diff --git a/M1/Numerical Optimisation/ComputerSession3.ipynb b/M1/Numerical Optimisation/ComputerSession3.ipynb new file mode 100644 index 0000000..ab42ef6 --- /dev/null +++ b/M1/Numerical Optimisation/ComputerSession3.ipynb @@ -0,0 +1,319 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Computer Session 3\n", + "\n", + "\n", + "\n", + "## A first geometric optimisation problem\n", + "\n", + "We consider a convex polygon inscribed in the unit disk in $\\R^d$. In other\n", + "words, we consider $0= \\theta_1\\leq \\theta_2\\leq \\dots\\leq \\theta_n< 2\\pi$, and\n", + "the associated polygon is the convex hull of $\\{e^{i\\theta_k}\\}_{k=1,\\dots n}$.\n", + "\n", + "Find numerically the polygon that maximize the perimeter. Your function to maximize must\n", + "take, as an argument, the geometric quantities of the problem: you should fix the number of sides or of angles. Then, computing the\n", + "perimeter, minimise it under constraints, using (for instance) a penalised\n", + "method (Exercise 3.2). Compute the gradient by finite differences.\n", + "\n", + "Plot your results graphically." + ] + }, + { + "cell_type": "code", + "execution_count": 123, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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qE7OarVNSU1NxdHQ0yTWqqqpYu3YtUVFRaLVak1yjKWqN/W6NfQbpd2vqd2vsM0i/W1O/G6PPhYWF+Pv7X3f7tlaZmNXcvnR0dDRpYmZra4ujo2Or+caG1tnv1thnkH63pn63xj6D9Ls19bsx+3y9IVQy+F8IIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQoomQxEwIIYQQookwaWK2ZcsWJkyYgI+PDyqVil9//fW6r9m8eTORkZFYW1sTHBzMF198UafN8uXLiYiIwMrKioiICH755RcTRC+EEEII0bhMmpiVlJTQtWtXPv3003q1P336NOPGjWPQoEEcPHiQl156iSeffJLly5cb2+zcuZNp06Yxc+ZMDh8+zMyZM5k6dSq7d+82VTeEEEIIIRqFhSlPPnbsWMaOHVvv9l988QUBAQHMnz8fgA4dOrBv3z7+/e9/c/vttwMwf/58Ro0axbx58wCYN28emzdvZv78+SxZsqTB+yCEaAJ0Oti6FTIzwdsbBg0CjcbcUQkhRIMzaWJ2o3bu3ElUVFStY6NHj2bhwoVUVVWh1WrZuXMnTz/9dJ02NcmcEKKFWbEC5syBtLSLx/z84KOPYPLkBr9caWkppaWl6PV644dOpzP+383Nzdi2uLiYwsJCVCoVarUatVqNhYUFlpaWaLVatFotKpWqwWMUQrRcTSoxy8rKwtPTs9YxT09PqqurycnJwdvb+6ptsrKyrnreiooKKioqjI8LCwsBqKqqoqqqqgF7cFHNeU11/qaqNfa7NfYZGqnfv/8OM2eCooCNzcXjeXmG4wATJhgPK4pCSUkJxcXFuLu7o7lQVUtISODkyZPGpKuyspLKykoqKiqorKxk1qxZxoRrx44dbN68+aohzbxw3aqqKg4ePMjatWuv2nbGjBm0b98egNjYWLZu3YqNjQ02NjbY2trW+jcoKAhHR8e/9GkyNfkel363dI3R5/qeu0klZkCdd5eKotQ5fqU213pX+s477/DGG2/UOb527VpsbW1vJtzriomJMen5m6rW2O/W2Gcwcb81Gli8+IpPZWVlkXX0KKW7d1NWVkZJSQllZWXo9XoAxo8fj4ODAwBHjhzh+PHjV73M6tWrcXFxASAuLo7k5ORaVTCVSmV8vHPnTpydnYmJiSEpKYmMjAzjNWuqa9XV1QBs376dxMREABITE9m/f/9VYxg8eDC+vr4ApKSkcPDgwVrJW83/HRwccHBwQKvV3shnskHI93jr0hr7bco+l5aW1qtdk0rMvLy86lS+srOzsbCwwNXV9ZptLq+iXWrevHnMnTvX+LiwsBB/f3+ioqJM9g61qqqKmJgYRo0aZZZfoObSGvvdGvsMput3dXU1ubm55MbEcH72bLI0Fvzm15n9bXwY6hbAvQlb6JkRzyadjjS9HssZM7AMCMDJyQkwvHGztbVlyJAheHl5AYbxqsnJycbkxsrKCisrKywtLbG0tMTJyQkLC8Ovw3HjxtW731drqygKVVVVWFhYoFYb5lgNHDiQCRMmUFZWRllZmbF6V/P/UaNGGX+P7dixg+zsbOP59Ho9xcXFFBcXc+7cOaZOnUp4eDgA6enpJCUl0aZNG9zc3HBzc8PS0vImvgLX7rN8j7d8rbHfjdHnmrt119OkErN+/frx+++/1zq2du1aevbsafxE9evXj5iYmFrjzNauXUv//v2vet6aX8KXqxkDYkqNcY2mqDX2uzX2Gf56vxVFIT8/HwcHB2NStG3bNjZs2GAYz3X0KHFOvuwM7EKxlaGy/Yd/Z9Z0HkX7nBRG7F5O14Tt+AQH43j77Tg5OeHo6Ii9vb3xFmaN0NBQQkNDb76zl7hevy9PjlxdXY1vMK+nd+/etG/fnsLCQuNHUVER58+f5/z583h6ehqvnZaWxrZt24yvValUtGnTBg8PDzw8POjRowfOzs433sErkO/x1qU19tuUfa7veU2amBUXF5OUlGR8fPr0aQ4dOoSLiwsBAQHMmzeP9PR0vvvuOwBmz57Np59+yty5c3nooYfYuXMnCxcurDXbcs6cOQwePJh3332XiRMnsnLlStatW1frF5MQomlRFIW8vDzS09NJT08nIyODs2fPUllZyf33309gYCAA9vb26PV6Mop1bNf5cW5AOGobe9pWV3F/7GZSTx9gVcfhJLkFkHTL01iOfoxb2tgww96Hjn5tWsxAexsbG3x9fY23Nq/Fy8uLHj16kJeXx7lz5ygpKSEvL4+8vDzi4+Pp2LGjsW1sbCwnT57E19cXHx+fWuPwhBBNg0kTs3379jFs2DDj45rbiffeey+LFi0iMzOTlJQU4/NBQUFER0fz9NNP89lnn+Hj48PHH39sXCoDoH///vz444+88sorvPrqq7Rr146lS5fSp08fU3ZFCHEDLh33GRsby2+//UZ5eXmddhqNplZ5X3H0Ic51ELvKylCFq/CsLOXxHT9y777fsdZVwfENvLbpG36NGMribmOJ8wzmlwwdv3yxkxAPe6b3DuD2Hn442baed/nt27c3TjAAw/qR2dnZxo9Lq3QnTpzg4MGDxrFuFhYWeHl54ePjg6+vLx06dGjw26BCiBtj0sRs6NChxsH7V7Jo0aI6x4YMGcKBAweued4pU6YwZcqUmw1PCNEAFEXh/PnzJCcnk5KSQnJyMkOGDKFLly4AODg4UF5ejoWFBd7e3sYkwNvbGxcXFzQaDZkFZfx7TSIrDqahKGBpoeaefm15vCSeNvNr7+zhUFnGzMOrufvwag4vWs4S23b8djiDE9nFvPlHLO+ujueWLt7M6B1AZGDLqaLVl52dHUFBQQQFBdV5rnPnztjZ2ZGenk5mZibl5eWkpaWRlpaGSqWqdbs3LS0NrVaLh4dHY4YvRKvXpMaYCSGah/Lycg4dOsSOHTtITEykpKSk1vPJycnGxMzb25vZs2df8bZZYXkVX8ScYOG201RUX5hN2cWb50eHE+BqC0SAdtkV1zFTzZ9Pt8m30Q14eXwHVh5M53+7U4jPKmLFgXRWHEgn1NNQRZvcvXVV0a4mODiY4OBg4OLt5YyMDNLT0yktLcXmkiVJYmJiSE5OxtraGh8fHzIzM4mMjMTX17fVJbtCNCZJzIQQ11VRUUFpaSlt2rQBoLKyklWrVpGcnGxcTNXHx4fAwEACAwPx9/c3vrbmdtmlqnR6Fu9O4aP1J8grqQSgd1sXXrqlA938nWtffPJkmDjxmiv/O1prmdmvLXf3DeRQaj6Ld6fw+5EMEs8W88bvsfzrT0MV7a4+AfQIaH1VtCtRqVTGCQmdO3eu9ZyiKFhbW2NpaUl5eTknTpzgxIkTFBcX4+TkRIcOHbjlllvMFLkQLZskZkKIOhRFISsri8TERE6ePElaWhrBwcHcfffdADg6OtKlSxesrKyYOnUqQUFB9ZpxpCgKa45n8e7qBE7nGKpswe52vDgmnFERnldPmDQaGDr0uudXqVR0D2hD94A2vDohgl8PprP4sipamKcD03v7c1sPP5xspIp2JSqViunTp6PX68nKyiIpKYni4mK0Wq1xt4NLbdmyxZiQ1ywPIoT4ayQxE0IYnTp1iri4OBISEur88S0uLq41qH/SpElER0fXOynbn3yet6Pj2J98HgA3e0vmjAzlzl7+aDUN/8fc0VrLPf3aMrNvIAdT81lyoYqWcLaI13+P5V+r4xnfxYfpvQPoEeAsVbQrUKvVxtmb58+fJyoqiqysLOPyJgDnz59nw4YNgGE2aWhoKGFhYbRr1+6KyxQJIa5NEjMhWrHKyspas/C2bt3K6dOnAcOaO+3atSMkJITg4GDjbcwbdTqnhPdWx/PnMcPC0NZaNQ8PCubhIe2wtzL9ryCVSkWPgDb0CGjDK+MvVtESzhaxbH8ay/anEe7lwPTeAUzq7itVtGuwsLCoM6lAURS6du1KYmIiZWVlHD58mMOHD6PRaAgKCmLAgAFXnIgghLgyScyEaGUqKytJSEjg2LFjnDx5kqeeegp7e3sAunbtiouLC2FhYfWuhF1NXkklH68/wQ+7kqnWK6hVcEekP3OjQvF0tG6o7twQJxst9/Zvyz39AjmQYhiL9seRDOKzinjtt+O882cc47v4MKNPAN39pYpWHy4uLtx2223o9XpSU1NJSEggISGB3NxckpKSiIyMNLYtKSlBURTj95sQoi5JzIRoBaqqqjhx4gTHjh3jxIkTtTbTPXPmDJ06dQKgW7dudOvW7aauVV6l4+vtp1mw8SRFFYY9I4eGufPi2HDCvZrGJt0qlYrIwDZEBrbh7+Mj+OVgGov3pJB4trhWFW1GH0MVzdFaqmjXo1arjZM/oqKiyMnJISEhgXbt2hnb7N27l82bNxMUFETHjh3p0KGDyfcrFqK5kcRMiBbu9OnTLFmyhMrKSuMxV1dXOnXqRMeOHRtsnSq9XmHFwXT+szaBzALDYrIdfRx5aVwHBrR3a5BrmIKTrZb7BgRxb/+2HEg5z+LdqcYq2t9XHuft6DgmXKii1ZkxKq6qZt/OS+Xm5qIoCqdOneLUqVOsWrWKdu3a0a1bN8LCwmqNXROitZKfAiFamNzcXMrLy43b+Xh6elJdXY2TkxOdOnWiU6dOeHl5Nehtuq0nzvF2dDxxmYYJA77ONjw7OpSJXX1Rq5vH7UBDFc2FyEAX/j4+ghUH01i8O4UT2cX8vD+Nn/en0cHbkWmRPlhXmzva5un2229n+PDhHD9+nOPHj5OZmWlcisPJyYk5c+bIrE7R6kliJkQLUFFRQWxsLAcPHiQlJQV/f39mzZoFgK2tLY888ghubm4NPmYqvQQe+HY/W5NyAXCwtuCxYe25r39brLXNdw9GJ1st9w8I4r7+bdmffJ7Fe1JYdSSTuMxCXv+jEEu1hn2649zdry1d/ZxkLNoNaNOmDQMHDmTgwIHk5uZy+PBhDh06RHBwsDEpUxSF/fv3ExYWhoODg5kjFqJxSWImRDOWmZnJ3r17OXr0qHHcmEqlwtramurqauOtIXd39wa9blZBOe+viWPFEQ0KuWg1Ku7uG8gTw0NwsWs5ey2qVCp6tnWhZ9sLVbQD6fxvdzInz5Ww7EA6yw6kE+HtyPQ+AUzq5oODjEW7Ia6urgwfPpyhQ4fWutWemZnJH3/8QXR0NGFhYfTs2ZPg4GBJgEWrIImZEM1UdHQ0e/bsMT52dXWle/fudOnSBUdH0wyyLyqv4r+bT/HVtlOUV+kBFWM7evLiuA4EutqZ5JpNhbOtJQ8MDOLu3r58uvRPUiz8iT5+ltjMQl799Rhvr4rj1q6GsWhdpIp2Q9RqNdbWF2fq6nQ6AgICSElJIS4ujri4OFxcXOjZsyfdunWTCQOiRZPETIhmIi8vD2tra+MfpbZt27J//34iIiLo2bMnAQEBJksGqnR6ftyTwvx1J8i9sIVSZIAzgx1zeHRa15taVqO5UalUtHOEJ8Z15vWJnVh+IJ0le1JIyi5m6b5Ulu5LJcLbkRl9ApgoVbS/xN/fnwceeIDs7Gz27dvH4cOHycvLY+3atWzYsIFZs2bh7e1t7jCFMAlJzIRowhRF4cyZM+zcuZPExESGDx/O4MGDAQgLC+Ppp5826ZpQhi2UzvLe6nhOXdhCKcjNjhfGhDM81IU///zTZNduDpxtLZk1MIgHBrRl75nzLNmTwqqjmcRmFvLKr8d4O/rSKpqzucNtdjw8PBg3bhwjR47k6NGj7N27l7KyMjw9PY1tcnNzadOmjUwaEC2GJGZCNEE6nY7Y2Fh27NhBZmam8Xh+fr7x/xqNxqRJ2YGU87wTHcfeM4YtlFztLHlqZAh39g5Aq1HXWguttVOpVPQOcqF3kGEs2vIDaSzZk8LJcyX8uDeVH/em0snXkem9A5jYzbdRdjxoSSwtLYmMjKRHjx6UlJQYkzCdTseiRYuwsLCgT58+dO/eXbaBEs2e/HYQoonZvXs3O3bsoKCgADBsg9O9e3f69u2Lq6urya+fnFvCe6sTWHXUkBBaa9U8ODCYvw0Jltty9dDGzpIHBwUza2AQe07nsWRPCtHHsjiWXsjLvxzjrVVxTOzmw4zegXT2czJ3uM2KSqWq9WYkJycHnU5HUVERq1evZtOmTURGRtK7d2+cnORzK5onScyEaGIyMjIoKCjAzs6O3r1706tXr0YZ7Hy+pJKPNxi2UKrSKahUMKWHH3OjQvF2sjH59VsalUpFn2BX+gS78lpJJcsPGHYXOHWuhCV7Ulmyx1BFm9E7kFu7+UgV7S/w9PTk6aef5vDhw+zatYucnBy2b9/Ozp076dKlC0OHDsXZ2dncYQpxQ+Q3gRBmVFRUxPbt24mMjDQuaTFgwAACAwPp0qVLo6yEXl6lY9GOM3y2MYmicsPKqYND3Zk3NpwO3k1jC6Xm7tIq2u4LVbQ/jxqqaC/9cpS3VsVyazdf7uoTQCdfqfTcCK1WS8+ePYmMjOTEiRPs2LGDM2fOcOjQIXr16iWJmWh2JDETwgwKCgrYtm0bBw8epLq6mtLSUiZPngwYBjw31DZJ16LXK6w8nM6/1ySSnl8GQAdvR14aF86gkIZd90wYqFQq+ga70jfYldcmVLLigGF3gVM5JSzZk8KSPSl08XNieu8Abu3qg51U0epNpVIRGhpKaGgoaWlpJCUlGXe/ADh48CBeXl4ym1M0efJTL0Qjys/PZ+vWrRw6dAidTgdAQEAAXbt2bdQ4tifl8HZ0HMczDFsoeTtZ80xUGLd190XTTLZQau5cLqmi7TplqKKtPpbFkbQCjqQd5Z9/xDKxuy8zeksV7Ub5+fnh5+dnfFxUVMSqVauorq4mNDSUYcOGSYImmixJzIRoJOvXr2fHjh3GhCwoKIghQ4YQGBjYaIuRJmQV8c6fcWxKOAeAvZUFjwxtx6yBQc16C6XmTKVS0a+dK/3auZJbXHFhRmcqp3NKWLw7hcW7DVW0Gb0DmCBVtL9Er9cTERHB0aNHSUxMJDExkYiICIYPH15no3UhzE1+woVoJFqtFp1OR3BwMEOHDiUgIKDRrn22sJwP1iby8/5U9ApYqGu2UGqPq70sL9BUuNpb8fDgdjw0KJidp3JZsieV1ccyL1bRamZ09gmgo49U0erLycmJyZMnM2TIEDZv3szRo0eJjY0lLi6Obt26MXz4cNmTUzQZkpgJYQJVVVXs2bMHHx8fgoKCAOjbty/+/v7Gx42huKKaLzef5P+2nqasylCpG9vJi+fHhBPk1rK3UGrOVCoV/du50b+dG7nFEbWqaP/bncL/dqfQ1d+ZGb39mdDVB1tL+VVeH66urkyePJkBAwawceNG4uPjOXbsGMOHDzd3aEIYyU+zEA1Ir9dz6NAhNm7cSFFREd7e3jz88MOoVCosLS0bLSmr1un5cW8q89clklNs2EKpR4AzL9/SgchAl0aJQTSMy6toi3ensOZ4FodT8zmcms8//ohjUnfDumgRPjKLtj48PT258847SUtL49y5c7WqZcePHyc0NLRVbTMmmhZJzIRoIGfOnGH9+vVkZWUB4OzsTJ8+fRo1BkVRiIk9y79Wx3PqnGELpbautrwwJpwxnbxkY+1m7NIqWk5xBcv3G3YXOJNbyg+7Uvhhl6GKdlfvAMZ39ZYqWj1cPkkgOTmZn3/+GUdHR0aOHEl4eLgZoxOtlfzkCnGT8vLy2LZtG/v27UOj0WBtbc2QIUPo1atXo6xDVuNQaj5vR8ex53QeYJj1N2dECDP6GLZQEi2Hm70VfxtySRVtTwpra1XRYpnU3ZcZfQJkLbobUF1djZOTEwUFBaxYsQIvL69G/RkWAiQxE+KmZWRkkJqaSlhYGL169WLYsGGNslJ/jZTcUt5bE88fRwxbKFlZqJk1MIjZQ9vhKFsotWhqtYoB7d0Y0N5QRVt2oYqWnFvK97uS+X5XMt38nZnRJ4AJXXywsZSZt9fSrl07Hn/8cXbt2sXWrVtJT0/nxIkT2NnZMXbsWFmsVjQKScyEuEGKopCfn0+bNm0A6NixI+Hh4Tz00EO1FrQ0tfMllXy6MYnvdp4xbqE0ubsfz0SF4uMsWyi1Nm72Vswe0o6HLxuLdig1n0MXqmi3XaiihXtJFe1qtFotgwYNonv37qxdu5akpCRiY2PJzs7miSeeMG6gLoSpSGImxA3Izs7mjz/+IC8vj8cffxxra2tUKhXdu3dvlNX6wbCF0rcXtlAqvLCF0qAQN14cGy5LKIhaVbRzRReraCl5pXy3M5nvdibTPcCZGb0DGC9VtKuyt7dnwoQJFBYWotPp6NOnjyRlolFIYiZEPVRWVrJp0yZ27dqFXq9Hq9WSkZFBcHBwo8Wg1yv8djiD99ckGLdQCvdy4KVxHRgcKlsoibrcHax4ZGg7/jY4mO0nc1iyJ4W1x89yMCWfgyn5vPlHLJO7+zKjTyBhXrKO15W0adOGsWPH1pqlefjwYRITExk9ejSOjlJ9FA1LEjMhrkFRFOLj41m9ejUFBQUAdOjQgTFjxuDk1HjVqR0nc3gnOp6j6YYYvByteSYqlMk9/GQLJXFdarWKQSHuDApxJ7uo3FhFS80r49udyXy7M5keAc7M6BPI+C7esgvEZVQqlXFGs06nY926dRQVFXHixAmGDh1Knz590GjkcyYahiRmQlyFTqdj6dKlJCYmAhffOYeGhjZaDCfOFvHOn/FsiM8GLm6h9MCAILkFJf4SDwdrHh3antmD27H9ZA6Ld6cQE3uWAyn5HEjJ583fjzO5hx8z+gQQ6ilVtMtpNBruuusuVq1aRWpqKmvXruXo0aNMnDgRLy8vc4cnWgBJzIS4ipqlLzQaDQMGDGDQoEGNtuhkdmE5H65LZOnei1sozegTwJMjQnCTLZREA7i8ivbzvjR+3Guooi3acYZFO84QGdiGGb0DiOog+0leysvLiwceeICDBw8SExNDZmYmX375JQMHDmTw4MGyxIa4KfLdI8Qlzp8/j4WFhXEl8DFjxjBo0CDc3RtnDFdJRTVfbjnF/209RWmlYQul0R09eWFMOMHu9o0Sg2h9PByseWxYex4Z0o5tSReqaHFn2Z98nv3J53G0tqCbs5qQs8VE+LUxd7hNgkqlokePHoSGhhIdHU1sbCxbtmyhffv2jboPrmh5JDETAsNYsj179rBu3TqCg4O58847UalU2NraNsqaZNU6PT/tS+PDdYmcK6oAoHuAMy+N60CvtrKFkmgcarWKwaHuDA51J7uwnJ8vjEVLO1/Gliw1Wz7dQc/ANszoE8C4zjIWDQyzN6dOnUpsbCxZWVm1kjJFUWS3DXHDJDETrV5eXh6//vorKSkpAFRUVFBZWYmVlelvGSqKwvq4bP61Op6k7GIAAi9soTRWtlASZuTheLGKtik+i/l/7ON4voZ9yefZl3yeN36PZXIPX2b0DiBExqIRERFBRESE8XF+fj5LlizhlltukQqauCGSmIlWS1EUDhw4wOrVq6mqqsLS0pKoqCgiIyMbJSE6kpbPW6vi2H1hC6U2tlqeHBHCXX0CsbSQ9ZJE02AYi+ZGUZieyIFD+fVwFkv2pJKeX8Y328/wzfYz9GprqKKN7SRVtBobN27k7NmzfPPNNwwcOJChQ4fKzE1RL5KYiVaptLSUlStXkpCQAEDbtm2ZNGlSo2y5kppXyvtrEvjtcAYAlhZqHhgQxCND2+FkI1soiabL09Gax4eH8MjQ9mw9cY7Fu1NYH5/N3jPn2XvmPK//FsvtPfyY0cef9h6tu4o2btw4VCoVhw4dYuvWrSQlJTF58uRGG68qmi9JzESrpNFoyM7ORqPRMGLECPr162fyKllBaRWfbjzBtzuSqdTpUangtm6+PDM6DF/ZQkk0Ixq1iqFhHgwN8+BsYTk/7U3lx72GKtrX20/z9fbT9G7rwow+AYzp5NUqq2hWVlZMmjSJ0NBQ/vjjDzIzM/nvf//LyJEj6dOnjwxTEFcliZloNaqqqrCwsEClUmFlZcWUKVPQaDQmX3uoolrH9zuT+WRDEgVlVQAMaO/KvLEd6OQrWyiJ5s3T0ZonRoTw6LD2bLlQRdsQn82eM3nsOZOH8+9abu/hx/TeAbT3aH0ziyMiIvD392flypUkJSWxevVqLCws6Nmzp7lDE02UJGaiVcjOzuann36id+/e9O7dG8DkG47r9Qq/HzFsoZR23rCFUpinAy+OC2doqLu8YxYtikatYliYB8PCPMgqKOenfan8uCeFjIJyFm47zcJtp+kd5MJdfQIY3bF1VdEcHBy466672LdvH4cPH6Zbt27mDkk0YZKYiRZNURQOHTpEdHQ0VVVV7Nq1i8jISJMPwt11Kpd3ouM4nGbYQsnDwYpnokKZEukvWyiJFs/LyZonR4Tw2LD2bEk8x/92p7Ah/ix7Tuex53QebWwvVNH6BNCulazPp1Kp6NWrFz179jS+KdPr9Rw4cIAePXrIBunCSBIz0WJVVlayatUqDh8+DED79u257bbbTJqUJWUX8a8/41kXZ9hCyc5Sw+wh7Zg1KAhbS/lxE62LRq1iWLgHw8I9yCwo46e9aSzda6iifbXtNF9tO02foItj0awsWn4V7dJK+ZYtW9i0aRNHjhzh9ttvb9T9d0XTJX8pRIt09uxZfv75Z3JyclCpVAwfPpyBAwea7PZhYSW8+lssP+9PR6dX0KhVTO/tz5wRobg7yBZKQng72TBnZAiPD2/P5sRs41i03afz2H2hijYl0o87e7eeKpqHhwdWVlakpKTwxRdfcNtttzXqXryiaZLETLQ4paWlLFy4kMrKShwcHJgyZQqBgYGmuVZlNV9sOskXBzVU6tMAGBVh2EKpNQ50FuJ6NGoVw8M9GR7uSUZ+GT/tS2Xp3lQyC8r5v62n+b+tp+kb7MKMPoGM7ujZoqtoEREReHl5sWzZMjIyMli8eDEDBw5k+PDhcmuzFZPETLQ4tra2DBo0iOTkZG677Tbs7Owa/BrVOj0/70/jg5iaLZRUdPFz5JVbOtI7SLZQEqI+fJxteGpkKI8Pa8/mRMOMzo0J2ew6lceuU3m42FkyJdIwozPIreF/jpsCFxcXHnjgAWJiYti9ezfbtm0jMzOTKVOmYGMjy+i0RpKYiRahqKiI6upq2rQxbLA8cOBAk9y6VBSFjQnZ/OvPeBLPGrZQ8m9jwwi3Yl6a2QdLS8sGvZ4QrYGFRs2IDp6M6GCooi3da6iiZRWW8+WWU3y55RT9gl2Z0SeAqBZYRbOwsGDs2LHGZTVSUlIoKCiQxKyVksRMNHupqan89NNP2NjY8OCDD2JpaWmSsWTH0gt4a1UcO0/lAuBsq+WJ4SFMi/Rh/drVsvyFEA3Ax9mGp0eF8sTw9mxKOMfiPYYq2s5Tuew8lYuLnSV3XBiL1tKqaJ06dcLd3Z28vDyTr68omi5JzESztn//fqKjo9HpdFhbW1NWVtbgVau086X8e00Cvx66uIXS/f3b8ujQ9jjZaqmqqmrQ6wkhDFW0kRGejIzwJN1YRUvhbGEF/91yiv9uOUX/dq5M721YF62l7C/r6emJp6en8XF6ejrHjx9nxIgRstdmKyGJmWiWdDodf/75J/v27QOgQ4cOTJo0CSurhpsBWVBaxeebkvhmxxkqq/UATOrmw7Ojw/BrY9tg1xFCXJuvsw1zR4Xy5PD2bEw4x+LdyWxKPMeOk7nsOJmLq50lU3r6Mb1XAG1bUBWtqqqKpUuXUlhYSFZWFnfccYfc3mwFJDETzU55eTk//fQTp06dMslSGDVbKH26MYn8UkM1rF+wKy+N60BnP1lnSAhzsdCoGRXhyagIT9LOl/LT3lSW7ks1VNE2n+K/m08xoL0rM3oHMirCs9lX0bRaLWPHjuWXX37h1KlTLFy4kBkzZuDiIhOMWrJG+a79/PPPCQoKwtramsjISLZu3XrVtvfddx8qlarOR8eOHY1tFi1adMU25eXljdEdYWarVq3i1KlTWFpacueddzJo0KAGScoUReH3wxmM/GAz/1wVR35pFaGe9nxzXy8WP9RHkjIhmhC/NrbMjQpj+wvD+XJmJEPD3FGpYHtSLo8tPkD/f63nX3/Gk5xbYu5Qb0qHDh144IEHcHR0JCcnh6+++ork5GRzhyVMyOQVs6VLl/LUU0/x+eefM2DAAP773/8yduxYYmNjCQgIqNP+o48+4l//+pfxcXV1NV27duWOO+6o1c7R0ZGEhIRax6ytrU3TCdGkREVFcf78ecaPH99gA2T3nM7jreg4DqfmA4YtlOaOCmVKpB8Wmub9rluIlsxCoyaqoxdRHb1IO19qnNGZXVTBF5tP8sXmkwxs78b03gHNtorm5eXFQw89xJIlS8jIyOC7777j1ltvpWvXruYOTZiAyROzDz74gFmzZvHggw8CMH/+fNasWcOCBQt455136rR3cnKqtS3Fr7/+yvnz57n//vtrtVOpVDJrpRU5d+4c7u7ugGFD4FmzZjVIlezkuWL+9Wc8MbFnAbC11PC3we14aLBsoSREc+PXxpZnosJ4ckQIG+INuwtsOXGObUk5bEvKwc3ekjt6+nNnL38CXZvXWDQHBwfuv/9+fvnlF2JjYzl+/DhdunSR2eAtkEn/8lRWVrJ//35efPHFWsejoqLYsWNHvc6xcOFCRo4cWWfl9uLiYgIDA9HpdHTr1o1//OMfdO/e/YrnqKiooKKiwvi4sLAQMAysNNWMuprztrYZew3db0VR2LZtG5s2bWLSpEl07ty5Qc6bU1zBJxtPsnTfxS2U7oj05clh7S5soaTUuw/ytZZ+t3TNsc/DQ10ZHupK2vkyftqfxrL96ZwrrmTBppMs2HSSAe1cmdbTl5EdPNBepSreFPs9adIkfHx86NatG9XV1Sa5RlPst6k1Rp/re26VoiiKqYLIyMjA19eX7du3079/f+Pxt99+m2+//bbOrcjLZWZm4u/vz+LFi5k6darx+K5du0hKSqJz584UFhby0UcfER0dzeHDhwkJCalzntdff5033nijzvHFixdjayuz65oqvV7PgQMHOHHiBGDYvuRmS/eVOtiYqWJ9upoKveGdZqc2eiYE6PGSbwUhWiydHo6dV7HjrIqEAhUKhp9/B61CHw+Ffh563JrhaBhFUThx4gRBQUFotVpzhyOuobS0lBkzZlBQUICjo+NV2zXKvZrLS62KotSr/Lpo0SKcnZ2ZNGlSreN9+/alb9++xscDBgygR48efPLJJ3z88cd1zjNv3jzmzp1rfFxYWIi/vz9RUVHX/OTcjKqqKmJiYhg1alSr+mFpqH5XV1fzyy+/ABAaGsqYMWPo1avXXz6fTq+w4mA6H60/ydkiQ/W0s68jL4wOpc9NbqEkX2vpd0vXUvo84cK/qedL+XlfOssOGKpo69JVrEtXM7C9K9N6+jEi3B2tRt0s+r1t2zYKCws5d+4cd955J/b2N79Hb3Pod0NrjD7X3K27HpMmZm5ubmg0GrKysmodz87OrrWA3pUoisLXX3/NzJkzr7tgqFqtplevXsbKyuWsrKyuuL6VVqs1+TddY1yjKbqZfldUVPDTTz9x+vRpLC0tmTx5cq1ZuTdCURQ2JZ7jX9HxJJwtAsCvjQ3PjwlnfGdv1OqGG58hX+vWpTX2u6X0OdjDiRfGOTF3dDjr487yv90pbD2Rw7akXLYl5eLuYMXUnn7c3t0baNr9Dg0NZe/evZw9e5bvv/+eu+++u8GW02jK/TYVU/a5vuc16fQUS0tLIiMjiYmJqXU8Jiam1q3NK9m8eTNJSUnMmjXrutdRFIVDhw7h7e19U/EK86uqqmLRokXGpOyuu+76y0nZsfQC7l64m/u/2UvC2SKcbLS8cksH1j8zhFu7+jRoUiaEaH60GjVjOnnz/aw+bHluGI8ObYebvRXniir4bONJRny4jQWxatYcP0uVTm/ucK/I19eXWbNm0aZNG/Ly8li4cCGZmZnmDkvcBJPfypw7dy4zZ86kZ8+e9OvXjy+//JKUlBRmz54NGG4zpqen891339V63cKFC+nTpw+dOnWqc8433niDvn37EhISQmFhIR9//DGHDh3is88+M3V3hIlptVratWtHYWEhd999919KttPzy/jPmgR+OZSOooClRs29/QN5fFgITrat692fEKJ+AlxteX5MOE+PCmVd7FkW7zFU0eIL1Dz+42E8VsUztac/03r54+/StAakurq6MmvWLH744QeysrL45ptvmDFjBm3btjV3aOIvMHliNm3aNHJzc3nzzTfJzMykU6dOREdHG2dZZmZmkpKSUus1BQUFLF++nI8++uiK58zPz+fhhx8mKysLJycnunfvzpYtW+jdu7epuyMawYgRI+jTpw8ODg439LrC8io+33iSr7efNm6hdGtXH54bHdbkfpEKIZomrUbN2M7ejO3szcmzBbyzdAsHC6zJLqrg041JfLYpicEh7kzvHcCIa8zobGz29vbcd999LF26lNOnT7N48WLmzJmDnV3zWhZENNLg/0cffZRHH330is8tWrSozjEnJydKS0uver4PP/yQDz/8sKHCE2Z29uxZtm7dysSJE9FqtahUqhtKyiqr9fywK5lPNpzg/IUtlPoEufDyLR3o4udsoqiFEC1dgIstEwL1fBQ1mM1JeSzencK2pBw2J55jc+I5PBysmNbLUEVrCvvnWltbc9ddd/HTTz8REREhSVkzJStoCrPKzMzku+++o6ysDHt7e8aMGVPv1yqKQvTRLN5bE09yriGRb+9hz7yx4QwP95CFF4UQDcLSQs24zt6M6+xNcm4JS/aksmy/YXeBTzYk8enGJIaEXqiihXuYdbcQCwsLpk+fXuv3n06nQ6PRmC0mcWMkMRNmk5aWxg8//EB5eTl+fn4MGTKk3q/dd8awhdLBlHwA3OwNWyhN7SlbKAkhTCfQ1Y4Xx4Yzd1QoMbFnWbwnme1JuWxKOMemhHN4Oloxrac/U81YRbs0KSsuLubbb79l4MCBsoVTMyGJmTCL5ORk/ve//1FZWUlAQAB33XXXFZc0udypc8W8uzqeNccNWyjZaDU8PDiYhwcHY2cl385CiMZhaaHmli7e3NLFmzM5JSzZm8KyfWmcLazg4w1JfLIxiaEXqmjDzVhF279/P+fOneOXX36hurqayMhIs8Qh6k/+kolGl5yczA8//EBVVRXBwcHceeed112rLqe4go/WnWDxnhR0egW1Cqb18ufpkaF4ODbD5bqFEC1GWzc75o3twDOjwlgbm8WSPSlsT8plY8I5Niacw8vRmqkXxqL5Ots0amyDBw+mtLSU3bt38/vvv6NWq6+6faFoGiQxE42qurqa5cuXU1VVRfv27Zk2bdo1F90rq9SxcNspvth8iuIKw75wI8I9eGFsOKGeNzZrUwghTMnSQs34Lj6M7+LD6ZwSftyTws/708gqLOfj9Sf4dMMJhoZ5ML13AMPC3BuliqZSqRgzZgwqlYpdu3bx22+/oVar5bZmEyaJmWhUFhYW3HnnnWzfvp3bbrsNC4srfwvq9ArLD6TxwdpEsgrLAejs68S8ceH0b+fWmCELIcQNC3KzY964DsyNCmXt8bMs3p3CzlO5bIjPZkN8Nl6O1sYZnT4mrqKpVCpGjx6NTqdj7969/Prrr6jVajp37mzS64q/RhIz0Sj0ej1qteHdoY+PD3fcccdV225OPMc70XHEZxm2UPJ1tuH5MWFM6CKr9QshmhcrCw0TuvowoasPp84V8+PeVJZdqKJ9tP4En2w4wbAwD2b0CWBomAcaE/2OU6lUjBs3Dr1ez/79+9m0aRMREREyW7MJksRMmFx2djZLly5l8uTJ+Pr6XrVdbEYh7/wZx9YTOQA4Wlvw+PD23NOvLdZa+eUhhGjegt3teWlcB56JCmXN8bMsuVBFWx+fzfr4bLydLlbRvJ0avoqmUqkYP348dnZ2REZGSlLWREliJkwqNzeX7777juLiYtatW8c999xTZ32xzIIy/r0mkRUH01AU0GpU3NOvLY8Pa08bu2tPChBCiObGykLDrV19uPVCFW3JnhSW7U8js6Cc+etO8PH6EwwPN4xFa+gqmkqlYvjw4bWOlZeXY20tk6iaCknMhMkUFhYakzIvLy+mTp1aKykrLK/ii00nWbjtNBUXtlAa38Wb50eHE+Bq/lW0hRDC1ILd7Xn5lgieHR3G6mNZLN6dwu7TeayLy2ZdXDY+ThdndJqiinbs2DFWrVrFXXfdhZ+fX4OfX9w4ScyESZSVlfHDDz9QUFCAq6srM2fOxMbG8EulslrP4t3JfLwhibySSgB6t3XhpVs60M3f2YxRCyGEeVhZaJjYzZeJ3Xw5ea6YJbtTWHYgjYxaVTRPZvTxZ0how1TRFEXh0KFDlJWV8b///Y8HHngAd3f3BuiNuBmSmIkGV11dzY8//kh2djYODg7MnDkTOzs7FEVh9bEs3l0dz5kLWyi1c7fjxbEdGNlBtlASQgiAdu72vDLeUEVbc/zSKtpZ1sWdxdfZhmm9/Jna0x8vp79+C1KlUjF16lS+/fZb0tPT+f7775k1axa2tnLHwpwkMRMNLjY2lsrKSuzs7Jg5cybOzs7sT87j7eh49iefB8DN3pKnRoZyZy9/2UJJCCGuwFp7sYqWlG0Yi7b8QBrp+WV8EJPIRxfGos3oHcDgUPe/VEWztLTkrrvu4uuvvyYnJ4fvv/+emTNnmqA3or4kMRMNLiIigqqqKvr370+J2o5HftjPn8eyAMMWSg8NCuLhIe2wly2UhBCiXtp72PPq+Aieu2Qs2p4zecTEniUm9mIVbVovfzxvcDcUW1tbZs6cycKFC8nJyWHJkiW4ucl6keYifxnFX6fTwdatkJkJ3t4waBBgWER24IgxLNhyhh92HaP6whZKd0T6Mzcq9IZ/aQghhDCw1mqY1N2XSd19ScouYvHu1DpVtBHhHkzvE8DgkPpX0ZycnJg5cybffPMN6enpFBQUmLgn4mokMRN/zYoVMGcOpKUBsB8odHMj8vMviDmn5eUPtxm3UBoa5s68sR0I85ItlIQQoqG093Dg7xMieH5MGH8ey2TJ7lT2nMljbexZ1l6oot3Zy5+p9ayiubu7M2PGDOLi4igpKWmEHogrkcRM3LgVK2DKFFAUAE4Cv6MiVuVA/IoECgO7AtV09HHkpXEdGNBeSuJCCGEq1loNt3X347bufpw4W8TiPSmsOJBOen4Z/4lJZP76E4zsYFgXbXCI+zV3UPHz88PT05Po6OhG7IG4lCRm4sbodIZK2YWkLBt4z9mb9YFdKQzugU1AF1wsFV6+pSOTe7WVLZSEEKIRhXg68NqEjrwwJpzoo5ks2ZPC3jPnWXP8LGuOn8WvzYUqWk9/PK5TRauqqmLlypV06tSJ8PDwRuqBkMRM3JitW423L5OtHZgS1p8T9i5YOHrg5deRR7b/gOcz05lYega1OsjMwQohROtkrdUwuYcfk3v4kXi2iMW7U1hxII2082X8e20i89edYGQHT6b3CWBQe7crvonet28fx44dIyEhgfvvvx8fHx8z9KT1kXUKxI3JzASgCrjvQlKmtbLjb2WFbP2/2Tx84De0aiAry6xhCiGEMAj1dOD1Wzuy5+WR/OeOrvQMbEO1XmH18Szu/XoPg9/fyGcbk8guKq/1uj59+tC+fXuqqqpYvHixTAhoJJKYiRvj7Y0C/NvFj4P2Lqg1WpYd28Bbm76hTXnRxXZeXmYLUQghRF3WWg23R/qx7JH+rHlqMPf1b4uDtQVp58t4f00C/d/ZwCM/7GdrUg56BdRqNXfccQeenp4UFxfz448/UlVVZRjSsmkTLFli+FenM3fXWhRJzMSNGTQIvb8/qwZMR6XRcicKQ7JPXXy+ZvX+fv3ME58QQojrCvO6UEV7aST/vqMrkReqaH8ey+KBbw/wz4Mavth8ioJKhRkzZmBnZ0dmZiYrX3oJJTAQhg2DGTMM/7Zta5gUJhqEjDETN0ajYdnLH5N2WotPcR7/+Prxi89duqWSRtP4sQkhhLghNpYapkT6MSXSj/isQn7cY1gXLbe8mv+sS+KjDSeJ6ujJsF4jiP3iPY4tXYo3MODSk6SnG2bqL1sGkyebqScth1TMRL2dP3+erNx83j9nB8DTCetxLSu82MDPD77/3kzRCSGEuBnhXo68fmtHtj83hBntdHT3d6JarxB9NIvnVmfya3Uoh/07Y2192ZqUF2bp89RTcluzAUjFTNRLRUUFixcvJvpwKmetOhMS6Ms9f/wf7Lyv9sr/ej3I+jdCCNFs2Vhq6OOh8Ma4PiTllLFkTwq/7E0mr11vcgO7Mk1tQdSJXfx9/f/hVZxreJGiQGqqYeb+0KFmjb+5k4qZuC5FUfj11185kZzOnlO5qCwsefmWDlhaaQ0/gNOnG/6V25dCCNGidPB25M2JndgdXsj7f35EZPYZqjUWRIcP5JFRsym//AUXZu6Lv04SM3Fd27ZtIy4ujm0n87AKHciQTgEMD/cwd1hCCCEaia2fN1OPruOXH55l5bdPw7kzbMpN5V2PIJRLG3p7myvEFkMSM3FNZ86cYcOGDaTmlZLu0AErZ3f+Pj4ClUpW9BdCiFZj0CDDOGKViq5ZJ5gWuwVFr+N7n3D2gGHyl7+/oZ24KZKYiasqLi5m+fLl6HR6DpQ4YeXVnrv7BBDiKZuRCyFEq6LRwEcfGf6vUjHvUDSuPmHk2Dkz3z2IDEWB+fNlSEsDkMRMXNW6desoKioiudSCPJeOONloeWpkqLnDEkIIYQ6TJxuWxPD1xbm8mGfOHELr4se2tl1ZfN/9lI8bZ+4IWwRJzMRVjR49muCQcA5owlBptDw9MoQ2dpbmDksIIYS5TJ4MZ87Axo088OQUgjr1o8TRnS04sHLlShRFue4pxLVJYiauysbGhjOOXShS2RHiYc9dfQPNHZIQQghz02hg6FCs75rOs7f1xDZsIHuT8zl09BhHjx41d3TNniRmopaSkhIOHjyIoigkZRfz3c4zALw6PgKtRr5dhBBCXDS5hy8d2gWCX1eybQLp2LGjuUNq9mSBWWGkKAorV64kMTGR8+fP832yPdV6hRHhHgwOdTd3eEIIIZoYC42a58eE81B2MdvL1ZwrrsLLSSYA3AwpgQij/fv3k5iYiIWFBflWHmxMOIdWo+LlWzqYOzQhhBBN1MgOHvQMbEN5lZ6P1iei1+tJSEgwd1jNliRmAoCcnBzWrFkDwNBhw/lsVw4A9/ZrS7C7vTlDE0II0YSpVCrmjQsH4MfdZ3j3owUsWbJEkrO/SBIzgU6nY8WKFVRVVREcHEyi4sXJcyW42FnyxIgQc4cnhBCiiYsMdCEqwhNFpWFrhmFm5sqVKykuLjZzZM2PJGaCzZs3k5GRgY2NDUNGjeOj9UkAPBMVipON1szRCSGEaA6eHxOGWgXHVQFUaB0oLS3l119/lSU0bpAkZq1cQUEB27ZtA2DChAks3JNFQVkV4V4O3NkrwMzRCSGEaC7aezgwtac/KrWGY9pwNBoNSUlJ7Nu3z9yhNSuSmLVyTk5O3HPPPQwcOBCNiz//250CwN8nRKBRy36YQggh6u+pkaFYa9UczQPnkJ4AxMTEcP78eTNH1nxIYiZo27YtI0aM4B9/xKLTK4zp6EX/dm7mDksIIUQz4+VkzQMDggBYmW6Dn78/lZWVREdHmzmy5kMSs1YqKyur1juYdXHZbEvKwVKj5qVxsjyGEEKIv+ZvQ9rhbKsl6VwJ6sDeBAUFERUVZe6wmg1JzFqh6upqli1bxueff87JkyepqNbx1qpYAGYNCiLA1dbMEQohhGiunGy0PD6sPQBf7slm2oy7cXeXRcrrSxKzVmjTpk3k5ORgZWWFj48P3+44w5ncUtwdrHjswg+TEEII8Vfd3TcQX2cbsgrLWbTjjPF4dna2zNK8DknMWpmMjAx27NgBwPjx4ynRqfnkwvIYz40Ow95KdukSQghxc6y1Gp6JCgXg841J5JdWsnHjRhYsWMCBAwfMHF3TJolZK6LT6Vi5ciV6vZ5OnToRHh7Of9YmUFRRTWdfJ6b08DN3iEIIIVqIid18CfdyoLC8ms83ncTKygpFUYiJiZGFZ69BErNWZNeuXZw9exZbW1vGjh3L8YwCftybChiWx1DL8hhCCCEaiEat4oWxhq2aFu04g394V7y9vSkvL2ft2rVmjq7pksSslSgoKGDTpk0AREVFYWtry5u/x6IoML6LN73aupg3QCGEEC3O0FB