vitillo/Bayes101.py

## Bayes101.py
{
 "metadata": {
  "name": "",
  "signature": "sha256:081b9937ad2575f1768d01c339462ad704226fa0c6551d14934aad2abf212241"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from IPython.core.pylabtools import figsize\n",
      "import numpy\n",
      "from matplotlib import pyplot as plt\n",
      "import pymc\n",
      "from pymc import deterministic\n",
      "from pymc.distributions import Binomial, Beta\n",
      "from __future__ import division\n",
      "figsize(11, 9)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = 8\n",
      "data = [4, 5, 6, 5, 5, 4, 3]\n",
      "\n",
      "p = Beta(\"p\", alpha=1, beta=1)\n",
      "y = Binomial(\"y\", n=n, p=p, value=data, observed=True)\n",
      "\n",
      "model = pm.Model([y, p])\n",
      "mcmc = pm.MCMC(model)\n",
      "mcmc.sample(40000, 10000, 1)\n",
      "\n",
      "pm.Matplot.plot(mcmc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 3596 of 40000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          20%                  ] 8126 of 40000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      29%                  ] 11996 of 40000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  39%                  ] 15868 of 40000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------49%                  ] 19852 of 40000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------59%--                ] 23891 of 40000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------69%------            ] 27911 of 40000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------79%----------        ] 31907 of 40000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------89%--------------    ] 35882 of 40000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------99%----------------- ] 39738 of 40000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 40000 of 40000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting p\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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V2yswX41VDXAn5mRVD7wFzAQy/6pexSSNioiUQidMLRWY89ifMcHVXGA6ppff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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ce64250>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n1 = 8\n",
      "data1 = [4, 5, 6, 5, 5, 4, 3]\n",
      "\n",
      "n2 = 20\n",
      "data2 = [16, 15, 17, 11, 18, 16, 18]\n",
      "\n",
      "p1 = Beta(\"p1\", alpha=1, beta=1)\n",
      "y1 = Binomial(\"y1\", n=n1, p=p1, value=data1, observed=True)\n",
      "\n",
      "p2 = Beta(\"p2\", alpha=1, beta=1)\n",
      "y2 = Binomial(\"y2\", n=n2, p=p2, value=data2, observed=True)\n",
      "\n",
      "@deterministic\n",
      "def diff(p1=p1, p2=p2):\n",
      "    return p2 - p1\n",
      "\n",
      "model = pm.Model([p1, y1, p2, y2, diff])\n",
      "mcmc = pm.MCMC(model)\n",
      "mcmc.sample(40000, 10000, 1)\n",
      "\n",
      "pm.Matplot.plot(mcmc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 4%                  ] 1810 of 40000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 3948 of 40000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            15%                  ] 6171 of 40000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          20%                  ] 8102 of 40000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        25%                  ] 10072 of 40000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      29%                  ] 11939 of 40000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    34%                  ] 13837 of 40000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------------   39%                  ] 15780 of 40000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------- 43%                  ] 17545 of 40000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------48%                  ] 19482 of 40000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------53%                  ] 21456 of 40000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------58%--                ] 23386 of 40000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------63%----              ] 25299 of 40000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------68%-----             ] 27259 of 40000 complete in 7.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------73%-------           ] 29203 of 40000 complete in 7.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------77%---------         ] 31120 of 40000 complete in 8.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------82%-----------       ] 33068 of 40000 complete in 8.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------87%-------------     ] 35008 of 40000 complete in 9.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------92%---------------   ] 36991 of 40000 complete in 9.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------97%----------------  ] 38943 of 40000 complete in 10.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 40000 of 40000 complete in 10.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting diff\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " p1\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " p2\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VceBVYCZwiTVud2CVNbzK+gywJ7DCsewKoIXL+CprvGRJ+T7Rp2PsTTldIhJV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\nh1gsRrNmzWjbti0AHTt25LHHHmPUqFE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hu7Rq1SrfRQksm3OY7l4UERERyYEwgq5uwCJg\nMTDIY557relzgCNC2KaIiIhIUQma01UGjABOAaqAGcBkYKFjnh7A/kAboAswEjgq4HZFRKQIKd8n\n+tId48mTJ7Prrrtmvf7DDjuMtm3bZr18PgXNpzgaGIKp7QK4znq/1THPA8AbwFPW50XACcCqpHVF\nMidCRNwpp6vwKacrKOV0JWvQ4Ca23/7TrJffunU5J5zQgqlTJ4ZYquxkcw4LWtPVAlju+LwCU5uV\nbp6W1A66JKCKigoqKiryXQwRERFXP/10Mz/9FGQNT/Pzz+PDKk7OBc3p8hu+J0eCvpbLRQARZBv5\nDHDctj10qPdjF4KW1e/yud4ndbU9t/WGta26WE+Q4xP2d1XgLyLiLmjV/lFABYnmxcFANTDMMc8D\nQCVgh6aezYumpdJWbr1EJBoqrZdtKKh5saDVRfNiaeV0lWbzYt0e46c59dTxvPzy03Ww7szkI0Vi\nO2Ap0BpoAHwEJGe39QCmWMNHAe97rCvuZciQIZ7T0i3jtmy69Tmnu63Hb3lSzZfNd8qG2371+50y\n2U+ZSnV8gsyXbt663O9B92em6wuyTKr/b37W7Wcb6RCtK1HW+6GQNW26RxxWxiGuV1YvrFe+yxGl\n18T4qaf+Nt//NeLx+Lbjm5EwIrTuwHDMnYxjgX8Cl1rTRlnvIzC1YZuAi4APXdZjfQcJk/K8xE0h\n/F0okb7wKZE+qNKs6apbxV3TVUgnvEietETEnYKuwqegKygFXeEr7qBLPdKLiEjOVFQM3ZbzI9Gk\nY+ytkH5lRvKXooi4U01X4VNNV1Cq6Qpfcdd0Be2nS0RECtDcuXN55JHHA63jhx82hFQaEQEFXSIi\nkfTSSy8xfPh7VFf/KsBa/gn8MqwiiZQ8BV0iIul1I3GX9hhq9kVYsOrV60J19aB8F6OG0uqnqzTp\nGHtT0BWyyspKysvL812MUOi7FJ6ofI8iU4bp9uYUoAqYAUwGFuazUNmpJN+dTvu7EFeS73L6V0lx\nlLWSXJUzWLBVSbpyrlq1gokTs3/2YllZGb/+9a9p0KBB1uvIloKukEXpoqjvUnii8j2KTGdgCbDM\n+jwe6IWCrjpUSXGUE4qnrJVEo5yHsnTpXvTtOyHrLfz00+u8/voLdO3aNet1ZEtBl4hIai2A5Y7P\nK4Audb3RVatWsXnz5qyXX7t2bYilESkUB7FpU/YBF8BOOx3DG2+8wVdffZX1Ovbdd9+sllPQJSKS\nWsb3+48d+zD9+l1cF2XJWNOmi7YN//DDJzRsOCuPpYFrr+0IwF13zfScpxDK6Veqsm6wbv5s2rRn\nDkvkLpf71M8x9pKLcq5f/y433vhuoHXstdf+WS1XSH3kfAS0z3chRCRn5gCH57sQPhwFVGCS6QEG\nA9XUTKZfAuyX22KJSJ4tBbKLvkRExNV2mJNra6AB5gdi23wWSERERCSqugOfYGq0Bue5LCIiIiIi\nIlLIugGLgMVAYfXil14r4A1gPjAPuMoavwvwCvAp8DLQLC+ly1wZMBt4wfpcrN+jGfA05pb+BZg7\nzYr1uwzG/H3NBZ4Atqd4vstDwCpM2W2pyj4Ycx5YBJyWozJmy+8xcNsHueDnvHqvNX0OcESOypUs\nXTkPAt4DfgD+lMNyuUlX1vP4/+2dT4gcRRTGfxpXFBeXRCVrXGUkICiYhZioG5RshGAIakQPXgQR\nD4I5KIJrIoI5eJCAKCgqKIQ1iHhQAmoSMHhQFBXMJp5yUJGg4ir+CeLBP7Aevm56tjOTqZ64VV34\n/WDY6ZmG/V5196tXr17VqC2/AD4C1sSTtohBOrchnXPA58BN8aQtIrTvXw/8A9wRQ1QPBumcBk6g\n9pwDHo+mbAiWoXR9Bxghv1qJcapC4FE0/XAlsBuYKT5/FHgqvrSheBh4DW38CPnaMQuUS8fOAsbI\n05YO8DUKtADeAO4hH1tuRJ15d8DRT/tV6PkfQXZ/CZwZReVwhF6DXm2w1IT41a3A/uL9dcAnscR1\nEaLzImAd8CRpg64QrVPI14A66ra26Xld768uzo9NaN+/DHgfeAe4M5a42v8fpHOaqs9sPVPAwa7j\nHcUrV/ahXauPASuLz8aL47YzARwCNlFlunK0YwwFKnVytGUFCuSXo+DxbWAzednSYXHA0U/7ThaP\nIg+iVYNtpck16BA36Arxqy8Bd3Udd9sTiyb+/wnSBl1N+6rlaD+32DTVOUWa4DBU50PAA8Ae0gRd\nITqnqfrMgaQeSfbadPCSRFpOlw4a0X6KnNd88fk88Z3ZMDwDPIKWwpfkaMflwE/oIT0MvIxGdjna\n8gvwNHAc+B74DU1p5WhLST/tq1jcSbXdF7T5GoT41V7nTCyxrjo5+f+mWu+jyiTGJFTn7aj84gBV\nWUxMQu/RbcCLxXHj/fL+A0J0LgAb0JTtfpS170vqoCtFIy4Fo8CbwIPA77XvFmi/nbcAP6L56H57\nt+VgBygjtBZ4ofj7ByePTHKxZTUa6XVQUDIK3F07JxdbejFIe2q73kMZqvrrttp5bbsGoVrqz3ps\nG9rUZoNoonUTKm9IUaMcqnMfmia7Fdi7dHL6EqLzWeS7F9C9mmJf0RCdh1F99yTwHGrbvqTekf47\nJLbkUtKkZE+HERRw7aVq7Hk05fADcDEKaNrMBtSRbAXOAc5H9uRmB+j++Rb9KDGooH4nsiE3W9YB\nHwM/F8dvoXR3jraU9Lun6r5govgsJZtP8V2bn40Qv9qG9s7J/4dqXYOy61uAXyPoqtO0TT9EccAF\nVH4mBiE6r0G/cwpwIdq25W/i1k+F6OxOtBxAA/4VaKaideS+6eAZwKtoaq6b3VSjnB20t9C5Fxup\n5qdzteMD4Iri/S5kR462TKJVseeie20W2E5etnQ4uZC+l/aykP5sNEX8Fe36xYw6Ta5Bh7g1XSF+\ntbuQ/nrS1PU08f+7SFvTFaL1MlR0nbIWMUTnaqpna21xfmya9v17SLN6MUTnSqr2vBb4JpK2ocl5\n08EbUA3UEarloltQlHuI9i/p78VGqpFErnZMokzXUZQdGiNfW2aotoyYRZnVXGx5HdWi/YXqIu7l\n1NofQ37gGHBzVKXN6WfHKuDdrvPKNviTqg1i0Muv3l+8Sp4vvj+KOt8UDNI5jtrtBMocHUfT7CkY\npPUVlC0q+4LPYgssGKRzBg3m5lCma31sgQUh92hJqqALBuvcjtrzCJqZaPMCIGOMMcYYY4wxxhhj\njDHGGGOMMcYYY4wxxhhjjDHGGGOMMcYYY4wxxhhjjDHGGGOMMcYYY8z/lX8BksCvhWEAqjQAAAAA\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cec1d10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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cldZNRKQ8eSVW1ZikydYB02rl5OxwngrcDWwLfF93dRW5xicikRIn9QeTxtmJ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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e7c86d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RsgVf7YEFrs8L7XleWgJHAU+75lnA68A0YEiBZRQRERGpGNkGWc2nnnQg8Baw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\nhBBCCCGEEEIIIYQQQgghhBAif3wGj/gXJ8EC9OYAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x110e7c150>"
       ]
      }
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n1 = 8\n",
      "data1 = [4, 5, 6, 5, 5, 4, 3]\n",
      "\n",
      "n2 = 20\n",
      "data2 = [16, 15, 17, 11, 18, 16, 18]\n",
      "\n",
      "p1 = Beta(\"p1\", alpha=500, beta=500)\n",
      "y1 = Binomial(\"y1\", n=n1, p=p1, value=data1, observed=True)\n",
      "\n",
      "p2 = Beta(\"p2\", alpha=500, beta=500)\n",
      "y2 = Binomial(\"y2\", n=n2, p=p2, value=data2, observed=True)\n",
      "\n",
      "@deterministic\n",
      "def diff(p1=p1, p2=p2):\n",
      "    return p2 - p1\n",
      "\n",
      "model = pm.Model([p1, y1, p2, y2, diff])\n",
      "mcmc = pm.MCMC(model)\n",
      "mcmc.sample(40000, 10000, 1)\n",
      "\n",
      "pm.Matplot.plot(mcmc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            15%                  ] 6158 of 40000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      29%                  ] 11637 of 40000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  40%                  ] 16017 of 40000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------50%                  ] 20050 of 40000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------60%---               ] 24328 of 40000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------72%-------           ] 28805 of 40000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------83%-----------       ] 33289 of 40000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------94%---------------   ] 37754 of 40000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 40000 of 40000 complete in 4.3 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting p1\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " diff\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " p2\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HGhMRERGpCAqORERERApMAZiIiFilcajs0vm3oxhyMJQDJlJxlAMmpUk5YFLo\nuSBFREREJEcUgImIiIgUmAIwERGxSjlIdun821EMORjKAROpOMoBk9KkHDBRDpiIiIhIiVIAJiIi\nIlJgCsBERMQq5SDZpfNvR5g2zAHE54F8EBjpez8KvAh87bx+Frg55L6gHDCRCqQcMClNygGTQs0F\nWQXcAxwG1AEzgInAF77t3gKOy3BfERERkYqSqgmyN/AVsBBYB0wABgVsFxQJht1XREREpKKkCsA6\nAN95Xi9y1nnFgL7AbGAy0DWNfUVEpMIpB8kunX87UjVBhmnE/gjoCKwBBgIvAF2yLJeIiFSI4cOH\n2y5CRdP5tyNVAFaHCa5cHTE1WV4rPctTgPuALZztUu3rqPEsR52HiJSPWuchUhwWLlzIa6+9lvZ+\na9f+kofSSCVKFYDNBDoDnYDFwKnAYN827YDvMbVlvTH5YMtC7uuoSbvgIlJKotT/YaXmDrHriSee\n4MYbn6Fx43R7GJ4HtMlHkaTCpArA1gOXAK9iejWOxfRivMB5fzRwEnChs+0a4LQU+4qIiGzi5h8V\nuils/fqjWLduREE/sxjZOv+VrhjG4dE4YCIVR+OAiV0jRozghhvWEIvlOgDTOGDlTnNBioiIiJQo\nBWAiIiIiBaYATERErNI4VHbp/NuRKglfREQkr5T8bZfOvx2qARMREREpMAVgIiIiIgWmAExERKxS\nDpJdOv92KAdMRESsUg6SXTr/dqgGTERERKTAFICJiIiIFFiYAGwAMBeYDwxLsl0vzPyPv/WsuwaY\nA3wKPAk0y6yY5alJE9slkEr2m9/ANtvYLoWIcpBs0/m3I1UOWBVwD3AYUAfMACbScFLtKmAk8Ipn\nXSfgfGB34D/AU5iJusdlW+hS1bo1LF8ef/3GG9Cvn73ySGVbtgz23x+WLLFdkrxYCKwANgDrgN7A\nFpjr0A7O+6cAPzvbXwOc42x/GfCas74H8AjQHJgMXF6Aslcc5SDZpfNvR6oasN7AV5iL1TpgAjAo\nYLtLgWeAHzzrVjj7tMQEei0xQVxa/vSndPcoXjvtVP9127Z2ypErHTvaLoFk67rrbJcgb2JAFNgX\ncx0DuBqYCnQB3nBeA3QFTnWeBwD3EZ9o937gXKCz8xiQ/6KLSCVIFYB1AL7zvF7krPNvMwhzoYL4\nFPDLgNuAb4HFmF+ar6dbwEMPTXePuKZNM9833zbfPNx2O+6Y33JIZTvmGIjFUm9XoiK+18cRr4Ef\nBxzvLA+RqNFBAAAgAElEQVQCxmN+MC7E/OjsA2wLVAPTne0e9ewjIpKVVAFYmEvzHZhfkjHMBc+9\n6O0M/B7TFNkeaAWcHqZQm20WX474L6FpyCTHyl9LlUve77J8ebgbX6FujlVVme+7xRa5K0ehZPN9\ny8Fdd9kuQd7FMD/4ZmJSIQDaAUud5aXOazDXp0Wefd0fmv71dTT8ASo5oBwku3T+7UiVA1YHeBua\nOlL/ggQmR2KCs9wWGIhJxm8G/AP4yXnvOaAv8ETDj6nxLEc58sgozz3nHDCLZrqgm+zatXDwwfDe\ne8H7XHYZ/P73mX9mMv/5T36OmwsnnQRPPZXePm5wGIlAo0awcWPuyyVGy5awZk3q7a6/Hm6+OfH7\nI0fCsGRdaTKw774wa1aqrWqdR8EcAPwL2ArT7DjX936McD8wpQCUg2SXzr8dqQKwmZi8h06YZsRT\ngcG+bbx1Rg8Dk4AXgW7An4AWwK+YRP7pBKoJXDthAnTtmqKESTz1FAwcWH9dkyYmyNptN3j44cyP\nnYn16+u/9tZubb01fP99w31KpXno6KNh0iTbpbDjmGPgpZfy+xlXXx3Phxw6FB57LHi7li2TH+eo\no0wAlk3Nst+f/wwPPAATJybe5rjjokycGPWsyfuv7X85zz8Az2PywJYC2wBLMM2L7v9x/h+a22F+\naNY5y971gXmsNTU1m5aj0SjRaDTL4otIsaitraW2tjbnx00VgK0HLgFexfR0HIvpAXmB8/7oJPvO\nxuRMzAQ2Ah8BDyTa+L//G15/Hb7+On5zaN489RdIpkOCxoLTTjOPoAAsnwFPsiZR24FWJp8/fDic\n7zTubNiQ2/Lkm//73nCDCSQy0bjA80lsu232x2iUwxEAq6rguOOSB2C5DPhCaIm5Xq0ENgOOwER8\nE4GzMD22zwJecLafiBkm53ZME2NnzI/FGKYzUR/n9VAgsPHWG4CJSHnx/6jKVXNtmMvwFGBXYBfg\nFmfdaIKDr7MxTY2uUcAewF6YC966RB8yerT5FZ1LmdxkchkIeW/M/fubcZcSfVaiz7UdmPl5b/7n\nnRdfXrs2P5+XKIhOxyJ/o3mAm25K/F63btCzp2lifeihhu8XIrjwBu9h/iYOOSR4faoaMr8DDki9\nTap8ujPPhMH+evP8age8A3wMfAC8hBlW4lbgcGAecKjzGuBz4GnneQpwEfHmyYuABzHjIH5F/aF2\nJEeUg2SXzr8dRTUSfqIbyysZXvJy+Ss/XeedV//zJ01qWFPi/b533BF8nKBz8tVX2ZcvLDfguvde\n8xxUKxmLwbqEoXV2wtZKub1Fe/Vq+F6HDvCDZ4CUP/4xvTL86U8wY4YJtIIGLvUGYEHnp317OPXU\n+uu8wWsY3u+VLABLFQy6gVzYoPHBB81zixaJt6mqipfpvvvg4ovrvz9uHOy3X7jPy5F/Avs4jz2J\n/3BchkmF6IKpFfvZs89fMD8yd8PU+Ls+xPyA3AUzPpjkwfDhw5WHZJHOvx1FGYD5bw5HHhm8/Tnn\nJD+e/zgjRqQuw8CB2Td9gsld8yelJ7txJhpuIigHLh+BZaKyJaqVPPHE+q/DNEHuvHPw+tatE+8T\ntidrM2eOhaFD4+uGD4/f+L2dOVq1qp+Ivv/+yY+dKlhJ9f7tt5t8Rq90e456P8P9t9pnn/SOAfEf\nAWGbMd3PWrYMpkwJ3sYbgF14YXCAW12dXjlFRMpdUQVg229vns88M9z2Bx3UcN3998eXu3QxvcJc\n7dunPuZuu8HLL4f7/FT8QYk/yAnTlBT0HXPVLOnWaiVy8cWJg4tnn63/+sknTa3OXnslPt6ee4Y7\nluvLL5OXz2vKFNMT79JL4+sOOCBxb9e//CW+/M47Dd8fPz6+HBTwduoUvmxB1q2DU07JbF/33z/Z\nWHKrVwevdwOwZr5Jwe67L/lnNm8O220X/J43AANzbm65pf42W2xRfM3pIiI2FVUAtuuu5iJ97LHJ\ntwsanPUPfzDPp50WX9eoUf2bZ9gbQDQKx+dguMVEAVfQjTcfNydvc9nmm5uedF7nn5+8iS8oYPIH\nZJ98Au+/b0bFHzMmOJhxJWr6cwfM7dat/vouXcI3lXXqlFmNEATnMHXuDG+/bZaD/ob23jv88YP+\nbauqTC9dfyCUSFANmBvg77JL/W233x6OOCL4OG4A5j+vF14YvH2Yv8ugALXSx1mT9CgHyS6dfzuK\nKgALa9ddG65zawPatKm/PpPAplEjGDUq/f0SHQvq53+5420lK1vnzub5ggtMDs3ixfH3Un2nK680\nz96ZAC68sGGtRJMmcMUViY/ZtKlprvO+729G3GuveFlTCQqmZs+GAw80y0E1Ov6mqzDNyLmSqEkc\nTK9dN4+rR4/0jx028PKXxbucqNn3m28SB9Zu83rQdwo6t97PTRQM+2vARNKlHCS7dP7tKJkALN0L\nvNucmanOnRPfJIN65p17bsN122xjamZiMRPsJGuC9AaOZ50VX27b1jTJbrttPEDx7vfhh4m/wxtv\nJH4vjCZNzGThX38dXzdmTObHC7qB77138lquY481Y1e5rr3WNCu6tVMAdWnOMNq3b/B6b5DrrT08\n7LCG2x59dPxcXHVV+n+f7ndOtwfljjvGP8vNMRw1Cm67LfXxDjwwnkwftF2iDhaurbYKPm7LlmYc\nOxERCa9kArB0nHdefFgB77RG6d4kE20f1Lzy4IMNm9A++8z0ngvz+XvsAT/9FH8ddIN0OyN4j9O9\ne+LjhglCk41e36yZKYe3g8AOO6R/Hp8ImPsAYNWq+q+DvnMk0rCJbb/96t/ww+T2eR1+ePB6b2J6\nhw7x7xm2U8ZOO5kcQj/v+brqqsT79+nTcJ0bmHsDNvd47vMJJ8Sb4JNJFewFzZ3qHyw46N9+r71M\nk713IGF/r08REamv5AIw7xx2ibrGjxkTr0XK1RhN3p6Y/foFb+Mf6X7LLev3dkuVhJ+qZ1ymtSzJ\nuM1Y7drVX9+mTf2ejgcfbMbCCsvbnDhkSHB5vMFxugrR5JXuZ8yeDe++m3ybVq3MkCRu06+XN9B0\nWwP+/e/620Qi8flKw07o7t03aNl1/vnp/Rv7j+2tIdt+e1M76+0EI5KIcpDs0vm3o+QCMG+i9Ukn\nmefzz09cSxFmsFPXF18kfs+9ubz9Njz6aP1t3VoPb05OUGJy2Bt6JJI8eEo1hIB7jpIdwx1XqmVL\n08z5P/9jXnd0JmQ59ND6eWt77lm/Ni8TYYaU+Mc/Er+Xba1KUA1TLrVqZYLKF19Mvt0xx8SD7f/9\n3+Btrr02eH0kYnp6rloV/PeU7N88VQDWrBn07m2W3XOdTaDbvXvmswtIZVEOkl06/3YUdQDmHzne\nz03+feABuPxy+OijzD/ryCODm49c7o3ooIPMzcu7rZuM7a0B2333hse48054/PGGx0yXmxifqJzu\nqOPJbsY77GCemzY1g5Q2bw6//tqwp2S63MDTX8Pz8cf1k9UTjWW2//71e7J6ecfSCnPu/E3F77+f\n3jnP9N/nuOMS50v5/03OOiu9HoN9+phzt9lmqcvnn3TbX8sZxPt37n0tIiK5FSYAGwDMxUzFMSzJ\ndr0wc0d6h+hsAzyDmT/ycyD0eNjff5+4qS/optC8Oey7b/JtvYNx+gUFK2FuPo88Eh/52+3Nd9pp\nwcMA9OwJp5/e8PhBN8ZcNJ2GrQ1xNWsWH/g17FhsftXVJtDxDxXSrVvqGph0pPq3eeopM5xIJu6+\nO73PDfou3nwod59+/YIHFQ4aPiPR97vhhtTbuG69Fb77DqZONdMxjR0bfy/swKhBI/97+fP4REQk\nnFTTCFcB92Cm76gDZmAmrvU31lVhJrh9BfDeju4EJgMnOZ8VOusnUQ1Cpr/Ily5teMzf/AbWrIH/\n/Mc0l2Sif/948+fDD5sbb7oDbH77bf3XucpbSxTwRKMNp4vxvpdtrUefPsnHA0vX6afDypX116Uq\n44EHZj5jgHvsPn0gl2kRb70VvH633ZL3Zk3kkkuCa1q9ttuu4QCq33yTuIOGf+iNdu0anuuhQ+Gx\nx8xyunl8O+8MCxakt4+UPzf/SM1gduj825EqAOuNmYB2ofN6AjCIhgHYpZiaLu9MfK2BgzCTcIOp\nHVueRVkz4t48grrJz59vbgZ9+sDNN6d/7OXLGyZCpzOKvlu7ENT7LIxEgVqy8asA/va3zActDSvV\nsATpBJm9e8dzk1ypArBcBLEtW5p5IPNt7FgzK4E3KPbPG+ryfq/f/tY80pXtEC2PPmp+0Lz2Wvr7\npjv+mVQG3fjt0vm3I1UdQQfgO8/rRc46/zaDAHcSIPfWuCPwA/Aw8BEwBmiZTWEhd7VDYHop9uhh\naq6SHffvfw9en24vND/vUAdekUjwsb3bHn44DBgQfNxkwcnUqQ2Hy8iHXXdNPPcjmHPv1axZ9qPL\n25Lob2fuXPOcqqzNmjWcD9M/uGnYuSNz+f9HPkyenF2upohIuUhVAxbmNncHcLWzbYR4E2RjoDtw\nCabp0t2uAHUKcYcemvzGXlUF//VfyY/Rt2/qeRNzqUsXuOwyWLIk8TbJah8aN4bf/S74vaBBRfMl\nWROgP79vxYr0ktELUQOWbTmCZmzIxMqVyTte5FJNjeml+c03+Tn+DjvEO4CIiFSyVAFYHdDR87oj\nphbMqwemaRKgLTAQWAd84GzrDl7wDCYAa+CKK2qoqTHL0WiUaKbZ0wH69DHjM5WKNWtMjUijRunX\nVLm5PpFIfFLyq66Cv/41t2UMK1Fw8sMPDWvA0m2GzVcNWPPmmU0tlAuJgsawwdcZZ5gemNlo186M\n8p9qcu50A9za2lpqa2szLpeUN+Ug2aXzb0eqAGwm0BnoBCwGTgUG+7bZybP8MDAJk6gPpvmyCzAP\nk8g/J+hDbr+9Jo0iF46NZq5Eg8uGMX58w3WjRpkALNM8s1x7443kvVHD8ieW+2VaA/bLL5ntVwzc\nxPhCSPf/Df8PKw36KF668dul829HqgBsPaYJ8VVMT8exmAT8C5z3R6fY/1LgCaApsAA4O+OSSkqJ\nBjqdOTN1b7l8ePZZU9vl5R+eIlNbbmmmf3LHYPMLG8g+9FB6n+udlimMrbc2Tcq5Uqim1WLPJRMR\nKXWpAjCAKc7DK1Hg5Q+wZlO/Z2TJ6tzZdgkyr5Gz1aSWTlJ9Js4+O7jJLZ3z5E9+T6Vr1/SOv3Rp\nescXEZHKUNQj4QdJNTp+vtxwQ/EPOllptRaNGiUeLy6MSZNMwnmpOOoo03NWpNxoLkK7dP7tCFMD\nVjSCxt3Kp3ffjc/vWFWV3eTRhZBOL0IpreAL0htjLt+K/f8FKS3KQbJL59+OkqoBK2TwBaYHZd++\nhf3MZK68EhL9f/LWW5mP5i/F4dJLbZcgvLFj4fPPbZdCRKR0lVQNWKXr2zdxQJho3kwpHb17w6BB\n8OKLtkuS2m9+Yy8dQESkHJRUDZiIiJQf5SDZpfNvR0nWgA0YAO+9Z7sUIiKSC8pBskvn346SrAEb\nNAg+/th2KUTKVzHNtSkiUo5KMgATKVeVNpSIiEilUgAmIg2oBkwKSTlIdun821GSOWAi5Uo1YFKJ\nlINkl86/HWFqwAYAc4H5wLAk2/XCzB15om99FTALM0m3SEp/+xtMm2a7FHYUS83T0UfDOefYLoWI\nSPlKVQNWBdwDHAbUATOAiZgJuf3bjQReAfy/4S8HPgeqsy2sVIZttjEPsadTJzPYqoiI5EeqGrDe\nwFfAQmAdMAEYFLDdpcAzwA++9dsBRwEP0jAwExEfNUFKJVIOkl06/3akqgHrAHzneb0I6BOwzSDg\nUEwzpLcR5W/AVUCBJxESEZFSoRwku3T+7UhVAxYmI+UO4Gpn2wjxmq5jgO8x+V/6XS8SgmrAREQq\nQ6oasDqgo+d1R0wtmFcPTNMkQFtgICYZvw9wHKYJsjmmFuxR4Ez/h9TU1GxajkajRKPRkMUXkVJQ\nW1tLbW2t7WKIiBSNVAHYTKAz0AlYDJwKDPZts5Nn+WFMb8cXnce1zvqDgT8SEHxB/QBMpJJdcQV0\n7Wq7FLnn/2GlfBPxcv8e1BRmh86/HakCsPXAJcCrmJ6OYzE9IC9w3h+dxmcVSQd7keJ14IHmIVJJ\ndOO3S+ffjjADsU5xHl6JAq+zE6x/y3mIiIiIVDxNRSQiIiJSYArARETEKo1DZZfOvx2aC1JEylEV\nphPRIuBYYAvgKWAHzMDSpwA/O9teA5wDbAAuA15z1vcAHsH04p6MmdVD8kA5SHbp/NuhGjARKUfu\nFGhu55+rgalAF+AN5zVAV0zv7q6YeW/vIz5u4f3AuZie4J2d90VEckIBmIiUm6Ap0I4DxjnL44Dj\nneVBwHjMVGsLMVOv9QG2xcxfO93Z7lHPPiIiWVMAJiLlxp0CbaNnXTtgqbO81HkN0J76g0svwkyv\n5l9f56yXPFAOkl06/3YoB0xEyol3CrRogm1i5HhcQs3mkR3lINml859cvmbyUAAmIuWkLw2nQHsM\nU+u1DbAE07z4vbO9f7q17TA1X3XOsnd9XaIP1WweIuUrXzN5qAlSRMrJtZiAakfgNOBNYCgwETjL\n2eYs4AVneaKzXVNnn86YvK8lwApMPljEOYa7j4hI1lQDJiLlzG1qvBV4GtOrcSFmGAowPSWfdp7X\nAxd59rkIMwxFC8wwFK8UosCVSHMR2qXzb0ck9SaA6X59B2ZsnQeBkQm26wW8h7m4PYf5JfoosDXm\novYAcJdvn1gspmkiRSpJJBKB8NefYqdrWAkaMWIEN9ywhlhsRI6P7P5ZZ/830bp1L6ZOvY9evXpl\nfSzJnVxdv8I0QVYB92CCsK7AYGD3BNuNxPxKdAu2DrgC2APYD7g4wb4lIR9JePmgcuZWqZQTSqus\nIpLcunXNOeSQgbRp0z6tx6mnnmO76BJCmACsN2ZsnIWYgGoCZuwcv0uBZ4AfPOuWAB87y6uALzDd\nu0tSqdzcVM7cKpVyQmmVVUSSW7PmFVav/oTly2em8biPzz770nbRJYQwOWAdgO88rxdhElP92wwC\nDsU0QwbVvXYC9gU+SLuUIiJStpSDlMhmziMdW6X9KTr/doQJwMI0ZN+Bmdojhml+9LeNtsLUjl2O\nqQkTEQnrUcxo9VNsF0TyQzd+u3T+7QiTRLYfUEN8HrRrMCNMexPxv/Ycqy2wBjgf08W7CfAS5uJ5\nR8DxvwJ2TrPcIlLaFgC7hNy2GWa+xqOBf2A6Aq3OU7kyoST8ElQKSfiZ+Ttdu/4/5sz5u6XPL3+5\nSsIPUwM2EzM2TidgMeZCONi3zU6e5YeBSZjgKwKMxXTxDgq+IPxFWEQq05aYa8xyzICqD2GuQyIi\nJStMALYeuAR4FdPTcSwmmf4C5/3RSfY9ADgD+AQzNQiYGjSNpyMiYV0J3IepNYP6OalSBpSDZJfO\nvx1hB2KdQsP8i0SB19me5XfRaPsikp1a4sHX0cDL9ooi+aAbv106/3bYDo4GAHOB+cAwS2VYSLyG\nbrqzbgtgKjAPeA1o49n+Gkx55wJHeNb3AD513rszB+V6CNPc8qlnXS7L1Qx4yln/PrBDDstZg+kt\nO8t5DCyCcnYEpgFzgM+Ay5z1xXhOE5W1huI6r80xvZo/xqQZ3OKsz/U5/aunnEdnUE4REfGowiTg\nd8Ik6n+MnUFa/4m5YXiNAv6fszwMM40JmIFoP8aUtxOm/G4i3nTMmGlgpi1xOy1k6iDMsB3ewCaX\n5boI06wDJp9mQg7LORz4Q8C2Nsu5DbCPs9wK+BLz91aM5zRRWYvxvLZ0nhtjAqQDyf05nQv0B27C\ndPgpNjEpPTfffHMsErk2BrEcP3AeuT5u2Me7sa5d+9o+vWWNHPWwsFkDFnaA10Lw92Y4DhjnLI8D\njneWB2G6w6/DlPsrzJho2wLVxGvQHvXsk6l3gH/nsVzeYz2LucHlqpwQ3EPEZjmDBgXuQHGe00Rl\nheI7r2uc56aYH1X/Jvfn9CKgC/A9sHmG5ZQiduONN27KQ5LC0/m3w+Zk3GEGeC2EGPA6sAGT1zYG\naIdpVsN5bucst8f8ynctwnyPdc6yq474DTOXclku7/lfj+lhtgWwLEdlvRQ4E9OL9krg5yIqZyfi\ngwIX+zl1y/o+plNLsZ3XRsBHmKFk7sc0m+b6nAK0xjRHRjIspxQx5SDZpfNvh80asGIZOOcAzA1u\nIGauyoN87+esujHHirVcYG7EO2Ka0f4F3Ga3OPW0wtT4XA6s9L1XbOfUP4BxMZ7XjZjybAf0Aw7x\nvZ+Lc/rfmLEEJ6CBnEWkTNgMwOowycaujtT/FVwo/3KefwCexzSNLsXk4YBpHvneWfaXeTtMmeuc\nZe/6ujyUNRflWuTZZ3tnuTGmhiFXtQrfE7/xPkg8t8d2OZtggq/HgBecdcV6Tt2yPu4pa7GeVzA1\naC9jkulzfU6XYjojLMDknKn2S0RKns0AzDvAa1NMIvDEApehJSb3BMyEW0dgksknAmc5688ifgOc\nCJyGKe+OmPJPx+TsrMA0oUaAoZ59cikX5Xox4FgnAW/ksJzbepZPIJ6gb7OciQYFLsZzmqisxXZe\n2xLv4dgCOBzTOzPX53QQZnDnd4FfMiinFDnlINml81+ZBmJ6eH2F6Z5eaDtikp0/xvzCdsuwBSYv\nLKgb/bWY8s4FjvSsd7vRfwXclYOyjcfMPLAWk6tzdo7L1Qx4mnj3/k45Kuc5mCTqT4DZmJtvO8/2\ntsp5IKa57GPiwzgMoDjPaVBZB1J853UvTP7Xx065rnLW5/qcPgd865RzvwzKmW+2O2VJBtQLUjJF\njlJVsp7LSEQkz8ZgAvyLMUNnXGS3OA0412QpJZoLUjJVyLkgRURsWkV8qBM1QYpIWbA9Er6ISCo/\nAn0xvT43Wi6L5IFykOzS+bdDNWAiUuxGALthfjB+brkskgcah8ounX87FICJSLEb7zy3cJ6znWVC\nyswrr7zCypX+Yf2S+/TTTzHjB4vYoQBMRIrdYOc5AlxhsyBSfNasWcNRRx1Nq1Ynpr1vLNYvDyUS\nCUcBmIgUuz0wXcqaOMtSZtz8o0yawmKxGFVVzVm58v9yXayKkc35l8xpGAoRKXbuXeE/wBTMOGjF\nRMNQWLR69WratNma9etX2y6KQ8NQlDsNQyEilWKmZ3k75/GypbKIiOSEAjARKXbnAX/HVCkcSH6m\n+RIRKSgFYCJS7OYC/+MsbwWMs1gWyQPlINml82+HcsBEpNjdAmyNqQFbClxntzgNKAfMIuWA+SkH\nLN+UAyYileI6TN7Xz5hEfBGRkqepiESk2N2B6Qm5ArjbcllERHJCAZiIFLuNwDfO8s82CyL5obkI\n7dL5t0M5YCJS7EYCO2B6Qu4NnG+3OA0oB8wi5YD5KQcs35QDJiKVIAI8A7R1lu+zWxwRkdxQACYi\nxSwGHAKMsl0QEZFcUgAmIsVskPM4EljmrDvZXnEkHzQOlV06/3ZYzwHr1q1bbPbsYpvaTUTybDaw\nT4jt7gcu9DwXI+WAWaQcMD/lgOVbrnLArPeCnD17NrFYrCwew4cPt14GfZfy/S7l8j1isRhAt5CX\niO2Bo53no5yHiEjJUxOkiBSz/8Mk4D+NmYZIRKQsKAATkWL2iO0CSP4pB8kunX87FIDlUDQatV2E\nnNF3KT7l8j0KoDnwFtAMaAq8CFwDbAE8hRlTbCFwCvGBXa8BzgE2AJcBrznre2CCwObAZODyApS/\n4ujGb5fOvx3Wk/BRAqtIxclVEmsSLYE1mB+Z7wJ/BI4DfsQMaTEM+A1wNdAVeBLoBXQAXgc6Y7Ko\npwOXOM+TgbuAV3yfpWuYRUrC91MSfr6VTRK+iEgerHGemwJVwL8xAdg4Z/044HhneRAwHliHqRn7\nCugDbAtUY4IvgEc9+4iIZCWbAOwhYCnwaZJt7gLmY7qc75vFZ4mIpKMR8DHmGjUNmAO0c17jPLdz\nltsDizz7LsLUhPnX1znrJcc0F6FdOv92ZJMD9jBwN+ZXYZCjgF0wVfl9MOP47JfF54mIhLURM85Y\na+BVzGj6XjFy2EZUU1OzaTkajSpfL03KQbJL5z+52tpaamtrc37cbAKwd4BOSd73Vvd/ALSh/i9Q\nEZF8Ww68jEmmXwpsAyzBNC9+72xTB3T07LMdpuarzln2rq8L+hBvACYi5cX/oypXtYX5zAHrAHzn\neb2I+hczEZF8aIv5wQfQAjgcmAVMBM5y1p8FvOAsTwROw+SL7YiptZ+OCdRWYGrwI8BQzz4iIlnJ\n9zAU/l4C6iokIvm2Lab2vZHzeAx4AxOEPQ2cS3wYCoDPnfWfA+uBi4hfqy7CDEPRAtML0t8DUnJA\n41DZpfNvRz4DsKBq/ZTV98qfECk/+cqhSOBToHvA+mXAYQn2+Yvz8PsQ2CtH5ZIEdOO3S+ffjmzH\nsegETCL4AnUUZvycozDJ93cQnISvMXREKkwBxgErJF3DLNI4YH4aByzfcnX9yqYGbDxwMCbf4jtg\nONDEeW80prr+KMyYOquBs7P4LBEREZGykU0ANjjENpdkcXwREakAykGyS+ffjmJoAsio+v7MM8/k\nlVdeYfjw4Vx88cV5KJaI5IuaICVX1ATppybIfCuGJkirRo4cSf/+/Vm1alXePiMWi7knmo0bN9Ko\nkWZuEhERkewVfQD2yCOP8MILL7Bu3TpWrlzJhAkTaN++Pdtuu23S/U4//XTq6urYsGEDTz75JB07\ndmTy5Mn8+c9/pnnz5px33nkMHjyYM888k0WLFtGqVSsef/xxfv75Z84880zat2/PPvvsw6uvvkrv\n3r2ZNWsWr732WoG+tYiIiJSzoq/SiUQitGrVipdffpnrrruOkSNHhtrvwQcfpLa2liuvvJLRo0cT\ni8W49tprmTp1KtOmTWPIkCE899xzbL/99tTW1nLaaadx9913E4lEWLx4MY8//jhXX301AAMGDFDw\nJSKSJ5qL0C6dfzuKvgYMoHt3M6RPz549ufPOO1Nuv3HjRq666io+/fRTfvnlF/baay9++OEHOnbs\nSAHjG/4AABeuSURBVKtWrQAT2C1YsICePXtuOrYbZHXr1o3GjeOnplevXrn+SiIi4lDyt106/3YU\nfQ1YLBZj1qxZAMycOZPOnTvXey/IrFmzWL58OW+99RbDhg1j48aNbLXVVixatIjVq1dv2neXXXZh\n+vTpAMyYMYMuXboANMj1Uu6XiIiI5FLR14BFIhHWrl3LwIEDWb16NePHjwfgmmuuYdKkSWzYsIGv\nv/6a2267bdM+u+++O9988w1HHHEEu+22G5FIhEgkwogRI+jfvz8tW7bk3HPP5bTTTuO5557j4IMP\nprq6mscff5zly5dvSrwXERERyYdiiDSSduEeN24cq1at0lATImVEw1CIVzbjUGkYCr/0h6HQOGDp\nqahhKFQjJSJSvnTjt0vn346iD8DOOuss20UQERERySlll4uIiIgUmAIwERGxSuNQ2aXzb0cxJFcp\ngVWkwigJX3JFSfh+mgsy33J1/VINmIiIiEiBKQATERERKTAFYCIiYpVykOzS+bejGHIwlD8hUmGU\nAya5ohwwP+WA5Vux5IANAOYC84FhAe+3BV4BPgY+A/4ry88TERERKXnZBGBVwD2YIKwrMBjY3bfN\nJcAsYB8gCtxGCQz+KiIiIpJP2QRgvYGvgIXAOmACMMi3zb+AzZ3lzYGfgPVZfKaIiJQZ5SDZpfNv\nRza1UR2A7zyvFwF9fNuMAd4EFgPVwClZfJ6IiJQhzUVol86/HdnUgIXJMLwWk//VHtMMeS8mEBMR\nERGpWNnUgNUBHT2vO2Jqwbz6AiOc5QXAP4FdgZnejWpqajYtR6NRotFoFsUSkWJTW1tLbW2t7WKI\niBSNbLpRNga+BPpjmhinYxLxv/BsczuwHLgRaAd8COwNLPNsoy7cIhVGw1CIl5t/lElTmIah8Et/\nGIpszn8lytX1K9sDDATuwPSIHAvcAlzgvDcaMwzFw8D2mObOW4AnfcfQxUukwigAk1xRAOanccDy\nLVfXr2yHhJjiPLxGe5Z/BI7N8jNEREREyoqmIhIREREpMAVgIiJilcahskvn345iyMFQ/oRIhVEO\nmOSKcsD8lAOWb8UyF6SIiIiIpEkBmIiIiEiBFVUA5h2QVUREKoNykOzS+bejGHIwNuVPRCIRlEsh\nUv6UAya5ohwwP+WA5ZtywERERERKlAIwERERkQJTACYi5aYjMA2YA3wGXOas3wKYCswDXgPaePa5\nBpgPzAWO8KzvAXzqvHdnXktdwZSDZJfOvx3FkIOhHDCRCpPnHLBtnMfHQCvgQ+B44GzM9GijgGHA\nb4Crga6YOWp7AR2A14HOmCSe6cAlzvNk4C7gFd/nKQfMIuWA+SkHLN+UAyYiEmwJJvgCWAV8gQms\njgPGOevHYYIygEHAeGAdsBD4CugDbAtUY4IvgEc9+4iIZEUBmIiUs07AvsAHQDtgqbN+qfMaoD2w\nyLPPIkzA5l9f56wXEcmaAjARKVetgGeBy4GVvvdi2GsjEh/lINml829HY9sFEBHJgyaY4Osx4AVn\n3VJMbtgSTPPi9876Okzivms7TM1XnbPsXV8X9GHeQaSj0SjRaDTL4leW4cOH2y5CRdP5T662tpba\n2tqcH1dJ+CJScHlOwo9gcrx+Aq7wrB/lrBuJSb5vQ/0k/N7Ek/B3wdSQfYDpRTkdeBkl4RcdJeH7\nKQk/34olCX8Aptv2fEyvoiBRYBamO3htlp8nIpLKAcAZwCGYa88szLXqVuBwzDAUhzqvAT4Hnnae\npwAXEb97XgQ8iLnGfUXD4EtEJCPZRHBVwJfAYZhq+RnAYEyPI1cb4O/AkZgq/baYbuBeqgETqTCa\niki83PyjTJrCVAPml34NWDbnvxLl6vqVzQH2B4ZjflmCqcqH+K9KML8etwH+lOQ4CsBEKowCMMkV\nBWB+aoLMt2JoguwAfOd57Xbd9uqMGX16GjATGJrF54mIiIiUhWx6QYYJ75sA3YH+QEvgPeB9TD6F\niIiISEXKJgDzd93uSP1BC8HUkP0I/OI83ga64QvAvF24a2tr1YVbpMzkqxu3lAflINml829HNm2Y\njTFJ+P2BxZhu2v4k/N2AezBJ+M0wXbpPxfQ2cikHTKTCKAdMckU5YH7KAcu3XF2/sqkBW4+ZpPZV\nTI/IsZjg6wLn/dGYISpeAT4BNgJjqB98iYiIiFScbEfCn+I8vEb7Xv+P8xARERERNBekiIhYprkI\n7dL5t6MYcjCUAyZSYZQDJrmiHDA/5YDlWzHkgImIiEhRacTXX8+hd+8j0tqrqirCAw/8D3vttVee\nyiV+CsBERETKRk9+/fVZZszYkNZeLVr8mblz5yoAKyAFYCIiYpXGocqlJpjRocKrqbkRM62zFFIx\n5GA0yAGrqampNziriJQX5YBJrigHLDeqq09m7NhTOPnkk20XpegVw1yQeaPeGCIiIlLO1AQpIiJF\n4aabbuVvf7s7rX02btxIJNI8TyUSyR8FYCIiYpXb6vHll4v4+efLgdPTPMJmOS9TJTE5YHvaLkbF\nKYYcjAY5YBoPTKS8KQdMggwZcj7jx/cGzrddlCwoB6zclXUOmIiIiEg5UwAmIiIiUmDKARMREavU\n890u5YDZUQw5GMoBE6kwygGTIMoBs0c5YOEpB0xERESkRCkAExERESkw5YCJiIhVygGzSzlgdmRb\nAzYAmAvMB4Yl2a4XsB44McvPExGRMjN8+HBNxG1RTc1wbrvtM9vFqDjZBGBVwD2YIKwrMBjYPcF2\nI4FXKJ+kWxEREZGMZROA9Qa+AhYC64AJwKCA7S4FngF+yOKzRERERMpGNjlgHYDvPK8XAX0CthkE\nHIpphiytfrkiIpJ3ygGzSzlgdmQTgIUJpu4Arna2jZCgCbKmpmbTcm1tbRZFEpFiVFtbq/+3JSE3\n/2vIkFIe/6t01dQMd8YB62q7KBUlm5ys/YAaTA4YwDXARky+l+trz2e0BdZgRtib6NlGA7GKVBgN\nxCpBNBCrPRqINbxiGIh1JtAZ6AQ0BU6lfmAFsBOwo/N4BrgwYJukvLVjIiIiIuUgmybI9cAlwKuY\nno5jgS+AC5z3R2dXNOPGG29UECYiUsaUA2aXcsDsKIYmgKRNkGqOFCk/aoKUIGqCtEdNkOEVQxOk\niIiIiGRAAZiIiIhIgWkuSBERsUo5YHYpB8yOYsjBUA6YSIVRDpgEUQ6YPcoBC085YCIiIiIlSgGY\niIiISIEpB0xEys1DwNHA98BezrotgKeAHYCFwCnAz8571wDnABuAy4DXnPU9gEeA5sBk4PK8l7xC\nKQfMLuWA2aEaMBEpNw8TnyLNdTUwFegCvOG8BuiKmcWjq7PPfcRzO+4HzsXM+NE54JiSI8OHD980\nH6QUXk3NcG677TPbxag4CsBEpNy8A/zbt+44YJyzPA443lkeBIwH1mFqxr4C+gDbAtXAdGe7Rz37\niIhkTQGYiFSCdsBSZ3mp8xqgPbDIs90ioEPA+jpnvYhITigHTEQqTYxSGyOgzCkHzC7lgNlRMgFY\nTU2NJuUWkUwtBbYBlmCaF7931tcBHT3bbYep+apzlr3r6xId3HttikajRKPRHBS5crj5X0OGlPL4\nX6Wrpma4Mw5YV9tFKUq1tbXU1tbm/LjFMBBiqIFYNSCrSPkowECsnYBJxHtBjgJ+AkZiEvDbOM9d\ngSeB3pgmxteBXTA1ZB9gekVOB14G7gJeCfgsDcSaIxqI1R4NxBperq5fJVMDJiIS0njgYKAt8B3w\nJ+BW4GlMr8aFmGEoAD531n8OrAcuIn7nvAgzDEULzDAUQcGXiEhGFICJSLkZnGD9YQnW/8V5+H1I\nvAZN8kg5YHYpB8wONUGKSMFpLkgJoiZIe9QEGV6xzAU5AJgLzAeGBbx/OjAb+AT4O7B3lp8nIiIi\nUvKyaYKsAu7BVOvXATOAicAXnm2+BvoByzHB2gPAfll8poiIiEjJyyYA640ZNXqh83oCZlRpbwD2\nnmf5A+p36xYREVEOmGXKAbMjmybIDpgeRi53BOlEzsX0JBIREdlEc0Hapbkg7cgmAEsnw/AQ4ByC\n88TSpgFZRUREpJRl0wTpH0G6I/XnTnPtDYzB5ID