{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## TP noté 2026." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import solve_ivp # solveur EDO de Python (initial value problem)\n", "from matplotlib import pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code du schéma du point milieu implicite" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def milimp(f,t0,tfinal,y0,h):\n", " \"methode du point milieu implicite\" \n", " #initialisation\n", " t=np.arange(t0,tfinal+h,h)\n", " N=len(t)\n", " yapp=np.zeros(N)\n", " yapp[0]=y0\n", "# code la methode du point milieu implicite pour le pas h\n", " for n in range(N-1):\n", " y=yapp[n]\n", " #initialisation avec Euler\n", " z=y +h* fun(t[n],y)\n", " # iterations de point fixe\n", " for i in range(3):\n", " z = y + h*(fun(t[n] + h/2,y + h/2*fun(t[n]+h,z)))\n", " yapp[n+1]=z\n", " return t,yapp\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Codage du schéma du point milieu explicite" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def milex(f,t0,tfinal,y0,h):\n", " \"methode du point milieu explicite\" \n", " #initialisation\n", " t=np.arange(t0,tfinal+h,h)\n", " N=len(t)\n", " yapp=np.zeros(N)\n", " yapp[0]=y0\n", "# code la methode du point milieu pour le pas h\n", " for n in range(N-1):\n", " y=yapp[n]\n", " yapp[n+1] = y + h*(fun(t[n] + h/2,y + h/2*fun(t[n],y)))\n", " return t,yapp\n", " " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def fun(t, y): \n", " return y**2 - y**3" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "t0, tfinal = 0, 2000\n", "y0 = 0.001" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "h=1\n", "timp,yapp = milimp(fun,t0,tfinal,y0,h)\n", "tex,zapp = milex(fun,t0,tfinal,y0,h)\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "#solveur basé sur schéma de Scipy\n", "sol = solve_ivp(fun, [t0, tfinal], [y0], 'Radau')" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(sol.t, sol.y.T, '-xb')\n", "# il faut transposer y pour qu'il ait le meme format que t \n", "plt.plot(timp,yapp,'-k')\n", "plt.plot(tex, zapp,'-r')\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n", "plt.legend(['Radau','point milieu implicite', 'point milieu explicite'], shadow=True)\n", "plt.title('Comparaison de méthodes de résolution d\\'EDO pas $h=1$')\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "h=2\n", "timp,yapp = milimp(fun,t0,tfinal,y0,h)\n", "tex,zapp = milex(fun,t0,tfinal,y0,h)\n", "plt.plot(sol.t, sol.y.T, '-xb')\n", "# il faut transposer y pour qu'il ait le meme format que t \n", "plt.plot(timp,yapp,'-k')\n", "plt.plot(tex, zapp,'-r')\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n", "plt.legend(['Radau','point milieu implicite', 'point milieu explicite'], shadow=True)\n", "plt.title('Comparaison de méthodes de résolution d\\'EDO pas $h=2$')\n", "plt.grid()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour $h=2$ la méthode implicite donne des résultats aberrants. L'algorithme de point fixe ne converge pas car $h$ n'est pas assez petit pour que l'itération soit contractante." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Codage des caractéristiques" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = lambda x: (0)*(x<0) + x*(0=1)\n", "x=np.linspace(-3,3,100)\n", "plt.plot(x, f(x),'-b', label='f(x)')\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)')\n", "plt.title('donnee initialef(x)')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "def caracdroit(x_0,t,f):\n", " \"calcule la caracteristique droite a partir de x_0, t et f\"\n", " return x_0 + t*f(x_0)" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t=np.linspace(0,2,100)\n", "for x_0 in np.linspace(-3,3,50):\n", " x= caracdroit(x_0,t,f) \n", " plt.plot(x,t,'-r')\n", "plt.xlabel('x')\n", "plt.ylabel('t')\n", "plt.title('caracteristiques de f(x)')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_0 = np.linspace(-3,3,200)\n", "x1= caracdroit(x_0,1,f)\n", "x2= caracdroit(x_0,2,f) \n", "plt.plot(x1, f(x_0),'-b', label='t=1')\n", "plt.plot(x2, f(x_0),'-r', label='t=2')\n", "plt.plot(x_0, f(x_0),'-k', label='t=0')\n", "plt.xlabel('x')\n", "plt.ylabel('u(x,.)')\n", "plt.title('solution u(.,t) a differents temps')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "g = lambda x: (1)*(x<0) + (1-x)*(0=1)\n", "x=np.linspace(-3,3,200)\n", "plt.plot(x, g(x),'-b', label='g(x)')\n", "plt.xlabel('x')\n", "plt.ylabel('g(x)')\n", "plt.title('donnee initiale g(x)')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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ioYceEl26dBGnT5++5bl27Zpo3bq1yJIliwgLCxMAIA4fPiyEcL+Ta/fu3aJGjRoiZcqUImPGjKJVq1Zi3rx58e4Ci4uLEx9//LF46KGHRMqUKUWZMmXEihUr4t0FZvq1L1y4UDz11FMie/bsIioqStx3332iTp06Yu3ata7fC1Xnzp0Tr776qrjnnntE6tSpRY0aNcTevXvjfb+EwPfDq6++KrJnzy4iIyNFlixZRMWKFUX//v0TPM7Zs2dFy5YtfY6zceNG17vQKleuLOrUqXPrz7GxsaJq1aoia9as4sSJEz7eTz75RACAmDNnzq3nLl68KFKnTi2GDBmSYF1WVrdTNgrDysoq2WrVqlXw+OOPw8qVK+PNV0rumjJlCrzyyiuwbt06n4nNs2bNgsaNG8ORI0cge/bsfr/uuHHjoFOnTnDs2DG7AmR1R2W3wKysrKySuaZOnQp///03FC1aFFKkSAEbN26ETz75BKpUqRIvruK5556DRx99FAYOHAiff/65X8eJjY2FwYMHQ8+ePW3zY3XHZRsgKysrq2SudOnSwbRp06B///5w6dIlyJYtG7Ro0QL69+8fzxsWFgZjx46F+fPnQ1xcnA8jlJCOHTsGTZo0gW7dugWzfCurRMlugVlZWVlZWVklO9nb4K2srKysrKySnWwDZGVlZWVlZZXsZBsgKysrKysrq2QnC0G7KC4uDo4fPw7p0qUzHt1vZWVlZWVldWclhICLFy/CAw88kCCgbxsgFx0/fhxy5sx5p8uwsrKysrKySoSOHTuWYPC0bYBclC5dOgDAb2D69OnvcDVWVlZWVlZWJrpw4QLkzJnz1nlcJ9sAuYi2vdKnT28bICsrKysrqxCTCb5iIWgrKysrKyurZCfbAFlZWVlZWVklO9kGyMrKysrKyirZyTZAVlZWVlZWVslOtgGysrKysrKySnayDZCVlZWVlZVVspNtgKysrKysrKySnWwDZGVlZWVlZZXsZBsgKysrKysrq2Qn2wBZWVlZWVlZJTvd0QZo4MCB8Oijj0K6dOngvvvug/r168O+ffsS/HerV6+G0qVLQ8qUKeGhhx6C0aNHx/PMmjULHnnkEYiOjoZHHnkE5syZczu+BCsrKysrK6sQ1B1tgFavXg3t27eHjRs3wrJlyyA2NhZq1qwJly5dYv/N4cOHoU6dOlC5cmXYunUrvPvuu9CxY0eYNWvWLc+GDRugcePG0LRpU/j999+hadOm0KhRI9i0aVNSfFlWVlZWVlZWXpfwkP755x8BAGL16tWsp3v37qJgwYI+z7Vp00aUL1/+1p8bNWokateu7eOpVauWePHFF43qOH/+vAAAcf78eT+qt7K6g/rtNyFOndJ7Dh0SYu9evefiRSHWrhUiLk7vW7pUiNhYvWfNGiFiYvSeLVuEOHlS7zl8WIg9e/SemBg8XkJ1L1smxI0bes/atQnXvXWrECdO6D1//inE7t16z+XLQqxeHby6L17Ue7ZtS7juI0eE2LXL97m4OPyexMTg748fF2LqVCHOnuV9MTFCjB8vxOnT+teaMEGIv//We2bNEmLHDr3n55/xfemU6jt+XIjRo4W4eVP/Wp9+KsSlS3rPl18mXLebTDzBfK2k9AT7tRIhf87fnmqADhw4IABA7HC+0RVVrlxZdOzY0ee52bNni4iICHH9+nUhhBA5c+YUQ4cO9fEMHTpU5MqVy/U1r169Ks6fP3/rcezYMdsAWYWO4uKEKFJEiOhoIRYv5n3NmwsBIMTHH/OeESPQ89JLvGf9evQUKiTE/z9z8XT2rBBp0giRMSM2XlzdxYph3T/8wB+vZUs83qBBvGfUKPQ0asR7Nm1CT4ECfN3//SdE2rRC3HuvEAcO8HWXKCFEVJQQCxbwx2vdGo/30Ue8Z/Ro9DRsyHs2b0ZP/vxCXLvm7jl/Xoj06YW45x4h9u/n6y5dGuueO5c/Xps2eLx+/eRzMTH4HAD+/rnn8PfOn6mqj/5PIiOFuHrV3XPokPz9+vXunosXhUidGn//7rt8TY88gr+vVo2v6ZVX8NesWXnPd9/hr+Hh+H118xw8KH8/fz5fk5tMPMF8raT0BPu1EiF/GiDPQNBCCOjatStUqlQJihQpwvpOnjwJWbNm9Xkua9asEBsbC6dPn9Z6Tp486fqaAwcOhAwZMtx65MyZM8CvxsoqCbV0KcDOnQCRkQDly7t7jh8HmDIFf1+1qrvn5k2Azz7D31eqxB9vyBD8tXx5PKabxowBuHQJIEcOgNy53T3LlwNs3w4QEQFQoYK75+RJgMmT8fdVqrh74uIAhg0LTt1jxwLExAA88ABA3rzunlWrALZtAwgP5+s+dQpg4sSE6x461LzucuUAoqLcPV9/DXDhAkC2bHzda9cC/PYbQIoUABUruntOnwb49tuE616zBn+fPTtfN/2/3XMPQHS0u2fkSPw1RQqAsmXdPatXA1y+jL9v2NDdc+YMwJ49+Psnn+RrmjcPfy1RgvcMGIC/3n8/QPr07p533sFfIyMBatfmX8vK2wpq6xWA2rVrJx588EFx7NgxrS9//vxiwIABPs/9/PPPAgDEif8v7UZGRoopU6b4eCZNmiSio6NdX9OuAFmFtGrWxCupTp14z7vvoqdSJd4zaxZ6Mmbkr8oOHhQiRQr0cSu1164J8cAD6JkwgT/eU0+h5803ec9776GnQgXeM3cueu65h98COnxY1r1tm7vn+nUhcuRAz7hx/PHq1kVPu3a8p3dv9JQtyy/xL1iAnvTphbhwwd1z9CiuRADgdqGbbtzAlRgAIcaO5Wt65hn0tGnDe/r1Q0/p0r51q1fss2fL33fo4PvvVV9YGP76xBO8J3Nm/PXBB3lPpUr4a8qUfE2dO8vf//cf/1r0+PnnhD3OlVLVExmJvz73HO/xykqKXQFi5YkGqEOHDiJHjhziELdUruh2bIE5ZRkgq5DR9u34QyRFCn6rKSYGmxo6eXF67LH42wxOdeyInpo1eQ9tIWTLxm/Z7NolT5J//OHuuXRJiEyZ0DdjBn+8KlXQ06MH7+nSBT1PPsl7Jk+W2yPqlo2qPXtk3dxW0+XLQmTJgr5p0/jjVauGnrfe4j1vvYWexx/nPdOmoSdLFiGuXHH37N8vGxKOp7p6Fb92ACEcF5A+JyyqGwAbVM5n0iTRw7l16eZxNu+qJ316/PWhh+J/Xc7XSp8+flPq9ERExH/vutXkvGD3YiNhGyBWd3QLTAgBHTp0gNmzZ8OKFSsgT548Cf6bChUqwLJly3yeW7p0KZQpUwYi/7+szXkqcsu+VlahKtr6adgQgPv8TJgAcPYsbo0884y7Z9MmgHXrcIulQwd3z7lzAOPG4e+7dXP3CCG3dTp04LdsqO4GDfgtm+++w62NPHnQ56bNm3E7JiKCr/v8edwiSqhu2mrq0IHfsqEtwqefBsif390zaRLAv/8CPPggv2WzZQtupUVEAHTs6O65eBHgq6/M627fHiBlSnffsGHorVcPoGBBd8/kybh1lyMHwPPPu3sAsO6wMPx9qlS8j+TAEVxVqFDCHm7rFgC3/wD494mqhg1l/ZyefJJ/75KKF8fvlVXoKqitl59q27atyJAhg1i1apU4ceLErcfly5dveXr06CGaNm1668+HDh0SqVOnFl26dBG7d+8W48aNE5GRkWLmzJm3POvWrRPh4eFi0KBBYs+ePWLQoEEiIiJCbNy40aguuwJkFRI6cQKBVgAhNmxw98TGCpEvH3pGjuRfq1Ej9DRvznsGD0ZPkSL8ts7y5ehJnVqIM2fcPSdPIvjsthVBunlTiIcfRs9nn/E1vfQSepSfEfH06afoeeQRvu5Vq9CTKpUQ//7r7vnnH9yGAcA7t7i6CxZEz5AhfE0E4+pg82HD0FOgQPy7lkhr16InOpq/C/D0afy6AIRYscLdExcnROHC6Pnkk/h/71z9oC23YcN4Hx3zq6/0rwWAq28JeebMSdizZEnCta9albBHBbI5z48/6j1eWUmxK0Cs7mgDBACuj/Hjx9/yNG/eXFStWtXn361atUqULFlSREVFidy5c4svv/wy3mvPmDFDFChQQERGRoqCBQuKWbNmGddlGyCrkBDxMRUr8p45c9Bz7738DxqVj/n9d3fP9etCZM+Onm++4Y9HfEz79ryH+Jhy5fiGZP589GTIwPMxR45IPmbrVnePysd8/TVfE/Exb7zBe4iPKVOGr/uHH9CTLp3vHUSqjh3DLRYAIX79la87d270jBnD11S/Pnpee4339O+PnpIl+bqXLEFP2rRCnDsX/++dJ/+qVfHX0aN9fefPSw/xVOpdUs7Xoobyl1/0x0touwkAv6duDJh6x1b69O7jBC5ckJ4sWdy/T+rxsmSJ//dOj1caCdsAsbqjDZBXZRsgK89L5WOU1c94qlwZPT178h4CSHV8zKRJ6NHxMbt3oycsjL+F/PJlCb5On84fj06wb7/Ne7p1Q0/16rxn6lR5wuL4mH37JB/DzUm6ckWI++5Dj5OPUVW9Onq6duU93bujp0oV3vP99+jJnBm/Z246cEDWzc0bunpViPvvR8/EifzxatRAT+fO7n+vnrAqVJDg/bff+vqIowKQIPymTb6eHTviNzdOcPnsWd+/v+++hLmdxx5zr52+3wC48uYm4qgAhHjnHXfPtm3S07evu8eLjYRtgFjZBshFtgGy8ry+/BJ/eOTJww8k/OUXeWX811/unnPn8KofQIhFi9w9cXFClCqFHnU2jFOvvYaeZ5/lPV99hZ4HH+QH+9Hcm4gIvAvKTTT3BkCIhQv5usuUQU/v3nxNbduip1493vP113JVg5shtHUresLDcQiimy5exFUtAP0snvLl0fP++7ynQwf0PPUU7xk/Hj3Zs/NAugrSHz7s7jl1Sp6wpkyRjbUTTqe6AeSdUs7vBX2/daspY8f6ety+Rnp/08MJZAuBFwr33is9U6e6f32lS0uPcwgkiZo+gPgDIElebCRsA8TKNkAusg2Qlael8jHDh/O+F19Ej46P+eQT9Oj4mJUr0ZMQH0Ncz5o1fN3Exzju0vTRyy+j5+WXeQ/xMQUL8nzMmjXoMeVjVq5098TFySF7bnwMqWlT9DRuzHuGD0dP/vx83evWybq5KdlnzsjhgD/9xNddtCh6dEMkadDkCy/wnqFD5Qnr/HnZWKrN58aN8Vd2AHxX3s6elXVzKzdq3fRwawSbNfP1LF8e30MXCvRwex84Gym3E/K5c3KbONQaCdsAsbINkItsA2Tlaal8DDf3xoSPuX5diJw50aPjY55+Gj06PqZPH/Q8+mjCfEz69GZ8zG+/uXtu3MAVJIDg8TGlSvF1L16MHo6PEQIjEWjFw8mzkGJj8TZtACG++IKvqWFD9LRqxXsGDkRP8eJ83UuXoidNGn7FwhSkp7rphEUNoQpVE0ivPjJk8H0tAunVR4sWvh4C6dWHc7Xs1ClZNwD+3rlVqF4o6E62jRsn7OnaNWGPEN5sJGwDxMo2QC6yDZCVpxVsPua++3g+Zu9e+YNq3z53z5Urcu4Nt8UghH98jOPGBx+Z8DHq3JvbzccIgYwVgH7Q5MyZ6MmYMX7OFMnfQZNOBkdV7droCXTQJIH06gkrTx7fpkkF6dXHww/L11FBevXhjAohkF59OAHoDz7w/fvKlePXTRcK9D5wO9keORK/bqfnxg1sIm0DZBug5CDbAFl5Viofw01NV/kYLmNL5WM4oFMIXPUBwFUgTsRr5MrFcz0qH3PkiLvnwgXJxzjvHFLrLlcOPR98wNfUvj166tThPSofw3E9v/+OHh0fExMjORPnrdqqKlZET69evIcGTdaqxXtMBk3u3CnrPnjQ3eMvSK+esGhgIk3VpkGTjz/u61VBbwLpCSanh8oREUivPpwAtArS08ON/1EHNnInW7pQ0HmI/7INkG2AkoNsA2TlWREfw93NIoTkNQoVSpiPSZkS+R03/fuv5GPcZqcIgSemQoXQ8+mnfE3Ex7z4Iu8hPubhh834GI7rUfkYNy6E6ibOZPBgvqYWLdCj42M+/xw9+fLxQPqGDeiJiuLT2ClAFsA91ZzqLlECPY5IIB+1aoUeXcgq8TEPPWQG0qsnLGqw9+3DbcF06WQDqDYKNOFZBemdqzdqNMnrr+Nz9erJv3dOHR8zBp+n2+wBhFi2zNfz22+yAeQal/PnZd2cJy5ObhPTKmeoNRK2AWJlGyAX2QbIypNSc6FM+BjnADpVzz6LHh0f8+GH6NHxMYsWoSddOp6P+euvhOfexMbKbRWXuV63RCnkOj5mwAD0BMrHHD9uxsfkzYuezz/na3rhBfQ4eRdVxMcULcrX/dNP6Elo0CTVvW6du8dfkJ5+pRMW8U5Hj8pBk4ULI5OmNhO0/aaC9EeOuDcc6qDJH3+Uf6/elq6C9LRaBhD//1BNfeeaGxXs5pqb1avl8/R5CLVGwjZArGwD5CLbAFl5Um+/jT8wqlXjPdOno8eUj+Fyoa5ckSePSZP44z35JHq6dOE9PXqgx43TIBEfkykTz8f88Yesm7tV+do13BoC0PMxtWrJkyinXr3QE+igyUOH5ErE9u183cTHKINg46lOHfToBk3SCku5cryH+BhdgKwK0tMKFgA2uvT7Eyd8QXr1xAaAkLkQviC96smWTR5PBenVRkqdF7VwIT6XPj3fkKggPdXv9KkXCgAYbOv2WhUq4HORkdhYhmIjYRsgVrYBcpFtgKw8J5WPWbDA3RMXh+njAPq5N/TDvm5d3vPNN+jRzb2hwXAJzb255x706ebe0InGjeUgmcy9mTABPQ88wPMxNIhPx8fExMgAWd0UeUoqNxk0WaMG7yE+5v77gzdo8vvv+eMRSM8N/RNC8jFPPOF7wjpxQv6eOCoC6Z0N0NixEqQPC8MtM9VDTbEzQPaff6RHDZ0lkL5bN19YWj2JEkhPW7P