3+ga7UFmt56P1SYwfPx6VSsWRI0c4deqUucNrkiQxayVsbW3p378/wcHBdO3aldXHsth9Og8rCzXzZHkMIYQQJqBSqZg31vA3ZvmBNIo0DvTq1QuAVatWUV1dbc7wmiRJzFoJrVbLsGHDmDlzJhXVet6KjgMM6834OtuYOTohhBAtVVd/Z27p7I2iwHurExg+fDj29vbk5uayfft2c4fX5DRKYvb5558TFBSEtbU1kZGRbN269aptN23ahEqlqvMRHx9fq93y5cuJiIjAysqKiIgIfvnlF1N3o1mqrq5Gr9cbH6tUKhZuO03a+TK8HK2ZPSTYjNEJIYRoDZ4dHYZGrWJDfDaHMkoYM2YMVlZW2Nvbmzu0JsfkidnSpUt56qmnePnllzl48CCDBg1i7NixpKSkXPN1CQkJZGZmGj9CQkKMz+3cuZNp06Yxc+ZMDh8+zMyZM5k6dSq7d+82dXeanc2bN/N///d/ZGRkAHC2sJzPNhqWx3hxbDi2lrI8hhBCCNMKcrNjem9/AP71ZzwRERHMmTOHyMhIM0fW9Jg8Mfvggw+YNWsWDz74IB06dGD+/Pn4+/uzYMGCa77Ow8MDLy8v44dGozE+N3/+fEaNGsW8efMIDw9n3rx5jBgxgvnz55u4N81Lbm4uO3bsIDMzk8LCQsBQRi6t1NE9wJmJ3XzMHKEQQojW4skRIdhaajiUms/aWMMKAaIuk5ZLKisr2b9/Py+++GKt41FRUcZFTq+me/fulJeXExERwSuvvMKwYcOMz+3cuZOnn366VvvRo0dfNTGrqKigoqLC+LgmSamqqqKqqupGulRvNec11fnrIzo6msrKStq3b0+7du3YfzqH5QfSAHh5bJhJBl02hX43ttbYZ5B+t6Z+t8Y+g/S7ofvdxlrDA/0D+XTTKd79M57B7V2wUKs4ceIE+/fvZ+rUqbWKMI2pMb7W9T23SROznJwcdDodnp6etY57enqSlZV1xdd4e3vz5ZdfEhkZSUVFBd9//z0jRoxg06ZNDB48GDBswH0j53znnXd444036hxfu3atyTP2mJgYk57/arKysti4cSNqtZrQ0FBWrYrmo+MaQEUvNz3pR7aTfsR01zdXv82pNfYZpN+tSWvsM0i/G5J/NdhbaDidW8rr362hj2sVf/zxB2VlZWRmZhIeHt7g17wRpvxal5aW1qtdowwwUqlqL1yqKEqdYzXCwsIICwszPu7Xrx+pqan8+9//NiZmN3rOefPmMXfuXOPjwsJC/P39iYqKwtHR8Yb7Ux9VVVXExMQwatQotFqtSa5xNXq9ni+//JKQkBB69+7NmDFj+P1IJqd3HcVGq+aD+wfj5Whtkmubs9/m0hr7DNLv1tTv1thnkH6bqt/FHin8Y1U8G7NtePmuUfj7+/P7779TVVXFkCFDsLOza/BrXk9jfK1r7tZdj0kTMzc3NzQaTZ1KVnZ2dp2K17X07duXH374wfjYy8vrhs5pZWWFlZVVneNardbkP2yNcY3L7du3j9zcXOzt7Rk5ciTVipr3154A4NGh7fF3dTB5DObot7m1xj6D9Ls1aY19Bul3Q5vZL4hvd6aQklfK97vTeGxYLw4ePEhmZiZbt25lwoQJDX7N+jLl17q+5zXp4H9LS0siIyPrlAZjYmLo379/vc9z8OBBvL29jY/79etX55xr1669oXO2ZImJiQAMHToUGxsb/rvlJJkF5fg62/DQYFkeQwghhPlYWqh5drThztgXm0+RV1LJmDFjADhw4MBVhyW1Fia/lTl37lxmzpxJz5496devH19++SUpKSnMnj0bMNxmTE9P57vvvgMMMy7btm1Lx44dqays5IcffmD58uUsX77ceM45c+YwePBg3n33XSZOnMjKlStZt24d27ZtM3V3moXp06cTGxtLeHg4GfllfLH5JAAvjeuAtdY8AyuFEEKIGuM7e/PllpMcSy/k041JvDahIx07duT48eOsXbuWe+65x9whmo3Jl8uYNm0a8+fP580336Rbt25s2bKF6OhoAgMDAcjMzKy1plllZSXPPvssXbp0YdCgQWzbto1Vq1YxefJkY5v+/fvz448/8s0339ClSxcWLVrE0qVL6dOnj6m70yyoVCo6duyIRqPhX3/GU16lp3dbF8Z19jJ3aEIIIQRqtYoXxxi2avphVzKpeaWMGjUKjUbDqVOnSE1NNXOE5tMog/8fffRRHn300Ss+t2jRolqPn3/+eZ5//vnrnnPKlClMmTKlIcJrMRITE2nbti2WlpYA7E/O47fDGahU8PcJEVedHCGEEEI0toEhbgwKcWPriRz+szaB+Xd2Z+TIkbi4uODn52fu8MxG9spsIc6dO8eSJUv4+OOPKS0tRa9XeOP3WACmRvrTydfJzBEKIYQQtb0wxrA8xq+HMjiWXkC/fv0ICwtr1YUEScxaiI0bN6IoCn5+ftja2rLiYDpH0gqwt7IwDrIUQgghmpJOvk7GXWjeXV17T+zy8nJ0Op05wjIrScxagPT0dGJjY1GpVAwfPpySimreu/AN/vjw9rg71F0qRAghhGgKno0KQ6tRsfVEDttO5ACGZZ8++ugjDh06ZN7gzEASsxZg/fr1AHTt2hUPDw8+35REdlEFga623D+grXmDE0IIIa7B38WWu/saJgS+uzoevV5Bp9NRVlbGpk2bWt2WWJKYNXOnTp3i1KlTaDQahg4dSmpeKf+39TQAL4/rgJWFLI8hhBCiaXt8WHvsrSw4ml7AH0cziYyMxNnZmaKiIvbt22fu8BqVJGbNmKIobNq0CYCePXvi7OzMO3/GUVmtZ0B7V0ZF1H93BSGEEMJcXO2t+NuFBdD/vSYBPWrjNozbt29vVVUzScyaserqauzt7bGwsGDAgAHsOpVL9NEs1Cp4dbwsjyGEEKL5mDUoCDd7K1LySlmyJ4WuXbvi7OxMcXEx+/fvN3d4jUYSs2ZMq9UydepUnn76aezsHYzLY8zoE0C4l2k2ZxdCCCFMwdbSgqdGhgDw8foTlFUrDBo0CDBUzaqrq80ZXqORxKwFsLOz46d9qcRlFuJobcHcUbI8hhBCiOZnWi9/gt3syC2p5Mstp+jatStOTk4UFxdz5swZc4fXKCQxa6Z27drF+fPnASgsr+LfaxIAmDMyFBc7S3OGJoQQQvwlWo2a5y6svfnV1lPklVUzceJEHnvsMdq3b2/m6BqHJGbNUHp6OqtXr+azzz6jtLSUTzckkVtSSbC7Hff0CzR3eEIIIcRfNqaTF139nSmt1PHJ+iSCg4Nxc3Mzd1iNRhKzZmjLli0AdOrUibOlCt9sNyyP8eotEWg18iUVQgjRfKlUKuaNNWzVtGRPCqdzSozP5efno9frzRVao5C/4s3MuXPnSEhIQKVSMWjQIN5aFUeVTmFIqDvDwj3MHZ4QQghx0/oGuzI83INqvcK/1xqG6kRHR/PRRx8RFxdn5uhMSxKzZmbXrl0AhIWFEZensC7uLBZqFa+O72DmyIQQQoiG8/yYMFQqWHUkk8Op+dja2qIoCjt27EBRFHOHZzKSmDUjxcXFHD58GIDeffry5h/HAZjZL5D2Hg7mDE0IIYRoUOFejkzu7gfAO3/G0bNnTywsLEhPTyclJcXM0ZmOJGbNyN69e6mursbX15etmQqJZ4tpY6vlqRGh5g5NCCGEaHBzo0KxtFCz61Qe+9JL6datGwA7duwwb2AmJIlZM6LVarG2tqZT9158uO4EAHNHheJkqzVzZEIIIUTD83W24b7+bQH415/x9OnTF5VKRUJCAufOnTNvcCYiiVkzMnDgQJ5++mlWp2nIL60izNOB6b0DzB2WEEIIYTKPDm2Hg7UF8VlFbE0tJzzcMGNz586dZo7MNCQxa2ZSCyr5YU8qYNgP00KWxxBCCNGCOdta8uhQw+Ky/1mbSI9efQCIj49vkds0WZg7AHF9mZmZlJeX07ZtW/7xRxw6vcLIDp4MDGk9C+4JIYRove4f0JZvd5whPb+MTWk6Jk+eTFhYGBYWLS+NkXJLM7Bp0ya+/fZbPvp+JZsTz6HVqHj5FlkeQwghROtgrdUwd5Rhottnm07SNrQDVlZWZo7KNCQxa+Ly8/NJTExEp1dYdkYFwAMDgghyszNzZEIIIUTjmdzDlxAPe/JLq/hi00kAFEWhoqLCzJE1LEnMmrj9+/ejKArpOgfSSi1ws7fk8eGtYyNXIYQQooaFRs3zYwwD/7/efpoDsUl8+eWXLFu2zMyRNSxJzJownU7HgQMHKK2sZmu+IwDPRoXhYC3LYwghhGh9RnbwoGdgG8qr9Hy3N5OsrCySkpLIy8szd2gNRhKzJiwuLo6SkhIOZJRTaedFhLcjd/T0N3dYQgghhFmoVCrmjTNUzX6LL8Te3Q9FUdi3b5+ZI2s4kpg1YXv37uVcUQXHK11RqTW8NiECjVpl7rCEEEIIs4kMdCEqwhO9AruLnQE4ePBgi1k6QxKzJqqiooKioiK2JuWg9WzPuM5e9Al2NXdYQgghhNk9PyYMtQp251pSoLOgrKyMhIQEc4fVICQxa6KsrKwIHX4H5wOGYm1nz7yxsjyGEEIIAdDew4GpPf1RqdTsL3JEURQOHTpk7rAahCRmTVRFtY53/oxHY+fMQ4OC8HexNXdIQgghRJPx1MhQrLVqTisenM4pISkpicLCQnOHddNa3pK5zZlOB1u3UnTqFN/pvEnO1ePhYGXcikIIIYQQBl5O1jwwIIjPN53keIEvL9wxBju75r/Gp1TMmooVK6BtWxg2jJ8eeYI3v/2BynPJvOBejJ2V5M9CCCHE5f42pB3OtlpynUI5XmKPRqMxd0g3TRKzpmDFCpgyBdLSKAMWBXSmAoXOBdncNvt2w/NCCCGEqMXJRsvjwwx3lT6ISaS8SmfmiG6eJGbmptPBnDmgKACsbOPDUY8gNHZteGvHj6hR4KmnDO2EEEIIUcvdfQPxdbYh41weL366hA0bNpg7pJsiiZm5bd0KaWnGh58E9wSVihEl+fTMTDAkbKmphnZCCCGEqMVaq+GZqFD05UUsWbmazdt2omvGxQxJzMwtM9P433wgS1cFqJiedeKq7YQQQghx0cRuvnQMCaZKbcW2+HROLl4MS5bApk3N7o6TJGbm5u1t/O9xwKM4DwsnD057h161nRBCCCEu0qhVvHhLBFq3QA6dyWPTw4/DjBkwbJhhYl0zGqstiZm5DRoEfn6gUnEM8CrKNXxj1SRmKhX4+xvaCSGEEOKKhh7bRp/KUnRqNd8HdKSq5on0dMMEu2aSnEliZm4aDXz0EQCTgfGVpWhd/TnsHYqiurAv5vz5hnZCCCGEqEunQ/XUHN7ctRy1tT1H3QJZ7XzhTtOFyXXNZSKdJGZNweTJsGwZ7n5+3FNwFmu1mgIbB0536AHLlhmeF0IIIcSVXZhI1+1sEoPKCkGl4pN2PS8+34wm0kli1lRMngxnzqBdv45OjoYvy+HvfpGkTAghhLieSybIzT59CJWFJame7VCu0a6pksSsCcjJyWHZsmUkJCXB0KF06x4CwKG0AjNHJoQQQjQDl0yQ65ebimPvyZR1HkmJpc1V2zVVkpg1AfHx8Rw7doy9e/cC0NXfCZDETAghhKiXSybSOVeW4lFq+Pt50sXP8HwzmkgniVkTkJCQAEB4eDgA3f3bABCXUUhFddMfqCiEEEKY1SUT6VCpaJ+biqIo7HHywPhXtJlMpJPEzMyKi4tJu7Dyf2ioYYkMfxcbXOwsqdTpicssMmd4QgghRPNwYSIdvr6E5KRSfHgNS8uLOePt3awm0kliZmaJiYkoioKPjw+Ojo4AqFQquvpduJ2Zct6c4QkhhBDNx4WJdO3vnozGvg15oZ2I/+KLZpOUgSRmZnf5bcwa3S7czjyUmt/YIQkhhBDNl0ZD+wHd0br4kadoSEhKQlHqzM9ssiQxM6OqqipOnToFQFhYWK3naiYAHJYJAEIIIcQNae9pj4WzF4WVkHc+n8xmsExGDUnMzKiwsBBXV1ecnZ3x8PCo9Vw3f2cATueUkF9aaYbohBBCiObJ3d4KJ1srNM7enC+tIjEx0dwh1ZskZmbk6urK7NmzeeSRR1DVbL90gbOtJW1dbQGpmgkhhBA3QqVSEeLpgEUbb/JKKjl58qS5Q6o3ScyaACsrqyser6maHUrJb7xghBBCiBagvbs92guJWVpaGmVlZeYOqV4aJTH7/PPPCQoKwtramsjISLZeY6+qFStWMGrUKNzd3XF0dKRfv36sWbOmVptFixahUqnqfJSXl5u6Kw2msrKSqqqqa7apScwOp+WbPiAhhBCiBQnxtEdtZYddUDdmzpyJpaWluUOqF5MnZkuXLuWpp57i5Zdf5uDBgwwaNIixY8eSkpJyxfZbtmxh1KhRREdHs3//foYNG8aECRM4ePBgrXaOjo5kZmbW+rC2tjZ1dxrMkSNHePfdd1m7du1V23StqZil5jerGSVCCCGEubXzsAeguE17goOD0TSDxWUBLEx9gQ8++IBZs2bx4IMPAjB//nzWrFnDggULeOedd+q0nz9/fq3Hb7/9NitXruT333+ne/fuxuMqlQovLy+Txm5KJ0+epLq6+prJZISPI1qNirySSlLzygi4MOZMCCGEENcWciExO51TQrVOj4WmeYzeMmmUlZWV7N+/n6ioqFrHo6Ki2LFjR73OodfrKSoqwsXFpdbx4uJiAgMD8fPzY/z48XUqak2ZXq83LpPRrl27q7azstAQ4W1YdPaQ3M4UQggh6s3HyQYbrYYqncLWA8dZs2YNeXl55g7rukxaMcvJyUGn0+Hp6VnruKenJ1lZWfU6x3/+8x9KSkqYOnWq8Vh4eDiLFi2ic+fOFBYW8tFHHzFgwAAOHz5MSEhInXNUVFRQUVFhfFxYWAgY1hG73jivv6rmvFc6f2pqKqWlpdjY2ODm5nbNGLr4OnI4rYADZ3IZG+Fuklgb0rX63VK1xj6D9Ls19bs19hmk3y2h3+3c7TiWUcjvq9djV5mLg4MDvXr1qtOuMfpc33OrFBMOXsrIyMDX15cdO3bQr18/4/G33nqL77//nvj4+Gu+fsmSJTz44IOsXLmSkSNHXrWdXq+nR48eDB48mI8//rjO86+//jpvvPFGneOLFy/G1rbxbw8eO3aMo0eP4u/vz8CBA6/Zdu85FT8kaQhyUHiqk2xoLoQQQtTX9yfU7MtR073iCFaZh+v1d9dUSktLmTFjBgUFBcYtGK/EpBUzNzc3NBpNnepYdnZ2nSra5ZYuXcqsWbP4+eefr5mUAajVanr16sWJEyeu+Py8efOYO3eu8XFhYSH+/v5ERUVd85NzM6qqqoiJiWHUqFFotdpaz+Xl5VFeXs7YsWOvmLlfqkNOCT98tJ2MMg2jRo9C28TvkV+r3y1Va+wzSL9bU79bY59B+t0S+p2y+RT71iXRJrgLvval2NnZMXbs2DprhzZGn2vu1l2PSRMzS0tLIiMjiYmJ4bbbbjMej4mJYeLEiVd93ZIlS3jggQdYsmQJt9xyy3WvoygKhw4donPnzld83srK6oprhWm1WpN/011+Db1eT2ZmJhqNhnbt2l33+iFeTjhaW1BYXs2p3HI6+TqZNN6G0hif26amNfYZpN+tSWvsM0i/m7NQb8PfzCydLcFWVpSXl1NYWIibm9sV25uyz/U9r8nLL3PnzuWrr77i66+/Ji4ujqeffpqUlBRmz54NGKpZ99xzj7H9kiVLuOeee/jPf/5D3759ycrKIisri4KCi6vfv/HGG6xZs4ZTp05x6NAhZs2axaFDh4znbMp0Oh1Dhw6lU6dOdbZhuhKVSmVcNuOgbGguhBBC1JtxZmZuBT4+vgBXXa6rqTB5YjZt2jTmz5/Pm2++Sbdu3diyZQvR0dEEBgYCkJmZWeuT9N///pfq6moee+wxvL29jR9z5swxtsnPz+fhhx+mQ4cOREVFkZ6ezpYtW+jdu7epu3PTtFot/fv3Z8qUKXVKqVfTXXYAEEIIIW5YgIstlho1ZVU67FwNS2wlJyebOaprM/k6ZgCPPvoojz766BWfW7RoUa3HmzZtuu75PvzwQz788MMGiKx56Co7AAghhBA3zEKjJsjNjoSzRVTbuQKGFSOaskZJzISBoigcO3YMf39/nJ2d6/26msTs5LliCsurcLRu3vf8hRBCiMbS3sOehLNFFKmdeeKJJ+qsi9rUNO0pfi1Mbm4uy5cv59NPP0Wnq//SF272Vvi1sUFR4GhawfVfIIQQQgjAkJgBnM4rx9XVtd7DiMxFErNGlJaWBoCvr+8N79nV7ZJ9M4UQQghRPzWJ2YnsIjNHUj+SmDWijIwMwJCY3ShJzIQQQogbF+JpSMySsos5e/YsP/30Ez///LOZo7o6GWPWiNLT0wHw8fG54ddempgpitLkS7FCCCFEUxDkZodaBYXl1eSVVhEbG4tWq0Wv16NWN736VNOLqIXS6XScPXsW+GuJWSdfJzRqFeeKKsgoKG/o8IQQQogWycpCQ6CrHQB51YYF56uqqsjOzjZzZFcmiVkjyc7Oprq6GhsbG9q0aXPDr7fWagj3cgDgsNzOFEIIIeqtnfuF25nnSozFkZrhRU2NJGaN5NLbmH/1NqSMMxNCCCFu3KXjzGrGedf8XW5qZIxZI+nQoQN2dnY3tQdXV39n/rc7RRIzIYQQ4ga0d7+YmE0PNVTMJDFr5ezs7OjQocNNnaNma6ajaQVU6/RYaKTgKYQQQlzPxSUzivH2DgPg3Llz6HS6G16+ytTkL3szEuxuj72VBWVVOk5kF5s7HCGEEKJZaHchMcsprgBLW+zs7PD09KS0tNTMkdUlFbNGUFhYyJEjR/Dy8qJ9+/Z/+TwatYoufk7sOJnLodR8Ong7NmCUQgghRMtkb2WBj5M1GQXlnDxXwrPPPttkl52SilkjSEtLY926dWzYsOGmz2WcAJCSf9PnEkIIIVqL9p6GlQ2SsoubbFIGkpg1ipq1Ujw9PW/6XDUbmh9Oy7/pcwkhhBCtRc0EgEuHAimKYq5wrkpuZTaCmsTMw8Pjps9VMwEg8WwRJRXV2FnJl1AIIYS4nkuXzDh37hzLli1Dp9Px+OOPmzmy2qRi1ggaMjHzcLTG28kavQJH0wtu+nxCCCFEa1AzMzMpuxg7OzvOnj1LTk4OFRUVZo6sNknMTKy6uprc3FygYRIzkIVmhRBCiBtVcyszPb8MRWOJvf2FmZo5OeYMqw5JzEwsLy8PRVGwtrY2fhPcLOM4M0nMhBBCiHppY2eJm70lACfPFePq6gpgLJ40FZKYmVheXh4ALi4uDTYLRCpmQgghxI279HZmTWJW83e6qZCR4ybWrl07Zs+eTXV1dYOds7OvE2oVZBaUc7awHE9H6wY7txBCCNFStfewZ9epPE5kFzPAxQWQxKzV0Wq1eHl5Neg57awsCPV0ID6riEOp+Yzu2LDnF+Kv0ul0VFVVmTsMk6qqqsLCwoLy8nJ0Op25wzEZrVbb5LaqEeJmhXhcXMtsQoAhMWtqtzIlMWumuvk7S2ImmgxFUcjKyiI/P9/coZicoih4eXmRmprapBepbAjOzs4N/sZSCHO69Famm1sAnp6eDTYxr6FIYmZiGzZswMHBge7du2NjY9Ng5+3q78yPe1NlAoBoEmqSMg8PD2xtbVt0wqLX6ykuLsbe3h61umUO01UUhdLSUuNSP25ubmaOSIiGEXIhMUvOLcHJxZVHHnkEoElV+iUxMyGdTsf27dtRq9V06dKlQc9dMwHgSFoBOr2CRt1y/xCKpk2n0xmTsprBtC2ZXq+nsrISa2vrFpuYAcY3ktnZ2bRp08bM0QjRMNwdrHCwtqCovJrTOSWEezW9Padb7m+VJqCkpARFUbC0tMTOzq5Bzx3iYY+NVkNxRTWnzhVf/wVCmEjNxBZbW1szRyIaWs3XtCEnLwlhTiqVylg1S7qwNZOiKOj1enOGVYskZiZUWloKGMZpNPStHQuNms5+TgAclNuZwoxq9pprybcvW6uar2lT3E9QiL+qZpzZibPFrFmzhrfffpvdu3ebOaqLJDEzoZrEzMHBwSTn7y7rmQkhhBA3xDgz81wxarWaqqoqCgsLzRzVRZKYmVBZWRkAjo6muYctOwAIYV6LFi3C2dnZ3GEIIW6AcWbm2WLj32dJzFqJmoqZqRKzmgkA8VlFlFW23PWUhBBCiIZSk5idzinB1s7w/6KiInOGVIskZiZk6sTM28kadwcrdHqF4xkFJrmGEEII0ZL4Ottgo9VQqdNTrBj2ziwoaDp/QyUxM6G+ffvy8MMPEx4ebpLzq1Qq2TdTiJswdOhQHn/8cR5//HGcnZ1xdXXllVdeMQ52P3/+PPfccw9t2rTB1taWsWPHcuLEiSue68yZM6jVavbt21fr+CeffEJgYKDxnL/99hshISHY2NgwbNgwvv32W1QqVa3FeZcvX07Hjh2xsrKibdu2/Oc//6l1zrZt2/L222/zwAMP4ODgQEBAAF9++WUDfmaEaLnUahXtPAwrJWSXG9Kg4uLiJrOThyRmJmRlZYWXl1eDL5VxKUnMRFOkKAqlldVm+bjRGYTffvstFhYW7N69m48//pgPP/yQr776CoD77ruPffv28dtvv7Fz504URWH8+PFXXIyybdu2jBw5km+++abW8W+++Yb77rsPlUrFmTNnmDJlCpMmTeLQoUP87W9/4+WXX67Vfv/+/UydOpU777yTo0eP8vrrr/Pqq6+yaNGiWu3+85//0