5J8gF6gdUYUabvfHGGxWEiZSQfI0kLSJSqrLp\nRtkY+BLoDyzGjBY9mPo5YNsDbwJnAO8nOE7aw1BoSAqR0qZhKMTLzQH78stFGobCApMDBl27dtUw\nFCHk6vqV7QEGAndgekSOBW4BLnDeGw08CJwAfOusW4dJ3vdSACZSYRSASRCNA2ZPdfXJjBjRj6OO\nOiqt/Vq3bk3btm3zVKriVCwBWC4oABOpMArAJIgCMHuaNv0TTZs+kdY+sdh6Nt+8isWLv85TqYqT\n5oIUERGRnFi79ibWrr0pzb3qaNLE36glYSkAExERqzQOmF1uDlhNjYYCKaRiaALIqgmypqZGPSJF\nSoyaICWImiBLTR1t/n979x+jRXHHcfwN3IEFAhdNcxWwuUbbRGKCiqX0asOlSS0aCk1NmtiaEJum\npjFFQ3MgpA3HHxI0/kox2sRGQ3+piTWNFmlaUo42aWpKFShUroKSCo3UAnqUQrzznv4x+/AsD7vP\n7T6zu7Oz93klT+7ZvWfvO7M3M888s7PzdC3i1KljrhNSqLJ8F6Rz+uQkIiIivvG+AyYiIiLiG80B\nExGRTNVqNfbt28fIyEii12/btg2AkyffzTNZEkNzwNwowxwMqzlg9eeaCybiD80Bq7ahoSGuuWYB\nM2ak+4LnsTE4ffohYEk+CSuE5oBVndYBa/F7ESk3dcCq7cCBA/T2fo3h4QOuk+KAOmBVp0n4IiIi\nIp5SB0xERJwaGNh4fh6SFE/n340yXALI/BKk5oOJlJsuQVabLkGCLkFWly5BtqC1wURERKTMKtkB\nq9MomIiIiJRRpTtg4ZEwdcZERMpJc5Dc0vl3owxzMDKfA9Zqn+aHibinOWDVpjlgoDlg1aU5YG3S\nqJiIiIi4ZtsBWwocBN4A1sa85ofB7/cC11nGy1S9M6aOmIiIiBTJpgM2BXgM0wmbD9wGXN30mluA\nq4BPAt8GnrCIlxvdNSki4o7mILml8++GzZdxLwIOAUeC7WeBFcDrodcsB7YGz18BuoBu4LhF3Fxp\njpiISLH0JdBu6fy7YTMCNhd4O7R9NNg33mvmWcTMXdRlyfrzuI5Z1O9t9k1kOg/xVL5ERATgVuDJ\n0PbtwJam17wEfC60vQO4vuk1tbr686T72jkmq30bNmwo5G/7rp6XcJ5a7Ys6D0Wdj7RpjdqXdVrC\nz/MoX0nzkvX/gmrdIpbJOamS/fv312bNml+D2gR8EDxcp6OIx9FaV9cc18WtcGTUftncRrkYGMDM\nAQNYB4wB94de8yNgEHN5EsyE/SVceAmyBhtCm33BQ0SqYzB41G0ELUNRWWmXoajPP6rGpTD/lqFo\n//xrGQpXOoDDQA8wFdhD9CT8l4Pni4E/R/wd151ZL7QzEpN0JKP+Pwj/L6L2FT0ilVZZ0xXHt/TG\naXc0ONvmyKliTrRHNAKmEbAqoyTt183AEGYy/rpg353Bo+6x4Pd7ufjyI6jxci5p505kPEnLEiVp\nwDJS3An2hDpg6oBVGRm1X2W4BBDkR0QmijIM4WdIbVgTrYQP1fqMEUeXIG3YLEMhIiJirVpzwPxj\nc/7PnHmPlSu/k/q4Vau+xcKFC1MfVyVl+ASqT48iE4xGwKpNI2AwMUbAxjBLfZ5LddTkyS+wefNN\n9Pf355KqvGkETEREcvfgg1vYvn1nqmPOnBnmww+r0r+WeJOBO9IfNfnN7JPiIXXAREQk1nPPvcju\n3b3AgpRHfjyP5IhUhjpgIiKtLQUexXz/7Y+5cK3DCeJG4Iu5/XXNAXNL598Nm68ikiaDg4Ouk5AZ\n5aV8qpIPz0zBLKWzFJgP3MbF6x06475MZBN/YGBDm2/+2cRvn8v42cVu7/xnF78d7su+PY2AZWhw\ncJC+vj7XyciE8lI+VcmHZxZh1jE8Emw/C6wAXneVoLA0ZaJWq3HixAnGxsZSxRgd/aBVCnD7zSUT\nOb7L2Pbxt2//DadOvZ/qmK6uLvr7v8ekSZMq0R6qAyYiEm8u8HZo+yjwGUdpOW90dJSRkRFGRkY4\ne/ZsomN27drFsmXL6ezsShWrVpsMfLSNVIpEGx39Ojt3zmZnuns7gDWsXn0PHR3V6LpUIxciIvko\n5VoC3d2Xc/LkfwDYtGlTqmNnzEjff5w27QeR+8+dG+KSS/6a+u81W736BgAefnh3quOyit+uqPjD\nw+bnrFlfLjx2u9o5/y7O/fBwjc7OzvPbGzduTHTcffdtZv36tXklq21luE94D+lvrxERv+0FrnWd\niAQWAwOYOWBgvnJtjAsn4h8Criw2WSLi0GHgKteJEBGpsg5MY9sDTMV8YCzNJHwRERGRqroZGMKM\ndK1znBYRERERERHx0VLgIPAGUL4ZcvGuAHYCB4D9wKpg/6XA74B/AL8F0t1u5NYU4DXgpWDb17x0\nAc9jlgn4O+aONV/zsg5Txv4G/AKYhh95eQo4jkl3Xat0r8O0AQeBmwpKYxJJ26dPA6PAV4PtuPah\nqPh1zXW6yPjN9XBxzrFvDe2LqjdpjRe/D3gfc35fA77fRtrziJ9F2bPJO+Rf7lrFty13tvGzKHuF\nmIIZ0u8BOvFrbsXHaEwgnom5PHE18ACwJti/FthcfNLathr4OfBisO1rXrYC3wyedwCz8TMvPcCb\nNCrwc8BK/MjL54HruLADFpfu+Zi634nJ8yHKsUB00vZpCvB74Nc0OgFx7UNR8eua63SR8aPqYRGx\ne4iuN2kkid9H9HnN4n3NJr5t2bOJXZd3uWsV36bc2cbvIWXZc9nQhRc4HKGxwKEP3sH8YwD+i+lt\nzwWWYwoAwc+vFJ+0tswDbsF8zUr9zlgf8zIb8+b/VLA9ivmk4mNehjH1YjqmIZkO/As/8vJH4FTT\nvrh0rwCeweT1CKZNWJR/EseVtH36LuYT97uhfVHtw5wC40N0nS4qflw9LCJ2VL05liJ2mvhR5zWL\n9zWb+LZlzyY2FFfuov62bbmzjZ+67LnsgEUtcDjXUVps9GA+7b8CdGMuvRD87HaUprQeAfoxt9fX\n+ZiXT2Aa46eBV4EngRn4mZeTwEPAPzEdr/cwl/B8zAvEp3sOpu7XlaUdSNI+zcU0zk8E21FrhvXQ\naB+KjB9Vp4uKH1UPpxcUO6re7EgRO2n8GtCLWU7lZcxIbtJj84wf1kP6smcbu4hyFxffttzZxk9d\n9lx2wEq5wGFKM4FfAncDp5t+V8OPPC4D/o25lh33icWXvHQA1wOPBz/PAPc2vcaXvFwJ3INpROdg\nytrtTa/xJS/Nxkt3GfKUJA2PYspXDVN3muvPTMwIzd2Y0Yii4iep03nGT1IP84odVW++kSJ20viv\nYuZbLQC2AL9KGSPv+O2WPZvYRZW7uPi25c42fuqy57IDdgyTiboruPCTcNl1YjpfP6XxDziOuQYP\ncDmmMJZdL+by0FuYS0FfwOTJx7wcDR5/Cbafx1TEd/AvLzcAfwJOYIbSXwA+i595gfjy1NwOzCP9\nJaM8JGmfFmIuUbyFmYP0OKYuQaN9+BntvTm3G38F0XX6JwXFX44ZQYiqh3nHXhHsb643vSliJ41/\nGvhf8Hw75v99afA62/c1m/hgV/bajX0ZxZW7VufeptzZxL+M6DY7bdkrjM8LHE7CFKxHmvY/QOOu\niXsp5wTpVpbQuHPF17z8AfhU8HwAkw8f87IAcxfTRzDlbStwF/7kpYeLJ+FHpbs+CX8q5hLCYcrx\nDR1p26enadwFGNc+FBU/LFyni4zfXA/vbz4gp9hx9SaNJPG7aZTTRTS+rD2L9zWb+LZlzyZ2WJ7l\nrlV8m3JnG/9a7MteoXxd4PBGzDXuPTRuRV2K6YXvoNxLBLSyhMbdHb7mZQHmE9BezCeQ2fiblzU0\nbmneSuOTXtnz8gxmDsQHmNGQO2id7vWYNuAg8KVCU9paVPt0Z/BoFu4ExLUPRcUPC9fpIuNH1cOi\nYkfVm7TGi38X5s12D2bUY/E4xxYVP4uyZ5P3ujzLXav4tuXONn4WZU9ERERERERERERERERERERE\nRERERERERERERERERERERERERERERERERKQ6/g8hMWRwSW1sDQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cd71f10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ERCQnjaMVbTo/8RLE3JoiIhJzSjSPNp2feFHNmYiIiEiEKDgTERERiRAFZyIi\nkpNymqJN5ydelHMmIiI5Kacp2nR+4kU1ZyIiIiIRouBMREREJEIUnImISE7KaYo2nZ94Uc6ZiDQ2\ni4EfgA3AemBfYEvgYWAn6/kTge+t7YcAZ1nbXwhMsdZ3B+4FWgDPAxc1QNlLRjlN0abzEy+qOROR\nxiYJVAJ7YwIzgMHAi8DuwMvWY4BOwEnWfV/gTlITGo8EBgAdrFvf8IsuIo2BgjMRaYwSrsfHAOOs\n5XHAsdZyP2ACpoZtMbAQ6AVsB7QGplvb3efYR0SkKArORKSxSQIvATOAc6x12wDLreXl1mOA7YGl\njn2XAjt4rK+x1seWcpqiTecnXpRzJiKNzYHAF8DWmKbMj1zPJ62bOCinKdp0fuJFwZmINDZfWPcr\ngCcxeWfLgW2BLzFNll9Z29QA7Rz7tsXUmNVYy871NV4vVlVVtXG5srKSysrKIosvIlFSXV1NdXV1\noMd0511EUVI/YkUam8TGfwK2KVABrAI2w/S8HAYcCnwDDMd0Bmhj3XcCHsQEcDtgmkPbY76UpmF6\nb04HngNGAC+4Xi+ZTOr7KwxTp07lqKMGs3Ll1CKOYv+J+TtHrVt3ZNq0J+jYsWMRrylxl0gU//2l\nmjMRaUy2wdSWgfn+ewAToM0AHsH0vlyMGUoDYK61fi5QCwwkdSUfiBlKoyVmKA13YBYrdj6Tms+i\nSecnXlRzJiIRFFrNWUNTzVlIVHMmURVEzZl6a4qIiIhEiIIzERERkQhRcCYiIjlpHK1o0/mJF3UI\nEBGRnJRoHm06P/GimjMRERGRCFFwJiIiIhIhCs5ERCQn5TRFm85PvCjnTEREclJOU7Tp/MSLas6A\n++9PLXfvXrpyiIiIiAQRnPUFPgIWAJdn2GaE9fwcYO889w3dFluklpuqLlFERERKqNjgrAK4HRNk\ndQL6A+55LY7ETBTcATgXGJnHvpLFGWeUugS57blnqUsgIkFQTlO06fzES7H1RPsCCzETBQM8BPQD\n5jm2OQYYZy1PA9oA2wK7+Ni3QURlmrRtt4Uvv/S//S9+EV5ZgtKmTalLICJBUE5TtOn8xEuxNWc7\nAEscj5da6/xss72PfRtE+/Zw8slmuVRzFB99NEzNc/7erl3DKUu+5cgmEYepq0VEgNralvTseRCb\nb75NXrctttiGl19+udTFlzJSbM2Z31Am8pfoUgVlTrvtlt/2++wTTjkOPDCc45aTtm1h6dJSl0JE\nomTNmje4IjSkAAAgAElEQVSAH/Peb7PNBvLFF18EXyCJrWKDsxqgneNxO0wNWLZt2lrbNPOxLwCn\nn17FfffZjyqtW7wUUsNUDrVS5VBGL4cfDmPHlroUpTd6NJxzTkO8UrV1k6iy85kad/PZZtYtP4lE\ny+CL4qLzEy/FBmczMIn+OwPLgJMwif1OzwCDMDll+wHfA8uBb3zsC8Bf/uIMzsK16ab57zNnTvFN\njIX0Eg0z8PnPf+CSS8I7ftS0aQPff596HHZQma1m7uyzYcyYcF/fr5bhX1Msldg/un75S/jmGyU2\nR40u+tGm8xMvxeac1WICr8nAXOBhTEL/edYN4HngE0zy/yhgYI59S2r33fPfJ9/mSKdp0+CGG2Dw\nYPO4WbP8j7HJJtmf99PhYfjw9McHH5x/OcrZZq4fw2EHZ+3bZ37uuuvCfe2oe/vtUpdARKS0ghjV\na5J1cxrlejwoj31Lws45KyT3rNgL+aWXFrZfEyu0Hj7c1LR88IH3du7yDRwId96Z/dg9ehRWprho\nEuLwzMkkTJwI1dXZXzvf3rtxEeZnLyJSDsria7AhkvWPO87/toV0umnVynt9Me/NDrp69apf8+W1\nnc3P8BZB1RzlOs7OO3uvv+iiYF7fyasshx7qf9sg7bGHuc9WU9u5c/7HDauTSKFatMh/n3LNU4w7\njaMVbTo/8VIWwVm+7Caqjz7yv8+JJ5p7PxeG3r3TH/vZp5Bctlycr1tXV9h+xbI/t0J98kn9JkWA\nbbYp7rhevGpkKivNvR0k22kbYQcIO+6Y+Tn783joofyPG3S5/fx46NYt83Nr1+b/mgrOomno0KHK\na4ownZ94KYvgzL5A/Pyzv+132cXc27UTmey3X/11zpyvUgzyms+FyW9w5j7m3nt7bwfw61/7f/1C\ntndLJKJxMbbL0L9/+uNSaNHC/M03b57/vs5y2z+i7XxGm58k/w4d8n/tXOXxa/PNg3ltEZFyVRbB\nmc3vF/3VV8P11+feLlM+z69+Ze7feSf3Mf78Z39lSiTg8cfrr3fXTPipqdh/f3NvdwRIJOB3v8u8\n/W9/m1o+8UTvJlz7db0C1mL4yR/yOq9e6666KvgLt3287bYz9/bnEIWAMZN99838nPPvPlPgvP32\nuV8jW22YWyIBI0Z4PzdggP/j2D8attzS/z4iInFUFsFZvhfKPn3q1xY42bk8ixd7v1b37mbZTy/M\nZBIqKnJvl0jA//2fWZ4yJff2XuzhOtq1Sx3Tvm/ZMvN7vumm1PJpp3lv4xUU2kNLZMvHy+fcZBpu\nxG/e3R/+kPmYhc7h+ec/wxtvwLhx+ZUlKNmCl0yf7VZbea/fbbf0HDp7/1NOSd9u221zlyvfpPwL\nLvBef9ddpjeyH1EYCFoyU05TtOn8xEtZBGfu2oy//tXf9l769YP33su+f76/3AtpfsplyZL66954\nAxYtqr/e/lyuvRaqqjI/7152XqS9aoy22KL+ukzHvuoq89lm88AD3uvtZmiv49quvrp+svuHH6aa\nITP1fMx2TDDjyx10EHTqBN98E36A4A6gL7ss/2NkKmOm9e4aNHtMvZ494Te/8d6nSxd45ZXiygPR\nabaW4imnKdp0fuKlLIKzfPzjH2YQy4bid2Jv9wXK7iDgvrDZ27VtW/8YrVvDrrumHtvNU/Y+TZqY\nnpu5XttLPh0KIL2X4eLF5nP3ymXz89p2M7IzKHY2xYI5vlunTvVrLXfaKffrZeJ8/SA6cHiNL2fX\nbDk/l5df9lf76uRnPLzevb2Dddv06fV7yzp7iB5yiL9g1X2O3TXDqhETEclPWQRnmQIYrwvo1VcX\n/0vdz6Cttkw/VLyCK6cdApji3b5AO99v377m87KH7kgm/c0+UOgFNJEwAVEi4X0MZ9lyvYaz2bOQ\n3LfBg03tYSZ+/i6CzDnzCpTt2sjmzVODrfbuDbW19bfNVgY/52uLLer/fbZo4a8mNB/ufey0AD/H\nc86EcO21/ptARUTirCyCM5szxwq8c8bcsl3E7BwwtyFDYM2a7Me98UZzb4/j5Jz6x4v7IvXWW97r\ngxoEN9dFcepUeOGF1ONCxtRyv06u4CwM9vE339wkw7vzq/ItS6bgLFsOY65jgamV++qr9MF9vYI3\nP7zeR7Nm2WsNB1nDQHfp4u81nAGWk7tGM1N5/HLOlHDkkYUPyCzhU05TtOn8xEtZBGfupkO7Jmjr\nrdPXZ0qUdnJeSDI1DTVpknnwzB9+MPfuWju7RiSTUY45E37xC9P0+sor2XveOTmDgwsvTD1+6qn8\netbZ43odeGCqpqqy0vuia+vYMT1vyTlGl/PzPOAAc////p/38/kGngMHZn7ODp7tGkL38BBetap+\nhv3Ip+bs8sv9HQtMJxX332u+Zs7M/NyXX8Izz2R+3u/QGPb7tmsuDzooPS/N+Rm634/9Y8f5vhMJ\nc4y2bc16d+cS5aOVD+U0RZvOT7yURXDWsSN8913qi/yKK+D1181ybW0qyFqxIvtx9tsPjjkm9dir\nR5p7bDR7aILRo01tU+vW5vE555gJz3Pp0sW85lFHmcfffJOqPTnkkPplyHSxcuZ4HXhgqlz9+nm/\nD/dxVq0y48R5DfiaqUkSzCCiVVUwYwY895xZ99ln3q9z+OHmOHatYi59+mR/PtuF2w6eBwyAuXPT\nn6uoME2F7qD19NP9lSvXa9vOP99/02MxzYUPPmjus43+v+WWmWehcJclG/d2u+wCr71m1tfWpnfG\nSSTg3/9ONSV7DRUDZugXu4PLuHGmBhFg5MjUNvfe6698IiKNQVkEZ5Bee7b55qmJufNJpH7rLTjz\nzNRjd1Czbh385S/p6wYPNkHf2WeboMjWrFn9JqIrrqj/mu++C08+mXqcb0/Q0aPNfb61Tg8/DI8+\nmnrcqlX2JHI76HTbZBPzOW2ySf69Utu0SR8qwh2gHHRQfsfz0rRp/RzBr7+GRx5JPe7c2QSmF16Y\n+3gdOsDf/pYK0j/+OPWcez7SXJ0PCgnO7GFSnA48sH4t4tFH+zueLVPt6uGHe9eqef29VVTUX3/J\nJeYYfm22WarGzdmT84wz/B9DRCTuyiY4C4M7sGve3Psi6qe5FEwNgrs3XkVF4RM5J5MmKCxE375w\n/PH+tk0kUk3FfpPF/QSLw4enJ/nnGnC3kAF5vbRpY5o5jzrKNBu/954JTP0ESC1amHHhTj/dBOvO\nwOX88+tvn62MhZTfa+DjHXeEO+4wy5Mnm+UnnkjlrPlpLs3UbP3HP5ohSWy5PiPntFpe23btagL9\nQw7JXSYwzaR9+/rbVkpLOU3RpvMTLz768UVHpgtHoRfxfIcvKKUwhyMoJu8niJ5/Yb23a64xt0Ik\nEplrCr/91tQA5Xp/+dac/fOf6T8ENtmkfgeHww7zPr5fv/iFyQl0zg/brJlpsvdTk7n55uZ1M41f\nNnu2uT/hBHj1VX/lmTTJX9mltJTPFG06P/FSVsGZzb44FGPKFNPUN3FiMGWyde0KL71U+P6TJ8P6\n9cGVJ0jF9sa054v8+We45Zb6vWUz9VxduDC/cobB+d5bt85/eBI/n9OVV6Y/btIExo/3Vz4/Fi82\nHVfatEmfSQBSTfZ2OXMFfhMnZu8Ek23+VhERya7sgrPXXy+smdA9NIA9F6WdnByUG26A//wnNe9l\nvuzelA3JviCfeCKcfHJh+/p9zr7oX3RR5udsnTqZez/TaOXrppvg4osL27eQGsEweiVmmmf0nntS\nA/s6FTNAr9vvf5/9+aAmThcRaYzKLufM7giQL69eimFo0gQWLCh8rsdMGmKU9Ycf9p8r5GfIiWIv\n0Oedl3k+zmKdcEJwx3J/BuedZ+6HDIFbbzW9LI88MrjXsz30kPf6P/0pnNeTxk05TdGm8xMvZVdz\nVg6cA2vGST4Bor2tM9k83wCzWbNUDlNQevf2P2dkJu5gzD0UyZVXmhrQLl3MzU8v0ULY05RFcayw\nDRtKXQIJmnKaok3nJ14UnJWJcuwQAPUHh/V6H6ecYmo2C20KzsfDD8OyZcF+nomEGcvrvfdMD9F2\n7fJvHo6S/v0zD63il4IzEZHCxSI4y3Whfeyx9EFcJV2Ywdmuu5pBa3fayfTM83LWWea2apU5V9lM\nnAg//VRYWcH0htxqq9SgqIXwqjn73/8KP14xrr46fXiLYiUSqUFvi+EOyr0UO2OCiEhcxSI4y8U9\nZUw5aoics3zkU54ddzSjy1dUmMFQMwVXrVubQGP58szHKjTn0C1ToFiIUjYr/uMfpXvtbNq0yd7r\n+Ouv8x+QWUrLzmdS81k06fzESyyCs6gFLuWmmPHI/O5rjyn3xhvROF+tWgVTjpYts0+b1JhlG27E\nzpcroQpgBrAUOBrYEngY2AlYDJwIfG9tOwQ4C9gAXAhMsdZ3B+4FWgDPAx59kONDF/1o0/mJl7Lr\nrVkurrkmfbLzYpVrzplbixbZm7yimNzu5izj/Pkwa1bpyiIFuwiYC9j/swYDLwK7Ay9bjwE6ASdZ\n932BOwH7L2AkMADoYN0014GIBCIWNWdR1K1b5vkM4yAKtV9R4DUXpkReW+BI4FrAHu3uGMCe5Goc\nUI0J0PoBE4D1mBq1hUAv4DOgNTDd2uc+4FjghbALHzcbNmxg2bJlee+3PFv+g0iZi0VwduyxZtR5\nKUxDNGv6dcstwQ8MHAR7Voq4B6XlUHMZgJuBSwHnML7bAPbVfrn1GGB74G3HdkuBHTDB2lLH+hpr\nfWyFldM0duxYBg26mObN808Eras7PNCylDPlnMVLLIKzxx8vdQnCF5dmzVxOOinY44m4HAV8BcwC\nKjNskyTV3Fm0qqqqjcuVlZVUlmIakACEddFfu3YtTZqcxerVI0I5fmOhoKx0qqurqa6uDvSYsQjO\npHAnnwx/+EPh+zeSmpZGoVev9InVY+oATBPmkZhE/s2B+zG1ZdsCXwLbYQI4MDVizsbrtpgasxpr\n2bm+xusFncGZiMSP+0dXEDM1qENAmQir5mzCBDOnZr6OOcbc+5kAXMrD229Hd2iOAF2BCbZ2AU4G\nXgFOA54BzrC2OQN4ylp+xtquubVPB0ye2ZfAD5j8s4R1DHsfEZGi6NIqvjknIL/5ZlPj1qtX6coj\nEgD7Z8+/gEcwvS8XY4bSANOj8xHrvhYY6NhnIGYojZaYoTRi3RlAOU3RpvMTL8UEZ9nGBXLqC9yC\nGVdoDDDcWl8FnA2ssB4PIeZfbsXYccdSl8DMGeqswfvNb0pXFpEAvGbdAL4FDs2w3XXWzW0m0DmE\nckWSLvrRpvMTL8U0a2YaF8ipArgdE6B1AvoDHa3nksBNwN7WrawDs6CTAZ3WroXf/z6444VZ1iCp\nnMEql3KKiDR2xQRnx2DGA8K6P9Zjm30x4wItxnQ9fwgzbpAtNunkYV74gp4QvFwu0ipnsMqlnCIi\njV0xwVmmcYGcdgCcU0zbYwTZLgDmAGOBNkWURSRUcR5QWMSPYcOGBdILTcKh8xMvuXLOXsR0L3e7\n0vU407hA2foYjgTsvmHXAP/BJOOKRErcB56Ngfswo/hPKnVB4kw5TdGm8xMvxTQrfoQZxNEeF+hV\nYE/XNvthEv/tOeeGAHWkOgXYdgaexTu5diGwm8d6EYmvRUB7n9tugpn/8vfA/zAdj1aHVK58JZOK\n7rMaMWIEl122kHXrSjEIrX0JDPcctWp1KiNH9uXUU08N9XUkGhJmANCi0raK6a1pjws0nPRxgZxm\nYMYF2hlYhvkC7W89tx3whbX8B+D9DK/j9wtaRBqnXwK7AisxKRb/xXzXiIiUpWKCs0zjAm0PjMb8\niq0FBgGTMT03xwLzrO2GA90wP1k+Bc4roiwi0nhdAtyJqW2D9DxXCYjG0Yo2nZ94KSY4yzQu0DJM\nYGabhHcuyOlFvLaIiK2aVGD2e+C50hUlvnTRjzadn3iJ8vRNfTF5bQuAy0tUhsXAe5hJkqdb67bE\ndJT4GJhCei/TIZjyfgQ4Zynsjmm2XQDcGlDZ/otpwnE2BwdZtk0wgwwvAN7GDDYcVDmrMD13Z1m3\nIyJQznaYvMkPgQ+AC631UftMM5Wzimh9pi2AacBszOj611vrw/g873OU8+ACyioiIj5UYDoC7Aw0\nw3zBd8y2Q0g+xVxMnG4ALrOWL8c074IZZHc2prw7Y8pvJwROx4z5BmaaF7uDRDEOxgze6wx6gizb\nQExTEZj8nYcCLOdQ4GKPbUtZzm0xzewArYD5mL+5qH2mmcoZxc90U+u+KSZ4OohwPs9xmB7frwD3\nFFjWsCQlu1tvvTW5ySYXJE2/6Ia+2SMNhPs6rVqdkrz//vtL/VFLAyGAHiZRrTnLNXhtQ3L3uMg0\n+G4/THf+9ZhyL8RMirwd0JpUzdt9eA/Ym683gO9CLJvzWI8DfQIsJ3j3ZCllOb/EBAcAP2JyI3cg\nep9ppnJC9D7Tn6z75pgfXN8Rzud5IeZz6Qn8tcCySg4aRyvadH7iJaoTn3sNXluKKbaTwEvABmAU\npqNDpsF3t8fUDtjsAXfXW8u2GtIH4g1SkGVznoNaTE+4LTG5hkG4AJN3OAOT0P19hMq5M6a2bxrR\n/kztcr4NHEj0PtMmwLuYoXBGYppiw/g8d8QEcD9jppEbkmc5xQflNEWbzk+8RLXmLCoDAx2Iufgd\nAfyF+vksgVRfhiTKZRsJ7IJpnvsCMwBxVLTC1BZdBKxyPRelz7QV8BimnD8Szc+0DlOetsBvgENc\nzwf1eV4MTMR8Dk8GcDwRkZKKanBWg0l8trUj/ddzQ7HHYVuB+dLfF/Nr3541YTvgK2vZXea2mDLX\nWMvO9TUhlTeIsi117LOjtdwU2ILgas2+InVhHkMqn6jU5WyGCczuJzVuXxQ/U7uc4x3ljOpnCqbm\n7TlMYn8Yn+cHmE4Em5Jq/hQRKVtRDc6cg9c2xyQlP9PAZdgU01QCsBmm99j7pAbfhfTBd58BTsaU\ndxdM+adjcmF+wDTLJoDT8B6wNwhBlO1pj2MdD7wcYDm3cyw7ByAuZTkTmHH45gK3ONZH7TPNVM6o\nfaZbkeqJ2RL4HaYXaRif5yGYJug1wKMFlFV8UE5TtOn8SEM5AtMTbSGlySHZBZN4PRvzy9wuw5aY\nPDSvoQCuwJT3I+Bwx3p7KICFQFBzlEzAjCn3Mybv5syAy7YJZpBheziFnQMq51mYpO73MJPeP0Uq\n76iU5TwI0ww3m9RwFH2J3mfqVc4jiN5n2hmTbzbbKtel1vowPs+F1vM7k17LFgWl7jgWeeqtKXFD\nAOkaRc39JCISAaMxwf9fMENrDCxtcdJY39WSiebWlLgp9dyaIiJR8COp4VrWlLIgIiJBiGrOmYiI\nX18DB2B6qNaVuCyxpZymaNP5iRfVnIlIubsW2BPzY3NuicsSWxpHK9p0fuJFwZmIlLsJ1n1L6z6I\nGThEREpGwZmIlLv+1n0C+FspCyIiEgQFZyJS7vbCdLdrZi1LCOx8JjWfRZPOT7woOBORcne8db+O\n4MYRFBdd9KNN5ydeFJyJSLmb4Vhua92eK1FZRESKpuBMRMrd2cCbmKbNgwhvejQRkQah4ExEyt1H\nwL+t5a2BcSUsS2wppynadH7iRcGZiMTBWEzN2fJSFySudNGPNp2feFFwJiLl7kpMntn3mE4BIiJl\nTdM3iUi5uwUYCvwA3FbisoiIFE3BmYiUuzrgM2v5+1IWJM40d2O06fzEi5o1RaTcrQM6ARcAvyhx\nWWJLOU3RpvMTLwrORKScJYDHgK2s5TtLWxwRkeIpOBORcpYEDgFuKHVBRESCouBMRMpZP+t2OPCt\nte6E0hUnvjSOVrTp/MRL5IOzrl27JufMmVPqYohIw5oDdPOxXV/gQGAk8OdQS9TI6aIfbTo/8RL5\n3ppz5swhmUzG4jZ06NCSl0HvQ++lHG5AV59fETsCv7fuj7RuIpFSW9uMCy+8nHbt9sr7dtddo0td\nfCmByNeciYhk8SimM8AjmKmbRCJn7dpbWLt2Kd99l++e43jvvblhFEkiTsGZiJSze0tdgMZCOU3F\n2MK65Ws74HNfW+r8xIuCswZUWVlZ6iIEIi7vA/ReGqEWwGvAJkBz4GlgCLAl8DCwE7AYOJHUgLZD\ngLOADcCFwBRrfXdMcNgCeB64qAHKXzK66Eebzk+8RD7nLE7icvGMy/sAvZdGaC1m6I1uQBdr+SBg\nMPAisDvwsvUYzOC2J1n3fTHjqCWs50YCA4AO1q1vg7wDEYk9BWci0tj8ZN03ByqA74BjgHHW+nHA\nsdZyP2ACsB5To7YQ6IVpb2oNTLe2u8