Waving 2D Gaussian.ipynb

waving-2d-gaussian.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Waving 2D Gaussian.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyO1WWQbmYpu81jmR7HVPOo/",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/ekellbuch/94ed72c460afca011e033f623e88a8f6/waving-2d-gaussian.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uOwRrYqjq_hY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "j-i3beylrVZj",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Make a 2D variable\n",
        "N = 100\n",
        "X = np.linspace(-10, 10, N)\n",
        "Y = np.linspace(-10, 10, N)\n",
        "X, Y = np.meshgrid(X, Y)\n",
        "# Pack X and Y into a single 3-dimensional array N x N x 2\n",
        "pos = np.empty(X.shape + (2,))\n",
        "pos[:, :, 0] = X\n",
        "pos[:, :, 1] = Y\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z2yqzA0Brana",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def multivariate_gaussian(pos, mu, Sigma):\n",
        "    \"\"\"\n",
        "    Find a multivariate Gaussian distribution on pos.\n",
        "    mu : D, \n",
        "    pos: N x N x D\n",
        "    Sigma D x D\n",
        "    \"\"\"\n",
        "    n = mu.shape[0]\n",
        "    Sigma_det = np.linalg.det(Sigma)\n",
        "    Sigma_inv = np.linalg.inv(Sigma)\n",
        "    # (x-mu)T Sigma-1 (x-mu)\n",
        "    exp_factor = np.einsum('...k,kl,...l->...', pos-mu, Sigma_inv, pos-mu)\n",
        "    return np.exp(-exp_factor / 2) / np.sqrt((2*np.pi)**n * Sigma_det)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bM04svlUsUnK",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Find the distribution of the variables X, Y\n",
        "mu = np.array([0, 0])\n",
        "Sigma = np.eye(2)\n",
        "Z = multivariate_gaussian(pos, mu, Sigma)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gUjbdDBestI_",
        "colab_type": "code",
        "outputId": "02a08f21-431f-4f39-f64c-2338fa561574",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        }
      },
      "source": [
        "find_max = lambda x : np.unravel_index(np.argmax(x),(N,N))\n",
        "plt.imshow(Z)\n",
        "plt.plot(*find_max(Z)[::-1],'ro', markerfacecolor='none')\n",
        "plt.show()"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MEQVGMOarYyY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Now make it an animation\n",
        "from IPython.display import HTML\n",
        "from matplotlib import animation"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y1P5-8K_y72W",
        "colab_type": "code",
        "outputId": "84f65f8a-7d56-4d0d-ef14-9535ec4998bf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 211
        }
      },
      "source": [
        "duration = 50 #sec\n",
        "fps = 10 # fps\n",
        "num_frames = int(duration*fps) # total # frames\n",
        "# First construct the noise we will add to our signal\n",
        "# a sinusoidal function\n",
        "time = np.arange(0, duration, 1/fps)\n",
        "offset = np.cos(time)\n",
        "plt.figure(figsize=(5,3))\n",
        "plt.plot(time, offset,'.')\n",
        "plt.xlim([0, duration])\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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/8U/Ptbnnz/+ak6dtVCubzjuzMkEYjGXliknaXTVoKwu+ZQj0RBtAgW8+eYx2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\nKCMiIiJGIAplRERExAhEoYyIiIgYgf8PMHhtxseXXcEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 360x216 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZEyASuS8w1jb",
        "colab_type": "code",
        "outputId": "0d539214-3752-48be-f236-e3a359fe91b2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "# Create a mu that changes over time\n",
        "mu_t = np.zeros((num_frames, 2))\n",
        "mu_t[0] = mu\n",
        "#mu_t = np.cumsum(mu_t + offset[:,None],0)\n",
        "mu_t = mu_t + offset[:,None]\n",
        "plt.plot(mu_t[:,1])\n",
        "plt.xlim([0, num_frames])\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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VNaGJnM3uaQ7VTYZGV7L9ElDVeUues7QbilTdXFqoNDAZC1ue/GsHIgjjSQBn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\nqDbbenMtFkprOx2je3pWoyLmIZFxXvBKvorDOhW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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oyDfhhZKv8n0",
        "colab_type": "code",
        "outputId": "3c1e8150-a20f-4a27-ee43-a7254a434685",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 309
        }
      },
      "source": [
        "# Make of our waving gaussian\n",
        "fig, ax = plt.subplots()\n",
        "\n",
        "Z = multivariate_gaussian(pos, mu_t[0], Sigma)\n",
        "im = ax.imshow(Z, cmap='viridis', animated=True)\n",
        "im2, = ax.plot(*find_max(Z)[::-1],'ro', markerfacecolor='none',animated=True)\n",
        "\n",
        "def init():\n",
        "    Z = multivariate_gaussian(pos, mu_t[0], Sigma)\n",
        "    im.set_array(Z)\n",
        "    im2.set_data(*find_max(Z)[::-1])\n",
        "    return im,im2,\n",
        "\n",
        "max_marker = np.zeros((num_frames, 2))#.astype('int')\n",
        "\n",
        "def make_frame(frame):\n",
        "    Z1 = multivariate_gaussian(pos, mu_t[frame], Sigma)\n",
        "    val = find_max(Z1)\n",
        "    max_marker[frame] = val\n",
        "    im.set_array(Z1)\n",
        "    im2.set_data(*val[::-1])\n",
        "    return im,im2,\n",
        "\n",
        "anim = animation.FuncAnimation(fig, make_frame,\n",
        "                               frames=num_frames, interval=fps, blit=True)\n",
        "plt.close(anim._fig)\n",
        "HTML(anim.to_html5_video())\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "\">\n",
              "  Your browser does not support the video tag.\n",
              "</video>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mpOj3KiN94We",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# compare our guessed argmax with ground truth\n",
        "xhat1, yhat1 = max_marker.astype('int').T\n",
        "mu_t_hat = pos[xhat1, yhat1]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cKadvFtq_KqG",
        "colab_type": "code",