LNnTw4ePMijjz7KI488Qnx8/A31XYjWqr274RZmWrEejUaDoiiUl5ebOSoDWWC2mZPETDRFZVU6Iv6+xizXjn1zNLaW9f/V5u/vz4cffohKpSIsLIyjR4/y4YcfMnToUH777Te2b99O//79Afjf//6Hv78/q1at4p577qlzrgcffJDZs2fzwQcfYGVlxeHDhzl06BArVqwA4IsvviAsLIz3338fgLCwMI4dO8Zbb71lPMcHH3zAiBEjePXVVwEIDQ0lNjaW999/n/vuu8/Ybty4cTz66KMAvPDCC3z44Yds2rTJZBV6IVqSEE/DzMyT2SX0bNeO6uobf1NnKlIxM5GysjIOHDjAtm3bTHqdzn5OqFSQdr6MnOIKk15LiJaob9++tdZg69evHydOnCA2NhYLCwv69OljfM7V1ZWwsDASExOveK5JkyZhYWHBL7/8AsDXX3/NsGHDaNu2LQAJCQn06tWr1mt69+5d63FcXBwDBgyodWzAgAGcOHGi1q2WS3cTUalUeHl5GbdQEkJcW7sLFbOkc8XMmDGD6dOnY29vb+aoDKRiZiJFRUUkJCRgbW3NsGHDTHYdR2st7dztScou5nBqPiM6eJrsWkLUl41WQ+ybo812bVNSFOWqi+laWloyc+ZMvvnmGyZPnszixYuZP3/+NV97+bv0+rQB0Gq1tR6rVKomtXq5EE1ZiOfF1f/1+qZRKashFTMTqZmR2Rjb1MjtTNHUqFQqbC0tzPJxozsQ7Nq1q87jkJAQIiIiqK6urrUieG5uLomJiYSGhl71fA8++CDr1q3j888/p6qqismTJxufCw8PZ+/evbXaXz5ZICIiok6lfceOHYSGhqLRmDbpFKK1CHSxRatRUVqpI7PQMLasqbyxkcTMRBozMesqiZkQf1lqaipz584lISGBJUuW8MknnzBnzhxCQkKYOHEiDz30ENu2bePw4cPcfffd+Pr6Mm7cuKuer0OHDvTt25cXXniB6dOnGzcDB/jb3/5GfHw8L7zwAomJifz000/GQf01CeUzzzzD+vXr+cc//kFiYiLffvstn376Kc8++6xJPw9CtCYWGjVtXQ0T85aujOadd97h6NGjZo7KQBIzE6lZ9d/a2trk1+p+yQ4ATa0kK0RTd88991BWVkbv3r157LHHeOKJJ3j44YcBw4zKyMhIxo8fT79+/VAUhT/++KPObcTLzZo1i8rKSh544IFax4OCgli2bBkrVqygS5cuLFiwwDgr08rKCoAePXrw008/8eOPP9KpUyf+/ve/8+abb9Ya+C+EuHk1tzMzCyqoqqqioqJpjNOWMWYmUpOYNUbFLMzLASsLNYXl1ZzJLSHYvWkMYBSiOdBqtcyfP58FCxbUea5NmzZ89913tY7p9Xrj9i333XffFROmzMxMOnXqVGegP8Ctt97Krbfeanz81ltv4efnV+tN3O23387tt99+1ZjPnDlT59ihQ4eu2l4IUVfNkhlnSxUCgcrKSvMGdIFUzEykMW9lajVqOvk6AXI7UwhzKi4uZu/evXzyySc8+eSTV2zz+eefs3fvXk6dOsX333/P+++/z7333tvIkQoh2l9YMiOzxHCnqalUzCQxM5Gaheoa41YmyAQAIZqCxx9/nIEDBzJkyJA6tzFrnDhxgokTJxIREcE//vEPnnnmGV5//fXGDVQIYayYpeYbKmXV1dXmDMdIbmWayPDhwykuLqZbt26Ncr2ul4wzE0LUz6ZNmxr0fIsWLaqzQv/lPvzwQz788MMGva4Q4sYFu9uhVkFxNZRW6ppMYiYVMxOxt7fH2dm50Rasq5kAEJtZSHlV09jvSwghhGiqrLUa/F1sQaMlr6RSEjPRsPza2OBiZ0mVTiEus9Dc4QghhBBNXoiHPWoLS9QO7ri6upo7HEASM5PZs2cPR48e5fz5841yPZVKJePMhBBCiBvQzsMetbU93r3HMnDgQHOHA0hiZjL79u3j2LFjFBQUNNo1u/o5AzLOTAghhKiPEI8Lm5mfKzFzJBdJYmYiVVVVgGHvvMbSLcAZkIqZEEIIUR/tPS7umdlUSGJmIjUL1V1vhfCG1NXPsJbZmdxSzpc0jYXyhBBCiKaqJjE7ufEnFi/9uVHvcl2NJGYmotMZZkY25qbDzraWBLkZ9v46nJbfaNcVQlzf0KFDeeqpp8wdhhDiEvZWFng7WaNUVVBQXt0kNjKXxMxEFMWwkrBa3bifYpkAIIR5bdq0CZVKRX5+fq3jK1as4B//+Id5ghJCXFV7D3tQqSiuUrWexOzzzz8nKCgIa2trIiMj2bp16zXbb968mcjISKytrQkODuaLL76o02b58uVERERgZWVFREQEv/zyi6nC/0tqvriNnZjV3M6UCQCiWdLpYNMmWLLE8K+uea3JVzO29EpcXFxwcHBoxGiEEPXR3tUW1GqKq0C/cCGYec9Mk2cNS5cu5amnnuLll1/m4MGDDBo0iLFjx5KSknLF9qdPn2bcuHEMGjSIgwcP8tJLL/Hkk0+yfPlyY5udO3cybdo0Zs6cyeHDh5k5cyZTp05l9+7dpu5OvdUkZiqVqlGv2y2gDWComNVU7YRoFlasgLZtYdgwmDHD8G/btobjJvDf//4XX1/fOu+Qb731VuPelb///nutN4lvvPFGrUUoVSoVX3zxBRMnTsTOzo4HH3yQYcOGAYYN0FUqlXGT88tvZVZUVPD888/j7++PlZUVISEhLFy40Ph8bGws48aNw97eHk9PT2bOnElOTo7x+WXLltG5c2dsbGxwdXVl5MiRlJQ0nZllQjQLzz9PyJsvAGqKq0H/z3+CrS08/7z5YlJMrHfv3srs2bNrHQsPD1defPHFK7Z//vnnlfDw8FrH/va3vyl9+/Y1Pp46daoyZsyYWm1Gjx6t3HnnnfWKqaCgQAGUgoKCerX/K5KTk5WFCxcqZWVlJrvGlZRXVSshL0UrgS/8oSTnlDTqtRVFUSorK5Vff/1VqaysbPRrm0tr7LOiXOx3YWGhEhsbe3Pf68uXK4pKpShQ+0OlMnwsX95wgV+Qm5urWFpaKuvWrTMey8vLUywtLZU1a9Yoq1evVhwdHZVFixYpJ0+eVNauXau0bdtWee2115Tz588rOp1OARQPDw9l4cKFysmTJ5UzZ84oy5cvVwAlISFByczMVPLz8xVFUZQhQ4Yoc+bMMV5r6tSpir+/v7JixQrl5MmTyrp165Qff/xRURRFycjIUNzc3JR58+YpcXFxyoEDB5RRo0Ypw4YNMz5vYWGhfPDBB8rp06eVI0eOKJ999plSVFTUoJ+jsrIyJTY2ViksLGzV3+PS7xbquecUBZTdfh2VNsNmKV6DpyvJ1tYXf/8891yDXq6+uYdJ98qsrKxk//79vPjii7WOR0VFsWPHjiu+ZufOnURFRdU6Nnr0aBYuXEhVVRVarZadO3fy9NNP12kzf/78Bo3/Znh7e+Pq6tqog/8BrCw0dPBx5HBqPgdTzxPgatuo1xfihul0MGeO4Vfh5RQFVCp46imYOBEa8OfJxcWFMWPGsHjxYkaMGAHAzz//jIuLCyNGjGDYsGG8+OKLxupZcHAw//jHP3j++edrVb5mzJhRa8Py06dPA+Dh4YGzs/MVr52YmMhPP/1ETEwMI0eONJ6/xoIFC+jRowdvv/228djXX3+Nv78/iYmJFBcXU11dzeTJkwkMDASgc+fON/9JEaK1qKyEDz4AICQnBUL7U6aDEo0lUG5o88EH8M9/QiMuewUm3sQ8JycHnU6Hp6dnreOenp5kZWVd8TVZWVlXbF9dXU1OTg7e3t5XbXO1c1ZUVFBRUWF8XFho2LKoqqrqmmNCbkbNeU11/mvp4mtIzA4k5zGuo0ejXtuc/TaX1thnuNjf6upqFEVBr9f/tYGzmzejTku7+vOKAqmp6DdvhqFD/1qwVzF9+nRmz57Np59+ipWVFf/73/+YNm0aKpWK/fv3s3fvXt566y1je51OR3l5OaWlpcbxYj169KjV75r/X+nzUfN5OnDgABqNhkGDBl3xc7Zv3z42btx4xb12T5w4QVRUFCNGjKBz585ERUUxatQopkyZQps2bRrk83JpXxRFMd6+ba3f49LvFmjBAmPCZU81Gvs2qCxtWNh3Cu/sWFK73aOPNsgl6/v5NGliVuPycVaKolxz7NWV2l9+/EbO+c477/DGG2/UOb527VpsbRu+oqTX64mLi0OlUqHT6Rq9aqbkqAANm48m04NTjXrtGjExMWa5rjm1xj4D7NixAy8vL4qLi43r990I7alT2NWjXdmpU1T16HHjAV7DkCFD0Ov1LFu2jO7du7N161beeOMNCgsL0ev1vPjii0yYMKHO66ytrSkqKgIME3xq3uwBlJaWAlBUVFRr8k91dTWVlZUUFhYaf6cVFhZeca3DyspKxowZw+uvv17nOU9PT0pKSvj555/ZvXs3Gzdu5OOPP+aVV15h3bp1xgpaQ6isrKSsrMx4h6O1fo9Lv1ugtm0Nk4yAjBKwO2JIh1zCdUQ/cWvtttHRDXLJmt8N12PSxMzNzQ2NRlOnkpWdnV2n4lXDy8vriu0tLCyMG4xerc3Vzjlv3jzmzp1rfFxYWIi/vz9RUVE4OjrecL+uR6fTsW/fPk6ePMnDDz9skmtcS0RuCT/M305GuYaRUaOwtGi8maFVVVXExMQwatSoRl1c15xaY5/hYr/79+9PZmYm9vb2WFtb3/iJLrmFdy02wcHYNPDPkqOjI7fddhu//PILGRkZhIaGMnjwYMBQCUtOTqZbt261XqMoCkVFRcaKmY2NTa2f8Zrbl7a2trWOW1hYYGlpiaOjI3369EGv13Pw4EHjrcxL9e7dmxUrVtCpUycsLK7+azoqKoqoqCj++c9/EhQUxLp16+oM87gZ5eXl2NjY0L9/f7Zs2dJqv8el3y3Q55/DvHkA/KffdCoDu9HOroqH5v4T5/Lyi+3eeafBKmaXvoG7FpMmZpaWlkRGRhITE8Ntt91mPB4TE8PEiROv+Jp+/frx+++/1zq2du1aevbsafwG6devHzExMbV+Aa1du5b+/ftf8ZxWVlZYWVnVOa7Vak3yTWdhYWF8p6zRaBr9G7u9pxNONloKyqo4lVtO5wtLaDQmU31um7LW2GcwfL+rVCrUavVfWx5myBDw84P09CuPM1OpwM8P9ZAhYILlZ+6++24mTJhAbGwsd999t7EPf//73xk/fjwBAQHccccdqNVqjhw5wpEjR3juueeMFfrL+x0UFIRKpSI6Oppx48ZhY2NjvCVZ83kKDg7m3nvv5cEHH+Tjjz+ma9euJCcnk52dzdSpU3n88cf56quvuOuuu3juuedwc3MjKSmJH3/8kf/7v/9j3759rF+/nqioKDw8PNi9ezfnzp0jIiKiQZfoUavVqFQqY3LYWr/Hpd8t0COPwDPPoOh0/BHSn/LEnWjsSygrK8O9JjHTaAztGuhzUN/PpclLKXPnzuWrr77i66+/Ji4ujqeffpqUlBRmz54NGKpZ99xzj7H97NmzSU5OZu7cucTFxfH111+zcOFCnn32WWObOXPmsHbtWt59913i4+N59913WbduXZNZVbvmly9c3AGgsa/f1bjQ7PlGv74QN0SjgY8+Mvz/8uEINY/nz2/Qgf+XGj58OC4uLiQkJDBjxgzj8dGjR/PHH38QExNDr1696Nu3Lx988AEBAQHXPJ+vry9vvPEGL774Ip6enjz++ONXbLdgwQKmTJnCo48+Snh4OA899JBxuQsfHx+2b9+OTqdj9OjRdOrUiTlz5uDk5IRarcbR0ZEtW7Ywbtw4QkNDeeWVV/jPf/7D2LFjG+4TI0RLZmkJc+dywCecNGcvtNWVuNso1PoNNHduow/8h0YYYzZt2jRyc3N58803yczMpFOnTkRHRxvHQWRmZtZa0ywoKIjo6GiefvppPvvsM3x8fPj444+5/fbbjW369+/Pjz/+yCuvvMKrr75Ku3btWLp0KX369DF1d+qtJjEz1yrC3fyc2JJ4jkOpBczsZ5YQhKi/yZNh2TLD7MxLJwL4+RmSssmTTXZpjUZDRkbGFZ8bPXo0o0ePrnVMr9cbb0koV1kr8NVXX+XVV1+tdWzTpk21HltbW/PBBx/wwYWZYZcLCQlhxVXWcOvQoQOrV6++4nNCiHp67z1+U7UHIDQ3BY2Pl6FapdEYkrL33jNLWI0y+P/RRx/l0avco120aFGdY0OGDOHAgQPXPOeUKVOYMmVKQ4RnEjUD/s1RMQPoFuAMSMVMNCOTJxuWxNi6FTIzwdsbBg0yWaVMCNG6Vev0/GEfBCWVhAe4UgSoXnkFnnvOLJWyGo2SmLVG5q6YdfVzBuDkuRIKyqpwsmmh4wREy6LRNPiSGEIIcSXbT+aSW1KJq50lvn27EB8Xh8VDD5k1KQPZxNxkaipm5krMXO2t8HexAeBoWoFZYhBCCCGaqpWH0gEY28kL3YW1+prCZAdJzEzkjjvuYOTIkQ2+4OON6OZfs2+m3M4UQgghapRX6Vh7/CwAt3R0Nx63NHO1DCQxMxl/f3/c3d3N+kXuemGZjEOpUjETQgghamyIz6a4ohpfZxt6BrkxY8YMBg4cKBUzYVrdjRMA8q86e0wIIYRobWpuY97azQet1oL27dvj7+9/zV2JGoskZiaSlJREfHw8Z8+eNVsMHX2csFCryCmuIKOg/PovEEIIIVq4grIqNsafA2BiNx8zR1OXJGYmcuDAAQ4ePEhqaqrZYrDWagj3Nmwbcygl32xxCCGEEE3FmmNZVOr0hHraE+7lSHFxMQcPHiQ9Pd3coQGSmJlMzdiyv7Kpc0PqJjsACCGEEEYrDxsSsIndfAHIycnh999/59ChQ2aM6iJJzEykZm/OiooKs8ZRs57ZYZkAIIRJbNq0CZVKRX5+foOet23btsyfP9/s5xCiJckuLGfHyVwAbu1quI1ZVlYGNI0ZmSCJmck0lYpZzQSAo+kFVOvMs6aaEC1Z//79yczMxMnJMAt60aJFODs73/R59+7dy8MPP3zT5xFCXPTHkUwUBXoEOOPvYgtIYtZq2NgYFnet+YKbS7CbPQ5WFpRV6Ug8W2zWWIRoiSwtLfHy8mrw2Vzu7u7Y2tpe9fmqqqoGvZ4QrcHKw4Z9cWtuYwKUlpYCF+90mZskZiZSk5iVlJSYNQ61WkUX/5r1zPLNGosQTc2VbvV169aN119/3fhYpVLx1Vdfcdttt2Fra0tYWBjR0dHG5y+9lblp0ybuv/9+CgoKUKlUqFSqWue63G+//UbPnj2xtrbGzc2NyZds1n55bCqVii+++IKJEydiZ2fHP//5z+ue43IFBQU8/PDDeHh44OjoyPDhwzl8+HD9PllCNHNncko4nJqPRq1iXGdv4/GaAookZi2cnZ0dcDETN6eL48zyzRqHaH0qKyuv+lF9YQuU+rS9vDp0tXam8sYbbzB16lSOHDnC2LFj+dvf/kZeXl6ddv3792f+/Pk4OjqSmZlJZmYmzz777BXPuWrVKiZPnswtt9zCwYMHWb9+PT179rxmHK+99hoTJ07k6NGjPPDAAzd0DkVRuOWWW8jKyiI6Opr9+/fTo0cPRowYccW+CNHS/HahWta/nSvuDheTsKZ2K1M2MTcRX19fhgwZwoQJE8wdyiUzM/PNGodofd5+++2rPhcSEsJdd91lfPz+++9f9fZc27Ztue+++4yP58+ff8U3PdeqTt2M++67j+nTpwPw1ltv8emnn7Jnzx7GjRtXq52lpSVOTk6oVCq8vLyuec633nqLO++8kzfeeMN4rGvXrtd8zYwZM3jggQeMj6dPn17vc2zcuJGjR4+SnZ1trAz8+9//5tdff2XZsmUynk20aIqi8Ouh2rMxa9T8LpHErIWzs7PDx8cHT09Pc4diTMwSs4sorqjG3kq+7ELciC5duhj/b2dnh729PdnZ2Td1zkOHDvHQQw/d0Gsur4bdyDn2799PcXExrq6utY6XlZVx8uTJG4pDiObmeEYhp86VYGmhZnTH2n+XBw8eTHh4OMeOHTNTdLXJX+hWwMPRGh8nazIKyjmaVkC/dq7Xf5EQDeCll1666nNqde2RFM8999xV214+sP6pp566qbgujeHy7cquVLW7fP88lUqFXn9zs5xrxqHeiJohEn/lHHq9Hm9vbzZt2lTnuYaYRSpEU/b7hduYIzt44GBd++fZx8cHd3d3kpOTzRFaHTLGzITOnDnDzp07m8Q4s26X7JspRGOxtLS86oeFhUW9216eGF2t3Y1yd3cnMzPT+LiwsJDTp0//tc5eEptOp7tuuy5durB+/fqbutaNnKNHjx5kZWVhYWHYF/DSDzc3t5uKQ4imTK9XjOPLbu3qe53W5ieJmQkdOXKEmJiYJjGwViYACFHX8OHD+f7779m6dSvHjh3j3nvvRaPR3NQ527ZtS3FxMevXrycnJ+eqb8xee+01lixZwmuvvUZcXBxHjx7lvffeu6Fr3cg5Ro4cSb9+/Zg0aRJr1qzhzJkz7Nixg1deeYV9+/bdcD+FaC72nskjs6AcB2sLhoa513quqqqKvXv3Eh8fX6d6bi6SmJlQzW2GwsJCM0ciEwCEuJJ58+YxePBgxo8fz7hx45g0aRLt2rW7qXP279+f2bNnM23aNNzd3a+aKA0dOpSff/6Z3377jW7dujF8+HB27959Q9e6kXOoVCqio6MZPHgwDzzwAKGhodx5552cOXOmSYyFFcJUatYuG9PRC2tt7TdeBQUFrFq1il9//bXB1yL8q2SMmQnVLA5ZUGD+7ZA6+TqhVkFWYTlZBeV4OVmbOyQhzM7R0ZGlS5fWOnbvvffWenyld9HJyck4OjoChuTo8jYLFixgwYIF173+5MmTr7ru2JkzZ64bx42ew8HBgY8//piPP/74urEJ0RJUVuuJPmoYrnD5bEyAoqIiAOPPc1MgFTMTqknMmkLFzM7KglBPB0CqZkIIIVqHrSfOkV9ahZu91RUnvtX8fba3t2/s0K5KEjMTakoVM5DbmUIIIVqXmkH/E7p6o1HXvVUpFbNWpilVzOBiYiYTAIQQQrR0pZXVrD1+FrjybUy4mJg5ODg0WlzXI4mZCdWsOdRkKmYXlsw4kpaPTt80Zp8IIYQQphATe5ayKh2BrrZ09XO6Ypv8/HwAnJyu/Lw5yOB/E3JwcODOO+9sMmsEhXg4YGupoaRSx8lzxcYxZ0LcjJqZTE1lqrloODVf06YyW02IG/HboZq1y3yu+j1cs5xVmzZtbno3j4YiFTMT0mq1hIaGNpmp6Bq1is6+hncFh1LyzRuMaDFqFoptCgspi4ZV8zW9fDFgIZq68yWVbE48B8DEbj5XbXfbbbdx++234+3t3VihXZf8tLUy3fyd2X06j0Np+Uzt5W/ucEQLoNFocHZ2Nr7btLW1bdEVFr1eT2VlJeXl5XW2lWopFEWhtLSU7OxsnJ2db3rRXSEaW/SxTKr1ChHejrT3uPrdIR8fH3x8fK64FZu5SGJmYqmpqaSnp+Pr60twcLC5w7k4M1MqZqIBeXl5ATSZWwGmpCgKZWVl2NjYtOgEFAx7aHp5eVFdXW3uUIS4ITW3Ma9VLWuqJDEzscTERHbt2kXv3r2bRGLW9UJilnC2iLJKHTaW8k5Y3DyVSoW3tzceHh5N6p2nKVRVVbFlyxYGDx5cZw/PlkSr1UqlTDRLGfll7DljGDs2oevVE7O0tDTS09Px8/PDw8OjscK7LknMTMzFxQWA3NxcM0di4O1kjYeDFdlFFRzLKKBXWxdzhyRaEI1G0+L/mGs0Gqqrq7G2tm7RiZkQzdUfRzJQFOgd5IKPs81V2yUmJrLl/9u78/goy3Px/5+ZZCb7QvaELCwhCWRhC0tAISgkYFkUAUFF9Fistp5q1Vo9/bXVfk+tS6u1HK3WolCFagURkTUgIBB2SAiEhC0J2TeSyZ5MZp7fHyFTYgJkm2SSXO/XKy8zM/fzPNftk2Guudfvvyc6Opr4+PgejPDW+ucACQvi7t600rClJGYqlUq6M4UQQvRbm2+YjXkrzTMymxtQLIUkZmbWfMN1Op3FjNNo7s5Myinv1TiEEEKI7nSpqJJzeRVYq1XcE3nrmZbNY2I9PT17IrR2k8TMzBwcHLCxsUFRFFN23tvGSouZEEKIfqh50P+0EE/cHLQ3LWcwGEw9WZKYDTAqlcp004uLi3s5miaR/i6oVJBbXktxZX1vhyOEEEJ0maIopr0xbzcb89q1axgMBrRarUWt+g+SmPWI5gVmCwsLezmSJk62GoI9HQHZN1MIIUT/cCZHR2ZpDXYaK2aOvPXC7s3dmF5eXha37I3MyuwBMTExTJw40WK2ZoKmcWYXi6pIyi5n5ijL2JlACCGE6KzmQf+zRnnjYHPr9MZSx5eBJGY9wpISsmZjAlzZcDKHZJkAIIQQoo8zGBW2nGnfbEyAKVOmMGLECLTam49D6y2SmA1QpiUzsssxGhXUastqyhVCCCHa68iVUoor63Gx0zAt5PatYDY2Nvj7+/dAZB0nY8x6yOnTp9m8eTMFBQW9HQoAoT5O2FirqaxrJKO0urfDEUIIITptc1IuAPdE+qK17tupTd+Ovg9JTU3l9OnT5OTk9HYoAGis1EQObpqJIstmCCGE6KvqGw1sP9vU6NGevTELCwvZunUr586dM3donSKJWQ9pnpmZn5/fy5H8R/NCszLOTAghRF+1L72YyrpGfJxtmdiObQYzMzM5fvw4ycnJPRBdx0li1kP