe5x2SE3rEffWAV6hDBKpWmUziRREhXgd9nxP3yvY00pwFsYcCwLyTKDVwMBvHbKgcYKl6ZBux4CHT2gB6tLMaH3KSQkPjWGPpCE3sjED3asd0pz8ZYPuhh9puB6zWzRVRY2jSj3Onm4myoxFfYgMBPH5WNnUWkvweXbgPJSD9glF9Dm8m7s7WY0D9r1EOjoAT1YXYoFI/hqSXxqDH0gCT2ymh9MF+ItD/Qy+kwvyxP0lIVdSZSzDIN1NhmbA8NYby3Fhq318HpSCzu9BO1G/6wUCsoAq4NRbHwkPjWGPpCEEdGLeMsVPY0+U2R5gpgAN3QM3MiJi69Xsw1i7Y7Ug+p1lIUFVhflYWsz3q6ohLcisOLr6CFoN/pnpVBQBlh5jGTjI/GpMfSBXIzefSrELHoSb7miqyHYBVyewI6chHDkYQwuFW2nfoNq3/q0mVS9ZGEvHk96Uf6T8y6Ujv4WQGDV19E6aDfDZ6UQUAZYeYxk4yPxqTH0gbyIEXwqxEV0Jd5yRM15h2qwaFf8kuzli4kY2idOr7grXncrbNOIcutAr6GCdi0/K3oJ6CkDrDxGsvGR+NQY+kDOYhSfCrEYM4i3dP7WhChpuoc7awq1K56zzno6Zfli2X74OCDL6cv2KmPEoF2Lz8qZoRCefLUDQ6OD4BJTsCKBBKx4xVqG2uo63LG7VdVRVJQBVhYj2fhIfGoMfSCN5VMhlqPFsGqlMWIWvlC74nMt26uJUYN2NT8rZ4ZCePjZ1xCd6kaVZRIb7H1wcxGERCfOxRrR0z2BHwVC+PTNV6gW0JuhWqJnjGTjI/GpA4r9A2kknwphfs4MhfD4wSNoEl7FrtK34bZEwLEsvC4eSbYb+0fqdZmFL8Su+HzL9mpBQfvKJEQJPznwFiL+83iX93Xc4juOCn5m/vsTQgme8W/Hfr+Inxxw4f/5yJWq/Y3MUC3RK0aqCJD41AnF/IE0kk+FMDcJUcLPDpxAZeAAdpUehic2DSubREKyoDdQCs7mwq3VM8Co/rLweW8pKlTZXiVMFbRnO51gFU72TaFnoA/v9b6JP685BJaRF32/gp/Bn9ccQlJi8cRgGU72bcLOdb40r1Z4zFgtyZdCeHONVBEg8akjivUDaSSfCmFunj02hJHBTny0+hC2ecZg5y72ncfEafSHXegZTmB3uQ0do+t1lYXPd0tRocr2amKGoF0Jm8MLHWMoZ0ZwW+Wby4Tn/M9lZNxW+SZeDG7GCx1jqopPYjEr2Xz2eerR2lSHiCCuKkqNVBEg8UlojpF8KoR5SYgSfn/0bWzlT6PdN4yl8svOiVjvDuF8CJgOWdHI6SsLn++WoozK9rKEaWEaZ4I9aP7TA+Au2ZNXhq4QGDloV8rmMOCfwQZb76JSeyoq+BlssPWh1x9e8XGEcqzUbNs1eRa/frsCvzizCTsrQlhfGljVe26UigCJT6LgZFs+MJJPhTAvHYNBCOEJNJYElgnPORgADa4wTobCsMrTiOsoC5/vlqLVyvZMdBLieAeisRB6hBjeHHkTQ+EhXTUiGQoFbQ4MI8PJrmxjmsPBxsAwmWXMicKyUrNtMCwgODmOD3jfxBrLGAalTXhfUz+srLzqBBgjVARIfBIFJZcuYSP5VIoBvcwFVJvOoRAqLAFE5ZUbduyciBJ2GiPTPOr0lIXPc0vRSmV7JjoJYegYhsQIxnkXLpeAs+4aHKxcr6tGJCOhpM2hrrwU4+NliIncIuvIUmIih4lkGerKS3P6HYj8SNdsK0kyescD8GIc6z0h+Bxv4nuDa3E64MH28kBGE2D0XhEg8UnkzZxYeaFjDK93vo013ADuaOjH1dXjsLKzfqOVIjUj+VS0Qi1BqNSIISMI2rggYF1JCD3hekwIJSuWLMOiDV3xBtygsyx8PluK0pbtZQnieAeGxAgGbW74ZBEbGSuOO2dvanprRDIKhZhOkI5rW6vww9PrcSJQldJCAgAygBOBKvSI63Hv5ursfwEib9I12wYiAsR4GA3uMBjM2iOarIM4HajD9vIAAONPgCHxSeTFnFiJBPpgmz6Nd7JDsFtZPN9Xj1dH1+O960bR4gmtGqkZxaeiBWrNnFRq0L9RZmbaeB4lvIxEksez/u24K0WXMABIMoMDgUshOtboMguf65aidGV7JuJHNBbCOO8CAxk3xeNg7OXodV682emtEckI5D2dYAUubSxDVe0G/HHicngsB9BUEl7SPMehd8aFPwYvR1XtBmxt8GZ7+EQBSNdsGwgLKGWnF71nHksYM+Li88XIE2BIfBI5s1CsXFHdhWmuG5e6h2DnREwIJXjWvx17z7bgoxuAFm9o1UjNCD4VtVFr85NSg/613lyVTcZ1znv8ntrX8UxvC34+AtycYj7i78cvw8vRy/GRd2zS7zmZy674NGV7JuJHQBZRCuCmWBSXW5w4VLkR4hLhlEuGrpjJdzrBSlg5Fh/bsw0/fiaM3wQsaBfeQj0/Cp5NQpAsGBCqcSSyFSOl1+BTe7bp9zw2OemabUVJAs8mF30tmHTByS0/X4w6AYbEJ5ETS8VKz9j0okitgp/BXTWH8PMR4ImeVty3bRpWVl41UtO7T0VN1Nz8pMSgf603V2WbcZ3zHr89cx4f3jCKJ3ta8b3BZjRZB+GxhBFMutCbqMOgUIG19Zfgpu21BTtWvZCqbD89PQZBSKAGIhh7OQ5VbsSA05vy+dlm6IqZfKcTrMbGNW588ubdePI1L54cuxRV8S6UsGHMSC6MMc0or12LT12p3npNYjnpmm05lkVCuijPJoQS9Cbq8AFvcNlrGHUCDIlPIieWipVUkRrLyLjZdxzfG2yeN0oDxo3U1EbNzU9KDPrXcnNVLhnXhd5jTB7FJzb2YTRmx+lAHWZEFpLEwiXYUe1rxkf2bDVttmhp2Z55+3mcHj2BP1RvQq+zbFnGcyHZZugKSoEHtStNvtMJMmFTrRtfvL0dHYMbL2T/E/DwVtxQxNUkPZGu2dbr4tEbKEVMnAbPSnjWvx1Omw2bl4hPI0+AIfFJ5MRSsbI0UpsjlVHaqJGa2qi5+UmJQf9aba7KJ+O6rqoE2zdtwjNHgYOjw2i29aPGKSDBlqJPaoLD14CP6MSjqigLyvZczTbYn/sHTPCulYVnjhm6QmCEffTLyHM6QaZQNUm/pGu29Tp5DNhcOBGowhmhGZ1CCz66cWS+gRcw/gQYEp9ETiwVKwsjtaWjPRYapY0cqamNmpuflBj0r9XmqlwzrgvL9Fc4ezFjYdA9U4VjkTLYXD7ccfkluHFbbdFli9TI0OWDUfbRpyKf6QSEOUjXbDsa2YDD42XgOQmf3tSDFk9o/jlmmABD4pPIiaViZS5S6w+7sN4dWjTaY84obfRITW1SCcKExOBUwIuOgBtxkYGNk9HqDWEy4YAzj2yyEoP+tdpclUvG1WbhVijTz17o3+xMYn21W5HGKF2jUoYuJwy2jz4VGU8nMJitgMicVM22Ht6KO7Zz6OgZxFN+H04GzTUBhsQnkRNLxQrLMmiq8qJrKIHzodktMHNd772JOtzgjGJvd7OhIzW1Wfo37gy48URPNSJxAWv5Abi5CEKiE78cbcTZeC0+upnL6vUXdoJHYnH0xSvwyLn1+HzLKUTjcQTCAkRJAsey8Lp4uB18VsGDVpurss24TsYETRujjIBeM3RG3EefklWmE2hmKyDBqxrp7BE3ba+d9+yaaQIMiU+do9fh3KmM0h4nj+Y1legdt+JkKAwnM40/Tu1Eb7wK+ybL4PIaO1JTm4V/48vKJ/DLc9Vo5Ttxc93F8T8ygCP+NfjvmavwZmclNtRklplb2glebominefxyqgXnxrZhlvLX8dudzd4NomEZMHxidnRLEPOHfjUtZkFD1ptrso24zoVSWrWGGUkcp0fqiRKDmrXC1rZCgzpozUhZvXskvjUMXoezp3OKO1x8djqqETXVBX+MFCL13EZLr10E65trdJcMBuNub/xLw6E8PzJLlxXcnTR4POYyKE/7AJjdeLTmwfx9OjRjDJz6TrBg2EBG+VpvDZZjycm2jGQqMIG5wiCSRfOxxswliyHw8FCXj53fcXjV3tzVbYZVxegSWOUIcllfqiCKDmoXRdoZCswso+WMAYkPnWK1sO5M2HVrUSVDfhbynTmxcY1bly2qQVPDfWjnh/DmZBnflD0jFQKzuZCc5UXHiefUWYuXSf43C7hjfYh3LixA48MRvFqZCeq7F44LRI+4p1Ci6cHv+6dwlOHPRmXnrXYXJVtxrXMycE9rX5jFJE/Sg5q1wOa2ApM4KMl9A+JzxxQuhSu9XDubKCtRMoTTYh4R80kttd6EQg7IVzwYTa5eHidPNgLJ0gmmbl0neALdwlbWQkfrH4DfYNNaKsIzo/IAnIrPat9jmSbcT3WO6VJYxSRP0oPatcaLWwFpvHRErqGxGeWqFEK13I4dy7C2qyeFL0QFwR4rDGUl9hQXmJb8bGrZebSdYIv3SWcaj4rkHvpWe1zJJuMaywhatIYReSP3sdA5YsWtoJi8NES2kPicwGrCa8zQyH88uBheKKn0cTHYIEIUWbQ5hvDe+y9eG6ktiClcK2Gc+vZY1rMFHJkUbpO8FQbqhbOZ138dWOUnjPNuGrVGEUUAD2PgSoAWtgKTO+jJXQBic8LrCa8bmnfiMcOnkZgpAsWfgaVyQGUXBh189vxejhtFbhj7SgwmVnTx0poMZzbCB7TYqWQI4vSCdlUG6rm5rMuxUil50wyrlo1RhGFQa9joAqBFrYCs/toCX1A4hOZCa8HnxzD8GQIH6k4itsq35wfdQMAE0IJnvVvxy/OteDmpil0+PMrhas9nNtIHtNipJCZuXRCdumGqrn5rB8w0S7hldCiMYooHJqMgVJhBqYWtgK1Ba9exwkSylL04jMT4fXhprfx9vAUInI17qo5BNuS9ZEV/AzuqjmEn48ALwy1ot6ZuhSe6YdM7eHcWnpMidUpZGYunZBduKGquXQaz/q3w2mzYfMC8Wn20jM1zxkcFcdAqTYDUwNbgZqCl6xexUvRi89MhFcoKqDN+RYCggUdkTrsKO1b9hiWkXGz7zi+N9gMq8UBbkkpPJsPmdoeNK08pkTmFCozl07Izm2oeqPXgt93V2OIacYnWoZhZWeHehZL6Zma54jVUHsGpuq2gkwEb2AA1zM2uJyVSL76UE5ZX7J6FTdFLz4zEV6BsIBG2xgusQ3i9Exq8Qlc7BB+Y2YnrlhQCs/2Q6a2B00LjymRPYXKzK0kZDvi9RiQnKhyCHhpDDgx6aXSM0HModEMTLVtBSsJ3s1iEpVCBEHehT/0HMgp60tWL6LoxWcmwkuUJDgsElxsFNNJ74qPdbJRTCTL0HIhUsv1Q6amB01tjymRO4XKzKUTsh+pdWNDTSnOjUxT6ZkglpDVDMyJs1h7fC8YMVEYT6jK26VSCV5LLIhQ3yvYZ7HgsLch56wvWb2IohefmQgvjmUhMlZMy24wSRYygFSfFxlAb6QMNpdvvhSez4dMLQ+a2h5TQh+sJGSp9EwQy8l0BqYnEUVy4ix6//Q9nHaVG3cv+kLBKyYQf/o+/BECnq9Yn1fWl6xeRNGLz0yEl9fF4/hENfqltWhzncf5kBsNrvD8QG5gds/2iUAVTgmteO+1l8wLw3w/ZGp40PQ255C6HwmC0CMLZ2BysoSm8CQaowFYxASSnBV9Di9EhsUVI2/h+eQMetyVCFZtmH++kfeiF3LzEVm9iKIXn5kIL7eDx5HIVvilCuxZex7Dk7U4GQqjhJ2e37MdEkvx3MzlqKlvwY3bauefa4QPmZ7mHFL3I0EUABXGABUjczMwGyJTaB8/BykWwjk5gQADeGVgOyxoTsbxFAscsFhQvyRDauS96IXcfERWL6LoxWemwmvIuQMOB4s/TkzhXTUDsEjTCIQFCJKEUNKJ16cvQbDsSnxsz7ZF4swoHzI9zDmk7keCyB/VxgAVIWLNNux48ydwDx7HISmGfTYb/Cw///13xqP4YDSMk5yMct4J2elb9hpG3YteyM1HZPUiil58ApkJr09d2wJZBp467MH3e1M8xtuAD6cQZ0b6kGk555C6Hwmzo4adRO0xQMWGWL0FbiGMjvgU9paUQ15yoaqVJLzMAj2SgPUiD9mR2i5lxL3ohdx8pDerF6E+JD4vkKnwylacGe1DptWcQ+p+JMyMYnaSheX1WAiJs8/goBDE87WXQma5RQ81cslXL3CjpzDOO9FpK0WtMI1x3gVhwd/ZKYmYkJMIcFZEOQtKolOQXZUpX8toe9ELuflIT1YvQhtIfC4g0z3Q2Ygz+pBlBnU/EmZFKTvJ0vK6TYjAG+jFQQsHcSAMrrIVsqN80XOMWvLVC9zICXRwFsTqd6JhvAMVsRACsggBAA+gXEyCZaxIusoQSMRRGvGnFZ9G24te6M1HG9e4cec1O/DmC/149Xg/KpgJ2CwM+i2NOGq5AjbvOporbGJIfKqAHvyUescIjVkEkS1K2UlSldevGz+PTosVr9rtqIxNoXboGPjaHcsEqBFLvnphzvcoO8rBNuxGScQ/KzClJBjWglHGgkv93fCxFgiIQ5aSKV+nUHvRVaXAqz7ZkZNofvNhOIVzeJ0L4+2EhNKEiFbOj7srwqi8/K/AFvE90eyQ+FSJQvopzTiKyCiNWQSRDYrYSdJs2bGIs13XAsth0OYG4iE0jHeAbdgNLGkUMVrJVy8s8j0yLGRX5XxmUwbQI0vYHp7ETbFJHJJlMKwF8pLXKNRedC0o1KrPZcFTxUUR25mIoT34Nva8+M/kTTYxJD5VpBB+SiW8Y3oQs0ZqzCKITFHCTpJu3mKSs8I7p3QYYJx3oSIWQkmK0q/RSr56YTXfo8iwOFy5Ee8cPIb6eBwn+RIEF3w/2+ygHsl71adGK0oJfUHi00Ao4R3Teq7mnPA9NRBEf9SNx8748OfN3Sh38WCXpIr01JhFEJmghJ0k3bzFPocX2xgrfJIIP8tBYDkEZHGZ79AQJV+dzinNxPc46PAg7vLhDr4UuxMiOsbO5ZQdTH0AOvm75LHqs5DD6gnjQuLTICjhHdN6ruZS4bvLIeP1sRpE35rBVRWD2F5ng8fJXzgeaswijIcSdpJ08xZ7XeXYYXfjptgk9todkBkGArDId2iEkq+u55Rm6Hu8zLMOtmu+jEY5mVt2MAW6/rtkQSGH1RPGhcSnQSi0d0zruZrphG9nrRu/eLsWjw3W4rnxAJrLOQhcCTVmEYZECTtJunmLcyXfq4ZPALEI9tls4IF536ERSr5GmFOare8xl+zgUozwd8mUQg6rJ4wLiU+DUGjvmJZzNVcSvi3eEL522TTemvLgJ29fgv0z63HDjmbcXu8xdEMVUZwoMed3Jd/hgNOLV9Zcivbxc2iLBhBKiogLMZSOncu/5Ks0BvIC5u17zAYD/V0yoZDD6gnjQuLTIBTaO6blXM3VhK+VlXGZL4AG11t4oNuHLfUemulJGBIl5vyu5jvsd5ZhuGEX3j/8Fm7jPcDGm8HZ3MoIowLCDRzF0OAbeJ2TgLFTYFkLZKdvdkXlhUyZrryAefges/oxJvNIFnJYPWFcSHwahEJ7x7Scq0kD5YliouBzfjP0HW7zXgL5uq9Cqtmq+8wRO3ISeO7/wbGp8zhl5eaHtnunuuGwuxcNzC82L6DZPJKFHlZPGJOcxOeDDz6I73znOxgeHsaWLVvwwAMP4Jprrkn7+Mceewzf/va3ce7cOXg8Htx88834l3/5F/h8vpwPvNgotHdMy7maNFCeKDbynvObosu5rOU23NL7J+yc6sp53qIemPMzDoYGcMZiQa+jdP57w5KYcmB+MXkBTeeRLPCwesKYZC0+f/nLX+KLX/wiHnzwQVx99dX44Q9/iFtuuQWnT59GY2Pjssf/6U9/wsc//nH867/+K2677TYMDg7i3nvvxT333IPf/e53BfklioFCe8fUmquZaoboxEwSUoIGyhPFRa5zftN2OXN2VJc3o+myv8A6YUZZ36FSLPAzSqXVKJmcXvTtdAPzi8kLaDiPZAbjoAo1rJ4wLlmLz+9973u4++67cc899wAAHnjgAezbtw8PPfQQ7r///mWPf/XVV7F27Vp8/vOfBwCsW7cOn/nMZ/Dtb387z0MvLgrtHVOiEWIp6WaIjs3U4migFtu9E7iyyp/2+TRQnih2Vu1y9ndiT2RqvsvZaGJsoZ+xIj6DbVMX55TOs2RgfilfWlReQCN5JLMZB6Vq0xahO7ISn4Ig4PXXX8dXvvKVRV+/8cYbcejQoZTPueqqq/C1r30NTz/9NG655RaMjY3h17/+Nd797nen/TnxeBzx+EVhFQqFsjlM01JI75gSjRALWWmG6FikG4+e8uBHHQ1w8wls9i5/f2mgPFH0mKzLORUL/YxhC79sTukccwPz3eEJtEdDReUFNIpHMqdxUCo1bRH6IyvxOTExAVEUUV1dvejr1dXVGBkZSfmcq666Co899hg+/OEPIxaLIZlM4vbbb8e//du/pf05999/P77+9a9nc2hFQyF3xBe8EeICq80QrXIK+PTmQfzwZBLfPbkB/++uU6hxxua/TwPlCcJ8Xc6pWOhnTDWndGEG1CVJ2DM9jutqdhaXF9AIHskiCJSIwpJTwxGz5MSSZXnZ1+Y4ffo0Pv/5z+N//+//jZtuugnDw8P48pe/jHvvvRePPPJIyud89atfxZe+9KX5/w6FQmhoaMjlUE1JIXbEz1FIMTtHJjNEy1w87twYwNffsuLrnddiZ2lPQYQvQZgFs3U5p2Kpn3HhnNLLYiGclWMIMIBXBnaLwGZ3IywXOviLCb17JIshUCIKS1bis6KiAhzHLctyjo2NLcuGznH//ffj6quvxpe//GUAwLZt2+ByuXDNNdfgm9/8JtasWbPsOTabDTabLZtDI/KgkGIWyHyUUnO5jKtrpuAvvxK28l0FEb4EYRZM1+WcglR+xn5nGYYa29AUmUJjZAq1YgIWALWSDOuffR1ikQnPOfTskSyGQKmgZNCUZXayEp88z2PXrl3Yv38/3ve+981/ff/+/bjjjjtSPicSicBiWfxjOG62lCLLcrbHSxiAbEYpea1RMCVW3Hllk8JHRRDGwnBdzjmQzs8oMiy6XD50uXxgZBnX+7vgrtgMsW6XBgepI6GgU49kMQRKhSKbpiwzk3XZ/Utf+hI+9rGPoa2tDbt378aPfvQj9PX14d577wUwWzIfHBzET37yEwDAbbfdhk9/+tN46KGH5svuX/ziF3H55Zejtra2sL8NoQu0nCGqGnq6IRGmxEhdzjmjcz8jCYXMKIZAqRDk1JRlUrIWnx/+8Ifh9/vxjW98A8PDw9i6dSuefvppNDXNZq6Gh4fR19c3//hPfOITmJ6exr//+7/jvvvug9frxfXXX49//ud/LtxvQegKtWaIagXdkAg1MEqXc77o1c9IQiFziiJQyhdqyloEIxug9h0KheDxeNAXDMLtNpZQKUYSooTv//4o1sYOrDhDdG93M3rse/D529oM4+9c6Ya0MEtDNySiELAjbyF08P4MzjcTNOGICXDDx8Gl8DOqfhMWE0g+fR+eWUX4X+/vwi0Vm00vFFaF/l6rwvUfQd9z/4AfuitXFeifCY2j8c++YUhfbCgUQqPHg+Aqeo12uxMFR+kZoppBkSuhMnrNCiqCjvyM1L2dJTq3T+gBaspaDIlPQhGUmiGqJXRDyo1UK1ZbaKJBxui5y9mskFDInqIKlHKAmrIWQ+KTUAwlZohqCd2QsifditUnO5uw39uA2wwWgGiGjrKCxQAJhdygQCk91JS1GBKfhKIUeoaoltANKTtWWrE6EevBvqE6PH5wGh+6th2bDNZ0RpgbEgp5QIFSSqgpazHGSj0RhIbkckMqVpauWF069aDCHsdH13WhlTmKpw53IiFm9nclCDUQa7ahlbPDnYit+LhiEQpE/sxPrwgOgknT5z0/vcK33vTnFIlPIicSooQTfVN4/NVe/PTFc3j81V6c6JsytYjQ5Q1JTIDrPwL+yCPgXv7+7P/2HwHEhPI/ewXmV6zWpl+xyjKzzWjRYD86BoPqHiBBrAAJBaLgzDVlOapnlyYsuY+4EzFc7++ab8oye7Mqld2JrClWH5/e5i7qed5opitWK+xxNFl60TkUMpY1g5YMmBvq3iYUgJqyLkLik8iKovbx6eiGpPcB2NmsWPVYoggK2mZqsyGV6PdIIi57PYlK3gmmdhdY3yUkRtWmwAEBCQVCCagpaxYSn0TGLPXxLS2nzvn49nYDTx0uRbOBhsdnii5uSAaYN2rWFaupRH9DZArt4+dwOhrAUDIMZvwUyjz1aLWXa56BLhaUqgKQUCAUgZqySHwSmTPv42te3cf3QHc/OgY3GKuUmiFa35CMMG/UlCtWU4j+hsgUdg+fxOFkBPvsNvgZH+riITSIM3ixdIPmGehiQPEqAAkFgig45kpLEYqSi4/PtFy4IQntd0O8+vOz/1vfpkqGMdt5o9zwccWPaSmtdR44vA3YN1QHKc0CX0kG9g3VweFpQGudR90DzAFu6BhGF4h+TpbQPn4Oh5MR7LU74Gc5gAHGeReisRCmE2E872vGgegohCMPa94EZkqWBARLPxNzVQB6D4ic0WlTp9GhzCeRMWb28RkJI8wbNeOK1aWivyk8CTkaxADH4MOxCGyyhDjDosNixbSURGnED8lVSRuvFMQIVQDCuOi5qdPokPgkUpJqJeLETBJSwnw+PqNhlAHYZluxulT0bw8OoTwexDsZ4JwsYoQBvDJwG8OBk4HO2Az6QRuvlIS2jhFKofemTqND4pNYRrpRSmMztTgaqMV27wSurPKnfb6hfHwGxEibMsy0YnWh6G+ITKE20I//lgQ8wnMYX5B1q5RF3Ckk8Y7pMSAyhX5nGW28UggjVAEIA2KApk6jQ+KTWMRKo5TGIt149JQHP+pogJtPYLN3uafTaD4+I6K3eaOrYZYVq3Oi/09CBO3j5/CyLOC/WHmR8AQAP2T8kgVsENE+fg5DjW20glEhjFIFUBSaOVtwyM6hPMZJOxCKs9pKxCqngE9vHsRGWy++e3IDRiKLs24TMRv2djejQ27DbQbx8RkS2pShCXOi/6bxc5BjQTxtc8DNsLAtFD8y4BCTYK08nnWUQI6FsDk0onkG2qzocuuYirAjJ5F8+j70PfcPePrEY/jVmSfx9InH0PfcPyD59H1gR97S+hANiRGaOo0OZT6JeTIZpVTm4nHnxgC+/pYVX++8FjtLewzt4zMqupg3WmxcEP1XDLyBXydmMOTyoI7j0SDGcZ5jwEKGQ0zCyVrA2L3wcxzOyjFcM9mL6nXXmU746AGjVQEKCXkSlYPsHMpD4pOYJ9NRSs3lMq6umYK//ErYyncZ2sdnCFYoq9EAbHWRaraCX3cNuLcG0JqII8xwaJRl2BNx+FkWosUGxu4FLDbwkggmGcMGpxNWWsGoDHrZOqZ26Zs8iYpCdg7lIfFJzJPNKCWvNQqmxIo7r2xS+KiKiBQ3MIl3Itb7MgYnu9KO+qAB2OrC+tbDU7YOJa4ylEb8QDwEd3gCtVISAZaBkIiDT8ThZTistTjhbHk34pSBVgytqwBajOMhT6KyGKmp06iQ+CTmMetKRCOQ8gYmzGBjaBgJ1oL9ay5Fp69h/vFUVtOO2RuTAy/ypQi5KgEAjCyhJOJHacQPWUqCYS0o5UvQmhCR3HSLwgdEDSdabR3TqvRNI6aUpZjtHGpB4pOYx5QrEfVGCqEgW12Y6vwvHIiOX7yByRKk/lcwwwjYDhnt42cQtvDod852jFNZTTtS3pgYFrKrEvIFMQpZRpu/S/EbEw3BXoDaazA1LH2TJ1Fh9GLnMDEkPol5Wus82H9hJeJH13WlbDqiUUq5k0ooeCQRbYEBvIAkDjbsgnThAsdE/IjGQjhrL8UphoUci8yP7REv3HSorKYROrkxUcOJtmhZ+iZPovJobecwOyQ+iXnMuBJRL6QTCs0zE7BN9eAJxOAYPg6+dgdkRzmYiB8BWYTAcgCAfTYbLouF0BSZQpfLN/+6VFZTgAzK2JrfmKjhRHO0LH2TJ1EdtLJzFAMkPouUVOszWy50q5tpJaIuWEEoNEYD6ICItxxe1MVDaBjvANuwG7KUhLDgJfzs7NiexiXiE6CyWiHJpoyt5Y2JGk60R8vSN3kSVURtO0eRQOKzCEm3PvPJzibs9zbgtita8HmTrETUAysJBYuYQIABwADjvAsVsRBKIn4wrAX8ktcJMECtmFj2+lRWKww5lbE1ujFRw4n2aFr61on1gyByhcSnWuikI3Wl9ZkTsR7sG6rD4wen8aFr202xElEPrCQUkpwVXnn2/wssh4AsznZMO33wTnVjWLpYevfKQGLJuUJltQJhsDI2NZxoj9alb82tHwSRByQ+VUAvHalL12cubSiqsMfx0XVd2NsNPHW4FM23tVGWswCsJBT6HF5sY6zwSSL8LAcBgCwlITt9cNjdqIxNYdDmhk8WsZGx4rjzYjBAZbXCoUgZO5uAM8vglBpOtEcPpW/yJBJGhcSnwuipIzWT9ZksM9to9EB3PzoGN1DmswCsJBR6XeXYYXfjptgk9tod4AEwrAUyw4KrbEXt0DEwsSCulzkwjgr0XhCfVFYrLIUuY2cTcOYSnGqddSNQ+NJ3rtUx8iQSBoTEp5LorJSX6frMCnscTZZedA6FSHwWgJWEgsiwOFy5EVcNn4AlOoMeMBCdsw1FsqMcFVWtuGnoJHbLMro5G66e6KaymgIUsoydTcAJIKfgVA9ZN6JwpW+9VMcIQi1IfCqI3jpSs1mf6bFEERSWN7cQ2bOaUBhwevFqzVbcMfAGbGDRGZ5CKBK6eAPb8G441l6DOmGGymoKUbAydjYB5+EfAjJyC06p4UQ35Fv61lN1jCDUgsSnguitI5XWZ2pEBkJhQ3QK1XWXw7v5vWhOITIXNhpRWa3wFKqMnU3AefXQccQYGUcqL8kpONWs4UQnzZO6ItfSt86qY5pA51NRQuJTQfTWkbp0fWZCYnAq4EVHwI24yMDGyWj1hlBjj9L6zAKTqVBILhAKJDLVo1Bl7GwCzql4AD2Q8gpOC9ZwkqEAoPJwYdFbdUxt6HwqXkh8KojeOlIXrs+8rHwCT/ZUIxIXsJYfgJuLICQ68dvxegwKzSirWUPrMwsMdabqmAKVsbMJOOOyhBAyuz6sGJzm2XCSqQAoxvLwSss4CjEJRG/VMTUpxvOJuAiJTwXRW0fq3PrMHz0TxHP957HH/SZuq3sTFfwMACAmcjgRqMIfg5djRGhC1+gMNmWY/VT6Im0ajNCZWqRlsEKUsbMJOG0Mi0xrC0oFpxkLgGv+FsIb/1lU5eFMlnHku+lNb9Ux1SC7QdFD4lNB9NiRuq6qBA6bA43OQWx29GA8akEwXgJBsmBGKoXF4cJnGkfx9OgxPHW4LKNZn2pcpAl1KPYyWL7Z6WwCzjKbFw5GxgtaBadZCIBbX/w2RmNTRVMezmYZR6YBeir0Vh0rCBkEr8VuNyBIfCqLDjtSOwaDsCVG8YktQVikWgTCAgRJAseyaHLx8Dp5sCyT8axPtS7ShPJQGewCeWSnswk43bXb4ZaB9slOTYLTbARA2+AJjHA8QhVNK76mGcrDai7j0Ft1LF8yDV6L2W5AzELiU2H0tgJtbtZnlVMAYEN5iS3l4zKZ9Ukbk0wElcHyY0G2x2otwQ2xKJjB4zhctREh3jn/sEUB5+X3AoBmwWk2AuC0GEWNlJkMN3p5WM1lHHqsjuVKNsFr0doNiHlIfKqAnhpNCjnrkzYmmQcqg+VOqmxPA0RcE57Eju5XcaakHEG+NG3AOR+cTpxFZ8yP6UQUpVISmzkHqipaYH3nlxUJTrMRANOsBevEZEaPNUx5OA2qLuPQYXUsJ7IMXp3VW81nNyCygsSnWuik0aSQsz5pY5J5oDJYbqyU7fEKEdw4fg57ZAv42nawvvUpA06p5lLwOz+Jupe+jbLpUYyIEqIsjyGOhxSbQvXrPwbPFr46ko3fsNTqQA2ScJukPLwSai/j0Ft1LBeyDV7X1rWhlbObxm5AZA+JzyJj6azPdEzEbKvO+qSNSeaBymA5sEq2J8A78avabfD7u3CLMA1b1WZww8eB3kOLmjDY8U6EXvoXHIiO40j9tuWZL4W8ttn4DVvsPjjLytAeHDR8eXg1tFjGoafqWC5kHbwmYqaxGxC5QeKzyFg46zOVTxMAJBnYN1QHW2k9kqKEx1/tTTk+iTYmmQdTdt0qTKbZnkG+BOGz+zA2fAynLfziJoyyZnCxgCZe22z9huzOT2HPS98xdnk4AwoZoGeFTqpjuZB18JqMmcNuQOQMic8iY27W5+MHp7G3e9aPubhD3YZ9Q3V4JbITDimBp184mHZ8kmYXaaLgmK3rVg0yyfY0RKawbfwMnkwE8TZbiUDVhvnvvZiI4fKhI7hiehSDdTvU99pm6zc0QXk4E7IJ0B2eBlrGgdyCV6FIziciNSQ+i5CNa9z40LXteOpwKR7o7keTZVZcBpMO9CabELWsgYWZxg725RXHJ73vml1w0EXaFJip61YtVsv2cLKE9vFzOJyM4KDFgnUpspoHeBumxAg2T/XiXGklxDSvp5TXNltBaYTycL4LLzIN0DvkNtx5RQtN8EDuwasRzidCGUh8Fimbat1ovq0NHYMb0DkUQlBIwMZbcWt1CZ47dh7N3LFVxyc9e7QUt7RtxG9foot0Tuhpk5BZum5VZLVsT1N4ElIshH02G0riSTCsBfKSx0iyiOc4Dp+MhdAUmUKXy5f29ZTy2mYtAHRcHi7UwovVAnSHpwF30vKMeVYMXmUJTMQPNjyBy6fHscbdCIiJ2X+cVdfnE6EcJD6LGCvHYltj2aIO9BN9U4gHBzIen5SUNtBFOgf0uEmoWMqqhWK1bE9jNIBzcgLT4FDPcJCdy4Ulw1oQZlmclRNoXEV8Kuq1NYEAKPTCi3QB+u20Nng5aYJXJjoJcbwDfCSA7UkBG1k7jsaDqDvwj0WxMY1ID4lPYhG5jE+688omukhnwdx4noORYYxaXfBJDHhRwAxnxbMch+rxt3CdRpuEtC6D5VsyVZPVrAoWMYEAA1QKYTjsZSnFp+z0wTvVjRlZQq2YfhoEeW1XRqmFF6kCdEOiQpVlafDaGfNjMjgIWRRQa3VBKq3Ek5UbMeD0KjrFgTAGJD6JReQ6Psk0F2mluTCe581gNzxCBCXxXpyTZ0WKVwY2MFZwtlK8mYhht1abhDTKghWqZKoaq1gVrACaEjH0ODzgKlshp/Bzyk4fHHY36oJjSLKpL8fktV0dWniRHjWrLPPB6+DraPzvf8Bp2ww6S6vxhqscvc6yeU8zbUxTAD3ZuDKAxCexCBqfpCzc0DFMDB+HLezHISmGfTYb/Cw//32fJOKm+BSuSkQRGD6O6iIZ5l7okqlarGRV2CnKiFjdOFXViqCjPPULMCzKyppxZXgGA4nIsiHu5LXNjKJeeLGC6GDHOzNeeVmw7CNnBRgOfSyHxxrb0jYg0ca0wqFHG9dqkPgkFkHjk5SFG3oT4WA/DjEi9tody0q1fpbDXrsDiEVRHewHN/iG6S/KSpVM1SKtVaF6C+Jv/gxtk514vkROO0GgLR5BXdM7UOvwommyi7y2OVCsCy9WFB2FmCGbYzaNNqapx0pb1hQLMAoAiU9iETTjTlnkiXOYSsawr6RkxbmO+2w2XDczA9l/TuUjVB9TlEzTWBV4viSjCQLWa78CqXKT+l5bg5Xq0lGMFZvVREcmM2RZyBizOCB0vwT7vr8HW9myKGuaazaNNqapxCpb1vRsbyDxSSyCZtwpiyU6ifNIws9yKz7Oz3J4W05gd2QS5sjRpMfMJdNsJwio6bU1YqkuHUVXsclAdKw2Q7YhMoX28XOQYiE8nZiG5fwzKBl+Ha2nfoNaRzmmY0E8L0VzyqbRxjR1yHTLmh7tDSQ+iWXQjDvlSDjKkQQLXhIhrCBAeUlEguGQTNEhbTbMXjLVeoJAKpQq1WU7raBQ0w2KrWKTiehYaYZsQ2QKu4dP4nAygn02G3hY0ez0QK7agD8JEXys+xBOinG8uPZKSEtK55lk02hjmjoY2d5A4pNICc24Uwa2cgN8FjsqhTAGbW4g1X1Dnh3PU2Gxg6lYr/oxqk1RlEz1NEdToVJdttMKCjndoNgqNpmIjnQzZBdu3prznTddeLwMoFyIYAAynmRFlEx0gm3YDSzJmq6WTaONaepgZHsDiU8iLTQ+qfCIay7DZk8jWmYGgXgI47xrUQaUl0RUCmG0MHZs9tRDrN2p4dGqQ9GVTDVGiVJdttMKlJhuUEwVm0xER7oZsgs3b8kMA14S4V2wBKExGsBZOYmz9lK0xkIoifghuyqXvf6K2TTamKYKRrY3kPgkCBURa3eges0OXDWUQCQRQkV8GgFZhACAB+BlODhtXlxldaPqQlnW7BRbyVRrCl2qy3ZaQeOtOxWbblAsFZtMREe6GbJzm7f8LD9fZVm4BGFuOYLAcgjIIkrTiE9g5Wya7jemmaDZzsj2BhKf2WKCE5bQkPmMgB+IjOCody1KhRnI0uzu71K+BG1CDHucNUWTEcirZEqfx6wpdKku22kFzxyvUXS6QTFUbDISHWlmyM6Jy7kqSy3nXLQEIclZ4ZVnX0IAIEvJtMexWjZNj35nwDzNdka2N5D4zAKznLBaYqT1iUqxLCMgcwix1tlzKSmjunJL0Z1LuZRM6fOYG4Uu1WU7reC188241KTTDdQiU9GRaobsmkgAsUQMrQzgsJfNCs8FSxD6HF5sY6zwSSJ4XPSCLiXjbJqe/M4w7lzMlBjY3kDiM0NMdcJqhOHWJyqYVdNrRkBLsimZ0ucxdwpdqst2WkE8GoPbUbjpBkUZ0GYhOpbOkJXHOlH29n6cLK9D0F27bO1rr6scO+xuvDs6gRMMO1+O52QJTeFJNEYDsCYFXBILoq5yC8Sqzar+6nlh4LmY6dC9vSENJD4zwYQnrNoYbX2iKlk1nWUE9EBGJVP6POZFoUt1WU8rsNkLNt3AcAFtAcl5hqyYQNXTcbRNnMbzYJZlNUWGxZGKDbi9149GjsNRqwueBTNBuyQBkhiHheVROj2I6n1f0aW4SYWR52KuhBGTGSQ+M8CsJ6xaGG19ImXV9A19HvOkwKW6bKcVXLHZh9On8p9uYLSAVglyEh0ZvP8bo5NoqN6OZocHV/n7EJrqwgtSHIc4DuCscLiqcKqyFS9bnIa6Hhp5LuaqGCyZQeIzAzQ/YQ3eVGGo9YmUVdM9mn8eTUAhS3XZTiu4ZXstugfzm25gtIBWUXIQHRm//+XNKPvN3Xg15sdJhxulnBWy0zf7j2ERAla+Hurs3mXkuZhmg8RnBmh5wpqhqcJI6xOLNatmJN8c3UAKQ6FKddlOK3DwlrwHwhsqoNUpmbz/XP8RDMaDOFy/a9mmoznSXQ/1eO8y8lxMs0HiMwO0OmHNUv410vrEYsyqGc03RzeQAlKgUl220wryHQhvpIBW16zy/ud6PdTrvcvIczHNBonPDNDkhDVR+ddI6xOLLatmRN8c3UD0SbYD3vMZCG+kgNbI5HQ91PG9y8hzMc0Gic8M0OKENVP510jrE4spq2ZU31yqz6Mky5gKCwhEBEiSBI5hcFdiGJW12+gGoiLZDnjPdSC8kQJaI5PL9RB6vndl02y381NgdORXNRskPjNBg0GuZir/Gml9YjFl1Qzrm1vyefxvvhJvTcaQFMIoZadRjRiujkexnq3B45GrcPlYFBvX0M3CTCgd0BrJA60kuVwPueHjGd27whYeo5EJrH/1IQhrtqsm7jJptrKv24PYGz/GqI78qmaDxGeGqD3I1Uzl37zWJ6pMMZVljOybm/s87j74IMr7juEq2Q/WJsDHSGhlrKipdCO+ph5dwV489IfX0NzQCK+DLVoRYTaUDGiN5oFWkpyuh72HVr13NVyYG8pOj+IpYRrBUK864m5B9z3jXYdmmxfNAJLOMnA2N8Q12yEzHAIv/Yvu/Kpmg8RnFqg5yNVs5d98GwxUw8DryrLF6L65eOUW/NT2MeyqtOITJacgiwmwnBWypwyyuwy9IS8GpznIgZOIRl9BQyWHGbE4RYTZUCqg1Y0HWg8jii4cg81Ziesj02CmD+FIeROC7lrggrhMdT1c7d7VEJnC7uGTOJyM4BQno9RdBanyEgDKiru03fec/aLgrdyE5NP3aetX1cN7rwIkPrNFpUGuy8odsgQm4gcT8UOWkrP7dp0+lFpdqpZ/8ylH5dNgoCZGXVeWLUb3zXUMBhEODmPnJYBsXw8AmLvldQbc2HuuGq18Jz657i0Mx9xoqqpFeYlNt41URHasqyrB9k2b8MxR4OBoHZpt/ahxCkiwpegTsw9o9eKB1sOIoqXHwHEcLo1EsHngGLq4U5h2r0GpxZF6k9IKpXpOltA+fg6HkxH8hufRkpDn13cCyom7TLvvva3v0dSvqof3Xi1IfKpFltHMwnLHAacXyYlORGMhBGQRAgAeQNlkF/bAgpqGq1URn4UoR+XaYKA2RlxXli1GagRLRTrbQEJi8ETPrPC8q+YQWEbGtMAgEBZQXmLTbSMVkTkLr0VXOHsxY2HQPVOFY5Ey2Fw+3HH5JbhxW21W76sePNB6GFGU7hg4eQs2h0Zw9WQvNiRlONfvQXLTLcuuhyuV6pvCk5BiIezjbahIhOGwly0Sn4AC4i6L7vv3vv4oOmRBk14LPbz3akLiUwVyimYulH+v3/cViD2v4klWxFlbCexSEiVJAaWSiHckBexgrEhEpmAd71T0hNRNOUpNDLauLFuM1AiWinS2gVMBLyJxATfXHQfLzG6u5tkkBOliKVCXjVRERqx8LZott7/ZmcT6andW1yLNPdB6GFG0wjGIDIuTnlq85V6D6/1duCUyDsua7cuPYQXrUmM0gC5JgD0hoZZzgqtshZzCH1pIcZfN5Jg9/W9i2pZZNaigvRZ6eO9VhsSnwuQTzUiVm+C0e3EpZ0ONlMBQyI+gnAQvy2gGh1KWg99qQcLfieYX/hnMB/9TkRNSL+UoorAYqREsFelsAx0BN9byA6jgZ+a/JkgWcOzi49djIxWxMkpei7T2QOthvF6hjiGddenS4DCOiAk0uCpmhaejPO2xFErcZTM5ZhQy3PGZFR83R8a9FhlUPfXw3qsNiU8lyTOa4YaOoS86iedqtuDqkVOo5HgEOQdGWQ4HLFZ0cFbUJaJ4TywE3/n9qPn9F5DY9cmCG5P1UI4ilMEwjWApSGcbiIsM3Fxk/r9jIocZqRRNLn7Za+ixkYpIj5LXIq090HoYr1fIY0hlXeKHj6Nn/CTYuu0pM54LKVQjbTaTY4Z4F1qFMF4o0Ki9TKueenjv1YbEp4LkG81wIyfQmYyiZSaA/Uhib6l3/nVKkgLqwxNgkwKOyxJaRIA98TgsfYfgrGwF+86/g1S3oyC/h+blKEJR9NIIlm0zWzrbgI2TERKdAAAZQH/YBc7mgte5XHzqsZGKSI+S1yI1PNArneOcDsbrFXzE3xLrktB/BC3P/QNeSK7sqyzkHOVsJscIVgdqeDfag4N5j9rLpuppptGKmULiU0HyjWZEIQw+EYUYC2GfzbZIeFZHJuERk7hGZmCTGbzMJHFKjoKPjGBrzxg2jpxE6Y3/iOSW9+X9e2hdjiKUR+tGsFya2dLZBlq9Ifx2vB4DUQ+iCRkBVKK5ygt2SapMr41URHqUvBYp7YFe7Rz/VCmn+Xg9pUf8aTFHOZtB+S0WB2yX/QX2dDyZ36i9LKuezqqtmr/3akPiU0HyjWY43oVaIYzn5QT87GzWhpGBymgQHjGJP5OA40jid4yISUjYxlhgt3D4Ge/CR8JjeP/+/wWPdy2kusvy+j20LkcR5iafZrZUtoESLoreeBUeHboGN9ecR3O1F54lWU89N1IR6VHyWqSkBzqTc/z3k6XYnbTAreF2NcU3vGkwRzlbwZvY+n64qzfnNWov26rn2to2tHL2otisNweJTwXJKYpcYE6WxjqxLj4Dr5SARZaRZBiUJmNgkwKukRkcRxI/YkTIkGEDEGcYOGUJfo7D/3V54ApP4H0vfhvcnT/JywNq9JE8hH4pRAPJUtvAjJDA1jIRfQP1eEvyoZ4dAmCcRioiPYW4Fq1U+lbCA53pOf6LriZMz5SjLTCAAxWXaLJdTfHMpJgAk4jCV7kJt3YNo23wBE5bLAjaSuGWocwc5RwEb76j9rKueoqxotmsNweJTwXJNoqU+RIkn75vgTkZ8IgRrBei+J+yjCedJZhOClgjS7DJDH7HiJABWGQZDMuCZ1hIFzKtcc6CfRyDqyc6UZ+nOdnoI3kI/VKoBpJUtoEzQ2vw1OFywzVSKYYJNqfkey3KxN5RaA90puf4jXUj+OXMlbiZeRmMVtvVFMxMLm2+mWaBRo7H7oQAlwXgm1PPDS0EOS0OyWPUXtZVz0SsaDbrzUHiU0GyiSJrnTWY6ngCB6Lji048hmPB9r2G2sQMPhIW8TzLYp3M4DxEjEGGRZZhYRjYWR5emYHfYpt/7TGWxWkxiqY8xafRR/IQ+kXJBhK9NFLpAbNsTsnnWpStvaNQHuhsznHeKaGj8tO4Jf6UZtvVlNjwtlLzzbywGu+Ee8t7FV1XmW6fux7WYwtFsllvDhKfSpJpFGmvhATgQHR8mUiVy9YhGejFy9MjYJIx3AoWQ5KEIUaCDbMZT4bj0SAB4HhMLxCfPIBp1lKQzji1R/Lks8aTMA5KN7Np3UilB8y2OSWXa5GWs4qzPceH7c2w3KDtdrWCbnjTcIB6RvvcFRBzuXpni2Gz3hwkPhUmkyjS3ngVet/8SWpzMsOCXbMDa+Q38VYsiCtEGfUMMC4zYK1W2MCiQZJQxVow4vBAvvB0XhLhZTiUWp0F64xTK5NUiDWehDGgZjaFyePGr+cAMNtrkZazinM6x/WwXa1Ax6DVAHUtg668vLN6eO9VgMSnCqwWzbBv/GRFc7LsKAdfexm48Q4Eg+PYybAokWI4IkqQGBngbBhxeBC2XOjolYFKIYxq3o0We3lBzclKZ5JWK409O1iLh5+eRGP9WngdnK5uiET2UDObsuR64zdCAJjNtUjLWcXFfo5rMkBd63WVGnT1Gw0Sn2qxQjSTiTlZdpSDbdiNOHcCTbZKlI+ewHuT03jUUYpJ3rUo41kphFHHOnAF70V1xUbDdMatVhqzitPYyr6GgRk/Tp3chJvqRxEW9XVDJLKDmtkU4oLPjX/tP9AZ6MaMFAbj9EF2+oBVdmmfZjfmPPpKr2g5q9hQ57gCTWlaDFDXw7pKJbyzZoLEpw7I2JzMsCi1uiBvfR+cl9+NW/f/L3DRCexLJjDGsuABeBkO1bwbV/Be7PE0GyqqWqk0FgwL6Boehxfj+ETtMB4cKcNmbwjby/sMe0MkqJlNCRb63GJTPXg75kd/MgTvVDccdnfandohhkUiPqOZN1JJtLR3GOUcV6opTenB9Sl/pk7WVRaThzNbSHzqgFzMyWJ9GzzetXjfi9/G1ROdOC1GMc1aUGp1osVejuqKjYaLqtKVxiRJRu94AF6MY707BAZAk3UQpwN12F4eMOwN0QwUwhdo5P3yemOpz22nFAeTnEGvw4VhSURlbAq1Q8fA1+5YJkDdsoTRCKuZN1JJtC596/0cV9Ifqfjg+lQ/U0/rKovEw5ktJD51QK7mZKnuMnB3/gT1w8dnxykZPKpaWBpLSAxOBbzoCLgxGRERni7FDb44ktIMrKwEjyWMGfHixcWIN0SjU0hfII1FKgApfG59Di+2MVb4JBF+lsOgzQ3EQ2gY7wDbsHu+BD934z8lrcVa6zlNvJFKoofSt27PcYX9kVqs1NQi20pkB4lPPZCPOdlEUdVcaawz4MYTPdWIxAWs5QfgEafByBx+P7oVz/k34/01byCYdMHJLb64GO2GaGTyWYmZDhqLlB+pfG69rnLssLtxU2wSe+0OyAyDcd6FilgIJRE/ZFflohv/Qft6uC0nMvp5hfZGKsHCzDxjceCp8R0YCDvwF5e8jRpnbP5xapW+9XiOK+6P1GKlpgbZViI7SHzqBDInz5bGfnJsLc5PAjvsp3Fz3XFU8DMIRgSwyRDicOLZqcvx44GrMM2U4561o8tewwg3RKOj5cxEIj2pfG4iw+Jw5UZcNXwCiEWwz2aDn+UQkEWURvwo5UsX3fitPU7TjL5amplfb4mitITHUX8F/urwbuwq92N9aUA3pW+tUMMfqfb9TYtsK5EdJD51RLGbkzfUlGI8xmMj24WP1hwCx8gAAIZhIMksKvkQ7qp8DmODbnTF1mKD+9yy19D7DdEMaDkzkUhPOp/bgNOLV9Zcivbxc7gsFsJZOQY5mcAloVG0sK5FN/4WYcoUY4FWysyPRfrwRE8NDoW3Qa65Fg0VpdqXvjVELX+kqvc3GnWke0h86g0TldGz5dzINOqdYVxqG0XXdCkaXGHYORG8hcNM3IqwCAzFy7CtpAd92IRzITe2lwfmn6/3G6JZ0HJmIpGelXxu/c4yDDW2oSkyhcbIFLYFh7GlfjeEKz+76MavB29kvqyWma9yCrintQ+ubgt6ktV4X/vmohSdc6jqj1Tx/kbVRH1D4pPQDZ1DIbS6BrGztgS947U4GQqjhJ2GlUkiGC9FOGJFqQ1o803gbbF3vtsd0P8NcSl63h6zGlrOTCTSs5rPTWRYdLl8mOBdaGdts8JzSfnUKGOBVoIy89lhZn9ksVcT9QyJT0I3zIkaj4vHVkclAhEPAmEBCUmCxSaDmZmByzoBOycu6nY3wg1xIUbYHrMStBJTnxTK56b3sUCrQZn57DCNP3KFAfnFWk3UMyQ+Cd2wUNSwLIPyEhvKS2zz3w+Gnegd53EyFMbZmQpMxr14+NwmQ9wQ51CiS1xttJ6ZSKShgD433Y4FygDKzGeJCfyRSg3IJ5SDxCehG1YTNXMZ0a6pKvRMXYb6hm2wVbkNcUMEzNMlbgZfoFkppM9Nj2OBMoEy89ljZH+kkgPyCeUg8UnohkxEDRgGrwWb0dS4AZ9/9xZdirN0mMWLZgZfoK7Jc7+2Hn1uanqc1c7M69K/ncM5pMfzZlUUHpBPKAeJT0I3mFXUzN2cHnu5B0IwgP1DNWj1hrDFG4CVlZc93gheNKP7AvVKTuXDVbxugLY+t5U8zvvc9WhdW4eIIKYUbrkIOzUz83r0b+dVgjbYtBXFB+QTisHIsrz87qczQqEQPB4P+oJBuN10MzM78xf0YGpRo/eGnIUsvDk5o50oE/tgs3LoEerhtPF477pRtHhCy573eHcjgms+jI+9c70GR505i8XBrC9Q86yPQVmpfLjQd7ewfDgnNEZTlUp14HVb5HFeEky+MlaB/3umCYLI4vLKKVQ7BYSSDvQkmuDwNuDS5nqc7BqYF3buC8Ju7vsrXQfODofw+MHUP3dREHtde87XkpV+t4U/Q03/di7nkJHhjzyCp088hqeqNqz62PeMncOt2/4cQvvdKhxZ8RIKhdDo8SC4il6jzCehO4zc7LCQpc1FoeAEpFA3WjwBTAgleNa/HXvPtuCjG4AW72IBahQvmlF9gbojVflQlsBE/GAifkxLSRxkODBT53Hzaz+E5T3/Cna8U9det5U8zp0BN57tLcOfuQ9jE98Fi8ODrY2VYFkGE7Ee/H9vX4KfPFuNm2vexnubR7NuzFM6M69L/3YRlqDVGpBPFB4Sn4QuMbqoSXVzYpM8egOliInTqOBncFfNIfx8BHiipxX3bZueL8FTl3jxsbR8yEQnIY53IBoLISCLEADwAA7KDHacm8TaE48jNvCaroVGOo9zQmLwRE81WvlO3FVzCILE4mTIgkDEg/ISGzy8ACGRwDvtf0KbbRDlfCWAiy+QqbBTMojVo3+7GEvQqg7IJwqKMVJIBGEw5m9OtRdvTl4nD87mQn/YBRkAy8i42XcckXgcpwOzvrNi7hJPiBJO9E3h8Vd78dMXz+HxV3txom8KCTGzm4uRWbhfm4lOQhg6hv7YFDp4O3odbgw73Oh1uPGq3YlDQhDii9/F6PCxjITGqP88uOHjKv9G6edtngp4EYkLuNl3HCwjw86JKGGnEQgL89+PxgXcueYoZCGMQERY9tpzwi4a7EfHYDDtMcwFsXde2YSPvXM97ryyCdsay/LOQuYyS1Rpst3RrsU5UWjEmm1o5exwJ2IrPs6IA/LNDmU+CUIBUt2cWJZBU5UXXUMJnA8BDa4wKvgZNFkHcTpQhzpn1HANVYXq9NVj44aazJcPZQnieAeGxAgGbe6FCT8AgMBy6OXt8Mf8OC1MIlSzacXXnRMa6zTIcqWbt9kRcGMtP4AKfmb+azybhCBJi75f7whiWmAQCAuL5v3OoWVjnh5niRZjCdo0A/KLkJzE54MPPojvfOc7GB4expYtW/DAAw/gmmuuSfv4eDyOb3zjG/jZz36GkZER1NfX42tf+xo+9alP5XzgBKEH0omvSCyO8hQ3J4+TR/OaSvSOW+fXhwrJJI6MVuNUfJOhusQLJRjNMHg/X+bKh0zEj2gshHHetUx4zuGVgUmrA/54AEzED9lVueJrayU00s3bjIsM3Fxk0dcEyQKOZZd9f6EoTYVWQ+L1OEu0KEvQJhiQX6xkLT5/+ctf4otf/CIefPBBXH311fjhD3+IW265BadPn0ZjY2PK59x5550YHR3FI488gvXr12NsbAzJZDLvgycILVlJfPXFK9DO8ymft3R96FSoCTbfTtx+9VrDNFQVSjDqsnFDA+b2a/9pegQDsgiB5VI+zieJ2MhYMeLwwBKfzEh8aiU00s3btHEyQqJz/r9jIocZqRRNLn7Z9xeK0lRo1Zinxy1fZt7RvhJGHpBfzGQtPr/3ve/h7rvvxj333AMAeOCBB7Bv3z489NBDuP/++5c9/tlnn8ULL7yArq4ulJeXAwDWrl2b31EThMasJr4eObceh8fL0DXJoLl8+TSzufWhksWNyOQm/PnVaw3TXFVIwajHxg0tmCsftr29H8fSTL9jZBk3xeNg7OU47q3D1YF+nEzEkN7xqK3QSDdvs9Ubwm/H6zEhlMDHz6A/7AJnc8Hr5Bd9fyDqWSRKl6JlY54et3wVcwnakAPycyXPJRR6IasUgiAIeP3113HjjTcu+vqNN96IQ4cOpXzOk08+iba2Nnz7299GXV0dNm7ciL/9279FNJqZX4Yg9MZS8bU081Fhj+OLm0+D5yT8+u0KJMXUYsKozUWpmqmWkmlDiB4bNzThQvnwels5PpBMwictzlP6JBEfjUVxucWJw5Ub0eXyocxiR3s8DGYFsdoeHES1b70mQmNuaUSH3Ia93c2YiM36Nrd4A3DaePx+/DKcDboRQCWaqrxgL5xMW7wBOGw8Hh9uA8NfFKUL0fqzk+53m2MiZsPe7mZ0yG24TS3/9lwJ2lGN6/1dy5pw3IkYrvd3zZegjSRUMuLCgHyh/W6IV39+9n/r21L/nmICXP8R8EceAffy92f/t/8IIKpv4cgGduQkkk/fh77n/gFPn3gMvzrzJJ4+8Rj6nvsHJJ++D+zIW1ofYsZklfmcmJiAKIqorq5e9PXq6mqMjIykfE5XVxf+9Kc/wW6343e/+x0mJibwuc99DpOTk/jxj3+c8jnxeBzx+MWbUShk0hsOYUgyydbZOBmf3tSDfznVih+fceD9y2YVGnNbE5CbYEyXrVSycUOXaw9XQKrZCs/uv8Ht//2/sC6WQAdiCDCzHs+NjBWMvRyHKjdiwOmFOxGDy9OAPbwLso69bunmbUqsA//lvwbDySp8cP0EPM6LAjoo8LBZLXgx8A644m+jXtDnZ0ePW76oBL06eW2A0hCz7bDPqeGIWZLOl2V52dfmkCQJDMPgscceg8czG6F+73vfwwc/+EH84Ac/gMOx3LR9//334+tf/3ouh0YQipOp+Lqyyo/LRkJ4VbgSfd0BXdycFpKrOCukYFSqccOo3fOJSz8AV9+fwA4dRZXViVopiQRnxXFnGXqdZRAZdj6j6V2zHfzOT+KWN/5T10Ij1bzN+iYrNvAcOns34scjA2iaWPLZKGvAx3fV42RX8zJh15NoRNRSjTWVVXjt3CiO9U5pFlTocSFGUZWgs8SwAs6ECwSyEp8VFRXgOG5ZlnNsbGxZNnSONWvWoK6ubl54AkBraytkWcbAwAA2bFi+FuurX/0qvvSlL83/dygUQkNDQzaHShCKkY342lAagK+6ETubd+rm5gTkJ84KKRiVaNwwdPc8ZwV/+b3YdvB+HIiO4rWydStnNGu2wlKzVfdCI93SiJu316JjcGPaz8aeLTWLhF0gKiI8NgFnYgRlE0fmV25qGVTociGGwXa0q4KBBZwZFwhkJT55nseuXbuwf/9+vO9975v/+v79+3HHHXekfM7VV1+NX/3qV5iZmUFJSQkA4OzZs2BZFvX19SmfY7PZYLMtn+tGEHogW/HltPO6ujnlK84KKRgL3bhhhu75rEunBhMa2WTcFwq7ufO23XoUNzUZLKjQCyZpVskFIwu4bBcIaDHXN1uyLrt/6Utfwsc+9jG0tbVh9+7d+NGPfoS+vj7ce++9AGazloODg/jJT34CALjrrrvwj//4j/jkJz+Jr3/965iYmMCXv/xlfOpTn0pZcicIvaPHMSuZUghxVkjBONe48fjBaeztnm1SysffZ5buebOWTnPNuJshqNAao3odc2aJ0OaHj6MzOoFQed2KT9OjgDPjAoGsxeeHP/xh+P1+fOMb38Dw8DC2bt2Kp59+Gk1NTQCA4eFh9PX1zT++pKQE+/fvx9/8zd+gra0NPp8Pd955J775zW8W7rcoBoo4YtUbehyzkimFEGeFFoyFbNwoZDOU5hgso7ka+WTczRJUaIVhvY45slRoTwO4crIXU/EpYGYQnLsWkqcBstMHpBB1ehNwZlwgkFPD0ec+9zl87nOfS/m9Rx99dNnXWlpasH///lx+FIEijFh1TqHFl5oUSpwVutO3UI0belx7SOSfuTRVUKE2BvY65sJSoe1JRNE+fg7xZBRxKYHOWBSueADloQE4nD5wla2QHeWLXkNvAs6MCwRot7vOKbaI1SjoccxKJhRSnBW607cQjRt6XHtI5J+5pKAid4zsdcyaJUK7PhrA7uGTOJyM4Ekbj3dKPCZYDn1SAmViDFXRKdQOHQNfu2NegOpRwJlxgQCJTz1TZBGr0dDjmJXVKLQ401unr5H9uGYm38wlBRW5Y8ZmFQAprWgya8HgxFkc8dSBhYz28XM4nIxgr90BDsAVQgy3iyIeZS2IigkM2XlAjKBhvANsw24wYPQp4Ey4w57Ep44pqojVoOhNfK2G2cWZkf24ZibfzKXZz1slMWOzSjor2ubwJJLxENxODyriM5BiIeyz2SAzDJIAnnSU4M6wCEgJPCfLiCVjGLeVoiIWQm1oCG2JuG4FnNkWCJD41DGmjVgJzTC7ODOyH9fM5Ju5NPt5qyRma1ZZyYr20tAxrA3P4KrhE0jYvTgrJ+BnL65nPWOx4nGXB7dHZ3C5IKNfSCCAGJqFKK6aGkLl2mt0LeDMNAWDxKcWZNi5bsaIldCWYhBnRvXjmpl8M5fFcN4qhamaVVaxok1b7XjGYkEwGcHtoSiOMvKylzhjseJfS7y4IQy02X2odfqwNhJA4yV/hsRN/1QYAafkdBqTTMEg8aky2XSumy1iJfRBMYgzI/pxzUwhMpfFcN4qgZmaVbihYxicOIsxiwPXTrwNi5hAkrOiz+FFr6scktMHz1Q3Dlgs2BOJYGMauxorSxix8DhYvQmyqxLvGTuHyypbCtIzQdNpMoPEp4pk27luqoiV0BXFIM6M5sc1M4XKXBbDeasEjsarccPA62C6XsJRVxmCpTXzMy6N1KxiOfsMkhNncQnD4JycQIABvDKwjbFih92NwxXr0Wd3g41N4QQLXCMBPkmEn+UuvogMVAphOOxlkJ2+gt4/aTpN5pD4LBSrpdlz6Fw3U8RK6A8SZ4SaFCpzSedt5izMwg1BxKaEgLUT3eib6ELUaoe3pBotdp8hmlXYkZOY7PwDnk/O4PES7yIvp08ScVNsEleNvAW2vAliIo64EISVdeCmeBx77Q7IDANeElEphFHLOcFVtgKF7G6n6TRZQeKzAGSSZmcS0Zw61802XoEgiOKFMpfqsSwL52sAJ0toikxh0/QYtob92CBbwV/2cSS3fkDf9485YSeG8YzFsjiTCcDPcthrdwCxCNpCoxhasw1r+15HpcWF24UQPNOTOMRxAGeFw14GrrIVpRYn2v1dBbt/0nSa7CDxmSeZptl9lS05da6bbbwCQRDFDWUuVSBNFk5kWHS5fOhy+cDIMq73d+GWvkOwbP2Axge8MvPCrrwJntEQeEmEsESAygyDfTYbLouF0JoQ0FrRAtf2P0frVDeaug7i5tgUTlusCNpK4J72o5ULF/T+SdNpsoPEZz5kkWa/vWsYIS7N6yxhaee6mcYrEARBEMpitizcnLALll8CR7AXlbEpDNrcwJJfzc9yOCvHcM1kL6rXXYfE9o8AnBXcdV9F/fBxNCl4/6TpNNlB4jNbFng7pbFORLpfwlhZPVjIEJd+EnDxA37DwAl4rJmd5Ck7100yXoEgCIJQFrNl4eaFHcOCq2xF7dAxIB7COO9alAHlJRFMMoYNTiesC0vpKtw/aTpNdpD4zIKl3s6Z8BiS4TFcIoSwITiAw5UbMeD0LnteyGpHp8WK1oSAF6hznSAIglAQw2XhVmnYXSjsZEc5+NodaBjvQEUshIAsQgDAA/AyHNZanHC2vBtxla1oNJ0mO0h8ZkgqbyczGkeXMAXBxs122g2fwCtrLkW/c7mXqddWgu1WoD04SJ3rBEEQhGIYKQuXScPuUmEnO8rBNuxGScSP0ogfspQEw1pQypegNSEiuekW1X8Pmk6THSQ+MyGNt5NhLeABDC/otGsfP4ehxjaIS6LOUgDO5j3YM95JnesEQRAKkRAldAwG0TkUQlwQYON5tBRZN71RsnAZz8W85m+XCzuGheyqhOyqnH2CLKPN36WdsOOsNJ0mC0h8ZkA687bs9ME71Y3hC513c512TZEpdLl884+b+4AnN90C95b3Uuc6QRQAEhnEUs4MhfDU4U5EA/1Ya52dIxpKOvBkZxP2extwW5FsQNI0C5fpasls5mK+8Z/gd30Ke178jq6FHU2nyRwSnxmQzrwtO31w2N3znXdznXaNC8Tnsg84Z6XOdYLIExIZC1Byj7SBODMUwq9eOIJW5ihual66QakH+4bq8PjBaXzo2nZsqjX5uaFRFi6r9dHZduRLSUMIO5pOkxkkPjMgrXk7ReddgAFqxQSAFT7g1LlOEDlDIuMitEd6loQo4anDnWhljqbcHV9hj+Oj67qwtxt46nApmm9rM312XO0sXLarJXPpyBfa7zaGsCvUPd7EgSWJzwxYyby9tPOuWYhibSSA94yd00U0RqVJwkyQyLgI7ZG+SMdgENFAP25qHlx2TszBMrM75R/o7kfH4AZsaywz/fVRtSxcLuujc+3IL5LkjdkDSxKfGbCaeXuu8642NISrpobQeMmf4bLKFs2jMSpNEmYjV5FhOmiP9CI6h0JYa+1dlAVPRYU9jiZLLzqHQrBZuOK4Pqox4zKHofZG6shXm2IILEl8ZkBG5m0waEvEUbn2GiRu+qfcL/QFSrNTaZIwI7mIDDOKT7NtsMmXuCDAY4lm9FiPJYrzE9M4232ero8FIqeh9gbpyFedfAJLA5XpSXxmgkrm7UKl2c1emjR7qYxIT7YiIygkFD4ibTDbBpt8sfE8QklHRo8NJBzoHPTjJo85r49akEsJneZipibXwNJoZXoSnxmitHm7kGn2haVJyDImwwICYQGiJIFjWXhdPLxOXrPSZD7ikawExU02IiOYdMDG6yvaLxSG22CjMC21bjzZ2YSJWM+KWfGJmA0d4Tq4JD9uqi1y60YByamETnMxU5JLYClbbIYr05P4zALFzNsF9m/NlSat4jTe6gtAjIdRyk6DZ5NISBb0BkoxYHOhqcqremkyH/FIVgIiG5HRm2zC7SY9D8gvt5jWOg/2exuwb6guZTYTACQZ2DdUhyBTgStKjxe9daOQLC2hc7KEpvAkGqMBWMQEkpwVfQ4vJnnnohI6zcVcTtaBZSxkSP83ic9sUcC8XWj/VlwQwIsz6BoehxfjaHCHYecuHmlMnEZ/2IWuoQR4cQZxlUqT+YhHs1sJiMzIRmQ4PA1orfOof5AqQH65FBUUhwd/mtgJsQu4tW7p9cWGfUN16JDbsL62GmVhA1s3dOjrW1hCP+coQ9vEeUixEM7JCQQYwCsD2xkL6sGgtmH3ovOR5mIuJtvA0hKdRJ8B/d8kPnVAof1bFosVvUHgnb5xrHeHsPR0tHMi1rtDOB8CegJAo0X50yBf8UhdzgQAWDkWt13RgscPTmNv9+z7nU5k3HlFi2kDkGL3y6WqoDBJBxxSHf4wugWvBddjI98FixhCMOlAT6IJJeWN+B97LsVb/UGEgsa0bujW13ehhP6uZ7+Klt7XsI+V8Qe7A36WBwDwkoiNsWncLnGoiQVROt65uPxbJOOTMiHbwBIMa0j/N4lPHVBo/5bNwuJcuAqOGmaZ8JyDAeCwMjgfqcIGq/I36HzFI3U5E3NsXOPGh65tx1OHS/FAdz+aLLPiI5h0oDfZBIenAXea3ftbxH651Soov+uuxtMjGzDAbECtzQ+XJYF6RxCxxBieOXIWmxprcTZhPOuG3sfvSJWbYHV40MFxOIEkSuJh8AB4AF6Gg8Ppw4sVLeAiAV2Vf/VGtoFl0uE1pP+bxKcOKLR/K56UwFksOBjYirvsh8Ay8rLHSDKDg4GtYC0WxBOZ/ex8yFc8UpczsZBNtW4039aGjsEN6BwKISgkYOOtuL2Iph4Uo19utQqKVZzGTksXoo5hTFovwdcuOwMrO3v9m8uKv9G5CwlrtbGsGwaY68oNHcNgdBJH170DrkQYJRE/ZCkJhrVAdvogO32QGBZHrC5dlX91R5aBJdf/miH93yQ+dUCh/VvJZAI7K4LoCLfg5yPAzb7jqOBn5r8/IZTgWf92dAgt2FURRDKZLNjvko58xSN1OescDXxoVo7Ftsayos5wF5tfbqUKiiTJ6B0PoJwZx8fqR/Gvg7U4HfBge3kAwGJrz5viNTgttRnGumGEua7z9jHeCfBOyK7K2eNa8ji9lX/1SDaBpZiIGtL/TeJTBxTav2XjeTBWBjduGMETPa343mAzmqyD8FjCCCZd6E3UwWmz4aMbR/DS2BpVhFq+4lEPXc40XzQ1uvWhFQtF5JdbqYISiAgQ4+H5Bssm6yBOB+rmxSdw0drT0T2M7ZdegbN9xrBuGGGuK43/KiyZBpZG9X+T+NQDBfZvzQm199p7cN+2czgd8OB0oA4zIgsnJ+ED3iA2e4MICrxqnqZ8xaPWXc40XzQ1evehEeZipQpKICyglJ2en+zhsYQxIy4XQ3PWnqjQhs8bxLphBGFH478UIJPA0qD+bxKfOqGQ/q2lQm17eWBR9A+o72nKVzxq2eVM80XTYAAfGmEuVqqgiJIEnr1oIQomXXByqcXQnLUnG+uGlpUPIwg7Gv+lHUb0f5P41BGF8m/pcRxNIY5Jiy5nmi+aHiP40AhzsVIFhWNZJKTZW9qEUILeRB0+4A2mfJ1sfeFaVz6MIOyMWv41C0bzf5P41BsF8m/pcRxNIY5J7S5nmi+aHiP40AhzsVIFxevi0RsoRSQ5g2f92+G02bA5hfjM1heuh8qHIYSdQcu/psJA/m8SnyZGj+NoCnFManY503zR9GTqQ5NkGcOCiDfOD+DN6Dlq1CJyZqUKitfJ4y22Av/RtxET3FrctXFkfszSHNnajXRT+TCIsDNi+ZfQBhKfJkeP42j0eEzpoPmi6cnEhxaICOgbC2DnzBQS0hl42MepUYvIi5UqKJ3hevQIVlzt60WFbXHAmIvdSE+VD6MIO6OVfwltIPFJECtA80XTs5oPLRAR0DU8jmZpGNc7oti0QYDs7QNQ5I1aRN6kq6B8uNYNjmHw7Otn8UB3Q952I71VPgwj7AxU/iW0gcQnQayAHuaL6pWVfGiSLKNvLIByeQwf5CbQUFIO2X3xplzMjVpEYVipgrKxtjB2I11WPkjYESaArvYEsQKtdR44LjQ4SMu3lALQ4So+tZjzoTmqcb2/C+5EbP5bU2EB7lgAn8A4buCdcDZtBNjFl5u5cmU02I+OwdRdyQSRC3PC9M4rm/Cxd67HnVc2YVtjWdYBDlU+CEIZSHwSxArMNTh0yG3Y292MiZht0fcnYjbs7W5Gh9yG23Syik9N5n1oFZvxmdA43jN2Du8cfxvvGT2H/y1N4A63F+UbtkF2e1M+f2G5kiD0RkutGz2JpmWf+6XMVT5aiqjyQRD5QGV3glgFPY6t0hOpfGhH+sKIxQfgaBEgsysL8mJr1FoIrWzVN1pvViMIs0LikyAyQI9jq3TFEh/aea4Xwtu/wfXsmVWfWqzlSq0HlxOro8eFHQRhBkh8EkSGGGlE1GoonXGjRq2V0cPgciIzqPJBEIWHxCdBFBlqZNyoXJke3QwuL3KyCcCo8kEQhYXEJ0EUEWpl3PRUrtSbr1JPg8uLlVwCMDNVPghCa0h8EkSRoHbGTQ/lSj36KvU2uLzYIMsDQWgPiU+CKBK0yLhpWa7Uq8jQ5eDyIoEsDwShD0h8EkSRoFXGTYtypZ5FBg0u1w6yPBCEPiDxSRBFQjFl3PQsMsw2CUBvntqVIMtDkSAmwA0dAzdyAqIQBse7INZsg1i7A+AomNMDJD4JVTDSDcqsFFPGTc8iw0yTAPToqV2JYgrAihV25CSEIw9j0H8eHWIMIYaFW5bQeuo3qPatB9/+l5Bqtmp9mEUPiU+dYiaxZrQblFkxW8ZtJfQsMvQ0CSAf9OqpXYliCsCKEXbkJEIHv4UD0VEc8dQhZLXPf+/FRAztE6ex5+D9cF/3FUg1l2p4pASJTx1iJrFmxBuUWTFTxm019C4y9DAJIB/07KldiWIKwIoOMQHhyMM4EB3F875myMzikzJkteN5XzPg78ItRx6G5dbvUgleQ0h86gwzibWFN6gPNnWjI+jF/qEaxEUGNk5GqzeEDzZ149e9+rpBmRWzZNwywQgiw8iDy/XsqV2JYgrAig1u6BgG/edxxFO3THjOITMMjnjqsNN/Ho3Dx+fXARPqQ+JTRxg1m5COuRtUc0UI/3pyPSJxAWv5Abi5CEKiE78dr4fTVoHraifR4dfPDcrMGD3jlilGERlGHVyuZ0/tShRTAFZscCMnZj2eC0rtqQhZ7egQY1iXq/ikZqaCQOJTRxg1m5COzqEQnMkRPNtbhla+EzfXHUcFPzP//QmhBM/6t+OZ3hY4bCO6uUGZHSNn3DKFRIay6NlTuxrFEoAVG6IQRojJ7HMcYliIQjjrn0HNTIWDxKeOmMsmlPMxTM4ICIQFiJIEjmXhdfHwOnmwLKO7bEI6IrE4eoIcrnd34q6aQ2AZedH3K/gZ3FVzCD8fAZ4LtsMXEzQ60uLDqBm3bFBDZJipMTAb9O6pXY1iCMCKDY53wS1LGT3WLUuzGcssXp+amQoLiU8dERcE8OIM3uobhxgPo5SdBs8mkZAs6A2UYsDmQlOVFx4nr7tsQiqmIiJkMYabfceXCc85WEbGzb7jeG5qK6YiSZWPkDA7SooMMzUGZosRPLWrUQwBWDEh1mxD66nf4MXEyqV3dyKGVs4Occ32LF6cmpkKDYlPHRGISpiZTOKdVUNocIdh5y7GZTFxGv1hF7qGEmheU6nLbEIqaq3jKOFWLs+VcFHUWsdVOqLcKdYsl9FRQmSYqTEwF4ziqSWKB7F2B6p969E+cTqlQAQARpbRHhxEdcXmrMQnNTMVHhKfOiEhShgcm0BM8MJrlxYJTwCwcyLWu0M4HwKOD7nRk2jEHTq/qZU5OURsIvrDLqx3h5DqIysD6A+74LGJcLo4tQ8xY4o5y0UsxmyNgbmgtqfWKIGfUY7TlHBW8O1/iT0H7wf8XctK4+5EDO3BQexxVM96M7PITKrWzFREkPjUCR2DQTiTI/CWMtjn357SI8kAqHNG8MveOkR91brPJjjtNiQcPgRQifMhoMG1NJvLoT/sQgCVsDp8cNpsGh5teoo9y0UsxmyNgbmiVuOOUQI/oxxn3ui421uq2Qr3dV/BLUcexs6lTUGcHdUVm3NqClKjmanYIPGpEzqHQmjme/GO+mHsPduCn48AN/tSd4efjq/HpZVVuo+kZ31hzfCUv43pkBUnQ2GUXPCxCpIFM1IpOJsLHk81RkeacYUOhRtluYilGHXMkBIo3bhjlMDPKMeZL0bo9pZqLoXl1u+icfj4bAZyTiCv2Q5xzfasMp5zKN3MVIyQ+NQJc6NLWjwhfHQD8ERPK7432Iwm6yA8ljCCSRd6E3Vw2mxoq5qBw6HfEvUcc76wVwLr8OEmCaGoB4GwAOFCB3+Ti4fbweOXvet06wujLJcyGLk8aeQxQ0qgVOOOUQI/oxxnvhiq25uzQqxvmy995ysEFW1mKlJIfOqEhaNLWrwh3LdtGqcDHpwO1GFGZOHkJHzAG8RmbxCPvr3REM1GC31hv+ydFWjN1Yt9Yb/s1fesRcpyFR49lCfzEb9GHzNkFIwS+Kl1nJoGbEXe7a1kM1OxQuJTJywdXWJlZWwvD2B7eWDR4/Q8uiQVRh/oTFmuwqKH8mS+4tcMY4aMgFECPzWOU+uAzTDd3kr5URVsZipWSHzqBDOPLjHyQGfKcl0k38yLHsqThRC/Zv6s6gmjBH5KH6ceAjYjdHsr7UdVqpmpWCHxqRPMvg7QqAOdKcs1SyEyL1qXUQslfjP9rJ6W2nBZYy1+d6TfcL5WPWCUwE/J49RDwAbov9tbLT+qEs1MxQqJTx1h9BK1GaEsV+EyL1qXUQspflf7rMat1ZBlFsdOvGbusTsKYpTAT8nj1Dpgm0PX3d5q+1EL3MxUrJD41BlGLlGbEbNnpFejkJkXrcuohRa/6T6rO3gOb3R2Ygv3Om5q0OfYHSNMGzBK4KfkcWodsM2h525vw/hRiUWQ+NQhRi1Rm5VizkgXMvOidRlVCfG79LOaECV8//dHsYV9Xbdjd7RuXskUpQO/QglwJY9T64BtDj13exvBj0osh8QnQWRAsWakC5l50bqMqob41UuZNB16aF7JBqUCv0ILcKWOU+uAbR4dd3vr3Y9KpIbEZ5FjhPKbXijGjHQhMy+ZlCfjIoNHzq1HX7ICb3SNo3MoVLDzUQ3xq5cyaSr00rySLYUO/JQS4EoEqFoHbAvRa7e3rv2oRFpIfBYxRim/EdpRyMzLauXJV8Yq8H/PNEEQWVxeeRjlo0JBz0c1PIR6KZOmQu9Z2ZUoVOCntAAvdICqN9+rHru9Nfej6njXvZ4h8VmkGK38RmhDoTMv6cqT56a9eNPvxuUlZ/DB9RNoLpMXvHZhzkc1msd0UyZNgZ6zsmphNAGuy4ZHnXV7a+lHNcKue71C4rMIMWr5jVAfJTIvS8uTkzEBXcE+3Fj9Kj61aQwWbvEPKeT5qHTzWCZiPSExeHm0Es+PN6O1JIDHX4UqVhc9Z2XVwogCvJgbHjNCIz+qoXbd6xASn0WI0aJ/QjuUyrwsLE+e6JvCQM8JvL95dJnwnKOQ56NSzWMJUUJSlNAXr8A3jm3FlVUT2OwNYYs3ACs7m8ntDLjxu55q9AZYtDpOYGP0FGbeVsfqouesrFoYVYAXa8NjpqjuRy3yXfeFgMRnEWLE6J/QDqUzL1qcj4X25i30T7fzXYgLY+gfEXFytAoeRwXeu24UkIFHz6xBrdyFD1ePYmdTCTxOHoA6Vhc9Na9ohZEFeDE2PGaDmn5Umi2aPyQ+ixCjRv+EdiiZeTH6+ZjKPx0MC+gdD8Af7sKx6QZ8+1grQqITbY5TeGfNINZVe+eFJ6CO1UVvzStaQALc5KjkR6XZovlD4rMIMXL0T2iHUpkXI5+P6fzTHhePrY5KBCICGmb8EPpH8MLUJrx3/TQ2+irBplB+SltddNm8ojIkwIlCQLNF84fEZxFC0T+hJ9ZXl+BXx2vxev9bcFsi4FgWXhcPr5NfJNL0eD6u5J9mWQblJTaUl9jwZ4kBnA+XI855wLKBtK+ntNUlEwvF+9s3IpYQ8firvaab/UsCnCgENFs0f0h8FiEU/RcnelwocGYohOfePI++APBi3IX3VrwFUebQGyjFgM2FpqrZ8rSa52M2f6dM/apuSwQbbH04HajA9vLAio9V2lqwkoWCYxg8c+SsqWf/Uvc4kS+azxY1ASQ+ixCK/ouPXBYKKC1WF3ol37UliGd6m/BaOIqbfcexlhtCf9iFrqEEPOX1eCWwTpXzMdu/U6Z+VY5l4WRjiIurH7sa1oJUFopimv2bq4dZjwEcoT563nVvFEh8ZoGZLjxmif7N9J4oRS6iQuntV6m8kl4+gSd6WvG9wWY0WQfhtoTx9owPHUNbsf6SzbjzylZFz8dc/k6Z+lW9Lh7jyTLYpJXPSa2sBcU4+zdbDzNthCPm0fGue6NA4jNDzHjhMfrsODO+J4UmF1HRNTqjeAYslVeyxRvCfdumcTrgwelAHcIiC5+NhTPswbWXNivqQ8xVfGXqn06ypegR18MpTEOSoTurC83+XZliygoTmaHXXfdGgcRnBpj5wmPU2XFmfk8KSbai4q3+9Xj+2HnFM2DpvJJWVsb28sAiX+T/e8KF/+/5E1jDBxQLMnIVX5n6p/eP1KOqdgOCiGFvd1R3Vhc1Z60arVpRjFlhIjP0uOveKJD4XAW68OgPek8yJ1tRcfD0qCoZsEy9kp0BN7qmGGx1v4SPNU8qFmTkKr6y8U9/bM82yDLw1GG37qwuC98PSZIRiAgIhAWIkrRs+sBKDVGrCUsjViv0lBU2mnAvCnS2694okPhcBT1deIhZ6D3JnGwHuB+fnMYOFTJgmXglExKDJ3qqsdXWgdvW+FFhL112DIUKMvIZdJ+tf1qPVpe592NuOL4YD6OUnQbPJpGQLIumD6RriFpNWF7a3IDDp04brlqhl41wRhTuhkFMgBs6Bm7kxMXsZc02iLU7aC2mQpD4XAW9XHiIi9B7kjnZDnCXZQZuq/LbhjLxSp4KeBGMJnGjux/lJd6UjylEkJEQJUzMJHF8tAaRJAsbJ6N1yU72haQSX9n4p/VodWmpdeMXJ+rwRt8rWGsdQoM7DDt3MYcTE6fRH3bhjV4LOuL1+MgScbiaDebZwVo8tn89Li8fxEc3G6taoYcNXGQzUg525CSEIw9jcKlv89RvUO1bT75NhSDxuQp6uPAAVG5ZiF7eEyOQ7UKB+soShKaU3zaUiVfydMANrzwGn4uBd8EqyqXkE2TMZZMmRrvgE7tgCw8jKtvx2/F6PGub3cne4gnNP36lbnQ9ispM2VBTisGICydj1bh+3SlwzGLRbedENJdO4/fd1RiQnNhQczELnYkN5uaqTgyM+TEdq4UoM2CZ5aJer9WKhQHcapYEJcZkkc1IOdiRkwgd/BYOREeXday/mIihfeI09hy8H+7rvgKp5lINj9R80Bm6CnpY/XdmKITv//4onnz+eQhv/wae4cchvP0bPPn88/j+74/i7HBo9RcxEXp4T4xCa50HjgsiT1p+vwewuMv62tYq9CSaMBGzrfi6cyKsJccsy5xXskNuw97u5kU/LyExODhchV91N0CQGHAcj0BEgJTuF8BskBHPMsiYyyatjR3AVze9jA/UncaVJafw6boD+FLd77CW6cTes9XoDMz+jmZevHBuZBqVdgFDTDP2jlyFCaFk0fcnhBL8bPhqvJXYjHgiiX975hQef7UXJ/qmcLJvatYGU5veBhOKCLjB8yakZBSnA+n/dgsDCb3QUutGT6IJXZMM3uobR+/gEKRQN/jI25BC3egdHMJbfePommLy+kykY95mtMLfd064R4P96BgMFvTnmxYxAeHIwzgQHcXzvuZlw+JDVjue9zXjQHQUwpGHAbF4kxhKQJnPVVBzFWWq7KaD53Cs8ww2s1RumYPWg2ZOtgsF1lWV4IBK269SeSUjgow3/B5IySRczDSsjARbrA+9g4s3Hi0l2yAjVTbJVuVF11AC50NAgyuMu2oO4ecjwBM9rfjERgHPjdSadvFC51AIO0p78I7K4UWzVj2WMIJJF45FLsF4vBT19ims5V6CZ+x1CDNleLKzCcOCF5ewIyt+FkVJQpUtiKbYIE4H6lbc8qS3asWGmlIMJ3z4xpst2Oq0Yo09gm2lA7jENQArKyEmTqN3xoXHz2xCvKK64IEJ2YyUgRs6hkH/eRzx1KUcEg8AMsPgiKcOO/3n0Th8fL6piMgfEp+roNYqylRm8qmEA/81WIsrSt7CrZsHUWZffNMt1nILrQfNjmwbYtTcfrXQK/lCxyhOnj2LXZ438e76IYRkL554uxIVjuSijUfNayrhcV38LOQSZKRqWvM4eTSvqUTvuBUnQ2GUsNNosZ3HcyNb8fXOa1FfU2+IxQu5MGdlWTprdUZkERJ4cDEOd1S8hlt8xxGMA4LzEmxY48FErAc/7SjHW1NV6Ay40eJNnbHkWBYJyQKPJYyZVbY86alacWYohCdf60BsqguN3BCccgjhOPCbme14xnIp3l/zBiqs0zgcuRRn400olwt//SWbkTJwIydmPZ4rrMcEZjOgHWJsdpQSic+CQeJzFdRYRZnOTH5ssgw9fgF/VnIIPcNOsEtuuoB+fVJKQutBsyebhhi1t19ZOXY2oHjjHG6q7MBH1w2BZYCEFMQfByrxrH877qo5hPXuEM6HgN5xK7Y6KsGyTM5BRrpsksfFY6ujEoGIB4GwAJckoTkSBRpb8dc3bTLtubTQyrJw1mpCYvDdE+txpes07qo5BJaRMR71gmNn/w4V9jhuW3MWiPvxRM9a3LdtOmWTltfFozdQCn+iBO4SKe1x6KlaMXddboy/indUHsG2kl4MR+xIiiISUidend6Cfzz/brgdDOpKZPxlaz+e8lehYzBY0Osw2YyUQRTCCDGZfZ5DDAtRCCt8RMUFic8MUPJmvJKZvCPgxgZ7H9p9wzgfci+66S6kGMstZlkPqgoXxojwIydwmRBGG++CuG7lMSJqb79KlYm0sjLeu24Ue8+24OcjwM2+42hwhXEyFEYg4oFkceccZKyUTWJZBuUlNpSXzPpQL4lJCJZYTSs8gfRWllMBLyJxATfXHQfLyIiJHGakUjQtCILLS3jsKO3HH0N1OB3wpCype5083mIr8Mb0Jbh37UjKY9BTtWLhdfmK8lPA9CiqHTFU2uOYEnhMxXncbD8FedKBfqYFn996Gk6LhJPBwl+HyWakDBzvgltOHwgtxC1Ls+OXFD6mgmCQsVEkPjNEqZvx3E33hrVDODFVho6AG3GRgY2T0TXtwno2CgZYdNOduykupBjLLUZfD6oG+YwRUbN7O10mssUTwkc3YJEPMZKQ8Wy4AWHHxpyDDMomLSadlaUj4MZafgAV/AxkAP1hFziba9H0Aa+Th8/FwBMcx6mAL7Wfk2FwTtyCCXYtTgYENLiiuq5WLAyGpqYk8GwSAMAyMny2OHy22WOvdB7G9wbrcC7kxvbygCLXYbIZKYNYsw2tp36DFxMrl97diRhaOTvENdtVPLrcMNLYKBKfWaDEzbhzKARncgSPnm1AJC5gLT8ANxdBSHSiP7ge58VLscvdixbXMErYaQTCQkrxmc0N0kxjm4w83kZpjDRGZKVM5FIf4smxciRcbfiLay/J+ZylbNJi0llZ4iIDNxdBTOTQH3YhgEo0V3kXVV9YlkFTlReWURavjFXgxtqRlMKy29qGv7hxM0521em+WrEwGApd8KumooKfQZP1YhOVEoEK2YxWII8sn1i7A9W+9WifOI3nfc0pm44YWUZ7cBDVFZt1Lz6NdL0HSHxqTv/ENLqmGLzL24mb646jgp+Z/961nuP41dAO/HjgKnyy7hB4dhqCtLxMkM0NkrZkFAlLxogsvbDOjRGBvwu3HHkYllu/q2lJZrVM5EIf4oxoh+2SyrwCDsomLSeVleVMwInyhA8nbbXgbC40p5k24HHy4EuqEBQ24YFu34rCcs+Wat1XKxYGQ3N+1Zg4vWjw/hxzTVRKBipkM1pO3lk+zgq+/S+x5+D9gL9rmWBzJ2JoDw5ij6N69rV0VLJehsGu9wCJT01JiBK6hkax1dYxb+ZfyAbXFG4tfx0Hp7bgt6M7cbvvFdjYxRfnbG6QtCWjeDDaGBG1M5GUTUrNUitL6WgIvb2lKK2YQXOZvMxvPsdEzIYxthmfvelScCyzorA0QrViYTDkdfIYsLnQH3ZhvTuEpX+BYNIFBycpHqiQzegihcrySTVb4b7uK7jlyMPYuVTEcnZUV2zWVak6HUa73gMkPjWlYzAItzyOHaX9ECR2WVTNMjKa3VFMJnqwd/wSvGLdjPfWXvQTZXOD1NuWDDOV/vWI0caIqJWJXHreecrr8Po4j9Ndo1hr7Sv6bBKwWBwmRAnf/30UrwUH0FzelfLxC9+XrQ3e+ecbmaXBUNOSGbBz1+oJoQTn4w3whp2Ydm5RPFAxgnBXnAJn+aSaS2G59btoHD4+ex2cK9+v2Q5xzXZ9ZzwvYLTrPUDiU1M6h0LY7BqEj2fSRtVeXsAu3wT2TQXxuP96JIeG4bVmf4NM1U28FLXGNlHpX3mMNkZErZFmS887JunAVKIJYcsaBCsuBRxc0WaTUlGsGeKlwVCqGbAWRsQTE1fgbHwtdjSsw527W+m6pQKKZPk4K8T6tvnHGaKrfQFGu94DJD41JS4I8FhjaaNqAIiJHCZidpQ7JGxu2AD7uqtyKrfoZUsGlf4VIIXpnglPwC1ndgnVyxgRJX1tmZx3HZNteBedd8soRr9hStHtwvwM2O4pFi9ONOI4twsf/bPLcNP2WtMIb71jxCyf0hhxbBSJTw2Z8xWliqp5NglBsmBGKgVnc8FeUoUd6ypx55VNOf0sPWzJ0Fvp3wykM93vTCTQMjOMlxylCJauSft8vY0RUcLXRudd7iy0Kfi8XkzxpZjAZohOC5x23tQZ4lVFd3UDvmQy0W0EjJjlUxojjo3KSXw++OCD+M53voPh4WFs2bIFDzzwAK655ppVn/fyyy/j2muvxdatW3Hs2LFcfrSpWOQrWhBVB8ICBEkCx7JocvFIsqUY7W3GFXlkZPQw11BPpX8zsJLp/k9CBB+bGcJl/W/gxbVXQnL6lj0/kzEiWnhzC+1ro/MuN5baFMotUViSDvQkmiB5G3BVEQgvavLRH0bM8imNEcdGZS0+f/nLX+KLX/wiHnzwQVx99dX44Q9/iFtuuQWnT59GY2Nj2ucFg0F8/OMfxw033IDR0dG8DtosLGuyWLJZBZg18+/trs+7i1IPcw31Uvo3BauY7gO8E0/U78Ltva+C7X8dR9e9AyHeOf/9TMaImMWbS+dd9pA95iLU5KMvjJjlUxwDjo3KWnx+73vfw91334177rkHAPDAAw9g3759eOihh3D//fenfd5nPvMZ3HXXXeA4Dk888UTOB2wm1DTz62GuoR5K/2ZhoemehYymGT8aowFYxASSnBV9Di96XeV4rn4nPjp8Cm0TPThtsWY8RsRM4oPOu+wgmwKRERqtcTRilk8NjDY2KivxKQgCXn/9dXzlK19Z9PUbb7wRhw4dSvu8//zP/8Tbb7+Nn/3sZ/jmN7+Z25GaFLXM/HroWtVD6f//b+/dw+Oo73v/98zsfaXd1c2SJUuyhS+SMbbBNmAo4VLAgcQQSmIeyKGkhRZOkh+h9LQHTnpOQtqG05yGUnpKQlyaPMkDDk5IKPEBHDfYxsEEy8a32JJvkiVZK8nSSrsrrfY6M78/ZMna1Uray8zsd2Y/r+fhAVaj1Xd3Zr7z/n4u769RmCy6d8fDuN17DFIkiDNyHH4O8MjAas6MtTYXDlQtx0HPItzdcBMWlzVmZCNiNPFB1112UJkCMR8F3cZRh1E+rdCTbVRW4nNoaAiiKKK6ujrp9erqavT396f9nTNnzuCZZ57Bvn37YDJl9uei0Sii0cvCKBgMZjNM3aFVXVGhu1ZZSP0bBTEWghCPYGPfcRxIjGOn1Qoff3nnmQpJxKbIMG7oO4aorQwJZyXEDY9O/O4872008UHXXXbMVqYgSTL84zH4QzGIl2rSq8QOnLiwjunzTygLC9s46i3Kpyk6sY3KqeGISwlzy7I84zUAEEURDz30EJ577jksX7484/d//vnn8dxzz+UyNN2iVV1RIQvoWUj9GwXBZEPTaD9+yYnYZrPPSD35eAHbbHYgMo77RqMQTLaMJyGj1UjSdZcd6coUAqEYugb9EKMhlF5y44hLJsRHq/GbIx1Yt6RcF/W/RJ4wtI2jnqJ8xEyyEp+VlZUQBGFGlPPixYszoqEAMDo6ioMHD+Lw4cP46le/CgCQJAmyLMNkMuHXv/41brvtthm/9+yzz+Lpp5+e+v9gMIj6+vpshkrMQaEK6M0Cj7s2LMcP3xvG0LEINno6UWmLweO0wOOwYDhm069htcb1T7LJClGMYrfdNqfR8m6zCfeEI5DNmaWdAePVSLJQcqInUssUAqEYOvoG4cEg6l3JPsSlwTiqxLPYvkfWRf0vkR/MbeOokygfMZOsxKfFYsG6deuwa9cu3HfffVOv79q1C/fee++M410uF44fP5702ssvv4z3338fP//5z7FkyZK0f8dqtcJqtab9GaE9StntnPIG8W7racjxcRweq0PbSCkaLF5YOBEhrgxBWzPKFyzWnWF1IeqfODGKc4IZfCICCBbM2BoLAGSAT0TQIZjRnMhMTALGrJEsdMmJnpheplBuiaBr0A8PBmfswDYUK0FvohZ/vPQcTgZGdFH/S+QHGbwTSpF12v3pp5/Gww8/jPXr12Pjxo34wQ9+gO7ubjzxxBMAJqKWvb29+PGPfwye57FqVfJDd8GCBbDZbDNeJ9hEKbud6d3Tj6/shdsSw0m/Gyf95fBFzOgdcyPCl+Ghdct1JQByrn/KM1IqxiMYcy1EbXgIiAYxaHEixgtTP7dIIqpiIdQKDoyWVEKMRzL+TFPiY7wDVdE+cEE/RDEOQTBDdnkgu8sBntddjSR5NmbG9DKFTVVtEKMh1LtCScJTkjm851sDh9WKVWUB1DvDuqj/NQQF6jIHitDgXanvuoDnjFWyFp8PPPAAfD4fvvWtb6Gvrw+rVq3CO++8g8bGiZ13+vr60N3drfhACe1Rym5ntu7pNeV+rCn3A5j0Mx3Be4fcWF6rk+hJjvVPSkRKBYsTpSY7LLVrUT/YhspIEH5ZRAyABYCHE2C3lUGoakHpqC8ro+WWOjeOWWPoO3wMQaEX7XIcQQ5wyUBLnxk1ThdsDcux03eN7mokybNxfqaXKQx1RHCD+UJSqn0oVoL3fGvQFmvGg8v7YeZl3dT/6p2CdpmjuAzelfquC33OWIWTZVku9CDmIxgMwu12ozsQgMuljyiL3omLEl761UEsjuyes0ljW2cTzttuxZNzpNuOdY/g7fffx1NNe+ftNn6x82bcc+ttuniACT2t6P7NN/CKq2pes+PHg4NouP1bkE3WWSOl0y1C5usUTfrbJgu4cR+4cR9kKQGON0F2VEB2VMCViE397UzTX3z/cXjf+1u8OXAOrWbAWRqdEh8uUcSasThaxAr8tuIJ3PTpLbqKVBOZc8obxAv/8THso8exwXUOblMIgYQTXfE6OKxWfG5JP5rdl51Itnc2ILDwATz8qaUFHLVxmSvLks3ckQ+5zHl6TLsr9V2zcM60JhgMosHtRmAevaaD8BJRCKbsdmrnt9sJB3rQ1huY9b1y6Z7WA9nWPwm9nyRFSlN/bzJSujs8gFjrVkCcvZFnymg50AsOHGRnFaSqZsjVqyb+7awCB27CaLliaeZGy5eiua3yMA42XoVucwOOB2vRHvCgY7QEB8Yq8E/iUrwvC/ic4xCWL8i8kYnQFytqXbhlzTLUltng8NRhzN4Mh6cO9y8L4C9Xn0kSnoB+6n91SUqWJXXuCJksOG9z4cLF45B/9TVYDvwAQk/rnHNITsOYPu/MEreaMnjPZt5hiXm+64znaaXex6DkZLVEKEch9s7OBCXtdozWPT1JtvVP8tAZDCjVKaqS0fL0bla32YpVjiqMhNzwj8cQkyTwPI8GhwW9loWIjHZBoIYCQ3PlIjfOna7GHbXt5JFaQObqMq8fH8GGwTOQIkHsl2I4ErqIqkP/hmZ7pfJp3SIweFeqo585ZwDGIPFZQFjeO1tJwWjE7mkg+/onU3hY0U5RNYyWU6O5PMehosSKipJk94kxgLpZDUa6hfDS6hJY3YvII7XAzJZlqR8fSdloogSN4SDqrXbsdVWpYvhudIN3pTr6yRlgbkh8FgjW985WUjAadYcZsWY1Wk68iQ/ic08wrngELYINcUc5gsGujN47005RpY2Wi66blQAw+0L4nfZGRMwL0RpbCzDkkcpqxkgt0t2Xgixhw+AZHEiMJ200EQMgSwlVDd+NbPCe8RwoSxiNh8Cdex9Cmg52mkvnhsRnAdDD3tlKCkaj7jAzVf80dDJttzswrf6pciX4ymVw9R3K6L2z6hRV0Gi5mLpZiQkyWQh/JF+DI9KNaOscKLhHKssZI7VId182hoYhRYLYabUmzT0WYKLpECqndQ1q8J7JHMiFhyEOtsEaHMLJ6DiOjg/M6GCnuXRujLdE1AFKNvOoRUudG/ZLglGaxQ8hU8E4ad3SJq/Hts4mDEWSU7hDESu2dTahTV6PzXraYWay/slejdt8HXCleGm64hHc5uuYqn8SF16NFsE247hUJiOlhSjWF2tWMz9GQjlSF8KpC83JhfBGxydw2cz4zM23wnrF/QgsfADWK+7HPbfehic3r9dUeP5sbysWR3bjqaa9eGzZKWxZ0o3Hlp3CU017sTiyG9v3tOKUTpoWMyXdfdkQ9uOMHIcvxd/XwwmQHRVTr001PPYd1XTMsyLGIfS0wtL6KoQPX5r4twrNUbky3xzIhYcR8x7B2LgPLpMd/696BT6ougI7FizDK64qvDt0EsE9z0OyOGgunQOKfBYAPeydrfSWhEbdYSar+icxnlWktCDiM8tobrFNmEZjaiHcNP9C+MXOCxD45dhyfaO2g7yEHjJGapHuvjSJcfinfwcyUBULwW4rSxKfADtpXT14Xs45B8oSxME29CVCuJkzQ7J50OW4/GxOKnXo+hDVZU3YMNxOc2kaSHwWgGybeYYjMRzrHtG8vklpwWjUHWYyrn/SQ6eoHsZIKIYeFsKTZCeUDbbbUpr7MiGY4bmUlZq+o5lQ1QI5pdaQhbRuzrvBac0ccyA37oNl3I/bIOAasxP7q5ZDTPmup0odhjuw+OpHcGt4hObSNJD4LADZNPOcGfWgI9CNC+ePFaS+SWnBaNgdZjKsf9JDp6gexkgog55s0PQklNUg9b4ciIxicSKBAyE/IJindjST7eVJv8dEWjfH3eAKxWxzoGfUiwUJEcOlNdhftRwXHJ60vz/VwR4bo7l0Fkh8FoBMm3k+uliJwz4X7qz+Hf6oaaBgHfGGFYwFQg+dogUZI+1/rDl6skHTk1BWi6T7svcThI/9FPeGL+L9qmWQnJUzIp6spHX16HmZbg409RzArpGz+I+6q2ZEPFOZLHXQw3xfCEh8FoBMur+jIod/O9WIa0tO4U9XXIRJSD7IyPVNRYEeOkU1HKMeasGMiJ5s0PQklFVl2n1pbrwBt+z5e2CkAwfHBhDguKntdUvNTmwI9jGR1tWt52XKHCi0vorYMe+8whNIKXXIdy414MKcxGcByKSZ59UzSxETeXx+6dAM4TnJXPVNxeaDR+gX3dSCFQKVHzp6skHTk1CegWrnUYaTE3BTaBiL42M4IYsIcUANeKw2l2Jh/XUw3/xMwRduRvG8zNbbWYlos1EX5iQ+C8R8zTzdiUpcW3UATWWz+BxdIl19UzH64BE6RWe1YFqixUNHaVcLNdGTUJ6OWudx+qLt0JLrUR4Po2F8BCViHAKAbjEGjyTCjLmfIVpgFM9Lrd1AjLwwJ/FZQOZq5vmkYxDlA7GM3md6fRPrOyexAEWF2UGPtWBaoOVDRy82aHoSypOodh7TLNr8Fgc6nJctljhZho+RRVshIoaqoKUbiMEX5iQ+C8xszTzt3mDW9U3F7IOXKRQVZgvd1oKpSQEeOnqxQdOLUAag6nnU26LNSP7BWrmB6O0cZwuJT0bJpb6pqH3wMoCiwuzBVC0YI0X9hXro6MXVQi9CWc3zqLtFm8H8g7XoYNfdOc4SEp+Mkkt90y9be4rKBy+b9DlFhdmElVowlor6jf7QUQI9CGU1zyMzi7YsFmyG8w9W2Q2EmXOsEiQ+GSWX+qZi8sHLNn2u26gwI9E4tWChFoy1on6jP3SKBTXPIwuLtlwWbOR5mTksnGM1IfHJMNnWNxWLD14u6XM97o7CTDRORQFc8FowBov6jf7QKRbUPI+FXrTltWDTg8cxAxT6HKsNiU/Gyaa+Sdc+eBmSa/pcb1FhVqJxqgvgAteCsVjUb/SHTrGg5nks6KKNwQWbESn4wlxlqKhNB0zWN225vhEPf2optlzfiNUNZTNqElvq3LBfqhOVZrF2Y9EHLxum0ue186fPw4EetPUGAOgsKpwyuac+uCYn993hAcRatwKiOkJ5UgC/O3QSr7iqsGPBMnxQdQV2LFiGV1xVeHfoJIJ7ngfffzyvvzNVC1a5Eo8HB/HZi2fwqcFz+OzFM3g8OIi7KlfCdcuzqkR5s63LE/qOKj6GVKYeOoFecHL6G3nqoVOxVHcPnWJB1fM4uWizV+M2Xwdc8UjSj13xCG7zdUwt2pQUf4L3CAYyXLAN+M5qcs8YkgKeYy2gyKeB0KMPXrbkmj7XU1SYiWicktGNDNL2haoFY7K+0mCdwUWLyuexUA081BCnHYZr0poGiU+DoSsfvBzINX3O1O4o84gxFiZ3pQRwVmn7AtSCsVpfaeSHjuow1KSn9nksxKKNyQWbgTFqkxaJTwOiFx+8XMg1fc5KVDgTMcbC5K6EAGalbnUuWK6vNOpDR02YadKbhurnUeNFG6sLNkNjwCYtEp8GRQ8+eLmQT/q80FHhTMVYRdWKgk/ueQtgnTQlMF/Ub8CHjlowvdgx0HlkecFG6AcSn4SuyDd9XrCocBZi7O6LElp4S0En93yjG0zUrWYC1VcaA50sdoyAKgs2hkolCG0g8UnoCiXS54WICmclxgIDqLOXYUOgt2DRuHyjGyzUrWYK1VfqH90sdoyAwgs2FkslCPUh8UnojkKnz3MhKzEmxdBUtRK3DrYXLBqXb3SDhbrVbKD6Sn2jp8WOEVBqwcZ0qQShKiQ+CV2it6aqbMVYwuYubDQuz+iGLpsSGKzLi4sS2noDaPcGEY3FYLVY0MzoNV5I9LbYmRUdpZ/zXrBRqURRQ+KT0C16aqrKRYzFChyNyye6QU0J+XPKG8SOA+0I+3uw2DwR3Q8m7Hi7vRG7PPXYzFh0v5DocrGTgi7Tz3ks2KhUorgh8UkQGpCzGCtwNC7X6AbzXeSMc8obxM/2tqKFO4hNTal1zeex01uH7XtG8YWbN2CFDrfJVRq9L3aKMf1MpRLFDeVtCEIDdL1l4iUBHNvwKMQbn5z496L1c6fADL41nJrERQk7DrSjhTuIB5d0zLAUq7RF8eCSDrRwB7HjQDviYmYRPyOj6/uLke10tcYwpRJETlDkkyC0wMiWPnPUqaVP24tYmYijxuyE1dMIrudjiPEwk3VthaCtN4CwvwebmnrTWokBAM9NOD282NmDtt5ls5ee6KiGMC90fH8Va/rZCKUSRO6Q+CQIjZBqVsFx01/jur0vY9GFM2gXwwjyAhaaeVxjd6JGh5Y+mdSpTU/bS76zkL2fYBAJ7JZiCHgPwNX7O7br2jSm3RvEYnPXnJsoABMR0EZTF9q9wbTiU5c1hHmgV8usgqefC7RA0XupBJEfJD4JQiNOeYPY0RpFNHobNjidWBvvRiwBDCZq8KFlA665+rNYVlNR6GFmTDZ1auKi9ZBNVgTPvY/dnIjWqqaiqGvLhWgsBrcpnNGxblMYgdjMNGwx1hAC+rTMKmT6uZALFKoLL25IfBKEBiQ1kFwx2UAyITSHIjx2evvxxr4j+mkgiY1D2v1tXBg8Ad7mxjX+C+i2e9DlLIfI8TNtUjb9b7JVyRCrxYJgwp7RsYGEHVZLyvdU7BY2DFpmzUWh0s8FX6DouFSCyB9qOCIIlTFaAwnffxzim3+Kjq4PsD8ygpPBLgz6zmB17xHc230Qi8b9AC7XqQ34zsL8+59jIMO6tgHfWQh9RzX8RGzRXOvC+XgjhiLWOY8biljRlWhEc8piRfAeoe9aR4g1q9Ei2GY05aWiaPqZkSanqVKJypV4PDiIz148g08NnsNnL57B48FB3FW5Eq5bnmWuVILIH4p8EoTKKNpAUmAmoyV7Bn+P/+AlHHVeFj4VkohNkWHc0HcMHy28Cj2Osqk6taUde8lWJUNa6tzY5anHTm8dHlzSkfaakWRgp7cOdnc9WurcST8reA0hkRWFSD+z1OSkx1IJIn9IfBKEyijVQFJwpkVLdttduBgbSfqxjxewzWYHIuPYMHgG3ob1Eyl4jkc8GiRblQwxCzw2X9eM7XtGsa1zYlGS7PNpxU5vHdrk9dhyXfOMnY7IwkZnFCD9zNwCRWelEqpRLO4UIPFJEKqjRAMJC0yPlsB/HpY0x8gch51WK66OBNE4PoIOZwVcsgSz1QVXxJfR3yFbFWD5Qhe+cPMG7DhQihc7e9BomtjhKJCwoyvRCLu7Hltm2eGILGz0h9ad+rpcoBhcmBWbOwWJT4JQmbwbSBhherSEc1TAM9KJPklEjBeSjvPxAk7LETSMj2DI4kSLYEOi6Wa0HOsjW5UsWFHrQtPm9WjrXYZ2bxCBWBxWixn3zLO3O1nY6BMt08+6WaBcEpym0+9ivGMPvOFhtJktCFhL4JJhGGFW8OavAkDik8iKuCihrTeAdm8Q0VgMVosFzfM8DFmhUGNvrnXh7fZGDEXOz5l6n2wguYfRbvfp0RLZUQG7zYWqyAh6rS4gpWzMzwG1YnyqTi2+6vOo7j1ItipZYhZ4rG4oy6oMgyxsdIxG6Wc9LFAmI4FDfUcRHOnAXimK/YIAxM2wSy4IVS34wOTQvzArUncKEp9ExpzyBrHjQDvC/h4sNk+kAYMJO95ub8QuTz02z5IGZIFMxr5kQYkq4jTfBhJWSIqWcDyEqhbUeo8A0SAGLc6kCGilJOGKsB+LFlw1EZWwOMhWRSvIwoaYB0UWKCqmwacaG8f7UBkZxu8EHtuc5ZA5DhZJRFVkBLXeIxitXat7YcZS85eWkPgkMiLJp7IptQHiPHZ667B9zyiTPpWZjP3f3x2BYC2FPd6nuLDOt4GEFVKjJbK9HJbatagfbENlJAi/LCIGYIEk4WaJR9OCK8FPs0nR6w40AHRXb6br75pQnzwXKKrWJ06LBJ63e1Ay3IWdVuuUMIvxwkS2JRpE/WAb+PqNuhZmzDV/aQSJT2JeUn0qUyN3kz6V2zqBHQdK0bR5PTMCKpOx372gHT2/H8GZkSb81boTqHFc9ttTSljn00DCCumiJbK9HHz9RpSM+1A67gPEOG4LB9FYdRXwR69CsjiS3kOPtip6bQTQ43etKTpbUChNrgsUtesTp0cCr/FfwBk5Dh+f0t7IAYMWJyojQZSM+xB0VulWmOmy+UsBSHwS86Jnn8r5xi5JMnqG/LjT3YXxoAsDEVuS+FRSWOfaQMIMs0VLOB6yswqlllJsCPTilgVLYL7l2RnCc/r76MVWRfeNAIX8rhkWdzktKBj+PLmS9QJFg/rE6ZFAkxiHf5ZnTowX4JdFlI77IDurtBVmCl4Lumn+UhgSn8S8pPpUxiUOJ/wetPldiIocrIKMFk8QV3r8zPlUzuex6R+PQYyGsNpzEYfDvTjpr8Oacn/SMUoK61waSFiiqNK5RdoIoATpxZ2IlYfiqDE7YK1bD67iioKIt1wWFHqNfmdEFgsULeoTp0cCE4IZHnn2Y2MAZCkBQDthpvS1oIfmLzUg8ckijK2wp/tUtvtdeOt8NcajMSy2XIBLGEdQdOAXg4vwnrUSDosMMORTOZ/Hpj8UQyk/Cpsgwm0KYUxMH31k3gBeQ5KiJb2fQB46A1N4GHFHOfjKZRDj4Ynt+HQuxIq1ESAvxDjMx99E4KN/wfvRYRx0liFQWgNwHMShU3hv3I81iRiuG2pHwFWLWnu5tuIthwUFP9iu7+i3gmhRnzg9Etht92A1Z0aFJMKXYukGABYAHG9CqUbCTI1MSLG6U5D4ZAwWV9iTPpXtfhe2nalGi6Udn647ikrL2NQxQ7ESvOdbg3cubsBVCxOajm8u5vPYFCUJFn5ivIGEEw5h9vQHywbwc6LGYkYwQzZZMX7x9xiYvFaDXXD1HULLybf0Hw1C8TYC5ArffxyxA68gcHon3o4H8KbJBHMgiAp/J4REFF7BjEG7G/u4EvgiYVwjRrG1tALrNBRvWS8oeg8hevR1in5fYjIqKcgSGkPDaAj7YRLjSAhmdNs96HKWQ7wUtcw1DT49EtjlLMdamwubIsPYZrMnff8WSYSHEwB7uTbCTK1MSJG6U5D4ZAhW68uaa114q60RF85xaLGcwEM1+8FzybmQSssY/qjqY5wfL0Pf4ErExeVM1DDO57Ep8DzikglDsRJ0xetwvycw63uxbAA/G2otZli9VpVEs0YAxjIduTB5PRz3n4MoJ/B6iQc+XgAnA6bRAQQSYVyURfCSEzBZp3bBKo+HNRVv2S4omtrfQTdFv6cQLE7UR8dwb/dBSJEgzsgTNZkeGVjNmbHW5sKBquW44PDklgYX44CUQIMk4ovdB9FeWg1vyQJcFw8DkTB2Wq0TEVAZqIqFUG1x4bpwELc6alQXZmpmQoqqnOkSJD5ZgeH6spY6N1431WB4tAtfW3p0hvAEABlA77gDN1T2Ymd8AG29ASbS0/N5bHqcFnSOlOKjwcVwWK1YOYv4ZN0APh2qCUSGr1Ul0aIRgMVMR9ZMux4kswMXIcLHT1xrpYkIRCmBsyYLTFICzogfnLM6aResDmeFZuIt2wUFhs9R9HsastmJxaP9eIMT8f9s9qQu9ApJxKbIMG7oO4ZjVSuyToMn3QuxAEaiAcjhQSwyOWE123GzyYmro1F0SOMQxRjqeTOuKl2ABVVXanKfqJ0JKTZ3ChKfjMByfZlZ4LFoQSVGfX74IzxKBQE24fJjNiIK6Ak54UcV1tRZcaq3m5nayPk8NhN8KX4zei3ax+vwV2s6YOZnCms9GMDPQEWByPK1qiRqNwIYJXo8/Xq41teZ1J1ckoghAAlR3ow4Z4ItEYMpEQHMtqldsADtxFu2CwqAK0obnLSIcYS7fouPeA7vQ4SPm7mt7jabHVwkhM/2HUf18rsyvidm3AsV9eDK6yEOtsEy7seacAjX8VY4bOXYwLngtJfB0nQrEivu0kyYaZIJ0ZETSL6Q+GQE1uvL3HYeVeUmjJpqcTwYQgk/CgufQEwyYUwqhWB1ommBB26HhbnayPk8NqNl1XDYw/hkOIgqW1SXBvCpqCkQWb9WlULVRgADRY+nXw+p3cmcLCF26b8ljkcUCZgTEchmGzwyEJ/2mbQQb9kuKFDeBFfIm9F7G8kGJx2C9wh6h89iqKwRXxw6i/HgEIbNVvzebMUJkxkJjoNZlnBUjuM+mYet8SYkMrlmZ7kXJj2ExXEfjoSGUDY6iLtLa2C+/TmIdesQ1fh+KFZLJLUg8ckIrBvNWi0WxIQSrGqogn/cDX8ohpgkQeB5NDot8Dgs4C/ltFmsjZzPY7NjYAw7Drh1awCfipoCkfVrVTFUbAQwUvR4+vWQ2p0sczym24NLAGRZRoUkYjlnxlHH5eyIFg/sbBcUiRV3ocV7sOhscNJhOv0uEkOn0cRxOAMJfjmO0kgEnw/z+Bxvwl6zGSMmC+yOCpwRnFgaG5v/TTHPvXDJQ1h0VuFA2RJcHRxEA28qyEKsWC2R1ILEJyOwvqqabNwZjp1HZQmH8hJr2uNYro2cy2NT9wbwKagpEFm/VpVErUYAI0WPp18Pqd3JYyYLyqM8rLKEKMeDB8AD2BSNgrOVo+uS+NTsgZ3lgkKsWlGUNjip8P3HMdz+//B+YgzbSzzw8W5AdgOJCCpjYWwSE/gczPhdxQp0ly9GYKgz4zlFL/dCsVoiqQWJT0ZgfVU1X+MOoNPayGno3QB+OmoKRNavVaVRoxGAmeixAp32qdfDgarluKHvGBAZx68tVnCCBfViFJ08UCtz+KzEY4PVgf1VyyFyvOYP7GwXFMVog5PEZFpcDOFdk+my3yYHwGzDkNmG12UZciSM9WND6C1fnNWcwsy9MB9FaomkFiQ+GYH1VdV8jTt6rY00KmoKRNavVVVQuBGAheixUp32qdfDBYcHHy28ChsGz+DqSBBdnAWSlIA1kcAiwQrZsQD7F6yYsOMp0AM7mwVFMdrgTGcqLV7eCPdAEBZJRCzF8F3muCn7rJXB/qzmFBbuhUwp9mtBSUh8soIOVlXzNe7osTbSqMwpEGUJ3LgPfGgI144OYqGrYcJfL9NdiXRwrbJOoaPHinbap7keehxl8DasR+P4CFaMXkRLsA8N8TiGSypx2FaKppAPa8cGC/vAzmJBUWw2ONOZTIsHyq+APdCFqsgIeq2uicjnNCbts24a7kL1klsyvmYLfS9kSzFfC0rCybI8x86pbBAMBuF2u9EdCMDlMrawmYxGDKRbVTHi+xcXJbT1BtDuDSJ6qTayOcfayOT3isFqseT8XkQyfP/vEdzzfJLA4MLDl+xLRrAmFsF1MCFgK0WduQTVVc0w3/wMpNq1Gb4/+9cqs4hxJN75S7w7T/T4Nl8H7qpcqWy3u0p/e97r4Zo/BScnIKR5YLPayU8Awocv4Wen3sYHVVeACw8j5j0CrziOQYszKQJqkUR8acyPP3E1wXz/v2V+7xfyXiAUJxgMosHtRmAevUbik0XEOIS+o4afpE95g9hxoB1hfw8Wm7vgMoURTNhxPt4Iu6cemymKmjfTBUF7xIfhQC/kRAQLZRlxAO+ZzTglCFggSdgkythkr0TZ7X+LxKr7MvsDRXKtqkG6xcEk06PHrlueVVTECz2t6P7NN/CKq2reSNPjwUE03P6tzBs86HowHJbWV/HOsdewY8EyAJhawIYjQfhlETFM7LHu4QQ8IPH4zDWPIvqH/zOrv1Goe4FQHhKfBNOc8gbxs72taOEOzlk/+oWbN2AFg53zukKMQ+g9BPznN3BypAMn4uNo5UV8ZCvFuHC58sYqJvBYKIAttgVwbvkJpLqrCzjo4qAQ0eNUMTEXn714Bnev/iJiGx5VdAyEfki7WLlUusON+yBLCXC8CaWWEvx5XETDHX+XUzd6UWVSDLCl7mxkKj6p5pPQnLgoYceBdrRwB9N2zlfaonhwSQe2dQI7DpSiafN6SsHng2AGOAHdHIefWEw4AaDXWjajZisqmPBTpwdrx4exZt93gC/8WPcTIesUon5MN93FRkNJwaGheElbP37Jf1N2Vk0cJMtY7+vIq8GwWGopDbGlrgKQ+CQ0p603gLC/B5uaetNaNgEAz0101L/Y2YO23mWGsD8qJEL/MbRHhjEQC2HQ4pwhPCfxCQI+4Xksu9iOUoa9JQ2Fxlvq6am72CgoKTg0Fy9aNhgafHtJo2ypqwQkPgnNafcGsdjclZRqT0elLYpGUxcz+8TrGTEWwmh8fKJGK8UmJZUhnke/GIWHxKch0Vt3sd5RUnAUSryQxZACGGhLXSUg8UloTjQWg9sUzuhY1vaJ1yuCxYlSSZzaZ3suPDIQ5k1spVsNXCOlNUXp01oolBQcBRYvxZIWVwsjbamrBCQ+Cc2xWiwIJuwZHcviPvF6RKxZjRbeigWShL45jpvccztitjOTbqUaKYUhn1bNUFJwMCFeDJ4WVxO9bCOqFSQ+Cc2Z3Cd+KHJ+ztQ7y/vE6w2xdi2qq5qx6Xw/2sUEosLMW5+TZWyKRmG1uFFjL2Mi4kU1UupAaVRtUFJwMCteWMtKsDaeyWFRo18SJD4JzSmGfeKZQzDDfPMz2DTwe4RCF/FTpwc+4XLtZ4UkYlM0imsFB+LWElRXLi+8+KQaKVWhNKrCpBE98sV2jGb46/MJDhbFC2tZCdbGMx1q9EuGxCehObRPfGGQatei7Pa/xZZd/xNrx4fxCc9jiOfhkYHlnBlWixtxawmudi9hIt3KRJrR6FAaVRFmEz0rQ8O4JhrEuZIqXHB45nyP+QQHa+KFtawEa+NJhRr9kiHxSRQE2ie+MCRW3Qdn2WKs2fcdLLvYjn4xijBvQsRsR429DNWVy5lJtzKbZiSIacwlevYFLuCqnn58qvcI9tWtQY8jvWtHJoKDKfHCWlaCtfGkGyI1+iVB4pMoGCtqXWjavB5tvcvQ7g0icGmf+Htob3dVkequBr7wY5T2HZ2wU2I03apImpHR+i/CIMwjegKuWuwrPY9rRgdx7cUz8Dauh5hyTWcqOFgSL6xlJVgbT/pBUqPfdEh8EgXFLPBY3VBGPp5ao4N0a75pRpbrvwhjMK/o4XjwC1aiPfYJ1oYGsDLYj+Pu2qkfZyU4GBIvc2Ylpm29OSolcCo0gqaTb0+IYZXGpJcsCTX6XYbEJ0EQTJJPmpH1+i/dQpHkJDIRPbK9HJFF12CwqxUPDl9AYzSUs+BgRbzMlpXgwsMQB9sQjgQnNrQAcD4eh6/tLdiiftXGxmIz1mxQo98EJD4JgmCSnNOMOqj/0iMUSZ5JpqJHtpcjWNEEd8163F21Ii/BwYJ4SZeV4MLDiHmPwCuOY9DinNpJTZRD+NDhQUzFBR9rzVjzooPMk9qQ+CSIHIiLEtp6A2j3BhGNxWC1WNBMtarKkmOaURf1XzqDIsnpyU70AFzVCsQ2PAogT8FRYPEyIyshSxAH2+AVx9FrdQGXbrvJTSuOli5Ap6NctQUfU81YREaQ+NQSSlkZglPeIHYcaEfY34PF5oku/WDCjrfbG7HLU4/N1KWvGLmkGfVS/6UbKJI8K8UqelKzEhj3IRwJYtDinBKek5tWcLZydDnKVF3wsdSMRWQGiU+NoJSVMTjlDeJne1vRwh3EpqZUf9Lz2Omtw/Y9o/jCzRuwgnZmUoRs04x6qv/SAxRJnh1Di555giXTsxKHEuO4IItTqfapTStMDuyvWj7V4a/ago+hZizN0WlQi8SnBlDKKjNYT2XHRQk7DrSjhTuYdmemSlsUDy7pwLZOYMeBUjRtXs/EuA1BFmlG3dV/MQ5FkufAoKIn02DJZFZiXcce7IvF0Y3Q1KYVnK0c+6uWzzDXV2vBx0ozlpboOahF4lNtKGWVEXpIZbf1BhD292BTU2/aLUEBgOcmdmx6sbMHbb3LyEKqADCdCtVhlEL3kWSVv3OjiZ5sgyWmu7+LJb/5W4TbfokSRxnighlHHWXocpTN8DQF1F3wsdCMpRV6D2qR+FQZSlnNH9HUSyq73RvEYnNX0vjSUWmLotHUhXZvkMRnAWA1FarXKIWeI8lafeeGET05BksSLZth8x7Ex66qwi/4iqGT3ABBLRKfKmPUlFWmKfL5Ipp3bViOd1tP6yKVHY3F4DaFMzrWbQojEIurPCIiLQymQvUcpWA6kjwHmn/nBhA9uQZLWF3wGRUjBLVIfObLPCkd3aes0pBpijyTiOYP3xuGHB/H4yvZT2VbLRYEE/aMjg0k7LBa2FppFhNMpUJ1HqXQpbDQ+XdeKHIOljC44DMyRghqkfjMg0xSOnpOWaUj0xT5fTetw3sH549oDh2L4PBYHdyW2Jx/l4VUdnOtC2+3N2Iocn7O1PtQxIquRCPuoW73gsJKKlT3UQodCgvdf+cFIp9gCVMLPoNjhKAWic8cyTSlU9a8GS2CTXcpq3Rk0+392h4LbPGL2HTF3BHNjZ5OtI2U4qTfjTXl/jn/fqFT2S11buzy1GOnty7t5wcASQZ2eutgd9ejpc6t/SCNTrbNIwykQo0QpdCbsDDCd14I8g2WsLLgMzpGCGqR+MyFbFI6Xb9FdXkTNvjasbd8MRrGR9AQ9sMkxpEQzOi2e9DtKGMrZTUL2XR77z3SDY89kEFzTgwNFi9O+svnFZ+FTmWbBR6br2vG9j2j2NY58TmTI79W7PTWoU1ejy3XNZPNksLMmmn4/c9QY/PAseBKJGxu5jrIjRClAPQlLIzynWuNIvW9DCz4jI5e67CnQ+IzB+ZM6cgSuHEfuHEfDsYjWN/9IRpXbcEdvk6sPLMbfbKENojwc4BHBq6BgM9wPOomIwcMTeCpZNPtvdjcheFY+bzv6XFaYOFE+CJzf25WUtnLF7rwhZs3YMeBUrzY2YNG00TNayBhR1eiEXZ3PbYwYAtlNGbLNHDhYewZ+D3W9h/BNd0fostdD9FsY6qD3AhRiil0IiwM9Z1riC7re4sQI5wnEp85MFtKhwsPQxxsQzgShF8WEQOwPxaD+8hPwIkJ9IoxvM3L6OJkxABYOOCULOFTMKOGAwC5AJ8mc7Lt9u4Zn19IexwWhLgy9I65IcnQRSp7Ra0LTZvXo613Gdq9QQRicVgtZtzDkCG+oZgl08CFhxHzHsF5cRx7naW4PxbDNYkwdtReiQ8SMWY6yI0QpdAb9J3niA7re4sSA5wnEp85kC6lM/kg9IrjGLQ4p7YZ60AIH8aD8IoxLLOVo7asHpIUgywlwPEmiI4K7LaXgxs+z3zXZTbd3gnBBb9UgaGIdSpSKkky/OMx+EMxiJIEgechmUoRsK1AhC/Hts4R3aSyzQKP1Q1l5OOpAWkzDbIEcbANXnEcvVYXwAE7rRyujgTROD6CDmcFM93MRohS6A36znNHb/W9xYrezxOJzxyYkdJJ8yCcxCPGMSJJ+DenG/fHwlg/NoTehvWQOD4pzqmHrstsur0v8ktQXVk11ZwzOh5D16AfYjSEUn4UFj6BqGjCL3x/gAuyEw/eshInz7splU3MIF2mgRv3IRwJYtDinLrffLyA03IEDZfEJzPdzAaIUugO+s7zQk/1vcWMns8Tic8cSE3ppHsQAkCFJGK5BPwnzyEqmGZEZqajh67LbLq9HZ4G3L9+OX6xL4J/P5XAFfIRLDZ7Ue8KwSaIGIqV4D3flfDzC3F9yVkcarPjvj9YB1GmVDaRTNpMw7hvorTlUoZhEj8H1IqXHRFYua/0HqXQI/Sd54lO6nuLHp2eJxKfOZCa0kn3IORkGZuiUfAmC05g4mGYGplJhfWuy2y7vZcvdEG+aR3+4edhlMUcuNa1AO7xEAIJJ7ridXBYrfhScx+Wu4LY1hnFe4dK8eTm9ZTKJpJI1zwiSwmkc4b1yEA8ZbXPyn2l5yiFXqHvnCDYhMRnLqSkdA7GI0kPwgpJxKZoFNeaHPidrRTCWO/Uz1IjM9PRQ9dltt3eoiRjqTuKTRXD8I7XYUzk4RAk3O8JYKUnADM/UXzAwg5GBJukax7heBMsKcdVSCKWc2YcdSRfP0zdVzqNUuga+s4JgjlIfObI9JTO+vP7sD8WQwdC8MjAcs4MzlaO/VXL0SvH4Qn1o0+aiIymi8wA+uq6zKbbu90bRJOlCzfXXJzzPVnYwYhgk3TNI7KjAp6Rzqn7ajLTwNnK0TVNfOrpviIIgigWSHymI8NdVKZSOke2wf3hP2G/1Y4xsx1HHWXocpRB5HhAlmC3uVAVGUHE7EwbmdFj12Wm3d7Z2jMVcgcjglHSNY84KpLuq02xiUzD/qrlE/cd9HlfEQRBFAMkPlPIZL/2pAJ1wYz42gdh8R5EeOgk9qbaenA8hKoW1PUexoaQH1ZnzYzIjJG7LrOxZyr0DkYEu6RrHhk1lcKRGEFNfAxhRyV+W92CCw4PAOPfVwRBEHqGxOc0Mt2vfYZp9Ty2HqUmBzY4qnALZ0PUVoa7Bs8VTddlNvZMLOxgRLBLuuYRUySA6OBJ9IZHsHZsEE0hX1HcVwRBEHqGk2WZ7W11AASDQbjdbnQHAnC5VBInYhyJd/4S785jSnybrwN3Va5Ma1o9GTUdSGfrUbEUlnV/Ck5KQEjTdcmqsXy+xEUJL/3qIBZHds9pz7Stswnnbbfiyc3ryVaJyA4xDqHvaFHdVwRBECwSDAbR4HYjMI9eI/F5CaGnFd2/+QZecVXNux3b48FBNNz+rfS+gfQgnMHpviC272lFC3dwTnumP7ppHRKSjHZvENFYDFaLBc3k80kQBSUuSmjrDdB9SRDEvGQqPintfonZ9mtPZV7TarL1mEEm9kzXNi3CuwdPI+zvwWLzxM+DCTvebm/ELk89NtMORwShOae8Qew40G7M+zLDxlKCIJSHxOcl0u2iMhusmFbribnsmQSewy/3HZqIjDalRkbPY6e3Dtv3jOILN2/ACqoJJQhNOOUN4md7Ww15X2bdWGpkSIQTBYDE5yXS7aIyG0yZVuuIdPZMkzWhLdzBtDWhlbYoHlzSgW2dwI4DpWiimlCCUJ24KGHHgXZD3pc5N5YaEBLhRKHQx2yhAWLNarQINrjikTmPI9NqZWnrDSDs78Gm2t60zUgAwHMTOyCFAz1o6w1oO0CCKEIMe1+KccRat2J3eADvVzTNKLMKmm14v6IJu8MDiLVuBWbZjc4ITIrwd4dO4hVXFXYsWIYPqq7AjgXL8IqrCu8OnURwz/Pg+48XeqiEAclJfL788stYsmQJbDYb1q1bh3379s167C9+8QvccccdqKqqgsvlwsaNG7Fz586cB6wWU7uoBHrBzdKDNWVaXbG0qMVnXJRwrHsE23/XhZ98cAbbf9eFY90jiIuZRY6n0+4NYrG5a04bJiB5BySCINTFqPel4D2CAd9ZtLrr0jqaAIDMcWh112HAdxZC31GNR6gRrIlwMQ6hpxWW1lchfPjSxL97Wg0t/oudrNPub7zxBp566im8/PLLuPHGG/HKK6/grrvuwsmTJ9HQ0DDj+A8++AB33HEHvv3tb8Pj8eCHP/whNm/ejI8//hhXX321Ih9CEebx6iTT6gmUbkCgHZAIgj2Mel8q1liqcwTvEfRmKMKv8Z1Fg4rfA6X+i5OsxecLL7yARx99FI899hgA4MUXX8TOnTvxve99D88///yM41988cWk///2t7+N//iP/8CvfvUrtsQn0u+iUixm8JmgRgMC7YDEGNR8QMC49yU1lk6giQjPYC4pyvpbmmMBZCk+Y7EYDh06hGeeeSbp9TvvvBP79+/P6D0kScLo6CjKy8tnPSYajSIavSxsgkHtUjrpdlGZ7tVZrBFPtRoQinYHJAYnIIpAEJMY9b5UtLGUwXs4U9QW4RnNJVUrklL/qRHYydQ/fB24q3Vr2o1d9AbNsZfJSnwODQ1BFEVUV1cnvV5dXY3+/v6M3uO73/0uQqEQtmzZMusxzz//PJ577rlshqYs5NU5g6kGhKb5GxBe7OxBW++ypK722Wipc2OXpx47vXVz7oC001sHu7seLXXuPD9J4WFxAirKCAQxK0a9L8Wa1Wg58SY+iM8d9ZuvsZTFezgb1HR3yXQu8bR8lpnUvxbQHJtMTg1HXMqFIsvyjNfSsW3bNnzzm9/EG2+8gQULFsx63LPPPotAIDD1T09PTy7DJBRErQYEs8Bj83XNaJPXY1tnE4Yi1qSfD0Ws2NbZhDZ5PTZf16wbO5fZYLLDlLXmA6LgGPW+VKKxlMl7OEtUc3fJYi6RD/0IbWI449S/rpu/aI6dQVaRz8rKSgiCMCPKefHixRnR0FTeeOMNPProo/jZz36G22+/fc5jrVYrrFbrnMcQ2qJmA0ImOyBt0fNOKpOkTECspJlYaj4g2MGQ92W+jaWM3sPZMiXCh06m/RzANBFeuTJj8ZnNXHJrz2GMWjOrK9Z7/S3NsTPJSnxaLBasW7cOu3btwn333Tf1+q5du3DvvffO+nvbtm3Dn/7pn2Lbtm34zGc+k/toiYKhdgPCXDsgGWUPaVYnIOoAJmbDiPdlPo2lrN7DWaOSu0s2c8kAZLiiYxm9r943dqE5diZZd7s//fTTePjhh7F+/Xps3LgRP/jBD9Dd3Y0nnngCwETKvLe3Fz/+8Y8BTAjPP/7jP8Y///M/4/rrr5+Kmtrtdrjd+qgTIrRpQEi3A5KRYHUCog5gYxEXJbT1BtDuDSIai8FqsaA5D7FoxPsy18ZSVu/hXFDD3SWbucRrcaIlFsLePOtv9QDNsTPJWnw+8MAD8Pl8+Na3voW+vj6sWrUK77zzDhobGwEAfX196O7unjr+lVdeQSKRwFe+8hV85StfmXr9kUcewY9+9KP8PwGhCUZtQNASVicg2lrWOCjtw2tocmgsZfUezhWl3V2ymUtiZjtqLC5sCPQqmvpnEZpjZ5LT3u5f/vKX8eUvfzntz1IF5Z49e3L5EwRjTDYgbN8zim2dE13tyT6fVuz01qFNXo8tOmpA0BJWJyClOoCJwqKGDy+RDKv3cF4o6O6SzVzSbLLDevUjuLXtbcNv7EJz7ExyEp9EcWLIBgQNYXUCUqv5gBl07MeYKWr58BLJsHoPs0K2c0l81R/BVb3S8Bu7GH6OzQESn0RWGLEBQSuYnYAMvLWs3v0YM0UtH14iGWbvYVbIYS7R3cYuuSxmDTzH5gony7OYnTFEMBiE2+1GdyAAl4uiaoR+4ft/j+Ce59MaDU+fgFy3PFsQo/lY61YMpItA6FCozWXqnPxd69/UefvvuhA79yYeW3Zq3mO3nlkB6xX3Y8v1jRqMzHiwfA+zgtHmkkny/VxG/V6mEwwG0eB2IzCPXiPxSRAaw/QEJMYh9B2FkCYCoasUtRhH4p2/xLvzRKhu83XgrsqVzPoxZspPPjgDd992bFnSPe+x2zsbEFj4AB7+1FINRmZMmL6HWcEoc8klFFvMGux7SSVT8Ulpd4JZlLaMYQWm00wG2VrWMH6MGaK2Dy+RDNP3cL4oVSNtkLkEgLKbCxjpe8kDEp8EkxjeMoYmIFUxkh9jJmjhw0ukwMI9rHAzXbHUSGdLsS1mtYDEJ8EcZBljUDTsOmfBj1HLyD358BYfSgvFudLKH8Qj2DB0Erfued4QNdLZUmyLWS0g8UkwBVnGGBOtIyqF9mPUOnJPPrzFheJC0SB71qsFC4tZo0Hik2AKsowxHoWIqBTSj7FQkXvy4S0SVBCKlFaem0IvZo0IiU+CKdq9QSw2d81ZtwZMREAbTV1o9wZJfKpNPunyAkVUCuXHWOjIPfnwakshmiLVEIqUVp4b2lxAeUh8EkwRjcXgNoUzOtZtCiMQi6s8ouIm33R5wSIqBTJ1ZiFybxZ4rG4oK7pFmdZCsFBNkWoIRcOklVWqK6fNBZSHxCfBDHFRwtBYAr4RHmdsAQg8D4/TAo/DAj7Nk5wsYzIgj8lYiXR5ISMqUs0quG55RtOt+yhyXxi0FoKFbIpUQygaIa2sal057VCkOCQ+CSaYfHhc6LuAxKgdIUc/SoQouvyluGB1onGBB26HZep4rSxj9Ow1mtdkrFC6vNARFa39GClyrz1aC8FCl1aoIRT1nlbWoq68EItZI0PiU0k0tJIxEtMfHo+2ePGj0/Vojy7FQzX7EZNG0RNyosMbR9PCKridFs0sY3KOpqS7DhasBAAIF09qcm3kOxkrlS5nIqKSox9jLgsPMnvXlkIIwUKXVqghFHWdVtawrtzQmwtoDIlPhSBz3txI9/D43JIBbDvdjNf7gU9XHMVSVxBng0DXoBk13CLs6l+kumVMrtGUdNdBfXQMy0M+jEJGe0klgpYSda8NBSZjpdLleo2o5Lrw0LPZux6j/IUQgoUurVBFKOo4rax5XTkLmwsYABKfCkDmvLmT7uHR7A7iwWXAW+db8EJvExrNvXDwYbSHFiI4shqV1UtUtYzJNZqS7jqoHx9BTbAXP5Ej+AQJ2CMc7GV1aJAAcWwQY+d+g2UXPoHlhq8gserzikRBlZiMlUqX6zGikk8aV69m73rdUawQQrDgpRUqCUW9ppWpU1+fkPjMFzLnzYvZHh7NniD+cvUoTvrdOOmvQ1TkMRSpwqL61fjqphWqRmJyiqbUlcy4DgRZwobBMziQGMc2uxMyONw0PoLNnfshm+w4IydwjAMaw4O4Ydf/RM35D2G57om8J3clJmPF0uU6i6jkm8bVg9l7aoTTH5bQ0dONjc5PcLfOdhQrhBBkobRCLaGox7RyoevKidwg8ZknZM6bH3M9PMy8jDXlfqwp9wMAHCYRgRKz6g/sXKIpV3NnZ1wHjaFhSJEgdlqtkDkOKxJx3JYQcSgRwS6LBT6rEwBgsdpwIDKOW7ytuGXPSN4RciUmYyXT5XqKqCiRxmXZ7D01wlkqhNE3KEIOl6BXEjAUtSZd96zvKFYIIchKaYVqQlFnaWUm6sqJrCHxmScU8s8PFqIIqeQSTUl3HTSE/Tgjx+HjLTDJMu4Jj+GQHMd2XoJTigFwAABivIAuTsZuixVyeCDvCLkSk7HS6XK9RFSUSuOyaPaerpxgeCyKFXEvFtYEsce/CttON+PBZROZh0lY3lGsEEKQqdIKnQlFNVCtrpwaiFWFxGeeUMg/P1iJIkwnF0Gc7jowiXH4Lz2YrkzEYRXjeFsARBGQZTnp2BgASRYViZArMhmrkS7XwYNSyTQuS2bvs5UT+EMxlPKjWGQP4CHbfrzeP1Fr/ZerR2HmL1+jrPqSFkII6qG0ophQo65c1QZiErUASHzmDYX884OpKMIlchHEwsDM6yAhmOG59PxuScRxRhYxyHEoAcBxHKbLTwsAjjcpEiFXajLWU7pcKeZaeEiSDP94DP5QDKIk4dwID5TGERcl5gXGbOUEoiTBwicAADwn49MVR/FCbxNO+t1T5S6TsOhLmosQVKKrn+XSiqJD4YWymg3E5IpzGRKfeaJXKxlWYDGKkIsgFrmZ10G33YPVnBkVkgirLKGfA3hZghUcZNPla8UiifBwAmRHBQAFIuQKTsZ6SZcrxWwLj0Aohq5BP8RoCKX8KEKiFR3B62HqasNLvxpltht8knZvEI2m8+ATQXQMTIhngecRiUuQpcuPgUrLGBrNvTjpr5shPln1Jc1GCCrZ1c9iaUWxothCWcUGYnLFSYbEZ57o0UqGNViLIuQiiNNdB13Ocqy1ubApMowoOHhkwC4mIJiswKT4lIGqWAh2W9mU+FQiQq5o1FIH6XKlSLfwCIRi6OgbhAeDqHeFYOElvN5/A67wiPjS8r34TX8ts93gk1wYCsIWHESX7EUpPwoLn0BcMiEcd2Iw5kSFJYJqewQA4DaFMCYmCycWfUmnk4kQVGMnJJZKK4odJRbKqjUQkyvODEh85ovOrGRYhbUoQtaCeJbr4EDVctzQdwz9ET/ckox6kwkjNg/ATUQ8q2Ih1AoOCFUtkDle0Qh5sUUtlSB14XFHzQX0D16EB4NY6grCFyvBexfXoC3WjAeX96PGEWG6GxyYaDQ63unFWjGGq1xe2ITLy4dwYhSnRixo85fAIkgos8QQSDjhEC6XkLDoS5qOuYRgobfEJDQiz4WyWg3E5IozExKfClCMtXFqwFoUIVtBPNt1YLa68YfxOGRewn+RE3gzFoE5HoWHE2C3lU0IT3u5OhHyIopaKsX0hcfzpzrhGj+GZmcZ3g/a0RWvg8NqxYPL+9HsnugIZ7kbfFJ0rXWcQmi8EmOiHTZhbOrndpOIlrIQ2nwSjvncWOKOoyteh/s9AQDGaZ4p9JaYhD5Qq4GYXHFmQuJTISjKZEyyFcSzXgfVV4If7sD9H/0ryqLDOOgsQ6C0BrKjYiriSRFydphcePzfnaXoPTuGqLMUDkHC/Z4AVnoCSZ3gALvd4JOi66tXnMOPTtfjPd8aPFSzHzx3efxWE48mTwytPh6v9v4BusQFOOmXccBXbZjmmUJviUnog2waiEtlEX0hDnt+1zVv4xq54syExKeSUJSJAGa9DsSG61FScxU+3boVV/vOoi3kR3A8SBFyRjELPCpLTLiiuh9blnTPezyL3eCToqvGEcHnlgxg2+lmvN4PfLriKCotlyOgMc6JTyJX4QRuxLqrWjBmFwzVPFPwLTEJXZBpA7EcDKJ0JI53E2EIJW/O27hGrjgzIfFJEBpCEXJ9weImCNkwXXQ1u4N4cNmEj+cLvU1oNPfCbQohkHCiK16HvngFVq9Yiv9v04oCj1p59H4eCW3IpIE4EIpi/YXTqLA4cf+KblQ6Li9ULo534q3zNXjhFwNY1rgE9ZWlaK514aoFq9Ai2MgVZxokPglCayhCrhtY3AQhG1JFV7MniL9cPYqTfjdO+uswJvJT5QQfDdngqCwt4GjVo9DnUQlvUUID5mkgLomFsaLnFG4TOKxatRDcNOEZCMXQP3gR6/hTCIn9OHlqFSr9Ibzd3ojfuBfiYVsDNgTOkivOJUh8EgRBzAKLmyBkQzrRZeZlrCn3J/l4DkWsuCCyJ56VopDnUUlvUUJ95mogbogL8HML0LjSDc7tnPqdJDs2dwhXlIzghd6FuL4ygPsdEzZe/xHegM9ww+SKcwkSnwRBELPA4iYI2aB38awUhTqPaniLEuozW3nUTt8C9A2141OVZy8fK8noGvRP2bFxAGxC8mYNkzZe/ynfhy2Oj3DNCLnikPgkCMLw5JP2ZG0ThGzQu3hWEq3PI3mL6pw05VEXPjgDt/lY0mH+8RjEaAj1rhCmn+LpmzVctvFailMb/wZrTd1FX/NP4pNgFqqTIpRAibQna5sgZIOexbPSaHkeyVvUeKRrXPOHYijlR5M2bwAwY7OGSRuvtv71uOp6qvkn8UkwCdVJEUqgZNqTtU0QskHP4llptDqP5C1qPNLVUIuSBAufSDpuKFaStFnDJKk2XsUcYCHxSTAH1UkRSqBE2tNIDweWxLORvtfZIG9R45GuhlrgecSly1JKkjm851sDh9WKlSnic7qNV7EHWEh8EkxBdVKEUuSb9iz2h4NaFPJ71VL0kreo8UhXQ+1xRtHlL0VEHMWYaMd7vjVoizXjweX9STuhTbfxogALiU+CMahOilCKfNKe9HDIj9lEnsBz+OW+QwX5XrUWvYX2FiXUIbWGukHowthoDXb6rsK4UAGH1YoHl/ej2R2c+p3pjhLLakrx8jufFH2AhcRnEcNi6ovqpAilyDXtSdH3/JhN5L3V1ohzASvuLD+KB1d0a/q9FmIxQTZXxiW1hnpoaBTHO3ux1nEKj1xxDjWOyNSxqY4SZ/pHKcACEp9FC6spRaqTIpQi17QnRd9zZy6Rt6dvBD8dLEOTfASj4yVwOy0zfl+N77VQiwmyuTI2qTXUp7wN2HGgDP+3q25OR4ntv+uiAAtIfBYlLKcUqU6KUIpc054Ufc+N+UReX9iOa91nsdjcja7BWqyyV4FPo+6V/l4LuZggm6viIVNHCQqwTEDis8hgPaVIdVKEUuSa9qSHQ27MJ/KiIgeXMI56ZwjHgyH4x90oL7GmfS8lv9dCLybI5qp4yMRRggIsE5D4LDLUigIoVT9KdVKEUuSa9qSHQ27MJ/Ksgoyg6IBNEFHCj8Ifis0qPpX8XllYTLBkc0UUFgqwTEDis8hQIwqgZP0o1UkRSpJL2pMeDrkxn8hr8QTxi8FFGIqVwMInEJOktMcp/b3SYoJgCQqwTEDis8hQOgqgRv0o1UkRSpJt2pMeDrkxn8i70uPHe9ZKvOdbg6vtJ2DmZy4c1fheaTFBsAQFWCYg8VlkKBkFULN+lOqkCCXJJu1JD4fcmE/kmXkZn1sygB+1r8T58TJ8viKY9HO1vtdiWUywaJ1HpIcCLCQ+iw4lowBqd5FSnRRRKOjhkD2ZiLzlriCqShbh48DNGB2IYPFwt+rfqxKLCdaF3Vzeqq+barBoQSXcdp65cRczxR5g4WRZluc/rLAEg0G43W50BwJwuWiyz4e4KOGlXx3E4sjuOaMA2zqbcN52K56cI1q5/XddiJ17E48tOzXv3916ZgWsV9yPLdc3zjouNSZ31h8aBNskXz8TDwe6fmbndF8Q2/dcKsOZQ+T90U3rkJBkTb/XKYEWSL+YmK02PVXYuS4Ju/PxRtgZ2GY1qfRp2nfe7nfhp+dq0T8qo9riR1O5CXGhhJlxE8YkGAyiwe1GYB69RuKzgBRKGGX6gNhyy4Y5J6effHAG7r7t2LKke96/ub2zAYGFD+DhTy2d8TO1JnfWHxoELQ6MSK4iTwuyXUzMJuyA5LmyUNuszhZMaPe7sO1MNVos7dhUcRT+CI9RUy1WNVRhOGYr+LiZR4xD8B6B0H8MYiwEweKEWLMaYu1aQKCGtLnIVHxS2r1AFHKHIaVSikrUj6pleK+6kT5NTnmj1j1AgrawsJxOzKaUh3VPZCB96VNc4vDW+Qnh+VDNfvCcjFJBmPJWrSzhCj5uluH7jyPWuhW9vrNoEyMIcjxcsoSWE2+iumIpLBv+HFLNqkIPU/eQ+CwALOwwpMQDIt/6UbUmd7UfGjQ55Y+aiw4Wt40tNoxQr610Tbsai6J01nkn/B6MR2P4dN1R8NxEYjPVW5W2h00P338cwT3/G7vDA2h11yFotk397IN4BBuGTuLWPc/DdcszkGquKuBI9Q+JT41RShgpMZHl+4DIt4tUrYYlNRuhaHLKH7UWByws6gjjoKQnslqLonTWeW1+FxZbLqDSMpb0eqq3Km0Pm4IYR6x1K3aHB/B+RRNkLnliCppteL+iCfB14K7WrTDd/V3KcuUBxdo1ZkoY1c4vjMKBHrT1Bmb8/JQ3iJd+dRBvv/8+YufehLtvO2Ln3sTb77+Pl351EKf7gmneVXkmu0jb5PXY1tmEoUjybiVDESu2dTahTV6PzWm6SHOZ3DNBrfdNnZymC0/g8uS0OzyAWOtWQKRtF9OhxD2QSqqgTT33k4K2hTuIHQfaERfTG5wTxCTRWAyuLDyRo7N4Ik8uihZHduOppr14bNkpbFnSjceWncJTTXuxOLIb2/e04lSm89A00pU+TW5jmkpMMkFI8Vada9zFhuA9ggHfWbS662YIz0lkjkOruw4DvrMQ+o5qPEJjQZFPjcl3Nc1adCef+lG1tr1T630F7xH0Zjg5XeM7i4a+oxAXrc/ovYsJNXbZUtv2iyg+lKhpV7sEKF3pk1WQMZJw4nCwAW2hOkREEwROhBlx3FItZDTuYkToPzZRRpUSVEglaLahTYxgCc3veUGRT43JZzXNanRnRa0LT25ej3tuvQ3WK+5HYOEDsF5xP+659TY8uXn9rOkktba9U+t9s52caGWcHqUiStNRLdpNFC3NtS6cjzfOyOikMlnT3pxmsa9GlH86LXVu2C+VPkmXfGvsJhE7h1Zjm/cahKIxOKVBBMIJfBxswqsdV6I94Jp33MWIGAshyGUmiYIcDzEWUnlExoYinxqTjzBiObqTS/2oWtveqfW+NDkpgxqLA7Wi3UTxosTOSGpE+aeTaqDfVBLEoQE7rnP+Hre7PsI1pR0IJUyIwY6Y6fd4P3A1tp1uxgPLgMPDlbre0UlpBIsTLjmzgI1LliYcTlQek5GhyKfG5LOaNlp0J92qPZVctr1T631zmZyImSgRUUpFrWg3UbzkW9MOqBPlT2Wy9KnDcgv+8eRVKBe78JmKgxgTHTg+Wo+Q7ILLYUOtYxwP1ezHUtNpfPf4MpyQ1s067mJErFmNFsEGVzwy53GueAQtgg3iwjUajcyY0FWnMfkIIy0mMi1RYnLX8n1pclIGJRcHcVHCse4R9A6P4+OhKhzqiWN4LAppljemVCORDZPC7rztVrzYeTO2nlmB7Z0N2HpmBV7svBnnbbfOuRmHVouiFbUu/OHVS9HgBj5VF4LZ3YjyioUI2xrRIy3BuVA5zo2W4FTQjUWWi0jIZqxrIdux6Yi1a1FdsRQbAr3gZtl7h5NlbAj0orpiKc3veUJpd43JZ59hI0Z31NpDW433nZqchk6mteIApk1OlStpckphuj0YZ7Jjx+BaXAjZ8cgV51DjuCzoM9lrG0i2r6k3daEz4cAHvU4gdApmmxONCzxwOyxTx+cS7SaIfDyR1SoBSsfZgTFcWeLFunozgInrW5Lc8I/H4A/FEJMkCDyPNU4LbjSPIBSlpHESghmWDX+OW/c8D/g6ZljpueIRbAj04lZ79YSXM9ks5QWJzwKQqzDSciLTErV2RFH8fWlyyplUn8OlpjBKSyw46KvEVw5sxLpyH5aW+jNeHKRzfWivdmHb6UacDEdxpXwWHd44mhZWwe20ZCxoCSIduXoiK1E3minp6p55nkN5iRXlJcnZH4+Z6p7TIdWsguuWZ3BX61Zck7qJiGBDdeVKpjcR0dPubrS3ewHJdp/h2fbxnY4kA9s6m3DediuepG3TVGFyh6OBdJMT7XA0g7n2x744bsFb52uwP7QayxqXoL6ydN7Jcq77oN3vwlvnazAejcIh+mCxmFHiWoBusfD7ihPFyem+ILbvmX9/+LnS95mw/XddiJ17E48tOzXvsVvPrID1ivux5frGnP+eoRHjEPqOQug7enn75IVrJrJZjAYVUhf4rksbGZyPN8Ku4e5ume7tTuJTZ2g1kRHzoMPJSQ3mW2mrsWA61j2Ct99/H0817U2bAYhLHE763TgwWIH/HFyKtc0t+MNVNUyu/oni4JQ3iLc/bsPwxfNYIHeghA9hTHLiIteE8gWLce/1LXnP1/PdF5MMRax4sfNm3HPrbeR1axDmWuBP1wVa+H9nKj4p7a4z1KqRJLJEMENctH7KZLgYq6cy2TIwEhcVtwebz/XBzMtYU+7HmnI/wJtgLV9HD1mi8MhARDKjN74AJsSRgBmi2QwoFP7RMsVPsIPaGxmoBYlPHaJWjSRBZEqmO225yxcp7nNInp6Enph+r/zXK9NHpbbvGcs7KpVPMyuhX1j2/54LEp86JdcCeILIl2xW2u+dAz5TrqxQzNb1wWQy4Vj3iC6K8AljoXVUijJjxYfaGxmoBYlPgiCyIpuV9o7+FRgYz6wGNlN7sGxcH9pCiyCd68W504dmLQ2gBzGhFoWISlFmrLjQayaIxCdBEFmRzUq72enFybE6DEUuKGYPlmlt21vnq9EVNOPe0t/i7sbZSwO0KMInipNCRaUoM1Y8TGaC4hKHE34P2vwuREUOVkFGiyeIKz1+mPmJwmKW/L9pCUQQRFZks9PW8tIRRMwLFN3qNJMdrF7vWIJdgytwY0UX/ktTx4yH/2S6s4U7iB0H2hEXM9s2lSCywWi70hHs0VzrwpHRxfj7wyvwizMuhAMXUBI+hXDgAn5xxoXvHluK9oCLud3dKPJJEERWZFNzOSbasaqpAW3DvKJNEPPVto0LC1DlHMQfX5E+MgpoW4SvJ/NnQjmMuCtdQRHjELxHIPQfu2xxV7MaYu3aorK4m47AcxgMSVhuPoeHF32MKsvY1M+GYiV4z7cGr59uhtthhr2MHZcDEp8EQWRF1jtttSyA1bRQ8SaIuWrbTlwIQOxsZaIIPxNLKkPVnZJAmMKou9IVgsnNPXpTN/c48WbRbu4RFyW8d/A07qw6hbXCefgjPEoFATZhwvyv0jKGP6r6GBe7bdjr+0N8/Y7lzCx2SXwqBEuRDZbGQhiPXPwEzQKvShPEbLVtR88PMVGEn6kllVHqTkkgJEPem8rA9x9HcM//xu7wwIxtjT+IR7Bh6CRu3fM8XLc8A6nmqgKOVFsmG9rubRqAWaxC16AZx4MhlPCjsPAJxCQTxqRSrK0YRlcojsRstU8FgMSnArAU2WBpLIQxydVPUMsmCBbSnXo1f84VEggzIe9NBRDjiLVuxe7wAN6vaILMJd9IQbMN71c0Ab4O3NW6Faa7v1s0EfbkhjYLVtmr4B93wx+KISZJEHgejU4LPA4LTp27wIzNEkDiM29YimywNBbC2LDuJ8hCulOv5s85YWCBkG8mifV7hXUE7xH0+s6i1V0347qaROY4tLrrcI3vLBr6jk7tPGd0Um2WeJ5DeYkV5SXWGceyZLMEkPjMC5YiGyyNhSgO5vMTBFAwc3cW0p16NX/OBaMKBKUySeS9mTtC/7GJEo5pkfR0BM02tIkRLGHw2lKrFI6FDE+ukPjMA5YiGyyNhWATNSbA2VLphS7/YCHdqVfz5yQybB4ygkBIRelMEnlv5oYYCyHIZXZ/BjkeYiyk8oiyQ825kIUMT66Q+MwDliIbLI2FYA8txSAr5R+FTnfqOSoBZNc8pHeBkErRZZIYdigQLE645Mx8eF2yNDF2lceUKWrPhSxkeHKFxGcesBTZYGksBFtoKQZZe2gXMt2p56hEts1DehYI6SimTBLrDgVizWq0nHgTH8Tnjqy74hG0CDaIC9doOLrZ0WIuTJfhKbdE4B+PwR+KYShiwUf+JTjLr8Gf3MSOzRJA4jMvWIpssDQWgh20FoMsPrQLle7UbVQih+YhvQqE2SiWTJIeHArE2rWorliKDUMn016PAMDJMjYEelFduZKZa2tyLvzDxV4cGymbddvLfOfC6Rmeb7efhzvSDqc8gpgsoDtWiwjvQknJON5tPQ0Tz05jGzsyWIc017pwPt44Y3u/VLTY1oqlsRDsMCUGa+cXg+FAD9p6A3n9vVwe2kYlk21At3U2oU1ej80M2ewI3iMYyLB5aMB3FkLf0csCIdALTk7vJTglECqWMiMQZqMotsVMWWSkLhomFxm7wwOItW4FxAJ9RsEMy4Y/x632atzm64ArHkn6sSsewW2+Dtxqr4Zlw58XvExgknZvEI5EP350un7ObS+VmAtX1Lrw6XXLEebL4OdrYHPXYklNOf7r6gFs/YOD+ObKPVgc2Y3te1pxipE5lyKfecBSZIOlsRDsoHUEh8o/kil03Wku5No8ZNnw57h1z/OAr2NGFM0Vj2BDoHdKIEiMCITZKIZMkp4cCqSaVXDd8gzuat2Ka1LLAwQbqitXFrw8IJWeoVF0jHC4w9OOT9cdRWWabS+3nW7Gg8vynwvjooT3Dp3GH5R8ggevKny5UyaQ+MwDFjpqWRwLwQ5ai0G1H9p63L1LbzY7uTYP6VEgzIae63UzRW8OBVLNVTDd/V009B2dGMtkY9TCNRAXrmFqQRMXJXR4B7DK2oaHavaD55KzAZWWMTxUsx+v9wNvnW+Bx8HBkccChsVyp/kg8ZknLEU2WBoLwQZaR3DUfGhPduyHRnpgSwwgGOMRSpjxrlSB6soq/PGtV2LlIk9e41cLPdns5NM8pCeBMBfFkEnSpUOBYIa4aP2UCGa1aa2tNwCXPIi1pT2ISfzUXuvT4TkZn644in/oWYouaTn+JI8FjB5rlEl8KgBLkQ2WxkIUHq0jOGo9tCc79ssiv0c8IiGRCGOl5QJc1nH44iU43NeEv//pRTxy5/W4c/XCvD5DsZN385BOBMJcFEMmSTOHAoZtnNSi3RvESmcvKiwcekJOLHUFkS4gWWEZg1seRC+3Ma8FjB7LnUh8KgRLkQ2WxkIUFq0jOGo8tCc79ssiv0dgPI6VlnZ8ujq5hmow9jF+cuE6vLZLRF357biS0QioHtBrd7HSGD2TpIVDAes2TmoRjcXgNkfQuMCDDm8cZ4NAvTOUFAGNiAJ6Qk6YBB7NdRWK73QUlzic8HtmdNkPx+15pfiVgsQnQRiYQkRwlH5ot/UGEBrpQTwiYaWlPW0NVZVlDE807MV4lx2v7anGcw/eqMtoFBNMdhcbpHkoH4ycSVJ7kaEHGye1mBSDbocFTQur0DVoxvFgCCX8KCx8AjHJhDGpFILVCWvJAiyoLM3r76VmuNr9Lrx1vhrj0RgWWy7AJYwjKDrwxkADTkdr8eBKQaFPmjskPgnC4BQigqPkQ7vdG4QtMYBEIoxPVx+dITwncZgSuM19GP82vBZtvaso8p8HRmoeyhfDZpLUXGTk4BVrpBR8khh0AqvsVfCPu+EPxRCTJAg8j0anBQm+FANdTbhOwXKnq8uH8MaZarRYkrvsZQCtvoX4z7EbcLi9CstqXKruMDcfJD4JoggoRARHqYd2NBZDMMZjpeVCUqo9HdXWABab2Sio1ztGaR4iZketRYaebJzUYEa5E8+hvMSK8pLLXr+SDGzrXKRoudNPdwfx/vEO3FJyMClDNJni58wO/NnKXrwzcLDglkskPgmiSNBrBMdqsSCUMMNlHZ/32Jhk0q/pN4sYoHmImBs1Fhl6s3FSmkKVO129ohk7vD1YZLmIU0H3jBR/0wIP3A4LE5ZLJD4JgmCa5loX3pUq4IuXzHlcRBQwJpUiIbhQykBBfVGSSWdzEXY/M4/Ciwxd2jgpTCHKncJxEX9QM4w1tR74Q46kFL/HYQF/qeOUBcslEp8EQTBNS50b1ZVVONzXhMHYx6hKk3qXAfSEnBjlK3GRX4KNOjT91juZdDYDclF2Pxcbmtk4MY7W5U6TXfapKf50FNpyicQnQRBMYxZ4/PGtV+Lvf3oRP7lwHZ5o2AuHKTH188l6pmG5CmfEK+HwNOjS9FvPZNLZfMd7z0LkZLwvRYqu+7nY0MLGSS9oWe6kp21hSXwSBME8Kxd58Mid1+O1XSLGu+y4zX0Y1dbAVD3TKF+JM+KV6DRfr1vTb92SQWfz3vLFWHlmN05Awu5lfwiZF2YcY+Tu52IjZxsnKsnICz1tC0vikyAIXXDn6oWoK78dr+2pxr8Nr8Vi80QNVUJw4SK/BA5Pg65Nv/VKJp3NDeMj6JMlfIA4EB4GnFUzjjFy93PRkYONU7Ea0iuJnraFJfFJEFkQFyW09QbQ7g0iGovBarGg2QCG03rhykUePPfgjWjrXXXpHMRRajFjI52DgpFJZ3ND2I82iOjiZNSP+yCnEZ+Acbufi5FsbJyK2ZBeSfS0LSyJT8LwKCUYT3mD2HGgHWF/z1TULZiw4+32Ruzy1GMzRd00Qa+WUUYlk85mkxiHnwNiAGQpMeexRu1+LkYysnEqckN6pdHLtrAkPglDo5RgPOUN4md7W9HCHcSmptTV5Hns9NZh+55RfOHmDQXdNYIgtCaTzuaEYIZHBiwcwPEmpN+jagIjdz8XJfPYOBW7Ib0a6GFbWBKfBHMoGalUQjDGRQk7DrSjhTuYto6m0hbFg0s6sK0TBd81giC0JpPO5m67B9dAwClZguiomPW9iqH7ueiYp4mo2A3p1YL1DBGJT4IplIpUKikY23oDCPt7sKmpN20BNwDwHJjYNYIgtCaTzuZuRxk+w/H4FMzYbS9P+z5pu58JXZNJExEZ0hcnJD4VhhpSckfJ1LaSgrHdG8Ric9ec1hUAG7tGqAld20RaMuxsrqtciRoO4IbPZ9T9TOibTJuIKqpWKGNITzZNuoLEp4JQQ0ruKJ3aVlIwRmMxuE3hjD5HoXeNUAu6tom5yLSzGZAz6n4mdE4WTUR3X5TQwlvyMqQnmyb9QeJTIaghJT+UTm0rKRj1tGuEGhjx2qYorvJk1NkMZHQMoW+yaiIKDKDOXoYNgd7sDOkvQTZN+oTEpwJQQ0r+KJ3aVlIw6mnXCKUx4rVNUVwVmaezOeNjCF2TVRORFENT1UrcOtiesSH9FGTTpFtyekq8/PLLWLJkCWw2G9atW4d9+/bNefzevXuxbt062Gw2NDU14fvf/35Og2WVqahd7fxRu3CgB229AW0HqAOisRhcWUQqo/OktptrXTgfb8RQxDrncZOCsXkOwdhS54b90q4R0iweMazsGqE0Rru2J6O4iyO78VTTXjy27BS2LOnGY8tO4ammvVgc2Y3te1pxyhss9FAJQrdk20SUsLknyjYqV+Lx4CA+e/EMPjV4Dp+9eAaPBwdxV+VKuG55dkbqXPAewUCGEdYB31kIfUfz/myEMmQtPt944w089dRT+PrXv47Dhw/jpptuwl133YXu7u60x3d2duLuu+/GTTfdhMOHD+N//I//gSeffBJvvvlm3oNnhVyidkQySqe2lRSMk7tGtMnrsa2zaYagHYpYsa2zCW3yemw22L7iRrq2U6O4qZ9pMorbwh3EjgPtiIuZNUEQBJFMJt6vk0w2EU2Vbdz+Ldy9+ov4wop7cPfqL6Lh9m/BdPd309ZsZmvTROKTHbJOu7/wwgt49NFH8dhjjwEAXnzxRezcuRPf+9738Pzzz884/vvf/z4aGhrw4osvAgBaWlpw8OBB/OM//iPuv//+/EbPCNSQkj9Kp7aV3mZML7tGKI2Rrm2yzCIIbcjE+xVI00SUZUkG2TTpl6zEZywWw6FDh/DMM88kvX7nnXdi//79aX/no48+wp133pn02qZNm/Dqq68iHo/DbNZ//UWxN6QoQUudG7suRSrT1RYC2ae2lRaMetg1QmmMdG2TZRZBaEMm3q9K+LrmEmGlGmM2yEp8Dg0NQRRFVFdXJ71eXV2N/v7+tL/T39+f9vhEIoGhoSEsXLhwxu9Eo1FEo5cfEMEgu6k8oLgbUpRC6UjlJEoLRtZ3jVAaI13bRoriEgTTZOj9mq+va84RVqLg5NTtzqWsYmRZnvHafMene32S559/Hs8991wuQysIakTtihG1UtvFJhiVxEjXtpGiuATBOpl6v+bjv6lVhJVQnqzEZ2VlJQRBmBHlvHjx4ozo5iQ1NTVpjzeZTKioSL/H77PPPounn3566v+DwSDq6+uzGaqmqBW1K0aKMbXNMka6to0UxSUIPZCp92vOaBRhJZQnK/FpsViwbt067Nq1C/fdd9/U67t27cK9996b9nc2btyIX/3qV0mv/frXv8b69etnrfe0Wq2wWue2yGGNYm1IUQOKVLKFUa5tI0VxCUI3qOzrqkWElVAeTp7MgWfIG2+8gYcffhjf//73sXHjRvzgBz/A1q1bceLECTQ2NuLZZ59Fb28vfvzjHwOYsFpatWoVHn/8cfzZn/0ZPvroIzzxxBPYtm1bxt3uwWAQbrcb3YEAXC62H3DJO6dMRO1o5xTCCBjh2j7dF8T2PZd2a5orinvLBubFNEEQ0xDjEPqOQkgTYSVjee0IBoNocLsRmEevZS0+gQmT+e985zvo6+vDqlWr8E//9E/41Kc+BQD40pe+hPPnz2PPnj1Tx+/duxd/8Rd/gRMnTqC2thb//b//dzzxxBNZfRi9iE+CINhmaoejQPooLu1wRBAEkRuqik+tIfFJEISSGCGKSxAEwRqZik/a250giKKD6ooJgiAKBy3xCYIgCIIgCM0g8UkQBEEQBEFoBolPgiAIgiAIQjNIfBIEQRAEQRCaQeKTIAiCIAiC0AwSnwRBEARBEIRmkPgkCIIgCIIgNIPEJ0EQBEEQBKEZJD4JgiAIgiAIzSDxSRAEQRAEQWgGiU+CIAiCIAhCM0h8EgRBEARBEJpB4pMgCIIgCILQDBKfBEEQBEEQhGaQ+CQIgiAIgiA0g8QnQRAEQRAEoRkkPgmCIAiCIAjNIPFJEARBEARBaAaJT4IgCIIgCEIzTIUeQCbIsgwAGA0GCzwSgiAIgiAIIh2TOm1St82GLsTn6OgoAODK+voCj4QgCIIgCIKYi9HRUbjd7ll/zsnzyVMGkCQJXq8XpaWl4DhO9b8XDAZRX1+Pnp4euFwu1f8eoSx0/vQPnUP9Q+dQ/9A51D9an0NZljE6Oora2lrw/OyVnbqIfPI8j0WLFmn+d10uF91wOobOn/6hc6h/6BzqHzqH+kfLczhXxHMSajgiCIIgCIIgNIPEJ0EQBEEQBKEZJD7TYLVa8Y1vfANWq7XQQyFygM6f/qFzqH/oHOofOof6h9VzqIuGI4IgnfKdwgAAB1VJREFUCIIgCMIYUOSTIAiCIAiC0AwSnwRBEARBEIRmkPgkCIIgCIIgNIPEJ0EQBEEQBKEZRSk+X375ZSxZsgQ2mw3r1q3Dvn375jx+7969WLduHWw2G5qamvD9739fo5ESs5HNOfzFL36BO+64A1VVVXC5XNi4cSN27typ4WiJdGR7H07y4YcfwmQyYe3ateoOkJiXbM9hNBrF17/+dTQ2NsJqteKKK67Av//7v2s0WiId2Z7D1157DWvWrIHD4cDChQvxJ3/yJ/D5fBqNlpjOBx98gM2bN6O2thYcx+Gtt96a93eY0TNykfHTn/5UNpvN8tatW+WTJ0/KX/va12Sn0yl3dXWlPb6jo0N2OBzy1772NfnkyZPy1q1bZbPZLP/85z/XeOTEJNmew6997WvyP/zDP8gHDhyQT58+LT/77LOy2WyWP/nkE41HTkyS7TmcxO/3y01NTfKdd94pr1mzRpvBEmnJ5Rzec8898nXXXSfv2rVL7uzslD/++GP5ww8/1HDUxHSyPYf79u2TeZ6X//mf/1nu6OiQ9+3bJ1955ZXy5z73OY1HTsiyLL/zzjvy17/+dfnNN9+UAci//OUv5zyeJT1TdOLz2muvlZ944omk15qbm+Vnnnkm7fF//dd/LTc3Nye99vjjj8vXX3+9amMk5ibbc5iOlStXys8995zSQyMyJNdz+MADD8h/8zd/I3/jG98g8Vlgsj2H7777rux2u2Wfz6fF8IgMyPYc/p//83/kpqampNdeeukledGiRaqNkciMTMQnS3qmqNLusVgMhw4dwp133pn0+p133on9+/en/Z2PPvpoxvGbNm3CwYMHEY/HVRsrkZ5czmEqkiRhdHQU5eXlagyRmIdcz+EPf/hDnDt3Dt/4xjfUHiIxD7mcw7fffhvr16/Hd77zHdTV1WH58uX4b//tvyEcDmsxZCKFXM7hDTfcgAsXLuCdd96BLMsYGBjAz3/+c3zmM5/RYshEnrCkZ0ya/rUCMzQ0BFEUUV1dnfR6dXU1+vv70/5Of39/2uMTiQSGhoawcOFC1cZLzCSXc5jKd7/7XYRCIWzZskWNIRLzkMs5PHPmDJ555hns27cPJlNRTVtMkss57OjowG9/+1vYbDb88pe/xNDQEL785S9jeHiY6j4LQC7n8IYbbsBrr72GBx54AJFIBIlEAvfccw/+5V/+RYshE3nCkp4pqsjnJBzHJf2/LMszXpvv+HSvE9qR7TmcZNu2bfjmN7+JN954AwsWLFBreEQGZHoORVHEQw89hOeeew7Lly/XanhEBmRzH0qSBI7j8Nprr+Haa6/F3XffjRdeeAE/+tGPKPpZQLI5hydPnsSTTz6J//W//hcOHTqE9957D52dnXjiiSe0GCqhAKzomaIKIVRWVkIQhBmruosXL85YDUxSU1OT9niTyYSKigrVxkqkJ5dzOMkbb7yBRx99FD/72c9w++23qzlMYg6yPYejo6M4ePAgDh8+jK9+9asAJoSMLMswmUz49a9/jdtuu02TsRMT5HIfLly4EHV1dXC73VOvtbS0QJZlXLhwAcuWLVN1zEQyuZzD559/HjfeeCP+6q/+CgCwevVqOJ1O3HTTTfi7v/s7ygQyDkt6pqginxaLBevWrcOuXbuSXt+1axduuOGGtL+zcePGGcf/+te/xvr162E2m1UbK5GeXM4hMBHx/NKXvoTXX3+d6pMKTLbn0OVy4fjx4zhy5MjUP0888QRWrFiBI0eO4LrrrtNq6MQlcrkPb7zxRni9XoyNjU29dvr0afA8j0WLFqk6XmImuZzD8fFx8HyybBAEAcDlCBrBLkzpGc1bnArMpLXEq6++Kp88eVJ+6qmnZKfTKZ8/f16WZVl+5pln5Icffnjq+Elrgr/4i7+QT548Kb/66qtktVRgsj2Hr7/+umwymeR//dd/lfv6+qb+8fv9hfoIRU+25zAV6nYvPNmew9HRUXnRokXy5z//efnEiRPy3r175WXLlsmPPfZYoT5C0ZPtOfzhD38om0wm+eWXX5bPnTsn//a3v5XXr18vX3vttYX6CEXN6OiofPjwYfnw4cMyAPmFF16QDx8+PGWVxbKeKTrxKcuy/K//+q9yY2OjbLFY5GuuuUbeu3fv1M8eeeQR+eabb046fs+ePfLVV18tWywWefHixfL3vvc9jUdMpJLNObz55ptlADP+eeSRR7QfODFFtvfhdEh8skG257CtrU2+/fbbZbvdLi9atEh++umn5fHxcY1HTUwn23P40ksvyStXrpTtdru8cOFC+Ytf/KJ84cIFjUdNyLIs7969e85nG8t6hpNlipUTBEEQBEEQ2lBUNZ8EQRAEQRBEYSHxSRAEQRAEQWgGiU+CIAiCIAhCM0h8EgRBEARBEJpB4pMgCIIgCILQDBKfBEEQBEEQhGaQ+CQIgiAIgiA0g8QnQRAEQRAEoRkkPgmCIAiCIAjNIPFJEARBEARBaAaJT4IgCIIgCEIzSHwSBEEQBEEQmvH/Ax+k/GoJwHgRAAAAAElFTkSuQmCC\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 3\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 4\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Converged, terminating.\n" - ] - } - ], - "source": [ - "seed(10) # For reproducible random numbers\n", - "\n", - "class Agent:\n", - "\n", - " def __init__(self, type):\n", - " self.type = type\n", - " self.draw_location()\n", - "\n", - " def draw_location(self):\n", - " self.location = uniform(0, 1), uniform(0, 1)\n", - "\n", - " def get_distance(self, other):\n", - " \"Computes the euclidean distance between self and other agent.\"\n", - " a = (self.location[0] - other.location[0])**2\n", - " b = (self.location[1] - other.location[1])**2\n", - " return sqrt(a + b)\n", - "\n", - " def happy(self, agents):\n", - " \"True if sufficient number of nearest neighbors are of the same type.\"\n", - " distances = []\n", - " # distances is a list of pairs (d, agent), where d is distance from\n", - " # agent to self\n", - " for agent in agents:\n", - " if self != agent:\n", - " distance = self.get_distance(agent)\n", - " distances.append((distance, agent))\n", - " # == Sort from smallest to largest, according to distance == #\n", - " distances.sort()\n", - " # == Extract the neighboring agents == #\n", - " neighbors = [agent for d, agent in distances[:num_neighbors]]\n", - " # == Count how many neighbors have the same type as self == #\n", - " num_same_type = sum(self.type == agent.type for agent in neighbors)\n", - " return num_same_type >= require_same_type\n", - "\n", - " def update(self, agents):\n", - " \"If not happy, then randomly choose new locations until happy.\"\n", - " while not self.happy(agents):\n", - " self.draw_location()\n", - "\n", - "\n", - "def plot_distribution(agents, cycle_num):\n", - " \"Plot the distribution of agents after cycle_num rounds of the loop.\"\n", - " x_values_0, y_values_0 = [], []\n", - " x_values_1, y_values_1 = [], []\n", - " # == Obtain locations of each type == #\n", - " for agent in agents:\n", - " x, y = agent.location\n", - " if agent.type == 0:\n", - " x_values_0.append(x)\n", - " y_values_0.append(y)\n", - " else:\n", - " x_values_1.append(x)\n", - " y_values_1.append(y)\n", - " fig, ax = plt.subplots(figsize=(8, 8))\n", - " plot_args = {'markersize': 8, 'alpha': 0.6}\n", - " ax.set_facecolor('azure')\n", - " ax.plot(x_values_0, y_values_0, 'o', markerfacecolor='orange', **plot_args)\n", - " ax.plot(x_values_1, y_values_1, 'o', markerfacecolor='green', **plot_args)\n", - " ax.set_title(f'Cycle {cycle_num-1}')\n", - " plt.show()\n", - "\n", - "# == Main == #\n", - "\n", - "num_of_type_0 = 250\n", - "num_of_type_1 = 250\n", - "num_neighbors = 10 # Number of agents regarded as neighbors\n", - "require_same_type = 5 # Want at least this many neighbors to be same type\n", - "\n", - "# == Create a list of agents == #\n", - "agents = [Agent(0) for i in range(num_of_type_0)]\n", - "agents.extend(Agent(1) for i in range(num_of_type_1))\n", - "\n", - "\n", - "count = 1\n", - "# == Loop until none wishes to move == #\n", - "while True:\n", - " print('Entering loop ', count)\n", - " plot_distribution(agents, count)\n", - " count += 1\n", - " no_one_moved = True\n", - " for agent in agents:\n", - " old_location = agent.location\n", - " agent.update(agents)\n", - " if agent.location != old_location:\n", - " no_one_moved = False\n", - " if no_one_moved:\n", - " break\n", - "\n", - "print('Converged, terminating.')" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 49, - 55, - 187, - 277 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/.jupyter_cache/executed/ca484b75c9e681c89cc70bdfd6b7cfb6/base.ipynb b/lectures/_build/.jupyter_cache/executed/ca484b75c9e681c89cc70bdfd6b7cfb6/base.ipynb deleted file mode 100644 index c3ed3844e..000000000 --- a/lectures/_build/.jupyter_cache/executed/ca484b75c9e681c89cc70bdfd6b7cfb6/base.ipynb +++ /dev/null @@ -1,33 +0,0 @@ -{ - "cells": [], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/.jupyter_cache/global.db b/lectures/_build/.jupyter_cache/global.db deleted file mode 100644 index 061a35897..000000000 Binary files a/lectures/_build/.jupyter_cache/global.db and /dev/null differ diff --git a/lectures/_build/html/.buildinfo b/lectures/_build/html/.buildinfo deleted file mode 100644 index b91199edd..000000000 --- a/lectures/_build/html/.buildinfo +++ /dev/null @@ -1,4 +0,0 @@ -# Sphinx build info version 1 -# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. -config: e1ff3a093d7148b2e032d4be7b8765d9 -tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/lectures/_build/html/_images/geom_series_11_0.png b/lectures/_build/html/_images/geom_series_11_0.png deleted file mode 100644 index 06577c854..000000000 Binary files a/lectures/_build/html/_images/geom_series_11_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/geom_series_17_0.png b/lectures/_build/html/_images/geom_series_17_0.png deleted file mode 100644 index 31c55864a..000000000 Binary files a/lectures/_build/html/_images/geom_series_17_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/geom_series_19_0.png b/lectures/_build/html/_images/geom_series_19_0.png deleted file mode 100644 index 2700425b7..000000000 Binary files a/lectures/_build/html/_images/geom_series_19_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/geom_series_21_0.png b/lectures/_build/html/_images/geom_series_21_0.png deleted file mode 100644 index 1748dbb7e..000000000 Binary files a/lectures/_build/html/_images/geom_series_21_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/geom_series_5_0.png b/lectures/_build/html/_images/geom_series_5_0.png deleted file mode 100644 index 6bdf090de..000000000 Binary files a/lectures/_build/html/_images/geom_series_5_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/geom_series_7_0.png b/lectures/_build/html/_images/geom_series_7_0.png deleted file mode 100644 index 53a391f02..000000000 Binary files a/lectures/_build/html/_images/geom_series_7_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/geom_series_9_0.png b/lectures/_build/html/_images/geom_series_9_0.png deleted file mode 100644 index dc93fe784..000000000 Binary files a/lectures/_build/html/_images/geom_series_9_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/graph.png b/lectures/_build/html/_images/graph.png deleted file mode 100644 index e900ec762..000000000 Binary files a/lectures/_build/html/_images/graph.png and /dev/null differ diff --git a/lectures/_build/html/_images/graph2.png b/lectures/_build/html/_images/graph2.png deleted file mode 100644 index 00d6a8f89..000000000 Binary files a/lectures/_build/html/_images/graph2.png and /dev/null differ diff --git a/lectures/_build/html/_images/graph3.png b/lectures/_build/html/_images/graph3.png deleted file mode 100644 index f125d2104..000000000 Binary files a/lectures/_build/html/_images/graph3.png and /dev/null differ diff --git a/lectures/_build/html/_images/graph4.png b/lectures/_build/html/_images/graph4.png deleted file mode 100644 index b1b2ea472..000000000 Binary files a/lectures/_build/html/_images/graph4.png and /dev/null differ diff --git a/lectures/_build/html/_images/launch.png b/lectures/_build/html/_images/launch.png deleted file mode 100644 index ac536f4b8..000000000 Binary files a/lectures/_build/html/_images/launch.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_11_1.png b/lectures/_build/html/_images/scalar_dynam_11_1.png deleted file mode 100644 index 582881a77..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_11_1.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_13_0.png b/lectures/_build/html/_images/scalar_dynam_13_0.png deleted file mode 100644 index 407dcc669..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_13_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_15_0.png b/lectures/_build/html/_images/scalar_dynam_15_0.png deleted file mode 100644 index 3b3a1be92..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_15_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_17_1.png b/lectures/_build/html/_images/scalar_dynam_17_1.png deleted file mode 100644 index a672a1ab8..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_17_1.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_19_0.png b/lectures/_build/html/_images/scalar_dynam_19_0.png deleted file mode 100644 index 1b249c534..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_19_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_21_0.png b/lectures/_build/html/_images/scalar_dynam_21_0.png deleted file mode 100644 index 4aaad7e4f..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_21_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_23_1.png b/lectures/_build/html/_images/scalar_dynam_23_1.png deleted file mode 100644 index e0e9a3e28..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_23_1.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_25_0.png b/lectures/_build/html/_images/scalar_dynam_25_0.png deleted file mode 100644 index 41c2172e2..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_25_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_27_0.png b/lectures/_build/html/_images/scalar_dynam_27_0.png deleted file mode 100644 index 13fdde0a4..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_27_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_31_1.png b/lectures/_build/html/_images/scalar_dynam_31_1.png deleted file mode 100644 index 9c499967b..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_31_1.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_33_0.png b/lectures/_build/html/_images/scalar_dynam_33_0.png deleted file mode 100644 index 63fb878a3..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_33_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_37_1.png b/lectures/_build/html/_images/scalar_dynam_37_1.png deleted file mode 100644 index 19e47d8ac..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_37_1.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_39_0.png b/lectures/_build/html/_images/scalar_dynam_39_0.png deleted file mode 100644 index ee8cbb5eb..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_39_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/scalar_dynam_9_0.png b/lectures/_build/html/_images/scalar_dynam_9_0.png deleted file mode 100644 index 0d0f47889..000000000 Binary files a/lectures/_build/html/_images/scalar_dynam_9_0.png and /dev/null differ diff --git a/lectures/_build/html/_images/schelling_3_1.png b/lectures/_build/html/_images/schelling_3_1.png deleted file mode 100644 index c188d6d0c..000000000 Binary files a/lectures/_build/html/_images/schelling_3_1.png and /dev/null differ diff --git a/lectures/_build/html/_images/schelling_3_3.png b/lectures/_build/html/_images/schelling_3_3.png deleted file mode 100644 index cd14b0ae7..000000000 Binary files a/lectures/_build/html/_images/schelling_3_3.png and /dev/null differ diff --git a/lectures/_build/html/_images/schelling_3_5.png b/lectures/_build/html/_images/schelling_3_5.png deleted file mode 100644 index 7e42b9b88..000000000 Binary files a/lectures/_build/html/_images/schelling_3_5.png and /dev/null differ diff --git a/lectures/_build/html/_images/schelling_3_7.png b/lectures/_build/html/_images/schelling_3_7.png deleted file mode 100644 index a9319b412..000000000 Binary files a/lectures/_build/html/_images/schelling_3_7.png and /dev/null differ diff --git a/lectures/_build/html/_images/schelling_fig1.png b/lectures/_build/html/_images/schelling_fig1.png deleted file mode 100644 index 432419427..000000000 Binary files a/lectures/_build/html/_images/schelling_fig1.png and /dev/null differ diff --git a/lectures/_build/html/_images/schelling_fig2.png b/lectures/_build/html/_images/schelling_fig2.png deleted file mode 100644 index faf3aaf2d..000000000 Binary files a/lectures/_build/html/_images/schelling_fig2.png and /dev/null differ diff --git a/lectures/_build/html/_images/schelling_fig3.png b/lectures/_build/html/_images/schelling_fig3.png deleted file mode 100644 index b6cf89105..000000000 Binary files a/lectures/_build/html/_images/schelling_fig3.png and /dev/null differ diff --git a/lectures/_build/html/_images/schelling_fig4.png b/lectures/_build/html/_images/schelling_fig4.png deleted file mode 100644 index 9625a207e..000000000 Binary files a/lectures/_build/html/_images/schelling_fig4.png and /dev/null differ diff --git a/lectures/_build/html/_panels_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css b/lectures/_build/html/_panels_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css deleted file mode 100644 index fc14abc85..000000000 --- a/lectures/_build/html/_panels_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css +++ /dev/null @@ -1 +0,0 @@ -details.dropdown .summary-title{padding-right:3em !important;-moz-user-select:none;-ms-user-select:none;-webkit-user-select:none;user-select:none}details.dropdown:hover{cursor:pointer}details.dropdown .summary-content{cursor:default}details.dropdown summary{list-style:none;padding:1em}details.dropdown summary .octicon.no-title{vertical-align:middle}details.dropdown[open] summary .octicon.no-title{visibility:hidden}details.dropdown summary::-webkit-details-marker{display:none}details.dropdown summary:focus{outline:none}details.dropdown summary:hover .summary-up svg,details.dropdown summary:hover .summary-down svg{opacity:1}details.dropdown .summary-up svg,details.dropdown .summary-down svg{display:block;opacity:.6}details.dropdown .summary-up,details.dropdown .summary-down{pointer-events:none;position:absolute;right:1em;top:.75em}details.dropdown[open] .summary-down{visibility:hidden}details.dropdown:not([open]) .summary-up{visibility:hidden}details.dropdown.fade-in[open] summary~*{-moz-animation:panels-fade-in .5s ease-in-out;-webkit-animation:panels-fade-in .5s ease-in-out;animation:panels-fade-in .5s ease-in-out}details.dropdown.fade-in-slide-down[open] summary~*{-moz-animation:panels-fade-in .5s ease-in-out, panels-slide-down .5s ease-in-out;-webkit-animation:panels-fade-in .5s ease-in-out, panels-slide-down .5s ease-in-out;animation:panels-fade-in .5s ease-in-out, panels-slide-down .5s ease-in-out}@keyframes panels-fade-in{0%{opacity:0}100%{opacity:1}}@keyframes panels-slide-down{0%{transform:translate(0, -10px)}100%{transform:translate(0, 0)}}.octicon{display:inline-block;fill:currentColor;vertical-align:text-top}.tabbed-content{box-shadow:0 -.0625rem var(--tabs-color-overline),0 .0625rem var(--tabs-color-underline);display:none;order:99;padding-bottom:.75rem;padding-top:.75rem;width:100%}.tabbed-content>:first-child{margin-top:0 !important}.tabbed-content>:last-child{margin-bottom:0 !important}.tabbed-content>.tabbed-set{margin:0}.tabbed-set{border-radius:.125rem;display:flex;flex-wrap:wrap;margin:1em 0;position:relative}.tabbed-set>input{opacity:0;position:absolute}.tabbed-set>input:checked+label{border-color:var(--tabs-color-label-active);color:var(--tabs-color-label-active)}.tabbed-set>input:checked+label+.tabbed-content{display:block}.tabbed-set>input:focus+label{outline-style:auto}.tabbed-set>input:not(.focus-visible)+label{outline:none;-webkit-tap-highlight-color:transparent}.tabbed-set>label{border-bottom:.125rem solid transparent;color:var(--tabs-color-label-inactive);cursor:pointer;font-size:var(--tabs-size-label);font-weight:700;padding:1em 1.25em .5em;transition:color 250ms;width:auto;z-index:1}html .tabbed-set>label:hover{color:var(--tabs-color-label-active)} diff --git a/lectures/_build/html/_panels_static/panels-variables.06eb56fa6e07937060861dad626602ad.css b/lectures/_build/html/_panels_static/panels-variables.06eb56fa6e07937060861dad626602ad.css deleted file mode 100644 index adc616622..000000000 --- a/lectures/_build/html/_panels_static/panels-variables.06eb56fa6e07937060861dad626602ad.css +++ /dev/null @@ -1,7 +0,0 @@ -:root { ---tabs-color-label-active: hsla(231, 99%, 66%, 1); ---tabs-color-label-inactive: rgba(178, 206, 245, 0.62); ---tabs-color-overline: rgb(207, 236, 238); ---tabs-color-underline: rgb(207, 236, 238); ---tabs-size-label: 1rem; -} \ No newline at end of file diff --git a/lectures/_build/html/_rediraffe_redirected.json b/lectures/_build/html/_rediraffe_redirected.json deleted file mode 100644 index 7316bcc24..000000000 --- a/lectures/_build/html/_rediraffe_redirected.json +++ /dev/null @@ -1 +0,0 @@ -{"index_toc.md": "intro.md"} \ No newline at end of file diff --git a/lectures/_build/html/_sources/geom_series.ipynb b/lectures/_build/html/_sources/geom_series.ipynb deleted file mode 100644 index 4c5062b5c..000000000 --- a/lectures/_build/html/_sources/geom_series.ipynb +++ /dev/null @@ -1,1288 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "d413a06a", - "metadata": {}, - "source": [ - "(geom_series)=\n", - "```{raw} html\n", - "
\n", - " \n", - " \"QuantEcon\"\n", - " \n", - "
