Microeconomic_hw.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import linprog\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Polygon\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aSSkoYMm5c1X6vqqqjB8/ntTUVFauXHnD6PHgwYNMnDiRcePG8fnnn5e+b21tjZeX1y3b/eWXX8jMzCQzM5Pp06czffr00te//PJLhWpTFAVVVW9Zi7+/P/b29gBYWVmh0938f7mQkBDmzp1LbGwsBw8eZPDgwaxevZq2bdvyyCOPVKiWoqIikpOTadWqFUVFRZw8ebL0s/3795dethdCiLqiygGsKEoA8A8gVFXVDoAeeMhShTUU/d3c6OHszOsJCRSWlFT6+xMnTuTo0aOsXr26NMgAkpKSuPvuu/n444/56KOPOHjw4A1zspaWmZnJunXryMvLo6ioiOXLl7N161aGDBlSoVrOnDnDmjVryh1dX+Pr68ujjz7Kt99+S1paGrNmzbrpmLS0NFasWEFOTg7FxcWsW7eOr7/+mq5du+Lo6Mj999/PK6+8Qm5uLn/88QerVq1i7NixlvxxCCFEtVX3ErQVYK8oihXgACRXv6SGRVEUXjIaOZuXx9cVuKR6vfj4eP7973+zb98+fH19S/ffLl26lLvuuospU6YwfPhwHBwcePHFF8sMK0spLCzkpZdewsvLC09PTxYtWsRPP/2En5/fbWvJzs5m3LhxLFu2DBsbm5va7tu3b+lK5uv/WFlZMX78+JuOVxSFxYsXExgYiLu7Oy+88ALvvvsuvXv3Bsxzw1euXMHb25tRo0axePFiGQELIeqcKi/CUlU1SVGUtwATcAVYr6rqeotV1oD8zcODTo6OzI+PZ7SPD3pFqdD3jEZj6SXevxo3btwNr1944QVeeOGFKtVXkT3AXl5e7N69u8zP9u/fX24tRUVFjBo1ijlz5pR7447Kjty9vLzYsmVLue00adKEn376qVJtCiFEbVPK+wf+tl9UFHdgJfAgkAl8B3yvquqXfzluAjABwMfHJ2TFihXVKrimTZ48meLiYhYtWmTRdn8HXgNmA30t2nLZpk+fzqlTp/Dx8eHuu+8mMjISgJycHJycnGqhArP169fz4Ycf0rRpU8C84rl///41cq7a7lttkr7VPw21XyB9q4x+/frFqqoaWtZn1QngkUCkqqrjr75+BAhXVfWp8r4TGhqq7tmzp0rnqy19+/YlMzOTffv2WbTdYlWl3a5d2Ot07A0NRangKNjSNm/eTN++fTU5d02TvtVPDbVvDbVfIH2rDEVRyg3g6swBm4BwRVEcFHOaDACOVqO9Bk2vKEw3GNifm8tvGRlalyOEEEJjVQ5gVVV3At8DccDBq239x0J1NUhjfHww2NoyLz6+3LldIYQQjUO1VkGrqjpbVdU2qqp2UFV1rKqq8hT6W7DW6ZhmMBCdnc3mzEytyxFCCKEhuRNWLXvc1xdfGxvmxcdrXYoQQggNSQDXMju9nucDA9mUmUlMVpbW5QghhNBI/Q3gzENwaC6olb+7lNae9PeniZUV800mrUsRQgihkfobwPEr4MDLsHkY5NevVcVOVlZMDgxk9YUL7M/J0bocIYQQGqi/AdzpNQhbDKkbYW0IZMRpXVGlPB0QgLNez3yZCxZCiEap/gawokDLJ2HgNlCLYEMv+PO/WldVYe7W1kwKCOC78+c5fvmy1uUIIYSoZXUjgPfPgs1/q9p3PXtAZBx49oSdj8Ou/wfF9WM31HOBgdjpdCyUuWAhhGh06kYAp22DjNiqf9/OC/qth3bT4dR/YMMdkFv3Q83bxob/8/Pjy9RU4vPytC5HCCFELaobAZx5EPLSoKAa23J0euiyAO74ES4dh7XdIGWD5WqsIS8GBaEAb8ooWAghGhXtAzgvDYqvgLUzZO6//fG3E3QvDNkNdn4QNQQOz6/TW5UC7ewY5+vLpykppOTXj0vnQgghqk/7AM7YC3pb87ytpVYyu7SCITFgfMg8v7z1Xiiou7d+nBYURKGq8q/ERK1LEUIIUUvqQADHQtFlKMmH839Yrl0rR+i5HELeh+Q1sDYULh6wXPsW1MLBgYe8vVmclMSFwkKtyxFCCFELtA/g81e3EQFk7LZs24oCrZ+BgVvMl7nXh8OZLy17DguZaTSSW1LC+zIKFkKIRkH7AL64939/v5wExTWwGtirp3mrkkd3iB4LuydBcYHlz1MN7R0duc/Tk/eTksguKtK6HCGEEDVM2wAuzL7xNpJ6B/M9nmuCvQ/03whtX4CTH8HGPnC5bo02ZxmNZBYV8VFSktalCCGEqGHaBvDFfWBl/7/XahFcrMFbSuqsoOub0Pt7yDoMa7rBud9r7nyVFOLszBB3d/6VmMjl4mKtyxFCCFGDtA3gjLgb71pVfBnOR9f8eQ1/N29VsvWEqEFw5A1Q1Zo/bwXMMho5X1jIZykpWpcihBCiBmkbwMV55tXPOlvz5edr79UG1zYwZCcE/R32TYNtfzdfEtfYHW5u3OHqyhsJCRSU1N39y0IIIapH2wBuNw1GFV9dBa3C3aeg11e1d35rZ+j1DXR9G5J+hrVhBLvn1t75yzHLaCQxP58vzp3TuhQhhBA1RNsAVhRQdIBy9bXO/F5t19B2Cgz4HQqzWHxvHEPaXKzdGv5isLs7IU5OLDSZKJJRsBBCNEjab0OqK7z7QGQcpy448fpwE8ROhhJtboqhKAqzjEb+zMvj2/PnNalBCCFEzZIAvp6DP5NXd2b5Hk84/h5s6g9XtFkMdY+nJ+0dHJgfH09JHVkgJoQQwnIkgP+iWNXx5u8B0PMr8yrtNd3Mj0usZTpFYYbRyOHLl1mVnl7r5xdCCFGzJIDLEzwKhuwCaxfY1A+O/qvWtyo96OVFczs75sXHo8ooWAghGhQJ4Ftxaw+RuyHwHtj7PPzxEBTm1NrprXQ6phsMxObksP6itgvDhBBCWJYE8O1Yu5jvnNVlISR8D+u6Q9axWjv9I76+BNraMi8+vtbOKYQQouZJAFeEopj3LPfbAPnpsC4MTCtr5dQ2Oh0vBgWxLSuLbZl195nGQgghKkcCuDJ8+8PQOHBtD9tHwN4XoaTmn1z0hJ8fXtbWMgoWQogGRAK4shwCYeBWaPkUHH0Lfh8IV1Jr9pR6PVMCA1l38SJ7srW/XaYQQojqkwCuCr0NhH0IEV/AhV2wthuc31Gjp3wqIAA3Kyvmm0w1eh4hhBC1o94GcNTFi7x0+jQJebX08IayNB0Lg2NAbw8b74Tji2psq5KLlRXPBATwY3o6h3O1v1+1EEKI6qm3AbwjO5v5JhPBMTHcf+gQGzMytNkr694JIveAXyTE/gN2jIGimgnIZwMDcdTpmC9zwUIIUe/V2wCeZTRyukcPphoMbMvKYtCBA7TdtYv3EhPJLKzlezjbuMGdq6DTXIj/GtaFQ/ZJi5/Gw9qaJ/39WZGWxqnLly3evhBCiNpTbwMYINjengXNmpEQHs4XbdrQxNqayadOERAdzYTjx9l36VLtFaPooMMs6LcW8lJgXSgk/GTx0zwfFIS1ovB6QoLF2xZCCFF76nUAX2On1zPW15cd3boRGxLCwz4+fJmaStfYWHrFxbE8NZX82nqsn99giIwF51aw7T7YN8OiW5X8bG0Z7+fH0nPntJ3/FkIIUS0NIoCv183ZmU9atyYpIoJ3mjfnfGEhY44eJSg6mpmnTxNfG6HlaIRB26DFBDiyEKIiIc9yjxWcajCgAm/JKFgIIeqt+hvAeecheV25H7tbWzM5KIhj3buzvlMnerq48LrJRLOYGO45eJB1GRk1+5g/vR10/zf0+BzObzdvVUrfaZGmjXZ2jPHx4ZOUFNIKCizSphBCiNpVrQBWFMVNUZTvFUU5pijKUUVRIixV2G0deg02R8KBV6CkuNzDdIrCoCZN+KljR86EhzPdYCA6O5vIAwdovWsX/0pI4GJNLtpq/hgM3gGKFWy8A04utshWpekGA3klJbyTmGiBIoUQQtS26o6A3wPWqqraBugMHK1+SRXU5XVo9ujVIL4L8i/c9isGOzvmNWtGQkQEy9u2xdvamuf//JOA6GjGHztGXE0t2mrSzTwv7DMQdj8FMY9CUfVWMbd2cGCklxcfJiXV7C8QQgghakSVA1hRFBegD/AZgKqqBaqq1t7TAqzszZd3wz6GtM2wNgQyYiv0VVudjod9fPijWzf2hoQw1seHFWlphMTGEvfEE2SEhpJXXP6oukpsm0DfX6DDbDizDNb3hEt/VqvJmUYjl4qL+SApyUJFCiGEqC1KVW9eoShKF+A/wBHMo99Y4FlVVXP/ctwEYAKAj49PyIoVK25uLCPO/MQh1/ags6l0Lc4Fx2h/cTY2xRc54fos5xz/Vuk2coC1wCepqRT4+OAEDAFGAL6Vbu3WmuTtpO3FeYDKMfeZXLCr+pX7mcBhYAVgX4Hjc3JycHJyqvL56jLpW/3UUPvWUPsF0rfK6NevX6yqqqFlfqiqapX+AKFAEdDj6uv3gNdu9Z2QkBC1TF9ZqeoKe1W9dLrszyviynlV3TRIVZejqjFPqGrRlSo10/bOO1W/ESNUDh5UiYpSiYpS2x04oH6Xnq4Wl5RUvb6/unRaVX/raq53/8uqWlxUpWaiMzNVoqLUt0ymCh0fFRVVpfPUB9K3+qmh9q2h9ktVpW+VAexRy8nE6swBJwKJqqpeW9r7PdCtGu1Vj50n9F0D7WfCn5/Cht6Qc7bSzSiAw8mT0KEDhIeD0ciR7GxGHjyI686dPG8yccESc65OTWHQH9DsMfM89pa/VWge+6/CXV0Z4ObGWwkJlr9sLoQQosZUOYBVVT0HJCiK0vrqWwMwX47Wjk4PnedBn1Vw6ZR5XvgWW5Vuy84OmjaFiAho144cW1v+dfo0XtHR3HnsGNHVfTSglT30+My8XSk1qlLz2NebZTRyrqCAz8+dq149Qgghak11V0E/AyxXFOUA0AWYX/2SLCBwuPkBCQ4BsHkoHHwV1GrcCUunA29v6NoVQkNRfX3ZmpZGz7g4/GJjeTslhStVHX0qivmGHYO2m2tc3wtOfVqpJvq6uRHh4sIbJhOFtXXHLyGEENVSrQBWVXWfqqqhqqp2UlX1XlVVL1qqsGpzbgGDoyH4YTg4G7YMhwILlOfkBK1aQc+e0KIF54qLeeH4cVyjoxn555+cunKlau16hEFkHHj3gV3/BzufgOKK3bVLURRmGY3E5+ezPDW1aucXQghRq+rvnbAqwsoRIpZB6Idwbj2sDYWL+yzUthUEBkJYGHTuTKGbG98nJNBy507aHjjANxcuUFzZFeal89iz4M/PKjWPfVeTJnRxcmKByVT58wohhKh1DTuAwXyJt9VTMGALFOfD+gg4vdSy7bu7mxdtRUSA0cixnBweurpo61mTifTK3C5Sp4fOc6HPz5Wax1YUhZkGAyeuXGHlecvdd1oIIUTNaPgBfI1XhPluVB7h5jtR7ZpoDmRLsrU1L9oKD4d27ci1teX906fxjo6m99GjbMvOvraF6/YC7670PPb9Xl60trdnfnx8xc8jhBBCE40ngAHsfaD/Bmg7FU59DBv7QG4NPFHo+kVbYWGofn78kZ5On6uLtt5MSeFyRRZtObeAwTEQPLpC89h6RWGG0cj+3Fx+vVD5LU2WZDKZcHJyorgGtkbNmTOHMWPG1Ll2hw4dytKlFry6IoRo0BpXAAPorKDr63DHSsg6Yn5K0blNNXc+R0fzoq2ICGjZkrSSEqZeXbT191OnOH75NveEtnKAiC8g9IMKzWM/7O1NsJ0d80ymSo2ClyxZQseOHXFwcMDX15eJEyeSmVnxO4sGBwezcePG0tcGg4GcnBz0en2F27CU+fPn07RpU5ycnAgMDOTBBx+0+DnKCus1a9Ywbtw4i59LCNEwNb4AvibofvMlXjtviBoMhxdY5ClF5bKygoAA1LAw6NKFInd3fkhKos2uXbTev5/l6enlL55SFGg1qULz2NY6HVODgojJziaqggH69ttvM23aNN58802ysrKIiYkhPj6eQYMGUVDPHne4dOlSli1bxsaNG8nJyWHPnj0MGDBA67KEEOImjTeAAVxaw+CdEDQS9s+EbffhZF1Us+dUFHBzg/btzXPFwcGcyM1lzKFDuMTE8Ex8POfLC70KzmM/5uuLn40Nc+Pjb1tOdnY2s2fPZtGiRURGRmJtbU1wcDDffvst8fHxfPnll4B5xDdixAgefPBBnHjgQJkAACAASURBVJ2d6datG/v37wdg7NixmEwm7r77bpycnHjjjTc4e/YsiqJQVGT+efbt25eXXnqJnj174uTkxN13382FCxcYPXo0Li4uhIWFcfbs2dK6nn32WYKCgnBxcSEkJIRt27ZV6Me7e/duhgwZQvPmzQHw9fVlwoQJpZ8nJyczfPhwmjRpQosWLfjkk0/KbGfz5s0EBgbe8N61Uf7atWuZP38+33zzDU5OTnTu3Lm0j59+at7DXVJSwty5czEajXh7e/PII4+QlZUFUPqzWbp0KQaDAU9PT+bNm1eh/gkhGo7GHcAA1k7Q62vo9g4k/co398XR0rOKe3kry9YWgoPNQdy+PZft7fngzBl8oqPpeeQIm7Oybr6MXDqP/eJ189imGw6x0+t5ISiIqMxMoq/+o1+eHTt2kJeXx/3333/D+05OTgwdOpQNGzaUvrdq1SpGjhxJRkYGDz/8MPfeey+FhYUsW7YMg8HA6tWrycnJYerUqWWea8WKFSxbtoykpCT+/PNPIiIieOyxx8jIyKBt27b885//LD02LCyMffv2lZ5r5MiR5OXdfl90eHg4X3zxBW+++SZ79uy5aQ561KhRBAYGkpyczPfff8/MmTPZtKlyUxCRkZHMnDmTBx98kJycnNJfRK63ZMkSlixZQlRUFKdPnyYnJ4enn376hmO2b9/O8ePH2bRpE6+++ipHj9be0zyFENqTAAbzqLTNZBgQhaNNMSvHnGLU2a9q7/w6HXh5QZcu5kVb/v5EX7hAv7178YmNZUFyMrnXB4nOCrq+cXUe+6h5q9K5jTc0+f/8/fGwsmLebUbB6enpeHp6YmVlddNnfn5+pKenl74OCQlhxIgRWFtbM2XKFPLy8oiJialwNx977DGaN2+Oq6srQ4cOpXnz5gwcOBArKytGjhzJ3r17S48dM2YMHh4eWFlZ8fzzz5Ofn8/x48dve44xY8awaNEi1q1bx5133om3tzcLFy4EICEhge3bt/P6669jZ2dHly5deOKJJ1i2bFmF+1BRy5cvZ8qUKTRr1gwnJycWLFjAihUrSq8IAMyePRt7e3s6d+5M586dywxyIUTDJQF8Pe/ejFjZjUOp9ny1YzTv7fkH1sW1PAfq6AgtW5oXbbVqxXlVZeaJE7ju2MG9p05x7PpFW0H3Q+Tuq/PYQ+DwwtJ5bEe9nsmBgfyakcHeS5fKPZ2npyfp6ek3BMM1KSkpeHp6/u90QUGlf9fpdKUjyYry8fEp/bu9vf1Nr3Nyckpfv/3227Rt2xZXV1fc3NzIysq64ZeBWxk9ejQbN24kMzOTjz/+mFdeeYV169aRnJxMkyZNcHZ2Lj3WaDSSVAPPU05OTsZoNN5wnqKiIlKvu1OZr+//HnTp4OBwQ/+FEA2fBPBfpF+x5ZFvmvOv1s/xjxOLiNrUD7/LFQ8Zi7GyAn9/CA2FLl0o9vBgVVISbXftouX+/Sw7f56ikpK/zGPPgG33Q4H5svPTAQG46PUsMJnKPU1ERAS2trb88MMPN7yfm5vLmjVrbljAlJDwvy1bJSUlJCYm4u/vD5hvBGIp27Zt4/XXX+fbb7/l4sWLZGZm4urqWum9zdbW1owcOZJOnTpx6NAh/P39ycjI4NJ1v5CYTCYCAgJu+q6joyOXr/tlp7i4mPPX3eDkdv319/cn/rqrDyaTCSsrqxt+6RBCNG4SwGUoKlF4PuRfPNDrGzpn7mfv2q70Sd2iTTHXFm21a1e6aOvPy5d55PBhXHbuZGJ8PKmqzXXz2L/AujDIPIibtTWTAgL4/vx5juXmltm8q6srs2fP5plnnmHt2rUUFhZy9uxZRo4cSWBgIGPHji09NjY2lh9++IGioiLeffddbG1tCQ8PB8yj29OnT1uky5cuXcLKygovLy+Kiop49dVXya7gk6eWLFnCr7/+yqVLlygpKWHNmjUcPnyYHj16EBQURM+ePZkxYwZ5eXkcOHCAzz77jNGjR9/UTqtWrcjLy+PXX3+lsLCQuXPnkp//vwVvPj4+nD17lpJyHn4xatQo3nnnHc6cOUNOTk7pnHFZl/qFEI2TBPAtfGd8gO5DdnHRxp1Nvw9gytG3a3ar0u1cXbSl9ugB7dtzxcGBj8+cwTc6mvCjR/nd7zHU/pug8BKsC4ezX/FcYCB2Oh0LbzEKnjp1KvPnz+eFF17AxcWlNKw2bdqEra1t6XH33HMP33zzDe7u7ixbtowffvgBa2trAGbMmMHcuXNxc3PjrbfeqlY3hwwZwtChQ2nVqhVGoxE7O7sbLn/fiouLC/Pnz8dgMODm5sbUqVNZvHgxvXv3BuDrr7/m7Nmz+Pv7c9999/HPf/6TQYMG3dSOq6srH330EU888QQBAQE4OjresCp65MiRAHh4eNCt282PwX788ccZO3Ysffr0oWnTptjZ2bFo0aKq/DiEEA2Vqqq19ickJEQt01dWqrrCXlUvnS7781rU7s471eadO99QuHNBlvrd1r+r6nLUb7eOUJ0Ksmvvh3a7P7m5KidOqGzdqhIVpXrs2qW+ezpOLVrXW1WXo6q7n1GnHDuk6qOi1DOXL6tRUVFV+rnMnj1bHT16dJW+W1uq2rf6QPpW/zTUfqmq9K0ygD1qOf98ywi4Ai5ZuzCy93e82OUN7k/8gV3rutMmq45sGXFwMC/a6tkTWrXigqIwOT4LR7tX+cnnUTixiPlnxhNYks7s2FieffZZzp07p3XVQgjR6EkAV5Si8Fa7FxnQfxNNCjLYta47I0zfaV3V/+j15kVbISHQtSv5nj7cZ/UoD7i/QtHFA8SlP8mm16dz8OBBXn31Va2rFUKIRq/uBHBJDd+BykK2+PSlW2QcB9068t32B3g7dgpWJYVal/U/igKuruZFWxERfNfucZwfLcLjwQsk/fIHqqqyePFiFEXB3t6+ws3OmTOn9K5YQgghqq9uBHC76dD8cbD317qSCkl2CKDvgM0savU0U46/w6ZNA/C5Ugcv69rYgNGIeuYsVvcNx8ZGd/VtHU3vGsJX+/bJYwuFEEIjdSOAO78G3T8Gve3tj60jCvU2/CN0EaMjviQkI5a4td3olbZd67LK5u9PkY8/BUWgt9ZTVFhCeOEfzDJF02nPHhYnJXGpjBtxCCGEqDl1I4Drsa+ajiZ8SAy5ekeiNvXjH8fe03arUnlSU+HJJ2n60cf4DevFlawC9mdM4m85G3nq5EkCoqN5+sQJDpezX1gIIYRlSQBbwCG3joRG7uHXgL/xXtxkvtrxMI6Fdey2gj/8AB9+yLAWLUiaMpd2y7Zi7d6FhSkzSbb9nr97uPJJSgoddu+m7969fJeWRmE5N5kQQghRfRLAFpJt48r9d/zAjM7zecD0LTHrw2mZfULrsm4SCNCkCW+dL+Jy343Q6hn8znzIf5OeJqlrUxY2a8bZvDweOHIEY0wMc86cITn/5kceCiGEqB4JYAtSFR0L289gSL91+OSlsmdtKPcm/Kh1WTczGCgoLOTVtAsQ+j5EfAkZsXhuCmeanYk/w8NZ3aEDXZyceDU+HkN0NCMPH2bzxYuyaEsIISxEArgGbPIdSEhkLMdc2vDjtvtZuHca+rq0zcrNDVxdec9kIr+kBJqOhiExoHeETf3QH3+fYR4e/NapEyd79OC5oCB+v3iRfvv30373bj5ITCRbFm0JIUS11N8ALi6AnLNaV1GuBEcDdwzaxuIWTzLt6BusjxqMV16a1mX9j9FIXkEBb127K5ZbR4jcAwF/g7jJsONhKMyhub09bzZvTmJEBP9t3RpHvZ5nTp0iIDqap06c4JA8Qk8IIaqk/gbwgZdhTRfz03/qqAK9LU91X8yj4f8lIj2auDXd6JFe8QfY1yh3d3B2ZqHJZH6sIYCNK9zxA3SeD6ZvYX0PyD4OgL1ez6N+fuwOCWFnt2783dOTz1NS6LhnD3fu3cs3aWkUyKItIYSosPobwC2fBKfmsOVu2P8ylBRrXVG5ljZ7lIjB0RTobNi6sQ8TT3yk/VYlRQGjkZy8PBZf95xbFB20nwH91kNeGqwNg7/MY3d3cWFJ27Yk9ezJm82akZifz0NXF229cuYMiXl5tdwZIYSof+pvADs1hcF/QLPH4fBc2HwX5KVrXVW59rt3IWRoLBt8B/HRnkl8Ef0I9kWXb//FmuThgeLoyOz4eEr++guB7wCIjAPXtrDtftg77abbhXpYW/OCwcDJHj34rWNHQpycmBsfT3BMDH8/dIhNsmhLCCHKVX8DGEBvB+GfQfdPIG0LrA2BC3u0rqpcmTbu3H3nal7p+E9Gn11O9PoIml86pV1BioJqMHDx8mWWppfxy4tjEAzcCi2ehKNvQNRg86j4L3SKwlAPD37p1Ik/e/Tg+aAgtmRmMnD/ftrt3s37iYlkyaItIYS4Qf0O4GtaPAGDrt4GckMvOPWJ9pd4y6EqOl7r+Ap39f2NwMuJ7Fkbyt2JP2tXkLc3ir090+Pjyx6t6m2h+2IIXwLp0bCmG5yPLre5pvb2vH510dbSNm1w1et59tQpAnbs4Mnjxzkgi7aEEAJoKAEM4BEKkbHg3Rd2TYCdT0DRFa2rKtc6/0hCImP506k5P2+9h7n7Z6HTYh776ig4LSeH7zMyyj+u2TgYHA06G9h0J9xmHttOr+cRX19iQkLYExLCg97eLE1NpfOePfSOi+Pr1FRZtCWEaNQaTgAD2HlC39+g/Utw+nPY0BtyzmhdVbninYLpNfgPPm0+nlmH57Nm81A8tJjH9vEBW1ueL28UfI17FxgaC76DYM8kiH4EKjCPHeLszGdt2pAUEcFbzZtzrqCAh48eJSg6mpdOn8Yki7aEEI1QwwpgAJ3e/HSlO1dDzp/meeHkNVpXVa58vR3/1+NTnuj+CX3SthK7NoTQC7trtwidDoKCSMjOZl1W1q2PtXE3/2w7vgpnl8P6CKjgPHYTa2ueDwriRI8erO3UiR4uLsw3mWgaE8O9Bw+yISPj5sVgQgjRQDW8AL4mYJj5krSDATb/DQ6+CmrdveT5WYsn6H11Hnv7ht48Udvz2H5+YG3NP+Ljb3+sooOOL5uvNlxOgLWhkLi6wqfSKQpDmjTh544dOd2jB1MNBnZkZzP4wAHa7trFuwkJXCwsrEZnhBCi7mu4AQzg3BwG74CmY+HgbPOe4fxbzHNqLNYjlJDIWDZ79+WTXRP4dOcT2NXWPLZeD0FBnLx4ke3Z2RX7jn+keauSU3PYOhz2v1Tp/djB9vYsaNaMhIgIvmzbFg9ra577808CoqP5v+PH2XvpUhU6I4QQdV/DDmAAKwfzCt6wj+DcBvNoLWOv1lWV64KdJ3f1/Y1XO7zM+NOf88eGXgTX1jy2vz9YWTHJZKr4d5yCzfuxm4+Hw/Ng89Aq7ce21ekY7ePDjm7diAsJYbSPD8tTU+kWG0tEXBxfnjtnvm+1EEI0ENUOYEVR9Iqi7FUUpe7eE1JRoOVE855WtRA29ITTS7SuqlwlOj2zO73KsDtX0yznNLFrQ4isjXlsKysICOBAejpxldkupLeDHp9e3Y+9FdZ2g2rMY3d1duaT1q1JjojgnebNuVBYyNhjxwiMjmbG6dPEy6ItIUQDYIkR8LPAUQu0U/M8w82XTD17QsxjsOtJKK67z7r9NWAYoZF7SHAI4tfNf+Plg6+i1PQ8dmAg6PU8VZlR8DUtnjCPhhWdeQV6Neex3aytmRwUxLHu3VnfqRO9XV15w2SiWUwM9xw8yDpZtCWEqMeqFcCKogQCfwM+tUw5tcDOC/qtg3bT4NS/YcMdkFuFsKklfzq3IGJwNMuajuXVg7P5ZfMw3GtyHtvaGvz92ZmWxvHLVbhVZpOQv+zHHl/t/dg6RWFQkyb82KEDZ8PDmWEwEJOdTeSBA7TetYt/JSSQIYu2hBD1THVHwO8CU4H6NTmns4IuC+GOH+HScfMl05QNWldVritWDjwavoQnwxYzMHUjsWtD6FKT89iBgaAoTKzKKBjA1sO8QrrDy3D6v+a7k1loHjvIzo65VxdtfdW2LT7W1jx/ddHW60CsLNoSQtQTSlVvlq8oyjDgLlVVn1IUpS/wgqqqw8o4bgIwAcDHxydkxYoV1SjX8uyLEuiQ8QoORSbOOD/GPS/vpqS4hMcXLdK6tDL5FhxheMYc7Eqy2OQ2mcMOQyv1/cCcHBKdnG573A/ATuArwLtKlZp55EXT9uI8VHQcdZ9Fhl2ParRWtlPAKmCDqpKvKLQF7gH6ATYWP5s2cnJycKrAf7f6qKH2raH2C6RvldGvX79YVVVDy/xQVdUq/QEWAInAWeAccBn48lbfCQkJUeukwhxV3T5KVZejbprnoXbp3qFqP5Ra+uN5JU3dsHGAqi5H/XjnBNWmKK/C330rKqpix165orJ5szrsxInq/3yzT6nqr51VdbmiqgfmqGpJcfXbLMPqqCj1/YQEtc3OnSpRUarHtm3q1FOn1NOXL9fI+WpTVFSU1iXUmIbat4baL1WVvlUGsEct55/ZKl+CVlV1hqqqgaqqBgMPAb+rqjqmqu1pysoRei6HkPe4w5DBj4+coOPFA1pXVa50Oy8i+61lQbvp/L9T/2HbhjsIsvQ8tp0d+Pjwa0oK5woKqtfWDfux58DmYTWyH9sJeCYwkCNhYWzq3Jk73dx4OyGB5jt3MuzAAX67cEEWbQkh6oyGvw+4ohQFWv+Dx1Z3xt66hJj14Yw+86XWVZWrWGfFzC4LuPeOH2l96Thxa7sx0NLz2AYDakkJzyUkVL+t0v3YiyF1o/kWoRlx1W+3DIqi0N/dnZVXF229ZDSy59Il/nbwIC137uRNk4kLsmhLCKExiwSwqqqb1TLmf+ujvamu3LO0Fbs9wvgyeiyLdj+NdXE1R4A1aFXQvYQO2UOKnR9rN0cy4/B8y21VcnAALy++TU62zCpjRYGWT8LAbaAWwfqe8Od/q9/uLQTa2fFq06aYIiJY0a4dgba2TD19msDoaB47dozdFb3rlxBCWJiMgMuQnmvNwP4beavN8zx98kO2bLyTgMuJWpdVrlMuLQkfEsMKw0PM3z+Ln7bei2tBpmUaNxopKS5mWlKSZdoD8Oxh3o/t1Rt2Pg67/l+N78e20el40NubLV27cjA0lMd8ffn+/Hm6x8URFhvLkpQUrhRr8DhIIUSjJQFcjiKdNS92e4uRvb+lY9ZB4tZ0o29qlNZlleuylSNjen7JMyHvMzR5DXvWhlpmHtvJCTw8WJKYyKWiouq3d03pfuzpcOo/V/djV+BBEBbQwcmJj1q1Iikigg9atiS3uJjHjh8nMDqaF//8k9NX6u5zpIUQDYcE8G18bxhJ2JDdXLD1YOPvA3nxyBu1+5SiylAUPmj9DH0Hbsa++Irl5rGNRoqKinglObn6bV1Pp4cuC67bjx1Sq/uxXaysmBQQwOGwMH7v3Jn+7u68k5BAi507uevAAX5JT6e4rv63FkLUexLAFXDMtS3dh+zih8D7eWPfNL7fPgLnwro7d7jDqxfdIuPY5dHdMvPYLi7g7s7ihISauUwbdC8M2QN2fhA1BA7Nq9VHRyqKQj93d75r3574iAhmBwezLyeHuw8dosXOnbxuMpFe3ZXgQgjxFxLAFZRj7cwDvb9lSte3uSdxFbvWdadt1hGtyypXmr2PZeexDQbyCwtZcO6c5Yq8nktLGBIDxlFw4CXYei9Yah67EgJsbZkdHEx8eDjftmtHsJ0d068u2nrk6FFisrKu7YMXQohqkQCuDEXhnbZTGNB/E24Fmexa150H4r/RuqpyFeusSuexO2QdIm5NN4Lyq3gLSzc3cHHhbZOJwpp6LKCVI/T8EkLeh+Q15kdHarQf21qnY6S3N1FdunAoLIzxfn78lJ5OxN69hMbG8llKCpdl0ZYQohokgKtgq8+ddIuMY597F7754yH+FfscViV1d1/p94aRdB+yi3RbT0ZceKFq89iKAkYjl/PzeTc1tWYKvXae1s/AwC1QfAXWh4PG+7HbOzry4dVFWx+1bEl+SQlPHD9OQHQ0U06d4mRVHlohhGj0JICrKMXBn34Doni39bM8d/xdft/UH98rKVqXVa5jrm3pMWQnJ+3uqPo8dpMm4OTEXJOp5hcnefU0b1Xy6A7RY2H306DxfmxnKysmBgRwMCyMLV26MMTdnUVJSbTatYsh+/fzsyzaEkJUggRwNRTprHku5F0e6vk13TLiiFvTjd5p27Quq1w51s784j67dB5799ow2mUerngDigIGA9lXrvDJ+fM1V+g19j7QfyO0fQFOfggb74Q6sB9bURT6uLmxon17TOHhvBoczOHcXO45dIhmMTEsiI8nTRZtCSFuQwLYAr4JfogeQ3ZyydqZqE39ePbYu3V6q9I7bafQf8DvuBZmsXN9Dx48W4knVHl5gYMDL8XH1859lXVW0PVN6P0dZB2CNd2gDu3H9rO15eXgYM6Gh7OyfXta2tsz88wZAqOjGX3kCDtk0ZYQohwSwBZy2K0DYUN2szrgbt6Ne46v/xiFY2GO1mWVa5t3n9J57BU7RlV8HvvqKPhCbi5fXbhQ84VeYxgBQ3aDrSf8PhDq2H5sK52O+7282NilC0fDwpjo788vFy7Qa+9eusXG8klyMrmyaEsIcR0JYAvKtnHl/jt+YFqXhYxM+I6d63vQKvu41mWV69o89nut/sFzx98lalO/is1je3uj2NkxNT6+dkd3rm1gyE4IGgH7psH2kVAH92O3cXTkvZYtSYqI4N+tWlGiqkw4cYKAHTuYfPIkJ2TRlhACCWDLUxTeaDeNQf024JV3nj1rQ7nftFLrqspVpLNmcuh7jOr5FV0z9rJ3TVfuSNt66y/pdKgGAymXLvHzxYu1U+g11s7QawV0fRsSf4K1YVCZeexa5GRlxQR/f/aFhrK9a1fu8vDgo+RkWu/axaD9+/nx/HmKampLlxCizpMAriFRvv3pNjSOw67tWbl9BG/sfRF9iQXvpWxhK4JH0WPITrKtXfh9U38mH3vn1pd4fX3BxobnTBZ+DnFFKAq0nQIDfofCLFjXHSozj13LFEWhl6srX7VrR0JEBHObNuXY5cvcf/gwTXfuZO7Zs6TKoi0hGh0J4BqU5BDInQO38GHLp3jx6Fts+H0Q3ldqcA9tNV2bx/45YDjvxE1hxR8PlT+PrdNBUBBnMjP5PSurdgu9xruPeatSk66wYxQtsj6AOrwfG8DHxoZZRiNnevTgx/btaevgwMtnzxIUHc3DR46wPTNTFm0J0UhIANewAr0tT4d9yCPhSwm/EEPc2m6En4/WuqxyZdu48vc7VjKty0JGJHzPzvU9aJ11rOyD/f3B2ppJ8bXzFKMyOfjDgCho/SyBuSthUz+ow/uxr7HS6bjXy4v1nTtzrHt3JgUE8NuFC9yxbx9d9uzh38nJ5Fjy6VNCiDpHAriWLGv2COGDY8jT27Fl051MOv5BnVrFe4O/zGPvXhdW9jy2Xg+BgRzLyCDm0qXar/ManTWEvMsR95chYy+s6Qq3m8euQ1o7OPBOixYk9ezJJ61aoVMUnjxxgoDoaJ45eZKjublalyiEqAESwLXogHtnQiP3sM53CB/EPsOy6LE4FNXdf1yvzWMfcu1Q/jx2QADo9UzSYi74L9Ls+5tXSVu7wqb+cPRfdfeXnDI46vU84e9PXEgIO7p25W4PD/6TnEy73buZAqyURVtCNCgSwLUs08ade+5cxUudXuPhs18Rsy6cFtkntS6rXEkOgfQduLn8eWwrKwgIIO78eQ7WhZGaWweI3A0Bw2Hv8/DHg1Co4ei8ChRFIcLVlS+vLtqa37QpycCIw4cJjonhtbNnScnP17pMIUQ1SQBrQFV0zOvwEpH91uKXl8KedaEMT1yldVnlujaPPTbiC3pc2Enc2m5EnN/xvwMCA0GnY2IdGAUDYO0Cd6yELgshYSWs6wHlzWPXcd42NswwGlkOrOrQgQ6Ojrxy9iyGmBgePHyYLbJoS4h6SwJYQxv8BhMSGctJ55as2nov8/bNRFdSd++W9GXTsUQMjjbPY2+8bh7bxgb8/fkjNZVTV65oXaaZokC7adBvA+Snw7owMH2vdVVVpgeGe3qytnNnTnTvzj8CAlh/8SJ99+2j4+7dfJSUxKUGsmjr5MmT2NnZMWbMGE3On5+fz/jx4zEajTg7O9O1a1fWrFlTJ2vJyMjgvvvuw9HREaPRyFdffaVJnaJqJIA1ZnI00nvQdj5p/gQzjyxgXdQQPPNq4UEHVXTAvTMhkbGs8R/KB7HP8OWOMeZ57KAgUJQ6MRd8A9/+MDQOXNub75wV9wLU4f3YFdHSwYG3W7QgKSKCz1q3xlanY9LJk/hHRzPpxAkO14WpgGqYNGkSYWFhNdL2nDlzmDNnzi2PKSoqIigoiC1btpCVlcVrr73GAw88wNmzZ2ukpurUMmnSJGxsbEhNTWX58uVMnDiRw4fr5o1pxM0kgOuAfL0dE3p8wvgen9L7/HZi14YQlr5L67LKlWXjxr19fmJWp7mMiv/aPI+dbwJfXzacO0diXZufdAiEgVuh5SQ49rb5XtJ1eD92RTno9Tzu58eekBBiunXjPk9PPktJocPu3fTdu5fv0tIorGeLtlasWIGbmxsDBgy44f2pU6dy3333lb5+8cUXGTBgAIWFlt/37ejoyJw5cwgODkan0zFs2DCaNm1KbGysxWvJzMzku+++4/HHH2fkyJGVqiU3N5eVK1fy2muv4eTkRO/evRk+fDjLli2reudFrZIArkM+bz6eXoP/oETRsW3jHUw4+e86u4pXVXTM7zDrxnlsq/2oqso/EhK0Lu9mehsI+wAivoALu2Dvi1pXZDGKotDDxYUv2rYlMSKC15s1Iz4/nweOHMEYE8OcM2dIqmu/FJUhOzubV155hbfffvumz6ZNm0ZUVBT79u3j448/5v+3d+dxWVX5A8c/h4d9kVX2xRVR3FgF0zQtFzJLf05ppZSmZTaNmVta5tiYKrPqLQAAIABJREFUjuPUNJna5s8yx7TRMjc0FcyFRUAQFUVQQBZBJUBcWe7vD5CfCyj7fYDzfr3uS3juufd+j+d5ni/3nnPPDQkJYcuWLejp6TV6XDk5OSQlJeHp6dkgscTHx7N06VIef/xx3Nzc+O677/D19WX58uW1iiUpKQmNRoO7u3vl+l69eskz4GZEV+0ApHvFWvngMyyGH468zJdH3yDgSgRv+q7kpq6R2qFV6U4/9uaD/8PWyBf42G4yH2aO45KrK2319dUO70Htx4NFLzByVDuSRmGjr89sV1fedXEhJC+PlZmZLEpL429paTxnY8M0JycGWlgghFA71Ad88MEHTJo0CRcXlwfWWVtbM336dCZMmEBBQQGHDh3C3NycgoICnnrqKU6dOkVERATdu3dv0JiKi4t56aWXCA4OxsPD46GxhIeHM2PGDPT19XF0dGTSpEkP7G/kyJFs27YNf39/PvzwQwYNGoShoWGdYjl48CDm5ub3lDE3N+eqmvfkS7Uiz4C1UJ6BNSMGbOev3Rfw6rm1HPmtL+2LzqkdVrXu9GN/1XEy83K+ZtelmSw8H692WNWz7AmGNmpH0ag0QvC0tTU7evbkbJ8+vOPiQmh+PoPi4/E8epQVGRkUatGgrbi4OPbu3cs777xTbRkvLy8SEhJYsmRJZZI2NjZmx44djBkzptrtRowYgYWFBRYWFixdupSlS5dW/j5ixIhqtysrK2P8+PHo6+uzYsWKR8bi5ubG/v37OXDgAB06dODw4cMP7PPDDz9k/vz5lJSUEBwczMSJE1m3bh25ubkP/f+pKhZTU1MKC+99GlhhYSFmZmYP3ZekPWQC1lJlOhoW9vwrQQN20K4olZhdPgzP3Kl2WNW6pTHk9T5fMbHPt/QrPsGcuBEU5Rx59IZSo+toZMQ/OnYkIzCQtR4emGo0/Dk5GccjR5ialERCkfrPrQ4LCyM1NRVXV1fs7e1Zvnw5mzdvxtvbG4CEhASmTp1KcHAwa9asqdxOT0+Ptm3bPnTf27dvJz8/n/z8fObOncvcuXMrf9++fXuV2yiKwqRJk8jJyWHz5s33XF6uLhZHR0eMjMqvVOnq6lZ5lcHHx4e//e1vxMTEkJCQwJAhQ9i2bRtdu3ZlwoQJtYrF3d2dkpISzp79/3kE4uPjKy+VS9pPJmAtt8spCJ/hMaSatmPngadZePxDrb5V6X87TqRvv72UooPB/idAi/uxWxsjjYZge3uifHyI8vbmeVtb1l68SM/oaB4/dowfc3K4rdKgrSlTppCSkkJcXBxxcXG88cYbPP300+zevZvMzEyeeeYZVq9ezcqVK0lISCAsLKxR45k6dSqJiYls27atMqkCNYrl/Pnz7Nq1i8DAwIcew97enldeeYVNmzaRm5vL/PnzaxWLiYkJo0ePZsGCBVy7do3Dhw+zdetWxo8fX/eKS01KJuBm4LxpB/o+dYS17YP58MQith8YgdWtK2qHVa1jLv3x7byRfQZecPQNiHgVSrTk/mAJAL82bVjj4UFGYCD/6NCBzFu3GJeYiGt4OB+cP0/GzZtNGo+xsTH29vaVi6mpKYaGhhgYGBAUFMSMGTMYOXIkxsbGzJo1q9pk1RDS0tL48ssviYuLq4zF1NSU77777pGxFBYWEhwczLp166oclDVw4ECEEA8surq6VfYZVxfL+vXrAVi5ciU3btzA1taWcePGsWrVKnkG3JwoitJki4+Pj6Ltug0YoHTs1avp/lNqs5SVKVOSVis3N+gr539xU7yvRNd6H8tDQ5sm1vx8RWf/XmXPwemKsl4oys7einI1pa7NUiOhoaGNun81NXbdSsvKlJ2XLytPx8crIjRU0YSGKqMSEpS9eXlKWVlZox67IeoWHBysJCQk1D+YeiguLlaCgoKUffv2KYoi34/NVUPXDYhWqvmalGfAzYkQfNX5dfo9dQgdpYzDex7j1ZQ1j95ODebmlFlaM1LnTxQ//isUpcIuH8jcoXZkUhV0hGC4tTXbe/YkpU8fZrq48Ht+Pk/Gx9M1Kop/Z2SQ3wj33DaEoKAg9uzZw+TJk1m7dq1qcWzYsIHIyEgWLVrEwIED2b9/v2qxSM1Di03ALXmKtmhrP7yHxXLQtj9rIifxVeRkDEqb9pJhjbi6cvP2bZbqeMPwGDBtBwdGwPEPQYv7sVu79kZGLK0YtPW9hwcWurr8JTkZp/BwXj9zhngtGLR1t507d5KVlUV4eDivvPKKanGMHz+ey5cvExYWRlhYGIMGDVItFql5aLEJuKVP0XbF0IZhA0NY7DmPySnfcOi3frheS1M7rHtZWoKZGcvS0ykxbgdPHYEOr8CJRXDgadDifmwJDDUaxtvbE+HjQ7SPD2Ntbfk+J4fe0dH0i43lPzk53GpmM21JkjZp0gSckZFR5yncxo4dy6uvvsqmTZvIz89/aNnWMkVbmY6G93st5tnHf6HT1WRid3kzJGu32mH9PyHAzY2imzdZkZsLukbQZw34rYacUNjlDVei1Y5SqgEfMzO+9fAgMzCQf3bsSE5xMS9VDNqaf+4c6U08aEuSWoImTcD29vZ1nsJt2bJl+Pv7s27dOtzc3Ojfvz8ff/wxcXFxD5RtbVO0/er8LL7Dosk0dmJX2HDmn/gbQtGSMxNrazAx4a/p6ZQpSnlS7vw6PHUIUOC3fpDyrdpRSjVkpafHDBcXzvj7s7tnTwLatGFpejrtIyJ4LiGB3/LyyttZkqRHatIErKurWzmF25IlS9i5c2flFG6BgYEMGDCAcePGVXlG7OrqytSpU9m2bRu5ubnMmzePbdu24eXlRVBQ0D1li4qKWt0UbSlmnQgcEs5/2r3I345/wNYDz2Jx+w+1w6o8C86/fp01l+56ypO1HwyLBdv+EPla+aKN/dhSlXSEYIiVFVt79OBcQABzXF05UljIkOPH8YiK4tMLF/hDSwdtSZK2aPI+4JpM4bZ1a9UPp7906RI//PADEydOZMKECdy8eZN58+axaNGie8q11inaruuaMD5wHdN8VzD04m6iQ3zp+YcWTAnZti3CyIh56en3Pjze0AYGhoDnvPKz4N/6lY+WlpoVN0NDPu7QgQuBgazz8MBGT48ZKSk4hYfz2unTxLbgP3wlqT7qnICFEC5CiFAhRKIQ4qQQ4i+P2ubGjRs1msJNR+fBsCZOnIiHhwdbt25l8ODBHD9+nGPHjrF48WJ8fX3vKduqp2gTgpXu0xgw+ACGpTeJ2BPA+HPfqx6T4urKpaIifsrLu3edjgZ6LYbHt8LVsxDiA9rUjy3VmIGODi/b23PE25tYHx9etrNjQ24uPjExBMbGsu7iRW6WytHvknRHfc6AS4B3FUXpCgQA04QQ3aorLIRwSk5OrtEUblVNkD5nzhxycnIqn53p4OBQbWByijaIaBuI97BYIqwD+D4imC+Ovol+qYqPpLOzAwMD3k1Lu/cs+A7nkTAsBoydIGw4JHwE2tKPLdWal5kZX3XpQmZgIP/q1Im84mImnD6NS0QE7507R+oNOTOaJNU5ASuKkq0oSmzFz1eBRMCpqrJCiDbATjs7uxpN4aZfxWPsXn/9dfT09Kqcxq1fv34PlJdTtEGukR1PDfqNZV1n8ebZVfy+93HMSh/+1JVGo6MDrq5kFBYSUt0odrNOMCQc2r0ECQvgwEjQhn5sqc4s9PT4i7Mzp/39+a1nT/qZm7MsPZ0OkZE8k5BAyJUryD+zpNaqQZ4HLIRoB3gBkVWtVxSlEOjl6+tbeeozc+ZMZs6cCUBJSQnjxo1j4cKFdOnSpcpj1HbydSsrK3755ZdabdMSleroMsdrGZHWfVgb8Qo9yqaw8aI1++0HN30w9vaQmsrb6emctbSsuoyuCQR+DzYBEPsOhPhC/81g2btpY5UalBCCJ62seNLKigs3b/JVdjZfZ2Ux/MoVHIEZFy7wqr09VjV8qL0ktQSiysuBtdmBEKbAAWCxoihbqlg/BZgCYGdn5/Pjjz8+sI89e/bwxRdf0L59e6D8odVqzSLz1vTpKKWlTPz8c1WO35gsS9L5n8vvY1aWySGz1zhqOrZ8lHITCgV2AF8A1fZXVGhz+ySeeQvRLSskyWIGOcZDH1q+qKgIU1PTBopUu7TEuhUDvwNbSks5pdGgDwwCngOq/jO8eWmJbXaHrFvNPfHEEzGKovhWta5eCVgIoQdsB3YrivLJo8r7+voq0dHaPfGC58CB3MrPJ6WK+4tbgs/278JW/zvGpm/kZ+fneCVgLYX65o/esKGUlEBEBD3MzTneo8ejy9/IgcNjITcMOk8F709BY1Bl0bCwMAYOHNig4WqLll43K19fVmZm8kNODtfKyvA3M+NNJydeaNsWQ41G7RDrpKW3maxbzQghqk3A9RkFLYBvgcSaJF9JOxTrGDHusQ1M9/6UEZnbObrbD8/8E00XgK4uODuTcOUKsTWZU9jIDgb9Bl1nw9lVsPdxuHah8eOUmlRPU1NWd+lCZt++/LtTJwpLS3nl9Gmcw8OZnZLCeTloS2qB6jMK+jFgPDBICBFXsQQ9aiNJCwjBZx7TGTR4P2bFV4nc3YdxqU34sAonJ9BomJqeXrPyOrrg9ffyvuCCRAjxhov7GjdGSRXmurr82dmZU35+7OvVi4EWFnxy4QIdIyN5+vhxdl65ImfaklqM+oyCPqQoilAUpaeiKL0rlp0NGZzUuA7Z9sd7eCwxVj7858hLfBb9Nnqltxv/wHp64OhIVG4uidev13w7l9Ew7CgY2kLoEDi5FOSXcYskhGCQpSX/7d6d1IAAPnBzI7aoiKcTEugcGck/0tO5Imfakpq5Fvs0JKlmLho5MHjwPj7tMp23kz4ndN8TOFzPavwDu7iAjk7Nz4LvaNMFhkSCy58g/j04OBpuFzROjJJWcDY05K/t25MeEMDGbt1wNjBg9rlzOB05wiuJiUTdN+udJDUXMgFLlOjoMcPnU55/bCO98uM5FuLF4zkHGveg+vrg4MCBnBzSavskHT1TeGxD+YCszG2w2w/yExonTklr6Ono8LytLQe8vEjw9WWigwObL1+mT2wsfjEx/G92NjfkTFtSMyITsFTpJ7fn8R8axR/6luzbP5gZif9s3Eu8FXOBT7tQh0FVQoDHdBgcCsVXYXcAttf3NnCAkrbqbmrKSnd3MgMDWdG5M9dLS5l45gxO4eHMTE4mRQ7akpoBmYCleySad8N/aBRbnZ/ln8dmsunQ85gWN9Jk+oaGYGfHzuxssm/VcZpM2/4wPBasfOiWvxii34am6MeWtEIbXV2mOTlxws+PsN69edLSks8yM+kUGcnw48fZfvkypXKcgKSlZAKWHnBVrw1j+v2XWb2XMTpjC1G7/fEoSGycg7m6opSVMT0jo+77MHKAwfu4YDIGkj6HfU9AU/RjS1pDCMEACws2eXqSFhDAwnbtiC8q4pkTJ+gYEcHStDQu3ZZ/mEnaRSZgqWpCsLzbLJ4ctBer23lE7fZnTPpPDX8cY2OwteW/WVn1G9Wqo0eK+TR47EfIj4cQL2jsfmxJKzkaGPBhu3akBQTwU7dutDcy4r3z53EOD2d8YiLhBQVVPxBEkpqYTMDSQ4XZPYH3sFgSLHrw06HnWR77LrplDXz7h6srZaWlzK7PWfAdbi/A0CjQt4T9gyFxubxVqZXS09FhjK0tob17c9LPjymOjmy9fJm+x47hExPDN1lZXJeDtiQVyQQsPVKWsRMDB4fxuftbvHv6E/bufxK7Gxcb7gCmpmBtzfeZmRSWlNR/f+bdypOw87NwbBYcer58oJbUanUzMeHzzp3JDAxkVefOFCsKk5OScAoPZ0ZyMmdrcz+6JDUQmYClGinW6PO27+e8HLgOvytHiQ3xpu+lww13ADc3SkpK+CCrgfpu9dpAv/9C72WQsQV2+0PBqYbZdy29/PLLODg40KZNG9zd3fnmm29UieNuZ8+exdDQkJdfflntUJqUma4ubzg5cdzXl99792aYlRWfZ2biHhXF0Ph4tl6+TEmZfECi1DRkApZqZX37l+kzNJJrGhPC9g7kz2f+3TCXeNu0AUtLVl+40HD3cgoB3WbBoL1wO688Cadtaph918J7771HamoqhYWF/Prrr7z//vvExMQ06DEWLlzIwoULa1x+2rRp+Pn5NWgMzYkQgv4WFmzo1o0LAQF81K4dp65f57kTJ+gQGcnitDRy5KAtqZHJBCzV2gmLHvgNO8pOxyD+HfMX1h95CeOSa/XfsZsbt4uLWZydXf993c3uCRgWCxY94fALEPsuVNOP/fzzz2Nqalq5CCFYsWJFvQ7v6emJgUH5E5yEEAghSElJAWD27NmMGjWqsuysWbMYPHgwxY04zeKPP/6IhYUFgwff+0xoNWLRBvYGBrzfrh3n+/Rhi6cn7kZGvH/+PC7h4bx06hRH5KAtqZHIBCzVSYG+BaMe/5l5vRbzQvpGInf3oXNhUv12am4ObdrwyYUL3G7oy4DGTjA4DNzfgtOfQNQbVRbbtGkTRUVFFBUVsWjRInr37s2LL75YuX7EiBFYWFhUuYwYMaLaw7/55psYGxvj4eGBg4MDQUHlzy2ZM2cOoaGhxMXFsXr1akJCQtiyZQt6jfRg+sLCQhYsWMA///nPB9Y1dSzaRldHh1Ft