+xj4hIUcIMzv4LLAfez7LNCGABptv83iGWRUTE1gSYjfl+\nehX4ENjGeox1v421vD2w1LHvUmAHj/U11vrY0tyN0abzEy9h5pzdA9yG+UXp5UigPaY5oBemiWC/\nEMsjIgJmovRumAztyZimTaekdQtEVVXVxuXKysqybX5WTlO06fyUTnV1NdXV1YEeM8zg7A1g5yzP\nO5sRpgFtSP/1KiISppXAc5jE/uXAtsCXmCbLr6xtaoB2jn3aYmrMaqxl5/oarxdxBmciEj/uH11B\n1GCWMudsB2CJ4/FS0r/sRESCthXmhyBAS+B3wCzgGeAMa/0ZwFPW8jPAyZj8tF0wNf3TMUHcD5ha\n/wRwmmMfEZGilHoojYTrcWBNCSIiHrbD1Ng3sW73Y3pnzsIMZDuA1FAaAHOt9XOBWmAgqe+pgZih\nNFpihtJ4oQHKXzIaRyvadH7ipZTBmVdzQc5mgXLO2RARb2HkbGTwPrCPx/pvgUMz7HOddXObCXQO\nqFyRp4t+tOn8xEspg7NngEHAQ5iOAN+TId9MORsi8RZGzoaISLkKMzibAPwWk+OxBBgKNLOeG4Vp\nBjgSM27QauDMEMsiIiIiUhbCDM76+9hmUIivLyIiAVFOU7Tp/MRLrGYImDhx4sY/0PPPPx+A2bNn\n06tXLy699FLmzJmzcVlERPwbOnSoLvwRpvMTL6XurRmau+66C4BJkyYxZMgQjj32WK6//vqNy0FL\nJpMkEqbzaV1dHU2axCruFRERkQZS9sHZypUrOemkk0gkErRp04aOHTsC0KNHD+6//35GjRrF5ptv\nzpIlS7j77rtp3bo1K1as4Jxzztl4jFNOOYWamho2bNjAgw8+SLt27Xj++ee55ppraNGiBWeffTb9\n+/fn9NNPZ+nSpbRq1Yrx48fz/fffc/rpp7P99tvTrVs3Jk+ezL777susWbOYMmVKqT4SERERKWNl\nH5yNHj2a448/nrPPPpshQ4ZsXJ9IJOjYsSNnnnkmPXv25Mgjj+Tbb7/duOw0ZswYWrZsyVNPPcWo\nUaO45ppruOKKK5g6dSqtWrUimUzy+OOPs+OOOzJ+/HjGjx/Pbbfdxumnn86yZct45ZVXaNq0KZMn\nT6Zv374MHz68oT8GEZFQKacp2nR+4qXsg7NFixZx7rnnAtCzZ0/ef7/+POvJZNJzGUwT5KWXXsr7\n77/PmjVr6Ny5MytWrKBdu3a0atUKMIHeokWL6NGjB2Bq5eyasa5du9K0aepj7NmzZ7BvUEQkAnTR\njzadn3gp+8So9u3b8+677wLwzjvv5L3/rFmzWLlyJa+99hqXX345dXV1bL311ixdupTVq1cDJqBr\n374906dP3/g6u+++O0C93DLlmomIiEgxyr7m7Oyzz+bEE0/kkUceYbvttmPXXXcF2Jicn20ZoGPH\njnz22Wccdthh7LnnniQSCRKJBNdeey19+vRh0003ZcCAAZx88sk88cQT/Pa3v6V169aMHz+elStX\n1jueiIiISDHKIbJIupsiRSTerB895fD9lEtsvr/CymkaMWIEl122kHXrRgR6XH/sP7GonqOb+fOf\nP+fOO2/OuaVyzqIjiO+vsq85ExGR8OmiH206P/GiBCkRERGRCFFwJiIiIhIhCs5ERCSnYcOGbcxr\nkujR+YkX5ZyJiEhOymmKNp2feFHNmYiIiEiEKDgTERERiRAFZyIikpNymqJN5ydelHMmIiI55cpp\nuuqqa7jjjlF5H3fdulVs2HBeocUSi3LO4iXM4KwvcAtQAYwBhrue3woYD2xrlePfwL0hlkdEREIy\nb95Cvv/+EuCEAvb+VdDFESlrYQVnFcDtwKFADfAO8Awwz7HNIGAWMAQTqM3HBGu1IZVJRERCtSXQ\nttSFECl7YeWc7QssBBYD64GHgH6ubb4ANreWNwe+QYGZiEgkKacp2nR+4iWsmrMdgCWOx0uBXq5t\nRgOvAMuA1sCJIZVFRESKpJymaNP5iZewas6SPra5ApgNbA90A+7ABGkiIiIijVZYNWc1QDvH43aY\n2jOnA4BrreVFwKfAHsAM98Gqqqo2LldWVlJZWRlcSUWk5Kqrq6muri51MUREIiGs4GwG0AHYGdNs\neRLQ37XNR5gOA28C22ACs0+8DuYMzkQkftw/upQ7Ez32OVHzWTTp/MRLWMFZLaY35mRMz82xmJ6a\n9mA2o4DrgHuAOZjm1cuAb0Mqj4iIFEEX/WjT+YmXMMc5m2TdnJwjFH4NHB3i64uIiIiUHU3fJCIi\nIhIhCs5ERCQnjaMVbTo/8aK5NUVEJCflNEWbzk+8qOZMREREJELKKjjTkBoiIiISd2UVnKk9XUSk\nNJTTFG06P/GinDMREclJOU3RpvMTL2VVcyYiIiISdwrORERERCJEwZmINCbtgFeBD4EPgAut9VsC\nLwIfA1OANo59hgALMPMBH+ZY3x1433ru1lBLHQHKaYo2nZ94Uc6ZiDQm64G/AbOBVsBMTFB2pnV/\nA3A5MNi6dQJOsu53AF4COgBJYCQwAJgOPA/0BV5ouLfSsJTTFG06P/GimjMRaUy+xARmAD8C8zBB\n1zHAOGv9OOBYa7kfMAET1C0GFgK9gO2A1pjADOA+xz4iIkVRcCYijdXOwN7ANGAbYLm1frn1GGB7\nYKljn6WYYM69vsZaLyJSNAVnItIYtQIeBy4CVrmeS1o3cVBOU7Tp/MSLcs5EpLFphgnM7geestYt\nBzzvjgYAABLRSURBVLbFNHtuB3xlra/BdCKwtcXUmNVYy871NV4v5pzZpLKyksrKyiKLXxrKaYo2\nnZ/Sqa6uprq6OtBjKjgTkcYkAYwF5gK3ONY/A5wBDLfun3KsfxC4CdNs2QGTZ5YEfsDkn00HTgNG\neL2gpp0TiTf3j64gajDDbNbsi+l6vgDT+8lLJTAL06W9OsSyiIgAHAicChyC+e6Zhfmu+hfwO8xQ\nGr2tx2CCuEes+0nAQFJNngOBMZjvuIXEuKemiDSssGrOKoDbgUMxVf3vYH6BznNs0wa4Azgc00yw\nVUhlERGxTSXzj9JDM6y/zrq5zQQ6B1GocmDXBqj5LJp0fuIlrOBsX8wvycXW44cwXdKdwdkfMXkf\ndo+nr0Mqi4iIFEkX/WjT+YmXsJo1dwCWOB7b3c+dOmBG5X4VmIHJ2RARERFp1MKqOfPTDb0ZsA/Q\nB9gUeAt4G5O/ISIiItIohRWcubuftyN9wEYwNWtfA2us2+tAVzyCM2dvp+rq6rLtii4i3sLoii7B\nUk5TtOn8xEsipOM2BeZjasWWYbqa9yc952xPTKeBw4FNMKN0n4TpFeWUTCZNRVwikcBeFpH4SiQS\nEN73U0NKNpbvrOOOO4MnnuiNGYmkXNh/YlE9Rzfz5z9/zp133lzqgkgegvj+CqvmrBYYBEzG9Nwc\niwnMzrOeH4UZZuMF4D2gDhhN/cBMREREpFEJcxDaSdbNaZTr8b+tm4iIiIiguTVFRMQHzd0YbTo/\n8aLpm0REJCclmkebzk+8qOZMREREJEIUnImIiIhESFkGZ85xz0REJHzKaYo2nZ94KYdxhOqNc6bx\nzkTiTeOclR+NcxYGjXNWjoL4/irLmjMRERGRuFJwJiIiIhIhCs5ERCQn5TRFm85PvGicMxERyUnj\naEWbzk+8qOZMREREJEIUnImIiIhEiIIzERHJSTlN0abzEy/KORMRkZyU0xRtOj/xopozERERkQhR\nzZmIiEgkNWP8+PFMmvRq3nseeeTvuOOOG0MokzQEBWciIpKTnc+k5rOGdDarVh3EqlW5t6yqetq6\n7wfMYOrU+8MtmoQqzOCsL3ALUAGMAYZn2K4n8BZwIvBEiOUREZECKSgrhRZAN19bVlU5t1sZSmmk\n4YSVc1YB3I4J0DoB/YGOGbYbDrxAPCY5FhERESlKWMHZvsBCYDGwHngI6Oex3QXAY8CKkMohIiIi\nUlbCCs52AJY4Hi+11rm36QeMtB4nQyqLiIgUSeNoRVtV1TCqqnR+4iKsnDM/gdYtwGBr2wRZmjWr\nqqo2LldXVxdXMhGJnOrqav3fjjjlnEVbVZXOT5yElee1H1CFyTkDGALUkd4p4BPH628F/AScAzzj\nOlYymTSxXiKRIJlMbrwHE7g5gzcRKX+JRALikYe68fsr7o477gyeeKI3cEapi5IH+08sbufoNbp0\n+Ttz5rxW6oI0SkF8f4XVrDkD6ADsDDQHTqJ+0LUrsIt1ewz4s8c2OamaXUREROIkrGbNWmAQMBnT\nI3MsMA84z3p+VEivKyIiIdA4Z9Fm55upeTMeyqHZIGuzpnNZROJBzZrlR82aUaJmzVKKcrOmiIiI\niBRAwZmIiIhIhCg4ExGRnDTOWbRpnLN40cTnIiKSkzoCRJs6AsSLas5EREREIkTBmYiIiEiEKDgT\nkcbmv8By4H3Hui2BF4GPgSlAG8dzQ4AFwEfAYY713a1jLABuDbG8kaCcs2hTzlm8KOdMRBqbe4Db\ngPsc6wZjgrMbgMutx4OBTpgZTjoBOwAvYWY/SQIjgQHAdOB5zHR1LzTIOygB5ZxFm3LO4kU1ZyLS\n2LwBfOdadwwwzloeBxxrLfcDJgDrgcXAQqAXsB3QGhOYgQn07H1ERIqimjMREdgG09SJdb+Ntbw9\n8LZju6WYGrT11rKtxlpf9qZNm8bixYvz3m/Jkk+DL4xIIxWb4KyqqoqqqqpSF0NEyl+S+M3n41v/\n/ufw1Vfb0aRJm7T1l1zSCYD//Geu5351ddsB+4RdPMlAc2vGS2yCs2HDhik4E5FCLQe2Bb7ENFl+\nZa2vAdo5tmuLqTGrsZad62u8Duz8XqqsrKSysjKgIodjw4Ykq1f/G+ictl5fr9GmoKx0qqurqa6u\nDvSY5TCxsK+JzzUBukh8NMDE5zsDz5KKQG4AvgGGYzoCtCHVIeBBYF9SHQLaY2rWpgEXYvLOngNG\nUL9DQNlNfL7TTp35/PMHcQdn8aSJzyV4QXx/xabmTETEpwnAb4GtgCXA34F/AY9gel8uBk60tp1r\nrZ8L1AIDSV3JBwL3Ai0xvTVj21NTRBqWgjMRaWz6Z1h/aIb111k3t5k0juolQDlNUafzEy8KzkRE\nJCdd9KNN5ydewh7nrC9mVO0FmIEd3U4B5gDvAW8CXUIuj4iIiEikhVlzVgHcjmkqqAHeAZ4B5jm2\n+QT4DbASE8jdDewXYplEREREIi3MmrN9MaNpL8YM2PgQZrRtp7cwgRmYnk9tERGRyNHcjdGm8xMv\nYdac7YDpCWVbipn2JJMBmB5PIiISMcppijadn3gJs+Ysn4FjDgHOwjsvLW8ajFZERETKVZg1Z+6R\ntduRPhedrQswGpNz5p6MGEgPtvyMwqvZAkTKSxgjbIuIlKswR+BuCswH+gDLMKNo9ye9Q8COwCvA\nqaRPLuyU9wwBmi1ApLw1wAwBDSU2MwTEcxyt+MwQkH5+NENAKUV9hoBaYBAwGdNzcywmMDvPen4U\nZmTuXwAjrXXrMR0JREQkQuIVlMWPzk+8hD0I7STr5jTKsXy2dRMRERERwh+EVkRERETyoOBMRERy\n0jha0abzEy+xnluzqqpKvTZFRAKgnKZo0/mJl1jXnA0bpl8RIiIiUl5iHZyJiIiIlBsFZyIikpNy\nmqJN5ydeYp1zJiIiwVBOU7Tp/MRLo6k5U8cAERERKQeNJjhT5wAREREpB40mOBMRkcIppynadH7i\nRTlnIiKSk3Kaok3nJ14aXc2Zcs9EREQkyhpdcKbcMxEREYmyRt2sqemdRCSu5s6dy6pVq/Leb926\nnzzX2/lMaj6LJvf5+e675YwfPz7v4/zqV7/isMMOC7Rskr9EqQvgQzKZTAKQSCRIJpMb74NaJyLR\nkkgkoDy+n3JJluI7Zv369bRo0ZLWrbvnvW9tbTNWr34c2Cb4gkWO/ScWt+vAF7RsOZiKig157ZVM\nrqe29nnWrs0/qJeUIL6/yuHLL/TgTDVoItGi4Kw4P//8My1btqKu7ucGf+3yEtfgrFA/0rz5tqxb\n92OpC1LWgvj+CjPnrC/wEbAAuDzDNiOs5+cAe4dYlqyceWgK0kRERKSUwgrOKoDbMQFaJ6A/0NG1\nzZFAe6ADcC4wMqSy5MUO1BSkiYikaBytaNP5ET/2B15wPB5s3ZzuAk5yPP4I7ySHpM1ebuh1Q4cO\nTUp02efHeZ68lnUeywfxaWcqyee3bt26ZJMmzZKQ1C3rDetW6nJE5bYq2bz5ZiX5m40T6+8qko4H\nRjsenwrc5trmWeAAx+OXAK/s1bQ37Lxv6HVSuFzBUrbAKde+uc6Z1/P5liEMChozI8Jfbnkqyeen\n4MzvTcFZ+k3BWRCsv6tIOg5/wdmBjscvAft4HCvtDTvvG3pdIRdyv0FJruMVUjuU7dhBBwS5ylXM\nZ1zMOStkn0I+10LOj1cZgg5cGzoIDerYRPjLLU+BfB75UnDm96bgLP2m4CwI1t9VUcLqDbUfUIXJ\nOQMYAtQBwx3b3AVUAw9Zjz8Cfgssdx0rCUMdDyutm4jER7V1sw0D9dYsWBi9NeM5zll8emsGc37U\nWzMIUR5KoykwH+gDLAOmYzoFzHNscyQwyLrfD7jFuncryZebiATLOWRNruFrNJRGcTSUhl/xCc6C\noeAsCFEOzgCOwARcFcBY4HrgPOu5Uda93aNzNXAm8K7HcRSciTQyCs6Ko+DMLwVn6RScBSHqwVlQ\nFJyJNDIKzoqj4MwvBWfpFJwFIeqD0IqISExoHK1o0/mJl3L4ZaqaM5FGRjVnxVHNmV+qOUunmrMg\nBPH91TSYooiIiEh5a8L69Wvo1OmA3Ju6bLZZcyZPfoItt9wyhHI1PgrOREREBNiUZHIW8+blX3O2\n6aYn8fXXXys4C4iCMxGRwvUl1St9DOljOcZKPMc5i4/gzk+XgvaqqGhZ5OuKUznkdMQm56y6uprK\nyspSF6NocXkfoPcSVWWSc1aBGc/xUKAGeIf64zkW9f01f/589tmnF7W1tXntl0wmSSZbUFv7TcGv\nHYxqoj1oeJg5Z9VE+70Hq3Xr3ZkxYyK77747EK/vo3ypt2aZqa6uLnURAhGX9wF6L1KUfYGFwGJg\nPWa2k35BvsB3331H06Yd+PnnL/O6rV+/nNraZUEWpUDVpS5ACVWXugAlpe+j4qhZU0SkMDsASxyP\nlwK9vDZcvHgxDz/8cN4v8Pnnn5NIVACtCiqgSEOpq4OLL76S1q23AOD9999l/vylOfdr0iRBVdVl\ndOjQIewilhUFZyIihfHdFjZp0iQGDx5c8AttvvnRBe8blIsv7gHATTfN8L3P2rXzadFiZlhFKtoP\nP5j7MD7fhn7vhZyfIK1atYTnnluQtu7DD2f52vfBB8cU9Jp33DGSgQPPL2jfqIt6TgfAbKBrqQsh\nIg1qDtCt1IXIYT+gCtMpAGAIUEd6p4CFwG4NWywRKbFFQPtSF0JEpDFqivkS3hlojvkh2bGUBRIR\nERFp7I7A9NhciKk5ExEREREREWkYfYGPgAXA5SUuS77aAa8CHwIfABda67cEXgQ+BqYAbUpSusJU\nALOAZ63H5fpe2gD/v71zCZGjisLwJ2Z8TNQBQZxMIkyUiLrxQfAZcRNfQaKudOEDBXEhoihGko0u\nXIggiogujJEoGoSoYUQ3ipuAGg2aUQizEB1CNDMG1PgAEUEXf5Vd00513+5KT+6Z/B8U1fW4cP66\n9546fV+1Ha1FtRfNrouoZSMqX18DbwDHE0fHFmAW2V7SyfaNyA9MAdcskI29kPrc63za42im55fF\ndt3/UuZHin9+rrg+CVzYY9rcaaJ/GvgK5fVngzNxYHTTfg7wCfAn8HCPaSPQRP80sfOeY1E3wTgw\nRLyxHKO0BjOfhLo9zgWeAjYU5x8Fnlx40/rmIeB1YKI4jqplK3B38XsJMEI8LePAtyggA3gTuJM4\nOq5EL6tqcFZn+3mo/g8h3d+Q3/qMKc+9k097DNWvKKT453XA+8XvS4BPe0ibO030A3yHAvqIpGg/\nDVgNPMHc4ORoyfs6/dBD3ufm5EoGvrjjgJlBmQbwO2qlWQ6sR8EBxf6mhTetL1YgZ7OZ1gzfiFpG\nUGCwpTj+GzhEPC2/onoxjALMYeAH4ujYCfzcdq7O9huBbUjvNPILFw/exJ5Iee7dfFqEmfMlKf65\n+kx2odbE0cS0udOv/tMr1yPld5UU7QeB3cX1XtPmThP9JUl5n2twNt/ijsuPkC1NGUetBLtQ5Zwt\nzs8yt7LmzDPAI2iZgJKIWlaiivMK8AXwErCUeFp+Ap4G9qGg7BfUrRZNR5U628dQ/S/J0RekPPdu\nPu1+1P31Mvl2R5ek+Oe6e8YS0uZOE/2g9fE+RC/wewZk46Bo8m5eDO/1phqS8z7X4GxxfExTXZpv\nAQ8Av7Vd+4cYOm8AfkR95HURfxQtS4CLgBeK/R9A+8qgEbScBTyIAv8xVM5ua7sngo46utl+JHR9\ngLph27f1bffV2d7J5hfRH4cLgAMo8M6Z1OcftXWoG031r0F/2K8H7kOt+VFoUvei+qMqTTVcQWLe\n5/qFgO/RoPqSM5j77zkCQygwew3YUZybRU37M8AyFPTkzuXoBbQOOAE4BWmKqGV/sX1eHG9Hg81n\niKVlNfAxUH7V+m3gMuLpqFJXntp9wYri3EJzdYdrKXWhk0+r3r+Z1qSbXEnxz/Pl237kF6P79n71\nl+W2/OjpQeAd1FW28/CbORCavJsXw3u9qYYDxb5r3ufacrYbWEVrccdbaA1Ej8AxqHtiL/Bs5fwE\nGrhNsd9B/mxCBXAlcCvwEXA7MbXMoCbps4vjtWjG47vE0jKFVqc/EZW1taisRdNRpa48TaBydxwq\ng6vIb5ZTSl3o5NOWVe67mbkTJXIkxT9PAHcUvy9FXe+ziWlzp4n+YeDk4vxSNPs49/yu0kv+tbcc\nHi15X9KuP3re/0fkxR3XoPFZe5g7Pf5U1N+c+1IHdVxFqyBG1XI+ajmbRC1OI8TUsoHWUhpbUYtE\nFB3bUOvBXyhYvovOtm9CfmAKuHZBLU2jzvYx4L3KfXU+7VU0vX4SBXYRxgrOp+XeYit5vrg+iYYR\ndEobjX71n4neC3vQMksR9XfTPorq9SE08WcfGnpRlzYa/epfDHlvjDHGGGOMMcYYY4wxxhhjjDHG\nGGOMMcYYY4wxxhhjjDHGGGOMMcYYY4wxxhhjjDHGGGOMMeZw8C+yWu2HMx0+gQAAAABJRU5ErkJg\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d4d8e10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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G0aVzE64gNWD9gI+BecBQj+VxYBUw0378MWV5lT1/Us6lFBERESkjmWrAqoA7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\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e50ce90>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Let's simulate some data of the height and weight of a population\n",
      "height_mu = 175.7\n",
      "height_sd = 7.3\n",
      "weight_mu = 72.6\n",
      "weight_sd = 15.9\n",
      "rho = 0.42\n",
      "mean = [height_mu, weight_mu]\n",
      "cov = [[height_sd**2, rho*height_sd*weight_sd],\n",
      "       [rho*height_sd*weight_sd, weight_sd**2]]\n",
      "men = numpy.random.multivariate_normal(mean, cov, 100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Linear Regression\n",
      "\n",
      "# Let's model the problem\n",
      "beta0 = pymc.distributions.Normal(\"beta0\", mu=0, tau=1e-12)\n",
      "beta1 = pymc.distributions.Normal(\"beta1\", mu=0, tau=1e-12)\n",
      "tau = pymc.distributions.Gamma(\"tau\", alpha=0.001, beta=0.001)\n",
      "\n",
      "@deterministic\n",
      "def mu(beta0=beta0, beta1=beta1):\n",
      "    return beta0 + men[:,0]*beta1\n",
      "\n",
      "likelihood = pymc.distributions.Normal(\"likelihood\", mu=mu, tau=tau, value=men[:,1], observed=True)\n",
      "\n",
      "model = pymc.Model([beta0, beta1, tau])\n",
      "mcmc = pymc.MCMC(model)\n",
      "mcmc.sample(iter=40000, burn=10000)\n",
      "\n",
      "pymc.Matplot.plot(mcmc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 3555 of 40000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------           17%                  ] 7021 of 40000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        26%                  ] 10489 of 40000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     33%                  ] 13391 of 40000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  40%                  ] 16329 of 40000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------48%                  ] 19274 of 40000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------55%-                 ] 22186 of 40000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------62%---               ] 25061 of 40000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------69%------            ] 27923 of 40000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------77%---------         ] 30818 of 40000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------84%------------      ] 33753 of 40000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------91%--------------    ] 36666 of 40000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------98%----------------- ] 39572 of 40000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 40000 of 40000 complete in 6.