\n", - "```\n", - "\n", - "```{index} single: python\n", - "```\n", - "\n", - "# Geometric Series for Elementary Economics\n", - "\n", - "```{contents} Contents\n", - ":depth: 2\n", - "```\n", - "\n", - "## Overview\n", - "\n", - "The lecture describes important ideas in economics that use the mathematics of geometric series.\n", - "\n", - "Among these are\n", - "\n", - "- the Keynesian **multiplier**\n", - "- the money **multiplier** that prevails in fractional reserve banking\n", - " systems\n", - "- interest rates and present values of streams of payouts from assets\n", - "\n", - "(As we shall see below, the term **multiplier** comes down to meaning **sum of a convergent geometric series**)\n", - "\n", - "These and other applications prove the truth of the wise crack that\n", - "\n", - "```{epigraph}\n", - "\"in economics, a little knowledge of geometric series goes a long way \"\n", - "```\n", - "\n", - "Below we'll use the following imports:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "c7215506", - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "plt.rcParams[\"figure.figsize\"] = (11, 5) #set default figure size\n", - "import numpy as np\n", - "import sympy as sym\n", - "from sympy import init_printing, latex\n", - "from matplotlib import cm\n", - "from mpl_toolkits.mplot3d import Axes3D" - ] - }, - { - "cell_type": "markdown", - "id": "c7a9fa2c", - "metadata": {}, - "source": [ - "## Key Formulas\n", - "\n", - "To start, let $c$ be a real number that lies strictly between\n", - "$-1$ and $1$.\n", - "\n", - "- We often write this as $c \\in (-1,1)$.\n", - "- Here $(-1,1)$ denotes the collection of all real numbers that\n", - " are strictly less than $1$ and strictly greater than $-1$.\n", - "- The symbol $\\in$ means *in* or *belongs to the set after the symbol*.\n", - "\n", - "We want to evaluate geometric series of two types -- infinite and finite.\n", - "\n", - "### Infinite Geometric Series\n", - "\n", - "The first type of geometric that interests us is the infinite series\n", - "\n", - "$$\n", - "1 + c + c^2 + c^3 + \\cdots\n", - "$$\n", - "\n", - "Where $\\cdots$ means that the series continues without end.\n", - "\n", - "The key formula is\n", - "\n", - "```{math}\n", - ":label: infinite\n", - "\n", - "1 + c + c^2 + c^3 + \\cdots = \\frac{1}{1 -c }\n", - "```\n", - "\n", - "To prove key formula {eq}`infinite`, multiply both sides by $(1-c)$ and verify\n", - "that if $c \\in (-1,1)$, then the outcome is the\n", - "equation $1 = 1$.\n", - "\n", - "### Finite Geometric Series\n", - "\n", - "The second series that interests us is the finite geometric series\n", - "\n", - "$$\n", - "1 + c + c^2 + c^3 + \\cdots + c^T\n", - "$$\n", - "\n", - "where $T$ is a positive integer.\n", - "\n", - "The key formula here is\n", - "\n", - "$$\n", - "1 + c + c^2 + c^3 + \\cdots + c^T = \\frac{1 - c^{T+1}}{1-c}\n", - "$$\n", - "\n", - "**Remark:** The above formula works for any value of the scalar\n", - "$c$. We don't have to restrict $c$ to be in the\n", - "set $(-1,1)$.\n", - "\n", - "We now move on to describe some famous economic applications of\n", - "geometric series.\n", - "\n", - "## Example: The Money Multiplier in Fractional Reserve Banking\n", - "\n", - "In a fractional reserve banking system, banks hold only a fraction\n", - "$r \\in (0,1)$ of cash behind each **deposit receipt** that they\n", - "issue\n", - "\n", - "* In recent times\n", - " - cash consists of pieces of paper issued by the government and\n", - " called dollars or pounds or $\\ldots$\n", - " - a *deposit* is a balance in a checking or savings account that\n", - " entitles the owner to ask the bank for immediate payment in cash\n", - "* When the UK and France and the US were on either a gold or silver\n", - " standard (before 1914, for example)\n", - " - cash was a gold or silver coin\n", - " - a *deposit receipt* was a *bank note* that the bank promised to\n", - " convert into gold or silver on demand; (sometimes it was also a\n", - " checking or savings account balance)\n", - "\n", - "Economists and financiers often define the **supply of money** as an\n", - "economy-wide sum of **cash** plus **deposits**.\n", - "\n", - "In a **fractional reserve banking system** (one in which the reserve\n", - "ratio $r$ satisfies $0 < r < 1$), **banks create money** by issuing deposits *backed* by fractional reserves plus loans that they make to their customers.\n", - "\n", - "A geometric series is a key tool for understanding how banks create\n", - "money (i.e., deposits) in a fractional reserve system.\n", - "\n", - "The geometric series formula {eq}`infinite` is at the heart of the classic model of the money creation process -- one that leads us to the celebrated\n", - "**money multiplier**.\n", - "\n", - "### A Simple Model\n", - "\n", - "There is a set of banks named $i = 0, 1, 2, \\ldots$.\n", - "\n", - "Bank $i$'s loans $L_i$, deposits $D_i$, and\n", - "reserves $R_i$ must satisfy the balance sheet equation (because\n", - "**balance sheets balance**):\n", - "\n", - "```{math}\n", - ":label: balance\n", - "\n", - "L_i + R_i = D_i\n", - "```\n", - "\n", - "The left side of the above equation is the sum of the bank's **assets**,\n", - "namely, the loans $L_i$ it has outstanding plus its reserves of\n", - "cash $R_i$.\n", - "\n", - "The right side records bank $i$'s liabilities,\n", - "namely, the deposits $D_i$ held by its depositors; these are\n", - "IOU's from the bank to its depositors in the form of either checking\n", - "accounts or savings accounts (or before 1914, bank notes issued by a\n", - "bank stating promises to redeem note for gold or silver on demand).\n", - "\n", - "Each bank $i$ sets its reserves to satisfy the equation\n", - "\n", - "```{math}\n", - ":label: reserves\n", - "\n", - "R_i = r D_i\n", - "```\n", - "\n", - "where $r \\in (0,1)$ is its **reserve-deposit ratio** or **reserve\n", - "ratio** for short\n", - "\n", - "- the reserve ratio is either set by a government or chosen by banks\n", - " for precautionary reasons\n", - "\n", - "Next we add a theory stating that bank $i+1$'s deposits depend\n", - "entirely on loans made by bank $i$, namely\n", - "\n", - "```{math}\n", - ":label: deposits\n", - "\n", - "D_{i+1} = L_i\n", - "```\n", - "\n", - "Thus, we can think of the banks as being arranged along a line with\n", - "loans from bank $i$ being immediately deposited in $i+1$\n", - "\n", - "- in this way, the debtors to bank $i$ become creditors of\n", - " bank $i+1$\n", - "\n", - "Finally, we add an *initial condition* about an exogenous level of bank\n", - "$0$'s deposits\n", - "\n", - "$$\n", - "D_0 \\ \\text{ is given exogenously}\n", - "$$\n", - "\n", - "We can think of $D_0$ as being the amount of cash that a first\n", - "depositor put into the first bank in the system, bank number $i=0$.\n", - "\n", - "Now we do a little algebra.\n", - "\n", - "Combining equations {eq}`balance` and {eq}`reserves` tells us that\n", - "\n", - "```{math}\n", - ":label: fraction\n", - "\n", - "L_i = (1-r) D_i\n", - "```\n", - "\n", - "This states that bank $i$ loans a fraction $(1-r)$ of its\n", - "deposits and keeps a fraction $r$ as cash reserves.\n", - "\n", - "Combining equation {eq}`fraction` with equation {eq}`deposits` tells us that\n", - "\n", - "$$\n", - "D_{i+1} = (1-r) D_i \\ \\text{ for } i \\geq 0\n", - "$$\n", - "\n", - "which implies that\n", - "\n", - "```{math}\n", - ":label: geomseries\n", - "\n", - "D_i = (1 - r)^i D_0 \\ \\text{ for } i \\geq 0\n", - "```\n", - "\n", - "Equation {eq}`geomseries` expresses $D_i$ as the $i$ th term in the\n", - "product of $D_0$ and the geometric series\n", - "\n", - "$$\n", - "1, (1-r), (1-r)^2, \\cdots\n", - "$$\n", - "\n", - "Therefore, the sum of all deposits in our banking system\n", - "$i=0, 1, 2, \\ldots$ is\n", - "\n", - "```{math}\n", - ":label: sumdeposits\n", - "\n", - "\\sum_{i=0}^\\infty (1-r)^i D_0 = \\frac{D_0}{1 - (1-r)} = \\frac{D_0}{r}\n", - "```\n", - "\n", - "### Money Multiplier\n", - "\n", - "The **money multiplier** is a number that tells the multiplicative\n", - "factor by which an exogenous injection of cash into bank $0$ leads\n", - "to an increase in the total deposits in the banking system.\n", - "\n", - "Equation {eq}`sumdeposits` asserts that the **money multiplier** is\n", - "$\\frac{1}{r}$\n", - "\n", - "- An initial deposit of cash of $D_0$ in bank $0$ leads\n", - " the banking system to create total deposits of $\\frac{D_0}{r}$.\n", - "- The initial deposit $D_0$ is held as reserves, distributed\n", - " throughout the banking system according to $D_0 = \\sum_{i=0}^\\infty R_i$.\n", - "\n", - "## Example: The Keynesian Multiplier\n", - "\n", - "The famous economist John Maynard Keynes and his followers created a\n", - "simple model intended to determine national income $y$ in\n", - "circumstances in which\n", - "\n", - "- there are substantial unemployed resources, in particular **excess\n", - " supply** of labor and capital\n", - "- prices and interest rates fail to adjust to make aggregate **supply\n", - " equal demand** (e.g., prices and interest rates are frozen)\n", - "- national income is entirely determined by aggregate demand\n", - "\n", - "### Static Version\n", - "\n", - "An elementary Keynesian model of national income determination consists\n", - "of three equations that describe aggregate demand for $y$ and its\n", - "components.\n", - "\n", - "The first equation is a national income identity asserting that\n", - "consumption $c$ plus investment $i$ equals national income\n", - "$y$:\n", - "\n", - "$$\n", - "c+ i = y\n", - "$$\n", - "\n", - "The second equation is a Keynesian consumption function asserting that\n", - "people consume a fraction $b \\in (0,1)$ of their income:\n", - "\n", - "$$\n", - "c = b y\n", - "$$\n", - "\n", - "The fraction $b \\in (0,1)$ is called the **marginal propensity to\n", - "consume**.\n", - "\n", - "The fraction $1-b \\in (0,1)$ is called the **marginal propensity\n", - "to save**.\n", - "\n", - "The third equation simply states that investment is exogenous at level\n", - "$i$.\n", - "\n", - "- *exogenous* means *determined outside this model*.\n", - "\n", - "Substituting the second equation into the first gives $(1-b) y = i$.\n", - "\n", - "Solving this equation for $y$ gives\n", - "\n", - "$$\n", - "y = \\frac{1}{1-b} i\n", - "$$\n", - "\n", - "The quantity $\\frac{1}{1-b}$ is called the **investment\n", - "multiplier** or simply the **multiplier**.\n", - "\n", - "Applying the formula for the sum of an infinite geometric series, we can\n", - "write the above equation as\n", - "\n", - "$$\n", - "y = i \\sum_{t=0}^\\infty b^t\n", - "$$\n", - "\n", - "where $t$ is a nonnegative integer.\n", - "\n", - "So we arrive at the following equivalent expressions for the multiplier:\n", - "\n", - "$$\n", - "\\frac{1}{1-b} = \\sum_{t=0}^\\infty b^t\n", - "$$\n", - "\n", - "The expression $\\sum_{t=0}^\\infty b^t$ motivates an interpretation\n", - "of the multiplier as the outcome of a dynamic process that we describe\n", - "next.\n", - "\n", - "### Dynamic Version\n", - "\n", - "We arrive at a dynamic version by interpreting the nonnegative integer\n", - "$t$ as indexing time and changing our specification of the\n", - "consumption function to take time into account\n", - "\n", - "- we add a one-period lag in how income affects consumption\n", - "\n", - "We let $c_t$ be consumption at time $t$ and $i_t$ be\n", - "investment at time $t$.\n", - "\n", - "We modify our consumption function to assume the form\n", - "\n", - "$$\n", - "c_t = b y_{t-1}\n", - "$$\n", - "\n", - "so that $b$ is the marginal propensity to consume (now) out of\n", - "last period's income.\n", - "\n", - "We begin with an initial condition stating that\n", - "\n", - "$$\n", - "y_{-1} = 0\n", - "$$\n", - "\n", - "We also assume that\n", - "\n", - "$$\n", - "i_t = i \\ \\ \\textrm {for all } t \\geq 0\n", - "$$\n", - "\n", - "so that investment is constant over time.\n", - "\n", - "It follows that\n", - "\n", - "$$\n", - "y_0 = i + c_0 = i + b y_{-1} = i\n", - "$$\n", - "\n", - "and\n", - "\n", - "$$\n", - "y_1 = c_1 + i = b y_0 + i = (1 + b) i\n", - "$$\n", - "\n", - "and\n", - "\n", - "$$\n", - "y_2 = c_2 + i = b y_1 + i = (1 + b + b^2) i\n", - "$$\n", - "\n", - "and more generally\n", - "\n", - "$$\n", - "y_t = b y_{t-1} + i = (1+ b + b^2 + \\cdots + b^t) i\n", - "$$\n", - "\n", - "or\n", - "\n", - "$$\n", - "y_t = \\frac{1-b^{t+1}}{1 -b } i\n", - "$$\n", - "\n", - "Evidently, as $t \\rightarrow + \\infty$,\n", - "\n", - "$$\n", - "y_t \\rightarrow \\frac{1}{1-b} i\n", - "$$\n", - "\n", - "**Remark 1:** The above formula is often applied to assert that an\n", - "exogenous increase in investment of $\\Delta i$ at time $0$\n", - "ignites a dynamic process of increases in national income by successive amounts\n", - "\n", - "$$\n", - "\\Delta i, (1 + b )\\Delta i, (1+b + b^2) \\Delta i , \\cdots\n", - "$$\n", - "\n", - "at times $0, 1, 2, \\ldots$.\n", - "\n", - "**Remark 2** Let $g_t$ be an exogenous sequence of government\n", - "expenditures.\n", - "\n", - "If we generalize the model so that the national income identity\n", - "becomes\n", - "\n", - "$$\n", - "c_t + i_t + g_t = y_t\n", - "$$\n", - "\n", - "then a version of the preceding argument shows that the **government\n", - "expenditures multiplier** is also $\\frac{1}{1-b}$, so that a\n", - "permanent increase in government expenditures ultimately leads to an\n", - "increase in national income equal to the multiplier times the increase\n", - "in government expenditures.\n", - "\n", - "## Example: Interest Rates and Present Values\n", - "\n", - "We can apply our formula for geometric series to study how interest\n", - "rates affect values of streams of dollar payments that extend over time.\n", - "\n", - "We work in discrete time and assume that $t = 0, 1, 2, \\ldots$\n", - "indexes time.\n", - "\n", - "We let $r \\in (0,1)$ be a one-period **net nominal interest rate**\n", - "\n", - "- if the nominal interest rate is $5$ percent,\n", - " then $r= .05$\n", - "\n", - "A one-period **gross nominal interest rate** $R$ is defined as\n", - "\n", - "$$\n", - "R = 1 + r \\in (1, 2)\n", - "$$\n", - "\n", - "- if $r=.05$, then $R = 1.05$\n", - "\n", - "**Remark:** The gross nominal interest rate $R$ is an **exchange\n", - "rate** or **relative price** of dollars at between times $t$ and\n", - "$t+1$. The units of $R$ are dollars at time $t+1$ per\n", - "dollar at time $t$.\n", - "\n", - "When people borrow and lend, they trade dollars now for dollars later or\n", - "dollars later for dollars now.\n", - "\n", - "The price at which these exchanges occur is the gross nominal interest\n", - "rate.\n", - "\n", - "- If I sell $x$ dollars to you today, you pay me $R x$\n", - " dollars tomorrow.\n", - "- This means that you borrowed $x$ dollars for me at a gross\n", - " interest rate $R$ and a net interest rate $r$.\n", - "\n", - "We assume that the net nominal interest rate $r$ is fixed over\n", - "time, so that $R$ is the gross nominal interest rate at times\n", - "$t=0, 1, 2, \\ldots$.\n", - "\n", - "Two important geometric sequences are\n", - "\n", - "```{math}\n", - ":label: geom1\n", - "\n", - "1, R, R^2, \\cdots\n", - "```\n", - "\n", - "and\n", - "\n", - "```{math}\n", - ":label: geom2\n", - "\n", - "1, R^{-1}, R^{-2}, \\cdots\n", - "```\n", - "\n", - "Sequence {eq}`geom1` tells us how dollar values of an investment **accumulate**\n", - "through time.\n", - "\n", - "Sequence {eq}`geom2` tells us how to **discount** future dollars to get their\n", - "values in terms of today's dollars.\n", - "\n", - "### Accumulation\n", - "\n", - "Geometric sequence {eq}`geom1` tells us how one dollar invested and re-invested\n", - "in a project with gross one period nominal rate of return accumulates\n", - "\n", - "- here we assume that net interest payments are reinvested in the\n", - " project\n", - "- thus, $1$ dollar invested at time $0$ pays interest\n", - " $r$ dollars after one period, so we have $r+1 = R$\n", - " dollars at time$1$\n", - "- at time $1$ we reinvest $1+r =R$ dollars and receive interest\n", - " of $r R$ dollars at time $2$ plus the *principal*\n", - " $R$ dollars, so we receive $r R + R = (1+r)R = R^2$\n", - " dollars at the end of period $2$\n", - "- and so on\n", - "\n", - "Evidently, if we invest $x$ dollars at time $0$ and\n", - "reinvest the proceeds, then the sequence\n", - "\n", - "$$\n", - "x , xR , x R^2, \\cdots\n", - "$$\n", - "\n", - "tells how our account accumulates at dates $t=0, 1, 2, \\ldots$.\n", - "\n", - "### Discounting\n", - "\n", - "Geometric sequence {eq}`geom2` tells us how much future dollars are worth in terms of today's dollars.\n", - "\n", - "Remember that the units of $R$ are dollars at $t+1$ per\n", - "dollar at $t$.\n", - "\n", - "It follows that\n", - "\n", - "- the units of $R^{-1}$ are dollars at $t$ per dollar at $t+1$\n", - "- the units of $R^{-2}$ are dollars at $t$ per dollar at $t+2$\n", - "- and so on; the units of $R^{-j}$ are dollars at $t$ per\n", - " dollar at $t+j$\n", - "\n", - "So if someone has a claim on $x$ dollars at time $t+j$, it\n", - "is worth $x R^{-j}$ dollars at time $t$ (e.g., today).\n", - "\n", - "### Application to Asset Pricing\n", - "\n", - "A **lease** requires a payments stream of $x_t$ dollars at\n", - "times $t = 0, 1, 2, \\ldots$ where\n", - "\n", - "$$\n", - "x_t = G^t x_0\n", - "$$\n", - "\n", - "where $G = (1+g)$ and $g \\in (0,1)$.\n", - "\n", - "Thus, lease payments increase at $g$ percent per period.\n", - "\n", - "For a reason soon to be revealed, we assume that $G < R$.\n", - "\n", - "The **present value** of the lease is\n", - "\n", - "$$\n", - "\\begin{aligned} p_0 & = x_0 + x_1/R + x_2/(R^2) + \\ddots \\\\\n", - " & = x_0 (1 + G R^{-1} + G^2 R^{-2} + \\cdots ) \\\\\n", - " & = x_0 \\frac{1}{1 - G R^{-1}} \\end{aligned}\n", - "$$\n", - "\n", - "where the last line uses the formula for an infinite geometric series.\n", - "\n", - "Recall that $R = 1+r$ and $G = 1+g$ and that $R > G$\n", - "and $r > g$ and that $r$ and $g$ are typically small\n", - "numbers, e.g., .05 or .03.\n", - "\n", - "Use the Taylor series of $\\frac{1}{1+r}$ about $r=0$,\n", - "namely,\n", - "\n", - "$$\n", - "\\frac{1}{1+r} = 1 - r + r^2 - r^3 + \\cdots\n", - "$$\n", - "\n", - "and the fact that $r$ is small to approximate\n", - "$\\frac{1}{1+r} \\approx 1 - r$.\n", - "\n", - "Use this approximation to write $p_0$ as\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - " p_0 &= x_0 \\frac{1}{1 - G R^{-1}} \\\\\n", - " &= x_0 \\frac{1}{1 - (1+g) (1-r) } \\\\\n", - " &= x_0 \\frac{1}{1 - (1+g - r - rg)} \\\\\n", - " & \\approx x_0 \\frac{1}{r -g }\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "where the last step uses the approximation $r g \\approx 0$.\n", - "\n", - "The approximation\n", - "\n", - "$$\n", - "p_0 = \\frac{x_0 }{r -g }\n", - "$$\n", - "\n", - "is known as the **Gordon formula** for the present value or current\n", - "price of an infinite payment stream $x_0 G^t$ when the nominal\n", - "one-period interest rate is $r$ and when $r > g$.\n", - "\n", - "We can also extend the asset pricing formula so that it applies to finite leases.\n", - "\n", - "Let the payment stream on the lease now be $x_t$ for $t= 1,2, \\dots,T$, where again\n", - "\n", - "$$\n", - "x_t = G^t x_0\n", - "$$\n", - "\n", - "The present value of this lease is:\n", - "\n", - "$$\n", - "\\begin{aligned} \\begin{split}p_0&=x_0 + x_1/R + \\dots +x_T/R^T \\\\ &= x_0(1+GR^{-1}+\\dots +G^{T}R^{-T}) \\\\ &= \\frac{x_0(1-G^{T+1}R^{-(T+1)})}{1-GR^{-1}} \\end{split}\\end{aligned}\n", - "$$\n", - "\n", - "Applying the Taylor series to $R^{-(T+1)}$ about $r=0$ we get:\n", - "\n", - "$$\n", - "\\frac{1}{(1+r)^{T+1}}= 1-r(T+1)+\\frac{1}{2}r^2(T+1)(T+2)+\\dots \\approx 1-r(T+1)\n", - "$$\n", - "\n", - "Similarly, applying the Taylor series to $G^{T+1}$ about $g=0$:\n", - "\n", - "$$\n", - "(1+g)^{T+1} = 1+(T+1)g+\\frac{T(T+1)}{2!}g^2+\\frac{(T-1)T(T+1)}{3!}g^3+\\dots \\approx 1+ (T+1)g\n", - "$$\n", - "\n", - "Thus, we get the following approximation:\n", - "\n", - "$$\n", - "p_0 =\\frac{x_0(1-(1+(T+1)g)(1-r(T+1)))}{1-(1-r)(1+g) }\n", - "$$\n", - "\n", - "Expanding:\n", - "\n", - "$$\n", - "\\begin{aligned} p_0 &=\\frac{x_0(1-1+(T+1)^2 rg -r(T+1)+g(T+1))}{1-1+r-g+rg} \\\\&=\\frac{x_0(T+1)((T+1)rg+r-g)}{r-g+rg} \\\\ &\\approx \\frac{x_0(T+1)(r-g)}{r-g}+\\frac{x_0rg(T+1)}{r-g}\\\\ &= x_0(T+1) + \\frac{x_0rg(T+1)}{r-g} \\end{aligned}\n", - "$$\n", - "\n", - "We could have also approximated by removing the second term\n", - "$rgx_0(T+1)$ when $T$ is relatively small compared to\n", - "$1/(rg)$ to get $x_0(T+1)$ as in the finite stream\n", - "approximation.\n", - "\n", - "We will plot the true finite stream present-value and the two\n", - "approximations, under different values of $T$, and $g$ and $r$ in Python.\n", - "\n", - "First we plot the true finite stream present-value after computing it\n", - "below" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "45dd667c", - "metadata": {}, - "outputs": [], - "source": [ - "# True present value of a finite lease\n", - "def finite_lease_pv_true(T, g, r, x_0):\n", - " G = (1 + g)\n", - " R = (1 + r)\n", - " return (x_0 * (1 - G**(T + 1) * R**(-T - 1))) / (1 - G * R**(-1))\n", - "# First approximation for our finite lease\n", - "\n", - "def finite_lease_pv_approx_1(T, g, r, x_0):\n", - " p = x_0 * (T + 1) + x_0 * r * g * (T + 1) / (r - g)\n", - " return p\n", - "\n", - "# Second approximation for our finite lease\n", - "def finite_lease_pv_approx_2(T, g, r, x_0):\n", - " return (x_0 * (T + 1))\n", - "\n", - "# Infinite lease\n", - "def infinite_lease(g, r, x_0):\n", - " G = (1 + g)\n", - " R = (1 + r)\n", - " return x_0 / (1 - G * R**(-1))" - ] - }, - { - "cell_type": "markdown", - "id": "53b55bbf", - "metadata": {}, - "source": [ - "Now that we have defined our functions, we can plot some outcomes.\n", - "\n", - "First we study the quality of our approximations" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "efde9d92", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_5_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "def plot_function(axes, x_vals, func, args):\n", - " axes.plot(x_vals, func(*args), label=func.__name__)\n", - "\n", - "T_max = 50\n", - "\n", - "T = np.arange(0, T_max+1)\n", - "g = 0.02\n", - "r = 0.03\n", - "x_0 = 1\n", - "\n", - "our_args = (T, g, r, x_0)\n", - "funcs = [finite_lease_pv_true,\n", - " finite_lease_pv_approx_1,\n", - " finite_lease_pv_approx_2]\n", - " ## the three functions we want to compare\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Finite Lease Present Value $T$ Periods Ahead')\n", - "for f in funcs:\n", - " plot_function(ax, T, f, our_args)\n", - "ax.legend()\n", - "ax.set_xlabel('$T$ Periods Ahead')\n", - "ax.set_ylabel('Present Value, $p_0$')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "c4f1780c", - "metadata": {}, - "source": [ - "Evidently our approximations perform well for small values of $T$.\n", - "\n", - "However, holding $g$ and r fixed, our approximations deteriorate as $T$ increases.\n", - "\n", - "Next we compare the infinite and finite duration lease present values\n", - "over different lease lengths $T$." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "ff816691", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_7_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "# Convergence of infinite and finite\n", - "T_max = 1000\n", - "T = np.arange(0, T_max+1)\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Infinite and Finite Lease Present Value $T$ Periods Ahead')\n", - "f_1 = finite_lease_pv_true(T, g, r, x_0)\n", - "f_2 = np.full(T_max+1, infinite_lease(g, r, x_0))\n", - "ax.plot(T, f_1, label='T-period lease PV')\n", - "ax.plot(T, f_2, '--', label='Infinite lease PV')\n", - "ax.set_xlabel('$T$ Periods Ahead')\n", - "ax.set_ylabel('Present Value, $p_0$')\n", - "ax.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "d4709249", - "metadata": {}, - "source": [ - "The graph above shows how as duration $T \\rightarrow +\\infty$,\n", - "the value of a lease of duration $T$ approaches the value of a\n", - "perpetual lease.\n", - "\n", - "Now we consider two different views of what happens as $r$ and\n", - "$g$ covary" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "50e7ed8a", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAA5sAAAHaCAYAAACO8F3wAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAAC7B0lEQVR4nOzdd3iT5foH8G+SpnvvFaAgm7ItszQVBVFQUQQFKkI5BxxHkAMKxyMqPwQn4EJEWTIEFBkqCBxtC5QpLQiCzALp3kln0ibv74+U0NDS3b5p+/1cVy/s87zvm7tPqPTu/QyJIAgCiIiIiIiIiBqQVOwAiIiIiIiIqOVhsklEREREREQNjskmERERERERNTgmm0RERERERNTgmGwSERERERFRg2OySURERERERA2OySYRERERERE1OCabRERERERE1OCYbBIREREREVGDY7JJREREREREDY7JJhERERERETU4JptERK3E2LFjYWdnh9zc3HteM2nSJMjlcqSlpdX4uevXr4dEIsGNGzfqH2Qj2rZtG7p37w47OztIJBKcOXOm0uuay9fTkJrr2Bw9ehRvv/12hb/Tb7/9NiQSCTIzM2v9zBs3bkAikdTo49KlSw30lRARtUxMNomIWonIyEgUFxdjy5Ytlfar1Wrs3LkTo0ePho+PTxNH17gyMjIQERGBDh064Ndff8WxY8fQqVMnscOyCM15bI4ePYp33nmnyl+g1Ja7uzuOHTtm+jh48CAA4IknnjBrb07jREQkFiuxAyAioqYxatQo+Pv7Y+3atXjxxRcr9H/33XcoKipCZGSkCNE1rsuXL6OkpASTJ09GWFiY2OFYFI6NOWdnZwwcOND0eWxsLABg+PDhZu1ERFQ9VjaJiFoJmUyGKVOm4PTp0zh37lyF/nXr1sHPzw+jRo0CAFy9ehVTp05Fx44dYW9vj4CAAIwZM6bSe+/2/PPPo127dhXab09vLO/KlSuYOHEivL29YWNjg65du+KLL76o8dd15MgRDB8+HE5OTrC3t8fgwYPxyy+/mMUydOhQAMCECRMgkUigVCpr/PzaxFnTMcvIyMA///lPKBQK2NjYwMvLC0OGDMH//ve/Wr9mVSxpbG6/93/99ReeffZZuLi4wMfHB9OmTYNarTa7dvfu3ejZsydsbGzQvn17fPLJJxX+7rz99tuYN28eACAoKMg0tTU6Otp0TVpaWrWvVZ24uDgAQN++fWt1HxERsbJJRNSqTJs2De+99x7Wrl2L5cuXm9ovXLiAkydPYv78+ZDJZACA5ORkeHh44L333oOXlxeys7OxYcMGDBgwAPHx8ejcuXO947lw4QIGDx6MNm3a4OOPP4avry/279+PV155BZmZmXjrrbeqvD8mJgYPPfQQevbsiTVr1sDGxgYrV67EmDFj8N1332HChAl48803ERISgpdeeglLlixBeHg4nJ2dGyXOmo5ZREQE4uLi8O6776JTp07Izc1FXFwcsrKyWuzY3PbUU09hwoQJiIyMxLlz57BgwQIAwNq1awEAv/76K5588kkMGzYM27ZtQ2lpKT766KMK64inT5+O7OxsfPbZZ/jxxx/h5+cHAOjWrZsp4azutWoiPj4eUqkUvXr1qtW4EBERAIGIiFqVsLAwwdPTU9DpdKa2f//73wIA4fLly/e8r7S0VNDpdELHjh2FV1991dS+bt06AYCQkJBgapsyZYrQtm3bCs946623hPL/9IwcOVIIDAwU1Gq12XUvv/yyYGtrK2RnZ1f5tQwcOFDw9vYW8vLyzOLs0aOHEBgYKBgMBkEQBCEqKkoAIHz//fdVPu9eX09d47zXmDk6OgqzZ8+uMo6WNja33/sPPvjA7LoXX3xRsLW1NcVz//33CwqFQtBqtaZr8vLyBA8PD+HuH1s+/PDDCvHU5rVqonfv3kKXLl1qfD0REd3BabRERK1MZGQkMjMzsWfPHgBAaWkpNm3ahNDQUHTs2NF0XWlpKZYsWYJu3brB2toaVlZWsLa2xpUrV3Dx4sV6x1FcXIzffvsNY8eOhb29PUpLS00fjzzyCIqLi3H8+PF73l9QUIATJ05g3LhxcHR0NLXLZDJEREQgMTGxQXYLrU2cNR2zkJAQrF+/HosXL8bx48dRUlLS4sfmtscee8zs8549e6K4uBjp6ekoKCjAH3/8gSeeeALW1tamaxwdHTFmzJhax1fVa9WETqfDX3/9xSm0RER1xGSTiKiVGTduHFxcXLBu3ToAwN69e5GWllZhY6A5c+bgzTffxBNPPIGffvoJJ06cwKlTp9CrVy8UFRXVO46srCyUlpbis88+g1wuN/t45JFHAKDKoytycnIgCIJp+mR5/v7+ptdoyjhrOmbbtm3DlClT8M0332DQoEFwd3fHc889h9TU1BY7Nrd5eHiYfW5jYwMAKCoqMsVd2W7IddkhuarXqonz58+jpKSEySYRUR1xzSYRUStjZ2eHZ599Fl9//TVSUlKwdu1aODk54emnnza7btOmTXjuueewZMkSs/bMzEy4urpW+Rq2trbQarUV2ssnHm5ubqZK20svvVTpc4KCgu75Gm5ubpBKpUhJSanQl5ycDADw9PSsMs6aqE2cNR0zT09PrFixAitWrMCtW7ewZ88ezJ8/H+np6fj1119b5NjU9HkSiaTSc15vJ+JNKT4+HgA3ByIiqismm0RErVBkZCRWrVqFDz/8EHv37sXzzz8Pe3t7s2skEompEnTbL7/8gqSkJNx3331VPr9du3ZIT09HWlqaqSKl0+mwf/9+0zX29vYIDw9HfHw8evbsaTZtsiYcHBwwYMAA/Pjjj/joo49gZ2cHADAYDNi0aRMCAwMb5BzE2sRZlzFr06YNXn75Zfz222+mYzZa4tjUNO7+/ftj165d+Oijj0zPy8/Px88//1zh+tpWKmvr9k60ffr0aZTnExG1dEw2iYhaof79+6Nnz55YsWIFBEGo9GzN0aNHY/369ejSpQt69uyJ06dP48MPP0RgYGC1z58wYQIWLlyIZ555BvPmzUNxcTE+/fRT6PV6s+s++eQTDB06FKGhoXjhhRfQrl075OXl4erVq/jpp5/w+++/V/k6S5cuxUMPPYTw8HDMnTsX1tbWWLlyJc6fP4/vvvuuwjErdVXTOGsyZmq1GuHh4Zg4cSK6dOkCJycnnDp1yrQLa0sdm5patGgRHn30UYwcORKzZs2CXq/Hhx9+CEdHR2RnZ5tdGxwcbIphypQpkMvlDbJL8m3x8fEICgqqtpJPRESVY7JJRNRKRUZGYtasWejWrRsGDBhQof+TTz6BXC7H0qVLkZ+fj759++LHH3/Ef//732qfHRQUhN27d+M///kPxo0bBz8/P8yZMwcZGRl45513TNd169YNcXFx+L//+z/897//RXp6OlxdXdGxY0fTmr+qhIWF4ffff8dbb72F559/HgaDAb169cKePXswevTo2g1IFWoaZ03GzNbWFgMGDMDGjRtx48YNlJSUoE2bNnj99dfx2muvtdixqamHH34YO3bswMKFCzFhwgT4+vrixRdfRHJyMjZu3Gh2rVKpxIIFC7BhwwZ8/fXXMBgMiIqKapCvy2Aw4M8//8TDDz/cIM8jImqNJIIgCGIHQURERHQvJSUl6N27NwICAnDgwAGxwyEiohpiZZOIiIgsSmRkJB566CH4+fkhNTUVq1atwsWLF/HJJ5+IHRoREdUCk00iIiKyKHl5eZg7dy4yMjIgl8vRt29f7N27Fw8++KDYoRERUS1wGi0RERERERE1OKnYARAREREREVHLw2STiIiIiIiIGhyTTSIiIiIiImpwrW6DIIPBgOTkZDg5OTXYgdZERERERESthSAIyMvLg7+/P6TSe9cvW12ymZycDIVCIXYYREREREREzZpKpUJgYOA9+1tdsunk5ATAODDOzs4iR0NERERERNS8aDQaKBQKU251L60u2bw9ddbZ2ZnJJhERERERUR1VtyyRGwQRERERERFRg2OySURERERERA2OySYRERERERE1uFa3ZrMmBEFAaWkp9Hq92KEQWTyZTAYrKyseJUREREREZphs3kWn0yElJQWFhYVih0LUbNjb28PPzw/W1tZih0JEREREFoLJZjkGgwEJCQmQyWTw9/eHtbU1qzVEVRAEATqdDhkZGUhISEDHjh2rPNiXiIiIiFoPJpvl6HQ6GAwGKBQK2Nvbix0OUbNgZ2cHuVyOmzdvQqfTwdbWVuyQiIiIiMgCsARRCVZmiGqH3zNEREREdDeL+gnx0KFDGDNmDPz9/SGRSLBr164K11y8eBGPPfYYXFxc4OTkhIEDB+LWrVtNHywRERERERHdk0UlmwUFBejVqxc+//zzSvuvXbuGoUOHokuXLoiOjsbZs2fx5ptvctoeERERERGRhbGoNZujRo3CqFGj7tn/xhtv4JFHHsEHH3xgamvfvn1ThEZERERERES1YFGVzaoYDAb88ssv6NSpE0aOHAlvb28MGDCg0qm25Wm1Wmg0GrMPIiIiIiIialzNJtlMT09Hfn4+3nvvPTz88MM4cOAAxo4diyeffBIxMTH3vG/p0qVwcXExfSgUiiaMWnxZWVnw9vbGjRs3xA7FzLhx47Bs2TKxw6gxSx1HoPmNJRERERFVTygthaG4WOww6qXZJJsGgwEA8Pjjj+PVV19F7969MX/+fIwePRqrVq26530LFiyAWq02fahUqqYK2SIsXboUY8aMQbt27er8jJUrVyIoKAi2trbo168fDh8+XO09eXl5mD17Ntq2bQs7OzsMHjwYp06dMvUvXLgQ7777brOpNIs1jnfHIJFIMHv2bLP25jaWRERERFS1wrg4JDw1DhnLl4sdSr00m2TT09MTVlZW6Natm1l7165dq9yN1sbGBs7OzmYfrYFOp0NRURHWrFmD6dOn1/k527Ztw+zZs/HGG28gPj4eoaGhGDVqVLU7AE+fPh0HDx7Exo0bce7cOYwYMQIPPvggkpKSAAA9e/ZEu3btsHnz5hrHcvLkyQptf/zxBwRBqN0XVUtijuNtp06dwurVq9GzZ88KfXUZSyIiIiKyPKVZWUievwA3J06C9tIlqH/+Bfr8ArHDqrNmk2xaW1vj/vvvx6VLl8zaL1++jLZt2zba6wqCgEJdaZN/1DaBUiqVePnllzFnzhx4enrioYcewr59+2BlZYVBgwbV+etftmwZIiMjMX36dHTt2hUrVqyAQqHAl19+ec97ioqKsGPHDnzwwQcYNmwY7rvvPrz99tsICgoyu++xxx7Dd999V+NYBg4ciBEjRuDQoUOmtldeeQU9e/bEd999B71eX6evMS8vD5MmTYKDgwP8/PywfPlyKJVKUwVRrHG8LT8/H5MmTcLXX38NNze3Sq+p7VgSERERkeUQ9Hpkb9mCa6MegbpsTxrXp59G+59/gszRQdzg6sGidqPNz8/H1atXTZ8nJCTgzJkzcHd3R5s2bTBv3jxMmDABw4YNQ3h4OH799Vf89NNPiI6ObrSYikr06LZwf6M9/14uLBoJe+vavT0bNmzACy+8gNjYWAiCgFWrVqF///4VrluyZAmWLFlS5bP27duHAQMG4PTp05g/f75Z34gRI3D06NF73ltaWgq9Xl/hSBo7OzscOXLE9HlISAiWLl0KrVYLGxubar+++Ph4LF68GOHh4RgyZAjeeOMN/PDDD/jwww8xffp0vPXWW5g/fz4iIiIgl8urfd5tc+bMQWxsLPbs2QMfHx8sXLgQcXFx6N27NwDj+a9ijONtL730Eh599FE8+OCDWLx4caXX1HYsiYiIiMgyFJ09i9R3FqH4wgUAgE23rvB76y3Y9eolcmT1Z1HJ5h9//IHw8HDT53PmzAEATJkyBevXr8fYsWOxatUqLF26FK+88go6d+6MHTt2YOjQoWKFbFHuu+8+s2Nhbty4AX9//wrXzZw5E+PHj6/yWQEBAcjMzIRer4ePj49Zn4+PD1JTU+95r5OTEwYNGoT/+7//Q9euXeHj44PvvvsOJ06cQMeOHc1eQ6vVIjU1tUbV6V69euH777/H33//jXfffRePPvoo+vTpgzfeeAPz58/H8uXLMXv2bLzzzjt47bXXEBkZWe0ZrHl5ediwYQO2bNmC4cOHAwDWrVtnNm5ijSMAbN26FXFxcWbrXe/1OrUZSyIiIiISV2lODjKWLUfuDz8AggCpkxO8Zs+C2zPPQCKTiR1eg7CoZFOpVFY7fXTatGmYNm1aE0UE2MlluLBoZJO9XvnXra27q29FRUWVJlvu7u5wd3ev9nk5OTkAAIlEYtYuCEKFtrtt3LgR06ZNQ0BAAGQyGfr27YuJEyciLi7OdI2dnR0AoLCwsNpYyuvSpQs2btyIt99+G08++STGjh2L3bt347333sPrr7+Of/zjH3j55ZeRlJRUbeXx+vXrKCkpQUhIiKnNxcUFnTt3Nn0u1jiqVCrMmjULBw4cqDZprutYEhEREVHTEgwG5P7wAzI+Xga9Wg0AcHniCXjPmwsrDw+Ro2tYFpVsWiKJRFLr6axicXAwn8/t6elpSnTKq830T5lMVqH6lp6eXqFKd7cOHTogJiYGBQUF0Gg08PPzw4QJExAUFGS6Jjs7GwDg5eVV5bPuJggCfvzxR7z77ru4du0a5syZg6FDh+L48eN49913sW/fPkyYMAHPP/98jZ4FVJ4I3ibWOJ4+fRrp6eno16+fqU2v1+PQoUP4/PPPodVqISv7rVddx5KIiIiImk7R+b+QumgRiv/8EwBg07kzfBe+CftyP++1JM0ji6I66dOnDzZt2lShvabTP62trdGvXz8cPHgQY8eONfUdPHgQjz/+eI1icHBwgIODA3JycrB//36zab7nz59HYGAgPD09a/QsvV6P7777DkuWLEFycjJefvllHDx4EH/++SeefvppHD58GJMmTcLFixfNputWpUOHDpDL5Th58qTpDFaNRoMrV64gLCwMgHjjOHz4cJw7d86sberUqejSpQtef/11U6IJ1H4siYiIiKjp6NVqZHzyCXK+22qcMuvgAK9X/gW3SZMgsWq5KVnL/coII0eOxIIFC5CTk2O2i2lNp38CxnWzERER6N+/PwYNGoTVq1fj1q1bmDlzpumazz//HDt37sRvv/1matu/fz8EQUDnzp1x9epVzJs3D507d8bUqVNN1xw+fBgjRoyo8dfTqVMnaDQazJ49Gy+//DJcXFwwadIk7NixA9OmTcPatWtrvV7RyckJU6ZMwbx58+Du7g5vb2+89dZbkEqlpmqnWOPo5OSEHj16mD3HwcEBHh4eFdprO5ZERERE1PgEgwHqXbuR/tFH0JfNRHMePRre8+ZB7uMtcnSNj8lmCxYcHIz+/ftj+/btmDFjRp2eMWHCBGRlZWHRokVISUlBjx49sHfvXrOkLjMzE9euXTO7T61WY8GCBUhMTIS7uzueeuopvPvuu6ZdYouLi7Fz507s31/znX5feuklzJgxw2y6cHh4OD766CP4+fnV6esDjMeSzJw5E6NHj4azszNee+01qFQq0zpJMcexJuoylkRERETUuIovXULqO4tQVLZniXWHDvB98004DBwgcmRNRyLU9kDHZk6j0cDFxQVqtRrOzs5mfcXFxUhISEBQUFC1G7I0F3v37sXcuXNx/vx5SKWWc6zqF198gd27d+PAgQNih1JBQUEBAgIC8PHHHyMyMhKA5Y4jYBlj2RK/d4iIiIjqQp+Xh4zPPkPO5i2AXg+JvT28XnoR7hERkFhbix1eg6gqpyqPlc0W7pFHHsGVK1eQlJRkWpNoCeRyOT777DOxwwBgPL/z77//RkhICNRqNRYtWgQAZuspLXUcAcsaSyIiIqLWShAEaH7+GWkffAB9RiYAwGnkSPgsmA+5r6/I0YmDlc1yWJ1pneLj4zF9+nRcunTJtJnPsmXLEBwcLHZozQa/d4iIiKg10169itRF/4fCkycBANZt28LnzTfhOHSIyJE1DlY2iWqoT58+OH36tNhhEBEREVEzYygoQMbKlcje8C1QWgqJrS08Z86E+7SpkLaQKbP1wWSTiIiIiIioFgRBQN7+/Uhb+h5K09IAAI7Dh8NnwQJYBwaIHJ3lYLJJRERERERUQ9rrCUhbvBgFR48CAOSBgfD57xtwUirFDcwCMdkkIiIiIiKqhqGoCJmrvkLW2rVASQkk1tbw+Mc/4PGP6ZByz4pKMdkkIiIiIiK6B0EQkP/bb0hdsgSlySkAAIewYfB94w1Yt2kjcnSWjckmERERERFRJXS3biH13XdREHMIAGDl7wff//wHjsOHQyKRiByd5WOySUREREREVI6huBhZX3+DrK+/hqDTAXI5PKZNg+eMf0Jqby92eM0Gk00iIiIiIqIy+TExSF38LkpUKgCAw+BB8Pnvm7BpHyRyZM0Pk00iIiIiImr1dIlJSFu6FPm//QYAsPLxgc+C+XAaOZJTZuuIySYREREREbVaBp0O2WvXInPVVxCKiwErK7g/9xw8X3wRMkcHscNr1phsEhERERFRq5QfG4u0/1sM3Y0bAAD7+++H78I3YdOxo7iBtRBSsQOgxpWVlQVvb2/cKPsGshTjxo3DsmXLxA6jSpY6dkDzGD8iIiIiS1WSmorE2a9CFTkduhs3IPPyhP+HH6LNtxuYaDYgJpst3NKlSzFmzBi0a9euzs9YuXIlgoKCYGtri379+uHw4cPV3vP2229DIpGYffj6+pr6Fy5ciHfffRcajabOcTW2hhg7oG7jVz4GiUSC2bNnm7U3h/EjIiIisjSCToesNWtw7ZFHkffrr4BUCrfnItBh7164jBnNtZkNjMlmC6XT6VBUVIQ1a9Zg+vTpdX7Otm3bMHv2bLzxxhuIj49HaGgoRo0ahVu3blV7b/fu3ZGSkmL6OHfunKmvZ8+eaNeuHTZv3lzjWJKTk1FaWlqnr6O2GmLsgPqN36lTp7B69Wr07NmzQl9dxo+IiIioNSs4fgLXxz6J9A8/glBYCLs+fRD04w74/uc/kDk5iR1ei8RkszqCAOgKmv5DEGoVplKpxMsvv4w5c+bA09MTDz30EPbt2wcrKysMGjSozl/+smXLEBkZienTp6Nr165YsWIFFAoFvvzyy2rvtbKygq+vr+nDy8vLrP+xxx7Dd999V+NYvv76awQGBuLf//63WeJaF3l5eZg0aRIcHBzg5+eH5cuXQ6lUmiqIDTF2QN3HLz8/H5MmTcLXX38NNze3Sq+p7fgRERERtUYl6elI+vdc3Hr+eeiuXYPM3R1+S5ag7eZNsO3SRezwWjRuEFSdkkJgiX/Tv+5/kgHr2u1+tWHDBrzwwguIjY2FIAhYtWoV+vfvX+G6JUuWYMmSJVU+a9++fRgwYABOnz6N+fPnm/WNGDECR48erTaeK1euwN/fHzY2NhgwYACWLFmC9u3bm/pDQkKwdOlSaLVa2NjYVPu8119/HV27dsW3336Lvn37Ijg4GFOmTMHEiRMrJLLVmTNnDmJjY7Fnzx74+Phg4cKFiIuLQ+/evQEAhw4dqtfYhYaGQqfT1Xn8XnrpJTz66KN48MEHsXjx4kqvqe34EREREbUmQmkpcjZvRsann8FQUABIJHB79hl4zZoFmYuL2OG1Ckw2W5D77rsPH3zwgenzGzduwN+/YqI8c+ZMjB8/vspnBQQEIDMzE3q9Hj4+PmZ9Pj4+SE1NrfL+AQMG4Ntvv0WnTp2QlpaGxYsXY/Dgwfjrr7/g4eFheg2tVovU1FS0bdu22q/P1tYW48ePx/jx45Geno4tW7Zgw4YNmDdvHh555BFMmTIFY8aMgZVV1X+t8/LysGHDBmzZsgXDhw8HAKxbt85srOo7dgDqPH5bt25FXFwcTp06Ve3r1Gb8iIiIiFqLwtOnkfrOImgvXwYA2PbsCd+FC2HXo7vIkbUuTDarI7c3VhnFeN1aursSV1RUBFtb2wrXubu7w93dvdrn5eTkAECFhdKCIFS7eHrUqFGm/w4ODsagQYPQoUMHbNiwAXPmzAEA2NnZAQAKCwurjeVu3t7emD17NmbPno19+/bh+eefx+7duxEfH2+qTt7L9evXUVJSgpCQEFObi4sLOnfubPq8vmNXXm3GT6VSYdasWThw4EClr19efcaPiIiIqCUqzcxE+kcfQ71rFwBA5uICr3/Pgeu4cZBIuYKwqTHZrI5EUuvprGJxcDCP09PT05QwllebabQymaxCFS49Pb1Cta4msQUHB+PKlSumtuzsbACo9RRYwFid/OGHH7Bx40YcOnQIYWFhmDJlCrp161btvULZetjKksDb6jt2oaGh8PT0rPX4nT59Gunp6ejXr5+pTa/X49ChQ/j888+h1Wohk8kA1G/8iIiIiFoSQa9HztatyFjxCQx5eQAA16efhtecV2F1j/0vqPEx2WzB+vTpg02bNlVor+lUUGtra/Tr1w8HDx7E2LFjTX0HDx7E448/XqtYtFotLl68iNDQUFPb+fPnERgYCE9Pzxo9Q6/X48CBA9i4cSN27dqFwMBAPPfcc1i/fj3atGlT41g6dOgAuVyOkydPQqFQAAA0Gg2uXLmCsLAwAPUfOwB1Gr/hw4dX2Pxo6tSp6NKlC15//XVTognUfvyIiIiIWqKiM2eQsmgRtBcuAgBsu3WD71sLYderl8iREZPNFmzkyJFYsGABcnJyzHY0rc1U0Dlz5iAiIgL9+/fHoEGDsHr1aty6dQszZ840XfP5559j586d+O2330xtc+fOxZgxY9CmTRukp6dj8eLF0Gg0mDJliumaw4cPY8SIETX+epYsWYKPP/4Y48ePx//+9z8MHjy4xveW5+TkhClTpmDevHlwd3eHt7c33nrrLUilUlO1syHGDqh+/O4eOycnJ/To0cPsGQ4ODvDw8KjQXtvxIyIiImpJSnNykLFsGXK//wEAIHVygters+E2YQIk5X5BT+JhstmCBQcHo3///ti+fTtmzJhRp2dMmDABWVlZWLRoEVJSUtCjRw/s3bvXbEOazMxMXLt2zey+xMREPPvss8jMzISXlxcGDhyI48ePm+4rLi7Gzp07sX///hrHEhERgXnz5lW7lrEmli1bhpkzZ2L06NFwdnbGa6+9BpVKZXp2Q4wdUP34VTZ2NVGX8SMiIiJqCQSDAbnf/4CMZcugV6sBAC5PPAHveXNhVbYRJVkGiSDU8kDHZk6j0cDFxQVqtRrOzs5mfcXFxUhISEBQUFCDJDSWYO/evZg7dy7Onz8PqQUtiv7iiy+we/duHDhwQOxQAAAFBQUICAjAxx9/jMjISACWO3aA5Y1fS/zeISIiIstTdP4vpC5ahOI//wQA2HTuDN+Fb8K+3H4X1PiqyqnKY2WzhXvkkUdw5coVJCUlmdYnWgK5XI7PPvtMtNePj4/H33//jZCQEKjVaixatAgAzNZSWurYAeKPHxEREVFT0qvVSF+xArlbtwGCAKmDA7xmvQK3iRMhqebYOxIPK5vlsDrTesTHx2P69Om4dOmSaSOfZcuWITg4WOzQmiV+7xAREVFjEAwGqHftRvpHH0FfthO/8+jR8H5tHuTe3iJH13qxsklUhT59+uD06dNih0FERERE91D8999IXfR/KIqLAwBYd+gA3zffhMPAASJHRjXFZJOIiIiIiCyGPi8PGZ99hpxNmwGDARJ7e3i99CLcIyIgsbYWOzyqBSabREREREQkOkEQoPn5Z6R98AH0GZkAAKeRI+GzYD7kvr4iR0d1wWSTiIiIiIhEpb1yBamL/g+Fp04BAKzbtoXPm2/CcegQkSOj+rCo8xwOHTqEMWPGwN/fHxKJBLt27brntTNmzIBEIsGKFSuaLD4iIiIiImo4+vwCpH3wIa6PfRKFp05BYmsLr9mzEfTTHiaaLYBFJZsFBQXo1asXPv/88yqv27VrF06cOAF/f/8mioyIiIiIiBqKIAjQ7NuH648+iuy1a4HSUjg+OBztf/4ZnjNnQMq1mS2CRU2jHTVqFEaNGlXlNUlJSXj55Zexf/9+PProo00UGRERERERNQTt9QSkLf4/FBw9BgCQKxTweeM/cFIqxQ2MGpxFJZvVMRgMiIiIwLx589C9e/ca3aPVaqHVak2fazSaxgqPiIiIiIjuwVBYiMxVXyFr3TqgpAQSa2t4/OMf8PjHdEh5TneL1KySzffffx9WVlZ45ZVXanzP0qVL8c477zRiVEREREREdC+CICD/t9+QumQJSpNTAAAOYcPg+8YbsG7TRuToqDE1m2Tz9OnT+OSTTxAXFweJRFLj+xYsWIA5c+aYPtdoNFAoFI0RIhERERERlVN8+TLSP/gQBUeOAADk/v7weeM/cHzggVr9TE/NU7NJNg8fPoz09HS0KffbD71ej3//+99YsWIFbty4Uel9NjY2sLGxaaIoiYiIiIioNCsLGZ9+htzvvwcMBkAuh8e0acbNf+zsxA6PmohF7UZblYiICPz55584c+aM6cPf3x/z5s3D/v37xQ7PYmVlZcHb2/ueyXhrMG7cOCxbtkzsMKpkqe9Tcxg7IiIishwGrRaZX3+NayNGInfbNsBggNNDD6HDLz/D+9XZTDRbGYtKNvPz802JJAAkJCTgzJkzuHXrFjw8PNCjRw+zD7lcDl9fX3Tu3FncwC3Y0qVLMWbMGLRr167Oz1i5ciWCgoJga2uLfv364fDhw7WOQSKRYPbs2bV+bnXX1ORs1oULF+Ldd9+16M2hxH6f7vUeNYexIyIiIvGZjjJ55FFkfLwMhoIC2HbvjrYbv0XgZ59ybWYrZVHJ5h9//IE+ffqgT58+AIA5c+agT58+WLhwociRNT86nQ5FRUVYs2YNpk+fXufnbNu2DbNnz8Ybb7yB+Ph4hIaGYtSoUbh161aN7j916hRWr16Nnj171vq5NbmmJmez9uzZE+3atcPmzZtr+dU3DbHfp3u9R4Dljx0RERGJr+jsWdx8diKSXp2DkqQkWHl7w++9pWj3/XbY33+/2OGRmIRWRq1WCwAEtVpdoa+oqEi4cOGCUFRUZGozGAxCga6gyT8MBkOtvq6wsDDhpZdeEl599VXBw8NDGDZsmLBjxw7B09OzXuMVEhIizJw506ytS5cuwvz586u9Ny8vT+jYsaNw8OBBISwsTJg1a1atnlvb1wYg7Ny5s9K+t99+WwgNDa025pqq6fuj0WiEiRMnCvb29oKvr6+wbNmyCmMh5vtU1Xt0W03GrrLvHSIiImrZdElJQuK/5woXOncRLnTuIlzs3UdI/+xzQV9QIHZo1MiqyqnKazYbBImlqLQIA7YMaPLXPTHxBOzl9rW6Z8OGDXjhhRcQGxsLQRCwatUq9O/fv8J1S5YswZIlS6p81r59+zBgwACcPn0a8+fPN+sbMWIEjh49Wm08L730Eh599FE8+OCDWLx4saldp9NV+9yaXFMbISEhWLp0KbRabbUbRuXl5eG9997Dr7/+ivz8fAwbNgzPPvssBgwYgJs3b2L58uWYPXt2jc56nTNnDmJjY7Fnzx74+Phg4cKFiIuLQ+/evU3XHDp0qML7VNP3KDQ0tF5jda/3qLzajB0RERG1fPr8AmR9/TWy16+HoNUCEglcnngCXrNnQe7jI3Z4ZEGYbLYg9913Hz744APT5zdu3IC/v3+F62bOnInx48dX+ayAgABkZmZCr9fD567/afj4+CA1NbXK+7du3Yq4uDicOnWqQl9Nnluf177X16PVapGamoq2bdtWee17772HjIwMfPjhhygsLMTPP/+Mp59+GtnZ2XB2dsY//vEPdOjQodrXzMvLw4YNG7BlyxYMHz4cALBu3boK70ll71NN3yOg7mNV1Xt09+vUdOyIiIio5RL0euT++CMyPvkU+sxMAID9/ffDe/7rsKvBL+Gp9WGyWQ07KzucmHhClNetrburY0VFRbC1ta1wnbu7O9zd3at9Xk5ODgBUOANJEIQqz0VSqVSYNWsWDhw4UOnr31aT59b2te/Frmzns8LCwmqvnTdvHlxdXZGYmAiDwYDRo0dj5cqVyMzMhJeXF7RaLUpKSqr82gDg+vXrKCkpQUhIiKnNxcWlwoZWlb1PNX2PyqvNWNX0PQJqN3ZERETUMhUcO4a0996H9tIlAIC8bRv4zJsHx+HDeV4m3ZNFbRBkiSQSCezl9k3+UZdvWgcHB7PPPT09TQljeUuWLIGjo2OVH4cPH4anpydkMlmF6lh6enqFKlp5p0+fRnp6Ovr16wcrKytYWVkhJiYGn376KaysrODh4VHtc+v62veSnZ0NAPDy8qr22pycHISHh0OhUKBt27YIDg7GypUrkZGRgf3792PQoEG4efNmtc8RBAFA5UlgeZW9TzV9j27fX9uxqu490uv1pmtrM3ZERETUsmivX4dq5gu4NXUatJcuQersDO/5r6PDTz/B6cEHmWhSlVjZbMH69OmDTZs2VWiv6RRNa2tr9OvXDwcPHsTYsWNNfQcPHsTjjz9+z3uHDx+Oc+fOmbVNnToVXbp0weuvvw4bG5tqn1vX176X8+fPIzAwEJ6entVeu3HjRowYMQJr1qxBQUEBfvnlF6xduxavvfYaOnTogBkzZqBbt27VPqdDhw6Qy+U4efIkFAoFAECj0eDKlSsICwszXVfZ+1SbabR1Gavq3iOZTGZqr83YERERUctQmpODzC9WImfrVqC0FLCygtuzz8LzxRdg5eYmdnjUTDDZbMFGjhyJBQsWICcnB27l/qdQmymac+bMQUREBPr3749BgwZh9erVuHXrFmbOnGm65vPPP8fOnTvx22+/AQCcnJzQo0cPs+c4ODiYzkqt6XNrck1+fj6uXr1q+vz22azu7u5oU+48p8OHD2PEiBE1+pr/85//wMrqzrdGcHBwhc13asLJyQlTpkzBvHnz4O7uDm9vb7z11luQSqVmvwWs7H2q7TTa2r5PNXmPbqvN2BEREVHzJuh0yN6yBZkrv4Sh7Jxtx/BweM+bB5v2QSJHR80Nk80WLDg4GP3798f27dsxY8aMOj1jwoQJyMrKwqJFi5CSkoIePXpg7969ZhvFZGZm4tq1aw3+3Jpc88cffyA8PNz0+Zw5cwAAU6ZMwfr16wEAxcXF2LlzJ/bv31+j2MonmvW1bNkyzJw5E6NHj4azszNee+01qFQqs3WSlvw+1XbsiIiIqHkSBAF5//sf0j/6CCU3jed023TuDJ/5r8Nh0CCRo6PmSiLcvYCshdNoNHBxcYFarYazs7NZX3FxMRISEhAUFFTtpinNxd69ezF37lycP38eUmnrXKL7xRdfYPfu3Thw4IDYoaCgoAABAQH4+OOPERkZaWq31PeppmPXEr93iIiIWouiv/5C+nvvo7Bsh3qZpye8Z8+Cy9ixkJRbWkN0W1U5VXmsbLZwjzzyCK5cuYKkpCTTusHWRi6X47PPPhPltePj4/H3338jJCQEarUaixYtAoAKaykt9X0Sc+yIiIiocZWkpSFj+Qqod+8GBAESGxu4T30eHtP/AZmjQ/UPIKoGK5vlsDpDDS0+Ph7Tp0/HpUuXTBv5LFu2DMHBwWKH1qD4vUNERNR8GAoLkbV2HbLWrIFQVAQAcB4zBt6vzoa8kjPaie7GyiaRBejTpw9Onz4tdhhEREREEAwGqHfvQcby5ShNTwcA2PXpA5/5r8OuVy+Ro6OWiMkmEREREVELV3DyJNLfex/FFy4AAOQBAfCeNxdOI0fyrExqNEw2iYiIiIhaKN3Nm0j/6CPkHfwfAEDq4ADPF2bCLSICUhsbkaOjlo7JJhERERFRC6NXq5H55Spkb94MlJQAUilcxz8Nr3/9C1YeHmKHR60Ek00iIiIiohZCKClBzrbtyPz8c+hzcwEADkOHwuf112DTsaO4wVGrw2STiIiIiKiZEwQB+dHRSP/gQ+gSEgAA1vd1gM/rr8MxNFTk6Ki1YrJJRERERNSMFV+6hPT330fB0WMAAJmbG7xe+Rdcn34aEiv+uE/i4d8+IiIiIqJmqDQjAxmfforcHT8CBgMkcjncpzwHjxkzIHNyEjs8IiabRERERETNiaG4GNnrNyBr9WoYCgsBAE4PPwzvf8+BtUIhcnREdzDZJCIiIiJqBgRBgOaXvUhf9jFKk1MAALbBwfBZMB/2ffuKHB1RRUw2iYiIiIgsXGF8PNLeew/FZ/8EAFj5+sL733Pg/OijkEilIkdHVDn+zWzhsrKy4O3tjRs3bogdiplx48Zh2bJlYodRJUsdO6B5jB8RERHVny4xCUlz5uDmsxNRfPZPSOzt4TXrFXTYtxcuY8Yw0SSLxr+dLdzSpUsxZswYtGvXrs7PWLlyJYKCgmBra4t+/frh8OHDtY5BIpFg9uzZpraFCxfi3XffhUajqXNcja0hxg6o/fi9/fbbkEgkZh++vr5m1zSH8SMiIqK60+fnI/3jZbj+yCPQ7N0HSCRwGfcUOvy6D54vvACpnZ3YIRJVi8lmC6XT6VBUVIQ1a9Zg+vTpdX7Otm3bMHv2bLzxxhuIj49HaGgoRo0ahVu3btXo/lOnTmH16tXo2bOnWXvPnj3Rrl07bN68uc6x3S0nJwf5+fkN8qyGGDug7uPXvXt3pKSkmD7OnTtn1t8Y40dERETiE0pLkbN1G66NGImsr7+GoNPBfuBABP24A/6LF0Pu7S12iEQ1xmSzGoIgwFBY2OQfgiDUKk6lUomXX34Zc+bMgaenJx566CHs27cPVlZWGDRoUJ2//mXLliEyMhLTp09H165dsWLFCigUCnz55ZfV3pufn49Jkybh66+/hpubW4X+xx57DN99912dYwOA0tJS/PLLLxg/fjz8/Pxw7dq1Gt2Xl5eHSZMmwcHBAX5+fli+fDmUSqWp+toQYwfUffysrKzg6+tr+vDy8qpwTUOMHxEREVmO/COxSBj7JFLffhv67GxYt2uHwJUr0WbdWth27Sp2eES1xg2CqiEUFeFS335N/rqd405DYm9fq3s2bNiAF154AbGxsRAEAatWrUL//v0rXLdkyRIsWbKkymft27cPAwYMwOnTpzF//nyzvhEjRuDo0aPVxvPSSy/h0UcfxYMPPojFixdX6A8JCcHSpUuh1WphY2NT7fPKO3fuHDZs2IBNmzahpKQE48ePR1RUFHr16lWj++fMmYPY2Fjs2bMHPj4+WLhwIeLi4tC7d28AwKFDh+o1dqGhodDpdHUevytXrsDf3x82NjYYMGAAlixZgvbt25tdU5/xIyIiIsuhvXoVaR98gIJDxqU2UhcXeL30EtyefQYSuVzk6IjqjslmC3Lffffhgw8+MH1+48YN+Pv7V7hu5syZGD9+fJXPCggIQGZmJvR6PXx8fMz6fHx8kJqaWuX9W7duRVxcHE6dOlXla2i1WqSmpqJt27ZVPg8wbtizefNmrF+/Hn/99RdGjRqFlStXYvTo0bC2tq72/tvy8vKwYcMGbNmyBcOHDwcArFu3zmys6jt2AOo8fgMGDMC3336LTp06IS0tDYsXL8bgwYPx119/wcPDw+x1ajN+REREZFlKs7OR+fnnyNm2HdDrASsruE+aBM8XZkLm6ip2eET1xmSzGhI7O3SOOy3K69bW3ZW4oqIi2NraVrjO3d0d7u7u1T4vJyfHGItEYtYuCEKFtvJUKhVmzZqFAwcOVPr6t9mVfY2FZYcRV+ezzz7DO++8g9DQUFy9ehWKOh5afP36dZSUlCAkJMTU5uLigs6dO5s+r+/YlVfb8Rs1apTpv4ODgzFo0CB06NABGzZswJw5c0x9tR0/IiIisgwGnQ45Gzchc9UqGPLyAACODw6Hz9y5sK7nxoREloTJZjUkEkmtp7OKxcHBwexzT09PU8JYXm2m0cpksgpVuPT09ArVuvJOnz6N9PR09Ot3Z/qxXq/HoUOH8Pnnn0Or1UImkyE7OxsAKl2PWJl//vOfkMvl2LBhA7p164annnoKERERCA8Ph7QW237fXg9bWRJ4W33HLjQ0FJ6ennUav7s5ODggODgYV65cMWuv7fgRERGRuARBQN7+A0j/6COUJCYCAGy6dYXP6/PhMCCkmruJmh8mmy1Ynz59sGnTpgrtNZ0Kam1tjX79+uHgwYMYO3asqe/gwYN4/PHH73nv8OHDK+yeOnXqVHTp0gWvv/46ZDIZAOD8+fMIDAyEp6dnjb4ef39/vPHGG3jjjTdw9OhRbNiwAU899RScnJwwadIkREREoHv37tU+p0OHDpDL5Th58qSpOqrRaHDlyhWEhYUBqP/YAajz+N1Nq9Xi4sWLCA0NNWuv7fgRERGReIrOnUPae++j6LRxxpyVlxe8Xn0VLo8/BknZz0ZELQ2TzRZs5MiRWLBgAXJycsx2g63NVNA5c+YgIiIC/fv3x6BBg7B69WrcunULM2fONF3z+eefY+fOnfjtt98AAE5OTujRo4fZcxwcHODh4WHWfvjwYYwYMaJOX9vgwYMxePBgfPLJJ9i1axc2bNiAjz76CPHx8QgODq7yXicnJ0yZMgXz5s2Du7s7vL298dZbb0EqlZqqnQ0xdkD143f32AHA3LlzMWbMGLRp0wbp6elYvHgxNBoNpkyZYvbs+owfERERNY2SlBSkL18OzZ6fAAASW1t4TJsGj8hpkN41K42opWGy2YIFBwejf//+2L59O2bMmFGnZ0yYMAFZWVlYtGgRUlJS0KNHD+zdu9dsQ5rMzMwaHzlyW3FxMXbu3In9+/fXKa7bbG1t8cwzz+CZZ55BcnIyHB0da3TfsmXLMHPmTIwePRrOzs547bXXoFKpTOs0G2LsgOrHr7KxS0xMxLPPPovMzEx4eXlh4MCBOH78uNmYN9T4ERERUeMwFBQga80aZK1dB6G4GADg8vhj8Hr1Vch9fUWOjqhpSITaHujYzGk0Gri4uECtVsPZ2dmsr7i4GAkJCQgKCqpyY5vmZO/evZg7dy7Onz9fq3WNje2LL77A7t27ceDAAbFDAQAUFBQgICAAH3/8MSIjIwFY7tgBljd+LfF7h4iIqC4EvR7qXbuQvmIF9BmZAAC7/v3g8/p82AX3qOZuouahqpyqPFY2W7hHHnkEV65cQVJSUp13b20Mcrkcn332mWivHx8fj7///hshISFQq9VYtGgRAJitpbTUsQPEHz8iIiKqqOD4CaS9/z60Fy8CAOQKBbznzoXTiIeq3ImeqKViZbMcVmdaj/j4eEyfPh2XLl0ybeSzbNmyatd7UuX4vUNERK2ZNiEB6R9+hPzffwcASJ2c4PnCC3CbPAnSWpwFTtRcsLJJVIU+ffrg9OmmPz+ViIiIWg59bi4yVq5EzpbvgNJSQCaD24QJ8Hz5JVjV8lxuopbIohaiHTp0CGPGjIG/vz8kEgl27dpl6ispKcHrr7+O4OBgODg4wN/fH8899xySk5PFC5iIiIiIWh1Bp0P2t9/i6siHkfPtRqC0FA5hw9B+z274LnyTiSZRGYtKNgsKCtCrVy98/vnnFfoKCwsRFxeHN998E3Fxcfjxxx9x+fJlPPbYYyJESkREREStjSAIyPvtN1wf8xjSliyFQa2GTceOUHzzDdp89RVsOnQQO0Qii2JR02hHjRqFUaNGVdrn4uKCgwcPmrV99tlnCAkJwa1bt9CmTZumCJGIiIiIWqGCkyeRsXwFiuLjAQAyDw94vfIKXJ96EhIri/qRmshiNOvvDLVaDYlEAldX13teo9VqodVqTZ9rNJpqn9vK9kwiqjd+zxARUUtVdP4vZKxYgYIjRwAAEltbuEdEwGPGPyGr4fneRK1Vs002i4uLMX/+fEycOLHKHZCWLl2Kd955p0bPlMvlAIxTdu3s7BokTqLWoLCwEMCd7yEiIqLmTnv9OjI++RR5+/cbG6ys4Pr0OHjOfAFyH29xgyNqJpplsllSUoJnnnkGBoMBK1eurPLaBQsWYM6cOabPNRrNPc9MlMlkcHV1RXp6OgDA3t6eZyIRVUEQBBQWFiI9PR2urq6QyWRih0RERFQvJcnJyPjiC6h37gIMBkAigfOY0fB6+WVYc9kWUa00u2SzpKQE48ePR0JCAn7//fcqq5oAYGNjAxsbmxo/39fXFwBMCScRVc/V1dX0vUNERNQclWZlIfOrr5D73VYIJSUAAMcHHoDXrFmw7dxJ5OiImqdmlWzeTjSvXLmCqKgoeHh4NPhrSCQS+Pn5wdvbGyVl/6MhonuTy+WsaBIRUbOlz8tD1tq1yN7wLYSyZSH2ISHwenU27Pv0ETk6oubNopLN/Px8XL161fR5QkICzpw5A3d3d/j7+2PcuHGIi4vDzz//DL1ej9TUVACAu7s7rK2tGzQWmUzGH6CJiIiIWihDcTFyNm9G1uqvoVerAQC2PXrA69XZcBg8mEupiBqARLCgbSSjo6MRHh5eoX3KlCl4++23ERQUVOl9UVFRUCqVNXoNjUYDFxcXqNXqaqfgEhEREVHLIpSUIHfHDmSu/BKlZcumrDt0gNesV+D00ENMMolqoKY5lUVVNpVKZZVHKFhQXkxEREREzYhgMEDzy15kfPYZSm7dAgBY+fvB6+V/weXxxyDhjDaiBmdRySYRERERUUMSBAH5UdHIWLEC2suXAQAyDw94zpwJ1wnjIW3gpVhEdAeTTSIiIiJqkQpOnETG8uUoOnMGACB1coJH5DS4R0RA6uAgbnBErQCTTSIiIiJqUYrO/4WM5ctREBsLAJDY2sI9YjI8IiMhc3UVNziiVoTJJhERERG1CNrr15Gx4hPkHThgbLCyguvT4+A58wXIfbzFDY6oFWKySURERETNWklSEjK+WAn1rl2AwQBIJHAeMxpe//oXrBUKscMjarWYbBIRERFRs1SalYXMVV8hd+tWCCUlAADH4cPh9corsO3cSeToiIjJJhERERE1K/q8PGStXYvsDd9CKCwEANgPGADvV2fDrndvcYMjIhMmm0RERETULBiKipCzeTMyv/4GBrUaAGDbowe8Xp0Nh8GDIZFIRI6QiMpjsklEREREFk0oKUHujh3I/GIlSjMyAADWHTrAa9YrcHroISaZRBaKySYRERERWSTBYIDml1+Q8elnKFGpAAByf394/utfcHlsDCQymcgRElFVmGwSERERkUURBAH5UVHIWPEJtJcvAwBkHh7wnDkTrhPGQ2ptLXKERFQTTDaJiIiIyGIUnDiJjOXLUXTmDABA6uQEj8hIuEdMhtTBQdzgiKhWmGwSERERkeiKzp1HxooVKIiNBQBIbG3hHjEZHpGRkLm6ihscEdUJk00iIiIiEo322jVkfPIp8g4cMDZYWcFt/NPwmDkTcm9vcYMjonphsklERERETa4kKQkZX6yEetcuwGAAJBI4jxkNr3/9C9YKhdjhEVEDYLJJRERERE2mNCsLmau+Qu7WrRBKSgAAjsOHw2vWK7Dt1Enk6IjEpzfocTbjLKITo+Fi7YLI4EixQ6ozJptERERE1Oj0Gg2y1q5F9rcbIRQWAgDsBwyA96uzYde7t7jBEYmsoKQAR5OPIloVjUOJh5CrzQUA+Dv4Y1qPac32LFkmm0RERETUaAxFRcjZvBmZX38Dg1oNALANDob3q7NhP2hQs/0hmqi+UvJTEJ0YjRhVDE6mnkSJocTU52TthNCAUCgVShgEA2SS5nmmLJNNIiIiImpwgk6H3B07kLnyS5RmZAAArDt0gNesV+D00ENMMqnVMQgGXMi6gGhVNKJV0biUc8msX+GkgFKhRLgiHL29e0MulYsSZ0NqkGQzNzcX+/fvR1JSEiQSCfz8/DBy5Ei4ubk1xOOJiIiIqJkQ9HpofvkFGZ99jhKVCgAg9/eH57/+BZfHxkAia54VGqK6KC4txomUE4hSReFQ4iFkFGWY+qQSKXp59YJSoYQyUIkgl6AW90uYeieba9aswfvvv49HH30UAQEBAIDjx4/jrbfewmuvvYbIyOa7oJWIiIiIakYQBORHRSFj+Qpor1wBAMg8PeE5cyZcxz8NqbW1yBESNY3MokzEqGIQnRiN48nHUawvNvXZW9ljSMAQhAWGITQwFO627iJG2vgkgiAI9XlA586dcfr0aTg6Opq15+XloV+/frh8+XK9AmxoGo0GLi4uUKvVcHZ2FjscIiIiomav4PgJZCxfjqKzZwEAUicneERGwv25CEjt7UWOjqhxCYKAyzmXEZMYg2hVNM5lnjPr93XwRVhgGMIV4bjf935Yy5r/L15qmlPVu7IpkUiQn59fIdnMz89vcWVgIiIiIrqj6Nx5ZCxfjoKjRwEAEltbuEdEwGN6JGQuLiJHR9R4SvQlOJV2yljBVEUjuSDZrL+7R3fj9FiFEp3dOrfavKjeyeZHH32EsLAw9OjRwzSNNjExEX/99Rc+/vjjegdIRERERJZFe+0aMlZ8gryDB40NVlZwG/80PGbOhNzbW9zgiBpJbnEuDicdRrQqGrHJsSgoKTD12chsMNBvIMIUYQgLDIO3Pb8PgAZINvv06YPffvsNKpUKycnJEAQBAQEBCAkJgYwLwImIiIhajJKkJGR8/gXUu3cDBgMgkcDlsTHwfPllWCsUYodH1OBuqG8Yd49NjEZ8ejwMgsHU52HrgTBFGJSBSgz0Hwg7KzvxArVQdU42Y2NjMXnyZNy6dQsA4OnpiSlTpuC///0v10ISERERtSClmZnIXPUVcrZtA0qMZwE6PjgcXq+8AttOnUSOjqjhlBpKcSb9jGn95Q3NDbP+jm4doQw0To/t4dkDUolUlDibizonmzNmzED37t2xY8cO2NjY4PTp0/j000+xc+dOHDt2DJ6eng0ZJxERERE1Mb1Gg6y1a5H97UYIhYUAAPuBA+H96mzY9eolcnREDSNfl4/Y5FhEq6JxOOkw1Fq1qc9KaoX7fe43VjAVSgQ4BogXaDNU591o7ezs8Oeff6Jjx46mNkEQMH78eMjlcmzZsqXBgmxI3I2WiIiIqGqGoiJkb9qErG/WwKA2/uBtGxwM71dnw2HwYJGjI6q/pPwkRKuiEaOKwam0Uyg1lJr6nK2dMSxwGJQKJYb4D4GjteO9H9RKNfputF27dkVqaqpZsimRSLBo0SKEhITU9bFEREREJBJBp0Pujh3IXPklSjOMh89b39cBXrNmwenBB1vtjprU/BkEA85nnjetv7ySc8Wsv51zO4QFGquXvb17w0pa761tCPVINp9//nn885//xP79+9GmTRtTu1qthgu3uiYiIiJqNgS9HppffkHGZ5+jRKUCAMgDAuD5r5fhMmYMJNz0kZqhotIiHE8+juhEYwUzqzjL1CeVSNHbqzfCFeEIU4QhyCVIxEhbrjonm7NnzwYAdOrUCU8++SR69+4NvV6PTZs24cMPP2yo+IiIiIiokQiCgPzff0fGik+gvWKs9Mg8PeE5cyZcxz8NqXXzP3yeWpf0wnTEJMYgRhWD4ynHodVrTX0OcgcM8R8CpUKJ0IBQuNq6ihdoK1HnNZvp6emIj4/H2bNncebMGZw5cwZXrlyBRCJB165dERwcjJ49e6Jnz554+OGHGzruOuOaTSIiImrtBEFA4fHjyFjxCYrOngUASJ2c4BEZCffnIiC1txc5QqKaEQQBl3MuI0oVhRhVDM5nnTfr93fwN23uc7/P/ZDL5CJF2rLUNKeqc7JZmeLiYpw7dw5nzpwxJaHnz59Hbm5uQ71EvTHZJCIiotZKEAQUHDmCzC9WoujMGQCAxNYW7hER8JgeCRmXQlEzoNPrcCr1lGn9ZWpBqll/sGcwlAolwgLD0MmtE9caN4JG3yCoMra2trj//vtx//33N+RjiYiIiKgeBEFAflQ0Mr/8EsXnzgEAJNbWcB0/Hh7//Afk3t4iR0hUtZziHBxOOoxoVTRik2JRWFpo6rOV2WKg/0AoA5UYFjgMXvZe4gVKZrjNEhEREVELJRgMyPvtN2R++SW0Fy4CMFYy3Z55Bu7TpjLJJIslCAISNAmm40nOZJyBQTCY+r3svDAscBjCFeEI8QuBnZWdeMHSPTHZJCIiImphBL0eeQcOIPPLVdBevgwAkNjbw33is3CfOhVWHh4iR0hUUamhFPHp8cbpsapo3Mq7Zdbf2a0zlAollAolunl0g1QiFSVOqjmLSjYPHTqEDz/8EKdPn0ZKSgp27tyJJ554wtQvCALeeecdrF69Gjk5ORgwYAC++OILdO/eXbygiYiIiCyEoNdDs3cfMletgu7aNQCA1MEBbhGT4T5lCqzc3ESOkMhcni4PsUmxiFJF4UjSEWh0GlOfldQKA3wHIEwRhrDAMPg7+osYKdWFRSWbBQUF6NWrF6ZOnYqnnnqqQv8HH3yAZcuWYf369ejUqRMWL16Mhx56CJcuXYKTk5MIERMRERGJTygthfrnn5G16ivobtwAAEidneEeEQH35yK48Q9ZFFWeCjGqGEQnRuN06mmUCqWmPlcbVwwLHAalQonB/oPhIHcQMVKqL4tKNkeNGoVRo0ZV2icIAlasWIE33ngDTz75JABgw4YN8PHxwZYtWzBjxoymDJWIiIhIdIJOB/WePcj8ajVKVCoAgMzFBe5Tn4fbpEmQ8ZfxZAEMggHnMs+Zpsdezb1q1h/kEgRloHF6bC+vXpBJZaLESQ2vUZJNqVQKpVKJDz/8EP369WuQZyYkJCA1NRUjRowwtdnY2CAsLAxHjx69Z7Kp1Wqh1d45zFWj0VR6HREREVFzYdDpoP7xR2St/holyckAAJm7uzHJfHYiZI6sBpG4CksKcSzlGGJUMYhJjEF2cbapTyaRoY93H9P6y7bObUWMlBpToySba9euxc2bN/HKK68gNja2QZ6Zmmo8P8fHx8es3cfHBzdv3rznfUuXLsU777zTIDEQERERicmg1SL3+x+Q9fXXKE1LAwDIPD3hERkJtwnjIbW3FzlCas3SCtIQkxiDaFU0TqScgM6gM/U5yh0xNGAowhRhCA0IhYsNp3a3Bo2SbD7//PMAgLfeeqvBn333oayCIFR5UOuCBQswZ84c0+cajQYKhaLB4yIiIiJqLIaiIuRs24bsNWtRmpEBALDy9obHP/4B16fHQWprK3KE1BoJgoC/s/82To9NjMaFrAtm/QGOAabqZT/vfpDL5OIESqKxqDWbVfH19QVgrHD6+fmZ2tPT0ytUO8uzsbGBjY1No8dHRERE1NAMBQXI2boVWWvXQZ+VBQCw8vOD5z//AZcnn4SUP+NQE9PqtTiZctJUwUwrTDP1SSBBsFcwwhXhCAsMw32u91VZFKKWr17J5uHDh/HVV1/h2rVr+OGHHxAQEICNGzciKCgIQ4cObagYAQBBQUHw9fXFwYMH0adPHwCATqdDTEwM3n///QZ9LSIiIiIx6fPzkbN5C7LXrYM+NxcAIA8MhMeMf8L18cchsbYWN0BqVbKLs3Eo8RCiVdE4mnwURaVFpj47KzsM8hsEpUKJ0MBQeNp5ihcoWZw6J5s7duxAREQEJk2ahPj4eNMmPHl5eViyZAn27t1b62fm5+fj6tU7u1MlJCTgzJkzcHd3R5s2bTB79mwsWbIEHTt2RMeOHbFkyRLY29tj4sSJdf0yiIiIiCyGXqNB9saNyP52IwxqNQBA3rYNPGfMhMuY0ZDIOQ2RGp8gCLiuvm7aPfZsxlkIEEz93nbeCFOEQalQIsQ3BLZWnMZNlZMIgiBUf1lFffr0wauvvornnnsOTk5OOHv2LNq3b48zZ87g4YcfNm3oUxvR0dEIDw+v0D5lyhSsX78egiDgnXfewVdffYWcnBwMGDAAX3zxBXr06FHj19BoNHBxcYFarYazs3OtYyQiIiJqaKU5Ocj+9lvkbNwEQ34+AMC6fXt4vjATzqNGQWLVbFY+UTNVYihBXFocolXRiEmMgSpPZdbf1b0rlAolwhRh6ObejdNjW7ma5lR1Tjbt7e1x4cIFtGvXzizZvH79Orp164bi4uI6B9+YmGwSERGRpSjNzkb2uvXI2bwZhsJCAIBNx47wfGEmnEaOhETG8wap8Wh0GhxJPILoxGgcSTyCvJI8U59cKkeIXwjCA8MRpgiDr4OviJGSpalpTlXnX5P5+fnh6tWraNeunVn7kSNH0L59+7o+loiIiKjFK83IQNbadcjZuhVCkXH9m02XLvB88QU4PfggJFKpyBFSS6XSqBCdaJweG5cWh1Kh1NTnZuOGYYHDoFQoMdh/MOzlPEqH6qfOyeaMGTMwa9YsrF27FhKJBMnJyTh27Bjmzp2LhQsXNmSMRERERC1CSVo6stZ8g9xt2yGU7Xdh26MHPF98AY7h4ZyaSA1Ob9DjXOY5RKmiEKOKwTX1NbP+Di4dEKYIQ7giHMGewZBJWU2nhlPnZPO1116DWq1GeHg4iouLMWzYMNjY2GDu3Ll4+eWXGzJGIiIiomatJDkZWd98g9wfdkDQGQ+6t+vVC54vvQiH0FAmmdSgCksKcTT5KKJV0TiUeAg52hxTn0wiQz+ffsbzLwOVUDjz/HlqPHVes3lbYWEhLly4AIPBgG7dusHR0bGhYmsUXLNJRERETUWXmIis1V8jd+dOoKQEAGDXrx+8XnoR9oMGMcmkBpNakIoYVQyiEqNwMuUkSgwlpj4nuROGBg6FMlCJIQFD4GLjImKk1BI0+prN2+zt7dG/f//6PoaIiIioxdDdvInMr1ZDvXs3oNcDAOwHDIDniy/CPuR+JplUb4Ig4EL2BePusaoYXMy+aNYf6BgIpUKJcEU4+vj0gVzKY3Oo6dU52Vy0aFGV/Vy3SURERK2N9noCsr5aBfVPPwMGAwDAYcgQeL74Auz79RM5OmrutHotTqScMB1Pkl6YbuqTQIJeXr2M02MVSrR3ac9fapDo6pxs7ty50+zzkpISJCQkwMrKCh06dGCySURERK2G9soVZH65Cpp9+4CyFUqOYWHwfPEF2PXqJXJ01JxlFmXicOJhRKuicSzlGIpKi0x9dlZ2GOw/GEqFEqEBofCw8xAvUKJK1DnZjI+Pr9Cm0Wjw/PPPY+zYsfUKioiIiKg5KP77b2R+uQp5+/eb2hyHD4fnCy/Arkd3ESOj5koQBFzNvYqYxBhEqaJwLuMcBNzZYsXb3hvhinCEBYYhxC8ENjIbEaMlqlq9Nwi62/nz5zF69GjcuHGjIR/bYLhBEBEREdVX0fm/kPnll8j/7TdTm9PIkfB8YSZsu3QRMTJqjkoMJTiddhrRKuP5l0n5SWb93Ty6QRlonB7bxb0Lp8eS6Jpsg6C75ebmQq1WN/RjiYiIiERXdPYsMld+ifyYGGODRALnUaPgMXMGbDt1Ejc4albUWjUOJx1GjCoGR5KOIL8k39RnLbXGAL8BUCqUCAsMg4+Dj4iREtVdnZPNTz/91OxzQRCQkpKCjRs34uGHH653YERERESWojAuDplfrERBbKyxQSqFy5jR8JgxAzbt24sbHDUbNzU3TdXL+PR46AW9qc/d1h1hgWEIU4RhkN8g2MvtRYuTqKHUOdlcvny52edSqRReXl6YMmUKFixYUO/AiIiIiMRWcPIkMld+icLjx40NMhlcHn8cnjP+Ceu2bcUNjiye3qDH2YyzxgQzMRoJ6gSz/vtc7zPtHhvsGQypRCpOoESNpM7JZkJCQvUXERERETUzgiCg8NgxZKxciaI/Thsb5XK4jh0Lj3/+A9aBgeIGSBatoKQAR5OPIloVjUOJh5CrzTX1WUms0M+3H5SBSoQpwqBwUogWJ1FTqFWyOWfOnBpfu2zZsloHQ0RERCQWQRBQcOQIMr9YiaIzZwAAErkcrk8/DY/pkZD7+4sbIFmslPwURCdGI0YVg5OpJ1FiKDH1OVk7ITQgFOGKcAwJGAInaycRIyVqWrVKNis77qQy3CGLiIiImgtBEJAfFY3MlStRfP48AEBiYwPXCePhERkJuQ83ZyFzBsGAC1kXTOsvL+VcMutv49TGND22t3dvyKVyUeIkElutks2oqKjGioOIiIioSQkGA/L+9z9krloF7YWLAACJnR3cnnkGHtOmwsrLS+QIyZIUlxbjRMoJRKmicCjxEDKKMkx9UokUvb16I0wRBqVCiSDnIBZfiNAIR58QERERWTJBr0fegQPIXPkltFeuAACk9vZwmzQJ7lOfh5W7u8gRkqXILMrEocRDiFJF4XjycRTri0199lb2GBIwBEqFEqEBoXCzdRMxUiLLVO9k88KFC7h16xZ0Op1Z+2OPPVbfRxMRERE1GKG0FJp9+5C56ivorl0DAEgdHeH+XATcIiJg5cZkobUTBAGXcy4jJjEGMaoY/Jn5p1m/r4MvwgKN1csQ3xBYy6xFipSoeahzsnn9+nWMHTsW586dg0QigSAIAO6s19Tr9VXdTkRERNQkhNJSqH/6GVmrVkF38yYAQOrsDPcpz8E9IgIyZ2eRIyQxlehLcCrtFGJUMYhWRSO5INmsv7tHd9P6y85unTk9lqgW6pxszpo1C0FBQfjf//6H9u3b4+TJk8jKysK///1vfPTRRw0ZIxEREVGtCTod1Hv2IPOr1ShRqQAAMldXuE+dCrdJEyFzdBQ5QhJLbnEuDicdRrQqGrHJsSgoKTD12chsMNBvIMIUYQgLDIO3vbd4gRI1c3VONo8dO4bff/8dXl5ekEqlkEqlGDp0KJYuXYpXXnmlxjvXEhERETUkg04H9Y8/InP1apQmpwAAZB4e8Jg2FW7PPAOpg4PIEZIYbqhvGHePTYxGfHo8DILB1Odh62Hc3CdQiYH+A2FnZSdeoEQtSJ2TTb1eD8ey3wh6enoiOTkZnTt3Rtu2bXHp0qVq7iYiIiJqWIbiYuR+/wOyvvkGpWlpAACZlyc8p0+H6/jxkNoxgWhNSg2lOJtx1nQ8yQ3NDbP+jm4doQw0To/t4dkDUolUjDCJWrQ6J5s9evTAn3/+ifbt22PAgAH44IMPYG1tjdWrV6N9+/YNGSMRERHRPRkKCpCz/XtkrV0DfUYmAMDK1xce06fDddxTkNraihwhNZV8XT5ik2MRo4rBoaRDUGvVpj4rqRXu97nfdDxJgGOAiJEStQ51Tjb/+9//oqDAOL998eLFGD16NEJDQ+Hh4YFt27Y1WIBERERElSnNyED2ps3I2boVBrUxqZD7+8Pjn/+Ey5NjIbXmTqGtQXJ+sql6eSrtFEoNpaY+FxsXhAaEQqlQYoj/EDhac50uUVOSCLe3ka2hM2fOoHfv3pX2ZWdnw83NzaJ36dJoNHBxcYFarYYzd58jIiJqdrTXE5C9bh3Uu3dDKDt6zbpdO3hMj4TL449DIpeLHCE1JoNgwF+ZfyFKFYWYxBhczrls1t/OuR2UCiXCAsPQ27s3rKQ8Vp6oodU0p6r1d1/fvn3Rp08fTJ8+HRMnToSLi4upz52HIBMREVEjKYyLR9aaNcj//Xeg7Hfldn36wCNyGhwfeAASKdfctVRFpUU4kXIC0apoxCTGILMo09QnlUjR26s3whXhCFOEIcglSLxAichMrSubx44dw9q1a7F9+3aUlJTgySefRGRkJMLDwxsrxgbFyiYREVHzIRgMyP/9d2StWYuicjvdOw4fDo/IabDv21fE6KgxZRRmICYxBjGqGBxLOQatXmvqc5A7YIj/ECgVSoQGhMLV1lW8QIlaoZrmVLVONm8rKirC9u3bsW7dOhw+fBjt2rXDtGnTMGXKFAQGBtY58MbGZJOIiMjyGbRaqHfvRva69dAlJAAAJHI5XJ54HO5Tp8KGmxG2OIIg4HLOZdP6y/NZ5836/R38TZv73O9zP+QyTpcmEkujJ5vlXbt2DevWrcO3336LlJQUPPTQQ9i7d299H9somGwSERFZLr1ajZzvtiJ70yboM41TJaXOznB79lm4T54EKy8vkSOkhqTT6/BH6h+m9ZcpBSlm/cGewab1l53cOln0viBErUmTJpsAkJ+fj82bN+M///kPcnNzodfrG+KxDY7JJhERkeUpSUpC9rffIuf7HyAUFgIArPz94DFlClyeGgeZo4PIEVJDyS3OxeGkw4hSRSE2KRaFpYWmPluZLQb6D4QyUIlhgcPgZc9fLhBZokbbIOhuMTExWLt2LXbs2AGZTIbx48cjMjKyvo8lIiKiVqD44kVkrVkLzb59QNkvqm26dIFH5DQ4P/wwd5ZtIRLUCabpsWcyzsAgGEx9XnZeGBY4DOGKcIT4hcDOyk60OImoYdUp2VSpVFi/fj3Wr1+PhIQEDB48GJ999hnGjx8PBwf+5pGIiIjuTRAEFBw9iuw1a1Fw9Kip3WHwILhHRsJh8GBOl2zmSg2liE+PR4wqBtGJ0bipuWnW39mtM5QKJZQKJbp5dINUwp2EiVqiWiebDz30EKKiouDl5YXnnnsO06ZNQ+fOnRsjNiIiImpBhJISaH7dj6y1a6G9eNHYKJPBedQoeEybCttu3cQNkOolT5eH2ORYRKuicTjxMDQ6janPSmqFEN8Q0/pLf0d/8QIloiZT62TTzs4OO3bswOjRoyGTyRojJiIiImpBDAUFyN2xA1nr16M02bgBjMTODq5Pj4P7c1NgHRggcoRUV0n5SabpsX+k/oFSodTU52rjimGBwxAWGIbB/oPhaO0oWpxEJI5aJ5t79uxpjDiIiIiohSnNyED2ps3I2boVBrUaACDz8IB7xGS4PfMMZK6u4gZItWYQDDiXec40PfZKzhWz/iCXICgDjdNje3n1gkzKwgRRa1bvDYKIiIiIytNeT0D2unVQ794NQacDAFi3awf3qVPh8sTjkNrYiBwh1UZhSSGOpxxHTGIMYlQxyCrOMvXJJDL08e5jWn/Z1rmtiJESkaVpVslmaWkp3n77bWzevBmpqanw8/PD888/j//+97+QSrmwnIiISEyFcfHIWrsG+b/9DpSdrGbXuzc8pkfC8YEHIOG/1c1GemE6YhJjEK2KxomUE9DqtaY+R7kjhgYMRZgiDKEBoXCxcREvUCKyaM0q2Xz//fexatUqbNiwAd27d8cff/yBqVOnwsXFBbNmzRI7PCIiolZHMBiQHxWFrDVrURQXZ2p3HD4cHpHTYN+3r4jRUU0JgoBLOZcQpYpCjCoGf2X9ZdYf4Bhgql728+4HuYxH0hBR9eqcbN66dQsKhaLC1uSCIEClUqFNmzb1Du5ux44dw+OPP45HH30UANCuXTt89913+OOPPxr8tYiIiOjeDFot1Hv2IHvtOugSEgAAErkcLk88DvepU2HTvr3IEVJ1dHodTqWeMiaYiTFILUg19UkgQbBXsGn95X2u9/E4GiKqtTonm0FBQUhJSYG3t7dZe3Z2NoKCgqAvO5i5IQ0dOhSrVq3C5cuX0alTJ5w9exZHjhzBihUr7nmPVquFVntn6odGo7nntURERFQ1vVqNnO+2InvTJugzMwEAUmdnuD3zDNwmT4L8rp8LyLJkF2fjcOJhxCTGIDYpFoWlhaY+Oys7DPQbiHBFOEIDQ+Fp5ylipEStkDYfyLpq/Mi8AmRdARx9gIeXih1ZndU52RQEodLfcOXn58PW1rZeQd3L66+/DrVajS5dukAmk0Gv1+Pdd9/Fs88+e897li5dinfeeadR4iEiImotSpKTkb1hA3K+/wFCoTFBsfLzg/uU5+A67mnIHB1EjpAqIwgCEtQJiE40Hk9yNuMsDILB1O9t540wRRiUCiVCfENga9U4P8MRURmDHsi9ZZ5QZl4xfp6XUvF69w6tK9mcM2cOAEAikeDNN9+Evb29qU+v1+PEiRPo3bt3gwVY3rZt27Bp0yZs2bIF3bt3x5kzZzB79mz4+/tjypQpld6zYMECU8yAsbKpUCgaJT4iIqKWpvjvv5G1Zi00e/cCZbOWbDp3hsf0SDg//DAkcq7dszSlhlLEp8eb1l/eyrtl1t/Vvaspwezm3o3TY4kaQ2F2uYTyallSeRXIvg6U23CrAntPwLMj4HGf8U+vLk0XcyOodbIZHx8PwPibsnPnzsHa2trUZ21tjV69emHu3LkNF2E58+bNw/z58/HMM88AAIKDg3Hz5k0sXbr0nsmmjY0NbLjFOhERUY0JgoDCY8eQ9c0aFBw9amp3GDwI7tMi4TBkMBMUC6PRaRCbFItoVTQOJx1Gni7P1CeXyhHiF4LwwHCEKcLg6+ArXqBELUmpDsi5Ua46WZZQZl0BCrPufZ/MBvDocCeh9OhY9mcHwM6tycJvCrVONqOiogAAU6dOxSeffAJnZ+cGD+peCgsLKxxxIpPJYDAY7nEHERER1ZRQWgrNvl+RtXYttBcvGhtlMjg//DDcp02FXffu4gZIZlR5KsSojMeTnE47jVKh1NTnZuOGYYHDoFQoMch/EBzknOZMVCeCAOSnm093vV2xzLkBCFXsU+PkD3jeVy6Z7Gj83EUBSGVN9iWIqc5rNtetW9eQcdTImDFj8O6776JNmzbo3r074uPjsWzZMkybNq3JYyEiImopDAUFyN2xA9nrN6AkORkAILGzg+u4cXCfMgXWgQEiR0gAoDfocS7znOn8y6u5V83627u0h1KhRLgiHMGewZC1kh9miRpESRGQdc28Onk7udRWscGo3OGuhLKsWuneAbBxbLr4LZREEMpOXa6D3377Db/99hvS09MrVBfXrl1b7+DulpeXhzfffBM7d+5Eeno6/P398eyzz2LhwoVm03mrotFo4OLiArVa3aRVWSIiIktTmpmJ7E2bkPPdVhjUagCAzMMD7pMnwfWZZ2Dl1rKmczVHhSWFOJZyDNGqaBxKPITs4mxTn0wiQz+ffggLNK6/bOPc8MfOEbUoBgOgSao8oVSr7n2fRAq4tjEmkrerk7eTSyc/oBUuK6hpTlXnZPOdd97BokWL0L9/f/j5+VVYu7Fz5866PLbRMdkkIqLWTns9Adnr1kG9ezcEnQ4AYN22LdynTYPLE49Dyr0ORJVWkGaqXp5IOQGdQWfqc5I7YWjAUCgVSgwJGAIXGxfxAiWyVMWaikeIZJZ9Xlp07/tsXc2nu95OKN2CADl3ai6vpjlVnafRrlq1CuvXr0dERERdH0FERERNqDA+Hllr1iD/t9+N65AA2PXqBffpkXB64AFIZJx2KQZBEPB39t+IVkUjOjEaF7IumPUHOgZCqVBCqVCir09fyKXcAZgI+lIg92YlCeUVID/t3vdJrYzJY/kpr7eTSnuPVlmlbEx1TjZ1Oh0GDx7ckLEQERFRAxMMBuRHRSFrzVoUxcWZ2h0feAAekdNg17cvd5YVgVavxcmUk6YKZlrhnR+OJZCgp1dP0/rL9i7t+R5R61WQZUwgyx8jknnFeISIoeTe9zl4V55QurYFZHVOgaiW6jzS06dPx5YtW/Dmm282ZDxERETUAAxaLdR79iB77TroEhIAABK5HM6PPwaPqVNh06GDyBG2PtnF2TiUeAjRqmgcTT6KonLT+eys7DDYfzDCAsMwLHAYPOw8xAuUqKmVaoHsBPM1lLerlUU5977PyrZsHWUH8x1fPToAdq5NFj7dW52TzeLiYqxevRr/+9//0LNnT8jvOtR52bJl9Q6OiIiIakevViNn6zZkb9wIfWYmAEDq5AS3Z56BW8RkyL29RY6w9RAEAdfV143TY1XROJtxFgLubJXhbe8NZaBxemyIXwhsZFwrSy2YIAB5qZUklFeN02GFKo4ydA6sfMdX50DgrmMRybLUOdn8888/0bt3bwDA+fPnzfo41YOIiKhplSQnI3vDBuR8/wOEwkIAgJWfH9ynPAfXcU9D5shzFptCiaEEcWlxiFZFIyYxBqo88x0uu7p3RbgiHGGKMHR178qfmajlMeiNyWPGJSDjbyDjsvHPzCuALu/e91k73UkoPe4r998dAGv+/6u5qnOyGRUV1ZBxEBERUR0U//03stashWbvXkBvPFzcpnNneEROg/OoUZDIuZlMY9PoNDiSeATRidE4kngEeSV3fqC2llpjgN8AKBVKDAscBl8HXxEjJWpA+hLjusnyCWXGJWPlsrS48nskUuOaycp2fHX04eY8LRBXxxIRETUzgiCg8NgxZK1Zi4LYWFO7/aCB8IicDochg1kxa2QqjQrRicbpsXFpcSgVSk197rbuGBY4DMpAJQb5D4K93F68QInqq6TYmEBmXCpXrbwEZF8DDKWV32Nla0wivTrf+fDsDLgHAVacLt6a1CvZPHz4ML766itcu3YNP/zwAwICArBx40YEBQVh6NChDRUjERERARBKS6H5dT+y1q6B9sJFY6NUCueHH4Z75DTYde8uboAtmN6gx7nMc4hSRSFGFYNr6mtm/fe53oewwDAoFUoEewZDJuUxMtTMaPOBzEvmVcrMS0DOjXuvp7R2BDw7AV5dAK/bf3Y2Vi/5PUCoR7K5Y8cOREREYNKkSYiPj4dWqwUA5OXlYcmSJdi7d2+DBUlERNSaGQoKkLvjR2SvX4+S5GQAgMTODq5PPQX356fAOjBQ5AhbpsKSQhxNPopoVTQOJx1GdnG2qc9KYoV+Pv2gVCgRpgiDwkkhXqBEtVGUY55QZvwNZF4G1Kp732PreieRNH10AZwDOPWVqlTnZHPx4sVYtWoVnnvuOWzdutXUPnjwYCxatKhBgiMiImrNSjMzkb1pE3K+2wqDWg0AkLm7wz1iMlyfeQZWbm4iR9jypBakIkYVg+jEaJxIOYGScuf4OVk7ITQgFEqFEkMChsDZ2lnESImqIAhAQYb5tNfMsmmw+Wn3vs/B2zyZvP2ngxeTSqqTOiebly5dwrBhwyq0Ozs7Izc3tz4xERERtWrahARkr1sP9a5dEHQ6AIB127ZwnzoVLk88DqmtrcgRthyCIOBC9gVjgqmKxsXsi2b9CicFlAollIFK9PHpA7mUGy6RBREEQJNkvp4ys6xqWdX5lM6BFauUnp0Ae/emi51ahTonm35+frh69SratWtn1n7kyBG0b9++vnERERG1KoIgoPD4cWRv3IT8qCjjD5EA7Hr1gvv0SDg98AAkMq6BaghavRYnUk6YjidJL0w39UkgQW/v3ggLDEO4IhxBLkHcbInEZzCYHydyO6HMuFzFcSISwK1dxfWUnp0AG6emjJ5asTonmzNmzMCsWbOwdu1aSCQSJCcn49ixY5g7dy4WLlzYkDESERG1WIbCQqj37EH2pk3QXb2z6YxjeDg8pkfCrm9fJjsNILMoE4cTDyNaFY1jKcdQVFpk6rOzssMQ/yFQKpQIDQyFuy2rOyQSfQmQnVCWUJavVlZxnIjUCnDvUHH6q8d9gNyuaeMnukudk83XXnsNarUa4eHhKC4uxrBhw2BjY4O5c+fi5ZdfbsgYiYiIWhydSoWczVuQu2MHDHnGyoTU3h4uY8fCbdIk2LQPEjnC5k0QBFzLvYboxGhEqaJwLuMcBAimfh97H+P0WIUS9/veDxsZj2OgJlRSDGRdvatKeQnIugaUWydsRmZTtvPrXdNf3YIAK+umjZ+ohiSCIAjVX3ZvhYWFuHDhAgwGA7p16wZHR8eGiq1RaDQauLi4QK1Ww9mZC/uJiKjpCIKAgqNHkbNpM/Kjo01TZa3btoXbpElweXIsZBb+76glKzGU4HTaacSoYhClikJSfpJZfzePblAqlAhXhKOzW2dWjKnxafONyWTmXbu/VnWciNyhYkLJ40TIwtQ0p6pzZbOoqAiCIMDe3h79+/fHzZs38c0336Bbt24YMWJEXR9LRETU4hgKCpC7ezdyNm+B7tqdqbIOoaFwj5gMh6FDIZFKRYyw+VJr1TiSdATRqmjEJsUir+TO+jVrqTUG+g9EWGAYwgLD4OPgI16g1LIV5VZMKDMuA+pb977H1gXw6nrXesrOgEsgd36lFqPOyebjjz+OJ598EjNnzkRubi4GDBgAuVyOzMxMLFu2DC+88EJDxklERNTs6G7eRM6WLcjd8SMM+fkAAKmDQ9lU2YmwCeJU2bq4pbmFKFUUYhJjEJcWB72gN/W527ojLDAMSoUSA/0Gwl5uL2Kk1OIUZgPpF8ollbePE0m99z2VHSfi2Rlw9GZSSS1enZPNuLg4LF++HADwww8/wMfHB/Hx8dixYwcWLlzIZJOIiFolwWBAwdFjyNm4EfmHDt2ZKtuunXGq7NgnOFW2lvQGPf7M/BNRqihEq6KRoE4w67/P9T4oFUqEBYahp1dPSCWsElM96QqNG/SkXTAml+kXjP9dVVLJ40SIKqhzsllYWAgnJ+O2yQcOHMCTTz4JqVSKgQMH4ubNmw0WIBERUXOgzy+Aevcu5GzaDF3CnWTIIWwY3CdPhsOQIZwqWwsFJQU4mnwU0apoHE48jBztnTMDrSRW6OfbD+GKcIQFhiHQKVC8QKl505cCOQlA2l/mSWX2dQD32NbEtS3g3bVcQtkZ8OwI2HIvEKK71TnZvO+++7Br1y6MHTsW+/fvx6uvvgoASE9P58Y7RETUauhu3kT25s1Q/7jTfKrsU0/CfeJEWN91HjXdW2pBKqJV0YhWReNk6kmUlNuV09naGaGBoVAGKjEkYAicrHlOINWCIAB5KWWVyr+A9IvGBDPjEqDXVn6PvSfg0w3wLvvw6W5MLm04M4GopuqcbC5cuBATJ07Eq6++igceeACDBg0CYKxy9unTp8ECJCIisjSCwYCC2Fhkb9qEgphDpnbroCC4TZ4El8efgMzRQcQImweDYMDFrIuITjQmmH9n/23W38apjel4kj7efWAlrfOPLdSaFOUak0lTUllWsSzOrfx6ub2xUundFfDufifBdPRuyqiJWqR6HX2SmpqKlJQU9O7d27R9+MmTJ+Hs7IwuXbo0WJANiUefEBFRXenz86HeuQs5mzdDd+OGsVEigeOwYXCLiIDD4EGcKluN4tJinEg5gejEaBxSHUJ6UbqpTyqRordXb4QpjBv8BDkH8XgSurdSrbEyWX76a/oFQJNU+fUSmXG6q1lS2RVwbQfw+5aoVhr96BMAuHLlCr766itcv34d33//PQICAnDp0iUEcXc9IiJqQbQJCcjZvAXqnTthKCgAAEgdHeH61JNwmzgR1m3bihyhZcssysShxEOIVkXjWPIxFOuLTX32VvYYEjAESoUSoQGhcLN1Ey9QskwGg3FdZfqFO9Nf0y8AWdeAcjsRm3FRlCWVZdNfvbsaN+uxsmna2IlauTonmzt27EBERAQmTZqEuLg4aLXG+e55eXlYsmQJ9u7d22BBEhERNTXBYEDBkSPI3rgJBYcPm9qt27eH2+RJcH38cUgdOFW2MoIg4EruFcSoYhCtisa5zHMQym224uvgC2WgcXrs/b73w1pmLV6wZDkEAchPv2v6a9m6ypLCyu+xdS1LJruVW1/Z1XiGJRGJrs7J5uLFi7Fq1So899xz2Lp1q6l98ODBWLRoUYMER0RE1NT0+flQ/7jTOFX29u7qEgkcw8LgFjEZDoMHc2pnJUr0Jfgj7Q9Eq6IRkxiDpHzzqYzdPbqb1l92duvMMWzttHll6yovmB8vUphV+fVWtsbdX73LqpQ+3Yz/7eTLsyqJLFidk81Lly5h2LBhFdqdnZ2Rm5tbn5iIiIianPZ6AnI2bzZOlS00VlGkTk5wffJJuE2aCOs2bUSO0PKotWocSjyEmMQYxCbFIr8k39RnI7PBQL+BCFOEISwwDN723GylVSrVAVlXzKe/pl8Acm9Vfr1ECri3L7cDbFlS6R4ESGVNGzsR1Vudk00/Pz9cvXoV7e7a0v3IkSNo3759feMiIiJqdILBgILDh41TZY8cMbVbd+gA98mT4PLYY5wqe5ebmpum40ni0+OhL7dmzsPWw7i5T6ASA/0Hws7KTrQ4qYkZDID61l1J5UUg8zJgKK38Hie/O9Neb0+F9eoMyPn3hqilqHOyOWPGDMyaNQtr166FRCJBcnIyjh07hrlz52LhwoUNGSMREVGD0uflQb1zJ7I3b0bJzbIKi0QCx/BwuE+eBPtBgzjNs0ypoRRnM84iRhWDKFUUbmhumPV3dOtoWn/Zw7MHpBLu6tniFWSWm/5atr4y/SKgy6/8ehvnuzbrKUsw7d2bNm4ianJ1TjZfe+01qNVqhIeHo7i4GMOGDYONjQ3mzp2Ll19+uSFjJCIiahDa69eRs2kzcnftglB+quy4cXCb+CysFQqRI7QMBSUFiE2KRbQqGoeTDiNXm2vqs5Jaob9Pf9P6ywDHANHipEamKwAy/jZfU5l2AShIr/x6qbxsXWX5zXq6AS6BXFdJ1ErV65xNACgsLMSFCxdgMBjQrVs3ODo6NlRsjYLnbBIRtS6CwYD8mBjkbNqMgthYU7v1fR3gPjkCLo+NgdTeXsQILUNyfrJpc5+TqSdRWm7qo7O1M4YFDkOYIgxD/IfAydpJvECp4elLgexr5tNf0/4Ccm4AuMePiW7tzM+q9O4OeHQAZPImDJyIxNKo52yWlJRgxIgR+Oqrr9CpUyf079+/zoESERE1Br1Gg9wff0TOlu9QcqvcVNkHHoB7xGTYDxjQqqfKGgQDLmRdQJQqCtGqaFzOuWzW39a5rWl6bG/v3rCS1utobrIUhdlA2nkg9VzZx3kg8xKg11V+vYOX+VmV3t2N1Usbyy4uEJFlqNO/HHK5HOfPn2/V/0gTEZFl0l67huxNm6DevefOVFln5ztTZQMDRY5QPEWlRTiRcsJUwcwsyjT1SSVS9PbqbZoeG+QSJF6gVH8GA5B7s1xSWfahSaz8erlDuSNFyn04ejVt3ETUotT515TPPfcc1qxZg/fee68h4yEiIqo1Qa9Hfswh5GzaiIKjx0ztNh3vg9vkCLiMGd1qp8pmFmUiRhWDaFU0jqccR7G+2NRnb2WPIQFDEK4Ix9CAoXCzdRMvUKq7kmIg4+JdieV5QJdX+fVu7QCfHoBvT8C3hzGpdG0LSLm5ExE1rDonmzqdDt988w0OHjyI/v37w+GureGXLVtW7+CIiIiqotdokLvjR+Rs3oySxLKKjVQKxwfC4T45AvYDQlrdLBxBEHA557Kpenku85xZv5+DH8ICwxCuCEd/3/6wllmLEyjVTUEWkPqnMaG8PR024xJQ7ggaE5m1sVrpG1yWWAYbp8PaujR93ETUKtU52Tx//jz69u0LALh82XydR2v7h52IiJqW9urVO1Nli4oAAFIXF7iOewpuz06EdWDr2iG1RF+CU2mnTOdfphSkmPX38Ohhmh7bya0T/51uDgwGICeh4jTYvOTKr7dzL0sqyyWWnh25YQ8RiarOyWZUVFRDxkFERFQlQa9HfnQ0sjdtQuGx46Z2m06d4DZ5ElzGjIHUrvUcBp9bnIvDSYcRrYpGbHIsCkoKTH02MhsM8huEMEUYwgLD4GXPdXcWraTIuAts+aQy7a97n1vp3t48sfTpATj783gRIrI4tU42CwsLMW/ePOzatQslJSV48MEH8emnn8LT07Mx4qsgKSkJr7/+Ovbt24eioiJ06tQJa9asQb9+/Zrk9YmIqGnp1eo7U2WTkoyNUimchj8At8kRsA+5v9VU6hLUCYhRxSBKFYUzGWdgEAymPk87T4QFhkGpUGKA3wDYWbWexLtZyc+4Mw329kfWFaDce2liZWtcT2lKLMumwdrw6Bkiah5qnWy+9dZbWL9+PSZNmgRbW1t89913eOGFF/D99983RnxmcnJyMGTIEISHh2Pfvn3w9vbGtWvX4Orq2uivTURETav48mXkbNoM9U8/mabKylxc4Pr0OLg9+yzkAS1/qmypoRRn0s+Y1l/e0Nww6+/k1sm0/rK7Z3dIJdzgxWIY9ED29bLEstxRI/mplV9v71lxGqzHfYCMR84QUfNV6/+D/fjjj1izZg2eeeYZAMDkyZMxZMgQ6PV6yGSyBg+wvPfffx8KhQLr1q0ztbVr165RX5OIiJqOoNcjPyoK2Zs2o/B4uamynTvDPWIynB99tMVPlc3X5SM2ORbRqmgcTjoMtVZt6rOSWuF+n/tN6y/9Hf3FC5Tu0BUAaReAtLumwZYUVnKxBPDoUDGxdPThNFgianEkgiAItbnB2toaCQkJCCj3G2U7OztcvnwZCoWiwQMsr1u3bhg5ciQSExMRExODgIAAvPjii/jHP/5xz3u0Wi20Wq3pc41GA4VCAbVaDWdn50aNl4iIakafm4vcHTuQs+U786myDz4It8mTYH9/y54qm5SfZKxeqmJwKu0USg2lpj4XGxcMCxiGMEUYhvgPgaO1o3iBEpCXVpZQlpsKm3UVQCU/TlnZGae9mq2v7AZYO1S8loioGdFoNHBxcak2p6p1ZVOv18Pa2nybdCsrK5SWlt7jjoZz/fp1fPnll5gzZw7+85//4OTJk3jllVdgY2OD5557rtJ7li5dinfeeafRYyMiotorvnQZOZs2GafKFhvPf5S5uMB1/Hi4PfsM5P4ts3JnEAw4n3neuHtsYjSu5Fwx62/n3A5KhRJhgWHo7d0bVlJOpWxyBr0xiTRLLM8DBemVX+/oc9faymBjBVPauLO+iIgsWa0rm1KpFKNGjYKNjY2p7aeffsIDDzxgdtbmjz/+2HBRlrG2tkb//v1x9OhRU9srr7yCU6dO4dixY5Xew8omEZFlEUpLkRcVhZyNm1B48qSp3aZLlztTZW1tRYywcRSVFuF48nFEJxormFnFWaY+qUSKPt59oAxUIkwRhiCXIBEjbYW0+cZpr6l/3jm7Mu0CUFpU8VqJFPDoWJZU9riTWDr5NH3cREQiabTK5pQpUyq0TZ48ubaPqRM/Pz9069bNrK1r167YsWPHPe+xsbExS4yJiEgcpTk5UO/YgewtW1CaXHYOpEwGpwcfhHvEZNj169fipspmFGYgJjEG0apoHE85Dq3+zi8/HeQOGOI/BEqFEqEBoXC1dRUtzlZDEIC8lLINe8pNg82+jkqnwcodjAmlT48702C9uwLW9k0eOhFRc1TrZLP85jxNbciQIbh06ZJZ2+XLl9G2bVuRIiIiouoUX7pknCq75ycIZTNNZK6ud6bK+vmJHGHDEQQBl3MuI0oVhRhVDM5nnTfr93fwR5jCeDzJ/T73Qy6TixRpK6AvNR4pcvf6ysKsyq938jOfBuvbE3ALAqTc4ZeIqK6a1SKQV199FYMHD8aSJUswfvx4nDx5EqtXr8bq1avFDo2IiMox6HTIO3AQuVu3ovCPP0ztNl27wn3yZDg/+kiLmSqr0+vwR+ofxgQzMQYpBSlm/cGewab1l53cOrW46q1F0OaXO7eybCps2gWgXCXZRCIDPDvdlVgGAw5Nc144EVFrUus1m2L7+eefsWDBAly5cgVBQUGYM2dOlbvR3q2m84uJiKj2tNcTkPv991Dv3Al9bq6xUSaD04iH4D55Muz69m0RyVZOcQ4OJx1GtCoasUmxKCy9c8SFrcwWA/0HQhmoxLDAYfCy9xIv0JZIVwCk/AmknAGSzxj/zLiESqfBWjvdWVfpG2ycDuvdFZC37ONziIgaW01zqmaXbNYXk00iooZl0GqNVczt21F46pSp3crXF65PPQXXp8dB7usrYoT1JwgCEjQJiFEZ11+eyTgDg2Aw9XvZeWFY4DCEK8IR4hcCOysmMw1CV2CsViafAZLjjYll5mWg3NibOPkBfr3Mq5Wu7TgNloioETTaBkFEREQAoL1+Hbnbv4d61647VUypFI5hYXAd/zQcQ0MhsWq+/8yUGkoRnx5vPP8yMQY3NTfN+ju7dUaYIgzhinB08+gGqYRJTb2UTyxTzhiTy6oSS/8+gF9vwL+38U/uBktEZHGa708BRETU5ExVzG3bzNZiWvn6wnXcOLiOe6pZVzHzdHmITY5FtCoahxMPQ6PTmPqspFYI8Q0xrb/0d2yZZ4A2CV1hWWIZf2c6bOalKiqWvY3JJRNLIqJmhckmERFVS3vt2p0qplptbJRK4ahU3qliyprn4fWJeYmm40n+SP0DpUKpqc/VxhWhAaFQKpQY7D8YjtaO4gXaXN1OLG9XK2uUWPa+86dT8/3lBRFRa8dkk4iIKmWsYh5AzrZtKPrjtKndys8PruOegutTzbOKaRAMOJd5DjGqGESponA196pZfzvndghXhCNMEYZeXr1gJeU/lTVmllieKdu85+/KE0tHX2MyWX46LBNLIqIWhf+CEhGRGWMVczvUu3ZXqGK6TRgPh6FDm10Vs7CkEMdTjiMmMQYxqhhkFd85a1EqkaKvd1/T9Nh2Lu3EC7Q50RUajxgpv3nPPRNLn3JJZR8mlkRErQSTTSIigqG42FjF3L7dvIrp72dci/nUU5D7NK91cumF6abpsSdSTkBb7sxFB7kDhgYMRVhgGEIDQuFq6ypanM1C+cTy9nTYjEuAoK94raNPxTWWzn5NGi4REVkGJptERK2Y9upV5GzfDvXuPTDcrmLKZMYq5vinm1UVUxAEXMq5hChVFGJUMfgr6y+z/gDHAIQFhkGpUKK/T3/IZXKRIrVwJUVA6nnzNZYZf1eTWPa+U7lkYklERGWYbBIRtTKG4mLk7d+PnO3fo+i0eRXT7emn4fLkk82miqnT63Aq9ZQxwUyMQWpBqll/T8+exumxijB0dO0IiUQiUqQWyiyxPFNWsbxHYungbV6t9O9t3NCHY0pERPfAZJOIqJXQXrmCnO+/r1jFDFfCbfx4OAwZ0iyqmDnFOTiUeAgxiTGITYpFYWmhqc9WZotB/oOgVCgxLHAYPO08RYzUwpQUAWl/3alWppwB0i9WkVj2vmvzHiaWRERUO0w2iYhaMENxMTS//orc7d+jKC7O1C7394fr+KfhMvZJyH28RYyweoIgIEGdgOjEaESronE24ywM5Tah8bLzQpgiDOGKcIT4hsDWyla8YC1FrRJLL/Ok0r8PE0siImoQTDaJiFog7ZUryNn+PdS7d8Og0RgbZTI4PRAO1/Hj4TB4sEVXMUsNpYhPjzetv7yVd8usv4t7F4QFGhPMrh5dIZVIRYrUApQUl23eU7YjbPJZIP3CvRPLCpv3+DOxJCKiRsFkk4iohTBVMbdtR1F8vKldHhAA16efhsuTYyH3ttwqZp4uD7FJsYhSReFI0hFodBpTn1wqR4hviOl4Ej/HVroJTUmxsWKZEl9WtTwLZFwEDKUVrzUllr3Lbd7DxJKIiJoOk00iomau+PJl5G7/Huo9e+6qYj5grGIOGQyJ1DIrf6o8FWJUMYhOjMbp1NMoFe4kTa42rhgWOAxKhRKD/QfDQe4gYqQiMEssz5TtCnuPxNLes+LmPc4BTCyJiEhUTDaJiJohQ1ERNL/uR+62bSg6c8bULg8MNFYxxz5hkVVMg2DAucxziFYZ119ezb1q1h/kEgSlQglloBK9vHpBJrXcqb4NyqA3nluZ9AeQ+AeQHGdcY3nPxLK3+XRYJpZERGSBmGwSETUjxZcuI3f7dmMVMy/P2GhldaeKOXiQxVUxC0sKcSzlGGJUMYhJjEF2cbapTyaRoa9PX9P5l22d24oYaRPKSzUmlabkMh7Q5Ve8zt7DfPMev96ASyATSyIiahaYbBIRWThDURE0+341VjHPnjW1365iuj45FlZeXiJGWFFaQRpiEmMQrYrGiZQT0Bl0pj5HuSOGBgxFmCIMoQGhcLFxES/QpqArME6BvZ1YJsUBmsSK18kdgIC+QEA/44d/HyaWRETUrDHZJCKyUMWXLiF323aof/rJvIo5fDhcxz8Nh0GWU8UUBAF/Z/9tOp7kQtYFs/4AxwDj9FiFEv28+0Euk4sTaGMzGIDMS+Wqlqcr3xlWIgW8ugKB/YCA/kBgf8CrC9Bapg0TEVGrwGSTiMiCGAoLodn3K3K2b0Px2T9N7XKFwljFHPuExVQxdXodTqaeNK2/TCtMM/VJIEGwVzCUgUqEKcLQ0bUjJC2xQpeXVq5i+QeQFA/o8ipe5+RnrFYG9jcml/59ABvHpo+XiIioCTHZJCKyAMV//122FvMnGPLL1u6VVTHdJoyH/cCBFlHFzC7OxqHEQ4hRxSA2ORZFpUWmPjsrOwz0G4hwRThCA0PhaecpYqSNQFdoPMcy8Q8g6bTxQ62qeJ3cwZhMlq9aOvs3ebhERERiY7JJRCQSYxVzH3K2b69YxRz/NFzHjoWVp7gJmyAISFAnIEoVhZjEGJxJPwMBgqnf284bYQrj5j4hviGwtbIVMdoGZDAAmZfNq5ZplUyHhQTw7mpetfTqAsj4zysRERH/NSQiamLFf/+NnG3boPnp5ztVTLkcTg8Oh9v48bAfMEDUKmaJoQTxafGm9ZeqPPPqXVf3rqYEs5t7t5YxPTY/veLusFpNxescfcuSyrLk0r8PYOPU9PESERE1A0w2iYiagKGgoKyK+T2K/yxXxWzTBm7jn4bL2LGw8vAQLT6NToPYpFhEqaJwJOkI8sqtO5RL5QjxC0F4YDjCFGHwdfAVLc4GoSsEUs6WrbE8bdzER32r4nVye2MyGdC33HRYnmdJRERUU0w2iYgaUfHFi8jZvh2aPT/BUFBgbLxdxZwwAfYhIaJVMVV5KkSrohGjisHptNMoFUpNfW42bggNDEW4IhyD/AfBQe4gSoz1ZjAAWVfMq5Zpf1U+Hdary127w3bldFgiIqJ64L+iREQNzFBQAPXevcjd/j2Kz50ztcvbtoHb+PFweeIJUaqYeoMe5zLPGRPMxBhczb1q1t/epb3peJKenj0ha47HcORnVNwdVquueJ2jT1lS2e/O7rC2zk0fLxERUQvGZJOIqIEUX7hgrGL+9LNZFdP5oQfhOn68KFXMwpJCHEs+hujEaBxKPITs4mxTn0wiQ1+fvlAGGhPMNs5tmjS2eispMk6HNSWWp4HcSqbDWtkB/r3NN/FxCeR0WCIiokbGZJOIqB5MVcxt21F8/ryp3bptW7iOHw+XsU/Ayt29SWNKLUjFocRDiFJF4WTKSegMOlOfk9wJQwOGIkwRhqEBQ+Fi49KksdWZwQBkXb1rd9i/AEPpXRdKAK/O5lVL766ATC5K2ERERK0Zk00iojoo+usv5G7/HpqffoKhsNDYKJfD+aGHjFXMASFNtkurIAi4mH0RMaoYRKmicDH7oll/gGMAwhXhUCqU6OvTF3JpM0i8CjLN11kmxVU+HdbBu+LusLbNJIEmIiJq4ZhsEhHVkD6/AJq9vxirmH/9ZWq3btfOWMV84vEmq2Jq9VqcTDlpWn+ZVphm6pNAgp5ePY3rLwOV6ODawbKPJykpvmt32D+A3JsVr7OyBfx6myeXLgpOhyUiIrJQTDaJiKogCAKK4uKg3rULml/2mqqYErkcTiNGlK3FvL9Jkrns4mwcSjyEaFU0jiYfRVFpkanPzsoOg/wGQalQYljgMHjYiXeMSpUMBiD72l27w56vZDosAM9O5tNhfbpzOiwREVEzwmSTiKgSJUlJyN29G+pdu1Fy686mM6Yq5tgnYOXm1qgxCIKA6+rriFJFIUYVg7MZZyFAMPV723lDqVAiTBGGAX4DYCOzadR46qQg667dYU8DxZVNh/UyTywD+nI6LBERUTPHZJOIqIyhoACaAwfx/+3deXRb9YEv8O+92mVL8hbvsuNgZ3X2hCQ4ieUGMoWwONPXnqEt0Clvhs4LS5oZCgVmpnQhJX1QTmFgCtPDdBYefa8lJhAITkNkZyGOE2eDBLJiy87iOHG0W+t9f1xZsrwkNpEt2/l+ztGRdH+/e+9Prkj99W+z19TA09AQPS7q9TB8/etIW10N3YIFw9qLGQgH0HShCVabFVabFa2u1rjyaRnTotuTTMuYNrqGx0oS0HEcsDUALQ2AbY+8qE9vSi2QNzs+XKYVcTgsERHROMOwSUQ3NCkchmdvozxMtrYWUvdiP4IA/eJFSFu9GoZbb4Wo1w9bG+w+O3a17YLVZsXOtp1wBpzRMpWowqK8RbAUyj2YuSm5w9aOIQt4gbMHgJY9csC0NQDezr71Msvi51nmlHM4LBER0Q2AYZOIbkj+5mbYu4fJnj0bPa4uLoZpdTVMd98NVX7+sN3f5rDJw2Nb67D/wn6EpFC0LEObgWUFy1BlrsKS/CXQq4Yv6A6Jqz0+WJ49CIQD8XWUWjlUmhcBRYuBwoWAfmS3fiEiIqLRgWGTiG4YIacTji1bYK95F979+6PHRYMBxttvh6m6Grq5c4ZlaGooHMKRjiPR+Zen7Kfiym8y3RQdHjszayYUoiLhbRiScBjo+CIWLlv2AJ1n+tZLzZGDZXe4zJ0FKNUj314iIiIadRg2iWhck0IhuD/ZA3tNDZxbt0Ly+eQCUURKRQVM1ffAsGIFRK024ff2BDzYfXY3rDYr6lvr0emLDTFVCArMz5kf3Z7EbDQn/P5D4vfIi/fY9sjzLVv39rOQjwBkT4sFS/MiIH0i51oSERFRvxg2iWhc8p0+DfvGGtg3bULwQmwPSnXpTUirrobxrruhyslO+H3Pu8+jzlYHa6sVDecaEOgxzNSgMmBp4VJYCi2oKKiASZPE1VYd52LDYVv2AOcP991+RKXvOyRWl5aU5hIREdHYM6bD5vr16/HUU0/hsccew0svvZTs5hBRkoXsdjg+/BBXNm5E16HD0eOiyQTTqlUwra6Gtrw8ocNkJUnC0ctH5YBps+LY5WNx5YWphbCYLagyV2FuzlyoxCQsjBMOAe3HYr2Wtj3AlZa+9Qx58b2WuTO5kA8RERF9ZWM2bDY2NuL111/HrFmzkt0UIkoiKRiEe9cuXNlYA9fHH0Py++UChQKpy5fDVF2N1CoLRHXi5hH6Qj40nGuA1WZFXWsd2j3t0TIBAmZPmI1KcyWqzFWYZJo08tuT+Fzynpa2vXKvZWsj4HP0qiTIq8IWLQLMi+Vnk5lDYomIiChhxmTYdLlc+M53voM33ngDP//5z5PdHCJKgq7jx2GveRf29zYhdLEjelwzZYq8muydd0KZlZWw+13yXkJ9az2sNis+OfcJvEFvtEyn1OGW/FtgMVuwrGAZMnWZCbvvoNjb4nstz38K9FjdFgCgTpW3HelezKdwIaA1jmw7iYiI6IYyJsPmmjVrsGrVKtx6663XDJs+nw++7gVBADgcvf+6T0RjRbCzE473N8O+cSO6jh6NHlekp8N4151IW70a2mnTEnIvSZJw6sopWFutsNqsOHzxMCRI0fJsfTaqzFWoLKzEzXk3Q6PQJOS+1xQOARc+jQVL217Abutbz1gY32uZPQNQjMl/8omIiGiMGnO/ebz99ttoampCY2PjoOqvX78ezz777DC3ioiGixQIwFVfL68ma60DApEFd1QqGCyVMK1ejdRlyyCorn9uYSAcQNOFJlhtVmy3bUebqy2ufFrGNFSZq2AxWzA1Y+rIDI/tcshDYrvDZes+wO+KryOI8vxK82LAfLM859JUOPxtIyIiIrqKMRU2bTYbHnvsMdTW1kI7yG0KfvzjH2PdunXR9w6HA2ZzkrcYIKKrkiQJvmPHcKWmBo733keoM7ZliHbGDJiqq2G8cxWU6enXfS+7z46dbTtRZ6vDzradcAac0TK1qMaivEWwmC1YXrgcuSm5132/q5IkuZeyO1i2NADtnwFSOL6e2gCYF8Z6LQsWAJrU4W0bERER0RAJkiRJ1642OtTU1GD16tVQKGKbnYdCIQiCAFEU4fP54sr643A4YDKZYLfbYTRyvhLRaBLs6ID9vfdhr6mB74svoscVE7JguutumKrvgXby5Ou+T4ujBVabFdZWK5ouNCHUY35jhjYDywuXw2K2YEneEuhV+uu+34BCQXnLEdveWLh0nu1bL60oFizNi+W9LsWr/1tHRERENFwGm6nGVM/mihUrcOTIkbhjf/3Xf42pU6fiiSeeuGbQJKLRJ+z3w/XxdthrauDasQMIycFPUKuRuuJrSKuuRkpFBQTlV//nKhQO4XDHYTlg2qw4bT8dV16aVorKwkpYzBbMzJoJxXAFuS47YGuMBMs9QNt+IOCJryMogLxZ8eHSmDc87SEiIiIaRmMqbBoMBpSXl8cdS0lJQWZmZp/jRDR6SZKEriNHYK+pgX3zBwjb7dEy3ezZMK2uhvH226Ewmb7yPTwBD3af3Y3ttu3Y0boDnb7YUFyloMT8nPmwmC2oNFfCbBiGofWSBHR+Cdga5GBp2wu0HwXQazCJ1gQU3hwLlgXzAHVK4ttDRERENMLGVNgkorEtcOEC7Js2wV7zLvynTkWPK3NyYLrnHpiq74Fm0qSvfP3z7vPR4bF7z+1FIByIlhnUBiwrWAaL2YKKggoY1QkeRh8KAOcOx3otbQ2A60Lfeukl8gI+5pvlcDlhKiCKiW0LERER0Sgw5sOm1WpNdhOI6CrCXV1wbtsG+8YauHfvBsLyYjeCVgvDrbfCtLoaKYsXQ/gKw+AlScLRy0dhtVlRZ6vDscvH4srNBjMsZgsshRbMzZkLlXj9K9ZGeS4DrY2xYNnWBPTYexMAIKqAvNmRcBnZ39KQk7g2EBER0bCQJAmhsIRQ5DkYlhCOPId6PIJxr8MIh4FgONy3jiQhFIpcR+o+L4xQGAiFw/1ePxiWkJGixr03FyX7x/GVjfmwSUSjjyRJ8B44CPvGjXBs2YKwM7bCq27+fKStrobh61+HInXoK6h2Bbuw9/zeaMBs97ZHywQImJM9B5WFlagyV6HEVJKY7Um6h8S2fBILlxc/71tPlx4LleZF8pBYle76709ERJQEkiQhEJJDVCAkIRiSQ1EgFEawx/FQ97F+yrpfB0M9w1k4Pqj1G8TiQ9zVQlk0DEpS9D6hQQa6foNkJGCOBlNzDQybREQAEDh7Vh4mu7EG/ubm6HFVfj5M1dUwVd8DddHQ/8Hs8HZgR+sObLdtx55ze+Dt0YOoU+pQkV8Bi9mCZYXLkKHNuP4PIknApVNA807gy11A8y7A0da3XsZNsV7LosVAZhmHxBIR3eB6Bq9gKBwNa8HQ1QNZIFInGAojEDm35/GBrxl5HXfOwPfuc7z3dXrUHS2Ba7RRiIL8EAQoRQEKhfxaIcrvxchztJ4o9j0uCFAqYq8Vovxe7L6mKEIhAnmmsf1Ha4ZNIrouYY8Hzq1bcWVjDTwNDXJQAyDo9TCuXAnT6tXQL1wAYQghTJIknLxyEnWtddhu244jF49A6rGwTo4+Rx4ea7ZgYe5CaBSa6/sQkgRc/CI+XPaebymqgPy5cqjsDpgpWdd3XyIiGrLusOQPhuELheAPxt77g2H4QyH4gxL8oXCkLBwt84XCCATD0bLucl+PYz3rR+v1KgsMEByDYQljZ1PBr0YUAKVChEoU5GeFAKUoQqkQoFLIoSp2PPZaIcrn9A1i8e+VoigHrt5BrJ9ze4aygQKdItKOvoFOvEobBmqnCFFAYkZN3SAYNoloyKRwGJ59+2CveRfOLVsQ9sS279AvWgRTdTWMK2+DmDL4VVUD4QD2X9gf3Z6kzRXfkzg9czosZguqzFWYkj7l+v6hD4fllWGbdwFf7gSadwOejvg6CjVQuBAorgAmVsgrxqqHcc9NIqJRZqihrmcYu95QF1fe63ksdrb1F8hUCvl9/Ov+w1vvcoXYX7DrPqfHdQY4v2dYVCoEqHqd239wjIU5osFi2CSiQfPbbLDXvAt7TQ0CbbEwqCoqgqn6HpjuvgfqwoJBX8/us2Nn205YbVbsbNsJV8AVLVOLaizOX4zKwkpUFlYiJ+U6FtYJh4ALn8Z6LZt3Ad7O+DpKrRwuJy6VA2bhAs63JKJRIRSW0BUIyY9gGF2BELz+EHzBELoC4UhZ5DnYXRaOnRMp80Zey+fFjvcMdb4eIW+shDq1UoRGIUKtlB+q7te9nyOvVT2OaZRykJLLFFApBagV8vGrXat3iOsOa/HBTYz2jLEnjG5UDJtEdFUhlxvOj7bAvrEGnn37osfFlBQY77gdpupq6ObNG/T/kbY4WrDdth11rXVoutCEkBSKlmVoM1BZWAmL2YLFeYuhV33FnsRQEDh/qEe4/ATw2ePrqPTyUNiJFUDxUnkxH+V1DsclohtCosJfVzDc47z4c7oCYXT55deBUPJTnyBADloJCnXqyPtrhbq4e/UTApUMckSjGsMmEfUhhULwNDTgSk0NnLVbIXV1yQWCgJRbboGpuhqGW1dA1F275y8UDuFwx2Fst22H1WbFGfuZuPLStNLo/MuZWTMhCl9hgZ1QADh7IDIkdhfQ0gD4nfF11AZ5rmV3uMyfAygSuBUKESWNJEnwRgJfV1yo6z/8xY71DX/9H48/J5nhT60UoVWK0KoUkYcInUoBTff7aJn8HCsToVXGn6NVKaLhjaGOiIYDwyYRRfnOnJGHyW7ahOC5c9Hj6pISmFavhunuu6DKzb3mddwBN3af3Q2rzYodrTvQ6YsNWVUKSszPnY8qcxUqCytRaCgcekODPnlfy+4FfWwNQMATX0djAoqXROZcLgVyZwEK/pNHNBr4g2G4fUG4/UF4/CG4fEF4fJFnfxBufwhuXxAeXxAuXwgefzBSFoqdF60fgtsfTNqiLP2Fv9jrvuEvrp5S0U8wjNRTxp+jiwRDzpcjorGEv3kR3eBCDgccH3wIe00NvAcPRo+LRiOMq+5AWnU1tLNmXfMv2ufd56OL++w9vxeBcCBaZlAbsKxgGarMVagoqIBBbRhaIwNdQGtjbEGf1kYg2BVfR5cuB8vuBX1yygFRMbT7EFEfobAEzzVCofwIRY7Jr7tDYffr7lDo9gWHtWdQrRB7Bbse4U09QPhTipGy3oFR7HFe78AoQqNUQMHwR0Q0IIZNohuQFArBvXs37Bs3wvnnbZD8frlAFJGybCnSVq9GalUVRM3AcxjDUhjHLh2DtVUOmJ9f/jyuvMhQFB0eOyd7DlTiEIas+t2AbW8kXO4C2vYBIX98HX1WbEjsxApgwjTucUk3PEmS4AuGrxEK5feeAUJhrEw+5g2Ern3jr0itFJGqUUKvVkSfUzRKpKiV0Gu6jymRqlFAr1YiRRMrT+lZX6NAiloJrYrhj4hoNGHYJLpBSJKErsOHYd+8Gc4PtyB48WK0TFNWJm9XctedUGVnD3iNrmAX9p7fi+227ai31aPd2x4tEwURcybMQaVZXuCnxFgy+Pk9Pqc8FPbLyLDYs01AOBhfJzU3Ei4jw2KzJssrVhCNcZIkwe0Pwe4NwO4JwO4NwNkViAZAeQhpCJ4eobDnsNLuYNkdGodrBVFRAFI0yj6hsDsA6tVKpPQMfz1CYYpaAb2mZ2iUr6FS8A9ERETjGcMm0TjnO3EC9s2b4dj8AQI2W/S4Ii0NxjvvhGl1NbTTpw8YDDu8HdjRugPbbdux59weeIPeaJleqUdFQQUqCyuxrHAZMrQZg2tUlx1o2RNb0OfsQUDq1XtiLIgFy4lLgYxJDJc0aoXDEpy+IBxeOSz2fvQ+3vO9oyuI0DAkRJ0qvtcvJRL0Unv3CHb3JHb3LvYMhT3CpEYpcoEYIiIaEoZNonHI39oKx+YP4Ni8Gb7jx6PHBZ0Ohq99DcZVq5C6tAKCWt3nXEmScPLKSXn+ZasVRy4egYTYL8K5KbmoLKxElbkKC3MXQq3oe40+PJeBlk8iW5HsBM4fAaRwfJ20otiQ2OIKIH0iwyWNqGAoDEfX1QOjo6ufMk8ATt/1L1CjUggw6VQw6lQwalXxw0ujgTE+FKb008OYolFCx+GkREQ0CjBsEo0TwYsX4fhwCxybN8N76FCsQKVC6rJlMK66A4aqKoj6vntXBkIB7G/fH13gp83VFlc+I3NGdP7llPQp1+7dcHfE5ls27wIufAag12/iGZNiPZfFFUCa+St9bqKe/MFwpLewn15ET6BPmd0bC5cuX/DaN7gGrUqUA6NWBZMu9jD2eu79MOrkgMieQyIiGk8YNonGsJDdDufWrbBv3gxPw14gHOktFEXoF90M06pVMNx2GxQmU59z7T47drTtQJ2tDjvbdsIVcEXLNAoNFuctRqW5EpWFlcjWDzyPEwDgvCCHyu6AefFY3zqZZbEhscW3AMb86/noNI51BUIDDj+N72ns2wuZiMVsUtSKQQfE3mFSo+QKyERERN0YNonGmLDHA+f27XBs/gCuHTuAQGyLEd3s2TCuWgXj7V+HcsKEPuc2O5qjvZcH2g8g1GOeZIY2Q+69LLRgUd4i6FV9e0CjHGdjQ2K/3AVcOtG3zoRpsSGxxRWAIec6PjWNNaGwhE6PH5dcflzx+K8+f7ErGPfeHwxf+wbXYNAqBwiIAwdIo1YJo07FRWuIiIgShGGTaAyQ/H64du6CY/NmOLdvh+TxRMs0kyfLAXPVHVAXFsadFwqHcOjioej2JGfsZ+LKy9LLYCmUh8eWZ5VDFAb4JftKS3y47DzTq4Ig72sZDZe3AClZCfjkNJoEQmFcdvtx0elDh8uHDpcfHS4fLvV4LZf5cdntu65VUUUB1wyIvYeqdj9StUrOVyQiIhoFGDaJRikpFIKnsRGOzZvhqN2KsN0eLVOZzTDecQeMq+6AdvLkuPPcATd2n90Nq82KHa070OnrjJYpBSUW5C6AxWxBZWElCg3x4VS+sQR0fhlbKfbLXYC9Jb6OIAK5s2LzLYsWA/pBrkRLo0pXIIRLbj86ogFSDosXe7y/FAmSnZ7AtS/YgyAA6Xo10vRXD4jGXkNSTTp5cRzOXyQiIhrbGDaJRpGr7YWpmJAF4+23w7RqFbSzZsX9In7efT46PHbv+b0IhGOhwKg2YlnhMljMFlTkV8CgNvS+KXDpVKzXsnkX4IhfIAiCAsifE1vQp2gxoO07D5RGB7cvGA2KF53+uMDYM1B2OH1wDnFRHIUoICNFjaxUDbJS1ZiQqkGWQX6dlapBZo/jGSlqKDkklYiI6IbFsEk0Cgy0F6ZoMsG48jYYV62CfuFCCAp58ZGwFMbRjqPYbtuOutY6fH7587jrFRmKUGWuQqW5EnOz50Ip9vhPXZKAjuPAlzti4dJ1Ib5BogoomBcJlxWAeRGg6RVSacRIkgRHVyRAOmNDVnsGykvuyHunf8iL5KgVohwWDRpkdgdJg6afQKlBmk4FkUNUiYiIaBAYNomSZKh7YXYFu9Bg2wlrqxV1tjpc9MZ6PUVBxJwJc+ThseZKlBhL4ocg2tuAM3XA6TrgtBVwnY9vjEINFC6MhcvCmwH1VRYIousWjiygEx8c/T0CZc85kX74Q0NbNEenUiDL0N0DKT8mpKojPY+aaLjMStXAqOWQVSIiIko8hk2iETTUvTA7vB2oP1EPq82KT85+gq5QV/QUvVKPioIKWMwWLCtYhnRteux63ivynMvTVvnRe7VYpVYOlxOXyeGyYAGg0g7Xx75hBLsX0OkxTLVPkIw8X3b7ERriCjoGrTIWFHuEyPhQKb9O0fCfdyIiIkou/jZCNMyGshemJEk4ceUE6k7WwWqz4kjHEUiIBZLclNzo6rELcxdCrZB7PRHoivVanqkDzh4ApB49YYII5M0BJlnkh3kRw+UQ2L0BtHV6cd7hRYezO0z2DZRDXUAHANL1qh6hUR7GOsHQK1BGjmtV3MORiIiIxg6GTaJh0HMvTPeOHZCushdmIBTA3gv7YP3cirrWOrS54hfnKc8sR6W5ElXmKkxOnywPdwyHgHOHIkNjrUDLHiDYFd+IzLJIuKyUF/XRpYP6kiQJF10+tHV60XbF2+/zUBbREQUgIyUy19Gg6dsT2SNQZqSouacjERERjVsMm0QJIvn9cO3aBcfmD+D8+OOr7oVp99mxpW0HrEet2NW2C66AK1ZXocHivMWoNFeisrAS2frs2Iqx+34X6b3cAXRdiW9Aaq4cLCdZgJJKwFQwIp97tAuGwjhn7+o/SEYe/uC150NmpqiRl6bFhOiKq70Dpfw+Xa/mAjpEREREYNgkui7yXpj7Inth1l51L8xmRzM227bB+qkVB9oPICTFVgzN0GbAYrbAUmjB4vzF0Cl1gPMCcNIamXdZBzha42+uMco9lt3hcsIUeWPDG0xXIITWuBDpiQuV5x1duNbUSFEAcoxaFKTpUJCui3suTNejIE0HnZpDWImIiIiGgmGTaIgkSULXkSNywPzgwwH3wlSVz8DhjsOw2t7H9o3b8aXjy7jrlKWXRedflmeVQ/S55G1Itj4rB8yLx+JvrFDLcy0nVQIlFiB/LqAY//8Jd8+XlMOjJ9YjGTnW4fJf8xpqhYj8NG0sSKbpe4RJHXJNWg5nJSIiIkqw8f+bKlGCRPfC/OBDBFpaosd77oUpzZmO3ef3oK71/6L+/9Xjiu9KtJ5SUGJB7gK5B9NsQYF2AtDaCBx5Dzj990DbfkDquT+iAOTNknstJ1mAoiXjbjuSRM2XTNUo++2VLEjXoTBNh6xUDYe2EhEREY0whk2iqxjMXpjOuTfBemEXrLY30fj/GhEIxxYDMqqNWFa4DBazBRW5S2DobJZ7Lfc/CjTvBgKe+Buml8RWjC1ZDugzRuRzDpdEzZfMSFFHeiTlnsj4MKmHUcd9IomIiIhGG4ZNol6utRem4Y7b0To7Fxs79sBq+xd8semLuPOLjcWwFFpQaa7EXGU6lM07gca3gTP/C/Bcir+ZPit+UZ/04uH/gAk0/PMldchP00Gv5j9VRERERGMNf4MjAhByOOS9MN9/P34vTEGAftEi6G9fiWMzTfjDlb2ob30RFz+OzdMUBRFzJsyRh8dmzUZJxxm593LXg8CV5vgbqVKAiRWxcJk9HRBH71zB/uZL9gyXl9ycL0lERERE/WPYpBtW2OuFa/t22Dd/AHd9fdxemNrZs6BYacHBch22uvdjz9kX0dUY28dSr9SjoqACltzFWBZWId22D9jxO+DCkfibiEqgcGEsXBbMB5TqEfqEV5eo+ZIpaoW8YivnSxIRERFRDwybdEO56l6YZWXwf20R9par8JH/EA53vAp8Hjs3NyUXloLlsGjzsPBKO9SndwD1/wH0mKMJAMgpjy3qU7wE0BhG5sMNoCsQwqmLLpxsd+HEBRdOtDtxot2F1s6hz5fsb5irSafifEkiIiIi6oNhk8a9nnthOmtrEeqxF6aysADOyjnYPV3Ee9IhnHW/DZyNnVueWY7K9OmoCkiY3PYphO3/Cvhd8TcwFcXPu0ydMDIfrBePP4hT7e5omOwOli2XPZAGmDfJ+ZJERERENFz4WySNS1fbC1PMysTlimmonxZGjeozuIIfAZH8qFFosDhrNiqV6ajsbEf2sU8A9wfxF9elR3ouIwEzvQQYwZ49ly8Y6aXsDpWxnsqBmHQqTM5JRWm2AWXZqSjLScXEzBTOlyQiIiKiYcOwSePKQHthwpiK9ptvwrbJPrxnPI2gsEc+HgQyNRmoNJTA4gticetn0J38Y/xFlTp5OGx3z2XurBFZ1MfuDeBkuzPSQyk/Tl5w4qy9a8BzMlPUKMtJRVm2AWU5qSjNll9npao51JWIiIiIRtSYCpvr16/HO++8g88//xw6nQ633HILnn/+eUyZMiXZTaMkGmgvTEmrwbm5hfiozIPa3HaEFJ9Fy8r0ebCIRlgunUP5mUMQcTB2QUGUF/LpDpfmmwGlZtja3+n2R8KkHCxPRl5fcPgGPCfboImGSjlQysEyM3X42klERERENBRjKmzW1dVhzZo1WLhwIYLBIJ5++mmsXLkSR48eRUpKSrKbRyPI39ICZ20tHLVb0XX4cPS4pFSgdcYEbCl1o36iBz61vPWIUlBisSYbFm8XLGePo8DfEn/BCVNji/pMrAC0poS2V5IkXHL7I2HSieOR+ZQn213ocA28fUieSRvtnSzLSZWHwk4wwKRXJbR9RERERESJJkjSQEuHjH4XL15EdnY26urqsHz58kGd43A4YDKZYLfbYTQah7mFlEi+kyfhqK2Fs3YrfJ/HlomVBMBWloYtZW58UhaGWycPFzWKGiyDDpaOs6hwXIKh51fdkC8Hy0kWoGQ5YMxLSBslSUK70xe36uvJyOtOT2DA8wrSdJEwGd9TadAyVBIRERHR6DLYTDWmejZ7s0dWFc3IyBiwjs/ng88XG47ocDiGvV2UGJIkwff559GA6T91KloWFgWcvkmP7ZO82DtZgD1VXuGnWNThf7jcqLR3YG6XL/YF15iAkmWxgJlZel2L+kiShHP2rugCPScjcypPXHDC0dX/3pSCABRl6CNBMrZQz00TUpGiGdP/KRIRERER9TFmf8OVJAnr1q3D0qVLUV5ePmC99evX49lnnx3BltH1kCQJXYcPRwNmwGaLloUUIo5NUqF+cgD7SgW49D6IEDEnKMJy+RIsHi9KApGgp9DIPZbd4TJvDiAqhtyecFhC2xVvdB7l8chiPafaXXD5+g+VogBMzEyReyh7zKsszU6FVjX0NhARERERjUVjdhjtmjVrsHnzZuzcuROFhYUD1uuvZ9NsNnMY7SgihULwHjgAx0e1cG7diuD589GygErEoUkCdk+WsL9UgFcrQA8BFR4vLG43lnm8SA+HAQhA/pzYoj5FiwGVbtBtCIUltHZ6YnMpI6HyZLsL3kCo33OUooCJWSlyD2V2KspyDNEtRRgqiYiIiGi8GtfDaB955BFs2rQJ9fX1Vw2aAKDRaKDRcIXO0UYKBOBpbJR7MP+8DaGOjmiZTyNi3yQJe6YKODhJgE8tIC8k4B63E1VXvFjg7YIaAIwFwJxvAKW3AhOXAfqBh1N3C4bCaL7siS7UIw99deHURRd8wXC/56gVIiZNSIlbqKcsOxXFmSlQK7lHJRERERFRf8ZU2JQkCY888gg2btwIq9WKkpKSZDeJhiDs98O9ezectVvh2rYNocicWwDwaAU0lgJ7pgo4XCIgoBRR7vPjf7o9qLroxWR/AIKoAopvkcNl2W3yCrIDzLv0B8NovuSOhsnulV9PX3TDH+o/VGqUIm6akBoNk6WRYFmcoYdSwVBJRERERDQUYypsrlmzBm+99RbeffddGAwGnI8MtzSZTNDpBj9kkkZO2OuFa+dOOWBu346wyxUtc+gF7J0MNEwR8GmxAKUILPZ24akrHiz3dCE7FALSioHZ34r1XmpS464fCIVx6mIkUF6I9FS2u/BlhxvBcP8jxHUqRWzF18icysk5qShM10MhfvVFg4iIiIiIKGZMzdkUBujFevPNN/G9731vUNfg1ifDL+Ryw1VnlQNmfT0krzdadjlVDpcNUwR8bhaQLoVh8XhR6fFisbcLOoUGmLhUDpeltwGZN8X1Xna4fGhq7sT+lk4caL6Cw21X0BXov6cyRa1AaY4Bk3st1FOQpoPIUElERERE9JWMyzmbYygX33BCdjucH2+Hs7YW7l27IPn90bJ2kxww90wRcbIAKA0EYPF48fR5L8p9foiZpcDM2yK9lxXRhX2CoTA+P+tAU0snmpo70dRyBS2XPX3ubdAoMTnXEN2bsixHfp1n0g74BwoiIiIiIhpeYyps0ugSvHwZzj//Gc7arXDv+QQIxlZtPZsRC5i2HAkLfT58w+OFpdWLAkErb0tSukIOmBny3NvLbj+aTnSiqaUZTS2dOGSz91kJVhCAsuxUzCtKlx/FaZiUlcqeSiIiIiKiUYZhk4YkcOECnFv/DGdtLTz79gHh2BDW5glAwxQRDVMF2NNDWN7VhTVuDypaupCaNRUov1UOl0VLEBLV+OK8E03HO9HUfBBNLZ348lI/vZZaJeaY0zCvKB3zi9Mx25wGk041kh+ZiIiIiIi+AoZNuiZ/axuctbVw1Nai6+DBuLJTuZGAOUWA2hiExePCTz1ezGnXQDmpElh8G1C6AldU2TjQcgX7T3SiadsBHLJdgdvfd//K0uxUzCtKi/RapqN0AnstiYiIiIjGIoZN6pfvzBk4a7fC/tEW+I8eiyv7vABomCpiXxlQoPOjyu3F971elOinA9NvReimW3FCPRVNrW40ne5Ek/UkTl881OceqZruXss0zC1Ox1xzGtL06pH6iERERERENIwYNgmAvPiS7/gJOGtr0fnRhwidPB0tCwvAUbOAhqkCPi2VMF3pQ5XHgyf9GqQVfg2euVU4qJ6LjRfVONDciYM7rsDp29PnHpOyUjA3Ms9yfnE6yrIN3GqEiIiIiGicYti8gUmShK5PP4Oj9iNc3vIBYDsbLQuKwKfFcsBsKQljATz4S68Xv9BOhytvOQ5oFuCX9kLsa3Hg5D4XgOa4a+vViuhcy3nFaZhrTkd6CnstiYiIiIhuFAybNxgpHIb34CHYP9qCS1s2Q3HhUrTMrwAOTZL3wPSaA1gkefGDsAZppltwQLUA/+2eih+0SXCcDkbOiIXTiZl6zCtKx9zidMwrSsOUHAOUCnGEPx0REREREY0WDJs3ACkYhGfffnR8+B4cf94K5SUHAEABoEsFHLhJQFMZoC7wYUnIh0dUk9CiWoh33TPw/KUJCLd3h8YAAECnUmBWoQnziuXtR+YWpSErVZOcD0dERERERKMSw+Y4Jfn9cDfsxdn3/4Suj+ugcnoByP+DezTA/lIBR0slZOZ2YYGkQnVoNrZcKcfPuqbCgdS4a5kzdNGtR+YVpWNqLnstiYiIiIjo6hg2x5GwzwfHjnrY3vu/kHY0QOWReyJVAJxaoHGygNZJIeRld6EwmIccx2zUtc/B7yQzAHmhHo1SxM2FaZhbnBbttcw2aJP3oYiIiIiIaExi2Bzjwh4POj6uRcu7/wfqvZ9C5QtH/0e9kgLsmyzAXhLAhHQRgnsyOvwLsKl9BtzQAQAK0nS4KzLPcl5ROqblGaFWsteSiIiIiIiuD8PmGBRyOmH7cCPO1byF1MMtUAYlpETKOgzAwcmAvzgARWoGLnvnYldwPk5dyodaqcBMswnfLkqLDonNNrLXkoiIiIiIEo9hc4wIXL6M4+/8Gy5/sAlpn1+CMgykRcrOpwGfl0rwFQlw6UpwwrsYe8MzkC6kYe60dHy7SO65nJ5vhEapSOKnICIiIiKiGwXD5ijmPNuMz/7rf8Nj3Y3sMx4oJCArUtaaCTTfJOFKYSraVLNxJLgUhoLJmFeUjm8VpeOXxWnIM+mS2n4iIiIiIrpxMWyOMi1HduLQf74Izf4TKGgLwgTAFClrzgbaJgk4m5eHNsPXoCr8GmZNzEFVcTpm5BuhVbHXkoiIiIiIRgeGzVHivVceh+aPm2E+L6G0x/Evc4HWEjXaS2ZCO+27mDx5Fr5enI58kxaCICStvURERERERFfDsDlKqLV6mM9LCANoLgAulGZCuPkOzKj8a1QVZ7PXkoiIiIiIxhSGzVGi4t7H8eGJI5jyjf+F2xeuYK8lERERERGNaQybo0RqSiq++fw7yW4GERERERFRQojJbgARERERERGNPwybRERERERElHAMm0RERERERJRwDJtERERERESUcAybRERERERElHAMm0RERERERJRwDJtERERERESUcAybRERERERElHAMm0RERERERJRwDJtERERERESUcAybRERERERElHAMm0RERERERJRwDJtERERERESUcAybRERERERElHDKZDdgpEmSBABwOBxJbgkREREREdHY052lurPVQG64sOl0OgEAZrM5yS0hIiIiIiIau5xOJ0wm04DlgnStODrOhMNhnD17FgaDAYIgJLs5cRwOB8xmM2w2G4xGY7KbQ+MYv2s0Uvhdo5HC7xqNFH7XaKSM5u+aJElwOp3Iz8+HKA48M/OG69kURRGFhYXJbsZVGY3GUfeFovGJ3zUaKfyu0Ujhd41GCr9rNFJG63ftaj2a3bhAEBERERERESUcwyYRERERERElHMPmKKLRaPDP//zP0Gg0yW4KjXP8rtFI4XeNRgq/azRS+F2jkTIevms33AJBRERERERENPzYs0lEREREREQJx7BJRERERERECcewSURERERERAnHsElEREREREQJx7A5Srz66qsoKSmBVqvF/PnzsWPHjmQ3icaZ9evXY+HChTAYDMjOzkZ1dTW++OKLZDeLbgDr16+HIAhYu3ZtsptC41BbWxu++93vIjMzE3q9HnPmzMH+/fuT3SwaZ4LBIJ555hmUlJRAp9Nh0qRJ+OlPf4pwOJzsptEYV19fj7vuugv5+fkQBAE1NTVx5ZIk4Sc/+Qny8/Oh0+lgsVjw2WefJaexXwHD5ijwhz/8AWvXrsXTTz+NAwcOYNmyZbj99tvR0tKS7KbROFJXV4c1a9Zgz5492Lp1K4LBIFauXAm3253sptE41tjYiNdffx2zZs1KdlNoHOrs7ERFRQVUKhU+/PBDHD16FC+88ALS0tKS3TQaZ55//nn867/+K1555RUcO3YMGzZswK9+9Su8/PLLyW4ajXFutxuzZ8/GK6+80m/5hg0b8OKLL+KVV15BY2MjcnNzcdttt8HpdI5wS78abn0yCixatAjz5s3Da6+9Fj02bdo0VFdXY/369UlsGY1nFy9eRHZ2Nurq6rB8+fJkN4fGIZfLhXnz5uHVV1/Fz3/+c8yZMwcvvfRSsptF48iTTz6JXbt2cTQQDbs777wTOTk5+N3vfhc99o1vfAN6vR7/+Z//mcSW0XgiCAI2btyI6upqAHKvZn5+PtauXYsnnngCAODz+ZCTk4Pnn38eDz30UBJbOzjs2Uwyv9+P/fv3Y+XKlXHHV65cid27dyepVXQjsNvtAICMjIwkt4TGqzVr1mDVqlW49dZbk90UGqc2bdqEBQsW4Jvf/Cays7Mxd+5cvPHGG8luFo1DS5cuxbZt23D8+HEAwKFDh7Bz507ccccdSW4ZjWdnzpzB+fPn43KCRqNBZWXlmMkJymQ34EbX0dGBUCiEnJycuOM5OTk4f/58klpF450kSVi3bh2WLl2K8vLyZDeHxqG3334bTU1NaGxsTHZTaBw7ffo0XnvtNaxbtw5PPfUU9u7di0cffRQajQb3339/sptH48gTTzwBu92OqVOnQqFQIBQK4Re/+AXuvffeZDeNxrHuLNBfTmhubk5Gk4aMYXOUEAQh7r0kSX2OESXKww8/jMOHD2Pnzp3JbgqNQzabDY899hhqa2uh1WqT3Rwax8LhMBYsWIDnnnsOADB37lx89tlneO211xg2KaH+8Ic/4L/+67/w1ltvYcaMGTh48CDWrl2L/Px8PPDAA8luHo1zYzknMGwmWVZWFhQKRZ9ezPb29j5/xSBKhEceeQSbNm1CfX09CgsLk90cGof279+P9vZ2zJ8/P3osFAqhvr4er7zyCnw+HxQKRRJbSONFXl4epk+fHnds2rRp+NOf/pSkFtF49fjjj+PJJ5/EX/3VXwEAZs6ciebmZqxfv55hk4ZNbm4uALmHMy8vL3p8LOUEztlMMrVajfnz52Pr1q1xx7du3YpbbrklSa2i8UiSJDz88MN455138PHHH6OkpCTZTaJxasWKFThy5AgOHjwYfSxYsADf+c53cPDgQQZNSpiKioo+WzgdP34cxcXFSWoRjVcejweiGP9rs0Kh4NYnNKxKSkqQm5sblxP8fj/q6urGTE5gz+YosG7dOtx3331YsGABlixZgtdffx0tLS34wQ9+kOym0TiyZs0avPXWW3j33XdhMBiivekmkwk6nS7JraPxxGAw9JkLnJKSgszMTM4RpoT64Q9/iFtuuQXPPfccvvWtb2Hv3r14/fXX8frrrye7aTTO3HXXXfjFL36BoqIizJgxAwcOHMCLL76I73//+8luGo1xLpcLJ0+ejL4/c+YMDh48iIyMDBQVFWHt2rV47rnnUFZWhrKyMjz33HPQ6/X49re/ncRWDx63PhklXn31VWzYsAHnzp1DeXk5fv3rX3M7Ckqogcb2v/nmm/je9743so2hG47FYuHWJzQs3n//ffz4xz/GiRMnUFJSgnXr1uFv/uZvkt0sGmecTif+8R//ERs3bkR7ezvy8/Nx77334p/+6Z+gVquT3Twaw6xWK6qqqvocf+CBB/Dv//7vkCQJzz77LH7729+is7MTixYtwr/8y7+MmT/eMmwSERERERFRwnHOJhERERERESUcwyYRERERERElHMMmERERERERJRzDJhERERERESUcwyYRERERERElHMMmERERERERJRzDJhERERERESUcwyYRERERERElHMMmERERERERJRzDJhERERERESUcwyYREVECWCwWrF27dtRcJ1nXH633JiKikcewSUREY9KWLVsgCMJVHx9++OGIteedd97Bz372sxG7HxER0WinTHYDiIiIvorKykqcO3cu+r68vBwPPfQQHnnkkeixrKysEWmL3+9HRkbGiNyLiIhorGDPJhERjUk6nQ65ubnIzc1FKBTCpUuXsHTp0uix3NxcKJXxf1O1WCx4+OGH8fDDDyMtLQ2ZmZl45plnIElStI4kSdiwYQMmTZoEnU6H2bNn449//GO/11m3bh2ysrJw22239Rki6vP58OijjyI7OxtarRZLly5FY2Nj3HXcbjfuv/9+pKamIi8vDy+88EKfz/nHP/4RM2fOhE6nQ2ZmJm699Va43e5+fyZbtmzB0qVLo5/tzjvvxKlTp/rUC4fD+NGPfoSMjAzk5ubiJz/5SVz5tX4Gg7nPYD4bERGNbwybREQ05h04cAAAMH/+/GvW/f3vfw+lUomGhgb85je/wa9//Wv827/9W7T8mWeewZtvvonXXnsNn332GX74wx/iu9/9Lurq6vq9zq5du/Db3/62z31+9KMf4U9/+hN+//vfo6mpCaWlpfiLv/gLXL58OVrn8ccfx/bt27Fx40bU1tbCarVi//790fJz587h3nvvxfe//30cO3YMVqsVf/mXfxkXjntyu91Yt24dGhsbsW3bNoiiiNWrVyMcDvdpe0pKChoaGrBhwwb89Kc/xdatWwf9MxjMfa712YiI6AYgERERjXHPPvusVFBQcM16lZWV0rRp06RwOBw99sQTT0jTpk2TJEmSXC6XpNVqpd27d8ed9+CDD0r33ntv3HXmzJnT59qPPfZY9DoqlUr67//+72i53++X8vPzpQ0bNkiSJElOp1NSq9XS22+/Ha1z6dIlSafTRa+zf/9+CYD05ZdfDuKn0Fd7e7sEQDpy5EhcO5cuXRpXb+HChdITTzwxpJ/B1e4zmM9GRETjH3s2iYhozGtqasK8efMGVXfx4sUQBCH6fsmSJThx4gRCoRCOHj2Krq4u3HbbbUhNTY0+/uM//qPPMNEFCxYMeI9Tp04hEAigoqIiekylUuHmm2/GsWPHonX8fj+WLFkSrZORkYEpU6ZE38+ePRsrVqzAzJkz8c1vfhNvvPEGOjs7r3rfb3/725g0aRKMRiNKSkoAAC0tLXH1Zs2aFfc+Ly8P7e3tADCon8G17jOYz0ZEROMfFwgiIqIxr6mpCQ8++OB1X6d7GOjmzZtRUFAQV6bRaOLep6SkDHgdKTLMtWeo7T7efUwaYChsTwqFAlu3bsXu3btRW1uLl19+GU8//TQaGhqiAa+nu+66C2azGW+88Qby8/MRDodRXl4Ov98fV0+lUsW9FwQh+tkH8zO41n0G89mIiGj8Y88mERGNaZcuXYLNZht0z+aePXv6vC8rK4NCocD06dOh0WjQ0tKC0tLSuIfZbB50m0pLS6FWq7Fz587osUAggH379mHatGnROiqVKq49nZ2dOH78eNy1BEFARUUFnn32WRw4cABqtRobN27s9+dw7NgxPPPMM1ixYgWmTZt21V7QgVzrZzCY+wz2sxER0fjGnk0iIhrTuhedGWzYtNlsWLduHR566CE0NTXh5Zdfjq6UajAY8A//8A/44Q9/iHA4jKVLl8LhcGD37t1ITU3FAw88MKh7pKSk4O/+7u/w+OOPIyMjA0VFRdiwYQM8Hk+0BzY1NRUPPvggHn/8cWRmZiInJwdPP/00RDH2d+CGhgZs27YNK1euRHZ2NhoaGnDx4sVoYO0pPT0dmZmZeP3115GXl4eWlhY8+eSTg2pvT9f6Gdx3333XvM9gPhsREY1/DJtERDSmHThwANnZ2X2GfA7k/vvvh9frxc033wyFQoFHHnkEf/u3fxst/9nPfobs7GysX78ep0+fRlpaGubNm4ennnpqSO365S9/iXA4jPvuuw9OpxMLFizARx99hPT09GidX/3qV3C5XLj77rthMBjw93//97Db7dFyo9GI+vp6vPTSS3A4HCguLsYLL7yA22+/vc/9RFHE22+/jUcffRTl5eWYMmUKfvOb38BisQyp3df6GQz2Ptf6bERENP4JEidWEBHRDcJisWDOnDl46aWXkt0UIiKicY/jWYiIiIiIiCjhGDaJiIiIiIgo4TiMloiIiIiIiBKOPZtERERERESUcAybRERERERElHAMm0RERERERJRwDJtERERERESUcAybRERERERElHAMm0RERERERJRwDJtERERERESUcAybRERERERElHAMm0RERERERJRwDJtERERERESUcP8ffwDkBHYh2pAAAAAASUVORK5CYII=\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_9_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "# First view\n", - "# Changing r and g\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Value of lease of length $T$')\n", - "ax.set_ylabel('Present Value, $p_0$')\n", - "ax.set_xlabel('$T$ periods ahead')\n", - "T_max = 10\n", - "T=np.arange(0, T_max+1)\n", - "\n", - "rs, gs = (0.9, 0.5, 0.4001, 0.4), (0.4, 0.4, 0.4, 0.5),\n", - "comparisons = ('$\\gg$', '$>$', r'$\\approx$', '$<$')\n", - "for r, g, comp in zip(rs, gs, comparisons):\n", - " ax.plot(finite_lease_pv_true(T, g, r, x_0), label=f'r(={r}) {comp} g(={g})')\n", - "\n", - "ax.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "7844a514", - "metadata": {}, - "source": [ - "This graph gives a big hint for why the condition $r > g$ is\n", - "necessary if a lease of length $T = +\\infty$ is to have finite\n", - "value.\n", - "\n", - "For fans of 3-d graphs the same point comes through in the following\n", - "graph.\n", - "\n", - "If you aren't enamored of 3-d graphs, feel free to skip the next\n", - "visualization!" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "142d0a9e", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_11_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "# Second view\n", - "fig = plt.figure()\n", - "T = 3\n", - "ax = plt.subplot(projection='3d')\n", - "r = np.arange(0.01, 0.99, 0.005)\n", - "g = np.arange(0.011, 0.991, 0.005)\n", - "\n", - "rr, gg = np.meshgrid(r, g)\n", - "z = finite_lease_pv_true(T, gg, rr, x_0)\n", - "\n", - "# Removes points where undefined\n", - "same = (rr == gg)\n", - "z[same] = np.nan\n", - "surf = ax.plot_surface(rr, gg, z, cmap=cm.coolwarm,\n", - " antialiased=True, clim=(0, 15))\n", - "fig.colorbar(surf, shrink=0.5, aspect=5)\n", - "ax.set_xlabel('$r$')\n", - "ax.set_ylabel('$g$')\n", - "ax.set_zlabel('Present Value, $p_0$')\n", - "ax.view_init(20, 10)\n", - "ax.set_title('Three Period Lease PV with Varying $g$ and $r$')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "5df0e132", - "metadata": {}, - "source": [ - "We can use a little calculus to study how the present value $p_0$\n", - "of a lease varies with $r$ and $g$.\n", - "\n", - "We will use a library called [SymPy](https://www.sympy.org/).\n", - "\n", - "SymPy enables us to do symbolic math calculations including\n", - "computing derivatives of algebraic equations.\n", - "\n", - "We will illustrate how it works by creating a symbolic expression that\n", - "represents our present value formula for an infinite lease.\n", - "\n", - "After that, we'll use SymPy to compute derivatives" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "bd0ad70e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Our formula is:\n" - ] - }, - { - "data": { - "text/latex": [ - "$\\displaystyle \\frac{x_{0}}{- \\frac{g + 1}{r + 1} + 1}$" - ], - "text/plain": [ - " x₀ \n", - "───────────\n", - " g + 1 \n", - "- ───── + 1\n", - " r + 1 " - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Creates algebraic symbols that can be used in an algebraic expression\n", - "g, r, x0 = sym.symbols('g, r, x0')\n", - "G = (1 + g)\n", - "R = (1 + r)\n", - "p0 = x0 / (1 - G * R**(-1))\n", - "init_printing(use_latex='mathjax')\n", - "print('Our formula is:')\n", - "p0" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "639487a8", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "dp0 / dg is:\n" - ] - }, - { - "data": { - "text/latex": [ - "$\\displaystyle \\frac{x_{0}}{\\left(r + 1\\right) \\left(- \\frac{g + 1}{r + 1} + 1\\right)^{2}}$" - ], - "text/plain": [ - " x₀ \n", - "──────────────────────\n", - " 2\n", - " ⎛ g + 1 ⎞ \n", - "(r + 1)⋅⎜- ───── + 1⎟ \n", - " ⎝ r + 1 ⎠ " - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "print('dp0 / dg is:')\n", - "dp_dg = sym.diff(p0, g)\n", - "dp_dg" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "e993d26f", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "dp0 / dr is:\n" - ] - }, - { - "data": { - "text/latex": [ - "$\\displaystyle - \\frac{x_{0} \\left(g + 1\\right)}{\\left(r + 1\\right)^{2} \\left(- \\frac{g + 1}{r + 1} + 1\\right)^{2}}$" - ], - "text/plain": [ - " -x₀⋅(g + 1) \n", - "───────────────────────\n", - " 2\n", - " 2 ⎛ g + 1 ⎞ \n", - "(r + 1) ⋅⎜- ───── + 1⎟ \n", - " ⎝ r + 1 ⎠ " - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "print('dp0 / dr is:')\n", - "dp_dr = sym.diff(p0, r)\n", - "dp_dr" - ] - }, - { - "cell_type": "markdown", - "id": "57283836", - "metadata": {}, - "source": [ - "We can see that for $\\frac{\\partial p_0}{\\partial r}<0$ as long as\n", - "$r>g$, $r>0$ and $g>0$ and $x_0$ is positive,\n", - "so $\\frac{\\partial p_0}{\\partial r}$ will always be negative.\n", - "\n", - "Similarly, $\\frac{\\partial p_0}{\\partial g}>0$ as long as $r>g$, $r>0$ and $g>0$ and $x_0$ is positive, so $\\frac{\\partial p_0}{\\partial g}$\n", - "will always be positive.\n", - "\n", - "## Back to the Keynesian Multiplier\n", - "\n", - "We will now go back to the case of the Keynesian multiplier and plot the\n", - "time path of $y_t$, given that consumption is a constant fraction\n", - "of national income, and investment is fixed." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "e64c49c0", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_17_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "# Function that calculates a path of y\n", - "def calculate_y(i, b, g, T, y_init):\n", - " y = np.zeros(T+1)\n", - " y[0] = i + b * y_init + g\n", - " for t in range(1, T+1):\n", - " y[t] = b * y[t-1] + i + g\n", - " return y\n", - "\n", - "# Initial values\n", - "i_0 = 0.3\n", - "g_0 = 0.3\n", - "# 2/3 of income goes towards consumption\n", - "b = 2/3\n", - "y_init = 0\n", - "T = 100\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Path of Aggregate Output Over Time')\n", - "ax.set_xlabel('$t$')\n", - "ax.set_ylabel('$y_t$')\n", - "ax.plot(np.arange(0, T+1), calculate_y(i_0, b, g_0, T, y_init))\n", - "# Output predicted by geometric series\n", - "ax.hlines(i_0 / (1 - b) + g_0 / (1 - b), xmin=-1, xmax=101, linestyles='--')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "df1abb00", - "metadata": {}, - "source": [ - "In this model, income grows over time, until it gradually converges to\n", - "the infinite geometric series sum of income.\n", - "\n", - "We now examine what will\n", - "happen if we vary the so-called **marginal propensity to consume**,\n", - "i.e., the fraction of income that is consumed" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "871f6b2d", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_19_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "bs = (1/3, 2/3, 5/6, 0.9)\n", - "\n", - "fig,ax = plt.subplots()\n", - "ax.set_title('Changing Consumption as a Fraction of Income')\n", - "ax.set_ylabel('$y_t$')\n", - "ax.set_xlabel('$t$')\n", - "x = np.arange(0, T+1)\n", - "for b in bs:\n", - " y = calculate_y(i_0, b, g_0, T, y_init)\n", - " ax.plot(x, y, label=r'$b=$'+f\"{b:.2f}\")\n", - "ax.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "03804c33", - "metadata": {}, - "source": [ - "Increasing the marginal propensity to consume $b$ increases the\n", - "path of output over time.\n", - "\n", - "Now we will compare the effects on output of increases in investment and government spending." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "1a08cc9c", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_21_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 10))\n", - "fig.subplots_adjust(hspace=0.3)\n", - "\n", - "x = np.arange(0, T+1)\n", - "values = [0.3, 0.4]\n", - "\n", - "for i in values:\n", - " y = calculate_y(i, b, g_0, T, y_init)\n", - " ax1.plot(x, y, label=f\"i={i}\")\n", - "for g in values:\n", - " y = calculate_y(i_0, b, g, T, y_init)\n", - " ax2.plot(x, y, label=f\"g={g}\")\n", - "\n", - "axes = ax1, ax2\n", - "param_labels = \"Investment\", \"Government Spending\"\n", - "for ax, param in zip(axes, param_labels):\n", - " ax.set_title(f'An Increase in {param} on Output')\n", - " ax.legend(loc =\"lower right\")\n", - " ax.set_ylabel('$y_t$')\n", - " ax.set_xlabel('$t$')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "b4a0192e", - "metadata": {}, - "source": [ - "Notice here, whether government spending increases from 0.3 to 0.4 or\n", - "investment increases from 0.3 to 0.4, the shifts in the graphs are\n", - "identical." - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 51, - 60, - 655, - 676, - 682, - 707, - 716, - 730, - 739, - 756, - 768, - 791, - 806, - 817, - 823, - 827, - 842, - 867, - 876, - 889, - 896, - 918 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/html/_sources/geom_series.md b/lectures/_build/html/_sources/geom_series.md deleted file mode 100644 index 6275f4794..000000000 --- a/lectures/_build/html/_sources/geom_series.md +++ /dev/null @@ -1,922 +0,0 @@ ---- -jupytext: - text_representation: - extension: .md - format_name: myst -kernelspec: - display_name: Python 3 - language: python - name: python3 ---- - -(geom_series)= -```{raw} html - -``` - -```{index} single: python -``` - -# Geometric Series for Elementary Economics - -```{contents} Contents -:depth: 2 -``` - -## Overview - -The lecture describes important ideas in economics that use the mathematics of geometric series. - -Among these are - -- the Keynesian **multiplier** -- the money **multiplier** that prevails in fractional reserve banking - systems -- interest rates and present values of streams of payouts from assets - -(As we shall see below, the term **multiplier** comes down to meaning **sum of a convergent geometric series**) - -These and other applications prove the truth of the wise crack that - -```{epigraph} -"in economics, a little knowledge of geometric series goes a long way " -``` - -Below we'll use the following imports: - -```{code-cell} ipython -%matplotlib inline -import matplotlib.pyplot as plt -plt.rcParams["figure.figsize"] = (11, 5) #set default figure size -import numpy as np -import sympy as sym -from sympy import init_printing, latex -from matplotlib import cm -from mpl_toolkits.mplot3d import Axes3D -``` - -## Key Formulas - -To start, let $c$ be a real number that lies strictly between -$-1$ and $1$. - -- We often write this as $c \in (-1,1)$. -- Here $(-1,1)$ denotes the collection of all real numbers that - are strictly less than $1$ and strictly greater than $-1$. -- The symbol $\in$ means *in* or *belongs to the set after the symbol*. - -We want to evaluate geometric series of two types -- infinite and finite. - -### Infinite Geometric Series - -The first type of geometric that interests us is the infinite series - -$$ -1 + c + c^2 + c^3 + \cdots -$$ - -Where $\cdots$ means that the series continues without end. - -The key formula is - -```{math} -:label: infinite - -1 + c + c^2 + c^3 + \cdots = \frac{1}{1 -c } -``` - -To prove key formula {eq}`infinite`, multiply both sides by $(1-c)$ and verify -that if $c \in (-1,1)$, then the outcome is the -equation $1 = 1$. - -### Finite Geometric Series - -The second series that interests us is the finite geometric series - -$$ -1 + c + c^2 + c^3 + \cdots + c^T -$$ - -where $T$ is a positive integer. - -The key formula here is - -$$ -1 + c + c^2 + c^3 + \cdots + c^T = \frac{1 - c^{T+1}}{1-c} -$$ - -**Remark:** The above formula works for any value of the scalar -$c$. We don't have to restrict $c$ to be in the -set $(-1,1)$. - -We now move on to describe some famous economic applications of -geometric series. - -## Example: The Money Multiplier in Fractional Reserve Banking - -In a fractional reserve banking system, banks hold only a fraction -$r \in (0,1)$ of cash behind each **deposit receipt** that they -issue - -* In recent times - - cash consists of pieces of paper issued by the government and - called dollars or pounds or $\ldots$ - - a *deposit* is a balance in a checking or savings account that - entitles the owner to ask the bank for immediate payment in cash -* When the UK and France and the US were on either a gold or silver - standard (before 1914, for example) - - cash was a gold or silver coin - - a *deposit receipt* was a *bank note* that the bank promised to - convert into gold or silver on demand; (sometimes it was also a - checking or savings account balance) - -Economists and financiers often define the **supply of money** as an -economy-wide sum of **cash** plus **deposits**. - -In a **fractional reserve banking system** (one in which the reserve -ratio $r$ satisfies $0 < r < 1$), **banks create money** by issuing deposits *backed* by fractional reserves plus loans that they make to their customers. - -A geometric series is a key tool for understanding how banks create -money (i.e., deposits) in a fractional reserve system. - -The geometric series formula {eq}`infinite` is at the heart of the classic model of the money creation process -- one that leads us to the celebrated -**money multiplier**. - -### A Simple Model - -There is a set of banks named $i = 0, 1, 2, \ldots$. - -Bank $i$'s loans $L_i$, deposits $D_i$, and -reserves $R_i$ must satisfy the balance sheet equation (because -**balance sheets balance**): - -```{math} -:label: balance - -L_i + R_i = D_i -``` - -The left side of the above equation is the sum of the bank's **assets**, -namely, the loans $L_i$ it has outstanding plus its reserves of -cash $R_i$. - -The right side records bank $i$'s liabilities, -namely, the deposits $D_i$ held by its depositors; these are -IOU's from the bank to its depositors in the form of either checking -accounts or savings accounts (or before 1914, bank notes issued by a -bank stating promises to redeem note for gold or silver on demand). - -Each bank $i$ sets its reserves to satisfy the equation - -```{math} -:label: reserves - -R_i = r D_i -``` - -where $r \in (0,1)$ is its **reserve-deposit ratio** or **reserve -ratio** for short - -- the reserve ratio is either set by a government or chosen by banks - for precautionary reasons - -Next we add a theory stating that bank $i+1$'s deposits depend -entirely on loans made by bank $i$, namely - -```{math} -:label: deposits - -D_{i+1} = L_i -``` - -Thus, we can think of the banks as being arranged along a line with -loans from bank $i$ being immediately deposited in $i+1$ - -- in this way, the debtors to bank $i$ become creditors of - bank $i+1$ - -Finally, we add an *initial condition* about an exogenous level of bank -$0$'s deposits - -$$ -D_0 \ \text{ is given exogenously} -$$ - -We can think of $D_0$ as being the amount of cash that a first -depositor put into the first bank in the system, bank number $i=0$. - -Now we do a little algebra. - -Combining equations {eq}`balance` and {eq}`reserves` tells us that - -```{math} -:label: fraction - -L_i = (1-r) D_i -``` - -This states that bank $i$ loans a fraction $(1-r)$ of its -deposits and keeps a fraction $r$ as cash reserves. - -Combining equation {eq}`fraction` with equation {eq}`deposits` tells us that - -$$ -D_{i+1} = (1-r) D_i \ \text{ for } i \geq 0 -$$ - -which implies that - -```{math} -:label: geomseries - -D_i = (1 - r)^i D_0 \ \text{ for } i \geq 0 -``` - -Equation {eq}`geomseries` expresses $D_i$ as the $i$ th term in the -product of $D_0$ and the geometric series - -$$ -1, (1-r), (1-r)^2, \cdots -$$ - -Therefore, the sum of all deposits in our banking system -$i=0, 1, 2, \ldots$ is - -```{math} -:label: sumdeposits - -\sum_{i=0}^\infty (1-r)^i D_0 = \frac{D_0}{1 - (1-r)} = \frac{D_0}{r} -``` - -### Money Multiplier - -The **money multiplier** is a number that tells the multiplicative -factor by which an exogenous injection of cash into bank $0$ leads -to an increase in the total deposits in the banking system. - -Equation {eq}`sumdeposits` asserts that the **money multiplier** is -$\frac{1}{r}$ - -- An initial deposit of cash of $D_0$ in bank $0$ leads - the banking system to create total deposits of $\frac{D_0}{r}$. -- The initial deposit $D_0$ is held as reserves, distributed - throughout the banking system according to $D_0 = \sum_{i=0}^\infty R_i$. - -## Example: The Keynesian Multiplier - -The famous economist John Maynard Keynes and his followers created a -simple model intended to determine national income $y$ in -circumstances in which - -- there are substantial unemployed resources, in particular **excess - supply** of labor and capital -- prices and interest rates fail to adjust to make aggregate **supply - equal demand** (e.g., prices and interest rates are frozen) -- national income is entirely determined by aggregate demand - -### Static Version - -An elementary Keynesian model of national income determination consists -of three equations that describe aggregate demand for $y$ and its -components. - -The first equation is a national income identity asserting that -consumption $c$ plus investment $i$ equals national income -$y$: - -$$ -c+ i = y -$$ - -The second equation is a Keynesian consumption function asserting that -people consume a fraction $b \in (0,1)$ of their income: - -$$ -c = b y -$$ - -The fraction $b \in (0,1)$ is called the **marginal propensity to -consume**. - -The fraction $1-b \in (0,1)$ is called the **marginal propensity -to save**. - -The third equation simply states that investment is exogenous at level -$i$. - -- *exogenous* means *determined outside this model*. - -Substituting the second equation into the first gives $(1-b) y = i$. - -Solving this equation for $y$ gives - -$$ -y = \frac{1}{1-b} i -$$ - -The quantity $\frac{1}{1-b}$ is called the **investment -multiplier** or simply the **multiplier**. - -Applying the formula for the sum of an infinite geometric series, we can -write the above equation as - -$$ -y = i \sum_{t=0}^\infty b^t -$$ - -where $t$ is a nonnegative integer. - -So we arrive at the following equivalent expressions for the multiplier: - -$$ -\frac{1}{1-b} = \sum_{t=0}^\infty b^t -$$ - -The expression $\sum_{t=0}^\infty b^t$ motivates an interpretation -of the multiplier as the outcome of a dynamic process that we describe -next. - -### Dynamic Version - -We arrive at a dynamic version by interpreting the nonnegative integer -$t$ as indexing time and changing our specification of the -consumption function to take time into account - -- we add a one-period lag in how income affects consumption - -We let $c_t$ be consumption at time $t$ and $i_t$ be -investment at time $t$. - -We modify our consumption function to assume the form - -$$ -c_t = b y_{t-1} -$$ - -so that $b$ is the marginal propensity to consume (now) out of -last period's income. - -We begin with an initial condition stating that - -$$ -y_{-1} = 0 -$$ - -We also assume that - -$$ -i_t = i \ \ \textrm {for all } t \geq 0 -$$ - -so that investment is constant over time. - -It follows that - -$$ -y_0 = i + c_0 = i + b y_{-1} = i -$$ - -and - -$$ -y_1 = c_1 + i = b y_0 + i = (1 + b) i -$$ - -and - -$$ -y_2 = c_2 + i = b y_1 + i = (1 + b + b^2) i -$$ - -and more generally - -$$ -y_t = b y_{t-1} + i = (1+ b + b^2 + \cdots + b^t) i -$$ - -or - -$$ -y_t = \frac{1-b^{t+1}}{1 -b } i -$$ - -Evidently, as $t \rightarrow + \infty$, - -$$ -y_t \rightarrow \frac{1}{1-b} i -$$ - -**Remark 1:** The above formula is often applied to assert that an -exogenous increase in investment of $\Delta i$ at time $0$ -ignites a dynamic process of increases in national income by successive amounts - -$$ -\Delta i, (1 + b )\Delta i, (1+b + b^2) \Delta i , \cdots -$$ - -at times $0, 1, 2, \ldots$. - -**Remark 2** Let $g_t$ be an exogenous sequence of government -expenditures. - -If we generalize the model so that the national income identity -becomes - -$$ -c_t + i_t + g_t = y_t -$$ - -then a version of the preceding argument shows that the **government -expenditures multiplier** is also $\frac{1}{1-b}$, so that a -permanent increase in government expenditures ultimately leads to an -increase in national income equal to the multiplier times the increase -in government expenditures. - -## Example: Interest Rates and Present Values - -We can apply our formula for geometric series to study how interest -rates affect values of streams of dollar payments that extend over time. - -We work in discrete time and assume that $t = 0, 1, 2, \ldots$ -indexes time. - -We let $r \in (0,1)$ be a one-period **net nominal interest rate** - -- if the nominal interest rate is $5$ percent, - then $r= .05$ - -A one-period **gross nominal interest rate** $R$ is defined as - -$$ -R = 1 + r \in (1, 2) -$$ - -- if $r=.05$, then $R = 1.05$ - -**Remark:** The gross nominal interest rate $R$ is an **exchange -rate** or **relative price** of dollars at between times $t$ and -$t+1$. The units of $R$ are dollars at time $t+1$ per -dollar at time $t$. - -When people borrow and lend, they trade dollars now for dollars later or -dollars later for dollars now. - -The price at which these exchanges occur is the gross nominal interest -rate. - -- If I sell $x$ dollars to you today, you pay me $R x$ - dollars tomorrow. -- This means that you borrowed $x$ dollars for me at a gross - interest rate $R$ and a net interest rate $r$. - -We assume that the net nominal interest rate $r$ is fixed over -time, so that $R$ is the gross nominal interest rate at times -$t=0, 1, 2, \ldots$. - -Two important geometric sequences are - -```{math} -:label: geom1 - -1, R, R^2, \cdots -``` - -and - -```{math} -:label: geom2 - -1, R^{-1}, R^{-2}, \cdots -``` - -Sequence {eq}`geom1` tells us how dollar values of an investment **accumulate** -through time. - -Sequence {eq}`geom2` tells us how to **discount** future dollars to get their -values in terms of today's dollars. - -### Accumulation - -Geometric sequence {eq}`geom1` tells us how one dollar invested and re-invested -in a project with gross one period nominal rate of return accumulates - -- here we assume that net interest payments are reinvested in the - project -- thus, $1$ dollar invested at time $0$ pays interest - $r$ dollars after one period, so we have $r+1 = R$ - dollars at time$1$ -- at time $1$ we reinvest $1+r =R$ dollars and receive interest - of $r R$ dollars at time $2$ plus the *principal* - $R$ dollars, so we receive $r R + R = (1+r)R = R^2$ - dollars at the end of period $2$ -- and so on - -Evidently, if we invest $x$ dollars at time $0$ and -reinvest the proceeds, then the sequence - -$$ -x , xR , x R^2, \cdots -$$ - -tells how our account accumulates at dates $t=0, 1, 2, \ldots$. - -### Discounting - -Geometric sequence {eq}`geom2` tells us how much future dollars are worth in terms of today's dollars. - -Remember that the units of $R$ are dollars at $t+1$ per -dollar at $t$. - -It follows that - -- the units of $R^{-1}$ are dollars at $t$ per dollar at $t+1$ -- the units of $R^{-2}$ are dollars at $t$ per dollar at $t+2$ -- and so on; the units of $R^{-j}$ are dollars at $t$ per - dollar at $t+j$ - -So if someone has a claim on $x$ dollars at time $t+j$, it -is worth $x R^{-j}$ dollars at time $t$ (e.g., today). - -### Application to Asset Pricing - -A **lease** requires a payments stream of $x_t$ dollars at -times $t = 0, 1, 2, \ldots$ where - -$$ -x_t = G^t x_0 -$$ - -where $G = (1+g)$ and $g \in (0,1)$. - -Thus, lease payments increase at $g$ percent per period. - -For a reason soon to be revealed, we assume that $G < R$. - -The **present value** of the lease is - -$$ -\begin{aligned} p_0 & = x_0 + x_1/R + x_2/(R^2) + \ddots \\ - & = x_0 (1 + G R^{-1} + G^2 R^{-2} + \cdots ) \\ - & = x_0 \frac{1}{1 - G R^{-1}} \end{aligned} -$$ - -where the last line uses the formula for an infinite geometric series. - -Recall that $R = 1+r$ and $G = 1+g$ and that $R > G$ -and $r > g$ and that $r$ and $g$ are typically small -numbers, e.g., .05 or .03. - -Use the Taylor series of $\frac{1}{1+r}$ about $r=0$, -namely, - -$$ -\frac{1}{1+r} = 1 - r + r^2 - r^3 + \cdots -$$ - -and the fact that $r$ is small to approximate -$\frac{1}{1+r} \approx 1 - r$. - -Use this approximation to write $p_0$ as - -$$ -\begin{aligned} - p_0 &= x_0 \frac{1}{1 - G R^{-1}} \\ - &= x_0 \frac{1}{1 - (1+g) (1-r) } \\ - &= x_0 \frac{1}{1 - (1+g - r - rg)} \\ - & \approx x_0 \frac{1}{r -g } -\end{aligned} -$$ - -where the last step uses the approximation $r g \approx 0$. - -The approximation - -$$ -p_0 = \frac{x_0 }{r -g } -$$ - -is known as the **Gordon formula** for the present value or current -price of an infinite payment stream $x_0 G^t$ when the nominal -one-period interest rate is $r$ and when $r > g$. - -We can also extend the asset pricing formula so that it applies to finite leases. - -Let the payment stream on the lease now be $x_t$ for $t= 1,2, \dots,T$, where again - -$$ -x_t = G^t x_0 -$$ - -The present value of this lease is: - -$$ -\begin{aligned} \begin{split}p_0&=x_0 + x_1/R + \dots +x_T/R^T \\ &= x_0(1+GR^{-1}+\dots +G^{T}R^{-T}) \\ &= \frac{x_0(1-G^{T+1}R^{-(T+1)})}{1-GR^{-1}} \end{split}\end{aligned} -$$ - -Applying the Taylor series to $R^{-(T+1)}$ about $r=0$ we get: - -$$ -\frac{1}{(1+r)^{T+1}}= 1-r(T+1)+\frac{1}{2}r^2(T+1)(T+2)+\dots \approx 1-r(T+1) -$$ - -Similarly, applying the Taylor series to $G^{T+1}$ about $g=0$: - -$$ -(1+g)^{T+1} = 1+(T+1)g+\frac{T(T+1)}{2!}g^2+\frac{(T-1)T(T+1)}{3!}g^3+\dots \approx 1+ (T+1)g -$$ - -Thus, we get the following approximation: - -$$ -p_0 =\frac{x_0(1-(1+(T+1)g)(1-r(T+1)))}{1-(1-r)(1+g) } -$$ - -Expanding: - -$$ -\begin{aligned} p_0 &=\frac{x_0(1-1+(T+1)^2 rg -r(T+1)+g(T+1))}{1-1+r-g+rg} \\&=\frac{x_0(T+1)((T+1)rg+r-g)}{r-g+rg} \\ &\approx \frac{x_0(T+1)(r-g)}{r-g}+\frac{x_0rg(T+1)}{r-g}\\ &= x_0(T+1) + \frac{x_0rg(T+1)}{r-g} \end{aligned} -$$ - -We could have also approximated by removing the second term -$rgx_0(T+1)$ when $T$ is relatively small compared to -$1/(rg)$ to get $x_0(T+1)$ as in the finite stream -approximation. - -We will plot the true finite stream present-value and the two -approximations, under different values of $T$, and $g$ and $r$ in Python. - -First we plot the true finite stream present-value after computing it -below - -```{code-cell} python3 -# True present value of a finite lease -def finite_lease_pv_true(T, g, r, x_0): - G = (1 + g) - R = (1 + r) - return (x_0 * (1 - G**(T + 1) * R**(-T - 1))) / (1 - G * R**(-1)) -# First approximation for our finite lease - -def finite_lease_pv_approx_1(T, g, r, x_0): - p = x_0 * (T + 1) + x_0 * r * g * (T + 1) / (r - g) - return p - -# Second approximation for our finite lease -def finite_lease_pv_approx_2(T, g, r, x_0): - return (x_0 * (T + 1)) - -# Infinite lease -def infinite_lease(g, r, x_0): - G = (1 + g) - R = (1 + r) - return x_0 / (1 - G * R**(-1)) -``` - -Now that we have defined our functions, we can plot some outcomes. - -First we study the quality of our approximations - -```{code-cell} python3 -def plot_function(axes, x_vals, func, args): - axes.plot(x_vals, func(*args), label=func.__name__) - -T_max = 50 - -T = np.arange(0, T_max+1) -g = 0.02 -r = 0.03 -x_0 = 1 - -our_args = (T, g, r, x_0) -funcs = [finite_lease_pv_true, - finite_lease_pv_approx_1, - finite_lease_pv_approx_2] - ## the three functions we want to compare - -fig, ax = plt.subplots() -ax.set_title('Finite Lease Present Value $T$ Periods Ahead') -for f in funcs: - plot_function(ax, T, f, our_args) -ax.legend() -ax.set_xlabel('$T$ Periods Ahead') -ax.set_ylabel('Present Value, $p_0$') -plt.show() -``` - -Evidently our approximations perform well for small values of $T$. - -However, holding $g$ and r fixed, our approximations deteriorate as $T$ increases. - -Next we compare the infinite and finite duration lease present values -over different lease lengths $T$. - -```{code-cell} python3 -# Convergence of infinite and finite -T_max = 1000 -T = np.arange(0, T_max+1) -fig, ax = plt.subplots() -ax.set_title('Infinite and Finite Lease Present Value $T$ Periods Ahead') -f_1 = finite_lease_pv_true(T, g, r, x_0) -f_2 = np.full(T_max+1, infinite_lease(g, r, x_0)) -ax.plot(T, f_1, label='T-period lease PV') -ax.plot(T, f_2, '--', label='Infinite lease PV') -ax.set_xlabel('$T$ Periods Ahead') -ax.set_ylabel('Present Value, $p_0$') -ax.legend() -plt.show() -``` - -The graph above shows how as duration $T \rightarrow +\infty$, -the value of a lease of duration $T$ approaches the value of a -perpetual lease. - -Now we consider two different views of what happens as $r$ and -$g$ covary - -```{code-cell} python3 -# First view -# Changing r and g -fig, ax = plt.subplots() -ax.set_title('Value of lease of length $T$') -ax.set_ylabel('Present Value, $p_0$') -ax.set_xlabel('$T$ periods ahead') -T_max = 10 -T=np.arange(0, T_max+1) - -rs, gs = (0.9, 0.5, 0.4001, 0.4), (0.4, 0.4, 0.4, 0.5), -comparisons = ('$\gg$', '$>$', r'$\approx$', '$<$') -for r, g, comp in zip(rs, gs, comparisons): - ax.plot(finite_lease_pv_true(T, g, r, x_0), label=f'r(={r}) {comp} g(={g})') - -ax.legend() -plt.show() -``` - -This graph gives a big hint for why the condition $r > g$ is -necessary if a lease of length $T = +\infty$ is to have finite -value. - -For fans of 3-d graphs the same point comes through in the following -graph. - -If you aren't enamored of 3-d graphs, feel free to skip the next -visualization! - -```{code-cell} python3 -# Second view -fig = plt.figure() -T = 3 -ax = plt.subplot(projection='3d') -r = np.arange(0.01, 0.99, 0.005) -g = np.arange(0.011, 0.991, 0.005) - -rr, gg = np.meshgrid(r, g) -z = finite_lease_pv_true(T, gg, rr, x_0) - -# Removes points where undefined -same = (rr == gg) -z[same] = np.nan -surf = ax.plot_surface(rr, gg, z, cmap=cm.coolwarm, - antialiased=True, clim=(0, 15)) -fig.colorbar(surf, shrink=0.5, aspect=5) -ax.set_xlabel('$r$') -ax.set_ylabel('$g$') -ax.set_zlabel('Present Value, $p_0$') -ax.view_init(20, 10) -ax.set_title('Three Period Lease PV with Varying $g$ and $r$') -plt.show() -``` - -We can use a little calculus to study how the present value $p_0$ -of a lease varies with $r$ and $g$. - -We will use a library called [SymPy](https://www.sympy.org/). - -SymPy enables us to do symbolic math calculations including -computing derivatives of algebraic equations. - -We will illustrate how it works by creating a symbolic expression that -represents our present value formula for an infinite lease. - -After that, we'll use SymPy to compute derivatives - -```{code-cell} python3 -# Creates algebraic symbols that can be used in an algebraic expression -g, r, x0 = sym.symbols('g, r, x0') -G = (1 + g) -R = (1 + r) -p0 = x0 / (1 - G * R**(-1)) -init_printing(use_latex='mathjax') -print('Our formula is:') -p0 -``` - -```{code-cell} python3 -print('dp0 / dg is:') -dp_dg = sym.diff(p0, g) -dp_dg -``` - -```{code-cell} python3 -print('dp0 / dr is:') -dp_dr = sym.diff(p0, r) -dp_dr -``` - -We can see that for $\frac{\partial p_0}{\partial r}<0$ as long as -$r>g$, $r>0$ and $g>0$ and $x_0$ is positive, -so $\frac{\partial p_0}{\partial r}$ will always be negative. - -Similarly, $\frac{\partial p_0}{\partial g}>0$ as long as $r>g$, $r>0$ and $g>0$ and $x_0$ is positive, so $\frac{\partial p_0}{\partial g}$ -will always be positive. - -## Back to the Keynesian Multiplier - -We will now go back to the case of the Keynesian multiplier and plot the -time path of $y_t$, given that consumption is a constant fraction -of national income, and investment is fixed. - -```{code-cell} python3 -# Function that calculates a path of y -def calculate_y(i, b, g, T, y_init): - y = np.zeros(T+1) - y[0] = i + b * y_init + g - for t in range(1, T+1): - y[t] = b * y[t-1] + i + g - return y - -# Initial values -i_0 = 0.3 -g_0 = 0.3 -# 2/3 of income goes towards consumption -b = 2/3 -y_init = 0 -T = 100 - -fig, ax = plt.subplots() -ax.set_title('Path of Aggregate Output Over Time') -ax.set_xlabel('$t$') -ax.set_ylabel('$y_t$') -ax.plot(np.arange(0, T+1), calculate_y(i_0, b, g_0, T, y_init)) -# Output predicted by geometric series -ax.hlines(i_0 / (1 - b) + g_0 / (1 - b), xmin=-1, xmax=101, linestyles='--') -plt.show() -``` - -In this model, income grows over time, until it gradually converges to -the infinite geometric series sum of income. - -We now examine what will -happen if we vary the so-called **marginal propensity to consume**, -i.e., the fraction of income that is consumed - -```{code-cell} python3 -bs = (1/3, 2/3, 5/6, 0.9) - -fig,ax = plt.subplots() -ax.set_title('Changing Consumption as a Fraction of Income') -ax.set_ylabel('$y_t$') -ax.set_xlabel('$t$') -x = np.arange(0, T+1) -for b in bs: - y = calculate_y(i_0, b, g_0, T, y_init) - ax.plot(x, y, label=r'$b=$'+f"{b:.2f}") -ax.legend() -plt.show() -``` - -Increasing the marginal propensity to consume $b$ increases the -path of output over time. - -Now we will compare the effects on output of increases in investment and government spending. - -```{code-cell} python3 -fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 10)) -fig.subplots_adjust(hspace=0.3) - -x = np.arange(0, T+1) -values = [0.3, 0.4] - -for i in values: - y = calculate_y(i, b, g_0, T, y_init) - ax1.plot(x, y, label=f"i={i}") -for g in values: - y = calculate_y(i_0, b, g, T, y_init) - ax2.plot(x, y, label=f"g={g}") - -axes = ax1, ax2 -param_labels = "Investment", "Government Spending" -for ax, param in zip(axes, param_labels): - ax.set_title(f'An Increase in {param} on Output') - ax.legend(loc ="lower right") - ax.set_ylabel('$y_t$') - ax.set_xlabel('$t$') -plt.show() -``` - -Notice here, whether government spending increases from 0.3 to 0.4 or -investment increases from 0.3 to 0.4, the shifts in the graphs are -identical. diff --git a/lectures/_build/html/_sources/intro.ipynb b/lectures/_build/html/_sources/intro.ipynb deleted file mode 100644 index 64ea7945b..000000000 --- a/lectures/_build/html/_sources/intro.ipynb +++ /dev/null @@ -1,50 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "a7f88dc4", - "metadata": {}, - "source": [ - "# Python Programming for Economics and Finance\n", - "\n", - "This website presents a set of lectures on Python programming for economics and finance, designed and written by\n", - "[Thomas J. Sargent](http://www.tomsargent.com/) and [John Stachurski](http://johnstachurski.net/). This is the first text in the series, which focuses on programming in Python.\n", - "\n", - "For an overview of the series, see [this page](https://quantecon.org/python-lectures/)\n", - "\n", - "```{tableofcontents}\n", - "```" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/html/_sources/intro.md b/lectures/_build/html/_sources/intro.md deleted file mode 100644 index 7f4d36397..000000000 --- a/lectures/_build/html/_sources/intro.md +++ /dev/null @@ -1,21 +0,0 @@ ---- -jupytext: - text_representation: - extension: .md - format_name: myst -kernelspec: - display_name: Python 3 - language: python - name: python3 ---- - -# Python Programming for Economics and Finance - -This website presents a set of lectures on Python programming for economics and finance, designed and written by -[Thomas J. Sargent](http://www.tomsargent.com/) and [John Stachurski](http://johnstachurski.net/). This is the first text in the series, which focuses on programming in Python. - -For an overview of the series, see [this page](https://quantecon.org/python-lectures/) - -```{tableofcontents} -``` - diff --git a/lectures/_build/html/_sources/scalar_dynam.ipynb b/lectures/_build/html/_sources/scalar_dynam.ipynb deleted file mode 100644 index 92ec7c681..000000000 --- a/lectures/_build/html/_sources/scalar_dynam.ipynb +++ /dev/null @@ -1,1080 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "7778fcad", - "metadata": {}, - "source": [ - "```{raw} html\n", - "
\n", - " \n", - " \"QuantEcon\"\n", - " \n", - "
\n", - "```\n", - "\n", - "# {index}`Dynamics in One Dimension `\n", - "\n", - "```{contents} Contents\n", - ":depth: 2\n", - "```\n", - "\n", - "## Overview\n", - "\n", - "In this lecture we give a quick introduction to discrete time dynamics in one\n", - "dimension.\n", - "\n", - "In one-dimensional models, the state of the system is described by a single variable.\n", - "\n", - "Although most interesting dynamic models have two or more state variables, the\n", - "one-dimensional setting is a good place to learn the foundations of dynamics and build\n", - "intuition.\n", - "\n", - "Let's start with some standard imports:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "726361e5", - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "plt.rcParams[\"figure.figsize\"] = (11, 5) #set default figure size\n", - "import numpy as np" - ] - }, - { - "cell_type": "markdown", - "id": "6a799320", - "metadata": {}, - "source": [ - "## Some Definitions\n", - "\n", - "This section sets out the objects of interest and the kinds of properties we study.\n", - "\n", - "### Difference Equations\n", - "\n", - "A **time homogeneous first order difference equation** is an equation of the\n", - "form\n", - "\n", - "```{math}\n", - ":label: sdsod\n", - "\n", - "x_{t+1} = g(x_t)\n", - "```\n", - "\n", - "where $g$ is a function from some subset $S$ of $\\mathbb R$ to itself.\n", - "\n", - "Here $S$ is called the **state space** and $x$ is called the **state variable**.\n", - "\n", - "In the definition,\n", - "\n", - "* time homogeneity means that $g$ is the same at each time $t$\n", - "* first order means dependence on only one lag (i.e., earlier states such as $x_{t-1}$ do not enter into {eq}`sdsod`).\n", - "\n", - "If $x_0 \\in S$ is given, then {eq}`sdsod` recursively defines the sequence\n", - "\n", - "```{math}\n", - ":label: sdstraj\n", - "\n", - "x_0, \\quad\n", - "x_1 = g(x_0), \\quad\n", - "x_2 = g(x_1) = g(g(x_0)), \\quad \\text{etc.}\n", - "```\n", - "\n", - "This sequence is called the **trajectory** of $x_0$ under $g$.\n", - "\n", - "If we define $g^n$ to be $n$ compositions of $g$ with itself, then we can write the trajectory more simply as $x_t = g^t(x_0)$ for $t \\geq 0$.\n", - "\n", - "### Example: A Linear Model\n", - "\n", - "One simple example is the **linear difference equation**\n", - "\n", - "$$\n", - "x_{t+1} = a x_t + b, \\qquad S = \\mathbb R\n", - "$$\n", - "\n", - "where $a, b$ are fixed constants.\n", - "\n", - "In this case, given $x_0$, the trajectory {eq}`sdstraj` is\n", - "\n", - "```{math}\n", - ":label: sdslinmodpath\n", - "\n", - "x_0, \\quad\n", - "a x_0 + b, \\quad\n", - "a^2 x_0 + a b + b, \\quad \\text{etc.}\n", - "```\n", - "\n", - "Continuing in this way, and using our knowledge of {doc}`geometric series `, we find that, for any $t \\geq 0$,\n", - "\n", - "```{math}\n", - ":label: sdslinmod\n", - "\n", - "x_t = a^t x_0 + b \\frac{1 - a^t}{1 - a}\n", - "```\n", - "\n", - "This is about all we need to know about the linear model.\n", - "\n", - "We have an exact expression for $x_t$ for all $t$ and hence a full\n", - "understanding of the dynamics.\n", - "\n", - "Notice in particular that $|a| < 1$, then, by {eq}`sdslinmod`, we have\n", - "\n", - "```{math}\n", - ":label: sdslinmodc\n", - "\n", - "x_t \\to \\frac{b}{1 - a} \\text{ as } t \\to \\infty\n", - "```\n", - "\n", - "regardless of $x_0$\n", - "\n", - "This is an example of what is called global stability, a topic we return to\n", - "below.\n", - "\n", - "### Example: A Nonlinear Model\n", - "\n", - "In the linear example above, we obtained an exact analytical expression for $x_t$\n", - "in terms of arbitrary $t$ and $x_0$.\n", - "\n", - "This made analysis of dynamics very easy.\n", - "\n", - "When models are nonlinear, however, the situation can be quite different.\n", - "\n", - "For example, recall how we [previously studied](https://python-programming.quantecon.org/python_oop.html#example-the-solow-growth-model) the law of motion for the Solow growth model, a simplified version of which is\n", - "\n", - "```{math}\n", - ":label: solow_lom2\n", - "\n", - "k_{t+1} = s z k_t^{\\alpha} + (1 - \\delta) k_t\n", - "```\n", - "\n", - "Here $k$ is capital stock and $s, z, \\alpha, \\delta$ are positive\n", - "parameters with $0 < \\alpha, \\delta < 1$.\n", - "\n", - "If you try to iterate like we did in {eq}`sdslinmodpath`, you will find that\n", - "the algebra gets messy quickly.\n", - "\n", - "Analyzing the dynamics of this model requires a different method (see below).\n", - "\n", - "### Stability\n", - "\n", - "A **steady state** of the difference equation $x_{t+1} = g(x_t)$ is a\n", - "point $x^*$ in $S$ such that $x^* = g(x^*)$.\n", - "\n", - "In other words, $x^*$ is a **fixed point** of the function $g$ in\n", - "$S$.\n", - "\n", - "For example, for the linear model $x_{t+1} = a x_t + b$, you can use the\n", - "definition to check that\n", - "\n", - "* $x^* := b/(1-a)$ is a steady state whenever $a \\not= 1$.\n", - "* if $a = 1$ and $b=0$, then every $x \\in \\mathbb R$ is a\n", - " steady state.\n", - "* if $a = 1$ and $b \\not= 0$, then the linear model has no steady\n", - " state in $\\mathbb R$.\n", - "\n", - "A steady state $x^*$ of $x_{t+1} = g(x_t)$ is called\n", - "**globally stable** if, for all $x_0 \\in S$,\n", - "\n", - "$$\n", - "x_t = g^t(x_0) \\to x^* \\text{ as } t \\to \\infty\n", - "$$\n", - "\n", - "For example, in the linear model $x_{t+1} = a x_t + b$ with $a\n", - "\\not= 1$, the steady state $x^*$\n", - "\n", - "* is globally stable if $|a| < 1$ and\n", - "* fails to be globally stable otherwise.\n", - "\n", - "This follows directly from {eq}`sdslinmod`.\n", - "\n", - "A steady state $x^*$ of $x_{t+1} = g(x_t)$ is called\n", - "**locally stable** if there exists an $\\epsilon > 0$ such that\n", - "\n", - "$$\n", - "| x_0 - x^* | < \\epsilon\n", - "\\; \\implies \\;\n", - "x_t = g^t(x_0) \\to x^* \\text{ as } t \\to \\infty\n", - "$$\n", - "\n", - "Obviously every globally stable steady state is also locally stable.\n", - "\n", - "We will see examples below where the converse is not true.\n", - "\n", - "## Graphical Analysis\n", - "\n", - "As we saw above, analyzing the dynamics for nonlinear models is nontrivial.\n", - "\n", - "There is no single way to tackle all nonlinear models.\n", - "\n", - "However, there is one technique for one-dimensional models that provides a\n", - "great deal of intuition.\n", - "\n", - "This is a graphical approach based on **45 degree diagrams**.\n", - "\n", - "Let's look at an example: the Solow model with dynamics given in {eq}`solow_lom2`.\n", - "\n", - "We begin with some plotting code that you can ignore at first reading.\n", - "\n", - "The function of the code is to produce 45 degree diagrams and time series\n", - "plots." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "6f5829b6", - "metadata": { - "tags": [ - "output_scroll" - ] - }, - "outputs": [], - "source": [ - "def subplots(fs):\n", - " \"Custom subplots with axes throught the origin\"\n", - " fig, ax = plt.subplots(figsize=fs)\n", - "\n", - " # Set the axes through the origin\n", - " for spine in ['left', 'bottom']:\n", - " ax.spines[spine].set_position('zero')\n", - " ax.spines[spine].set_color('green')\n", - " for spine in ['right', 'top']:\n", - " ax.spines[spine].set_color('none')\n", - "\n", - " return fig, ax\n", - "\n", - "\n", - "def plot45(g, xmin, xmax, x0, num_arrows=6, var='x'):\n", - "\n", - " xgrid = np.linspace(xmin, xmax, 200)\n", - "\n", - " fig, ax = subplots((6.5, 6))\n", - " ax.set_xlim(xmin, xmax)\n", - " ax.set_ylim(xmin, xmax)\n", - "\n", - " hw = (xmax - xmin) * 0.01\n", - " hl = 2 * hw\n", - " arrow_args = dict(fc=\"k\", ec=\"k\", head_width=hw,\n", - " length_includes_head=True, lw=1,\n", - " alpha=0.6, head_length=hl)\n", - "\n", - " ax.plot(xgrid, g(xgrid), 'b-', lw=2, alpha=0.6, label='g')\n", - " ax.plot(xgrid, xgrid, 'k-', lw=1, alpha=0.7, label='45')\n", - "\n", - " x = x0\n", - " xticks = [xmin]\n", - " xtick_labels = [xmin]\n", - "\n", - " for i in range(num_arrows):\n", - " if i == 0:\n", - " ax.arrow(x, 0.0, 0.0, g(x), **arrow_args) # x, y, dx, dy\n", - " else:\n", - " ax.arrow(x, x, 0.0, g(x) - x, **arrow_args)\n", - " ax.plot((x, x), (0, x), 'k', ls='dotted')\n", - "\n", - " ax.arrow(x, g(x), g(x) - x, 0, **arrow_args)\n", - " xticks.append(x)\n", - " xtick_labels.append(r'${}_{}$'.format(var, str(i)))\n", - "\n", - " x = g(x)\n", - " xticks.append(x)\n", - " xtick_labels.append(r'${}_{}$'.format(var, str(i+1)))\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n", - "\n", - " xticks.append(xmax)\n", - " xtick_labels.append(xmax)\n", - " ax.set_xticks(xticks)\n", - " ax.set_yticks(xticks)\n", - " ax.set_xticklabels(xtick_labels)\n", - " ax.set_yticklabels(xtick_labels)\n", - "\n", - " bbox = (0., 1.04, 1., .104)\n", - " legend_args = {'bbox_to_anchor': bbox, 'loc': 'upper right'}\n", - "\n", - " ax.legend(ncol=2, frameon=False, **legend_args, fontsize=14)\n", - " plt.show()\n", - "\n", - "def ts_plot(g, xmin, xmax, x0, ts_length=6, var='x'):\n", - " fig, ax = subplots((7, 5.5))\n", - " ax.set_ylim(xmin, xmax)\n", - " ax.set_xlabel(r'$t$', fontsize=14)\n", - " ax.set_ylabel(r'${}_t$'.format(var), fontsize=14)\n", - " x = np.empty(ts_length)\n", - " x[0] = x0\n", - " for t in range(ts_length-1):\n", - " x[t+1] = g(x[t])\n", - " ax.plot(range(ts_length),\n", - " x,\n", - " 'bo-',\n", - " alpha=0.6,\n", - " lw=2,\n", - " label=r'${}_t$'.format(var))\n", - " ax.legend(loc='best', fontsize=14)\n", - " ax.set_xticks(range(ts_length))\n", - " plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "08aa7b12", - "metadata": {}, - "source": [ - "Let's create a 45 degree diagram for the Solow model with a fixed set of\n", - "parameters" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "ef6950ac", - "metadata": {}, - "outputs": [], - "source": [ - "A, s, alpha, delta = 2, 0.3, 0.3, 0.4" - ] - }, - { - "cell_type": "markdown", - "id": "6b10d60c", - "metadata": {}, - "source": [ - "Here's the update function corresponding to the model." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "f409302c", - "metadata": {}, - "outputs": [], - "source": [ - "def g(k):\n", - " return A * s * k**alpha + (1 - delta) * k" - ] - }, - { - "cell_type": "markdown", - "id": "d1aa5b32", - "metadata": {}, - "source": [ - "Here is the 45 degree plot." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "276c761a", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiIAAAIyCAYAAAD2YqGxAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAABQUklEQVR4nO3deZyNdf/H8bcZzGSyZRkVIRHZsoSUKDslQrbI1qpFym7OLIZZlIRUkhYJ2ZIsWW6ihEJki+z7WMcYZsbMXL8/rt84I+ss51xneT0fj3ncc74z51yfx31L7/u6ru/7ymEYhiEAAAAL+Fg9AAAA8F4EEQAAYBmCCAAAsAxBBAAAWIYgAgAALEMQAQAAliGIAAAAyxBEAACAZQgiAADAMgQRAABgGYIIAACwDEEEAABYhiACAAAsQxABAACWIYgAAADLEEQAAIBlCCIAAMAyBBEAAGAZgggAAG4oOjpaOXLkUI4cObR27dprfh4SEnLl5//98vf3t2Di68tp9QAAACBjduzYIZvNpoCAAMXHx9/0d1988UWVKlXqqrWcOV3nX/+uMwkAALillJQUvfjii6patarKlSunb7/99qa/3717dzVo0MA5w2UCl2YAAEpOTlZERITKlCkjf39/PfDAA4qIiNDevXuVI0cOde/e3eoR8f+ioqK0efNmTZ48Wb6+vlaPk2WcEQEAqGfPnpoyZYrKlCmjPn36KDExUWPGjNHvv/9u9WhIZ+vWrQoNDdWwYcNUsWLF23rP6tWrtX79evn6+qp8+fJq1KiR/Pz8HDzp7SOIAMBNjBwpxcZaPcXN5c8vDRmS+fcvX75cU6ZMUc2aNbVq1SrdcccdkqRhw4apWrVq2TSlYyUmJurw4cNWj3FTxYsXz1IASE5OVvfu3VWhQgUNGjTott9ns9muen333Xfr66+/VuPGjTM9S3YiiADATcTGSufOWT2FY6XdYxAUFHQlhEhSsWLF9Pbbb2vw4MFWjXbbDh8+rL59+1o9xk2NGTNGZcqUyfT7R44cqc2bN2vdunXKlSvXLX//4Ycf1tdff6369esrMDBQhw8f1vTp0zVy5Ei1atVKa9euVdWqVTM9T3YhiADATeTPb/UEt5bVGTdv3ixJqlu37jU/u96aKypevLjGjBlj9Rg3Vbx48Uy/d/PmzQoPD9d7772n6tWr39Z7WrdufdXrBx54QMOGDVNgYKBefvllhYeHa+bMmZmeKbsQRADgJrJyycNdnD9/Xj4+PipUqNA1PwsMDLRgoozz8/PL0tkGV/fiiy+qTJkyCgkJyZbPev311/Xbb79lfbBsQBABAC+XL18+paam6vTp0ypcuPBVPztx4oRFUyG9tLNWNyoie/TRRyVJc+fOveZMyH/lzp1befPm1cWLF7N1xswiiACAl6tatao2bdqkNWvWqFWrVlf9bM2aNRZNhfR69ep13fVVq1Zp9+7datWqlYoUKXJNcdn17N69W2fPnnWJ+0MkgggAeL0uXbroq6++0vDhw9WkSZMr/6/7+PHj+uijjyyeDpI0adKk6653795du3fv1uDBg1WnTp0r63Fxcdq3b5+qVKly1e+fPXv2Sqjp1KmT4wbOAIIIAHi5Ro0aqUuXLpo6daoqV66sZ599VomJifr+++9Vu3ZtzZ8/Xz4+9F+6k9OnT6tq1aqqWbOmKleurKJFi+rIkSNatGiRTp8+rcaNG+udd96xekxJBBEAgKSvvvpK5cuX1+TJkzVu3DgVL15cffv2VcOGDTV//nzly5fP6hGRAXfddZf69OmjtWvXav78+Tp37pwCAgJUuXJlvfDCC+rdu7fLtLLmMAzDsHoIAIBrmjRpkl566SVNmDBBr732mtXjwAMRRAAAOn78uAIDA5UjR44ra0eOHNFjjz2mw4cPa9++fSpRooSFE8JTcWkGAKDIyEgtWLBA9erVU9GiRXXw4EH99NNPiouLU0hICCEEDkMQAQCoWbNm2r59uxYsWKCzZ8/K399fVapU0euvv67OnTtbPR48GJdmAACAZdiPBQAALEMQAQAAliGIAAAAyxBEAACAZQgiAADAMgQRAABgGYIIAACwDEEEAABYhiACAAAsQxABAACWIYgAAADLEEQAAIBlCCIAAMAyBBEAAGAZgggAALAMQQQAAFiGIAIAACxDEAEAAJYhiAAAAMsQRAAAgGUIIgAAwDIEEQAAYBmCCAAAsAxBBAAAWCZLQSQiIkI5cuRQ3759s2kcAADgTTIdRP744w9NnDhRVapUyc55AACAF8lUELlw4YK6dOmizz//XAULFszumQAAgJfIVBDp06ePWrZsqUaNGt3ydxMTE3X+/PkrX7GxsTp5/qQMw8jMoQEAgAfJcBCZPn26Nm7cqIiIiNv6/YiICOXPn//KV4HAAir6YVHFJcVleFgAAOBaTp8+rTfeeCPT789QEDl06JDefvttffvtt/L397+t9wwePFixsbFXvg4dOpSpQQEAgGs5cuSIBgwYoPj4+Ex/Rs6M/PKGDRsUExOjGjVqXFlLSUnRqlWrNH78eCUmJsrX1/eq9/j5+cnPz8++kJjpWQEAgIv4999/FRISorx582r48OGZ/pwMBZGGDRvq77//vmqtR48eKl++vAYOHHhNCAEAAJ5ny5YtCg8PV4kSJRQcHKx8+fJl+rMyFETy5s2rSpUqXbUWEBCgQoUKXbMOAAA8z5o1azRq1ChVqlRJQ4cOve1bNW4kQ0EEAAB4r59//lkff/yxHn/8cfXr1085c2Y9RmT5E1auXJnlIQAAgOsyDEOzZs3SN998oxYtWuiVV16Rj0/2PCWGMyIAAOCGDMPQF198oXnz5qlz587q2LGjcuTIkW2fTxABAADXlZycrLFjx2rlypV69dVX1bJly2w/BkEEAABcIzExUVFRUdq0aZPee+89PfHEEw45DkEEAABc5cKFCwoLC9PevXtls9lUrVo1hx2LIAIAAK44c+aMbDabzpw5oxEjRujBBx906PEIIgAAQJJ09OhRBQUFKTU1VVFRUSpRooTDj5k9e28AAIBb27t3rwYMGKBcuXIpOjraKSFEIogAAOD1/v77bw0aNEhFixZVdHS0ihQp4rRjc2kGAAAv9vvvvys6OlqVKlXSkCFDdMcddzj1+AQRAAC81JIlSzR+/Hg99thj6tevn3LlyuX0GQgiAAB4GcMwNHv2bH399ddq3ry5Xn311WyrbM8ogggAAF7EMAxNnjxZP/zwgzp27KjOnTtna2V7RhFEAADwEsnJyRo3bpxWrFihV155RU8//bTVIxFEAADwBmmV7Rs3bnRoZXtGEUQAAPBw8fHxCgsL0549e2Sz2VS9enWrR7qCIAIAgAc7c+aMgoODdfr0aadUtmcUQQQAAA917NgxDRs2TCkpKU6rbM8omlUBAPBAe/fuVf/+/Z1e2Z5RBBEAADzM1q1bNXjwYBUtWlRRUVEqWrSo1SPdEJdmAADwIGvXrlV0dLQeeughDR061OmV7RlFEAEAwEMsXbpU48aNU926dfXuu+9aUtmeUQQRAAA8wOzZs/XVV19ZXtmeUQQRAADcmGEY+vLLLzV37lyXqGzPKIIIAABuKjk5WePHj9fy5cv18ssv65lnnrF6pAwjiAAA4IaSkpIUGRl5pbK9fv36Vo+UKQQRAADcTFpl+7///qugoCDVqFHD6pEyjSACAIAbSatsP3XqlEaMGKHy5ctbPVKWEEQAAHATx44dk81m0+XLlxUVFaX77rvP6pGyzD329gAA4OX27t2rAQMGyNfXV9HR0R4RQiSCCAAALi+tsr1w4cIuX9meUVyaAQDAha1bt05RUVGqUKGChg0b5vKV7RlFEAEAwEUtW7ZMY8eO1aOPPqr33nvPLSrbM4ogAgCAC5ozZ46+/PJLNWvWTK+99prbVLZnFEEEAAAXkr6y/fnnn9cLL7zgVpXtGUUQAQDARaSkpGjcuHFavny5XnrpJbVq1crqkRyOIAIAgAtISkpSdHS0/vzzT7377rtq0KCB1SM5BUEEAACLxcfHKzw8XLt27XL7yvaMIogAAGChs2fPKjg4WDExMQoPD1eFChWsHsmpCCIAAFgkrbI9KSlJUVFRKlmypNUjOZ1n7gUCAMDF7du3TwMGDJCPj49GjRrllSFEIogAAOB027Zt0+DBg1WoUCFFR0d7VGV7RnFpBgAAJ1q/fr2ioqJUvnx5DR06VHny5LF6JEsRRAAAcJLly5dr7NixqlOnjt59913lzp3b6pEsRxABAMAJ5s6dq8mTJ6tp06Z6/fXXPbayPaMIIgAAOJBhGPr66681e/Zsr6hszyiCCAAADpKSkqKPP/5YS5cuVe/evfXss89aPZLLIYgAAOAAaZXtf/zxh/r166cnn3zS6pFcEkEEAIBslr6yfdiwYXrkkUesHsllEUQAAMhG586dU3BwsE6cOOGVle0ZRRABACCbHD9+XDabTYmJiYqMjFSpUqWsHsnlsXcIAIBssH//fg0YMECSNGrUKELIbSKIAACQRdu3b9egQYNUsGBBjRo1yqsr2zOKSzMAAGRBWmX7gw8+qGHDhnl9ZXtGEUQAAMiktMr22rVr67333qOyPRMIIgAAZEJaZXvjxo3Vp08f+fr6Wj2SWyKIAACQAYZh6JtvvtGsWbPUrl07devWjcr2LCCIAABwm9JXtvfq1UutW7e2eiS3RxABAOA2JCUladSoUVq/fr3eeecdPfXUU1aP5BEIIgAA3MLFixcVHh6uf/75h8r2bEYQAQDgJtJXtg8fPlwPPfSQ1SN5FIIIAAA3cOLECQUFBVHZ7kA0qwIAcB3pK9ujo6MJIQ5CEAEA4D/SKtsLFCig6OhoBQYGWj2Sx+LSDAAA6fzxxx+KjIxUuXLlNGzYMAUEBFg9kkcjiAAA8P9WrFihMWPGqFatWurfvz+V7U5AEAEAQNK8efM0adIkKtudjCACAPBqhmFoypQpmjlzJpXtFiCIAAC8VkpKiiZMmKAlS5aoZ8+eatOmjdUjeR2CCADAKyUlJen999/XunXr1LdvXzVs2NDqkbwSQQQA4HUuXryoESNGaOfOnRo6dKhq1apl9UheiyACAPAqsbGxCg4O1vHjxxUWFqaKFStaPZJXI4gAALxGTEyMhg0bpoSEBEVERKh06dJWj+QRzpyR7rorc++lWRUA4BUOHDig/v37SzIr2wkhWZeSIv38sxQcnPnP4IwIAMDj7dixQ6GhoSpatKhCQ0NVsGBBq0dye7t3S999Jx09mrXPIYgAADzan3/+qYiICCrbs0lcnDRnjrRmjX0tK7UrBBEAgMdasWKFPvroI9WsWVMDBgygsj0LDEP67TczhMTH29dLlpS6dMn85xJEAAAeKa2yvVGjRnrjjTeobM+Cw4elqVOlvXvta/7+Ups20hNPSD5ZuOOUIAIA8CiGYejbb7/V999/r+eee07du3ensj2TEhKk+fOl//1PSk21r9eqJbVvL+XLl/VjEEQAAB4jNTVVn3zyiRYvXqwePXroueees3okt2QY0qZN0owZ0rlz9vXAQKlzZ6l8+ew7FkEEAOARLl++rPfff19r166lsj0LTp2Spk2Ttm61r+XKJbVoITVpIuXM5uRAEAEAuL1Lly4pPDxcO3fu1JAhQ1S7dm2rR3I7ycnSkiXSwoXS5cv29UqVpE6dpMKFHXNcgggAwK3FxsYqJCRER48eVWhoqCpVqmT1SG7nn3/Mm1FPnLCvFSggdeggVauWte25t0IQAQC4rZiYGNlsNsXHxysyMpK21Aw6f16aNUtat86+5uMjPfWU9Mwz5s4YRyOIAADc0oEDB2Sz2ZQ7d25FR0fr7rvvtnokt5GaKq1eLc2dK126ZF+//36zE6R4cefNQhABALidHTt2KCwsTIULF1ZoaKjuyuwT17zQwYPmZZj9++1refJIzz0nPf64Yy/DXA9BBADgVjZs2KCRI0eqbNmyCgoKorL9NiUkSPPmSStWmNtz0zz6qNS2rZQ3rzVzEUQAAG5j5cqVGjNmjGrUqKGBAwdS2X4bDEPasEH6/nspNta+fvfd5mWYsmWtm00iiAAA3MT8+fM1ceJENWzYUG+++SaV7bchJsbsBNm+3b6WK5d5I2rDhtnfCZIZLjACAAA3ZhiGpk6dqhkzZqhNmzbq0aMHle23kJwsLV4sLVpkfp+malVzS26hQtbN9l8EEQCAy6KyPeN27pS+++7qTpCCBc1SsqpVrZvrRggiAACXdPnyZX3wwQdas2aN3n77bTVq1MjqkVzajTpBGjWSnn5a8vOzbrabIYgAAFxOWmX7jh07NHToUCrbb8Iw7J0gFy/a18uUMW9Gvfde62a7HQQRAIBLSV/ZHhYWRmX7TRw+bHaC7N1rX8uTx9yO+9hjzu8EyQyCCADAZaSvbI+IiND9999v9UguKTFR+vFH6X//M1tS01jdCZIZBBEAgEs4ePCgbDabcubMSWX7DRiGtHmzNH26dPasfb1YMfMyTLly1s2WWQQRAIDl/vnnH4WEhFDZfhOnT5sBZMsW+1quXFKLFlKTJq7RCZIZbjo2AMBTbNiwQRERESpTpoxsNhuV7f+RkiItWyb99JOUlGRfr1jR3JJbpIh1s2UHgggAwDKrVq3S6NGjVb16dQ0cOFB+rrrH1CL//mvejHr0qH0tf36zlKx6dfe4GfVWCCIAAEukVbY/9dRTevPNN5XTXa8tOEB8vDR7tvTbb/a1HDmkBg2k1q0lf3+rJst+/K8OAHAqwzD03Xffafr06VS2/4dhSL//boaQCxfs6yVLmjejlixp3WyOQhABADhNamqqPv30Uy1atEjdu3fXc889Rwj5f8eOmZdhdu+2r/n7m2dA6tc3W1I9EUEEAOAUly9f1ujRo/Xbb7/prbfeUuPGja0eySUkJUkLF0pLlpg3pqapWVNq314qUMCy0ZyCIAIAcLhLly5p5MiR2rZtm4YMGaI6depYPZJL2LpVmjZNOnXKvla4sNS5s7krxhsQRAAADnX+/HmFhITo8OHDCg0NVeXKla0eyXLnzkkzZkgbN9rXfH2lZs2k5s3NfhBvQRABADjMyZMnFRQUpAsXLigyMtLrK9tTU6WVK6V586SEBPt6uXLmzajFilk2mmUIIgAAhzh06JCCgoLk6+ur6Oho3XPPPVaPZKn9+82bUQ8etK/lzSu1ayfVru0ZnSCZQRABAGS7f/7550pVe1hYmFdXtl+6JP3wg/TLL+b23DT16klt2kjeXiRLEAEAZKuNGzdq5MiRuv/++2Wz2XTnnXdaPZIlDEP680/p+++l8+ft6/fea16GKVPGutlcCUEEAJBtVq1apQ8//FDVqlXz6sr2mBjpu++kHTvsa7lzS61aSU89Zd6YChNBBACQLRYsWKDPPvtMTz75pNdWticnS4sXS4sWmd+nqVpV6thR8uIrVDfkfX9KAADZyjAMTZs2TdOmTVPr1q3Vs2dPr2xL3bnTPAty4oR9rWBB8wm5VataN5erI4gAADItNTVVn332mRYuXKgXX3xRbdu29boQcv68NGuWtG6dfc3HR2rUSHr6aclLr07dNoIIACBT0le2v/nmm2rSpInVIzmVYUirV0tz50oXL9rXy5Qxm1GLF7duNndCEAEAZFhCQoJGjBihrVu3atCgQapbt67VIznV4cNmJ8jevfa1PHmktm2lxx7z3k6QzCCIAAAy5L+V7VWqVLF6JKdJTJR+/FH63//MltQ0deqYxWR581o3m7siiAAAbtvJkydls9kUFxeniIgIlfGSMgzDkDZvlqZPl86eta8HBkovvGBWtCNzCCIAgNty6NAh2Ww2+fj4eFVl++nTZgDZssW+liuX1KKF1KSJ5IW7lLMV//UBAG5p165dCgkJ8arK9pQUadky6aefpKQk+3rFiuaW3CJFrJvNkxBEAAA39ddff2nEiBEqXbq011S279kjffutdPSofS1/fqlDB6l6dW5GzU4EEQDADa1evVqjR4/Www8/rEGDBnl8ZXt8vLkdd/Vq+1qOHFKDBlLr1pK/v1WTeS6CCADguhYuXKhPP/1UDRo00FtvveXRle2GIa1fL82cKcXF2ddLljQfUFeypHWzeTrP/VMFAMiU9JXtzz77rHr16uXRbanXe0Cdv795BqR+fbMlFY5DEAEAXGEYhj777DMtWLBA3bp1U7t27Tw2hCQnS0uWSAsWXP2AuurVzXtBChSwbDSvQhABAEiSkpOTNXr0aP36669644031LRpU6tHcpjdu82bUY8ft6/ddZe5G8aL+tlcAkEEAKCEhASNHDlSf//9t0dXtsfHmw+oW7PGvsYD6qxFEAEALxcXF6fQ0FAdOHDAYyvbDUNau9YMIRcu2NdLlzabUXlAnXUIIgDgxU6dOiWbzabz588rIiJCDzzwgNUjZbsTJ8zLMLt22df8/aU2baQnnuBmVKsRRADASx0+fFhBQUHy8fFRVFSU7r33XqtHylaXL0uLF5tf6W9GrVlTev55s6AM1iOIAIAXSqtsL1iwoMLCwlSoUCGrR8pW//wjTZ1qng1JU7iw1LmzWdEO10EQAQAvk1bZXqpUKdlsNuX1oGfXx8WZ94GsXWtf8/ExH07XsqWUO7d1s+H6CCIA4EV+/fVXffDBB6pataoGDRokfw/pLDcMcyfM7Nnmzpg0ZcqYzagedtXJoxBEAMBLpFW2169fX2+//bbHVLYfO2Zehtm9276WJ4/03HPS44/zgDpX5xl/CgEAN2QYhmbMmKGpU6eqVatW6t27t0e0pV6+LC1cKP38s5SSYl+vVUtq317Kl8+62XD7CCIA4MEMw9DEiRP1008/qWvXrmrfvr1HhJAdO8yzICdP2teKFDEvw1SoYN1cyDiCCAB4qOTkZH344YdavXq1+vTpo2bNmlk9UpadP28+IXf9evuar6/UtKnUooWUK5d1syFzCCIA4IESEhIUERGhLVu2aODAgXrsscesHilLDEP69Vdpzhzp4kX7etmy5lmQu++2bjZkDUEEADxM+sr2kJAQVa1a1eqRsuTIEfMyzJ499rWAAKltW6luXW5GdXcEEQDwIGmV7bGxsRo5cqTKli1r9UiZlpQkLVggLVkipaba1+vUkdq1kzyo/sSrEUQAwEMcOXJEQUFBkqTo6Gi3rmzfulWaNk06dcq+VrSoeRmmfHnr5kL2I4gAgAfYvXu3QkJClD9/fg0fPtxtK9tjY6Xvv5f+/NO+ljOn1KyZ+cXNqJ6HIAIAbi6tsr1kyZIKDg52y8r21FRp1Spp7lwpIcG+Xq6c9MILUmCgdbPBsQgiAODGfvvtN73//vtuXdl+6JD07bfS/v32tYAA8wm5tWtzM6qnI4gAgJtatGiRPvnkE9WrV0/vvPOO21W2JyZKP/0kLVt29c2odeuaO2LuvNO62eA87vWnFgBwVWX7M888o5deesnt2lK3bDFvRj1zxr5WrJh5M2q5ctbNBecjiACAGzEMQ59//rnmz5+vLl26qEOHDm4VQs6dk6ZPlzZtsq/lzCm1bCk1aWJ+D+/C/+QA4CaSk5M1ZswYrVq1Sq+//rqaN29u9Ui3LTVVWrlSmjfv6ptRy5c3z4IULWrZaLAYQQQA3EBCQoIiIyO1efNmDRgwQI8//rjVI922gwfNm1EPHLCv5c1rPiG3Vi1uRvV2BBEAcHFxcXEKCwvT/v37FRwcrIcfftjqkW5LYqL044/S8uXms2LS1KsntWlj7owBCCIA4MJOnz4tm82mc+fOuVVl+/VuRr3nHvMyzAMPWDcXXA9BBABcVFplu2EYioqKUvHixa0e6ZZiY82bUTdutK/lymXejNq4MTej4lr8kQAAF5S+sj0sLEyFCxe2eqSbMgyzGXXOnKtvRq1QQercmZtRcWMEEQBwMZs3b1Z4eLjbVLYfPSpNmSLt3Wtfu/NOsxmVm1FxKwQRAHAhaZXtVapU0eDBg126sv3yZWnBAunnn69tRm3XjptRcXsIIgDgIhYvXqwJEya4RWX7jh3S1KnSyZP2taJFzQfUPfigdXPB/bjun3IA8BKGYWjmzJmaMmWKnn76ab388ssu25YaFyfNnCmtW2df8/WVmjWTmjc3b0wFMoIgAgAWMgxDkyZN0o8//ujSle2GIf3+uzRrlhQfb19/4AHzLMjdd1s3G9wbQQQALJKcnKyxY8dq5cqVeu2119SiRQurR7quEyfMyzD//GNfy5NHeu456fHHuRkVWUMQAQALuENle3KyeSPqwoXm92keecTcEZMvn3WzwXMQRADAydyhsv3ff83nwxw7Zl8rVMjsBKlUybq54HkIIgDgRGmV7WfPntWIESNUrlw5q0e6ysWLZinZ6tX2NR8fqVEj6emnJT8/62aDZyKIAICTHDlyRDabTampqYqOjnapynbDkP78U/r+e+n8eft6qVLmzaglSlg2GjwcQQQAnODff/9VSEiI8uXL53KV7adOSd99J23bZl/z8zOfkFu/vnlGBHAUgggAONiWLVsUHh6uEiVKKCQkxGUq21NTpWXLpB9/NFtS0zz8sNSxo1SwoGWjwYsQRADAgdasWaNRo0apcuXKGjJkiMtUtu/fb96MeuiQfa1AATOAVKtm1VTwRgQRAHCQn3/+WR9//LEef/xx9evXzyUq2xMSpHnzpBUrzPtCJLMHpEEDqXVryUVyEryI9f9UAICHSV/Z3qJFC73yyivycYEbLTZvlqZNk86eta8VL27ejFq6tHVzwbsRRAAgGxmGoS+++ELz5s1T586d1bFjR8sr28+dk6ZPlzZtsq/lyiU984y5LdfX17LRAIIIAGSX9JXtr776qlq2bGnpPKmp0i+/SD/8YF6SSVOxollM5kIbd+DFCCIAkA0SExMVFRWlTZs2qX///qpXr56l8xw+bN6Mum+ffS1vXqlDB6lmTZ4PA9dBEAGALLpw4YLCwsK0b98+2Ww2VbNw20lSkvTTT9LSpeYZkTSPP24+pC4gwLLRgOsiiABAFpw5c0Y2m01nzpxReHi4HnzwQctm2bbNLCY7dcq+VqyYeTNq2bKWjQXcFEEEADLp6NGjCgoKUmpqqqKiolTCoh70uDizmn39evtazpxS8+ZSs2bm94Cr4o8nAGTCnj17FBwcrDvvvFPDhw9XkSJFnD6DYUhr1kizZpkPq0tTrpx5FiQw0OkjARlGEAGADEqrbC9evPiV58c424kT5s2ou3bZ1/Lkkdq3lx59lJtR4T4IIgCQAb///ruio6NVqVIlDR061OmV7cnJ0pIl0oIF5vdpatc2Q4iLPMYGuG0EEQC4TUuWLNH48eP12GOPqV+/fsqVK5dTj79vn/TNN9LRo/a1QoWkLl3MbhDAHRFEAOAWDMPQ7Nmz9fXXX1tS2Z6QYJaSrVx59fNhGjeWnn5a8vNz2ihAtiOIAMBNGIahyZMn64cfflCnTp3UqVMnp1a2b9libslN/3yYEiWkbt2k++5z2hiAwxBEAOAGkpOTNW7cOK1YsUKvvPKKnn76aacd+/x58/kwGzbY13Llkp59VmrYUHKBZ+gB2YIgAgDXkVbZvnHjRr333nt64oknnHJcw5B+/VWaM+fqLbkPPWTeC8LzYeBpCCIA8B9ple179+6VzWZT9erVnXLcEyekKVOk3bvta3feKT3/vFSrFlty4ZkIIgCQzpkzZxQcHKzTp09rxIgRTqlsT06Wfv5ZWrjw6i25deqYW3LvvNPhIwCWIYgAwP87duyYhg0b5tTK9r17zbMg6bfkFi5sNqNWqODwwwOWI4gAgHTlMoyzKtsTEqS5c6VffrFvyfXxkRo1kp55Rsqd26GHB1wGQQSA19u6dauGDx+ue++9V8HBwcqfP79Dj7d5s7kl99w5+1rJklLXrubWXMCbEEQAeLW1a9cqOjpaDz30kIYOHao77rjDYceKjTW35G7caF/LndvckvvUU2zJhXciiADwWkuXLtW4ceNUt25dvfvuuw6rbE/bkjt7tnTpkn29YkVzS26hQg45LOAWCCIAvE76yvbmzZvr1VdfdVhl+/Hj5lNy02/JzZvX3JL7yCNsyQUIIgC8imEY+vLLLzV37lx17NhRnTt3dkhle3KytHixtGjR1Vty69aV2rWTAgKy/ZCAWyKIAPAaycnJGj9+vJYvX66XX35ZzzzzjEOOs2ePuSX32DH7WpEi5pbc8uUdckjAbRFEAHiFpKQkRUZGauPGjerfv79DKtsvXTKfkvvfLblpT8llSy5wLYIIAI8XHx+vsLAw7dmzR0FBQapRo0a2H+Ovv6Rp067ekluqlLklt3jxbD8c4DEIIgA8Wlpl+6lTpxQeHq7y2Xxt5Nw5c0vupk32NT8/c0vuk0+yJRe4FYIIAI917Ngx2Ww2Xb58WVFRUbrvvvuy7bMNQ1q92tySm5BgX69USercmS25wO0iiADwSHv37lVwcLACAgI0YsQIFS1aNNs++9gxc0vuv//a1/LmlTp0kGrWZEsukBEEEQAeJ62y/Z577lFISEi2VbYnJ5vbcRctklJS7OtsyQUyjyACwKOsW7dOUVFR2V7Zfr0tuUWLms2obMkFMo8gAsBjLFu2TGPHjs3Wyva0p+SuXGlf8/GRmjaVWraUHNQKD3gNgggAjzBnzhx9+eWXatasmV577bVsqWzfssV8Su7Zs/Y1tuQC2YsgAsCtpa9s79Chg7p06ZLlyva4OGnGDOmPP+xruXNLrVuzJRfIbgQRAG4rJSVF48aNy7bKdsOQ1q2Tvv9eio+3rz/0kFnPzpZcIPsRRAC4paSkJEVHR+vPP//Uu+++qwYNGmTp806fNrfkbt9uXwsIMJ+SW7s2W3IBRyGIAHA78fHxGj58uHbv3p3lyvbUVGnFCvMZMUlJ9vVHHjF7QfLmzfq8AG6MIALArZw9e1bBwcGKiYlReHi4KlSokOnPOnJE+uYbaf9++1rBgmYzapUqWZ8VwK0RRAC4jbTK9qSkJEVFRalkyZKZ+pzkZGnBAmnxYvOMSJoGDaQ2bSR//+yZF8CtEUQAuIV9+/bJZrMpT548GjVqVKYr2/fsMc+CHD9uXytWTOrWTSpTJpuGBXDbCCIAXN62bds0fPhwFStWTKGhoZmqbL9RMVnz5uYXxWSANQgiAFza+vXrFRUVpfLly2vo0KHKkydPhj/j77+lqVOvLSbr1k26997smxVAxhFEALis5cuXa+zYsapTp47effdd5c6dO0Pvp5gMcH0EEQAuae7cuZo8ebKaNm2q119/PUOV7RSTAe6DIALApRiGoa+++kpz5szR888/rxdeeCFDle2nT5uXYbZts69RTAa4LoIIAJeRkpKi8ePHa9myZerdu7eeffbZ234vxWSAeyKIAHAJ6Svb+/XrpyeffPK230sxGeC+CCIALBcfH6/w8HDt2rVLw4YNU82aNW/rfcnJ0sKF0qJFFJMB7oogAsBS586dU3BwsE6cOJGhyvYbFZN17So98ICDhgWQ7QgiACxz/Phx2Ww2JSYmKjIyUqVKlbrle9KKyX75xdwdI1FMBrgzgggAS+zfv182m03+/v63XdlOMRngeQgiAJwurbI9MDBQYWFht6xsp5gM8FwEEQBOlZHKdsOQ1q83Q0j6YrIKFcxissKFnTAwAIciiABwmoxUtp89a16G+ftv+xrFZIDnIYgAcIq0yvYmTZqoT58+N6xsNwxp9Wpp9mzzxtQ0NWuaxWT58jlpYABOQRAB4FCGYeibb77RrFmz1L59e3Xt2vWGle0xMdKUKdKuXfa1fPmkLl2khx92zrwAnIsgAsBhUlJS9PHHH2vp0qU3rWxPTZWWL5fmzZMuX7avP/aY1K6ddJPbSAC4OYIIAIdISkrSqFGjtH79er3zzjt66qmnrvt7R49KX399dT17oUJmMdltdpsBcGMEEQDZ7r+V7Y888sg1v5OcLC1ebFa0p6SYazlymNtxW7eW/PycOzMAaxBEAGSr9JXtw4cP10MPPXTN7+zfb54FOXrUvlasmFlMVqaM82YFYD2CCIBsc+LECQUFBd2wsj0pSfrxR2nZsqvr2Zs2lVq2pJ4d8EYEEQDZYv/+/QoODpafn5+io6MVGBh41c937TJ3xMTE2NdKlJBefNH8TwDeiSACIMu2b9+usLAwBQYGKjQ0VAUKFLjys4QEsxNk1Sr77+fMKT3zjNS4seTr6/x5AbgOggiALPnjjz8UGRmpcuXKadiwYQoICLjys61bpW+/vfohdWXKmPeCFCtmwbAAXA5BBECmrVixQmPGjFGtWrXUv3//K5XtFy5I338vrVtn/10/P6lNG6lBA+rZAdgRRABkyrx58zRp0iQ1btxYffr0ka+vrwxD2rBBmj7dfGJumgoVzF6QQoWsmxeAayKIAMiQ9JXt7dq1U7du3ZQjRw6dOyd99520ebP9d/Pkkdq3lx59lLMgAK6PIALgtqWkpGjChAlasmSJevbsqTZt2sgwpN9+k2bOlC5dsv9utWpSp05S/vzWzQvA9RFEANyWpKQkvf/++1q3bt2VyvZTp8ybUXfssP9e3rxS585mEOEsCIBbIYgAuKWLFy9qxIgR2rlzp4YOHaqaNWtp+XLphx/MkrI0depIzz8vpds4AwA3RRABcFOxsbEKDg7W8ePHNXz4cBUs+JBGjZL27rX/TsGC0gsvSJUqWTcnAPdEEAFwQzExMRo2bJgSEhI0YkSk/vmnlD7+2HxgXZoGDcxtuf7+lo0JwI0RRABc14EDB2Sz2eTn56e+faM1bVoxHTpk/3nRomYxWdmy1s0IwP0RRABcY8eOHQoNDVXhwkX12GOh+vzzgkpNNX+WI4fUpIlZ0c5D6gBkFUEEwFXSKtsDA8upQIFhWrnSfufpPfeYD6n7z0N1ASDTCCIArlixYoVGjx6jfPkeUXLyAJ08aVa2+/hIzZpJLVuaD6wDgOzCXykAJJmV7WPHTlLu3I2VJ08f5chhPha3eHGpe3epRAlr5wPgmQgigJczDENfffWtPv74e+XN21YlSryoHDlyyNfXPAPSrJnk62v1lAA8FUEE8GKpqakKC/tE3323WKVK9VTp0m0kSSVLmveC3HuvxQMC8HgEEcBLXbhwWS+99L5+/32tKlXqq3vvbaicOc3dME2amPeFAICjEUQAL7R580W9/voIHT26U9WqDVHRorV1//1mL8jdd1s9HQBvQhABvEhCgvTtt7H66KNgXbx4TDVrhiowsJKefVZq2JCzIACcjyACeIkdO6RPP43RkiVBSk6+qFq1IlW9eml16yYFBlo9HQBvRRABPNylS9KsWdKiRQf05582+frmVr16o9S1azE1aGA2pQKAVQgigAfbulWaMkXat2+HNm4Mk79/EXXsGKpXXy2owoWtng4ACCKAR7p4UZoxQ1q7Vjp5coM2bRqpu+4qq5Ejg9SkSQBnQQC4DIII4GE2b5a+/VY6f146enSl/v57jCpWrKlJkwbo7rtzWz0eAFyFIAJ4iAsXpOnTpT/+MF8fODBfu3ZN1LPPNtQHH7ypnDmpRwXgeggigAfYuFH67jspLs6sbP/336k6eXKG+vVroz59eigH12IAuCiCCODG4uLMALJxo/naMFL177+fKClpsUJCeqht2+esHRAAboEgAripP/80Q0h8vPk6NfWyTp78QP7+v2vIkLfVqFEjawcEgNtAEAHczH/PgkiSn98lxcWFy8dnh4KDh6h27drWDQgAGUAQAdzIhg1mCLlwwb5WoUKsdu8O0cWLRxUWFqZKlSpZNyAAZBBBBHADFy5I06aZl2PSBARIzZrFaM4cm+Lj4xUREaH777/fuiEBIBMIIoCL27RJmjrVvCSTplo1qV69gxo1yqacOXMqOjpad/PYXABuiCACuKj4ePMsSFoviGSeBenUSbrzzp0KCwtV4cKFFRoaqrvuusu6QQEgCwgigAtK346apmpV6YUXpN27NygoKEJlypSRzWZTQECAdYMCQBYRRAAXEh9vPiNm3Tr7Wp48UseOUq1a0qpVv+jDDz9UjRo1NHDgQOXOTWU7APdGEAFcxJYt5pNy058FqVLFPAuSP780f/58TZw4UQ0bNtSbb74pX18q2wG4P4IIYLH0T8pNkyeP1KGDZNaBGJo69TtNnz5dbdq0UY8eVLYD8BwEEcBCf/9t3gty7px9rVIlqWtXqUABKTU1VZ9++qkWLVqk7t27q23btlaNCgAOQRABLHDxojRzprRmjX3tjjuk55+XHn1UypFDunz5skaPHq3ffvtNb731lho3bmzdwADgIAQRwMm2bZO++ebqsyAVK5pnQQoWNF9funRJI0eO1LZt2zRkyBDVqVPHklkBwNEIIoCTXLpkngX57Tf7mr+/eRakbl3zLIgkxcbGKjQ0VIcPH1ZoaKgqV65szcAA4AQEEcAJtm83z4KcPWtfe+ghqVs3+1kQSTp58qSCgoJ04cIFRUZGUtkOwOMRRAAHSkiQZs2SVq+2r/n7S+3aSY8/bj8LIkmHDh1SUFCQcubMqVGjRlHZDsArEEQAB9mxwzwLcuaMfa1CBfNekEKFrv7df/75R6GhoSpUqBCV7QC8CkEEyGaJidLs2dIvv9jX/PzMsyD16l19FkSSNm7cqJEjR+r++++XzWbTnXfe6dyBAcBCBBEgG/37r/TVV9LJk/a18uXNe0H+exZEklatWqUPP/xQ1apV08CBA+Xn5+e0WQHAFRBEgGxw+bL044/S0qWSYZhruXNLbdtK9etfexZEkhYsWKDPPvtMTz75pN58803lzMk/jgC8D3/zAVl04ID05ZfSsWP2tTJlpO7dpaJFr/19wzD03XdmZXvr1q3Vs2dPKtsBeC2CCJBJKSnSokXSggVSaqq5ljOn9OyzUqNGko/Pte9JTU3VZ599poULF+rFF19U27ZtCSEAvBpBBMiEo0fNsyAHD9rXSpSQevaU7rnn+u+hsh0ArkUQATIgNVVatkyaN09KTjbXfHykFi3ML1/f678vISFBI0aM0LZt2zR48GA9+uijzhsaAFwYQQS4TTEx5o6YPXvsa3ffLfXoIZUseeP3nT9/XiEhIVS2A8B1EESAWzAMadUqsyE1Kclcy5FDatxYatVKypXrxu89efKkbDab4uLiFBERoTJlyjhnaABwEwQR4CbOnpW+/tpsSU1TuLC5I6Zs2Zu/99ChQ7LZbPLx8VF0dLTuudHNIwDgxQgiwHUYhrR2rTR9uvm8mDRPPGE2pN6qdyytsv2uu+5SWFgYle0AcAMEEeA/zp+Xvv1W2rzZvlaggNmOWrHird+/adMmjRw5UqVLl6ayHQBugSACpLNxozR1qnThgn2tTh2pQwcpT55bv3/16tUaPXo0le0AcJsIIoCkixeladOk9evta3nzSl26SNWq3d5nLFy4UJ9++qkaNGigt956i8p2ALgN/E0Jr7d1qzRlinTunH2tWjUzhOTNe+v3G4ahadOmadq0aXr22WfVq1cv2lIB4DYRROC1EhOlmTOl1avta3nySB07SrVqXf9Bdf9lGIY+++wzLViwQN26dVO7du0IIQCQAQQReKU9e6TJk6VTp+xrFSuaN6QWKHB7n5GcnKzRo0fr119/1RtvvKGmTZs6ZFYA8GQEEXiV5GTpp5+kxYvNLbqSuRW3XTupXr3bOwsimZXtI0eO1N9//61Bgwapbt26jhsaADwYQQRe4+hR8yzIoUP2tTJlzIr2IkVu/3POnz+v0NBQHTx4UKGhoapSpUr2DwsAXoIgAo9nGNLy5dLcuVc/qK5VK6lpU/P723Xq1CkFBQVdqWx/4IEHHDM0AHgJggg82pkz5oPq/vnHvnb33VKvXlKJEhn7rMOHDysoKEg+Pj6KiorSvffem62zAoA3IojAIxmGtG6d2Q2SvqK9USOpdeubP6juenbt2qWQkBAVLFhQYWFhKlSoULbOCwDeiiACjxMfb1a0b9xoXytY0LwX5MEHM/55f/31l0aMGKHSpUsrKChIeW+nXAQAcFsIIvAoW7eaT8s9f96+lpGK9v/69ddf9cEHH6hq1aoaPHgwle0AkM0IIvAIiYnSrFnSqlX2tYAA6YUXpOrVM/eZaZXt9evX19tvv01lOwA4AH+zwu3t22duy42Jsa9VqmSWk+XPn/HPMwxDM2bM0NSpU9WqVSv17t2btlQAcBCCCNxWSoq0YIG0aJGUmmqu5c4ttW+fsXKy9AzD0MSJE/XTTz+pa9euat++PSEEAByIIAK3dOyY9OWX0oED9rXSpaWePaWiRTP3mcnJyfrwww+1evVq9enTR82aNcueYQEAN0QQgVsxDGnFCmnOHOnyZXPNx0d6+mmpefOMlZOll5CQoIiICG3ZsoXKdgBwIoII3Ma5c2Y52Y4d9rVixcyzICVLZv5z4+LiFBoaqgMHDlDZDgBORhCBW9i4UZoyRbp40b721FPSc89lvJwsvVOnTslmsyk2NlYjR45U2bJlsz4sAOC2EUTg0hISpBkzpDVr7GsFCkjdu0sVKmTts48cOaKgoCBJUnR0NJXtAGABgghc1t690hdfSKdO2ddq1JC6dDE7QrJi9+7dCgkJUf78+TV8+HAq2wHAIgQRuJzUVHNb7sKF9m25fn5Sp05mS2pWd9OmVbaXLFlSwcHBVLYDgIUIInApJ0+a5WR799rX7r/fvCG1SJGsf376yvZBgwbJ398/6x8KAMg0gghcgmFIv/8uTZ9u1rVL5lbcli2lFi0yvy03vUWLFumTTz7RE088ob59+1LZDgAugL+JYbnrPS23cGGpVy/zbEhWpa9sf+aZZ/TSSy/RlgoALoIgAkvt3Gk2pJ47Z1+rW9d8Wm52XDUxDEOff/655s+frxdeeEHPP/88IQQAXAhBBJZITpZ++EFautS+lieP1LVr5p+We+0xkjVmzBitWrVKr7/+upo3b549HwwAyDYEETjd0aPmttzDh+1r5ctLPXqYHSHZISEhQZGRkdq8ebMGDBigxx9/PHs+GACQrQgicBrDkFaulGbPtj8nJmdOqXVrqVGjrG/LTZO+sj04OFgPP/xw9nwwACDbEUTgFOfPm8+J2bbNvnb33VLv3lLx4tl3HCrbAcC9EETgcH//LX39tRQXZ1978kmpbdusPSfmv6hsBwD3QxCBw1y+bF6GWbHCvpYvn/mcmIoVs/dY6Svbw8LCVLhw4ew9AADAIQgicIhjx6RJk66+IbVKFalbNym7G9U3b96s8PBwKtsBwA0RRJCtDEP69Vfzibnpb0ht316qXz/7bkhN89tvv+n9999XlSpVNHjwYCrbAcDNEESQbeLjpSlTpE2b7Gv33GPekOqI2zUWL16sCRMmqF69enrnnXeobAcAN8Tf3MgWu3aZD6s7e9a+Vr++eSYkO29Ilcy21JkzZ2rKlCl6+umn9fLLL9OWCgBuiiCCLElNlebPlxYtMi/LSFJAgHkviCPqOwzD0KRJk/Tjjz+qS5cu6tChAyEEANwYQQSZdvq0eUPq3r32tXLlpJ49pYIFs/94ycnJ+uijj/TLL7/otddeU4sWLbL/IAAApyKIIFP++MN8Ym5Cgvnax0dq1Upq2tT8PrtR2Q4AnokgggxJTJSmT5fWrLGvFS5s3pBaurRjjhkXF6ewsDDt37+fynYA8DAEEdy2AwfMSzExMfa12rWlzp0lR+2aPX36tGw2m86ePUtlOwB4IIIIbskwpOXLpTlzpJQUc83Pzwwgdeo47rhHjhyRzWZTamqqoqOjVTw7H0oDAHAJBBHcVHy8+bC6LVvsa6VKSb16SUWLOu64//77r0JCQpQvXz4q2wHAgxFEcEO7d0tffHF1N0jTpuZNqY7sDtuyZYvCw8NVokQJhYSEUNkOAB6MIIJrpKZKixdLP/5o7wbJm1fq0SP7H1b3X2vWrNGoUaNUuXJlDRkyhMp2APBwBBFcJTbWbEjdudO+Vq6ceSmmQAHHHvvnn3/Wxx9/TGU7AHgR/qbHFdu3myEkLs58nSOH9PTTUosWjukGSZO+sr1ly5Z65ZVXaEsFAC9BEIFSUszLMIsX29cKFDDPgpQr59hjG4ahL774QvPmzVPnzp3VsWNHQggAeBGCiJc7c8bsBtmzx75WqZLUvbt5X4gjJScna+zYsVq5ciWV7QDgpQgiXuyvv6Svv5YuXjRf+/hIzz0nNWpkXpZxpMTEREVFRWnTpk3q37+/6tWr59gDAgBcEkHECyUnS7NmSStW2NcKFZJeeslxNe3pXbhwQWFhYdq3b59sNpuqVavm+IMCAFwSQcTLxMRIn38uHTxoX6teXeraVcqTx/HHP3PmjGw2m86cOaPw8HA9+OCDjj8oAMBlEUS8yJ9/St98Yz64TjJLyZ5/XnriCcdfipGko0ePKigoSKmpqYqKilKJEiUcf1AAgEsjiHiB5GRp5kxp5Ur7WmCg9PLLkrMe37Jnzx4FBwcrb968Gj58OJXtAABJBBGPd+qUNHGi+eTcNLVrS126mA+uc4b0le3BwcHKly+fcw4MAHB5BBEPtnmz+cC6tF0xOXNKnTpJjz3mnEsxkvT7778rOjpalSpV0tChQ6lsBwBchSDigVJSpB9+kJYssa8VLWpeinHmbRlLlizR+PHj9dhjj6lfv37KlSuX8w4OAHALBBEPc/asuSsmfUFZ9epSt27SHXc4ZwbDMDR79mx9/fXXatGihV555RX5OLIjHgDgtggiHmT7dumLL6QLF8zXvr5Su3bSk08671KMYRiaPHmyfvjhB3Xq1EmdOnWish0AcEMEEQ+QmiotWGB+GYa5dtdd5qUYZxSUpUlf2f7KK6/o6aefdt7BAQBuiSDi5s6fN8+C7NxpX6tcWerRQwoIcN4c6Svb33vvPT3xxBPOOzgAwG0RRNzY7t3m/SCxseZrHx+pdWupSRPnXYqR7JXte/fupbIdAJAhBBE3ZBjSsmXSnDnmZRlJyp/ffFZM2bLOneXMmTMKDg7W6dOnNWLECCrbAQAZQhBxMwkJZk37hg32tfLlpV69JGf3hB07dkzDhg2jsh0AkGkEETdy/Lj06afSsWP2tebNpVatzMsyzpR2GebOO+/U8OHDVaRIEecOAADwCAQRN7Fpk9mSmpBgvvb3l3r2lKpWdf4sf//9t8LDw3XvvfcqODhY+fPnd/4QAACPQBBxcampZkvqzz/b1+65R3rtNbMt1dnWrl2r6OhoVaxYUUOGDNEdzmpJAwB4JIKIC4uLkyZNunpr7iOPSF27Ou+BdektXbpU48aNo7IdAJBtCCIuat8+6bPPzMp2ybwHpH1757akpklf2d68eXO9+uqrVLYDALIFQcTFGIa0erU0Y4aUnGyu5csnvfKK9MADVsxj6Msvv9TcuXPVsWNHde7cmcp2AEC2IYi4kMuXpe++k9assa+VKWOGECvuB01OTtb48eO1fPlyvfzyy3rmmWecPwQAwKMRRFzEqVPm1txDh+xrTz1lPrTO19f58yQlJSkyMlIbN25U//79qWwHADgEQcQF7NwpTZwoxcebr3PnNm9IrVXLmnni4+MVFhamPXv2KCgoSDVq1LBmEACAxyOIWMgwpBUrpJkz7VXtRYtKr74q3XuvNTOlVbafOnVK4eHhKl++vDWDAAC8AkHEIte7H6RiRal3bylPHmtmOnbsmIKCgpScnKyoqCjdd9991gwCAPAaBBELnDtn3g+yb599rWlT88m5Vu2K3bt3r4KDgxUQEKCRI0eqqBVtaQAAr0MQcbJ9+6RPPpFiY83XuXJJL75oFpVZZevWrRo+fDiV7QAApyOIONGaNdLUqfZ+kLvukl5/XbLyobXr1q1TVFSUHnroIQ0dOpTKdgCAUxFEnCA1VZo1S1q+3L5WtqzZD5I3r3VzLVu2TGPHjlXdunX17rvvUtkOAHA6goiDxcebW3PTPy+mQQPp+eet6QdJM2fOHH355Zdq1qyZXnvtNSrbAQCWIIg40LFj0vjxZlmZZAaPTp2kevWsmyl9ZXuHDh3UpUsXKtsBAJYhiDjI9u3mQ+sSEszX+fKZ/SBlylg3U0pKisaNG0dlOwDAZRBEHGDlSvOhdWklZSVKSH36SAULWjdTUlKSoqKitGHDBr333nuqX7++dcMAAPD/CCLZKDVV+v57sy01zcMPSz17Sn5+lo2l+Ph4DR8+XLt376ayHQDgUggi2eTSJenzz6Vt2+xrTZtKbdpIVt6CcfbsWQUHB+vkyZMaMWIEle0AAJdCEMkGp05JH38sHT1qvvb1lV54Qapb19q5jh07JpvNduWyDJXtAABXQxDJoj17zKbUuDjzdUCAeVNquXLWzrVv3z7ZbDblyZNHo0aNorIdAOCSCCJZsG6d9M039qbUwEDpjTfMJ+haadu2bRo+fLiKFSum0NBQKtsBAC6LIJIJhiHNny8tWGBfK1/ebEq16sm5adatW6fo6GiVL19eQ4cOVR6rBwIA4CYIIhmUnGyeBVm3zr72xBNSx47WNqVK0vLlyzV27FjVqVNH7733HpXtAACXRxDJgEuXpE8/tde158ghtW8vPfWUtTtjJCrbAQDuiSBym86elcaNk44cMV/nyiX16iVVq2btXIZh6KuvvtKcOXP0/PPP64UXXqCyHQDgNggit+HIEWnsWOncOfN1QIB5U+r991s6llJSUjR+/HgtW7ZML730klq1amXtQAAAZBBB5BZ27jS356Y9M6ZIEemtt6zfGZOUlKTo6Gj9+eef6tevn5588klrBwIAIBMIIjexdq15Y2pKivm6VCnzTEjevJaOpfj4eIWHh2vXrl0aNmyYatasae1AAABkEkHkOgxDWrJEmjPHvlalitS7t7XPjJHsle0xMTEKDw9XhQoVrB0IAIAsIIj8h2GYAWTJEvta/frm9lyrN6IcP35cNptNiYmJioqKUsmSJa0dCACALCKIpJOaKk2ZIq1ZY19r3Vpq1sz67bn79++XzWbTHXfcQWU7AMBjEET+3+XL0qRJ0l9/ma9z5JC6dJHq1bN0LElUtgMAPBdBROaOmAkTpH/+MV/7+pr3g1Svbu1ckrR+/XpFRUVR2Q4A8EheH0Ti4syisgMHzNd+ftJrr0mucA9o+sr2d999V7lz57Z6JAAAspVXB5GzZ6UPP5ROnDBfBwRIb74plS5t7VySNHfuXE2ePFlNmjRRnz59qGwHAHgkrw0iMTHS6NFmGJGkAgWkt9+W7rnH0rFkGIa++eYbzZo1S+3bt1fXrl2pbAcAeCyvDCLHjpkh5Px583XRolLfvlKhQpaOpZSUFH388cdaunSpevfurWeffdbagQAAcDCvCyJHjpiXY+LizNfFi5tnQvLls3aupKQkjRo1SuvXr6eyHQDgNbwqiBw6ZIaQ+Hjz9X33mWdCAgIsHeuayvZHHnnE2oEAAHASrwki+/dLH30kXbxovi5d2nx4ndW7Yc+dO6fg4GCdOHGCynYAgNfxiiCyb580Zoz9CbplypghxN/f0rF04sQJBQUFKTExUZGRkSpVqpS1AwEA4GQevyf0wAHzTEhaCClXzrwnxOoQsn//fg0YMECSFB0dTQgBAHgljw4ihw+bZ0IuXTJfP/ig2RNi9RN0t2/frkGDBqlAgQKKjo5WYGCgtQMBAGARj700c/SoeWNq2j0hZctKffpIVpeT/vHHH4qMjNSDDz6ooUOHKsDqO2UBALCQRwaR48fNEHLhgvn6/vulN96w/kzI//73P3300UeqXbu23nvvPSrbAQBez+OCyMmTV5eVlSzpGjem/vDDD/riiy/UuHFj9enTR76+vtYOBACAC/CoIHL+vHlPSGys+bpECbMn5I47rJspfWV7u3bt1K1bNyrbAQD4fx4TRC5dksaOlU6dMl/ffbcZQqzsCUlJSdGECRO0ZMkS9erVS61bt7ZuGAAAXJBHBJHLl6UJE8zmVEkqWNDconvnndbNlJSUpPfff1/r1q3TO++8o6eeesq6YQAAcFFuH0RSU6XJk6Vdu8zXAQHmmZCCBa2b6eLFixoxYoR27typoUOHqlatWtYNAwCAC3PrIGIY0rRp0saN5uvcuc2ekGLFrJspNjZWwcHBOn78uIYPH66HHnrIumEAAHBxbh1EFi+WVq0yv/fxkV591XyGjFXSKtsTEhKobAcA4Da4bbPqpk3SDz/YX3fvLlWsaNU0V1e2jxo1ihACAMBtcMsgcviw9OWX9tetW0u1a1s2jnbs2EFlOwAAmeB2l2bOn5fGj5cSE83XtWpJzZpZN09aZXu5cuU0bNgwKtsBAMgAtwoiycnSJ59IZ8+ar0uVkrp1k6zqB1uxYoXGjBmjRx55RAMGDKCyHQCADHKbIGIY0pQp0t695usCBaTXX5dy5bJmnnnz5mnSpElUtgMAkAVuE0SWL5fWrjW/z5XLfJJu/vzOn8MwDH377bf6/vvv1bZtW7344otUtgMAkEluEUT27pVmz7a/7tFDuu8+58+RmpqqCRMm6Oeff1bPnj3Vpk0b5w8BAIAHcfkgEh8vTZxoNqhKUtOmUo0azp8jKSlJH3zwgdauXau+ffuqYcOGzh8CAAAP49JBxDDM+va0m1PLljW36joble0AADiGSweRX36Rtm41v8+bV+rd22xQdab0le1hYWGqaGVrGgAAHsZlg8jx49KsWfbXPXqYO2WcKSYmRkFBQbp06ZIiIiJU2sr+eAAAPJBLNqumpJiXZC5fNl8/+aTz69sPHDig/v37KzU1VdHR0YQQAAAcwCWDyOLF0oED5veBgdJzzzn3+GmV7fnz51d0dLSKWfk4XwAAPJjLBZETJ6SFC83vfXyknj0lZxaWbtiwQcOGDVPJkiUVERGhggULOu/gAAB4GZe6R8QwpO++M6vcJalxY7PG3VlWrlypMWPGqGbNmlS2AwDgBC4VRNavl3buNL8vVEhq2dJ5x/7xxx/1+eefq1GjRnrjjTeobAcAwAlcJohcuiTNnGl/3amT5Ofn+OOmr2x/7rnn1L17dyrbAQBwEpcJIkuWSHFx5vfVqkmVKzv+mKmpqfrkk0+0ePFi9ejRQ885+65YAAC8nEsEkbg486F2kuTrK7Vr5/hjXr58WR988IF+//13vf3222rUqJHjDwoAAK7iEkFk0SIpMdH8vl49qXBhxx7v0qVLCg8P144dOzRkyBDVrl3bsQcEAADXZXkQOX3arHKXpFy5pBYtHHu82NhYhYSE6OjRowoLC1OlSpUce0AAAHBDlgeRRYvs23UbNpTy53fcsWJiYmSz2RQfH6+IiAjdf//9jjsYAAC4JUsLzRISpHXrzO/9/aWmTR13rIMHD6p///5KSUlRdHQ0IQQAABdgaRBZv15KSjK/r1NHypPHMcfZuXOnBg4cqHz58ikqKkp33323Yw4EAAAyxLIgYhjSqlX21/XqOeY46SvbIyMjdddddznmQAAAIMMsu0fk0CHzSzJr3IsXz/5j/PLLL/rwww9Vo0YNDRw4kMp2AABcjGVB5Pff7d8/8UT2f/78+fM1ceJENWzYUG+++SaV7QAAuCDLgsiGDeZ/+vtLNWtm3+cahqHvvvtO06dPV5s2bdSjRw8q2wEAcFGWBZHERCm3pEceyb5nyqSmpurTTz/VokWLqGwHAMANWN4jct992fM5ly9f1ujRo/Xbb79R2Q4AgJuwPIgULJj1z7h06ZJGjBih7du3a+jQoVS2AwDgJtw+iMTGxio0NFRHjhyhsh0AADfj1kHk5MmTCgoK0oULF6hsBwDADVkaRHLlynyb6qFDhxQUFKScOXNq1KhRtKUCAOCGLK14L1hQyszO2n/++UcDBw5U3rx5FR0dTQgBAMBNWRpEMtO2vnHjRg0dOlTFixdXREQEle0AALgxSy/NFCiQsd9ftWqVPvzwQ1WrVk0DBw6UX3YVkAAAAEtYGkQycqPqTz/9pIkTJ+rJJ5/Um2++qZw5Lb/PFgAAZJGl/za/nasqVLYDAOC5XPrSTGpqqj777DMtXLhQL774otq2bUsIAQDAg7jspZn0le1vvfWWGjdu7LzBAACAU7jkpZmEhASNGDFC27Zt0+DBg/Xoo486dzAAAOAUlgWRG5WZnT9/XiEhITp8+LBCQ0NVuXJl5w8HAACcwrIgUqDAtWVm6SvbIyMjqWwHAMDDWRpE0jt06JBsNpt8fHwUHR2te+65x5K5AACA81jWrJo+iKRVtgcEBGjUqFGEEAAAvITlQWTTpk0aNmyYihcvrsjISCrbAQDwIpkKIhMmTFDp0qXl7++vGjVqaPXq1Rn+jAIFpNWrVyssLEyVK1fW8OHDdeedd2ZmHAAA4KYyHERmzJihvn37aujQodq0aZPq1aun5s2b6+DBgxn6nO3bl2jUqFGqV6+ehgwZwnNjAADwQjkMwzAy8obatWurevXq+uSTT66sVahQQa1bt1ZERMQt338+8bzyR+ZX/TVN9UL7durVqxdtqQAAeKkM7ZpJSkrShg0bNGjQoKvWmzRpojVr1lz3PYmJiUpMTLzyOjYhVpLUpmNrte/UXnFJcRmdGQAAuKC8ufNm+ORChoLIqVOnlJKSosDAwKvWAwMDdfz48eu+JyIiQqGhoemmlPSu1Pfga+ob9VqGhgUAAK4r5p0YFclXJEPvyVSPyH/TjmEYN0xAgwcPVr9+/a68PnfunEpWKqmD/x5U/vz5M3N4AADgQs6fP68SJUood9/cGX5vhoJI4cKF5evre83Zj5iYmGvOkqTx8/O79kbUOCm/f37l88uXsWkBAIDr8ZOUeO2JituRoV0zuXPnVo0aNbR06dKr1pcuXaq6detm+OAAAMC7ZfjSTL9+/dS1a1fVrFlTjz76qCZOnKiDBw/q1VdfdcR8AADAg2U4iHTo0EGnT59WWFiYjh07pkqVKmnhwoUqWbLkbb3fz89PwcHB9IYAAOAhsvLv9gz3iAAAAGQXy541AwAAQBABAACWIYgAAADLEEQAAIBlCCIAAMAyTg0iEyZMUOnSpeXv768aNWpo9erVzjw8AABwoIiICOXIkUN9+/a97fc4LYjMmDFDffv21dChQ7Vp0ybVq1dPzZs318GDB501AgAAcJA//vhDEydOVJUqVTL0PqcFkdGjR6tXr17q3bu3KlSooDFjxqhEiRL65JNPnDUCAABwgAsXLqhLly76/PPPVbBgwQy91ylBJCkpSRs2bFCTJk2uWm/SpInWrFnjjBEAAICD9OnTRy1btlSjRo0y/N4MV7xnxqlTp5SSknLNE3oDAwOveZIvAABwH9OnT9fGjRv1xx9/ZOr9Tgkiaf77eGDDMDL1yGAAAGC9Q4cO6e2339aSJUvk7++fqc9wShApXLiwfH19rzn7ERMTc81ZEgAA4B42bNigmJgY1ahR48paSkqKVq1apfHjxysxMVG+vr43/Qyn3COSO3du1ahRQ0uXLr1qfenSpapbt64zRgAAANmsYcOG+vvvv/XXX39d+apZs6a6dOmiv/7665YhRHLipZl+/fqpa9euqlmzph599FFNnDhRBw8e1KuvvuqsEQAAQDbKmzevKlWqdNVaQECAChUqdM36jTgtiHTo0EGnT59WWFiYjh07pkqVKmnhwoUqWbKks0YAAAAuJodhGIbVQwAAAO/Es2YAAIBlCCIAAMAyBBEAAGAZgggAALAMQQQAAFiGIAIAACxDEAEAAJYhiAAAAMsQRAAAgGUIIgAAwDIEEQAAYJn/AzZgV8JFiPQLAAAAAElFTkSuQmCC\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_9_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "xmin, xmax = 0, 4 # Suitable plotting region.\n", - "\n", - "plot45(g, xmin, xmax, 0, num_arrows=0)" - ] - }, - { - "cell_type": "markdown", - "id": "4018b5f1", - "metadata": {}, - "source": [ - "The plot shows the function $g$ and the 45 degree line.\n", - "\n", - "Think of $k_t$ as a value on the horizontal axis.\n", - "\n", - "To calculate $k_{t+1}$, we can use the graph of $g$ to see its\n", - "value on the vertical axis.\n", - "\n", - "Clearly,\n", - "\n", - "* If $g$ lies above the 45 degree line at this point, then we have $k_{t+1} > k_t$.\n", - "* If $g$ lies below the 45 degree line at this point, then we have $k_{t+1} < k_t$.\n", - "* If $g$ hits the 45 degree line at this point, then we have $k_{t+1} = k_t$, so $k_t$ is a steady state.\n", - "\n", - "For the Solow model, there are two steady states when $S = \\mathbb R_+ =\n", - "[0, \\infty)$.\n", - "\n", - "* the origin $k=0$\n", - "* the unique positive number such that $k = s z k^{\\alpha} + (1 - \\delta) k$.\n", - "\n", - "By using some algebra, we can show that in the second case, the steady state is\n", - "\n", - "$$\n", - "k^* = \\left( \\frac{sz}{\\delta} \\right)^{1/(1-\\alpha)}\n", - "$$\n", - "\n", - "### Trajectories\n", - "\n", - "By the preceding discussion, in regions where $g$ lies above the 45 degree line, we know that the trajectory is increasing.\n", - "\n", - "The next figure traces out a trajectory in such a region so we can see this more clearly.\n", - "\n", - "The initial condition is $k_0 = 0.25$." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "5bddd6ca", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAAAikAAAI1CAYAAAATh2r+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/NK7nSAAAACXBIWXMAAA9hAAAPYQGoP6dpAAB0GElEQVR4nO3deVhUZRsG8JsdQVZRVDAX0BR3RTNNy9RKzX3L1LTU/NIs09xlFUXQzMq0zCxz19yXLDW3NHdBRcQVZBNkHWQf5nx/nJgBVwbOzBng/l2XV2deZt73sQgfz3nPfYwEQRBAREREZGCM5S6AiIiI6GnYpBAREZFBYpNCREREBolNChERERkkNilERERkkNikEBERkUFik0JEREQGiU0KERERGSQ2KURERGSQ2KQQERGRQWKTQkRERAaJTQoREREZJDYpREREZJDYpBAREZFBYpNCREREBolNChERERkkNilERERkkNikEBERkUFik0JERFTBBAcHw8jICEZGRjhz5swTX/f19VV//fFflpaWMlT8dKZyF0BERETSCQ8Ph7e3N6ytrZGZmfnc944ePRr16tUrNmZqajitgeFUQkRERGVSUFCA0aNHo2XLlmjUqBHWr1//3PePGTMGb7zxhn6KKwVe7iEiomdSKpUIDAyEm5sbLC0t4e7ujsDAQNy9exdGRkYYM2aM3CVSEUFBQQgNDcWaNWtgYmIidzllxjMpRET0TB999BHWrVsHNzc3TJo0Cbm5uVi2bBn+/fdfuUujx1y7dg1+fn6YN28emjZtWqLPnDx5EufOnYOJiQkaN26M7t27w8LCQseVlhybFCKiUlq4EEhPl7uK57OzA+bMKd1njxw5gnXr1sHT0xMnTpxAlSpVAADz5s1D69atJaxSd3JzcxETEyN3Gc/l6upa5sZAqVRizJgxaNKkCWbNmlXiz3l7exd7XatWLaxduxY9evQoUz1SYZNCRFRK6elAWprcVehO4X4GLy8vdYMCADVr1sTnn3+O2bNny1VaicXExGDKlClyl/Fcy5Ytg5ubW5nmWLhwIUJDQ3H27FmYmZm98P2tWrXC2rVr8frrr8PZ2RkxMTHYvHkzFi5ciL59++LMmTNo2bJlmWqSApsUIqJSsrOTu4IXK0uNoaGhAICOHTs+8bWnjRkiV1dXLFu2TO4ynsvV1bVMnw8NDUVAQAC+/PJLtGnTpkSf6d+/f7HX7u7umDdvHpydnfHxxx8jICAA27ZtK1NdUmCTQkRUSqW9jFJeKBQKGBsbo1q1ak98zdnZWYaKtGdhYVHmsxSGbvTo0XBzc4Ovr68kc02cOBGnTp0qe2ESYJNCRERPZWtrC5VKheTkZDg5ORX7WkJCgkxV0eMKz3g9K4Tt1VdfBQDs3LnziTMojzM3N4eNjQ2ysrIkrbG02KQQEdFTtWzZEpcvX8bp06fRt2/fYl87ffq0TFXR48aOHfvU8RMnTuDWrVvo27cvqlev/kRo29PcunULqampBrEfBWCTQkREzzBixAj8+uuvmD9/Pt566y3139QfPHiAb775RubqqNDq1aufOj5mzBjcunULs2fPRocOHdTjGRkZuHfvHlq0aFHs/ampqeqGZ/jw4borWAtsUoiI6Km6d++OESNGYMOGDWjevDn69euH3NxcbN26Fa+88gr27t0LY2NmgpY3ycnJaNmyJTw9PdG8eXPUqFEDsbGx+OOPP5CcnIwePXrgiy++kLtMAGxSiIjoOX799Vc0btwYa9aswXfffQdXV1dMmTIF3bp1w969e2Frayt3iaQlR0dHTJo0CWfOnMHevXuRlpYGa2trNG/eHCNHjsS4ceMMJq3WSBAEQe4iiIiofFm9ejXGjx+PFStW4JNPPpG7HKqg2KQQEdEzPXjwAM7OzjAyMlKPxcbGolOnToiJicG9e/dQp04dGSukioyXe4iI6JkWLVqE/fv3o3PnzqhRowbu37+Pffv2ISMjA76+vmxQSKfYpBAR0TO98847uH79Ovbv34/U1FRYWlqiRYsWmDhxIt5//325y6MKjpd7iIiIyCDx3jEiIiIySGxSiIiIyCCxSSEiIiKDxCaFiIiIDBKbFCIiIjJIbFKIiIjIILFJISIiIoPEJoWIiIgMEpsUIiIiMkhsUoiIiMggsUkhIiIig8QmhYiIiAwSmxQiIiIySGxSiIiIyCCxSSEiIiKDxCaFiIiIDBKbFCIiIjJIbFKIiIjIILFJISIiIoPEJoWIiIgMEpsUIiIiMkhsUoiIiMggsUkhIiIig8QmhYiIiAySTpqUwMBAGBkZYcqUKbqYnoiIiCoByZuU8+fPY9WqVWjRooXUUxMREVElImmT8ujRI4wYMQI//fQTHBwcpJyaiIiIKhlJm5RJkyahd+/e6N69+wvfm5ubC4VCof6Vnp6Oh4qHEARBypKIiIionJKsSdm8eTMuXbqEwMDAEr0/MDAQdnZ26l/2zvao8XUNZORlSFUSERERyaSgoADffPMN+vTpU+o5JGlSoqOj8fnnn2P9+vWwtLQs0Wdmz56N9PR09a/o6GgpSiEiIiKZ5eXlITAwEEePHsW0adNKPY+RIMH1lV27dmHAgAEwMTFRjxUUFMDIyAjGxsbIzc0t9rWnUeQqYLfIDumz0mFrYVvWkoiIiEgGmZmZCAgIwM2bNzFnzhy0bdu21HOZSlFQt27dcPXq1WJjH374IRo3boyZM2e+sEEhIiKi8i81NRU+Pj5ITExEQEAAmjRpUqb5JGlSbGxs0KxZs2Jj1tbWqFat2hPjREREVPE8ePAA3t7eyM3NRVBQEOrWrVvmOZk4S0RERGUSGRmJGTNmwMjICIsXL5akQQEkOpPyNMeOHdPV1ERERGQgwsLCMH/+fNSsWRN+fn6ws7OTbG6dNSlERERUsZ07dw5BQUFo3Lgx5s6dCysrK0nnZ5NCREREWjty5Ai+/fZbdOjQAdOmTYO5ubnka7BJISIiIq3s3LkTa9aswdtvv42JEyfC2Fg3W1zZpBAREVGJCIKAtWvXYvv27Rg6dChGjhwJIyMjna3HJoWIiIheqKCgAN9//z0OHTqEcePGoV+/fjpfk00KERERPVdeXh4WL16M8+fPY+rUqejatate1mWTQkRERM9UNOZ+3rx58PT01NvabFKIiIjoqdLS0uDj44OEhARJYu61xSaFiIiInlA05n7RokWoV6+e3mtgLD4REREVUxhzDwCLFy+WpUEB2KQQERFREdevX8esWbPg4OCAxYsXo0aNGrLVwss9REREBAA4f/48Fi1ahJdffhnz5s2TPOZeW2xSiIiICH///Te++eYbvPLKK/jyyy91EnOvLTYpREREldyuXbvw888/46233sKkSZN0FnOvLTYpRERElZQgCPjtt9/w+++/Y8iQIRg1apROY+61xSaFiIioEpIj5l5bbFKIiIgqmcKY+3PnzuGLL77Am2++KXdJT8UmhYiIqBLJyspCQEAAIiIiMG/ePLRr107ukp6JTQoREVElUTTmfv78+fDw8JC7pOdik0JERFQJJCQkwMvLS9aYe20Zxj1GREREpDNFY+6Dg4PLRYMCsEkhIiKq0MLDwzFr1izY29sjODgYzs7OcpdUYrzcQ0REVEEVxtw3atQI8+bNg7W1tdwlaYVNChERUQV09OhRLFu2DO3bt8f06dMNIuZeW2xSiIiIKpjdu3dj9erV6NGjByZNmgQTExO5SyoVNilEREQVhCAIWLduHbZt24bBgwfjgw8+MKiYe22xSSEiIqoAVCoVVqxYgT///BMfffQRBgwYIHdJZcYmhYiIqJzLy8vDV199hTNnzmDKlCno1q2b3CVJgk0KERFROZaVlYUFCxbgxo0bmDt3Ltq3by93SZJhk0JERFROpaenw8fHBw8ePCgXMffaYpNCRERUDiUmJmLevHnIyckpNzH32mLiLBERUTkTFRWF6dOnAyhfMffaYpNCRERUjoSHh2PmzJmws7NDUFAQatasKXdJOsPLPUREROXEhQsXEBgYWG5j7rXFJoWIiKgcOHbsGJYtWwZPT0/MmDGjXMbca4tNChERkYHbs2cPfvrpJ3Tv3h2ffvppuY251xabFCIiIgMlCALWr1+PrVu3YtCgQRg9enS5jrnXFpsUIiIiA6RSqbBy5UocPHiwwsTca4tNChERkYHJz8/HkiVLKlzMvbbYpBARERmQ7OxsBAQE4MaNG5gzZw5eeeUVuUuSDZsUIiIiA5Geng5fX1/ExcXBz88PzZo1k7skWbFJISIiMgCJiYnw9vZGZmYmFi1ahPr168tdkuyYOEtERCSz+/fvY/r06SgoKEBwcDAblP+wSSEiIpLRjRs31DH3wcHBqFWrltwlGQw2KURERDK5ePEi5s2bh7p16yIwMBAODg5yl2RQuCeFiIhIBpUx5l5bbFKIiIj0bO/evVi1ahW6deuGyZMnV5qYe22xSSEiItITQRCwYcMGbNmyBQMGDMCHH35YqWLutcUmhYiISA+Kxtx/+OGHGDhwoNwlGTw2KURERDqWn5+Pr776CqdPn8bnn3+O7t27y11SucAmhYiISIeys7OxYMECXL9+HXPnzq3UMffaYpNCRESkI+np6fDz80NsbCz8/f0rfcy9ttikEBER6UDRmPvAwEA0aNBA7pLKHTYpREREErt//z68vb1hamrKFNkyYOIsERGRhCIiIjBz5kzY2NiwQSkjNilEREQSuXjxIubOnYuXXnoJixYtgqOjo9wllWu83ENERCSBEydOYOnSpWjTpg1mzpwJCwsLuUsq99ikEBERldG+ffuwatUqvPnmm/j0009haso/XqXAf4tERESlJAgCNm7ciM2bNzPmXgfYpBAREZWCSqXCjz/+iAMHDmDMmDEYNGiQ3CVVOGxSiIiItJSfn4+lS5fi1KlT+Oyzz9CjRw+5S6qQ2KQQERFpITs7GwsXLkRYWBjmzJmDDh06yF1ShcUmhYiIqIQUCgV8fX0RExMDPz8/NG/eXO6SKjQ2KURERCXw8OFDeHl54dGjR1i0aBFj7vWATQoREdELREdHw9vbG8bGxggODkbt2rXlLqlSYOIsERHRcxTG3FetWhWLFy9mg6JHbFKIiIie4dKlS5g7dy5cXV0RGBjImHs94+UeIiKipzhx4gS+/vprtG7dmjH3MmGTQkRE9Jj9+/fjxx9/RNeuXTF58mTG3MuE/9aJiIj+IwgCNm3ahE2bNqF///746KOPGHMvIzYpREREKB5zP3r0aAwaNIgNisy4cZaIiCo9pVKJJUuW4I8//sDkyZMxePBgNigSUCiANWtK/3meSSEiokotJycHCxYsQFhYGGbPno1XX31V7pLKPZUKOHEC2LULyM4GPvqodPOwSSEiokpLoVDAz88P0dHRjLmXSFQUsGGD+M+yYpNCRESV0sOHD+Ht7Y2MjAwEBgbCzc1N7pLKtexsYPdu4NgxQBA04x07ln5ONilERFTpMOZeOoIAXLgAbN0q7kEpVKsWMGIE0LBh6edmk0JERJXKzZs34evrC0dHR/j7+zNFtgwSE4GNG4HwcM2YmRnQpw/QrRtQ1ngZNilERFRphISEYMGCBahfvz68vb1RtWpVuUsql/LzgYMHxV9KpWa8ZUtg2DCgWjVp1mGTQkRElcI///yDr776Cq1atcKsWbMYc19K168DmzaJZ1EKOToC770nNilSYpNCREQV3oEDB/DDDz/gjTfewGeffcaY+1JISwO2bRP3nxQyNgZ69AB69wZ00fPxvxIREVVYgiBg8+bN2LhxI/r164exY8cypE1LKhVw9CiwZw+Qk6MZb9gQeP99QJd7jtmkEBFRhSQIAn788Ufs378fH3zwAVNkS+HePTHzJDpaM1a1KjBoEPDqq4Cu/3WySSEiogpHqVRi6dKl+Oeff/Dpp5/i7bfflrukciUrC9i5Ezh5snjmyWuvAQMHAtbW+qmDTQoREVUoOTk5WLhwIa5evYpZs2ahY1nSxCoZQQDOngV+/x3IyNCMu7qKl3b0nXfHJoWIiCqMjIwM+Pn5ISoqCn5+fmjRooXcJZUb8fFi5snNm5oxCwugb1/gzTfFTbL6xiaFiIgqhKSkJHh7e0OhUCAwMBDu7u5yl1Qu5OUBBw4Af/0FFBRoxtu0AYYOBRwc5KuNTQoREZV7MTEx8PLygrGxMYKCguDi4iJ3SeXC1ati5klysmbMyQkYPhxo1ky+ugqxSSEionLt1q1b8PHxgYODA/z9/VFNqrjTCiw1FdiyBbh8WTNmYgK8/TbQsydgbi5fbUWxSSEionKraMy9l5cXbGxs5C7JoKlUwN9/i5knubma8ZdfFjfG1qwpX21PwyaFiIjKpcKY+5YtW2L27NmMuX+Be/eA9euBmBjNmI0NMGQI0L697jNPSoNNChERlTuFMfevv/46Pv/8c8bcP0dWFrBrF3DihCbzxMgI6NwZGDAAsLKStbzn4n9VIiIqNwRBwJYtW7Bhwwb07dsX48aNY4rsMwgCcP48sHXrk5knI0YADRrIV1tJsUkhIqJyQRAErFq1Cvv27cOoUaMwZMgQNijPkJAgZp7cuKEZkzvzpDTYpBARkcFTKpX4+uuvcfLkSUyaNAnvvPOO3CUZpPx84OBB8ZdSqRlv3RoYNkzezJPSYJNCREQGLScnB4GBgbhy5QpmzpyJTp06yV2SQQoPF8+eJCZqxqpVA957DyivwbtsUoiIyGAVjbn39fVFy5Yt5S7J4CgUwLZtwLlzmjFjY6BHD6B3b/EyT3nFJoWIiAxSYcx9eno6Fi5ciIYNG8pdkkFRqcSnFO/cCWRna8bd3ICRI4HateWrTSpsUoiIyODExsbCy8sLABAcHMyY+8dER4uZJ5GRmjFra2DQIKBjR8PMPCkNNilERGRQbt26BV9fX9jZ2WH+/PmMuS8iJ0dMi/37b03mCSA2JgMHiuFsFQmbFCIiMhiFMfd169aFj48PY+7/Iwjic3a2bAHS0jTjtWqJcfaNGslWmk6xSSEiIoNw6tQpLFmyBC1btsSsWbNgaWkpd0kGISlJfFLxtWuaMTMzcVNsjx5ARQ7brcC/NSIiKi8OHjyIFStWoHPnzvjiiy8Ycw8x5+TwYWDfPjH/pFCzZsDw4YCTk3y16Qu/C4iISDaCIGDr1q1Yv349+vTpg/HjxzNFFsCtW8CGDUB8vGbM3l4MZGvduuJsjH0RNilERCQLQRDw008/Ye/evRg5ciSGDh1a6RuUR4+A7duB06c1Y0ZGYpR9375AZbsCxiaFiIj0TqlUYtmyZThx4gQmTpyInj17yl2SrAQB+Pdf4PffgcxMzXjdumLmyUsvyVebnNikEBGRXuXk5GDRokUIDQ3FjBkz8Nprr8ldkqzi4sQ4+1u3NGOWlsCAAUCXLuXnYYC6wCaFiIj0JiMjA/7+/oiMjISPjw9atWold0myycsD9u8H/vpLTI8t1K4dMGQIYGcnX22Ggk0KERHpRXJyMry9vZGWllbpY+6vXhVvK05O1oxVry5mnnh4yFeXoWGTQkREOlcYcy8IAoKCguDq6ip3SbJITRUD2S5f1oyZmgLvvCP+MjOTrzZDxCaFiIh06vbt2/Dx8YGdnR38/f3hVBkCPh6jUgFHjwK7dwO5uZrxxo3FsyfOzvLVZsjYpBARkc5cuXIF8+fPr9Qx95GR4sMAo6M1YzY24r6T9u0rT+ZJabBJISIinSiMuW/RogVmz55d6WLus7KAXbuAEyc0DwM0MgI6dxbv3LGykrW8coFNChERSa4yx9wLAnD+PLBtG6BQaMZdXYERI4AGDeSrrbypPN81RESkc4IgYNu2bVi3bh3effddfPzxx5UqRTYxUcw8CQ/XjFlYiGmxb75ZuTNPSoNNChERSUIQBKxevRp79uzBiBEjMGzYsErToOTnA3/+Cfzxh/hgwEKtW4vP23FwkK+28oxNChERlZlSqcS3336LY8eO4ZNPPkGvXr3kLklvwsPFsyeJiZoxR0fxScUtWshXV0XAJoWIiMokNzcXixYtQkhISKWKuVcoxH0n585pxoyNgR49gN69xcs8VDZsUoiIqNQyMjIwf/583Lt3r9LE3AuCeMfOzp1AdrZm3M1N3Bjr4iJfbRUNmxQiIiqV5ORk+Pj4ICUlpdLE3MfEiJkn9+5pxqytgUGDgI4dmXkiNTYpRESktdjYWHh7e0OlUiE4OLjCx9zn5gJ79wJHjhR/GGDHjsDAgWI4G0mPTQoREWnl9u3b8PX1ha2tbaWIub9yRXwYYEqKZqxmTfHSTqNG8tVVGbBJISKiErty5QoCAgJQp04d+Pr6VuiY+7Q0YPPmJx8G2Ls38NZb4jHpFv8VExFRiZw+fRqLFy9G8+bNMWfOnAobc69SAceOiQ8DzMnRjDdpIj4MsEYN2UqrdNikEBHRC/3555/4/vvv8dprr2Hq1KkVNub+/n1xY2xUlGbMxgYYOhRo144bY/WtYn6XERGRJARBwO+//47ffvsNvXr1woQJE2BcAbPdc3KAPXuAv//WPAwQEB8GOHAgHwYoFzYpRET0VIIg4Oeff8bu3bvx/vvv47333quQMfchIeLek9RUzVjt2sDIkWL2CcmHTQoRET2hMsTcp6SIzUloqGbMzAx4912ge3dujDUE/E9ARETF5ObmIigoCJcvX8b06dPRuXNnuUuSlEolXtbZs0fMPynUtKm4MbaC31FdrrBJISIitUePHsHf3x/37t2Dt7c3WrduLXdJkoqMFDfGRkdrxmxtxScVt23LjbGGhk0KEREBAFJSUuDt7Y2UlBQEBATg5ZdflrskyWRni7cUHzum2RhrZAR06QL078+NsYaKTQoRESEuLg5eXl5QqVQICgpCnTp15C5JEoIghrFt3gykp2vGXV3FxNgGDeSrjV6MTQoRUSV39+5deHt7o2rVqpg/fz6qV68ud0mSSE4W4+yvXtWMmZsDffoA3boBJiby1UYlwyaFiKgSu3r1KubPnw9XV1f183jKu4IC8UGAe/cCeXma8ebNgeHDgWrV5KuNtMMmhYiokvr3338RHByMZs2aYe7cuRUi5v7uXXFjbGysZszeXtwY27o1N8aWN2xSiIgqob/++gvLly9Hp06dMHXqVJiZmcldUplkZQE7dwInTxbfGPvGG+LG2ArQf1VKbFKIiCoRQRCwfft2rF27tkLE3AsCcOECsHUroFBoxuvUERNj69WTrTSSAJsUIqJKQhAErFmzBrt27cLw4cMxfPjwch1zn5QEbNwIhIVpxiwsgL59gTffBMpx70X/YZNCRFQJKJVKfPfddzh69CgmTJiAd999V+6SSk2pBA4dAvbvB/LzNeMtWwLvvQc4OspXG0mLTQoRUQVXGHN/6dIlfPnll+jSpYvcJZXa7dvAhg1AXJxmzMFBbE5atZKtLNIRNilERBVYZmYm/P39cefOHXh7e6NNmzZyl1QqmZnAjh3AP/9oxoyMxLyTPn24MbaiYpNCRFRBpaSkwMfHB8nJyViwYEG5jLkXBODcOWDbNiAjQzNet664Mfall+SrjXSPTQoRUQUUHx+PefPmleuY+8RE8dLOjRuaMUtL8Zbi11/nxtjKgE0KEVEFU95j7pVK4M8/gQMHxONCbdqIoWz29rKVRnrGJoWIqAK5du0a5s+fDxcXF/j4+MDOzk7ukrRy86Z49uTBA82Yo6MYZ9+ihXx1kTzYpBARVRBnzpxBcHAwPDw8MHfuXFSpUkXukkrs0SNg+3bg9GnNmLEx0L078O67Yv4JVT5sUoiIKoBDhw7hu+++Q8eOHTFt2rRyE3MvCMCZM+LG2MxMzXj9+uLGWFdX+Woj+bFJISIq57Zv345ff/0VPXv2xP/+979yE3OfkCA+DPDmTc2YpSUwYADQpQs3xhKbFCKicksQBPzyyy/YuXMn3nvvPbz//vvlIuZeqQQOHgT++KP4xlhPT2DoUKCcbaMhHWKTQkRUDimVSixfvhxHjhzBxx9/jD59+shdUoncuiWePSm6MbZaNeD994FmzeSriwwTmxQionImLy8PixYtwqVLlzB9+vRyEXOfmSlujD11SjNmbAz06CFujDU3l682MlxsUoiIypGiMfdeXl5o27at3CU9lyAA588DW7cWT4ytVw8YNYobY+n52KQQEZUThTH3SUlJCAgIQOPGjeUu6bmSkoCNG4GwMM0YE2NJG2xSiIjKgfj4eHh7eyM/Px9BQUF4yYAfWlNQABw+DOzdC+Tna8ZbtxYTYx0c5KuNyhc2KUREBu7u3bvw8fGBtbU1FixYgBo1ashd0jNFRgLr1gExMZoxe3txY2zLlnJVReUVmxQiIgNWGHNfu3Zt+Pr6GmzMfU4OsGsXcOyYuA8FAIyMgK5dgX79xMs8RNpik0JEZKDOnj2LoKAgg4+5v3wZ2LwZSEvTjLm6ihtj69WTqyqqCNikEBEZoMOHD+Pbb7816Jj71FRg0yYgNFQzZm4O9OkjPnOHG2OprNikEBEZmB07duCXX37BO++8g08++cTgYu5VKvGyzq5dQG6uZrxZM3HvSbVqclVGFQ2bFCIiA1E05n7YsGEYMWKEwcXcR0eLibGRkZoxW1vxrp22bcV9KERSYZNCRGQACgoK8N133xlszH1uLrBvn3hrsUqlGe/cGRg4ELCykq82qrjYpBARySwvLw/BwcG4cOECpk2bhjfeeEPukoq5dk0MZUtO1ozVqgWMHAm4u8tXF1V8bFKIiGSUmZmJgIAA3Lx50+Bi7hUKYMsW4MIFzZipKdCrF/D22+IxkS7xW4yISCapqanw8fHBw4cPsWDBAoOJuRcE4J9/gB07gKwszfjLLwMjRgDOzvLVRpULmxQiIhkUxtzn5eUZVMx9fLy4Mfb2bc2YtTUweDDw6qvcGEv6xSaFiEjP7t27B29vb1hZWWHx4sUGEXOfnw8cOAD8+af47J1CHTqIDYqNjXy1UeXFJoWISI/CwsIwf/581KxZE35+fgYRcx8RIZ49SUzUjFWvLl7aadJEvrqI2KQQEenJuXPnEBQUhMaNG2Pu3Lmwkvm+3cxM4PffgdOnNWPGxuKm2N69AQMMuaVKhk0KEZEeHDlyBN9++y06dOiAadOmwdzcXLZaBAE4exbYtg149Egz7uYm3lZcu7ZspREVwyaFiEjHdu7ciTVr1uDtt9/GxIkTZY25T0wUM0/CwzVjVaqIgWydO3NjLBkWNilERDoiCALWrl2L7du3Y+jQoRg5cqRsMfdKJXDoELB/v7hJtlDbtmKkvQFsjSF6ApsUIiIdKCgowPLly3H48GGMGzcO/fr1k62WO3fEjbFxcZoxR0fxYYDNm8tWFtELsUkhIpJY0Zj7qVOnomvXrrLUkZUF7NwJnDwp7kMBxMs53boBffsCFhaylEVUYmxSiIgkVDTmft68efD09NR7DYIAXL4MbN4MpKdrxuvWFTfGGkhuHNELsUkhIpJIWloafHx8kJCQgICAADSRIWQkNRXYtAkIDdWMWViIZ07efFO8xZiovGCTQkQkgQcPHsDb2xu5ublYtGgR6tWrp9f1BQE4fly8vJOToxlv3lzce+LoqNdyiCTBJoWIqIwiIyPh7e0NS0tLWWLu4+KAdeuAu3c1Y7a24l07bdvytmIqv9ikEBGVwfXr1+Hv7w9nZ2f4+/vrNeY+Px/44w/g4MHiz9t57TVg0CBA5kBbojJjk0JEVEpyxtzfuiWePUlI0Iw5O4sbYxs10lsZRDrFJoWIqBTkirnPygJ27BBvKy5kbAy88w7Qqxeft0MVC5sUIiItFcbcv/XWW5g0aZJeYu4FAbh0SbytWKHQjDdoAIwaxeftUMXEJoWIqIQEQcBvv/2G33//HUOGDMGoUaP0EnOfmio+b+fKFc2YhQUwYADw+uu8rZgqLjYpREQlUFBQgO+//x6HDh3SW8y9SqW5rTg3VzPesiUwfDjg4KDzEohkxSaFiOgF8vLysHjxYpw7dw5ffPEF3nzzTZ2vGRsrPm/n8duKhw8HWrfmbcVUObBJISJ6jqysLAQEBCAiIgLz5s1Du3btdLpefj5w4IB4W7FKpRnv3BkYOJC3FVPlwiaFiOgZisbcz58/Hx4eHjpd7+ZN8ezJ47cVjxoFNGyo06WJDBKbFCKip0hISICXl5deYu6zsoDffwdOndKMmZgAPXuKtxbztmKqrNikEBE9JjIyEj4+PrCwsEBwcDCcnZ11so4gABcvAlu28LZioqdhk0JEVETRmHs/Pz/Y29vrZJ2UFPFpxUVvK7a01NxWzI2xRGxSiIjUzp8/j0WLFqFRo0aYN28erK2tJV9DpQKOHQN27eJtxUQvwiaFiAjA0aNHsWzZMrRv3x7Tp0/XScx9bCzw229AZKRmzM5Oc1sxERXHJoWIKr3du3dj9erV6NGjByZNmgQTExNJ58/PB/bvB/78s/htxV26iJd3eFsx0dOxSSGiSksQBKxbtw7btm3D4MGD8cEHH0gecx8RId5WnJioGatZU9wY6+4u6VJEFQ6bFCKqlAoKCrBixQr89ddf+OijjzBgwABJ58/MFG8rPn1aM1Z4W3HPnoApf/oSvRD/NyGiSicvLw9LlizB2bNnJY+5FwTgwgXxtuKMDM24m5t49qRWLcmWIqrw2KQQUaWSlZWFBQsW4MaNG5g7dy7at28v2dzJyeLTiq9d04xZWgKDBomx9rytmEg7bFKIqNJIT0+Hj48PHjx4IGnMvUoFHD0K7N5d/Lbi1q2B994DdBS1QlThsUkhokohMTER8+bNQ05OjqQx9zExwLp1xW8rtrcXmxPeVkxUNmxSiKjCi4qKgre3tzrmvmbNmmWe81lPK379dfG24ipVyrwEUaXHJoWIKrTw8HD4+fmhRo0a8PPzg4MEka63bolnT4o+rbhWLXFjrJtbmacnov+wSSGiCuvChQsIDAyULOY+JwfYsQM4flwzxtuKiXSH/0sRUYVUGHPfrl07zJgxo8wx91euABs2AGlpmrH69YEPPuDTiol0hU0KEVU4UsbcKxRi5smFC5oxCwugf3/gjTcAY+Myl0tEz8AmhYgqDEEQsH79emzduhWDBg3C6NGjSx1zLwjAmTPA1q1AVpZmvGlTYMQIoFo1iYomomdik0JEFYJKpcLKlStx8ODBMsfcJyWJz9sJD9eMWVsDw4YB7dszlI1IX9ikEFG5l5+fjyVLluDMmTOYMmUKunXrVqp5VCrg77/FULa8PM14u3Zig2JjI1HBRFQibFKIqFzLzs5GQEAAbty4gTlz5uCVV14p1TxPC2VzcBAv7TRvLk2tRKQdNilEVG6lp6fD19cXcXFx8PPzQ7NmzbSe42mhbEZG4qbY/v3FZ+8QkTzYpBBRuZSYmAgvLy9kZWVh0aJFqF+/vtZz3L4tnj158EAzxlA2IsPBJoWIyp3CmHtzc3MsXrxY65j7nBxg507g2DHNGEPZiAwP/1ckonIlPDwc/v7+qF69eqli7q9cATZuBFJTNWMMZSMyTGxSiKjcuHjxIhYuXIiGDRvCy8tLq5j7jAxg8+bioWzm5uK+k65dGcpGZIjYpBBRuXDs2DEsW7YMnp6eWsXcF4aybdsGZGZqxj08gJEjGcpGZMjYpBCRwdu7dy9WrVqFbt26YfLkySWOuU9KEp+3c/26ZszaGhg6FHjlFYayERk6NilEZLAEQcCGDRuwZcsWDBgwAB9++GGJYu4ZykZUMbBJISKDVDTm/sMPP8TAgQNL9LnYWOC33xjKRlQRsEkhIoOTn5+Pr776CqdPn8bnn3+O7t27v/AzSiWwf/+ToWyvvw4MGMBQNqLyiE0KERmUwpj78PBwzJ07t0Qx93fuiGdPioay1awp3lbMUDai8otNChEZjKIx9/7+/i+MuX9aKJuxsRjI1qsXQ9mIyjv+L0xEBiExMRHe3t7IzMxEYGAgGjRo8Nz3h4WJkfZFQ9nq1RPPnri46LZWItIPNilEJLv79+/D29sbpqamCA4ORq1atZ753sxMYOtWMfukEEPZiComNilEJKuIiAj4+vrCyckJfn5+cHR0fOZ7L10SI+0zMjRjTZqIoWxOTnooloj0ik0KEcnm4sWLCAwMhJubG7y9vZ8Zc5+eDmzaBFy+rBmrUgUYMgTo2JGhbEQVFZsUIpLF8ePH8fXXX6Nt27aYOXPmU2PuBQH4918x0j4rSzPesiXw/vuAvb3+6iUi/WOTQkR6V5KY++RkYP364pH2NjbAe+8Bbdvy7AlRZcAmhYj0RhAEbNy4EZs3b35mzL0giLcU79wJ5OZqxl95RXzmTtWq+q2ZiOTDJoWI9EKlUuGHH37AH3/8gTFjxmDQoEFPvCchAVi7VgxnK8RIe6LKi00KEelcfn4+li5dilOnTuGzzz5Djx49in1dpQL++gvYu1eMty/UpQswaBAj7YkqKzYpRKRT2dnZWLhwIcLCwjBnzhx06NCh2Nejo8VI+/v3NWPVq4uhbI0a6blYIjIobFKISGfS09Ph5+eHmJgY+Pn5oXmRazb5+cCBA08+ELB7d6BvXzGgjYgqNzYpRKQTDx8+hJeXFx49eoRFixYVi7m/e1fce1L0gYC1awOjR4vR9kREAJsUItKB6OhoeHl5wdTUFIsXL1bH3OfmArt3A3//Ld7FAwAmJuIDAXv25AMBiag4/kggIklFRETAz88P1apVKxZzHx4uPhAwOVnzXj4QkIieh00KEUnm0qVLWLhwIRo0aABvb29UrVoVWVnA778Dp05p3mdmJu476d6dDwQkomdjk0JEkjhx4gS+/vprtG7dGjNnzoSFhQVCQ4ENG8Rn7xRq1AgYNQqoUUO+WomofGCTQkRltn//fvz444/o2rUrJk+ejOxsU/z2G3DhguY9lpZi5knnzoy0J6KSYZNCRKUmCAI2bdqETZs2oX///vjww49w/rwRtmwBMjM172vWDBg5UkyPJSIqKTYpRFQqKpUKP/74Iw4cOIDRo0fjzTcHYcUKI1y9qnmPtTUwbBjQvj3PnhCR9tikEJHWisbcf/rpZFhZvQU/PyAnR/MeT0/xicU2NvLVSUTlG5sUItJKTk4OFixYgLCwMHzyyWxcv/4qbtzQfN3ODnj/faBVK9lKJKIKgk0KEZWYQqGAr68vYmJi0Lu3H/74ozlyczVf79gRGDIEsLKSr0YiqjjYpBBRiTx8+BDe3t54+DAD7u6BOHfOTf01BwfxtuKmTWUskIgqHDYpRPRCYsy9NxISjFGzZjBSU2urv9ali3hrsaWljAUSUYXEJoWInuvmzZuYNcsXDx44omFDf5ibizH31aqJkfaNG8tcIBFVWGxSiOiZLl68jClTFuLRo/po3dobZmZVAQBduwIDBgAWFjIXSEQVGpsUInqqnTtPYt68pahSpRXatp0FExML1Kghnj1p2FDu6oioMmCTQkTFFBQAAQEH8MsvP6BWrTfQrNlnMDExRbduQL9+gLm53BUSUWXBJoWI1KKjBUydugnnzm1CvXr98PLLY1GrlhFGjwYaNJC7OiKqbNikEBGUSuDAAQFLlvyIqKj9aNToAzRoMBhvv22EPn0AMzO5KySiyohNClElFxUFrFmjxMGDS/HgwT9o2vRTvPLK2xg9GqhXT+7qiKgyY5NCVEnl5wP79wP79+fg0qWFSEm5ijZtZmHMmI7o3Rsw5U8HIpIZfwwRVUL37gFr1wJRUQpcvOiHR4/uo1cvP8ya1QJ16shdHRGRiE0KUSWSnw/s3g0cPgxkZyfh/HkvKJUZmD07EB995A4TE7krJCLSYJNCVEncvi2ePUlMBB49isGFC16wsTHGDz8EwdPTRe7yiIiewCaFqILLzQV27QKOHgUEAUhLu4nLl33x8ssOWLPGH9WrV5O7RCKip2KTQlSB3bwpnj1JShJfJyWF4NatBejevT6CgrxgY2Mjb4FERM/BJoWoAsrNBXbsAI4d04w9fPgPEhK+woABLTFnzmxY8ME7RGTg2KQQVTAREeLZk+RkzVh+/gFkZv6AgQNfx+effw5T3l9MROUAf1IRVRBPO3tiZibA3n4LQkM3YPDgvhg3bhyMjIxkq5GISBtsUogqgMf3ngCAu7sAI6NVOH58H0aNGoUhQ4awQSGicoVNClE5Vnjnzt9/a8bMzIB+/ZS4fPlrnDx5EpMmTcI777wjW41ERKXFJoWonLp1Szx78vChZszdHRg2LAc//xyIK1euYObMmejUqZN8RRIRlQGbFKJyJi9Pc/ZEEMQxMzNgwADA0zMD8+f7ISoqCn5+fmjRooWstRIRlQWbFKJy5M4d4NdfxdTYQm5uwOjRgIlJEmbP9kZ6ejoWLlyIhg0bylYnEZEU2KQQlQP5+eLZkyNHip896d8fePNNID4+FrNnewEAgoOD4eLCmHsiKv/YpBAZuLt3xbMnCQmasQYNgDFjAGdn4NatW/D19YWdnR3mz5+PatUYc09EFQObFCIDlZ8P7NkDHDqkOXtiagr06wd07w4YGwMhISFYsGAB6tatCx8fH8bcE1GFwiaFyADduyeePXnwQDNWr5549qRWLfH1P//8g6+++gotW7bErFmzYGlpKUOlRES6wyaFyIAolcDevcCffxY/e9K3L9Cjh3j2BAD++OMPrFy5El26dMGUKVMYc09EFRJ/shEZiMhI8exJfLxmrG5d8exJ7dria0EQsGXLFmzYsAF9+vTB+PHjmSJLRBUWmxQimSmVwL594tkTlUocMzEB+vQB3n5bc/ZEEAT89NNP2Lt3L0aOHImhQ4eyQSGiCo1NCpGMoqLEsydxcZqxl14Sz54UvYtYqVRi2bJlOHHiBCZOnIiePXvqu1QiIr1jk0IkA6US2L8fOHiw+NmTd98Vz56YmGjem5OTg0WLFiE0NBQzZszAa6+9Jk/RRER6xiaFSM+io8WzJzExmrE6dcSzJ66uxd+bkZEBPz8x5t7HxwetWrXSY6VERPJik0KkJyoV8Mcf4v6TwrMnxsZA795Az57Fz54AQFJSEry9GXNPRJUXmxQiPYiPF8+eREZqxlxdxbMndeo8+f7Y2Fh4eXlBEAQEBQXB9fFTLERElQCbFCIdEgTxeTs7d4r7UADAyEg8c9K7t5iB8riiMff+/v5wcnLSb9FERAaCTQqRjiQliWdPbt3SjDk7Ax9+CNSv//TPhIaGIiAggDH3RERgk0IkOUEATp4Efv8dyM3VjHfrBgwYID69+GlOnTqFJUuWoEWLFpg9ezZj7omo0mOTQiShtDTgt9+AsDDNWLVq4t6TRo2e/bmDBw9ixYoV6Ny5M7744gvG3BMRgU0KkSQEATh3Dti8GcjK0ox37gwMHgw866SIIAjYtm0b1q1bh3fffRcff/wxU2SJiP7DJoWojDIygA0bgMuXNWN2dsAHHwDNmj37c4IgYPXq1dizZw9GjBiBYcOGsUEhIiqCTQpRGYSEAOvXi41KoVdeAYYNA6ytn/05pVKJb775BsePH8cnn3yCXr166bxWIqLyhk0KUSlkZQFbtgBnzmjGqlYFRowA2rR5/mcZc09EVDJsUoi0dP06sHatuEm2UMuWwMiRgK3t8z+bkZEBf39/REZGMuaeiOgF2KQQlVBurnhb8YkTmrEqVYD33hMv8bxoO0lycjK8vb2RmprKmHsiohJgk0JUArduicFsSUmasSZNgNGjAQeHF38+NjYW3t7eUKlUCA4OZsw9EVEJsEkheo78fGD3buDwYfE2YwAwNxdvK+7S5cVnTwDg9u3b8PX1ha2tLWPuiYi0wCaF6BmiooBffhEfDljI3V0MZqtevWRzXLlyBQEBAahTpw58fX0Zc09EpAU2KUSPKSgADhwQf6lU4pipKdC/vxhtb2xcsnlOnz6NxYsXo3nz5pgzZw5j7omItMQmhaiIhARgzRogMlIzVreuePakdu2Sz/Pnn3/i+++/x2uvvYapU6cy5p6IqBRK9ZNz2rRpuHnzJvbu3St1PUSyEATg+HHx7p38fHHM2Bjo1Uv8ZWJS0nk0Mfe9e/fGxx9/DOOSnnohIqJiStWkhISEoGPHjlLXQiSLpz0U0NkZGDEiF//8sx5bt1rB3d0dbm5ucHR0fOY8giDg559/xu7du/H+++/jvffeY8w9EVEZlKpJCQ0NxaRJk6SuhUjvLlwQn7tT9KGAXbsCAwcCkZFR2Lx5MzIzM2Fubg5bW1vUqVMHLVq0QMOGDeHm5oY6derA2NgYSqUS3377LY4dO8aYeyIiiWjdpERHRyM5OVmdlJmWloZRo0YhOTkZ27dvR61atUo0T25uLnJzc9WvFbkKbUshKrWsLPGJxbt3P8Dt27cBCDA3z8HLL5/BiRPxOHECKCgoAAC4u7vDxMQECoUCN2/eRGhoKIyMjFC1alVUq1YNHh4euHfvHpKSkjB9+nR07txZ3t8cEVEFoXWTEhISAjs7O9SvXx9Xr17FwIED0bVrV2zfvh3m5uYlnicwMBB+fn6aAQsAs7Wthkh7N26IwWxxcdk4deofWFpa4qWXHqJ+/X9hZpZX7KyKUqkEAJibm6NatWqoWrUqFAoF0tLSkJCQAIVCgVOnTiE2Nhb29vbYsGGDPL8pIqIKyEgQCiOqSmb+/Pk4fPgwJkyYgEmTJmHRokWYMGGC+uumpqZo9t/z6T09PbF69eqnzvO0Myl1VtRB+qx02Fq84AEoRKWQnw/s3AkcOSK+jo+Px8WL/6B//ywsXz76iWC2mzdvYtKkSTAyMkJOTg5UKhUsLCxga2uLhg0bom7duvj7778hCAIWLlyIxo0b6/83RURUgZXqTMrVq1fx6aefYv/+/U9soLW3t0dISMgL57GwsICFhYVmIPfZ7yUqq/v3xVuLiwazmZvfhZ3dMiQluSIv773i348AbG1tUbNmTRQUFKB58+Zo0qQJGjRoADc3N6Snp8PLy0udIlunTh09/46IiCq+UjUpgwYNwoYNG5BW9DGwRAZIpQIOHgT27tUEs5mZAf36qbBx48+oXt0UycnJuHXrlvoMYKGaNWtixYoVqFKlSrGckzt37sDHxwc2Njbw9/dH9ZLGzxIRkVa0CnDIyMjAvXv3MHHiRKxYsQLDhw9HWNH7NgEoFAq0bdsWr732Go4fPy5psUTaSEwEFi8Wn71T2KC89BIwdy7g5haJ+Pg41K5dGzk5Obh+/fpT57CxsSnWoFy5cgWzZ8+Gs7MzgoKCUL16deTk5GDIkCEYMmQIcnJy9PFbIyKqFLQ6kxISEgITExN4eHigdevWCAsLQ58+fXDu3Dn1Q9MiIyNRu3ZtXLt2Db1798bVq1dha8s9JqQ/ggCcPAls2wbk5YljRkZAz55A795ixP2+fdfx6NEjvPTSSzAzM8OFCxcwdOjQ587777//Ijg4GM2aNcPcuXPVMfcFBQX4/fffAQC//vqrLn9rRESVilZNSmhoKBo3bqy+dh8UFITw8HAMHDgQhw8fhrm5OWr/lx3erFkzeHh44ObNm/D09JS+cqKnUCiAtWuBa9c0YzVqAB9+CDRooBkLCQmBsbExjIyM4ODggIiICKSmpsLBweGp8/71119Yvnw5OnXqhKlTp8LMzEz9NXNzcyxfvlx9TERE0tD67p7nSU1NhZWVFSwsLBATE4NOnTrh8uXLz03pLKTIVcBukR3v7qFSu3wZWLcOyMzUjHXpAgweDBTdE5uTk4NRo0YhNzcXtWrVQn5+Pu7cuYPAwMAnNoILgoDt27dj7dq16NWrFyZMmMCYeyIiPZH0qWfh4eHqH+JGRkb45ptvStSgEJVFTg6wZQtw+rRmzNYW+OADoHnzJ98fERGB5ORk2NjYICUlBcbGxsjOzsa1a9eKNSmCIGDNmjXYtWsXhg8fjuHDhzPmnohIjyRtUjp27IirV69KOSXRc929C/z8M5CUpBlr3RoYORKoWvXZn7Ozs0N+fj4UCgXMzMxQo0YNdXAbgGIx9xMmTMC77777zLlUKhXu3LkDAHBzc+OZFiIiiUh6uacseLmHtKFSAfv3AwcOaO7csbQE3nsP6NABTwSzPS4pKQkZGRnw9fWFm5sb/ve//8HBwQFmZmbIzc1FUFAQLl26hKlTp6JLly7PnSszMxNV/+uIHj16BGtrayl+i0RElZ6kZ1KI9OHhQzGY7e5dzZibG/DRR8B/N5m9kJOTk3oDuI2NDWrUqAFAbDL8/f1x9+5deHt7o02bNiWaz87OTqvfAxERvVipmhRPT09ER0cjISFB6nqInkkQgH//FR8MWPhEBWNj4N13xduLy3qVJSUlBT4+PkhOTsaCBQvw8ssvl+hz1tbWDDYkItKBUjUpd+/eRdOmTaWuheiZMjOB9euBS5c0Y9WrA2PHAvXrP/n+qKgo5Obmol69eiW6LTg+Ph7z5s2DSqVCUFAQY+6JiAxAqZqUtLQ0vPrqq1LXQvRU4eHiU4uLnqzo1AkYOlTch/K4zMxMzJgxA6mpqbC3t4eHhwc8PDzg7u6OBg0awN7evtj7k5OTMX36dFStWhXz589nzD0RkYHQukk5e/YsBEFAr169AIh/Y23fvj2ysrJw8uRJtGrVSuoaqZJSKsWnFu/a9QgFBeKdN1WqCOjXTwEPj1zcv//0zz169AjZ2dkwMzNDdnY2jh49isOHD8PMzAy2traoW7cuWrRogdq1ayM+Ph5XrlxB165d4ePjU6q9Jbm5ueongf/4449PPKiQiIhKR+u7e7y8vBAQEICCggLs3LkTw4cPh5ubG86fP6++w6EkFAoFFAqF+nVGXgY81nnw7h4CAMTFibcW//vvfVy6dBm2tjawt38Ad/d/YG6e9cLPJyYmwsLCQr0hFhCbifj4eMTFxcHIyAjm5ua4desWevXqhTVr1qBKlSqlqpV39xAR6YbWZ1JOnz4NOzs7TJ48GStXrsTw4cOxYcOGYu9JSkpCzZo10apVK1y4cOGp8/Tt27f4AwgtAMzWthqqaAQBOHoU2L5dPJOSnp4OQcjDW28p0LWrJYyMur9wjqysLGzduhWAmIKsUCiQmZkJQRBgZWUFDw8PWFpaIjQ0FPb29khLS0NBQUGpazYzM0NwcLD6mIiIpKH1mRQXFxfEx8cDAFauXKk+zV1Up06dcP/+fTg7Oz+zSeGZFHpcerr43J3CB2sLggpnz+4C8DN8fcdhwIABJZpHoVBgzJgxePjwIezs7ODs7IyWLVuiUaNGaNCgAS5duoQNGzagZ8+e+N///sfwNSIiA6X1mZTExEQ0atQIERERePDgwRNfP3ToECIjI9GzZ0+EhIQ8cx5bW9tiT0dW5Cqe+V6q+EJDgd9+Ax490ow1bZqAe/dWIyUlAZcvXy5xk2Jra4t58+YhOzsbbm5ucHZ2hpGREQRBwC+//IKdO3fivffew/vvv8+YeyIiA6ZVkxIXFwelUgkfHx8cOXIEvr6+aNWqFfr166d+zwcffIBff/0V27Ztk7xYqnhyc4Ft24CTJzVjtrbAmDHA7dvnkJ2tgKurK65evYqMjAzY2NiUaN7HQ9iUSiWWL1+OI0eO4OOPP0afPn2gVCrVjXSrVq1galq6bEOVSqU+u1irVi2emSEikohWP0137NgBAOjduzdWr14NT09PDB48GBEREQCAOXPmwNXVFW+//bb0lVKFEx0NLFhQvEFp2RLw9gaaNgVCQ0NhYmICBwcHpKam4saNG6VaJy8vDwsXLsSxY8cwffp09OnTB4AY3tauXTu0a9cOKSkppf59ZGdnw9XVFa6ursjOzi71PEREVJxWf3U8fvw4LCws1Jdp/v33X7i4uKB9+/aIjY3F0aNHcfnyZZiamkKlUkEQBLz55pv4+++/dVI8lU+CAPz9N7Bjh7g5FgDMzcXck9deE5+7k5mZqd7YamFhAaVSibCwMLRr106rtTIzM+Hv7487d+7Ay8sLbdu21cHvCKU+C0NERM+m1U/Wxy/hmJqaFovG//fff9XH48aNQ0hICBsUKkahEDfHXrumGatTBxg/HnB21oxFREQgJSUFdevWBQBUqVIF58+fx+jRo0u8j6Qw5j4pKQkBAQFo3Lhxsa/XqFEDUjxf09raGvn5+WWeh4iIiuNf/0hvwsLE5NgiN3WhRw+gf3/g8RMRYWFhyMvLUwej2dvbIyoqCg8ePECtWrVeuFZ8fDy8vLygVCoRFBSEl156SbrfCBER6YXOmpTVq1framoqZwqTYw8f1owVbo591iOgIiIioFQqcenSJahUKlSpUgWWlpaIiop6YZNy9+5d+Pj4wNraGgsXLiwW6EZEROUHz6SQTiUkAD/9JG6SLdSsmdigPO9GnY8++givvPIK9u3bh5ycHAwYMADm5ubw9PR87nrXrl3D/Pnz4eLi8sKYe4VCgU6dOgEATp06VeyWeG3k5uZi6tSpAIClS5cyFp+ISCJah7npiiJXAbtFdgxzqyAEATh9Gti8GcjLE8dMTYGBA4E33xQ3x5aEn58f7t69i59++umFTzM+e/YsgoKC4OHhgblz574w5j4xMRHO/22ESUhIKPUZF8biExHpBs+kkOSysoANG4CiYcM1awLjxombZHXh8OHD+Pbbb9GxY0dMmzatRPH0VlZWeP3119XHpWVmZgYfHx/1MRERSYNNCknqzh1g9WqgaOxI587AkCGArq6C7NixA7/88gveeecdfPLJJyUOU6tatSqOHTtW5vXNzc3h6+tb5nmIiKg4NikkCZUKOHAA2LdPvNQDAFZWwKhRwGPhr5IpGnM/bNgwjBgxgjH3REQVCJsUKrOUFODnn4HbtzVjDRsCY8cCDg66WbOgoADfffddsZh7balUKkT/t6O3Tp06pY6zFwQB6enpAAA7Ozs2SkREEmGTQmUSGipmn2Rlia+NjYF33wV69hSPdSEvLw9BQUG4ePEipk2bhjfeeKNU8yQlJaFevXoAyrZxNisrCw7/dWPcOEtEJB02KVQqSqUYa3/kiGasWjXx7Imbm+7WzczMxPz583Hr1i2dxtwTEZH8StWkeHp6Ijo6ulgkPlUeiYli9sn9+5qxNm3E/SdluEnmhVJTU+Hj44OHDx9iwYIFT8Tca8vJyQmZmZkAAEtLy1LPY2Vlhbz/7rPmM3yIiKRTqp+od+/eRdNnRYVShXb+PLB+PZCTI742NRXv3Hn99ZJnnwDArVu3sHz5cjRo0ACNGjWCm5sb6tWr98wslPj4eAQEBKgv9UgRc29sbFymW48LGRkZ8dZjIiIdKFWTkpaWhldffVXqWsiA5eUBW7YA//yjGXN2Fh8MWJrsk5s3b+Ls2bO4ePEiAPFshL29PTw8PODh4QF3d3e4/XfdKCMjA3PmzEHVqlWxePFixtwTEVUSWjcpZ8+ehSAI6NWrFwAgKioK7du3R1ZWFk6ePIlWrVqVaB6FQgFFkSfNZeRlaFsK6UlcHPDDDwU4dCgMKSkpMDY2Qo0ad5Gffw7+/spSz1tQUICWLVtCEARkZmZCoVDg6NGjOHz4MMzMzGBra4uoqCgkJiZi0KBBCAgIeG7MvbYePXqErl27AgCOHj2qTo3VVl5eHubOnQsAWLBgwQuTcYmIqGS0blL27dsHAOjSpQu2b9+O4cOHw83NDXfu3NHqh3zfvn1x/PhxzYAFgNnaVkO6VBhtv2kTkJiowK1bt2BtbYrmza+hRo07AICCAmnWMjExUf8qKChAQUEB4uLiEBoaCgCYOnWqpA0KIN6Vc+G/WNysrKxSNyn5+flYsmQJAMDX15dNChGRRLRuUk6fPg07OztMnjwZK1euxPDhw7FhwwYAQFxcHBo2bAiVSgVBEDB06FD89ttvT51nz549T5xJ8VjnUcrfBkktJ0fce3L+vPg6LS0NlpZJGDvWCN7ec8s8//79+xEeHo7w8HCoVCpYWFjAzs4Onp6eaNasGdLS0rBnzx64uLigZs2aqF69epnXfJyVlZX6gYVljcX/8ssv1cdERCQNrR8w6OLigvj4eADAypUrMWHCBPXX8vLyoFAo4OTkhKSkJNSqVQvXr19Hw4YNXzgvHzBoOKKixLt3Hj7UjCUkbMPNmwFo06Y5fv311zLfxXLjxg0sXboUDRo0QOPGjeHm5oYGDRrA2tpaHXP/9ttvY+LEiaUOWSMiovJN6z9pEhMT0ahRI0RERODBgwfFvmZubg4nJycAQHp6OgRBgEqlkqZS0jlBAI4eBX7/XXMZx9ISGDjwEb7+egNcXGogMTERd+7cwcsvv1ymtRo3bowff/yxWDprYcz9jh07MHToUIwcOZLprURElZhWf0WNi4uDUqmEj48Pxo4dC19fX+zevbvYe6KiolClShW4u7tj4MCBZf7DjPQjMxNYuVK8g6ewQalXD/DyAiwtw5CWlgZXV1dkZWUhPDxckjWLNiAFBQX49ttvsWPHDowfPx6jRo2CIAjIyspCVlaWTppdlUolyfyCICA/Px/5+fnQ8sQkERE9h1ZNyo4dOwAAvXv3xurVq+Hp6YnBgwcjIiJC/Z66desiOzsbV69excGDB3Ht2jVpKybJ3bsHBASIEfeFevQApk8HnJyA69evQ6lUwtzcHCYmJrh8+bKk6+fl5SEwMBBHjx7F1KlT0bdvXwBibL21tTWsra2RlJQk6ZpSzp+VlQVzc3OYm5sjq/D5AEREVGZaNSnHjx+HhYUFbG3FPSP//vsvHB0d0b59ezx69KjYe5s1a4Y6depgzZo10lVLkhIE4O+/gcWLxYcEAoC1NfDpp8DgwWJQmyAIOHfuHKpUqQIAcHBwwNWrV5/4711amZmZ8PHxweXLlzFv3jz1LcFERERa7UnZtm1b8Q+bmhaLxr927Rrs7e3h6uqKmJgY3LlzBx07dpSmUpJUdjbw22/ApUuaMTc3MZyt6JOL4+Pjcf/+ffUD9Ozt7REVFYUbN26o74wprcKY+8TERAQEBKBJkybFvu7k5ITIyEj1sdSkmt/KygqpqanqYyIikoakDxoJCQnB+PHj1a8HDBiAwYMHS7kESSA6Gli1SnwGT6G33gL69wdMTIq/9/r160hNTYUgCEhJSYGlpSUyMjIQFhZWpiblwYMH8Pb2Rm5uLhYtWqR+GnFRxsbGqFu3bqnXeBGp5jcyMoK9vX3ZCyIiomIkbVJGjhyJkSNHSjklSUgQgFOnxHA25X9BsVZWwJgxQMuWT/9MzZo10aBBA+Tl5SE/Px9mZmZ4+eWX4ezsXOo6IiMj4e3tDUtLS8bcExHRM2mdk6IrzEnRrdxcYONG4MwZzVjdusDHH4ubY1/k7t278PPzQ+/evTF06NBS1xEWFob58+ejZs2a8PPze26K7KNHj/Duu+8CEJOOS5sIq+v58/LysHDhQgDAnDlzmDhLRCQRPle+EoiPB378UfxnoTfeEJ9eXMZMNq2cO3cOQUFBaNy4MebOnfvC/RtZWVnqRyeUJbZe1/Pn5+fDz88PADB9+nQ2KUREEmGTUsGdOyfG2+fmiq8tLIBRo4B27fRbx5EjR/Dtt9+iQ4cOmDZtWon+ILe0tESzZs3Ux1KTan5TU1NMnDhRfUxERNLgT9QKKj8f2LoVOHFCM1a7NvC//wFl2E5SKjt37sSaNWvw1ltvYdKkSSWOube1tcXVq1d1VpdU81tYWOD777+XoCIiIiqKTUoFlJQE/PCDeBdPoY4dgeHDAX1eiRAEAb/99ht+//13DBkyBKNGjWLMPRERlRiblArm2jXg55+BwuBTMzPg/ffFJkWfCgoK8P333+PQoUMYN24c+vXrp98CiIio3OPjZSsIQQD27QOWL9c0KDVqALNn679BycvLw6JFi3DkyBF88cUXpW5QEhMTYWRkBCMjIyQWDXWRiFTzZ2ZmwszMDGZmZsjMzJSwQiKiyo1nUiqArCzx7EnRxyS1aiXmn/yXZq83mZmZCAgIwM2bNzFv3jy00/cOXZkoC4NniIhIMmxSyrnoaHH/SeHz8YyMgAEDxARZfW//SEtLg4+PDxISEjB//nx4eHiUaT5HR0ecP39efSw1qeavUqUKYmJi1MdERCQNNinl2Jkz4u3F+fnia2tr8dk7jz0CRy8SEhLg5eX13Jh7bZmampb5+UD6mN/Y2BguLi4SVEREREWxSSmHlEpg2zbg2DHNWN264u3FOjjh8EKRkZHw8fGBhYUFgoODyxSZT0REVIhNSjmTliamx969qxnr3BkYNky8k0ffrl+/Dn9/fzg7O8PPz0/SB+09evQIw4YNAwBs2bJFJ7H4Usyfl5eHb775BgDw+eefM3GWiEgibFLKkZs3xacXZ2SIr01NxduLO3WSp57z589j0aJFaNSoEebNmwdra2tJ58/KysKBAwfUx7qIxZdi/vz8fMyYMQMAMHHiRDYpREQSKVWT4unpiejoaCQkJEhdDz2FIACHDwM7dgAqlTjm6Che3qlbV56a/v77b3zzzTdo3769zp5XY2lpCTc3N/Wxoc5vamqK0aNHq4+JiEgapfqJevfuXTRt2lTqWugpcnOB334DLlzQjDVpAowbB0hxYkGpVGLXrl0wMjKCu7s7GjRoABsbm+d+ZteuXfj555/Ro0cPTJo0CSYmJmUv5ClsbW1x+/Ztncwt5fwWFhb49ddfy14QEREVU6omJS0tDa+++qrUtdBjkpKAlSuB/+5uBQD07An07QuU8PE3L/TgwQP8/PPPSEtLQ5UqVWBraws3Nzc0b94cbm5ucHd3R82aNQGIMffHjx/H/fv3MXjwYHzwwQeMuSciIp3Rukk5e/YsBEFAr169AABRUVFo3749srKycPLkSbRq1apE8ygUCigUCvXrjLwMbUup0CIigO++y8X58+HIy8uDqakSLVtexPnzD/BftIck0tPTAQD169eHmZkZFAoFQkJCcPbsWRgbG8PGxgbOzs6oWbMmLly4gCpVqsDLywv9+/eXrggiIqKn0LpJ2bdvHwCgS5cu2L59O4YPHw43NzfcuXNHq42Hffv2xfHjxzUDFgBma1tNxSMI4q3FW7cCp09fQkxMDFxdLVC//hEolemIjZV+TaVSCUEQYGlpCUtLSzg6OkKhUCA1NRUxMTFISkrC0aNHERkZCQDoqKec/cTERPXtzAkJCahRo4ZBzp+ZmanOSYmNjZV8AzERUWWldZNy+vRp2NnZYfLkyVi5ciWGDx+ODRs2ABDPsrz99tvIzs6GsbExPvnkEyxduvSp8+zZs+eJMyke68qWUFreKZXAhg3A6dOASlWArKws1KqVit27++Oll97VyZoxMTGYMGECUlJSkJCQgLy8PBgbG8POzg4NGjTAu+++i3PnzsHKykrdpNCTCs9IERGRdLRuUm7cuAGFQoGVK1di5cqVmDBhgvprFhYW+PHHHzFs2DCEhYWhRYsWmDVr1lP/hmprawtbW1v1a0Wu4on3VCZpaWK8/b174muFQgErq39gY3ME0dFNUK+etGcRCllbW8PJyQmZmZlo1KgRmjVrBnd3d7i5ucHU1BS+vr5QqVT45ptv1Hdz6SKi/mkcHR3x119/6WxNqeavUqUKbt68qT4mIiJpaN2kJCYmolGjRoiIiMCDBw+Kfa1Vq1bqPSlNmzaFubk57t27J/lp+orm3j1xg2zhX8bNzIC2bUMQG3sIgiDg2rVr6Ny5s07WrlatGr799ltYWFjAyspKPZ6QkICZM2ciJydHsph7bZmamqJHjx4GP7+xsTEaNmwoQUVERFSUVveIxMXFQalUwsfHB2PHjoWvry9279791Pf+9ttvEAQBr7zyiiSFVlSnTwNLlmgaFEdHYOZMICPjb5iamsLGxgbnzp2DqjAgRQccHByKNSiRkZHqcLLg4GBZGhQiIiKtmpQdO3YAAHr37o3Vq1fD09MTgwcPRkRERLH33bp1C+PHj1dHhdOTVCpxc+zateJeFABo2BCYMwewt8/AtWvX4ODgAAcHB8THx+ttP0h4eDhmzZoFOzs7BAUFqW8/zsrKwtChQzF06FBkZWXppRZdrynV/Pn5+fj+++/x/fffI7/waY9ERFRmRoIgCCV985AhQ7B3717k5OQAEO8KcXFxQU5ODmJjY1G1alUoFArUqVMHw4cPxw8//FDiQhS5CtgtskP6rHTYWti++APlWHY28NNPQFiYZuyNN4ChQwETE+DcuXOYMWOG+rbg69evY/bs2ejdu7dO63pezL2u77R5mvJ0d0/hnW2PHj3i3T1ERBLRak/Ktm3bin/Y1LRYNL5KpULz5s3RunVrrRqUyiQpCVi+HIiPF1+bmADDh4sPCSwUFhYGpVKpjpo3NjZGSEiITpuUo0ePYtmyZWjXrh1mzJjxRMy9ubm5+jZbfT2bRtdrSjW/iYkJBg8erD4mIiJpSPqgkR9++AH3799HYmKi+i6H9evXY9CgQVIuU27duQOsWAE8eiS+trYGPvlEvMxTSBAEnDt3DsbGxsj470mCFhYWCAkJQU5Ojk6eYbN7926sXr36uTH39vb2iCkafasHul5TqvktLS2faOCJiKjsJG1SJk6ciIkTJ0o5ZYVx9qz4DJ7C/SfOzsCnnwKPX2FQ/vcGKysrpKSkQKlUwtTUFBYWFsjOzpa0SREEAevXr8fWrVsxaNAgjB49mjH3RERkMPjIVh0TBGDPHuDAAc1Y48bAhAlAkRtq1MzMzBAYGAiFQoEFCxYgJycH8+fPh5WVFRwcHCSrS6VSYcWKFfjzzz/x0UcfYcCAAZLNTUREJAWJHlNHT5OXB6xaVbxB6dIF+Oyzpzcohezt7fHSSy+pX7/00ktwcnKSsK48BAUF4dChQ5gyZUqJGpSkpCSYmJjAxMQESUlJktUi55pSzZ+VlQUXFxe4uLjo7c4nIqLKgGdSdCQ9Hfj+eyAqSnxtZAQMGQK8+aZ4LJesrCwsWLAAN27cwJw5c0qcY6NSqdRZLbrMbNHnmlLNLwgC4uLi1MdERCQNNik6EB0tNiipqeJrCwtg/HigeXN560pPT4ePjw8ePHgAPz8/NGvWrMSftbe3x+bNm9XH+qDrNaWa39LSEpcvX1YfExGRNNikSOzqVTEDJTdXfO3oKG6Q/e9OV9kkJibCy8sL2dnZCAwMRP369bX6vLm5OYYNG6aj6uRZU6r5TUxM1I+DICIi6bBJkdDJk+JTjAvP+DdoIN5ibCtzNl1UVBS8vb1hbm6O4OBgdYosERGRIePGWQkIArB7N7B+vaZBadsWmDpV/galaMx9WRqUrKwsjBs3DuPGjdNrLL4u15Rq/vz8fPz666/49ddfGYtPRCQhrWLxdam8xuIrlcC6dcCZM5qxHj2AQYPKvkF2woQJyMnJwdq1a0v1+YsXL2LhwoVo2LAhvLy8yhTXzlj8Z2MsPhGRbvByTxlkZwM//ADcuCG+NjISn7/z5pvy1gUAx44dw7Jly+Dp6fnUmHttmZubo3r16upjfdD1mlLNb2Jigl69eqmPiYhIGmxSSik1FfjuOyA2VnxtZgaMHQu0bi1vXQCwZ88e/PTTT+jWrRsmT54syR+c9vb2SExMlKA6w1lTqvktLS2xf/9+CSoiIqKi2KSUQlwc8O23mluMra2BSZMANzd56yoacz9gwAB8+OGHjLknIqJyi02Klu7cEc+gZGeLr52cxATZ/7Y2yEalUmHlypU4ePAgPvzwQwwcOFDegoiIiMqId/do4do14OuvNQ1K3brAzJnyNyj5+fkIDg7GX3/9hc8//1wnDUpSUhLMzc1hbm6u11h8Xa4p1fxZWVlo2LAhGjZsyFh8IiIJ8UxKCZ07B/zyC1CYnt6kiZiBYmEhb13Z2dkICAhAeHi4VjH32lKpVOrba/UZi6/LNaWaXxAE3L59W31MRETSYJNSAseOAZs3F89A+egjwFTmf3vp6enw9fVFXFwc/P39tYq515a9vT1WrFihPtYHXa8p1fyWlpb4559/1MdERCQN5qQ8hyAA+/cDe/dqxrp0AYYPB4z1cKHseTkpiYmJ8Pb2RmZmJvz8/NCgQQPdF0RERKRHPJPyDIIAbNkCHD2qGevZE+jXT96nGAPA/fv34eXlBTMzMwQHB6NWrVryFkRERKQD3Dj7FAUF4v6Tog3KkCFA//7yNyg3btzAzJkzYWtrq9cGJScnB1OnTsXUqVORk5NTIdaUan6lUolt27Zh27ZtUCqVElZIRFS58XLPY5RKYNUqIDRUfG1sDIwaBXTsqP9aHr/cc/HiRQQGBsLd3b3MMffaYiz+szEWn4hIN0p1ucfT0xPR0dFISEiQuh5Z5eeLMffXromvTU2Bjz8GWraUdh1BEJCVlaXVH2bHjx/H119/jbZt22LmzJl6i6YvZGpqCjs7O/VxRVhTqvmNjY3x+uuvq4+JiEgapfrJfPfuXTRt2lTqWmSVlwesWAGEh4uvzczEFNkmTaRfa8eOHVi3bh3c3NzQvHlzuLu7w83NDTVr1nxqQuzevXuxatUqSWPuteXo6Ii0tLQKtaZU81epUgXHjh0r8zxERFRcqZqUtLQ0vPrqq1LXIpvcXGD5cuDmTfG1hQXw6adAo0a6WS8+Ph4xMTHIyMjA2bNnYWxsDBsbG9SsWRMtWrRAo0aN4O7ujoKCAty9exerVq1izD0REVU6WjcpZ8+ehSAI6qe+RkVFoX379sjKysLJkyfRqlWrEs2jUCigUCjUrzPyMrQtRRI5OeJzeLZtu4jk5BRYWgpo3PgQFi58qLM1Cy/3tG3bFoC48TIjIwOxsbEICwsDANjY2CAkJASmpqZYvnw5Bg0apLN6iIiIDJHWTcq+ffsAAF26dMH27dsxfPhwuLm54c6dO+rNgyXRt29fHD9+XDNgAWC2ttWUTU4O8M03wI0buYiLi4cgPEKHDldgY6P4ryDdEAQB1tbWEAQB2dnZ6oYtPz8fFhYWqFq1Kh48eIDk5GSYmpqia9euOqulpFJSUuDi4gIAiI2NhaOjY7lfU6r5s7Oz1WcW//33X1SpUkWyGomIKjOtm5TTp0/Dzs4OkydPxsqVKzF8+HBs2LBB/fXatWvjwYMHqF27NmJiYp45z549e544k+KxzkPbckqt8BLP3btAamoajIyy0K7dKfz229c63xi6fPlynDlzBtevX4elpSXs7OzQoUMHNGvWDC4uLtizZw8EQYAgCMjPzzeI21qVSqX6Nl191aPrNaWaX6VSIfS/28H09cgAIqLKQOs/jW/cuAGFQoGVK1di5cqVmDBhQrGvf/nll0hNTcUvv/zy3HlsbW1ha6u51ViRq3jOu6WVny9ukr11S3ydmfkQjo5rkZWVj9u3b6Nx48Y6Xb9Lly7IyclBw4YN4e7ujvr168PKygrp6enw8/NDTEwM5s+fjy5dugDQXwz989jb2yMwMFB9XBHWlGp+S0tL/PXXX+pjIiKShtY5KWZmZnBzc0NERAR8fX3h4+PzxHuWLVuGJUuWPPdMyuP0lZOSnw+sXAn8t/UDlpYCkpLmIjHxPLKzszFt2jQMGDBAZ+s/y8OHD+Hl5YVHjx7B39+fMfdERFTpaRXqEBcXB6VSCR8fH4wdOxa+vr7YvXu3rmqTXGFQW2GDYmEBDB36AKmpIXB0dISJiQkuXbqk97qio6Mxffp0KJVKLF68mA0KERERtGxSduzYAQDo3bs3Vq9eDU9PTwwePBgRERE6KU5KKhWwZg1w5Yr42twc+OwzIDPzKhQKBWxtbeHg4IBr164hI0N/dxpFRERg5syZsLGxKRZzn5OTA19fX/j6+uothv555KhH12tKNb9SqcT+/fuxf/9+g9g/RERUUWh1uWfIkCHYu3dvsc2GLi4uyMnJQWxsrPruHkO73CMIwKZNQOHNRGZmYoPSqBGwZMkS7N69Gx4eHsjLy8O9e/ewePFitGvXTtIanubSpUtYuHAhGjRoAG9v72J3R8kRQ/88jMV/NsbiExHphlYbZ7dt21b8w6am5SIaf/9+TYNibAz8739ig5Kfn4+LFy+qN/Cam5sjPz8fYWFhOm9STpw4gaVLl6JNmzaYOXMmLCyK3/JsamoKKysr9bHc5KhH12tKNb+xsTE8PT3Vx0REJA3Jf/I7OTkhJSUFgiDAxMQEa9aswejRo6VepsROnAD27tW8HjMGaNZMPL59+zaSkpKQlZWFuLg4WFtbIysrC+fPn8eYMWN0VtO+ffuwatUqdO3aFZMnT37qH5COjo7IzMzUWQ3akqMeXa8p1fxVqlTB+fPnJaiIiIiKkrxJSUpKknrKUrt0Cdi4UfN6yBDglVc0r+vVq4eePXsiKysL4eHhsLCwQIMGDdBS6icK/kcQBGzcuBGbN29G//798dFHHzHmnoiI6Bnkv46gIxERwM8/i/tRAODtt4Hu3Yu/p0qVKpg6dSoAYPTo0TAzM8O8efN0Uo9KpcKPP/6IAwcOYPTo0Rg0aBAbFCIioueokBfQExKAH34QbzkGgI4dARmiT9Ty8/OxePFi/PHHH/jss88wePDgFzYoKSkp6sC7lJQUPVVqWPXoek2p5s/OzkanTp3QqVMnZGdnS1ghEVHlVuHOpGRlAd9/L/4TEPefjBoFyHXSIicnBwsWLEBYWBhmz55d4qdHFz50sPBYbnLUo+s1pZpfpVLh9OnT6mMiIpJGhWpSVCoxrK3whqPatYHx48U7euSgUCjg6+uLmJgY+Pn5oXnz5iX+rK2tLWbNmqU+lpsc9eh6Tanmt7CwwM6dO9XHREQkDa1j8XVFipyUzZuBo0fF46pVgdmzASenkn129OjRsLS0xI8//liqtR9XNObez88Pbm5uksxLRERUWVSYMyknTmgaFBMTMQulpA2K1KKjo+Ht7Q1jY2MEBwejdu3a8hRCRERUjlWIJuXmTTFRttCIEUDDhvLUEhERAT8/Pzg6OsLf3x+Ojo6lmicvLw8rVqwAAEycOBHm5uZSllku6tH1mlLNX1BQgJMnTwIAOnfuDBMTE8lqJCKqzMr95Z60NCAgACh83E737mIeirakuNxz+fJlLFy4EPXr138i5l5bjMVnLD4RUWVXrs+kqFTA6tWaBqVpU2DQIHlqOXnyJJYuXYrWrVs/NeZeW8bGxuo5DCFqXY56dL2mVPMbGRnBw8NDfUxERNIo103K7t3ArVvisYMDMHasPHfyHDhwAD/88APeeOMNfPbZZ5I8Z8bJyckgnn5cSI56dL2mVPNbWVkhLCxMgoqIiKioctukhIUBBw+Kx8bGwMcfA/o+yy4IAjZt2oRNmzahX79+GDt2LP8mTUREJJFy2aRkZgJr12peDxwINGig3xqKxtx/8MEHJUqRJSIiopKTf7ODlgQB2LABSE8XXzdt+uQzeXRNqVRiyZIl+OOPP/Dpp59iyJAhkjcoKSkpqFatGqpVq2Ywsfj6rkfXa0o1f3Z2Nnr06IEePXowFp+ISELl7kzKuXPAxYvisZUV8MEH+o28L4y5v3btGmbNmoWOHTvqZB2lUqn+g9NQYvH1XY+u15RqfpVKhcOHD6uPiYhIGuWqScnIEFNlC40cCdjb6299hUIBPz8/3L9/H35+fmjRooXO1rK1tcUnn3yiPpabHPXoek2p5rewsMD69evVx0REJI1ylZPyyy/AmTPicbt2wLhx0q3/opyUpKQkeHl5ISMjA76+vnB3d5ducSIiInpCuTmTcuOGpkGxsgKGDdPf2jExMfDy8oKxsTGCgoLg4uKiv8WJiIgqqXLRpCiVwMaNmtcDBwI2NvpZ++bNm/D19YWDgwP8/f1RrVo1vaybl5eHTf9l/Q8fPtwgYvH1XY+u15Rq/oKCAly6dAkA0KZNG8biExFJpFxc7vnzT2DHDvHYzQ2YPl36zbJPu9wTEhKCBQsWoH79+vDy8oKNvjojMBZfH2syFp+IyLAZ/JmUrCxNaJuREfD++/q5m+eff/7BV199hZYtW2L27Nl63xBpbGys/hu5ocTi67seXa8p1fxGRkaoW7eu+piIiKRRqiZl2rRpuHnzJvbu3St1PU84dEhsVACgQwfA1VXnS6pj7l9//XV8/vnnksTca8vJyckgbj0uJEc9ul5TqvmtrKwQGRlZ9oKIiKiYUv3pGxISorN8kKIUCuDIEfHYxATo00e36xXG3G/cuBF9+/bFuHHj+DdjIiIimZSqSQkNDcWkSZOkruUJBw4AubnicZcugC73rAqCgPDwcMTHx2PUqFE6SZElIiKiktP6Qnx0dDSSk5PRqlUrAEBaWhr69OmDjh07Ij4+vsTz5ObmQqFQFPtVVGYmcPKkeGxuDvTqpW2lJadUKhEWFob79+9j0qRJGDp0qOwNSlpaGmrVqoVatWohLS1N1lrkqkfXa0o1f05ODvr374/+/fsb1JOriYjKO63PpISEhMDOzg7169fH1atXMXDgQHTt2hXbt2/X6hbOwMBA+Pn5aQYsAMzWvDxzRrz1GAA6dwZ0FXKak5ODwMBAPHz4EK1bt8Y777yjm4W0lJeXhwcPHqiP5SZHPbpeU6r5CwoKsHv3bvUxERFJo1RNSsuWLbFp0yZMmjQJixYtwoQJE9Rf37dvH6ZNmwaVSoWZM2di3DNiYWfPno2pU6eqXytyFaizog4A8SGChWdRAPFSjy5kZGTAz88PUVFRaNWqFWrWrKmbhUqhatWqGDVqlPpYbnLUo+s1pZrf3Nwcq1atUh8TEZE0tM5JGTRoEI4ePQpAbEiKbqBVKpXw8PDA0aNHYWtrizZt2uDs2bNwdHR84bxFc1ISo22xeLE43rAh8OWX2lRYMklJSfD29kZ6ejp8fX0REBDw3Fh8IiIi0i+t96SEhIRg0KBByMnJeeI6/rlz59C0aVO4uLjAxsYGvXr1wp9//ql1UUXPonTurPXHXygmJgbTp09HTk4OgoOD0bBhQ+kXISIiojLR6nJPRkYG7t27h4kTJ6JTp04YPnw4Tp8+jaZNmwIA4uLiij3XxtXVFbGxsVoVlJkJXLggHltZAW3aaPXxF7p16xZ8fHxgb2+P+fPn6y3mXltKpRL79+8HAPTu3VuWrBa569H1mlLNr1KpEB4eDgBo0qSJQYTvERFVBFr9VA4JCYGJiQk8PDzQunVrhIWFoU+fPjh37hycnJzwtCtH2t4lc/myZsPsq68CZmZaffy5CmPu69atCx8fH73G3GsrJSUF/fv3B2AYsfhy1KPrNaWaPzs7G82aNQPAWHwiIilp9Ve+0NBQNG7cWB0RHxQUBA8PDwwcOBB5eXlwcXEpduYkJiYGtWrV0qqg2DjNsaenVh99rn/++Qd+fn5o2rQpAgICDLpBKWRkZCT7rdBFyVGPrteUan4nJyc4OTlJUBERERWS9AGDSqUSTZo0wbFjx9QbZ8+cOVOiSyqFG2eDHdJxO0y833jxYmluPf7jjz+wcuVKdOnSBVOmTHnqaf2nPWCQiIiI5CPpRX5TU1N89dVX6Nq1K1QqFWbMmKH1no/CvbgmJkBZT3YIgoAtW7Zgw4YN6NOnD8aPH29QZyaIiIjo2STf/di3b1/07du31J8vbFLs7cv2tGNBEPDTTz9h7969GDlypEGkyBIREVHJGdxtCIVPPC5BtMozKZVKLFmyBPv27cPEiRMxbNiwctegpKWloV69eqhXr57BxOLrux5drynV/Dk5ORgxYgRGjBjBWHwiIgnJe1/rc9jbl+5zhTH3V65cwYwZM/Daa69JWpe+5OXlISoqSn0sNznq0fWaUs1fUFCAjRs3AoA6eZaIiMrOYJsUBwftP1M05t7Hx0f9EMTyqGrVqurbYw0lFl/f9eh6TanmNzc3x9dff60+JiIiaUh6d09ZFN7dMyY+HeaCLd57D+jateSffzzmXtsUWd7dQ0REZFgM9kyKNpd7YmNj4eXlBUDMbnF1ddVNUURERKQ3BtuklHTj7K1bt+Dr6ws7Ozv4+/tXmEAtpVKJM2fOAAA6dOhgELH4+q5H12tKNb9KpcL9+/cBAC+99BJj8YmIJGKwTUpJ9qSEhoYiICCgXMTcayslJQWd/3u6oqHE4uu7Hl2vKdX82dnZqF+/PgDG4hMRSckgm5SSBLmdOnUKS5YsQYsWLTB79mxYWlrqpziip7CyspK7BCKiCscgm5QXBbkdPHgQK1asQOfOnfHFF1/IfilEF2rUqPHUBzbKRY56dL2mVPNbW1sjMzNTgoqIiKgog/zT/VmXegRBwNatW7F+/Xq8++67+Pjjj8tdSBsRERGVTLlpUorG3I8YMaJcpsgSERFRyRnkbQiPNylKpRJLly7Fvn378Mknn+C9996r8A2KQqFA48aN0bhxYygUCrnLkaUeXa8p1fy5ubkYP348xo8fj9zcXAkrJCKq3Az+TEpOTg4WLVqE0NDQch1zr62cnBxERESoj21tbStdPbpeU6r5lUolVq9eDQBYtmwZLCwsJKuRiKgyM+gmJSMjA/7+/oiMjCz3MffasrKyQvfu3dXHcpOjHl2vKdX8ZmZmCAgIUB8TEZE0DDIW32eWLWxskuHt7Y3U1FT4+flpHXOvLcbiExERGRbJ96SsWLEC9evXh6WlJdq2bYuTJ09qPUd2diymT5+OrKwsBAcH67xBISIiIsMjaZOyZcsWTJkyBXPnzsXly5fRuXNn9OzZUx0ZXhKPHt3B/PkzYGlpicWLF1fa5/CoVCqEh4cjPDwcKpVK7nJkqUfXa0o1vyAIePjwIR4+fGhQ2TZEROWdpJd7XnnlFbRp0wYrV65UjzVp0gT9+/dHYGDgcz9beLmn4e/90OctN/j6+uo15t7QLvckJibC2dkZgGHE4stRj67XlGr+zMxMVK1aFQBj8YmIpCTZxtm8vDxcvHgRs2bNKjb+1ltv4fTp00+8Pzc3t9jtmuk56QCAGnXqYab3TAjmAhS5+rv1Nt84H841nPW65vNk5GUAFppjy1x5Y//lqEfXa0o1f2ZupnoeRa4CBaYFElVIRFRx2JjbaB0fItmZlLi4OLi4uODUqVPo2LGjenzhwoVYu3at+lbPQr6+vvDz89MM2ACYJkUlREREZGgSv0hEddvqWn1G8luQH++SBEF4auc0e/ZsTJ06Vf06LS0NdZvVxf3b92FnZyd1WS+kUChQp04dREdHy55JUig2NhYeHh64fv06XFxc5C5Hlnp0vaZU8xvi9w8RkSEo/PloPsVc689K1qQ4OTnBxMQEDx48KDZe9Lp/URYWFk+GXmUAdpZ2sLWQ4Ye8BYBcwNbCVp71n0JhrgByxVNkhlCTHPXoek3J5jfA7x8iIoPw38/H0iTFS3Z3j7m5Odq2bYtDhw4VGz906FCxyz9EREREJSHp5Z6pU6di1KhR8PT0xKuvvopVq1bh/v37+N///iflMkRERFQJSNqkDBs2DMnJyfD390d8fDyaNWuGAwcOoG7dui/8rIWFBXx8fGR77onc6z+Nra0tXn/9dYPZ4yBHPbpeU6r5DfH7h4jIEJTl56PBxOITERERFSV5LD4RERGRFNikEBERkUFik0JEREQGiU0KERERGSQ2KURERGSQDKZJWbFiBerXrw9LS0u0bdsWJ0+e1Ol606ZNQ58+fXS6hrY8PT2fms4rF7nq0eW6Us1tiN8/RESGKjAwEEZGRpgyZYpWnzOIJmXLli2YMmUK5s6di8uXL6Nz587o2bMn7t+/r7M1Q0JC0KpVK53NXxp3795Fo0aN5C5DTa56dLmuVHMb4vcPEZEhOn/+PFatWoUWLVpo/VmDaFKWLl2KsWPHYty4cWjSpAmWLVuGOnXqYOXKlTpbMzQ0FK1bt9bZ/KWRlpaGV199Ve4y1OSqR5frSjW3IX7/EBEZmkePHmHEiBH46aef4ODgoPXnZW9S8vLycPHiRbz11lvFxt966y2cPn1aJ2tGR0cjOTlZ/TfhtLQ09OnTBx07dkR8fLxO1nyRs2fPQhAE9OrVCwAQFRUFZ2dn2NjYICQkpNLUo8t1pZrbEL9/iIgM0aRJk9C7d2907969VJ+XvUlJSkpCQUHBE/sEnJ2dn3iislRCQkJgZ2eH+vXr4+rVq2jXrh1q1aqFY8eOoVatWjpZ80X27dsHAOjSpQu2b9+Ohg0bwtHREfHx8bJcVpCrHl2uK9Xchvj9Q0RkaDZv3oxLly4hMDCw1HPI3qQUevwRzoIglOqxziUREhKCli1bYtOmTejSpQu+/PJLrFq1Cubm5gDEP8xefvllNGzYEKtXr9ZJDY87ffo07OzsMHnyZAwZMgRDhgxBeHg4qlatCgCoXbs2jI2N4erqKns9Z8+ehb29PSwsLFClShVMnTpVL+vGxcXB2toaVapUgaWlJT744APJ5i6UlJQEU1NTeHp6PnOeF33/mJqaolWrVmjVqhXGjRtXun8RRETlWHR0ND7//HOsX78elpaWpZ9IkFlubq5gYmIi7Nixo9j4Z599JnTp0kUnaw4cOFBwcHAQHBwchFOnThX7Wn5+vtCwYUMhJiZGUCgUgru7u5CcnKyTOoqqXbu2YGRkJBgZGQk//PDDE1//6quvhHnz5gkuLi46r+VF9Vy+fFnYvHmzIAiCcO3aNcHY2FhISEjQ+bq5ubnCw4cPBUEQhIcPHwqmpqbCzZs3JZm7UMeOHQVXV1ehbdu2z5zned8/giAI1apVK3FNREQV0c6dOwUAgomJifoXAMHIyEgwMTERlEplieaR/UyKubk52rZti0OHDhUbP3ToEDp27KiTNUNCQjBo0CDk5OQgLS2t2NfOnTuHpk2bwsXFBTY2NujVqxf+/PNPndRRVGJiIho1agRBEJ56mWvq1KmoVq2azusoST2tWrXCsGHDAABNmzaFubk57t27p/N1zc3N4eTkBABIT0+HIAhQqVSSzA2I33ORkZF4++23nzvP875/iIgI6NatG65evYqQkBD1L09PT4wYMQIhISEwMTEp2US666NKbvPmzYKZmZnw888/C9evXxemTJkiWFtbC5GRkZKvpVAoBCMjI+HSpUvCL7/8Itja2grXrl1Tf33btm3CpEmT1K+Dg4OFxYsXS15HUbGxsQIAYePGjcLYsWMFAMKuXbueeN/XX3+tlzMpJa1HEARh7dq1goWFhd7WjYyMFCwtLQUAwpAhQySdu2bNmsLBgweFsWPHPvNMyou+fwRBEMzMzIQ2bdoInTp1Eo4dO1biGomIKrLXX39d+Pzzz7X6jEE0KYIgCN9//71Qt25dwdzcXGjTpo1w/Phxnaxz4sQJwdTUVMjJyREEQRC+/PJLoX79+urLCFu3bn2iSVmyZIlOain03XffCQCE9PR0QRAEwdPTUzA1NRVu3LhR7H36alJKWs/NmzcFc3PzZ1460dW6giAIV69eFWxsbISrV69KMvfs2bMFT09PQRCE5zYpL/r+EQSxISqs8aWXXlKvSURUmZXrJkVfvvvuO6FZs2bq1wUFBULv3r2Fzp07C7m5ucKpU6eE/v37q7/+2WefCRs2bNBpTYMHDy52NiI/P1+oUaOGYGtrK2RkZKjH9dWklKSe9PR0wdbWVpgwYYJe1y3Kw8ND+OKLLySZu0OHDurrpkZGRgIAoWvXrk/M86Lvn8e98847wvnz50tUIxERFWckCIIg9bWo8kypVKJJkyY4duwYbG1t0aZNG5w5c0av+0GeZdmyZViyZAliYmJkrUOlUqF+/fqoX78+jh07prd1r127Bnt7e7i6uiImJgbu7u5Yv349Bg8eLOk648aNQ0hICC5cuKD1Z1NTU2FlZQULCwvExMSgU6dOuHz5MhwdHSWtkYioMjCVuwBDY2pqiq+++gpdu3aFSqXCjBkzDKJBcXJyQkpKCgRBgImJCdasWYPRo0fLUssPP/yA+/fvIzExEVWqVAEArF+/HoMGDdLpuiEhIRg/frz69YABAyRvUMoqPDwcEyZMgLGxMYyMjPDNN9+wQSEiKiWeSSEiIiKDJPstyERERERPwyaFiIiIDBKbFCIiIjJIbFKIiIjIILFJISIiIoPEJoWIiIgMEpsUIiIiMkhsUoiIiMggsUkhIiIig8QmhYiIiAwSmxQiIiIySP8HTCMzJsPm1RUAAAAASUVORK5CYII=\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_11_1.