{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "![Py4Eng](img/logo.png)\n", "\n", "# Optimization\n", "## Yoav Ram" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import scipy\n", "import scipy.optimize as opt\n", "import scipy.special as spec\n", "import seaborn as sns\n", "sns.set(\n", " style='ticks',\n", " context='talk'\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Optimization\n", "\n", "*Scipy* has several methods for optimizing (minimizing or maximizing) functions.\n", "\n", "This session is roughly based on [Tutorial on \"Modern Optimization Methods in Python\" ](https://github.com/mmckerns/tutmom/blob/aae5de033cbbf7565f196fc8e92181fe0bbe9926/intro.ipynb)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simple minimization\n", "\n", "Consider the following polynomial, defined using `np.poly1d1`, which, given the polynomial coeffcients $a_i$ returns a polynomial $\\sum_{i=0}^n{a_i x^i}$:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 2\n", "1.3 x + 4 x + 0.6\n" ] } ], "source": [ "p = np.poly1d((1.3, 4, 0.6))\n", "print(p)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def minplot(x, f, xmin=None):\n", " plt.plot(x, f(x))\n", " if xmin is not None:\n", " plt.plot(xmin, f(xmin), 'ok')\n", " plt.axvline(xmin, color='k', ls='--')\n", " plt.xlabel('x')\n", " plt.ylabel('f(x)')\n", " sns.despine()\n", "\n", "x = np.linspace(-10, 7)\n", "minplot(x, p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll use `scipy.optimize.fmin` (aliasing `scipy.optimize` as `opt`) to find a minimum for `p`, our polynomial. `fmin` uses the *downhill simplex algorithm* and we start with the guess 3:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: -2.476923\n", " Iterations: 20\n", " Function evaluations: 40\n", "x = [-1.53845215], p(x) = [-2.47692308]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xmin = opt.fmin(p, [3])\n", "print(\"x = {0}, p(x) = {1}\".format(xmin, p(xmin)))\n", "minplot(x, p, xmin)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise\n", "\n", "Find the minimum of the function $f(x) = (x-2)(x+1)^3$ using either `fmin` or `minimize_scalar`. The later doesn't require a guess (`x0`)." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "f(1.250) = -8.543\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Minimizing with \"box\" constraints\n", "\n", "Suppose we want to find the minimum of a 1st order Bessel function with the constraint $2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 20, 500)\n", "minplot(x, spec.j1)\n", "plt.axvspan(8, 16, alpha=0.3);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use `opt.minimize_scalar` and give it constraints:" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " fun: -0.23330441717143405\n", " message: 'Solution found.'\n", " nfev: 9\n", " status: 0\n", " success: True\n", " x: 11.706004881285123\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "result = opt.minimize_scalar(spec.j1, method=\"bounded\", bounds=[8, 16])\n", "print(result)\n", "minplot(x, spec.j1, result.x)\n", "plt.axvspan(8, 16, alpha=0.3);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise\n", "\n", "Find the **maximum** of the *Fresnel sin integral*, which is the first value returned from the $\\mathbb R \\to \\mathbb R^2$ function [`scipy.special.fresnel`](http://docs.scipy.org/doc/scipy/reference/generated/scipy.special.fresnel.html#scipy.special.fresnel). Constrain maximization to $x \\in (2, 3)$. Plot the result and the maximum to make sure you got it right." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Minimize a multivariate function\n", "\n", "Follows example from [SciPy Tutorial](http://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html#tutorial-sqlsp).\n", "\n", "The `opt.minimize` provides interface to other contrained methods. Let's use *SLSQP* (Sequential Least SQuares Programming) method to deal with the following problem:\n", "\n", "$$\n", "f(x,y) = 2xy + 2x - x^2 -2y^2 \\\\\n", "x^3 = y \\\\\n", "y \\ge 1\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def f(arr, sign=1.0):\n", " x, y = arr\n", " return (2 * x * y + 2 * x - x**2 - 2 * y**2) * sign\n", "\n", "x = np.linspace(-10, 10)\n", "y = np.linspace(-10, 10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We load the `mplot3d` module that will allow us to do some 3D plotting." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "from mpl_toolkits.mplot3d import Axes3D" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def minplot3d(x, y, f, xmin=None, ymin=None):\n", " z = np.array([[f([xi, yi]) for yi in y] for xi in x])\n", " fig = plt.figure()\n", " ax = fig.add_subplot(111, projection='3d')\n", " ax.plot_surface(x, y, z, rstride=4, cstride=4, cmap='viridis', alpha=0.5)\n", " if xmin is not None and ymin is not None:\n", " ax.scatter3D(xmin, ymin, f([xmin, ymin]), s=50, c='k')\n", " \n", "minplot3d(x, y, f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this method we also need the derivative of `f` with respect to `x` and `y`:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def df(arr, sign=1.0):\n", " x, y = arr\n", " dfdx = -2*x + 2*y + 2\n", " dfdy = 2*x - 4*y\n", " return np.array([ dfdx, dfdy ]) * sign" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "minplot3d(x, y, lambda x: df(x)[0])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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liKSX4RpylK9FKfXA+5osYyS9KEnn48jOm6T/1t/6W3S7XT772c/y8z//83zrW9/iq1/9Kr/xG7/BG2+8wWc/+1m+9KUvNYH3AD8B/O+LHLcm6QWRRzb51jMMwyIZKKUsxlOdZbRx0lLlvChmf39/7lQWOJxQ7wXVhzevVNzc3Cw+r6rDodynuMYsjpOO7ndfE2vtUnUczKXFRa4przk4b006CAJ+67d+i09/+tP84A/+IO12m0984hN8//d/P7/8y7/MJz/5SYBbpDLHx27evPmnixy3fkKOQbUApTqeKv/f2tramZ970VFX+TX1er2Zoph5x4TzIWmtddGAKS+GyUt2y1v1co/ivNNZ3vY0J44HtbVelmjxtPr+efU1WbZI+iS9RPr9PnD+JA1w/fp1/v2/n61RWV1d5dd//dcB1k96zJqkD8Gi46lu3bp1btvk4zrW5dfU7/dpNBqHjsyqHhPOlqTzY73yyisFOV++fBmlFHEco5SayW6Xt+r7+/tF35LyVr0cced/LhNRnCfO2oJ3VF+TJEmmIu95fU3yxPgy9DWBA7nuJCR93nLHeaEm6QqqBSjl8VTtdpsbN25M3eRSyqnJFWeJwyLpvGJxMBjQbDbnViwehrP0X5dlDYCVlRWuXr06JWEcZsGrJsl6vR7Xr1+fifbmEUaVuO9nL437ifvxnsrkXUa1r8nu7i5xHC9NX5NcRluEpAeDAVLKI8fKLTNqkmbW4wyp53Fzc5MwDOl2u1y7dm3GMgXpTZLfMGeNsiZdLicfDoe0Wq2ZBWMRnEUkXe6OZ4xhZWWF3d1d1tfXT60x55HjUV3sytFev98veljPq+jLfcUnIYxlSxw+yIWn2tek1+uxurrK6urqwn1NznMhPWkk3W63l86dsije0iR9WHVguan9ceOpFtWNT4N8AcjLyUejEe12+9hhs0chb+V4GkLK+0rnskRuM8x/fl4WvMMa7cwrxy5X9D3M8xKXacGAA3fHcX1Nyt9Fr9c7l74m+fXA4iR9P/To88JbkqSrTfbvZTxVXhl2XteYzxDsdDo8++yzc6P5k+KkJF0l52rr0uqw2er7OC8cVtFX1rvn+YpzvbvsNDmPXg73ggcdSVdxnE+6TN5lQlxkxFaVuI/ra5IfN+8bfRxqkn6IUPU4l1tzAgu35izjrCNpay29Xq9oxOS6Ljdu3FhoEviiOC4hmeM4ci4fL7/2eedahKjPksznDVSdZ02ruhvynhnb29sPXO9eNpI+rbvjJH1N9vb2Du1rUpWwTlrIUpP0kqNKzkmSFN3flFL31P3trEg6t6DlOvjKykpBEGdJ0HA8cZbJWWtduDWOavqfv4fTXs954yhrWp4g29vbYzKZzOjdVW/3afTuk2KZKvxOYndbFIv0NSm7Tcrk7ft+0dBrNBod67e/H307zhMXmqTzgZgvvfQSjz32WNHUfW9vD8dxzqTBUE7Sp418yjp43iUv18Fv3749NbzzrHBYkUx10Oxx5FzFvUTDD0qDLevdYRiSJAlPP/10ce/kcsm8DnbzLIJnPaBhGTBvCO15YZG+JvlsRGMMt27dAmbzD+XF9H6UhOfY2tri7/7dv8uv/uqv8sM//MPcunWLj3/843zrW9/i6tWrvPbaax+4efPml05yzAtJ0lWP82Qy4e7du4xGI3zf59q1a6yurp7JTVfusXGSB/Swydvl5NiissRJUY2kq9eyvr7OlStXFibnhyGSPinKJFxGlSyO07tPO6V8meSO84ikT4p5ElYYhly7du3QvibGGD796U9jjMF1XX7v936Pd7/73bznPe85t+v8+Mc/zt7eXvH3n/3Zn+UHf/AH+Xf/7t/xjW98g5/+6Z/+T88999yzN2/e3Fz0mBeKpOeNp9ra2gLS5NZRlXinRU7Mi5L0vMnbh7UwPa8J1jn53ys5l493r1g2N8NhWFTvHo/HU3p3NTF2nKd4mUj6fkbSiyLXpI/qaxKGIT/6oz/KH/7hH7K7u8s//+f/nH6/z1e/+tVqb+czwX/+z/+ZRqPBY489BsDLL7/Md7/7XX7nd34H13V5//vfD/B/AR8GPrvocS8MSWutC4KujqdSShUlymeNRbvVLTp5u3rs87L3jcdjXnzxxYKcF3WzzMN5VDE+KJx1KXZ1CvY8T3HVaZInMJcFyxBJV3FU4rD8fXzoQx/iv/yX/8JHPvIRPvzhDxeccNZ47bXX+I3f+A1+93d/l7/399Je/q+88gqPP/54VXe/SdpgaWFcGJKGgwKUyWRCp9Mp/MQvvvjiwmQn4v8XK9ogHwG5euy/P46ktdZFEi7vL72oznvWcoe1lt3dXcIwZDKZFJrzWdjP7mXO4TJFaGeJakFIjuqsxDAMZ5wNeWJsb2/vgfu7lzWSXvS+zTVpIcS5EHSSJHzsYx/j4x//OKurB5wxGo3mWWZHwImGK14Yku71enzve99jZWVlZjyVUmrhqkBt/gph9xFIBA6IVZCPYOUjKXGLaVkiJ+nq8U87ebt67LOIqPKHfWNjo+h122q1im3ZWeAwkl70wV6GyPF+XcNRsxJz4s6dNeWm/+XWo/eid58UyxpJL7ponbe743Of+xzvete7cjmjQKPRuKdm/zkuDEl3u13e8Y53zNV2T1ZwIjCmX/rbLpg7COEgACGaIC4XpC1F2v0uP34+3PW0k7fLuFe5o0rOa2trXLlyhdu3b5/6mMed7zRYpgjtQaLsbNjd3aXb7bK+vj7Vz2Se3u267tzinLP6XJc1kl5k0dBaMxwOz5Wkv/zlL7O5ucmXv/xlIF0Ufu7nfo4XXniBN954gyiKyrz0HPD1kxz/wpB0bn4/7HeL99eYPobFgB1ywD/7CLGNMK8hrEQKxXpzgIjfxvbdNTa2FQj/TCZvn9beV7b1xXFckHO+PbwXaeIwVI+ZSyvb29uFU6JMItUHbBki6WVC+Ts/rG903r2ubEvLZ1jO07sXqeQ76lqWiaQXHZ01HA6B8+2A99/+23+b+vvf/tt/m1/8xV/kh3/4h/nKV77Cr/3ar/GP/tE/4o//+I8B/jfgoyc5/oUh6aOglComkhyHyLoYApRwUBgEEdjpLnfWRlibJn+sNki1w6C3hZQeT11t02ytI9UVjH0Era8i5WWEOPlW8aSzA48j5xznkZAsX2s5el9ZWQGYsaqVo7/8Z8vgaHjQ58+xSNP/vBnVcXp3uQy7umAuMuR22XpJw+KR9P3sJT0P//pf/2t+6Zd+iR/4gR/g8uXLAP/HzZs3v3eSY1wYkj7qJjqR3CFctB2iS4GdxEdKD4VEkiBsiDGa0WjEeDwGLH5g6XZ9hEgwdgOb7GK4RR+NBJTootQjOPIaSj2KFMcnMBZt0J9XK25sbBTkfNRk8vOIpCFNlGxvbxNFUbFAlJOf1cbzYRgyGAwKt8NLL700FW2X3Q5vNdyLdHSc3l2OvMtDbucV5+R5kWXSo/Ok6rL2kv6jP/qj4r8ff/zx6hCAExWywAUiaTi6d/HicsdsCbYhxJiQhHSbNRqNmYwsrvLoth9hMtrDcabLhC0xiAmxTiN4awcovY2SLyKsTUlfXMJRj6HkYyh5BSGmyei4QpkqOa+urnLlypVjp4CfpWskbwSfT2VZXV3l+vXrxTWUe20f1oq03+/z5ptvcvXq1aIcuNrNrkza55UwWybJ5ax3FYdV8lX7d88btZXfL/1+/772jD4MJ+mANxgMEEJM7TYeNlwokj4MJ9GkNT4hDRQuSgA2QhBmwyzTyFkpRbvbIgh8hIgJxxFWN3BpooQqom3sAREKcUD26YmGwD5K30YJiSCPtq+g5GM48lFE5iSpEmqZnMtR63HkfHAt9x5J5/2t7969y3g8RkrJ+vr6jGNkkYc5f9iq8xjzgoQygVQLRKrR32lbXy4b7pf0c5zenbcctdYWDf/L1sIH8dmXp6Qfh36/T6vVWqqdwEnxliDpXO5Y5MaX0sPYCENEbNNIYzQaE401nuPT6azRCARCxKXXSAwxie2T5NxnBUJ4GJpIYYAIbFUXN2g7KqQVawcos43kZaQAowWOPyGMeyjnKQSP0O8PiyZMa2trM6Xki+BerX05OY9GI7rdLo8//jjf+9737lmWqH4/h1WTVWcmHqW5ntRjvEwE/6CupTqtRWvNeDzmySefnGp8NO+zP6w45yxx0kj6YW6uBBeMpI+SO3Id69gG86RaXpIkDEdDwkmI4zi0V5r4vo8QlgkWYQMc4SEBS3QQIRcHslhGTMxBBC8JcKSHQiBEAnYCHPxeCDA2xBCCBWMNidxhFBuG4f/Hm3uaWDustB7n2uNvpxO0ceXJCPqoz+k4jEYjNjY2GAwGtNvtqf7W90IoJ3ntYQUi5daXZb0730GVh6yeh03tLLHovXq/kOu/x/WMLmve8/Tu6sJ52uj2JKOzer1eTdIPA8oFJ8d9sePQcmd3QjLR+G6T7splAs+CqDg8iIltGkGEIsZqQcO2UNJB2jRyFoQIZGrjAwyayIzLV4YjfBzpImzmJKFK9oad3l2MNuA9SrPlgrPPbvLn7A3/HCUUnlzBV1cI1FUCdRUpzlaTzhtU5VvHeZNhzkpCOS3mtb4s93CYNzOx2oY0juOl0qWXBce5O44avlD+7CeTyYzDZ15xznGLUx1JP8Q47MvNt1ta60NLSfPJ23vDNzGthPZaK7WHASMrUDRxhIsUFkGcRcG2OK+2Gs0EXeI+gYexHYQUCBJgjLXT2nhiYxIdl17j4wiXOIwZDfawVqGUZHVllVCtMjYRxiaEJPnpGekhTrKFEjcRgCMa+GqdQD1CoK7iyumOf4sSahiGbGxssL+/T6PR4Omnnz40AXNejpF7wVE9NaqRXzlR+fLLLx/qdLgfyD/HZYukT4rD5KqjppPnUstRuYbyKK/jcD/blJ4XLhRJH4Zyp7oqqpO3n3ziGXp8F5iOnLWN0bY8JsrFFR5KKNIqxd7MsS2aWMQkmeRhrYMrGrhSkd7yIdaGFGwLTMIxw+EWiU4IgoCJlgT+JYTTBuMhhcRUXmOxxDYkLn40ZmT6qOQNJCAReLJL4FwlUI+AcI4k1CiK2NjYYG9vjyAIuH79Ou12+9iH4mGpODzMpnbnzh0mkwmrq6tFZV/Z6VBOluX/O49k2bKR9Enb8B6Fqt6dI881lCPvw/RurTVCiKLFwVF42KeywAUj6cNu6mp/jdyZMG/ydmwG3OkrlPBxhYskjZytTf3QBzggxpCIsbW0Mp26rDlLJLnuLAQkxCSmHDkHuMIlCSOGwz10MiJoOKysrKCUIgojtI0JzZiIJkNtwHp4KvNtC43loLgmR3VRGekxjt5FiReZJEN2hMIb7tJ2LtNWl2moFZJEs7Gxwe7uLr7v8+STT844Lo767B+k3HEWkFLiOM5Uk5xqZV91UnmZPE6TqJyHZSPp++GTLucajtO7J5MJxhheeeWVGb07/zO/3sFgwFNPPXWu137euFAkfRjypEeSJMdO3s71XG0TdLnS0Pq40sMREokGoiwKPiAoYzWRndacY+OBaKQOD5ukScGM7K2FMBqzPUx7SwdBQLNzFd/1MvudBQYHD22+SAhLVElUKtHAFQ5KCLAJaXqzrL1YEhuSFIuK4E54GzfaQFjLaDAgHhmaap3HH3uWR1efwFOLD729X4nD+43DKvuOS5blzf+rBHLSJOky4EEmMefp3VtbWwyHQ65cuTK32T+kn91v/uZv0u/3uXPnDt/97ndP5YRaBN/85jf5Z//sn/HKK6+wtrbG888/z4//+I+zv7/PL/zCL/Anf/IndDod/sE/+Ad86EMfOvHx3xIknd9kedHHUZO3JS5SNDAlzRkAUZUUQNLEFS4ID6MNQqgZzdkKGJuDTlgCrxQ575MkY/yGQ7e7guNk2rnV6IzsxwDax6GLwUcJF2tjDNMTutPXlM5tnXRRkRKJTUvZi6SkACyJjumN9hmNR0gpabXbiGbEpniRrf53cYVHU3VpO5dpOZdpqlWkmB8hHhVJn6Ss/UHiJOc/LFlWraicl6isRt7VeYnLFkmfZOjr/YDW+ki9O+/b7TgOb7zxBt/61rf46le/Srfb5etf//qZFrbs7+/z0Y9+lE984hN84AMf4C//8i/5yEc+wlNPPcUXv/htX/5/AAAgAElEQVRFms0m3/jGN7h58yY/9VM/xSc+8Ynvu3nz5rdOco4LRdLVm9rag8nbef/Zt73tbUcOdhVCMDESbTw85eIgEcJkJDctKRg0odWERIxswkA7OCKVL5Q0YCNkpelQGIVsD7dJkgTf92mtXcZ3014hUlggyTTng4jAYohtiLZNBjoBBFI08ITCESJ7zQQ7tahAbCPiEm9LAjzpIvCwdsj29i5CWNqtNo1GI91t2ISk2EGE9JMhO/EWCoEUlkC2aTprqUziXMaTzYPrfEg06fPEYcUhZb216i8uz+crb9WX5XNZJjsgHL5oVCtaP/WpT/HBD36QT37yk/z1v/7X2dnZOfN+0rdv3+b9738/H/zgBwF4z3vew/ve9z7+5//8n3zta1/jK1/5Cr7v833f93184AMf4Ld/+7d/CviHJznHhSLpHDk5b2xsFJO3rbV0Op2FJm9L4aJFTGSiKVrOSU4hQORkqqeaC2mRySQZOcbWx1ifJIoYDnrEyRg/UHS73SLpMSutOLjSxREqq1xMfyxEaS6h1UxKkbO1Lr50cIRCijRyNlR1as12v89oNCK2bQharLa7eMop/N7aVhciQ1iSVvpJiJf0cMQtpLA4wsEVV9nXEW3b5TH7WJZMPTkedCR9XjhKby0Td3XLfuvWLYIgWHjk1nlh2SLpkyQy+/0+q6ur3Lhxgxs3bpz5tbzrXe/iM5/5TPH3/f19vvnNb/Lcc8/hOM7UmK7s/CcesHjhSDqfHxiG4dTk7ddee21hb7ArOmgRY+y0pGAwTEqEZa3ClT4QgImzQpiYsuYchRPe7O1XImcfR6hUPyZBz0grENvUhz0WCbF2cEwAwkOJAIFG23BKcxYCIpsQlche4uNJD2kt43GfwXAXi8b3fZLE0mg0iKwmSkoFN8LPyF4i0FlxzXTBTX5tKUIsO9xJ9pG8wcb2HRoyYMVdZcVdpSNX8Jh2UdRIMa+fRp7Uvn37Np1Op8ijlEduVbXu825CtYyR9CJTWYwx99Un3e/3eeGFF4po+j/+x/849fssQGzOffERuFAkHUURt2/fnmnyAydrshRZyVALFAGuTHt45IRlK4SV2ISEhDExgyTBdVwc4aGjmNGgxzAMUb5TiZw14yn92M2kFZW6NWxUaM6CLCmJAWvoJzk5Kjzp4wqFEhZrY/RM5GzYHe4xHA6x1tJotFlpdREW+oMejvCw6CmZxFjDWE/vHzzh4UqFEmBJ0BULIEBoE6yxuElIn5DdeIg0bzAc9pEWum6X9eAylxtXWA8u44iDW2+ZCOBBX4sQoiDctbW14p4xxsxIJtVE5TyXyVm8n2WMpBe5ntFohLX2vvikv/e97/HCCy/w5JNP8mu/9mu8/PLLM1NZsr+faCoLXDCS9n2fd77znXOjCilloQEeB0dkPQsw6Erk7Ek/8zlbbKYFl+WOSRgyHO2QxGnk3Ln0GGPh4MhcP56NghEQmZioSAaKLAp2kWiE1QgUVTEgMglRyc8t8PCVi4MgHA/pDXfRNqbZSBMsUko0hkQnxEA/MbjKPYichZnjB88idF2O0F086eBKicASG5EuJtkVGpMuDuPxGKkkSir2wjvc6t1FCYGSgqbbYNVbY92/zKq7hsU+cLnjQZ+/ijLB5j1Jqt7uclVfGIaMRqNDm1CdpvH/spWow+Jyx2CQ8uF5R9Lf/va3ef755/ngBz/IP/kn/wQpJdevXydJEm7fvs21a9cAePXVVwG+c9LjXyiSLkchVSil5s0bm/9vRRNHNNA2momcY5sQ6zIxptKFNRP6vRidTPACRXc9j5wd+rEmmYriFZ4M8Aqyn6cFWyYmYkyM0QbHKBwclGikkTOaxIRTUbDFsj/qMxgMMMYQBA267as0Hb+Igk25yZNNzzM206TsEOBLhZICS0JiI2ypo196bTGT7EeSAG09pLFEQ8Nw2MNKQ6fTwff9VGYSYI0l0Qk60ezrCfvD27zefwOJRSL4q1sv0XEfZT1Y49HmZdqN1lu6l/QixHhUE6qjCkPmSSbzotNlnW+4LA3/t7a2eP755/nIRz7CT//0Txc/b7fb/J2/83f47Gc/y6/8yq/w4osv8qUvfQngd056jgtF0nB0k6VFNWmNopckgMQVHp