27K3d28S/fyY6ujI9itXeOzYMbyio/kqK4trctCW1IBkApbqTBE6LPGcx9AndmN/8yLRIb48d+Hnuu9QCHBz48atW3yak9Nwgd6h0Qffz6HvevCY8dCin332Gd9//z179+7Fysqq8vXt27eTn59f5bJ9+/Zq97dy5UquXr3KwYMHGT16dOUZsbW1NdOnT2fChAksWbKEnTt3Ym5uTkFBAf7+/piamnLiRMM9LvKDDz5g0qRJuFTMQna36mIJDw8nMDCQAQMGMG7cuBZ/RgzgYWLCZ507k9W3L1+6uwPwelISjkeO8JezZzl9rQGu+EitnkzAUr3ts38S72GxnG7jwc8HR7P02Bw0ZXUczWxlBaamLE5Pb7wZjNq9CBae1a5esWIF3377LXv37sXa2rrBDqvRaOjXrx8ZGRmsWrWq8nUvLy8SEhJYsmRJZWI0NjZmx44djBkzptr93X02vnTpUpYuXfrQs/G4uDj27t3LO++8U+0+q4rFzc2N/fv3c+DAATp06MDWrVvr+l/Q7JhoNExxdOSYry+HvLwYYW3Nqqwsuh49ypNxcfx86ZIctCXVmUzAUoO4YOJK/6cOsqrTG8xJXMbu0KG0vZlb+x1VnAVfvXGDL3PrsH09rVq1ii+//JJ9+/ZhY2PzwPrhw4ff00d89zJ8+PAaHaOkpKSyDzghIYGpU6cSHBzMmjVrKsvo6enRtm3bh+7n7rPxuXPnMnfu3IeejYeFhZGamoqrqyv29vYsX76czZs34+3t/dBYHB0dMTIyAkBXVxcdndb3tSGE4DFzc9Z368aFwEAWt29P0o0bjD55kvaRkfwtNZWLdZ1OVWq1Wt8nSWo0tzUGvOm/ilcC/pe+l48QE+KD/+XI2u/IxgZhbMwH6elN+vD1r776ihUrVrB3795qk9+uXbsq+4jvX3bt2vVA+dzcXH788UeKioooLS1l9+7dbNiwgUGDBpGZmckzzzzD6tWrWblyJQkJCYSFhTVa/aZMmUJKSgpxcXHExcXxxhtv8PTTT7N79+4axXL+/Hl27dr10L7u1sBOX595bm6c69OHX7p3p6uxMR+kpuIaEcG4U6c4mJ8vB21JNSITsNTgvuvwCn2fOkKx0OPg3v5MTVpZu1uVhEBxdSXv2jXWX7nSeIHeZ/bs2aSkpNCxY8fKs9p169bVa59CCFatWoWzszOWlpbMnDmTf/3rXzzxxBMEBQUxY8YMRo4cibGxMbNmzWL+/PkNVJsHGRsbY29vX7mYmppiaGiIgYHBI2MpLCwkODiYdevWoa+v32gxNie6Ojo8a2PDnl69OOPvz1tOToTk5fF4XBy9oqP5FShqiIllpJZLUZQmW3x8fBRt123AAKVjr15N95/SxMvy0NAmO5bFrTxle2iQoqxH+e7weMWo+FrNty8tVQgPV+yjo5WysrIatV1oaGiNyjUnwcHBSkJCgqp1Ky4uVoKCgpR9+/Y1yv5bUrsVlZQoX2dmKr2PHlUIDVXMfv9deSspSTlVVKR2aA2qJbXZ/Rq6bkC0Us3XnDwDlhpNvr4lzwzYxoc9FvJy6g+E7wmkw9WUmm2sowOurly8epVf/vijcQPVUkFBQezZs4fJkycTEhKiWhwbNmwgMjKSRYsWMXDgQDZu3KhaLNrORKPhNUdHYn18WAE8a2PDV1lZdDt6lEFxcWy+dIliOWhLqqCrdgBSy6YIHRb1+JAoa3/WH3mJmBAfXu77AzucatCPaG8Pqam8k5bGqLtuBWotdu7cWflzY/YNP8r48eMZP368asdvjoQQeALTunblk44d+TY7m9VZWYw5eRJHfX2mODoyxcEBh4rb0aTWSZ4BS00ixHE4PsNiOGfage0HnuGj+PfRKXvEpAY6OuDiQlpBAb/l5zdNoJLUwNrq6zPXzY2UgAB+7d6dnqamLKwYtPX8yZOE/fGHHLTVSskELDWZVNP29B1yhG87TOT9k4vZFTYc65uXH76RoyPo6fHn9PSmCVKSGolGCJ6xsWFXz56c9ffnL05O7P3jD56Ij6f70aN80VBPA5OaDZmApSZ1S2PIawHf8pr/1wzIPUBMiA8+V6Kr30CjAWdnzuTlEX5VPlJQahk6GRuzvFMnMgIDWdOlC0Y6Orx19ixO4eG8mZTESTnTVqsgE7Ckim87vcZjT5U/zvDwb4/xWvLX1Rd2cgKNhjfT0pooOklqGsYaDa86OHDUx4dIb29G29iwJjub7kePMuDYMTbl5spBWy2YTMCSamKsffEZFkOY7UC+jprCNxGTMCy58WBBXV1wdibu8mWOyzMDqQUSQuDfpg3fde1KRmAgf+/QgQu3bvHCqVO4RkTw4fnzZMqZtlocmYAlVV0xtCFo4E4+8nyfSefWcPi3x2hXdP7Bgk5OoKPDVNkXLLVwNvr6zHZ15WyfPuzo0QNvU1M+SkvDLTycMSdOsF8O2moxZAKWVFemo2FBr48YMWAbHYrOERPiw7Cs+6Z11NcHR0eO5OSQfKOKs2RJamE0QhBkbc2Onj1J7tOHGS4uhObnMzg+nm5Hj/J5RgYFctBWsyYTsKQ1djiNwHdYNBeMXdgR9jQLEv6KUO7q/3JxASF4U54FS61MByMjlnXsSEZgIN95eNBGo+Ht5GScjhzhjTNnSCgqUjtEqQ5kApa0SopZJwKHhPNDu5f5a8JCth14BstbeeUrDQzAwYG9Fy9y4eZNdQOVJBUYaTRMsLcn0seHo97ePG9ry3c5OfSMjqb/sWNsyMnhthy01WzIBCxpnRu6xgQHfsdUv5U8dfE3YkJ86J13rHyliwuKovDnCxfUDVKSVObbpg1rPDzIDAxkeceOZN+6xYuJibiGh/PB+fPyj9RmQCZgSTsJwerOU+n/5EF0lRKO/NaX4HNrwcgI7Oz4NTubnNu31Y5SklRnpafHuy4uJPXpw64ePfBv04bFaWm0j4hg9IkT7M3Lk4O2tJRMwJJWi7Lpg8+wGMJtAlkb8Sqro15H39kepayMdzMy1A5PkrSGjhAMs7bm1x49ONenD7NcXTlYUMBTx4/TNSqKzzIyyC8uVjtM6S4yAUta75KhLUOe2MPSbnN4PfkrDh4eiot5CT9mZsovFEmqQjsjI5Z06MCFgAC+9/DAQleX6cnJOIWHM+XMGeLloC2tIBOw1CyU6ujyXu+lPNf/Z7pcPUNs8gsMvB7F3MxMtUOTJK1lqNEw3t6eCB8fYnx8GGdryw85OfSOjuax2Fj+k5PDLTloSzUyAUvNylaX5/AbepSLxg7svjKbtic/pqhY9gVL0qN4m5nxTcWgrU87duRScTEvJSbiEh7OvHPnSJeDtpqcTMBSs3O2jTt9hkay0XE0HxV8Tdq+EXBbPq5QkmrCUk+P6S4unPb3Z3fPngS2acPf09NpHxHBswkJ7MnLo0wO2moSMgFLzdJ1XRNeGrCJt+1m4Z63n7IQP0yKU9QOS5KaDR0hGGJlxdYePTgXEMAcV1fCCwsZevw4HlFRfHrhAn/IMRaNql4JWAgxTAhxRgiRLISY21BBSVKNCMHn3u8x0PpTrt2+ivflaXD+B7WjkqRmx83QkI87dOBCYCDru3bFVk+PGSkpOIWH89rp0xyTjwJtFHVOwEIIDfAFMBzoBowTQnRrqMAkqUYsLDjS9jF62X1DoV4XCB8P0X+GUtkvLEm1ZaCjw4t2dhzy9uaYjw8v29mxITcX75gYAmNjWXfxIjdLS9UOs8XQrce2/kCyoijnAIQQPwLPAqcaIrCaGDhwYIPvMzUujrKSEmiEfWuDlfn5YGGhdhgNy92d8y++iPceX5Za5fECKzh58DsW7vXk0jUDtaNrEPn5+Vi0tHar0FLr1lLq5WVoyMVevYj382NCYSGTYmKwCA+n/b/+hVF+yxt7sXDhwiY7Vn0SsBNw93yAGUCf+wsJIaYAUwDs7OwICwurxyHvld8IjS9KStBRFNxb4BsLQLe0tMXVTYmKIm3AALIGD+HjpbFEn9ewcPgFvnwumtnb3IhON1U7xHorLS1tlPe7NmipdWtJ9TK9eJHOu3dT5O7Olcce49KgQVwaNAizxERsDh3C7PRpRAsZuFVUVNSgeephRF2nKBNC/AkYqijKaxW/jwf8FUX5c3Xb+Pr6KtHR0XU6XlMZOHAg+fn5xMXFqR1KowgLC2uUKwdq25iby9hTp9jUrRt/srWFgkQ4OBquJkGvpdB1Jgihdph11lLbDVpu3VpqvQA2hYWR4ObG11lZ5BQX08HQkKmOjkx0cMBKT0/t8OqlodtNCBGjKIpvVevqMwgrA3C563dnIKse+5OkOhvTti0uwMfp6eXz3pp3haGuxLCJAAAN2ElEQVRR4Dwa4mbDoTFQXKh2mJLUItgCH7VvT3pgIBu6dsXJwIBZ587hFB7Oq6dPE10oP2s1UZ8EfBToLIRoL4TQB8YCvzZMWJJUOxoheBGIKypiZ17F4wv1zKDfJvBaDhlbYbc/5J9UNU5Jakn0dXQYa2fH715eHPf15RV7e37KzcUvNhb/mBjWZmdzQw7aqladE7CiKCXAW8BuIBHYpCiK/HaTVPMk4GZgwOK0tP9/+osQ0PVdGLSvfLKOPX0gbaOqcUpSS9TD1JRV7u5k9e3L5506cbW0lFfPnME5PJzZKSmcu3FD7RC1Tr3uA1YUZaeiKO6KonRUFGVxQwUlSXWhC8yumEwg7P7BL3YDYFgsWPSCw2Ph+IeqxChJLV0bXV3ecnbmlJ8f+3v1YpClJZ9cuECnyEiePn6cHVeuUNpCBmzVl5wJS2pRJtrbY6+vz+K0tAdXGjvC4FBwfxus/Zs+OElqRYQQPGFpyU+enqQFBvKBmxvHiooYkZBA58hIlqWnc7mVP9NbJmCp0eXl5TFq1ChMTExwc3PjP//5T6Mdy1CjYaaLC/vy84koKHiwgEYffD8Dp6cbLQZJku7lZGDAX9u3Jy0ggE3duuFqYMCcc+dwDg8nODGRqMJC6npHTnMmE7DU6KZNm4a+vj45OTmsX7+eqVOncvJk4w0XeN3BAStdXT5OT2+0Y0iSVHt6Ojr8ydaWMC8vEnx9meTgwJbLl+kTG4tfTAxrWtmgLZmAW6nZs2czatSoyt9nzZrF4MGDKa7B5Otjx47l1VdfZdOmTY+caODatWts3ryZjz76CFNTU/r168fIkSNZt25dvetQHVNdXaY7O7PtyhX54HFJ0lLdTU35wt2drMBAvujcmZtlZUw6cwan8HBmJieTfP262iE2OpmAW6k5c+YQGhpKXFwcq1evJiQkhC1btqBXg5voly1bhr+/P+vWrcPNzY3+/fvz8ccfVzl5SVJSEhqNBnd398rXevXq1ahnwABvOTlhptHwcVV9wZIkaQ0zXV3edHIiwc+PsN69ecrSks8yM+kcFcWw+Hi2Xb7cYgdtyQTcSllbWzN9+nQmTJjAkiVL2LlzJ+bm5hQUFODv74+pqSknTpyocltXV1emTp3Ktm3byM3NZd68eWzbtg0vLy+CgoLuKVtUVIS5ufk9r5mbm3O1kZ+uYqmnxzQnJ366dIkzreAvaUlq7oQQDLCwYKOnJ2kBAfy1XTsSrl1j5IkTdIyIYGlaGpda2KAtmYBbMS8vLxISEliyZAkuLuWTmhkbG7Njxw7GjBnz0G0vXbrEDz/8wMSJE5kwYQI3b95k3rx5LFq06J5ypqamFN43K05hYSFmZmYNW5kqvOPsjKGODktlX7AkNSuOBgYsaNeO1IAA/uvpSQcjI947fx7n8HDGJyYSXlDQIgZtyQTcSiUkJDB16lSCg4NZs2ZN5et6enq0bdv2odtOnDgRDw8Ptm7dyuDBgzl+/DjHjh1j8eLF+PreO+Wpu7s7JSUlnD17tvK1+Ph4PD09G7ZCVbDV12eygwM/5OSQdvNmox9PkqSGpaejw/+0bcv+3r055efHFEdHtl6+TN9jx/CJieGbrCyuNeNBWzIBt0KZmZk888wzrF69mpUrV5KQkFCrp3/MmTOHnJwcfvrpJyZOnIiDg0O1ZU1MTBg9ejQLFizg2rVrHD58mK1btzJ+/PgGqMmjzXJxQQDL5FmwJDVrXU1M+LxzZ7ICA1nVuTPFisLkpCScjhzhneRkkpphV5NMwK3MtWvXCAoKYsaMGYwcORJjY2NmzZrF/Pnza7yP119/HT09PYQQDyz9+vV7oPzKlSu5ceMGtra2jBs3jlWrVjXJGTCAs6Ehwfb2fJudTfatW01yTEmSGo+pri5vODlx3NeX33v3Zri1NSsyM+kSFcWQ+Hh+uXSJkrIytcOskfo8D1hqhkxMTIiPj7/ntZkzZzJz5swa76O2z8q0srLil19+qdU2DWmOiwtrsrP5JCODf3TsqFockiQ1HCEE/S0s6G9hwae3bvFNdjZfZmcz6uRJXAwMeN3RkdccHLDT11c71GrJM2DpAUFBQezZs4fJkyezdu1atcOpt07GxoyztWVVZiZXanCfsyRJzYu9gQHvt2vH+T592OLpSRdjY94/fx6X8HBePHWKw1o6aEueAUsP2Llzp9ohNLj33NxYn5vLZxkZLGrfXu1wJElqBLo6Ooxq25ZRbdty5vp1VmVmsvbiRTbk5tLTxIQ3nZx4ydYWU13tSH3yDFhqFTxNTBhlY8PnmZkUlpSoHY4kSY2si7Ex/+rcmcy+ffnK3R0BvJGUhFN4OG+fPcvpa9fUDlEmYKn1mO/mRn5JCSszM9UORZKkJmKi0TDZ0ZFjvr4c9vLiGWtrvszKouvRozwZF8cWFQdtyQQstRo+ZmYMtbTkk4wMrjfjewclSao9IQR9zc35oVs3LgQG8nH79py9cYP/OXmSdhERfJSaysUmvlNCJmCpVZnv5sal4mK+yc5WOxRJklRiq6/Pe25unAsIYGv37niamLAgNRWXiAg+hiYbsKUdPdFaJCwsrNa32UjNR38LC0bb2KAnhNqhSJKkMo0QjLSxYaSNDWevX2d1VhbJGRmIJvp+kAlYanU2d++udgiSJGmZzsbG/LNTJ8IyMprsmPIStCRJkiSpQCZgSZIkSVKBTMCSJEmSpAKZgCVJkiRJBTIBS5IkSZIKZAKWJEmSJBXIBCxJkiRJKpAJWJIkSZJUIBOwJEmSJKlAJmBJkiRJUoFMwJIkSZKkApmAJUmSJEkFMgFLkiRJkgpEUz33EEAIcQlIa7ID1p0NcFntIBqJrFvzJOvW/LTUeoGsW224KYrStqoVTZqAmwshRLSiKL5qx9EYZN2aJ1m35qel1gtk3RqKvAQtSZIkSSqQCViSJEmSVCATcNW+UjuARiTr1jzJujU/LbVeIOvWIGQfsCRJkiSpQJ4BS5IkSZIKWnUCFkIME0KcEUIkCyHmVrHeQAixsWJ9pBCiXdNHWXtCCBchRKgQIlEIcVII8ZcqygwUQhQIIeIqlgVqxFoXQohUIURCRdzRVawXQoh/V7TbcSGEtxpx1pYQostd7REnhCgUQky/r0yzaTchxBohRK4Q4sRdr1kJIX4TQpyt+Neymm2DK8qcFUIEN13Uj1ZNvf4hhDhd8X77WQhhUc22D33vqq2aui0UQmTe9Z4Lqmbbh36fqq2aum28q16pQoi4arZtnHZTFKVVLoAGSAE6APpAPNDtvjJvAqsrfh4LbFQ77hrWzQHwrvjZDEiqom4Dge1qx1rH+qUCNg9ZHwTsAgQQAESqHXMd6qgBLlJ+D2GzbDfgccAbOHHXa8uAuRU/zwX+XsV2VsC5in8tK362VLs+j6jXEEC34ue/V1WvinUPfe+qvVRTt4XAzEds98jvU7WXqup23/p/Aguast1a8xmwP5CsKMo5RVFuAz8Cz95X5lngu4qf/wsMFkKIJoyxThRFyVYUJbbi56tAIuCkblRN6lnge6VcBGAhhHBQO6haGgykKIrSHCauqZKiKL8Defe9fPdn6jvguSo2HQr8pihKnqIofwC/AcMaLdBaqqpeiqLsURSlpOLXCMC5yQNrANW0WU3U5PtUVQ+rW8X3+vPAhqaMqTUnYCfgwl2/Z/BgkqosU/HhKgCsmyS6BlJx2dwLiKxidaAQIl4IsUsI4dmkgdWPAuwRQsQIIaZUsb4mbavtxlL9l0FzbTcAO0VRsqH8D0XAtooyzb39JlJ+BaYqj3rvaqu3Ki6vr6mm26C5t1l/IEdRlLPVrG+UdmvNCbiqM9n7h4TXpIzWEkKYApuB6YqiFN63Opbyy5u9gM+BX5o6vnp4TFEUb2A4ME0I8fh965t7u+kDI4GfqljdnNutpppt+wkh5gMlwPpqijzqvauNVgEdgd5ANuWXau/XbNuswjgefvbbKO3WmhNwBuBy1+/OQFZ1ZYQQuoA5dbs80+SEEHqUJ9/1iqJsuX+9oiiFiqIUVfy8E9ATQtg0cZh1oihKVsW/ucDPlF/+ultN2labDQdiFUXJuX9Fc263Cjl3ugMq/s2tokyzbL+KwWIjgJeUio7D+9Xgvat1FEXJURSlVFGUMuBrqo65WbYZVH63jwY2VlemsdqtNSfgo0BnIUT7ijOOscCv95X5FbgzAnMMsL+6D5Y2qejP+BZIVBTlk2rK2N/pzxZC+FP+XrjSdFHWjRDCRAhhdudnyge/nLiv2K/AhIrR0AFAwZ3Lns1EtX+NN9d2u8vdn6lgYGsVZXYDQ4QQlhWXO4dUvKa1hBDDgDnASEVRrldTpibvXa1z3/iJUVQdc02+T7XVk8BpRVEyqlrZqO2m9sg0NRfKR8smUT56b37Fa4so/xABGFJ+GTAZiAI6qB1zDevVj/LLP8eBuIolCHgDeKOizFvAScpHK0YAfdWOu4Z161ARc3xF/Hfa7e66CeCLinZNAHzVjrsW9TOmPKGa3/Vas2w3yv+IyAaKKT9DmkT5GIp9wNmKf60qyvoC39y17cSKz10y8KradalBvZIp7wO983m7c/eEI7DzYe9dbVqqqdu6is/RccqTqsP9dav4/YHvU21aqqpbxetr73y+7irbJO0mZ8KSJEmSJBW05kvQkiRJkqQamYAlSZIkSQUyAUuSJEmSCmQCliRJkiQVyAQsSZIkSSqQCViSJEmSVCATsCRJkiSpQCZgSZIkSVLB/wH70XTbc42LEwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "ax.grid()\n",
    "\n",
    "# Draw constraint lines\n",
    "ax.hlines(0, -1, 17.5)\n",
    "ax.vlines(0, -1, 12)\n",
    "ax.plot(np.linspace(-1, 17.5, 100), 6-0.4*np.linspace(-1, 17.5, 100), color=\"c\")\n",
    "ax.plot(np.linspace(-1, 5.5, 100), 10-2*np.linspace(-1, 5.5, 100), color=\"c\")\n",
    "ax.text(1.5, 8, \"$2x_1 + 5x_2 \\leq 30$\", size=12)\n",
    "ax.text(10, 2.5, \"$4x_1 + 2x_2 \\leq 20$\", size=12)\n",