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "k0 = 0.25\n", - "\n", - "plot45(g, xmin, xmax, k0, num_arrows=5, var='k')" - ] - }, - { - "cell_type": "markdown", - "id": "a10e45d1", - "metadata": {}, - "source": [ - "We can plot the time series of capital corresponding to the figure above as\n", - "follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "7e93df3f", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_13_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, k0, var='k')" - ] - }, - { - "cell_type": "markdown", - "id": "c86cbdd6", - "metadata": {}, - "source": [ - "Here's a somewhat longer view:" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "d3307a3b", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_15_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, k0, ts_length=20, var='k')" - ] - }, - { - "cell_type": "markdown", - "id": "766077b3", - "metadata": {}, - "source": [ - "When capital stock is higher than the unique positive steady state, we see that\n", - "it declines:" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "432b70e0", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_17_1.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "k0 = 2.95\n", - "\n", - "plot45(g, xmin, xmax, k0, num_arrows=5, var='k')" - ] - }, - { - "cell_type": "markdown", - "id": "9069e20c", - "metadata": {}, - "source": [ - "Here is the time series:" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "1c71062a", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_19_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, k0, var='k')" - ] - }, - { - "cell_type": "markdown", - "id": "cdefce6a", - "metadata": {}, - "source": [ - "### Complex Dynamics\n", - "\n", - "The Solow model is nonlinear but still generates very regular dynamics.\n", - "\n", - "One model that generates irregular dynamics is the **quadratic map**\n", - "\n", - "$$\n", - "g(x) = 4 x (1 - x),\n", - "\\qquad x \\in [0, 1]\n", - "$$\n", - "\n", - "Let's have a look at the 45 degree diagram." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "e8358b87", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_21_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "xmin, xmax = 0, 1\n", - "g = lambda x: 4 * x * (1 - x)\n", - "\n", - "x0 = 0.3\n", - "plot45(g, xmin, xmax, x0, num_arrows=0)" - ] - }, - { - "cell_type": "markdown", - "id": "9ba1efba", - "metadata": {}, - "source": [ - "Now let's look at a typical trajectory." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "0d315786", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_23_1.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "plot45(g, xmin, xmax, x0, num_arrows=6)" - ] - }, - { - "cell_type": "markdown", - "id": "bf4c28cd", - "metadata": {}, - "source": [ - "Notice how irregular it is.\n", - "\n", - "Here is the corresponding time series plot." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "baeb20a5", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_25_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=6)" - ] - }, - { - "cell_type": "markdown", - "id": "d95d17ae", - "metadata": {}, - "source": [ - "The irregularity is even clearer over a longer time horizon:" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "2df1bca8", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_27_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=20)" - ] - }, - { - "cell_type": "markdown", - "id": "1655ad15", - "metadata": {}, - "source": [ - "## Exercises\n", - "\n", - "```{exercise}\n", - ":label: sd_ex1\n", - "\n", - "Consider again the linear model $x_{t+1} = a x_t + b$ with $a\n", - "\\not=1$.\n", - "\n", - "The unique steady state is $b / (1 - a)$.\n", - "\n", - "The steady state is globally stable if $|a| < 1$.\n", - "\n", - "Try to illustrate this graphically by looking at a range of initial conditions.\n", - "\n", - "What differences do you notice in the cases $a \\in (-1, 0)$ and $a\n", - "\\in (0, 1)$?\n", - "\n", - "Use $a=0.5$ and then $a=-0.5$ and study the trajectories\n", - "\n", - "Set $b=1$ throughout.\n", - "```\n", - "\n", - "```{solution-start} sd_ex1\n", - ":class: dropdown\n", - "```\n", - "\n", - "We will start with the case $a=0.5$.\n", - "\n", - "Let's set up the model and plotting region:" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "99a7fe4f", - "metadata": {}, - "outputs": [], - "source": [ - "a, b = 0.5, 1\n", - "xmin, xmax = -1, 3\n", - "g = lambda x: a * x + b" - ] - }, - { - "cell_type": "markdown", - "id": "d475fb8c", - "metadata": {}, - "source": [ - "Now let's plot a trajectory:" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "4f9c7a05", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_31_1.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "x0 = -0.5\n", - "plot45(g, xmin, xmax, x0, num_arrows=5)" - ] - }, - { - "cell_type": "markdown", - "id": "8719daf0", - "metadata": {}, - "source": [ - "Here is the corresponding time series, which converges towards the steady\n", - "state." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "05d6634c", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_33_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=10)" - ] - }, - { - "cell_type": "markdown", - "id": "413f6020", - "metadata": {}, - "source": [ - "Now let's try $a=-0.5$ and see what differences we observe.\n", - "\n", - "Let's set up the model and plotting region:" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "5121798a", - "metadata": {}, - "outputs": [], - "source": [ - "a, b = -0.5, 1\n", - "xmin, xmax = -1, 3\n", - "g = lambda x: a * x + b" - ] - }, - { - "cell_type": "markdown", - "id": "1721e272", - "metadata": {}, - "source": [ - "Now let's plot a trajectory:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "08d70fea", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_37_1.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "x0 = -0.5\n", - "plot45(g, xmin, xmax, x0, num_arrows=5)" - ] - }, - { - "cell_type": "markdown", - "id": "800eec50", - "metadata": {}, - "source": [ - "Here is the corresponding time series, which converges towards the steady\n", - "state." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "78e6f8e3", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_39_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=10)" - ] - }, - { - "cell_type": "markdown", - "id": "7d6d7f18", - "metadata": {}, - "source": [ - "Once again, we have convergence to the steady state but the nature of\n", - "convergence differs.\n", - "\n", - "In particular, the time series jumps from above the steady state to below it\n", - "and back again.\n", - "\n", - "In the current context, the series is said to exhibit **damped oscillations**.\n", - "\n", - "```{solution-end}\n", - "```" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 39, - 44, - 218, - 304, - 309, - 311, - 315, - 318, - 322, - 326, - 361, - 365, - 370, - 372, - 376, - 378, - 383, - 387, - 391, - 393, - 408, - 414, - 418, - 420, - 426, - 428, - 432, - 434, - 466, - 470, - 474, - 477, - 482, - 484, - 490, - 494, - 498, - 501, - 506, - 508 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/html/_sources/scalar_dynam.md b/lectures/_build/html/_sources/scalar_dynam.md deleted file mode 100644 index 1090909e0..000000000 --- a/lectures/_build/html/_sources/scalar_dynam.md +++ /dev/null @@ -1,519 +0,0 @@ ---- -jupytext: - text_representation: - extension: .md - format_name: myst -kernelspec: - display_name: Python 3 - language: python - name: python3 ---- - -```{raw} html - -``` - -# {index}`Dynamics in One Dimension ` - -```{contents} Contents -:depth: 2 -``` - -## Overview - -In this lecture we give a quick introduction to discrete time dynamics in one -dimension. - -In one-dimensional models, the state of the system is described by a single variable. - -Although most interesting dynamic models have two or more state variables, the -one-dimensional setting is a good place to learn the foundations of dynamics and build -intuition. - -Let's start with some standard imports: - -```{code-cell} ipython -%matplotlib inline -import matplotlib.pyplot as plt -plt.rcParams["figure.figsize"] = (11, 5) #set default figure size -import numpy as np -``` - -## Some Definitions - -This section sets out the objects of interest and the kinds of properties we study. - -### Difference Equations - -A **time homogeneous first order difference equation** is an equation of the -form - -```{math} -:label: sdsod - -x_{t+1} = g(x_t) -``` - -where $g$ is a function from some subset $S$ of $\mathbb R$ to itself. - -Here $S$ is called the **state space** and $x$ is called the **state variable**. - -In the definition, - -* time homogeneity means that $g$ is the same at each time $t$ -* first order means dependence on only one lag (i.e., earlier states such as $x_{t-1}$ do not enter into {eq}`sdsod`). - -If $x_0 \in S$ is given, then {eq}`sdsod` recursively defines the sequence - -```{math} -:label: sdstraj - -x_0, \quad -x_1 = g(x_0), \quad -x_2 = g(x_1) = g(g(x_0)), \quad \text{etc.} -``` - -This sequence is called the **trajectory** of $x_0$ under $g$. - -If we define $g^n$ to be $n$ compositions of $g$ with itself, then we can write the trajectory more simply as $x_t = g^t(x_0)$ for $t \geq 0$. - -### Example: A Linear Model - -One simple example is the **linear difference equation** - -$$ -x_{t+1} = a x_t + b, \qquad S = \mathbb R -$$ - -where $a, b$ are fixed constants. - -In this case, given $x_0$, the trajectory {eq}`sdstraj` is - -```{math} -:label: sdslinmodpath - -x_0, \quad -a x_0 + b, \quad -a^2 x_0 + a b + b, \quad \text{etc.} -``` - -Continuing in this way, and using our knowledge of {doc}`geometric series `, we find that, for any $t \geq 0$, - -```{math} -:label: sdslinmod - -x_t = a^t x_0 + b \frac{1 - a^t}{1 - a} -``` - -This is about all we need to know about the linear model. - -We have an exact expression for $x_t$ for all $t$ and hence a full -understanding of the dynamics. - -Notice in particular that $|a| < 1$, then, by {eq}`sdslinmod`, we have - -```{math} -:label: sdslinmodc - -x_t \to \frac{b}{1 - a} \text{ as } t \to \infty -``` - -regardless of $x_0$ - -This is an example of what is called global stability, a topic we return to -below. - -### Example: A Nonlinear Model - -In the linear example above, we obtained an exact analytical expression for $x_t$ -in terms of arbitrary $t$ and $x_0$. - -This made analysis of dynamics very easy. - -When models are nonlinear, however, the situation can be quite different. - -For example, recall how we [previously studied](https://python-programming.quantecon.org/python_oop.html#example-the-solow-growth-model) the law of motion for the Solow growth model, a simplified version of which is - -```{math} -:label: solow_lom2 - -k_{t+1} = s z k_t^{\alpha} + (1 - \delta) k_t -``` - -Here $k$ is capital stock and $s, z, \alpha, \delta$ are positive -parameters with $0 < \alpha, \delta < 1$. - -If you try to iterate like we did in {eq}`sdslinmodpath`, you will find that -the algebra gets messy quickly. - -Analyzing the dynamics of this model requires a different method (see below). - -### Stability - -A **steady state** of the difference equation $x_{t+1} = g(x_t)$ is a -point $x^*$ in $S$ such that $x^* = g(x^*)$. - -In other words, $x^*$ is a **fixed point** of the function $g$ in -$S$. - -For example, for the linear model $x_{t+1} = a x_t + b$, you can use the -definition to check that - -* $x^* := b/(1-a)$ is a steady state whenever $a \not= 1$. -* if $a = 1$ and $b=0$, then every $x \in \mathbb R$ is a - steady state. -* if $a = 1$ and $b \not= 0$, then the linear model has no steady - state in $\mathbb R$. - -A steady state $x^*$ of $x_{t+1} = g(x_t)$ is called -**globally stable** if, for all $x_0 \in S$, - -$$ -x_t = g^t(x_0) \to x^* \text{ as } t \to \infty -$$ - -For example, in the linear model $x_{t+1} = a x_t + b$ with $a -\not= 1$, the steady state $x^*$ - -* is globally stable if $|a| < 1$ and -* fails to be globally stable otherwise. - -This follows directly from {eq}`sdslinmod`. - -A steady state $x^*$ of $x_{t+1} = g(x_t)$ is called -**locally stable** if there exists an $\epsilon > 0$ such that - -$$ -| x_0 - x^* | < \epsilon -\; \implies \; -x_t = g^t(x_0) \to x^* \text{ as } t \to \infty -$$ - -Obviously every globally stable steady state is also locally stable. - -We will see examples below where the converse is not true. - -## Graphical Analysis - -As we saw above, analyzing the dynamics for nonlinear models is nontrivial. - -There is no single way to tackle all nonlinear models. - -However, there is one technique for one-dimensional models that provides a -great deal of intuition. - -This is a graphical approach based on **45 degree diagrams**. - -Let's look at an example: the Solow model with dynamics given in {eq}`solow_lom2`. - -We begin with some plotting code that you can ignore at first reading. - -The function of the code is to produce 45 degree diagrams and time series -plots. - -```{code-cell} ipython ---- -tags: [output_scroll] ---- -def subplots(fs): - "Custom subplots with axes throught the origin" - fig, ax = plt.subplots(figsize=fs) - - # Set the axes through the origin - for spine in ['left', 'bottom']: - ax.spines[spine].set_position('zero') - ax.spines[spine].set_color('green') - for spine in ['right', 'top']: - ax.spines[spine].set_color('none') - - return fig, ax - - -def plot45(g, xmin, xmax, x0, num_arrows=6, var='x'): - - xgrid = np.linspace(xmin, xmax, 200) - - fig, ax = subplots((6.5, 6)) - ax.set_xlim(xmin, xmax) - ax.set_ylim(xmin, xmax) - - hw = (xmax - xmin) * 0.01 - hl = 2 * hw - arrow_args = dict(fc="k", ec="k", head_width=hw, - length_includes_head=True, lw=1, - alpha=0.6, head_length=hl) - - ax.plot(xgrid, g(xgrid), 'b-', lw=2, alpha=0.6, label='g') - ax.plot(xgrid, xgrid, 'k-', lw=1, alpha=0.7, label='45') - - x = x0 - xticks = [xmin] - xtick_labels = [xmin] - - for i in range(num_arrows): - if i == 0: - ax.arrow(x, 0.0, 0.0, g(x), **arrow_args) # x, y, dx, dy - else: - ax.arrow(x, x, 0.0, g(x) - x, **arrow_args) - ax.plot((x, x), (0, x), 'k', ls='dotted') - - ax.arrow(x, g(x), g(x) - x, 0, **arrow_args) - xticks.append(x) - xtick_labels.append(r'${}_{}$'.format(var, str(i))) - - x = g(x) - xticks.append(x) - xtick_labels.append(r'${}_{}$'.format(var, str(i+1))) - ax.plot((x, x), (0, x), 'k-', ls='dotted') - - xticks.append(xmax) - xtick_labels.append(xmax) - ax.set_xticks(xticks) - ax.set_yticks(xticks) - ax.set_xticklabels(xtick_labels) - ax.set_yticklabels(xtick_labels) - - bbox = (0., 1.04, 1., .104) - legend_args = {'bbox_to_anchor': bbox, 'loc': 'upper right'} - - ax.legend(ncol=2, frameon=False, **legend_args, fontsize=14) - plt.show() - -def ts_plot(g, xmin, xmax, x0, ts_length=6, var='x'): - fig, ax = subplots((7, 5.5)) - ax.set_ylim(xmin, xmax) - ax.set_xlabel(r'$t$', fontsize=14) - ax.set_ylabel(r'${}_t$'.format(var), fontsize=14) - x = np.empty(ts_length) - x[0] = x0 - for t in range(ts_length-1): - x[t+1] = g(x[t]) - ax.plot(range(ts_length), - x, - 'bo-', - alpha=0.6, - lw=2, - label=r'${}_t$'.format(var)) - ax.legend(loc='best', fontsize=14) - ax.set_xticks(range(ts_length)) - plt.show() -``` - -Let's create a 45 degree diagram for the Solow model with a fixed set of -parameters - -```{code-cell} ipython -A, s, alpha, delta = 2, 0.3, 0.3, 0.4 -``` - -Here's the update function corresponding to the model. - -```{code-cell} ipython -def g(k): - return A * s * k**alpha + (1 - delta) * k -``` - -Here is the 45 degree plot. - -```{code-cell} ipython -xmin, xmax = 0, 4 # Suitable plotting region. - -plot45(g, xmin, xmax, 0, num_arrows=0) -``` - -The plot shows the function $g$ and the 45 degree line. - -Think of $k_t$ as a value on the horizontal axis. - -To calculate $k_{t+1}$, we can use the graph of $g$ to see its -value on the vertical axis. - -Clearly, - -* If $g$ lies above the 45 degree line at this point, then we have $k_{t+1} > k_t$. -* If $g$ lies below the 45 degree line at this point, then we have $k_{t+1} < k_t$. -* If $g$ hits the 45 degree line at this point, then we have $k_{t+1} = k_t$, so $k_t$ is a steady state. - -For the Solow model, there are two steady states when $S = \mathbb R_+ = -[0, \infty)$. - -* the origin $k=0$ -* the unique positive number such that $k = s z k^{\alpha} + (1 - \delta) k$. - -By using some algebra, we can show that in the second case, the steady state is - -$$ -k^* = \left( \frac{sz}{\delta} \right)^{1/(1-\alpha)} -$$ - -### Trajectories - -By the preceding discussion, in regions where $g$ lies above the 45 degree line, we know that the trajectory is increasing. - -The next figure traces out a trajectory in such a region so we can see this more clearly. - -The initial condition is $k_0 = 0.25$. - -```{code-cell} ipython -k0 = 0.25 - -plot45(g, xmin, xmax, k0, num_arrows=5, var='k') -``` - -We can plot the time series of capital corresponding to the figure above as -follows: - -```{code-cell} ipython -ts_plot(g, xmin, xmax, k0, var='k') -``` - -Here's a somewhat longer view: - -```{code-cell} ipython -ts_plot(g, xmin, xmax, k0, ts_length=20, var='k') -``` - -When capital stock is higher than the unique positive steady state, we see that -it declines: - -```{code-cell} ipython -k0 = 2.95 - -plot45(g, xmin, xmax, k0, num_arrows=5, var='k') -``` - -Here is the time series: - -```{code-cell} ipython -ts_plot(g, xmin, xmax, k0, var='k') -``` - -### Complex Dynamics - -The Solow model is nonlinear but still generates very regular dynamics. - -One model that generates irregular dynamics is the **quadratic map** - -$$ -g(x) = 4 x (1 - x), -\qquad x \in [0, 1] -$$ - -Let's have a look at the 45 degree diagram. - -```{code-cell} ipython -xmin, xmax = 0, 1 -g = lambda x: 4 * x * (1 - x) - -x0 = 0.3 -plot45(g, xmin, xmax, x0, num_arrows=0) -``` - -Now let's look at a typical trajectory. - -```{code-cell} ipython -plot45(g, xmin, xmax, x0, num_arrows=6) -``` - -Notice how irregular it is. - -Here is the corresponding time series plot. - -```{code-cell} ipython -ts_plot(g, xmin, xmax, x0, ts_length=6) -``` - -The irregularity is even clearer over a longer time horizon: - -```{code-cell} ipython -ts_plot(g, xmin, xmax, x0, ts_length=20) -``` - -## Exercises - -```{exercise} -:label: sd_ex1 - -Consider again the linear model $x_{t+1} = a x_t + b$ with $a -\not=1$. - -The unique steady state is $b / (1 - a)$. - -The steady state is globally stable if $|a| < 1$. - -Try to illustrate this graphically by looking at a range of initial conditions. - -What differences do you notice in the cases $a \in (-1, 0)$ and $a -\in (0, 1)$? - -Use $a=0.5$ and then $a=-0.5$ and study the trajectories - -Set $b=1$ throughout. -``` - -```{solution-start} sd_ex1 -:class: dropdown -``` - -We will start with the case $a=0.5$. - -Let's set up the model and plotting region: - -```{code-cell} ipython -a, b = 0.5, 1 -xmin, xmax = -1, 3 -g = lambda x: a * x + b -``` - -Now let's plot a trajectory: - -```{code-cell} ipython -x0 = -0.5 -plot45(g, xmin, xmax, x0, num_arrows=5) -``` - -Here is the corresponding time series, which converges towards the steady -state. - -```{code-cell} ipython -ts_plot(g, xmin, xmax, x0, ts_length=10) -``` - -Now let's try $a=-0.5$ and see what differences we observe. - -Let's set up the model and plotting region: - -```{code-cell} ipython -a, b = -0.5, 1 -xmin, xmax = -1, 3 -g = lambda x: a * x + b -``` - -Now let's plot a trajectory: - -```{code-cell} ipython -x0 = -0.5 -plot45(g, xmin, xmax, x0, num_arrows=5) -``` - -Here is the corresponding time series, which converges towards the steady -state. - -```{code-cell} ipython -ts_plot(g, xmin, xmax, x0, ts_length=10) -``` - -Once again, we have convergence to the steady state but the nature of -convergence differs. - -In particular, the time series jumps from above the steady state to below it -and back again. - -In the current context, the series is said to exhibit **damped oscillations**. - -```{solution-end} -``` \ No newline at end of file diff --git a/lectures/_build/html/_sources/schelling.ipynb b/lectures/_build/html/_sources/schelling.ipynb deleted file mode 100644 index fa086ddc0..000000000 --- a/lectures/_build/html/_sources/schelling.ipynb +++ /dev/null @@ -1,430 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "003bb3c9", - "metadata": {}, - "source": [ - "(schelling)=\n", - "```{raw} html\n", - "
\n", - " \n", - " \"QuantEcon\"\n", - " \n", - "
\n", - "```\n", - "\n", - "# Schelling's Segregation Model\n", - "\n", - "```{index} single: Schelling Segregation Model\n", - "```\n", - "\n", - "```{index} single: Models; Schelling's Segregation Model\n", - "```\n", - "\n", - "```{contents} Contents\n", - ":depth: 2\n", - "```\n", - "\n", - "## Outline\n", - "\n", - "In 1969, Thomas C. Schelling developed a simple but striking model of racial segregation {cite}`Schelling1969`.\n", - "\n", - "His model studies the dynamics of racially mixed neighborhoods.\n", - "\n", - "Like much of Schelling's work, the model shows how local interactions can lead to surprising aggregate structure.\n", - "\n", - "In particular, it shows that relatively mild preference for neighbors of similar race can lead in aggregate to the collapse of mixed neighborhoods, and high levels of segregation.\n", - "\n", - "In recognition of this and other research, Schelling was awarded the 2005 Nobel Prize in Economic Sciences (joint with Robert Aumann).\n", - "\n", - "In this lecture, we (in fact you) will build and run a version of Schelling's model.\n", - "\n", - "Let's start with some imports:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "54000f82", - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "plt.rcParams[\"figure.figsize\"] = (11, 5) #set default figure size\n", - "from random import uniform, seed\n", - "from math import sqrt" - ] - }, - { - "cell_type": "markdown", - "id": "bae7bc55", - "metadata": {}, - "source": [ - "## The Model\n", - "\n", - "We will cover a variation of Schelling's model that is easy to program and captures the main idea.\n", - "\n", - "### Set-Up\n", - "\n", - "Suppose we have two types of people: orange people and green people.\n", - "\n", - "For the purpose of this lecture, we will assume there are 250 of each type.\n", - "\n", - "These agents all live on a single unit square.\n", - "\n", - "The location of an agent is just a point $(x, y)$, where $0 < x, y < 1$.\n", - "\n", - "### Preferences\n", - "\n", - "We will say that an agent is *happy* if half or more of her 10 nearest neighbors are of the same type.\n", - "\n", - "Here 'nearest' is in terms of [Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance).\n", - "\n", - "An agent who is not happy is called *unhappy*.\n", - "\n", - "An important point here is that agents are not averse to living in mixed areas.\n", - "\n", - "They are perfectly happy if half their neighbors are of the other color.\n", - "\n", - "### Behavior\n", - "\n", - "Initially, agents are mixed together (integrated).\n", - "\n", - "In particular, the initial location of each agent is an independent draw from a bivariate uniform distribution on $S = (0, 1)^2$.\n", - "\n", - "Now, cycling through the set of all agents, each agent is now given the chance to stay or move.\n", - "\n", - "We assume that each agent will stay put if they are happy and move if unhappy.\n", - "\n", - "The algorithm for moving is as follows\n", - "\n", - "1. Draw a random location in $S$\n", - "1. If happy at new location, move there\n", - "1. Else, go to step 1\n", - "\n", - "In this way, we cycle continuously through the agents, moving as required.\n", - "\n", - "We continue to cycle until no one wishes to move.\n", - "\n", - "## Results\n", - "\n", - "Let's have a look at the results we got when we coded and ran this model.\n", - "\n", - "As discussed above, agents are initially mixed randomly together.\n", - "\n", - "```{figure} /_static/lecture_specific/schelling/schelling_fig1.png\n", - "\n", - "```\n", - "\n", - "But after several cycles, they become segregated into distinct regions.\n", - "\n", - "```{figure} /_static/lecture_specific/schelling/schelling_fig2.png\n", - "\n", - "```\n", - "\n", - "```{figure} /_static/lecture_specific/schelling/schelling_fig3.png\n", - "\n", - "```\n", - "\n", - "```{figure} /_static/lecture_specific/schelling/schelling_fig4.png\n", - "\n", - "```\n", - "\n", - "In this instance, the program terminated after 4 cycles through the set of\n", - "agents, indicating that all agents had reached a state of happiness.\n", - "\n", - "What is striking about the pictures is how rapidly racial integration breaks down.\n", - "\n", - "This is despite the fact that people in the model don't actually mind living mixed with the other type.\n", - "\n", - "Even with these preferences, the outcome is a high degree of segregation.\n", - "\n", - "## Exercises\n", - "\n", - "```{exercise-start}\n", - ":label: schelling_ex1\n", - "```\n", - "\n", - "Implement and run this simulation for yourself.\n", - "\n", - "Consider the following structure for your program.\n", - "\n", - "Agents can be modeled as [objects](https://python-programming.quantecon.org/python_oop.html).\n", - "\n", - "Here's an indication of how they might look\n", - "\n", - "```{code-block} none\n", - "* Data:\n", - "\n", - " * type (green or orange)\n", - " * location\n", - "\n", - "* Methods:\n", - "\n", - " * determine whether happy or not given locations of other agents\n", - "\n", - " * If not happy, move\n", - "\n", - " * find a new location where happy\n", - "```\n", - "\n", - "And here's some pseudocode for the main loop\n", - "\n", - "```{code-block} none\n", - "while agents are still moving\n", - " for agent in agents\n", - " give agent the opportunity to move\n", - "```\n", - "\n", - "Use 250 agents of each type.\n", - "\n", - "```{exercise-end}\n", - "```\n", - "\n", - "```{solution-start} schelling_ex1\n", - ":class: dropdown\n", - "```\n", - "\n", - "Here's one solution that does the job we want.\n", - "\n", - "If you feel like a further exercise, you can probably speed up some of the computations and\n", - "then increase the number of agents." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "1f0c2a34", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 1\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/schelling_3_1.png" - } - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 2\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/schelling_3_3.png" - } - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 3\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/schelling_3_5.png" - } - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 4\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/schelling_3_7.png" - } - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Converged, terminating.\n" - ] - } - ], - "source": [ - "seed(10) # For reproducible random numbers\n", - "\n", - "class Agent:\n", - "\n", - " def __init__(self, type):\n", - " self.type = type\n", - " self.draw_location()\n", - "\n", - " def draw_location(self):\n", - " self.location = uniform(0, 1), uniform(0, 1)\n", - "\n", - " def get_distance(self, other):\n", - " \"Computes the euclidean distance between self and other agent.\"\n", - " a = (self.location[0] - other.location[0])**2\n", - " b = (self.location[1] - other.location[1])**2\n", - " return sqrt(a + b)\n", - "\n", - " def happy(self, agents):\n", - " \"True if sufficient number of nearest neighbors are of the same type.\"\n", - " distances = []\n", - " # distances is a list of pairs (d, agent), where d is distance from\n", - " # agent to self\n", - " for agent in agents:\n", - " if self != agent:\n", - " distance = self.get_distance(agent)\n", - " distances.append((distance, agent))\n", - " # == Sort from smallest to largest, according to distance == #\n", - " distances.sort()\n", - " # == Extract the neighboring agents == #\n", - " neighbors = [agent for d, agent in distances[:num_neighbors]]\n", - " # == Count how many neighbors have the same type as self == #\n", - " num_same_type = sum(self.type == agent.type for agent in neighbors)\n", - " return num_same_type >= require_same_type\n", - "\n", - " def update(self, agents):\n", - " \"If not happy, then randomly choose new locations until happy.\"\n", - " while not self.happy(agents):\n", - " self.draw_location()\n", - "\n", - "\n", - "def plot_distribution(agents, cycle_num):\n", - " \"Plot the distribution of agents after cycle_num rounds of the loop.\"\n", - " x_values_0, y_values_0 = [], []\n", - " x_values_1, y_values_1 = [], []\n", - " # == Obtain locations of each type == #\n", - " for agent in agents:\n", - " x, y = agent.location\n", - " if agent.type == 0:\n", - " x_values_0.append(x)\n", - " y_values_0.append(y)\n", - " else:\n", - " x_values_1.append(x)\n", - " y_values_1.append(y)\n", - " fig, ax = plt.subplots(figsize=(8, 8))\n", - " plot_args = {'markersize': 8, 'alpha': 0.6}\n", - " ax.set_facecolor('azure')\n", - " ax.plot(x_values_0, y_values_0, 'o', markerfacecolor='orange', **plot_args)\n", - " ax.plot(x_values_1, y_values_1, 'o', markerfacecolor='green', **plot_args)\n", - " ax.set_title(f'Cycle {cycle_num-1}')\n", - " plt.show()\n", - "\n", - "# == Main == #\n", - "\n", - "num_of_type_0 = 250\n", - "num_of_type_1 = 250\n", - "num_neighbors = 10 # Number of agents regarded as neighbors\n", - "require_same_type = 5 # Want at least this many neighbors to be same type\n", - "\n", - "# == Create a list of agents == #\n", - "agents = [Agent(0) for i in range(num_of_type_0)]\n", - "agents.extend(Agent(1) for i in range(num_of_type_1))\n", - "\n", - "\n", - "count = 1\n", - "# == Loop until none wishes to move == #\n", - "while True:\n", - " print('Entering loop ', count)\n", - " plot_distribution(agents, count)\n", - " count += 1\n", - " no_one_moved = True\n", - " for agent in agents:\n", - " old_location = agent.location\n", - " agent.update(agents)\n", - " if agent.location != old_location:\n", - " no_one_moved = False\n", - " if no_one_moved:\n", - " break\n", - "\n", - "print('Converged, terminating.')" - ] - }, - { - "cell_type": "markdown", - "id": "bb5e865e", - "metadata": {}, - "source": [ - "```{solution-end}\n", - "```" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 49, - 55, - 187, - 277 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/html/_sources/schelling.md b/lectures/_build/html/_sources/schelling.md deleted file mode 100644 index 874140185..000000000 --- a/lectures/_build/html/_sources/schelling.md +++ /dev/null @@ -1,280 +0,0 @@ ---- -jupytext: - text_representation: - extension: .md - format_name: myst -kernelspec: - display_name: Python 3 - language: python - name: python3 ---- - -(schelling)= -```{raw} html - -``` - -# Schelling's Segregation Model - -```{index} single: Schelling Segregation Model -``` - -```{index} single: Models; Schelling's Segregation Model -``` - -```{contents} Contents -:depth: 2 -``` - -## Outline - -In 1969, Thomas C. Schelling developed a simple but striking model of racial segregation {cite}`Schelling1969`. - -His model studies the dynamics of racially mixed neighborhoods. - -Like much of Schelling's work, the model shows how local interactions can lead to surprising aggregate structure. - -In particular, it shows that relatively mild preference for neighbors of similar race can lead in aggregate to the collapse of mixed neighborhoods, and high levels of segregation. - -In recognition of this and other research, Schelling was awarded the 2005 Nobel Prize in Economic Sciences (joint with Robert Aumann). - -In this lecture, we (in fact you) will build and run a version of Schelling's model. - -Let's start with some imports: - -```{code-cell} ipython -%matplotlib inline -import matplotlib.pyplot as plt -plt.rcParams["figure.figsize"] = (11, 5) #set default figure size -from random import uniform, seed -from math import sqrt -``` - -## The Model - -We will cover a variation of Schelling's model that is easy to program and captures the main idea. - -### Set-Up - -Suppose we have two types of people: orange people and green people. - -For the purpose of this lecture, we will assume there are 250 of each type. - -These agents all live on a single unit square. - -The location of an agent is just a point $(x, y)$, where $0 < x, y < 1$. - -### Preferences - -We will say that an agent is *happy* if half or more of her 10 nearest neighbors are of the same type. - -Here 'nearest' is in terms of [Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance). - -An agent who is not happy is called *unhappy*. - -An important point here is that agents are not averse to living in mixed areas. - -They are perfectly happy if half their neighbors are of the other color. - -### Behavior - -Initially, agents are mixed together (integrated). - -In particular, the initial location of each agent is an independent draw from a bivariate uniform distribution on $S = (0, 1)^2$. - -Now, cycling through the set of all agents, each agent is now given the chance to stay or move. - -We assume that each agent will stay put if they are happy and move if unhappy. - -The algorithm for moving is as follows - -1. Draw a random location in $S$ -1. If happy at new location, move there -1. Else, go to step 1 - -In this way, we cycle continuously through the agents, moving as required. - -We continue to cycle until no one wishes to move. - -## Results - -Let's have a look at the results we got when we coded and ran this model. - -As discussed above, agents are initially mixed randomly together. - -```{figure} /_static/lecture_specific/schelling/schelling_fig1.png - -``` - -But after several cycles, they become segregated into distinct regions. - -```{figure} /_static/lecture_specific/schelling/schelling_fig2.png - -``` - -```{figure} /_static/lecture_specific/schelling/schelling_fig3.png - -``` - -```{figure} /_static/lecture_specific/schelling/schelling_fig4.png - -``` - -In this instance, the program terminated after 4 cycles through the set of -agents, indicating that all agents had reached a state of happiness. - -What is striking about the pictures is how rapidly racial integration breaks down. - -This is despite the fact that people in the model don't actually mind living mixed with the other type. - -Even with these preferences, the outcome is a high degree of segregation. - -## Exercises - -```{exercise-start} -:label: schelling_ex1 -``` - -Implement and run this simulation for yourself. - -Consider the following structure for your program. - -Agents can be modeled as [objects](https://python-programming.quantecon.org/python_oop.html). - -Here's an indication of how they might look - -```{code-block} none -* Data: - - * type (green or orange) - * location - -* Methods: - - * determine whether happy or not given locations of other agents - - * If not happy, move - - * find a new location where happy -``` - -And here's some pseudocode for the main loop - -```{code-block} none -while agents are still moving - for agent in agents - give agent the opportunity to move -``` - -Use 250 agents of each type. - -```{exercise-end} -``` - -```{solution-start} schelling_ex1 -:class: dropdown -``` - -Here's one solution that does the job we want. - -If you feel like a further exercise, you can probably speed up some of the computations and -then increase the number of agents. - -```{code-cell} python3 -seed(10) # For reproducible random numbers - -class Agent: - - def __init__(self, type): - self.type = type - self.draw_location() - - def draw_location(self): - self.location = uniform(0, 1), uniform(0, 1) - - def get_distance(self, other): - "Computes the euclidean distance between self and other agent." - a = (self.location[0] - other.location[0])**2 - b = (self.location[1] - other.location[1])**2 - return sqrt(a + b) - - def happy(self, agents): - "True if sufficient number of nearest neighbors are of the same type." - distances = [] - # distances is a list of pairs (d, agent), where d is distance from - # agent to self - for agent in agents: - if self != agent: - distance = self.get_distance(agent) - distances.append((distance, agent)) - # == Sort from smallest to largest, according to distance == # - distances.sort() - # == Extract the neighboring agents == # - neighbors = [agent for d, agent in distances[:num_neighbors]] - # == Count how many neighbors have the same type as self == # - num_same_type = sum(self.type == agent.type for agent in neighbors) - return num_same_type >= require_same_type - - def update(self, agents): - "If not happy, then randomly choose new locations until happy." - while not self.happy(agents): - self.draw_location() - - -def plot_distribution(agents, cycle_num): - "Plot the distribution of agents after cycle_num rounds of the loop." - x_values_0, y_values_0 = [], [] - x_values_1, y_values_1 = [], [] - # == Obtain locations of each type == # - for agent in agents: - x, y = agent.location - if agent.type == 0: - x_values_0.append(x) - y_values_0.append(y) - else: - x_values_1.append(x) - y_values_1.append(y) - fig, ax = plt.subplots(figsize=(8, 8)) - plot_args = {'markersize': 8, 'alpha': 0.6} - ax.set_facecolor('azure') - ax.plot(x_values_0, y_values_0, 'o', markerfacecolor='orange', **plot_args) - ax.plot(x_values_1, y_values_1, 'o', markerfacecolor='green', **plot_args) - ax.set_title(f'Cycle {cycle_num-1}') - plt.show() - -# == Main == # - -num_of_type_0 = 250 -num_of_type_1 = 250 -num_neighbors = 10 # Number of agents regarded as neighbors -require_same_type = 5 # Want at least this many neighbors to be same type - -# == Create a list of agents == # -agents = [Agent(0) for i in range(num_of_type_0)] -agents.extend(Agent(1) for i in range(num_of_type_1)) - - -count = 1 -# == Loop until none wishes to move == # -while True: - print('Entering loop ', count) - plot_distribution(agents, count) - count += 1 - no_one_moved = True - for agent in agents: - old_location = agent.location - agent.update(agents) - if agent.location != old_location: - no_one_moved = False - if no_one_moved: - break - -print('Converged, terminating.') -``` - -```{solution-end} -``` \ No newline at end of file diff --git a/lectures/_build/html/_sources/short_path.ipynb b/lectures/_build/html/_sources/short_path.ipynb deleted file mode 100644 index 66d9acbdf..000000000 --- a/lectures/_build/html/_sources/short_path.ipynb +++ /dev/null @@ -1,702 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "12189301", - "metadata": {}, - "source": [ - "(short_path)=\n", - "```{raw} html\n", - "
\n", - " \n", - " \"QuantEcon\"\n", - " \n", - "
\n", - "```\n", - "\n", - "# Shortest Paths\n", - "\n", - "```{index} single: Dynamic Programming; Shortest Paths\n", - "```\n", - "\n", - "```{contents} Contents\n", - ":depth: 2\n", - "```\n", - "\n", - "## Overview\n", - "\n", - "The shortest path problem is a [classic problem](https://en.wikipedia.org/wiki/Shortest_path) in mathematics and computer science with applications in\n", - "\n", - "* Economics (sequential decision making, analysis of social networks, etc.)\n", - "* Operations research and transportation\n", - "* Robotics and artificial intelligence\n", - "* Telecommunication network design and routing\n", - "* etc., etc.\n", - "\n", - "Variations of the methods we discuss in this lecture are used millions of times every day, in applications such as\n", - "\n", - "* Google Maps\n", - "* routing packets on the internet\n", - "\n", - "For us, the shortest path problem also provides a nice introduction to the logic of **dynamic programming**.\n", - "\n", - "Dynamic programming is an extremely powerful optimization technique that we apply in many lectures on this site.\n", - "\n", - "The only scientific library we'll need in what follows is NumPy:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "0cdc4241", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np" - ] - }, - { - "cell_type": "markdown", - "id": "12745deb", - "metadata": {}, - "source": [ - "## Outline of the Problem\n", - "\n", - "The shortest path problem is one of finding how to traverse a [graph](https://en.wikipedia.org/wiki/Graph_%28mathematics%29) from one specified node to another at minimum cost.\n", - "\n", - "Consider the following graph\n", - "\n", - "```{figure} /_static/lecture_specific/short_path/graph.png\n", - "\n", - "```\n", - "\n", - "We wish to travel from node (vertex) A to node G at minimum cost\n", - "\n", - "* Arrows (edges) indicate the movements we can take.\n", - "* Numbers on edges indicate the cost of traveling that edge.\n", - "\n", - "(Graphs such as the one above are called weighted [directed graphs](https://en.wikipedia.org/wiki/Directed_graph).)\n", - "\n", - "Possible interpretations of the graph include\n", - "\n", - "* Minimum cost for supplier to reach a destination.\n", - "* Routing of packets on the internet (minimize time).\n", - "* Etc., etc.\n", - "\n", - "For this simple graph, a quick scan of the edges shows that the optimal paths are\n", - "\n", - "* A, C, F, G at cost 8\n", - "\n", - "```{figure} /_static/lecture_specific/short_path/graph4.png\n", - "\n", - "```\n", - "\n", - "* A, D, F, G at cost 8\n", - "\n", - "```{figure} /_static/lecture_specific/short_path/graph3.png\n", - "\n", - "```\n", - "\n", - "## Finding Least-Cost Paths\n", - "\n", - "For large graphs, we need a systematic solution.\n", - "\n", - "Let $J(v)$ denote the minimum cost-to-go from node $v$, understood as the total cost from $v$ if we take the best route.\n", - "\n", - "Suppose that we know $J(v)$ for each node $v$, as shown below for the graph from the preceding example\n", - "\n", - "```{figure} /_static/lecture_specific/short_path/graph2.png\n", - "\n", - "```\n", - "\n", - "Note that $J(G) = 0$.\n", - "\n", - "The best path can now be found as follows\n", - "\n", - "1. Start at node $v = A$\n", - "1. From current node $v$, move to any node that solves\n", - "\n", - "```{math}\n", - ":label: spprebell\n", - "\n", - "\\min_{w \\in F_v} \\{ c(v, w) + J(w) \\}\n", - "```\n", - "\n", - "where\n", - "\n", - "* $F_v$ is the set of nodes that can be reached from $v$ in one step.\n", - "* $c(v, w)$ is the cost of traveling from $v$ to $w$.\n", - "\n", - "Hence, if we know the function $J$, then finding the best path is almost trivial.\n", - "\n", - "But how can we find the cost-to-go function $J$?\n", - "\n", - "Some thought will convince you that, for every node $v$,\n", - "the function $J$ satisfies\n", - "\n", - "```{math}\n", - ":label: spbell\n", - "\n", - "J(v) = \\min_{w \\in F_v} \\{ c(v, w) + J(w) \\}\n", - "```\n", - "\n", - "This is known as the *Bellman equation*, after the mathematician Richard Bellman.\n", - "\n", - "The Bellman equation can be thought of as a restriction that $J$ must\n", - "satisfy.\n", - "\n", - "What we want to do now is use this restriction to compute $J$.\n", - "\n", - "## Solving for Minimum Cost-to-Go\n", - "\n", - "Let's look at an algorithm for computing $J$ and then think about how to\n", - "implement it.\n", - "\n", - "### The Algorithm\n", - "\n", - "The standard algorithm for finding $J$ is to start an initial guess and then iterate.\n", - "\n", - "This is a standard approach to solving nonlinear equations, often called\n", - "the method of **successive approximations**.\n", - "\n", - "Our initial guess will be\n", - "\n", - "```{math}\n", - ":label: spguess\n", - "\n", - "J_0(v) = 0 \\text{ for all } v\n", - "```\n", - "\n", - "Now\n", - "\n", - "1. Set $n = 0$\n", - "1. Set $J_{n+1} (v) = \\min_{w \\in F_v} \\{ c(v, w) + J_n(w) \\}$ for all $v$\n", - "1. If $J_{n+1}$ and $J_n$ are not equal then increment $n$, go to 2\n", - "\n", - "This sequence converges to $J$.\n", - "\n", - "Although we omit the proof, we'll prove similar claims in our other lectures\n", - "on dynamic programming.\n", - "\n", - "### Implementation\n", - "\n", - "Having an algorithm is a good start, but we also need to think about how to\n", - "implement it on a computer.\n", - "\n", - "First, for the cost function $c$, we'll implement it as a matrix\n", - "$Q$, where a typical element is\n", - "\n", - "$$\n", - "Q(v, w)\n", - "=\n", - "\\begin{cases}\n", - " & c(v, w) \\text{ if } w \\in F_v \\\\\n", - " & +\\infty \\text{ otherwise }\n", - "\\end{cases}\n", - "$$\n", - "\n", - "In this context $Q$ is usually called the **distance matrix**.\n", - "\n", - "We're also numbering the nodes now, with $A = 0$, so, for example\n", - "\n", - "$$\n", - "Q(1, 2)\n", - "=\n", - "\\text{ the cost of traveling from B to C }\n", - "$$\n", - "\n", - "For example, for the simple graph above, we set" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "2d5a435c", - "metadata": {}, - "outputs": [], - "source": [ - "from numpy import inf\n", - "\n", - "Q = np.array([[inf, 1, 5, 3, inf, inf, inf],\n", - " [inf, inf, inf, 9, 6, inf, inf],\n", - " [inf, inf, inf, inf, inf, 2, inf],\n", - " [inf, inf, inf, inf, inf, 4, 8],\n", - " [inf, inf, inf, inf, inf, inf, 4],\n", - " [inf, inf, inf, inf, inf, inf, 1],\n", - " [inf, inf, inf, inf, inf, inf, 0]])" - ] - }, - { - "cell_type": "markdown", - "id": "4ade5693", - "metadata": {}, - "source": [ - "Notice that the cost of staying still (on the principle diagonal) is set to\n", - "\n", - "* np.inf for non-destination nodes --- moving on is required.\n", - "* 0 for the destination node --- here is where we stop.\n", - "\n", - "For the sequence of approximations $\\{J_n\\}$ of the cost-to-go functions, we can use NumPy arrays.\n", - "\n", - "Let's try with this example and see how we go:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "1841811a", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The cost-to-go function is [ 8 10 3 5 4 1 0]\n" - ] - } - ], - "source": [ - "nodes = range(7) # Nodes = 0, 1, ..., 6\n", - "J = np.zeros_like(nodes, dtype=int) # Initial guess\n", - "next_J = np.empty_like(nodes, dtype=int) # Stores updated guess\n", - "\n", - "max_iter = 500\n", - "i = 0\n", - "\n", - "while i < max_iter:\n", - " for v in nodes:\n", - " # minimize Q[v, w] + J[w] over all choices of w\n", - " lowest_cost = inf\n", - " for w in nodes:\n", - " cost = Q[v, w] + J[w]\n", - " if cost < lowest_cost:\n", - " lowest_cost = cost\n", - " next_J[v] = lowest_cost\n", - " if np.equal(next_J, J).all():\n", - " break\n", - " else:\n", - " J[:] = next_J # Copy contents of next_J to J\n", - " i += 1\n", - "\n", - "print(\"The cost-to-go function is\", J)" - ] - }, - { - "cell_type": "markdown", - "id": "b348a870", - "metadata": {}, - "source": [ - "This matches with the numbers we obtained by inspection above.\n", - "\n", - "But, importantly, we now have a methodology for tackling large graphs.\n", - "\n", - "## Exercises\n", - "\n", - "\n", - "```{exercise-start}\n", - ":label: short_path_ex1\n", - "```\n", - "\n", - "The text below describes a weighted directed graph.\n", - "\n", - "The line `node0, node1 0.04, node8 11.11, node14 72.21` means that from node0 we can go to\n", - "\n", - "* node1 at cost 0.04\n", - "* node8 at cost 11.11\n", - "* node14 at cost 72.21\n", - "\n", - "No other nodes can be reached directly from node0.\n", - "\n", - "Other lines have a similar interpretation.\n", - "\n", - "Your task is to use the algorithm given above to find the optimal path and its cost.\n", - "\n", - "```{note}\n", - "You will be dealing with floating point numbers now, rather than\n", - "integers, so consider replacing `np.equal()` with `np.allclose()`.\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "cfacfaa8", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Writing graph.txt\n" - ] - } - ], - "source": [ - "%%file graph.txt\n", - "node0, node1 0.04, node8 11.11, node14 72.21\n", - "node1, node46 1247.25, node6 20.59, node13 64.94\n", - "node2, node66 54.18, node31 166.80, node45 1561.45\n", - "node3, node20 133.65, node6 2.06, node11 42.43\n", - "node4, node75 3706.67, node5 0.73, node7 1.02\n", - "node5, node45 1382.97, node7 3.33, node11 34.54\n", - "node6, node31 63.17, node9 0.72, node10 13.10\n", - "node7, node50 478.14, node9 3.15, node10 5.85\n", - "node8, node69 577.91, node11 7.45, node12 3.18\n", - "node9, node70 2454.28, node13 4.42, node20 16.53\n", - "node10, node89 5352.79, node12 1.87, node16 25.16\n", - "node11, node94 4961.32, node18 37.55, node20 65.08\n", - "node12, node84 3914.62, node24 34.32, node28 170.04\n", - "node13, node60 2135.95, node38 236.33, node40 475.33\n", - "node14, node67 1878.96, node16 2.70, node24 38.65\n", - "node15, node91 3597.11, node17 1.01, node18 2.57\n", - "node16, node36 392.92, node19 3.49, node38 278.71\n", - "node17, node76 783.29, node22 24.78, node23 26.45\n", - "node18, node91 3363.17, node23 16.23, node28 55.84\n", - "node19, node26 20.09, node20 0.24, node28 70.54\n", - "node20, node98 3523.33, node24 9.81, node33 145.80\n", - "node21, node56 626.04, node28 36.65, node31 27.06\n", - "node22, node72 1447.22, node39 136.32, node40 124.22\n", - "node23, node52 336.73, node26 2.66, node33 22.37\n", - "node24, node66 875.19, node26 1.80, node28 14.25\n", - "node25, node70 1343.63, node32 36.58, node35 45.55\n", - "node26, node47 135.78, node27 0.01, node42 122.00\n", - "node27, node65 480.55, node35 48.10, node43 246.24\n", - "node28, node82 2538.18, node34 21.79, node36 15.52\n", - "node29, node64 635.52, node32 4.22, node33 12.61\n", - "node30, node98 2616.03, node33 5.61, node35 13.95\n", - "node31, node98 3350.98, node36 20.44, node44 125.88\n", - "node32, node97 2613.92, node34 3.33, node35 1.46\n", - "node33, node81 1854.73, node41 3.23, node47 111.54\n", - "node34, node73 1075.38, node42 51.52, node48 129.45\n", - "node35, node52 17.57, node41 2.09, node50 78.81\n", - "node36, node71 1171.60, node54 101.08, node57 260.46\n", - "node37, node75 269.97, node38 0.36, node46 80.49\n", - "node38, node93 2767.85, node40 1.79, node42 8.78\n", - "node39, node50 39.88, node40 0.95, node41 1.34\n", - "node40, node75 548.68, node47 28.57, node54 53.46\n", - "node41, node53 18.23, node46 0.28, node54 162.24\n", - "node42, node59 141.86, node47 10.08, node72 437.49\n", - "node43, node98 2984.83, node54 95.06, node60 116.23\n", - "node44, node91 807.39, node46 1.56, node47 2.14\n", - "node45, node58 79.93, node47 3.68, node49 15.51\n", - "node46, node52 22.68, node57 27.50, node67 65.48\n", - "node47, node50 2.82, node56 49.31, node61 172.64\n", - "node48, node99 2564.12, node59 34.52, node60 66.44\n", - "node49, node78 53.79, node50 0.51, node56 10.89\n", - "node50, node85 251.76, node53 1.38, node55 20.10\n", - "node51, node98 2110.67, node59 23.67, node60 73.79\n", - "node52, node94 1471.80, node64 102.41, node66 123.03\n", - "node53, node72 22.85, node56 4.33, node67 88.35\n", - "node54, node88 967.59, node59 24.30, node73 238.61\n", - "node55, node84 86.09, node57 2.13, node64 60.80\n", - "node56, node76 197.03, node57 0.02, node61 11.06\n", - "node57, node86 701.09, node58 0.46, node60 7.01\n", - "node58, node83 556.70, node64 29.85, node65 34.32\n", - "node59, node90 820.66, node60 0.72, node71 0.67\n", - "node60, node76 48.03, node65 4.76, node67 1.63\n", - "node61, node98 1057.59, node63 0.95, node64 4.88\n", - "node62, node91 132.23, node64 2.94, node76 38.43\n", - "node63, node66 4.43, node72 70.08, node75 56.34\n", - "node64, node80 47.73, node65 0.30, node76 11.98\n", - "node65, node94 594.93, node66 0.64, node73 33.23\n", - "node66, node98 395.63, node68 2.66, node73 37.53\n", - "node67, node82 153.53, node68 0.09, node70 0.98\n", - "node68, node94 232.10, node70 3.35, node71 1.66\n", - "node69, node99 247.80, node70 0.06, node73 8.99\n", - "node70, node76 27.18, node72 1.50, node73 8.37\n", - "node71, node89 104.50, node74 8.86, node91 284.64\n", - "node72, node76 15.32, node84 102.77, node92 133.06\n", - "node73, node83 52.22, node76 1.40, node90 243.00\n", - "node74, node81 1.07, node76 0.52, node78 8.08\n", - "node75, node92 68.53, node76 0.81, node77 1.19\n", - "node76, node85 13.18, node77 0.45, node78 2.36\n", - "node77, node80 8.94, node78 0.98, node86 64.32\n", - "node78, node98 355.90, node81 2.59\n", - "node79, node81 0.09, node85 1.45, node91 22.35\n", - "node80, node92 121.87, node88 28.78, node98 264.34\n", - "node81, node94 99.78, node89 39.52, node92 99.89\n", - "node82, node91 47.44, node88 28.05, node93 11.99\n", - "node83, node94 114.95, node86 8.75, node88 5.78\n", - "node84, node89 19.14, node94 30.41, node98 121.05\n", - "node85, node97 94.51, node87 2.66, node89 4.90\n", - "node86, node97 85.09\n", - "node87, node88 0.21, node91 11.14, node92 21.23\n", - "node88, node93 1.31, node91 6.83, node98 6.12\n", - "node89, node97 36.97, node99 82.12\n", - "node90, node96 23.53, node94 10.47, node99 50.99\n", - "node91, node97 22.17\n", - "node92, node96 10.83, node97 11.24, node99 34.68\n", - "node93, node94 0.19, node97 6.71, node99 32.77\n", - "node94, node98 5.91, node96 2.03\n", - "node95, node98 6.17, node99 0.27\n", - "node96, node98 3.32, node97 0.43, node99 5.87\n", - "node97, node98 0.30\n", - "node98, node99 0.33\n", - "node99," - ] - }, - { - "cell_type": "markdown", - "id": "6647d22d", - "metadata": {}, - "source": [ - "```{exercise-end}\n", - "```\n", - "\n", - "```{solution-start} short_path_ex1\n", - ":class: dropdown\n", - "```\n", - "\n", - "First let's write a function that reads in the graph data above and builds a distance matrix." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "7eb79595", - "metadata": {}, - "outputs": [], - "source": [ - "num_nodes = 100\n", - "destination_node = 99\n", - "\n", - "def map_graph_to_distance_matrix(in_file):\n", - "\n", - " # First let's set of the distance matrix Q with inf everywhere\n", - " Q = np.full((num_nodes, num_nodes), np.inf)\n", - "\n", - " # Now we read in the data and modify Q\n", - " with open(in_file) as infile:\n", - " for line in infile:\n", - " elements = line.split(',')\n", - " node = elements.pop(0)\n", - " node = int(node[4:]) # convert node description to integer\n", - " if node != destination_node:\n", - " for element in elements:\n", - " destination, cost = element.split()\n", - " destination = int(destination[4:])\n", - " Q[node, destination] = float(cost)\n", - " Q[destination_node, destination_node] = 0\n", - " return Q" - ] - }, - { - "cell_type": "markdown", - "id": "9fe7ca07", - "metadata": {}, - "source": [ - "In addition, let's write\n", - "\n", - "1. a \"Bellman operator\" function that takes a distance matrix and current guess of J and returns an updated guess of J, and\n", - "1. a function that takes a distance matrix and returns a cost-to-go function.\n", - "\n", - "We'll use the algorithm described above.\n", - "\n", - "The minimization step is vectorized to make it faster." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "520c29a7", - "metadata": {}, - "outputs": [], - "source": [ - "def bellman(J, Q):\n", - " num_nodes = Q.shape[0]\n", - " next_J = np.empty_like(J)\n", - " for v in range(num_nodes):\n", - " next_J[v] = np.min(Q[v, :] + J)\n", - " return next_J\n", - "\n", - "\n", - "def compute_cost_to_go(Q):\n", - " num_nodes = Q.shape[0]\n", - " J = np.zeros(num_nodes) # Initial guess\n", - " max_iter = 500\n", - " i = 0\n", - "\n", - " while i < max_iter:\n", - " next_J = bellman(J, Q)\n", - " if np.allclose(next_J, J):\n", - " break\n", - " else:\n", - " J[:] = next_J # Copy contents of next_J to J\n", - " i += 1\n", - "\n", - " return(J)" - ] - }, - { - "cell_type": "markdown", - "id": "ca360928", - "metadata": {}, - "source": [ - "We used np.allclose() rather than testing exact equality because we are\n", - "dealing with floating point numbers now.\n", - "\n", - "Finally, here's a function that uses the cost-to-go function to obtain the\n", - "optimal path (and its cost)." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "bb110ac7", - "metadata": {}, - "outputs": [], - "source": [ - "def print_best_path(J, Q):\n", - " sum_costs = 0\n", - " current_node = 0\n", - " while current_node != destination_node:\n", - " print(current_node)\n", - " # Move to the next node and increment costs\n", - " next_node = np.argmin(Q[current_node, :] + J)\n", - " sum_costs += Q[current_node, next_node]\n", - " current_node = next_node\n", - "\n", - " print(destination_node)\n", - " print('Cost: ', sum_costs)" - ] - }, - { - "cell_type": "markdown", - "id": "0c788917", - "metadata": {}, - "source": [ - "Okay, now we have the necessary functions, let's call them to do the job we were assigned." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "4e2930bb", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0\n", - "8\n", - "11\n", - "18\n", - "23\n", - "33\n", - "41\n", - "53\n", - "56\n", - "57\n", - "60\n", - "67\n", - "70\n", - "73\n", - "76\n", - "85\n", - "87\n", - "88\n", - "93\n", - "94\n", - "96\n", - "97\n", - "98\n", - "99\n", - "Cost: 160.55000000000007\n" - ] - } - ], - "source": [ - "Q = map_graph_to_distance_matrix('graph.txt')\n", - "J = compute_cost_to_go(Q)\n", - "print_best_path(J, Q)" - ] - }, - { - "cell_type": "markdown", - "id": "5e9ff1a8", - "metadata": {}, - "source": [ - "The total cost of the path should agree with $J[0]$ so let's check this." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "07cdaf8d", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "160.55" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "J[0]" - ] - }, - { - "cell_type": "markdown", - "id": "db431ffd", - "metadata": {}, - "source": [ - "```{solution-end}\n", - "```" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 51, - 53, - 202, - 212, - 223, - 247, - 279, - 381, - 392, - 414, - 425, - 449, - 457, - 470, - 474, - 478, - 482, - 484 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/html/_sources/short_path.md b/lectures/_build/html/_sources/short_path.md deleted file mode 100644 index 13bd06d0e..000000000 --- a/lectures/_build/html/_sources/short_path.md +++ /dev/null @@ -1,487 +0,0 @@ ---- -jupytext: - text_representation: - extension: .md - format_name: myst -kernelspec: - display_name: Python 3 - language: python - name: python3 ---- - -(short_path)= -```{raw} html - -``` - -# Shortest Paths - -```{index} single: Dynamic Programming; Shortest Paths -``` - -```{contents} Contents -:depth: 2 -``` - -## Overview - -The shortest path problem is a [classic problem](https://en.wikipedia.org/wiki/Shortest_path) in mathematics and computer science with applications in - -* Economics (sequential decision making, analysis of social networks, etc.) -* Operations research and transportation -* Robotics and artificial intelligence -* Telecommunication network design and routing -* etc., etc. - -Variations of the methods we discuss in this lecture are used millions of times every day, in applications such as - -* Google Maps -* routing packets on the internet - -For us, the shortest path problem also provides a nice introduction to the logic of **dynamic programming**. - -Dynamic programming is an extremely powerful optimization technique that we apply in many lectures on this site. - -The only scientific library we'll need in what follows is NumPy: - -```{code-cell} python3 -import numpy as np -``` - -## Outline of the Problem - -The shortest path problem is one of finding how to traverse a [graph](https://en.wikipedia.org/wiki/Graph_%28mathematics%29) from one specified node to another at minimum cost. - -Consider the following graph - -```{figure} /_static/lecture_specific/short_path/graph.png - -``` - -We wish to travel from node (vertex) A to node G at minimum cost - -* Arrows (edges) indicate the movements we can take. -* Numbers on edges indicate the cost of traveling that edge. - -(Graphs such as the one above are called weighted [directed graphs](https://en.wikipedia.org/wiki/Directed_graph).) - -Possible interpretations of the graph include - -* Minimum cost for supplier to reach a destination. -* Routing of packets on the internet (minimize time). -* Etc., etc. - -For this simple graph, a quick scan of the edges shows that the optimal paths are - -* A, C, F, G at cost 8 - -```{figure} /_static/lecture_specific/short_path/graph4.png - -``` - -* A, D, F, G at cost 8 - -```{figure} /_static/lecture_specific/short_path/graph3.png - -``` - -## Finding Least-Cost Paths - -For large graphs, we need a systematic solution. - -Let $J(v)$ denote the minimum cost-to-go from node $v$, understood as the total cost from $v$ if we take the best route. - -Suppose that we know $J(v)$ for each node $v$, as shown below for the graph from the preceding example - -```{figure} /_static/lecture_specific/short_path/graph2.png - -``` - -Note that $J(G) = 0$. - -The best path can now be found as follows - -1. Start at node $v = A$ -1. From current node $v$, move to any node that solves - -```{math} -:label: spprebell - -\min_{w \in F_v} \{ c(v, w) + J(w) \} -``` - -where - -* $F_v$ is the set of nodes that can be reached from $v$ in one step. -* $c(v, w)$ is the cost of traveling from $v$ to $w$. - -Hence, if we know the function $J$, then finding the best path is almost trivial. - -But how can we find the cost-to-go function $J$? - -Some thought will convince you that, for every node $v$, -the function $J$ satisfies - -```{math} -:label: spbell - -J(v) = \min_{w \in F_v} \{ c(v, w) + J(w) \} -``` - -This is known as the *Bellman equation*, after the mathematician Richard Bellman. - -The Bellman equation can be thought of as a restriction that $J$ must -satisfy. - -What we want to do now is use this restriction to compute $J$. - -## Solving for Minimum Cost-to-Go - -Let's look at an algorithm for computing $J$ and then think about how to -implement it. - -### The Algorithm - -The standard algorithm for finding $J$ is to start an initial guess and then iterate. - -This is a standard approach to solving nonlinear equations, often called -the method of **successive approximations**. - -Our initial guess will be - -```{math} -:label: spguess - -J_0(v) = 0 \text{ for all } v -``` - -Now - -1. Set $n = 0$ -1. Set $J_{n+1} (v) = \min_{w \in F_v} \{ c(v, w) + J_n(w) \}$ for all $v$ -1. If $J_{n+1}$ and $J_n$ are not equal then increment $n$, go to 2 - -This sequence converges to $J$. - -Although we omit the proof, we'll prove similar claims in our other lectures -on dynamic programming. - -### Implementation - -Having an algorithm is a good start, but we also need to think about how to -implement it on a computer. - -First, for the cost function $c$, we'll implement it as a matrix -$Q$, where a typical element is - -$$ -Q(v, w) -= -\begin{cases} - & c(v, w) \text{ if } w \in F_v \\ - & +\infty \text{ otherwise } -\end{cases} -$$ - -In this context $Q$ is usually called the **distance matrix**. - -We're also numbering the nodes now, with $A = 0$, so, for example - -$$ -Q(1, 2) -= -\text{ the cost of traveling from B to C } -$$ - -For example, for the simple graph above, we set - -```{code-cell} python3 -from numpy import inf - -Q = np.array([[inf, 1, 5, 3, inf, inf, inf], - [inf, inf, inf, 9, 6, inf, inf], - [inf, inf, inf, inf, inf, 2, inf], - [inf, inf, inf, inf, inf, 4, 8], - [inf, inf, inf, inf, inf, inf, 4], - [inf, inf, inf, inf, inf, inf, 1], - [inf, inf, inf, inf, inf, inf, 0]]) -``` - -Notice that the cost of staying still (on the principle diagonal) is set to - -* np.inf for non-destination nodes --- moving on is required. -* 0 for the destination node --- here is where we stop. - -For the sequence of approximations $\{J_n\}$ of the cost-to-go functions, we can use NumPy arrays. - -Let's try with this example and see how we go: - -```{code-cell} python3 -nodes = range(7) # Nodes = 0, 1, ..., 6 -J = np.zeros_like(nodes, dtype=int) # Initial guess -next_J = np.empty_like(nodes, dtype=int) # Stores updated guess - -max_iter = 500 -i = 0 - -while i < max_iter: - for v in nodes: - # minimize Q[v, w] + J[w] over all choices of w - lowest_cost = inf - for w in nodes: - cost = Q[v, w] + J[w] - if cost < lowest_cost: - lowest_cost = cost - next_J[v] = lowest_cost - if np.equal(next_J, J).all(): - break - else: - J[:] = next_J # Copy contents of next_J to J - i += 1 - -print("The cost-to-go function is", J) -``` - -This matches with the numbers we obtained by inspection above. - -But, importantly, we now have a methodology for tackling large graphs. - -## Exercises - - -```{exercise-start} -:label: short_path_ex1 -``` - -The text below describes a weighted directed graph. - -The line `node0, node1 0.04, node8 11.11, node14 72.21` means that from node0 we can go to - -* node1 at cost 0.04 -* node8 at cost 11.11 -* node14 at cost 72.21 - -No other nodes can be reached directly from node0. - -Other lines have a similar interpretation. - -Your task is to use the algorithm given above to find the optimal path and its cost. - -```{note} -You will be dealing with floating point numbers now, rather than -integers, so consider replacing `np.equal()` with `np.allclose()`. -``` - -```{code-cell} python3 -%%file graph.txt -node0, node1 0.04, node8 11.11, node14 72.21 -node1, node46 1247.25, node6 20.59, node13 64.94 -node2, node66 54.18, node31 166.80, node45 1561.45 -node3, node20 133.65, node6 2.06, node11 42.43 -node4, node75 3706.67, node5 0.73, node7 1.02 -node5, node45 1382.97, node7 3.33, node11 34.54 -node6, node31 63.17, node9 0.72, node10 13.10 -node7, node50 478.14, node9 3.15, node10 5.85 -node8, node69 577.91, node11 7.45, node12 3.18 -node9, node70 2454.28, node13 4.42, node20 16.53 -node10, node89 5352.79, node12 1.87, node16 25.16 -node11, node94 4961.32, node18 37.55, node20 65.08 -node12, node84 3914.62, node24 34.32, node28 170.04 -node13, node60 2135.95, node38 236.33, node40 475.33 -node14, node67 1878.96, node16 2.70, node24 38.65 -node15, node91 3597.11, node17 1.01, node18 2.57 -node16, node36 392.92, node19 3.49, node38 278.71 -node17, node76 783.29, node22 24.78, node23 26.45 -node18, node91 3363.17, node23 16.23, node28 55.84 -node19, node26 20.09, node20 0.24, node28 70.54 -node20, node98 3523.33, node24 9.81, node33 145.80 -node21, node56 626.04, node28 36.65, node31 27.06 -node22, node72 1447.22, node39 136.32, node40 124.22 -node23, node52 336.73, node26 2.66, node33 22.37 -node24, node66 875.19, node26 1.80, node28 14.25 -node25, node70 1343.63, node32 36.58, node35 45.55 -node26, node47 135.78, node27 0.01, node42 122.00 -node27, node65 480.55, node35 48.10, node43 246.24 -node28, node82 2538.18, node34 21.79, node36 15.52 -node29, node64 635.52, node32 4.22, node33 12.61 -node30, node98 2616.03, node33 5.61, node35 13.95 -node31, node98 3350.98, node36 20.44, node44 125.88 -node32, node97 2613.92, node34 3.33, node35 1.46 -node33, node81 1854.73, node41 3.23, node47 111.54 -node34, node73 1075.38, node42 51.52, node48 129.45 -node35, node52 17.57, node41 2.09, node50 78.81 -node36, node71 1171.60, node54 101.08, node57 260.46 -node37, node75 269.97, node38 0.36, node46 80.49 -node38, node93 2767.85, node40 1.79, node42 8.78 -node39, node50 39.88, node40 0.95, node41 1.34 -node40, node75 548.68, node47 28.57, node54 53.46 -node41, node53 18.23, node46 0.28, node54 162.24 -node42, node59 141.86, node47 10.08, node72 437.49 -node43, node98 2984.83, node54 95.06, node60 116.23 -node44, node91 807.39, node46 1.56, node47 2.14 -node45, node58 79.93, node47 3.68, node49 15.51 -node46, node52 22.68, node57 27.50, node67 65.48 -node47, node50 2.82, node56 49.31, node61 172.64 -node48, node99 2564.12, node59 34.52, node60 66.44 -node49, node78 53.79, node50 0.51, node56 10.89 -node50, node85 251.76, node53 1.38, node55 20.10 -node51, node98 2110.67, node59 23.67, node60 73.79 -node52, node94 1471.80, node64 102.41, node66 123.03 -node53, node72 22.85, node56 4.33, node67 88.35 -node54, node88 967.59, node59 24.30, node73 238.61 -node55, node84 86.09, node57 2.13, node64 60.80 -node56, node76 197.03, node57 0.02, node61 11.06 -node57, node86 701.09, node58 0.46, node60 7.01 -node58, node83 556.70, node64 29.85, node65 34.32 -node59, node90 820.66, node60 0.72, node71 0.67 -node60, node76 48.03, node65 4.76, node67 1.63 -node61, node98 1057.59, node63 0.95, node64 4.88 -node62, node91 132.23, node64 2.94, node76 38.43 -node63, node66 4.43, node72 70.08, node75 56.34 -node64, node80 47.73, node65 0.30, node76 11.98 -node65, node94 594.93, node66 0.64, node73 33.23 -node66, node98 395.63, node68 2.66, node73 37.53 -node67, node82 153.53, node68 0.09, node70 0.98 -node68, node94 232.10, node70 3.35, node71 1.66 -node69, node99 247.80, node70 0.06, node73 8.99 -node70, node76 27.18, node72 1.50, node73 8.37 -node71, node89 104.50, node74 8.86, node91 284.64 -node72, node76 15.32, node84 102.77, node92 133.06 -node73, node83 52.22, node76 1.40, node90 243.00 -node74, node81 1.07, node76 0.52, node78 8.08 -node75, node92 68.53, node76 0.81, node77 1.19 -node76, node85 13.18, node77 0.45, node78 2.36 -node77, node80 8.94, node78 0.98, node86 64.32 -node78, node98 355.90, node81 2.59 -node79, node81 0.09, node85 1.45, node91 22.35 -node80, node92 121.87, node88 28.78, node98 264.34 -node81, node94 99.78, node89 39.52, node92 99.89 -node82, node91 47.44, node88 28.05, node93 11.99 -node83, node94 114.95, node86 8.75, node88 5.78 -node84, node89 19.14, node94 30.41, node98 121.05 -node85, node97 94.51, node87 2.66, node89 4.90 -node86, node97 85.09 -node87, node88 0.21, node91 11.14, node92 21.23 -node88, node93 1.31, node91 6.83, node98 6.12 -node89, node97 36.97, node99 82.12 -node90, node96 23.53, node94 10.47, node99 50.99 -node91, node97 22.17 -node92, node96 10.83, node97 11.24, node99 34.68 -node93, node94 0.19, node97 6.71, node99 32.77 -node94, node98 5.91, node96 2.03 -node95, node98 6.17, node99 0.27 -node96, node98 3.32, node97 0.43, node99 5.87 -node97, node98 0.30 -node98, node99 0.33 -node99, -``` - -```{exercise-end} -``` - -```{solution-start} short_path_ex1 -:class: dropdown -``` - -First let's write a function that reads in the graph data above and builds a distance matrix. - -```{code-cell} python3 -num_nodes = 100 -destination_node = 99 - -def map_graph_to_distance_matrix(in_file): - - # First let's set of the distance matrix Q with inf everywhere - Q = np.full((num_nodes, num_nodes), np.inf) - - # Now we read in the data and modify Q - with open(in_file) as infile: - for line in infile: - elements = line.split(',') - node = elements.pop(0) - node = int(node[4:]) # convert node description to integer - if node != destination_node: - for element in elements: - destination, cost = element.split() - destination = int(destination[4:]) - Q[node, destination] = float(cost) - Q[destination_node, destination_node] = 0 - return Q -``` - -In addition, let's write - -1. a "Bellman operator" function that takes a distance matrix and current guess of J and returns an updated guess of J, and -1. a function that takes a distance matrix and returns a cost-to-go function. - -We'll use the algorithm described above. - -The minimization step is vectorized to make it faster. - -```{code-cell} python3 -def bellman(J, Q): - num_nodes = Q.shape[0] - next_J = np.empty_like(J) - for v in range(num_nodes): - next_J[v] = np.min(Q[v, :] + J) - return next_J - - -def compute_cost_to_go(Q): - num_nodes = Q.shape[0] - J = np.zeros(num_nodes) # Initial guess - max_iter = 500 - i = 0 - - while i < max_iter: - next_J = bellman(J, Q) - if np.allclose(next_J, J): - break - else: - J[:] = next_J # Copy contents of next_J to J - i += 1 - - return(J) -``` - -We used np.allclose() rather than testing exact equality because we are -dealing with floating point numbers now. - -Finally, here's a function that uses the cost-to-go function to obtain the -optimal path (and its cost). - -```{code-cell} python3 -def print_best_path(J, Q): - sum_costs = 0 - current_node = 0 - while current_node != destination_node: - print(current_node) - # Move to the next node and increment costs - next_node = np.argmin(Q[current_node, :] + J) - sum_costs += Q[current_node, next_node] - current_node = next_node - - print(destination_node) - print('Cost: ', sum_costs) -``` - -Okay, now we have the necessary functions, let's call them to do the job we were assigned. - -```{code-cell} python3 -Q = map_graph_to_distance_matrix('graph.txt') -J = compute_cost_to_go(Q) -print_best_path(J, Q) -``` - -The total cost of the path should agree with $J[0]$ so let's check this. - -```{code-cell} python3 -J[0] -``` - -```{solution-end} -``` \ No newline at end of file diff --git a/lectures/_build/html/_sources/status.ipynb b/lectures/_build/html/_sources/status.ipynb deleted file mode 100644 index 4e505d231..000000000 --- a/lectures/_build/html/_sources/status.ipynb +++ /dev/null @@ -1,53 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "5b0438dd", - "metadata": {}, - "source": [ - "# Execution Statistics\n", - "\n", - "This table contains the latest execution statistics.\n", - "\n", - "```{nb-exec-table}\n", - "```\n", - "\n", - "(status:machine-details)=\n", - "\n", - "These lectures are built on `linux` instances through `github actions` and `amazon web services (aws)` to\n", - "enable access to a `gpu`. These lectures are built on a [p3.2xlarge](https://aws.amazon.com/ec2/instance-types/p3/)\n", - "that has access to `8 vcpu's`, a `V100 NVIDIA Tesla GPU`, and `61 Gb` of memory." - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/html/_sources/status.md b/lectures/_build/html/_sources/status.md deleted file mode 100644 index 8309f5100..000000000 --- a/lectures/_build/html/_sources/status.md +++ /dev/null @@ -1,23 +0,0 @@ ---- -jupytext: - text_representation: - extension: .md - format_name: myst -kernelspec: - display_name: Python 3 - language: python - name: python3 ---- - -# Execution Statistics - -This table contains the latest execution statistics. - -```{nb-exec-table} -``` - -(status:machine-details)= - -These lectures are built on `linux` instances through `github actions` and `amazon web services (aws)` to -enable access to a `gpu`. These lectures are built on a [p3.2xlarge](https://aws.amazon.com/ec2/instance-types/p3/) -that has access to `8 vcpu's`, a `V100 NVIDIA Tesla GPU`, and `61 Gb` of memory. \ No newline at end of file diff --git a/lectures/_build/html/_sources/troubleshooting.ipynb b/lectures/_build/html/_sources/troubleshooting.ipynb deleted file mode 100644 index d7f7bd220..000000000 --- a/lectures/_build/html/_sources/troubleshooting.ipynb +++ /dev/null @@ -1,104 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "a8d21bed", - "metadata": {}, - "source": [ - "(troubleshooting)=\n", - "```{raw} html\n", - "
\n", - " \n", - " \"QuantEcon\"\n", - " \n", - "
\n", - "```\n", - "\n", - "# Troubleshooting\n", - "\n", - "```{contents} Contents\n", - ":depth: 2\n", - "```\n", - "\n", - "This page is for readers experiencing errors when running the code from the lectures.\n", - "\n", - "## Fixing Your Local Environment\n", - "\n", - "The basic assumption of the lectures is that code in a lecture should execute whenever\n", - "\n", - "1. it is executed in a Jupyter notebook and\n", - "1. the notebook is running on a machine with the latest version of Anaconda Python.\n", - "\n", - "You have installed Anaconda, haven't you, following the instructions in [this lecture](https://python-programming.quantecon.org/getting_started.html)?\n", - "\n", - "Assuming that you have, the most common source of problems for our readers is that their Anaconda distribution is not up to date.\n", - "\n", - "[Here's a useful article](https://www.anaconda.com/blog/keeping-anaconda-date)\n", - "on how to update Anaconda.\n", - "\n", - "Another option is to simply remove Anaconda and reinstall.\n", - "\n", - "You also need to keep the external code libraries, such as [QuantEcon.py](https://quantecon.org/quantecon-py) up to date.\n", - "\n", - "For this task you can either\n", - "\n", - "* use conda install -y quantecon on the command line, or\n", - "* execute !conda install -y quantecon within a Jupyter notebook.\n", - "\n", - "If your local environment is still not working you can do two things.\n", - "\n", - "First, you can use a remote machine instead, by clicking on the Launch Notebook icon available for each lecture\n", - "\n", - "```{image} _static/lecture_specific/troubleshooting/launch.png\n", - "\n", - "```\n", - "\n", - "Second, you can report an issue, so we can try to fix your local set up.\n", - "\n", - "We like getting feedback on the lectures so please don't hesitate to get in\n", - "touch.\n", - "\n", - "## Reporting an Issue\n", - "\n", - "One way to give feedback is to raise an issue through our [issue tracker](https://github.com/QuantEcon/lecture-python/issues).\n", - "\n", - "Please be as specific as possible. Tell us where the problem is and as much\n", - "detail about your local set up as you can provide.\n", - "\n", - "Another feedback option is to use our [discourse forum](https://discourse.quantecon.org/).\n", - "\n", - "Finally, you can provide direct feedback to [contact@quantecon.org](mailto:contact@quantecon.org)" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/html/_sources/troubleshooting.md b/lectures/_build/html/_sources/troubleshooting.md deleted file mode 100644 index e68f030fb..000000000 --- a/lectures/_build/html/_sources/troubleshooting.md +++ /dev/null @@ -1,75 +0,0 @@ ---- -jupytext: - text_representation: - extension: .md - format_name: myst -kernelspec: - display_name: Python 3 - language: python - name: python3 ---- - -(troubleshooting)= -```{raw} html - -``` - -# Troubleshooting - -```{contents} Contents -:depth: 2 -``` - -This page is for readers experiencing errors when running the code from the lectures. - -## Fixing Your Local Environment - -The basic assumption of the lectures is that code in a lecture should execute whenever - -1. it is executed in a Jupyter notebook and -1. the notebook is running on a machine with the latest version of Anaconda Python. - -You have installed Anaconda, haven't you, following the instructions in [this lecture](https://python-programming.quantecon.org/getting_started.html)? - -Assuming that you have, the most common source of problems for our readers is that their Anaconda distribution is not up to date. - -[Here's a useful article](https://www.anaconda.com/blog/keeping-anaconda-date) -on how to update Anaconda. - -Another option is to simply remove Anaconda and reinstall. - -You also need to keep the external code libraries, such as [QuantEcon.py](https://quantecon.org/quantecon-py) up to date. - -For this task you can either - -* use conda install -y quantecon on the command line, or -* execute !conda install -y quantecon within a Jupyter notebook. - -If your local environment is still not working you can do two things. - -First, you can use a remote machine instead, by clicking on the Launch Notebook icon available for each lecture - -```{image} _static/lecture_specific/troubleshooting/launch.png - -``` - -Second, you can report an issue, so we can try to fix your local set up. - -We like getting feedback on the lectures so please don't hesitate to get in -touch. - -## Reporting an Issue - -One way to give feedback is to raise an issue through our [issue tracker](https://github.com/QuantEcon/lecture-python/issues). - -Please be as specific as possible. Tell us where the problem is and as much -detail about your local set up as you can provide. - -Another feedback option is to use our [discourse forum](https://discourse.quantecon.org/). - -Finally, you can provide direct feedback to [contact@quantecon.org](mailto:contact@quantecon.org) - diff --git a/lectures/_build/html/_sources/zreferences.ipynb b/lectures/_build/html/_sources/zreferences.ipynb deleted file mode 100644 index e8fb5c71e..000000000 --- a/lectures/_build/html/_sources/zreferences.ipynb +++ /dev/null @@ -1,46 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "f995fbab", - "metadata": {}, - "source": [ - "(references)=\n", - "# References\n", - "\n", - "```{bibliography} _static/quant-econ.bib\n", - "```" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/html/_sources/zreferences.md b/lectures/_build/html/_sources/zreferences.md deleted file mode 100644 index 5f17e8922..000000000 --- a/lectures/_build/html/_sources/zreferences.md +++ /dev/null @@ -1,17 +0,0 @@ ---- -jupytext: - text_representation: - extension: .md - format_name: myst -kernelspec: - display_name: Python 3 - language: python - name: python3 ---- - -(references)= -# References - -```{bibliography} _static/quant-econ.bib -``` - diff --git a/lectures/_build/html/_static/basic.css b/lectures/_build/html/_static/basic.css deleted file mode 100644 index d54be8067..000000000 --- a/lectures/_build/html/_static/basic.css +++ /dev/null @@ -1,906 +0,0 @@ -/* - * basic.css - * ~~~~~~~~~ - * - * Sphinx stylesheet -- basic theme. - * - * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * - */ - -/* -- main layout ----------------------------------------------------------- */ - -div.clearer { - clear: both; -} - -div.section::after { - display: block; - content: ''; - clear: left; -} - -/* -- relbar ---------------------------------------------------------------- */ - -div.related { - width: 100%; - font-size: 90%; -} - -div.related h3 { - display: none; -} - -div.related ul { - margin: 0; - padding: 0 0 0 10px; - list-style: none; -} - -div.related li { - display: inline; -} - -div.related li.right { - float: right; - margin-right: 5px; -} - -/* -- sidebar --------------------------------------------------------------- */ - -div.sphinxsidebarwrapper { - padding: 10px 5px 0 10px; -} - -div.sphinxsidebar { - float: left; - width: 270px; - margin-left: -100%; - font-size: 90%; - word-wrap: break-word; - overflow-wrap : break-word; -} - -div.sphinxsidebar ul { - list-style: none; -} - -div.sphinxsidebar ul ul, -div.sphinxsidebar ul.want-points { - margin-left: 20px; - list-style: square; -} - -div.sphinxsidebar ul ul { - margin-top: 0; - margin-bottom: 0; -} - -div.sphinxsidebar form { - margin-top: 10px; -} - -div.sphinxsidebar input { - border: 1px solid #98dbcc; - font-family: sans-serif; - font-size: 1em; -} - -div.sphinxsidebar #searchbox form.search { - overflow: hidden; -} - -div.sphinxsidebar #searchbox input[type="text"] { - float: left; - width: 80%; - padding: 0.25em; - box-sizing: border-box; -} - -div.sphinxsidebar #searchbox input[type="submit"] { - float: left; - width: 20%; - border-left: none; - padding: 0.25em; - box-sizing: border-box; -} - - -img { - border: 0; - max-width: 100%; -} - -/* -- search page ----------------------------------------------------------- */ - -ul.search { - margin: 10px 0 0 20px; - padding: 0; -} - -ul.search li { - padding: 5px 0 5px 20px; - background-image: url(file.png); - background-repeat: no-repeat; - background-position: 0 7px; -} - -ul.search li a { - font-weight: bold; -} - -ul.search li p.context { - color: #888; - margin: 2px 0 0 30px; - text-align: left; -} - -ul.keywordmatches li.goodmatch a { - font-weight: bold; -} - -/* -- index page ------------------------------------------------------------ */ - -table.contentstable { - width: 90%; - margin-left: auto; - margin-right: auto; -} - -table.contentstable p.biglink { - line-height: 150%; -} - -a.biglink { - font-size: 1.3em; -} - -span.linkdescr { - font-style: italic; - padding-top: 5px; - font-size: 90%; -} - -/* -- general index --------------------------------------------------------- */ - -table.indextable { - width: 100%; -} - -table.indextable td { - text-align: left; - vertical-align: top; -} - -table.indextable ul { - margin-top: 0; - margin-bottom: 0; - list-style-type: none; -} - -table.indextable > tbody > tr > td > ul { - padding-left: 0em; -} - -table.indextable tr.pcap { - height: 10px; -} - -table.indextable tr.cap { - margin-top: 10px; - background-color: #f2f2f2; -} - -img.toggler { - margin-right: 3px; - margin-top: 3px; - cursor: pointer; -} - -div.modindex-jumpbox { - border-top: 1px solid #ddd; - border-bottom: 1px solid #ddd; - margin: 1em 0 1em 0; - padding: 0.4em; -} - -div.genindex-jumpbox { - border-top: 1px solid #ddd; - border-bottom: 1px solid #ddd; - margin: 1em 0 1em 0; - padding: 0.4em; -} - -/* -- domain module index --------------------------------------------------- */ - -table.modindextable td { - padding: 2px; - border-collapse: collapse; -} - -/* -- general body styles --------------------------------------------------- */ - -div.body { - min-width: 450px; - max-width: 800px; -} - -div.body p, div.body dd, div.body li, div.body blockquote { - -moz-hyphens: auto; - -ms-hyphens: auto; - -webkit-hyphens: auto; - hyphens: auto; -} - -a.headerlink { - visibility: hidden; -} - -a.brackets:before, -span.brackets > a:before{ - content: "["; -} - -a.brackets:after, -span.brackets > a:after { - content: "]"; -} - -h1:hover > a.headerlink, -h2:hover > a.headerlink, -h3:hover > a.headerlink, -h4:hover > a.headerlink, -h5:hover > a.headerlink, -h6:hover > a.headerlink, -dt:hover > a.headerlink, -caption:hover > a.headerlink, -p.caption:hover > a.headerlink, -div.code-block-caption:hover > a.headerlink { - visibility: visible; -} - -div.body p.caption { - text-align: inherit; -} - -div.body td { - text-align: left; -} - -.first { - margin-top: 0 !important; -} - -p.rubric { - margin-top: 30px; - font-weight: bold; -} - -img.align-left, figure.align-left, .figure.align-left, object.align-left { - clear: left; - float: left; - margin-right: 1em; -} - -img.align-right, figure.align-right, .figure.align-right, object.align-right { - clear: right; - float: right; - margin-left: 1em; -} - -img.align-center, figure.align-center, .figure.align-center, object.align-center { - display: block; - margin-left: auto; - margin-right: auto; -} - -img.align-default, figure.align-default, .figure.align-default { - display: block; - margin-left: auto; - margin-right: auto; -} - -.align-left { - text-align: left; -} - -.align-center { - text-align: center; -} - -.align-default { - text-align: center; -} - -.align-right { - text-align: right; -} - -/* -- sidebars -------------------------------------------------------------- */ - -div.sidebar, -aside.sidebar { - margin: 0 0 0.5em 1em; - border: 1px solid #ddb; - padding: 7px; - background-color: #ffe; - width: 40%; - float: right; - clear: right; - overflow-x: auto; -} - -p.sidebar-title { - font-weight: bold; -} - -div.admonition, div.topic, blockquote { - clear: left; -} - -/* -- topics ---------------------------------------------------------------- */ - -div.topic { - border: 1px solid #ccc; - padding: 7px; - margin: 10px 0 10px 0; -} - -p.topic-title { - font-size: 1.1em; - font-weight: bold; - margin-top: 10px; -} - -/* -- admonitions ----------------------------------------------------------- */ - -div.admonition { - margin-top: 10px; - margin-bottom: 10px; - padding: 7px; -} - -div.admonition dt { - font-weight: bold; -} - -p.admonition-title { - margin: 0px 10px 5px 0px; - font-weight: bold; -} - -div.body p.centered { - text-align: center; - margin-top: 25px; -} - -/* -- content of sidebars/topics/admonitions -------------------------------- */ - -div.sidebar > :last-child, -aside.sidebar > :last-child, -div.topic > :last-child, -div.admonition > :last-child { - margin-bottom: 0; -} - -div.sidebar::after, -aside.sidebar::after, -div.topic::after, -div.admonition::after, -blockquote::after { - display: block; - content: ''; - clear: both; -} - -/* -- tables ---------------------------------------------------------------- */ - -table.docutils { - margin-top: 10px; - margin-bottom: 10px; - border: 0; - border-collapse: collapse; -} - -table.align-center { - margin-left: auto; - margin-right: auto; -} - -table.align-default { - margin-left: auto; - margin-right: auto; -} - -table caption span.caption-number { - font-style: italic; -} - -table caption span.caption-text { -} - -table.docutils td, table.docutils th { - padding: 1px 8px 1px 5px; - border-top: 0; - border-left: 0; - border-right: 0; - border-bottom: 1px solid #aaa; -} - -table.footnote td, table.footnote th { - border: 0 !important; -} - -th { - text-align: left; - padding-right: 5px; -} - -table.citation { - border-left: solid 1px gray; - margin-left: 1px; -} - -table.citation td { - border-bottom: none; -} - -th > :first-child, -td > :first-child { - margin-top: 0px; -} - -th > :last-child, -td > :last-child { - margin-bottom: 0px; -} - -/* -- figures --------------------------------------------------------------- */ - -div.figure, figure { - margin: 0.5em; - padding: 0.5em; -} - -div.figure p.caption, figcaption { - padding: 0.3em; -} - -div.figure p.caption span.caption-number, -figcaption span.caption-number { - font-style: italic; -} - -div.figure p.caption span.caption-text, -figcaption span.caption-text { -} - -/* -- field list styles ----------------------------------------------------- */ - -table.field-list td, table.field-list th { - border: 0 !important; -} - -.field-list ul { - margin: 0; - padding-left: 1em; -} - -.field-list p { - margin: 0; -} - -.field-name { - -moz-hyphens: manual; - -ms-hyphens: manual; - -webkit-hyphens: manual; - hyphens: manual; -} - -/* -- hlist styles ---------------------------------------------------------- */ - -table.hlist { - margin: 1em 0; -} - -table.hlist td { - vertical-align: top; -} - -/* -- object description styles --------------------------------------------- */ - -.sig { - font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace; -} - -.sig-name, code.descname { - background-color: transparent; - font-weight: bold; -} - -.sig-name { - font-size: 1.1em; -} - -code.descname { - font-size: 1.2em; -} - -.sig-prename, code.descclassname { - background-color: transparent; -} - -.optional { - font-size: 1.3em; -} - -.sig-paren { - font-size: larger; -} - -.sig-param.n { - font-style: italic; -} - -/* C++ specific styling */ - -.sig-inline.c-texpr, -.sig-inline.cpp-texpr { - font-family: unset; -} - -.sig.c .k, .sig.c .kt, -.sig.cpp .k, .sig.cpp .kt { - color: #0033B3; -} - -.sig.c .m, -.sig.cpp .m { - color: #1750EB; -} - -.sig.c .s, .sig.c .sc, -.sig.cpp .s, .sig.cpp .sc { - color: #067D17; -} - - -/* -- other body styles ----------------------------------------------------- */ - -ol.arabic { - list-style: decimal; -} - -ol.loweralpha { - list-style: lower-alpha; -} - -ol.upperalpha { - list-style: upper-alpha; -} - -ol.lowerroman { - list-style: lower-roman; -} - -ol.upperroman { - list-style: upper-roman; -} - -:not(li) > ol > li:first-child > :first-child, -:not(li) > ul > li:first-child > :first-child { - margin-top: 0px; -} - -:not(li) > ol > li:last-child > :last-child, -:not(li) > ul > li:last-child > :last-child { - margin-bottom: 0px; -} - -ol.simple ol p, -ol.simple ul p, -ul.simple ol p, -ul.simple ul p { - margin-top: 0; -} - -ol.simple > li:not(:first-child) > p, -ul.simple > li:not(:first-child) > p { - margin-top: 0; -} - -ol.simple p, -ul.simple p { - margin-bottom: 0; -} - -dl.footnote > dt, -dl.citation > dt { - float: left; - margin-right: 0.5em; -} - -dl.footnote > dd, -dl.citation > dd { - margin-bottom: 0em; -} - -dl.footnote > dd:after, -dl.citation > dd:after { - content: ""; - clear: both; -} - -dl.field-list { - display: grid; - grid-template-columns: fit-content(30%) auto; -} - -dl.field-list > dt { - font-weight: bold; - word-break: break-word; - padding-left: 0.5em; - padding-right: 5px; -} - -dl.field-list > dt:after { - content: ":"; -} - -dl.field-list > dd { - padding-left: 0.5em; - margin-top: 0em; - margin-left: 0em; - margin-bottom: 0em; -} - -dl { - margin-bottom: 15px; -} - -dd > :first-child { - margin-top: 0px; -} - -dd ul, dd table { - margin-bottom: 10px; -} - -dd { - margin-top: 3px; - margin-bottom: 10px; - margin-left: 30px; -} - -dl > dd:last-child, -dl > dd:last-child > :last-child { - margin-bottom: 0; -} - -dt:target, span.highlighted { - background-color: #fbe54e; -} - -rect.highlighted { - fill: #fbe54e; -} - -dl.glossary dt { - font-weight: bold; - font-size: 1.1em; -} - -.versionmodified { - font-style: italic; -} - -.system-message { - background-color: #fda; - padding: 5px; - border: 3px solid red; -} - -.footnote:target { - background-color: #ffa; -} - -.line-block { - display: block; - margin-top: 1em; - margin-bottom: 1em; -} - -.line-block .line-block { - margin-top: 0; - margin-bottom: 0; - margin-left: 1.5em; -} - -.guilabel, .menuselection { - font-family: sans-serif; -} - -.accelerator { - text-decoration: underline; -} - -.classifier { - font-style: oblique; -} - -.classifier:before { - font-style: normal; - margin: 0 0.5em; - content: ":"; - display: inline-block; -} - -abbr, acronym { - border-bottom: dotted 1px; - cursor: help; -} - -/* -- code displays --------------------------------------------------------- */ - -pre { - overflow: auto; - overflow-y: hidden; /* fixes display issues on Chrome browsers */ -} - -pre, div[class*="highlight-"] { - clear: both; -} - -span.pre { - -moz-hyphens: none; - -ms-hyphens: none; - -webkit-hyphens: none; - hyphens: none; - white-space: nowrap; -} - -div[class*="highlight-"] { - margin: 1em 0; -} - -td.linenos pre { - border: 0; - background-color: transparent; - color: #aaa; -} - -table.highlighttable { - display: block; -} - -table.highlighttable tbody { - display: block; -} - -table.highlighttable tr { - display: flex; -} - -table.highlighttable td { - margin: 0; - padding: 0; -} - -table.highlighttable td.linenos { - padding-right: 0.5em; -} - -table.highlighttable td.code { - flex: 1; - overflow: hidden; -} - -.highlight .hll { - display: block; -} - -div.highlight pre, -table.highlighttable pre { - margin: 0; -} - -div.code-block-caption + div { - margin-top: 0; -} - -div.code-block-caption { - margin-top: 1em; - padding: 2px 5px; - font-size: small; -} - -div.code-block-caption code { - background-color: transparent; -} - -table.highlighttable td.linenos, -span.linenos, -div.highlight span.gp { /* gp: Generic.Prompt */ - user-select: none; - -webkit-user-select: text; /* Safari fallback only */ - -webkit-user-select: none; /* Chrome/Safari */ - -moz-user-select: none; /* Firefox */ - -ms-user-select: none; /* IE10+ */ -} - -div.code-block-caption span.caption-number { - padding: 0.1em 0.3em; - font-style: italic; -} - -div.code-block-caption span.caption-text { -} - -div.literal-block-wrapper { - margin: 1em 0; -} - -code.xref, a code { - background-color: transparent; - font-weight: bold; -} - -h1 code, h2 code, h3 code, h4 code, h5 code, h6 code { - background-color: transparent; -} - -.viewcode-link { - float: right; -} - -.viewcode-back { - float: right; - font-family: sans-serif; -} - -div.viewcode-block:target { - margin: -1px -10px; - padding: 0 10px; -} - -/* -- math display ---------------------------------------------------------- */ - -img.math { - vertical-align: middle; -} - -div.body div.math p { - text-align: center; -} - -span.eqno { - float: right; -} - -span.eqno a.headerlink { - position: absolute; - z-index: 1; -} - -div.math:hover a.headerlink { - visibility: visible; -} - -/* -- printout stylesheet --------------------------------------------------- */ - -@media print { - div.document, - div.documentwrapper, - div.bodywrapper { - margin: 0 !important; - width: 100%; - } - - div.sphinxsidebar, - div.related, - div.footer, - #top-link { - display: none; - } -} \ No newline at end of file diff --git a/lectures/_build/html/_static/check-solid.svg b/lectures/_build/html/_static/check-solid.svg deleted file mode 100644 index 92fad4b5c..000000000 --- a/lectures/_build/html/_static/check-solid.svg +++ /dev/null @@ -1,4 +0,0 @@ - - - - diff --git a/lectures/_build/html/_static/clipboard.min.js b/lectures/_build/html/_static/clipboard.min.js deleted file mode 100644 index 54b3c4638..000000000 --- a/lectures/_build/html/_static/clipboard.min.js +++ /dev/null @@ -1,7 +0,0 @@ -/*! - * clipboard.js v2.0.8 - * https://clipboardjs.com/ - * - * Licensed MIT © Zeno Rocha - */ -!function(t,e){"object"==typeof exports&&"object"==typeof module?module.exports=e():"function"==typeof define&&define.amd?define([],e):"object"==typeof exports?exports.ClipboardJS=e():t.ClipboardJS=e()}(this,function(){return n={686:function(t,e,n){"use strict";n.d(e,{default:function(){return o}});var e=n(279),i=n.n(e),e=n(370),u=n.n(e),e=n(817),c=n.n(e);function a(t){try{return document.execCommand(t)}catch(t){return}}var f=function(t){t=c()(t);return a("cut"),t};var l=function(t){var e,n,o,r=1 - - - - diff --git a/lectures/_build/html/_static/copybutton.css b/lectures/_build/html/_static/copybutton.css deleted file mode 100644 index f1916ec7d..000000000 --- a/lectures/_build/html/_static/copybutton.css +++ /dev/null @@ -1,94 +0,0 @@ -/* Copy buttons */ -button.copybtn { - position: absolute; - display: flex; - top: .3em; - right: .3em; - width: 1.7em; - height: 1.7em; - opacity: 0; - transition: opacity 0.3s, border .3s, background-color .3s; - user-select: none; - padding: 0; - border: none; - outline: none; - border-radius: 0.4em; - /* The colors that GitHub uses */ - border: #1b1f2426 1px solid; - background-color: #f6f8fa; - color: #57606a; -} - -button.copybtn.success { - border-color: #22863a; - color: #22863a; -} - -button.copybtn svg { - stroke: currentColor; - width: 1.5em; - height: 1.5em; - padding: 0.1em; -} - -div.highlight { - position: relative; -} - -/* Show the copybutton */ -.highlight:hover button.copybtn, button.copybtn.success { - opacity: 1; -} - -.highlight button.copybtn:hover { - background-color: rgb(235, 235, 235); -} - -.highlight button.copybtn:active { - background-color: rgb(187, 187, 187); -} - -/** - * A minimal CSS-only tooltip copied from: - * https://codepen.io/mildrenben/pen/rVBrpK - * - * To use, write HTML like the following: - * - *

