CS166 Session 10.1 Pre-Class Work.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "CS166 Session 10.1 PCW.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XqBXfN8VrhFx",
        "colab_type": "text"
      },
      "source": [
        "# Random walk with drift"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0l4nDh26XIeQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        },
        "outputId": "334f1f9d-2704-4277-bb07-f03a2c5a5c5d"
      },
      "source": [
        "import random\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "class randomWalk:\n",
        "    def __init__(self, position=0, p_heads=0.6):\n",
        "        self.position = position\n",
        "        self.p_heads = p_heads\n",
        "\n",
        "    def step(self):\n",
        "        # when the coin lands on heads\n",
        "        if random.random() < self.p_heads:\n",
        "            self.position += 1\n",
        "        else: \n",
        "            self.position -= 1\n",
        "\n",
        "    def display(self):\n",
        "        return(self.position)\n",
        "\n",
        "sim = randomWalk()\n",
        "path = []\n",
        "for _ in range(30):\n",
        "    sim.step()\n",
        "    path.append(sim.display())\n",
        "\n",
        "plt.figure(figsize=(16,8))\n",
        "x = np.linspace(1, 31, 30)\n",
        "plt.xlabel(\"Time step\")\n",
        "plt.ylabel(\"Position\")\n",
        "plt.plot(x, path)\n",
        "plt.title(\"Posiiton of random walk based on coinflip outcome\")\n",
        "plt.show()"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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F2IFK6NS21da947K+uqhPe81bnqtjZdVeW2dF1kG9t/WI/uvGQeodH+21deAM\nClMAAADAz5VU1ujht7KV1D1WP7q6f6uuHRpilJY6XKWVNZq/PMcraxSX1+jRpTka3itOd13Zzytr\nwFkUpgAAAICfe+yfW1VYWqW01BSFh7b+n/iDu8Xo3msHKP2LAn2YV+jx7S9cmavj5dVKSx2u0BBa\neAMRhSkAAADgx/61+5he/3Sv7rqyny7o3d6xHPeNSVT/zm01MyNL5dW1HtvuRzuL9PeN+/Sjq/tr\naI9Yj20XvoXCFAAAAPBTVbV1mr44Uz3bt9GvbxjkaJao8FClpQ7X/uMVempVnke2WVlTp5npWerb\nMVq/HDvQI9uEb6IwBQAAAPzUH9bs1M7CMi2Ymqy2kWFOx9GofvG6bVQfvbQ+X1n7i1u8vf9+b7t2\nHy3XwqkpigoP9UBC+CoKUwAAAMAPbT9cqj98sEOTL+yh0YO7OB3nK9MnDFGndpGanp6p2rr6895O\n7sESPf/hLn3jkl66MrGTBxPCF1GYAgAAAH6mvt5qenqW2kaG6aGbhzod5z/EtQnXnEnDtOVAiV5a\nn39e26irt5q+OFNxbcI166YkDyeEL6IwBQAAAPzM65/t1aY9xzV74lB1ahfpdJyvGZ/cTTcM7aqn\nVudp79Hyc37+qx/t1ub9xXr4lqHq0DbCCwnhayhMAQAAAD9yqLhSj/1zq65K7KRpF/d0Os5pGWM0\nb3KywkJCNDMjS9baZj93//FyPf7uNo0e3FmTLujhxZTwJRSmAAAAgJ+w1uqht7JVW1+vBVOTZYzv\nzvTsFhelB8cP1vodRUr/vKBZz7HW6qEl2ZKk+VN8+/XBsyhMAQAAAD/xdvYhrco5rF+NHaS+Hds6\nHadJt1/aV5f07aB5K3JUdLKqyccvyzyoNdsKdf+Ng9WrQ3QrJISvoDAFAAAA/EBxRY0eXrpFw3rE\n6gdX9XM6TrOEhBilpaaorKpW85bnnPWxx8uqNWfpFl3Qu72+f0VC6wSEz6AwBQAAAPxA2j+36ujJ\nKqWlDldYqP/8GT+wa4zuG52ot748oDXbjpzxcQtW5qq4okZpqSkKDaGFN9j4zxENAAAABKlPdx3V\nXz/bqx9c1U8pveKcjnPO7hszQIld2ml2RrbKqmq/dv+GHUV6c9N+3X1NfyV1j3UgIZxGYQoAAAD4\nsMqaOs3IyFKvDm30qxsGOR3nvESGhWpRaooKTlToyVV5/3FfZU2dZmZkKaFjtH5+/UCHEsJpFKYA\nAACAD/vDmh3aVVimhVNTFB0R5nSc8zYyIV63X9pHL2/I1+Z9J766/enV27XnaLkWpqYoKjzUwYRw\nEoUpAAAA4KPyDpfqj2t3aiATAkkAACAASURBVOpFPXXNoM5Ox2mxBycMUeeYSE1Pz1JNXb22HCjW\nC+t26dYRvXTFgE5Ox4ODKEwBAAAAH1RXb/Xg4ky1iwzT7IlJTsfxiNiocM2ZlKzcgyV6/sNdmpGe\npQ7R4Zp5U2C8Ppw//+0FAAAAXld0skrhoSGKaxPudBQg6Lz2yR59sfeEnrz1AnVsF+l0HI8Zn9xN\n44Z11e/e2SZJ+v1tF6l9dITDqeA0zpgCAIDTKq6o0cT/XqfUP2xQVW2d03GAoHLgRIV+9842XT2w\nk6Ze1NPpOB43d3Ky4tqEa2xSV908vLvTceADOGMKAABO67G3t+pIaZUOl1Tp2TU79Ws/fTdQwN9Y\na/XwW9mqq7daODVFxgTeTM+usVH64P7RiokKC8jXh3PHGVMAAPA1n+Uf018+3asfXNlPUy7soT9+\nsEN5h0udjgUEhZVZh7Q694h+fcMg9Y6PdjqO13RoG6GwUMoRuHAkAACA/1BVW6cZ6Znq1aGNfn3j\nID1081C1iwzTjPQs1ddbp+MBAa24vEaPLN2ilJ5xuuvKBKfjAK2GwhQAAPyHZ9fs1M7CMi1wz0zs\n2C5SsycO1aY9x/X6p3ucjgcEtEX/zNXx8motSk3hbCKCCkc7AAD4St7hUv3xgx2acmEPXdtoZmLq\nxT119cBOeuztbTpYXOFgQiBwfbLrqP72r3364VX9lNwzzuk4QKuiMAUAAJKk+nqrGelZahcZpodu\nHvof9xljtGBKimrr6/XwW1tkLS29gCdV1tRpZnqW+sRH65djeaMxBB8KUwAAIEl6/dM92rTnuGZP\nHHramYl9OkbrV2MHaVXOYb2dfciBhEDg+p/3d2hXUZkWTE1Wm4hQp+MArY7CFAAA6GBxhR572zUz\nMfXiM89M/MFV/TSsR6weXrpFxeU1rZgQCFy5B0v03Nqd7pb5zk0/AQhAFKYAAAQ5a60eWrJFtfX1\nWjDl7DMTw0JD9Ni04TpWVq20t3NbMSUQmOrqraanZym2TbhmTxza9BOAAEVhCgBAkPtn9iGtzj2s\nX98wSH06Nj0zMblnnH5wVT/99bN9+mTX0VZICASu//t4tzbvO6FHbhmq+LYRTscBHENhCgBAEGuY\nmZjcM1b/78p+zX7er8YOUu/4NpqZnqXKmjovJgQCV8GJCv3unW26dlBnTbqgh9NxAEdRmAIAEMTS\n3s51teWmDj+nmYltIkK1cGqKdhWV6dk1O7yYEAhMrhb6bFkrzZ+SfNYWeiAYUJgCABCkPtl1VH/9\nbJ9+cJ4zE68e2FmpF/XUHz/YqW2HSr2QEAhcyzMP6v2tR/RfNw5S7/imW+iBQEdhCgBAEGqYmdg7\nvo1+1YKZibNvHqrYNuGanp6punpmmwLNcaK8WnOWbdHwXnG66xxa6IFARmEKAEAQenaNa2biwqkp\nLZqZGN82Qg/dnKQv9p7Qa5/s8WBCIHAtXJmr4+U1SksdrtAQWngBicIUAICgs/VQif74wU6lXuSZ\nmYlTLuypawZ11m/f3qoDJyo8kBAIXB/tKNI/Nu7Xj67ur6E9Yp2OA/gMClMAAIJIXb3V9MXumYk3\ne2ZmojFGC6Ykq97K/WYutPQCp1NZU6cZGVnq2zFavxw70Ok4gE+hMAUAIIj8+ePd+nLfCT10c5JH\nZyb2jo/Wr28YpPe2HtGKrIMe2y4QSJ55b7v2HC3Xwqkpigo//xZ6IBBRmAIAECQOuGcmXjOos6Zc\n2NPj27/rygSl9IzTo0tzVFxe4/HtA/4s50CJnv9wl75xSS9dmdjJ6TiAz6EwBQAgCDTMTKy30gIv\nzUwMCw1R2rQUHS+v1sKVuR7fPuCv6uqtZqRnqkN0uGbdlOR0HMAnUZgCABAEVmQd1HutMDNxWI84\n/fDqfvr7xn36eOdRr60D+JNXPtqtzfuL9fAtw9TBgy30QCChMAUAIMAVl9fo0aU5SukZpzuvSPD6\ner+8fpD6xEdrZkaWKmvqvL4e4Mv2Hy/XE+9u05jBnXXL8O5OxwF8FoUpAAABzjUzsVpp01IUFur9\nX/1tIkK1cGqK8ovK9Pv3t3t9PcBXWWs1e0m2JGn+1BSvtNADgYLCFACAAPbRziL9feM+/fDqfhrW\nI67V1r1qYCdNu7iX/rR2l3IPlrTauoAvWbr5gD7YVqj7bxysnu3bOB0H8GkUpgAABKjKmjrNTM9S\nn/ho/fL6Qa2+/uyJSYprE67pizNVV89sUwSX42XVmrssRxf0bq/vt0ILPeDvKEwBAAhQ//3edu12\nz0xsE9H6MxM7tI3Qw7cM1eb9xXr1o92tvj7gpPkrclVcUaO01BSFhtDCCzSFwhQAgACUe9A1M3Ha\nxb101UDnZiZOuqCHrh3UWY+/u037j5c7lgNoTeu3F2nx5/t19zX9ldQ91uk4gF+gMAUAIMDU1VtN\nX5ypuDbhmj3R2ZmJxhjNn5Isa6WHlmTLWlp6Edgqqus0MyNLCR2j9fPrBzodB/AbFKYAAASYV7+a\nmTjUJ2Ym9o6P1v3jBmvNtkItyzzodBzAq55+L097j5VrYWqKosJbv4Ue8FcUpgAABJD9x8v1+Lvb\nNHpwZ026oIfTcb5y5xUJuqBXnOYu26IT5dVOxwG8IrugWC+uy9e3RvTWFQOca6EH/BGFKQAAAcJa\nq4caZiZOSfapmYmhIUaLUofreHmNFqzIdToO4HG1dfWakZ6lDtERmnmTsy30gD+iMAUAIEAsyzyo\nNdsK9V83DlavDtFOx/maoT1idfc1/fXGpv36aEeR03EAj3rlo93KKijWo5OGKi463Ok4gN+hMAUA\nIAAcL6vWnKVbdEGvON3pwzMTf3H9QCV0jNaMjCxV1tQ5HQfwiH3HyvXEu3m6fkgXTUzp7nQcwC9R\nmAIAEAAWrMzViYoaLUod7tMzE6PCQ7Vwaor2HC3X06u3Ox0HaDFrrWZmZCnESPN8rIUe8CcUpgAA\n+LkNO4r05ibXzMShPXx/ZuIViZ30zUt66YV1u7TlQLHTcYAWWfJlgdZtL9Jvxg1Wj/ZtnI4D+C0K\nUwAA/Fhlzb9nJv7Cj2YmzpqYpA7R4ZqRnqW6emabwj8dK6vWvOW5urB3e3338gSn4wB+jcIUAAA/\n9vTq7dpztFwLp/rXzMT20RF6+JZhytxfrJc35DsdBzgv85fnqKSiRmnTUny6hR7wBxSmAAD4qS0H\nivXCul365iW9dEWi/81MvGV4d40Z3FlPvJunfcfKnY4DnJMP8wqV/kWB7rl2gIZ08/0WesDXUZgC\nAOCH6uqte2ZiuGZN9M+ZicYYzZ+aImOk2UuyZS0tvfAP5dW1mrUkS/07tdVPr0t0Og4QEChMAQDw\nQy9vyFfm/mI9csswtY+OcDrOeevZvo1+M26w1uYVaunmA07HAZrl6dXbte9YhRam+lcLPeDLvF6Y\nGmNCjTFfGGOWe3stAACCQcPMxOuGdNHNw/1/ZuL3Lk/Qhb3ba86yHB0rq3Y6DnBW2QXFenHdLt02\nqrcu69/R6ThAwGiNM6a/kJTbCusAABDwrLWatSQ7oGYmhoYYpU1LUUlFjeavyHE6DnBGtXX1enBx\npjq2i9T0Cf7ZQg/4Kq8WpsaYXpImSnrRm+sAABAs3vrygD7MK9T94warZwDNTBzSLVY/vra/0j8v\n0LrthU7HAU7rpfX52nKgRHMmDVNcm3Cn4wABxdtnTJ+W9ICk+jM9wBhztzFmozFmY2Ehv4gAADiT\nY2XVmrs8Rxf0bq/vBeDMxJ9dN1D9OrXVrIxsVVTXOR0H+A97j5brqdV5GpvUVROSuzkdBwg4XitM\njTE3Szpird10tsdZa5+31o6w1o7o3Lmzt+IAAOD35q9wzUx8LEBnJkaFh2rh1BTtPVaup1fnOR0H\n+Iq1VjMzshQWEqJ5U4YFRAs94Gu8ecb0SkmTjDG7Jf1N0nXGmNe8uB4AAAFr3fZCpX9eoB9f2z+g\nZyZePqCjvjWit15cn6/sgmKn4wCSpPTPC7R+R5EeGD9Y3eMCp4Ue8CVeK0yttTOstb2stQmSvi3p\nfWvtHd5aDwCAQFVRXadZGdnq16mtfnbdQKfjeN3Mm5LUITpC09MzVVt3xquBgFZx9GSV5q/I0cV9\n2uuOS/s6HQcIWMwxBQDAxz29Ok97j5Vr4dTgmJkYFx2uRycNVXZBiV7esNvpOAhy85bn6GRVrdKm\nDVdIALbQA74irLkPNMZcISmh8XOstf/XnOdaaz+Q9MG5RQMAANkFxXpxfb6+PbK3Lh8QPDMTJ6Z0\nV8aQAj25Kk/jk7upd3y005EQhNbmFWrJlwf08+sHalDXGKfjAAGtWWdMjTF/lvS4pKskjXR/jPBi\nLgAAgl5tXb2mp2eqQ3SEZgTZzERjjOZNSVaIkWZmZMla63QkBJny6lrNysjSgM5t9ZMxA5yOAwS8\n5p4xHSFpqOW3AgAAreblDbuVXVCiZ79zseKig29mYo/2bfTA+CF6ZOkWLfmyQFMv6uV0JASRJ9/N\n0/7jFXrjnssVGRb4LfSA05p7jWm2JAY2AQDQSvYeLdcTq7ZpbFIX3ZQSvL+C77isry7q017zlufq\nWFm103EQJDL3n9D/bsjXdy7to5EJ8U7HAYJCcwvTTpJyjDHvGGOWNnx4MxgAAMHKWqtZS7IUaozm\nTk4O6pmJoSFGaanDVVpZo/nLc5yOgyBQU1ev6Yuz1KldpKZPGOJ0HCBoNLeV91FvhgAAAP+W8UWB\n1m0v0pxJw9SjPTMTB3eL0T3XDtDv39+hyRf11LWDOjsdCQHsxXX5yjlYoufuuFixUcHXQg84pVln\nTK21ayVtlRTj/sh13wYAADzo6MkqzVueo4v6tNcdlzEzscFPxiSqf+e2mpWRpfLqWqfjIEDtLirT\n06vzdOPQrhqf3N3pOEBQae678t4q6TNJ35R0q6RPjTHf8GYwAACC0fwVua6ZianDFcrMxK9EhYdq\n0dQU7T9eoadW5TkdBwGooYU+IjREcycnOx0HCDrNvcZ0lqSR1trvW2u/J2mUpIe8FwsAgOCzNq9Q\nGV8U6N5rB2hwN2YmnurS/h1126jeeml9vrL2FzsdBwHmzU37tWHHUT04YYi6xUU5HQcIOs0tTEOs\ntUcafX30HJ4LAACa0DAzsX/ntrpvTKLTcXzW9AlJ6tguUtPTM1VbV+90HASIopNVWrAyVyMTOug7\no/o4HQcISs0tLt92vyPvncaYOyWtkLTSe7EAAAguT61yzUxMSx2uqHBmJp5JXJtwzZk0TFsOlOil\n9flOx0GAmLssR+VVdVqUmqIQWugBRzT3zY9+I+l5ScPdH89bax/0ZjAAAIJF1v5ivbQ+X7eN6qNR\n/ZiZ2JQJyd00Nqmrnlqdp71Hy52OAz+3ZtsRLd18QPeNGaDELrTQA05pdjuutXaxtfbX7o8Mb4YC\nACBY1NTV68HFmcxMPAfGGM2bMkxhISGamZEla63TkeCnyqpqNTsjW4ld2une0QOcjgMEtbMWpsaY\n9e5/S40xJY0+So0xJa0TEQCAwPXSetfMxDmThimuDTMTm6t7XBs9OH6w1u8oUvrnBU7HgZ964t08\nFZyoUFpqiiLDaKEHnHTWwtRae5X73xhrbWyjjxhrbWzrRAQAIDDtOVqmp1bl6YahXTU+uZvTcfzO\n7Zf21SV9O2j+ihwdPVnldBz4mc37TuiVj/J1x2V9NCKBFnrAac2dY/rn5twGAACax1qrmRlZCg8N\n0bzJyTKGN1w5VyEhRmmpKTpZVat5y3OcjgM/0tBC3zkmUg+Mp4Ue8AXNvcZ0WOMvjDFhki7xfBwA\nAILD4s8LXDMTxw9mZmILDOwao3tHJ2rJlwf0wbYjTT8BkPTCul3aeqhUcycnKzaKFnrAFzR1jekM\nY0yppOGNry+VdFjSW62SEACAAFN0skrzV+Tokr4ddPulfZ2O4/d+MmaABnRuq1kZ2SqrqnU6Dnxc\nflGZnl69XROSu2ncMFroAV/R1DWmi6y1MZJ+d8r1pR2ttTNaKSMAAAFl3vIclVXVKo2ZiR4RGRaq\ntGnDVXCiQk+uynM6DnyYtVYz07MUGRaiOZOGNf0EAK2mqTOmDU33bxhjLj71oxXyAQAQUNZsO6K3\nvjyg+0YnamBXZiZ6ysiEeH3n0j56eUO+Nu874XQc+Kg3Nu7Xx7uOasaEJHWJpYUe8CVhTdz/a0l3\nS3riNPdZSdd5PBEAAAGq8czE+8YwM9HTpk8YotU5hzU9PUtLf3qlwkObPa4dQaCwtEoLVuZqVEK8\nvj2yt9NxAJyiqVbeu93/jjnNB0UpAADn4MlVrpmJi5iZ6BWxUeGaO3mYcg+W6MV1+U7HgY+Zs2yL\nKqrrtJAWesAnNXdczDeNMTHuz2cbY9KNMRd5NxoAAIFj874TenlDvm6/tI9GMjPRa8Ynd9e4YV31\n9Oo87S4qczoOfMT7Ww9reeZB/fS6RCV2aed0HACn0dwel4estaXGmKskjZX0kqTnvBcLAIDA0Xhm\n4oMTmJnobXMnJysiNESzlmTJWut0HDjspLuFflDXdrrnWlroAV/V3MK0zv3vREnPW2tXSIrwTiQA\nAAJLw8zEOZOYmdgausZG6cEJQ7Rhx1G9uWm/03HgsMff2aaDJZValDpcEWFcdwz4qub+dBYYY/4k\n6VuSVhpjIs/huQAABK3dRWV6ZvV2jRvWVeOTmZnYWr4zqo9GJnTQgpW5KjpZ5XQcOOSLvcf16se7\n9d3L+uqSvh2cjgPgLJpbXN4q6R1J46y1JyTFS/qN11IBABAArLWamZGliNAQzZ2c7HScoBISYrQo\nNUXlVXWauyzH6ThwQE1dvWakZ6lbbJR+M26w03EANKFZham1tlzSTknjjDE/ldTFWvuuV5MBAODn\n3ti0Xx/tPKrpNw1RV2YmtrrELjG6b8wALd18QGu2HXE6DlrZ8x+6WujnTU5WDC30gM9r7rvy/kLS\n65K6uD9eM8b8zJvBAADwZ4WlVVqwwjUz8baRfZyOE7TuHT1AiV3aaXZGtsqqap2Og1ayq/Cknnlv\nuyamdNfYoV2djgOgGZrbyvsDSZdaax+21j4s6TJJP/JeLAAA/Nvc5TnMTPQBkWGhSktNUcGJCj3x\nbp7TcdAK6uutZqRnKSosRI9MGup0HADN1NzC1Ojf78wr9+f8lgUA4DTWbD2iZZsP6CdjmJnoC0Yk\nxOuOy/ro5Y/y9eW+E07HgZf9Y+M+fZp/TDNvSlKXGFroAX/R3ML0ZUmfGmMeNcY8KukTuWaZAgCA\nRk5W1WpWRpYGdmmne0czM9FXPDB+iLrERGr64kzV1NU7HQdecqS0UgtX5urSfvH61sjeTscBcA6a\n++ZHT0q6S9Ix98dd1tqnvRkMAAB/1DAzMW1aCjMTfUhsVLjmTk7W1kOlev7DXU7HgZfMWZqjytp6\nLUpNkTE09wH+JOxsdxpjoiTdIylRUpakP1hreecAAABOo2Fm4h2X9tUlfeOdjoNTjBvWTROSu+mZ\n97brppTu6teprdOR4EGrcw5rRdZB3X/jIPXvTAs94G+a+q/cVyWNkKsonSDpca8nAgDADzXMTOwa\nE6UHxjMz0VfNmTRMkWEhmpmeJWut03HgIaWVNXrorWwN6Raju6+hhR7wR00VpkOttXdYa/8k6RuS\nrmmFTAAA+J2vZiZOYWaiL+sSG6UZE5L08a6jemPjfqfjwEMef2ebDpVUalEqLfSAv2rqJ7em4RNa\neAEAOL2GmYk3pXTTDcxM9HnfHtlboxLitWBlrgpLq5yOgxbatOe4/u+TPfr+5Qm6qE8Hp+MAOE9N\nFaYXGGNK3B+lkoY3fG6MKWmNgAAA+DJrrWZmZCkyLESP3jLM6ThohpAQo4WpKaqortOcZVucjoMW\nqK6t14z0THWPjdL942ihB/zZWQtTa22otTbW/RFjrQ1r9Hlsa4UEAPivHUdKlXe41OkYXvOPjfv0\nyS73zMRYZib6i8Qu7fTT6xK1PPOg3ss97HQcr8naX6x9x8qdjuE1f1q7U3mHT2r+1GS1izzre3oC\n8HE04QMAvOZYWbVu/dMnuvVPH6voZOC1TB4prdSCFbka1S9e3xrBzER/c8+1AzSoazs9tCRbJ6sC\n74qlPUfL9I3nPtJ3XvxE5dWB9/p2Fp7U79/foZuHd9d1Q2ihB/wdhSkAwGvmL89RSUWNyqpqNW95\njtNxPG7Osn/PTAwJYWaiv4kIC9Gi1OE6WFKpx9/Z5nQcj2poMQ8xRvuOVejp1dudjuRR9fVWM9Kz\n1CYiVI/QQg8EBApTAIBXfJhXqPQvCnTv6AG6b3Si3vrygNZsO+J0LI9ZnXNYKzIP6mdjEjWAmYl+\n65K+HfTdy/rq1Y9364u9x52O4zGLPy/Qhh1HNXNikm4b1Vsvrtul7IJip2N5zN837tNn+cc066Yk\ndY6JdDoOAA+gMAUAeFx5da1mZmSpf+e2+smYRN03ZoASu7TT7IxslQVAy2TDzMTBXWP042uZmejv\nfjNusLrGRGn64ixV19Y7HafFik5Waf6KHI3o20G3j+qj6ROS1LFdpB5cnKnaOv9/fUdKKrVwZa4u\n799R3xzRy+k4ADyEwhQA4HFPrcrT/uMVSksdrqjwUEWGhSotNUUFJyr0xLt5Tsdrsa9mJk5jZmIg\niIkK17wpydp2uFTPf7jT6TgtNndZjsqr6pQ2zdViHtcmXHMnDdOWAyV6aX2+0/Fa7JGlW1RVW6+F\nqSkyhhZ6IFDw2xQA4FFZ+4v10vp83Taqj0b1i//q9hEJ8brjsj565aN8bd53wsGELdN4ZuLFzEwM\nGDcM7aqJKd313+/v0K7Ck07HOW9rth3R0s0H3F0KMV/dPj7ZNWP3qdV52nvUf9+l990th/TP7EP6\n5diB6teprdNxAHgQhSkAwGNq6+o1PT1TndpFavqEIV+7/4HxQ9Q5xtVSWOOHLYXMTAxsj0waqqiw\nEM1Iz1J9vXU6zjkrq6rV7IxsJXZpp3tH/2eLuTFG8yYnKywkRDMzsmSt/72+0soaPfzWFiV1j9WP\nru7vdBwAHkZhCgDwmJfW52vLgRLNmTRMcW3Cv3Z/bFS45k5O1tZDpXph3S4HErZMw8zEeVOYmRiI\nusREaeZNSfo0/5j+sXGf03HO2RPv5qngRIXSUlMUGRb6tfu7xUXpwfGDtX5HkdI/L3AgYcv89u1t\nOlJaqbTUFIWH8icsEGj4qQYAeMTeo+V6anWebhjaVeOTu53xceOGddP4Yd30zOrt2l1U1ooJW6Zh\nZuLE4d11fRIzEwPVt0b21qX94rVwZa6OlFY6HafZNu87oVc+ytcdl/XRiIT4Mz7u9kv76pK+HTR/\nRY6O+tFs4U17jum1T/foziv66YLe7Z2OA8ALKEwBAC3WMDMxLCRE8yYnN/mGJHMmD1NEmP+0FDbM\nTIwKD9Ejtwx1Og68yBijRakpqqyt15yl/jF7t6auXg8uzlTnmEg9MP7rLfSNhYQYpaWm6KQfzRau\nqq3T9MVZ6hHXRv914yCn4wDwEgpTAECLpX9eoPU7ivTg+MHqFhfV5OO7xkZp+oQh+mjnUb2xaX8r\nJGyZr2YmTkxSl5imXx/8W//O7fTz6xK1IuugVuccdjpOk15Yt0tbD5Vq7uRkxUZ9vYX+VAO7xuje\n0Yla8uUBrc0rbIWELfPcB7u0/chJzZ+arLa00AMBi8IUANAiRSerNG9Fji7p20G3X9q32c+7bWQf\njUqI14IVuSos9d2WwoaZiZf1j9etI3o7HQet5O5rBmhw1xg99Fa2SitrnI5zRvlFZXpm9XaNH9ZN\n44aduYX+VD8ZM0ADOrfVzPQsn54tvONIqZ5ds0OTLuihMYO7OB0HgBdRmAIAWmTe8hyVVdUqLdU1\nM7G5QkKMFqamqKK6TnN9uKWwYWbiotThzEwMIhFhIUqblqJDJZX63TvbnI5zWtZazUzPUkRYiOZM\nHnZOz40MC1XatOEqOFGhJ1f55mzh+nqr6YuzFB0ZqodpoQcCHoUpAOC8rdl2RG99eUD3jU7UwK4x\nTT/hFIld2uknYxK1bPMBrdl6xAsJW6ZhZuIvrmdmYjC6qE8Hff/yBP35kz3atOe403G+5o2N+/Xx\nrqOaMSFJXWPPvcV8ZEK8br+0j17e4Juzhf/y2V5t3HNcs25KUqd2kU7HAeBlFKYAgPPSeGbifWMG\nNP2EM7h39AAN6tpOszKydNKHWgobZiYO6Raju69hZmKwun/cYHWPjdKM9ExV1/rO7N3C0iotWJmr\nUQnx+vbI828xf3CCa7bw9PQsn5otfKi4Uo/9c6uuTOyob1zSy+k4AFoBhSkA4Lw8uco1M3HRGWYm\nNldEWIgWpQ7XwZJKPe5DLZO/fXubDpdWKm3acGYmBrF2kWGaPzVZeYdP6rm1O52O85U5y7aoorpO\nC8+xhf5UsVHhmjMpWbkHS/TiunwPJmyZR5Zmq7quXgumpNBCDwQJftMCAM7Z5n0n9PKGfN1+aR+N\nPMvMxOa6pG8Hffeyvnr14936Yq/zLZP/npmYoAuZmRj0rhvSVTcP767/eX+Hdhw56XQcvb/1sJZn\nHtRPr0tUYpd2Ld7e+ORuGjesq55enecTs4Xfzj6kd7Yc1q9uGKQEWuiBoEFhCuD/t3ff8VWW5//A\nP/fJ3iGTkEESIPsEVEBliiKyIaG1y37Vam2tbR11JExZIc5q+1Nba1vbr3Z9TdgbZAnKUsjJ3oNA\n9t7j3L8/ckAKBBLOeM5JPu/Xi5fJOee578/TPj7m4lw5F9GgdPdqkZCqgbeLHV6Zd/OZiYPx0kPh\n8HWxR6LCLYVXz0x8cU64YjnIvKxZFA0HWyssT9VAq1Vu9m6LroU+zNcZP595+y3011q3JAa2Viqs\n2KLsbOGmjm6s3pqOKD9XPDktRLEcRGR6LEyJiGhQPjpWhKxLTVi7eGAzEwfKxd4G65fGILuiGR8e\nLTTYuoN1ZWbiUs5MpG95u9hhxfxInCquw79OlymW4829ObjU1IFN8bGwtTbcj3G+rvZ4ZV4EjufX\n4jMFZwu/tjsbNS2dU0aH3wAAIABJREFUeG1ZLKzZQk80rPDfeCIiGrDimla8cyAXD0X7Ym7MwGcm\nDtSDUb6Yrx6Jdw/mobDa9C2Tl2cmLho/CrMiODOR/tt3Jwbg3lBPbNqdhaqmDpPv/01pPf72ZTF+\nfM9o3DV6hMHX/+HkIEwKHoGNu7JQ02L62cKni+vw6clS/GRqCNQBbibfn4iUxcKUiIgGREqJ5Zs1\nsLVSYd2SGKPt8+qiaNhZq7B8s2lbCrVaicRUDRxsrbB6IWcm0vWE6Ju929mjxZptGSbdu6tHi8RU\nDUa62uOlh4zTYq5SCWyKV6Otsxfrtpt2tnBfC30aAkY44IU5YSbdm4jMAwtTIiIakP87ewEnCmqR\nMD/itmYmDpSPqz2Wz4/EV4V1+M8Z07VM/uNUKU4X12Plgkh4u3BmIt1YiJcTnps9DrvTK7A3o8Jk\n+354tADZFc1YvyQGLgZsob/WWB8XPDNrLLaZeLbwe4cKUFDdio1xajjasoWeaDhiYUpERLdU3dyJ\njTv7Zib+YFKQ0ff73sRATA7xwMadWahqNn7LJGcm0mD8dHooIv1csXprOpo6uo2+X2F1C373eT4W\nqP0wO8rX6Ps9fd8YjPNxxsot6Wg1wWzh3MpmfHA4H0snjMLMMG+j70dE5omFKRER3dK6HZkGmZk4\nUJdbCjt6tFhrgpZCzkykwbCxUiE5Xo3q5k68vifbqHtdbjG3t1ZhzWLTtJjbWquQvEyNi43teHOf\ncWcLXz4/ZztrrGILPdGwxsKUiIhu6lB2Fbafv4hnZhlmZuJAjfF2xq9mjcXOtEs4mFVptH0uz0x8\nbjZnJtLAjQ90x2NTQvDJV6U4U1xntH3+c6YMJ4vqsHx+JHxcjNdCf627RnvgkbtH4+MTxThX1mC0\nfT49WYKzJfVYuSAKns5soScazliYEhFRv1o7e7BySzrG+Tjj6fsMNzNxoH42cwzCfV2wcks6WozQ\nUnh5ZmKknyuenM6ZiTQ4v5kTBn93BySkatDZ02vw9auaO5C0Kwt3h3jge5MCDb7+rbw8t2+2cEJK\nmlFmC19qbMdre3IwfZwX4u/0N/j6RGRZWJgSEVG/3tyXg4uN7UhepjbozMSButxSWNHUgTeM0DL5\n7cxENWw4M5EGycnOGhviYpBf1YIPDhcYfP212zLR0aPFpnhlWsxd7G2wbkm0UWYLSymxemsGerRs\noSeiPvyvMBER3dC5sgZ8fKIYj9w9GneN9lAsxx1BI/DovcH4+1d9LX+Gcnlm4uNTQxAb4G6wdWl4\nmRXug8XjR+H9QwXIr2o22LoHMiuxU3MJv75/LEK9TddCf6050SMxL6ZvtnBRTavB1t2TXoH9mZV4\n4cEwBHk6GmxdIrJcLEyJiOg63b1aJKSkwdfFHi/PNc7MxMF48aFw+LnaIzE1DV09+rcUXp6Z6O/u\ngBce5MxE0s/qRVFwtLNCQooGWq3+s3ebO7qxams6wn1d8NQM07fQX2vt4r7ZwompaQaZLdzY3o3V\n2zIQ4++Kn0xlCz0R9WFhSkRE1/nwaGHfzMSlxp2ZOFDOdtZYvzQGuZUt+OMR/Vsmv52ZGAMnO85M\nJP14OdthxfxInCmpx6enSvVe7429Oaho6lCshf5ahp4tnLw7C3WtXUiOj4U1W+iJSId3AyIi+i+F\n1S1492Ae5qtH4kETzEwcqAcifbEg1g+//zwfBdUtt73O1TMT7wv3MWBCGs6+c1cApo71xGu7s1HR\nePuzd8+W1ON/vyrBo/cG446gEQZMqB9DzRb+qrAW/zxVhiemhSDG382ACYnI0rEwJSKiK6SUWL5Z\nAztrFV5dFK10nOusWRQFexsVElNvr2WSMxPJWIQQSIpTo0erxeqt6be1RlePFompafBztceLDynf\nQn81Q8wW7ujuxfJUDQI9HPD8bLbQE9F/Y2FKRERX/OdMGb4q1M1MdDXdzMSB8nGxx4oFkThVVId/\n30ZLIWcmkjGN9nTCc7PDsC+zEnvSLw36+D8cKUBuZQs2xMXA2QxbzPWdLfzeoXwU1rQiKU4NB1sr\nIyQkIkvGwpSIiAD0zUzcuDMLk0M88L2Jpp+ZOFAPTwzEPaEeSNqVhaqmgbcUcmYimcKT00IQ5eeK\n1Vsz0NjePeDj8qta8P8+z8fCWD/cH2E+LfTXut3ZwjkVzfjgcAHi7/DH9HHeRkxIRJaKhSkREQEA\n1m7/dmaiSmW+MwWFENgUH4vOHi1e3Z4xoGM4M5FMxdpKhdeWxfbNxx3g7F2tVmJ5qgYOtlZYY4Yt\n9FeztVZhk2628Jt7cwZ0TK9WIiE1Da4ONljJFnoi6gcLUyIiwsGsSuxMu4RfzRqLMQrOTByoEC8n\nPPvAOOzS9M1CvJXLMxOfn82ZiWR86gA3/GRqCP5xshSniupu+fp/nS7DqeI6rJgfCW8X828xvzNo\nBP7nntH425fF+Lr01rOFP/mqBN+UNmDVwkh4ONkaPyARWSQWpkREw1xLZw9WbumbmfizmcrPTByo\np2aEImKkC1ZtSUdzR/8tk5dnJkaPcsUT0zgzkUzjhTlhCBjhgMTUNHT29Pb7uqqmDmzanYV7Qz3x\n3YkBJkyon5fmRmCkqz0SUzQ3nS18saEdr+/JxowwbyydwBZ6IuofC1MiomHujT3ZqGjqwCYzmZk4\nUDZWKiQvi0Vlcwde39N/S2Hy7mzUtnRyZiKZlKOtNTbGqVFQ3Yr3DvU/e3fNtgx09miRFG9ZLebO\ndtZYvyQGOZXN+PDojc9PSolVW9KhlcDGpTEWdX5EZHr8LzQR0TB2tqQef9fNTLzTjGYmDtSEQHc8\nNiUYn5wswdmS61sm+2YmluLJ6aFQB3BmIpnWzDBvxN3hjw8O5yO3svm65/dmVGB3egWemz0OIV5O\nCiTUz+yovtnCvzt449nCOzWXcDC7Cr+ZE4ZAD7bQE9HNsTAlIhqmzHlm4mC8OCcco9wckJCi+a+W\nSc5MJHOwckEknO2skZCS9l+zd5s6urF6azoi/Vzx0+mhCibUT3+zhRvbuvHqtkyo/d3w2JRg5QIS\nkcVgYUpENEz9UTczcf1S85yZOFBOdtbYsDQGeVUt+MPhwiuPc2YimQNPZzusWhiFr0sb8MnJkiuP\nv74nG9XNnUiOV8PGglvM+5stnLQrC/VtXUhepmYLPRENiNHuFEKIQCHEISFEphAiQwjxrLH2IiKi\nwSmobsHvP8/Hglg/PBBpvjMTB2pWhA8WjR+F9w7lI7+qmTMTyazE3eGP6eO88PqeHFxqbMeZ4jp8\n8lUpHpsSgvGB7krH09u1s4W/LKjFv8+U4cnpIYgexRZ6IhoYIaW89atuZ2Eh/AD4SSm/FkK4ADgL\nYKmUMrO/YyZOnCjPnDljlDxERNRHq5X4/p++QvalJhz4zUz4uNgrHckgqps7MfvtIwjzdUaPVqKk\ntg0HXpjJ8RRkFkpr2zDnnSOYMsYLpXVtaO/qxb7nZ8DJgrsVrlZU04qH3jmKmWHeyK9qQa9WYu9z\nM9itQET/RQhxVko58UbPGe0dUynlJSnl17qvmwFkAeDnhBMRKezfZ8pwqqgOKxZEDpmiFAC8Xeyw\nYkEkThfXc2YimZ0gT0e88GAYPs+uQn5VCzbExQyZohT4drbw/sxKFLGFnohug0nuiEKIYAB3ADh5\ng+eeAvAUAAQFBZkiDhHRsFXV1IGkXVm4J9QDD08MVDqOwX33rgAcyamGlUpwZiKZnZ9MDcGxvBqE\neDlhVriP0nEM7qkZoTiWV40oPzdMG+eldBwisjBGa+W9soEQzgCOANgopUy92WvZyktEZFy/+PQs\nDmRVYe9zMyxyPAURERFZLkVaeXUb2wBIAfDprYpSIiIyrn0ZFdilqcCzD1jmzEQiIiIauoz5qbwC\nwJ8BZEkp3zbWPkREdGvNHd1YvTUDESNd8NQMy52ZSEREREOTMd8xnQrgxwDuF0Kc0/2Zb8T9iIio\nH6/vyUFlcweSl8Va9MxEIiIiGpqM9uFHUsovAAhjrU9ERANztqQOn5wswWNTgjFhCMxMJCIioqGH\nf21ORDSEdfb0IiFFg1FuDnhxTrjScYiIiIhuaOgM0CIiouv84XAh8qpa8NfHJg2pmYlEREQ0tPAd\nUyKiISq/qhnvHcrHovGjMCti6M1MJCIioqGDhSkR0RCk1UokpmrgYGuF1QujlI5DREREdFMsTImI\nhqB/nCrF6eJ6rFgQCW8XO6XjEBEREd0UC1MioiGmorEDr+3OxpQxnvjuXQFKxyEiIiK6JRamRERD\nzJpt6ejq1SIpTg0hOLWLiIiIzB8LUyKiIWRPegX2ZlTiudlhCPZyUjoOERER0YCwMCUiGiKaOrqx\nems6Iv1c8eT0EKXjEBEREQ0YC1MioiHitd3ZqGnpxGvL1LCx4u2diIiILAd/ciEiGgJOF9fh05Ol\neHxqCGID3JWOQ0RERDQoLEyJiCxcZ08vElLS4O/ugBceDFM6DhEREdGgWSsdgIiI9PP+oQIUVLfi\n48cnwcmOt3UiIiKyPHzHlIjIguVWNuP9w/lYMmEU7gv3UToOERER0W1hYUpEZKG0WonEVA2c7Kyx\namGU0nGIiIiIbhsLUyIiC/XpyRKcLanHygVR8HK2UzoOERER0W1jYUpEZIEuNbbjtT05mDbWC8vu\n9Fc6DhEREZFeWJgSEVkYKSVWb81Aj1aLjXExEEIoHYmIiIhILyxMiYgszJ70CuzPrMTzs8Mw2tNJ\n6ThEREREemNhSkRkQRrbu7F6WwaiR7niiWkhSschIiIiMggOvCMisiDJu7NR29KJvzw6CdZW/LtF\nIiIiGhr4Uw0RkYU4WViLf54qxRPTQqAOcFM6DhEREZHBsDAlIrIAHd29SEzVIGCEA55/MEzpOERE\nREQGxVZeIiIL8N6hfBTWtOLvP5kMR1veuomIiGho4TumRERmLqeiGR8cLkDcHf6YEeatdBwiIiIi\ng2NhSkRkxnq1EgmpaXCxt8bKBZFKxyEiIiIyChamRERm7JOvSvBNaQNWLYyCp7Od0nGIiIiIjIKF\nKRGRmbrY0I7X92Rj+jgvxN3hr3QcIiIiIqNhYUpEZIaklFi9NR1aCSTFqSGEUDoSERERkdGwMCUi\nMkO7NBU4kFWFFx4MQ6CHo9JxiIiIiIyKhSkRkZlpbOvGmm0ZUPu74fGpwUrHISIiIjI6DsMjIjIz\nSbuyUN/WhY8fnwRrK/79IREREQ19/ImHiMiMfFlQi3+fKcOT00IQ4++mdBwiIiIik2BhSkRkJjq6\ne7F8swZBHo54bnaY0nGIiIiITIatvEREZuL3n+ehqKYV//vEZDjYWikdh4iIiMhk+I4pEZEZyLrU\nhD8eKUT8nf6YPs5b6ThEREREJsXClIhIYb1aiYRUDVwdbLByQZTScYiIiIhMjoXpAH2eXYk39mYr\nHcNoNBcasf38RaVjGM03pfXYpbmkdAyiG/r7l8U4X9aANYui4OFkq3QcIiIiIpPj75gO0Kmievzh\nSAGmjvXClDFeSscxqMa2bvzkb6dR3dyJkW72mBTsoXQkg6pr7cITfzuD+rYupD49BXcEjVA6EtEV\n5Q3teGNvDmaGeWPx+FFKxyEiIiJSBN8xHaDnZo/DaE9HLE/VoKO7V+k4BrVpdxbqWrvg7WKHhJQ0\ndPYMrfPbsCMTTe3d8HSyRWKqBt29WqUjEQEApJRYuVkDKYENS2MghFA6EhEREZEiWJgOkL2NFZLi\n1CiubcPvDuYpHcdgviqsxb9Ol+GJaSF44zuxKKhuxXuHCpSOZTBHc6uR+k05fj5zDJLi1MiuaMaH\nRwuVjkUEANiedgmHcqrxmzlhCPRwVDoOERERkWJYmA7C1LFe+M5dAfjwaCGyLjUpHUdvHd29WJ6q\nQaCHA56fHYb7wn2wZMIofHA4H7mVzUrH01tbVw9WbNEg1MsJv7x/LOZEj8S8mJF492AeCqtblI5H\nw1xDWxfWbc9AbIAbHp8aonQcIiIiIkWxMB2kFfMj4eZgg4SUNPRqpdJx9PL/Ps9HYU0rkuLUV2Ym\nrloYBSc7aySmaqC18PN750AeyurakRSvhr1N3/mtXRwNO2sVlm/WQErLPj+ybBt3ZqG+rRvJ8bGw\nUrGFl4iIiIY3FqaDNMLJFqsXReH8hUZ8fKJY6Ti3LbuiCX84UoD4O/57ZqKXsx1WLojC2ZJ6fHqy\nRMGE+kkvb8RHxwrx/UmBuCfU88rjPq72SJwXia8K6/CfM2UKJqTh7ER+Df7v7AX8dHoooka5Kh2H\niIiISHEsTG/D4vGjMCvcG2/ty8GF+jal4wxar1YiIUU3M3Hh9TMTl93pj2ljvfDanhxcamxXIKF+\nenq1eCUlDZ7OdkicF3nd89+fFIjJIR7YuDMLVc0dCiSk4ayjuxeJmzUY7emI52aPUzoOERERkVlg\nYXobhBDYEKcGAKzckm5xLaH/+2UxzpU1YPXCG89MFEIgKU6NHq0Wq7dmWNz5/eV4ETIuNmHt4mi4\nOdpc97xKJbApXo2OHi3Wbs9UICENZ+8ezENJbRuS4r5tMSciIiIa7liY3iZ/dwe8OCcch3Oqse38\nRaXjDNhF3czEGWHeWDKh/5mJQZ6OeH52GPZnVmJPeoUJE+qntLYNb+/PxexIX8yLGdnv68Z4O+NX\ns8ZiZ9olHMyqNGFCGs4yLzbhw6OF+O5dAZg6dmjNQyYiIiLSBwtTPTw6JRjjA92xbnsm6lu7lI5z\nS1JKrNqSDq0ENg5gZuIT00IQPcoVq7dloLG920Qpb5+UEiu2aGCtUmH90uhbnt/PZo5BuK8LVm5J\nR0tnj4lS0nDVq5VITE3DCEcbrFhwfYs5ERER0XDGwlQPViqB5Hg1Gtu7sXFXltJxbmmn5hIOZlcN\neGaitZUKyfGxqG3pRPLubBMk1M/mb8pxLK8GL88Nh5+bwy1fb2utwqZlalQ0deDNvTkmSEjD2ccn\ninH+QiNWL4qGu+P1LfREREREwxkLUz1F+rniqRmh+OzsBRzPr1E6Tr8a2rrw6rYMqP3d8NiU4AEf\npw5wwxPTQvDPU6X4qrDWeAH1VNvSifU7MnFnkDseuXv0gI+7M2gE/uee0fjbl8U4W1JvvIA0rJXV\nteHNvTmYFe6NRbF+SschIiIiMjssTA3g1w+MQ7CnI5Zv1qCju1fpODeUtEs3M3GZGtZWg/u//fkH\nwxAwwgHLU833/DbszEJLZw+Sl8VCNciZkC/NjcBIV3skpqahq0drpIQ0XEkpsXJLOoQANsSpb9li\nTkRERDQcsTA1AHsbKyTFq1FS24Z3DuQpHec6Jwpq8J8zF/Dk9BBEj3Ib9PGOttZIilOjsKYV7x3K\nN0JC/RzJrcbmb8rx9MwxCPN1GfTxznbWWL8kBrmVLfjjkQIjJKThbNv5iziSW40X54TD3/3WLeZE\nREREwxELUwOZMsYLD08MwJ+OFSK9vFHpOFd0dPdieaoGQR6OeO6BsNteZ0aYN+Lu8McHhwuQU9Fs\nwIT6aevqwYrNGoR6O+EXs8be9jqzo3yxQO2H33+ej4LqFgMmpOGsvrUL67ZnYnygOx4dRAs9ERER\n0XDDwtSAls+PxAhHWySmatDTax4tob87mIfi2jZsilfDwVa/mYmrFkbB1cEGCalp6NWax2zTt/fl\n4kJ9O5LjY/WeCblmcRTsbVRITNVAaybnR5Ztw84sNLZ3IzleDatBtpgTERERDScsTA3I3dEWry6O\ngqa8ER+fKFY6DrIu9c1M/I6BZiZ6ONli1cJIfFPagE++KjFAQv2kXWjAX44X4Yd3B2FyiIfe6/m4\n2GPFgkicKqrDv8+UGSAhDWdf5NUg5esL+NnMUET6uSodh4iIiMissTA1sAVqPzwQ4YO39uWirK5N\nsRy9WomElDS4OdhgxXzDzUxcOsEfM8K88fqebFxsaDfYuoPV3atFQooGXs52SJgXYbB1H54YiHtC\nPZC0KwtVTR0GW5eGl/auXizfrEGIlxN+df84peMQERERmT0WpgYmhMD6pTFQCWDFlnRIqUxL6N+u\nzEyMwggnw81MFEJg49IYaCWweqty5/fnL4qQeakJ65ZEw9XexmDrCiGwKT4WnT1avLo9w2Dr0vDy\nzsFclNa1ISlOrXeLOREREdFwwMLUCEa5O+Clh8JxNLcaW89dNPn+F+rb8Oa+HNwX7o3F40cZfP1A\nD0e88GAYDmRVYZemwuDr30pJbSt+uz8Xc6J8MTfG8DMhQ7yc8OwD47BLU4H9mZUGX5+GtvTyRnx0\nrAjfmxiIe8d4Kh2HiIiIyCKwMDWSH98bjAmB7li3IxN1rV0m21dKiVVb0gEAG5bGGG1m4uNTg6H2\nd8OabRlobOs2yh43IqXE8s0a2FqpsG5JjNH2eWpGKCJGumDVlnQ0d5ju/Miy9fRqkZiqwQhHWyw3\nYAs9ERER0VDHwtRIrFQCycvUaGrvxoadmSbbd3vaJRzKqcZv5oQjYISj0faxtlJhU7wa9W1d2LQ7\ny2j7XCvl63Icz6/Fy/MiMNLN3mj72OjOr7K5A6/vyTHaPjS0/PV4MTTljXh1cRTcHA3XYk5EREQ0\n1LEwNaKIka74+cwxSP26HMfyqo2+X31rF9Zuy8D4ADc8ZoKZiTH+bnhyWgj+dboMXxbUGn2/mpZO\nbNiZiYmjR+BHk4OMvt8dQSPw6L3B+ORkCc6W1Bl9P7JsZXVteHt/Lh6I8MECteFbzImIiIiGMham\nRvbL+8ci1MsJyzdr0NbVY9S9Nu7KQkN7NzbFx5psZuJzs8MQ5OGI5Zs16OjuNepe63dkorWzB5vi\n1VCZ6PxefCgcfq72SEjRoLPHuOdHlutyi7lKAOuN2EJPRERENFSxMDUyexsrJMWrUVbXjncO5Blt\nn+P5Nfjs7AX8bEYookaZbmaig60VkuLUKKppxe8/N975HcqpwtZzF/HMrLEY5+titH2u5WxnjQ1x\nMcirasEfDheabF+yLFvOleNYXg1eeigco9wdlI5DREREZHFYmJrAPaGe+MHkQHx0rBDp5Y0GX7+j\nu29mYrCnI379gOlnJk4b54Vldwbgj0cKkXWpyeDrt3b2YOXmdIz1ccbT940x+Pq3cn+ELxaNH4X3\nDuUjv6rZ5PuTeatr7cL6HVm4I8gdP743WOk4RERERBaJhamJJMyLhKezHV5JSUNPr9aga79zIA8l\ntW1IilduZuLKBZFwc7BBQqoGvVrDzjZ9e38uyhvakRyvhp21Mue3emEUHGytkJiqgdbA50eWbcOO\nTDR3dCPZhC30REREREMNC1MTcXOwwdrF0ci42IS/HC8y2LoZFxvxp2OFeHhiAKaM8TLYuoM1wskW\nqxdF4XxZA/7+ZbHB1j1f1oC/Hi/CI/cEYWKwh8HWHSxvFzusWBCJ08X1+OfpUsVykHk5mluN1G/K\n8fOZYxA+0nQt5kRERERDDQtTE5oXMxKzI33x9v5clNa26b1er1bqZibamMXMxMXjR2FmmDfe2JuD\n8oZ2vdfr7tXilZQ0eLvY4eW5EQZIqJ/v3hWAKWM8kbwrG5VNHUrHIYW1dfVgxRYNQr2d8MyssUrH\nISIiIrJoLExNSAiB9UujYa1SYcUWDaTUryX0r8eLkHahEWsWRcPd0dZAKW+fEAIblsZASmDVlnS9\nz+9PxwqRXdGMdUti4Gqv/ExIIQSS4tTo6tVizdYMpeOQwt45kIeyunZsilOuhZ6IiIhoqGBhamJ+\nbg54eW44juXVYPM35be9TlldG97al4v7I3ywMNZ8ZiYGejjiN3PC8Hl2FXakXbrtdYprWvHugTzM\njR6Jh6JHGjChfoK9nPDs7HHYk1GBPekVSschhaSXN+KjY4X4weRA3B3qqXQcIiIiIovHwlQBj9w9\nGncGuWP9jkzUtnQO+ngpJVZsSTfbmYmPTw1BbIAb1m7PQENb16CPvzwT0tZahbVLoo2QUD8/nR6K\nSD9XrN6ajqaObqXjkIn16FrMPZ3tkDBP+RZ6IiIioqGAhakCVCqB5GWxaOnswYadWYM+fuu5izia\nW40XHwqHvxnOTLRSCSTHx6K+rRsbb+P8/u/sBZwoqEXCvAj4utobIaF+bKxUSI5Xo6alE6/tzlY6\nDpnYn78oQsbFJqxdHA03B+VbzImIiIiGAhamCgnzdcHT943F5m/KcSS3esDH1bV2Yd2OTEwIdMf/\nmPHMxKhRrnhqRmhfkZlfM+Djqps7sXFnFiYHe+AHk4KMmFA/4wPd8fjUEHx6shSni+uUjkMmUlrb\nht8eyMWDUb6YF2M+LeZERERElo6FqYKemTUGY7ydsGKzBm1dPQM6ZsPOTDS1dyN5mdrsZyY++8A4\nBHs6InGzBh3dvQM6Zt2OTLR39SIpXg2VmZ/fCw+Gwd/dAQkpaejsGdj5keW63GJurVJh/RLza6En\nIiIismQsTBVkZ22F5GWxuFDfjrf35d7y9cfyqpH6dd/MxIiRriZIqB97GyskxalRUtuGdw/m3fL1\nh7KrsP38Rfzy/rEY6+NsgoT6cbKzxsa4GBRUt+L9QwVKxyEjS/26HF/k1+CVueEY6WZ+LeZERERE\nloyFqcImBXvgh3cH4S/Hi5B2oaHf17V39WLF5nSEejnhl/dbzszEKWO98N27AvDh0UJkXmzq93Wt\nnT1YuSUdYb7O+PnMMSZMqJ/7wn2wZMIovH84H3mVzUrHISOpbenEhp2ZuGv0CPzo7tFKxyEiIiIa\ncliYmoGEeRHwcrZDQooG3b3aG77mnQO5KK1rQ1K85c1MXLEgEiMcbZCYmoZe7Y1nm765LwcXG9ux\nKT4WttaWdVmuWhgFJztrJKRqoO3n/Miyrd+RiZbOHiRbQIs5ERERkSWyrApgiHK1t8G6JdHIvNSE\nP39RdN3z6eWN+OiLInx/UiDuscCZie6Otli9KBrnLzTi4xPF1z1/rqwBH58oxo/vGY27Ro8wfUA9\neTnbYeWCKJwtqcenp0qVjkMGdiS3GlvOXcTT943FOF8XpeMQERERDUksTM3E3Bg/zInyxW/356Kk\ntvXK4z29WiTq1Ml1AAAXvklEQVSkpmGEoy0SLXhm4qJYP8wK98Zb+3Jwob7tyuPdvVokpKTB18Ue\nLz0UrmBC/Sy70x/Txnrhtd3ZqGjsUDoOGUhrZw+Wp2owxtsJz8yynBZzIiIiIktj1MJUCDFXCJEj\nhMgXQiQYc6+hYN2SGNhaqbB8swZS9rWE/vV4MdLLdTMTHS13ZqIQAhvi1ACAlVvSr5zfh0cLkV3R\njPVLY+Bib9nntzEuBj1aLVZt/fb8yLK9vT8X5Q3tSF4WCztry2qhJyIiIrIkRitMhRBWAN4DMA9A\nFIAfCCGijLXfUDDSzR4vz4vA8fxapHxdjtLaNry1PwezI30wX235MxP93R3w4pxwHM6pxrbzF1FU\n04p3D+ZhvnokHozyVTqe3kZ7OuG52WHYn1mJPekVSschPZ0va8Bfjxfhh3cHYVKwh9JxiIiIiIY0\nayOuPRlAvpSyEACEEP8CsARAphH3tHg/mhyErd+UY/2OTIT7uvTNTFw6dGYmPjolGFvPX8S67ZkI\n9nKCvbUKry6OVjqWwTw5LQTbz1/E6m0ZmDLWC24Olvsu8HDW3atFQqqm70PJ5kUoHYeIiIhoyDNm\nK68/gLKrvr+ge4xuQqUSSF6mRntXL04V1+HlueHwc3NQOpbBWKkEXlumRmN7N86W1GP5/Ej4uAyd\nmZDWViokx8eitqUTybuzlY5jNIdyqvDZ2QtKxzCaj44VIetSE9YtiYGrBbeYExEREVkKY75jOiBC\niKcAPAUAQUFBCqcxD2N9XPDq4micLanHI0NwZmLESFesWRSFjItN+N6kQKXjGJw6wA1PTAvBn44V\nYemEUbjbAj9J+WYu1LfhmU+/Rnt3L0K8nCzyk5RvprimFe8cyMVD0b6YG2P5LfRERERElkAY60Na\nhBD3AnhVSvmQ7vtEAJBSburvmIkTJ8ozZ84YJQ+RKbV19WDOb4/C1lqFXb+ebnGzZ/sjpcTjH5/G\nqaI6uNrbwNXBGjt+Nd3iZs/2R0qJR/58EmlljTjwm5nwdR067+YTERERKU0IcVZKOfFGzxnzp8nT\nAMYJIUKEELYAvg9gmxH3IzIbjrbWSIpTo7C6Fe8fylc6jsFsO38Rh3Oq8eKccGyMi0FuZQv+eKRA\n6VgG89nZCzieX4tX5kWwKCUiIiIyIaMVplLKHgC/BLAXQBaA/0gpM4y1H5G5mRHmjbg7/PHBkQLk\nVjYrHUdv9a1dWLc9E+MD3fHolGA8EOmLBbF++P3n+SioblE6nt5qWjqxcVcWJgWPwA8n89cKiIiI\niEzJqP13UspdUsowKeUYKeVGY+5FZI5WLoiEs501ElLSoNVa9mzTjbuy0NjejeR4NaxUfZ8SvWZR\nFOxtVEhM1Vj8+a3bnom2zl5sildDpRoan4JNREREZCmGxi+GEZkpT2c7rFoYha9LG/DJyRKl49y2\nL/Jq8NnZC3hqRigi/VyvPO7jYo8VCyJxqqgO/z5TdpMVzNuh7CpsO38Rv5g1BmN9XJSOQ0RERDTs\nsDAlMrK4O/wxfZwXXtudjYsN7UrHGbT2rl4s36xBiJcTfv3AuOuef3hiIO4N9UTSrixUNXUokFA/\nrZ09WLklHWN9nPH0fWOUjkNEREQ0LLEwJTIyIQQ2LlWjV0qs3poOY30StrG8czAXpXVtSIpT3/DT\nhYUQSIpXo7NHizXbLO/XyN/cl4PyhnYkx6thZz00Pj2ZiIiIyNKwMCUygSBPR/zmwXAcyKrCLk2F\n0nEGLL28ER8dK8L3Jgbi3jH9z2MN8XLCsw+Mw+70CuzLsJzzO1fWgI9PFOPH94zGxGAPpeMQERER\nDVssTIlM5PGpwVD7u2HNtgw0tnUrHeeWenq1SEzVYISjLZbPj7zl65+aEYqIkS5YvTUDzR3mf37d\nvVokpKTB18UeL88NVzoOERER0bDGwpTIRKytVNgUr0Z9Wxc27c5SOs4tfXyiGJryRry6OApujja3\nfL2NlQrJy2JR2dyB1/fkmCChfj48WojsimasWxINF/tbnx8RERERGQ8LUyITivF3w5PTQvCv02X4\nqrBW6Tj9Kqtrw1v7cvFAhA8WqP0GfNyEQHc8NiUYn5wswdmSOiMm1E9RTSvePZiHeTEjMSd6pNJx\niIiIiIY9FqZEJvbc7DAEeThieaoGHd29Sse5jpQSK7akQyWA9UtjIMTgZnq+OCcco9wckJCiQWeP\neZ7f8lQN7KxVWLs4Wuk4RERERAQWpkQm52BrhY1xMSisacX/+zxf6TjX2XruIo7mVuOlh8Ixyt1h\n0Mc72Vljw9IY5FW14A+HC42QUD//d+YCviysReK8SPi42isdh4iIiIjAwpRIEdPHeSP+Tn/84UgB\nsiualI5zRV1rF9btyMSEQHf8+N7g215nVoQPFo0fhfcO5SO/qtlwAfVU1dyBjbuyMDnYA9+fFKh0\nHCIiIiLSYWFKpJCVC6Lg6mCDV1I06NWax2zTDTsy0dTejeRlalipBtfCe63VC6PgYGuFxFQNtGZy\nfmu3Z6K9qxdJ8Wqo9Dw/IiIiIjIcFqZECvFwssXqhVE4X9aAv39ZrHQcHM2tRuo35Xj6vjGIGOmq\n93reLnZYuSASp4vr8c/TpQZIqJ+DWZXYmXYJv7x/LMb6OCsdh4iIiIiuwsKUSEFLJozCzDBvvLE3\nB+UN7YrlaOvqwYotGoR6O+GZWWMNtu537grA1LGeSN6VjcqmDoOtO1gtnT1YuSUdYb7O+PnMMYrl\nICIiIqIbY2FKpCAhBDYsjYGUwKot6ZBSmZbXdw7koayuHZvi1LC3sTLYukIIbFyqRlevFqu3phts\n3cF6c28OKpo6kLwsFrbWvO0RERERmRv+hEaksEAPR/xmThg+z67CjrRLJt8/vbwRHx0rxA8mB+Lu\nUE+Drx/s5YTnZodhb0Yl9qRXGHz9W/m6tB5/+7IY/3PPaNwZNMLk+xMRERHRrbEwJTIDj08NQWyA\nG9Zuz0BDW5fJ9u3p1eKVlDR4OtshYV6k0fZ5cnoIIv1csXprOpo6uo22z7W6erRITNFgpKs9Xpob\nYbJ9iYiIiGhwWJgSmQErlUByfCzq27qRtCvLZPv+5XgRMi42Ye3iaLg52BhtHxsrFV5bpkZNSyde\n251ttH2u9eHRAuRUNmP9khg421mbbF8iIiIiGhwWpkRmImqUK346PRT/OXMBJ/JrjL5faW0b3t6f\ni9mRvpgXM9Lo+8UGuOPxqSH49GQpThfXGX2/guoW/O7zfCxQ+2F2lK/R9yMiIiKi28fClMiMPDd7\nHEZ7OiJxswYd3b1G20dKieWbNbBWqbB+aTSEMM1MzxceDIO/uwMSUtLQ2WO889NqJRJTNbC3VmHN\n4iij7UNEREREhsHClMiM2NtYISlOjZLaNrx7MM9o+6R+XY4v8mvw8txw+Lk5GG2faznZWWNjXAwK\nqlvx/qECo+3z7zNlOFVUh+XzI+HjYm+0fYiIiIjIMFiYEpmZqWO98J27AvDh0UJkXmwy+Pq1LZ3Y\nsDMTdwa545G7Rxt8/Vu5L9wHSyaMwvuH85FX2Wzw9auaOpC0Kwt3h3jge5MCDb4+ERERERkeC1Mi\nM7RifiTcHWyQmJqGXq1hZ5uu35GJls4eJC+LhUplmhbea61aGAUnO2skpGqgNfD5vbo9A509WmyK\nV5usRZmIiIiI9MPClMgMjXCyxZrF0Th/oREfnyg22LpHcqux5dxFPH3fWIT5uhhs3cHycrbDqgVR\nOFtSj09PlRps3f2ZldilqcCzD4xDqLezwdYlIiIiIuNiYUpkphbF+mFWuDfe2peDC/Vteq/X1tWD\nFZs1GOPthGdmjTFAQv3E3+mP6eO88NrubFQ0dui9XnNHN1ZtSUfESBc8NSPUAAmJiIiIyFRYmBKZ\nKSEENsSpAQArt6RDSv1aXt/el4sL9e1IXhYLO2srQ0TUixACG5eq0aPVYtVW/c/vjb05qGzuwKZ4\nNWyseGsjIiIisiT86Y3IjPm7O+DFOeE4nFONbecv3vY6aRca8JfjRfjh3UGYFOxhwIT6CfJ0xPOz\nw7A/sxJ70itue52zJfX4369K8Oi9wbgjaIQBExIRERGRKbAwJTJzj04JxvhAd6zbnon61q5BH9/d\nq0VCigZeznZImBdhhIT6eWJaCKJHuWL1tgw0tncP+viuHi0SUtLg52qPFx8KN0JCIiIiIjI2FqZE\nZs5KJZAcr0Zjezc27Mwa9PEfHStC5qUmrFsSDVd7GyMk1I+1lQrJ8bGobelE8u7sQR//weEC5FW1\nYENcDJztrI2QkIiIiIiMjYUpkQWI9HPFUzNCkfL1BXyRVzPg44prWvHOgVzMifLF3Bg/IybUjzrA\nDU9MC8E/T5XiZGHtgI/Lr2rGe4fysTDWD/dH+BoxIREREREZEwtTIgvx6wfGIdjTEcs3a9De1XvL\n10spsWKLBrZWKqxbEmOChPp5/sEwBIxwQOJmDTq6b31+Wq1EYqoGDrZWWLMo2gQJiYiIiMhYWJgS\nWQh7GyskxatRWteGdw7m3vL1n529gOP5tXh5XgRGutmbIKF+HG2tkRSnRmF1K94/lH/L1//zdClO\nF9djxfxIeLvYmSAhERERERkLC1MiCzJljBcenhiAj44VIb28sd/X1bR0YuOuLEwcPQI/mhxkwoT6\nmRHmjbg7/PHBkQLkVjb3+7rKpg4k78rGvaGe+O7EABMmJCIiIiJjYGFKZGGWz4/ECEdbJKZq0NOr\nveFr1m3PRFtnLzbFq6FSCRMn1M+qhVFwsbdBQkoatNobzzZdszUDXb1aJMWrIYRlnR8RERERXY+F\nKZGFcXe0xauLo6Apb8THJ4qve/5QThW2nb+IX8wag3G+LqYPqCcPJ1usWhiJr0sb8MnJkuue35tR\ngT0ZFXh29jiEeDkpkJCIiIiIDI2FKZEFWqD2wwMRPnhrXy7K6tquPN7a2YOVm9Mx1scZT983RsGE\n+lk6wR8zwrzx+p4cXGpsv/J4U0c3Vm9NR6SfK346PVTBhERERERkSCxMiSyQEALrl8ZAJYAVW9Ih\nZV/L61v7clHe0I7keDXsrK0UTnn7hBDYuDQGvVqJVVed3+t7slHd3InkeDVsrHj7IiIiIhoq+JMd\nkYUa5e6Alx4Kx9Hcamw5V45zZQ3464kiPHJPECYGeygdT2+BHo544cEwHMiqwi5NBU4X1+GTr0rx\n2JQQjA90VzoeERERERmQuPxOhDmYOHGiPHPmjNIxiCxGr1Zi2QcnUFrXBi9nWzS2d2P/CzPham+j\ndDSD6OnVIu79E7jU2AE3B2t0dGux7/kZcLKzVjoaEREREQ2SEOKslHLijZ7jO6ZEFsxKJZC8TI2m\n9m7kVrZg3ZKYIVOUAoC1lQqb4tWob+tCQXUrNsTFsCglIiIiGoL4Ex6RhYsY6YqNcTG4UN+Oh6JH\nKh3H4GL83bB2cTTqWrswK9xH6ThEREREZAQsTImGgO9NClI6glE9cs9opSMQERERkRGxlZeIiIiI\niIgUxcKUiIiIiIiIFMXClIiIiIiIiBTFwpSIiIiIiIgUxcKUiIiIiIiIFMXClIiIiIiIiBTFwpSI\niIiIiIgUxcKUiIiIiIiIFMXClIiIiIiIiBTFwpSIiIiIiIgUxcKUiIiIiIiIFMXClIiIiIiIiBTF\nwpSIiIiIiIgUxcKUiIiIiIiIFMXClIiIiIiIiBTFwpSIiIiIiIgUxcKUiIiIiIiIFMXClIiIiIiI\niBQlpJRKZ7hCCFENoGSQh3kBqDFCHLJ8vDboZnh9UH94bVB/eG1Qf3ht0M3w+vjWaCml942eMKvC\n9HYIIc5IKScqnYPMD68NuhleH9QfXhvUH14b1B9eG3QzvD4Ghq28REREREREpCgWpkRERERERKSo\noVCYfqh0ADJbvDboZnh9UH94bVB/eG1Qf3ht0M3w+hgAi/8dUyIiIiIiIrJsQ+EdUyIiIiIiIrJg\nFl2YCiHmCiFyhBD5QogEpfOQ+RBCFAshNEKIc0KIM0rnIeUIIf4ihKgSQqRf9ZiHEGK/ECJP988R\nSmYk5fRzfbwqhCjX3T/OCSHmK5mRlCGECBRCHBJCZAohMoQQz+oe5/1jmLvJtcF7xzAnhLAXQpwS\nQpzXXRtrdY+HCCFO6mqWfwshbJXOao4stpVXCGEFIBfAgwAuADgN4AdSykxFg5FZEEIUA5gopeTM\nqGFOCDEDQAuAv0spY3SPvQ6gTkqZrPtLrRFSyleUzEnK6Of6eBVAi5TyTSWzkbKEEH4A/KSUXwsh\nXACcBbAUwGPg/WNYu8m18TB47xjWhBACgJOUskUIYQPgCwDPAngBQKqU8l9CiD8AOC+l/EDJrObI\nkt8xnQwgX0pZKKXsAvAvAEsUzkREZkZKeRRA3TUPLwHwN93Xf0PfDxQ0DPVzfRBBSnlJSvm17utm\nAFkA/MH7x7B3k2uDhjnZp0X3rY3ujwRwP4DPdI/zvtEPSy5M/QGUXfX9BfCmQN+SAPYJIc4KIZ5S\nOgyZHV8p5SXd1xUAfJUMQ2bpl0KINF2rL1s1hzkhRDCAOwCcBO8fdJVrrg2A945hTwhhJYQ4B6AK\nwH4ABQAapJQ9upewZumHJRemRDczTUp5J4B5AJ7RtesRXUf2/T6DZf5OAxnLBwDGAJgA4BKAt5SN\nQ0oSQjgDSAHwnJSy6erneP8Y3m5wbfDeQZBS9kopJwAIQF+HZ4TCkSyGJRem5QACr/o+QPcYEaSU\n5bp/VgHYjL4bA9FllbrfEbr8u0JVCuchMyKlrNT9YKEF8Cfw/jFs6X5HLAXAp1LKVN3DvH/QDa8N\n3jvoalLKBgCHANwLwF0IYa17ijVLPyy5MD0NYJzuU65sAXwfwDaFM5EZEEI46T6MAEIIJwBzAKTf\n/CgaZrYBeFT39aMAtiqYhczM5aJDJw68fwxLug8x+TOALCnl21c9xfvHMNfftcF7BwkhvIUQ7rqv\nHdD3Ia1Z6CtQv6N7Ge8b/bDYT+UFAN3HcL8DwArAX6SUGxWORGZACBGKvndJAcAawD94bQxfQoh/\nArgPgBeASgBrAGwB8B8AQQBKADwspeQH4AxD/Vwf96GvFU8CKAbws6t+p5CGCSHENADHAGgAaHUP\nL0ff7xLy/jGM3eTa+AF47xjWhBCx6PtwIyv0vQH4HynlOt3Ppv8C4AHgGwCPSCk7lUtqniy6MCUi\nIiIiIiLLZ8mtvERERERERDQEsDAlIiIiIiIiRbEwJSIiIiIiIkWxMCUiIiIiIiJFsTAlIiIiIiIi\nRVnf+iVERETDjxDCE8BB3bcjAfQCqNZ93yalnGKCDO4AfiilfN/YexERESmJ42KIiIhuQQjxKoAW\nKeWbJt43GMAOKWWMKfclIiIyNbbyEhERDZIQokX3z/uEEEeEEFuFEIVCiGQhxI+EEKeEEBohxBjd\n67yFEClCiNO6P1NvsGa07rhzQog0IcQ4AMkAxugee0P3upd0a6QJIdbqHgsWQmQLIT4VQmQJIT4T\nQjia7n8RIiIi/bAwJSIi0s94AD8HEAngxwDCpJSTAXwE4Fe617wL4LdSykkAlumeu9bPAbwrpZwA\nYCKACwASABRIKSdIKV8SQswBMA7AZAATANwlhJihOz4cwPtSykgATQB+YfhTJSIiMg7+jikREZF+\nTkspLwGAEKIAwD7d4xoAs3RfzwYQJYS4fIyrEMJZStly1TpfAlghhAgAkCqlzLvq9ZfN0f35Rve9\nM/oK1VIAZVLK47rHPwHwawAmbT0mIiK6XSxMiYiI9NN51dfaq77X4tv/zqoA3COl7OhvESnlP4QQ\nJwEsALBLCPEzAIXXvEwA2CSl/ON/Pdj3u6jXfmgEP0SCiIgsBlt5iYiIjG8fvm3rhRBiwrUvEEKE\nAiiUUv4OwFYAsQCaAbhc9bK9AH4ihHDWHeMvhPDRPRckhLhX9/UPAXxh8LMgIiIyEhamRERExvdr\nABN1H1iUib7fJ73WwwDShRDnAMQA+LuUshbAcSFEuhDiDSnlPgD/APClEEID4DN8W7jmAHhGCJEF\nYASAD4x8TkRERAbDcTFEREQWjmNliIjI0vEdUyIiIiIiIlIU3zElIiIiIiIiRfEdUyIiIiIiIlIU\nC1MiIiIiIiJSFAtTIiIiIiIiUhQLUyIiIiIiIlIUC1MiIiIiIiJSFAtTIiIiIiIiUtT/B51EMrLO\nkPzrAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1152x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "48Qvxp5iYgqg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 548
        },
        "outputId": "26823efd-2d0a-4b51-c7ba-aa0a584993e9"
      },
      "source": [
        "final_pos_list = []\n",
        "\n",
        "for _ in range(200):\n",
        "    sim2 = randomWalk()\n",
        "    for _ in range(30):\n",
        "        sim2.step()\n",
        "    final_pos_list.append(sim2.display())\n",
        "\n",
        "plt.figure(figsize=(16,8))\n",
        "plt.hist(final_pos_list, bins=50)\n",
        "plt.axvline(np.mean(final_pos_list), color='r', linestyle='dashed', linewidth=2)\n",
        "plt.axvline(6, color='g', linestyle='dashed', linewidth=2)\n",
        "plt.xlabel(\"Final position\")\n",
        "plt.ylabel(\"Frequency\")\n",
        "plt.title(\"Histogram of the final posiiton of random walk based on coinflip outcome\")\n",
        "plt.show()\n",
        "\n",
        "print(f\"The sample mean is {round(np.mean(final_pos_list), 4)}.\")\n",
        "print(f\"The sample variance is {round(np.var(final_pos_list), 4)}.\")"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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A0Wy1Vwm+IMn2JCelu1rwk5P8UpJvmF9qAHCIrrlmlDAnPXDRKHEAgGFWOyT4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\n",
            "text/plain": [
              "<Figure size 1152x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "The sample mean is 5.42.\n",
            "The sample variance is 28.8236.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BFyjoa7ArerL",
        "colab_type": "text"
      },
      "source": [
        "# Gambler's Ruin"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9GdDpr73p_9_",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        },
        "outputId": "0a08406d-4da3-44c9-b063-4d100495ea2c"
      },
      "source": [
        "def gamblersRuin():\n",
        "    gambler = 100\n",
        "    casino = 2000\n",
        "    count = 0\n",
        "    while gambler != 0 and casino != 0:\n",
        "        i = random.random()\n",
        "        if i < 0.5:\n",
        "            gambler+=1\n",
        "            casino-=1\n",
        "            count+=1\n",
        "        else:\n",
        "            gambler-=1\n",
        "            casino+=1\n",
        "            count+=1\n",
        "    if gambler == 0:\n",
