tutorials/Gradient_Descent_With_DeepC.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Gradient Descent With DeepC.ipynb",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5bndlKgejLGt",
        "colab_type": "text"
      },
      "source": [
        "##Install DeepC \n",
        "<img src=\"https://raw.githubusercontent.com/ai-techsystems/dnnCompiler/master/misc/dnnCompilerLogo.jpg\" alt=\"DNNC\" width=\"300\"/>\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jnBgVf3LdPdF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "!pip install deepC"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "scvwzKb7jPqk",
        "colab_type": "text"
      },
      "source": [
        "##Import DNNC"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4Bpi3nCKMMN7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import deepC.dnnc as dc"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "19Saplu-MgkU",
        "colab_type": "text"
      },
      "source": [
        "# Model\n",
        "\n",
        "$f(w) = w^4/2 - 11*w^3/3,$\n",
        "\n",
        " => $df/dw = 2w^3-11w^2$\n",
        "\n",
        "Model above has *local minima at w=11/2=5.5*"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RWzduK41tmaS",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def f(w):\n",
        "  return 1/2*w**4 - 11/3*w**3"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YSwxArsky8VA",
        "colab_type": "text"
      },
      "source": [
        "# Gradients\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zqmt4xr0zGcC",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# gradient computation\n",
        "def df(w):\n",
        "    return 2 * w**3 - 11 * w**2"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "v1WnxaVxzOkl",
        "colab_type": "text"
      },
      "source": [
        "# Plot"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vaTRykmyty_y",
        "colab_type": "code",
        "outputId": "d552270d-fb55-47d0-a66d-4ed1cbf0d29b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 537
        }
      },
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig = plt.figure(figsize=(12,9))\n",
        "ax = plt.axes()\n",
        "\n",
        "x = dc.arange(60)/10;\n",
        "ax.plot(list(x), list(f(x)), label=\"f(x)\");\n",
        "ax.plot(list(x), list(df(x)), label=\"df(x)\");\n",
        "ax.legend()\n",
        "ax.grid(True)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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2+frAFtu2twFYljUaaAesd6ieC9q+bjHHti9lpTuZbLcftsuXbJcftssP2+1nvnabfdku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\n",
            "text/plain": [
              "<Figure size 864x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DpX__SNgtwoY",
        "colab_type": "text"
      },
      "source": [
        "# Model Parameters\n",
        "\n",
        "**Effect of learning rage $\\alpha$ on convergence speed and accuracy**\n",
        "\n",
        "\n",
        "|Learning Rate $\\alpha$ |  Iterations   |  final value   |   accuracy   |\n",
        "|-----------------------|---------------|----------------|--------------|\n",
        "|     1e-1              |   infinite    |       NA       |      NA      |\n",
        "|     8e-2              |       5       |    0.0483      |      fair    |\n",
        "|     1e-2              |      22       |    5.499       |  excellent   |\n",
        "|     5e-2              |      44       |    5.494       |      good    |\n",
        "|     1e-3              |     208       |    5.48        |      good    |\n",
        "|     1e-4              |    1875       |    5.45        |      fair    |\n",
        "|     5e-5              |    3633       |    5.42        |      fair    |\n",
        "|     2e-5              |    8667       |    5.37        |      ok      |\n",
        "|     1e-5              |     nan       |    NA          |      NA      |\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y--CTjk3EFqP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# learning rate\n",
        "alpha = 5e-3; # \n",
        "\n",
        "w      = dc.arange(2)\n",
        "w_next = 0.9 * w"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vBN59-wcMOkp",
        "colab_type": "text"
      },
      "source": [
        "# Test Convergence"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8nRWKsrqdS66",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def all(result):\n",
        "  for r in result:\n",
        "    if ( False == r ):\n",
        "      return False;\n",
        "  return True;\n",
        "\n",
        "def convergence_not_reached(step_sz):\n",
        "  precision = 1e-3\n",
        "  return not all(abs(step_sz) < dc.array([precision]))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g2K_4ew5OTqQ",
        "colab_type": "text"
      },
      "source": [
        "# Gradient Descecnt"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B_if7vM4MGtu",
        "colab_type": "code",
        "outputId": "4ec4d73e-a9fa-4f39-cdae-151ef7149b81",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 773
        }
      },
      "source": [
        "ws = []\n",
        "iter   = 1\n",
        "while convergence_not_reached(f(w_next)-f(w)):\n",