8/Jqy+Ly8vF6O5D9uHGcmhBBC9EXNi8rOH+PXrvHSzZ/DzZ/LlkYSsx7SPMiwsLAQvV7fy9E0aU7MzudXUKc39G4wQgghRAdV1unZfb5pjdD2zMYESczEdU5OTjg5OWE0Gi2mO9N/kB3uDlr0BoXU/IreDkcIIYTokF3nCqlvNDLM04FwP+fblm9oaKCkpASQxGzAU6lUDB48GIDc3NxejqaJSqX6T3emTAAQQgjRx2xu3oJp9OB2reCfn5+Poig4Ozvj6Oho7vA6RRKzHjR4cNMfTmVlZW+HYiITAIQQQvRFJVX1HLrU1Po1vx2zMeE/3Zi+vr5mi6urZIHZHhQdHc3EiROxsbHp7VBMZAKAEEKIvmhbSj4Go8JofxeGeji065hr164BEBAQYM7QukQSsx5kZ2fX2yG0MtrfFYCs0hrKqhsY5GB521MIIYQQP7TZNBtzcLuP+dGPfsT06dNRqy23w9ByIxM9wsVew7Dr3zSSpDtTCCFEH5B9rYaTWWWoVDA3qmPdko6Ojtjb25spsq6TxKyHpaWlsXr1ahISEno7FJPRMgFACCFEH/LN9UH/McPc8Xa27eVoupckZj2ssbGR7Oxsrly50tuhmIyRCQBCCCH6kOZFZduzBVOzHTt28Omnn5KRkWGusLqFWROzsrIyli9fjouLCy4uLixfvpzy8vKbltfr9fzqV78iMjISBwcH/Pz8eOSRR1qtlh8bG4tKpWrxs3TpUnNWpdsEBQUBUFBQQF1dXS9H08SUmGWXoyhK7wYjhBBC3EJaQQXphZVordTMDm9/N+bFixe5fPmyxSzyfjNmTcwefPBBkpKS2LFjBzt27CApKYnly5fftHxNTQ2nTp3iN7/5DadOneKrr77iwoULzJ8/v1XZlStXkp+fb/r58MMPzVmVbuPk5IS7uzuKonD16tXeDgeAMF8ntFZqymr0XL1W09vhCCGEEDfV3FoWG+qJi72mXcdUV1dTWlqKSqWy6BmZYMZZmefPn2fHjh0cOXKESZMmAfDRRx8RExNDeno6oaGhrY5xcXFpNfZq1apVTJw4katXrxIYGGh63t7eHh8fH3OFb1ZBQUGUlpaSmZlJSEhIb4eDjbUVo/ycScouJym7nCD39k07FkIIIXqSoig3zMZsfzdmZmYmAF5eXha5QsKNzJaYHT58GBcXF1NSBjB58mRcXFxITExsMzFri06nQ6VS4erq2uL5devW8dlnn+Ht7c2cOXP43e9+h5OTU5vnqK+vp76+3vS4oqJp+yG9Xm+2Js3m87Z1/sGDB3P8+HGuXLliMU2qkYObErNTWde4J9yr0+e5Vb37q4FYZ5B6D6R6D8Q6g9TbEut96mo5ueW1OGitmDbcrd0xpqenYzAYCAwMbPOYnqhze89ttsSsoKAAL6/WH/BeXl4UFBS06xx1dXW89NJLPPjggzg7/2cPrIceeoihQ4fi4+PD2bNnefnll0lOTr7pTMc//vGPvPrqq62e37Vrl9mnzLYVU3V1tamv293dHa3WAtYOK1EBVuxPyWIcXZ+YYEmzTnvKQKwzSL0HkoFYZ5B6W5INV9SAmlHOevbu3tmuYxRFYevWrVRXV+Pn58e2bdtuWtacda6pad9QoQ4nZq+88kqbSc6Njh8/DtDmvlWKorRrPyu9Xs/SpUsxGo28//77LV5buXKl6feIiAhGjBhBdHQ0p06dYty4ca3O9fLLL/Pcc8+ZHldUVBAQEEBcXFyLhK876fV6EhISmDVrFhpN6z7wyspKnJyciI2NbdUa2BtGlVbz6V8OkVdnxcy4WWitOzf88Hb17o8GYp1B6j2Q6j0Q6wxSb0urd6PByKtv7Qf0PHlPNNNGeLTruNLSUk6ePImVlRWPPPJIm40hPVHn5t662+lwYvb000/fdgbkkCFDOHPmDIWFha1eKy4uxtvb+5bH6/V6lixZQkZGBt99991tk6dx48ah0Wi4ePFim4mZjY1Nm9sgaTQas//R3ewaTzzxRLsS1J4S7O2Cq72G8ho9l0tribq+I0Bn9cT/W0szEOsMUu+BZCDWGaTeliIxo5hr1XrcHbRMC/VGY9X+BoTQ0FBUKhUODrceQ23OOrf3vB1OzDw8PPDwuH2WGhMTg06n49ixY0ycOBGAo0ePotPpmDJlyk2Pa07KLl68yN69e3F3d7/ttc6dO4der7foTUl/yJKSMmiKZ7S/K/svFJOUXd7lxEwIIYToTpuTcgH4UZRvh5IyHx8fHn744T6zHJTZlssYOXIks2fPZuXKlRw5coQjR46wcuVK5s6d22Lgf1hYGJs2bQKaFl9dtGgRJ06cYN26dRgMBgoKCigoKKChoQGAy5cv8/vf/54TJ06QmZnJtm3bWLx4MWPHjmXq1Knmqo5ZKIpCaWkp1dXVvR0KcMMOALKhuRBCCAtSpzew82zT+PT5o9s/G/NGltYgcjNmXcds3bp1REZGEhcXR1xcHFFRUXz66actyqSnp6PT6QDIycnhm2++IScnhzFjxuDr62v6SUxMBECr1bJnzx7i4+MJDQ3l5z//OXFxcezevRsrKytzVqfbbdq0iVWrVpGSktLboQAwVhIzIYQQFmjP+SKqGwwMdrVjXOCgdh9XWVnZ7rFdlsJsszIB3Nzc+Oyzz25Z5samxSFDhty2qTEgIID9+/d3S3y9zcfHhzNnznDp0iUmT57c2+EQ5e8CwJXianS1elzsLGdsgRBCiIGruRtz/hg/1Or2t3wdO3aMAwcOMHXqVGbNmmWu8LqV7JXZi4KDg4Gmhe8sYb0Yd0cbAt2alg85I/tmCiGEsAC6Wj370ouBju2NCU29ckCfWpBeErNe5OnpiYuLC42NjRazqblpnNnV8l6NQwghhADYebaABoORUG8nwnzav8RVWVkZRUVFqNVqU0NIXyCJWS9SqVSEhYUBkJaW1svRNDFtaC4tZkIIISzA5uT/dGN2xIULFwAIDAy0+G2YbiSJWS9rTszS09MxGo29HM1/ErOk7PI+M7VYCCFE/1RUUUfi5VKg47Mxm7sx27sFpKWQxKyXNWfyNTU1ZGdn93Y4hPs5Y61WUVLVQG55bW+HI4QQYgDbciYfRYFxga4EuLV/C8W6ujrTxuV9LTEz66xMcXtWVlbExcXh6OjI4MGDezscbDVWjPR1JiVXR1J2Of6DzLuXqBBCCHEz31yfjblgTMc+Hy9duoTRaMTT0xM3NzdzhGY2kphZgLFjx/Z2CC2MDnAhJVdHcnY5c6M6t5CfEEII0RUZJdUk5+iwUqu4J7JjO/uEhISwaNEiixgi1FHSlSlaGRPQtHifLDQrhBCit2xJzgNgarAHnk6t97u+Fa1WS0REBFFRUeYIzaykxcxClJaWcurUKZydnZk0aVKvxjImoGmh2ZRcHXqDsUN7kgkhhBBdpSgKXzd3Y3ZyC6a+Sj5xLUR+fj6HDh3iyJEjvT4bcpiHI0621tTpjVworOzVWIQQQgw85/IquFJcjY21mrhw7w4dm5CQwIEDB6iqqjJTdOYliZmFCAkJQaPRUFZWRl5eXq/GolarGO3vCkh3phBCiJ73zfVuzLtHeuFk2/7tAevr6zl69Ch79uyhurraXOGZlSRmFkKr1ZrWNLOETc1HX+/OTJbETAghRA8yGhW+SWpKzOaP7thszPT0dBobG/Hw8MDLy8sc4ZmdJGYWJCIiAoCzZ8/2+kwSmQAghBCiNxzLvEZBRR1OttbEhnp26Nhz584BEB4ejkrV/s3OLYkkZhYkODgYOzs7qqqqyMrK6tVYmlvMLhZVUVXf2KuxCCGEGDiauzHnRPhgq7Fq93E1NTVcunQJ+E9DR18kiZkFsbKyYtSoUUDvd2d6Odky2NUORYEzsm+mEEKIHtDQaGRbSj7Q8UVlU1JSMBgM+Pr64unZsZY2SyKJmYWJiIjAzs4OR0fH3g7F1Gom3ZlCCCF6woGLxZTX6PF0smHyMPcOHZucnAzAmDFjzBBZz5F1zCzMkCFDeP7557G27v1bMybAlW0pBTIBQAghRI/YfH3Q/9woX6zU7R8j1tjYiKenJ9euXSMyMtJc4fWI3v/0Fy2oVCqLSMoAWTJDCCFEj6mubyQhtRDoeDemtbU19913H42NjRbzGdpZ0pVpoRRFITMzk4qKil6LIdLfBSu1isKKegp0db0WhxBCiP5v9/lCavUGgtztGe3v0qlz9PWkDCQxs1hff/01a9as4eTJk70Wg73WmhBvJwCSsst6LQ4hhBD9X/PaZQtG+3VoqYuioiIKCgrMFVaPk8TMQgUHBwOQlJTUq2uajTFNAND1WgxCCCH6t7LqBvZfKAZg/piO7Y25d+9ePvjgAw4ePGiO0HqcJGYWKiwsDFtbW3Q6HRkZGb0Wx5gAV0BazIQQQpjPtrP5NBoVRvk6E+zl1O7jKioqSE9PB5q2NuwPJDGzUBqNhqioKABOnTrVa3GMvp6YpeToMBh7d3N1IYQQ/VPzbMwFHWwtO3XqFEajkcDAwD67BdMPSWJmwcaNGwfA+fPnqays7JUYRng5Ya+1orrBwKWiql6JQQghRP+VV17LsYxrAMwb3f7EzGg0mhouJkyYYJbYeoMkZhbMx8eHwMBAjEZjr00CsFKriBzcPM5MujOFEEJ0ry3Xt2CaONQNP1e7dh+Xnp5ORUUFDg4OjBw50lzh9ThJzCzcxIkTAXp178wxga6ATAAQQgjR/TrbjXnixAkAxo4d2y+WyWjWf2rST40cOZIVK1YwZMiQXothrGkCQHmvxSCEEKL/uVRUSWp+BdZqFfdE+Lb7uPr6eoqLi1GpVIwfP96MEfY8ScwsnJWVFUOHDu3VGJonAFworKSmoRF7rfzZCCGE6LrmtcumhXgyyEHb7uNsbGx45plnyMnJYdCgQeYKr1dIV2Yfotfrqa6u7vHr+rrY4e1sg8GocDa393YiEEII0X8oisLm5M51Y0JTw0VQUFB3h9XrJDHrI1JSUvjzn//M7t27e+X6/9k3UyYACCGE6LrkHB1ZpTXYaayYOdK73ceVlpZiMBjMGFnvksSsj3B1daWuro4zZ870ytIZzRMAkmUCgBBCiG6wOSkXgFmjvHGwad8QGaPRyD//+U/++te/UlhYaM7weo0kZn1EQEAAgYGBGAwGjh492uPXH2NqMSvv8WsLIYToXwxGhW/P5AMd68ZMTU1Fp9PR2NiIu7u7ucLrVZKY9SFTpkwBmqYI19fX9+i1I/1dUKkgt7yWosq6Hr22EEKI/uXIlVKKK+txtddw5wjPdh2jKAqHDx8GmhaU7U9LZNxIErM+JDQ0FA8PD+rq6np8myYnWw0jvBwB6c4UQgjRNc3dmHMifNFaty8Vyc7OJjc3F2tr63610v8PSWLWh6hUKlOr2eHDh3t88GPzBIBk6c4UQgjRSXV6A9vPFgAd68ZMTEwEYPTo0Tg4OJglNksgiVkfExUVhaOjI5WVlWRnZ/fotf+zA0B5j15XCCFE/7EvvZjKukZ8nG2ZOMStXccUFhaSlpaGSqUiJibGzBH2rv7ZQduPWVtbc++99zJo0KAeH/h4Y4uZ0aigVqt69PpCCCH6vm+Sm7ox54/xa/fnSHp6OgDh4eF4eHiYLTZLIIlZHxQcHNwr1w31ccJWo6ayvpErJdUEXx9zJoQQQrRHZZ2e3eeLAJg/uv3dmNOmTWPYsGHY2bV/k/O+Sroy+7hr166hKEqPXEtjpSbCzwWQ7kwhhBAdt+tcIQ2NRoZ7OhDu59yhY/39/fvtEhk3ksSsD/v2229ZtWoVaWlpPXbNMdf3zZQJAEIIITqqeQum+aMHo1LdvhuzqqqKqqoqc4dlUSQx68Ps7e1RFIX9+/f3WKuZTAAQQgjRGcWV9Ry6VAI0jS9rj++++453332XkydPmjM0iyKJWR82efJktFotBQUFpoGR5tY8AeB8fgV1+v67V5kQQojutS0lH4NRYbS/C0M9br/cRXl5OcnJyej1ejw927cIbX8giVkfZm9vz6RJkwB6rNXMf5AdHo5aGo0K5/IqzH49IYQQ/UPzorLzxwxuV/l9+/ZhMBgYNmwYgYGB5gzNokhi1sfFxMSg1WrJz8/vkbFmKpXK1Gom3ZlCCCHaI/taDaeulqNSwbwo39uWLy4uJjk5GYC7777b3OFZFEnM+jh7e3smT54MwJ49ezAajWa/pkwAEEII0RHfXB/0HzPMHS9n29uW37t3L4qiEBYWxuDB7Wth6y8kMesHpkyZgp2dHTU1NZSUlJj9eqOvJ2bSYiaEEKI9vklqSszaswVTXl4eqampqFQq7rrrLnOHZnFkgdl+wNbWlmXLluHt7Y2NjY3Zr9ecmF29VsO16gbcHLRmv6YQQoi+Ka2ggvTCSrRWamaH374bs7CwEGtra8LDw/Hy8uqBCC2LJGb9RE8OjHSx0zDM04ErxdUkZ5czI2zgvXGEEEK0z+brrWWxoZ642GtuW37s2LEMHz68Xeuc9UfSldnPKIrC+fPnqa2tNet1xsgEACGEELdhNCo3dGO2f6yYs7MzTk5O5grLokli1s9s3ryZL774goMHD5r1OrLQrBBCiNs5dbWM3PJaHLRW3D3y1r0rly5dIjs7u4cis1xmTczKyspYvnw5Li4uuLi4sHz5csrLy295zKOPPopKpWrx0zzrsFl9fT3//d//jYeHBw4ODsyfP5+cnBwz1qTvGDVqFABHjx6lrKzMbNdpXjIjOae8x3YdEEII0bc0z8aMD/fBVmN103INDQ188803rF69uke3GbREZk3MHnzwQZKSktixYwc7duwgKSmJ5cuX3/a42bNnk5+fb/rZtm1bi9efffZZNm3axOeff87Bgwepqqpi7ty5GAyyEv2IESMYOnQojY2NJCQkmO06I32d0VqpKa/Rk1VaY7brCCGE6Jv0BiNbz+QDt9+CKTExkYqKClxdXQkODu6J8CyW2RKz8+fPs2PHDv7xj38QExNDTEwMH330Ed9+++1ttw+ysbHBx8fH9OPm5mZ6TafTsXr1av785z8zc+ZMxo4dy2effUZKSgq7d+82V3X6DJVKxezZs1GpVKSmppKRkWGW62it1YzycwakO1MIIURrhy6VUFrdgLuDlqnBHjctV1FRwaFDhwCYNWsW1tYDe16i2Wp/+PBhXFxcTFsGQdPeji4uLiQmJhIaGnrTY/ft24eXlxeurq5Mnz6dP/zhD6YpsydPnkSv1xMXF2cq7+fnR0REBImJicTHx7c6X319PfX19abHFRVNWwnp9Xr0en2X69qW5vOa6/y34ubmxtixYzl+/Dhbt25l5cqVqNXdn4NHDXYmKbucU1nX+FFE0/3pzXr3loFYZ5B6D6R6D8Q6g9S7q/X++lTTEKM5Ed5gNKA3tt2rtXPnTurq6ggMDGTEiBG98v+7J+51e89ttsSsoKCgzfVHvLy8KCgouOlxc+bMYfHixQQFBZGRkcFvfvMb7rrrLk6ePImNjQ0FBQVotVoGDRrU4jhvb++bnvePf/wjr776aqvnd+3ahb29fQdr1jHm7E68lfr6eq5evcrFixepq6tjxIgR3X4NpUQFWLH/bBbjVVdavNZb9e5NA7HOIPUeSAZinUHq3RkNBtieYgWo8KjOYNu2tntvrl27xs6dOwEYOnQo27dv7/Q1u4M573VNTfuG/XQ4MXvllVfaTHJudPz4cYA21yBRFOWWa5M88MADpt8jIiKIjo4mKCiIrVu3snDhwpsed6vzvvzyyzz33HOmxxUVFQQEBBAXF4ezs/Mt69JZer2ehIQEZs2ahUZz+3VbzMHf359Tp04RHx/PkCFDuv384aU1fPqXg+TVqpkZNwuttdoi6t3TBmKdQeo9kOo9EOsMUu+u1HtbSgH1x87g72rLT5fcedN84OOPP2bEiBFERkZy3333dTX0TuuJe93cW3c7HU7Mnn76aZYuXXrLMkOGDOHMmTMUFha2eq24uBhvb+92X8/X15egoCAuXrwIgI+PDw0NDZSVlbVoNSsqKmLKlCltnsPGxqbNFfE1Go3Z32w9cY2bmTx5MpMnTzZLNybAcG9nXO01lNfouVRSa9oRAHq33r1lINYZpN4DyUCsM0i9O2Pr2abP/3ljBqPVtr07jKIoTJkyhf379zNnzhyL+H9sznvd3vN2ODHz8PDAw+Pmg/iaxcTEoNPpOHbsGBMnTgSalnDQ6XQ3TaDaUlpaSnZ2Nr6+Tds4jB8/Ho1GQ0JCAkuWLAEgPz+fs2fP8uabb3a0Ov3aDxOy27VWdpRKpWK0vyv7LxSTlF3eIjETQggxMOlq9OxLLwZuvTemSqUiKiqKyMjIAbvKf1vMNitz5MiRzJ49m5UrV3LkyBGOHDnCypUrmTt3bouB/2FhYWzatAmAqqoqXnjhBQ4fPkxmZib79u1j3rx5eHh4mJo4XVxcePzxx3n++efZs2cPp0+f5uGHHyYyMpKZM2eaqzp9msFg4MCBA6xZswaj0dit5x5zPRlLlpmZQgghgB3n8mkwGAn1diLMp+3hQo2NjabfJSlryazrmK1bt47IyEji4uKIi4sjKiqKTz/9tEWZ9PR0dDodAFZWVqSkpLBgwQJCQkJYsWIFISEhHD58uMXWDO+88w733nsvS5YsYerUqdjb27NlyxasrG6+eN1AVltby8GDB8nKyjKN/+suzYmZLJkhhBAC/rM35s3WLrt69SrvvvsuZ8+e7cmw+gyzLhbi5ubGZ599dssyN64ab2dnZ5qdcSu2trasWrWKVatWdTnGgcDR0ZGZM2eydetWvvvuO0aOHNltkx6auy+vlFSjq9HTjv1phRBC9FOFFXUcvlIKwPzRrRMzg8HA1q1bqays5MqVK0RERPR0iBZP9socIKKjo/H396e+vp4dO3Z023ndHLQEuTctOZKcU95t5xVCCNH3bEnOQ1FgfNAgAtxaL0d15MgRCgsLsbe3l+FHNyGJ2QChUqmYO3cuarWa1NRU0yzX7mDaN1O6M4UQYkDbcn1vzLZay0pLS9m7dy/QtMK/udcR7askMRtAfHx8TBvCf/vtty12Q+gKGWcmhBAio6Sa5BwdVmoV90T6tnhNURS++eYbGhsbGTZsGGPGjOmdIPsAScwGmNjYWFxdXamuriYnJ6dbzjn6hsTsxjGDQgghBo5vrg/6nxrsgadTy7VDT5w4QVZWFhqNhnnz5slMzFsY2DuFDkBarZZFixZhY2ODp6dnt5wz3M8Za7WK0uoGcsvruuWcQggh+g5FUdicnAvAgpt0YwLMnDmz1ZaKoiVJzAYgf3//bj2frcaKkb7OpOTqSM7RId+DhBBiYDmXV8GV4mpsrNXEhbfe3Wf27NmEh4d3++dPfyRdmQNcTk4OBw4c6PJ5mseZncnRdflcQggh+pbNSU2tZTNHeuNk2/a6SQEBAdKF2Q6SmA1gZWVlfPzxx+zZs4crV6506VymHQAkMRNCiAHFaFTYkpwPwLwbujF1Oh2ff/65aRF50T6SmA1ggwYNYvz48QB88803XZql2TwB4Fx+BYbu3fVJCCGEBTuWeY2CijqcbK2JDW0au6woCps2bSItLY1vv/22lyPsWyQxG+BmzZqFq6sr5eXlbNu2rdPnGebhgJOtNXV6I/m13RigEEIIi9a8BdOcCB9sNU1bIzbvea3VapkzZ05vhtfnSGI2wGm1WhYuXIhKpSI5ObnTe5ep1SrTQrOZlTKGQAghBoKGRiPbUpq6MReMGQxAYWEhe/bsAZoG/bu5ufVafH2RJGaCwMBApk2bBjQtPFteXt6p8zSPM7taJYmZEEIMBN9fKEZXq8fTyYbJw9xpbGxk48aNGAwGQkNDGTt2bG+H2OdIYiYAmDZtGv7+/tTV1XHq1KlOnaN5nFmWJGZCCDEgbL6+BdO8KD+s1Cr27NlDUVERDg4OzJ8/X2ZhdoKsYyYAsLKyYuHChVy5csU0IaCjmlvMCmuhsq4RN03bU6aFEEL0fdX1jexOLQRg/hg/GhsbTTP8FyxYgIODQ2+G12dJYiZM3NzcujQWwNPJhsGutuSW13E2T8e0ULtujE4IIYQl2X2+kFq9gSB3e0b7u6BSqfjxj39MWloaISEhvR1enyVdmaJN9fX1bN++ndrajk2xjBrsAsCZnApzhCWEEMJCNM/GXDDaz9RlqdFoiIyM7M2w+jxJzESbvvzyS44ePcrXX3/doY3JRwc0JWay0KwQQvRf16ob+P5CMQDe1Zc5cOBAhz4rxM1JYibadPfdd2NtbU16ejqJiYntPq65xSw5RydvUiGE6Ke2peTTaFQYoq3k0pnj7Nmzh4yMjN4Oq1+QxEy0ydfXl9mzZwOwZ88esrKy2nVcuJ8TahSKKuspqKgzZ4hCCCF6msEA+/bxTUISxvoa3ItOoygK48ePZ9iwYb0dXb8giZm4qfHjxxMVFYXRaGTDhg1UV1ff9hh7rTW+9k2/J10tN2+AQgghes5XX8GQIeTNX8zRShU16YcY8uUavPPyTF/kRddJYiZuSqVSMXfuXDw9PamsrGTjxo0YjbffCDPIsakLMymn3MwRCiGE6BFffQWLFkFODltGTqMu4zTe2WfxuFbE4o8+QrNlS29H2G9IYiZuSavVsmTJEjQaDSUlJVRU3H62ZWBzYiYtZkII0fcZDPDMM3B93PCnPsHU56cTWpzJfYCHSgXPPttUTnSZrGMmbsvT05OlS5fi7e2No6PjbcsHOTW9eVNydRiMClZqWflZCCH6rAMHICcHBfh6VCxX3PxRl2bz6LU8wqApYcvObioXG9u7sfYDkpiJdhk+fHiLxwaDASsrqzbL+tiBg9aK6gYDF4sqCfNx7okQhRBCmEN+PkUOrvx/cT9jV0gMWmBeTirz9LWtyomuk65M0WFnzpzhb3/7200nA6hVEDG4KRmT7kwhhOi7FEVho9GDmf/1HjuGjsPa0MizB9ex6rt/0KovxNe3N0LsdyQxEx3S2NjI/v37KSkp4d///jeGm4wpGO3fvJ5ZeQ9GJ4QQorvk6+r4rzXHeT6lgcL8izgd+JSPP3maZw/9C62x8T8FVSoICIA77+y9YPsRScxEh1hbW7Ns2TJsbGzIyspi+/btbZZrXmj2tLSYCSFEn6IoCocLVdyzKpG96cUYCy8yvvo8C09sxqM0p2Xh61sx8Ze/wE2Gt4iOkcRMdJiHhwf3338/KpWKEydOcOTIkVZlmrdmulBYSU1DY6vXhRBCWJ7sazU8uvYkn1+xoqq+kWDbKu71KGLixDDifv97Rvn7tzzA3x82bICFC3sn4H5IEjPRKSEhIcycOROAnTt3kpaW1uJ1H2dbvJ1tMCqQIvtmCiGERTMaFT49nMnsv3xP4uVraFQKP53kzgztZdwctIwZM4Y7fv1ryMyEvXth/fqm/2ZkSFLWzSQxE502ZcoUoqOjmwaHbtxIaWlpi9fHBLgCMs5MCCEsWVZpNcs+OsJvNp+jusFAdJArPw+tQn35IPqGBoYMGcK8efNQqVRN3ZWxsbBsWdN/pfuy28lyGaLTVCoV99xzDzqdDh8fH9zc3Ghs/E+35ZiAQew8V0hSdnnvBSmEEKJNBqPCmsRM3tqZRp3eiJ3Gil/NDmVZ9GB+97staDQavLy8WLJkyU2XRxLdTxIz0SVqtZply5ahVrdufG0eZyZLZgghhGW5VFTFrzae4WRWGQAxw9x54/4oAt3t0ev1jBs3jsbGRuLj47G3t+/laAcWScxEl92YlDU2NnLu3Dni4uKI8ndFpYI8XR1FFXV4Odv2YpRCCCEaDUb+cTCDtxMu0NBoxNHGmpfvCWPZhEDUN+zSYmNjw3333YdGo+nFaAcmGWMmuo2iKHzxxRecOXOGr7/+GnuNmhFeTVs4SXemEEL0rvSCSu7/WyKvb0+jodHItBBPdv5iGg9NCkKtVrF///42Z9mLniUtZqLbqFQqJk+ezK5du0hNTWXbtm2MHjyYC4VVJO9MJK7YrWkBQhmrIIQQPUZvMPLBvsv89buL6A0KTrbW/GbuKBaP928a0A+cOHGCvXv3AuDt7d2b4Q540mImutXw4cOJiYlpWuPs00/RvPY8AEnHzsOMGTBkCHz1Ve8GKYQQA8S5PB0L/u8Qf064gN6gcHeYFwm/mM6S6ABTUpaamsrWrVsBiI2Nxf+Ha5WJHiUtZqLbBQYGMqG2lh3//jfl9q7UR57njO8IjKhQ5+bCokWyIKEQQphRfaOB9767xPv7LtNoVHC11/DKvHAWjPEzJWQAmZmZbNy4EUVRiI6OZvr06S1m14ueJ4mZMIvxH32EHkioKUd/6RilGhuuuA8muDSnaQuPZ5+FBQukW1MIIbpZcnY5v9yQzIXCKgDmRPjw+wUReDrZtCiXnZ3N+vXrMRgMjBw5knvuuadF0iZ6h3RlCvPIzeUOYCrgW1eF2taZ1dELqNLagaJAdjYcONDbUQohRL9Rpzfw+vY07nv/EBcKq3B30PLeg+P428PjWyVlVVVVrFu3joaGBoYOHcr999/f5rJHoufJXRBmowLigCdRsHb24F9j5jDtJ/9gdfR86qw0kJ/f2yEKIUS/cDLrGvf89QAf7L+MUYH5o/1IeG46P4rybbO8o6MjsbGxBAUFsWzZMqytpQPNUsidEGalAn6atIOguir+fOdyLlrb8Ntxc1k94V6eNXiw0GDE2kq+HwghRGfUNhh4a2c6nyRmoCjg6WTDH+6NIC7c57bHTp48mYkTJ0pLmYWRuyHMY/DgprFkNCVnc9MO8tk/nuKOTX9AnbSDLKORF882EP+X79meko+iKL0brxBC9DFHrpQy+93v+fhQU1J2/zh/dv9i+k2TsrKyMr744gvq6upMz0lSZnmkxUyYxxtvNM2+VKmaxpQBPoqRewsuElx0hRQvWy7YxXO5GJ5ad4rR/i78Mj6MO0Z49HLgQghh2arqG3ljexqfHskCwNfFltcWRjIj1Oumx5SVlbF27VrKy8uxtrbm/vvv76lwRQdJYibMY968piUxnnkGcnIAsAIW+/tjXLQIaxcXolSZKEMH89UlPck5Oh5efZQpw915cXYYYwJcezV8IYSwRAcvlvCrjWfILa8FYNnEAF6+ZyTOtjffOunatWusXbsWnU6Hu7s7cXFxPRWu6ARJzIT5LFzYtCTGgQNNA/19fbG6806WKAqff/45ly5dQpN9hLWLFrI108i6o1kkXi7l3vcOER/uzQtxoYzwdurtWgghRK+rqNPz2tbzfH48GwD/QXa8vjDqtr0MJSUlrF27lsrKSjw8PFixYgVOTvLvqiWTzmVhXlZWEBsLy5Y1/dfKCmtra5YuXUpwcDB6vZ6d32zkx+Nc+O75WO4f549aBTvPFRL/l+954ctkcspqersWQgjRa/amFRH39vempGxFTBA7n51226SsqKiITz75hMrKSry8vHj00UclKesDpMVM9Irm5Gzjxo3o9Xp8fHywtrbmz0tG85Ppw/jTznR2pRay4WQO3yTl8dDkQH42IxgPR5vbn1wIIfqB8poGfv9tKl+dygUgyN2eN++PYtIw99seqygKX331FdXV1fj4+PDII49gb29v7pBFN5DETPQaa2trFi9ejMFgaLGGToi3E39/JJpTV8t4a0c6h6+U8smhTP59PJvH7xzGyjuH4nSL8RRCCNHX7TxXwP/39VmKK+tRqeDxqUN5Pi4UO237dktRqVQsWrSIXbt2cd9992FnZ2fmiEV3kcRM9Cq1Wm2arq0oCrt27cLNzY0JEyYwLnAQ61dO4uClEt7ckU5Kro6/7rnIp4cz+WlsMMtjgrDVyJZOQoj+o7Sqnle2pLIlOQ+A4Z4OvLloNOODBrXr+JqaGlPLmIeHBw8++KDZYhXmIYmZsBiXLl3i8OHDANTV1XHHHXegUqm4c4QndwR7sP1sAX/alc6V4mr+sO08Hx/K4Jm7R7BovL8sUiuE6NMURWFrSj6/23yO0uoG1Cr4yfThPHP3iHZ/AT137hybN29m6dKlDBs2zMwRC3Mx66dZWVkZy5cvx8XFBRcXF5YvX055efktj1GpVG3+vPXWW6YysbGxrV5funSpOasiekBwcDB33nknAHv27GH79u0YjUag6e/inkhfdj07jTfuj8TXxZZ8XR0vfZVC3F++Z+uZfIxGWaRWCNH3FFXW8dRnp3h6/WlKqxsI9Xbi659N5Vezw9qdlB0/fpwNGzbQ0NBASkqKmSMW5mTWFrMHH3yQnJwcduzYAcATTzzB8uXL2bJly02Pyf/B/onbt2/n8ccfb7UY3sqVK/n9739veiz9532fSqXi7rvvxsHBgZ07d3Ls2DGqqqpYuHChaQyatZWaByYEsmDMYD47ksV7ey9xpbian60/ReRgF34ZH8qdIzxQXd91QAghLJWiKHydlMurW1Ipr9FjrVbx0xnBPD0jGK11+9pNFEVh//797Nu3D4AJEyYwZ84cM0YtzM1sidn58+fZsWMHR44cYdKkSQB89NFHxMTEkJ6eTmhoaJvH+fi03Epi8+bNzJgxo1WzrL29fauyon+YPHkyjo6ObNq0idTUVKqrq1m2bBm2tramMrYaK3585zAemBDARwcyWH3gCim5Oh75+BiTh7nx4uwwxgW2b0yGEEL0tAJdHb/elMKetCIAwv2ceXNRFOF+Lu0+h9FoZPv27Rw/fhxo6k2aPn26fDHt48zWlXn48GFcXFxMSRk0feC6uLiQmJjYrnMUFhaydetWHn/88VavrVu3Dg8PD8LDw3nhhReorKzstthF74uIiODhhx/GxsaGq1evknN994AfcrLV8NysEPa/OIPHpg5Ba6XmyJVrLHw/kZX/PMGFQvm7EEJYDkVR+PfxbGa9s589aUVordS8EBfC1z+b2qGkrLGxkS+++ILjx4+jUqn40Y9+ZBrmI/o2s7WYFRQU4OXVet8uLy8vCgoK2nWOtWvX4uTkxMKFC1s8/9BDDzF06FB8fHw4e/YsL7/8MsnJySQkJLR5nvr6eurr602PKyoqANDr9ej1+vZWqUOaz2uu81uq7qy3v78/Dz/8MIWFhQQFBd3ynC42av5ndggrJgewau9lNp3OIyG1kN3nC7l3tC8/vysY/0Hm6e6Wey317u8GYp2h++udW17L/7c5lYOXSgGI8nfm9XsjGOHtCEYDeqOh3edSFAVra2tUKhULFiwgPDy82+IciPe7J+rc3nOrFEXp0IjpV155hVdfffWWZY4fP86uXbtYu3Yt6enpLV4bMWIEjz/+OC+99NJtrxUWFsasWbNYtWrVLcudPHmS6OhoTp48ybhx49od8/r162XBvT6msrKSyspK/Pz8blmuoAa2Zqs5c62pUdhKpTDVW2HWYCPO2p6IVAghmhgVSCxU8U2WmnqjCmuVwj0BRmL9FKy60MBlMBjQ6XS4ubl1X7DCbGpqanjwwQfR6XQ4OzvftFyHE7OSkhJKSkpuWWbIkCGsX7+e5557rtUsTFdXV9555x0ee+yxW57jwIEDTJs2jaSkJEaPHn3LsoqiYGNjw6effsoDDzzQ6vW2WswCAgIoKSm55f+crtDr9SQkJDBr1iw0moGzGKo5611XV8fHH39MaWkpcXFxTJw48bbN9sk5Ot5OuEjilWsA2GuteDQmiB/fEdRti9TKvZZ693cDsc7QPfW+eq2GX399jiMZZQCMD3TltXvDGebp0OFzXbp0iZSUFBYsWGBa/9EcBuL97ok6V1RU4OHhcdvErMNdmR4eHnh43Hp/LoCYmBh0Oh3Hjh1j4sSJABw9ehSdTseUKVNue/zq1asZP378bZMyaFq7Ra/X4+vr2+brNjY22Ni03spHo9GY/Y+uJ65hicxRb7VazdChQykrK2P37t2Ul5czZ84crKxuPp08eqgH65/w4ODFEt7cmcaZHB3v77/C+uPZ/DR2OI/EDOm2RWrlXg8sA7HeA7HO0Ll6G40KaxIzeWtnOrV6A3YaK16cHcojMUOwUne8mezEiRNs27YNo9HI0KFDmTBhQofP0VED8X6bs87tPa/ZUu6RI0cye/ZsVq5cyZEjRzhy5AgrV65k7ty5LWZkhoWFsWnTphbHVlRU8OWXX/LjH/+41XkvX77M73//e06cOEFmZibbtm1j8eLFjB07lqlTp5qrOsICWFlZMW/ePOLj41GpVJw4cYJ169ZRW1t722PvGOHB5p9N5YOHxzHc04HyGj2vbUsj9q19/OvYVRoNxh6ogRBiILhSXMWSDw/z+29TqdUbmDzMjR3P3sljU4d2OCkzGAxs3bqVb7/9FqPRyJgxY9ocsiP6D7MuMLtu3ToiIyOJi4sjLi6OqKgoPv300xZl0tPT0el0LZ77/PPPURSFZcuWtTqnVqtlz549xMfHExoays9//nPi4uLYvXv3LVtORP+gUqmIiYlh6dKlaLVarly5wj/+8Q+Ki4vbdezsCF92PjuNNxdF4ediS0FFHS9/lcKsd77n2zN5skitEKLTDEaFD/dfZs67BziRVYaD1or/vTeC9T+eTJB7x7suq6qq+Oc//2maeXnXXXexYMEC+azr58y6wKybmxufffbZLcu0NcTtiSee4IknnmizfEBAAPv37++W+ETfFRoayuOPP8769espLS1l165dPPTQQ+061tpKzZLoAOaP9mPd0au8t/cSGSXVPL3+NOF+l/llfCjTQzxl2rkQot0uFlbywoYzJGeXA3DnCA/+uDAS/0Gdm2CWl5fH559/TkVFBTY2NixcuPCm63+K/kX2yhR9lre3N0888QTbt29n9uzZHT7eVmPF43cM5YEJAfzjwBX+cSCDc3kVPPrJcSYNbVqktr0bBwshBia9wcjfv7/Cu7sv0mAw4mRrzW9+NIrF0f5d+nKnUqmoqanBw8ODpUuXtmtst+gfJDETfZqDgwOLFi1q8dzJkycZOXJku5dCcbSx5tmZISyfHMT7+y7z6ZEsjmZc4/6/JTJzpDe/jA8l1MfJHOELIfqw1LwKfrkhmXN5TWtj3hXmxWv3ReLjYnubI9umKIopmfP19eWhhx7C19e3xa4nov8z6xgzIXra2bNn2bJlC3//+99b7bt6O+6ONvxm7ij2vRDLA9EBqFWw+3whs9/9nl98kcTV0hozRS2E6EsaGo28nXCB+f93kHN5FbjYaXjngdGsXhHd6aRMp9Oxdu3aFrucDB06VJKyAUgSM9GveHp64ubmRnl5OatXr+bEiRNtjmO8FT9XO95YFMWuX0znnkgfFAU2nc7l7rf38dvNZymqrDNT9EIIS5eSo2P+/x3kr3su0mhUiA/3JuG5adw3tvNdlxcvXuTDDz8kMzOTLVu2dPjfLNG/SGIm+pXmcWchISE0Njby7bffsmHDBurqOp5MBXs58v5D4/nm6ancOcIDvUHhn4ezmP7mPt7amYauduBsVyLEQFenN/DGjjTuff8QaQWVuDlo+b8Hx/LBw+Pxcupcq5bRaGT37t2sW7eOmpoafH19Wbp0qUw8GuBkjJnod2xtbVm2bBmHDx9m9+7dnDt3jry8PBYtWsTgwYM7fL4of1c+fXwSiZdKeGNnOsnZ5by39zKfHbnKU7HDeTC64+cUQvQdp6+W8/LX57hcXA3AvNF+vDJvFO6OrRcub6+Kigo2btxIVlYWABMnTiQuLg5ra/lYHujkL0D0SyqViilTphAYGMiGDRsoKyujqqqqS+ecEuzB18Pd2ZVayJ92pnOxqIrXt6fx8cEMYj1VzDIYGWCLZAvRr9U2GNiUqWb/kWMoCng42vCH+yKID/fp0nl1Oh0ffvghNTU12NjYMH/+fMLDw7spatHXSWIm+jV/f3+efPJJ0tLSWqwBdOPsp45QqVTEh/swc6Q3m07n8k7CBXLLa/l3pRVH/5rIc3EhzIvyQ92JLVeEEJbj6JVSXtxwhqxrTSN+Fo4bzG/njsLVXtvlczs7OxMQEIBOp2Px4sW4u7t3+Zyi/5DETPR7tra2jBkzxvRYp9Px2WefMWvWLEJCQjp1Tiu1ikXj/Zk32pdPEzP4y640sq7V8MznSXyw/wovxocSGyqL1ArR11TXN/LmjjTWHm7qYnTRKvzpgXHMCvfr0nkLCgpwdXXF1tYWlUrFvffei0ajka5L0Yr8RYgB58CBAxQXF7N+/XrGjx9PfHw8Wm3nvgXbWFuxIiYIp5Jz5DmG8vGhLM7nV/DYmuNMHOLGi7NDiR7i1s01EEKYw6FLJfxq4xlyypr2310yfjDj1FnEhnh2+pxGo5HDhw/z3XffER4ezsKFCwGws7PrlphF/yOzMsWAM3v2bGJiYoCmxWg/+OADsrOzu3ROWyt4esZwvn9xBk9MG4bWWs2xzGss+uAw/7XmOOfzK7ojdCGEGVTU6Xn5qxQe+sdRcspqGexqx6ePT+QP94Zj14XmC51Oxz//+U8SEhIwGAw0NDTQ2NjYfYGLfklazMSAY21tTXx8PCEhIXz99ddcu3aNjz/+mDvuuIPY2NgubRA8yEHL/9wzksemDuGvey7y7xM5fJdWxN70IuaP9uO5WSGd2sxYCGEe+9KLePmrFPJ1TUvqPBITxIuzw3C0sUav79ySOIqicOrUKXbt2kV9fT1arZbZs2czduxYGd4gbksSMzFgDR06lKeeeort27eTnJzMgQMHsLOzY8qUKV0+t6+LHX9cGMXKO4fx54QLbD2Tz+akPLaeyWfpxAB+ftcIvJxlRW8heouuRs//25rKhpNNK+0Hudvzxv1RTB7WtYH4lZWVbNq0iStXrgAQEBDAvffeKwP8RbtJYiYGNFtbW+677z5CQ0M5fPgwEyZM6NbzD/N05L0Hx/HUdB1v7kzn+wvFfHbkKhtO5vDY1KE8OW04LvayxoYQPSkhtZBfb0qhqLIelQoemzKUF+JDsNd2/SPR2tqa4uJiNBoNd911F5MmTUKtllFDov0kMRMCGDVqFCNHjjR1MxiNRr766ivGjx/P0KFDu3z+iMEu/PO/JnL4cilv7kzj9NVy/rbvMuuOZPFk7HAemzIUO23nu1CFELd3rbqBV745xzfJeQAM83TgrUVRjA/q2gSdiooKnJycUKlU2NnZsWjRIpycnHBzk4k/ouMkjRfiuhvHfpw8eZKzZ8+ydu1atmzZ0qktndoSM9ydr56awkePRBPq7URFXSNv7khn+lt7+fRIFnqDsVuuI4RoaVtKPnHv7Oeb5DzUKvjJ9GFs+/mdXUrKDAYDBw8eZNWqVZw5c8b0fFBQkCRlotOkxUyINkRFRVFYWMiJEyc4efIkFy5cYPbs2YwaNarLg3dVKhWzRnlzV5gXm5NyeTvhAjlltfzm67N89P0VnpdFaoXoNsWV9fx281m2ny0AIMTbkbcWjWZ0gGuXzpuVlcW3335LcXExAOnp6YwePbqr4QohiZkQbbGxsWHu3LlERESwZcsWSktL+fLLLxk+fDhz5szBw8Ojy9ewUqtYOM6fuVF+/OvYVVZ9d4mr1xep/du+y7w4O5QZoV4yi0uITlAUhc1Jebyy5RzlNXqs1Sp+Gjucn90VjI1154cN1NTUkJCQwOnTpwFwcHAgLi6OqKio7gpdDHCSmAlxC0OGDOHJJ5/k0KFDHDx4kMuXL/Ptt9/y6KOPdts1tNZqVkwZwqLx/nxyKIMP918hraCS/1pzguigQbw4O4yJQ6VbRIj2Kqyo49ebUth9vgiAUb7OvLU4inA/ly6dNy0tjc2bN1Nb27QA7fjx45k5c6YsFiu6lSRmQtyGRqMhNjaWqKgodu7cyYwZM0yvGY1GFEXplus42Fjz9F0jeHhyEH/bf5k1hzI5kVXGkg8PMyPUkxfiQ7v8wSJEf6YoCl+ezOH/fZtKZV0jGisVP79rBE/GDkdj1fUh1fb29tTW1uLt7c3cuXMJCAjohqiFaEkSMyHayc3NjWXLlrV4bs+ePeTm5nZrd6OrvZaX54zksSlD+et3F/nieDZ704vZm15sWqR2iIcsUivEjXLLa3n5qxS+v9A05mu0vwtvLhpNqI9Tp89ZUVHRYleQwMBAli9fztChQ2UJDGE2kpgJ0Um1tbUcP36c2tpaLl26hIuLCzNnzsTR0bFbzu/jYstr90Wy8s5hvJ1wgS3JeXyTnMe2lHyWTAjgmbtH4C2L1IoBTlEU1h+7yh+3pVFV34jWWs1zs0L48R1Dse5kK5lerycxMZH9+/eTnp7OAw88gKdn036Zw4cP787whWhFEjMhOsnOzo4nn3ySHTt2cPHiRU6ePMn58+e58847mTx5MtbW3fP2GurhwKplY/nJtGH8aVc6+9KLWX/0Kl+dymHFlCE8NX04rvad24RdiL7samkNL311hsTLpQCMC3TlzUWjCfbq3JcjRVE4d+4cCQkJ6HQ6DAYDgwYN6vTWTEJ0hiRmQnSBm5sbixcvprq6msbGRgoLC9m9ezfHjx9n8eLF+Pv7d9u1Iga7sOaxiRy9UsqbO9M5mVXGh/uvsP7oVZ6cPpzHpg7plpXLhbB0RqPCPw9n8saOdGr1Bmw1an4ZH8ajU4Zg1cllZjIyMti9eze5ubkAuLi4EBsbS1ZWlqm1TIieIP+KC9ENvLy8mDNnDmlpaezevZva2lpcXV3Ncq1Jw9zZ8GQM36UV8dbOdNIKKnlrZzqfHMrk53cHs3RCIFprGf8i+qeMkmpe3JDM8cwyACYNdePNRVEEuXd+3GVNTQ3r169Hr9ej0Wi44447THvmXr16tVviFqK9JDETopuoVCqioqIYOXIk+fn5LcaaJSQkEBISQlBQULdd6+6R3sSGerElOY8/J6STfa2W324+x0cHrvDcrBDmjx7c6dYDISyNwajw8cEM/rQrnfpGI/ZaK16eE8ZDk4I6tRhzZWUlTk5NEwPs7e2ZOnUqNTU1TJs2zfTelS5M0RskMROim2k0GgIDA02PMzMzOXToEIcOHSI4OJi77roLPz+/brmWlVrFvWMHc0+kL18cv8q7ey6Rfa2WX3yRzAf7rvDL+FDuHimL1Iq+7WJhJb/ccIak7HIA7hzhwWv3RRLgZt/hc+l0Og4cOMCpU6dYsWKF6ctSbGxsN0YsROdJYiaEmbm5uREdHc2pU6e4dOkSly5dYuTIkcTGxuLt7d0t19Baq1keM4T7x/vzyaFMPth/mfTCSn78zxOMC3TlxdlhTB7m3i3XEqKnNBqMfPj9Fd7dfZEGgxEnG2t+/aORPDAhoMNfNsrLyzl48CCnT5/GYDAAcPHixW5rxRaiu0hiJoSZOTs7M3fuXKZMmcK+fftISUnh/PnznD9/ntDQUObPn4+DQ/esS2avteZnM4J5aFIgH+y/wprEDE5dLWfp348wPcSTX8aHEjFYFqkVlu98fgW/3JDM2dwKAGaEevLawkh8XTq2yn5ZWRkHDhwgKSkJo9EINO3oMWPGDEnKhEWSxEyIHuLm5sbChQu544472L9/P6mpqRQVFZllOxdXey0vzQnjsalD+OuepkVq918oZv+FYuZG+fJ8XChDZZFaYYEaGo28v+8S7+29hN6g4GKn4XfzRnHf2MEdbiVTFIV169ZRUlICwLBhw5g+fbokZMKiSWImRA/z8vJi8eLFlJSUUFVVZVpB3GAwsHHjRsaOHUtwcHC3jAvzdrblD9cXqX1n9wU2J+Xx7Zl8tp8tYEl00yK1Pi6ySK2wDCk5On65IZm0gkoA4kZ587/3RuDVgYWUc3Nz8fLyQqPRoFKpmDp1KufOnWP69OmyhZLoEyQxE6KXeHh44OHhYXqcnJxMamoqqampeHt7M3nyZCIjI7tlodohHg68u3QsP5k2nD/tSue7tCL+daxpkdpHpwzhyenDGeQgi9SK3lHfaODd3Rf58PsrGIwKbg5aXp0fztwo33Z9QVEUhQsXLpCYmEhWVhbz5s1j/PjxAIwZM4axY8eauwpCdBtJzISwECNGjCAmJoYTJ05QWFjI5s2b2bNnDxMmTCA6OrpbxqGN8nPm40cncDzzGm/uSON4Zhkfft+0SO0T04bxX3cMxcFG/lkQPef01TJ+ueEMl4qqAJgb5cur88Nxd7S57bGNjY2cOXOGxMREU3elWq1Gp9OZysiMZNHXyL/AQlgIJycn4uPjmTZtGidPnuTYsWNUVFSwd+9eDhw4wDPPPGNad6mrJgxx498/iWFfejFv7EgjraCSPydcYO3hTJ6eEcyySYHYWFt1y7WEaEud3sCfd6Wz+mAGRgU8HG3433sjmB3hc9tjFUVh//79nDhxgqqqpoTOxsaG6OhoJk2ahLOzs7nDF8JsJDETwsLY2dlxxx13EBMTQ2pqKocPH8bW1rZFUpaTk4Ovry9WVp1PnlQqFTPCvJge4smWM3m8nXCBrNIaXtmSyj8OZvCLmSHcO1YWqRXd73jmNV7ccIaMkmoAFo4dzG/mjrpld7qiKKbWL5VKRV5eHlVVVbi4uDB58mTGjRuHjc3tW9mEsHSSmAlhoaysrIiMjCQiIoKGhgbT81VVVXz88cfY29szbtw4xo8fj4tL55fAUKtVLBjTvEhtNn/dc5Gcslqe/zKZD7+/zAtxocwa5S1dQqLLahoaeXNHOmsPZ6Io4O1sw2v3RXL3yJuv51dfX09ycjInTpzgwQcfNG11Nm3aNEaPHk1YWFiXvqAIYWkkMRPCwqlUqhYtASUlJdjZ2VFVVcX333/PgQMHGDFiBNHR0QQHB5tmeXaUxkrNw5ODuH+cP2sSM/nbvktcKKziiU9PMjbQlRfjw4gZLovUis5JvFTCr746Q/a1WgAeiA7gf340Ehc7TauyiqKQnZ1NUlISZ8+eNX0xOXnyJHfffTcA/v7++Pv791wFhOghkpgJ0ccMGTKE5557jrS0NE6cOEFGRgYXLlzgwoULODs7s2TJki59YNlprXgqdjgPTgzkw+8v88mhTE5fLWfZR0e4c4QHL8aHEekvi9SK9qms0/PH7WmsP9q0GfhgVzv+uDCSaSGercrW19dz/PhxTp8+TWlpqel5T09PJkyYwOjRo3ssbiF6iyRmQvRBVlZWhIeHEx4eTklJCSdPniQpKYnq6mrc3f/TqlVUVISjoyP29h3fU9DFXsOLs8N4dOoQ/u+7S6w/epUDF0s4cPEgP4r05eczhnVnlUQ/tP9CMS9vPEOerg6AhycH8tKckTjeMPP3xrFjarWaAwcOUF9fj1arZdSoUYwdO5bAwEDpShcDhiRmQvRxHh4exMfHc/fdd5Ofn99iJ4FvvvmG/Px8QkJCGD16NMHBwR1eF83LyZbfL4jgx3c0LVL7dVIuW1Py2XGugIkeasbq6gj0aN0dJQYuXY2e/92aypcncwAIdLPn9fsjmTK8ad0+o9FIZmYmKSkpFBUV8eMf/xiVSoVGoyE2NhZbW1tGjRolg/nFgCSJmRD9hLW1dYuVzRsaGmhsbMRgMJj25rSxsSE0NJTw8HCGDx/eoSQt0N2edx4Yw0+mD+NPO9PZfb6Iw0VqZv7lICtigngqNhg3WaR2wNudWsj/bEqhqLIelQoenTKEX8aHYqex4urVq5w9e5Zz585RXV1tOqagoABfX18AYmJieit0ISyCJGZC9FNarZYnn3ySwsJCkpKSOHfuHBUVFZw5c4YzZ84QGRnJ/fff3+Hzhvk4848VEzh6uZj/+fwolyuNfHQgg38dy2blncN4/M6hLbqqRD9kMMCBA5CfD76+cOedlNUZeHXLOb5OygNgmIcDby6KInqIG+fPn2fHjh0tFn61t7dn1KhRRERE4O1981mZQgw08q+nEP2ct7c38fHxxMXFkZOTw7lz5zh37hyhoaGmMsXFxezfv5/Q0FCCg4PbtbH6uEBX/jvcgFPIRP6ccInU/Are2X2Bfx7O5GczgnlosixS2y999RU88wzk5Jie2h4zj9/c9QQljSpUxkYWjtDy7I/CCPBzA5q+JOh0OmxsbAgLCyMiIoJhw4bJMhdCtEESMyEGCJVKRUBAAAEBAcTHx6Moium1tLQ0zp49y9mzZ1Gr1QQGBhISEkJoaGiLyQStzwnTRngwI8yHrSn5vJ1wgYySan7/bSqrD2bw7MwRLBznL4vU9hdbtsCiRXD9b6fE3oXfznqKb4dF05iXgXtlNtOHanHKtSY1RU2AX9Mq/kOGDOGBBx4gODgYjUbGIwpxK5KYCTEAqVSqFrPcRowYQX19PRcuXKCoqIjMzEwyMzPZtWsX7u7uPPzwwwwaNOim51OrVcwb7cfsCB++PJHDu3sukFteyy83nOHD76/wQlwo8eGySG1fpihQ8z+/od7ehSqtPSd8Q/ifETGU1VVgPLqBCTnnmKjLxvrn/42zs3OLVlcrKytGjhzZi9EL0XdIYiaEwMfHBx8fH2bOnElZWRkXLlwgPT2drKwsKioqWmwHdezYMWprawkICMBoNLY4j8ZKzYOTAlk4bjBrEzN5f99lLhVV8eRnJxkd4Mqv4kOZEuzR09UbsBRFoVZvoKq+kaq6RqrrDVTW66muN1BVr6eq3nD9+camMs3lGm74vb6Rijo9FWVVGKY/i2aQn+nclce/xu1aLnEXjzC6ppwQIGz0aHwWLpQkXIhOksRMCNHCoEGDmDRpEpMmTaK+vp6CgoIWszePHz9OcXExBoOBzMxMqqqqGD58OIGBgab9O201Vvxk+nCWTgzko++vsPpgBsnZ5Tz4j6PcEezBL+NDGR3g2vLCbQwoZwCOQTIlU3U3JEs3Jkx1jVTVG9pMpip/kGRV1zdiVG5/zbZiMNaU06gravqpKELR16HS2OAy4V6cGupwqasipjSbpSl7CFUMODYf3NDQ1McthOgUScyEEDdlY2NDUFCQ6bGiKEyaNIkrV65w6dIl9Ho9Fy5c4PLlywB4eXnx05/+1FTeQaPihfhQVkwZwnt7L7HuaBYHL5Vw8FIJcyJ8eD4ulGAvxzYHlOPvD+++CwsX9lh9O0tRFGoampKlyusJUXNidWMyVXW9teqHCVRzEtWVZOpW1CpwsLHGycYah+s/TrbWOGitcbS1xtGm6cfBxpqslKPkXjoLxga0rmq0HmqsVV7k5WZz9+YveGTfmv8kYW25vuyFEKJzJDETQrSbSqUiOjqa6Oho6uvrWb9+PcOGDSM/P5+rV6/i5+dnKms0GvnTn/6Es7Mzfn5+3OPnx5ylwaxP0fFNShHbzxaw81wBi9wNPPP/nmJwRVHLi+XmNg0037DBLMlZczLVIjGqa5kotUyymhKryjo9uYVW/PXSoabjr7dWmTuZ+mEC1fy7o23zYyscbTQ42FjhdP2/zcfYaaxMXYtGo5Hi4mLy8vLIzc0lNzeX5cuXm3aH2GPI5EDpBbRaRwICAggKCmLw4MEkJycz7+QxNJcvmwb/t6BSNSXTd97Zvf8jhBhgJDETQnSKWq3Gzc2NKVOmoNFoUBTFtNk0NC3BUVdXR11dHUVFRSQlJQHgrlazwtWJ0zWDSK735N8lVny98gOWn97GTw//G/faiqYTKErTh/2zz8KCBWBl1SqZah4DVVnfxjip+h+0Ut2QZFXXN1LV0NhmftE+KqiqbvWsWkUbCdPNkymnNp+3apVMddXVq1dJSUmhsLCQgoKCFvcJIDc3lxEjRgAwbtw4wsLC8PHxMS1nodfrOXv2LLzxRlOyrFK1TM6a4/zLXwZk97MQ3cmsidkf/vAHtm7dSlJSElqtlvLy8tseoygKr776Kn//+98pKytj0qRJvPfee4SHh5vK1NfX88ILL/Cvf/2L2tpa7r77bt5///0ubdwshOgalUrVYgsdb29vXnjhBXJzc8nPzycvL4+8vDyqqqqgVsdzd43DqayRN784xiHvYbxtNPDBnQ8zvrwAazsXjE7uNDp5UOvgQvXvd1KFFdVdSqbadqtkqjmhcrrheVtrFWkpScROnYSLva0pmXKy0WCrUffKoPfa2lquXbtGaWkpJSUlFBYWMn36dFMLZmlpKcePHzeV12q1DB482PRz47+dgwYNuvkM3Hnzmlow2+p2/stf+kS3sxCWzqyJWUNDA4sXLyYmJobVq1e365g333yTt99+mzVr1hASEsL//u//MmvWLNLT000zw5599lm2bNnC559/jru7O88//zxz587l5MmTsmChEBbE0dGR0NBQ02K2iqJQWVlJfn4+7u7ueCQk8K/P/4d1g0fye49Aihzd+F5jA411UJYLZbmorLXYNtRh49vUoqM0NqDUlOPk7IKLszOOdpqWCZS2dTJ1syTL0ca6w8mUXq9Hk3uaSUPdemxNLqPRSFVVFVqtFltbWwCysrLYvXs3paWl1NTUtDomODjYlJgFBgZyxx134OXlhY+PDx4eHqjV6s4Fs3BhUwumTNQQwizMmpi9+uqrAKxZs6Zd5RVF4S9/+Qu//vWvWXj9m9fatWvx9vZm/fr1/OQnP0Gn07F69Wo+/fRTZs6cCcBnn31GQEAAu3fvJj4+3ix1EUJ0nUqlwtnZGWdn56YnfH1RAQ/knmd67nm+DQgnzd6VhtpK6uuqaNTXoTE0cs99Uxn3UCyONtYUZmfy5RfrUalUqBvVOCqOOGmccHZ0xsnJiaioKFMLUENDA3V1ddjZ2VnkwqYGgwFFUUyzXnU6HefPn6eyspKKigp0Oh06nY7KykqMRiNz584lOjradHx2drbpdycnJ9zd3XF3d8fLy4uhQ4eaXnN3dzf9e9ktrKwgNrb7zieEMLGoMWYZGRkUFBQQFxdnes7Gxobp06eTmJjIT37yE06ePIler29Rxs/Pj4iICBITEyUxE6IvufNO8PdHk5tLgKLwVPa5Fi/rgTI/P5weX4adowMA16yaEo3y8nKMRiMVFRVUVFSQm5sL0KJrLiMjg3/9618AaDQa7OzssLe3x87ODjs7OyZMmGBKYK5du0ZqaiparRaNRoO1tXVT8qdualHz8fExdfHV19dz8eJFrKysMBgMGI1GDAaD6feAgADT/o/FxcUcPHiQ+vp66uvrTclidXU1dXV13HPPPUycOBGA8vJyduzY0eb/KrVaTV1dnemxt7c3ixcvxt3dHTc3N7Ra2UBeiP7AohKzgoICgFYb2np7e5OVlWUqo9VqW42B8Pb2Nh3/Q83/IDarqGgaXKzX69Hr9d0W/42az2uu81uqgVjvgVhn6MZ6v/suLF/e9HsbA8oHrVoFNjam6wwbNoynnnrK1L1XWVnZ4sfT09NUtrq6umlNruuJU11dHWVlZaZLDB8+3JTE5eXlsXPnzpuG+aMf/Yjx48ej1+spKytj3bp1N+0OjI+Px82taZ/IiooKTp06ddPz6nQ6U7wODg6Ehobi6OiIi4uLqXXRxcUFR0dH1Gq1qayVlRUhISGm85jz70/+xqXe/V1P1Lm95+5wYvbKK6+Yuihv5vjx4y2a2zvqh+M9FEW57RiQW5X54x//2GbMu3btMk0RN5eEhASznt9SDcR6D8Q6QzfU28oK1q+/dZlt29p9uhsHuQOMHTsWvV5PQ0MDDQ0Npi9qer2e1NRUcq4PYr927RqNjY00NjaaWr+a9xM1Go2cOnWKwsLC6yFbUVZWZmpNU6vVpt+trKw4c+YMpaWlQNPAfEdHR6ytrbG2tkaj0aDRaLCxscHW1paqqiq23VA/e3t7jEYjZWVlLZJISyB/4wPLQKy3Oevc1ljQtnQ4MXv66adZunTpLcsMGTKko6cFmraFgaZWMd8bFiksKioytaL5+PjQ0NBAWVlZi1azoqIipkyZ0uZ5X375ZZ577jnT44qKCgICAoiLi/vPWJduptfrSUhIYNasWRY5tsVcBmK9B2KdwQz1Nhjg8GEoKAAfH4iJscgB5c31/tOf/jRg7rf8jUu9+7ueqHNzb93tdDgx8/DwwMPDPHvdDR06FB8fHxISEhg7dizQNHh3//79vPHGGwCMHz8ejUZDQkICS5YsASA/P5+zZ8/y5ptvtnleGxubFtP4mzV/czWnnriGJRqI9R6IdYZurLdGAzNmdP08PWQg3u+BWGeQeg8k5qxze89r1jFmV69e5dq1a1y9ehWDwWBaYDI4OBhHx6ZNPcLCwvjjH//Ifffdh0ql4tlnn+W1115jxIgRjBgxgtdeew17e3sefPBBAFxcXHj88cd5/vnnTYNeX3jhBSIjI7t31pEQQgghRA8za2L229/+lrVr15oeN7eC7d27l9jrU63T09PR6XSmMi+++CK1tbX89Kc/NS0wu2vXLtMaZgDvvPMO1tbWLFmyxLTA7Jo1a2QNMyGEEEL0aWZNzNasWXPbNcyUHyzjrVKpeOWVV3jllVdueoytrS2rVq1i1apV3RClEEIIIYRl6OTSz0IIIYQQortJYiaEEEIIYSEkMRNCCCGEsBCSmAkhhBBCWAhJzIQQQgghLIQkZkIIIYQQFkISMyGEEEIICyGJmRBCCCGEhZDETAghhBDCQkhiJoQQQghhISQxE0IIIYSwEJKYCSGEEEJYCEnMhBBCCCEshCRmQgghhBAWQhIzIYQQQggLIYmZEEIIIYSFkMRMCCGEEMJCWPd2AL1BURQAKioqzHYNvV5PTU0NFRUVaDQas13H0gzEeg/EOoPUeyDVeyDWGaTeA6nePVHn5pyjOQe5mQGZmFVWVgIQEBDQy5EIIYQQYiCprKzExcXlpq+rlNulbv2Q0WgkLy8PJycnVCqVWa5RUVFBQEAA2dnZODs7m+Ualmgg1nsg1hmk3gOp3gOxziD1Hkj17ok6K4pCZWUlfn5+qNU3H0k2IFvM1Go1/v7+PXItZ2fnAfOHfaOBWO+BWGeQeg8kA7HOIPUeSMxd51u1lDWTwf9CCCGEEBZCEjMhhBBCCAshiZmZ2NjY8Lvf/Q4bG5veDqVHDcR6D8Q6g9R7INV7INYZpN4Dqd6WVOcBOfhfCCGEEMISSYuZEEIIIYSFkMRMCCGEEMJCSGImhBBCCGEhJDETQgghhLAQkph10h/+8AemTJmCvb09rq6u7TpGURReeeUV/Pz8sLOzIzY2lnPnzrUoU19fz3//93/j4eGBg4MD8+fPJycnxww16JyysjKWL1+Oi4sLLi4uLF++nPLy8lseo1Kp2vx56623TGViY2Nbvb506VIz16Z9OlPnRx99tFV9Jk+e3KJMf7vXer2eX/3qV0RGRuLg4ICfnx+PPPIIeXl5LcpZ2r1+//33GTp0KLa2towfP54DBw7csvz+/fsZP348tra2DBs2jA8++KBVmY0bNzJq1ChsbGwYNWoUmzZtMlf4ndaRen/11VfMmjULT09PnJ2diYmJYefOnS3KrFmzps33eV1dnbmr0m4dqfO+ffvarE9aWlqLcv3tXrf1b5dKpSI8PNxUxtLv9ffff8+8efPw8/NDpVLx9ddf3/YYi3pfK6JTfvvb3ypvv/228txzzykuLi7tOub1119XnJyclI0bNyopKSnKAw88oPj6+ioVFRWmMk8++aQyePBgJSEhQTl16pQyY8YMZfTo0UpjY6OZatIxs2fPViIiIpTExEQlMTFRiYiIUObOnXvLY/Lz81v8fPzxx4pKpVIuX75sKjN9+nRl5cqVLcqVl5ebuzrt0pk6r1ixQpk9e3aL+pSWlrYo09/udXl5uTJz5kzliy++UNLS0pTDhw8rkyZNUsaPH9+inCXd688//1zRaDTKRx99pKSmpirPPPOM4uDgoGRlZbVZ/sqVK4q9vb3yzDPPKKmpqcpHH32kaDQaZcOGDaYyiYmJipWVlfLaa68p58+fV1577TXF2tpaOXLkSE9V67Y6Wu9nnnlGeeONN5Rjx44pFy5cUF5++WVFo9Eop06dMpX55JNPFGdn51bvd0vR0Trv3btXAZT09PQW9bnx/dkf73V5eXmL+mZnZytubm7K7373O1MZS7/X27ZtU379618rGzduVABl06ZNtyxvae9rScy66JNPPmlXYmY0GhUfHx/l9ddfNz1XV1enuLi4KB988IGiKE1vCI1Go3z++eemMrm5uYparVZ27NjR7bF3VGpqqgK0+EM8fPiwAihpaWntPs+CBQuUu+66q8Vz06dPV5555pnuCrXbdLbOK1asUBYsWHDT1wfKvT527JgCtPgQsKR7PXHiROXJJ59s8VxYWJjy0ksvtVn+xRdfVMLCwlo895Of/ESZPHmy6fGSJUuU2bNntygTHx+vLF26tJui7rqO1rsto0aNUl599VXT4/b+W9hbOlrn5sSsrKzspuccCPd606ZNikqlUjIzM03PWfq9vlF7EjNLe19LV2YPycjIoKCggLi4ONNzNjY2TJ8+ncTERABOnjyJXq9vUcbPz4+IiAhTmd50+PBhXFxcmDRpkum5yZMn4+Li0u74CgsL2bp1K48//nir19atW4eHhwfh4eG88MILVFZWdlvsndWVOu/btw8vLy9CQkJYuXIlRUVFptcGwr0G0Ol0qFSqVt39lnCvGxoaOHnyZIt7ABAXF3fTOh4+fLhV+fj4eE6cOIFer79lGUu4r9C5ev+Q0WiksrISNze3Fs9XVVURFBSEv78/c+fO5fTp090Wd1d0pc5jx47F19eXu+++m71797Z4bSDc69WrVzNz5kyCgoJaPG+p97ozLO19PSA3Me8NBQUFAHh7e7d43tvbm6ysLFMZrVbLoEGDWpVpPr43FRQU4OXl1ep5Ly+vdse3du1anJycWLhwYYvnH3roIYYOHYqPjw9nz57l5ZdfJjk5mYSEhG6JvbM6W+c5c+awePFigoKCyMjI4De/+Q133XUXJ0+exMbGZkDc67q6Ol566SUefPDBFpsCW8q9LikpwWAwtPmevFkdCwoK2izf2NhISUkJvr6+Ny1jCfcVOlfvH/rzn/9MdXU1S5YsMT0XFhbGmjVriIyMpKKignfffZepU6eSnJzMiBEjurUOHdWZOvv6+vL3v/+d8ePHU19fz6effsrdd9/Nvn37mDZtGnDzv4f+cq/z8/PZvn0769evb/G8Jd/rzrC097UkZjd45ZVXePXVV29Z5vjx40RHR3f6GiqVqsVjRVFaPfdD7SnTFe2tN7SOHzoW38cff8xDDz2Era1ti+dXrlxp+j0iIoIRI0YQHR3NqVOnGDduXLvO3RHmrvMDDzxg+j0iIoLo6GiCgoLYunVrq6S0I+ftqp6613q9nqVLl2I0Gnn//fdbvNbT9/p2OvqebKv8D5/vzPu8p3U2xn/961+88sorbN68uUXyPnny5BYTXKZOncq4ceNYtWoVf/3rX7sv8C7oSJ1DQ0MJDQ01PY6JiSE7O5s//elPpsSso+fsLZ2Ncc2aNbi6unLvvfe2eL4v3OuOsqT3tSRmN3j66advOztsyJAhnTq3j48P0JSZ+/r6mp4vKioyZeE+Pj40NDRQVlbWoiWlqKiIKVOmdOq67dHeep85c4bCwsJWrxUXF7f6JtGWAwcOkJ6ezhdffHHbsuPGjUOj0XDx4kWzfFj3VJ2b+fr6EhQUxMWLF4H+fa/1ej1LliwhIyOD7777rkVrWVvMfa9vxsPDAysrq1bfeG98T/6Qj49Pm+Wtra1xd3e/ZZmO/L2YU2fq3eyLL77g8ccf58svv2TmzJm3LKtWq5kwYYLpb743daXON5o8eTKfffaZ6XF/vteKovDxxx+zfPlytFrtLcta0r3uDIt7X3f7qLUBpqOD/9944w3Tc/X19W0O/v/iiy9MZfLy8ixuQPjRo0dNzx05cqTdA8JXrFjRaobezaSkpCiAsn///k7H2x26WudmJSUlio2NjbJ27VpFUfrvvW5oaFDuvfdeJTw8XCkqKmrXtXrzXk+cOFF56qmnWjw3cuTIWw7+HzlyZIvnnnzyyVaDhOfMmdOizOzZsy1uQHhH6q0oirJ+/XrF1tb2tgOpmxmNRiU6Olp57LHHuhJqt+lMnX/o/vvvV2bMmGF63F/vtaL8Z/JDSkrKba9haff6RrRz8L8lva8lMeukrKws5fTp08qrr76qODo6KqdPn1ZOnz6tVFZWmsqEhoYqX331lenx66+/rri4uChfffWVkpKSoixbtqzN5TL8/f2V3bt3K6dOnVLuuusui1tCISoqSjl8+LBy+PBhJTIystUSCj+st6Ioik6nU+zt7ZW//e1vrc556dIl5dVXX1WOHz+uZGRkKFu3blXCwsKUsWPHWkS9O1rnyspK5fnnn1cSExOVjIwMZe/evUpMTIwyePDgfn2v9Xq9Mn/+fMXf319JSkpqMY2+vr5eURTLu9fNSwmsXr1aSU1NVZ599lnFwcHBNAPtpZdeUpYvX24q3zyt/he/+IWSmpqqrF69utW0+kOHDilWVlbK66+/rpw/f155/fXXLXYJhfbWe/369Yq1tbXy3nvv3XSZk1deeUXZsWOHcvnyZeX06dPKY489plhbW7dI7ntTR+v8zjvvKJs2bVIuXLignD17VnnppZcUQNm4caOpTH+8180efvhhZdKkSW2e09LvdWVlpekzGVDefvtt5fTp06bZ4Zb+vpbErJNWrFihAK1+9u7dayoDKJ988onpsdFoVH73u98pPj4+io2NjTJt2rRW30Zqa2uVp59+WnFzc1Ps7OyUuXPnKlevXu2hWt1eaWmp8tBDDylOTk6Kk5OT8tBDD7WaTv7DeiuKonz44YeKnZ1dm+tVXb16VZk2bZri5uamaLVaZfjw4crPf/7zVut+9ZaO1rmmpkaJi4tTPD09FY1GowQGBiorVqxodR/7273OyMho8z1x4/vCEu/1e++9pwQFBSlarVYZN25ci5a7FStWKNOnT29Rft++fcrYsWMVrVarDBkypM0vG19++aUSGhqqaDQaJSwsrMWHuaXoSL2nT5/e5n1dsWKFqcyzzz6rBAYGKlqtVvH09FTi4uKUxMTEHqzR7XWkzm+88YYyfPhwxdbWVhk0aJByxx13KFu3bm11zv52rxWlqUXfzs5O+fvf/97m+Sz9Xje39t3s79XS39cqRbk+wk0IIYQQQvQqWcdMCCGEEMJCSGImhBBCCGEhJDETQgghhLAQkpgJIYQQQlgIScyEEEIIISyEJGZCCCGEEBZCEjMhhBBCCAshiZkQQgghhIWQxEwIIYQQwkJIYiaEEEIIYSEkMRNCCCGEsBCSmAkhhBBCWIj/Hwz0WpEfs+65AAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def