        "        print(\"Gambler is broke!\")\n",
        "        print(count)\n",
        "    if casino == 0:\n",
        "        print(\"Casino is broke!\")\n",
        "        print(count)\n",
        "\n",
        "gamblersRuin()"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Gambler is broke!\n",
            "45678\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bz54tqQOr2bV",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 548
        },
        "outputId": "ed567eec-81dc-4160-fae5-af89c6af23bd"
      },
      "source": [
        "def gamblersRuinMC():\n",
        "    gambler = 100\n",
        "    casino = 2000\n",
        "    count = 0\n",
        "    while gambler != 0 and casino != 0:\n",
        "        i = random.random()\n",
        "        if i < 0.5:\n",
        "            gambler+=1\n",
        "            casino-=1\n",
        "            count+=1\n",
        "        else:\n",
        "            gambler-=1\n",
        "            casino+=1\n",
        "            count+=1\n",
        "    return(count)\n",
        "\n",
        "outcomes = []\n",
        "\n",
        "for _ in range(200):\n",
        "    outcomes.append(gamblersRuinMC())\n",
        "\n",
        "plt.figure(figsize=(16,8))\n",
        "plt.hist(outcomes, bins=50)\n",
        "plt.axvline(np.mean(outcomes), color='r', linestyle='dashed', linewidth=2)\n",
        "plt.xlabel(\"Outcome\")\n",
        "plt.ylabel(\"Frequency\")\n",
        "plt.title(\"Histogram of the outcome of 200 gambling events\")\n",
        "plt.show()\n",
        "\n",
        "print(f\"The sample mean is {round(np.mean(outcomes), 4)}.\")\n",
        "print(f\"The sample variance is {round(np.var(outcomes), 4)}.\")"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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kz+rB65IcW1W3XVRtAAAATNuGXjNbVWckuby737LXqhOTfGjm8WVjGwAAAFzHhn3PbFXd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\n",
            "text/plain": [
              "<Figure size 1152x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "The sample mean is 228061.9.\n",
            "The sample variance is 409446730787.87.\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LSP-eENL00lH",
        "colab_type": "text"
      },
      "source": [
        "# Monty Hall"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8bZdcmVltv58",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "required_experiments = 100000"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sSlnggQM07HH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "33f9eadc-67ce-4277-8ac4-b9a374b068b3"
      },
      "source": [
        "# The Monty Hall scenario.\n",
        "\n",
        "experiments = 0\n",
        "successes = 0\n",
        "while experiments < required_experiments:\n",
        "\n",
        "    # The car is hidden behind a random door\n",
        "    car_door = random.randint(1, 3)\n",
        "\n",
        "    # The contestant selects a random door\n",
        "    contestant_door = random.randint(1, 3)\n",
        "\n",
        "    # The host opens a different door that has a goat behind it\n",
        "    host_door = random.choice(list(set([1, 2, 3]) - set([car_door, contestant_door]))) \n",
        "\n",
        "    # The contestant switches to the other door (not the one she chose originally and not the goat)\n",
        "    contestant_door = (set([1, 2, 3]) - set([contestant_door, host_door])).pop()\n",
        "\n",
        "    # Did the contestant win? Count that as a success.\n",
        "    if contestant_door == car_door:\n",
        "        successes += 1\n",
        "    experiments += 1\n",
        "\n",
        "print(successes / experiments)"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.66829\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YLgD2IWN09Uu",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "f41c4958-7f32-4e19-dbff-373d849b7716"
      },
      "source": [
        "# The earthquake scenario.\n",
        "\n",
        "experiments = 0\n",
        "successes = 0\n",
        "while experiments < required_experiments:\n",
        "\n",
        "    car_door = random.randint(1, 3)  # The car is hidden behind a random door\n",
        "\n",
        "    contestant_door = random.randint(1, 3)  # The contestant selects a random door\n",
        "\n",
        "    earthquake_door = random.randint(1, 3)  # The earthquake opens a random door\n",
        "\n",
        "    # What if the earthquake opened the contestant's door? Nothing, the contestant just switches to another one.\n",
        "    # What if the earthquake opened the door with a car behind it?\n",
        "    if earthquake_door == car_door:\n",
        "        # This does not fit the scenario so don't count it as a valid experiment.\n",
        "        continue\n",
        "\n",
        "    # The contestant switches to another door (not the one she chose originally and not the goat).\n",
        "    contestant_door = random.choice(list(set([1, 2, 3]) - set([contestant_door, earthquake_door])))\n",
        "\n",
        "    # Did the contestant get the car? Count that as a success.\n",
        "    if contestant_door == car_door:\n",
        "        successes += 1\n",
        "    experiments += 1\n",
        "\n",
        "print(successes / experiments)"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.50073\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f5j_w0Zw1D3i",
        "colab_type": "text"
      },
      "source": [
        "### Analyzing how quickly the error converges to the true value for the (standard) Monty Hall scenario"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HznEuvm70_7u",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 393
        },
        "outputId": "b9abc5c5-2718-4568-8c9f-0ce177649ae7"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "true_value = 2/3\n",
        "errors = []\n",
        "\n",
        "experiments = 0\n",
        "successes = 0\n",
        "while experiments < required_experiments:\n",
        "    car_door = random.randint(1, 3)\n",
        "    contestant_door = random.randint(1, 3)\n",
        "    host_door = random.choice(list(set([1, 2, 3]) - set([car_door, contestant_door]))) \n",
        "    contestant_door = (set([1, 2, 3]) - set([contestant_door, host_door])).pop()\n",
        "    if contestant_door == car_door:\n",
        "        successes += 1\n",
        "    experiments += 1\n",
        "    errors.append(abs(true_value - successes / experiments))\n",
        "\n",
        "plt.figure(figsize=(12, 6))\n",
        "plt.loglog(range(1, experiments + 1), errors, 'k.', alpha = 0.4)\n",
        "plt.xlabel('Number of simulations')\n",
        "plt.ylabel('Absolute error')\n",
        "plt.show()"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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TCUOHDkVDQwNKSkqQn58PlUoFlUqFGzduQK/Xo6SkBOnp6QgJCUFERATmzp2L9PR05OTk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\niIiIiATs/wN8gVztbGi4HgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "37gzfQlZ1MDD",
        "colab_type": "text"
      },
      "source": [
        "### Analyzing how quickly the error converges to the true value for the Earthquake version of the Monty Hall scenario"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hjThAH-m1Ggp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def simulate_Monty_hall_earthquake(n):\n",
        "    random.seed(2)\n",
        "    switchscore = 0\n",
        "    stayscore = 0\n",
        "    doors = [1,2,3]\n",
        "    counter = 0\n",
        "    errors = []\n",
        "    for i in range(1, n+1):\n",
        "        car = random.sample(doors, 1)\n",
        "        my_guess = random.sample(doors, 1)\n",
        "        earthquake_door = random.sample(set(doors) - set(my_guess), 1)\n",
        "        if earthquake_door != car:\n",
        "            counter+=1\n",
        "            if my_guess == car:\n",
        "                stayscore+= 1\n",
        "            else:\n",
        "                switchscore += 1\n",
        "            errors.append(abs(1/2 - switchscore/counter) )\n",
        "\n",
        "        else:\n",
        "            continue\n",
        "    plt.figure(figsize=(12, 6))\n",
        "    plt.loglog(range(1, counter + 1), errors, 'k.', alpha=0.4)\n",
        "    plt.xlabel('Number of simulations')\n",
        "    plt.ylabel('Absolute error')\n",
        "    plt.show()\n",
        "    return stayscore/counter, switchscore/counter"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_jg1RF6e1OqI",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 410
        },
        "outputId": "a45ebfb1-42e8-4c6d-b6dd-d822d53ce36d"
      },
      "source": [
