pwsode_1.ipynb

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  "metadata": {
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      "authorship_tag": "ABX9TyNjxcsCgCn2Pyi8FRwOKfMg",
      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/slashssab/piecewise-smooth-ode/blob/main/pwsode_1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fFPGf9mlRz0d"
      },
      "source": [
        "# Introduction\n",
        "\n",
        "The following paper shows several ways to analyze and vizualize pierce-wise smooth problems given by LTI systems. We will use well known python packages like:\n",
        "- scipy\n",
        "- numpy\n",
        "\n",
        "to provide tools concerning stability and periodic behaviors of concidered systems. Let us bring a following example of the LTI system with switching:\n",
        "$$\\ddot{\\theta}=A\\theta + \\mathcal{T}$$\n",
        "where\n",
        "$$\\mathcal{T} = \\begin{cases}\n",
        "     B \\theta + C \\dot{\\theta},& \\text{if }  |\\theta|\\geq \\theta_0\\\\\n",
        "    0,              & \\text{otherwise}\n",
        "\\end{cases},$$\n",
        "where $\\theta_0$ is fixed border value of $\\theta$ where switching is trigered. Most software tools offering solving ODEs accepts problems defined as the first order differential equations in a following form:\n",
        " $$\\dot{x} = f(x),$$\n",
        " where $x$ is a function of time. Having hnown that fact we have to transform equation:\n",
        " $$\\ddot{\\theta}=A\\theta + \\mathcal{T}$$\n",
        " to the first order representation using Jacobian:\n",
        " $$\n",
        "    \\ddot{\\theta}=A\\theta \\Rightarrow \\dot{x}=L_1 x,\n",
        " $$\n",
        "\n",
        "where $x$ is a state vector:\n",
        "$$x = \\begin{bmatrix}\n",
        "\\theta \\\\\n",
        "\\dot{\\theta}\n",
        "\\end{bmatrix},$$\n",
        "and $L_1$ is Jacobian:\n",
        "$$L_1=\\begin{bmatrix}\n",
        "0 & 1\\\\\n",
        "A & 0\n",
        "\\end{bmatrix}.$$\n",
        "The same can be applied for the system with control:\n",
        "$$\n",
        "    \\ddot{\\theta}=A\\theta+B\\theta+C\\dot{\\theta} \\Rightarrow \\dot{x}=L_2 x,\n",
        "$$\n",
        "where\n",
        "$$L_2=\\begin{bmatrix}\n",
        "0 & 1\\\\\n",
        "A+B & C\n",
        "\\end{bmatrix}.$$\n",
        "Problem defined as above will be an example for our consideration."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cAFF6CXHiCBR"
      },
      "source": [
        "# Implementation\n",
        "Before we get started we have to import necessary packages"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o7kWt2t3idgA"
      },
      "source": [
        "import numpy as np\n",
        "from scipy.integrate import odeint"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O_gPjn51RzKn"
      },
      "source": [
        "\n",
        "## defining variables\n",
        "We define constants $A$, $B$ and $C$ form our example:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wKhiE90ZhnS8"
      },
      "source": [
        "A = 0.5\n",
        "B = -0.7\n",
        "C = 0"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "769Ht8gFiqLG"
      },
      "source": [
        "and Jacobians $L_1$ and $L_2$:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PRTLf_DRh4rt"
      },
      "source": [
        "L1 = np.array([[0,1],[A, 0]])\n",
        "L2 = np.array([[0,1],[A + B , C]])"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lhpQzhkajoRP"
      },
      "source": [
        "Having defined those elements we can define our problm with switching by using particular jacobian in dependence of a defined condition. In our case:\n",
        "$$|\\theta| \\ge \\theta_0,$$\n",
        "functionlooks as follows:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y3Tde7a9k_oy"
      },
      "source": [
        "def func(y, t, Ain, Aout, theta_0):\n",
        "    if abs(y[0])>theta_0:\n",
        "        return np.dot(Aout,y)\n",
        "    else:\n",
        "        return np.dot(Ain,y)"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ygwZhQadlP1H"
      },
      "source": [
        "## Initial value problem\n",
        "Now we define the initial problem for our system:\n",
        "- IVP $$\\begin{bmatrix}\n",
        "\\theta \\\\\n",
        "\\dot{\\theta}\n",
        "\\end{bmatrix}= \\begin{bmatrix}\n",
        "1 \\\\\n",
        "1\n",
        "\\end{bmatrix}$$\n",
        "- time of simuation $T=20$, $N=1000$ samples\n",
        "- $\\theta_0 = 1$\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kYdVZCqrlbAv"
      },
      "source": [
        "ivp = np.array([1,1])\n",
        "theta_0 = 1\n",
        "T = 20\n",
        "N = 1000\n",
        "tspan = np.linspace(0, T, N)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3xN3EFiylZ5P"
      },
      "source": [
        "and run the simulation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zNxU3xEMi1o-"
      },
      "source": [
        "args = (L1,L2,theta_0)\n",
        "y = odeint(func,ivp,tspan,args=args)"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7h53FAMLoSHH"
      },
      "source": [
        "## Results\n",
        "Now we can observe simulation results on a phase portrait"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 479
        },
        "id": "yjiJiJ8WoOgr",
        "outputId": "a0ddce28-85be-4a11-e559-7f393f3c2692"
      },
      "source": [
        "from matplotlib import pyplot\n",
