rédaction

parent 3082119a
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 1 À propos du calcul de $\\pi$\n",
"## 1.1 En demandant à la lib maths\n",
"Mon ordianteur m'indique que $\\pi$ vaut *approximativement*"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.141592653589793\n"
]
}
],
"source": [
"from math import *\n",
"print (pi)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1.2 En utilisant la méthode des aiguilles de Buffon\n",
"Mais calculé avec la __méthode__ des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon) on obtiendrait comme __approximation__ :\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.128911138923655"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"np.random.seed(seed=42)\n",
"N=10000\n",
"x = np.random.uniform(size=N, low=0, high=1)\n",
"theta = np.random.uniform(size=N, low=0, high=pi/2)\n",
"2/(sum((x+np.sin(theta))>1)/N)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1.3 Avec un argument \"fréquentiel\" de surface\n",
"Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d'appel à la fonction sinus se base sur le faut que si $X\\sim U(0,1)$ et $Y\\sim U(0,1)$ alors $P[X^2+Y^2\\leq 1] = \\pi/4$ (voir [méthode de Monte Carlo sur Wikipédia](https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo). Le code suivant illustre ce fait:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"\n",
"np.random.seed(seed=42)\n",
"N=10000\n",
"x = np.random.uniform(size=N, low=0, high=1)\n",
"y = np.random.uniform(size=N, low=0, high=1)\n",
"accept = (x*x+y*y) <= 1\n",
"reject = np.logical_not(accept)\n",
"\n",
"fig, ax = plt.subplots(1)\n",
"ax.scatter(x[accept], y[accept], c='b', alpha=0.2, edgecolor=None)\n",
"ax.scatter(x[reject], y[reject], c='r', alpha=0.2, edgecolor=None)\n",
"ax.set_aspect('equal')"
]
},
{
"cell_type": "raw",
"metadata": {
"hideCode": true
},
"source": [
"il est alors aisé d'obtenir une approximation (pas terrible) de pi en comptant combien de fois, en moyennen X² + Y& est inférieur à 1:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.1556"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"4*np.mean(accept)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
{
"cells": [],
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 1 À propos du calcul de $\\pi$\n",
"## 1.1 En demandant à la lib maths\n",
"Mon ordianteur m'indique que $\\pi$ vaut *approximativement*"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"3.141592653589793\n"
]
}
],
"source": [
"from math import *\n",
"print (pi)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1.2 En utilisant la méthode des aiguilles de Buffon\n",
"Mais calculé avec la __méthode__ des [aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon) on obtiendrait comme __approximation__ :"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.128911138923655"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"np.random.seed(seed=42)\n",
"N = 10000\n",
"x = np.random.uniform(size=N, low=0, high=1)\n",
"theta = np.random.uniform(size=N, low=0, high=pi/2)\n",
"2/(sum((x+np.sin(theta))>1)/N)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1.3 Avec un argument \"fréquentiel\" de surface\n",
"Sinon, une méthode plus simple à comprendre et ne faisant pas intervenir d'appel à la fonction sinus se base sur le faut que si $X\\sim U(0,1)$ et $Y\\sim U(0,1)$ alors $P[X^2+Y^2\\leq 1] = \\pi/4$ (voir [méthode de Monte Carlo sur Wikipédia](https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo). Le code suivant illustre ce fait:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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tYJqU3nLDy5cVx7I6qrq7KdGDwcwwZUMDf0sG4+QkuWxhoTIrAgGVheeG6M3NKplJCKWhwT7Zxw1c1aks4MWs0K8vIcbjx3l9Ozu+uXk7Q5mcVI7BB1zWuy9CffkAPRW8qQn4gz+gLwYgDp44QdwS/8zWFpl3VRW1hIICvm8YxO+REdKeW14LkBnp0yM6ppkZVWpoUM5fa7RwG0QiwGc+owh9bQ2pSAMmSjsQmyzF3bENJAo0CaXXHnR1kXhv3iRn29xkVl17u7qhnrS0tKSkr5RLbm2p7EV5oHPn+HtwkJ9Ppfj91lYyj/FxcjinIg3rpokT8exZ/vb5cg+D7SZ33y18u9Pr2yGDJDHtpkBph/CRkfxWCdzcDHzqUyS2hga+/8lPEm+PHaPw8vmIw+vrxHfRiMfH+XmJeLlpk06m6eXL2+tS6uspKD05fyMReid/8xsk78YxsRhE0SYQXJ9DsrIZ1+ejeEL8SFb1t7ubRDo6SuKySl9d6pWXk3OaJtVUyV4ULqXb2pWVvG5BAaV7JMLvmyYleCxG+yqbGp7PtNvdOAWzmRVO129s5OtW7cbuuZqaVDaawAMqu953xJ/P2hJJwrPr4XH8uIpaHTlCwSha7tISzQK9SMvtvOxwyMkcyKmW477X/F58AiWJuyhKryNd14SV576GokhE0ZRdTLy7mwvOFicNBOhIjEZJ0JI88+Uv87OxGDmZHMbZs5Toov6nUsqsmJmhAxFQzSsWF8lZneoBdgP5YiK5XL+xkQzQyclo91y7RoSdgcG6nAcP3d3dZq6DOnXi1BmtnXq800Y6Tt/T79vXR5zt7lYMYWVFaYb5fpZsF3r7+zFEChawWRHGWnMUm6HIbzN+n38eStXWESyXBXvZFHmAzk6F/BIulLi/aVK1EsYgdftbWzQPPoz2YtmeM9f1yF6n0ypNWeL9zz1nf8+8IIICwzCumKbZnfVz+4n4rTicSBDP1tYytVev+5nLWTt1adrNeeWrfVxW2t4DBHO9qYSvrA+m5xgUFHAj9XBhLtwzXyCHMD7On2g00+Oa6x5duMBnuXZNOUpTKfpVvvUt5zqFPLZ380r8+0rt17VXScAqKSEe6ZEkLxGenYaABeS8vGiTTmcracjynvh+8m7a7kb9dVq8nSd9Y4OJPvLZM2fsVXndLyB+BFFVHiToSDA1ReIfHOTeHD2qHG9uDMm6P4bB/6WxB8DXamqcr5UPE2cHsK+IX7eTBwYYJZGqPj0WPzmZPT9jt+3bvJ6XG5MBMt/Ti76am70zAk+0vRMEc1u812YaVm4aiSi/wIO0c+2YmLVMORIhwU5MEJmOH1dRC6drWvdnfp7ZgYcPk6GtrvIax4/veWeeXGFfEb9IuMVF+piWl2lOhsM8r8ZGEntjI02t/n6Vh2LFrZ2EgHeinVnxS0xAn4/rEgYkuTRS9OWluc+egxuH9NJMQz5rZTp7kZrrBk5MbHmZYcRr15TULiri69IH7vHHna9rtz/Smam/n9dqa1NmTXm5+xofcBvzfUX8Irx+8ANKybU1EnpxMWPx9+4xrb2lRdVkSCsvK27l6m332hpcumyZJn9u3OB6JFcmFKIg6O1lircU0cn74guTuhCfj34iN9zIZW2e8SoeZz88Uc+lVZhwSDmMK1eo6g8MeO8U7KSqACpEJpu4uKiSilpasi/eTcJbmZiojktLvPbQkNJITJPRCbfcArsqwKEhlfBTUMADldBSV5e781S6/169ShXwxRdpFu0R7CviB3juW1sknKkp2vxSEr64yN+hEM/yyhXuYXs7w3V6U5hEgvstGZiFhfbCR87q7bfJZOwEm94a3O9X5cOnT/M7r73Gz4gJODNDQfnOO7ze008T/3w+MgspzBMm0dHhHj3yIqBz6k+h16enUkwIevttbk5ra2amXTpN6Sg1/W7qlvUgrU4U6yYmk1yDtPQqLeXnnBafTcLrUFamQpd+Pwm1slJFIVKp7T4LK1glyPg4r9PaSmYpffinp1Vo1G59UqA1PMx7BwKslfhP/wn46le9zTDYAew74hcwTZ7n3Bz3UKSq5JOMjXEP6+v5s7jIcxgdVbMinn6aBPLWW8Qnu2iAnFVBAX/6+8lYEgkKjnv3SAuRCAl5YoI4BPDvzk6aKFNTPO+xMc6nED9XIsE29Z2dxBFJZ796VfWiuHiRzMvJP+FmwuzItyFfamgAfvpTSl3pgTY3x350+ucCARLCBx/wAaQSMFsttLW4obaW1+rv5/3m55lJJX3a5uZ46E6LzybhrWqeOFb8fs4JmJ5mTYRk3yUS7hV3VvNlZoZSRLQk3ZEZiShksq7v3Xf52dJSMoGhIRUSHRri7z2w//Zleu/Ro9yjdJoJUi0tVP+rqniOUo05PU0mXFhIIn39dQqUiQmFr2fOsIZFEtJ00HGpooLX3NoC3niDeHn3rjItUinirGgjJSWqhPvxx4lrohUeOaImOJ06RTwfHVV9Of1+pYmsrfE7bu3l3bJMd9SaXr60sEAVq7ycnnzDYA7y7Gzm54TbtrSo1l6xGDmaWwjEqd25pBRLQQWgNtRt8U4PKxLerrehVBiePs17ADyQI0d4IG5zFawpwFLOq/cR1LUfp/UB3NOSEoVAhsF1uLUv3yXsS+Lv7iYOJpPc8+VlEmUwSEFx6xb/rqvjuQwNcS8Ng87XWCxzjoWOT3