        "    print (\"iteration=\", iter, \" w=\", w, \" and w_next\", w_next)\n",
        "    iter += 1\n",
        "    \n",
        "    w      = w_next\n",
        "    w_next = w - alpha * df(w)\n",
        "    ws.append(w[1])\n",
        "\n",
        "    \n",
        "print(\"GD found minima at \", w_next, \"with learning rate\", alpha)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "iteration= 1  w= [0.000000 1.000000]  and w_next [0.000000 0.900000]\n",
            "iteration= 2  w= [0.000000 0.900000]  and w_next [0.000000 0.937260]\n",
            "iteration= 3  w= [0.000000 0.937260]  and w_next [0.000000 0.977342]\n",
            "iteration= 4  w= [0.000000 0.977342]  and w_next [0.000000 1.020542]\n",
            "iteration= 5  w= [0.000000 1.020542]  and w_next [0.000000 1.067196]\n",
            "iteration= 6  w= [0.000000 1.067196]  and w_next [0.000000 1.117681]\n",
            "iteration= 7  w= [0.000000 1.117681]  and w_next [0.000000 1.172426]\n",
            "iteration= 8  w= [0.000000 1.172426]  and w_next [0.000000 1.231912]\n",
            "iteration= 9  w= [0.000000 1.231912]  and w_next [0.000000 1.296685]\n",
            "iteration= 10  w= [0.000000 1.296685]  and w_next [0.000000 1.367359]\n",
            "iteration= 11  w= [0.000000 1.367359]  and w_next [0.000000 1.444625]\n",
            "iteration= 12  w= [0.000000 1.444625]  and w_next [0.000000 1.529259]\n",
            "iteration= 13  w= [0.000000 1.529259]  and w_next [0.000000 1.622120]\n",
            "iteration= 14  w= [0.000000 1.622120]  and w_next [0.000000 1.724157]\n",
            "iteration= 15  w= [0.000000 1.724157]  and w_next [0.000000 1.836403]\n",
            "iteration= 16  w= [0.000000 1.836403]  and w_next [0.000000 1.959953]\n",
            "iteration= 17  w= [0.000000 1.959953]  and w_next [0.000000 2.095941]\n",
            "iteration= 18  w= [0.000000 2.095941]  and w_next [0.000000 2.245480]\n",
            "iteration= 19  w= [0.000000 2.245480]  and w_next [0.000000 2.409579]\n",
            "iteration= 20  w= [0.000000 2.409579]  and w_next [0.000000 2.589010]\n",
            "iteration= 21  w= [0.000000 2.589010]  and w_next [0.000000 2.784133]\n",
            "iteration= 22  w= [0.000000 2.784133]  and w_next [0.000000 2.994651]\n",
            "iteration= 23  w= [0.000000 2.994651]  and w_next [0.000000 3.219329]\n",
            "iteration= 24  w= [0.000000 3.219329]  and w_next [0.000000 3.455700]\n",
            "iteration= 25  w= [0.000000 3.455700]  and w_next [0.000000 3.699827]\n",
            "iteration= 26  w= [0.000000 3.699827]  and w_next [0.000000 3.946248]\n",
            "iteration= 27  w= [0.000000 3.946248]  and w_next [0.000000 4.188211]\n",
            "iteration= 28  w= [0.000000 4.188211]  and w_next [0.000000 4.418314]\n",
            "iteration= 29  w= [0.000000 4.418314]  and w_next [0.000000 4.629475]\n",
            "iteration= 30  w= [0.000000 4.629475]  and w_next [0.000000 4.816046]\n",
            "iteration= 31  w= [0.000000 4.816046]  and w_next [0.000000 4.974685]\n",
            "iteration= 32  w= [0.000000 4.974685]  and w_next [0.000000 5.104687]\n",
            "iteration= 33  w= [0.000000 5.104687]  and w_next [0.000000 5.207697]\n",
            "iteration= 34  w= [0.000000 5.207697]  and w_next [0.000000 5.286970]\n",
            "iteration= 35  w= [0.000000 5.286970]  and w_next [0.000000 5.346516]\n",
            "iteration= 36  w= [0.000000 5.346516]  and w_next [0.000000 5.390390]\n",
            "iteration= 37  w= [0.000000 5.390390]  and w_next [0.000000 5.422238]\n",
            "iteration= 38  w= [0.000000 5.422238]  and w_next [0.000000 5.445101]\n",
            "iteration= 39  w= [0.000000 5.445101]  and w_next [0.000000 5.461378]\n",
            "iteration= 40  w= [0.000000 5.461378]  and w_next [0.000000 5.472898]\n",
            "iteration= 41  w= [0.000000 5.472898]  and w_next [0.000000 5.481016]\n",
            "iteration= 42  w= [0.000000 5.481016]  and w_next [0.000000 5.486719]\n",
            "iteration= 43  w= [0.000000 5.486719]  and w_next [0.000000 5.490717]\n",
            "iteration= 44  w= [0.000000 5.490717]  and w_next [0.000000 5.493515]\n",
            "GD found minima at  [0.000000 5.495472] with learning rate 0.005\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iVw3GlIOzjKW",
        "colab_type": "code",
        "outputId": "0e5539d5-fb01-4ce5-fee3-c8f0e0deb88d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 537
        }
      },
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "fig = plt.figure(figsize=(12,9))\n",
        "ax = plt.axes()\n",
        "\n",
        "tws=dc.array(ws)\n",
        "x = dc.arange(60)/10;\n",
        "ax.scatter(ws, f(tws.numpy()), label=\"GD(x)\");\n",
        "ax.plot(list(x), list(f(x)), label=\"f(x)\");\n",
        "ax.plot(list(x), list(df(x)), label=\"df(x)\");\n",
        "ax.legend()\n",
        "ax.grid(True)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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QERERKfTW/Qixy6HrZ+BX0u5qXKJQT9UQEREREQ+QlgxzX4LwKGjc1+5qXKZQjziLiIiI\niAdY9D4kxcNt34Oj6I7LFt1PJiIiIiKud3QX/PUpNOoNlZrbXY1LKTiLiIiISP6cuiHQ4Q2dXra7\nGpdTcBYRERGR/Nk0Dbb/Bte9ACUr2F2Nyyk4i4iIiMjlS020RpvDGsHVA+2uxi10c6CIiIiIXL75\nr0PyAegzDpzFI1JqxFlERERELk/cKlg+Eq4eABFN7a7GbRScRUREROTSZWXCjMehRHm47n92V+NW\nxWNcXUREREQKxvKvYP866PUt+AXbXY1bacRZRERERC5NYizMfwNqXQ/1utpdjdspOIuIiIjIpfn1\nGTCz4ab3wDDsrsbtFJxFRERE5OK2/AJbZkL7Z6BUFbursYWCs4iIiIhcWFoyzHoaQutBq4ftrsY2\nujlQRERERC4s+i04Hgs9fwOnt93V2EYjziIiIiKSt/h1sPQLaHo3VG5hdzW2UnAWERERkdxlZ8HM\nxyGgNHR62e5qbKepGiIiIiKSu5VjrFUCu48C/1J2V2M7jTiLiIiIyPmOx8O8V6F6e2jY0+5qPIKC\ns4iIiIicb/azkJkGXT4olj2bc6PgLCIiIiLn2jQNNk2FdkOhTA27q/EYCs4iIiIicsaJwzDzCajQ\nGFo/bnc1HkU3B4qIiIjIGbOegtREuGt6se7ZnBuNOIuIiIiIZeNU2DjFWla7fH27q/E4Cs4iIiIi\nYk3R+OVJqNAEWg+xuxqPpKkaIiIiInLWFI0Z4FREzI1GnEVERESKu3OmaNSzuxqPpeAsIiIiUpxp\nisYlU3AWERERKc5mPQVpx6HbF5qicREKziIiIiLF1akpGu00ReNSKDiLiIiIFEfnTNHQQieXQsFZ\nREREpDj65UlN0bhMtgVnwzBuMAxjq2EYOwzDeNauOkRERESKnY1TYNNUTdG4TLYEZ8MwnMBnwI1A\nPaCPYRi6aiIiIiKudmqKRnikpmhcJrvG5a8GdpimuQvAMIwJQFdgk0315OrvjctI+HsFaxxJZDt9\nyHZ4Yzp8MJ2+Zx47fch2WJvD6cTAwGGAYRgYBjhOfwVyjjkdBk6HgbfTgdNh4JXz2Mtx1mOngbfD\nga+XA4f1YhEREZEr98uTkJakKRr5YJim6f6TGkZP4AbTNO/PedwPaGGa5sP/et4DwAMA5cuXbzph\nwgT31vnXh7RLi77k5x83AzhmluAYJThmBnGMIBLMEhw1g0jI2XeUIA6YpYgzy5KGzyW9r9MAb0fO\n5jROf+/lsL73cYKv08DXC/ydBr5eBn5O8Dvrq68T/L0MArwNSnhDoLeBj7NwB/Lk5GRKlChhdxmS\nC10bz6br47l0bTxXUbk2oQeiqbf5Q3ZV68eeKj3tLqdAFPS16dChwyrTNJvldsyj/5lhmuYIYARA\ns2bNzPbt27v1/HGVQ5n+1wLq1KyKIysdIzsDMtNxZGdgZKVjZKfhyMrAyE7HkZmKMy2BwLRjBKce\no2baMbzS/sEr7RheGcm5vn+abxlOBoRzwj+cZL8KJPuFc9yvAsd9wkj0DeOEEUB6ZjbpmdmkZWaT\nlplFWob1ffqpx5nZpGZkcTI9i0OpmZxIy+JEWiZpmdkX/Xx+3g5C/H0ICfC2Nn8fSgV6E+zvQ5lA\nH0JL+lIuyJfyJf0IDfKlhK8XhuE5YTs6Ohp3/52QS6Nr49l0fTyXro3nKhLX5ujf8OUoqNSS6ncO\np3oRGW1257Wx608sDqh01uOKOfs8SkT1emzfc5CrWrS/sjfKTIeUY3DyiLUd3weJe/BN2INvwl5K\nJe6EA9GQlXbu6wLKQLm6UK42hNaFcnWsrUS5i54yIyubk+lWiD6ZnklyTqBOTMkg4WQGx06mk5iS\nwbET6SSkZJBwMp2dh5I59k8GiSnpZGSd/5sIf28noSV9CQ3yJTTIj3JBvoQF+1GxlD8VSwVQqZQ/\npQN9PCpci4iICJCVCZMHgOGAHiM1RSOf7PpTWwHUMgyjGlZg7g30takW1/PygaDy1paX7Gw4cQgS\n90LCP5CwF47uhINbYP0kSEs889zcAnWFxuBX8vRTvJ0Ogv0dBPt7X3a5pmlyPDWTQ0mpHDyexsGk\nNA6e9f2B46lsjj/OH9vSSE7LPOe1AT5OKpUKoGIpfyqVDjgTqkv7U61sIAE+ef+VmxoTx7A5W9mX\nkEJ4iD9DO9emW2TEZdcvIiIi//LHOxC7AnqMhpDKdldTaNkSnE3TzDQM42FgDuAExpimudGOWjyG\nw3EmXFf817Qa04SkeDi0xQrSh3K2cwK1AWVrQXgURERZX8MagrffZZdiGAbB/t4E+3tTMzTogs9N\nTssk9thJ9h5NOf1177GT7D16kmV/Hz0vWEeE+FMztMS5W7kS/LHtEM9NXk9KRhYAcQkpDP1pLa/M\n2EjCyQwFaRERkfz6509Y9B407gsNi8a8ZrvYNk5vmuYsYJZd5y9UDANKhltbjevO7DdNSNoPBzbC\nvhiIWwW7FsC6nJsoHV4QWu9MkI6Ish47nAVWWglfL+qElaROWMnzjpmmSWJKBnuPprDn6El2HUpm\nx6Fkth9IZtnfR0jNODMP22FA9r9mh2Rkmxw7mQHkEaQbZxXY5xARESmSUhJg8gMQUgVuetfuago9\nTXApzAwDSlawtlqdrH2mac2h3rca4lZbXzdMgVXfWMd9g6FyS6hyDVS91pri4bz86RyXVp5BSIAP\nIQE+NKwYfM6x7GyTuIQUdhxMZsfBZN6Ytfmi7/fvIB17NIvIV3/TiLSIiEhuTBNmPm791vre38D3\nwr9FlotTcC5qDAOCI6yt7n+tfdnZcHSXNSK950/YvQS2z7GOeQdC5RZQpbUVpMOjrDnZLuZwGFQq\nHUCl0gF0qBPKN3/uJi4h5bLeY8UhzgnSz01ez8p/jrJgyyHNkxYREVkzzlohsOOLULGp3dUUCQrO\nxYHDAWVrWlvj2619SQfgnyU5258w/zVrv5c/VGoO1dpCzU4Q1th6vYsN7Vz7nDnOl+KP/edOOUnJ\nyOKHpXtOP1aYFhGRYuvITpg1FKq20eqABUjBubgKKg8NulsbwIkjZ0aj/1kM81+3toCyULOjFaJr\nXAeBZV1Szqkge6qrRrC/NyfSM3Nti3fKoDqZfLnlwn+F8wrTZ59TRESkSMlMh5/vs6Zi3vpVgd7b\nVNwpOIslsIw1tePU9I7kQ9aNhjvmwo55sG4iYEB4EytE1+wEEc0KtA9kt8iIc8Ls2e3pcgvSgfmc\nmp2SkcWwOVsB1P5ORESKnug3raYBt31nTd2UAqPgLLkrUQ4a3WZt2dmwf+2ZEL3oA1g4zLrRsEZ7\nqN0Frroe/EsVaAkXC9KGce60DgO41AXk4xJSeOqntWTmtPLQSLSIiBQJfy+ExcMhqj/U62p3NUWO\ngrNcnMMB4ZHW1nao1drm7z+sIL3tN9g0zWp9V/VaqHMz1L7JJf/CPS9I//o7ESHO0yPGHeqU4+dV\ncefMk75QmM78V/+7lIws3v51C6CRaBERKYROHoXJA6FMDbjhbburKZIUnOXy+YdY/4qt19Uajd4X\nA1tmwJZfYNZT1hYeBXW6WEG6XG2r20cBC/H3Zsmz7c/Z16xK6XNCb25h2t/bmedNiPuPp/LEj2tO\n95TWSLSIiBQKpgnTH7FWIe4zF3wC7a6oSFJwlivjcFgtbio2hU4vw6FtsPUX2DzT6tQx/zUoXcMK\n0fW7WYHaBSH6lH+PSsP5YXpo59oMm7M11/Z3BucvxJKSkcWbszbTtUk409bs02i0iIh4npVjYMtM\n+M9r1v1I4hIKzlKwyl1lbdcOgePxsHWWNRK99Av482MoVRUa9LC20HouDdGn5BamgfPa311oJPpg\nUhrN35hLwskMzYsWERHPErcKZj8LNTpCq4ftrqZIc32DXim+SlaA5vdBv8kwdDt0/cwafV48HL64\nBj5vCX+8C4d3uL20bpERvNW9IREh/hhARIj/6ce5CfH3Jik1M9d50ac6dEyNiaP12/Op9uwvtH57\nPlNj4lz9MUREpLg7eRR+vAtKlIceo9yy9kJxphFncQ//UhB5p7WdOGzdULhhMix4Exa8AWGNckai\nu0NIZbeUdDkj0S/fUp8hE9fk+j5xCSk8Oj6G3zbuJzUz+/Q+jUaLiIhLZWfBz/dD8gG4dzYElLa7\noiJP/ywR9wssa41E3/MLPLEJOr8FTh+Y+xIMbwijO8PKr63uHW6W10h0t8gIwvMYjfZ2Gkxfu+90\naD7l7NFoERGRAvfHu7BzHtz4LkRoSW130Iiz2KtkOLR6yNqO7bZGoddNhJmPw6/PWDcVNu5jrVpY\ngIutXEheI9G5LQvu7+3kre4NefwCo9FZ2SZOh3FOH2rdWCgiIldk++/wxzvQuC80vdvuaooNBWfx\nHKWqQpsnrBsL98XA2gmw/ifYOBkCQ63FWBr3gbAGtpT372XBzw6/eXXpAGjzznyaVAph/paDmsoh\nIiJX7tg/MHkAlK8PXd53y432YlFwFs9jGBARZW3Xvw7bf4O142HZV/DXpxDWEBr3wTvd/YHzckaj\n/bwc9GlRmR0Hk5m1Yf95rzk1lUPBWURELllGKvzY31pH4bbvwCfA7oqKFQVn8WxePlD3Zms7cQQ2\n/Axrx8Gc52llOOHoT9avqGpcBw6nbWVeaDQaoOqzv+T6urxGqUVERHI1+xmIXwO9x1krBIpbKThL\n4RFYBlo8YG0HtxA74y0q71lkNXwPrmR17GhyB4RUsqW8vEajwbrJMK+QPGTiGu5oUZmmVUppgRUR\nEclbzFhY9Y01pbFOF7urKZYUnKVwCq3Drhr3UPmukdZKhau+hei3IPptqNkJmt4FV90ATm+7KwVy\nn8rh6+WgedXS/L7pAFNi4ogI8edgUioZWVpgRURE/mX/evjlCajaBjr8z+5qii0FZyncvHyg/q3W\ndmw3xPxgbRPvtJrBN+kLUf2hdHVby7zQVI4TaZlMW7OPF6dtyHOBFQVnEZFiLCUBJvaz1kToOcZt\nXabkfPqTl6KjVFW47n/Q7lnY8bs1Cr3kI1j8IVTvAM3vzxmFtuevfV5TOQJ9vejbojLPT1mf6+s0\nD1pEpBjLzoapD0LiXrh7FpQItbuiYk0LoEjR4/SC2jdC3wkwZCN0eAEOb4OJd8BHjWHhMEg+aHeV\n58lruW+AJyauYdO+426sRkREPMKS4bB1Flz/BlRuYXc1xZ5GnKVoKxkO7Z6Ga5+Abb/CilEw/3WI\nfgfq3QLNB0Dllh7RAzOvedAtqpVm9sb9TI6Jo02tsjQID2bamjjiE1N1A6GISFG2ZRbMexUa9IAW\nA+2uRlBwluLC6QV1/2tth7fDyjHW3ckbfobQ+tYS4I1uA98g20q80DzoxJMZjF3+D19G72TR9sOn\nX6MbCEVEiqj96+Hn+yG8CdzyqUcM8IiCsxRHZWvBDW9Z86HXT4IVI607lX9/CZr0gasHQtmatpSW\n1zzo4ABvHmpfkx/++ofjqZnnHEvJyOLd2VsUnEVEioqkAzCuN/gFQ+/xWuTEg2iOsxRfPoFW27qB\ni+C+uVDnJlj5NXzaFMb2gh3zwDQv/j5uFJ+Ymuv+fYmpLNp+CNPD6hURkcuUkQoT+kLKUegzHkpW\nsLsiOYuCs4hhQKXm0H2EdTNhu2dhXwz80B0+awErRkP6CburBCA8jxsInYZBv9HL6fXlXyzeflgB\nWkSkMDJNmDYY4lbCrV9Z0zTEoyg4i5wtqDx0eM4K0N2+BG8/axrHB3Xht/9Bwh5byxvauTb+3ucu\nLe7v7eSdHg15rVsD4hJSuHP0stMBesrqWFq/PZ9qz/5C67fnMzUmzqbKRUTkohYOgw2ToOOL1g3s\n4nE0x1kkN16+1nznxr1hz1JY9gX89Tn89Zm1zGmLB6HKNW6/WeNCNxAC3NasIj+u2MtnC3Zy5+hl\nOAw4taaKbiQUEfFgG6fAgjegUW+rE5R4JAVnkQsxDKjSytoS9lrt7FZ9A5tnQHgktHoY6nV169Le\ned1ACODr5aRfq6rc1rwSV78xj8SUjHOOayVCEREPFLcapjwIlVrALR+rg4YH01QNkUsVUgn+8wo8\nsRm6fABpSfDzffBRE/jzE0hNtLvC03y9nBz/V2g+RSsRioh4kMQ4GN8HSpSD28dav/EUj6XgLHK5\nfAKsvs+DV0CfCdZS37/9Dz6oD7Oft30e9Cl53UhoGDB68d+kZWblelxERNwk/QRM6APpydBnohWe\nxaMpOIvkl8NhLe19zy8wYKPpHsoAACAASURBVAFc1RmWfWmNQP90D8StsrW83G4k9PVycFVoEK/N\n3ESnD/5g+tp96sAhImKH7GyYMtBa6KTnGChfz+6K5BIoOIsUhIgo6DkaHlsLrR6CHXNh5HUw5gZr\nydTsbLeX1C0ygre6NyQixB8DiAjx550ejZgzpC3f3ns1gT5ePDo+hm6fLWHF7qMATI2JUxcOERF3\nWPC6db/M9a9bAy9SKOjmQJGCFFLJ+iHY9mmI+R6WfmH9Gq5sbWj9KDTs5db5a3ndSNjuqnJcW7Ms\nk1fH8v5v2+j15V80q1KKDXGJpGZaIV9dOEREXGTl17DofYi6C1o+ZHc1chk04iziCn4lodVgeDQG\nuo8Cp4/V1P6jxrB4uEfcSOh0GPRqVon5T7XjofY1WPnPsdOh+ZRTXThERKSAbJpmrQ9Q63ro8r46\naBQyCs4iruT0hka9YNAiuHMylL0K5r5k3Uj42//B8Xi7KyTAx4unb6iT5/F96sIhIlIw/l4IP98P\nEc2g17dubWUqBUPBWcQdDANqdoS7psMD0VDrP/DXpzC8IUwdDAe32F0hEXl04Shf0s/NlYiIFEHx\na2F8XyhdHfpOtDo0SaGj4CzibuGR0OtreGQ1NLsHNvwMn7ew+njuXW5bWbl14QA4djKdEQt3kpHl\n/hscRUSKhCM74Yce4B9i/fYxoLTdFUk+KTiL2KV0NbhpGAzZCO2ehT1/wej/wNddYPtccHObuNy6\ncPyvS11a1yzLm7O2cONHi/hzx2G31iQiUugl7YfvbwUzG/pNgWDdbF2YqauGiN0Cy0CH5+CaR2D1\nd9YUjrE9IKwhXDsE6nUDx/kjwa6QWxeO+9tUZ97mA7wyYxN9Ry2jV9OK/K9LPYIDNDdPROSCUhKs\nkeYTh+HuGVC2lt0VyRVScBbxFL4lrB7Qze+H9T9a3Tcm3QulXoPWj0GTvrYtxdqxbnla1yzLR/O2\nM2LhLhZsPcRrXeuTlpnNsDlb2ZeQQniIP0M711brOhERgIwUmNAXDm2FO36EiKZ2VyQFQMFZxNN4\n+UDkndC4L2yZCYs/gJmPQ/TbVrBueo/V7s7N/LydPHNDHbo0rMAzP6/jwbGrcRiQnTOj5Oy+zyFu\nr05ExINkZcKk++CfP63FsWpcZ3dFUkA0x1nEUzkcUO8Waznv/tMgtA78/iIMbwDzX4cTR2wpq0FE\nMNMGt6akn9fp0HyK+j6LSLFnmjDzMdj6C9z4LjToYXdFUoAUnEU8nWFA9fZWeB6wAKq1hYXDrAA9\n+3k4vs/tJXk5HSSlZuZ6TH2fRaRYm/cKxPxgrSDb4gG7q5ECpuAsUphERMHtP8BDy6BeV1j2JQxv\nBNMftdoduVF4Hn2fg/y8yPr3ULSISHGweDgs/tCaUtfheburERdQcBYpjELrwK1fWkt6R/WHtRPg\n02bWnLoDG91SQm59nx0GHE/N5LWlqWw7kOSWOkREPMLi4dbKsA16aCntIkzBWaQwK1UFbv4AHl8H\nrR6GbbPhi2tgXG/Yu8Klp86t7/P7vRrzad9IjqRmc/Mnixm1aBfZGn0WkaJuyUdnQvOtI9zWQlTc\nT101RIqCoDC4/jWr7/PykbDsCxjdyZoP3eYp66sLRj9y6/sMkB2/len7g3j9l83M23yQ925rnOeS\n3iIihdqSj6wbt0+FZqeiVVGmEWeRoiSgNLR/Bh7fANe/bvUP/e4Wa0XCrbPdthphSV+Dkf2b8k6P\nhqyLTeCGDxcyeXUspptXQxQRcaklH1uhuX53heZiQsFZpCjyLWGtRPjYOmuuXdIBGH87fNkGNkyG\n7CyXl2AYBrc3r8yvj7WldlgQT/y4lsHjVnPsRLrLzy0i4nJLPobf/88Kzd1HKjQXE7rKIkWZt5+1\nEmHUXbDuR2sxlUn3QJla0OYJaNgLnK5dOrtymQAmDmzFiIW7+OD3razYfYxbIyP4ZV28VhwUkcLp\nz09yQvOtCs3FjEacRYoDpzdE3gGDl0PPr8HLD6Y+CJ9EwYpRkJHq2tM7DB5sX4Opg1vj5TAYsXAX\ncQkpmJxZcXBqTJxLaxARKRB/fgK//S8nNI9SaC5mXBacDcMYZhjGFsMw1hmGMcUwjJCc/VUNw0gx\nDGNNzvalq2oQkX9xOKFBdxi0CPpMhBLl4Zcn4aPG8OenkH7CpaevHx5MbrcoasVBESkU/vzUCs31\nuik0F1OuHHH+HWhgmmYjYBvw3FnHdpqm2SRnG+TCGkQkN4YBtW+A+36H/tOh3FXw2wvwYQP4Yxik\nJLjs1PGJuY9ux2nFQRHxYBX3TrN+TtbrBj1GKzQXUy4LzqZp/maa5qk1eZcCFV11LhHJJ8OA6u3g\nrhlWiK7YHBa8DsMbwrxX4cThAj9lXisO+no5OKobB0XEEy35mJo7x+SEZo00F2eGO9pDGYYxA5ho\nmuYPhmFUBTZijUIfB/5nmuaiPF73APAAQPny5ZtOmDDB5bX+W3JyMiVKlHD7eeXidG1co0TSLirv\nmUS5Q3+S7fBhX/j17K10K+m+ZS75PS50bRJSMog7lkJ2zs8e04S1Rx1ExzsI8jEY1NiXOqW1eIAr\n6b8dz6Vr42FMk+q7vqPy3snsK9WC7Q2fxnQoNHuagv7vpkOHDqtM02yW27ErCs6GYcwFwnI59IJp\nmtNynvMC0AzobpqmaRiGL1DCNM0jhmE0BaYC9U3TPH6hczVr1sxcuXJlvmvNr+joaNq3b+/288rF\n6dq42KGtsPhDqxuHwwlN7oBrH4dSVS/60otdm6kxcQybs/Wcrho1Q0vwyPgY/jlygsc6XsXD19XE\n6dCSta6g/3Y8l66NB8nKhJmPQcwP0OxeogNvpn2HjnZXJbko6P9uDMPIMzhf0T+bTNPsdJET3w3c\nDHQ0cxK6aZppQFrO96sMw9gJXAW4PxWLSN7K1YZbv4T2z1orY8X8AKu/s1rYtXnCOp5Pea04OOOR\na/nflPV8OHcbS3cd4aPeTQgt6Xcln0JE5PJlpMCke2HrLGj3rPVz8I8/7K5KPIAru2rcADwN3GKa\n5smz9pczDMOZ8311oBawy1V1iMgVKlUVbv4QHlsLLQbB5unwWQuY2A/i1xboqUr4evHh7U14t2cj\nYvYe48aPFvHHtkMFeg4RkQtKOQbf3wpbf4Wb3oMOz1n3g4jg2q4anwJBwO//ajvXFlhnGMYaYBIw\nyDTNoy6sQ0QKQslwuOFNaznvNk/Crj/gq7bwQ0/Ys7TATmMYBrc1q8SMh6+lbAlf7hqznLd/3UJG\nVnaBnUNEJFfH4+HrmyB2JfQcA1cPsLsi8TAum+FummbNPPb/DPzsqvOKiIsFloGO/wetH7UWT/nr\nMxjTGapcC22fhOodCuQ0tcoHMXVwa16duZEv/9jJit1H+axvFGHBmrohIi5weIc10pxyFO6cBNXb\n212ReCDdGioi+eMXbI08t3gQVn8LSz62/qcTHkXZUp0huy04ruyXWv4+Tt7q3ohWNcry7M/ruPmT\nxXzWN5L4xNTzbi7Ukt0ikm9xq2FsT8CAu2dCeKTdFYmHUnAWkSvjEwAtH4Rm98La8bD4QxrsewsO\nToVrh0CDHlfc8/SWxuHUCQti4Per6DNyKU7DICPb6gh0asluQOFZRC7fzgUw8U4IKA39pkKZGnZX\nJB7MlXOcRaQ48fKFpnfDw6vYVHeIdTPNlAfgkyhrSkdG7isGXqqrygcx7eHW+Dgdp0PzKVqyW0Ty\nZcPPMLYXhFSBe39TaJaLUnAWkYLl9OJg+fYwaAn0Hg+B5eCXJ+GjRrB4OKResGX7BZX08yY1M/eb\nBPdpyW4RuVSmCQuHWS3nKjaDe2ZByQp2VyWFgIKziLiGwwF1boL751pLeofWhbkvwfAGMP8NOHEk\nX28bkceS3Xkt5S0ico70k/DzfTD/dasvfb8p4B9id1VSSCg4i4hrGQZUawv9p8GA+VC1DSx81wrQ\ns5+DxLjLeruhnWvj733+ktwNIkqSnZ3/lVBFpBhIjIOvb4QNk6HTy9B9JHjrH91y6RScRcR9IppC\n77Hw0FKoewss+wo+agxTH7KW+L4E3SIjeKt7QyJC/DGA8GA/rq5amjkbD3DftytIPJnh2s8gIoXT\n3hUwsgMc2QF9xls3L2thE7lM6qohIu4XWhe6fwUdnoe/PoXV38OasVDnZmj9OFRqfsGX/3vJbtM0\nGbtsD6/M2Mh/P13MyP7NqB0W5OpPISKFxdoJMP1Rax5z/2nWzyCRfNCIs4jYp1QVuGkYDNkAbZ+G\n3YthdCf4ugtsn2vdwHMJDMPgzpZVmDiwFakZWXT/fAnzNh9wcfEi4vGys+C3/4MpA6HS1TBggUKz\nXBEFZxGxX2BZuO4FGLIROr8JR3fB2B7wZRtYPwmyMi/pbaIql2Law62pVi6Q+79byYiFOzEvMXyL\nSBGTmgjje8OfH0Pz+62bAANK212VFHIKziLiOXxLQKvB8Nha6Po5ZKVZd79/EgXLR1p3w19EhWB/\nfhp4DTc1qMCbs7YwdNI60jKz3FC8iHiMIzthVCfYOR+6fABd3gent91VSRGg4CwinsfLByLvgIeW\nwe1jrV7Qs56yOnEseAtOHL7gy/19nHzSJ5LHOtZi0qpY7hi5jMPJaW4qXkRste03GHmd9XOi31Ro\nfp/dFUkRouAsIp7L4YC6N1u9oO+eBRWbwx9vw4f1YeYT1qhSni81GPKfq/i0byTr4xLp+ukSNsfn\nf/EVEfFwmekw5wUY1wuCK1rtL6u1sbsqKWIUnEXE8xkGVG0NfSdao9ANe0LM9/BJU5jYD2JX5vnS\nmxuF89OgVmRmZ9Pjiz/5fZNuGhQpco7+DV/fYHXpaX4/3D8PSlezuyopgtSOTkQKl9A60PUzuO7/\nYNmXsGIMbJ4OVVrDNY9CreutkeqzNKoYwvSHr2XAdyt54PuVPN25DmElfXnvt23sS0ghPMSfoZ1r\nn9PiTkQKiY1TrFZzGHDbd1Cvq90VSRGm4CwihVNQmLXyV5snrT7QSz+H8bdD2drQ6iFodPs5K4KV\nL+nHxAdaMXTSWt6ZvQWnYZCV03EjLiGF5yavB1B4FiksMlKs1UdXfQ0RzaDnGKvFpYgLaaqGiBRu\nvkFWUH40BrqPAi9fmPGYNQ96/huQdGZqxqmbBoP8vE6H5lNSMrIYNufSVi8UEZsd2gojO1qhufVj\ncO9shWZxC404i0jR4PSGRr2s+c+7F1sj0AuHwZLh0LAXtHwIwhpgGAbJqbn3hd6XkOLmokXkspgm\nxPwAvz5t/UbpjklQ6z92VyXFiIKziBQthmHdSV+tjdV1Y+kX1nLea8ZCtXbQ6mEign2JTTy/PV14\niH8ubygiHiEtCWYOgfU/QdU20H2ktYS2iBtpqoaIFF1lakCX96wVCTu9DIe3w7he/Or9FHf7zMeP\nc8PzjQ3CbClTRC5iVzR8cQ1s+Bk6vAD9pyk0iy0UnEWk6AsoDdcOgcfXQfdRBAUF87JjFMv9HuE5\nr3FEBh2nUil/xiz5m+//2m13tSJySmqi1THju67g8LL6ubd7GhxOuyuTYkpTNUSk+Dh7HvSevyi5\n7CsGbp7BwMxZZFa7gQ9LduD/ppnEJqTwTOc6OByG3RWLFF/b5sCMxyF5v9VqssPz53TKEbGDgrOI\nFD+GAVWusbbEWFgxGq9V3zA0ZRb9Q6rx0eLreOpID968vSV+3hrZEnGrk0etNnPrJkC5unD7D1Cx\nqd1ViQCaqiEixV1wRej0EjyxGbp+TmhIEG96j+al7T35/cMBHN+33e4KRYqPTdPhsxawYRK0fRoG\n/qHQLB5FI84iIgDefhB5B0aTvrB3GclzPuTG2Ck4RkwmpWon/K95AGp21NxKEVdIPgSznoJNUyGs\nEdz5M1RoZHdVIudRcBYROZthQOWWRAyYSMyGTayY9B7dd8/Df/fvEFIZmt4Dkf2gRDm7KxUp/EzT\nai/36zOQngwdX7TmMzu97a5MJFcKziIieYhsUI+g0I+4ddQSWqT9xf/5LSN43iuw4E2odws0uxeq\ntLbCtohcnn0x1lzmPX9BxebQ9TMoV9vuqkQuSMFZROQCaoYGMeGhdvQf7cfVsS0Zc/OLtE6YYS2o\nsuFnKFvbCtCNe4N/iN3lini+5IMw71VrBcCAMvDfjyHyTk2DkkJBNweKiFxERIg/Pw26hjoVStJ/\negI/lX0IntgCXT8H3xIw+xl4vw5MGwx7l1u/fhaRc2WmwZKP4OMoWDsBrnkYHl0NTe9SaJZCQyPO\nIiKXoHSgD+Pub8GgH1YxdNI6jp6ow8B2d0DkHbBvDawcA+snWaNoZWtDVD9o1FtzoUVME7b+CnOe\nh2N/w1U3Quc3rJU9RQoZjTiLiFyiQF8vRt3VjJsbVeCtX7fw5qzNmKYJ4U3glo/hqa1wyyfgFwy/\n/Q8+qAMT7rAWcsjKtLt8Efc7uBm+vxUm9AGnj9Uto+8EhWYptDTiLCJyGXy9nHzUO5JSAT6MWLiL\nNXsSiD12kvjEVMJD/BnauSPd7u8PB7dAzPfWr6S3zISgCtCkrzWXs3R1uz+GiGslH4KF78KK0dZ0\nphvfte4FULcMKeQUnEVELpPTYfBq1/ocSkpj9sb9p/fHJaTw3OT1AHSLrGP9OrrjS7B9Dqz+HhZ/\nCIveh6ptoHEfqzOHb5BdH0Ok4CUfgj8/hhWjIDMVmt1nLZUdUNruykQKhIKziEg+GIbB+rjE8/an\nZGQxbM5WukVGWDu8fKDuf63t+D5YO96aBz3tIfjlSajTBRrdDjWuA6d+JEsh9e/A3LAXtB0KZWvZ\nXZlIgdJPaRGRfNqXkHJZ+ykZDm2ehGufgNgVsG6i1dJuwyQILAcNelghOjxSvaGlcFBglmJGwVlE\nJJ/CQ/yJyyUkly/pd+EXGgZUutraOr8FO+bCugmw8mtY9iWUqQWNb4eGt0GpKi6qXuQKKDBLMaXg\nLCKST0M71+a5yetJycg6Z396VjZ7jpykcpmAi7+Jlw/UucnaUhJg0zRY9yPMf93aKrWE+t2gXldr\nxFrETskH4c9PFJil2FJwFhHJp1PzmIfN2cq+hBTCQ/y5vXklxiz5m9u++osf7m9BzdASl/6G/iHW\nYhBN74KEPVaA3jgFZj9rbQrRYpfYVbD8K9gwGcwsBWYpthScRUSuQLfIiDM3Aua4vn557hy1jN4j\n/uL7+1pQt0LJy3/jkMrQ9ilrO7wdNk6FTVMVosV9MtOsv3fLv4K4VeATZLWUazFQfZil2NICKCIi\nBaxOWEkmDmyFl8NB7xFLWbs34cresGwtaDcUHlwCD6+EDv+D9GQrQH9QF0Z3hqVfwLHdBVK/FHPH\n42H+G/BhA5jyAKQehxuHwROb4KZ3FZqlWNOIs4iIC9QoV4KfBrWi76il3DFqGWPubs7V1Qqgl+2p\nEN1u6JmR6LOnc4TWg9o3WssaRzQFh8ZH5BKYJuxdbo0ub5oG2VlQ63po8QBUv05/j0RyKDiLiLhI\npdIB/DTwGvqOWkr/McsY2b8ZbWqVK7gTnB2ij+yEbbNh66+weLi10EpgKFzV2QrS1duDT2DBnVuK\nhuPxVkvEdRNg/3rwDYarB0Lz+zSyLJILBWcRERcKC/Zj4gOt6Dd6Gfd9s5LP74iiU73yBX+iMjWg\n1WBrSzkG2+fC1lnW6GHM9+DlZ4Xnq27AN/UybliUoic1ETbPsG4+/XshYEKFJtDlfWjU21oiW0Ry\npeAsIuJi5YJ8mfBAS+4as5xBP6xieO8m3NzIhTf0+ZeCRr2sLTMd9vwJW2dbQXrbbFoBbH8bqneA\nGh2sJcD98nEDoxQemWmw/XdY/6P1dyErDUpVtTpjNLpN3TFELpGCs4iIG4QE+PDD/S2475uVPDo+\nhrSMbHo0rej6E3v5WCPN1dvDDW/BoS3smDOSmo69sGYsrBgJhhMqNrOW/a7ewZobreW/C7/sLNjz\nlzWyvGkapCZAQFmr3WHD26xrrhUqRS6LfjKKiLhJkJ8339zbnAHfreSpSWsxgZ7uCM+nGAaE1iW2\n0i3UbN/eGoXcuxx2LYCdCyD6bYh+C3xLWqPQ1dpC5RZQvqGCdGGRfAh2zoPtv8GOeVZY9g6EOl2s\nkeXq7cHpbXeVIoWWfhKKiLhRgI8Xo++ywvPQSWvJNk1ua1bJnmK8fKFaG2vr+CKcPGrNeT0VpLf+\nYj3POxAqNYfKraBSC6jYXPNgPUV2NuyLsYLy9t+s7zGtG0Nr3wS1/mPdIKobQ0UKhIKziIib+Xk7\nGdm/GQO+W8kzP68DE25rblN4PltAaWtRlfrdrMeJsbBnqbXtXWqNSGNaUzvCGlhBunJLK0wHVdCv\n/d0l+aD1D5xTo8onDwOG9Q+aDs9bYTmssVrIibiAgrOIiA1OhecHvl/F0z+vI9s06X11ZbvLOldw\nRWjY09rA6sYQu+JMmF71LSz70joWGAoVGkGFxtYW1si6+Uxh+spkZcCBDbB3BcQut6bWJPxjHQso\nAzU7Wf2Wa1xn/cNHRFxKwVlExCZ+3k5G9GvKwO9X8ezk9ZhAH08Lz2fzC7aCWs1O1uOsDIhfZ4Xp\n/esgfq01xcPMOvP8sH+F6TI1NMf2ArzTE2DLL1ZAjl0BcashM8U6GFTBGlW+egBUvgbCm4DDaW/B\nIsWMgrOIiI38vJ181a8pD/6wiucmr8c0oW8LDw7PZ3N6Q8Wm1nZKRioc3GSF6FPb8pFW+zMAh5c1\nEl2mFpStmfO1lvU1sGzxGaE+eRQObYXDW+HQtpyvW2mduBf+BBze1gh+07ut+eUVr7Z+A1Bc/nxE\nPJSCs4iIzfy8nXzZrykP/rCa56es593ZW0hMySA8xJ+hnWvTLTLC7hIvnbcfRERZ2ylZGXB4mzU6\nfWS7tVT4kR2wc/6ZQA3WCPWpIB1SBUqGW1tQBeurf6nCExxN05rakrQfjsdZn/nQFuvP4dDWnHnJ\nObz8rc9cuSU7T3SkRvs+1oIk3n721S8iuXJZcDYM42VgAHAoZ9fzpmnOyjn2HHAfkAU8aprmHFfV\nISJSGPh6ObmpQRjRWw+SkJIBQFxCCs9NXg9QuMLzvzm9oXx9aztbdhYk7oXDO6xAfWSHFTD/XgjH\n9wHmuc/38jsTok8F6qAwq32eX0krePue/bWk1TmkIGRnQ8YJSD8J6cmQcRJSEqxgnBSf+9dTUyxO\n8QuBcrWtJdDL1YaytaHcVRBc+fSNfHujo6lRuWXB1CwiBc7VI84fmqb53tk7DMOoB/QG6gPhwFzD\nMK4yzVOT4kREiqcP524n+19ZMSUji2Fzthbu4JwXh9OatlGqKtTqdO6xrIwzIfT4PmtLyvl6PN6a\nA5wUD1npFz6H0zcnSAdZ00QcTjAc1si14bA6hBiOM5vDafW3Tj9xVlA+cX4I/jfvgJwgX8FaQCYo\n7EywD6pgjSgHlis8I+Yikis7pmp0BSaYppkG/G0Yxg7gauAvG2oREfEY+xJyD2d57S/SnN4QUsna\n8mKa1gIfqcch7fhZXxNzvk88sy8tCbIzwcy2XmdmWyPeZvZZW5Z1zK8klKxg9a/2CQSfAPApYYVj\nn8Azm2/Js0a9gxSKRYoBVwfnhw3D6A+sBJ40TfMYEAEsPes5sTn7RESKtfAQf+JyCcnB/upCkSvD\nsOY9+5eyuxIRKSYM0zQv/qy8XmwYc4GwXA69gBWOD2NNUnsNqGCa5r2GYXwKLDVN84ec9xgN/Gqa\n5qRc3v8B4AGA8uXLN50wYUK+a82v5ORkSpTQClmeSNfGc+na5E9CSgZxx1LIzvm5nJkNM/Y42ZVk\ncH9DH66NKJgArevjuXRtPJeujecq6GvToUOHVaZpNsvt2BWNOJum2enizwLDMEYCM3MexgFn/+6t\nYs6+3N5/BDACoFmzZmb79u3zXWt+RUdHY8d55eJ0bTyXrk3+TY2JY9icrexLSCE8xJ/HO9di+tp9\njNlwmIb169G1yZX/gk7Xx3Pp2nguXRvP5c5r48quGhVM04zPeXgrsCHn++nAOMMwPsC6ObAWsNxV\ndYiIFCbdIiPOuxHw5kbh3PPNcp74cS0+Tgc3NqxgU3UiIsWbKxeyf9cwjPWGYawDOgBDAEzT3Aj8\nCGwCZgOD1VFDRCRv/j5ORt/VnMhKITwyPobfNx2wuyQRkWLJZcHZNM1+pmk2NE2zkWmat5w1+oxp\nmm+YplnDNM3apmn+6qoaRESKikBfL76+pzn1I4IZPHY10VsP2l2SiEix48oRZxERKUBBft58d8/V\n1CpfgoHfr2LJjsMXf5GIiBQYBWcRkUIkOMCb7+9rQbWygdz/7UqW/33U7pJERIoNBWcRkUKmdKAP\nP9zfgvAQP+75ejmr/jlmd0kiIsWCgrOISCFUtoQv4wa0pFyQL3ePWc662AS7SxIRKfIUnEVECqny\nJf0YN6AlIYHe9Bu9nM3xx+0uSUSkSFNwFhEpxMJD/Bl3f0v8vZ30G72cvw+fsLskEZEiS8FZRKSQ\nq1Q6gB/ub0G2aXLnqGXsS0ixuyQRkSJJwVlEpAioGVqC7+69muOpGdw5ahmHktLsLklEpMhRcBYR\nKSIaRATz9d3NiU9Mpf+Y5SSezLC7JBGRIkXBWUSkCGlWtTRf9WvKzoPJ3PPNck6kZdpdkohIkaHg\nLCJSxLS9qhwf94lkbWwiD3y/ktSMLLtLEhEpEhScRUSKoBsahPFuj0Ys2XGER8bHkJGVbXdJIiKF\nnpfdBYiIiGv0aFqRE+mZvDhtI71HLCU+IYX4xFSebZJNQkwc3SIj7C5RRKRQUXAWESnC+reqyrJd\nR/llffzpfelZ2Tw3eT2AwrOIyGXQVA0RkSIuZs+xcx6bJqRkZDFszlabKhIRKZwUnEVEirj4xNRz\nHi8/9P/t3Xl0VfW9/vHnk5PphCSEMZAwKhAFQUICOBe0ildtG3GoVkAUixattb3FytWOV6/e0sGf\nrRMKgopiFbC2WlGvUpwQiCCIEoSAQigzYQgnA8n39wcHy5BAIMPe55z3a60scvZJsp+ub1k+7Hz3\nZ5sk8aAUADhOFGcATDbgEgAAIABJREFUiHJZGcFDXr+3KVDrcQDA0VGcASDKjR+Wo2BC4OvX3VL3\nT9i4qE+mV5EAICJRnAEgyhXkZuv+4X2VnRGUSbqiu9StTYqmz/9KH6ze6nU8AIgYFGcAiAEFudl6\n/67zteaBS9U3O00v33q2urVN0dinC/VpyU6v4wFARKA4A0AMykhJ1NM3DlbLYIKun7JAxVv2eB0J\nAHyP4gwAMapDy2Q9M2aQJGnk5AXaeNj0DQDAoSjOABDDTmqXqqk3DNLOUJVGTflIpXsrvY4EAL5F\ncQaAGNe3U0tNGpWntVv36sapC7W3cp/XkQDAlyjOAACddXJbPXRtfy1ZV6px0z9WVXWN15EAwHco\nzgAASdLFp3XUfZf31dyiLfrpi5+opsZ5HQkAfCXe6wAAAP+4dlAXbS+r1MQ5RWqVkqhffqu3zMzr\nWADgCxRnAMAhxg05WdvLKjX5vTXq0DJZt3zjZK8jAYAvUJwBAIcwM919yanasrtCD/xjhdqlJumK\nvE5exwIAz1GcAQBHiIszTbyqn7aVVehnM5eqTWqihuS09zoWAHiKmwMBALVKig/osRF56pWZpnHT\nP9Yn60q9jgQAnqI4AwDqlJacoKk3DlTrFom6cepCrd1a5nUkAPAMxRkAcFTt05L19I2D5CSNmrJA\nW3ZXeB0JADxBcQYAHNNJ7VI1+fp8bdldoRumLtCeCp4uCCD2UJwBAPWS26WVHrlugD7/12794NlC\nVe7j6YIAYgvFGQBQb0NPaa8HhvfVu19s1Z0v8XRBALGFcXQAgONyVX5nbd5doYlzipSZnqwJl5zq\ndSQAaBYUZwDAcRs35GRt2lWux+cVq11akm469ySvIwFAk6M4AwCOm5npl9/qoy27K3Tvq5/r4XdW\nqXRvlbIygho/LEcFudleRwSARsceZwDACQnEmc4/pb3iTNqxt0pOUklpSBNmLdPLi0u8jgcAjY7i\nDAA4YQ++9YUOvz8wVFWtiXOKvAkEAE2I4gwAOGEbSkPHdRwAIhnFGQBwwrIygrUe79AyuZmTAEDT\nozgDAE7Y+GE5CiYEjjjeMpigqmoekAIgulCcAQAnrCA3W/cP76vsjKBMUnZGUN/N76wVG3frntmf\nyjkekAIgejCODgDQIAW52UeMn2ufnqQ/vb1K2a2Cuv2Cnh4lA4DGRXEGADS6n1zYSyWlIf3hzZXq\n2DJZV+V39joSADQYxRkA0OjMTA8M76fNuyo0YdYyZaYn67xe7byOBQANwh5nAECTSIyP0yMjBqhH\n+1SNm/6xlm/Y6XUkAGgQijMAoMmkJydo6g2DlJYcrxueWqgS5jsDiGAUZwBAk+rQMllTbxikUGW1\nbnxqoXaVV3kdCQBOCMUZANDkcjqk6dEReVq9ZY/GPfsxM54BRCSKMwCgWZzTs63+Z3hfvbdqq+6e\nvYwZzwAiTpNN1TCzFyTlhF9mSCp1zvU3s26SPpdUFH5vvnPulqbKAQDwj6vzO2v99r166O1V6tI6\nRbedz4xnAJGjyYqzc+67Bz43s99LOvh26tXOuf5NdW4AgH/9+MJeWrcjpN+9sVKdWqUc8fAUAPCr\nJp/jbGYm6WpJ5zf1uQAA/mdmeuCKvtpQGtKdLy1Vh5bJOuOkNl7HAoBjsqbeY2Zm50n6g3MuP/y6\nm6TlklZK2iXpHufcu3V871hJYyUpMzMzb8aMGU2atTZ79uxRampqs58Xx8ba+Bdr429+WZ+yKqd7\n54e0q9Lp7sFBZaVy241f1gZHYm38q7HXZujQoYUHeuvhGlSczewtSR1qeetu59xfw1/zqKRVzrnf\nh18nSUp1zm0zszxJL0vq45zbdbRz5efnu0WLFp1w1hM1d+5cDRkypNnPi2NjbfyLtfE3P63Puu17\ndfkj7yuYGNDscWerbWqS15E85ae1waFYG/9q7LUxszqLc4P+ee+c+6Zz7rRaPg6U5nhJwyW9cND3\nVDjntoU/L5S0WlKvhuQAAESmzq1T9OT1A7Vld4VumrZIocpqryMBQJ2a+vdi35S0wjm3/sABM2tn\nZoHw5ydJ6impuIlzAAB8qn/nDD343Vx9sr5Ud7ywWNU1jKkD4E9NXZyvkfT8YcfOk7TUzJZIeknS\nLc657U2cAwDgYxef1kH3XNpbc5Zv0v2vfe51HACoVZNO1XDOja7l2ExJM5vyvACAyHPj2d20bvte\nPfneGnVunaLrz+rmdSQAOESTj6MDAKA+zEw/v6y31u/Yq1//bbk6tw7q/FMyvY4FAF9j9g8AwDcC\ncab/d02uTu2Yrh8+t1jLN+w89jcBQDOhOAMAfKVFUrymjB6o9GCCxkxdpI07y72OBACSKM4AAB/K\nTE/W5OsHand5lcZMW6iyin1eRwIA9jgDAPypd1a6/vy9ARozbaGufvxD7Sir1L92lisrI6jxw3JU\nkJvtdUQAMYYrzgAA3xp6Sntdnput5Rt2acPOcjlJJaUhTZi1TC8vLvE6HoAYQ3EGAPja/OIjR/2H\nqqo1cU6RB2kAxDKKMwDA1zaUho7rOAA0FYozAMDXsjKCx3UcAJoKxRkA4Gvjh+UomBA44vj3z+3u\nQRoAsYziDADwtYLcbN0/vK+yM4IySe3TkpQUH6cXC9czpg5As2IcHQDA9wpysw8ZP/fOis0aM22h\nbn9+sSaNylcgzjxMByBWcMUZABBxhp7SXr/+dh/934rNuu/Vz72OAyBGcMUZABCRRp7ZTcVbyzTl\n/TXq3jZFI8/s5nUkAFGO4gwAiFj3XNpbX27bq1/97TN1bp2iITntvY4EIIqxVQMAELECcaaHrs1V\nr8w03fbcYhVt3O11JABRjOIMAIhoqUnxmnx9vlISA7px6kJt3l3udSQAUYriDACIeFkZQU2+fqC2\nl1Xq+08Xqryq2utIAKIQxRkAEBX6dmqpB6/pr6XrS/Wff/lENTXO60gAogzFGQAQNYb16aD/+o9T\n9eqyf+kPb670Og6AKMNUDQBAVLnp3O4q3lqmP7+zSt3attCVeZ28jgQgSlCcAQBRxcz0m+/00brt\nezVh1lJ1ahXUGSe18ToWgCjAVg0AQNRJCMTp4esGqGubFrr5mUIVb9njdSQAUYDiDACISi2DCXpq\n9EDFx5nGTFukHWWVXkcCEOEozgCAqNW5dYomjcpTSWlItzxbqMp9NV5HAhDBKM4AgKiW17W1Jl7Z\nTx+t2a4Js5bJOcbUATgx3BwIAIh63+mfrTVby/TgW1/opHYtdOvQHl5HAhCBKM4AgJjwowt6as3W\nMk2cU6TubVvokr4dvY4EIMKwVQMAEBPMTP97RT/ldW2lH7+wREvWlXodCUCEoTgDAGJGckJAk0bm\nqX16km6atkglpSGvIwGIIBRnAEBMaZOapCnXD1RFVbXGTF2o3eVVXkcCECEozgCAmNMzM02PjBig\nLzbv0e3PL9a+asbUATg2ijMAICad27Odfv3tPnqnaIvuffVzr+MAiABM1QAAxKwRZ3TVmq1lmvze\nGu0ur9L84u3aUBpSVkZQ44flqCA32+uIAHyE4gwAiGn/