        "outputId": "37016423-e29f-44d1-8948-21d195dbd1ef",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "plt.plot(mu_t[:,0],'k')\n",
        "plt.plot(mu_t_hat[:,0],'--r')\n",
        "plt.xlim([0, num_frames])\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IWr0sAZ0Z0iNGjOj2ndvtxp6ebnmnAVC7ahVeenYYNpuNtDytbpnFg5q+ridATnFxxy8W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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9Ne7109r_UOF",
        "colab_type": "code",
        "outputId": "c8fa917d-694a-4f63-eaf3-5ea477574982",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "plt.plot(mu_t[:,1],'k')\n",
        "plt.plot(mu_t_hat[:,1],'--r')\n",
        "plt.xlim([0, num_frames])\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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IWr0sAZ0Z0iNGjOj2ndvtxp6ebnmnAVC7ahVeenYYNpuNtDytbpnFg5q+ridATnFxxy8W\nX1N9ObSnFQXo2NsALL+evoYGqlpaGNGLnYlyxDuMdiBqdUGlSITb//Mf/qeXyI2hQ4fSDofFCO6q\nhx/m3x4Prh5szczKoh3wHwZ7GLOfe473HI5OCYtYhBBE3G4ih0H2fMaSJTwLDNFHvl1wZmdjPwxk\nTI6/9VZ+Su8dcbomwWF1R1x6ww28Rs+ODSBvyJCOXyzuiMUf/8gr9DxTBxikD3Qsvp41r73GA0C5\ngg1vOMIdRmFhIUGbzfKbgqbTktZbp+F04srO7vjD6gc9EMDZRzhq0G6nvaHBRIt6xl1Tw7A+IkyE\nx0P0MAj/dW/fztcBZw8zSwBXdjbOw0C+xhYMErTbKSws7PH7bL1Dsfj5lD4fTnp3GAXaWrzVg0T7\n558zCxjeS+KoHgTRbrEIof/DD/k+MFKfmaXIEe0whBDsyc/n0zxry4DrIaDp+fm9HlMxYgRPlZRY\nHg5oDwZx6s6rB0IOB/7DYIkv2tKC7KUTBqgtLmbrYdAR++vrCUOv2bw148bxlBDWRvJFozgjEdw5\nOb1GyvinTuU6wO92m2tbF6J+PxGnk8xeBjWeyZOZBVT3sndgFoGmJgLQKY7YleElJR25GJdfbqpd\nXWmsqgJgmKKAmyPaYQC8N2UKP1A03UqW+gMHAMjs5eEBaJo4kXsdDuhhicUsgsEgrkgETx8O9q5v\nfYvro1ETreoZ2d6O6MNhvH/xxVzZ3m55redAYyPhPgYB9aeeys2RCHV1dSZa1QVt1pDWx33PnjGD\nR4A9Fs8uhd+PvQ9ZmqHl5awF9lgcSBBqbibkdPbqgIcPH04I2Ltvn7mGdaG5pgboCKtVwRHvMEaO\nHNm5QWoVVdoGWPagQb0eUzpkCMG9e4laqOe/d+9ePPQ9Exo+YgT19fWWquu2tbXhCIWw9bF0Nnz4\ncKLRKPv37zfRskORUhJqaiLch1bQsGHDsAMVVnYcmsPo676PKixkOlDx2WcmGdUztlAIRx8z4JLi\nYq4FGpYvN8+oHoi2tBDtYzY2YsQIfg64X3jBPKN6oLWujggo07M64h3GxZWVbDh4EL+Fa5p7g0HO\nBey6LEgPHN/czJ5gkHoLk6P27t3LL4Hwqaf2esyZH33ErcA+Czu4iooKVgBNMeqvXTlx2TKWaMda\nRV1dHQ2RCK19zCynrVxJGKj+/HPzDOtC0G7neqChDwHEMU1NrAP8FnbEUkqeA6p6SC7UGTFoEI8C\nLourbe4Ih6nu474XFxdzBZBrsbpuW0MDQbsdFCTtgbqKe2cKIbYKIXYIIW7v4fvfCyE+0X62CSEa\nYr6LxHz3WqL/dn5WFsVAxY4dKf5fJM+eujreAIr6eCHztM266t27zTGqB/bv3899QJpWOrYnSj//\nnLOx1mHs27ePHwL13/lOr8fkh0JMwXo7bwc+XLiw12NyteXSgxbOgit9Pv4GePrQNdLzBuotnLHV\n19fzvVCIg2ee2esxWdqmfYuFod9SSq4LBHi9D204u91O2OkkZPHS2Q+k5Pvf/ray9lLegRVC2IG/\nAKcBFcBaIcRrUsrOua2U8nsxx98CTI1pwi+lTDqrJEd7ISt37qRs8uRkm0mJ+m3bOF8IivuY9hVq\nL2SthSPiqspKhgODc3J6PcaVnY0H+NziGQbQY66ITmZhIWGsdRh6zkBvkTLwZfRRjYWZyfu2bmUa\nMKqPJSl930Bf87aCfXv3YqP30F8AXC6iQJuFod8+n49AINDn8wkgXS5LQ78DgQB1dXUM1kORFaBi\nhjEL2CGl3CWlDALPAn2VdroMUKY9kaW9kHUWdsTOTZt4RUocfcxyCrWXwEo7m774gr1A1ksv9XqM\nOyeHNLC0ZOe+ffvYDJT89a+9HuPKycGDtXsD+/bt45fAeK0OQk/YtI64zsJKhs2rV7MeKNOCM3pE\nE9Brs3Bzvqqigggwc8mS3g8SgqDdTsjCpM2Kigr+DZyh1fPulbQ0IhaGfldVVXE9cM6aNcraVOEw\nhgKxb22F9lk3hBAjgVLg3ZiPPUKIdUKIVUKIr/b2jwghrtOOW1cTMwrSR3A+C6fSTQcPdvzSRbUy\nFn1DvMXCEZy+3CD6iNSyZWSQ5XBYvtQzVAgcfYTNirQ07MB+ix3bcUKQ3tf+hBbp1dBXZ20wjdXV\nQEzSW09oz67fwryBWu2Zy+xjJgQQdjgIWzhyr6ysZDKQ30/OSjQzk/ZAwLKQ6gMHDnA6MEahnpXZ\nm96XAi9KKWN7gpFSyhnA5cAfhBDdxYMAKeXDUsoZUsoZsclHnmOO4Xm7nQMWPuidTqCPMFAxbBi/\nzM3FSikyPSa7LzvJyyPidFKlH2sBFRUVpEGfDpgxY/jI6+WAhY6tqqqKbKezz/Bfysp4dexYtlg4\ncm/WBjR9hdWSn88jJ53EYgtHxPosrK/wdIC/XXMNPwkEiFoU/q0/n31eT+CNW27hDClptGgf48CB\nA6RBn2HKiaLCYVQCsYu4w7TPeuJSuixHSSkrtf/uAt7j0P2NfhFz53LHyJFstTIMVF9P7auDy8/n\n1fJyNliYSauPNPu0829/4/snn0y1fqwFVB84gEvKvh3b17/OH887jz367M4CqqqqyLTb+76eY8fy\n/tlns7qqyrKRpr4v0dfMkrQ09h1/PGvr64lYlBCpz4Ddubl9HuecOJH94TA+i/YxKisr8dC7soNO\nsZb7YNXg68CBA3igzzDlRFHhMNYCZUKIUiGEiw6n0C3aSQgxDsgDVsZ8lieEcGu/FwBzgYQDwSfn\n5fHV5cthw4Yk/xeSp6WlBb/fT0tWVt8dRzTKHI+Ha9etg7feMs/AGFpqa4nYbH13xMDXWlq4ets2\ny2oO6ImQfV5PYLLNxncrK5G7dplgVXeqq6sp8/v7ve8THA7ua2uj7d13ez/OQJp9Plr7c2zAzPp6\nnohGaXriCXMM60JDPDNgYNb27SwFgr/7nfFG9UBFRQV59D9yn7ZuHfsAz/33d8oHmcmBAwc4CXBl\nZSlrM2WHIaUMAzcDbwNbgOellJuFEPcIIWLjNy8FnpWHDrPGA+uEEBuA/wL3x0ZXxcX+/fxp61Yu\n3rcP/vSnlP5fkuHAgQM8DVTMng19jTiiUf5v0yYurquDO+80zT6d1tZW3m9r4/NJk6CHGhOxTPP5\n+N+WFqJLl5pk3ZdEo1Eqamr4bMwY6EuSeetWLl26lFujUdr72HQ2kqqqKj4bOhRmz+79oIYGLn38\ncb4DyF/9yjTbYnklGmX94MHQT1TPcUuWcBWQfvfdptjVlQ0tLXzo9cKECX0eN2LvXk4Ahtx3H1iw\nslBVVcW6zMyOssF9kOPxUAiUPPkkrF1rjnExHDhwgDVOJ6IH6f1kUbKHIaVcLKUsl1KOllL+Qvvs\nLinlazHH3C2lvL3LeR9KKSdJKSdr//17wv/4kCHcd8017LJIhDDzhz/kNmDPbbf1XWfY4eDhm27i\nJTqqn5lN02OPcSOw/tZboR+p483nnQdYE+veuHYtZ0QivHPDDXDGGb0fOHYs7/7ylwSANgvsjDQ3\n4z54kOevvhr+9397P9DrZcXTT7MGrInseeABztm9m2fPOw/6WZrY/sQTPMKX2mim8sEHTN++nYXz\n5/c9UABaH3iAzitu9rt08CC5X3zBPXPnwiWX9Hmo6/vfpzNF1mw7o1Gq9u/n+mOOAYUDgCM+0xs6\n1gpbo1EiFmR7Z65ezRQ6itD0R3FxMW1gSWy24+WXuQEYPHhwv8fmasc0W7CPEXrmGV4DiuPQBxs0\naFCHHLsFAQ9Nr77KHimZGIdc/aBBgzrqtlhw36MvvshJbW2d6+l9UVxcjB8QVuyzPf00/1ddHbed\nnRaa3RG/9BL/3LKF0j5ymXTy8vII6TpjZtu5ejWL3nyTcxVJgugcNQ6jHQhaEY3g9+OHuAqs63Za\nIcsdbGqinfgchl7O0Yokrra6OqJAYRzJRnpHHLDCYWjONCeODq6oqMiyui3h5mb8EHdH3AKEFclI\nJEK4pQW/lHE9n5mZmdS63ewcOhRs5nZhMqZGdn/YbDYihYUsGT8eeigEZiianVm9yNkny1HjMG4C\ndlx7ren/ti0QoB16rTMQS3FxMd8D3n/oIcPt6kpE6zjieSELRo3iN8BeC2Tj/Q0N+IFBcXZwNwDr\nFJWfTAQ996bP3AaNwsJCvg3886u9phkZRqS1NW6H4fF4eCAvjx9+4xuG29WV9vr6uO0UQrBp6FDu\nOvHEfvdlVBPQ1Hzjue8AYuhQfjdyJPShi2YE+mpLX4KoyXBUOIzBgwezFvhCYfhYvNhCIaTbjTOO\nqV9xcTGtQKUFa9nR1lYCQuDtJxQQoGjkSH4AbLLgegYbGmgnviW+/Px8Xrfb2dhPVI0R6Lk3BXF0\nWE6nk7b8fLZbsNQj29rivp7Q8YxaEQYabGyM22GAdXa2ajPggjgdxqCioo5wYZOjpPScK1Wy5jpH\nhcMoLi5mDuDsS1LAIA6mpdEWx3omdLy0pwDjH3vM9Nresr2dqNvdq35/LLm5ueQ7nfgsSIoLNTXh\np2P9tz9sNhun5Obi3rzZeMO60KrlABT0oSMVy1czMpi6cmX/ByomLCUtxN8Rn+t2c/1774HJRbRC\nLS20E7+dc91uHvngA1i1yljDuuD3+ToccJx2jvJ6WfXpp/Dgg8Ya1gV9Bpwbx4pCIhwVDqOoqIj/\nBWY+o0yiKm6umjyZRePHx3VsRkYGx7tczF6+3PQRx/dmzuSuPmSjYxFCsDccZu5//mOwVd15ccwY\nbiwsxBbn2vRv/H7Os0Ay/tPsbH7gdJIZ5wu5IBzmYgtqTfzpu9/lFuKfYYx1OplfV2e6w3jrkku4\nnPiWTAGKvF5GBYNg8v7V59On8w3i27ME8GozEbP3LQ/k5vJbILuXmuPJclQ4DKfTiXS7ERYkx1RX\nV8f9MgJflkc1OWpif10dWQlMT0M2G2ELSrVubG+nMs5RO0DU47EkquejaJQXhg5FxFnS1J6VhdOC\n6oBVVVXk5ubiiXPZrrMao8nXdGd7O3tttl5LnnZFX5sPmfyMbktP5wXid8D6kqXf5Kz0Xbm53Abk\nje5RaSlpjgqHAR2yB444QhyVUl/P4zt3ckoC0S9uffnK5Bfyqm3bODuBUU7I6bQkTLlk+3bOTCDy\nRaSlIYJBAy3qmfDevcyKcykSOrJtPWZLg0QifP3VV7k0AS0hXR/J7IjDsmXLuCQzE7vdHtfxuuho\ns9nSMBs3MpPea3l3ZZAWqtxqspaYr7KSTKBIcZRUyvUwDhds6ek4TN5MDtbVcVwkQl0fNZ270qmT\nY/IM44rGRjYnMBqLuFyWhP9esXcv+f1oCcVi0wYKUsq49mdUcc5nn3FBAp2qKycHB+BvbiZNoVRD\nn/j9zNu3j40JLEvoZVzrDxxg0NSEZN1SYv66deQm8B7p4cwtNTX0H8ahjmPffpuT7XYccdqq5wq1\nm1wrffyiRTQDUcXP2lEzw3BkZuIyWTRNl1TP6EeOORYrpvx+v580wJnAwyPdbmzt7aYqgkopsQeD\niH40j2JxZGXhlpJmk5cmoq2tRBJIivJo0WmmVt7TBiXOBKLdMoqL2Q80mLw34AiFErrvOcOGsRio\n7UtdwQBkW1tC972goIBfA7vLyowzqgdCTU2EAJvi63PUOIy1M2ZwZm6uqdFHukheRpzTU4C9M2fi\nFILouHFGmdWNmoMHSaNjlBsvm04+mX8BDSaOjBoaGnBLmZAc8xdf+xrXYq4iaDQaRQQCRBJ4GX0X\nXcQgoNrMbG9tUJLIfRcnn8xQYG+cm7qqcIXDncWm4iFv1CjOAbb2I3OjGj3aMF4KCwu5H9iQwL6c\nCkItLQQMSGo8ahyGo7SU95qaiJrpMLQZRiLJMflFRYSlNLUjrtXqDHgSWOqpOu88XgBqTdRpqq2t\n7dDvz8yM+xzHzJm8D9SZuEbc2NiIR8qEOo6C0lIOAtUmZs/rmeX91W2IRV+brzE5y98ZjeJIwGHo\nibJm22kLBPpV040lLy+PPKDV5EJf0ZYWgnHuByXCUeMwyqNRvh2NUm9iKcy65mbWAVkJpP2XSsmD\nQOOHHxplVjd8+/cToX/9/lgGO50MwXyH4SGxpbOhLS18FWvsTGQJZUh9PfcAzTt3GmZXV5rq6zkA\nuBKYAQ8KBnkdcJmYMxKNREgnsaWzvLw8dgETXn7ZMLt6wh4M9l1XpAsOh4N37XbOeeEFA63qTjTB\npbN4OWocRllNDQ8B9du3mwlevekAACAASURBVPZvbk1PZyaQPX9+3OcU2e1cD/hNjMk/4PfjAMI3\n3RT3OdP++lfewPyO+Ayg7jvfifucYcuW8TJQa+JIs6amhj8Cu6+5Ju5zvLW13AkETdzDqPZ6GQK0\nnHxy3OfkpKVxLoCJdtbX1zMI2HruuXGfY7fbKRQCTAxXDQaD3BSNsub00xM6L+xymR7k8mI0ynvT\npilv96hxGBna6LnBxLXsuro6HA4HWQmMiGOjO8xCn7YXJrAu7crOJg3zHcZWIHvSpLjP0aN6zLzv\ntbW1LAWimgx8POjLgWZKxuv3Lt4QUKBzH6HdxE3vmtpaDgLZCa7zB2w2UxWAfT4fHwDByZMTOk+6\nXKbmCoVCIZ5pbWXLaacpb/vocRjaS9FooiT3kE8+YT0gElif1FP120xcc2/fsYPHhCBnx464z3Hl\n5uLB3DXi2tpabgKKEhjd6stXZt732tpapgDFCYRx68sYZiZwhVau5FVgWCLh0doym5l5GL7du7kH\nGJXgvl7Y4UCamCvk8/k4GyhN9N/0eLCZmCtUW1vLIGB4Akum8aLEYQghzhRCbBVC7BBC3N7D998Q\nQtQIIT7Rfv5fzHfXCCG2az/xz/G7oCfyNJmYyOOoqeErCWbv5mkOw8waDuHKSr4pJULbpI8HR0aG\n6TMM38GD/BlIe//9uM/RO2IzE7hqa2v5B1C8cGH8J2kbpWaO3EO7drEA8CawOa/bGTQxp6l5927u\nBAYn+KyFnU5Ti5H5fD6eAcYnuP8o0tNxmphUXFNTw/PAOU8+qbztlB2GEMIO/AU4C5gAXCaE6KnG\n4nNSyinaz6PauV7gp8BsYBbwUyFEUpraeqRSq1kdnJScr4veJeDJ07xe2oBWE/MG5nzyifaPx2+n\nSE/HabOZ5zAqK5n/xhsd/3YiIyOPhwqXy7zaHe3tzHjpJYbTIfcRN1pHbOZAYbx2PRMSoPN42J+Z\nSY2JSygFixYBkJnA0hnA5lGjWGFm7tXy5WSTWJgywGfTp/MbKZEmRXC2fPIJJ5Dg8xknKmYYs4Ad\nUspdUsog8CxwfpznngEskVL6pJT1wBLgzGSMcM2bx7T0dD41S+p63z6G6C9VInUjvF4mjBzJ61qR\nIjM4vqKi45c4xQcBOPZYHi8uNs9hvPIKp27ZQo3D0W+t5EOYPJkXR41ii1lZ6evXc8qaNUghEHPn\nxn/epElccf75vGqcZYfS0sIwbak0LZGkMSH4+VVXsdBE3asxmnhk5pw5CZ237LzzuN/vNy25dPiL\nLwJgS9DO2mOP5ZFolEaTlvmyXn8dgHCCdsaDCocxFIjVwa7QPuvKhUKIT4UQLwoh9N2teM9FCHGd\nEGKdEGJdj+vqGRmECwsJmRXvrE2FHzz+eEgwfG1sTg5lGzeCSbkYNil5bfx4GDEi/pMuvpgV5eV8\n9eOP4aOPjDNOJy+PzzMy+ObcuXDKKfGfN2UKq6dM4ccbN8Ijjxhnn04gQBT43ujRcMMN8Z9ntzMk\nK4vRVVVgxvKE9nze6fVCAnktAKPcbi6vqyOye7cBhvVAOMwTDgfuBKN6Bmdn80g0SstLLxlk2KFE\n29pYA3guvTSh8woLC3kTiP7kJ4bY1ZVAfT0BwPajHylv26xN79eBEinlV+iYRSS8uCalfFhKOUNK\nOaO36nY3hsP8/rXXwIzR0ZgxjMjI4Iskqr3Nsdv5yccfQwKb0KlwcXo6GxIZtWsMzs7m2spKcxzG\n5Zdz/tChZCZR8KWgoIDZra2wcaMBhnXhlFOYO3s2lUmU3Dy+pobXGhqQZmx85+Vx47x5rEyiIl2J\nEPwRaF6zRr1dPfDUlCm8kYRIXkFBAd8C2k2yc+PIkTwvBNkJFhYrKCigDIiYFPJf7XSyHOIqlpYo\nKhxGJRAbDzdM+6wTKWWdlFLXHn8UmB7vuYng0NfsTNgIC0Yi7Gtt7dxsT4TOBDoT7AyHw7ze2kp0\nzJiEz+38fzNpPbu2tjahEFCdgoIC2qQ0rWZ2TW0tBUl0cLrwZJMZEV0OB+sCARxJFNDpDCAxKfJs\nUUYGe5OQzvDqASQmRZ69WVrKUwUFCYtcFhQU4AfTygW8NWYMl+Tlxa38mwgqHMZaoEwIUSqEcAGX\nAq/FHiCEiH1qFwBbtN/fBk4XQuRpm92na58lRad0uAkdcdP69dwHjExiIytddxgmdMQNVVV8HShJ\nYnNQDyQwQ+Y8cv/9/NvnS9phtGNSKOjy5fx0715GJiBjoaNLdDRoGmSGcvAgZ+/cyfgkQiuzNGdo\niiS3lAzbvZuxCS6bARQUFxPCPCXY5oMHKUiizn1hYWGHwzApZ8Tn8xkyuwAFDkNKGQZupqOj3wI8\nL6XcLIS4RwixQDvsO0KIzUKIDcB3gG9o5/qAe+lwOmuBe7TPksJlYq2Jtg0buB0YlISkdqb2QprR\nwTV+8QXPAuOSkEzR6wGbkTMS3LqV8SSWZKaTn5+PH3NCQSMbN3JVKERhArpcOnqSoSmh37t2cbfP\nx7gkBjT6QMGUkXsgwN+3bePcJKLH9JG7WTkj9731FguTeBf0AY1Z5QIuXrGCvxv0ziqphyGlXAws\n7vLZXTG/3wHc0cu5jwGPqbBDn/IHGhpwJ7LBmwR6+G6ioYDwpcNoqq4m8bMTQ19WcCcxMsofNIgQ\nHaGgRldwCDQ04Cc5h1FQUMB2wJueTmKry4nTWltLNl9m7CeCLoNvRs5IsLERF186qUQw1WEkIcGu\nk5+fTyXQZlKOgzMUgiRG7hkZGayz25G5uYw0wK6u5Dc2MtigcOOjJtMbwD9xIjcDPgNkfbvSpr1M\nyexhuMrLmQdUTZyo2Kru6J1TehIOo6CggDxg89e/rtiq7oSammgneYdxAbDq6quV29UV/b7nJuEw\nPMcey9eAfQZk4HZFz0tJpFaLTl55OaXAWhMk+EParNCVhMNIS0tjktvNS7NnqzarRxyRCLYEhAd1\nhBD8triYJxOUFEkWWyCQkJJyQm0b0qpFOMaP5y+AGaIbesZuItLmOrlDhrACqDEhkUdfh06kZodO\nQUEBrUCtCclmoZaWlGYYYE5Wun7f85JwGLljx/IKsN+E2vP6DDiZ+56RnU2l00mVCWvuuqSLO4kl\nPiEEXq8Xn0mb3u5oNKFaLbGYaac9FEIOOIz+KUhP5xigwYRcjIC2bprMSNOblcVVQPjjjxVb1R19\n/yGZpTOv18uPgfzFi/s9NlWq8/NZRccyQ6IUFBRwLzDnoYeU29WVtmCQasCbhJ05DgdnC0Hwiy/U\nG9YF/b5nJTEDFkJwl9tNoQlhyvqSqSeJGTDAz0MhTjGhVEAoFMJDYrVaYrm9oYF7ly5Va1QPRKNR\nnOFwYmoJCXBUOYyhPh8bAZsJD9C748eTZrORlUC9ZB1vdjZPATlahquRbEtPZxaQcdJJCZ/r9Xq5\nCihev161Wd34z4kncgPJOQyPx8M4u51iExLNVs6fTzHJxbjbqqp4Q0oKN21Sb1gXdhxzDKWAZ/z4\npM6/rbWVMSbkDdS43VwAhGfOTOr82YEAZSZEnTXU13MfUPeVryR1fr7DwWATNr0bGxtZBdQlEUYf\nD0eVw9DDAdtMmPr56uvJ9HoRSeyXeIcMAcyJ7qhqbWVbTg6OJDritLQ0AkIgTXjQfT4fbrebtCRH\nRtLtxmbC5qe+rJBU2KImWxMwIZqrpq2N3YA3iSVTgKDdTsSE+14TDPIykJGIbE0MUbfbFCVYX309\nPwXajjsuqfNtGRm4TJAw8fl83AxsSzAbPV6OKoehR66YoQg6+tNPeSDJjPK09HTTEnmcu3dzvdMJ\nSTqnsMNhSl7L1f/8J3+12xNOiurE48FhgsMY//bb/NFmIyOZtWzNGYZNcBie9eu5HchLcgkl5HCA\nCQ6jbfduzqBjBJ4UHg92E+573cGDDAIKkhT0s2dm4jZBgLBe6/sO2zyMwwk9McqMRJ6R+/ZxUZIv\nvhCCgBCmJMQN2b2b+2trk65MFna5wIRNWm9DA0XJdhp0KNw6TJCEGbxrF6cJkZxj02YYIRMGCoWb\nNnEfkJ2gsqpOxOk0JZ/Js2EDbwH5yQ7yTLrvbdu3UwWUrV6d1PnOzExcQJvB997n8/EZMPmVVwxp\n/6hyGHptBFMSedraOkZhSRK0202RsuicxSSp4ht1u4maMIJzhMMJya93paGggM8NigyJRfj9hJOt\nlazdAzMGCuHmZkKASNLWqMuFzYSBgr4akExQBkCgoIBqKWkzeDakV8hMJq8FoH30aF6ko+aLkfh8\nPkqA9GRn6v1wVDkMcnL4yZAhrEoy9C0hUuk4gP+bPJmHktD5SZROOYIkO+Nfn3AClxucBAkdDiOV\nyI5VM2awIMnRdEIEAh2j72RwOHj0kkv4eyBg+NJEpKWFYAqdxjM33sjl0Sh+g5cjA9pqQLLRRx9/\n85vMB8NDVvXSusnktQA0n346FwM+gwcLvro60gCPQe/C0eUwXC6WjR7NRhOmqCIQIJqCw2gaPpxt\nJsS5d85ikpxhePPzTYkfTyXGHTrWbOtN2LuyB4MpJUX5pk9nazBIq8EdR7StjUAK4nMZw4bhx/iO\nuFPOJdnnU1urN9pOPUw52RmGWXY2ajMYz8AeRnzMBjwGh9mFQiFC4TChJLI+dU5ramJmEvpOiRCN\nRr/Ur0myk5u/fz93VFcbPiJ+y2bDl4QUt85xFRWsaW/Hb/A1rYlGaUlh9DalooJZQJ3B+lzS7+8I\nWEiSqRs2cAvG29m5n5Pk7HLC6tUsxng7dZkUW5KDmpKPPqIOCOpVOg1CXzpzGLTKctQ5jHtXruRr\neoU5g2hoaOAy4OU7epTHiouztm7lKoP3Wpqbm1kIPH7bbZDk8kRZQwOXRSKGLk0Eg0EujETYNW9e\n0m147XYmAQ0J1C1PhgscDl4699ykz5/37LPcgPEd3B1ZWdyVgp0ln3zCNzF+RPyG282Ppk+HJKOP\nvI2NnEXHUoyR7IxG+U1+PowendT5WZmZeDFeR8zX0MCr6emQZP5Nfxx1DiPicHBda2vSYaTx0PzJ\nJ3yPFEPX0tI4ORql3cBs2tAf/sC3ACb0VGI9PpyZmeQDrVp9aCNoe/ZZ5pDa9dQzhW2PKdGx7JHQ\n6tV8q7k55ft+ApD15z8rs6sblZWcWV2NK4U9MmdmJlOBsJFJm8Eg4w4cYHd5OSQ5G/JokiLZBmdR\nbwsGeXH0aEiibgd8KTha9uabKs06lC1bmLRpE3eXl8MZZxjyTxx1DqNek0IIGPgA2V99ld8BBSlM\n+2o04cHA008rsqo7efffz92k1hG3TJ0KgPPRR9UY1QOuhQtZCYxKwclLTdgta9EiRVZ1J/Too/yB\n1K5n+4kn4gXKHn/csLDV6OLF/NjvZ3gKey3y5JMBKHo76fI0/fPpp3yzro4pKew5ujUFg7IlSxQZ\n1QOhEH9atoxLU5hl6+Vny4zM8n/uOf7fpk14k5RZiYejzmGs/MY3gC+jGowgoG2u5iah06Oz78or\niWJskqEIhVhIah1c4Mwz+Rhji79EW1t5AxAJ1nSOxT19Ok+AobkDwYYGKkjteoYfeIDbgMaCAjAo\nQ9lfV4cXyEmh43B/5zvUYmzOSLSlhQmRCIUuV9JteM46i//abEgjc0b8fsr8fopSCHJh5Ej+mpFB\n0Egl7bY2IiSncxYvSqwXQpwphNgqhNghhLi9h+9vFUJ8JoT4VAixVAgxMua7iBDiE+3nta7nJkra\n0KH8C6g3UEI60NhIEPAmUaZTx5ufz/8B+ydNUmbXIYTD2CIR2kmtg/N6vVwPfHLhhcpM60rU71di\n5y3Ai3ffrcqsbugS7KnYmZeXx9+BP37nO5CEpHc8tOlKyikMaNLT07nZ6WRFWZkqs7qhS/ikpxjR\n84OCAv56/PEqTOoZvWZHkvssOg+WlvLN009XYVHPKHiP+iNlhyGEsAN/Ac4CJgCXCSG6Lpp/DMyQ\nUn4FeBH4dcx3finlFO1nASmSUVbGFUBFkmuN8RBubsZPckJ5Ol6vl98BXwwdqsyuQ9BGXH5S74jX\nALsN6tygIxlOhZ0tQLWBCVwRTYI9L4WRu9PpJCsry9DNZH0GnIxSbSzLCwvZkMqouh9STYbTaS8q\nYoeBM4yINrt2pZjbkG9wiLpsa6NNysPbYQCzgB1Syl1SyiDwLHB+7AFSyv9KKfU3eRWQfPxkP5gR\n7xzWOo6cFB4gr9fLCMC/c6cyuw4hEmHfyJHsIbUOzuv1chyQs2KFMtO6EgZaSc1hZGRkcKbdzuwX\nX1RmV1cira1KRnBnpKfz/559FgySOQ8qmAEDHJ+WRs6uXWqM6oHWFKT3YzlTCOYZuDfQpDk2TxI1\nO2I5NRTi9g0bDNPo0p/PVN73/lDhMIYC+2L+rtA+641rgdhQAY8QYp0QYpUQ4qu9nSSEuE47bl2N\ndgN7Ij8tjWZgyDPPxGd9ErwxfjzXZGVhS2E9Mj8/n3eAKf/6lzrDYsnJYeFFF/FGejqeJJOioGNp\n4jabjeMN3Ez+/fXXc4MQKTlgIQQnejycsGYNGJS4+dYFF3AJqTuMoRkZTKyqSlrfqz8+nzKFq0nd\nzrsPHuSSDRvUGNUDB3NzeQBILylJqZ3Tm5q4ykBp+4bWVpYCthRXLUZJyVmNjWDQfmDNt7+t5L73\nhamb3kKIK4EZwG9iPh4ppZwBXA78QQjRY6CzlPJhKeUMKeWMwj5GTt7Bg8kEQgYKEG6LRtmVpGy0\nji4dbmRheJ/Pl/LDI4QwXFeovr6e3NzclBwwgF1PpDRoeWJfNMpuIDfFkWanbINBdu7KyuI5Uu84\njL7ve7xe/g/IHjUqpXZsGRk4DaphDXAwM5P5QDhJaXOdzjK0Bt33gwUFfMjh7zAqgVjXO0z77BCE\nEPOBHwMLpJSdT6GUslL77y7gPWBqKsakZWYSxFjp8JHbt3N2ip2bEKIjE9coh/H55/zshRc4U8Ea\ntDRSOlxKLnv9dS5RIBzYqUdkUJJh2QcfcEl6OvYUJDcgphypQXbat2xhJqkvTUiDpcMbq6rIgpTD\nQO2ZmXgMlA5PqQZKDG7t/9Nv0MxSLlnCCRz+DmMtUCaEKBVCuIBLgUOinYQQU4G/0eEsDsZ8nieE\ncGu/FwBzgc9SMUYIQbsQhoaBnr9tG9drpSVTIex0IozarGtsZHhLC/lJirrFYqh0eCDAcXv2MCnF\nThhiolgMuqYnr13LVQpUQDvLkRrkMOYsWcLTNhuOFKRBoOO+O8Nhwzri8jfeoAnIS1HGwpmVRRrg\nN2jw5Vy+nB1AcYpZ2mnaQKHJoGzv4Y88wk84zB2GlDIM3Ay8DWwBnpdSbhZC3COE0KOefgNkAi90\nCZ8dD6wTQmwA/gvcL6VMyWGA8dLh9mCQaAr7AjrS5UIYNeXXOk13issnoFULM2rKr9mZrFppLE6D\np/yOYBCp4L67i4rYAEra6gnp9xNS4IBFejpuA6XDQ83NRAFXivdev+91BsnCBKurGY2CpciiIvYD\njQblXkkF0Yb9oWQPQ0q5WEpZLqUcLaX8hfbZXVLK17Tf50spB3UNn5VSfiilnCSlnKz99+8q7Hl7\n8GDWGlgbwREKJa2uGcvb48bxsFERDdro1a1A5njF1Kl8LcWIm15RFOMOsG3aNHIzM8Gg3AFHOIxQ\nMVAYM4YpQPPs2akb1QOivT15CfYYtp5/PtdhnO5VpKWFgBBJ65zpVF1wAYMwTjpcL8iWleI7ED7p\nJIYC+1Pc/+wN0d5+ZDiMw42XZszgOYPixyORCM5IJKXaDTpfTJjAS0aN3LWOOE3BwyNGjuR9o/aE\ntNmAU0GeR15BAY0tLYQMWnd3RaNJq5XGYnToty0QIKJgwCSnTmUZBjqMtjYCCjKfs4cN4yAddbeN\nINWaHTr6fTfqeopAgJDNRpqBSctHpcPw5uXRaNBNaWhoII3kZY5jGeVwMNwgCZNAVhZvAm6tznkq\nlIVCXO334zfghYyGQlQBDgWOrTQc5kGgKckymv3hVuQwitLSWAVE//nP1I3qAVsohFTgMIY1N7MA\njKsz0tZGWMHS2ZC6Ou4Bmo3Ka9FrdqTYERf5/bwOOA16Ph3aUnlS5YPj5Kh0GD956y0eq6oypG2f\nz8c5wJYrrki5rbM++YRXAwFDpMNrx4/nbMCRpBxzLONqangIaDQg1r150CAGA1XHHptyW0U2G9cD\nbVu2pNxWV6SUjLTZWKOJ8qVCXmEhs4GIQR3cHR4Pb8+Zk3I7I5cv7ygratBM6E2Xi9fHjUu5nYKa\nGu4E2vfsSd2oHvgiGuX93FxIof4NQK7Hw7kA+/b1d2hS/Oy44/iXUcoRGkelwxAeD24pDemIfT4f\nWwH32LEpt+XMysKDMVNUVaGA8GWGa6OCyLCuqLRTl5BuNWDW1tzczIFolIwhQ1JuK1dbww4YkCsk\npeQ/ra00KeiI3Tk5OIH6PhJlU+HfoRArFezj6GVTWw1ybG85nfxy1qyUHYYeHRcwaMb2UTRKm4IV\nhb44Oh1GejppGDMy8vl83ACMUFDVz5mdTRrGTPndjz/OXqBQwXpmmvagG1H8xf/hh7wKjFCwYak7\nDCOWzur37eNnQJmCOiveggLagaAB+0Ktra3MD4UoVxB9p+9/NRvgMKSUOOvqGKYi6kwb0LQb5DBU\nJMBCR78Extx3olFO2b6daQqW+PriqHQYtowMPBjkMOrq+Csw+OOPU27LlZ2NE/AZ0BGHq6oYDuSk\nKEAHkK5p/RjhMAK7drEA8KYgca2jq7MakRjVtGcPdwHDFcwG8/LyaMeY5FKfz8fTwCwFkh565FqL\nAQ6jra2NJ0Ihvvn666k3pg2KjEqIu6GigoUqCh9pzjGs74moxO/nzspKjjUw/wyOUodhz8w0bOTe\nWWRdQX6D28BEnmBTE2HAqyCEL1Of8huwdKa/5JkKwnZziotpA9oMeGn0UXaagjBot9vNh3Y7BxQ4\nya74fD48qIk600fERizx+Xw+0kBJtKHeEQcMqLIZjUZJ8/tJV5G4mpZGhcdDnRF1ULRoQ5eC8PS+\nOCodRvv8+TyKMTMMvXP3qMifOO88vg7UGTDSDDU3K9PGTz/tNMqBHQZInPu1dfxUajfoZI8ZQ6YQ\nLFewv9QVVVLcOtcPGcIrpaVK2orFV1eHB3CruFfnnMOVJSXsNSARsr6+Hg9qog2ZOpXTjzuOJQY4\n4KamJjx06GqljMPBzWecwZMGJGzq+2GpSrD3x1HpMGyXXcb9GOMwxn7wAQB2BQ969qxZPA/kL1uW\nclvd2q6oIEiH7HeqZA4axBcOB+NVl+uUkpkvvwxAtoKZkN1uJzc3l1Nffll5NbuRL70EQEaKUtw6\nXq+XK995Byq7ya6lRPrixdgAl4IZMMXF7B06lNmfpSy+0I3gypVMRU2GP3Y7GV4vV372GSiWMWnc\nsoVvgJIwZYCC7Gx+uHMnKB4khv74R0BNom5fHJUOIy8vj8eBshdeUN52lZRsdTph1qyU28rMzOQb\nNhtTDag/vrykhDfS0pTEZAshuCIjgzPefx+iUQXWaUQiPHXmmbxut+MZMUJJk6emp3PCxo2gOLR2\ny8iRrAYyFGVnj83M5NSKCnjnHSXt6YSrq6kE7Ioq0H21rY3LDaiJYf/oIwCCJ56opL0T/X6+VVMD\nipehw//9LwAt5eVK2jsmHOby1lZYt05JezpNeXlsBYJf+YrSdrtyVDqMrKwsZgG5BuQNvJ6Tw5WT\nJ0MK9ad1hBCc53TiNCD8922vl/tSrDMQyyR9Sq5S+8rh4OOMDG4oLgZFmflD9NBHxdd0xfDhnOTx\n4FHUcWQbpFi7YtIkhgGZZ5+tpL3JbW3YVQ4SNNbPnIkAuPZaJe0N1QdGiq/njunTEcCe++5T0l6O\ntlQYUrzxvWv+fMYBTqNKPmsclQ5Dlw6XBnTEnv37KVExjdZxu9VLSH/4Id9asYJSFevDGp1LcCqv\naW0tc9auZZLC62mUdHj+li1MVDjd76wyp3h/oKm6mjSXS5k8hD0jA7cBDkNl/g18uXYfVLzxrdpO\nfQ9MdeSZ//PPycZYHSk4Sh0G0FFrwoDNuoc2beL6vXvVNZiWpr7WxJYtnHXgAIMUdnAOvVNXeU13\n7+bbGzcyJUUZ7lg6HYZKO8Nhbn/jDb6hcH1cjwqTipVgb3r8cZ6z2ZTJQzg06fCgYlXlY194gcVC\nkJ5iMpyOx6CIw5z33uMpwKtoUKMPFFQnGZ54yy3czYDDSJqIy4XNAIehSoBOx5aerr5amPb/rSqi\nB2LCNFWO3BVKsOuk6y+MSju1tlTe92zNYYQUb36q0pHScWZlYUd9tndGbS0ldrsyx9aZZKjYYWRs\n385VdAhbqqAzuVRxiLo9GDRcqRaOYodxMDeXvYqzHqPRKB4pvxxtK6Bi2DBeVTTK6kTr4DIVPeQA\ndWPGcJvHAyofSIUS7DrhkhJOEIKook1foNNOh8IYd29+PplA1XXXKWsTOqT3VUiw6zRPncrPgHrF\nI2Lh9xNSOLOMTpvG14CDivMQws3NBAGnomuaMWYMpcD2GTOUtAdAOIw9GiUgBNkGhL7HctQ6jGdP\nOIGbFYeYNTU04EFtx7F96lRuVOzYIlrimopkOJ3w6NH8tr2dkMr9G22GoUKCXSdz0CCWS0mTSnl7\nXYJdpcPwemkF6hTrSbkikc6EOxVE5s7lbsCnOBlSBAJEFOZNZI4ZwyvAQcWVIcOtrbQrVH/1FhWx\nG6hRuRSpPZ9CUVRkXyhxGEKIM4UQW4UQO4QQt/fwvVsI8Zz2/WohREnMd3don28VQpyhwh7oeCFV\n52HUawq4LoVe3Ov10tjYSFjhPoY/GMRHhyqqKooyMzkGaKyoUNamvkGpcumsICuLq4DmVauUtanP\nMFQmRXm9Xu4EXM8/r6xNUL9kmp+ZySDUL0nZgkGlS2dep5MzgXbFCsCytZWgwgGdNy+P24H0NWuU\ntWnEkmlvpOwwhBB24C/AWcAE4DIhxIQuh10L1EspxwC/B36lnTuBjhrgE4Ezgb9q7aXMuZs381xj\nIxGF+wN1DQ38D9AyMLvwkAAAIABJREFUd66yNo/fsoUI0Lhjh7I2K66+mnzUrmeOamxkI+DX4tJV\nUHfssZQCQmGFvPysLJ4CWLxYWZvteXlcAPgmTlTWZn5+PtcAmVoiqCp+73CwT1HoL8CwNWuoAkKK\n81rW2WzsVaD8q5Pf1sabQMb69craBGgKhahXWJAoOyeHe4CiTz5R1ibp6fxl7Fi2GaxUC2pmGLOA\nHVLKXVLKIPAscH6XY84HntR+fxE4VXTMnc4HnpVSBqSUXwA7tPZSpjAUYhYdBY9UUdfczMOAU0HS\nnk5adjY2oFFh/Q7VoYDwpYR0m8LNOl97O7uBHIUzoRztpVGpK1QfifAy4Bw1SlmbXq8XPxBRWFY0\nGAzyo1CImqlTlbWpZ7ar1hH7X2DZKacoa08vn9queInvruxsfnLWWcras9lstPPlsrESMjJ4IisL\n37Bh6trsBRUOYygQWxGkQvusx2OklGGgEciP81wAhBDXCSHWCSHW1cQxPXZq4YAql6Uaq6qYBhQo\n3KxLMyAcMPuJJ/gTah1Glqb1pDIcMLRsGbfTseyhCm9RESHUxuM37tjBGUCRwjV3XbE2qnAtu762\nlkFAocK9Fj3qTOVAIRgM0tLSovT51JdjjMjDUB15FLDbld532tooqKpisMHCg3AEbXpLKR+WUs6Q\nUs4ojGNE6srO7pA4V/igR7ZtYz0w6NNPlbWpb/i2KFQEzfj0U05DscPQR3AKHYZr5UruA7wKw2r1\njlhluGpk9WreAoYqHBWmpaURtNmUJpc2bd9OFTBt40ZlbeoJmyprjNTX1/MpcOaKFcra1CXOVd53\nKSXfq63l6wrfd4CQ3a42/2bjRt6sqGCGAYnKXVHhMCqB4TF/D9M+6/EYIYQDyAHq4jw3KfQNygaF\nSz36tDxD4SatPuVX6TCira3KlGp19KUelVN+fdkob/BgZW3m5eXhB8IKO3f9vmcpXDoDCDmdRBSK\nJOoVEZUoKetoHbHK6oA+n48SINOmcLyq15pQ6DCam5uZJyWlinM7wk4nUmGOmL6sqUJ6vz9U3LG1\nQJkQolQI4aJjE/u1Lse8Blyj/X4R8K6UUmqfX6pFUZUCZYCS8AFneTnvA40KZxh67QaVYbXpkybx\nB6BaofyCbGvDD+QojOrJKSnhm8BmlaG6TU34gTyFjs3tdnNOWhqLpkxR1qZ+37MUSLDHcktZGXco\nqL2to9fsSFe5hDJyJAuHDeNzhc+nXgtDZbQhbjc/mj5daU6TbqdNcZ7UPWedxa0K3029XonKaMPe\nSNlhaHsSNwNvA1uA56WUm4UQ9wghFmiH/R3IF0LsAG4FbtfO3Qw8D3wGvAXcJKVUEtbkvPJKTgIO\nKpymdU7LFSZGZU+fzveA3QpHW7K9nbDDgU1hm/aMDF7JzWW7wjbDLS20g/Jko+qCAnYrHLnro+sc\nBRLssXjz85XWc9dnqaok2AEoLmbxhAlsVigN0lBbiwPFtRuEYHd5OZsVBhHoDkNFKYNYPMXF7Fc4\nY9N1qVSufPSGkt1bKeViYHGXz+6K+b0duLiXc38B/EKFHbHkadMzlZvendNyhWF2DrudoqwsGhTG\nuTfYbNQZUKTl5LQ0HPv29X9gnERaWwko1D3S+boQ5Cms4aAvnalMhAS4qKWFbIV5A7rchFKHEQ4z\nzuFghcLnU48IVLp0BpzQ2Eg8ATHx4vP5KEXtigLAqbt3Q3090WhUyaCuTWHVyv44Yja9E8Xx7rts\nEwL7zp3K2lwXjfLLiRNBZaW07dupbm6mXGFc9l3HHMMvxo9X1p7Ov6qqOE7hBuDDEyawQKEEu843\n6+uZv22bsvZWDRrERVlZ2BRHy0xqbeUshSPNvULwQyBDYVgtDQ0sXLyY+dr+iArq6+t5BnCrtBO4\nfPlyvt7YSFTR8pnP56MCsCmq1aIzeedOrgYaFUV0VQwdyjeB9NGjlbTXF0etwyAQoExKggo3k7e2\ntrJh4kS1ekraTCCoUB/fiFBAgKDicMDq5mZsBoyKom43NoVLUruCQT5VWLNDx56RgSsaRSpSwd0d\nifCo14tNpRPWns9oW5uyjri6rY0rhCDjoouUtKcTdbnw0FFWVQU+n4+TgPC99yppT8eWkaE05L/S\n7eYJIGf48P4OTZmj12FoD7rKqB5PTQ2z29tBpRy5trylMrrjzs8+43LFUg6gScYrdBjztm7lSgPq\nmUuPR2mNkdzdu7lAWWtfYtdyhfyK9tn8VVVMycxU+3xq75FHSpoV3Sufz0deXp7SPTbouO8qO2K9\nnTzFS2eOjIyOkH9FdgZ37mQO4DW4PCsczQ5D64gv2rxZSXMyFGK5z8etr70GKrM0tRfy5j171Lzo\nS5dybksLJYprWgNEnU4uaWqC/ftTb2zrVu7cs4fTDHBspKUxNRRSUwazsZEHV63iZwqXNnVcWVm4\nAP/TT6femJT8YvFilu7dCyrrtWhJqvcADYrqj3/trbeo8/lg0SIl7emItDQuBFoV5aEMXr0aCbif\ne05Je/+/vfMOj6u69va7Z0ajGfUuWZZcMca9YBs3wMY2oRhIKBcIAXJD+S4llUsIaYSEcAklBJJL\nQkK4GAIJgVBNCbbB2AZXirvlhoxly2qjLk3RzP7+mHPGY3k0mnKKQfM+jx5LR2eOl05be6+91m+p\n2LKzOQmQK1cmfzCPh/+86y7WAnk6K9XCl9lhjA3KWU3XKE7YsW0b2YAnPR209ORZWTRlZdEOoIGw\nn1wSVGA5OLa3nFfyVI8cyadA4MCB5A+maD3t02EN4/OJE1kOeLQYESvaRDUaFheqdEyfzjNAkxbZ\nLS4XZepMRWOJiKYxY9gBdGqkJzVJvc/Hj9fkeCptc+bwHtClkcOcovQdR+M1DN/ChTwPNGuhrKtc\nk0NCYNMwGacvvrwOo6CAW667jiEa5c63KYt+H1x3HWg5lRaCh779bQZZrUgNXp6+9nZ2AQ2zZiV9\nrN6suvpqpgDtGjgjdS1k06JFSR+rN4fOPptFQKMWInxKgdXLGuoeqQTmzuUa4JAW602KnU9Mnw4a\nqsAC7Hj8ccYBhzUaKNn8fl4fMgQ0Hix0/PCHnAVUa/TMC7ebTzMyYN48TY6nknbFFVwB7NPifCrX\n/aca1wj1xZfXYRDsanakuVmTRUVdiqIUCgoK6OnpoUODUJevvV23zltqLLdZA5kIT0sLAbQVHlQp\nKChgKNC2a1fSx1KraPUoiiosLGQukLZiRfIHU3t26BDH1jpFXeueHSoF+fnkAG21tZocz+Lx4NfY\n+ULwfE4DbFqEy5VZZZoB4Sj4kjuMCa2tPOTz0amBPEiT388SIE2H1LWRnZ2sAjo0kA7f84MfcAn6\nOIwSh4N2wPqHPyR9rIZ587iKYPGa1uTn57MSKHjggaSP1VFayoNAmg5KoAUFBfw3MGbJkn737Y+A\nxcIKIKCDxHVxSwv7gez339fkeJ0AOrzg8vPzaQbGvPqqJsez+nxIHeqZ7HY7T1gszHnrreQPVljI\n8sJCfFrW3kThS+0wKjs6+DbQqkGx2aGMDL4JOKZPT/pYvcl3Ojkd6KquTvpYdVYrn6GPw8gtKSEL\n8Ggw0jxSXMw/0D4DBYJ/uxvwaTBjaygv53YgXeM4NhyVOEcDXaHWvDwWAi1TpyZ9rN7k5uUxHOjR\nIEHB7/dTCmw855ykj9WbdIcDN9plHF6Znc3zCxZocqze9Nhs2uhJTZzIrUVFdBmQUgtfcofhUKXD\nNSg6UiUc9HgRqxWaXRq8iHNfeYUL0CkkVVpKAPBokOfu/eQTZqCPneqLOKCBw2iprSWbYLhDa1TF\nWi1qRtRwUaEOMzb1OXJrkEDS2tqKlFKX6w7gsVg06TEipWRXays2nXpM9NjtWDSSW9Gr7ioSX2qH\noa43tGugNln6/vu4gUINCwFVVBXUbg0cxqhXX+VadHoRFxYGR+4avDgqnn6a59DZYWhQM5K9ZAlt\nQKEOGShCiGDNiAYOw7t8OXuBYRrKkIdQpcM1GCi0VFfzIjBOi9TsCHg1kg7v6uriZq+XqTo87wDS\nbseqgcOQTz7J3oYGhmlcVNoXX26HoYy2tJAO97a0kE4wd15rchRRu24NigyFxxNUgNVhRBySDtdg\nyu/v7NTNzqysLDwQWhBMBlU/TEsJ9mNwOrFpkF7ZXVvLSCBXj8VPDaXD2w4e5BKgWEN573B6rFZN\nrrvL5eIuYKzGPcJVpNOJVYPr7na5yAGyDRAehC+5w8gsKsIHdGigCBrq5KXDIlje4MFsBFwaSC9Y\nPR78NhtpOow4HA4HT9tsVGlwcwYUCXY9ZhhCCJ7IyeEtDfL8vW1teIFCndIWl44YwXcmTkz6OGpH\nvBw97HQ4WF1YyF4tsg2V2b5TpxDKG6NH87oGs8Gmpiac6Jd9tGL6dG7XQAVXFZzUWnq/L77cDuOC\nC7ADuzTIIAh18tIhNOEsL+f09HTWlpcnfSy9MjtUHiot5V0tMnG6u/FZrbo4NoCPBg1ipQYPe097\nO270mQkB9AwezAYNKvxVCZwcjSXYAbBaeWjuXF7VoDVxu85S3BumTeNFDUbursbGYERBJ4fRMXo0\nb3Z0JJ3yH7ruKYeRPBmZmdjtdk3yx0NN23WqpiwoKNCkviGtp0eXHHeVgvx8WjQI8Qm3G7+Ocdex\nmZnka1CR3tPZiVsIbBr2cQ9nghCcd/AgJBnPDvXs0CGtFoL3pxbPkToTytRJirvC4SBdg4iCLt0L\nwxjl9fIVr5euJNdbPC0t+Aj2sjcCfZ6CEwRRV8cSq5VqDSQNPpKSt0eM4BydXnJvt7Tw0fr1SR/n\n4ilTsGVmhtobas3zBw7QqoGm0J9GjaLB5eJ0DWyKxP+rr2eKBtlx6woLeT8/n59oYFMkprS28rWW\nFmhrgyReojUWC2/YbJyvkwDdva+9xqlaZEm1tXEAGKzTmtA177zDVzweuru7cSYxuGtTQ2c6OYxp\n27fzdaCpuZnMJEJTh8rLeROY/0VYwxBCFAghlgkh9ij/Hnd2hRCThRBrhRDbhRBbhBCXh/3uKSHE\nZ0KIT5Uv7fpqArjdXNHdTZYGL7jXvF5eWrAANG72ozLS6yVLgxnGvo4OHDqNMiEoIa1FGugHUnJY\nx9xxkZmJ3Z9888b3MjJ4Wcv+J71IV17wyaoqf5Cby60VFaBDUgaAw+8nq6cHT5Izoa2ZmUzMycF2\nxhkaWXYslowMnCSvRlDb3U0+YL/lFk3s6k1abm5QWTfJ2dCWkSO5FX3WAiORbEjqR8AKKeUoYIXy\nc2+6gGuklOOAc4DfCSHCldxul1JOVr606yIEoQXqZAu4pJS0NzZSpIMAnYpPC+nwri6u//zzoFKr\nXqSna5IGOv7gQaZYrRoYFBm110SyyCNHGJ6VpYFFkUlX7qnWJNUIXC6XLjUYKjI9HQfJv4j1rhnQ\nqteEq6UFj9OJU6dzqg4UWpKcBTcr4eEvisO4CFB1DZYAX+29g5Ryt5Ryj/L9YaAe0L+XIIQchj/J\ndMDOzk4e6enhzscf18KqiPTYbElX/Aaam/nv7m7GaNjH/DgyMjRJA/314cMs1rDda29sWVlkAD1J\nOs8f79rFr7dt08aoCDg1qhW6+NNPWaqRlH9EnE5NXsSVVVU819SkjUR+BGzZ2Zr0mvDX1PCA1Qo6\nnVOHRgOFc599ll1CYLfbtTCrX5J1GKVSSlXp6wgQNUVDCDEDsAPhzQV+rYSqHhZC9Kn0JYS4UQix\nSQixKea+vUoMM5Bk5afL5cJBcJSlFwENKj/VepN0HRupCKeTdCmTavoTCARwSIlNx5G7mg6Z7AjO\n6vXqmnWmFpe2Jekw0jo7ydKoI14kREaGJi/izMZGZrW3gwbhwkikKU2pkp0JWWtruaWjA3Sqw9Bq\noEBXF36dEjIi0a/DEEIsF0Jsi/B1Ufh+Mpgf1meOmBBiEPAM8J9SSvXOvhM4BZgOFAB39PV5KeWf\npZTTpJTTimNdHLTb6UxPpyPJEbfL5cJJsNhGLw6NGMEWvz+pGLE6WtErxx2gdvp0niS5B7KtrQ0H\nwdGgXjTNncvlQHMS1cmBQABbTw9CR4dhmTePk4GDSV4z0d1Nj45ZZx3z5rGc5F/EPTqmpwP4L7mE\nn5C8Y+tW/06d7Ey/7DLmAEeSDR+73bpe99706zCklAullOMjfL0K1CmOQHUIEd2lECIHeAP4iZRy\nXdixa2UQD/B/wAwt/qiw/5jf/uQn/MrrxZfEhVEdhtDRYay77jp+SZIvYmU0rafDcJ1zDg+Q3APZ\nVF+PHX0lma0TJvBPwJVEOLK1tTV43XVMU86rqGAP0JjEOlsgEAhKcesYlvDedlvS1x3CZvs6OeGM\n887jCZK3U89CXYCMkSPZmJZGQ5JyKxaPh4COkY/j/r8kP/8ahDI4rwWO0xUWQtiBl4GnpZQv9vqd\n6mwEwfUPzYPF6mJQMi9iNSRl1aAysy9UO5O50dWQlF5FUQCFWVnkk5ydLUq/gnQdkwhKgLOA1iRi\n5aHrrmPorCAQ4DaAJHp3tLe3k46+IVMt7s9AIIBUZ/s6vYizvV4mWyw0J5l9FBLY1GmQKGpr+S+n\nE2+SGZwWr1fX637c/5fk5+8DFgkh9gALlZ8RQkwTQjyh7PMfwBnANyOkzz4rhNgKbAWKgHuStOc4\nvvLSS9QDrVVVCR/D5XLxHOC94grN7OrNnKeeQgLetWsTPsa+khIyAevChZrZ1ZuxL7yAC0h/442E\nj9HU2clcoOuCCzSzqzflVVWsAIb//vcJH8PlcnEP0PCVr2hmV28yu7t5EPjaX/4CCVb9NjU1sQo4\nrIP0vkru97+PBBb95S/BmpEEaG9vp0lKGgYNCvUK1xrx1FN8Eggwfs2apI4TCp3pFY7cvp1H29r4\n+rJlSR3meZuNbaecopFR/ZOUw5BSNkkpF0gpRymhK5eyfZOU8nrl+79JKdPCUmdD6bNSyrOklBOU\nENc3pJTJ61H3Isvtphjwf/BBYgdwuRj2+uu8BzhuvVVL047BpzzsziS6r9k//pgCoFDHOgyUl2dZ\nEjd6c30964CsMWM0Mup40pU8/9LNmxM+hsvlYgng16GNrIpQajwKWlshwbCUy+XiUeDADTdoaNmx\niPPPp8piYfzOnZDgOXW5XPwv8Ma992prXDjz5wMwMYkZW3d3N8/6fNx/zz2g18t40iQAxibRYyQQ\nCHBfdzdVc+ZoZVW/fKmlQQDqv/tdIAnp8IMHOXvpUqbZ7UlVjvaH/OY3cRMWO437AJJLH36Y69FP\n9wgg87zz2EBy0uELfvITXkSf3g0quZMm8WdAJFEzUvn73/MWOue4Oxz8StV/SjA5w/LmmzwNFOkY\nMuXSS7lLrc5OMP27Y9s2vg8M0kDEsE9OPZV1ubnJZRxeeCEvAwWlpWDR6RVZUsKLI0diTSKzzf3g\ng/wzEND1OerNl95hqKJc3YmuYSgPsV4iZCqhLnGJLtIqD7FMT9dN9wiC0uFuOBqLTgSPR1dBPwCb\nzUbAbseaRLJD2uHDDEVfxwZh2WIJvoht27dzNZCvc5vO0JpTgte+Z/NmfguU6llYCgQcjqSue6Cu\nDif6X3drZiZ2KSFBp+H79FPmYlzRHgwAh6GKsXkSlV5QHmK7jrUNADk5OcFeE4nWjCh26rlAC0Hp\n8GqHg7okYrtWjwd/Wpqujg1ge04Oa4cOTfjzUseeHeEcrKjgfwYPhgTvMW9bGwGUEbGOtJaVceOY\nMTB3bkKf7zJIirtm0CA2JHFvBZTrXqSzAz40ahT32e2JO4zWVrrR37GF86V3GDnDhzMD2DhsWGIH\nUEZTGTp7cYvFwuT8fJ6eOTOxAyh26u0wAO4dOpTfTU5c9svq8+m3mBjGB5WV/O7kkxP+vFQk2PV2\nbN3DhvFHiyVhh+Fraws6Np3v0YySEt7z+SDB/0cNC+stxf3BGWdwaxKyM7K7O9hdU+cXcfOkSdzp\n9eJLMETn6+jATWqGoSnW9HT25OVRk2hMU3kR6yVzHE5OYSGuRENnygwjTcdiOJVkpa5tPT26pSuG\nU1BQEBR3SzRmrrMEu0pZdjaDGhsTXvT2d3TgFkK33iIqJTk5LKqthR07Evq8R1mf00uCXaWgoICW\nlhb8CVaTC7cbN/rPMIqzsykDmhNc+PZ3dKRmGHpwQ1oa+bt3J/bhc85hSm4u3hEjtDUqAt91uzn9\nk08S+3BJCbeUlXHQADv/n8vFXRs2JPz5Z8vK2DF4sIYWReZKl4tVa9dCguHIHZmZ7NSxVkRlbGcn\n67u78SaYydfe00ODAfIQxVlZPNbZSeDf/07o82pCh97h3UUbN7IPaEnwum8fPZpV6D9yn1RVRS3Q\nkaBelSsjg12kZhia84umJiYm6DD86elsbmsj14AGJWd1dDA10UKzrCz+7vEghwzR1qgIVEjJmCQq\nk+93Otk/erSGFkXGkZ2NFRJepL2/rIznJ0zQ1KZIZCbZe/6xESO4ygA71bUHT4Kz4LcGD2ZGeTno\nPFvPtloZCjQnOAt+bvp0Xs7L0z0U6VB1xBLUO3t54UK+jv5rbOEMCIfhs1qRCaaBti9fzh1SUmJA\nqCeQhHS4v76e05qbGWxAqMeSjHR4IICtsZESnbPO4KgiqD/BRIKmpiZDRm+ZSuijM0GHobdkuIo6\naEq0d8eRtjZ8JSX6paoq2HNzsZJ4qKepqcmQME+mcs0SHSg0NTWRm5uru2ML50vdcU+lx2ZLeJTp\nXbGC/wH+aYQXdziwJXjzdK5ezVvAC0kq3saCLSsLJ9DT0xP3zRpoaGBnSwtLP/9cH+PCCFcEzRs1\nKu7P/2v/fg4bkESQpYhpJuowvl5VRaXO8XaAgsJCukk84/Ckffu4KEkJ/1hQBwqqBE1c9PTw9N//\nzp8MCJkmO1D4+quvknhKR2IMiBmG325HJPgiVes38nRqKRmOcDpJ8/sJJDB6N0JHSsWWk4MNEurt\nrU6/9ZRgV1HPRSIvjkAgQIXfT44Bo7fsJGuFJrW1MSZJEbtYKCwsxM3Rxet4mVxbyxU69kBRUR1G\nQpLxbjdWKXEYMFBQr3tXgrpXQxsaGKljE7JIDAiHEUhPD6o6JvAi9rS00AMU6pzjDkBODn6CKqnx\n0qFMv/XOcQcIDB3K+wQlPuKlVXEYRmSd2U45hd8BiYzfWltbgxLsBrw4ckeM4D+B/QmMaqWUpPl8\nhmSdFRUVcTqwKUGpFNndHZzt64xj8mSeBVyJODYlEmFEtmHm+PHcDnyeoMqw1aBsw3AGhMN484Yb\nuJnEsia8BhbHfHTLLUwiGJuMFzXH3QiH0bZ4MfOApgTWhdQZht51LQDOqVP5PnAogXRTV1MTTvSv\n8AfIHzyYp4DqBF4c7e3tONBXel+lqKiI7UBNAumqgUAA4fEQMKAzXNZFF3G1EBxKJPylfMaIGbC1\nspIn8vLYm+B6oN3vx6Kj9H4kBoTDsJ9yCkeAxgRCKGpxjN452XDUKSXkMJRwRq4BM6FkpK7VmVCG\nAQ64qLAQB9CYQEiqWWlGpXcKKEB2VhZzLBYC+/fH/dnGxkbdJdhV8vLyuEIICj/8MO7Ptra24pDS\nECluq9VKQUFBQs+7mvqrp/R+iJ4epubk0J3IWgtgDwSwGHDdwxkQDmPs7t1cQ2IO48WZM5mYlkam\nnsJuCidv3swzJGbntmHDOBvIHTlSc7t6U7F1K7sATwIFXLVWKz8E0hW1Tj0pbmwMzg5XrYr7s67G\nRv4OMG6c1mYdh7BYWBkIMD4BafuGhgYOAdKARVqLxcIdViuT1q3rf+deqI7NkBDKihV87nKRl4Bi\nrcvn41HAn0CSRNw0NLDi88+ZkEAdht/vZwPQXV6uvV1RGBAOY8SqVfyAxF7EdW1tWIqLCfZ40pei\nujq+ATQmkA74ud/PciHIMyAkledwMBroTKCBfQ3wAJBjgMNwKusk7gQWk+va2/k6YPva1zS2KjIe\nIRJK/21sbGQB0HhHn92NNcWflpZQxmFDQwOXAR89/LD2RvXGZiNDyoQUqhtsNr4LyKlTtberN4rz\n9CaQsNDS0sJ84DMdpfcjkZTDEEIUCCGWCSH2KP9GXMkUQvjDmie9FrZ9uBBivRBirxDieaU7n+ak\n5eQEQxMJOIyJH33EzdqbFBH1BdecwBTVuXs312RmYtE5xx2Orj+0J+DY2g8d4iQg34AZm/pAJlI3\noN4rMfePTxKv1YpM0GGAcXYG0tMTyjhsbGzEC+RXVmpvVG8UnbJEBgpNdXWkA4VGVE8rdvoTKIJV\nw8FGyoJA8jOMHwErpJSjgBXKz5HoDmuedGHY9t8AD0spTwKageuStCci9txcnCTmMGZWV/O1JPpC\nx4MaN21NoPJz3ObNPJ6o0m2cqD2uE0kHHLRpE3sAqwF1GOoDmcgITuzcSRuQ+957GhsVGZ/NlpBk\nfENDA+8CZW+/rb1REZAOB5YEiksbGxv5b2CYEedTGSgkkv5re+893EBlEq19Y0ZZzwl0diLj1Dtr\n2b2bncC4BHW9EiVZh3ERsET5fgnBvtwxofTxPgtQ+3zH9fl4sGVl4SD4cMWL8HgM65mrZrokIhXQ\n09GB14DZBRB6IBNxGKHRvhGxbMVh+BJwGB0NDWQDwqA8d7/djkggq8dVX898wJFg8Ve8CKczmMYb\nJ42NjVwL5CXa+TIewq57vC/iDuWe1ltRFwAh8Nls2Px+OuMc7LUcOsQpQJ4BWWfhJPuGKZVSqvGT\nI0BfKToOIcQmIcQ6IYTqFAqBFillj/JzDaDLyp3IyGBXenr8M4wNG5je3Y00Ktc5L496my3+grja\nWi6uqcFvlERAURHrCgqoiTettqeH61RxRYMcxivjxrEmgTTQ89VMIIOu/asLFvBQvB/asYNvPPss\nYExaLcA7ixdzFsT3Im5tZfGf/8xIwGpAfQOFhWw57TR2+/10xBPukZLZf/87YEyhLsD6b3yDl4g/\n+jHk6acByDIgezOcfh2GEGK5EGJbhK+LwveTwTuor7toqJRyGvB14HdCiLhTeYQQNypOZ1PcM4UL\nLuDJIUPivihH3xCtAAAgAElEQVSBt94CoMqABVoALr+cK884g/0dHfF1X1OUY/cZdJMzciS/XbCA\n9+ONZR86RLqUtKelgRGxVyF4b8EC3kwgVDdavVemTNHYqMg0TJnC+11d+OIZvb/7LmMPH2ZTZiYs\nXKifcWE4hg7F6vfTHo+Y55YtjN23j/1paYhLL9XPOJXCQj656SbSgM6XXor9cx0d5CizUXsSfVTi\nofniiykA0u++O67PlSqZVVkn2qK3lHKhlHJ8hK9XgTohxCAA5d+Ipb9SykPKv/uBlcAUoAnIE0Ko\nw+IK4FAUO/4spZwmpZwW9wLfvHn4Skr4w/Ll8MorMX+sfeFCrgI+P+us+P6/JCguLubN9evhZz+L\n+TNy+HB+KwTvXHCBjpYdyyyfj9sOHIB4ZhlWK6vS0njy7LN1F6BTGe/zsbStDV+ccuwdQvDimDFg\n0AhuUHo67YD7oTjmGbNn89iQIfxsxgxIoqFVPBQVFbEG4ro/KShgVXk5Pxs5Ei66qP/9NaCoqIg7\ngOzf/Cb2D/X0cDgnh9uKikLrC3pTVFTEXKD0mWfi+pzw+XjSasVpgOpzOMk+ta8B1yrfXwu82nsH\nIUS+ECJd+b4ImAPsUGYk7wGXRvu8VuQVFDDU7YY4ZhkNpaU8hzFFeypFRUW4Ia4ZRktlJbdJiWP4\ncN3s6s0oj4cb3G78cWQgBcrLme/302jQqB2gKDOT04G2ffvi+tzYvDzemz9fH6MikFNcTBbQHc8s\neOpUHnE4yDNCtkZBvT+98SwojxvHHUOG0F5RoZtdvSkqKqIbCMQzoMnP5/o5c3g/iba+8VJcXEw3\nYPH7oaen3/1Vvn/hhfzG4BoMSN5h3AcsEkLsARYqPyOEmCaEeELZZwywSQixmaCDuE9KqS7t3wH8\nQAixl+Caxl+TtKdPQhXQcbyIOzdu5DSMTV0rKiqiS8q4bvTGgwfJBooNdGyqEmxLHLUYLpeLQCBg\nWAooQLbyf8WTAuz3+3G5XIYOFNT7M64U4Pp6Mo4cMXxA001QASEeGhsbzRl4xbnOZpS0uUrITojr\n3XTY5SLHwIGCSlIOQ0rZJKVcIKUcpYSuXMr2TVLK65XvP5RSTpBSTlL+/WvY5/dLKWdIKU+SUl4m\npdRNm1vVWIon57ngr3/leYx1GOqII56UQNsTT9AGDDJQVyZUMxJH+mHHO++wFzg5QbXTRFAfqo44\nHEbzgQO8ICWnGpR5BFBQXIyX+KTDA/fey/ttbaY4jLhqB/72Nz7au5eTDczoUe2Mq2Zk925+v2UL\nsxNt6ZsAubm5R7MbY02rDgS49uOPOduAYuLeDIhKb4A8pY9wVxzVnz3t7XRjTkgqntoBtaK1wMAp\naqYyco+nZqSjpoaRQL4ROj0K6sg9nhRg14EDXAIMSrCZVSIUKr0m