Assn3_P452_1911007.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyOjsgLyjlUHchcri0v3VCxz",
      "include_colab_link": true
    },
    "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/abhich2507/Numerical_Python/blob/main/Assn3_P452_1911007.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 22,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bOJkdQJTxrYK",
        "outputId": "b9a93d6f-1d95-4557-ecaf-4294e2093f56"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "A= [[ 6.00000000e+00  3.31152776e-15 -5.24604773e-14  3.44156801e-09]\n",
            " [ 3.28225807e-15  4.00000000e+00  1.21079839e-11 -1.90734863e-06]\n",
            " [-5.30689896e-14  1.21084736e-11  8.00000000e+00  3.27398426e-11]\n",
            " [ 3.44156639e-09 -1.90734863e-06  3.27418150e-11  2.00000000e+00]]\n",
            "Q= [[ 1.00000000e+00 -1.64109789e-15  6.63363074e-15 -1.72078319e-09]\n",
            " [ 3.28216462e-15  1.00000000e+00 -1.51356311e-12  9.53674316e-07]\n",
            " [-6.63365891e-15  1.51357872e-12  1.00000000e+00 -1.63709061e-11]\n",
            " [ 1.72078319e-09 -9.53674316e-07  1.63709075e-11  1.00000000e+00]]\n",
            "eigenvalues= [6. 4. 8. 2.]\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-22-8d2af50ea353>:15: ComplexWarning: Casting complex values to real discards the imaginary part\n",
            "  R[j,j] = mag(Ap[:,j])\n",
            "<ipython-input-22-8d2af50ea353>:16: ComplexWarning: Casting complex values to real discards the imaginary part\n",
            "  Q[:,j] = Ap[:,j]/R[j,j]\n",
            "<ipython-input-22-8d2af50ea353>:13: ComplexWarning: Casting complex values to real discards the imaginary part\n",
            "  R[i,j] = Q[:,i]@A[:,j]\n"
          ]
        }
      ],
      "source": [
        "#1\n",
        "\n",
        "import numpy as np\n",
        "def mag(xs):\n",
        "    return np.sqrt(np.sum(xs*xs))\n",
        "def qrdec(A):\n",
        "    n = A.shape[0]\n",
        "    Ap = np.copy(A)\n",
        "    Q = np.zeros((n,n))\n",
        "    R = np.zeros((n,n))\n",
        "    for j in range(n):\n",
        "        for i in range(j):\n",
        "            R[i,j] = Q[:,i]@A[:,j]\n",
        "            Ap[:,j] -= R[i,j]*Q[:,i]\n",
        "        R[j,j] = mag(Ap[:,j])\n",
        "        Q[:,j] = Ap[:,j]/R[j,j]\n",
        "    return Q, R\n",
        "A=np.array([[4.0,2.0/3.0,-4.0/3.0,4.0/3.0],[2.0/3.0,4.0,0,0],[-4.0/3.0,0,6,2],[4.0/3.0,0.0,2.0,6.0]],dtype=complex)\n",
        "'''\n",
        "Q,R=qrdec(A)\n",
        "print('Q=',Q)\n",
        "print('R=',R)\n",
        "'''\n",
        "for k in range(1,20):\n",
        "    Q,R=qrdec(A)\n",
        "    A=R@Q\n",
        "    m=[]\n",
        "    for i in range(1,np.shape(A)[0]):\n",
        "        for j in range(i+1):\n",
        "            m.append(abs(A[i][j]))\n",
        "    f=sum(m)\n",
        "    if f<=0.00001:\n",
        "        break\n",
        "eigenvalues=np.diagonal(A)\n",
        "print('A=',A)\n",
        "print('Q=',Q)\n",
        "print('eigenvalues=',eigenvalues)"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#1b"
      ],
      "metadata": {
        "id": "QHheiWWbyGxr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Define the matrix\n",
        "A = np.array([[4.0, 2.0/3.0, -4.0/3.0, 4.0/3.0],\n",
        "              [2.0/3.0, 4.0, 0, 0],\n",
        "              [-4.0/3.0, 0, 6, 2],\n",
        "              [4.0/3.0, 0.0, 2.0, 6.0]], dtype=complex)\n",
        "\n",
        "# Choose an initial guess for the eigenvector\n",
        "v_initial = np.array([1, 1, 1, 1])\n",
        "\n",
        "# Define a function to calculate the relative error\n",
        "def relative_error(new_val, old_val):\n",
        "    return abs((new_val - old_val) / new_val) * 100\n",
        "\n",
        "# Initialize variables\n",
        "old_eigenvalue = 0.0\n",
        "tolerance = 0.0001\n",
        "\n",
        "# Iterative method to find the largest eigenvalue and its corresponding eigenvector\n",
        "while True:\n",
        "    v_updated = np.dot(A, v_initial)\n",
        "    eigenvalue = np.linalg.norm(v_updated)\n",
        "    error = relative_error(eigenvalue, old_eigenvalue)\n",
        "    v_updated = v_updated / eigenvalue\n",
        "\n",
        "    # Check if the error is within tolerance\n",
        "    if error < tolerance:\n",
        "        break\n",
        "\n",
        "    old_eigenvalue = eigenvalue\n",
        "    v_initial = v_updated\n",
        "\n",
        "# Print the results\n",
        "print('Largest eigenvalue =', eigenvalue)\n",
        "print('Eigenvector =', v_updated)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qDFFXw2dyUw3",
        "outputId": "3a72c0ea-5605-42f5-a065-0fbbcf49b7d1"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Largest eigenvalue = 7.999992178241464\n",
            "Eigenvector = [1.12119132e-03+0.j 3.74030152e-04+0.j 7.06358506e-01+0.j\n",
            " 7.07853278e-01+0.j]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#2A"
      ],
      "metadata": {
        "id": "BVHjEZjmyaOb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "x=np.arange(0.00,1.05,0.05)\n",
        "y=np.array([0.486,0.866,0.944,1.144,1.103,1.202,1.166,1.191,1.124,1.095,1.122,1.102,1.099,1.017,1.111,1.117,1.152,1.265,1.380,1.575,1.857])\n",
        "x2=x**2\n",
        "x3=x**3\n",
        "x4=x**4\n",
        "x5=x**5\n",
        "x6=x**6\n",
        "xy=x*y\n",
        "x2y=x2*y\n",
        "x3y=x3*y\n",
        "sumx=np.sum(x)\n",
        "sumy=np.sum(y)\n",
        "sumx2=np.sum(x2)\n",
        "sumx3=np.sum(x3)\n",
        "sumx4=np.sum(x4)\n",
        "sumx5=np.sum(x5)\n",
        "sumx6=np.sum(x6)\n",
        "sumxy=np.sum(xy)\n",
        "sumx2y=np.sum(x2y)\n",
        "sumx3y=np.sum(x3y)\n",
        "A=np.array([[len(x),sumx,sumx2,sumx3],[sumx,sumx2,sumx3,sumx4],[sumx2,sumx3,sumx4,sumx5],[sumx3,sumx4,sumx5,sumx6]])\n",
        "B=np.array([sumy,sumxy,sumx2y,sumx3y])\n",
        "X=np.linalg.solve(A, B)\n",
        "def f(x,a,b,c,d):\n",
        "    return a + b*x + c*x**2 + d*x**3\n",
        "plt.scatter(x,y)\n",
        "plt.plot(x,f(x,X[0],X[1],X[2],X[3]))\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 447
        },
        "id": "DAOpPKN5wMcE",
        "outputId": "d11f0c42-29e8-4124-adc2-03040d9ee86d"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7bc8995580d0>]"
            ]
          },
          "metadata": {},
          "execution_count": 24
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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SV+O8GEaIiIjs4GKBAfvSCyGTAS+M5ajInTCMEBER2cHqg+Zuq5OjdOjTo7PE1Tg3hhEiIiIbyy6uwJdn8gBwVKQtGEaIiIhsbM2hKzAJ4IGBARgcrJW6HKfHMEJERGRDebeqsP10LgBgwdi+ElfjGqwOI4cPH0ZCQgKCg4Mhk8mwc+fONh979OhReHl5YdiwYda+LRERkUv44HAm6owC8b27IbZXV6nLcQlWh5GKigpER0dj1apVVh1369YtzJ49Gw8++KC1b0lEROQSbpTVYEvyNQDAiw9wVKStvKw9YNKkSZg0aZLVbzRv3jxMnz4dCoXCqtEUIiIiV7H+SBZq6k0YFtYFo/p0k7ocl+GQNSMffvghMjMzkZiY2Kb9a2pqYDAYmjyIiIicWeaNcmw4mgUAeHFsX8hkMokrch12DyPfffcdXnvtNWzatAleXm0biFm5ciW0Wq3lERYWZucqiYiI2s9kEli8/Sxq600YpPODr1IBo0lIXZbLsGsYMRqNmD59OpYtW4b+/fu3+bjFixdDr9dbHjk5OXaskoiIqGN+8/k5nMwqBQBcyC/D9H+cxJi3DiDpXL7ElbkGq9eMWKOsrAynTp3C6dOn8eKLLwIATCYThBDw8vLCV199hQceeKDZcSqVCiqVyp6lERER2cTW5KvYfPJas+0F+mrM35SKNTNjMDFKJ0FlrsOuYUSj0eDs2bNNtq1evRoHDhzAtm3bEBERYc+3JyIisiujSSDxi/QWXxMAZACW7UrH+MggKORcQ9Iaq8NIeXk5MjIyLM+zsrKQlpYGf39/9OzZE4sXL8b169fx8ccfQy6XIyoqqsnxAQEBUKvVzbYTERG5mvcPZKCm3tTq6wJAvr4ayVmliOfVNa2yOoycOnUKY8eOtTxftGgRAGDOnDnYuHEj8vPzce1a8+EqIiIid6KvqsP6I5lt2reorNrO1bg2mRDC6Zf7GgwGaLVa6PV6aDQaqcshIiLC4u1nsCW5bRdYbHnuHo8cGWnr5zfvTUNERGSl41dKLEGkWyclWlsNIgOg06oRF+HvsNpcEcMIERGRFarrjHh9h/nijBkje+IPPzWvgfxhIGl4npgQycWrd8EwQkREZIW/7v8OWcUVCNSo8OqkgZgYpcOamTEI0qqb7BekVfOy3jay66W9RERE7iQ9z4C/HzYvWl3+SBQ0am8AwMQoHcZHBiE5qxRFZdUI8DNPzXBEpG0YRoiIiNqg3mjCa9vPwGgSmDJEh4cGBzV5XSGXeeQiVVvgNA0REVEbfHg0G2dy9dCovZD4cKTU5bgVhhEiIqK7uFZSiT/tuwQAeGNKJAL81Hc5gqzBMEJERHQHQgi8vuMsqutMGNWnG342IlTqktwOwwgREdEd/Dv1Oo5kFEPlJceKnw6BTMZFqbbGMEJERNSKG2U1WP6l+UZ4C8f3R3j3ThJX5J4YRoiIiFrxuy/Toa+qw+BgDZ4dwzvN2wvDCBERUQv2XyjErm/zoJDL8NbjQ+Gl4EemvfDMEhER/UB5TT3e2HkOAPDsmAhEhWglrsi9MYwQERH9wB+TLiJfX42e/r745bj+Upfj9hhGiIiIGkm5WoqPT1wFAKx8bAh8lAqJK3J/DCNERES31dQb8eq/z0II4GexoRjdt7vUJXkEhhEiIqLbVh+8goyicnTvrMKSKYOkLsdjMIwQEREBuFxYhtWHMgAAyx4ejC6+Sokr8hwMI0RE5PGMJoFX/30GdUaBcYMCMXlI0N0PIpthGCEiIo+36cRVnL52C51VXlj+6GC2fHcwhhEiIvJo129V4e2kiwCAVycNhE7rI3FFnodhhIiIPJYQAm/sOIuKWiNG9OqKGXE9pS7JI3lJXQAREZEjGU0CyVmlKCqrRkZROQ5eugGlQo43Hx8CuZzTM1JgGCEiIo+RdC4fy3alI19f3WT7hMGB6BvgJ1FVxGkaIiLyCEnn8jF/U2qzIAIAu87kI+lcvgRVEcAwQkREHsBoEli2Kx2ilddlAJbtSofR1NoeZE8MI0RE5PaSs0pbHBFpIADk66uRnFXquKLIgmGEiIjcXlFZ60GkPfuRbTGMEBGR2wvwU9t0P7IthhEiInJ7cRH+6KRStPq6DIBOq0ZchL/jiiILhhEiInJ7Hx3LRkWNscXXGjqLJCZEQsE+I5JgGCEiIrf2edp1/O7LdADAo8OCodM2nYoJ0qqxZmYMJkbppCiPwKZnRETkxg5fvoFfffYtAOCpUeFITIiEScDSgTXAzzw1wxERaTGMEBGRW/o25xbmbUpBnVHg4ehgLP1JJGQyGRQyIL5PN6nLo0Y4TUNERG4n80Y5nt74DSprjRjTtzve+Vk07zvjxBhGiIjIrRQaqjFrfTJKK2oxJESLtbNiofTix50z498OERG5DX1VHeZsSMb1W1WI6N4JHz79I3RWcUWCs+PfELmsxrcB5yI0IqquM+K5j0/hYkEZevip8PHcOHTvrJK6LGoDq0dGDh8+jISEBAQHB0Mmk2Hnzp133H/79u0YP348evToAY1Gg/j4eOzdu7e99RIBMN99c8xbB/DkuhN4eWsanlx3AmPeOsC7bhJ5KKNJ4KUtp5GcVQo/lRc+ejoOYf6+UpdFbWR1GKmoqEB0dDRWrVrVpv0PHz6M8ePHY8+ePUhJScHYsWORkJCA06dPW10sEdD6bcAL9NWYvymVgYTIwwgh8MbOc/gqvRBKLznWzRmByGCN1GWRFWRCiHbfL1kmk2HHjh149NFHrTpu8ODBmDZtGpYuXdqm/Q0GA7RaLfR6PTQa/gPzZEaTwJi3DrR6900ZzA2Mjrz6gFNO2XBqicj23v3qEv56IANyGbB6BpuXOZO2fn47fM2IyWRCWVkZ/P1b7/9fU1ODmpoay3ODweCI0sgFWHMb8I72EagzmiCXyWwWFpLO5WPZrvQm9eu0aiQmRPKHJ1E7fXw8G389kAEAWP5oFP9fclEODyPvvPMOysvLMXXq1Fb3WblyJZYtW+bAqshV2Os24CXlNTifZ0B6vgHn8ww4n6dHVnEFhACUXnL4eCvMD6UCam8FfLzl8FGat6m9FfBt+PPt/zbdV4EL+XqsPpTZ7H0bppbYiprIervP5CPxi/MAgIXj+mPGyF4SV0Tt5dAw8sknn2DZsmX4/PPPERAQ0Op+ixcvxqJFiyzPDQYDwsLCHFEiObmO3gZcCIHcm1U4n6c3h488c/goMLQeXmrrTaitN0FfVdeumu+kYY508faziOnZFQEa3r6cqC2OZRRj4adpEAKYdU8vvPRgX6lLog5wWBjZunUrnn32WXz22WcYN27cHfdVqVRQqXg5FjUXF+EPnVaNAn01Wlrs1LBmJC7CH3VGEzKKyhuFDj3S8w0oq65v8WtHdO+ESJ0GkcEaDA7WYJBOA6VCjqo6o/lR2/S/1Y231RlRXWtEZePnt18vNNQgPf/OU403K+sQt2I/Qrr4IDpMi6GhXTA0VIuoEC00au+OnzgiN3Luuh7P/zMFtUYTJg8Jwm8fHgyZjGuvXJlDwsiWLVswd+5cbN26FVOmTHHEW5KbUshlSEyIxPxNqZABzQKJANC7eyc8uuooLhWWobbe1OxreCtk6B/oh8HBGgwO1iLydvBorTFS1w7W/Hnadby8Na1N+16/VYXrt6qw52yBZVvvHp0QfTucDA3tgsHBGqi9FR2sisg1XS2pwFMfJqO8ph7xvbvhz9OGcRG4G7A6jJSXlyMjI8PyPCsrC2lpafD390fPnj2xePFiXL9+HR9//DEA89TMnDlz8Je//AUjR45EQYH5h6yPjw+0Wq2Nvg3yJBOjdFgzMwZLPz+PorKaZq8fvVJi+bOfyguDbo90ROrM4aNvQOe7toa25VUvbZ1aWj9nBHyUCpzJ1eNM7i18m6PH9VtVyLxRgcwbFdhx+joAwEtuDlONR1D6B/rBW8GGyuTebpTVYNb6ZBSX1yJSp8EHs2Oh8mIwdwdWX9p76NAhjB07ttn2OXPmYOPGjXjqqaeQnZ2NQ4cOAQB+/OMf47///W+r+7cFL+2lxq6WVGDNoSv4d2ou6ozf//MN1KjMIx06jWXUI7Srj9U3x7L1VS8NlyPfbWqppcuRi8trcDZX/31AydWjuLx5AFN5yREZrEF0aBfE9+mG+/r1gI+SP6TJfZRV1+H/PjiB83kG9PT3xbb58W0O+iSdtn5+d6jPiKMwjBAAXC4sw+qDGfji2zyYbv+rje/dDXPHRGB4zy42afvc0FDth/9TNESE9l710vB1gaZTS9Z+XSEE8vXVlmByJvcWzuTqm62DUXvLcW+/HhgfGYgHBwagG1tikwurqTfiqQ3f4HhmCbp3VmLbvFEI795J6rKoDRhGyG2cu67H+wcykHT++3UUYwf0wIsP9EVsr9b71VjL3g3V7NVnxGQSuFpaiTO5t5B69Sb2XyxC7s0qy+tyGTAi3B8PRQbiocgg9OzGFtnk/BqmSgv0Vdj6TQ5OZpWis8oLW5+/B1EhnOJ3FQwj5PJOZZfibwcy8N/LNwAAMhkwcXAQFozta5cfRsevlODJdSfuut+W5+5pd0M1R3RgFULgQn4Z9qUX4qv0ApzPa3olz8AgP3MwGRyEwcEaXoVATqel4A4AvxzXD78c11+iqqg9nLYDKzknZ2lTLoTA0YwSvH/wO5zILAVgvoLm4ehgvPDjPugX6Ge397ZXQ7XGFHJZhzvD3o1MJkNksPkS5ZfH9UPuzUrsSy/EvvRCnMwqxcWCMlwsKMNfD2QgWKvG+NvBJC7Cn4tgSXKtTZUCwF++/g4Dg/zYINANMYyQU7QpF0Jg/4UivH8wA2k5twCYL8F9IjYU8+7vg17d7D8/3NGGas4qtKsvnh4dgadHR+BWZS0OXCzCvvRCHLp0A3n6anx0/Co+On4VGrUXHhgYgIcGB+G+/j1avdSZyF6MJoFlu9JbDCINlu1Kx/jIIF7O62Y4TePh7LVgs62MJoH/nMvH+wcycLGgDID5ypAn43ri+ft6I7iLj93eu6Va2nvViyuqrjPiaEYxvjpfiK8vFKKkotbymtJLjtF9uuGhwUF4cFCAywUwck2OmColx+I0Dd3VnX4LETB/+Nrrt5A6owmfp+Vh9aEMZN6oAAB0UiowKz4cz4yJQA8/x1/9caeGag3ffWJCpFsEEQBQeyvw4KBAPDgoEEaTwOlrN/FVeiG+Ol+A7JJKHLx0Awcv3YBMBgwP64IJg4Pwk+hghDgwIJLnKKuuw7v7LrVp345MlZJz4siIB5Pit5DqOiO2peRi7X+vWK740Pp44+nR4XhqVDi6+Cpt8j4d4QzTVlISQiCjqNwSTL7N1Td5PS7cHw8PC8aUITp07ST93xe5vm+yS7Hw07QmV4HdCUdGXAdHRuiuHLFgs0FlbT0+OXkNHxzOtHRN7d5ZiWfv7Y2Z9/RyqvUJE6N0GB8Z5BQLeq1hq0XIMpkM/QL90C/QDwvG9kWBvhr70guw+2w+TmaVIjnb/PjtF+dxf/8eeGR4CMYNCoCv0nn+Dsk11BlN+MvX32H1oQyYBBDW1QeVtUaUVtTe9d5T5F7408ODOWrB5r70Qrz67zMovb0mQadV4+f39ca0H/V02i6hjrjqxZbsOZoTpFVjVnw4ZsWHI19fhV3f5uHztDyczzNg/8Ui7L9YBF+lAhMGB+HhYcEY07d7m6/KcZaruMjxsoor8Mutpy0jb4/HhOK3D0fiaEaxx0yV0vc4TePB7L1gUwiBvx/OxFtJFyEE0KubL+bf3wePxYTe9d4w1HZSLULOKCrD52nmYHKttNKyvVsnJaYM1eGRYSGI6dml1T4mnj4d5i6sDZRCCGz9Jge/25WOqjojtD7eWPHTIZgy9Pu/c/7bcB9sekZtYqs25T9UU2/Ekh3nsC0lFwAw856eSEwYzD4WNmbvrrFtIYTA6Zxb+Pz0dXx5Jr/JVTlh/j54JDoEjwwLbtIjRuqruDyNvUagrA0NpRW1ePXfZ7AvvRAAMKpPN/xpajR02uaLojlq5h4YRqjNbP1bSEl5DeZtSsE32TchlwGJCYMxZ1S4DSumBs52KWS90YQjGcX4Ii0Pe88XoKLWaHktUqfBI8OCMWWoDj9be1zSAOVJ7DXKYG2gPHSpCK9sO4MbZTVQKuR4ZcIAPDMmwuobWZJrYRghq9jqt5DLhWV45qNvkFNaBT+VF1bNiMHovt35G46dfJ52HS9vTbvrfn/5v2F4ZFiI/QtqpKrWiK8vFOLztOs4dOkG6m/f3fCHawFawysmOs5eI1DWjMjVGU148z8XsfFYNgCgX0Bn/OX/hiMymD/LPQGvpiGr2GLB5sFLRfjFJ6dRXlOPnv6+2PDUCGQUlTf7ocW5X9tx5q6xPkoFEqKDkRAdjJsVtdhzLh+fn85DcnZpm47vyFVc9hzid5XpA3v2EUrOKm01iDR8/Xx9NT47lYMNR7NwubAcAPDUqHC8Nmkg1N7OuXCdpMMwQh0mhMCGo9n4w+50mAQwMsIfa2fG4mRWSYu/lRXoqzF/UyrXBdhAXIQ/dFr1XRchd+RSSFt8+HbtpMSMkb0wY2Qv7Po2D7/Ycvqux7Q3QNlz8aMrLaxsa2BIziq1+heRtgbFJTvPwWgS6N5ZhT/+bCjGDgiw6n3Ic3A1IXVIbb0Jr+84i+VfmoPItBFh+OczI6Hx8b7jb2WA+bcyo8npZwmdWkPXWOD7ofcGtrgUMulcPsa8dQBPrjuBl7em4cl1JzDmrQNIOpff7ponD9FBp1U3q/eHNh7Lwhff5qGipt6qeudvSm32IdwQgDtStz2/tj3Ys49QW4Oi0SQwblAg9v7yXgYRuiOGEWq3W5W1mL3hJLYk50AmA96YMghvPj4ESi+5Vb+VUcdMjNJhzcwYBGmbfkAEadUdGn2y14fvnQJUY3vPF+KlLacRs3wf5v0z5a7B5G7TEkD7A7A9v7a92HMKr2FE7k5/fzIAv380Cutmx6JbZ8ff3oFcC6dpqF2u3CjHMxu/QXZJJTopFfjb9OF4YGCg5XVHdncl23eNtfd9ixoCVEtTHkt/Mghh/p2w52w+9pzNR3ZJJZLOFyDpfAFUXnKMHRCAyUN1eHBgADo16txrz2kJe35te7HnFN6d7uPU4LcPR2LmPb2s/trkmRhGyGr/++4GXticirLqeoR08cH6p0ZgYFDTVdLOvLDSXdmya6wjPnzvFqCiQrR4ZcIApOcbsPtMy8HkxwN6YMrQYDw4MMCuAdgVw7W9b/w4MUqHP00dit9+kQ5D9fcjVp1VCrz1+FBMGRrc7trJ8zCMkFX+eTwbv709HB3bqyv+PisW3VsYgnXEwkqyH0d9+N4tQMlkMgwO1mJw8PfBZM/ZfOw+Yw4me88XYu/5Qqi85Bgaqm3Te7YnALtquG5tBCqoA4tujSaB/313A9tScvFVeiFq600AAH9fb/zigX6YPSrcKa8uIufGMEJtUm804XdfpuPj41cBAI/FhGDlY0Og8mr5Ej17/1ZG9uWMH76Ng8mvHvo+mOw5W4Cs4gp8k33zzsej/QHYlcO1rabwvissw7bUXOxIvW652SUADAj0wxOxofi/uDD4qb1tXT55CIYRuit9VR1e/CQV//uuGADw64kDMP/+Pq3ec6SBPX4rI8dw9g/fHwaTC/ll2H02D5+dym3yQdmYAPD65IHtCsCuHq7bO4V3q7IWu77Nw7aUXMsN7QCgq683HhkWgidiQzE4WHPXnwVEd8MOrHRH2cUVeOajb3DlRgV8vBX487RhmBgVZNXXcJUmUdSUve5bZE9CCKw/kok/f/0dKmqMzV5XeskR07ML7undDff07oZhYV2sasDlSn1G2qveaMLh29MwX6cXodZonobxksswdmAAnogNxdgBAbzZJbUJ28FThx2/UoL5m1Nwq7IOOq0a62aPQFRI2+blyT246oev0SRwMrME5/L0KDLUoNBQjRNZpbjxg1GT9oQTdw3XFwsM+HdKLnaczkNx+ffnKVKnwROxoXh4WHCL68OI7oRhhDpka/I1vLHzHOpNAtFhXbBuViwCNM61OI8cw10+fIUQyCyuwInMEpzILMWJzJJm4UTlJUdMz663w4k/oq0cOXE1pRW1+CLtOral5uLcdYNle7dOSjw6PASPx4TyHjLUIQwj1C5Gk8CKPRew/kgWACAhOhh/fGKoW/9AJs/UnnAyrGeXVhdtu4o6owmHLt3AtpQcHLhYhDqj+SPAWyHDgwMD8XhsKH48oAe8FZyGoY5jGCGrlVXX4aUtp3Hw0g0AwMJx/fHSg325OI08grXhZHCwBkFaNQI1anTrpITcCUeLhBAor6lHoaEa+fpqHLx4A5+nXUdJRa1lnyEhWjwRG4qE6GD4d1JKWC25I4YRskp5TT2mrj2O9HwDVF5y/GlqNH7CpkXkwRrCyfErJZaA0ngtRWPeChkC/NQI0KgQpDEHlCCt2vLnQI0KQVo1fJW2u4Cxus6IG2Xm9TAFhmoU3l4b8/3D/LyytvlC3u6dVXgsxjwNMyDIz2Y1Ef0Qwwi1mRACL2xOxX/OFaB7ZyXWz/kRosO6SF0WkVMRQuDKjYaRkxJkl1SgQF+DkooatPWnqJ/aC0G3g4olpPwgvHTtpMTNilpLwCgwVKPodsAoMNRY/nyzsq7NtTe874AgPzwWE4L7+vWAF6dhyAEYRqjNVh/KwNtJl+CtkGHr8/GI7dVV6pKIXEad0YQbZebQUKg3j1I0/nPR7UDR0ghFRym95LfDjAoBGrXlz4GWERnzc1uOyBBZo62f3/wX6uEOXSrCH/deAgAseziKQYTISt4KOYK7+CC4i0+r+wghUFZTbwkoDVMoBZbn5j8Xl9fAJAC5DOjhp2oSKAL91Aj8wYiK1seba7rILTCMeLCrJRV4actpCAE8GReG6SN7Sl0SkVuSyWTQqL2hUXujX2DrazTqjSYYquuhUXtxGoU8CsOIh6qsrcfP/5kCQ3U9hoV1wW8fHix1SUQez0sh5xUt5JEYRjyQEAK/3nYGFwvK0L2zCmtnxrp87wQiV+cuzeWI2oNhxAN9cDgTX57Jh5dchjUzYxCkZWdVIim5att9IlvhpKSH+d93N/BW0kUA5ruM/ijc+W55TuRJGm5I2DiIAECBvhrzN6Ui6Vy+RJUROQ7DiAfJKa3EL7achkkAP4sNxcx7ekldEpFHM5oElu1KR0v9FRq2LduVDqPJ6TswEHUIw4iHqKo14vl/mu/AOzRUi+WPRvGSQCKJJWeVNhsRaUwAyNdXIzmr1HFFEUnA6jBy+PBhJCQkIDg4GDKZDDt37rzrMYcOHUJMTAxUKhX69u2LjRs3tqNUai8hBF7bfgYX8g3o1kmJtTNjeeM7IidQVNZ6EGnPfkSuyuowUlFRgejoaKxatapN+2dlZWHKlCkYO3Ys0tLS8Mtf/hLPPvss9u7da3Wx1D7rj2Th87Q8eMllWDUj5o7NmYjIcQL82rZ4vK37Ebkqq6+mmTRpEiZNmtTm/deuXYuIiAj86U9/AgAMGjQIR44cwZ///GdMmDDB2rcnKx3LKMbK/5gXrL4xZRDu6d1N4oqIqEFchD90WjUK9NUtrhuRAQjSmi/zJXJndl8zcvz4cYwbN67JtgkTJuD48eP2fmuPl3uzEi9uOQ2jSeCxmBDMGRUudUlE1IhCLkNiQiQAc/BorOF5YkIk+42Q27N7GCkoKEBgYGCTbYGBgTAYDKiqqmrxmJqaGhgMhiYPsk51nRHzNqWgtKIWUSEarPjpEC5YJXJCE6N0Lfb7CdKqsWZmDPuMkEdwyqZnK1euxLJly6Quw2UJIfD6jrM4d90Afy5YJXJ6E6N0GB8ZxA6s5LHsHkaCgoJQWFjYZFthYSE0Gg18fFpeSLl48WIsWrTI8txgMCAsLMyudbqTj45lY3vqdSjkMrw/fThCu/pKXRIR3YVCLkN8H67pIs9k9zASHx+PPXv2NNm2b98+xMfHt3qMSqWCSqWyd2lu6URmCZbvvgAAWDxpIEb16S5xRURERHdm9ZqR8vJypKWlIS0tDYD50t20tDRcu3YNgHlUY/bs2Zb9582bh8zMTPz617/GxYsXsXr1avzrX//CwoULbfMdkEXerSos2JwKo0ngkWHBeGZMhNQlERER3ZXVYeTUqVMYPnw4hg8fDgBYtGgRhg8fjqVLlwIA8vPzLcEEACIiIrB7927s27cP0dHR+NOf/oR//OMfvKzXxhoWrJZU1GKQToM3HxvKBatEROQSZEIIp7/pgcFggFarhV6vh0ajkbocpyOEwCvbzmBbSi66+Hpj14tjEObPdSJERCSttn5+8940bmDTiavYlpILuQz425PDGUSIiMilMIy4uG+yS7FsVzoA4NWJA3Fvvx4SV0RERGQdp+wzQi0zmkSTPgQ9/X0xf1Mq6k0CU4bq8Px9vaUukYiIyGoMIy4i6Vw+lu1Kb3K7cW+FDHVGgYFBfvjjE1ywSkRErolhxAUkncvH/E2pzW6kVWc0b5kxsid8lfyrJCIi18Q1I07OaBJYtiu9xTt6Nlh96AqMJqe/KIqIiKhFDCNOLjmrtMnUTEvy9dVIzip1UEVERES2xTDi5IrK7hxErN2PiIjI2TCMOLkAP/Xdd7JiPyIiImfDMOLk4iL8odO2HjRkAHRa8+3GiYiIXBHDiJNTyGVITIhs8bWGC3kTEyKhkPOyXiIick0MIy6gX6AfWsoaQVo11syMwcQoneOLIiIishE2p3ABv/8yHSYBPDAwAM/d29vSgTUuwp8jIkRE5PIYRpzcwUtFOHjpBrwVMrwxZRB69+gsdUlEREQ2xWkaJ1ZnNGH5l+ab4D01KpxBhIiI3BLDiBP7+PhVZN6oQLdOSvziwX5Sl0NERGQXDCNOqqS8Bu99fRkA8KsJA6BRe0tcERERkX0wjDipd/ddRll1PSJ1GkwdESZ1OURERHbDMOKELuQbsCX5GgD2ECEiIvfHMOJkhBD43S7zpbxThugwsnc3qUsiIiKyK4YRJ7P3fAGOZ5ZA5SXHa5MGSl0OERGR3bHPiB0YTQLJWaVWNyerrjPi97svAACev683wvx97V0qERGR5BhGbCzpXD6W7UpHvr7ask2nVSMxIfKubdvXH8lC7s0qBGnUmP/jPvYulYiIyClwmsaGks7lY/6m1CZBBAAK9NWYvykVSefyWz220FCNVQczAACvTRoIXyVzIhEReQaGERsxmgSW7UqHaOG1hm3LdqXDaGppD+DtpEuorDVieM8ueGRYsN3qJCIicjYMIzaSnFXabESkMQEgX1+N5KzSZq+l5dzCv1NzAQCJCYMhk/FSXiIi8hwMIzZSVNZ6ELnTfkIILNt1HgDweEwohoV1sXVpRERETo1hxEYC/NTt2u/ztDycvnYLvkoFfj1xgD1KIyIicmoMIzYSF+EPnVaN1iZYZDBfVRMX4W/ZVllbjzf/cxEAsGBsXwRq2hZoiIiI3AnDiI0o5DIkJkQCQLNA0vD8h63d1x66ggJDNcL8ffDMmAjHFEpERORkGEZsaGKUDmtmxiBI23SEI0irxpqZMU36jOSUVuLvhzMBAEsmD4LaW+HQWomIiJwFm1nY2MQoHcZHBt21A+ub/7mImnoT4nt3w4TBQRJVS0REJD2GETtQyGWI79P6De5OZpZg99l8yGXA0oRIXspLREQejdM0DtbQHA0AnozriUE6jcQVERERSYthxMH+dSoH6fkGaNReWDS+v9TlEBERSY5hxIEM1XV4Z+8lAMDL4/qjW2eVxBURERFJj2HEgf62/zuUVNSiT49OmB3fS+pyiIiInALDiINk3ijHxmPZAIA3fhIJbwVPPREREdDOMLJq1SqEh4dDrVZj5MiRSE5OvuP+7733HgYMGAAfHx+EhYVh4cKFqK5u271c3MUfdl9AnVFg7IAeGDsgQOpyiIiInIbVYeTTTz/FokWLkJiYiNTUVERHR2PChAkoKipqcf9PPvkEr732GhITE3HhwgWsX78en376KV5//fUOF+8q/nv5BvZfLIKXXIY3fhIpdTlEREROxeow8u677+K5557D008/jcjISKxduxa+vr7YsGFDi/sfO3YMo0ePxvTp0xEeHo6HHnoITz755F1HU9xFndGE5V+aL+WdMyocfXp0lrgiIiIi52JVGKmtrUVKSgrGjRv3/ReQyzFu3DgcP368xWNGjRqFlJQUS/jIzMzEnj17MHny5A6U7To2nbiKjKJy+HdS4qUH+0ldDhERkdOxqgNrcXExjEYjAgMDm2wPDAzExYsXWzxm+vTpKC4uxpgxYyCEQH19PebNm3fHaZqamhrU1NRYnhsMBmvKdBqlFbX4877LAIBfPTQAWh9viSsiIiJyPna/pOPQoUNYsWIFVq9ejdTUVGzfvh27d+/G8uXLWz1m5cqV0Gq1lkdYWJi9y7SLP++7DEN1PQbpNJj2I9f8HoiIiOzNqpGR7t27Q6FQoLCwsMn2wsJCBAW1fLO33/zmN5g1axaeffZZAMCQIUNQUVGB559/HkuWLIFc3jwPLV68GIsWLbI8NxgMLhdILhYYsPnkVQDA0p9ENrtRHhEREZlZNTKiVCoRGxuL/fv3W7aZTCbs378f8fHxLR5TWVnZLHAoFAoAgBCixWNUKhU0Gk2ThysRQmD5l+kwCWBSVNAdb5pHRETk6ay+a++iRYswZ84cjBgxAnFxcXjvvfdQUVGBp59+GgAwe/ZshISEYOXKlQCAhIQEvPvuuxg+fDhGjhyJjIwM/OY3v0FCQoIllLibb7Jv4mhGCZRecrw+eZDU5RARETk1q8PItGnTcOPGDSxduhQFBQUYNmwYkpKSLItar1271mQk5I033oBMJsMbb7yB69evo0ePHkhISMAf/vAH230XTmbDkSwAwOMxIQjz95W4GiIiIucmE63NlTgRg8EArVYLvV7v9FM2OaWVuP+PB2ESwL6F96FfoJ/UJREREUmirZ/fvEGKjW08lg2TAO7t151BhIiIqA0YRmyorLoOn36TAwB4ZkyExNUQERG5BoYRG/rsVC7Ka+rRp0cn3Nevh9TlEBERuQSGERsxmgQ2HssGAMwdEwE5+4oQERG1CcOIjXx9oRDXSivRxdcbjw0PlbocIiIil8EwYiMNl/NOj+sJH6V79k8hIiKyB4YRGzh3XY+TWaXwksswK76X1OUQERG5FIYRG9hw1DwqMnmIDjqtj8TVEBERuRaGkQ4qKqvGrm/zAJgXrhIREZF1GEY6aNPxq6gzCsT26ophYV2kLoeIiMjlMIx0QHWdEZtOXgPAJmdERETtxTDSAZ+nXUdpRS1CuvjgochAqcshIiJySQwj7SSEwIYj2QCAp0aFw0vBU0lERNQe/ARtp6MZJbhUWAZfpQJTfxQmdTlEREQui2GknRou5506IgxaH2+JqyEiInJdDCPtcOVGOQ5cLIJMZp6iISIiovZjGGmHjUezAQAPDgxEePdO0hZDRETk4hhGrHSrshbbUnIBAHPHhEtbDBERkRtgGLHS1m9yUFVnxMAgP8T37iZ1OURERC6PYcQKdUYTPjqWDcDc5Ewmk0lbEBERkRtgGLFC0rkC5Our0b2zEgnRwVKXQ0RE5BYYRqzQcDnvzHt6Qe2tkLgaIiIi98Aw0kap127i9LVbUCrkmDGyl9TlEBERuQ2GkTbacMQ8KvLIsGD08FNJXA0REZH7YBhpg+u3qvCfcwUAgKdH8+68REREtsQw0gYfH8+G0SQwqk83RAZrpC6HiIjIrTCM3EVFTT22nLwGAJjLUREiIiKbYxi5i+2puTBU1yO8my8eGBggdTlERERuh2HkDkwmgQ9v34fm6dERkMvZ5IyIiMjWGEbu4NDlImQWV8BP7YUnYkOlLoeIiMgtMYzcwYYj2QCAJ+N6opPKS9piiIiI3BTDSCsuFhhwJKMYchkwO55NzoiIiOyFYaQVH94eFZkUpUNoV19piyEiInJjDCMtKC6vwY606wCAuWPCpS2GiIjIzTGMtOCTk9dQW29CdFgXxPTsKnU5REREbo1h5Adq6o34+PhVAMDc0eGQyXg5LxERkT0xjPzAl9/mo7i8BkEaNSYP0UldDhERkdtjGGlECIENR8135509qhe8FTw9RERE9tauT9tVq1YhPDwcarUaI0eORHJy8h33v3XrFhYsWACdTgeVSoX+/ftjz5497SrYnk5mleJ8ngFqbzmmx/WUuhwiIiKPYHUnr08//RSLFi3C2rVrMXLkSLz33nuYMGECLl26hICA5vduqa2txfjx4xEQEIBt27YhJCQEV69eRZcuXWxRv01tOGIeFXk8JhRdfJUSV0NEROQZrA4j7777Lp577jk8/fTTAIC1a9di9+7d2LBhA1577bVm+2/YsAGlpaU4duwYvL29AQDh4eEdq9oOrpZUYN+FQgDm+9AQERGRY1g1TVNbW4uUlBSMGzfu+y8gl2PcuHE4fvx4i8d88cUXiI+Px4IFCxAYGIioqCisWLECRqOxY5Xb2MZj2RAC+PGAHugb0FnqcoiIiDyGVSMjxcXFMBqNCAwMbLI9MDAQFy9ebPGYzMxMHDhwADNmzMCePXuQkZGBF154AXV1dUhMTGzxmJqaGtTU1FieGwwGa8q0mqG6Dv/6JgcAMJejIkRERA5l98tFTCYTAgIC8MEHHyA2NhbTpk3DkiVLsHbt2laPWblyJbRareURFhZm1xr/9U0OKmqN6BfQGff2627X9yIiIqKmrAoj3bt3h0KhQGFhYZPthYWFCAoKavEYnU6H/v37Q6FQWLYNGjQIBQUFqK2tbfGYxYsXQ6/XWx45OTnWlGkVo0lg47FsAMDcMRFsckZERORgVoURpVKJ2NhY7N+/37LNZDJh//79iI+Pb/GY0aNHIyMjAyaTybLt8uXL0Ol0UCpbvmJFpVJBo9E0edjLvvQC5N6sQldfb/x0eIjd3oeIiIhaZvU0zaJFi7Bu3Tp89NFHuHDhAubPn4+KigrL1TWzZ8/G4sWLLfvPnz8fpaWlePnll3H58mXs3r0bK1aswIIFC2z3XXTA+tuX884Y2Qtqb8Vd9iYiIiJbs/rS3mnTpuHGjRtYunQpCgoKMGzYMCQlJVkWtV67dg1y+fcZJywsDHv37sXChQsxdOhQhISE4OWXX8arr75qu++inc7k3sI32TfhrZBhVnwvqcshIiLySDIhhJC6iLsxGAzQarXQ6/U2nbJZ+Gkadpy+jp8OD8Gfpw2z2dclIiKitn9+e/TNV/oGdEb3zkpezktERCQhjx4ZAYDaehOUXh6dyYiIiOyCIyNtxCBCREQkLX4SExERkaQYRoiIiEhSDCNEREQkKYYRIiIikhTDCBEREUmKYYSIiIgkxTBCREREkmIYISIiIkkxjBAREZGkGEaIiIhIUgwjREREJCmGESIiIpIUwwgRERFJykvqAqRiNAkkZ5WiqKwaAX5qxEX4QyGXSV0WERGRx/HIMJJ0Lh/LdqUjX19t2abTqpGYEImJUToJKyMiIvI8HjdNk3QuH/M3pTYJIgBQoK/G/E2pSDqXL1FlREREnsmjwojRJLBsVzpEC681bFu2Kx1GU0t7EBERkT14VBhJziptNiLSmACQr69Gclap44oiIiLycB4VRorKWg8i7dmPiIiIOs6jwkiAn9qm+xEREVHHeVQYiYvwh06rRmsX8MpgvqomLsLfkWURERF5NI8KIwq5DIkJkQDQLJA0PE9MiGS/ESIiIgfyqDACABOjdFgzMwZB2qZTMUFaNdbMjGGfESIiIgfzyKZnE6N0GB8ZxA6sRERETsAjwwhgnrKJ79NN6jKIiIg8nsdN0xAREZFzYRghIiIiSTGMEBERkaQYRoiIiEhSDCNEREQkKYYRIiIikhTDCBEREUmKYYSIiIgkxTBCREREknKJDqxCCACAwWCQuBIiIiJqq4bP7YbP8da4RBgpKysDAISFhUlcCREREVmrrKwMWq221ddl4m5xxQmYTCbk5eXBz88PMpntbmZnMBgQFhaGnJwcaDQam31dao7n2jF4nh2D59kxeJ4dw57nWQiBsrIyBAcHQy5vfWWIS4yMyOVyhIaG2u3razQa/kN3EJ5rx+B5dgyeZ8fgeXYMe53nO42INOACViIiIpIUwwgRERFJyqPDiEqlQmJiIlQqldSluD2ea8fgeXYMnmfH4Hl2DGc4zy6xgJWIiIjcl0ePjBAREZH0GEaIiIhIUgwjREREJCmGESIiIpKU24eRVatWITw8HGq1GiNHjkRycvId9//ss88wcOBAqNVqDBkyBHv27HFQpa7PmnO9bt063HvvvejatSu6du2KcePG3fXvhsys/TfdYOvWrZDJZHj00UftW6CbsPY837p1CwsWLIBOp4NKpUL//v3586MNrD3P7733HgYMGAAfHx+EhYVh4cKFqK6udlC1runw4cNISEhAcHAwZDIZdu7ceddjDh06hJiYGKhUKvTt2xcbN260b5HCjW3dulUolUqxYcMGcf78efHcc8+JLl26iMLCwhb3P3r0qFAoFOLtt98W6enp4o033hDe3t7i7NmzDq7c9Vh7rqdPny5WrVolTp8+LS5cuCCeeuopodVqRW5uroMrdy3WnucGWVlZIiQkRNx7773ikUcecUyxLsza81xTUyNGjBghJk+eLI4cOSKysrLEoUOHRFpamoMrdy3WnufNmzcLlUolNm/eLLKyssTevXuFTqcTCxcudHDlrmXPnj1iyZIlYvv27QKA2LFjxx33z8zMFL6+vmLRokUiPT1d/O1vfxMKhUIkJSXZrUa3DiNxcXFiwYIFludGo1EEBweLlStXtrj/1KlTxZQpU5psGzlypPj5z39u1zrdgbXn+ofq6+uFn5+f+Oijj+xVoltoz3mur68Xo0aNEv/4xz/EnDlzGEbawNrzvGbNGtG7d29RW1vrqBLdgrXnecGCBeKBBx5osm3RokVi9OjRdq3TnbQljPz6178WgwcPbrJt2rRpYsKECXary22naWpra5GSkoJx48ZZtsnlcowbNw7Hjx9v8Zjjx4832R8AJkyY0Or+ZNaec/1DlZWVqKurg7+/v73KdHntPc+/+93vEBAQgGeeecYRZbq89pznL774AvHx8ViwYAECAwMRFRWFFStWwGg0Oqpsl9Oe8zxq1CikpKRYpnIyMzOxZ88eTJ482SE1ewopPgtd4kZ57VFcXAyj0YjAwMAm2wMDA3Hx4sUWjykoKGhx/4KCArvV6Q7ac65/6NVXX0VwcHCz/wHoe+05z0eOHMH69euRlpbmgArdQ3vOc2ZmJg4cOIAZM2Zgz549yMjIwAsvvIC6ujokJiY6omyX057zPH36dBQXF2PMmDEQQqC+vh7z5s3D66+/7oiSPUZrn4UGgwFVVVXw8fGx+Xu67cgIuY4333wTW7duxY4dO6BWq6Uux22UlZVh1qxZWLduHbp37y51OW7NZDIhICAAH3zwAWJjYzFt2jQsWbIEa9eulbo0t3Lo0CGsWLECq1evRmpqKrZv347du3dj+fLlUpdGHeS2IyPdu3eHQqFAYWFhk+2FhYUICgpq8ZigoCCr9iez9pzrBu+88w7efPNNfP311xg6dKg9y3R51p7nK1euIDs7GwkJCZZtJpMJAODl5YVLly6hT58+9i3aBbXn37NOp4O3tzcUCoVl26BBg1BQUIDa2loolUq71uyK2nOef/Ob32DWrFl49tlnAQBDhgxBRUUFnn/+eSxZsgRyOX+/toXWPgs1Go1dRkUANx4ZUSqViI2Nxf79+y3bTCYT9u/fj/j4+BaPiY+Pb7I/AOzbt6/V/cmsPecaAN5++20sX74cSUlJGDFihCNKdWnWnueBAwfi7NmzSEtLszwefvhhjB07FmlpaQgLC3Nk+S6jPf+eR48ejYyMDEvYA4DLly9Dp9MxiLSiPee5srKyWeBoCICCt1mzGUk+C+22NNYJbN26VahUKrFx40aRnp4unn/+edGlSxdRUFAghBBi1qxZ4rXXXrPsf/ToUeHl5SXeeecdceHCBZGYmMhLe9vI2nP95ptvCqVSKbZt2yby8/Mtj7KyMqm+BZdg7Xn+IV5N0zbWnudr164JPz8/8eKLL4pLly6JL7/8UgQEBIjf//73Un0LLsHa85yYmCj8/PzEli1bRGZmpvjqq69Enz59xNSpU6X6FlxCWVmZOH36tDh9+rQAIN59911x+vRpcfXqVSGEEK+99pqYNWuWZf+GS3tfeeUVceHCBbFq1Spe2ttRf/vb30TPnj2FUqkUcXFx4sSJE5bX7r//fjFnzpwm+//rX/8S/fv3F0qlUgwePFjs3r3bwRW7LmvOda9evQSAZo/ExETHF+5irP033RjDSNtZe56PHTsmRo4cKVQqlejdu7f4wx/+IOrr6x1cteux5jzX1dWJ3/72t6JPnz5CrVaLsLAw8cILL4ibN286vnAXcvDgwRZ/3jac2zlz5oj777+/2THDhg0TSqVS9O7dW3z44Yd2rVEmBMe2iIiISDpuu2aEiIiIXAPDCBEREUmKYYSIiIgkxTBCREREkmIYISIiIkkxjBAREZGkGEaIiIhIUgwjREREJCmGESIiIpIUwwgRERFJimGEiIiIJMUwQkRERJL6/3iIr9SZjoflAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#2B"
      ],
      "metadata": {
        "id": "MD1tOXUNy-7U"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#2b\n",
        "data = np.genfromtxt(\"assign3fit.txt\")\n",
        "x, y = data[:, 0], data[:, 1]\n",
        "x, y"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "COVjhKRE3ExP",
        "outputId": "ec0a88f8-277d-410f-fa69-1e25c774991d"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0.  , 0.05, 0.1 , 0.15, 0.2 , 0.25, 0.3 , 0.35, 0.4 , 0.45, 0.5 ,\n",
              "        0.55, 0.6 , 0.65, 0.7 , 0.75, 0.8 , 0.85, 0.9 , 0.95, 1.  ]),\n",
              " array([0.486, 0.866, 0.944, 1.144, 1.103, 1.202, 1.166, 1.191, 1.124,\n",
              "        1.095, 1.122, 1.102, 1.099, 1.017, 1.111, 1.117, 1.152, 1.265,\n",
              "        1.38 , 1.575, 1.857]))"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "yerr = np.tile([0.001], x.shape[0])\n",
        "yerr"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KYMiTEQ_3Z6l",
        "outputId": "f5ed90a5-fa1c-4f89-fa45-2991da2a2524"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001,\n",
              "       0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001, 0.001,\n",
              "       0.001, 0.001, 0.001])"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "\n",
        "import numpy as np\n",
        "from matplotlib import pyplot as plt\n",
        "\n",
        "from assn_3_utils import mlcgList, gauss_seidel, gauss_elim\n",
        "\n",
        "def poly(n, x):\n",
        "    return x ** n\n",
        "\n",
        "def cheby(n, x):\n",
        "    chebyshev = {\n",
        "        0: 1,\n",
        "        1: x,\n",
        "        2: 2 * x ** 2 - 1,\n",
        "        3: 4 * x ** 3 - 3 * x,\n",
        "    }\n",
        "\n",
        "    return chebyshev[n]\n",
        "\n",
        "def polyfit(x, y, yerr, n=2, basis=\"poly\"):\n",
        "    \"\"\"\n",
        "    Polynomial Least-Squares Fitting\n",
        "\n",
        "    \"\"\"\n",
        "    bases = {\n",
        "        \"poly\": poly,\n",
        "        \"cheby\": cheby\n",
        "    }\n",
        "\n",
        "    basis = bases[basis]\n",
        "\n",
        "    N = n + 1\n",
        "    A = np.empty((N, N))\n",
        "    b = np.empty(N)\n",
        "\n",
        "    for i in range(N):\n",
        "        for j in range(N):\n",
        "            A[i, j] = np.sum(basis(i, x) * basis(j, x) / yerr ** 2)\n",
        "            b[j] = np.sum((basis(j, x) * y) / yerr ** 2)\n",
        "\n",
        "    # Using Gauss-Elimination to calculate x\n",
        "    return gauss_elim(A, b)"
      ],
      "metadata": {
        "id": "zbQCZb-V3_h0"
      },
      "execution_count": 27,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Cubic LSq fit"
      ],
      "metadata": {
        "id": "uibqZ7xy4F-s"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "_, (a0, a1, a2, a3), _ = polyfit(x, y, yerr, n=3)\n",
        "polytuple = (a0, a1, a2, a3)\n",
        "polytuple\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DzBHTNfh4EPH",
        "outputId": "d7594819-5749-4549-ca82-ddba17343e7c"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.5746586674194756,\n",
              " 4.7258614421437075,\n",
              " -11.128217777647695,\n",
              " 7.668677622912345)"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Cheby LSq fit\n",
        "_, (a0, a1, a2, a3), _ = polyfit(x, y, yerr, n=3, basis=\"cheby\")\n",
        "chebytuple = (a0, a1, a2, a3)\n",
        "chebytuple"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rzb3aXZD4I8t",
        "outputId": "6a4087df-e437-4335-d8ff-a9be9ccfca0c"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(-4.9894502214032475,\n",
              " 10.477369659326074,\n",
              " -5.564108888822789,\n",
              " 1.917169405727739)"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def func(x, a0, a1, a2, a3, basis=\"poly\"):\n",
        "    if basis == \"cheby\":\n",
        "        ch = cheby\n",
        "        return a0 * ch(0, x) + a1 * ch(1, x) + a2 * ch(2, x) + a3 * ch(3, x)\n",
        "\n",
        "    return a0 + a1 * x + a2 * x ** 2 + a3 * x ** 3\n"
      ],
      "metadata": {
        "id": "incKGAuR46BV"
      },
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fig, axs = plt.subplots(1, 2, figsize=(15,6))\n",
        "fig.suptitle(\"Plots\", fontsize=20)\n",
        "axs[0].plot(x, func(x, *polytuple), label=\"Polynomial LSQ\")\n",
        "axs[0].plot(x, y, label=\"Original Data\")\n",
        "axs[1].plot(x, func(x, *chebytuple, basis=\"cheby\"), label=\"Chebyshev LSQ\")\n",
        "axs[1].plot(x, y, label=\"Original Data\")\n",
        "\n",
        "axs[0].legend()\n",
        "axs[1].legend()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 582
        },
        "id": "POXaVTai49x8",
        "outputId": "40c76032-f14b-437b-b6ab-03a64c471d1d"