        "pyplot.title('Phase portrait, T = {0}'.format(T), fontsize=16)\n",
        "pyplot.xlabel(r'$\\theta$', fontsize=14)\n",
        "pyplot.ylabel(r'$\\dot{\\theta}$', rotation = 0, fontsize=14)\n",
        "pyplot.plot(y[:,0], y[:,1])\n",
        "pyplot.show()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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O0LJlS2H69OnC+fPnK/x+H55sMDY2Vhg4cKDg7OwsGBsbC/Xq1ROmTZv2yCKnD/v777+FHj16CLVq1RIMDQ0FFxcX4bXXXhNOnDhR7vGPm/Twvy5cuCC89NJLgqOjoziBZrt27Sp9ncr+TJ527cOHDwvh4eGCnZ2dWNfD/xa++eYbAYDwzjvvPLGup4GOLO5a0ckfH/7Z/df69euFtm3bCtbW1oKZmZng7+8vfPXVV0JxcXH1vRHSaTJBqKFDI4io2syYMQMzZ87E9OnTMWPGDKnL0XmdO3fGsWPHcOPGjXLndSIizWMfIiIiLVJYWIh///0XH374IcMQUTXSjxvUREQ6wszMTK1TOhFVD7YQERERkd5jHyIiIiLSe2whIiIiIr3HQERERER6j52qK0ClUiE5ORlWVlZ6M3MsERGRrhMEAbm5uXB1dX3qYtsMRBWQnJwMd3d3qcsgIiKiZ5CYmCgum/M4DEQVYGVlBaDsG2ptbS1xNURERFQROTk5cHd3Fz/Hn4SBqALu3yaztrZmICIiItIxFenuwk7VREREpPcYiIiIiEjvMRARERGR3mMgIiIiIr3HQERERER6j4GIiIiI9B4DEREREek9BiIiIiLSewxEREREpPcYiIiIiEjvaV0gOnz4MF588UW4urpCJpNh8+bNTz3n4MGDaN68OUxMTFCvXj2sXLnykWMWLVoET09PmJqaIjQ0FCdPntR88URERKSTtC4Q5efnIyAgAIsWLarQ8XFxcejZsyc6dOiAqKgojBs3Dm+//Tb++ecf8Zj169dj/PjxmD59Os6cOYOAgAB07doV6enpVfU2iIiISIfIBEEQpC7icWQyGTZt2oQ+ffo89piPP/4YO3bswMWLF8V9AwYMQFZWFnbt2gUACA0NRYsWLbBw4UIAgEqlgru7O8aOHYvJkyc/tY6cnBzY2NggOzubi7sSET2HO3nFSLpbiAB3W6lLIT1Qmc9vnV/tPiIiAuHh4Wr7unbtinHjxgEASkpKEBkZiSlTpoivy+VyhIeHIyIiotxrFhcXo7i4WHyek5Oj+cKJ/iM1uwj/i0zE4at30NDFCq8F10HTOrZSl0WkMYIgoN03B5BfogQA1HOyxK9DglG3loXElRHVgECUmpoKZ2dntX3Ozs7IyclBYWEh7t69C6VSWe4xMTEx5V5zzpw5mDlzZpXVTHRfiUKFfdFpWH86EYev3obqXnvtyfhM/Hb8JoaE1cW0FxvDQC6TtlCi56RQqjB1y0UxDAHA9fQ8tPv2IADgnbbemNi1IYwMtK4nB+kJnQ9EVWHKlCkYP368+DwnJwfu7u4SVkQ1zbW0XKw/lYhNZ5OQkV8i7g/xskfPJrURefMutp1PxqqIm0jNKcKPA5rB1MhAwoqJnl1esQJjfj+Dg1duQy4D3m3ng50XUhCfUSAe8/PhWPx8OBYAsG7kC3jBu5ZU5ZKe0vlA5OLigrS0NLV9aWlpsLa2hpmZGQwMDGBgYFDuMS4uLuVe08TEBCYmJlVWM+mnUqUK/1xKxapj8TgVf1fc72hlgleD6qBfsDu8HMpuHQxp6YmujV3w4foo/HMpDYOWncCyIcGwNTeWqnyiZ5KWU4S3Vp7CpeQcmBrJsWBgc3T2c8ZH3XwhCAI2nE7Ex39eUDtnwC/HAQAj2nhhcvdGbCGlaqHzgSgsLAw7d+5U27dnzx6EhYUBAIyNjREUFIR9+/aJnbNVKhX27duHMWPGVHe5pIfSc4vwx4lErD1xE+m5ZX3TDOQydPR1Qv9gd7Rv6AjDcm4T9GxaG7UsjTFy9WmcvnkXfRcfw6q3QlDHzry63wLRM7malothK04hKasQDpbGWDakBQIf6kwtk8nQv4UH+rfwQHZhKSZuPIc9lx/88br0SByWHolDHTszrBv5Av/tU5XSulFmeXl5uH79OgCgWbNmmDt3Ljp06AB7e3t4eHhgypQpSEpKwurVqwGUDbv39/fH6NGj8dZbb2H//v14//33sWPHDnTt2hVA2bD7IUOG4Oeff0ZISAjmzZuHDRs2ICYm5pG+ReXhKDOqLEEQcCYhC6sj4rHzQgpKlWX/mzlYmuD1UA+8HuIBFxvTCl3ralouhiw/iZTsIjhamWDlsBZo7GpTleUTPbej1+/g3TWRyC1SwNvRAiuHhsCjVsUCze5LqRj5W2S5r/04IBC9A900WSrVYJX5/Na6QHTw4EF06NDhkf1DhgzBypUrMXToUMTHx+PgwYNq53z44Ye4fPky6tSpg6lTp2Lo0KFq5y9cuBDffvstUlNTERgYiPnz5yM0NLRCNTEQUUUpVQL+uZSKnw/dwLlb2eL+5h62GNLSE939a8PYsPKdRlOyCzFsxSnEpObC0sQQiwc1R5v6jposnUhjNp5OxJS/LkChEhDiaY9fBgc90+3e9NwiDFl+CtEpj470Hd3BBxO7NIRMxttp9Hg6HYi0EQMRPU1RqRL/i7yFpUdicfNeR1FjQzleCnDFkDBPNKnz/C06OUWleGd1JCJiM2Aol+Hrvk3RN6jOc1+XSFMEQcDcPVexYH9ZK3/vQFd882pTmBg+34AAQRAwf991/LD36iOvhTdyxsLXOeiAysdApGEMRPQ4WQUl+C3iJlYeixdHi9maG2HwC3UxuKUnHCw12zm/WKHExI3nse1cMgBgTId6GN+5AeTsdEoSK1Yo8fH/zmNzVNm/zbEdy/5taroF599rdzDo1xOP7He3N8Ofo1rCyapit6JJPzAQaRgDEf1Xem4Rfj4Ui99PJKCwtGxeFTdbM4xo44V+Ldxhblx14xVUKgHf77mCRQduACjrfP39awH8C5kkk1VQgpG/ReJkXCYM5TJ8+XIT9GtRtVOV3Lidh64/HIZCpf4RZmIox8FJ7VHbxqxKvz7pBgYiDWMgovvuB6E1x2+iWKECAPjVtsY77bzRs0ntckeLVZWNpxPxyaYLKFUKCHS3xdLBwXC04nQRVL0SMgowdOVJxN7Oh5WJIRYPCkLr+g7V9vWzCkrw+tITuPyffkZGBjIcnNQBbrYMRvqMgUjDGIiovCDUzMMWH3Sqj3YNHCXr2Hk8NgPvrolEVkEp3GzN8OvQYPi68N8oVY/jsRl4b+0ZZOaXwNXGFCuGhaChi5UktZQoVHh3TST2x6gv2i2TAYcndYC7PYfs6yMGIg1jINJfjwtCH4Y3QJv6DloxwiXuTj6GrzyF2Dv5sDQxxILXm6FDQyepy6Ia7vcTCZi25SIUKgFN3Gzw65BgOFlL33+nVKnCqDVnsDdafTJemQw4PqUTnLWgRqo+DEQaxkCkf/KKFfjl0A0sPRIn9hFq5mGLceEN0FZLgtDDsgpK8O6aSByPzYRcBnza0w9vtfLUujpJ95UqVfh8+2WsirgJAHgxwBXfvtpU6/qwlSpVeP+Ps/j7Yqrafm8HC2wb2xoWJjo/LzFVAAORhjEQ6Y8ShQp/nEzA/H3XxFFjAXVsML5LQ60MQg8rUajw2eYL2HD6FgDgleZu+PLlJlr3QUW6K6ugBO+tPYNjNzIAABO7NMDoDvW0+v8LhVKFseUEo/BGTvj5zWAuC1LDMRBpGANRzadSCdhxIQXf7b4iziPk5WCBSV0boru/i1b/wn+YIAhYcTQeX+yMhlIloGkdGywZFARXdiyl53Q9PRfDV53GzYwCmBsbYF7/QHRpXP56kNqoqFSJvouP4VKyeufrt1t74dOejXTm/3GqHAYiDWMgqtlOxmXi8x2Xcf7ezNIOlib4ILw+BrRwh1E1jhrTpKPX72DM72dwt6AUDpbGWDwoCC087aUui3TUvug0fLAuCnnFCtSxM8OyIbrbef9OXjHafH1AvBV+309vNEePJrUlqoqqCgORhjEQ1Uwp2YWYszMGW+9NcmhhbICRbX3wdhuvGtG/IDGzACN/i0R0Sg4M5TLMeKkx3gj14F/CVGFKlYB5ex/MPB3iZY/FbzRHLQ1POCqFG7fz0On7Q4/sPzypQ4XXXCPtx0CkYQxENUtRqRLLjsRi0YEbKCxVQiYDBrTwwPjODWrcPD4FJQp89L/z2H4+BQAwoIU7ZrzUmP2K6Kky80vwwbqzOHLtDgBgcFhdfNbT75nW4tNmR67dxpu/nlTb16i2NbaMblXj3qs+YiDSMAaimkEQBOy+nIbPd1xGYmYhACC4rh1mvNQY/m41d/V4QRCw5FAsvvknBoIANHGzwaLXm/OvYHqs87eyMGrNGSRlFcLUSI6vXmmKPs1q9grzX/0dgyWHbqjtGxdeH+PCG0hUEWkCA5GGMRDpvpsZ+fhs80Xxr10Xa1NM6eGLlwJc9eYW0qGrtzFu3VncLSiFlakhvn8tQKc6xVLVEwQB604lYvqWSyhRquBZyxyLBwWhUW39+L1XVKpEjx+PIPZOvtr+3R+2RQNnaSacpOfDQKRhDES6q1Spwi+HYzF/3zUUK1QwNpBjZFtvjGrvUyP6CVVWclYhxvx+BmcSsgAAI9p44aNuvjrbeZw0p7BEiWlbLmJjZNm0DZ39nPHdawGwMTOSuLLqV17/oqC6dtjwThiH6esYBiINYyDSTZE37+KTvy7gSlouAKB1PQd83scfng4WElcmrVKlCl//HYNl/8YBKLttuOD1ZlwMU4/FpOZg7O9ncS09D3IZMKFLQ4xq5wO5nn/4r46Ix7Qtl9T2LRkUhG7+bFnVFQxEGsZApFtyikrx7a4rWHPiJgQBsLcwxtRejdAn0E1vbo9VxK6LqZj0v3PILVLA3sIYc/sFoD2X/NArgiBgzYkEfL79MooVKjhamWBe/0C0qld9i7Nqu6JSJdp9ewBpOcVq+89N76KXrWe6hoFIwxiIdMfey2n4ZNMFpOeW/fJ6NagOPunRCPYWxhJXpp1uZuTjvbVnxMnqhrb0xOTuvhyFpgeyCkrw8Z/n8c+lsjW/2jd0xHevBcChBgyprwon4zLR7+cItX0zX2qMIS09pSmIKoSBSMMYiLRfTlEpZm27jP/d6//g5WCBL/r4oyX/0n2qolIlvvo7BiuPxQMAGjpb4ceBgTo78R493an4THzwx1kkZxfByECGj7v54q1WXnp/i+xpBEHAB+uixLnL7rswowusTNlapI0YiDSMgUi7Hb56Gx//eR4p2UWQyYARbbwxvnMDtnJU0oEr6Zi