0q+qjCwV6/PxzfM/+/fK5pk1Dt5EI1boTKdsABSjbAFl5Tp99hj8sAs2FUvkYXS5UkSLo+fhjvqbmzdGjm3szciR6dHzM+vXoMeVjnLyHWnexYugZOJCv6dVX0aPjY774Aj06PmbTJrk68Pff7p7//pODJt1yqqjukiV9V0zc1Lo1eurX5z2jR6Mnd26zQZOmIL16wjp0SP6eBggSSO9sgObPF6JNG/z9M8/E97Rsic85QXr1VnhaoVJB+kOH5AWBehJVLxQeewx/pZVT8qkgPQDe0q+uONFrEbcGgE1cqDYSoVp3ImUboABlGyArT0nNhXJmL6lq0AA9rVvzno8+Qk+JEjxnQvxF2rTxIwpIx49LDsQZdUBS58fo+Jjnn/c9Gbpp0CD06PiYZcvQkzq12dwbt8BLIbDBzJ8fPSNG8DXR/JhmzXgPDZosXJive8UK9KRKhYMZ3XTqlBw0uXYtX3eBAuhxhpSq8gekp0GT6gmLVqLo+6iC9M4GaOlSyfUQSK96PvrIHaSn75tbQ/Lii7KJc3roQiFfPtl4qhxPTIxc7aHt1IED45+Qz5yR22ilS8evO5QaiVCtO5GyDVCAsg2Qlac0Ywb+oNDxMWouFMfHqHNvvvuOPx7xMZ068R7iY3Rzb2bPRo8pH2My92bCBP54Tz2Fng4deM/776NHN/dm3jz06PiYP/+UfIl6F5MqddDkuHH88eiOp3bteA/xMWXL8o2UysdwAbJHj/o3aJJAevWERXdYUQP8+uvy3zobINpGK11a1q16pk+XgyZVkJ6aNDpBOkF6tUEiT2ysvFCg7dIHHvANOo2JkSA9NUHHjsU/IdP3G0Bu3YZqIxGqdSdStgEKULYBsvKUgpUL5S8fc+iQu0flY2bP5o9HWxDvvst7OnVCj/NWZ1UTJ6JHx8fs2iVPaH/84e5R5944M6xUVamCHh0fQ5OBn3iC90yZgh7doMk9e2Td3KBJJx/DiWbwvPUW7zEB6SkYNEsWCdKrJyyVlwHwBemdDRDN/Jk8WXrU7abNm91Beie34wTpCQZXPeqFAo0BaNvWt6bt230HI9KgUNVz5ozc/sucWW6BhmojEap1J1K2AQpQtgGy8oxM+BjTXCh/+Jjnn+c9xMfkzcvzMZQLFUw+xjkxWBXxMQ0a8B4TPubXX9GTEB9D82N0AbI0aFIXIOvkY9xkMmhyyxb0mA6a1IH0jz6KHhWkV09YtNUIEB+kV300Q8oJ0h88KD00j0oF6WNifJuUkyd9Qfrr1+X7Rj2JEkjfq5e8E3DJEt+aaLAnfV7ojjvVQ+8TAF8mK1QbiVCtO5GyDVCAsg2QlWdEuVCvvsp7KBeqWDEzPoabHxNMPoZyoZo35z0ff4yeYPIxP//M101zb3R8zEsvoUfHxwwZgh7doEniTlKm1AfIOvkYt7pNBk02aYIe3aDJQEB69YRFd6wBxAfpVR9tkTkHTaozfmiriwYmChF/hYm2uwikp1vy1ZR3gqajonwz565d861JDWJNlUpuFaoe4tYiInz/70K1kQjVuhMp2wAFKNsAWXlCwcyFChYfM3cuenR8jJoLpeNjaJKvjo+hW511fEzv3ujR8TELFqAnQwY9H0Ncz5Yt7p4bN3AlBgBXZjjRoMk2bXhPv37oUfkYp4I5aNIfkN45IFM9YdFQxNSp49ft3AJzA+lpBZGaDABfkJ4mgtOD6h41Cv+eQP5nnpEeCr5t2VLmstHdic6aaBtUbXKdHgBshrmvLZQaiVCtO5GyDVCAsg2QlScUrFwof/kYXS4U8TE9evAeyoV68kneM3kyerJm5bkelY9RZ8GoUvkYdWCeU5QLpQuQfest9Dz+OO9x42OcUgdN7t3r7rlyRfIxU6bwx3viCfToAmTfeQc9au6WUyofw9WtA+nVExbxMQULxn8NZyPhBtLT+4MeTpC+WbP4zUjGjPJESd8TmkBN7xG6UKAVM/q+OmuicQo//sjXDYAxINzXFkqNRKjWnUjZBihA2QbI6o7rv//cf1CriovDuAcAPR9DQKiOj6FcqDx5eK5H5WP++svdo+ZC6fgYyoXS8TGUC/Xss7znq6/Qo+Nj6K6liAhc5XGTOvfGXz7GqbZt0VOvHu8ZNw49STVoMlCQ3q1BcGvMnT43kF5duQGID9I/8kj8YxFIf/Wq3Dak9yM9atZEkBwAt99oxUytiRiobNl83+fOuosV039todRIhGrdiZRtgAKUbYCs7riIj9HNvSHuIaFcKH/4GF0uFPExTZvyHroqf+QRvu5Vq9BjysesWcPXTVf7Q4fyNREf8/LLvGfYMPQEOmjy9GkJ/65c6e6Ji0PuCQD5Fk4mgyZHjEBPvnx83SpIf/Kku+fsWT1I79YAuQ2SVH2FCrkfS21wnA33xYvxA0wjInDulBDyvZM1a/zcsR9/lJ8bdeq26qP3i/NOOefX57adHKqNRKjWnUjZBihA2QbI6o5K5WNMcqF0fAzlQun4GMqFCpSPUefe6PgYyoXS8TF9+6KnTBm+boJd06XDFRw3qblQmze7e9S5Nzo+hjgT3aDJ/v3RU7IkX/eSJejRDZr8+2//Bk0SH+OmYID0bnBzkybxfeodXm6349+8KRtygPhgNzWZNK/K2bgS7/Xii741UcNNoxfU7wfNR1Jr//133+Oq060zZHAfWxCqjUSo1p1I2QYoQNkGyOqOyoSPUXOhdHwM5UIlBR8zdSp6smTh597QFgVA0vIxVavynu+/R48uQFblY3bvdveogyYnTuSPV7Mmejp35j3vvose3aDJWbPQkzEjPyAzWCC9esKi2/udoLQQMocLwJ0lcybBO1ek6E41ek8C4F1fpMqV8bkxY7B5JM+XX+Jr0f+ROsKABnvSw217i8Bp3f9LqDYSoVp3ImUboABlGyCrOyaVj9HlQhEfo8uFGjMGPQ8+GDw+ZuFCvm46MVIulJtoDouOj/n6a/To+Bg1F4qbe6PyMfPm8XVTLpSOj2nfHj26QZMUDKobNLl9O3pSpMC75dwUEyNv8dYNmqxYET26QZME0usGTZqA9CpvQ7OinIDzpUtyQCaA+9blTz/5NiPOkx/FXRBrpXouXZIrOAcOSI4KALeAaV4SRVcIIS8U1Idz1enyZd9cMa7BDdVGIlTrTqRsAxSgbANkdce0ciX+UEiVKnA+pmBB9Oj4mFdeQY8JH0O5UG6igXZqLpRT//5rxscQI6LjY+hOId3cG7qd+uGH+brXrUNPdDTPx5gOmixaFD2DBvE1tWiBnhde4D2ff44e3aBJmoUTFSX5GKdMQfoSJdAzYABfk3pnVrt2+KvzTkAC6enhtsKnrhC5nfyI0aH3t+qhWVY5cuD/J9VNHooU+fBD+Xp0oUCPsLD43y+6ULhbG4lQrTuRsg1QgLINkNUdE/Exb7zBe0z4GDUXyoSPMcmFGjOGr4n4GDUXyqkPP0RPqVJ83W65UE6pfIzzVmVSbCwCtgB4YuZEuVCtWvGeAQPQU7w4X/fSpehJk4YPYlUDZDdu5OvOlw89ugDZF15AT4sWvGfwYPQEA6SnAZkAOGsHwHelTwXp1VUZpyis1e3kd/Gi7wRop4e2qZo2lTA0PVTYf/t29KsXCvRwRpeogz3v1kYiVOtOpGwDFKBsA2R1R7R3r/yhwOVCqXzM1Kn8a1Wvjp5u3XgPXY3rcqFM+Bh17o2Oj8maFT2TJvHHq1EDPTo+hk6ElAvlppkz0aMLkP3jD1n3zp3unmvXZKyCbtBk7dro6diR91CAbMWKvGfOHPTce6/ZoEknzEu6fl2I7NnRYwLSt2/PewikpwcNQlRX6AikpxUntxObk/9xegiAJtje6aFb+cePlxcK9CBu7qGHZLNHFwrqStHXX/vWRCC9bYC8V3ciZRugAGUbIKs7IuJjnn6a9xAfkzNn4HyMSS4U8TG6uTe0JeLMhVJFfEz27Hzd/vIxurk3xMe89x7vIT6mdm3eQ3yMjuvZuVPWffCgu0flY2bN4o9HkG/PnryHBgmqt3o7RQ2BLkBWBekPHHD3qCA9PWjKtXqnFUHLdMeZ24mNkuG5ZoO2WgHkcEvyXLggGyOKR3FrygiIVy8UCCgHiD++gAJkbQPkvboTKdsABSjbAFkluVQ+hsuFUvkYXS4UgaQmfIxu7o3Kx3Bzb86ckXUvX87XTXyMMxdKFfExai6UU8THUC6Um1Q+hguQPXtWrlYsXcrXTasHugBZGjTpNheHRPEPDz3E1/3LL+jRBciqgyYXL+brNgHpX3sNPSYgPY03AJB3sX3zDXpUkF6dzqye2NQAWa7ZoHlNAHK1jDy0UvPQQ/JCgeJdAGRTvHo1vpZ6oUDzlJzHowsFAPkevhsbiVCtO5GyDVCAsg2QVZLLhI/xNxcqWHyMbu4N5TKVKMHXTeGXadLwc29UPka97dlZd9688VcfnDLhYwYNQo+Oj6E7lkz5mHXr3D0qZ6IbNEmrGLpBkxQMqhs0qYL0XIDsP/9IZsYEpKc5QQAyDoW2YCnQ9OWXfX3qiW3oUPm8OgdI9VDGWmQkrgCqHhrD8MorslmhzwM9MmVCZk29UBgwwPcOL/V4dKEAIJvYu7GRCNW6EynbAAUo2wBZJalUPmbyZN735JPo6dKF9/TogZ6k4GPUuTfffccfj+awBJOP4X5oqnwMwbBOqXNvgsXHlC/Pe4iP0QXIHjkit3h0AbK0EuNkWVQRH9O2Le8hPubRR81A+uPH5QmLxh3Mm4ejE1SQXs35ov8jFaSn5s3puXBBPte0afwTJK1oUXNbqlT8SdDU8Kog/bff+nroeH/95csabdp09zYSoVp3ImUboABlGyCrJNU33+APAt3cm99/R08wcqEqVECPbu7Nm2+iR8fHTJiAHh0fs2MHenR8TEyMGR9TqRJ6dHxM587o0c29mTgRPcHkY2bM4I9XtSp63nmH9xAf47xLSdWUKei57z5+0CSB9GFhZiD9tGn88VSQXj1hFSmCvy5disMzASRIT2MV1BPb9On4Z9pyVAFm8hCzBIAhuOrxjh2TzTixQZMn+3rU97x6oeDMHaPj0YUC1X43NxKhWnciZRugAGUbIKskU1ycPKF8/DHvI45Bx8eMHIkeHR+j5kIFyscUK4YeHR9DQ/MC5WPoCl3Hx/z3H8ZLAGDcBFd3yZLoCZSPGT0aPblz84MmN29GT0SE73RiVeqgyR9+4Os2GTTZpg16nnmG99DAQF2ArBOkV09YtA35449ye2n+fPx31HzQiS0uDmNYAORwQ2pS1ZMfRVhkzYp/Vo9HE8ZptZEuFFRPypS4mkkXCilS4IoUrU6px1NvAKDm9W5uJEK17kQqZBqg1atXi3r16ols2bIJABBz5szR+ps3by4AIN7jkUceueUZP368q+cKd8XkItsAWSWZiI9Jqlyo559HT8uWvIf4GC4XSgg5lC51an7uzYkTko9Zv97do/IxI0bwNTVujJ5mzXgPBWEWLszXTXcQ6fiYU6ckp7J2LV83zb0ZNoyvifiYV17hPUOGoKdQIR5IX71anui5QZPq3BsdSE/DBnUgPQHJBNKrJywaC0CrVuqgSWqK6cT288/4++hoeafYqFG+ntOn5XYUbWOpx2vbFn+lVUIC6VVPnTr4nHqhQBcExYv7Ho+eB5B3Jd7NjUSo1p1IhUwDtGjRItGrVy8xa9Ysowbo3Llz4sSJE7cex44dExkzZhS9lVt0x48fL9KnT+/jO8Fd6TKyDZBVkonuqHHGCqii23gfe4z3zJ4tTxLcD5RDh/zLhZowgT8e3YHToQPvef999FSowHvmzUOPjo/5808zPoYCZMeN449H04J1AbJ9+qBHFyC7YAF60qcPLED2xg0J/+oCZOnWc12AbL9+6CldOngg/a+/4nPqCYvuuKI5Q2qArBpiGhMjRIMG+PvWrSV4T00/eQikB5ArYOrxVGZIvVBQPV9+6QvSb9okV55oICQArrbRChYAfs+cr3W3NRKhWnciFTINkCqTBsipOXPmiLCwMPGnwkSMHz9eZMiQIaBabANklSRS594cOuTuUfkYXS4UbSHocqE6dUJPoHzMrl3oCQtDWNpNly4hZA2g52PojiIdH9O1K3p0fIxJgOyePbJuXYAscSY6Pobmx7glnpOIj9EFyE6bhh5dgKw6aHLPHnePyvWYgPQmAbJVqsjn1BOWeheXCtLfvOkLFm/fLuveskU232pi/Jkzsm4AOW7ByffQQ71QoP9PAITf1QsFYqHCw32T3omjAsBmiS6O7+ZGIlTrTqSSTQNUr149UcMxDGz8+PEiPDxc5MqVS2TPnl3UrVtXbOGuvv6vq1evivPnz996HDt2zDZAVrdfFCnw/PO8h7YLdHzMxo3yB7ouF8qEj6G5Nx99xNfUujV6GjTgPSofw9VNAZsREbjq4CZ17s2iRXzddJdQUvAxW7bIkysXIHvhQnw+xq1u4mICHTRJwaA6kH7bNtlwc4MmOZCea0jUQZP//uv7d/T9rl1bQuVp0/revaXmcOXMqT+eE6SnkQDUOKkgPd1VWLeu72vRDQAAQrz0kvvx7rZGIlTrTqSSRQN0/PhxER4eLqZPn+7z/IYNG8TEiRPFtm3bxJo1a0TDhg1FqlSpxH7uik8I0bt3b+HGDdkGyOq2SeVjdHNvKBdq5Ej+tRo1Qk/z5ryH+JgiRRLmY3Rzb1Q+5uef3T0qH/PZZ3xNL72EniZNeA/xMbq5N5QLZcrH0LA8t7qJjxkyhK+J+Bj1BOrUZ5+hRzdokqIfdIMmT5+Wc29WrHD3xMUh9wQQOEg/YgR68uf3rdutIVFXUISQd/zRg+petkxudZYq5ftaVLezoXY7nhOkJ6YIQM4ZeughbABpW3HaNL55U+c23c2NRKjWnUgliwZowIABIlOmTOIad/vt/3Xz5k1RvHhx8eabb7IeuwJkleR67z15RcqJ5t4kxMeY5EIRH0PTe91Uty56dHwMzb0x4WMyZDDjY7ZudfeY8jF0q3Mw+Rjus6/yMZs3u3vUQZMqH+MU8TGvvcZ7iI8pWTLhQZM6kN7Jx3B1E0j/xRe+f+fWRDgbbhocqT4IpKfVmsaN478WvQ/Uu/LcjqeC9GfP+m63EdczYoQcBJk+PW5pur2Wc3Dn3dxIhGrdidRd3wDFxcWJfPnyic66wERFrVu3FrV180wcsgyQ1W2VKR9DuVA6PoYGzyUVH0Nzbxwrrz6iK3MdH0OTfQPlY/btk5zJ3r3uHlM+5okn0KMbNOnGxzg1YwZ6MmXiA2QPHJB179rl7lEHTU6cyB8vWCD9rFnocRs06dZEOEH6SZPiewikf/11/PN778V/LdpyU6M9nJ4yZRI+Fl0o0OiFVq342p2DJO/mRiJU606k7voGaOXKlQIAxA7uThZFcXFxokyZMqKl7rZfh2wDZHVb9eWX+MHPkyfhXKhg8jEffsjXRCeoZ5/lPcRr6PgYNReK42PUuTcLF/J1Ex/Tpw9fE+VC1avHeygXSsfHqHNvTAZNzpvHH49Sy3WDJtu3R89TT/EefwNkdSA93bmlA+kpQNYNpHc2ERER8T20XUmPrFnlgEyCxr/7jt+S+vdf/njOCwWaCK0+3nkHG076TNAoALeGyzkB/W5uJEK17kQqZBqgixcviq1bt4qtW7cKABBDhw4VW7duFUf+n2Ddo0cP0dQlF6dJkyaiXLlyrq/Zp08fsWTJEnHw4EGxdetW0bJlSxERESE2ccu+LrINkNVtk8rHBJoLRcGTJnxMqlS+JxhVKh9jkgs1dChfE00Cfvll3kOp3wULmvExHNej8jErV7p71FyoTz7ha2rWDD2NG/Mejo9RRYMmo6MxJ8xNZ84gZwWA20Zc3SYBsgTSv/AC7yGQPm/exIP0ziYiY8b4nu7dfT0q2E23zG/Y4Pta1HQ9+CB/vPTpfeu+elUC/fQID8cLBRqa+OCD8v/o7799vW53wN3NjUSo1p1IhUwDRCs5zkfz/+8tN2/eXFStWtXn35w7d06kSpVKfPXVV66v2blzZ5ErVy4RFRUlsmTJImrWrCnWc0PYGNkGyOq2iXKhdHyMmgul42NMcqGIj3njDd5DuVA6PobSuNOn5/mYY8cS5mPUXCgdH1O/Pnp0Qaz9+6NHx8dQLlTatPzcG38HTTr5GFUNG6Ln1Vd5DwWGFi/O1710KXrSpDEbNGkC0usGTSYE0jsboDx54nvU1HUAuQKo/tvTp31vg6eVx+ee830tNRvMuXpPrJY6c4gGNlJ+m3p3mjpnCMA92uRubiRCte5EKmQaIK/KNkBWt03Ex7z9Nu+hCbvVq/MeutLV5UL5y8dMmcIfT82F4kQrAI6LFh99/z16Mmc242N273b3mPIxNWqgR8cL9uyJnkqVeA/xMbpBkwcPSiCdC5BVB01++y1/vNq10aO5ecMIpJ87Fz06kF4NkOUGTf73n28ToUzfvyUKvXWe2Oj2e1o1ou83gJxM7hy78PnnfMNCTROtkgLgytvJk/LCgXLQbtyQq08A+H5w093cSIRq3YmUbYAClG2ArG6LVD4mKXKhKELg6ad5D/ExOXOa8TH/356OJzVfSTf3plw59HzwAV8T8TEUb+AmlY/h7gRVc6G4uTcqH6NjEGmrplcv3tOxI3p0N1x89x16smXj6965Ez1hYXyArArSz5zJH49A+h49eA+B9E8+yXvofUKP0qXje2iL1Hlio6a3fHlseqluAN9cMVUUj+I8Qd68KRtfmo5NHtpaVfEIulCgBxe2ezc3EqFadyJlG6AAZRsgq9si4mN0uVA0z0THx6xZgx7d3Bt/+RhdLlTTpvKKm9Pw4ehRc6GcUnOhTPiY5cv5uomPGTSIr6lFC/To+BhaadDxMRs2oCcqih80aRogS4MmBwzga2rVCj3ObSFVFCBrAtLrAmRNQXo1TwvAfbWM/t+cJzbagmra1HfwofpQc9noQsHtBEmsUrp0vhxQTIwMuaUsPBWkpwe37Xw3NxKhWnciZRugAGUbIKugS+VjfvvN3aPyMWPG8K9FfIxufgzxMaVKJczHmOZC/fKLu0ede6PjY557Dj10e7KbBgxAT6B8jDr3RsfH0AqEbtAk3XGkGzRJeVNFi/J1L1+OntSp+SDWkycl16MbNEkrJLpBk8EC6WmujvpwxqmcPBnfQyc2akT79o2/SgQQH4CmAFm3E2SPHvgcNZL02LRJNnv0vaULBe61VN3NjUSo1p1I2QYoQNkGyCroolwoHR8zfTp6smTh+RiTXCiVj5k0iT8e5ULp5t7QCadyZd4zcyZ61Fwop/74Q9at42Moafy77/jjEWvSsSPvoSiEihV5Dw2adJt7Q1IDZLlBk9euSc5k/Hj+eATotm/Pe2jQZLlyfENCU5VNQXpdgKwJSP/00/EbCee4BHp/uzUbtH1IjBitONFDnfB87JjvgEPnCZImddM8Knp07oy/1q8vvXShYBug0Kw7kbINUICyDZBVUGWaC0V8jC4XivgYXS4U8TG6uTf+8jFqLpRTdIJT77xx6s030aPjY779Fj0PPJAwH+PMhVJ16ZJvLhQn4mN69uQ9dGLl4Fkh5FA+XYAsZWGFhbnfhSSE76DJ77/nj1e1qmwoOBFIrxuQaQrSO5sIAN8YkCtX5PuEtgHVExuFy9J2FLFS9FC3A5230quvQ7VQg6SyRNQ40/+3CtLbBig0606kbAMUoGwDZBVUUS6UKR/D5UL5y8fo5sfQLcs6PmbkSPTky2fGx6i5UKpUPmbZMr7uYsXQM3AgXxPxMc5cKFXEx+gCZE35GOJM1CnFzrqJPVGjHJx67bX4KxROER/z4IP8oMnNm9GTVCA9DZp86infRkK9zV8FpAsU8D2xOe8eCw/3TXEHkAC0CtK7NS2UZ0dfG61O0uPee2UDShcKzibIC02CbYBsA+Rl2QbIKmiKjcVEdACcAM3JhI8hmNSZY6TK31yojRv5uomP+fxzvia6jblFC94zaBB6dHwM5UjpglhVPkYNslSl8jG6QZONG6NHx8dQfpUJH5MqFc/1qAGyukGT1DzoBk0SH6MbNBkskP7ff+WATJq9Q48OHdCjgvQAcnWKTmzUaBKQ/+KLvic/APl9I5Ce2wKjlUa6UFDnCQHIWVfqhQKAXFn1SpNgGyDbAHlZtgGyCppM+JiDB/3LhTLhY3S5UMTH6HKh/OVjtm939/jLx9CJ1U3Ex5Qvz3to0GRCAbLB5mPatuU9ffqg59FH+UZq4UK5usH93Dl61D+QnhkWK4SQfMzrr/OeDz9ET6lS+L1Umw2aY0UgPTV4akRFTIzMoaPHr7/6nvxy5cLXUUF6aszU1zl50nc1p1Wr+I0UNcUE0tP3atw4bzUJtgGyDZCXZRsgq6CpQgX8kOtyoYiP0eVCmfAxO3agJ6FcKBM+plIl9LjlQpGIj3HeEaRq4kT0BJOP0QXI0gqELkDWhI+ZMgU9Oj5m715ZNw3ec+rKFcnATJvGH4+ysnQBsgQaV6vGe0xAepWP4UD6K1cwywsAmxhns0FznGjQZOnS+CttPdGJjZo/AAnSq69FMDVdKNDKDX0/6HXGjvU9/s6dvq+TJw82lypID4Bfw9mz3moSbANkGyAvyzZAVkER5UIlFR9DuVA6PoZyoXR8jHpLMcfH/Pef5GOWLOHrptuVdXxM69boadCA94wejZ7cuZOGj6ETuo6PadMGPc88w3voxK0LkN2yBT26QZOmIH3ZsujRgfTt2qFHB9J/8w16CKR3NkADB/qC9LSF26+f74mNIjYAJEivvhYF3dKFAm0Dqo1TTAyG3dKfCaRXX4cadbpQoK1SZ/q8F5oE2wDZBsjLsg2QVVBEfIwuF4r4mGLFEuZjTHOhuOy7mzfNcqGIj9HNvSE+pkgRvu4VK9Bjysfo5t7QiVE394b4mCZNeA/xMYUK8XzM6tXoMeVjVq9296h8zJAhfE00aFK9s8opAukLFAgcpCceZ8UKvu4iRdDz8cf4nLMBGj5czvdp1AhXAQF8Bx3GxGDjB4ArgFS3+lrz5kmQPjISty6pNvKcPCnfI+qFwoED8rnt2+MPbKSAVK81CbYBsg2Ql2UbIKuApfIxO3a4e9RcqAkT+NeiO3CSIhfKlI/JkQM933zDH69uXfS0a8d7evdGT9myfCO1YAF60qfn5974y8eMHcvXRAGybdrwHlrp0AXIEjicLh3P9aiDJn/9la+bQHpdgGyDBujRBcgmFqR3NkCffOIbIEuNB7FjAHgXHX0G1AiRY8ek5+hReaFA33cazEkelSNSG2415DQmRl4o0Pfz+efj1+6FJsE2QLYB8rJsA2QVsGjWiY6PoVwoHR+zaxd6wsJwmKCb1FwoHR9Dc290fAzlQun4GDohZc3K1023OoeF4fBGN6lcj46PoQBZHR/z1lvo0fEx06ahJ0sWswBZHR9DAbKTJ/PHe+IJ9HTtynveeQc9Varwnhkz0KMD6VWu53aA9M4GiJoVAunpddetkx7atgTAFTMSNbQAyPJQk0RsVp06vsejFUkAX5C+cGHfkyhdKFBjRhEwXmsSbANkGyAvyzZAVgHpv/8k1+MMeSSpfIwzCVuVP3yMSS5URASuOrjJNBeqVCn09OvH10R8jHNisKqvvkKPbu4N5UIlxMcQ17NgAV83DeILlI+hu4p0gyYpAT08HFfV3HTxotzymTePPx7xMbpBkx06oEcH0k+YgJ7EgPTOBoj4r1mz8D1HTcwff/iu1gDg/40qlROi73eNGnLF8NNPfY9HYHTGjLLhpu8vPX791ffPhQvLlSKvNQm2AbINkJdlGyCrgES5UDo+Rs2F4ube+MvH6ObeBCsXatUq9KRM6XtVr8qEj7l5U+ZC6ebeUICsjo+hFHAdH7N2LXp0fIwaIKvjY2jl4ZNP+JqaNZOrF5xGjEBPvnx83SYgvTr35qef+LpNQPpXX0UPbR+RnA0QgAyQPXUK/xwW5rt1RQ9ncCpt1QHIC4UffpDN92+/uR9Pbbi7dvX9OxrsSY2ZmknntSbBNkC2AfKybANklWhdvy7n3gSLj9HlQtF2gmku1JYt7p4bN+Tcm6TgY374AT06PkYNkA0WH6MLkCWmpGRJvu4lS+SJlhs0+fffvnyMm2Jj8U48AJle7iYTkH7gQPToQPply2TDbQLSOwNk3RoSCpClu8EyZ3b30YBCEnFY9ChSRILQ99yD3xvn64SHS5D+xg255UYPqhsAV5xUxs1rTYJtgGwD5GXZBsgq0bodfMz06fzxiI/R5UIRH1O9Ou+5HXzMlCn88YiP6daN9/jLx5jMvdm9292j8jETJ/LHo7udOnfmPe++ix7doMlZs9CTMSN/AvAXpP/2W/54xMfoBk3qQHq3LTBqMpYulY2MWwOkrvCdORP/78eNk00cRYU4X0fNkKPhizTPih60nei8WcBrTYJtgGwD5GXZBsgqUVL5mA8/5H2vv44eHR9jkgtFfIzp3JuFC/m6iY+huSxuolyoevV4D+VCmfIxHNdjyseUL48e3aBJGs5Xpw7voQDZ7Nl5Pmb7dvSYDpqcPZs/HsU66AZNEkhfqxbvIZA+Wza+bn9B+pkz3b8utdlQI1uohiee8PXR9pbKZdFKFD3uuw+bTxqoSNu4zuP9/rt8jZdewueIM6MH15x7rUmwDZBtgLws2wBZJUrEx6RKxfMx//wj+RhdLpQ/fIwuF4r4GF0ulMrH6ObeEB9Dd9c4pc69MeFjXnyR9xAfowuQVfmYkyfdPaZ8DAXIDhrE10SDJnUBsjRokvgYN6lzb44fd/f4C9KriepOEUj/3HO858sv0cOB9M6GRGXSaCbUyy/j9h95aFtKnZJNKz30eP99bNzo/4hWutTj3Xef/Pfnz8v3Ic1rApD80JNP6mv3QpNgGyDbAHlZtgGySpQoF8rJPKjq2xc9ZcokzMfocqFUPmbzZnePOvdmzBi+JsqF0vEx/fujR8fH0NaEKR/zyy/uHpWPUWFWpxo2RI+Oj6FcqOLF+bppC8d00KSTj1HrpkGTxMe4iaYj6wZNBgukV4cI6kD6hx9GDzdo0tkAqRPCaYu1a1ff2TwAuMqnrkwR00SPP/+UDXjmzLLZPXxYetTtRppQXaAAfjbIQ00RTZvmavdCk2AbINsAeVm2AbLyW/v2yQ+0LhfKhI+pXh09Oj6me3f0VK3Ke77/Xp5YgsXHTJrEH4+2MXR8TM+e6HHeGaRK5WN0AbImfAzlQun4mNq10ROsQZO6ANnDh2Xd6raOqqQG6SlAVgfSE7dGD7XBbdIEnxs4UNZNj3z5fF9HDTylkx9dFKgra5SPB+C73UgZYf37y/cJPbi4Ea81CbYBsg2Ql2UbICu/RXzM00/zHuJjcubk+ZitW+WVswkfo8uFKlcOPRRc6SZ/+RiubjUX6vBhd09MDDYHADgxmBPxMer0YKdM+BjKhdLxMTt3yroPHnT3JMTHkGjQZI8evIcGTdaowXsmTUKPKUivC5ClIFYdSE8BsjqQnr7f9FDrosa3bVtfD4DvXCI3ADomRoL8X36JvitX5PafeoI8ckQ+d+SIrJse3O39XmsSbANkGyAvyzZAVn7JXz7m00/516JcKB0fM3w4evLn5/kYmsgbTD5m8GC+JsqF0vExn3+OHhM+Rjf3xpSPoXgGHR/TqhV6AuFjhPB/0OTixXzdwQLpTQZNmgbIUt30UFeTaL5Q/vzxG5yOHaWPthrVx7//yq3FvXvRR4MmnSdI2s6sVk1eKNAjKorn17zWJNgGyDZAXpZtgKz80ocf4ge5VKmE+RjKOXKTmgul42NoG0HHx1A6t3q3jlP+8jEc13P8uOR6Nm7k686bFz2ff87X9MIL6GnRgvcQH1O0aPD4mHXr3D0qH5MUgyZXrkSPF0F6eqRK5fv3WbPKv1NDS53/17SNqD4WLsRfs2XD70lcnKxbPUHGxWGALQBuCxJITw/doEyvNQm2AbINkJdlGyArY129Kk8AOj7mySfR06UL7+nRAz2VK/OemTPRo8uF+uMPyfXs3OnuUfkYk1wo9UreqV690FOxIu+ZPRs9Oj5GnXuzfbu7R+Vj1Fwop+rUQU/79rzngw/QU74875k3Dz0ZMvABsuqgya1b+bpp0OTXX/PHq1cPPTqQvk8f9Dz6KN9IUWMRDJCeBk3SI2NG+fdqDAaAvFOOHuoKHa2A0vsOQIi33/ZtwOhCwdkAUdRFypS4UkQNNz1WreK/X15rEmwDZBsgL8s2QFbGortSAuVjVK7H7U4WkkkuFAGk6vA4p4iPMc2F0vExNPdm1iz+eJUqoadnT97TuTN6TPgYXYDs7t3oSYiPoUGT33/PH8+Ej6EQT92gyalT0XPfffygyb175UlBB9IT1zN1Kn+8YIP0xEDRe4Z08qRvI0KzqehBAPPVq7JRorvGACSnNm4c+ogncjZA9J5+8UUJ0lNDaRsJ73iC/VqJkG2AApRtgKyMFBcnAx91fAzlFOn4mJEj0ZMvH8+ZmORCnT0r+Zhly/i6TfgYyoVq2JD3fPEFeh56iK970yb0REb63j6t6r//ZI6Tjo8pWRI9/fvzNb32GnpoqrCbaNBk7tyB8zE0aPKHH/i6y5RBT9++fE3+gPTcHU9CmIH0Fy7gqhYAP2hSBelpdZLeoyRq7gHip7hHRsr3BL2/AfDWd/o9rZwdOuT7Wurjv/9kszprlgTp1abMNhLe8AT7tRIh2wAFKNsAWRnpxx/xAxwMPsafXKiWLXnPoEHo0eVC/fQTehLiYwhOXb/e3XPzpgRfR4zga2rcGD3NmvEeGqanpng7pfIxlAvl1D//SA5l7Vq+buJMhg3ja3r5ZfQ0acJ7hg5FT6FCPJC+Zg16UqbUD5okrofbzlFB+iFD+Jr8Ael1gyYJpI+OxhVAOmEVLSo9tCULgNyVemIrUEDWTdtobnlhDz6IPgLpAXyzvmgVKmtWWbczC8w2Et7wBPu1EiHbAAUo2wBZGcmEjzHJhQoWH3PtmuRjJkzgj0d8jC4X6v330WPCx9xzjxkfs22bu+f6dYzOAJBbIW4iPqZtW97jLx/Dzb1R+ZjffnP3qIMmv/qKr+nZZ9Hz+uu853aA9FyArArS063nblJBevWEVbas9FBTni4d1q366tZFj3r313PPxW+AWrb0vVAAkNOrAWSQbadOEqQvUMA2QF70BPu1EiHbAAUo2wBZJSgTPiYmxj8+RpcL1akTemrW5D0TJ8qrYxM+hsuFunxZbi/MmMEfr0oV9LzzDu/p2hU9TzzBe6ZMQY8JHxMWxvMx6tybadP449Ewvbfe4j0E51arxnumT0dPliz8oMn9+80CZAmknzyZP16wQXrdoEknSK+esIgZunpV3h5PALzqowsDulAAwJU+ZwM0caIE6akJoqGSAHIlku6ioy1H2wB5zxPs10qEbAMUoGwDZJWgiI95/nneY5ILpfIxulwo4mN0c2+Ij/noI74m4mMaNOA9o0ejRzf3hu7K0c29UefHLFrE1126NHr69eNrouDLZ57hPWPHokfHx2zZgp7wcCGOHnX3qHyMGuTprLtsWfT07s3X1K4denQBsgTS6wJkVZD+zz/dPbcDpKdBhuoJi+D6CRPkczT9W/WNGCEvFOixcmX8Bmj/ft9k9/TpkWVTPYULywGZ9H6hlUzbSHjHE+zXSoRCpgFavXq1qFevnsiWLZsAADFHNx1WCLFy5UoBAPEeexxXVjNnzhSFChUSUVFRolChQmK2LpXZRbYBstLKXz5GlwtFfIwuF+rjj9Gjy4VasQI9Oj7m1CmzXCjaXuByoYSQidw6PmbIEPTo+BgKtDTlY1av5uumOTE6PoZiG3RzYz77DD0FCvB1//wzeqKj8fvqpjNn5IDMFSvcPSpI//HHfE0E0jdqxHtMQHqTQZNuIL16wmrQAOumAYhq7apv0SJ5oUCPc+d8PXnzSpCems7GjeM3SR06yIabmmragrWNhHc8wX6tRChkGqBFixaJXr16iVmzZvnVAO3bt0+cOHHi1iNW+bCvX79ehIeHiwEDBog9e/aIAQMGiIiICLGRA1BdZBsgK61ooJuOj6ElfB0f8+efko/R5UKZ8DGUC6XjYygXSsfHLFggT0YcH3P0qKx7yxZ3z40buBIDoOdjnnkGPTo+pl8/eeXP1b1oEXrSpTObe8PxMercGx0fQ1yKbtAkBYPqAmQJpDcNkDUB6XWDJhML0qsnrJdewsYIQHJplLX233/St26dvFAAwAsC52u1bCkvFGgbcMqU+A0Q8V90V9rDD+P70zYS3vIE+7USoZBpgFT50wD9x/2gEEI0atRI1HbMP6lVq5Z4UXdHhEO2AbJipeZCBYuPefJJ3jN5sjw5mORC7d/v7vGXj3n7bd5Dc1wef5z3TJuGnixZeK5n3z4zPoYCZHV8zBNPoKdrV97zzjvoqVKF98yYgR7TQZO7drl71ADZiRP549WsiZ5OnXiPCUhPwaCmIL0uQPaBB9CjgvTqCatVK9wao+8TgNyaVSMqaM4QzeuhVTcnJ0SNKwA2es5VovLlZd0EQX/2mW0kvOgJ9mslQnd9A5Q7d25x//33i+rVq4sVjqXlnDlziqGO0e9Dhw4VuXLlYl/36tWr4vz587cex44dsw2QlbtMcqFM+Bgv5kIRH6Obe3PhgoRQFy7k6370UfT06cPXROGZOj6GcqF0fMy2begJDzfjY7i5N0LgyRYA74LjRNsxatCnU8THZM9uNmhSTTxXFRMj597otvIfeww9JiC9LkCWQHpngKxzBYgabmqA6A4/aiABJNdDrBRl4KlzgOh9QoGoBPlfvCg9BH/TZ4HGTthGwnueYL9WInTXNkB79+4VX331lfjtt9/E+vXrRdu2bUVYWJhYrXABkZGRYrLjSnHy5MkiKiqKfd3evXsLN7bINkBWPkrqXKhVq9DjxVwoHR+zdi16oqN5ruf0abMA2cKF0fPJJ3xNlAvVuDHvGTECPUkVIEt8zKBBfE0UG6ED6U0CZDdulKsntwukV09YFI7boIFcCSOeaOBA6aMLBdoKpf9nmuZNj4gICTbTHCxi2qjhAZBNHsWE2EbCe55gv1YidNc2QG6qV6+eeFqZnBoZGSmmTJni45k0aZKIjo5mX8OuAFkZaf58/MDq+Bh17o2Oj6FtgbFj+eMRH9OmDe/p2xc9Oj7mhx/QE8xcqNGj+ZqIj2ndmvf0748eHR+zZAl6TPmYTZvcPaaDJhs2RI+Oj6ETvG7QJPExadIgUOymEycSBuljYxFoBtAPmmzUCD23E6RXT1i0HUWcW4oUsjlr1cq3uaH/ZwD53qM7EenRsKFspGjl0enJl09+rmgOlm0kvOcJ9mslQsmqAerfv78oWLDgrT8nZgvMKcsAWbmKlul1fIw/uVCmfMzeve4elY9xNP0+Ij4mmLlQ3NybAwdk3bt3u3tUPkYXIEu5UHSLtZsoF6pSJd5DfIxu7s3Bg/7xMQT9uql2bfS8+SbvIZC+QgXeYwLSHz4s6zYB6b/5hj8egfTt2sX/O/WEBYDbWrRlmjWr9NFnhBpu+t7TVGgh4g8xpKGbZcrg31+9Krf96EG1qe9P20h4zxPs10qEklUD1LBhQ/G4AmM2atRIPOXYm69du7aFoK0CE4U8muZCBYuP0eVCER+TM6cZH8PlQl28mHAulBD+8TF16vAelY/h6t6+Xa4uBIuP6dWL95jwMd99hx4nH6Nq50706AZN+gvS9+jBe5IKpHc2QNOnyxW6YsWkjyaRA+D3lCZc07bq8eO+r1OlimxuKN+NJqPTI1Mm2eir3y/bSHjPE+zXSoRCpgG6ePGi2Lp1q9i6dasAADF06FCxdetWceT/P6h79OghmiocxbBhw8ScOXPE/v37xc6dO0WPHj0EAIhZypTddevWifDwcDFo0CCxZ88eMWjQIHsbvFXgMuFjKBeqYMHAcqGSmo+hfKWk4mOIIdHxMZQL5SU+hgJkdYMmaQvoued4z+0A6XWDJoMB0qsnrHvvxe1QamRr1EDP5cu+jcu+fTIGhGYz0dRvenz3nZxNRStvtIVKD9oKfuAB34bZNhLe8wT7tRKhkGmAuMGGzf+/l928eXNRVVnyHDx4sMibN69ImTKluPfee0WlSpXEDy4JzDNmzBAFChQQkZGRomDBgj4NkolsA2TlI1M+hnKhxozhX6t+ffQEKxcqbVo+F0rlY375xd2TmFwoTgMGoKd4cb5uyoXS8TFqLtSGDXzddEu0bu7NCy+gp0UL3jN4MHp0fMzy5ehJKECWTubr1rl7QhWkV2fu0O3s9H2jGp1Tn2Ni5NYb3ajiZHtoVS1vXvwaTp/2zQSjzwFA/EnhtpHwnifYr5UIhUwD5FXZBsjKR/7wMZkzm/Ex3Nybq1flQLhg8TG6XChiNEzn3uzc6e65dg23hgDM+BhdgCzxMZQv5aY5c+RqBPcD1JSPoW0bEz6mfXveQ4Mmy5XjGxJ/QfqtW909Kkj/9dd8TbR6QndOuYlA+jJl+LrpfaL+/9L2G2Wq0agFehw6hL+GhcmvlaBuelCjR3waTYV25n1FRsafXG0bCe95gv1aiZBtgAKUbYCsbknNheL4mLg4OaFWx8e0b48eHR9DuVA6PkbNhTp82N1jysdQvpKOj6FcKB0f8+236EkqPoYCZHV8TOfO6NHxMXRLto6PUQNkdYMmM2dG3/Tp/PGqVkWPCUivGzTpL0jPBciagvRUN4DMR3v5ZfwzbcGqHnrfAUgA+uhR378HkLOZaOWJODPnw43htI2E9zzBfq1EyDZAAco2QFa3RHzMww8nzMdER5vxMcuXu3vUXKjBg/maiI954QXeY8LH+JsLtXQpXzfxMQMG8DUFi49RA2T//tvdc+6c5Hq8Mmhy82b0BAOkL1MGPYGC9F9/jR4dSK9OdwaQfBfdXThxIl4oOLeuaCXvlVfQT02y85E5M/5f798vG02nxy27zjYS3vME+7USIdsABSjbAFkJIW4PH1OihBkfw829UfkYXS6UP3yMbu4NcR5FiwbOx9Dcm2DxMc2a8R4TPmblSvQEc9DksGF8TQTSU0PgJn9AetNBk6tWuXvi4vD7AyCnNLuJQHp60P8fNetLl8oLBfVB24b0PaH4DGeDQ++/Dz7AP9O2JT24955tJLznCfZrJUK2AQpQtgGyEkL4nwtlwsd89x1/vFq10KPjYygXSsfH0NaDKR9Dg+WcUvmY8eP549Wpgx4dH0OzXnR8DKV7B8rHXL9uxsdQwKaOj+nTBz06PmbhQvQEY9CkCUhPd1a99hrvuR0gPT1++w3/jrLltmyRFwrqg97za9ZgDdSQ0coRPebOxb9XX4OaK10TbxsJ73mC/VqJkG2AApRtgKyEEDikDsCMj3EE8PrIhI9Rc6EOHnT3xMTIfKWZM/njER/TsyfvIT6GbmF2k798zIED7p7LlyXX8/33/PGIIenenff4M2jyvvt4PmbvXvkDWMfH0El+6lT+eNWroyfQQZPTp6NHB9Lv3282aDLYID19FgAQ4L9xQ9ZB22huj7AwnDNFq4QAeEcY/T5lSry4oPgUek2aJwXAr3LZRsJ7nmC/ViJkG6AAZRsgK7F+PX44TfmYZcvcPWou1MCB/PFefRU9DRvyHrpD5qGHAuNj1Lk3S5bwdVMuFA2ocxPd1ly/Pu8ZMwY9uXMHj49xGX9xq27iY/r25Wt64w306PiYsWPRkysXXzfxMbpBkypIP38+XzeFhn7wAV8TgfR16/Ke2wHSq/ldhw/LgYbh4b7NETWM9ChUCF+LmkRalaS/p69DvT0+WzbfVSKvnJBDtZEI1boTKdsABSjbAFkZ8TGDBqFHlwv100/oCQYfkz8/enS5UCZ8zCefoKdwYTM+xpkLRfrnHzn3Zu1avm4TPobuKAoWH6MbNPnvv2Z8TKFC6NHxMU2bokc3aT7UQfp8+bCZphPWqVMyBoNW9mhb0nkXV5MmeKFAf//KK74nvy+/xJU2ahAB5Cqf107IodpIhGrdiZRtgAKUbYCSuQ4dSpiPUXOhdHwMgZ+mfAwnlY/hcqFUPmbbNnePmgsVLD7m0UfN+BiO6zl6VNZNfIlTSc3HLFqEnnTpeD7mr78k12MyaPKLL/iaCKR/9VXeYwLS//gjekxBepNBkyNH4qoPnbAuXJDfH2pcaLWQQG96DBvmmxC/YoWM3QDA16UZWtRwt2tnGyAv1mQboOQh2wAlc1EulI6PmTgRPfffz/Mxu3ahR8fHqHNvdHwM5ULp+BgaTPfEE7yHogh0fIyaC8XxMZcvm/Exjz+OHhqW56a330ZPtWq8Z9o09GTJYsbHcIMmr1wx42OefBI9Xbrwnh490KMbNHm3gPRq0xITg02/2qRQw0zDINWGh94nERH4/acVSHqtp5+Wf379dTkbyGsn5FBtJEK17kTKNkAByjZAyVj+8jG6XCjiGho04D2jR6NHx8eouVA6PsYkF4r4GGesgKo2bdDzzDO8x4SPoW2S8HBc5XGTysfQgD23uilAtndvviZaOTDhY3LkMONj/vzT3XPxojxRz53LH4/4mPfe4z3+gPQPPBA8kF4XEeQE6SkMmE5YtP0LIETNmnLri6ItqIFWAWlqcNWBiYcOyVU0+jzR58FrJ+RQbSRCte5EyjZAAco2QMlYH3+MH0pdLtSKFejR8TGnTkk+xm2ImxDIgxQogJ7PPuNreukl9DRpwnuGDEFPoUI8Z0J335jOvaH8Jre6iY+hkEs3NWmCHsqOctNnn6GnQAG+brpDKDoav69uUuferFjh7lH5mI8/5mtq3hw9jRrxnpEj0aMLkA0mSE+DJgMF6UeNQo9uQKYbSE+MEp2w1G2qJUvkKiZ9zQDIatGFAgBuPZ496zvnhz5vAAjSlyjh2wh56YQcqo1EqNadSNkGKEDZBiiZSuVjxo3jfbTc37Yt7yE+pmxZvpFasAA9urk3Kh+zZYu758YNXIkBwInEnIiPadOG9/Trh57Spc34GO4zovIxv/7q7omNlVf6ukGTlA7eujXvoROmCR+TNm3wBk2OGsXX9Pzz6PESSE9ZXDqQvnFj9Kgg/bJlvicsalSyZsXmk/7u1Cn5e7rzix7r1smtY3oULSp/T81ZypTIs3nthByqjUSo1p1I2QYoQNkGKJlq8mT5Q53jelQ+RpcLRdyDLheK+BhdLtRbb6FHlwul8jEc16PyMXv3untMc6GIj+nalfe88w56qlThPf7yMbt2uXuuXkUWCwBPsJxq1kRPp068h/iYxx7jPcTHZMzI//BWQfodO9w9Kkg/YQJ/PALpO3TgPQTSly/Pewikv+ceHqT/8093kJ5CXAGweaTVzddew0YRAL8W9cRGq4QAuMp1/bpsCp2PkiXlSuerr3rzhByqjUSo1p1I2QYoQNkGKBkqqXOhiI+JiNDzMSa5UMTHmORC1avHe8aNQ48JHxMebsbHcAGyQkhuRBcgSwPxnnqK90yYgJ7s2Xk+Zvt29KRIgc2Jm1Q+Rhcg+9hj6Hn3Xd5DIH3NmryHeBndgEwVpA80QJZA+nfe4T0E0jsDZNU7teh9AoDzmOjrqFbN98SmPmrXxgabtvucj9Gj5crbb79584Qcqo1EqNadSNkGKEDZBigZatUq/DB6iY8ZNgw9ScXHFC6MHhM+pnFj3jNiBHqCwcfQ3BuTQZODBvE1tWyJnuef5z20BaMbNEmrHZGRuF3mJlOQXuVdOLVujZ5ggvR//eXu0YH01GQCSB4JABtLWn167TW821FtbOiOu8GDsVkCkKt19MicWW4ZV6iAx/PiCTlUG4lQrTuRsg1QgLINUDLUM8/gh1E396ZvX/TocqHoh3wwcqGIj9HNvSE+Rjf3pn9/9JQsyde9ZAl6dHyMmgu1aZO7JzYWGwgA/dybhg3Ro5t7Q/NjdHwMsSlp0mDD5KYTJyQfo5t7Q3zMyJF8TY0aoad5c97jD0iv43pMQXoKkA0WSO8WIEtNlvPxzz9y+OYnn/iuFNH7CQAbMLorkpo6enz0kdwKnDwZj+fFE3KoNhKhWnciZRugAGUboGSmffv842OSIheKTiS6XKgDB8xyoeiKO1i5UJUq8Z5Zs9CTMSPP9Rw8KPkY3dwbOil++y1/vNq10fPmm7znvfd8VxfcNGcOekwDZH//3d2jgvTffMMfj5LS27XjPTRTRxcgS2yOaYCsCUg/dmz8v6fVSPURHo4NGG0dz50r3yMA8g7HDBnw+0LvQ2KRAPBCgFaX7rtPsndePCGHaiMRqnUnUrYBClC2AUpmMuFjaJ5Jzpw8H2OSC3Xxopx7Eyw+pk4d3kMD64LBx1AulAkfowuQ7dgRPbVq8Z6k5mMqV0ZPjx68p0sX9Dj5GFVJDdJXq4ae2w3S0xRq9XH//diY0bbZrl2ykQaQcTJPP40rbwC4MvrXX9Lz3HNyLpD6nvHiCTlUG4lQrTuRsg1QgLINUDKSysesXOnuiYvDbQEAfS5Us2boMcmF0vExNHMlKirwXCi6zThYuVC6+THEx+i4nv/+kyDs0qV83cTHDBjA19SqlTyJcvryS/TkycPX/csv6NEFyJ47J0/0ixfzdSclSE/DCU0DZAMB6T/4QJ6wSpfGX0uUwP9nauauXpXHApCBpsOGybsCX3xRbiVTM00XDerX4MUTcqg2EqFadyJlG6AAZRugZCTKhdLxMYsXoydtWj4XSuVjkjIXqnhxvu6lS9Gj42MSkwvFia74W7TgPYMHo0fHxyxfjh7TuTeB8jHEsDRtyns+/RQ9bnwMSQ2QDRSkpwDZoUP5mih36+WXeQ8FyOpAegqQ1YH0tNoIgNukALj9SP82d27flR36/wPA2+np65k2zReCpibWObzRiyfkUG0kQrXuRMo2QAHKNkDJRFevmuVC+cPH6HKhZs5Ej27uzcGD/uVCBcrH9OqFHl0uVDD5mOzZ0WPCx+gCZGlFIph8zNat7h6Vj9EFyFKmlZdAepMA2fr10aMD6cuVkycsumOreXO5NVyzZvwcMHqv796Nv4+MlHctOpsk5+qrF0/IodpIhGrdiZRtgAKUbYCSiSgXKnt2s1yow4fdPSofM2cOf7yKFdGj42MoF0rHx1AulI6P2bkTPQnxMTT3ZuZM/ngmfAytCuj4mEmT0KPjY+hkqQuQvXwZ4XAAPR9DbImOj+nWDT06PmbqVPToAmT37ZM/0AMdNEkgvW7QJIH0ukGTwQTpadWKGlMArIG2ttq3l3f/qY+GDeWqX82acltMfbitqnnxhByqjUSo1p1I2QYoQNkGKBlIzYUKFh+TLx/PmRAEapoLpeNjaA5LoHzMF1+gJxh8DN3uHCw+pn593jNmDHp0fMzmzegJBh9DAbJ9+/I1vfEGep5+mvckJUgfFydXbT74gK+JmhkTkJ4eNM156FC5XUuNkPMxapQMhB02TK62qQ+37WAvnpBDtZEI1boTKdsABSjbACUDUS5UmjTBy4X6/HP+eCZ8DOVCFS0aeC4UzY/R5ULlz4+e4cP5moiPUXOhnPrkE/5KnuQvH7NmDV838STDhvE1vfwyel55hfcQH1OwYMJ8TMqUWJ+bggnSN22KnmCB9NHRwQPp6UETpSdPlhcRbis7AMg50QqTyhHRI21a9+1JL56QQ7WRCNW6EynbAAUo2wAlA9WqhR++jh15D+VC6fgYuotFx8eouVAcH6POvRk/nj9enTro0fExNJlXx8fQLJYMGfhcKBM+5vp1XNEA0PMxFCCr42OILdHxMQsXokfHxxw9KvmY335z95jyMRQgq+Nj/AHp06XjQXo1QNZrIL2a4E4N6NKlsmGl94nqu+8+uVpXpoxctaKmCYAP5vXiCTlUG4lQrTuRsg1QgLIN0F2uHTvkD+uDB909MTGSj5k1i3+tSpXQ07Mn7yE+pkYN3kMp2fffHzgfQ3Nvvv+ePx7xMd278x7iY554gvdMmSJPdhwfs3evrHvfPnfPlSty7o3JoMm33uI9b7+NnmrVeM/06ejJkoXnY9QA2T173D2mID0FyHbpwnt69EBPoCC9GiBrAtJ/9x1/PLpQoOacmn1qgJxND8WpAOCqJwHtNIkaQK4Y6hpUL56QQ7WRCNW6EynbAAUo2wDd5Xr1VfzgOW+9VWWSC7VpE3p0fIxpLlTJkujp35+viaIEAs2F8peP+eEHvm7iY/r142tq0wY9zzzDe8aORU+uXHzdJnzMhQtypWH+fL7usmXR07s3X1O7duipW5f3BAukVwNk587lj0c8zXvv8R4C6WvX5j0E0j/wAA/SqxcKlLemPmjqt9oAUcYdNTq0FUvbxClTyqDYUDshh2ojEap1J1K2AQpQtgG6i6XOj1m/3t2j8jEjRvCv1bgxekz4mMKFzfiY06fdPSofs3YtXzfFDwSLjylUKDA+5t9/Zd2rVrl7/OVjdAGyxMc8/DBf988/o0c398aUj/EHpG/UiPfcKZB+4EC+JnVGj7ptRU0o1UzvXXo9eo5mJ1E0CL3naIUy1E7IodpIhGrdiZRtgAKUbYDuYql8DKe5c9Fzzz08H/Pnn5J72LbN3aPmQgWLj3n0Ub6RWrAAPenT83Nvjh6VdQeLj3n9dd7Trx96SpXi6160CD1JxcdQgGyrVrzno4/QU6IEX7e/IL3JoEkdSE93XyUVSK8OmqT66PHAA3JrF0CuclIQLIAE6ClkFkB+/kLxhByqjUSo1p1I2QYoQNkG6C6Vmgul42PoLpd33uE9XbuiR8fHUC6Ujo9Rc6E4PkbNhZo2jT/e44+jR8fHUC6Ujo9Rc6EC4WPUuTeU8u0mEz6GbrPW8TEzZqAnUD5GDZDV8TE1a6InqUH67dvdPaYg/VNPoccfkF5lgABwy5biM2ibKzxc5rzRBYT6b3LlklumoXhCDtVGIlTrTqRsAxSgbAN0lyqYfAzlQi1a5O6Ji5OZSUnBx2zZIk9COj6GuJ4FC/i6g83H5MiRMB8THo6ram7yOh/DBciqgya9AtKrAbL+gPT0ddDjqafkthcF4BYvHr/BIQ+AnPFEK2KhdkIO1UYiVOtOpEKmAVq9erWoV6+eyJYtmwAAMUc3RVcIMWvWLPHkk0+KzJkzi3Tp0ony5cuLJQ6wdPz48QIA4j2ucFfgLrIN0F0oNRdKx8fQ3So6PmbIEPQUKsRvM6xejZ6UKc3m3nB8zM2beBwAPR9D8Klufsxnn6FHlwtlwseoc28C5WOaN0ePjo8ZORI9+fLxda9fj55g8DEE/Or4mDsF0usGTfoD0usGTdKFgjpoUm1kqPGl3xPj1KSJLxBNFxL0e9p6pK2xUDshh2ojEap1J1Ih0wAtWrRI9OrVS8yaNcuoAerUqZMYPHiw+OWXX8T+/ftFz549RWRkpNiyZcstz/jx40X69OnFiRMnfB7+yDZAd6GIj9HlQql8jPKe8pGaCzV2LH+8Z55BDzfnRAjJx5QuHTw+5tdf+bpz50bP6NF8TXSSat2a9/jDx6RNa8bHbNrk7omNlRELo0bxNREf07Il7yE+plixhPkYXYDsiRNmID2xL0kB0q9YIVdcOJD+1Cm5XeUPSB8X59vUUDMKgJ8XulW+bdv4PnqULy+PvWpVaJ6QQ7WRCNW6E6mQaYBUmTRAbnrkkUdEX2VE/fjx40WGDBkCqsU2QHehqlXDD5suF4r4GF0ulMrH6HKhiDMJNBeKJuzqcqGIj9HlQql8DMf1qHyMLheK+JiJE/njER/TqRPvIT6mUiXeQ3xMxow816PyMTt2uHtUPmbCBP54xMfoAmSJj6lQgffcDpB+3Dj+eATSt2vHewikL1s2YZBevVC4ciV+Q0Pvk7x5JZ9Gdxe6PaixLlMmdE/Itm7bAN0uJaYBunnzpsiZM6cYOXLkrefGjx8vwsPDRa5cuUT27NlF3bp1fVaI3HT16lVx/vz5W49jx47ZBuhu0m+/4QdNx/WY8jEEfur4GLoS1vEx48ahR5cLtW2bvMoOlI8pXx49Oj6Gogqeeor3TJiAnuzZeT5m+3b06PiYmBgzPob4knff5T00V6ZmTd6j8jFc3SofowuQvRMgvS5A9naD9GfP8o1N7dryPUq31jsf0dGyiRs/PnRPyLZu2wDdLiWmAfr4449FxowZxSmFVdiwYYOYOHGi2LZtm1izZo1o2LChSJUqldi/fz/7Or179xZu3JBtgO4SvfKKvELlNGwYenR8zNq18ge6CR+zYoW7Jy5OTsz95BO+pmbN0NO4Me8ZMQI9ulwoUz6G5t789BNfN+VCDRrE19SyJXqef573EB+TNy/Px2zcKOs+ftzdo/IxP/7I112iBHo++oivqXVruVrByQSk//VX2XD/9Ze759w5M5CeAmSDBdLrAmQJpI+IwO1g0t9/8w0QrewUKSJXhZyPihXxV1p9DNUTsq3bNkC3S/42QFOmTBGpU6cWy5Yt0/pu3rwpihcvLt7ULGnbFaC7WMeOST5m82Z3j8rH6Obe1K+PHl0uVP/+6NHlQi1Zgp60aXmu5++/JR+jm3tDfIxu7k3DhujR5ULRADtdLtSyZegx5WN0c2+IIVFWb+OpUSP06Obe0NyZIkUS5mNMA2R//tndo4L0n33G10QgfdOmvIdAel2ALLEypgGyq1fzdRNIP3QoXxOB9M4LhQMH4jc1dEzKpqOtWno/qg9qPil2JVRPyLZu2wDdLvnTAE2bNk2kSpVKLFy40MjfunVrUVt326tDlgG6i9S9O37IqlblPd9/j57MmXk+5sAB//gYXS5UjRro6dyZ9/TsiR6TXCgdH3PwoORjdLlQxMd8+y1/PNru0PExvXrJq35Oc+agRzf35vDhhANkVT7mm2/449EdS7q5Nx98gB5dgOz8+ejRgfRqgKwJSK8bkPn00+jRDcjs2xc9ugDZH35AT7p0fICsDqSnLU31QXlgNDKBGDta7aEHbXOGhckYkFA9Idu6bQN0u2TaAE2ZMkWkTJnSuFmKi4sTZcqUES11d4c4ZBugu0QXL8pcqHnzeB/xMR98wHvat5dXvJzGj0dPMPgYOsHo3ud0sunVi/fQYLpatXjPd9+hJ1s2njPZuVOeyHR8DJ3wZs7kj1e5Mnp69OA9Xbqg58kneY/Kx5gMmuS2wS9fxuYXAENSOQUbpNcNyNy3T54g7jRIT7fqqw+6GKD3KU3gVqc+A8iRAk8/LV8vVE/Itm7bAAVTFy9eFFu3bhVbt24VACCGDh0qtm7dKo78f5Bbjx49RFNlGXnKlCkiIiJCjBo1yucW93PKNkKfPn3EkiVLxMGDB8XWrVtFy5YtRUREhNjE3WbrItsA3SWiXCgdH7NuHXqio3EbxE2muVDEx5jkQr3wAu+5U7lQAwbwNVEu1HPP8Z4vv5QnQ67uX35Bj27ujcrH6ObeEB/z4Yd8TTR8Tzf35quv0KPjY0xAejVAlludVkF65e7VeCKQXm0cnPr6a/ToQHo1QNYEpHe7UKCsOnrQZ4HYK3XWj/NB7z+VzwrVE7Kt2zZAwdTKlSuFG3zcvHlzIYQQzZs3F1WVrYuqVatq/UII0blzZ5ErVy4RFRUlsmTJImrWrCnWc7M6GNkG6C6QaS7Uc8+hR5cLNWAAenR8jJoLxfExprlQdBWty4V64QX0JFUulD98zPDhfE00BE/Hx9DcGx0fowbImvAxa9bwdZvwMXSLtw6kpwBZHUhPAbLR0XyArArSr1zp7lEDZHUgPQXI6kD6hC4UaBYVPWj7jngf4ufU0FMAuTrlfN1QPSHbum0DlBxkG6C7QCZ8jEku1LVruDUEoM+FomFwulyopORjTHOhCGJNaj5m61Z3z/XruKIBkLR8TPr0PB9z9KgZSG8SIBsskH7xYrkKc7sDZGfN8m1sqNGlxrFgQfxVTXkHkLfdO4HxUD0h27ptA5QcZBugu0B3Khfq4EF3T0xM0uZCTZqEHl0u1O7d6EkoF4r4GN3cm6pV0UN3+ripWzf06ObeTJ0qVw84PmbvXvnDk5t7o/IxU6fyx6teHT26AFkC6XUBstOno0cH0qsBssEC6XUBssEC6emONXrQCiWtANH32e2ROnX8SeChekK2ddsGKDnINkAhrmDmQhEfo8uFIj5Glwv1xRfypBFILtS5c2a5UMTH6HKhTPiYMWPQo+NjTANkiY/54Qe+bgrT1PExb7yBnmDyMVyArArSz5/P1013QwUTpOfqVkF6urPKqZiY4IH01CTSg7a66H1ITbRbA+QWBROqJ2Rbt22AkoNsAxTi8icXKph8zLp17p6bN5GDAAheLlQw+RhdLhRtb+gCZImP0QXIEh9TsGDCfEzKlDwf8++/ko/hAmRVPkYXIEt8jC5A1gSkVwNk70aQnuY60YMaWWoe1V/ps0CP7dvjv2aonpBt3bYBSg6yDVAIS82FcvvhK4Q5H0O5UDo+hnKhdHzMvHnoCWYulI6PoVwoHR9DuVCPPsrXvXChPOHp+Biq+7ff3D2mfMyzz6Ln9dd5z4cfoqdUqYT5GNMA2UD4GCG8CdLnzYueYIH03MPJ/agPjnUL1ROyrds2QMlBtgEKYREfo8uFMuFj1FwoHR9jkgtFfIwuF8qEj5kyBT0mfIwuF+rKFbNcKBM+5u230WPCx2TJYsbH7Nnj7rl6FWf+AOAMIE4mfEyPHugx4WMyZbq7QXqTCwXng1YP1W0wej16cEM1Q/WEbOu2DVBykG2AQlQqH7NkibsnLg7vrgFImlwof/kYXS5U6dLoCVYuVK5cfN0mfMyFC5KP0QXIEh+jC5Bt1w49ugDZb75BjykfE2iArNdAenXQZFKA9BQgS1t36oP+39UHrUzRwwk/k0L1hGzrtg1QcpBtgEJUxMcULmzGx5w+7e45dUqyDDo+pkAB9ASLjylUiOdMVq+WV946PoauzHV8DN2+HCgf89ln6Hn44cD5GOJ6dHxMkSLoMeFjGjXiPSNHokfHxyQ1SP/qq+jxEkhPFwrlysVvdpxcED3UoYh32wnZ1m0boOQg2wCFoFQ+Ztw43kd8TLt2vIf4mLJl+UZqwQL0pE/Pz73xl48ZO5avifgYt7tqSP36oad0ab5uGmpnysc4c6FIsbFyAN7o0XxNxMe0bs17PvoIPSVKmPEx3MqCysdwk99VPmbUKL6m2wHSc1zPyZOyoeCGtt5JkJ6aeOdDvfPL7S6wu+2EbOu2DVBykG2AQlCUC6XjY9RcKI6PuXzZjI+hXCgdH0O5UDo+hnKhAuVj1Lk3Oj6GcqF0fAzlQun4mBkz0GPKx+za5e5R597o+JiaNdGj42PefRc9jz3Ge2bPRo+Oj7kdIH2HDryHQPry5XnP3LnoSWqQvm1bOb3b+VCZH9sA2bpvx2slQrYBClC2AQoxJTUfQ7lQ4eG4yuOmpOZjxo1DT44cPB+zbZusOyn5mKee4j0TJqAnqQdNvvsu7+nUCT06kJ74mGCA9CaDJqtUQY8OpO/aFT3BBulp9TGhh7MJuttOyLZu2wAlB9kGKMS0ahV+kFKmNJt7s3q1u8c0F6pJE/TocqGGDUOPLhdq7Vr0REcjd+QmNRdqxQp3T1wcck8A+lyo5s3Ro8uFGjECPfny8XX7y8f89BNfN6WFDxrE19SyJXqef573jBqFHlM+5vhxd89//0k+Rg3wdNadlCD9r7+iJyICtyfddP68DJANNkhPd9WZPIjTuhtPyLZu2wAlB9kGKMT0zDP4QQomH8P935vwMTdumPExDRqgJ1h8TNq0gfMxFG8QLD6mWLHA+JgTJ8z4GIpnMOFjlPDkePIySN+kCe+5nSA9rZqZPAgwvxtPyLZu2wAlB9kGKIS0b59cet+7192j8jFTpvCvRXxM1668h/iYKlV4z/ffo0eXC3XggH+5UBMn8scjPqZTJ95DfEylSryHQi91uVAqH7Njh7tH5WMmTOCPZ8LHvPceeipU4D3B5GMoiDVQkL53b/SYgPS6AFk1iHXLFnePKUif2AsFWjVK6HHPPdj43a0nZFu3bYCSg2wDFEJq2xY/RPXq8R7iY0xzoQLlY8qXR8/77/OeDh3Qo+NjKBdKx8eoc28OHXL3xMTIXKjZs/njPfYYenR8TMeO6NHxMd99hx5TPuaPP9w9ly7JQZMzZvDHM+FjunRBj46P8Rek37/f3XMnQXqubn8vFFSQnraFE3p06XJ3n5Bt3bYBSg6yDVCISOVjVq5095jyMc2aoceEj9HlQhEfo5t7c/asHC6n42MoFypYfEzevDwfs3EjeqKi9HwMcT06PqZECfQEi4/Jk4ev24SPOXfOjI+hAFkTPubZZ3kPgfS6AFkC6SMi9CA9DcjUgfSPPoqePn34mgikN7lQcIL0tJ2b0GP//rv7hGzrtg1QcpBtgEJE/fvjB0iXC7VkCXp0c2/+/lvyMbpcKOJjdLlQDRuiR5cLNXAgenS5UEuXokeXC6XyMbpcKOJjdLlQjRqhR5cLNXgwenRzb5YvR48uQFblY37+2d2j8jHDh/M1vfQSepo25T2ffooe3dwbAul1AbIqH7NmDV+3CUj/yivoCSZIz3E9gV4oUPyI7kGTsO/mE7Kt2zZAyUG2AQoB+cvHdO7Me3r2RE+gfMzBg/7xMVxWkhB4QgHAW8k5+cvHcD9o1Fyo339391y/jhEUABhJwaluXfQkFR9DXM/Wre6eGzck13M7+BinCKTXBcgeOya5ns2b+bqDDdKXLJnwhULatPEvFNT0d+5BK1R38wnZ1m0boOQg2wCFgIiPMc2FOnzY3RMTI/mYOXP441WsiJ5evXgP8TG1avEe4mOyZeO5np070RMWps+FIj5m5kz+eJUro6dHD95DfMyTT/IeCpDNmpXnenbvlnWbzL2ZPp0/HvExb7/Ne4iPqV6d90ydih4d13M7QPpu3XhP9+7oqVqV9yQ1SE+3urtdKKjxFm6P3LnlFuXdfEK2ddsGKDnINkAel8rHmORCvfAC7/n8c/TocqE2bEBPMHOhBgzga2rVCj3PPcd7KBdKx8f88gt6EsqFIj5GlwtFfMyHH/I1vf46eurX5z1jxqDHlI8xCZBduJCvu0wZ9PTty9f0xhvoefpp3vP11+gxBem5ANmLF+WAzHnz+Lopf+uDD/ia2rdHT506vEe9UEgMSH/jhr75ARDi44+l/24+Idu6bQOUHGQbII9LzYXi+JjjxyUfs3Gju8eUj3nhBfQEyseoc284PubkScnHrFvn7lFzoXR8DEUY6PgYf3OhTAZN6viYggXRo+NjaO6Njo+huTcFC/J8zJo16Elo7o0JH/PII+jRgfQmAbLDh6NHB9KvW4eehAJkgwXS6y4ULlzQNz9RUb6zkO7mE7Kt2zZAyUG2AfK4atXCD44uF6pXL/RUrMh75sxBTzByoYiP0eVC1amDnvbtec8HH6CnXDm+IZk3Dz0ZMvBzb44cSZiPUefe6HKhnn4aPW+8wXv69kVPmTJ83QsXokfHx6hzb0wCZMeM4WuqXx89r73Gez78ED06PmbxYvSYBsjqQPo8edCjA+kpQPbVV3nPgAHoCRSkVwdkuoH0J0/qGyDnMMy7+YRs67YNUHKQbYA8rNuRC9WzJ+/p3Bk9NWrwHuJjdHNv/OVjdLlQVauip3t33tOtG3qClQsFwAfIqnzM1Kn88apXR4+Oj3n7bfTo5t5Mn44eHR9jEiB79aq8w2nSJP54xMfoAmR79ECPLkB25kz06EB6NUB25053z7VryJAB6ANkg3GhcPiwvgFyNql38wnZ1m0boOQg2wB5WK++ih+ahg15D/ExulwoUz6GcqGWLHH3qHxM//58Ta+9hp5A+ZjNm9Fjysf88ANfd7D5GF2ArAkfowbIzp/P1+0PH6MLkPUySE+3lbuJQHrdgEwC6XUXCpcuyQsFDqSngZVuj9Kl4/vv5hOyrds2QMlBtgHyqNS5N4HyMZQLFUw+xiQXSsfH0NybpOBj/M2FChYfoxs0+dln6Hn4Yb7un39Gjxf4GBLlX+kGTaogPTdoUgXpdYMmTUB6ulAIFKT/9lu+AXJbNbubT8i2btsAJQfZBsijev99/MCUL897iI8JRi5Ujhzo0fExlAvVti3v6dMHPY8+mvDcm4T4GKrbhI/56iu+pmefRc/rr/MemnujGzSpBsgGysfQ3Jsvv+RrIj5GN2iS5t7o+BhTkJ74GB1InzcvenQgPQXI6kB6CpANBkgfrAsF2rZ0PtKnd9/uvZtPyLZu2wAlB9kGyIO6fNksF4r4GF0uVNeu6AkWHxMWpudjTHKhHn8cPbpcKH/4mCxZAuNjuFwop558Ej3B4mMyZTLjY3btcveoc2+Cxcc89hjvCSZITwMyTUB6XYAsgfTBuFCgup0P7vN1N5+Qbd22AUoOsg2QB0W5ULlzm/ExXC7U+fNy7o2Oj6EEbB0fQ7lQOj6GcqF0fMyWLegJD9fnQpnwMWXLokfHx1AulG5+zDffoMeZC6Xq99/Ro+Nj1ABZHR9ToQJ6dHzMm2+iR8fH0JaNjo/xF6TXDZr0MkivGzTpD0jv9uD4s7v5hGzrtg1QcpBtgDwmlY8ZNoz3ER/TpAnvGTIEPYUKBY+PWbXK3RMXJ3Ohhgzha2rSBD0vvcR7iI/R5UKpfMypU+6eM2fk3Jvly/m6ixRBjzrkzqnmzdHTqBHvIT5GN2iSAmRNB00uW8bXXawYegYO5GsKFki/aRN6dCD9f/+ZgfQlS6LHiyC986EbLXE3n5Bt3bYBSg6yDZDHpPIxJrlQW7a4e27cwJUYgKTNhTLlY379la872LlQJUokzMekTYsncDepfMymTe4eNUB21Ci+JuJjnDNlVBEfU6yYGR9jEiC7fr27R+VjRozgayKQvlkz3kMgfeHCwQPp167l6/bnQuGVV3gPgfS0nag+uGR6Ie7uE7Kt2zZAyUG2AfKYKBdKx8dQLtTjj/OeadPQkyWLWS6Ujo+h+TE6PoZyobp25T3vvIOeKlV4z4wZ6AkGH2MyP4YCZDt14j3vvoseHR8zezZ6gjlocsIE/nhPPYUeHR+T1CA9DZocN44/XlKD9P4MmqQhmOqD+54IcXefkG3dtgFKDrINkIek5kLp+BharueuTuPi8OQBgGnknNq2RY9ufsy4cejR8THbtqEnPBxPlm5S+Zi5c/njlS+Pnvfe4z0dOqDnqad4z4QJ6AkmH6MbNPnYY+jR8TGdOqGnZk3eM3GiXI3g+BiaVxMWhs2gm9QAWd2gySpV0OMVkP7y5TsH0hPnpj5C6aTtxZps3bYBEkKI1atXi3r16ols2bIJABBzdJDk/7Vq1SpRqlQpER0dLfLkySO+dLlldubMmaJQoUIiKipKFCpUSMyePduvumwD5CG98gp+SHRzb4YNQ4+Oj1m7Fj06Pub0acnHrFjh7omLw+0MAP3cm2bN0KObezNiBHry5ePrNuVjgjX3pmVL9Dz/PO8ZNQo9urk3Gzeix5SP0c29KVECPR99xNfUujV6GjTgPSYg/a+/yoabA+nVANlFi/i6CaTv14+viRqMZ57hPbcDpNddKBBI37u3+wpQKJ20vViTrds2QEIIsWjRItGrVy8xa9Ysowbo0KFDInXq1KJTp05i9+7dYuzYsSIyMlLMVO7SWL9+vQgPDxcDBgwQe/bsEQMGDBARERFiIzfHw0W2AfKIjh2Ty/WbN7t7/OVjdLlQxMfocqFM+Ji//w4+H6PLhTLhY5YtQ49u7o2/fMzIkXxNxMc0b857Pv4YPUWK8HWvWIEeUz7m55/5uomP+ewzvqY7BdKvXu3uUQdN3gmQniB+2wDZum0DJMSRI0dEnMsPq7i4OHGEG3FvIJMGqHv37qJgwYI+z7Vp00aUV/bzGzVqJGo7bpOtVauWeFGX0OyQbYA8ou7d8QOi42O+/x49mTLxc28OHAje/BgTPqZnT/To+JhZs9Bjysfs2OHuUefH6PiY2rXRo+Nj3nsPPTo+Zu5c9ARz0KSOj6lbFz06PqZ3b/SY8jHBAul1gyYJpA/moEnu55F6oWAC0usGTdKFAg2apAbNNkC2btsACZEiRQpxymUL4fTp0yJFihT+vpwsxKABqly5sujoGFw2e/ZsERERIa7/n8XImTOnGOqIEhg6dKjIlSsX+7pXr14V58+fv/U4duyYbYDutC5elMv18+bxPuJj3n+f91AulI6PoVwoHR+j5kIdOuTuiYmRuVC6rVfKhXr3Xd5DuVA6PoZyobJlSzgXypSP0Q2arFwZPTo+pksX9Oj4mMmT0ZM1K8/17Nkj696/392jzr3R8TFeBOlNBk0GC6RXLxQ4kN7tQsHZ/ITaSduLNdm6Q7cBCgsLE/+4LOn++eefInXq1P6+nCzEoAHKnz+/+MjBAaxbt04AgDj+/3ydyMhIMdnxA2Xy5MkiKiqKfd3evXsLAIj3sA3QHRTxMfnzJ8zHJFUuFPExulwoEz7GJBfqv//McqGIj9HlQhEfo8uF+vJL9OhyoShANhh8DAXIfvghXxPxMc8+y3u++go9urk3/oL0CxfydRNI36cPXxOB9PXq8Z7bAdIHeqHgBOkvXZInKVoZC7WTthdrsnV7pgGKAEN17doVAADCwsLg/fffh9SpU9/6u5s3b8KmTZugRIkSpi+XaIWFhfn8WQgR73k3j/M5VT179rz19QEAXLhwAXLmzBmMcq0So5s3AT77DH/fpQtAihTuviFD8NcmTQCyZnX3jBkDcPkyQPHiANWru3t++glgxw6ANGkAXn/d3XPyJMDkyfh75b0Sr+5hw2Td4eHuvqFD8deXXwbIls3d89VXAJcuARQtClCjhrtn5UqAbdsAUqcGaNPG3fPPPwATJ+rrjouTdXfunHDdL70EkD27u+frrwEuXgR45BGA2rXdPWvWAGzZApAqFcAbb7h7/v0X4Ntv8ffduvF1U02dOgFEMD/OyNOoEQD3uR43DuDCBYACBQCeesrds24dwK+/AqRMCdCunbvnzBmACRP0dQvhW3dkpL7u558HePBBd8/48QDnzgHkzw9Qr567Z/16gI0bAaKjAdq3d/ecPQvwzTe+davvqUcewc+IldVdJOMGaOvWrQCAzcSOHTsgKirq1t9FRUVB8eLF4a233gp+hYruv/9+OHnypM9z//zzD0RERECmTJm0nqzcCRIAoqOjITo6OvgFWyVOc+cCHDoEkDEjQPPm7p5DhwDmzMHfd+ni7rl+HWDkSPx9164AXBNMjdSrrwLce6+75/PP8fUqVAAoX97ds2ABwB9/4Gu0aOHu+fNPgFmz9HXfuAEwYoT0JFR3ixb4vXLTqFEA164BlC0LULGiu+eHHwD27wfIkAGgZUt3z9GjADNm4O+5RurGDYDhw83rbtYMIHNmd8+XXwJcvQpQpgxApUruniVLAPbuBUifHqBVK3fPX38BTJ+urzs21r+Gu2lTgCxZ3D2jRwNcuQJQsiRA1arunqVLAXbtAkibFqB1a3fP8eMAU6fq61YvFDp35uumRuqVV/gLha++wguFYsXkhcK0afLvy5e3DZDV3Sd/l5datGhxW7aGwGALrHv37qJQoUI+z73xxhvxIOinHKxH7dq1LQQdSiI+RpcLRXyMLhfKhI8xmXtz6ZJZLhTxMbq5N8TH6HKhiI9Jqlwo4mN0uVDEx1SvznumTkWPbu7Nvn1y6XvvXnePysdMncofj/iYbt14D4H0VavyHuJjMmc2A+l373b3qCD9pEn88Qik79yZ9xBIX6kS7yGQPmNGnus5eFCC9Dt3untUkP7bb/E5uouNHgMHhua2jRdrsnV7ZgvM7wYomLp48aLYunWr2Lp1qwAAMXToULF169Zbd5P16NFDNG3a9JafboPv0qWL2L17txg3bly82+DXrVsnwsPDxaBBg8SePXvEoEGD7G3woSSVjzHJhVq61N1jysf4kwtlwsfo5t6ofMzixXzdxMckRS6UyseY5ELpAmTLlEGPLkD2jTfQowuQ/fpr9OTMGRgfYxogW64cenQBsgTS6wJkCaTPnt0MpOcCZFWQXndR6M+FQq1avMftQoG+J/Sgry3UTtperMnWbRsgIYRYuXKlAIgPHzf//+yQ5s2bi6qOK7dVq1aJkiVLiqioKJE7d27XQYgzZswQBQoUEJGRkaJgwYJilm5arYtsA3QHRXNvWrTgPTT3pmhRs1yoM2fcPSdPyrk369a5e9S5N8OH8zXR3BulYY8nyoV65BGzXKh//3X3/POPnHuzZg1fN829cdwV6SOae6MbNEm5UAUL8kD6mjXoMZ17s3Klu0ede6MbNNm0KXp0gyaHD0fPww/zda9bh56kAulbtECPDqT//HP0mID0kZE8SK9eKOhA+uLFfS8U/v3Xt/kBkPEgoXbS9mJNtm7bAHlZtgG6QzLNhaLl+vHj+deqUwc97dvzng8+QI9u7s38+egJZi7U11/zx6PJu7q5N337okc392bhQvQEMxdKN/emfn306ObefPghenRzbxYvRo9pgOwvv7h7YmNxxQ5AP/emYUP00NwbNw0YgJ7ixfm6ly5Fj27QpBogy61Ix8biZHAAbIQ4vfBCwhcKgwcnfKGwfHn8CwXKeVMfNEgz1E7aXqzJ1m0bIC/LNkB3SMHKhfKXj9HlQlWtip6kzIUC4HOhVD4mKXOhgsHHmATIPvkkerp04T09eqCncmXeM3MmeoLBx5gEyNaqhR7HnDIf9eqFnooVec+cOejRDcg8fDjhC4Xr12WArD8XCrGx8rZ69UETokPtpO3FmmzdtgHysmwDdAek5kItWeLuiYvDmAqApOFjNm9GT0J8DHE9ScnHmOZCcdPZTfkYyoUKlI/55hv06Obe/P47enR8jDr3Jlh8jA6k//Zb9HgJpO/cGT06kH7SJPToBk2qFwo0aFLd6lIf9FkItZO2F2uyddsGyMuyDdAdEPExhQub8TEmuVBr17p7VD5m2DC+JpNcKOJjgpkLtWqVu8c0F4r4GJNcKB0fo+ZCmfAxy5fzdRcpgp6PP+ZrIj6mUSPeM3IkevLlMxs0aQLSL1vG1018zMCBfE1JDdKbXCgkFqSngYnOBzVLoXbS9mJNtm7bAHlZtgFKYpnmQtWrh55g5kLp+BjiegLlY25HLpQJHxPsXCg3UYCsjo+hANk0afgAWVM+hgJkdXxMUoL0aoBssED6Zs14j78gvcmFAoH06has83HoUGietL1Yk63bNkBelm2Aklj+8DEJ5UJlyYK+pORjdLlQ+/cnnAuV1HzMjBno0eVC/fFHwgGyt4OP0QXIzp6NHtMAWR1I7w8fowuQff999OhAetpW0oH0R44kLUjfp0/8CwWKwnB7nDwZmidtL9Zk67YNkJdlG6AkVFycEKVL4wdBx8dQLtQzz/CesWPRk9R8TO/efE3t2qGnbl3eY8LH0NybYPAxFSqg5733eM+bb6JHx8dMmIAeXYCsCR8TEyP5GN3IikqV0KPjYwik1/ExwQTpKUDWBKTXDZokkF43aNLfCwUdSE8XCjRo8uJFuZXp9jh/PjRP2l6sydZtGyAvyzZASSh/+ZjVq909N28ihwOg52OaNEGPCR9ToIAZH3PqlLvn9GnchgAQYsUKd48pH9O8OXoC5WMoQDYYfEyxYugJFh/z0EN83Zs2oUfHx9wOkL5BA94zejR6cuf2Hkjv74UCheG6PSIiQvek7cWabN22AfKybAOUhCI+pk0b3kN8TOnSScvHjB7N10R8TOvWvIf4mBIlEuZj0qY142M2bXL3xMbi4DwATKTnRHxMy5a8h/iYYsX4umkuTOrU/NwbddDk+vXuHpWPGTGCr8mEj/n4Y/ToQPoVK9DjJZB+yBD0BAOkp4bbH5A+Lk5ePLg90qUL3ZO2F2uyddsGyMuyDVASad++hPkYde6Njo+hXCgdH/POO+ipUoX3mPAx6twbjo9Rc6F0fAzlQnXqxHtoMJ2Oj6FcqGDwMTRocsIE/nhPPYUeHR/z3nvo0fExc+eiJxiDJu8USH/hgrvHFKTPlQs9dwqkX7WKb34AkE8L1ZO2F2uyddsGyMuyDVASqW1b/ADUq8d7xo1Djwkfo8uFUvmYefP44xEf8/77vIdgUUforo/85WMOHXL3xMRIPmb2bP54jz2Gnnff5T3+DJrUzb3ZtQs9YWEIS7vp0iXJx8yYwR+vShX0BGvQpG7uzZ0C6R9/nPeYgPTBvFAgkL5rV/kcTZXmHg89FLonbS/WZOu2DZCXZRugJJDKx+hyoQoXRo8uF6pZM/TocqFGjEBPvnz8NoPKxyRFLlTLluh5/nneM2oUenS5UBs3okeXC6XyMbpcKAqQ/egjvqbWrdGj42OIKdHNvfn1V/REROD2pJvUANlFi/i6CaTv14+viUD6Z5/lPV99hR5TkP7oUXePCtIvWMDXTSB9nz58TcG+UEiRQl4o/PWXXBXkHoULh+5J24s12bptA+Rl2QYoCdS/P775S5bkl+uXLEGPjo/5+28zPobmx5jwMa++ynsGDkSPCR+jy4VS58eY8DEjR/I1NWqEnv+HCLuK+JgiRZKGj3n4YfR89hlf00svoSep+BgL0qNHBekpD0/3KFMmdE/aXqzJ1m0bIC/LNkC3WSofM3Ei7zPhY3r2RI8JH5MxI/9hU/mYHTvcPaZ8TO3a6EkKPkbNhfr9d3ePKR9Tty56gsXHZMhgxsds2eLuuR18jClIz332jx0L/qDJpADp1QsFGjR57ZrcNtM9KlcO3ZO2F2uyddsGyMuyDdBt1vjx+MbPnp1frt++HT0J8TH33ou+YPExtWrxnu++Q4+Oj9m5Ez3B5GN69OA9Xbqg58knec/kyejR8TF79si6A+VjqlVDz9tv85633kKPjo+ZNg09weRjpkzhj0cgvcrHOBUskF4dNKkLkA3WhYIbSE/cVEKPWrVC96TtxZps3bYB8rJsA3QbpfIxgwfzPuJjXniB93z+OXpM+JioKDM+ZulSvm7iYwYM4Gtq1Qo9zz3He/zhYxLKhSI+ZvFivm7iYz78kK/p9dfRY8LH6AJkiY/Rzb25cAHvngIQYuFCvu5HH0VPsPiYnDmTBqSnPC0TkF4XIEsgffbstwekpwuDhB7164fuSduLNdm6bQPkZdkG6DZq6VJ805vyMRs2uHtiYxFoBtDzMXSHiy4XavBg9Oj4mOXL0ZM6Nc/HnDwp+Ziff3b3qHyMLhfqxRfR07Qp7/n0U/TocqHoFudUqZCDcdM//0g+hnKh3OouWBA9Q4fyNb3yCnpefpn3DBuGnoIFeT5m7Vr0REfzXM+dAunz5w99kH7rVrPmBwBZp1A9aXuxJlu3bYC8LNsA3UYRH6PLhSI+pmJF3jNnDnp0c29UPoabe3P9ulkuFPEx7dvzHgJKy5XjG5L589GTIYNZLtTWre6eGzfMcqGIj3njDd7Tty96dFzPDz+gRxcgq/IxmzfzdRMfM2YMX1P9+uh57TXeQyC9bu6NCtJzAzL9Bem/+IKvqWFD9OgCZAmk1wXI+gvSm1woqAGydCcfgNyK4x6tWoXuSduLNdm6bQPkZdkG6DaJ+BhdLpTKx+hyoSpXRo8uF6pzZ/TocqEmTUKPLhdK5WN0uVCZM6NPlwtFfIwuF6pbN/TocqGmTkWPLhdK5WN0uVDEx1AulJuqV0dPt268p3t39FStynu+/x49mTPj98xN6qBJEz5m0iT+eDVqoKdzZ95DIH2lSrxHBek5rkcF6XfudPeoIP233/LHowuFN9/kPSYXCgTSqxcKZ8/KlTOuCaIGnGoI1ZO2F2uyddsGyMuyDdBtEuVC6fgYyoXS8TG//IKehObHENej42NKlUKPjo+hXCgdHzNmDHp0fMxvv8m6dblQJnwM5ULp+BjKhdLxMV9/jZ6cOfm6abvENECW42Pi4nB1DEDPx7Rvjx7doEl/QXouQDYmxgykr1gRPTqQvmNH9HgJpKcLBRWkp9ECzqZHnQek/r5799A9aXuxJlu3bYC8LNsA3QapuVDr1rl71Lk3gfIxn3yCHl0u1MqV6NHNvfnnH8n1BIuPeeUV3jN0KHp0fMyaNegxzYXS8TGUC/Xpp3xNTZui58UXec/w4eh5+GG+7nXr0BMdHTw+RgfSt2iBnkBB+g0b0JMQSE8BsjqQvnhx9CQFSE8XCipIf/OmzIyjptat6VEfvXuH7knbizXZum0D5GXZBug26P338c2um3szbx56dHNvVD5GlwtFfIxu7s3TT6NHN/emTx/06PiYhQvRY8rH6HKhHnwQPbq5N88+ix7d3JsPP0SPjo9ZvBg9gQbIxsbiiRhAP/fmuefQo+NjBgxAj46PUUF6kwBZmnvjVjc1Ayof45Q/IH3RomYg/Zkz7h7TCwV/QHo1QJZmHamND/3/On9PnsGDQ/ek7cWabN22AfKybAMUZN2pXCgdH6PmQnF8zO3IhapWjfeouVAcH7N/f8Jzb65exZk/AGa5ULoA2R490FO5Mu/xd+6Njo/Jlg09ugDZWrXQowPpe/VCj25A5uzZ6AkUpL92zQykr1MHPboBmf5cKCQGpCeYX31Qowggt42pwQTAu99C9aTtxZps3bYB8rJsAxRkjR6Nb/TcuXnORM2F0vExNPfmhx/cPSof07cvXxPxMU8/zXvGjkWPaS6UCR8zfz5fN+VCffABX1O7dujRzY/55hv06HKhfv8dPTo+Rp17M2cOfzwKkO3Vi/e8+SZ6atfmPd9+ix7TAFkdSE9zb2bO5I9XqRJ6dIMmgwXS794tG24dSE8XCtOn88erWhU9/oL0Bw/6cj+01QggV53UZojYqLFjQ/ek7cWabN22AfKybAMURN28iXlIADj/hdPLL6MnqXOhVq1y98TFyVwoHR/jTy6Ujo8xyYU6c0ZyPcuX83UnNhfKqZEj0ZMvH8+ZqHNvTpxw95w9K1cTli3j6y5WDD0DB/I1EUjfsCHvIZD+oYf4ujdtkid8btCkOiBzyRK+7pIl0dO/P18TgfT16/MeE5B+82azCwUC6dULBZq+rTY+tLpFzQ41aQBy9XPy5NA9aXuxJlu3bYC8LNsABVEqH6PLhSL2INBcKH/4GF0u1J3iY3S5UMTH6HKhiI/R5ULdDj6mZUveQ3yMLkD2p5/kyTlQPoZA+hEj+Jrc+BinbgdIrwuQJZBed6GQWJD+8mXfJofet7TipK780GolbaPOnh26J20v1mTrtg2Ql2UboCAqWHyMmgsVCB9z5Urw+BjKhQo1PsYtF8opEz5GnXsTKB/z1FPo0Q2avN18jCo1QFY3aLJePfR4HaSnOBDaQqbGhxpKALkqSv9fNGdp8eLQPWl7sSZbt22AvCzbAAVJKh9z9Ki7R+VjFixw96i5UL1788fzJxdKx8dQLlSKFGa5UHPn8scjPsYkF0o394ZyoUz5GH9zoZzyJ0C2Zk3eM3GiPJlyfMyuXejR8TEWpE88SK9u09H2l8oCUVNEd07SiiVdKKxeHbonbS/WZOu2DZCXZRugIMkfPqZAgcD4GDUXasUKd4+aCxVMPsYkF0rHx9BJKVh8jC4XivgYkwDZYPIxH33E10R8TIMGvOdOgfT9+vE1EUj/zDO853aA9LoLBQLp1QsFeh/SNhe9Dq300FYnbR3SChJNNv/ll9A9aXuxJlu3bYC8LNsABUHqcj3Hx6i5UDo+pkED9Ojmx1AuVMmSZrlQHB9jmgtlwsc8/zx6dHwM5ULp+BjKhUqd2iwXKlA+plEj9Oj4mI8/Ro+Oj1mxAj06PubUKbNBkyYg/UsvoUfHxwQTpKeGmwPpb970D6TXDZoMBKSnGwyosaEVHso2o88grQDRyg+tcO7YEbonbS/WZOu2DZCXZRugIIj4mCpVeI+/fMyuXe4eNRdq4kT+eDVroqdTJ95zO/iYHTvcPWou1IQJ/PGIjwnW/BjdoEl17o1u0CTxMbpBk8HiYxYskCsXOpCeuB6vgPQ0dDAYIL3JhYIbSH/ypGzo6VdqlJ2/UiNKLBCtTP7xR+ietL1Yk63bNkBelm2AApTKx3C5UELgyRogeHxM9uyB8zEmuVD+8DG6XCjiY3S5UCofE2guFPExurk3xMc8+STvIT4ma1azANlg8TFvv817iI95/HHecztA+ilT+OMRSN+1K++53RcK1KjRqg81gNR40zYXbWe6RWMcPx66J20v1mTrtg0QadSoUSJ37twiOjpalCpVSqzhlsGFEM2bNxcAEO/xyCOP3PKMHz/e1XOFAxldZBugADViBL6x8+dPOBdKx8eouVAmfMygQXxNLVuiR8fHmORC+cvH/PgjX7cJH9O6NXp0fAzlQpnyMVyArMrHLFrE1126NHp0fMzrr6NHx8d89ZU8KZvwMUkJ0tety3tMQHp10GSgID1dKLz3Hu9xu1C4cUOu1NHWJ4X/0mvSr5RRRo2SOivov/9C96TtxZps3bYBEkKIadOmicjISDF27Fixe/du0alTJ5EmTRpxhAEBz507J06cOHHrcezYMZExY0bRW/mBNn78eJE+fXof3wnuBMvINkABKDZWsgVffMH7GjZEz6uv8h5/+Jg0acz4mA0b+Lrz5UOPCR/TvDnvCRYfc/Kk3Jb4+Wd3j5oL9dlnfE3ExwRz0OS//7p7/vlHbqOsXs3XTXzMkCF8TcEC6deuRY+XQHq6ULhdIP3Mmfgc3fUXFiYbRQqTrVYNf6XVKkq9J14IAFf5QvWk7cWabN22ARJCiLJly4o33njD57mCBQuKHrolekVz5swRYWFh4k/lCmv8+PEiQ4YMAdVlG6AANGuW/KHLLdcfPCiX13Vzb2iZ/ttv+ePVro2eN9/kPe+9J3+4c5o7Fz2mfMzvv7t7VD7mm2/441EmU7t2vKd3b/SUK8c3UvPno0fHx6hzb0z4mLFj+ZqeeQY9js+tj/r2RU+ZMnzdP/yAnnTp+Lk3JnyMCtKPGcPXRCC9btBkUoP0dKEwahRfUyAXCtTcUOQHrdxlziy/r7TyQ+9H4rboLrgUKfA1Q/Wk7cWabN22Abp27ZoIDw8Xsx2sRceOHUUV3X64onr16okajoye8ePHi/DwcJErVy6RPXt2UbduXbGF+6H/f129elWcP3/+1uPYsWO2AUqsiI/R5UJ17IgeHR/z3Xfo0fExO3fKK1sTPkaXC2XCx3TpIq+WOU2ejB5TPmb/fnfP5cuSz9DlQtFJTsfHUASCKR/DbRfv2yc5k7173T1XruDsHAA9H/PEE+gJFh+TOTPP9XgZpM+YkT8BqBcK/oL06meDGluqnX7NlUuuMBJnRROyyZMmDb5eqJ60vViTrds2QH///bcAALHOccvuRx99JB5++OEE//3x48dFeHi4mO44OWzYsEFMnDhRbNu2TaxZs0Y0bNhQpEqVSuznTjRCiN69ews3bsg2QH6K+Bjdcv1//8lcqKVL3T1xcRj3AKDnY1q1Qs9zz/Ee4mPy5OG5HhM+5tw5yccsXszXTYzFhx/yNfnDx+hyoX77TdZtkgu1cCFftz98jC5AlviYnDl5PmbrVvSEh5vxMSYgvS5Atn179OiCWMePR48OpN++Xa6KmAyanDWLPx5tNfXsyXtMQHq6ULj/ft+66f+KGvvUqeXKJK2GPf00/pohgxwzQFuOtNWbObP8ukLxpO3FmmzdtgGiBmj9+vU+z/fv318UKFAgwX8/YMAAkSlTJnGN+2H1f928eVMUL15cvKnZIrErQEES5UK1aMF7KBeqaFF+m2H5cvlD2yQXyoSPGT6cr4muenV8zKefoueRR8xyoQLlYygXauhQvibKhXr5Zd4zbBh6gsnHrFzp7lH5mE8+4Wtq2hQ9jRvznuHD0aObe0MgfXQ0vh/cZArSExOjA+lbtECPDqQfNQo9OpB+wwb0BAOkd7tQOHdOXmQ4t7ZSpZJbYTQ4s1o1uSVGM4NoOGWuXPiaoXrS9mJNtm7bAAWyBRYXFyfy5csnOnfubHSs1q1bi9q6qz+HLAOUCJnyMSa5UHXqoEeXC/XBB+gx5WMCyYW6cUMOidPlQtEVdZs2vMcfPsY0F2rzZr5uEz6mfn150uPkLx/Dzb3xl48JFKSnAFkdSE8BsqYgveOizaduAulHjuRrogsFE5C+SBH/LxQIri5QQK6iUdNZt678nNJqD91pmDKlZLxoHAJdjIbqSduLNdm6bQMkBELQbR1D0goVKpQgBL1y5UoBAGIHty+uKC4uTpQpU0a01E3jdcg2QIkQ8TEOJstHkyahR5cLtXs3enS5UKZ8TNWq6Onenfd064ae6tV5z9Sp6NHlQu3bJz/QJnzM1Kn88apXlychTt27o6dqVd7z/ffo0fExBw5IPmb3bnePysdMmsQfr0YN9OguTHr2RE+lSrwnmCA9BcgGC6SvUIH3EEivG5B5O0B69UIhLk5uZ9EWcY4cEnambbX8+eW2J7FWRYr43nIPgCtMQoTuSduLNdm6bQMkhLwNfty4cWL37t2ic+fOIk2aNLfu6urRo4do2rRpvH/XpEkTUa5cOdfX7NOnj1iyZIk4ePCg2Lp1q2jZsqWIiIgQm7irTRfZBshPqXyMLheK+Jj+/fnXoqX3+vV5z5gx6NHxMZs3oycYfAzdEdO3L18T5ULp+Jivv0aPKR/D5UJdvChvZ54/nz+eP3xMnTq8R+VjuLpVPubwYXdPTIwcNDlnDn884mNMQHrdyu6336LHFKQ/eNDdYwrSV66MHt0FXOfO6AkUpOcuFGgsRNq0ciW1TRv5f0Pv01atJABNU8QbNJArhnRnGd05GaonbS/WZOu2DRBp1KhR4sEHHxRRUVGiVKlSYrXCRTRv3lxUdVzhnjt3TqRKlUp8xYyy79y5s8iVK5eIiooSWbJkETVr1ozHGSUk2wD5KeJjdHNvVD6Gm3uj8jFr17p7VD5GlwtFfIwuF2roUPQULMhzJmvWoMc0F0rHxzzyCHpM+BhdLtTt4GOWL+frJj5m8GC+JuJjXniB95gMmlT5mOPH3T2mID2tegwYwNcUbJBex/WcOye5nmCB9M4LBdrOfPVVuUVKKzxVq8rvCTU499wjm+Du3eX7mNixJ57A1w3Vk7YXa7J12wbIy7INkB+6fl3yMUmRC7VwIXpM+ZjffnP33Lghh73p+Bh/cqFKleLrXrwYPcHIhaJpvSa5ULoAWeJjihc342O4uTfHj0uuZ+NGvm7iY3QBssEC6X/6CT0JgfS0CqILkPUHpHdZsb6lTz5BTzBBenVy/pEjcnutVy/5nqRb3Ol9CiAvWp54Qt7yPnKk/HuCuWlFM1RP2l6sydZtGyAvyzZAfsiEj9m7Fz3ByIUiPqZbN95DfEy1arxn+nT06PgYk1yoq1dlLlSgfEyPHuipXJn30HRf01woEz7mu+/44xEf07Ej76GTrW7Q5Jw56AkGH+MPSK8LkPUXpDcZNMmB9OqFgglIrxs0yV0oEF9VvboQZcvi7/v3l7V98QX+Wriw3Bbr3l021MTopU0rQWqaZB2qJ20v1mTrtg2Ql2UbIEOpfIwuF4q4A93cm7Fj0aPLhTLhY0xzoegEoZt7064denS5UN98gx7TXCiOjzHNhapQAT26XKg330SPCR/zwAMJ8zEpUuj5GJO5NzSNWDf3hviYpAbpv/+eP15SgvQmFwpXrsgLBRWkv3JFfj3UvISHy23HokXlVleHDvJzO3mybDqpSc2XT66y0Z1qoXrS9mJNtm7bAHlZtgEylJoLpeNj/MmF+vRT/njByoX6+Wf0BCMXqkgR9ASaC0XbD/ny8ZyJaS4U8TEmAbIDB/I10ZyYhg15D60qPPQQX/emTegxnXujA+kpQDZQkH70aPToAmTvFEhvcqHgBOlpIGLOnHIlsW5duRX63nuSQZs2Td7S/+OP+GvatPKuwccekzEstBIVqidtL9Zk67YNkJdlGyBDER+jm3tD3EHp0vw2w6JF6PESH/PRR+gpUYKvWz15BMrH5M2LHh0f8/zz6NGNdBg0SF7xB8rHJDT35uZNmTKuC5Bt3Bg9zZrxHuJjggHSE9ej8jHOuulWcR1IT0MBkwqkpwuFVavcPSpI77xQKFcOn+/XT0ZffPedbIZpRlNYmAziveceuepTqpRcLXruObmN3KULvn6onrS9WJOt2zZAXpZtgAxkwsdcuSL5GF0uFCVRBysXKlA+xjQXqlYt9AQrF0rHxxw6lPhcKKeeego9Oj6Gbo0uX573zJuHHtNBk9u2uXvUuTdJDdJzXI+/ID1zV6oQwj+QXnehwIH0dAdaVJR8L6VPL3mxHDnw80cNPcWsPPmkbDwbN5azf9q1k9uoNIogVE/aXqzJ1u2ZBigFWFklRp99hm/funUBChZ090yZAnDqFECOHADPP+/u+f13gJ9+AggPB+jY0d0TEwMwZgz+vmtXvqYhQ/DXtm0BUqfW1127NkDhwu6eadMATp4EeOABgEaN3D07dwL8+CNAihR83ZcuAXz5pXndb7wBkCaNu2fECIC4OICaNQGKFHH3fP89wPHjAPffD/Dii+6e3bsBFi8GCAsD6NTJ3XPlCsAXXyRc99Ch+GubNgBp0/J137wJ8MQTAMWLu3tmzgT46y+A++4DePlld8++fQALF2LdnTu7e65eBRg1StYdFqav+/XXAdKlc/eMHAkQGwtQrRpAqVLuntmzAY4cAciSBaBJE3fPgQMA8+fj77t0cfdcuwbw+ecJ103vk9atATJkkM/T19yoEX6PAABeeAFgyRL8/bPPAqxcib9//HGAzZvx96VLY30AAA8/jJ9VAICsWQEuX8bfp0rlXouV1d2goLZed4nsClACCiYf06yZvALlRFBn/vz8NoMpH2OSC+UPHxNoLpS/fIwuF4r4GF2ALMUeNGjAe24HH7NoEV83ZVPpQHq6aymYIP3Ro+6eUALpT5+WW36rVsmBpCtWyKnjS5fKEQQLFsjv94wZ8hb5776TMRijR8vtP8qiC9VVCy/WZOv2zAqQbYBcZBugBGTCx6i5UBwf428u1KhRfE2UC6XjY2j4my4Xiibp6vgYk1yomzflSUfHx1Dqto6PoVwoHR9DXIeOjzl1Sp4sdYMmTfiYl15Cj46PGTIEPYUK8Y2rvyA9x8eoIP2QIXxNwQLp/Q2QDRZI7xw0SXdrlS4tt7kefFDWlz49bvtS83TqlPzMHTokRwps2CAbujlz5EBFYulC9aTtxZps3bYB8rJsA6SRKR9Dw9V0fAzNLdHxMWouFPdBUXOhkpKPMcmFuuceno9R594Ei49p14730J09ZcvyjdSCBfLEyfExR49KrkfHxxCMq+NjaNVBB9L36ydP8sEC6X/5xd0TGyvjIEaP5mtq0AA9rVvzHn9A+sQMmoyNlQzSN9/I926vXhJifvFFOfKgbFm5cpcxI74v6SR05ox8rQ0bJN9GGWqhetL2Yk22btsAeVm2AdJowgR802bPzs+P2bFDXnEeOuTuiYmRuVCzZ/PHe+wx9Lz7Lu+hgMdatXgP3Sasy4XatQs9YWF41ewm01yoKlXQ8847vIcCZAPNhdqzR9a9f7+7R50foxs0SVsib7/Ne956Cz2PP857pk1DT5YsZoMmuQBZddBkUoP0XN0qSL9rF193sC4UOJCehjRmzIjNNDWl+/bJ6dXTp8vVo3fekdubNWpg003/Pi5Org4ePixzzWhGUqietL1Yk63bNkBelm2AGKm5UIMG8b6WLdGj42NMcqE2bkRPQrlQJnxMiRLo0fExlAul42MoFyp37oRzoSIicNXBTWqArI6PoVwoHR9DuVA6Pobu/NHxMVu2oCchPoa4Hh0fQ0njOj6mbVv06PiYcePQo+Nj6EQeHi7E/4OU48l00KSahs6pQwf0PPUU76ELBd2gSfVCgRs0qbtQoObprbfk7fjlysmGODIS32e0Evfjj3JGUo8estkrVw59dEK6fFnOLaL/41A9aXuxJlu3bYC8LNsAMSI+Jk0aBIrdpPIxGza4e9RcqJEj+eMRH0PTaN1EfEyRIvw2w/Ll6DHNhfr5Z3ePmgv12Wd8TcTHNGnCeyiLSZcLtWoVekxzoUwGTZrwMS+/zHsoJDOp+JjChdGjC5ClFQ4TkD5fvuCB9D/9xNdNIH2gFwoE0jsHTe7bh8+HheEqKwHwo0ZJ1q12bWysqBmKiZEN9cyZcouuaVP5eunT4+vT951CckP1pO3FmmzdtgHysmwDxIhyod58k/fQLBGTXChTPkaXC0V8zDff8MerWxc9Oj7mduRCbdni7rlxQ+ZCjR3L10R8jC4Xqm9f9JQpw9f9ww/oSZfOLEB282a+buJjdAGyBNC+9hrv6d8fPSVLmoH0HNdzO0D6V1/lPf6A9LfzQoG2fevVkytJkZHYWNIq1pdfyjvjKlXCbVD6Xh0+jIGzALi6SDB6/vz4+vT9Isg/VE/aXqzJ1m0bIC/LNkAuUvkYXS6UCR9DfEGPHrzHhI+hXKhA+Rg1F2r6dP541aqhR8fHUC6UKR/D5UKZ8DFXrshbnXV8zBNPoMeEj6lalffQlokuQPbAAVn37t3uHn/5GF2ArMmgyVAH6Z0DMi9elLfpL14sgednn8XGik4sf/8tb2d//30EvwHwMxoXJ/m6adNkDEalSngMCsqlcNdQPWl7sSZbt22AvCzbALnIHz4mTx6ej6EfwsHkYz78kK/JHz7mwQd5Pua332TdHB9jmgvlDx9Trx7v+fpr9DhzoVSpc29M+Jh58/jj0crC++/zHgrc1PEx48ejR8fHbN+OHl2AbEyM5GN0QawmIH3HjugxAel1Qaz+gvQzZvDHI5DeeaFAIHO+fPj/Treyz5yJK3MA8k4/amRWrpSfz5o18XUIiv/tN5lFR7lv1GBRKGuonrS9WJOt2zZAXpZtgBxSc6FM+Jjhw/nXevFF9DRtynv84WNSpgycjylYED009M1Nr7yCnkD5GMqFMuVjVq5096i5UDo+xmTQ5PDh6NENmly3TtZ98qS758wZMz7GH5DeOfdGlT8gfVSUHqSnzCwdSF+8OHpMQPrnnuM9JhcKHEivzg0aOlTmut17LzZltPr00Udy9TM6GlcLaQhmz574NdMJ6MIFvHUeABtYIeTnnZr9UD1pe7EmW7dtgLws2wA55C8fY5ILRUvrTql8zNdf8zU9/TR6gsXHpE8fOB9Dc1SCxceUKpVwLpTpoEnd3BsKkP3iC74m4mN0AbIDBqCneHG+7qVL0ZPUIH2LFryHhgkmNUivu1AgkN55oUCsTurU+P2jBrdNG2xk6Pu2axf+fwIIUb06/lsCpWfNkiux99+Pf0fNUb9++L2lkxNdXITqSduLNdm6bQPkZdkGSJEpH1O1Knq6d+c9xMfQD2Q3TZ2Knvvu4/kYumMFQC7RO6XyMVOn8serXh093brxHmIsdHwMMRQ6Pkblekz4mEmT+OPVqIEek0GTlSvzHuJjdAGyKh/DBcheuya3W2h4npuCBdL7O2hSB9LTFlIogPQvvCAb6JgYuXL188/yPZgvHx7/+efxzx9+iJ8HauL//FPOl6L3Bl1QjBnjOyCRTk6hetL2Yk22btsAeVm2AVJETIGOj/E3F0rHx9D8kb59+ZreeAM9Tz/Ne/zlY44ccfeowCnHx8TF4UkPAE+CnIiPqVOH9xAfkz27WS6UyaDJOXP441WsiB5K/XaTP3yMbtDkzp3oMeVjdFxPsEF6Hdeze7es+8ABd09SgPTqJOtt2xAgB8AtwLg4uU371lu40kT1rFsnV3wyZ0YvTQWnFT3i0ubNw61jOjnRlmionrS9WJOt2zZAXpZtgP4vlY/R5ULRnSY6PoYGtRUsmDAfk1AuVLD4mKZN0WPCxzz8cNLyMYMH8zVxuVCqiI/Jl4/nTDZsQE9Cc29olWHpUr5u4mMGDOBrChYfQydzXYCsCtIvXszXTSB9//58TQTS16/Pe0wuFFSQPjEXCrTCRHdq0V1yffpgs0wg+9q1sklOkwb/jrbDqImlzyxxWDQscdMmXCGi9zMpVE/aXqzJ1m0bIC/LNkD/18KF+AbV5UKpfIwuF4r4GF0u1LPPouf113nPhx+ix4SPSSgXyh8+hkIh3fTcc75X027yl4/xNxfKWTfxMZ9/ztdE2ym6AFniY4oW5esmEDchPob4lHXr3D1JDdKvXIke00GTa9bwdfsD0usCZLkLhWvX5Nbo1KnY+NH23sGD8v8gSxb8/6dAV2p4qPmkO+FoxWfWLPz+0P/Nn39KePqee+TxQ/Wk7cWabN22AfKybAP0fxEf89ZbvOftt9FTrRrvmT4dPaZ8zJ497h41F2ryZP54lAvVpQvv6dEDPTo+ZuZM9GTMyPMxai6UCR/z3Xf88SiAsmNH3kNzb0wGTTrnx6g6dEieQLdv5+smPmb8eP54deqgh+4gcpM/fIyO6zEB6a9fDz5I/+ijfN3qhYIJSG9yoeAE6YmNoy3GTz7BP9P8ozffxD/TEEe6mKAVHlqhmz0bvw7a1t2xw/eOsCtX5ErVAw/I44fqSduLNdm6bQPkZdkGSPjyMbpcKPpBqsuFKlsWPbq5N+3aoUeXC/XNN+jR5UKpfAw3P8Y0F6pCBfTocqHoxFO7Nu+hNG7TXCgd15Mxo7xy51SpEnp69uQ9nTujp0YN3nM7+BgK13QTgfS6ANlggfR798q6kxKkN7lQcAuQpf9T+gzRVumYMfgZoy2s+fNxBYg+l7/84gtAHzniy/hcvixXfCgG4+ef8c/58snjh+pJ24s12bptA+Rl2QZIyFyol17iPbTMnlS5UDT/5OOP+ZqIj2nUiPcEMxeK+Jhly/i66ep74EC+pldfRU9icqFUbdqEHh0fowbILlnC1023Tevm3tDt07oBmTS4L3fupAXpdQGybdqgRzcgk2Ikcubk6zYB6f29UHCC9BT2GhGB/6f056gofA9SiG3q1NjQ0PcyfXqsm94TBEBTg5MrF74+zdSiGAzaii1aVNYQqidtL9Zk67YNkJeV7Bsg9W6TX39198TGylyo0aP51yI+pnVr3kOhjCVK8NsMP/6IHt3cG1M+xiQXyoSPGTRIniiCxcdQ9pJTN29KrmfECL6mxo3R06wZ76Htk8KFzfiY06fdPf/8I+ferF3L112gAHpMQPrE8DGq/AXpV61y98TFyQDZTz/layKQ/sUXeY8JSE9NiduFAiW4U1Pftatvs0x3dFETSgHBdJckNc7EA9Gdhk88gX+mlSfaDp43D/9ctqysIVRP2l6sydZtGyAvK9k3QJQLVaUK76FcqEyZeK5H5WN27XL3+JsLpZt7Y5ILNXs2enS5UOr8GK/kQtFJScfH/Pmn5GO2bXP3qAGy48bxx6tXDz26uTd9+sgTJddILVggVyM4kP7o0cD4GFXEvrRpw3sIpC9dmq970SL0JATSm1woEEhvcqHgBOnPnpXN2po1+H2gzwuNZaAVRnof0nuOgGxaXaStXPqcEPtEK6LUUFFWnTr3KlRP2l6sydZtGyAvK1k3QKZ8jEkuFPExulyoCRPQY5oLFSgfY5ILRXwMZSa5yd9cKB0f408ulI6Pobk3dGXvJhqAFww+hrKkpk3jj/f44+gJFKRXA2STAqSnANlggfS6QZM6kJ5WvWiVke5wzJwZPy+HD8vPxr//YoNL27LUBBcrhn+meVA0IJEaJGqIqEmnFSL1cxuqJ20v1mTrtg2Ql5WsGyC6GtTlQgWTj6Efzia5UIHyMZQLFQw+pkQJ9CQFH6PmQnF8jL8BssHiY3Ll4usmNiUYIL1JgGywQHpibEwDZG8XSK9ue9LqEW0VUrNCHB6t1tJMqowZ8d9fvixXBen/gFaM6PtNt8hTqDDNDFLnNYXqSduLNdm6bQPkZSXbBkjlY0xyoeiWWzcNHIieYsX4bYZly9CT1LlQzZvzHuIndHzMihXoCUYuFPExn33G10S5UE2a8J4hQ9Cjm3tDOVK6ANl//zULkCU+ZsgQvqZQB+l1AzJVkJ5ruAO9UKDVngwZ8CRx4YL8Gml2FU2WptUcypGjVHcadnnfffj1x8XJgZx796KHYj7GjsU/0wwllccK1ZO2F2uyddsGyMtKtg2QyseY5EIFi4/R5UKZ8DH+5kIlBR9DYKoJH6PLhTp6lM+FIt24IW+DppOYm0z4mH790JNUfIwJSN+gAXqSAqRXA2Q3beLrNgHpaavJBKR3u1Cg91nnzvhn2poqUAC9Z87I98bBg+ihW/JpACZNBKftrL/+wj+Hh8stZ7prbv58/DMxUmpgb6ietL1Yk63bNkBeVrJtgIiPSYpcKJWPMcmFmjmTP16wcqGIj8maled6aGaKjo8xzYUiPkaXC/XWW+hx5kKp8pePoSt/p9S5N1Om8McjPqZrV94TqiA9BcgGCtKrgyYTc6Fw6JD8uvfvx+fo/ULbrvQ5K1YM/3z1qly9o+8VbR/TFhzd3Zc3rzwWNf3U8NH3QB3IGaonbS/WZOu2DRBp1KhRInfu3CI6OlqUKlVKrOHGzQshVq5cKQAg3mOPA3icOXOmKFSokIiKihKFChUSs2fP9qumZNkAqXzM8ePunv/+k8v1P/7o7lHn3uj4GOIOdHyMP7lQERF4deumYPIxlAul42O++go9ulwo4mMiIng+Rp17Eygf07YteurV4z3jxqFHx8eoc29M+BguQFYIM5C+QwffFQw3BROkpwBZ3c8ME5C+Uyf06EB6CjN1A+kJDKcLjaNHZUNE33e6c4y+fzTP5/775WoSDUwkTonem8QbqTEYNMeIbgJQgftQPWl7sSZbt22AhBBi2rRpIjIyUowdO1bs3r1bdOrUSaRJk0YcYQaKUQO0b98+ceLEiVuPWOXkuH79ehEeHi4GDBgg9uzZIwYMGCAiIiLERm4ujIuSZQNEfEyLFryH+Bjd3Jvly9GTKlXgfIxJLhTxMbpcKBM+hk4eOj5GzYUy4WN0uVAmfMywYegJJh+jC5AtXBg9Oj6mWTP0BHPQpEmArAlIrxs0SSshxMa4ibaLTEF63YWCPyC9M4j18mV5RyNtS1GWHN0pd/myvBjZvBmfo7gRmkl06ZLcIqOLA1pRpFWws2fliYjuCiQIvm9fWVOonrS9WJOt2zZAQghRtmxZ8YYjh6dgwYKiB7OVQQ3Qf9z+vRCiUaNGorbjbopatWqJF3WDyhxKdg2Qysf8/ru7R+VjTHKhdHyMP7lQweRjTHKhdHwM5UKVKcPX/cMP6EmXjs+FUvkYOnm51U18jG7uTf366FF5DacIjC1Zkq97yRL0JBUfc6dAem7QpArS6wZN+gPSFymSMEjvNmiS7lR78EGsSx3KSGwa8WM5c8pj0FYwBQ5Tk5k1q/QQB0aMEEWZqMGnNNxRbYRD9aTtxZps3bYBunbtmggPD4+3PdWxY0dRheEGqAHKnTu3uP/++0X16tXFCscdHzlz5hRDHVfeQ4cOFblo7LuLrl69Ks6fP3/rcezYseTVAAWLj1FzoYhbcMqUj6G7W7p35z3+8jHc3Jt9+5KWj6FcKHXQnFPff48eXYDsgQN3ho+pVIn3zJqFHh0f4y9I/+23/PFq10aPDqR/7z306EB6CpANJkj/zTf88ejOK+eFgroVS6MhaAxCypSyqaYRCxRAe+mSbE5p5tTIkfjnOnXk6z/yCD5HW9jEBBUoID0Eb6t3VIbqSduLNdm6bQP0999/CwAQ69at83n+o48+Eg8//LDrv9m7d6/46quvxG+//SbWr18v2rZtK8LCwsRqZTsiMjJSTHYMOJs8ebKIiopia+ndu7dwY4uSRQOk8jGLF7t71B/KzuV6VcTH1K/Pe0z4GEqjDkYuFPEx6nK+U2+8gR6KDnDT11/LK+5A+Riae0PbG24iPsaZC6Wqffv4Jzin6M6h7NmDx8fQQD03VayInqQA6XfulA033QXllNdBeueFAt22Hh0tt2Lp+0Wr2LGxshmnrUHK71JXhOh2fnoPxcbKlTAKCqYLBPWik5oz9U7IUD1pe7EmW7dtgKgBWu9Yku7fv78ooF6NJKB69eqJp5UTV2RkpJjiuEKfNGmSiI6OZl8jWa8AUS6Ujo9Rc6FM+BgOZL95E3OcAPR8zCuvoOfll3kPTcjV8TGUCxUdbZYLpeNj6Mr5k0/4mmjrwGR+jC4XiobZmfIxP/3E100QrG7QZIsW6DEZNJk3L8/H0Mk7Kip4IP2AAXxNtAqiDuxz6k6B9DRU0E10ofDss/H/jt77xOJdvy4nbv/wAz5H748MGWQzTqtzagYczTwiEP3QIfn/Q98LmsP0wgvy39HdZlOnyudC9aTtxZps3bYBSswWmJv69+8vChYseOvPidkCcyrZMEDXr+MVI4AZH+PgtXzkDx+TPj3Pxxw7FrxcKBM+hmaelCrF100D6dKm5efe+MvHfPklX5MJH0NQbPHifN20KhDMQZPEjriJAmR1IP3gwejR8TEE0usGTZ46JUF6xyryLZmC9C++iB7doEkaDmgC0pteKDhB+pMn5XuIZicR65M1q1wxpTvEVIC+XDl8jvi8S5fkdh01dTQHqVAh+e+ocVKz6mj1UZ1wHaonbS/WZOu2DZAQCEG3bdvW57lChQqxELSbGjZsKB5XGJBGjRqJpxy3zNauXdtC0G6aMgXfgCa5UAD6XChaklevGp2iIW26XCjiY3S5UJRereNj1Lk3u3e7e9RcqEmT+OPVqIGeQHOhiI/R5UKpfIwzF4p07RpuDQHgVhEnEz6mVy/0VKzIe4iPufde/oeVKUifPTt6dHwMgfTEt7iJBk0GCtIfOSJB+q1b+bpNLhSeeSawCwWC1cuVk88RdK2+96ipI4bu/Hn5NdDWK60SqbfE011u6ggHCkpVt7Zp9U1doQvVk7YXa7J12wZICHkb/Lhx48Tu3btF586dRZo0acSf//8Q9+jRQzRVbm8eNmyYmDNnjti/f7/YuXOn6NGjhwAAMUsJv1y3bp0IDw8XgwYNEnv27BGDBg2yt8G7KS5OToBNaj6GGXNgxMfExeF0ZYDA+Ri62yZ7dr5ulY8hbsKtbpp7Y8LHmORCJQUfExMjb7c24WN69uQ9NDumRg3eM2mSXM0wAel1AbIE0n//PX+8qlXRowPpu3VDT/XqvGfq1IQvFFSQ3uRCwQnS37gh4Wlqav/7T65y0V2OxA9FRspV1IUL8bmHHpKvR1ut6twnmk2kXoBQs6lOEKcGS93KDtWTthdrsnXbBog0atQo8eCDD4qoqChRqlQpH6C5efPmoqpyp8zgwYNF3rx5RcqUKcW9994rKlWqJH6gfXFFM2bMEAUKFBCRkZGiYMGCPg2SiZJFA6TmQun4GFquX7XK3aPyMZ9+yh+P+BjdStzw4ejR8TE//4we3dwblY9ZvpyvmxiJwYP5moiPURkJp+huG10ulMrHmORCLV3K103zY3R8DA2a1PExFHqpm3tDfIwuQPbcOTn3xgSk1/Exr72GnkBB+s2b0WMK0rv8HLlVt8mFAg2aTOyFAq0OqncrUuCsmktHowHUUR/UxKlRITSvSR2OSdEz6rZx6dLxLzioEVMjTEL1pO3FmmzdtgHyspJFA0TzQF5/nffcjlwoCnF0KjYWQVUAPR9D029bteI9xMeY5EKlScPPvTl+XDIZOj4mb170mPAxJrlQukGTP/2EnoSCWInr0fEx+fOjRzf3pnFj9KhwrVP+gvTOuTcklesxAemHDeNrotR0NdDTKQLpCxYMDKRXB00m9kKBwGN1lY1W3lSAnfgc9TNCjaV69ysNtVQbG+K41NEhtCWpfi7prjl1tEKonrS9WJOt2zZAXtZd3wCpfIwjRuSWVD7GMVbAR08+iR4dH0O5UDo+ZuZM9Oj4GJNcKFM+plYt9Kh5R06Z8DGUC2XKx2zfztdNc29MBk3q+BgaNFm+PO8hPkY39+bPPyVbopt74w9I72D+fNSnD3oCBemPHk1akJ7YHROQ3u1CgXLxUqSQ28N0x1ZYmFzBOn5cnjRoNe7MGfmZoDvvYmLk+41816/HnwodFycbfDWOhZo5dSRCqJ60vViTrds2QF7WXd8AtWuHb7y6dXmPSS7Utm3yB7dJLpR6V4lTFSqgx4SP0eVCffstenS5UDt2yLp182OIj9FtoVaqhB5dLhTxMYnNhSLdDj5GzXtyqmtX9DzxBO/xB6RPKECWbvcOFKSnu6RMQHrTAFndhQINmkzshQJ9HtVcPFp9VWcOjRmDz5UtK58jQF25E/bWNnG2bPK5ffvwudSpZZN25ow8CdF7Li5OPqeOYAjVk7YXa7J12wbIy7qrGyB1ud4xRfuWTHOhaNCaLhdK5WNMcqEC5WPoDhZdLhTd+aLLhTLhYzZtQo8pH6PLhSpZEj26AFkTPoZOksHgY2juTaB8jAlIT7xLrlx83SYg/YUL/oH0ugBZkwsFGjSpu1D4/XfZcDtB+vPn5fuD5jnFxcntKnUKNjE8KvtFFwXqyhqxdCoATbfTU3K8EO4xGJcvyxOT+vMvVE/aXqzJ1m0bIC/rrm6APvoI33Q6PsbfXCjuDjvTXCgavW/Cx+hyoVQ+JpBcqNvBx6ggq1O6XCiSysesXcvXXaAAeoLFxxQqxDeupiB9QnyMGiBrAtLrAmT9Bel1gyapbh1IT4MmTS4U3EB6ukAoWFC+PwiYT51abk9euCDft+r2L4H8M2bI5wiA7tNHPkf/n+qwS3rfqatH6qqQ2tCF6knbizXZum0D5GXdtQ2Qulyv42NMcqHefRc9jz3Ge4iP0eVCHTrkXy7UhAn88egKWR3q5tT776NHlws1d668Mg6Uj6E7atRYAafq1Yt/Fe8Uzb0pW5ZvpOgqP316swBZEz6GgjXdRCC9LkCWBk0GE6RX705SZQrSN2iAHvWuKadMLhQIpNddKKggvfNCIS5OAt1q7hatPCkjQG5lw+XLJ+s5dUqeRNTBiwRbL1ggn6O71NStWrq9X82k++svfC4iwrfWUD1pe7EmW7dtgLysu7YBmjAB33A6PsY0F8qEj3nssfg/dJ2i2SSB8jEEkoaFISztJjUXSr1idqpKFfQEyseY5EL5y8dMm8Yfj+4k0vExFCCbFHzMlSvBA+lp0KRuSvydAulNLhTcQHpasUybVm43XbsmP1vqVi9FZHTrJp+j/6eiReVzFy/Gh6KFkCG9KmA/bBg+p25h798vm1FVoXrS9mJNtm7bAHlZd2UDZJoL1bIlekxyoXR8zMaN6ImM1OdCEf+gy4WiuTc6PoZyoVSQ1KnRo9GTOzfPmVDydjBzofr142tq0wY96nRep2jujY6P2bJF1q3e0aPqwgU590ZdHXDWHSw+hgZNmoD0CQXIBguk79ABPeocHadMLhRUkD6xFwp0h5maCE9Q8wMPyM/W9evy6//5Z+kltkptwNaulf9eVa5c+Lw6FoGaSnVSOPFKWbPG/1pC8aTtxZps3bYB8rLuygZo2TJ8swUzF0pdtneKRvg3b857Pv4YPbpcKOIUEpp7Q3yMeoJQpeZCffYZX9NLL6FHlws1ZAh6THKhUqZMXC6UWjfxMUOG8DU1aYIeXYAsXfHrAmTpBGo6aFIH0hOfYsLH6AJkgwnSU92Uou5Wd7FiCV8omID0uguFI0fk1q+6EkXbc+oqHq0UZcni+zr0flabQgo3VYHzy5flqpDKatGQT/XCgi5ccuf2rTdUT9perMnWbRsgL+uubICIj9HlQr33HnqCwceY5EIRH6PLhapbN/5VslP+8DG6XCiVj6HoAadu3JBX02p8gFOUC6XjY/wdNGkSILt5M1937tzoGT2ar8kfPqZkycD4GH8DZJMCpPf3QiGxID2FkKoRHGfOyO+HOi+K7vRSw3GJ1UmRwvf7S6C4elcerVbdc4/v100/E9T5TTSw8pFHfOsN1ZO2F2uyddsGyMu66xqgYPIxNJ1Wx8d06YKeQPkYyj0KC0M2wU2mfEy1avGvrJ0y4WOmTZNX4ya5UHv3unvUXCgdH0PshsmgSRVmdYog2kyZeK7nwAH/+JiJE/nj+QPSV6rEe24HSK8bNGlyoRAoSH/1qnzPqltjNHqhRAn5XFycbLjV2/qJiytd2ve1abVw4UL5HH0PH33U10ujF9TtUBo06XzdUD1pe7EmW7dtgLysu64BMsmF+vJL9OTJk3AuVDD4GMog0uVCvf46ep59lveY5EL99pusm+Nj1FwoHR/z6KPoUW8xdoruuFHnsDhFuVA6Pkade2PCx8ybxx+PIhTef5/3UICsbtBkMEH6e+9F3+zZ/PFMQPqOHdETKiA91ZIjh+97lhgmdauT2K7UqX0bV9qCe/tt+ZwKQKvbgIMH43PO7VFqCNW76ggkdzaloXrS9mJNtm7bAHlZd1UDpPIxulwo4gmGD+df68UX0aPenuvUp5+ix4SPSZXKjI/R5ULRFe/QoXxNdAdNMPkYk1yolSvdPWou1Cef8DXRPBcdH0Op3/nzm/Exurk3xMfQQD63uk34GH9A+rx5AwfpaUBmsEB63YUCgfS6C4WEQHpqRvv3l8/R3VcpUvg2LxRr4oT76XZ/NXyWcsuyZ/f10gWQ2rTfvCm3TdVhmNSc1ajh+xqhetL2Yk22btsAeVl3VQNEP0B1fAzlQun4mCNHJB+zdau758YNmQul42MoF+qNN3hP377oCTQXypSPobk3Oj4mWLlQ6qBJbu6Nv3zMF1/wNTVsiB4dH0Mp40nBxyQ1SL98OXqCAdLToEkdSE8XCm4gPU3hjoz0bUbpc+q8O40mm6vzrw4flg2Wur1Gww6ddxTSapS61Xr6tDwBqSt5NEnc+RqhetL2Yk22btsAeVl3TQOk5kJNn877iI9Rl9OdIj5GhTadosFqulwoyiQC4OfeqHyMLheK+Bh1NopT/vAxmTOb8TG7d7t71EGTkybxx6tRAz2dO/MegmR1fMysWejJmJGfe3PwoH98jBq94FSwQXrTANlQAunVCwU3kJ5Wx9Qp3DdvSkB9yhT5PAWihof7Tgin8QLO2UK00ukcu0DvSTXxfedO+d5RRXeRvfii7/OhetL2Yk22btsAeVl3TQNkkgul8jG6XCjiY5IiF4r4mEBzoVQ+RpcLVa4cej74gK+J+Jg6dXgP5UJlz85zPf7yMXPm8MerWBE9vXrxHuJjatXiPd99h55s2XiuR+VjdAGyxMfMnMkfj0D6nj15D4H0zq0YVf6C9CYBsoFeKHTrhp7HH4//d6dPy21ddcwEbV2lS+fbyFIz4mzeaeSB8/+dpkqrn9Hz5+WJRl1tpFWxQoV8X2PAAHzeuVoYqidtL9Zk67YNkJd1VzRAN2/KH4g6PsafXKiCBXnOhH6IB5oLZcrH0O2+zitVVSa5UOvWoSehXCgTPoYGTQ4ezNdEs1fccqFIn3+OnkD5GDVA1oSPUUM2nQo2SJ9QgKw/gyZNQHqTAFldw+3vhYJ6FxaJtuuc26MUcutsOqjhUj+/cXHYYAP4ZpRduCBXKNX3MdWdJYvva0+Zgs8773ikO9ycq2WhetL2Yk22btsAeVl3RQO0cCG+uXR8zNGjko8xyYUaM4Y/ngkfQ7lQOj5m8WJ5NWySC6Uu66syzYV67jn0tGrFe+iquHhxvu6lS9Gj42PUXCjdoMm8edHz+ed8TSZ8DN39Y8rHcEGs/g6aDDWQ3uRCwQSkpwsFN5A+NlZuc6m5cFeuyPR6dajk6dNyK01dcSNYOirKd7uWgmlz5PA9Lo1tcG6XUa1OwJ62up3jIkL1pO3FmmzdtgHysu6KBqh6dfcfZKrefhs9Oj6G8oZ0fIxJLtTVqzIXSsfH+JMLpeNj6HZeHR+j5kLt3Onu8TcXqmNH3tOrl/vJSBVFIQTKx1y7JlcKdHNv6tRBT/v2vIcA3XLlbj9If/26BOnVAX1O+QPS6wZNmlwoBAOkp+9Pxoy+nyPiz3Lm9G2avv0Wn1dzvoSQd6E5P7PU0DhXumjYZosWvs8TG+ec00QRJ85xCaF60vZiTbZu2wB5WSHfAJnwMRcuyCvPYPExulwoEz6GcohSpMCTvJtiYvzjY3S5UMTH6HKhiI8xzYXS8TGUCxUoH9O5M3p0fMykSejRzb3ZvRs9pnzM99/zx6Ptmu7deQ/xMUkN0qtgsVN0oaAD6bt3T/hCISGQnhpk5wVJvXru/9+0MulsRBo3xuednB1tZTu3A2mr2Hn7P0WQOLc9CdIeOND3+VA9aXuxJlu3bYC8rJBvgILFx/z8M3qCycfo5sfQD2UdH6PmQnGcyYYN6AkGH0O3Iev4GJNcKJryqwuQNRk0qQbIqjNgnHXTlF911oxTxJ6Y8DHBBOnd+BiqO9ggfc6cZoMmg3Wh4DZokho2J0B+6pRcWVLvLLx8WX6m1K3puDjZ1Dm39Oj2fCczRTOHnM1r7dr4vLodJ4RssJy3+YfqSduLNdm6bQPkZYV0A6TyMeqEV1XB5GMoFyqYfMzGjXzdJnwM5UI5l/1VUS5U0aJ83RRCmdD8mEBzoUgmfMwnn6BHx8dQnlOqVDzX888/kutZu5avm/iYYcP4mkIdpH/pJd4TDJCeVuycK6T02mXK+D5Pt9vnyOH7f0y3rqdK5bsaqd7p5fy+0arjtm2+zxP47ryrkzLsvvrK9/lQPWl7sSZbt22AvKyQboCIj6lShfcQH5MpU2B8jDr3JlA+hnKhHnuM91CmkY6PUXOh1EBJVaa5UMTHdOjAe+iumfLlec+8eejRBciqfIzzZEVS597o+BjaVmnblvf06YOeRx8NjI/xF6R3nlhVPfssel5/nfeEGkgfEyNXkJyrM7Ta5WyKaSK1831HU7+dW58EhOfM6fv8mTP8SYa4Nuf/Gc2ocua8hepJ24s12bptA+RlhWwDpM69mTuX91HmkI6P6dABPTo+hkDNQPmYmBh5paqGQzpVqRJ6dLlQnTqhJ9BcKFM+xiQXqmpV9OgCZImP0QXI0q3LOj5m715Zt46PMQmQ9Qek1wXIEkifJUvwQHpdgKw/IH3lyrwnGBcKtIWYN6/vChK9vyIifFdtYmPlNteyZb6v1aABPu/cjh0yBJ93bmXSVvADD/g+f/OmbLadW630GXNyaqF60vZiTbZu2wB5WSHbAJnwMWoulJo5pOrsWckgOH8Ik9RcKCcwqcqEj6FcKB0fs2kTenTzY1Q+ZskSvm5a/tfxMXQVruNj6I6c3Ll5PoaiD4IxaJICZHV8TJs26HFGGagaOxY9gQ6aNOVjypZFT+/efE1095EOpKcJyLoAWROQPpgXCm++yV8oqOybGnAqhJz07QzMpe20DBl8v8abNyX879wifukl9/czAfxOePuff+TJx/l9pNlKztWqUD1pe7EmW7dtgLyskGyAVD5m1CjeR3yMSS6UKR8TSC7UzZsyF0rHxxCcqZt7Q3yMbu7NihXo0fExp06Z8TEmuVDEx7jlQpGIjylUiOdMaM5LQnwMzb1ZvdrdExcnA2SdJ2VVJnwMTSrWBciagvTE9aizcJx1FymCno8/5msikL5RI94TzAsFAumXLo3/98Q0pUrl+xm5eVPe6u+Ek2lFzTlviFLh06WL37TS/CVn00/bs84tRVqVzZQpfs303nAG+YbqSduLNdm6bQPkZYVkA+QvH2OSC6UGMDpFuVAmfIxJLpSOj/nzTzM+hk4qSZkLlT49P/fGXz5GFyBLcKqOj6GZL7q5N4sWyRNpIHzMjRtysJ8uQJa2bVq35j0E0pcowdf944/oSZMGV/rcpIL0ugBZf0B63YVCQiA9Dat0Dgf9X3vnHh9Vde3xlTevEA2B8EoAeUgAAcNL8IlalFokXqTaWkARJRR5Wio+Qavgq+CDQJVitCiEykOoIh/QCkgBkVsQC1WuoASSgEQkBJC8Zt8/totzMrPXnj3OZM4ZZ/0+Hz/3NmcxszKZmbP22t+9fliEp6TU3sr0eCxY3rswwuGQ3h2ykyetG4n3QEiE6r1BcFy8dOnimzP+Tb27TJF603ZjTpw3F0BuVkQWQJdfLt9MwfIx2DbX8TF2X6ivvlLH2H2hdHwMzr3R8THoC3X99XRMoL5Q+/erY86eNeNjcO5NsHwMTupt2lQ/98YfH2Ofe2PCx0ydSseYgPRvv211EUz4mL171TE/V5C+qMgqIr2HPqIdindhhFxQYqJvUY1A/vPP1/45nvjLzPTNAbezvLf58LOi8ivD95D3gM1IvWm7MSfOmwsgNyviCiATXyg7H2PiC+U9OM0u5GNuuYWOMeFjTObehNIXCvmYoUPpGBM+xj73prBQHWPnY/7xDzrvPn1kzMyZdE7Ix3jzInYtWiRjdHzM7t0yJi5OdtVUsvMxq1fTz4d8jGruDQpB+sGD6ZjXX5cxPzeQHruI3tPKz5yxPofe26u49ezNE1VVWZ8Bb4d53Pb19mjzeKx/Y58xJIQFTau2N/HfeIP/kXrTdmNOnDcXQG5WxBVAdeELRc29sfMxOl8oEz4GW/Q6PgZb/zo+Bo8B16tH+0KZ8DE1NWZ8jIkv1Ny5MkbHx3z8sYxJSpKvq0qlpRYf481loDweIbp2lTG6uTcjR8oYb/8nu/CodceOdN4mfIzpgEwE6XUDMnE6cShBepOFgglIr1ooVFRYXa2lS2tfw5N87dr5fg5xaKH3liIucC680Pdvgp8h7zxKSqyi0btAw8nWkyf75k6dDovUm7Ybc+K8uQBysyKqADLxhaqstHyh3MLH2OfeeK9qUVVVFtdjwseMHUvHBMrHmPhCUYMm64KPufRSOu9162RMo0Y0H1NUZMbHXHSRjJk/n84J+ZjRo+kY7GZ0707nvWGDVXD/nEB63NZs3ty3q4UTmL07Z8XF1g3B+5QjmvGqTiQiM+RdrCGA3bat779BUNz79GZlpZWD9wIoUm/absyJ8+YCyM2KqAII+RidL1Qo+Rj0hVq2jH4+5GOmTaNj0HVa5wsVKB/zxRfqGFNfqOuukzE6Xyg0kTTxhWrShJ57EygfozOQHTSIXtGj8Ni1zkB2xQoZk5pKfykFCtK/8Qb9fAjST5hAxzzyiIwJJUivWyiEAqTHbTbvY/8lJdZr5/0Zwy3jvn19Hw+HE3oXdzoAGq1AVN8LyFN5s0v2x/P+vEXqTduNOXHeXACh8vLyRNu2bUVSUpLIzs4Wm709bmxasWKFuP7660VaWppITk4Wl112mVjntfLJz88XAODz3w/UDVShiCmA7HyMzhcK58fo+Jh775UxOj4mUF8oio8x9YUy4WPQF0rHx+DNIFx8DG5lBMvH2A1kKT5mzx4ZExsrixOVTp+2ZsisXEk/X6hAeuRjWrSg8w4lSH/VVTJGB9JPnSpjdCA9bk+lp9MFt31ApmqhgO+j+HjfTg6yN6qp4dgZ8h5yeO6ctQXqXXBiJ0rV5cFCffx432u4fefN1OG2WUyMb/crUm/absyJ8+YCSAghCgoKREJCgli4cKHYt2+fmDRpkmjYsKE4RAxemzRpknjmmWfEjh07xP79+8WDDz4oEhISxL9tWyj5+fmicePGoqSkpNZ/gShiCiDkY3S+UMjH1K9P8zHffmvxMVQBaveFmjOHzinUfIxu7o1TfIyJL1RiYngMZJGPufVWOmbePBnTvj3Nx4QbpL/7bhnjDe/atWCBjGnXjs7700+tgiNYkD4UCwU0mFXNIUJjXe/txVOnrG0+b2AZt7KaNvX9jD/7rLymYqNwe/XFF32vYVfRezTDwYPy5w0a+P6bSL1puzEnzpsLICGE6Nu3r8jNza31s86dO4vp06cbP0aXLl3E47bJuPn5+SIlJSWovCKiALK363V8zJAhMkbHxzz+uIzp3ZsupN57T8bofKHsfMzOneoY+9wbHR+TkyNjvI8K2/XkkzLGTXzMsGEyJlg+xsRA1oSPqa62+JiXX6ZzCidIf/SoGUiPA/50ID1OQdaB9Nh5MVko6EB6+0JBBdJ//71V2Hpfx05dQoIvN4Rbph07+uaHn01VQYVMk3fXSAhraKR3wVddbW0Feneo0GxVNSAxUm/absyJ8+YCqKKiQsTFxYmVXi35iRMniqt080dsqqmpERkZGeJl2xd7fn6+iIuLE5mZmaJVq1bipptuqtUhUuncuXOirKzs/H+HDx92fwG0dKl885j4QgGEh4/B0yW6vx9+2ael0XzM//2fxcd4r4hRpnwM8hMmfIxufoydj6Hm3hw4ELpBk7glEko+hvqiqQuQXmfE+thjMsYEpE9JCR6kz8yUMTojVhOQ3t9CATubqsGIOBNKBTJj11Q1Uwp95FRmrFjYek+hrqmxCjXv4+zHjlnfCd7bwdhN8zZVFSJyb9puzInz5gKoqKhIAID417/+VevnTz31lOjUqZPRYzz77LMiNTVVHLMdId62bZtYvHix2L17t9i8ebMYNmyYqF+/vthPgb1CiBkzZggVN+TaAsjjsZykdb5QyMcMGULHIB+TkUHzMSa+UOXl1twbio/xeITo10/GPPYYndP48TLml7+kY+x8DJW3nY+hfKFOnzbjYwYMkDEPP0zHTJwoY264gY7BQZM6PgZX4jEx9NwbOx/jbVxpFw6a1HVVTUD6N9+UMTqQ3h8fI0TdgPSqgX6ougDpvY+2CyGLDjyR5d3ZrK62il7v91hlpcWVeXfDzp61Onzexrbff2/dQLw7SocOyZ/Hx/uyeviZSEvz/R1wu031/RupN2035sR5cwGEBdBWr9b9k08+KS6++GK//37JkiWiQYMGYgNl1vmjampqRI8ePcQEzUo64jpA+EVl6gul42O6dJEx3hNm7UJfqNtvp2NefNH68gzWFwq3ET78kM7bhI/BibvDh9MxJnwMumrr+Bi7L5SOj0EORLVtgTLhY+bPlzE6PibQQZM6kN5k0GSoQfq4OPeB9NRCAbdaGzf2PYmG25mpqb7FI9pSNGvm+3fEay1b+naUcKtRBUDjv1MVMjh6oGtX32toN9Kjh++1SL1puzEnzpsLoGC2wAoKCkT9+vXFu9QXn5fGjBkjblS5NRNyPQM0dKh84+j4mD/9ScZkZ9PbDO+/L2NMfaGouTfV1fJGDKBu1aP+539kzN130zE486RHj9DxMd6+Rva8cRtB5ws1fLiMufNOOgb5GJ2BbKB8jFd39Lzs3QYV5IrCIXkjRtAxkQ7Sd+5sNmhSt1AwAelxoUCB9MjaTZrke+13v5PXVNuCeBpQ9Zl4+GF5TcU34ftNBb8jPK4q6LCTpxo/sWqVvKY6pRapN2035sR5cwEkhISgx3l9KWRlZWkh6CVLloh69eqJVatWGT2Hx+MRvXv3FnfpTA295OoCaP9+M1+o9HQZo+Nj0BdqyhQ6Bn2hrrySjlm+XMaY+kL95z/qmIoKuTUEoJ8fg3NMdHwM3jwGDKBj8As/FL5QyMeofKFQ6OekOpqMQj5GdRNCrV4tY1JS6Lk3dj7G24sKZQfp//pX+vnw5u51YKGWZs6UMTqQ/t13ZUwoQfpXXqFzChVI72+hcPCg9d723qoqL7c6mtu21b7m8Viv/5o1vo+L266LFvleQ2hd1QHFI/+qzzUWvKriEscAqIqjSL1puzEnzpsLICGsY/CLFi0S+/btE5MnTxYNGzYU3/w4h2X69OlihG31umTJEhEfHy/y8vJqHXE/aftSmjlzpli3bp04cOCA2LVrl7jrrrtEfHy8+IQ63aOQqwsg9IXydoW267XXZIxu7s1nn8kYUz7G21DRLhM+ZsIEGaPrxL3xhowJ1hfqzBkzXyjkYx58kI6ZPFnGmPAxOgNZOx/jDaai7HyMtxu4XQjG/vGPdMz999M3M5QJSG/Kx6CBrIqPQV17rYzRgfQIC5sMmgw3SE8tFBD+V81Gwve06oQXbvU1aOD7e5SXW4Wgar4TnkhUIQC/+pW8pjqtiK+v6nfBbT7Vd0uk3rTdmBPnzQUQKi8vT7Rp00YkJiaK7Oxsscl2fHTUqFHiatsX4dVXXy1UsPIo29HdyZMni8zMTJGYmCiaNm0qBg0a5MMZ+ZNrC6DvvrPa9To+Bo/APvMM/Vg4Dl/Hx7z8sozp0ME/H5OYaMbHUMyWnY/xHtFv1+jRMkbnCxUIH5OQ4HscGHXypDX3RsfHXHqpjNHxMTgfxoSP0RnI7twpY+LjZbdEJVM+BkH6uuZjhDAD6e0GsqqOCOaNIL1u0GSoQHp/C4WzZ61iW5UzdlmfeML32qOPymsqU2HsOqkYnxMnrJuHaisVffhUnzWcd6X6bsDPu2pbLVJv2m7MifPmAsjNcm0BhL5QPXvS7XoEGXVzb4qLrbk3Oj6mfXsZk5dH52TCxzz9tIzR8TEIbup8oY4etbieUPExI0fSMegL1bXrT/eFEqK2gawJHzN3Lp3Tb38rY+64g46ZM0fG6PgYU5A+ED4mHCA9DpoMJUivWyj4A+mx29qmjW+xffiw1YVSdXHQCFa13YudGtXWPX5WLrrI91pVlfXZVgHkaJuiGsGAgxVVn4lIvWm7MSfOmwsgN8uVBZCdj/nb3+g45GNUMCbqoYdkjG7uzcqVMiaUfIxu7g3yMffdR8fgitmEj9H5Qtn5mN271TF2PkbFYKBwu0E39wb5mD59zPgYau5NYaGVt/cUX5Sdj9HNvUGQ/t576ZhIB+l1CwU7SP9TFwr26dEqFgdBZRU/9/XX8lpcnLpwxu7c4sW+13BBoSrKvvrKKmxVRSQWXSqne3yfqmYhRepN2405cd5cALlZriyAXn9dvlmC5WNOn7a4Hh0fg4aOJr5QOj4GfaFM+RjKF+rsWWvujY6PCcQX6rrr6BgEQk0GTcbE+MKvKDsfU1BAP9/AgTJGNQwPhV2Ba66hY5YtkzFNm9J8jAlIf+6cBdK/9Rb9fIGA9LrTnXUB0pssFCZOpGNwoUCB9Lj9m5TkezrObsGiKkRfeIH+W37/vbWwUG1zYtdVVXRhQdqtmzpn/JuqwHj0D1MNDY3Um7Ybc+K8uQBys1xXAHk81spNN/cG+RidL1RenozRzb355BMZY+oLpVpNYt4mvlBjxsgYFQuBQrdsHR9j4gtVVmbmC4UrcBW7gRo7VsbcfDMds3ChjMnMpPP+97+tbgA198aUj+nbV8bouB4E6XVcT6hAeruBrA6k799fxjzyCB0TCEivGzRpulDwB9Lj8XaVfQj+TZOS1B0mHPSo2u7ELiY1EBY7ZSofOdxGVM2Qqq62CivV5xoHeaoWPZF603ZjTpw3F0BulusKIBxeppt7Y+djgvWFQo8hnS8U8gKh5GN0vlAIdobKFyori+ZMNm2SMcH4QmHeWVky5s9/pnPCG+lvfkPH4Nwb00GTtunotWQH6f/5T3WMHaR/9lk6JwTpVT5VKDSQ7dCBztsO0lPGxaYgPS4UggXpcaFw0UXqhcKxY9bnbccO3+t4elC1TVVaahUiKjYI/61qK+q776wbh+q7AOcKqTqgR4/KazEx6mIcQX0VzB+pN2035sR5cwHkZrmuABo8WL5RdHNvkI8x9YWi+JhvvrE4E50vVOvWMkbHx5j4Qs2YIWNMfKFM+ZhQ+ULp+JgnnpAxvXrRea9dK2OC5WOqqmTnC0DPx6AD+JgxdAyC9Lq5NyYgvd1AVgfS43FtHUh/660yxgSk1xnI2kF6atCkfUCmDqTHhcJLL6lj8HXs08f3WlWVZZuh6tZhl6p7d/VjYxGn2jJFdkkFQAthQc6quU7YsVPZYAhhDaBUweyRetN2Y06cNxdAbparCqC9e61VG8XH2H2h3n6bfqxAfKGuv56OeestGaPjY/77XyvvYH2hTPiYuvCF0g2aDMRAdupUOga5CxMDWVM+Zu9edYx97o0KrkXhTTRYkB4NZEMB0qOXlm7QJC4U6hqkr6qyFgAqzui996xCQ7V9iIWqyg/v+HHrxqDq4s2eLa9RXTfcHlOdNsTiieKDEDBXzQ+K1Ju2G3PivLkAcrNcVQCZ+ELh6Hvd3BsTPsbuC6XjY9AXSsfHmPhCvfqqjDHhY+Lj9XxMqHyhxo2TMTo+ZtEiGaPjY3bvljFxcbKrppKdj6EMZIWQN2sAPR+DWx+DB9MxCNK3amXGx6i2Z4SQX1gmIP3ll8sYE5BeNUQQhQayOpDevlCgBk2aLhT8gfR4QjItTV1I44gFVcf27FnriL7qJN/bb+uLFOyWqY7unztnFZOqrUQ8kEDB/1hAqorMSL1puzEnzpsLIDfLNQWQ3RdKx8d06iRjwukLFQo+Bufe6PiYQHyhLr7YzBeK4mNKS83m3uDpHh0fgwPnTPiYjh3pvLdulTE6PsY+90YFxmLeJiD9XXfJGB0fgwayFB8jRG2Qnho0aQfpdQayoQbpg10o4ERr1QTxkyet975qS3PNGnktI0P9GUNAndru1gHQeJqyUSP1Y+NcK+qzhBPGVVtvkXrTdmNOnDcXQG6Wawog9IXS8TH4hZqSQvMx9rk3Oj4mEF8oFaCJevxxGaPzhcJtglD4QiEf85e/0DnhtkOwvlDo+m3Kx1AWLIHyMaNH0zG4LaLjY0xAejsfYwLSU3yMEIGB9N26+TeQdQtIj52m2Fh1Zw+7g507q38n7OhSfnAIzau8DktLrZuG6r2HjF92tvqxcZuY2pLFE4QqbilSb9puzInz5gLIzXJFAWTKx+BxWp0vlAkfY+oLhW9anS9UIHyMzhcKPZZMfKGaNAmdL5QJH6OalYJ68EEZc8UVdAzyMampNNdj52N0c2+Qj9EZyJqA9I88ImPCDdK/9hr9fIGA9P36+Qfpg10ooMVGTo76OnZRZs3yvVZdbc2EUp1kKy6W12Ji1EUqMjwdOqifGzs8t92mvo6nDanOJZ78U+UWqTdtN+bEeXMB5Ga5ogBCPqZNG5qPQTNFnS9UoHzM44/TOQXCx+h8oex8DOULVV5uzb0x4WN0vlDIx+h8oUz4mD17rNW/CR+zciX9fMjH6AxkkY+54QY6BrkO3dybUIL0yMfoQHocNGkC0qen01yPKUiPRYUJSD9tGh3jb6Fw6pS1ZafagvrmGytf1fsaxxSkpKg/Gzh8k+rg4IRrqsBB7o5ixdDUlSqU0fpG1UWL1Ju2G3PivLkAcrMcL4DsfMycOXRcIHxMsL5QgfIxzz1H54R8DPVFLoQZH4O+UImJZr5QOj4GfaFM+BidgSzyMbpBk9u3yxjTQZOh4mPCDdLrDGQRpNcZyAYC0usWCoGC9P/4hzoG/7bU9hYejacKKCywqM8r/p2oriie0qI6OFjkUQUOvsepwaXYSVTB2ZF603ZjTpw3F0BuluMFUCj5GPSFeuUV+vlycmSMbu4N8jEmvlCNGtFzb+x8jGqAnBC1+RjVkVxUIL5QPXqY+UKZ8DHbttF5Ix8zbx6dk4mBbCB8jG7ujSkfgyC9CR+jA+lx0KQJSF+/vhlIrzOQRWZGt1DArR/dQgGtKSiQ3uOxnks1RNTjsRgj1Skqj8cy6aU6VdiBee899XX8LFMDLNFzj3p/4tY05X+HJxJV4x8i9abtxpw4by6A3CzHCyA8ZRIqPiYtzYyP0flCIR/z5pv082GL3YSPURlEotAXSsfHBOoLpeNjbrxRxgTLx6xaJWN0c2++/triekLFx1BArRBmgyYDBelVPlJC1B40uXAhnRMOmnQjSE8tFLDYbNRI/Vw7dlhFneo1xBNaiYnq64cOyetxcerrdgBatbiw31BUsLjdBoM6TYiFsmr7LlJv2m7MifPmAsjNcrQA2rXL+iI04WN0vlD9+skYHR+DUKeOj0FfqFatgvOFOn3ajI9BXygdH4O+RTo+xsQX6j//kTGmfMzy5fTzoYGs6ng0Cm0OdHzMm2/KGB0fYzeQDXbQpAlIf//9Mubaa+kYU5AeC1cTkH7pUvr5Qg3S6xYKeIqQgrGRM6PsTLATSfmYIYPWr5/6Ok7npgBo5OpSU9XXS0qs94tqq7CmxrohqbbBI/Wm7cacOG8ugNwsRwugESPkm+L22+kYNDzU+UIhH5OUZMbHfPihOsbuC6Uavoa6804ZEywfYzL35vvvLV+o9evpvHv0kDGqEzmoUA2aNJl7c/KkxfUEy8egb1OwfIwJSF9WZgbSo4FssCD9X/8qY3QgfaALBROQXjWZWQj5+LrTeBUVVqFJ/V1xMUJZmaCvGlU8I19EfS/gAEWqgMICqVkz9XV/N6RIvWm7MSfOmwsgN8uxAsjOx1C+UHY+RucLFQgf07NncL5QxcVmvlDIOOj4GBNfqGeekTGXXBIcH2M3kNX5QpkMmsS5NyNH0jF4TFnHx3z0kYzxx8fgdoWOjwkEpL/jDjpmzhwZEy6QvksXGaPypEIhSG+yUAgWpEfbDwpuRuuM9HR1oVlUZH3Zq4pjj8eawUUV9Ph5pl4T/CxTfBZ+ji+5RH3dbsGheq0i9abtxpw4by6A3CzHCqDp0+UbQucLhXyMqS+UCR+j8jNC3XCDjDHxhRowgI4x4WNMfaEQ9tT5Qv3ylzJGx8fgoEnd/Bi8uaWkmM29oQDTykqzQZO/+pWM0c29MeFj3n1XxpjyMaqTP0LUBul1BrJDh8oYE5BeN2gSQXqdgazpQgGnJgezUDh3zjpmT21/YtFODRjECdRUd+arr+T1hAT6M41sFVU4YgeW6hqinQi19VpYaBWCKkXqTduNOXHeXAC5WY4UQHZfqHfeoeMGDJAxOl+oCRNkDMUbCGHGx5j6QqWm6m8QQlhGrDo+Bufe/OIXdAzyMTpfKDsfQ/lC2fmYv/+dfj4cbKfjY3DuDeWxJIQZH/PFF9aXwpdfqmNM+ZhAQPprrqFjli2TMU2b0nzM/v2BDZrUgfTXXy9jpkyhY0wGTYZqoYBzllq1Und3TpywuogUHI6QPbUVi1uV1MGAb7+13hfUdxLOlVLZWAhhnSqkOn045DQlRX09Um/absyJ8+YCyM1ypAB6+WX5ZujQgW7Xb9tmrdIoPubECYuPUU10FaI2HzN7Np3T6NEy5tZb6Zj582WMzhcKT8iY+kJRc0o8Htk90K10hbD4GGparxDytA+APP1D8TE7d8oYf3wMzr2hji/b+RidgWxurowZMoSOsfMxVN4mfMypU2YgPdojzJhB54Qg/U030TH5+VYhYQLSUwayp09bIL3KLgIVqoUC8kHU+w3fR9R27KlTVoFEFYfo00e9xtgV69SJzhO7VFQnDyF2qiDG90yLFurrkXrTdmNOnDcXQG5W2AsgOx+j84XC+TF33UXHIB+j84X64AMZY8rHUL5QNTXWbBMTXygTPqZrVzM+hvKFsvMxH39M540zW+bOpXP67W/1q2YhzPiYTZtkjI6POX7c4mM2blTHmPIxdQHSUwaypiA9DuEzAel1BrII0nfoQBfcgS4UKO4GAfGEBJoPws4LNZwQT5h17Kh+X3s8kh3S/d1x65A6YXbypHUzocYYIOtFDSjFwwcXXaS+Hqk3bTfmxHlzAeRmhb0AWrlSvhHCzcfcdx8d8+ijMuayy+iYUPIxOPcmWD5m5kwZ06dPcHxMYaGVtwkfoxs0acLH/OlPMsZk0KSOjzlyxOJ6dIMmQ8HHCGEG0tsHTYYKpFcNI0SZLBSeflrG6EB6nPxNDVBEdicmhp6MjYXHH/6gvo42JfXq0Vu6eASfKnqxw9q8ufq6ENbWIsX74aKoa1f19Ui9absxJ86bCyA3K+wFEK4ig+VjkFcIlo+xz73R8THoCxUsH4MeSDo+xu4LRfExdl8oHR+DlgHUTUkI6RkFoOdjCgpkjCkfQw2a/OEHqwsQLB+DIL1u0CQemQ43SD9xIh1jAtKHaqFQWel/oVBaak2ipjqgWGxTn8nKSovro6ZwY0dL9/lAeJ7qEKGvmu5vjqMsKFsVNIvt00d9PVJv2m7MifPmAsjNCmsBZPeFChUfo/OFQj7mllvoGDy1ouNj7L5Q4eBjxo6VMTffTMcsXChjMjP9+0KZ8jGUL5TdQFbHx/z+9zJGx8fgoMnWrYMbNGkK0uOgyVCB9C1bmoH0Bw6oY06ftkD6FSvo5wtk0OSgQXSMCUiP0DB1Ys3jsbpR/roqzZrR23XDhsmYJ59UXz92zCr8qe8jnPat69ThwoCaPo6wO3UCNVJv2m7MifPmAsjNCmsB9OtfyzfBqFF0jIkv1D//KWN0fIypLxTyMSa+UL/7HR2DvlBZWcHxMXZfqE2b6LzRq+nPf6ZzQl8oiqcQwr8vlBCSLwLQ8zH2uTeUf5N90CTFkQhhDcrT8TEI0uvm3pgMmqwLkH7YMDomL0/G6EB6k0GTpgsFHDRJFR32LcJFi9QxyEc1bEhv/+J0aKowqamxOq3UHKq1a633IiVk1Sgj36oqq5tHsUw4iZqarB6pN2035sR5cwHkZoWtAArUF4r6MhbC8oUy4WN0vlDYCtf5Qtn5mH//Wx1j94UKdn7ME0/ImF696LzxRpGcTK+U7XyMbn4M+kLp+BjkMsaMoWNwem+4B03qQHqcWWPCx5iC9CYGsjqQHg1kgwXpcaEQLEiPn4ELL6S3CPHEHjV40D7ckOoi4nTmhg3pzh+yYToQHzuRVPesuFhej42lC0ycdk51hiP1pu3GnDhvLoDcrLAVQFOmyDeAzhcK9/d1vlB2PkbnC4VtcBNfqGnT6Jg//EHGUJNxhajNx1BcT6B8zJIl9PMhH0MNoxNCiAcekDG6QZMmfIzdQHbvXnWMfe7N4sX08w0aJGNMBk1efjkdg3xMair9hWLnYz7/XB1TUSG3tABkV4DS4MEyJliQ/p13ZMwFF4QOpNctFExAepzbQx0ZP3fOOopPdcjwBFmDBjQfhicIdduMuECgpnl7PNZ2LfU3xSPu6en082C3lgK+I/Wm7cacOG8ugNyssBRAJ09afMzateoYU1+oe++VMaH0hSosVMecOmXmC4Wr0pkz6ZxMfKEWLZIxJnxMXBw9P8bOx5j4QukMZHFrQ2cgi1sKOj5mzx5rZW4yaFJnIIsg/UMP0TEI0uv4GATpdQMy8eSSzkD27Flre+ftt+nnQ5B++nQ6BkF63UIBQXrThQIF0u/f7/93W7FCxrRqRXdUcMq4zmNuyBAZo9v6xKKO2vq1D0mkCq116+T17t3p58Gj9lRHM1Jv2m7MifPmAsjNCksB9Pzz8o+v84XauFHG+POFCoSPMfGF0vExc+fKGFM+JlhfqK5dZQw1v0QIi4+57TY65qWXZEywfIx97s0HH9B5d+8uY3R8DB6z1g2aNOFj7CB9cbE6xpSP6dlTxuhA+jFjZEwoQXrqGLnpQqFXLxkTLEiPXVldcZuTI2N0px/x7//GG+rrVVXWQoLajj161CrGqO1oZJEyMuhcsBjXnSDFLuOECerrkXrTdmNOnDcXQG5WnRdAVVUWH7BwIR2HK8TcXDoGfaF0fMx778kYU1+onTvpvJGP0c29wRvEPffQMSa+ULhy1fExdl+oTz5Rx9gNZOfPp3PCEzmjR9Mxs2dbq2kq7w0bZEzDhmZ8zLZt6hg7H6ObexNqkF43ILMuQHqKoxHC2prRLRTsIH0wC4XTp63tJKrYKi213m/UltPBg/J6XBzNGeHsnpQUurDFz23nzurrQlgTtnXH6HE4qu51xsLvgQfU1yP1pu3GnDhvLoDcrDovgEz4GPTmAZAeUSrZfaF0fMx118kYE1+oq6+mY3CqbVoa3W638zHB+kL94hcyRsfHmPhC4ZZFairN9Rw4YPExurk3JnwMMiTUaloIeQQdQB5Jp4R8jG7uTaAg/Wuv0c+HIP3vf0/H4JHrYEH6Q4csrofy0LKD9LqFws03y5ixY+kYk4UC2lq0b093CbEjd+ml9HNhl1Q3QwqLEl03CuF/3UlL7NzoFklY3Oi4PoS6qS3rSL1puzEnzpsLIFReXp5o27atSEpKEtnZ2WLz5s3a+I0bN4rs7GyRlJQk2rVrJxYoTuosX75cZGVlicTERJGVlSVW6tgJheq0ADLlYwL1haL4GBNfqPJya+Vrwsc89hgdg75Qui0Euy9UsHwMwqjB8jETJ8oY6hiwEJajdosWNGdiwsfYB00Gy8c4BdJTpptCWIMmwwHSf/mlVXCbLBTeeksdY9+21NmM9OsnY3QWKniQQBeDwyF1HTIs7HSPg6f6dFvbeExe93vhNjJlVRKpN2035sR5cwEkhBAFBQUiISFBLFy4UOzbt09MmjRJNGzYUBwibtQHDx4UDRo0EJMmTRL79u0TCxcuFAkJCWK5zYV869atIi4uTsyaNUv897//FbNmzRLx8fFiO3V8WKE6LYA2b5Z/dFNfKB0fY+ILNXKkjAmWj7H7QlGzREz5GPSFouaWCGH5Qg0fTsfgFN327f3zMYmJNB9j4gtln3tDuXoLIWe+AOjhVzxy3K4dnTfyMbq5N3Y+5v336bzDCdLjoEkdSF9WFl6Q3mShgJ/L+vXpbUvsysbF0Z+B0lKrI0cNrKyosN5vVNdOCGtaNeVpJ4T1nqSO2gshxLXXyhhdtxW3Uamt1ki9absxJ86bCyAhhOjbt6/I9Wrddu7cWUwnVrx//OMfRWev/fCxY8eKy2zHbH/961+LG72Old5www3idp0xpJfqtABCPiYcvlB2PkbnCxUIH2PiC6XjY+y+UNSNxj73huJjqqstPmbePDon/GK/8046BrcjdL5QH34oY/wZyCIfQw22q6mRBqQA0pCUkgkfUxcgPdWBDRSkp45TC2FtEekMZEMJ0uNCQQfS45wh3Vwn3LbUdTdxOnaPHnTMli0ypkkT+vcvKZExMTH0eACPx1pwUKfahLAOElBH9oWwxgNQXnyRetN2Y06cNxdAFRUVIi4uzmd7auLEieIqYk7LlVdeKSZ6+QmtXLlSxMfHi8ofV3YZGRlijtcX9Jw5c0RmZiaZy7lz50RZWdn5/w4fPlw3BZDJ3Jtz56y5N1S7XgiLj9H5QiEfo/MIQj5GN/fGlI9BXyjq5IsQgfExOl+oVatkTCj4GBMDWeRjxo+nY/Doc79+dEGyZo2MCQUfgyC9zkAWt1FMQPrevX/eID21UCgutvKmXu+aGitvnc8cDsjUbRPjAkd3+g8Ne7Oy6JgjR2RMXBzd2RJCMnsAtDeaEBYnSH3nROpN2405cd6uKYDiwSGVlpZCTU0NpKen1/p5eno6HD16VPlvjh49qoyvrq6G0tJSaNGiBRlDPSYAwOzZs+Hxxx//ib9JAPr6a4DmzQGyswE6d1bHFBYCpKUBJCQADB+ujjl3DsDjAYiLA5g4kX6+U6dkzNSpdMzRowCNGgGMGwfQoIE65uBBmfcllwB07aqOOXxY5g0AcPvt6piKCoCaGoDYWIDJk+mcysoA4uP9552cDJCbC9CwIZ13ixYAXboAdO+ujjlyBKBJE5nXb36jjqmsBKiqMs/7/vsBYmLUMSUlAI0bA4wdK/PX5d2pE0DPnuqYoiKA1FT5mt5xhzqmqkrmHhMDMGUKnffJk/7zLi6Wed9zj/y/urwvugigVy91TEkJwAUXyPfKiBHqmOpq+XuZ5J2Q4D/vlBSAu+6S/1elAwdk3pmZ9Ot97Jj8eyUnAwwdqo4RAuD0aZkLFYN5JyUBDBxIxxw/Ll/n3r3pmGPHAJo2lb9XQoI6pqZG/m1jYgC8vhdrKTYWIDERoH59OobF+rkppKVXACoqKhIAILZ6jch/8sknxcWE703Hjh3FLC/+YsuWLQIARMmPc1sSEhLEEq8TUW+++aZISkoicwlbB0gI2SmhWBSUx0MDy3ZRQ//sKiykORPUyZP0MXNUuPM+fNh/3mVl9DYaqrKSZmhQocz7yBGaj0G5NW9dF0EI2bGitv9QlZX0TB9UKPMuKqJBepRJ3lVV/l9vIfz/bkLIrVCqI4X64Qf/K9+aGrrbZhfVubWrqsp/Tjp5PDLf06f1j2MSF84YN+bEeZs/1k9QRHSA0tLSIC4uzqcz8+233/p0cFDNmzdXxsfHx0OTJk20MdRjAgAkJSVBUlLST/k1Aldiolxt6hQTI1ej/tSmjf+YjAz/MdTK2K5w5926tf8YqhNhV0ICQMuW+phQ5t2qlf+YSM2b6ljZlZDg/7FCmbe/1wjALO/4eLPHMnmddJ0WVL16/mNiY83eK1Tn1q74IL/qY2LoTmugceGMcWNOnLf5Y9WxYp164sTEROjVqxds2LCh1s834nziMgAACjlJREFUbNgAAwYMUP6b/v37+8SvX78eevfuDQk/toCpGOoxWSwWi8ViRZ8c6wABAEydOhVGjBgBvXv3hv79+8Orr74KhYWFkJubCwAADz74IBQVFcHf/vY3AADIzc2FefPmwdSpU+Gee+6Bbdu2waJFi2Dp0qXnH3PSpElw1VVXwTPPPANDhw6F1atXwwcffABbtmxx5HdksVgsFovlPjlaAN12223w3XffwRNPPAElJSXQrVs3WLt2LbT5sfVdUlIChYWF5+PbtWsHa9euhSlTpkBeXh60bNkSXnrpJRg2bNj5mAEDBkBBQQE88sgj8Oijj0L79u1h2bJl0K9fv7D/fiwWi8VisdypGCGEcDoJt+nUqVOQkpICZWVl0NhkD57FYrFYLJbjCuT+7RgDxGKxWCwWi+WUuABisVgsFosVdeICiMVisVgsVtSJCyAWi8VisVhRJy6AWCwWi8ViRZ24AGKxWCwWixV14gKIxWKxWCxW1IkLIBaLxWKxWFEnLoBYLBaLxWJFnRy1wnCrcDj2qVOnHM6ExWKxWCyWqfC+bWJywQWQQuXl5QAAkJGR4XAmLBaLxWKxAlV5eTmkpKRoY9gLTCGPxwPFxcWQnJwMMTExIX3sU6dOQUZGBhw+fJh9xvyIXytz8WtlLn6tzMWvVWDi18tcdfVaCSGgvLwcWrZsCbGxesqHO0AKxcbGQuvWrev0ORo3bswfEEPxa2Uufq3Mxa+Vufi1Ckz8epmrLl4rf50fFEPQLBaLxWKxok5cALFYLBaLxYo6cQEUZiUlJcGMGTMgKSnJ6VRcL36tzMWvlbn4tTIXv1aBiV8vc7nhtWIImsVisVgsVtSJO0AsFovFYrGiTlwAsVgsFovFijpxAcRisVgsFivqxAUQi8VisVisqBMXQA7q5ptvhszMTKhXrx60aNECRowYAcXFxU6n5Tp98803cPfdd0O7du2gfv360L59e5gxYwZUVlY6nZor9dRTT8GAAQOgQYMGcMEFFzidjus0f/58aNeuHdSrVw969eoFH3/8sdMpuVKbN2+GIUOGQMuWLSEmJgbeeecdp1NypWbPng19+vSB5ORkaNasGeTk5MCXX37pdFqu1IIFC6B79+7nhx/2798f3n//fcfy4QLIQQ0cOBD+/ve/w5dffgkrVqyAAwcOwK233up0Wq7TF198AR6PB1555RXYu3cvzJ07F/7yl7/AQw895HRqrlRlZSUMHz4cxo0b53QqrtOyZctg8uTJ8PDDD8OuXbvgyiuvhMGDB0NhYaHTqblOZ86cgR49esC8efOcTsXV2rRpE4wfPx62b98OGzZsgOrqahg0aBCcOXPG6dRcp9atW8PTTz8NO3fuhJ07d8K1114LQ4cOhb179zqSDx+Dd5HWrFkDOTk5UFFRAQkJCU6n42o999xzsGDBAjh48KDTqbhWr7/+OkyePBlOnjzpdCquUb9+/SA7OxsWLFhw/mdZWVmQk5MDs2fPdjAzdysmJgZWrVoFOTk5Tqfieh0/fhyaNWsGmzZtgquuusrpdFyv1NRUeO655+Duu+8O+3NzB8glOnHiBLz11lswYMAALn4MVFZWBqmpqU6nwYogVVZWwv/+7//CoEGDav180KBBsHXrVoeyYv3cVFZWBgDA309+VFNTAwUFBXDmzBno37+/IzlwAeSwHnjgAWjYsCE0adIECgsLYfXq1U6n5HodOHAAXn75ZcjNzXU6FVYEqbS0FGpqaiA9Pb3Wz9PT0+Ho0aMOZcX6OUkIAVOnToUrrrgCunXr5nQ6rtTnn38OjRo1gqSkJMjNzYVVq1ZBly5dHMmFC6AQa+bMmRATE6P9b+fOnefjp02bBrt27YL169dDXFwcjBw5EqJlVzLQ1woAoLi4GG688UYYPnw4jBkzxqHMw6+f8lqx1IqJian1v4UQPj9jsX6K7rvvPtizZw8sXbrU6VRcq4svvhh2794N27dvh3HjxsGoUaNg3759juQS78iz/ox13333we23366Nadu27fn/Py0tDdLS0qBTp06QlZUFGRkZsH37dsdaguFUoK9VcXExDBw4EPr37w+vvvpqHWfnLgX6WrF8lZaWBnFxcT7dnm+//danK8RiBaoJEybAmjVrYPPmzdC6dWun03GtEhMToUOHDgAA0Lt3b/j000/hxRdfhFdeeSXsuXABFGJhQfNThJ2fioqKUKbkWgXyWhUVFcHAgQOhV69ekJ+fD7Gx0dW8DOZ9xZJKTEyEXr16wYYNG+CWW245//MNGzbA0KFDHcyMFckSQsCECRNg1apVsHHjRmjXrp3TKUWUhBCO3fO4AHJIO3bsgB07dsAVV1wBF154IRw8eBAee+wxaN++fVR0fwJRcXExXHPNNZCZmQnPP/88HD9+/Py15s2bO5iZO1VYWAgnTpyAwsJCqKmpgd27dwMAQIcOHaBRo0bOJuewpk6dCiNGjIDevXuf7yQWFhYyT6bQ6dOn4auvvjr/v7/++mvYvXs3pKamQmZmpoOZuUvjx4+HJUuWwOrVqyE5Ofl8hzElJQXq16/vcHbu0kMPPQSDBw+GjIwMKC8vh4KCAti4cSOsW7fOmYQEyxHt2bNHDBw4UKSmpoqkpCTRtm1bkZubK44cOeJ0aq5Tfn6+AADlfyxfjRo1SvlaffTRR06n5grl5eWJNm3aiMTERJGdnS02bdrkdEqu1EcffaR8H40aNcrp1Fwl6rspPz/f6dRcp9GjR5//7DVt2lRcd911Yv369Y7lw3OAWCwWi8ViRZ2iC6RgsVgsFovFAi6AWCwWi8ViRaG4AGKxWCwWixV14gKIxWKxWCxW1IkLIBaLxWKxWFEnLoBYLBaLxWJFnbgAYrFYLBaLFXXiAojFYrFYLFbUiQsgFovFYrFYUScugFgsFovFYkWduABisVhRoePHj0Pz5s1h1qxZ53/2ySefQGJiIqxfv97BzFgslhNiLzAWixU1Wrt2LeTk5MDWrVuhc+fOcOmll8JNN90EL7zwgtOpsVisMIsLIBaLFVUaP348fPDBB9CnTx/47LPP4NNPP4V69eo5nRaLxQqzuABisVhRpR9++AG6desGhw8fhp07d0L37t2dTonFYjkgZoBYLFZU6eDBg1BcXAwejwcOHTrkdDosFsshcQeIxWJFjSorK6Fv377Qs2dP6Ny5M8yZMwc+//xzSE9Pdzo1FosVZnEBxGKxokbTpk2D5cuXw2effQaNGjWCgQMHQnJyMrz77rtOp8ZiscIs3gJjsVhRoY0bN8ILL7wAixcvhsaNG0NsbCwsXrwYtmzZAgsWLHA6PRaLFWZxB4jFYrFYLFbUiTtALBaLxWKxok5cALFYLBaLxYo6cQHEYrFYLBYr6sQFEIvFYrFYrKgTF0AsFovFYrGiTlwAsVgsFovFijpxAcRisVgsFivqxAUQi8VisVisqBMXQCwWi8VisaJOXACxWCwWi8WKOnEBxGKxWCwWK+rEBRCLxWKxWKyo0/8DluQ5Izgu688AAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t=np.linspace(0,2,100)\n", "for x_0 in np.linspace(-3,3,50):\n", " x= caracdroit(x_0,t,g) \n", " plt.plot(x,t,'-r')\n", "plt.xlabel('x')\n", "plt.ylabel('t')\n", "plt.title('caracteristiques de g(x)')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_0 = np.linspace(-3,3,200)\n", "x2= caracdroit(x_0,2,g)\n", "x1 = caracdroit(x_0,1,g)\n", "plt.plot(x2, g(x_0),'-r', label='t=2')\n", "plt.plot(x1, g(x_0),'-b', label='t=1')\n", "plt.plot(x_0, g(x_0),'-k', label='t=0')\n", "plt.xlabel('x')\n", "plt.ylabel('u(x,.)')\n", "plt.title('solution u(.,t) a differents temps')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour $t>=1$ les caractéristiques se coupent et la solution donnée par la méthode n'est plus une fonction car elle prend plusieurs valeurs aux points $x>1$. Il y a apparition d'une discontinuité." ] } ], "metadata": { "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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 2 }