        "simulate_Monty_hall_earthquake(required_experiments)"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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uz8sRcCIKVjCTIbcIIe4Vff3XmYiIIqJt6UhcXFyfJl8eOXIEBoMBGRkZMBgM\nOHLkSAgjDZ2///3vqK2t7bD9/PnzWLFiBQBg3bp1cLlcaG5uhsvlwqZNm7o8p6ZpWLBgAQoKCjBn\nzhxYrdawxE5Eg0cwNdo/BjAfQIsQwgVAAJBSyuSwRkZERCERysmXY8eORWNjIxoaGgC0TrSMNlar\nFb/97W8D7l+zZg0mT56Mffv2tdt+6tSpLs+7YcMGrFq1Ck1NTRBCoLGxEX/72984sk1EAXU7oi2l\nTJJS6qSUMVLK5AuPmWQTEQ0Qqqpi5syZuOaaa/q8QI7RaMSkSZNgMpmQmZmJzz//POra/G3atAl2\nuz3g/pMnT+LnP/95h5H9r776CoWFhV2e1+12Q0oJr9eLXbt2cVSbiLoUVB9tIcR3hRAvXfj5TriD\nIiKi0PEtkLN//36sXr2614mxpmn46KOPYLfb4XQ6kZSUBCllWPuA95SmaUGVs5w+fRpSynbbXC4X\n3nrrrYDHXDzi7XQ6sWPHjt4FSkSXhG4TbSHECwB+BuDrCz8/E0L8LtyBERFRaIRigRxN01BYWIiW\nlhZMmzYNXq8X58+fx6FDh6Ao0dEpVtM0LFu2DFVVVdDperce2/79+zvdvnbtWuzdu7fD9o8//rhX\n1yGiS0Mw/zreCSBXSukFACHEXwHsA/CrcAZGRESh0dcabV8C63A4UFRUhGHDhmHkyJGYOnUqvF4v\nPB5PmCLvGZvNhrKyMpw7dw7x8fFobGyEEAKjR4+Gqqr4/PPPuz3H119/jcLCQmRnZ/u7iwDAY489\nhpaWlg7Pr6+vD/l9ENHgEewwxFAAvoI3Y5hiISKiMPAtkLN9+3bU1NSgqqqqR3XaNpsNDocDOp3O\nX6MshICmaRgxYkTYV7YM1tatW7Fq1Sp/QpycnIwhQ4bgP/7jP/DFF18ElWh7vV4888wziIuLQ2Nj\nI0aMGIHMzMyA5TYTJkyApmn+13bKlCkwm80hvS8iGriCSbR/B2CfEGIrWjuO3Azg6bBGRUREIVVV\nVYWlS5fC6XTiD3/4A+6//37MnDkzqKRQURTs27cPlZWVqK6uxoQJE/x12tHS+dVqteKZZ55pN+p8\n7tw5OJ1OnDt3rkM9dlc+++wz/3ni4uKg1+u7vG5ubi4qKysBAMOGDcPatWthsVh6dyNENKh0WcR2\noXf2DgA3AlgL4H0A35BSruqH2IiIKERKSkrgdDrhcDhQVlaGpUuX4sEHH+yyy4aPpmkYMmQIzp07\nB7fb7e8/fdNNN/W5L3eoLFmyxN9ysC2Px4ODBw/ihhtuQFxcXFDnapusu91uOJ3OgM/1fQDxqa2t\nxYMPPhh1nViIKDK6TLRl62D5tJgAACAASURBVBDARimlTUq5/sJPZVfHEBFR9MnJyYHX60VNTQ2E\nENDpdNA0Da+99lqXSaGv08jhw4fhcDgQExMDRVFQX1+PL7/8Eo2NjREvHSksLMTq1asD7h8xYgSm\nT5/ub3GYmJjYbv+wYcNCGk9lZSU2bNgQ0nMS0cAUzLTsL4UQ14c9EiIiChuz2Yyf/vSnGDlyJOLj\n4+HxeJCYmIiUlJQuR6RtNhtaWlqQnp4Or9eLhoYG6HQ6xMXFRUXpiKZpmD9/Ptxud6f7hwwZ4u8d\n/uKLL+Ltt9/G3LlzoSiK/0NDTk5OyOMK5psCIhr8gqnRzgPwkBDiOIAG/N/KkBPDGlkvCCGmA5g+\nZsyYSIdCRBRVrFYr3n77bXi9XsTGxiItLQ3XXXcdTCZTlyPSdXV1sFqtqK2thaIocLlc/omR11xz\nDZqbm2Gz2SK2OuKGDRtQUlIScP8999zjr0NXVRWqqkJRFHz88cdwOBwwGo344Q9/iL1798LlcnV7\nPbPZjLKysm6fG8y5iGjwCybRviPsUYSIlHIDgA2TJk2aG+lYiAY6TdP87c24xPTAV1JSAofDgbNn\nz8LhcMDpdCItLQ1z584N+P5arVY8/fTTOHv2LCorKyGEQGxsLPR6PdxuN3bv3o3s7OyIlY5omoYP\nPvgATU1NHfb5RqxvvvnmDvvMZjPeffddlJSUICcnB+np6fj973+PgwcPdnvN22+/HZWVld0m0ufP\nnw/+Roho0Ooy0RZC6AH8U0p5VT/FQ0RRwNc32ePxQFEUFBQUMNke4HJycuB2u1FfXw8pJTweD0pK\nSrB8+XJkZ2d3+v7u3LkTx48fR1NTk78nNdCaxPomFkaydMRms3Va9mIwGJCVlYWYmBhcccUVnR5r\nNpvbdVy5+eabg0q0R40ahdzc3G4XqikqKvLXvvMDK9Glq7vJkC0ADgkhRvdTPEQUBUKxkiBFF7PZ\njP/+7//G8OHDERMTAyEEEhMT0dLSEvD9TU1Nhdfr9SfZMTEx/vpsVVUxbdq0iHYdKS8v73Qlx4kT\nJyIvLw+33HJL0D2tg02CT506hf/8z/9EUlJSl887d+4cnnvuOTzyyCMoKCjAk08+yU4kRJegYEpH\nhgEoEULsRmuNNgBASvndsEVFRBHV15UEKTrdc889AIDFixejpqYGKSkpXdZo5+fnIzc3F59//jn0\nej1iYmIQGxvr79px8uRJGI3GiP1+bN++HV6vt922+Ph4LFiwAFlZWT0aRZ44cSLi4uICTqr00TQN\nFosF69evx8cff4wDBw6gqakJBw8exPHjx9s994033oDX64UQAnv37sXNN9+MOXPm9OwmiWhACybR\nfibsURBRVPGtJMivvAcXTdNQXFyMG2+8ETU1NZgxYwby8/MDvr+lpaWwWq2QUsLr9fpLRsaNG4fh\nw4cjKSkJEydGbl58Z/2tp0yZgqysLOTm5vboXFdddRWGDBnSbaI9YsQIAIDFYoHFYvHPZairq8P0\n6dPbLcnu+xAgpYTb7cZ7773HRJvoEtNtez8p5TYAFQBiLvz5CwBfhjkuIoowVVWRm5vLJHsQ8ZUE\n5eTkIDU1td3CLJ0pKipCU1MTWlpa0NLSArfbjaSkJAwfPhxlZWXYvHkz/vCHP2DJkiURKYtQVbVd\njXhaWpp/JLunPB4P0tLS2m0zGAztHsfExOAb3/hGhxhyc3NhsVhwyy23dHmNXbt2wWq19jg2Ihq4\nuk20hRBzAawB8MaFTRkA1oUzKCIiCj1fSVBJSQn27duHXbt2YdmyZQGT5Ly8PHi9XrjdbiiKgqFD\nh+LKK6/ExIkTkZWVhdTUVCQlJaGuri4iddrV1dWQUkIIASEExowZg3nz5vXqw6HJZMLw4cMBtE7w\n1Ov1HUbrJ0yYgPz8/IDn6O7Dhsvl6nJhHSIafIIpHSkAcAOAIgCQUh4RQgwPa1RERBRyvpIg32Iq\nOTk5qKioCNgHOzs7G/PmzcObb76JpqYm6PV6ZGZm4q677oKmaThx4gQAYOjQof1ep11YWIj33nvP\n/zgxMbFdz+yeUlUVixYtwty5c+FyuZCSkoJvfvObKCsrA9A64j1r1qwuk/jOloC/WFc9v6n/WK1W\nlJSU4MyZM/jXv/4FAJgzZ45/HgNRqASTaLullE2+r+eEEAoAGdaoiIgoLFRVhcViQUlJSZeTXdu2\neLz11luRmpoKs9mM6dOnQ1VVPPXUU9iwYQMqKipw22239XuJUVFRkb/9pNfrxdChQ/Htb3+7T+e0\nWCz44IMP/P21AWDz5s1wuVwwGAzdnj8zM7PbRLqxsbFPMQ5Gs2bNwrZt2zB16tR2H55CbcGCBdi8\neTOGDBmCXbt2ddi/adMmvP/++0y2KaSCSbS3CSH+A4BBCHE7gMcAbAhvWEREFC7BTHb11XOnpKTg\n008/RWxsrH8EGwCqqqrwzjvvwOPx4NNPP8Xrr7/e69Hk3nC73e0WhZk+fXpIrn9xf+233nrLn3h3\nd/4ZM2Zg48aNkDLwWNTFky01TfPXbZvN5ktuTsSsWbOwatUqAMCqVaugaRq2bt0a1ut05d577+3y\n/SPqqW5rtAE8DaAKwFcAfgxgI4D/CmdQREQUWb567tLSUgCtZSRte6qXlJTA4/EgKyvLv/hNf6qp\nqUFsbCwSEhIQGxsLRQlm3KjnzGYzHnjggaCS+OnTp2P8+PFdPqdtoq1pGubMmYPvfe97+M53voO7\n7777kum1PXv2bAwfPrxD8ltYWOgvbQqVGTNmBJVk+3z/+9/HihUrQhoDXbqC6TrilVL+f1LK+6WU\n9134Mz/uERENUL6ykL/85S945plnOu2EoaoqZs6ciRtuuAFmsxl2u71dmUlOTg4URUF5eTkURfGX\nWvQX32JKLpfLv7hSpKmqiqlTp3b5HN+ESwD4+9//jn/84x9oaGhAY2MjPvvsM/zmN78Jc5Shp2ka\n1qxZgzfeeKPbrioLFy5ETEwM3n77bVRVVXX6nFtuuQVr167tUQwzZsxAWloaZsyY0W57QUEBPvzw\nwx6da+XKlXjkkUeYbFNIBDOiTUREg4jNZoPD4UBZWRmsViuWLl3aYSRV0zSsXr0ax48fR0JCAqZN\nm4aCggJ/aYPZbMbChQvxve99DwsXLuzXshEAGDlyJDIzMzF69GhkZmZi5MiR/Xr9QBISEjrdLoSA\nTqfDlClT/Ns6G2Vdt25gNfUqLCzEiBEjcP/99+PRRx9FXl5ewGR74cKFePbZZ+HxeLo977333ht0\nsj1jxgx8+OGHqKmpwYcfftgu2f7Tn/4U3I104pFHHun1sUQ+4fmujYiIopbJZILL5YLdbkdKSgoM\nBoO/JMRXt+2r0c7MzERFRQVSU1Pb1Q9rmoZPPvkENpsNu3fvBtA6mbC/qKqK5uZmtLS0wOv1Rk1t\ns2/VzLYURYHBYEBsbCxGjx7t337s2LEOz/VNliwsLMTHH3+MzMxM/wTUaGO1Wjv0Dnc6nbjrrruw\ne/duzJs3D1988QW+/e1vY9myZXj11Vd7dP6ZM2cGlZRfPGLd9nFfv4AXQrBmm/ok6ERbCJEgpey4\nDBcREQ0oqqpi3rx5WLp0KQwGA4xGIxRF8XcZURQFM2fOhKIoATuT2Gw22Gw2FBYWwul04tixY3jn\nnXf6bWR76NChuOOOO9o9jgY6XccvihVFQXJycrvl4gsLCzstnXC5XJg2bRq++OILOJ1OSCmxfPly\nrFu3LiqSbV9bvJycHCxZsqTT55w4cQJjx471T1Z9/fXXsXnzZtjt9h5dq6WlBSkpKT0+DgDWrl2L\nH/zgBz0+rjMxMTFobm4OuL/tokmVlZX+1UOBvif6NPB1m2gLISYDeAtAIoDRQohrAPxYSvlYuIMj\nIqLwMJvNWLRoUcARbI/H02VnEpPJBLvdDqfTidTUVOj1epSUlPRbom0ymZCcnIy6urqI9PEO5MyZ\nMx22JScnY8iQIWhsbERdXR00TcMzzzzT6fFutxuffPJJu22ff/45/vznP+PZZ58NS8zBys3Nxf79\n+wG0rpqZnJwc8LltO8IAwNGjR3t1zdraWkyZMgU7d+7sdH+gyaMPPfRQyFopejweCCGwdevWDt/a\ntE2yAbRLsn37pZRYu3atv4Uh2wdeWoIZ0X4FwB0A1gOAlHK/EOLmsEZFRERhpWlahyS6qxHsi6mq\niscffxzHjh2DXq+HwWDo9wmRvtHCaBo1vLh0xGg0YsiQISgvLwcALF68GEOHDm3XKjEYb775ZkQT\n7SlTpviTbKB15N3lcvXLtTvree0zefLkTrcHk2RnZGTgzJkzQf/+3HLLLXjuuefw+eefA2hd4CYY\na9euxb333gsAWLp0KSwWS1haGFJ0Et39ggkhiqSUeUKIfVLKay9s2y+lvKZfIuyFSZMmyT179kQ6\nDCKiqOTrOmKz2WC32/H444/DYrG0S74BtCslaTsRsu152i5a05812lu2bMG7776L7Oxs2O12zJw5\nE7m5uf12/UDWrFmDn/zkJ3C73ZBS4qGHHsL69ev9NfBCCDz00ENYuXIlWlpagj5vXFxcRBe7uXjk\ntr9VVlZ2WjrT07j+/d//HT/72c86fEvT3/en1+uDqj+n6CeE2CulnBRofzAj2icvlI9IIUQMgJ8B\nKA1VgERE1L+6qq/2JR/FxcXtSkkuXqZd0zQsXrwYW7duxblz51BcXIy0tLR+KR3RNA0fffQRDh06\nhEOHDiEvLy9qSkfy8/Nx7733+mt1b7vtNqxcudK/X0qJTz/9tEdJNgCkpqb6/1xYWIiioiLk5eX1\n64ebUFMUJehkc8SIER2S7d702/7LX/7S6fbRo0f3+FuGvmhpaUFSUhKOHj0aFbX3FD7BJNqPAngV\nQAaA0wA2o3V1SCIiGoA6q6/euXOnv97VbDb7F6zpajLksWPHcOzYMbhcLthsNjzxxBN45ZVXwp5s\n22w2xMfHY8aMGSgtLcWdd94ZNcmKqqp47rnn2n0zcPFiOr7R7Z6oq6vDmjVroNPp8PDDD/uXhV+3\nbt2ATbbfeOMNnDp1Cv/85z+Rm5uLvXv3oqioKODz8/PzcfjwYf/jizue9MXx48dx+eWX4+TJk/1W\nilRfX48RI0YgNTUV1dXV/XJN6n/BlI5MkVLu7G5bNGHpCBFR1woLCzF//nzo9Xro9XqMGzcOBw8e\nRFNTE2688UY899xzABBwMqSmaZg9eza2bdsGr9cLr9eLUaNGYdq0aVi0aFFYE19N07BkyRL/RMgF\nCxZETaLdmcsvvzwko6XDhw+HoijtJlzm5eXh7rvvDvvotqIoPR6F705n+UdBQQFef/31bo/RNK3D\nxMPuXH311UGtYBqpMpmXX34ZTzzxRESuTb0XitKR1wBcF8Q2IiIaICwWC9555x2UlJRAr9dj7dq1\nsNvtkFKiqKgIVqsV06ZNC5jAqqqKBQsW4NixY6isrERzczMyMjL8PbnDnfhG40TIcDt79myHbUVF\nRSgqKoKiKHjmmWfw61//OiTXWrFiBT7++GPcdttt2Lx5c8iT7ECWLVuGP/3pT92+r3fffXePzhts\nkg20/k5FItmeP38+ADDZHmQCJtpCiG8AmAwgXQgxv82uZAD6cAdGREThZTabYTaboWka1q1bB7fb\njbi4OMTExADovDNJW9nZ2Vi0aBEOHDiA0tJSjBw5EkajMez10r7SkauuuqrT+vFok5eXF/b6X4/H\ng2effRZms7nP7eNeeeUV/PKXv4SUstPVK0PB941JZ26++WZs27at033f+ta3cOWVV+Kzzz4L+loZ\nGRlBJ9k+UkrMnj0bb7/9do+O66v58+fjqaeewtVXX43i4uJ+vTaFR8DSESHEVAAWtNZo/7nNrvMA\nNkgpj4Q9utY4ZgC4C60J/nIp5ebujmHpCBFRz1itVixevBgtLS0wmUyYPXs2Vq9eHbDriK9zicPh\nQE1NDSwWC6644op2EyrDRdM0PPvss/4Jh88991xUJ9pWqxXXXHNNuwVrwuXaa6/Fl19+2evjNU1D\nTk4Oampq+hyLwWDA1KlTkZWVheXLl8PtdgNo7fwRaFKiL4bc3FxUVlb26HpXXHEFjh8/3u51TkhI\nQENDQ+9u4IJIdly5lL6xGah6XToipdwGYJsQ4m0p5fFeXnwFgO8AOCulNLfZ/i20TrDUA3hLSvlC\nF3GsA7BOCDEMwEtonYxJRER9pGkarFYrgNbR7ZdeeingAjYXjxrbbDY4HA58/fXXsFqt2L59O8aO\nHYv/+q//CnvSW1VVheLiYrhcLlRWVqKqqiqqE22z2YyUlJSAE970en3ISjMOHTrUp+P/9re/9TrJ\nNhqNcDgc/sfPP/+8vxzi/vvvD7pTiqqqKC4u7nEN9meffYaqqio8/fTTOHLkCL73ve8FXL2yJ4It\nJUlNTcXs2bOxZ88enDlzpt3Ezd7q7cqYFD2CqdF+WwjR4SOVlPLWYI4F8EcA7/g2CCH0AJYBuB3A\nKQBfCCHWozXp/t1Fxz8spfQVpf3XheOIiKiPfO35du/eDaC1vGHBggXtelF31XXEZDLB5XLh9OnT\naGhogN1uR3V1NR5//HGsXLkyrJ1HSkpKoNPpMGHCBJSXl/fripS9NWLEiE4TbUVRMHTo0JB1nXC7\n3SguLg5Y7tOdjRs3dvuchIQEOJ3OdttuuOEGLF++HPPnz8fZs2cxduxYPPTQQ/79FoulR5M1VVXF\n5MmTu1ysprNjVFXFP/7xj6CPCVbbkeXx48f7k2hVVfHYY48FrI2/OEHfunVrj7ql1NbW9iJaiibB\nJNq/bPPneAD3Agiq8aWU8lMhROZFm28AcFRKWQ4AQoj3AHxPSvk7tI5+tyNaf0tfALBJShnw+zAh\nxI8A/Aho7YdJRESB+Uakk5KS/I8LCwthsVj8CUtXS7Crqop58+bh1KlTOHPmDIQQiI+Ph9frDXvi\nm5OTA0VRUF5eDkVR+n1Fyt6YMmWK/9sDn7i4OCQnJ+Mb3/gG1q9fH5LrtLS04Fe/+hUuv/zyXpXU\n1NfXd/scnU4Hg8HgXxnSYDBg8eLFMJvN+J//+Z8u6/p7YufOnRFfKKczPfnWoLPSj61bt6KoqAhP\nP/10KMOiKKXr7glSyr1tfnZKKeejtXa7tzIAnGzz+NSFbYE8DuA2APcJIR7tIs43pZSTpJST0tPT\n+xAeEdHgZzKZYDQacf78edTU1KC8vBzr16/Hww8/jLfeeguapkFVVeTm5gZMmMxmM5YsWYKbbroJ\nSUlJiI2NRVJSUtgTX7PZjJ///Oe4/vrr8fOf/zzqR7MB4LbbbvNPMvUZMmQIMjIykJiYiPj4eCQk\nJITkWjt27MAHH3yA7du39/jYYJZVb2howMaNGzFnzhzMnTsXGzdu9I9Wd/c701MPPPBAUM/76quv\nQnK9/mCxWPDUU0+x/voS0e2IthAipc1DHYB/A2AMW0QXkVIuBbC0v65HRHQpUFUVTz31FKxWK44e\nPYpPP/0Uu3btQnV1Nfbu3Ys9e/YENSJqNpuxfPlybN++HTU1NZgyZUrYE1+r1Yo//OEP8Hg82Ldv\nH8aNGxf1yXZ+fj6GDRvWrkWf0+mETqfDuHHjEBMTA51Oh9jYWDQ1NfXpWvX19WhsbMSBAwdw3333\nBX2c1WoNKmGVUva4FKS33nvvvW47n7z//vtR//4HEkz9txCCSfkA1u2INoC9APZc+O9nAH4B4JE+\nXPM0gMvaPB51YRsREfUjVVUxbdo0zJgxA42NjWhoaIDBYEB8fDwqKythtVpRXFzsXzGyq/Pcd999\n+PGPf9wvCU9JSQk8Hg+ysrLg8Xh63LotElRVRUZG+y9vFUWBXq9HTk4OZsyYgWuvvRY333wzRo0a\nhfj4+A4rSvaEx+Pp9n27WLATB43GfhtrAwA8+eSTXe7vazvDSHv//fe7fU5P30uKHt3+LZZSXhHi\na34BYKwQ4gq0JtizAHw/xNcgIqIgqaqKxx9/HIcPH0ZNTQ1aWlqQnJyMjRs3Ii4urtP2fm1ZrVZs\n2rQJAPDtb3877Ml2Tk4OvF4vvvrqKxgMhgFRow0AY8aMwb59+/yP4+LiAADDhg3Diy++CJvNBkVR\n8Nprr2Hnzp04f/58n/pvb9++3V8CFIxAvasv9t3vfrfXMfXGkiVLsHTpUn97wLYG6vLzbd1zzz14\n//338be//Q0ffPBBp88ZMWIER7UHqK4WrOnyI6KUcm13JxdCrERrPXeaEOIUgGellMuFED8F8E+0\ndhpZIaUMyXCEEGI6gOljxowJxemIiC4ZFosFK1euxM6dO5Gamophw4Zhy5YtAdv7+VitVvzwhz/E\nkSOtSyu89957+Otf/xrWZDs9PR3XXHONP4kcKPNykpOTodPpIKWElBIejwc6nc4/+dT3+i5cuBBW\nqxW1tbVYtWoVPvzwQzQ3N/f4eqdOnerRYj7BTITMyMjAggULehxLXx0/fhxZWVn+bieKouCmm27C\n1q1b+z2WcLjnnntwzz33ROXkT+qbrka0p3exTwLoNtGWUj4YYPtGAN33EOohKeUGABsmTZo0N9Tn\nJiIa7HwrRQKtX1Vv27YtYHs/n5KSEpw/fx6xsbEQQuD8+fNh6zriW6mypqYGqamp+Ld/+7cBsTKk\nz5133omVK1eisbERUkoMHz4cEyZMgMfTvpFX26Q7Pz8fDzzwAF599VXs2LGjR9c7f/48ysvL27Vs\n7Ep3SZ6iKPjf//3fiNRDq6qK8vLykHU0iVaRWv6dwqerBWtm92cgRETU/wIts95dez+fnJwcJCUl\n+VfxC1fXEV/f78rKSrjdbv8odlcfAqLNPffcgwMHDuCVV15Bc3Mzqqur0djY2GX8vvr34uJifP75\n5+2S8oSEBH/nmECj0Zs2bQq6hnnkyJFdLlaj0+kiOumw7QeQwYzJ9uASTNcRI4BnAdx8YdM2AAul\nlI7ARxERUbTzLaNus9lgt9vx+OOPt6t5DSaxMZvN+Otf/xr2Gm2r1YodO3bAbrfD7XbjmmuuwbXX\nXospU6YMuOSrvr4eUko0NjYGnTzedttteOutt1BXVwcAuPHGG/Hggw9iypQpmDVrVsAJoWfOnAk6\nrnHjxnXZdSQ5OTnoc1Ho9aTenqJHMFOaVwCwAph54fH/C+AvAKJumi9rtImIgmez2fwL1fhKPv78\n5z/3eIJZ25KTcGpqaoKUEnq9HhUVFdi9ezdOnz6N9PT0AZOAnD59GlJK6HQ6eL3edkuWd8ViseC9\n997Dxx9/jMzMTEyfPt1/z/fff3/ARLuzCYSBxMfHd7n/hhtuCPpcFHqcEDkwBdPe70op5bNSyvIL\nP88ByAp3YL0hpdwgpfxRf7ceIiIaiEwmE+x2O86fPw8pJRwOB55//nm88cYbHVYxjDSz2Ywbb7wR\nycnJSExMREJCArKzs+HxeGCz2SIdXtA8Hg+klGhpafFPiAyWxWLB888/jzlz5rT7YPHoo48iNja2\n02N6soR3YmJiwH2KouDuu+8O+lxE1CqYRNslhLjJ90AIMQVA90tHERFRVPO19Rs6dCh0Oh1iYmJQ\nUlKC119/HY899ljQybamaUH12w6G1WrFqlWrOlxbVVXMmjULkyZNQm5uLrKzs2G32wdUjTYAfy17\noMe9oaoqxo4d2+m+noxoNzQ0BNw3ceJETJ/eVY8E6g+hrN1euHAhpkyZgoULF4bsnNRRMKUjPwHw\n1wu12gKAHcC/hzMoIiLqHxaLBX/+85/x2muvoba2FkeOHMHYsWNRUVGBjz76qNuyDF+dt8PhgMvl\nwrx583pdRmK1WvHYY4/B4/FAURS8/vrr/nNZrVb84he/wKFDhyClxOjRo7Fo0SLk5+cPmLIRoONi\nL6H6Bnbq1Kmdlo/o9fqgz7F///6A+6SUA+p1HsyEEP4PaL3twrJw4UI8++yzAIBdu3YBAH7961+H\nNlACEMSItpSyWEp5DYCJACZIKa+VUgb+20hERAOKxWLxj2JnZGSgoqICZ8+exdGjR7Fs2bIuR6pt\nNhscDgfKyspgtVqxdOnSXo9sd7XiY0lJCWpra/0lFzabDcXFxb26TiTpdK3/2/WNTPoe99XBgwc7\n3d6TEe3jx48H3FdeXt7jmCh8RowYgREjRuDaa6+FyWRq93dOCOH/KSws7PR4X5Ld9jE7nYRHt3/D\nhRA/E0IkAzgP4GUhxJdCiG+GP7SeE0JMF0K8GezkEiIiauVrI/fWW2/h/vvvxx133IHrr7++2xpo\nk8kEl8sFu92OlJQUGAyGXtdM5+TkQFEUlJeXQ1GUdm0Cc3JyEBcXh5aWFrS0tKC5uRlff/11tx8E\nos2oUaMAwD+pzfe4rwIl1J01B+is1GfFihU4d+5cwPMnJCT0PUgKWk8W4pFS4rLLLgPQsbTklltu\n8SfbBQUFGD9+PAoKCgKei8l26AVTOvKwlPJVIcQdAFLR2nXkfwBsDmtkvcAFa4iI+sZsNiM9PR3L\nli3rdrEaoDVBnzdvHpYuXQqDwQCj0djrmmmz2YzXX38dJSUlyMnJabd4jsfjwW9/+1u8/vrrcDgc\naGlpweTJk2G32wfMgjUAkJqaiiFDhrR7HArf/OY3sXPnzg7bDx48iFdeeQVPPPEEgNbXcsGCBThx\n4gRGjx6NJUuWQFVVLFq0qMvzP/rooyGJk4LT084/zc3NSEtL63TfLbfc0u7x4cOHexsW9UIwibbv\n482dAN6RUpYIfuQhIhq0gl2sxsdsNmPRokUhWbXv4laBvhpwj8eDmpoa3HHHHRg2bBhKS0sH5GTI\n9PR0NDc3w+v1QqfThWz5+PHjxyM1NbXDgjNlZWX4xS9+AQB44oknsGHDBqxatQrNzc3Q6/W45ppr\nMH/+fJw+fbrDOX/4wx/iyJEjuOOOO1i/OwB0tdgQRU4wifZeIcRmAFcA+JUQIgmAN7xhERFRJPV0\nFb5QrNqnaRo2bNiAiooK3HbbbbBYLLDZbPB4PIiJicGmTZsQHx8PnU6HBQsW4Lrrrhtwy3EPGTIE\no0aNQktLC/R6fbvRqt77wQAAIABJREFU7b7IyclBenp6p8mWlBJ//OMf8cQTT2DVqlX+MhOv14tX\nX30VDz30UIdacZ1Oh8WLFw+o15ZCY8WKFXj44YcjHcagEcwsjEcAPA3geimlE0AsAC7PTkREPaJp\nGrZs2YItW7Z0qKvWNA2//OUvMX/+fCxduhQPPfQQCgsLYTKZoCgK9u/fD7fbDbvdjpMnT+I3v/kN\n9uzZE6E76b2YmBhUVVWhuroaVVVViImJCcl5zWYz/vSnP2H8+PGd7q+qqoKmaThy5Ei77WfOnMG6\ndeswfPjwdtszMjKYZF+iHnnkkUiHMKh0O6ItpfQKITIB/D9CCAlgh5Tyg3AHRkRE4We1WrFz506k\npqaGtVWepmlYvHgxdu/eDQDIy8vDggUL/Nez2Ww4deoUdDodEhIS0NzcjI8//hhDhw7FzJkzMXHi\nRFitVthsNkgpUVNTg5deegmlpaXtzhPtmpubkZWVhaSkJJw/fx7Nzc0hO7fFYsGaNWvwgx/8APv2\n7etw3e3bt8Plar8MhsfjwYsvvthhJHwgleMMVi+//DLmz58f6TCoj4LpOvI6gEcBfIXWpdh/LIRY\nFu7AeoNdR4iIgme1WjFnzhz85je/wU9+8hM88sgjYVsR0tcGMCkpCUlJSairq2vXncRkMmHUqFHw\ner2or6+HTqfD4cOH8dprr2HFihXIz8/HkiVLMHz4cMTHxyMuLg7p6ekdzhPtcnJyEB8fj3PnziE+\nPr5dZ5VQMJvNePDBBzuUgjQ1NeHYsWOdJvZlZWVwOp3ttrHeN/KeeOIJvPzyy/jWt76Fl19+OSSL\nG1H/C6ZG+1YA2fJCLyIhxF8BfB3WqHqJXUeIiIJXUlKCc+fOoampCfX19di1axcWL16Ml156qVcj\nxJqmBZwQaTKZYDQacejQIQDA0KFD242aqqqKl156CVOnTkVFRQVSUlKwdu1aJCUl4csvv0RCQgJm\nzZqFv/zlL3jxxRf9I9sXnyfapaenIzc3F5WVlRgxYkTIJkO2VVFRAa+3/VQqr9cLvV4fdPs2X/tB\niqwnnnjC3zEGaG37d3EXEYpuwSTaRwGMBuDrZH8ZgCOBn05ERANBTk4O9Ho9XC4XhBBITExEfX09\nCgsLYbFYepRst+0O0tjYiLvuugtms9l/DlVV8dRTT/lHzNvu81FVFXPmzAEAbNmyBWvXrsX58+dR\nVlaGDz74AJs2bcKsWbPw5JNPoqWlJeB5opnNZkNKSgquu+46VFRUhKU14fr16zvd/sknn8Butwd1\njoyMjFCGRCFisViQnp6OqqqqsF7H928A9V3A0hEhxAYhxHoASQBKhRCFQoitAEovbCMiogHMbDbj\ntddew+TJk5GZmYnU1FTYbDb/yHZnkxYD8XUHSUlJwe7du7F8+XI888wz7UpRVFXFtGnTMO3/b+/e\nw6Mu77yPf76TA4ZTEIEhgsixgA6tWjxdnkbBIkVYm2WVwnXtWky7FqrVlIPbKq6y9RQOFtdDhVV0\nH+wjIktNW3BXFpC1fRTaYgniCQULJiEcDOckk9zPH5lkE8hpkpn5JTPv13VxtfM7zXfmZuQz99y/\n+x4zpkVTBl5++eVKS0tTly5ddO655+qTTz7Rs88+q9zcXKWkpLToOu1Nzc2dLZmjvLVqvoScbvv2\n7S2+Rrdu/DPfXu3fv7/NX4QWLVok51yjv1zQax49TfVoL2hiH78pAUACCAaDGjlypAoKCvTpp5/q\ngw8+0Hnnnac1a9aotLRU/fr108yZM5sNtDUBcufOnSovL1dJSYl2796tJUuWaP78+S0KxKffmDln\nzhxt3rxZCxYs0J49e2qHP/z1r3/VnDlz9MQTT3S4XrdI5yhvjUGDBjU4br2plR9P19jsJWgf9u7d\nK6nxlRyLiork9/tVXFysYcOG6ejRo0pJSdGUKVOUk5PT4T43HVmjQds5t6mh7WZ2taTvSno7VkUB\nAOKnZg7sQCCgffv2aefOnZKkkSNHtnjlxZoAWVBQoOXLl2vXrl31lmRv7vyaGzNrAvW4ceOUl5en\nyZMna8SIEVq7dq1eeOEFHThwQMeOHdPu3buVm5url19+ud4CNx1BNOYcj1TNDagtxTzKHUNNmG5o\ne83/RvIFC9HXknm0ZWYXm1meme2WNF/Vw0cAAAmkJixPnTpVl19+ecQrL9YMDZk7d64CgYCGDBlS\nb0n24uJibdu2rcFgUHNjZigUUllZmd59911t3rxZ27ZtU+/evTV79mw9++yzGjRokLp166a+ffsq\nJSVFO3bsiOp7kAgaGg7Q2HCShnTv3r3DfXlJVs8888wZ215//fWoXJtFwKOj0R5tM/uaqnuuvyvp\ngKRXJZlzjoE7AJCg6vZut3Z4Q0NLstcsSPPhhx/qrLPO0vz58+v9fF1zY+apU6eUmpqq9PR0LV++\nXKFQSF26dNFDDz2kYDCoJ554onaMdkZGRtSnx0sEDU3hd/r0fU3hPe04srOz9frrr2vZsmWSpJyc\nHGVnZ0d0Dedco6HazJiBpo2ssTfQzKokbZZ0h3Pu0/C2z5xzg+NYX0TMbKKkiUOHDv3+6atfAQC8\ns2zZMv34xz/WqVOnJEmDBw/Wf/zHf9TrOd24caPy8vLUqVMnlZeXa8uWLSovL1d5eblGjRqlxx57\nTMFgUAUFBdqxY4cuvPBCel4bMGXKFL366qutPv+GG27Q+vXro1gR2rvmeq/rZsWrrrpKv//975s8\nJpmY2R+dc6Mb29/U0JFsSYWSNpjZUjMbI6ld/47gnMt3zv0gMzPT61IAAHXUzO3s8/nk8/lUWlqq\npUuX1puVJBgM6oUXXtC8efN03XXX1W4vKyvTBx98oJycHC1btky9e/fWbbfdRshuhN/vV0pKSqvP\nZ2q/5NPS+dwbC9kSQ00a02jQds6tcc5NkTRC0gZJ90jqY2bPmtm34lUgAKDjGzt2rLp27SqpevGU\n48ePa9OmTZoxY8YZUwBedNFFGj9+vPr37187ttjn86moqEiPPfaYZs2aFbMVLBPBwIEDW927mJ6e\nrkmTJkW5IrR3+/fvb9FxjYVsNK7ZmyGdc8edc6845yZK6i/pz5LmxrwyAEDCCAaDeu211zRz5kzd\ncsstGjZsmAKBgEKhUIM3NAYCAb300ku65557NGDAAKWmpio1NVXl5eV65513NH36dK1evdqDV9L+\nnXvuuRo4cKDS0tLO2NerVy+lp6c3em5KSop69eoVy/LQAfXp00cbN270uowOqSUrQ9Zyzh2W9Hz4\nDwAAtZobOx0MBmvHWM+YMUOfffaZUlNTa2++O30J90AgoEAgoBtuuEF5eXnatWuXDh48qCNHjqi4\nuFgzZ85Uz549mRP4NH6/XxUVFWcswy5Jhw8fbnB7jbKyMn300Ue8p0moqZsiS0pKWrSIDTdPnimi\noA0AQENqwvOJEydUVVWlRYsWNRrWAoGAnnnmmXqhvGYJ98LCQh06dEh33XVX7fk1i+ps3rxZP//5\nz/Xxxx/r7LPPVmVlpd59911C4Wl69OihcePGac2aNTpw4MAZ+32+6h+zG5ryr2ZYD4DoIGgDANps\nx44dOnHihMrKyvTll18qJydHkyZN0vTp0xvs3a7pra5RWFiowsJCbdy4USdOnNDnn39ebzEav9+v\nyZMny+fzaebMmaqsrFRaWpouv/zyuL3GjiIrK0tZWVmNDhFJS0uTmenkyZMN7q9ZdRBoDTNTv379\n+HsURtAGgCR2+nCN1rrwwgtVVVWlL7/8UocPH9bhw4f11FNPaf369VqxYkWzM4RkZWXp0KFDOnHi\nhM455xylpKTonXfeUSgUqldbdna2evbsqXfffVeXX345vdkNqFl46KOPPtLKlSvr7ausrFSvXr00\nevRorV+/XlVVVSovL6/db2ZNDi0BWmLfvn0MIwlr0cqQHYWZTTSz50tLS70uBQDavZrhGi+++KIe\neOCBNs3kEQgEtGjRImVlZdXeuJiamqqvvvqqRas3+v1+3XXXXfL7/erUqVNt0M7NzdW4ceP0wgsv\n1B4bDAY1d+5cQnYT/H6/Ro8+c2rfLl26aOLEiRo5cmTtHOV1Oef09a9/PV5lop2JdjBmyr8EC9rM\now0ALVdYWKjS0lLt2rVLBQUFWrJkSYPLo7dUMBjUww8/rO7du0uq7j3t0aNHi1caDAaDevnllzVr\n1izl5OTovffe09tvv633339fd955p2bNmtWm+lC9QmRpaak6deqkzMxMdevWTVJ1IEpJSVHv3r3V\npUsXj6uElzZs2BDV6/Xo0SOq1+toGDoCAEkqKytLJ0+e1KFDh9SzZ09lZGSooKCgtmc7EAhEPJyk\nZmjHmjVr1L17d9166621Nztu3rxZn3/+uQYNGqRrrrmmwWvXjN1ev369SktLa4cxVFRUaMmSJXr/\n/fe1ePFiFqtpgSFDhpyxzTmnP//5z7ryyisVCoUUCoXq7Ttx4kSD0wIieUTyS1FRUZH69u3b5DGl\npaXq06dPi+fqTjQEbQBIUn6/X3fffbeWLFmijIwMpaSk6LXXXlNBQYGOHz+uc889V7Nnz454iEbN\nNH41iouLNW/ePP3mN79RaWmpMjIyNH78eOXl5TUa5AOBgEaPHq3f/e53tT9nh0Ihbd68WTk5Ofrb\nv/1bjR8/nsDdhIqKCmVkZJxx0+NXX32l8vJyTZw4USdPntRnn32mvXv3qmvXrurUqZMqKio8qhjt\nRVNT/dXV0i/iJSUlSRu2E2roCAAgMoFAQPPnz9f3vvc9TZgwoTZk7dmzR1u2bFFubm6bV2EsLCxU\ncXGxqqqqVFVVpVOnTum///u/9bOf/azRRTD8fr+WLVum3Nxcde3aVT6fT2amyspK/elPf9L8+fM1\ndepUVohsgt/vr53Kr67Dhw+rd+/eGjJkiEaMGKGhQ4eqrKxMBw4cUGFhIT3aaJGioqKIji8pKYlR\nJe0bQRsAklzNsueBQECZmZkqKSlRKBSqnf2jJTczNqVm1pDKykqFQiFVVVVp//79Wr16taZMmdLo\nCo9+v195eXl66aWXNGDAgNol3CsrK1VeXq5du3Zp7dq1baotkfXo0UNf+9rXztielpamLl26aObM\nmbr11lt14403asCAARo2bJjOO+88erTRrKKiojbNUpRMCNoAAEnVwXbu3LmaPXu2zj//fHXt2lUZ\nGRktvpmxqes+/PDDeuSRR3Tttddq4MCBSk1NVadOnXTs2DE9/fTTTd7kmJ2drfz8fN1///0aOXKk\nfD5fbQ83GpeVlaWGZuGqqKiQ3++v/YI1fPhwHT16VPv379fRo0cJUGhW3b8jkfRsz5kzJxbltGuM\n0QYA1PL7/crJydEVV1zR5HLqrb3uxIkTlZ+fr5/+9Kc6evSo0tPT1bdvXxUWFjYZ8Gpukrz00ks1\nY8YMlZWVqUePHho/fnyba0tUfr9fN910k5555pl624cNG1ZvJoialSTrPgZaKpIvZnl5eXriiSdi\nWE37Q9AGAJzh9JUbo6UmcPfs