08Tzu5BXD2ECOj7v7YlhLT35I1iAlChUW7r+GhQeuQyUAnrXMsWBgczSpU3OnnagK8Xfy0f67g2r75rzSBANDPKQpiB6LgUjDGIi0U36xAl/ujMbaEwkAyn65f/daAIK5RMUzu5NXjI//dx77YtIBAG3qO+D71wLgZG0qcWX0vGJSczB+/TlcTim7PfpKMzfM6uMPSz0cbakp49dH4a+zSWr7Ls/qCnNjfk+1BQORhjEQaZ9T8ZkYvyFKnGBxSFhdfNzdl7+INOB+R9svdlxGUakKtuZGmP6iHzul6yiFUoVfjsTihz1XUaoUYGduhNl9/NGrqavUpdUI19PzED5XfYj+z28GoSvn+NIKDEQaxkCkPZQqAQv3X8eP+65CJQButmb45tWmHBVTBa6n52Lc+ihcTCprUejo64QvXvbn8HwdEns7DxM2nsPZe/NOhTdywpevNIGTFVv8NG3Umkj8fTFVfN7cwxZ/jmrJPyIkxkCkYQxE2iE5qxDj1kfhZFwmAODlZm6Y1bsxOzNWofsTW/649xpKlCpYmRji056N0L+FO3/RazGFUoUVR+Px/Z4rKCot+7lNf6kx+jZnK19VunArGy8u/Fdt35GPOsDdnsvkSIWBSMMYiKT3z6VUfPzneWQVlMLC2ACz+/jjleZ1pC5Lb1xLy8Wk/51HVGIWgLJJLue80oS/6LXQucQsTPnrgthXqHU9B3zzalO42rJlrzoolCoEf7EXWQWl4r7J3X3xbjsfCavSXwxEGsZAJJ2iUiW+2BGN347fBFC2MOmCgc30frZpKShVApb/G4fvdl9BsUIFMyMDjO1UD2+39uaq4Fogt6gU3+++ilUR8RAEwMbMCFO6+6JfsDtHCkrgv7NcGxnIED2rGwy5TE61YiDSMAYiaSRmFuCd3yLFv3RHtvXGxC4N+eErsbg7+fj4z/PirUtvRwvMeskfreuzH5cUBEHAP5dSMX3rJXE25ZebueHTno04yaLEUrOL8MKcfWr7Dk5szz/oqhEDkYYxEFW/A1fSMW5dFLILS7mshBYSBAGbo5LwxY4Y3Mkr+xDu2aQ2PuvViJ2uq9H19FzM3h6NQ1dvAyibeuLzPk0YTrXM60uP49iNDPE55yyqPgxEGsZAVH1UKgEL9l/HvH1XIQhAgLstFr/RnP0ftFROUSl+2HMVq47FQyUA5sYGGNOxHt5q5cWJMatQdkEp5u27it8ibkKhEmBkIMO77XwwukM9ft+11J+RtzBh4znxeTMPW2x6r5WEFekHBiINYyCqHtkFpfhwQxT235sU8PVQD0x/0Q8mhvwFr+0uJ+dg2paLOH3zLgDA1cYUE7s2RJ9AN/Zf0aAShQrrTiXghz1Xcfdep93wRs74tGcjePE2jNZLzCxAm28OqO07N60LbMw5UraqMBBpGANR1YtJzcHI1ZFIyCyAsaEcn/fxR79gd6nLokpQqcpuo333zxUkZxcBAPxqW2NKD1+0rufA4d7PQaUSsPVcMubuuYqEzAIAQANnS0zt5Yc29R0lro4qQ6kS0HTGP8gvUYr7toxuhQB3W+mKqsEYiDSMgahq7Y9Jw9jfzyK/RIk6dmZYMigI/m5cW0lXFZUqseJoPH46cB25xQoAQKiXPT7s3AAveNeSuDrdIggC9sek49t/riAmNRcA4GBpgg861cPAEA+OWNJhX/0dgyWHbojPv3jZH2+E1pWwopqpMp/fWvl/06JFi+Dp6QlTU1OEhobi5MmTjz22ffv2kMlkjzx69uwpHjN06NBHXu/WrVt1vBV6AkEQsOxILN5edRr5JUqEedfCtjGtGYZ0nKmRAUa198GhjzpgaEtPGBvIcSIuEwN+OY6BvxwXR6fR46lUAnZdTMWLC//F8FWnEZOaCytTQ0zq2hCHP2qPN8M8GYZ03OTuvlgzPFR8/ummixj9+xkJKyKtayFav349Bg8ejCVLliA0NBTz5s3Dxo0bceXKFTg5PTrKKDMzEyUlJeLzjIwMBAQEYNmyZRg6dCiAskCUlpaGFStWiMeZmJjAzs6uQjWxhUjzSpUqTNtyCX+cLFuYdUALd8zq7c8h9TVQclYhfjp4HetPJaJUWfbrJsTTHiPbeqOjrxP7GD1EoVRhx4UULDpwHVfT8gAAZkYGGNyyLka184GtubHEFZKmJWcVouVX+8XnhnIZrn7enf9faIhO3zILDQ1FixYtsHDhQgCASqWCu7s7xo4di8mTJz/1/Hnz5mHatGlISUmBhUVZJ8OhQ4ciKysLmzdvfqaaGIg0K7ugFKPWRuLYjQzIZMCnPRpheGsv9jGp4ZKyCrHowHVsPP0gGPk4WmBkW2/0DnTT69FR2QWlWHcqAasjbiIpq2zBYisTQwxp6Ym3WnvB3oJBqCYrUajQ4LO/1faxs7Vm6GwgKikpgbm5Of73v/+hT58+4v4hQ4YgKysLW7Zseeo1mjRpgrCwMPzyyy/ivqFDh2Lz5s0wNjaGnZ0dOnbsiM8//xy1apXfn6G4uBjFxcXi85ycHLi7uzMQaUBiZgGGLD+J2Dv5sDA2wPyBzdCpkbPUZVE1Ssspwoqj8Vh74iZyi8r6GNmZG+G1YHe8HuKhV5PWXUnNxW/H4/FnZBIKS8s62dayMMawVp54M8wTNmb8QNQnvRcdxbl7y+MAwKFJ7VG3lv78/1AVdDYQJScnw83NDceOHUNYWJi4/6OPPsKhQ4dw4sSJJ55/8uRJhIaG4sSJEwgJCRH3r1u3Dubm5vDy8sKNGzfwySefwNLSEhERETAwePSv0hkzZmDmzJmP7Gcgej6XkrMxdMUp3M4thputGZYNCUaj2vx+6qvcolKsP5WIFUfjxVYRAGhT3wH9gt3R2c+5RrYa5RSVYtu5ZGw4lYhzt7LF/b4uVnirtRdeCnCtke+bKmbunquYv++a+PzPUWEIqmsvYUW6TW8D0TvvvIOIiAicP3/+icfFxsbCx8cHe/fuRadOnR55nS1Emnfsxh28szoSucUK+LpYYfVbIXCyNpW6LNICSpWAAzHpWHviJg5evY37v5EsTQzR3d8FLzdzQ6h3LRjocJ+KolIlDl29jR3nU7D7ciqKSlUAyvqLhDdyxpCWnnjB2563jQkAsCUqCR+sixKfzx/YDC8FuEpXkA6rTCAyrKaaKsTBwQEGBgZIS0tT25+WlgYXF5cnnpufn49169Zh1qxZT/063t7ecHBwwPXr18sNRCYmJjAx4RpAmrLjfAo+XB+FEqUKoV72WDokGNamvBVAZQzkMoT7OSPczxmJmQVYdyoBm88mIymrEBsjb2Fj5C04WBqjo68TOvu5oE19B51oQckuLMXR63ew+1Iq9kanI+/eFAQAUM/JEv2D3fFyczeuN0aP6B3oBjdbM7y6JAIA8P4fZ5GQkY8xHetLXFnNplUtREBZp+qQkBAsWLAAQFmnag8PD4wZM+aJnapXrlyJd999F0lJSY/tG3TfrVu34OHhgc2bN+Oll156ak3sVP3sVkfEY/rWSxAEoLu/C37oH6gTH2YkLZVKwOmbd7E5Kgk7zqcgu7BUfM3USI4w71po6eOAMJ9aaFTbWitaj0oUKlxMzkbEjQwcvJKOMwlZUKoe/Hp1tTFFjya10bNpbQS627I1iJ7qZkY+2n17UHz+cjM3/NA/ULJ6dJHO3jIDyobdDxkyBD///DNCQkIwb948bNiwATExMXB2dsbgwYPh5uaGOXPmqJ3Xpk0buLm5Yd26dWr78/LyMHPmTPTt2xcuLi64ceMGPvroI+Tm5uLChQsVagliIKo8QRAwf991/LD3KgBg0AsemPmSv1Z8cJFuKVWqcDIuE3sup2HP5TS1/kYAYGNmhOYetmhSxxZN3WzQpI4NnKv4dqxKJSDxbgGiU3JxISkLp+Lv4lxiFooVKrXjfBwt0L6hE3o0qY1m7rYcSk2VllVQgsBZe8TnbRs4YvVbIU84gx6m04EIABYuXIhvv/0WqampCAwMxPz58xEaWjaBVfv27eHp6YmVK1eKx1+5cgW+vr7YvXs3OnfurHatwsJC9OnTB2fPnkVWVhZcXV3RpUsXzJ49G87OFRvdxEBUOYIg4Nt/ruCng2WzsH4Y3gDvd6rHv4jpuQmCgOiUXBy7cQcRNzJwIi5T7VbUfbbmRvBysICXgwW8HSxQ28YMTtYmcLQygYOlCSxNDGFiKC/336QgCCgsVSKroBRZBaXIyC9G0t1CJGUV4tbdQsTdycfVtFwUPLT0wn125kYI9rRH2waOaN/AEe725lXyfSD9UqxQouFnu8Tnge622DyaC8NWhM4HIm3DQFRxgiDgix3RWPZvHADgs56N8HYbb4mroppKoVThYnIOziVm4UJSNi7cysa19FyoKvBbTS4rm/TQxMgAgiBAoRKgVAkoVarEeZKexNhQjgbOlmjkYo2gunYI9rSHj6MFgz9VCaVKgM8nO8Xn3o4W2D+hvXQF6QgGIg1jIKoYlUrAjG2XsDriJgBgdu/GeDPMU9qiSO8UligRdyf/3iMPcXcKkJ5bhPScYtzOK0ZmfsnTLwLAyEAGGzNj2Jkbwc3ODG62ZqhjZw53ezP4uljBs5YFl8+gaqVSCfB+KBQ5WBrj9Gedn3AGMRBpGAPR06lUAj7ZdAHrTiVCJgPmvNwEA0I8pC6L6BEKpQqFpUoUlipRVKJCkUIJuQwwkMthKJfBQC6DjZkRzI0N2NpDWkcQBHhNeRCKDOQy3Piyh4QVaTcGIg1jIHoylUrAR3+ex/8ib0EuA757LQCvNK8jdVlERDWW37RdYj82UyM5YmZ3l7gi7aTzq92T7hAEAdO2XsT/Im/BQC7DjwOaMQwREVWxy7O6wcGybI27olIVwubsk7gi3cdARM9MEATM+TsGa44nQCYD5vYLwIucTZWIqFqc/qwzDO9N5ZCSXYRu8w5LXJFuYyCiZzZv7zX8cjgWQFmfod6BbhJXRESkX6598eBWWUxqLvr9HCFhNbqNgYieyc+HbuDHewsQTn/Rjx2oiYgkIJPJEDfnQafqk3GZGLH6tIQV6S4GIqq0347fxJy/YwAAk7o2xLBWXhJXRESkv2QyGWIfGmm253IaZmy9JGFFuomBiCpl18VUTNtyEQAwuoMPRneoJ3FFREQkl8tw/aHbZyuPxeO3iHjpCtJBDERUYZE3M/HBurMQBGBgiAcmdmkodUlERHSPoYEcl2d1FZ9P3XIJB6+kS1iRbmEgogq5cTsPw1edRrFChfBGTpjduzEnrSMi0jLmxoY4+Ukn8fnQFacQk5ojYUW6g4GInio9pwhDlp9EVkEpAt1tsWBgcy5ZQESkpZysTfH3B23E593mHUF6bpGEFekGfqrRE+UVKzBs5SnculsIz1rm+HVIMMyMDaQui4iInqBRbWusGNpCfB7yxT4UK5QSVqT9GIjosZQqAR/8cRaXknPgYGmMVW+FoJalidRlERFRBXTwdcKs3o3F5w0/2yVhNdqPgYge67vdV7AvJh0mhnIsG9ICdWtZSF0SERFVwuAwT/QOfLCCwMs/HZWwGu3GQETl2hKVhMUHbwAAvnm1KQLdbaUtiIiInsmPA5rByKBsEMzZhCwsuDepLqljIKJHnEvMwkf/Ow8AeK+9D5fkICLScVdmP5ij6Ps9V3Hs+h0Jq9FODESkJi2nCCNWPxhez7mGiIh0n1wuw9mpncXnry87gbQcjjx7GAMRiYoVSoz8LRLpucVo4GyJeQOaQS7nXENERDWBnYUxNo9uJT4P/XIfBEGQsCLtwkBEoi93RONcYhZszY2wbHALWJoYSl0SERFpUKC7Lab28hOft//uoHTFaBkGIgIAbDuXjFURNwEAP/QPhEctc4krIiKiqjC8tRc87/2Ov5lRgGVHYiWuSDswEBFib+dh8p9lnahHd/BBh4ZOEldERERV6cDE9uL25zuicT09V7pitAQDkZ4rLFHivbVnkF+iRKiXPT4MbyB1SUREVMVkMhlOPLTmWfjcwyhVqiSsSHoMRHpu2paLiEnNhYOlCRYMbMY1yoiI9ISztSnmD2wmPm80Vb9nsuannx7bEpWEjZG3IJcB8wcGwsnaVOqSiIioGr0U4Io29R0AAAqVgF//jZO4IukwEOmppKxCfLb5IgDg/U710dLHQeKKiIhICr8NDxW3Z2+/rLfzEzEQ6SGVSsCEDVHILVKgmYctxnSoJ3VJREQkoaOTO4rboV/uk7AS6TAQ6aFl/8bieGwmzI0N8EO/QPYbIiLSc262ZpjU9cHKBGP/OCthNdLgJ6GeuZycg2//uQIAmNbLD54OXMGeiIiA0Q/dLdh2LhlRiVnSFSMBBiI9UlSqxLj1Z1GqFBDeyBn9W7hLXRIREWmR6FndxO0+i47q1dIeDER6ZMH+a7ialgcHS2N81bcJZDKuU0ZERA+YGRtg6eBg8fnApcclrKZ6aWUgWrRoETw9PWFqaorQ0FCcPHnysceuXLkSMplM7WFqqj58XBAETJs2DbVr14aZmRnCw8Nx7dq1qn4bWuVycg5+PlQ2PfvnffzhYGkicUVERKSNOvs5w9bcCABwPDYTl5KzJa6oemhdIFq/fj3Gjx+P6dOn48yZMwgICEDXrl2Rnp7+2HOsra2RkpIiPm7evKn2+jfffIP58+djyZIlOHHiBCwsLNC1a1cUFenH0EKFUoXJf52HQiWgW2MXdPOvLXVJRESkxY5PeTCLdc/5/0pYSfXRukA0d+5cjBgxAsOGDYOfnx+WLFkCc3NzLF++/LHnyGQyuLi4iA9nZ2fxNUEQMG/ePHz22Wfo3bs3mjZtitWrVyM5ORmbN2+uhnckvRVH43H+VjasTQ0xq3djqcshIiItZ2pkgO9fCxCfj1tX80edaVUgKikpQWRkJMLDw8V9crkc4eHhiIiIeOx5eXl5qFu3Ltzd3dG7d29cunRJfC0uLg6pqalq17SxsUFoaOhjr1lcXIycnBy1h666mZGP7/eUjSr7tGcjzkZNREQV0jeojri9OSoZNzPyJaym6mlVILpz5w6USqVaCw8AODs7IzU1tdxzGjZsiOXLl2PLli1Ys2YNVCoVWrZsiVu3bgGAeF5lrjlnzhzY2NiID3d33RyNJQgCPtl0AUWlKrT0qYV+wbr5PoiISBrnZ3QRt9t9e1C6QqqBVgWiZxEWFobBgwcjMDAQ7dq1w19//QVHR0f8/PPPz3zNKVOmIDs7W3wkJiZqsOLqs+NCCo5ez4CJoRxfvsxRZUREVDnWpkZqEzauOX7zCUfrNq0KRA4ODjAwMEBaWpra/rS0NLi4uFToGkZGRmjWrBmuX78OAOJ5lbmmiYkJrK2t1R66pqBEgS92RAMARrX34QSMRET0TB6esPGzzRehVNXMuYm0KhAZGxsjKCgI+/Y9WEdFpVJh3759CAsLq9A1lEolLly4gNq1y0ZSeXl5wcXFRe2aOTk5OHHiRIWvqYt+OnADKdlFqGNnhnfb+UhdDhER6bDtY1uL2wN+eXyfXl1mKHUB/zV+/HgMGTIEwcHBCAkJwbx585Cfn49hw4YBAAYPHgw3NzfMmTMHADBr1iy88MILqFevHrKysvDtt9/i5s2bePvttwGUjUAbN24cPv/8c9SvXx9eXl6YOnUqXF1d0adPH6neZpW6mZGPXw6XzTn0WU8/mBoZSFwRERHpMn83GzhZmSA9txin4u8iMbMA7vbmUpelUVoXiPr374/bt29j2rRpSE1NRWBgIHbt2iV2ik5ISIBc/qBh6+7duxgxYgRSU1NhZ2eHoKAgHDt2DH5+fuIxH330EfLz8zFy5EhkZWWhdevW2LVr1yMTONYUs7dHo0SpQut6Duja2PnpJxARET3FoUkd0GjaLgBAm28OIP6rnhJXpFkyQZ8WKnlGOTk5sLGxQXZ2ttb3Jzp09TaGLD8JQ7kMu8a1QT0nK6lLIiKiGuKbXTH46eANAMCSQUHo5l+x/r1Sqcznt1b1IaLno1QJmLOzrCP1kJaeDENERKRRH3XzFbffXRMpYSWax0BUg2yJSkJMai6sTA0xtmO9p59ARERUSUsGNRe3l97rr1oTMBDVEMUKJb7ffRVA2TB7W3NjiSsiIqKa6OH1ML/YGY2a0vOGgaiGWHs8AUlZhXC2NsGwll5Sl0NERDXY5tGtxO3Jf16QsBLNYSCqAXKLSrHwQNlElOPCG8DMmMPsiYio6gS624rb608nolihlK4YDWEgqgGWHolDZn4JvB0t8NpDi/ERERFVlX8/7iBuD1txSsJKNIOBSMdlF5Ri+b9xAICJXRrC0IA/UiIiqnp17Mxha24EADh2IwMlCpXEFT0ffnrquFUR8cgrVqChsxW6Ndbu+SCIiKhm2T2urbj93tozElby/BiIdFhesQLLj5a1Do3uWA9yOVezJyKi6uNkbQpjw7IosTc6DQql7rYSMRDpsLXHbyKroBReDhbo2aT2008gIiLSsAMT24vb4zeck66Q58RApKOKSpVYeqRsQqz32vvAgK1DREQkATdbM3F767lkqFS6OS8RA5GOWncyAXfySuBma4Y+zdykLoeIiPTYwYdaiaZtvShdIc+BgUgHKVUClt0bWfZuex8YcWQZERFJyNPBQtxeczxBwkqeHT9JddCey2m4dbcQtuZGeLU55x0iIiLpbXgnTNzeEpUkYSXPhoFIB624N7JsYIgHZ6UmIiKtEOJlL25/sC5KukKeEQORjrmUnI0TcZkwkMvw5gt1pS6HiIhI9GmPRuL21bRcCSupPAYiHbPyaDwAoLu/C1wf6tlPREQktbfbPFhcvOf8IxJWUnkMRDokI68YW84lAwCGteKK9kREpF1kMhnCGzkBAEqVAgpKFBJXVHEMRDpk/elElChUCKhjg+YetlKXQ0RE9IgFA5uL25/8dUHCSiqHgUhHCIKAjadvAQDeCK0LmYwTMRIRkfZ5eLDP5qhkCSupHAYiHXEq/i7i7uTDwtgAPZtymQ4iItJeK4e1ELcjb2ZKWEnFMRDpiPWnEgEAvZq6wsLEUOJqiIiIHq99Qydxu9/PxyWspOIYiHRAblEpdl5IAQD0a+EucTVERERP176hI4Cy1RUUSpXE1TwdA5EO2H4+BYWlSvg4WrAzNRER6YQf+zcTt7/eFSNhJRXDQKQDNp4uu13Wv4U7O1MTEZFOsDE3EreXHomTsJKKYSDScomZBTiTkAW5DFzVnoiIdMonPXzF7ezCUgkreToGIi13v+9QqFctOFmZSlwNERFRxQ1v7S1uz9x6ScJKno6BSMvtuBeIONSeiIh0jYH8QTePv84mSVjJ0zEQabGEjAKcv5UNuaxs7TIiIiJd88XL/uL2nbxiCSt5MgYiLbb9QtkMny19HFDL0kTiaoiIiCrv9RAPcXuKFi/lwUCkxXacL7td1ou3y4iISEc9PDp6z+U0CSt5Mq0MRIsWLYKnpydMTU0RGhqKkydPPvbYpUuXok2bNrCzs4OdnR3Cw8MfOX7o0KGQyWRqj27dulX123guSVmFuJScA7kM6NqYt8uIiEh3PXzbLK9YIWElj6d1gWj9+vUYP348pk+fjjNnziAgIABdu3ZFenp6uccfPHgQAwcOxIEDBxAREQF3d3d06dIFSUnqnbe6deuGlJQU8fHHH39Ux9t5Zgdiyt5vUF072FkYS1wNERHRsxvQ4sFts4X7r0tYyeNpXSCaO3cuRowYgWHDhsHPzw9LliyBubk5li9fXu7xa9euxXvvvYfAwED4+vpi2bJlUKlU2Ldvn9pxJiYmcHFxER92dnbV8Xae2f1A9PB6MERERLro4dFmSw7dkLCSx9OqQFRSUoLIyEiEh4eL++RyOcLDwxEREVGhaxQUFKC0tBT29vZq+w8ePAgnJyc0bNgQo0aNQkZGxmOvUVxcjJycHLVHdSoqVeLojTsAgI6+DERERKT7XnlocmFBECSspHxaFYju3LkDpVIJZ2dntf3Ozs5ITU2t0DU+/vhjuLq6qoWqbt26YfXq1di3bx++/vprHDp0CN27d4dSqSz3GnPmzIGNjY34cHev3gVVj8dmoKhUhdo2pvB1sarWr01ERFQVJnd/MGv13ujyu8FIyVDqAjTpq6++wrp163Dw4EGYmj6Y1XnAgAHidpMmTdC0aVP4+Pjg4MGD6NSp0yPXmTJlCsaPHy8+z8nJqdZQdPDKbQBlt8u4dhkREdUETtYPPpc/3XQBnf2cn3B09dOqFiIHBwcYGBggLU19WF5aWhpcXJ480uq7777DV199hd27d6Np06ZPPNbb2xsODg64fr38jl0mJiawtrZWe1SnQ1fvByLHav26REREVcnVpiwUpedq3wSNWhWIjI2NERQUpNYh+n4H6bCwsMee980332D27NnYtWsXgoODn/p1bt26hYyMDNSurX3z+6TlFCHuTj7kMiDMp5bU5RAREWnMuM4NxO2i0vK7rUhFqwIRAIwfPx5Lly7FqlWrEB0djVGjRiE/Px/Dhg0DAAwePBhTpkwRj//6668xdepULF++HJ6enkhNTUVqairy8vIAAHl5eZg0aRKOHz+O+Ph47Nu3D71790a9evXQtWtXSd7jkxyPLevs7edqDWtTI4mrISIi0pyXH+pYveF0ooSVPErr+hD1798ft2/fxrRp05CamorAwEDs2rVL7GidkJAAufxBjlu8eDFKSkrw6quvql1n+vTpmDFjBgwMDHD+/HmsWrUKWVlZcHV1RZcuXTB79myYmGjfchgn4jIBlK1uT0REVJMYGTz4/P5x7zUMDvOUrpj/0LpABABjxozBmDFjyn3t4MGDas/j4+OfeC0zMzP8888/Gqqs6p28F4hCvOyfciQREZHucbUxRXJ2ETLyS6QuRY3W3TLTZ3fyinE9vexWX4gnAxEREdU8H4TXF7eLFdrTj4iBSIvcbx3ydbHich1ERFQjvdK8jri96UzSE46sXgxEWiQqMQsAEOyp3cuKEBERPauH+xGtPZEgYSXqGIi0yPlbWQCApm62ktZBRERUHS4kZUtdgoiBSEuoVAIuJZWtmebvZiNxNURERFWnT6Cr1CU8goFIS9zMLEBusQLGhnLUd7aUuhwiIqIq88