r/yrffVrgnwmdqSqXDS/eoykoymtJS4pTeMgyg47etjUVB0qdydZUaSXk58NhjZGLd3XxvY4O+omPHMjt16aDjlFP9QDS6w/R2+ZI0P+zoADo7sXT4BK7O1uPyaxxwkigIZw6dqK7mg3ziEyQmYRJ2YG2ZVVND1Ur63K+uKi4IqA11W7zTwzY3Z8/Tn5jgAXV3k/Crq3m969ft7yWIcvky/z9zhqq9WwNVp/UdO8bvLSyo766t8fPB4J718N+XxB+JcJ+/9CUSeCpFbeCLX6Qkrari2dXXUyAVFys7vaxMVV8KCD5ZhZE+8EaahCaTxMmNDSUUW1pU+ntZGbWC+XnSgWTDvviiak6ztkb8EudvIqGa1cq5b22pStYjR7YT99QUTZkLF0hHtbWqke2tW0roujEGR5Av+f3c3FQK02Mp/Ox6M/ovJTG1GsbMDHB5PorFyRWqu+If8Dp0wioF9YKhpiZuoHDK+XlufFWV++LdHlaktHTp3Y0K7TRFBsjsKKwfhNv6Tp8mgqTT6tAbG8kMm5v3LAy6b23+SIRe8FBoe8hYHLzRKPFGiKypSYVtpShNjzJZTcbOTqbyDg5SIPj9lODRKAXI+jo/5/fz+zIB6NgxlYQE8P/KSgrQ6mpGKzY2+PlEgmt8+mmaE3V1xC2ZyfH442Rs3d3KOS4NZoqLST9TU6ocWEqOr1yhib61xfVJuNlTfo8Qit8P9PZiqbQaF2ePwyjyo6ZwBXerurAwDLS3RzBY1IPulUmqPjU1/BFHl4Qa7EIOhrHdDk+nafsXFnKzgsFMb7+1Pt5p3XoUIRBQyR8NDaw+tPOgHz3KhiWGoaoYFxYoTazg5FuQKTLSUTiZJPJUVjoX9shhRCLAH/4hryGNWMUfsUdh0H2V3msHFy6Q+UpDGoCEMTJCpvnaa6q7Un29YqTT09sbc9hda2GBRPzoo8pOHxxUfpmCAhKY9Prr6SExy4yN6mr+yHuRCL938WImPs7Okl76+9XIN2lc88ILwO//vsJ5a2Ztfz+fsaKCOCLdiSsqyDR2lc0bj6P/5RgG3lpA4FAYyw1RrJdHkEqRRhsagOfPxFWoym5T9Hx/ievLxJr6ej6sHiIRh8duJfTQEDltZaXyrs7P02FpZQDxOJElHleDVKV02roGJ6T7zW/IrXdaQ6GvZRcx/9/J9F47KCggouvTef1+ZebpoS6naj6BXHtCrq5uF0qAmrEhHbeHhxluFCd1R8d23Lt1i3Rw/TrP3OfjfQoKlN9Jmv5avfviWFxc5P+5lBxnxbNIBHcae7DyMWBhQ4UrS0ro9zh6FEqivfwyCUcfIbayYh+uaGggBysupre7ooJMQneW7ba91cWL3EQJv8jvixe3H4AQuheic0oSAewdetK2qa9P9Yk7dsw5hPeA0n33NfFLD8jFRZ7H2hr3t7VVEUouae1eE8/kmnbnIwJQZmwIsczOKt+VHQg+TU9zHeIb8Pv53qVLqgHOnTt89vV11X14eVm1APNacuy1vsHaPbykRDGo35rfkQhVqZMnMyViWVlmiy/9dWnIKdzM+j2919nYGB9MEo68SMPJSdWEQSAUynT46OCV6LJNkbFWnsXjdAym0+zpD5DhxeNUzdxGne0h7Gvij8VUL0mpnqyoUCaWgNczzUf5tz5jw1ZK3gerxBVzYn2dhLu2xmuIs290VPmX5ueBf/kXahOGwWefnGQ+iIQKFxaIVwJ2PiOvOQAyS1K6h9+7p5yYujlv3ggjWJxEU2dACXC9xZddOqXe/VbXGPReZ5ubjKsWFKgwoFuyj4AM/RSJDyjvqldwUo3cMhSBTFOmooIpqOm0CvEYhhrjJX3cCgt50Hamxh7AviZ+XWAIsu22OCyXgh07nHCTktXVxA2pHm1oIIFLQs8zz5DY33+f3nsxmYeGMud5rq0pM6KuTiWUSfPR9nYyCBkI5KTBZKtv0J9RUo1lvKBd+XSwK4qtK70Y6AOOni5DqDCpWnxJ7r94KGMxLvbNN1ULI+vQUZ+PF759m9+TzLtsyT4Cjz0G/Nf/yuvU1vL76+vA5z+f/YBlA9xUI7t7C1PQTZnr18m4ysvJOcvLiRjvvMP1SHLT6iqdVX199rX/eYZ9TfxOppdMrnLKg99JQw+nzD8rTjhJyWeeUT4vKdx5/XU6EuvqeK833qA0ra9XfifDIA7pTuelJTX4V6S7afJe4uvwUnLsVt9g94x2Pjhde9hCBJvdPSgajOFu/xxCZ7Ubi6Pk9m1KvGiUGyQdflpbKZX1dFjpdSZODUA1EvVShTU9zV5t165RuygvB/7dv/OeL7+b7r+6ZJIBpAA3ESChS5sovUW5TJZ5WIjfMIzPAfgLAD4A/800zT+3vB8C8P8BaLl/zf/TNM3/ka9FOhGjbnpJ05ixMeLFqVOqJ4O1hNatfsKLHZwNJ6wzNiT0KPM1Ll0iwxc8lnySe/e4rtOn6ZOS2ZfiABcIBonPdXXqtdVVXkdC6140GDcfh9MzWpvvjo8ziUlgMxSB2d2DsTngqH5/fUF1dbzgyAgvsrqaOUFVsuWEO+ltxr0k++iHVFurHBOTk1SrpBQ0W3un3XT/1Tlrc7Oa21dZydclz0HGeX0IkJX4DcPwAfg2gM8CmABw2TCM86Zp6qlP3wJw3TTN3zMMowbATcMwfmCa5vpuF+hF85LQaE0N/SkyFl2fXCXZkdb6iViM9RP/6l+pWHo2Zp8NJ+wIb3ycwkfOWxqRrK3x/fl54vT162Raeqh4akqFBcvK6BOYnFSzO8NhapXSiNQruPk4nHp19PZSi5GzGB/nc3iaNwCQO6+sUP2RoQgyPtn6ZeFOVVW0fSQBpqHBPfZtV5EI8Bp6//VXX1XhRjvkMgz7UJJb6addu6eKCraH3tzkmmR+XEeHmkSUTnNvpqcpuYaG9twR6EXyPwnglmmawwBgGMYPAXwJgE78JoCgYRgGgHIAcQA5joi1h2zEGImQwGVYzFtvKWEyPp5ZhQqomZA6E5C/NzeJU7okA7Yzezt1eWqK53bhgv1ZLS6qITT19fTzJBL8TjhMnAoEKJhqajKft76ez1NcTGE5NcVsxuvX+f1EQtXR2CW/uZkxThqCXQg1FqN2ofcm2NrimisqPJTmx+NU+YWA0mmWMR4+zIeUjDf5ss6dUinl0XVL9tErEgsKqGL196vKLOm/HgiQOAGl9lnLIe1CSYcP0yHndF9dSt1vq45Uivf9kz/Zbj+m02qsd1kZ11JTw/wEfYjDHjR38EL8jQD02MgEACu6/CWA8wDuAggC+APTNLfysUAvmpf+GdEQRaUGMoXJ1avUOoeHiR9AZv2EUwGYzuz1piKzs9Tm7txh628nUyEYVENoAgGaAxcuqCw9ielXVvKauiTVo2KA8g+1t6tkumSSZqLVt2HXmi4bHjmFUOfngSefVFWvUnY8O+sxg/CUEBQyAAAgAElEQVQ+Ua1cHcbk5CqSG1Wo8B1G7cgUyo4c4WZYv+wWV7UDsa+EQ4XD3LBYjOqUHvrb2CCz6e/n4QSDKg00FlODQqyhJGC7U8lOStXXuyf4SFHRyy+rCT9SClxZqew+T6WYuYMX4jdsXrOmBT4P4D0AnwLQAeBVwzB+ZZrmYsaFDOMbAL4BAC0tLZ4W6KXphtW86u8nMhoGfUbSPLa9XdVPLC9TfV5fJyJPT1OCLS3RL1Rf7yzJpHxXsvjSaV57ZoaMRTc15KxaWngfGULT1MSU3sJCnrlI17Gx7fUw1sIw65AY3UwGMoWQNAWxM4PsehLq1bXd3Zl4LyFLa3u61lZeNyteLiwgUVqPGyhDhTmOEBJIVtTjhnEEhz/1Va5fFr9TdVe3r06e5P83b3Kh1oq7hQUeelOT0kTu3aPabQ0lSeXi668Twazc1IvK6ARLS0oSyf961lYu18oBvBD/BAA9U6IJlPA6/BGAPzeZK3zLMIzbAB4FcEn/kGma3wHwHYDpvV4WaHVKSZRIGHg0mvmZigoSosyVbGlRQ2MHB2mvvvEGpZnPp5xWjz7K/S8szGy95iTJxDEnpkYo5GxqyDrjcUaohKnE43xdl/LV1ZSwTiPlvTBDXQgtL7ubQcB2jfXqVeLfiRPqvpIyPTCgSt5zbk8XDmPi3SQKq0NAcwhJAAWpFWCzmMwo6sHbmi0Uo9tXABNv5ue5YJ+Pqt3sLAlZbMRAQMVnxdaXXINAIHNcd0EBuenVq6o5hN+fGbJzOhgrDA1RggwPU+JsbvJePh9/67MJ96C4x0tV32UAUcMw2gzDKALwNVDF12EMwKcBwDCMOgCPABjOxwJFyt66BfzTPzH9ur6eTFYvptIrNmtq+P/nPsdKSznfQIDM/Q//EPi93+N+Ly6qGPrqKu/V0MCzdysA04vSdFND8vGtZ6WXft++zecJh4nHk5OqyEuvALSrPs1WpSe+rvffV4VF2dbmVl0roFfGSkFSURGZQ2GhR7yMRpGaWUGZycUXpFZgpFZgRKNkHtaFyN/irXWqptPHfYl9de0aN0GcEw0NPNxYjMQvU1EjEdU3IBAg95UhIrK5+rju8nIS+9QUbXVp1zU5ydecSi+t64zHVR74sWP8/O3bZACrq2RYVVU5lGLmDlklv2maacMw/hTABTDU913TNK8ZhvHN++//FYD/HcBfG4ZxFTQT/oNpmi7F3N4hHqfEPnJEJXg5qde62nnhguozIapreTnPt6dH9W/4/vd53aKi7F2knabq6qZGMLjdbyUg4cl4nOvXNZnVVV5HtAynULSbhz4epwP77l1eLxAgMykr47M7rc3qV2lupmCzq3wEiJ96rYTnorP7i08Ox1CemMNmMIy1ji4s+SMIl9ssBMhUU7J5f+NxEuH163xwses2N7kBw8OZ6prU3st9VlZoIkgZbmcnY65vvMFNOX2aCHXjRmaDE7F9KisV17aWXtr1XtPzwI8doyYxMUF19aWXyKT2YtLQffAU5zdN8ycAfmJ57a+0v+8C2JOsBL37rWhekm129qyzKRQOk7DEox8KkWCnpvi+9IL02kVaNDQ5r9LSzKm6knFXXm7vt7I+j9xPIkG5FH45eeivXCH+NDQQhzY2lG9DHJp2a7OaEm7j+IDsvTfdTPX27gh6N3uwbMc8Yllsmmzzznt7+dCRCAnvzh3WGxiGilM+9RS/FwxyU2ZmKB1OnFBdV+fneeAidZJJSuULF2i3SU+2QED1MDh+XLXbAoBXXuF1ZmaUQ0ef837jhiodLi0l4hw7Rp/D2bP21V95hoc+w09SS69dIxJL7Udfn7I79bJxgWiUCTx+v5r2PDJCc0HaY/X2qmpTwFmS6Rqa5O0vLvIe09PKaff009mZ827yRrLB9eukk7Iy5ZxbX+f6nYbFAN7mGOpgZT65DEBx01zmq6O4d74XiU2grLoMLdVJhHxZHB4SY5XR4+k0QynvvEOVbmGByR9DQyTC997jjPbmZhUOCod56AUFVAkrK1UlYjpNtVG45/y88hrX1CiVUaqyLlwgkr7+OpFNnEG9vUTYoiLV0mlqir+rqx2qpfYWHnriD4eZJl1aqrorp1I8q+Fhalu1tduRLRLh+S4vqz6Mjz6q8kkEfyQS4JYKa9XQxJckrcOtU3XdfFK5tgy3gtdS7/Jy/jQ0cL/cmNJuC5pyzYK101zicaB3MIJQtAeVszGkZ+dwbT6Moy92oVJ3eFi9v6J+CfHeu0eCqqzkYd+6RRu+pkYh0yOPKHXt2jVKXLHfxO6TSsRr13jwlZWK0Rw9SoJ+6im1jl//mvdYWaHaNTdHxJSahKUlIoxUPXZ2UoL4fKrJpF4t9QDgoSf+aJR2rDhSZfqxxMVPnFBl41Zka25WKr3ukZdSV2sLeicYGyPDkM68kp1qrdQDskvB3cyryHZtu2Y0d++qRiVuzGI3JeT50GaEgRQHIkg2cCHpFWBwFugR7dfKpaanSfgNDaq1kgxJkIyokhLVrtnnY7GPrq599av8rJUbSyWihN0Mg8jX1kYV//ZtZd/fvk0Cl3jorVtEzps3ed2SEqVuSpgqFKIPob9/e7XUA4KHnvjlvKWxa2Wl6nhbXOw8jgvIJDTrmHnAm8SVpDQx75aXiQ/V1WompQ5eMhJ3KmWzXVvi8oODFCoyz6C7O4ee/R7ByfkpkGtkyjMD0bmUdNQBlNe1rIxEXVjIsMfJk6pKMJUi8qTTSl0Tjio3FG4slYjSx1CGioqK39Ki1nHjBh9eVMLKSt4/maSan0iQAejz4wD7TjEPEB564gfIIMXkkmw3L/XqOqGVl28fM+82pEPUarHth4eZC7KwQMExNQX82Z9tJyIvSOxkM2dT5bNde35eZSiWlSnfV1lZ9o4+uYCsVwqkJiaoWX3608o/Jnvr1UzZkTmkf0k6rA4OkgjPnqVNODtL5NnaojR+991MJ5Fbbb7fz8+NjlJNP3XKW089acmUTivHlMw+cErgOBjXZQ/6+YyMULubn+c569N2xCSw67vgpczVTq3+xS94XfEzBAJMcTVN4pXE6/V6/lyQOBdnWbYS3PPnSQOtrcS3d94ho5PkHiA/zkXxgUgkpa2NAu7ttylgW1oyIwCBAGnm3XfpBBctxeqgzdkcsn7J7+fDy+ZVV3NTlpaIFFLTb3USWbmxHto5dEh5+ONx9XD64q32ls+negfMzqpGjisrlBx37vB7x47xd64jo/ME+6Z1t9jLgQAZsNRWvPmmSs4ZHHTO/xgaYpTltde499XV2/dVV6ulr0R/P+8hxWGlpVT3Fxbs75Vrq+xseS06uF1bCFIa48o6332Xa3v7bf68/rpqA7ZTWFhQBVKlpcoclgEqeihbwrTXrpEmpK7CmvOiJ0E5tdYHkDlYQQaD2H1JEkSiUapAq6skvMOHVb683SbroZ26On5XZvbpD6dDdzevu7nJzb11i8wiGqVP4sQJdc/xcZVQ8v77wPe+x2lBXpEgj7BviB/IJJRwmNl7585xH2dnnfdPmriurJCAV1b4/9BQ5vX1ATT9/VRnjxyhnX/jBpFYGoUII7LeyzMSW+6pg1PLe7dr6+3DAOWbuHWLTr9f/pIO6eFh4t/3vrf9+b1COKwGzAhY+wnozyYzPeTHaQiNPJ9jZqVdhp8QuPVLgiwyEKG2lqq/DGJw2mQ7Llpaqspr7SASoTRqbyezaGujNhAMEpEkpDg7S6ki7Znr6shkXnlFTYcR2KNBHTrsC7VfIJvN6/TetWvemrhKYtClSzwjSRU+epTm4tAQNT4p/HFaRy6e81zNBKdrW9uHDQ9TYNXWqjTme/fIKNvbuZfnzzPV2YtmaZ1CLG3tpW4gldreT0CeTW/EI+bvjsyPXGKKgiyJhAqjyfy//n5ugj5wVP+elyaMVrDWlvf3q6oxyZN+5x0ygMOHqUVIxlo8TrW0uzuzh6FbS6o8wL4i/myE4vReX5+3Jq7V1dQmZ2dJNGLTnzvH/xMJ4szWlvs6cvHd5GtUvbV9mCSQ9fQQb6Wib2WFOCWdg9ycf3rjXOm8JYVsDQ10Lq6tcd8kkqabN/JsTg7znOtUcmk6KCGIuTkS2sSEqnIyDH7u6ae330PnoisrysNbVMQH9bq+UAj41a9U3cDt22qmnGGopKOrV/n+xARtp4UFtUGmyUPcIz/AvlL73Wxeu/cmJ0mws7P0xywvq2vZNXGdnaWJJpV1jY38zOwsf8bHqS1UVPDaduvwUnuiQzYzQTdxvVynpoZr7uhgDorkJCwtqTZygL2aroP+HDK5a3iYGkQgwGft6eFYPil7t+KlrElShTc3GSIXh3nOiWzC/XWwNh2Uja+tpaQdGOBhLi+TIQgBNjfbE5EgUiLBw756lYfc06PacGdbn5T/ytiymRn+nD3LzZN6g4sXuZ72djoqZ2ZUh5fKSuUn2CM/wL6S/Nli5Pp7BQXK+frMM8CPfkQGcPIk931+fnsTV+kwJaWwDQ08k3ffJd489hidjYWFNA+kSYu+DqcpzF56PlohVyewfh2JaqVSpINr17gvjz6q0tHd2n55KQvWG4y4nZkUUYlQ3twkA7h8OUdtNpemgw0N/PzLL/PidXV8+IICcj07lV/AMPjQLS1qyq/Y524HKesbHVWTdmWTKyv54M88Q41ANJPWVq6ps1Nl+zU0kCk4DQDJE+wr4gfcCUVvn3bjhiLO5mZmTb71FkfIP/kkCV+394eGOG1pbY3EUlVFZiCNYJ56KlNTsGvSYtc6zql+3otZsJPmsQKnT6uOPOk0Hc6S7yD45ZZGnkt3JDuwe0YJt1onKHnWZm24/3xjFwZjERS8toCSxqrMPJq1Naoa4TBtb8mfd1L5h4aA736X9lAyqaq2UilyvePH1UHazVzr6FAagiBBRwe/u7ZG9aurC/jCF1ifXlCgcvulHHh1ldeScJN1lkEea/r3xay+XFppy6yEmzdV19tUinteUcGzs8vF/973eD6zs6oaU7L4mpvpo7GOZtOvJT6bX/5Sdb5pbWVrL79fMQo75HcaS+c2O7CxUY0KkwpF6/ftBoN47QmpzwPUe1kEg9RS3UbpuT1jLLa9inIn4+ys96kZ7sXa0hpWzAC6uu4zgF/+kg8tKb96Xfe//teZF5OQ0O3b5IrikX/uOR5+IqEKcmTaqtMMQOswRbvhiVeukLGMjJCBBIP8jjgcJQ3ZbhhkFi75OzOrL9dW2v39PBNp2xYO81zGxsigpXekjvgS3ZHBnffu8Tuzs/zMnTv8Wx8lZ2XCv/gFQ2nhMBnD+jrDuEVFPG9x4OUiza0OzkSCOOPzcU3S36C01H6AjZ2W5LVK1K47kpeS5WzPmM+qRv0+ay1RlPX3AgYwNlaGE+1JNSlF+p0BitNY4eJFHtbGBpGhpYWM4PXX2S21tFSZGC+/7B4+sks+OnxY9eWT0dsDA7TzCwpUYVJnp0oQOnFCNWmUWQYfJW9/rq20l5Z45svLVME7O3n+16+TQH7v95QTzi5GLtVwS0tk1qIeX75MLewzn1Fj4nWP/G9+o6I95eWMrd+7x6Sis2fV53JBfisOSelxcTF/ch1g4wROGsLUFKMdhkHi1+cbuIHbM0o4dW5O9cysqnI3wZ3WnGliRYCuHhSPxbB8Zw44GlY9227cyByXbBdKmZwkwdXVkdB8PqpuQ0P8/le/qgZrZpsBaOeckhFcIs1qa8kMXn6ZiHfiBEOJ16/zgRYXnZs05gkeem+/lyQYqxP4xg0iWGUlz/GNN2junTypvNW641QQXhxhpqneW18noXV38/fPfsazskrZVIqCQ2Bri5pEVRW/J556N4e1FayRgLU14h/A5xEHdm8vtdSxsdz2FtjuJJ+ZoUYrnv36ehJmbW12Z7eA2zNWV9MJLyPFFxf5f7Yomt2ahQlKd+44Iphp78HWZ55XzRaiUcXNJCPQjogaGvjwoRBTFX0+Lrqzkx7Lz35WfU9mAOpgDR85ZSxZM9W6u+lLKC/nvYNBXkufsroH/fuAfSD5vSTB6BISUK272ttJJDIT4e5dJT2lQ7N83zpia2VF4Ynkejz+uEqUseLP8eOq9Fuk+Ooqr6lrK7nG9XXVXcLTIyN8nnRapapPTW3vUrSTSsG5OTLNgQGVzpyrdpHNKf/EE7yeMIC2Nu57rlO0OjtVG/GSEp5ta6t0BdIeTIhyZcX5RufO0SMsElZ68507t13KnztHDglk2vx2MwCtapV1xJG1Z1pVFaMF1dV8fXZW1fnnGR56ye8lV16XkDL+qrVVNVZtbOQZ3L1LKba+TttZHGnWGPknPsEJPj5f9hRWgc9/XjGquTnV6/HjH+f7urYiRS6/+Y29FmEX29d76Tc28lnGxni/wkIyBJl7kS23QAerZiXZeHr6bjpNPHz/fara2a6bLQ25vp4E+tRT/F1fn1smq6xZCvlkqvHamraXueRNA2QI3/ymmp5bUkIiFweR9bMvvaRy9QMB5ezTwU6t+vWvgR//WKX9Ss+0SESllH7hC+TkUhQUjXpXu3KAh17ye61/1yXkr36lJiGZJv02iQQZqgy8TCYZETDNzFAUwD3u6+N+373L99bWVOhva2t727CODuDf/3v6fJJJnulTTymhoWdrBgLAxz6mJKIOTg5Ovz9zhoQMejVNrs2uS5FM2LGLSIlAku5X4swUrVNvV3bpkspEranxFpqTQiwReqL17LaTEbC9klcyF4uLlVl9904YK1eTKKsJoOV+pCzrjU6fVupNtpCIlx57uvaRSNCWqq+n+midSKw78155RRVBGIZyGn4IQzs+dMglV15698ko9EuXKM2iUUqIoSGeb3GxYsh6BAFQxPfCC8DPf04JHQwqbWJ+Hvj2t7eXplZWUv2XMlrriGwZyeXmvHRycL77LhmGPo58bY1aDGDfpejqVTX8RVrW/eAHFCzT07x2Vxe1oL4+4r5onUePUpu4dInab2srn0OS07LhoRMTy9Yz0Sl8bj1jJ7NC7huqjaJ6qRfJRaD/ahm6Oiz9AK2L3Ytaet3zKdVNlZVq9LKdF18eQNpTr65SSzh+XNmpeYJ9QfxO4HRmL77IopXRUSJOYyMR9tgxMtnxcUqwiortTS4ARXyBAPCVr1D9TiZVFKCigkQm8/2sTOPwYUrlWIznJSXgMnFaB7fRY/pngEyJ2dxMR6b4M0yTtv+TT6rP3rpFBmiNSP3jP9IPJdfq7iZB9vczMiFdo2/fVpWtoRB/+3x8T58abAdWJpZO8zwGB3kOdkNRJNRuZVYvvaQmfMtZd3aqNcqZxGLKoVsciCBZ1oPi8Rh8M3MYnw4j9GUblXEva+l1FUXsqdVVZffYefFjMTVPUG8YGYvR6ZRH2LfE73ZmHR2sVpOe/BIP9/ko8Scn+R3dj+NWHSjOtelp5QA0TaViW5kGYN+S24vK6xQKO3o0s8V8Mkk8qq1VdSGrq5l+EV1LEAiFKOl1JhQKkQHMzam1dnSoxrcbG3zm5WXe5+5dRqYkGcpOWOpMTJKESkpUUpueJCRn+cMf8v3aWjW3EKCJLCXUVVXcnzff5H0XFrZPzpLu3JuhCJKhnt/SWJcdLe8mjTIb6EMd791jGE98CYC9GSIPdO0a/xfbbnb2wQ/teJjAbp6c05lFIpk9+SUCMD3N71nHttlVB46PU7qOjFDqiwovzVqspak605DaDmnaYh0r5uTpl8pCPXlsYIDEPzFBHJDZfh//uHJkJxKZ0rurSxU2CRHJ5xobvdnd1gI3mQXg8/Es3nuPpoI1b0K+K0zs6lWaXBLalvteucI9lfHqiYSaYHzkiIp+vfkmfTW66SyFRrW1mXMIq6uJA2fOuD/bb2Eve6lHImqoY2EhEae2lgjl89nnHITD3NCuLiJgIsGH3YOuPg+9t1/A6jiNx1VTTwGrM1ePFEhI6fhx4I//WA1rcaoOnJwk4W9uksBKSmjrp1IkaqkZEMTSY9si6ZaWSGhOY8XsGn1IZaHEwAvun9Dly6q3gN/P9YlGCCjp/eij6prnznHN8/N0UsrfX/mKt25D0Sj3qb2dhC+NQCRLUkKCt29TUL38snJI6/F8w6Cv4MYNRYQyQ2N4WJkTiQQJ984dMgZpu15aqjQVMZ3DYeUA1kvmo1Ga0m7jzPRISqIgh8SLnYBI7NZWPmgyqcqE7QhaENDvJ7KePMnvSoJHHmHfEL+13ZU+T06IzdqiyinkJPUXdkQo35meJuJWVlLFlQ7Rd++SqK2lqU6j3Vpa7Dv9OHWrkVBYczOl++3bvOfGBglAxnmL000HK846RaROn/bWbUjWWlTE/ZB8F7+fzCCRINHLjEohrHg8k4nJrIpHH1XMWSIRkqsgE7WmpsgIlpaoWdy5Qw1H6HNpSbUll4iEPoewsND52ezKrS/PR7E4mUPfNa8gN/vRj+g1npigxFhcVNVnbqWZXltB7QL2jdrvNE9uZER1lykszN6bUcAtghCJUGJ//OPK3gVINOKMSqeJrHYlxTIlSqaQ9/fzzGX+o9s5irosYeCRERXuXV5WIb7KSiXh3JKFnCJSTqE4OwYQCrEITvpSVlZyLVev0icgiUA1NYrJLSyofaupIfMwTe7DygrX/vTTar6FMJFIhHu7vq60mU9+0r4F+xNPkNFaZyQ60YqteV8fweBqD7qLY2rG3o7qjaHs0uvXmRQhhSFbW1zo4cMqnv/++9vjxfqmP4B23vuG+K3OMsmNeOstEqhe+Wg3wCNXKCjgGUl33pYWImVFhbcxVmtrar6gNNPc2spkTHbRChlSMjGhaubjcV7r+nV681dX+fn2diUgcp2yk4uT2+qDqq3lPaem+PlUigyqooI4vbXFDMqhITKKQ4e4zliMTFGEWWEhz+utt2iOlJeTwZSXc8KytMD7xS+o/Swvq3F6p05RQ5Lwt1PBkb7HN25sZ45lZcBcKuKt3tgtJCgdf5eWeFChEDmdzDaPRFQVVmGhCk9kq0/fwzbe+4b4nebJPf749nLbXP01doUt8/NURTs76ajt66PP4Otfz34O1p4OAAm2pSUz3DU/TwS2El9BAb83Okoc8vv52Xff5Ro2NvjM1vbXds+Sj14BVh/U2hrNUL9fOUABqvamSeIfGCDDEmdjIMDvnDqVSWdTU5yelUrxGR99VA0alTOWCsZAQHW40sexy4xEu3McHFQMrriYvoTubofqTLdNkUO145aA6vi7tUXEEUklHE6cLocOkTNKqCLboiW0Ia2R88gI9g3xO2X6xWK7n31nPdPz57nHMgGnsJDE1t7uLf9c1qr3dKipoeYn4a6hIQoGmf+n41kgQAFx9CgRNpmk8JiY4DVeeMGZ8HOR5l7b4RUUKEZ1/LgyMb78ZT7j6Ki61uoqz2V5mc8qA2uCQTV8xbpHfj+98/okpMuXqcnJNaw1BnaNVJzOUVqHT07ydyzGhKltRX5um+LGGAA1zFGyqmS8U0kJ1ZJkkpsnQyCKi5lieukSkUPSSGXR1tCGnredJx+AJ+I3DONzAP4CgA/AfzNN889tPvMsgP8MoBDArGma53a9OgvYmUK7bYBpd6YyiUbmAAIqHyOXteqhRlH/ATKDpSVV52EdqHHsGDsO1dfzvj4f8ePUKa5tYECF/3QmkIs0NwxqM4mEal0mnX3tCEkGz4gjNBhUPQ6sjWsk5DY7q2LuAO9TXu68R3o41u8nsxgYUJqFdBKy0+ycznFkhEJ3a4v3r6+nJjE2RoaWMRfTLRFDxkVLGCcYzKwOE++j3FjstePHyQzef185psrL1YLr6ngY164RaQX5GhpUaEMePJ85CPBA/IZh+AB8G8BnAUwAuGwYxnnTNK9rnwkD+H8AfM40zTHDMGp3vTKP4DX33wnsmL0gLqDi7Ddu8OwLClRZdzbQGdPiIpn96ur2zk4CgmfyvXicji+/nwQ1N0cEfuwxfv6997h+KRX3GrKWIqF79/icMoQklSKeXrlCHJTsOUk0Aoh/Mnw2mSThHz1K/NRpRkynbA5Ja9OQtjZe/+RJ0om0ECstVY49p9wYu3N85x0y8Tt3uMaSEpWqva2a0E2S9PVxYyQBY3WV/586xf8lISIU4qbJvDRJCPmP/5EqiCSpPPEEOZNMPQGIFDry6VmB1umyeQAvkv9JALdM0xwGAMMwfgjgSwCua5/5twD+0TTNMQAwTXM6L6vzCLtxjtoxe0HcyUlK4LExqp4tLbS74/HM8u5s64rFKHkkTHX5Ms93cpJa4NGjauSYMK6vf11NjJIy4du3iZ8S8zYMpZ739HgvmonFVFfi1VUVZpMW3L/+tfJ5Ce4NDXF9H//4ds1COvwCmTTT3Mz9AqjNOIUTOzu35/NXVpIOq6p479VV7mFDw3YmEo+Tnqwt76qruTaJ4BUVkZm2tyv6zKAjN0miO5V0MIztNeGJBAn97Fk+uNVOv3CBHH16mveqrFRxzooKXmtycufTZT2CF+JvBKB3uJ8AYCW1TgCFhmG8DiAI4C9M0/wb64UMw/gGgG8AQIvEwT5kcHIkvviiQshIhIRfXq4cU141L8Enafsm05/SaZ5/eTm93T09mcQhKcpidycSfG9+np7vsjJqjCJMnJ7FTtqKlDRN4qbkJIhKPTNDQSNmSmmpytQLBrc3J5UuvtbOybW19JXYVS8KyFStI0co7UWbkP2IxVR1YTCozGNrHUxtLQnaWiz33HOqVF5oyOdT+7ONjpwkydYWVT5JcNCdGDrTKCykU88w+B07MAxqDZGIqgG/coWb2tysYrDhMK+fbbrsDsEL8duxPGvXTz+A0wA+DaAUwFuGYbxtmuZgxpdM8zsAvgOwgWfuy905OHnB5dx+8QtW76VSNNM6OymVV1bUnAdANYDNdZKSJL1cuqS84G1t6reUo+pgbeRx/jwJMRikBBsYoPoqCOzVBBINQVep5+a4R6+/zj0QLaWkRGkdEk6TzjldXSrbT1+rdNnx4nvI5qeQHyfQvy+jwX1UIrAAACAASURBVPRiOVmPhB43NqgN2GkQriAhj+Zm1Qz0vfdUhZMg1fy8CvltbHCD3nwzsweaIJOEL95+W7XqFkeTxESFEezEps0CXoh/AoDeyqQJwF2bz8yaprkCYMUwjDcAPAZgEA8BZPOCz88zNNvervLpf/ADSsXCwszJTaurfC1XzUsy92preZ5WaZvNjDMMag/xuGoXtr7O9dg1NnED0RBEpRbibmvjs0WjxN31deJ7PM73dGaxrXOO5Vm9psvvNrXeOiTHruWdFw0iK0gCxuioKnq4do0qod/PjXrtNRW+kLxm0yQR67PRdC1ibU1NPNna2u793cOEHy/EfxlA1DCMNgB3AHwNtPF1+GcAf2kYhh9AEWgW/F/5XOhuIJt0uXjRvhnr5CRV65ERniFAZGttzT370yptNzeJRyIc2tvdv7+1xQ5DN26QUAESXV1d7oJA1xBSKQowmU4klY59fVSPu7upDRQW0jchPfdmZsgA7HwfuTTs2G1zDy/fl+f1SkP2WmJEzfqTGfEnT/LGExOqmcC9e4rAZVrqwgKZhO6ckcQJgEghPc12sgk7hKzEb5pm2jCMPwVwAQz1fdc0zWuGYXzz/vt/ZZrmgGEYPwPwAYAtMBzYn69F7jbhKZt0cWvG+tJLJISBAb7++OP23v54nGbb9ftuUGsYTpe2uhNRRr/LAFcx+ewIam2NPqSzZ1UV3927ampwLnuiE0RFxfb5AKdPU7UX4VN7P34jU6iamojfg4OkCf3euYRfdxuqzdesQwFXLdE0eaiGQUeNSGmpLtvY4KHKAI7iYuXAk/7xPT3bFy0dVNraMru/5Mm2d4KHfmhHLkMunMA6QwHIHBTx3e/yf730dX6en//jP85+/Xg8UyMEyHAOH1ZhOPlcLMY6D3HgSYOQQMB9IIbdYJJkUoWXxUnptQlmLvsj9x4dVc48GYSiDySx7olXhr1b5p6PbFi5xttvZ7Y18yXi2BqMoXRtAUeD9+vIGxrUFF6ABC/dWlZWKC2k0cHKCrnkiRP8riCU20QVaeSxtbWjB/qdGdqRj14L2aRDLs1YddAR5u5d4oRTGA5Q0lbyRSYm6JmWDNDlZefn00Nily4R38JhImoolPvI7Vz2xy5jUZJ5nJKfcjFV3T7rhbB3axbrjFWav/T3A6da4qgf68VWSQDzBVVA7QZtnieeoOpz5QovcPo0N0xMg+lpqo2zszyo48fpKNHVertFS3PFHc8zyw0eeuK3qux2TTJyibfbOU2l9PXiRZ5ZQ8P2WX5WsCLM6qpq+iqVdxIVsCLw8rIqejEMfv/GDeVHcErMkZDYygqfXzrtZBu5nY2A9P0ZGVFOMb3Sz5qNJ7CXpqloVPPz1HakS7GXHAuv17dK+4oKCvTSUmDxnRjqmgNIIoDyChAxnniCxN3YSBvQNFWJ52c+wwtLymQ6zd9SwOFlMsledhaywENP/LpDR58ZpzfJ8MIUs0kHvfRVkEIq+uwYjH5GFRUk2HSa5t6RIyoqoHfsFRtSL3oJBFQpudjcTok5+v1kvPu9e8Q7p7biVhtWb4FlmipmLxWF8XhmBp++v/m2r7PBlSs0NWSfVlf5/5UrZAC7ASdp39KiajDSMwtYaapCalUTBPX1PFjrwEcdvvxle1tV9xI7ceS97CxkgYee+HWEu36dhy81EsJYd8IUrVN9xcQyDEqahoZMYtHzL6xn1NxMtf/uXUoNadYi1YZWRi7xcylYWVykr0fyz90Sc+R+H3yguve6jdy26x69tsbvS6ZbSQn3I1t34d2mUns9D6GF69dVpx5A9RH8yU92bA7b7otI+60tavWBADWrQoQR3UqioyugWr4lk+QUvb3eVCm7jXLzKuajt7lHeOiJX/axr4+2bmMjJavUWOyko7GUXm9uEvFnZ8lcZYb84iI1tMVFVVS1vJypaVh7x/f0MJVVGracOkXHsF3HXr3opatLee7X1pyHYFrv94lPUCWWWhGnkdt23aPjcUp9KT6TSjlpD66DVejkO+wcj3OY7iuvkBk+8giZZjxOJqi3KlteZphTBttkM4fdzB0rM+3tJfOWxqErK8BESRSPzfUCSQAV9yX45CQ5enGx+yLcNspL6TCw5+rVQ0/8APfR2k1GINeOxvG4Kr2urqYKvrxM5JiYoDYh1XaAc1GV3SDWY8eAP/qjTBxwqx2Qohe/n7kDbuaL9X6RCOdQVlbad9C1G8ohdSJCDEBmpRzwwITOb9f46qscshIMcp2Dg1yndAf+4AOVRbiwoIbXWsug7fwcTnMDZme3DyuRNvprazz7I0eAsrII3l/qwWoshq7UHCpawtxwvYopm01ux4HcVPu9VK8ssC+IH8hfR+NYTBXLGIbKB+/rozknY9Sk2s6pqErO6MoVVbxy9Oj2+7nVDszOej9fO5xwcnzpiK8P5ZAGpwUFiqD1Sjm79uB7adPHYmSCfr+aoWAYPI+REVXfv7bGzw0Ps6JR32cnc9hOuC4ukvGfPr19WEkqpRqUiDlmmkBiPYL0yR4MSDjzwoXswxcEnDiQDAF14rJ7mNWnw74gfqnaisdJ9Ovran5dKOTcf84O9HHcm5tEKoB/FxUR4dbWyAjEY+9WVDU/TwkiFZ16iS3gzshzjcl7xQkr4stQjnicSP3kk3QUzs9T6ykqorTr6VGScY+FDgDu1cYG7yPTkOUMbt5UNRaSSi+9CwFVVu/32++jXZSot5dMRXI4xFHa368SmUZGMrsvWduz52STO6n3MzOUYiKFrF1FDtp4EfSqrakp2mXinGpqIsLm4vXXe9FPTvK6o6Pce2nMubmphlbMzzsXVfX1EVl0b/TICF9/7jl1zwfEyH8LVsTXh3KcOUO88vn4/IuLqr1WYaGqqLP6pvYiWSccVnUSErqVNmDr6/y+5OsDlPivvcb9DYfJKOSMrL0w7aJEd+6oPhvSCkwGuX7qU2omYiqlEpmkbdhvaTsXm9xOvd/YoK156hS57OxsZleRvZwgZIGHnviFeabTatpLKqWm72Sz/aygl16PjhIZZBrzq6/ymh0dKoVXEFpKVX0+1di1r49MW/dGmybPVif+Bw1uwklP67XL7APUPuaChzvB2WiUzHJ0lPkKo6N0xkoJ9Xvv8TyCQTJmcWxKXX4wSKZmN8NSp1FppZ5KcW0VFXzuyUni1cgIr9/ZyfOVISJ6e/bf0nYuNrndQUjP8oYG+9HhB3F+BcI8r13j76Ym1QdOWqZJXbmXUKh+dtKRV+rl6+qIFAsLZARiUzs1dh0dzRwo8bCAVThNTfF5m5rU+15Cyrng4U5wNhLhHl+5QoaaSgHPPkvG/P77PPMTJ3gmfX30xxw6tL1hq12WoX7O0kq9s1O1wkun6fRrbeU119aU1tPdrTQYa3v2jItnAzstQXqW66Bv+kGcX4EwT/FUA5QApqk81UBuXmlJWFlcBP7+73nt+nrlcDpyZHvDDjvk7uykpCovJzKNjTH5q6ODzGNhQQ2RdCrYcYLdmH3WjL3xcX6/tJTOyVdf5fuG4W6+PojSXGEAIo0DAarojY1cRzyuOl1XVvJ3Msn9Fl+Ak92v0+jamsrhmJxUmbkbG1yjRBX8fq4nL0LWTkuQnuU66Jt+EOdXIMxTt8XE876wkDmswatXWpfiEt8eHSXRd3TwdWvDDjvkPnWKZ7q4yPMtK6MUWV9nYpD0oNMTabyYbvkw+3TEr63NnCFQW5uZXlxfb2++PsjSXH1/hdGXlPDcn3qK7wtTePddajPl5Vy3NEJxmoGhV1TeuaNCm4cO8f/6eqr7krvjtUejJ7BqCXK4gP2mH8T5Fcje+f3ck+pqeqtTKRKcdViDF4mpS/GGBtVyrbRUteqyNuywQ+7CQqqpExNkHDU1yns+PKx69euJNBKZcFtjPs0+3WwqLc2cMNzQoBKL7MxXNzx0ajdv91kd5Hvj46qGoKWFhCf7Kz0PAP6dSFBSi/S/d4/XKShQoctgMDPt17o+iWIA96v1fDwr0Yju3SNjkUGfss95d7xn8xkcxPkzQVRDycBbWFDDGgC+dvmyUusCAR701avbOygB27O7JicpAfTUXGvDDidC6OkhMZ08qcq8S0qUXwLITKQZGSFCuUl1NxXarm9AR4eqBrUiqJ3ZpIewpP+e077b5TLMz5PQpcv01askpmee4XM74awIvc1NNYhDhthIe/CGhu0Fc8JUJOxXXq4YbGUlmdf4OJ9F5llaNSex52VvFxeBv/s7nk1hodIajh9XGt+ONLB8lCEexPm3g5MGJYfT10d1sLiYHLyuzr7U1Zoq++STmam5dg073Biyfj2RWn5tZ/VEmsVF99Hi1vUJSEq5tW/Am2+y/+DHP545o95ajJM1hOUC6TT3RJje+fN8noEBEnI4TCJ64w33kmLRaG7f5rWsgzhWV1U059QprjWdpnZy+jTP6vp1En5/P5lFKESmPTxMRh6LqX2122PZW4BM5NYt3qepSfUnkNkCXjQwndZrl4bQefM8AsX34/cbG95tvQ8B9hXxW5mqpNzKoQiirK+rzjx2pa5eU3Ot4MSQ9euJ1BKJIuOxpWGkSFwdrI4xJy3D5+P1KitVeHF9XTmtGhqci3GyhrAcwClTrrdXdfBdX1ez+txME5G6uhaia0VOWoh0MQK4fxsb/Kyc1cYGryPzBwBnzenMGcVAxcsvA0Il+1L2xMtUIxE+tf44gr88j5FNP1oeq0ZwY5Ucqb19T8J0+YB9M6Lbbrxyby8PXkCkq/6aXamrEEQuU5Dl/jLXPR63v146Tan19NNq6lJjo+rR2NKiJI+AnQT2+aiN/OY3fFYxLwTRBTY2lPosIGm8+vqeew741rcowdNp75OfFxa2M6t0mvZyMKhqXAyDa3HramztYwi4D+IQ0MefNzWpMWfl5WQcppk5wFSX7gJ6noNEDQoLaUqcOKHGkOt74nYdIJMxlkzEUOzfREFVGFPThnKwiD32EMK+kfx2Eqimhq+fOcPXmptZ+Sfz3cfGuO9HjpAAge3aw5kz2QlArwJ00ubstAL9XgLZnLm6NPnYxzJ73ktGnN5NuLCQzEEiIAC/I30ErKankwAaGto+OKOjw9nRKVEMaSNumtm7Glu7BrsN4tBBN7nEJFhYYLZnOKzyNaTFPeC+x3orPgFrx18vZ6VrBr6lBaTD1ShJr2Jp5f7hlJRQ7bQr+ngIYN8Qv50KFo3SwaZXx50+TcTq6yNz6Owksc7PUx1/4w17IgbsvdDV1ZlVgKsetTk3Z5GbMzdbtadkxEnrxaIiEpAM4Ugm6feQPAgvjqqhIbYxq6wkA5XW5S+9lEkAGxtcx8QEE2303HwZsOlWZKUTca5ttHXGdeaMchxKhqwUS8k13PbYjqFNTVHyX7iwnVl6uc5mMAwjzbzxsnIA5v3CELs664cEHvoGngJOTSbX1qjC6RKur48Emk6r1NBkknnhIs1WVylFZMa95PQPDVGN3tpS2ZZLS3RIiaSQUGBDg3NDl95eJnPNzWXOuxP13wkuXNjeSVdGvDc3U5uZmlJNP8XbPzSkOgwXFHC9kj0qe2XXaBPI3sBUIgwSaq2r475IA9G5OX7+scfsp1PtBpz6XFqZdK4JVHq25tSUas0nTlOJ5ADOznv9OuZcHMs/70ViYRNd9bNoD86ivGIXXVV3Ab8zDTwF3EJt1kO3U+vGxlTdvmEotVlGqz3+uL0XenOT0k1Xtb1oc2NjaqyWPu/OLbQGOEul8XFGCdraSHyTk6qWf2iIxCce+ddf52tyb9kzp2w7t9blAPe3ooKhPFlXKKQqBSsqqHEJ4bz6qnOfgVzAam7Nz5M5PvFE5hiwnbYtF4k+Pc1rCrOUZ7xyRXWL8vszsyMlGiSh0N5rETS29eB4cQzGaiE+8B3F0RejqOx4+Lz8AvvG4efFSSec+MYNNX5aQKYei6MJUF18VlaoKfT2UqWVsepSTy6FWH19DA3duZNdm1taogSWIaylpdsdc3agO7dkwKSo/IGACn+NjnLNVVX8PTrK1w2D2kVBgSJewN2hJolOOkgSkIDV8SeVgoEACaGhwX5t4pjVHaReYGgI+C//hc++vMz7S9fiubnM9mgS3ssFBJ+ef57+oPr6zPfLyhhWlKKya9d45pIdKc+kM8aTz0bge6oH6598HunTPRicfXgJH9hHkh9wd1g5NbA4fZoqus/HENf0/fnBUqsvU1yXlniwKysk8KYmSi9Bto4OSu3paTKDb37TXdoYBglAes1JKq3evdntGXU7s6kpEznHx1UNvBCcdB8KhSjFr15VAyqzZYh6aV0uGok1p355OZMpWNcmUrSvL7OLULbS4PPnVV+FjQ0y3GRSzREU0JOfdpqJ55RXIde3y44UpqMnDumwR7U4eYV9RfxOMDREu3V6WnVXlgYW/f20Q5ubKb3LyigVEwkiV0EBkev2beU029hQuf6xGGu919eJdO3t/JyewWeFeJwIUVdHTWNhgUTS3b1dvbYDOyanI+fSEpmSePiDQT6L3n2oo4P74SVD1Evr8miUPpORkcxaetOkWSJDMnt71ZxJgY0Nvn7unDcHpHRbCgZ5v81NMu90mgxNH22mRzb0jEO7zE4ncDIpjx7dnh0pjOb998nYo9EHWouTV9j3xC+e6vl5NVX3Zz8DPvc5Etvt20Sa2lpK31iMCHL0KJFlbIzfi8f5dzDIQ93aovqcSmU6+wDnQRUCoqaL6iuNQaam3Ds+O4FdUtLCAp8PIEPp66NWIZLe52MHaa/ST29dbgcSHx8fV+m2hw/z3m+9RWYq+fLJJNeSSJBo3nuPr3/wgXLAbm4CL7+sqveszTVFM0ul+MymSd8EkBnZWFnhfmxucr9LS50zO92ezc6rD2RmRyaTNCkffZRm59aW6gvopa7hYYN9T/w//rEqnU2lqCYGg/TeRiJ8va5OceUzZ5Rqf+QIv7O2Rts+EFDz83TPeK5cXSbyijRMJFT57OXL1DZkXrybiqqrsj4f13nvnpoTOTjI7xYWkhArK/e2FiSRICE88giJUzoXDQ2RiAsKVJ8Aw1D97197jR750lIy4rv3ZzwXFrImwqoJSEafjCNfXOTzhsNskVZTk/mcly+ToYtqDthndrqBk0mpZ0cuL/PZA4HMcWWzsw+sFievsK+JPx6nxGtq4s/ICCV9ayulxMqKGqihQ1kZ3z95klKov5+fnZ9XvQJffJGfzbXCUvoNXr1KJNWn3lZVEVn0ohWnFmR2eQLSNfrUKfov3nsP+J//k8975kyeS1FtYHFROTEB/p6ZodSVXHxA9QC8dYsE095OgkinuTfimHzsMftOTDIN+/BhMhwxAZ55hve0Emk4zP2uq1Ov2WV27sQvINmR3d3A97/P5y8q2j6u7EG3assH7Dvi1w/wzh3Vk6+igsgiXWuOHlXc2E5yNzTwdyhEqfTGG2rwRTSaOX3WK1fX+w1KV+CrV5V/QKrSJJ4uk52B7RLKLtlHmo12dJAoCgv5fWl7vUet3n4LktWXSinJn0ySyemhUPGJSIl1IEDtQAhFzKFnnuFzSMxebGjZ86EhPmNbG5moDAW1QjRKG1+IWnI49CEmu+2REImocWXpNP1Ht2/z/85Ob5miDxt4In7DMD4H4C/AEd3/zTTNP3f43BkAbwP4A9M0/z5vq7wP1gO8ejUzHl1eztc3N5mcole1AZmS+9w5EvjiIiWxIG93t0o3tRbHWNdhlSA6wYrKPzNDJvXFL6qqNOtkZzvPsFPvRwEZwGGdKSB173vR+FVU97k53jMYVOFOGZxSoiW2BYPKodrQQFNMuiQfOqSSkiQ7UGxoiaNLjD2bxhWJUFM7f56qvrTI08Ox+eiREI0C//RP9HHMzKhmIjJ/oLvbubT6YYSsxG8Yhg/AtwF8FsAEgMuGYZw3TfO6zef+DwAX9mKhQGYzz2vXKOW3tijxt7Z48MEg8KUvKedVNsl9/jyvc+gQJfLoKK9hmkzqsB6kmwTRCVa6zpomi3Okc5O1UQVg70NwyqkXEA+0PlNAvOrPPKOSUl55RfWl2yki6g04JBpgmmrIRUMDtZ3ZWZ6BPpdgZoaSfnaW5yQVdM3NjEZI+bU0PhkdJVM+eza3NuIdHXTueZnQI7CTcNzkJM+ltJRMTKYkT0zQl3H69A67Lz2gdt06eJH8TwK4ZZrmMAAYhvFDAF8CcN3yuT8D8A8AzuR1hRrIaGuJu3Z0UJrEYiyCOXmSBPzJT2Z+z0lyv/02r/PYYzxEyewbGFD+AutBukkQp5DPsWOqOMdusrOdRLPTWCRXYGWFUsc6U0AawwpzFM/38DAl7k5MAp3ZHT5MBvOLX9DB19rK+62skBAaGmhuCd5WVmZ2Sk6nyRief54MS5y1RUU0HcRBWFCQ2VDTumanIiQ3u9sw6HfRU75lEpDdM9vRYSzG9TU2qopGGSiyvJxZUp2TZvEA23Xr4CXDrxGAliuGifuv/RYMw2gE8PsA/ip/S9sO4TA3U7y6Mt46GKSE4Vrcr6GXBst01qUlSphUikzg5k1+trNzeyaZXYmrlNDaZeetrJDI9ZLfxx+ng8yttNYuo/Gzn6W3u7hYNQ1tb1czBWZmuAYxCeRHH2iaK+jMzjDUuKzDh/lbOlCHQiRqu0rHmhpK9aNHaf40NfHz0SgZr8wrlDOtqHDO3pPQ7soKCXhlhf8PDbmf+fw8TbyiItUNeGpqe5amU+m45G5UV5NprK/z85LvsL7O93Swllbb3ujCBcY8NzdVs4Tbt8m9X34599TIHMCL5LcjJ2s10H8G8B9M09w0XKjPMIxvAPgGALS0tHhd428hGqUaW1dH4hobIyGcOsW9kzCeG7fVkVmms1ZX87fUdPt8qnOMgKiIXnriO5kY+fAGyz2knbjcyzC4XmluKdqA7dSZHMCqLou5sbioXnO7tqxX7ygkMXpdk1lc5FmuauOw7a578SK/J05T+X3xonOeQixGBlVSQq1rdpZ7ItqC9bNumt3GhhoeI8lV6TSvbyV+x5CwnfNqaUm1gJYuq9PTe6oBeCH+CQB6XloTgLuWz3QD+OF9wq8G8HnDMNKmab6sf8g0ze8A+A7Aqr5cFyuINDxMSbG+Tmni9ytpnA3Jrf37+vuJFFtb9CrX1tJ8EPtavNEzM7z/kSPuCR35Cvno+OFkv8u95LPt7ZSAW1s0Xdrbqdnk0rLLClZmJw019TRlL9e2Y4zSbDMWU4lVXV2K6VqvG48zvz8Y5DXq66kB6U5fOxBzcXRUtVAX887a8dfNN3DmDD/f1cX7ymTl556jABocVOXlriFhK4eRkdDiHBL7qKkpM484z+CF+C8DiBqG0QbgDoCvAfi3+gdM02yTvw3D+GsA/2Il/J2CxPLFM9zUxMOSg5c6bInxStmsE1j793V18dC2tlQXYIDEtLioSnwLC8kYBgcfzDw7q3PTzX63Rhn8fvpCJieJmF5bdtmB1fdQVUUiamvzVjegg84YrXb1F7/IvdU1A7smJ6EQnz+dVolaEk1wgnCYzFNPAjKM7Z165bNeNLvCQjID3S8nGaRZ8cLKYZqb6YD64ANVjCKxYulZtgeQlfhN00wbhvGnoBffB+C7pmleMwzjm/ff3zM7Px7PzCcHSIxVVfxfylk7OlRl2ugo89SdQHLU43Hua2EhD0gfrgnwkF9+mZ+RZJ1QSE1W2uuEDr3l9tYWw4XiS2hqykRaa5Th7Fk6pS5eJE6JUwzwPndPwCqxa2q4v7thfnb+rWxMVRjc008DP/0pibeoiK/L+HanZ7Oai5IHoHfqFciW1OWm2emamHSUtt1nK4cJhSh5amuVPXTsGKV/LJbbDPocwFOc3zTNnwD4ieU1W6I3TfN/3f2yCLEYN1JvWCm94iSUJqmei4tURdva1Ngz5+dx/x/gYTU2qpbcAvmu1nLyLAt+TE3R5CgpIbILw1tdde72m0iQmB55hCZCMkntSQZ05OpQtkP43fSncLKr3ZiqMLhAAHjhBdrusi9f+AK1P6uzXJjJwgJxZWlJzfjr6Mjs1Gt91p2m6npy3NtxmFQK+MpXMhM4Uinlxd0DeKgz/KRNlGlSxZP4ammp4tj19Zkqn7Xoxkpci4v8/JEj6jNOTsK9rtZyQxTBD93Zu75OpN3YyHS4WXFJ73Mv0Qo9OxDYWZJLvmAnMXf9LCSdW7oTSTTD2mH4/HkVd29vpyn0yCOZ3XqsA0i81l04gadkIjsOI6EdcWBIIcUehvseauKXuvBYjFK9vJzce26OZbuhkHN/+95elZQSjaoDlxg1oOK9FRX2iLfXk5OyIUpPD23VsTGaJ+3tqsBHb9hpxSW9zz1APJI059JSZcLsVotxy0txe28nTNXuLKamqBVeusQzbWlRzzw7q6JngCr1np5WjUZ1/444Vr3UXbiBU2bm9oQxizplbVt0+DAPW0o39wAe6k4+0SjVW+kOu7amKvAMwz6uPjlJKbe2xsQLv59OssVFSojFRf4v/eb7+4lEdojnpXuQG7i1+wbccwbk/p/+NJ1hjz6qUmM7Oojodmt9/nna/Hq0QgZcCDPt7+fru9Fi3OLhbu8B289NBmdKPwC70Lb1LFZX+d3iYhL+0pJ6LoDEbw291dfzs3o+gs6AJyZU3P6nP2W4fXPTe35EPE6t63vfA/72b+lvmZjgsxUXu3Q2ki9Go6pJYSxG1W0Pk3weaskfifD5QyE6/QCqbY8+qgpHrNpTZSXNpUBA9exbXVWhoCNH6FQdGCBH3twkQ/iTP3Few07UYi+2ny4BrSFFCUFFo/y7rS1T+3AzA+1m0+sRkJIS4lpr6861GDetRf530mj0c7t9mwSia2dO0lY/i95edc4tLSR8KSMWDclL3H1sjPu5vEyckLi9zFyU+oVsOCD5/TpR37xJid/UpHpK2poB+maKDSue5T1s/vlQEz/Ag62r46RWAUlvBbYT54ULSppKHr0+yhtQ7ZgAcmRJvc0neLH9hEjtwzYCQgAAIABJREFUQoo6AXR2ZqazPvaYexq4Tlwym/74cb6nV9Dtxpy0qreJBAlJzIu6Oq7VycTQz02KhUZGVJfjbL4Ia4Sjq4v3v3OHdRotLWoEm/Q8sJps8TjflzTfuTnuj4STCwoYPdLNEyeIxahxHjrEZ793j/8nEswBsEsYc9xM2w/lHx564s/V7talqSTxSJbb6io7sXR2KqmQSinVLp+OLy/nKQTgFFKUjkCDg9RYTp6kifLjH2e2mbaTlDpx6S3P5doy1nqnYNVa+vuV09owSITCdKXphZ2Jka8ux6EQJX5jIyW3DHKNxViFJz4U/Zn1jkurq/xeQYGaHQiQaSwv269B92vcuME1Nzby+cvLKWB8vsymsYCNBvIh9QF76Ik/19CLziykH5+ouI88opp7ZIv37ha8qPTyfG4hRasGMTenOvbYzeZz2498OS3jcTWvTwqJDIPOtJYWMtNf/Yp97goLgZ//nOO0vva17dfSuxwD/L266q3LsdM8Q32/JOXbjtnpHZeuX+eeysyGlRU+m2RJ2u2Bni9y965q9Z5Oq/Zi4TDX5Jr5t9eeZQd4qB1+ArozS7f53Obmra6ywUMgAPybf8MptmVl9OJubZEgi4q4v9nGTO0ExKk1OcnU7cVFpdK/+iqTTmT90uJLB2H8Vqeg5Na7zebTYbdOSyuIL6O4WJlily7xGerq+Prt2ySIpSXu9fQ0JeN//+98bv28Kir4mVSKDDmV4v9euxxbn8s03Z2oOgiDBnjPxx6jtnbokIq6bWzYz2fo66OZ4vPxOpJkdvGi6mwcjxMHnnkmy/7n+5A8wkMv+a3gxZEWifDgzp3bbq9JHYBTk4h8lVU7qfQApcz8vErAmZ9XCTjWNVk7Ee0kt94trXa3cWyZkwhw/Tdvcu1bW6p6T8aHmeb29OTmZpoHeoOQhgb3FG275xLIRYOWUWzDw1TTa2rUvmxskHGfPm0fbRsY4OdEY6mupgYn1X5S/djaSk0gq0mZr6KQHGBfSH4drCWmTqWfTmE0cXRZmSxAqfTtb9NR5PfvfOCEgKj0zz6rClakr72oyuLgray0Z/zV1QwV/fKX1CCKisgspIOthMy8JIFlC8F5Abt9jUZp0lRV8VpLS9S8JH+irk7NF7CWF0ejlJ5tbQxRtrXtbrydU1m1XemuRNeKisggZG6jVHuur+fWF9E06Zv5+tf5c/YsGeJDOqR3/0l+LzPT///2viy2ruNM8yvey03cN5G0REokTdmkJduy6DhOlMROvCaA0+nkIY6R7gm6ESRIBvPSQAbz0DPAYIDMW3ejkw6CIAimgU6A9HSnM0AyhjVJJ2nEi8jIi0QtFElxkUiREvd9q3n4+Lvqnlvn3LrkJX3Zuj8giLw895w6VfXXv39/Tw/huzc2GBbs6DAJQXaBhpAwxdCQ2ajnz1MKLS9TAqQDg21TUBKNj5vMRTvJyOXgsjeo3ZDy7FmqnO+8Y/L2fcaWCSirsOYdHR2mbn9x0WD7i4YyPc13Li5OrFXZbTptkHzvZ8/Fww+T0QXV+cEHqbVsbSViOdrU2UkhoZTBM9zcTM6/SNtvt4+IPgeO+SsryUCuBpgSax0a4iIMDlJazs5ygWMxtw/FrqATb/itW/yso2N3ZdXBLrcjI3zOI4+YhJvWVrea6wr/jo2R6c+cMbDXYRs0SJmIKAmO3YULnE9JQ6+q4t8EeffKFR5WCwumIUpNDcfY08Pwl1CmNV6f+7lKu2/fNmCrKysmSuE6HM+cMSAhMzP055w+zf3oVdbron1G9DlwzB+PA//yL5zsujpuLqnkk1irFAIVFzOUNDZG9StMeku998QET/7FRS7i5iZV47q6nZdV25LowgWqtWtrfJ5IjL4+hqVc4woyazBtNR3p7RuBSEXj45TqsZiRfPb8PPss7/XWWybkV1Ji4uaSbSloPnvs10ogEaxXrtC8kiQy8a8UFLihuYNUXc33DAppYBdaTCZUszToQDH/1BQhttvaTBus+XmGkaR6a33dzFlpKSX3zAxt77BFyMujNKquNg642Vl6fZeX+bzd5FzIASDMPDdHxrt1i4fX1paJOdtjdDmvXGmrvmPzTSqKor4+Ms3p04kty+/cMSnFwhjPPgv89Kf8zvw83/XmTTKV4PTtA1Td+5Sqn2NrK+fILhSLUtvDNIwd8+k+J/scKIdfXx+l3pEjdKx0dZG55SCQ3PXeXqbwXr/OeUsVypNsv5ISw+gLCwYX3/YX7IaEmaWZpqA1tbe7nW8u55Vv2iqQXFsAGCSk69cphWMxE/3wyWEXHDtXt2PXGCSOL5DeJSX8WQ61nWIL7oRswVpZyf1TXk6Vv7CQiMMSk0/XmZoRkg0iWVOvv87TyZVokAE6UMyfauPV1lKNnZ42HWTffZdqXNQCas3Tv6DAhKE+9jE6/wQcMxObwGZmybnXmv4JFyO4wr++GzTMsy9azalTBrX44kVqTD5eaZnn5WUTmxecftf8KEWbf2GB10rXHtEaIkEuM0xhbcYffJDz3Nb2gYTbDbW300bt7uaCFRSYXmV7AOSZ9Wq/jRl/4QKZc32dkrOmJnHj9fXREz40xA0HMHuvqSl6AaU3nO2YGRvz73LrS66ce7sM1aXhuVTLMLioYDejw4eTzcff/IY+DKX4T+LUvoAxUmjU2pqI0//xj7ud1FrTz7GywufF4zSnRNuK0qh24vjebSlxlLMwE474yHtUV3Nxp6cN6khXV7jXcZeU1cwv0mtzkx7tmRkytbTaamigZH7pJc6bpGs2NjLGCqTuqAu4syvT7XLrS7K5xO7u7U2NIx92D5vCAGElZ17ebWyMc3PpEj8rKuIc3bnjp9nYB1h+Ps2u2lquj8tJXV7OcdTUUJO6coV/v3OHuQvS4CNIO3F8p/rObrJoM+GId4GyvvYa7/F+PoHWpgRQyGcT74CyWu0XG21oyAA3SDnv2hp//9M/NVWPdrqmUCrJ8uabjOnH45RO+6HuheHIj43t3LQIJj/V1dFUtFFtpUeh+DIKCmgCpFvhF0y3vnMnPPGqvJzrdfUqD7vKSj5PfBdSuBTUan2TudL5zm6yaH3Gkwq/IQjKGotRO+vvt65PdxPvgrJa8ovzc3DQNKMsKCCjSntte+HSOdldJ/ni4s6ZPh2VsK+PGkptrUmUKS/3i9WHkQsQ9r336AOx0XClR2FJCU0i6f6rNTdtMGSVCtpqaoqgFXl5fAe7hPfGDWpt4qSdmCCUVn09QUok3dkFoybvIyHJ+XlGb0pKUuP82RRVSryb+ZV7C87E8HBqXAIblFVC0VqbXot9fcAT+1jkk9XM7zoE19bC66vTyRbbaUjVxeRAeiqhbAJptAHsXrNzlbi2tbn9FrbPIC/PxOplr732mqk1iIK2kvcuLOR9JGlJkmPm5nhIFxayym9zk88oLSWzlJeHw4lJMtfAAJmkooLzJr6v4Ly6WqNnKkrjml+A4xsZofSWKr6BgURTy95Pcg8pzgIcTVUynfIYQVnN/HIINjZS9Rc4L+m77nJQiW0nDOqKnwM7C6mG2X3BMtKNjcSGkz7x+91u0lR+izDNRJjXPgRtsM+LF8Nbisv1jY10JG5tmfTdzk6zqQcHDQyZJGUdOsQD48kn3e8ubbftZCitzdq60rODrdHb2sKzOjMxv7K3XKhRrkPN7lokuAeSR5IwB/tU5JPVNr/MwalTlBZ5eWT8oiJWS505k/wd3+KVnZhWYXbf5csmhCQhWukD6Bu/jwrXhdmQrrmy7dkTJzjmn/6UuHJSfBPsPxcs1FlfN+3A5+c530VFpoxYwnOSVCXp1DKngsHf3Gwk3cYGbVtRd0VLGBtzv7tU/EkVo5RfuwplZF0aG7lXyss5rokJPzPOZ55d83v0KMcDJKJGyTyFRRJaWxkl2dyk6SVNVd6fg3QWfheU1ZIf4IQ99xwdoD42dU+P6QgrXnRXam7wJB8f5zVih/pqC+vrtPukbHd+3oTPpOEkkPh8H81uJ97lYOmufD9MJe3udqvKdivwVC3F7U44Ev/f3DTRA5F0Q0O8vqiIh7YkX01MhEdVmpoSUYgAUzSUal0KC1MDggTnKdU8uwRyGGpUWPdl134uLbXW3w5x3bnDxfn97xkSyTCeX9Yzv5CPJmSrfwIJdfEiT9dgxyObAX1BJIMVbWLzNTRwI8/N0ZnzwANUN6MaToaF61LF6X3DvbaW4gIy7e2lHV5fz3GXlJjuPnl5/F/alJ87x++ePk1JbavSUZ1w5B1jMe5fyWuIxzlfn/qUAWJ1ka/vy16Xixd5EBUW0gyx19Fl+uwmnd4eX3k5JXpfH5lZWr/5HNRJC7e5aZwd9fUc8M9/ztBWBm3/A8P8Pt70nh7TbruqivNWXByewGIvQH19+AawE42uXjVdWWdmTE/F48dNddf4OMNgroaTYe/hG6f3dQra0tBWSW/dohp99arpTxiL8bARZ+pTT3HMk5PUDuJxXie5Fi+/bOZe0oUFiCPYCUckHcDrNjb4HmEdc1zrk8r3JUw4NMR3BJKr8uSaoIRfWDB4fUK+81xdnQyuumsBPTPDDWw3FqyspJ2Q4USfA8H8PpqQXNPQwI28sEDmOXKEP0fFz6MaLdiNP44f5wYbGOAmW19nimw8znucPEk78Nw5Mor0AqyqYpFLlIoZlEDSuPXyZdOsJB7331hhQKYLCybZ5/hxSiw5LO+7j2q2SP233+bnra3G6XbzJgFEH3iAz2hrM1WGUdK5qyv8uqgD0cfUk0Pi2jUTcgxW5YVJ+LGxnTtfBW9BwFWjyqu9Q8GVldzg0nkW4MSLlzuDlNUOPyFbE1pf57zE49SExBfS3U0GEVy1vDzTSz2V0yfo/JudNY0Wgo0/CgvJ8A0NdC6JN1rsy+Xl5FCkJGsFkzzefZeHSU9PsuOtqYnP/sMfEtO8h4cT8f/CfEG2U1FU0o0NSnuByhLBIgg7NgmopUBVKcU1EEYSx6E491IlzoQl2ABuB60kvviiDlVXM7LyyCPuNt9hyE527cbMDBO+fvtbznXYs+QQ//u/N/6lqEQk2wktmX3f/W4yzv/7CxeLcTACari8TObPcKLPgZD8qTQhUelE6m9tcd6OHycDpep4FNXrThhA7OWyMi7i/DzDWUEnT18fgSrsslD5XPwEly7xns3NprXYhz6UHKcvKOCaS5r3iRNGoxD8P5dvQqSMAIiWlfFZAmW9usq/Xb3KTRuLmUYVoiFJay+bbt8m0wKJDShcDTbDJF3wOtGEghgD//ZvDAOmY4tH+QiCWIjyjk1N/F53N79bV8fn5ueHz62MWSI6ktsQlrMQPPSlmrO/3+D7JeT3v/QSJdvt29wAjY27wzYLoQMh+SsrucHEngMSNaG+Pi5aaSlVsNJSTqqP1AeSpZLd6y4YwmlqMuAftkQtKeH3m5p4CNlVmQMDPERGRvhzdTXXsr+fG1Daj9lov7/+tckTePJJbq7Z2WT8v7AU09VVHn4yH8J8ohEcO2acm4BB4+noMJLw7Fm+q1TvSb2JbSO7qvLSwQoUiSzztbZGxpiY4PzYzVZSVQBGpe9GhVdlf9TVcW5HR5OxBoVs86G83BRHiSPVZTLIO0oDXvkX9gy0tdG597GPGTTTPcg395L8SqkXAPw1gBiAH2itvx34+ysAvrX96wKAr2ut38nUICXhQ6SIeJUbG41K195uTtXWVv59YsK/z6EtlaTKD0gO4cTjZBzBzpfmEPa6uDLT+vvJyNeu8XPJ6R8eZovpjQ1KdrtXo1LcGNKOfH7etJASCuIX/uxn/N8O3QFGYtpOtPZ2HgyCD1BaSgZvajI2++amyQcQPPuFBc5JWDFSOh50MblsxpC1ldoEl+NU3tdHu7DXN6wa8s03aU6mihLZ7b2UonkgAC1jY7z/0aO8VsYj7zg+zvtJAtbRoxHOxX1I9EnJ/EqpGIDvAHgWwCiA80qpn2ute63LBgF8Qms9rZR6EcD3AWRs5FGaUG0tmX5qitJrbc3YVjs9LMNCOCLdBaYq7LuuzLSqKuOBHh3l5ikp4WbPzyfj3blDjUOYZXaW6ui1a6ayc2Ym8UAThpANPDVFybm6atTRYBdi2Ve2BzzYB1De75lnjMki8FtVVaYY6fhxXmNTOtmTMobJSY5bTNzHHqM9HaxNsCHWd5MHYZNojqJ9SautmzcZjhQKtveSMuX5ec6HHKjBcHF7O53Aw8MmDCmZiOPjETDlewzm6