2VNPP/20+vbtqyFDhigrK6tFi+cEg0GtXLkyql8CEtm1116rF198\nsd4NkT6fT1lZWbWPa1aSDIVCSk1NrbcPQNtYIq7aM3r0aLd161avywAANKFusJakp59+WqFQSKdO\nndKECRNaNb0g6isoKNAll1xSb9x1165d9emnn9Z7b6O1QigSR2NDsxrKjZEM49qwYUNCLTZlZn90\nzp25OlQYPdoAAE/UjBOWpG3btikUCtXOwV1UVCSfz6dbbrml0Tm30bxAIKAbbrhBb775Zu22tLS0\nM4bq1G0LQGp4ir/bb7+9wWPHjRtX7+9YU66//vqkWpqdmyEBAJ6rWbp9586dKi8v1969e7Vx40bN\nnTtXkydPbnRmEjTv9AVFDh8+rKVLl3pUDToS55xuv/12DRgwQLfffrtefPHFBo9bt26dxo0bp8zM\nTLE6d30JNXTEzCZKmjh06NDvf/LJJ16XAwBJpaCgoE1jp4uLi1VQUKDly5frL3/5i0pKSnTgwAFJ\nUnp6umbNmqUf/vCH9LxG6IILLtDOnTvrbfvGN76hbdu2eVQREt3111+vP/zhDyorK2twf5cuXXTs\n2LE4VxUbzQ0dSagebedcvnPuB3ybAoD4Kigo0IwZM/TII4/olltu0cKFC5ucsq8hfr9fY8aM0dy5\nczVq1Cg551RRUaGKigodP35cjz76qHJyciK+brK7+eabz9j2rW99y4NKkCw2bNigU6dONbr/+PHj\ncazGWwkVtAEA3tixY4dKS0u1b98+7dmzR/PmzdPkyZMbXfmxKYFAQAsXLtTUqVPrrVJYXl6u//qv\n/2p23m3UN2LEiDO2ffzxxx5UgmSzYcMGr0vwHEEbANBmF154ocrKynTs2LHaZdbfe+895eTktCps\n+/1+zZkzRzfddFNt2E5NTVVlZaXWrl2rBx54gOXXW+itt946Y9v//M//eFAJkk1Ts4ssXrw4foV4\niKANAGizQCCgRx55RH369FFqavWEVj6fT4cOHdL8+fNbFYr9fr+WLl2qn/3sZ8rMzFRGRobS09OV\nkpKigoICLVmyhJ7tFhg7duwZ266++moPKgH+V25ubqu+hHc0BG0AQFRkZ2fr5Zdf1mWXXaauXbvK\nzFRVVaWioiLdcccdmjZtWsSzh/j9fj344INas2aN7r77bt1www3y+Xzq2bOnMjIyVFhYGKNXkzgm\nTJigUaNG1ds2adIkj6oB/teYMWO8LiHmmEcbABA1wWBQq1atUn5+vl566SUdOnRIBw8e1M6dO/XH\nP/5Rb7zxhqTqUB7pdYPBYG1PdkZGhjIzM1nFsAUKCwsVCoWUkpKi9PR0lZeX66233tL06dO9Lg1J\nYMCAAfriiy8a3FdVVRXnauKPoA0AiKqaZdavuOIKPfjgg9q8ebN8Pp86d+6siooKLV26VCUlJbrq\nqqsingYwEAho/vz5rGIYgaysLA0ePFgfffSRysrKlJKS0uBwEiAW9uzZE9HKkYkmoebRrsES7ADQ\nPhQUFOiee+7R22+/LeecnHPq1q2bfD6funfvroULF0bcu43IFRcXa8GCBdq6dasmTZqke++91+uS\nkESaCtodPYcm1TzaAID2JRAIaMWKFXrsscd08803KxAIKBQK6ciRI/riiy80Y8YMVn2Mk4yMDF15\n5ZU6fPgwN5Eirk5fnbSuRO/tJmgDAGLK7/crNzdXzz33nIYMGaJQKKTKyko553T48GHdc889WrZs\nGeEvhmrGaQ8cOFChUIibSBFXyfz3jaANAIgLv9+vhx56SNdcc40yMjLk8/lkZjp48KD+5V/+RZMn\nT9a8efOYHzsGsrKylJqaqt27dys1NZWbSIE4YYw2ACCuiouLtWLFCj355JM6duxYbQ93eXm50tPT\nNWLECL300ksR3yiJphUXF3MTKTyTqOO0mxujTdAGAHhi48aNysvL044dO2qHjXTu3FkZGRm69NJL\nNWHCBE2cOJFQCCQAgnYCIWgDQMdQXFys/Px8Pf744yoqKlJlZaUqKirk8/lUWVmpiy66SMuXL6d3\nG+jgCNoJhKANAB1LQUGB1q5dqw0bNmjTpk06ceJE7b4bb7xR//7v/07PNtCBJWvQTqibIc1sopk9\nX1pa6nUpAIAIBAIBzZ49W3PmzKm33cy0d+9erVmzRuvXr2dmEqCDeuihh7wuwRMJFbSdc/nOuR9k\nZmZ6XQoAdFgFBQV69dVXPZn9IxgMau7cuUpLS1NKSopSUlIUCoX03HPP6Sc/+YkefPBBwjbQAc2b\nNy8pwzZDRwAAtQoKCpSTk6MjR44oJSVFTz31lILBYNzrWL16tdauXatu3brp888/1/bt2+WcU/fu\n3bVgwQKNGTMm7jUBaLuGhpB05Cza3NCR1HgWAwBo39555x3t2bNHoVBIp06dUl5enkaOHBn38dHZ\n2dnKzs5WcXGxfvKTn6isrEydOnVSWlpaXOsAgLYgaAMAap1zzjmqqqpSRUWFUlNT1alTJxUWFnp2\nI6Lf79d9990nM1NlZaWysrKYgQRAh0HQBgDUuuaaazRu3Di9++676tKliwYNGuT5KoKBQEALFixg\nsRUgQfXv31979+71uoyYYIw2AKCe4uLi2hshA4EAwRZA1DQ2zV9HzaOM0QYARMTv9xOuAcTV4sWL\nde+993pdRtQl1PR+AAAA6Hhyc3O9LiEmCNoAAABol/r37y8zk5npqquu8rqciBG0AQAA0O70799f\n+/btq338+9//XsOHDz9jMa3OnTvLzNS5c+d4l9gsgjYAAADanbohu8bHH3+sUaNG1Ybtzp076+TJ\nk5KkkydPtruwzc2QAICoKC4uVn5+vnbv3q2xY8d6sqIkgPatW7duOnr0aIP7unbtqmPHjrXoOqNG\njZJzrjZk1zj9sdfo0QYAtFlxcbFmzZql3NxcLVmyRNOmTdPGjRu9LgtAO/Pkk082uu/48eMRXatX\nr15tLSfmCNoAgDYrLCzU3r175fP51LVrV5WVlWnJkiW6//77CdwAak2fPj1q1zp48GDUrhUrBG0A\nQJtlZWWpf//+qqqq0pEjR3T8+HGtW7dOCxYs0IQJEzRr1iwVFxd7XSaAdmDEiBFelxA3BG0AQJv5\n/X4tWLBAixYt0pQpUzR48GCVl5errKxMJ06c0MKFC3XjjTfSuw1As2fPbvaYjjiVX0NYgh0AEFXF\nxcWaPn261q1bp6qqqnr7Bg4cqPz8fAUCAY+qA9AeNLcUe2P7WyKe2ba5Jdjp0QYARJXf79fjjz+u\nSy+9VD5f/X9mSkpK9Itf/EK//OUvz5gLFwASDUEbABB1gUBAv/71r5Wbm6tOnTpJqu6hqqys1MqV\nKzV37lx95zvfYSgJgIRG0AYAxITf71deXp5eeeUVXXbZZfr617+us88+WydPntTx48e1a9cu/cM/\n/IMWLlzIjZIAaoeLJNKvXQRtAEBMZWdn64033tDChQs1ZMgQOecUCoXknNMXX3yh2bNn6+qrr9bq\n1au9LhWAh4YPHy6pejGa1mpvC2URtAEAMef3+zVmzBjNnz9fgwYNqh1OIlXfuPTpp5/qtttu05w5\nczysEkC89OvX74xtaWlpbb7uhg0b2nyNaGr3QdvMRprZc2a2ysx+6HU9AIDWCwaDWr16tWbMmKGz\nzjqr3r5QKKQFCxZo8eLFHlUHIF727t17xrbt27d7UElsxTRom9kLZrbfzApO236TmX1kZp+a2X1N\nXcM5t9M5d6ekWyUlxqSKAJDEAoGAFi1apEceeaRez7ZU3bv9i1/8ghUlASSEWPdoL5d0U90NZpYi\n6WlJ4yVdIOm7ZnaBmY0ys9+c9qdP+JxJkn4r6XcxrhcAECf33nuvXnnlFZ133nn1thcVFWnx4sWa\nMGGCHn74YY+qA+CFRPvMx3zBGjMbKOk3zrlA+PGVkv7ZOTcu/PifJMk592gLrvVb59yE5o5jwRoA\n6DiKi4u1YMEC5efnq6KiQrt3765d6CY9PV2/+tWvlJ2d7XGVAKKtoUVpUlJSVFlZ2eprxnshxva4\nYE0/SX+t83hveFuDzCxoZkvM7JdqokfbzH5gZlvNbGtJSUn0qgUAxFTNNICbNm3StGnTav/xNTOZ\nmTZt2uRxhQDipS0huz1q9zdDOuc2Oufuds79o3Pu6SaOe945N9o5N7p3797xLBEAEAV+v18zZ87U\n1VdfLZ/PJ5/Pp7S0NF133XVelwYArZLqwXPuk1R3QF7/8DYAQJLz+/169dVXtWLFCn3wwQf69re/\nzbARAB2WF0F7i6RhZjZI1QF7iqSpHtQBAGiH/H6/cnNzvS4DANos1tP7/UrSHyQNN7O9ZnaHcy4k\n6UeS3pS0U9JK59yOKD3fRDN7vrS0NBqXAwAAQDtx2223qW/fvrrtttu8LqXFYj7riBeYdQQAAKB9\na2jWkcakpaWpvLy82XOZdQQAAACIwLhx47wuoVUI2gAAAGi3+vXrp0cfbXa5lXaJoA0AAIB2a926\ndQoEAl6X0SoJFbS5GRIAACCxdNSQLSVY0HbO5TvnfpCZmel1KQAAAEhyCRW0AQAAkPgaWgV8xIgR\nHlTSNII2AAAA4q5Xr171Hp911lktPve5554749zXXnstKnVFE0EbAAAAcXfxxRfXe3zq1KkWn5ud\nna3XX39dU6dO1b333qstW7a0y7HcXizBHjNmNlHSxKFDh3pdCgAAAJoQyYI1DcnOzlZ2dnaUqomN\nhOrR5mZIAACAjuHDDz/0uoSYS6igDQAAgI4hGTpGCdoAAACIu+HDh3tdQswRtAEAABB3Z599ttcl\nxBxBGwAAAHHXr18/r0uIuYQK2izBDgAA0DF07tzZ6xJiLqGCNrOOAAAAdAwnTpzwuoSYS6igDQAA\ngI6hoqKi2WOysrLiUEnsELQBAAAQd2PHjm32mNmzZ8ehktgx55zXNUTd6NGj3datW70uAwAAAE1o\nbnXI9p5TzeyPzrnRje2nRxsAAACIAYI2AAAAEAMJFbSZ3g8AAADtRUIFbab3AwAAQHuRUEEbAAAA\naC8I2gAAAEAMELQBAACAGCBoAwAAADFA0AYAAABigKANAAAAxABBGwAAAIiBhAraLFgDAACA9iKh\ngjYL1gAAAKC9SKigDQAAALQXBG0AAAB4ok+fPl6XEFMEbQAAAHhi7ty5XpcQUwRtAAAAeGLatGk6\n77zzvC4jZgjaAAAA8ITf79eECRO8LiNmCNoAAADwzNGjR70uIWYI2gAAAPBM586dvS4hZgjaAAAA\n8MzUqVO9LiFmCNoAAADwTDAYVGpqqtdlxERCBW2WYAcAAOh4nHNnbEuEISUJFbRZgh0AAKDjOeec\nc87YNmDAAA8qia6ECtoAAADoeC6++OIztn3zm9/0oJLoImgDAADAU8eOHTtjG0EbAAAAaKPBgwfX\ne+zz+XTw4EGPqokegjYAAAA8NWfOnHrjtDMyMjRw4EDvCoqSxJxLBQAAAB1GIBDQqlWr9MADD+jU\nqVMaOXKkJk5ZXz+7AAAJY0lEQVSc6HVZbUbQBgAAgOeCwaBWrVqlwsJCZWVlye/3e11SmxG0AQAA\n0C74/f6ECNg1GKMNAAAAxABBGwAAAIgBgjYAAAAQAwRtAAAAIAYI2gAAAEAMELQBAACAGCBoAwAA\nADGQUEHbzCaa2fOlpaVelwIAAIAkl1BB2zmX75z7QWZmptelAAAAIMklVNAGAAAA2guCNgAAABAD\n5pzzuoaoM7MSSXskZUpqbsB2U8c0tq+x7b0kHWhhmfHUkvfBi+tGen5Lj49Vuze2L9nava3Xbs25\n0Wr7aLa7lHxt31E/87S7t9dtj+3e1H7aPTrXTZZ2P98517vRvc65hP0j6fm2HNPYvia2b/X6Nbf2\nffDiupGe39LjY9Xuje1LtnZv67Vbc2602j6a7Z6Mbd9RP/O0O+0eYfvS7rR71No90YeO5LfxmMb2\nteS67Ums6m3rdSM9v6XHx6rdI6mhPYhlrW25dmvOjVbbJ0O7S3zmI9lPu8f+uu2x3ZvaT7tH57q0\nuxJ06IhXzGyrc26013Ugvmj35EXbJyfaPTnR7smpre2e6D3a8fa81wXAE7R78qLtkxPtnpxo9+TU\npnanRxsAAACIAXq0AQAAgBggaAMAAAAxQNAGAAAAYoCgHUNm1sXMXjKzpWY2zet6EB9mNtjM/s3M\nVnldC+LHzG4Jf9ZfNbNveV0P4sPMRprZc2a2ysx+6HU9iJ/wv/Fbzexmr2tB/JhZ0Mw2hz/3weaO\nJ2hHyMxeMLP9ZlZw2vabzOwjM/vUzO4Lb86WtMo5931Jk+JeLKImknZ3zn3mnLvDm0oRTRG2+5rw\nZ/1OSbd5US+iI8J23+mcu1PSrZKu8qJeREeE/75L0lxJK+NbJWIhwrZ3ko5JOkvS3uauTdCO3HJJ\nN9XdYGYpkp6WNF7SBZK+a2YXSOov6a/hwyrjWCOib7la3u5IHMsVebvfH96Pjmu5Imh3M5sk6beS\nfhffMhFly9XCdjezGyV9IGl/vItETCxXyz/zm51z41X9Reuh5i5M0I6Qc+5tSYdO23yZpE/DPZnl\nkv6vpL9R9Ted/uFjeK87sAjbHQkikna3ao9LWuuc+1O8a0X0RPp5d869Ef6HlyGCHViE7R6UdIWk\nqZK+b2b8G9+BRdL2zrmq8P7Dkjo1d+3UqFaavPrpf3uupeqAfbmkJZL+1cwmqOMt6YrmNdjuZnaO\npJ9LutjM/sk596gn1SFWGvu83yVprKRMMxvqnHvOi+IQM4193oOqHibYSfRoJ6IG29059yNJMrPb\nJR2oE76QOBr7zGdLGieph6R/be4iBO0Ycs4dl/Q9r+tAfDnnDqp6nC6SiHNuiaq/XCOJOOc2Stro\ncRnwiHNuudc1IL6cc6slrW7p8fzUER37JJ1X53H/8DYkNto9OdHuyYl2T060e/KKStsTtKNji6Rh\nZjbIzNIlTZH0hsc1IfZo9+REuycn2j050e7JKyptT9COkJn9StIfJA03s71mdodzLiTpR5LelLRT\n0krn3A4v60R00e7JiXZPTrR7cqLdk1cs296cc9GtFgAAAAA92gAAAEAsELQBAACAGCBoAwAAADFA\n0AYAAABigKANAAAAxABBGwAAAIgBgjYAtJCZOTNbWOfxLDP75yhde7mZTY7GtZp5nr8zs51mtqGF\nx//OzHpE6bmPNbO/h5nNqPP4XDNbFY3nBgAvELQBoOXKJGWbWS+vC6nLzFIjOPwOSd93zl3fkoOd\nc992zn3Vusoi1kNSbdB2zn3pnIv5lw8AiBWCNgC0XEjS85LuPX3H6T3SNb23ZhY0s01m9msz+8zM\nHjOzaWb2npltN7MhdS4z1sy2mtnHZnZz+PwUM8szsy1m9hcz+8c6191sZm9I+qCBer4bvn6BmT0e\n3jZP0tWS/s3M8k47PsvM3jazbeFzrglv321mvcxsoJl9GH6dH5vZCjMba2bvmNknZnZZ+Ph/NrNZ\nda5bYGYDT3uurma23sz+FK7xb8K7HpM0JFxDXvg5C8LnnGVmL4aP/7OZXR/efruZrTazdeE6nqjz\nvi0PP/92MzujzQAg1iLpBQEASE9L+ktNoGuhb0gaKemQpM8kLXPOXWZmP5Z0l6R7wscNlHSZpCGS\nNpjZUEl/L6nUOXepmXWS9I6Z/Wf4+EskBZxzn9d9MjM7V9Ljkr4p6bCk/zSzW5xzD5vZDZJmOee2\nnlbjVElvOud+bmYpkjo38DqGSvo7SdMlbQmfc7WkSZJ+KumWFr4fpyR9xzl3JPzrwP8Lf2G4L/x6\nLgq/joF1zpkpyTnnRpnZiPBr+lp430WSLlb1Lw4fmdlTkvpI6uecC4SvFZXhLwAQCXq0ASACzrkj\nkl6WdHcEp21xzhU658ok7ZJUE5S3qzpc11jpnKtyzn2i6kA+QtK3JP29mW2T9K6kcyQNCx//3ukh\nO+xSSRudcyXOuZCkFZKuba5GSd8Ljzkf5Zw72sAxnzvntjvnqiTtkLTeOecaeB3NMUmPmNlfJL0l\nqZ8kfzPnXC3p/0iSc+5DSXsk1QTt9c65UufcKVX37p+v6vdvsJk9ZWY3SToSQX0AEBUEbQCI3JOq\nHuvcpc62kML/TTUzn6T0OvvK6vz/qjqPq1T/l0V32vM4VYfSu5xzF4X/DHLO1QT14216FXWfyLm3\nVR3G90labmZ/38BhLXkdte9D2FkNXGeapN6SvhnuvS5u5LiWqltXpaRU59xhVf+SsFHSnZKWteH6\nANAqBG0AiJBz7pCklaoO2zV2q3qohlQ9lCKtFZf+OzPzhcdtD5b0kaQ3Jf3QzNIkycy+ZmZdmrqI\npPckXRceW50i6buSNjV1gpmdL6nYObdU1aH0klbUL1W/D5eEr3mJpEENHJMpab9zriI81vr88Paj\nkro1ct3Nqg7oCg8ZGaDq96dB4SEpPufc65LuV+tfDwC0GmO0AaB1Fkr6UZ3HSyX92szel7ROrett\n/kLVIbm7pDudc6fMbJmqh2X8ycxMUomaGQvtnCs0s/skbVB1j/hvnXO/bua5g5Jmm1mFpGOqHhve\nGq+reqjLDlUPdfm4gWNWSMo3s+2Stkr6MFz3wfDNlQWS1qp6PHyNZyQ9Gz4nJOl251xZ9VvSoH6S\nXgz/uiBJ/9TK1wMArWbVw+sAAAAARBNDRwAAAIAYIGgDAAAAMUDQBgAAAGKAoA0AAADEAEEbAAAA\niAGCNgAAABADBG0AAAAgBgjaAAAAQAz8f4wrdkYZrzsPAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.4987066194171564, 0.5012933805828437)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        }
      ]
    }
  ]
}