dcmpml+8TTM/Lvn6WElpSBNmLZMkyjOA\nr7FVAwAQ0wJxpu1llUccD1VVa+KcIg8SAfArijMAIOZt3Fle6/ENjKsDcBCKMwAg5mVlBI/rOIDY\nRHEGAMS88cNyFEwIHHIsYKb/vKiXR4kA+BE3BwIAYt6BGwAnzinShtKQ0pLjtat8n4q3lHmcDICf\nUJwBAND+8nygQDvnNGHWMv35nVXq3raFrsjr5HE6AH7AVg0AAA5jZvrvgtN01sltdNespfqoeJvX\nkQD4AMUZAIBaJATi9Oh1eercOkU3P1uoNVvZtgHEOoozAAB1aJmSoKdGD5RJGjN1oUr3HjnvGUDs\noDgDAHAUXdu00KRR+Vq/I6Rbni1U5b4aryMB8AjFGQCAYxjYrbV+e2U/zS/errtnL5NzzutIADzA\nVA0AAOqhIDdbxVvL9ND/faGT2qXqB0NO9joSgGZGcQYAoJ5+/M2eWru1TP/7+gp1bZOiS/p29DoS\ngGbEVg0AAOrJzPTbK/tpQJcM/fiFJVqyrtTrSACaEcUZAIDjkJwQ0BOj8tU+PUk3TVuk9Tv2eh0J\nQDOhOAMAcJzapCbpqdEDVbGvWjdOXahd5VVeRwLQDCjOAACcgB7t0/TYiDwVbynTbc8t1r5qxtQB\n0Y7iDADACTq7R1vdd/lpmrdyi375ynLG1AFRrsHF2cyuMrPlZlZjZvmHvTfBzFaZWZGZDTvo+MXh\nY6vM7K6GZgAAwCvfHdhFt3zjZE3/6CtNfm+N13EANKHGGEf3qaThkh4/+KCZ9ZZ0jaQ+krIkvWVm\nvcJvPyzpQknrJS00s1ecc581QhYAAJrdncNy9NX2Mt332ufq3DpFw/p08DoSgCbQ4CvOzrnPnXNF\ntbz1HUkznHMVzrk1klZJGhT+WOWcK3bOVUqaEf5aAAAiUlyc6Q9X91e/Thm6Y8YSLVu/0+tIAJqA\nNdZ+LDObK+mnzrlF4dd/ljTfOfds+PVkSf8If/nFzrmbwsdHShrsnLutlp85VtJYScrMzMybMWNG\no2Q9Hnv27FFqamqznxfHxtr4F2vjb6xP09lZ4fSbD0OqdtLPz0hWm+DxXZ9ibfyLtfGvxl6boUOH\nFjrn8mt7r15bNczsLUm1/d7pbufcXxsS7micc5MkTZKk/Px8N2TIkKY6VZ3mzp0rL86LY2Nt/Iu1\n8TfWp2md2n+3rnjkAz1RFK+XfnCWUpPqvyuStfEv1sa/mnNt6vVPYefcN51zp9XycbTSXCKp80Gv\nO4WP1XUcAICI1yszTY+MGKAvNu/Rbc99zJg6IIo05Ti6VyRdY2ZJZtZdUk9JCyQtlNTTzLqbWaL2\n30D4ShPmAACgWZ3bs53++zunaW7RFv3m758xpg6IEg2eqmFml0v6k6R2kl41syXOuWHOueVm9hdJ\nn0naJ+lW51x1+HtukzRHUkDSFOfc8obmAADAT743uIvWbivTpHnF6tqmhcac093rSAAaqMHF2Tk3\nW9LsOt67T9J9tRx/TdJrDT03AAB+dtfFp+irbXt176ufqVOrIGPqgAjHkwMBAGgicXGmP363v07v\nlKEfzVisJetKvY4EoAEa4wEoAACgDsHEgJ68Pl+XP/K+Rjz5kVokBrR5d4WyMoIaPyxHBbnZXkcE\nUE9ccQYAoIm1TU3SiMFdtadinzbtrpCTVFIa0oRZy/TyYgZLAZGC4gwAQDN4+sMvjzgWqqrWxDm1\nPXwXgB9RnAEAaAYbSkPHdRyA/1CcAQBoBlkZweM6DsB/KM4AADSD8cNyFEwIHHH8G73aeZAGwImg\nOAMA0AwKcrN1//C+ys4IyiRltUxWz/aperFwnT5YvdXreADqgXF0AAA0k4Lc7EPGz+0MVenKRz/Q\nzc8Uava4szxMBqA+uOIMAIBHWgYTNGX0QCXFBzT6qYXaWeG8jgTgKCjOAAB4qHPrFE0Zna9teyr1\nYGG59lbu8zoSgDpQnAEA8Fi/Thl66Npcrd1Vox8+t1j7qmu8jgSgFhRnAAB84MLemRrZO1H/t2Kz\nfvnKcjnHtg3Ab7g5EAAAnzi/S4JS2nXWY/9crexWQY0b0sPrSAAOQnEGAMBH7hyWow2lIf329SJl\ntQweMoUDgLcozgAA+EhcnGniVf20eXe5xr/0idqnJemsHm29jgVA7HEGAMB3kuIDenxkvrq3baGb\nnylU0cbdXkcCIIozAAC+1DKYoKduGKSUpIBGP7VAG3eWex0JiHkUZwAAfCo7I6gpowdqV6hKo59a\noN3lVV5HAmIaxRkAAB/rk9VSj47I06rNe/SDZz9W5T5mPANeoTgDAOBz5/Vqp/uH99V7q7bqrllL\nmfEMeISpGgAARICr8jtrQ2m5/vjWSmVnBPWfF+V4HQmIORRnAAAixO0X9NCG0pD+9PYqZaYna8QZ\nXb2OBMQUijMAABHCzHTf5adpy54K/eKvn6ptapIuPq2D17GAmMEeZwAAIkh8IE4Pf2+ATu+codtn\nLNaCNdu9jgTEDIozAAARJpgY0OTrB6pTq6BumraQB6QAzYTiDABABGrdIlFP3zhIyQkBXT9lgTaU\nhryOBEQ9ijMAABGqU6sUTbtxkMoq9mnUlAUq3VvpdSQgqlGcAQCIYKd2TNekUfn6attejZm2SOVV\n1V5HAqIWUzUAAIhwZ57cRg9e01+3Pvexrnz0A20vq9S/dpYrKyOo8cNyVJCb7XVEICpwxRkAgChw\nSd+OGp6brU837NKGneVykkpKQ5owa5leXlzidTwgKlCcAQCIEvOLjxxNF6qq1sQ5RR6kAaIPxRkA\ngChR12QNJm4AjYPiDABAlMjKCB7XcQDHh+IMAECUGD8sR8GEwBHHv316lgdpgOhDcQYAIEoU5Gbr\n/uF9lZ0RlEnqmJ6sji2TNe3DtVr81Q6v4wERj3F0AABEkYLc7EPGz23eVa4rH/tQN0xdqL/cfKZ6\nZaZ5mA6IbFxxBgAgirVPT9azYwYrMRCnkZM/0rrte72OBEQsijMAAFGuS5sUPT1mkEKV1Ro5+SNt\n2V3hdSQgIlGcAQCIAad0SNdTNwzSpl0VGjVlgXaGqryOBEQcijMAADEir2srPT4yT6s279ZN0xYq\nVFntdSQgolCcAQCIIef1aqc/fre/Fn25Q+OmF6qqusbrSEDEoDgDABBjLuuXpfsK+uqdoi366Yuf\nqKbGeR0JiAiMowMAIAZ9b3AXlYYq9dvXi9QymKBff7uPzMzrWICvUZwBAIhRP/jGySrdW6VJ84qV\nnpygnw7L8ToS4GsUZwAAYpSZacJ/nKJdoSr9+Z1VCiYGdOvQHl7HAnyL4gwAQAwzM913eV+VV1Vr\n4pwiJScENOac7l7HAnyJ4gwAQIwLxJl+d9XpqthXo//++2dKTojTdYO7eh0L8B2magAAAMUH4vT/\nrsnV0Jx2uuflTzWzcL3XkQDfoTgDAABJUmJ8nB4dkaezTm6j8S99or8v3eB1JMBXKM4AAOBryQkB\nPTEqX3ldW+mOGUv05mebvI4E+AbFGQAAHCIlMV5TRg9Un6x03Tr9Y81bucXrSIAvNKg4m9lVZrbc\nzGrMLP+g4xeaWaGZLQv/ef5B7801syIzWxL+aN+QDAAAoPGlJSdo2o2DdHL7VI19ZpHmF2/zOhLg\nuYZecf5U0nBJ8w47vlXSt5xzfSVdL+mZw96/zjnXP/yxuYEZAABAE8hISdQzYwapU6sUjZm6UIVf\n7vA6EuCpBo2jc859LumIR3Q65xYf9HK5pKCZJTnnKhpyPgAA0LzapiZp+k2DdfXjH2r0Uws09tyT\nNGPhOm0oDSkrI6jxw3JUkJvtdUygWTTHHucrJH18WGl+KrxN4+d2eOsGAAC+kpmerOk3DVZ8nOn3\nb65USWlITlJJaUgTZi3Ty4tLvI4INAtzzh39C8zektShlrfuds79Nfw1cyX91Dm36LDv7SPpFUkX\nOedWh49lO+dKzCxN0kxJzzrnnq7j3GMljZWkzMzMvBkzZhzP/7ZGsWfPHqWmpjb7eXFsrI1/sTb+\nxvr4l9/XZv6XuzV9lamqRrqye7Uyg/uPJwbilNMhzdtwTczvaxPLGntthg4dWuicy6/tvWMW5/qo\nrTibWSdJb0u6wTn3fh3fN1pSvnPutmOdIz8/3y1atOhYX9bo5s6dqyFDhjT7eXFsrI1/sTb+xvr4\nl9/Xpvtdr6q21mCS1jxwaXPHaVZ+X5tY1thrY2Z1Fucm2aphZhmSXpV018Gl2czizaxt+PMESZdp\n/w2GAADA57Iygsd1HIg2DR1Hd7mZrZd0pqRXzWxO+K3bJPWQ9IvDxs4lSZpjZkslLZFUIumJhmQA\nAADNY/ywHAUTAkcc/25+Zw/SAM2voVM1ZkuaXcvxeyXdW8e35TXknAAAwBsHpmdMnFOkDaUhtU9P\nUlW10xPvFeu8nHbq3znD44RA02pQcQYAALGlIDf7kPFzJaUhXTPpQ4188iM9PWaQcru08jAd0LR4\n5DYAADhh2RlBvTD2TLVqkahRkxfo4694SAqiF8UZAAA0SFZGUC/cfIZap+4vzzxhENGK4gwAABqs\nY8ugZow9Q21TE3X9lAUq/HK715GARkdxBgAAjWJ/eT5T7dKSNGryAs0v3uZ1JKBRUZwBAECj6dAy\nWTPGnqGOGUFdP2WB3l6xyetIQKOhOAMAgEaVmZ6sv9x8pnplpmns04X62ycbvI4ENAqKMwAAaHSt\nWyTque8P1oCurXT7jMV6fsFXXkcCGoziDAAAmkRacoKm3TBI3+jVThNmLdOkeau9jgQ0CMUZAAA0\nmWBiQJNG5uvSfh31P6+t0O/fKJJzzutYwAnhyYEAAKBJJcbH6aFrcpWWFK8/vb1Ku8v36ReX9VZc\nnHkdDTguFGcAANDkAnGm+4f3VWpSvJ58b412lVfpt1f0U3yAX34jclCcAQBAszAz3X3pqUoPJugP\nb65UWcU+PXRtrpLiA15HA+qFf+YBAIBmY2a6/YKe+sVlvTVn+SbdNG2R9lbu8zoWUC9ccQYAAM3u\nxnO6Ky05Xj+buVTXTpqvK/M66bF/FmtDaUhZGUGNH5ajgtxsr2MCh6A4AwAAT1yV31kZKYkaN71Q\nv/jrch2YtVFSGtKEWcskifIMX2GrBgAA8MyFvTOVEUzU4QPqQlXVmjinyJNMQF0ozgAAwFNb91TU\nenxDaaiZkwBHR3EGAACeysoIHtdxwCsUZwAA4Knxw3IUTDhyJF2P9qmqqeEpg/APijMAAPBUQW62\n7h/eV9kZQZmkrJbJOq9nW/1z5Rbd+tzHKq+q9joiIImpGgAAwAcKcrOPmKDx5LvFuu+1z7X5yY/0\nxKh8tW6R6FE6YD+uOAMAAF+66dyT9PD3BmhZyU5d8egH+nJbmdeREOMozgAAwLcu6dtR028arB17\nK1Xw8Pv6YPVWryMhhlGcAQCArw3s1lqzx52tNqlJGjl5gaa+v0bOcdMgmh/FGQAA+F73ti00e9xZ\nGprTTr/622e686Wl3DSIZkdxBgAAESEtOUGTRubr9vN76MXC9bpm0nxt2lXudSzEEIozAACIGHFx\npp9clKPHRgzQyk27ddmf3lPhlzu8joUYQXEGAAAR5+LTOmrWuLMUTAjo2knz9cLCr7yOhBhAcQYA\nABHplA7peuW2szWoe2v9bOYy/fKvn6qqusbrWIhiPAAFAABErIyURE29YaD+9/UVeuLdNVqxcbe+\n1S9Lj/5ztTaUhpSVEdT4YTlHPFwFOBEUZwAAENHiA3G6+9Le6p2VrvEvLtWCNdt1YFhdSWlIE2Yt\nkyTKMxqMrRoAACAqXJ7bSa1SEnX4hOdQVbUmzinyJBOiC8UZAABEja17Kmo9vqE01MxJEI0ozgAA\nIGpkZQRrPd66RWIzJ0E0ojgDAICoMX5YjoIJgUOOmaRtZZW69++fqXIfUzdw4rg5EAAARI0DNwBO\nnFP09VSNH13QU8tKdurJ99ZowdrteuiaXHVr28LjpIhEFGcAABBVCnKzj5igcfXAzjq7R1v9bOZS\nXfrQu7rv8r5M2cBxY6sGAACICRef1kGv/ehc9c5K1x0vLNFP/rJEeyr2eR0LEYTiDAAAYkZ2RlDP\nf/8M3X5BT728uETD/jhP7xRt9joWIgTFGQAAxJT4QJx+cmEvvXjLWQomBnTDUwt1x4zF2lbHKDvg\nAPY4AwCAmJTXtZVevf0cPfLOaj0yd5XmfbFVv7ist5xz+t0bKw95ZHeG12HhCxRnAAAQs5LiA/rx\nhb10Sd+O+tnMpbrjhSWKM6km/PjBA4/svv+swNF/EGICWzUAAEDMy+mQppk/OEstgwlfl+YDQlXV\n2rSz3Jtg8BWKMwAAgKRAnGlXqKrW9yqreXAKKM4AAABfq+uR3fM3B1TG6LqYR3EGAAAIq+2R3QEz\nvb/J9I2JczX9oy+1j6vPMYviDAAAEFaQm637h/dVdkZQpv1zn39/9en6+RnJ6t42RXfP/lQXPThP\nbyzfKOfcMX8eogtTNQAAAA5S2yO75+78Qn/5zpl687NNeuD1FRr7TKEGdWutCZecotwurTxKGr0W\nrNmu1KR49c5K9zrKISjOAAAA9WBmuqhPB51/Snu9sGid/vjmF7r8kQ90ad+OGj8sR0vWlWrinKJD\n5j8fXsBxdOu279UD/1ihV5f9S5f07aBHrsvzOtIhKM4AAADHIT4Qp+sGd9V3+mfriXnFmjSvWK8v\n3yhJqg7Psjsw/1kS5bkeyir26dG5qzXp3WLFmXTHN3vq5vNO9jrWESjOAAAAJyA1KV4/vrCXrhvc\nRUN+N1d7K6sPeT9UVa2Jc4oozkdRU+M0a3GJfvv6Cm3eXaGC/lm68+JT6pxu4jWKMwAAQAO0T09W\n6LDSfEBJaUjOOZlZM6fyv0Vrt+s3f/9MS9fv1OmdM/TYyDwN8Pl+8QZN1TCzq8xsuZnVmFn+Qce7\nmVnIzJaEPx476L08M1tmZqvM7CHj/0kAACDCHe0KacHD7+uVTzaoijF2kvb/Y+KHzy/WlY99qE27\nyvWHq0/X7B+c5fvSLDX8ivOnkoZLeryW91Y75/rXcvxRSd+X9JGk1yRdLOkfDcwBAADgmfHDcjRh\n1jKFqv595Tk5Pk6X9ctS4Vc7dPvzi9WxZbJGn9VNacnxevid1TF3E+G2PRWa9sFaPT6vWJJ0+/k9\ndMuQk5WSGDkbIBqU1Dn3uaR6//rBzDpKSnfOzQ+/flpSgSjOAAAggh0ovrVN1aipcXqnaLOefHeN\n7v/HikO+L9pvIqypcXp/9VbNWLBOb3y2UVXVTt86PUs/uzhHnVqleB3vuFljDO82s7mSfuqcWxR+\n3U3SckkrJe2SdI9z7t3wdo4HnHPfDH/duZJ+5py7rI6fO1bSWEnKzMzMmzFjRoOzHq89e/YoNTW1\n2c+LY2Nt/Iu18TfWx79YG/9qrLWZV7xb8zdLK3aaapypZaJTr3Sn3q2lId1Tv74YWRqq0qad5aqs\nrlFiIE6ZLZPazQwgAAAH8ElEQVSVEUxo8PmbS2l5jd4t2ad56/dpS8ipRYJ0Tla8zuucoOzUxn3+\nXmP/vRk6dGihcy6/tveOecXZzN6S1KGWt+52zv21jm/7l6QuzrltZpYn6WUz61PvxGHOuUmSJklS\nfn6+GzJkyPH+iAabO3euvDgvjo218S/Wxt9YH/9ibfyrsdbmhtdf1cGXLHdWmhZuNS3cKr212emS\nvplqkRivx95frfJ9cTpwO1owoVr3D+/t66vS1TVO/1y5Wc8vWKe3V2xWdY3TmSe10T2DOmtYnw5K\nPuxR5o2lOf/eHLM4H7g6fDyccxWSKsKfF5rZakm9JJVI6nTQl3YKHwMAAIh6WRlBlZSGjjiekZKg\nnA5pmvrBWlVVH7kb4MBoO6n27SBeqa5xWrFxl95YvkkvLlqnDTvL1TY1UTed213XDOyi7m1beJat\nKTTJbmwzaydpu3Ou2sxOktRTUrFzbruZ7TKzM7T/5sBRkv7UFBkAAAD8prabCIMJAf3qW31UkJut\nXeVV6verN2r93pLSkO58aakqw9M5SkpDGv/iJ/r135ardG+VsjKCGnpKO72zYotKSkMKmKnaOZn0\n9VXuVikJ+mX4XCdiT8U+Lf5qhxat3aHCL3do8Vc7VFZZLTPpnB5t9fPLeuuCUzOVGN+42zH8okHF\n2cwu1/7i207Sq2a2xDk3TNJ5kn5jZlWSaiTd4pzbHv62cZKmSgpq/02B3BgIAABiwtFuIpSk9OQE\nZddxVVrS16X5gKoapx17qyTtL9LPzv/q6/eqw/exHXz9esfeKt3xwhLd8cISjTiji+4t6FtnVuec\nSkpDKvxyf1Fe9OUOFW3cpRonmUmndEjX5QOyld+1tQZ1b+3bh5Y0poZO1ZgtaXYtx2dKmlnH9yyS\ndFpDzgsAABCpCnKzj3rFt66r0ge/bgzPzv9KRRt36+webVW6t0o79lZqx94q7Qz/uaOsUrsr9kmS\nWiQGlNullX54fk/ldW2l3C4ZSkuOnJsVG0vkDM4DAACIAXVdlZ44p6jOK9EnauHaHVq4dofSkuPV\nKiVRrVIS1DIlUd3atlCrlESd1K6F8rq2Uk5mmuID0bn94nhQnAEAAHymrqvSh1+Jbgxf3PcfSqAU\n1wvFGQAAIAIcfiW6ZTBBZZX7ap3CUV8BM0rzcaA4AwAARIjDr0S/vLjkkC0dtU3VOJprB3du6shR\nheIMAAAQoY51o+EB97y87JCJGybpumNM1cCRKM4AAABR7t6CvpTkRsCmFgAAAKAeKM4AAABAPVCc\nAQAAgHqgOAMAAAD1QHEGAAAA6oHiDAAAANQDxRkAAACoB4ozAAAAUA8UZwAAAKAeKM4AAABAPVCc\nAQAAgHqgOAMAAAD1QHEGAAAA6oHiDAAAANQDxRkAAACoB4ozAAAAUA8UZwAAAKAezDnndYZ6MbMt\nkr704NRtJW314Lw4NtbGv1gbf2N9/Iu18S/Wxr8ae226Oufa1fZGxBRnr5jZIudcvtc5cCTWxr9Y\nG39jffyLtfEv1sa/mnNt2KoBAAAA1APFGQAAAKgHivOxTfI6AOrE2vgXa+NvrI9/sTb+xdr4V7Ot\nDXucAQAAgHrgijMAAABQDxTnozCzi82syMxWmdldXufBfmY2xcw2m9mnXmfBocyss5m9Y2afmdly\nM/uR15mwn5klm9kCM/skvDa/9joTDmVmATNbbGZ/9zoLDmVma81smZktMbNFXufBv5lZhpm9ZGYr\nzOxzMzuzSc/HVo3amVlA0kpJF0paL2mhpGudc595Ggwys/Mk7ZH0tHPuNK/z4N/MrKOkjs65j80s\nTVKhpAL+3njPzExSC+fcHjNLkPSepB855+Z7HA1hZvYTSfmS0p1zl3mdB/9mZmsl5TvnmOPsM2Y2\nTdK7zrknzSxRUopzrrSpzscV57oNkrTKOVfsnKuUNEPSdzzOBEnOuXmStnudA0dyzv3LOfdx+PPd\nkj6XlO1tKkiS229P+GVC+IMrJz5hZp0kXSrpSa+zAJHCzFpKOk/SZElyzlU2ZWmWKM5Hky1p3UGv\n14sCANSbmXWTlCvpI2+T4IDwVoAlkjZLetM5x9r4x4OS7pRU43UQ1MpJesPMCs1srNdh8LXukrZI\neiq8zelJM2vRlCekOANodGaWKmmmpDucc7u8zoP9nHPVzrn+kjpJGmRmbHXyATO7TNJm51yh11lQ\np3OccwMk/YekW8NbBuG9eEkDJD3qnMuVVCapSe9JozjXrURS54NedwofA3AU4f2zMyVNd87N8joP\njhT+VeY7ki72OgskSWdL+nZ4H+0MSeeb2bPeRsLBnHMl4T83S5qt/ds54b31ktYf9Nuzl7S/SDcZ\ninPdFkrqaWbdw5vNr5H0iseZAF8L34A2WdLnzrk/eJ0H/2Zm7cwsI/x5UPtvfF7hbSpIknNugnOu\nk3Oum/b/t+Zt59wIj2MhzMxahG92VngbwEWSmOrkA865jZLWmVlO+NAFkpr0ZvT4pvzhkcw5t8/M\nbpM0R1JA0hTn3HKPY0GSmT0vaYiktma2XtIvnXOTvU2FsLMljZS0LLyXVpL+yzn3moeZsF9HSdPC\nE4PiJP3FOcfYM+DYMiXN3n9dQPGSnnPOve5tJBzkh5Kmhy9yFku6oSlPxjg6AAAAoB7YqgEAAADU\nA8UZAAAAqAeKMwAAAFAPFGcAAACgHijOAAAAQD1QnAEAAIB6oDgDAAAA9UBxBgAAAOrh/wN4dLC4\n12T5LQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x648 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}