Short

- */ - .o-tooltip--left { - position: relative; - } - - .o-tooltip--left:after { - opacity: 0; - visibility: hidden; - position: absolute; - content: attr(data-tooltip); - padding: .2em; - font-size: .8em; - left: -.2em; - background: grey; - color: white; - white-space: nowrap; - z-index: 2; - border-radius: 2px; - transform: translateX(-102%) translateY(0); - transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); -} - -.o-tooltip--left:hover:after { - display: block; - opacity: 1; - visibility: visible; - transform: translateX(-100%) translateY(0); - transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1); - transition-delay: .5s; -} - -/* By default the copy button shouldn't show up when printing a page */ -@media print { - button.copybtn { - display: none; - } -} diff --git a/lectures/_build/html/_static/copybutton.js b/lectures/_build/html/_static/copybutton.js deleted file mode 100644 index 02c5c82d9..000000000 --- a/lectures/_build/html/_static/copybutton.js +++ /dev/null @@ -1,248 +0,0 @@ -// Localization support -const messages = { - 'en': { - 'copy': 'Copy', - 'copy_to_clipboard': 'Copy to clipboard', - 'copy_success': 'Copied!', - 'copy_failure': 'Failed to copy', - }, - 'es' : { - 'copy': 'Copiar', - 'copy_to_clipboard': 'Copiar al portapapeles', - 'copy_success': '¡Copiado!', - 'copy_failure': 'Error al copiar', - }, - 'de' : { - 'copy': 'Kopieren', - 'copy_to_clipboard': 'In die Zwischenablage kopieren', - 'copy_success': 'Kopiert!', - 'copy_failure': 'Fehler beim Kopieren', - }, - 'fr' : { - 'copy': 'Copier', - 'copy_to_clipboard': 'Copié dans le presse-papier', - 'copy_success': 'Copié !', - 'copy_failure': 'Échec de la copie', - }, - 'ru': { - 'copy': 'Скопировать', - 'copy_to_clipboard': 'Скопировать в буфер', - 'copy_success': 'Скопировано!', - 'copy_failure': 'Не удалось скопировать', - }, - 'zh-CN': { - 'copy': '复制', - 'copy_to_clipboard': '复制到剪贴板', - 'copy_success': '复制成功!', - 'copy_failure': '复制失败', - }, - 'it' : { - 'copy': 'Copiare', - 'copy_to_clipboard': 'Copiato negli appunti', - 'copy_success': 'Copiato!', - 'copy_failure': 'Errore durante la copia', - } -} - -let locale = 'en' -if( document.documentElement.lang !== undefined - && messages[document.documentElement.lang] !== undefined ) { - locale = document.documentElement.lang -} - -let doc_url_root = DOCUMENTATION_OPTIONS.URL_ROOT; -if (doc_url_root == '#') { - doc_url_root = ''; -} - -/** - * SVG files for our copy buttons - */ -let iconCheck = ` - ${messages[locale]['copy_success']} - - -` - -// If the user specified their own SVG use that, otherwise use the default -let iconCopy = ``; -if (!iconCopy) { - iconCopy = ` - ${messages[locale]['copy_to_clipboard']} - - - -` -} - -/** - * Set up copy/paste for code blocks - */ - -const runWhenDOMLoaded = cb => { - if (document.readyState != 'loading') { - cb() - } else if (document.addEventListener) { - document.addEventListener('DOMContentLoaded', cb) - } else { - document.attachEvent('onreadystatechange', function() { - if (document.readyState == 'complete') cb() - }) - } -} - -const codeCellId = index => `codecell${index}` - -// Clears selected text since ClipboardJS will select the text when copying -const clearSelection = () => { - if (window.getSelection) { - window.getSelection().removeAllRanges() - } else if (document.selection) { - document.selection.empty() - } -} - -// Changes tooltip text for a moment, then changes it back -// We want the timeout of our `success` class to be a bit shorter than the -// tooltip and icon change, so that we can hide the icon before changing back. -var timeoutIcon = 2000; -var timeoutSuccessClass = 1500; - -const temporarilyChangeTooltip = (el, oldText, newText) => { - el.setAttribute('data-tooltip', newText) - el.classList.add('success') - // Remove success a little bit sooner than we change the tooltip - // So that we can use CSS to hide the copybutton first - setTimeout(() => el.classList.remove('success'), timeoutSuccessClass) - setTimeout(() => el.setAttribute('data-tooltip', oldText), timeoutIcon) -} - -// Changes the copy button icon for two seconds, then changes it back -const temporarilyChangeIcon = (el) => { - el.innerHTML = iconCheck; - setTimeout(() => {el.innerHTML = iconCopy}, timeoutIcon) -} - -const addCopyButtonToCodeCells = () => { - // If ClipboardJS hasn't loaded, wait a bit and try again. This - // happens because we load ClipboardJS asynchronously. - if (window.ClipboardJS === undefined) { - setTimeout(addCopyButtonToCodeCells, 250) - return - } - - // Add copybuttons to all of our code cells - const COPYBUTTON_SELECTOR = 'div.highlight pre'; - const codeCells = document.querySelectorAll(COPYBUTTON_SELECTOR) - codeCells.forEach((codeCell, index) => { - const id = codeCellId(index) - codeCell.setAttribute('id', id) - - const clipboardButton = id => - `` - codeCell.insertAdjacentHTML('afterend', clipboardButton(id)) - }) - -function escapeRegExp(string) { - return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string -} - -/** - * Removes excluded text from a Node. - * - * @param {Node} target Node to filter. - * @param {string} exclude CSS selector of nodes to exclude. - * @returns {DOMString} Text from `target` with text removed. - */ -function filterText(target, exclude) { - const clone = target.cloneNode(true); // clone as to not modify the live DOM - if (exclude) { - // remove excluded nodes - clone.querySelectorAll(exclude).forEach(node => node.remove()); - } - return clone.innerText; -} - -// Callback when a copy button is clicked. Will be passed the node that was clicked -// should then grab the text and replace pieces of text that shouldn't be used in output -function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { - var regexp; - var match; - - // Do we check for line continuation characters and "HERE-documents"? - var useLineCont = !!lineContinuationChar - var useHereDoc = !!hereDocDelim - - // create regexp to capture prompt and remaining line - if (isRegexp) { - regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') - } else { - regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') - } - - const outputLines = []; - var promptFound = false; - var gotLineCont = false; - var gotHereDoc = false; - const lineGotPrompt = []; - for (const line of textContent.split('\n')) { - match = line.match(regexp) - if (match || gotLineCont || gotHereDoc) { - promptFound = regexp.test(line) - lineGotPrompt.push(promptFound) - if (removePrompts && promptFound) { - outputLines.push(match[2]) - } else { - outputLines.push(line) - } - gotLineCont = line.endsWith(lineContinuationChar) & useLineCont - if (line.includes(hereDocDelim) & useHereDoc) - gotHereDoc = !gotHereDoc - } else if (!onlyCopyPromptLines) { - outputLines.push(line) - } else if (copyEmptyLines && line.trim() === '') { - outputLines.push(line) - } - } - - // If no lines with the prompt were found then just use original lines - if (lineGotPrompt.some(v => v === true)) { - textContent = outputLines.join('\n'); - } - - // Remove a trailing newline to avoid auto-running when pasting - if (textContent.endsWith("\n")) { - textContent = textContent.slice(0, -1) - } - return textContent -} - - -var copyTargetText = (trigger) => { - var target = document.querySelector(trigger.attributes['data-clipboard-target'].value); - - // get filtered text - let exclude = '.linenos, .gp'; - - let text = filterText(target, exclude); - return formatCopyText(text, '', false, true, true, true, '', '') -} - - // Initialize with a callback so we can modify the text before copy - const clipboard = new ClipboardJS('.copybtn', {text: copyTargetText}) - - // Update UI with error/success messages - clipboard.on('success', event => { - clearSelection() - temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_success']) - temporarilyChangeIcon(event.trigger) - }) - - clipboard.on('error', event => { - temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_failure']) - }) -} - -runWhenDOMLoaded(addCopyButtonToCodeCells) \ No newline at end of file diff --git a/lectures/_build/html/_static/copybutton_funcs.js b/lectures/_build/html/_static/copybutton_funcs.js deleted file mode 100644 index dbe1aaad7..000000000 --- a/lectures/_build/html/_static/copybutton_funcs.js +++ /dev/null @@ -1,73 +0,0 @@ -function escapeRegExp(string) { - return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string -} - -/** - * Removes excluded text from a Node. - * - * @param {Node} target Node to filter. - * @param {string} exclude CSS selector of nodes to exclude. - * @returns {DOMString} Text from `target` with text removed. - */ -export function filterText(target, exclude) { - const clone = target.cloneNode(true); // clone as to not modify the live DOM - if (exclude) { - // remove excluded nodes - clone.querySelectorAll(exclude).forEach(node => node.remove()); - } - return clone.innerText; -} - -// Callback when a copy button is clicked. Will be passed the node that was clicked -// should then grab the text and replace pieces of text that shouldn't be used in output -export function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") { - var regexp; - var match; - - // Do we check for line continuation characters and "HERE-documents"? - var useLineCont = !!lineContinuationChar - var useHereDoc = !!hereDocDelim - - // create regexp to capture prompt and remaining line - if (isRegexp) { - regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)') - } else { - regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)') - } - - const outputLines = []; - var promptFound = false; - var gotLineCont = false; - var gotHereDoc = false; - const lineGotPrompt = []; - for (const line of textContent.split('\n')) { - match = line.match(regexp) - if (match || gotLineCont || gotHereDoc) { - promptFound = regexp.test(line) - lineGotPrompt.push(promptFound) - if (removePrompts && promptFound) { - outputLines.push(match[2]) - } else { - outputLines.push(line) - } - gotLineCont = line.endsWith(lineContinuationChar) & useLineCont - if (line.includes(hereDocDelim) & useHereDoc) - gotHereDoc = !gotHereDoc - } else if (!onlyCopyPromptLines) { - outputLines.push(line) - } else if (copyEmptyLines && line.trim() === '') { - outputLines.push(line) - } - } - - // If no lines with the prompt were found then just use original lines - if (lineGotPrompt.some(v => v === true)) { - textContent = outputLines.join('\n'); - } - - // Remove a trailing newline to avoid auto-running when pasting - if (textContent.endsWith("\n")) { - textContent = textContent.slice(0, -1) - } - return textContent -} diff --git a/lectures/_build/html/_static/css/blank.css b/lectures/_build/html/_static/css/blank.css deleted file mode 100644 index 8a686ec75..000000000 --- a/lectures/_build/html/_static/css/blank.css +++ /dev/null @@ -1,2 +0,0 @@ -/* This file is intentionally left blank to override the stylesheet of the -parent theme via theme.conf. The parent style we import directly in theme.css */ \ No newline at end of file diff --git a/lectures/_build/html/_static/css/index.ff1ffe594081f20da1ef19478df9384b.css b/lectures/_build/html/_static/css/index.ff1ffe594081f20da1ef19478df9384b.css deleted file mode 100644 index 9b1c5d792..000000000 --- a/lectures/_build/html/_static/css/index.ff1ffe594081f20da1ef19478df9384b.css +++ /dev/null @@ -1,6 +0,0 @@ -/*! - * Bootstrap v4.5.0 (https://getbootstrap.com/) - * Copyright 2011-2020 The Bootstrap Authors - * Copyright 2011-2020 Twitter, Inc. - * Licensed under MIT (https://github.com/twbs/bootstrap/blob/master/LICENSE) - */:root{--blue:#007bff;--indigo:#6610f2;--purple:#6f42c1;--pink:#e83e8c;--red:#dc3545;--orange:#fd7e14;--yellow:#ffc107;--green:#28a745;--teal:#20c997;--cyan:#17a2b8;--white:#fff;--gray:#6c757d;--gray-dark:#343a40;--primary:#007bff;--secondary:#6c757d;--success:#28a745;--info:#17a2b8;--warning:#ffc107;--danger:#dc3545;--light:#f8f9fa;--dark:#343a40;--breakpoint-xs:0;--breakpoint-sm:540px;--breakpoint-md:720px;--breakpoint-lg:960px;--breakpoint-xl:1200px;--font-family-sans-serif:-apple-system,BlinkMacSystemFont,"Segoe UI",Roboto,"Helvetica Neue",Arial,"Noto Sans",sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";--font-family-monospace:SFMono-Regular,Menlo,Monaco,Consolas,"Liberation Mono","Courier New",monospace}*,:after,:before{box-sizing:border-box}html{font-family:sans-serif;line-height:1.15;-webkit-text-size-adjust:100%;-webkit-tap-highlight-color:rgba(0,0,0,0)}article,aside,figcaption,figure,footer,header,hgroup,main,nav,section{display:block}body{margin:0;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji;font-size:1rem;line-height:1.5;color:#212529;text-align:left}[tabindex="-1"]:focus:not(:focus-visible){outline:0!important}hr{box-sizing:content-box;height:0;overflow:visible}h1,h2,h3,h4,h5,h6{margin-top:0;margin-bottom:.5rem}p{margin-top:0;margin-bottom:1rem}abbr[data-original-title],abbr[title]{text-decoration:underline;text-decoration:underline dotted;cursor:help;border-bottom:0;text-decoration-skip-ink:none}address{font-style:normal;line-height:inherit}address,dl,ol,ul{margin-bottom:1rem}dl,ol,ul{margin-top:0}ol ol,ol ul,ul ol,ul ul{margin-bottom:0}dt{font-weight:700}dd{margin-bottom:.5rem;margin-left:0}blockquote{margin:0 0 1rem}b,strong{font-weight:bolder}small{font-size:80%}sub,sup{position:relative;font-size:75%;line-height:0;vertical-align:baseline}sub{bottom:-.25em}sup{top:-.5em}a{color:#007bff;background-color:transparent}a:hover{color:#0056b3}a:not([href]),a:not([href]):hover{color:inherit;text-decoration:none}code,kbd,pre,samp{font-family:SFMono-Regular,Menlo,Monaco,Consolas,Liberation Mono,Courier New,monospace;font-size:1em}pre{margin-top:0;margin-bottom:1rem;overflow:auto;-ms-overflow-style:scrollbar}figure{margin:0 0 1rem}img{border-style:none}img,svg{vertical-align:middle}svg{overflow:hidden}table{border-collapse:collapse}caption{padding-top:.75rem;padding-bottom:.75rem;color:#6c757d;text-align:left;caption-side:bottom}th{text-align:inherit}label{display:inline-block;margin-bottom:.5rem}button{border-radius:0}button:focus{outline:1px dotted;outline:5px auto -webkit-focus-ring-color}button,input,optgroup,select,textarea{margin:0;font-family:inherit;font-size:inherit;line-height:inherit}button,input{overflow:visible}button,select{text-transform:none}[role=button]{cursor:pointer}select{word-wrap:normal}[type=button],[type=reset],[type=submit],button{-webkit-appearance:button}[type=button]:not(:disabled),[type=reset]:not(:disabled),[type=submit]:not(:disabled),button:not(:disabled){cursor:pointer}[type=button]::-moz-focus-inner,[type=reset]::-moz-focus-inner,[type=submit]::-moz-focus-inner,button::-moz-focus-inner{padding:0;border-style:none}input[type=checkbox],input[type=radio]{box-sizing:border-box;padding:0}textarea{overflow:auto;resize:vertical}fieldset{min-width:0;padding:0;margin:0;border:0}legend{display:block;width:100%;max-width:100%;padding:0;margin-bottom:.5rem;font-size:1.5rem;line-height:inherit;color:inherit;white-space:normal}progress{vertical-align:baseline}[type=number]::-webkit-inner-spin-button,[type=number]::-webkit-outer-spin-button{height:auto}[type=search]{outline-offset:-2px;-webkit-appearance:none}[type=search]::-webkit-search-decoration{-webkit-appearance:none}::-webkit-file-upload-button{font:inherit;-webkit-appearance:button}output{display:inline-block}summary{display:list-item;cursor:pointer}template{display:none}[hidden]{display:none!important}.h1,.h2,.h3,.h4,.h5,.h6,h1,h2,h3,h4,h5,h6{margin-bottom:.5rem;font-weight:500;line-height:1.2}.h1,h1{font-size:2.5rem}.h2,h2{font-size:2rem}.h3,h3{font-size:1.75rem}.h4,h4{font-size:1.5rem}.h5,h5{font-size:1.25rem}.h6,h6{font-size:1rem}.lead{font-size:1.25rem;font-weight:300}.display-1{font-size:6rem}.display-1,.display-2{font-weight:300;line-height:1.2}.display-2{font-size:5.5rem}.display-3{font-size:4.5rem}.display-3,.display-4{font-weight:300;line-height:1.2}.display-4{font-size:3.5rem}hr{margin-top:1rem;margin-bottom:1rem;border-top:1px solid rgba(0,0,0,.1)}.small,small{font-size:80%;font-weight:400}.mark,mark{padding:.2em;background-color:#fcf8e3}.list-inline,.list-unstyled{padding-left:0;list-style:none}.list-inline-item{display:inline-block}.list-inline-item:not(:last-child){margin-right:.5rem}.initialism{font-size:90%;text-transform:uppercase}.blockquote{margin-bottom:1rem;font-size:1.25rem}.blockquote-footer{display:block;font-size:80%;color:#6c757d}.blockquote-footer:before{content:"\2014\00A0"}.img-fluid,.img-thumbnail{max-width:100%;height:auto}.img-thumbnail{padding:.25rem;background-color:#fff;border:1px solid #dee2e6;border-radius:.25rem}.figure{display:inline-block}.figure-img{margin-bottom:.5rem;line-height:1}.figure-caption{font-size:90%;color:#6c757d}code{font-size:87.5%;color:#e83e8c;word-wrap:break-word}a>code{color:inherit}kbd{padding:.2rem .4rem;font-size:87.5%;color:#fff;background-color:#212529;border-radius:.2rem}kbd kbd{padding:0;font-size:100%;font-weight:700}pre{display:block;font-size:87.5%;color:#212529}pre code{font-size:inherit;color:inherit;word-break:normal}.pre-scrollable{max-height:340px;overflow-y:scroll}.container{width:100%;padding-right:15px;padding-left:15px;margin-right:auto;margin-left:auto}@media (min-width:540px){.container{max-width:540px}}@media (min-width:720px){.container{max-width:720px}}@media (min-width:960px){.container{max-width:960px}}@media (min-width:1200px){.container{max-width:1400px}}.container-fluid,.container-lg,.container-md,.container-sm,.container-xl{width:100%;padding-right:15px;padding-left:15px;margin-right:auto;margin-left:auto}@media (min-width:540px){.container,.container-sm{max-width:540px}}@media (min-width:720px){.container,.container-md,.container-sm{max-width:720px}}@media (min-width:960px){.container,.container-lg,.container-md,.container-sm{max-width:960px}}@media (min-width:1200px){.container,.container-lg,.container-md,.container-sm,.container-xl{max-width:1400px}}.row{display:flex;flex-wrap:wrap;margin-right:-15px;margin-left:-15px}.no-gutters{margin-right:0;margin-left:0}.no-gutters>.col,.no-gutters>[class*=col-]{padding-right:0;padding-left:0}.col,.col-1,.col-2,.col-3,.col-4,.col-5,.col-6,.col-7,.col-8,.col-9,.col-10,.col-11,.col-12,.col-auto,.col-lg,.col-lg-1,.col-lg-2,.col-lg-3,.col-lg-4,.col-lg-5,.col-lg-6,.col-lg-7,.col-lg-8,.col-lg-9,.col-lg-10,.col-lg-11,.col-lg-12,.col-lg-auto,.col-md,.col-md-1,.col-md-2,.col-md-3,.col-md-4,.col-md-5,.col-md-6,.col-md-7,.col-md-8,.col-md-9,.col-md-10,.col-md-11,.col-md-12,.col-md-auto,.col-sm,.col-sm-1,.col-sm-2,.col-sm-3,.col-sm-4,.col-sm-5,.col-sm-6,.col-sm-7,.col-sm-8,.col-sm-9,.col-sm-10,.col-sm-11,.col-sm-12,.col-sm-auto,.col-xl,.col-xl-1,.col-xl-2,.col-xl-3,.col-xl-4,.col-xl-5,.col-xl-6,.col-xl-7,.col-xl-8,.col-xl-9,.col-xl-10,.col-xl-11,.col-xl-12,.col-xl-auto{position:relative;width:100%;padding-right:15px;padding-left:15px}.col{flex-basis:0;flex-grow:1;min-width:0;max-width:100%}.row-cols-1>*{flex:0 0 100%;max-width:100%}.row-cols-2>*{flex:0 0 50%;max-width:50%}.row-cols-3>*{flex:0 0 33.33333%;max-width:33.33333%}.row-cols-4>*{flex:0 0 25%;max-width:25%}.row-cols-5>*{flex:0 0 20%;max-width:20%}.row-cols-6>*{flex:0 0 16.66667%;max-width:16.66667%}.col-auto{flex:0 0 auto;width:auto;max-width:100%}.col-1{flex:0 0 8.33333%;max-width:8.33333%}.col-2{flex:0 0 16.66667%;max-width:16.66667%}.col-3{flex:0 0 25%;max-width:25%}.col-4{flex:0 0 33.33333%;max-width:33.33333%}.col-5{flex:0 0 41.66667%;max-width:41.66667%}.col-6{flex:0 0 50%;max-width:50%}.col-7{flex:0 0 58.33333%;max-width:58.33333%}.col-8{flex:0 0 66.66667%;max-width:66.66667%}.col-9{flex:0 0 75%;max-width:75%}.col-10{flex:0 0 83.33333%;max-width:83.33333%}.col-11{flex:0 0 91.66667%;max-width:91.66667%}.col-12{flex:0 0 100%;max-width:100%}.order-first{order:-1}.order-last{order:13}.order-0{order:0}.order-1{order:1}.order-2{order:2}.order-3{order:3}.order-4{order:4}.order-5{order:5}.order-6{order:6}.order-7{order:7}.order-8{order:8}.order-9{order:9}.order-10{order:10}.order-11{order:11}.order-12{order:12}.offset-1{margin-left:8.33333%}.offset-2{margin-left:16.66667%}.offset-3{margin-left:25%}.offset-4{margin-left:33.33333%}.offset-5{margin-left:41.66667%}.offset-6{margin-left:50%}.offset-7{margin-left:58.33333%}.offset-8{margin-left:66.66667%}.offset-9{margin-left:75%}.offset-10{margin-left:83.33333%}.offset-11{margin-left:91.66667%}@media (min-width:540px){.col-sm{flex-basis:0;flex-grow:1;min-width:0;max-width:100%}.row-cols-sm-1>*{flex:0 0 100%;max-width:100%}.row-cols-sm-2>*{flex:0 0 50%;max-width:50%}.row-cols-sm-3>*{flex:0 0 33.33333%;max-width:33.33333%}.row-cols-sm-4>*{flex:0 0 25%;max-width:25%}.row-cols-sm-5>*{flex:0 0 20%;max-width:20%}.row-cols-sm-6>*{flex:0 0 16.66667%;max-width:16.66667%}.col-sm-auto{flex:0 0 auto;width:auto;max-width:100%}.col-sm-1{flex:0 0 8.33333%;max-width:8.33333%}.col-sm-2{flex:0 0 16.66667%;max-width:16.66667%}.col-sm-3{flex:0 0 25%;max-width:25%}.col-sm-4{flex:0 0 33.33333%;max-width:33.33333%}.col-sm-5{flex:0 0 41.66667%;max-width:41.66667%}.col-sm-6{flex:0 0 50%;max-width:50%}.col-sm-7{flex:0 0 58.33333%;max-width:58.33333%}.col-sm-8{flex:0 0 66.66667%;max-width:66.66667%}.col-sm-9{flex:0 0 75%;max-width:75%}.col-sm-10{flex:0 0 83.33333%;max-width:83.33333%}.col-sm-11{flex:0 0 91.66667%;max-width:91.66667%}.col-sm-12{flex:0 0 100%;max-width:100%}.order-sm-first{order:-1}.order-sm-last{order:13}.order-sm-0{order:0}.order-sm-1{order:1}.order-sm-2{order:2}.order-sm-3{order:3}.order-sm-4{order:4}.order-sm-5{order:5}.order-sm-6{order:6}.order-sm-7{order:7}.order-sm-8{order:8}.order-sm-9{order:9}.order-sm-10{order:10}.order-sm-11{order:11}.order-sm-12{order:12}.offset-sm-0{margin-left:0}.offset-sm-1{margin-left:8.33333%}.offset-sm-2{margin-left:16.66667%}.offset-sm-3{margin-left:25%}.offset-sm-4{margin-left:33.33333%}.offset-sm-5{margin-left:41.66667%}.offset-sm-6{margin-left:50%}.offset-sm-7{margin-left:58.33333%}.offset-sm-8{margin-left:66.66667%}.offset-sm-9{margin-left:75%}.offset-sm-10{margin-left:83.33333%}.offset-sm-11{margin-left:91.66667%}}@media (min-width:720px){.col-md{flex-basis:0;flex-grow:1;min-width:0;max-width:100%}.row-cols-md-1>*{flex:0 0 100%;max-width:100%}.row-cols-md-2>*{flex:0 0 50%;max-width:50%}.row-cols-md-3>*{flex:0 0 33.33333%;max-width:33.33333%}.row-cols-md-4>*{flex:0 0 25%;max-width:25%}.row-cols-md-5>*{flex:0 0 20%;max-width:20%}.row-cols-md-6>*{flex:0 0 16.66667%;max-width:16.66667%}.col-md-auto{flex:0 0 auto;width:auto;max-width:100%}.col-md-1{flex:0 0 8.33333%;max-width:8.33333%}.col-md-2{flex:0 0 16.66667%;max-width:16.66667%}.col-md-3{flex:0 0 25%;max-width:25%}.col-md-4{flex:0 0 33.33333%;max-width:33.33333%}.col-md-5{flex:0 0 41.66667%;max-width:41.66667%}.col-md-6{flex:0 0 50%;max-width:50%}.col-md-7{flex:0 0 58.33333%;max-width:58.33333%}.col-md-8{flex:0 0 66.66667%;max-width:66.66667%}.col-md-9{flex:0 0 75%;max-width:75%}.col-md-10{flex:0 0 83.33333%;max-width:83.33333%}.col-md-11{flex:0 0 91.66667%;max-width:91.66667%}.col-md-12{flex:0 0 100%;max-width:100%}.order-md-first{order:-1}.order-md-last{order:13}.order-md-0{order:0}.order-md-1{order:1}.order-md-2{order:2}.order-md-3{order:3}.order-md-4{order:4}.order-md-5{order:5}.order-md-6{order:6}.order-md-7{order:7}.order-md-8{order:8}.order-md-9{order:9}.order-md-10{order:10}.order-md-11{order:11}.order-md-12{order:12}.offset-md-0{margin-left:0}.offset-md-1{margin-left:8.33333%}.offset-md-2{margin-left:16.66667%}.offset-md-3{margin-left:25%}.offset-md-4{margin-left:33.33333%}.offset-md-5{margin-left:41.66667%}.offset-md-6{margin-left:50%}.offset-md-7{margin-left:58.33333%}.offset-md-8{margin-left:66.66667%}.offset-md-9{margin-left:75%}.offset-md-10{margin-left:83.33333%}.offset-md-11{margin-left:91.66667%}}@media (min-width:960px){.col-lg{flex-basis:0;flex-grow:1;min-width:0;max-width:100%}.row-cols-lg-1>*{flex:0 0 100%;max-width:100%}.row-cols-lg-2>*{flex:0 0 50%;max-width:50%}.row-cols-lg-3>*{flex:0 0 33.33333%;max-width:33.33333%}.row-cols-lg-4>*{flex:0 0 25%;max-width:25%}.row-cols-lg-5>*{flex:0 0 20%;max-width:20%}.row-cols-lg-6>*{flex:0 0 16.66667%;max-width:16.66667%}.col-lg-auto{flex:0 0 auto;width:auto;max-width:100%}.col-lg-1{flex:0 0 8.33333%;max-width:8.33333%}.col-lg-2{flex:0 0 16.66667%;max-width:16.66667%}.col-lg-3{flex:0 0 25%;max-width:25%}.col-lg-4{flex:0 0 33.33333%;max-width:33.33333%}.col-lg-5{flex:0 0 41.66667%;max-width:41.66667%}.col-lg-6{flex:0 0 50%;max-width:50%}.col-lg-7{flex:0 0 58.33333%;max-width:58.33333%}.col-lg-8{flex:0 0 66.66667%;max-width:66.66667%}.col-lg-9{flex:0 0 75%;max-width:75%}.col-lg-10{flex:0 0 83.33333%;max-width:83.33333%}.col-lg-11{flex:0 0 91.66667%;max-width:91.66667%}.col-lg-12{flex:0 0 100%;max-width:100%}.order-lg-first{order:-1}.order-lg-last{order:13}.order-lg-0{order:0}.order-lg-1{order:1}.order-lg-2{order:2}.order-lg-3{order:3}.order-lg-4{order:4}.order-lg-5{order:5}.order-lg-6{order:6}.order-lg-7{order:7}.order-lg-8{order:8}.order-lg-9{order:9}.order-lg-10{order:10}.order-lg-11{order:11}.order-lg-12{order:12}.offset-lg-0{margin-left:0}.offset-lg-1{margin-left:8.33333%}.offset-lg-2{margin-left:16.66667%}.offset-lg-3{margin-left:25%}.offset-lg-4{margin-left:33.33333%}.offset-lg-5{margin-left:41.66667%}.offset-lg-6{margin-left:50%}.offset-lg-7{margin-left:58.33333%}.offset-lg-8{margin-left:66.66667%}.offset-lg-9{margin-left:75%}.offset-lg-10{margin-left:83.33333%}.offset-lg-11{margin-left:91.66667%}}@media (min-width:1200px){.col-xl{flex-basis:0;flex-grow:1;min-width:0;max-width:100%}.row-cols-xl-1>*{flex:0 0 100%;max-width:100%}.row-cols-xl-2>*{flex:0 0 50%;max-width:50%}.row-cols-xl-3>*{flex:0 0 33.33333%;max-width:33.33333%}.row-cols-xl-4>*{flex:0 0 25%;max-width:25%}.row-cols-xl-5>*{flex:0 0 20%;max-width:20%}.row-cols-xl-6>*{flex:0 0 16.66667%;max-width:16.66667%}.col-xl-auto{flex:0 0 auto;width:auto;max-width:100%}.col-xl-1{flex:0 0 8.33333%;max-width:8.33333%}.col-xl-2{flex:0 0 16.66667%;max-width:16.66667%}.col-xl-3{flex:0 0 25%;max-width:25%}.col-xl-4{flex:0 0 33.33333%;max-width:33.33333%}.col-xl-5{flex:0 0 41.66667%;max-width:41.66667%}.col-xl-6{flex:0 0 50%;max-width:50%}.col-xl-7{flex:0 0 58.33333%;max-width:58.33333%}.col-xl-8{flex:0 0 66.66667%;max-width:66.66667%}.col-xl-9{flex:0 0 75%;max-width:75%}.col-xl-10{flex:0 0 83.33333%;max-width:83.33333%}.col-xl-11{flex:0 0 91.66667%;max-width:91.66667%}.col-xl-12{flex:0 0 100%;max-width:100%}.order-xl-first{order:-1}.order-xl-last{order:13}.order-xl-0{order:0}.order-xl-1{order:1}.order-xl-2{order:2}.order-xl-3{order:3}.order-xl-4{order:4}.order-xl-5{order:5}.order-xl-6{order:6}.order-xl-7{order:7}.order-xl-8{order:8}.order-xl-9{order:9}.order-xl-10{order:10}.order-xl-11{order:11}.order-xl-12{order:12}.offset-xl-0{margin-left:0}.offset-xl-1{margin-left:8.33333%}.offset-xl-2{margin-left:16.66667%}.offset-xl-3{margin-left:25%}.offset-xl-4{margin-left:33.33333%}.offset-xl-5{margin-left:41.66667%}.offset-xl-6{margin-left:50%}.offset-xl-7{margin-left:58.33333%}.offset-xl-8{margin-left:66.66667%}.offset-xl-9{margin-left:75%}.offset-xl-10{margin-left:83.33333%}.offset-xl-11{margin-left:91.66667%}}.table{width:100%;margin-bottom:1rem;color:#212529}.table td,.table th{padding:.75rem;vertical-align:top;border-top:1px solid #dee2e6}.table thead th{vertical-align:bottom;border-bottom:2px solid #dee2e6}.table tbody+tbody{border-top:2px solid #dee2e6}.table-sm td,.table-sm th{padding:.3rem}.table-bordered,.table-bordered td,.table-bordered th{border:1px solid #dee2e6}.table-bordered thead td,.table-bordered thead th{border-bottom-width:2px}.table-borderless tbody+tbody,.table-borderless td,.table-borderless th,.table-borderless thead th{border:0}.table-striped tbody tr:nth-of-type(odd){background-color:rgba(0,0,0,.05)}.table-hover tbody tr:hover{color:#212529;background-color:rgba(0,0,0,.075)}.table-primary,.table-primary>td,.table-primary>th{background-color:#b8daff}.table-primary tbody+tbody,.table-primary td,.table-primary th,.table-primary thead th{border-color:#7abaff}.table-hover .table-primary:hover,.table-hover .table-primary:hover>td,.table-hover .table-primary:hover>th{background-color:#9fcdff}.table-secondary,.table-secondary>td,.table-secondary>th{background-color:#d6d8db}.table-secondary tbody+tbody,.table-secondary td,.table-secondary th,.table-secondary thead th{border-color:#b3b7bb}.table-hover .table-secondary:hover,.table-hover .table-secondary:hover>td,.table-hover .table-secondary:hover>th{background-color:#c8cbcf}.table-success,.table-success>td,.table-success>th{background-color:#c3e6cb}.table-success tbody+tbody,.table-success td,.table-success th,.table-success thead th{border-color:#8fd19e}.table-hover .table-success:hover,.table-hover .table-success:hover>td,.table-hover .table-success:hover>th{background-color:#b1dfbb}.table-info,.table-info>td,.table-info>th{background-color:#bee5eb}.table-info tbody+tbody,.table-info td,.table-info th,.table-info thead th{border-color:#86cfda}.table-hover .table-info:hover,.table-hover .table-info:hover>td,.table-hover .table-info:hover>th{background-color:#abdde5}.table-warning,.table-warning>td,.table-warning>th{background-color:#ffeeba}.table-warning tbody+tbody,.table-warning td,.table-warning th,.table-warning thead th{border-color:#ffdf7e}.table-hover .table-warning:hover,.table-hover .table-warning:hover>td,.table-hover .table-warning:hover>th{background-color:#ffe8a1}.table-danger,.table-danger>td,.table-danger>th{background-color:#f5c6cb}.table-danger tbody+tbody,.table-danger td,.table-danger th,.table-danger thead th{border-color:#ed969e}.table-hover .table-danger:hover,.table-hover .table-danger:hover>td,.table-hover .table-danger:hover>th{background-color:#f1b0b7}.table-light,.table-light>td,.table-light>th{background-color:#fdfdfe}.table-light tbody+tbody,.table-light td,.table-light th,.table-light thead th{border-color:#fbfcfc}.table-hover .table-light:hover,.table-hover .table-light:hover>td,.table-hover .table-light:hover>th{background-color:#ececf6}.table-dark,.table-dark>td,.table-dark>th{background-color:#c6c8ca}.table-dark tbody+tbody,.table-dark td,.table-dark th,.table-dark thead th{border-color:#95999c}.table-hover .table-dark:hover,.table-hover .table-dark:hover>td,.table-hover .table-dark:hover>th{background-color:#b9bbbe}.table-active,.table-active>td,.table-active>th,.table-hover .table-active:hover,.table-hover .table-active:hover>td,.table-hover .table-active:hover>th{background-color:rgba(0,0,0,.075)}.table .thead-dark th{color:#fff;background-color:#343a40;border-color:#454d55}.table .thead-light th{color:#495057;background-color:#e9ecef;border-color:#dee2e6}.table-dark{color:#fff;background-color:#343a40}.table-dark td,.table-dark th,.table-dark thead th{border-color:#454d55}.table-dark.table-bordered{border:0}.table-dark.table-striped tbody tr:nth-of-type(odd){background-color:hsla(0,0%,100%,.05)}.table-dark.table-hover tbody tr:hover{color:#fff;background-color:hsla(0,0%,100%,.075)}@media (max-width:539.98px){.table-responsive-sm{display:block;width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch}.table-responsive-sm>.table-bordered{border:0}}@media (max-width:719.98px){.table-responsive-md{display:block;width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch}.table-responsive-md>.table-bordered{border:0}}@media (max-width:959.98px){.table-responsive-lg{display:block;width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch}.table-responsive-lg>.table-bordered{border:0}}@media (max-width:1199.98px){.table-responsive-xl{display:block;width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch}.table-responsive-xl>.table-bordered{border:0}}.table-responsive{display:block;width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch}.table-responsive>.table-bordered{border:0}.form-control{display:block;width:100%;height:calc(1.5em + .75rem + 2px);padding:.375rem .75rem;font-size:1rem;font-weight:400;line-height:1.5;color:#495057;background-color:#fff;background-clip:padding-box;border:1px solid #ced4da;border-radius:.25rem;transition:border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media (prefers-reduced-motion:reduce){.form-control{transition:none}}.form-control::-ms-expand{background-color:transparent;border:0}.form-control:-moz-focusring{color:transparent;text-shadow:0 0 0 #495057}.form-control:focus{color:#495057;background-color:#fff;border-color:#80bdff;outline:0;box-shadow:0 0 0 .2rem rgba(0,123,255,.25)}.form-control::placeholder{color:#6c757d;opacity:1}.form-control:disabled,.form-control[readonly]{background-color:#e9ecef;opacity:1}input[type=date].form-control,input[type=datetime-local].form-control,input[type=month].form-control,input[type=time].form-control{appearance:none}select.form-control:focus::-ms-value{color:#495057;background-color:#fff}.form-control-file,.form-control-range{display:block;width:100%}.col-form-label{padding-top:calc(.375rem + 1px);padding-bottom:calc(.375rem + 1px);margin-bottom:0;font-size:inherit;line-height:1.5}.col-form-label-lg{padding-top:calc(.5rem + 1px);padding-bottom:calc(.5rem + 1px);font-size:1.25rem;line-height:1.5}.col-form-label-sm{padding-top:calc(.25rem + 1px);padding-bottom:calc(.25rem + 1px);font-size:.875rem;line-height:1.5}.form-control-plaintext{display:block;width:100%;padding:.375rem 0;margin-bottom:0;font-size:1rem;line-height:1.5;color:#212529;background-color:transparent;border:solid transparent;border-width:1px 0}.form-control-plaintext.form-control-lg,.form-control-plaintext.form-control-sm{padding-right:0;padding-left:0}.form-control-sm{height:calc(1.5em + .5rem + 2px);padding:.25rem .5rem;font-size:.875rem;line-height:1.5;border-radius:.2rem}.form-control-lg{height:calc(1.5em + 1rem + 2px);padding:.5rem 1rem;font-size:1.25rem;line-height:1.5;border-radius:.3rem}select.form-control[multiple],select.form-control[size],textarea.form-control{height:auto}.form-group{margin-bottom:1rem}.form-text{display:block;margin-top:.25rem}.form-row{display:flex;flex-wrap:wrap;margin-right:-5px;margin-left:-5px}.form-row>.col,.form-row>[class*=col-]{padding-right:5px;padding-left:5px}.form-check{position:relative;display:block;padding-left:1.25rem}.form-check-input{position:absolute;margin-top:.3rem;margin-left:-1.25rem}.form-check-input:disabled~.form-check-label,.form-check-input[disabled]~.form-check-label{color:#6c757d}.form-check-label{margin-bottom:0}.form-check-inline{display:inline-flex;align-items:center;padding-left:0;margin-right:.75rem}.form-check-inline .form-check-input{position:static;margin-top:0;margin-right:.3125rem;margin-left:0}.valid-feedback{display:none;width:100%;margin-top:.25rem;font-size:80%;color:#28a745}.valid-tooltip{position:absolute;top:100%;z-index:5;display:none;max-width:100%;padding:.25rem .5rem;margin-top:.1rem;font-size:.875rem;line-height:1.5;color:#fff;background-color:rgba(40,167,69,.9);border-radius:.25rem}.is-valid~.valid-feedback,.is-valid~.valid-tooltip,.was-validated :valid~.valid-feedback,.was-validated :valid~.valid-tooltip{display:block}.form-control.is-valid,.was-validated .form-control:valid{border-color:#28a745;padding-right:calc(1.5em + .75rem);background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='8' height='8'%3E%3Cpath fill='%2328a745' d='M2.3 6.73L.6 4.53c-.4-1.04.46-1.4 1.1-.8l1.1 1.4 3.4-3.8c.6-.63 1.6-.27 1.2.7l-4 4.6c-.43.5-.8.4-1.1.1z'/%3E%3C/svg%3E");background-repeat:no-repeat;background-position:right calc(.375em + .1875rem) center;background-size:calc(.75em + .375rem) calc(.75em + .375rem)}.form-control.is-valid:focus,.was-validated .form-control:valid:focus{border-color:#28a745;box-shadow:0 0 0 .2rem rgba(40,167,69,.25)}.was-validated textarea.form-control:valid,textarea.form-control.is-valid{padding-right:calc(1.5em + .75rem);background-position:top calc(.375em + .1875rem) right calc(.375em + .1875rem)}.custom-select.is-valid,.was-validated .custom-select:valid{border-color:#28a745;padding-right:calc(.75em + 2.3125rem);background:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='4' height='5'%3E%3Cpath fill='%23343a40' d='M2 0L0 2h4zm0 5L0 3h4z'/%3E%3C/svg%3E") no-repeat right .75rem center/8px 10px,url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='8' height='8'%3E%3Cpath fill='%2328a745' d='M2.3 6.73L.6 4.53c-.4-1.04.46-1.4 1.1-.8l1.1 1.4 3.4-3.8c.6-.63 1.6-.27 1.2.7l-4 4.6c-.43.5-.8.4-1.1.1z'/%3E%3C/svg%3E") #fff no-repeat center right 1.75rem/calc(.75em + .375rem) calc(.75em + .375rem)}.custom-select.is-valid:focus,.was-validated .custom-select:valid:focus{border-color:#28a745;box-shadow:0 0 0 .2rem rgba(40,167,69,.25)}.form-check-input.is-valid~.form-check-label,.was-validated .form-check-input:valid~.form-check-label{color:#28a745}.form-check-input.is-valid~.valid-feedback,.form-check-input.is-valid~.valid-tooltip,.was-validated .form-check-input:valid~.valid-feedback,.was-validated .form-check-input:valid~.valid-tooltip{display:block}.custom-control-input.is-valid~.custom-control-label,.was-validated .custom-control-input:valid~.custom-control-label{color:#28a745}.custom-control-input.is-valid~.custom-control-label:before,.was-validated .custom-control-input:valid~.custom-control-label:before{border-color:#28a745}.custom-control-input.is-valid:checked~.custom-control-label:before,.was-validated .custom-control-input:valid:checked~.custom-control-label:before{border-color:#34ce57;background-color:#34ce57}.custom-control-input.is-valid:focus~.custom-control-label:before,.was-validated .custom-control-input:valid:focus~.custom-control-label:before{box-shadow:0 0 0 .2rem rgba(40,167,69,.25)}.custom-control-input.is-valid:focus:not(:checked)~.custom-control-label:before,.custom-file-input.is-valid~.custom-file-label,.was-validated .custom-control-input:valid:focus:not(:checked)~.custom-control-label:before,.was-validated .custom-file-input:valid~.custom-file-label{border-color:#28a745}.custom-file-input.is-valid:focus~.custom-file-label,.was-validated .custom-file-input:valid:focus~.custom-file-label{border-color:#28a745;box-shadow:0 0 0 .2rem rgba(40,167,69,.25)}.invalid-feedback{display:none;width:100%;margin-top:.25rem;font-size:80%;color:#dc3545}.invalid-tooltip{position:absolute;top:100%;z-index:5;display:none;max-width:100%;padding:.25rem .5rem;margin-top:.1rem;font-size:.875rem;line-height:1.5;color:#fff;background-color:rgba(220,53,69,.9);border-radius:.25rem}.is-invalid~.invalid-feedback,.is-invalid~.invalid-tooltip,.was-validated :invalid~.invalid-feedback,.was-validated :invalid~.invalid-tooltip{display:block}.form-control.is-invalid,.was-validated .form-control:invalid{border-color:#dc3545;padding-right:calc(1.5em + .75rem);background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='12' height='12' fill='none' stroke='%23dc3545'%3E%3Ccircle cx='6' cy='6' r='4.5'/%3E%3Cpath stroke-linejoin='round' d='M5.8 3.6h.4L6 6.5z'/%3E%3Ccircle cx='6' cy='8.2' r='.6' fill='%23dc3545' stroke='none'/%3E%3C/svg%3E");background-repeat:no-repeat;background-position:right calc(.375em + .1875rem) center;background-size:calc(.75em + .375rem) calc(.75em + .375rem)}.form-control.is-invalid:focus,.was-validated .form-control:invalid:focus{border-color:#dc3545;box-shadow:0 0 0 .2rem rgba(220,53,69,.25)}.was-validated textarea.form-control:invalid,textarea.form-control.is-invalid{padding-right:calc(1.5em + .75rem);background-position:top calc(.375em + .1875rem) right calc(.375em + .1875rem)}.custom-select.is-invalid,.was-validated .custom-select:invalid{border-color:#dc3545;padding-right:calc(.75em + 2.3125rem);background:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='4' height='5'%3E%3Cpath fill='%23343a40' d='M2 0L0 2h4zm0 5L0 3h4z'/%3E%3C/svg%3E") no-repeat right .75rem center/8px 10px,url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='12' height='12' fill='none' stroke='%23dc3545'%3E%3Ccircle cx='6' cy='6' r='4.5'/%3E%3Cpath stroke-linejoin='round' d='M5.8 3.6h.4L6 6.5z'/%3E%3Ccircle cx='6' cy='8.2' r='.6' fill='%23dc3545' stroke='none'/%3E%3C/svg%3E") #fff no-repeat center right 1.75rem/calc(.75em + .375rem) calc(.75em + .375rem)}.custom-select.is-invalid:focus,.was-validated .custom-select:invalid:focus{border-color:#dc3545;box-shadow:0 0 0 .2rem rgba(220,53,69,.25)}.form-check-input.is-invalid~.form-check-label,.was-validated .form-check-input:invalid~.form-check-label{color:#dc3545}.form-check-input.is-invalid~.invalid-feedback,.form-check-input.is-invalid~.invalid-tooltip,.was-validated .form-check-input:invalid~.invalid-feedback,.was-validated .form-check-input:invalid~.invalid-tooltip{display:block}.custom-control-input.is-invalid~.custom-control-label,.was-validated .custom-control-input:invalid~.custom-control-label{color:#dc3545}.custom-control-input.is-invalid~.custom-control-label:before,.was-validated .custom-control-input:invalid~.custom-control-label:before{border-color:#dc3545}.custom-control-input.is-invalid:checked~.custom-control-label:before,.was-validated .custom-control-input:invalid:checked~.custom-control-label:before{border-color:#e4606d;background-color:#e4606d}.custom-control-input.is-invalid:focus~.custom-control-label:before,.was-validated .custom-control-input:invalid:focus~.custom-control-label:before{box-shadow:0 0 0 .2rem rgba(220,53,69,.25)}.custom-control-input.is-invalid:focus:not(:checked)~.custom-control-label:before,.custom-file-input.is-invalid~.custom-file-label,.was-validated .custom-control-input:invalid:focus:not(:checked)~.custom-control-label:before,.was-validated .custom-file-input:invalid~.custom-file-label{border-color:#dc3545}.custom-file-input.is-invalid:focus~.custom-file-label,.was-validated .custom-file-input:invalid:focus~.custom-file-label{border-color:#dc3545;box-shadow:0 0 0 .2rem rgba(220,53,69,.25)}.form-inline{display:flex;flex-flow:row wrap;align-items:center}.form-inline .form-check{width:100%}@media (min-width:540px){.form-inline label{justify-content:center}.form-inline .form-group,.form-inline label{display:flex;align-items:center;margin-bottom:0}.form-inline .form-group{flex:0 0 auto;flex-flow:row wrap}.form-inline .form-control{display:inline-block;width:auto;vertical-align:middle}.form-inline .form-control-plaintext{display:inline-block}.form-inline .custom-select,.form-inline .input-group{width:auto}.form-inline .form-check{display:flex;align-items:center;justify-content:center;width:auto;padding-left:0}.form-inline .form-check-input{position:relative;flex-shrink:0;margin-top:0;margin-right:.25rem;margin-left:0}.form-inline .custom-control{align-items:center;justify-content:center}.form-inline .custom-control-label{margin-bottom:0}}.btn{display:inline-block;font-weight:400;color:#212529;text-align:center;vertical-align:middle;user-select:none;background-color:transparent;border:1px solid transparent;padding:.375rem .75rem;font-size:1rem;line-height:1.5;border-radius:.25rem;transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media (prefers-reduced-motion:reduce){.btn{transition:none}}.btn:hover{color:#212529;text-decoration:none}.btn.focus,.btn:focus{outline:0;box-shadow:0 0 0 .2rem rgba(0,123,255,.25)}.btn.disabled,.btn:disabled{opacity:.65}.btn:not(:disabled):not(.disabled){cursor:pointer}a.btn.disabled,fieldset:disabled a.btn{pointer-events:none}.btn-primary{color:#fff;background-color:#007bff;border-color:#007bff}.btn-primary.focus,.btn-primary:focus,.btn-primary:hover{color:#fff;background-color:#0069d9;border-color:#0062cc}.btn-primary.focus,.btn-primary:focus{box-shadow:0 0 0 .2rem rgba(38,143,255,.5)}.btn-primary.disabled,.btn-primary:disabled{color:#fff;background-color:#007bff;border-color:#007bff}.btn-primary:not(:disabled):not(.disabled).active,.btn-primary:not(:disabled):not(.disabled):active,.show>.btn-primary.dropdown-toggle{color:#fff;background-color:#0062cc;border-color:#005cbf}.btn-primary:not(:disabled):not(.disabled).active:focus,.btn-primary:not(:disabled):not(.disabled):active:focus,.show>.btn-primary.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(38,143,255,.5)}.btn-secondary{color:#fff;background-color:#6c757d;border-color:#6c757d}.btn-secondary.focus,.btn-secondary:focus,.btn-secondary:hover{color:#fff;background-color:#5a6268;border-color:#545b62}.btn-secondary.focus,.btn-secondary:focus{box-shadow:0 0 0 .2rem rgba(130,138,145,.5)}.btn-secondary.disabled,.btn-secondary:disabled{color:#fff;background-color:#6c757d;border-color:#6c757d}.btn-secondary:not(:disabled):not(.disabled).active,.btn-secondary:not(:disabled):not(.disabled):active,.show>.btn-secondary.dropdown-toggle{color:#fff;background-color:#545b62;border-color:#4e555b}.btn-secondary:not(:disabled):not(.disabled).active:focus,.btn-secondary:not(:disabled):not(.disabled):active:focus,.show>.btn-secondary.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(130,138,145,.5)}.btn-success{color:#fff;background-color:#28a745;border-color:#28a745}.btn-success.focus,.btn-success:focus,.btn-success:hover{color:#fff;background-color:#218838;border-color:#1e7e34}.btn-success.focus,.btn-success:focus{box-shadow:0 0 0 .2rem rgba(72,180,97,.5)}.btn-success.disabled,.btn-success:disabled{color:#fff;background-color:#28a745;border-color:#28a745}.btn-success:not(:disabled):not(.disabled).active,.btn-success:not(:disabled):not(.disabled):active,.show>.btn-success.dropdown-toggle{color:#fff;background-color:#1e7e34;border-color:#1c7430}.btn-success:not(:disabled):not(.disabled).active:focus,.btn-success:not(:disabled):not(.disabled):active:focus,.show>.btn-success.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(72,180,97,.5)}.btn-info{color:#fff;background-color:#17a2b8;border-color:#17a2b8}.btn-info.focus,.btn-info:focus,.btn-info:hover{color:#fff;background-color:#138496;border-color:#117a8b}.btn-info.focus,.btn-info:focus{box-shadow:0 0 0 .2rem rgba(58,176,195,.5)}.btn-info.disabled,.btn-info:disabled{color:#fff;background-color:#17a2b8;border-color:#17a2b8}.btn-info:not(:disabled):not(.disabled).active,.btn-info:not(:disabled):not(.disabled):active,.show>.btn-info.dropdown-toggle{color:#fff;background-color:#117a8b;border-color:#10707f}.btn-info:not(:disabled):not(.disabled).active:focus,.btn-info:not(:disabled):not(.disabled):active:focus,.show>.btn-info.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(58,176,195,.5)}.btn-warning{color:#212529;background-color:#ffc107;border-color:#ffc107}.btn-warning.focus,.btn-warning:focus,.btn-warning:hover{color:#212529;background-color:#e0a800;border-color:#d39e00}.btn-warning.focus,.btn-warning:focus{box-shadow:0 0 0 .2rem rgba(222,170,12,.5)}.btn-warning.disabled,.btn-warning:disabled{color:#212529;background-color:#ffc107;border-color:#ffc107}.btn-warning:not(:disabled):not(.disabled).active,.btn-warning:not(:disabled):not(.disabled):active,.show>.btn-warning.dropdown-toggle{color:#212529;background-color:#d39e00;border-color:#c69500}.btn-warning:not(:disabled):not(.disabled).active:focus,.btn-warning:not(:disabled):not(.disabled):active:focus,.show>.btn-warning.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(222,170,12,.5)}.btn-danger{color:#fff;background-color:#dc3545;border-color:#dc3545}.btn-danger.focus,.btn-danger:focus,.btn-danger:hover{color:#fff;background-color:#c82333;border-color:#bd2130}.btn-danger.focus,.btn-danger:focus{box-shadow:0 0 0 .2rem rgba(225,83,97,.5)}.btn-danger.disabled,.btn-danger:disabled{color:#fff;background-color:#dc3545;border-color:#dc3545}.btn-danger:not(:disabled):not(.disabled).active,.btn-danger:not(:disabled):not(.disabled):active,.show>.btn-danger.dropdown-toggle{color:#fff;background-color:#bd2130;border-color:#b21f2d}.btn-danger:not(:disabled):not(.disabled).active:focus,.btn-danger:not(:disabled):not(.disabled):active:focus,.show>.btn-danger.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(225,83,97,.5)}.btn-light{color:#212529;background-color:#f8f9fa;border-color:#f8f9fa}.btn-light.focus,.btn-light:focus,.btn-light:hover{color:#212529;background-color:#e2e6ea;border-color:#dae0e5}.btn-light.focus,.btn-light:focus{box-shadow:0 0 0 .2rem rgba(216,217,219,.5)}.btn-light.disabled,.btn-light:disabled{color:#212529;background-color:#f8f9fa;border-color:#f8f9fa}.btn-light:not(:disabled):not(.disabled).active,.btn-light:not(:disabled):not(.disabled):active,.show>.btn-light.dropdown-toggle{color:#212529;background-color:#dae0e5;border-color:#d3d9df}.btn-light:not(:disabled):not(.disabled).active:focus,.btn-light:not(:disabled):not(.disabled):active:focus,.show>.btn-light.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(216,217,219,.5)}.btn-dark{color:#fff;background-color:#343a40;border-color:#343a40}.btn-dark.focus,.btn-dark:focus,.btn-dark:hover{color:#fff;background-color:#23272b;border-color:#1d2124}.btn-dark.focus,.btn-dark:focus{box-shadow:0 0 0 .2rem rgba(82,88,93,.5)}.btn-dark.disabled,.btn-dark:disabled{color:#fff;background-color:#343a40;border-color:#343a40}.btn-dark:not(:disabled):not(.disabled).active,.btn-dark:not(:disabled):not(.disabled):active,.show>.btn-dark.dropdown-toggle{color:#fff;background-color:#1d2124;border-color:#171a1d}.btn-dark:not(:disabled):not(.disabled).active:focus,.btn-dark:not(:disabled):not(.disabled):active:focus,.show>.btn-dark.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(82,88,93,.5)}.btn-outline-primary{color:#007bff;border-color:#007bff}.btn-outline-primary:hover{color:#fff;background-color:#007bff;border-color:#007bff}.btn-outline-primary.focus,.btn-outline-primary:focus{box-shadow:0 0 0 .2rem rgba(0,123,255,.5)}.btn-outline-primary.disabled,.btn-outline-primary:disabled{color:#007bff;background-color:transparent}.btn-outline-primary:not(:disabled):not(.disabled).active,.btn-outline-primary:not(:disabled):not(.disabled):active,.show>.btn-outline-primary.dropdown-toggle{color:#fff;background-color:#007bff;border-color:#007bff}.btn-outline-primary:not(:disabled):not(.disabled).active:focus,.btn-outline-primary:not(:disabled):not(.disabled):active:focus,.show>.btn-outline-primary.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(0,123,255,.5)}.btn-outline-secondary{color:#6c757d;border-color:#6c757d}.btn-outline-secondary:hover{color:#fff;background-color:#6c757d;border-color:#6c757d}.btn-outline-secondary.focus,.btn-outline-secondary:focus{box-shadow:0 0 0 .2rem rgba(108,117,125,.5)}.btn-outline-secondary.disabled,.btn-outline-secondary:disabled{color:#6c757d;background-color:transparent}.btn-outline-secondary:not(:disabled):not(.disabled).active,.btn-outline-secondary:not(:disabled):not(.disabled):active,.show>.btn-outline-secondary.dropdown-toggle{color:#fff;background-color:#6c757d;border-color:#6c757d}.btn-outline-secondary:not(:disabled):not(.disabled).active:focus,.btn-outline-secondary:not(:disabled):not(.disabled):active:focus,.show>.btn-outline-secondary.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(108,117,125,.5)}.btn-outline-success{color:#28a745;border-color:#28a745}.btn-outline-success:hover{color:#fff;background-color:#28a745;border-color:#28a745}.btn-outline-success.focus,.btn-outline-success:focus{box-shadow:0 0 0 .2rem rgba(40,167,69,.5)}.btn-outline-success.disabled,.btn-outline-success:disabled{color:#28a745;background-color:transparent}.btn-outline-success:not(:disabled):not(.disabled).active,.btn-outline-success:not(:disabled):not(.disabled):active,.show>.btn-outline-success.dropdown-toggle{color:#fff;background-color:#28a745;border-color:#28a745}.btn-outline-success:not(:disabled):not(.disabled).active:focus,.btn-outline-success:not(:disabled):not(.disabled):active:focus,.show>.btn-outline-success.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(40,167,69,.5)}.btn-outline-info{color:#17a2b8;border-color:#17a2b8}.btn-outline-info:hover{color:#fff;background-color:#17a2b8;border-color:#17a2b8}.btn-outline-info.focus,.btn-outline-info:focus{box-shadow:0 0 0 .2rem rgba(23,162,184,.5)}.btn-outline-info.disabled,.btn-outline-info:disabled{color:#17a2b8;background-color:transparent}.btn-outline-info:not(:disabled):not(.disabled).active,.btn-outline-info:not(:disabled):not(.disabled):active,.show>.btn-outline-info.dropdown-toggle{color:#fff;background-color:#17a2b8;border-color:#17a2b8}.btn-outline-info:not(:disabled):not(.disabled).active:focus,.btn-outline-info:not(:disabled):not(.disabled):active:focus,.show>.btn-outline-info.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(23,162,184,.5)}.btn-outline-warning{color:#ffc107;border-color:#ffc107}.btn-outline-warning:hover{color:#212529;background-color:#ffc107;border-color:#ffc107}.btn-outline-warning.focus,.btn-outline-warning:focus{box-shadow:0 0 0 .2rem rgba(255,193,7,.5)}.btn-outline-warning.disabled,.btn-outline-warning:disabled{color:#ffc107;background-color:transparent}.btn-outline-warning:not(:disabled):not(.disabled).active,.btn-outline-warning:not(:disabled):not(.disabled):active,.show>.btn-outline-warning.dropdown-toggle{color:#212529;background-color:#ffc107;border-color:#ffc107}.btn-outline-warning:not(:disabled):not(.disabled).active:focus,.btn-outline-warning:not(:disabled):not(.disabled):active:focus,.show>.btn-outline-warning.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(255,193,7,.5)}.btn-outline-danger{color:#dc3545;border-color:#dc3545}.btn-outline-danger:hover{color:#fff;background-color:#dc3545;border-color:#dc3545}.btn-outline-danger.focus,.btn-outline-danger:focus{box-shadow:0 0 0 .2rem rgba(220,53,69,.5)}.btn-outline-danger.disabled,.btn-outline-danger:disabled{color:#dc3545;background-color:transparent}.btn-outline-danger:not(:disabled):not(.disabled).active,.btn-outline-danger:not(:disabled):not(.disabled):active,.show>.btn-outline-danger.dropdown-toggle{color:#fff;background-color:#dc3545;border-color:#dc3545}.btn-outline-danger:not(:disabled):not(.disabled).active:focus,.btn-outline-danger:not(:disabled):not(.disabled):active:focus,.show>.btn-outline-danger.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(220,53,69,.5)}.btn-outline-light{color:#f8f9fa;border-color:#f8f9fa}.btn-outline-light:hover{color:#212529;background-color:#f8f9fa;border-color:#f8f9fa}.btn-outline-light.focus,.btn-outline-light:focus{box-shadow:0 0 0 .2rem rgba(248,249,250,.5)}.btn-outline-light.disabled,.btn-outline-light:disabled{color:#f8f9fa;background-color:transparent}.btn-outline-light:not(:disabled):not(.disabled).active,.btn-outline-light:not(:disabled):not(.disabled):active,.show>.btn-outline-light.dropdown-toggle{color:#212529;background-color:#f8f9fa;border-color:#f8f9fa}.btn-outline-light:not(:disabled):not(.disabled).active:focus,.btn-outline-light:not(:disabled):not(.disabled):active:focus,.show>.btn-outline-light.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(248,249,250,.5)}.btn-outline-dark{color:#343a40;border-color:#343a40}.btn-outline-dark:hover{color:#fff;background-color:#343a40;border-color:#343a40}.btn-outline-dark.focus,.btn-outline-dark:focus{box-shadow:0 0 0 .2rem rgba(52,58,64,.5)}.btn-outline-dark.disabled,.btn-outline-dark:disabled{color:#343a40;background-color:transparent}.btn-outline-dark:not(:disabled):not(.disabled).active,.btn-outline-dark:not(:disabled):not(.disabled):active,.show>.btn-outline-dark.dropdown-toggle{color:#fff;background-color:#343a40;border-color:#343a40}.btn-outline-dark:not(:disabled):not(.disabled).active:focus,.btn-outline-dark:not(:disabled):not(.disabled):active:focus,.show>.btn-outline-dark.dropdown-toggle:focus{box-shadow:0 0 0 .2rem rgba(52,58,64,.5)}.btn-link{font-weight:400;color:#007bff;text-decoration:none}.btn-link:hover{color:#0056b3}.btn-link.focus,.btn-link:focus,.btn-link:hover{text-decoration:underline}.btn-link.disabled,.btn-link:disabled{color:#6c757d;pointer-events:none}.btn-group-lg>.btn,.btn-lg{padding:.5rem 1rem;font-size:1.25rem;line-height:1.5;border-radius:.3rem}.btn-group-sm>.btn,.btn-sm{padding:.25rem .5rem;font-size:.875rem;line-height:1.5;border-radius:.2rem}.btn-block{display:block;width:100%}.btn-block+.btn-block{margin-top:.5rem}input[type=button].btn-block,input[type=reset].btn-block,input[type=submit].btn-block{width:100%}.fade{transition:opacity .15s linear}@media (prefers-reduced-motion:reduce){.fade{transition:none}}.fade:not(.show){opacity:0}.collapse:not(.show){display:none}.collapsing{position:relative;height:0;overflow:hidden;transition:height .35s ease}@media (prefers-reduced-motion:reduce){.collapsing{transition:none}}.dropdown,.dropleft,.dropright,.dropup{position:relative}.dropdown-toggle{white-space:nowrap}.dropdown-toggle:after{display:inline-block;margin-left:.255em;vertical-align:.255em;content:"";border-top:.3em solid;border-right:.3em solid transparent;border-bottom:0;border-left:.3em solid transparent}.dropdown-toggle:empty:after{margin-left:0}.dropdown-menu{position:absolute;top:100%;left:0;z-index:1000;display:none;float:left;min-width:10rem;padding:.5rem 0;margin:.125rem 0 0;font-size:1rem;color:#212529;text-align:left;list-style:none;background-color:#fff;background-clip:padding-box;border:1px solid rgba(0,0,0,.15);border-radius:.25rem}.dropdown-menu-left{right:auto;left:0}.dropdown-menu-right{right:0;left:auto}@media (min-width:540px){.dropdown-menu-sm-left{right:auto;left:0}.dropdown-menu-sm-right{right:0;left:auto}}@media (min-width:720px){.dropdown-menu-md-left{right:auto;left:0}.dropdown-menu-md-right{right:0;left:auto}}@media (min-width:960px){.dropdown-menu-lg-left{right:auto;left:0}.dropdown-menu-lg-right{right:0;left:auto}}@media (min-width:1200px){.dropdown-menu-xl-left{right:auto;left:0}.dropdown-menu-xl-right{right:0;left:auto}}.dropup .dropdown-menu{top:auto;bottom:100%;margin-top:0;margin-bottom:.125rem}.dropup .dropdown-toggle:after{display:inline-block;margin-left:.255em;vertical-align:.255em;content:"";border-top:0;border-right:.3em solid transparent;border-bottom:.3em solid;border-left:.3em solid transparent}.dropup .dropdown-toggle:empty:after{margin-left:0}.dropright .dropdown-menu{top:0;right:auto;left:100%;margin-top:0;margin-left:.125rem}.dropright .dropdown-toggle:after{display:inline-block;margin-left:.255em;vertical-align:.255em;content:"";border-top:.3em solid transparent;border-right:0;border-bottom:.3em solid transparent;border-left:.3em solid}.dropright .dropdown-toggle:empty:after{margin-left:0}.dropright .dropdown-toggle:after{vertical-align:0}.dropleft .dropdown-menu{top:0;right:100%;left:auto;margin-top:0;margin-right:.125rem}.dropleft .dropdown-toggle:after{display:inline-block;margin-left:.255em;vertical-align:.255em;content:"";display:none}.dropleft .dropdown-toggle:before{display:inline-block;margin-right:.255em;vertical-align:.255em;content:"";border-top:.3em solid transparent;border-right:.3em solid;border-bottom:.3em solid transparent}.dropleft .dropdown-toggle:empty:after{margin-left:0}.dropleft .dropdown-toggle:before{vertical-align:0}.dropdown-menu[x-placement^=bottom],.dropdown-menu[x-placement^=left],.dropdown-menu[x-placement^=right],.dropdown-menu[x-placement^=top]{right:auto;bottom:auto}.dropdown-divider{height:0;margin:.5rem 0;overflow:hidden;border-top:1px solid #e9ecef}.dropdown-item{display:block;width:100%;padding:.25rem 1.5rem;clear:both;font-weight:400;color:#212529;text-align:inherit;white-space:nowrap;background-color:transparent;border:0}.dropdown-item:focus,.dropdown-item:hover{color:#16181b;text-decoration:none;background-color:#f8f9fa}.dropdown-item.active,.dropdown-item:active{color:#fff;text-decoration:none;background-color:#007bff}.dropdown-item.disabled,.dropdown-item:disabled{color:#6c757d;pointer-events:none;background-color:transparent}.dropdown-menu.show{display:block}.dropdown-header{display:block;padding:.5rem 1.5rem;margin-bottom:0;font-size:.875rem;color:#6c757d;white-space:nowrap}.dropdown-item-text{display:block;padding:.25rem 1.5rem;color:#212529}.btn-group,.btn-group-vertical{position:relative;display:inline-flex;vertical-align:middle}.btn-group-vertical>.btn,.btn-group>.btn{position:relative;flex:1 1 auto}.btn-group-vertical>.btn.active,.btn-group-vertical>.btn:active,.btn-group-vertical>.btn:focus,.btn-group-vertical>.btn:hover,.btn-group>.btn.active,.btn-group>.btn:active,.btn-group>.btn:focus,.btn-group>.btn:hover{z-index:1}.btn-toolbar{display:flex;flex-wrap:wrap;justify-content:flex-start}.btn-toolbar .input-group{width:auto}.btn-group>.btn-group:not(:first-child),.btn-group>.btn:not(:first-child){margin-left:-1px}.btn-group>.btn-group:not(:last-child)>.btn,.btn-group>.btn:not(:last-child):not(.dropdown-toggle){border-top-right-radius:0;border-bottom-right-radius:0}.btn-group>.btn-group:not(:first-child)>.btn,.btn-group>.btn:not(:first-child){border-top-left-radius:0;border-bottom-left-radius:0}.dropdown-toggle-split{padding-right:.5625rem;padding-left:.5625rem}.dropdown-toggle-split:after,.dropright .dropdown-toggle-split:after,.dropup .dropdown-toggle-split:after{margin-left:0}.dropleft .dropdown-toggle-split:before{margin-right:0}.btn-group-sm>.btn+.dropdown-toggle-split,.btn-sm+.dropdown-toggle-split{padding-right:.375rem;padding-left:.375rem}.btn-group-lg>.btn+.dropdown-toggle-split,.btn-lg+.dropdown-toggle-split{padding-right:.75rem;padding-left:.75rem}.btn-group-vertical{flex-direction:column;align-items:flex-start;justify-content:center}.btn-group-vertical>.btn,.btn-group-vertical>.btn-group{width:100%}.btn-group-vertical>.btn-group:not(:first-child),.btn-group-vertical>.btn:not(:first-child){margin-top:-1px}.btn-group-vertical>.btn-group:not(:last-child)>.btn,.btn-group-vertical>.btn:not(:last-child):not(.dropdown-toggle){border-bottom-right-radius:0;border-bottom-left-radius:0}.btn-group-vertical>.btn-group:not(:first-child)>.btn,.btn-group-vertical>.btn:not(:first-child){border-top-left-radius:0;border-top-right-radius:0}.btn-group-toggle>.btn,.btn-group-toggle>.btn-group>.btn{margin-bottom:0}.btn-group-toggle>.btn-group>.btn input[type=checkbox],.btn-group-toggle>.btn-group>.btn input[type=radio],.btn-group-toggle>.btn input[type=checkbox],.btn-group-toggle>.btn input[type=radio]{position:absolute;clip:rect(0,0,0,0);pointer-events:none}.input-group{position:relative;display:flex;flex-wrap:wrap;align-items:stretch;width:100%}.input-group>.custom-file,.input-group>.custom-select,.input-group>.form-control,.input-group>.form-control-plaintext{position:relative;flex:1 1 auto;width:1%;min-width:0;margin-bottom:0}.input-group>.custom-file+.custom-file,.input-group>.custom-file+.custom-select,.input-group>.custom-file+.form-control,.input-group>.custom-select+.custom-file,.input-group>.custom-select+.custom-select,.input-group>.custom-select+.form-control,.input-group>.form-control+.custom-file,.input-group>.form-control+.custom-select,.input-group>.form-control+.form-control,.input-group>.form-control-plaintext+.custom-file,.input-group>.form-control-plaintext+.custom-select,.input-group>.form-control-plaintext+.form-control{margin-left:-1px}.input-group>.custom-file .custom-file-input:focus~.custom-file-label,.input-group>.custom-select:focus,.input-group>.form-control:focus{z-index:3}.input-group>.custom-file .custom-file-input:focus{z-index:4}.input-group>.custom-select:not(:last-child),.input-group>.form-control:not(:last-child){border-top-right-radius:0;border-bottom-right-radius:0}.input-group>.custom-select:not(:first-child),.input-group>.form-control:not(:first-child){border-top-left-radius:0;border-bottom-left-radius:0}.input-group>.custom-file{display:flex;align-items:center}.input-group>.custom-file:not(:last-child) .custom-file-label,.input-group>.custom-file:not(:last-child) .custom-file-label:after{border-top-right-radius:0;border-bottom-right-radius:0}.input-group>.custom-file:not(:first-child) .custom-file-label{border-top-left-radius:0;border-bottom-left-radius:0}.input-group-append,.input-group-prepend{display:flex}.input-group-append .btn,.input-group-prepend .btn{position:relative;z-index:2}.input-group-append .btn:focus,.input-group-prepend .btn:focus{z-index:3}.input-group-append .btn+.btn,.input-group-append .btn+.input-group-text,.input-group-append .input-group-text+.btn,.input-group-append .input-group-text+.input-group-text,.input-group-prepend .btn+.btn,.input-group-prepend .btn+.input-group-text,.input-group-prepend .input-group-text+.btn,.input-group-prepend .input-group-text+.input-group-text{margin-left:-1px}.input-group-prepend{margin-right:-1px}.input-group-append{margin-left:-1px}.input-group-text{display:flex;align-items:center;padding:.375rem .75rem;margin-bottom:0;font-size:1rem;font-weight:400;line-height:1.5;color:#495057;text-align:center;white-space:nowrap;background-color:#e9ecef;border:1px solid #ced4da;border-radius:.25rem}.input-group-text input[type=checkbox],.input-group-text input[type=radio]{margin-top:0}.input-group-lg>.custom-select,.input-group-lg>.form-control:not(textarea){height:calc(1.5em + 1rem + 2px)}.input-group-lg>.custom-select,.input-group-lg>.form-control,.input-group-lg>.input-group-append>.btn,.input-group-lg>.input-group-append>.input-group-text,.input-group-lg>.input-group-prepend>.btn,.input-group-lg>.input-group-prepend>.input-group-text{padding:.5rem 1rem;font-size:1.25rem;line-height:1.5;border-radius:.3rem}.input-group-sm>.custom-select,.input-group-sm>.form-control:not(textarea){height:calc(1.5em + .5rem + 2px)}.input-group-sm>.custom-select,.input-group-sm>.form-control,.input-group-sm>.input-group-append>.btn,.input-group-sm>.input-group-append>.input-group-text,.input-group-sm>.input-group-prepend>.btn,.input-group-sm>.input-group-prepend>.input-group-text{padding:.25rem .5rem;font-size:.875rem;line-height:1.5;border-radius:.2rem}.input-group-lg>.custom-select,.input-group-sm>.custom-select{padding-right:1.75rem}.input-group>.input-group-append:last-child>.btn:not(:last-child):not(.dropdown-toggle),.input-group>.input-group-append:last-child>.input-group-text:not(:last-child),.input-group>.input-group-append:not(:last-child)>.btn,.input-group>.input-group-append:not(:last-child)>.input-group-text,.input-group>.input-group-prepend>.btn,.input-group>.input-group-prepend>.input-group-text{border-top-right-radius:0;border-bottom-right-radius:0}.input-group>.input-group-append>.btn,.input-group>.input-group-append>.input-group-text,.input-group>.input-group-prepend:first-child>.btn:not(:first-child),.input-group>.input-group-prepend:first-child>.input-group-text:not(:first-child),.input-group>.input-group-prepend:not(:first-child)>.btn,.input-group>.input-group-prepend:not(:first-child)>.input-group-text{border-top-left-radius:0;border-bottom-left-radius:0}.custom-control{position:relative;display:block;min-height:1.5rem;padding-left:1.5rem}.custom-control-inline{display:inline-flex;margin-right:1rem}.custom-control-input{position:absolute;left:0;z-index:-1;width:1rem;height:1.25rem;opacity:0}.custom-control-input:checked~.custom-control-label:before{color:#fff;border-color:#007bff;background-color:#007bff}.custom-control-input:focus~.custom-control-label:before{box-shadow:0 0 0 .2rem rgba(0,123,255,.25)}.custom-control-input:focus:not(:checked)~.custom-control-label:before{border-color:#80bdff}.custom-control-input:not(:disabled):active~.custom-control-label:before{color:#fff;background-color:#b3d7ff;border-color:#b3d7ff}.custom-control-input:disabled~.custom-control-label,.custom-control-input[disabled]~.custom-control-label{color:#6c757d}.custom-control-input:disabled~.custom-control-label:before,.custom-control-input[disabled]~.custom-control-label:before{background-color:#e9ecef}.custom-control-label{position:relative;margin-bottom:0;vertical-align:top}.custom-control-label:before{pointer-events:none;background-color:#fff;border:1px solid #adb5bd}.custom-control-label:after,.custom-control-label:before{position:absolute;top:.25rem;left:-1.5rem;display:block;width:1rem;height:1rem;content:""}.custom-control-label:after{background:no-repeat 50%/50% 50%}.custom-checkbox .custom-control-label:before{border-radius:.25rem}.custom-checkbox .custom-control-input:checked~.custom-control-label:after{background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='8' height='8'%3E%3Cpath fill='%23fff' d='M6.564.75l-3.59 3.612-1.538-1.55L0 4.26l2.974 2.99L8 2.193z'/%3E%3C/svg%3E")}.custom-checkbox .custom-control-input:indeterminate~.custom-control-label:before{border-color:#007bff;background-color:#007bff}.custom-checkbox .custom-control-input:indeterminate~.custom-control-label:after{background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='4' height='4'%3E%3Cpath stroke='%23fff' d='M0 2h4'/%3E%3C/svg%3E")}.custom-checkbox .custom-control-input:disabled:checked~.custom-control-label:before{background-color:rgba(0,123,255,.5)}.custom-checkbox .custom-control-input:disabled:indeterminate~.custom-control-label:before{background-color:rgba(0,123,255,.5)}.custom-radio .custom-control-label:before{border-radius:50%}.custom-radio .custom-control-input:checked~.custom-control-label:after{background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='12' height='12' viewBox='-4 -4 8 8'%3E%3Ccircle r='3' fill='%23fff'/%3E%3C/svg%3E")}.custom-radio .custom-control-input:disabled:checked~.custom-control-label:before{background-color:rgba(0,123,255,.5)}.custom-switch{padding-left:2.25rem}.custom-switch .custom-control-label:before{left:-2.25rem;width:1.75rem;pointer-events:all;border-radius:.5rem}.custom-switch .custom-control-label:after{top:calc(.25rem + 2px);left:calc(-2.25rem + 2px);width:calc(1rem - 4px);height:calc(1rem - 4px);background-color:#adb5bd;border-radius:.5rem;transition:transform .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media (prefers-reduced-motion:reduce){.custom-switch .custom-control-label:after{transition:none}}.custom-switch .custom-control-input:checked~.custom-control-label:after{background-color:#fff;transform:translateX(.75rem)}.custom-switch .custom-control-input:disabled:checked~.custom-control-label:before{background-color:rgba(0,123,255,.5)}.custom-select{display:inline-block;width:100%;height:calc(1.5em + .75rem + 2px);padding:.375rem 1.75rem .375rem .75rem;font-size:1rem;font-weight:400;line-height:1.5;color:#495057;vertical-align:middle;background:#fff url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='4' height='5'%3E%3Cpath fill='%23343a40' d='M2 0L0 2h4zm0 5L0 3h4z'/%3E%3C/svg%3E") no-repeat right .75rem center/8px 10px;border:1px solid #ced4da;border-radius:.25rem;appearance:none}.custom-select:focus{border-color:#80bdff;outline:0;box-shadow:0 0 0 .2rem rgba(0,123,255,.25)}.custom-select:focus::-ms-value{color:#495057;background-color:#fff}.custom-select[multiple],.custom-select[size]:not([size="1"]){height:auto;padding-right:.75rem;background-image:none}.custom-select:disabled{color:#6c757d;background-color:#e9ecef}.custom-select::-ms-expand{display:none}.custom-select:-moz-focusring{color:transparent;text-shadow:0 0 0 #495057}.custom-select-sm{height:calc(1.5em + .5rem + 2px);padding-top:.25rem;padding-bottom:.25rem;padding-left:.5rem;font-size:.875rem}.custom-select-lg{height:calc(1.5em + 1rem + 2px);padding-top:.5rem;padding-bottom:.5rem;padding-left:1rem;font-size:1.25rem}.custom-file{display:inline-block;margin-bottom:0}.custom-file,.custom-file-input{position:relative;width:100%;height:calc(1.5em + .75rem + 2px)}.custom-file-input{z-index:2;margin:0;opacity:0}.custom-file-input:focus~.custom-file-label{border-color:#80bdff;box-shadow:0 0 0 .2rem rgba(0,123,255,.25)}.custom-file-input:disabled~.custom-file-label,.custom-file-input[disabled]~.custom-file-label{background-color:#e9ecef}.custom-file-input:lang(en)~.custom-file-label:after{content:"Browse"}.custom-file-input~.custom-file-label[data-browse]:after{content:attr(data-browse)}.custom-file-label{left:0;z-index:1;height:calc(1.5em + .75rem + 2px);font-weight:400;background-color:#fff;border:1px solid #ced4da;border-radius:.25rem}.custom-file-label,.custom-file-label:after{position:absolute;top:0;right:0;padding:.375rem .75rem;line-height:1.5;color:#495057}.custom-file-label:after{bottom:0;z-index:3;display:block;height:calc(1.5em + .75rem);content:"Browse";background-color:#e9ecef;border-left:inherit;border-radius:0 .25rem .25rem 0}.custom-range{width:100%;height:1.4rem;padding:0;background-color:transparent;appearance:none}.custom-range:focus{outline:none}.custom-range:focus::-webkit-slider-thumb{box-shadow:0 0 0 1px #fff,0 0 0 .2rem rgba(0,123,255,.25)}.custom-range:focus::-moz-range-thumb{box-shadow:0 0 0 1px #fff,0 0 0 .2rem rgba(0,123,255,.25)}.custom-range:focus::-ms-thumb{box-shadow:0 0 0 1px #fff,0 0 0 .2rem rgba(0,123,255,.25)}.custom-range::-moz-focus-outer{border:0}.custom-range::-webkit-slider-thumb{width:1rem;height:1rem;margin-top:-.25rem;background-color:#007bff;border:0;border-radius:1rem;transition:background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out;appearance:none}@media (prefers-reduced-motion:reduce){.custom-range::-webkit-slider-thumb{transition:none}}.custom-range::-webkit-slider-thumb:active{background-color:#b3d7ff}.custom-range::-webkit-slider-runnable-track{width:100%;height:.5rem;color:transparent;cursor:pointer;background-color:#dee2e6;border-color:transparent;border-radius:1rem}.custom-range::-moz-range-thumb{width:1rem;height:1rem;background-color:#007bff;border:0;border-radius:1rem;transition:background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out;appearance:none}@media (prefers-reduced-motion:reduce){.custom-range::-moz-range-thumb{transition:none}}.custom-range::-moz-range-thumb:active{background-color:#b3d7ff}.custom-range::-moz-range-track{width:100%;height:.5rem;color:transparent;cursor:pointer;background-color:#dee2e6;border-color:transparent;border-radius:1rem}.custom-range::-ms-thumb{width:1rem;height:1rem;margin-top:0;margin-right:.2rem;margin-left:.2rem;background-color:#007bff;border:0;border-radius:1rem;transition:background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out;appearance:none}@media (prefers-reduced-motion:reduce){.custom-range::-ms-thumb{transition:none}}.custom-range::-ms-thumb:active{background-color:#b3d7ff}.custom-range::-ms-track{width:100%;height:.5rem;color:transparent;cursor:pointer;background-color:transparent;border-color:transparent;border-width:.5rem}.custom-range::-ms-fill-lower,.custom-range::-ms-fill-upper{background-color:#dee2e6;border-radius:1rem}.custom-range::-ms-fill-upper{margin-right:15px}.custom-range:disabled::-webkit-slider-thumb{background-color:#adb5bd}.custom-range:disabled::-webkit-slider-runnable-track{cursor:default}.custom-range:disabled::-moz-range-thumb{background-color:#adb5bd}.custom-range:disabled::-moz-range-track{cursor:default}.custom-range:disabled::-ms-thumb{background-color:#adb5bd}.custom-control-label:before,.custom-file-label,.custom-select{transition:background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media (prefers-reduced-motion:reduce){.custom-control-label:before,.custom-file-label,.custom-select{transition:none}}.nav{display:flex;flex-wrap:wrap;padding-left:0;margin-bottom:0;list-style:none}.nav-link{display:block;padding:.5rem 1rem}.nav-link:focus,.nav-link:hover{text-decoration:none}.nav-link.disabled{color:#6c757d;pointer-events:none;cursor:default}.nav-tabs{border-bottom:1px solid #dee2e6}.nav-tabs .nav-item{margin-bottom:-1px}.nav-tabs .nav-link{border:1px solid transparent;border-top-left-radius:.25rem;border-top-right-radius:.25rem}.nav-tabs .nav-link:focus,.nav-tabs .nav-link:hover{border-color:#e9ecef #e9ecef #dee2e6}.nav-tabs .nav-link.disabled{color:#6c757d;background-color:transparent;border-color:transparent}.nav-tabs .nav-item.show .nav-link,.nav-tabs .nav-link.active{color:#495057;background-color:#fff;border-color:#dee2e6 #dee2e6 #fff}.nav-tabs .dropdown-menu{margin-top:-1px;border-top-left-radius:0;border-top-right-radius:0}.nav-pills .nav-link{border-radius:.25rem}.nav-pills .nav-link.active,.nav-pills .show>.nav-link{color:#fff;background-color:#007bff}.nav-fill .nav-item{flex:1 1 auto;text-align:center}.nav-justified .nav-item{flex-basis:0;flex-grow:1;text-align:center}.tab-content>.tab-pane{display:none}.tab-content>.active{display:block}.navbar{position:relative;padding:.5rem 1rem}.navbar,.navbar .container,.navbar .container-fluid,.navbar .container-lg,.navbar .container-md,.navbar .container-sm,.navbar .container-xl{display:flex;flex-wrap:wrap;align-items:center;justify-content:space-between}.navbar-brand{display:inline-block;padding-top:.3125rem;padding-bottom:.3125rem;margin-right:1rem;font-size:1.25rem;line-height:inherit;white-space:nowrap}.navbar-brand:focus,.navbar-brand:hover{text-decoration:none}.navbar-nav{display:flex;flex-direction:column;padding-left:0;margin-bottom:0;list-style:none}.navbar-nav .nav-link{padding-right:0;padding-left:0}.navbar-nav .dropdown-menu{position:static;float:none}.navbar-text{display:inline-block;padding-top:.5rem;padding-bottom:.5rem}.navbar-collapse{flex-basis:100%;flex-grow:1;align-items:center}.navbar-toggler{padding:.25rem .75rem;font-size:1.25rem;line-height:1;background-color:transparent;border:1px solid transparent;border-radius:.25rem}.navbar-toggler:focus,.navbar-toggler:hover{text-decoration:none}.navbar-toggler-icon{display:inline-block;width:1.5em;height:1.5em;vertical-align:middle;content:"";background:no-repeat 50%;background-size:100% 100%}@media (max-width:539.98px){.navbar-expand-sm>.container,.navbar-expand-sm>.container-fluid,.navbar-expand-sm>.container-lg,.navbar-expand-sm>.container-md,.navbar-expand-sm>.container-sm,.navbar-expand-sm>.container-xl{padding-right:0;padding-left:0}}@media (min-width:540px){.navbar-expand-sm{flex-flow:row nowrap;justify-content:flex-start}.navbar-expand-sm .navbar-nav{flex-direction:row}.navbar-expand-sm .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-sm .navbar-nav .nav-link{padding-right:.5rem;padding-left:.5rem}.navbar-expand-sm>.container,.navbar-expand-sm>.container-fluid,.navbar-expand-sm>.container-lg,.navbar-expand-sm>.container-md,.navbar-expand-sm>.container-sm,.navbar-expand-sm>.container-xl{flex-wrap:nowrap}.navbar-expand-sm .navbar-collapse{display:flex!important;flex-basis:auto}.navbar-expand-sm .navbar-toggler{display:none}}@media (max-width:719.98px){.navbar-expand-md>.container,.navbar-expand-md>.container-fluid,.navbar-expand-md>.container-lg,.navbar-expand-md>.container-md,.navbar-expand-md>.container-sm,.navbar-expand-md>.container-xl{padding-right:0;padding-left:0}}@media (min-width:720px){.navbar-expand-md{flex-flow:row nowrap;justify-content:flex-start}.navbar-expand-md .navbar-nav{flex-direction:row}.navbar-expand-md .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-md .navbar-nav .nav-link{padding-right:.5rem;padding-left:.5rem}.navbar-expand-md>.container,.navbar-expand-md>.container-fluid,.navbar-expand-md>.container-lg,.navbar-expand-md>.container-md,.navbar-expand-md>.container-sm,.navbar-expand-md>.container-xl{flex-wrap:nowrap}.navbar-expand-md .navbar-collapse{display:flex!important;flex-basis:auto}.navbar-expand-md .navbar-toggler{display:none}}@media (max-width:959.98px){.navbar-expand-lg>.container,.navbar-expand-lg>.container-fluid,.navbar-expand-lg>.container-lg,.navbar-expand-lg>.container-md,.navbar-expand-lg>.container-sm,.navbar-expand-lg>.container-xl{padding-right:0;padding-left:0}}@media (min-width:960px){.navbar-expand-lg{flex-flow:row nowrap;justify-content:flex-start}.navbar-expand-lg .navbar-nav{flex-direction:row}.navbar-expand-lg .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-lg .navbar-nav .nav-link{padding-right:.5rem;padding-left:.5rem}.navbar-expand-lg>.container,.navbar-expand-lg>.container-fluid,.navbar-expand-lg>.container-lg,.navbar-expand-lg>.container-md,.navbar-expand-lg>.container-sm,.navbar-expand-lg>.container-xl{flex-wrap:nowrap}.navbar-expand-lg .navbar-collapse{display:flex!important;flex-basis:auto}.navbar-expand-lg .navbar-toggler{display:none}}@media (max-width:1199.98px){.navbar-expand-xl>.container,.navbar-expand-xl>.container-fluid,.navbar-expand-xl>.container-lg,.navbar-expand-xl>.container-md,.navbar-expand-xl>.container-sm,.navbar-expand-xl>.container-xl{padding-right:0;padding-left:0}}@media (min-width:1200px){.navbar-expand-xl{flex-flow:row nowrap;justify-content:flex-start}.navbar-expand-xl .navbar-nav{flex-direction:row}.navbar-expand-xl .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-xl .navbar-nav .nav-link{padding-right:.5rem;padding-left:.5rem}.navbar-expand-xl>.container,.navbar-expand-xl>.container-fluid,.navbar-expand-xl>.container-lg,.navbar-expand-xl>.container-md,.navbar-expand-xl>.container-sm,.navbar-expand-xl>.container-xl{flex-wrap:nowrap}.navbar-expand-xl .navbar-collapse{display:flex!important;flex-basis:auto}.navbar-expand-xl .navbar-toggler{display:none}}.navbar-expand{flex-flow:row nowrap;justify-content:flex-start}.navbar-expand>.container,.navbar-expand>.container-fluid,.navbar-expand>.container-lg,.navbar-expand>.container-md,.navbar-expand>.container-sm,.navbar-expand>.container-xl{padding-right:0;padding-left:0}.navbar-expand .navbar-nav{flex-direction:row}.navbar-expand .navbar-nav .dropdown-menu{position:absolute}.navbar-expand .navbar-nav .nav-link{padding-right:.5rem;padding-left:.5rem}.navbar-expand>.container,.navbar-expand>.container-fluid,.navbar-expand>.container-lg,.navbar-expand>.container-md,.navbar-expand>.container-sm,.navbar-expand>.container-xl{flex-wrap:nowrap}.navbar-expand .navbar-collapse{display:flex!important;flex-basis:auto}.navbar-expand .navbar-toggler{display:none}.navbar-light .navbar-brand,.navbar-light .navbar-brand:focus,.navbar-light .navbar-brand:hover{color:rgba(0,0,0,.9)}.navbar-light .navbar-nav .nav-link{color:rgba(0,0,0,.5)}.navbar-light .navbar-nav .nav-link:focus,.navbar-light .navbar-nav .nav-link:hover{color:rgba(0,0,0,.7)}.navbar-light .navbar-nav .nav-link.disabled{color:rgba(0,0,0,.3)}.navbar-light .navbar-nav .active>.nav-link,.navbar-light .navbar-nav .nav-link.active,.navbar-light .navbar-nav .nav-link.show,.navbar-light .navbar-nav .show>.nav-link{color:rgba(0,0,0,.9)}.navbar-light .navbar-toggler{color:rgba(0,0,0,.5);border-color:rgba(0,0,0,.1)}.navbar-light .navbar-toggler-icon{background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='30' height='30'%3E%3Cpath stroke='rgba(0,0,0,0.5)' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3E%3C/svg%3E")}.navbar-light .navbar-text{color:rgba(0,0,0,.5)}.navbar-light .navbar-text a,.navbar-light .navbar-text a:focus,.navbar-light .navbar-text a:hover{color:rgba(0,0,0,.9)}.navbar-dark .navbar-brand,.navbar-dark .navbar-brand:focus,.navbar-dark .navbar-brand:hover{color:#fff}.navbar-dark .navbar-nav .nav-link{color:hsla(0,0%,100%,.5)}.navbar-dark .navbar-nav .nav-link:focus,.navbar-dark .navbar-nav .nav-link:hover{color:hsla(0,0%,100%,.75)}.navbar-dark .navbar-nav .nav-link.disabled{color:hsla(0,0%,100%,.25)}.navbar-dark .navbar-nav .active>.nav-link,.navbar-dark .navbar-nav .nav-link.active,.navbar-dark .navbar-nav .nav-link.show,.navbar-dark .navbar-nav .show>.nav-link{color:#fff}.navbar-dark .navbar-toggler{color:hsla(0,0%,100%,.5);border-color:hsla(0,0%,100%,.1)}.navbar-dark .navbar-toggler-icon{background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' width='30' height='30'%3E%3Cpath stroke='rgba(255,255,255,0.5)' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3E%3C/svg%3E")}.navbar-dark .navbar-text{color:hsla(0,0%,100%,.5)}.navbar-dark .navbar-text a,.navbar-dark .navbar-text a:focus,.navbar-dark .navbar-text a:hover{color:#fff}.card{position:relative;display:flex;flex-direction:column;min-width:0;word-wrap:break-word;background-color:#fff;background-clip:border-box;border:1px solid rgba(0,0,0,.125);border-radius:.25rem}.card>hr{margin-right:0;margin-left:0}.card>.list-group{border-top:inherit;border-bottom:inherit}.card>.list-group:first-child{border-top-width:0;border-top-left-radius:calc(.25rem - 1px);border-top-right-radius:calc(.25rem - 1px)}.card>.list-group:last-child{border-bottom-width:0;border-bottom-right-radius:calc(.25rem - 1px);border-bottom-left-radius:calc(.25rem - 1px)}.card-body{flex:1 1 auto;min-height:1px;padding:1.25rem}.card-title{margin-bottom:.75rem}.card-subtitle{margin-top:-.375rem}.card-subtitle,.card-text:last-child{margin-bottom:0}.card-link:hover{text-decoration:none}.card-link+.card-link{margin-left:1.25rem}.card-header{padding:.75rem 1.25rem;margin-bottom:0;background-color:rgba(0,0,0,.03);border-bottom:1px solid rgba(0,0,0,.125)}.card-header:first-child{border-radius:calc(.25rem - 1px) calc(.25rem - 1px) 0 0}.card-header+.list-group .list-group-item:first-child{border-top:0}.card-footer{padding:.75rem 1.25rem;background-color:rgba(0,0,0,.03);border-top:1px solid rgba(0,0,0,.125)}.card-footer:last-child{border-radius:0 0 calc(.25rem - 1px) calc(.25rem - 1px)}.card-header-tabs{margin-bottom:-.75rem;border-bottom:0}.card-header-pills,.card-header-tabs{margin-right:-.625rem;margin-left:-.625rem}.card-img-overlay{position:absolute;top:0;right:0;bottom:0;left:0;padding:1.25rem}.card-img,.card-img-bottom,.card-img-top{flex-shrink:0;width:100%}.card-img,.card-img-top{border-top-left-radius:calc(.25rem - 1px);border-top-right-radius:calc(.25rem - 1px)}.card-img,.card-img-bottom{border-bottom-right-radius:calc(.25rem - 1px);border-bottom-left-radius:calc(.25rem - 1px)}.card-deck .card{margin-bottom:15px}@media (min-width:540px){.card-deck{display:flex;flex-flow:row wrap;margin-right:-15px;margin-left:-15px}.card-deck .card{flex:1 0 0%;margin-right:15px;margin-bottom:0;margin-left:15px}}.card-group>.card{margin-bottom:15px}@media (min-width:540px){.card-group{display:flex;flex-flow:row wrap}.card-group>.card{flex:1 0 0%;margin-bottom:0}.card-group>.card+.card{margin-left:0;border-left:0}.card-group>.card:not(:last-child){border-top-right-radius:0;border-bottom-right-radius:0}.card-group>.card:not(:last-child) .card-header,.card-group>.card:not(:last-child) .card-img-top{border-top-right-radius:0}.card-group>.card:not(:last-child) .card-footer,.card-group>.card:not(:last-child) .card-img-bottom{border-bottom-right-radius:0}.card-group>.card:not(:first-child){border-top-left-radius:0;border-bottom-left-radius:0}.card-group>.card:not(:first-child) .card-header,.card-group>.card:not(:first-child) .card-img-top{border-top-left-radius:0}.card-group>.card:not(:first-child) .card-footer,.card-group>.card:not(:first-child) .card-img-bottom{border-bottom-left-radius:0}}.card-columns .card{margin-bottom:.75rem}@media (min-width:540px){.card-columns{column-count:3;column-gap:1.25rem;orphans:1;widows:1}.card-columns .card{display:inline-block;width:100%}}.accordion>.card{overflow:hidden}.accordion>.card:not(:last-of-type){border-bottom:0;border-bottom-right-radius:0;border-bottom-left-radius:0}.accordion>.card:not(:first-of-type){border-top-left-radius:0;border-top-right-radius:0}.accordion>.card>.card-header{border-radius:0;margin-bottom:-1px}.breadcrumb{flex-wrap:wrap;padding:.75rem 1rem;margin-bottom:1rem;list-style:none;background-color:#e9ecef;border-radius:.25rem}.breadcrumb,.breadcrumb-item{display:flex}.breadcrumb-item+.breadcrumb-item{padding-left:.5rem}.breadcrumb-item+.breadcrumb-item:before{display:inline-block;padding-right:.5rem;color:#6c757d;content:"/"}.breadcrumb-item+.breadcrumb-item:hover:before{text-decoration:underline;text-decoration:none}.breadcrumb-item.active{color:#6c757d}.pagination{display:flex;padding-left:0;list-style:none;border-radius:.25rem}.page-link{position:relative;display:block;padding:.5rem .75rem;margin-left:-1px;line-height:1.25;color:#007bff;background-color:#fff;border:1px solid #dee2e6}.page-link:hover{z-index:2;color:#0056b3;text-decoration:none;background-color:#e9ecef;border-color:#dee2e6}.page-link:focus{z-index:3;outline:0;box-shadow:0 0 0 .2rem rgba(0,123,255,.25)}.page-item:first-child .page-link{margin-left:0;border-top-left-radius:.25rem;border-bottom-left-radius:.25rem}.page-item:last-child .page-link{border-top-right-radius:.25rem;border-bottom-right-radius:.25rem}.page-item.active .page-link{z-index:3;color:#fff;background-color:#007bff;border-color:#007bff}.page-item.disabled .page-link{color:#6c757d;pointer-events:none;cursor:auto;background-color:#fff;border-color:#dee2e6}.pagination-lg .page-link{padding:.75rem 1.5rem;font-size:1.25rem;line-height:1.5}.pagination-lg .page-item:first-child .page-link{border-top-left-radius:.3rem;border-bottom-left-radius:.3rem}.pagination-lg .page-item:last-child .page-link{border-top-right-radius:.3rem;border-bottom-right-radius:.3rem}.pagination-sm .page-link{padding:.25rem .5rem;font-size:.875rem;line-height:1.5}.pagination-sm .page-item:first-child .page-link{border-top-left-radius:.2rem;border-bottom-left-radius:.2rem}.pagination-sm .page-item:last-child .page-link{border-top-right-radius:.2rem;border-bottom-right-radius:.2rem}.badge{display:inline-block;padding:.25em .4em;font-size:75%;font-weight:700;line-height:1;text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:.25rem;transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media (prefers-reduced-motion:reduce){.badge{transition:none}}a.badge:focus,a.badge:hover{text-decoration:none}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.badge-pill{padding-right:.6em;padding-left:.6em;border-radius:10rem}.badge-primary{color:#fff;background-color:#007bff}a.badge-primary:focus,a.badge-primary:hover{color:#fff;background-color:#0062cc}a.badge-primary.focus,a.badge-primary:focus{outline:0;box-shadow:0 0 0 .2rem rgba(0,123,255,.5)}.badge-secondary{color:#fff;background-color:#6c757d}a.badge-secondary:focus,a.badge-secondary:hover{color:#fff;background-color:#545b62}a.badge-secondary.focus,a.badge-secondary:focus{outline:0;box-shadow:0 0 0 .2rem rgba(108,117,125,.5)}.badge-success{color:#fff;background-color:#28a745}a.badge-success:focus,a.badge-success:hover{color:#fff;background-color:#1e7e34}a.badge-success.focus,a.badge-success:focus{outline:0;box-shadow:0 0 0 .2rem rgba(40,167,69,.5)}.badge-info{color:#fff;background-color:#17a2b8}a.badge-info:focus,a.badge-info:hover{color:#fff;background-color:#117a8b}a.badge-info.focus,a.badge-info:focus{outline:0;box-shadow:0 0 0 .2rem rgba(23,162,184,.5)}.badge-warning{color:#212529;background-color:#ffc107}a.badge-warning:focus,a.badge-warning:hover{color:#212529;background-color:#d39e00}a.badge-warning.focus,a.badge-warning:focus{outline:0;box-shadow:0 0 0 .2rem rgba(255,193,7,.5)}.badge-danger{color:#fff;background-color:#dc3545}a.badge-danger:focus,a.badge-danger:hover{color:#fff;background-color:#bd2130}a.badge-danger.focus,a.badge-danger:focus{outline:0;box-shadow:0 0 0 .2rem rgba(220,53,69,.5)}.badge-light{color:#212529;background-color:#f8f9fa}a.badge-light:focus,a.badge-light:hover{color:#212529;background-color:#dae0e5}a.badge-light.focus,a.badge-light:focus{outline:0;box-shadow:0 0 0 .2rem rgba(248,249,250,.5)}.badge-dark{color:#fff;background-color:#343a40}a.badge-dark:focus,a.badge-dark:hover{color:#fff;background-color:#1d2124}a.badge-dark.focus,a.badge-dark:focus{outline:0;box-shadow:0 0 0 .2rem rgba(52,58,64,.5)}.jumbotron{padding:2rem 1rem;margin-bottom:2rem;background-color:#e9ecef;border-radius:.3rem}@media (min-width:540px){.jumbotron{padding:4rem 2rem}}.jumbotron-fluid{padding-right:0;padding-left:0;border-radius:0}.alert{position:relative;padding:.75rem 1.25rem;margin-bottom:1rem;border:1px solid transparent;border-radius:.25rem}.alert-heading{color:inherit}.alert-link{font-weight:700}.alert-dismissible{padding-right:4rem}.alert-dismissible .close{position:absolute;top:0;right:0;padding:.75rem 1.25rem;color:inherit}.alert-primary{color:#004085;background-color:#cce5ff;border-color:#b8daff}.alert-primary hr{border-top-color:#9fcdff}.alert-primary .alert-link{color:#002752}.alert-secondary{color:#383d41;background-color:#e2e3e5;border-color:#d6d8db}.alert-secondary hr{border-top-color:#c8cbcf}.alert-secondary .alert-link{color:#202326}.alert-success{color:#155724;background-color:#d4edda;border-color:#c3e6cb}.alert-success hr{border-top-color:#b1dfbb}.alert-success .alert-link{color:#0b2e13}.alert-info{color:#0c5460;background-color:#d1ecf1;border-color:#bee5eb}.alert-info hr{border-top-color:#abdde5}.alert-info .alert-link{color:#062c33}.alert-warning{color:#856404;background-color:#fff3cd;border-color:#ffeeba}.alert-warning hr{border-top-color:#ffe8a1}.alert-warning .alert-link{color:#533f03}.alert-danger{color:#721c24;background-color:#f8d7da;border-color:#f5c6cb}.alert-danger hr{border-top-color:#f1b0b7}.alert-danger .alert-link{color:#491217}.alert-light{color:#818182;background-color:#fefefe;border-color:#fdfdfe}.alert-light hr{border-top-color:#ececf6}.alert-light .alert-link{color:#686868}.alert-dark{color:#1b1e21;background-color:#d6d8d9;border-color:#c6c8ca}.alert-dark hr{border-top-color:#b9bbbe}.alert-dark .alert-link{color:#040505}@keyframes progress-bar-stripes{0%{background-position:1rem 0}to{background-position:0 0}}.progress{height:1rem;line-height:0;font-size:.75rem;background-color:#e9ecef;border-radius:.25rem}.progress,.progress-bar{display:flex;overflow:hidden}.progress-bar{flex-direction:column;justify-content:center;color:#fff;text-align:center;white-space:nowrap;background-color:#007bff;transition:width .6s ease}@media (prefers-reduced-motion:reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg,hsla(0,0%,100%,.15) 25%,transparent 0,transparent 50%,hsla(0,0%,100%,.15) 0,hsla(0,0%,100%,.15) 75%,transparent 0,transparent);background-size:1rem 1rem}.progress-bar-animated{animation:progress-bar-stripes 1s linear infinite}@media (prefers-reduced-motion:reduce){.progress-bar-animated{animation:none}}.media{display:flex;align-items:flex-start}.media-body{flex:1}.list-group{display:flex;flex-direction:column;padding-left:0;margin-bottom:0;border-radius:.25rem}.list-group-item-action{width:100%;color:#495057;text-align:inherit}.list-group-item-action:focus,.list-group-item-action:hover{z-index:1;color:#495057;text-decoration:none;background-color:#f8f9fa}.list-group-item-action:active{color:#212529;background-color:#e9ecef}.list-group-item{position:relative;display:block;padding:.75rem 1.25rem;background-color:#fff;border:1px solid rgba(0,0,0,.125)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:#6c757d;pointer-events:none;background-color:#fff}.list-group-item.active{z-index:2;color:#fff;background-color:#007bff;border-color:#007bff}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:-1px;border-top-width:1px}.list-group-horizontal{flex-direction:row}.list-group-horizontal>.list-group-item:first-child{border-bottom-left-radius:.25rem;border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child{border-top-right-radius:.25rem;border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:1px;border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:-1px;border-left-width:1px}@media (min-width:540px){.list-group-horizontal-sm{flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child{border-bottom-left-radius:.25rem;border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child{border-top-right-radius:.25rem;border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:1px;border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:-1px;border-left-width:1px}}@media (min-width:720px){.list-group-horizontal-md{flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child{border-bottom-left-radius:.25rem;border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child{border-top-right-radius:.25rem;border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:1px;border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:-1px;border-left-width:1px}}@media (min-width:960px){.list-group-horizontal-lg{flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child{border-bottom-left-radius:.25rem;border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child{border-top-right-radius:.25rem;border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:1px;border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:-1px;border-left-width:1px}}@media (min-width:1200px){.list-group-horizontal-xl{flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child{border-bottom-left-radius:.25rem;border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child{border-top-right-radius:.25rem;border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:1px;border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:-1px;border-left-width:1px}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 1px}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-primary{color:#004085;background-color:#b8daff}.list-group-item-primary.list-group-item-action:focus,.list-group-item-primary.list-group-item-action:hover{color:#004085;background-color:#9fcdff}.list-group-item-primary.list-group-item-action.active{color:#fff;background-color:#004085;border-color:#004085}.list-group-item-secondary{color:#383d41;background-color:#d6d8db}.list-group-item-secondary.list-group-item-action:focus,.list-group-item-secondary.list-group-item-action:hover{color:#383d41;background-color:#c8cbcf}.list-group-item-secondary.list-group-item-action.active{color:#fff;background-color:#383d41;border-color:#383d41}.list-group-item-success{color:#155724;background-color:#c3e6cb}.list-group-item-success.list-group-item-action:focus,.list-group-item-success.list-group-item-action:hover{color:#155724;background-color:#b1dfbb}.list-group-item-success.list-group-item-action.active{color:#fff;background-color:#155724;border-color:#155724}.list-group-item-info{color:#0c5460;background-color:#bee5eb}.list-group-item-info.list-group-item-action:focus,.list-group-item-info.list-group-item-action:hover{color:#0c5460;background-color:#abdde5}.list-group-item-info.list-group-item-action.active{color:#fff;background-color:#0c5460;border-color:#0c5460}.list-group-item-warning{color:#856404;background-color:#ffeeba}.list-group-item-warning.list-group-item-action:focus,.list-group-item-warning.list-group-item-action:hover{color:#856404;background-color:#ffe8a1}.list-group-item-warning.list-group-item-action.active{color:#fff;background-color:#856404;border-color:#856404}.list-group-item-danger{color:#721c24;background-color:#f5c6cb}.list-group-item-danger.list-group-item-action:focus,.list-group-item-danger.list-group-item-action:hover{color:#721c24;background-color:#f1b0b7}.list-group-item-danger.list-group-item-action.active{color:#fff;background-color:#721c24;border-color:#721c24}.list-group-item-light{color:#818182;background-color:#fdfdfe}.list-group-item-light.list-group-item-action:focus,.list-group-item-light.list-group-item-action:hover{color:#818182;background-color:#ececf6}.list-group-item-light.list-group-item-action.active{color:#fff;background-color:#818182;border-color:#818182}.list-group-item-dark{color:#1b1e21;background-color:#c6c8ca}.list-group-item-dark.list-group-item-action:focus,.list-group-item-dark.list-group-item-action:hover{color:#1b1e21;background-color:#b9bbbe}.list-group-item-dark.list-group-item-action.active{color:#fff;background-color:#1b1e21;border-color:#1b1e21}.close{float:right;font-size:1.5rem;font-weight:700;line-height:1;color:#000;text-shadow:0 1px 0 #fff;opacity:.5}.close:hover{color:#000;text-decoration:none}.close:not(:disabled):not(.disabled):focus,.close:not(:disabled):not(.disabled):hover{opacity:.75}button.close{padding:0;background-color:transparent;border:0}a.close.disabled{pointer-events:none}.toast{max-width:350px;overflow:hidden;font-size:.875rem;background-color:hsla(0,0%,100%,.85);background-clip:padding-box;border:1px solid rgba(0,0,0,.1);box-shadow:0 .25rem .75rem rgba(0,0,0,.1);backdrop-filter:blur(10px);opacity:0;border-radius:.25rem}.toast:not(:last-child){margin-bottom:.75rem}.toast.showing{opacity:1}.toast.show{display:block;opacity:1}.toast.hide{display:none}.toast-header{display:flex;align-items:center;padding:.25rem .75rem;color:#6c757d;background-color:hsla(0,0%,100%,.85);background-clip:padding-box;border-bottom:1px solid rgba(0,0,0,.05)}.toast-body{padding:.75rem}.modal-open{overflow:hidden}.modal-open .modal{overflow-x:hidden;overflow-y:auto}.modal{position:fixed;top:0;left:0;z-index:1050;display:none;width:100%;height:100%;overflow:hidden;outline:0}.modal-dialog{position:relative;width:auto;margin:.5rem;pointer-events:none}.modal.fade .modal-dialog{transition:transform .3s ease-out;transform:translateY(-50px)}@media (prefers-reduced-motion:reduce){.modal.fade .modal-dialog{transition:none}}.modal.show .modal-dialog{transform:none}.modal.modal-static .modal-dialog{transform:scale(1.02)}.modal-dialog-scrollable{display:flex;max-height:calc(100% - 1rem)}.modal-dialog-scrollable .modal-content{max-height:calc(100vh - 1rem);overflow:hidden}.modal-dialog-scrollable .modal-footer,.modal-dialog-scrollable .modal-header{flex-shrink:0}.modal-dialog-scrollable .modal-body{overflow-y:auto}.modal-dialog-centered{display:flex;align-items:center;min-height:calc(100% - 1rem)}.modal-dialog-centered:before{display:block;height:calc(100vh - 1rem);height:min-content;content:""}.modal-dialog-centered.modal-dialog-scrollable{flex-direction:column;justify-content:center;height:100%}.modal-dialog-centered.modal-dialog-scrollable .modal-content{max-height:none}.modal-dialog-centered.modal-dialog-scrollable:before{content:none}.modal-content{position:relative;display:flex;flex-direction:column;width:100%;pointer-events:auto;background-color:#fff;background-clip:padding-box;border:1px solid rgba(0,0,0,.2);border-radius:.3rem;outline:0}.modal-backdrop{position:fixed;top:0;left:0;z-index:1040;width:100vw;height:100vh;background-color:#000}.modal-backdrop.fade{opacity:0}.modal-backdrop.show{opacity:.5}.modal-header{display:flex;align-items:flex-start;justify-content:space-between;padding:1rem;border-bottom:1px solid #dee2e6;border-top-left-radius:calc(.3rem - 1px);border-top-right-radius:calc(.3rem - 1px)}.modal-header .close{padding:1rem;margin:-1rem -1rem -1rem auto}.modal-title{margin-bottom:0;line-height:1.5}.modal-body{position:relative;flex:1 1 auto;padding:1rem}.modal-footer{display:flex;flex-wrap:wrap;align-items:center;justify-content:flex-end;padding:.75rem;border-top:1px solid #dee2e6;border-bottom-right-radius:calc(.3rem - 1px);border-bottom-left-radius:calc(.3rem - 1px)}.modal-footer>*{margin:.25rem}.modal-scrollbar-measure{position:absolute;top:-9999px;width:50px;height:50px;overflow:scroll}@media (min-width:540px){.modal-dialog{max-width:500px;margin:1.75rem auto}.modal-dialog-scrollable{max-height:calc(100% - 3.5rem)}.modal-dialog-scrollable .modal-content{max-height:calc(100vh - 3.5rem)}.modal-dialog-centered{min-height:calc(100% - 3.5rem)}.modal-dialog-centered:before{height:calc(100vh - 3.5rem);height:min-content}.modal-sm{max-width:300px}}@media (min-width:960px){.modal-lg,.modal-xl{max-width:800px}}@media (min-width:1200px){.modal-xl{max-width:1140px}}.tooltip{position:absolute;z-index:1070;display:block;margin:0;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji;font-style:normal;font-weight:400;line-height:1.5;text-align:left;text-align:start;text-decoration:none;text-shadow:none;text-transform:none;letter-spacing:normal;word-break:normal;word-spacing:normal;white-space:normal;line-break:auto;font-size:.875rem;word-wrap:break-word;opacity:0}.tooltip.show{opacity:.9}.tooltip .arrow{position:absolute;display:block;width:.8rem;height:.4rem}.tooltip .arrow:before{position:absolute;content:"";border-color:transparent;border-style:solid}.bs-tooltip-auto[x-placement^=top],.bs-tooltip-top{padding:.4rem 0}.bs-tooltip-auto[x-placement^=top] .arrow,.bs-tooltip-top .arrow{bottom:0}.bs-tooltip-auto[x-placement^=top] .arrow:before,.bs-tooltip-top .arrow:before{top:0;border-width:.4rem .4rem 0;border-top-color:#000}.bs-tooltip-auto[x-placement^=right],.bs-tooltip-right{padding:0 .4rem}.bs-tooltip-auto[x-placement^=right] .arrow,.bs-tooltip-right .arrow{left:0;width:.4rem;height:.8rem}.bs-tooltip-auto[x-placement^=right] .arrow:before,.bs-tooltip-right .arrow:before{right:0;border-width:.4rem .4rem .4rem 0;border-right-color:#000}.bs-tooltip-auto[x-placement^=bottom],.bs-tooltip-bottom{padding:.4rem 0}.bs-tooltip-auto[x-placement^=bottom] .arrow,.bs-tooltip-bottom .arrow{top:0}.bs-tooltip-auto[x-placement^=bottom] .arrow:before,.bs-tooltip-bottom .arrow:before{bottom:0;border-width:0 .4rem .4rem;border-bottom-color:#000}.bs-tooltip-auto[x-placement^=left],.bs-tooltip-left{padding:0 .4rem}.bs-tooltip-auto[x-placement^=left] .arrow,.bs-tooltip-left .arrow{right:0;width:.4rem;height:.8rem}.bs-tooltip-auto[x-placement^=left] .arrow:before,.bs-tooltip-left .arrow:before{left:0;border-width:.4rem 0 .4rem .4rem;border-left-color:#000}.tooltip-inner{max-width:200px;padding:.25rem .5rem;color:#fff;text-align:center;background-color:#000;border-radius:.25rem}.popover{top:0;left:0;z-index:1060;max-width:276px;font-family:-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji;font-style:normal;font-weight:400;line-height:1.5;text-align:left;text-align:start;text-decoration:none;text-shadow:none;text-transform:none;letter-spacing:normal;word-break:normal;word-spacing:normal;white-space:normal;line-break:auto;font-size:.875rem;word-wrap:break-word;background-color:#fff;background-clip:padding-box;border:1px solid rgba(0,0,0,.2);border-radius:.3rem}.popover,.popover .arrow{position:absolute;display:block}.popover .arrow{width:1rem;height:.5rem;margin:0 .3rem}.popover .arrow:after,.popover .arrow:before{position:absolute;display:block;content:"";border-color:transparent;border-style:solid}.bs-popover-auto[x-placement^=top],.bs-popover-top{margin-bottom:.5rem}.bs-popover-auto[x-placement^=top]>.arrow,.bs-popover-top>.arrow{bottom:calc(-.5rem - 1px)}.bs-popover-auto[x-placement^=top]>.arrow:before,.bs-popover-top>.arrow:before{bottom:0;border-width:.5rem .5rem 0;border-top-color:rgba(0,0,0,.25)}.bs-popover-auto[x-placement^=top]>.arrow:after,.bs-popover-top>.arrow:after{bottom:1px;border-width:.5rem .5rem 0;border-top-color:#fff}.bs-popover-auto[x-placement^=right],.bs-popover-right{margin-left:.5rem}.bs-popover-auto[x-placement^=right]>.arrow,.bs-popover-right>.arrow{left:calc(-.5rem - 1px);width:.5rem;height:1rem;margin:.3rem 0}.bs-popover-auto[x-placement^=right]>.arrow:before,.bs-popover-right>.arrow:before{left:0;border-width:.5rem .5rem .5rem 0;border-right-color:rgba(0,0,0,.25)}.bs-popover-auto[x-placement^=right]>.arrow:after,.bs-popover-right>.arrow:after{left:1px;border-width:.5rem .5rem .5rem 0;border-right-color:#fff}.bs-popover-auto[x-placement^=bottom],.bs-popover-bottom{margin-top:.5rem}.bs-popover-auto[x-placement^=bottom]>.arrow,.bs-popover-bottom>.arrow{top:calc(-.5rem - 1px)}.bs-popover-auto[x-placement^=bottom]>.arrow:before,.bs-popover-bottom>.arrow:before{top:0;border-width:0 .5rem .5rem;border-bottom-color:rgba(0,0,0,.25)}.bs-popover-auto[x-placement^=bottom]>.arrow:after,.bs-popover-bottom>.arrow:after{top:1px;border-width:0 .5rem .5rem;border-bottom-color:#fff}.bs-popover-auto[x-placement^=bottom] .popover-header:before,.bs-popover-bottom .popover-header:before{position:absolute;top:0;left:50%;display:block;width:1rem;margin-left:-.5rem;content:"";border-bottom:1px solid #f7f7f7}.bs-popover-auto[x-placement^=left],.bs-popover-left{margin-right:.5rem}.bs-popover-auto[x-placement^=left]>.arrow,.bs-popover-left>.arrow{right:calc(-.5rem - 1px);width:.5rem;height:1rem;margin:.3rem 0}.bs-popover-auto[x-placement^=left]>.arrow:before,.bs-popover-left>.arrow:before{right:0;border-width:.5rem 0 .5rem .5rem;border-left-color:rgba(0,0,0,.25)}.bs-popover-auto[x-placement^=left]>.arrow:after,.bs-popover-left>.arrow:after{right:1px;border-width:.5rem 0 .5rem .5rem;border-left-color:#fff}.popover-header{padding:.5rem .75rem;margin-bottom:0;font-size:1rem;background-color:#f7f7f7;border-bottom:1px solid #ebebeb;border-top-left-radius:calc(.3rem - 1px);border-top-right-radius:calc(.3rem - 1px)}.popover-header:empty{display:none}.popover-body{padding:.5rem .75rem;color:#212529}.carousel{position:relative}.carousel.pointer-event{touch-action:pan-y}.carousel-inner{position:relative;width:100%;overflow:hidden}.carousel-inner:after{display:block;clear:both;content:""}.carousel-item{position:relative;display:none;float:left;width:100%;margin-right:-100%;backface-visibility:hidden;transition:transform .6s ease-in-out}@media (prefers-reduced-motion:reduce){.carousel-item{transition:none}}.carousel-item-next,.carousel-item-prev,.carousel-item.active{display:block}.active.carousel-item-right,.carousel-item-next:not(.carousel-item-left){transform:translateX(100%)}.active.carousel-item-left,.carousel-item-prev:not(.carousel-item-right){transform:translateX(-100%)}.carousel-fade .carousel-item{opacity:0;transition-property:opacity;transform:none}.carousel-fade .carousel-item-next.carousel-item-left,.carousel-fade .carousel-item-prev.carousel-item-right,.carousel-fade .carousel-item.active{z-index:1;opacity:1}.carousel-fade .active.carousel-item-left,.carousel-fade .active.carousel-item-right{z-index:0;opacity:0;transition:opacity 0s .6s}@media (prefers-reduced-motion:reduce){.carousel-fade .active.carousel-item-left,.carousel-fade .active.carousel-item-right{transition:none}}.carousel-control-next,.carousel-control-prev{position:absolute;top:0;bottom:0;z-index:1;display:flex;align-items:center;justify-content:center;width:15%;color:#fff;text-align:center;opacity:.5;transition:opacity .15s ease}@media (prefers-reduced-motion:reduce){.carousel-control-next,.carousel-control-prev{transition:none}}.carousel-control-next:focus,.carousel-control-next:hover,.carousel-control-prev:focus,.carousel-control-prev:hover{color:#fff;text-decoration:none;outline:0;opacity:.9}.carousel-control-prev{left:0}.carousel-control-next{right:0}.carousel-control-next-icon,.carousel-control-prev-icon{display:inline-block;width:20px;height:20px;background:no-repeat 50%/100% 100%}.carousel-control-prev-icon{background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='%23fff' width='8' height='8'%3E%3Cpath d='M5.25 0l-4 4 4 4 1.5-1.5L4.25 4l2.5-2.5L5.25 0z'/%3E%3C/svg%3E")}.carousel-control-next-icon{background-image:url("data:image/svg+xml;charset=utf-8,%3Csvg xmlns='http://www.w3.org/2000/svg' fill='%23fff' width='8' height='8'%3E%3Cpath d='M2.75 0l-1.5 1.5L3.75 4l-2.5 2.5L2.75 8l4-4-4-4z'/%3E%3C/svg%3E")}.carousel-indicators{position:absolute;right:0;bottom:0;left:0;z-index:15;display:flex;justify-content:center;padding-left:0;margin-right:15%;margin-left:15%;list-style:none}.carousel-indicators li{box-sizing:content-box;flex:0 1 auto;width:30px;height:3px;margin-right:3px;margin-left:3px;text-indent:-999px;cursor:pointer;background-color:#fff;background-clip:padding-box;border-top:10px solid transparent;border-bottom:10px solid transparent;opacity:.5;transition:opacity .6s ease}@media (prefers-reduced-motion:reduce){.carousel-indicators li{transition:none}}.carousel-indicators .active{opacity:1}.carousel-caption{position:absolute;right:15%;bottom:20px;left:15%;z-index:10;padding-top:20px;padding-bottom:20px;color:#fff;text-align:center}@keyframes spinner-border{to{transform:rotate(1turn)}}.spinner-border{display:inline-block;width:2rem;height:2rem;vertical-align:text-bottom;border:.25em solid;border-right:.25em solid transparent;border-radius:50%;animation:spinner-border .75s linear infinite}.spinner-border-sm{width:1rem;height:1rem;border-width:.2em}@keyframes spinner-grow{0%{transform:scale(0)}50%{opacity:1;transform:none}}.spinner-grow{display:inline-block;width:2rem;height:2rem;vertical-align:text-bottom;background-color:currentColor;border-radius:50%;opacity:0;animation:spinner-grow .75s linear infinite}.spinner-grow-sm{width:1rem;height:1rem}.align-baseline{vertical-align:baseline!important}.align-top{vertical-align:top!important}.align-middle{vertical-align:middle!important}.align-bottom{vertical-align:bottom!important}.align-text-bottom{vertical-align:text-bottom!important}.align-text-top{vertical-align:text-top!important}.bg-primary{background-color:#007bff!important}a.bg-primary:focus,a.bg-primary:hover,button.bg-primary:focus,button.bg-primary:hover{background-color:#0062cc!important}.bg-secondary{background-color:#6c757d!important}a.bg-secondary:focus,a.bg-secondary:hover,button.bg-secondary:focus,button.bg-secondary:hover{background-color:#545b62!important}.bg-success{background-color:#28a745!important}a.bg-success:focus,a.bg-success:hover,button.bg-success:focus,button.bg-success:hover{background-color:#1e7e34!important}.bg-info{background-color:#17a2b8!important}a.bg-info:focus,a.bg-info:hover,button.bg-info:focus,button.bg-info:hover{background-color:#117a8b!important}.bg-warning{background-color:#ffc107!important}a.bg-warning:focus,a.bg-warning:hover,button.bg-warning:focus,button.bg-warning:hover{background-color:#d39e00!important}.bg-danger{background-color:#dc3545!important}a.bg-danger:focus,a.bg-danger:hover,button.bg-danger:focus,button.bg-danger:hover{background-color:#bd2130!important}.bg-light{background-color:#f8f9fa!important}a.bg-light:focus,a.bg-light:hover,button.bg-light:focus,button.bg-light:hover{background-color:#dae0e5!important}.bg-dark{background-color:#343a40!important}a.bg-dark:focus,a.bg-dark:hover,button.bg-dark:focus,button.bg-dark:hover{background-color:#1d2124!important}.bg-white{background-color:#fff!important}.bg-transparent{background-color:transparent!important}.border{border:1px solid #dee2e6!important}.border-top{border-top:1px solid #dee2e6!important}.border-right{border-right:1px solid #dee2e6!important}.border-bottom{border-bottom:1px solid #dee2e6!important}.border-left{border-left:1px solid #dee2e6!important}.border-0{border:0!important}.border-top-0{border-top:0!important}.border-right-0{border-right:0!important}.border-bottom-0{border-bottom:0!important}.border-left-0{border-left:0!important}.border-primary{border-color:#007bff!important}.border-secondary{border-color:#6c757d!important}.border-success{border-color:#28a745!important}.border-info{border-color:#17a2b8!important}.border-warning{border-color:#ffc107!important}.border-danger{border-color:#dc3545!important}.border-light{border-color:#f8f9fa!important}.border-dark{border-color:#343a40!important}.border-white{border-color:#fff!important}.rounded-sm{border-radius:.2rem!important}.rounded{border-radius:.25rem!important}.rounded-top{border-top-left-radius:.25rem!important}.rounded-right,.rounded-top{border-top-right-radius:.25rem!important}.rounded-bottom,.rounded-right{border-bottom-right-radius:.25rem!important}.rounded-bottom,.rounded-left{border-bottom-left-radius:.25rem!important}.rounded-left{border-top-left-radius:.25rem!important}.rounded-lg{border-radius:.3rem!important}.rounded-circle{border-radius:50%!important}.rounded-pill{border-radius:50rem!important}.rounded-0{border-radius:0!important}.clearfix:after{display:block;clear:both;content:""}.d-none{display:none!important}.d-inline{display:inline!important}.d-inline-block{display:inline-block!important}.d-block{display:block!important}.d-table{display:table!important}.d-table-row{display:table-row!important}.d-table-cell{display:table-cell!important}.d-flex{display:flex!important}.d-inline-flex{display:inline-flex!important}@media (min-width:540px){.d-sm-none{display:none!important}.d-sm-inline{display:inline!important}.d-sm-inline-block{display:inline-block!important}.d-sm-block{display:block!important}.d-sm-table{display:table!important}.d-sm-table-row{display:table-row!important}.d-sm-table-cell{display:table-cell!important}.d-sm-flex{display:flex!important}.d-sm-inline-flex{display:inline-flex!important}}@media (min-width:720px){.d-md-none{display:none!important}.d-md-inline{display:inline!important}.d-md-inline-block{display:inline-block!important}.d-md-block{display:block!important}.d-md-table{display:table!important}.d-md-table-row{display:table-row!important}.d-md-table-cell{display:table-cell!important}.d-md-flex{display:flex!important}.d-md-inline-flex{display:inline-flex!important}}@media (min-width:960px){.d-lg-none{display:none!important}.d-lg-inline{display:inline!important}.d-lg-inline-block{display:inline-block!important}.d-lg-block{display:block!important}.d-lg-table{display:table!important}.d-lg-table-row{display:table-row!important}.d-lg-table-cell{display:table-cell!important}.d-lg-flex{display:flex!important}.d-lg-inline-flex{display:inline-flex!important}}@media (min-width:1200px){.d-xl-none{display:none!important}.d-xl-inline{display:inline!important}.d-xl-inline-block{display:inline-block!important}.d-xl-block{display:block!important}.d-xl-table{display:table!important}.d-xl-table-row{display:table-row!important}.d-xl-table-cell{display:table-cell!important}.d-xl-flex{display:flex!important}.d-xl-inline-flex{display:inline-flex!important}}@media print{.d-print-none{display:none!important}.d-print-inline{display:inline!important}.d-print-inline-block{display:inline-block!important}.d-print-block{display:block!important}.d-print-table{display:table!important}.d-print-table-row{display:table-row!important}.d-print-table-cell{display:table-cell!important}.d-print-flex{display:flex!important}.d-print-inline-flex{display:inline-flex!important}}.embed-responsive{position:relative;display:block;width:100%;padding:0;overflow:hidden}.embed-responsive:before{display:block;content:""}.embed-responsive .embed-responsive-item,.embed-responsive embed,.embed-responsive iframe,.embed-responsive object,.embed-responsive video{position:absolute;top:0;bottom:0;left:0;width:100%;height:100%;border:0}.embed-responsive-21by9:before{padding-top:42.85714%}.embed-responsive-16by9:before{padding-top:56.25%}.embed-responsive-4by3:before{padding-top:75%}.embed-responsive-1by1:before{padding-top:100%}.flex-row{flex-direction:row!important}.flex-column{flex-direction:column!important}.flex-row-reverse{flex-direction:row-reverse!important}.flex-column-reverse{flex-direction:column-reverse!important}.flex-wrap{flex-wrap:wrap!important}.flex-nowrap{flex-wrap:nowrap!important}.flex-wrap-reverse{flex-wrap:wrap-reverse!important}.flex-fill{flex:1 1 auto!important}.flex-grow-0{flex-grow:0!important}.flex-grow-1{flex-grow:1!important}.flex-shrink-0{flex-shrink:0!important}.flex-shrink-1{flex-shrink:1!important}.justify-content-start{justify-content:flex-start!important}.justify-content-end{justify-content:flex-end!important}.justify-content-center{justify-content:center!important}.justify-content-between{justify-content:space-between!important}.justify-content-around{justify-content:space-around!important}.align-items-start{align-items:flex-start!important}.align-items-end{align-items:flex-end!important}.align-items-center{align-items:center!important}.align-items-baseline{align-items:baseline!important}.align-items-stretch{align-items:stretch!important}.align-content-start{align-content:flex-start!important}.align-content-end{align-content:flex-end!important}.align-content-center{align-content:center!important}.align-content-between{align-content:space-between!important}.align-content-around{align-content:space-around!important}.align-content-stretch{align-content:stretch!important}.align-self-auto{align-self:auto!important}.align-self-start{align-self:flex-start!important}.align-self-end{align-self:flex-end!important}.align-self-center{align-self:center!important}.align-self-baseline{align-self:baseline!important}.align-self-stretch{align-self:stretch!important}@media (min-width:540px){.flex-sm-row{flex-direction:row!important}.flex-sm-column{flex-direction:column!important}.flex-sm-row-reverse{flex-direction:row-reverse!important}.flex-sm-column-reverse{flex-direction:column-reverse!important}.flex-sm-wrap{flex-wrap:wrap!important}.flex-sm-nowrap{flex-wrap:nowrap!important}.flex-sm-wrap-reverse{flex-wrap:wrap-reverse!important}.flex-sm-fill{flex:1 1 auto!important}.flex-sm-grow-0{flex-grow:0!important}.flex-sm-grow-1{flex-grow:1!important}.flex-sm-shrink-0{flex-shrink:0!important}.flex-sm-shrink-1{flex-shrink:1!important}.justify-content-sm-start{justify-content:flex-start!important}.justify-content-sm-end{justify-content:flex-end!important}.justify-content-sm-center{justify-content:center!important}.justify-content-sm-between{justify-content:space-between!important}.justify-content-sm-around{justify-content:space-around!important}.align-items-sm-start{align-items:flex-start!important}.align-items-sm-end{align-items:flex-end!important}.align-items-sm-center{align-items:center!important}.align-items-sm-baseline{align-items:baseline!important}.align-items-sm-stretch{align-items:stretch!important}.align-content-sm-start{align-content:flex-start!important}.align-content-sm-end{align-content:flex-end!important}.align-content-sm-center{align-content:center!important}.align-content-sm-between{align-content:space-between!important}.align-content-sm-around{align-content:space-around!important}.align-content-sm-stretch{align-content:stretch!important}.align-self-sm-auto{align-self:auto!important}.align-self-sm-start{align-self:flex-start!important}.align-self-sm-end{align-self:flex-end!important}.align-self-sm-center{align-self:center!important}.align-self-sm-baseline{align-self:baseline!important}.align-self-sm-stretch{align-self:stretch!important}}@media (min-width:720px){.flex-md-row{flex-direction:row!important}.flex-md-column{flex-direction:column!important}.flex-md-row-reverse{flex-direction:row-reverse!important}.flex-md-column-reverse{flex-direction:column-reverse!important}.flex-md-wrap{flex-wrap:wrap!important}.flex-md-nowrap{flex-wrap:nowrap!important}.flex-md-wrap-reverse{flex-wrap:wrap-reverse!important}.flex-md-fill{flex:1 1 auto!important}.flex-md-grow-0{flex-grow:0!important}.flex-md-grow-1{flex-grow:1!important}.flex-md-shrink-0{flex-shrink:0!important}.flex-md-shrink-1{flex-shrink:1!important}.justify-content-md-start{justify-content:flex-start!important}.justify-content-md-end{justify-content:flex-end!important}.justify-content-md-center{justify-content:center!important}.justify-content-md-between{justify-content:space-between!important}.justify-content-md-around{justify-content:space-around!important}.align-items-md-start{align-items:flex-start!important}.align-items-md-end{align-items:flex-end!important}.align-items-md-center{align-items:center!important}.align-items-md-baseline{align-items:baseline!important}.align-items-md-stretch{align-items:stretch!important}.align-content-md-start{align-content:flex-start!important}.align-content-md-end{align-content:flex-end!important}.align-content-md-center{align-content:center!important}.align-content-md-between{align-content:space-between!important}.align-content-md-around{align-content:space-around!important}.align-content-md-stretch{align-content:stretch!important}.align-self-md-auto{align-self:auto!important}.align-self-md-start{align-self:flex-start!important}.align-self-md-end{align-self:flex-end!important}.align-self-md-center{align-self:center!important}.align-self-md-baseline{align-self:baseline!important}.align-self-md-stretch{align-self:stretch!important}}@media (min-width:960px){.flex-lg-row{flex-direction:row!important}.flex-lg-column{flex-direction:column!important}.flex-lg-row-reverse{flex-direction:row-reverse!important}.flex-lg-column-reverse{flex-direction:column-reverse!important}.flex-lg-wrap{flex-wrap:wrap!important}.flex-lg-nowrap{flex-wrap:nowrap!important}.flex-lg-wrap-reverse{flex-wrap:wrap-reverse!important}.flex-lg-fill{flex:1 1 auto!important}.flex-lg-grow-0{flex-grow:0!important}.flex-lg-grow-1{flex-grow:1!important}.flex-lg-shrink-0{flex-shrink:0!important}.flex-lg-shrink-1{flex-shrink:1!important}.justify-content-lg-start{justify-content:flex-start!important}.justify-content-lg-end{justify-content:flex-end!important}.justify-content-lg-center{justify-content:center!important}.justify-content-lg-between{justify-content:space-between!important}.justify-content-lg-around{justify-content:space-around!important}.align-items-lg-start{align-items:flex-start!important}.align-items-lg-end{align-items:flex-end!important}.align-items-lg-center{align-items:center!important}.align-items-lg-baseline{align-items:baseline!important}.align-items-lg-stretch{align-items:stretch!important}.align-content-lg-start{align-content:flex-start!important}.align-content-lg-end{align-content:flex-end!important}.align-content-lg-center{align-content:center!important}.align-content-lg-between{align-content:space-between!important}.align-content-lg-around{align-content:space-around!important}.align-content-lg-stretch{align-content:stretch!important}.align-self-lg-auto{align-self:auto!important}.align-self-lg-start{align-self:flex-start!important}.align-self-lg-end{align-self:flex-end!important}.align-self-lg-center{align-self:center!important}.align-self-lg-baseline{align-self:baseline!important}.align-self-lg-stretch{align-self:stretch!important}}@media (min-width:1200px){.flex-xl-row{flex-direction:row!important}.flex-xl-column{flex-direction:column!important}.flex-xl-row-reverse{flex-direction:row-reverse!important}.flex-xl-column-reverse{flex-direction:column-reverse!important}.flex-xl-wrap{flex-wrap:wrap!important}.flex-xl-nowrap{flex-wrap:nowrap!important}.flex-xl-wrap-reverse{flex-wrap:wrap-reverse!important}.flex-xl-fill{flex:1 1 auto!important}.flex-xl-grow-0{flex-grow:0!important}.flex-xl-grow-1{flex-grow:1!important}.flex-xl-shrink-0{flex-shrink:0!important}.flex-xl-shrink-1{flex-shrink:1!important}.justify-content-xl-start{justify-content:flex-start!important}.justify-content-xl-end{justify-content:flex-end!important}.justify-content-xl-center{justify-content:center!important}.justify-content-xl-between{justify-content:space-between!important}.justify-content-xl-around{justify-content:space-around!important}.align-items-xl-start{align-items:flex-start!important}.align-items-xl-end{align-items:flex-end!important}.align-items-xl-center{align-items:center!important}.align-items-xl-baseline{align-items:baseline!important}.align-items-xl-stretch{align-items:stretch!important}.align-content-xl-start{align-content:flex-start!important}.align-content-xl-end{align-content:flex-end!important}.align-content-xl-center{align-content:center!important}.align-content-xl-between{align-content:space-between!important}.align-content-xl-around{align-content:space-around!important}.align-content-xl-stretch{align-content:stretch!important}.align-self-xl-auto{align-self:auto!important}.align-self-xl-start{align-self:flex-start!important}.align-self-xl-end{align-self:flex-end!important}.align-self-xl-center{align-self:center!important}.align-self-xl-baseline{align-self:baseline!important}.align-self-xl-stretch{align-self:stretch!important}}.float-left{float:left!important}.float-right{float:right!important}.float-none{float:none!important}@media (min-width:540px){.float-sm-left{float:left!important}.float-sm-right{float:right!important}.float-sm-none{float:none!important}}@media (min-width:720px){.float-md-left{float:left!important}.float-md-right{float:right!important}.float-md-none{float:none!important}}@media (min-width:960px){.float-lg-left{float:left!important}.float-lg-right{float:right!important}.float-lg-none{float:none!important}}@media (min-width:1200px){.float-xl-left{float:left!important}.float-xl-right{float:right!important}.float-xl-none{float:none!important}}.user-select-all{user-select:all!important}.user-select-auto{user-select:auto!important}.user-select-none{user-select:none!important}.overflow-auto{overflow:auto!important}.overflow-hidden{overflow:hidden!important}.position-static{position:static!important}.position-relative{position:relative!important}.position-absolute{position:absolute!important}.position-fixed{position:fixed!important}.position-sticky{position:sticky!important}.fixed-top{top:0}.fixed-bottom,.fixed-top{position:fixed;right:0;left:0;z-index:1030}.fixed-bottom{bottom:0}@supports (position:sticky){.sticky-top{position:sticky;top:0;z-index:1020}}.sr-only{position:absolute;width:1px;height:1px;padding:0;margin:-1px;overflow:hidden;clip:rect(0,0,0,0);white-space:nowrap;border:0}.sr-only-focusable:active,.sr-only-focusable:focus{position:static;width:auto;height:auto;overflow:visible;clip:auto;white-space:normal}.shadow-sm{box-shadow:0 .125rem .25rem rgba(0,0,0,.075)!important}.shadow{box-shadow:0 .5rem 1rem rgba(0,0,0,.15)!important}.shadow-lg{box-shadow:0 1rem 3rem rgba(0,0,0,.175)!important}.shadow-none{box-shadow:none!important}.w-25{width:25%!important}.w-50{width:50%!important}.w-75{width:75%!important}.w-100{width:100%!important}.w-auto{width:auto!important}.h-25{height:25%!important}.h-50{height:50%!important}.h-75{height:75%!important}.h-100{height:100%!important}.h-auto{height:auto!important}.mw-100{max-width:100%!important}.mh-100{max-height:100%!important}.min-vw-100{min-width:100vw!important}.min-vh-100{min-height:100vh!important}.vw-100{width:100vw!important}.vh-100{height:100vh!important}.m-0{margin:0!important}.mt-0,.my-0{margin-top:0!important}.mr-0,.mx-0{margin-right:0!important}.mb-0,.my-0{margin-bottom:0!important}.ml-0,.mx-0{margin-left:0!important}.m-1{margin:.25rem!important}.mt-1,.my-1{margin-top:.25rem!important}.mr-1,.mx-1{margin-right:.25rem!important}.mb-1,.my-1{margin-bottom:.25rem!important}.ml-1,.mx-1{margin-left:.25rem!important}.m-2{margin:.5rem!important}.mt-2,.my-2{margin-top:.5rem!important}.mr-2,.mx-2{margin-right:.5rem!important}.mb-2,.my-2{margin-bottom:.5rem!important}.ml-2,.mx-2{margin-left:.5rem!important}.m-3{margin:1rem!important}.mt-3,.my-3{margin-top:1rem!important}.mr-3,.mx-3{margin-right:1rem!important}.mb-3,.my-3{margin-bottom:1rem!important}.ml-3,.mx-3{margin-left:1rem!important}.m-4{margin:1.5rem!important}.mt-4,.my-4{margin-top:1.5rem!important}.mr-4,.mx-4{margin-right:1.5rem!important}.mb-4,.my-4{margin-bottom:1.5rem!important}.ml-4,.mx-4{margin-left:1.5rem!important}.m-5{margin:3rem!important}.mt-5,.my-5{margin-top:3rem!important}.mr-5,.mx-5{margin-right:3rem!important}.mb-5,.my-5{margin-bottom:3rem!important}.ml-5,.mx-5{margin-left:3rem!important}.p-0{padding:0!important}.pt-0,.py-0{padding-top:0!important}.pr-0,.px-0{padding-right:0!important}.pb-0,.py-0{padding-bottom:0!important}.pl-0,.px-0{padding-left:0!important}.p-1{padding:.25rem!important}.pt-1,.py-1{padding-top:.25rem!important}.pr-1,.px-1{padding-right:.25rem!important}.pb-1,.py-1{padding-bottom:.25rem!important}.pl-1,.px-1{padding-left:.25rem!important}.p-2{padding:.5rem!important}.pt-2,.py-2{padding-top:.5rem!important}.pr-2,.px-2{padding-right:.5rem!important}.pb-2,.py-2{padding-bottom:.5rem!important}.pl-2,.px-2{padding-left:.5rem!important}.p-3{padding:1rem!important}.pt-3,.py-3{padding-top:1rem!important}.pr-3,.px-3{padding-right:1rem!important}.pb-3,.py-3{padding-bottom:1rem!important}.pl-3,.px-3{padding-left:1rem!important}.p-4{padding:1.5rem!important}.pt-4,.py-4{padding-top:1.5rem!important}.pr-4,.px-4{padding-right:1.5rem!important}.pb-4,.py-4{padding-bottom:1.5rem!important}.pl-4,.px-4{padding-left:1.5rem!important}.p-5{padding:3rem!important}.pt-5,.py-5{padding-top:3rem!important}.pr-5,.px-5{padding-right:3rem!important}.pb-5,.py-5{padding-bottom:3rem!important}.pl-5,.px-5{padding-left:3rem!important}.m-n1{margin:-.25rem!important}.mt-n1,.my-n1{margin-top:-.25rem!important}.mr-n1,.mx-n1{margin-right:-.25rem!important}.mb-n1,.my-n1{margin-bottom:-.25rem!important}.ml-n1,.mx-n1{margin-left:-.25rem!important}.m-n2{margin:-.5rem!important}.mt-n2,.my-n2{margin-top:-.5rem!important}.mr-n2,.mx-n2{margin-right:-.5rem!important}.mb-n2,.my-n2{margin-bottom:-.5rem!important}.ml-n2,.mx-n2{margin-left:-.5rem!important}.m-n3{margin:-1rem!important}.mt-n3,.my-n3{margin-top:-1rem!important}.mr-n3,.mx-n3{margin-right:-1rem!important}.mb-n3,.my-n3{margin-bottom:-1rem!important}.ml-n3,.mx-n3{margin-left:-1rem!important}.m-n4{margin:-1.5rem!important}.mt-n4,.my-n4{margin-top:-1.5rem!important}.mr-n4,.mx-n4{margin-right:-1.5rem!important}.mb-n4,.my-n4{margin-bottom:-1.5rem!important}.ml-n4,.mx-n4{margin-left:-1.5rem!important}.m-n5{margin:-3rem!important}.mt-n5,.my-n5{margin-top:-3rem!important}.mr-n5,.mx-n5{margin-right:-3rem!important}.mb-n5,.my-n5{margin-bottom:-3rem!important}.ml-n5,.mx-n5{margin-left:-3rem!important}.m-auto{margin:auto!important}.mt-auto,.my-auto{margin-top:auto!important}.mr-auto,.mx-auto{margin-right:auto!important}.mb-auto,.my-auto{margin-bottom:auto!important}.ml-auto,.mx-auto{margin-left:auto!important}@media (min-width:540px){.m-sm-0{margin:0!important}.mt-sm-0,.my-sm-0{margin-top:0!important}.mr-sm-0,.mx-sm-0{margin-right:0!important}.mb-sm-0,.my-sm-0{margin-bottom:0!important}.ml-sm-0,.mx-sm-0{margin-left:0!important}.m-sm-1{margin:.25rem!important}.mt-sm-1,.my-sm-1{margin-top:.25rem!important}.mr-sm-1,.mx-sm-1{margin-right:.25rem!important}.mb-sm-1,.my-sm-1{margin-bottom:.25rem!important}.ml-sm-1,.mx-sm-1{margin-left:.25rem!important}.m-sm-2{margin:.5rem!important}.mt-sm-2,.my-sm-2{margin-top:.5rem!important}.mr-sm-2,.mx-sm-2{margin-right:.5rem!important}.mb-sm-2,.my-sm-2{margin-bottom:.5rem!important}.ml-sm-2,.mx-sm-2{margin-left:.5rem!important}.m-sm-3{margin:1rem!important}.mt-sm-3,.my-sm-3{margin-top:1rem!important}.mr-sm-3,.mx-sm-3{margin-right:1rem!important}.mb-sm-3,.my-sm-3{margin-bottom:1rem!important}.ml-sm-3,.mx-sm-3{margin-left:1rem!important}.m-sm-4{margin:1.5rem!important}.mt-sm-4,.my-sm-4{margin-top:1.5rem!important}.mr-sm-4,.mx-sm-4{margin-right:1.5rem!important}.mb-sm-4,.my-sm-4{margin-bottom:1.5rem!important}.ml-sm-4,.mx-sm-4{margin-left:1.5rem!important}.m-sm-5{margin:3rem!important}.mt-sm-5,.my-sm-5{margin-top:3rem!important}.mr-sm-5,.mx-sm-5{margin-right:3rem!important}.mb-sm-5,.my-sm-5{margin-bottom:3rem!important}.ml-sm-5,.mx-sm-5{margin-left:3rem!important}.p-sm-0{padding:0!important}.pt-sm-0,.py-sm-0{padding-top:0!important}.pr-sm-0,.px-sm-0{padding-right:0!important}.pb-sm-0,.py-sm-0{padding-bottom:0!important}.pl-sm-0,.px-sm-0{padding-left:0!important}.p-sm-1{padding:.25rem!important}.pt-sm-1,.py-sm-1{padding-top:.25rem!important}.pr-sm-1,.px-sm-1{padding-right:.25rem!important}.pb-sm-1,.py-sm-1{padding-bottom:.25rem!important}.pl-sm-1,.px-sm-1{padding-left:.25rem!important}.p-sm-2{padding:.5rem!important}.pt-sm-2,.py-sm-2{padding-top:.5rem!important}.pr-sm-2,.px-sm-2{padding-right:.5rem!important}.pb-sm-2,.py-sm-2{padding-bottom:.5rem!important}.pl-sm-2,.px-sm-2{padding-left:.5rem!important}.p-sm-3{padding:1rem!important}.pt-sm-3,.py-sm-3{padding-top:1rem!important}.pr-sm-3,.px-sm-3{padding-right:1rem!important}.pb-sm-3,.py-sm-3{padding-bottom:1rem!important}.pl-sm-3,.px-sm-3{padding-left:1rem!important}.p-sm-4{padding:1.5rem!important}.pt-sm-4,.py-sm-4{padding-top:1.5rem!important}.pr-sm-4,.px-sm-4{padding-right:1.5rem!important}.pb-sm-4,.py-sm-4{padding-bottom:1.5rem!important}.pl-sm-4,.px-sm-4{padding-left:1.5rem!important}.p-sm-5{padding:3rem!important}.pt-sm-5,.py-sm-5{padding-top:3rem!important}.pr-sm-5,.px-sm-5{padding-right:3rem!important}.pb-sm-5,.py-sm-5{padding-bottom:3rem!important}.pl-sm-5,.px-sm-5{padding-left:3rem!important}.m-sm-n1{margin:-.25rem!important}.mt-sm-n1,.my-sm-n1{margin-top:-.25rem!important}.mr-sm-n1,.mx-sm-n1{margin-right:-.25rem!important}.mb-sm-n1,.my-sm-n1{margin-bottom:-.25rem!important}.ml-sm-n1,.mx-sm-n1{margin-left:-.25rem!important}.m-sm-n2{margin:-.5rem!important}.mt-sm-n2,.my-sm-n2{margin-top:-.5rem!important}.mr-sm-n2,.mx-sm-n2{margin-right:-.5rem!important}.mb-sm-n2,.my-sm-n2{margin-bottom:-.5rem!important}.ml-sm-n2,.mx-sm-n2{margin-left:-.5rem!important}.m-sm-n3{margin:-1rem!important}.mt-sm-n3,.my-sm-n3{margin-top:-1rem!important}.mr-sm-n3,.mx-sm-n3{margin-right:-1rem!important}.mb-sm-n3,.my-sm-n3{margin-bottom:-1rem!important}.ml-sm-n3,.mx-sm-n3{margin-left:-1rem!important}.m-sm-n4{margin:-1.5rem!important}.mt-sm-n4,.my-sm-n4{margin-top:-1.5rem!important}.mr-sm-n4,.mx-sm-n4{margin-right:-1.5rem!important}.mb-sm-n4,.my-sm-n4{margin-bottom:-1.5rem!important}.ml-sm-n4,.mx-sm-n4{margin-left:-1.5rem!important}.m-sm-n5{margin:-3rem!important}.mt-sm-n5,.my-sm-n5{margin-top:-3rem!important}.mr-sm-n5,.mx-sm-n5{margin-right:-3rem!important}.mb-sm-n5,.my-sm-n5{margin-bottom:-3rem!important}.ml-sm-n5,.mx-sm-n5{margin-left:-3rem!important}.m-sm-auto{margin:auto!important}.mt-sm-auto,.my-sm-auto{margin-top:auto!important}.mr-sm-auto,.mx-sm-auto{margin-right:auto!important}.mb-sm-auto,.my-sm-auto{margin-bottom:auto!important}.ml-sm-auto,.mx-sm-auto{margin-left:auto!important}}@media (min-width:720px){.m-md-0{margin:0!important}.mt-md-0,.my-md-0{margin-top:0!important}.mr-md-0,.mx-md-0{margin-right:0!important}.mb-md-0,.my-md-0{margin-bottom:0!important}.ml-md-0,.mx-md-0{margin-left:0!important}.m-md-1{margin:.25rem!important}.mt-md-1,.my-md-1{margin-top:.25rem!important}.mr-md-1,.mx-md-1{margin-right:.25rem!important}.mb-md-1,.my-md-1{margin-bottom:.25rem!important}.ml-md-1,.mx-md-1{margin-left:.25rem!important}.m-md-2{margin:.5rem!important}.mt-md-2,.my-md-2{margin-top:.5rem!important}.mr-md-2,.mx-md-2{margin-right:.5rem!important}.mb-md-2,.my-md-2{margin-bottom:.5rem!important}.ml-md-2,.mx-md-2{margin-left:.5rem!important}.m-md-3{margin:1rem!important}.mt-md-3,.my-md-3{margin-top:1rem!important}.mr-md-3,.mx-md-3{margin-right:1rem!important}.mb-md-3,.my-md-3{margin-bottom:1rem!important}.ml-md-3,.mx-md-3{margin-left:1rem!important}.m-md-4{margin:1.5rem!important}.mt-md-4,.my-md-4{margin-top:1.5rem!important}.mr-md-4,.mx-md-4{margin-right:1.5rem!important}.mb-md-4,.my-md-4{margin-bottom:1.5rem!important}.ml-md-4,.mx-md-4{margin-left:1.5rem!important}.m-md-5{margin:3rem!important}.mt-md-5,.my-md-5{margin-top:3rem!important}.mr-md-5,.mx-md-5{margin-right:3rem!important}.mb-md-5,.my-md-5{margin-bottom:3rem!important}.ml-md-5,.mx-md-5{margin-left:3rem!important}.p-md-0{padding:0!important}.pt-md-0,.py-md-0{padding-top:0!important}.pr-md-0,.px-md-0{padding-right:0!important}.pb-md-0,.py-md-0{padding-bottom:0!important}.pl-md-0,.px-md-0{padding-left:0!important}.p-md-1{padding:.25rem!important}.pt-md-1,.py-md-1{padding-top:.25rem!important}.pr-md-1,.px-md-1{padding-right:.25rem!important}.pb-md-1,.py-md-1{padding-bottom:.25rem!important}.pl-md-1,.px-md-1{padding-left:.25rem!important}.p-md-2{padding:.5rem!important}.pt-md-2,.py-md-2{padding-top:.5rem!important}.pr-md-2,.px-md-2{padding-right:.5rem!important}.pb-md-2,.py-md-2{padding-bottom:.5rem!important}.pl-md-2,.px-md-2{padding-left:.5rem!important}.p-md-3{padding:1rem!important}.pt-md-3,.py-md-3{padding-top:1rem!important}.pr-md-3,.px-md-3{padding-right:1rem!important}.pb-md-3,.py-md-3{padding-bottom:1rem!important}.pl-md-3,.px-md-3{padding-left:1rem!important}.p-md-4{padding:1.5rem!important}.pt-md-4,.py-md-4{padding-top:1.5rem!important}.pr-md-4,.px-md-4{padding-right:1.5rem!important}.pb-md-4,.py-md-4{padding-bottom:1.5rem!important}.pl-md-4,.px-md-4{padding-left:1.5rem!important}.p-md-5{padding:3rem!important}.pt-md-5,.py-md-5{padding-top:3rem!important}.pr-md-5,.px-md-5{padding-right:3rem!important}.pb-md-5,.py-md-5{padding-bottom:3rem!important}.pl-md-5,.px-md-5{padding-left:3rem!important}.m-md-n1{margin:-.25rem!important}.mt-md-n1,.my-md-n1{margin-top:-.25rem!important}.mr-md-n1,.mx-md-n1{margin-right:-.25rem!important}.mb-md-n1,.my-md-n1{margin-bottom:-.25rem!important}.ml-md-n1,.mx-md-n1{margin-left:-.25rem!important}.m-md-n2{margin:-.5rem!important}.mt-md-n2,.my-md-n2{margin-top:-.5rem!important}.mr-md-n2,.mx-md-n2{margin-right:-.5rem!important}.mb-md-n2,.my-md-n2{margin-bottom:-.5rem!important}.ml-md-n2,.mx-md-n2{margin-left:-.5rem!important}.m-md-n3{margin:-1rem!important}.mt-md-n3,.my-md-n3{margin-top:-1rem!important}.mr-md-n3,.mx-md-n3{margin-right:-1rem!important}.mb-md-n3,.my-md-n3{margin-bottom:-1rem!important}.ml-md-n3,.mx-md-n3{margin-left:-1rem!important}.m-md-n4{margin:-1.5rem!important}.mt-md-n4,.my-md-n4{margin-top:-1.5rem!important}.mr-md-n4,.mx-md-n4{margin-right:-1.5rem!important}.mb-md-n4,.my-md-n4{margin-bottom:-1.5rem!important}.ml-md-n4,.mx-md-n4{margin-left:-1.5rem!important}.m-md-n5{margin:-3rem!important}.mt-md-n5,.my-md-n5{margin-top:-3rem!important}.mr-md-n5,.mx-md-n5{margin-right:-3rem!important}.mb-md-n5,.my-md-n5{margin-bottom:-3rem!important}.ml-md-n5,.mx-md-n5{margin-left:-3rem!important}.m-md-auto{margin:auto!important}.mt-md-auto,.my-md-auto{margin-top:auto!important}.mr-md-auto,.mx-md-auto{margin-right:auto!important}.mb-md-auto,.my-md-auto{margin-bottom:auto!important}.ml-md-auto,.mx-md-auto{margin-left:auto!important}}@media (min-width:960px){.m-lg-0{margin:0!important}.mt-lg-0,.my-lg-0{margin-top:0!important}.mr-lg-0,.mx-lg-0{margin-right:0!important}.mb-lg-0,.my-lg-0{margin-bottom:0!important}.ml-lg-0,.mx-lg-0{margin-left:0!important}.m-lg-1{margin:.25rem!important}.mt-lg-1,.my-lg-1{margin-top:.25rem!important}.mr-lg-1,.mx-lg-1{margin-right:.25rem!important}.mb-lg-1,.my-lg-1{margin-bottom:.25rem!important}.ml-lg-1,.mx-lg-1{margin-left:.25rem!important}.m-lg-2{margin:.5rem!important}.mt-lg-2,.my-lg-2{margin-top:.5rem!important}.mr-lg-2,.mx-lg-2{margin-right:.5rem!important}.mb-lg-2,.my-lg-2{margin-bottom:.5rem!important}.ml-lg-2,.mx-lg-2{margin-left:.5rem!important}.m-lg-3{margin:1rem!important}.mt-lg-3,.my-lg-3{margin-top:1rem!important}.mr-lg-3,.mx-lg-3{margin-right:1rem!important}.mb-lg-3,.my-lg-3{margin-bottom:1rem!important}.ml-lg-3,.mx-lg-3{margin-left:1rem!important}.m-lg-4{margin:1.5rem!important}.mt-lg-4,.my-lg-4{margin-top:1.5rem!important}.mr-lg-4,.mx-lg-4{margin-right:1.5rem!important}.mb-lg-4,.my-lg-4{margin-bottom:1.5rem!important}.ml-lg-4,.mx-lg-4{margin-left:1.5rem!important}.m-lg-5{margin:3rem!important}.mt-lg-5,.my-lg-5{margin-top:3rem!important}.mr-lg-5,.mx-lg-5{margin-right:3rem!important}.mb-lg-5,.my-lg-5{margin-bottom:3rem!important}.ml-lg-5,.mx-lg-5{margin-left:3rem!important}.p-lg-0{padding:0!important}.pt-lg-0,.py-lg-0{padding-top:0!important}.pr-lg-0,.px-lg-0{padding-right:0!important}.pb-lg-0,.py-lg-0{padding-bottom:0!important}.pl-lg-0,.px-lg-0{padding-left:0!important}.p-lg-1{padding:.25rem!important}.pt-lg-1,.py-lg-1{padding-top:.25rem!important}.pr-lg-1,.px-lg-1{padding-right:.25rem!important}.pb-lg-1,.py-lg-1{padding-bottom:.25rem!important}.pl-lg-1,.px-lg-1{padding-left:.25rem!important}.p-lg-2{padding:.5rem!important}.pt-lg-2,.py-lg-2{padding-top:.5rem!important}.pr-lg-2,.px-lg-2{padding-right:.5rem!important}.pb-lg-2,.py-lg-2{padding-bottom:.5rem!important}.pl-lg-2,.px-lg-2{padding-left:.5rem!important}.p-lg-3{padding:1rem!important}.pt-lg-3,.py-lg-3{padding-top:1rem!important}.pr-lg-3,.px-lg-3{padding-right:1rem!important}.pb-lg-3,.py-lg-3{padding-bottom:1rem!important}.pl-lg-3,.px-lg-3{padding-left:1rem!important}.p-lg-4{padding:1.5rem!important}.pt-lg-4,.py-lg-4{padding-top:1.5rem!important}.pr-lg-4,.px-lg-4{padding-right:1.5rem!important}.pb-lg-4,.py-lg-4{padding-bottom:1.5rem!important}.pl-lg-4,.px-lg-4{padding-left:1.5rem!important}.p-lg-5{padding:3rem!important}.pt-lg-5,.py-lg-5{padding-top:3rem!important}.pr-lg-5,.px-lg-5{padding-right:3rem!important}.pb-lg-5,.py-lg-5{padding-bottom:3rem!important}.pl-lg-5,.px-lg-5{padding-left:3rem!important}.m-lg-n1{margin:-.25rem!important}.mt-lg-n1,.my-lg-n1{margin-top:-.25rem!important}.mr-lg-n1,.mx-lg-n1{margin-right:-.25rem!important}.mb-lg-n1,.my-lg-n1{margin-bottom:-.25rem!important}.ml-lg-n1,.mx-lg-n1{margin-left:-.25rem!important}.m-lg-n2{margin:-.5rem!important}.mt-lg-n2,.my-lg-n2{margin-top:-.5rem!important}.mr-lg-n2,.mx-lg-n2{margin-right:-.5rem!important}.mb-lg-n2,.my-lg-n2{margin-bottom:-.5rem!important}.ml-lg-n2,.mx-lg-n2{margin-left:-.5rem!important}.m-lg-n3{margin:-1rem!important}.mt-lg-n3,.my-lg-n3{margin-top:-1rem!important}.mr-lg-n3,.mx-lg-n3{margin-right:-1rem!important}.mb-lg-n3,.my-lg-n3{margin-bottom:-1rem!important}.ml-lg-n3,.mx-lg-n3{margin-left:-1rem!important}.m-lg-n4{margin:-1.5rem!important}.mt-lg-n4,.my-lg-n4{margin-top:-1.5rem!important}.mr-lg-n4,.mx-lg-n4{margin-right:-1.5rem!important}.mb-lg-n4,.my-lg-n4{margin-bottom:-1.5rem!important}.ml-lg-n4,.mx-lg-n4{margin-left:-1.5rem!important}.m-lg-n5{margin:-3rem!important}.mt-lg-n5,.my-lg-n5{margin-top:-3rem!important}.mr-lg-n5,.mx-lg-n5{margin-right:-3rem!important}.mb-lg-n5,.my-lg-n5{margin-bottom:-3rem!important}.ml-lg-n5,.mx-lg-n5{margin-left:-3rem!important}.m-lg-auto{margin:auto!important}.mt-lg-auto,.my-lg-auto{margin-top:auto!important}.mr-lg-auto,.mx-lg-auto{margin-right:auto!important}.mb-lg-auto,.my-lg-auto{margin-bottom:auto!important}.ml-lg-auto,.mx-lg-auto{margin-left:auto!important}}@media (min-width:1200px){.m-xl-0{margin:0!important}.mt-xl-0,.my-xl-0{margin-top:0!important}.mr-xl-0,.mx-xl-0{margin-right:0!important}.mb-xl-0,.my-xl-0{margin-bottom:0!important}.ml-xl-0,.mx-xl-0{margin-left:0!important}.m-xl-1{margin:.25rem!important}.mt-xl-1,.my-xl-1{margin-top:.25rem!important}.mr-xl-1,.mx-xl-1{margin-right:.25rem!important}.mb-xl-1,.my-xl-1{margin-bottom:.25rem!important}.ml-xl-1,.mx-xl-1{margin-left:.25rem!important}.m-xl-2{margin:.5rem!important}.mt-xl-2,.my-xl-2{margin-top:.5rem!important}.mr-xl-2,.mx-xl-2{margin-right:.5rem!important}.mb-xl-2,.my-xl-2{margin-bottom:.5rem!important}.ml-xl-2,.mx-xl-2{margin-left:.5rem!important}.m-xl-3{margin:1rem!important}.mt-xl-3,.my-xl-3{margin-top:1rem!important}.mr-xl-3,.mx-xl-3{margin-right:1rem!important}.mb-xl-3,.my-xl-3{margin-bottom:1rem!important}.ml-xl-3,.mx-xl-3{margin-left:1rem!important}.m-xl-4{margin:1.5rem!important}.mt-xl-4,.my-xl-4{margin-top:1.5rem!important}.mr-xl-4,.mx-xl-4{margin-right:1.5rem!important}.mb-xl-4,.my-xl-4{margin-bottom:1.5rem!important}.ml-xl-4,.mx-xl-4{margin-left:1.5rem!important}.m-xl-5{margin:3rem!important}.mt-xl-5,.my-xl-5{margin-top:3rem!important}.mr-xl-5,.mx-xl-5{margin-right:3rem!important}.mb-xl-5,.my-xl-5{margin-bottom:3rem!important}.ml-xl-5,.mx-xl-5{margin-left:3rem!important}.p-xl-0{padding:0!important}.pt-xl-0,.py-xl-0{padding-top:0!important}.pr-xl-0,.px-xl-0{padding-right:0!important}.pb-xl-0,.py-xl-0{padding-bottom:0!important}.pl-xl-0,.px-xl-0{padding-left:0!important}.p-xl-1{padding:.25rem!important}.pt-xl-1,.py-xl-1{padding-top:.25rem!important}.pr-xl-1,.px-xl-1{padding-right:.25rem!important}.pb-xl-1,.py-xl-1{padding-bottom:.25rem!important}.pl-xl-1,.px-xl-1{padding-left:.25rem!important}.p-xl-2{padding:.5rem!important}.pt-xl-2,.py-xl-2{padding-top:.5rem!important}.pr-xl-2,.px-xl-2{padding-right:.5rem!important}.pb-xl-2,.py-xl-2{padding-bottom:.5rem!important}.pl-xl-2,.px-xl-2{padding-left:.5rem!important}.p-xl-3{padding:1rem!important}.pt-xl-3,.py-xl-3{padding-top:1rem!important}.pr-xl-3,.px-xl-3{padding-right:1rem!important}.pb-xl-3,.py-xl-3{padding-bottom:1rem!important}.pl-xl-3,.px-xl-3{padding-left:1rem!important}.p-xl-4{padding:1.5rem!important}.pt-xl-4,.py-xl-4{padding-top:1.5rem!important}.pr-xl-4,.px-xl-4{padding-right:1.5rem!important}.pb-xl-4,.py-xl-4{padding-bottom:1.5rem!important}.pl-xl-4,.px-xl-4{padding-left:1.5rem!important}.p-xl-5{padding:3rem!important}.pt-xl-5,.py-xl-5{padding-top:3rem!important}.pr-xl-5,.px-xl-5{padding-right:3rem!important}.pb-xl-5,.py-xl-5{padding-bottom:3rem!important}.pl-xl-5,.px-xl-5{padding-left:3rem!important}.m-xl-n1{margin:-.25rem!important}.mt-xl-n1,.my-xl-n1{margin-top:-.25rem!important}.mr-xl-n1,.mx-xl-n1{margin-right:-.25rem!important}.mb-xl-n1,.my-xl-n1{margin-bottom:-.25rem!important}.ml-xl-n1,.mx-xl-n1{margin-left:-.25rem!important}.m-xl-n2{margin:-.5rem!important}.mt-xl-n2,.my-xl-n2{margin-top:-.5rem!important}.mr-xl-n2,.mx-xl-n2{margin-right:-.5rem!important}.mb-xl-n2,.my-xl-n2{margin-bottom:-.5rem!important}.ml-xl-n2,.mx-xl-n2{margin-left:-.5rem!important}.m-xl-n3{margin:-1rem!important}.mt-xl-n3,.my-xl-n3{margin-top:-1rem!important}.mr-xl-n3,.mx-xl-n3{margin-right:-1rem!important}.mb-xl-n3,.my-xl-n3{margin-bottom:-1rem!important}.ml-xl-n3,.mx-xl-n3{margin-left:-1rem!important}.m-xl-n4{margin:-1.5rem!important}.mt-xl-n4,.my-xl-n4{margin-top:-1.5rem!important}.mr-xl-n4,.mx-xl-n4{margin-right:-1.5rem!important}.mb-xl-n4,.my-xl-n4{margin-bottom:-1.5rem!important}.ml-xl-n4,.mx-xl-n4{margin-left:-1.5rem!important}.m-xl-n5{margin:-3rem!important}.mt-xl-n5,.my-xl-n5{margin-top:-3rem!important}.mr-xl-n5,.mx-xl-n5{margin-right:-3rem!important}.mb-xl-n5,.my-xl-n5{margin-bottom:-3rem!important}.ml-xl-n5,.mx-xl-n5{margin-left:-3rem!important}.m-xl-auto{margin:auto!important}.mt-xl-auto,.my-xl-auto{margin-top:auto!important}.mr-xl-auto,.mx-xl-auto{margin-right:auto!important}.mb-xl-auto,.my-xl-auto{margin-bottom:auto!important}.ml-xl-auto,.mx-xl-auto{margin-left:auto!important}}.stretched-link:after{position:absolute;top:0;right:0;bottom:0;left:0;z-index:1;pointer-events:auto;content:"";background-color:transparent}.text-monospace{font-family:SFMono-Regular,Menlo,Monaco,Consolas,Liberation Mono,Courier New,monospace!important}.text-justify{text-align:justify!important}.text-wrap{white-space:normal!important}.text-nowrap{white-space:nowrap!important}.text-truncate{overflow:hidden;text-overflow:ellipsis;white-space:nowrap}.text-left{text-align:left!important}.text-right{text-align:right!important}.text-center{text-align:center!important}@media (min-width:540px){.text-sm-left{text-align:left!important}.text-sm-right{text-align:right!important}.text-sm-center{text-align:center!important}}@media (min-width:720px){.text-md-left{text-align:left!important}.text-md-right{text-align:right!important}.text-md-center{text-align:center!important}}@media (min-width:960px){.text-lg-left{text-align:left!important}.text-lg-right{text-align:right!important}.text-lg-center{text-align:center!important}}@media (min-width:1200px){.text-xl-left{text-align:left!important}.text-xl-right{text-align:right!important}.text-xl-center{text-align:center!important}}.text-lowercase{text-transform:lowercase!important}.text-uppercase{text-transform:uppercase!important}.text-capitalize{text-transform:capitalize!important}.font-weight-light{font-weight:300!important}.font-weight-lighter{font-weight:lighter!important}.font-weight-normal{font-weight:400!important}.font-weight-bold{font-weight:700!important}.font-weight-bolder{font-weight:bolder!important}.font-italic{font-style:italic!important}.text-white{color:#fff!important}.text-primary{color:#007bff!important}a.text-primary:focus,a.text-primary:hover{color:#0056b3!important}.text-secondary{color:#6c757d!important}a.text-secondary:focus,a.text-secondary:hover{color:#494f54!important}.text-success{color:#28a745!important}a.text-success:focus,a.text-success:hover{color:#19692c!important}.text-info{color:#17a2b8!important}a.text-info:focus,a.text-info:hover{color:#0f6674!important}.text-warning{color:#ffc107!important}a.text-warning:focus,a.text-warning:hover{color:#ba8b00!important}.text-danger{color:#dc3545!important}a.text-danger:focus,a.text-danger:hover{color:#a71d2a!important}.text-light{color:#f8f9fa!important}a.text-light:focus,a.text-light:hover{color:#cbd3da!important}.text-dark{color:#343a40!important}a.text-dark:focus,a.text-dark:hover{color:#121416!important}.text-body{color:#212529!important}.text-muted{color:#6c757d!important}.text-black-50{color:rgba(0,0,0,.5)!important}.text-white-50{color:hsla(0,0%,100%,.5)!important}.text-hide{font:0/0 a;color:transparent;text-shadow:none;background-color:transparent;border:0}.text-decoration-none{text-decoration:none!important}.text-break{word-wrap:break-word!important}.text-reset{color:inherit!important}.visible{visibility:visible!important}.invisible{visibility:hidden!important}@media print{*,:after,:before{text-shadow:none!important;box-shadow:none!important}a:not(.btn){text-decoration:underline}abbr[title]:after{content:" (" attr(title) ")"}pre{white-space:pre-wrap!important}blockquote,pre{border:1px solid #adb5bd;page-break-inside:avoid}thead{display:table-header-group}img,tr{page-break-inside:avoid}h2,h3,p{orphans:3;widows:3}h2,h3{page-break-after:avoid}@page{size:a3}.container,body{min-width:960px!important}.navbar{display:none}.badge{border:1px solid #000}.table{border-collapse:collapse!important}.table td,.table th{background-color:#fff!important}.table-bordered td,.table-bordered th{border:1px solid #dee2e6!important}.table-dark{color:inherit}.table-dark tbody+tbody,.table-dark td,.table-dark th,.table-dark thead th{border-color:#dee2e6}.table .thead-dark th{color:inherit;border-color:#dee2e6}}html{font-size:var(--pst-font-size-base);scroll-padding-top:calc(var(--pst-header-height) + 12px)}body{padding-top:calc(var(--pst-header-height) + 20px);background-color:#fff;font-family:var(--pst-font-family-base);font-weight:400;line-height:1.65;color:rgba(var(--pst-color-text-base),1)}p{margin-bottom:1.15rem;font-size:1em;color:rgba(var(--pst-color-paragraph),1)}p.rubric{border-bottom:1px solid #c9c9c9}a{color:rgba(var(--pst-color-link),1);text-decoration:none}a:hover{color:rgba(var(--pst-color-link-hover),1);text-decoration:underline}a.headerlink{color:rgba(var(--pst-color-headerlink),1);font-size:.8em;padding:0 4px;text-decoration:none}a.headerlink:hover{background-color:rgba(var(--pst-color-headerlink),1);color:rgba(var(--pst-color-headerlink-hover),1)}.heading-style,h1,h2,h3,h4,h5,h6{margin:2.75rem 0 1.05rem;font-family:var(--pst-font-family-heading);font-weight:400;line-height:1.15}h1{margin-top:0;font-size:var(--pst-font-size-h1);color:rgba(var(--pst-color-h1),1)}h2{font-size:var(--pst-font-size-h2);color:rgba(var(--pst-color-h2),1)}h3{font-size:var(--pst-font-size-h3);color:rgba(var(--pst-color-h3),1)}h4{font-size:var(--pst-font-size-h4);color:rgba(var(--pst-color-h4),1)}h5{font-size:var(--pst-font-size-h5);color:rgba(var(--pst-color-h5),1)}h6{font-size:var(--pst-font-size-h6);color:rgba(var(--pst-color-h6),1)}.text_small,small{font-size:var(--pst-font-size-milli)}hr{border:0;border-top:1px solid #e5e5e5}code,kbd,pre,samp{font-family:var(--pst-font-family-monospace)}code{color:rgba(var(--pst-color-inline-code),1)}pre{margin:1.5em 0;padding:10px;background-color:rgba(var(--pst-color-preformatted-background),1);color:rgba(var(--pst-color-preformatted-text),1);line-height:1.2em;border:1px solid #c9c9c9;border-radius:.2rem;box-shadow:1px 1px 1px #d8d8d8}dd{margin-top:3px;margin-bottom:10px;margin-left:30px}.navbar{position:fixed;min-height:var(--pst-header-height);width:100%;padding:0}.navbar .container-xl{height:100%}@media (min-width:960px){.navbar #navbar-end>.navbar-end-item{display:inline-block}}.navbar-brand{position:relative;height:var(--pst-header-height);width:auto;padding:.5rem 0}.navbar-brand img{max-width:100%;height:100%;width:auto}.navbar-light{background:#fff!important;box-shadow:0 .125rem .25rem 0 rgba(0,0,0,.11)}.navbar-light .navbar-nav li a.nav-link{padding:0 .5rem;color:rgba(var(--pst-color-navbar-link),1)}.navbar-light .navbar-nav li a.nav-link:hover{color:rgba(var(--pst-color-navbar-link-hover),1)}.navbar-light .navbar-nav>.active>.nav-link{font-weight:600;color:rgba(var(--pst-color-navbar-link-active),1)}.navbar-header a{padding:0 15px}.admonition,div.admonition{margin:1.5625em auto;padding:0 .6rem .8rem;overflow:hidden;page-break-inside:avoid;border-left:.2rem solid;border-left-color:rgba(var(--pst-color-admonition-default),1);border-bottom-color:rgba(var(--pst-color-admonition-default),1);border-right-color:rgba(var(--pst-color-admonition-default),1);border-top-color:rgba(var(--pst-color-admonition-default),1);border-radius:.2rem;box-shadow:0 .2rem .5rem rgba(0,0,0,.05),0 0 .0625rem rgba(0,0,0,.1);transition:color .25s,background-color .25s,border-color .25s}.admonition :last-child,div.admonition :last-child{margin-bottom:0}.admonition p.admonition-title~*,div.admonition p.admonition-title~*{padding:0 1.4rem}.admonition>ol,.admonition>ul,div.admonition>ol,div.admonition>ul{margin-left:1em}.admonition>.admonition-title,div.admonition>.admonition-title{position:relative;margin:0 -.6rem;padding:.4rem .6rem .4rem 2rem;font-weight:700;background-color:rgba(var(--pst-color-admonition-default),.1)}.admonition>.admonition-title:before,div.admonition>.admonition-title:before{position:absolute;left:.6rem;width:1rem;height:1rem;color:rgba(var(--pst-color-admonition-default),1);font-family:Font Awesome\ 5 Free;font-weight:900;content:var(--pst-icon-admonition-default)}.admonition>.admonition-title+*,div.admonition>.admonition-title+*{margin-top:.4em}.admonition.attention,div.admonition.attention{border-color:rgba(var(--pst-color-admonition-attention),1)}.admonition.attention>.admonition-title,div.admonition.attention>.admonition-title{background-color:rgba(var(--pst-color-admonition-attention),.1)}.admonition.attention>.admonition-title:before,div.admonition.attention>.admonition-title:before{color:rgba(var(--pst-color-admonition-attention),1);content:var(--pst-icon-admonition-attention)}.admonition.caution,div.admonition.caution{border-color:rgba(var(--pst-color-admonition-caution),1)}.admonition.caution>.admonition-title,div.admonition.caution>.admonition-title{background-color:rgba(var(--pst-color-admonition-caution),.1)}.admonition.caution>.admonition-title:before,div.admonition.caution>.admonition-title:before{color:rgba(var(--pst-color-admonition-caution),1);content:var(--pst-icon-admonition-caution)}.admonition.warning,div.admonition.warning{border-color:rgba(var(--pst-color-admonition-warning),1)}.admonition.warning>.admonition-title,div.admonition.warning>.admonition-title{background-color:rgba(var(--pst-color-admonition-warning),.1)}.admonition.warning>.admonition-title:before,div.admonition.warning>.admonition-title:before{color:rgba(var(--pst-color-admonition-warning),1);content:var(--pst-icon-admonition-warning)}.admonition.danger,div.admonition.danger{border-color:rgba(var(--pst-color-admonition-danger),1)}.admonition.danger>.admonition-title,div.admonition.danger>.admonition-title{background-color:rgba(var(--pst-color-admonition-danger),.1)}.admonition.danger>.admonition-title:before,div.admonition.danger>.admonition-title:before{color:rgba(var(--pst-color-admonition-danger),1);content:var(--pst-icon-admonition-danger)}.admonition.error,div.admonition.error{border-color:rgba(var(--pst-color-admonition-error),1)}.admonition.error>.admonition-title,div.admonition.error>.admonition-title{background-color:rgba(var(--pst-color-admonition-error),.1)}.admonition.error>.admonition-title:before,div.admonition.error>.admonition-title:before{color:rgba(var(--pst-color-admonition-error),1);content:var(--pst-icon-admonition-error)}.admonition.hint,div.admonition.hint{border-color:rgba(var(--pst-color-admonition-hint),1)}.admonition.hint>.admonition-title,div.admonition.hint>.admonition-title{background-color:rgba(var(--pst-color-admonition-hint),.1)}.admonition.hint>.admonition-title:before,div.admonition.hint>.admonition-title:before{color:rgba(var(--pst-color-admonition-hint),1);content:var(--pst-icon-admonition-hint)}.admonition.tip,div.admonition.tip{border-color:rgba(var(--pst-color-admonition-tip),1)}.admonition.tip>.admonition-title,div.admonition.tip>.admonition-title{background-color:rgba(var(--pst-color-admonition-tip),.1)}.admonition.tip>.admonition-title:before,div.admonition.tip>.admonition-title:before{color:rgba(var(--pst-color-admonition-tip),1);content:var(--pst-icon-admonition-tip)}.admonition.important,div.admonition.important{border-color:rgba(var(--pst-color-admonition-important),1)}.admonition.important>.admonition-title,div.admonition.important>.admonition-title{background-color:rgba(var(--pst-color-admonition-important),.1)}.admonition.important>.admonition-title:before,div.admonition.important>.admonition-title:before{color:rgba(var(--pst-color-admonition-important),1);content:var(--pst-icon-admonition-important)}.admonition.note,div.admonition.note{border-color:rgba(var(--pst-color-admonition-note),1)}.admonition.note>.admonition-title,div.admonition.note>.admonition-title{background-color:rgba(var(--pst-color-admonition-note),.1)}.admonition.note>.admonition-title:before,div.admonition.note>.admonition-title:before{color:rgba(var(--pst-color-admonition-note),1);content:var(--pst-icon-admonition-note)}table.field-list{border-collapse:separate;border-spacing:10px;margin-left:1px}table.field-list th.field-name{padding:1px 8px 1px 5px;white-space:nowrap;background-color:#eee}table.field-list td.field-body p{font-style:italic}table.field-list td.field-body p>strong{font-style:normal}table.field-list td.field-body blockquote{border-left:none;margin:0 0 .3em;padding-left:30px}.table.autosummary td:first-child{white-space:nowrap}.sig{font-family:var(--pst-font-family-monospace)}.sig-inline.c-texpr,.sig-inline.cpp-texpr{font-family:unset}.sig.c .k,.sig.c .kt,.sig.c .m,.sig.c .s,.sig.c .sc,.sig.cpp .k,.sig.cpp .kt,.sig.cpp .m,.sig.cpp .s,.sig.cpp .sc{color:rgba(var(--pst-color-text-base),1)}.sig-name{color:rgba(var(--pst-color-inline-code),1)}blockquote{padding:0 1em;color:#6a737d;border-left:.25em solid #dfe2e5}dt.label>span.brackets:not(:only-child):before{content:"["}dt.label>span.brackets:not(:only-child):after{content:"]"}a.footnote-reference{vertical-align:super;font-size:small}div.deprecated{margin-bottom:10px;margin-top:10px;padding:7px;background-color:#f3e5e5;border:1px solid #eed3d7;border-radius:.5rem}div.deprecated p{color:#b94a48;display:inline}.topic{background-color:#eee}.seealso dd{margin-top:0;margin-bottom:0}.viewcode-back{font-family:var(--pst-font-family-base)}.viewcode-block:target{background-color:#f4debf;border-top:1px solid #ac9;border-bottom:1px solid #ac9}span.guilabel{border:1px solid #7fbbe3;background:#e7f2fa;font-size:80%;font-weight:700;border-radius:4px;padding:2.4px 6px;margin:auto 2px}footer{width:100%;border-top:1px solid #ccc;padding:10px}footer .footer-item p{margin-bottom:0}.bd-search{position:relative;padding:1rem 15px;margin-right:-15px;margin-left:-15px}.bd-search .icon{position:absolute;color:#a4a6a7;left:25px;top:25px}.bd-search input{border-radius:0;border:0;border-bottom:1px solid #e5e5e5;padding-left:35px}.bd-toc{-ms-flex-order:2;order:2;height:calc(100vh - 2rem);overflow-y:auto}@supports (position:-webkit-sticky) or (position:sticky){.bd-toc{position:-webkit-sticky;position:sticky;top:calc(var(--pst-header-height) + 20px);height:calc(100vh - 5rem);overflow-y:auto}}.bd-toc .onthispage{color:#a4a6a7}.section-nav{padding-left:0;border-left:1px solid #eee;border-bottom:none}.section-nav ul{padding-left:1rem}.toc-entry,.toc-entry a{display:block}.toc-entry a{padding:.125rem 1.5rem;color:rgba(var(--pst-color-toc-link),1)}@media (min-width:1200px){.toc-entry a{padding-right:0}}.toc-entry a:hover{color:rgba(var(--pst-color-toc-link-hover),1);text-decoration:none}.bd-sidebar{padding-top:1em}@media (min-width:720px){.bd-sidebar{border-right:1px solid rgba(0,0,0,.1)}@supports (position:-webkit-sticky) or (position:sticky){.bd-sidebar{position:-webkit-sticky;position:sticky;top:calc(var(--pst-header-height) + 20px);z-index:1000;height:calc(100vh - var(--pst-header-height) - 20px)}}}.bd-sidebar.no-sidebar{border-right:0}.bd-links{padding-top:1rem;padding-bottom:1rem;margin-right:-15px;margin-left:-15px}@media (min-width:720px){.bd-links{display:block}@supports (position:-webkit-sticky) or (position:sticky){.bd-links{max-height:calc(100vh - 11rem);overflow-y:auto}}}.bd-sidenav{display:none}.bd-content{padding-top:20px}.bd-content .section{max-width:100%}.bd-content .section table{display:block;overflow:auto}.bd-toc-link{display:block;padding:.25rem 1.5rem;font-weight:600;color:rgba(0,0,0,.65)}.bd-toc-link:hover{color:rgba(0,0,0,.85);text-decoration:none}.bd-toc-item.active{margin-bottom:1rem}.bd-toc-item.active:not(:first-child){margin-top:1rem}.bd-toc-item.active>.bd-toc-link{color:rgba(0,0,0,.85)}.bd-toc-item.active>.bd-toc-link:hover{background-color:transparent}.bd-toc-item.active>.bd-sidenav{display:block}nav.bd-links p.caption{font-size:var(--pst-sidebar-caption-font-size);text-transform:uppercase;font-weight:700;position:relative;margin-top:1.25em;margin-bottom:.5em;padding:0 1.5rem;color:rgba(var(--pst-color-sidebar-caption),1)}nav.bd-links p.caption:first-child{margin-top:0}.bd-sidebar .nav{font-size:var(--pst-sidebar-font-size)}.bd-sidebar .nav ul{list-style:none;padding:0 0 0 1.5rem}.bd-sidebar .nav li>a{display:block;padding:.25rem 1.5rem;color:rgba(var(--pst-color-sidebar-link),1)}.bd-sidebar .nav li>a:hover{color:rgba(var(--pst-color-sidebar-link-hover),1);text-decoration:none;background-color:transparent}.bd-sidebar .nav li>a.reference.external:after{font-family:Font Awesome\ 5 Free;font-weight:900;content:"\f35d";font-size:.75em;margin-left:.3em}.bd-sidebar .nav .active:hover>a,.bd-sidebar .nav .active>a{font-weight:600;color:rgba(var(--pst-color-sidebar-link-active),1)}.toc-h2{font-size:.85rem}.toc-h3{font-size:.75rem}.toc-h4{font-size:.65rem}.toc-entry>.nav-link.active{font-weight:600;color:#130654;color:rgba(var(--pst-color-toc-link-active),1);background-color:transparent;border-left:2px solid rgba(var(--pst-color-toc-link-active),1)}.nav-link:hover{border-style:none}#navbar-main-elements li.nav-item i{font-size:.7rem;padding-left:2px;vertical-align:middle}.bd-toc .nav .nav{display:none}.bd-toc .nav .nav.visible,.bd-toc .nav>.active>ul{display:block}.prev-next-area{margin:20px 0}.prev-next-area p{margin:0 .3em;line-height:1.3em}.prev-next-area i{font-size:1.2em}.prev-next-area a{display:flex;align-items:center;border:none;padding:10px;max-width:45%;overflow-x:hidden;color:rgba(0,0,0,.65);text-decoration:none}.prev-next-area a p.prev-next-title{color:rgba(var(--pst-color-link),1);font-weight:600;font-size:1.1em}.prev-next-area a:hover p.prev-next-title{text-decoration:underline}.prev-next-area a .prev-next-info{flex-direction:column;margin:0 .5em}.prev-next-area a .prev-next-info .prev-next-subtitle{text-transform:capitalize}.prev-next-area a.left-prev{float:left}.prev-next-area a.right-next{float:right}.prev-next-area a.right-next div.prev-next-info{text-align:right}.alert{padding-bottom:0}.alert-info a{color:#e83e8c}#navbar-icon-links i.fa,#navbar-icon-links i.fab,#navbar-icon-links i.far,#navbar-icon-links i.fas{vertical-align:middle;font-style:normal;font-size:1.5rem;line-height:1.25}#navbar-icon-links i.fa-github-square:before{color:#333}#navbar-icon-links i.fa-twitter-square:before{color:#55acee}#navbar-icon-links i.fa-gitlab:before{color:#548}#navbar-icon-links i.fa-bitbucket:before{color:#0052cc}.tocsection{border-left:1px solid #eee;padding:.3rem 1.5rem}.tocsection i{padding-right:.5rem}.editthispage{padding-top:2rem}.editthispage a{color:var(--pst-color-sidebar-link-active)}.xr-wrap[hidden]{display:block!important}.toctree-checkbox{position:absolute;display:none}.toctree-checkbox~ul{display:none}.toctree-checkbox~label i{transform:rotate(0deg)}.toctree-checkbox:checked~ul{display:block}.toctree-checkbox:checked~label i{transform:rotate(180deg)}.bd-sidebar li{position:relative}.bd-sidebar label{position:absolute;top:0;right:0;height:30px;width:30px;cursor:pointer;display:flex;justify-content:center;align-items:center}.bd-sidebar label:hover{background:rgba(var(--pst-color-sidebar-expander-background-hover),1)}.bd-sidebar label i{display:inline-block;font-size:.75rem;text-align:center}.bd-sidebar label i:hover{color:rgba(var(--pst-color-sidebar-link-hover),1)}.bd-sidebar li.has-children>.reference{padding-right:30px}div.doctest>div.highlight span.gp,span.linenos,table.highlighttable td.linenos{user-select:none;-webkit-user-select:text;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none}.docutils.container{padding-left:unset;padding-right:unset} \ No newline at end of file diff --git a/lectures/_build/html/_static/css/theme.css b/lectures/_build/html/_static/css/theme.css deleted file mode 100644 index 2e03fe372..000000000 --- a/lectures/_build/html/_static/css/theme.css +++ /dev/null @@ -1,120 +0,0 @@ -/* Provided by the Sphinx base theme template at build time */ -@import "../basic.css"; - -:root { - /***************************************************************************** - * Theme config - **/ - --pst-header-height: 60px; - - /***************************************************************************** - * Font size - **/ - --pst-font-size-base: 15px; /* base font size - applied at body / html level */ - - /* heading font sizes */ - --pst-font-size-h1: 36px; - --pst-font-size-h2: 32px; - --pst-font-size-h3: 26px; - --pst-font-size-h4: 21px; - --pst-font-size-h5: 18px; - --pst-font-size-h6: 16px; - - /* smaller then heading font sizes*/ - --pst-font-size-milli: 12px; - - --pst-sidebar-font-size: .9em; - --pst-sidebar-caption-font-size: .9em; - - /***************************************************************************** - * Font family - **/ - /* These are adapted from https://systemfontstack.com/ */ - --pst-font-family-base-system: -apple-system, BlinkMacSystemFont, Segoe UI, "Helvetica Neue", - Arial, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol; - --pst-font-family-monospace-system: "SFMono-Regular", Menlo, Consolas, Monaco, - Liberation Mono, Lucida Console, monospace; - - --pst-font-family-base: var(--pst-font-family-base-system); - --pst-font-family-heading: var(--pst-font-family-base); - --pst-font-family-monospace: var(--pst-font-family-monospace-system); - - /***************************************************************************** - * Color - * - * Colors are defined in rgb string way, "red, green, blue" - **/ - --pst-color-primary: 19, 6, 84; - --pst-color-success: 40, 167, 69; - --pst-color-info: 0, 123, 255; /*23, 162, 184;*/ - --pst-color-warning: 255, 193, 7; - --pst-color-danger: 220, 53, 69; - --pst-color-text-base: 51, 51, 51; - - --pst-color-h1: var(--pst-color-primary); - --pst-color-h2: var(--pst-color-primary); - --pst-color-h3: var(--pst-color-text-base); - --pst-color-h4: var(--pst-color-text-base); - --pst-color-h5: var(--pst-color-text-base); - --pst-color-h6: var(--pst-color-text-base); - --pst-color-paragraph: var(--pst-color-text-base); - --pst-color-link: 0, 91, 129; - --pst-color-link-hover: 227, 46, 0; - --pst-color-headerlink: 198, 15, 15; - --pst-color-headerlink-hover: 255, 255, 255; - --pst-color-preformatted-text: 34, 34, 34; - --pst-color-preformatted-background: 250, 250, 250; - --pst-color-inline-code: 232, 62, 140; - - --pst-color-active-navigation: 19, 6, 84; - --pst-color-navbar-link: 77, 77, 77; - --pst-color-navbar-link-hover: var(--pst-color-active-navigation); - --pst-color-navbar-link-active: var(--pst-color-active-navigation); - --pst-color-sidebar-link: 77, 77, 77; - --pst-color-sidebar-link-hover: var(--pst-color-active-navigation); - --pst-color-sidebar-link-active: var(--pst-color-active-navigation); - --pst-color-sidebar-expander-background-hover: 244, 244, 244; - --pst-color-sidebar-caption: 77, 77, 77; - --pst-color-toc-link: 119, 117, 122; - --pst-color-toc-link-hover: var(--pst-color-active-navigation); - --pst-color-toc-link-active: var(--pst-color-active-navigation); - - /***************************************************************************** - * Icon - **/ - - /* font awesome icons*/ - --pst-icon-check-circle: '\f058'; - --pst-icon-info-circle: '\f05a'; - --pst-icon-exclamation-triangle: '\f071'; - --pst-icon-exclamation-circle: '\f06a'; - --pst-icon-times-circle: '\f057'; - --pst-icon-lightbulb: '\f0eb'; - - /***************************************************************************** - * Admonitions - **/ - - --pst-color-admonition-default: var(--pst-color-info); - --pst-color-admonition-note: var(--pst-color-info); - --pst-color-admonition-attention: var(--pst-color-warning); - --pst-color-admonition-caution: var(--pst-color-warning); - --pst-color-admonition-warning: var(--pst-color-warning); - --pst-color-admonition-danger: var(--pst-color-danger); - --pst-color-admonition-error: var(--pst-color-danger); - --pst-color-admonition-hint: var(--pst-color-success); - --pst-color-admonition-tip: var(--pst-color-success); - --pst-color-admonition-important: var(--pst-color-success); - - --pst-icon-admonition-default: var(--pst-icon-info-circle); - --pst-icon-admonition-note: var(--pst-icon-info-circle); - --pst-icon-admonition-attention: var(--pst-icon-exclamation-circle); - --pst-icon-admonition-caution: var(--pst-icon-exclamation-triangle); - --pst-icon-admonition-warning: var(--pst-icon-exclamation-triangle); - --pst-icon-admonition-danger: var(--pst-icon-exclamation-triangle); - --pst-icon-admonition-error: var(--pst-icon-times-circle); - --pst-icon-admonition-hint: var(--pst-icon-lightbulb); - --pst-icon-admonition-tip: var(--pst-icon-lightbulb); - --pst-icon-admonition-important: var(--pst-icon-exclamation-circle); - -} diff --git a/lectures/_build/html/_static/doctools.js b/lectures/_build/html/_static/doctools.js deleted file mode 100644 index e1bfd708b..000000000 --- a/lectures/_build/html/_static/doctools.js +++ /dev/null @@ -1,358 +0,0 @@ -/* - * doctools.js - * ~~~~~~~~~~~ - * - * Sphinx JavaScript utilities for all documentation. - * - * :copyright: Copyright 2007-2022 by the Sphinx team, see AUTHORS. - * :license: BSD, see LICENSE for details. - * - */ - -/** - * select a different prefix for underscore - */ -$u = _.noConflict(); - -/** - * make the code below compatible with browsers without - * an installed firebug like debugger -if (!window.console || !console.firebug) { - var names = ["log", "debug", "info", "warn", "error", "assert", "dir", - "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace", - "profile", "profileEnd"]; - window.console = {}; - for (var i = 0; i < names.length; ++i) - window.console[names[i]] = function() {}; -} - */ - -/** - * small helper function to urldecode strings - * - * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL - */ -jQuery.urldecode = function(x) { - if (!x) { - return x - } - return decodeURIComponent(x.replace(/\+/g, ' ')); -}; - -/** - * small helper function to urlencode strings - */ -jQuery.urlencode = encodeURIComponent; - -/** - * This function returns the parsed url parameters of the - * current request. Multiple values per key are supported, - * it will always return arrays of strings for the value parts. - */ -jQuery.getQueryParameters = function(s) { - if (typeof s === 'undefined') - s = document.location.search; - var parts = s.substr(s.indexOf('?') + 1).split('&'); - var result = {}; - for (var i = 0; i < parts.length; i++) { - var tmp = parts[i].split('=', 2); - var key = jQuery.urldecode(tmp[0]); - var value = jQuery.urldecode(tmp[1]); - if (key in result) - result[key].push(value); - else - result[key] = [value]; - } - return result; -}; - -/** - * highlight a given string on a jquery object by wrapping it in - * span elements with the given class name. - */ -jQuery.fn.highlightText = function(text, className) { - function highlight(node, addItems) { - if (node.nodeType === 3) { - var val = node.nodeValue; - var pos = val.toLowerCase().indexOf(text); - if (pos >= 0 && - !jQuery(node.parentNode).hasClass(className) && - !jQuery(node.parentNode).hasClass("nohighlight")) { - var span; - var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); - if (isInSVG) { - span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); - } else { - span = document.createElement("span"); - span.className = className; - } - span.appendChild(document.createTextNode(val.substr(pos, text.length))); - node.parentNode.insertBefore(span, node.parentNode.insertBefore( - document.createTextNode(val.substr(pos + text.length)), - node.nextSibling)); - node.nodeValue = val.substr(0, pos); - if (isInSVG) { - var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); - var bbox = node.parentElement.getBBox(); - rect.x.baseVal.value = bbox.x; - rect.y.baseVal.value = bbox.y; - rect.width.baseVal.value = bbox.width; - rect.height.baseVal.value = bbox.height; - rect.setAttribute('class', className); - addItems.push({ - "parent": node.parentNode, - "target": rect}); - } - } - } - else if (!jQuery(node).is("button, select, textarea")) { - jQuery.each(node.childNodes, function() { - highlight(this, addItems); - }); - } - } - var addItems = []; - var result = this.each(function() { - highlight(this, addItems); - }); - for (var i = 0; i < addItems.length; ++i) { - jQuery(addItems[i].parent).before(addItems[i].target); - } - return result; -}; - -/* - * backward compatibility for jQuery.browser - * This will be supported until firefox bug is fixed. - */ -if (!jQuery.browser) { - jQuery.uaMatch = function(ua) { - ua = ua.toLowerCase(); - - var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || - /(webkit)[ \/]([\w.]+)/.exec(ua) || - /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || - /(msie) ([\w.]+)/.exec(ua) || - ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || - []; - - return { - browser: match[ 1 ] || "", - version: match[ 2 ] || "0" - }; - }; - jQuery.browser = {}; - jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; -} - -/** - * Small JavaScript module for the documentation. - */ -var Documentation = { - - init : function() { - this.fixFirefoxAnchorBug(); - this.highlightSearchWords(); - this.initIndexTable(); - this.initOnKeyListeners(); - }, - - /** - * i18n support - */ - TRANSLATIONS : {}, - PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; }, - LOCALE : 'unknown', - - // gettext and ngettext don't access this so that the functions - // can safely bound to a different name (_ = Documentation.gettext) - gettext : function(string) { - var translated = Documentation.TRANSLATIONS[string]; - if (typeof translated === 'undefined') - return string; - return (typeof translated === 'string') ? translated : translated[0]; - }, - - ngettext : function(singular, plural, n) { - var translated = Documentation.TRANSLATIONS[singular]; - if (typeof translated === 'undefined') - return (n == 1) ? singular : plural; - return translated[Documentation.PLURALEXPR(n)]; - }, - - addTranslations : function(catalog) { - for (var key in catalog.messages) - this.TRANSLATIONS[key] = catalog.messages[key]; - this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')'); - this.LOCALE = catalog.locale; - }, - - /** - * add context elements like header anchor links - */ - addContextElements : function() { - $('div[id] > :header:first').each(function() { - $('\u00B6'). - attr('href', '#' + this.id). - attr('title', _('Permalink to this headline')). - appendTo(this); - }); - $('dt[id]').each(function() { - $('\u00B6'). - attr('href', '#' + this.id). - attr('title', _('Permalink to this definition')). - appendTo(this); - }); - }, - - /** - * workaround a firefox stupidity - * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075 - */ - fixFirefoxAnchorBug : function() { - if (document.location.hash && $.browser.mozilla) - window.setTimeout(function() { - document.location.href += ''; - }, 10); - }, - - /** - * highlight the search words provided in the url in the text - */ - highlightSearchWords : function() { - var params = $.getQueryParameters(); - var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : []; - if (terms.length) { - var body = $('div.body'); - if (!body.length) { - body = $('body'); - } - window.setTimeout(function() { - $.each(terms, function() { - body.highlightText(this.toLowerCase(), 'highlighted'); - }); - }, 10); - $('