4kkBdre0GKZzpqLen/HMgP2t\nreQAOQbamZOTg9diia9mpKmJGW43JQYqwAohjuqAxeowPB6ubGhgUhwhLK0YMA6jsLSU14GWOCo4\n/Z2dhjdZLyoq4jHg0MyZMX/G3dJCACgyQE9IJbu4GB/QGofEudqzwwiBRJW8yko2Ak1xpNaqYTYj\nBBJViouLeQLYG0e4zqMoKRsZ4svJyeFhi4X34lhkVwdpucqgzQiEECwpLOTB886L+TM9yqzJaWDL\nU4AVlZVc8tWvQoztldXuoXYDB14qA8ZhFBUVcSGwL44XcaCzE48Q5BqgWKpSXFzMH4EdEyfG/Blv\naytuoNiIYiMFx4UXYgf2xOGA1c5iRuW4AxScfDIzgI1xONNWxWEY0YxKJSsri585nayK49z4lOtu\n5AxDCMH60lJWxSH7rs7ujLzuAO6yMj6NI7ykXncjWgSEU1BcTEMcM2DVATtSDkM/1FFYPDUcsrsb\nf1qaIcKDKkVFReQAHXFIXfva23EDDqXC1QiKEjifaugs38AXR1paGrm5uXHV4LQZ2IxKRQhBSXEx\nDXHoiPV0dBgeMgWYnJ9Pxp49Me8fCpka7DCmOxzM2rwZYqxtUcOreQbOhAAmp6dzy9atEGMmn+tQ\nsPrAiJ4yvRkwDqO0tJS1wOg//CHmz/xp+HD+MmyYbjZFoqioiGeAc+JQ9Vybn8+fDL557A0NPJOW\nRua2bTF/pkYI3rDZSDf4BbfG7ebUOCQpWpqbOQDkGCGUF8bbjY3817JlMe//8cyZ3IPxDuP7LS38\neP36mPc/qMyaSw1+EZ/Z08Pt+/dDjAv0TR4Pm4DcGENDWjHUbufylhaoqYlp/+YjR/BjbMhUZcA4\njMLCQvIgrjqMVV4v9Qb0lwjHbrcHJaTjSLFbYbfz6kkn6WhVBLq6+IbPR3ocIoKrMzL4zpAhYPBU\n+iSfD2ccU/6t6elMzMkhzcCCTSCoWRaHAOGmggJeEsLQNQwINmtKi2PB9eMhQ7gZKDPYYYRCNjE+\nSzsqKpgO5BlUBKmizmR7YhQ5PZidjQ3o+aou0ntRGTAOw2q10mOzEYgjHfCUAweYZpQ+UxjC6Ywr\nu8N/+DAnGdBK9BiU8Fd3HBLSDQ0Nhr/cICgdHohDHqSuro5SE3LccTiwxJEGat25k1Pz80lLoAVt\nMqRlZ2MPBGLWk6o7fBib1Uq+wYvJ6gg81nu0XkngMPraq6nfsYqOqmFgI9csVQaMw4CgImggxhGc\nlJL7m5q44MABna06HktmJrY4NIXu3LuXe1RRP6NQJaTjqBv46pYtLN28WS+L+sSflhZXGmjZzp38\nraEBDh7U0arjsWRkYPH5CMTY4/mat9/mf0xIrVTbBbTFmAK8+F//YjcY0qslHFWYrynGUM+QFSv4\nRAiyDLZTXdOLNUVdbtnCE0CJQW0XwhlQDoP0dESMDqO5uRknYDN65A7YsrOxx/gikFJi9XiMU9RV\nUf6/eOoGrG1tZCagHJssAbsdurtjfhE76uqY0dISl1SDFlgzM3ESe690q8cT6k1iJI78fNKAukN9\nSr8dQ6CzMxhmNZgsZTbrijGRwFpby2QpEQbpSKkUVFTQBbTFOBMS1dVcB2Sl6jD0pWroUFbGOHqo\nq6vDAaQbmFKrsn/8eH4Z4wPW0tJCupRYjX5xOBy4HQ7aurrwxhA+6+npCWadGazfD1A3ejQ7pKQp\nxnWMUJW9gVlnAA1z5/IUR0Mj/WHt6cFmROfCXnSefTaXE3xGYqKrC2nCdbctWsTJQHWMz4a3vZ0e\nIcDgMHT+pElkAh+PHRvT/u3KOqxRkvbhDCiHsWnRIu70eGKKvdYdOUIGxhfxAHRMn84DXm9MTVVq\na2txYFCfgXCsVp5+5BF+S2wvuIaGBhwEW3wazfbbbuPXBM9Vf7jd7qOd7wx+IN2XXspDxPYillJi\n9/uxGX3dgayZM/knUBdrIoHHgzTY+QIUjxjBHqA2xhmbv70dr0ENs8JR10yOxKjLFlItSDkMfSkt\nLcXj8cQUe21Q4p5OE1LXKnNyGE1wsbA/amtrcQJ2E0JnatZLLDe66tjMGBUNUmLEsdhZV1dHyEKD\nX3Jl+fnkE5vDaG9vD153E2bAZUJwFkHRy/6QUmL1ek257iXAbYBP6R3RH/7OTnpMSHLJcDj4R1oa\npWvWxLS/W3WAKYehL+f/+9/sJbYXx5GmJuYCadde2+++WjNl61Z2AY0xFEfV1tZyL+C78krd7erN\nzCef5CZiPJ9HjrAGaDM4VRVg4sMP8wqxzTCOHDlCM9A+ZIhhPRFUhv71r9QQ24ytrq6ObwL1BjVO\nCqfwk09YAXj27u133+bmZp6TkgOnnaa/Yb1Ia27mQSC9qqrfff1+P1vdbg4Y2CIghMXCJT4fedXV\nMe3e2tZGt91u+IAGBpjDyHA6ySO2EdyRhgbWWa3kG9VtL4xQdkcMi4q1tbU8A2RffrnOVh1PwaZN\nnEbsDuN/Ad8vf6m7Xb3JcLsZSux2/gnY8/LLYLAaqDMvjwyC4dD+OHLkCC8AdhNexFZl3SSWNNC6\nujr+ADSYUDOgjsC7YwidNTU18VspWXnTTXpbFRGvxRJTAonH4+Hhri4e/OlPwYRw+YByGM78fPKA\nU26+GaJ58w8+4MbHH+f36elYTEirVfOyhz31VPQdDx7kq7//PT9PSyM7npauGmHJzGQxMOMPf4Bo\n60JeL3MefJC3ML54C8CWlcVo4KLHHoN+pNWHP/IIb2COnWrG0zeffBL6CaNkPfkkPwEqDE4BBUIv\n4quXLYM33uh7v6YmSq++mlsIhtsMRxmBX7ptGzz6aN/7BQLYv/lNXsL4GoyQCVYrl9fUQD+z4O4f\n/pB/cTTMajQDymFYL7uMNUDJ9u2hPtgRWbaMoU1NnGJCPBMgS1HYLN61K/qOGzcy6uBBFlutiBim\n3Vpjuflmmi0WJm7eDNEKzmpqGL1zJ7lWq6F6VyG+8Q32pqdzyuefw86dUXcd/cEHlGGsAmyI885j\nbVYWo+rqoB8pk9JVq7gHKDEhXZXp01lVXMywtjZ4992+99u6lYKPPuJqYESM4RZNKSvjvREjKPd4\nIFr4rK2NvLfeIh/zHMY+VYamn3oq5/PPczFfUIchhCgQQiwTQuxR/j1uGCGEmC+E+DTsyy2E+Kry\nu6eEEJ+F/U7Xmvzcc85hsRA8edVVMG9e3zt2d+MRgvtmzgQTYpq2ESP4VWYme/rTCFJmFQ+PHQun\nn26AZb347nf5VWUlL/XXV1ix858mPYxccAE/nzyZu8eMgX4kVGw9PaxyOg2vngZg0iTunTuXi8eO\nhSuuiLqr7OriTSBvzhxjbAunuJjHFy1ixPDhEK0HuXLdvwdkXXaZMbaFY7Xy2oUXkp2VFX2Godj5\nD8xzGO9cdRVzAXc/7Yul282fMGcGDMnPMH4ErJBSjgJWKD8fg5TyPSnlZCnlZOAsoAt4J2yX29Xf\nSyk/TdKeqFitVrJKS1nrdEK0snq3GzdQbkLPXJUXRozgN2PGRN9JSf/MNWm0AVAzciS/LSqKvgCn\n2GmkXHhv0oYM4Tm/H6I54Z4erIEAaSakqqoMqqzkg8ZG6C/rze0m4HBgNSENFGDw4MEcPnw4eoq6\nct19JsiCqJSWltLR0RE9RV2x003w7zKDgqFD+QCo66emyeLx0M0XdIYBXAQsUb5fAvS3snUp8JaU\nMr5GuxpSWVbGyI0bYceOPvfx5+SwQ0oqDVYrDaesrKz/RVplZGS0bHQ4g0tK6D50KHpVtPJAmqGu\nqTKksJDRNTUQ7Zwq59OMVFWViooKrqqvx7diRdT9LCalqqpUVFTwM4+Hzp//vO+dlPOZXVxsuCyI\nSnl5Ob8GRLTsPOX+FE4n2SYNFsrz87kaaO1HBdji9eIGSkzQkYLkHUaplFJdpTkC9DefuwL4e69t\nvxZCbBFCPCyE6DOPUQhxoxBikxBiUzw9GHozbPBgfrR5M7z+ep/7HL7xRmYTfCjM4j+bm/nnpk1R\n9+m+9lqygCyDJdjDWdjezkfV1RBlDUVOmMDC9HQ6+5sx6cgop5PXurrwvPVW3zvZbNyVn8/no0YZ\nZ1gvKioquBfoeuGFqPsty8pin0mjYQjauQAILF/e906LF3PNjBkETLw/KysrKQSs0VLUy8t5aPp0\nDpr4vA/OzeVpIPDOO33vJCXLxo9nc14eNpPWV/t1GEKI5UKIbRG+LgrfTwbnpn3OT4UQg4AJwL/D\nNt8JnAJMBwqAO/r6vJTyz1LKaVLKacksSJapN28UTamDSkGSmQ6jJDOTIX4/PVGyn2rr6+kEBpn4\n4shWrkV7FCfeYbGwwuMhz4wcd4V8JbzYFqXGIWC3c19nJ97x440y6zgqKiro5mh3wr74gd/Pzrlz\njTEqApWVlXQTlNPok+xsPmxqYtDQoYbZ1RvVThEtizAvj+cJrh2aRbnSRiHac4QQPDZkCFUmOuB+\nHYaUcqGUcnyEr1eBOsURqA4hWsXRfwAvSylDMqxSyloZxAP8HzAjuT+nfyqGDMFNmF5QBAruu48/\ngqkhKbUWozZK5z33Cy9wP+bFMwEKFGdVFyULpn7dOq4GhpjQUlKlWLmWrVFCUnUHDnCy18tJJk33\nIRhD7+Zol7pIdHV10dTUxBCDG/2EU1FRgRvwR2kXINet4+LqaoaZuBao2hm1XUBjI0P27jX1uhcq\nz1HUgYLfT+fBgww20c5kQ1KvAWop9LXAq1H2vZJe4agwZyMIrn/E3r4tQSorK3EDHVEujHPnTsZj\n7gxDrcU4FKVto3X1am7C3MX5IuVF3BhFQrrrnXd4GhhpgnyJymAlOyqaw2hYs4atwNQYtYf0QH3B\nuaMMaA5+/jle4LyPPjLMrt6UlpbiFiKqbHznq69yv99v6nPkcDiwZGRg8/uhD6Vk3+rVvNjczCQz\nUr4VRFoaPqIPFDh8mHc3b+ayOKT6tSZZh3EfsEgIsQdYqPyMEGKaEOIJdSchxDCgEni/1+efFUJs\nBbYCRcA9SdrTL+oUtStK9WegsxOfxUKeiSPiXCVtLtrIvaupiW5gqIlT/lLl/45Wld6sFCMNMnHK\nX6E4jGhT/nqle2ChiSG+nJwcPBYLPVGqfmv27SMNyDGhp7OKxWKhMzOT1ijV8O319fiBwSaGUABc\npaWsKynpMzGjRbk/C010bBDMJnNH6S/jVuTPc81KTydJhyGlbJJSLpBSjlJCVy5l+yYp5fVh+1VL\nKQdLKQO9Pn+WlHKCEuL6hpQy9nZ4CVJZWcm5wJozz+xzH9ndDU4nwmBpiHDyTj2VF4GDUUbE3S0t\neC0WckwcuRdMmsRdVis7ojR8UiUkykx8cWTk5nJVTg7LoqTVqo12ikwMRQohuH7ECB4aN67PfWo/\n+wyAHBNDEwCPT57Mf0VJZOhsbMQNVJoYOgPYNXEiN5SU9KkN5lJEPotNvO4A/7N4Mb+JkqZ8RBk8\n5ps4oBlQld4QDN9sEYJdUaZ1wu3GYkKfgXAyzjuPG/Pz2RllxOFtbaXHjAKzMCyDBvHssGF8HCXP\nXdXvt2ZlGWVWRPaMHs2mKE1q1FlSlhlV3mFkDBvGnig6TUcUh5FrUvGWSkVFBTXRQpEuF92YuxaI\n8v8fjKKsqw5oSk2eCVknT2ZLfX2f/WXU615k4kxowDmMtLQ0rs3Lo+DDD/vcZxfQZvLDCP3f6J6O\nDlP6DByD38+0khIao6y1hMTfTOiFEc6F6elkRUn/Da1vmHxOL3O7mR9FFqZBCZ2Z0QsjnK+2tvLb\nzz7rs3jP09JCNybJrIRxVmsru1pb6diyJeLv25Qw5SATs/gA5tXWcq6UHOojvFuv6NqVmDhjG3AO\nA+B7Ph+n97Fg2NPTw2Kvl40XXRTx94bx4Yes2bmTwj4KDKWUfK2nh99/61sGG9aL1lb+sXYts3fv\n7nOXR3t6+PkFF4BJxVsqt2zezEU1NX2+4FZ3dvK7SZPAxDUhgDOOHOHSlhb8fSzS7q+vD8qsxNih\nTS+G+/2cHwjQ2Me60B9Hj+ayoUNNK9pTKS4ooAyo6yPjcE1+Pv/hdJJtYqgH4NTly7kR+FwZEPRm\nV3c3v7BYKJihezJpnwxIhyEyMo52VetFbW0