    "ax.text(-2, 2, \"$x_2 \\geq 0$\", size=12)\n",
    "ax.text(2.5, -0.7, \"$x_1 \\geq 0$\", size=12)\n",
    "\n",
    "# Draw the feasible region\n",
    "feasible_set = Polygon(np.array([[0, 0], \n",
    "                                 [0, 6], \n",
    "                                 [2.5, 5], \n",
    "                                 [5, 0]]), \n",
    "                       color=\"cyan\")\n",
    "ax.add_patch(feasible_set)\n",
    "\n",
    "# Draw the objective function\n",
    "ax.plot(np.linspace(-1, 5.5, 100), 3.875-0.75*np.linspace(-1, 5.5, 100), color=\"orange\")\n",
    "ax.plot(np.linspace(-1, 5.5, 100), 5.375-0.75*np.linspace(-1, 5.5, 100), color=\"orange\")\n",
    "ax.plot(np.linspace(-1, 5.5, 100), 6.875-0.75*np.linspace(-1, 5.5, 100), color=\"orange\")\n",
    "ax.arrow(-1.6, 5, 0, 2, width = 0.05, head_width=0.2, head_length=0.5, color=\"orange\")\n",
    "ax.text(5.7, 1, \"$z = 3x_1 + 4x_2$\", size=12)\n",
    "\n",
    "# Draw the optimal solution\n",
    "ax.plot(2.5, 5, \"*\", color=\"black\")\n",
    "ax.text(2.7, 5.2, \"Optimal Solution\", size=12)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (11, 5)  #set default figure size\n",
    "import numpy as np\n",
    "from numpy import exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.integrate import odeint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "pop_size = 3.3e8\n",
    "γ = 1 / 18\n",
    "σ = 1 / 5.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def F(x, t, R0=1.6):\n",
    "    \"\"\"\n",
    "    Time derivative of the state vector.\n",
    "\n",
    "        * x is the state vector (array_like)\n",
    "        * t is time (scalar)\n",
    "        * R0 is the effective transmission rate, defaulting to a constant\n",
    "\n",
    "    \"\"\"\n",
    "    s, e, i = x\n",
    "\n",
    "    # New exposure of susceptibles\n",
    "    β = R0(t) * γ if callable(R0) else R0 * γ\n",
    "    ne = β * s * i\n",
    "\n",
    "    # Time derivatives\n",
    "    ds = - ne\n",
    "    de = ne - σ * e\n",
    "    di = σ * e - γ * i\n",
    "\n",
    "    return ds, de, di"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initial conditions of s, e, i\n",
    "i_0 = 1e-7\n",
    "e_0 = 4 * i_0\n",
    "s_0 = 1 - i_0 - e_0\n",
    "x_0 = s_0, e_0, i_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_path(R0, t_vec, x_init=x_0):\n",
    "    \"\"\"\n",
    "    Solve for i(t) and c(t) via numerical integration,\n",
    "    given the time path for R0.\n",
    "\n",
    "    \"\"\"\n",
    "    G = lambda x, t: F(x, t, R0)\n",
    "    s_path, e_path, i_path = odeint(G, x_init, t_vec).transpose()\n",
    "\n",
    "    c_path = 1 - s_path - e_path       # cumulative cases\n",
    "    return i_path, c_path\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#homework\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"figure.figsize\"] = (11, 5)  #set default figure size\n",
    "import numpy as np\n",
    "from scipy.interpolate import interp1d\n",
    "from scipy.optimize import minimize_scalar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'R' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-1-e47767cad66b>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0mquantecon\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mmarkov\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mDiscreteDP\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0maiyagari_ddp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mDiscreteDP\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mR\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mQ\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mbeta\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mresults\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0maiyagari_ddp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmethod\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'policy_iteration'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'R' is not defined"
     ]
    }
   ],
   "source": [
    "from quantecon.markov import DiscreteDP\n",
    "aiyagari_ddp = DiscreteDP(R, Q, beta)\n",
    "results = aiyagari_ddp.solve(method='policy_iteration')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from quantecon.markov import DiscreteDP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.21059096994885]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from scipy.optimize import root\n",
    "import time \n",
    "import sympy\n",
    "beta=0.95\n",
    "delta=0.05\n",
    "alpha=0.3\n",
    "k=0\n",
    "x=sympy.Symbol('x')\n",
    "k=sympy.solve(k**alpha+(1-delta)*x-beta*(alpha*((x)**(alpha-1))+(1-delta))*(x**alpha+(1-delta)*x-x),x)\n",
    "print(k)"
   ]
  }
 ],
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