6UKCFmtvq5W2M4HJKQkFiH7tplfNfDyTzL2jppR7uKNS8yMVGJHGUeBQsBmEzySKYeVCMsQx2WXpNGtI4QROGY/mCPUE9oBA2azWbaWAqmXgMuDh7GJPgiQIq0NL2MBJ1WSWYfl7AOnlS4Kl1UjI1JyouKtUziiDiO6ccTms0mrUaDwEmTrJYEgyaRMa6sVJtZiOOYXr9HIsZsTe5wc3AbazSecFhxWlz2V7naWOdyY+1Mt/HLinu14B2XqDzMWzyvCdWyOU1guUj693//99nZ2eHzn/88n//854uff/jDH+aXf/mX+eQnP8n73/9+ms0mH/vYx/ixH/uxPz3pOS4cSR+Gk/SULuulaeR88DuBgydcbJIwHPSI4hFeoEiShGazieM4aGsYZyQmhcsokXjKwxMyJWwSEhNR1nUNtqIFCxzRAGsQJkaJYEbuMNbSGw8ZDofESUzgB3RX12l5fraopNKKseXFyRJZTQzEcYSLixIevnJIR+1qEiJ06TVWWEKbEJYa+Cvh4wmHaDxiv7eFTlLv6vr6evFAT3SS6ul5/1/hZdIKWAyJjTDiYOvqN3w80QWdFFH3tg7Zje7w3fEbGK1pCpeuTIn7SrBOt9G+cBNczkt2OSxROW9aTnlWIsDOzg7NZvOBf9Z5y+FFSTp/Js8LL7zwAi+88MKhv//1X//1ez7HhSPps5jO4ogAT7ZKW/2D44VRxM5wlziJ8T2f1uolfNdjEu4gTBNH+BWZxGaac8I0Bbv40sUV4lAtOLEJExJCHeEmGke4CFwcIUniiP3+LpN4jO/7rHfXi5txWCZ7q/BUkC0QaRQci+nEn7aGUVJJFsp8B5EmOhMbHUgrFkaTMRvDAUYbWsElrNCgDZ5spa/JFqLyN6GtYVRJSvrSw5Xg2jGu8IjyKFIKXOlCOYlvIdSaHRuzq+/yv/pvIPcsTevRlU3W3S6XgjUamW3tNJa1ZYgY72cxy2HTcvImVMPhkK2trTTP8ACm5VRxkg54F6FvB1xAkj4MJ+sp7dDLSEtYF0+qLHLuE8ZjXF+yvrZecmsYIjR9HaITxYFMosA6eEIQl0mOVD+emIiySu5k9rdyFFy91v5kzHA4JIqiNDG58gjtoIGDwAqNNjGaqdA/S0qWfmQ9EuPQoIEvXRIbT/u0yRaVUgAuSSUPEycMBvtEyQQ3cGmttvCdLnvb+0RJQr9E9hIXXyocYRDCZueZXihDk6RWKZOgEoOSDi4ujpSAISq/RoDKqjKtq5AZg08sxCZiU9/FTN7AG0maOqBhm1xSTVZK0fZZ9NY4byxDoi63+uULxqOPPorrug98Wk5N0hcAi7QrPW77U5Y7wjhkZzgkjrPIeWUdz3XTohaZuzWimQg+TzA6QtBPBAIHXzm4QiKERdt4Vgu2hqQSBRsaYEBoj71+j91hhOe5rK2tFdrudBQscGWAn0XBxuo5CwRoLPtxiJ/d667wCVRqszNoEhOntr/ic4jYKS0OrZVLNFwfT6lMs/aIZioyLSOdJj4R2bUJj0ClXQCt0MQmrnxngpE+KAZK34+PL1OpSNuE2CbTtkEBRgFKAYrQgpCK7TDmdb2NnGzRGCna1mUFjxUZ4LuzA2/PeoL6veBBk3SOauLwQUzLKeOkvaQf9jalcAFJ+jCUO+EdT9IeNnIYDvuE8QTHyyJnN/OsYhmZiAMOk2gbgPEzmUQXjojUaqfSyFnHU5FzWQs+LAoOdcwoiRhs3iVwGzQ7l+k2mrhSgjBoE5fKuFPEJiGecvhlC0RmmdM2I8aSFhFbTVwqahFW4jseUhsGgx6TcIj01NTikL/GEy7DxBAlEmkz4saS2IS44lqJrSFOSkU4OHhC4lgfT/gzunv6fjRxacKNQOFLlX0GaYSe2OnPzQATDCgJCmIhCSXs2pBED/GtoD126Yxc2tqhmU24kVJy9+7ducmz+4VliKRzlBsWHYbTTsspN6FaVJ466XzDh3kAbY63DEkf1VO6jOFwyO033+RWfwPf92l2V/E9H0+qAy+xiUmq/aZFGjWqQiZJ5QEhUh9yHtFOvWZGCz6Igo3WDAb7jCYjLJbVlVUCv8lu5DDScXnqFq7w8ZXKEnKa2MZTycJigSi9JjIKD5+GbKa9QUyELkXOidHs7/aYTCa4jkurs0bTDzJyFFni70CKSHuMQGg04dTIsNS3nb8mNvHUeVLZJ2FgNDJO8JXEagdf5RZAQ2SSqajeAhOjS6PJBI7wMttgunuopiVSPTy3q8BEWEZCs69AECHMEEYhKybg6iih2VcIkx6k3IT+PPtIF+9viUj6XvTxs5iWU5ZMYLFFI8dFaPgPF5CkF5E75mE4HLKxscFwOMRtTEeMaRXeNLm7wsdTTuY/1ijpTHmJc0dErC37Wes8hYevsgiwILlpsp/EITujdCp5Gml0iccTWsEaEosrFImNpyLOahSMlQQq1cSlsOish/UUbwkYJjEmjvILxlM+LjAcDBiOB1hlWVlZwfd8ELkcY6akCE/6IBQN6RMTZf31DqCtJdIJwuTfi8QTLp7K5QtNVF68BCRUzmMhUB6ulEhpSawmMtOfW/XaXBwc6+Aqgcg/o+qOo/K5DeMxOzJiry0RriUQio7waBtJR0cE/ejIPtJnFXUvU1HNSaagLILTTsvJE5X5McIwPDZRORgMZqbXP4y4cCR9GPKbrErSZXLO+0vHjuGlzZ1MHjCZDjqtH1cf8ImWODh4opUSY+GIOCBuTRbNTUXBHoFywGj6wz6DcQ8hBd1ulyAI0khjNKQfT5BSMkokSripTFJ0yKsk5ARMTMKkRGQHC0TqwxZMTww31rLT22c8HiOEoNVq0wgCGo5bSCuJSWaILjIaaS39OGGUGFpaEigXT8rs2pKZz7zaLwSrUMbHJ0iJVVjiue/n4EcSRaAcnDxCt8mUbRABE62ndg+OcAicNEI3No3Q9ZwIvR+nvvIesCsifBuTWFBC0m16rCmfVeES4BRtMcte43uNupctkr4fcs9h03K01jOtX621vP7668DR03L6/T7veMc7zv3ac3znO9/hl37pl3jppZe4fv06n/rUp/j+7//+ez7uhSPpw27uvBoxJ4zRaMTdu3enyDlPhoyScEZSyLfTjhApYVWIUUqZuRsOCkcEDoFyaMgGaeSsZ8g+1Am7/R7j0RgpJc3WCmvNNp5SSAHp/4nCmYJNk36jpHwckVnm0qZNmoTIxFPJteoCMdYCKR18fCaTEYNBjxhNq9Uq2pam/y5hXPkcDhKMqfuC9BKBlOjGOj54jQVhHDznwLUS2QRjpxOZE6vpJzFNYRnH4Eo3kzwy94yJMRVfefU78mS6OEiRRs9pi9mD1yTWMoinFxlfpVZDISyhGE8vDqSLsTWGUfa6vTDkrhrhqpS4mo7LervBZbfNinBpWVkQdznqrhL3UVHgMpH0cUNozxtKqSlv9/b2Nr1ejyeeeOLQaTlRFPG5z32O0WjESy+9VHSlO0+nRxiGhWf6Qx/6EH/wB3/Az/zMz/BHf/RH9zxo4MKR9FHIS8NfffXVueScw5VqZttebKcLCHzpZ5ICRCIirpRXWyxjHTNKHHRGFkq4BMpBYukP+vRHPYywtNttgkaQ9rO2mkkWaSaJJdQKYX186aGlIkbPkElkDNGU3q5oZNG2lGkycUomETAKQ/aH6eSXZrNJp9Gk4bhp4k9YEjPdVS//HAalxB9W4ChFQwZoInzpEplp90ViLUl5UbEC33GysnimEp95N9bYGGJTTjBKAqVwlTwozzfJ1HcUGU2U6dSecDCJSBOmKk0wxqXf50cNtSbMF+7YIoXEwy9F6JrqPMmJTooIvR9FbI/HvK4UUgqkEKx6AVfaLa74l1iTPiLRcyv8DosCl4mk71ckvSjyvh1HTcvp9/s8++yz/I//8T94/fXX+e///b/T7Xb54z/+43MrbPmTP/kTpJT8xE/8BAA/9mM/xn/4D/+Br3/96/zIj/zIPR37LUPSo9GIJEmKxt83spmG8+BKB2NSf3Tu142nmuGnKCfJRhrGsWSNII3MsEWyMG36mT7osdb0BgNGoxEArVaH9VYLX6WTyA2pLS2PGvOE3ChJCLHEOiC2Flekjg2VVe+FleQapFFwGSpLYiZRiNSCJIoJGgHNVrN4EGdkEuEQKJWSlrXENiaZkhXS9zaIE/qxJogMUqQLRBpsWsZmQlJpKFUmRwCtFS4ejlC0lCS0CYmZliLGWjMuvUZJh0CqglDDkuSRN3wqEyqAIxR+JnnoXPKYiuoFo2T6c2ugaCknc6xYwplFyJCUFq5eGHJ3NMxkIgiUw7rX4LF2l8uX1lhxPOJKaXbZriZlKkXt7+/f90nlVTzoSLqKo5orlROVP//zP8+Xv/xlfuVXfoW/8Tf+RjGp5bzw6quv8uyzz0797MaNG7z44os1SVdRvaFGoxEbGxsMBgOklHQ6Ha5fv37scaRQFb9uqh97mYvCkG/ByxNUZklB4eEJFwcYjobsD3skVtNsNmk0Gml3PmuJk2l/dBo1KoxKcHBKflVA51a28mvSrbufRZra6kzyyH5tLaMwZHM4JEkSpJBIt0G3vYZfJPEMYVUmsYZhUkmaSrfwOhsMB7MIsi541jIsImeL1iKVIo6TL5IEJS39KM7Oky4QIktahjaZki+0sQynEogCX3p4SuIIQaBSOWmGUMv+RAt+prtrOUELOzf5OY7LXQAlvpK4KmuPZaZ3Nhamo20ididj7g5G6CRt1NXxfa40mjzabvPolSsESs14jPOJQjDbzW7e2K3zwDJG0otcj7W28ElfunSJS5cunet1jUajmXF8QRAs3NTtKFw4ks5RJuc8ct7e3l74hlt1m2yEvamfVT2+WIGvfDwlEQpCG0617ARIrKY/HLDV66eyQqPJpXaLhuMhsyi4ajFLE2WpxcwYw1hDQzs03AAlPJSyqRe6klwLTUI4dZg0iUeS0B/sM44mKN+l2+3S7/exWhBpTVSKTgWSwMldEalEkBaPlD6Him+5IX18XBJc2o6fyQoJ2pi0+VQSo5TCcRyUclBKIUVZvrD0s2ku4ojzCARBJl9Y0uTitHxxsLvxpcM4skgkgZPbBtPPaOZz0wmhhkGUIKTAN5JAOYUFsKJipV0AtWZS+txcofCcVPLQ1hDqZGoRSqxFm4MFqDcJ2RyOeFHupOdUijU/4JFmG0dYWp7H9SefnJlUXh27Na9I5CxJddkiaa31Qg3/x+MxWuv7VnHYaDTm9o+uSqmnwYUjaWMMf/VXf0W/35+RNXZ3dxfu3/GBa+8l1DGbYZ/NsMdWlP450aUnVoiCFEKtGSaGVqJSkhOCyWTEfn+fKEq3YQc9nWFwWBRM2oUuzqLg/AEx1jDSCUI7jDK92lNuliwEIzLJoyRFxEnC3t4+YZTaldrddQIvTfzFMiIxKRFpM53EGycJ41KAqoSD7yhcIbDCEplpySP1OmsGSUJvklY3huMxyWSCIxWBHzCOI4bhqIiEU9JWKOXgOIpRDJ5RSKPoOBKTyQrV88wmMmUq+0iRjfrSUy4Pg03fT+m7daSDr2QheYQVyUPb6cRsYDw8k5KwyCyCE11ZuKwljsstbAVeXkAk0zL7KWudmF4gB8DuaMwbgz7j4RBjNE8kIy43mjzabHO10y6iwerYrclkwv7+/qE9pMs+45PiYY2k8w5498sn/cwzz/Dbv/3bUz979dVX+cAHPnDPx75wJJ37V59++umZaiOlVDGGaBH4yuWJ5jpPNNeLn/XjCVtRryDv7XBAYvUUme4NBwyHQ7TWNBoNLncuY6TEFQKDzfTt46PghnJREnzSgbgAshTVRNoQVfzbgfJQ1jIY9hmOR1hHsLq6WmSY88TfMNGYRCNj8KST+pZLpGWqpBVXZQUXz0mH50orkCK9vvF4zHA0BAvNVhM/aGCsoeEFdEUmFZmEKI4YxinB5Fv6/f4A4xgmJk1GKseh4TrZeTLJY06EOp2UBN9x8HGRKnW1VAk1MWZK704JVdGUbhrVSidLfmaHtFkiM5pOZDYchVIy9cSbZCrRaZnV3X0haEoXKdP7INTTi4MBxnHCIIoxxnC7P2BrOOZltYsQ4CrFqh9wrdnhStDkSrfLakZYiwy7necwOS5KXrZIellJ+gd+4AeIoojf+q3f4sd//Mf5gz/4A7a2tvihH/qhez72hSNpIQTXrl27557Sh6HjBnTcgButq0Cqv+7FQ17f2+A7g5cY9Mb0oxF+4LO6uopSCoVkEE4nowqNVqREEs/x7I6yqH2oDTI2tJSDLxQdR6GxRGY6uWaMZbO/x2QyRilFq9Wl4fsErlNEwbHVxCYBcSAtRBXXg0Cku4Es8RWZhNjoKaILjSHMFrxAOoTjGM8q9HDCpVYXv9kgJqv8M5DObdSkdT0CXJ+W6xM4DgrY3tlGeg7SSOIoLBKE+4BynIK0Xceh5Xm4Tlpqn2SLSuniU2I0gjA8SL42nNRTbbIFcZZQDcM4QUqJiA1KpHkBRwmsESTCTrdvzSL0cuFp2nNbIpVA24yEy84QIRiXpwNZi+8efM5xtisruzumv5uYvXHI7mCCSdLuii3P5VKzyaOtFldbLVY7naktftVnXG2INK/5fznqttYuVTOqRUk6n8pyv8rCPc/jC1/4Av/0n/5T/sW/+Bdcv36dz3/+87XccVKcpF3pohCAG1pa+5rv86/R6XS4fPUKAxGzlUXbe2HEflgtAqla5iBQLq5SWVdnXVjZ8j4bGkNiLb3w4EFPx1gJRqMhg+GARJSnogsMVKJgcKSLj4cViqbyUrKfQ0BTEoFItWqVRYH5AhHHEcNhj+EovabW6go4DqG2KKFoKIUVJpVAZs6TSisAw0TT8gK6rS6tILUNRknCKA6ZxBE6SQijtG3sHplckhG377i0fA8nI+6JmX6/1jKV+Es/N5VaDVUaWVe17VTySEk40A4mselrHFVUX4ZVySO3DZZ4uOG4OOmQTGQ1PhCCKNFEpey0QhCI9HNuOi6R0RWXi8VYwyC7BwaTiO3hmL/a3UtrAaRkNfC52mrxSEbc83pIV6Puvb29uW1Ioygq3CbLEFGfZHRWEAT37FE+Cd75znfyxS9+8cyPeyFJ+rCe0idp/L8IBoMBGxsbjEYjOp0OYRhy9epVGo0GLeCRYKX4txMdszEesBEO2BgPuDvpzxSkTLRhUpIvZKa3BsIjEOkUlnJ+0VrLXr9fsvO1aDcCAjct6sij11QPPXhdYgxjYxCJQEYJWIvnHJRqJzaXCCqyQikKTJKEaDTCxDFNP+Dqaputvd2pKEdbyzCO0SWSSaUVhZCpNDTJ5AuRxfUWwah0Hkd6rDWDzLsNkY4ZRCFJkpBoTTiZMDIjdkmlIJWVHHc8nwAfx5GpbW4BQvWswpcOHeURZfa8LBY/eE00LZMEjsJREkO+45hm4kkp2u5ID2UkvpPa7A6TPMIklc9UtrDni0PucplOr0Kipz38++OQu/0h38mKdJqux3qzwSMZca9l5FWd3DJvXmIcx8RxzGAwONRhcr+QD5B4K7UphQtK0ochlzvuNSooVyt2Oh2effZZPM/jL//yLw+VUwLl8lR7jafaa8XP+nHIxqTP3fGAjcmAzXAw5bQwNo00R8Zgopim49EWgkC4ROGEXr9PZDSNZoNmo4mQ2USUJJnqtpc6KdLoLC/qoOxCEfNcHoLAcXGkyCSPVCbROnVsjCdjXMel3enSCBoMehE2hgYOnnKy7XtFimB2ByFIC06a0qWpXOZ9K7E2xLpM9D7dZhMnq/qb6JhxHBXEHUcR+5OIeJK6c4peEZ6H77soRxFZM0OokTYkNkFkUapE4rsKXzi4jiSciWpJi45KJe6uVIW+n2AItS70fWvTSHAcTZ/XdxSuoyDzYfetTX16+fuvLA6uVDSlgyoWB01cDj6sZVLaOQwmMTvDMa/v7acLmZR0fY/HWm0uN5pcbbcIXGduG9JXX321qELNybvcU6PayS4n//OIuk8yb7HX69Ukvcw4rsnSolumKsbjMRsbG4VzpFytmN9AJ9G8O65Px/V5tnO5OMZONGJjMsiIu89OOCIvCwfLeDLhzZ19jNY0mk1Wmk0CN++4l9vDKh5kWy0jB2kUjoau46MzMjlMigCwxjAZjdHhBNdxWF27jPAcEmumyH4cJ0Qlt4gUkpZQSEkmk2jiynkmWjOME0yU0FCgTGqbk1Jk2vs0OcIsOQbSx2s2cbLXWGsZ9CO01iRJ2j9kp9/H9g7cJb7r0PB8PM9BOIpB5bYxpP5oo21hvfRUSqgi85Ufl5TE2rS6UklcFNqxU2PIgFTyKLeJ1YKGcug43sFnNrWwZfJN6St1pcRzFVKIYudQTv4mxpCUMtP7own9/oT/pS0gaHguq02fRzptrnZarDcbRZLadV06c7TuctR9VCe7s4q6813wopp0TdIPIco9pU9yw0wmEzY2Nuj1ejSbzbnVinmnsHuRU4QQXPJbXPJbvGvlESB9uL5pv03PxtwZ9dkdjvFcl9bqKjJ7D1WXRx6dull5d1zop9Pb6tha+pMDt0teQi2kILGpM0Fbw3g8ZjQcAqmk4jcaJKkXDU85BDhIVzKWs8UVJtd2S/BkSnRSpNFmlFd4ZFdvZtwkKTl6WfFGYlMP+VRhS6XgxFeKpuPh+Q5CZhKPTsk6J+5Ea3azyepAkchjHOO4ChxFSsGlqFZXolYhCpcHGaFO5RpKu5S2gChMUEKkVY8qlzymFyFjLWGiGZS+G1dJ/EwPFyaVdo4iYQFp8teRWLIEZOXeTAyMJ1lyehKxOxjzxk4/LW+Xgk7gE/f2eEYo/FabpnfgTz6s+X+1fzGze5oAACAASURBVHTucoLT9Y8u4604lQUuKEkvEkkvgjAM2djYYH9/n0ajwfXr12m324ceX0p55tM9osmErlG0jeCdl2/wyHsewSqV6tqjIXfHA+6OBqUKv4PotFxsIYVIk1gitYxFcjIzGaYseVhrCcOQeDJGYrnSWcFtBMTWTEWOkTZYkxCGCWFsaMeWIMgKToQgNgmjCjlUt+8AvlG0RNprxFdqyroGs5IHpCSUSx65M6L8IcTJdFWmEIK246P8jFCtIdJpwZDWmsFgQGJhfzQqiEUIwYr0cBwP5Sq0ENhy685cWih9lI5Ke5NIAQmWSOtp3TlfUMp6uMp0ZykIZXqeMsq6c0e6EFsCN02eImwqI5U+MwuESUI5X+3IlOjzHYpIpvM2uiLF9Ech/f0eOwn8xdY+vqNYbTa42m5xtdPicquBKhHmUZ3sjoq651kD5wVRJyXpi9BLGi4oSR+G43pK54iiiM3NTXZ3d/F9n6eeeopOp3Psin8WFr8ck8mEu3fv0u/3UUrRbrd56qmnit8/1Vnlqc5q8fd+FBaEfXc8ZGM0nHIsGDvt8ogTizKClnJRQhZ+Yp2R8zArH280GjRaLZCSOGtAlEsRRqQEVH7UU3LQhKXtu9IC382dIakFripfRMYwjBJaniUKdRptumU3iZ7RkGfOI2TRl0MgsDKZkR5mCFXKlFA9CWGEloKg2Sya02utsRNLfzxB9zXGGpSUqa3RcxCOgxYgpULItBhJa1vYJ3P4jsJF0vG8VKtP9NTOphyhh1GC67o0ZLoIWcFMzgAgijVRXNbDBZ7rFCQcJpUiHWMYlUi4RWrpdB0FkuK6ylnmKNGMogRNxBDYG0y4vdtDKYkQgo7vcbXR5HKnxdVui3Yw66ZYNOo+bmrLSeWOK1euHPvvHga8pUi6LHfMQ94vYXd3F9d1efLJJ+l2uwtvx84iko6iiLt37xbR+9NPP83u7u6xr+t4Ph3P520raVWatZbdcMydUrS9PRkdPLTZdnkUlYg7jglHI4xO6DYCmustpjt5MF+KkIq24xEqh4ZyMELMLdIow80scFKmUkWviEzzoiDLOJomOlfJUul12ifFzItQs2vSscFTEk85qdXOpiRkDiGucaRxlMIjPY9wBYk1aGnwggBs6khJkgSdaEZhgh6GGKNxlMRzHBzXwaq0qlQ5aTJOkJKdh2ScJyXzRShL/sW65Ie2qWRVXVBcmZ3DphpymOip+00bWxw/R+AoHCcl1NikuYeDb1QQJcmUHp4uji4q83rvSTl1/xtrmZTumcEoZG93zCtyF0S6I1hp+VzppqR9udMqdjtlHBZ1V8vgB4MBOzs7xWsANjc3jx20MBgMeOaZZ2Z+/jDiQpL0UT2l59nwkiRha2uL7e1tHMfh2rVrrK6unjhDfS8kXV4gPM+bit739/eLbPqiEEKwHjRZD5q8mzSiSIxhazLk7mjISxt3uD3ZTsvQs61+GIZp+8dOF9d1SYO01GaWyxeJ0Uwq3fViowkjyyhM8MME13EyKSJ1hoRCpFa0EqoJNpOA5ytcIWm7HnEmRUz1g9bVdrElZ0ReDJLLFPm1aUNcGu5baLVKYovosfJ+kukeLb5J3RQyL+5xp6Naay060SQ6IYw1yTjCWIMrBUpJpJIYKZHCIzGkEgVMkR2QLiiuIlYK13Xm685RhBQuk0mcVld6KivsSX9/XFJSCYGXkbDUAkfKGT08XxytsZjY4CNpul6aq8jOUf5eokgTZj7DPNq+szNAORKBoBW4rLebXO02udpt0W0ejNOq4qipLbu7u/T7/cISmD/H1UELSZLQ6/Xuq9zxuc99jt/93d9lMBjwrne9i1/8xV8sBg584xvf4Fd/9Ve5desW4/H4/wb+z5s3b3530WNfSJI+CmVJQmtdkLOUkscee4zV1dVT9yo4jQ9ba83m5uaRC8RZad2OlDza/P/be/Mouco6ffy5ay29791ZOkknpLIKSHAgIjJAGAdRVMLoOHM8AgMTNCOjooIEErOBGAUZJZwOo6AoMAKK4iBB88NlIsH5OmSnIAshoZfq6rWWu9/7++PWe/u9t6q6q7qru7o79ZzDCV3dXfet21Wf9/M+n+fzfCrQHKxAK+dDJ0SUVVbieFcXhiqrYAT8GDQMl04ZyEArwM4CeW5Y66uRhozUh5fmQw3TBAu7WMZz7LDREa1YYBhoqSCcSBXMGCYlA+SY7Ed+TxBiGcAn2Fpsn8DZv2OOzNVyjL0RGRwPlufTApdlWZBV93XTqAXWAG9RHyfL/tvqhp1165oORdNgWZZddGVZGAwDNtWUw/M8NNgbUVLR4QeHACMgIPDgOAZgGNu4yqDoCCad8uAZBqJgFyWNFB9Ob2x2Jmz/fQMgpw0OAs+CYVnopuFQMSTj1k0LSdnN7fvJ39+yoBumq5hqwU0rxSUFfUNJnOqxeXqe41AZ9KGhIojGqnI0VARTEsTMoLNuSZIwZ86ctFmJxPj/xIkT+PznPw9BEPCzn/0MnZ2duPjii3HVVVdlff7x4rnnnsPzzz+PH//4x2hpaUF7ezv+9V//Fb/73e/Q19eH9evXY8eOHbjkkkuwcuXK3wJ4EsAFuT7/jAzSI2XAHMdB0zREIhFEo1EwDIPGxkbU1taO20gmn2BqmiZ6e3sRjUYBAM3Nzaipqcm4BoZhClqQNE3TGfkkxeM4f+FC18YQV1V0J+LoTiQQiaf4bVq/jXQJmAgOAYZHuSCAF0Sb3/YGugwFNtu+lIWSoVBk/47m/p0UTeDI8zzKCMuyM1SLs6CnnJhcNEkGrpZQOElFB28ALE/RJGyqiGpZME2aJslMLbj4XYYBx3NA6kQftDhIsuZk3dB1MIYG3VKgMwwM2K3jpmlCNwzoKb6foS7DsQwEjgUv+mxDKd39+g3LgpSWoXMQBMryVTdSjSH2972KFQYM/CIPsBYU3t7w6HefRVEeHMMAimVTMaJ9j3XLvsf0KcB7ohmMy+juj0PgorAYoMrvQ6Xfh4aqMjRWlaGqzJ/2OTYMw/l8ZJuV2Nraisceewz33HMPWltbcfz4cYTDYaxZs2bCOib7+/uxbt06zJ07FwDwmc98Bt/97nfR1dWFV155BUuXLsXll19OfnwrgH8PhUIXhMPh/5fL88/IIJ0NpIpPMueGhgbU1dUVzOUrl0zasiz09/cjEonANE3U19ejrq5uREkgacsdL+hrk3UuXrw47fWXiyLKxVosrKkd/j1ZRncijkgige5EAtFk0n0UN0zIuo64pEJM3QJfKkPTDR0GbE8Nl2zOsJzBBLJqQgTAmQzKedGRzdHNIECqXdvDVdPKCJuO8bR4G+mDhP2C7dftKphRoIOKqDGAaTnZo8XkRi2wFL9rAYBmd8uxIgsBw3I2mi6xTBM8Y4IxDCjxuH3aYFkn27bb4FkoVGYv8kS7bRtkyZqetSgJpIKwwEMEA5/I2soQ3ZMJq/YJQFJ0+DULYopW4Tj7lKHqtjyTTZmGGaYJiRpCyQD2/RLs95ZqmNAoTbkFC4qmg+xzjAFEo3Gc7h4ExzLgBQ4fX73MdX9z6TZkWRZLly7FmTNnsGHDBnzgAx8Y8edzha7rTmev93o33XST67E9e/aguroazc3NOHHihGsYQDgcNkKh0HEAywGUgjSBaZro7+9HT08PdF2H3+/HggULCt7SSrL0TCCTNiKRCDRNQ11dHerr63OykBwv3WFZFmKxGLq7u6GqKurq6uD3+3HmzJmcsguGYVAbCKA2EMDS+mF+uzeZRHcqaPf0xREF43LLT8gy4vE4NE2zMx+OQ9Dvg08UwAsCTJZx0xeWZWe1stup0H3kt3XVrhbvDEFIEFj4BQ5WiqtWPUHYSxOwDAMfWAR4HkFB9OiKmbSgAnipBUA1dBe1YFHUAmDTCwLs4h8pmCq6vYHxgl10BID+PgWBoB8+QYCg62Bg2lNhNBWKLKNHG4JpsuB4DjzHQ039SzhzkglzHAmQHg49RUeYGuucdgSWsZt6WCal09ahU7RKWj3Agt2NmTop6IYJVaeDMKBqOlSPkoZk2/aJxnCuz8A+nRipG+zT0z8XubaEK4ptG1BITvq1117DDTfckPb47NmzsWfPHufrv/zlL9i4cSM2b94MlmUhSVImk6ckgJydl2ZkkCaBx7IsDAwMIBKJQNd11NXVOValE+E5kCmYkgkR3d3dkGUZNTU1aGxszMm4nGA8dEcymURXVxeSySSqq6sxb948iKLouISNtUWeZ1k0lZejKfUGtBZY+D8BCNbVY1DV8da7HXg3FgPDsKisrIRpmNANHUlZxVA8aRtHwT6yBn0iggwLzuYW0q6leGgSjmXsQMfZwVM1TNdwAAsWNMOETI3I4RgGPjHln43MAVXVDZiKDnD2e4TwzgJsz20vtZKJWhA41uaqHRMmw6FJLItJ0RgeL3HBpiMApJ7fcgYn0+9TAXagEjXA0HVYsLNTOSFDS1mK8jwPnuMhK3bg5ji7qCpwLIRUR6KZgY4wTMtpbHHWxbAIchwqfD7oqfsz3F1qnxxYMNATuvN3EQRbTWKkft51vzzZNizAL9q+4jxjU1JkM83EUefrgFfIZpbVq1cjHA6P+DO/+MUv8I1vfAN33303PvKRjwDIPAwAdoCO53rtGRmkSdba3d0NTdNQW1uLhoYG8DyPjo4OKIoy+pOMAd4gnUgk0N3djWQyiaqqKsydOzdNcpTr8+ZLdyiKgq6uLsRiMZSXl2PRokUpZzwb9EZWCDAMA5FjETA0GFIcf9Nch6ZzlwGCiI6BQURicfTEk+hJJO1gaJn2EV/XkVRV+wQiqzASCgyNQcAvQBQFMDwHA4xbBmi6