SP5PwTgutZ6AACUUj8B8FkA7zO/1vr31vVvADiasRFuk2hC9lxIKamkdWpNSSVpna4MQB+STdLdTecMwE3nA+NcXW16x9vhr+FhMvdjj3GMUtQh0vTkSTqbbKapqOAzL14k47S1GaCSIEPI4VRXx40o9vrICNV0l6/IR0LbDHP4cCJqb1gxUjrpy3J/wU+oqzOeesFVdIX5Mgl3J5rj+fMMhUpashwCUksgzC3tvQSbcGOD/QuCadL2eCRqcv06tbeODn4vDL9xP8A8fZj/CACrMBSjiJbqfwbgl64/KKW+CuCrANAcxDj2oODJbTuLxKaanIzOGkuHNjeZH7C+zkV64w0+v6sr+t7NzcmZabW1hnEfeoj3m5xMvF+QaWZnjT3oAojMy+Mhd/486+RPnjRmCsDNODFh7Hm7ak/wD3wldDrFSOkWplVXc71sLUQgy6JAV2Xs4iiUBqTpCkgx88rK+Pz1da7T6dPUMIWB7fZeIyPmcC8t5XPFdxGsQmxvp8+noIBrL5ET+a5zrPsA5unD/MrxmXZeqNTTIPOfdf1da/190CRAV1eX8x5h5NKAgp1a7bjubhnf5aGtr+epPzNDZtracmtjYUU2L71E6b+8zI0VTPCxcwqKi8Or6STxyGaWwkJe39VFJhsZIeMXFiZX7b35Jv0L6VTBpZLmwfU5cYLv6luYlm4xm29Wnw/Jei0vUyKvrvLnzs7Ew1ApaoOSOt7ZaRKgALevZ3SUe1IqH6WYRxKQ5LtJtA9gnj7MPwqgyfr9KIBbwYuUUg8D+AGAF7XWGYUdCdOA4vG9a24aVnt965aJAYeF22Qj9/QYs6GjgwdGMEnHfrfjx8mkb79NxszPZzKNq697UDCcOJHoH2hpoZoeixn1FOD/c3PAj3/Md7p+nSr3zZuJvQ2CzCwm1txcYgORl15yr8+1a6lRd3yddS7yyerzvVeU6SG1BDYAi2gKQZ+Hy9dTXMzvnjhhDqnNTWphZWXmIJe1lfl4MK8SFXu1ubfJJ9R3HkC7UqpFKVUA4IsAfm5foJRqBvBPAL6stb6WsdFtU1g1nR2yyTTaql17bW8u2QypEjsAXnP6NPDRj/IeUegu8m6HDhnAkq4u/nzxItVJO9QlFXUSThSNYXU1dePKGzdYz1BebkA8+/sptcISb8S30tdn4MMFhae7270+Yag7mWgbJgy7umqSoOxYe6pkOBey8R/9EdXylpZk4Na+PpoAXV2cr7W1RJ9HWBViQQHXSXoDrK0xv2JpiSHcwkI6A197LXE+zk+3Y25sjzb3NqWU/FrrDaXUNwG8Cob6fqi1vqSU+tr2378H4C8B1AD4rmI624bW2jPIlprCNCBpceWrKtrSJgqdBkiuvV5aotNOmO6o5dKMSuxIZbIF3016+U1MRDvulKJmUVVlwlOSYCS59IBbXb96lYws9+7spAQTZCTbl2KPXToFBavsLlzgAWdTlIbqmpu5OYYpy8v5syQmRdnvktUX9K9EQZlL5EIOy6BnPmw/+fg8pApRnKK9vVT7Dx/m3ysqaOM/9BDf0zaZAOZkvD/fDdW4tvIEugo9N/cOyCvOr7X+BYBfBD77nvXznwP484yNKkBR9mYqVdG14FH2dFB1j8eZcDM3R1VQGmWWl/OED7OTfU224LtJLL+lxcSYxXF3+LBxmimXJ8bxucv/IIk0YRQ29rExmgbBz4H0zK/g/WdnqXmIypuXZ0qjb9zgAWcf0kDiIT48bDAI7FoKm2zTxE7ZlvFHga8AfhEMaVU2NMTPCwr4DpOTpmvU5CTH2GQZ0oKdEJzXu8t7G+s/EOm9O4E1m5pKTNnc2DALHouFo9PYc11dbTaRpGKKY0ygqFpb3WMJOofCEmKC7xaM5YvjTg4j2ZRbWzy4RkeN1/nMmeQcfZcj7bnn+D7Ly8Y+tZGRwja6oCYHP+/s5Bz4rk/w/iMjZGKB+ZJEn6Eh3sduZ37uHA+CxkYeIILDUFdHZpO5D1JYifPly3xuUVF0FyGfPVhdnYy8/fGP89qJCTJ9dbUpORey8RPsed0DzM4EOhDMH9zAgv9+/rxbZXd13X3nHUqteJxq7yOP8FpJHxWp7HJEbW0loinPzpLxb96kI88FxJHKORT2bq2tJiR46JBx3LmwBVZXeahIaKmvj98Pmz+h9nYeEnaTSRsZSZJSpqaMNK2uNuCfMl826ClgsBEkByAMQi3ISCINS0qMf6WoiOt04gQZSXwJQRX57l1WbpaXG0YMAoIGQUaVMnH6q1fpVAXCwVdc6xSmhc/N8b4LC+YzwXt4/nmzN+1mntXVxqzfY8zOBDoQzA+YyQ+GuFzedjtMV1HBxa6sJJN0dPAaFzqNUn5RhYoKMllHR3jGmIxPmKWxMRydN8iccgClqmE/d45qsaiYUQCXwee5mkza39GBQKxkKUYxgDT0qK8PXxv7feU+Ig3v3uW6FBcndmWy05lFRZZ4umh2S0uGWYIpz0GQ0bk5/q201Ph9VlaiwVfscYfR1BTHZGcAurowS2UfwD0kAsHXd5UpOjDML+TjSLOdM729VOsASpjGRkpgAak8c8Y4UuNx973Fyw/4ncwjI9QKDh2ihrGywu/YRSpR5BPyEhVzampnzV2iniGebZGuQKI0jfqeb16KFNv09ZEZ+/oMPt/KCrUtAUyx05nz8zkWCZsdPsy1nJ93+2BkTHaorabG4ArW1PBZrjLgdMmVAWh3YbYF10c/avaRzMc+YHYm0IFjfh88d4F9npvjBJeWUkWOxfg9AaKQ3nGCoXb+vLvmO92owtgYTQ45TOrrKXVE4mSKguYIkJnmLjvNL3E58oaHOW+XLiV68AHDCC0tBnFJ1qWsjD8H05mrqzmOggIyl6z18eM86ONxU2IsBUkiCCT5aW6O1335y2YcrpTpMArLUQjLAJRDMFXR1X7TgWN+WewoPHcpriktJWS0VGJ1dNDuD3qC7Xu7HFp5ebTZL1/mZ52d4eObmiLzr68blNreXm4KQXrdDQVx/tbXzWYLQ/tJtz7ENzc/eN+8PPM9KdFdWuJ1Ei5tbzcefLuO/+5damhaJ6b0Bk2gZ57hcxYW+L2qKuCFF+j4fOstSli7Hj8WM2OSLFBJ5hGfUTrZiFEp9zJv8pzZWZp9t25xfPPzPKSiiq72k7Ke+V2ZZqnw3KW45vZterUBxlalmCKMXB5dgZYeHuaiSfba8DDwuc8lb5K+Pkq3lRUu/uKiqQb0KWewQ5PBeDeQuPHW1wl6UVxMFdll9++kPsTHs+267/S08cRLF+KRkUQv/p07/L2/n1EHOSREhZ+YSByfSx12ofqOj5PxH3888VoBLpF3GR8nOtJjj/lnI9oUZdrY87a+bsLJ5eWmM49Un46NcY7uvz/joLzelNVgHq5MsGvXeAikwnOvqOBGy8/nJrx5k2i1YfFxwA0GIaGbqSnD/LdvA7/8JfCrXyXfQyrE8vKIiXfqFNVakXo+7zs5yfEuLlJqTE7y856exEw6wXmQ2H1hIc2AhgaTXReWHRmWfRc2D0HmcN23oYHzVVjI8Yujrq6OnxUWkvErK/lOwTr+1VVem2p8tbWci1//mrUJY2PuRqOHDpk+hPIuExNk/MZG//mw1+eNNxg5kqxLeY6NVixtz8vLjb+ispKH1rVr1CAFGer8eQNbtt+U1ZI/7JTVmqdlMNPMVkvn53my1tRQ/V9YINOeOhX9zKCkefVVMmA8zg1bUMB73r1LLL1PftIdghP7cnbWH1tA3ndwMDHeffcuDxBXJl1BAbWcJ580n9l2/07t91QOqFRZl4BRb4XsVmt1dVyzYB1/W1v0+AQ0s73d1BhMT1OrC8bLXYlgr766s/lwRQ3s1mSy9+RZtq9B0KDkd6UYYtSa8zA1BfzkJ8DXv773Hn6bslryh4Eu2k0RwtKeR0dNp5/FRf5/6hQ/T4cqK7nQU1NktIIC4yQsLEyWGAIXJaW7Dz/MGLoPopC8r11PIPBhdiadTfn5ZiO+/jr/Hx83mzEITir32G0CSar7yjw0NhrgipUVzsu77/KaWIzzOTGRmJsfNT45IKU7z9NPM2Lj2hNjYzx8bbBT17jHx6mpRIGi2lEDCUMWFfEgkr1n1wvcvMn7ApT4y8tcX1nXeJy+I0mzHhigX2k/Kaslf5jjSWzgVN73kpLE+OrSUjIsUyqS/O+BAYOQs7REle6BB6hdAInOtGBk4MgRP4ebvK9ICol3S7bg4iLVXTsnPT/faCTiZBoaAl55xYw/3exIoShHYar72unR4swrKKAWJZB0+fkmCUu85GGdboR86zwWFvhzURHNhPV1U11nJyq5fABBn0gwSai5mfMs+AF2MZTtj5H7NjQYNKiaGlZt3n9/Yp3G4cM0B6QuY49BfABkueT37Wnnos7ORPBJOXk7O9PvgffFL/L0npujlG1ooBpeU0NNIlidBnBDPP64KZ+9cIGMEFXBJu9rO9AmJ/lvbs5AQkkmnQCGnj1rCmLKy7nh7twx4xc79MYNlvAKY0S9d6rKOx+/gCQT/cVfAH/8x2TCU6eY8lpZaSS4+AmioL+FwjQOwTuUfP/Ll3kY1teTEQcGTN+HdHwAtrov1XzDw5z3Rx5hLYCg/AT9MY89ZpCI6uqIRPW1rxkYNCn+GRxMFHCZqHr0IaWDqVz7RF1dXbrbQ8+xT0CxlwQkwZaAkmZqn9avvUYGsgs+urpMf/pgimrUydrfnwiuWVtrPLxBmO7CwsQe3Fk1AAAT7ElEQVR68zAQB5dNHfT2j49zXCdOmLiwPOOJJ4wN64r1P/984n1deH1h7y2bL+hXCRu3D/mONYpc7zE+bqIMhw5RSzp/nmstTsflZe6BxsbEZ8mY5uYS80ZKS4EvfMHMgw0aIvBrx46Z+Uvn3X70I+Af/9HkKRQXc24/8xng85/nvpVaErsuxHfulVI9PlW1Wa32A+60Xp9e6GEprEGEHomNx+Ph8X/AYAj29PC0np3lhgpi24vzyJViDHCDPfRQuINJ3jfooLI3le2g8o3Jd3eHNzCVeQlDSXI9dycULHaqqCDjrq76q7auHHvRHGQONjaoRg8Pc64BMtrt2ya9WyiYNxKLMYKwsGBySFpakpOERN2X8aaDW3jkCA8mOVTicc51eXl6/SZ3S1nP/EJhVVlhvdABt8d6eJiboKeHCyjFHENDBqAzyt4SgA6RMAKd5eoQU1OTaL8XFfHQ8HG4yRiuXDHttl3pp+nE5EtL+fzr1+l0O3uW7zM1lZwHsLhIdTRVVaIvBYudpqbY4665mfD0YdV0LnJFZGzHcFkZmefaNVO5ODPj7nthoy1vbNBcUIrJYVL5KHkUkryzuMg1FUEAMOKyuWl8F1G+la0tvrMk/pSV8fsC6Cmw7dITAODnrn6Tu6EDw/xhjScl1urLUKOj3PxLSyYpBuCC9PTwALAdN+Pj3BxHj3Kh7M65QeisIJru0lIioKbWphd7lMPNNjGKikyq8pkzJrc96FiLcn729XFDCnpPdTXf5dw5Oi0ffTQZWOPqVT4rVVVi1FwHbXAJ9a2v0xsuSVv2uu0k1TUodZuaeMDffz/f4fZtAzkWPFgkIUzqBUpLeSBJ5qFoReXliWbG/LyZb1mzmhr+vrwcnSloh4MBkwkovSKam00TkKIi7pvJyYw37Dk4zG8vsG8v9CCJivu735EJFxa40ScnKQV7e40mIIs/MGAYdmSEKqGk6jY1JUJr2wtuY+KHofW6aGqKjB+PkzFWVkwn3YsX6WAKbiqXhmMz35UryYARBQW8Rhp32rUSt2+TaZ58MjVMt2v8No5CQwM39tWr5vBaXubfGhsT6x18zYowfEG5h6jRi4s8ZBobWY4clkknaMui6ot/pqyM45c1sM2MqSn+L5JZKQPXlerwCssEPHOG79XXR8EyO5tenki6dGCYfze90GWznDtHe0tCPLEY77W+TjVYVEc5RCT7zG5tvbXFjbG2xvEI3l7QPLAlssSxH3wwEcTBRX19iR17iov5szirfKRiMPW2sJDvJ624BMnm9Gky329+Q22ospKMYLdGk7lIVTBkM/3kJKX93bu898mT1JhGRw3wx9WrNLVqa6MRkcKeUVdnMAulWajk5+flkXHb2420DuueCyRDtgnzt7UZ7S1oZqyvJ9r3Ylr4NNK198aFC9yDYtaJNjk+nqhN+naeSocODPMH1VtXmywX2Yxw5AilmNhxhw/zVL99mxumuTkRAnt+3jhdFhf599FRLnB9PTewNAK9cIGb+ZlnEsc0O0uVt66On6eybWdmjMQXqRLmrAojF7LvxYs8wE6fNu3OpDpSQk2inivF94