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting beta0\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " beta1\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " tau\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mMRsLtNy8G94JVA+oaldgC+7e5+OOIS2jk9Tzj/m2lSY2b+VBtsfyrQHWuPSX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\nzMysCweJZmZmZtaFg0QzMzMz6+L/A41FT8Chwv0XAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113873f90>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZsCBqw4bwfN5/P/w6+Pzr+L//W31dutrjKFIFX4UMssaOzVxrnuz556FRhE+v\nzZsrgAobVLsesfZppcfueXxyChJFRICHgSWqGuyWMAkYgNeBZADwfCD9SRG5B+8VcHtgnqqqiGwS\nkTJgHnAJMCYprznABYDfum46MMr1nBagBzDY5TULuBCYkHT8KvbZZ3jK2TpUE6/WotSShA12Hbbv\n//2f91otFx9+mHpdcBgSv31gIfzud4XLO1kwQDnuOO819HXXVd8urIdu8liNtSnTYODJY0WKeLPH\nXH89HHBA6v3SBWypgqGoPeqXLAmfXjJTkPjgg6nXFeJV75Yt4VMxJh9rzz3LgXL22stvY2oD8tZ1\nFiiUHrvn8cm1JvEkoD/wloj4Q/wOAW4HJorIQGAlcBGAqi4RkYnAEmAHMMi9jgYYBDwGNAGmuJ7N\n4AWhT4jIcmAdrkOKqq4XkVuA1912I/xOLHgNQsaLyEhgocujmky9Hf2aoVSDAQd95zuZtwGvpuah\nh6Jtm2kg6LCaqOuvj5Z3OmFtwo45purfo0Z5v4OzcuQqVTCRPHh0qg4gucx8k41sa9W+/jo8sA/L\nx79/6c4ln7V6yUMBPf98+PiNhX5dm+o1c678DlRR54s2xhiTkGvv5ldJ3a7x9BT7jAJGhaQvADqG\npG/FBZkh6x4Fqg3KoaofAGUpC+5E7XmcTY/mZLnUomR61ZxpqJd8StVppTa+4CW3n1SFX/2q+owr\nNe09nK1sAqYHH0w9Pt/27eG9wDP5wQ+y3ydVmaM2Z8glSJw50+t4lK4JRrailiddrbsxxpj0bMaV\nFFK1FwvK9tVevqWaSzrZ3LmJ5bBhX4pF1IBJNf9jLmYjOMxNJjfcAEcemXp9sAYt3biKcXe8mDUr\nt/1nz4amTfNTFl/YjD3Wi7n+s3l8S4/d8/jkbQic+iZTezKAvfYKTx83LrFcDA+t4Hh/2QQ4tS04\nuHe614/5mrGmprKZBjFTID9xYrR8cp2DeN68zNukE3UA7FReeCG3/cMk9yaH/AxTZYqbtU8rPXbP\n42M1iSmEPYCiuvzyvBUjb5Yvh2bN0s8XXEzSzZdcV84hn9L1do4iU/vWQgv2UM+HVF8IbFYVY4zJ\nH6tJLLD/9//iLoHHf+X52mvxliMfsh1/0RSvsDaDt92Web9LL828jTHGmNxYTWKJmT497hLkbsWK\nuEtg8iVsuJ3aGOjd1F3WPq302D2Pj2jcLeJjIiJaexPBGGPCNGsWrf1v/giqWgQthXMnIlqqn9/F\nrHHjvdnzIVMIAAAgAElEQVS6dQ2Fm5bP/+dbiHu/gMMP/xkrViwoQN4mVyK1//llNYnGmNjUboBo\njDEmGxYkGmOMMcaYaixINMYYU2dY+7TSY/c8PtYm0RhTQgrbpkdEVgKbgJ3AdlU9QURa4M0jfyhu\nmlJ/ClERGQJc4ba/RlWnu/SueNOUNsabpvTakGNZm8QiZG0STaHUyTaJIvKIiKwVkcWBtBYiMkNE\nlonIdBFpHlg3RESWi8hSEekZSO8qIovduvsC6XuIyASXPkdEDg2sG+COsUxELg2ktxORuW6f8SKy\nW67naYwxEShQrqqdVfUEl3YDMENVjwRecn8jIh2Ai4EOQC/gfpFdw++PBQaqanugvYj0qs2TMMYY\nyM/r5kfxPuCC8vmhOBBY59L/AIx2ebUAbgJOcD/DRKSZ22c0cLfb5wuXhzHG1Ibkb/pnA/48TOOA\nc9xyX+ApVd2uqiuBFUCZiBwE7K2q/jw5jwf2McaYWpNzkKiqs/ECsaB8figG83oG6O6WzwCmq+oG\n9+pmBtDbBZ3dgKdDjm+MMYWkwIsiMl9ErnRpLVV1rVteC7R0y62AVYF9VwEHh6SvdukGa59Wiuye\nx6dQM66k+1CcE9jO/1DcTuoPxYOBjwFUdYeIbBSR/Uj9AdsC2KCqlSF5GWNMIZ2kqp+IyAHADBFZ\nGlypquq1hzY1ZfP4lh675/Ep+LR8tfyhaB++xpjYqOon7vfnIvIcXlOYtSJyoKp+6t6afOY2Xw20\nCezeGu/L7mq3HExfHXa84YFJ5svLyykvL8/PiRhjYldRUUFFzBPSFypIzMeH4qrAPocAa0SkEdBM\nVdeJyGqgPLBPG2AmsB5oLiINXG1iyg9YGB5YLk/KzhhT91W4n8ITkaZAQ1X9UkT2BHoCI4BJwAC8\nttIDgOfdLpOAJ0XkHry3He2Bee6L9SYRKQPmAZcAY8KOGQwSjTH1S/IXvzheuRcqSMznh6Kf1xzg\nAryOMADTgVGu57QAPYDBLq9ZwIV4w04Ej59keJ5O1xhTnMqp+uWvoB+yLYHnXF+8RsDfVHW6iMwH\nJorIQNwQOACqukREJgJLgB3AoMCYNoPwhsBpgjcEztRCFrwu8R+U9gqydNg9j0/O4ySKyFPAqcD+\neO0PbwL+AUzEqwFcSdVxwYbijQu2A7hWVae5dH9cMP9D8RqXvgfwBNAZWAf0c51eEJHLgaGuKCNV\ndZxLbweMx2ufuBDor6rbk8pt4yQaU3Js7mZTWDZOoimUOMZJtMG0jTElxIJEU1gWJJpCqZODaRtj\njDHGmPrHgkRjjDF1ho2ZV3rsnsfHXjcbY0qIvW42hWWvm02h2OtmY4wxxhhTFCxINMYYY4wx1ViQ\naIwxps6w9mmlx+55fKxNojGmhFibRFNY1ibRFIq1STTGGGOMMUXBgkRjjDHGGFONBYnGGGPqDGuf\nVnrsnsen3rZJFJFewL1AQ+AhVR2dtN7aJBpTcqxNoiksa5NoCsXaJOaJiDQE/gT0AjoAPxKR78Rb\nKmOMMcaYuqNeBonACcAKVV2pqtuB8UDfmMtkjDHGGFNn1Ncg8WDg48Dfq1yaMcaYOszap5Ueu+fx\naRR3AQrEGuoYY0w9NGzYsLiLYGqZ3fP41NcgcTXQJvB3G7zaxCTDA8vl7scYU39UuB9jjDHZqq9B\n4nygvYi0BdYAFwM/qr7Z8FoskjGm9pVT9cufvbIyxpio6mWQqKo7ROQqYBreEDgPq+q7MRfLGGNM\njvy2afYKsnTYPY9PvR0nMRMbJ9GYUmTjJJrCsnESTaHYOInGGGOMMaYoWJBojDHGGGOqsSDRGGNM\nnWFj5pUeu+fxsTaJxpgSYm0STWFZm0RTKNYm0RhjjDHGFAULEo0xxhhjTDUWJBpjjKkzrH1a6bF7\nHh9rk2iMKSHWJtEUlrVJNIVibRKNMcYYY0xRsCDRGGOMMcZUU+MgUUQuFJF3RGSniHRJWjdERJaL\nyFIR6RlI7yoii926+wLpe4jIBJc+R0QODawbICLL3M+lgfR2IjLX7TNeRHYLrBvj0t8Ukc41PUdj\njDHFxdqnlR675/GpcZtEETkKqAT+AlynqgtdegfgSeB44GDgRaC9qqqIzAOuUtV5IjIFGKOqU0Vk\nEPBdVR0kIhcD56pqPxFpAbwOdHWHXQB0UdWNIjIReFpVJ4rIWOBNVX1ARPq4Y/QRkTLgPlU9MaT8\n1ibRmJJjbRJNYVmbRFModapNoqouVdVlIav6Ak+p6nZVXQmsAMpE5CBgb1Wd57Z7HDjHLZ8NjHPL\nzwDd3fIZwHRV3aCqG4AZQG8REaAb8LTbblwgr75+Xqo6F2guIi1rep7GGGOMMaWoEG0SWwGrAn+v\nwqtRTE5f7dJxvz8GUNUdwEYR2S9NXi2ADapaGZJXKz+vwD6tczslY4wxxpjS0ijdShGZARwYsmqo\nqk4uTJEyilLHnlwda+9kjDGmHvDbpg0bNizmkpjaYvc8PmmDRFXtUYM8VwNtAn+3xqvNW03VGj0/\n3d/nEGCNiDQCmqnqOhFZDZQH9mkDzATW471GbuBqE1u7PFIdfzWhhgeWy5MOZYyp+yrcj6kvLFAo\nPXbP45M2SMxCsOZuEvCkiNyD9wq4PTDPdVzZ5DqTzAMuAcYE9hkAzAEuAF5y6dOBUSLS3B2jBzDY\n5TULuBCY4PZ9PpDXVcB4ETkR77X02vBiD8/xtI0xxa2cql/+rIekMcZEVeMgUUTOxQvy9gdeEJFF\nqtpbVZe4nsdLgB3AoEAXvEHAY0ATYIqqTnXpDwNPiMhyYB3QD0BV14vILXg9nAFGuA4sAIPxAsGR\nwEKXB6o6RUT6iMgKYDNweU3P0RhjjDGmVNm0fMaYEmJD4NR1xd4+zYbAyb9iv+e1JY4hcCxINMaU\nEAsSTWFZkGgKpU6Nk2iMMcYYY+ovCxKNMcYYY0w1FiQaY4ypM2we39Jj9zw+1ibRGFNCrE2iKSxr\nk2gKxdokGmOMMcaYomBBYpFolK9hzUvcnnsmlr///fjKYYwxxtR1FiQWiXy8NXrvvdzzyLcuXWr3\neBKoiG/cuHaPna2bb467BMbUPdY+rfTYPY+PBYkRdOxY831feinzNpCfIPGww3LPI99uvTW+Yx96\naHzHjuKAA8LTr722do7fv3/tHKeUiEhDEVkkIpPd3y1EZIaILBOR6W6KUX/bISKyXESWikjPQHpX\nEVns1t0Xx3kUs2HDhpX8oMqlxu55fCxIjKBBDlfptNOibVdf259XVsZ3bCny7gmpylcb5U73Kr5J\nk5rnO3JkzfetJ67Fm5LU/x99AzBDVY/Em5P+BgAR6QBcDHQAegH3i+y682OBgaraHmgvIr1qsfzG\nGLNLjcMfEblTRN4VkTdF5FkRaRZYl9U3ZBHZQ0QmuPQ5InJoYN0A9y18mYhcGkhvJyJz3T7jRWS3\nwLoxLv1NEelc03OsTX6QeMwxtX/ss84qXN61HfzWNMBq3752jhMlj7iD23ffjff4YfbdN/W6uK+X\nT0RaA32Ah0h0QT0bGOeWxwHnuOW+wFOqul1VVwIrgDIROQjYW1Xnue0eD+xjjDG1KpeaxOnA0ap6\nLLAMGAI1/oY8EFjn0v8AjHZ5tQBuAk5wP8MCweho4G63zxcuD0SkD3CES/+ZO2ad8aMf5bZ/ixbZ\n77P//qnXDR+eW9u+mpQn2Y03Rt82GDD0yqL+paIi+raZ/O530bZLVUNdG0FPumMEO/8ENW2aOd8o\n29REuvLus09iecsWWL++MGWI4A/Ab4Fg/XlLVV3rltcCLd1yK2BVYLtVwMEh6atdunGsfVrpsXse\nnxoHiao6Q1X9D8O5QGu3XJNvyMFv288A3d3yGcB0Vd2gqhuAGUBvF3R2A5522yV/Qx/nyjgXaC4i\n/gdzLHbfPbH89tuFOUa3bt7vk0/Oft90tX277w6bN6fff0HSkFrBh3azZuSkb1/YbbfM2/mCwcSF\nF0bfL581nrk0T6gtIrmf8/33V6+FLi/PLc9cNW6cvtaxUETkLOAzVV1EohaxCjeoYT1tWFJ7rH1a\n6bF7Hp98Pc6uAKa45Zp8Qz4Y+BhAVXcAG0VkvzR5tQA2BILUYF6t/LwC+7Qmgj59wtNzrdn54x8T\ny0cfHb7Nt7+dXZ7du8PUqYm/W7owuCYP/nT7NG+eOehJ7sEcvF65BiK//W122xfLq8eauM81wMgm\nKM7GpZeGp5+T9DIz1T27996qf//85zB5cvpjnnBCtLJl4t/XBx6AI4+suq5I2vN+HzhbRD4AngJO\nE5EngLUiciCA+6L8mdt+NdAmsH9rvM+q1VT9vGrt0kINHz58109FPqvDjTGxq6ioqPJ/PA5pH/+u\nV97ikJ8fBrb5HbBNVZ8seGk9UR4JyaFCpMfICy+Ep6cKkvbYI0qu0SxcCB9+GH37Fi3gjDPgwAOr\npkd9YB5ySLR9ahJ05TNIPOmk7PL47ner/h31VXnLkLrm0aMz79ewYbT8w4Rd25Ur4X/+J/1+77xT\n82OGHbtHj2j7XHklLF1aPT3d/j/+cdW/p03zfiffp0yOOw569/aujd8ko40LsYohSFTVoaraRlXb\nAf2Amap6CTAJGOA2GwA875YnAf1EZHcRaQe0B+ap6qfAJhEpc29MLgnsU03wAVIedzWuMSavysvL\niztIVNUeqtox5Mcf3uEyvIbaPwnsls035FWBfQ5xeTYCmqnqupC82ri09XivkRsE8lodyCv5+Cm+\niQ8P/FSEb0LqoUry2XO3adOqgVu2zjzT+x21Z2rr1vDUU95yvh+ycbzuA+88snnFHNSoUfXrEGUw\n7n/9q3pa1M5HfqA2d24i7dBDoV279PuFBbTphH3JyRT8J9fW+cJqvFP14H/yyerD+fi1zvPmVd8+\nlW9/Gx57DKa4dxV+2a++OsreFVT9f15r/H9NtwM9RGQZcJr7G1VdAkzE6wn9L2BQYI69QXidX5YD\nK1R1KmYXa59Weuyex6fG83y4Tie/BU5V1W8CqyYBT4rIPXivgP1vyCoim0SkDJiH9w15TGCfAcAc\n4AK8oSLA6xwzyo0tJkAPYLDLaxZwITCB6t/QrwLGi8iJeK+l/YbjSYbvWmrbNvtrcNRRXnu9998P\nX58q+GrWDDZuzJx/8+awYUO0vP0x7x54wGuXmGmsveD++axJ3HtvGD8eysoy5x1VNnkkB6jB8s+c\nCVdc4dXWFdIFF8DOnZlrGf2y+a9ko55nqu1+/Wu4555oeYSVI/j3f/4T/d7/+McwZEi0bf2yB7/M\nfPvb3vFS6d69eo15MK/0163c/fgK/6BR1ZeBl93yeuD0FNuNAkaFpC8AchidtX6ztmmlx+55fHJp\nk/hHYC9ghhs89n6o8Tfkh4H9RGQ58EvcWGLuA/YW4HW8wHKE68ACMBj4tdtnX5cHqjoFeF9EVgB/\nccdM67rr4M03s78Ar70Gb7xRNe2jj6oPUpz8EFu40AtYAKZPh88/D9+2b9/EcnLtUaoHY4sW0K9f\n5rJHyQuyDxJ/+MOq7dAOOiixvGJFdnlFdf750bbr1g0++CDzdt27Z97GF7x22U4DmO/2kyeeGJ4e\nvAdhx/bPIZvy/OY31fdPpWXL9D3o77or/d/JkmtGMx2/prXLxhhT6nLp3dxeVQ9V1c7uZ1Bg3ShV\nPUJVj1LVaYH0Be519RGqek0gfauqXuTyPNH1ivbXPerS26vquED6B6pa5tIvVtXtgXVXuWMcq6oL\nM53LPvskeuTOmuX9FoEbbkgsh9lrL6/mLKhNm9RDiPgOOyzxOq9Hj/QPUN9RR2XeJhvB3q35qO3z\na4KC16pBA+/c/HWHH55Yd/zxqfM6/3y4+OLE3/37J+5FmEsuSb2uJoHYnXeGt73LpHWgMUU+OxCl\nqx2N4plnvN9HHJF+O7/5RLA3fio/+Unmbfzz+fRT7zVz48bVz7Fjx+o9pDN1TPnVr7z/p1GvcZTz\nMcYYU10dGKyjdvltv5s0gfPOi7ZPcg1SLm0Lg4LBwOWXV12X7gGZbZvAsLx27KhehnT8B3tYXkce\nCf/9b9W0GTNS5/X00/DXvyb+PvxwuO221NunuxZlZdmP1bjXXtXb3vltPgEGDswuPwifw7pRxMYe\nuXaQ8r/IpBq/MXiP//vfqkMY5ctzz8Enn2TeLlN7TPDuT3l5IqgNu/9hHX2LcdpKkz1rn1Z67J7H\nx4JEUgdCxx0Hb72VOVB69VWvLaAvuSYxrAZn//293snJ/Ade27aJsQ+h+iu2k05KXZ6oQ6gk1yT+\n+9+JdQ0bwoMPVn9VN20aRPm/2qWLd/18++0XrUy5Sg7Qp03z7mFUDz6YCCb8+/7LXyY6+QTT02nQ\noOrA0qeHtErba69oZbrmmqp/pwouUwXLfnlTvaYN7hf1PkW5BsFtmjb12tjmmk+YsPMOe8WefB1N\n3WRj5pUeu+fxsSAxDRHvdViU7dI9yMLauO2xR9VxDpN98EHVce2S8//1rzOXC7wHs1+r4gcqxx1X\ndUzIVG3Srryy+oO9Z0849tjUx/MDkddeg9mz05ct3evPmrbXO/VU+MtfEn/vtlt24w5eeWV4h5O9\n94b58xNly1Q+Efjqq+jHhdRBXnKnkFQDlKfa/9BDveFjksvn+973atZxK27pmkvU5fEyjTGmWFiQ\nSPgDJZgW5YFTqLHa5syJXoag9eu9wOCCCxJjBfrT1L3+uvfq0S/z8OHw8MPR827VKvU6P0jcY4/M\nbcHCanu+/jrz8V9/3Zvtw5d87Qs1GHXXrtWPma6XeHL7zCVLClOuTJo2TQwfE6Zz52gdelI55BC4\n7LJo20b5f9Kpk/f7lFPSb5c8BFWwFjRY2+ofM5cxLY0xphRZkEjqWVDyafDgaNslP0TLyrwH/AUX\nhG9/0EHhD7999/X2C7btS+U73/GGhkkn+Or4+ONTB4rZBGhhAYM/NEq6oPi447zZPlJJ7kyUKcDO\nNCROcP9zz63aqSYoXQA0ZIh3nQsprkGlRbxe7ZC501bYvlB1uso2bbxzeeWV9PsmB+rBwejbtfNG\nEfC9/DL89KfZlc0UJ2ufVnrsnsenxuMk1he/+Y334C+0Qw+t+b7JrwonTEgsv/QSbNtWs3yzCSou\nuSTxuhVS1xJmEySkO37jxuGdPVonTbD4wgvV29qddx4sX574O1MNUqZ7c9FFieVnnw3f5sorqwen\nQWGdQYJtTqFmQd5hh6UepzOdRo288Q23bMl+3zB+sHfkkV6+T6aYfynVYO/+F7VsasyTg8Tkf3ud\nOyeWf/CD6Pma4mZt00qP3fP4lHyQWGxtl6IECsGgJZ+zm+Sj92emeZ7Be5hn6kHbsCEsWFA17bjj\nwmt9zzgDFi+uWoZge8cWLaoGuFH5NX9RagAffBBuvDG7/LPtRdytW/Ugeb/9EkFiNkFmkyZej+1g\nr+1cBL80+ANfh808s88+sN0NVtW9e2I0gVRuvbXqeKFB/vkedhhs2pQ6j2AHImOMMdGVfJAYRbEF\nktlK1dEkOahINf1gNqJcq4EDq47TGNXrr6c+Zqa5gIPtCZctSz3tXFCLFl6nn7COIn75g23fUjVb\niDqUUqbr0bdv6pl0Tjkl2nibhdK7d2J6Qf88Ul0P/5q9+GLmfIcOTb3Ob5M4Z07qKTKXLKkeWBtj\njImm5IPE2goAox6nEO3K/I4r+cz7+OPh44+96eeCotQk+oLluf32zIFemJrcv/btvWNH2ffUU9Ov\n79bNGwIJwmsGP/oofK7lbMduhPAg3r+Gr7wS3ps87JU9ZHfdzj8/MSB3Kg0aVJ1ppzZcdBGsWZO6\ntzcUvh2oqX1+2zR7BVk67J7Hp+SDxCiiPFD79Uvfm3fAgGgDBf/oR9Hmdc5W+/bV03r0gEEZJy30\nJAeYTz0F69ZVDYCOOy7RgzrbPDt2rDosT13RoEFizMreveG996qub9MmfD8/SA1OyZjO2rWZa3oL\nERD16eO98s0UJMbh6KOjdcwy9YsFCqXH7nl8aty7WURuEZE3ReQNEXlJRNoE1g0RkeUislREegbS\nu4rIYrfuvkD6HiIywaXPEZFDA+sGiMgy93NpIL2diMx1+4wXkd0C68a49DdFJNB8Pew8sksH7/Xh\nxx9XTWvWrPqsKEFNmoQPnp3siCMyz11bE8uWVT+nAw+EP/+5+rZPPJE5v4YN4Vvfgm++SaS9/nr4\noNGlQiT7dp3BV8Tpanq/9a3MX1bCXjfX5N938nbf/nbt9Jz+9a+rzgltjDEmXrkMgXOHmxu5E/A8\nMAxARDoAFwMdgF7A/SK7HkljgYGq2h5oLyJ+vdNAYJ1L/wMw2uXVArgJOMH9DBMR/+XSaOBut88X\nLg9EpA9whEv/mTtmTv7wB29aMfBeEz79dPp2TjV5lVgbor7OTVX7FSaXKePSjTEYVa7NBTLNZ5zK\nM894/w4KKd25RX2tn2kWlkxqcn1qei/vvjv90EbGGGNqV41fN6vql4E/9wL82Xn7Ak+p6nZgpYis\nAMpE5ENgb1Wd57Z7HDgHmAqcjQsygWeAP7nlM4DpqroBQERmAL1FZALQDejnthsHDAcecMcf58o4\nV0Sai0hLVV0bdh5RHpZHHJF4WDZokHmfn/yk+vAmxeCMM+ILxsLENa5fUE3nKT7nnPyWI0xNrk+X\nLlXHB0zlxBOj5ZdqkOy63pnL1F3WPq2w1q79kEsv/X813r9Tpw78+tf5nQPT7nl8cmqTKCK3ApcA\nW/Bq+gBaAXMCm60CDga2u2XfapeO+/0xgKruEJGNIrKfy2tVSF4tgA2qWhmSVys/r8A+rYHQIDHM\n/Pnh7QsnT04/Fp6vQYPC9aiM2lM2F2HBSSEDujZtatZppS7L9RpPmeL16L3ppqrpCxZkDuAeesjr\nYR5FqrwKNauNMZlYoFBIh/DVVyMjNTkK9w7Llk3Je5Bo9zw+aYNEV3N3YMiqoao6WVV/B/xORG4A\n7gXStMrLmyiP0uRHW8p9wh6CweFSgs46K8KRCyzTzCj5UFs1fPff7w163a9f5m1TybVGq67WiPnt\nW5ODRN9ee6WeOzrqOY8ZAx06hK9rZF3ejKmHDgBqXovovRi8N09lMcUg7Ue9qvaImM+TgD877Gog\n2KqtNV5t3mq3nJzu73MIsEZEGgHNVHWdiKwGygP7tAFmAuuB5iLSwNUmtnZ5pDr+akINZ/Zsb+7i\n8vJyyjON7GvyqmvX1AF5fTVgAIwbF74u2Ht5xAjYuhVGjcr+GM2be9Mm5jpX9NVXp15XV2oSKyoq\nqKioiLsYxhhTJ9W4PkBE2quqP/lZX2CRW54EPCki9+C9Am4PzFNVFZFNIlIGzMN7TT0msM8AvNfU\nFwAvufTpwCgRaY5XO9gDGOzymgVcCExw+z4fyOsqYLyInIj3WjrFq+bhnHKKFyTWBVOnerNUFFox\ntBWM4gc/gE6d4i5Fdh57zAsSk69x8hA3N90Er71WsyBx+XKvpi+fs/EkS1eTWEz/fpK//Nn8r3Wf\ntU8rPXbP45PLS6PbROTbwE7gPeDnAKq6REQmAkuAHcAg1V2PjUHAY0ATYIqqTnXpDwNPiMhyYB2u\nQ4qqrheRWwB/ro0RficWYDBeIDgSWOjyQFWniEgf12FmM7XzCrxWRBlCp1BOPjk/0/bl08svx12C\n/PnWt2q23/jx3oDSQZlmXsnHK3Z73WziYoFC6bF7Hp9cejdfkGbdKKBaHYiqLgA6hqRvBS5KTnfr\nHgUeDUn/AChLsc9VKQuepK62SSuksJqgrl2rDxRtCitKjdzhh3s/+c43naefDp9FxhhjTP1i9QHG\n1GOFCObOPz//eRpjjCk+JR8kWk1idQeG9Wc3eRWlNm/PPXM7xpo1Xi/n2lZMbRJN/WPt00qP3fP4\nlHyQaKrauTP6bB71QTF/SejUCd5/v+b7H3RQeHoxn7MxmRQ6UPjqq6/QHL7p5LKvCWfBYXxKPki0\nB2ZVpRQg1gXt2sVdAmNKy1FHHcvatZ8iUrMPw8pKe6iY+qPkg0RTuw47rDinLKxNhx6aupbPGBOv\n7dthx463gCx7hBlTD5V8kGg1ibXLekjDO+/EW2Nr/+ZNXWbt00qP3fP4lHyQaExty7VDSrG77jo4\n9ti4S2HqKwsUSo/d8/iUfAs0q1UxJr8OOaR25hg3xhhTWCVfk9i0adwlMHG56y747nfjLkXtsy9G\nxhhjoijpIPHtt+GII+IuhYnLddfFXQJjTLasfVrpsXsen5yDRBG5DrgT2F9V17u0IcAVePM6X6Oq\n0116V7y5mxvjzd18rUvfA3gc6II3d/PFqvqhWzcA+J073EhVfdyltwPGAy2ABcAlqrrdrRsD9Aa+\nBi5T1UVhZT/66FzP3pi6Z5994i6BMTVngULpsXsen5zaJIpIG6AH8GEgrQNwMdAB6AXcL7LrBddY\nYKCqtgfai0gvlz4QWOfS/wCMdnm1AG4CTnA/w0SkmdtnNHC32+cLlwci0gc4wqX/zB2zTquoqIi7\nCJFYOfOrEOX84AM455y8Z1tnrqkxxpjocu24cg9wfVJaX+ApVd2uqiuBFUCZiBwE7K2q89x2jwP+\n4+psYJxbfgbo7pbPAKar6gZV3QDMAHq7oLMb8LTbblwgr75+Xqo6F2guIgWYwbb21JUHsJUzvwpR\nzrZtC9Mmsa5cU2OMMdHVOEgUkb7AKlV9K2lVK2BV4O9VwMEh6atdOu73xwCqugPYKCL7pcmrBbBB\nVStD8mrl5xXYp3W252eMMab4jBgxYlcbNVMa7J7HJ22bRBGZARwYsup3wBCgZ3DzPJYrnSgTYyaX\nxSbTNMZkRUQex3sr8q+4y2ISrH1a6bF7Hp+0QaKq9ghLF5HvAu2AN11zw9bAAhEpw6vVaxPYvDVe\nbd5qqtbo+em4dYcAa0SkEdBMVdeJyGqgPLBPG2AmsB7vNXIDV5vY2uXh55V8/NWEkDo0Fkhd+RZl\n5cyvulJOqFtljehK4GIRmQC8BjykqptjLpMxxtSaGvVuVtW3gV3t/ETkA6Crqq4XkUnAkyJyD94r\n4CZlpXIAACAASURBVPbAPFVVEdnkAsl5wCXAGJfFJGAAMAe4AHjJpU8HRolIc7zawR7AYJfXLOBC\nYILb9/lAXlcB40XkRLzX0mtDzqHuRIjGmDjsBxwGbATWAo/gdcozxpiSkK9xEne9zlXVJSIyEVgC\n7AAGqaq/fhDeEDhN8IbAmerSHwaeEJHleEPg9HN5rReRW4DX3XYjXAcWgMF4geBIYKHLA1WdIiJ9\nRGQFsBm4PE/naIwpLdcB96vqewAi8nGG7U0tsDHzSo/d8/hIIn4zxhjjE5Efqupkt3ymqr4Qd5mC\nRETt8zv/WrY8nM8+mw4cHndRUvBfghXjvZ9KWdm9zJkzNfOmJmsiUutvQUty7mYR6SUiS0VkuYgM\njqkMK0XkLRFZJCLzXFoLEZkhIstEZLp7ze5vP8SVd6mI9AykdxWRxW7dfXko1yMislZEFgfS8lYu\nEdlDRCa49DkicmgeyzlcRFa5a7pIRHoXQTnbiMgsEXlHRN4WkWtcejFe01RlLarrKiKNRWSuiLwh\nIktE5DaXntdrCtzplxM4M9tyGmNMnaeqJfUDNMQbu7EtsBvwBvCdGMrxAdAiKe0O4Hq3PBi43S13\ncOXczZV7BYla4HnACW55CtArx3KdAnQGFheiXHhNDu53yxcD4/NYzmHAr0O2jbOcBwKd3PJewH+A\n7xTpNU1V1mK8rk3d70Z4bZlPLsA1XYo3ZuvNwPu5/L8qxA+gJv++9a3DFFYoaJH+4H7iLkfYz7+0\nrOyMuG9hveX+z9fq50wp1iSeAKxQ1ZXqTeM3Hm8A7jgkVxsHBxVPHiA82wHKa0RVZ+PNYFOocqUa\nOD0f5YTwoZjiLOenqvqGW/4KeBevQ1cxXtNUZYXiu65fu8Xd8b74fUH+r+kg4EjgM8AmMywSNmZe\n6bF7Hp98dVypS3YN3O2sAspiKIcCL4rITuAvqvpXoKUmemKvJdGDvBVebYnPH1R8O6kHKM+nfJar\nysDpIrJRRFqom/c7D64WkUuB+cB16nV0KopyikhbvNrPuRT5NQ2UdQ5wEkV2XUWkAV6HtcOBsar6\njojk+5oCNAP28A6Z13+npoas80LpsXsen1KsSdS4C+CcpKqdgd7AL0TklOBKv2o5lpKlUazlcsbi\njd/ZCfgEuDve4iSIyF54NWfXquqXwXXFdk1dWZ/GK+tXFOF1VdVKVe2ENw7qD0SkW9L6fFzTnwH/\nxHvb8FWOeRljTJ1TikFi8mDbbaham1ArVPUT9/tz4Dm81+BrReRAAPcq7DO3eTYDlIcOHJ6jfJQr\neeB0JDFwel5qZ1T1s0DbjYfwrmns5RSR3fACxCdU1R/PsyivaaCs/+uXtVivqyvbRuAFoCv5v6Zr\n1RsT9j28NpBWi2iMKSmlGCTOB9qLSFsR2R2v8fyk2iyAiDQVkb3d8p540xsuJjGoOFQfILyfiOwu\nIu1IDFD+KbBJRMpERPAGKH+e/MtHuf4Rkldw4PScucDAdy7eNY21nC7fh4ElqnpvYFXRXdNUZS22\n6yoi+/s9l0WkCd4g+4vI/zXtKyKTgVeBLdmW0xSGtU8rPXbPY1TbPWWK4QfvFe9/8BqwD4nh+O3w\nelu+AbztlwFoAbwILMObbaZ5YJ+hrrxLgTMC6V3xHtorgDF5KNtTwBpgG17bscvzWS689l0TgeV4\n7cTa5qmcV+B1PHgLeBMvQGhZBOU8Gah093qR++lVpNc0rKy9i+26Ah3x2iO+4cr123z//3HlfBb4\nyJXzxAjlaozX3vQNvMkEbguUa0aKcg1x12Ip0DOkXMuB+1IcT03+We/mXH6sd3MhEUPvZhtM2xhj\nQojIX4FtqvoLEblfVQdF2Kepqn7tXqW/CvwGr6f0f1X1DvHGZd1XVW8QkQ7Ak8DxeB1lXgTaq6qK\nN3bqVao6T0Sm4AWwU5OOpfb5nX82mHYubDDtQhIbTNsYY4rGV3i9pCHi62Yt/NA8xhhTayxINMaY\ncP8Fvi8id+O9hs9IRBqIyBt4weUsVX2H9MMdBTvN+UPzJKcXamirOsnap5Ueu+fxKcVxEo0xJiNV\nvVVEjgIaqOqSiPtUAp1EpBkwLWxoHhHJ23vC4cOH71ouLy+nvLw8X1kXLRszr/SU6j2vqKigoqIi\n1jJYkGiMMSFE5Cm32MS1BYr8yldVN4pIlaF5VPXTfA9tFQwSjTH1S/IXvzhqU+11szHGhFDVH6nq\nj/CG/Xkl0/YFHpqnEENbGWNMWlaTaIwxIUTkaLwupLsBR0fY5SBgnJsysAHe4OkvicgiYKKIDARW\nAhcBqOoSEZmIN1zODmBQoLvyIOAxoAkwJblncynza1NK9RVkKbJ7Hh8bAscYY0KIiP9E2gr8S1Xf\njLM8yWwInMKwIXByYUPgFFIcQ+BYTaIxxoSbH1huLSKtVfWF2EpjjDG1zIJEY4wJ91Pg//CqbE7G\n2gUaY0qMBYnGGBNuqareBSAiB6jquEw7mMKz9mmlx+55fCxINMaYFETkYbyaxLWZtjW1wwKF0mP3\nPD4WJBpjTLjf4Y1RuAGv84oxxpQUGyfRGGPC3QsMU9VNwB/jLowxxtQ2CxKNMSZcJfChW94QZ0FM\ngs3jW3rsnsfHXjcbY0y4rUAHEbka2DfuwhiPtU8rPXbP42NBojHGJHHT4T0N7I83evH98ZbIGGNq\nnwWJxhiTRFVVRLqp6h1xl8UYY+JiQaIxxiQRkb5AXxE5A1gPoKoXxlsqAzZmXimyex6fkg0SRaQY\nJ740xhRYxLlPe6nqSSIyVlV/XvBCmcgsUCg9ds/jU9K9m1W1XvwMGzYs9jLYudTfc6kv56Ga1ffC\nQ0TkTPe7j4j0KdDHkDHGFK2SrUk0xpg0/o7XaWUicEDMZTHGmFhYkGiMMUlU9bG4y2DCWfu00mP3\nPD4WJNYD5eXlcRchb+xcik99OQ9TP1igUHrsnsdHsmynU2+IiJbquRtTqkQEjdZxpejZZ1hhtGx5\nOJ99Nh04PO6ipOD/8y3Gez+VsrJ7mTNnatwFqZfi+Pwq6Y4rxhhjjDEmXJ0LEkXkERFZKyKL02wz\nRkSWi8ibItK5NstnjDGmcGwe39Jj9zw+dbFN4qPAH4HHw1a6oSqOUNX2IlIGjAVOrMXyGWOMKRBr\nn1Z67J7Hp87VJKrqbOCLNJucDYxz284FmotIy9oomzHGGGNMfVHngsQIDgY+Dvy9CmgdU1mMMcYY\nY+qk+hgkQqL7l68Yu4EZY4zJkrVPKz12z+NTF9skZrIaaBP4u7VLq2b48OG7lsvLy208OGPqmYqK\nCioqKuIuhskja59Weuyex6dOjpMoIm2ByaraMWRdH+AqVe0jIicC96pqtY4rNsaYMaXHxkk0mdg4\nibmwcRILKY7PrzpXkygiT/3/9u49TKrq3PP497XFG9EgOsEIHDWR42WCIhohXqBNPLG9oMxoFDLJ\n8caMRjGOJhGJ84QmPnrAHOMlGuVoTtAk3mKioyeIkUdqOMmoeAFFuchFRmgiKkaNILfDO3/sVd2b\nrqruprqqdu/av8/z7Kd37UuttWrt2vvttdbeBYwE9jWzVcAkoBeAu09z9xlmdpqZLQPWAxcml1sR\nERGRdEpdkOjuY7uwzfha5EVERGpLv+ObParz5KSyu7kSOuuqmT59OuvXr+fyyy/v9L3uu+8+vvnN\nb9KrV6+i65cuXco3vvENlixZwrp169hjjz3KzreIlE/dzdIZdTd3h7qbq0k/y9eDmHW9HqZPn87m\nzZtLrh8wYABz5sxh+PDqPtM7fsHQxUNERES6Q0FiB2bNmsXpp5/OiBEjWLNmDRAFhCNGjOD4449n\n9uzZPPfcc8yfP59TTz2VW265hVmzZtHY2Mixxx7L1KlTAdh9993Za6+9Sqbz+uuv09jYyHHHHccV\nV1wBREHe5ZdfzogRI/jqV7/K+++/z4IFCzjxxBM54YQTmDJlChDdoX3BBRdw+umn89prrzFixAjG\njBnTmraIiIhIOVI3JrFW3J3evXvz2GOP8fTTTzN16lQmTZrEww8/zJw5c1i/fj1nnHEGs2fPZsiQ\nIfzhD39gjz324NNPPyWXy7Ft2zaGDx/OlVdeyW677dZhWgcffHDrYzpGjx7NsmXLWLhwIQ0NDcyZ\nM6c1PxdddBH33nsvhxxyCKeccgpjx47FzDjggAOYPn06K1euZM2aNTz77LPsvLOqVkTqj8anZY/q\nPDmKJEowM4YOHQrAMcccw2233cby5ct54403OOmkkwB4//33C/Z76aWX+PGPf8yWLVtYuXIl7733\nHgMHDizYLm7FihV8//vfZ8OGDaxYsYI1a9awePFiRo4cuV1+3nnnHQ455BAAhg4dyvLly1vzl3fk\nkUcqQBSRuqVAIXtU58lRd3MJ7s68efOAKPAbNGgQX/jCFzjiiCOYPXs2s2fPbl3fq1cvtm7dCsBP\nfvITpk2bxrPPPkv//v0LxgYWGyt49913873vfY9cLsdRRx2Fu3PYYYe1tiICbNu2jX79+rF48WLc\nnVdeeYUvfjEaWL3TTm3VGJ8XERERKZeanEowMzZv3sypp57K+vXrefDBB9lnn30YM2YMI0eOpKGh\ngcGDB3Pbbbdx5plncu6553L22Wdz9tlnM3r0aAYPHtw6DvHDDz/knHPO4dVXX2XUqFFcc801NDU1\ntaY1atQorrzySg499FDcHTNj1KhRzJw5kxNPPJFevXrxyCOPcMMNNzBu3DjcnTPOOIMDDjigNa/5\nvztyw42IiIhIKXoEjohkhh6Bk37VHp+mR+B0R3UegaMxiZEkzl8KEkUkMxQkSmcUJHaHnpNYTXpO\nooiIiIj0CAoSRURERKSAgkQREUmNyZMnt45Rk2xQnSdHYxJFJDM0JlE6ozGJ3aExidWkMYkiIiIi\n0iMoSBQRERGRAgoSRUQkNTQ+LXtU58nRmEQRyQyNSZTOaExid2hMYjVpTGIXmVmTmS02s6VmNqHI\n+n3NbKaZzTez183sggSyKSIiIpJaqQsSzawBuANoAg4HxprZYe02Gw/Mc/chQCNws5npd6pFRERE\nuih1QSJwLLDM3Ve6+xbgIeCsdtv8BdgrzO8FrHP3rTXMo4hkjJkNNLPZZvZG6MH4blje18yeMbM3\nzeyPZtYnts/E0COy2My+Hlt+tJktCOtuS6I8PZXGp2WP6jw5aWxd6w+sir1eDQxrt809wLNmtgbY\nEzi3RnkTkezaAlzl7vPN7DPAy2b2DHAh8Iy73xSGx1wLXGtmhwPnEfWI9AdmmdmgMNDwLuBid59r\nZjPMrMndNdALmDRpUtJZkBpTnScnjS2JXRmt+0NgvrvvDwwB7jSzPaubLRHJMnd/x93nh/lPgEVE\nwd+ZwH1hs/uA0WH+LOBBd9/i7iuBZcAwM/s8sKe7zw3b3R/bR0SkZtLYktgCDIy9HkjUmhh3HHAD\ngLsvN7O3gEOAl+IbNTc3t843NjbS2NhY+dyKSGJyuRy5XK7m6ZrZgcBRwAtAP3dfG1atBfqF+f2B\n52O7rSYKKrew/TmtJSwXEampNAaJLwGDwkl4DVF3zdh22ywGTgb+bGb9iALEFe3fKB4kikj9af/P\nXy3GNYWu5t8BV7r738zanljh7m5mPfHZJamRr0N1QWaH6jw5qQsS3X2rmY0HngYagF+4+yIzuySs\nnwbcCPzSzF4l6lK/xt0/SCzTIpIJZtaLKED8lbs/HhavNbP93P2d0JX8bljevldkAFELYkuYjy9v\nKZZeFntDFChkT1brPKmekDg9TFtEMqOaD6O1qMnwPqKnKVwVW35TWDbVzK4F+rh7/saVB4ie2NAf\nmAUcHFobXwC+C8wF/gDc3v7GFZ3DqkMP0+4OPUy7mpJ4mHbqWhJFRHqo44FvAa+Z2bywbCIwBXjE\nzC4GVhKetuDuC83sEWAhsBW4LBb1XQZMB3YHZujOZhFJgoJEEZEKcPc/UfqJESeX2OdGouEx7Ze/\nDAyuXO7qh8anZY/qPDnqbhaRzNBvN0tn1N3cHepurib9drOIiIik1gsvPI2ZlT2NGfOPSRdBYtTd\nLCIideOEE07m5Zdf6nzDEjZu/LiCucmaJrrXwnk/mzbNqlRmpAIUJIqISGp0Nj7t/fc/YePG3wJf\n7kYq+oGunkRjEpOjIFFERFKja4HCnkCfamdFakTBYXI0JlFERERECihIFBEREZECChJFRCQ1Jk+e\nXJPf4JaeQ3WeHI1JFBGR1ND4tOxRnSdHLYkiIiIiUkBBooiIiIgUUJAoIiKpofFp2aM6T47GJIqI\nSGpofFr2qM6To5ZEERERESmQyiDRzJrMbLGZLTWzCSW2aTSzeWb2upnlapxFERERkVRLXZBoZg3A\nHUS/JH44MNbMDmu3TR/gTmCUu38JOKej92xubq5OZkVEpKI0Pi17VOfJMXdPOg87xMy+Akxy96bw\n+loAd58S2+YyYD93/1EH7+P5spsZafscRGTHhe+6JZ2PSoifw6TNoYcOZ8mSW4HhSWelSvKHbz3W\n/f2MHj2Lxx67P+mM9EhJnL9S15II9AdWxV6vDsviBgF9zWy2mb1kZt+uWe5ERERE6kAa727uyr9P\nvYChwNeAPYDnzOx5d19a1ZyJiIiI1Ik0BoktwMDY64FErYlxq4D33f1T4FMzmwMcCWwXJMbHIuZy\nORobG6uQXRFJSi6XI5fLJZ0NqaD82DQ9FiU7VOfJSeOYxJ2BJUSthGuAucBYd18U2+ZQoptbTgF2\nBV4AznP3hbFtNCZRJGM0JrH+aUximmlMYkeSOH+lriXR3bea2XjgaaAB+IW7LzKzS8L6ae6+2Mxm\nAq8B24B74gGiiIiIiHQsdUEigLs/BTzVbtm0dq//GfjnWuZLREREpF6k8e5mERHJKD0zL3tU58lJ\nZUuiiIhkk25eyB7VeXLUkigiIiIiBRQkioiIiEgBBYkiIpIaGp+WParz5GhMooiIpIbGp2WP6jw5\nakkUERERkQIKEkVERESkgIJEERFJDY1Pyx7VeXI0JlFERFJD49OyR3WeHLUkioiIiEgBBYkiIiIi\nUkBBooiIpIbGp2WP6jw5GpMoIiKpofFp2aM6T45aEkVERESkgIJEERERESmgIFFERFJD49OyR3We\nnFSOSTSzJuBWoAG4192nltjuy8BzwLnu/vsaZlFERKpA49OyR3WenNS1JJpZA3AH0AQcDow1s8NK\nbDcVmAlYTTMpIiIiknKpCxKBY4Fl7r7S3bcADwFnFdnuCuBR4L1aZk5ERESkHqQxSOwPrIq9Xh2W\ntTKz/kSB411hkdcmayIiUk0an5Y9qvPkpHFMYlcCvluBa93dzcwo0d3c3NzcOp/L5cjlctstE5F0\ny3+vpX5ofFr2qM6TY+7pamQzs+FAs7s3hdcTgW3xm1fMbAVtgeG+wAbgv7v7E7FtPF92M8PdW/+K\nSH0K3/G6GKMcP4dJm0MPHc6SJbcCw5POSpXkD996rPv7GT16Fo89dn/SGemRkjh/pbEl8SVgkJkd\nCKwBzgPGxjdw9y/k583sl8CT8QBRRERERDqWujGJ7r4VGA88DSwEHnb3RWZ2iZldkmzuRCSrzOxf\nzWytmS2ILetrZs+Y2Ztm9kcz6xNbN9HMlprZYjP7emz50Wa2IKy7rdbl6Ok0Pi17VOfJSV13c6Wo\nu1kke6rZXWNmJwKfAPe7++Cw7CbgfXe/ycwmAHu7+7VmdjjwAPBlohvvZgGDwjjqucB4d59rZjOA\n2919ZpH01N1chLqb00zdzR1Jors5dS2JIiI9kbv/O/DXdovPBO4L8/cBo8P8WcCD7r7F3VcCy4Bh\nZvZ5YE93nxu2uz+2j4hITSlIFBGpnn7uvjbMrwX6hfn9iR7flZd/lFf75S20e8SXiEitKEgUEamB\n0Ddcj32ENaXxadmjOk9OGu9uFhFJi7Vmtp+7vxO6kt8Ny1uAgbHtBhC1ILaE+fjyllJvHn+ua2Nj\nI42NjZXJdQ+mZ+ZlT1brvCc851VBoohI9TwBnE/0O/LnA4/Hlj9gZj8l6k4eBMwNN658bGbDgLnA\nt4HbS725Hv4vUr/a/+OXRGuqgkQRkQowsweBkcC+ZrYK+BEwBXjEzC4GVgLnArj7QjN7hOgxXluB\ny2K3Kl8GTAd2B2YUu7NZRKQWFCSKiFSAu48tserkEtvfCNxYZPnLwOAKZq2u5FtTstoFmUWq8+Qo\nSBQRkdRQoJA9qvPkKEgUERGRHmHFisXceeedZe8/ZMgQjj/++ArmKNsUJIqIiEgPcAhLlnyZ739/\nYVl7b906j0svXaEgsYIUJIqISGpofFo9G8amTcMKljY3Tw5/O6vzm4E1lc9WhilIFBGR1FBwmD2d\nB4dSLQoSRUSkx1i4cCEffPBB2ftv2PBxBXMjkm0KEktobm7Wg2pFRGrsiiuu5fnnl9Kr1z5l7b9l\nS19gz8pmSiSjFCSWMHnyZAWJIiI1tnUrbNgwFTiz6Pquj0+TeqE6T46CRBERSQ0FCtmjOk/OTkln\noBxm1mRmi81sqZlNKLL+v5nZq2b2mpn92cyOSCKfIiIiImmVuiDRzBqAO4Am4HBgrJkd1m6zFcAI\ndz8CuB74l9rmUkRERCTdUhckAscCy9x9pbtvAR4Czopv4O7PuftH4eULwIAa51FERKqguXly6xg1\nyQbVeXLSOCaxP7Aq9no1UPj0zTYXAzOqmiMREakJjU/LHtV5ctIYJHpXNzSzk4CLAP1Gj4iIiMgO\nSGOQ2AIMjL0eSNSauJ1ws8o9QJO7/7XYG8UfcZPL5SqZRxHpAXK5nL7bIiJlMvcuN8z1CGa2M7AE\n+BrRjzTOBca6+6LYNn8HPAt8y92fL/E+ni+7meHurX/jy0SkfoTvtSWdj0qIn8PqyciRZzJnzjj0\nnMRS8odv/dV9KTvy283jx6/hZz+7ufqZSkAS56/UtSS6+1YzGw88DTQAv3D3RWZ2SVg/DfgRsDdw\nl5kBbHH3Y5PKs4iIVEZ2g8PsUp0nJ3VBIoC7PwU81W7ZtNj8OGBcrfMlIiIiUi/S+AicmtJP84mI\niEgWKUjsxOTJejaTiEhPoWfmZY/qPDmp7G4WEZFs0vi07FGdJ0ctiSIiIiJSQEGiiIiIiBRQkCgi\nIqmh8WnZozpPjsYkiohIamh8WvaozpOjlkQRERERKaAgcQfomYkiIiKSFQoSd4CemSgikiyNT8se\n1XlyNCZRRERSQ+PTskd1nhy1JIqIiIhIAQWJZdL4RBEREalnChLLpPGJIiK1p/Fp2aM6T47GJIqI\nSGpofFr2qM6To5bEblK3s4iIiNQjc/ek87DDzKwJuBVoAO5196lFtrkdOBXYAFzg7vParfd82c0M\nd2/929myUutFpGcL31dLOh+VED+H1ZORI89kzpxxwJlJZ6WHyh++9Vf33XczvXvfyN5771f2O0ya\ndBXjxo2rYJ4qJ4nzV+q6m82sAbgDOBloAV40syfcfVFsm9OAg919kJkNA+4Chlc7b83NzWpZFBGp\novzYNHVBZkfX6/x81q9vYv368tJpaPgp69atK2/nOpW6lkQz+wowyd2bwutrAdx9Smybu4HZ7v5w\neL0YGOnua2PbVLwlUa2KIj2bWhKr74c/nMRvfvNY2fuvXbuSTZt+jVoSS1FLYrU0NEzghhv6MmHC\nhKSzUlQS5680jknsD6yKvV4dlnW2zYAq56tVpVoT8+8Tf79y3rsS+VELadd0t65E0m7FitW8/fZ/\n5e23f13WtGnTn4CRSRdDRADcPVUTcDZwT+z1t4CftdvmSeD42OtZwNB223hefr6ry3Zkn0mTJnm5\nOstD/r3jaRRblt+n2HadyW9XqTIlqRb5LlZXndWPVEcH34XEz2OVmOLHWk9y3nkXOdzr4JqqMhGm\npPNRf1NDwzU+ZcqUpL9CJSVx/kpjd/NwoNnbupsnAts8dvNK6G7OuftD4XXR7maYFHvnxjCJSP3I\nhSlvMq7u5qoaM+ZiHn74OODiqry/xiRmr7u5VnWu7uYiah2VdnciutlmOXAgsAswHzis3TanATPC\n/HDg+SLv08XYXcq1o62V8fnOWj07266jtMtJrxa62iIcP3bz853lv7N9Onqf7nw2ndVPreuMBP4T\nr9bUU89hakms9qSWxGpNakkscp6pdYIVyXT0aJslwDJgYlh2CXBJbJs7wvpXadfVHNbvcAWJJKk7\nwVFXg+56pyCx+hQkVntSkFitSUFi4ZS67uZK6aldNSJSPbq7ufqq3d0s2eturhV1NxdK493NIiKS\nUfod3+xRnScndQ/TFhGR7MruDSvZpTpPjloSRURERKSAgkQRERERKaDuZhGRHsjMmoBbgQbgXo89\nC7aa3n333W79fu3HH39YwdwU0nMSs6eWdf7RRx/R0tJS9v59+vShd+/eFcxRsnR3cx3I5XI0NjYm\nnY2KUFl6nnopB6Tn7mYzayB6zNfJQAvwIjDW3RfFtqnKOeyaayZy++33sssu+5bcZuvW9ey8c/EL\noTt88sn1wDkVz1ubHMn++EGS6Sd9d3OOev3szW5g991/3uE2//Efm2ho2LXous2b/8q0aXdw0UUX\nVSN7iZy/1JJYB+rpIq6y9Dz1Uo6UORZY5u4rAczsIeAsYFFHOwF88MEHvPfee2UnvG7dOjZtuppN\nmyZ2sFVzmJKSo14DlZ4vR71+9u7XsWHDdZ1s1UypY7937+oEh0lSkCgi0vP0B1bFXq8GhnVlx+nT\npzNx4vXsuuvnyko4apw8uqx9RbJsyxb4zneu4IorflDW/jvtBI8++gCnnHJKhXNWPgWJIiI9T7f6\nEnfaaW/M/r6sfc1gr73+Dfi3ktts3LiE3XZ7uczcdc/VVx/D7Nk55s0blUj6kGz5P/44+rvXXsmU\nP4myX331MQD89KcvJfrZQ8fl37btE9yPLPu9N29exJYtW8revxoyPSYx6TyISO2lZEzicKDZ3ZvC\n64nAtvjNKzqHiWRPrc9fmQ0SRUR6KjPbmejGla8Ba4C5tLtxRUSk2tTdLCLSw7j7VjMbDzxNLuAK\nWQAACH9JREFU9AicXyhAFJFaU0uiiIiIiBTI5C+umFmTmS02s6VmNiHp/HSVmQ00s9lm9oaZvW5m\n3w3L+5rZM2b2ppn90cz6JJ3XrjKzBjObZ2ZPhtepLIuZ9TGzR81skZktNLNhKS7LxHCMLTCzB8xs\n1zSUxcz+1czWmtmC2LKS+Q7lXBrOBV+vcV6/Z2bbzKxvZ/kxs6NDXSw1s9tiy3c1s4fD8ufN7IDY\nuvNDmd80s3+MLf+Zma03s01m9o6ZHRRb92cz22xmG83sO1VK/1/M7NOQ/ioz26dW6ZvZN8JrN7O3\nzewhM+sV++w/DOkvN7OjqlD2g8zshbBPa9ph3e1h+av5tIuxHbx2Veo7UebncJWZbQh1vdrarldD\nzOyj8Fn/xcz2rVL648KxttHMWszsn2qcfvw4WGlt17gk0u/ScViUu2dqIuq6WQYcCPQC5gOHJZ2v\nLuZ9P2BImP8M0Zilw4CbgGvC8gnAlKTzugNluhr4DfBEeJ3KsgD3AReF+Z2Bz6axLOF7sQLYNbx+\nGDg/DWUBTgSOAhbElhXNN3B4+O73CmVeBuxUo3wOBGYCbwF9O8hPvqdnLnBsmJ8BNIX5y4Cfh/nz\ngIfCfF9gOdAnTMuBz4Z1vwfODfP/DvwpzF8CfBzSHw1srFL6/wc4L8y/AsysVfrAoWH/14GhwF3A\npeGzXw48FT77VcDzVSj7I7HP/i7g0jB/GjAjzA/Lp13kuNnhaxfd/050pw5WhvT7EJ1TlhJdrxYD\nvw7bPRc7BqrxHfh8rB5eBE6ocfp9gB8Cf4vVca3T79JxWPIYqsVJsSdNwFfylRJeXwtcm3S+yizL\n40S/yLAY6BeW7QcsTjpvXcz/AGAWcBLwZFiWurIQXYBWFFmexrL0JfrnY2+iYPdJ4B/SUpZwco1f\nEIvmG5gITIhtNxMYXqM8/hY4gu2DxKL5IbrILYotHwPcHdtmWJjfGXgvzI8F7ortc3fYz4D3CMEw\n8PP8cQu8APwmts8nwKlVTn8CsCaB9GcTBYnDw3tMBJ6nLXidSRTgDK5i2YfTFhxMy6fd/phtd9yU\nde2im9+JCtbBi0TXq63AfmH5acAnNUj/XqJA6T/XMn3arnFPAC+H4yCJ8nd6HJaastjdXOwhtf0T\nykvZzOxAov8QXyD6wq8Nq9YC/RLK1o66BfgBsC22LI1lOQh4z8x+aWavmNk9ZtabFJbF3T8Abgbe\nJrqr9kN3f4YUliUole/9ib77eTU5D5jZWcBqd3+t3apS+Wm/vIW2fLaey9x9K/CRRd23pd6rL/Ah\ncL2ZvQ2cAnwatvkcUUtP3kfAl6qRvrvnv+/5gKGm6Rd5r/2BXWi7LqwmatU8ooplj7/X/hRekwZQ\nqFLXrh39TlSiDj4BvkhUx+bu74TlC4Ddq5W+me1kZvOBbxOd096pZfq0XePeBXYjOg5qmX779+ro\nOCwqi3c3e9IZ6C4z+wzwO+BKd/+bWdtjk9zdLQXPTzOzM4B33X2emTUW2yYtZSH6Hg0Fxrv7i2Z2\nK9F/+a3SUhYz+yLwP4laHz4Cfmtm34pvk5aytNeFfFekTGb2DFELTXvXEbUWxMc/VuOZZ/8D+KyZ\njQmv/xNR2f4C4O7XAdeFMVqXdJCXcj+PDtMHMLPrgC1Ex1gl0/8dcEiUxHbpl34yeOn0K6Ur5ehK\n2Sv+navFdzlcr8YS9Xx9Uiwb1Uo7BENDzOx6okDxhBqmfwht17iOjq1anUvLSieLLYktRGOC8gay\nfcTdo4VBpr8DfuXuj4fFa81sv7D+80T/tfR0xwFnmtlbwIPAV83sV6SzLKuJWodeDK8fJQoa30lh\nWY4B/q+7rwv/mf6eqJsrjWWB0sdT+/PAgLCs29z9H9x9cPuJaFzWQcCr4bgfALxsZv1K5Gd1WD6g\nyPJ8Gf4ulG1nojFH64BJwOOxdP83UeD/INDHzPLn/ReIxj9B1KI0KJbOZ4E3qpT+hUTdbFNp+8wr\nlX4jcFWR9J8BPiAanxV/r5Ywbabt8x8A7AW8WkbZi11fWvJpxz77+PHW1WOxUteuHflOlHsMtgAD\nY9er/0f0OKcPAA/pAhxJNP60KunH9vkc0fE+qIbpf4m2a9wYopbUWxMqf1eOw+I6G89QbxNRq89y\nopaSXUjXjSsG3A/c0m75TYSxDEQtWD3upoJOyjWStjGJqSwLMAf4+zDfHMqRurKEk9brRF0gRnRD\nzuVpKQuF46+K5pu2QeK7EAVuywmDxGuY1/iYxJL5Ibq4DQv10X7Q+l1hfgzbD1pfQRQQ7Z2fD+tm\n0Db27k+03aCRv3FkF+C/sP2NI5VMfw5R99i+ROOkLq1x+o8QBZ9H59Nn+xtXDiK6AD9fpbTzn328\n7PEbV4ZT+saVsq5dVOA70Y3P4UHC2NfY57CYMP6UaCxo+xs3KpX+SuCAUA9vAX8mejh9rdKPHwdr\ngKdqXP4dOg5LHj+1PCn2lIloQPQSoruHJiadnx3I9wlE4/fmA/PC1BQOiFnAm8Af8wdDWiaiIDF/\nd3Mqy0IUXL1I1Prwe6KWkLSW5RqiC+kCoiCxVxrKQnRBWkPUKrQKuLCjfBPddbgsnLRPSSC/KwhB\nYkf5IQpoFoR1t8eW7xpO+EvDxebA2LoLw/KlwPmx5TOADcCm8BntH1v3XPjsNgKXVyn9t0LaG4G/\nEgbg1yJ9ouBzDdE5dCtR93ev2Gf/YUh/BTC0CmU/iOhiv5ToqQG9YuvuCGm8mk+7xDGzQ9cuKvSd\nKPNzuJGoi3MTUUti/no1hGiYwWaiMYL7Vin9/xWOpfyx/oOwvFbpx4+DG2m7xiWRfpeOw2KTHqYt\nIiIiIgWyOCZRRERERDqhIFFERERECihIFBEREZECChJFREREpICCRBEREREpoCBRRERERAooSBQR\nERGRAgoSRURERKTA/wchryejkr67mQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x115794090>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SZY3CCZUViW9pY9aPKC3D/N3v8o3DzKyonFiZ9ROf+tTK5cMOyy8OM7Mi86VA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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x115130cd0>"
       ]
      }
     ],
     "prompt_number": 108
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Linear Regression \n",
      "\n",
      "# Standardize the input data to reduce autocorrelation\n",
      "mean_height = men[:,0].mean()\n",
      "mean_weight = men[:,1].mean()\n",
      "sd_height = men[:,0].std()\n",
      "sd_weight = men[:,1].std()\n",
      "men[:,0] = (men[:,0] - mean_height)/sd_height\n",
      "men[:,1] = (men[:,1] - mean_weight)/sd_weight\n",
      "\n",
      "beta0 = pymc.distributions.Normal(\"beta0\", mu=0, tau=1e-12)\n",
      "beta1 = pymc.distributions.Normal(\"beta1\", mu=0, tau=1e-12)\n",
      "tau = pymc.distributions.Gamma(\"tau\", alpha=0.001, beta=0.001)\n",
      "\n",
      "@deterministic\n",
      "def mu(beta0=beta0, beta1=beta1):\n",
      "    return beta0 + men[:,0]*beta1\n",
      "\n",
      "likelihood = pymc.distributions.Normal(\"likelihood\", mu=mu, tau=tau, value=men[:,1], observed=True)\n",
      "\n",
      "model = pymc.Model([beta0, beta1, tau])\n",
      "map_ = pymc.MAP(model)\n",
      "map_.fit()\n",
      "mcmc = pymc.MCMC(model)\n",
      "mcmc.sample(iter=40000, burn=10000)\n",
      "\n",
      "pymc.Matplot.plot(mcmc)\n",
      "\n",
      "beta0_samples = mcmc.trace('beta0')[:]\n",
      "beta1_samples = mcmc.trace('beta1')[:]\n",
      "beta0_unstd = beta0_samples*sd_weight + mean_weight - beta1_samples*sd_weight*mean_height/sd_height\n",
      "beta1_unstd = beta1_samples*sd_weight/sd_height\n",
      "\n",
      "print \"\\n\"\n",
      "print \"Unstandardized beta0 HDI: \" + \",\".join(map(str, pymc.utils.hpd(beta0_unstd , 1.- 0.95)))\n",