M1TAVkYIPJcaqmDCMi168pmtWlAy/I4TUC3EGGLzZIPwzro+PBjBVpOw9mzHFM/uMqIyTFcQttUkqUBkWGAs3pVxkmDnbgsHAhyHMlG0vTmokwLLsim3PztYcTzgEy3AMsEwtkOeoqqQEgoMywSDVLBPZdvkX4Zh4LdYiKJgZ8qmCUVzB2FF1SErBqSkPRGeYxiIok3fmLCDMH3HTNOym5qoj5fIcxAFm1bKdA1yoikXRWiyAY4FRJFHZQa9tWmaObnaES/pyew4/P73v48f/ehHePjhh3HxxRc7j7e1teE3v/mN83UoFOIALAJwJNfnnpFBGgCi0SjKysrQ0NDg+sMWsuHEC8JJ040o5eXlWLhwYdr8s3yfN9c1k6Jof3+/o7PO5KnrDCkYo48JDUInAfbG1NLSgqqqKmcDOKexHuc01sM0TftnkxIi8QR64klE4gn0JiX0DwxA4AVUBoKIDcmQVB3xpALDNFJSMx5+UQAnCGB5DjoDMAzrhAjvcVzkuOFGDYdD9jaQuItZ0C34BA7lqfeLRnTV1K1PC6gpaoE44WmmAU03XMd+oo7xGxw03UgFO94V7Gili2lZUFQTFjO8Np5l4RPtTQiKCcOwnCk8DMMAqfFjLAME/CICPsumiGAXIWVVRVKWnPcRz3GQNG/w5uATeVsyCAumrttBmBlel+zZ6HwiZ2+mLAPdIPI86pbqBnSP+kZMUTHkxEMrVkwTkGUdRjA9eaALhyNhsg3/n332WTz++ON48skn04bRrlmzBjt27MDu3btx2WWXAcAGAGcA/F+uzz8jgzTDMFi0aFFW4/9Ce0oTmKbd6HDs2DEEAoERJ5LnA5JJj0RNEDlhNBrNqRGHvNnHk0lbloWhoSHnxAIATU1NToD2XptMwm6orEBDpZ3lSJKEru4IOspEIFAGzeLQJcQwmJTtQGfBkbHJmg5dtr0gGACiwMEniuAEHmBZmClJm33V9EYNhrHbtXk+FSBM0x1QLTsIJ6Th4MiCQZDlwPIpxzlDd7WnkyIbDY6YHaU6LFVdd2gMIHOwE3n7uA+WQSKlRKFhmCaSKapA1BjAMO3NIZXVp2epDOxlsmAYFgGfgKC/HAJnz23UNB1KTIGiqJAMybk/JGjzPA/DNCCAQZlgB2HDsq9B0ySMBUhJjzxP5MDxw006tObcsgDFOwCDY8FbDMr9gs3Ta4adfXuQj00pMXiaDLS3tyORSGDt2rWux5955hksXLgQDz/8MLZv346vfe1rAHAlgE+Ew+GcP3gzMkgDk+cpDQw3opDOqFzbyHPFSFkvyWIjkQiAkaV8mZ5zrEGa5rpramrQ0NCA48ePO0ZUfr/f+S+TiQ5pIOrv74ff78f5ocVO27CZUg9EBuOIDMURjSXRE0va+unU0xCTJFU3oCsSDJ0EbhaCKIDhBZgaYLGsM1XbstKLfySgciwLhbdbu2nYRTYDFhWIBZaFT7TleU7xz9PFKCnuk4/IcfBxtj+4YaZzwrpuQtdtG11VNuAXgIDPzm6tlO2rwwlbAMBAVQ2oqpt3F0XeDpCWmyYBCO9uX1PgRfAih8ogB0FIBWBVQ1JWoGk6ZEV2isCdXT0uqiQY8EEQOYBhwFmAizy0bMqDfpDn7HoAw6W4fd1wzdXUDRM6Y0KW7D8MA8DPji9ITybV8dJLL434/Ysuugi//OUvyZd5y01mdJDOhEJ5SgPpjSj19fWIRqMjmjCNBZmyXpp313Ud9fX1qK+vz5m6oAN/PqDb1gmV4/P5YJomWltbkUwmIadUHb29vc76ScAWRdHpHuM4DrNmzUrL+FmWhV9k0dpQg9aGGmedCUVNBe4EeoYSiMaTtkKDgd2ybdrFSV03YOoqlJgKlmHA8wx4wZavGWDAcKzNy7KMK6AqigHBYiH6WfACB45JtYVrBgxqL7OzWnfxzy96NNJaujcHo5kwyRMxSNEkjNMtqFJZvc0JG1DgDcICRAGpDD1Do4onQAq8vQkxqVZ6RbM3BybF8xu6AdJAyoJDuS8IodyWzsUTCSSSElhegG7o0CR79uLQEMBy9uZXFfDDki0EyuyxW4TeMeh1GRYkKZ0mEQTbd1w1DFiu0wkytpLnUzicKQ54wAwO0tnAcdyo1MFoII0oPT09YFnWyV5lWUY0Gs35zZQryHORgBqPx9HV1QVZlp2iaD5qESD/TNowDEQiEfT19UEURccRkPDMDMM4gZiAOOnJsgxJkhCPx12DgHmeRzKZhGma8Pv9WX0YyD2oCPhREfBjYfOw//ZAQkJkKI7uQTvj7o0lYQgWBI5FkLM3Yztw69CSGnRdB8sCPM+C41kg5TjHcZyjOPE67vGqlaIWUu3nhpmudPBK+mBntYRaUQ0T0NzKBlXRQYsNOdbufJQFHkGfAIthMwRhDbo8/DcTOBaCaCtdSKB3Nd3oJiSd3ojt1+LjecDP2hk6TddYgKbq0FRAkXSYqonq8qAtz+OY1AalQFE16IYOVVGQHJQxOEjoEnsepd8vwh/wgRd4u7lFcxs3aaoBjToFCCyHIM+D5e3Nw0t3kM/sVMykJxpnZZAGci9C0LAsC319fejp6YFpmmnNMLSBUy7651xBAqokSejo6EA8HkdlZeWY1SL0WkcL0qZpOq+ZDPklBRnDMBwf7Wzr9vv9jhRSVVVUVVWhuroamqZBlmXIsoyhoSFnA/L5fC6qZCSzeIZhUFMeRE15EKFZ9mBgwzQRTWXaPb1xRAcTGEzYniRkY6abRwzF/tdkLfhYFtBVSAkDYFhwqSM+Z7EZqQUhVfyzGNvvw6tFVlQdChWF/Yad0bOpduq0TDglg5MlHaKoQeAFiDwLQUw1qjh2pHRDkAlDcuvKfSIPQWCdDUXRaHrPpklYi4EeT8lRWQaij5r0oqXkian7ZZqW7RWSAg8O/oAAQeQhsizUgIqkpELTdcene2AwBgzYk3HISLNAUITPJ4LjeeimBY2qFxiGTfcQCJ7PJnl/5HJSnEk2pcAMDtKjFcwMw8g5+/RSC9kaUbwZb6FAOPTTp08jGAy6JsKMFaNl0nRRkNAptbW1Lq5/tJMIUZoMDQ2hrKwMCxYscGXaVVVVzrV0XYckSU7m3dvb65hKkSIQHbyzbYIcy6KpugJN1RVAytlV1Q309McQGUigZyCO6GASCUW1m0coT/+BgQFwHAfWBCxTg8WoMFkGhgqYjF2A4/hU5x/HwVTc907gbF01wxEtsuFqjTcMC7pnQo7AcxBFzjEvklJRnUjbCFdNwDCAPyWpIyPKVE/hkmTCw/eEcak2VN2gp3PBMi0oUnoh0+I5CCwQ8Ak2TULzyLoJXVfBiSLUpA6BYVEWLAOX2hxUzYCsqNANA0YqcA8NDA9YYFkWok+AP+CD6BPAmvagAXINnk+vvZDfGw0lumOaIx/j/3wbUfIdKjAadF13FSSbmppQX19fEL57JE46mUyis7MTkiQ5RUGe53Pm8knrfV9fn6M0KSsrGzHjFgQh7b7quu5k27IsY2BgwFGR8DzvCtokcGe6hshzmN1QjdkNw/7bSUVDpD+G6GAC3f1xnOnug2VaEPwC/D4/xXMbsHQ91TxiwNQ1aAwDGRZMMGBZ0q7NwbJ4GC4faWu4UYVhAMNwfDOce6UbkOhuSNOEj2FQ7hPACbwta/N0RqqKDtohimOpgiHsDNWlqPBkwgDA+VjwogA2VcxTNB2WJwhLKQ5a4dVhDp3nYMKCblpQNR0kq7dVG5qLD/dxPMoDvuGTg2bLEw0q444NptQ6WooyC/jg94vQFAmyLEMURZcENVe6o7q6etSfmy6YsUE6l0x6JIylEaVQmbSX825paUFHRwf8/nTTmbEiUyatKAq6u7sxNDTkKgqSKc2jXZvQGj09PQCAxsZG1NTUjHnNPM+jvLzcpfMmOnRZlh3nM2JSxXFcGlWSbShq0CdgfnMtGiv9qBN1tFXVQgy0Qmd96I1J6BmIo3coafOsIgtLFEnchkUMkDQNjGXB0lRoqgnZtGCAcWmPTcuCluKiedm+hz6RZML27ESXb4YFaJoJKamB41K/xzIQUrI2ywIMHi7tsWVaUOT0DF1IZehmihP2vi/lpIcm8dlrZlhbcRGPW8OtKoRDpzYHnrXVHeUBcZi+0emTgwkjmcEzpVx0yQYBC2ZSc6SW8ZiEwcEBvPNOyjtFFJ2Tk6IoYFOKnWyIxWKuARnTHTM2SGcDmzIxzxakJUlCd3c34vF43o0ohJ8da5D2mi/RnHdHR0fBugMJiP6azth9Ph/mz5+PsrIyV1FwtEBLNjVVVVFTU5OX0iQfcByHsrIyl/7cNE2HJpFlGYlEAn19fU6hKRPPreu6Q8WQv7O3m80wTfQNSejtSyDaH0e0P46BIQkWy0JkWTvztyw7S07dR8M0wDAWYOrQJAWSacG0UpNGNLtt2zBsnw1yR+lMWNU1xFM+JcOvz4Ii28FR4DmYsg6eHy4YGqadpboGAOgGDI9fiU/k7NmNDAOWSZepejN0Rrfg9/Eo94vDahLqOU3TgqmbkGPDwd6WQNqUj25aUFU3TaJpBjTPycDv58GV8ylu34CmmWhrm4/6uqBr5BYAdHR0ABh5XmIikSgKJ/3MM8/gW9/6Fvbt2+c89sILL+CBBx5AX18f3ve+9+GVV15pCofD3fk871kXpIHMXYf0PMNsw2ZzwVh02F4DJLqNnX7eieiUHBoaQkdHB1iWzasoSEDuG+EB58yZk1PrbiHBsqw95ovaTGllCflvcHDQdQ9ZlkVNTQ2qqqoyctwcy6KhugwN1WUA7MKkphvoHUgg2p8yleqLI55UAELZYLhAKcL22DAtEyxjApoOVU5CMy1YpuW42vEcB02zeW5D12EpttG+TxTsYGeYUPXUhplam6GbMHR3JiymgjBDZ6lZFBVlfgGsYUL0CcPTYXTDVcwzTROqaiARH+YweMKhpzYHeNwFdc2EThPiKZqEE4aVMZo23JVoF3FNKInhkwDHMymuXoQoiqioqIAoiuju7kZbW1vWyS2yLKO9vd1pKDt06BDOOeecSWlqOX36NO677z5XYvLGG29g48aN+MEPfoBQKIQtW7YAwMMArsvnuWdskB7NU5oEUroRxe/3jzpsdjTkG0zpppCqqirHAGm8zzsSSFGQ+Eo3NDTkXRT0NqPMmzdv3MXMQsIrCaQ3QsMwEAgEwDAMhoaGnJZ2kpHRWbf3NCDwHJrrK9FcP5ypSbKWyrRTgXsgAUXVwViWE/xZhgGjG/AJhGozU3asOlRVQiJhD/glg10TSQmqqjmNOICdCft4DgikArfm5re9sjaOhZ1tp4pw3iBsmUgrGPI868jtFHnYI4TAy6GXsSx8HJMKwsPZM90Xn4lDF/wpNYll2T7X1DVM3UqT4BFZa6Z5ifZmoiIWi2Hu3Lk4efIkXn75ZfzqV7/C/PnzR202GS8Mw8BXv/pV/MM//AOeffZZ5/Ff/epXuOKKK3DuuecCAG6//XY888wz14ZCocZwOBzJ9flnbJAeCSzLQtM0dHV1OY0oc+bMQVVV1bg531y9QTLxvyPRKoUy/k8kEujq6oIkSWBZ1lGq5FoUJB2O0WjUlX1PlKF6IUDudSKRQFVVFRobG53gSegeOuPu6+tzlCWCIGQsUNII+AXMbanB3JYa57GhuIxofwLRATtwD8Uk6LJ9j+3AbwchkRMgcgGYogmWA3RDg6qp0DUFydQRn6O8pMv8IizJBMuwYFmkpHN2Mc/OUulMGCmahOKRedtUSmQYwM/bNAnVqWPqJuRUhq4kVAiCADHIOh2G3s3BtCyosg7IniDsE8AJqQxdc3PVpmlBSQ5vDn4/D4FhIPjsjk/dMB1XwOHfye4xQzdLfe1rX8Mvf/lLPPTQQ1i0aFFBzNRG8pIuLy9He3s7zjnnHHzwgx90BekTJ07g/PPPd76uqakBgAEASwCUgnS2oEGM/0nHW65t1LlitIzXm7lnM0DK9Lzj4aQzbQpnzpxBf38/ZFlGIBDImj0Cw5koGRhQV1dXkGk2EwnSEUqbTXk3QlpZQsu26MCtKAoGBwedgihRltBZt7f1vbLcj8pyP9rm1qXWYmJwUEJvXxzR3gR6++IYHEzCNKkmDQswNEBOaHbB1c+A5WwjyksJrAAAIABJREFUJU3XISsKhlQZekwDm+qapL02WJaFwNkBkk0NktU0txab0CS8T4ASswOY4OMgijwsZpjftky7/ZxlWOiqAV1188iijwcrsOA0A5bIuTJ407SgSCogDd9nQeDA+1ITdSy4uGoGDHRNh04NK84UpHP1klYUBZWVlZgzZ86oP58LRvKSfuihh/D888/j2WefxaFDh1zflyTJJTlNIS8vaWAGB2nAXRjxGv/7fD4sXLiw4EEmW5CmDZDGkrmPle4YqSjY0tKCRCIBWZbR39/vyNu82SNguwpKkoTq6uo0vnyqgVaZ0A04+WT72ZQlNM+drfWdboEn1+Q4FrW1ZaitLcM5i+zn0zQDff0J9PYl0NMzhFPv2Nk+/XumwQCw/ZYrAj4ERA6GqMG0DKi6DklSICVTBkks4wRsErzZlI+06ONt0yXDrSYBAF0xoCvUY6link9gEQwI4EXOztApHlmRNUAGRMMO4DzPpjaHlNxOdbeG65oBXXNfV/Tx4EV7yLEp8tBSGTrD2JNZaOTafEa8pAtZOMzmJS3LMtauXYutW7dmrF/5/f5xe0kDMzxIA5kbUTRNG1PHYS7wFg7HaoDkRb50B+kUjEQiWYuC3mIbLW/z6pIZhkEwGATP85AkCYFAYEoGasLxkwLsaKPJ8kE2PpQO3MlkEv39/U6w8QZun8/nBGBB4NDYUAFRMMCzMcxqbkF1zQooCtDbl0Rvbxy9fQkoikZZGbAwVBMAA97iUekXIFTa8wh104CiapBlFZKU7mxHGnF4jgPL8ygLirZviO4u5sGym1uUhArO4gEfA55jIfjtQiZxCzR0E2TWgp2hu6kFUbSDMFIJhqJ4OHRFh6boYIMitKQKlgUEnwBfIN2Qq5iG/9lw6NAhnD59GuvWrQNgf34kScKqVavwy1/+EgsXLsTJkyedn08VOGsBHM3nOlPvU1ZAxGIxdHZ2QlEUl8cF+RBPBEiQ9tp45muAlOl5c6E76E3JMIy8OgWJvM3v96O3txexWAyCIDhDakkLN9El59NQMtGguxvLy8snTWWSTVmiqmpWZQmhSTiOc/xMSG2ABKI5s2ud54vFZIcmiQ8l0SPp0FNZp2VZ0KiOQxF2kBNrBHsWo6FDVlS73Zw42zGAkhBgJHWH6xZEAX6/ADalxdZSjnwEhmHCSLiDsCBwEEUWDMPBNO3smU4k7M5HqiTIMPD57Myc3hwIzFQhk8sQjHP1PZ9ML+lVq1Zh//79ztf79u3DF77wBUeCd8011+Cf//mfcd1112HlypX4zne+AwAvhsPh3nyuM6ODdG9vL/x+P1pbW10ynIk0/uc4DrIs48SJE07HXr7jsjIhF7qDLgqSTSkf1z9vM0pTU5NrijiBaZquADRSQwnJuCcqcJMTA+2jnQvHP5FgGMZRitCt78SvRJIkDA0NOcVJwA4umqZlVJZUVPhRUeHH/Hm2sZRpWhjsT6AvGkdvNI6+nhgGB4YN/S3L3eYtWDx8QRGCz9ZVa7oOQ1YQN1UkJQkW6ebjhjNtjuPAmRaCfh5+0qzioTAM3YQkDQduBoCYCsJgGOi6XWSk9HZQZRUqxQCwLAvOslAWFGCadjs5GV5LwzTNnD5D8XjcSR6KjaVLl2LLli2466670NPTg1WrVgFAOrk9CmZ0kJ4/f/6kGv+TTFPTNFRUVBRUozlSkKaLghUVFXl3CgL2mzsSieREE7Asm/HYTwdumq/1Bu5sHtP5wFvIHG9340SDFCiTySQGBwfBMAxaWloQDAYdukRRlIy1AbpAaRcIGdTUlaOmrhwLQ/bza5qB/t64Hbh74uiLxhx9M8m4VSpwBwUf+ArWUVSomoZkUoGmapAVBWbq8xGN9IPnY3bg5nkEgn6IfgEMy9rZs6w6nzELgKpoUCnDboZl4POLdoaeWqeuuelAQzeQHBxWT/hq0lVO+XpJF+N98Dd/8zeuRhYAuPrqq3H11VfTD+Ws6iCY0UE6W2NJoY3/VVVFJBLBwMCAoxSYN29ewZ4fyMxJk645WimSb6cgLU8bTzNKtsDt7QTMVmgLBAI5B24yv5EM153qhUzA3sDpUw5NfZGGDQJvbYCmmLJteILAobG5Co3NVcPXlFT09SbQ1xNzMm4yFYVlGZiGCTkx/DnwMTyCFbbhkQULPdFe8LxoFxtVFYYkIR6LOZakfp8IRlIRrAhA9Pvs7Nlj2WqZFuSkmybhhNTILdIQ48mjOH58dMdMMlcCZniQzoZCeEoDbuWEKIpobW2FqqrOB6qQoDlpr7fH7Nmz8+4UJGsfGBiYsGaUbHwtHYDoQttoColcJHVTDUTV09fX54xUG+0onq31PdtJJdt98wdEzJojYtacYf12PCajtyeGwZ4YejoG0N8Tg6EP0ySmbiKpSpAkCZqsoqwqCF+lD7zIg2FgFyVlJTW7UIMSjyNGAneKLhFFEYFyPwS/fYpUVdOVFBmaAYkK5AEfB5FlwPvtTdoXSE8S8plvWArS0wgjFciAsfs+ZzJAIkft/v7+CeG7SfY/MDDgFAUbGhqc6+baKVjsZpRMqhJvC7ckSWkKCYZhnAYcMuh2qlIbgLvD0bKsca8500lltPuWybOkvMKP8go/0NYAwH4/DPUn0dc9hN5IDJ2ne9Bx2qaQKsorbK8R1YBGURgBXoRQxkEQeRhlZZAlBYqsOiPNYrEYhoZSXtKpwO0L+BAoC0DwCbAs28nPGR9mWi6apGHW8GmAvM6pOjprMjCjg3Q2jNWcnxTWuru7YZqmo9ig3zyFHM9FQ9M0KIqCM2fOjLkoOFWbUbJNdVFVFYODgxgYGHAyMcMw0NXV5ZwAMknbig2aQiJWrxNhNjXSffPSJSMNVaiuK0d5lR++KgvlTSbOu3QeRDaIwT4SvIeQGJJd19BkA4wFyAN2V2TAJ4AXA+AE3qZHUkFX13UYhoH4UBxDA8OBm+M5+Mv8CAT8AMtA9AvQFA2WZbey0yAJSK4SvJlk+A+cpUE6X99n4itN62+z8aD0xJNCBA3Cv5Ij5aJFiyCKoot3Hg3E2W+6NKMAw94gRFLX1NQEQRCyStuyZY6TuQmZpoloNOqoiopBx4ymLCEFSnqoAtnsGYZBQ0MDqqurwfM8mlPdkgCgSCp6IzH0RYbQl/qXgQU2NYvQMiyoSRWw7EKiBQsBUYBQGQAYu8ioKJrdWZgK3InBBIb6hsAzFgzVgCDyCJQHYRgqVFV1ahT5ekmXgvQ0Qi50x2jI1QCJgPaUHk+A8BYF6+rqnBZuy7JyKrKNNhllKoJQSb29vRkldaNJ2zJljnTL+0QEbnoTtywLzc3NGaWLxQLDMI6jHB3AiL2soigQRRGWZaGnpwc9PT0ZNfAtrbWYNW84cMcHkujtGkB/16D9b/cQdE13psqYhgk5rgDWcNJSFhDB8gF7CK5h2U00mgZFkqHrOuIDcfQP9OPtt992bGZJQkH6D0a6r/F4HLNnz56YG1kkzOggnQ10ISobaFlbWVlZzr7S451zSPPdHMdhzpw5qKiocIpFZ86cATBc5acDENGRZpqMUmzt8GgYq6QuUwDyZo5Ey03+3t6M2+/3jzlwq6qKrq4uJBKJaXNKoTdCn8/n2ry9ypKRNPD+oB+toRbMWzLLed6h3jh6OwfR1zWAvs4BDPbGUxar9t9RU3RYsjYcuFl7CEIwUAnTtKBrBha0zcfcec1O1k+6Jzs6Opy/N/kbkk2b/P0mk5N++eWX8e1vfxvd3d0455xzsHnzZixZsgQAsHfvXmzfvh1nzpzBsmXLsG3bNixYsGBM15na76ZxYqRxTdm00plkbfkEuLFOZ/F2CnqLgj6fD21tbY6sjWSN9IeIzN5TVRUMw6C+vh51dXVTJqPLBlmWnSk4hQh02QI3MU0i9y4ajWYN3CMNwAXcgU4UxWmhNAGGR6Ppup5xIxz3UIUKP9rq52Dhe+YCsD07+rtTQbtrEH1dg4gNJABmeI6jmlSd0V22S+Cw6VV5ebkzgLm1tdXZfAllQ/5+pmni6aefdk4DfX19qK0d7tosNI4cOYKvf/3r2LlzJ9773vfi0UcfxW233YaXXnoJ0WgU69evx44dO3DJJZegvb0dX/7yl/Hcc8+N6VozOkiPBG/XIZFK9fb2OhnsWKrxY5lzSI7KsiyPWhTMJGsjio2+vj4oiuJsQESuRmuRM1ltFguTKanL5HaXyabUOwDXm3GTVu6urq5p0URDYBiGo+WvqKhAa2trzl2w+Q5V8NYHyusCqJtV7SQwSlJFX/cg+joH0Ns9iOipCJRUyznDMLYKRBBgmqbTZEX+dqIoIhgMOskLkXQODg4iFovh1KlTOHjwIH7605/iwgsvxBNPPFH4mwngqaeewvXXX0+6CHHDDTdg9erVME0Tu3fvxtKlS3H55ZcDAG699VY8/vjjOHToEFasWJH3tabGp3WCMNIHh/bYIEZEgD2Xbzyqh3wyabooSDeS5FMUpJUElZWVaGhocJ6DlmZ5PTdommSyA3chXOoKgVxsSiVJcvlLk+Dg9/vR2Ng44oDdqQDaQ4ZhGIc+Gy9GUpbQwTsTzeTz+VDZGERja62T1MQHEujr6EdvZz/KqoLQdd2hG6urq9HY2OhKgOhuWrKBbN++HX/7t3+LHTt2oLGxcdxS2JF8pI8cOYLLLrsMn/nMZxAOh7Fs2TLcc889YFkWJ06cwMKFC52f5zgOc+fOxbFjx0pBOh+wLAtJkvDWW29B0zTU1dUVRCqVy5xDmlIhDQ6BQCCvNm66GSUQCKQ1o2TS1RKrTXLcpz2SvfakgUBgQmRjXpc6r4RxKsBrU0qO0L29vc7xXtM0vPvuuwByGwxQDNB8+URKAQloZUkmmmm0oQq1rdWYtbgZyWQSJ06cAMuyaG1tTbMBJe8X+rWcOnUKmzdvhqZpaG1tdaahjAcj+UhzHIennnoKO3fuRCgUwkMPPYRbb70VL7zwAiRJSqNIA4GAw63ni+K/kyYY3mGbABwPZdM0C2aARCNb23m2oiD5Xi6dgsRQiNAys2fPztmrIJPV5kj2pOQDNNpAgFygaRq6u7sRi8Um1aVuvCCmVYTDJY6CwMj3jlZHTDbNRE6HPT09RefLczmteBMGwH7vVVZWwjAMaJqW1aTLNE08+eST+N73vodzzz0Xu3fvxty5cwuy9mw+0gDw4Q9/GGvWrMHKlSsBALfddhsee+wxnDhxAoFAIM1HWpKkMXf0zvggTYMUqGKxmPMhmgi5jtcMiRzviXKBzBQk3wNG7xQkx9aenp6CNqNkKhTRwYd0sdGB20uV5FpgEwQhY2Y0FUHLFysrKzNu5KPdu2JYu0qShM7OTqiq6ppdOdVAn1bIe7urqwssy6KiosLhozO1vvM8j4GBAQDA1q1b8eabb+KOO+7Apz71qUl7rQsWLHBsUYFhEyvLstDW1obf/OY3zvcMw8A777yDRYsWjelaMz5IMwzjTLQm1MCCBQswNDQ05uPHaKCDNF0UJJ7BdNEylzdVMplEJBKZtGaUbMGH0CTeSS50gS0QCDiSqOnkUkdAslAyQSffTSXbvfPytIW2dqWLsGVlZdPmpKJpGjo7O5FIJJyiOZ14ZBqq8PLLL2Pnzp3OyfCqq67CueeeO6nvrY9//OO4/fbbce211+Lcc8/Fgw8+iHnz5mHx4sWora3Fjh07sHv3blx22WVob29Hc3Mzli1bNqZrMWOcmzf2YXuTjDNnzjjV4ebmZocaIFnSWHe3kXDixAmIogjDMJwOqMbGRqegB+QWnFVVRU9Pj6PVbmpqmpTx9LnCe2SVJCmtwBYIBFBXV4eysrIpxz17QfPlZFjCRK3Za5hEZGVA/tausVjM1UhTLKvOfECfLgVBQEtLS06UzNtvv41Nmzahv78f73vf+1BWVoajR4/iQx/6EP7pn/5pElY+jOeffx6PPPIIurq6sHz5cmzduhXz588HALz66qvYvn07Tp8+jaVLl9I66bz/MDM+SJM3rzeL6+3tRTQaRSgUKuj1dF3HsWPHoOs6AoEAmpubnaJgrq3idDOKKIpobGyc8s0ogL3u7u5uDA4OOm5oqqo6gbuQTSSFBCnkDg4Oory8HM3NzQWtUeQKb9ZI/gPcx31CNwFAd3c34vF4mgJiKkNVVXR2diKZTDpa/tHeB4Zh4Cc/+QkefvhhrFq1Clu3bsWsWbMmacUFRd5BesbTHfX19ZPiKU18G6LRqJNBkl0116JgrpNRphosy3Kc9TJJ6nRdd1El2ZpIaKpkMtedqZBbDGTTwGeboQjYJ5aKigoEg7ZsjWXZKft+Ifc7EolAFMWcbQpOnjyJjRs34uTJk7j77ruxdu3aKfsaJwIzPkhnQ6Hc6rzOeI2NjZAkCclk0mm7zUXOFo/HnXmIhR6gOpEg/g8jSep4nkdFRYUrANJt25IkZQzcJGOciMAtSRK6urqgKArq6upyyuaKAW/glmUZHR0dUBQF5eXl4HkeiqKgs7Mzp+G3xQJZoyzLOXfCGoaBH//4x9i5cyfe97734YUXXkBLS8skrXjqYMYH6dFMlnKd+JAJpChIBt2SAEW4Z29xjQQdOmOUZRmRSMRpRsmnE6yYoCV1Y5noMlL3H8m6iZIFSDdKIh7T+YLWl5eVlaGtrW1aFNhoh71gMIi2tjZXfSJTB+DAwEDRAzctB/T7/ViwYEFOdZXjx49j06ZNOHXqFDZt2oRPfOITRd9oioUZz0kTI3IvJEnC8ePHsXjx4rw/pGQUEvGuHako6A08kiQ5gYe0bwuCgPr6+ilvZA+ke1Y0NTVNmKSOBG6aKpFl2Zk+k4kqyXb/vF2OTU1N06LABgwnA+Skluv7JJO3NOkPmAxrV1mW0dnZCUVRclb36LqOH/3oR3jkkUewevVqbNmyBU1NTQVb0xRAqXDohWmaTjZLQ1VVvPnmm1i0aFHO9p1EO0u8JsZaFIxGo+jv73eE/pqmOR8cb3GIHh9VTNCTRkzTdBlATfY6vFRJpsBDUyWk/V6SJEcGORWpDS/o1ujKyko0NTWNW3pJ7p934yMJRqaMO997ZVmWU58JBoNoaWnJKRE6fvw47rnnHpw+fRp33XUXPvaxj02J936BUSoc5op8PKXpoiDpwydqi3yKgkNDQ4hEIq4gR2YX0h8cSZKcoyqp6tNUSaEbIEZDoV3qxoPRrEkzeUoDNi/e0NCA8vLyKf/Bpx0Rve+38YK+f9mGAozH2pU002ialrOvtq7reOyxx9De3o73v//9eOSRR2Za9jwuzPhMmhz5Mj1++PBhtLa2Zp3kkKkoSNuH5po9J5NJdHd3Q5Zl1NTUoL6+ftQgR3OMdNYDpHtJk8BdaHj9QZqbm6f80ADArcEFbN8EopKY6icWehJ6MbP+kagmID1wi6Lo2BWUlZWhpaUlp9rKW2+9hY0bN+Ldd9/Fhg0b8NGPfnRK/B0mEKVMOlcwDDOiDC9bUZAOzqO9mVRVRSQSQSwWc4pUuTaj0IGkuroagFuOJUlSmpc0HbTH47NBS9PINPLpwt+SeoEkSc7fjdwHL0dLn1jI/aaLk5MZuGmunxTYirkh0p4bI5kl0daugE2XlJWVQVVVsCyb9T2oaRp++MMfYteuXbj00kvR3t6OxsbGSXlt0w1nbSYNAOFw2JEDEXiLgmS2Xj6dgpPZjEI612iqJFu7di7NI7SkbipL07wgXD9xFsw166cDN5010lQTfQ9zGVuWL2gTp2Jx/WOBaZqOwb7f70cwGHTuJe1yRycNlmUhEolg06ZN6OzsxN13341rrrlmWrzeAqGUSXsx0h+fns7iLQq2tbXB7/fnZR9ajGaUbJakdMChrSG9hTUiZRuvpK5YoAualmWhpaUlL5VMtsGttJyNmEx5Aze5h2MN3HSHZr5G/MVGIpFAZ2cnTNPMeNLyZtz9/f149NFH8dJLL0EURVRXV+NTn/oUVq9efTYF6DFhxgdpILNdKWAHONISPN6iIMlAp0IzCsdxLj9kwN31J0mSo0Emo8R0XbcnRE+xIaojgR54UEi/5GyG9jTVRHf+eYu7owXuiTLinwzQE15GUpx4PbnD4TA6OjqwZMkSLFq0CIZhYPfu3ViyZAmuvvrqyX4Z0woznu4AbG7Y+zoty8KxY8cc7sw7UzDXoqC3GaXQ3tQTBdM0nazfNE0IggDDMFyFNZrjnohj/lhBN3b4/X5HCjnZIIHbW1wDsrvbaZrmGPFncn2byojH4+js7AQAx8hpNGiahl27duGHP/whLr/8cmzatMlFL56FKOmkM4HokAmIaxgZZd/W1ubKtscyGaWpqWlaDCIFskvqRuNnvYXJyZYCWpblFHQty0JDQ8OUy/q9XhuSJDnuduQ9xnEcamtrUVVVNen3cCygaZmqqio0NTXldGI5evQo7rnnHvT29mLjxo34+7//+0lY7ZRHKUhnAgnSdFGQ8I+yLKOxsTHnyRneySiNjY3TRvlAbyzBYBBNTU2jFte82SIddDiOyxi4JwL0KKhia7XzBeFvNU1z6hxeW1IvVTJVQMz4GYZBS0tLTgVwVVXR3t6Oxx57DGvWrMHGjRsndHL3NEMpSGcCGWNPghOp/BNeMJu/Bu0P4W1Gqa+vd5pRpjq8krrxtkSTbJEO3ERBU8iRW+RadBt6rr7DUwFeI/7m5manGOu9h14/afr+TZQOfiTouu4MSc6H7z98+DA2bdqEvr4+bNy4ER/60IcmYbX548CBA/jc5z6HP/3pTwCAwcFBfP3rX8err76KiooKfP7zn8f1118/EZcuqTsygXjXeouCxJmN9tegHdlI5V8QBMiyDE3TpmUWV2hJXSZLzZFGbmUzlxoNhNqYTpNdCEgCYFlWRvVDNltSb9dfptFbE3lqoYua2QbBZoKqqnjkkUfwox/9CB/60IewYcOGKZk9W5aFZ599Fvfdd59r07n77rsRDAaxd+9ehMNh3HzzzVi5ciWWLFlSxNXaOCsyadrbIZeiIGmTjcfj6Ovrc3l/eLnZYmQ5uYBupKmoqHBMoCYTI5lL0a52XnMkWg5YVVWFxsbGKXmPM4EUBgtlxE8HbnIfyamFbmCi5/8VYu35FDUPHjyITZs2YXBwEJs2bcJVV1015jVMNHbu3IkXX3wRH/3oR7Fr1y7s27cPiUQCF154IV566SVniO2WLVsA2MG7wChl0l5YloWbb74Zfr8fK1aswMqVK7F8+fIRK9PEZrS/vx+iKKK1tRXBYNB1PKWHZJIPCx10ikWDeOmBYg5+9cqwMrUaE48NoigBbP+H6TS0FnBTSjzPY968eWOeDk0jmw6efi/Sk7YJ3URn3aNtErRXCM/zOU8XVxTFyZ6vvvpqbNiwATU1NeN7wROM6667DuvWrcNrr73mPHbq1CnwPO+aMr5gwQLs3r27GEtMw4wP0gzD4LOf/Sz+8Ic/4JVXXkF7ezt0Xcf8+fOxfPlyJ3AvXrwYlmXh+PHjzpu6ubnZ1Rjh1c7S3X7eIz7dNDKajWYh4OXMpyI9kK3VWNM0DAwMoL+/31HhaJqGM2fO5KU/LhZoS85cDe3HAzKA1Ru4vV7S9IT3bHUCehBsPl4h+/fvx6ZNmxCPx/Ef//EfuPLKKyfmxRYYmVrPk8lkWgHd7/c7cspiY8YHaQC44oorcMUVVwCwP1BHjx7FgQMHsH//fvz0pz/F6dOnwXEcKisrIQgC7rnnHsyePXvUzrVMWY63aYQEzYnUHtN+FdONMyeKk6GhIVRUVDjNEXTjSCKRcE4tk2UulQvotuhgMJizof1EINuU8mx1AkEQwLIsVFXNK/OXZRkPP/wwfvKTn+Caa67BXXfd5XjLTFcEAoG0gCzLckFOQoXA9PgkFxB+vx/nn38+zj//fOexLVu24IknnkBTUxOampqwYcMGp6OKzraXL18+ajHEOyqKtiGlM26ilx1PwPFK6optypMPyMSOaDQKnufTqI2xmkvlesQfL2gj/nxb0ScL2QI3uXeKooBlWWiahlOnTqV5vfh8Ptd9fP3117Fp0yYkk0l873vfcxKf6Y558+ZB13V0dHQ4w21PnjyJRYsWFXllNs6KwuFoOHz4MABg+fLlAOwAcvr0aezfvx/79+/HgQMHcPToUaiqitmzZ7sCdygUylsSZllWWjGIyK/oo2k2U6RCS+omG8lkEl1dXVBVFfX19aitrR0Thz+SuRRt7JOruVQuoI34p1tRkx5l5fP5MGvWLPh8vjSfDUmSHK+XU6dO4eWXX4au6/jjH/+ID3/4w7jnnnucPoPpin379uELX/gC9u3bBwD4t3/7N4iiiK1bt+Ktt97CzTffjPb2dpx77rmFvnRJJz1RIJNcCE1y4MABnDhxAhzH4ZxzznEF7vnz5+edyXmPpvQHhVZCAHDsIaeTSx0AxydlcHAQ5eXlaGpqKrjixGsu5b2P3qktud472qOa4zi0tLRMm6ImYBf5yADbhoYG1NbWjripk8D9+9//Ho8//jjeeecdJ/O+4YYb8NWvfnUSV194eIP0wMAANm7ciD//+c8IBoNYv3491q5dOxGXLgXpyUQsFsOhQ4dcGXc0GkVZWRmWLl3qBO0VK1aMySuXnjaSTCYhSZLzPWINOV4ntskAnflzHOdk/pMFb50g05xEOnB77yOZdD3dxm8B9r3v7e1FNBqF3+/HrFmzctoYJUnC9773PTz55JP4+Mc/jjvvvBOKouDw4cNoamrC0qVLJ2H1MxKlIF1MWJaFrq4uHDhwAAcOHMDrr7+Ow4cPQ5IkNDY2urLtZcuW5ZSJETOhvr4+CILgKAdItq0oisNvT1aLdj6QJMnxSZkqmX+mcVu0lp7mZInN5nSaTEMgyzI6Ojqgqmpeap///d//xebNm6GqKrZu3YpLL710ElZ71qAUpKcaDMPAsWPHXDTJW2+9Bcuy0NbW5grcCxcudHwbaEmdZVlOG7r3QzZaizbNbReKl80FdFHT2xI9FeE1l0okEs59ZBgmTQc/lY3R1GJCAAARuklEQVSRaJfAfO69JEl46KGH8PTTT+O6667DHXfcMW0sVKcRSkF6OiCZTOLIkSMOTXLw4EF0dHTA7/djyZIlmDNnDt5++21ceumluOaaa/KW1BF+m2Tb9KQMwm+PdLwfD+jBBwzDTLuippc3r6mpcWXdxTCXygeSJKGjowO6rqOpqSln1clf/vIXbN68GbquY+vWrfjABz4wCasdOx599FE8+OCDLjOqXbt2YdWqVUVcVU4oBenpimg0iv379+P73/++w/uxLAtZltNkgGOprHunkZPjfSGnkdN67enI3dJG/Nn8kifTXCof0Jrt8vJyNDc35+Sml0wm8d3vfhc/+9nPsHbtWtxxxx0TNuqtkPjyl7+MZcuW4aabbir2UvJFKUhPZ0iShC996Uv42Mc+hiuvvBKnTp1y0SRvvPEGdF1Ha2trmgwwXyqBHO+9gRsYzhLpwD1SsKHd3ojLYLGaOsYC2gZ1LEb8XmUOMeMC3OZSE0U50aOsmpqaUFlZmdMmu2/fPmzevBkAsHXrVrz//e8v6LomEqQNffXq1cVeSr4oBemZDFVVcfToUSdoHzhwwPEdCIVCrsDd2tqadzCgs0SvmQ9pdPC2uQ8ODiISiYBhGDQ2NuYcIKYCaOWDz+cr6ISXsZpL5QN6c6yoqEBzc3NOlEsikcB3v/tdPPPMM/jkJz+Jr3zlK9MieyaQJAkXXHABLr30Uhw8eBCVlZW46aabJkoyV2iUgvTZhoGBARw8eNCVcZMP7fLly7F8+XJHBjiWsUW07pgEbxJsiKtgWVkZ6uvrEQgEpk2AliQJnZ2dUFU1J93weJHJXEqSJJeihKZKRFEccT1klJVlWWhubna8UEbDq6++is2bN4NlWWzbtg0XX3xxoV7ipOH06dO48847cfPNN+Piiy/GgQMHsG7dOnz729/GBz/4wWIvbzSUgvTZDsuy8O677zoBe//+/Thy5AgURUFzczNWrFjhZNtLly7NO3OkC2s8zzs+G5kGshJ/kqkEOvvMh7udCNCWAXTWPdJUctM0xzTKKh6P48EHH8Rzzz2Hf/zHf8Ttt98+rZpxRsOWLVugaZpD30xhlIJ0CenQNA3Hjh3D66+/7tAkx48fB8uyWLhwoYsmaWtry/ihtywLsVjMMbJvbGx0lAPeSdq0CoL21SD/FmOKOr1+AFNWdeK9l/RwW5ZlnTmcdXV1qKmpyYne2Lt3L7Zs2QKe57Ft2zZcdNFFE/oaJhqHDx/G//zP/+CWW25xHtuwYQP8fj82bNhQxJXlhFKQLiE3xONxHDp0yEWTRCIRBAIBp1uSBO5YLIYzZ86gubk551FKXrN62ldjpDFlE4FCG/FPNujCJikQ08b/3tMLeW2xWAwPPPAAfvGLX+DTn/40br/99inj7DYenDx5Etdeey3uv/9+XHXVVdi3bx8+97nP4YknnnD8d6YwSkG6hLGju7vbFbQPHjyIZDIJlmVx4YUX4oMf/CAWLFgw6tCEbMhWTCPt2bSiZDRONheQdvRIJAJRFNHc3DytghTJ/ru6usCyrMsvZCRzqUcffRSJRAJvvvkmBEHAtm3bZlzX4J49e/DAAw/g9OnTaGpqwhe/+MUpO0/Rg1KQLqFwuOWWW/DXv/4VV155JQRBwMGDB/Hmm2/CMAzMnz/f0W2vWLECixcvzpvb9bZneznZ8Ywpm2wj/kKDHiFWU1ODxsbGUdU6hmGgr68PDz74IN544w10dXUhmUyC53k89dRTWLly5SStvoQRUArSJRQOJ0+eRHV1tWskkizLTrckybrfffddiKKIUCjkoknmzJmTd2AknCydIXr57ZGaRbxG/C0tLVO6Hd0L7yirlpaWnLP/P/7xj9i6dSsCgQC2b9+OVatWoaenB8ePH8d55503rXxHZjBKQbqEyUdfXx8OHjzoFCYPHjzoqA9Ipk3+G8sMPO+YMrpZhHaxI7pny7LyauqYKhjrKKuhoSHs2LEDv/71r/GZz3wG//7v/14wvXcJBUcpSJdQfFiWhXfeecfVdEOGJsyZM8cVuJcsWTKmDI/WHBMbV/JeJjauhR5TNlGgvaoFQUBLS0vOQfaVV17Btm3bUF5eju3bt+OCCy6Y4NWWME6UgnQJUxOqqiIcDrtokrfffhs8z2PRokUufnvBggU5ZZBeI/76+nowDJOmOZ5KcxG9UFUVnZ2dSCaTqK+vd17DaBgcHMS3vvUtvPjii/jsZz+L2267bVrQGUeOHME999yDY8eOYd68efjGN76B8847r9jLmkyUgrQXW7duhSAI+NrXvuY8tnfvXmzfvh1nzpzBsmXLsG3bNixYsKCIqzw7MTQ0lDY0obe3F+Xl5a6hCcuXL08bmpCLEf94x5RNJGjlic/nQ0tLS85BlmTPFRUVuPfee13zOqcyFEXBmjVrsG7dOlx//fV4/vnn8eCDD2LPnj3Tqm4wTpSCNEF/fz+++c1v4uc//zluvPFGJ0hHo1FcddVV2LFjBy655BK0t7djz549eO6554q84hIsy0JnZ6dLBnjo0CHIsoympiYsX74cS5YsQWdnJ4LBINauXYuWlpa8zJxyHVM2Hk+N0UA2GFmW82pJHxgYwP3334+XXnoJN954I77whS9MKyOr3//+99i4cSNeeeUV57GPfOQjWL9+Pf7u7/6ueAubXOT9hpoaZ74JwKc//Wm8973vTfvj7969G0uXLsXll18OALj11lvx+OOP49ChQ1ixYkUxllpCCgzDYNasWZg1a5ajedV1HceOHcP+/fuxZ88e7Nq1CwCwdOlSvPbaa1i2bJlraMJoNEamCdreKS1DQ0NpU1oKMabMO8pqwYIFOQfZ3/3ud7j33ntRXV2Np556aiIGpE44Tp48iYULF7oeW7BgAd56662zKUjnjWkbpHVdRzKZTHucZVmUl5fjscceQ1NTE+644w7X90+cOOF6o3Ach7lz5+LYsWOlID0FwfM8lixZgiVLluDVV1/FmjVrcNttt6Gnp8ehSf7zP/8TXV1dztAEQpGsXLkSLS0towZVQRAgCILToOOd0pJMJtHf3z+uMWW0bjufUVbkRPjb3/4WN910E9avXz+tsmcayWQyrSDq9/udtvcSMmPaBunXXnsNN9xwQ9rjs2fPxp49e9DU1JTx9yRJSrNlDAQCriGvJUxNPPDAA87/z58/HxdeeKHzdSQSwcGDBx2a5Oc//zni8Thqa2tdToDLly8f1TGOdED6fD5nwALht+lsOxqNAhh5TJllWYhGo4hGowgGg2hra8uZf/3tb3+Le++9F7W1tXjqqafwnve8J6/7NdUQCATSArIsy9OqC7QYmLZBevXq1QiHw3n/XqY3iiRJpTfKNEdjYyOuuOIKXHHFFQBsbfXJkycdfvv3v/892tvboes65s2b5zKVWrx48aiBk55