generate_thetas(n):\n", + " random_steps = np.random.random(n)\n", + " return np.concatenate(([0], np.cumsum(random_steps / np.sum(random_steps) * (2*np.pi))))\n", + "\n", + "n = 10\n", + "thetas = generate_thetas(n)\n", + "thetas_inf = np.linspace(0, 2*np.pi, 1000)\n", + "\n", + "plt.figure(figsize=(7, 7))\n", + "plt.plot(np.cos(thetas), np.sin(thetas), label='polygon')\n", + "plt.scatter(np.cos(thetas), np.sin(thetas), color='red', label='vertices')\n", + "plt.plot(np.cos(thetas_inf), np.sin(thetas_inf), 'k--', label='unit circle', alpha=0.5)\n", + "plt.legend()\n", + "plt.title(f'Polygon with {n} sides')\n", + "plt.grid(True)\n", + "plt.xlim(-1.1, 1.1)\n", + "plt.ylim(-1.1, 1.1)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 122, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Optimal angles (radians): [0. 0.63040051 1.25944297 1.88997226 2.51787685 3.14660756\n", + " 3.7751046 4.40249926 5.02981518 5.6572878 6.28318531 6.28318531]\n", + "Maximum perimeter: 5.564607445922133\n", + "2 * pi = 6.283185307179586\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "from scipy.optimize import minimize\n", + "import matplotlib.pyplot as plt\n", + "\n", + "def polygon_perimeter(theta, n):\n", + " points = np.array([[np.cos(t), np.sin(t)] for t in theta])\n", + " perimeter = 0\n", + " for i in range(n-1):\n", + " perimeter += np.sqrt(np.sum((points[i+1] - points[i])**2))\n", + " perimeter += np.sqrt(np.sum((points[0] - points[-1])**2))\n", + " return -perimeter\n", + "\n", + "def constraint_increasing(theta):\n", + " return np.array([theta[i+1] - theta[i] for i in range(len(theta)-1)])\n", + "\n", + "\n", + "def optimize_polygon(n):\n", + " theta0 = generate_thetas(n)\n", + " \n", + " constraints = [\n", + " {'type': 'ineq', 'fun': constraint_increasing},\n", + " {'type': 'eq', 'fun': lambda x: x[0]},\n", + " {'type': 'ineq', 'fun': lambda x: 2*np.pi - x[-1]}\n", + " ]\n", + "\n", + " result = minimize(\n", + " lambda x: polygon_perimeter(x, n),\n", + " theta0,\n", + " constraints=constraints,\n", + " method='SLSQP'\n", + " )\n", + " \n", + " return result.x\n", + "\n", + "n = 10\n", + "optimal_angles = optimize_polygon(n + 1)\n", + "\n", + "plt.figure(figsize=(7, 7))\n", + "t = np.linspace(0, 2*np.pi, 100)\n", + "plt.plot(np.cos(t), np.sin(t), 'k--', alpha=0.5)\n", + "\n", + "points = np.array([[np.cos(t), np.sin(t)] for t in optimal_angles])\n", + "points = np.vstack([points, points[0]])\n", + "plt.plot(points[:, 0], points[:, 1], 'b-', linewidth=2)\n", + "plt.scatter(points[:-1, 0], points[:-1, 1], color='red')\n", + "\n", + "plt.axis('equal')\n", + "plt.grid(True)\n", + "plt.title(f'Optimal {n}-sided Polygon Inscribed in Unit Circle')\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "\n", + "print(f\"Optimal angles (radians): {optimal_angles}\")\n", + "print(f\"Maximum perimeter: {-polygon_perimeter(optimal_angles, n)}\")\n", + "print(f\"2 * pi = {2 * np.pi}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Projection on convex sets $K=\\{x\\in\\R^d, Cx\\leq b\\}$\n", + "\n", + "Let compute the projection of a point $x_0$ on the convex set $K=\\{x\\in\\R^d,\n", + "Cx\\leq b\\}$, where $C$ is a matrix and $b$ is a vector. The projection is\n", + "defined as: \n", + "$$\n", + "\\Pi_K(x_0) = \\arg\\min_{x\\in K} \\|x-x_0\\|^2.$$\n", + "\n", + "1. Define the projection operator when $C=\\mathrm{Id}$ and $b=0$. We denote by $\\Pi_{\\mathbb{K}_-}$ this projection operator. \n", + " How can you compute it using Python?\n", + "2. Write the KKT conditions for the quadratic optimization problem when $K=\\{x\\in\\R^d, Cx\\leq b\\}$: \n", + " $$\n", + " \\min_{x\\in K}\\left\\{ \\frac12 ||x||^2-\\langle x_0,x\\rangle\\right\\}.$$\n", + " How is it related to the projection operator?\n", + "3. Show that, for all $\\tau>0$, we have \n", + " $$\\forall \\mu\\in\\mathrm{K}_-, \\quad\n", + " \\langle\\lambda^*-\\mu,\\lambda^*-(\\lambda^*+\\tau(b-Cx^*))\\rangle\\leq 0.$$\n", + " Express this condition in terms of the projection operator\n", + " $\\Pi_{\\mathbb{K}_-}$.\n", + "4. Implement Uzawa’s algorithm to compute numerically the projection operator on $K=\\{x\\in\\R^d, Cx\\leq b\\}$:\n", + " $$\\lambda_{n+1}=\\Pi_{\\mathbb{K}_-}(\\lambda_n+\\tau(b-Cx_n)),\\text{ then }\n", + " x_{n+1}=C^T\\lambda_{n+1}+x_0.$$\n", + "5. You can adapte the code of the first exercise to use the projection operator. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The polygonal isoperimetric inequality\n", + "\n", + "Given an perimeter constraint $L$ and a fixed number of sides $N$, what is the polygon with $N$ sides that maximises the enclosed area? We represent a polygon in $\\R^2$ by a collection of point $\\{(x_i,y_i)\\}_{i=1,\\dots,N}$, ordered in a counterclockwise fashion.\n", + " We admit that the area of this polygon is given by \n", + "$$A=\\frac12\\sum_{k=1}^N (x_ky_{k+1}-y_{k}x_{k+1}).$$\n", + "\n", + "\n", + "You must enter as parameters the number of sides of the polygon you seek and use whichever algorithm you see fit (typically, a Uzawa method).\n", + "\n", + "Plot your results graphically." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The obstacle problem\n", + "\n", + "Let $g$ be a given continuous function on the interval $[0,1]$. We consider an \\textit{obstacle problem}: find a function $ u: [0,1] \\longrightarrow \\mathbb{R}$ such that:\n", + "\n", + "$$\n", + "\\left\\{\n", + "\\begin{array}{ll}\n", + "-u''(x) \\geq 1 & x \\in (0,1) \\\\\n", + "u(x) \\geq g(x) & x \\in (0,1) \\\\\n", + "\\left( -u''(x) - 1 \\right)(u(x) - g(x)) = 0 & x \\in (0,1) \\\\\n", + "u(0) = u(1) = 0 & \\\\\n", + "\\end{array}\n", + "\\right.\n", + "$$\n", + "\n", + "The first equation represents a minimum concavity for the function $u$, the second equation represents the obstacle: $u$ must remain above $g$. The third equation expresses the fact that we must satisfy at least one of the two previous equations with equality: either we solve $-u''(x) = 1$, or $u(x) = g(x)$, and we are on the obstacle." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "### Associated minimization problem\n", + "\n", + "We discretize this problem by introducing a uniform mesh: $x_j = jh$, where $h$ is the step size of the mesh, and $j \\in \\{0, \\dots, n+1\\}$, with $n \\geq 1$ an integer and $h = \\frac{1}{n+1}$. Let $ g_j = g(x_j) $ for $ j \\in \\{0, \\dots, n+1\\} $. We seek values $ u_j = u(x_j) $ for $ j \\in \\{0, \\dots, n+1\\} $ such that:\n", + "\n", + "$$\n", + "\\left\\{\n", + "\\begin{array}{ll}\n", + "\\displaystyle -\\frac{u_{j-1} - 2u_j + u_{j+1}}{h^2} \\geq 1 & j \\in \\{0, \\dots, n+1\\} \\\\\n", + "u_j \\geq g_j & j \\in \\{0, \\dots, n+1\\} \\\\\n", + "\\displaystyle \\left( -\\frac{u_{j-1} - 2u_j + u_{j+1}}{h^2} \\right) (u_j - g_j) = 0 & j \\in \\{0, \\dots, n+1\\} \\\\\n", + "u_0 = u_{n+1} = 0 & \\\\\n", + "\\end{array}\n", + "\\right.\n", + "$$\n", + "\n", + "Recall that $ -\\frac{u_{j-1} - 2u_j + u_{j+1}}{h^2} $ is the finite difference approximation of $ -u''(x_j) $.\n", + "\n", + "We introduce the matrix $ A \\in S_n(\\mathbb{R}) $, defined by:\n", + "\n", + "$$\n", + "A = \\frac{1}{h^2} \\left( \\begin{array}{ccccc}\n", + "2 & -1 & 0 & \\dots & 0 \\\\\n", + "-1 & 2 & -1 & \\vdots \\\\\n", + "0 & \\ddots & \\ddots & \\ddots & 0 \\\\\n", + "\\vdots & & -1 & 2 & -1 \\\\\n", + "0 & \\dots & 0 & -1 & 2\n", + "\\end{array} \\right).\n", + "$$\n", + "\n", + "We also define the column vectors $ b $ and $ g $ of $ \\mathbb{R}^n $ as follows:\n", + "\n", + "$$\n", + "b = \\left( \\begin{array}{c}\n", + "1 \\\\\n", + "\\vdots \\\\\n", + "1\n", + "\\end{array} \\right), \\quad g = \\left( \\begin{array}{c}\n", + "g_1 \\\\\n", + "\\vdots \\\\\n", + "g_n\n", + "\\end{array} \\right).\n", + "$$\n", + "\n", + "Recall that if $ u = \\left( \\begin{array}{c} u_1 \\\\ \\vdots \\\\ u_n \\end{array} \\right) $, then\n", + "\n", + "$$\n", + "u \\text{ is a solution of (2)} \\Longleftrightarrow u \\text{ is a solution of } \\left\\{\n", + "\\begin{array}{l}\n", + "\\displaystyle \\min_{v \\in K} \\left\\{ \\frac{1}{2}(Av, v) - (b, v) \\right\\} \\\\\n", + "K = \\{v \\in \\mathbb{R}^n : v \\geq g \\}\n", + "\\end{array}\n", + "\\right.\n", + "$$\n", + "\n", + "We define the function $J$ on $\\mathbb{R}^n$ by:\n", + "\n", + "$$\n", + "J(v) = \\frac{1}{2} (Av, v) - (b, v).\n", + "$$\n", + "\n", + "### Problem Resolution\n", + "\n", + "Consider the specific case where $g(x) = \\max \\left( 0, 1 - 100(x - 0.7)^2 \\right)$.\n", + "\n", + "We want to solve this problem using the projected gradient algorithm. Denote by $\\Pi_K =\\{v\\geq g\\}$ the projection onto the convex set $K$. Without proving it, we can use the fact that:\n", + "\n", + "$$\n", + "\\Pi_K(v) = \\left( \\max(v_i, g_i) \\right)_{1 \\leq i \\leq n}.\n", + "$$\n", + "\n", + "1. Write a gradient method with a fixed step size to find the minimum of $J$ over $\\mathbb{R}^n$. Test this method and verify that it converges to the desired result.\n", + "2. Adapt the previous program to implement the projected gradient method with a constant step size. For instance, you can choose the optimal step size $\\rho_{\\textrm{opt}} = \\frac{2}{\\lambda_1(A) + \\lambda_n(A)}$ of the gradient method without constraints. Also, don't forget to set a maximum number of iterations and a relevant stopping criterion.\n", + "3. Test the program for different values of $n$. Represent the graph of the solution and the graph of the obstacle on the same plot. Verify that if $u(x) \\neq g(x)$, then $-u''(x) = 1$ (using the finite difference approximation).\n", + "4. Implement the Uzawa algorithm to solve this problem and compare the efficiency of the methods implemented. Test with different choices of obstacles.\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "base", + "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": "3.12.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}