' + _('Hide Search Matches') + '

') - .appendTo($('#searchbox')); - } - }, - - /** - * init the domain index toggle buttons - */ - initIndexTable : function() { - var togglers = $('img.toggler').click(function() { - var src = $(this).attr('src'); - var idnum = $(this).attr('id').substr(7); - $('tr.cg-' + idnum).toggle(); - if (src.substr(-9) === 'minus.png') - $(this).attr('src', src.substr(0, src.length-9) + 'plus.png'); - else - $(this).attr('src', src.substr(0, src.length-8) + 'minus.png'); - }).css('display', ''); - if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) { - togglers.click(); - } - }, - - /** - * helper function to hide the search marks again - */ - hideSearchWords : function() { - $('#searchbox .highlight-link').fadeOut(300); - $('span.highlighted').removeClass('highlighted'); - var url = new URL(window.location); - url.searchParams.delete('highlight'); - window.history.replaceState({}, '', url); - }, - - /** - * helper function to focus on search bar - */ - focusSearchBar : function() { - $('input[name=q]').first().focus(); - }, - - /** - * make the url absolute - */ - makeURL : function(relativeURL) { - return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL; - }, - - /** - * get the current relative url - */ - getCurrentURL : function() { - var path = document.location.pathname; - var parts = path.split(/\//); - $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() { - if (this === '..') - parts.pop(); - }); - var url = parts.join('/'); - return path.substring(url.lastIndexOf('/') + 1, path.length - 1); - }, - - initOnKeyListeners: function() { - // only install a listener if it is really needed - if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS && - !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) - return; - - $(document).keydown(function(event) { - var activeElementType = document.activeElement.tagName; - // don't navigate when in search box, textarea, dropdown or button - if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT' - && activeElementType !== 'BUTTON') { - if (event.altKey || event.ctrlKey || event.metaKey) - return; - - if (!event.shiftKey) { - switch (event.key) { - case 'ArrowLeft': - if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) - break; - var prevHref = $('link[rel="prev"]').prop('href'); - if (prevHref) { - window.location.href = prevHref; - return false; - } - break; - case 'ArrowRight': - if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) - break; - var nextHref = $('link[rel="next"]').prop('href'); - if (nextHref) { - window.location.href = nextHref; - return false; - } - break; - case 'Escape': - if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) - break; - Documentation.hideSearchWords(); - return false; - } - } - - // some keyboard layouts may need Shift to get / - switch (event.key) { - case '/': - if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) - break; - Documentation.focusSearchBar(); - return false; - } - } - }); - } -}; - -// quick alias for translations -_ = Documentation.gettext; - -$(document).ready(function() { - Documentation.init(); -}); diff --git a/lectures/_build/html/_static/documentation_options.js b/lectures/_build/html/_static/documentation_options.js deleted file mode 100644 index 877e3c311..000000000 --- a/lectures/_build/html/_static/documentation_options.js +++ /dev/null @@ -1,14 +0,0 @@ -var DOCUMENTATION_OPTIONS = { - URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'), - VERSION: '', - LANGUAGE: 'None', - COLLAPSE_INDEX: false, - BUILDER: 'html', - FILE_SUFFIX: '.html', - LINK_SUFFIX: '.html', - HAS_SOURCE: true, - SOURCELINK_SUFFIX: '', - NAVIGATION_WITH_KEYS: true, - SHOW_SEARCH_SUMMARY: true, - ENABLE_SEARCH_SHORTCUTS: true, -}; \ No newline at end of file diff --git a/lectures/_build/html/_static/exercise.css b/lectures/_build/html/_static/exercise.css deleted file mode 100644 index e3446a879..000000000 --- a/lectures/_build/html/_static/exercise.css +++ /dev/null @@ -1,43 +0,0 @@ -/********************************************* -* Variables * -*********************************************/ -:root { - --note-title-color: rgba(68,138,255,.1); - --note-border-color: #007bff; - --grey-border-color: #ccc; -} - -/********************************************* -* Exercise * -*********************************************/ -div.exercise { - border-color: var(--note-border-color); - background-color: var(--note-title-color); -} - -div.exercise p.admonition-title { - background-color: var(--note-title-color); -} - -/* Remove content box */ -div.exercise p.admonition-title::before { - content: "\f303"; -} - -/********************************************* -* Solution * -*********************************************/ -div.solution{ - border-color: var(--grey-border-color); - background-color: none; -} - -div.solution p.admonition-title { - background-color: transparent; - text-decoration: none; -} - -/* Remove content box */ -div.solution p.admonition-title::before { - content: none; -} diff --git a/lectures/_build/html/_static/file.png b/lectures/_build/html/_static/file.png deleted file mode 100644 index a858a410e..000000000 Binary files a/lectures/_build/html/_static/file.png and /dev/null differ diff --git a/lectures/_build/html/_static/jquery-3.5.1.js b/lectures/_build/html/_static/jquery-3.5.1.js deleted file mode 100644 index 50937333b..000000000 --- a/lectures/_build/html/_static/jquery-3.5.1.js +++ /dev/null @@ -1,10872 +0,0 @@ -/*! - * jQuery JavaScript Library v3.5.1 - * https://jquery.com/ - * - * Includes Sizzle.js - * https://sizzlejs.com/ - * - * Copyright JS Foundation and other contributors - * Released under the MIT license - * https://jquery.org/license - * - * Date: 2020-05-04T22:49Z - */ -( function( global, factory ) { - - "use strict"; - - if ( typeof module === "object" && typeof module.exports === "object" ) { - - // For CommonJS and CommonJS-like environments where a proper `window` - // is present, execute the factory and get jQuery. - // For environments that do not have a `window` with a `document` - // (such as Node.js), expose a factory as module.exports. - // This accentuates the need for the creation of a real `window`. - // e.g. var jQuery = require("jquery")(window); - // See ticket #14549 for more info. - module.exports = global.document ? - factory( global, true ) : - function( w ) { - if ( !w.document ) { - throw new Error( "jQuery requires a window with a document" ); - } - return factory( w ); - }; - } else { - factory( global ); - } - -// Pass this if window is not defined yet -} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { - -// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 -// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode -// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common -// enough that all such attempts are guarded in a try block. -"use strict"; - -var arr = []; - -var getProto = Object.getPrototypeOf; - -var slice = arr.slice; - -var flat = arr.flat ? function( array ) { - return arr.flat.call( array ); -} : function( array ) { - return arr.concat.apply( [], array ); -}; - - -var push = arr.push; - -var indexOf = arr.indexOf; - -var class2type = {}; - -var toString = class2type.toString; - -var hasOwn = class2type.hasOwnProperty; - -var fnToString = hasOwn.toString; - -var ObjectFunctionString = fnToString.call( Object ); - -var support = {}; - -var isFunction = function isFunction( obj ) { - - // Support: Chrome <=57, Firefox <=52 - // In some browsers, typeof returns "function" for HTML elements - // (i.e., `typeof document.createElement( "object" ) === "function"`). - // We don't want to classify *any* DOM node as a function. - return typeof obj === "function" && typeof obj.nodeType !== "number"; - }; - - -var isWindow = function isWindow( obj ) { - return obj != null && obj === obj.window; - }; - - -var document = window.document; - - - - var preservedScriptAttributes = { - type: true, - src: true, - nonce: true, - noModule: true - }; - - function DOMEval( code, node, doc ) { - doc = doc || document; - - var i, val, - script = doc.createElement( "script" ); - - script.text = code; - if ( node ) { - for ( i in preservedScriptAttributes ) { - - // Support: Firefox 64+, Edge 18+ - // Some browsers don't support the "nonce" property on scripts. - // On the other hand, just using `getAttribute` is not enough as - // the `nonce` attribute is reset to an empty string whenever it - // becomes browsing-context connected. - // See https://github.com/whatwg/html/issues/2369 - // See https://html.spec.whatwg.org/#nonce-attributes - // The `node.getAttribute` check was added for the sake of - // `jQuery.globalEval` so that it can fake a nonce-containing node - // via an object. - val = node[ i ] || node.getAttribute && node.getAttribute( i ); - if ( val ) { - script.setAttribute( i, val ); - } - } - } - doc.head.appendChild( script ).parentNode.removeChild( script ); - } - - -function toType( obj ) { - if ( obj == null ) { - return obj + ""; - } - - // Support: Android <=2.3 only (functionish RegExp) - return typeof obj === "object" || typeof obj === "function" ? - class2type[ toString.call( obj ) ] || "object" : - typeof obj; -} -/* global Symbol */ -// Defining this global in .eslintrc.json would create a danger of using the global -// unguarded in another place, it seems safer to define global only for this module - - - -var - version = "3.5.1", - - // Define a local copy of jQuery - jQuery = function( selector, context ) { - - // The jQuery object is actually just the init constructor 'enhanced' - // Need init if jQuery is called (just allow error to be thrown if not included) - return new jQuery.fn.init( selector, context ); - }; - -jQuery.fn = jQuery.prototype = { - - // The current version of jQuery being used - jquery: version, - - constructor: jQuery, - - // The default length of a jQuery object is 0 - length: 0, - - toArray: function() { - return slice.call( this ); - }, - - // Get the Nth element in the matched element set OR - // Get the whole matched element set as a clean array - get: function( num ) { - - // Return all the elements in a clean array - if ( num == null ) { - return slice.call( this ); - } - - // Return just the one element from the set - return num < 0 ? this[ num + this.length ] : this[ num ]; - }, - - // Take an array of elements and push it onto the stack - // (returning the new matched element set) - pushStack: function( elems ) { - - // Build a new jQuery matched element set - var ret = jQuery.merge( this.constructor(), elems ); - - // Add the old object onto the stack (as a reference) - ret.prevObject = this; - - // Return the newly-formed element set - return ret; - }, - - // Execute a callback for every element in the matched set. - each: function( callback ) { - return jQuery.each( this, callback ); - }, - - map: function( callback ) { - return this.pushStack( jQuery.map( this, function( elem, i ) { - return callback.call( elem, i, elem ); - } ) ); - }, - - slice: function() { - return this.pushStack( slice.apply( this, arguments ) ); - }, - - first: function() { - return this.eq( 0 ); - }, - - last: function() { - return this.eq( -1 ); - }, - - even: function() { - return this.pushStack( jQuery.grep( this, function( _elem, i ) { - return ( i + 1 ) % 2; - } ) ); - }, - - odd: function() { - return this.pushStack( jQuery.grep( this, function( _elem, i ) { - return i % 2; - } ) ); - }, - - eq: function( i ) { - var len = this.length, - j = +i + ( i < 0 ? len : 0 ); - return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); - }, - - end: function() { - return this.prevObject || this.constructor(); - }, - - // For internal use only. - // Behaves like an Array's method, not like a jQuery method. - push: push, - sort: arr.sort, - splice: arr.splice -}; - -jQuery.extend = jQuery.fn.extend = function() { - var options, name, src, copy, copyIsArray, clone, - target = arguments[ 0 ] || {}, - i = 1, - length = arguments.length, - deep = false; - - // Handle a deep copy situation - if ( typeof target === "boolean" ) { - deep = target; - - // Skip the boolean and the target - target = arguments[ i ] || {}; - i++; - } - - // Handle case when target is a string or something (possible in deep copy) - if ( typeof target !== "object" && !isFunction( target ) ) { - target = {}; - } - - // Extend jQuery itself if only one argument is passed - if ( i === length ) { - target = this; - i--; - } - - for ( ; i < length; i++ ) { - - // Only deal with non-null/undefined values - if ( ( options = arguments[ i ] ) != null ) { - - // Extend the base object - for ( name in options ) { - copy = options[ name ]; - - // Prevent Object.prototype pollution - // Prevent never-ending loop - if ( name === "__proto__" || target === copy ) { - continue; - } - - // Recurse if we're merging plain objects or arrays - if ( deep && copy && ( jQuery.isPlainObject( copy ) || - ( copyIsArray = Array.isArray( copy ) ) ) ) { - src = target[ name ]; - - // Ensure proper type for the source value - if ( copyIsArray && !Array.isArray( src ) ) { - clone = []; - } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { - clone = {}; - } else { - clone = src; - } - copyIsArray = false; - - // Never move original objects, clone them - target[ name ] = jQuery.extend( deep, clone, copy ); - - // Don't bring in undefined values - } else if ( copy !== undefined ) { - target[ name ] = copy; - } - } - } - } - - // Return the modified object - return target; -}; - -jQuery.extend( { - - // Unique for each copy of jQuery on the page - expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), - - // Assume jQuery is ready without the ready module - isReady: true, - - error: function( msg ) { - throw new Error( msg ); - }, - - noop: function() {}, - - isPlainObject: function( obj ) { - var proto, Ctor; - - // Detect obvious negatives - // Use toString instead of jQuery.type to catch host objects - if ( !obj || toString.call( obj ) !== "[object Object]" ) { - return false; - } - - proto = getProto( obj ); - - // Objects with no prototype (e.g., `Object.create( null )`) are plain - if ( !proto ) { - return true; - } - - // Objects with prototype are plain iff they were constructed by a global Object function - Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; - return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; - }, - - isEmptyObject: function( obj ) { - var name; - - for ( name in obj ) { - return false; - } - return true; - }, - - // Evaluates a script in a provided context; falls back to the global one - // if not specified. - globalEval: function( code, options, doc ) { - DOMEval( code, { nonce: options && options.nonce }, doc ); - }, - - each: function( obj, callback ) { - var length, i = 0; - - if ( isArrayLike( obj ) ) { - length = obj.length; - for ( ; i < length; i++ ) { - if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { - break; - } - } - } else { - for ( i in obj ) { - if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { - break; - } - } - } - - return obj; - }, - - // results is for internal usage only - makeArray: function( arr, results ) { - var ret = results || []; - - if ( arr != null ) { - if ( isArrayLike( Object( arr ) ) ) { - jQuery.merge( ret, - typeof arr === "string" ? - [ arr ] : arr - ); - } else { - push.call( ret, arr ); - } - } - - return ret; - }, - - inArray: function( elem, arr, i ) { - return arr == null ? -1 : indexOf.call( arr, elem, i ); - }, - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - merge: function( first, second ) { - var len = +second.length, - j = 0, - i = first.length; - - for ( ; j < len; j++ ) { - first[ i++ ] = second[ j ]; - } - - first.length = i; - - return first; - }, - - grep: function( elems, callback, invert ) { - var callbackInverse, - matches = [], - i = 0, - length = elems.length, - callbackExpect = !invert; - - // Go through the array, only saving the items - // that pass the validator function - for ( ; i < length; i++ ) { - callbackInverse = !callback( elems[ i ], i ); - if ( callbackInverse !== callbackExpect ) { - matches.push( elems[ i ] ); - } - } - - return matches; - }, - - // arg is for internal usage only - map: function( elems, callback, arg ) { - var length, value, - i = 0, - ret = []; - - // Go through the array, translating each of the items to their new values - if ( isArrayLike( elems ) ) { - length = elems.length; - for ( ; i < length; i++ ) { - value = callback( elems[ i ], i, arg ); - - if ( value != null ) { - ret.push( value ); - } - } - - // Go through every key on the object, - } else { - for ( i in elems ) { - value = callback( elems[ i ], i, arg ); - - if ( value != null ) { - ret.push( value ); - } - } - } - - // Flatten any nested arrays - return flat( ret ); - }, - - // A global GUID counter for objects - guid: 1, - - // jQuery.support is not used in Core but other projects attach their - // properties to it so it needs to exist. - support: support -} ); - -if ( typeof Symbol === "function" ) { - jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; -} - -// Populate the class2type map -jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), -function( _i, name ) { - class2type[ "[object " + name + "]" ] = name.toLowerCase(); -} ); - -function isArrayLike( obj ) { - - // Support: real iOS 8.2 only (not reproducible in simulator) - // `in` check used to prevent JIT error (gh-2145) - // hasOwn isn't used here due to false negatives - // regarding Nodelist length in IE - var length = !!obj && "length" in obj && obj.length, - type = toType( obj ); - - if ( isFunction( obj ) || isWindow( obj ) ) { - return false; - } - - return type === "array" || length === 0 || - typeof length === "number" && length > 0 && ( length - 1 ) in obj; -} -var Sizzle = -/*! - * Sizzle CSS Selector Engine v2.3.5 - * https://sizzlejs.com/ - * - * Copyright JS Foundation and other contributors - * Released under the MIT license - * https://js.foundation/ - * - * Date: 2020-03-14 - */ -( function( window ) { -var i, - support, - Expr, - getText, - isXML, - tokenize, - compile, - select, - outermostContext, - sortInput, - hasDuplicate, - - // Local document vars - setDocument, - document, - docElem, - documentIsHTML, - rbuggyQSA, - rbuggyMatches, - matches, - contains, - - // Instance-specific data - expando = "sizzle" + 1 * new Date(), - preferredDoc = window.document, - dirruns = 0, - done = 0, - classCache = createCache(), - tokenCache = createCache(), - compilerCache = createCache(), - nonnativeSelectorCache = createCache(), - sortOrder = function( a, b ) { - if ( a === b ) { - hasDuplicate = true; - } - return 0; - }, - - // Instance methods - hasOwn = ( {} ).hasOwnProperty, - arr = [], - pop = arr.pop, - pushNative = arr.push, - push = arr.push, - slice = arr.slice, - - // Use a stripped-down indexOf as it's faster than native - // https://jsperf.com/thor-indexof-vs-for/5 - indexOf = function( list, elem ) { - var i = 0, - len = list.length; - for ( ; i < len; i++ ) { - if ( list[ i ] === elem ) { - return i; - } - } - return -1; - }, - - booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + - "ismap|loop|multiple|open|readonly|required|scoped", - - // Regular expressions - - // http://www.w3.org/TR/css3-selectors/#whitespace - whitespace = "[\\x20\\t\\r\\n\\f]", - - // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram - identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + - "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", - - // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors - attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + - - // Operator (capture 2) - "*([*^$|!~]?=)" + whitespace + - - // "Attribute values must be CSS identifiers [capture 5] - // or strings [capture 3 or capture 4]" - "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + - whitespace + "*\\]", - - pseudos = ":(" + identifier + ")(?:\\((" + - - // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: - // 1. quoted (capture 3; capture 4 or capture 5) - "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + - - // 2. simple (capture 6) - "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + - - // 3. anything else (capture 2) - ".*" + - ")\\)|)", - - // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter - rwhitespace = new RegExp( whitespace + "+", "g" ), - rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + - whitespace + "+$", "g" ), - - rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), - rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + - "*" ), - rdescend = new RegExp( whitespace + "|>" ), - - rpseudo = new RegExp( pseudos ), - ridentifier = new RegExp( "^" + identifier + "$" ), - - matchExpr = { - "ID": new RegExp( "^#(" + identifier + ")" ), - "CLASS": new RegExp( "^\\.(" + identifier + ")" ), - "TAG": new RegExp( "^(" + identifier + "|[*])" ), - "ATTR": new RegExp( "^" + attributes ), - "PSEUDO": new RegExp( "^" + pseudos ), - "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + - whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + - whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), - "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), - - // For use in libraries implementing .is() - // We use this for POS matching in `select` - "needsContext": new RegExp( "^" + whitespace + - "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + - "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) - }, - - rhtml = /HTML$/i, - rinputs = /^(?:input|select|textarea|button)$/i, - rheader = /^h\d$/i, - - rnative = /^[^{]+\{\s*\[native \w/, - - // Easily-parseable/retrievable ID or TAG or CLASS selectors - rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, - - rsibling = /[+~]/, - - // CSS escapes - // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters - runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), - funescape = function( escape, nonHex ) { - var high = "0x" + escape.slice( 1 ) - 0x10000; - - return nonHex ? - - // Strip the backslash prefix from a non-hex escape sequence - nonHex : - - // Replace a hexadecimal escape sequence with the encoded Unicode code point - // Support: IE <=11+ - // For values outside the Basic Multilingual Plane (BMP), manually construct a - // surrogate pair - high < 0 ? - String.fromCharCode( high + 0x10000 ) : - String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); - }, - - // CSS string/identifier serialization - // https://drafts.csswg.org/cssom/#common-serializing-idioms - rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, - fcssescape = function( ch, asCodePoint ) { - if ( asCodePoint ) { - - // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER - if ( ch === "\0" ) { - return "\uFFFD"; - } - - // Control characters and (dependent upon position) numbers get escaped as code points - return ch.slice( 0, -1 ) + "\\" + - ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; - } - - // Other potentially-special ASCII characters get backslash-escaped - return "\\" + ch; - }, - - // Used for iframes - // See setDocument() - // Removing the function wrapper causes a "Permission Denied" - // error in IE - unloadHandler = function() { - setDocument(); - }, - - inDisabledFieldset = addCombinator( - function( elem ) { - return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; - }, - { dir: "parentNode", next: "legend" } - ); - -// Optimize for push.apply( _, NodeList ) -try { - push.apply( - ( arr = slice.call( preferredDoc.childNodes ) ), - preferredDoc.childNodes - ); - - // Support: Android<4.0 - // Detect silently failing push.apply - // eslint-disable-next-line no-unused-expressions - arr[ preferredDoc.childNodes.length ].nodeType; -} catch ( e ) { - push = { apply: arr.length ? - - // Leverage slice if possible - function( target, els ) { - pushNative.apply( target, slice.call( els ) ); - } : - - // Support: IE<9 - // Otherwise append directly - function( target, els ) { - var j = target.length, - i = 0; - - // Can't trust NodeList.length - while ( ( target[ j++ ] = els[ i++ ] ) ) {} - target.length = j - 1; - } - }; -} - -function Sizzle( selector, context, results, seed ) { - var m, i, elem, nid, match, groups, newSelector, - newContext = context && context.ownerDocument, - - // nodeType defaults to 9, since context defaults to document - nodeType = context ? context.nodeType : 9; - - results = results || []; - - // Return early from calls with invalid selector or context - if ( typeof selector !== "string" || !selector || - nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { - - return results; - } - - // Try to shortcut find operations (as opposed to filters) in HTML documents - if ( !seed ) { - setDocument( context ); - context = context || document; - - if ( documentIsHTML ) { - - // If the selector is sufficiently simple, try using a "get*By*" DOM method - // (excepting DocumentFragment context, where the methods don't exist) - if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { - - // ID selector - if ( ( m = match[ 1 ] ) ) { - - // Document context - if ( nodeType === 9 ) { - if ( ( elem = context.getElementById( m ) ) ) { - - // Support: IE, Opera, Webkit - // TODO: identify versions - // getElementById can match elements by name instead of ID - if ( elem.id === m ) { - results.push( elem ); - return results; - } - } else { - return results; - } - - // Element context - } else { - - // Support: IE, Opera, Webkit - // TODO: identify versions - // getElementById can match elements by name instead of ID - if ( newContext && ( elem = newContext.getElementById( m ) ) && - contains( context, elem ) && - elem.id === m ) { - - results.push( elem ); - return results; - } - } - - // Type selector - } else if ( match[ 2 ] ) { - push.apply( results, context.getElementsByTagName( selector ) ); - return results; - - // Class selector - } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && - context.getElementsByClassName ) { - - push.apply( results, context.getElementsByClassName( m ) ); - return results; - } - } - - // Take advantage of querySelectorAll - if ( support.qsa && - !nonnativeSelectorCache[ selector + " " ] && - ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && - - // Support: IE 8 only - // Exclude object elements - ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { - - newSelector = selector; - newContext = context; - - // qSA considers elements outside a scoping root when evaluating child or - // descendant combinators, which is not what we want. - // In such cases, we work around the behavior by prefixing every selector in the - // list with an ID selector referencing the scope context. - // The technique has to be used as well when a leading combinator is used - // as such selectors are not recognized by querySelectorAll. - // Thanks to Andrew Dupont for this technique. - if ( nodeType === 1 && - ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { - - // Expand context for sibling selectors - newContext = rsibling.test( selector ) && testContext( context.parentNode ) || - context; - - // We can use :scope instead of the ID hack if the browser - // supports it & if we're not changing the context. - if ( newContext !== context || !support.scope ) { - - // Capture the context ID, setting it first if necessary - if ( ( nid = context.getAttribute( "id" ) ) ) { - nid = nid.replace( rcssescape, fcssescape ); - } else { - context.setAttribute( "id", ( nid = expando ) ); - } - } - - // Prefix every selector in the list - groups = tokenize( selector ); - i = groups.length; - while ( i-- ) { - groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + - toSelector( groups[ i ] ); - } - newSelector = groups.join( "," ); - } - - try { - push.apply( results, - newContext.querySelectorAll( newSelector ) - ); - return results; - } catch ( qsaError ) { - nonnativeSelectorCache( selector, true ); - } finally { - if ( nid === expando ) { - context.removeAttribute( "id" ); - } - } - } - } - } - - // All others - return select( selector.replace( rtrim, "$1" ), context, results, seed ); -} - -/** - * Create key-value caches of limited size - * @returns {function(string, object)} Returns the Object data after storing it on itself with - * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) - * deleting the oldest entry - */ -function createCache() { - var keys = []; - - function cache( key, value ) { - - // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) - if ( keys.push( key + " " ) > Expr.cacheLength ) { - - // Only keep the most recent entries - delete cache[ keys.shift() ]; - } - return ( cache[ key + " " ] = value ); - } - return cache; -} - -/** - * Mark a function for special use by Sizzle - * @param {Function} fn The function to mark - */ -function markFunction( fn ) { - fn[ expando ] = true; - return fn; -} - -/** - * Support testing using an element - * @param {Function} fn Passed the created element and returns a boolean result - */ -function assert( fn ) { - var el = document.createElement( "fieldset" ); - - try { - return !!fn( el ); - } catch ( e ) { - return false; - } finally { - - // Remove from its parent by default - if ( el.parentNode ) { - el.parentNode.removeChild( el ); - } - - // release memory in IE - el = null; - } -} - -/** - * Adds the same handler for all of the specified attrs - * @param {String} attrs Pipe-separated list of attributes - * @param {Function} handler The method that will be applied - */ -function addHandle( attrs, handler ) { - var arr = attrs.split( "|" ), - i = arr.length; - - while ( i-- ) { - Expr.attrHandle[ arr[ i ] ] = handler; - } -} - -/** - * Checks document order of two siblings - * @param {Element} a - * @param {Element} b - * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b - */ -function siblingCheck( a, b ) { - var cur = b && a, - diff = cur && a.nodeType === 1 && b.nodeType === 1 && - a.sourceIndex - b.sourceIndex; - - // Use IE sourceIndex if available on both nodes - if ( diff ) { - return diff; - } - - // Check if b follows a - if ( cur ) { - while ( ( cur = cur.nextSibling ) ) { - if ( cur === b ) { - return -1; - } - } - } - - return a ? 1 : -1; -} - -/** - * Returns a function to use in pseudos for input types - * @param {String} type - */ -function createInputPseudo( type ) { - return function( elem ) { - var name = elem.nodeName.toLowerCase(); - return name === "input" && elem.type === type; - }; -} - -/** - * Returns a function to use in pseudos for buttons - * @param {String} type - */ -function createButtonPseudo( type ) { - return function( elem ) { - var name = elem.nodeName.toLowerCase(); - return ( name === "input" || name === "button" ) && elem.type === type; - }; -} - -/** - * Returns a function to use in pseudos for :enabled/:disabled - * @param {Boolean} disabled true for :disabled; false for :enabled - */ -function createDisabledPseudo( disabled ) { - - // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable - return function( elem ) { - - // Only certain elements can match :enabled or :disabled - // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled - // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled - if ( "form" in elem ) { - - // Check for inherited disabledness on relevant non-disabled elements: - // * listed form-associated elements in a disabled fieldset - // https://html.spec.whatwg.org/multipage/forms.html#category-listed - // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled - // * option elements in a disabled optgroup - // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled - // All such elements have a "form" property. - if ( elem.parentNode && elem.disabled === false ) { - - // Option elements defer to a parent optgroup if present - if ( "label" in elem ) { - if ( "label" in elem.parentNode ) { - return elem.parentNode.disabled === disabled; - } else { - return elem.disabled === disabled; - } - } - - // Support: IE 6 - 11 - // Use the isDisabled shortcut property to check for disabled fieldset ancestors - return elem.isDisabled === disabled || - - // Where there is no isDisabled, check manually - /* jshint -W018 */ - elem.isDisabled !== !disabled && - inDisabledFieldset( elem ) === disabled; - } - - return elem.disabled === disabled; - - // Try to winnow out elements that can't be disabled before trusting the disabled property. - // Some victims get caught in our net (label, legend, menu, track), but it shouldn't - // even exist on them, let alone have a boolean value. - } else if ( "label" in elem ) { - return elem.disabled === disabled; - } - - // Remaining elements are neither :enabled nor :disabled - return false; - }; -} - -/** - * Returns a function to use in pseudos for positionals - * @param {Function} fn - */ -function createPositionalPseudo( fn ) { - return markFunction( function( argument ) { - argument = +argument; - return markFunction( function( seed, matches ) { - var j, - matchIndexes = fn( [], seed.length, argument ), - i = matchIndexes.length; - - // Match elements found at the specified indexes - while ( i-- ) { - if ( seed[ ( j = matchIndexes[ i ] ) ] ) { - seed[ j ] = !( matches[ j ] = seed[ j ] ); - } - } - } ); - } ); -} - -/** - * Checks a node for validity as a Sizzle context - * @param {Element|Object=} context - * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value - */ -function testContext( context ) { - return context && typeof context.getElementsByTagName !== "undefined" && context; -} - -// Expose support vars for convenience -support = Sizzle.support = {}; - -/** - * Detects XML nodes - * @param {Element|Object} elem An element or a document - * @returns {Boolean} True iff elem is a non-HTML XML node - */ -isXML = Sizzle.isXML = function( elem ) { - var namespace = elem.namespaceURI, - docElem = ( elem.ownerDocument || elem ).documentElement; - - // Support: IE <=8 - // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes - // https://bugs.jquery.com/ticket/4833 - return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); -}; - -/** - * Sets document-related variables once based on the current document - * @param {Element|Object} [doc] An element or document object to use to set the document - * @returns {Object} Returns the current document - */ -setDocument = Sizzle.setDocument = function( node ) { - var hasCompare, subWindow, - doc = node ? node.ownerDocument || node : preferredDoc; - - // Return early if doc is invalid or already selected - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { - return document; - } - - // Update global variables - document = doc; - docElem = document.documentElement; - documentIsHTML = !isXML( document ); - - // Support: IE 9 - 11+, Edge 12 - 18+ - // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( preferredDoc != document && - ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { - - // Support: IE 11, Edge - if ( subWindow.addEventListener ) { - subWindow.addEventListener( "unload", unloadHandler, false ); - - // Support: IE 9 - 10 only - } else if ( subWindow.attachEvent ) { - subWindow.attachEvent( "onunload", unloadHandler ); - } - } - - // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, - // Safari 4 - 5 only, Opera <=11.6 - 12.x only - // IE/Edge & older browsers don't support the :scope pseudo-class. - // Support: Safari 6.0 only - // Safari 6.0 supports :scope but it's an alias of :root there. - support.scope = assert( function( el ) { - docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); - return typeof el.querySelectorAll !== "undefined" && - !el.querySelectorAll( ":scope fieldset div" ).length; - } ); - - /* Attributes - ---------------------------------------------------------------------- */ - - // Support: IE<8 - // Verify that getAttribute really returns attributes and not properties - // (excepting IE8 booleans) - support.attributes = assert( function( el ) { - el.className = "i"; - return !el.getAttribute( "className" ); - } ); - - /* getElement(s)By* - ---------------------------------------------------------------------- */ - - // Check if getElementsByTagName("*") returns only elements - support.getElementsByTagName = assert( function( el ) { - el.appendChild( document.createComment( "" ) ); - return !el.getElementsByTagName( "*" ).length; - } ); - - // Support: IE<9 - support.getElementsByClassName = rnative.test( document.getElementsByClassName ); - - // Support: IE<10 - // Check if getElementById returns elements by name - // The broken getElementById methods don't pick up programmatically-set names, - // so use a roundabout getElementsByName test - support.getById = assert( function( el ) { - docElem.appendChild( el ).id = expando; - return !document.getElementsByName || !document.getElementsByName( expando ).length; - } ); - - // ID filter and find - if ( support.getById ) { - Expr.filter[ "ID" ] = function( id ) { - var attrId = id.replace( runescape, funescape ); - return function( elem ) { - return elem.getAttribute( "id" ) === attrId; - }; - }; - Expr.find[ "ID" ] = function( id, context ) { - if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { - var elem = context.getElementById( id ); - return elem ? [ elem ] : []; - } - }; - } else { - Expr.filter[ "ID" ] = function( id ) { - var attrId = id.replace( runescape, funescape ); - return function( elem ) { - var node = typeof elem.getAttributeNode !== "undefined" && - elem.getAttributeNode( "id" ); - return node && node.value === attrId; - }; - }; - - // Support: IE 6 - 7 only - // getElementById is not reliable as a find shortcut - Expr.find[ "ID" ] = function( id, context ) { - if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { - var node, i, elems, - elem = context.getElementById( id ); - - if ( elem ) { - - // Verify the id attribute - node = elem.getAttributeNode( "id" ); - if ( node && node.value === id ) { - return [ elem ]; - } - - // Fall back on getElementsByName - elems = context.getElementsByName( id ); - i = 0; - while ( ( elem = elems[ i++ ] ) ) { - node = elem.getAttributeNode( "id" ); - if ( node && node.value === id ) { - return [ elem ]; - } - } - } - - return []; - } - }; - } - - // Tag - Expr.find[ "TAG" ] = support.getElementsByTagName ? - function( tag, context ) { - if ( typeof context.getElementsByTagName !== "undefined" ) { - return context.getElementsByTagName( tag ); - - // DocumentFragment nodes don't have gEBTN - } else if ( support.qsa ) { - return context.querySelectorAll( tag ); - } - } : - - function( tag, context ) { - var elem, - tmp = [], - i = 0, - - // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too - results = context.getElementsByTagName( tag ); - - // Filter out possible comments - if ( tag === "*" ) { - while ( ( elem = results[ i++ ] ) ) { - if ( elem.nodeType === 1 ) { - tmp.push( elem ); - } - } - - return tmp; - } - return results; - }; - - // Class - Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { - if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { - return context.getElementsByClassName( className ); - } - }; - - /* QSA/matchesSelector - ---------------------------------------------------------------------- */ - - // QSA and matchesSelector support - - // matchesSelector(:active) reports false when true (IE9/Opera 11.5) - rbuggyMatches = []; - - // qSa(:focus) reports false when true (Chrome 21) - // We allow this because of a bug in IE8/9 that throws an error - // whenever `document.activeElement` is accessed on an iframe - // So, we allow :focus to pass through QSA all the time to avoid the IE error - // See https://bugs.jquery.com/ticket/13378 - rbuggyQSA = []; - - if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { - - // Build QSA regex - // Regex strategy adopted from Diego Perini - assert( function( el ) { - - var input; - - // Select is set to empty string on purpose - // This is to test IE's treatment of not explicitly - // setting a boolean content attribute, - // since its presence should be enough - // https://bugs.jquery.com/ticket/12359 - docElem.appendChild( el ).innerHTML = "" + - ""; - - // Support: IE8, Opera 11-12.16 - // Nothing should be selected when empty strings follow ^= or $= or *= - // The test attribute must be unknown in Opera but "safe" for WinRT - // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section - if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { - rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); - } - - // Support: IE8 - // Boolean attributes and "value" are not treated correctly - if ( !el.querySelectorAll( "[selected]" ).length ) { - rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); - } - - // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ - if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { - rbuggyQSA.push( "~=" ); - } - - // Support: IE 11+, Edge 15 - 18+ - // IE 11/Edge don't find elements on a `[name='']` query in some cases. - // Adding a temporary attribute to the document before the selection works - // around the issue. - // Interestingly, IE 10 & older don't seem to have the issue. - input = document.createElement( "input" ); - input.setAttribute( "name", "" ); - el.appendChild( input ); - if ( !el.querySelectorAll( "[name='']" ).length ) { - rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + - whitespace + "*(?:''|\"\")" ); - } - - // Webkit/Opera - :checked should return selected option elements - // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked - // IE8 throws error here and will not see later tests - if ( !el.querySelectorAll( ":checked" ).length ) { - rbuggyQSA.push( ":checked" ); - } - - // Support: Safari 8+, iOS 8+ - // https://bugs.webkit.org/show_bug.cgi?id=136851 - // In-page `selector#id sibling-combinator selector` fails - if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { - rbuggyQSA.push( ".#.+[+~]" ); - } - - // Support: Firefox <=3.6 - 5 only - // Old Firefox doesn't throw on a badly-escaped identifier. - el.querySelectorAll( "\\\f" ); - rbuggyQSA.push( "[\\r\\n\\f]" ); - } ); - - assert( function( el ) { - el.innerHTML = "" + - ""; - - // Support: Windows 8 Native Apps - // The type and name attributes are restricted during .innerHTML assignment - var input = document.createElement( "input" ); - input.setAttribute( "type", "hidden" ); - el.appendChild( input ).setAttribute( "name", "D" ); - - // Support: IE8 - // Enforce case-sensitivity of name attribute - if ( el.querySelectorAll( "[name=d]" ).length ) { - rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); - } - - // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) - // IE8 throws error here and will not see later tests - if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { - rbuggyQSA.push( ":enabled", ":disabled" ); - } - - // Support: IE9-11+ - // IE's :disabled selector does not pick up the children of disabled fieldsets - docElem.appendChild( el ).disabled = true; - if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { - rbuggyQSA.push( ":enabled", ":disabled" ); - } - - // Support: Opera 10 - 11 only - // Opera 10-11 does not throw on post-comma invalid pseudos - el.querySelectorAll( "*,:x" ); - rbuggyQSA.push( ",.*:" ); - } ); - } - - if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || - docElem.webkitMatchesSelector || - docElem.mozMatchesSelector || - docElem.oMatchesSelector || - docElem.msMatchesSelector ) ) ) ) { - - assert( function( el ) { - - // Check to see if it's possible to do matchesSelector - // on a disconnected node (IE 9) - support.disconnectedMatch = matches.call( el, "*" ); - - // This should fail with an exception - // Gecko does not error, returns false instead - matches.call( el, "[s!='']:x" ); - rbuggyMatches.push( "!=", pseudos ); - } ); - } - - rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); - rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); - - /* Contains - ---------------------------------------------------------------------- */ - hasCompare = rnative.test( docElem.compareDocumentPosition ); - - // Element contains another - // Purposefully self-exclusive - // As in, an element does not contain itself - contains = hasCompare || rnative.test( docElem.contains ) ? - function( a, b ) { - var adown = a.nodeType === 9 ? a.documentElement : a, - bup = b && b.parentNode; - return a === bup || !!( bup && bup.nodeType === 1 && ( - adown.contains ? - adown.contains( bup ) : - a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 - ) ); - } : - function( a, b ) { - if ( b ) { - while ( ( b = b.parentNode ) ) { - if ( b === a ) { - return true; - } - } - } - return false; - }; - - /* Sorting - ---------------------------------------------------------------------- */ - - // Document order sorting - sortOrder = hasCompare ? - function( a, b ) { - - // Flag for duplicate removal - if ( a === b ) { - hasDuplicate = true; - return 0; - } - - // Sort on method existence if only one input has compareDocumentPosition - var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; - if ( compare ) { - return compare; - } - - // Calculate position if both inputs belong to the same document - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? - a.compareDocumentPosition( b ) : - - // Otherwise we know they are disconnected - 1; - - // Disconnected nodes - if ( compare & 1 || - ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { - - // Choose the first element that is related to our preferred document - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( a == document || a.ownerDocument == preferredDoc && - contains( preferredDoc, a ) ) { - return -1; - } - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( b == document || b.ownerDocument == preferredDoc && - contains( preferredDoc, b ) ) { - return 1; - } - - // Maintain original order - return sortInput ? - ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : - 0; - } - - return compare & 4 ? -1 : 1; - } : - function( a, b ) { - - // Exit early if the nodes are identical - if ( a === b ) { - hasDuplicate = true; - return 0; - } - - var cur, - i = 0, - aup = a.parentNode, - bup = b.parentNode, - ap = [ a ], - bp = [ b ]; - - // Parentless nodes are either documents or disconnected - if ( !aup || !bup ) { - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - /* eslint-disable eqeqeq */ - return a == document ? -1 : - b == document ? 1 : - /* eslint-enable eqeqeq */ - aup ? -1 : - bup ? 1 : - sortInput ? - ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : - 0; - - // If the nodes are siblings, we can do a quick check - } else if ( aup === bup ) { - return siblingCheck( a, b ); - } - - // Otherwise we need full lists of their ancestors for comparison - cur = a; - while ( ( cur = cur.parentNode ) ) { - ap.unshift( cur ); - } - cur = b; - while ( ( cur = cur.parentNode ) ) { - bp.unshift( cur ); - } - - // Walk down the tree looking for a discrepancy - while ( ap[ i ] === bp[ i ] ) { - i++; - } - - return i ? - - // Do a sibling check if the nodes have a common ancestor - siblingCheck( ap[ i ], bp[ i ] ) : - - // Otherwise nodes in our document sort first - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - /* eslint-disable eqeqeq */ - ap[ i ] == preferredDoc ? -1 : - bp[ i ] == preferredDoc ? 1 : - /* eslint-enable eqeqeq */ - 0; - }; - - return document; -}; - -Sizzle.matches = function( expr, elements ) { - return Sizzle( expr, null, null, elements ); -}; - -Sizzle.matchesSelector = function( elem, expr ) { - setDocument( elem ); - - if ( support.matchesSelector && documentIsHTML && - !nonnativeSelectorCache[ expr + " " ] && - ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && - ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { - - try { - var ret = matches.call( elem, expr ); - - // IE 9's matchesSelector returns false on disconnected nodes - if ( ret || support.disconnectedMatch || - - // As well, disconnected nodes are said to be in a document - // fragment in IE 9 - elem.document && elem.document.nodeType !== 11 ) { - return ret; - } - } catch ( e ) { - nonnativeSelectorCache( expr, true ); - } - } - - return Sizzle( expr, document, null, [ elem ] ).length > 0; -}; - -Sizzle.contains = function( context, elem ) { - - // Set document vars if needed - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( ( context.ownerDocument || context ) != document ) { - setDocument( context ); - } - return contains( context, elem ); -}; - -Sizzle.attr = function( elem, name ) { - - // Set document vars if needed - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( ( elem.ownerDocument || elem ) != document ) { - setDocument( elem ); - } - - var fn = Expr.attrHandle[ name.toLowerCase() ], - - // Don't get fooled by Object.prototype properties (jQuery #13807) - val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? - fn( elem, name, !documentIsHTML ) : - undefined; - - return val !== undefined ? - val : - support.attributes || !documentIsHTML ? - elem.getAttribute( name ) : - ( val = elem.getAttributeNode( name ) ) && val.specified ? - val.value : - null; -}; - -Sizzle.escape = function( sel ) { - return ( sel + "" ).replace( rcssescape, fcssescape ); -}; - -Sizzle.error = function( msg ) { - throw new Error( "Syntax error, unrecognized expression: " + msg ); -}; - -/** - * Document sorting and removing duplicates - * @param {ArrayLike} results - */ -Sizzle.uniqueSort = function( results ) { - var elem, - duplicates = [], - j = 0, - i = 0; - - // Unless we *know* we can detect duplicates, assume their presence - hasDuplicate = !support.detectDuplicates; - sortInput = !support.sortStable && results.slice( 0 ); - results.sort( sortOrder ); - - if ( hasDuplicate ) { - while ( ( elem = results[ i++ ] ) ) { - if ( elem === results[ i ] ) { - j = duplicates.push( i ); - } - } - while ( j-- ) { - results.splice( duplicates[ j ], 1 ); - } - } - - // Clear input after sorting to release objects - // See https://github.com/jquery/sizzle/pull/225 - sortInput = null; - - return results; -}; - -/** - * Utility function for retrieving the text value of an array of DOM nodes - * @param {Array|Element} elem - */ -getText = Sizzle.getText = function( elem ) { - var node, - ret = "", - i = 0, - nodeType = elem.nodeType; - - if ( !nodeType ) { - - // If no nodeType, this is expected to be an array - while ( ( node = elem[ i++ ] ) ) { - - // Do not traverse comment nodes - ret += getText( node ); - } - } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { - - // Use textContent for elements - // innerText usage removed for consistency of new lines (jQuery #11153) - if ( typeof elem.textContent === "string" ) { - return elem.textContent; - } else { - - // Traverse its children - for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { - ret += getText( elem ); - } - } - } else if ( nodeType === 3 || nodeType === 4 ) { - return elem.nodeValue; - } - - // Do not include comment or processing instruction nodes - - return ret; -}; - -Expr = Sizzle.selectors = { - - // Can be adjusted by the user - cacheLength: 50, - - createPseudo: markFunction, - - match: matchExpr, - - attrHandle: {}, - - find: {}, - - relative: { - ">": { dir: "parentNode", first: true }, - " ": { dir: "parentNode" }, - "+": { dir: "previousSibling", first: true }, - "~": { dir: "previousSibling" } - }, - - preFilter: { - "ATTR": function( match ) { - match[ 1 ] = match[ 1 ].replace( runescape, funescape ); - - // Move the given value to match[3] whether quoted or unquoted - match[ 3 ] = ( match[ 3 ] || match[ 4 ] || - match[ 5 ] || "" ).replace( runescape, funescape ); - - if ( match[ 2 ] === "~=" ) { - match[ 3 ] = " " + match[ 3 ] + " "; - } - - return match.slice( 0, 4 ); - }, - - "CHILD": function( match ) { - - /* matches from matchExpr["CHILD"] - 1 type (only|nth|...) - 2 what (child|of-type) - 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) - 4 xn-component of xn+y argument ([+-]?\d*n|) - 5 sign of xn-component - 6 x of xn-component - 7 sign of y-component - 8 y of y-component - */ - match[ 1 ] = match[ 1 ].toLowerCase(); - - if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { - - // nth-* requires argument - if ( !match[ 3 ] ) { - Sizzle.error( match[ 0 ] ); - } - - // numeric x and y parameters for Expr.filter.CHILD - // remember that false/true cast respectively to 0/1 - match[ 4 ] = +( match[ 4 ] ? - match[ 5 ] + ( match[ 6 ] || 1 ) : - 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); - match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); - - // other types prohibit arguments - } else if ( match[ 3 ] ) { - Sizzle.error( match[ 0 ] ); - } - - return match; - }, - - "PSEUDO": function( match ) { - var excess, - unquoted = !match[ 6 ] && match[ 2 ]; - - if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { - return null; - } - - // Accept quoted arguments as-is - if ( match[ 3 ] ) { - match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; - - // Strip excess characters from unquoted arguments - } else if ( unquoted && rpseudo.test( unquoted ) && - - // Get excess from tokenize (recursively) - ( excess = tokenize( unquoted, true ) ) && - - // advance to the next closing parenthesis - ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { - - // excess is a negative index - match[ 0 ] = match[ 0 ].slice( 0, excess ); - match[ 2 ] = unquoted.slice( 0, excess ); - } - - // Return only captures needed by the pseudo filter method (type and argument) - return match.slice( 0, 3 ); - } - }, - - filter: { - - "TAG": function( nodeNameSelector ) { - var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); - return nodeNameSelector === "*" ? - function() { - return true; - } : - function( elem ) { - return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; - }; - }, - - "CLASS": function( className ) { - var pattern = classCache[ className + " " ]; - - return pattern || - ( pattern = new RegExp( "(^|" + whitespace + - ")" + className + "(" + whitespace + "|$)" ) ) && classCache( - className, function( elem ) { - return pattern.test( - typeof elem.className === "string" && elem.className || - typeof elem.getAttribute !== "undefined" && - elem.getAttribute( "class" ) || - "" - ); - } ); - }, - - "ATTR": function( name, operator, check ) { - return function( elem ) { - var result = Sizzle.attr( elem, name ); - - if ( result == null ) { - return operator === "!="; - } - if ( !operator ) { - return true; - } - - result += ""; - - /* eslint-disable max-len */ - - return operator === "=" ? result === check : - operator === "!=" ? result !== check : - operator === "^=" ? check && result.indexOf( check ) === 0 : - operator === "*=" ? check && result.indexOf( check ) > -1 : - operator === "$=" ? check && result.slice( -check.length ) === check : - operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : - operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : - false; - /* eslint-enable max-len */ - - }; - }, - - "CHILD": function( type, what, _argument, first, last ) { - var simple = type.slice( 0, 3 ) !== "nth", - forward = type.slice( -4 ) !== "last", - ofType = what === "of-type"; - - return first === 1 && last === 0 ? - - // Shortcut for :nth-*(n) - function( elem ) { - return !!elem.parentNode; - } : - - function( elem, _context, xml ) { - var cache, uniqueCache, outerCache, node, nodeIndex, start, - dir = simple !== forward ? "nextSibling" : "previousSibling", - parent = elem.parentNode, - name = ofType && elem.nodeName.toLowerCase(), - useCache = !xml && !ofType, - diff = false; - - if ( parent ) { - - // :(first|last|only)-(child|of-type) - if ( simple ) { - while ( dir ) { - node = elem; - while ( ( node = node[ dir ] ) ) { - if ( ofType ? - node.nodeName.toLowerCase() === name : - node.nodeType === 1 ) { - - return false; - } - } - - // Reverse direction for :only-* (if we haven't yet done so) - start = dir = type === "only" && !start && "nextSibling"; - } - return true; - } - - start = [ forward ? parent.firstChild : parent.lastChild ]; - - // non-xml :nth-child(...) stores cache data on `parent` - if ( forward && useCache ) { - - // Seek `elem` from a previously-cached index - - // ...in a gzip-friendly way - node = parent; - outerCache = node[ expando ] || ( node[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ node.uniqueID ] || - ( outerCache[ node.uniqueID ] = {} ); - - cache = uniqueCache[ type ] || []; - nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; - diff = nodeIndex && cache[ 2 ]; - node = nodeIndex && parent.childNodes[ nodeIndex ]; - - while ( ( node = ++nodeIndex && node && node[ dir ] || - - // Fallback to seeking `elem` from the start - ( diff = nodeIndex = 0 ) || start.pop() ) ) { - - // When found, cache indexes on `parent` and break - if ( node.nodeType === 1 && ++diff && node === elem ) { - uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; - break; - } - } - - } else { - - // Use previously-cached element index if available - if ( useCache ) { - - // ...in a gzip-friendly way - node = elem; - outerCache = node[ expando ] || ( node[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ node.uniqueID ] || - ( outerCache[ node.uniqueID ] = {} ); - - cache = uniqueCache[ type ] || []; - nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; - diff = nodeIndex; - } - - // xml :nth-child(...) - // or :nth-last-child(...) or :nth(-last)?-of-type(...) - if ( diff === false ) { - - // Use the same loop as above to seek `elem` from the start - while ( ( node = ++nodeIndex && node && node[ dir ] || - ( diff = nodeIndex = 0 ) || start.pop() ) ) { - - if ( ( ofType ? - node.nodeName.toLowerCase() === name : - node.nodeType === 1 ) && - ++diff ) { - - // Cache the index of each encountered element - if ( useCache ) { - outerCache = node[ expando ] || - ( node[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ node.uniqueID ] || - ( outerCache[ node.uniqueID ] = {} ); - - uniqueCache[ type ] = [ dirruns, diff ]; - } - - if ( node === elem ) { - break; - } - } - } - } - } - - // Incorporate the offset, then check against cycle size - diff -= last; - return diff === first || ( diff % first === 0 && diff / first >= 0 ); - } - }; - }, - - "PSEUDO": function( pseudo, argument ) { - - // pseudo-class names are case-insensitive - // http://www.w3.org/TR/selectors/#pseudo-classes - // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters - // Remember that setFilters inherits from pseudos - var args, - fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || - Sizzle.error( "unsupported pseudo: " + pseudo ); - - // The user may use createPseudo to indicate that - // arguments are needed to create the filter function - // just as Sizzle does - if ( fn[ expando ] ) { - return fn( argument ); - } - - // But maintain support for old signatures - if ( fn.length > 1 ) { - args = [ pseudo, pseudo, "", argument ]; - return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? - markFunction( function( seed, matches ) { - var idx, - matched = fn( seed, argument ), - i = matched.length; - while ( i-- ) { - idx = indexOf( seed, matched[ i ] ); - seed[ idx ] = !( matches[ idx ] = matched[ i ] ); - } - } ) : - function( elem ) { - return fn( elem, 0, args ); - }; - } - - return fn; - } - }, - - pseudos: { - - // Potentially complex pseudos - "not": markFunction( function( selector ) { - - // Trim the selector passed to compile - // to avoid treating leading and trailing - // spaces as combinators - var input = [], - results = [], - matcher = compile( selector.replace( rtrim, "$1" ) ); - - return matcher[ expando ] ? - markFunction( function( seed, matches, _context, xml ) { - var elem, - unmatched = matcher( seed, null, xml, [] ), - i = seed.length; - - // Match elements unmatched by `matcher` - while ( i-- ) { - if ( ( elem = unmatched[ i ] ) ) { - seed[ i ] = !( matches[ i ] = elem ); - } - } - } ) : - function( elem, _context, xml ) { - input[ 0 ] = elem; - matcher( input, null, xml, results ); - - // Don't keep the element (issue #299) - input[ 0 ] = null; - return !results.pop(); - }; - } ), - - "has": markFunction( function( selector ) { - return function( elem ) { - return Sizzle( selector, elem ).length > 0; - }; - } ), - - "contains": markFunction( function( text ) { - text = text.replace( runescape, funescape ); - return function( elem ) { - return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; - }; - } ), - - // "Whether an element is represented by a :lang() selector - // is based solely on the element's language value - // being equal to the identifier C, - // or beginning with the identifier C immediately followed by "-". - // The matching of C against the element's language value is performed case-insensitively. - // The identifier C does not have to be a valid language name." - // http://www.w3.org/TR/selectors/#lang-pseudo - "lang": markFunction( function( lang ) { - - // lang value must be a valid identifier - if ( !ridentifier.test( lang || "" ) ) { - Sizzle.error( "unsupported lang: " + lang ); - } - lang = lang.replace( runescape, funescape ).toLowerCase(); - return function( elem ) { - var elemLang; - do { - if ( ( elemLang = documentIsHTML ? - elem.lang : - elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { - - elemLang = elemLang.toLowerCase(); - return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; - } - } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); - return false; - }; - } ), - - // Miscellaneous - "target": function( elem ) { - var hash = window.location && window.location.hash; - return hash && hash.slice( 1 ) === elem.id; - }, - - "root": function( elem ) { - return elem === docElem; - }, - - "focus": function( elem ) { - return elem === document.activeElement && - ( !document.hasFocus || document.hasFocus() ) && - !!( elem.type || elem.href || ~elem.tabIndex ); - }, - - // Boolean properties - "enabled": createDisabledPseudo( false ), - "disabled": createDisabledPseudo( true ), - - "checked": function( elem ) { - - // In CSS3, :checked should return both checked and selected elements - // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked - var nodeName = elem.nodeName.toLowerCase(); - return ( nodeName === "input" && !!elem.checked ) || - ( nodeName === "option" && !!elem.selected ); - }, - - "selected": function( elem ) { - - // Accessing this property makes selected-by-default - // options in Safari work properly - if ( elem.parentNode ) { - // eslint-disable-next-line no-unused-expressions - elem.parentNode.selectedIndex; - } - - return elem.selected === true; - }, - - // Contents - "empty": function( elem ) { - - // http://www.w3.org/TR/selectors/#empty-pseudo - // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), - // but not by others (comment: 8; processing instruction: 7; etc.) - // nodeType < 6 works because attributes (2) do not appear as children - for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { - if ( elem.nodeType < 6 ) { - return false; - } - } - return true; - }, - - "parent": function( elem ) { - return !Expr.pseudos[ "empty" ]( elem ); - }, - - // Element/input types - "header": function( elem ) { - return rheader.test( elem.nodeName ); - }, - - "input": function( elem ) { - return rinputs.test( elem.nodeName ); - }, - - "button": function( elem ) { - var name = elem.nodeName.toLowerCase(); - return name === "input" && elem.type === "button" || name === "button"; - }, - - "text": function( elem ) { - var attr; - return elem.nodeName.toLowerCase() === "input" && - elem.type === "text" && - - // Support: IE<8 - // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" - ( ( attr = elem.getAttribute( "type" ) ) == null || - attr.toLowerCase() === "text" ); - }, - - // Position-in-collection - "first": createPositionalPseudo( function() { - return [ 0 ]; - } ), - - "last": createPositionalPseudo( function( _matchIndexes, length ) { - return [ length - 1 ]; - } ), - - "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { - return [ argument < 0 ? argument + length : argument ]; - } ), - - "even": createPositionalPseudo( function( matchIndexes, length ) { - var i = 0; - for ( ; i < length; i += 2 ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ), - - "odd": createPositionalPseudo( function( matchIndexes, length ) { - var i = 1; - for ( ; i < length; i += 2 ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ), - - "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { - var i = argument < 0 ? - argument + length : - argument > length ? - length : - argument; - for ( ; --i >= 0; ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ), - - "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { - var i = argument < 0 ? argument + length : argument; - for ( ; ++i < length; ) { - matchIndexes.push( i ); - } - return matchIndexes; - } ) - } -}; - -Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; - -// Add button/input type pseudos -for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { - Expr.pseudos[ i ] = createInputPseudo( i ); -} -for ( i in { submit: true, reset: true } ) { - Expr.pseudos[ i ] = createButtonPseudo( i ); -} - -// Easy API for creating new setFilters -function setFilters() {} -setFilters.prototype = Expr.filters = Expr.pseudos; -Expr.setFilters = new setFilters(); - -tokenize = Sizzle.tokenize = function( selector, parseOnly ) { - var matched, match, tokens, type, - soFar, groups, preFilters, - cached = tokenCache[ selector + " " ]; - - if ( cached ) { - return parseOnly ? 0 : cached.slice( 0 ); - } - - soFar = selector; - groups = []; - preFilters = Expr.preFilter; - - while ( soFar ) { - - // Comma and first run - if ( !matched || ( match = rcomma.exec( soFar ) ) ) { - if ( match ) { - - // Don't consume trailing commas as valid - soFar = soFar.slice( match[ 0 ].length ) || soFar; - } - groups.push( ( tokens = [] ) ); - } - - matched = false; - - // Combinators - if ( ( match = rcombinators.exec( soFar ) ) ) { - matched = match.shift(); - tokens.push( { - value: matched, - - // Cast descendant combinators to space - type: match[ 0 ].replace( rtrim, " " ) - } ); - soFar = soFar.slice( matched.length ); - } - - // Filters - for ( type in Expr.filter ) { - if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || - ( match = preFilters[ type ]( match ) ) ) ) { - matched = match.shift(); - tokens.push( { - value: matched, - type: type, - matches: match - } ); - soFar = soFar.slice( matched.length ); - } - } - - if ( !matched ) { - break; - } - } - - // Return the length of the invalid excess - // if we're just parsing - // Otherwise, throw an error or return tokens - return parseOnly ? - soFar.length : - soFar ? - Sizzle.error( selector ) : - - // Cache the tokens - tokenCache( selector, groups ).slice( 0 ); -}; - -function toSelector( tokens ) { - var i = 0, - len = tokens.length, - selector = ""; - for ( ; i < len; i++ ) { - selector += tokens[ i ].value; - } - return selector; -} - -function addCombinator( matcher, combinator, base ) { - var dir = combinator.dir, - skip = combinator.next, - key = skip || dir, - checkNonElements = base && key === "parentNode", - doneName = done++; - - return combinator.first ? - - // Check against closest ancestor/preceding element - function( elem, context, xml ) { - while ( ( elem = elem[ dir ] ) ) { - if ( elem.nodeType === 1 || checkNonElements ) { - return matcher( elem, context, xml ); - } - } - return false; - } : - - // Check against all ancestor/preceding elements - function( elem, context, xml ) { - var oldCache, uniqueCache, outerCache, - newCache = [ dirruns, doneName ]; - - // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching - if ( xml ) { - while ( ( elem = elem[ dir ] ) ) { - if ( elem.nodeType === 1 || checkNonElements ) { - if ( matcher( elem, context, xml ) ) { - return true; - } - } - } - } else { - while ( ( elem = elem[ dir ] ) ) { - if ( elem.nodeType === 1 || checkNonElements ) { - outerCache = elem[ expando ] || ( elem[ expando ] = {} ); - - // Support: IE <9 only - // Defend against cloned attroperties (jQuery gh-1709) - uniqueCache = outerCache[ elem.uniqueID ] || - ( outerCache[ elem.uniqueID ] = {} ); - - if ( skip && skip === elem.nodeName.toLowerCase() ) { - elem = elem[ dir ] || elem; - } else if ( ( oldCache = uniqueCache[ key ] ) && - oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { - - // Assign to newCache so results back-propagate to previous elements - return ( newCache[ 2 ] = oldCache[ 2 ] ); - } else { - - // Reuse newcache so results back-propagate to previous elements - uniqueCache[ key ] = newCache; - - // A match means we're done; a fail means we have to keep checking - if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { - return true; - } - } - } - } - } - return false; - }; -} - -function elementMatcher( matchers ) { - return matchers.length > 1 ? - function( elem, context, xml ) { - var i = matchers.length; - while ( i-- ) { - if ( !matchers[ i ]( elem, context, xml ) ) { - return false; - } - } - return true; - } : - matchers[ 0 ]; -} - -function multipleContexts( selector, contexts, results ) { - var i = 0, - len = contexts.length; - for ( ; i < len; i++ ) { - Sizzle( selector, contexts[ i ], results ); - } - return results; -} - -function condense( unmatched, map, filter, context, xml ) { - var elem, - newUnmatched = [], - i = 0, - len = unmatched.length, - mapped = map != null; - - for ( ; i < len; i++ ) { - if ( ( elem = unmatched[ i ] ) ) { - if ( !filter || filter( elem, context, xml ) ) { - newUnmatched.push( elem ); - if ( mapped ) { - map.push( i ); - } - } - } - } - - return newUnmatched; -} - -function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { - if ( postFilter && !postFilter[ expando ] ) { - postFilter = setMatcher( postFilter ); - } - if ( postFinder && !postFinder[ expando ] ) { - postFinder = setMatcher( postFinder, postSelector ); - } - return markFunction( function( seed, results, context, xml ) { - var temp, i, elem, - preMap = [], - postMap = [], - preexisting = results.length, - - // Get initial elements from seed or context - elems = seed || multipleContexts( - selector || "*", - context.nodeType ? [ context ] : context, - [] - ), - - // Prefilter to get matcher input, preserving a map for seed-results synchronization - matcherIn = preFilter && ( seed || !selector ) ? - condense( elems, preMap, preFilter, context, xml ) : - elems, - - matcherOut = matcher ? - - // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, - postFinder || ( seed ? preFilter : preexisting || postFilter ) ? - - // ...intermediate processing is necessary - [] : - - // ...otherwise use results directly - results : - matcherIn; - - // Find primary matches - if ( matcher ) { - matcher( matcherIn, matcherOut, context, xml ); - } - - // Apply postFilter - if ( postFilter ) { - temp = condense( matcherOut, postMap ); - postFilter( temp, [], context, xml ); - - // Un-match failing elements by moving them back to matcherIn - i = temp.length; - while ( i-- ) { - if ( ( elem = temp[ i ] ) ) { - matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); - } - } - } - - if ( seed ) { - if ( postFinder || preFilter ) { - if ( postFinder ) { - - // Get the final matcherOut by condensing this intermediate into postFinder contexts - temp = []; - i = matcherOut.length; - while ( i-- ) { - if ( ( elem = matcherOut[ i ] ) ) { - - // Restore matcherIn since elem is not yet a final match - temp.push( ( matcherIn[ i ] = elem ) ); - } - } - postFinder( null, ( matcherOut = [] ), temp, xml ); - } - - // Move matched elements from seed to results to keep them synchronized - i = matcherOut.length; - while ( i-- ) { - if ( ( elem = matcherOut[ i ] ) && - ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { - - seed[ temp ] = !( results[ temp ] = elem ); - } - } - } - - // Add elements to results, through postFinder if defined - } else { - matcherOut = condense( - matcherOut === results ? - matcherOut.splice( preexisting, matcherOut.length ) : - matcherOut - ); - if ( postFinder ) { - postFinder( null, results, matcherOut, xml ); - } else { - push.apply( results, matcherOut ); - } - } - } ); -} - -function matcherFromTokens( tokens ) { - var checkContext, matcher, j, - len = tokens.length, - leadingRelative = Expr.relative[ tokens[ 0 ].type ], - implicitRelative = leadingRelative || Expr.relative[ " " ], - i = leadingRelative ? 1 : 0, - - // The foundational matcher ensures that elements are reachable from top-level context(s) - matchContext = addCombinator( function( elem ) { - return elem === checkContext; - }, implicitRelative, true ), - matchAnyContext = addCombinator( function( elem ) { - return indexOf( checkContext, elem ) > -1; - }, implicitRelative, true ), - matchers = [ function( elem, context, xml ) { - var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( - ( checkContext = context ).nodeType ? - matchContext( elem, context, xml ) : - matchAnyContext( elem, context, xml ) ); - - // Avoid hanging onto element (issue #299) - checkContext = null; - return ret; - } ]; - - for ( ; i < len; i++ ) { - if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { - matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; - } else { - matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); - - // Return special upon seeing a positional matcher - if ( matcher[ expando ] ) { - - // Find the next relative operator (if any) for proper handling - j = ++i; - for ( ; j < len; j++ ) { - if ( Expr.relative[ tokens[ j ].type ] ) { - break; - } - } - return setMatcher( - i > 1 && elementMatcher( matchers ), - i > 1 && toSelector( - - // If the preceding token was a descendant combinator, insert an implicit any-element `*` - tokens - .slice( 0, i - 1 ) - .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) - ).replace( rtrim, "$1" ), - matcher, - i < j && matcherFromTokens( tokens.slice( i, j ) ), - j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), - j < len && toSelector( tokens ) - ); - } - matchers.push( matcher ); - } - } - - return elementMatcher( matchers ); -} - -function matcherFromGroupMatchers( elementMatchers, setMatchers ) { - var bySet = setMatchers.length > 0, - byElement = elementMatchers.length > 0, - superMatcher = function( seed, context, xml, results, outermost ) { - var elem, j, matcher, - matchedCount = 0, - i = "0", - unmatched = seed && [], - setMatched = [], - contextBackup = outermostContext, - - // We must always have either seed elements or outermost context - elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), - - // Use integer dirruns iff this is the outermost matcher - dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), - len = elems.length; - - if ( outermost ) { - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - outermostContext = context == document || context || outermost; - } - - // Add elements passing elementMatchers directly to results - // Support: IE<9, Safari - // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id - for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { - if ( byElement && elem ) { - j = 0; - - // Support: IE 11+, Edge 17 - 18+ - // IE/Edge sometimes throw a "Permission denied" error when strict-comparing - // two documents; shallow comparisons work. - // eslint-disable-next-line eqeqeq - if ( !context && elem.ownerDocument != document ) { - setDocument( elem ); - xml = !documentIsHTML; - } - while ( ( matcher = elementMatchers[ j++ ] ) ) { - if ( matcher( elem, context || document, xml ) ) { - results.push( elem ); - break; - } - } - if ( outermost ) { - dirruns = dirrunsUnique; - } - } - - // Track unmatched elements for set filters - if ( bySet ) { - - // They will have gone through all possible matchers - if ( ( elem = !matcher && elem ) ) { - matchedCount--; - } - - // Lengthen the array for every element, matched or not - if ( seed ) { - unmatched.push( elem ); - } - } - } - - // `i` is now the count of elements visited above, and adding it to `matchedCount` - // makes the latter nonnegative. - matchedCount += i; - - // Apply set filters to unmatched elements - // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` - // equals `i`), unless we didn't visit _any_ elements in the above loop because we have - // no element matchers and no seed. - // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that - // case, which will result in a "00" `matchedCount` that differs from `i` but is also - // numerically zero. - if ( bySet && i !== matchedCount ) { - j = 0; - while ( ( matcher = setMatchers[ j++ ] ) ) { - matcher( unmatched, setMatched, context, xml ); - } - - if ( seed ) { - - // Reintegrate element matches to eliminate the need for sorting - if ( matchedCount > 0 ) { - while ( i-- ) { - if ( !( unmatched[ i ] || setMatched[ i ] ) ) { - setMatched[ i ] = pop.call( results ); - } - } - } - - // Discard index placeholder values to get only actual matches - setMatched = condense( setMatched ); - } - - // Add matches to results - push.apply( results, setMatched ); - - // Seedless set matches succeeding multiple successful matchers stipulate sorting - if ( outermost && !seed && setMatched.length > 0 && - ( matchedCount + setMatchers.length ) > 1 ) { - - Sizzle.uniqueSort( results ); - } - } - - // Override manipulation of globals by nested matchers - if ( outermost ) { - dirruns = dirrunsUnique; - outermostContext = contextBackup; - } - - return unmatched; - }; - - return bySet ? - markFunction( superMatcher ) : - superMatcher; -} - -compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { - var i, - setMatchers = [], - elementMatchers = [], - cached = compilerCache[ selector + " " ]; - - if ( !cached ) { - - // Generate a function of recursive functions that can be used to check each element - if ( !match ) { - match = tokenize( selector ); - } - i = match.length; - while ( i-- ) { - cached = matcherFromTokens( match[ i ] ); - if ( cached[ expando ] ) { - setMatchers.push( cached ); - } else { - elementMatchers.push( cached ); - } - } - - // Cache the compiled function - cached = compilerCache( - selector, - matcherFromGroupMatchers( elementMatchers, setMatchers ) - ); - - // Save selector and tokenization - cached.selector = selector; - } - return cached; -}; - -/** - * A low-level selection function that works with Sizzle's compiled - * selector functions - * @param {String|Function} selector A selector or a pre-compiled - * selector function built with Sizzle.compile - * @param {Element} context - * @param {Array} [results] - * @param {Array} [seed] A set of elements to match against - */ -select = Sizzle.select = function( selector, context, results, seed ) { - var i, tokens, token, type, find, - compiled = typeof selector === "function" && selector, - match = !seed && tokenize( ( selector = compiled.selector || selector ) ); - - results = results || []; - - // Try to minimize operations if there is only one selector in the list and no seed - // (the latter of which guarantees us context) - if ( match.length === 1 ) { - - // Reduce context if the leading compound selector is an ID - tokens = match[ 0 ] = match[ 0 ].slice( 0 ); - if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && - context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { - - context = ( Expr.find[ "ID" ]( token.matches[ 0 ] - .replace( runescape, funescape ), context ) || [] )[ 0 ]; - if ( !context ) { - return results; - - // Precompiled matchers will still verify ancestry, so step up a level - } else if ( compiled ) { - context = context.parentNode; - } - - selector = selector.slice( tokens.shift().value.length ); - } - - // Fetch a seed set for right-to-left matching - i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; - while ( i-- ) { - token = tokens[ i ]; - - // Abort if we hit a combinator - if ( Expr.relative[ ( type = token.type ) ] ) { - break; - } - if ( ( find = Expr.find[ type ] ) ) { - - // Search, expanding context for leading sibling combinators - if ( ( seed = find( - token.matches[ 0 ].replace( runescape, funescape ), - rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || - context - ) ) ) { - - // If seed is empty or no tokens remain, we can return early - tokens.splice( i, 1 ); - selector = seed.length && toSelector( tokens ); - if ( !selector ) { - push.apply( results, seed ); - return results; - } - - break; - } - } - } - } - - // Compile and execute a filtering function if one is not provided - // Provide `match` to avoid retokenization if we modified the selector above - ( compiled || compile( selector, match ) )( - seed, - context, - !documentIsHTML, - results, - !context || rsibling.test( selector ) && testContext( context.parentNode ) || context - ); - return results; -}; - -// One-time assignments - -// Sort stability -support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; - -// Support: Chrome 14-35+ -// Always assume duplicates if they aren't passed to the comparison function -support.detectDuplicates = !!hasDuplicate; - -// Initialize against the default document -setDocument(); - -// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) -// Detached nodes confoundingly follow *each other* -support.sortDetached = assert( function( el ) { - - // Should return 1, but returns 4 (following) - return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; -} ); - -// Support: IE<8 -// Prevent attribute/property "interpolation" -// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx -if ( !assert( function( el ) { - el.innerHTML = ""; - return el.firstChild.getAttribute( "href" ) === "#"; -} ) ) { - addHandle( "type|href|height|width", function( elem, name, isXML ) { - if ( !isXML ) { - return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); - } - } ); -} - -// Support: IE<9 -// Use defaultValue in place of getAttribute("value") -if ( !support.attributes || !assert( function( el ) { - el.innerHTML = ""; - el.firstChild.setAttribute( "value", "" ); - return el.firstChild.getAttribute( "value" ) === ""; -} ) ) { - addHandle( "value", function( elem, _name, isXML ) { - if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { - return elem.defaultValue; - } - } ); -} - -// Support: IE<9 -// Use getAttributeNode to fetch booleans when getAttribute lies -if ( !assert( function( el ) { - return el.getAttribute( "disabled" ) == null; -} ) ) { - addHandle( booleans, function( elem, name, isXML ) { - var val; - if ( !isXML ) { - return elem[ name ] === true ? name.toLowerCase() : - ( val = elem.getAttributeNode( name ) ) && val.specified ? - val.value : - null; - } - } ); -} - -return Sizzle; - -} )( window ); - - - -jQuery.find = Sizzle; -jQuery.expr = Sizzle.selectors; - -// Deprecated -jQuery.expr[ ":" ] = jQuery.expr.pseudos; -jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; -jQuery.text = Sizzle.getText; -jQuery.isXMLDoc = Sizzle.isXML; -jQuery.contains = Sizzle.contains; -jQuery.escapeSelector = Sizzle.escape; - - - - -var dir = function( elem, dir, until ) { - var matched = [], - truncate = until !== undefined; - - while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { - if ( elem.nodeType === 1 ) { - if ( truncate && jQuery( elem ).is( until ) ) { - break; - } - matched.push( elem ); - } - } - return matched; -}; - - -var siblings = function( n, elem ) { - var matched = []; - - for ( ; n; n = n.nextSibling ) { - if ( n.nodeType === 1 && n !== elem ) { - matched.push( n ); - } - } - - return matched; -}; - - -var rneedsContext = jQuery.expr.match.needsContext; - - - -function nodeName( elem, name ) { - - return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); - -}; -var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); - - - -// Implement the identical functionality for filter and not -function winnow( elements, qualifier, not ) { - if ( isFunction( qualifier ) ) { - return jQuery.grep( elements, function( elem, i ) { - return !!qualifier.call( elem, i, elem ) !== not; - } ); - } - - // Single element - if ( qualifier.nodeType ) { - return jQuery.grep( elements, function( elem ) { - return ( elem === qualifier ) !== not; - } ); - } - - // Arraylike of elements (jQuery, arguments, Array) - if ( typeof qualifier !== "string" ) { - return jQuery.grep( elements, function( elem ) { - return ( indexOf.call( qualifier, elem ) > -1 ) !== not; - } ); - } - - // Filtered directly for both simple and complex selectors - return jQuery.filter( qualifier, elements, not ); -} - -jQuery.filter = function( expr, elems, not ) { - var elem = elems[ 0 ]; - - if ( not ) { - expr = ":not(" + expr + ")"; - } - - if ( elems.length === 1 && elem.nodeType === 1 ) { - return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; - } - - return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { - return elem.nodeType === 1; - } ) ); -}; - -jQuery.fn.extend( { - find: function( selector ) { - var i, ret, - len = this.length, - self = this; - - if ( typeof selector !== "string" ) { - return this.pushStack( jQuery( selector ).filter( function() { - for ( i = 0; i < len; i++ ) { - if ( jQuery.contains( self[ i ], this ) ) { - return true; - } - } - } ) ); - } - - ret = this.pushStack( [] ); - - for ( i = 0; i < len; i++ ) { - jQuery.find( selector, self[ i ], ret ); - } - - return len > 1 ? jQuery.uniqueSort( ret ) : ret; - }, - filter: function( selector ) { - return this.pushStack( winnow( this, selector || [], false ) ); - }, - not: function( selector ) { - return this.pushStack( winnow( this, selector || [], true ) ); - }, - is: function( selector ) { - return !!winnow( - this, - - // If this is a positional/relative selector, check membership in the returned set - // so $("p:first").is("p:last") won't return true for a doc with two "p". - typeof selector === "string" && rneedsContext.test( selector ) ? - jQuery( selector ) : - selector || [], - false - ).length; - } -} ); - - -// Initialize a jQuery object - - -// A central reference to the root jQuery(document) -var rootjQuery, - - // A simple way to check for HTML strings - // Prioritize #id over to avoid XSS via location.hash (#9521) - // Strict HTML recognition (#11290: must start with <) - // Shortcut simple #id case for speed - rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, - - init = jQuery.fn.init = function( selector, context, root ) { - var match, elem; - - // HANDLE: $(""), $(null), $(undefined), $(false) - if ( !selector ) { - return this; - } - - // Method init() accepts an alternate rootjQuery - // so migrate can support jQuery.sub (gh-2101) - root = root || rootjQuery; - - // Handle HTML strings - if ( typeof selector === "string" ) { - if ( selector[ 0 ] === "<" && - selector[ selector.length - 1 ] === ">" && - selector.length >= 3 ) { - - // Assume that strings that start and end with <> are HTML and skip the regex check - match = [ null, selector, null ]; - - } else { - match = rquickExpr.exec( selector ); - } - - // Match html or make sure no context is specified for #id - if ( match && ( match[ 1 ] || !context ) ) { - - // HANDLE: $(html) -> $(array) - if ( match[ 1 ] ) { - context = context instanceof jQuery ? context[ 0 ] : context; - - // Option to run scripts is true for back-compat - // Intentionally let the error be thrown if parseHTML is not present - jQuery.merge( this, jQuery.parseHTML( - match[ 1 ], - context && context.nodeType ? context.ownerDocument || context : document, - true - ) ); - - // HANDLE: $(html, props) - if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { - for ( match in context ) { - - // Properties of context are called as methods if possible - if ( isFunction( this[ match ] ) ) { - this[ match ]( context[ match ] ); - - // ...and otherwise set as attributes - } else { - this.attr( match, context[ match ] ); - } - } - } - - return this; - - // HANDLE: $(#id) - } else { - elem = document.getElementById( match[ 2 ] ); - - if ( elem ) { - - // Inject the element directly into the jQuery object - this[ 0 ] = elem; - this.length = 1; - } - return this; - } - - // HANDLE: $(expr, $(...)) - } else if ( !context || context.jquery ) { - return ( context || root ).find( selector ); - - // HANDLE: $(expr, context) - // (which is just equivalent to: $(context).find(expr) - } else { - return this.constructor( context ).find( selector ); - } - - // HANDLE: $(DOMElement) - } else if ( selector.nodeType ) { - this[ 0 ] = selector; - this.length = 1; - return this; - - // HANDLE: $(function) - // Shortcut for document ready - } else if ( isFunction( selector ) ) { - return root.ready !== undefined ? - root.ready( selector ) : - - // Execute immediately if ready is not present - selector( jQuery ); - } - - return jQuery.makeArray( selector, this ); - }; - -// Give the init function the jQuery prototype for later instantiation -init.prototype = jQuery.fn; - -// Initialize central reference -rootjQuery = jQuery( document ); - - -var rparentsprev = /^(?:parents|prev(?:Until|All))/, - - // Methods guaranteed to produce a unique set when starting from a unique set - guaranteedUnique = { - children: true, - contents: true, - next: true, - prev: true - }; - -jQuery.fn.extend( { - has: function( target ) { - var targets = jQuery( target, this ), - l = targets.length; - - return this.filter( function() { - var i = 0; - for ( ; i < l; i++ ) { - if ( jQuery.contains( this, targets[ i ] ) ) { - return true; - } - } - } ); - }, - - closest: function( selectors, context ) { - var cur, - i = 0, - l = this.length, - matched = [], - targets = typeof selectors !== "string" && jQuery( selectors ); - - // Positional selectors never match, since there's no _selection_ context - if ( !rneedsContext.test( selectors ) ) { - for ( ; i < l; i++ ) { - for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { - - // Always skip document fragments - if ( cur.nodeType < 11 && ( targets ? - targets.index( cur ) > -1 : - - // Don't pass non-elements to Sizzle - cur.nodeType === 1 && - jQuery.find.matchesSelector( cur, selectors ) ) ) { - - matched.push( cur ); - break; - } - } - } - } - - return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); - }, - - // Determine the position of an element within the set - index: function( elem ) { - - // No argument, return index in parent - if ( !elem ) { - return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; - } - - // Index in selector - if ( typeof elem === "string" ) { - return indexOf.call( jQuery( elem ), this[ 0 ] ); - } - - // Locate the position of the desired element - return indexOf.call( this, - - // If it receives a jQuery object, the first element is used - elem.jquery ? elem[ 0 ] : elem - ); - }, - - add: function( selector, context ) { - return this.pushStack( - jQuery.uniqueSort( - jQuery.merge( this.get(), jQuery( selector, context ) ) - ) - ); - }, - - addBack: function( selector ) { - return this.add( selector == null ? - this.prevObject : this.prevObject.filter( selector ) - ); - } -} ); - -function sibling( cur, dir ) { - while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} - return cur; -} - -jQuery.each( { - parent: function( elem ) { - var parent = elem.parentNode; - return parent && parent.nodeType !== 11 ? parent : null; - }, - parents: function( elem ) { - return dir( elem, "parentNode" ); - }, - parentsUntil: function( elem, _i, until ) { - return dir( elem, "parentNode", until ); - }, - next: function( elem ) { - return sibling( elem, "nextSibling" ); - }, - prev: function( elem ) { - return sibling( elem, "previousSibling" ); - }, - nextAll: function( elem ) { - return dir( elem, "nextSibling" ); - }, - prevAll: function( elem ) { - return dir( elem, "previousSibling" ); - }, - nextUntil: function( elem, _i, until ) { - return dir( elem, "nextSibling", until ); - }, - prevUntil: function( elem, _i, until ) { - return dir( elem, "previousSibling", until ); - }, - siblings: function( elem ) { - return siblings( ( elem.parentNode || {} ).firstChild, elem ); - }, - children: function( elem ) { - return siblings( elem.firstChild ); - }, - contents: function( elem ) { - if ( elem.contentDocument != null && - - // Support: IE 11+ - // elements with no `data` attribute has an object - // `contentDocument` with a `null` prototype. - getProto( elem.contentDocument ) ) { - - return elem.contentDocument; - } - - // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only - // Treat the template element as a regular one in browsers that - // don't support it. - if ( nodeName( elem, "template" ) ) { - elem = elem.content || elem; - } - - return jQuery.merge( [], elem.childNodes ); - } -}, function( name, fn ) { - jQuery.fn[ name ] = function( until, selector ) { - var matched = jQuery.map( this, fn, until ); - - if ( name.slice( -5 ) !== "Until" ) { - selector = until; - } - - if ( selector && typeof selector === "string" ) { - matched = jQuery.filter( selector, matched ); - } - - if ( this.length > 1 ) { - - // Remove duplicates - if ( !guaranteedUnique[ name ] ) { - jQuery.uniqueSort( matched ); - } - - // Reverse order for parents* and prev-derivatives - if ( rparentsprev.test( name ) ) { - matched.reverse(); - } - } - - return this.pushStack( matched ); - }; -} ); -var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); - - - -// Convert String-formatted options into Object-formatted ones -function createOptions( options ) { - var object = {}; - jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { - object[ flag ] = true; - } ); - return object; -} - -/* - * Create a callback list using the following parameters: - * - * options: an optional list of space-separated options that will change how - * the callback list behaves or a more traditional option object - * - * By default a callback list will act like an event callback list and can be - * "fired" multiple times. - * - * Possible options: - * - * once: will ensure the callback list can only be fired once (like a Deferred) - * - * memory: will keep track of previous values and will call any callback added - * after the list has been fired right away with the latest "memorized" - * values (like a Deferred) - * - * unique: will ensure a callback can only be added once (no duplicate in the list) - * - * stopOnFalse: interrupt callings when a callback returns false - * - */ -jQuery.Callbacks = function( options ) { - - // Convert options from String-formatted to Object-formatted if needed - // (we check in cache first) - options = typeof options === "string" ? - createOptions( options ) : - jQuery.extend( {}, options ); - - var // Flag to know if list is currently firing - firing, - - // Last fire value for non-forgettable lists - memory, - - // Flag to know if list was already fired - fired, - - // Flag to prevent firing - locked, - - // Actual callback list - list = [], - - // Queue of execution data for repeatable lists - queue = [], - - // Index of currently firing callback (modified by add/remove as needed) - firingIndex = -1, - - // Fire callbacks - fire = function() { - - // Enforce single-firing - locked = locked || options.once; - - // Execute callbacks for all pending executions, - // respecting firingIndex overrides and runtime changes - fired = firing = true; - for ( ; queue.length; firingIndex = -1 ) { - memory = queue.shift(); - while ( ++firingIndex < list.length ) { - - // Run callback and check for early termination - if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && - options.stopOnFalse ) { - - // Jump to end and forget the data so .add doesn't re-fire - firingIndex = list.length; - memory = false; - } - } - } - - // Forget the data if we're done with it - if ( !options.memory ) { - memory = false; - } - - firing = false; - - // Clean up if we're done firing for good - if ( locked ) { - - // Keep an empty list if we have data for future add calls - if ( memory ) { - list = []; - - // Otherwise, this object is spent - } else { - list = ""; - } - } - }, - - // Actual Callbacks object - self = { - - // Add a callback or a collection of callbacks to the list - add: function() { - if ( list ) { - - // If we have memory from a past run, we should fire after adding - if ( memory && !firing ) { - firingIndex = list.length - 1; - queue.push( memory ); - } - - ( function add( args ) { - jQuery.each( args, function( _, arg ) { - if ( isFunction( arg ) ) { - if ( !options.unique || !self.has( arg ) ) { - list.push( arg ); - } - } else if ( arg && arg.length && toType( arg ) !== "string" ) { - - // Inspect recursively - add( arg ); - } - } ); - } )( arguments ); - - if ( memory && !firing ) { - fire(); - } - } - return this; - }, - - // Remove a callback from the list - remove: function() { - jQuery.each( arguments, function( _, arg ) { - var index; - while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { - list.splice( index, 1 ); - - // Handle firing indexes - if ( index <= firingIndex ) { - firingIndex--; - } - } - } ); - return this; - }, - - // Check if a given callback is in the list. - // If no argument is given, return whether or not list has callbacks attached. - has: function( fn ) { - return fn ? - jQuery.inArray( fn, list ) > -1 : - list.length > 0; - }, - - // Remove all callbacks from the list - empty: function() { - if ( list ) { - list = []; - } - return this; - }, - - // Disable .fire and .add - // Abort any current/pending executions - // Clear all callbacks and values - disable: function() { - locked = queue = []; - list = memory = ""; - return this; - }, - disabled: function() { - return !list; - }, - - // Disable .fire - // Also disable .add unless we have memory (since it would have no effect) - // Abort any pending executions - lock: function() { - locked = queue = []; - if ( !memory && !firing ) { - list = memory = ""; - } - return this; - }, - locked: function() { - return !!locked; - }, - - // Call all callbacks with the given context and arguments - fireWith: function( context, args ) { - if ( !locked ) { - args = args || []; - args = [ context, args.slice ? args.slice() : args ]; - queue.push( args ); - if ( !firing ) { - fire(); - } - } - return this; - }, - - // Call all the callbacks with the given arguments - fire: function() { - self.fireWith( this, arguments ); - return this; - }, - - // To know if the callbacks have already been called at least once - fired: function() { - return !!fired; - } - }; - - return self; -}; - - -function Identity( v ) { - return v; -} -function Thrower( ex ) { - throw ex; -} - -function adoptValue( value, resolve, reject, noValue ) { - var method; - - try { - - // Check for promise aspect first to privilege synchronous behavior - if ( value && isFunction( ( method = value.promise ) ) ) { - method.call( value ).done( resolve ).fail( reject ); - - // Other thenables - } else if ( value && isFunction( ( method = value.then ) ) ) { - method.call( value, resolve, reject ); - - // Other non-thenables - } else { - - // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: - // * false: [ value ].slice( 0 ) => resolve( value ) - // * true: [ value ].slice( 1 ) => resolve() - resolve.apply( undefined, [ value ].slice( noValue ) ); - } - - // For Promises/A+, convert exceptions into rejections - // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in - // Deferred#then to conditionally suppress rejection. - } catch ( value ) { - - // Support: Android 4.0 only - // Strict mode functions invoked without .call/.apply get global-object context - reject.apply( undefined, [ value ] ); - } -} - -jQuery.extend( { - - Deferred: function( func ) { - var tuples = [ - - // action, add listener, callbacks, - // ... .then handlers, argument index, [final state] - [ "notify", "progress", jQuery.Callbacks( "memory" ), - jQuery.Callbacks( "memory" ), 2 ], - [ "resolve", "done", jQuery.Callbacks( "once memory" ), - jQuery.Callbacks( "once memory" ), 0, "resolved" ], - [ "reject", "fail", jQuery.Callbacks( "once memory" ), - jQuery.Callbacks( "once memory" ), 1, "rejected" ] - ], - state = "pending", - promise = { - state: function() { - return state; - }, - always: function() { - deferred.done( arguments ).fail( arguments ); - return this; - }, - "catch": function( fn ) { - return promise.then( null, fn ); - }, - - // Keep pipe for back-compat - pipe: function( /* fnDone, fnFail, fnProgress */ ) { - var fns = arguments; - - return jQuery.Deferred( function( newDefer ) { - jQuery.each( tuples, function( _i, tuple ) { - - // Map tuples (progress, done, fail) to arguments (done, fail, progress) - var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; - - // deferred.progress(function() { bind to newDefer or newDefer.notify }) - // deferred.done(function() { bind to newDefer or newDefer.resolve }) - // deferred.fail(function() { bind to newDefer or newDefer.reject }) - deferred[ tuple[ 1 ] ]( function() { - var returned = fn && fn.apply( this, arguments ); - if ( returned && isFunction( returned.promise ) ) { - returned.promise() - .progress( newDefer.notify ) - .done( newDefer.resolve ) - .fail( newDefer.reject ); - } else { - newDefer[ tuple[ 0 ] + "With" ]( - this, - fn ? [ returned ] : arguments - ); - } - } ); - } ); - fns = null; - } ).promise(); - }, - then: function( onFulfilled, onRejected, onProgress ) { - var maxDepth = 0; - function resolve( depth, deferred, handler, special ) { - return function() { - var that = this, - args = arguments, - mightThrow = function() { - var returned, then; - - // Support: Promises/A+ section 2.3.3.3.3 - // https://promisesaplus.com/#point-59 - // Ignore double-resolution attempts - if ( depth < maxDepth ) { - return; - } - - returned = handler.apply( that, args ); - - // Support: Promises/A+ section 2.3.1 - // https://promisesaplus.com/#point-48 - if ( returned === deferred.promise() ) { - throw new TypeError( "Thenable self-resolution" ); - } - - // Support: Promises/A+ sections 2.3.3.1, 3.5 - // https://promisesaplus.com/#point-54 - // https://promisesaplus.com/#point-75 - // Retrieve `then` only once - then = returned && - - // Support: Promises/A+ section 2.3.4 - // https://promisesaplus.com/#point-64 - // Only check objects and functions for thenability - ( typeof returned === "object" || - typeof returned === "function" ) && - returned.then; - - // Handle a returned thenable - if ( isFunction( then ) ) { - - // Special processors (notify) just wait for resolution - if ( special ) { - then.call( - returned, - resolve( maxDepth, deferred, Identity, special ), - resolve( maxDepth, deferred, Thrower, special ) - ); - - // Normal processors (resolve) also hook into progress - } else { - - // ...and disregard older resolution values - maxDepth++; - - then.call( - returned, - resolve( maxDepth, deferred, Identity, special ), - resolve( maxDepth, deferred, Thrower, special ), - resolve( maxDepth, deferred, Identity, - deferred.notifyWith ) - ); - } - - // Handle all other returned values - } else { - - // Only substitute handlers pass on context - // and multiple values (non-spec behavior) - if ( handler !== Identity ) { - that = undefined; - args = [ returned ]; - } - - // Process the value(s) - // Default process is resolve - ( special || deferred.resolveWith )( that, args ); - } - }, - - // Only normal processors (resolve) catch and reject exceptions - process = special ? - mightThrow : - function() { - try { - mightThrow(); - } catch ( e ) { - - if ( jQuery.Deferred.exceptionHook ) { - jQuery.Deferred.exceptionHook( e, - process.stackTrace ); - } - - // Support: Promises/A+ section 2.3.3.3.4.1 - // https://promisesaplus.com/#point-61 - // Ignore post-resolution exceptions - if ( depth + 1 >= maxDepth ) { - - // Only substitute handlers pass on context - // and multiple values (non-spec behavior) - if ( handler !== Thrower ) { - that = undefined; - args = [ e ]; - } - - deferred.rejectWith( that, args ); - } - } - }; - - // Support: Promises/A+ section 2.3.3.3.1 - // https://promisesaplus.com/#point-57 - // Re-resolve promises immediately to dodge false rejection from - // subsequent errors - if ( depth ) { - process(); - } else { - - // Call an optional hook to record the stack, in case of exception - // since it's otherwise lost when execution goes async - if ( jQuery.Deferred.getStackHook ) { - process.stackTrace = jQuery.Deferred.getStackHook(); - } - window.setTimeout( process ); - } - }; - } - - return jQuery.Deferred( function( newDefer ) { - - // progress_handlers.add( ... ) - tuples[ 0 ][ 3 ].add( - resolve( - 0, - newDefer, - isFunction( onProgress ) ? - onProgress : - Identity, - newDefer.notifyWith - ) - ); - - // fulfilled_handlers.add( ... ) - tuples[ 1 ][ 3 ].add( - resolve( - 0, - newDefer, - isFunction( onFulfilled ) ? - onFulfilled : - Identity - ) - ); - - // rejected_handlers.add( ... ) - tuples[ 2 ][ 3 ].add( - resolve( - 0, - newDefer, - isFunction( onRejected ) ? - onRejected : - Thrower - ) - ); - } ).promise(); - }, - - // Get a promise for this deferred - // If obj is provided, the promise aspect is added to the object - promise: function( obj ) { - return obj != null ? jQuery.extend( obj, promise ) : promise; - } - }, - deferred = {}; - - // Add list-specific methods - jQuery.each( tuples, function( i, tuple ) { - var list = tuple[ 2 ], - stateString = tuple[ 5 ]; - - // promise.progress = list.add - // promise.done = list.add - // promise.fail = list.add - promise[ tuple[ 1 ] ] = list.add; - - // Handle state - if ( stateString ) { - list.add( - function() { - - // state = "resolved" (i.e., fulfilled) - // state = "rejected" - state = stateString; - }, - - // rejected_callbacks.disable - // fulfilled_callbacks.disable - tuples[ 3 - i ][ 2 ].disable, - - // rejected_handlers.disable - // fulfilled_handlers.disable - tuples[ 3 - i ][ 3 ].disable, - - // progress_callbacks.lock - tuples[ 0 ][ 2 ].lock, - - // progress_handlers.lock - tuples[ 0 ][ 3 ].lock - ); - } - - // progress_handlers.fire - // fulfilled_handlers.fire - // rejected_handlers.fire - list.add( tuple[ 3 ].fire ); - - // deferred.notify = function() { deferred.notifyWith(...) } - // deferred.resolve = function() { deferred.resolveWith(...) } - // deferred.reject = function() { deferred.rejectWith(...) } - deferred[ tuple[ 0 ] ] = function() { - deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); - return this; - }; - - // deferred.notifyWith = list.fireWith - // deferred.resolveWith = list.fireWith - // deferred.rejectWith = list.fireWith - deferred[ tuple[ 0 ] + "With" ] = list.fireWith; - } ); - - // Make the deferred a promise - promise.promise( deferred ); - - // Call given func if any - if ( func ) { - func.call( deferred, deferred ); - } - - // All done! - return deferred; - }, - - // Deferred helper - when: function( singleValue ) { - var - - // count of uncompleted subordinates - remaining = arguments.length, - - // count of unprocessed arguments - i = remaining, - - // subordinate fulfillment data - resolveContexts = Array( i ), - resolveValues = slice.call( arguments ), - - // the master Deferred - master = jQuery.Deferred(), - - // subordinate callback factory - updateFunc = function( i ) { - return function( value ) { - resolveContexts[ i ] = this; - resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; - if ( !( --remaining ) ) { - master.resolveWith( resolveContexts, resolveValues ); - } - }; - }; - - // Single- and empty arguments are adopted like Promise.resolve - if ( remaining <= 1 ) { - adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject, - !remaining ); - - // Use .then() to unwrap secondary thenables (cf. gh-3000) - if ( master.state() === "pending" || - isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { - - return master.then(); - } - } - - // Multiple arguments are aggregated like Promise.all array elements - while ( i-- ) { - adoptValue( resolveValues[ i ], updateFunc( i ), master.reject ); - } - - return master.promise(); - } -} ); - - -// These usually indicate a programmer mistake during development, -// warn about them ASAP rather than swallowing them by default. -var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; - -jQuery.Deferred.exceptionHook = function( error, stack ) { - - // Support: IE 8 - 9 only - // Console exists when dev tools are open, which can happen at any time - if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { - window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); - } -}; - - - - -jQuery.readyException = function( error ) { - window.setTimeout( function() { - throw error; - } ); -}; - - - - -// The deferred used on DOM ready -var readyList = jQuery.Deferred(); - -jQuery.fn.ready = function( fn ) { - - readyList - .then( fn ) - - // Wrap jQuery.readyException in a function so that the lookup - // happens at the time of error handling instead of callback - // registration. - .catch( function( error ) { - jQuery.readyException( error ); - } ); - - return this; -}; - -jQuery.extend( { - - // Is the DOM ready to be used? Set to true once it occurs. - isReady: false, - - // A counter to track how many items to wait for before - // the ready event fires. See #6781 - readyWait: 1, - - // Handle when the DOM is ready - ready: function( wait ) { - - // Abort if there are pending holds or we're already ready - if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { - return; - } - - // Remember that the DOM is ready - jQuery.isReady = true; - - // If a normal DOM Ready event fired, decrement, and wait if need be - if ( wait !== true && --jQuery.readyWait > 0 ) { - return; - } - - // If there are functions bound, to execute - readyList.resolveWith( document, [ jQuery ] ); - } -} ); - -jQuery.ready.then = readyList.then; - -// The ready event handler and self cleanup method -function completed() { - document.removeEventListener( "DOMContentLoaded", completed ); - window.removeEventListener( "load", completed ); - jQuery.ready(); -} - -// Catch cases where $(document).ready() is called -// after the browser event has already occurred. -// Support: IE <=9 - 10 only -// Older IE sometimes signals "interactive" too soon -if ( document.readyState === "complete" || - ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { - - // Handle it asynchronously to allow scripts the opportunity to delay ready - window.setTimeout( jQuery.ready ); - -} else { - - // Use the handy event callback - document.addEventListener( "DOMContentLoaded", completed ); - - // A fallback to window.onload, that will always work - window.addEventListener( "load", completed ); -} - - - - -// Multifunctional method to get and set values of a collection -// The value/s can optionally be executed if it's a function -var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { - var i = 0, - len = elems.length, - bulk = key == null; - - // Sets many values - if ( toType( key ) === "object" ) { - chainable = true; - for ( i in key ) { - access( elems, fn, i, key[ i ], true, emptyGet, raw ); - } - - // Sets one value - } else if ( value !== undefined ) { - chainable = true; - - if ( !isFunction( value ) ) { - raw = true; - } - - if ( bulk ) { - - // Bulk operations run against the entire set - if ( raw ) { - fn.call( elems, value ); - fn = null; - - // ...except when executing function values - } else { - bulk = fn; - fn = function( elem, _key, value ) { - return bulk.call( jQuery( elem ), value ); - }; - } - } - - if ( fn ) { - for ( ; i < len; i++ ) { - fn( - elems[ i ], key, raw ? - value : - value.call( elems[ i ], i, fn( elems[ i ], key ) ) - ); - } - } - } - - if ( chainable ) { - return elems; - } - - // Gets - if ( bulk ) { - return fn.call( elems ); - } - - return len ? fn( elems[ 0 ], key ) : emptyGet; -}; - - -// Matches dashed string for camelizing -var rmsPrefix = /^-ms-/, - rdashAlpha = /-([a-z])/g; - -// Used by camelCase as callback to replace() -function fcamelCase( _all, letter ) { - return letter.toUpperCase(); -} - -// Convert dashed to camelCase; used by the css and data modules -// Support: IE <=9 - 11, Edge 12 - 15 -// Microsoft forgot to hump their vendor prefix (#9572) -function camelCase( string ) { - return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); -} -var acceptData = function( owner ) { - - // Accepts only: - // - Node - // - Node.ELEMENT_NODE - // - Node.DOCUMENT_NODE - // - Object - // - Any - return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); -}; - - - - -function Data() { - this.expando = jQuery.expando + Data.uid++; -} - -Data.uid = 1; - -Data.prototype = { - - cache: function( owner ) { - - // Check if the owner object already has a cache - var value = owner[ this.expando ]; - - // If not, create one - if ( !value ) { - value = {}; - - // We can accept data for non-element nodes in modern browsers, - // but we should not, see #8335. - // Always return an empty object. - if ( acceptData( owner ) ) { - - // If it is a node unlikely to be stringify-ed or looped over - // use plain assignment - if ( owner.nodeType ) { - owner[ this.expando ] = value; - - // Otherwise secure it in a non-enumerable property - // configurable must be true to allow the property to be - // deleted when data is removed - } else { - Object.defineProperty( owner, this.expando, { - value: value, - configurable: true - } ); - } - } - } - - return value; - }, - set: function( owner, data, value ) { - var prop, - cache = this.cache( owner ); - - // Handle: [ owner, key, value ] args - // Always use camelCase key (gh-2257) - if ( typeof data === "string" ) { - cache[ camelCase( data ) ] = value; - - // Handle: [ owner, { properties } ] args - } else { - - // Copy the properties one-by-one to the cache object - for ( prop in data ) { - cache[ camelCase( prop ) ] = data[ prop ]; - } - } - return cache; - }, - get: function( owner, key ) { - return key === undefined ? - this.cache( owner ) : - - // Always use camelCase key (gh-2257) - owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; - }, - access: function( owner, key, value ) { - - // In cases where either: - // - // 1. No key was specified - // 2. A string key was specified, but no value provided - // - // Take the "read" path and allow the get method to determine - // which value to return, respectively either: - // - // 1. The entire cache object - // 2. The data stored at the key - // - if ( key === undefined || - ( ( key && typeof key === "string" ) && value === undefined ) ) { - - return this.get( owner, key ); - } - - // When the key is not a string, or both a key and value - // are specified, set or extend (existing objects) with either: - // - // 1. An object of properties - // 2. A key and value - // - this.set( owner, key, value ); - - // Since the "set" path can have two possible entry points - // return the expected data based on which path was taken[*] - return value !== undefined ? value : key; - }, - remove: function( owner, key ) { - var i, - cache = owner[ this.expando ]; - - if ( cache === undefined ) { - return; - } - - if ( key !== undefined ) { - - // Support array or space separated string of keys - if ( Array.isArray( key ) ) { - - // If key is an array of keys... - // We always set camelCase keys, so remove that. - key = key.map( camelCase ); - } else { - key = camelCase( key ); - - // If a key with the spaces exists, use it. - // Otherwise, create an array by matching non-whitespace - key = key in cache ? - [ key ] : - ( key.match( rnothtmlwhite ) || [] ); - } - - i = key.length; - - while ( i-- ) { - delete cache[ key[ i ] ]; - } - } - - // Remove the expando if there's no more data - if ( key === undefined || jQuery.isEmptyObject( cache ) ) { - - // Support: Chrome <=35 - 45 - // Webkit & Blink performance suffers when deleting properties - // from DOM nodes, so set to undefined instead - // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) - if ( owner.nodeType ) { - owner[ this.expando ] = undefined; - } else { - delete owner[ this.expando ]; - } - } - }, - hasData: function( owner ) { - var cache = owner[ this.expando ]; - return cache !== undefined && !jQuery.isEmptyObject( cache ); - } -}; -var dataPriv = new Data(); - -var dataUser = new Data(); - - - -// Implementation Summary -// -// 1. Enforce API surface and semantic compatibility with 1.9.x branch -// 2. Improve the module's maintainability by reducing the storage -// paths to a single mechanism. -// 3. Use the same single mechanism to support "private" and "user" data. -// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) -// 5. Avoid exposing implementation details on user objects (eg. expando properties) -// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 - -var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, - rmultiDash = /[A-Z]/g; - -function getData( data ) { - if ( data === "true" ) { - return true; - } - - if ( data === "false" ) { - return false; - } - - if ( data === "null" ) { - return null; - } - - // Only convert to a number if it doesn't change the string - if ( data === +data + "" ) { - return +data; - } - - if ( rbrace.test( data ) ) { - return JSON.parse( data ); - } - - return data; -} - -function dataAttr( elem, key, data ) { - var name; - - // If nothing was found internally, try to fetch any - // data from the HTML5 data-* attribute - if ( data === undefined && elem.nodeType === 1 ) { - name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); - data = elem.getAttribute( name ); - - if ( typeof data === "string" ) { - try { - data = getData( data ); - } catch ( e ) {} - - // Make sure we set the data so it isn't changed later - dataUser.set( elem, key, data ); - } else { - data = undefined; - } - } - return data; -} - -jQuery.extend( { - hasData: function( elem ) { - return dataUser.hasData( elem ) || dataPriv.hasData( elem ); - }, - - data: function( elem, name, data ) { - return dataUser.access( elem, name, data ); - }, - - removeData: function( elem, name ) { - dataUser.remove( elem, name ); - }, - - // TODO: Now that all calls to _data and _removeData have been replaced - // with direct calls to dataPriv methods, these can be deprecated. - _data: function( elem, name, data ) { - return dataPriv.access( elem, name, data ); - }, - - _removeData: function( elem, name ) { - dataPriv.remove( elem, name ); - } -} ); - -jQuery.fn.extend( { - data: function( key, value ) { - var i, name, data, - elem = this[ 0 ], - attrs = elem && elem.attributes; - - // Gets all values - if ( key === undefined ) { - if ( this.length ) { - data = dataUser.get( elem ); - - if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { - i = attrs.length; - while ( i-- ) { - - // Support: IE 11 only - // The attrs elements can be null (#14894) - if ( attrs[ i ] ) { - name = attrs[ i ].name; - if ( name.indexOf( "data-" ) === 0 ) { - name = camelCase( name.slice( 5 ) ); - dataAttr( elem, name, data[ name ] ); - } - } - } - dataPriv.set( elem, "hasDataAttrs", true ); - } - } - - return data; - } - - // Sets multiple values - if ( typeof key === "object" ) { - return this.each( function() { - dataUser.set( this, key ); - } ); - } - - return access( this, function( value ) { - var data; - - // The calling jQuery object (element matches) is not empty - // (and therefore has an element appears at this[ 0 ]) and the - // `value` parameter was not undefined. An empty jQuery object - // will result in `undefined` for elem = this[ 0 ] which will - // throw an exception if an attempt to read a data cache is made. - if ( elem && value === undefined ) { - - // Attempt to get data from the cache - // The key will always be camelCased in Data - data = dataUser.get( elem, key ); - if ( data !== undefined ) { - return data; - } - - // Attempt to "discover" the data in - // HTML5 custom data-* attrs - data = dataAttr( elem, key ); - if ( data !== undefined ) { - return data; - } - - // We tried really hard, but the data doesn't exist. - return; - } - - // Set the data... - this.each( function() { - - // We always store the camelCased key - dataUser.set( this, key, value ); - } ); - }, null, value, arguments.length > 1, null, true ); - }, - - removeData: function( key ) { - return this.each( function() { - dataUser.remove( this, key ); - } ); - } -} ); - - -jQuery.extend( { - queue: function( elem, type, data ) { - var queue; - - if ( elem ) { - type = ( type || "fx" ) + "queue"; - queue = dataPriv.get( elem, type ); - - // Speed up dequeue by getting out quickly if this is just a lookup - if ( data ) { - if ( !queue || Array.isArray( data ) ) { - queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); - } else { - queue.push( data ); - } - } - return queue || []; - } - }, - - dequeue: function( elem, type ) { - type = type || "fx"; - - var queue = jQuery.queue( elem, type ), - startLength = queue.length, - fn = queue.shift(), - hooks = jQuery._queueHooks( elem, type ), - next = function() { - jQuery.dequeue( elem, type ); - }; - - // If the fx queue is dequeued, always remove the progress sentinel - if ( fn === "inprogress" ) { - fn = queue.shift(); - startLength--; - } - - if ( fn ) { - - // Add a progress sentinel to prevent the fx queue from being - // automatically dequeued - if ( type === "fx" ) { - queue.unshift( "inprogress" ); - } - - // Clear up the last queue stop function - delete hooks.stop; - fn.call( elem, next, hooks ); - } - - if ( !startLength && hooks ) { - hooks.empty.fire(); - } - }, - - // Not public - generate a queueHooks object, or return the current one - _queueHooks: function( elem, type ) { - var key = type + "queueHooks"; - return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { - empty: jQuery.Callbacks( "once memory" ).add( function() { - dataPriv.remove( elem, [ type + "queue", key ] ); - } ) - } ); - } -} ); - -jQuery.fn.extend( { - queue: function( type, data ) { - var setter = 2; - - if ( typeof type !== "string" ) { - data = type; - type = "fx"; - setter--; - } - - if ( arguments.length < setter ) { - return jQuery.queue( this[ 0 ], type ); - } - - return data === undefined ? - this : - this.each( function() { - var queue = jQuery.queue( this, type, data ); - - // Ensure a hooks for this queue - jQuery._queueHooks( this, type ); - - if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { - jQuery.dequeue( this, type ); - } - } ); - }, - dequeue: function( type ) { - return this.each( function() { - jQuery.dequeue( this, type ); - } ); - }, - clearQueue: function( type ) { - return this.queue( type || "fx", [] ); - }, - - // Get a promise resolved when queues of a certain type - // are emptied (fx is the type by default) - promise: function( type, obj ) { - var tmp, - count = 1, - defer = jQuery.Deferred(), - elements = this, - i = this.length, - resolve = function() { - if ( !( --count ) ) { - defer.resolveWith( elements, [ elements ] ); - } - }; - - if ( typeof type !== "string" ) { - obj = type; - type = undefined; - } - type = type || "fx"; - - while ( i-- ) { - tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); - if ( tmp && tmp.empty ) { - count++; - tmp.empty.add( resolve ); - } - } - resolve(); - return defer.promise( obj ); - } -} ); -var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; - -var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); - - -var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; - -var documentElement = document.documentElement; - - - - var isAttached = function( elem ) { - return jQuery.contains( elem.ownerDocument, elem ); - }, - composed = { composed: true }; - - // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only - // Check attachment across shadow DOM boundaries when possible (gh-3504) - // Support: iOS 10.0-10.2 only - // Early iOS 10 versions support `attachShadow` but not `getRootNode`, - // leading to errors. We need to check for `getRootNode`. - if ( documentElement.getRootNode ) { - isAttached = function( elem ) { - return jQuery.contains( elem.ownerDocument, elem ) || - elem.getRootNode( composed ) === elem.ownerDocument; - }; - } -var isHiddenWithinTree = function( elem, el ) { - - // isHiddenWithinTree might be called from jQuery#filter function; - // in that case, element will be second argument - elem = el || elem; - - // Inline style trumps all - return elem.style.display === "none" || - elem.style.display === "" && - - // Otherwise, check computed style - // Support: Firefox <=43 - 45 - // Disconnected elements can have computed display: none, so first confirm that elem is - // in the document. - isAttached( elem ) && - - jQuery.css( elem, "display" ) === "none"; - }; - - - -function adjustCSS( elem, prop, valueParts, tween ) { - var adjusted, scale, - maxIterations = 20, - currentValue = tween ? - function() { - return tween.cur(); - } : - function() { - return jQuery.css( elem, prop, "" ); - }, - initial = currentValue(), - unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), - - // Starting value computation is required for potential unit mismatches - initialInUnit = elem.nodeType && - ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && - rcssNum.exec( jQuery.css( elem, prop ) ); - - if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { - - // Support: Firefox <=54 - // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) - initial = initial / 2; - - // Trust units reported by jQuery.css - unit = unit || initialInUnit[ 3 ]; - - // Iteratively approximate from a nonzero starting point - initialInUnit = +initial || 1; - - while ( maxIterations-- ) { - - // Evaluate and update our best guess (doubling guesses that zero out). - // Finish if the scale equals or crosses 1 (making the old*new product non-positive). - jQuery.style( elem, prop, initialInUnit + unit ); - if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { - maxIterations = 0; - } - initialInUnit = initialInUnit / scale; - - } - - initialInUnit = initialInUnit * 2; - jQuery.style( elem, prop, initialInUnit + unit ); - - // Make sure we update the tween properties later on - valueParts = valueParts || []; - } - - if ( valueParts ) { - initialInUnit = +initialInUnit || +initial || 0; - - // Apply relative offset (+=/-=) if specified - adjusted = valueParts[ 1 ] ? - initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : - +valueParts[ 2 ]; - if ( tween ) { - tween.unit = unit; - tween.start = initialInUnit; - tween.end = adjusted; - } - } - return adjusted; -} - - -var defaultDisplayMap = {}; - -function getDefaultDisplay( elem ) { - var temp, - doc = elem.ownerDocument, - nodeName = elem.nodeName, - display = defaultDisplayMap[ nodeName ]; - - if ( display ) { - return display; - } - - temp = doc.body.appendChild( doc.createElement( nodeName ) ); - display = jQuery.css( temp, "display" ); - - temp.parentNode.removeChild( temp ); - - if ( display === "none" ) { - display = "block"; - } - defaultDisplayMap[ nodeName ] = display; - - return display; -} - -function showHide( elements, show ) { - var display, elem, - values = [], - index = 0, - length = elements.length; - - // Determine new display value for elements that need to change - for ( ; index < length; index++ ) { - elem = elements[ index ]; - if ( !elem.style ) { - continue; - } - - display = elem.style.display; - if ( show ) { - - // Since we force visibility upon cascade-hidden elements, an immediate (and slow) - // check is required in this first loop unless we have a nonempty display value (either - // inline or about-to-be-restored) - if ( display === "none" ) { - values[ index ] = dataPriv.get( elem, "display" ) || null; - if ( !values[ index ] ) { - elem.style.display = ""; - } - } - if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { - values[ index ] = getDefaultDisplay( elem ); - } - } else { - if ( display !== "none" ) { - values[ index ] = "none"; - - // Remember what we're overwriting - dataPriv.set( elem, "display", display ); - } - } - } - - // Set the display of the elements in a second loop to avoid constant reflow - for ( index = 0; index < length; index++ ) { - if ( values[ index ] != null ) { - elements[ index ].style.display = values[ index ]; - } - } - - return elements; -} - -jQuery.fn.extend( { - show: function() { - return showHide( this, true ); - }, - hide: function() { - return showHide( this ); - }, - toggle: function( state ) { - if ( typeof state === "boolean" ) { - return state ? this.show() : this.hide(); - } - - return this.each( function() { - if ( isHiddenWithinTree( this ) ) { - jQuery( this ).show(); - } else { - jQuery( this ).hide(); - } - } ); - } -} ); -var rcheckableType = ( /^(?:checkbox|radio)$/i ); - -var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); - -var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); - - - -( function() { - var fragment = document.createDocumentFragment(), - div = fragment.appendChild( document.createElement( "div" ) ), - input = document.createElement( "input" ); - - // Support: Android 4.0 - 4.3 only - // Check state lost if the name is set (#11217) - // Support: Windows Web Apps (WWA) - // `name` and `type` must use .setAttribute for WWA (#14901) - input.setAttribute( "type", "radio" ); - input.setAttribute( "checked", "checked" ); - input.setAttribute( "name", "t" ); - - div.appendChild( input ); - - // Support: Android <=4.1 only - // Older WebKit doesn't clone checked state correctly in fragments - support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; - - // Support: IE <=11 only - // Make sure textarea (and checkbox) defaultValue is properly cloned - div.innerHTML = ""; - support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; - - // Support: IE <=9 only - // IE <=9 replaces "; - support.option = !!div.lastChild; -} )(); - - -// We have to close these tags to support XHTML (#13200) -var wrapMap = { - - // XHTML parsers do not magically insert elements in the - // same way that tag soup parsers do. So we cannot shorten - // this by omitting or other required elements. - thead: [ 1, "", "
" ], - col: [ 2, "", "
" ], - tr: [ 2, "", "
" ], - td: [ 3, "", "
" ], - - _default: [ 0, "", "" ] -}; - -wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; -wrapMap.th = wrapMap.td; - -// Support: IE <=9 only -if ( !support.option ) { - wrapMap.optgroup = wrapMap.option = [ 1, "" ]; -} - - -function getAll( context, tag ) { - - // Support: IE <=9 - 11 only - // Use typeof to avoid zero-argument method invocation on host objects (#15151) - var ret; - - if ( typeof context.getElementsByTagName !== "undefined" ) { - ret = context.getElementsByTagName( tag || "*" ); - - } else if ( typeof context.querySelectorAll !== "undefined" ) { - ret = context.querySelectorAll( tag || "*" ); - - } else { - ret = []; - } - - if ( tag === undefined || tag && nodeName( context, tag ) ) { - return jQuery.merge( [ context ], ret ); - } - - return ret; -} - - -// Mark scripts as having already been evaluated -function setGlobalEval( elems, refElements ) { - var i = 0, - l = elems.length; - - for ( ; i < l; i++ ) { - dataPriv.set( - elems[ i ], - "globalEval", - !refElements || dataPriv.get( refElements[ i ], "globalEval" ) - ); - } -} - - -var rhtml = /<|&#?\w+;/; - -function buildFragment( elems, context, scripts, selection, ignored ) { - var elem, tmp, tag, wrap, attached, j, - fragment = context.createDocumentFragment(), - nodes = [], - i = 0, - l = elems.length; - - for ( ; i < l; i++ ) { - elem = elems[ i ]; - - if ( elem || elem === 0 ) { - - // Add nodes directly - if ( toType( elem ) === "object" ) { - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); - - // Convert non-html into a text node - } else if ( !rhtml.test( elem ) ) { - nodes.push( context.createTextNode( elem ) ); - - // Convert html into DOM nodes - } else { - tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); - - // Deserialize a standard representation - tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); - wrap = wrapMap[ tag ] || wrapMap._default; - tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; - - // Descend through wrappers to the right content - j = wrap[ 0 ]; - while ( j-- ) { - tmp = tmp.lastChild; - } - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - jQuery.merge( nodes, tmp.childNodes ); - - // Remember the top-level container - tmp = fragment.firstChild; - - // Ensure the created nodes are orphaned (#12392) - tmp.textContent = ""; - } - } - } - - // Remove wrapper from fragment - fragment.textContent = ""; - - i = 0; - while ( ( elem = nodes[ i++ ] ) ) { - - // Skip elements already in the context collection (trac-4087) - if ( selection && jQuery.inArray( elem, selection ) > -1 ) { - if ( ignored ) { - ignored.push( elem ); - } - continue; - } - - attached = isAttached( elem ); - - // Append to fragment - tmp = getAll( fragment.appendChild( elem ), "script" ); - - // Preserve script evaluation history - if ( attached ) { - setGlobalEval( tmp ); - } - - // Capture executables - if ( scripts ) { - j = 0; - while ( ( elem = tmp[ j++ ] ) ) { - if ( rscriptType.test( elem.type || "" ) ) { - scripts.push( elem ); - } - } - } - } - - return fragment; -} - - -var - rkeyEvent = /^key/, - rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/, - rtypenamespace = /^([^.]*)(?:\.(.+)|)/; - -function returnTrue() { - return true; -} - -function returnFalse() { - return false; -} - -// Support: IE <=9 - 11+ -// focus() and blur() are asynchronous, except when they are no-op. -// So expect focus to be synchronous when the element is already active, -// and blur to be synchronous when the element is not already active. -// (focus and blur are always synchronous in other supported browsers, -// this just defines when we can count on it). -function expectSync( elem, type ) { - return ( elem === safeActiveElement() ) === ( type === "focus" ); -} - -// Support: IE <=9 only -// Accessing document.activeElement can throw unexpectedly -// https://bugs.jquery.com/ticket/13393 -function safeActiveElement() { - try { - return document.activeElement; - } catch ( err ) { } -} - -function on( elem, types, selector, data, fn, one ) { - var origFn, type; - - // Types can be a map of types/handlers - if ( typeof types === "object" ) { - - // ( types-Object, selector, data ) - if ( typeof selector !== "string" ) { - - // ( types-Object, data ) - data = data || selector; - selector = undefined; - } - for ( type in types ) { - on( elem, type, selector, data, types[ type ], one ); - } - return elem; - } - - if ( data == null && fn == null ) { - - // ( types, fn ) - fn = selector; - data = selector = undefined; - } else if ( fn == null ) { - if ( typeof selector === "string" ) { - - // ( types, selector, fn ) - fn = data; - data = undefined; - } else { - - // ( types, data, fn ) - fn = data; - data = selector; - selector = undefined; - } - } - if ( fn === false ) { - fn = returnFalse; - } else if ( !fn ) { - return elem; - } - - if ( one === 1 ) { - origFn = fn; - fn = function( event ) { - - // Can use an empty set, since event contains the info - jQuery().off( event ); - return origFn.apply( this, arguments ); - }; - - // Use same guid so caller can remove using origFn - fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); - } - return elem.each( function() { - jQuery.event.add( this, types, fn, data, selector ); - } ); -} - -/* - * Helper functions for managing events -- not part of the public interface. - * Props to Dean Edwards' addEvent library for many of the ideas. - */ -jQuery.event = { - - global: {}, - - add: function( elem, types, handler, data, selector ) { - - var handleObjIn, eventHandle, tmp, - events, t, handleObj, - special, handlers, type, namespaces, origType, - elemData = dataPriv.get( elem ); - - // Only attach events to objects that accept data - if ( !acceptData( elem ) ) { - return; - } - - // Caller can pass in an object of custom data in lieu of the handler - if ( handler.handler ) { - handleObjIn = handler; - handler = handleObjIn.handler; - selector = handleObjIn.selector; - } - - // Ensure that invalid selectors throw exceptions at attach time - // Evaluate against documentElement in case elem is a non-element node (e.g., document) - if ( selector ) { - jQuery.find.matchesSelector( documentElement, selector ); - } - - // Make sure that the handler has a unique ID, used to find/remove it later - if ( !handler.guid ) { - handler.guid = jQuery.guid++; - } - - // Init the element's event structure and main handler, if this is the first - if ( !( events = elemData.events ) ) { - events = elemData.events = Object.create( null ); - } - if ( !( eventHandle = elemData.handle ) ) { - eventHandle = elemData.handle = function( e ) { - - // Discard the second event of a jQuery.event.trigger() and - // when an event is called after a page has unloaded - return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? - jQuery.event.dispatch.apply( elem, arguments ) : undefined; - }; - } - - // Handle multiple events separated by a space - types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; - t = types.length; - while ( t-- ) { - tmp = rtypenamespace.exec( types[ t ] ) || []; - type = origType = tmp[ 1 ]; - namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); - - // There *must* be a type, no attaching namespace-only handlers - if ( !type ) { - continue; - } - - // If event changes its type, use the special event handlers for the changed type - special = jQuery.event.special[ type ] || {}; - - // If selector defined, determine special event api type, otherwise given type - type = ( selector ? special.delegateType : special.bindType ) || type; - - // Update special based on newly reset type - special = jQuery.event.special[ type ] || {}; - - // handleObj is passed to all event handlers - handleObj = jQuery.extend( { - type: type, - origType: origType, - data: data, - handler: handler, - guid: handler.guid, - selector: selector, - needsContext: selector && jQuery.expr.match.needsContext.test( selector ), - namespace: namespaces.join( "." ) - }, handleObjIn ); - - // Init the event handler queue if we're the first - if ( !( handlers = events[ type ] ) ) { - handlers = events[ type ] = []; - handlers.delegateCount = 0; - - // Only use addEventListener if the special events handler returns false - if ( !special.setup || - special.setup.call( elem, data, namespaces, eventHandle ) === false ) { - - if ( elem.addEventListener ) { - elem.addEventListener( type, eventHandle ); - } - } - } - - if ( special.add ) { - special.add.call( elem, handleObj ); - - if ( !handleObj.handler.guid ) { - handleObj.handler.guid = handler.guid; - } - } - - // Add to the element's handler list, delegates in front - if ( selector ) { - handlers.splice( handlers.delegateCount++, 0, handleObj ); - } else { - handlers.push( handleObj ); - } - - // Keep track of which events have ever been used, for event optimization - jQuery.event.global[ type ] = true; - } - - }, - - // Detach an event or set of events from an element - remove: function( elem, types, handler, selector, mappedTypes ) { - - var j, origCount, tmp, - events, t, handleObj, - special, handlers, type, namespaces, origType, - elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); - - if ( !elemData || !( events = elemData.events ) ) { - return; - } - - // Once for each type.namespace in types; type may be omitted - types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; - t = types.length; - while ( t-- ) { - tmp = rtypenamespace.exec( types[ t ] ) || []; - type = origType = tmp[ 1 ]; - namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); - - // Unbind all events (on this namespace, if provided) for the element - if ( !type ) { - for ( type in events ) { - jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); - } - continue; - } - - special = jQuery.event.special[ type ] || {}; - type = ( selector ? special.delegateType : special.bindType ) || type; - handlers = events[ type ] || []; - tmp = tmp[ 2 ] && - new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); - - // Remove matching events - origCount = j = handlers.length; - while ( j-- ) { - handleObj = handlers[ j ]; - - if ( ( mappedTypes || origType === handleObj.origType ) && - ( !handler || handler.guid === handleObj.guid ) && - ( !tmp || tmp.test( handleObj.namespace ) ) && - ( !selector || selector === handleObj.selector || - selector === "**" && handleObj.selector ) ) { - handlers.splice( j, 1 ); - - if ( handleObj.selector ) { - handlers.delegateCount--; - } - if ( special.remove ) { - special.remove.call( elem, handleObj ); - } - } - } - - // Remove generic event handler if we removed something and no more handlers exist - // (avoids potential for endless recursion during removal of special event handlers) - if ( origCount && !handlers.length ) { - if ( !special.teardown || - special.teardown.call( elem, namespaces, elemData.handle ) === false ) { - - jQuery.removeEvent( elem, type, elemData.handle ); - } - - delete events[ type ]; - } - } - - // Remove data and the expando if it's no longer used - if ( jQuery.isEmptyObject( events ) ) { - dataPriv.remove( elem, "handle events" ); - } - }, - - dispatch: function( nativeEvent ) { - - var i, j, ret, matched, handleObj, handlerQueue, - args = new Array( arguments.length ), - - // Make a writable jQuery.Event from the native event object - event = jQuery.event.fix( nativeEvent ), - - handlers = ( - dataPriv.get( this, "events" ) || Object.create( null ) - )[ event.type ] || [], - special = jQuery.event.special[ event.type ] || {}; - - // Use the fix-ed jQuery.Event rather than the (read-only) native event - args[ 0 ] = event; - - for ( i = 1; i < arguments.length; i++ ) { - args[ i ] = arguments[ i ]; - } - - event.delegateTarget = this; - - // Call the preDispatch hook for the mapped type, and let it bail if desired - if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { - return; - } - - // Determine handlers - handlerQueue = jQuery.event.handlers.call( this, event, handlers ); - - // Run delegates first; they may want to stop propagation beneath us - i = 0; - while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { - event.currentTarget = matched.elem; - - j = 0; - while ( ( handleObj = matched.handlers[ j++ ] ) && - !event.isImmediatePropagationStopped() ) { - - // If the event is namespaced, then each handler is only invoked if it is - // specially universal or its namespaces are a superset of the event's. - if ( !event.rnamespace || handleObj.namespace === false || - event.rnamespace.test( handleObj.namespace ) ) { - - event.handleObj = handleObj; - event.data = handleObj.data; - - ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || - handleObj.handler ).apply( matched.elem, args ); - - if ( ret !== undefined ) { - if ( ( event.result = ret ) === false ) { - event.preventDefault(); - event.stopPropagation(); - } - } - } - } - } - - // Call the postDispatch hook for the mapped type - if ( special.postDispatch ) { - special.postDispatch.call( this, event ); - } - - return event.result; - }, - - handlers: function( event, handlers ) { - var i, handleObj, sel, matchedHandlers, matchedSelectors, - handlerQueue = [], - delegateCount = handlers.delegateCount, - cur = event.target; - - // Find delegate handlers - if ( delegateCount && - - // Support: IE <=9 - // Black-hole SVG instance trees (trac-13180) - cur.nodeType && - - // Support: Firefox <=42 - // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) - // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click - // Support: IE 11 only - // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) - !( event.type === "click" && event.button >= 1 ) ) { - - for ( ; cur !== this; cur = cur.parentNode || this ) { - - // Don't check non-elements (#13208) - // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) - if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { - matchedHandlers = []; - matchedSelectors = {}; - for ( i = 0; i < delegateCount; i++ ) { - handleObj = handlers[ i ]; - - // Don't conflict with Object.prototype properties (#13203) - sel = handleObj.selector + " "; - - if ( matchedSelectors[ sel ] === undefined ) { - matchedSelectors[ sel ] = handleObj.needsContext ? - jQuery( sel, this ).index( cur ) > -1 : - jQuery.find( sel, this, null, [ cur ] ).length; - } - if ( matchedSelectors[ sel ] ) { - matchedHandlers.push( handleObj ); - } - } - if ( matchedHandlers.length ) { - handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); - } - } - } - } - - // Add the remaining (directly-bound) handlers - cur = this; - if ( delegateCount < handlers.length ) { - handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); - } - - return handlerQueue; - }, - - addProp: function( name, hook ) { - Object.defineProperty( jQuery.Event.prototype, name, { - enumerable: true, - configurable: true, - - get: isFunction( hook ) ? - function() { - if ( this.originalEvent ) { - return hook( this.originalEvent ); - } - } : - function() { - if ( this.originalEvent ) { - return this.originalEvent[ name ]; - } - }, - - set: function( value ) { - Object.defineProperty( this, name, { - enumerable: true, - configurable: true, - writable: true, - value: value - } ); - } - } ); - }, - - fix: function( originalEvent ) { - return originalEvent[ jQuery.expando ] ? - originalEvent : - new jQuery.Event( originalEvent ); - }, - - special: { - load: { - - // Prevent triggered image.load events from bubbling to window.load - noBubble: true - }, - click: { - - // Utilize native event to ensure correct state for checkable inputs - setup: function( data ) { - - // For mutual compressibility with _default, replace `this` access with a local var. - // `|| data` is dead code meant only to preserve the variable through minification. - var el = this || data; - - // Claim the first handler - if ( rcheckableType.test( el.type ) && - el.click && nodeName( el, "input" ) ) { - - // dataPriv.set( el, "click", ... ) - leverageNative( el, "click", returnTrue ); - } - - // Return false to allow normal processing in the caller - return false; - }, - trigger: function( data ) { - - // For mutual compressibility with _default, replace `this` access with a local var. - // `|| data` is dead code meant only to preserve the variable through minification. - var el = this || data; - - // Force setup before triggering a click - if ( rcheckableType.test( el.type ) && - el.click && nodeName( el, "input" ) ) { - - leverageNative( el, "click" ); - } - - // Return non-false to allow normal event-path propagation - return true; - }, - - // For cross-browser consistency, suppress native .click() on links - // Also prevent it if we're currently inside a leveraged native-event stack - _default: function( event ) { - var target = event.target; - return rcheckableType.test( target.type ) && - target.click && nodeName( target, "input" ) && - dataPriv.get( target, "click" ) || - nodeName( target, "a" ); - } - }, - - beforeunload: { - postDispatch: function( event ) { - - // Support: Firefox 20+ - // Firefox doesn't alert if the returnValue field is not set. - if ( event.result !== undefined && event.originalEvent ) { - event.originalEvent.returnValue = event.result; - } - } - } - } -}; - -// Ensure the presence of an event listener that handles manually-triggered -// synthetic events by interrupting progress until reinvoked in response to -// *native* events that it fires directly, ensuring that state changes have -// already occurred before other listeners are invoked. -function leverageNative( el, type, expectSync ) { - - // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add - if ( !expectSync ) { - if ( dataPriv.get( el, type ) === undefined ) { - jQuery.event.add( el, type, returnTrue ); - } - return; - } - - // Register the controller as a special universal handler for all event namespaces - dataPriv.set( el, type, false ); - jQuery.event.add( el, type, { - namespace: false, - handler: function( event ) { - var notAsync, result, - saved = dataPriv.get( this, type ); - - if ( ( event.isTrigger & 1 ) && this[ type ] ) { - - // Interrupt processing of the outer synthetic .trigger()ed event - // Saved data should be false in such cases, but might be a leftover capture object - // from an async native handler (gh-4350) - if ( !saved.length ) { - - // Store arguments for use when handling the inner native event - // There will always be at least one argument (an event object), so this array - // will not be confused with a leftover capture object. - saved = slice.call( arguments ); - dataPriv.set( this, type, saved ); - - // Trigger the native event and capture its result - // Support: IE <=9 - 11+ - // focus() and blur() are asynchronous - notAsync = expectSync( this, type ); - this[ type ](); - result = dataPriv.get( this, type ); - if ( saved !== result || notAsync ) { - dataPriv.set( this, type, false ); - } else { - result = {}; - } - if ( saved !== result ) { - - // Cancel the outer synthetic event - event.stopImmediatePropagation(); - event.preventDefault(); - return result.value; - } - - // If this is an inner synthetic event for an event with a bubbling surrogate - // (focus or blur), assume that the surrogate already propagated from triggering the - // native event and prevent that from happening again here. - // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the - // bubbling surrogate propagates *after* the non-bubbling base), but that seems - // less bad than duplication. - } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { - event.stopPropagation(); - } - - // If this is a native event triggered above, everything is now in order - // Fire an inner synthetic event with the original arguments - } else if ( saved.length ) { - - // ...and capture the result - dataPriv.set( this, type, { - value: jQuery.event.trigger( - - // Support: IE <=9 - 11+ - // Extend with the prototype to reset the above stopImmediatePropagation() - jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), - saved.slice( 1 ), - this - ) - } ); - - // Abort handling of the native event - event.stopImmediatePropagation(); - } - } - } ); -} - -jQuery.removeEvent = function( elem, type, handle ) { - - // This "if" is needed for plain objects - if ( elem.removeEventListener ) { - elem.removeEventListener( type, handle ); - } -}; - -jQuery.Event = function( src, props ) { - - // Allow instantiation without the 'new' keyword - if ( !( this instanceof jQuery.Event ) ) { - return new jQuery.Event( src, props ); - } - - // Event object - if ( src && src.type ) { - this.originalEvent = src; - this.type = src.type; - - // Events bubbling up the document may have been marked as prevented - // by a handler lower down the tree; reflect the correct value. - this.isDefaultPrevented = src.defaultPrevented || - src.defaultPrevented === undefined && - - // Support: Android <=2.3 only - src.returnValue === false ? - returnTrue : - returnFalse; - - // Create target properties - // Support: Safari <=6 - 7 only - // Target should not be a text node (#504, #13143) - this.target = ( src.target && src.target.nodeType === 3 ) ? - src.target.parentNode : - src.target; - - this.currentTarget = src.currentTarget; - this.relatedTarget = src.relatedTarget; - - // Event type - } else { - this.type = src; - } - - // Put explicitly provided properties onto the event object - if ( props ) { - jQuery.extend( this, props ); - } - - // Create a timestamp if incoming event doesn't have one - this.timeStamp = src && src.timeStamp || Date.now(); - - // Mark it as fixed - this[ jQuery.expando ] = true; -}; - -// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding -// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html -jQuery.Event.prototype = { - constructor: jQuery.Event, - isDefaultPrevented: returnFalse, - isPropagationStopped: returnFalse, - isImmediatePropagationStopped: returnFalse, - isSimulated: false, - - preventDefault: function() { - var e = this.originalEvent; - - this.isDefaultPrevented = returnTrue; - - if ( e && !this.isSimulated ) { - e.preventDefault(); - } - }, - stopPropagation: function() { - var e = this.originalEvent; - - this.isPropagationStopped = returnTrue; - - if ( e && !this.isSimulated ) { - e.stopPropagation(); - } - }, - stopImmediatePropagation: function() { - var e = this.originalEvent; - - this.isImmediatePropagationStopped = returnTrue; - - if ( e && !this.isSimulated ) { - e.stopImmediatePropagation(); - } - - this.stopPropagation(); - } -}; - -// Includes all common event props including KeyEvent and MouseEvent specific props -jQuery.each( { - altKey: true, - bubbles: true, - cancelable: true, - changedTouches: true, - ctrlKey: true, - detail: true, - eventPhase: true, - metaKey: true, - pageX: true, - pageY: true, - shiftKey: true, - view: true, - "char": true, - code: true, - charCode: true, - key: true, - keyCode: true, - button: true, - buttons: true, - clientX: true, - clientY: true, - offsetX: true, - offsetY: true, - pointerId: true, - pointerType: true, - screenX: true, - screenY: true, - targetTouches: true, - toElement: true, - touches: true, - - which: function( event ) { - var button = event.button; - - // Add which for key events - if ( event.which == null && rkeyEvent.test( event.type ) ) { - return event.charCode != null ? event.charCode : event.keyCode; - } - - // Add which for click: 1 === left; 2 === middle; 3 === right - if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) { - if ( button & 1 ) { - return 1; - } - - if ( button & 2 ) { - return 3; - } - - if ( button & 4 ) { - return 2; - } - - return 0; - } - - return event.which; - } -}, jQuery.event.addProp ); - -jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { - jQuery.event.special[ type ] = { - - // Utilize native event if possible so blur/focus sequence is correct - setup: function() { - - // Claim the first handler - // dataPriv.set( this, "focus", ... ) - // dataPriv.set( this, "blur", ... ) - leverageNative( this, type, expectSync ); - - // Return false to allow normal processing in the caller - return false; - }, - trigger: function() { - - // Force setup before trigger - leverageNative( this, type ); - - // Return non-false to allow normal event-path propagation - return true; - }, - - delegateType: delegateType - }; -} ); - -// Create mouseenter/leave events using mouseover/out and event-time checks -// so that event delegation works in jQuery. -// Do the same for pointerenter/pointerleave and pointerover/pointerout -// -// Support: Safari 7 only -// Safari sends mouseenter too often; see: -// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 -// for the description of the bug (it existed in older Chrome versions as well). -jQuery.each( { - mouseenter: "mouseover", - mouseleave: "mouseout", - pointerenter: "pointerover", - pointerleave: "pointerout" -}, function( orig, fix ) { - jQuery.event.special[ orig ] = { - delegateType: fix, - bindType: fix, - - handle: function( event ) { - var ret, - target = this, - related = event.relatedTarget, - handleObj = event.handleObj; - - // For mouseenter/leave call the handler if related is outside the target. - // NB: No relatedTarget if the mouse left/entered the browser window - if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { - event.type = handleObj.origType; - ret = handleObj.handler.apply( this, arguments ); - event.type = fix; - } - return ret; - } - }; -} ); - -jQuery.fn.extend( { - - on: function( types, selector, data, fn ) { - return on( this, types, selector, data, fn ); - }, - one: function( types, selector, data, fn ) { - return on( this, types, selector, data, fn, 1 ); - }, - off: function( types, selector, fn ) { - var handleObj, type; - if ( types && types.preventDefault && types.handleObj ) { - - // ( event ) dispatched jQuery.Event - handleObj = types.handleObj; - jQuery( types.delegateTarget ).off( - handleObj.namespace ? - handleObj.origType + "." + handleObj.namespace : - handleObj.origType, - handleObj.selector, - handleObj.handler - ); - return this; - } - if ( typeof types === "object" ) { - - // ( types-object [, selector] ) - for ( type in types ) { - this.off( type, selector, types[ type ] ); - } - return this; - } - if ( selector === false || typeof selector === "function" ) { - - // ( types [, fn] ) - fn = selector; - selector = undefined; - } - if ( fn === false ) { - fn = returnFalse; - } - return this.each( function() { - jQuery.event.remove( this, types, fn, selector ); - } ); - } -} ); - - -var - - // Support: IE <=10 - 11, Edge 12 - 13 only - // In IE/Edge using regex groups here causes severe slowdowns. - // See https://connect.microsoft.com/IE/feedback/details/1736512/ - rnoInnerhtml = /\s*$/g; - -// Prefer a tbody over its parent table for containing new rows -function manipulationTarget( elem, content ) { - if ( nodeName( elem, "table" ) && - nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { - - return jQuery( elem ).children( "tbody" )[ 0 ] || elem; - } - - return elem; -} - -// Replace/restore the type attribute of script elements for safe DOM manipulation -function disableScript( elem ) { - elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; - return elem; -} -function restoreScript( elem ) { - if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { - elem.type = elem.type.slice( 5 ); - } else { - elem.removeAttribute( "type" ); - } - - return elem; -} - -function cloneCopyEvent( src, dest ) { - var i, l, type, pdataOld, udataOld, udataCur, events; - - if ( dest.nodeType !== 1 ) { - return; - } - - // 1. Copy private data: events, handlers, etc. - if ( dataPriv.hasData( src ) ) { - pdataOld = dataPriv.get( src ); - events = pdataOld.events; - - if ( events ) { - dataPriv.remove( dest, "handle events" ); - - for ( type in events ) { - for ( i = 0, l = events[ type ].length; i < l; i++ ) { - jQuery.event.add( dest, type, events[ type ][ i ] ); - } - } - } - } - - // 2. Copy user data - if ( dataUser.hasData( src ) ) { - udataOld = dataUser.access( src ); - udataCur = jQuery.extend( {}, udataOld ); - - dataUser.set( dest, udataCur ); - } -} - -// Fix IE bugs, see support tests -function fixInput( src, dest ) { - var nodeName = dest.nodeName.toLowerCase(); - - // Fails to persist the checked state of a cloned checkbox or radio button. - if ( nodeName === "input" && rcheckableType.test( src.type ) ) { - dest.checked = src.checked; - - // Fails to return the selected option to the default selected state when cloning options - } else if ( nodeName === "input" || nodeName === "textarea" ) { - dest.defaultValue = src.defaultValue; - } -} - -function domManip( collection, args, callback, ignored ) { - - // Flatten any nested arrays - args = flat( args ); - - var fragment, first, scripts, hasScripts, node, doc, - i = 0, - l = collection.length, - iNoClone = l - 1, - value = args[ 0 ], - valueIsFunction = isFunction( value ); - - // We can't cloneNode fragments that contain checked, in WebKit - if ( valueIsFunction || - ( l > 1 && typeof value === "string" && - !support.checkClone && rchecked.test( value ) ) ) { - return collection.each( function( index ) { - var self = collection.eq( index ); - if ( valueIsFunction ) { - args[ 0 ] = value.call( this, index, self.html() ); - } - domManip( self, args, callback, ignored ); - } ); - } - - if ( l ) { - fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); - first = fragment.firstChild; - - if ( fragment.childNodes.length === 1 ) { - fragment = first; - } - - // Require either new content or an interest in ignored elements to invoke the callback - if ( first || ignored ) { - scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); - hasScripts = scripts.length; - - // Use the original fragment for the last item - // instead of the first because it can end up - // being emptied incorrectly in certain situations (#8070). - for ( ; i < l; i++ ) { - node = fragment; - - if ( i !== iNoClone ) { - node = jQuery.clone( node, true, true ); - - // Keep references to cloned scripts for later restoration - if ( hasScripts ) { - - // Support: Android <=4.0 only, PhantomJS 1 only - // push.apply(_, arraylike) throws on ancient WebKit - jQuery.merge( scripts, getAll( node, "script" ) ); - } - } - - callback.call( collection[ i ], node, i ); - } - - if ( hasScripts ) { - doc = scripts[ scripts.length - 1 ].ownerDocument; - - // Reenable scripts - jQuery.map( scripts, restoreScript ); - - // Evaluate executable scripts on first document insertion - for ( i = 0; i < hasScripts; i++ ) { - node = scripts[ i ]; - if ( rscriptType.test( node.type || "" ) && - !dataPriv.access( node, "globalEval" ) && - jQuery.contains( doc, node ) ) { - - if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { - - // Optional AJAX dependency, but won't run scripts if not present - if ( jQuery._evalUrl && !node.noModule ) { - jQuery._evalUrl( node.src, { - nonce: node.nonce || node.getAttribute( "nonce" ) - }, doc ); - } - } else { - DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); - } - } - } - } - } - } - - return collection; -} - -function remove( elem, selector, keepData ) { - var node, - nodes = selector ? jQuery.filter( selector, elem ) : elem, - i = 0; - - for ( ; ( node = nodes[ i ] ) != null; i++ ) { - if ( !keepData && node.nodeType === 1 ) { - jQuery.cleanData( getAll( node ) ); - } - - if ( node.parentNode ) { - if ( keepData && isAttached( node ) ) { - setGlobalEval( getAll( node, "script" ) ); - } - node.parentNode.removeChild( node ); - } - } - - return elem; -} - -jQuery.extend( { - htmlPrefilter: function( html ) { - return html; - }, - - clone: function( elem, dataAndEvents, deepDataAndEvents ) { - var i, l, srcElements, destElements, - clone = elem.cloneNode( true ), - inPage = isAttached( elem ); - - // Fix IE cloning issues - if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && - !jQuery.isXMLDoc( elem ) ) { - - // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 - destElements = getAll( clone ); - srcElements = getAll( elem ); - - for ( i = 0, l = srcElements.length; i < l; i++ ) { - fixInput( srcElements[ i ], destElements[ i ] ); - } - } - - // Copy the events from the original to the clone - if ( dataAndEvents ) { - if ( deepDataAndEvents ) { - srcElements = srcElements || getAll( elem ); - destElements = destElements || getAll( clone ); - - for ( i = 0, l = srcElements.length; i < l; i++ ) { - cloneCopyEvent( srcElements[ i ], destElements[ i ] ); - } - } else { - cloneCopyEvent( elem, clone ); - } - } - - // Preserve script evaluation history - destElements = getAll( clone, "script" ); - if ( destElements.length > 0 ) { - setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); - } - - // Return the cloned set - return clone; - }, - - cleanData: function( elems ) { - var data, elem, type, - special = jQuery.event.special, - i = 0; - - for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { - if ( acceptData( elem ) ) { - if ( ( data = elem[ dataPriv.expando ] ) ) { - if ( data.events ) { - for ( type in data.events ) { - if ( special[ type ] ) { - jQuery.event.remove( elem, type ); - - // This is a shortcut to avoid jQuery.event.remove's overhead - } else { - jQuery.removeEvent( elem, type, data.handle ); - } - } - } - - // Support: Chrome <=35 - 45+ - // Assign undefined instead of using delete, see Data#remove - elem[ dataPriv.expando ] = undefined; - } - if ( elem[ dataUser.expando ] ) { - - // Support: Chrome <=35 - 45+ - // Assign undefined instead of using delete, see Data#remove - elem[ dataUser.expando ] = undefined; - } - } - } - } -} ); - -jQuery.fn.extend( { - detach: function( selector ) { - return remove( this, selector, true ); - }, - - remove: function( selector ) { - return remove( this, selector ); - }, - - text: function( value ) { - return access( this, function( value ) { - return value === undefined ? - jQuery.text( this ) : - this.empty().each( function() { - if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { - this.textContent = value; - } - } ); - }, null, value, arguments.length ); - }, - - append: function() { - return domManip( this, arguments, function( elem ) { - if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { - var target = manipulationTarget( this, elem ); - target.appendChild( elem ); - } - } ); - }, - - prepend: function() { - return domManip( this, arguments, function( elem ) { - if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { - var target = manipulationTarget( this, elem ); - target.insertBefore( elem, target.firstChild ); - } - } ); - }, - - before: function() { - return domManip( this, arguments, function( elem ) { - if ( this.parentNode ) { - this.parentNode.insertBefore( elem, this ); - } - } ); - }, - - after: function() { - return domManip( this, arguments, function( elem ) { - if ( this.parentNode ) { - this.parentNode.insertBefore( elem, this.nextSibling ); - } - } ); - }, - - empty: function() { - var elem, - i = 0; - - for ( ; ( elem = this[ i ] ) != null; i++ ) { - if ( elem.nodeType === 1 ) { - - // Prevent memory leaks - jQuery.cleanData( getAll( elem, false ) ); - - // Remove any remaining nodes - elem.textContent = ""; - } - } - - return this; - }, - - clone: function( dataAndEvents, deepDataAndEvents ) { - dataAndEvents = dataAndEvents == null ? false : dataAndEvents; - deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; - - return this.map( function() { - return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); - } ); - }, - - html: function( value ) { - return access( this, function( value ) { - var elem = this[ 0 ] || {}, - i = 0, - l = this.length; - - if ( value === undefined && elem.nodeType === 1 ) { - return elem.innerHTML; - } - - // See if we can take a shortcut and just use innerHTML - if ( typeof value === "string" && !rnoInnerhtml.test( value ) && - !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { - - value = jQuery.htmlPrefilter( value ); - - try { - for ( ; i < l; i++ ) { - elem = this[ i ] || {}; - - // Remove element nodes and prevent memory leaks - if ( elem.nodeType === 1 ) { - jQuery.cleanData( getAll( elem, false ) ); - elem.innerHTML = value; - } - } - - elem = 0; - - // If using innerHTML throws an exception, use the fallback method - } catch ( e ) {} - } - - if ( elem ) { - this.empty().append( value ); - } - }, null, value, arguments.length ); - }, - - replaceWith: function() { - var ignored = []; - - // Make the changes, replacing each non-ignored context element with the new content - return domManip( this, arguments, function( elem ) { - var parent = this.parentNode; - - if ( jQuery.inArray( this, ignored ) < 0 ) { - jQuery.cleanData( getAll( this ) ); - if ( parent ) { - parent.replaceChild( elem, this ); - } - } - - // Force callback invocation - }, ignored ); - } -} ); - -jQuery.each( { - appendTo: "append", - prependTo: "prepend", - insertBefore: "before", - insertAfter: "after", - replaceAll: "replaceWith" -}, function( name, original ) { - jQuery.fn[ name ] = function( selector ) { - var elems, - ret = [], - insert = jQuery( selector ), - last = insert.length - 1, - i = 0; - - for ( ; i <= last; i++ ) { - elems = i === last ? this : this.clone( true ); - jQuery( insert[ i ] )[ original ]( elems ); - - // Support: Android <=4.0 only, PhantomJS 1 only - // .get() because push.apply(_, arraylike) throws on ancient WebKit - push.apply( ret, elems.get() ); - } - - return this.pushStack( ret ); - }; -} ); -var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); - -var getStyles = function( elem ) { - - // Support: IE <=11 only, Firefox <=30 (#15098, #14150) - // IE throws on elements created in popups - // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" - var view = elem.ownerDocument.defaultView; - - if ( !view || !view.opener ) { - view = window; - } - - return view.getComputedStyle( elem ); - }; - -var swap = function( elem, options, callback ) { - var ret, name, - old = {}; - - // Remember the old values, and insert the new ones - for ( name in options ) { - old[ name ] = elem.style[ name ]; - elem.style[ name ] = options[ name ]; - } - - ret = callback.call( elem ); - - // Revert the old values - for ( name in options ) { - elem.style[ name ] = old[ name ]; - } - - return ret; -}; - - -var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); - - - -( function() { - - // Executing both pixelPosition & boxSizingReliable tests require only one layout - // so they're executed at the same time to save the second computation. - function computeStyleTests() { - - // This is a singleton, we need to execute it only once - if ( !div ) { - return; - } - - container.style.cssText = "position:absolute;left:-11111px;width:60px;" + - "margin-top:1px;padding:0;border:0"; - div.style.cssText = - "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + - "margin:auto;border:1px;padding:1px;" + - "width:60%;top:1%"; - documentElement.appendChild( container ).appendChild( div ); - - var divStyle = window.getComputedStyle( div ); - pixelPositionVal = divStyle.top !== "1%"; - - // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 - reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; - - // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 - // Some styles come back with percentage values, even though they shouldn't - div.style.right = "60%"; - pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; - - // Support: IE 9 - 11 only - // Detect misreporting of content dimensions for box-sizing:border-box elements - boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; - - // Support: IE 9 only - // Detect overflow:scroll screwiness (gh-3699) - // Support: Chrome <=64 - // Don't get tricked when zoom affects offsetWidth (gh-4029) - div.style.position = "absolute"; - scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; - - documentElement.removeChild( container ); - - // Nullify the div so it wouldn't be stored in the memory and - // it will also be a sign that checks already performed - div = null; - } - - function roundPixelMeasures( measure ) { - return Math.round( parseFloat( measure ) ); - } - - var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, - reliableTrDimensionsVal, reliableMarginLeftVal, - container = document.createElement( "div" ), - div = document.createElement( "div" ); - - // Finish early in limited (non-browser) environments - if ( !div.style ) { - return; - } - - // Support: IE <=9 - 11 only - // Style of cloned element affects source element cloned (#8908) - div.style.backgroundClip = "content-box"; - div.cloneNode( true ).style.backgroundClip = ""; - support.clearCloneStyle = div.style.backgroundClip === "content-box"; - - jQuery.extend( support, { - boxSizingReliable: function() { - computeStyleTests(); - return boxSizingReliableVal; - }, - pixelBoxStyles: function() { - computeStyleTests(); - return pixelBoxStylesVal; - }, - pixelPosition: function() { - computeStyleTests(); - return pixelPositionVal; - }, - reliableMarginLeft: function() { - computeStyleTests(); - return reliableMarginLeftVal; - }, - scrollboxSize: function() { - computeStyleTests(); - return scrollboxSizeVal; - }, - - // Support: IE 9 - 11+, Edge 15 - 18+ - // IE/Edge misreport `getComputedStyle` of table rows with width/height - // set in CSS while `offset*` properties report correct values. - // Behavior in IE 9 is more subtle than in newer versions & it passes - // some versions of this test; make sure not to make it pass there! - reliableTrDimensions: function() { - var table, tr, trChild, trStyle; - if ( reliableTrDimensionsVal == null ) { - table = document.createElement( "table" ); - tr = document.createElement( "tr" ); - trChild = document.createElement( "div" ); - - table.style.cssText = "position:absolute;left:-11111px"; - tr.style.height = "1px"; - trChild.style.height = "9px"; - - documentElement - .appendChild( table ) - .appendChild( tr ) - .appendChild( trChild ); - - trStyle = window.getComputedStyle( tr ); - reliableTrDimensionsVal = parseInt( trStyle.height ) > 3; - - documentElement.removeChild( table ); - } - return reliableTrDimensionsVal; - } - } ); -} )(); - - -function curCSS( elem, name, computed ) { - var width, minWidth, maxWidth, ret, - - // Support: Firefox 51+ - // Retrieving style before computed somehow - // fixes an issue with getting wrong values - // on detached elements - style = elem.style; - - computed = computed || getStyles( elem ); - - // getPropertyValue is needed for: - // .css('filter') (IE 9 only, #12537) - // .css('--customProperty) (#3144) - if ( computed ) { - ret = computed.getPropertyValue( name ) || computed[ name ]; - - if ( ret === "" && !isAttached( elem ) ) { - ret = jQuery.style( elem, name ); - } - - // A tribute to the "awesome hack by Dean Edwards" - // Android Browser returns percentage for some values, - // but width seems to be reliably pixels. - // This is against the CSSOM draft spec: - // https://drafts.csswg.org/cssom/#resolved-values - if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { - - // Remember the original values - width = style.width; - minWidth = style.minWidth; - maxWidth = style.maxWidth; - - // Put in the new values to get a computed value out - style.minWidth = style.maxWidth = style.width = ret; - ret = computed.width; - - // Revert the changed values - style.width = width; - style.minWidth = minWidth; - style.maxWidth = maxWidth; - } - } - - return ret !== undefined ? - - // Support: IE <=9 - 11 only - // IE returns zIndex value as an integer. - ret + "" : - ret; -} - - -function addGetHookIf( conditionFn, hookFn ) { - - // Define the hook, we'll check on the first run if it's really needed. - return { - get: function() { - if ( conditionFn() ) { - - // Hook not needed (or it's not possible to use it due - // to missing dependency), remove it. - delete this.get; - return; - } - - // Hook needed; redefine it so that the support test is not executed again. - return ( this.get = hookFn ).apply( this, arguments ); - } - }; -} - - -var cssPrefixes = [ "Webkit", "Moz", "ms" ], - emptyStyle = document.createElement( "div" ).style, - vendorProps = {}; - -// Return a vendor-prefixed property or undefined -function vendorPropName( name ) { - - // Check for vendor prefixed names - var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), - i = cssPrefixes.length; - - while ( i-- ) { - name = cssPrefixes[ i ] + capName; - if ( name in emptyStyle ) { - return name; - } - } -} - -// Return a potentially-mapped jQuery.cssProps or vendor prefixed property -function finalPropName( name ) { - var final = jQuery.cssProps[ name ] || vendorProps[ name ]; - - if ( final ) { - return final; - } - if ( name in emptyStyle ) { - return name; - } - return vendorProps[ name ] = vendorPropName( name ) || name; -} - - -var - - // Swappable if display is none or starts with table - // except "table", "table-cell", or "table-caption" - // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display - rdisplayswap = /^(none|table(?!-c[ea]).+)/, - rcustomProp = /^--/, - cssShow = { position: "absolute", visibility: "hidden", display: "block" }, - cssNormalTransform = { - letterSpacing: "0", - fontWeight: "400" - }; - -function setPositiveNumber( _elem, value, subtract ) { - - // Any relative (+/-) values have already been - // normalized at this point - var matches = rcssNum.exec( value ); - return matches ? - - // Guard against undefined "subtract", e.g., when used as in cssHooks - Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : - value; -} - -function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { - var i = dimension === "width" ? 1 : 0, - extra = 0, - delta = 0; - - // Adjustment may not be necessary - if ( box === ( isBorderBox ? "border" : "content" ) ) { - return 0; - } - - for ( ; i < 4; i += 2 ) { - - // Both box models exclude margin - if ( box === "margin" ) { - delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); - } - - // If we get here with a content-box, we're seeking "padding" or "border" or "margin" - if ( !isBorderBox ) { - - // Add padding - delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); - - // For "border" or "margin", add border - if ( box !== "padding" ) { - delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); - - // But still keep track of it otherwise - } else { - extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); - } - - // If we get here with a border-box (content + padding + border), we're seeking "content" or - // "padding" or "margin" - } else { - - // For "content", subtract padding - if ( box === "content" ) { - delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); - } - - // For "content" or "padding", subtract border - if ( box !== "margin" ) { - delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); - } - } - } - - // Account for positive content-box scroll gutter when requested by providing computedVal - if ( !isBorderBox && computedVal >= 0 ) { - - // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border - // Assuming integer scroll gutter, subtract the rest and round down - delta += Math.max( 0, Math.ceil( - elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - - computedVal - - delta - - extra - - 0.5 - - // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter - // Use an explicit zero to avoid NaN (gh-3964) - ) ) || 0; - } - - return delta; -} - -function getWidthOrHeight( elem, dimension, extra ) { - - // Start with computed style - var styles = getStyles( elem ), - - // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). - // Fake content-box until we know it's needed to know the true value. - boxSizingNeeded = !support.boxSizingReliable() || extra, - isBorderBox = boxSizingNeeded && - jQuery.css( elem, "boxSizing", false, styles ) === "border-box", - valueIsBorderBox = isBorderBox, - - val = curCSS( elem, dimension, styles ), - offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); - - // Support: Firefox <=54 - // Return a confounding non-pixel value or feign ignorance, as appropriate. - if ( rnumnonpx.test( val ) ) { - if ( !extra ) { - return val; - } - val = "auto"; - } - - - // Support: IE 9 - 11 only - // Use offsetWidth/offsetHeight for when box sizing is unreliable. - // In those cases, the computed value can be trusted to be border-box. - if ( ( !support.boxSizingReliable() && isBorderBox || - - // Support: IE 10 - 11+, Edge 15 - 18+ - // IE/Edge misreport `getComputedStyle` of table rows with width/height - // set in CSS while `offset*` properties report correct values. - // Interestingly, in some cases IE 9 doesn't suffer from this issue. - !support.reliableTrDimensions() && nodeName( elem, "tr" ) || - - // Fall back to offsetWidth/offsetHeight when value is "auto" - // This happens for inline elements with no explicit setting (gh-3571) - val === "auto" || - - // Support: Android <=4.1 - 4.3 only - // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) - !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && - - // Make sure the element is visible & connected - elem.getClientRects().length ) { - - isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; - - // Where available, offsetWidth/offsetHeight approximate border box dimensions. - // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the - // retrieved value as a content box dimension. - valueIsBorderBox = offsetProp in elem; - if ( valueIsBorderBox ) { - val = elem[ offsetProp ]; - } - } - - // Normalize "" and auto - val = parseFloat( val ) || 0; - - // Adjust for the element's box model - return ( val + - boxModelAdjustment( - elem, - dimension, - extra || ( isBorderBox ? "border" : "content" ), - valueIsBorderBox, - styles, - - // Provide the current computed size to request scroll gutter calculation (gh-3589) - val - ) - ) + "px"; -} - -jQuery.extend( { - - // Add in style property hooks for overriding the default - // behavior of getting and setting a style property - cssHooks: { - opacity: { - get: function( elem, computed ) { - if ( computed ) { - - // We should always get a number back from opacity - var ret = curCSS( elem, "opacity" ); - return ret === "" ? "1" : ret; - } - } - } - }, - - // Don't automatically add "px" to these possibly-unitless properties - cssNumber: { - "animationIterationCount": true, - "columnCount": true, - "fillOpacity": true, - "flexGrow": true, - "flexShrink": true, - "fontWeight": true, - "gridArea": true, - "gridColumn": true, - "gridColumnEnd": true, - "gridColumnStart": true, - "gridRow": true, - "gridRowEnd": true, - "gridRowStart": true, - "lineHeight": true, - "opacity": true, - "order": true, - "orphans": true, - "widows": true, - "zIndex": true, - "zoom": true - }, - - // Add in properties whose names you wish to fix before - // setting or getting the value - cssProps: {}, - - // Get and set the style property on a DOM Node - style: function( elem, name, value, extra ) { - - // Don't set styles on text and comment nodes - if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { - return; - } - - // Make sure that we're working with the right name - var ret, type, hooks, - origName = camelCase( name ), - isCustomProp = rcustomProp.test( name ), - style = elem.style; - - // Make sure that we're working with the right name. We don't - // want to query the value if it is a CSS custom property - // since they are user-defined. - if ( !isCustomProp ) { - name = finalPropName( origName ); - } - - // Gets hook for the prefixed version, then unprefixed version - hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; - - // Check if we're setting a value - if ( value !== undefined ) { - type = typeof value; - - // Convert "+=" or "-=" to relative numbers (#7345) - if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { - value = adjustCSS( elem, name, ret ); - - // Fixes bug #9237 - type = "number"; - } - - // Make sure that null and NaN values aren't set (#7116) - if ( value == null || value !== value ) { - return; - } - - // If a number was passed in, add the unit (except for certain CSS properties) - // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append - // "px" to a few hardcoded values. - if ( type === "number" && !isCustomProp ) { - value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); - } - - // background-* props affect original clone's values - if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { - style[ name ] = "inherit"; - } - - // If a hook was provided, use that value, otherwise just set the specified value - if ( !hooks || !( "set" in hooks ) || - ( value = hooks.set( elem, value, extra ) ) !== undefined ) { - - if ( isCustomProp ) { - style.setProperty( name, value ); - } else { - style[ name ] = value; - } - } - - } else { - - // If a hook was provided get the non-computed value from there - if ( hooks && "get" in hooks && - ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { - - return ret; - } - - // Otherwise just get the value from the style object - return style[ name ]; - } - }, - - css: function( elem, name, extra, styles ) { - var val, num, hooks, - origName = camelCase( name ), - isCustomProp = rcustomProp.test( name ); - - // Make sure that we're working with the right name. We don't - // want to modify the value if it is a CSS custom property - // since they are user-defined. - if ( !isCustomProp ) { - name = finalPropName( origName ); - } - - // Try prefixed name followed by the unprefixed name - hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; - - // If a hook was provided get the computed value from there - if ( hooks && "get" in hooks ) { - val = hooks.get( elem, true, extra ); - } - - // Otherwise, if a way to get the computed value exists, use that - if ( val === undefined ) { - val = curCSS( elem, name, styles ); - } - - // Convert "normal" to computed value - if ( val === "normal" && name in cssNormalTransform ) { - val = cssNormalTransform[ name ]; - } - - // Make numeric if forced or a qualifier was provided and val looks numeric - if ( extra === "" || extra ) { - num = parseFloat( val ); - return extra === true || isFinite( num ) ? num || 0 : val; - } - - return val; - } -} ); - -jQuery.each( [ "height", "width" ], function( _i, dimension ) { - jQuery.cssHooks[ dimension ] = { - get: function( elem, computed, extra ) { - if ( computed ) { - - // Certain elements can have dimension info if we invisibly show them - // but it must have a current display style that would benefit - return rdisplayswap.test( jQuery.css( elem, "display" ) ) && - - // Support: Safari 8+ - // Table columns in Safari have non-zero offsetWidth & zero - // getBoundingClientRect().width unless display is changed. - // Support: IE <=11 only - // Running getBoundingClientRect on a disconnected node - // in IE throws an error. - ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? - swap( elem, cssShow, function() { - return getWidthOrHeight( elem, dimension, extra ); - } ) : - getWidthOrHeight( elem, dimension, extra ); - } - }, - - set: function( elem, value, extra ) { - var matches, - styles = getStyles( elem ), - - // Only read styles.position if the test has a chance to fail - // to avoid forcing a reflow. - scrollboxSizeBuggy = !support.scrollboxSize() && - styles.position === "absolute", - - // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) - boxSizingNeeded = scrollboxSizeBuggy || extra, - isBorderBox = boxSizingNeeded && - jQuery.css( elem, "boxSizing", false, styles ) === "border-box", - subtract = extra ? - boxModelAdjustment( - elem, - dimension, - extra, - isBorderBox, - styles - ) : - 0; - - // Account for unreliable border-box dimensions by comparing offset* to computed and - // faking a content-box to get border and padding (gh-3699) - if ( isBorderBox && scrollboxSizeBuggy ) { - subtract -= Math.ceil( - elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - - parseFloat( styles[ dimension ] ) - - boxModelAdjustment( elem, dimension, "border", false, styles ) - - 0.5 - ); - } - - // Convert to pixels if value adjustment is needed - if ( subtract && ( matches = rcssNum.exec( value ) ) && - ( matches[ 3 ] || "px" ) !== "px" ) { - - elem.style[ dimension ] = value; - value = jQuery.css( elem, dimension ); - } - - return setPositiveNumber( elem, value, subtract ); - } - }; -} ); - -jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, - function( elem, computed ) { - if ( computed ) { - return ( parseFloat( curCSS( elem, "marginLeft" ) ) || - elem.getBoundingClientRect().left - - swap( elem, { marginLeft: 0 }, function() { - return elem.getBoundingClientRect().left; - } ) - ) + "px"; - } - } -); - -// These hooks are used by animate to expand properties -jQuery.each( { - margin: "", - padding: "", - border: "Width" -}, function( prefix, suffix ) { - jQuery.cssHooks[ prefix + suffix ] = { - expand: function( value ) { - var i = 0, - expanded = {}, - - // Assumes a single number if not a string - parts = typeof value === "string" ? value.split( " " ) : [ value ]; - - for ( ; i < 4; i++ ) { - expanded[ prefix + cssExpand[ i ] + suffix ] = - parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; - } - - return expanded; - } - }; - - if ( prefix !== "margin" ) { - jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; - } -} ); - -jQuery.fn.extend( { - css: function( name, value ) { - return access( this, function( elem, name, value ) { - var styles, len, - map = {}, - i = 0; - - if ( Array.isArray( name ) ) { - styles = getStyles( elem ); - len = name.length; - - for ( ; i < len; i++ ) { - map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); - } - - return map; - } - - return value !== undefined ? - jQuery.style( elem, name, value ) : - jQuery.css( elem, name ); - }, name, value, arguments.length > 1 ); - } -} ); - - -function Tween( elem, options, prop, end, easing ) { - return new Tween.prototype.init( elem, options, prop, end, easing ); -} -jQuery.Tween = Tween; - -Tween.prototype = { - constructor: Tween, - init: function( elem, options, prop, end, easing, unit ) { - this.elem = elem; - this.prop = prop; - this.easing = easing || jQuery.easing._default; - this.options = options; - this.start = this.now = this.cur(); - this.end = end; - this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); - }, - cur: function() { - var hooks = Tween.propHooks[ this.prop ]; - - return hooks && hooks.get ? - hooks.get( this ) : - Tween.propHooks._default.get( this ); - }, - run: function( percent ) { - var eased, - hooks = Tween.propHooks[ this.prop ]; - - if ( this.options.duration ) { - this.pos = eased = jQuery.easing[ this.easing ]( - percent, this.options.duration * percent, 0, 1, this.options.duration - ); - } else { - this.pos = eased = percent; - } - this.now = ( this.end - this.start ) * eased + this.start; - - if ( this.options.step ) { - this.options.step.call( this.elem, this.now, this ); - } - - if ( hooks && hooks.set ) { - hooks.set( this ); - } else { - Tween.propHooks._default.set( this ); - } - return this; - } -}; - -Tween.prototype.init.prototype = Tween.prototype; - -Tween.propHooks = { - _default: { - get: function( tween ) { - var result; - - // Use a property on the element directly when it is not a DOM element, - // or when there is no matching style property that exists. - if ( tween.elem.nodeType !== 1 || - tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { - return tween.elem[ tween.prop ]; - } - - // Passing an empty string as a 3rd parameter to .css will automatically - // attempt a parseFloat and fallback to a string if the parse fails. - // Simple values such as "10px" are parsed to Float; - // complex values such as "rotate(1rad)" are returned as-is. - result = jQuery.css( tween.elem, tween.prop, "" ); - - // Empty strings, null, undefined and "auto" are converted to 0. - return !result || result === "auto" ? 0 : result; - }, - set: function( tween ) { - - // Use step hook for back compat. - // Use cssHook if its there. - // Use .style if available and use plain properties where available. - if ( jQuery.fx.step[ tween.prop ] ) { - jQuery.fx.step[ tween.prop ]( tween ); - } else if ( tween.elem.nodeType === 1 && ( - jQuery.cssHooks[ tween.prop ] || - tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { - jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); - } else { - tween.elem[ tween.prop ] = tween.now; - } - } - } -}; - -// Support: IE <=9 only -// Panic based approach to setting things on disconnected nodes -Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { - set: function( tween ) { - if ( tween.elem.nodeType && tween.elem.parentNode ) { - tween.elem[ tween.prop ] = tween.now; - } - } -}; - -jQuery.easing = { - linear: function( p ) { - return p; - }, - swing: function( p ) { - return 0.5 - Math.cos( p * Math.PI ) / 2; - }, - _default: "swing" -}; - -jQuery.fx = Tween.prototype.init; - -// Back compat <1.8 extension point -jQuery.fx.step = {}; - - - - -var - fxNow, inProgress, - rfxtypes = /^(?:toggle|show|hide)$/, - rrun = /queueHooks$/; - -function schedule() { - if ( inProgress ) { - if ( document.hidden === false && window.requestAnimationFrame ) { - window.requestAnimationFrame( schedule ); - } else { - window.setTimeout( schedule, jQuery.fx.interval ); - } - - jQuery.fx.tick(); - } -} - -// Animations created synchronously will run synchronously -function createFxNow() { - window.setTimeout( function() { - fxNow = undefined; - } ); - return ( fxNow = Date.now() ); -} - -// Generate parameters to create a standard animation -function genFx( type, includeWidth ) { - var which, - i = 0, - attrs = { height: type }; - - // If we include width, step value is 1 to do all cssExpand values, - // otherwise step value is 2 to skip over Left and Right - includeWidth = includeWidth ? 1 : 0; - for ( ; i < 4; i += 2 - includeWidth ) { - which = cssExpand[ i ]; - attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; - } - - if ( includeWidth ) { - attrs.opacity = attrs.width = type; - } - - return attrs; -} - -function createTween( value, prop, animation ) { - var tween, - collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), - index = 0, - length = collection.length; - for ( ; index < length; index++ ) { - if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { - - // We're done with this property - return tween; - } - } -} - -function defaultPrefilter( elem, props, opts ) { - var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, - isBox = "width" in props || "height" in props, - anim = this, - orig = {}, - style = elem.style, - hidden = elem.nodeType && isHiddenWithinTree( elem ), - dataShow = dataPriv.get( elem, "fxshow" ); - - // Queue-skipping animations hijack the fx hooks - if ( !opts.queue ) { - hooks = jQuery._queueHooks( elem, "fx" ); - if ( hooks.unqueued == null ) { - hooks.unqueued = 0; - oldfire = hooks.empty.fire; - hooks.empty.fire = function() { - if ( !hooks.unqueued ) { - oldfire(); - } - }; - } - hooks.unqueued++; - - anim.always( function() { - - // Ensure the complete handler is called before this completes - anim.always( function() { - hooks.unqueued--; - if ( !jQuery.queue( elem, "fx" ).length ) { - hooks.empty.fire(); - } - } ); - } ); - } - - // Detect show/hide animations - for ( prop in props ) { - value = props[ prop ]; - if ( rfxtypes.test( value ) ) { - delete props[ prop ]; - toggle = toggle || value === "toggle"; - if ( value === ( hidden ? "hide" : "show" ) ) { - - // Pretend to be hidden if this is a "show" and - // there is still data from a stopped show/hide - if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { - hidden = true; - - // Ignore all other no-op show/hide data - } else { - continue; - } - } - orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); - } - } - - // Bail out if this is a no-op like .hide().hide() - propTween = !jQuery.isEmptyObject( props ); - if ( !propTween && jQuery.isEmptyObject( orig ) ) { - return; - } - - // Restrict "overflow" and "display" styles during box animations - if ( isBox && elem.nodeType === 1 ) { - - // Support: IE <=9 - 11, Edge 12 - 15 - // Record all 3 overflow attributes because IE does not infer the shorthand - // from identically-valued overflowX and overflowY and Edge just mirrors - // the overflowX value there. - opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; - - // Identify a display type, preferring old show/hide data over the CSS cascade - restoreDisplay = dataShow && dataShow.display; - if ( restoreDisplay == null ) { - restoreDisplay = dataPriv.get( elem, "display" ); - } - display = jQuery.css( elem, "display" ); - if ( display === "none" ) { - if ( restoreDisplay ) { - display = restoreDisplay; - } else { - - // Get nonempty value(s) by temporarily forcing visibility - showHide( [ elem ], true ); - restoreDisplay = elem.style.display || restoreDisplay; - display = jQuery.css( elem, "display" ); - showHide( [ elem ] ); - } - } - - // Animate inline elements as inline-block - if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { - if ( jQuery.css( elem, "float" ) === "none" ) { - - // Restore the original display value at the end of pure show/hide animations - if ( !propTween ) { - anim.done( function() { - style.display = restoreDisplay; - } ); - if ( restoreDisplay == null ) { - display = style.display; - restoreDisplay = display === "none" ? "" : display; - } - } - style.display = "inline-block"; - } - } - } - - if ( opts.overflow ) { - style.overflow = "hidden"; - anim.always( function() { - style.overflow = opts.overflow[ 0 ]; - style.overflowX = opts.overflow[ 1 ]; - style.overflowY = opts.overflow[ 2 ]; - } ); - } - - // Implement show/hide animations - propTween = false; - for ( prop in orig ) { - - // General show/hide setup for this element animation - if ( !propTween ) { - if ( dataShow ) { - if ( "hidden" in dataShow ) { - hidden = dataShow.hidden; - } - } else { - dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); - } - - // Store hidden/visible for toggle so `.stop().toggle()` "reverses" - if ( toggle ) { - dataShow.hidden = !hidden; - } - - // Show elements before animating them - if ( hidden ) { - showHide( [ elem ], true ); - } - - /* eslint-disable no-loop-func */ - - anim.done( function() { - - /* eslint-enable no-loop-func */ - - // The final step of a "hide" animation is actually hiding the element - if ( !hidden ) { - showHide( [ elem ] ); - } - dataPriv.remove( elem, "fxshow" ); - for ( prop in orig ) { - jQuery.style( elem, prop, orig[ prop ] ); - } - } ); - } - - // Per-property setup - propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); - if ( !( prop in dataShow ) ) { - dataShow[ prop ] = propTween.start; - if ( hidden ) { - propTween.end = propTween.start; - propTween.start = 0; - } - } - } -} - -function propFilter( props, specialEasing ) { - var index, name, easing, value, hooks; - - // camelCase, specialEasing and expand cssHook pass - for ( index in props ) { - name = camelCase( index ); - easing = specialEasing[ name ]; - value = props[ index ]; - if ( Array.isArray( value ) ) { - easing = value[ 1 ]; - value = props[ index ] = value[ 0 ]; - } - - if ( index !== name ) { - props[ name ] = value; - delete props[ index ]; - } - - hooks = jQuery.cssHooks[ name ]; - if ( hooks && "expand" in hooks ) { - value = hooks.expand( value ); - delete props[ name ]; - - // Not quite $.extend, this won't overwrite existing keys. - // Reusing 'index' because we have the correct "name" - for ( index in value ) { - if ( !( index in props ) ) { - props[ index ] = value[ index ]; - specialEasing[ index ] = easing; - } - } - } else { - specialEasing[ name ] = easing; - } - } -} - -function Animation( elem, properties, options ) { - var result, - stopped, - index = 0, - length = Animation.prefilters.length, - deferred = jQuery.Deferred().always( function() { - - // Don't match elem in the :animated selector - delete tick.elem; - } ), - tick = function() { - if ( stopped ) { - return false; - } - var currentTime = fxNow || createFxNow(), - remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), - - // Support: Android 2.3 only - // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) - temp = remaining / animation.duration || 0, - percent = 1 - temp, - index = 0, - length = animation.tweens.length; - - for ( ; index < length; index++ ) { - animation.tweens[ index ].run( percent ); - } - - deferred.notifyWith( elem, [ animation, percent, remaining ] ); - - // If there's more to do, yield - if ( percent < 1 && length ) { - return remaining; - } - - // If this was an empty animation, synthesize a final progress notification - if ( !length ) { - deferred.notifyWith( elem, [ animation, 1, 0 ] ); - } - - // Resolve the animation and report its conclusion - deferred.resolveWith( elem, [ animation ] ); - return false; - }, - animation = deferred.promise( { - elem: elem, - props: jQuery.extend( {}, properties ), - opts: jQuery.extend( true, { - specialEasing: {}, - easing: jQuery.easing._default - }, options ), - originalProperties: properties, - originalOptions: options, - startTime: fxNow || createFxNow(), - duration: options.duration, - tweens: [], - createTween: function( prop, end ) { - var tween = jQuery.Tween( elem, animation.opts, prop, end, - animation.opts.specialEasing[ prop ] || animation.opts.easing ); - animation.tweens.push( tween ); - return tween; - }, - stop: function( gotoEnd ) { - var index = 0, - - // If we are going to the end, we want to run all the tweens - // otherwise we skip this part - length = gotoEnd ? animation.tweens.length : 0; - if ( stopped ) { - return this; - } - stopped = true; - for ( ; index < length; index++ ) { - animation.tweens[ index ].run( 1 ); - } - - // Resolve when we played the last frame; otherwise, reject - if ( gotoEnd ) { - deferred.notifyWith( elem, [ animation, 1, 0 ] ); - deferred.resolveWith( elem, [ animation, gotoEnd ] ); - } else { - deferred.rejectWith( elem, [ animation, gotoEnd ] ); - } - return this; - } - } ), - props = animation.props; - - propFilter( props, animation.opts.specialEasing ); - - for ( ; index < length; index++ ) { - result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); - if ( result ) { - if ( isFunction( result.stop ) ) { - jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = - result.stop.bind( result ); - } - return result; - } - } - - jQuery.map( props, createTween, animation ); - - if ( isFunction( animation.opts.start ) ) { - animation.opts.start.call( elem, animation ); - } - - // Attach callbacks from options - animation - .progress( animation.opts.progress ) - .done( animation.opts.done, animation.opts.complete ) - .fail( animation.opts.fail ) - .always( animation.opts.always ); - - jQuery.fx.timer( - jQuery.extend( tick, { - elem: elem, - anim: animation, - queue: animation.opts.queue - } ) - ); - - return animation; -} - -jQuery.Animation = jQuery.extend( Animation, { - - tweeners: { - "*": [ function( prop, value ) { - var tween = this.createTween( prop, value ); - adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); - return tween; - } ] - }, - - tweener: function( props, callback ) { - if ( isFunction( props ) ) { - callback = props; - props = [ "*" ]; - } else { - props = props.match( rnothtmlwhite ); - } - - var prop, - index = 0, - length = props.length; - - for ( ; index < length; index++ ) { - prop = props[ index ]; - Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; - Animation.tweeners[ prop ].unshift( callback ); - } - }, - - prefilters: [ defaultPrefilter ], - - prefilter: function( callback, prepend ) { - if ( prepend ) { - Animation.prefilters.unshift( callback ); - } else { - Animation.prefilters.push( callback ); - } - } -} ); - -jQuery.speed = function( speed, easing, fn ) { - var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { - complete: fn || !fn && easing || - isFunction( speed ) && speed, - duration: speed, - easing: fn && easing || easing && !isFunction( easing ) && easing - }; - - // Go to the end state if fx are off - if ( jQuery.fx.off ) { - opt.duration = 0; - - } else { - if ( typeof opt.duration !== "number" ) { - if ( opt.duration in jQuery.fx.speeds ) { - opt.duration = jQuery.fx.speeds[ opt.duration ]; - - } else { - opt.duration = jQuery.fx.speeds._default; - } - } - } - - // Normalize opt.queue - true/undefined/null -> "fx" - if ( opt.queue == null || opt.queue === true ) { - opt.queue = "fx"; - } - - // Queueing - opt.old = opt.complete; - - opt.complete = function() { - if ( isFunction( opt.old ) ) { - opt.old.call( this ); - } - - if ( opt.queue ) { - jQuery.dequeue( this, opt.queue ); - } - }; - - return opt; -}; - -jQuery.fn.extend( { - fadeTo: function( speed, to, easing, callback ) { - - // Show any hidden elements after setting opacity to 0 - return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() - - // Animate to the value specified - .end().animate( { opacity: to }, speed, easing, callback ); - }, - animate: function( prop, speed, easing, callback ) { - var empty = jQuery.isEmptyObject( prop ), - optall = jQuery.speed( speed, easing, callback ), - doAnimation = function() { - - // Operate on a copy of prop so per-property easing won't be lost - var anim = Animation( this, jQuery.extend( {}, prop ), optall ); - - // Empty animations, or finishing resolves immediately - if ( empty || dataPriv.get( this, "finish" ) ) { - anim.stop( true ); - } - }; - doAnimation.finish = doAnimation; - - return empty || optall.queue === false ? - this.each( doAnimation ) : - this.queue( optall.queue, doAnimation ); - }, - stop: function( type, clearQueue, gotoEnd ) { - var stopQueue = function( hooks ) { - var stop = hooks.stop; - delete hooks.stop; - stop( gotoEnd ); - }; - - if ( typeof type !== "string" ) { - gotoEnd = clearQueue; - clearQueue = type; - type = undefined; - } - if ( clearQueue ) { - this.queue( type || "fx", [] ); - } - - return this.each( function() { - var dequeue = true, - index = type != null && type + "queueHooks", - timers = jQuery.timers, - data = dataPriv.get( this ); - - if ( index ) { - if ( data[ index ] && data[ index ].stop ) { - stopQueue( data[ index ] ); - } - } else { - for ( index in data ) { - if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { - stopQueue( data[ index ] ); - } - } - } - - for ( index = timers.length; index--; ) { - if ( timers[ index ].elem === this && - ( type == null || timers[ index ].queue === type ) ) { - - timers[ index ].anim.stop( gotoEnd ); - dequeue = false; - timers.splice( index, 1 ); - } - } - - // Start the next in the queue if the last step wasn't forced. - // Timers currently will call their complete callbacks, which - // will dequeue but only if they were gotoEnd. - if ( dequeue || !gotoEnd ) { - jQuery.dequeue( this, type ); - } - } ); - }, - finish: function( type ) { - if ( type !== false ) { - type = type || "fx"; - } - return this.each( function() { - var index, - data = dataPriv.get( this ), - queue = data[ type + "queue" ], - hooks = data[ type + "queueHooks" ], - timers = jQuery.timers, - length = queue ? queue.length : 0; - - // Enable finishing flag on private data - data.finish = true; - - // Empty the queue first - jQuery.queue( this, type, [] ); - - if ( hooks && hooks.stop ) { - hooks.stop.call( this, true ); - } - - // Look for any active animations, and finish them - for ( index = timers.length; index--; ) { - if ( timers[ index ].elem === this && timers[ index ].queue === type ) { - timers[ index ].anim.stop( true ); - timers.splice( index, 1 ); - } - } - - // Look for any animations in the old queue and finish them - for ( index = 0; index < length; index++ ) { - if ( queue[ index ] && queue[ index ].finish ) { - queue[ index ].finish.call( this ); - } - } - - // Turn off finishing flag - delete data.finish; - } ); - } -} ); - -jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { - var cssFn = jQuery.fn[ name ]; - jQuery.fn[ name ] = function( speed, easing, callback ) { - return speed == null || typeof speed === "boolean" ? - cssFn.apply( this, arguments ) : - this.animate( genFx( name, true ), speed, easing, callback ); - }; -} ); - -// Generate shortcuts for custom animations -jQuery.each( { - slideDown: genFx( "show" ), - slideUp: genFx( "hide" ), - slideToggle: genFx( "toggle" ), - fadeIn: { opacity: "show" }, - fadeOut: { opacity: "hide" }, - fadeToggle: { opacity: "toggle" } -}, function( name, props ) { - jQuery.fn[ name ] = function( speed, easing, callback ) { - return this.animate( props, speed, easing, callback ); - }; -} ); - -jQuery.timers = []; -jQuery.fx.tick = function() { - var timer, - i = 0, - timers = jQuery.timers; - - fxNow = Date.now(); - - for ( ; i < timers.length; i++ ) { - timer = timers[ i ]; - - // Run the timer and safely remove it when done (allowing for external removal) - if ( !timer() && timers[ i ] === timer ) { - timers.splice( i--, 1 ); - } - } - - if ( !timers.length ) { - jQuery.fx.stop(); - } - fxNow = undefined; -}; - -jQuery.fx.timer = function( timer ) { - jQuery.timers.push( timer ); - jQuery.fx.start(); -}; - -jQuery.fx.interval = 13; -jQuery.fx.start = function() { - if ( inProgress ) { - return; - } - - inProgress = true; - schedule(); -}; - -jQuery.fx.stop = function() { - inProgress = null; -}; - -jQuery.fx.speeds = { - slow: 600, - fast: 200, - - // Default speed - _default: 400 -}; - - -// Based off of the plugin by Clint Helfers, with permission. -// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ -jQuery.fn.delay = function( time, type ) { - time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; - type = type || "fx"; - - return this.queue( type, function( next, hooks ) { - var timeout = window.setTimeout( next, time ); - hooks.stop = function() { - window.clearTimeout( timeout ); - }; - } ); -}; - - -( function() { - var input = document.createElement( "input" ), - select = document.createElement( "select" ), - opt = select.appendChild( document.createElement( "option" ) ); - - input.type = "checkbox"; - - // Support: Android <=4.3 only - // Default value for a checkbox should be "on" - support.checkOn = input.value !== ""; - - // Support: IE <=11 only - // Must access selectedIndex to make default options select - support.optSelected = opt.selected; - - // Support: IE <=11 only - // An input loses its value after becoming a radio - input = document.createElement( "input" ); - input.value = "t"; - input.type = "radio"; - support.radioValue = input.value === "t"; -} )(); - - -var boolHook, - attrHandle = jQuery.expr.attrHandle; - -jQuery.fn.extend( { - attr: function( name, value ) { - return access( this, jQuery.attr, name, value, arguments.length > 1 ); - }, - - removeAttr: function( name ) { - return this.each( function() { - jQuery.removeAttr( this, name ); - } ); - } -} ); - -jQuery.extend( { - attr: function( elem, name, value ) { - var ret, hooks, - nType = elem.nodeType; - - // Don't get/set attributes on text, comment and attribute nodes - if ( nType === 3 || nType === 8 || nType === 2 ) { - return; - } - - // Fallback to prop when attributes are not supported - if ( typeof elem.getAttribute === "undefined" ) { - return jQuery.prop( elem, name, value ); - } - - // Attribute hooks are determined by the lowercase version - // Grab necessary hook if one is defined - if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { - hooks = jQuery.attrHooks[ name.toLowerCase() ] || - ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); - } - - if ( value !== undefined ) { - if ( value === null ) { - jQuery.removeAttr( elem, name ); - return; - } - - if ( hooks && "set" in hooks && - ( ret = hooks.set( elem, value, name ) ) !== undefined ) { - return ret; - } - - elem.setAttribute( name, value + "" ); - return value; - } - - if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { - return ret; - } - - ret = jQuery.find.attr( elem, name ); - - // Non-existent attributes return null, we normalize to undefined - return ret == null ? undefined : ret; - }, - - attrHooks: { - type: { - set: function( elem, value ) { - if ( !support.radioValue && value === "radio" && - nodeName( elem, "input" ) ) { - var val = elem.value; - elem.setAttribute( "type", value ); - if ( val ) { - elem.value = val; - } - return value; - } - } - } - }, - - removeAttr: function( elem, value ) { - var name, - i = 0, - - // Attribute names can contain non-HTML whitespace characters - // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 - attrNames = value && value.match( rnothtmlwhite ); - - if ( attrNames && elem.nodeType === 1 ) { - while ( ( name = attrNames[ i++ ] ) ) { - elem.removeAttribute( name ); - } - } - } -} ); - -// Hooks for boolean attributes -boolHook = { - set: function( elem, value, name ) { - if ( value === false ) { - - // Remove boolean attributes when set to false - jQuery.removeAttr( elem, name ); - } else { - elem.setAttribute( name, name ); - } - return name; - } -}; - -jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { - var getter = attrHandle[ name ] || jQuery.find.attr; - - attrHandle[ name ] = function( elem, name, isXML ) { - var ret, handle, - lowercaseName = name.toLowerCase(); - - if ( !isXML ) { - - // Avoid an infinite loop by temporarily removing this function from the getter - handle = attrHandle[ lowercaseName ]; - attrHandle[ lowercaseName ] = ret; - ret = getter( elem, name, isXML ) != null ? - lowercaseName : - null; - attrHandle[ lowercaseName ] = handle; - } - return ret; - }; -} ); - - - - -var rfocusable = /^(?:input|select|textarea|button)$/i, - rclickable = /^(?:a|area)$/i; - -jQuery.fn.extend( { - prop: function( name, value ) { - return access( this, jQuery.prop, name, value, arguments.length > 1 ); - }, - - removeProp: function( name ) { - return this.each( function() { - delete this[ jQuery.propFix[ name ] || name ]; - } ); - } -} ); - -jQuery.extend( { - prop: function( elem, name, value ) { - var ret, hooks, - nType = elem.nodeType; - - // Don't get/set properties on text, comment and attribute nodes - if ( nType === 3 || nType === 8 || nType === 2 ) { - return; - } - - if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { - - // Fix name and attach hooks - name = jQuery.propFix[ name ] || name; - hooks = jQuery.propHooks[ name ]; - } - - if ( value !== undefined ) { - if ( hooks && "set" in hooks && - ( ret = hooks.set( elem, value, name ) ) !== undefined ) { - return ret; - } - - return ( elem[ name ] = value ); - } - - if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { - return ret; - } - - return elem[ name ]; - }, - - propHooks: { - tabIndex: { - get: function( elem ) { - - // Support: IE <=9 - 11 only - // elem.tabIndex doesn't always return the - // correct value when it hasn't been explicitly set - // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ - // Use proper attribute retrieval(#12072) - var tabindex = jQuery.find.attr( elem, "tabindex" ); - - if ( tabindex ) { - return parseInt( tabindex, 10 ); - } - - if ( - rfocusable.test( elem.nodeName ) || - rclickable.test( elem.nodeName ) && - elem.href - ) { - return 0; - } - - return -1; - } - } - }, - - propFix: { - "for": "htmlFor", - "class": "className" - } -} ); - -// Support: IE <=11 only -// Accessing the selectedIndex property -// forces the browser to respect setting selected -// on the option -// The getter ensures a default option is selected -// when in an optgroup -// eslint rule "no-unused-expressions" is disabled for this code -// since it considers such accessions noop -if ( !support.optSelected ) { - jQuery.propHooks.selected = { - get: function( elem ) { - - /* eslint no-unused-expressions: "off" */ - - var parent = elem.parentNode; - if ( parent && parent.parentNode ) { - parent.parentNode.selectedIndex; - } - return null; - }, - set: function( elem ) { - - /* eslint no-unused-expressions: "off" */ - - var parent = elem.parentNode; - if ( parent ) { - parent.selectedIndex; - - if ( parent.parentNode ) { - parent.parentNode.selectedIndex; - } - } - } - }; -} - -jQuery.each( [ - "tabIndex", - "readOnly", - "maxLength", - "cellSpacing", - "cellPadding", - "rowSpan", - "colSpan", - "useMap", - "frameBorder", - "contentEditable" -], function() { - jQuery.propFix[ this.toLowerCase() ] = this; -} ); - - - - - // Strip and collapse whitespace according to HTML spec - // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace - function stripAndCollapse( value ) { - var tokens = value.match( rnothtmlwhite ) || []; - return tokens.join( " " ); - } - - -function getClass( elem ) { - return elem.getAttribute && elem.getAttribute( "class" ) || ""; -} - -function classesToArray( value ) { - if ( Array.isArray( value ) ) { - return value; - } - if ( typeof value === "string" ) { - return value.match( rnothtmlwhite ) || []; - } - return []; -} - -jQuery.fn.extend( { - addClass: function( value ) { - var classes, elem, cur, curValue, clazz, j, finalValue, - i = 0; - - if ( isFunction( value ) ) { - return this.each( function( j ) { - jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); - } ); - } - - classes = classesToArray( value ); - - if ( classes.length ) { - while ( ( elem = this[ i++ ] ) ) { - curValue = getClass( elem ); - cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); - - if ( cur ) { - j = 0; - while ( ( clazz = classes[ j++ ] ) ) { - if ( cur.indexOf( " " + clazz + " " ) < 0 ) { - cur += clazz + " "; - } - } - - // Only assign if different to avoid unneeded rendering. - finalValue = stripAndCollapse( cur ); - if ( curValue !== finalValue ) { - elem.setAttribute( "class", finalValue ); - } - } - } - } - - return this; - }, - - removeClass: function( value ) { - var classes, elem, cur, curValue, clazz, j, finalValue, - i = 0; - - if ( isFunction( value ) ) { - return this.each( function( j ) { - jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); - } ); - } - - if ( !arguments.length ) { - return this.attr( "class", "" ); - } - - classes = classesToArray( value ); - - if ( classes.length ) { - while ( ( elem = this[ i++ ] ) ) { - curValue = getClass( elem ); - - // This expression is here for better compressibility (see addClass) - cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); - - if ( cur ) { - j = 0; - while ( ( clazz = classes[ j++ ] ) ) { - - // Remove *all* instances - while ( cur.indexOf( " " + clazz + " " ) > -1 ) { - cur = cur.replace( " " + clazz + " ", " " ); - } - } - - // Only assign if different to avoid unneeded rendering. - finalValue = stripAndCollapse( cur ); - if ( curValue !== finalValue ) { - elem.setAttribute( "class", finalValue ); - } - } - } - } - - return this; - }, - - toggleClass: function( value, stateVal ) { - var type = typeof value, - isValidValue = type === "string" || Array.isArray( value ); - - if ( typeof stateVal === "boolean" && isValidValue ) { - return stateVal ? this.addClass( value ) : this.removeClass( value ); - } - - if ( isFunction( value ) ) { - return this.each( function( i ) { - jQuery( this ).toggleClass( - value.call( this, i, getClass( this ), stateVal ), - stateVal - ); - } ); - } - - return this.each( function() { - var className, i, self, classNames; - - if ( isValidValue ) { - - // Toggle individual class names - i = 0; - self = jQuery( this ); - classNames = classesToArray( value ); - - while ( ( className = classNames[ i++ ] ) ) { - - // Check each className given, space separated list - if ( self.hasClass( className ) ) { - self.removeClass( className ); - } else { - self.addClass( className ); - } - } - - // Toggle whole class name - } else if ( value === undefined || type === "boolean" ) { - className = getClass( this ); - if ( className ) { - - // Store className if set - dataPriv.set( this, "__className__", className ); - } - - // If the element has a class name or if we're passed `false`, - // then remove the whole classname (if there was one, the above saved it). - // Otherwise bring back whatever was previously saved (if anything), - // falling back to the empty string if nothing was stored. - if ( this.setAttribute ) { - this.setAttribute( "class", - className || value === false ? - "" : - dataPriv.get( this, "__className__" ) || "" - ); - } - } - } ); - }, - - hasClass: function( selector ) { - var className, elem, - i = 0; - - className = " " + selector + " "; - while ( ( elem = this[ i++ ] ) ) { - if ( elem.nodeType === 1 && - ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { - return true; - } - } - - return false; - } -} ); - - - - -var rreturn = /\r/g; - -jQuery.fn.extend( { - val: function( value ) { - var hooks, ret, valueIsFunction, - elem = this[ 0 ]; - - if ( !arguments.length ) { - if ( elem ) { - hooks = jQuery.valHooks[ elem.type ] || - jQuery.valHooks[ elem.nodeName.toLowerCase() ]; - - if ( hooks && - "get" in hooks && - ( ret = hooks.get( elem, "value" ) ) !== undefined - ) { - return ret; - } - - ret = elem.value; - - // Handle most common string cases - if ( typeof ret === "string" ) { - return ret.replace( rreturn, "" ); - } - - // Handle cases where value is null/undef or number - return ret == null ? "" : ret; - } - - return; - } - - valueIsFunction = isFunction( value ); - - return this.each( function( i ) { - var val; - - if ( this.nodeType !== 1 ) { - return; - } - - if ( valueIsFunction ) { - val = value.call( this, i, jQuery( this ).val() ); - } else { - val = value; - } - - // Treat null/undefined as ""; convert numbers to string - if ( val == null ) { - val = ""; - - } else if ( typeof val === "number" ) { - val += ""; - - } else if ( Array.isArray( val ) ) { - val = jQuery.map( val, function( value ) { - return value == null ? "" : value + ""; - } ); - } - - hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; - - // If set returns undefined, fall back to normal setting - if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { - this.value = val; - } - } ); - } -} ); - -jQuery.extend( { - valHooks: { - option: { - get: function( elem ) { - - var val = jQuery.find.attr( elem, "value" ); - return val != null ? - val : - - // Support: IE <=10 - 11 only - // option.text throws exceptions (#14686, #14858) - // Strip and collapse whitespace - // https://html.spec.whatwg.org/#strip-and-collapse-whitespace - stripAndCollapse( jQuery.text( elem ) ); - } - }, - select: { - get: function( elem ) { - var value, option, i, - options = elem.options, - index = elem.selectedIndex, - one = elem.type === "select-one", - values = one ? null : [], - max = one ? index + 1 : options.length; - - if ( index < 0 ) { - i = max; - - } else { - i = one ? index : 0; - } - - // Loop through all the selected options - for ( ; i < max; i++ ) { - option = options[ i ]; - - // Support: IE <=9 only - // IE8-9 doesn't update selected after form reset (#2551) - if ( ( option.selected || i === index ) && - - // Don't return options that are disabled or in a disabled optgroup - !option.disabled && - ( !option.parentNode.disabled || - !nodeName( option.parentNode, "optgroup" ) ) ) { - - // Get the specific value for the option - value = jQuery( option ).val(); - - // We don't need an array for one selects - if ( one ) { - return value; - } - - // Multi-Selects return an array - values.push( value ); - } - } - - return values; - }, - - set: function( elem, value ) { - var optionSet, option, - options = elem.options, - values = jQuery.makeArray( value ), - i = options.length; - - while ( i-- ) { - option = options[ i ]; - - /* eslint-disable no-cond-assign */ - - if ( option.selected = - jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 - ) { - optionSet = true; - } - - /* eslint-enable no-cond-assign */ - } - - // Force browsers to behave consistently when non-matching value is set - if ( !optionSet ) { - elem.selectedIndex = -1; - } - return values; - } - } - } -} ); - -// Radios and checkboxes getter/setter -jQuery.each( [ "radio", "checkbox" ], function() { - jQuery.valHooks[ this ] = { - set: function( elem, value ) { - if ( Array.isArray( value ) ) { - return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); - } - } - }; - if ( !support.checkOn ) { - jQuery.valHooks[ this ].get = function( elem ) { - return elem.getAttribute( "value" ) === null ? "on" : elem.value; - }; - } -} ); - - - - -// Return jQuery for attributes-only inclusion - - -support.focusin = "onfocusin" in window; - - -var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, - stopPropagationCallback = function( e ) { - e.stopPropagation(); - }; - -jQuery.extend( jQuery.event, { - - trigger: function( event, data, elem, onlyHandlers ) { - - var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, - eventPath = [ elem || document ], - type = hasOwn.call( event, "type" ) ? event.type : event, - namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; - - cur = lastElement = tmp = elem = elem || document; - - // Don't do events on text and comment nodes - if ( elem.nodeType === 3 || elem.nodeType === 8 ) { - return; - } - - // focus/blur morphs to focusin/out; ensure we're not firing them right now - if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { - return; - } - - if ( type.indexOf( "." ) > -1 ) { - - // Namespaced trigger; create a regexp to match event type in handle() - namespaces = type.split( "." ); - type = namespaces.shift(); - namespaces.sort(); - } - ontype = type.indexOf( ":" ) < 0 && "on" + type; - - // Caller can pass in a jQuery.Event object, Object, or just an event type string - event = event[ jQuery.expando ] ? - event : - new jQuery.Event( type, typeof event === "object" && event ); - - // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) - event.isTrigger = onlyHandlers ? 2 : 3; - event.namespace = namespaces.join( "." ); - event.rnamespace = event.namespace ? - new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : - null; - - // Clean up the event in case it is being reused - event.result = undefined; - if ( !event.target ) { - event.target = elem; - } - - // Clone any incoming data and prepend the event, creating the handler arg list - data = data == null ? - [ event ] : - jQuery.makeArray( data, [ event ] ); - - // Allow special events to draw outside the lines - special = jQuery.event.special[ type ] || {}; - if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { - return; - } - - // Determine event propagation path in advance, per W3C events spec (#9951) - // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) - if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { - - bubbleType = special.delegateType || type; - if ( !rfocusMorph.test( bubbleType + type ) ) { - cur = cur.parentNode; - } - for ( ; cur; cur = cur.parentNode ) { - eventPath.push( cur ); - tmp = cur; - } - - // Only add window if we got to document (e.g., not plain obj or detached DOM) - if ( tmp === ( elem.ownerDocument || document ) ) { - eventPath.push( tmp.defaultView || tmp.parentWindow || window ); - } - } - - // Fire handlers on the event path - i = 0; - while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { - lastElement = cur; - event.type = i > 1 ? - bubbleType : - special.bindType || type; - - // jQuery handler - handle = ( - dataPriv.get( cur, "events" ) || Object.create( null ) - )[ event.type ] && - dataPriv.get( cur, "handle" ); - if ( handle ) { - handle.apply( cur, data ); - } - - // Native handler - handle = ontype && cur[ ontype ]; - if ( handle && handle.apply && acceptData( cur ) ) { - event.result = handle.apply( cur, data ); - if ( event.result === false ) { - event.preventDefault(); - } - } - } - event.type = type; - - // If nobody prevented the default action, do it now - if ( !onlyHandlers && !event.isDefaultPrevented() ) { - - if ( ( !special._default || - special._default.apply( eventPath.pop(), data ) === false ) && - acceptData( elem ) ) { - - // Call a native DOM method on the target with the same name as the event. - // Don't do default actions on window, that's where global variables be (#6170) - if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { - - // Don't re-trigger an onFOO event when we call its FOO() method - tmp = elem[ ontype ]; - - if ( tmp ) { - elem[ ontype ] = null; - } - - // Prevent re-triggering of the same event, since we already bubbled it above - jQuery.event.triggered = type; - - if ( event.isPropagationStopped() ) { - lastElement.addEventListener( type, stopPropagationCallback ); - } - - elem[ type ](); - - if ( event.isPropagationStopped() ) { - lastElement.removeEventListener( type, stopPropagationCallback ); - } - - jQuery.event.triggered = undefined; - - if ( tmp ) { - elem[ ontype ] = tmp; - } - } - } - } - - return event.result; - }, - - // Piggyback on a donor event to simulate a different one - // Used only for `focus(in | out)` events - simulate: function( type, elem, event ) { - var e = jQuery.extend( - new jQuery.Event(), - event, - { - type: type, - isSimulated: true - } - ); - - jQuery.event.trigger( e, null, elem ); - } - -} ); - -jQuery.fn.extend( { - - trigger: function( type, data ) { - return this.each( function() { - jQuery.event.trigger( type, data, this ); - } ); - }, - triggerHandler: function( type, data ) { - var elem = this[ 0 ]; - if ( elem ) { - return jQuery.event.trigger( type, data, elem, true ); - } - } -} ); - - -// Support: Firefox <=44 -// Firefox doesn't have focus(in | out) events -// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 -// -// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 -// focus(in | out) events fire after focus & blur events, -// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order -// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 -if ( !support.focusin ) { - jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { - - // Attach a single capturing handler on the document while someone wants focusin/focusout - var handler = function( event ) { - jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); - }; - - jQuery.event.special[ fix ] = { - setup: function() { - - // Handle: regular nodes (via `this.ownerDocument`), window - // (via `this.document`) & document (via `this`). - var doc = this.ownerDocument || this.document || this, - attaches = dataPriv.access( doc, fix ); - - if ( !attaches ) { - doc.addEventListener( orig, handler, true ); - } - dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); - }, - teardown: function() { - var doc = this.ownerDocument || this.document || this, - attaches = dataPriv.access( doc, fix ) - 1; - - if ( !attaches ) { - doc.removeEventListener( orig, handler, true ); - dataPriv.remove( doc, fix ); - - } else { - dataPriv.access( doc, fix, attaches ); - } - } - }; - } ); -} -var location = window.location; - -var nonce = { guid: Date.now() }; - -var rquery = ( /\?/ ); - - - -// Cross-browser xml parsing -jQuery.parseXML = function( data ) { - var xml; - if ( !data || typeof data !== "string" ) { - return null; - } - - // Support: IE 9 - 11 only - // IE throws on parseFromString with invalid input. - try { - xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); - } catch ( e ) { - xml = undefined; - } - - if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) { - jQuery.error( "Invalid XML: " + data ); - } - return xml; -}; - - -var - rbracket = /\[\]$/, - rCRLF = /\r?\n/g, - rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, - rsubmittable = /^(?:input|select|textarea|keygen)/i; - -function buildParams( prefix, obj, traditional, add ) { - var name; - - if ( Array.isArray( obj ) ) { - - // Serialize array item. - jQuery.each( obj, function( i, v ) { - if ( traditional || rbracket.test( prefix ) ) { - - // Treat each array item as a scalar. - add( prefix, v ); - - } else { - - // Item is non-scalar (array or object), encode its numeric index. - buildParams( - prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", - v, - traditional, - add - ); - } - } ); - - } else if ( !traditional && toType( obj ) === "object" ) { - - // Serialize object item. - for ( name in obj ) { - buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); - } - - } else { - - // Serialize scalar item. - add( prefix, obj ); - } -} - -// Serialize an array of form elements or a set of -// key/values into a query string -jQuery.param = function( a, traditional ) { - var prefix, - s = [], - add = function( key, valueOrFunction ) { - - // If value is a function, invoke it and use its return value - var value = isFunction( valueOrFunction ) ? - valueOrFunction() : - valueOrFunction; - - s[ s.length ] = encodeURIComponent( key ) + "=" + - encodeURIComponent( value == null ? "" : value ); - }; - - if ( a == null ) { - return ""; - } - - // If an array was passed in, assume that it is an array of form elements. - if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { - - // Serialize the form elements - jQuery.each( a, function() { - add( this.name, this.value ); - } ); - - } else { - - // If traditional, encode the "old" way (the way 1.3.2 or older - // did it), otherwise encode params recursively. - for ( prefix in a ) { - buildParams( prefix, a[ prefix ], traditional, add ); - } - } - - // Return the resulting serialization - return s.join( "&" ); -}; - -jQuery.fn.extend( { - serialize: function() { - return jQuery.param( this.serializeArray() ); - }, - serializeArray: function() { - return this.map( function() { - - // Can add propHook for "elements" to filter or add form elements - var elements = jQuery.prop( this, "elements" ); - return elements ? jQuery.makeArray( elements ) : this; - } ) - .filter( function() { - var type = this.type; - - // Use .is( ":disabled" ) so that fieldset[disabled] works - return this.name && !jQuery( this ).is( ":disabled" ) && - rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && - ( this.checked || !rcheckableType.test( type ) ); - } ) - .map( function( _i, elem ) { - var val = jQuery( this ).val(); - - if ( val == null ) { - return null; - } - - if ( Array.isArray( val ) ) { - return jQuery.map( val, function( val ) { - return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; - } ); - } - - return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; - } ).get(); - } -} ); - - -var - r20 = /%20/g, - rhash = /#.*$/, - rantiCache = /([?&])_=[^&]*/, - rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, - - // #7653, #8125, #8152: local protocol detection - rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, - rnoContent = /^(?:GET|HEAD)$/, - rprotocol = /^\/\//, - - /* Prefilters - * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) - * 2) These are called: - * - BEFORE asking for a transport - * - AFTER param serialization (s.data is a string if s.processData is true) - * 3) key is the dataType - * 4) the catchall symbol "*" can be used - * 5) execution will start with transport dataType and THEN continue down to "*" if needed - */ - prefilters = {}, - - /* Transports bindings - * 1) key is the dataType - * 2) the catchall symbol "*" can be used - * 3) selection will start with transport dataType and THEN go to "*" if needed - */ - transports = {}, - - // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression - allTypes = "*/".concat( "*" ), - - // Anchor tag for parsing the document origin - originAnchor = document.createElement( "a" ); - originAnchor.href = location.href; - -// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport -function addToPrefiltersOrTransports( structure ) { - - // dataTypeExpression is optional and defaults to "*" - return function( dataTypeExpression, func ) { - - if ( typeof dataTypeExpression !== "string" ) { - func = dataTypeExpression; - dataTypeExpression = "*"; - } - - var dataType, - i = 0, - dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; - - if ( isFunction( func ) ) { - - // For each dataType in the dataTypeExpression - while ( ( dataType = dataTypes[ i++ ] ) ) { - - // Prepend if requested - if ( dataType[ 0 ] === "+" ) { - dataType = dataType.slice( 1 ) || "*"; - ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); - - // Otherwise append - } else { - ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); - } - } - } - }; -} - -// Base inspection function for prefilters and transports -function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { - - var inspected = {}, - seekingTransport = ( structure === transports ); - - function inspect( dataType ) { - var selected; - inspected[ dataType ] = true; - jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { - var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); - if ( typeof dataTypeOrTransport === "string" && - !seekingTransport && !inspected[ dataTypeOrTransport ] ) { - - options.dataTypes.unshift( dataTypeOrTransport ); - inspect( dataTypeOrTransport ); - return false; - } else if ( seekingTransport ) { - return !( selected = dataTypeOrTransport ); - } - } ); - return selected; - } - - return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); -} - -// A special extend for ajax options -// that takes "flat" options (not to be deep extended) -// Fixes #9887 -function ajaxExtend( target, src ) { - var key, deep, - flatOptions = jQuery.ajaxSettings.flatOptions || {}; - - for ( key in src ) { - if ( src[ key ] !== undefined ) { - ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; - } - } - if ( deep ) { - jQuery.extend( true, target, deep ); - } - - return target; -} - -/* Handles responses to an ajax request: - * - finds the right dataType (mediates between content-type and expected dataType) - * - returns the corresponding response - */ -function ajaxHandleResponses( s, jqXHR, responses ) { - - var ct, type, finalDataType, firstDataType, - contents = s.contents, - dataTypes = s.dataTypes; - - // Remove auto dataType and get content-type in the process - while ( dataTypes[ 0 ] === "*" ) { - dataTypes.shift(); - if ( ct === undefined ) { - ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); - } - } - - // Check if we're dealing with a known content-type - if ( ct ) { - for ( type in contents ) { - if ( contents[ type ] && contents[ type ].test( ct ) ) { - dataTypes.unshift( type ); - break; - } - } - } - - // Check to see if we have a response for the expected dataType - if ( dataTypes[ 0 ] in responses ) { - finalDataType = dataTypes[ 0 ]; - } else { - - // Try convertible dataTypes - for ( type in responses ) { - if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { - finalDataType = type; - break; - } - if ( !firstDataType ) { - firstDataType = type; - } - } - - // Or just use first one - finalDataType = finalDataType || firstDataType; - } - - // If we found a dataType - // We add the dataType to the list if needed - // and return the corresponding response - if ( finalDataType ) { - if ( finalDataType !== dataTypes[ 0 ] ) { - dataTypes.unshift( finalDataType ); - } - return responses[ finalDataType ]; - } -} - -/* Chain conversions given the request and the original response - * Also sets the responseXXX fields on the jqXHR instance - */ -function ajaxConvert( s, response, jqXHR, isSuccess ) { - var conv2, current, conv, tmp, prev, - converters = {}, - - // Work with a copy of dataTypes in case we need to modify it for conversion - dataTypes = s.dataTypes.slice(); - - // Create converters map with lowercased keys - if ( dataTypes[ 1 ] ) { - for ( conv in s.converters ) { - converters[ conv.toLowerCase() ] = s.converters[ conv ]; - } - } - - current = dataTypes.shift(); - - // Convert to each sequential dataType - while ( current ) { - - if ( s.responseFields[ current ] ) { - jqXHR[ s.responseFields[ current ] ] = response; - } - - // Apply the dataFilter if provided - if ( !prev && isSuccess && s.dataFilter ) { - response = s.dataFilter( response, s.dataType ); - } - - prev = current; - current = dataTypes.shift(); - - if ( current ) { - - // There's only work to do if current dataType is non-auto - if ( current === "*" ) { - - current = prev; - - // Convert response if prev dataType is non-auto and differs from current - } else if ( prev !== "*" && prev !== current ) { - - // Seek a direct converter - conv = converters[ prev + " " + current ] || converters[ "* " + current ]; - - // If none found, seek a pair - if ( !conv ) { - for ( conv2 in converters ) { - - // If conv2 outputs current - tmp = conv2.split( " " ); - if ( tmp[ 1 ] === current ) { - - // If prev can be converted to accepted input - conv = converters[ prev + " " + tmp[ 0 ] ] || - converters[ "* " + tmp[ 0 ] ]; - if ( conv ) { - - // Condense equivalence converters - if ( conv === true ) { - conv = converters[ conv2 ]; - - // Otherwise, insert the intermediate dataType - } else if ( converters[ conv2 ] !== true ) { - current = tmp[ 0 ]; - dataTypes.unshift( tmp[ 1 ] ); - } - break; - } - } - } - } - - // Apply converter (if not an equivalence) - if ( conv !== true ) { - - // Unless errors are allowed to bubble, catch and return them - if ( conv && s.throws ) { - response = conv( response ); - } else { - try { - response = conv( response ); - } catch ( e ) { - return { - state: "parsererror", - error: conv ? e : "No conversion from " + prev + " to " + current - }; - } - } - } - } - } - } - - return { state: "success", data: response }; -} - -jQuery.extend( { - - // Counter for holding the number of active queries - active: 0, - - // Last-Modified header cache for next request - lastModified: {}, - etag: {}, - - ajaxSettings: { - url: location.href, - type: "GET", - isLocal: rlocalProtocol.test( location.protocol ), - global: true, - processData: true, - async: true, - contentType: "application/x-www-form-urlencoded; charset=UTF-8", - - /* - timeout: 0, - data: null, - dataType: null, - username: null, - password: null, - cache: null, - throws: false, - traditional: false, - headers: {}, - */ - - accepts: { - "*": allTypes, - text: "text/plain", - html: "text/html", - xml: "application/xml, text/xml", - json: "application/json, text/javascript" - }, - - contents: { - xml: /\bxml\b/, - html: /\bhtml/, - json: /\bjson\b/ - }, - - responseFields: { - xml: "responseXML", - text: "responseText", - json: "responseJSON" - }, - - // Data converters - // Keys separate source (or catchall "*") and destination types with a single space - converters: { - - // Convert anything to text - "* text": String, - - // Text to html (true = no transformation) - "text html": true, - - // Evaluate text as a json expression - "text json": JSON.parse, - - // Parse text as xml - "text xml": jQuery.parseXML - }, - - // For options that shouldn't be deep extended: - // you can add your own custom options here if - // and when you create one that shouldn't be - // deep extended (see ajaxExtend) - flatOptions: { - url: true, - context: true - } - }, - - // Creates a full fledged settings object into target - // with both ajaxSettings and settings fields. - // If target is omitted, writes into ajaxSettings. - ajaxSetup: function( target, settings ) { - return settings ? - - // Building a settings object - ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : - - // Extending ajaxSettings - ajaxExtend( jQuery.ajaxSettings, target ); - }, - - ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), - ajaxTransport: addToPrefiltersOrTransports( transports ), - - // Main method - ajax: function( url, options ) { - - // If url is an object, simulate pre-1.5 signature - if ( typeof url === "object" ) { - options = url; - url = undefined; - } - - // Force options to be an object - options = options || {}; - - var transport, - - // URL without anti-cache param - cacheURL, - - // Response headers - responseHeadersString, - responseHeaders, - - // timeout handle - timeoutTimer, - - // Url cleanup var - urlAnchor, - - // Request state (becomes false upon send and true upon completion) - completed, - - // To know if global events are to be dispatched - fireGlobals, - - // Loop variable - i, - - // uncached part of the url - uncached, - - // Create the final options object - s = jQuery.ajaxSetup( {}, options ), - - // Callbacks context - callbackContext = s.context || s, - - // Context for global events is callbackContext if it is a DOM node or jQuery collection - globalEventContext = s.context && - ( callbackContext.nodeType || callbackContext.jquery ) ? - jQuery( callbackContext ) : - jQuery.event, - - // Deferreds - deferred = jQuery.Deferred(), - completeDeferred = jQuery.Callbacks( "once memory" ), - - // Status-dependent callbacks - statusCode = s.statusCode || {}, - - // Headers (they are sent all at once) - requestHeaders = {}, - requestHeadersNames = {}, - - // Default abort message - strAbort = "canceled", - - // Fake xhr - jqXHR = { - readyState: 0, - - // Builds headers hashtable if needed - getResponseHeader: function( key ) { - var match; - if ( completed ) { - if ( !responseHeaders ) { - responseHeaders = {}; - while ( ( match = rheaders.exec( responseHeadersString ) ) ) { - responseHeaders[ match[ 1 ].toLowerCase() + " " ] = - ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) - .concat( match[ 2 ] ); - } - } - match = responseHeaders[ key.toLowerCase() + " " ]; - } - return match == null ? null : match.join( ", " ); - }, - - // Raw string - getAllResponseHeaders: function() { - return completed ? responseHeadersString : null; - }, - - // Caches the header - setRequestHeader: function( name, value ) { - if ( completed == null ) { - name = requestHeadersNames[ name.toLowerCase() ] = - requestHeadersNames[ name.toLowerCase() ] || name; - requestHeaders[ name ] = value; - } - return this; - }, - - // Overrides response content-type header - overrideMimeType: function( type ) { - if ( completed == null ) { - s.mimeType = type; - } - return this; - }, - - // Status-dependent callbacks - statusCode: function( map ) { - var code; - if ( map ) { - if ( completed ) { - - // Execute the appropriate callbacks - jqXHR.always( map[ jqXHR.status ] ); - } else { - - // Lazy-add the new callbacks in a way that preserves old ones - for ( code in map ) { - statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; - } - } - } - return this; - }, - - // Cancel the request - abort: function( statusText ) { - var finalText = statusText || strAbort; - if ( transport ) { - transport.abort( finalText ); - } - done( 0, finalText ); - return this; - } - }; - - // Attach deferreds - deferred.promise( jqXHR ); - - // Add protocol if not provided (prefilters might expect it) - // Handle falsy url in the settings object (#10093: consistency with old signature) - // We also use the url parameter if available - s.url = ( ( url || s.url || location.href ) + "" ) - .replace( rprotocol, location.protocol + "//" ); - - // Alias method option to type as per ticket #12004 - s.type = options.method || options.type || s.method || s.type; - - // Extract dataTypes list - s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; - - // A cross-domain request is in order when the origin doesn't match the current origin. - if ( s.crossDomain == null ) { - urlAnchor = document.createElement( "a" ); - - // Support: IE <=8 - 11, Edge 12 - 15 - // IE throws exception on accessing the href property if url is malformed, - // e.g. http://example.com:80x/ - try { - urlAnchor.href = s.url; - - // Support: IE <=8 - 11 only - // Anchor's host property isn't correctly set when s.url is relative - urlAnchor.href = urlAnchor.href; - s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== - urlAnchor.protocol + "//" + urlAnchor.host; - } catch ( e ) { - - // If there is an error parsing the URL, assume it is crossDomain, - // it can be rejected by the transport if it is invalid - s.crossDomain = true; - } - } - - // Convert data if not already a string - if ( s.data && s.processData && typeof s.data !== "string" ) { - s.data = jQuery.param( s.data, s.traditional ); - } - - // Apply prefilters - inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); - - // If request was aborted inside a prefilter, stop there - if ( completed ) { - return jqXHR; - } - - // We can fire global events as of now if asked to - // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) - fireGlobals = jQuery.event && s.global; - - // Watch for a new set of requests - if ( fireGlobals && jQuery.active++ === 0 ) { - jQuery.event.trigger( "ajaxStart" ); - } - - // Uppercase the type - s.type = s.type.toUpperCase(); - - // Determine if request has content - s.hasContent = !rnoContent.test( s.type ); - - // Save the URL in case we're toying with the If-Modified-Since - // and/or If-None-Match header later on - // Remove hash to simplify url manipulation - cacheURL = s.url.replace( rhash, "" ); - - // More options handling for requests with no content - if ( !s.hasContent ) { - - // Remember the hash so we can put it back - uncached = s.url.slice( cacheURL.length ); - - // If data is available and should be processed, append data to url - if ( s.data && ( s.processData || typeof s.data === "string" ) ) { - cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; - - // #9682: remove data so that it's not used in an eventual retry - delete s.data; - } - - // Add or update anti-cache param if needed - if ( s.cache === false ) { - cacheURL = cacheURL.replace( rantiCache, "$1" ); - uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + - uncached; - } - - // Put hash and anti-cache on the URL that will be requested (gh-1732) - s.url = cacheURL + uncached; - - // Change '%20' to '+' if this is encoded form body content (gh-2658) - } else if ( s.data && s.processData && - ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { - s.data = s.data.replace( r20, "+" ); - } - - // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. - if ( s.ifModified ) { - if ( jQuery.lastModified[ cacheURL ] ) { - jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); - } - if ( jQuery.etag[ cacheURL ] ) { - jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); - } - } - - // Set the correct header, if data is being sent - if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { - jqXHR.setRequestHeader( "Content-Type", s.contentType ); - } - - // Set the Accepts header for the server, depending on the dataType - jqXHR.setRequestHeader( - "Accept", - s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? - s.accepts[ s.dataTypes[ 0 ] ] + - ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : - s.accepts[ "*" ] - ); - - // Check for headers option - for ( i in s.headers ) { - jqXHR.setRequestHeader( i, s.headers[ i ] ); - } - - // Allow custom headers/mimetypes and early abort - if ( s.beforeSend && - ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { - - // Abort if not done already and return - return jqXHR.abort(); - } - - // Aborting is no longer a cancellation - strAbort = "abort"; - - // Install callbacks on deferreds - completeDeferred.add( s.complete ); - jqXHR.done( s.success ); - jqXHR.fail( s.error ); - - // Get transport - transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); - - // If no transport, we auto-abort - if ( !transport ) { - done( -1, "No Transport" ); - } else { - jqXHR.readyState = 1; - - // Send global event - if ( fireGlobals ) { - globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); - } - - // If request was aborted inside ajaxSend, stop there - if ( completed ) { - return jqXHR; - } - - // Timeout - if ( s.async && s.timeout > 0 ) { - timeoutTimer = window.setTimeout( function() { - jqXHR.abort( "timeout" ); - }, s.timeout ); - } - - try { - completed = false; - transport.send( requestHeaders, done ); - } catch ( e ) { - - // Rethrow post-completion exceptions - if ( completed ) { - throw e; - } - - // Propagate others as results - done( -1, e ); - } - } - - // Callback for when everything is done - function done( status, nativeStatusText, responses, headers ) { - var isSuccess, success, error, response, modified, - statusText = nativeStatusText; - - // Ignore repeat invocations - if ( completed ) { - return; - } - - completed = true; - - // Clear timeout if it exists - if ( timeoutTimer ) { - window.clearTimeout( timeoutTimer ); - } - - // Dereference transport for early garbage collection - // (no matter how long the jqXHR object will be used) - transport = undefined; - - // Cache response headers - responseHeadersString = headers || ""; - - // Set readyState - jqXHR.readyState = status > 0 ? 4 : 0; - - // Determine if successful - isSuccess = status >= 200 && status < 300 || status === 304; - - // Get response data - if ( responses ) { - response = ajaxHandleResponses( s, jqXHR, responses ); - } - - // Use a noop converter for missing script - if ( !isSuccess && jQuery.inArray( "script", s.dataTypes ) > -1 ) { - s.converters[ "text script" ] = function() {}; - } - - // Convert no matter what (that way responseXXX fields are always set) - response = ajaxConvert( s, response, jqXHR, isSuccess ); - - // If successful, handle type chaining - if ( isSuccess ) { - - // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. - if ( s.ifModified ) { - modified = jqXHR.getResponseHeader( "Last-Modified" ); - if ( modified ) { - jQuery.lastModified[ cacheURL ] = modified; - } - modified = jqXHR.getResponseHeader( "etag" ); - if ( modified ) { - jQuery.etag[ cacheURL ] = modified; - } - } - - // if no content - if ( status === 204 || s.type === "HEAD" ) { - statusText = "nocontent"; - - // if not modified - } else if ( status === 304 ) { - statusText = "notmodified"; - - // If we have data, let's convert it - } else { - statusText = response.state; - success = response.data; - error = response.error; - isSuccess = !error; - } - } else { - - // Extract error from statusText and normalize for non-aborts - error = statusText; - if ( status || !statusText ) { - statusText = "error"; - if ( status < 0 ) { - status = 0; - } - } - } - - // Set data for the fake xhr object - jqXHR.status = status; - jqXHR.statusText = ( nativeStatusText || statusText ) + ""; - - // Success/Error - if ( isSuccess ) { - deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); - } else { - deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); - } - - // Status-dependent callbacks - jqXHR.statusCode( statusCode ); - statusCode = undefined; - - if ( fireGlobals ) { - globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", - [ jqXHR, s, isSuccess ? success : error ] ); - } - - // Complete - completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); - - if ( fireGlobals ) { - globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); - - // Handle the global AJAX counter - if ( !( --jQuery.active ) ) { - jQuery.event.trigger( "ajaxStop" ); - } - } - } - - return jqXHR; - }, - - getJSON: function( url, data, callback ) { - return jQuery.get( url, data, callback, "json" ); - }, - - getScript: function( url, callback ) { - return jQuery.get( url, undefined, callback, "script" ); - } -} ); - -jQuery.each( [ "get", "post" ], function( _i, method ) { - jQuery[ method ] = function( url, data, callback, type ) { - - // Shift arguments if data argument was omitted - if ( isFunction( data ) ) { - type = type || callback; - callback = data; - data = undefined; - } - - // The url can be an options object (which then must have .url) - return jQuery.ajax( jQuery.extend( { - url: url, - type: method, - dataType: type, - data: data, - success: callback - }, jQuery.isPlainObject( url ) && url ) ); - }; -} ); - -jQuery.ajaxPrefilter( function( s ) { - var i; - for ( i in s.headers ) { - if ( i.toLowerCase() === "content-type" ) { - s.contentType = s.headers[ i ] || ""; - } - } -} ); - - -jQuery._evalUrl = function( url, options, doc ) { - return jQuery.ajax( { - url: url, - - // Make this explicit, since user can override this through ajaxSetup (#11264) - type: "GET", - dataType: "script", - cache: true, - async: false, - global: false, - - // Only evaluate the response if it is successful (gh-4126) - // dataFilter is not invoked for failure responses, so using it instead - // of the default converter is kludgy but it works. - converters: { - "text script": function() {} - }, - dataFilter: function( response ) { - jQuery.globalEval( response, options, doc ); - } - } ); -}; - - -jQuery.fn.extend( { - wrapAll: function( html ) { - var wrap; - - if ( this[ 0 ] ) { - if ( isFunction( html ) ) { - html = html.call( this[ 0 ] ); - } - - // The elements to wrap the target around - wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); - - if ( this[ 0 ].parentNode ) { - wrap.insertBefore( this[ 0 ] ); - } - - wrap.map( function() { - var elem = this; - - while ( elem.firstElementChild ) { - elem = elem.firstElementChild; - } - - return elem; - } ).append( this ); - } - - return this; - }, - - wrapInner: function( html ) { - if ( isFunction( html ) ) { - return this.each( function( i ) { - jQuery( this ).wrapInner( html.call( this, i ) ); - } ); - } - - return this.each( function() { - var self = jQuery( this ), - contents = self.contents(); - - if ( contents.length ) { - contents.wrapAll( html ); - - } else { - self.append( html ); - } - } ); - }, - - wrap: function( html ) { - var htmlIsFunction = isFunction( html ); - - return this.each( function( i ) { - jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html ); - } ); - }, - - unwrap: function( selector ) { - this.parent( selector ).not( "body" ).each( function() { - jQuery( this ).replaceWith( this.childNodes ); - } ); - return this; - } -} ); - - -jQuery.expr.pseudos.hidden = function( elem ) { - return !jQuery.expr.pseudos.visible( elem ); -}; -jQuery.expr.pseudos.visible = function( elem ) { - return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); -}; - - - - -jQuery.ajaxSettings.xhr = function() { - try { - return new window.XMLHttpRequest(); - } catch ( e ) {} -}; - -var xhrSuccessStatus = { - - // File protocol always yields status code 0, assume 200 - 0: 200, - - // Support: IE <=9 only - // #1450: sometimes IE returns 1223 when it should be 204 - 1223: 204 - }, - xhrSupported = jQuery.ajaxSettings.xhr(); - -support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); -support.ajax = xhrSupported = !!xhrSupported; - -jQuery.ajaxTransport( function( options ) { - var callback, errorCallback; - - // Cross domain only allowed if supported through XMLHttpRequest - if ( support.cors || xhrSupported && !options.crossDomain ) { - return { - send: function( headers, complete ) { - var i, - xhr = options.xhr(); - - xhr.open( - options.type, - options.url, - options.async, - options.username, - options.password - ); - - // Apply custom fields if provided - if ( options.xhrFields ) { - for ( i in options.xhrFields ) { - xhr[ i ] = options.xhrFields[ i ]; - } - } - - // Override mime type if needed - if ( options.mimeType && xhr.overrideMimeType ) { - xhr.overrideMimeType( options.mimeType ); - } - - // X-Requested-With header - // For cross-domain requests, seeing as conditions for a preflight are - // akin to a jigsaw puzzle, we simply never set it to be sure. - // (it can always be set on a per-request basis or even using ajaxSetup) - // For same-domain requests, won't change header if already provided. - if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { - headers[ "X-Requested-With" ] = "XMLHttpRequest"; - } - - // Set headers - for ( i in headers ) { - xhr.setRequestHeader( i, headers[ i ] ); - } - - // Callback - callback = function( type ) { - return function() { - if ( callback ) { - callback = errorCallback = xhr.onload = - xhr.onerror = xhr.onabort = xhr.ontimeout = - xhr.onreadystatechange = null; - - if ( type === "abort" ) { - xhr.abort(); - } else if ( type === "error" ) { - - // Support: IE <=9 only - // On a manual native abort, IE9 throws - // errors on any property access that is not readyState - if ( typeof xhr.status !== "number" ) { - complete( 0, "error" ); - } else { - complete( - - // File: protocol always yields status 0; see #8605, #14207 - xhr.status, - xhr.statusText - ); - } - } else { - complete( - xhrSuccessStatus[ xhr.status ] || xhr.status, - xhr.statusText, - - // Support: IE <=9 only - // IE9 has no XHR2 but throws on binary (trac-11426) - // For XHR2 non-text, let the caller handle it (gh-2498) - ( xhr.responseType || "text" ) !== "text" || - typeof xhr.responseText !== "string" ? - { binary: xhr.response } : - { text: xhr.responseText }, - xhr.getAllResponseHeaders() - ); - } - } - }; - }; - - // Listen to events - xhr.onload = callback(); - errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" ); - - // Support: IE 9 only - // Use onreadystatechange to replace onabort - // to handle uncaught aborts - if ( xhr.onabort !== undefined ) { - xhr.onabort = errorCallback; - } else { - xhr.onreadystatechange = function() { - - // Check readyState before timeout as it changes - if ( xhr.readyState === 4 ) { - - // Allow onerror to be called first, - // but that will not handle a native abort - // Also, save errorCallback to a variable - // as xhr.onerror cannot be accessed - window.setTimeout( function() { - if ( callback ) { - errorCallback(); - } - } ); - } - }; - } - - // Create the abort callback - callback = callback( "abort" ); - - try { - - // Do send the request (this may raise an exception) - xhr.send( options.hasContent && options.data || null ); - } catch ( e ) { - - // #14683: Only rethrow if this hasn't been notified as an error yet - if ( callback ) { - throw e; - } - } - }, - - abort: function() { - if ( callback ) { - callback(); - } - } - }; - } -} ); - - - - -// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432) -jQuery.ajaxPrefilter( function( s ) { - if ( s.crossDomain ) { - s.contents.script = false; - } -} ); - -// Install script dataType -jQuery.ajaxSetup( { - accepts: { - script: "text/javascript, application/javascript, " + - "application/ecmascript, application/x-ecmascript" - }, - contents: { - script: /\b(?:java|ecma)script\b/ - }, - converters: { - "text script": function( text ) { - jQuery.globalEval( text ); - return text; - } - } -} ); - -// Handle cache's special case and crossDomain -jQuery.ajaxPrefilter( "script", function( s ) { - if ( s.cache === undefined ) { - s.cache = false; - } - if ( s.crossDomain ) { - s.type = "GET"; - } -} ); - -// Bind script tag hack transport -jQuery.ajaxTransport( "script", function( s ) { - - // This transport only deals with cross domain or forced-by-attrs requests - if ( s.crossDomain || s.scriptAttrs ) { - var script, callback; - return { - send: function( _, complete ) { - script = jQuery( " -{% endmacro %} \ No newline at end of file diff --git a/lectures/_build/html/genindex.html b/lectures/_build/html/genindex.html deleted file mode 100644 index 592f39755..000000000 --- a/lectures/_build/html/genindex.html +++ /dev/null @@ -1,496 +0,0 @@ - - - - - - - - Index — Introductory Computational Economics and Finance - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- -
- -
- -
- -
- - - - - - -
- - -