zSOAdU9bb2+vitwVBcCaTNzU15Zw99/X14b777sOePXvwL//yL1i/fv2MKKy1tbXhiSeecD128uRJXHPNNUVa0fTAtA3SY0VbWxt+85vfOF8bhoF33nkHixYtKuKqSig0iMPfwoUL8fGPfxyAXbAjQxP279+Pp556Cvfffz8EQcg4NGG0gJqN304mk+jr60M8Hncej0QiiMViaW3u3mvs3r0b9957LxoaGvBf//VfM4qCu/jii6GqKn784x/jU5/6FJ5//nlEo1FccsklxV7alMZZF6TXrFmDHTt2YPfu3bjsssvQ3t6O5uZmLFu2bFKu/+EPfxhnzpxxjsOzZs3Cr3/960m59tkOn8+H8847z6XL7e/vd9Eku3fvdg1NIEF7xYoVqK2tHfUamqYhGo1C13XMmjULFRUVLs9oEsCB4TFlf/7zn1FWVobdu3dj7969uOWWW3DrrbfOiOyZhiiK2LVrFzZt2oTvfOc7mDdvHnbu3Fk6xY6CGSvBI7jjjjtQU1Pj0km/+uqr2L59O06fPo2lS5dOmk5almW8973vxZ/+9KecPvAlTD4sy8KZM2dc2u2jR49CURTMmjXLFbiXLFni0B+maSISieQ0yooeUxaLxfDFL34RJ0+eBGBv2hdddBHuvPPOnKetlDCtUNJJT2UcOHAA69evxx/+8IdiL6WEPKBpGt58800cOHAAr7/+Og4ePIgTJ06AZVksWrQIs2fPRjgcxqc//WlcffXVqK6uzul5o9Eo7r33XvzhD3/AjTfeiAsuuABHjx7FqVOn8JWvfGVM485KmPIoBeliYyRp4AsvvID29nY0NDTg1KlTWLZsGe6666407WgJUx+xWAwHDx7EAw88gAMHDmDevHno7e2FaZpYtmyZS1HiVRpZloUXX3wR999/P1paWvDNb34TS5YsKdIrKWGSUQrSxcbevXuzSgNvueUW/PnPf8ZXvvIV1NfX4+GHH8YLL7yA//7v/54WvgsluKEoCr70pS/huuuuw+WXX46uri7HUOr111/H4cOHkUwm0dDQ4Mj/Wltb8cILL2Dv3r343Oc+h1tuuWXKzYEsYUJRCtLTCZZlYdWqVXj00Uenjf9CCbnDMAwcP37cRZOEw2G0tLRg586d0zJ7LhW+x41SW/hUxtNPP425c+di9erVAOwPsa7r07aDrISRwXEcFi9ejMWLF2Pt2rUA7OLxdD01ybKMkydPlgrfk4zJs/0qAZFIBNu2bXPMde677z60tbVNy4yqhLFhugZoAHjzzTdRX19fCtCTjFKQnkSsW7cOl1xyCa6//npcfPHFeOedd/D9739/Ui0yjxw5grVr1+K8887Dtddei9dff33Srl3C1Ieu6xgaGkr7Lx6P48iRI+B5Hp/85Cdx0UUX4cYbb8Tx48eLveQZjxInfRah5OdbwmgoFb4nHKXCYQnZUfLzLaGQKBW+x4S8g3SJ7jiLMJKfbwkljIann34ae/fudb4uFb4nB6UgfRah5OdbwnhQKnwXByUJ3lmEkp9vCePBunXrEI/Hcf311yORSODCCy+c9ML32YhSkD6LUPLzLWE8EAQBd955J+68885iL+WsQmkLPItA+/lqmoZnnnmm5OdbQglTHCV1x1mGN954A5s2bUI4HMa8efOwadMml7/yZOPRRx/Fgw8+6PKv2LVrF1atWlW0NZVQwgSiJMErYXrhy1/+MpYtW4abbrqp2EspoYTJQEmCV8L0wtGjR7F06dJiL6OEEqYsxppJl1DCuBEKhYIAhgC8COBCAP0AvhUOh39Q1IXNEIRCoe8C0MLh8O3UY1cCeBDAAgB/BXBTOBx+s0hLLCEHlDLpEoqJJgD/A2AngFYAtwD4TigU+vuirmqaIxQK1YVCoccAfMHzeBOA5wDcCaAGwG8BPDnpCywhL5Qy6RKmFEKh0H8AEMPh8L8Wey3TFaFQ6Cjsza8awNskkw6FQrcC+MdwOHxp6msOQBTAleFw+P8Va70ljIySTrqEoiEUCr0XwFXhcPg+6mE/gPT5YyU4CIVCPIDyDN8yw+HwEIArwuFwRyqbprEEwBHyRTgcNkKh0HEAywGUgvQURSlIl1BMxAFsDIVCx2Afw/8WwKcAfLCoq5r6uAzAyxkePwVgfjgc7sjye2WwawA0kgBKLadTGKUgXULREA6H3wyFQv8AYBuAxwGcAXBDOBz+azHWEwqF3gfgF+FweFbq6xoAPwBwOYBBAN8Ih8P/WYy10QiHw7/FGKRcsANywPNYEPZmWcIURSlIl1BUhMPhXwH4VTHXEAqFGAA3APgOAJ361i7YAawJwHsAvBgKhf4SDocPTP4qC4KjAK4nX6Q46UWgKJASph5K6o4SSgC+DuA22Bk9ACAUCpUD+BiAjeFwWA6Hw68B+CmAm4uzxILg5wBWhUKhT4RCIRHABtinl/8r7rJKGAmlIF1CCTalcR6Av1CPnQNbY3yCeiwMu8g2LREOh7sAXAtgI4BeAFcC+EQ4HC5JvKYwSnRHCWc9wuFwJwCEQiH64TIAkudHp1WRLRwOfzbDY/8fgHMnfzUljBWlTLqEEjKjVGQrYUqgFKRLKCEz3gIghEKhVuqxEEpFthImGaUgXUIJGRAOh2MAngdwbygUCoZCoQsBfBrAT4q7shLONvz/Hfm0ip7B81MAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "minplot3d(x, y, lambda x: df(x)[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now an **unconstrained optimization** can be performed as:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. (Exit mode 0)\n", " Current function value: -2.0\n", " Iterations: 4\n", " Function evaluations: 5\n", " Gradient evaluations: 4\n", " fun: -2.0\n", " jac: array([-0., -0.])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 5\n", " nit: 4\n", " njev: 4\n", " status: 0\n", " success: True\n", " x: array([2., 1.])\n", "Min at [2. 1.]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "res = opt.minimize(\n", " f, \n", " x0=[-1, 1],\n", " args=(-1.0,),\n", " jac=df,\n", " method='SLSQP', \n", " options={'disp': True}\n", ")\n", "print(res)\n", "print(\"Min at \", res.x)\n", "xmin, ymin = res.x\n", "minplot3d(x, y, f, xmin, ymin)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then constraints are defined as a sequence of dictionaries, with keys `type`, `fun` and `jac`. Reminder:\n", "\n", "$$\n", "x^3 = y \\Rightarrow x^3 - y = 0 \\\\\n", "y \\ge 1 \\Rightarrow y - 1 \\ge 0\n", "$$\n", "\n", "If we had a $<=$ inequality, we would have multiplied both sides by -1." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "cons = (\n", " dict(\n", " type='eq',\n", " fun=lambda v: np.array([v[0]**3 - v[1]]), # v[0] -> x, v[1] -> y\n", " jac=lambda v: np.array([3 * (v[0]**2), -1])\n", " ),\n", " dict(\n", " type='ineq',\n", " fun=lambda v: np.array([v[1] - 1]),\n", " jac=lambda v: np.array([0, 1])\n", " )\n", ")" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully. (Exit mode 0)\n", " Current function value: -1.0000001831052137\n", " Iterations: 9\n", " Function evaluations: 14\n", " Gradient evaluations: 9\n", " fun: -1.0000001831052137\n", " jac: array([-1.99999982, 1.99999982])\n", " message: 'Optimization terminated successfully.'\n", " nfev: 14\n", " nit: 9\n", " njev: 9\n", " status: 0\n", " success: True\n", " x: array([1.00000009, 1. ])\n", "\n", "Min at [1.00000009 1. ]\n", "2.746578582346615e-07\n", "0.0\n" ] } ], "source": [ "res = opt.minimize(\n", " f, \n", " x0=[-1, 1],\n", " args=(-1.0,),\n", " jac=df,\n", " constraints=cons,\n", " method='SLSQP', \n", " options={'disp': True}\n", ")\n", "print(res)\n", "print()\n", "print(\"Min at \", res.x)\n", "xmin, ymin = res.x\n", "print(xmin**3 - ymin)\n", "print(ymin - 1)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "minplot3d(x, y, f, xmin, ymin)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise\n", "\n", "Minimize the Rosenbrock function:\n", "$$\n", "f(x) = \\sum_{i=1}^{N-1}{100(x_i - x_{i-1}^2)^2 + (1-x_{i-1})^2}\n", "$$\n", "defined in `opt.rosen` as a function that accepts an array `x`.\n", "\n", "Use how many dimensions you want (determined by the initial guess), use the function `opt.minimize` with `method` set to either `nelder-mead` or `powell`.\n", "\n", "The result should be an array of `1`s. If you get something close but not quite, you can change the tolerance by giving `opt.minimize` the argument `options={'xtol':tol}`, where `tol` is the error tolerance you want." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# References\n", "\n", "- [`scipy.optimize` tutorial](http://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html#univariate-function-minimizers-minimize-scalar)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Colophon\n", "This notebook was written by [Yoav Ram](http://python.yoavram.com) and is part of the [_Python for Engineers_](https://github.com/yoavram/Py4Eng) course.\n", "\n", "The notebook was written using [Python](http://python.org/) 3.6.1.\n", "Dependencies listed in [environment.yml](../environment.yml), full versions in [environment_full.yml](../environment_full.yml).\n", "\n", "This work is licensed under a CC BY-NC-SA 4.0 International License.\n", "\n", "![Python logo](https://www.python.org/static/community_logos/python-logo.png)" ] } ], "metadata": { "kernelspec": { "display_name": "Python [conda env:Py4Eng]", "language": "python", "name": "conda-env-Py4Eng-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 1 }