      "print \"Unstandardized beta1 HDI: \" + \",\".join(map(str, pymc.utils.hpd(beta1_unstd , 1.- 0.95)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 3629 of 40000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------           18%                  ] 7254 of 40000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----------       26%                  ] 10697 of 40000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     33%                  ] 13547 of 40000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  40%                  ] 16391 of 40000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------48%                  ] 19260 of 40000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------55%                  ] 22083 of 40000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------62%---               ] 24909 of 40000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------69%------            ] 27692 of 40000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------76%---------         ] 30536 of 40000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------83%-----------       ] 33414 of 40000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------90%--------------    ] 36319 of 40000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------97%----------------- ] 39189 of 40000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 40000 of 40000 complete in 6.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting beta1\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " tau\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " beta0\n",
        "\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Unstandardized beta0 HDI: -0.187313759236,0.194719066091\n",
        "Unstandardized beta1 HDI: 0.0833251532747,0.471270731396\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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18a+FP+MIat7HAamG/anAn83sMoLPtb7AjLA2bIWZDQNmAD8Grsp0zmjQJSLV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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x110adcb10>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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231OataLQeyx0jvLJfmIw+1jjx7d0zVCsuGT86P5ffrklb05ERApr1xqrOXOC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\nAGyYAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1109cbb50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ARBaLyEciUmcAbBHZT0Rmicj3IpKDG/KNMSbUHsAaEXlQRP4rIveKyLZAG1Vd\n7ZZZDbRxp3chfpzZ5cCuAfNXuPNNPbGcodJixytcpBwvEakA7gT643whvS0ik1V1ka/Yl8DF2K9E\nY0z9aQT0AC5S1bdF5Dbcy4oeVVURyfHATCbXLGeotNjxChc1ub4XsMRtmkdEHsNpsq8JvFR1Dc4v\nz0ERt2WMMelaDixXVa+nuyeBEcAqEWmrqqvcy4ifu6+vADr4lm/vrmOFO+2fHzhIV2VlZc10LBYj\nFotFfxfGmKJRVVVFVQ4GJY4aeO0KfOZ7vhzoHXGdxhgTiRtYfSYi+6jqhzit8gvcx1nAaPfvs+4i\nk4F/isjfcb7XOgGz3Vax9SLSG5gNnAHcHrRNf+BljGl4En9QZXtJNWrgZc30xphidTHwqIg0AT7G\n6U6iApgkIufidicBoKoLRWQSsBDYDFyoWjMWxIU43UlsjXOX5NT6fBPlzsb+Ky12vMJFDbwSm+c7\nEJ+ImqFK33TMfRhjGoYq91E/VPUd4JCAl/onKX8DcEPA/LlA19zWzqSr3E7g33zzDV9kOZ5b06ZN\nad68eY5rlJlyO17ZEM10gD//wiKNgA+Ao4GVOE3xwxOS672ylcA3qvq3JOtSa0AzppwIqtog+uMX\nEY3yXWoajh12aM+6dW8SnxqYyPvYx39mGjf+DRUVT2S13c2bv2fo0KE8+ugDWS1vMieS3XdYpBYv\nVd0sIhcBL+E04d+vqotE5Ffu6+NEpC3wNtAC+FFELgW6qGoGfYobY4wxDVt19Viqq8dmufQDVFe/\nntP6mPyIPGSQqk4BpiTMG+ebXkX85UhjjDEmLZYzVFrseIWzsRqNMcYULTuBlxY7XuFsyCBjjDHG\nmHpigZcxxhhjTD2xwMsYY0zRsrH/Sosdr3CW42WMMaZoWc5QabHjFc5avIwxxhhj6okFXsYYY4wx\n9cQCL2OMMUXLcoZKix2vcJFzvERkAHAbTs/196nq6IAytwMDgY3A2ao6L+p2jTHGNHyWM1Ra7HiF\ni9TiJSIVwJ3AAKALMFxEOieUOR7YW1U7ARcA2Y6HYIwxxhhT0qJeauwFLFHVZapaDTwGDEkoMxiY\nAKCqbwEtRaRNxO0aY4wxxpScqIHXrsBnvufL3XlhZVIN226MMcYAljNUaux4hYua46VplpMslzPG\nGFPGLGeotNjxChc18FoBdPA974DTopWqTHt3XoBK33TMfRhjGoYq92GMMeUrauA1B+gkIh2BlcBp\nwPCEMpMybhdJAAAgAElEQVSBi4DHRORQYJ2qrg5eXWXE6hhjileM+B9TdjnCGFN+IgVeqrpZRC4C\nXsLpTuJ+VV0kIr9yXx+nqi+KyPEisgTYAPwycq2NMcaUBS9fyC5hlQY7XuFEtTjSrURELfXLmHIi\nqGpi/mdJEhEtlu9SU1g77NCedeveJPU9ZN7HPpefmQc49dTXmTTpgRyu06Qikt13mA2SbYwxxrhW\nr17NFVf8gS1bslt+w4a1ua2QaXAs8DLGGGNc69ev58knJ/PDDzdkuYZDgR1yWSXTwFjgZYwxpmgV\nImeocePt+eGH8+ptew2J5XiFs8DLGGNM0bITeGmx4xUuas/1xhhjjDEmTRZ4GWOMMcbUEwu8jDHG\nFC0b+6+02PEKZzlexhhjipblDJUWO17hsm7xEpEdRWS6iHwoItNEpGWScg+IyGoReS/7ahpjjDHG\nlL4olxqvBqar6j7Ay+7zIA8CAyJsxxhjjDGmQYgSeA0GJrjTE4CTggqp6mvAVxG2Y4wxpkxZzlBp\nseMVLkqOVxtVXe1Orwba5KA+xhhjTA3LGSotdrzCpQy8RGQ60DbgpT/4n6iqOoNcG2OMMcaYZFIG\nXqp6TLLX3IT5tqq6SkTaAZ9Hr06lbzrmPowxDUOV+zDGmPIV5VLjZOAsYLT799no1amMvgpjTJGK\nEf9jyvJATDgb+6+02PEKFyXwuhGYJCLnAsuAoQAisgtwr6oOcp9PBI4AdhKRz4A/q+qDkWptjDGm\nLNgJvLTY8QqXdeClqmuB/gHzVwKDfM+HZ7sNY4wxxpiGxIYMMsYYY4ypJxZ45cgFFxS6Bsmde26h\na2CMMdmxfqFKix2vcDZWY45oEXemse22ha6BMfVPRJYB64EtQLWq9hKRHYHHgd1xc1NVdZ1bfgRw\njlv+ElWd5s7vCYwHmgEvquql9ftOypvlDJUWO17hrMWrDDTKY3j90EP5W7cxESkQU9XuqtrLnRc4\n1JmIdAFOA7rgDHF2l4iIu8xY4FxV7QR0EhEbAs0Yk7UGEXg1aVLoGhR3i1c+A68zzoC99srf+o2J\nSBKeJxvqbAgwUVWrVXUZsATo7fZR2FxVZ7vlHiLJ8GjGGJOOBhF4nXxyZuWvuy73dSjmwKtZs/yu\n/5Zb0i97xBH5q0cyZ5xR/9ssVoXY/wWkwAwRmSMi57vzkg11tguw3LfscmDXgPkr3PmmnljOUGmx\n4xWuQQReEydmVn7kyPTKnX568Pw+fTLbXqFddVV+19+6dfplmzbNXz2SmTAhvEwxatEi9+vcf//s\nl73kktzVo570UdXuwEDgtyLS1/+iqipOcGaK2KhRoyxvqITY8QpXlsn1knjxAdhuO/j2W2f6ggvg\nnnvgkUfg3nthm23iy+62G7zxRvy8QrR4bbMNbNyYXrlEe+wBS5fmph6ZvPdC7Keg451M797w1lv5\nq0smfvITeOml+HlTp8KALDOMBgyANr6h7H/yE5g1K/3lf/pTuP32+Hn+/5tio6r/c/+uEZFngF5A\nsqHOVgAdfIu3x2npWuFO++evCNpeZWVlzXQsFiMWi+XmjRhjikJVVRVVVVWR1xOpxUtEdhSR6SLy\noYhME5GWAWU6iMhMEVkgIu+LSFH+bv7mm9rpO+6AL790prfeum7ZTE7kyXTunN1y221XO92xY/bb\n33nn7JfNpWnT6s7r0aN2etiw+qsLQIcO4WUycf/9zt/tt8982aDP2YEHZl+XKVPinx93XPT6FOsl\ndhHZRkSau9PbAscC71E71BnED3U2GRgmIk1EZA+gEzBbVVcB60Wkt5tsfwZJhkerrKyseVjQZUzD\nE4vF4v7PsxX1UmPgHUIJqoHLVXV/4FCcJv8sw45aLeuEeLnTpAnsuGPy16OcgM4/H1auhPvuy65u\nvXs7f3ffPbvlPYnv4Zikw6Hnln+78+YFb/fYY2uncx0I1be+7sWtrbL4T7s66L+pgII+494873NZ\nRNoAr4nIfOAt4Hm3e4gbgWNE5EPgKPc5qroQmAQsBKYAF7qXIgEuBO4DPgKWqOrUen0nZc5yhkqL\nHa9wUQOvZHcI1VDVVao6353+FliEk7AaSVBLlGfiRNgl8haSCwu8Lrss+bLNmkG7dnDIIdlt2wvY\njjsufpvffRdcPt3LZlFa8bK91HjQQXVfnz8/+3qUinRbKo84InrHvEcdlfy13/wm/nmzZsHH8o9/\njLadQlDVpap6kPs4QFX/6s5fq6r9VXUfVT3W68PLfe0GVd1bVfdT1Zd88+eqalf3taJssW/ILGeo\ntNjxChc18Ep2h1AgEekIdMf5BRptwym21KQJnH02HH988jJBLSlBuVBBwoKUdu3SW082km072Z2L\nXlcPt92Wej0isMMOdZc/9NDM6hdVlEtpACNG5KYeuZLNpbghQ2qnE1vKMg2QEz/T/uUTLzcnW3ev\nXuHb/vHHzOpljDHlKjTwcnO43gt4DPaXC7tDSES2A54ELnVbvgJU+h5V6b2DJK6/Hl54wZlu2zax\nLrBgQfbrDjoBDRzo/P38c7jiiuzXnc2203FpQl/bieu59154++309svIkdDel268eXNwuVSXpnIh\nMaho2zb5+h9/vO68f/0rN/XwB6yJLZmZHq+5c9P/ARBm223hsMOc6SeeyH49/fs7N5t4l/cffbRu\nmfSOaxXx/+PGGFN+QgMvVT3GbWZPfEzGvUMIIOEOoTgi0hh4CnhEVQMTUx2VvkcsozcSv73a6Tlz\nnLu3EjVvnvl6vaTvoJPp0KHOyad1a6ioSH+dmfarFHSC807UmfRnlvgeOnRwWse6dKmdt9tudZPb\n27Rxglp/0LJlS/rbzTTwShW4bNgQ//xPf0peNujS8+DBdedFFRR0T5uWfg///hsLILhlMl2qtS2A\n2eSYebbe2slNPPBAWLMGfv7z+G1Aui1eMSzwMpmynKHSYscrXNRLjcnuEKrh3gl0P7BQVW9LfD3f\nevZ0uk4I8tOfZrauuXOzr4d3uSbRzJnZr9PjBSDZtibNmBE8/+67oWtXZ/r3v3f+eif+Hj1Sn3Sf\nfjp4nd7yJ6XR97dq+u/pwAPhwgvh8sth0qTgdYVp1Sq9baVy2ml15x1zTHxAmxg8Jd7IkY87BVMF\nbF6LcDpBXbJ9lCzw8t+Fa0w2LGeotNjxChc18Aq8Q0hEdhER90IffYBfAEeKyDz3kbexzn7zm9o7\nyWoqeWNwWS+oyJQIrF4dXi5xGT/v5JrppSgvNy2oBcN/wva6CkhnOKWjjw4vc9NNyV8LChQSg1r/\nnYoAzzyTfH2nn1438TuMtz923hlOPbXu6/7A4Mor675+663wt79lts1UN3hkYvx45+/Ysc5f//5M\nt8WrU6e68/wdniYu5+8f7Npr06pmSsmCxTLrKd8YY0JFCryS3SGkqitVdZA7/bqqbuXeXdTdfSS9\nHTvq5Z+77qr7q7xx4+Cyv/tddtsQSa8fLK+Xdn8nlf7cqGx4AUZY4KUK33+f3SXVTKXTQpNOmV/8\nwvl7wAHOcYT0A9PE/ZF4N6B/+0GXHS+7DM48M71teSZNgk8+Se+9ee9jwYLw8v4gMajsvffWnZd4\nefvss+Gvf619nrh//IFwlL7SvPeVrMVr8uTs122MMQ1R0Q0ZlHi34rRptZ1Q+v3yl5mtN+jk0rx5\n5t1OHH88/Oxn6ZXdaafaae8E5SU7R7mctO++zuWrxHUknnyDhufZd9/4+mTi3/+GF1+sO99fj8RW\no3bt4vd9qu0+/HDdeYmtl8kkBhbjxtXeXAHxgXIu+oB79FGnVTHZZexk/Jcck0kMoP1atw7uhiNM\nOsc7m89Ey5bwn/8kf19RcsuMAcsZKjV2vMIV3ddiUMeeQWMmXnIJ/P3v6a83236zwLkjzrsr7oUX\nUndT4Rd0Ijv88Ozr4QUhixcH50iNHQuzZ6deh5cUn+5J1n/i79cPunevW8bf2pH4+rJlTkDlrWfg\nwLrB29Spye+mPOEEeO652ufeOJtvvx1fLuwE36ULLFrkjBhwxhm1wyUlG48zleeecxLMvZbUdILo\nTHKdwtbnvf7AA+mvM18BUN++zs0r55+f/O5WY6KwnKHSYscrXNEHXpD8RHTMMel33BilhWnoUOcR\nxbnnwvDh6dfn/PPrznv11fjniftq553DA8xME8ijXkZs0gQa+UYEbdSotusNz3HHpdcS5Hfwwc7f\nfv2cv+ncSbrffrBwoROEeJ2YJgYkqYb28fb3CScEv56Yx+bXujX88EP8vGSjD/jfS6ocPX+Qe8EF\nTkCZTLJAu1275H3ApRq9wcsp818SzuRuXmOMKVdFF3il88v8lFOcvwccAC+/XDs/VY/g9T2m3P77\n17ZQicB558E//5l+fe65J3wbydZRUQHdugWX9y5/pmrx8gd46ew3f4tXsktvudr/iTlr//638zdX\nLTqJHc369emTetmwVsTEIMpryUsMfO68s3bEgRYtaucntnL6LzlefrnTZUWy/ezVLXFbK1fWttwl\n1j9VK52Xt5iLcUuNMaacFF3gFXQpK/Fk8uSTma+3vgOv996LD7TStc02TseXUXz3HYwenf3y/ryq\n7t1hQMg9qP7Aq2PH1Pt6t90yr49/fZdf7lwyTJSrwMsfbCRehtxvv9TLZhuE9O/v/PXeZ+vWtd2P\n/OEP8MEH8eWz+Sx7++f88+H558PLn3FG6v8zf/6in9dSu+eewV1rQHafAVO+LGeotNjxCtcovEj9\n8U4oF1zg5K+cc07u1h120sy1dFo/Djig7vxLL4Ubboi27WR3cfp59bv55tTlWrWCKVNSl8nkcqR/\nOJxsNG0afCyDLnNFvUzqP4aVlbB8efj6MuG1ZqX6rDRrBvvsE31b3jZatoRBg+q+PmNGfGtY797Z\n9Wt2zz3OckcdVRtQGhOF5QuVFjte4Yoq8PLzt5x4J9VGjbJP4D3xRGedy5bloHI5UFHhtIoVcvuf\nfpqbwcTzPU5fOgFUJr32hznuuPh+rgBGjYrvnsEvsU+2ESOcoaOC7sYFp+f/Tz91cry+TTJ4VhBv\n/WH744kn4nP9rrgifMzNoL7cMukmwy/sh0M6fcsZY0xDVbSBl1+TJk6fVAsWZDY8TaJkScTZ2nln\n5wSbS+l0Zuq5555orTCpLvlcdVVt1xdhctWPV5hUger++0dfv2fqVCegSAwqrrwSLroofPkbboA7\n7kj+un/IHf9l5Ww79E2U2N3JLbdkt558XJ5ftMh5z3a50RhTrrIOvERkR+BxYHdgGTDU60DVV6YZ\n8G+gKdAE+Jeqjkhn/YkdjTZtWnccu8TyQflhfo1yHGauWOFcukkcMzBbJ5+cWeCVbh9X2UjW23+Q\nfLd4eYIuzaaS68ChoiK4Q1ovQAtq/Ul1w4dffecgpiPbFq9U6vuSvyl9Xr6QXcIqDXa8wkUJRa4G\npqvqTSJylfv8an8BVf1eRI5U1Y0i0gh4XUQOV9XXU604m5PQkiXht7MHnSSeegq++sqZ7tkTvvwy\n/W02apTb/pGSncT22cepW7EqxqAhXaecAv/7X/LXu3eHefPSW9dee9Wdl06+Xabqa3+Hbee882ws\nRpN/dgIvLXa8wkUJvAYD3khsE4AqEgIvAFXd6E42ASqAtRG2mVRQL+3p8Oe+zJiR+UktlyfBZIHX\n4YcnzxcqBl7Am2q4p3wGC6NGJR+EPMxJJyUfsFvECXrDAi/vvfl77c9HNwvp5njVl6Chi4wxxqQW\npb2mjap6Q0WvBtoEFRKRrURkvltmpqoujLDNvGrSJPsALgovMby++kQ68MDwLiIy4QUu2dwFlwuV\nldG74EgmkyAnH61bhbTbbs6Yj8YYY3InZYuXiEwH2ga89Af/E1VVEQk8Ranqj8BBIrI98JKIxFS1\nKqhsZWVlzXQsFiMWi6WqXoPx1FPBQdeVV8JNN+V+e/Pn53Z9jRo5rUKp8pkuvdQJ+LJRqBaeKIFw\nPoPoffd1unvIJ1XnR8iDD+ZyrVVUVlblcoWmDFjOUGmx4xUuZeClqscke01EVotIW1VdJSLtgJT3\n96nq1yLyAnAwzmXJOvyBVzlKPFmPHp2fwCsfwgZuTnVJL19yEbBlu44OHaJv2++GG+DII53pHXeE\nN990pmfNcsZKLA0xKitjADjfzdbJoglnJ/DSYscrXJRLjZOBs9zps4BnEwuISCsRaelObw0cA6SZ\nqlx+bPiVhmPw4Mz66AozYkRwX1yHHlo8OV/JFOLyvTHGFKsogdeNwDEi8iFwlPscEdnFbdkC2AV4\nxc3xegt4TlVfDlxbPSj2wKbY61co2QYW7drlth7JJKtfvvLOSs3nn8PYsYWuhTHGFIes72pU1bVA\nnUFBVHUlMMidfhdI0ftW6dt55/z2Y9W3b+q7BU1yBx8MP/wQbR3F3ppUClq0cMZwPOKI2nnHHw8v\nvli4OpnSYTlDpcWOV7iS6Lm+mL35ZvbDGCUKavF69dXcrLtcRRmeplxbIDt3Ds/Zy1RFhbNezwsv\nlO/+NZmxE3hpseMVrqwCr/79c9861bp16tfvuSe8R31Pm8AOOUwhlWOL18Ki7fDFGGNKX1kFXv4O\nLuvL+eenV27FCthpp/zWxWQm3RYZa7kxxhiTrrIKvIrZLrsUugbFq5CtTvU1ALgxJpjlDJUWO17h\nLPAyxhhTtOwEXlrseIXL4RDPxjQsIs4decYYY0yuWOBlTBLbbgu33w4ffFDomhhjjGkosr7UKCI7\nAo8DuwPLgKGqui5J2QpgDrBcVU/MdpvG1JcFC5xBorfbDpo3T13WcryMyR/LGSotdrzCRcnxuhqY\nrqo3ichV7vOrk5S9FFgIhJzCjKmrEIFNly71v01jTF12Ai8tdrzCRbnUOBiY4E5PAAKHQBaR9sDx\nwH2A3XhvjDHGmLIVJfBqo6qr3enVQLLuP28Ffg/kcWAdY4wxxpjil/JSo4hMB9oGvPQH/xNVVRGp\nc0FIRE4APlfVeSISi1JRU74sh8qY8mU5Q6XFjle4lIGXqh6T7DURWS0ibVV1lYi0Az4PKHYYMFhE\njgeaAS1E5CFVPTNonZWVlTXTsViMWCwW/g6MKbCbb4Zvvil0LYpfVVUVVVVVha6GKTF2Ai8tdrzC\niWbZnCAiNwFfqupoEbkaaKmqyZLrEZEjgN8lu6tRRDTbupiG7amn4Gc/s5avhkZEUNUGkfdp318N\nx0cffUSPHsfz7bcf5XEr3sc+l5+ZBzj11NeZNOmBHK7TpJLtd1iUHK8bgWNE5EPgKPc5IrKLiLyQ\nZBn7ZjIZO+AAaNq00LUwxhhjosu6OwlVXQv0D5i/EhgUMP/fwL+z3Z4pX/vuC99/X+haGGMKwXKG\nSosdr3A2VqMxpsFK7Lw5VcfPIjICOAfYAlyiqtPc+T2B8Th5qi+q6qX1/T7KmZ3AS4sdr3A2ZJAx\npiHzOm/20hy8jp/3AV52nyMiXYDTgC7AAOAuEfFyN8YC56pqJ6CTiAyox/obYxoYC7yMMQ1Sks6b\nk3X8PASYqKrVqroMWAL0du/Ybq6qs91yD5Gks2hjjEmHBV7GmIYqqPPmZB0/7wIs95VbDuwaMH+F\nO9/Uk2uuuaYmb8gUPzte4SzHyxjT4KTTeXOyjp+zZf0Q5oflDJWWhny8ctUXoQVexpiGKKjz5oeB\nZB0/rwA6+JZvj9PStcKd9s9fEbRBf+BljGl4En9QZduyZ5cajTENjqqOVNUOqroHMAx4RVXPACYD\nZ7nFzgKedacnA8NEpImI7AF0Amar6ipgvYj0dpPtz/AtY4wxGbMWL2NMOfAuKd4ITBKRc3G7kwBQ\n1YUiMgnnDsjNwIW+rugvxOlOYmuc7iSm1mO9y571C1Va7HiFizJkUNL+cBLKLQPW4/SNU62qvZKs\nz4bcMKaM2JBBphjZkEEmXYUYMiiwP5wACsRUtXuyoKuUlMogv6VSTyidulo9jTHGRBUl8ErWH06Q\nBvGrFkrnpFYq9YTSqavV0xhjTFRRAq9k/eEkUmCGiMwRkfMjbM8YY0yZsX6hSosdr3Apk+tFZDrQ\nNuClP/ifhPSH00dV/ycirYHpIrJYVV/LrrrGmHIlIg/h9C4/pdB1MfXHkrTT99RTj7DtttnddNuh\nw24sXjw/ch3seIWLkly/GCd3y+sPZ6aq7heyzCjgW1X9W8BrlplqTJnJJDFVRJrijKc4CPgPcJ+q\nbshX3TJhyfUNR+km1/8AZPvv8CmtWp3MmjVLc1ifhi/b5Poo3Ul4/eGMJr4/HH+ltgEqVPUbEdkW\nOBYIbINsKHc3GWPyZidgT+BrnPSGB3ACMWMMTd1HNr7OZUVMiCiBV2B/OCKyC3Cvqg7CuUz5tNPv\nII2AR1V1WqQaG2PK1RXAXar6MYCIfFbg+ph6YP1ClRY7XuGyvtRojDH1SUROVNXn3OlBqvpCoevk\nsUuNDUfpXmqMYimtWh1llxozVIh+vHJCRAaIyGIR+UhEripQHZaJyLsiMk9EZrvzdhSR6SLyoYhM\nE5GWvvIj3PouFpFjffN7ish77mtjclCvB0RktYi855uXs3qJSFMRedyd/6aI7J7julaKyHJ3v84T\nkYGFrquIdBCRmSKyQETeF5FL3PlFtV9T1LOo9qmINBORt0RkvogsFJG/uvNzvj+Bh3z17JtpXY0x\npiioasEeQAWwBOgINAbmA50LUI+lwI4J824CrnSnrwJudKe7uPVs7NZ7CbUth7OBXu70i8CAiPXq\nC3QH3stHvXCGQrnLnT4NeCzHdR0F/L+AsgWrK87l74Pc6e2AD4DOxbZfU9SzGPfpNu7fRsCbwOH5\n2J84/QVeB7wCPBjlfyvXD5ybu00D8OGHH+p22+2toHl84D7yuY1MHp9oq1YdC73rS477f5/x90Wh\nW7x6AUtUdZmqVgOPAUMKVJfE5sJkHcQOwbmlvVpVl+GcOHqLc2dnc1Wd7ZZ7iNSdyoZSp9uNr/JY\nL/+6ngKOznFdIbjz3ILVVVVXqep8d/pbYBGwK0W2X1PUE4pvn250J5vg/Jj6ivzsz0uAVcAhwGXZ\n1NWUHusXqrTY8QpX6EGydwX8CbLLgd4FqIfidPK6BRinqveSvIPYXXB+1XuW47yPanfas4LaE2Uu\n5bJeNftfVTeLyNcisqOqrs1hfS8WkTOBOcAV6oznWRR1FZGOOK10b1HE+9VXzzeBPhTZPhWRrYD/\nAnsBY1V1gYjkY3/uBjQHNuEMUTYik3qa0mRJ2qXFjle4Qrd4FUtmYR9V7Q4MBH4rInH5I16TYkFq\nlkKx1stnLLAHcBDwP6BO/22FIiLb4bTyXKqq3/hfK6b96tbzSZx6fksR7lNV/VFVDwLaA/1E5MiE\n13O1P/8f8DzwLfBMDtZnjDH1rtCB1wqgg+95B+J/9dYLVf2f+3cNzhd6L2C1iLQFcC+DfO4WT6xz\ne5w6r3Cn/fNX5KG6uajXct8yu7nragRsn8vWLlX93Hct/D6c/VrwuopIY5yg62FV9fqfK7r96qvn\nI149i3WfunX7GngB6El+9uf7wGKcnLLZGGNMCSp04DUH6CQiHUWkCU6C7+T6rICIbCMizd1pr5PX\n96jtIBbiO4idDAwTkSYisgfQCZitqquA9SLSW0QEOIOATmVzIBf1+lfAun4GvJzLironXM9PcfZr\nQevqrvd+YKGq3uZ7qaj2a7J6Fts+FZFW3h2LIrI1cAwwj/zszyNxLgt/JyJPZFpXU5osZ6i02PFK\nQzYZ+bl84Fze+wAnyXZEAba/B85dVvNxflGPcOfvCMwAPgSmAS19y4x067sYOM43vyfOiXAJcHsO\n6jYRWImT0/IZ8Mtc1gunm+NJwEc4eTcdc1jXc3ASpN8F3sE58bYpdF1x7rj70T3e89zHgGLbr0nq\nObDY9inQFSe/a75br9/n+v/HV88l7usdgfb18f2QwX5Q0zDYXY0mXWR5V6N1oGqMKQkici+wSVV/\nKyJ3qeqFha6TR6wD1QbDOlA16ZICjNVojDH16Vtquyz5rpAVMcaYbBU6x8sYY9L1BXCYiPwN5zKs\nKQOWM1Ra7HiFs0uNxpiSISL7AVup6sJC18XPLjU2HHap0aTLLjUaYxo0EZnoTm7tfuFFGhnCGGMK\nwQIvY0xJUNXhUNPVxuUFro4xxmTFAi9jTEkQkf1xrs00BvYvcHVMPfHyhWwomtJgxyuc5XgZY0qC\niHjf5D8AU1T1nULWx89yvBoOy/Ey6bIcL2NMQzfHN91eRNqr6gsFq40xxmTBAi9jTKk4D3gDp5ng\ncPIzJJcxxuSVBV7GmFKxWFVvARCR1qo6odAVMvlnOUOlxY5XOMvxMsaUBBH5K7AzTovXalX9Q4Gr\nVMNyvBoOy/Ey6bIcL2NMQ/cHoD2wDifB3hhjSo4NGWSMKRW3AaNUdT1wR6ErY4wx2bDAyxhTKn4E\nPnWn1xWyIqb+2Nh/pcWOVzjL8TLGlAQRGQ3sjnNnYzdVPb/AVaphOV7FZcaMGfztb/eQzSHZsOEb\n/vvfJWzcaDleJjXL8TLGNFjuMEFPAq1wzlp3FbZGpph98sknvPLKl2za9Kss17BdTutjjJ8FXsaY\noqeqKiJHqupNha6LKQ0VFXsBQwtdDWPqsMDLGFP0RGQIMEREjgPWAqjqqYWtlakP1i9UabHjFa5o\nAi8RKZaL3caYepJBfsQAVe0jImNV9Td5rZQpKnYCLy12vMIV1V2NqtogHqNGjSp4Hex92Hsp9keG\ndhORQe7f40Xk+Dx8BRljTN4VTYuXMcak8AROYv0koHWB62KMMVmzwMsYU/RUdXyh62AKw3KGSosd\nr3AWeOVBLBYrdBVyoqG8D7D3Um5EpBnwb6Ap0AT4l6qOEJEdgcdx+gNbBgxV1XXuMiOAc4AtwCWq\nOs2d3xMYDzQDXlTVS+v33ZQ3O4GXFjte4Yoqx6uhaCgnxobyPsDeS7lR1e+BI1X1IKAbcKSIHA5c\nDUxX1X2Al93niEgX4DSgCzAAuMvtOwxgLHCuqnYCOonIgPp9N8aYhsQCL2NMg6SqG93JJkAF8BUw\nGNdqmNEAAB8kSURBVJjgzp8AnORODwEmqmq1qi4DlgC9RaQd0FxVZ7vlHvItY4wxGYsceInIAyKy\nWkTeS1HmdhH5SETeEZHuUbdpjDFhRGQrEZkPrAZmquoCoI2qrnaLrAbauNO7AMt9iy8Hdg2Yv8Kd\nb+qJjf1XWux4hctFjteDwB04vwTrcG/73ltVO4lIb5xm+0NzsF1jjElKVX8EDhKR7YGXROTIhNc1\nl/0HVlZW1kzHYjG7JJwjljNUWhry8aqqqqKqqiryeiIHXqr6moh0TFGkpmlfVd8SkZYi4v/VaYwx\neaOqX4vIC0BPYLWItFXVVe5lxM/dYiuADr7F2uO0dK1wp/3zVwRtxx94GWMansQfVNm27NVHjteu\nwGe+58uJ/yIzxpicEpFWItLSnd4aOAaYB0wGznKLnQU8605PBoaJSBMR2QPoBMxW1VXAehHp7Sbb\nn+FbxhhjMlZf3UkkDgtiwwMZY/KpHTBBRLbC+YH5sKq+LCLzgEkici5udxIAqrpQRCYBC4HNwIVa\n273+hTjdSWyN053E1Hp9J2XO+oUqLXa8wtVH4BXUhB/aVG85EsY0LLnKj0iHqr4H9AiYvxbon2SZ\nG4AbAubPBbrmuo4mPXYCLy12vMLVR+A1GbgIeExEDgXWJcvvshwJYxquXOVHGGNMKYsceInIROAI\noJWIfAaMAhoDqOo4VX3RHdR2CbAB+GXUbRpjjDHGlKJc3NU4PI0yF0XdjjHGmPJjOUOlxY5XuJIZ\nq3H8+PFs2LCB3/72t6FlJ0yYwM9//nMaN24c+PqWLVs4//zzWbJkCT179uTWW2/NdXWNMcbkgJ3A\nS4sdr3AlM2RQ7bBp4caPH8+mTZuSvv7888/Tvn17Xn31VTZs2MCbb76ZiyrWUXtTVPy0McYYY8pT\nyQReADNmzGDQoEH069ePlStXAk6Q1a9fP/r06cPMmTOZNWsW8+fPZ+DAgdx6663MmDGDWCxGr169\nGD16NACzZs3i2GOPBWDAgAG88cYbcdt5//33icViHHbYYVx88cWAEzj99re/pV+/fhx11FF88cUX\nvPfee/Tt25fDDz+cG2+8EXBuEDj77LMZNGgQ7777Lv369WPYsGE12zbGGGNM+SqZS42qyrbbbssz\nzzzDSy+9xOjRoxk1ahSPP/54TcvVCSecwMyZMznooIN44YUX2Gabbfjuu++oqqrixx9/5NBDD+XS\nSy/lq6++onnz5gBsv/32rF27Nm5be++9d81t7yeddBJLlixh4cKFVFRU8Oqrr9bU55xzzuG+++5j\n33335bjjjmP48OGICLvvvjvjx49n2bJlrFy5kldeeYVGjUpmVxtjTNGwnKHSYscrXMlEAyJCjx5O\ntzwHH3wwY8aM4eOPP2bBggUceaQzBNsXX3xRZ7k5c+Zw7bXXUl1dzaeffsrnn39Oy5YtWb9+PQDr\n1q1jxx13jFvmk08+4Xe/+x0bN27kk08+YeXKlSxevJgjjjgirj6rVq1i3333BaBHjx58/PHHNfXz\nHHjggRZ0GWNMluwEXlrseIUrmUuNqsq8efMAJ5jq1KkTe+65J926dWPmzJnMnDmz5vXGjRuzefNm\nAG6++WbGjRvHK6+8wi677IKqcthhhzFjxgwApk2bxuGHHx63rbvvvpsrrriCqqoqunfvjqrSuXPn\nmtYugB9//JE2bdqwePFiVJX//ve/7LXXXgBstVXtbvVPG2OMMaa8lUxTjIiwadMmBg4cyIYNG5g4\ncSI77bQTw4YN44gjjqCiooKuXbsyZswYBg8ezNChQznllFM45ZRTOOmkk+jatSstWrRARDjhhBN4\n9tln6devHz169KB3795x2zrxxBO59NJL2W+//VBVRIQTTzyRqVOn0rdvXxo3bsykSZO4/vrrOe+8\n81BVTjjhBHbfffeaunp/M7kpwBhjjDENmxTL3XYiosVSF2NM/okIqtogfpnY91f+ZJMzdM8993DZ\nZXP47rt78lWtiLyPfbF8ZpbSqtVRrFmzNPKayinHK9vvsJJp8TLGGFN+yuEE3pDY8QpnCUjGGGOM\nMfXEAi9jjDHGmHpigZcxxpiidc0119TkDZniZ8crnOV4GWOMKVqWM1Ra7HiFsxYvY4wxxph6YoGX\nMcYYY0w9scDLGGNM0bKcodJixyuc5XgZY4wpWpYzVFrseIWL3OIlIgNEZLGIfCQiVwW83kpEporI\nfBF5X0TOjrpNY4wxxphSFCnwEpEK4E5gANAFGC4inROKXQTMU9WDgBjwNxGxljZjjDHGlJ2oLV69\ngCWqukxVq4HHgCEJZf4HtHCnWwBfqurmiNs1xhhTBixnqLTY8QoXteVpV+Az3/PlQO+EMvcCr4jI\nSqA5MDTiNo0xxpQJyxkqLXa8wkVt8UpnaPWRwHxV3QU4CPiHiDSPuF1jjDHGmJITtcVrBdDB97wD\nTquX32HA9QCq+rGILAX2BeYkrqyysrJmOhaLEYvFIlbPGFMsqqqqqKqqKnQ1jDGmoEQ1nUarJAs7\nSfIfAEcDK4HZwHBVXeQr83fga1W9RkTaAHOBbqq6NmFdGqUuxpjSIiKoqhS6Hrlg31/54+ULZXIJ\n65577uGyy+bw3Xf35KtaEXkf+2L5zCylVaujWLNmaeQ1ZXO8SlW232GRWrxUdbOIXAS8BFQA96vq\nIhH5lfv6OOAG4EEReQfn0uaViUGXMcYYE6QcTuANiR2vcJG7dVDVKcCUhHnjfNNfACdG3Y4xxhhj\nTKmzIYOMMcYYY+qJBV7GGGOKlvULVVrseIWzHuSNMcYULcsZKi12vMJZi5cxxhhjTD2xwMsYY4wx\npp5Y4GWMMaZoWc5QabHjFc5yvIwxxhQtyxkqLXa8wlmLlzHGGGNMPbHAyxhjjDGmnljgZYxpcESk\ng4jMFJEFIvK+iFzizt9RRKaLyIciMk1EWvqWGSEiH4nIYhE51je/p4i85742phDvp5xZzlBpseMV\nLtIg2blkg8waU17yOUi2iLQF2qrqfBHZDpgLnAT8EvhCVW8SkauAHVT1ahHpAvwTOATYFZgBdFJV\nFZHZwEWqOltEXgRuV9WpCduz768iYoNkZyp3g2SXk2y/w6zFyxjT4KjqKlWd705/CyzCCagGAxPc\nYhNwgjGAIcBEVa1W1WXAEqC3iLQDmqvqbLfcQ75ljDEmYxZ4GWMaNBHpCHQH3gLaqOpq96XVQBt3\nehdguW+x5TiBWuL8Fe58Y4zJigVexpgGy73M+BRwqap+43/NvTZYLNd6TBKWM1Ra7HiFs368jDEN\nkog0xgm6HlbVZ93Zq0Wkraquci8jfu7OXwF08C3eHqela4U77Z+/Imh7lZWVNdOxWIxYLJaDd2Gs\nX6jS0pCPV1VVFVVVVZHXY8n1xpiCyHNyveDkcH2pqpf75t/kzhstIlcDLROS63tRm1y/t5tc/xZw\nCTAbeAFLri96llyfKUuuz0a232GRW7xEZABwG1AB3KeqowPKxIBbgcY4dxTFom7XGGNS6AP8AnhX\nROa580YANwKTROT/t3f30XLU9R3H3x9yIYRACAgHJMRetKmCFRXloQXqtYDGgIB6fEgBLQGbIwe1\n4lGIPcpybKl40FIeDlIEDVoeLIiNJYhwdK1SIARJICQXiDY2AYmASrBASci3f8xsMlnu3n2YfZq9\nn9c5e+7s7Ox8f7+d2dnv/c1vfnMasAb4AEBErJT0HWAlsAk4I5NJnQF8E5gCLK5OuswGwYYNT/Ke\n93y4pfduvz1cdtlX2HPPPdtcqsGUq8VL0iTgYeBokub3e4G5EbEqs8x04E7gnRGxTtIeEfHUGOvy\nf4xmE0gnW7y6zcevzqn0F2rmFJZbvJr1LHBzy++ePPksRkeXMjw83NL2KqpetXgdAqxOL79G0vUk\nl2WvyizzV8BNEbEOYKykK6tUKm3TV8LMzCauifAD3nu7AK21dgEMDX1hy7S3V315r2qcAazNPK9c\ngp01C9g9HUV6qaRTxluhr4YwMzOzQZW3xauRdtLtgYOAo4CdgLsk3R0Rj+aMbWZmZlYoeROv6kuw\nZ7LtYIOQtIg9FRHPA89L+k/gjcDLEq/KKcZSqeTLsc0GTLsuxbaJZSL1GRoE3l715e1cP0TSuf4o\n4HGSy62rO9e/DrgUeCcwmWT06A9GxMqqdUVEVDqrtVwmMysGd663TnHn+u6aOnWYFSvKDA8P97oo\nXdWTzvURsUnSmcBtJMNJXBURqyTNT1+/IiJGJf0AeADYDFxZnXSZmZmZTQS5x/GKiFuBW6vmXVH1\n/ELgwryxzMzMzIrM92o0M7O+5Xv/FYu3V32+V6OZmfUtd9IuFm+v+tziZWZmZtYlTrzMzMzMusSJ\nl5mZ9S33GSoWb6/63MfLzMz6lvsMFYu3V31u8TIzMzPrEideZmZmZl3ixMvMzPqW+wwVi7dXfe7j\nZWZmfct9horF26s+t3iZmZmZdYkTLzMzM7MuceJlZmZ9y32GisXbqz738TIzs77lPkPF4u1Vn1u8\nzMzMzLrEiZeZmZlZl/hUo5mZ9Z3LLvsaP/nJEl7/+j8C4KGHftXwe3/xi1Ei/rRTRbNxVPp3+ZRj\nbYqIfCuQZgMXAZOAr0fEBTWWOxi4C/hARHx3jNcjIpBE3jKZWf9Lv+vqdTnaoXL8svY59ti5LF48\nDTi0xTW8Fji8jSVqp8puPxj7zNSpw6xYUWZ4eLjXRemqVo9huVq8JE0CLgWOBh4D7pW0KCJWjbHc\nBcAP2LrHmZmZjWMEmNvrQpi1Vd4+XocAqyNiTURsBK4HThhjuY8DNwJP5oxnZmZmVlh5E68ZwNrM\n83XpvC0kzSBJxi5PZw1G26qZmXVcqXQepZLHhSoKj+NVX97O9Y0kURcB50RESBLjnGoslUpb/o6M\njDAyMpKzeGbWL8rlMuVyudfFsIIpldxJu0jcqb6+XJ3rJR0GlCJidvp8AbA528Fe0i/ZmmztATwH\nfDQiFlWty53rzSYQd6638SSd649nMPt4uXP9IGj1GJb3VONSYJakYUk7AB8EtkmoIuLVEbFfROxH\n0s/rY9VJVy2VFjAzMzOzQZAr8YqITcCZwG3ASuCGiFglab6k+XkL5/PEZmYTm/t4FYv7eNWXexyv\ndhnrVKNPO5oNLp9qtPH4VGNx+FRjc3zLIDMzM7MuceJlZmZm1iVOvMzMrG+5j1exuI9Xfb5JtpmZ\n9S2P41UsHserPrd4mZmZmXWJEy8zMzOzLnHiZWYDSdLVktZLejAzb3dJt0t6RNIPJU3PvLZA0qOS\nRiW9IzP/LZIeTF/7527XY6JzH69icR+v+jyOl5n1RKfH8ZJ0JPAH4JqIeEM678vAUxHxZUlnA7tF\nxDmSDgCuBQ4GZgB3ALPSe8wuAc6MiCWSFgMXR8QPqmJ5HK828zhexeFxvJrjFi8zG0gR8VPgd1Wz\njwcWptMLgRPT6ROA6yJiY0SsAVYDh0p6JbBLRCxJl7sm8x4zs6Y58TKziWSviFifTq8H9kqn9wHW\nZZZbR9LyVT3/sXS+mVlLnHiZ2YSUnhscjHM9A8x9vIrFfbzq8zheZjaRrJe0d0Q8kZ5G/E06/zFg\nZma5fUlauh5Lp7PzHxtrxaVSacv0yMgIIyMj7Sv1BOZxvIplkMfxKpfLlMvl3Otx4mVmE8ki4CPA\nBenf72XmXyvpqySnEmcBS9LO9RskHQosAU4BLh5rxdnEy8wGT/U/VK227DnxMrOBJOk64G3AHpLW\nAl8AvgR8R9JpwBrgAwARsVLSd4CVwCbgjMxlimcA3wSmAIurr2g0M2uGEy8zG0gRUWscgqNrLH8+\ncP4Y8+8D3tDGolkTKv27fMqxGCqtQIN8yjEvJ15mZta3nHAVixOu+nJf1ShpdjrS86PpgITVr58k\nabmkByTdKenAZmO474SZmZkNglyJl6RJwKXAbOAAYK6k/asW+yXwFxFxIPBF4F+ajeNLU83MzGwQ\n5G3xOgRYHRFrImIjcD3JCNBbRMRdEfFM+vQetr0028zMrCaP41UsHservrx9vGYAazPP1wGHjrP8\nacDinDHNzGyCcB+vYnEfr/ryJl4Nj/os6e3APODwnDHNzMzMCilv4lU92vNMtr2vGQBph/orgdkR\nUX3T2i0qnehLpZJHfTYbMO0a9dnMrMi0dYzAFt4sDQEPA0cBj5OM7Dw3IlZllnkV8CPg5Ii4e5x1\nRUQgiUqZKtPZeWY2GNLvtXpdjnaoHL+sfY49di6LFx9PqfQIMGinHCu7/WDsM1OnDrNiRZnh4eEJ\nNY5Xq8ewXC1eEbFJ0pnAbcAk4KqIWCVpfvr6FSSjRe8GXC4JYGNEHJInrpmZTQyDlXANvomQcOWV\newDViLgVuLVq3hWZ6dOB0/PGMTMzMys6j1xvZmZmLdu8Gd7//nnsuONOTb9Xgs9//pMcc8wxHShZ\nf3LiZWZmfcv3aux/zz9/FUuXPg9AqXRf+vctDb138uSLWLfuZdfkDbTCJV6lUsm3EDIzmyCccBXB\nUVumSqXjmnrn0NBN7S5M38t9r8Zu84i4ZmZmVlSFS7zMzMzMisqJl5mZ9S3fq7FYvL3qK1wfLzMz\nmzjcx6tYvL3qc+JlZmYd8cUv/gMbNvyhpfeOji4Hjm9vgcz6gBMvMzPriAsvvIQNG+YBu7Tw7lOA\nA9tcIrPeK3Ti5aElzMz63SeAvVt+t8fxKhZvr/py3SS7nRq9SXataTMrFt8ke/DtuuvebNiwjDyJ\n12AarJtk5zF16qlccslfcOqpp/a6KE1r9RjmqxrNzMzMusSJl5mZmVmXDETi5X5eZmaDyeNCFYu3\nV30D0cfLfb3Misd9vAaf+3jV4j5eFe7jZWZmZmYdkzvxkjRb0qikRyWdXWOZi9PXl0t6c96YZmZm\nZkWUK/GSNAm4FJgNHADMlbR/1TJzgD+OiFnA3wCX54lZj/t7mZkNDvcZKhZvr/rytngdAqyOiDUR\nsRG4HjihapnjgYUAEXEPMF3SXjnj1nTeeZXB20pb5lWmnZSZmRVLqXSuB+MsEG+v+vImXjOAtZnn\n69J59ZbZN2fcuioJWHY6O6+IyVi9ZLKTyeZ46yvSZ2hmZtZTEdHyA3gfcGXm+cnAJVXLfB84PPP8\nDuCgMdYV6WVBUTHevHqvtzLv3HPPjX6RLUtlOu9nU1nPWOuuN2+89fXrZ9hL432u9V6v9Z52lqFd\n22ms9TRap3S/yXUM6pdH9jtgW02btlfArwPCj20epI9el6P3j6lT/zquvvrqXu+qLWn1GJZrOAlJ\nhwGliJidPl8AbI6ICzLLfA0oR8T16fNR4G0Rsb5qXQHnZuaMpA8zGwzl9FFxHuHhJAZaO4aTGMx7\n/w3ucBLNbq+JOJxE05la9kFyk+1fAMPADsAyYP+qZeYAi9Ppw4C7a6yr/eloFzX6n3+2npXpQW8l\naleLS57WubGm683rRotREXSqrrT432I/Pop+/OoUt3jVerjFq/KYiC1eTb/hZSuAdwEPA6uBBem8\n+cD8zDKXpq8vZ4zTjOkynfx8+ka7TiNZbe06zWed5cRr8DnxqvVw4lV5TMTEq+9GrjezicEj1w8+\nj1xfy+CeamzWRDzV6JHrzcysb3lcqGJpdnu9+CKcfvpHGRqa3NLjpJPmdbA2neEWLzPrCbd49b+I\nYPPmzS2/f7fd9uHZZ5fjFq9qbvHaaiPQ6j72bU488SfcfPM17SxQw1o9hg11ojBmZlZ8o6OjHHDA\nAUitnRwZwFzU2m77Hr23d5x4mZlZTbvs8jqefXZVr4thNjDcx8vMrA5JsyWNSnpU0tm9Ls9E4j5e\nxeLtVZ8Trw4ol8u9LkJbDEo9wHWx1kmaRDIkzmzgAGCupP17Wabe7APdjpnE6969/8pdiNFL5a5E\n2bq9uhMvqyjHRp9q7IByuczIyEivi5HboNQDXBfL5RBgdUSsAZB0PXAC0LPzb73ZB8p0924igx6v\n28oM4uf5+OO/4qabbgLghhtu4Omnn274vVOmTGHOnDmdKlpNTrzMzMY3A1ibeb4OOLRHZWnawoUL\n+dSnPtdSR/eXXtrIxo2vaH+hzNriVaxcuQfz5l0LwAsvrOS2215q6J2bNq3nuefu5Igjjm0p8vY5\n+vU78TIzG1/Pr8077rgTueWWf99m3nnnNdePZsqUN7cUe7vthpg27d288MLD7LjjfS2toxWVeGed\n9VYAvvrVpV2J1w0bNiR/p017d1fiQffqV9le559/bVf3l8RLwIsNLTlp0o4A/Oxnt3SwPGPrq3G8\nel0GM+uuIozjJekwoBQRs9PnC4DNEXFBZhkfv8wmoFaOYX2TeJmZ9SNJQyT3oz0KeBxYAsyNCI+x\nYGZN86lGM7NxRMQmSWcCtwGTgKucdJlZq9ziZWZmZtYlPR/Hq8gDE0qaKenHkh6StELSJ9L5u0u6\nXdIjkn4oaXqvy9oISZMk3S/p++nzotZjuqQbJa2StFLSoQWuy4J0/3pQ0rWSJhelLpKulrRe0oOZ\neTXLntb10fR48I7elLoxjW4DSWskPZB+r5Z0Ol667Dbf407Fk7SjpHskLUu/Z//YarwmYo55zO1U\nvHS5l+3HTcap+xsn6eL09eWSWrsKosF4kl4n6S5JL0j6dJ5YDcY7Ka3XA5LulHRgh+OdkMa7X9J9\nkv6yk/Eyyx0saZOk99ZdaUT07EHSbL8aGCa56dIyYP9elqnJ8u8NvCmd3pmkH8j+wJeBz6bzzwa+\n1OuyNlifs4B/BRalz4taj4XAvHR6CNi1iHVJvxe/BCanz28APlKUugBHAm8GHszMG7PsJAOTLkuP\nA8PpcWG7XtdhnLo1tA2A/wZ271a89PVtvscdrt9O6d8h4G7giE7GrHXM7XAdX7YfNxGj7m8cMAdY\nnE4fCtyd4zNsJN6ewFuBvwc+nXO/bCTenwG7ptOzu1C/qZnpN5CMwdexeJnlfgT8B/C+euvtdYvX\nloEJI2IjUBmYsBAi4omIWJZO/4FkQMUZwPEkP/6kf0/sTQkbJ2lfkgPA14HKVRpFrMeuwJERcTUk\n/XMi4hkKWBdgA7AR2ElJB++dSDp3F6IuEfFT4HdVs2uV/QTguojYGMlApatJjg/9qplt0I4rNxuK\nV+N73LF4EfFcOrkDyY/PbzsZs8Yxd59OxUvjjLUfN6qR37gt5YiIe4DpkvbqVLyIeDIilpIcW/Jq\nJN5d6TEY4B5g3w7H+9/M052BpzoZL/Vx4EbgyUZW2uvEa6yBCWf0qCy5SBom+a/oHmCviFifvrQe\naPVL1E3/BHwG2JyZV8R67Ac8Kekbkn4u6UpJUylgXSLit8BXgP8hSbh+HxG3U8C6ZNQq+z4k3/+K\nfj8WNLoNArhD0lJJH+1CvLG+xx2LJ2k7ScvSZX4cESs7HTMTe5itx9yOx2tRI79xYy3TanLS7d/U\nZuOdBizudDxJJ0paBdwKtHw6upF4kmaQJGOXp7Pqdpzv9VWNA9GzX9LOwE3AJyPiWWnrP5oREerz\nMX4kHQf8JiLulzQy1jJFqEdqCDgIODMi7pV0EXBOdoGi1EXSa4C/JWnmfgb4N0knZ5cpSl3G0kDZ\ne1ovSbeTnNqq9nfZJ3XqcXhE/FrSnsDtkkbTFpS2x2vke9zOeOlrm4E3pS3Nt0kaiYhyJ2Om69mZ\npIXhk2nLV0fj5dDoOqtbJ1stS7e/Mw3Hk/R2YB5weKfjRcT3gO9JOhL4FvDaDsa7CDgn3YdEAy3N\nvU68HgNmZp7PZNv/evuepO1Jkq5vpRsbYL2kvSPiCUmvBH7TuxI25M+B4yXNAXYEpkn6FsWrByT7\nz7qIuDd9fiOwAHiigHV5K/BfEfE0gKTvkvSXKGJdKmrtU9XHgn3TeT0TEcfUei3tbF13G0TEr9O/\nT0q6meTUxZiJVxvijfU9viYiPtyp+mXW9YykW0j22fI4y+WOmTnmfjtzzO1YvJwa+Y1r577f7d/U\nhuKlHeqvBGZHRKunbRuOVxERP5U0JOkVleNoB+K9Bbg+bXDZA3iXpI0RsajWSnt9qnEpMEvSsKQd\ngA8CNQvbb9Ls9ipgZURclHlpEUknaNK/4x4cei0iPhcRMyNiP+BDwI8i4hQKVg9I+oAAayX9STrr\naOAh4PsUrC7AKHCYpCnpvnY0sJJi1qWi1j61CPiQpB0k7QfMIhmotF/V/W5I2knSLun0VOAdQEtX\nxjUSr8b3eMykqx3xJO2h9EpASVOAY4D7W4zXaMxax9yOxGuDRn7jFgEfhi13Sfh95hRoJ+JVtKPv\nYd14kl4FfBc4OSJWdyHea9L9BEkHAbSYdDUULyJeHRH7pd+7G4GPjZd0Vd7U0wfwLpIrU1YDC3pd\nnibLfgRJX4plJAec+0mu2tgduAN4BPghML3XZW2iTm9j61WNhawH8EbgXmA5yRd+1wLX5bMkieOD\nJB1wty9KXYDrSPqmvUjST+LU8coOfC49DowC7+x1+evUbcx6kPRVuyWdfnV6bFgGrMhzfGskXtXy\nW77HHazfgcDP0/o9AHymC5/pmMfcTn6mmf34/yr7cZNxXvYbB8wH5meWuTR9fTlwUM7Pcdx4JKde\n15J0X/gdSR/SnTsY7+vA05nttaTD9fts+n27n6R1+eBOxqta9hvAe+ut0wOompmZmXVJr081mpmZ\nmU0YTrzMzMzMusSJl5mZmVmXOPEyMzMz6xInXmZmZmZd4sTLzMzMrEuceJmZmZl1iRMvMzMzsy75\nf4DgOLyR6PcRAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11288ba90>"
       ]
      }
     ],
     "prompt_number": 119
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Let's simulate some data of the height of three different populations\n",
      "\n",
      "sd = 5.3\n",
      "n = 100\n",
      "numpy.random.seed(42)\n",
      "grp1 = numpy.random.normal(177.5, sd, n)\n",
      "grp2 = numpy.random.normal(181.3, sd, n)\n",
      "data = numpy.concatenate((grp1, grp2))\n",
      "\n",
      "origin_mean = data.mean()\n",
      "origin_std = data.std(ddof=1)\n",
      "data = (data - origin_mean)/origin_std # standardize\n",
      "grp = n*[0] + n*[1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha_sd = pymc.distributions.Gamma(\"alpha_sd\", alpha=1.01005, beta=0.1005) # mode=0.1, sd=10.0\n",
      "\n",
      "alpha0 = pymc.distributions.Normal(\"alpha0\", mu=0, tau=0.001) # y values are assumed to be standardized\n",
      "alpha = pymc.distributions.Normal(\"alpha\", mu=0, tau=1/alpha_sd**2, size=len(numpy.bincount(grp)))\n",
      "\n",
      "sigma = pymc.distributions.Uniform(\"sigma\", 0, 10) # y values are assumed to be standardized\n",
      "likelihood = pymc.distributions.Normal(\"likelihood\", mu=alpha0 + alpha[grp], tau=1/sigma**2, value=data, observed=True)\n",
      "\n",
      "model = pymc.Model([alpha0, alpha, sigma, alpha_sd])\n",
      "\n",
      "map_ = pymc.MAP(model)\n",
      "map_.fit()\n",
      "\n",
      "thin = 750\n",
      "burn = 10000\n",
      "steps = 5000*thin + burn\n",
      "\n",
      "mcmc = pymc.MCMC(model)\n",
      "mcmc.sample(iter=steps, burn=burn, thin=thin)\n",
      "\n",
      "pymc.Matplot.plot(mcmc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
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       ]
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      {
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        "\r",
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      },
      {
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      {
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      {
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        "\r",
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      {
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      {
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      {
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      {
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        "\r",
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      {
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      {
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