tqleWa46EhHsbd3Ryz9DG8cIHf7e01lXeFhTzQDh2iNiWNVsK0NxdAy6VLvL6kJLFZqITmfEqLAbO3YjFzsDz0kNH4jhzh53YBU35+4hqtrBgzyYdcmYBAcqOWvaztz+o4f5BkwqR4Q/Kio+KfNiM0N1OClZebXnm3bpm867o6MgpASVFaanIFRIoePcrvS8VaTQ03RyzGOLpEL2WzDgxws8Zipq3Y0BDbO7vGLmqspLtqbWrc5+b8chOCmZEVFWw7Ja2o8vPJmOPjjFU3NfFd19f5/7FjBnvOJ7/CjmzMzhq/wTvv8HAcHKRNfOwYnzE6ync7e5bazPo6taMo1dZ+ht3scmQkGa03LDM0VZPP554DvvENHpAbGwaH4R/+ITFPY3qaczg9zb9LToaYez4k++PKFe4ZG+shP5/m3fPP7426L3SgmB9IPwHC3ggCnywNEltbGcY5edLkDMjJu7pquv22tpKBxXn11FPceM3NLN4R9byy0pT9ujbr1hb9DdLa2TV2ac/e2mqcVbOzZJLCQr93diXC1NQwbm03fj161PgvjhxhKnJHB8fd1mZq58MSb2Qtzp3jIQcwpXZjw/xbXeW8LS2R+cvL+X9zswHReOopPj9qk8s6irMXMKnPQa1kNynNtoDZ3OQBaB/eGxvG33P6tDmkH300WesLI3sPnzzJg7K7m++4BwjdoXRg1H6hdNBigGRPsDhkqqvJ5AMDps+fIKrKySv5BX19XODpaS5KebnxzNpoNza5Qn3T09xQSoXjxdnmTX4+D5erV/ndwcFEEIieHt4nGJIMC/+5GDgsIhHVKgtwm1MLC6aS8vBhU9IsHv2tLR6oZWW8//y8GUMqxpR19Ime7CalWShVnsbyMjWFqNyQVPeW9ZfEszCH7l5R1jN/MOOtv5+L29xsmCDKS1xbm5yZZ7fOkrbUwtRSEBLsbWcfBHfvmkKOlRWqzzMz3ChPP83nujbrzIyp1GtrSwQCBQzzBhObVlf5jleuMMf8oYfIcJcuMVXWlZPugzyUbkQiCCQiYc/mZhMmk1bi0u5qbY2mVVUVNYuFBRMbB2i6yTOjsAftsTY1cR7EKXbiRDRG4E7s5t3maQTnK4j4E2zI2tXFse4nok9WM79s/s1NbjZBipG4d6oqsKkpk8wj0Fr19cDLL5P52tqSmVpScYO97WymAqgW/vM/0xaMxUy/POln72KslRUyysmTZJBXX6VaX1jI5924kdj+WyREcTEZX2L0t27x95aWcA3IFwdQmCTYP9CeQzl87UYX771nqg3FnBoepi/lwx82CLZ37phIweQk7ymq7d27PBA+8hGDvBNm48pYu7t50LS0UPLm57s9+bvFxEtH03CRD+KPTzbgXlJWM7+rvv3YMW6ylhaDmz8+7u5C291tIKME6urKFeA732EM2+4Ik66nuLqaG2N9PTkLzga6tBnr2We5UZeWCAZy6xbfqaGBB9PCgklLBoyE0NqondI0ZHk5ucnjTtJvw5gkqu/BoUP8TPLhJfOttZVmyuamQetpbuYzNjZYzQaQ4QsLDXKuqxdh2FgrKhizt1uFS3q2xMkzUQnnOrwlouDTqt0X8UfCzn19xuzciwo+F2U188vml5AbYBxeZWXUBu67z3RBDUrq7m5+d2SEm7migsx644bxaE9NGWkTLN0U+zqMqbSOBtB0MVZVFYEcpeAHMHH3/n5qKOXl3AC24+rBB+kRl25B99+fCG8N7F56iJQfHqZHfmsrse9BWxvfTQ7f+XmuhQ18Ke/7s59xriVsVlFBFR+g1vT666lTtF1q88wM50oaqFZU8CD81a84Nw0NmWln76MVRVFUbYR978HB5CK13Yw7Hcpq5g+rb5eSWol7B7vQAlT3h4b43dVVMtrgoEFTlYVoaUk8jQWpZXqaG76+nhusri4x1mszZzrqW3U1mbe4OLFWQWCv6uqMN19qz+NxAwtWVUWVc2mJ415cJJPZkikVbr+LXIVTvb2U0mVlnJe33uJ7K2UaUJaVue1qiR7YB6OdZZgqRTtMbY7F+K4SQQH4jK0tfkey+Hw0ibB58NEeUl0neyOooUhTFVsw1Nf7O7AzSVkd6nPVt0tsXcIhYTHd3l4yz/q6sU3X1niP++5LRMiZmUlEarl7lwdFXh7/Nj5uHFN2qK22dmd4A3NzJr69vs7vKMX/W1vNoSDM3NpK38Dmpkk+EaflygprDwDT9XUntd+uwqmqKgNWUljI97ahuIqLWRvgike7wm35+QZqy0a3EbQle+7CsAeVMvkHgtOwvMyxBlOYfbr12uQbRva5rr2d+6a723QRnpszeJBCO8lJyBRlNfPL6VhXR0lSUkKpOTFhmkgo5Y7pAoy9NjRwk0hIb2HBZPaVlSVW4YnzSoo4JF9bni+twoLM6QtEIVRWZlpMbW2ZBiL19UabsUEhg8kn8hzpIf+JT1CVFoAMX0BKm+xNKFK5qYkb+NIlhhuLijjvxcXczGfOJHf2EXIBsYhTbnHRpGjPztL3IUk0QDRQppTSbm0lArhWVoZj+PmSL9ipfd3cHAXFpUsGlx/ge1ZV8T2np6naa82fJZcf2DuYNR/yUvuVUi8A+GuwRfcPtNbfDvxdbf/90wCWAPwHrfUfMjFAu759asr0kBPv/d27nNRjx7jhpOpNAB07Oqh2LS9zIaRssrmZammwCq+khPfr7CQDFBQYn4OrCGUnXuXmZmOvDg5SMlRVcaxh6bRhz0m37j5MXbVNmMpK5uRPT5PBiovJDLW1TAx6/HFT2lpa6n6OK9wmjkz5rKAgUQPq76emIfUaYUCZ7e3UgmxAj6oqoz3tNLbvO5d245go2PGtLY710iX+XlTEffjmm8ZpmImchJ1SSsmvlIoB+A6AFwF0AnhZKRVsW/EigPbtf18F8HcZHicA472PxbgRhocNKCNAJ9LqqolTLy5Scj36KOPvx47x54oKg5wqC2VLKjutt6nJwITbPeN2czpLFt+pU4QI+9KXKPWPH08friwdyRGlrsr7j41xjgVRV5BmPv95qvjSndhnjHIA2GaB/ZlSZKxYjM+JxYh7NzoaDZTpghB79llm2KWrhe1kLuW6VLDjlZWJ/gmp0RcUKHuOdjPunZKP5P8QgOta6wEAUEr9BMBnAVipGvgsgP+liQn2hlKqUinVqLUey+RgL182m7G/n8xYWkob8JlnDMyUTNwTT3DT5OWZJBNh/GBChS2pSkoSE39qaqhltLT4t3SKIleR0iuv+HeNsSkdyZEqO/KJJ4yXXjDt7ruPTLi5aWL5Yd2J06XeXrOeAP+Px2kGPPVUNHJOmCa0GyeZ71zKdalgx9vbCe9eX2+agS4v029j2/S7zUnYKfkw/xEAI9bvowCCQ3VdcwRARpnfJpHQkmYLJKto1dVMOAli0YVJxqCJkQnmDCPXgu+kc0s62Wyp1Nrq6mQvve2RT9WdOBMkCL5AInKOfajvFfnOpVwnbb/q6oz/xe4fIdcNDBjNsa2NB1yYubSf5MP8rh43QTePzzVQSn0VNAvQ7NO7KkCdnXQMKWXw7dfWjOrpYuqd2lSZYs79IF/J4ROazARoii91dDDxRzIqBTRDwo37bQMD/nNZXc3aBxtM1DU/XV3J/on9fJ8o8vH2jwJosn4/CuDWDq6B1vr7WusurXVXnQ2o70lnztBuF3grCfEISIXLBv0gbapsIx8odPsa8cjbTUoyOXddXfRzbG5SK9nc5AH/8ssHY7189lY277+U0N1KqTiAawA+BeAmgPMAvqS1vmRd8xkA3wS9/U8A+But9Yei7usL3R2kIDacxHv3qrHBvzfySWLZj4YRH8Sz7hXyhe72wu1XSn0awF+Bob4faq3/h1LqawCgtf7edqjvbwG8AIb6vqK1juTsnTJ/jnKUo2jKKG6/1voXAH4R+Ox71s8awDfSHWSOcpSjD46yOsMvRznK0d5RjvlzlKN7lHLMn6Mc3aOUY/4c5egepRzz5yhH9yjlmD9HObpHKcf8OcrRPUpeST578mClJgEMeV5eC+DOHg5np5St4wKyd2zZOi7g38/YjmmtU+bPf2DMnw4ppbp9Mpb2m7J1XED2ji1bxwXce2PLqf05ytE9Sjnmz1GO7lE6KMz//Q96ACGUreMCsnds2Tou4B4b24Gw+XOUoxxlng6K5M9RjnKUYcoa5ldKvaCUuqqUuq6U+s+Ovyul1N9s//1dpdRjWTS2V7bH9K5S6vdKqUeyZWzWdY8rpTaVUl/IlnEppZ5SSr2tlLqklPrNfozLZ2xKqQql1P9RSr2zPbav7NO4fqiUmlBKXQz5e2Z5QGv9gf8DQUL6AbQCKADwDoDOwDWfBvBLEC/wwwDezKKxfQRA1fbPL2bT2KzrfgViMnwhG8YFoBJEgG7e/v1wtswZgP8C4H9u/1wHYApAwT6M7eMAHgNwMeTvGeWBbJH878ODa63XAAg8uE3vw4Nrrd8AUKmUasyGsWmtf6+13u67gzdADMP9IJ95A4D/COB/A5jIonF9CcA/aa2HAUBrnU1j0wDKthGqSkHm39jrgWmtf7v9rDDKKA9kC/OHQX+ne81eULrP/TPwdN4PSjk2pdQRAJ8D8D3sH/nM2QkAVUqpf1VK9Sil/iSLxva3ADpAENr3APwnrfXW/gwvkjLKA9nSpTdj8OB7QN7PVUo9DTL/2T0dkfVIx2fBsf0VgG9prTeVcl2+J+QzrjiAMyAwbDGA15VSb2itr2XB2J4H8DaATwJoA/CaUup3Wuu5pG/uL2WUB7KF+TMGD74H5PVcpdTDAH4A4EWtdUinvA9kbF0AfrLN+LUAPq2U2tBa/+wDHtcogDta60UAi0qp3wJ4BESK3kvyGdtXAHxb09C+rpQaBPAggLf2eGypKLM8sB9OFg9HRxzAAIAWGCfMQ4FrPoNEZ8dbWTS2ZgDXAXwk2+YtcP2PsD8OP5856wDw/7avPQTgIoCTWTK2vwPw37Z/rgch62v3aU2PI9zhl1EeyArJr7XeUEp9E8CrMPDgl2x4cNBT/WmQyZbA0zlbxvaXAGoAfHdbwm7ofSgQ8RzbvpPPuLTWl5VS/xfAuwC2wO7PzhDXfo8NwH8H8COl1Hsgo31La73n1X5KqR8DeApArVJqFMB/BZBvjSujPJDL8MtRju5RyhZvf45ylKN9phzz5yhH9yjlmD9HObpHKcf8OcrRPUo55s9Rju5RyjF/jnJ0j1KO+XOUo3uUcsyfoxzdo/T/AUC7Rv8D5vBgAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"import matplotlib.pyplot as plt\n",
"np.random.seed(seed=42)\n",
"N = 1000\n",
"x = np.random.uniform(size=N, low=0, high=1)\n",
"y = np.random.uniform(size=N, low=0, high=1)\n",
"1\n",
"accept = (x*x+y*y) <= 1\n",
"reject = np.logical_not(accept)\n",
"fig, ax = plt.subplots(1)\n",
"ax.scatter(x[accept], y[accept], c='b', alpha=0.2, edgecolor=None)\n",
"ax.scatter(x[reject], y[reject], c='r', alpha=0.2, edgecolor=None)\n",
"ax.set_aspect('equal')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Il est alors aisé d’obtenir une approximation (pas terrible) de π en comptant combien de fois,\n",
"en moyenne, X² + Y² est inférieur à 1 :"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.112"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"4*np.mean(accept)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
......@@ -16,10 +147,9 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.3"
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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