tgUDA1MwOACwWsn0+OvoITTQ0NNDd3c0wk0dFqnKp\nt7UVX4R1DJ/Px9a6OkQ/GjmG4HCQ5vf32W9iXW0te+bMMUU2Ohx7Tg4O6HOkueXIEV484wyYPt1Y\nw3qRWVSEFahRQiW92X3kCE6z708gX0k7r+/jRby5tZVtw4aByeFdW3Y2DugzqvBJSwt/Gz4cq4nn\ndEA6DGtmJpY+WrV+9tlnbARO37zZeMPCUV7EPR0ddETIda+urubnwLxtumciR0cJ3zggYjy7pqaG\n+YEAC2Lo7aE3lsxMnMCBCJL17e3tOJubmSlldJkTA3AWFOAE9kUI80kpOXTgACPKy6NLyhuAmq3z\neR9hvtN27uQqE2T3exNK/e7jRWzbsYP/MHnNEoKSNE76nmHU79vH9LIyU+/PAekw0nNzSZcyolbT\n3t27mQaUmVR6H0J5Eff1gquuruYSYEgMXfl0RQj8aWk4iHyjHzhwgGuB6dH6JhhEWlYWDiKfz4MH\nD3IFcPUf/wgm5rlDcNG9L4fR2NjITI+H+x55pF8JdL1R048PRrgHPR4PF7hcLIyhy6HeqHZGmmFI\nKZm3fz8/7GN9w0isGRlk2WwR70+ACVVV/P2DDyBKooHeDEiH4SwsxAHsiXCjH1BGSzlmL3orMwwH\nsDeCln91dTUOzOk5fhxOJ06Cs7PeVFdX4+RolzYzUUdwkR7Izz777GgvbxNF/SCo6usA9keIue/Z\ns4fQkrzJi/POoUOpslo5EMHO/fv348CcXvO9sVVU8Hp2NjsjFOs2NDRg8/nMTx4BcDrJTUuL+Ly7\n3W68am2OiffngHQYPb/6FfOJ/CKuUZyI6S+43Fw8V17JfmB3hAXl6upqMoXAbnKmDIC87z5esVoj\n2rlv3z6cgO1EeHE89hg/zsmJOHKvqqrCAUir1fRYtuWBB5gzcmREO3fv3n3UsZn9krv0Ur45fTof\nR5ip79mzByfgMHk9CICRI3n8jDNYFsFh7N27FweYqvwb4rHHeGTx4ojP0YEDB44OFFIOw1gGT5/O\nYZst4gyjRnUiZj+MubmkP/ccO4qLI9q5e/duMq1W00fDALabbuLwSSexK0Iq6K5duyhwOrEo7UdN\nZeJE5LhxEe2sqqqiwOFAmH3dARwOho0eTVWEtYHdu3eTpWYdnQDX/qSTTop4f+7duxcnwYXxE4FR\no0axd+/e49YtVTvNrhECoKyM0kmTqKmpOa5/x4kyUDA5UG8OtvXrWW23U/bYY/Dmm6Ht/p/+lD37\n9rG7spKTTa5OBWDfPj7s7ITnnoNwnfxf/ILt27fjT0/vv9GOEezbxxPt7RS/+SZMmnR0+y9/yc6d\nO2kpKTHfAQN8+CF/OngQ65Ejx9p5zz1UVVUxLz8/1MPBVFau5M+bNtHe0ICcNImQ3sC997J7927m\nFBRAY6P553TTJv73tdcQbW34J0zAqjqy3/yGqqoqBtvtnHwi3J/19Tz8u9/xMOAdNw67OoO8/362\nb9/OaIvlhJips3w5/7VkCYsBy5QpRwcEDz3Ejh07CAWfTZwBD0iHQXo65OWxp7WVYWH6Rkc6OvjM\n7Wb1XXdx8jnnmGiggt1OW3ExtbW1jBwxIvTiaFMW7J+8/35uv/12U00EYMUK8jIz2VVby6jhw7Eo\nkir+jAx2797N9muu4dyvfMVkI4GODpy5uWyrqWFUZeXRF0dWFrt27WL77Nkwa5a5NgKUlOAdMoSd\n9fVUlJaSpYZHs7LYvn075RMmBGswTFQpBmDkSFqnTmXTypWcWVhIgRp+ysxk69ateCdO5PKrrzbX\nRoDiYg5ffDHrX3qJWXl5lKlaTMr53DdiBN/6znfMtRHA6cQ2ZAj79+yhICfnaIV8ZiY7duygtriY\nH9x0E5goWYSU8gv3deqpp8pkufvuu6UQQnZ0dIS2vfLKKxKQ69atS/r4WvHoo49KQB46dCi0bc2a\nNRKQS5cuNdGyY3nmmWckILdt2xbatnPnTgnIp556ykTLjmXp0qUSkKtXrw5tq62tlYB8+OGHTbTs\nWNatWycB+corr4S2dXV1SYvFIu+66y7zDOvFvn37JCCfeOKJ0Da/3y+zs7PlrbfeaqJlx+JyuSQg\n77vvvmO2Dx06VF555ZUmWXU8Xq9X2u12efvttx+zfdq0aXLRokVJHx/YJJN49w7INQyACRMmIKVk\nR1gl9RYltW6syRW04UxSQieffnq03fknn3wCBP+GE4UpSmHexx9/HNr2kVJNP3XqVFNsioRq50dh\nlf7q+ZxyIhQXKowbNw6LxXLMdd+2bRuBQCB0T5wIDBs2jIyMjNCzA8EF2vb29hPq/szPz6eyspKt\nW7eGtrW2tnLgwAHGRRF6NJq0tDTGjRvH5rA6MK/Xy9atW5k4caKJlgUZsA5DfTls3LgxtG39+vWM\nGTPGtL6+kVBfDupLDWDDhg2UlZWZLuoWzujRo3E6ncc4jE2bNuF0OhljYmvW3pSXl1NeXs6msPa3\n6rmdPHmyWWYdR1ZWFmPHjmV92NqVaueJ5DAsFgunnnrqMXaq5/ZEcsAQvL7h133Dhg0AzDBRaiMS\nkyZN4tNPPw0t0G/duhWPx8Npp51msmUD2GEMHTqU8vJy1qxZAwRDc2vXrmXWiRDDDiM3N5exY8eG\n7ITgjT5jxgxT5dd7Y7PZmDJlCh+GiTpu2LCByZMnm9Z/uC+mTZt2zAvuww8/ZNSoUeTm5ppo1fGc\ndtppbNiwIfTiWL16NaWlpQw/AeQ2wpk1axYff/wxbiVhYM2aNWRkZJxQDhhgzpw5VFVVhaRh1q5d\nixDihHgRhzNr1izq6+tD2WcnkmMbsA5DCMHcuXNZvXp1KDTlcrlOOIcBMG/ePNasWYPP5+PQoUNU\nVVUxe/Zss806jgULFrBp0yZaWlpobW1l/fr1zJs3z2yzjuPMM89kz549HDhwAJ/Px/vvv8+CBQvM\nNus4Zs+eTVNTE1u2bEFKycqVKznzzDNPqIECBO30+XwhJ7x69WpmzpxJmsn1LL05/fTTAUKDr1Wr\nVjFu3DhT+8lEQn1mVq5cCcC7775LeXm5qS15VZJyGEKIy4QQ24UQASHEtCj7nSOEqBJC7BVC/Chs\n+3AhxHpl+/NCCHsy9sTLwoULqamp4eOPP+bll18G4NxzzzXShJg466yz6OjoYNWqVSxduhSACy64\nwGSrjmfhwoUEAgGWLVvG8uXL8fv9J+T5VG16++23+eCDD+jo6DghHcb555+PEILXX3+dLVu2BHW5\n5s8326zjmD9/Punp6bz88stUV1fzySefsHDhQrPNOo5p06aRm5vLK6+8gsvl4v333+f8888326zj\nGDVqFBUVFSxduhSPx8Pbb7/N4sWLT4yBQjIr5sAYYDSwEpjWxz5WYB8wArADm4Gxyu/+CVyhfP8n\n4KZY/l8tsqSkDGZO2O12+a1vfUuefPLJcvbs2ZocV2u6urpkXl6evOSSS+TUqVPlqFGjZCAQMNus\n4/D5fP9WC8MAAAczSURBVLKyslLOnz9fLliwQJaVlUmv12u2WccRCATkKaecIidNmiQvu+wymZub\ne0y23InE7Nmz5YgRI+R1110n7Xa7bGxsNNukiFx44YWytLRUfu9735OA/Oyzz8w2KSLXX3+9zMzM\nlD/96U8lIDds2GC2SRG54447pNVqlb/61a8kIN98801NjkuSWVKapLn24zBmAf8O+/lO5UsAjYAt\n0n7RvrRyGFJKefPNN0vghEtT7c2Pf/zjkJ1Lliwx25w+efDBB0N2Pvjgg2ab0ydLliwJ2XnHHXeY\nbU6fvPHGGyE7b7jhBrPN6ZMPP/wwZOdll11mtjl9snnzZpmWliYBuWjRohNy4CWllPv375cZGRkS\nkNOmTZN+v1+T4ybrMIxYjRwMhOsK1wCnAYVAi5SyJ2x7nx1MhBA3AjcCmsbyHnjgAQYPHsyQIUNO\nyOmpyt13301aWhrl5eVcfSIUQ/XB97///eCNZbPx7W9/22xz+uTqq6/G4/FQW1vLj3/8Y7PN6ZNz\nzz2XZ599li1btvCLX/zCbHP6ZNasWbz00kts3bqV75wIRXB9MHHiRN58801WrlzJt7/97RMjzBOB\n4cOH88Ybb7B06VK+853vmN6ESkVIGV1TXwixHIgk3foTKeWryj4rgf+WUm7qvZMQ4lLgHCnl9crP\nVxN0GL8A1kkpT1K2VwJvSSnH92f0tGnTZHh6XIoUKVKk6B8hxEdSyj7Xm/uj3xmGlDLZ1atDQHjB\nQIWyrQnIE0LYlFmGuj1FihQpUpyAGDHP2QiMUjKi7MAVwGtKPO094FJlv2uBVw2wJ0WKFClSJECy\nabVfE0LUEFywfkMI8W9le7kQ4k0AZfZwK/BvYCfwTynlduUQdwA/EELsJbim8ddk7EmRIkWKFPrR\n7xrGiUhqDSNFihQp4ifZNYwTY+k9RYoUKVKc8KQcRooUKVKkiImUw0iRIkWKFDGRchgpUqRIkSIm\nvpCL3kKIdqDKbDtOEIoISqykSJ2LcFLn4iipc3GU0VLKhBv+nFiNCmKnKpmV/i8TQohNqXMRJHUu\njpI6F0dJnYujCCGSSi9NhaRSpEiRIkVMpBxGihQpUqSIiS+qw/iz2QacQKTOxVFS5+IoqXNxlNS5\nOEpS5+ILueidIkWKFCmM54s6w0iRIkWKFAaTchgpUqRIkSImvlAOQwhxjhCiSgixVwjxI7Pt0Rsh\nxJNCiHohxLawbQVCiGVCiD3Kv/nKdiGEeFQ5N1uEEFPNs1x7hBCVQoj3hBA7hBDbhRDfVbYPuPMh\nhHAIITYIITYr5+JuZftwIcR65W9+XmkngBAiXfl5r/L7YWbarwdCCKsQ4hMhxFLl5wF5LoQQ1UKI\nrUKIT9UUWi2fkS+MwxBCWIH/Bc4FxgJXCiHGmmuV7jwFnNNr24+AFVLKUcAK5WcInpdRyteNwB8N\nstEoeoDbpJRjgZnALcr1H4jnwwOcJaWcBEwGzhFCzAR+AzysdLFsBq5T9r8OaFa2P6zs92XjuwTb\nJ6gM5HMxX0o5Oaz2RLtnJJmG4EZ+Eey58e+wn+8E7jTbLgP+7mHAtrCfq4BByveDCBYxAjwOXBlp\nvy/jF8FmW4sG+vkAMoCPCbY9bgRsyvbQ80KwF80s5Xubsp8w23YNz0GF8iI8C1gKiAF8LqqBol7b\nNHtGvjAzDGAwcDDs5xpl20CjVEpZq3x/BChVvh8w50cJI0wB1jNAz4cSgvkUqAeWAfuAFhlsWAbH\n/r2hc6H8vpVgw7IvC78DfggElJ8LGbjnQgLvCCE+EkLcqGzT7Bn5okqDpACklFIIMaDyooUQWcC/\ngO9JKduEEKHfDaTzIaX0A5OFEHnAy8ApJptkCkKIxUC9lPIjIcQ8s+05AZgrpTwkhCgBlgkhdoX/\nMtln5Is0wzgEVIb9XKFsG2jUCSEGASj/1ivbv/TnRwiRRtBZPCulfEnZPGDPB4CUsgV4j2DYJU8I\noQ4Cw//e0LlQfp8LNBlsql7MAS4UQlQD/yAYlnqEgXkukFIeUv6tJziQmIGGz8gXyWFsBEYp2Q92\n4ArgNZNtMoPXgGuV768lGMtXt1+jZD7MBFrDpqFfeERwKvFXYKeU8rdhvxpw50MIUazMLBBCOAmu\n5ewk6DguVXbrfS7Uc3Qp8K5UgtZfdKSUd0opK6SUwwi+E96VUl7FADwXQohMIUS2+j1wNrANLZ8R\nsxdp4lzQOQ/YTTBe+xOz7THg7/07UAv4CMYXryMYb10B7AGWAwXKvoJgFtk+YCswzWz7NT4XcwnG\nZ7cAnypf5w3E8wFMBD5RzsU24OfK9hHABmAv8AKQrmx3KD/vVX4/wuy/QafzMg9YOlDPhfI3b1a+\ntqvvSC2fkZQ0SIoUKVKkiIkvUkgqRYoUKVKYSMphpEiRIkWKmEg5jBQpUqRIERMph5EiRYoUKWIi\n5TBSpEiRIkVMpBxGihQpUqSIiZTDSJEiRYoUMfH/AVnxktgRj86fAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XGDFSTQjIe9S",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}