Back to top

-
- -
- -
- -
- -
- -

Introductory Computational Economics and Finance

- -

- -
- -

Thomas J. Sargent & John Stachurski

- -
- - - - -
- -
- - -

Index

- -
- D - | M - | P - | S - -
-

D

- - - -
- -

M

- - -
- -

P

- - -
- -

S

- - -
- - - -
- -
- - - -
- -

- -

Creative Commons License – This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International.

- -
- -
- - - - - - -
- -
- -
- - - -
    -
    • -
    • -
    • -
    • -
    • -
    • -
    • -
- -
- -
- - - -
- - - \ No newline at end of file diff --git a/lectures/_build/html/geom_series.html b/lectures/_build/html/geom_series.html deleted file mode 100644 index 85a63c6ab..000000000 --- a/lectures/_build/html/geom_series.html +++ /dev/null @@ -1,1406 +0,0 @@ - - - - - - - - 1. Geometric Series for Elementary Economics — Introductory Computational Economics and Finance - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- -
- -
- -
- -
- - -
- On this page -
- - - - -
- - -

Back to top

-
- -
- -
- -
- -
- -

Introductory Computational Economics and Finance

- -

Geometric Series for Elementary Economics

- -
- -

Thomas J. Sargent & John Stachurski

- -
- - - - -
- -
- -
-

1. Geometric Series for Elementary Economics

- -
-

1.1. Overview

-

The lecture describes important ideas in economics that use the mathematics of geometric series.

-

Among these are

-
    -

  • the Keynesian multiplier

    • -

  • the money multiplier that prevails in fractional reserve banking -systems

    • -

  • interest rates and present values of streams of payouts from assets

    • -
-

(As we shall see below, the term multiplier comes down to meaning sum of a convergent geometric series)

-

These and other applications prove the truth of the wise crack that

-
-

“in economics, a little knowledge of geometric series goes a long way “

-
-

Below we’ll use the following imports:

-
-
-
%matplotlib inline
-import matplotlib.pyplot as plt
-plt.rcParams["figure.figsize"] = (11, 5)  #set default figure size
-import numpy as np
-import sympy as sym
-from sympy import init_printing, latex
-from matplotlib import cm
-from mpl_toolkits.mplot3d import Axes3D
-
-
-
-
-
-
-

1.2. Key Formulas

-

To start, let \(c\) be a real number that lies strictly between -\(-1\) and \(1\).

-
    -

  • We often write this as \(c \in (-1,1)\).

    • -

  • Here \((-1,1)\) denotes the collection of all real numbers that -are strictly less than \(1\) and strictly greater than \(-1\).

    • -

  • The symbol \(\in\) means in or belongs to the set after the symbol.

    • -
-

We want to evaluate geometric series of two types – infinite and finite.

-
-

1.2.1. Infinite Geometric Series

-

The first type of geometric that interests us is the infinite series

-
-\[ -1 + c + c^2 + c^3 + \cdots -\]
-

Where \(\cdots\) means that the series continues without end.

-

The key formula is

-
-(1.1)\[1 + c + c^2 + c^3 + \cdots = \frac{1}{1 -c }\]
-

To prove key formula (1.1), multiply both sides by \((1-c)\) and verify -that if \(c \in (-1,1)\), then the outcome is the -equation \(1 = 1\).

-
-
-

1.2.2. Finite Geometric Series

-

The second series that interests us is the finite geometric series

-
-\[ -1 + c + c^2 + c^3 + \cdots + c^T -\]
-

where \(T\) is a positive integer.

-

The key formula here is

-
-\[ -1 + c + c^2 + c^3 + \cdots + c^T = \frac{1 - c^{T+1}}{1-c} -\]
-

Remark: The above formula works for any value of the scalar -\(c\). We don’t have to restrict \(c\) to be in the -set \((-1,1)\).

-

We now move on to describe some famous economic applications of -geometric series.

-
-
-
-

1.3. Example: The Money Multiplier in Fractional Reserve Banking

-

In a fractional reserve banking system, banks hold only a fraction -\(r \in (0,1)\) of cash behind each deposit receipt that they -issue

-
    -

  • In recent times

    -
      -

    • cash consists of pieces of paper issued by the government and -called dollars or pounds or \(\ldots\)

      • -

    • a deposit is a balance in a checking or savings account that -entitles the owner to ask the bank for immediate payment in cash

      • -
    -
    • -

  • When the UK and France and the US were on either a gold or silver -standard (before 1914, for example)

    -
      -

    • cash was a gold or silver coin

      • -

    • a deposit receipt was a bank note that the bank promised to -convert into gold or silver on demand; (sometimes it was also a -checking or savings account balance)

      • -
    -
    • -
-

Economists and financiers often define the supply of money as an -economy-wide sum of cash plus deposits.

-

In a fractional reserve banking system (one in which the reserve -ratio \(r\) satisfies \(0 < r < 1\)), banks create money by issuing deposits backed by fractional reserves plus loans that they make to their customers.

-

A geometric series is a key tool for understanding how banks create -money (i.e., deposits) in a fractional reserve system.

-

The geometric series formula (1.1) is at the heart of the classic model of the money creation process – one that leads us to the celebrated -money multiplier.

-
-

1.3.1. A Simple Model

-

There is a set of banks named \(i = 0, 1, 2, \ldots\).

-

Bank \(i\)’s loans \(L_i\), deposits \(D_i\), and -reserves \(R_i\) must satisfy the balance sheet equation (because -balance sheets balance):

-
-(1.2)\[L_i + R_i = D_i\]
-

The left side of the above equation is the sum of the bank’s assets, -namely, the loans \(L_i\) it has outstanding plus its reserves of -cash \(R_i\).

-

The right side records bank \(i\)’s liabilities, -namely, the deposits \(D_i\) held by its depositors; these are -IOU’s from the bank to its depositors in the form of either checking -accounts or savings accounts (or before 1914, bank notes issued by a -bank stating promises to redeem note for gold or silver on demand).

-

Each bank \(i\) sets its reserves to satisfy the equation

-
-(1.3)\[R_i = r D_i\]
-

where \(r \in (0,1)\) is its reserve-deposit ratio or reserve -ratio for short

-
    -

  • the reserve ratio is either set by a government or chosen by banks -for precautionary reasons

    • -
-

Next we add a theory stating that bank \(i+1\)’s deposits depend -entirely on loans made by bank \(i\), namely

-
-(1.4)\[D_{i+1} = L_i\]
-

Thus, we can think of the banks as being arranged along a line with -loans from bank \(i\) being immediately deposited in \(i+1\)

-
    -

  • in this way, the debtors to bank \(i\) become creditors of -bank \(i+1\)

    • -
-

Finally, we add an initial condition about an exogenous level of bank -\(0\)’s deposits

-
-\[ -D_0 \ \text{ is given exogenously} -\]
-

We can think of \(D_0\) as being the amount of cash that a first -depositor put into the first bank in the system, bank number \(i=0\).

-

Now we do a little algebra.

-

Combining equations (1.2) and (1.3) tells us that

-
-(1.5)\[L_i = (1-r) D_i\]
-

This states that bank \(i\) loans a fraction \((1-r)\) of its -deposits and keeps a fraction \(r\) as cash reserves.

-

Combining equation (1.5) with equation (1.4) tells us that

-
-\[ -D_{i+1} = (1-r) D_i \ \text{ for } i \geq 0 -\]
-

which implies that

-
-(1.6)\[D_i = (1 - r)^i D_0 \ \text{ for } i \geq 0\]
-

Equation (1.6) expresses \(D_i\) as the \(i\) th term in the -product of \(D_0\) and the geometric series

-
-\[ -1, (1-r), (1-r)^2, \cdots -\]
-

Therefore, the sum of all deposits in our banking system -\(i=0, 1, 2, \ldots\) is

-
-(1.7)\[\sum_{i=0}^\infty (1-r)^i D_0 = \frac{D_0}{1 - (1-r)} = \frac{D_0}{r}\]
-
-
-

1.3.2. Money Multiplier

-

The money multiplier is a number that tells the multiplicative -factor by which an exogenous injection of cash into bank \(0\) leads -to an increase in the total deposits in the banking system.

-

Equation (1.7) asserts that the money multiplier is -\(\frac{1}{r}\)

-
    -

  • An initial deposit of cash of \(D_0\) in bank \(0\) leads -the banking system to create total deposits of \(\frac{D_0}{r}\).

    • -

  • The initial deposit \(D_0\) is held as reserves, distributed -throughout the banking system according to \(D_0 = \sum_{i=0}^\infty R_i\).

    • -
-
-
-
-

1.4. Example: The Keynesian Multiplier

-

The famous economist John Maynard Keynes and his followers created a -simple model intended to determine national income \(y\) in -circumstances in which

-
    -

  • there are substantial unemployed resources, in particular excess -supply of labor and capital

    • -

  • prices and interest rates fail to adjust to make aggregate supply -equal demand (e.g., prices and interest rates are frozen)

    • -

  • national income is entirely determined by aggregate demand

    • -
-
-

1.4.1. Static Version

-

An elementary Keynesian model of national income determination consists -of three equations that describe aggregate demand for \(y\) and its -components.

-

The first equation is a national income identity asserting that -consumption \(c\) plus investment \(i\) equals national income -\(y\):

-
-\[ -c+ i = y -\]
-

The second equation is a Keynesian consumption function asserting that -people consume a fraction \(b \in (0,1)\) of their income:

-
-\[ -c = b y -\]
-

The fraction \(b \in (0,1)\) is called the marginal propensity to -consume.

-

The fraction \(1-b \in (0,1)\) is called the marginal propensity -to save.

-

The third equation simply states that investment is exogenous at level -\(i\).

-
    -

  • exogenous means determined outside this model.

    • -
-

Substituting the second equation into the first gives \((1-b) y = i\).

-

Solving this equation for \(y\) gives

-
-\[ -y = \frac{1}{1-b} i -\]
-

The quantity \(\frac{1}{1-b}\) is called the investment -multiplier or simply the multiplier.

-

Applying the formula for the sum of an infinite geometric series, we can -write the above equation as

-
-\[ -y = i \sum_{t=0}^\infty b^t -\]
-

where \(t\) is a nonnegative integer.

-

So we arrive at the following equivalent expressions for the multiplier:

-
-\[ -\frac{1}{1-b} = \sum_{t=0}^\infty b^t -\]
-

The expression \(\sum_{t=0}^\infty b^t\) motivates an interpretation -of the multiplier as the outcome of a dynamic process that we describe -next.

-
-
-

1.4.2. Dynamic Version

-

We arrive at a dynamic version by interpreting the nonnegative integer -\(t\) as indexing time and changing our specification of the -consumption function to take time into account

-
    -

  • we add a one-period lag in how income affects consumption

    • -
-

We let \(c_t\) be consumption at time \(t\) and \(i_t\) be -investment at time \(t\).

-

We modify our consumption function to assume the form

-
-\[ -c_t = b y_{t-1} -\]
-

so that \(b\) is the marginal propensity to consume (now) out of -last period’s income.

-

We begin with an initial condition stating that

-
-\[ -y_{-1} = 0 -\]
-

We also assume that

-
-\[ -i_t = i \ \ \textrm {for all } t \geq 0 -\]
-

so that investment is constant over time.

-

It follows that

-
-\[ -y_0 = i + c_0 = i + b y_{-1} = i -\]
-

and

-
-\[ -y_1 = c_1 + i = b y_0 + i = (1 + b) i -\]
-

and

-
-\[ -y_2 = c_2 + i = b y_1 + i = (1 + b + b^2) i -\]
-

and more generally

-
-\[ -y_t = b y_{t-1} + i = (1+ b + b^2 + \cdots + b^t) i -\]
-

or

-
-\[ -y_t = \frac{1-b^{t+1}}{1 -b } i -\]
-

Evidently, as \(t \rightarrow + \infty\),

-
-\[ -y_t \rightarrow \frac{1}{1-b} i -\]
-

Remark 1: The above formula is often applied to assert that an -exogenous increase in investment of \(\Delta i\) at time \(0\) -ignites a dynamic process of increases in national income by successive amounts

-
-\[ -\Delta i, (1 + b )\Delta i, (1+b + b^2) \Delta i , \cdots -\]
-

at times \(0, 1, 2, \ldots\).

-

Remark 2 Let \(g_t\) be an exogenous sequence of government -expenditures.

-

If we generalize the model so that the national income identity -becomes

-
-\[ -c_t + i_t + g_t = y_t -\]
-

then a version of the preceding argument shows that the government -expenditures multiplier is also \(\frac{1}{1-b}\), so that a -permanent increase in government expenditures ultimately leads to an -increase in national income equal to the multiplier times the increase -in government expenditures.

-
-
-
-

1.5. Example: Interest Rates and Present Values

-

We can apply our formula for geometric series to study how interest -rates affect values of streams of dollar payments that extend over time.

-

We work in discrete time and assume that \(t = 0, 1, 2, \ldots\) -indexes time.

-

We let \(r \in (0,1)\) be a one-period net nominal interest rate

-
    -

  • if the nominal interest rate is \(5\) percent, -then \(r= .05\)

    • -
-

A one-period gross nominal interest rate \(R\) is defined as

-
-\[ -R = 1 + r \in (1, 2) -\]
-
    -

  • if \(r=.05\), then \(R = 1.05\)

    • -
-

Remark: The gross nominal interest rate \(R\) is an exchange -rate or relative price of dollars at between times \(t\) and -\(t+1\). The units of \(R\) are dollars at time \(t+1\) per -dollar at time \(t\).

-

When people borrow and lend, they trade dollars now for dollars later or -dollars later for dollars now.

-

The price at which these exchanges occur is the gross nominal interest -rate.

-
    -

  • If I sell \(x\) dollars to you today, you pay me \(R x\) -dollars tomorrow.

    • -

  • This means that you borrowed \(x\) dollars for me at a gross -interest rate \(R\) and a net interest rate \(r\).

    • -
-

We assume that the net nominal interest rate \(r\) is fixed over -time, so that \(R\) is the gross nominal interest rate at times -\(t=0, 1, 2, \ldots\).

-

Two important geometric sequences are

-
-(1.8)\[1, R, R^2, \cdots\]
-

and

-
-(1.9)\[1, R^{-1}, R^{-2}, \cdots\]
-

Sequence (1.8) tells us how dollar values of an investment accumulate -through time.

-

Sequence (1.9) tells us how to discount future dollars to get their -values in terms of today’s dollars.

-
-

1.5.1. Accumulation

-

Geometric sequence (1.8) tells us how one dollar invested and re-invested -in a project with gross one period nominal rate of return accumulates

-
    -

  • here we assume that net interest payments are reinvested in the -project

    • -

  • thus, \(1\) dollar invested at time \(0\) pays interest -\(r\) dollars after one period, so we have \(r+1 = R\) -dollars at time\(1\)

    • -

  • at time \(1\) we reinvest \(1+r =R\) dollars and receive interest -of \(r R\) dollars at time \(2\) plus the principal -\(R\) dollars, so we receive \(r R + R = (1+r)R = R^2\) -dollars at the end of period \(2\)

    • -

  • and so on

    • -
-

Evidently, if we invest \(x\) dollars at time \(0\) and -reinvest the proceeds, then the sequence

-
-\[ -x , xR , x R^2, \cdots -\]
-

tells how our account accumulates at dates \(t=0, 1, 2, \ldots\).

-
-
-

1.5.2. Discounting

-

Geometric sequence (1.9) tells us how much future dollars are worth in terms of today’s dollars.

-

Remember that the units of \(R\) are dollars at \(t+1\) per -dollar at \(t\).

-

It follows that

-
    -

  • the units of \(R^{-1}\) are dollars at \(t\) per dollar at \(t+1\)

    • -

  • the units of \(R^{-2}\) are dollars at \(t\) per dollar at \(t+2\)

    • -

  • and so on; the units of \(R^{-j}\) are dollars at \(t\) per -dollar at \(t+j\)

    • -
-

So if someone has a claim on \(x\) dollars at time \(t+j\), it -is worth \(x R^{-j}\) dollars at time \(t\) (e.g., today).

-
-
-

1.5.3. Application to Asset Pricing

-

A lease requires a payments stream of \(x_t\) dollars at -times \(t = 0, 1, 2, \ldots\) where

-
-\[ -x_t = G^t x_0 -\]
-

where \(G = (1+g)\) and \(g \in (0,1)\).

-

Thus, lease payments increase at \(g\) percent per period.

-

For a reason soon to be revealed, we assume that \(G < R\).

-

The present value of the lease is

-
-\[\begin{split} -\begin{aligned} p_0 & = x_0 + x_1/R + x_2/(R^2) + \ddots \\ - & = x_0 (1 + G R^{-1} + G^2 R^{-2} + \cdots ) \\ - & = x_0 \frac{1}{1 - G R^{-1}} \end{aligned} -\end{split}\]
-

where the last line uses the formula for an infinite geometric series.

-

Recall that \(R = 1+r\) and \(G = 1+g\) and that \(R > G\) -and \(r > g\) and that \(r\) and \(g\) are typically small -numbers, e.g., .05 or .03.

-

Use the Taylor series of \(\frac{1}{1+r}\) about \(r=0\), -namely,

-
-\[ -\frac{1}{1+r} = 1 - r + r^2 - r^3 + \cdots -\]
-

and the fact that \(r\) is small to approximate -\(\frac{1}{1+r} \approx 1 - r\).

-

Use this approximation to write \(p_0\) as

-
-\[\begin{split} -\begin{aligned} - p_0 &= x_0 \frac{1}{1 - G R^{-1}} \\ - &= x_0 \frac{1}{1 - (1+g) (1-r) } \\ - &= x_0 \frac{1}{1 - (1+g - r - rg)} \\ - & \approx x_0 \frac{1}{r -g } -\end{aligned} -\end{split}\]
-

where the last step uses the approximation \(r g \approx 0\).

-

The approximation

-
-\[ -p_0 = \frac{x_0 }{r -g } -\]
-

is known as the Gordon formula for the present value or current -price of an infinite payment stream \(x_0 G^t\) when the nominal -one-period interest rate is \(r\) and when \(r > g\).

-

We can also extend the asset pricing formula so that it applies to finite leases.

-

Let the payment stream on the lease now be \(x_t\) for \(t= 1,2, \dots,T\), where again

-
-\[ -x_t = G^t x_0 -\]
-

The present value of this lease is:

-
-\[\begin{split} -\begin{aligned} \begin{split}p_0&=x_0 + x_1/R + \dots +x_T/R^T \\ &= x_0(1+GR^{-1}+\dots +G^{T}R^{-T}) \\ &= \frac{x_0(1-G^{T+1}R^{-(T+1)})}{1-GR^{-1}} \end{split}\end{aligned} -\end{split}\]
-

Applying the Taylor series to \(R^{-(T+1)}\) about \(r=0\) we get:

-
-\[ -\frac{1}{(1+r)^{T+1}}= 1-r(T+1)+\frac{1}{2}r^2(T+1)(T+2)+\dots \approx 1-r(T+1) -\]
-

Similarly, applying the Taylor series to \(G^{T+1}\) about \(g=0\):

-
-\[ -(1+g)^{T+1} = 1+(T+1)g+\frac{T(T+1)}{2!}g^2+\frac{(T-1)T(T+1)}{3!}g^3+\dots \approx 1+ (T+1)g -\]
-

Thus, we get the following approximation:

-
-\[ -p_0 =\frac{x_0(1-(1+(T+1)g)(1-r(T+1)))}{1-(1-r)(1+g) } -\]
-

Expanding:

-
-\[\begin{split} -\begin{aligned} p_0 &=\frac{x_0(1-1+(T+1)^2 rg -r(T+1)+g(T+1))}{1-1+r-g+rg} \\&=\frac{x_0(T+1)((T+1)rg+r-g)}{r-g+rg} \\ &\approx \frac{x_0(T+1)(r-g)}{r-g}+\frac{x_0rg(T+1)}{r-g}\\ &= x_0(T+1) + \frac{x_0rg(T+1)}{r-g} \end{aligned} -\end{split}\]
-

We could have also approximated by removing the second term -\(rgx_0(T+1)\) when \(T\) is relatively small compared to -\(1/(rg)\) to get \(x_0(T+1)\) as in the finite stream -approximation.

-

We will plot the true finite stream present-value and the two -approximations, under different values of \(T\), and \(g\) and \(r\) in Python.

-

First we plot the true finite stream present-value after computing it -below

-
-
-
# True present value of a finite lease
-def finite_lease_pv_true(T, g, r, x_0):
-    G = (1 + g)
-    R = (1 + r)
-    return (x_0 * (1 - G**(T + 1) * R**(-T - 1))) / (1 - G * R**(-1))
-# First approximation for our finite lease
-
-def finite_lease_pv_approx_1(T, g, r, x_0):
-    p = x_0 * (T + 1) + x_0 * r * g * (T + 1) / (r - g)
-    return p
-
-# Second approximation for our finite lease
-def finite_lease_pv_approx_2(T, g, r, x_0):
-    return (x_0 * (T + 1))
-
-# Infinite lease
-def infinite_lease(g, r, x_0):
-    G = (1 + g)
-    R = (1 + r)
-    return x_0 / (1 - G * R**(-1))
-
-
-
-
-

Now that we have defined our functions, we can plot some outcomes.

-

First we study the quality of our approximations

-
-
-
def plot_function(axes, x_vals, func, args):
-    axes.plot(x_vals, func(*args), label=func.__name__)
-
-T_max = 50
-
-T = np.arange(0, T_max+1)
-g = 0.02
-r = 0.03
-x_0 = 1
-
-our_args = (T, g, r, x_0)
-funcs = [finite_lease_pv_true,
-        finite_lease_pv_approx_1,
-        finite_lease_pv_approx_2]
-        ## the three functions we want to compare
-
-fig, ax = plt.subplots()
-ax.set_title('Finite Lease Present Value $T$ Periods Ahead')
-for f in funcs:
-    plot_function(ax, T, f, our_args)
-ax.legend()
-ax.set_xlabel('$T$ Periods Ahead')
-ax.set_ylabel('Present Value, $p_0$')
-plt.show()
-
-
-
-
-_images/geom_series_5_0.png -
-
-

Evidently our approximations perform well for small values of \(T\).

-

However, holding \(g\) and r fixed, our approximations deteriorate as \(T\) increases.

-

Next we compare the infinite and finite duration lease present values -over different lease lengths \(T\).

-
-
-
# Convergence of infinite and finite
-T_max = 1000
-T = np.arange(0, T_max+1)
-fig, ax = plt.subplots()
-ax.set_title('Infinite and Finite Lease Present Value $T$ Periods Ahead')
-f_1 = finite_lease_pv_true(T, g, r, x_0)
-f_2 = np.full(T_max+1, infinite_lease(g, r, x_0))
-ax.plot(T, f_1, label='T-period lease PV')
-ax.plot(T, f_2, '--', label='Infinite lease PV')
-ax.set_xlabel('$T$ Periods Ahead')
-ax.set_ylabel('Present Value, $p_0$')
-ax.legend()
-plt.show()
-
-
-
-
-_images/geom_series_7_0.png -
-
-

The graph above shows how as duration \(T \rightarrow +\infty\), -the value of a lease of duration \(T\) approaches the value of a -perpetual lease.

-

Now we consider two different views of what happens as \(r\) and -\(g\) covary

-
-
-
# First view
-# Changing r and g
-fig, ax = plt.subplots()
-ax.set_title('Value of lease of length $T$')
-ax.set_ylabel('Present Value, $p_0$')
-ax.set_xlabel('$T$ periods ahead')
-T_max = 10
-T=np.arange(0, T_max+1)
-
-rs, gs = (0.9, 0.5, 0.4001, 0.4), (0.4, 0.4, 0.4, 0.5),
-comparisons = ('$\gg$', '$>$', r'$\approx$', '$<$')
-for r, g, comp in zip(rs, gs, comparisons):
-    ax.plot(finite_lease_pv_true(T, g, r, x_0), label=f'r(={r}) {comp} g(={g})')
-
-ax.legend()
-plt.show()
-
-
-
-
-_images/geom_series_9_0.png -
-
-

This graph gives a big hint for why the condition \(r > g\) is -necessary if a lease of length \(T = +\infty\) is to have finite -value.

-

For fans of 3-d graphs the same point comes through in the following -graph.

-

If you aren’t enamored of 3-d graphs, feel free to skip the next -visualization!

-
-
-
# Second view
-fig = plt.figure()
-T = 3
-ax = plt.subplot(projection='3d')
-r = np.arange(0.01, 0.99, 0.005)
-g = np.arange(0.011, 0.991, 0.005)
-
-rr, gg = np.meshgrid(r, g)
-z = finite_lease_pv_true(T, gg, rr, x_0)
-
-# Removes points where undefined
-same = (rr == gg)
-z[same] = np.nan
-surf = ax.plot_surface(rr, gg, z, cmap=cm.coolwarm,
-    antialiased=True, clim=(0, 15))
-fig.colorbar(surf, shrink=0.5, aspect=5)
-ax.set_xlabel('$r$')
-ax.set_ylabel('$g$')
-ax.set_zlabel('Present Value, $p_0$')
-ax.view_init(20, 10)
-ax.set_title('Three Period Lease PV with Varying $g$ and $r$')
-plt.show()
-
-
-
-
-_images/geom_series_11_0.png -
-
-

We can use a little calculus to study how the present value \(p_0\) -of a lease varies with \(r\) and \(g\).

-

We will use a library called SymPy.

-

SymPy enables us to do symbolic math calculations including -computing derivatives of algebraic equations.

-

We will illustrate how it works by creating a symbolic expression that -represents our present value formula for an infinite lease.

-

After that, we’ll use SymPy to compute derivatives

-
-
-
# Creates algebraic symbols that can be used in an algebraic expression
-g, r, x0 = sym.symbols('g, r, x0')
-G = (1 + g)
-R = (1 + r)
-p0 = x0 / (1 - G * R**(-1))
-init_printing(use_latex='mathjax')
-print('Our formula is:')
-p0
-
-
-
-
-
Our formula is:
-
-
-
-\[\displaystyle \frac{x_{0}}{- \frac{g + 1}{r + 1} + 1}\]
-
-
-
-
-
print('dp0 / dg is:')
-dp_dg = sym.diff(p0, g)
-dp_dg
-
-
-
-
-
dp0 / dg is:
-
-
-
-\[\displaystyle \frac{x_{0}}{\left(r + 1\right) \left(- \frac{g + 1}{r + 1} + 1\right)^{2}}\]
-
-
-
-
-
print('dp0 / dr is:')
-dp_dr = sym.diff(p0, r)
-dp_dr
-
-
-
-
-
dp0 / dr is:
-
-
-
-\[\displaystyle - \frac{x_{0} \left(g + 1\right)}{\left(r + 1\right)^{2} \left(- \frac{g + 1}{r + 1} + 1\right)^{2}}\]
-
-
-

We can see that for \(\frac{\partial p_0}{\partial r}<0\) as long as -\(r>g\), \(r>0\) and \(g>0\) and \(x_0\) is positive, -so \(\frac{\partial p_0}{\partial r}\) will always be negative.

-

Similarly, \(\frac{\partial p_0}{\partial g}>0\) as long as \(r>g\), \(r>0\) and \(g>0\) and \(x_0\) is positive, so \(\frac{\partial p_0}{\partial g}\) -will always be positive.

-
-
-
-

1.6. Back to the Keynesian Multiplier

-

We will now go back to the case of the Keynesian multiplier and plot the -time path of \(y_t\), given that consumption is a constant fraction -of national income, and investment is fixed.

-
-
-
# Function that calculates a path of y
-def calculate_y(i, b, g, T, y_init):
-    y = np.zeros(T+1)
-    y[0] = i + b * y_init + g
-    for t in range(1, T+1):
-        y[t] = b * y[t-1] + i + g
-    return y
-
-# Initial values
-i_0 = 0.3
-g_0 = 0.3
-# 2/3 of income goes towards consumption
-b = 2/3
-y_init = 0
-T = 100
-
-fig, ax = plt.subplots()
-ax.set_title('Path of Aggregate Output Over Time')
-ax.set_xlabel('$t$')
-ax.set_ylabel('$y_t$')
-ax.plot(np.arange(0, T+1), calculate_y(i_0, b, g_0, T, y_init))
-# Output predicted by geometric series
-ax.hlines(i_0 / (1 - b) + g_0 / (1 - b), xmin=-1, xmax=101, linestyles='--')
-plt.show()
-
-
-
-
-_images/geom_series_17_0.png -
-
-

In this model, income grows over time, until it gradually converges to -the infinite geometric series sum of income.

-

We now examine what will -happen if we vary the so-called marginal propensity to consume, -i.e., the fraction of income that is consumed

-
-
-
bs = (1/3, 2/3, 5/6, 0.9)
-
-fig,ax = plt.subplots()
-ax.set_title('Changing Consumption as a Fraction of Income')
-ax.set_ylabel('$y_t$')
-ax.set_xlabel('$t$')
-x = np.arange(0, T+1)
-for b in bs:
-    y = calculate_y(i_0, b, g_0, T, y_init)
-    ax.plot(x, y, label=r'$b=$'+f"{b:.2f}")
-ax.legend()
-plt.show()
-
-
-
-
-_images/geom_series_19_0.png -
-
-

Increasing the marginal propensity to consume \(b\) increases the -path of output over time.

-

Now we will compare the effects on output of increases in investment and government spending.

-
-
-
fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 10))
-fig.subplots_adjust(hspace=0.3)
-
-x = np.arange(0, T+1)
-values = [0.3, 0.4]
-
-for i in values:
-    y = calculate_y(i, b, g_0, T, y_init)
-    ax1.plot(x, y, label=f"i={i}")
-for g in values:
-    y = calculate_y(i_0, b, g, T, y_init)
-    ax2.plot(x, y, label=f"g={g}")
-
-axes = ax1, ax2
-param_labels = "Investment", "Government Spending"
-for ax, param in zip(axes, param_labels):
-    ax.set_title(f'An Increase in {param} on Output')
-    ax.legend(loc ="lower right")
-    ax.set_ylabel('$y_t$')
-    ax.set_xlabel('$t$')
-plt.show()
-
-
-
-
-_images/geom_series_21_0.png -
-
-

Notice here, whether government spending increases from 0.3 to 0.4 or -investment increases from 0.3 to 0.4, the shifts in the graphs are -identical.

-
-
- - - - -
- -
- - - -
- -

- -

Creative Commons License – This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International.

- -
- -
- - - - - - -
- -
- -
- - - -
    -
    • -
    • -
    • -
    • -
    • -
    • -
    • -
- -
- -
- - - -
- - - \ No newline at end of file diff --git a/lectures/_build/html/index.html b/lectures/_build/html/index.html deleted file mode 100644 index 3157386d7..000000000 --- a/lectures/_build/html/index.html +++ /dev/null @@ -1 +0,0 @@ - diff --git a/lectures/_build/html/index_toc.html b/lectures/_build/html/index_toc.html deleted file mode 100644 index 0453403b1..000000000 --- a/lectures/_build/html/index_toc.html +++ /dev/null @@ -1,15 +0,0 @@ - - - - - - - -

You should have been redirected.

- If not, click here to continue. - - diff --git a/lectures/_build/html/intro.html b/lectures/_build/html/intro.html deleted file mode 100644 index 3f45cd5c9..000000000 --- a/lectures/_build/html/intro.html +++ /dev/null @@ -1,488 +0,0 @@ - - - - - - - - Python Programming for Economics and Finance — Introductory Computational Economics and Finance - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- -
- -
- -
- -
- - - - - - -
- - -

Back to top

-
- -
- -
- -
- -
- -

Introductory Computational Economics and Finance

- -

Python Programming for Economics and Finance

- -
- -

Thomas J. Sargent & John Stachurski

- -
- - - - -
- -
- -
-

Python Programming for Economics and Finance

-

This website presents a set of lectures on Python programming for economics and finance, designed and written by -Thomas J. Sargent and John Stachurski. This is the first text in the series, which focuses on programming in Python.

-

For an overview of the series, see this page

-
-

Tools & Techniques

- -
-
-

Models

- -
-
-

Other

- -
-
- - - - -
- -
- - - -
- -

- -

Creative Commons License – This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International.

- -
- -
- - - - - - -
- -
- -
- - - -
    -
    • -
    • -
    • -
    • -
    • -
    • -
    • -
- -
- -
- - - -
- - - \ No newline at end of file diff --git a/lectures/_build/html/objects.inv b/lectures/_build/html/objects.inv deleted file mode 100644 index 1236fa388..000000000 Binary files a/lectures/_build/html/objects.inv and /dev/null differ diff --git a/lectures/_build/html/scalar_dynam.html b/lectures/_build/html/scalar_dynam.html deleted file mode 100644 index bed6697f1..000000000 --- a/lectures/_build/html/scalar_dynam.html +++ /dev/null @@ -1,1063 +0,0 @@ - - - - - - - - 3. Dynamics in One Dimension — Introductory Computational Economics and Finance - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- -
- -
- -
- -
- - -
- On this page -
- - - - -
- - -

Back to top

-
- -
- -
- -
- -
- -

Introductory Computational Economics and Finance

- -

Dynamics in One Dimension

- -
- -

Thomas J. Sargent & John Stachurski

- -
- - - - -
- -
- -
-

3. Dynamics in One Dimension

- -
-

3.1. Overview

-

In this lecture we give a quick introduction to discrete time dynamics in one -dimension.

-

In one-dimensional models, the state of the system is described by a single variable.

-

Although most interesting dynamic models have two or more state variables, the -one-dimensional setting is a good place to learn the foundations of dynamics and build -intuition.

-

Let’s start with some standard imports:

-
-
-
%matplotlib inline
-import matplotlib.pyplot as plt
-plt.rcParams["figure.figsize"] = (11, 5)  #set default figure size
-import numpy as np
-
-
-
-
-
-
-

3.2. Some Definitions

-

This section sets out the objects of interest and the kinds of properties we study.

-
-

3.2.1. Difference Equations

-

A time homogeneous first order difference equation is an equation of the -form

-
-(3.1)\[x_{t+1} = g(x_t)\]
-

where \(g\) is a function from some subset \(S\) of \(\mathbb R\) to itself.

-

Here \(S\) is called the state space and \(x\) is called the state variable.

-

In the definition,

-
    -

  • time homogeneity means that \(g\) is the same at each time \(t\)

    • -

  • first order means dependence on only one lag (i.e., earlier states such as \(x_{t-1}\) do not enter into (3.1)).

    • -
-

If \(x_0 \in S\) is given, then (3.1) recursively defines the sequence

-
-(3.2)\[x_0, \quad -x_1 = g(x_0), \quad -x_2 = g(x_1) = g(g(x_0)), \quad \text{etc.}\]
-

This sequence is called the trajectory of \(x_0\) under \(g\).

-

If we define \(g^n\) to be \(n\) compositions of \(g\) with itself, then we can write the trajectory more simply as \(x_t = g^t(x_0)\) for \(t \geq 0\).

-
-
-

3.2.2. Example: A Linear Model

-

One simple example is the linear difference equation

-
-\[ -x_{t+1} = a x_t + b, \qquad S = \mathbb R -\]
-

where \(a, b\) are fixed constants.

-

In this case, given \(x_0\), the trajectory (3.2) is

-
-(3.3)\[x_0, \quad -a x_0 + b, \quad -a^2 x_0 + a b + b, \quad \text{etc.}\]
-

Continuing in this way, and using our knowledge of geometric series, we find that, for any \(t \geq 0\),

-
-(3.4)\[x_t = a^t x_0 + b \frac{1 - a^t}{1 - a}\]
-

This is about all we need to know about the linear model.

-

We have an exact expression for \(x_t\) for all \(t\) and hence a full -understanding of the dynamics.

-

Notice in particular that \(|a| < 1\), then, by (3.4), we have

-
-(3.5)\[x_t \to \frac{b}{1 - a} \text{ as } t \to \infty\]
-

regardless of \(x_0\)

-

This is an example of what is called global stability, a topic we return to -below.

-
-
-

3.2.3. Example: A Nonlinear Model

-

In the linear example above, we obtained an exact analytical expression for \(x_t\) -in terms of arbitrary \(t\) and \(x_0\).

-

This made analysis of dynamics very easy.

-

When models are nonlinear, however, the situation can be quite different.

-

For example, recall how we previously studied the law of motion for the Solow growth model, a simplified version of which is

-
-(3.6)\[k_{t+1} = s z k_t^{\alpha} + (1 - \delta) k_t\]
-

Here \(k\) is capital stock and \(s, z, \alpha, \delta\) are positive -parameters with \(0 < \alpha, \delta < 1\).

-

If you try to iterate like we did in (3.3), you will find that -the algebra gets messy quickly.

-

Analyzing the dynamics of this model requires a different method (see below).

-
-
-

3.2.4. Stability

-

A steady state of the difference equation \(x_{t+1} = g(x_t)\) is a -point \(x^*\) in \(S\) such that \(x^* = g(x^*)\).

-

In other words, \(x^*\) is a fixed point of the function \(g\) in -\(S\).

-

For example, for the linear model \(x_{t+1} = a x_t + b\), you can use the -definition to check that

-
    -

  • \(x^* := b/(1-a)\) is a steady state whenever \(a \not= 1\).

    • -

  • if \(a = 1\) and \(b=0\), then every \(x \in \mathbb R\) is a -steady state.

    • -

  • if \(a = 1\) and \(b \not= 0\), then the linear model has no steady -state in \(\mathbb R\).

    • -
-

A steady state \(x^*\) of \(x_{t+1} = g(x_t)\) is called -globally stable if, for all \(x_0 \in S\),

-
-\[ -x_t = g^t(x_0) \to x^* \text{ as } t \to \infty -\]
-

For example, in the linear model \(x_{t+1} = a x_t + b\) with \(a -\not= 1\), the steady state \(x^*\)

-
    -

  • is globally stable if \(|a| < 1\) and

    • -

  • fails to be globally stable otherwise.

    • -
-

This follows directly from (3.4).

-

A steady state \(x^*\) of \(x_{t+1} = g(x_t)\) is called -locally stable if there exists an \(\epsilon > 0\) such that

-
-\[ -| x_0 - x^* | < \epsilon -\; \implies \; -x_t = g^t(x_0) \to x^* \text{ as } t \to \infty -\]
-

Obviously every globally stable steady state is also locally stable.

-

We will see examples below where the converse is not true.

-
-
-
-

3.3. Graphical Analysis

-

As we saw above, analyzing the dynamics for nonlinear models is nontrivial.

-

There is no single way to tackle all nonlinear models.

-

However, there is one technique for one-dimensional models that provides a -great deal of intuition.

-

This is a graphical approach based on 45 degree diagrams.

-

Let’s look at an example: the Solow model with dynamics given in (3.6).

-

We begin with some plotting code that you can ignore at first reading.

-

The function of the code is to produce 45 degree diagrams and time series -plots.

-
-
-
def subplots(fs):
-    "Custom subplots with axes throught the origin"
-    fig, ax = plt.subplots(figsize=fs)
-
-    # Set the axes through the origin
-    for spine in ['left', 'bottom']:
-        ax.spines[spine].set_position('zero')
-        ax.spines[spine].set_color('green')
-    for spine in ['right', 'top']:
-        ax.spines[spine].set_color('none')
-
-    return fig, ax
-
-
-def plot45(g, xmin, xmax, x0, num_arrows=6, var='x'):
-
-    xgrid = np.linspace(xmin, xmax, 200)
-
-    fig, ax = subplots((6.5, 6))
-    ax.set_xlim(xmin, xmax)
-    ax.set_ylim(xmin, xmax)
-
-    hw = (xmax - xmin) * 0.01
-    hl = 2 * hw
-    arrow_args = dict(fc="k", ec="k", head_width=hw,
-            length_includes_head=True, lw=1,
-            alpha=0.6, head_length=hl)
-
-    ax.plot(xgrid, g(xgrid), 'b-', lw=2, alpha=0.6, label='g')
-    ax.plot(xgrid, xgrid, 'k-', lw=1, alpha=0.7, label='45')
-
-    x = x0
-    xticks = [xmin]
-    xtick_labels = [xmin]
-
-    for i in range(num_arrows):
-        if i == 0:
-            ax.arrow(x, 0.0, 0.0, g(x), **arrow_args) # x, y, dx, dy
-        else:
-            ax.arrow(x, x, 0.0, g(x) - x, **arrow_args)
-            ax.plot((x, x), (0, x), 'k', ls='dotted')
-
-        ax.arrow(x, g(x), g(x) - x, 0, **arrow_args)
-        xticks.append(x)
-        xtick_labels.append(r'${}_{}$'.format(var, str(i)))
-
-        x = g(x)
-        xticks.append(x)
-        xtick_labels.append(r'${}_{}$'.format(var, str(i+1)))
-        ax.plot((x, x), (0, x), 'k-', ls='dotted')
-
-    xticks.append(xmax)
-    xtick_labels.append(xmax)
-    ax.set_xticks(xticks)
-    ax.set_yticks(xticks)
-    ax.set_xticklabels(xtick_labels)
-    ax.set_yticklabels(xtick_labels)
-
-    bbox = (0., 1.04, 1., .104)
-    legend_args = {'bbox_to_anchor': bbox, 'loc': 'upper right'}
-
-    ax.legend(ncol=2, frameon=False, **legend_args, fontsize=14)
-    plt.show()
-
-def ts_plot(g, xmin, xmax, x0, ts_length=6, var='x'):
-    fig, ax = subplots((7, 5.5))
-    ax.set_ylim(xmin, xmax)
-    ax.set_xlabel(r'$t$', fontsize=14)
-    ax.set_ylabel(r'${}_t$'.format(var), fontsize=14)
-    x = np.empty(ts_length)
-    x[0] = x0
-    for t in range(ts_length-1):
-        x[t+1] = g(x[t])
-    ax.plot(range(ts_length),
-            x,
-            'bo-',
-            alpha=0.6,
-            lw=2,
-            label=r'${}_t$'.format(var))
-    ax.legend(loc='best', fontsize=14)
-    ax.set_xticks(range(ts_length))
-    plt.show()
-
-
-
-
-

Let’s create a 45 degree diagram for the Solow model with a fixed set of -parameters

-
-
-
A, s, alpha, delta = 2, 0.3, 0.3, 0.4
-
-
-
-
-

Here’s the update function corresponding to the model.

-
-
-
def g(k):
-    return A * s * k**alpha + (1 - delta) * k
-
-
-
-
-

Here is the 45 degree plot.

-
-
-
xmin, xmax = 0, 4  # Suitable plotting region.
-
-plot45(g, xmin, xmax, 0, num_arrows=0)
-
-
-
-
-_images/scalar_dynam_9_0.png -
-
-

The plot shows the function \(g\) and the 45 degree line.

-

Think of \(k_t\) as a value on the horizontal axis.

-

To calculate \(k_{t+1}\), we can use the graph of \(g\) to see its -value on the vertical axis.

-

Clearly,

-
    -

  • If \(g\) lies above the 45 degree line at this point, then we have \(k_{t+1} > k_t\).

    • -

  • If \(g\) lies below the 45 degree line at this point, then we have \(k_{t+1} < k_t\).

    • -

  • If \(g\) hits the 45 degree line at this point, then we have \(k_{t+1} = k_t\), so \(k_t\) is a steady state.

    • -
-

For the Solow model, there are two steady states when \(S = \mathbb R_+ = -[0, \infty)\).

-
    -

  • the origin \(k=0\)

    • -

  • the unique positive number such that \(k = s z k^{\alpha} + (1 - \delta) k\).

    • -
-

By using some algebra, we can show that in the second case, the steady state is

-
-\[ -k^* = \left( \frac{sz}{\delta} \right)^{1/(1-\alpha)} -\]
-
-

3.3.1. Trajectories

-

By the preceding discussion, in regions where \(g\) lies above the 45 degree line, we know that the trajectory is increasing.

-

The next figure traces out a trajectory in such a region so we can see this more clearly.

-

The initial condition is \(k_0 = 0.25\).

-
-
-
k0 = 0.25
-
-plot45(g, xmin, xmax, k0, num_arrows=5, var='k')
-
-
-
-
-
/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string "k-" (-> linestyle='-'). The keyword argument will take precedence.
-  ax.plot((x, x), (0, x), 'k-', ls='dotted')
-
-
-_images/scalar_dynam_11_1.png -
-
-

We can plot the time series of capital corresponding to the figure above as -follows:

-
-
-
ts_plot(g, xmin, xmax, k0, var='k')
-
-
-
-
-_images/scalar_dynam_13_0.png -
-
-

Here’s a somewhat longer view:

-
-
-
ts_plot(g, xmin, xmax, k0, ts_length=20, var='k')
-
-
-
-
-_images/scalar_dynam_15_0.png -
-
-

When capital stock is higher than the unique positive steady state, we see that -it declines:

-
-
-
k0 = 2.95
-
-plot45(g, xmin, xmax, k0, num_arrows=5, var='k')
-
-
-
-
-
/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string "k-" (-> linestyle='-'). The keyword argument will take precedence.
-  ax.plot((x, x), (0, x), 'k-', ls='dotted')
-
-
-_images/scalar_dynam_17_1.png -
-
-

Here is the time series:

-
-
-
ts_plot(g, xmin, xmax, k0, var='k')
-
-
-
-
-_images/scalar_dynam_19_0.png -
-
-
-
-

3.3.2. Complex Dynamics

-

The Solow model is nonlinear but still generates very regular dynamics.

-

One model that generates irregular dynamics is the quadratic map

-
-\[ -g(x) = 4 x (1 - x), -\qquad x \in [0, 1] -\]
-

Let’s have a look at the 45 degree diagram.

-
-
-
xmin, xmax = 0, 1
-g = lambda x: 4 * x * (1 - x)
-
-x0 = 0.3
-plot45(g, xmin, xmax, x0, num_arrows=0)
-
-
-
-
-_images/scalar_dynam_21_0.png -
-
-

Now let’s look at a typical trajectory.

-
-
-
plot45(g, xmin, xmax, x0, num_arrows=6)
-
-
-
-
-
/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string "k-" (-> linestyle='-'). The keyword argument will take precedence.
-  ax.plot((x, x), (0, x), 'k-', ls='dotted')
-
-
-_images/scalar_dynam_23_1.png -
-
-

Notice how irregular it is.

-

Here is the corresponding time series plot.

-
-
-
ts_plot(g, xmin, xmax, x0, ts_length=6)
-
-
-
-
-_images/scalar_dynam_25_0.png -
-
-

The irregularity is even clearer over a longer time horizon:

-
-
-
ts_plot(g, xmin, xmax, x0, ts_length=20)
-
-
-
-
-_images/scalar_dynam_27_0.png -
-
-
-
-
-

3.4. Exercises

-
- -

Exercise 3.1

-
-

Consider again the linear model \(x_{t+1} = a x_t + b\) with \(a -\not=1\).

-

The unique steady state is \(b / (1 - a)\).

-

The steady state is globally stable if \(|a| < 1\).

-

Try to illustrate this graphically by looking at a range of initial conditions.

-

What differences do you notice in the cases \(a \in (-1, 0)\) and \(a -\in (0, 1)\)?

-

Use \(a=0.5\) and then \(a=-0.5\) and study the trajectories

-

Set \(b=1\) throughout.

-
-
- -
-
- - - - -
- -
- - - -
- -

- -

Creative Commons License – This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International.

- -
- -
- - - - - - -
- -
- -
- - - -
    -
    • -
    • -
    • -
    • -
    • -
    • -
    • -
- -
- -
- - - -
- - - \ No newline at end of file diff --git a/lectures/_build/html/schelling.html b/lectures/_build/html/schelling.html deleted file mode 100644 index f5db14999..000000000 --- a/lectures/_build/html/schelling.html +++ /dev/null @@ -1,762 +0,0 @@ - - - - - - - - 4. Schelling’s Segregation Model — Introductory Computational Economics and Finance - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- -
- -
- -
- -
- - -
- On this page -
- - - - -
- - -

Back to top

-
- -
- -
- -
- -
- -

Introductory Computational Economics and Finance

- -

Schelling’s Segregation Model

- -
- -

Thomas J. Sargent & John Stachurski

- -
- - - - -
- -
- -
-

4. Schelling’s Segregation Model

- -
-

4.1. Outline

-

In 1969, Thomas C. Schelling developed a simple but striking model of racial segregation [Sch69].

-

His model studies the dynamics of racially mixed neighborhoods.

-

Like much of Schelling’s work, the model shows how local interactions can lead to surprising aggregate structure.

-

In particular, it shows that relatively mild preference for neighbors of similar race can lead in aggregate to the collapse of mixed neighborhoods, and high levels of segregation.

-

In recognition of this and other research, Schelling was awarded the 2005 Nobel Prize in Economic Sciences (joint with Robert Aumann).

-

In this lecture, we (in fact you) will build and run a version of Schelling’s model.

-

Let’s start with some imports:

-
-
-
%matplotlib inline
-import matplotlib.pyplot as plt
-plt.rcParams["figure.figsize"] = (11, 5)  #set default figure size
-from random import uniform, seed
-from math import sqrt
-
-
-
-
-
-
-

4.2. The Model

-

We will cover a variation of Schelling’s model that is easy to program and captures the main idea.

-
-

4.2.1. Set-Up

-

Suppose we have two types of people: orange people and green people.

-

For the purpose of this lecture, we will assume there are 250 of each type.

-

These agents all live on a single unit square.

-

The location of an agent is just a point \((x, y)\), where \(0 < x, y < 1\).

-
-
-

4.2.2. Preferences

-

We will say that an agent is happy if half or more of her 10 nearest neighbors are of the same type.

-

Here ‘nearest’ is in terms of Euclidean distance.

-

An agent who is not happy is called unhappy.

-

An important point here is that agents are not averse to living in mixed areas.

-

They are perfectly happy if half their neighbors are of the other color.

-
-
-

4.2.3. Behavior

-

Initially, agents are mixed together (integrated).

-

In particular, the initial location of each agent is an independent draw from a bivariate uniform distribution on \(S = (0, 1)^2\).

-

Now, cycling through the set of all agents, each agent is now given the chance to stay or move.

-

We assume that each agent will stay put if they are happy and move if unhappy.

-

The algorithm for moving is as follows

-
    -

  1. Draw a random location in \(S\)

    2. -

  2. If happy at new location, move there

    3. -

  3. Else, go to step 1

    4. -
-

In this way, we cycle continuously through the agents, moving as required.

-

We continue to cycle until no one wishes to move.

-
-
-
-

4.3. Results

-

Let’s have a look at the results we got when we coded and ran this model.

-

As discussed above, agents are initially mixed randomly together.

-
-_images/schelling_fig1.png -
-

But after several cycles, they become segregated into distinct regions.

-
-_images/schelling_fig2.png -
-
-_images/schelling_fig3.png -
-
-_images/schelling_fig4.png -
-

In this instance, the program terminated after 4 cycles through the set of -agents, indicating that all agents had reached a state of happiness.

-

What is striking about the pictures is how rapidly racial integration breaks down.

-

This is despite the fact that people in the model don’t actually mind living mixed with the other type.

-

Even with these preferences, the outcome is a high degree of segregation.

-
-
-

4.4. Exercises

-
- -

Exercise 4.1

-
-

Implement and run this simulation for yourself.

-

Consider the following structure for your program.

-

Agents can be modeled as objects.

-

Here’s an indication of how they might look

-
* Data:
-
-    * type (green or orange)
-    * location
-
-* Methods:
-
-    * determine whether happy or not given locations of other agents
-
-    * If not happy, move
-
-        * find a new location where happy
-
-
-

And here’s some pseudocode for the main loop

-
while agents are still moving
-    for agent in agents
-        give agent the opportunity to move
-
-
-

Use 250 agents of each type.

-
-
- -
-
- - - - -
- -
- - - -
- -

- -

Creative Commons License – This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International.

- -
- -
- - - - - - -
- -
- -
- - - -
    -
    • -
    • -
    • -
    • -
    • -
    • -
    • -
- -
- -
- - - -
- - - \ No newline at end of file diff --git a/lectures/_build/html/search.html b/lectures/_build/html/search.html deleted file mode 100644 index f41084412..000000000 --- a/lectures/_build/html/search.html +++ /dev/null @@ -1,475 +0,0 @@ - - - - - - - - Search — Introductory Computational Economics and Finance - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- -
- -
- -
- -
- - - - - - -
- - -

Back to top

-
- -
- -
- -
- -
- -

Introductory Computational Economics and Finance

- -

- -
- -

Thomas J. Sargent & John Stachurski

- -
- - - - -
- -
- -

Search

- - - - -

- Searching for multiple words only shows matches that contain - all words. -

- - -
- - - -
- - - -
- -
- - -
- -
- - - -
- -

- -

Creative Commons License – This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International.

- -
- -
- - - - - - -
- -
- -
- - - -
    -
    • -
    • -
    • -
    • -
    • -
    • -
    • -
- -
- -
- - - -
- - - \ No newline at end of file diff --git a/lectures/_build/html/searchindex.js b/lectures/_build/html/searchindex.js deleted file mode 100644 index 99d3f7329..000000000 --- a/lectures/_build/html/searchindex.js +++ /dev/null @@ -1 +0,0 @@ -Search.setIndex({docnames:["geom_series","intro","scalar_dynam","schelling","short_path","status","troubleshooting","zreferences"],envversion:{"sphinx.domains.c":2,"sphinx.domains.changeset":1,"sphinx.domains.citation":1,"sphinx.domains.cpp":5,"sphinx.domains.index":1,"sphinx.domains.javascript":2,"sphinx.domains.math":2,"sphinx.domains.python":3,"sphinx.domains.rst":2,"sphinx.domains.std":2,"sphinx.ext.intersphinx":1,"sphinxcontrib.bibtex":9,sphinx:56},filenames:["geom_series.md","intro.md","scalar_dynam.md","schelling.md","short_path.md","status.md","troubleshooting.md","zreferences.md"],objects:{},objnames:{},objtypes:{},terms:{"0":[0,2,3,4,5],"00":4,"005":0,"01":[0,2,4,5],"011":0,"02":[0,4],"03":[0,4],"04":[2,4],"05":[0,4],"06":4,"07":4,"08":[4,5],"09":4,"1":[0,5],"10":[0,2,3,4],"100":[0,4],"1000":0,"101":[0,4],"102":4,"104":[2,4],"1057":4,"1075":4,"11":[0,2,3,4],"111":4,"114":4,"116":4,"1171":4,"12":4,"121":4,"122":4,"123":4,"124":4,"1247":4,"125":4,"129":4,"13":4,"132":4,"133":4,"1343":4,"135":4,"136":4,"1382":4,"14":[2,4],"141":4,"1447":4,"145":4,"1471":4,"15":[0,4],"153":4,"1561":4,"16":4,"160":4,"162":4,"166":4,"17":4,"170":4,"172":4,"18":4,"1854":4,"1878":4,"19":4,"1914":0,"1969":[3,7],"197":4,"2":[0,2,3,5,7],"20":[0,2,4],"200":2,"2005":3,"2023":5,"21":4,"2110":4,"2135":4,"22":4,"2261905364":2,"23":4,"232":4,"236":4,"238":4,"24":4,"243":4,"2454":4,"246":4,"247":4,"25":[2,4,5],"250":3,"251":4,"2538":4,"2564":4,"26":4,"260":4,"2613":4,"2616":4,"264":4,"269":4,"27":4,"2767":4,"278":4,"28":4,"284":4,"29":4,"2984":4,"2f":0,"2xlarg":5,"3":[0,3,4],"30":4,"31":4,"32":4,"33":[4,5],"3350":4,"336":4,"3363":4,"34":4,"35":4,"3523":4,"355":4,"3597":4,"36":4,"37":4,"3706":4,"38":4,"39":4,"3914":4,"392":4,"395":4,"3d":0,"4":[0,2,4],"40":4,"4001":0,"41":4,"42":4,"43":4,"437":4,"44":4,"45":[2,4],"46":4,"47":4,"475":4,"478":4,"48":4,"480":4,"488":7,"49":4,"493":7,"4961":4,"5":[0,2,3,4],"50":[0,2,4,5],"500":4,"51":4,"52":4,"53":4,"5352":4,"54":4,"548":4,"55":4,"55000000000007":4,"556":4,"56":4,"57":4,"577":4,"58":4,"59":[4,7],"594":4,"6":[0,2,3,4],"60":4,"61":[4,5],"62":4,"626":4,"63":4,"635":4,"64":4,"65":4,"66":4,"67":4,"68":4,"7":[0,2,4],"70":4,"701":4,"71":4,"72":4,"73":4,"75":4,"76":4,"77":4,"78":[4,5],"783":4,"79":4,"8":[0,3,4,5],"80":4,"807":4,"81":4,"82":4,"820":4,"83":4,"84":4,"85":4,"86":4,"87":4,"875":4,"88":4,"89":4,"9":[0,4,5],"90":4,"91":4,"92":4,"93":4,"94":4,"95":[2,4],"96":4,"967":4,"97":[4,5],"98":4,"99":[0,4],"991":0,"break":[3,4],"case":[0,2,4],"class":3,"default":[0,2,3],"do":[0,2,4,6],"final":[0,4,6],"float":4,"function":[0,2,4],"import":[0,2,3,4],"int":4,"long":0,"new":3,"return":[0,2,3,4],"short":0,"true":[0,2,3],"try":[2,4,6],"var":2,"while":[3,4],A:4,And:3,As:[0,2,3],But:[3,4],By:2,For:[0,1,2,3,4,6],If:[0,2,3,4,6],In:[0,2,3,4],It:0,No:4,One:[1,6],The:[2,6],There:[0,2],These:[0,3,5],To:[0,2],_:2,__init__:3,__name__:0,_t:2,about:[0,2,3,4,6],abov:[0,2,3,4],access:5,accord:[0,3],account:0,action:5,actual:3,add:0,addit:4,adjust:0,affect:0,after:[0,3,4],again:[0,2],agent:3,aggreg:[0,3],agre:4,ahead:0,algebra:[0,2],algorithm:3,align:0,all:[0,2,3,4],allclos:4,almost:4,along:0,alpha:[2,3],also:[0,2,4,6],although:[2,4],alwai:0,amazon:5,american:7,among:0,amount:0,an:[0,1,2,3,4],anaconda:6,analysi:4,analyt:2,analyz:2,ani:[0,2,4],anoth:[4,6],antialias:0,append:[2,3],appli:[0,4],applic:4,approach:[0,2,4],approx:0,approxim:[0,4],ar:[0,2,3,4,5],arang:0,arbitrari:2,area:3,aren:0,arg:0,argmin:4,argument:[0,2],arrai:4,arrang:0,arriv:0,arrow:[2,4],arrow_arg:2,articl:6,artifici:4,ask:0,aspect:0,assert:0,assign:4,assum:[0,3,6],assumpt:6,aumann:3,avail:6,avers:3,aw:5,award:3,ax1:0,ax2:0,ax:[0,2,3],axes3d:0,axi:2,azur:3,b:[0,2,3,4],back:2,balanc:0,base:2,basic:6,bbox:2,bbox_to_anchor:2,becaus:[0,4],becom:[0,3],befor:0,begin:[0,2,4],behind:0,being:0,bellman:4,belong:0,below:[0,2,4],best:[2,4],between:[0,3],big:0,bivari:3,bo:2,borrow:0,both:0,bottom:2,bs:0,build:[2,3,4],built:5,c:[0,3,4,7],c_0:0,c_1:0,c_2:0,c_t:0,cach:5,calcul:[0,2],calculate_i:0,calculu:0,call:[0,2,3,4],can:[0,2,3,4,6],capit:[0,2],captur:3,cash:0,cdot:0,celebr:0,chanc:3,chang:0,check:[0,2,4],choic:4,choos:3,chosen:0,circumst:0,claim:[0,4],classic:[0,4],clearer:2,clearli:2,click:6,clim:0,cm:0,cmap:0,code:[2,3,6],coin:0,collaps:3,collect:0,color:3,colorbar:0,combin:0,come:0,command:6,common:6,comp:0,compar:0,comparison:0,compon:0,composit:2,comput:[0,3,4],compute_cost_to_go:4,conda:6,condit:[0,2],consid:[0,2,3,4],consist:0,constant:[0,2],consum:0,consumpt:0,contact:6,contain:5,context:[2,4],continu:[0,2,3],converg:[0,2,3,4],convers:2,convert:[0,4],convinc:4,coolwarm:0,copi:4,correspond:2,could:0,count:3,covari:0,cover:3,crack:0,creat:[0,2,3],creation:0,creditor:0,current:[0,2,4],current_nod:4,custom:[0,2],cycl:3,cycle_num:3,d:[0,3,4],d_0:0,d_:0,d_i:0,dai:4,damp:2,data:[3,4],date:[0,6],ddot:0,deal:[2,4],debtor:0,decis:4,declin:2,def:[0,2,3,4],defin:[0,2],degre:[2,3],delta:[0,2],demand:0,denot:[0,4],depend:[0,2],deposit:0,depositor:0,deriv:0,describ:[0,2,4],descript:4,design:[1,4],despit:3,destin:4,destination_nod:4,detail:6,deterior:0,determin:[0,3],develop:3,dg:0,diagon:4,diagram:2,dict:2,did:2,diff:0,differ:0,dimens:1,dimension:2,direct:[4,6],directli:[2,4],discours:6,discret:[0,2],discuss:[2,3,4],displaystyl:0,distanc:[3,4],distinct:3,distribut:[0,3,6],document:5,doe:3,dollar:0,don:[0,3,6],dot:[0,2],down:[0,3],dp0:0,dp_dg:0,dp_dr:0,dpt7pvt11fvcm_yxjd7kmv880000gn:2,dr:0,draw:3,draw_loc:3,dtype:4,durat:0,dx:2,dy:2,dynam:[1,3,4],e:[0,2],each:[0,2,3,4,6],earlier:2,easi:[2,3],ec:2,econom:[3,4,7],economi:0,economist:0,edg:4,effect:0,either:[0,6],element:4,elementari:1,els:[2,3,4],empti:2,empty_lik:4,enabl:[0,5],enamor:0,end:[0,4],enter:[2,3],entir:0,entitl:0,epsilon:2,equal:[0,4],equat:[0,4],equival:0,error:6,etc:[2,4],euclidean:3,evalu:0,even:[2,3],everi:[2,4],everywher:4,evid:0,exact:[2,4],examin:0,exampl:4,excess:0,exchang:0,execut:[1,6],exhibit:2,exist:2,exogen:0,expand:0,expenditur:0,experienc:6,express:[0,2],extend:[0,3],extern:6,extract:3,extrem:4,f:[0,3,4],f_1:0,f_2:0,f_v:4,fact:[0,3],factor:0,fail:[0,2],fals:[2,3],famou:0,fan:0,faster:4,fc:2,feedback:6,feel:[0,3],fig:[0,2,3],figsiz:[0,2,3],figur:[0,2,3],file:4,financi:0,find:[2,3],finite_lease_pv_approx_1:0,finite_lease_pv_approx_2:0,finite_lease_pv_tru:0,first:[0,1,2,4,6],fix:[0,2],fmt:2,focus:1,folder:2,follow:[0,2,3,4,6],fontsiz:2,form:[0,2],format:2,forum:6,found:4,foundat:2,frac:[0,2],frameon:2,franc:0,free:0,from:[0,2,3,4,6],frozen:0,fs:2,full:[0,2,4],func:0,further:3,futur:0,g:[0,2,4],g_0:0,g_t:0,gb:5,gener:[0,2],geom_seri:5,geometr:[1,2],geq:[0,2],get:[0,2,6],get_dist:3,gg:0,github:5,give:[0,2,3,6],given:[0,2,3,4],global:2,go:[0,3],goe:0,gold:0,good:[2,4],googl:4,gordon:0,got:3,govern:0,gpu:5,gr:0,gradual:0,graph:[0,2,4],great:2,greater:0,green:[2,3],gross:0,grow:0,growth:2,gs:0,guess:4,ha:[0,2,5],had:3,half:3,happen:0,happi:3,have:[0,2,3,4,6],haven:6,head_length:2,head_width:2,heart:0,held:0,henc:[2,4],her:3,here:[0,2,3,4,6],hesit:6,hi:[0,3],high:3,higher:2,hint:0,hit:2,hl:2,hline:0,hold:0,homogen:2,horizon:2,horizont:2,how:[0,2,3,4,6],howev:[0,2],hspace:0,hw:2,i:[0,2,3,4],i_0:0,i_t:0,icon:6,idea:[0,3],ident:0,ignit:0,ignor:2,illustr:[0,2],immedi:0,implement:3,impli:[0,2],importantli:4,in_fil:4,includ:[0,4],incom:0,increas:[0,2,3],increment:4,independ:3,index:0,indic:[3,4],inf:4,infil:4,infinite_leas:0,infti:[0,2,4],init_print:0,initi:[0,2,3,4],inject:0,inlin:[0,2,3],inspect:4,instal:6,instanc:[3,5],instead:6,instruct:6,integ:[0,4],integr:3,intellig:4,intend:0,interact:3,interest:2,internet:4,interpret:[0,4],intro:5,introduct:[2,4],intuit:2,invest:0,iou:0,ipykernel_27068:2,irregular:2,issu:0,iter:[2,4],its:[0,2,4],itself:2,j:[0,1,4],j_0:4,j_:4,j_n:4,job:[3,4],john:[0,1],joint:3,jump:2,jupyt:6,just:3,k0:2,k:2,k_0:2,k_:2,k_t:2,keep:[0,6],keyn:0,keyword:2,kind:2,know:[2,4],knowledg:[0,2],known:[0,4],l_i:0,label:[0,2],labor:0,lag:[0,2],lambda:2,larg:4,largest:3,last:0,later:0,latest:[5,6],latex:0,launch:6,law:2,ldot:0,lead:[0,3],learn:2,leas:0,least:3,lectur:[0,1,2,3,4,5,6],left:[0,2],legend:[0,2],legend_arg:2,lend:0,length:0,length_includes_head:2,less:0,let:[0,2,3,4],level:[0,3],li:[0,2],liabil:0,librari:[0,4,6],like:[2,3,6],line:[0,2,4,6],linestyl:[0,2],linspac:2,linux:5,list:3,littl:0,live:3,ll:[0,4],loan:0,loc:[0,2],local:[2,3],locat:3,logic:4,longer:2,look:[2,3,4],loop:3,lower:0,lowest_cost:4,ls:2,lw:2,machin:6,made:[0,2],main:3,make:[0,4],mani:[3,4],map:[2,4],map_graph_to_distance_matrix:4,margin:0,markerfacecolor:3,markers:3,match:4,math:[0,3],mathbb:2,mathemat:[0,4],mathematician:4,mathjax:0,matplotlib:[0,2,3],matrix:4,max_it:4,maynard:0,me:0,mean:[0,2,4],memori:5,meshgrid:0,messi:2,method:[2,3,4,5],methodolog:4,might:3,mild:3,million:4,min:4,min_:4,mind:3,minim:4,mix:3,model:7,modifi:[0,4,5],more:[0,2,3],most:[2,6],motion:2,motiv:0,move:[0,3,4],movement:4,mpl_toolkit:0,mplot3d:0,much:[0,3,6],multipl:0,must:[0,4],n:[2,4],name:0,nan:0,nation:0,natur:2,ncol:2,nearest:3,necessari:[0,4],need:[2,4,6],neg:0,neighbor:3,neighborhood:3,net:0,network:4,next:[0,2,4],next_j:4,next_nod:4,nice:4,no_one_mov:3,nobel:3,node0:4,node10:4,node11:4,node12:4,node13:4,node14:4,node15:4,node16:4,node17:4,node18:4,node19:4,node1:4,node20:4,node21:4,node22:4,node23:4,node24:4,node25:4,node26:4,node27:4,node28:4,node29:4,node2:4,node30:4,node31:4,node32:4,node33:4,node34:4,node35:4,node36:4,node37:4,node38:4,node39:4,node3:4,node40:4,node41:4,node42:4,node43:4,node44:4,node45:4,node46:4,node47:4,node48:4,node49:4,node4:4,node50:4,node51:4,node52:4,node53:4,node54:4,node55:4,node56:4,node57:4,node58:4,node59:4,node5:4,node60:4,node61:4,node62:4,node63:4,node64:4,node65:4,node66:4,node67:4,node68:4,node69:4,node6:4,node70:4,node71:4,node72:4,node73:4,node74:4,node75:4,node76:4,node77:4,node78:4,node79:4,node7:4,node80:4,node81:4,node82:4,node83:4,node84:4,node85:4,node86:4,node87:4,node88:4,node89:4,node8:4,node90:4,node91:4,node92:4,node93:4,node94:4,node95:4,node96:4,node97:4,node98:4,node99:4,node9:4,node:4,nomin:0,non:4,none:[2,3],nonlinear:4,nonneg:0,nontrivi:2,note:[0,4],notebook:6,notic:[0,2,4],now:[0,2,3,4],np:[0,2,4],num_arrow:2,num_neighbor:3,num_nod:4,num_of_type_0:3,num_of_type_1:3,num_same_typ:3,number:[0,2,3,4],numpi:[0,2,4],nvidia:5,o:3,object:[2,3],observ:2,obtain:[2,3,4],obvious:2,occur:0,often:[0,4],okai:4,old_loc:3,omit:4,onc:2,one:[0,2,3,4],onli:[0,2,4],open:4,oper:4,opportun:3,optim:4,option:6,orang:3,order:2,org:6,origin:2,oscil:2,other:[0,2,3,4],otherwis:[2,4],our:[0,2,4,6],our_arg:0,out:[0,2],outcom:[0,3],output:0,outsid:0,outstand:0,over:[0,2,4],overview:1,owner:0,p0:0,p3:5,p:0,p_0:0,packet:4,page:[1,6],pai:0,pair:3,paper:0,param:0,param_label:0,paramet:2,partial:0,particular:[0,2,3],path:[0,1],payment:0,payout:0,peopl:[0,3],per:0,percent:0,perfectli:3,perform:0,period:0,perman:0,perpetu:0,pictur:3,piec:0,place:2,pleas:6,plot45:2,plot:[0,2,3],plot_arg:3,plot_distribut:3,plot_funct:0,plot_surfac:0,plt:[0,2,3],plu:0,point:[0,2,3,4],pop:4,posit:[0,2],possibl:[4,6],pound:0,power:4,precautionari:0,preced:[0,2,4],predict:0,present:1,prevail:0,previous:2,princip:0,principl:4,print:[0,3,4],print_best_path:4,prize:3,probabl:3,problem:6,proce:0,process:0,produc:2,product:0,program:[3,4],project:0,promis:0,proof:4,propens:0,properti:2,prove:[0,4],provid:[2,4,6],pseudocod:3,purpos:3,put:[0,3],pv:0,py:[2,6],pyplot:[0,2,3],python:[0,6],q:4,qquad:2,quad:2,quadrat:2,qualiti:0,quantecon:6,quantiti:0,quick:[2,4],quickli:2,quit:2,r:[0,2],r_:2,r_i:0,race:3,racial:3,rais:6,ran:3,random:3,randomli:3,rang:[0,2,3,4],rapidli:3,rather:4,ratio:0,rcparam:[0,2,3],re:[0,4],reach:[3,4],read:[2,4],reader:6,real:0,reason:0,recal:[0,2],receipt:0,receiv:0,recent:0,recognit:3,record:0,recurs:2,redeem:0,redundantli:2,refer:1,regard:3,regardless:2,region:[2,3],regular:2,reinstal:6,reinvest:0,rel:[0,3],remark:0,rememb:0,remot:6,remov:[0,6],replac:4,repres:0,reproduc:3,requir:[0,2,3,4],require_same_typ:3,research:[3,4],resourc:0,restrict:[0,4],reveal:0,review:7,rg:0,rgx_0:0,richard:4,right:[0,2],rightarrow:0,robert:3,robot:4,round:3,rout:4,rr:0,rs:0,run:[3,5,6],s:[0,1,2,4,5,6],sai:3,said:2,same:[0,2,3],sargent:1,satisfi:[0,4],save:0,saw:2,scalar:0,scalar_dynam:5,scan:4,sch69:[3,7],schell:[1,5,7],scienc:[3,4],scientif:4,second:[0,2,6],section:2,see:[0,1,2,4],seed:3,segreg:[1,7],self:3,sell:0,sequenc:[0,2,4],sequenti:4,seri:[1,2],servic:5,set:[0,1,2,4,6],set_color:2,set_facecolor:3,set_posit:2,set_titl:[0,3],set_xlabel:[0,2],set_xlim:2,set_xtick:2,set_xticklabel:2,set_ylabel:[0,2],set_ylim:2,set_ytick:2,set_yticklabel:2,set_zlabel:0,sever:3,shall:0,shape:4,sheet:0,shift:0,short_path:5,shortest:1,should:[4,6],show:[0,2,3,4],shown:4,shrink:0,side:0,silver:0,similar:[3,4],similarli:0,simpl:[2,3,4],simpli:[0,2,6],simplifi:2,simul:3,singl:[2,3],site:4,situat:2,size:[0,2,3],skip:0,small:0,smallest:3,so:[0,2,4,6],social:4,solow:2,solv:0,some:[0,3,4],someon:0,sometim:0,somewhat:2,soon:0,sort:3,sourc:6,space:2,specif:[0,6],specifi:4,speed:3,spend:0,spine:2,split:[0,4],sqrt:3,squar:3,stabl:2,stachurski:1,stai:[3,4],standard:[0,2,4],start:[0,2,3,4],state:[0,2,3],statist:1,statu:5,steadi:2,step:[0,3,4],still:[2,3,4,6],stock:2,stop:4,store:4,str:2,stream:0,strictli:0,strike:3,string:2,structur:3,studi:[0,2,3],subplot:[0,2,3],subplots_adjust:0,subset:2,substanti:0,substitut:0,success:[0,4],suffici:3,suitabl:2,sum:[0,3],sum_:0,sum_cost:4,suppli:0,supplier:4,suppos:[3,4],surf:0,surpris:3,sym:0,symbol:0,sympi:0,system:[0,2],systemat:4,sz:2,t:[0,2,3,6],t_max:0,tabl:5,tackl:[2,4],take:[0,2,4],task:[4,6],taylor:0,techniqu:[2,4],telecommun:4,tell:[0,6],term:[0,2,3],termin:3,tesla:5,test:4,text:[0,1,2,4],textrm:0,th:0,than:[0,2,4],thei:[0,3],them:4,theori:0,therefor:0,thi:[0,1,2,3,4,5,6],thing:6,think:[0,2,4],third:0,thoma:[1,3,7],thought:4,three:0,through:[0,2,3,5,6],throughout:[0,2],throught:2,thu:0,time:[0,2,4,5],todai:0,togeth:3,tomorrow:0,tool:0,top:2,topic:2,total:[0,4],touch:6,toward:[0,2],trace:2,tracker:6,trade:0,transport:4,travel:4,travers:4,trivial:4,troubleshoot:[1,5],truth:0,ts_length:2,ts_plot:2,two:[0,2,3,6],txt:4,type:[0,3],typic:[0,2,4],uk:0,ultim:0,undefin:0,under:[0,2],understand:[0,2],understood:4,unemploi:0,unhappi:3,uniform:3,uniqu:2,unit:[0,3],until:[0,3],up:[2,6],updat:[2,3,4,6],upper:2,us:[0,2,3,4,6],use_latex:0,userwarn:2,usual:4,v100:5,v:4,valu:2,vari:0,variabl:2,variat:[3,4],vcpu:5,vector:4,veri:2,verifi:0,version:[2,3,6],vertex:4,vertic:2,view:[0,2],view_init:0,visual:0,w:4,wa:[0,3],wai:[0,2,3,6],want:[0,3,4],we:[0,2,3,4,6],web:5,websit:1,weight:4,well:0,were:[0,4],what:[0,2,3,4],when:[0,2,3,6],whenev:[2,6],where:[0,2,3,4,6],whether:[0,3],which:[0,1,2],who:3,why:0,wide:0,wise:0,wish:[3,4],within:6,without:0,word:2,work:[0,3,6],worth:0,write:[0,2,4],written:1,x0:[0,2],x:[0,2,3],x_0:[0,2],x_0rg:0,x_1:[0,2],x_2:[0,2],x_:[0,2],x_t:[0,2],x_val:0,x_values_0:3,x_values_1:3,xgrid:2,xmax:[0,2],xmin:[0,2],xr:0,xtick:2,xtick_label:2,y:[0,2,3,6],y_0:0,y_1:0,y_2:0,y_:0,y_init:0,y_t:0,y_values_0:3,y_values_1:3,you:[0,2,3,4,6],your:[3,4],yourself:3,z:[0,2],zero:[0,2,4],zeros_lik:4,zip:0,zrefer:5,zy:2},titles:["1. Geometric Series for Elementary Economics","Python Programming for Economics and Finance","3. Dynamics in One Dimension","4. Schelling\u2019s Segregation Model","2. Shortest Paths","7. Execution Statistics","5. Troubleshooting","6. References"],titleterms:{"1":[2,3,4],"2":4,"3":2,"4":3,"static":0,A:[0,2],One:2,The:[0,3,4],accumul:0,algorithm:4,an:6,analysi:2,applic:0,asset:0,back:0,bank:0,behavior:3,complex:2,content:[0,2,3,4,6],cost:4,definit:2,differ:2,dimens:2,discount:0,dynam:[0,2],econom:[0,1],elementari:0,environ:6,equat:2,exampl:[0,2],execut:5,exercis:[2,3,4],financ:1,find:4,finit:0,fix:6,formula:0,fraction:0,geometr:0,go:4,graphic:2,implement:4,infinit:0,interest:0,issu:6,kei:0,keynesian:0,least:4,linear:2,local:6,minimum:4,model:[0,1,2,3],monei:0,multipli:0,nonlinear:2,other:1,outlin:[3,4],overview:[0,2,4],path:4,prefer:3,present:0,price:0,problem:4,program:1,python:1,rate:0,refer:7,report:6,reserv:0,result:3,s:3,schell:3,segreg:3,seri:0,set:3,shortest:4,simpl:0,solut:[2,3,4],solv:4,some:2,stabil:2,statist:5,techniqu:1,tool:1,trajectori:2,troubleshoot:6,up:3,valu:0,version:0,your:6}}) \ No newline at end of file diff --git a/lectures/_build/html/short_path.html b/lectures/_build/html/short_path.html deleted file mode 100644 index 1803f9749..000000000 --- a/lectures/_build/html/short_path.html +++ /dev/null @@ -1,1003 +0,0 @@ - - - - - - - - 2. Shortest Paths — Introductory Computational Economics and Finance - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- -
- -
- -
- -
- - -
- On this page -
- - - - -
- - -

Back to top

-
- -
- -
- -
- -
- -

Introductory Computational Economics and Finance

- -

Shortest Paths

- -
- -

Thomas J. Sargent & John Stachurski

- -
- - - - -
- -
- -
-

2. Shortest Paths

- -
-

2.1. Overview

-

The shortest path problem is a classic problem in mathematics and computer science with applications in

-
    -

  • Economics (sequential decision making, analysis of social networks, etc.)

    • -

  • Operations research and transportation

    • -

  • Robotics and artificial intelligence

    • -

  • Telecommunication network design and routing

    • -

  • etc., etc.

    • -
-

Variations of the methods we discuss in this lecture are used millions of times every day, in applications such as

-
    -

  • Google Maps

    • -

  • routing packets on the internet

    • -
-

For us, the shortest path problem also provides a nice introduction to the logic of dynamic programming.

-

Dynamic programming is an extremely powerful optimization technique that we apply in many lectures on this site.

-

The only scientific library we’ll need in what follows is NumPy:

-
-
-
import numpy as np
-
-
-
-
-
-
-

2.2. Outline of the Problem

-

The shortest path problem is one of finding how to traverse a graph from one specified node to another at minimum cost.

-

Consider the following graph

-
-_images/graph.png -
-

We wish to travel from node (vertex) A to node G at minimum cost

-
    -

  • Arrows (edges) indicate the movements we can take.

    • -

  • Numbers on edges indicate the cost of traveling that edge.

    • -
-

(Graphs such as the one above are called weighted directed graphs.)

-

Possible interpretations of the graph include

-
    -

  • Minimum cost for supplier to reach a destination.

    • -

  • Routing of packets on the internet (minimize time).

    • -

  • Etc., etc.

    • -
-

For this simple graph, a quick scan of the edges shows that the optimal paths are

-
    -

  • A, C, F, G at cost 8

    • -
-
-_images/graph4.png -
-
    -

  • A, D, F, G at cost 8

    • -
-
-_images/graph3.png -
-
-
-

2.3. Finding Least-Cost Paths

-

For large graphs, we need a systematic solution.

-

Let \(J(v)\) denote the minimum cost-to-go from node \(v\), understood as the total cost from \(v\) if we take the best route.

-

Suppose that we know \(J(v)\) for each node \(v\), as shown below for the graph from the preceding example

-
-_images/graph2.png -
-

Note that \(J(G) = 0\).

-

The best path can now be found as follows

-
    -

  1. Start at node \(v = A\)

    2. -

  2. From current node \(v\), move to any node that solves

    3. -
-
-(2.1)\[\min_{w \in F_v} \{ c(v, w) + J(w) \}\]
-

where

-
    -

  • \(F_v\) is the set of nodes that can be reached from \(v\) in one step.

    • -

  • \(c(v, w)\) is the cost of traveling from \(v\) to \(w\).

    • -
-

Hence, if we know the function \(J\), then finding the best path is almost trivial.

-

But how can we find the cost-to-go function \(J\)?

-

Some thought will convince you that, for every node \(v\), -the function \(J\) satisfies

-
-(2.2)\[J(v) = \min_{w \in F_v} \{ c(v, w) + J(w) \}\]
-

This is known as the Bellman equation, after the mathematician Richard Bellman.

-

The Bellman equation can be thought of as a restriction that \(J\) must -satisfy.

-

What we want to do now is use this restriction to compute \(J\).

-
-
-

2.4. Solving for Minimum Cost-to-Go

-

Let’s look at an algorithm for computing \(J\) and then think about how to -implement it.

-
-

2.4.1. The Algorithm

-

The standard algorithm for finding \(J\) is to start an initial guess and then iterate.

-

This is a standard approach to solving nonlinear equations, often called -the method of successive approximations.

-

Our initial guess will be

-
-(2.3)\[J_0(v) = 0 \text{ for all } v\]
-

Now

-
    -

  1. Set \(n = 0\)

    2. -

  2. Set \(J_{n+1} (v) = \min_{w \in F_v} \{ c(v, w) + J_n(w) \}\) for all \(v\)

    3. -

  3. If \(J_{n+1}\) and \(J_n\) are not equal then increment \(n\), go to 2

    4. -
-

This sequence converges to \(J\).

-

Although we omit the proof, we’ll prove similar claims in our other lectures -on dynamic programming.

-
-
-

2.4.2. Implementation

-

Having an algorithm is a good start, but we also need to think about how to -implement it on a computer.

-

First, for the cost function \(c\), we’ll implement it as a matrix -\(Q\), where a typical element is

-
-\[\begin{split} -Q(v, w) -= -\begin{cases} - & c(v, w) \text{ if } w \in F_v \\ - & +\infty \text{ otherwise } -\end{cases} -\end{split}\]
-

In this context \(Q\) is usually called the distance matrix.

-

We’re also numbering the nodes now, with \(A = 0\), so, for example

-
-\[ -Q(1, 2) -= -\text{ the cost of traveling from B to C } -\]
-

For example, for the simple graph above, we set

-
-
-
from numpy import inf
-
-Q = np.array([[inf, 1,   5,   3,   inf, inf, inf],
-              [inf, inf, inf, 9,   6,   inf, inf],
-              [inf, inf, inf, inf, inf, 2,   inf],
-              [inf, inf, inf, inf, inf, 4,   8],
-              [inf, inf, inf, inf, inf, inf, 4],
-              [inf, inf, inf, inf, inf, inf, 1],
-              [inf, inf, inf, inf, inf, inf, 0]])
-
-
-
-
-

Notice that the cost of staying still (on the principle diagonal) is set to

-
    -

  • np.inf for non-destination nodes — moving on is required.

    • -

  • 0 for the destination node — here is where we stop.

    • -
-

For the sequence of approximations \(\{J_n\}\) of the cost-to-go functions, we can use NumPy arrays.

-

Let’s try with this example and see how we go:

-
-
-
nodes = range(7)                              # Nodes = 0, 1, ..., 6
-J = np.zeros_like(nodes, dtype=int)        # Initial guess
-next_J = np.empty_like(nodes, dtype=int)   # Stores updated guess
-
-max_iter = 500
-i = 0
-
-while i < max_iter:
-    for v in nodes:
-        # minimize Q[v, w] + J[w] over all choices of w
-        lowest_cost = inf
-        for w in nodes:
-            cost = Q[v, w] + J[w]
-            if cost < lowest_cost:
-                lowest_cost = cost
-        next_J[v] = lowest_cost
-    if np.equal(next_J, J).all():
-        break
-    else:
-        J[:] = next_J   # Copy contents of next_J to J
-        i += 1
-
-print("The cost-to-go function is", J)
-
-
-
-
-
The cost-to-go function is [ 8 10  3  5  4  1  0]
-
-
-
-
-

This matches with the numbers we obtained by inspection above.

-

But, importantly, we now have a methodology for tackling large graphs.

-
-
-
-

2.5. Exercises

-
- -

Exercise 2.1

-
-

The text below describes a weighted directed graph.

-

The line node0, node1 0.04, node8 11.11, node14 72.21 means that from node0 we can go to

-
    -

  • node1 at cost 0.04

    • -

  • node8 at cost 11.11

    • -

  • node14 at cost 72.21

    • -
-

No other nodes can be reached directly from node0.

-

Other lines have a similar interpretation.

-

Your task is to use the algorithm given above to find the optimal path and its cost.

-
-

Note

-

You will be dealing with floating point numbers now, rather than -integers, so consider replacing np.equal() with np.allclose().

-
-
-
-
%%file graph.txt
-node0, node1 0.04, node8 11.11, node14 72.21
-node1, node46 1247.25, node6 20.59, node13 64.94
-node2, node66 54.18, node31 166.80, node45 1561.45
-node3, node20 133.65, node6 2.06, node11 42.43
-node4, node75 3706.67, node5 0.73, node7 1.02
-node5, node45 1382.97, node7 3.33, node11 34.54
-node6, node31 63.17, node9 0.72, node10 13.10
-node7, node50 478.14, node9 3.15, node10 5.85
-node8, node69 577.91, node11 7.45, node12 3.18
-node9, node70 2454.28, node13 4.42, node20 16.53
-node10, node89 5352.79, node12 1.87, node16 25.16
-node11, node94 4961.32, node18 37.55, node20 65.08
-node12, node84 3914.62, node24 34.32, node28 170.04
-node13, node60 2135.95, node38 236.33, node40 475.33
-node14, node67 1878.96, node16 2.70, node24 38.65
-node15, node91 3597.11, node17 1.01, node18 2.57
-node16, node36 392.92, node19 3.49, node38 278.71
-node17, node76 783.29, node22 24.78, node23 26.45
-node18, node91 3363.17, node23 16.23, node28 55.84
-node19, node26 20.09, node20 0.24, node28 70.54
-node20, node98 3523.33, node24 9.81, node33 145.80
-node21, node56 626.04, node28 36.65, node31 27.06
-node22, node72 1447.22, node39 136.32, node40 124.22
-node23, node52 336.73, node26 2.66, node33 22.37
-node24, node66 875.19, node26 1.80, node28 14.25
-node25, node70 1343.63, node32 36.58, node35 45.55
-node26, node47 135.78, node27 0.01, node42 122.00
-node27, node65 480.55, node35 48.10, node43 246.24
-node28, node82 2538.18, node34 21.79, node36 15.52
-node29, node64 635.52, node32 4.22, node33 12.61
-node30, node98 2616.03, node33 5.61, node35 13.95
-node31, node98 3350.98, node36 20.44, node44 125.88
-node32, node97 2613.92, node34 3.33, node35 1.46
-node33, node81 1854.73, node41 3.23, node47 111.54
-node34, node73 1075.38, node42 51.52, node48 129.45
-node35, node52 17.57, node41 2.09, node50 78.81
-node36, node71 1171.60, node54 101.08, node57 260.46
-node37, node75 269.97, node38 0.36, node46 80.49
-node38, node93 2767.85, node40 1.79, node42 8.78
-node39, node50 39.88, node40 0.95, node41 1.34
-node40, node75 548.68, node47 28.57, node54 53.46
-node41, node53 18.23, node46 0.28, node54 162.24
-node42, node59 141.86, node47 10.08, node72 437.49
-node43, node98 2984.83, node54 95.06, node60 116.23
-node44, node91 807.39, node46 1.56, node47 2.14
-node45, node58 79.93, node47 3.68, node49 15.51
-node46, node52 22.68, node57 27.50, node67 65.48
-node47, node50 2.82, node56 49.31, node61 172.64
-node48, node99 2564.12, node59 34.52, node60 66.44
-node49, node78 53.79, node50 0.51, node56 10.89
-node50, node85 251.76, node53 1.38, node55 20.10
-node51, node98 2110.67, node59 23.67, node60 73.79
-node52, node94 1471.80, node64 102.41, node66 123.03
-node53, node72 22.85, node56 4.33, node67 88.35
-node54, node88 967.59, node59 24.30, node73 238.61
-node55, node84 86.09, node57 2.13, node64 60.80
-node56, node76 197.03, node57 0.02, node61 11.06
-node57, node86 701.09, node58 0.46, node60 7.01
-node58, node83 556.70, node64 29.85, node65 34.32
-node59, node90 820.66, node60 0.72, node71 0.67
-node60, node76 48.03, node65 4.76, node67 1.63
-node61, node98 1057.59, node63 0.95, node64 4.88
-node62, node91 132.23, node64 2.94, node76 38.43
-node63, node66 4.43, node72 70.08, node75 56.34
-node64, node80 47.73, node65 0.30, node76 11.98
-node65, node94 594.93, node66 0.64, node73 33.23
-node66, node98 395.63, node68 2.66, node73 37.53
-node67, node82 153.53, node68 0.09, node70 0.98
-node68, node94 232.10, node70 3.35, node71 1.66
-node69, node99 247.80, node70 0.06, node73 8.99
-node70, node76 27.18, node72 1.50, node73 8.37
-node71, node89 104.50, node74 8.86, node91 284.64
-node72, node76 15.32, node84 102.77, node92 133.06
-node73, node83 52.22, node76 1.40, node90 243.00
-node74, node81 1.07, node76 0.52, node78 8.08
-node75, node92 68.53, node76 0.81, node77 1.19
-node76, node85 13.18, node77 0.45, node78 2.36
-node77, node80 8.94, node78 0.98, node86 64.32
-node78, node98 355.90, node81 2.59
-node79, node81 0.09, node85 1.45, node91 22.35
-node80, node92 121.87, node88 28.78, node98 264.34
-node81, node94 99.78, node89 39.52, node92 99.89
-node82, node91 47.44, node88 28.05, node93 11.99
-node83, node94 114.95, node86 8.75, node88 5.78
-node84, node89 19.14, node94 30.41, node98 121.05
-node85, node97 94.51, node87 2.66, node89 4.90
-node86, node97 85.09
-node87, node88 0.21, node91 11.14, node92 21.23
-node88, node93 1.31, node91 6.83, node98 6.12
-node89, node97 36.97, node99 82.12
-node90, node96 23.53, node94 10.47, node99 50.99
-node91, node97 22.17
-node92, node96 10.83, node97 11.24, node99 34.68
-node93, node94 0.19, node97 6.71, node99 32.77
-node94, node98 5.91, node96 2.03
-node95, node98 6.17, node99 0.27
-node96, node98 3.32, node97 0.43, node99 5.87
-node97, node98 0.30
-node98, node99 0.33
-node99,
-
-
-
-
-
Writing graph.txt
-
-
-
-
-
-
- -
-
- - - - -
- -
- - - -
- -

- -

Creative Commons License – This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International.

- -
- -
- - - - - - -
- -
- -
- - - -
    -
    • -
    • -
    • -
    • -
    • -
    • -
    • -
- -
- -
- - - -
- - - \ No newline at end of file diff --git a/lectures/_build/html/status.html b/lectures/_build/html/status.html deleted file mode 100644 index 4747e4b87..000000000 --- a/lectures/_build/html/status.html +++ /dev/null @@ -1,527 +0,0 @@ - - - - - - - - 7. Execution Statistics — Introductory Computational Economics and Finance - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- -
- -
- -
- -
- - - - - - -
- - -

Back to top

-
- -
- -
- -
- -
- -

Introductory Computational Economics and Finance

- -

Execution Statistics

- -
- -

Thomas J. Sargent & John Stachurski

- -
- - - - -
- -
- -
-

7. Execution Statistics

-

This table contains the latest execution statistics.

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Document

Modified

Method

Run Time (s)

Status

geom_series

2023-01-25 08:50

cache

2.78

✅

intro

2023-01-25 08:50

cache

0.9

✅

scalar_dynam

2023-01-25 08:50

cache

2.25

✅

schelling

2023-01-25 08:50

cache

1.97

✅

short_path

2023-01-25 08:50

cache

1.33

✅

status

2023-01-25 08:50

cache

0.9

✅

troubleshooting

2023-01-25 08:50

cache

0.9

✅

zreferences

2023-01-25 08:50

cache

0.9

✅

-

These lectures are built on linux instances through github actions and amazon web services (aws) to -enable access to a gpu. These lectures are built on a p3.2xlarge -that has access to 8 vcpu's, a V100 NVIDIA Tesla GPU, and 61 Gb of memory.

-
- - - - -
- -
- - - -
- -

- -

Creative Commons License – This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International.

- -
- -
- - - - - - -
- -
- -
- - - -
    -
    • -
    • -
    • -
    • -
    • -
    • -
    • -
- -
- -
- - - -
- - - \ No newline at end of file diff --git a/lectures/_build/html/troubleshooting.html b/lectures/_build/html/troubleshooting.html deleted file mode 100644 index e19874751..000000000 --- a/lectures/_build/html/troubleshooting.html +++ /dev/null @@ -1,528 +0,0 @@ - - - - - - - - 5. Troubleshooting — Introductory Computational Economics and Finance - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- -
- -
- -
- -
- - -
- On this page -
- - - - -
- - -

Back to top

-
- -
- -
- -
- -
- -

Introductory Computational Economics and Finance

- -

Troubleshooting

- -
- -

Thomas J. Sargent & John Stachurski

- -
- - - - -
- -
- -
-

5. Troubleshooting

- -

This page is for readers experiencing errors when running the code from the lectures.

-
-

5.1. Fixing Your Local Environment

-

The basic assumption of the lectures is that code in a lecture should execute whenever

-
    -

  1. it is executed in a Jupyter notebook and

    2. -

  2. the notebook is running on a machine with the latest version of Anaconda Python.

    3. -
-

You have installed Anaconda, haven’t you, following the instructions in this lecture?

-

Assuming that you have, the most common source of problems for our readers is that their Anaconda distribution is not up to date.

-

Here’s a useful article -on how to update Anaconda.

-

Another option is to simply remove Anaconda and reinstall.

-

You also need to keep the external code libraries, such as QuantEcon.py up to date.

-

For this task you can either

-
    -

  • use conda install -y quantecon on the command line, or

    • -

  • execute !conda install -y quantecon within a Jupyter notebook.

    • -
-

If your local environment is still not working you can do two things.

-

First, you can use a remote machine instead, by clicking on the Launch Notebook icon available for each lecture

-_images/launch.png -

Second, you can report an issue, so we can try to fix your local set up.

-

We like getting feedback on the lectures so please don’t hesitate to get in -touch.

-
-
-

5.2. Reporting an Issue

-

One way to give feedback is to raise an issue through our issue tracker.

-

Please be as specific as possible. Tell us where the problem is and as much -detail about your local set up as you can provide.

-

Another feedback option is to use our discourse forum.

-

Finally, you can provide direct feedback to contact@quantecon.org

-
-
- - - - -
- -
- - - -
- -

- -

Creative Commons License – This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International.

- -
- -
- - - - - - -
- -
- -
- - - -
    -
    • -
    • -
    • -
    • -
    • -
    • -
    • -
- -
- -
- - - -
- - - \ No newline at end of file diff --git a/lectures/_build/html/zreferences.html b/lectures/_build/html/zreferences.html deleted file mode 100644 index 76ae9a471..000000000 --- a/lectures/_build/html/zreferences.html +++ /dev/null @@ -1,471 +0,0 @@ - - - - - - - - 6. References — Introductory Computational Economics and Finance - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- -
- -
- -
- -
- - - - - - -
- - -

Back to top

-
- -
- -
- -
- -
- -

Introductory Computational Economics and Finance

- -

References

- -
- -

Thomas J. Sargent & John Stachurski

- -
- - - - -
- -
- -
-

6. References

-
-
-
Sch69
-

Thomas C Schelling. Models of Segregation. American Economic Review, 59(2):488–493, 1969.

-
-
-
-
- - - - -
- -
- - - -
- -

- -

Creative Commons License – This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International.