YLdcXt7MJSCSt5gIFIS9xvNmxU21rt/ioREVFNE1z3QV/Zv87ckrCSB/jJqyUu3gtETdyqd900IiKi6vbwwuVrjt+UsJIHNBKIEhISEBMTo4lL6a1LyWWByN+V/YeIiEh/3LidL3UJADQUiAYPHoxGjRpp4lJ66/6EjA1crCSuhIiIqOq1qe8gdQlqeMtMC+QVK5CWUwwA8HFgh2oiIqr5uvm7SF2CGo0EooMHD0IQBE1cSi/F3i5rHXKwNIGNOVe4JyKimq+zn7O4HX9H+ttmbCHSAjfuBSJvRwuJKyEiIqoeTlam4vY/l1IlrKQMA5EWiL3XoczHkbfLiIhI/zAQEYAHLUQ+bCEiIiI9dCYhS+oSni8QZWZm4sMPP4SnpydMTU3h5+eHVatWaao2vZGQWQAA8KzFQERERPqjto3p0w+qJobPeuKVK1fQqVMnZGVloV+/frC1tcXatWsxdOhQmJmZoV+/fpqss0ZLzS4CANS21Z5/GERERFWteV077DifInUZAJ6xhSg3Nxc9evSAUqnEmTNnsHz5csydOxf79++HgYEB5syZo+k6a6xihRJ38koAAK42ZhJXQ0REVH0eXsJDas/UQjRr1izExsZi69ataNCggbi/cePGCAgIwJkzZ5CXlwdLS3YSfpq07LL5h0wM5bDlkHsiItIjwXXtxe1ihRImhgaS1VLpFqKsrCwsWrQI/v7+ePHFFx953d6+7M2lpaU9f3V6ICW7EEDZfdSH13YhIiKq6RrVfrA6w/01PaVS6UC0ceNGFBYWYvDgweW+Xlxc1uJhbGz8fJXpidSce/2HeLuMiIj0jKHBgxhyKv6uhJU8wy2zv//+GwAQExODGTNmPPL6tWvXYGBgABcX7ZqSW1ul3OtQ7aJFPe2JiIiqW0xKjqRfv9KB6OjRowCA5cuXP/aYhg0bwsiI/WEq4m5BWYdqewu2qBERkf6KzyiQ9OtX6pbZ3bt3kZ6ejrZt20IQhEce+/btAwC0bt26SoqtiXIKSwEANmYMkEREpL9uZki7nlmlAtGtW7cAAK6uruW+vnPnTgBA9+7dn7Ms/ZHNQERERIS7BaWSfv1KBaLS0rJiTUxMyn3tjz/+QK1atdCrVy/NVKcHGIiIiEifGRloxwjrSgUiZ2dnAOUPqV+2bBmSk5MxadKkcgMTlY+BiIiI9Jm2LFtVqUDk5uYGb29vHDx4EDdv3hT3Hz9+HJMmTUKzZs3w4YcfarzImux+ILJmICIiIj1Ut5a51CUAeIZ5iKZMmYKioiK0atUKkyZNwqBBg9CuXTu4ublh27ZtnH+okvKKFAAAK9NnXlaOiIhIZ9maa0duqHQgevvtt/HTTz/B3NwcCxYswLFjxzB+/HicPn0abm5uVVFjjVaqFAAAxgbPtKwcERGRTrM00Y4GgWeqYtSoURg1apSma9FLJUoVAMDIkIGIiIj0j7bcIdHKT+FFixbB09MTpqamCA0NxcmTJ594/MaNG+Hr6wtTU1M0adJEHP5/nyAImDZtGmrXrg0zMzOEh4fj2rVrVfkWKkxxPxBpSS97IiKi6qQtLURaF4jWr1+P8ePHY/r06Thz5gwCAgLQtWtXpKenl3v8sWPHMHDgQAwfPhxnz55Fnz590KdPH1y8eFE85ptvvsH8+fOxZMkSnDhxAhYWFujatSuKioqq622VS6kSoCq7Y8ZbZkREpJcs2UJUvrlz52LEiBEYNmwY/Pz8sGTJEpibmz92qZAff/wR3bp1w6RJk9CoUSPMnj0bzZs3x8KFCwGUtQ7NmzcPn332GXr37o2mTZti9erVSE5OxubNm6vxnT2q9F7rEKC+wB0REZG+YAtROUpKShAZGYnw8HBxn1wuR3h4OCIiIso9JyIiQu14AOjatat4fFxcHFJTU9WOsbGxQWho6GOvWVxcjJycHLVHVSh5OBDJecuMiIj0j4mW9KHVjiruuXPnDpRKpTgB5H3Ozs5ITU0t95zU1NQnHn//v5W55pw5c2BjYyM+3N3dn+n9PI1cxhBERET6rVihevpB1UCrApG2mDJlCrKzs8VHYmJilXydh1uFHr59RkREpC+KSpVSlwBAywKRg4MDDAwMHlkaJC0tDS4uLuWe4+Li8sTj7/+3Mtc0MTGBtbW12qMqGD3Ub0hxbz4iIiIifVJUqh0NAloViIyNjREUFIR9+/aJ+1QqFfbt24ewsLByzwkLC1M7HgD27NkjHu/l5QUXFxe1Y3JycnDixInHXrO6GMhluN9IxBYiIiLSR8UK7Wgh0o6u3Q8ZP348hgwZguDgYISEhGDevHnIz8/HsGHDAACDBw+Gm5sb5syZAwD44IMP0K5dO3z//ffo2bMn1q1bh9OnT+OXX34BAMhkMowbNw6ff/456tevDy8vL0ydOhWurq7o06ePVG9TZGggR4lChVIVW4iIiEj/aEsLkdYFov79++P27duYNm0aUlNTERgYiF27domdohMSEiCXP2jYatmyJX7//Xd89tln+OSTT1C/fn1s3rwZ/v7+4jEfffQR8vPzMXLkSGRlZaF169bYtWsXTE1Nq/39/Zfx/UCkJZ3KiIiIqpO29CGSCYLApomnyMnJgY2NDbKzszXen6j57D3IzC/B7g/booGzlUavTUREpO0mbjyH/0XeAgDEf9VTo9euzOe3VvUh0kf313DJKSyVuBIiIqLql3S3UOoSADAQSc7a1AgAkM1AREREeigpi4GIANiYlQWinCIGIiIi0j8MRATgQSDKLmAgIiIi/aPUklHWDEQSs74fiAoVEldCREQkHakXeWUgkpi1Wdk/APYhIiIifVbHzkzSr89AJDEHCxMAQEZ+scSVEBERSadpHRtJvz4DkcRcbMomh0zJLpK4EiIiIukEuNtK+vUZiCRW+14gSmUgIiIiPfPwOmYBdWylKwQMRJJzeSgQcdJwIiLSJzEpueJ2QxdpV2tgIJKYk5UpZDKgRKlCZn6J1OUQERFVm3O3ssRtIwNpIwkDkcSMDeVwsCzrWM1+REREpE+iErOkLkHEQKQF7vcjStaS2TqJiIiqw7/X7khdgoiBSAvUrWUBAIi7ky9xJURERNUnPVd7ppxhINIC3g5lgejG7TyJKyEiIqp+bRs4Sl0CA5E28HYsC0Sxt9lCRERE+ie8kZPUJTAQaQMfR0sAQCxvmRERkZ5Iy3kwkKijLwMR4UELUWZ+Ce5y6D0REemBAzHp4nYdO3MJKynDQKQFzI0NxZFm7EdERET6YNelVKlLUMNApCXqOZXdNotJzX3KkURERLrv4JXbUpeghoFIS/i7la3yeyk5W+JKiIiIqk9wXTupSwDAQKQ1mtwLRBeSGIiIiKhmU6kerN3Zv4W7hJU8wECkJe4HoiupuWqr/xIREdU0x2MzxO2eTWtLWMkDDERaoo6dGWzMjFCqFHA1lR2riYio5lp3KlHcNjc2lLCSBxiItIRMJhNbiS6yHxEREdVgW88lS13CIxiItMj9jtXnb2VJWwgREVE18HezlroEEQORFgm619P+ZFymxJUQERFVjfxihbg9pkM9CStRx0CkRVp4lgWiG7fzcVuLVgAmIiLSlD9OJojbXfxcJKxEHQORFrE1N4avixUA4FQ8W4mIiKjmWXTgurgtl8skrEQdA5GWCfWyB8DbZkREVDPdLSgFAHHJKm3BQKRlQrxqAVCfo4GIiKgmUChV4vZoLeo/BGhZIMrMzMQbb7wBa2tr2NraYvjw4cjLe/ycPJmZmRg7diwaNmwIMzMzeHh44P3330d2tvqwdZlM9shj3bp1Vf12nknIvRaiK2m5yCookbgaIiIizfnrTJK4/WpQHQkreZRWBaI33ngDly5dwp49e7B9+3YcPnwYI0eOfOzxycnJSE5OxnfffYeLFy9i5cqV2LVrF4YPH/7IsStWrEBKSor46NOnTxW+k2fnaGWCek6WEATg6HW2EhERUc0xY9slcdvUyEDCSh6lHdNDAoiOjsauXbtw6tQpBAcHAwAWLFiAHj164LvvvoOrq+sj5/j7++PPP/8Un/v4+OCLL77AoEGDoFAoYGj44O3Z2trCxUV7erM/SfsGjrienocDV9K1ZkpzIiKi51VQUrY0VaPa2jP/0H1a00IUEREBW1tbMQwBQHh4OORyOU6cOFHh62RnZ8Pa2lotDAHA6NGj4eDggJCQECxfvhyCIDzmCkBxcTFycnLUHtWpo68TAODgldtqC+ARERHpqsTMAnF7xot+ElZSPq0JRKmpqXByclLbZ2hoCHt7e6SmplboGnfu3MHs2bMfuc02a9YsbNiwAXv27EHfvn3x3nvvYcGCBY+9zpw5c2BjYyM+3N2rdyXeYE97WBgb4E5eMS4lV28YIyIiqgpf7YoRt0O9a0lYSfmqPBBNnjy53E7NDz9iYmKefqGnyMnJQc+ePeHn54cZM2aovTZ16lS0atUKzZo1w8cff4yPPvoI33777WOvNWXKFGRnZ4uPxMTExx5bFYwN5Whd3wEAcOBKerV+bSIioqqw43yK1CU8UZX3IZowYQKGDh36xGO8vb3h4uKC9HT1D3+FQoHMzMyn9v3Jzc1Ft27dYGVlhU2bNsHIyOiJx4eGhmL27NkoLi6GiYnJI6+bmJiUu786dWjohH8upeHAlXS836m+pLUQERE9D+VD3T/ebecjYSWPV+WByNHREY6Ojk89LiwsDFlZWYiMjERQUBAAYP/+/VCpVAgNDX3seTk5OejatStMTEywdetWmJo+faKnqKgo2NnZSR56nqR9w7Lbh1GJWUjPLYKTlXZNYEVERFRRv/4bK26P7qCdgUhr+hA1atQI3bp1w4gRI3Dy5EkcPXoUY8aMwYABA8QRZklJSfD19cXJkycBlIWhLl26ID8/H7/++itycnKQmpqK1NRUKJVlPdm3bduGZcuW4eLFi7h+/ToWL16ML7/8EmPHjpXsvVaEi40pAt1tIQjArosV60NFRESkjb7c+aBrjJXpk+/iSEVrht0DwNq1azFmzBh06tQJcrkcffv2xfz588XXS0tLceXKFRQUlPVUP3PmjDgCrV499Rkv4+Li4OnpCSMjIyxatAgffvghBEFAvXr1MHfuXIwYMaL63tgz6tW0NqISs7D9fAoGh3lKXQ4REVGlPXy7bECL6h2kVBky4UnjzwlAWUuUjY2NOKS/uiRnFaLlV/shkwHHp3SCszVvmxERkW5ZdiQWn++IBgCcn9EF1tXYQlSZz2+tuWVGj3K1NUNQXTsIAvD3Be3unU9ERFSe+2EIQLWGocpiINJyPZuUzVS9g4GIiIh0zMO3y/oFa9faZf/FQKTletwLRKfi7yI5q1DiaoiIiCpu0YHr4vanPbVvduqHMRBpORcbU4R62QMA/oy8JXE1REREFTd3z1Vx28ZMe2+XAQxEOqFfcFmv/I2Rt7i2GRER6YS0nCJx+7OejSSspGIYiHRAjya1YWliiITMAhyPy5C6HCIioqcavfaMuD28tZeElVQMA5EOMDM2wIsBZZNTbjzN22ZERKT9Tt+8CwCwNTeCTCaTuJqnYyDSEfd75++8kIKcolKJqyEiInq8AzEP1ib97a3HL7+lTRiIdESguy0aOFuiWKHC1qhkqcshIiJ6rGErT4nbTerYSFhJxTEQ6QiZTCZ2rv4t4iY4wTgREWmjzPwScXtgiPYu1fFfDEQ65LVgd5gbG+BKWi4ibrBzNRERaZ9hK06K27N6+0tYSeUwEOkQGzMj9G1e1pdo+dF4aYshIiL6D0EQcO5WNgCgto0pjAx0J2boTqUEABjS0hMAsC8mDQkZBdIWQ0RE9JB5e6+J2xveCZOwkspjINIx9Zws0baBIwQBWBURL3U5REREoh/3PQhE7vbmElZSeQxEOmhYK08AwIZTicgrVkhbDBEREYCj1++I2z+90VzCSp4NA5EOalffEd6OFsgtVmDdyQSpyyEiIsIby06I2/cXJtclDEQ6SC6X4Z223gCAnw/HoqhUKXFFRESkz87fyhK3J3ZpIF0hz4GBSEe93KwOXG1McTu3GBtPJ0pdDhER6bGXFh4Vt0d3qCdhJc+OgUhHGRvK8W57HwDAkkOxKFWqJK6IiIj0UeztPHF7aEtPnVi3rDwMRDqsX7A7HCxNkJRViE1nk6Quh4iI9FDH7w+J29N6+UlYyfNhINJhpkYGGNnWCwCw+OANKFVczoOIiKpPUlahuN2zaW3I5brZOgQwEOm8N0LrwtbcCHF38rGZrURERFSNWn21X9ye1z9QukI0gIFIx1mYGOKdtmV9iebuuYpiBUecERFR1YtOyRG3X27mplPLdJRHt6snAGWd2Jyty/oSrT3OeYmIiKjqdf/xiLj9/WsBElaiGQxENYCZsQHGhZfN+7DwwHXkFpVKXBEREdVkx248mJV6dAcfne47dB8DUQ3xWlAdeDtYIDO/BEuPxEldDhER1WCvL30wK/Wkrr4SVqI5DEQ1hKGBHBO7NgQALDsSi9u5xRJXRERENdGWqAcDeGb38ZewEs1iIKpBuvu7oGkdGxSUKDF3z1WpyyEiohpGEAR8sC5KfP7mC3WlK0bDGIhqEJlMhs96lk2Kte5UAi4mZUtcERER1STj1keJ23+MeEG6QqoAA1ENE+Jlj5cCXCEIwPStlyAInKyRiIieX3ZBKbZEJYvPw3xqSViN5jEQ1UBTevjCzMgAkTfvqv3jJSIielYtvtgrbkd+Fi5hJVVDqwJRZmYm3njjDVhbW8PW1hbDhw9HXl7eE89p3749ZDKZ2uPdd99VOyYhIQE9e/aEubk5nJycMGnSJCgUiqp8K5KqbWOGMR3LVhv+cmc08opr7nslIqKqF3nzLkruLSLexc8ZtSxNJK5I87QqEL3xxhu4dOkS9uzZg+3bt+Pw4cMYOXLkU88bMWIEUlJSxMc333wjvqZUKtGzZ0+UlJTg2LFjWLVqFVauXIlp06ZV5VuR3NttvFC3ljnSc4uxYP81qcshIiId1nfxMXF7yaAgCSupOloTiKKjo7Fr1y4sW7YMoaGhaN26NRYsWIB169YhOfnJt33Mzc3h4uIiPqytrcXXdu/ejcuXL2PNmjUIDAxE9+7dMXv2bCxatAglJSVV/bYkY2JoIK46vPzfOFxJzZW4IiIi0kWfbb4gbn/3WkCNmISxPFoTiCIiImBra4vg4GBxX3h4OORyOU6cOPGEM4G1a9fCwcEB/v7+mDJlCgoKCtSu26RJEzg7O4v7unbtipycHFy6dKnc6xUXFyMnJ0ftoYs6NXJGFz9nlCoFfPzneShV7GBNREQVl55ThDUPLQn1alAdCaupWloTiFJTU+Hk5KS2z9DQEPb29khNTX3sea+//jrWrFmDAwcOYMqUKfjtt98waNAgtes+HIYAiM8fd905c+bAxsZGfLi7uz/r25LcrN7+sDIxRFRiFlZHxEtdDhER6ZCQL/eJ22emdpawkqpX5YFo8uTJj3R6/u8jJibmma8/cuRIdO3aFU2aNMEbb7yB1atXY9OmTbhx48YzX3PKlCnIzs4WH4mJic98Lam52Jhico+yadW//ecKbt0teMoZREREwIqjD5aBeqetN+wtjCWspuoZVvUXmDBhAoYOHfrEY7y9veHi4oL09HS1/QqFApmZmXBxcanw1wsNDQUAXL9+HT4+PnBxccHJkyfVjklLSwOAx17XxMQEJiY1pwf9wBYe2BKVjJNxmfhk00WsGtYCMlnNvAdMRETPr6BEgZnbLovPp/RoJGE11aPKA5GjoyMcHR2felxYWBiysrIQGRmJoKCyHuz79++HSqUSQ05FREVFAQBq164tXveLL75Aenq6eEtuz549sLa2hp+fXyXfjW6Sy2WY80oTdP/xCA5fvY3NUUl4uVnNvQ9MRETPx3/6P+L23vHtJKyk+mhNH6JGjRqhW7duGDFiBE6ePImjR49izJgxGDBgAFxdXQEASUlJ8PX1FVt8bty4gdmzZyMyMhLx8fHYunUrBg8ejLZt26Jp06YAgC5dusDPzw9vvvkmzp07h3/++QefffYZRo8eXaNagZ7Gx9ESH3SqDwCYvuUSkrMKJa6IiIi00W8R8bg/BqeTrxPqOVlKW1A10ZpABJSNFvP19UWnTp3Qo0cPtG7dGr/88ov4emlpKa5cuSKOIjM2NsbevXvRpUsX+Pr6YsKECejbty+2bdsmnmNgYIDt27fDwMAAYWFhGDRoEAYPHoxZs2ZV+/uT2si23gioY4OcIgUmbjwHFUedERHRQzLzSzB1y4MR2MuGBD/h6JpFJnCxq6fKycmBjY0NsrOz1eY40kWxt/PQc/6/KCxV4rOejfB2G2+pSyIiIi3hOXmHuH1wYnt4OlhIWM3zq8znt1a1EFHV83a0xKc9yzrHffPPFU7YSEREAIAvdjzoRP12ay+dD0OVxUCkh94I9UBHXyeUKFT4YN1ZFCuUUpdEREQSupmRj6VHHgyz/6yXfgw6ehgDkR6SyWT4qm8T2FsYIyY1F9/9c0XqkoiISCIqlYB23x4Un9f0CRgfh4FITzlZmeLrvmUj8ZYeicOey2kSV0RERFJo/fV+cXvOK01q/ASMj8NApMc6+znjrVZeAIAJG6KQmMlZrImI9Mnyf+OQnF0EAKjvZImBIR4SVyQdBiI9N7m7LwLdbZFTpMDo38+wPxERkZ6Iv5OPWdsfdKTe/WFbCauRHgORnjM2lGPRG81ha26E87ey8eWOaKlLIiKiKqZSCWj/3UHxecSUjnq/pBMDEcHN1gw/9AsEAKyKuInt55OlLYiIiKpU8Bd7xe1vXm2K2jZmElajHRiICADQwdcJ77X3AQB8/L/ziEnNkbgiIiKqCrO2XUZmfgkAwK+2NfoFu0tckXZgICLR+M4N0NKnFvJLlBix+rT4PwwREdUM+6LTsPzog/mGdrzfWsJqtAsDEYkMDeRY9HpzeNibIzGzEO+tjUSpUiV1WUREpAHJWYUYvuq0+PzizK5632/oYQxEpMbOwhjLhgTD0sQQx2MzMWvb5aefREREWq1UqULLrx7MN7Tz/TawNDGUsCLtw0BEj2jgbIV5/QMhkwG/Hb+JNcdvSl0SERE9h/qf/i1uf/lyE/i56vZC5VWBgYjKFe7njEldGwIAZmy9hGPX70hcERERPYt+P0eI2518nfB6qP5OvvgkDET0WKPa+aB3oCsUKgHv/BbJkWdERDrm8+2XcTIuU3z+69AWElaj3RiI6LFkMhm+7tsUIV72yC1WYOjyU0jJLpS6LCIiqoCNpxOx7N8HI8piv+whYTXaj4GInsjUyABL3wxGPSdLpOYUYejyU8guLJW6LCIieoJT8ZmY9L/z4vNLM7tCLueIsidhIKKnsjE3wqq3QuBkZYIrabl457fTXPOMiEhLJWYW4LUlD/oN/ftxB1hwRNlTMRBRhbjZmmHlsBBxOP7EjeehUglSl0VERA+5m1+CNt8cEJ//Oaol6tiZS1iR7mAgogrzc7XGkkFBMJTLsO1cMqZuuQhBYCgiItIG+cUKNJu9R3z+Q/8ABNW1k7Ai3cJARJXSur4D5t6bo2jtiQR8uTOaoYiISGLFCiUaT/9HfP5xN1+83KyOhBXpHgYiqrSXAlzx1StNAABLj8Thx33XJK6IiEh/KVUCGn62S3z+TltvjLq3WDdVHAMRPZP+LTww/UU/AMC8vdfwy+EbEldERKR/BEGAzyc7xeevBtXBlB6NJKxIdzEQ0TMb1spLnM36y50x+C0iXtqCiIj0iCAI8JryIAx1aOiI714LkLAi3cZARM9ldId6GN2hrGl26pZL+I3rnhERVbn/hqHGrtZYMSxEwop0HwMRPbeJXRri7dZeAICpmy9i+UMzoxIRkWapVOphqIGzJXa830bCimoGztREz00mk+HTno1gaCDHkkM3MGv7ZZQoVXi3HTv1kXYRBAE5RQrczS9BYakSpUoVSpUqlCgEGBnIYGJoABMjOUwNDWBrYQQrE0PIZJzdl7SHUqXeZ6hpHRtsHdNawopqDgYi0giZTIaPuzWEsaEc8/ddw1d/x6BEocL7nepLXRrpmYy8YlxOyUHcnXwkZBQg8W4BEjILcTu3GHcLSqCsxISixgZy1LI0hoOlCdztzVC3lgU8a5mjbi0LNHKxho25URW+EyJ1CqUK9T79W3we4mmPDe+GSVhRzcJARBojk8kwvnMDGBvI8N3uq5i75ypKlSqM79yAf2VTlcgvVuBsQhZOxmfiwq0sXE7JQVpO8VPPMzc2gLmxIYwNZDAylMNQLoNSJaBYoUKxQoXCEiUKS5UoUaqQkl2ElOwiXEjKfuQ67vZmaFzbBk3q2CC4rh0CPWxhYmhQFW+V9FyxQqk2tL5NfQf8NjxUwopqHgYi0rgxHevD2FCOL3fGYMH+68gtUmBaLz8uLEjPTaFUIfLmXRy4chsRN+7gYnJOuS0+Xg4W8HG0RN1a5vCwN4e7vRlcrM1gb2EMW3MjmBo9PbQUlSqRkV+CjLxipOcUIyGzADcz8hGfUYAbt/Nw624hEjPLHrsupQIATAzlaOZhixe8a6FDQyc0cbPhv3t6btkFpQiYtVt8Ht7IGcuGBEtYUc0kEzjN8FPl5OTAxsYG2dnZsLa2lrocnbHqWDymb70EAOjVtDa+7xfAv56p0vKLFdgbnYY9l9Nw+Opt5BQp1F53szVDC087NK9rh8au1mjoYg3LaljIMrugFJdSsnEpKQdRiVk4EZeJO3nqrVOOVibo5OuETo2c0aa+Q4WCGNHDEjML1NYmezWoDofWV0JlPr+1KhBlZmZi7Nix2LZtG+RyOfr27Ysff/wRlpaW5R4fHx8PLy+vcl/bsGEDXnvtNQAo93bNH3/8gQEDBlSoLgaiZ7clKgkTN55DqVJAq3q1sGRQEKxM2e+CnqyoVImDV9Kx7VwK9sWkoahUJb5mZ26Edg0c0baBI0K87LVm4UpBEHDjdj5OxGXg32t3cPjqbeSXKMXXrUwM0c3fBb0D3RDmUwsGbDmip7hwKxsvLvxXfD6xSwOM6ch+mZWhs4Goe/fuSElJwc8//4zS0lIMGzYMLVq0wO+//17u8UqlErdv31bb98svv+Dbb79FSkqKGKRkMhlWrFiBbt26icfZ2trC1NS0QnUxED2fI9du493fIpFfooS/mzVWDA2Bo5WJ1GWRFrqcnIN1pxKw6WwSch9qCfJysEB3fxd0auSEQHc7nQgTxQolTsZlYl90Ov65lIqU7CLxNUcrE7zS3A2vh3igbi0LCaskbXUgJh3DVp4Sn8/tF4BXmnNtssrSyUAUHR0NPz8/nDp1CsHBZfdGd+3ahR49euDWrVtwdXWt0HWaNWuG5s2b49dffxX3yWQybNq0CX369Hmm2hiInt/5W1kYtuIUMvJLULeWOVa/FcIPAgJQ1hq0+WwSfj+ZgPO3HnRcdrUxxYsBrngxwBWNXa11umO+SiXg9M272BKVhB0XUpBVUCq+1rqeA14P9UBnP2cYGXBqOFLvbgAAa98ORat6DhJWpLt0MhAtX74cEyZMwN27d8V9CoUCpqam2LhxI15++eWnXiMyMhLBwcE4evQoWrZsKe6XyWRwdXVFcXExvL298e6772LYsGGP/QVbXFyM4uIHfQFycnLg7u7OQPSc4u7kY/DyE0jMLIS9hTF+fjMILTztpS6LJJKeW4TfIm5izfGbuHsvIBgZyNDFzwUDQtzRysehRnZILlGocOBKOn4/kYDD127j/m9gVxtTDG3liQEhHrDmbWW9NXrtGey4kCI+3zWuDXxd+LnzrCoTiLRmlFlqaiqcnJzU9hkaGsLe3h6pqakVusavv/6KRo0aqYUhAJg1axY6duwIc3Nz7N69G++99x7y8vLw/vvvl3udOXPmYObMmc/2RuixvBws8Oeolnhr5SlcTMrBG0tP4Ku+TdgMrGeup+dh8cEb2HouCaXKsjTgZmuGwWF10TeoDhwsa/btVGNDObo2dkHXxi5IzCzA+lOJWHcqEcnZRfhyZwzm77uO/i3cMby1F1xtzaQul6qJIAjwm/YPCksf9Ds7+UknOFlXrGsHPb8qbyGaPHkyvv766yceEx0djb/++gurVq3ClStX1F5zcnLCzJkzMWrUqCdeo7CwELVr18bUqVMxYcKEJx47bdo0rFixAomJieW+zhaiqlVQosD49efEocpjOtTD+M4NamRrAD1wJTUXC/Zfw44LKWKrSHMPW7zdxhtd/JxhqMe3i4pKldgalYylR2JxLT0PQFlrWb9gd7zXoR7cGIxqtLxiBfyn/6O27+rn3WFsqL//T2iKVt0yu337NjIyMp54jLe3N9asWfNct8x+++03DB8+HElJSXB0dHzisTt27ECvXr1QVFQEE5On/zXKPkSap1IJ+G73Ffx08AYAoEcTF3z/WiDMjDksuaa5kpqLeXuv4u+LD1p6O/s5Y1R7HzT3sJOwMu0jCAIOXr2Nnw/dwPHYTABlwejVIHeM7uCjNSPqSHNib+eh4/eHxOe+LlbYNa6thBXVLFp1y8zR0fGpAQUAwsLCkJWVhcjISAQFBQEA9u/fD5VKhdDQp8/G+euvv+Kll16q0NeKioqCnZ1dhcIQVQ25XIaPuvnCx9ESk/86j50XUnHrbgR+fjMItW3413BNkJRViB/2XMWfZ26JLULd/V0wpmM9NHa1kbY4LSWTydChoRM6NHTCidgM/LjvGo7dyMAfJxPwZ+QtDGlZF2M61OeSITXEprO38OH6c+Lzt1t74bNefhJWpN+0plM1UDbsPi0tDUuWLBGH3QcHB4vD7pOSktCpUyesXr0aISEh4nnXr19HgwYNsHPnTrWh9QCwbds2pKWl4YUXXoCpqSn27NmDiRMnYuLEiRXuJ8QWoqp1Mi4T7/x2GncLSuFgaYwFA5sjzKeW1GXRM8oqKMGiA9exKuImShRl8wd1a+yCDzs3QEMXK4mr0z0n4zLxw56riIgta2m3MTPC2I718GZYXU50qsOGrzyFfTHp4vOFrzdDr6YVG01NFadVt8wqIzMzE2PGjFGbmHH+/PnifEL3J2I8cOAA2rdvL573ySefYM2aNYiPj4dcrn7PddeuXZgyZQquX78OQRBQr149jBo1CiNGjHjk2MdhIKp6CRkFeGdNJKJTcmAgl2FyN1+83cZLp4da6xuFUoW1JxIwd89VZBeWjRp7wdseH3fzRTPeGnsu92+lfbUzBlfScgGUraP2UVdf9Gpam/+f6JCiUiV8p+5S23dgYnt4OXAakqqgs4FIWzEQVY/CEiU+3XQBf51NAgD0bFIbX7/atFqWYaDnc+z6Hczcdln8sPZ1scLk7r5o18CRH9YapFQJ+F9kIr7ffRXpuWUDP5p72OLzPk3g58rfTdouJjUH3eYdUdvHztNVi4FIwxiIqo8gCFhz/CZmbb+MUqWAek6W+PnNIPg4lr98C0krJbsQs7ZdFjtM25obYUKXhhjYwl2vR41VtYISBX49Eoclh24gv0QJuQwY2tILH3auz6VxtNSv/8Zh9vbL4vNXmrlhbv9A6QrSEwxEGsZAVP0ib97Fe2sjkZZTDAtjA3z5ShP0DnSTuiy6R6kS8FtEPL795wryS5QwkMswKNQDH3ZuAFtzY6nL0xup2UWYveMydpwvm8jPycoEU3v58TaaFlGqBAR/vkecfBQAfn4zCF0bu0hYlf5gINIwBiJppOcWYezvZ3Eirmz48atBdTDzpcaw4C00SUWn5GDyXxdwLjELQNktmy9facLZdCV05NptTNtyCXF38gGULQcyu48/+6VI7EpqLrrOO6y27/iUTnCx4WSL1YWBSMMYiKSjUKqwYP91LNh/DSoB8HawwILXm3HYtgQKS5T4cd81LD0SC6VKgJWJIT7q7os3Qjw4qaYWKFYo8cuhWCw8cB3FChVMDOWY1LUhhrXy0onFcGuab3bFiPOsAUCAuy02v9eSLXfVjIFIwxiIpHc8NgPj1kUhNacIxgZyTOnhi6EtPfnLpZqcjMvExI3nkJBZAKBsPqEZLzWGM5cV0DoJGQX4dPMFHLl2B0BZC963rwWwH141KW8UGYfUS4eBSMMYiLTD3fwSTPrfeeyNTgMAhDdywpxXmsLRihNsVpWiUiXm7rmKpUdiIQhAbRtTzOrtj85+zlKXRk8gCALWn0rE5zuikVesgImhHBO6NMDw1t5sLapC+6LTMHzVabV9Z6d2hp0F+9VJhYFIwxiItIcgCFgdcRNf7IhGiVIFewtjfN7HHz2a1Ja6tBrnYlI2xm+IwtW0srW1+gXXwdRefhzFpEOSsgox5a8LOHz1NgCgmYctvn01APWc2FqkSUqVgM5zDyH2Xh8uoGwy0iVvBklYFQEMRBrHQKR9olNyMH7DOUSn5AAAXgpwxazejTnCSQMUShV+OngD8/ddg0IlwMHSBF+90gThbBXSSYIgYMPpRHy+PRq5xQqYGskxtZcfXg/x4C1nDTgdn4lXl0So7ftzVBiC6tpLVBE9jIFIwxiItFOJQoUF+6/hp4M3oFQJcLIywVd9m6CjLz+4n1XcnXyMWx8ljiDr7u+CL15uAns2+eu85KxCfPS/8/j3elnfoi5+zvi6b1PeznlGgiDg9aUnxCVVAKCekyX+GdeWtyW1CAORhjEQabeoxCxM2BCFG7fLmqv7BdfBpz39YGPGWzuVsSUqCZ/8dQH5JUpYmxpiVm9/9A50ZStCDaJSCfj13zh8808MSpUCnK1N8EO/QLSs5yB1aTrlbMJdvPzTMbV9y4cG848xLcRApGEMRNqvqFSJ7/65gl+PxkEQyiaom/FSY3T3d+EH+lMUlCgwY+slbDh9CwAQ4mWPHwcEoraNmcSVUVW5mJSN99edReztfMhkwDttfTC+cwMuIfEUCqUK3X88gmvpeeI+K1NDnP4snAvtaikGIg1jINIdJ+MyMfnP82LnxvBGTpjV2x+utvxwL09Mag7G/H4W19PzIJcBYzvWx/ud6rPJXw8UlCgwe3s0/jiZAABoWscGi15vDnd7c4kr007bzydjzO9n1fbNH9gMLwVwOL02YyDSMAYi3VJUqsRPB65j8aEbKFUKMDc2wMQuDTGkpSc/6O8RBAFrTyRg9vbLKFao4Gxtgnn9myHMp5bUpVE123UxFZP/Oo+sglLYmBlhbr8AdGrEWz/35RSVoumM3Wr76jlZ4u8P2sCI6/VpPQYiDWMg0k3X0nIx5a8LOH3zLoCyv4C/fLkJ/N30e5br/GIFPv7zPLbfW/+qQ0NHfPdaAGpZcj4nfZWUVYj31p4RO9O/177sFpq+L9D75c5o/HI4Vm3fX++1RHMPO4kqospiINIwBiLdpVIJ+ONUAr76Owa5RQrIZMDAEA9M7NJQL0dOxd7Ow7trInE1LQ+Gchkmd/fFW628uPQGoUShwpc7o7HyWDwAINTLHgtebwYnK/2bjfzYjTt4fekJtX0vBbjixwGB7JOoYxiINIyBSPel5xRh9o5obDuXDACwNjXEhC4N8Uaoh978FfzPpVRM2HAOecUKOFmZYPGg5pwrhR6x/XwyPv7feeSXKOFoZYIFA5vhBW/9uJV6N78EzWbveWT/vx93QB079q3SRQxEGsZAVHOciM3AjG2XxQkdGzpbYfpLfmjpU3OHHStVAr7ffUVcaDLE0x4L39DPv/ypYq6n5+G9tWUtiXIZMKV7I7zdxqvGto4IgoAP10dhc1Sy2n6uQab7GIg0jIGoZlGqBPxxMgHf7b6CrIJSAECPJi74uJsv6taykLg6zcrML8EH686KC30Ob+2Fyd192RmUnqqgRIHPNl3EX2eTAAAvN3PDnFeawNSoZg0vP3glHUNXnFLb16tpbSwY2KzGBkB9wkCkYQxENVNWQQnm7rmKNcdvQiUARgYyvBFaF2M71qsRHYwvJmXjnd8ikZRVCDMjA3z9alMOEaZKEQQBq47FY/aOaChVAprWscHPbwbViDmqEjML8O0/V7D1nHqr0JmpnfWyf2FNxUCkYQxENVt0Sg6+3BkttqJYmhji3XbeeKu1F8yNDSWu7tn8fSEF4zecQ2GpEp61zPHzm8Fo6GIldVmko45dv4PRv5/B3YJSOFiaYMmg5gj21M3+Z1kFJViw/zp+i7iJEqUKANDA2RIzXmpco2+d6ysGIg1jINIP/167gzl/R+NScln/IicrE4wLb4B+wXV0puO1IAhYsP865u65CgBoU98BC19vzmVM6LklZhZgxOrTiEnNhZGBDLN7+2NAiIfUZVVYUakSq47FY9GB68gpUgAAWtWrhSndG+n9VBw1GQORhjEQ6Q+VSsC288n4bvcVJGYWAgC8HS3wQaf66NXUVasndiwsUWLS/86J8wsNa+WJT3s00pkwR9ovv1iBiRvP4e+LqQCAwWF1MbWXn1b3SSsqVeKPkwlYfPAG0nOLAQC+LlaY0qMR2tZ3YD+hGo6BSMMYiPRPsUKJtccTsGD/Ndy91/Fam4NRanYRRqw+jQtJ2TCUyzC7jz8G6tBf76Q7BEHAwv3X8f1DrZCL3mgOa1PtaoUsViix/lQiFh24jrScsiDkZmuGceH18UrzOlr3/zBVDQYiDWMg0l+5RaVYdSweS4/EIbuwLBj5OFrgfS0KRlGJWRi5+jTSc4thZ26ExYOC9GbeGJLO7kup+GBdFApLlWjgbIlfh7TQinXQShQqbDhdFoRSsosAAK42phjdsR5eC3LnArZ6hoFIwxiIqLxgVM/JEmM71kPPJrUluy3194UUjFsfhWKFCg2cLbFscAt41JL+Q4n0w8WkbAxfdQppOcVwsDTG0sHBaCbRshaFJUpsOJ2IXw7HIimr7Ha3s7UJxnSoh34t3LkavZ5iINIwBiK6L6eoFKuOxmPpkVixY2YdOzO83doL/Vq4V9uoNEEQ8Ou/cfhiZzQEoWw9svkDm8FKy25bUM2Xkl2It1aeRnRKDkwM5fihfyB6NKldbV//bn4JVkfcxKqIeGTmlwAAHK1MMLq9DwaEeNS4eZOochiINIyBiP4rp6gUq4/FY8XReGTc+yVsZ26EwWGeGNLSs0rnMVGqBMzadgmrIm4CAAa94IEZLzZm52mSTH6xAmP/OIv9MekAgI+7+eLddt5V2mE5OasQy47EYd2pBBSUKAEA7vZmGNnGG68FuzMIEQAGIo1jIKLHKSpVYmPkLSw9HIuEzAIAgKmRHP2C3fF2a2+N374qKFHg/T+isDc6DQDwSQ9fjGhTtR88RBWhVAmYvf2yuDhs/2B3fP6yv8ZHoF1Kzsbyf+OxJSoJClXZx1ej2tYY1d4HPfxd+IcBqWEg0jAGInoapUrAroupWHLoBi4kZQMAZDKgk68ThrT0ROt6zz+8Nz23CG+vOo3zt7JhbCjHD/0C0bNp9d2aIKqIVcfiMXPbJagEoF0DR/z0RnNYmDzfreRSpQq7L6Vh1bF4nIzPFPeHedfCu+19OHyeHouBSMMYiKiiBEFARGwGfj4Ui0NXb4v7vR0tMPiFuugbVOeZ+vlcT8/F0BWncOtuIezMjbBsSDBXqiettS86DaN/P4OiUhWa1rHB8qEt4PAMy+Fk5BVj3alErDl+UxwxZiiXoXuT2hje2guB7rYarpxqGgYiDWMgomdx43Yefou4if9F3kJecVkHbAtjA/QNqoPBYXVRz6liS2mcis/E8JWnkFOkgGctc6wYFgIvh5q1CC3VPGcT7mL4qtPIzC9B3VrmWDUsBJ4V+HcrCAKiErOw9kQCtp5LRomibHkNB0tjvB7igTdeqAtna9OqLp9qCJ0NRF988QV27NiBqKgoGBsbIysr66nnCIKA6dOnY+nSpcjKykKrVq2wePFi1K9fXzwmMzMTY8eOxbZt2yCXy9G3b1/8+OOPsLS0rFBdDET0PPKKFfjrzC2sOhaPG7fzxf3Bde3Qr4U7ejWt/djRabsupuL9dWdRolChuYctlg1pwYUnSWfE3s7DkBUnkZhZiFoWxlg+tAUCHtOqk1VQgr/OJGH9qURcScsV9zetY4OhLT3Rs2ltDp2nStPZQDR9+nTY2tri1q1b+PXXXysUiL7++mvMmTMHq1atgpeXF6ZOnYoLFy7g8uXLMDUt+yuie/fuSElJwc8//4zS0lIMGzYMLVq0wO+//16huhiISBMEQcDR6xlYeSwe+2PScK8/KCxNDPFiQG30b+GBgDo2Yl+INcdvYtqWi1AJQHgjZyx8vRlHzpDOSc8twrAVp3ApOQdmRgb4aVBzdGjoBKBsqZzjsRlYdyoRuy6liq1BJoZy9GxSG4PC6qKZuy37B9Ez09lAdN/KlSsxbty4pwYiQRDg6uqKCRMmYOLEiQCA7OxsODs7Y+XKlRgwYACio6Ph5+eHU6dOITg4GACwa9cu9OjRA7du3YKrq+tT62EgIk1LzS7Cn2duYcPpRNzMKBD3N3S2Qmc/Z8Sk5mBvdNkQ5oEh7pjd25+jZ0hn5RUrMGpNJI5cuwMDuQyTu/kit6gUm6OSxdGZAOBX2xoDQ9zxUqAbFyQmjajM53f1zCJXReLi4pCamorw8HBxn42NDUJDQxEREYEBAwYgIiICtra2YhgCgPDwcMjlcpw4cQIvv/zyI9ctLi5GcXGx+DwnJ6dq3wjpHRcbU4zuUA+j2vngRFwmNpxOxM4LKbiSlqt2u+D9TvXxYXh9/oVMOs3SxBC/DmmBj/88j01nk/DFzmjxNSsTQ/Ru5ooBLTy46jxJSqcDUWpq2YrLzs7OavudnZ3F11JTU+Hk5KT2uqGhIezt7cVj/mvOnDmYOXNmFVRMpE4ulyHMpxbCfGphxkuNsTUqCWcSstDA2Qqt6zmgSR1+QFDNYGwox/evBcDN1gzrTiUixMsOnf2c0bWxS7XN8E70JFX+r3Dy5Mn4+uuvn3hMdHQ0fH19q7qUCpsyZQrGjx8vPs/JyYG7u7uEFZE+sDEzwpthnngzTOpKiKqGXC7DxK4NMbFrQ6lLIXpElQeiCRMmYOjQoU88xtvb+5mu7eLiAgBIS0tD7doPJqhLS0tDYGCgeEx6erraeQqFApmZmeL5/2ViYgITk8rPmUFERES6qcoDkaOjIxwdHavk2l5eXnBxccG+ffvEAJSTk4MTJ05g1KhRAICwsDBkZWUhMjISQUFBAID9+/dDpVIhNDS0SuoiIiIi3aJVw1YSEhIQFRWFhIQEKJVKREVFISoqCnl5eeIxvr6+2LRpEwBAJpNh3Lhx+Pzzz7F161ZcuHABgwcPhqurK/r06QMAaNSoEbp164YRI0bg5MmTOHr0KMaMGYMBAwZUaIQZERER1Xxa1ZNt2rRpWLVqlfi8WbNmAIADBw6gffv2AIArV64gOztbPOajjz5Cfn4+Ro4ciaysLLRu3Rq7du0S5yACgLVr12LMmDHo1KmTODHj/Pnzq+dNERERkdbTynmItA3nISIiItI9lfn81qpbZkRERERSYCAiIiIivcdARERERHqPgYiIiIj0HgMRERER6T0GIiIiItJ7DERERESk9xiIiIiISO8xEBEREZHe06qlO7TV/cm8c3JyJK6EiIiIKur+53ZFFuVgIKqA3NxcAIC7u7vElRAREVFl5ebmwsbG5onHcC2zClCpVEhOToaVlRVkMpnU5VS7nJwcuLu7IzExkWu5VQN+v6sXv9/Vi9/v6qfP33NBEJCbmwtXV1fI5U/uJcQWogqQy+WoU6eO1GVIztraWu/+Z5ISv9/Vi9/v6sXvd/XT1+/501qG7mOnaiIiItJ7DERERESk9xiI6KlMTEwwffp0mJiYSF2KXuD3u3rx+129+P2ufvyeVww7VRMREZHeYwsRERER6T0GIiIiItJ7DERERESk9xiIiIiISO8xEFGlxMfHY/jw4fDy8oKZmRl8fHwwffp0lJSUSF1ajfXFF1+gZcuWMDc3h62trdTl1DiLFi2Cp6cnTE1NERoaipMnT0pdUo11+PBhvPjii3B1dYVMJsPmzZulLqnGmjNnDlq0aAErKys4OTmhT58+uHLlitRlaTUGIqqUmJgYqFQq/Pzzz7h06RJ++OEHLFmyBJ988onUpdVYJSUleO211zBq1CipS6lx1q9fj/Hjx2P69Ok4c+YMAgIC0LVrV6Snp0tdWo2Un5+PgIAALFq0SOpSarxDhw5h9OjROH78OPbs2YPS0lJ06dIF+fn5UpemtTjsnp7bt99+i8WLFyM2NlbqUmq0lStXYty4ccjKypK6lBojNDQULVq0wMKFCwGUrVvo7u6OsWPHYvLkyRJXV7PJZDJs2rQJffr0kboUvXD79m04OTnh0KFDaNu2rdTlaCW2ENFzy87Ohr29vdRlEFVKSUkJIiMjER4eLu6Ty+UIDw9HRESEhJURaV52djYA8Hf1EzAQ0XO5fv06FixYgHfeeUfqUogq5c6dO1AqlXB2dlbb7+zsjNTUVImqItI8lUqFcePGoVWrVvD395e6HK3FQEQAgMmTJ0Mmkz3xERMTo3ZOUlISunXrhtdeew0jRoyQqHLd9CzfbyKiZzF69GhcvHgR69atk7oUrWYodQGkHSZMmIChQ4c+8Rhvb29xOzk5GR06dEDLli3xyy+/VHF1NU9lv9+keQ4ODjAwMEBaWpra/rS0NLi4uEhUFZFmjRkzBtu3b8fhw4dRp04dqcvRagxEBABwdHSEo6NjhY5NSkpChw4dEBQUhBUrVkAuZ0NjZVXm+01Vw9jYGEFBQdi3b5/YsVelUmHfvn0YM2aMtMURPSdBEDB27Fhs2rQJBw8ehJeXl9QlaT0GIqqUpKQktG/fHnXr1sV3332H27dvi6/xr+qqkZCQgMzMTCQkJECpVCIqKgoAUK9ePVhaWkpbnI4bP348hgwZguDgYISEhGDevHnIz8/HsGHDpC6tRsrLy8P169fF53FxcYiKioK9vT08PDwkrKzmGT16NH7//Xds2bIFVlZWYr84GxsbmJmZSVydduKwe6qUlStXPvbDgv+UqsbQoUOxatWqR/YfOHAA7du3r/6CapiFCxfi22+/RWpqKgIDAzF//nyEhoZKXVaNdPDgQXTo0OGR/UOGDMHKlSurv6AaTCaTlbt/xYoVT71dr68YiIiIiEjvsfMHERER6T0GIiIiItJ7DERERESk9xiIiIiISO8xEBEREZHeYyAiIiIivcdARERERHqPgYiI9FpmZiY+/PBDeHp6wtTUFH5+fuVOhElENRuX7iAivXXlyhV06tQJWVlZ6NevH2xtbbF27VoMHToUZmZm6Nevn9QlElE14UzVRKSXcnNzERgYiIKCAhw6dAgNGjQAAFy6dAkBAQFo0qQJzp49K3GVRFRd2EJERHpp1qxZiI2NxdatW8UwBACNGzdGQEAAzpw5g7y8PC6gS6Qn2IeIiPROVlYWFi1aBH9/f7z44ouPvG5vbw8ASEtLq+7SiEgiDEREpHc2btyIwsJCDB48uNzXi4uLAQDGxsbVWRYRSYi3zIhI7/z9998AgJiYGMyYMeOR169duwYDAwO4uLhUc2VEJBV2qiYivePs7Iz09PQnHtOwYUPExMRUU0VEJDXeMiMivXL37l2kp6ejbdu2EAThkce+ffsAAK1bt5a4UiKqTgxERKRXbt26BQBwdXUt9/WdO3cCALp3715tNRGR9BiIiEivlJaWAgBMTEzKfe2PP/5ArVq10KtXr+oujYgkxEBERHrF2dkZQPlD6pctW4bk5GRMmjSp3MBERDUXO1UTkd7x8fFBcnIyYmJiULduXQDA8ePHER4ejgYNGuD48eMcck+kZxiIiEjvLFu2DCNGjICbmxsGDhyIlJQUbNy4EZ6enti/fz/c3NykLpGIqhkDERHppcWLF+OHH35AQkICXF1d0b9/f3zyySewsrKSujQikgADEREREek9dqomIiIivcdARERERHqPgYiIiIj0HgMRERER6T0GIiIiItJ7DERERESk9xiIiIiISO8xEBEREZHeYyAiIiIivcdARERERHqPgYiIiIj0HgMRERER6T0GIiIiItJ7/wfwHCGu5BXP6AAAAABJRU5ErkJggg==\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "7lHeMTjUPH-n"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}