- -
- -
- - - - - - -
- -
- -
- - - -
    -
    • -
    • -
    • -
    • -
    • -
    • -
    • -
- -
- -
- - - -
- - - \ No newline at end of file diff --git a/lectures/_build/jupyter_execute/geom_series.ipynb b/lectures/_build/jupyter_execute/geom_series.ipynb deleted file mode 100644 index 4c5062b5c..000000000 --- a/lectures/_build/jupyter_execute/geom_series.ipynb +++ /dev/null @@ -1,1288 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "d413a06a", - "metadata": {}, - "source": [ - "(geom_series)=\n", - "```{raw} html\n", - "
\n", - " \n", - " \"QuantEcon\"\n", - " \n", - "
\n", - "```\n", - "\n", - "```{index} single: python\n", - "```\n", - "\n", - "# Geometric Series for Elementary Economics\n", - "\n", - "```{contents} Contents\n", - ":depth: 2\n", - "```\n", - "\n", - "## Overview\n", - "\n", - "The lecture describes important ideas in economics that use the mathematics of geometric series.\n", - "\n", - "Among these are\n", - "\n", - "- the Keynesian **multiplier**\n", - "- the money **multiplier** that prevails in fractional reserve banking\n", - " systems\n", - "- interest rates and present values of streams of payouts from assets\n", - "\n", - "(As we shall see below, the term **multiplier** comes down to meaning **sum of a convergent geometric series**)\n", - "\n", - "These and other applications prove the truth of the wise crack that\n", - "\n", - "```{epigraph}\n", - "\"in economics, a little knowledge of geometric series goes a long way \"\n", - "```\n", - "\n", - "Below we'll use the following imports:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "c7215506", - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "plt.rcParams[\"figure.figsize\"] = (11, 5) #set default figure size\n", - "import numpy as np\n", - "import sympy as sym\n", - "from sympy import init_printing, latex\n", - "from matplotlib import cm\n", - "from mpl_toolkits.mplot3d import Axes3D" - ] - }, - { - "cell_type": "markdown", - "id": "c7a9fa2c", - "metadata": {}, - "source": [ - "## Key Formulas\n", - "\n", - "To start, let $c$ be a real number that lies strictly between\n", - "$-1$ and $1$.\n", - "\n", - "- We often write this as $c \\in (-1,1)$.\n", - "- Here $(-1,1)$ denotes the collection of all real numbers that\n", - " are strictly less than $1$ and strictly greater than $-1$.\n", - "- The symbol $\\in$ means *in* or *belongs to the set after the symbol*.\n", - "\n", - "We want to evaluate geometric series of two types -- infinite and finite.\n", - "\n", - "### Infinite Geometric Series\n", - "\n", - "The first type of geometric that interests us is the infinite series\n", - "\n", - "$$\n", - "1 + c + c^2 + c^3 + \\cdots\n", - "$$\n", - "\n", - "Where $\\cdots$ means that the series continues without end.\n", - "\n", - "The key formula is\n", - "\n", - "```{math}\n", - ":label: infinite\n", - "\n", - "1 + c + c^2 + c^3 + \\cdots = \\frac{1}{1 -c }\n", - "```\n", - "\n", - "To prove key formula {eq}`infinite`, multiply both sides by $(1-c)$ and verify\n", - "that if $c \\in (-1,1)$, then the outcome is the\n", - "equation $1 = 1$.\n", - "\n", - "### Finite Geometric Series\n", - "\n", - "The second series that interests us is the finite geometric series\n", - "\n", - "$$\n", - "1 + c + c^2 + c^3 + \\cdots + c^T\n", - "$$\n", - "\n", - "where $T$ is a positive integer.\n", - "\n", - "The key formula here is\n", - "\n", - "$$\n", - "1 + c + c^2 + c^3 + \\cdots + c^T = \\frac{1 - c^{T+1}}{1-c}\n", - "$$\n", - "\n", - "**Remark:** The above formula works for any value of the scalar\n", - "$c$. We don't have to restrict $c$ to be in the\n", - "set $(-1,1)$.\n", - "\n", - "We now move on to describe some famous economic applications of\n", - "geometric series.\n", - "\n", - "## Example: The Money Multiplier in Fractional Reserve Banking\n", - "\n", - "In a fractional reserve banking system, banks hold only a fraction\n", - "$r \\in (0,1)$ of cash behind each **deposit receipt** that they\n", - "issue\n", - "\n", - "* In recent times\n", - " - cash consists of pieces of paper issued by the government and\n", - " called dollars or pounds or $\\ldots$\n", - " - a *deposit* is a balance in a checking or savings account that\n", - " entitles the owner to ask the bank for immediate payment in cash\n", - "* When the UK and France and the US were on either a gold or silver\n", - " standard (before 1914, for example)\n", - " - cash was a gold or silver coin\n", - " - a *deposit receipt* was a *bank note* that the bank promised to\n", - " convert into gold or silver on demand; (sometimes it was also a\n", - " checking or savings account balance)\n", - "\n", - "Economists and financiers often define the **supply of money** as an\n", - "economy-wide sum of **cash** plus **deposits**.\n", - "\n", - "In a **fractional reserve banking system** (one in which the reserve\n", - "ratio $r$ satisfies $0 < r < 1$), **banks create money** by issuing deposits *backed* by fractional reserves plus loans that they make to their customers.\n", - "\n", - "A geometric series is a key tool for understanding how banks create\n", - "money (i.e., deposits) in a fractional reserve system.\n", - "\n", - "The geometric series formula {eq}`infinite` is at the heart of the classic model of the money creation process -- one that leads us to the celebrated\n", - "**money multiplier**.\n", - "\n", - "### A Simple Model\n", - "\n", - "There is a set of banks named $i = 0, 1, 2, \\ldots$.\n", - "\n", - "Bank $i$'s loans $L_i$, deposits $D_i$, and\n", - "reserves $R_i$ must satisfy the balance sheet equation (because\n", - "**balance sheets balance**):\n", - "\n", - "```{math}\n", - ":label: balance\n", - "\n", - "L_i + R_i = D_i\n", - "```\n", - "\n", - "The left side of the above equation is the sum of the bank's **assets**,\n", - "namely, the loans $L_i$ it has outstanding plus its reserves of\n", - "cash $R_i$.\n", - "\n", - "The right side records bank $i$'s liabilities,\n", - "namely, the deposits $D_i$ held by its depositors; these are\n", - "IOU's from the bank to its depositors in the form of either checking\n", - "accounts or savings accounts (or before 1914, bank notes issued by a\n", - "bank stating promises to redeem note for gold or silver on demand).\n", - "\n", - "Each bank $i$ sets its reserves to satisfy the equation\n", - "\n", - "```{math}\n", - ":label: reserves\n", - "\n", - "R_i = r D_i\n", - "```\n", - "\n", - "where $r \\in (0,1)$ is its **reserve-deposit ratio** or **reserve\n", - "ratio** for short\n", - "\n", - "- the reserve ratio is either set by a government or chosen by banks\n", - " for precautionary reasons\n", - "\n", - "Next we add a theory stating that bank $i+1$'s deposits depend\n", - "entirely on loans made by bank $i$, namely\n", - "\n", - "```{math}\n", - ":label: deposits\n", - "\n", - "D_{i+1} = L_i\n", - "```\n", - "\n", - "Thus, we can think of the banks as being arranged along a line with\n", - "loans from bank $i$ being immediately deposited in $i+1$\n", - "\n", - "- in this way, the debtors to bank $i$ become creditors of\n", - " bank $i+1$\n", - "\n", - "Finally, we add an *initial condition* about an exogenous level of bank\n", - "$0$'s deposits\n", - "\n", - "$$\n", - "D_0 \\ \\text{ is given exogenously}\n", - "$$\n", - "\n", - "We can think of $D_0$ as being the amount of cash that a first\n", - "depositor put into the first bank in the system, bank number $i=0$.\n", - "\n", - "Now we do a little algebra.\n", - "\n", - "Combining equations {eq}`balance` and {eq}`reserves` tells us that\n", - "\n", - "```{math}\n", - ":label: fraction\n", - "\n", - "L_i = (1-r) D_i\n", - "```\n", - "\n", - "This states that bank $i$ loans a fraction $(1-r)$ of its\n", - "deposits and keeps a fraction $r$ as cash reserves.\n", - "\n", - "Combining equation {eq}`fraction` with equation {eq}`deposits` tells us that\n", - "\n", - "$$\n", - "D_{i+1} = (1-r) D_i \\ \\text{ for } i \\geq 0\n", - "$$\n", - "\n", - "which implies that\n", - "\n", - "```{math}\n", - ":label: geomseries\n", - "\n", - "D_i = (1 - r)^i D_0 \\ \\text{ for } i \\geq 0\n", - "```\n", - "\n", - "Equation {eq}`geomseries` expresses $D_i$ as the $i$ th term in the\n", - "product of $D_0$ and the geometric series\n", - "\n", - "$$\n", - "1, (1-r), (1-r)^2, \\cdots\n", - "$$\n", - "\n", - "Therefore, the sum of all deposits in our banking system\n", - "$i=0, 1, 2, \\ldots$ is\n", - "\n", - "```{math}\n", - ":label: sumdeposits\n", - "\n", - "\\sum_{i=0}^\\infty (1-r)^i D_0 = \\frac{D_0}{1 - (1-r)} = \\frac{D_0}{r}\n", - "```\n", - "\n", - "### Money Multiplier\n", - "\n", - "The **money multiplier** is a number that tells the multiplicative\n", - "factor by which an exogenous injection of cash into bank $0$ leads\n", - "to an increase in the total deposits in the banking system.\n", - "\n", - "Equation {eq}`sumdeposits` asserts that the **money multiplier** is\n", - "$\\frac{1}{r}$\n", - "\n", - "- An initial deposit of cash of $D_0$ in bank $0$ leads\n", - " the banking system to create total deposits of $\\frac{D_0}{r}$.\n", - "- The initial deposit $D_0$ is held as reserves, distributed\n", - " throughout the banking system according to $D_0 = \\sum_{i=0}^\\infty R_i$.\n", - "\n", - "## Example: The Keynesian Multiplier\n", - "\n", - "The famous economist John Maynard Keynes and his followers created a\n", - "simple model intended to determine national income $y$ in\n", - "circumstances in which\n", - "\n", - "- there are substantial unemployed resources, in particular **excess\n", - " supply** of labor and capital\n", - "- prices and interest rates fail to adjust to make aggregate **supply\n", - " equal demand** (e.g., prices and interest rates are frozen)\n", - "- national income is entirely determined by aggregate demand\n", - "\n", - "### Static Version\n", - "\n", - "An elementary Keynesian model of national income determination consists\n", - "of three equations that describe aggregate demand for $y$ and its\n", - "components.\n", - "\n", - "The first equation is a national income identity asserting that\n", - "consumption $c$ plus investment $i$ equals national income\n", - "$y$:\n", - "\n", - "$$\n", - "c+ i = y\n", - "$$\n", - "\n", - "The second equation is a Keynesian consumption function asserting that\n", - "people consume a fraction $b \\in (0,1)$ of their income:\n", - "\n", - "$$\n", - "c = b y\n", - "$$\n", - "\n", - "The fraction $b \\in (0,1)$ is called the **marginal propensity to\n", - "consume**.\n", - "\n", - "The fraction $1-b \\in (0,1)$ is called the **marginal propensity\n", - "to save**.\n", - "\n", - "The third equation simply states that investment is exogenous at level\n", - "$i$.\n", - "\n", - "- *exogenous* means *determined outside this model*.\n", - "\n", - "Substituting the second equation into the first gives $(1-b) y = i$.\n", - "\n", - "Solving this equation for $y$ gives\n", - "\n", - "$$\n", - "y = \\frac{1}{1-b} i\n", - "$$\n", - "\n", - "The quantity $\\frac{1}{1-b}$ is called the **investment\n", - "multiplier** or simply the **multiplier**.\n", - "\n", - "Applying the formula for the sum of an infinite geometric series, we can\n", - "write the above equation as\n", - "\n", - "$$\n", - "y = i \\sum_{t=0}^\\infty b^t\n", - "$$\n", - "\n", - "where $t$ is a nonnegative integer.\n", - "\n", - "So we arrive at the following equivalent expressions for the multiplier:\n", - "\n", - "$$\n", - "\\frac{1}{1-b} = \\sum_{t=0}^\\infty b^t\n", - "$$\n", - "\n", - "The expression $\\sum_{t=0}^\\infty b^t$ motivates an interpretation\n", - "of the multiplier as the outcome of a dynamic process that we describe\n", - "next.\n", - "\n", - "### Dynamic Version\n", - "\n", - "We arrive at a dynamic version by interpreting the nonnegative integer\n", - "$t$ as indexing time and changing our specification of the\n", - "consumption function to take time into account\n", - "\n", - "- we add a one-period lag in how income affects consumption\n", - "\n", - "We let $c_t$ be consumption at time $t$ and $i_t$ be\n", - "investment at time $t$.\n", - "\n", - "We modify our consumption function to assume the form\n", - "\n", - "$$\n", - "c_t = b y_{t-1}\n", - "$$\n", - "\n", - "so that $b$ is the marginal propensity to consume (now) out of\n", - "last period's income.\n", - "\n", - "We begin with an initial condition stating that\n", - "\n", - "$$\n", - "y_{-1} = 0\n", - "$$\n", - "\n", - "We also assume that\n", - "\n", - "$$\n", - "i_t = i \\ \\ \\textrm {for all } t \\geq 0\n", - "$$\n", - "\n", - "so that investment is constant over time.\n", - "\n", - "It follows that\n", - "\n", - "$$\n", - "y_0 = i + c_0 = i + b y_{-1} = i\n", - "$$\n", - "\n", - "and\n", - "\n", - "$$\n", - "y_1 = c_1 + i = b y_0 + i = (1 + b) i\n", - "$$\n", - "\n", - "and\n", - "\n", - "$$\n", - "y_2 = c_2 + i = b y_1 + i = (1 + b + b^2) i\n", - "$$\n", - "\n", - "and more generally\n", - "\n", - "$$\n", - "y_t = b y_{t-1} + i = (1+ b + b^2 + \\cdots + b^t) i\n", - "$$\n", - "\n", - "or\n", - "\n", - "$$\n", - "y_t = \\frac{1-b^{t+1}}{1 -b } i\n", - "$$\n", - "\n", - "Evidently, as $t \\rightarrow + \\infty$,\n", - "\n", - "$$\n", - "y_t \\rightarrow \\frac{1}{1-b} i\n", - "$$\n", - "\n", - "**Remark 1:** The above formula is often applied to assert that an\n", - "exogenous increase in investment of $\\Delta i$ at time $0$\n", - "ignites a dynamic process of increases in national income by successive amounts\n", - "\n", - "$$\n", - "\\Delta i, (1 + b )\\Delta i, (1+b + b^2) \\Delta i , \\cdots\n", - "$$\n", - "\n", - "at times $0, 1, 2, \\ldots$.\n", - "\n", - "**Remark 2** Let $g_t$ be an exogenous sequence of government\n", - "expenditures.\n", - "\n", - "If we generalize the model so that the national income identity\n", - "becomes\n", - "\n", - "$$\n", - "c_t + i_t + g_t = y_t\n", - "$$\n", - "\n", - "then a version of the preceding argument shows that the **government\n", - "expenditures multiplier** is also $\\frac{1}{1-b}$, so that a\n", - "permanent increase in government expenditures ultimately leads to an\n", - "increase in national income equal to the multiplier times the increase\n", - "in government expenditures.\n", - "\n", - "## Example: Interest Rates and Present Values\n", - "\n", - "We can apply our formula for geometric series to study how interest\n", - "rates affect values of streams of dollar payments that extend over time.\n", - "\n", - "We work in discrete time and assume that $t = 0, 1, 2, \\ldots$\n", - "indexes time.\n", - "\n", - "We let $r \\in (0,1)$ be a one-period **net nominal interest rate**\n", - "\n", - "- if the nominal interest rate is $5$ percent,\n", - " then $r= .05$\n", - "\n", - "A one-period **gross nominal interest rate** $R$ is defined as\n", - "\n", - "$$\n", - "R = 1 + r \\in (1, 2)\n", - "$$\n", - "\n", - "- if $r=.05$, then $R = 1.05$\n", - "\n", - "**Remark:** The gross nominal interest rate $R$ is an **exchange\n", - "rate** or **relative price** of dollars at between times $t$ and\n", - "$t+1$. The units of $R$ are dollars at time $t+1$ per\n", - "dollar at time $t$.\n", - "\n", - "When people borrow and lend, they trade dollars now for dollars later or\n", - "dollars later for dollars now.\n", - "\n", - "The price at which these exchanges occur is the gross nominal interest\n", - "rate.\n", - "\n", - "- If I sell $x$ dollars to you today, you pay me $R x$\n", - " dollars tomorrow.\n", - "- This means that you borrowed $x$ dollars for me at a gross\n", - " interest rate $R$ and a net interest rate $r$.\n", - "\n", - "We assume that the net nominal interest rate $r$ is fixed over\n", - "time, so that $R$ is the gross nominal interest rate at times\n", - "$t=0, 1, 2, \\ldots$.\n", - "\n", - "Two important geometric sequences are\n", - "\n", - "```{math}\n", - ":label: geom1\n", - "\n", - "1, R, R^2, \\cdots\n", - "```\n", - "\n", - "and\n", - "\n", - "```{math}\n", - ":label: geom2\n", - "\n", - "1, R^{-1}, R^{-2}, \\cdots\n", - "```\n", - "\n", - "Sequence {eq}`geom1` tells us how dollar values of an investment **accumulate**\n", - "through time.\n", - "\n", - "Sequence {eq}`geom2` tells us how to **discount** future dollars to get their\n", - "values in terms of today's dollars.\n", - "\n", - "### Accumulation\n", - "\n", - "Geometric sequence {eq}`geom1` tells us how one dollar invested and re-invested\n", - "in a project with gross one period nominal rate of return accumulates\n", - "\n", - "- here we assume that net interest payments are reinvested in the\n", - " project\n", - "- thus, $1$ dollar invested at time $0$ pays interest\n", - " $r$ dollars after one period, so we have $r+1 = R$\n", - " dollars at time$1$\n", - "- at time $1$ we reinvest $1+r =R$ dollars and receive interest\n", - " of $r R$ dollars at time $2$ plus the *principal*\n", - " $R$ dollars, so we receive $r R + R = (1+r)R = R^2$\n", - " dollars at the end of period $2$\n", - "- and so on\n", - "\n", - "Evidently, if we invest $x$ dollars at time $0$ and\n", - "reinvest the proceeds, then the sequence\n", - "\n", - "$$\n", - "x , xR , x R^2, \\cdots\n", - "$$\n", - "\n", - "tells how our account accumulates at dates $t=0, 1, 2, \\ldots$.\n", - "\n", - "### Discounting\n", - "\n", - "Geometric sequence {eq}`geom2` tells us how much future dollars are worth in terms of today's dollars.\n", - "\n", - "Remember that the units of $R$ are dollars at $t+1$ per\n", - "dollar at $t$.\n", - "\n", - "It follows that\n", - "\n", - "- the units of $R^{-1}$ are dollars at $t$ per dollar at $t+1$\n", - "- the units of $R^{-2}$ are dollars at $t$ per dollar at $t+2$\n", - "- and so on; the units of $R^{-j}$ are dollars at $t$ per\n", - " dollar at $t+j$\n", - "\n", - "So if someone has a claim on $x$ dollars at time $t+j$, it\n", - "is worth $x R^{-j}$ dollars at time $t$ (e.g., today).\n", - "\n", - "### Application to Asset Pricing\n", - "\n", - "A **lease** requires a payments stream of $x_t$ dollars at\n", - "times $t = 0, 1, 2, \\ldots$ where\n", - "\n", - "$$\n", - "x_t = G^t x_0\n", - "$$\n", - "\n", - "where $G = (1+g)$ and $g \\in (0,1)$.\n", - "\n", - "Thus, lease payments increase at $g$ percent per period.\n", - "\n", - "For a reason soon to be revealed, we assume that $G < R$.\n", - "\n", - "The **present value** of the lease is\n", - "\n", - "$$\n", - "\\begin{aligned} p_0 & = x_0 + x_1/R + x_2/(R^2) + \\ddots \\\\\n", - " & = x_0 (1 + G R^{-1} + G^2 R^{-2} + \\cdots ) \\\\\n", - " & = x_0 \\frac{1}{1 - G R^{-1}} \\end{aligned}\n", - "$$\n", - "\n", - "where the last line uses the formula for an infinite geometric series.\n", - "\n", - "Recall that $R = 1+r$ and $G = 1+g$ and that $R > G$\n", - "and $r > g$ and that $r$ and $g$ are typically small\n", - "numbers, e.g., .05 or .03.\n", - "\n", - "Use the Taylor series of $\\frac{1}{1+r}$ about $r=0$,\n", - "namely,\n", - "\n", - "$$\n", - "\\frac{1}{1+r} = 1 - r + r^2 - r^3 + \\cdots\n", - "$$\n", - "\n", - "and the fact that $r$ is small to approximate\n", - "$\\frac{1}{1+r} \\approx 1 - r$.\n", - "\n", - "Use this approximation to write $p_0$ as\n", - "\n", - "$$\n", - "\\begin{aligned}\n", - " p_0 &= x_0 \\frac{1}{1 - G R^{-1}} \\\\\n", - " &= x_0 \\frac{1}{1 - (1+g) (1-r) } \\\\\n", - " &= x_0 \\frac{1}{1 - (1+g - r - rg)} \\\\\n", - " & \\approx x_0 \\frac{1}{r -g }\n", - "\\end{aligned}\n", - "$$\n", - "\n", - "where the last step uses the approximation $r g \\approx 0$.\n", - "\n", - "The approximation\n", - "\n", - "$$\n", - "p_0 = \\frac{x_0 }{r -g }\n", - "$$\n", - "\n", - "is known as the **Gordon formula** for the present value or current\n", - "price of an infinite payment stream $x_0 G^t$ when the nominal\n", - "one-period interest rate is $r$ and when $r > g$.\n", - "\n", - "We can also extend the asset pricing formula so that it applies to finite leases.\n", - "\n", - "Let the payment stream on the lease now be $x_t$ for $t= 1,2, \\dots,T$, where again\n", - "\n", - "$$\n", - "x_t = G^t x_0\n", - "$$\n", - "\n", - "The present value of this lease is:\n", - "\n", - "$$\n", - "\\begin{aligned} \\begin{split}p_0&=x_0 + x_1/R + \\dots +x_T/R^T \\\\ &= x_0(1+GR^{-1}+\\dots +G^{T}R^{-T}) \\\\ &= \\frac{x_0(1-G^{T+1}R^{-(T+1)})}{1-GR^{-1}} \\end{split}\\end{aligned}\n", - "$$\n", - "\n", - "Applying the Taylor series to $R^{-(T+1)}$ about $r=0$ we get:\n", - "\n", - "$$\n", - "\\frac{1}{(1+r)^{T+1}}= 1-r(T+1)+\\frac{1}{2}r^2(T+1)(T+2)+\\dots \\approx 1-r(T+1)\n", - "$$\n", - "\n", - "Similarly, applying the Taylor series to $G^{T+1}$ about $g=0$:\n", - "\n", - "$$\n", - "(1+g)^{T+1} = 1+(T+1)g+\\frac{T(T+1)}{2!}g^2+\\frac{(T-1)T(T+1)}{3!}g^3+\\dots \\approx 1+ (T+1)g\n", - "$$\n", - "\n", - "Thus, we get the following approximation:\n", - "\n", - "$$\n", - "p_0 =\\frac{x_0(1-(1+(T+1)g)(1-r(T+1)))}{1-(1-r)(1+g) }\n", - "$$\n", - "\n", - "Expanding:\n", - "\n", - "$$\n", - "\\begin{aligned} p_0 &=\\frac{x_0(1-1+(T+1)^2 rg -r(T+1)+g(T+1))}{1-1+r-g+rg} \\\\&=\\frac{x_0(T+1)((T+1)rg+r-g)}{r-g+rg} \\\\ &\\approx \\frac{x_0(T+1)(r-g)}{r-g}+\\frac{x_0rg(T+1)}{r-g}\\\\ &= x_0(T+1) + \\frac{x_0rg(T+1)}{r-g} \\end{aligned}\n", - "$$\n", - "\n", - "We could have also approximated by removing the second term\n", - "$rgx_0(T+1)$ when $T$ is relatively small compared to\n", - "$1/(rg)$ to get $x_0(T+1)$ as in the finite stream\n", - "approximation.\n", - "\n", - "We will plot the true finite stream present-value and the two\n", - "approximations, under different values of $T$, and $g$ and $r$ in Python.\n", - "\n", - "First we plot the true finite stream present-value after computing it\n", - "below" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "45dd667c", - "metadata": {}, - "outputs": [], - "source": [ - "# True present value of a finite lease\n", - "def finite_lease_pv_true(T, g, r, x_0):\n", - " G = (1 + g)\n", - " R = (1 + r)\n", - " return (x_0 * (1 - G**(T + 1) * R**(-T - 1))) / (1 - G * R**(-1))\n", - "# First approximation for our finite lease\n", - "\n", - "def finite_lease_pv_approx_1(T, g, r, x_0):\n", - " p = x_0 * (T + 1) + x_0 * r * g * (T + 1) / (r - g)\n", - " return p\n", - "\n", - "# Second approximation for our finite lease\n", - "def finite_lease_pv_approx_2(T, g, r, x_0):\n", - " return (x_0 * (T + 1))\n", - "\n", - "# Infinite lease\n", - "def infinite_lease(g, r, x_0):\n", - " G = (1 + g)\n", - " R = (1 + r)\n", - " return x_0 / (1 - G * R**(-1))" - ] - }, - { - "cell_type": "markdown", - "id": "53b55bbf", - "metadata": {}, - "source": [ - "Now that we have defined our functions, we can plot some outcomes.\n", - "\n", - "First we study the quality of our approximations" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "efde9d92", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_5_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "def plot_function(axes, x_vals, func, args):\n", - " axes.plot(x_vals, func(*args), label=func.__name__)\n", - "\n", - "T_max = 50\n", - "\n", - "T = np.arange(0, T_max+1)\n", - "g = 0.02\n", - "r = 0.03\n", - "x_0 = 1\n", - "\n", - "our_args = (T, g, r, x_0)\n", - "funcs = [finite_lease_pv_true,\n", - " finite_lease_pv_approx_1,\n", - " finite_lease_pv_approx_2]\n", - " ## the three functions we want to compare\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Finite Lease Present Value $T$ Periods Ahead')\n", - "for f in funcs:\n", - " plot_function(ax, T, f, our_args)\n", - "ax.legend()\n", - "ax.set_xlabel('$T$ Periods Ahead')\n", - "ax.set_ylabel('Present Value, $p_0$')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "c4f1780c", - "metadata": {}, - "source": [ - "Evidently our approximations perform well for small values of $T$.\n", - "\n", - "However, holding $g$ and r fixed, our approximations deteriorate as $T$ increases.\n", - "\n", - "Next we compare the infinite and finite duration lease present values\n", - "over different lease lengths $T$." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "ff816691", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_7_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "# Convergence of infinite and finite\n", - "T_max = 1000\n", - "T = np.arange(0, T_max+1)\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Infinite and Finite Lease Present Value $T$ Periods Ahead')\n", - "f_1 = finite_lease_pv_true(T, g, r, x_0)\n", - "f_2 = np.full(T_max+1, infinite_lease(g, r, x_0))\n", - "ax.plot(T, f_1, label='T-period lease PV')\n", - "ax.plot(T, f_2, '--', label='Infinite lease PV')\n", - "ax.set_xlabel('$T$ Periods Ahead')\n", - "ax.set_ylabel('Present Value, $p_0$')\n", - "ax.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "d4709249", - "metadata": {}, - "source": [ - "The graph above shows how as duration $T \\rightarrow +\\infty$,\n", - "the value of a lease of duration $T$ approaches the value of a\n", - "perpetual lease.\n", - "\n", - "Now we consider two different views of what happens as $r$ and\n", - "$g$ covary" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "50e7ed8a", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_9_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "# First view\n", - "# Changing r and g\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Value of lease of length $T$')\n", - "ax.set_ylabel('Present Value, $p_0$')\n", - "ax.set_xlabel('$T$ periods ahead')\n", - "T_max = 10\n", - "T=np.arange(0, T_max+1)\n", - "\n", - "rs, gs = (0.9, 0.5, 0.4001, 0.4), (0.4, 0.4, 0.4, 0.5),\n", - "comparisons = ('$\\gg$', '$>$', r'$\\approx$', '$<$')\n", - "for r, g, comp in zip(rs, gs, comparisons):\n", - " ax.plot(finite_lease_pv_true(T, g, r, x_0), label=f'r(={r}) {comp} g(={g})')\n", - "\n", - "ax.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "7844a514", - "metadata": {}, - "source": [ - "This graph gives a big hint for why the condition $r > g$ is\n", - "necessary if a lease of length $T = +\\infty$ is to have finite\n", - "value.\n", - "\n", - "For fans of 3-d graphs the same point comes through in the following\n", - "graph.\n", - "\n", - "If you aren't enamored of 3-d graphs, feel free to skip the next\n", - "visualization!" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "142d0a9e", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_11_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "# Second view\n", - "fig = plt.figure()\n", - "T = 3\n", - "ax = plt.subplot(projection='3d')\n", - "r = np.arange(0.01, 0.99, 0.005)\n", - "g = np.arange(0.011, 0.991, 0.005)\n", - "\n", - "rr, gg = np.meshgrid(r, g)\n", - "z = finite_lease_pv_true(T, gg, rr, x_0)\n", - "\n", - "# Removes points where undefined\n", - "same = (rr == gg)\n", - "z[same] = np.nan\n", - "surf = ax.plot_surface(rr, gg, z, cmap=cm.coolwarm,\n", - " antialiased=True, clim=(0, 15))\n", - "fig.colorbar(surf, shrink=0.5, aspect=5)\n", - "ax.set_xlabel('$r$')\n", - "ax.set_ylabel('$g$')\n", - "ax.set_zlabel('Present Value, $p_0$')\n", - "ax.view_init(20, 10)\n", - "ax.set_title('Three Period Lease PV with Varying $g$ and $r$')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "5df0e132", - "metadata": {}, - "source": [ - "We can use a little calculus to study how the present value $p_0$\n", - "of a lease varies with $r$ and $g$.\n", - "\n", - "We will use a library called [SymPy](https://www.sympy.org/).\n", - "\n", - "SymPy enables us to do symbolic math calculations including\n", - "computing derivatives of algebraic equations.\n", - "\n", - "We will illustrate how it works by creating a symbolic expression that\n", - "represents our present value formula for an infinite lease.\n", - "\n", - "After that, we'll use SymPy to compute derivatives" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "bd0ad70e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Our formula is:\n" - ] - }, - { - "data": { - "text/latex": [ - "$\\displaystyle \\frac{x_{0}}{- \\frac{g + 1}{r + 1} + 1}$" - ], - "text/plain": [ - " x₀ \n", - "───────────\n", - " g + 1 \n", - "- ───── + 1\n", - " r + 1 " - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Creates algebraic symbols that can be used in an algebraic expression\n", - "g, r, x0 = sym.symbols('g, r, x0')\n", - "G = (1 + g)\n", - "R = (1 + r)\n", - "p0 = x0 / (1 - G * R**(-1))\n", - "init_printing(use_latex='mathjax')\n", - "print('Our formula is:')\n", - "p0" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "639487a8", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "dp0 / dg is:\n" - ] - }, - { - "data": { - "text/latex": [ - "$\\displaystyle \\frac{x_{0}}{\\left(r + 1\\right) \\left(- \\frac{g + 1}{r + 1} + 1\\right)^{2}}$" - ], - "text/plain": [ - " x₀ \n", - "──────────────────────\n", - " 2\n", - " ⎛ g + 1 ⎞ \n", - "(r + 1)⋅⎜- ───── + 1⎟ \n", - " ⎝ r + 1 ⎠ " - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "print('dp0 / dg is:')\n", - "dp_dg = sym.diff(p0, g)\n", - "dp_dg" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "e993d26f", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "dp0 / dr is:\n" - ] - }, - { - "data": { - "text/latex": [ - "$\\displaystyle - \\frac{x_{0} \\left(g + 1\\right)}{\\left(r + 1\\right)^{2} \\left(- \\frac{g + 1}{r + 1} + 1\\right)^{2}}$" - ], - "text/plain": [ - " -x₀⋅(g + 1) \n", - "───────────────────────\n", - " 2\n", - " 2 ⎛ g + 1 ⎞ \n", - "(r + 1) ⋅⎜- ───── + 1⎟ \n", - " ⎝ r + 1 ⎠ " - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "print('dp0 / dr is:')\n", - "dp_dr = sym.diff(p0, r)\n", - "dp_dr" - ] - }, - { - "cell_type": "markdown", - "id": "57283836", - "metadata": {}, - "source": [ - "We can see that for $\\frac{\\partial p_0}{\\partial r}<0$ as long as\n", - "$r>g$, $r>0$ and $g>0$ and $x_0$ is positive,\n", - "so $\\frac{\\partial p_0}{\\partial r}$ will always be negative.\n", - "\n", - "Similarly, $\\frac{\\partial p_0}{\\partial g}>0$ as long as $r>g$, $r>0$ and $g>0$ and $x_0$ is positive, so $\\frac{\\partial p_0}{\\partial g}$\n", - "will always be positive.\n", - "\n", - "## Back to the Keynesian Multiplier\n", - "\n", - "We will now go back to the case of the Keynesian multiplier and plot the\n", - "time path of $y_t$, given that consumption is a constant fraction\n", - "of national income, and investment is fixed." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "e64c49c0", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_17_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "# Function that calculates a path of y\n", - "def calculate_y(i, b, g, T, y_init):\n", - " y = np.zeros(T+1)\n", - " y[0] = i + b * y_init + g\n", - " for t in range(1, T+1):\n", - " y[t] = b * y[t-1] + i + g\n", - " return y\n", - "\n", - "# Initial values\n", - "i_0 = 0.3\n", - "g_0 = 0.3\n", - "# 2/3 of income goes towards consumption\n", - "b = 2/3\n", - "y_init = 0\n", - "T = 100\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.set_title('Path of Aggregate Output Over Time')\n", - "ax.set_xlabel('$t$')\n", - "ax.set_ylabel('$y_t$')\n", - "ax.plot(np.arange(0, T+1), calculate_y(i_0, b, g_0, T, y_init))\n", - "# Output predicted by geometric series\n", - "ax.hlines(i_0 / (1 - b) + g_0 / (1 - b), xmin=-1, xmax=101, linestyles='--')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "df1abb00", - "metadata": {}, - "source": [ - "In this model, income grows over time, until it gradually converges to\n", - "the infinite geometric series sum of income.\n", - "\n", - "We now examine what will\n", - "happen if we vary the so-called **marginal propensity to consume**,\n", - "i.e., the fraction of income that is consumed" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "871f6b2d", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_19_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "bs = (1/3, 2/3, 5/6, 0.9)\n", - "\n", - "fig,ax = plt.subplots()\n", - "ax.set_title('Changing Consumption as a Fraction of Income')\n", - "ax.set_ylabel('$y_t$')\n", - "ax.set_xlabel('$t$')\n", - "x = np.arange(0, T+1)\n", - "for b in bs:\n", - " y = calculate_y(i_0, b, g_0, T, y_init)\n", - " ax.plot(x, y, label=r'$b=$'+f\"{b:.2f}\")\n", - "ax.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "03804c33", - "metadata": {}, - "source": [ - "Increasing the marginal propensity to consume $b$ increases the\n", - "path of output over time.\n", - "\n", - "Now we will compare the effects on output of increases in investment and government spending." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "1a08cc9c", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/geom_series_21_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 10))\n", - "fig.subplots_adjust(hspace=0.3)\n", - "\n", - "x = np.arange(0, T+1)\n", - "values = [0.3, 0.4]\n", - "\n", - "for i in values:\n", - " y = calculate_y(i, b, g_0, T, y_init)\n", - " ax1.plot(x, y, label=f\"i={i}\")\n", - "for g in values:\n", - " y = calculate_y(i_0, b, g, T, y_init)\n", - " ax2.plot(x, y, label=f\"g={g}\")\n", - "\n", - "axes = ax1, ax2\n", - "param_labels = \"Investment\", \"Government Spending\"\n", - "for ax, param in zip(axes, param_labels):\n", - " ax.set_title(f'An Increase in {param} on Output')\n", - " ax.legend(loc =\"lower right\")\n", - " ax.set_ylabel('$y_t$')\n", - " ax.set_xlabel('$t$')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "b4a0192e", - "metadata": {}, - "source": [ - "Notice here, whether government spending increases from 0.3 to 0.4 or\n", - "investment increases from 0.3 to 0.4, the shifts in the graphs are\n", - "identical." - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 51, - 60, - 655, - 676, - 682, - 707, - 716, - 730, - 739, - 756, - 768, - 791, - 806, - 817, - 823, - 827, - 842, - 867, - 876, - 889, - 896, - 918 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/jupyter_execute/geom_series.py b/lectures/_build/jupyter_execute/geom_series.py deleted file mode 100644 index fb0dd0ba1..000000000 --- a/lectures/_build/jupyter_execute/geom_series.py +++ /dev/null @@ -1,938 +0,0 @@ -#!/usr/bin/env python -# coding: utf-8 - -# (geom_series)= -# ```{raw} html -#
-# -# QuantEcon -# -#
-# ``` -# -# ```{index} single: python -# ``` -# -# # Geometric Series for Elementary Economics -# -# ```{contents} Contents -# :depth: 2 -# ``` -# -# ## Overview -# -# The lecture describes important ideas in economics that use the mathematics of geometric series. -# -# Among these are -# -# - the Keynesian **multiplier** -# - the money **multiplier** that prevails in fractional reserve banking -# systems -# - interest rates and present values of streams of payouts from assets -# -# (As we shall see below, the term **multiplier** comes down to meaning **sum of a convergent geometric series**) -# -# These and other applications prove the truth of the wise crack that -# -# ```{epigraph} -# "in economics, a little knowledge of geometric series goes a long way " -# ``` -# -# Below we'll use the following imports: - -# In[1]: - - -get_ipython().run_line_magic('matplotlib', 'inline') -import matplotlib.pyplot as plt -plt.rcParams["figure.figsize"] = (11, 5) #set default figure size -import numpy as np -import sympy as sym -from sympy import init_printing, latex -from matplotlib import cm -from mpl_toolkits.mplot3d import Axes3D - - -# ## Key Formulas -# -# To start, let $c$ be a real number that lies strictly between -# $-1$ and $1$. -# -# - We often write this as $c \in (-1,1)$. -# - Here $(-1,1)$ denotes the collection of all real numbers that -# are strictly less than $1$ and strictly greater than $-1$. -# - The symbol $\in$ means *in* or *belongs to the set after the symbol*. -# -# We want to evaluate geometric series of two types -- infinite and finite. -# -# ### Infinite Geometric Series -# -# The first type of geometric that interests us is the infinite series -# -# $$ -# 1 + c + c^2 + c^3 + \cdots -# $$ -# -# Where $\cdots$ means that the series continues without end. -# -# The key formula is -# -# ```{math} -# :label: infinite -# -# 1 + c + c^2 + c^3 + \cdots = \frac{1}{1 -c } -# ``` -# -# To prove key formula {eq}`infinite`, multiply both sides by $(1-c)$ and verify -# that if $c \in (-1,1)$, then the outcome is the -# equation $1 = 1$. -# -# ### Finite Geometric Series -# -# The second series that interests us is the finite geometric series -# -# $$ -# 1 + c + c^2 + c^3 + \cdots + c^T -# $$ -# -# where $T$ is a positive integer. -# -# The key formula here is -# -# $$ -# 1 + c + c^2 + c^3 + \cdots + c^T = \frac{1 - c^{T+1}}{1-c} -# $$ -# -# **Remark:** The above formula works for any value of the scalar -# $c$. We don't have to restrict $c$ to be in the -# set $(-1,1)$. -# -# We now move on to describe some famous economic applications of -# geometric series. -# -# ## Example: The Money Multiplier in Fractional Reserve Banking -# -# In a fractional reserve banking system, banks hold only a fraction -# $r \in (0,1)$ of cash behind each **deposit receipt** that they -# issue -# -# * In recent times -# - cash consists of pieces of paper issued by the government and -# called dollars or pounds or $\ldots$ -# - a *deposit* is a balance in a checking or savings account that -# entitles the owner to ask the bank for immediate payment in cash -# * When the UK and France and the US were on either a gold or silver -# standard (before 1914, for example) -# - cash was a gold or silver coin -# - a *deposit receipt* was a *bank note* that the bank promised to -# convert into gold or silver on demand; (sometimes it was also a -# checking or savings account balance) -# -# Economists and financiers often define the **supply of money** as an -# economy-wide sum of **cash** plus **deposits**. -# -# In a **fractional reserve banking system** (one in which the reserve -# ratio $r$ satisfies $0 < r < 1$), **banks create money** by issuing deposits *backed* by fractional reserves plus loans that they make to their customers. -# -# A geometric series is a key tool for understanding how banks create -# money (i.e., deposits) in a fractional reserve system. -# -# The geometric series formula {eq}`infinite` is at the heart of the classic model of the money creation process -- one that leads us to the celebrated -# **money multiplier**. -# -# ### A Simple Model -# -# There is a set of banks named $i = 0, 1, 2, \ldots$. -# -# Bank $i$'s loans $L_i$, deposits $D_i$, and -# reserves $R_i$ must satisfy the balance sheet equation (because -# **balance sheets balance**): -# -# ```{math} -# :label: balance -# -# L_i + R_i = D_i -# ``` -# -# The left side of the above equation is the sum of the bank's **assets**, -# namely, the loans $L_i$ it has outstanding plus its reserves of -# cash $R_i$. -# -# The right side records bank $i$'s liabilities, -# namely, the deposits $D_i$ held by its depositors; these are -# IOU's from the bank to its depositors in the form of either checking -# accounts or savings accounts (or before 1914, bank notes issued by a -# bank stating promises to redeem note for gold or silver on demand). -# -# Each bank $i$ sets its reserves to satisfy the equation -# -# ```{math} -# :label: reserves -# -# R_i = r D_i -# ``` -# -# where $r \in (0,1)$ is its **reserve-deposit ratio** or **reserve -# ratio** for short -# -# - the reserve ratio is either set by a government or chosen by banks -# for precautionary reasons -# -# Next we add a theory stating that bank $i+1$'s deposits depend -# entirely on loans made by bank $i$, namely -# -# ```{math} -# :label: deposits -# -# D_{i+1} = L_i -# ``` -# -# Thus, we can think of the banks as being arranged along a line with -# loans from bank $i$ being immediately deposited in $i+1$ -# -# - in this way, the debtors to bank $i$ become creditors of -# bank $i+1$ -# -# Finally, we add an *initial condition* about an exogenous level of bank -# $0$'s deposits -# -# $$ -# D_0 \ \text{ is given exogenously} -# $$ -# -# We can think of $D_0$ as being the amount of cash that a first -# depositor put into the first bank in the system, bank number $i=0$. -# -# Now we do a little algebra. -# -# Combining equations {eq}`balance` and {eq}`reserves` tells us that -# -# ```{math} -# :label: fraction -# -# L_i = (1-r) D_i -# ``` -# -# This states that bank $i$ loans a fraction $(1-r)$ of its -# deposits and keeps a fraction $r$ as cash reserves. -# -# Combining equation {eq}`fraction` with equation {eq}`deposits` tells us that -# -# $$ -# D_{i+1} = (1-r) D_i \ \text{ for } i \geq 0 -# $$ -# -# which implies that -# -# ```{math} -# :label: geomseries -# -# D_i = (1 - r)^i D_0 \ \text{ for } i \geq 0 -# ``` -# -# Equation {eq}`geomseries` expresses $D_i$ as the $i$ th term in the -# product of $D_0$ and the geometric series -# -# $$ -# 1, (1-r), (1-r)^2, \cdots -# $$ -# -# Therefore, the sum of all deposits in our banking system -# $i=0, 1, 2, \ldots$ is -# -# ```{math} -# :label: sumdeposits -# -# \sum_{i=0}^\infty (1-r)^i D_0 = \frac{D_0}{1 - (1-r)} = \frac{D_0}{r} -# ``` -# -# ### Money Multiplier -# -# The **money multiplier** is a number that tells the multiplicative -# factor by which an exogenous injection of cash into bank $0$ leads -# to an increase in the total deposits in the banking system. -# -# Equation {eq}`sumdeposits` asserts that the **money multiplier** is -# $\frac{1}{r}$ -# -# - An initial deposit of cash of $D_0$ in bank $0$ leads -# the banking system to create total deposits of $\frac{D_0}{r}$. -# - The initial deposit $D_0$ is held as reserves, distributed -# throughout the banking system according to $D_0 = \sum_{i=0}^\infty R_i$. -# -# ## Example: The Keynesian Multiplier -# -# The famous economist John Maynard Keynes and his followers created a -# simple model intended to determine national income $y$ in -# circumstances in which -# -# - there are substantial unemployed resources, in particular **excess -# supply** of labor and capital -# - prices and interest rates fail to adjust to make aggregate **supply -# equal demand** (e.g., prices and interest rates are frozen) -# - national income is entirely determined by aggregate demand -# -# ### Static Version -# -# An elementary Keynesian model of national income determination consists -# of three equations that describe aggregate demand for $y$ and its -# components. -# -# The first equation is a national income identity asserting that -# consumption $c$ plus investment $i$ equals national income -# $y$: -# -# $$ -# c+ i = y -# $$ -# -# The second equation is a Keynesian consumption function asserting that -# people consume a fraction $b \in (0,1)$ of their income: -# -# $$ -# c = b y -# $$ -# -# The fraction $b \in (0,1)$ is called the **marginal propensity to -# consume**. -# -# The fraction $1-b \in (0,1)$ is called the **marginal propensity -# to save**. -# -# The third equation simply states that investment is exogenous at level -# $i$. -# -# - *exogenous* means *determined outside this model*. -# -# Substituting the second equation into the first gives $(1-b) y = i$. -# -# Solving this equation for $y$ gives -# -# $$ -# y = \frac{1}{1-b} i -# $$ -# -# The quantity $\frac{1}{1-b}$ is called the **investment -# multiplier** or simply the **multiplier**. -# -# Applying the formula for the sum of an infinite geometric series, we can -# write the above equation as -# -# $$ -# y = i \sum_{t=0}^\infty b^t -# $$ -# -# where $t$ is a nonnegative integer. -# -# So we arrive at the following equivalent expressions for the multiplier: -# -# $$ -# \frac{1}{1-b} = \sum_{t=0}^\infty b^t -# $$ -# -# The expression $\sum_{t=0}^\infty b^t$ motivates an interpretation -# of the multiplier as the outcome of a dynamic process that we describe -# next. -# -# ### Dynamic Version -# -# We arrive at a dynamic version by interpreting the nonnegative integer -# $t$ as indexing time and changing our specification of the -# consumption function to take time into account -# -# - we add a one-period lag in how income affects consumption -# -# We let $c_t$ be consumption at time $t$ and $i_t$ be -# investment at time $t$. -# -# We modify our consumption function to assume the form -# -# $$ -# c_t = b y_{t-1} -# $$ -# -# so that $b$ is the marginal propensity to consume (now) out of -# last period's income. -# -# We begin with an initial condition stating that -# -# $$ -# y_{-1} = 0 -# $$ -# -# We also assume that -# -# $$ -# i_t = i \ \ \textrm {for all } t \geq 0 -# $$ -# -# so that investment is constant over time. -# -# It follows that -# -# $$ -# y_0 = i + c_0 = i + b y_{-1} = i -# $$ -# -# and -# -# $$ -# y_1 = c_1 + i = b y_0 + i = (1 + b) i -# $$ -# -# and -# -# $$ -# y_2 = c_2 + i = b y_1 + i = (1 + b + b^2) i -# $$ -# -# and more generally -# -# $$ -# y_t = b y_{t-1} + i = (1+ b + b^2 + \cdots + b^t) i -# $$ -# -# or -# -# $$ -# y_t = \frac{1-b^{t+1}}{1 -b } i -# $$ -# -# Evidently, as $t \rightarrow + \infty$, -# -# $$ -# y_t \rightarrow \frac{1}{1-b} i -# $$ -# -# **Remark 1:** The above formula is often applied to assert that an -# exogenous increase in investment of $\Delta i$ at time $0$ -# ignites a dynamic process of increases in national income by successive amounts -# -# $$ -# \Delta i, (1 + b )\Delta i, (1+b + b^2) \Delta i , \cdots -# $$ -# -# at times $0, 1, 2, \ldots$. -# -# **Remark 2** Let $g_t$ be an exogenous sequence of government -# expenditures. -# -# If we generalize the model so that the national income identity -# becomes -# -# $$ -# c_t + i_t + g_t = y_t -# $$ -# -# then a version of the preceding argument shows that the **government -# expenditures multiplier** is also $\frac{1}{1-b}$, so that a -# permanent increase in government expenditures ultimately leads to an -# increase in national income equal to the multiplier times the increase -# in government expenditures. -# -# ## Example: Interest Rates and Present Values -# -# We can apply our formula for geometric series to study how interest -# rates affect values of streams of dollar payments that extend over time. -# -# We work in discrete time and assume that $t = 0, 1, 2, \ldots$ -# indexes time. -# -# We let $r \in (0,1)$ be a one-period **net nominal interest rate** -# -# - if the nominal interest rate is $5$ percent, -# then $r= .05$ -# -# A one-period **gross nominal interest rate** $R$ is defined as -# -# $$ -# R = 1 + r \in (1, 2) -# $$ -# -# - if $r=.05$, then $R = 1.05$ -# -# **Remark:** The gross nominal interest rate $R$ is an **exchange -# rate** or **relative price** of dollars at between times $t$ and -# $t+1$. The units of $R$ are dollars at time $t+1$ per -# dollar at time $t$. -# -# When people borrow and lend, they trade dollars now for dollars later or -# dollars later for dollars now. -# -# The price at which these exchanges occur is the gross nominal interest -# rate. -# -# - If I sell $x$ dollars to you today, you pay me $R x$ -# dollars tomorrow. -# - This means that you borrowed $x$ dollars for me at a gross -# interest rate $R$ and a net interest rate $r$. -# -# We assume that the net nominal interest rate $r$ is fixed over -# time, so that $R$ is the gross nominal interest rate at times -# $t=0, 1, 2, \ldots$. -# -# Two important geometric sequences are -# -# ```{math} -# :label: geom1 -# -# 1, R, R^2, \cdots -# ``` -# -# and -# -# ```{math} -# :label: geom2 -# -# 1, R^{-1}, R^{-2}, \cdots -# ``` -# -# Sequence {eq}`geom1` tells us how dollar values of an investment **accumulate** -# through time. -# -# Sequence {eq}`geom2` tells us how to **discount** future dollars to get their -# values in terms of today's dollars. -# -# ### Accumulation -# -# Geometric sequence {eq}`geom1` tells us how one dollar invested and re-invested -# in a project with gross one period nominal rate of return accumulates -# -# - here we assume that net interest payments are reinvested in the -# project -# - thus, $1$ dollar invested at time $0$ pays interest -# $r$ dollars after one period, so we have $r+1 = R$ -# dollars at time$1$ -# - at time $1$ we reinvest $1+r =R$ dollars and receive interest -# of $r R$ dollars at time $2$ plus the *principal* -# $R$ dollars, so we receive $r R + R = (1+r)R = R^2$ -# dollars at the end of period $2$ -# - and so on -# -# Evidently, if we invest $x$ dollars at time $0$ and -# reinvest the proceeds, then the sequence -# -# $$ -# x , xR , x R^2, \cdots -# $$ -# -# tells how our account accumulates at dates $t=0, 1, 2, \ldots$. -# -# ### Discounting -# -# Geometric sequence {eq}`geom2` tells us how much future dollars are worth in terms of today's dollars. -# -# Remember that the units of $R$ are dollars at $t+1$ per -# dollar at $t$. -# -# It follows that -# -# - the units of $R^{-1}$ are dollars at $t$ per dollar at $t+1$ -# - the units of $R^{-2}$ are dollars at $t$ per dollar at $t+2$ -# - and so on; the units of $R^{-j}$ are dollars at $t$ per -# dollar at $t+j$ -# -# So if someone has a claim on $x$ dollars at time $t+j$, it -# is worth $x R^{-j}$ dollars at time $t$ (e.g., today). -# -# ### Application to Asset Pricing -# -# A **lease** requires a payments stream of $x_t$ dollars at -# times $t = 0, 1, 2, \ldots$ where -# -# $$ -# x_t = G^t x_0 -# $$ -# -# where $G = (1+g)$ and $g \in (0,1)$. -# -# Thus, lease payments increase at $g$ percent per period. -# -# For a reason soon to be revealed, we assume that $G < R$. -# -# The **present value** of the lease is -# -# $$ -# \begin{aligned} p_0 & = x_0 + x_1/R + x_2/(R^2) + \ddots \\ -# & = x_0 (1 + G R^{-1} + G^2 R^{-2} + \cdots ) \\ -# & = x_0 \frac{1}{1 - G R^{-1}} \end{aligned} -# $$ -# -# where the last line uses the formula for an infinite geometric series. -# -# Recall that $R = 1+r$ and $G = 1+g$ and that $R > G$ -# and $r > g$ and that $r$ and $g$ are typically small -# numbers, e.g., .05 or .03. -# -# Use the Taylor series of $\frac{1}{1+r}$ about $r=0$, -# namely, -# -# $$ -# \frac{1}{1+r} = 1 - r + r^2 - r^3 + \cdots -# $$ -# -# and the fact that $r$ is small to approximate -# $\frac{1}{1+r} \approx 1 - r$. -# -# Use this approximation to write $p_0$ as -# -# $$ -# \begin{aligned} -# p_0 &= x_0 \frac{1}{1 - G R^{-1}} \\ -# &= x_0 \frac{1}{1 - (1+g) (1-r) } \\ -# &= x_0 \frac{1}{1 - (1+g - r - rg)} \\ -# & \approx x_0 \frac{1}{r -g } -# \end{aligned} -# $$ -# -# where the last step uses the approximation $r g \approx 0$. -# -# The approximation -# -# $$ -# p_0 = \frac{x_0 }{r -g } -# $$ -# -# is known as the **Gordon formula** for the present value or current -# price of an infinite payment stream $x_0 G^t$ when the nominal -# one-period interest rate is $r$ and when $r > g$. -# -# We can also extend the asset pricing formula so that it applies to finite leases. -# -# Let the payment stream on the lease now be $x_t$ for $t= 1,2, \dots,T$, where again -# -# $$ -# x_t = G^t x_0 -# $$ -# -# The present value of this lease is: -# -# $$ -# \begin{aligned} \begin{split}p_0&=x_0 + x_1/R + \dots +x_T/R^T \\ &= x_0(1+GR^{-1}+\dots +G^{T}R^{-T}) \\ &= \frac{x_0(1-G^{T+1}R^{-(T+1)})}{1-GR^{-1}} \end{split}\end{aligned} -# $$ -# -# Applying the Taylor series to $R^{-(T+1)}$ about $r=0$ we get: -# -# $$ -# \frac{1}{(1+r)^{T+1}}= 1-r(T+1)+\frac{1}{2}r^2(T+1)(T+2)+\dots \approx 1-r(T+1) -# $$ -# -# Similarly, applying the Taylor series to $G^{T+1}$ about $g=0$: -# -# $$ -# (1+g)^{T+1} = 1+(T+1)g+\frac{T(T+1)}{2!}g^2+\frac{(T-1)T(T+1)}{3!}g^3+\dots \approx 1+ (T+1)g -# $$ -# -# Thus, we get the following approximation: -# -# $$ -# p_0 =\frac{x_0(1-(1+(T+1)g)(1-r(T+1)))}{1-(1-r)(1+g) } -# $$ -# -# Expanding: -# -# $$ -# \begin{aligned} p_0 &=\frac{x_0(1-1+(T+1)^2 rg -r(T+1)+g(T+1))}{1-1+r-g+rg} \\&=\frac{x_0(T+1)((T+1)rg+r-g)}{r-g+rg} \\ &\approx \frac{x_0(T+1)(r-g)}{r-g}+\frac{x_0rg(T+1)}{r-g}\\ &= x_0(T+1) + \frac{x_0rg(T+1)}{r-g} \end{aligned} -# $$ -# -# We could have also approximated by removing the second term -# $rgx_0(T+1)$ when $T$ is relatively small compared to -# $1/(rg)$ to get $x_0(T+1)$ as in the finite stream -# approximation. -# -# We will plot the true finite stream present-value and the two -# approximations, under different values of $T$, and $g$ and $r$ in Python. -# -# First we plot the true finite stream present-value after computing it -# below - -# In[2]: - - -# True present value of a finite lease -def finite_lease_pv_true(T, g, r, x_0): - G = (1 + g) - R = (1 + r) - return (x_0 * (1 - G**(T + 1) * R**(-T - 1))) / (1 - G * R**(-1)) -# First approximation for our finite lease - -def finite_lease_pv_approx_1(T, g, r, x_0): - p = x_0 * (T + 1) + x_0 * r * g * (T + 1) / (r - g) - return p - -# Second approximation for our finite lease -def finite_lease_pv_approx_2(T, g, r, x_0): - return (x_0 * (T + 1)) - -# Infinite lease -def infinite_lease(g, r, x_0): - G = (1 + g) - R = (1 + r) - return x_0 / (1 - G * R**(-1)) - - -# Now that we have defined our functions, we can plot some outcomes. -# -# First we study the quality of our approximations - -# In[3]: - - -def plot_function(axes, x_vals, func, args): - axes.plot(x_vals, func(*args), label=func.__name__) - -T_max = 50 - -T = np.arange(0, T_max+1) -g = 0.02 -r = 0.03 -x_0 = 1 - -our_args = (T, g, r, x_0) -funcs = [finite_lease_pv_true, - finite_lease_pv_approx_1, - finite_lease_pv_approx_2] - ## the three functions we want to compare - -fig, ax = plt.subplots() -ax.set_title('Finite Lease Present Value $T$ Periods Ahead') -for f in funcs: - plot_function(ax, T, f, our_args) -ax.legend() -ax.set_xlabel('$T$ Periods Ahead') -ax.set_ylabel('Present Value, $p_0$') -plt.show() - - -# Evidently our approximations perform well for small values of $T$. -# -# However, holding $g$ and r fixed, our approximations deteriorate as $T$ increases. -# -# Next we compare the infinite and finite duration lease present values -# over different lease lengths $T$. - -# In[4]: - - -# Convergence of infinite and finite -T_max = 1000 -T = np.arange(0, T_max+1) -fig, ax = plt.subplots() -ax.set_title('Infinite and Finite Lease Present Value $T$ Periods Ahead') -f_1 = finite_lease_pv_true(T, g, r, x_0) -f_2 = np.full(T_max+1, infinite_lease(g, r, x_0)) -ax.plot(T, f_1, label='T-period lease PV') -ax.plot(T, f_2, '--', label='Infinite lease PV') -ax.set_xlabel('$T$ Periods Ahead') -ax.set_ylabel('Present Value, $p_0$') -ax.legend() -plt.show() - - -# The graph above shows how as duration $T \rightarrow +\infty$, -# the value of a lease of duration $T$ approaches the value of a -# perpetual lease. -# -# Now we consider two different views of what happens as $r$ and -# $g$ covary - -# In[5]: - - -# First view -# Changing r and g -fig, ax = plt.subplots() -ax.set_title('Value of lease of length $T$') -ax.set_ylabel('Present Value, $p_0$') -ax.set_xlabel('$T$ periods ahead') -T_max = 10 -T=np.arange(0, T_max+1) - -rs, gs = (0.9, 0.5, 0.4001, 0.4), (0.4, 0.4, 0.4, 0.5), -comparisons = ('$\gg$', '$>$', r'$\approx$', '$<$') -for r, g, comp in zip(rs, gs, comparisons): - ax.plot(finite_lease_pv_true(T, g, r, x_0), label=f'r(={r}) {comp} g(={g})') - -ax.legend() -plt.show() - - -# This graph gives a big hint for why the condition $r > g$ is -# necessary if a lease of length $T = +\infty$ is to have finite -# value. -# -# For fans of 3-d graphs the same point comes through in the following -# graph. -# -# If you aren't enamored of 3-d graphs, feel free to skip the next -# visualization! - -# In[6]: - - -# Second view -fig = plt.figure() -T = 3 -ax = plt.subplot(projection='3d') -r = np.arange(0.01, 0.99, 0.005) -g = np.arange(0.011, 0.991, 0.005) - -rr, gg = np.meshgrid(r, g) -z = finite_lease_pv_true(T, gg, rr, x_0) - -# Removes points where undefined -same = (rr == gg) -z[same] = np.nan -surf = ax.plot_surface(rr, gg, z, cmap=cm.coolwarm, - antialiased=True, clim=(0, 15)) -fig.colorbar(surf, shrink=0.5, aspect=5) -ax.set_xlabel('$r$') -ax.set_ylabel('$g$') -ax.set_zlabel('Present Value, $p_0$') -ax.view_init(20, 10) -ax.set_title('Three Period Lease PV with Varying $g$ and $r$') -plt.show() - - -# We can use a little calculus to study how the present value $p_0$ -# of a lease varies with $r$ and $g$. -# -# We will use a library called [SymPy](https://www.sympy.org/). -# -# SymPy enables us to do symbolic math calculations including -# computing derivatives of algebraic equations. -# -# We will illustrate how it works by creating a symbolic expression that -# represents our present value formula for an infinite lease. -# -# After that, we'll use SymPy to compute derivatives - -# In[7]: - - -# Creates algebraic symbols that can be used in an algebraic expression -g, r, x0 = sym.symbols('g, r, x0') -G = (1 + g) -R = (1 + r) -p0 = x0 / (1 - G * R**(-1)) -init_printing(use_latex='mathjax') -print('Our formula is:') -p0 - - -# In[8]: - - -print('dp0 / dg is:') -dp_dg = sym.diff(p0, g) -dp_dg - - -# In[9]: - - -print('dp0 / dr is:') -dp_dr = sym.diff(p0, r) -dp_dr - - -# We can see that for $\frac{\partial p_0}{\partial r}<0$ as long as -# $r>g$, $r>0$ and $g>0$ and $x_0$ is positive, -# so $\frac{\partial p_0}{\partial r}$ will always be negative. -# -# Similarly, $\frac{\partial p_0}{\partial g}>0$ as long as $r>g$, $r>0$ and $g>0$ and $x_0$ is positive, so $\frac{\partial p_0}{\partial g}$ -# will always be positive. -# -# ## Back to the Keynesian Multiplier -# -# We will now go back to the case of the Keynesian multiplier and plot the -# time path of $y_t$, given that consumption is a constant fraction -# of national income, and investment is fixed. - -# In[10]: - - -# Function that calculates a path of y -def calculate_y(i, b, g, T, y_init): - y = np.zeros(T+1) - y[0] = i + b * y_init + g - for t in range(1, T+1): - y[t] = b * y[t-1] + i + g - return y - -# Initial values -i_0 = 0.3 -g_0 = 0.3 -# 2/3 of income goes towards consumption -b = 2/3 -y_init = 0 -T = 100 - -fig, ax = plt.subplots() -ax.set_title('Path of Aggregate Output Over Time') -ax.set_xlabel('$t$') -ax.set_ylabel('$y_t$') -ax.plot(np.arange(0, T+1), calculate_y(i_0, b, g_0, T, y_init)) -# Output predicted by geometric series -ax.hlines(i_0 / (1 - b) + g_0 / (1 - b), xmin=-1, xmax=101, linestyles='--') -plt.show() - - -# In this model, income grows over time, until it gradually converges to -# the infinite geometric series sum of income. -# -# We now examine what will -# happen if we vary the so-called **marginal propensity to consume**, -# i.e., the fraction of income that is consumed - -# In[11]: - - -bs = (1/3, 2/3, 5/6, 0.9) - -fig,ax = plt.subplots() -ax.set_title('Changing Consumption as a Fraction of Income') -ax.set_ylabel('$y_t$') -ax.set_xlabel('$t$') -x = np.arange(0, T+1) -for b in bs: - y = calculate_y(i_0, b, g_0, T, y_init) - ax.plot(x, y, label=r'$b=$'+f"{b:.2f}") -ax.legend() -plt.show() - - -# Increasing the marginal propensity to consume $b$ increases the -# path of output over time. -# -# Now we will compare the effects on output of increases in investment and government spending. - -# In[12]: - - -fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(6, 10)) -fig.subplots_adjust(hspace=0.3) - -x = np.arange(0, T+1) -values = [0.3, 0.4] - -for i in values: - y = calculate_y(i, b, g_0, T, y_init) - ax1.plot(x, y, label=f"i={i}") -for g in values: - y = calculate_y(i_0, b, g, T, y_init) - ax2.plot(x, y, label=f"g={g}") - -axes = ax1, ax2 -param_labels = "Investment", "Government Spending" -for ax, param in zip(axes, param_labels): - ax.set_title(f'An Increase in {param} on Output') - ax.legend(loc ="lower right") - ax.set_ylabel('$y_t$') - ax.set_xlabel('$t$') -plt.show() - - -# Notice here, whether government spending increases from 0.3 to 0.4 or -# investment increases from 0.3 to 0.4, the shifts in the graphs are -# identical. diff --git a/lectures/_build/jupyter_execute/geom_series_11_0.png b/lectures/_build/jupyter_execute/geom_series_11_0.png deleted file mode 100644 index 06577c854..000000000 Binary files a/lectures/_build/jupyter_execute/geom_series_11_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/geom_series_17_0.png b/lectures/_build/jupyter_execute/geom_series_17_0.png deleted file mode 100644 index 31c55864a..000000000 Binary files a/lectures/_build/jupyter_execute/geom_series_17_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/geom_series_19_0.png b/lectures/_build/jupyter_execute/geom_series_19_0.png deleted file mode 100644 index 2700425b7..000000000 Binary files a/lectures/_build/jupyter_execute/geom_series_19_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/geom_series_21_0.png b/lectures/_build/jupyter_execute/geom_series_21_0.png deleted file mode 100644 index 1748dbb7e..000000000 Binary files a/lectures/_build/jupyter_execute/geom_series_21_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/geom_series_5_0.png b/lectures/_build/jupyter_execute/geom_series_5_0.png deleted file mode 100644 index 6bdf090de..000000000 Binary files a/lectures/_build/jupyter_execute/geom_series_5_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/geom_series_7_0.png b/lectures/_build/jupyter_execute/geom_series_7_0.png deleted file mode 100644 index 53a391f02..000000000 Binary files a/lectures/_build/jupyter_execute/geom_series_7_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/geom_series_9_0.png b/lectures/_build/jupyter_execute/geom_series_9_0.png deleted file mode 100644 index dc93fe784..000000000 Binary files a/lectures/_build/jupyter_execute/geom_series_9_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/intro.ipynb b/lectures/_build/jupyter_execute/intro.ipynb deleted file mode 100644 index 64ea7945b..000000000 --- a/lectures/_build/jupyter_execute/intro.ipynb +++ /dev/null @@ -1,50 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "a7f88dc4", - "metadata": {}, - "source": [ - "# Python Programming for Economics and Finance\n", - "\n", - "This website presents a set of lectures on Python programming for economics and finance, designed and written by\n", - "[Thomas J. Sargent](http://www.tomsargent.com/) and [John Stachurski](http://johnstachurski.net/). This is the first text in the series, which focuses on programming in Python.\n", - "\n", - "For an overview of the series, see [this page](https://quantecon.org/python-lectures/)\n", - "\n", - "```{tableofcontents}\n", - "```" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/jupyter_execute/intro.py b/lectures/_build/jupyter_execute/intro.py deleted file mode 100644 index 97bc24a79..000000000 --- a/lectures/_build/jupyter_execute/intro.py +++ /dev/null @@ -1,12 +0,0 @@ -#!/usr/bin/env python -# coding: utf-8 - -# # Python Programming for Economics and Finance -# -# This website presents a set of lectures on Python programming for economics and finance, designed and written by -# [Thomas J. Sargent](http://www.tomsargent.com/) and [John Stachurski](http://johnstachurski.net/). This is the first text in the series, which focuses on programming in Python. -# -# For an overview of the series, see [this page](https://quantecon.org/python-lectures/) -# -# ```{tableofcontents} -# ``` diff --git a/lectures/_build/jupyter_execute/scalar_dynam.ipynb b/lectures/_build/jupyter_execute/scalar_dynam.ipynb deleted file mode 100644 index 92ec7c681..000000000 --- a/lectures/_build/jupyter_execute/scalar_dynam.ipynb +++ /dev/null @@ -1,1080 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "7778fcad", - "metadata": {}, - "source": [ - "```{raw} html\n", - "
\n", - " \n", - " \"QuantEcon\"\n", - " \n", - "
\n", - "```\n", - "\n", - "# {index}`Dynamics in One Dimension `\n", - "\n", - "```{contents} Contents\n", - ":depth: 2\n", - "```\n", - "\n", - "## Overview\n", - "\n", - "In this lecture we give a quick introduction to discrete time dynamics in one\n", - "dimension.\n", - "\n", - "In one-dimensional models, the state of the system is described by a single variable.\n", - "\n", - "Although most interesting dynamic models have two or more state variables, the\n", - "one-dimensional setting is a good place to learn the foundations of dynamics and build\n", - "intuition.\n", - "\n", - "Let's start with some standard imports:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "726361e5", - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "plt.rcParams[\"figure.figsize\"] = (11, 5) #set default figure size\n", - "import numpy as np" - ] - }, - { - "cell_type": "markdown", - "id": "6a799320", - "metadata": {}, - "source": [ - "## Some Definitions\n", - "\n", - "This section sets out the objects of interest and the kinds of properties we study.\n", - "\n", - "### Difference Equations\n", - "\n", - "A **time homogeneous first order difference equation** is an equation of the\n", - "form\n", - "\n", - "```{math}\n", - ":label: sdsod\n", - "\n", - "x_{t+1} = g(x_t)\n", - "```\n", - "\n", - "where $g$ is a function from some subset $S$ of $\\mathbb R$ to itself.\n", - "\n", - "Here $S$ is called the **state space** and $x$ is called the **state variable**.\n", - "\n", - "In the definition,\n", - "\n", - "* time homogeneity means that $g$ is the same at each time $t$\n", - "* first order means dependence on only one lag (i.e., earlier states such as $x_{t-1}$ do not enter into {eq}`sdsod`).\n", - "\n", - "If $x_0 \\in S$ is given, then {eq}`sdsod` recursively defines the sequence\n", - "\n", - "```{math}\n", - ":label: sdstraj\n", - "\n", - "x_0, \\quad\n", - "x_1 = g(x_0), \\quad\n", - "x_2 = g(x_1) = g(g(x_0)), \\quad \\text{etc.}\n", - "```\n", - "\n", - "This sequence is called the **trajectory** of $x_0$ under $g$.\n", - "\n", - "If we define $g^n$ to be $n$ compositions of $g$ with itself, then we can write the trajectory more simply as $x_t = g^t(x_0)$ for $t \\geq 0$.\n", - "\n", - "### Example: A Linear Model\n", - "\n", - "One simple example is the **linear difference equation**\n", - "\n", - "$$\n", - "x_{t+1} = a x_t + b, \\qquad S = \\mathbb R\n", - "$$\n", - "\n", - "where $a, b$ are fixed constants.\n", - "\n", - "In this case, given $x_0$, the trajectory {eq}`sdstraj` is\n", - "\n", - "```{math}\n", - ":label: sdslinmodpath\n", - "\n", - "x_0, \\quad\n", - "a x_0 + b, \\quad\n", - "a^2 x_0 + a b + b, \\quad \\text{etc.}\n", - "```\n", - "\n", - "Continuing in this way, and using our knowledge of {doc}`geometric series `, we find that, for any $t \\geq 0$,\n", - "\n", - "```{math}\n", - ":label: sdslinmod\n", - "\n", - "x_t = a^t x_0 + b \\frac{1 - a^t}{1 - a}\n", - "```\n", - "\n", - "This is about all we need to know about the linear model.\n", - "\n", - "We have an exact expression for $x_t$ for all $t$ and hence a full\n", - "understanding of the dynamics.\n", - "\n", - "Notice in particular that $|a| < 1$, then, by {eq}`sdslinmod`, we have\n", - "\n", - "```{math}\n", - ":label: sdslinmodc\n", - "\n", - "x_t \\to \\frac{b}{1 - a} \\text{ as } t \\to \\infty\n", - "```\n", - "\n", - "regardless of $x_0$\n", - "\n", - "This is an example of what is called global stability, a topic we return to\n", - "below.\n", - "\n", - "### Example: A Nonlinear Model\n", - "\n", - "In the linear example above, we obtained an exact analytical expression for $x_t$\n", - "in terms of arbitrary $t$ and $x_0$.\n", - "\n", - "This made analysis of dynamics very easy.\n", - "\n", - "When models are nonlinear, however, the situation can be quite different.\n", - "\n", - "For example, recall how we [previously studied](https://python-programming.quantecon.org/python_oop.html#example-the-solow-growth-model) the law of motion for the Solow growth model, a simplified version of which is\n", - "\n", - "```{math}\n", - ":label: solow_lom2\n", - "\n", - "k_{t+1} = s z k_t^{\\alpha} + (1 - \\delta) k_t\n", - "```\n", - "\n", - "Here $k$ is capital stock and $s, z, \\alpha, \\delta$ are positive\n", - "parameters with $0 < \\alpha, \\delta < 1$.\n", - "\n", - "If you try to iterate like we did in {eq}`sdslinmodpath`, you will find that\n", - "the algebra gets messy quickly.\n", - "\n", - "Analyzing the dynamics of this model requires a different method (see below).\n", - "\n", - "### Stability\n", - "\n", - "A **steady state** of the difference equation $x_{t+1} = g(x_t)$ is a\n", - "point $x^*$ in $S$ such that $x^* = g(x^*)$.\n", - "\n", - "In other words, $x^*$ is a **fixed point** of the function $g$ in\n", - "$S$.\n", - "\n", - "For example, for the linear model $x_{t+1} = a x_t + b$, you can use the\n", - "definition to check that\n", - "\n", - "* $x^* := b/(1-a)$ is a steady state whenever $a \\not= 1$.\n", - "* if $a = 1$ and $b=0$, then every $x \\in \\mathbb R$ is a\n", - " steady state.\n", - "* if $a = 1$ and $b \\not= 0$, then the linear model has no steady\n", - " state in $\\mathbb R$.\n", - "\n", - "A steady state $x^*$ of $x_{t+1} = g(x_t)$ is called\n", - "**globally stable** if, for all $x_0 \\in S$,\n", - "\n", - "$$\n", - "x_t = g^t(x_0) \\to x^* \\text{ as } t \\to \\infty\n", - "$$\n", - "\n", - "For example, in the linear model $x_{t+1} = a x_t + b$ with $a\n", - "\\not= 1$, the steady state $x^*$\n", - "\n", - "* is globally stable if $|a| < 1$ and\n", - "* fails to be globally stable otherwise.\n", - "\n", - "This follows directly from {eq}`sdslinmod`.\n", - "\n", - "A steady state $x^*$ of $x_{t+1} = g(x_t)$ is called\n", - "**locally stable** if there exists an $\\epsilon > 0$ such that\n", - "\n", - "$$\n", - "| x_0 - x^* | < \\epsilon\n", - "\\; \\implies \\;\n", - "x_t = g^t(x_0) \\to x^* \\text{ as } t \\to \\infty\n", - "$$\n", - "\n", - "Obviously every globally stable steady state is also locally stable.\n", - "\n", - "We will see examples below where the converse is not true.\n", - "\n", - "## Graphical Analysis\n", - "\n", - "As we saw above, analyzing the dynamics for nonlinear models is nontrivial.\n", - "\n", - "There is no single way to tackle all nonlinear models.\n", - "\n", - "However, there is one technique for one-dimensional models that provides a\n", - "great deal of intuition.\n", - "\n", - "This is a graphical approach based on **45 degree diagrams**.\n", - "\n", - "Let's look at an example: the Solow model with dynamics given in {eq}`solow_lom2`.\n", - "\n", - "We begin with some plotting code that you can ignore at first reading.\n", - "\n", - "The function of the code is to produce 45 degree diagrams and time series\n", - "plots." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "6f5829b6", - "metadata": { - "tags": [ - "output_scroll" - ] - }, - "outputs": [], - "source": [ - "def subplots(fs):\n", - " \"Custom subplots with axes throught the origin\"\n", - " fig, ax = plt.subplots(figsize=fs)\n", - "\n", - " # Set the axes through the origin\n", - " for spine in ['left', 'bottom']:\n", - " ax.spines[spine].set_position('zero')\n", - " ax.spines[spine].set_color('green')\n", - " for spine in ['right', 'top']:\n", - " ax.spines[spine].set_color('none')\n", - "\n", - " return fig, ax\n", - "\n", - "\n", - "def plot45(g, xmin, xmax, x0, num_arrows=6, var='x'):\n", - "\n", - " xgrid = np.linspace(xmin, xmax, 200)\n", - "\n", - " fig, ax = subplots((6.5, 6))\n", - " ax.set_xlim(xmin, xmax)\n", - " ax.set_ylim(xmin, xmax)\n", - "\n", - " hw = (xmax - xmin) * 0.01\n", - " hl = 2 * hw\n", - " arrow_args = dict(fc=\"k\", ec=\"k\", head_width=hw,\n", - " length_includes_head=True, lw=1,\n", - " alpha=0.6, head_length=hl)\n", - "\n", - " ax.plot(xgrid, g(xgrid), 'b-', lw=2, alpha=0.6, label='g')\n", - " ax.plot(xgrid, xgrid, 'k-', lw=1, alpha=0.7, label='45')\n", - "\n", - " x = x0\n", - " xticks = [xmin]\n", - " xtick_labels = [xmin]\n", - "\n", - " for i in range(num_arrows):\n", - " if i == 0:\n", - " ax.arrow(x, 0.0, 0.0, g(x), **arrow_args) # x, y, dx, dy\n", - " else:\n", - " ax.arrow(x, x, 0.0, g(x) - x, **arrow_args)\n", - " ax.plot((x, x), (0, x), 'k', ls='dotted')\n", - "\n", - " ax.arrow(x, g(x), g(x) - x, 0, **arrow_args)\n", - " xticks.append(x)\n", - " xtick_labels.append(r'${}_{}$'.format(var, str(i)))\n", - "\n", - " x = g(x)\n", - " xticks.append(x)\n", - " xtick_labels.append(r'${}_{}$'.format(var, str(i+1)))\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n", - "\n", - " xticks.append(xmax)\n", - " xtick_labels.append(xmax)\n", - " ax.set_xticks(xticks)\n", - " ax.set_yticks(xticks)\n", - " ax.set_xticklabels(xtick_labels)\n", - " ax.set_yticklabels(xtick_labels)\n", - "\n", - " bbox = (0., 1.04, 1., .104)\n", - " legend_args = {'bbox_to_anchor': bbox, 'loc': 'upper right'}\n", - "\n", - " ax.legend(ncol=2, frameon=False, **legend_args, fontsize=14)\n", - " plt.show()\n", - "\n", - "def ts_plot(g, xmin, xmax, x0, ts_length=6, var='x'):\n", - " fig, ax = subplots((7, 5.5))\n", - " ax.set_ylim(xmin, xmax)\n", - " ax.set_xlabel(r'$t$', fontsize=14)\n", - " ax.set_ylabel(r'${}_t$'.format(var), fontsize=14)\n", - " x = np.empty(ts_length)\n", - " x[0] = x0\n", - " for t in range(ts_length-1):\n", - " x[t+1] = g(x[t])\n", - " ax.plot(range(ts_length),\n", - " x,\n", - " 'bo-',\n", - " alpha=0.6,\n", - " lw=2,\n", - " label=r'${}_t$'.format(var))\n", - " ax.legend(loc='best', fontsize=14)\n", - " ax.set_xticks(range(ts_length))\n", - " plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "08aa7b12", - "metadata": {}, - "source": [ - "Let's create a 45 degree diagram for the Solow model with a fixed set of\n", - "parameters" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "ef6950ac", - "metadata": {}, - "outputs": [], - "source": [ - "A, s, alpha, delta = 2, 0.3, 0.3, 0.4" - ] - }, - { - "cell_type": "markdown", - "id": "6b10d60c", - "metadata": {}, - "source": [ - "Here's the update function corresponding to the model." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "f409302c", - "metadata": {}, - "outputs": [], - "source": [ - "def g(k):\n", - " return A * s * k**alpha + (1 - delta) * k" - ] - }, - { - "cell_type": "markdown", - "id": "d1aa5b32", - "metadata": {}, - "source": [ - "Here is the 45 degree plot." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "276c761a", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_9_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "xmin, xmax = 0, 4 # Suitable plotting region.\n", - "\n", - "plot45(g, xmin, xmax, 0, num_arrows=0)" - ] - }, - { - "cell_type": "markdown", - "id": "4018b5f1", - "metadata": {}, - "source": [ - "The plot shows the function $g$ and the 45 degree line.\n", - "\n", - "Think of $k_t$ as a value on the horizontal axis.\n", - "\n", - "To calculate $k_{t+1}$, we can use the graph of $g$ to see its\n", - "value on the vertical axis.\n", - "\n", - "Clearly,\n", - "\n", - "* If $g$ lies above the 45 degree line at this point, then we have $k_{t+1} > k_t$.\n", - "* If $g$ lies below the 45 degree line at this point, then we have $k_{t+1} < k_t$.\n", - "* If $g$ hits the 45 degree line at this point, then we have $k_{t+1} = k_t$, so $k_t$ is a steady state.\n", - "\n", - "For the Solow model, there are two steady states when $S = \\mathbb R_+ =\n", - "[0, \\infty)$.\n", - "\n", - "* the origin $k=0$\n", - "* the unique positive number such that $k = s z k^{\\alpha} + (1 - \\delta) k$.\n", - "\n", - "By using some algebra, we can show that in the second case, the steady state is\n", - "\n", - "$$\n", - "k^* = \\left( \\frac{sz}{\\delta} \\right)^{1/(1-\\alpha)}\n", - "$$\n", - "\n", - "### Trajectories\n", - "\n", - "By the preceding discussion, in regions where $g$ lies above the 45 degree line, we know that the trajectory is increasing.\n", - "\n", - "The next figure traces out a trajectory in such a region so we can see this more clearly.\n", - "\n", - "The initial condition is $k_0 = 0.25$." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "5bddd6ca", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_11_1.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "k0 = 0.25\n", - "\n", - "plot45(g, xmin, xmax, k0, num_arrows=5, var='k')" - ] - }, - { - "cell_type": "markdown", - "id": "a10e45d1", - "metadata": {}, - "source": [ - "We can plot the time series of capital corresponding to the figure above as\n", - "follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "7e93df3f", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_13_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, k0, var='k')" - ] - }, - { - "cell_type": "markdown", - "id": "c86cbdd6", - "metadata": {}, - "source": [ - "Here's a somewhat longer view:" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "d3307a3b", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_15_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, k0, ts_length=20, var='k')" - ] - }, - { - "cell_type": "markdown", - "id": "766077b3", - "metadata": {}, - "source": [ - "When capital stock is higher than the unique positive steady state, we see that\n", - "it declines:" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "432b70e0", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_17_1.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "k0 = 2.95\n", - "\n", - "plot45(g, xmin, xmax, k0, num_arrows=5, var='k')" - ] - }, - { - "cell_type": "markdown", - "id": "9069e20c", - "metadata": {}, - "source": [ - "Here is the time series:" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "1c71062a", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_19_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, k0, var='k')" - ] - }, - { - "cell_type": "markdown", - "id": "cdefce6a", - "metadata": {}, - "source": [ - "### Complex Dynamics\n", - "\n", - "The Solow model is nonlinear but still generates very regular dynamics.\n", - "\n", - "One model that generates irregular dynamics is the **quadratic map**\n", - "\n", - "$$\n", - "g(x) = 4 x (1 - x),\n", - "\\qquad x \\in [0, 1]\n", - "$$\n", - "\n", - "Let's have a look at the 45 degree diagram." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "e8358b87", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_21_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "xmin, xmax = 0, 1\n", - "g = lambda x: 4 * x * (1 - x)\n", - "\n", - "x0 = 0.3\n", - "plot45(g, xmin, xmax, x0, num_arrows=0)" - ] - }, - { - "cell_type": "markdown", - "id": "9ba1efba", - "metadata": {}, - "source": [ - "Now let's look at a typical trajectory." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "0d315786", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_23_1.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "plot45(g, xmin, xmax, x0, num_arrows=6)" - ] - }, - { - "cell_type": "markdown", - "id": "bf4c28cd", - "metadata": {}, - "source": [ - "Notice how irregular it is.\n", - "\n", - "Here is the corresponding time series plot." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "baeb20a5", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_25_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=6)" - ] - }, - { - "cell_type": "markdown", - "id": "d95d17ae", - "metadata": {}, - "source": [ - "The irregularity is even clearer over a longer time horizon:" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "2df1bca8", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_27_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=20)" - ] - }, - { - "cell_type": "markdown", - "id": "1655ad15", - "metadata": {}, - "source": [ - "## Exercises\n", - "\n", - "```{exercise}\n", - ":label: sd_ex1\n", - "\n", - "Consider again the linear model $x_{t+1} = a x_t + b$ with $a\n", - "\\not=1$.\n", - "\n", - "The unique steady state is $b / (1 - a)$.\n", - "\n", - "The steady state is globally stable if $|a| < 1$.\n", - "\n", - "Try to illustrate this graphically by looking at a range of initial conditions.\n", - "\n", - "What differences do you notice in the cases $a \\in (-1, 0)$ and $a\n", - "\\in (0, 1)$?\n", - "\n", - "Use $a=0.5$ and then $a=-0.5$ and study the trajectories\n", - "\n", - "Set $b=1$ throughout.\n", - "```\n", - "\n", - "```{solution-start} sd_ex1\n", - ":class: dropdown\n", - "```\n", - "\n", - "We will start with the case $a=0.5$.\n", - "\n", - "Let's set up the model and plotting region:" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "99a7fe4f", - "metadata": {}, - "outputs": [], - "source": [ - "a, b = 0.5, 1\n", - "xmin, xmax = -1, 3\n", - "g = lambda x: a * x + b" - ] - }, - { - "cell_type": "markdown", - "id": "d475fb8c", - "metadata": {}, - "source": [ - "Now let's plot a trajectory:" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "4f9c7a05", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_31_1.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "x0 = -0.5\n", - "plot45(g, xmin, xmax, x0, num_arrows=5)" - ] - }, - { - "cell_type": "markdown", - "id": "8719daf0", - "metadata": {}, - "source": [ - "Here is the corresponding time series, which converges towards the steady\n", - "state." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "05d6634c", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_33_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=10)" - ] - }, - { - "cell_type": "markdown", - "id": "413f6020", - "metadata": {}, - "source": [ - "Now let's try $a=-0.5$ and see what differences we observe.\n", - "\n", - "Let's set up the model and plotting region:" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "5121798a", - "metadata": {}, - "outputs": [], - "source": [ - "a, b = -0.5, 1\n", - "xmin, xmax = -1, 3\n", - "g = lambda x: a * x + b" - ] - }, - { - "cell_type": "markdown", - "id": "1721e272", - "metadata": {}, - "source": [ - "Now let's plot a trajectory:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "08d70fea", - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/var/folders/zy/dpt7pvt11fvcm_yxjd7kmv880000gn/T/ipykernel_27068/2261905364.py:50: UserWarning: linestyle is redundantly defined by the 'linestyle' keyword argument and the fmt string \"k-\" (-> linestyle='-'). The keyword argument will take precedence.\n", - " ax.plot((x, x), (0, x), 'k-', ls='dotted')\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_37_1.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "x0 = -0.5\n", - "plot45(g, xmin, xmax, x0, num_arrows=5)" - ] - }, - { - "cell_type": "markdown", - "id": "800eec50", - "metadata": {}, - "source": [ - "Here is the corresponding time series, which converges towards the steady\n", - "state." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "78e6f8e3", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/scalar_dynam_39_0.png" - } - }, - "output_type": "display_data" - } - ], - "source": [ - "ts_plot(g, xmin, xmax, x0, ts_length=10)" - ] - }, - { - "cell_type": "markdown", - "id": "7d6d7f18", - "metadata": {}, - "source": [ - "Once again, we have convergence to the steady state but the nature of\n", - "convergence differs.\n", - "\n", - "In particular, the time series jumps from above the steady state to below it\n", - "and back again.\n", - "\n", - "In the current context, the series is said to exhibit **damped oscillations**.\n", - "\n", - "```{solution-end}\n", - "```" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 39, - 44, - 218, - 304, - 309, - 311, - 315, - 318, - 322, - 326, - 361, - 365, - 370, - 372, - 376, - 378, - 383, - 387, - 391, - 393, - 408, - 414, - 418, - 420, - 426, - 428, - 432, - 434, - 466, - 470, - 474, - 477, - 482, - 484, - 490, - 494, - 498, - 501, - 506, - 508 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/jupyter_execute/scalar_dynam.py b/lectures/_build/jupyter_execute/scalar_dynam.py deleted file mode 100644 index 6711628a3..000000000 --- a/lectures/_build/jupyter_execute/scalar_dynam.py +++ /dev/null @@ -1,548 +0,0 @@ -#!/usr/bin/env python -# coding: utf-8 - -# ```{raw} html -#
-# -# QuantEcon -# -#
-# ``` -# -# # {index}`Dynamics in One Dimension ` -# -# ```{contents} Contents -# :depth: 2 -# ``` -# -# ## Overview -# -# In this lecture we give a quick introduction to discrete time dynamics in one -# dimension. -# -# In one-dimensional models, the state of the system is described by a single variable. -# -# Although most interesting dynamic models have two or more state variables, the -# one-dimensional setting is a good place to learn the foundations of dynamics and build -# intuition. -# -# Let's start with some standard imports: - -# In[1]: - - -get_ipython().run_line_magic('matplotlib', 'inline') -import matplotlib.pyplot as plt -plt.rcParams["figure.figsize"] = (11, 5) #set default figure size -import numpy as np - - -# ## Some Definitions -# -# This section sets out the objects of interest and the kinds of properties we study. -# -# ### Difference Equations -# -# A **time homogeneous first order difference equation** is an equation of the -# form -# -# ```{math} -# :label: sdsod -# -# x_{t+1} = g(x_t) -# ``` -# -# where $g$ is a function from some subset $S$ of $\mathbb R$ to itself. -# -# Here $S$ is called the **state space** and $x$ is called the **state variable**. -# -# In the definition, -# -# * time homogeneity means that $g$ is the same at each time $t$ -# * first order means dependence on only one lag (i.e., earlier states such as $x_{t-1}$ do not enter into {eq}`sdsod`). -# -# If $x_0 \in S$ is given, then {eq}`sdsod` recursively defines the sequence -# -# ```{math} -# :label: sdstraj -# -# x_0, \quad -# x_1 = g(x_0), \quad -# x_2 = g(x_1) = g(g(x_0)), \quad \text{etc.} -# ``` -# -# This sequence is called the **trajectory** of $x_0$ under $g$. -# -# If we define $g^n$ to be $n$ compositions of $g$ with itself, then we can write the trajectory more simply as $x_t = g^t(x_0)$ for $t \geq 0$. -# -# ### Example: A Linear Model -# -# One simple example is the **linear difference equation** -# -# $$ -# x_{t+1} = a x_t + b, \qquad S = \mathbb R -# $$ -# -# where $a, b$ are fixed constants. -# -# In this case, given $x_0$, the trajectory {eq}`sdstraj` is -# -# ```{math} -# :label: sdslinmodpath -# -# x_0, \quad -# a x_0 + b, \quad -# a^2 x_0 + a b + b, \quad \text{etc.} -# ``` -# -# Continuing in this way, and using our knowledge of {doc}`geometric series `, we find that, for any $t \geq 0$, -# -# ```{math} -# :label: sdslinmod -# -# x_t = a^t x_0 + b \frac{1 - a^t}{1 - a} -# ``` -# -# This is about all we need to know about the linear model. -# -# We have an exact expression for $x_t$ for all $t$ and hence a full -# understanding of the dynamics. -# -# Notice in particular that $|a| < 1$, then, by {eq}`sdslinmod`, we have -# -# ```{math} -# :label: sdslinmodc -# -# x_t \to \frac{b}{1 - a} \text{ as } t \to \infty -# ``` -# -# regardless of $x_0$ -# -# This is an example of what is called global stability, a topic we return to -# below. -# -# ### Example: A Nonlinear Model -# -# In the linear example above, we obtained an exact analytical expression for $x_t$ -# in terms of arbitrary $t$ and $x_0$. -# -# This made analysis of dynamics very easy. -# -# When models are nonlinear, however, the situation can be quite different. -# -# For example, recall how we [previously studied](https://python-programming.quantecon.org/python_oop.html#example-the-solow-growth-model) the law of motion for the Solow growth model, a simplified version of which is -# -# ```{math} -# :label: solow_lom2 -# -# k_{t+1} = s z k_t^{\alpha} + (1 - \delta) k_t -# ``` -# -# Here $k$ is capital stock and $s, z, \alpha, \delta$ are positive -# parameters with $0 < \alpha, \delta < 1$. -# -# If you try to iterate like we did in {eq}`sdslinmodpath`, you will find that -# the algebra gets messy quickly. -# -# Analyzing the dynamics of this model requires a different method (see below). -# -# ### Stability -# -# A **steady state** of the difference equation $x_{t+1} = g(x_t)$ is a -# point $x^*$ in $S$ such that $x^* = g(x^*)$. -# -# In other words, $x^*$ is a **fixed point** of the function $g$ in -# $S$. -# -# For example, for the linear model $x_{t+1} = a x_t + b$, you can use the -# definition to check that -# -# * $x^* := b/(1-a)$ is a steady state whenever $a \not= 1$. -# * if $a = 1$ and $b=0$, then every $x \in \mathbb R$ is a -# steady state. -# * if $a = 1$ and $b \not= 0$, then the linear model has no steady -# state in $\mathbb R$. -# -# A steady state $x^*$ of $x_{t+1} = g(x_t)$ is called -# **globally stable** if, for all $x_0 \in S$, -# -# $$ -# x_t = g^t(x_0) \to x^* \text{ as } t \to \infty -# $$ -# -# For example, in the linear model $x_{t+1} = a x_t + b$ with $a -# \not= 1$, the steady state $x^*$ -# -# * is globally stable if $|a| < 1$ and -# * fails to be globally stable otherwise. -# -# This follows directly from {eq}`sdslinmod`. -# -# A steady state $x^*$ of $x_{t+1} = g(x_t)$ is called -# **locally stable** if there exists an $\epsilon > 0$ such that -# -# $$ -# | x_0 - x^* | < \epsilon -# \; \implies \; -# x_t = g^t(x_0) \to x^* \text{ as } t \to \infty -# $$ -# -# Obviously every globally stable steady state is also locally stable. -# -# We will see examples below where the converse is not true. -# -# ## Graphical Analysis -# -# As we saw above, analyzing the dynamics for nonlinear models is nontrivial. -# -# There is no single way to tackle all nonlinear models. -# -# However, there is one technique for one-dimensional models that provides a -# great deal of intuition. -# -# This is a graphical approach based on **45 degree diagrams**. -# -# Let's look at an example: the Solow model with dynamics given in {eq}`solow_lom2`. -# -# We begin with some plotting code that you can ignore at first reading. -# -# The function of the code is to produce 45 degree diagrams and time series -# plots. - -# In[2]: - - -def subplots(fs): - "Custom subplots with axes throught the origin" - fig, ax = plt.subplots(figsize=fs) - - # Set the axes through the origin - for spine in ['left', 'bottom']: - ax.spines[spine].set_position('zero') - ax.spines[spine].set_color('green') - for spine in ['right', 'top']: - ax.spines[spine].set_color('none') - - return fig, ax - - -def plot45(g, xmin, xmax, x0, num_arrows=6, var='x'): - - xgrid = np.linspace(xmin, xmax, 200) - - fig, ax = subplots((6.5, 6)) - ax.set_xlim(xmin, xmax) - ax.set_ylim(xmin, xmax) - - hw = (xmax - xmin) * 0.01 - hl = 2 * hw - arrow_args = dict(fc="k", ec="k", head_width=hw, - length_includes_head=True, lw=1, - alpha=0.6, head_length=hl) - - ax.plot(xgrid, g(xgrid), 'b-', lw=2, alpha=0.6, label='g') - ax.plot(xgrid, xgrid, 'k-', lw=1, alpha=0.7, label='45') - - x = x0 - xticks = [xmin] - xtick_labels = [xmin] - - for i in range(num_arrows): - if i == 0: - ax.arrow(x, 0.0, 0.0, g(x), **arrow_args) # x, y, dx, dy - else: - ax.arrow(x, x, 0.0, g(x) - x, **arrow_args) - ax.plot((x, x), (0, x), 'k', ls='dotted') - - ax.arrow(x, g(x), g(x) - x, 0, **arrow_args) - xticks.append(x) - xtick_labels.append(r'${}_{}$'.format(var, str(i))) - - x = g(x) - xticks.append(x) - xtick_labels.append(r'${}_{}$'.format(var, str(i+1))) - ax.plot((x, x), (0, x), 'k-', ls='dotted') - - xticks.append(xmax) - xtick_labels.append(xmax) - ax.set_xticks(xticks) - ax.set_yticks(xticks) - ax.set_xticklabels(xtick_labels) - ax.set_yticklabels(xtick_labels) - - bbox = (0., 1.04, 1., .104) - legend_args = {'bbox_to_anchor': bbox, 'loc': 'upper right'} - - ax.legend(ncol=2, frameon=False, **legend_args, fontsize=14) - plt.show() - -def ts_plot(g, xmin, xmax, x0, ts_length=6, var='x'): - fig, ax = subplots((7, 5.5)) - ax.set_ylim(xmin, xmax) - ax.set_xlabel(r'$t$', fontsize=14) - ax.set_ylabel(r'${}_t$'.format(var), fontsize=14) - x = np.empty(ts_length) - x[0] = x0 - for t in range(ts_length-1): - x[t+1] = g(x[t]) - ax.plot(range(ts_length), - x, - 'bo-', - alpha=0.6, - lw=2, - label=r'${}_t$'.format(var)) - ax.legend(loc='best', fontsize=14) - ax.set_xticks(range(ts_length)) - plt.show() - - -# Let's create a 45 degree diagram for the Solow model with a fixed set of -# parameters - -# In[3]: - - -A, s, alpha, delta = 2, 0.3, 0.3, 0.4 - - -# Here's the update function corresponding to the model. - -# In[4]: - - -def g(k): - return A * s * k**alpha + (1 - delta) * k - - -# Here is the 45 degree plot. - -# In[5]: - - -xmin, xmax = 0, 4 # Suitable plotting region. - -plot45(g, xmin, xmax, 0, num_arrows=0) - - -# The plot shows the function $g$ and the 45 degree line. -# -# Think of $k_t$ as a value on the horizontal axis. -# -# To calculate $k_{t+1}$, we can use the graph of $g$ to see its -# value on the vertical axis. -# -# Clearly, -# -# * If $g$ lies above the 45 degree line at this point, then we have $k_{t+1} > k_t$. -# * If $g$ lies below the 45 degree line at this point, then we have $k_{t+1} < k_t$. -# * If $g$ hits the 45 degree line at this point, then we have $k_{t+1} = k_t$, so $k_t$ is a steady state. -# -# For the Solow model, there are two steady states when $S = \mathbb R_+ = -# [0, \infty)$. -# -# * the origin $k=0$ -# * the unique positive number such that $k = s z k^{\alpha} + (1 - \delta) k$. -# -# By using some algebra, we can show that in the second case, the steady state is -# -# $$ -# k^* = \left( \frac{sz}{\delta} \right)^{1/(1-\alpha)} -# $$ -# -# ### Trajectories -# -# By the preceding discussion, in regions where $g$ lies above the 45 degree line, we know that the trajectory is increasing. -# -# The next figure traces out a trajectory in such a region so we can see this more clearly. -# -# The initial condition is $k_0 = 0.25$. - -# In[6]: - - -k0 = 0.25 - -plot45(g, xmin, xmax, k0, num_arrows=5, var='k') - - -# We can plot the time series of capital corresponding to the figure above as -# follows: - -# In[7]: - - -ts_plot(g, xmin, xmax, k0, var='k') - - -# Here's a somewhat longer view: - -# In[8]: - - -ts_plot(g, xmin, xmax, k0, ts_length=20, var='k') - - -# When capital stock is higher than the unique positive steady state, we see that -# it declines: - -# In[9]: - - -k0 = 2.95 - -plot45(g, xmin, xmax, k0, num_arrows=5, var='k') - - -# Here is the time series: - -# In[10]: - - -ts_plot(g, xmin, xmax, k0, var='k') - - -# ### Complex Dynamics -# -# The Solow model is nonlinear but still generates very regular dynamics. -# -# One model that generates irregular dynamics is the **quadratic map** -# -# $$ -# g(x) = 4 x (1 - x), -# \qquad x \in [0, 1] -# $$ -# -# Let's have a look at the 45 degree diagram. - -# In[11]: - - -xmin, xmax = 0, 1 -g = lambda x: 4 * x * (1 - x) - -x0 = 0.3 -plot45(g, xmin, xmax, x0, num_arrows=0) - - -# Now let's look at a typical trajectory. - -# In[12]: - - -plot45(g, xmin, xmax, x0, num_arrows=6) - - -# Notice how irregular it is. -# -# Here is the corresponding time series plot. - -# In[13]: - - -ts_plot(g, xmin, xmax, x0, ts_length=6) - - -# The irregularity is even clearer over a longer time horizon: - -# In[14]: - - -ts_plot(g, xmin, xmax, x0, ts_length=20) - - -# ## Exercises -# -# ```{exercise} -# :label: sd_ex1 -# -# Consider again the linear model $x_{t+1} = a x_t + b$ with $a -# \not=1$. -# -# The unique steady state is $b / (1 - a)$. -# -# The steady state is globally stable if $|a| < 1$. -# -# Try to illustrate this graphically by looking at a range of initial conditions. -# -# What differences do you notice in the cases $a \in (-1, 0)$ and $a -# \in (0, 1)$? -# -# Use $a=0.5$ and then $a=-0.5$ and study the trajectories -# -# Set $b=1$ throughout. -# ``` -# -# ```{solution-start} sd_ex1 -# :class: dropdown -# ``` -# -# We will start with the case $a=0.5$. -# -# Let's set up the model and plotting region: - -# In[15]: - - -a, b = 0.5, 1 -xmin, xmax = -1, 3 -g = lambda x: a * x + b - - -# Now let's plot a trajectory: - -# In[16]: - - -x0 = -0.5 -plot45(g, xmin, xmax, x0, num_arrows=5) - - -# Here is the corresponding time series, which converges towards the steady -# state. - -# In[17]: - - -ts_plot(g, xmin, xmax, x0, ts_length=10) - - -# Now let's try $a=-0.5$ and see what differences we observe. -# -# Let's set up the model and plotting region: - -# In[18]: - - -a, b = -0.5, 1 -xmin, xmax = -1, 3 -g = lambda x: a * x + b - - -# Now let's plot a trajectory: - -# In[19]: - - -x0 = -0.5 -plot45(g, xmin, xmax, x0, num_arrows=5) - - -# Here is the corresponding time series, which converges towards the steady -# state. - -# In[20]: - - -ts_plot(g, xmin, xmax, x0, ts_length=10) - - -# Once again, we have convergence to the steady state but the nature of -# convergence differs. -# -# In particular, the time series jumps from above the steady state to below it -# and back again. -# -# In the current context, the series is said to exhibit **damped oscillations**. -# -# ```{solution-end} -# ``` diff --git a/lectures/_build/jupyter_execute/scalar_dynam_11_1.png b/lectures/_build/jupyter_execute/scalar_dynam_11_1.png deleted file mode 100644 index 582881a77..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_11_1.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_13_0.png b/lectures/_build/jupyter_execute/scalar_dynam_13_0.png deleted file mode 100644 index 407dcc669..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_13_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_15_0.png b/lectures/_build/jupyter_execute/scalar_dynam_15_0.png deleted file mode 100644 index 3b3a1be92..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_15_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_17_1.png b/lectures/_build/jupyter_execute/scalar_dynam_17_1.png deleted file mode 100644 index a672a1ab8..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_17_1.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_19_0.png b/lectures/_build/jupyter_execute/scalar_dynam_19_0.png deleted file mode 100644 index 1b249c534..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_19_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_21_0.png b/lectures/_build/jupyter_execute/scalar_dynam_21_0.png deleted file mode 100644 index 4aaad7e4f..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_21_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_23_1.png b/lectures/_build/jupyter_execute/scalar_dynam_23_1.png deleted file mode 100644 index e0e9a3e28..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_23_1.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_25_0.png b/lectures/_build/jupyter_execute/scalar_dynam_25_0.png deleted file mode 100644 index 41c2172e2..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_25_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_27_0.png b/lectures/_build/jupyter_execute/scalar_dynam_27_0.png deleted file mode 100644 index 13fdde0a4..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_27_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_31_1.png b/lectures/_build/jupyter_execute/scalar_dynam_31_1.png deleted file mode 100644 index 9c499967b..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_31_1.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_33_0.png b/lectures/_build/jupyter_execute/scalar_dynam_33_0.png deleted file mode 100644 index 63fb878a3..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_33_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_37_1.png b/lectures/_build/jupyter_execute/scalar_dynam_37_1.png deleted file mode 100644 index 19e47d8ac..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_37_1.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_39_0.png b/lectures/_build/jupyter_execute/scalar_dynam_39_0.png deleted file mode 100644 index ee8cbb5eb..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_39_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/scalar_dynam_9_0.png b/lectures/_build/jupyter_execute/scalar_dynam_9_0.png deleted file mode 100644 index 0d0f47889..000000000 Binary files a/lectures/_build/jupyter_execute/scalar_dynam_9_0.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/schelling.ipynb b/lectures/_build/jupyter_execute/schelling.ipynb deleted file mode 100644 index fa086ddc0..000000000 --- a/lectures/_build/jupyter_execute/schelling.ipynb +++ /dev/null @@ -1,430 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "003bb3c9", - "metadata": {}, - "source": [ - "(schelling)=\n", - "```{raw} html\n", - "
\n", - " \n", - " \"QuantEcon\"\n", - " \n", - "
\n", - "```\n", - "\n", - "# Schelling's Segregation Model\n", - "\n", - "```{index} single: Schelling Segregation Model\n", - "```\n", - "\n", - "```{index} single: Models; Schelling's Segregation Model\n", - "```\n", - "\n", - "```{contents} Contents\n", - ":depth: 2\n", - "```\n", - "\n", - "## Outline\n", - "\n", - "In 1969, Thomas C. Schelling developed a simple but striking model of racial segregation {cite}`Schelling1969`.\n", - "\n", - "His model studies the dynamics of racially mixed neighborhoods.\n", - "\n", - "Like much of Schelling's work, the model shows how local interactions can lead to surprising aggregate structure.\n", - "\n", - "In particular, it shows that relatively mild preference for neighbors of similar race can lead in aggregate to the collapse of mixed neighborhoods, and high levels of segregation.\n", - "\n", - "In recognition of this and other research, Schelling was awarded the 2005 Nobel Prize in Economic Sciences (joint with Robert Aumann).\n", - "\n", - "In this lecture, we (in fact you) will build and run a version of Schelling's model.\n", - "\n", - "Let's start with some imports:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "54000f82", - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib inline\n", - "import matplotlib.pyplot as plt\n", - "plt.rcParams[\"figure.figsize\"] = (11, 5) #set default figure size\n", - "from random import uniform, seed\n", - "from math import sqrt" - ] - }, - { - "cell_type": "markdown", - "id": "bae7bc55", - "metadata": {}, - "source": [ - "## The Model\n", - "\n", - "We will cover a variation of Schelling's model that is easy to program and captures the main idea.\n", - "\n", - "### Set-Up\n", - "\n", - "Suppose we have two types of people: orange people and green people.\n", - "\n", - "For the purpose of this lecture, we will assume there are 250 of each type.\n", - "\n", - "These agents all live on a single unit square.\n", - "\n", - "The location of an agent is just a point $(x, y)$, where $0 < x, y < 1$.\n", - "\n", - "### Preferences\n", - "\n", - "We will say that an agent is *happy* if half or more of her 10 nearest neighbors are of the same type.\n", - "\n", - "Here 'nearest' is in terms of [Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance).\n", - "\n", - "An agent who is not happy is called *unhappy*.\n", - "\n", - "An important point here is that agents are not averse to living in mixed areas.\n", - "\n", - "They are perfectly happy if half their neighbors are of the other color.\n", - "\n", - "### Behavior\n", - "\n", - "Initially, agents are mixed together (integrated).\n", - "\n", - "In particular, the initial location of each agent is an independent draw from a bivariate uniform distribution on $S = (0, 1)^2$.\n", - "\n", - "Now, cycling through the set of all agents, each agent is now given the chance to stay or move.\n", - "\n", - "We assume that each agent will stay put if they are happy and move if unhappy.\n", - "\n", - "The algorithm for moving is as follows\n", - "\n", - "1. Draw a random location in $S$\n", - "1. If happy at new location, move there\n", - "1. Else, go to step 1\n", - "\n", - "In this way, we cycle continuously through the agents, moving as required.\n", - "\n", - "We continue to cycle until no one wishes to move.\n", - "\n", - "## Results\n", - "\n", - "Let's have a look at the results we got when we coded and ran this model.\n", - "\n", - "As discussed above, agents are initially mixed randomly together.\n", - "\n", - "```{figure} /_static/lecture_specific/schelling/schelling_fig1.png\n", - "\n", - "```\n", - "\n", - "But after several cycles, they become segregated into distinct regions.\n", - "\n", - "```{figure} /_static/lecture_specific/schelling/schelling_fig2.png\n", - "\n", - "```\n", - "\n", - "```{figure} /_static/lecture_specific/schelling/schelling_fig3.png\n", - "\n", - "```\n", - "\n", - "```{figure} /_static/lecture_specific/schelling/schelling_fig4.png\n", - "\n", - "```\n", - "\n", - "In this instance, the program terminated after 4 cycles through the set of\n", - "agents, indicating that all agents had reached a state of happiness.\n", - "\n", - "What is striking about the pictures is how rapidly racial integration breaks down.\n", - "\n", - "This is despite the fact that people in the model don't actually mind living mixed with the other type.\n", - "\n", - "Even with these preferences, the outcome is a high degree of segregation.\n", - "\n", - "## Exercises\n", - "\n", - "```{exercise-start}\n", - ":label: schelling_ex1\n", - "```\n", - "\n", - "Implement and run this simulation for yourself.\n", - "\n", - "Consider the following structure for your program.\n", - "\n", - "Agents can be modeled as [objects](https://python-programming.quantecon.org/python_oop.html).\n", - "\n", - "Here's an indication of how they might look\n", - "\n", - "```{code-block} none\n", - "* Data:\n", - "\n", - " * type (green or orange)\n", - " * location\n", - "\n", - "* Methods:\n", - "\n", - " * determine whether happy or not given locations of other agents\n", - "\n", - " * If not happy, move\n", - "\n", - " * find a new location where happy\n", - "```\n", - "\n", - "And here's some pseudocode for the main loop\n", - "\n", - "```{code-block} none\n", - "while agents are still moving\n", - " for agent in agents\n", - " give agent the opportunity to move\n", - "```\n", - "\n", - "Use 250 agents of each type.\n", - "\n", - "```{exercise-end}\n", - "```\n", - "\n", - "```{solution-start} schelling_ex1\n", - ":class: dropdown\n", - "```\n", - "\n", - "Here's one solution that does the job we want.\n", - "\n", - "If you feel like a further exercise, you can probably speed up some of the computations and\n", - "then increase the number of agents." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "1f0c2a34", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 1\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/schelling_3_1.png" - } - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 2\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/schelling_3_3.png" - } - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 3\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/schelling_3_5.png" - } - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Entering loop 4\n" - ] - }, - { - "data": { - "image/png": "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\n", - "text/plain": [ - "
" - ] - }, - "metadata": { - "filenames": { - "image/png": "/Users/mmcky/work/quantecon/lecture-python-intro/lectures/_build/jupyter_execute/schelling_3_7.png" - } - }, - "output_type": "display_data" - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Converged, terminating.\n" - ] - } - ], - "source": [ - "seed(10) # For reproducible random numbers\n", - "\n", - "class Agent:\n", - "\n", - " def __init__(self, type):\n", - " self.type = type\n", - " self.draw_location()\n", - "\n", - " def draw_location(self):\n", - " self.location = uniform(0, 1), uniform(0, 1)\n", - "\n", - " def get_distance(self, other):\n", - " \"Computes the euclidean distance between self and other agent.\"\n", - " a = (self.location[0] - other.location[0])**2\n", - " b = (self.location[1] - other.location[1])**2\n", - " return sqrt(a + b)\n", - "\n", - " def happy(self, agents):\n", - " \"True if sufficient number of nearest neighbors are of the same type.\"\n", - " distances = []\n", - " # distances is a list of pairs (d, agent), where d is distance from\n", - " # agent to self\n", - " for agent in agents:\n", - " if self != agent:\n", - " distance = self.get_distance(agent)\n", - " distances.append((distance, agent))\n", - " # == Sort from smallest to largest, according to distance == #\n", - " distances.sort()\n", - " # == Extract the neighboring agents == #\n", - " neighbors = [agent for d, agent in distances[:num_neighbors]]\n", - " # == Count how many neighbors have the same type as self == #\n", - " num_same_type = sum(self.type == agent.type for agent in neighbors)\n", - " return num_same_type >= require_same_type\n", - "\n", - " def update(self, agents):\n", - " \"If not happy, then randomly choose new locations until happy.\"\n", - " while not self.happy(agents):\n", - " self.draw_location()\n", - "\n", - "\n", - "def plot_distribution(agents, cycle_num):\n", - " \"Plot the distribution of agents after cycle_num rounds of the loop.\"\n", - " x_values_0, y_values_0 = [], []\n", - " x_values_1, y_values_1 = [], []\n", - " # == Obtain locations of each type == #\n", - " for agent in agents:\n", - " x, y = agent.location\n", - " if agent.type == 0:\n", - " x_values_0.append(x)\n", - " y_values_0.append(y)\n", - " else:\n", - " x_values_1.append(x)\n", - " y_values_1.append(y)\n", - " fig, ax = plt.subplots(figsize=(8, 8))\n", - " plot_args = {'markersize': 8, 'alpha': 0.6}\n", - " ax.set_facecolor('azure')\n", - " ax.plot(x_values_0, y_values_0, 'o', markerfacecolor='orange', **plot_args)\n", - " ax.plot(x_values_1, y_values_1, 'o', markerfacecolor='green', **plot_args)\n", - " ax.set_title(f'Cycle {cycle_num-1}')\n", - " plt.show()\n", - "\n", - "# == Main == #\n", - "\n", - "num_of_type_0 = 250\n", - "num_of_type_1 = 250\n", - "num_neighbors = 10 # Number of agents regarded as neighbors\n", - "require_same_type = 5 # Want at least this many neighbors to be same type\n", - "\n", - "# == Create a list of agents == #\n", - "agents = [Agent(0) for i in range(num_of_type_0)]\n", - "agents.extend(Agent(1) for i in range(num_of_type_1))\n", - "\n", - "\n", - "count = 1\n", - "# == Loop until none wishes to move == #\n", - "while True:\n", - " print('Entering loop ', count)\n", - " plot_distribution(agents, count)\n", - " count += 1\n", - " no_one_moved = True\n", - " for agent in agents:\n", - " old_location = agent.location\n", - " agent.update(agents)\n", - " if agent.location != old_location:\n", - " no_one_moved = False\n", - " if no_one_moved:\n", - " break\n", - "\n", - "print('Converged, terminating.')" - ] - }, - { - "cell_type": "markdown", - "id": "bb5e865e", - "metadata": {}, - "source": [ - "```{solution-end}\n", - "```" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 49, - 55, - 187, - 277 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/jupyter_execute/schelling.py b/lectures/_build/jupyter_execute/schelling.py deleted file mode 100644 index 044af2add..000000000 --- a/lectures/_build/jupyter_execute/schelling.py +++ /dev/null @@ -1,276 +0,0 @@ -#!/usr/bin/env python -# coding: utf-8 - -# (schelling)= -# ```{raw} html -#
-# -# QuantEcon -# -#
-# ``` -# -# # Schelling's Segregation Model -# -# ```{index} single: Schelling Segregation Model -# ``` -# -# ```{index} single: Models; Schelling's Segregation Model -# ``` -# -# ```{contents} Contents -# :depth: 2 -# ``` -# -# ## Outline -# -# In 1969, Thomas C. Schelling developed a simple but striking model of racial segregation {cite}`Schelling1969`. -# -# His model studies the dynamics of racially mixed neighborhoods. -# -# Like much of Schelling's work, the model shows how local interactions can lead to surprising aggregate structure. -# -# In particular, it shows that relatively mild preference for neighbors of similar race can lead in aggregate to the collapse of mixed neighborhoods, and high levels of segregation. -# -# In recognition of this and other research, Schelling was awarded the 2005 Nobel Prize in Economic Sciences (joint with Robert Aumann). -# -# In this lecture, we (in fact you) will build and run a version of Schelling's model. -# -# Let's start with some imports: - -# In[1]: - - -get_ipython().run_line_magic('matplotlib', 'inline') -import matplotlib.pyplot as plt -plt.rcParams["figure.figsize"] = (11, 5) #set default figure size -from random import uniform, seed -from math import sqrt - - -# ## The Model -# -# We will cover a variation of Schelling's model that is easy to program and captures the main idea. -# -# ### Set-Up -# -# Suppose we have two types of people: orange people and green people. -# -# For the purpose of this lecture, we will assume there are 250 of each type. -# -# These agents all live on a single unit square. -# -# The location of an agent is just a point $(x, y)$, where $0 < x, y < 1$. -# -# ### Preferences -# -# We will say that an agent is *happy* if half or more of her 10 nearest neighbors are of the same type. -# -# Here 'nearest' is in terms of [Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance). -# -# An agent who is not happy is called *unhappy*. -# -# An important point here is that agents are not averse to living in mixed areas. -# -# They are perfectly happy if half their neighbors are of the other color. -# -# ### Behavior -# -# Initially, agents are mixed together (integrated). -# -# In particular, the initial location of each agent is an independent draw from a bivariate uniform distribution on $S = (0, 1)^2$. -# -# Now, cycling through the set of all agents, each agent is now given the chance to stay or move. -# -# We assume that each agent will stay put if they are happy and move if unhappy. -# -# The algorithm for moving is as follows -# -# 1. Draw a random location in $S$ -# 1. If happy at new location, move there -# 1. Else, go to step 1 -# -# In this way, we cycle continuously through the agents, moving as required. -# -# We continue to cycle until no one wishes to move. -# -# ## Results -# -# Let's have a look at the results we got when we coded and ran this model. -# -# As discussed above, agents are initially mixed randomly together. -# -# ```{figure} /_static/lecture_specific/schelling/schelling_fig1.png -# -# ``` -# -# But after several cycles, they become segregated into distinct regions. -# -# ```{figure} /_static/lecture_specific/schelling/schelling_fig2.png -# -# ``` -# -# ```{figure} /_static/lecture_specific/schelling/schelling_fig3.png -# -# ``` -# -# ```{figure} /_static/lecture_specific/schelling/schelling_fig4.png -# -# ``` -# -# In this instance, the program terminated after 4 cycles through the set of -# agents, indicating that all agents had reached a state of happiness. -# -# What is striking about the pictures is how rapidly racial integration breaks down. -# -# This is despite the fact that people in the model don't actually mind living mixed with the other type. -# -# Even with these preferences, the outcome is a high degree of segregation. -# -# ## Exercises -# -# ```{exercise-start} -# :label: schelling_ex1 -# ``` -# -# Implement and run this simulation for yourself. -# -# Consider the following structure for your program. -# -# Agents can be modeled as [objects](https://python-programming.quantecon.org/python_oop.html). -# -# Here's an indication of how they might look -# -# ```{code-block} none -# * Data: -# -# * type (green or orange) -# * location -# -# * Methods: -# -# * determine whether happy or not given locations of other agents -# -# * If not happy, move -# -# * find a new location where happy -# ``` -# -# And here's some pseudocode for the main loop -# -# ```{code-block} none -# while agents are still moving -# for agent in agents -# give agent the opportunity to move -# ``` -# -# Use 250 agents of each type. -# -# ```{exercise-end} -# ``` -# -# ```{solution-start} schelling_ex1 -# :class: dropdown -# ``` -# -# Here's one solution that does the job we want. -# -# If you feel like a further exercise, you can probably speed up some of the computations and -# then increase the number of agents. - -# In[2]: - - -seed(10) # For reproducible random numbers - -class Agent: - - def __init__(self, type): - self.type = type - self.draw_location() - - def draw_location(self): - self.location = uniform(0, 1), uniform(0, 1) - - def get_distance(self, other): - "Computes the euclidean distance between self and other agent." - a = (self.location[0] - other.location[0])**2 - b = (self.location[1] - other.location[1])**2 - return sqrt(a + b) - - def happy(self, agents): - "True if sufficient number of nearest neighbors are of the same type." - distances = [] - # distances is a list of pairs (d, agent), where d is distance from - # agent to self - for agent in agents: - if self != agent: - distance = self.get_distance(agent) - distances.append((distance, agent)) - # == Sort from smallest to largest, according to distance == # - distances.sort() - # == Extract the neighboring agents == # - neighbors = [agent for d, agent in distances[:num_neighbors]] - # == Count how many neighbors have the same type as self == # - num_same_type = sum(self.type == agent.type for agent in neighbors) - return num_same_type >= require_same_type - - def update(self, agents): - "If not happy, then randomly choose new locations until happy." - while not self.happy(agents): - self.draw_location() - - -def plot_distribution(agents, cycle_num): - "Plot the distribution of agents after cycle_num rounds of the loop." - x_values_0, y_values_0 = [], [] - x_values_1, y_values_1 = [], [] - # == Obtain locations of each type == # - for agent in agents: - x, y = agent.location - if agent.type == 0: - x_values_0.append(x) - y_values_0.append(y) - else: - x_values_1.append(x) - y_values_1.append(y) - fig, ax = plt.subplots(figsize=(8, 8)) - plot_args = {'markersize': 8, 'alpha': 0.6} - ax.set_facecolor('azure') - ax.plot(x_values_0, y_values_0, 'o', markerfacecolor='orange', **plot_args) - ax.plot(x_values_1, y_values_1, 'o', markerfacecolor='green', **plot_args) - ax.set_title(f'Cycle {cycle_num-1}') - plt.show() - -# == Main == # - -num_of_type_0 = 250 -num_of_type_1 = 250 -num_neighbors = 10 # Number of agents regarded as neighbors -require_same_type = 5 # Want at least this many neighbors to be same type - -# == Create a list of agents == # -agents = [Agent(0) for i in range(num_of_type_0)] -agents.extend(Agent(1) for i in range(num_of_type_1)) - - -count = 1 -# == Loop until none wishes to move == # -while True: - print('Entering loop ', count) - plot_distribution(agents, count) - count += 1 - no_one_moved = True - for agent in agents: - old_location = agent.location - agent.update(agents) - if agent.location != old_location: - no_one_moved = False - if no_one_moved: - break - -print('Converged, terminating.') - - -# ```{solution-end} -# ``` diff --git a/lectures/_build/jupyter_execute/schelling_3_1.png b/lectures/_build/jupyter_execute/schelling_3_1.png deleted file mode 100644 index c188d6d0c..000000000 Binary files a/lectures/_build/jupyter_execute/schelling_3_1.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/schelling_3_3.png b/lectures/_build/jupyter_execute/schelling_3_3.png deleted file mode 100644 index cd14b0ae7..000000000 Binary files a/lectures/_build/jupyter_execute/schelling_3_3.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/schelling_3_5.png b/lectures/_build/jupyter_execute/schelling_3_5.png deleted file mode 100644 index 7e42b9b88..000000000 Binary files a/lectures/_build/jupyter_execute/schelling_3_5.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/schelling_3_7.png b/lectures/_build/jupyter_execute/schelling_3_7.png deleted file mode 100644 index a9319b412..000000000 Binary files a/lectures/_build/jupyter_execute/schelling_3_7.png and /dev/null differ diff --git a/lectures/_build/jupyter_execute/short_path.ipynb b/lectures/_build/jupyter_execute/short_path.ipynb deleted file mode 100644 index 66d9acbdf..000000000 --- a/lectures/_build/jupyter_execute/short_path.ipynb +++ /dev/null @@ -1,702 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "12189301", - "metadata": {}, - "source": [ - "(short_path)=\n", - "```{raw} html\n", - "
\n", - " \n", - " \"QuantEcon\"\n", - " \n", - "
\n", - "```\n", - "\n", - "# Shortest Paths\n", - "\n", - "```{index} single: Dynamic Programming; Shortest Paths\n", - "```\n", - "\n", - "```{contents} Contents\n", - ":depth: 2\n", - "```\n", - "\n", - "## Overview\n", - "\n", - "The shortest path problem is a [classic problem](https://en.wikipedia.org/wiki/Shortest_path) in mathematics and computer science with applications in\n", - "\n", - "* Economics (sequential decision making, analysis of social networks, etc.)\n", - "* Operations research and transportation\n", - "* Robotics and artificial intelligence\n", - "* Telecommunication network design and routing\n", - "* etc., etc.\n", - "\n", - "Variations of the methods we discuss in this lecture are used millions of times every day, in applications such as\n", - "\n", - "* Google Maps\n", - "* routing packets on the internet\n", - "\n", - "For us, the shortest path problem also provides a nice introduction to the logic of **dynamic programming**.\n", - "\n", - "Dynamic programming is an extremely powerful optimization technique that we apply in many lectures on this site.\n", - "\n", - "The only scientific library we'll need in what follows is NumPy:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "0cdc4241", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np" - ] - }, - { - "cell_type": "markdown", - "id": "12745deb", - "metadata": {}, - "source": [ - "## Outline of the Problem\n", - "\n", - "The shortest path problem is one of finding how to traverse a [graph](https://en.wikipedia.org/wiki/Graph_%28mathematics%29) from one specified node to another at minimum cost.\n", - "\n", - "Consider the following graph\n", - "\n", - "```{figure} /_static/lecture_specific/short_path/graph.png\n", - "\n", - "```\n", - "\n", - "We wish to travel from node (vertex) A to node G at minimum cost\n", - "\n", - "* Arrows (edges) indicate the movements we can take.\n", - "* Numbers on edges indicate the cost of traveling that edge.\n", - "\n", - "(Graphs such as the one above are called weighted [directed graphs](https://en.wikipedia.org/wiki/Directed_graph).)\n", - "\n", - "Possible interpretations of the graph include\n", - "\n", - "* Minimum cost for supplier to reach a destination.\n", - "* Routing of packets on the internet (minimize time).\n", - "* Etc., etc.\n", - "\n", - "For this simple graph, a quick scan of the edges shows that the optimal paths are\n", - "\n", - "* A, C, F, G at cost 8\n", - "\n", - "```{figure} /_static/lecture_specific/short_path/graph4.png\n", - "\n", - "```\n", - "\n", - "* A, D, F, G at cost 8\n", - "\n", - "```{figure} /_static/lecture_specific/short_path/graph3.png\n", - "\n", - "```\n", - "\n", - "## Finding Least-Cost Paths\n", - "\n", - "For large graphs, we need a systematic solution.\n", - "\n", - "Let $J(v)$ denote the minimum cost-to-go from node $v$, understood as the total cost from $v$ if we take the best route.\n", - "\n", - "Suppose that we know $J(v)$ for each node $v$, as shown below for the graph from the preceding example\n", - "\n", - "```{figure} /_static/lecture_specific/short_path/graph2.png\n", - "\n", - "```\n", - "\n", - "Note that $J(G) = 0$.\n", - "\n", - "The best path can now be found as follows\n", - "\n", - "1. Start at node $v = A$\n", - "1. From current node $v$, move to any node that solves\n", - "\n", - "```{math}\n", - ":label: spprebell\n", - "\n", - "\\min_{w \\in F_v} \\{ c(v, w) + J(w) \\}\n", - "```\n", - "\n", - "where\n", - "\n", - "* $F_v$ is the set of nodes that can be reached from $v$ in one step.\n", - "* $c(v, w)$ is the cost of traveling from $v$ to $w$.\n", - "\n", - "Hence, if we know the function $J$, then finding the best path is almost trivial.\n", - "\n", - "But how can we find the cost-to-go function $J$?\n", - "\n", - "Some thought will convince you that, for every node $v$,\n", - "the function $J$ satisfies\n", - "\n", - "```{math}\n", - ":label: spbell\n", - "\n", - "J(v) = \\min_{w \\in F_v} \\{ c(v, w) + J(w) \\}\n", - "```\n", - "\n", - "This is known as the *Bellman equation*, after the mathematician Richard Bellman.\n", - "\n", - "The Bellman equation can be thought of as a restriction that $J$ must\n", - "satisfy.\n", - "\n", - "What we want to do now is use this restriction to compute $J$.\n", - "\n", - "## Solving for Minimum Cost-to-Go\n", - "\n", - "Let's look at an algorithm for computing $J$ and then think about how to\n", - "implement it.\n", - "\n", - "### The Algorithm\n", - "\n", - "The standard algorithm for finding $J$ is to start an initial guess and then iterate.\n", - "\n", - "This is a standard approach to solving nonlinear equations, often called\n", - "the method of **successive approximations**.\n", - "\n", - "Our initial guess will be\n", - "\n", - "```{math}\n", - ":label: spguess\n", - "\n", - "J_0(v) = 0 \\text{ for all } v\n", - "```\n", - "\n", - "Now\n", - "\n", - "1. Set $n = 0$\n", - "1. Set $J_{n+1} (v) = \\min_{w \\in F_v} \\{ c(v, w) + J_n(w) \\}$ for all $v$\n", - "1. If $J_{n+1}$ and $J_n$ are not equal then increment $n$, go to 2\n", - "\n", - "This sequence converges to $J$.\n", - "\n", - "Although we omit the proof, we'll prove similar claims in our other lectures\n", - "on dynamic programming.\n", - "\n", - "### Implementation\n", - "\n", - "Having an algorithm is a good start, but we also need to think about how to\n", - "implement it on a computer.\n", - "\n", - "First, for the cost function $c$, we'll implement it as a matrix\n", - "$Q$, where a typical element is\n", - "\n", - "$$\n", - "Q(v, w)\n", - "=\n", - "\\begin{cases}\n", - " & c(v, w) \\text{ if } w \\in F_v \\\\\n", - " & +\\infty \\text{ otherwise }\n", - "\\end{cases}\n", - "$$\n", - "\n", - "In this context $Q$ is usually called the **distance matrix**.\n", - "\n", - "We're also numbering the nodes now, with $A = 0$, so, for example\n", - "\n", - "$$\n", - "Q(1, 2)\n", - "=\n", - "\\text{ the cost of traveling from B to C }\n", - "$$\n", - "\n", - "For example, for the simple graph above, we set" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "2d5a435c", - "metadata": {}, - "outputs": [], - "source": [ - "from numpy import inf\n", - "\n", - "Q = np.array([[inf, 1, 5, 3, inf, inf, inf],\n", - " [inf, inf, inf, 9, 6, inf, inf],\n", - " [inf, inf, inf, inf, inf, 2, inf],\n", - " [inf, inf, inf, inf, inf, 4, 8],\n", - " [inf, inf, inf, inf, inf, inf, 4],\n", - " [inf, inf, inf, inf, inf, inf, 1],\n", - " [inf, inf, inf, inf, inf, inf, 0]])" - ] - }, - { - "cell_type": "markdown", - "id": "4ade5693", - "metadata": {}, - "source": [ - "Notice that the cost of staying still (on the principle diagonal) is set to\n", - "\n", - "* np.inf for non-destination nodes --- moving on is required.\n", - "* 0 for the destination node --- here is where we stop.\n", - "\n", - "For the sequence of approximations $\\{J_n\\}$ of the cost-to-go functions, we can use NumPy arrays.\n", - "\n", - "Let's try with this example and see how we go:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "1841811a", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The cost-to-go function is [ 8 10 3 5 4 1 0]\n" - ] - } - ], - "source": [ - "nodes = range(7) # Nodes = 0, 1, ..., 6\n", - "J = np.zeros_like(nodes, dtype=int) # Initial guess\n", - "next_J = np.empty_like(nodes, dtype=int) # Stores updated guess\n", - "\n", - "max_iter = 500\n", - "i = 0\n", - "\n", - "while i < max_iter:\n", - " for v in nodes:\n", - " # minimize Q[v, w] + J[w] over all choices of w\n", - " lowest_cost = inf\n", - " for w in nodes:\n", - " cost = Q[v, w] + J[w]\n", - " if cost < lowest_cost:\n", - " lowest_cost = cost\n", - " next_J[v] = lowest_cost\n", - " if np.equal(next_J, J).all():\n", - " break\n", - " else:\n", - " J[:] = next_J # Copy contents of next_J to J\n", - " i += 1\n", - "\n", - "print(\"The cost-to-go function is\", J)" - ] - }, - { - "cell_type": "markdown", - "id": "b348a870", - "metadata": {}, - "source": [ - "This matches with the numbers we obtained by inspection above.\n", - "\n", - "But, importantly, we now have a methodology for tackling large graphs.\n", - "\n", - "## Exercises\n", - "\n", - "\n", - "```{exercise-start}\n", - ":label: short_path_ex1\n", - "```\n", - "\n", - "The text below describes a weighted directed graph.\n", - "\n", - "The line `node0, node1 0.04, node8 11.11, node14 72.21` means that from node0 we can go to\n", - "\n", - "* node1 at cost 0.04\n", - "* node8 at cost 11.11\n", - "* node14 at cost 72.21\n", - "\n", - "No other nodes can be reached directly from node0.\n", - "\n", - "Other lines have a similar interpretation.\n", - "\n", - "Your task is to use the algorithm given above to find the optimal path and its cost.\n", - "\n", - "```{note}\n", - "You will be dealing with floating point numbers now, rather than\n", - "integers, so consider replacing `np.equal()` with `np.allclose()`.\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "cfacfaa8", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Writing graph.txt\n" - ] - } - ], - "source": [ - "%%file graph.txt\n", - "node0, node1 0.04, node8 11.11, node14 72.21\n", - "node1, node46 1247.25, node6 20.59, node13 64.94\n", - "node2, node66 54.18, node31 166.80, node45 1561.45\n", - "node3, node20 133.65, node6 2.06, node11 42.43\n", - "node4, node75 3706.67, node5 0.73, node7 1.02\n", - "node5, node45 1382.97, node7 3.33, node11 34.54\n", - "node6, node31 63.17, node9 0.72, node10 13.10\n", - "node7, node50 478.14, node9 3.15, node10 5.85\n", - "node8, node69 577.91, node11 7.45, node12 3.18\n", - "node9, node70 2454.28, node13 4.42, node20 16.53\n", - "node10, node89 5352.79, node12 1.87, node16 25.16\n", - "node11, node94 4961.32, node18 37.55, node20 65.08\n", - "node12, node84 3914.62, node24 34.32, node28 170.04\n", - "node13, node60 2135.95, node38 236.33, node40 475.33\n", - "node14, node67 1878.96, node16 2.70, node24 38.65\n", - "node15, node91 3597.11, node17 1.01, node18 2.57\n", - "node16, node36 392.92, node19 3.49, node38 278.71\n", - "node17, node76 783.29, node22 24.78, node23 26.45\n", - "node18, node91 3363.17, node23 16.23, node28 55.84\n", - "node19, node26 20.09, node20 0.24, node28 70.54\n", - "node20, node98 3523.33, node24 9.81, node33 145.80\n", - "node21, node56 626.04, node28 36.65, node31 27.06\n", - "node22, node72 1447.22, node39 136.32, node40 124.22\n", - "node23, node52 336.73, node26 2.66, node33 22.37\n", - "node24, node66 875.19, node26 1.80, node28 14.25\n", - "node25, node70 1343.63, node32 36.58, node35 45.55\n", - "node26, node47 135.78, node27 0.01, node42 122.00\n", - "node27, node65 480.55, node35 48.10, node43 246.24\n", - "node28, node82 2538.18, node34 21.79, node36 15.52\n", - "node29, node64 635.52, node32 4.22, node33 12.61\n", - "node30, node98 2616.03, node33 5.61, node35 13.95\n", - "node31, node98 3350.98, node36 20.44, node44 125.88\n", - "node32, node97 2613.92, node34 3.33, node35 1.46\n", - "node33, node81 1854.73, node41 3.23, node47 111.54\n", - "node34, node73 1075.38, node42 51.52, node48 129.45\n", - "node35, node52 17.57, node41 2.09, node50 78.81\n", - "node36, node71 1171.60, node54 101.08, node57 260.46\n", - "node37, node75 269.97, node38 0.36, node46 80.49\n", - "node38, node93 2767.85, node40 1.79, node42 8.78\n", - "node39, node50 39.88, node40 0.95, node41 1.34\n", - "node40, node75 548.68, node47 28.57, node54 53.46\n", - "node41, node53 18.23, node46 0.28, node54 162.24\n", - "node42, node59 141.86, node47 10.08, node72 437.49\n", - "node43, node98 2984.83, node54 95.06, node60 116.23\n", - "node44, node91 807.39, node46 1.56, node47 2.14\n", - "node45, node58 79.93, node47 3.68, node49 15.51\n", - "node46, node52 22.68, node57 27.50, node67 65.48\n", - "node47, node50 2.82, node56 49.31, node61 172.64\n", - "node48, node99 2564.12, node59 34.52, node60 66.44\n", - "node49, node78 53.79, node50 0.51, node56 10.89\n", - "node50, node85 251.76, node53 1.38, node55 20.10\n", - "node51, node98 2110.67, node59 23.67, node60 73.79\n", - "node52, node94 1471.80, node64 102.41, node66 123.03\n", - "node53, node72 22.85, node56 4.33, node67 88.35\n", - "node54, node88 967.59, node59 24.30, node73 238.61\n", - "node55, node84 86.09, node57 2.13, node64 60.80\n", - "node56, node76 197.03, node57 0.02, node61 11.06\n", - "node57, node86 701.09, node58 0.46, node60 7.01\n", - "node58, node83 556.70, node64 29.85, node65 34.32\n", - "node59, node90 820.66, node60 0.72, node71 0.67\n", - "node60, node76 48.03, node65 4.76, node67 1.63\n", - "node61, node98 1057.59, node63 0.95, node64 4.88\n", - "node62, node91 132.23, node64 2.94, node76 38.43\n", - "node63, node66 4.43, node72 70.08, node75 56.34\n", - "node64, node80 47.73, node65 0.30, node76 11.98\n", - "node65, node94 594.93, node66 0.64, node73 33.23\n", - "node66, node98 395.63, node68 2.66, node73 37.53\n", - "node67, node82 153.53, node68 0.09, node70 0.98\n", - "node68, node94 232.10, node70 3.35, node71 1.66\n", - "node69, node99 247.80, node70 0.06, node73 8.99\n", - "node70, node76 27.18, node72 1.50, node73 8.37\n", - "node71, node89 104.50, node74 8.86, node91 284.64\n", - "node72, node76 15.32, node84 102.77, node92 133.06\n", - "node73, node83 52.22, node76 1.40, node90 243.00\n", - "node74, node81 1.07, node76 0.52, node78 8.08\n", - "node75, node92 68.53, node76 0.81, node77 1.19\n", - "node76, node85 13.18, node77 0.45, node78 2.36\n", - "node77, node80 8.94, node78 0.98, node86 64.32\n", - "node78, node98 355.90, node81 2.59\n", - "node79, node81 0.09, node85 1.45, node91 22.35\n", - "node80, node92 121.87, node88 28.78, node98 264.34\n", - "node81, node94 99.78, node89 39.52, node92 99.89\n", - "node82, node91 47.44, node88 28.05, node93 11.99\n", - "node83, node94 114.95, node86 8.75, node88 5.78\n", - "node84, node89 19.14, node94 30.41, node98 121.05\n", - "node85, node97 94.51, node87 2.66, node89 4.90\n", - "node86, node97 85.09\n", - "node87, node88 0.21, node91 11.14, node92 21.23\n", - "node88, node93 1.31, node91 6.83, node98 6.12\n", - "node89, node97 36.97, node99 82.12\n", - "node90, node96 23.53, node94 10.47, node99 50.99\n", - "node91, node97 22.17\n", - "node92, node96 10.83, node97 11.24, node99 34.68\n", - "node93, node94 0.19, node97 6.71, node99 32.77\n", - "node94, node98 5.91, node96 2.03\n", - "node95, node98 6.17, node99 0.27\n", - "node96, node98 3.32, node97 0.43, node99 5.87\n", - "node97, node98 0.30\n", - "node98, node99 0.33\n", - "node99," - ] - }, - { - "cell_type": "markdown", - "id": "6647d22d", - "metadata": {}, - "source": [ - "```{exercise-end}\n", - "```\n", - "\n", - "```{solution-start} short_path_ex1\n", - ":class: dropdown\n", - "```\n", - "\n", - "First let's write a function that reads in the graph data above and builds a distance matrix." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "7eb79595", - "metadata": {}, - "outputs": [], - "source": [ - "num_nodes = 100\n", - "destination_node = 99\n", - "\n", - "def map_graph_to_distance_matrix(in_file):\n", - "\n", - " # First let's set of the distance matrix Q with inf everywhere\n", - " Q = np.full((num_nodes, num_nodes), np.inf)\n", - "\n", - " # Now we read in the data and modify Q\n", - " with open(in_file) as infile:\n", - " for line in infile:\n", - " elements = line.split(',')\n", - " node = elements.pop(0)\n", - " node = int(node[4:]) # convert node description to integer\n", - " if node != destination_node:\n", - " for element in elements:\n", - " destination, cost = element.split()\n", - " destination = int(destination[4:])\n", - " Q[node, destination] = float(cost)\n", - " Q[destination_node, destination_node] = 0\n", - " return Q" - ] - }, - { - "cell_type": "markdown", - "id": "9fe7ca07", - "metadata": {}, - "source": [ - "In addition, let's write\n", - "\n", - "1. a \"Bellman operator\" function that takes a distance matrix and current guess of J and returns an updated guess of J, and\n", - "1. a function that takes a distance matrix and returns a cost-to-go function.\n", - "\n", - "We'll use the algorithm described above.\n", - "\n", - "The minimization step is vectorized to make it faster." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "520c29a7", - "metadata": {}, - "outputs": [], - "source": [ - "def bellman(J, Q):\n", - " num_nodes = Q.shape[0]\n", - " next_J = np.empty_like(J)\n", - " for v in range(num_nodes):\n", - " next_J[v] = np.min(Q[v, :] + J)\n", - " return next_J\n", - "\n", - "\n", - "def compute_cost_to_go(Q):\n", - " num_nodes = Q.shape[0]\n", - " J = np.zeros(num_nodes) # Initial guess\n", - " max_iter = 500\n", - " i = 0\n", - "\n", - " while i < max_iter:\n", - " next_J = bellman(J, Q)\n", - " if np.allclose(next_J, J):\n", - " break\n", - " else:\n", - " J[:] = next_J # Copy contents of next_J to J\n", - " i += 1\n", - "\n", - " return(J)" - ] - }, - { - "cell_type": "markdown", - "id": "ca360928", - "metadata": {}, - "source": [ - "We used np.allclose() rather than testing exact equality because we are\n", - "dealing with floating point numbers now.\n", - "\n", - "Finally, here's a function that uses the cost-to-go function to obtain the\n", - "optimal path (and its cost)." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "bb110ac7", - "metadata": {}, - "outputs": [], - "source": [ - "def print_best_path(J, Q):\n", - " sum_costs = 0\n", - " current_node = 0\n", - " while current_node != destination_node:\n", - " print(current_node)\n", - " # Move to the next node and increment costs\n", - " next_node = np.argmin(Q[current_node, :] + J)\n", - " sum_costs += Q[current_node, next_node]\n", - " current_node = next_node\n", - "\n", - " print(destination_node)\n", - " print('Cost: ', sum_costs)" - ] - }, - { - "cell_type": "markdown", - "id": "0c788917", - "metadata": {}, - "source": [ - "Okay, now we have the necessary functions, let's call them to do the job we were assigned." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "4e2930bb", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0\n", - "8\n", - "11\n", - "18\n", - "23\n", - "33\n", - "41\n", - "53\n", - "56\n", - "57\n", - "60\n", - "67\n", - "70\n", - "73\n", - "76\n", - "85\n", - "87\n", - "88\n", - "93\n", - "94\n", - "96\n", - "97\n", - "98\n", - "99\n", - "Cost: 160.55000000000007\n" - ] - } - ], - "source": [ - "Q = map_graph_to_distance_matrix('graph.txt')\n", - "J = compute_cost_to_go(Q)\n", - "print_best_path(J, Q)" - ] - }, - { - "cell_type": "markdown", - "id": "5e9ff1a8", - "metadata": {}, - "source": [ - "The total cost of the path should agree with $J[0]$ so let's check this." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "07cdaf8d", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "160.55" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "J[0]" - ] - }, - { - "cell_type": "markdown", - "id": "db431ffd", - "metadata": {}, - "source": [ - "```{solution-end}\n", - "```" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10, - 51, - 53, - 202, - 212, - 223, - 247, - 279, - 381, - 392, - 414, - 425, - 449, - 457, - 470, - 474, - 478, - 482, - 484 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/jupyter_execute/short_path.py b/lectures/_build/jupyter_execute/short_path.py deleted file mode 100644 index b30876f07..000000000 --- a/lectures/_build/jupyter_execute/short_path.py +++ /dev/null @@ -1,397 +0,0 @@ -#!/usr/bin/env python -# coding: utf-8 - -# (short_path)= -# ```{raw} html -#
-# -# QuantEcon -# -#
-# ``` -# -# # Shortest Paths -# -# ```{index} single: Dynamic Programming; Shortest Paths -# ``` -# -# ```{contents} Contents -# :depth: 2 -# ``` -# -# ## Overview -# -# The shortest path problem is a [classic problem](https://en.wikipedia.org/wiki/Shortest_path) in mathematics and computer science with applications in -# -# * Economics (sequential decision making, analysis of social networks, etc.) -# * Operations research and transportation -# * Robotics and artificial intelligence -# * Telecommunication network design and routing -# * etc., etc. -# -# Variations of the methods we discuss in this lecture are used millions of times every day, in applications such as -# -# * Google Maps -# * routing packets on the internet -# -# For us, the shortest path problem also provides a nice introduction to the logic of **dynamic programming**. -# -# Dynamic programming is an extremely powerful optimization technique that we apply in many lectures on this site. -# -# The only scientific library we'll need in what follows is NumPy: - -# In[1]: - - -import numpy as np - - -# ## Outline of the Problem -# -# The shortest path problem is one of finding how to traverse a [graph](https://en.wikipedia.org/wiki/Graph_%28mathematics%29) from one specified node to another at minimum cost. -# -# Consider the following graph -# -# ```{figure} /_static/lecture_specific/short_path/graph.png -# -# ``` -# -# We wish to travel from node (vertex) A to node G at minimum cost -# -# * Arrows (edges) indicate the movements we can take. -# * Numbers on edges indicate the cost of traveling that edge. -# -# (Graphs such as the one above are called weighted [directed graphs](https://en.wikipedia.org/wiki/Directed_graph).) -# -# Possible interpretations of the graph include -# -# * Minimum cost for supplier to reach a destination. -# * Routing of packets on the internet (minimize time). -# * Etc., etc. -# -# For this simple graph, a quick scan of the edges shows that the optimal paths are -# -# * A, C, F, G at cost 8 -# -# ```{figure} /_static/lecture_specific/short_path/graph4.png -# -# ``` -# -# * A, D, F, G at cost 8 -# -# ```{figure} /_static/lecture_specific/short_path/graph3.png -# -# ``` -# -# ## Finding Least-Cost Paths -# -# For large graphs, we need a systematic solution. -# -# Let $J(v)$ denote the minimum cost-to-go from node $v$, understood as the total cost from $v$ if we take the best route. -# -# Suppose that we know $J(v)$ for each node $v$, as shown below for the graph from the preceding example -# -# ```{figure} /_static/lecture_specific/short_path/graph2.png -# -# ``` -# -# Note that $J(G) = 0$. -# -# The best path can now be found as follows -# -# 1. Start at node $v = A$ -# 1. From current node $v$, move to any node that solves -# -# ```{math} -# :label: spprebell -# -# \min_{w \in F_v} \{ c(v, w) + J(w) \} -# ``` -# -# where -# -# * $F_v$ is the set of nodes that can be reached from $v$ in one step. -# * $c(v, w)$ is the cost of traveling from $v$ to $w$. -# -# Hence, if we know the function $J$, then finding the best path is almost trivial. -# -# But how can we find the cost-to-go function $J$? -# -# Some thought will convince you that, for every node $v$, -# the function $J$ satisfies -# -# ```{math} -# :label: spbell -# -# J(v) = \min_{w \in F_v} \{ c(v, w) + J(w) \} -# ``` -# -# This is known as the *Bellman equation*, after the mathematician Richard Bellman. -# -# The Bellman equation can be thought of as a restriction that $J$ must -# satisfy. -# -# What we want to do now is use this restriction to compute $J$. -# -# ## Solving for Minimum Cost-to-Go -# -# Let's look at an algorithm for computing $J$ and then think about how to -# implement it. -# -# ### The Algorithm -# -# The standard algorithm for finding $J$ is to start an initial guess and then iterate. -# -# This is a standard approach to solving nonlinear equations, often called -# the method of **successive approximations**. -# -# Our initial guess will be -# -# ```{math} -# :label: spguess -# -# J_0(v) = 0 \text{ for all } v -# ``` -# -# Now -# -# 1. Set $n = 0$ -# 1. Set $J_{n+1} (v) = \min_{w \in F_v} \{ c(v, w) + J_n(w) \}$ for all $v$ -# 1. If $J_{n+1}$ and $J_n$ are not equal then increment $n$, go to 2 -# -# This sequence converges to $J$. -# -# Although we omit the proof, we'll prove similar claims in our other lectures -# on dynamic programming. -# -# ### Implementation -# -# Having an algorithm is a good start, but we also need to think about how to -# implement it on a computer. -# -# First, for the cost function $c$, we'll implement it as a matrix -# $Q$, where a typical element is -# -# $$ -# Q(v, w) -# = -# \begin{cases} -# & c(v, w) \text{ if } w \in F_v \\ -# & +\infty \text{ otherwise } -# \end{cases} -# $$ -# -# In this context $Q$ is usually called the **distance matrix**. -# -# We're also numbering the nodes now, with $A = 0$, so, for example -# -# $$ -# Q(1, 2) -# = -# \text{ the cost of traveling from B to C } -# $$ -# -# For example, for the simple graph above, we set - -# In[2]: - - -from numpy import inf - -Q = np.array([[inf, 1, 5, 3, inf, inf, inf], - [inf, inf, inf, 9, 6, inf, inf], - [inf, inf, inf, inf, inf, 2, inf], - [inf, inf, inf, inf, inf, 4, 8], - [inf, inf, inf, inf, inf, inf, 4], - [inf, inf, inf, inf, inf, inf, 1], - [inf, inf, inf, inf, inf, inf, 0]]) - - -# Notice that the cost of staying still (on the principle diagonal) is set to -# -# * np.inf for non-destination nodes --- moving on is required. -# * 0 for the destination node --- here is where we stop. -# -# For the sequence of approximations $\{J_n\}$ of the cost-to-go functions, we can use NumPy arrays. -# -# Let's try with this example and see how we go: - -# In[3]: - - -nodes = range(7) # Nodes = 0, 1, ..., 6 -J = np.zeros_like(nodes, dtype=int) # Initial guess -next_J = np.empty_like(nodes, dtype=int) # Stores updated guess - -max_iter = 500 -i = 0 - -while i < max_iter: - for v in nodes: - # minimize Q[v, w] + J[w] over all choices of w - lowest_cost = inf - for w in nodes: - cost = Q[v, w] + J[w] - if cost < lowest_cost: - lowest_cost = cost - next_J[v] = lowest_cost - if np.equal(next_J, J).all(): - break - else: - J[:] = next_J # Copy contents of next_J to J - i += 1 - -print("The cost-to-go function is", J) - - -# This matches with the numbers we obtained by inspection above. -# -# But, importantly, we now have a methodology for tackling large graphs. -# -# ## Exercises -# -# -# ```{exercise-start} -# :label: short_path_ex1 -# ``` -# -# The text below describes a weighted directed graph. -# -# The line `node0, node1 0.04, node8 11.11, node14 72.21` means that from node0 we can go to -# -# * node1 at cost 0.04 -# * node8 at cost 11.11 -# * node14 at cost 72.21 -# -# No other nodes can be reached directly from node0. -# -# Other lines have a similar interpretation. -# -# Your task is to use the algorithm given above to find the optimal path and its cost. -# -# ```{note} -# You will be dealing with floating point numbers now, rather than -# integers, so consider replacing `np.equal()` with `np.allclose()`. -# ``` - -# In[4]: - - -get_ipython().run_cell_magic('file', 'graph.txt', 'node0, node1 0.04, node8 11.11, node14 72.21\nnode1, node46 1247.25, node6 20.59, node13 64.94\nnode2, node66 54.18, node31 166.80, node45 1561.45\nnode3, node20 133.65, node6 2.06, node11 42.43\nnode4, node75 3706.67, node5 0.73, node7 1.02\nnode5, node45 1382.97, node7 3.33, node11 34.54\nnode6, node31 63.17, node9 0.72, node10 13.10\nnode7, node50 478.14, node9 3.15, node10 5.85\nnode8, node69 577.91, node11 7.45, node12 3.18\nnode9, node70 2454.28, node13 4.42, node20 16.53\nnode10, node89 5352.79, node12 1.87, node16 25.16\nnode11, node94 4961.32, node18 37.55, node20 65.08\nnode12, node84 3914.62, node24 34.32, node28 170.04\nnode13, node60 2135.95, node38 236.33, node40 475.33\nnode14, node67 1878.96, node16 2.70, node24 38.65\nnode15, node91 3597.11, node17 1.01, node18 2.57\nnode16, node36 392.92, node19 3.49, node38 278.71\nnode17, node76 783.29, node22 24.78, node23 26.45\nnode18, node91 3363.17, node23 16.23, node28 55.84\nnode19, node26 20.09, node20 0.24, node28 70.54\nnode20, node98 3523.33, node24 9.81, node33 145.80\nnode21, node56 626.04, node28 36.65, node31 27.06\nnode22, node72 1447.22, node39 136.32, node40 124.22\nnode23, node52 336.73, node26 2.66, node33 22.37\nnode24, node66 875.19, node26 1.80, node28 14.25\nnode25, node70 1343.63, node32 36.58, node35 45.55\nnode26, node47 135.78, node27 0.01, node42 122.00\nnode27, node65 480.55, node35 48.10, node43 246.24\nnode28, node82 2538.18, node34 21.79, node36 15.52\nnode29, node64 635.52, node32 4.22, node33 12.61\nnode30, node98 2616.03, node33 5.61, node35 13.95\nnode31, node98 3350.98, node36 20.44, node44 125.88\nnode32, node97 2613.92, node34 3.33, node35 1.46\nnode33, node81 1854.73, node41 3.23, node47 111.54\nnode34, node73 1075.38, node42 51.52, node48 129.45\nnode35, node52 17.57, node41 2.09, node50 78.81\nnode36, node71 1171.60, node54 101.08, node57 260.46\nnode37, node75 269.97, node38 0.36, node46 80.49\nnode38, node93 2767.85, node40 1.79, node42 8.78\nnode39, node50 39.88, node40 0.95, node41 1.34\nnode40, node75 548.68, node47 28.57, node54 53.46\nnode41, node53 18.23, node46 0.28, node54 162.24\nnode42, node59 141.86, node47 10.08, node72 437.49\nnode43, node98 2984.83, node54 95.06, node60 116.23\nnode44, node91 807.39, node46 1.56, node47 2.14\nnode45, node58 79.93, node47 3.68, node49 15.51\nnode46, node52 22.68, node57 27.50, node67 65.48\nnode47, node50 2.82, node56 49.31, node61 172.64\nnode48, node99 2564.12, node59 34.52, node60 66.44\nnode49, node78 53.79, node50 0.51, node56 10.89\nnode50, node85 251.76, node53 1.38, node55 20.10\nnode51, node98 2110.67, node59 23.67, node60 73.79\nnode52, node94 1471.80, node64 102.41, node66 123.03\nnode53, node72 22.85, node56 4.33, node67 88.35\nnode54, node88 967.59, node59 24.30, node73 238.61\nnode55, node84 86.09, node57 2.13, node64 60.80\nnode56, node76 197.03, node57 0.02, node61 11.06\nnode57, node86 701.09, node58 0.46, node60 7.01\nnode58, node83 556.70, node64 29.85, node65 34.32\nnode59, node90 820.66, node60 0.72, node71 0.67\nnode60, node76 48.03, node65 4.76, node67 1.63\nnode61, node98 1057.59, node63 0.95, node64 4.88\nnode62, node91 132.23, node64 2.94, node76 38.43\nnode63, node66 4.43, node72 70.08, node75 56.34\nnode64, node80 47.73, node65 0.30, node76 11.98\nnode65, node94 594.93, node66 0.64, node73 33.23\nnode66, node98 395.63, node68 2.66, node73 37.53\nnode67, node82 153.53, node68 0.09, node70 0.98\nnode68, node94 232.10, node70 3.35, node71 1.66\nnode69, node99 247.80, node70 0.06, node73 8.99\nnode70, node76 27.18, node72 1.50, node73 8.37\nnode71, node89 104.50, node74 8.86, node91 284.64\nnode72, node76 15.32, node84 102.77, node92 133.06\nnode73, node83 52.22, node76 1.40, node90 243.00\nnode74, node81 1.07, node76 0.52, node78 8.08\nnode75, node92 68.53, node76 0.81, node77 1.19\nnode76, node85 13.18, node77 0.45, node78 2.36\nnode77, node80 8.94, node78 0.98, node86 64.32\nnode78, node98 355.90, node81 2.59\nnode79, node81 0.09, node85 1.45, node91 22.35\nnode80, node92 121.87, node88 28.78, node98 264.34\nnode81, node94 99.78, node89 39.52, node92 99.89\nnode82, node91 47.44, node88 28.05, node93 11.99\nnode83, node94 114.95, node86 8.75, node88 5.78\nnode84, node89 19.14, node94 30.41, node98 121.05\nnode85, node97 94.51, node87 2.66, node89 4.90\nnode86, node97 85.09\nnode87, node88 0.21, node91 11.14, node92 21.23\nnode88, node93 1.31, node91 6.83, node98 6.12\nnode89, node97 36.97, node99 82.12\nnode90, node96 23.53, node94 10.47, node99 50.99\nnode91, node97 22.17\nnode92, node96 10.83, node97 11.24, node99 34.68\nnode93, node94 0.19, node97 6.71, node99 32.77\nnode94, node98 5.91, node96 2.03\nnode95, node98 6.17, node99 0.27\nnode96, node98 3.32, node97 0.43, node99 5.87\nnode97, node98 0.30\nnode98, node99 0.33\nnode99,\n') - - -# ```{exercise-end} -# ``` -# -# ```{solution-start} short_path_ex1 -# :class: dropdown -# ``` -# -# First let's write a function that reads in the graph data above and builds a distance matrix. - -# In[5]: - - -num_nodes = 100 -destination_node = 99 - -def map_graph_to_distance_matrix(in_file): - - # First let's set of the distance matrix Q with inf everywhere - Q = np.full((num_nodes, num_nodes), np.inf) - - # Now we read in the data and modify Q - with open(in_file) as infile: - for line in infile: - elements = line.split(',') - node = elements.pop(0) - node = int(node[4:]) # convert node description to integer - if node != destination_node: - for element in elements: - destination, cost = element.split() - destination = int(destination[4:]) - Q[node, destination] = float(cost) - Q[destination_node, destination_node] = 0 - return Q - - -# In addition, let's write -# -# 1. a "Bellman operator" function that takes a distance matrix and current guess of J and returns an updated guess of J, and -# 1. a function that takes a distance matrix and returns a cost-to-go function. -# -# We'll use the algorithm described above. -# -# The minimization step is vectorized to make it faster. - -# In[6]: - - -def bellman(J, Q): - num_nodes = Q.shape[0] - next_J = np.empty_like(J) - for v in range(num_nodes): - next_J[v] = np.min(Q[v, :] + J) - return next_J - - -def compute_cost_to_go(Q): - num_nodes = Q.shape[0] - J = np.zeros(num_nodes) # Initial guess - max_iter = 500 - i = 0 - - while i < max_iter: - next_J = bellman(J, Q) - if np.allclose(next_J, J): - break - else: - J[:] = next_J # Copy contents of next_J to J - i += 1 - - return(J) - - -# We used np.allclose() rather than testing exact equality because we are -# dealing with floating point numbers now. -# -# Finally, here's a function that uses the cost-to-go function to obtain the -# optimal path (and its cost). - -# In[7]: - - -def print_best_path(J, Q): - sum_costs = 0 - current_node = 0 - while current_node != destination_node: - print(current_node) - # Move to the next node and increment costs - next_node = np.argmin(Q[current_node, :] + J) - sum_costs += Q[current_node, next_node] - current_node = next_node - - print(destination_node) - print('Cost: ', sum_costs) - - -# Okay, now we have the necessary functions, let's call them to do the job we were assigned. - -# In[8]: - - -Q = map_graph_to_distance_matrix('graph.txt') -J = compute_cost_to_go(Q) -print_best_path(J, Q) - - -# The total cost of the path should agree with $J[0]$ so let's check this. - -# In[9]: - - -J[0] - - -# ```{solution-end} -# ``` diff --git a/lectures/_build/jupyter_execute/status.ipynb b/lectures/_build/jupyter_execute/status.ipynb deleted file mode 100644 index 4e505d231..000000000 --- a/lectures/_build/jupyter_execute/status.ipynb +++ /dev/null @@ -1,53 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "5b0438dd", - "metadata": {}, - "source": [ - "# Execution Statistics\n", - "\n", - "This table contains the latest execution statistics.\n", - "\n", - "```{nb-exec-table}\n", - "```\n", - "\n", - "(status:machine-details)=\n", - "\n", - "These lectures are built on `linux` instances through `github actions` and `amazon web services (aws)` to\n", - "enable access to a `gpu`. These lectures are built on a [p3.2xlarge](https://aws.amazon.com/ec2/instance-types/p3/)\n", - "that has access to `8 vcpu's`, a `V100 NVIDIA Tesla GPU`, and `61 Gb` of memory." - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/jupyter_execute/status.py b/lectures/_build/jupyter_execute/status.py deleted file mode 100644 index 724616a9e..000000000 --- a/lectures/_build/jupyter_execute/status.py +++ /dev/null @@ -1,15 +0,0 @@ -#!/usr/bin/env python -# coding: utf-8 - -# # Execution Statistics -# -# This table contains the latest execution statistics. -# -# ```{nb-exec-table} -# ``` -# -# (status:machine-details)= -# -# These lectures are built on `linux` instances through `github actions` and `amazon web services (aws)` to -# enable access to a `gpu`. These lectures are built on a [p3.2xlarge](https://aws.amazon.com/ec2/instance-types/p3/) -# that has access to `8 vcpu's`, a `V100 NVIDIA Tesla GPU`, and `61 Gb` of memory. diff --git a/lectures/_build/jupyter_execute/troubleshooting.ipynb b/lectures/_build/jupyter_execute/troubleshooting.ipynb deleted file mode 100644 index d7f7bd220..000000000 --- a/lectures/_build/jupyter_execute/troubleshooting.ipynb +++ /dev/null @@ -1,104 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "a8d21bed", - "metadata": {}, - "source": [ - "(troubleshooting)=\n", - "```{raw} html\n", - "
\n", - " \n", - " \"QuantEcon\"\n", - " \n", - "
\n", - "```\n", - "\n", - "# Troubleshooting\n", - "\n", - "```{contents} Contents\n", - ":depth: 2\n", - "```\n", - "\n", - "This page is for readers experiencing errors when running the code from the lectures.\n", - "\n", - "## Fixing Your Local Environment\n", - "\n", - "The basic assumption of the lectures is that code in a lecture should execute whenever\n", - "\n", - "1. it is executed in a Jupyter notebook and\n", - "1. the notebook is running on a machine with the latest version of Anaconda Python.\n", - "\n", - "You have installed Anaconda, haven't you, following the instructions in [this lecture](https://python-programming.quantecon.org/getting_started.html)?\n", - "\n", - "Assuming that you have, the most common source of problems for our readers is that their Anaconda distribution is not up to date.\n", - "\n", - "[Here's a useful article](https://www.anaconda.com/blog/keeping-anaconda-date)\n", - "on how to update Anaconda.\n", - "\n", - "Another option is to simply remove Anaconda and reinstall.\n", - "\n", - "You also need to keep the external code libraries, such as [QuantEcon.py](https://quantecon.org/quantecon-py) up to date.\n", - "\n", - "For this task you can either\n", - "\n", - "* use conda install -y quantecon on the command line, or\n", - "* execute !conda install -y quantecon within a Jupyter notebook.\n", - "\n", - "If your local environment is still not working you can do two things.\n", - "\n", - "First, you can use a remote machine instead, by clicking on the Launch Notebook icon available for each lecture\n", - "\n", - "```{image} _static/lecture_specific/troubleshooting/launch.png\n", - "\n", - "```\n", - "\n", - "Second, you can report an issue, so we can try to fix your local set up.\n", - "\n", - "We like getting feedback on the lectures so please don't hesitate to get in\n", - "touch.\n", - "\n", - "## Reporting an Issue\n", - "\n", - "One way to give feedback is to raise an issue through our [issue tracker](https://github.com/QuantEcon/lecture-python/issues).\n", - "\n", - "Please be as specific as possible. Tell us where the problem is and as much\n", - "detail about your local set up as you can provide.\n", - "\n", - "Another feedback option is to use our [discourse forum](https://discourse.quantecon.org/).\n", - "\n", - "Finally, you can provide direct feedback to [contact@quantecon.org](mailto:contact@quantecon.org)" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/jupyter_execute/troubleshooting.py b/lectures/_build/jupyter_execute/troubleshooting.py deleted file mode 100644 index 95be2164f..000000000 --- a/lectures/_build/jupyter_execute/troubleshooting.py +++ /dev/null @@ -1,66 +0,0 @@ -#!/usr/bin/env python -# coding: utf-8 - -# (troubleshooting)= -# ```{raw} html -#
-# -# QuantEcon -# -#
-# ``` -# -# # Troubleshooting -# -# ```{contents} Contents -# :depth: 2 -# ``` -# -# This page is for readers experiencing errors when running the code from the lectures. -# -# ## Fixing Your Local Environment -# -# The basic assumption of the lectures is that code in a lecture should execute whenever -# -# 1. it is executed in a Jupyter notebook and -# 1. the notebook is running on a machine with the latest version of Anaconda Python. -# -# You have installed Anaconda, haven't you, following the instructions in [this lecture](https://python-programming.quantecon.org/getting_started.html)? -# -# Assuming that you have, the most common source of problems for our readers is that their Anaconda distribution is not up to date. -# -# [Here's a useful article](https://www.anaconda.com/blog/keeping-anaconda-date) -# on how to update Anaconda. -# -# Another option is to simply remove Anaconda and reinstall. -# -# You also need to keep the external code libraries, such as [QuantEcon.py](https://quantecon.org/quantecon-py) up to date. -# -# For this task you can either -# -# * use conda install -y quantecon on the command line, or -# * execute !conda install -y quantecon within a Jupyter notebook. -# -# If your local environment is still not working you can do two things. -# -# First, you can use a remote machine instead, by clicking on the Launch Notebook icon available for each lecture -# -# ```{image} _static/lecture_specific/troubleshooting/launch.png -# -# ``` -# -# Second, you can report an issue, so we can try to fix your local set up. -# -# We like getting feedback on the lectures so please don't hesitate to get in -# touch. -# -# ## Reporting an Issue -# -# One way to give feedback is to raise an issue through our [issue tracker](https://github.com/QuantEcon/lecture-python/issues). -# -# Please be as specific as possible. Tell us where the problem is and as much -# detail about your local set up as you can provide. -# -# Another feedback option is to use our [discourse forum](https://discourse.quantecon.org/). -# -# Finally, you can provide direct feedback to [contact@quantecon.org](mailto:contact@quantecon.org) diff --git a/lectures/_build/jupyter_execute/zreferences.ipynb b/lectures/_build/jupyter_execute/zreferences.ipynb deleted file mode 100644 index e8fb5c71e..000000000 --- a/lectures/_build/jupyter_execute/zreferences.ipynb +++ /dev/null @@ -1,46 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "f995fbab", - "metadata": {}, - "source": [ - "(references)=\n", - "# References\n", - "\n", - "```{bibliography} _static/quant-econ.bib\n", - "```" - ] - } - ], - "metadata": { - "jupytext": { - "text_representation": { - "extension": ".md", - "format_name": "myst" - } - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.15" - }, - "source_map": [ - 10 - ] - }, - "nbformat": 4, - "nbformat_minor": 5 -} \ No newline at end of file diff --git a/lectures/_build/jupyter_execute/zreferences.py b/lectures/_build/jupyter_execute/zreferences.py deleted file mode 100644 index 118e06f1f..000000000 --- a/lectures/_build/jupyter_execute/zreferences.py +++ /dev/null @@ -1,8 +0,0 @@ -#!/usr/bin/env python -# coding: utf-8 - -# (references)= -# # References -# -# ```{bibliography} _static/quant-econ.bib -# ``` diff --git a/lectures/_config.yml b/lectures/_config.yml index 4f7eea35d..6361f7583 100644 --- a/lectures/_config.yml +++ b/lectures/_config.yml @@ -12,14 +12,14 @@ html: baseurl: https://intro.quantecon.org/ bibtex_bibfiles: - - _static/quant-econ.bib + - _static/quant-econ.bib latex: latex_documents: - targetname: quantecon-python-intro.tex + targetname: quantecon-python-intro.tex sphinx: - extra_extensions: [sphinx_multitoc_numbering, sphinxext.rediraffe, sphinx_exercise, sphinx_togglebutton] + extra_extensions: [sphinx_multitoc_numbering, sphinxext.rediraffe, sphinx_exercise, sphinx_togglebutton, sphinx_tojupyter] config: html_favicon: _static/lectures-favicon.ico html_theme: quantecon_book_theme diff --git a/lectures/_static/lecture_specific/short_path/graph.png b/lectures/_static/lecture_specific/short_path/graph.png index e900ec762..d5c31af9e 100644 Binary files a/lectures/_static/lecture_specific/short_path/graph.png and b/lectures/_static/lecture_specific/short_path/graph.png differ diff --git a/lectures/_static/lecture_specific/short_path/graph2.png b/lectures/_static/lecture_specific/short_path/graph2.png index 00d6a8f89..c287eac5d 100644 Binary files a/lectures/_static/lecture_specific/short_path/graph2.png and b/lectures/_static/lecture_specific/short_path/graph2.png differ diff --git a/lectures/_static/lecture_specific/short_path/graph3.png b/lectures/_static/lecture_specific/short_path/graph3.png index f125d2104..35af75ef5 100644 Binary files a/lectures/_static/lecture_specific/short_path/graph3.png and b/lectures/_static/lecture_specific/short_path/graph3.png differ diff --git a/lectures/_static/lecture_specific/short_path/graph4.png b/lectures/_static/lecture_specific/short_path/graph4.png index b1b2ea472..abc9e84e5 100644 Binary files a/lectures/_static/lecture_specific/short_path/graph4.png and b/lectures/_static/lecture_specific/short_path/graph4.png differ diff --git a/lectures/_toc.yml b/lectures/_toc.yml index 61ae6730c..906d736c7 100644 --- a/lectures/_toc.yml +++ b/lectures/_toc.yml @@ -11,6 +11,7 @@ parts: numbered: true chapters: - file: schelling + # - file: solow - caption: Other numbered: true chapters: diff --git a/solow.md b/solow.md index ad0652451..b92b139d2 100644 --- a/solow.md +++ b/solow.md @@ -1,3 +1,14 @@ +--- +jupytext: + text_representation: + extension: .md + format_name: myst +kernelspec: + display_name: Python 3 + language: python + name: python3 +--- + # The Solow-Swan Growth Model We consider a model due @@ -16,7 +27,7 @@ To keep things simple, we ignore population and productivity growth. We will use the following imports -```{code-cell} ipython +```{code-cell} python3 import matplotlib.pyplot as plt plt.rcParams["figure.figsize"] = (11, 5) #set default figure size import numpy as np @@ -100,7 +111,7 @@ The function $g$ from \eqref{eq:solow} is then plotted, along with the 45 degree line. -```{code-cell} ipython +```{code-cell} python3 A, s, alpha, delta = 2, 0.3, 0.3, 0.4 x0 = 0.25 num_arrows = 8 @@ -182,7 +193,7 @@ At this parameterization, $k^* \approx 1.78$. As expected, the time paths in the figure both converge to this value. -```{code-cell} ipython +```{code-cell} python3 A, s, alpha, delta = 2, 0.3, 0.3, 0.4 x0 = np.array([.25, 1.25, 3.25]) ts_length = 20 @@ -284,7 +295,7 @@ savings at low levels of capital combined with low rates of return at high levels of capital combine to yield global stability. -```{code-cell} ipython +```{code-cell} python3 A, s, alpha, delta = 2, 0.3, 0.3, 0.4 @@ -412,7 +423,7 @@ Now the long run convergence obtained in in the deterministic case breaks down, since the system is hit with new shocks at each point in time. -```{code-cell} ipython +```{code-cell} python3 sig = 0.2 mu = np.log(2) - sig**2 / 2