      },
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x600 with 2 Axes>"
            ],
            "image/png": 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x2WysWbOGG2+8kWbNmtG6dWsee+wxVq1aVejYEydOcMMNN+Dr60vTpk0LcsEztm3bRv/+/fH396dOnTqMHDmSEydOFDomPz+fBx98kKCgIGrVqsXzzz+PYRgAvPTSS7Rp0+a8GDt06MDzzz8PwOLFi+natSt+fn7UqFGDXr16cejQoULHf/3110RFRREUFMQtt9xCWlpawT6n08nrr79Ow4YN8fHxoX379kyfPr1gX/369fnoo48KXW/jxo3Y7fbz7lMU27dvZ//+/Xz44Yd0796dBg0a0KtXL1555RW6d+8OQGxsLOPGjeORRx7htddeo1WrVjRp0oRx48Yxfvx43nzzTVavXl3se4uISOVT5QpfhmGQmZtvydeZBKOkfHx8yM3NBcxH+datW8fs2bNZuXIlhmEwYMCAgmW9zxUVFcVVV13FhAkTCm2fMGECo0ePxm4/+zH/85//5M0332TdunW4u7tzxx13FOybOXMmDz/8MOPGjWPbtm3cc889jBkzht9//73QdV9++WVGjRrFpk2baNGiBcOHD+eee+7hmWeeYd26dRiGwYMPPnjR95mWlsbtt9/OsmXLWLVqFU2bNmXAgAGFEqjSqFu3Lvn5+cycOfOin8nUqVPx9/fnnnvuOW/fuHHjyMvL44cffnBJPCIiIuIalSHPS0pKYt68eTzwwAP4+fmdt//PPVpffPFFhg4dypYtWxgwYAAjRowgKSkJgOTkZK644gqio6NZt24d8+bN4+jRowwdOrTQNSZNmoS7uztr1qzhnXfe4a233uLzzz8H4I477mDnzp2sXbu24PiNGzeyZcsWxowZQ35+PoMHD6Z3795s2bKFlStXcvfddxda2XD//v3MmjWLOXPmMGfOHJYsWcK///3vgv2vv/46X331FR9//DHbt2/n0Ucf5bbbbmPJkiXY7XZuvfVWpkyZUijmyZMn06tXLxo0aFCk39dzhYaGYrfbmT59Og6H44LHTJ8+nby8vAvO7Lrnnnvw9/dn6tSpxb63iIhUPu5WB+BqWXkOWv1rviX33vFSP3w9i/9bahgGCxcuZP78+Tz00EPs3buX2bNns3z5cnr27AmYyUFERASzZs3i5ptvPu8ad911F/feey9vvfUWXl5ebNiwga1bt/Ljjz8WOu7VV1+ld+/eADz99NNce+21ZGdn4+3tzRtvvMHo0aO5//77AQpGJd944w369OlTcI0xY8YUJFxPPfUUPXr04Pnnn6dfv34APPzww4wZM+ai7/eKK64o9PrTTz+lRo0aLFmyhIEDBxb3t+883bt359lnn2X48OHce++9dO3alSuuuIJRo0ZRp04dAPbs2VMws+3PwsLCCAwMZM+ePaWORURERFynMuR5+/btwzAMWrRoUaTrjh49mltvvRWA1157jXfffZc1a9ZwzTXX8P777xMdHc1rr71WcPyXX35JREQEe/bsoVmzZgBERETw9ttvY7PZaN68OVu3buXtt99m7Nix1K9fn379+jFhwgS6dOkCmIOjvXv3plGjRiQlJZGSksLAgQNp3LgxAC1btiwUo9PpZOLEiQQEBAAwcuRIFi5cyKuvvkpOTg6vvfYaCxYsoEePHgA0atSIZcuW8cknn9C7d29GjBjBm2++yeHDh4mMjMTpdDJt2jSee+65Iv0e/Vl4eDjvvvsuTz75JC+++CKdO3emT58+jBgxgkaNGgFmrhcUFES9evXOO9/T05NGjRop1xMRqSaq3IyvymTOnDn4+/vj7e1N//79GTZsGC+88AI7d+7E3d2dbt26FRwbEhJC8+bN2blz5wWvNXjwYNzc3Jg5cyZgrvrYp08foqKiCh3Xrl27gu/PJAJnGr7v3LmTXr16FTq+V69e593z3GucKSS1bdu20Lbs7GxSU1MvGOvRo0cZO3YsTZs2JSgoiMDAQNLT0zl8+PAFjy+JV199lcTERD7++GNat27Nxx9/TIsWLdi6dWvBMX83cnuhopiIiLhQKWdKi1RExX0C4Ny8ys/Pj8DAwILcbPPmzfz+++/4+/sXfJ0pqJ3bVqJ79+6FZmj16NGDvXv3FsyGGjt2LFOnTiU7O5vc3FymTJlSMOs/ODiY0aNH069fPwYNGsQ777xDQkJCoRijoqIKil5g5pBnYty3bx+ZmZn07du3UJxfffVVQYwdOnSgZcuWBbO+lixZwrFjxy44mFtUDzzwAImJiUyePJkePXrw/fff07p1a3777bciX0O5nohIGapAeV6Vm/Hl4+HGjpf6WXbv4ujTpw8fffQRnp6ehIWF4e5e8o/D09OTUaNGMWHCBIYMGcKUKVN45513zjvOw8Oj4PszCZLT6SzWvS50jeJc9/bbb+fkyZO88847NGjQAC8vL3r06FHwmKerhISEcPPNN3PzzTfz2muvER0dzRtvvMGkSZNo2rQpy5YtIzc397ykJz4+ntTU1IJRVBERKSM/PQzJh+CyJyGq198fL9VeZcjzmjZtis1mO291wYs5N4cCM486k0Olp6czaNAg/vOf/5x33oVmMl3MoEGD8PLyYubMmXh6epKXl8dNN91UsH/ChAn84x//YN68eXz77bc899xz/PbbbwX9sv4uRoCff/6Z8PDwQsd5eXkVfD9ixAimTJnC008/zZQpU7jmmmtKvfhRQEAAgwYNYtCgQbzyyiv069ePV155hb59+9K0aVNSUlKIj48nLCys0Hm5ubns37+/4GkFEREpA4tehkMrodfD0PwaS0OpcjO+bDYbvp7ulnydO9JWFH5+fjRp0oTIyMhCRa+WLVuSn59fqOHmyZMn2b17N61atbro9e666y4WLFjAhx9+SH5+PkOGDClWPC1btmT58uWFti1fvvwv71kSy5cv5x//+AcDBgygdevWeHl5ndek1dU8PT1p3LhxwaqOt956K+np6XzyySfnHfvGG2/g7e3NsGHDyjQmEZFqzemE3b/AgcXgzLc6GqkkKkOeFxwcTL9+/fjggw8KrSZ9xrmrDv6djh07sn37dqKiomjSpEmhr3P7h/25SfuZHqpubmaxzt3dndtvv50JEyYwYcIEbrnlFnx8fAqdEx0dzTPPPMOKFSto06bNeT25LqZVq1Z4eXlx+PDh82KMiIgoOG748OFs27aN9evXM336dEaMGFHk34eisNlstGjRouD3/KabbsLd3Z0333zzvGM//vhjMjMzGTVqlEtjEBGRc+yZD4dXQG661ZFUvRlfVUHTpk25/vrrGTt2LJ988gkBAQE8/fTThIeHc/3111/0vJYtW9K9e3eeeuop7rjjjvMSmr/zxBNPMHToUKKjo7nqqqv46aefmDFjBgsWLCjtWyqkadOmfP3113Tu3JnU1FSeeOKJYscKkJKSwqZNmwptCwkJYfPmzUybNo1bbrmFZs2aYRgGP/30E3Pnzi1YAKBHjx48/PDDPPHEE+Tm5jJ48GDy8vL45ptvePfdd5k4cWKpRyFFROQvHN0GGcfAww8iu1sdjYhLffDBB/Tq1YuuXbvy0ksv0a5dO/Lz8/ntt9/46KOPLtq64s8eeOABPvvsM2699VaefPJJgoOD2bdvH9OmTePzzz8vKGwdPnyYxx57jHvuuYcNGzbw3nvvnVfwueuuuwp6d5070BkTE8Onn37KddddR1hYGLt372bv3r1FLgoFBATw+OOP8+ijj+J0OrnkkktISUlh+fLlBAYGcvvttwPm45I9e/bkzjvvxOFwcN111/3ttbOyss7L9QICAkhLS+P//u//GDlyJK1atcLT05MlS5bw5Zdf8tRTTwEQGRnJf//7Xx5//HG8vb0ZOXIkHh4e/Pjjjzz77LO88sorF1ztUkREXCAt0cz1sEGjPn97eFlT4auCmjBhAg8//DADBw4kNzeXyy67jLlz55431fzP7rzzTlasWFFotcaiGjx4MO+88w5vvPEGDz/8MA0bNmTChAlcfvnlJXwXF/bFF19w991307FjRyIiInjttdcuuOLO31m8eDHR0dGFtt155508++yz+Pr6Mm7cOGJjY/Hy8qJp06Z8/vnnjBw5suDY//3vf7Rr144PP/yQ5557juzsbDw9PVm0aBGXXXZZqd+niIj8hf0LzV8bXgruXn99rEgl06hRIzZs2MCrr77KuHHjSEhIIDQ0lE6dOvHRRx8V+TphYWEsX76cp556iquvvpqcnBwaNGjANddcU2jV7lGjRpGVlUXXrl1xc3Pj4Ycf5u677y50raZNm9KzZ0+SkpIK9ZH19fVl165dTJo0iZMnT1KvXj0eeOCBC658fTEvv/wyoaGhvP766xw4cIAaNWrQsWNHnn322ULHjRgxgvvvv59Ro0YVadBzz5495+V6V155JdOmTSMqKooXX3yRgwcPYrPZCl4/+uijBcc++uijNGrUiDfffJN33nmnYDbY1KlTueWWW4r8/kREpJj2LzJ/DYsGP+snlNiM4nbgtEBqaipBQUGkpKQQGBhYaF92djYxMTE0bNgQb29viyKsOF5++WW+//57tmzZYnUolc7Bgwfp3bs3PXr0YPLkyQWjqH+mP3MiIi4wcSAc/AP6j4dud//98SXwV/mDVBzK88qHYRg0bdqU+++/n8cee8zqcCyRlJTElVdeSWBgIL/88gu+vr4XPE5/7kRESmn6HbDtB4xLH8d25fNlcovi5HlVrsdXdZWens62bdt4//33eeihh6wOp1KKiopi8eLFtGjR4rxp9SIi4kI56XB4FQBj/ghkyZ7jFgckUrUdP36c999/n8TERMaMGWN1OJYJDg5mwYIFXHnllaxcudLqcEREqianA/b/DsA/1gbz0+Z4iwPSo45VxoMPPsjUqVMZPHhwiR5zFFPDhg154YUXrA5DRKRqO/gHOPM4YtTm9xP+POBZvFWRRaR4ateuTa1atfj000+pWbOm1eFYKiQkhH/9619WhyEiUnUlbIKsJNLx5Zfk+lzrVrxFAMuCCl9VxMSJE5k4caLVYYiIiPy9fWZ/r8WOtoQGeNMxsnr/R1ykrFWCziYiIlJV7DP7ey1ztMbdw5PLmoVaHJAedRQREZHydrqx/RJne65uVQe73fqRQBERERFxgYI8rx29m4Xi62n9fCsVvkRERKT8JB2ApAPk48ZKZyuuaVPX6ohERERExBWyUyB2DQBLHe0qTJ6nwpeIiIiUn9OPOa53NsXuHUj3RtYvcS0iIiIiLnBgCRgO9jvrcdRemyta1LE6IkCFLxERESlP+82+D0sc7biqVR083JSKiIiIiFQJpx9zXOpsR88mtQjy8bA4IJOyTRERESkf+bkYMUsBMyG6pnXFmP4uIiIiIqVkGAWN7ZdUsDxPhS8REREpH0fWYMtN54QRyAH3xhVilR8RERERcYGT+yDlMDmGO2uMlvRtVTEecwQVviqtgwcPYrPZ2LRpU5HPmThxIjVq1LA8DhERqaZO9/f6w9mWy1vUwdvDzeKARCom5XkiIlLpnM7z1jhb0KZBGKEBXhYHdFaxC19Lly5l0KBBhIWFYbPZmDVr1t+eM3nyZNq3b4+vry/16tXjjjvu4OTJkyWJt0qJjY3ljjvuICwsDE9PTxo0aMDDDz9cpN+biIgIEhISaNOmTZHvN2zYMPbs2VOakEvk8ssvx2azYbPZ8PLyIjw8nEGDBjFjxoxiX+uFF16gQ4cOrg9SRETK3pm+D4529KtA09/lLOV5rqM8T3meiEi1sm8BYLaz6FdBVnM8o9iFr4yMDNq3b88HH3xQpOOXL1/OqFGjuPPOO9m+fTvff/89a9asYezYscUOtio5cOAAnTt3Zu/evUydOpV9+/bx8ccfs3DhQnr06EFSUtJFz83NzcXNzY26devi7u5e5Hv6+PhQu3ZtV4RfbGPHjiUhIYH9+/fzww8/0KpVK2655RbuvvtuS+IREZFyln4MEjYDsNLWjj4trPl5JH9NeZ5rKM9TniciUq3kZWMcXAaYha+rK9BjjlCCwlf//v155ZVXuOGGG4p0/MqVK4mKiuIf//gHDRs25JJLLuGee+5hzZo1xQ62KnnggQfw9PTk119/pXfv3kRGRtK/f38WLFhAXFwc//znPwuOjYqK4uWXX2bUqFEEBgZy9913X3Dq+ezZs2natCne3t706dOHSZMmYbPZSE5OBs6fAn9mVO3rr78mKiqKoKAgbrnlFtLS0gqOmTdvHpdccgk1atQgJCSEgQMHsn///mK/X19fX+rWrUv9+vXp3r07//nPf/jkk0/47LPPWLBgQcFxTz31FM2aNcPX15dGjRrx/PPPk5eXVxD/iy++yObNmwtGFidOnAjAW2+9Rdu2bfHz8yMiIoL777+f9PT0YscpIiJlZP/vAGx3NqBFkyYEeleMVX6kMOV5rqE8T3meiEi1cngltvwsEo2aeNRrTUSwr9URFVLmPb569OhBbGwsc+fOxTAMjh49yvTp0xkwYMBFz8nJySE1NbXQV5EZBuRmWPNlGEUKMSkpifnz53P//ffj4+NTaF/dunUZMWIE3377LcY513vjjTdo3749Gzdu5Pnnnz/vmjExMdx0000MHjyYzZs3c8899xRKqi5m//79zJo1izlz5jBnzhyWLFnCv//974L9GRkZPPbYY6xbt46FCxdit9u54YYbcDqdRXqvf+X222+nZs2ahabCBwQEMHHiRHbs2ME777zDZ599xttvvw2YU/jHjRtH69atSUhIICEhgWHDhgFgt9t599132b59O5MmTWLRokU8+eSTpY5RRERc5JzlrSvSKj9SOsrzzqc8z6Q8T0SkGjmd5/3haMs1bepZHMz5ij5/uoR69erF5MmTGTZsGNnZ2eTn5zNo0KC/nEL/+uuv8+KLL5bshnmZ8FpYCaMtpWfjwdPvbw/bu3cvhmHQsmXLC+5v2bIlp06d4vjx4wVT1q+44grGjRtXcMzBgwcLnfPJJ5/QvHlzxo8fD0Dz5s3Ztm0br7766l/G4nQ6mThxIgEBAQCMHDmShQsXFpx34403Fjr+yy+/JDQ0lB07dhSr78SF2O12mjVrVui9PPfccwXfR0VF8fjjjzNt2jSefPJJfHx88Pf3x93dnbp1C/+n6ZFHHil03iuvvMK9997Lhx9+WKoYRUTEBZxOHHsX4gYsdbbnvQo2/V1KTnne+ZTnmZTniYhUH2fyvCXO9jxSwfp7QTnM+NqxYwcPP/ww//rXv1i/fj3z5s3j4MGD3HvvvRc955lnniElJaXgKzY2tqzDtIRRxJFDgM6dO//l/t27d9OlS5dC27p27fq3142KiipIhgDq1avHsWPHCl7v3buXW2+9lUaNGhEYGEhUVBQAhw8fLnLsf8UwDGw2W8Hrb7/9ll69elG3bl38/f157rnninSvBQsWcOWVVxIeHk5AQAAjR47k5MmTZGZmuiROEREphaNbccs6QbrhjS2yG7X8K84qP1I6yvMuTnme8jwRkWohNQG34ztwGjbigrvSpHbA359Tzsp8xtfrr79Or169eOKJJwBo164dfn5+XHrppbzyyivUq3f+NDgvLy+8vEqYFHv4miNyVvAo2nOsTZo0wWazsXPnzgv20Ni5cyc1a9YkNDS0YJuf39+PMJaEh0fhHis2m63Q9PZBgwbRoEEDPvvsM8LCwnA6nbRp04bc3NxS39vhcLB3796CRG7lypWMGDGCF198kX79+hEUFMS0adN48803//I6Bw8eZODAgdx33328+uqrBAcHs2zZMu68805yc3Px9a1YzxeLiFQ7p5e3XulsRd+2ERYHI66kPO98yvNMyvNERKqJ0485bjEa0bNtM4uDubAyL3xlZmaetyKNm5sbULyRsCKz2Yo0Dd1KISEh9O3blw8//JBHH320UP+HxMREJk+ezKhRowqNkP2d5s2bM3fu3ELb1q5dW6o4T548ye7du/nss8+49NJLAVi2bFmprnmuSZMmcerUqYJp9itWrKBBgwaFelYcOnSo0Dmenp44HI5C29avX4/T6eTNN9/EbjcnMX733Xcui1NEREond/dveGL297pP/b2qFOV551OeZ1KeJyJSPTj2Ljj9mGM7rmld8fp7QQkedUxPT2fTpk0Fq8zExMSwadOmgmnKzzzzDKNGjSo4ftCgQcyYMYOPPvqIAwcOsHz5cv7xj3/QtWtXwsIs6tFQAbz//vvk5OTQr18/li5dSmxsLPPmzaNv376Eh4f/bc+GP7vnnnvYtWsXTz31FHv27OG7774rWAmnOInVuWrWrElISAiffvop+/btY9GiRTz22GMlulZmZiaJiYkcOXKEVatW8dRTT3Hvvfdy33330adPHwCaNm3K4cOHmTZtGvv37+fdd99l5syZha4TFRVV8GfuxIkT5OTk0KRJE/Ly8njvvfc4cOAAX3/9NR9//HGJ4hQRERfLScM9zlzh71jtXoTV8PmbE8RKyvNcQ3me8jwRkWrB6cCxz1y5e6dvF9qEB1oc0IUVu/C1bt06oqOjiY6OBuCxxx4jOjqaf/3rXwAkJCQUelZ/9OjRvPXWW7z//vu0adOGm2++mebNmxda4aU6atq0KevWraNRo0YMHTqUxo0bc/fdd9OnTx9WrlxJcHBwsa7XsGFDpk+fzowZM2jXrh0fffRRwYhaSR8nsNvtTJs2jfXr19OmTRseffTRgqaqxfXZZ59Rr149GjduzJAhQ9ixYwfffvttoaak1113HY8++igPPvggHTp0YMWKFeetbHTjjTdyzTXX0KdPH0JDQ5k6dSrt27fnrbfe4j//+Q9t2rRh8uTJvP766yWKU0REXCzmD+xGPoectWnfvqPV0cjfUJ7nGsrzlOeJiFQL8ZvwzE0m1fAlvM2lJR6MKWs2o0zmobtWamoqQUFBpKSkEBhYuIKYnZ1NTEwMDRs2xNvb26IIK6ZXX32Vjz/+uMo2jbWK/syJiBRdzo+P4rXxS77K78slD0+kUah/ud37r/IHqTiU55WM8ryyoz93IiJF4/j9P7gteY25jq7UuuNbujYs3sBOaRQnzyvzHl9Sfj788EO6dOlCSEgIy5cvZ/z48Tz44INWhyUiItVY3p7f8AL2BXZlVDkWvUSqGuV5IiJS0aRvn0cQsMEjmmca1LQ6nItS4asK2bt3L6+88gpJSUlERkYybtw4nnnmGavDEhGR6urkfvwzYskz3KjV9iqroxGp1JTniYhIhZKVjP+JzQC4N+uLm71iPuYIKnxVKW+//TZvv/221WGIiIgAZ1dzXG8044p2ja0OR6RSU54nIiIVifPAYtxwsM8ZRvfo9laH85eK3dxeREREpCiSt84DYJNnJ1qHqceWiIiISFVxcvMvAKy0daBn41oWR/PXVPgSERER18vPJfDoKgDcm15VYVf5EREREZFiMgw8Dy4GIDOiN57uFbu0VLGjKwan02l1CFJN6M+aiMjfyzu4Cm9nFseNQDp0vdTqcKSS089eKU+VYNF7ERFLGcd3E5SbSI7hQcPOV1sdzt+q9D2+PD09sdvtxMfHExoaiqenp0aVpUwYhkFubi7Hjx/Hbrfj6elpdUgiIhVWwoY5RAJr7R24pkGI1eFIJaU8T8qbYRgcP34cm82Gh4eH1eGIiFRIiRt/ph6wjhZc0irS6nD+VqUvfNntdho2bEhCQgLx8fFWhyPVgK+vL5GRkdjtVWbCpIiIy7kfWARAekRv7BV4lR+p2JTniRVsNhv169fHzc3N6lBERCqk7J2/ARBfqye9PCt+WaniR1gEnp6eREZGkp+fj8PhsDocqcLc3Nxwd3fXaLOIyF9wpB4lLHsvAJFdBlocjVR2yvOkvHl4eKjoJSJyMXnZ1EteD0DNdv0tDqZoqkThCyiYjqwpySIiItY6uOYnGgM7aUinVs2sDkeqAOV5IiIiFUP81kWEkUuiEUyXLr2sDqdI9KyWiIiIuFTGjl8BiA/piYebUg0RERGRquLYhp8B2OPfhSDfytH3WtmoiIiIuIzhdBCRtBKAwLbXWByNiIiIiLhSzYQ/ALA3vcriSIpOhS8RERFxmX1bVlKTVDIMb9p272t1OCIiIiLiIomx+2ngOITDsNGi53VWh1NkKnyJiIiIyySsnwPAPv+OeHv7WByNiIiIiLjKvpWzAdjv2YxatetaHE3RqfAlIiIiLhMUv9T8pvGV1gYiIiIiIi7ldmARAOn1e1scSfGo8CUiIiIusf9IPK3ydwHQqEflmf4uIiIiIn/tZGomLbPWAxDeeaDF0RSPCl8iIiLiErtW/IyHzUGiexgB9ZpZHY6IiIiIuMjGVQupYcsg3eZHnRa9rA6nWFT4EhEREZew7Tenv6eGX2ZxJCIiIiLiSunbfwUgMaQ7uLlbHE3xqPAlIiIipXYkKYM2WWsBqNvxWoujERERERFXSc3OI/LUSgAC2/SzOJriU+FLRERESm3lurVE2o+TjzuBLa6wOhwRERERcZFlW/bS3rYPgNrRlW+AU4UvERERKbXUrfMBOF6zA3j5WxuMiIiIiLhM3IZ5uNkMTvhEQVB9q8MpNhW+REREpFSOp+UQlWxOf/drVfmmv4uIiIjIhWXnOagR/4f5ovGV1gZTQip8iYiISKks3HaE7vYdAAS2ucbiaERERETEVf7Yc5xetk0AhLQfYG0wJaTCl4iIiJRKzMaF+NlyyPQIgTptrA5HRERERFxk44bVhNmSyLN5YovqZXU4JaLCl4iIiJRYSlYewQnm9HdHo8vBrtRCREREpCrIczix7V8IQEbdbuDhY3FEJaPsVEREREps0a6jXGrbDEBAaz3mKCIiIlJVrD6QRFfHRgAC21TePq4qfImIiEiJrdi0g1b2Q+aLRn2sDUZEREREXGbB1oN0s+8EwN70KoujKTkVvkRERKREsnId2GN+N7+v1Qb8Qy2OSERERERcwek0OLn9d7xteeT41IHQFlaHVGIqfImIiEiJLNlznB7GJgC8W1Te6e8iIiIiUtjG2FO0z1kPgHvzq8FmsziiklPhS0RERErk123xXGrfCoCtyZUWRyMiIiIirjJvWyKX2bcA4Na0cud5KnyJiIhIseXmO4nbtZoQWxoOD3+I6Gp1SCIiIiLiAoZhsGHrNprZ4zCwQ6PLrQ6pVFT4EhERkWJbeeAknfM2AGBvdBm4eVgckYiIiIi4wo6EVBqnrQHAGd4RfGpaHFHpqPAlIiIixTZvWyKXuZnT3/WYo4iIiEjVMX/7UXrbNwPg1qTyruZ4hgpfIiIiUiwOp8GK7QfoaNtrbmiswpeIiIhIVfHb1jgusW8zX6jwJSIiItXN+kOnaJ61EQ+bAyO4MQQ3tDokEREREXGBA8fT8Tm+iSBbJk7vGhDe0eqQSk2FLxERESmWc1f50WOOIiIiIlXH/O1HC9pZ2BtdDnY3awNyARW+REREpMgMw2D+tgR6ny586TFHERERkapj3vazA5xUkQFOFb5ERESkyLbFpeKZGkOE/TiG3QOiLrE6JBERERFxgfjkLA7GHqG9bb+5oYoMcKrwJSIiIkU2b3vC2cccI7uDl7/FEYmIiIiIK/y6PZFL7NtwsxkQ2gKCwq0OySVU+BIREZEiO7e/V1VY5UdERERETIUfc6w6eZ4KXyIiIlIk+46lEXs8mR72HeaGKtL3QURERKS6O5mew5qYkwWN7Wl8hbUBuZAKXyIiIlIk87cfpZN9D762HPCvA3XaWB2SiIiIiLjAgp1HaUwc9WxJ4O4NDXpaHZLLqPAlIiIiRTJvWyK97ZvNF42vAJvN2oBERERExCXmbz/KZWfyvAa9wMPH2oBcSIUvERER+VtHTmWyNS6F3mf6PlSRVX5EREREqru07DyW7T1xNs+rYu0sVPgSERGRvzV/+1FCOUVL+2HABo37WB2SiIiIiLjA77uPY3dk0d1tl7mhig1wqvAlIiIif2v+tkQus281X4R1AL9alsYjIiIiIq4xf1si3ey78CQPAutDaHOrQ3IpFb5ERETkLx1Py2HtoaRzVvmpWqOAIiIiItVVdp6D33cf47KCxxyrXh9XFb5ERETkL/224yg2w0kf923mhirW90FERESkuvpj7wkycx1c4XF6Zn8VHOBU4UtERET+0rztibSxxRBopIJnANTvYnVIIiIiIuIC87YlEsYJGhpHwGaHRr2tDsnlVPgSERGRi0rJymPFvhNnp7836g1uHtYGJSIiIiKlludwsmDn0bPtLMI7g09Na4MqA8UufC1dupRBgwYRFhaGzWZj1qxZf3tOTk4O//znP2nQoAFeXl5ERUXx5ZdfliReERERKUeLdh0l32nQz3u7uaHxFdYGJGVKeZ6IiEj1sfpAEilZeVzlUbXbWbgX94SMjAzat2/PHXfcwZAhQ4p0ztChQzl69ChffPEFTZo0ISEhAafTWexgRUREpHzN33aUADJp7dhtbqiiCZGYlOeJiIhUH/O2J+CGg172beAEmlxldUhlotiFr/79+9O/f/8iHz9v3jyWLFnCgQMHCA4OBiAqKqq4txUREZFylpXrYPGeY/S2b8eOA0KaQM0oq8OSMqQ8T0REpHpwOg1+3X6U9rb9+DjTzUccw6KtDqtMlHmPr9mzZ9O5c2f++9//Eh4eTrNmzXj88cfJysq66Dk5OTmkpqYW+hIREZHytWTPcbLznPT3OfOYo2Z7SWHK80RERCqnjbHJHEvLoa/n6cccG10OdjdLYyorxZ7xVVwHDhxg2bJleHt7M3PmTE6cOMH999/PyZMnmTBhwgXPef3113nxxRfLOjQRERH5C/O3JwIGl7ttAQd6zFHOozxPRESkcjLzPBjgsx2yqdIDnGU+48vpdGKz2Zg8eTJdu3ZlwIABvPXWW0yaNOmio4HPPPMMKSkpBV+xsbFlHaaIiIicIzU7j3nbEmlkS6BGbiK4eULUJVaHJRWM8jwREZHKJ8/hZObGOGqQRmT2LnNjFV7AqMxnfNWrV4/w8HCCgoIKtrVs2RLDMDhy5AhNmzY97xwvLy+8vLzKOjQRERG5iJkb4sjKc3Bj0G7IASJ7gKef1WFJBaM8T0REpPL5bcdRjqflcKvvbmxOA2q3gqBwq8MqM2U+46tXr17Ex8eTnp5esG3Pnj3Y7Xbq169f1rcXERGRYjIMg29WHQLguoCd5kY95igXoDxPRESk8jmT5w0P2WtuqMKzvaAEha/09HQ2bdrEpk2bAIiJiWHTpk0cPnwYMKevjxo1quD44cOHExISwpgxY9ixYwdLly7liSee4I477sDHx8c170JERERcZk1MEnuPpRPk4aB+ygZzYxXu+yBnKc8TERGp2vYfT2fF/pPYbQatMteaG6v4AGexC1/r1q0jOjqa6GhzmcvHHnuM6Oho/vWvfwGQkJBQkBwB+Pv789tvv5GcnEznzp0ZMWIEgwYN4t1333XRWxARERFX+ma1+XP8oSYnsOVlgn9dqNPa4qikPCjPExERqdomrzJ/jt/WKBO3jERw94HInhZHVbaK3ePr8ssvxzCMi+6fOHHiedtatGjBb7/9VtxbiYiISDk7npbDvG0JAFwfcE6zU5vNwqikvCjPExERqbqych1MX28uKjMqdB/EAVG9wMPb2sDKWJn3+BIREZHK47t1seQ5DNrXDyI0bpG5sYpPfxcRERGpDn7aEk9qdj4RwT40TlpqbqwG7SxU+BIREREAHE6DqWvM6e+PND0OJ/eChx80vdriyERERESktCafbmp/f2sntsMrwWaHVtdZHFXZU+FLREREAFi65zhHTmUR6O3OZalzzI1tbwTvQGsDExEREZFS2Xokhc1HUvBwszHY+au5sWk/CKr6qzCr8CUiIiLA2aWtR7YPwG3XbHNjpzEWRiQiIiIirjB5tZnnDWoVjM+O78yNnatHnqfCl4iIiHDkVCaLdh8DYIzfCnDkQr32EN7R4shEREREpDRSs/P4cVM8AA/U2Q5ZpyAoAppcZXFk5UOFLxEREWHqmsMYBvRsFEyt3VPNjZrtJSIiIlLpzVh/hKw8B83q+NPo8Pfmxo6jwO5mbWDlRIUvERGRai4338m3a82lrf/ROBFO7gNPf2h7k8WRiYiIiEhpGIbBN6vNxYseaJN3uqm9G0TfZnFk5UeFLxERkWpu/vZETqTnUjvAi64nfzQ3tr0JvAKsDUxERERESmV1TBL7jqXj6+lG/+z55sZm10BgmLWBlSMVvkRERKq5M03tx7T3w77r9GqOesxRREREpNI7k+fd2K4Wntu/NTdWk6b2Z6jwJSIiUo3tO5bG6pgk7DYY4b0MnHkQFg1hHawOTURERERK4XhaDvO3JwJwT61NkJ0CQZHQ+AprAytnKnyJiIhUY9+sMns+XNUilMAdU8yNmu0lIiIiUul9ty6WPIdBdGQN6u//ztzYqfo0tT9DhS8REZFqKjM3nx82HAHg/qh4SDoAngHQ5kaLIxMRERGR0nA4Daacbmp/X8tciF0NdneIHmlxZOVPhS8REZFq6qfN8aRl5xMZ7Ev7ozPNje2Ggpe/tYGJiIiISKks2XOMuOQsgnw8uCLjZ3Nj8/4QUNfawCygwpeIiEg1deYxxzuj/bCdaWpfzZqdioiIiFRFZ/K8WzvUwn3rmcccq2eep8KXiIhINbQ5NpmtcSl4utm5yb4EnPkQ3hnqtrU6NBEREREphdikTH7ffQyAO2tuhJwUqBkFjfpYG5hFVPgSERGphs4sbX1tm9r4bfvG3KjZXiIiIiKV3tQ1hzEMuKRJLUJ3n168qOPtYK+eJaDq+a5FRESqsZTMPH7aEg/AfZGxcOogeAVB6yHWBiYiIiIipZKb7+S7dbEA3NciE+LWnW5qf5vFkVlHhS8REZFq5ocNR8jOc9KibgBNj0w3N7YfBp6+1gYmIiIiIqUyb3siJ9JzqRPoRY9Ts82NLQaCf21rA7OQCl8iIiLViGEYTF5tPuZ4VwdfbLvmmjuqabNTERERkarkTDuLkR1rYd/6vbmxmrezUOFLRESkGll54CT7j2fg6+nGIOdCMBwQ0Q3qtLI6NBEREREphb1H01gTk4Sb3cZt/usgNw2CG0HUZVaHZikVvkRERKqRyaeXtr6hQ128Np9uaq/ZXiIiIiKV3uTVZp53ZYva1NhxJs8bXW2b2p9Rvd+9iIhINXIsNZv52xMBuCfsEKQcBu8gaD3Y2sBEREREpFQyc/P5Yf0RAO5tlgbxG8HuAR1GWByZ9VT4EhERqSa+XRtLvtOgY2QNImO+NTe2vxU8fKwNTERERERKZfameNJy8mkQ4kv0sVnmxpaDwK+WpXFVBCp8iYiIVAMOp8HUNeb097vae8OeeeYOPeYoIiIiUqkZhsE3pxcvGt0pBNu206t2V/Om9meo8CUiIlIN/L7rGPEp2dT09aBvzm9mU/vIHlC7hdWhiYiIiEgpbD6Swra4VDzd7Qz1XgO56RDSBKIutTq0CkGFLxERkWrgzCjg0E5heGz62tyo2V4iIiIild43q8w8b2Dbevht/crc2Gk02GzWBVWBqPAlIiJSxcUmZbJkz3EAxtTZD6lHwKcmtLre4shEREREpDSSM3P5aXM8AGObJEPCZnDzhPbDrQ2sAlHhS0REpIqbvPowhgGXNq1F3T1TzY3th4OHt7WBiYiIiEip/LAhjpx8Jy3qBtDiyA/mxlbXg1+ItYFVICp8iYiIVGE5+Q6+WxcLwJ1tPWHvfHNHp9HWBSUiIiIipWYYBpNPt7MY0zkE27bThS+1syhEhS8REZEqbN62RJIycqkb6M1l6b+A4YQGl0BoM6tDExEREZFSWLn/JAeOZ+Dn6cb1bsshLwNqNYcGPa0OrUJR4UtERKQKm7zqMAC3dqmHfePppvZa2lpERESk0juzeNEN0WF4b1JT+4tR4UtERKSK2p2YxpqDSbjZbYwK2QNp8eAbAi0HWR2aiIiIiJTCsdRsft1+FIC7Gp2Co1vBzQva32JxZBWPCl8iIiJV1JmeD31b1qHmzsnmxg7Dwd3LwqhEREREpLSmrY0l32nQuUFNomK+Mze2vgF8g60NrAJS4UtERKQKysjJZ8aGOADubOMOe38zd6jZqYiIiEillu9wMnWN2c5iTKeacKapvdpZXJAKXyIiIlXQj5viSc/JJyrEl85JswEDGl4GIY2tDk1ERERESmHRrmMkpGRT09eDq/OXQH4WhLaEiG5Wh1YhqfAlIiJSxRiGwTerzMccb+sShm3jN+YOzfYSERERqfS+WW3O9hraqT4emyaZGzuPUVP7i1DhS0REpIrZGJvMjoRUPN3t3BK0A9ITwbcWtBhodWgiIiIiUgqHT2aydM9xAMY0OAbHdoC7N7QbZnFkFZcKXyIiIlXMmdleA9vVw3/76dle0SPA3dPCqERERESktCavMfO8y5qFUnfvt+bG1kPAp4Z1QVVwKnyJiIhUIcmZuczZkgDAHa3tsG+huaPj7RZGJSIiIiKllZPv4Pt1RwAYHR0E22eYO9TU/i+p8CUiIlKFTF9/hNx8J63qBdI6YRZgQKPL1dReREREpJL7ZWsiSRm51Avypnf2IsjPhtqtoX4Xq0Or0FT4EhERqSKcToPJp5udjuwahm2TmtqLiIiIVBVn2lnc2iUCtw0TzY1qav+3VPgSERGpIlbsP0nMiQz8vdy5wXczpB8Fv9rQ4lqrQxMRERGRUtiVmMq6Q6dws9sYGZ4Ax3eBhy+0G2p1aBWeCl8iIiJVxJlRwBuiw/He/JW5Mfo2cPOwMCoRERERKa0zed7VrepQc+dkc2ObIeAdZGFUlYMKXyIiIlVAYko2v+08CsCYlgYc+B2wQSc1tRcRERGpzNJz8pm5IQ6A0dGBsH2WuaPTHdYFVYmo8CUiIlIFTFt7GIfToEtUTRodnm5ubHwF1IyyNC4RERERKZ0fN8WRkeugUS0/uqbMB0cO1G0L4R2tDq1SUOFLRESkkst3OJm2JhaAkV3rwabT09+1tLWIiIhIpWYYBt+sMhcvGt41Atv6ieaOTmpqX1QqfImIiFRyC3cdIzE1mxA/T/q7r4eM4+BfF5pdY3VoIiIiIlIKGw4nszMhFS93O8NqH4aTe8HDD9rebHVolYYKXyIiIpXcmWanN3eOwGPjJHNjx5Fqai8iIiJSyU0+necNah9GwLZvzI1tbwLvQAujqlxU+BIREanEDp7I4I+9J7DZ4Pbm+RCzFLBBx1FWhyYiIiIipXAqI5c5WxMAuL1DAOycbe5QO4tiUeFLRESkEpuyxuz50LtZKPX2TTM3Nu0LNSItjEpERERESuv79bHk5jtpEx5Im2NzwJEL9TpAWLTVoVUqxS58LV26lEGDBhEWFobNZmPWrFlFPnf58uW4u7vToUOH4t5WRERE/iQ7z8H368ym9rd1rgebppg7OmkUUEpGeZ6IiEjF4HQaTF5tDnCO6Bp5tqm9ZnsVW7ELXxkZGbRv354PPvigWOclJyczatQorrzyyuLeUkRERC5g7tYETmXmERbkzRXGasg8CQFh0PRqq0OTSkp5noiISMWwbN8JDp3MJMDLnRtqHoCk/eDpD21utDq0Sse9uCf079+f/v37F/tG9957L8OHD8fNza1Yo4ciIiJyPsMwmLTiIAC3do3EvuFtc0fHkeBW7B/vIoDyPBERkYpi4uk8b0jHcLw3v2lubHszeAVYF1QlVS49viZMmMCBAwf4v//7vyIdn5OTQ2pqaqEvEREROWvetkQ2H0nBx8ONEU1y4eAfYLOrqb2UO+V5IiIirrUmJolFu45ht8GYDv6w8ydzhx5zLJEyL3zt3buXp59+mm+++QZ396KNQL/++usEBQUVfEVERJRxlCIiIpVHnsPJf+btAmDsZY0I3nW6t1fTqyGovoWRSXWjPE9ERMS1DMPgtbk7ARjWJZKo2FngzIOwjlCvvbXBVVJlWvhyOBwMHz6cF198kWbNmhX5vGeeeYaUlJSCr9jY2DKMUkREpHKZuuYwB09mUsvfk7t7hsGmyeYONbWXcqQ8T0RExPV+2ZbIpthkfDzcePTKxqCm9qVWpk1A0tLSWLduHRs3buTBBx8EwOl0YhgG7u7u/Prrr1xxxRXnnefl5YWXl1dZhiYiIlIppWXn8c6CvQA8fFUz/PfPhaxTEFgfmva1ODqpTpTniYiIuFZuvpP/njOrv/aJ1XAqBrwC1dS+FMq08BUYGMjWrVsLbfvwww9ZtGgR06dPp2HDhmV5exERkSrn06UHOJmRS6NaftzSJQIm3Wvu6DgK7G7WBifVivI8ERER1yo0q/+yRvDjK+aOdkPB08/a4CqxYhe+0tPT2bdvX8HrmJgYNm3aRHBwMJGRkTzzzDPExcXx1VdfYbfbadOmTaHza9eujbe393nbRURE5K8dTc3m8z9iAHjymuZ4nNwDh1eAzc1czVGklJTniYiIWCMtO493F54zqz/3JOz62dypdhalUuzC17p16+jTp0/B68ceewyA22+/nYkTJ5KQkMDhw4ddF6GIiIgA8L8Fe8jKc9Axsgb9WteFee+YO5pdA4Fh1gYnVYLyPBEREWucN6t/xdvgzIf6XaCuBpRKw2YYhmF1EH8nNTWVoKAgUlJSCAwMtDocERGRcrf3aBr9/rcUpwHT7+1BZ99j8Mll4MiBEdPV3+sClD9UDvqcRESkujuamk3v8b+Tnefk49s6ck2kAR92h+wUuP5DiB5hdYgVTnHyhzLt8SUiIiKu8Z95u3Aa0K91HTpHBMAXQ8yiV5OrzC8RERERqZTe/m0P2XlOc1Z/qzow+Saz6BXWEdoNszq8Ss9udQAiIiLy11YdOMmCncdws9t48poW8MdbEL8RvIPguvfAZrM6RBEREREpgT1H0/huXSwAzw5oiW3DRNi/ENy84IaPwU3zlUpLhS8REZEKzDAMXp+7E4Bbu0bQOG8fLP2vuXPAm+rtJSIiIlKJ/eeXc2b1B6bA/OfMHVf9H4Q2tza4KkKlQxERkQrs560JbD6Sgq+nGw/3joQp/cxGpy2vg7Y3WR2eiIiIiJTQqgMnWbjr9Kz+q5vCrFsgLwMa9IJu91kdXpWhGV8iIiIVVG6+k/HzdwNw92WNCF33JhzfCX6hMPBtPeIoIiIiUkmdN6t//9dweAV4+MHgD8Guco2r6HdSRESkgpqy+hCHTmZSy9+Lexoeh+XvmjsGvQt+tawNTkRERERK7NxZ/Y91MGDhS+aOfq9CzShLY6tq9KijiIhIBZSance7i/YB8HifcHzm3AoY0H44tBhgbXAiIiIiUmK5+U7+O8+c1X/vJZEE/3r/2dW6O422NrgqSDO+REREKqBPluwnKSOXRqF+DD31GZyKgcD60P/fVocmIiIiIqUwefUhDieZs/rvdftRq3WXMRW+REREKpiElCw+/yMGgP9Gn8S+7gtzx/Xvm0mRiIiIiFRKqdl5vLtwLwAvd83Dc/kb5g6t1l1m9KijiIhIBfP2b3vIyXfSO9KDTpueMDd2GQuN+1gbmIiIiIiUyseL93MqM4/mtTy4Zu/z5mrdra7Xat1lSDO+REREKpDdiWlMX38EgLcCpmJLjYPgRtD3RYsjExEREZHSSEjJ4otl5qz+j8PnYTu+y1yt+9q39IhjGVLhS0REpAL5z7xdOA14OmofIftngM0Ogz8GTz+rQxMRERGRUjgzq/+2sHiidn9pbtRq3WVOhS8REZEKYsX+EyzadYza9jTuSnnX3NjzIYjsZm1gIiIiIlIquxJTmb7+CL5k81zee9i0Wne5UeFLRESkAnA6Df79yy7AYELoFNyzTkBoS+jzT6tDExEREZFS+s8v5qz+j+r8iHfaIa3WXY5U+BIREakA5mxNYMuRFIZ6rqR1yhKwu8OQT8Ddy+rQRERERKQUVuw7we+7j9PbbSu9U340N2q17nKjwpeIiIjFcvIdjJ+/izok8ZLnJHNj76egXntrAxMRERGRUnE6DV7/ZReBZPCu7xfmRq3WXa7crQ5ARESkuvtm1WFikzKZ4vMF3vlpENYRLnnM6rBEREREpJR+2hLP1rgU3vH6mqC8Y1qt2wKa8SUiImKhlKw83l+0l1vdFtHT2AhuXnDDx+CmsSkRERGRyiwn38Ebv+7mavtarrct1WrdFlHhS0RExEIfL9mPf9YR/uUx2dxw1f9BaHNrgxIRERGRUvtm1WEyko7yuueX5gat1m0JDSeLiIhYJD45iwnL9jPJ4xN8yIYGvaDbfVaHJSIiIiKllJKVx3sL9/C6xxeEkKLVui2kGV8iIiIWeeu3PYwwfqabfReGhx8M/hDs+tEsIiIiUtl9tHg/vXMW099tLYZW67aUZnyJiIhYYGdCKps3rmKOx3cA2Pq9CjWjrA1KREREREotLjmLn5evZ47HRABsWq3bUhpWFhERscD4udt4w/1jvGx50OQq6DTa6pBERERExAXemr+bV2wfE2TLxAiLhksetTqkak2FLxERkXK2fN8J2hz4gvb2Azi8guC698BmszosERERESmlHfGpeG35it5uW3C6eWG74RNw87A6rGpNhS8REZFy5HQafPfTTzzkPhMAt2vfhMAwi6MSEREREVf4cs7v/NP9GwDsV/5Lq3VXACp8iYiIlKOfN8Zw/6k38LA5yGk6ENreZHVIIiIiIuICy3Yf5eYjr+FnyyE7rDt0v9/qkAQVvkRERMpNTr6DlLkv0dx+hEyPYLwGv6NHHEVERESqAKfTYOes/9DNvotcuw/eN32s1borCH0KIiIi5eTXX35keP4sANyufw/8alkbkIiIiIi4xO9/LGVU5lcA5F75MgQ3tDgiOUOFLxERkXKQkpxM+/VPY7cZxNS/Dq82A60OSURERERcIDs7m7DFj+Fly+NQzZ7497zL6pDkHCp8iYiIlIN9Ux4jkqMcs9Ui4tZ3rQ5HRERERFxk27f/R0tjH6n4Ufu2T9XKooJR4UtERKSMndg8j07HfgAgrvd43P1qWhyRiIiIiLhC2oF1tI/5DIAdHZ7HJyTC4ojkz1T4EhERKUtZybj99CAA830H0aH3DRYHJCIiIiIukZdN9vdj8cDBH+496TLoHqsjkgtQ4UtERKQMnZo5jpr5x4lx1iHspv9i09R3ERERkSohbd5LhGYd4LgRiG3gW7i5qcRSEelTERERKSu7fqbmnuk4DBszo56nbaMwqyMSEREREVc4vAq/9R8C8FXwo/Rq38LigORiVPgSEREpC+nHyZ31EABfOAdy0/U3WhyQiIiIiLhETjo50+/GjsEPjkvpe+MdmtVfganwJSIi4mqGQf7sh/DMPslOZwTHOo8jMsTX6qhERERExAUc85/FK/UQcUYIq5s/Sbv6NawOSf6CCl8iIiIuZmz8Gvc9v5BjuPOS5yPcf1Vrq0MSEREREVfYPQ+3DZMAeI4HeGhAZ4sDkr+jwpeIiIgrJcWQ//NTAPzPcTOPDL+BYD9Pi4MSERERkVLLOEHOjPsB+Dy/P8NuHkFEsGb1V3QqfImIiLiK00H6t2PxcGSy2tmCkL7j6NYoxOqoRERERKS0DIP06Q/glXOSPc5wkro/zTVt6lodlRSBCl8iIiIukrn4bfyPriXd8GZ21PPceVkTq0MSERERERfIWf81/jHzyDXc+Lz2MzzWv53VIUkRqfAlIiLiAo74zXgufR2AD7zH8vTwflrdR0RERKQKME4dxJhrtrL4zO0WHr/9ZtzdVE6pLPRJiYiIlFZeNqe+GYM7+SwwujB49JMEeHtYHZWIiIiIlJbTwbGvxuDtzGS9sxldRrxI7QBvq6OSYlDhS0REpJQOT3+WWpn7OW4Ektv/bZrXC7Q6JBERERFxgbhfxlPn1AbSDW/2XfImXRuHWh2SFJMKXyIiIqVwbMsC6u/+EoD5jf7JgO5tLY5IRERERFwhOWYDoWvHAzCr9gMM7XupxRFJSajwJSIiUkLZaadg1r3YMZjvfQ03jxhrdUgiIiIi4gKO3GxSp9yBJ/mscOvC9Xc8rf6tlZQKXyIiIiW048t7qe08Tix1aHvHB3i5u1kdkoiIiIi4wIaJ44jMi+GkEUjtEZ8S4ONpdUhSQip8iYiIlMCKn76k46l5OAwbJ/u+S1jtWlaHJCIiIiIusGHpHDrFTQZgX7dXaNKokcURSWmo8CUiIlJMe/btpeW6fwGwIXI0HXpdY3FEIiIiIuIKRxKOUmfRI9htBuuDB9JtwO1WhySlpMKXiIhIMaRk5pI09W5q2tI45NGYTqP+Y3VIIiIiIuIC2XkOdk68n3COc9RehzZ3vm91SOICKnyJiIgUkdNp8OMXr9LdsYEcPKg5ciJ2Dy+rwxIRERERF/j+m4/om7MAJzbcbvwEL7+aVockLqDCl4iISBFNm7eYm058BMDJbs8QGNnO4ohERERExBVmL9vIgIP/BiCu1Vhqte5jcUTiKsUufC1dupRBgwYRFhaGzWZj1qxZf3n8jBkz6Nu3L6GhoQQGBtKjRw/mz59f0nhFREQssWJvIi1XPY6vLYejIV0J6/eo1SGJuJzyPBERqY62xyUT8OujhNjSOOHXlIghr1gdkrhQsQtfGRkZtG/fng8++KBIxy9dupS+ffsyd+5c1q9fT58+fRg0aBAbN24sdrAiJZKfC458q6MQkUosMSWbzVP/j2j7PrLs/tQe+QXYNWlaqh7leVLpOPLMLxGREkrJyuPnSf+hj30jeXgQfNtEcFcri6rEvbgn9O/fn/79+xf5+P/973+FXr/22mv8+OOP/PTTT0RHRxf39iLFkxwLX14DeRnQZSx0vRv8Q62OSkQqkTyHkzcnfctrju/BBm4D38BWI9LqsETKhPI8qVQyk8w8LzUeOt0O3e+HoHCroxKRSsTpNPj35Lk8l/MF2CD/8ufwqNfG6rDExYpd+Cotp9NJWloawcHBFz0mJyeHnJycgtepqanlEZpUNXnZ8N1ISD1ivl76X1jxLnQYDj0ehJDGJb50fHIW6w+dYsPhU2yKTSY1Kw8/L3d8Pd3w83TH18sdXw83fL3OvD79q6cbfl7u+HgWfu3n6VZwjt1uc9FvgIi4wvg5m7jnxL/xsDvIaDIIv+hbrA5JpMJSniflxumAH+6CE7vN1yvfh9UfQ9uboedDUKd1iS99LC2bDYeS2XjYzPVOZuReII9zw9fTHT+v07+ezuXOHHfm2HN/9fV0x015nkiF8sni3dx0+GX87Dmk1+2O/2X/sDokKQPlXvh64403SE9PZ+jQoRc95vXXX+fFF18sx6ikyjEMmDsO4jeCTzBc9QKsnwjxG2Ddl7BuArS6Dno+DPU7/eWlcvIdbItLLUh+NhxKJjE1u8xC9/Ewk6Vzi2VhNXzo1jCYrg1DaFrbX8UxkXIyZ0s89db+mybu8WR7h+I35F2w6e+fyMUoz5Ny8/ursH8huPvANa/Dth/g4B+wear51aQv9PoHRF36l/9u5zmc7ExIZcOhU2w4nMyGw6c4ciqrzML2crf/abDUjToB3nRpGEy3hsG0rBeo4phIOVmx7wQZi96kk/te8tz98L/lM7WyqKJshmEYJT7ZZmPmzJkMHjy4SMdPmTKFsWPH8uOPP3LVVVdd9LgLjQRGRESQkpJCYGBgScOV6mTtF/DzY2Czw20zoHEfsxh2cJk562vvr2ePbXCJmRg16Qt2O4kp2Ww4fKpgRtf2uFRyHc5Cl3ez22hVL5COkTXo2KAmtQO8ycrLJzPXQWaOg4xc8/uMnHN+zXOQmZNPRq6DzNz8s8ed/tX5p7+J3uRwmX0Lfe3rSSKAN/OHkosHNXw96BIVfLoQFkyreoG4u+kfaBFX23csjX+//xGf2181N4z4AZpe/GeXVDypqakEBQUpfygh5XlSYe38Cb69zfz+xi+g7U3m93HrYfm7sHM2GKdzt7Bo6PUwtLwO7G6cSM85W+Q6dIotcclk5xXO82w2aF4ngOjImnSMrEFEsC9ZeefkeOfkcxk5DrJyL5D7nZvr5Tpw/CnR8ySPnvbtXG1fhwM7/86/lQx8CPByp1NUTbo2DKZbwxDahgfh6a48T8TVElOyGffOJCY6nsHD5sAY/BG2DsOtDkuKoTh5XrnN+Jo2bRp33XUX33///V8mQwBeXl54eamZnJRQ7Br45Snz+yv/zyx6gZnFNLzU/Dq6A1a8h7H1O2yHlsGhZcR7RvGlcyCT0ruS96e/GiF+nmby06AGHSNr0q5+EL6ervvrYxgGOflOslKTcO7+Bc+9c/E7/Dt2x9mZZb39DjEm6xESMn35bcdRfttxFAA/Tzc6nVMIa1c/CC93N5fFJlIdZeTk8/jXS/nI9hEAzs53YlfRS+SilOdJuTm+G2bea37f/YGzRS+A8E4wdBIkHYCVH2Bs/AZb/Eb4fjQnPML4ioF8mtaDbAr/+Qv0dqdjg5p0jDS/2kcEEeDt4bKQDcMg1+EkMy0F594FeOyZg9+hRbjlpRUc09vnAHfkPsG+nCAW7z7O4t3HAfD2sNMx0iyEdW0YTHRETXw8leeJlEZuvpNHvlnBS/nv4GF34Gg+ELf2t1odlpShcil8TZ06lTvuuINp06Zx7bXXlsctpbpKOwrfjQJnHrS63hzhO8ex1DOzuWBD4kiO5fbiNuYy3G0RYbkHeY73udMrmLm+1xPfZBitG0bQqUFNIoN9sZXV401pR7Ht/hnvnXPwjlkCznNWoAyKNGeYbJ1Oi5xtrKj1Gruu+IKlJ4NYE5PEmoNJpGXns3TPcZbuMRMkL3c7HSJq0K1RCN0aBhMdWcOlRTqRqs4wDJ6esZUxye9Tzy2J/JqNcL/6ZavDEqmwlOdJuclOhWkjIDfdfISx70uFdidl5J6ezZXLhribOJzTjaHGL4xy+5VaefE8xqfc7jWVn70HcrDRcFo0akjHBjVoVKsM20hkJmHbMw+vnT/htX8R5J/TLsO/LjS/Bnb9TGTGAX4LfIn9V33O0rTwgjwvKSOXFftPsmL/SQA83Gy0q1+joBDWqUFNAl1YpBOpDl7/ZSd9Ez6lmXscDt9Q3K5TK4uqrtiPOqanp7Nv3z4AoqOjeeutt+jTpw/BwcFERkbyzDPPEBcXx1dffQWY095vv/123nnnHYYMGVJwHR8fH4KCgop0Tz2qIEWSnwtfXQeHV0JoC7hrAfnufvy4KZ7Fe46z4dAp4pLP79lQ09eDXvU9GO62iM6J0/DMOmbu8AqETqOh+30QGObaWE8dhJ1zYNccOLwKOOevYWhLaDkQWg6Cuu3Mf4SP7YTJQyHlMPjUhGGTIaoXDqfB7sQ01sScZM3BJNbEJHEiPbfQrdztNtrWDzo9ZT6YTg2CCfJRgiRyMROXx7D+5895z/N9DJsbtjt/hfqdrQ5LSkD5Q/Epz5MKy+k0Fy3aNQcCw+HuJRh+tfhlWyILdhxlw+FTHDyZed5pAd7udAv3YrjXMnocnYZPRqy5w90Hom+DHg9AcEPXxpoaD7t+Nh/JPLgMDMfZfTUbmjley+vMGWp2O5w6BFOGwfGd4OFrPr7ZYgCGYbD/eDqrY8wcb/WBpPP6zNpt0CoskK5RIQXFsGA/T9e+H5Eq5KfN8Uz99mumeL5mbhj+PTS72tqgpESKkz8Uu/C1ePFi+vTpc97222+/nYkTJzJ69GgOHjzI4sWLAbj88stZsmTJRY8vCiVEUiRzn4A1n5oFq7G/szQpiFd/3snuo2enkdtt0KxOwDnT2WvQsJbf2dlc+Tmw9XuzP8SZVYLsHtBuqLlCUO2WJYvNMOD4LjMB2jkbErcW3h/eCVqcLnbVanrha6Qfg6m3Qtw6M6br3oMOhafkGobBgRMZp5Ojk6yOSSIhpXCCZLNBy7qBBYWwLg2DqeWvR05EANYfOsU/PvmZuR5PEGTLhN5PQ59nrA5LSkj5Q/Epz5MKa+l4WPQKuHnCmHmsdzTi5Tk72BSbXOiwJrX9zR6skTXp2KAmTULPmc3lyIedP5p5XsImc5vNbj4l0PMfEN6x5PGd3G/mebvmwJG1hffVaXO62DUIare68MyS7BT4fjTsXwTYoN+r0P3+QscahkFsUharY04WzAg7dIFiX7M6/qeLYCF0jQqmbpB3yd+XSBWy71gaI97/lZm2xwmzJUGnMTDof1aHJSVUpoUvKyghkr+1aSrMMvs9xA+YwD+31+f3070Rgnw8uL1HA7o1CqF9RA38vYrw2J/TaTbAX/4OHF5xdnuza8zEqEHPv58O63Saq0ju/Mn8Stp/dp/NDg16mQlQi2shqH7R3mdeltnXYscs8/VlT0KfZy8ai2EYHDmVZSZHpxOkmBMZ5x3Xql4gN0SHc32HMGoHKjmS6ulEeg6D3lnKf7Jf5DK3rRhh0dju/A3cNEOyslL+UDnoc5K/tfc3mHwzYJB05Zv8K7Yjc7YkAODr6cbI7g3o3jiE6Iga1PAtwmwnw4CYpeaCR/sWnN0edSn0egSaXPn3eZ5hwNFtp/O8OXBse+H99bueLnYNhOBGRXufjnyY+zisn2C+7nwn9P8vuF08d01MyT49698shu05mn7eMY1D/RjcIZzB0eFEBPsWLRaRKiY9J5/r31/Gg8n/5Qa35RjBjbDd8wd4+VsdmpSQCl9SvcRvgi/7QX42i+uO4c7DV+NwGrjbbYzs0YCHr2xatCToYmLXwop3zKTmzCOJ4Z3NlSBbDAT7OQ1GHflwaLk52rdzDqTFn93n5gmNrzDPaT4A/EJKFo/TCYtehmVvma/b3AjXfwgeRStYHUvNLngsck1MErsSC8+Iu6RpKEOiw7m6dR31BpNqw+E0GPnFapocnMJLHpMw3H2w3fvHxWdgSqWg/KFy0OckfynpAHx6OWSnsKn2DQyNH0ZuvhObDW7uVJ/Hr25eukG7xG2w4j3YNv1sn9Xarc08r82NhQc/nE5zNtfO2WbBK/nQ2X12d4i6xCx2Nb8WAuuVLB7DgJUfwK/PAQY0vhJungjeRfu7kZSRe86A50l2xKcWWjm8a8NgbuwYTv+29dQbTKoNwzB4aOpGjG0z+cDzXQybHdsdv0JEF6tDk1JQ4Uuqj4yTGJ/2xpYSyxI6Mjr7MQzsXNWyNs8MaEnjUBdW8E/sg5Xvw6Yp4Di9DHtwI+jxoNkDbOcc2D0XspLOnuPpD02vNpOgpn3BK8B18Wz8Bn562EzSIrrBLVPAr1axL5OUkcvcrQnM3BjH+kOnCrb7ebrRv209hkSH071RSNk1fRWpAMbP38W8xUv52fNZvG150H88dLvb6rCklJQ/VA76nOSicjMwvuiL7eh2ttCMm7L/SS4edG8UzHPXtqJNeNH6yBVJciys+gg2TDKb54PZS6z7fWari10/m1/pR8+e4+4NTa4yBzWb9QPfYNfFs3MOzBgLeZnm45HDv4UakcW+TGp2Hr9uP8rMjUdYsf8kZ/7n5+Vup2+rOgzpGM6lTUPxcLO7LnaRCmbC8hg+/mkZ872eooYtAy57Aq54zuqwpJRU+JJqwXDkk/TJIEKOreCgsw7X5b5CWN26PD+wFb2aFL8AVGTpx8xeYms+g+zk8/f7BEOLAWbT0oa9izwTq0RilsK3t5l9IWpGmc0ZQ5uV+HIHT2Qwc2McMzYeITbp7EIAYUHeXB8dzpDocJrWcWHxTqQCWLDjKPd+tYoZnv9HO3uMOTNzxA9mw2Gp1JQ/VA76nOSCDIPjk0YSevAnjhtBDMx5FZ+Q+jwzoCVXt6pTdqttZ52CdV/Cqo8h49j5+70CzdYXLQeaRS9Pv7KJAyB+I0y5BdITwa82DJ9m9oUt6eWSs5i1KY6ZG+LYe+zsI5G1/D0Z1D6MGzvWp3VYYNn93opYYP2hJIZ9spIv3P5Nb7ctUK8D3LVArSyqABW+pMrbHp/CvimPc336d2QaXoxx/zc39LuKmztH4FZeM5Ny0s1ZV2s+BUceNO9vzuyK7PGXvRhc7vgemHKzuVKkdxAM/Roa9S7VJQ3DYP2hU/ywIY6ft8STmp1fsK9teBBDOoYzqH2YmuJLpXf4ZCbXvvcHd+VP42H3GeBdA+5f6fqVXMUSyh8qB31O8mcxJzJYM+VlhiV9RJ7hxl22f3HpldcxqkcUnu7lNCiRlw1bvoXVH0NWsrnqW4tB0PAycC/HVRNTjpgrPh7dZq5EOeRTaHVdqS5pGAbb4lKZsfEIszfFczLj7IrgTWv7M6RjfQZHh1EvyKe00YtY6kR6Dte++wd9M+bwiscEDHdvbPcshdDmVocmLqDCl1RZx9KyeXP+HtI2TudDj3cA+LHpq1x5071Fa1pfVWWcgGnDIXa12WNi4P+g40iXXDo7z8GiXceYsSGOxbuPkX+6UYSb3cblzUK5oWM4V7Wsg7eH299cSaRiiTmRwZ0T1xJ0chPTvV7EDSfc9KXZ00WqBOUPlYM+JzkjJTOPdxbuZfequUxyfxV3m5Of6z9Cj1v/SbBfORabKpqcNJh+h7nwEkDfl8zFllwwMyvP4eSPvcf5YUMcv+04Sm6+EzAv3bNxCDdE1+eaNnWrd54tldLR1GzumrSOjPidzPV6Fm9y4Zr/QPd7rQ5NXESFL6lysvMcfLEshg9/30dY3iFmeT6Pny2H1I73EXjdv60Or2LIy4YfHzCbswJc8ihc8S+XPq51Mj2HOVsSmLHhCJuPpBRsD/B259q29RjSsT6dG9RUPzCp8JbvO8H9kzeQm5XGrz7/JMJIgLY3w42fWx2auJDyh8pBn5PkOZxMXnWI/y3ci09mIj95/ZNatlRSmw0h8NYvXVLgqfQc+TD/GfNJA4COt8O1b7r0ca2UrDx+2ZrAjI1xrIk527PWx8ONfq3rMKRjfXo1qVV+T1eIlNDm2GTu/nodJ1MzmOX9Im3YD40uh9tmqpVFFaLCl1QZhmHw05YE/vPLLuKSswggk3l+/yLcEW9ONb9tZvk+VljRGQYsfh2W/Md83ep6uOET8HD9VPV9x9KZufEIszbGE5d8th9Y/Zo+DIkO54aO9WlYqwz7XoiU0NcrD/LCTzuIMo7wesB0uuauNhsY37ccfGpaHZ64kPKHykGfU/VlGAa/7z7Gqz/vZP/xDLzI5Ue/V2nh2At128Idv4Knr9VhViyrPjYLYIbT/I/8zZPAp4bLbxOblMmsjXHM2BhHzImMgu21A7wYHB3OkI7htKirv69S8fy0OZ7Hv99MqOMoL/jP5Kq8xWY7mPtWQlC41eGJC6nwJVXChsOneHnODjYeTgYgLNCTH4I/oF7i7xAUAXcvLtEqhtXCpqkw+yFw5plNUG+dBv61y+RWTqfB6pgkZm48wtytiaTnnO0HFh1ZgyHR4QxsF0bN6vyIglQIeQ4nL83ezr61v3CX21yudNto7rDZ4bYZ0LiPtQGKyyl/qBz0OVVPuxPTeOXnHfyx9wQAwb4efBc2hSZHZpqDEHcvgZoNLI6ygto9z3z0MS8DajWHEd+ZixyVAcMw2BSbzIwNcfy0JZ7kzLyCfS3rBTIkOpzrO4RRO7AMF3MSKQKn0+B/C/bwx++/cKf7XAa4rcWO+eguN34BbW+yNkBxORW+xLWO7wG7G4Q0LpfbxSVn8Z9fdjF7czxgTq++7/LG3Md0PP74N7h5wZ3zISy6XOKptA4uh29HmKsTBUWaSVHtlmV6y6xcB7/tPMqMDUf4Y+8JHKf7gXm62xnYrh4juzegQ0QNrRYk5S45LZ2pX75N75Pf08p+CAADG7bmA+CSRyCiq7UBSplQ/lA56HOyWFIM5GeXeY5wxon0HN76bQ/T1hzGaYCnm50xvaJ4JHg5PvPGnR6M+MFcYVcuLmGL2fQ+LR58a8GtU8v8Z1luvpPfdx9j5oY4Fu46Sp7jbN/Xfq3rcFv3BvRoFKI8T8pdZnYOX0/4kM4Jk+lk33t2R6M+0OthDW5WUSp8ieucOgQfdDUTojY3wuXPQq0mZXKrjJx8Plq8n8/+OEBOvhObDW7sWJ8n+jWnTuIS84c7Blz/IUSPKJMYqpyT+2HyTZB0wFx+e+ikckskj6VlM3tTPDM2xLEjIbVge9vwIEZ2b8Cg9mH4eKohvpSxzCROLvkEY80n1DJOAeBw88at423Q/f5yK+iLNZQ/VA76nCyUdQreaQ/ZKdDsGrjiOfMRwzKQk+9gwvKDfLBoH2mnZ4f3b1OXp/u3oEHmDpjQ35ypfuX/waWPlUkMVU5qvJkfJ24xB4Zv+BjaDCmXWydn5jJnSwI/bDhS8HQGQJPa/ozs3oAbOoYT6O26/mMiF5STRvKKCWT98T71nEcBcNrcsbcfZuZ5ddtYHKCUJRW+xHUWvQJLx599bXMzi069n4Kg+i65hcNp8MP6I4z/dTfH03IA6NowmH8NbEWb8CCzePNpH8hJgc53wsC3XHLfaiMzCaaNgMMrzM/v2jeh85hyu71hGGw+ksJXKw8yZ0tCwWpBgd7u3Nw5gtu6N1AvMHG9k/th1Uc4NnyDm8PsQXeCmji73k3ty+8F32CLA5TyoPyhctDnZKHVn8IvTxTe5uKBTsMw+GVbIq//spPYJPPf47bhQTx3bUu6NQqBtKPwaW9IS4CW18HQr9TMvjhy0mHGWNg913x9xfNw6bhy/T3cmZDKN6sOMXNjHJm5DgB8Pd0YHB3OyO4NaFlPf6/FxVKOwOpPyF83AffcNACS8Sez3WjC+j4EAXUtDlDKgwpf4hqOfPhfW3MK9eXPQNwG2Dvf3OfmCV3ugkseA//QEt/iZHoOd0xax+bYZAAig315dkAL+rWua06TzkmHL/rCsR0Q0Q1unwPu6hVVbPk5Zs+vLd+ar3s8CH1fLvdVTZIycvl+XSzfrD5UkPwCXNq0FiO7N+CKFrVxd9NKK1JChgGHV8KK9zF2z8WG+eNth7MBC2vexPA7HiUkKMDiIKU8KX+oHPQ5WcQw4ONL4Og2My9IjYftM8x9LhroTM/J575v1hf08aoT6MUT/VowJDrcXAHakQeTrjMH50JbwF0LwEv/Theb0wG/Pg+rPjBfdxgBA/9X7jlzWnYeMzfG8dXKQ+w7ll6wvUtUTW7r3oD+berh6a48T0ohfiOseB+2zwTDLLLud9bjZ78buHHMOMJrq/9zdaLCl7jG7nkwdRj4BMO4XeDuBYdXwcKX4NBy8xgPP+hxv5kwFXNFmeNpOYz4fBV7jqYT4OXOQ1c24faeUXi5n378zTBg+hjzHzb/OmaT08B6rn2P1YlhmLP3fn/VfN1iIAz5FDzLf7aV02mwZO9xvl55iN93H+PMv0JhQd4M7xbJsC6RhAZ4lXtcUkk58mDHj7DyfTMhOm2RowOfOa4lIvpqXrmhnZLtakj5Q+Wgz8kicevhsyvMR+TG7TJnwiZsMWf7u2CgMzU7j9FfrmHD4WS8PezcfVlj7u3dCF/Pc1bj/uUpWP2x2Y5h7CKo1dSFb7AaWvs5zH3SLAhEXWrOnrNghrNhGKw6kMQ3qw4xf3si+ad7vtby92RYlwiGd2tAeA3XrzguVZTTCXvmmXnemf+DAisdrfjc0R/35tfw1i0d8fNy/4uLSFWkwpe4xtThsPtns6jV79Wz2w0D9i+CRS+f/U+mdw2zQXTXu4tUSDmWms2tn61i//EM6gR6MXVsdxqF+hc+aMV78OtzYHeH0T9DZHeXvbVqbet0mHUfOHKhXgdzxUcLC4qxSZlMXn2Yb9ce5tTplYI83Gz0b1OPkT0a0LlBTTVJlQvLSoYNX8HqTyD1CACGuzcLPPrw7+QriCGcZwe05M5LGurPUDWl/KFy0OdkkZ8ehvUToe1QuPGzwvsOrz490LnMfF3Mgc6UrDxGfbmGzbHJBPl48M2d3WhbP6jwQZu/hZl3m9/fMhVaDCj1WxJg7wL4fjTkpkFIExj+naX9LI+mZjN1zWGmrjnM0VSzpYndBle2rMPI7g24pEktc/afyJ/lZsCmKbDqI0jaD4Bhd2eVz+W8ktSH7UZDHuzThMf6NtOfoWpKhS8pvbREeKuVOWL0wBoIbX7+MYYBu+aYI4PHd5nb/OvApY9Dp9vNGWIXkJhiFr1iTmQQFuTNlLHdifpzj6cDS+DrwWA4YcAb0HWsa99fdXd4FUwbDpknITDcLH7Va2dpSNl5DuZuTeDrVYcKNUltUTeA27o3YHB0OP4ayRGAUwdh1cew8WvIPf0ohV8ox1uOYsy2tmxL9iTAy513h0fTp3ltS0MVayl/qBz0OVkgJx3ebG7+G3r7HGh46fnHGAYc+N0sgJ070NnrYeh2z0UHOpMzcxn5xRq2xqVQ09eDr+/sZvZsPVfCZvjianPxpMuehCv+6dr3V90d3W42vU+JNZ/cuGUyNOhpaUh5DicLdhzl61WHWLH/ZMH2hrX8GNEtkps7RRDkq2b4AqQmwNrPYN2X5gIcAN5BpLYeyX17OrH8uBee7nbG39SO6zuEWxurWEqFLym9P940E52I7nDn/L8+1umArd/D769B8iFzW1AkXP40tBsGbmeLFXHJWQz/bBWHTmYSXsOHaXd3JyLYt/D1kmPNJqeZJ6H9cBj8oZqcloWkAzB5KJzcC9ig4WXQYTi0HGTJ44/n2haXwjerDjFrUxzZeWYzfH8vd27sGM5t3RvQtM7p/h9JMeYjbnmZENnD7APn6fsXV5ZKLXaNOc19509mURwgtCX0eICFHr35x/c7yMh10CDEly9u70yT2uoTU90pf6gc9DlZYMPXMPtBCG4ED2346zzrQgOdfrXhsifOG+hMysjlts9XsyMhlWA/Tybf1e38xuaZSWael3wYml4Nt35b7j1Hq4W0o2bLkjNFy4ju0P4WaH1DsduTuNq+Y2l8s+owP6w/UrDCp7eHnevahzGye9TZ2YGp8bB9FmSeMONv0EM94KqyxK2w8gPz6RSn+RQINaOg+wOsrXENd3+7i1OZedQO8OLTUZ3pEFHDymilAlDhS0rH6YT3OsKpGLj+Q7O5aVHk58LGr2DJeEhPNLfVagZ9/gktryM22ZzpdeRUFhHBPkwd2536Nf9UpMjLgi+vgYRNUK893DEfPNQDoMxknYJZD5iPtJ7h4QetrocOt0KDSyxNRlMy85i+4QjfrDpEzIkMAOqQxAO1tzDIbRU1T20pfIKbJ9TvYva1aHip+f1FZh5KJZGfA7t/MROhI2vObm98BfR4AKPRFXy8NIb/zt+FYUDPxiF8MLwjNf20CIYof6gs9DlZ4PO+5r+pV70AlzxatHP+ZqDzZJaDEZ+vZldiGrX8PZl8V3ea1w04/xrf3GjOJKvZEO7+HXxquvStyTlyM2HOo7D1u7MDRm5e0OJaaH+r+bPUzbrZ9Bk5+fy4KZ6vVh5kV6K5Ml8wqYyttZWbPFdTK2l9wUI1gLnoQnjHs3leRHcNeFZ2jjzY/7s5sBmz5Oz2yB7Q4wFoPoBp6+J4btY28p0GbcOD+GxUZ+oGeVsXs1QYKnxJ6RxYAl9dZzYaHber+LN/cjPN5prL3iqYnpob2pankwczI60FUSF+TBnbnbA/N7U0DPjxAdg02ZyWfc8SqBHpojclf+nUIXPFx81TzZlgZwRFmLP22t/qsmXNS8KZdpwDS6fi3Po9TbK2YreZ/2w5sHMkqDO1wxrgE7cCUuMKn+jubc4Ca3gpRF1mJktumkZvmbxsyEoyZ3Nmnv41K+ns94W2nX6de3ZVKNw8od1Q6H4/1GlNdp6DZ2ZsZeZG83O/rXsk/zeoNR5aGVROU/5QOehzKmfHdsKH3c0eqo/ugIA6xTs/P9d81HzJfwsGOvODm/J69hC+TGpLrQAfpo7tduFZtwtegGVvg4evuYJjndalfz/y91ITzKLl5qnmSuln+NeBtjebeV7dNpaFZ2Sd4uCy78ne9B1N09fjbnMW7Iv1b0/NiBb4J642Wx2cy+5hDnI2vNQshtXvAh4qiFgmP/ecHO5Cud45+85sy0k9e77NzRx87/Eg1O9EvsPJq3N3MmH5QQCubVePN25qj4+nmzXvTyocFb6kdKbfCdumQ+c7YODbJb9Odiqs/ADnivew55mzdbbYWxF+4+uEtL78/OPXfg4/jwObHW6bAY37lPzeUjKGYT5OtnkKbJsJOSln99Xvak6RbzOkfEZns5Jh18+w7Qc4sLhgyWKAuID2fJPRhe8zO3GCIOw2uKJ5KKNbQg/7dtwOLYOYpZBxrPA1PfzMafJnRgrrdQC7fniWSm4GHFl7ToLz56TmJGSeMn89/e9AsfmGQOc7zZXFTv8H7VhaNvd8vZ6Nh5Nxs9t4YVArRvaIct37kipB+UPloM+pnM17BlZ9aK7ufMvkkl8nLwvWfIbzj7ewZ5sDnbtsjQi69iXqdRp4/uOTO36E70aZ39/4BbS9qeT3lpIxDLO/2uapZiEs82yvLeq2NVuMtL0J/MuhP2Zuhjmje9sM2PebuejSacf8W/JtdjempHcigRAALmlSi9Gt3ejtuQuPw8sg5o+ChW0KuHtDRFdzsLOhBjxdIj8HYlf/qZj154HK07leblrJ7uEVCB1Hmb0DT096SMnK46GpG1m65zgAj/VtxkNXNNFiRVKICl9ScplJZrNTRy7cvRjCokt1uf3H07nv01+5KWs6t7v/hhenf6g16QtXPAdhHczXh1fDxGvN57n7vmQ2ThVr5WXB7rmweRrsW3DOFHlPaN7fTI6aXOnahCI3w1yueOsP5yVB1OsAbW40e1PUiCA338n87Yl8veoQa2KSCg6rHeDFTZ3qM7RTfaKIMwtgMUvh4DLzB/S5vILMZq8NLzUTpNqt1WekONKOwhdXmX1aisrmZhayfIPNX31qnn597rbgc14Hm5/TOZ/LtrgUxn61joSUbIJ8PPhwREd6NalVBm9QKjvlD5WDPqdylJ9j5nlZp2D499Ds6lJdLjElmzs/XUTflO8Z6/4LfmSZOyJ7wpXPn22ofmwXfH6lOYv3z6uFizUcebD3N3Owc/e8sz2VbG7QtK85C6zZNa6dQZWfY+aU234wi155mWf3hbaANjeZA6whjXE4DX7fdYyvVh3ij73HOfM/1hq+HgyJrs+wzvVp7nXidJ73Bxz8A9KPFr6fh5+5KvyZPK9ue0sf7ax0slNhQn84uq3o59jsp/O44LP5XUGud+62c3I97xqF8ryYExncOWktB45n4O1h562hHRjQ1roV6KXiUuFLSm7VRzDvaXPU554/StVUfu/RNIZ/vprjaTk0q+PP1GENCNnwDmz4CpxmI0taXQ9dxsIPd5nT5VsNhpsnqpl9RZN21OwPsWkqHNt+drtf6Nkp8iVdFbIYSdDF7DuWzvfrYpm+/ggnM84Wy3o0CuGWrhH0a10XbzebGfuZ5Ojg8sIz2sD8IRzVCxr2NmeFhTbXn8WLycuGSQPN2V6+IWaTed/gCxSvzilg+QSDd1Cpfk9/2ZrAY99tJivPQaNQP764vQsN/7wqrMhpyh8qB31O5WjrdPjhTnNF50e2lmrW858XLPpuZFPCt38Caz4zV2sEaHIV9HoE5jwCJ/eZP1tHzlLxoaLJTDLzsM1TIW792e3eQeagY/tbzccIS/Lz25Fn9m7aNgN2zimce9WMMq/f5iao0+qil4hNyuT79Uf4fl0sCSnZBdujI2twS5cIBrYLw8/TDU7sOT3Y+Yc54HnujDYwZxY16Hl65v9lUKeNBjwvxumAqbfA3l/NAcg6rQvneecNVIZccLCyuJbtPcEDUzaQkpVHvSBvPhvV+fxVYUVOU+FLSsYw4KOe5rP/A96ArmNLfKndiWmM+HwVJ9JzaVE3gMl3dSPE/3ST8aQDsPjfsOU7OLdhZWhLs9+Dl3/p3oeUHcMwV1zZPNX8/DJPnN1Xp435KGTboX/fL8SRf04S9NNFkqAboXarYiVZuflOFu06yrS1sSzZc3Z0MMjHgxuiwxnWJeLs6lJOhznd/+AfZjHs0IrzH8Xzqw1Rl5hFPQ8/c6GFQl++5q/uf37tXbUTKcOAGXebxVDvGjB20V8WJl1zS4N3F+7j7QV7ALisWSjv3RpNkI8eYZCLU/5QOehzKkeTrjN//vZ+Cvo8W+LLxCZlXnzBotR4WDq+8EAnQGB9s3+rn2boVmjHd5t53uZvIS3+7PaQJmae127Y3/fgdTrh8EqzdcqOHwsXoALCzAHNNkMgrGOx8jyH02Dp3uN8uyaWBTuPku80Ez0/TzcGtQ9jWJcIOkTUMB+HczrN/9OcyfMOLrvAgGdNaNDLfMLFK+BsLufuXTiv8/A1Z76dm/dV5TwPYP4/zYbz7j4wZq752GgZ+2rlQV78aQcOp0GHiBp8OqoTtQPUs00uToUvKZkj68xp6O7eMG53iZc63hGfym1frCYpI5fWYYF8c2e3C6+wdnQH/P6quUS2V5C5sk8Z/+dZXMiRB/sWnp4i/8vZxxJtbuYjkO1vgebXnp0iX5AE/QA7Zv0pCaoHrYdA2xuLnQRdTFxyFt+vi+X7dUeIS84q2N6+fhDDukQyqH09ArzPKZo48swlv888Ghm7+uyIdUmclzRdoEB25issGjqMqDyzy/54Exa+ZDZGvm0GNOpdprfLynXw+PTN/LwlAYA7ejXk2QEtcFcTe/kbyh8qB31O5SQpBt7tANjg4c1Qs0GJLnP4pFn0ikvOIirE98ILFkHhgU53LxjzS7n851lcxOkw86HNU81BynNn5EddCh2GQ8vrzg5YGwbEbTDzvO0zIC3h7PG+IeZTHW1vMldidEHR6FhaNjM2xPHt2tiClb8BmtcJYFiXCG6IDi/8/w+nAxK3mEWwmKVmTnruAjrF5eZ1keLYn7a5e0PtltBpTOWZ6bjhK5j9kPn9TRPMImUZynM4efGn7XyzymydcUN0OK8PaYu3h/rwyl9T4UtK5scHzVV62t0CQz4p0SW2xaVw2xerSc7Mo139IL6+oxtBvn8zI+PEXvMHQ1B4ie4pFUBmkpnkbJ5mPvp2hlcQtLnBnC21fWbhkcMzSVCbG80li8to5MzhNFi27wTfrj3MbzuOkucw/8nz8XBjYLt63NI1go6RNc9vlpmfYxaDY5aay7bnZZ3+yjQLYme+L/g1Gxw5JQ+050PQ9+WKX/za+RN8e5v5/bVvQZc7y/R2CSlZ3P3VerbGpeDhZuPl69twS1et9ipFo/yhctDnVE4WvmQOXDS+AkbOLNElYk5kMPyzVSSkZNOolrlKd92gv5mRkRRj/myrGVWie0oFkJMGO2abRbCDf5zd7uFrFr8C6pp5XvKhs/u8gqDlILNo0rB3mRV9DMNgTUwS366N5eetCeTkmz1pPd3s9GtTl1u6RNCjUQh2+5/yK0cexG8yZ0Ce3A/5WYVzuj/nefnZpRsQbX8rXP9hxZ8pdnA5fHW92fPt8mfg8qfL9HanMnK5f/IGVh44ic0GT/Zrwb29G6mJvRSJCl9SfDlp8EZz81GvMb+cbUZaDFuOJHPb56tJzc6nQ0QNJt3RVY8hVUcn9p6dIv/n1XbKKQm6aGjpOczcEMe0tYfZf/zs6GDT2v4M6xLBkI71Cb7Q7MSicjrOFsgKJVB/kUilxsPaz8zzyyHBKJWEzfDlNWbcXe+BAf8ts1vtOZrGhOUxzNgQR06+k2A/Tz4a0ZFujULK7J5S9Sh/qBz0OZUDRz683drsp3rzJGg9uNiX2H88neGfreJoag5Navsz5a5u1A7UY0jVTvJhM8fbPMWc1XcuD19zAaQ2N5r93dy9yjW0lKw8Zm+KY+qaWHYkpBZsjwj2YVjnCG7qFPH3hdq/4nReoECWWTi3y//TtsyTsPJDc3XyznfCtW9W3EHOpBj47ApzMajWQ+CmL8ss1kMnM5i44iDfrztCek4+fp5u/O+WaPq2+pt2KSLnUOFLim/9RPjpYQhpCg+uLfY/chsPn2LUl2tIy86nU4OaTBzTpfBjZFL9OJ3mqODW781RtVbXWZIEXYhhGKw/dIppa2OZsyWe7DxzdNDDzcbVrc3RwV6Na50/OlhWVn0M854yv+/7MvT6R/nctzjSjsJnfSA1zpwtMPx7lxcunU6DJXuP8+WyGP7Ye7Z/XIeIGrx3azQRwb4uvZ9UfcofKgd9TuVg9y9mo2rfEHhsF7gXb5Dn3AWLmtcJ4Ju7uhEaYP3Pc7GQYZiz/DdPg+wUaDHAXAXSs2IsOLMtLoVpaw/z48Z40nLMXnN2G/RpXpthXSLo06I2HuXVMmHrdHMhL4yKO8M/OxW+6AvHd5ktOMb8Yj6u6UKGYbA6JokvlsWwYOfRgl68zer48+6t0bSoq3//pXhU+JLi++wKcxWXEvyne93BJEZPWEt6Tj5do4L5ckwX/L0qyTPsUu2lZufx0+Z4vl0by5YjZ5uehtfwYViXCG7uXJ96Qa79wX9BZ/pmQakXl3C5vGyYeC3ErTOL43ctKHEPwAvJzM3nhw1xTFgew4HTM/HsNri6VV3uuKQhXaIu8CiqSBEof6gc9DmVgym3wJ5foMeD0O/VYp26OzGN4Z+t4mTGBRYsEqngsnIdzN2awLdrY1lzMKlge2iAFzd1qs+wzhFElcfq0Of2zer9NPR5puzvWVROB0wZBvt+M/vujv0dAuu57PI5+Q5+2pzAl8tiCs3E690slDsuachlTWspz5MSUeFLiidxG3zcy2xU/dgu8A8t8qmrD5xkzMS1ZOY66N4omC9Hd8HXU0UvqZy2x6fw3dpYZm6MIzX77Ohgrya1uLJFba5oUYfIkDKcdbTwZfjjDfP76z+E6BFld6+iMgyYMdacuefiFRzjk7P4auUhpq45TEpWHgABXv/f3p3HR1Vf/x9/z0wyk32B7CEQFtkhYVGM4IZYXIq7olhAqrW2tFrpt+5KW63211a/tn61tip1FxV3obiAqChuQNj3sGYPkIXsmbm/P24SCCRAkkluZvJ6Ph55cL1zJzm5QTicez7nE6Cpp6Zo5hmpdHih3cgffAM/pw5WmmMuczQ80uzvpdiBJ/3Wk96wCPAB2wsO6c0f9mrByn3aX17TeP601B6aNDROEwfHqX9sWMcVYZp0+P9RGn9bx3yd1lp8j/TNk+YmTD/9r9nx5QVFh6r1yjd79NI3u1V0yJyDGxRo15Wje2nW+FQNiAv3ytdB90XhC62z6A7pu3+ZwymnvnTSb/t6R5FufP4HVda6NWFAjJ6ZMVbBTnbfgO+rqnVr8fo8zf9+j77JOtDktQFxYZo4OE7nDorT2NRo77bJG4a0+G7p239KNrt05XMdvpPOCX3xN2npg2ZhfPo7Ut+z2v0pV+05qHnLd+q/6/Pkrt+KvE/PEN1wRqquHptCxyi8hvzBN/Bz6mANf473zpB+uvik39amDYsAH1BT59HSzfma//1efb61UEf+a7h3jxAzzxscp3F9e3h/Z8Gu1uG/8gXpg/rVPlc/Lw27vN2fclNuqeYt36n3MnNU4zbHiSREBGnGGX103am9KZ7Dayh84eTVVkqPDjLX5v/kLXMG00lYvq1IN734vapqPTprYKz+PX0MW87CL+0qKtfHG/O0ZFOBfth9sLFQI0nhQQE665RYTRwcp3MGxXpn6YdhmPP2Vr1gFpumvmwOirXCxvelN6abxz/+X2nsT9v8qWrdHi1en6fnlu9U5t7ixvMZ/XrqpxP6auLgODk6a6Yaug3yB9/Az6kDeTzSP9LN3fYu+6eUPu2k3saGRegucoor9dGGPC3dXKBvsw40FmokcwfwCafEND7wbNdg/CN1lQ7/Xcvrd3Csk865RzrnzjZ/Ko/H0NLNBZr31U59vWN/4/m0lCjdOKGvLhye0Hkz1dBtUPjCyVv7pvT2TVJkinTbGsl+4uLV51sLdfOLP6i6zqOJg+P01PWjKXqhWyiprNWX2wq1dHOBlm0p1IEj2uRtNimtV5QmDjZb5YclRbS9Vd7jlt65RVr3huRwStPekPqf66Xv4iQduYPjuFukC/9fmz5NcUWNXvtur15csUu5JeY24E6HXZekJ2nW+FQNS4r0ZtRAE+QPvoGfUwfKWmb+w9YVIf12i+Q88RJyNixCd1VeXaevthdp6eYCfbalQPml1U1eH5oY0dgNlp4S1fYHdoYhfXSP9M1T9R3+z5o7YXamA1nSM+eZOzgOv9JcZdCGvLW8uk4LVu7Tf77aqV37KyRJDrtNFwxP0E/H99WYPtHejhxoROELJ+/5H5s7751zt3TOXSe8fOnmfN3y0irVuD2aNCReT14/Sq4Ail7oftweQ2v2FeuzzQVaurlAG3JKm7weH+HSuYPM5GjCgBiFtnb5nrtOenOmtPlDc3vwn7wt9cnw4ndwHGV55oYXpdlS//PMwlsrd3DcXnBI//lqp95ata9x18yYMKd+cnofXT+uD7uBoVOQP/gGfk4daMFPpfVvSWNvlH782AkvZ8MiwGQYhjbklJp53pYCZe4tbrIkskeoU+cMjNW5g+N01sDY1ndEGob04W+klc93fod/VYn07PlS0RYpabQ0a1Grd3Dce6BCL67Ypfnf71VZ/VzciKAAXTeut2ZkpCo5qhM2hkK3R+ELJ2f/DumJ0ZJs0u3rpchex738k435+uUrK1XrNnTBsAT947pRcgbQsgpIUn5pVWMRbPn2IlXUuBtfczrsGtevh84dZHaDnfTuQXXV0vxp0vZPJWe4NPN9KXl0B30H9Wor63dwXCnFDJRu/OSkd3A0DENfbivSvK92atmWwsbzQxIjdOOEvpqSlkihHJ2K/ME38HPqIOX7pccGS+4a6ebPpaT0417OhkVAy/YfqtayLYVauqVAX2wtbCz2SGaH05g+0Zo4OE7nDY7TgLiTHJBvRYe/u056baqZW4YnmZsWneQOjoZhaOXug3pu+U59tCFPDdM/+sWEatb4VF05phd/ZqBTUfjCyflkrvTV49KA86WfLDjupYvX5+pXr65WncfQxSMS9fi16azTBlpQXefWt1kHtLS+ELbnQEWT1/vFhmpifRFsbGqP4xeQayulV642OzODo6UbFkrxwzomcMOQ3rpJWr/A/Fo3LTmpHRyrat16Z3W25i3fqW0FhySZ3fKThsTrp+P76vR+PdimGpYgf/AN/Jw6yIqnpI/ulhLTpJ9/cdxL2bAIOHm1bo9W7j6ozzYXaMnmAm2vz30a9IoOblwSmdGv5/FHwrjrpAU3SJs+6JwO/8V3m0ssA4LNzS5OUBCXzM0AFq3L1byvdmrtvpLG82eeEqOfju+rswfGys6cVliAwhdOzF0rPTZUKi8wW2uHTGnx0oVrc3Xr/NVyewxdkpakx65JUwBFL+CkGIahHYXljd1g3+86oLojBuSHuQI0NjVaKdEh6hUdrOToYPWKDlFyVLBiwpxmwai6THrpcmnf91JorDTrv1LMKd4P9vO/Sp891OIOjlW1buWWVCn7YKWyiyuUfbBS+w5W6rMtBTpYUStJCnU6dM2pKbrhjFT16XmSnW1AByF/8A38nDqAYUhPZUiFm6SLH5VOvanFS9mwCGifvQcqGh92rsjar5q6wwPygwLtGtunh3r3rM/zosw8r1d0sGLDXGbBqK6mvsP/k/oO//ek5DHeD3Tl8+YGSpJ09QvSsMuavFxT51FuSWV9nlf/cbBSX2wrbJx35gyw64pRyZo1vq8GJYR7P0agFSh84cQ2fSi9fr35j+g5myRH8+vS1+4r1hVPfa06j6ErRiXrr1ensfMa0A6lVbVavq2ofkB+gYoO1bR4rSvA3lgI6x9ep1/u/o1iD21RTUiCSq59Xz17DfTeE7aN70lvzDAPxzyo73te0pjw7CuuVE5xpQrLqlt8e6/oYN1wRqquOTVFEQxBRhdB/uAb+Dl1gL3fSc+db3Z1/M8WKaj5jUR27y/XhX//UhU1bjYsArygoqZOX2/fryWbC/TZ5gLllVa1eK3TYVdSVJB6RYeoT4Rdv8i+U71KVqrOGan9V7+jmP6jvffvrp1fynjpMtk8dcoafpu+6nXj4QLXwQplF1eqoKxaLVUG4sJdmpHRR9ed1ts7u5gDXkDhCyf2ytXSto+l8bdJ5/+x2Uuqat368RPLtb3gkCYPi9dT14+h6AV4kcdjaG12iTbmlCq7uEL7DlY2dlHll1Udk3z0UKnmOx/UQHu29nhidb37D7JHJTV5gmj+anaOJUQENXZnGoahokM1jcWsho6t7OJKBRWu018P3alg1Whe3QX6Y92MFmMOcTqUHGV+/oZfhyRE6KyBsfz5gC6H/ME38HPqAO/Nlla/LKVNky7/Z7OXuD2Grv33Cn2/66BO69tDL914GnMYAS8yDEObcsu0Lru4Mb/bV5+H5ZZUynNUnheqSr3kfESj7dtVaERoWu1cVUb2q8/zjlwZEKxeUSFKjApqHD1jGIYOVtQ25nj7Dh7u2PLs36G/lcxRlA7pfXeGbq39laTmc7aGh66N+WRUsAbEhWni4HhmO6PLaU3+wPS57qhknznQUJJGz2zxssc+2artBYcUE+bSI1eM5B+1gJfZ7Talp0QpPSXqmNeObDdvSJT2HazQo0V/0f2Fv1Vve57+o4c0df/9+mp/80/yHXabEiKC5AqwK7u4UtVHtN43iNVBve96UMG2Gi1zp+mpwBs0PD7MLGpFhRyT/ESFBDKvCwC6sqpSaf3b5vHolh9kzFu+U9/vOqhQp0OPXp1G0QvwMpvNpqFJERqadOw/yGvdHuWVVCm7uPKIB58VeurA/9Mdeb/TQGXpxcA/6eriB/TNwThJB475HHabFB8RpBCnQznFVaqsdR9zTbgq9I7z94qyH1Kmp58edMzWkJjIJrndkQ8ze4Y6yfPglyh8dUeZr0qGR+ozocXB1d/vOqBnvsySJD1yxQj1CHV2ZoRAt+cMsKtPz9Bm5mSlS8UjZcy7QANKs/VF4t+1dNxz2lnuql+WeLiTq9ZtKLu4svGdNpsUHx7UmOD0ibRp5paHFVNyQNXRp+jUG97VD5E9OvX7BAB42fq3pNoKc2fe3qc3e8m2/DL99eMtkqT7fzxUKT1COjNCoNsLdNiV0iOk+f/3yj+V8fxFSizcrCU9H9VnZ7ygHdWR5oPQ+mWJ2QfNB5q5JU2XUsaGuxqLWCmRgZqedYeS9+eoNjRBA2a9r+9jUjrpOwS6Fgpf3Y3HI616yTxu4SlgeXWdfvvGGhmGdNWYXjp/aHwnBgjghKJ6yzbzA+k/Fyr04GZNWftracZ7UtDhJ4oej6HCQ9Xad7BCNXWGkqOClRAZdLhN3TCkt26UStZLwdFyTX9DLopeAOD7Vr1o/jp6hvnE4yi1bo9+++Ya1dR5dM6gWE09lX8IA11KaE/ZZrwnzbtAroM7dcHKn0uzFklhAxovaRhhse9ghSpr3EqMClZiZFDTGX3/vUva/7UUEKzA619XIEUvdGMs1O1usj6TSvaYQ06HXtLsJX/+72btOVChpMggPTBlaCcHCOCk9OxvFruCe0g5q6RXp0o1FY0v2+02xUcEaUyfHsro31O9e4Y0nc3wxV/NrgB7gHTNS1KPfhZ8EwAAr8pbZ/6dYA+U0q5r9pJ/LtuhtftKFBkcqP935UiWNQFdUXiCNPN9KaKXtH+bubt3xeHljjabTbHhLo3qHa0zBsSob0xo06LXD/+Rvq2f73fFv6Sk9M6NH+hiKHx1Nw1PAUdOlQKDj3n5y22Feumb3ZKkv1yVxu5sQFcWN0Sa/o7kipT2fG3u1FrX8s6LjTa8K332J/P44sekvmd2aJgAgE7SkOcNvlgKjTnm5fXZJfrHkm2SpD9eOkzxEUGdGR2A1ojqbRa/wuKl/PXSy1eaM/xOZOcX0qL/MY/PvU8aemnHxgn4AApf3Ul5kbR5oXnczDLH0qpa3bFgrSRp+ul9NOGUYxMmAF1MUrr0kwVSYKi0Y6n05g2Su7bl63NWS+/cYh6f/ktpTMsbXAAAfEhtpbT2dfO4mTyvus6t376xRnUeQxcOT9AlaUmdHCCAVmu2w7+85ev375Beny556qThV0ln/U/nxQp0YRS+upM1r0meWilptJQw4piXH/xgo3JLqtSnZ4juunCwBQECaJOU06Rp86WAIGnLIuntmyXPsTv7qDRXem2aVFcpDThfOv/Bzo8VANAxNr4vVZVIkb2lfuce8/Ljn27Tlvwy9Qx16qHLhrPEEfAVR3f4z79eqq069rrKYum1a6WqYil5jHTp/zU75w/ojih8dReGIa18wTxu5ingpxvz9ebKfbLZpL9dnaZQF/seAD6l71nmrC57oLThben9W83NLBrUVkrzp0llOVLMIOmq5yQH/58DgN9oHGo/XbI3TfFX7j6of32+Q5L08BUj1DPM1dnRAWiPIzv8sz47tsPfXSctmCUVbZUikqVrX212rA3QXVH46i72fGMORgwMlUZc1eSlg+U1uuvtdZKkn53ZT6emsrMb4JMG/sgsaNnsUubL0uI7zaK3YUjv/tJskQ/uYXaHBUVaHS0AwFuKtku7l5t//qdPa/JSZY1b//PmGnkM6YpRyZo8LMGiIAG0y5Ed/lv/27TD/+N7zZEXgSHSda+Zw/EBNOJxf3fR8BRw+OWSK7zJS/e/t15Fh6o1IC5Mc84faEFwALxm6KXSZU9L7/xc+u7fZgIUGGJ2gdkDpKns4AgAfmd1fZ43YJIU2avJS3/5aLN2FpUrISJIc6cMsyA4AF7T9yxp6svSa9eZuV1giJQ8Svr2afP1y/8lJaZZGyPQBVH46g4qi6UN75jHo5sOsv5gTY4+XJsrh92mx65Ja7oNLgDflDZVqq2QPvyN9NXjh8//+H+l1AlWRQUA6AjuWinzVfP4qDzv6x1F+s9XuyRJf75yhCJD2K0b8HmnnC9dNc9c7pj5svkhSRPvk4ZeYmloQFfFUsfuYP0Cc5h17BCp16mNpwvKqnT/e+slSbPPHaCRvaIsChCA142dJU1++PB/nz672fl+AAAft3WxVF4ohcZJAyc3nj5UXaffvWnu1n3dab11zqA4qyIE4G1DL5Eu+6ek+uH1I66WzmQHR6AldHx1B43DTmc07uxhGIbufmudiitqNSwpQr86d4CFAQLoEBmzpbB4qWSvdMatVkcDAOgIDZsXpU+THIc7uv60cKOyiyvVKzpY9148xKLgAHSYtKnmzNbcTGn8bezgCBxHqzu+vvjiC02ZMkVJSUmy2Wx69913T/ieZcuWafTo0XK5XBowYICef/75NoSKNsnJlHLXSA6nNHJq4+kFK/dpyeYCOR12PXpNmpwBNP8BfmnEVdKE2yU7y5gBnBh5no8p2Sdt/9Q8PqKr97MtBXrtu72SzN26w9itG/BPgy6QzrmLHRyBE2h1taO8vFxpaWl68sknT+r6nTt36uKLL9a5556rzMxM/eY3v9FNN92kjz76qNXBog0aur2GTJFCe0qSsosr9ccPNkqSbj9/oAYnRFgVHQAA6ELI83zM6lckGVLqmVLP/pKk4ooa3bnAXOL40/F9dXq/nhYGCACA9Vr9+OfCCy/UhRdeeNLXP/300+rbt68effRRSdKQIUO0fPly/e///q8mT558gnejXWoqpHVvmsf1TwENw9CdC9aqrLpOo3pH6eaz2N0NAACYyPN8iMctrX7JPD5iqP3v39+ggrJq9YsN1R0XDLIoOAAAuo4OX9+2YsUKTZo0qcm5yZMna8WKFS2+p7q6WqWlpU0+0AYb35WqS6XoVCn1LEnSy9/u0fLtRQoKtOvRq9PksLMWHAAAtA15noWyPjNnOAZFmZ39kv67LlfvZubIbpMevZrdugEAkDqh8JWXl6f4+Pgm5+Lj41VaWqrKyspm3/PII48oMjKy8SMlJaWjw/RPDcscR02X7Hbt3l+uhxdukiTdecFg9YsNszA4AADg68jzLNSQ542cKgUGqehQte5919yt+xfn9Neo3tEWBgcAQNfRJSea33333SopKWn82Lt3r9Uh+Z7CLdKeFZLNIaVfL7fH0P+8uUaVtW6d3q+HZmakWh0hAADohsjzvOBQobR5kXk8eoYMw9A9b6/TgfIaDU4I163nnWJtfAAAdCEdvsVLQkKC8vPzm5zLz89XRESEgoOb333C5XLJ5XJ1dGj+reEp4MDJUkSi5n2Rpe93HVSo06G/XpUmO0scAQBAO5HnWWTNa5KnVkoeIyUM17ur9+njjfkKdNj02DXpcgWwxBEAgAYd3vGVkZGhJUuWNDn3ySefKCMjo6O/dPdVV2MmRJI0eoa25Zfprx9vkSTd/+OhSukRYmFwAADAX5DnWcAwDj/gHD1DuSWVeuC9DZKk2847RUOT2K0bAIAjtbrwdejQIWVmZiozM1OSuY11Zmam9uzZI8lsX58xY0bj9bfccouysrJ0xx13aPPmzXrqqaf0xhtv6Pbbb/fOd4BjbVkoVeyXwhNV2+88/fbNNaqp8+icQbGaeipzNAAAQPPI83zAnhXS/m1SYKiMYVfozrfWqayqTmm9InXL2f2tjg4AgC6n1YWvH374QaNGjdKoUaMkSXPmzNGoUaP0wAMPSJJyc3MbkyNJ6tu3rxYuXKhPPvlEaWlpevTRR/Xss8+yxXVHangKmH69/vnFbq3dV6LI4ED9vytHymZjiSMAAGgeeZ4PaMjzhl+h+WuL9cXWQjkD7Hr0mjQFOLrk+F4AACxlMwzDsDqIEyktLVVkZKRKSkoUEUH79nEd3C39PU2SoS1Tv9TFL+1TncfQ369N16XpyVZHBwBApyF/8A38nFqhslh6dLBUV6n8qz/UxNfLVV7j1n0XD9FNZ/azOjoAADpNa/IHHgv5m9UvSzLk6Xu2bl1crDqPoQuHJ+iStCSrIwMAAEB7rHtTqquUETdUt37pUHmNW6el9tCs8X2tjgwAgC6Lwpc/8bjrC1/Sh47ztSW/TD1DnXrosuEscQQAAPB19cscv426WN/uOqgQp0N/vXqkHOzWDQBAiyh8+ZPtS6SyHNW5onXHBnOI/cNXjFDPMLYMBwAA8Gk5q6W8tTLsTt22caAk6Z6LhqhPz1CLAwMAoGuj8OVPVr0gSXrHc6aqjEBdMSpZk4clWBwUAAAA2q2+2+vLwAzl14XqzFNidP243hYHBQBA10fhy1+U5Utb/itJ+vehCUqICNLcKcMsDgoAAADtVlMurVsgSfpn2QSFBwWwWzcAACcpwOoA4CWZr0iGWys9p2ib0UsvXDVSkSGBVkcFAACA9trwrlRdqj1GnL7xDNHfpgxTUlSw1VEBAOAT6PjyB4Yhz0qz/X2++1xNG9dbZw+MtTgoAAAAeINnpTnOYn7duZo0NFFXjE62OCIAAHwHHV/+YNdy2Yt3qswI1pqIc/T2RUOsjggAAADeULhF9n3fqs6w6xPneXr18hEscQQAoBXo+PIDecv+JUn6wJOhP159usJc1DMBAAD8QcHn/5YkLfWM0u1XnKXYcHbrBgCgNSh8+biKPZmK3r3YPB7+E53er6fFEQEAAMAbaouyFLThdUnSzt5X6qIRiRZHBACA76Hw5cty18r+4iVyqVar7cP1k8svtToiAAAAeMOBLNU+e6EijDJtU29dc+0sqyMCAMAnUfjyVblrZLwwRUF1Jcr09NeeHz2rICdLHAEAAHze/h0ynr9YIVV52u5J0ooznlF0eIjVUQEA4JOolPiinEzpxUtlqyrWas8A3RP6B31w6iCrowIAAEB77d8hPf9j2cpytN2TpFscv9d7Z4+1OioAAHwWHV++Jme19OKlUlWx1mqgptfcpVkT0xTg4EcJAADg0+qLXirL0W57L11bc78uP2uMQtm4CACANqNa4kuyVzUWvQoiR2pa1R2KjOqpy0cnWx0ZAAAA2qNou/T8xVJZjsrC++vKintVE9RTMzL6WB0ZAAA+jcKXr8heJb10mVRVIk+v03Rtxe90SCGafe4ABdLtBQAA4Lsai165MmKH6EY9oCJF6sYJ/RQeFGh1dAAA+DQqJr4ge6X04mVSVYmUcrpeH/S4ssocSowM0pVj6PYCAADwWUXbzKLXoTwpbqiWnvasvisMVLgrQDeMT7U6OgAAfB6Fr65u30rpxcul6hKpd4Zqrn1DTyzPkyT94pz+cgU4LA4QAAAAbVK41ZzpVV/0Mma8r799fVCSdMP4VEUG0+0FAEB7Ufjqyvb9YC5vrC6Rep8hXf+m3tpQopySKsWFu3TN2BSrIwQAAEBbFG6VXmgoeg2TZn6gT/d4tCm3VKFOh346vq/VEQIA4BcofHVVe7+XXrpcqi6V+oyXrn9TtQGhevKz7ZKkW87ur6BAur0AAAB8TuGW+uWN+VL8cGnmBzJCeuofS7ZJkmackaroUKfFQQIA4B8ofHVFe79rWvSa9obkCtM7q7O172ClYsJcuu603lZHCQAAgNYq2GwubywvkOJHSDPel0J7atmWQq3LLlFwoEM3TaDbCwAAbwmwOgAcZc+30stXSjVlUuqZ0rTXJWeo6tyexm6vm8/qq2An3V4AAAA+pWCT9MIUqbxQSqgveoX0kGEY+nt9t9f0jD7qGeayOFAAAPwHha+uZM+30stXSDWHmhS9JOmDtTnavb9CPUKdun5cH4sDBQAAQKsUbDI7vSqKpISR0oz3pJAekqTl24uUubdYrgC7bjqTbi8AALyJpY5dxZ5vjip6vdFY9HJ7DD2x1Oz2uunMvgp1Ua8EAADwGfkbWyx6GYahv39qdntNG9dbceFBVkYKAIDfoYLSFexeYS5vrC2X+p4lXfe65AxpfHnhulxlFZYrKiRQMzJSrYsTAAAArZO/wVzeWLFfSkyTpr/bWPSSpBVZ+/XD7oNyBth1y9n9rYsTAAA/RceX1XZ/fbjo1e+cY4peHo+hJ+pnPtw4vq/C6PYCAADwDXnrjyh6pTfp9GrQsJPjtaemKD6Cbi8AALyNKoqVdn0lvXJ1fdHrXOm616TA4CaXLN6Qp20FhxQeFKCZ41OtiRMAAACt01D0qjwgJY2Spr8jBUc3ueS7nQf0TdYBBTpsdHsBANBB6Piyyq7lh4te/Sc2W/TyeIzGp4CzxvdVRFCgFZECAACgNfLWHVH0Gm0ubzyq6CVJTyw187yrx6YoKSr4mNcBAED70fFlhZ1fSq9eI9VWSP3Pk6595ZiilyR9uilfm/PKFOYK0E/p9gIAAOj6ctdKL14iVR6UksdIP3lbCo465rKVuw/qy21FCrDb9Au6vQAA6DAUvjrbkUWvAZOkqa9IgcfOczAMQ/+ofwo484w+igpxdnakAAAAaI3cNdKLl9YXvcZK09+WgiKbvbSh2+uK0clK6RHS7DUAAKD9KHx1pqzPpVenSnWV0oDzpakvN1v0kqTPthRofXapQpwO3TihXycHCgAAgFbJyTSLXlXFUq9TpZ+81WLRa83eYi3bUiiH3abZ5w7o1DABAOhumPHVWbKWHS56nfKj4xa9DMPQ35dslyRNP72PeoTS7QUAANBlHVP0arnTSzrc7XVpepL69AztnBgBAOim6PjqDI1FryrplMnS1JekAFeLl3+xrUhr9hYrKNCum86k2wsAAKDLylldX/QqkXqdVt/pFdHi5euzS/TppgLZbaLbCwCATkDhq6OV75dem2YWvQZeIF3z4nGLXoZxeCfH68f1UWx4y9cCAADAQrVV5i7dVSVSyjiz6OUKP+5b/m+p2dX/45FJ6h8b1hlRAgDQrbHUsaPtWSHVlks9+p+w6CVJK3bs18rdB+UMsOvnZ9HtBQAA0GXlrZPKC6WQnidV9NqcV6rFG/Jks0m/mki3FwAAnYHCV0fLWWX+2ueMExa9JOnv9d1e007rrbiI5meAAQAAoAtoyPOSx56w6CVJT9R3e100PFED4098PQAAaD8KXx0tuyEhGn3CS7/J2q9vdx6Q02HXz8+m2wsAAKBLa0Wety2/TIvW5Uqi2wsAgM5E4asjGYY58FSSkk6cEDXs8HP12F5KjAzuyMgAAADQXg0dXyeR5/3fZ9tlGNLkYfEaktjy8HsAAOBdFL460oEsc1trh0uKG3rcS1fuPqCvtu9XgN2mX5zTv3PiAwAAQNtUlUpF5kNLJY067qVZhYf0wZocSdKvJ57S0ZEBAIAjUPjqSA3dXgnDpQDncS/9xxJz5sNVY3qpV3RIR0cGAACA9sjNlGRIkSlSWOxxL33ysx3yGNJ5g+M0PDmyU8IDAAAmCl8d6SSXOWbuLdbnWwvlsNv0y3OY+QAAANDlNeZ5x+/22r2/XO9mZkuSfn0e3V4AAHQ2Cl8d6SQHnj5Rv5PjZenJ6t2Tbi8AAIAu7yTzvKc+2yG3x9DZA2OVnhLV8XEBAIAmKHx1FI9byl1jHh+n42t9domWbC6Q3SbNPpfZXgAAAD7hJAbb7z1QobdW7ZMk3Uq3FwAAlqDw1VEKt0i15ZIzTIppOdFp2MnxkrQk9YsN66zoAAAA0FblRVLxHvM4Kb3Fy57+fIfqPIYmDIjRmD7RnRMbAABogsJXR2l4CpiYJtkdzV6yKbdUH23Il80m/Wois70AAAB8QsN8r56nSEHND6vPKa7UGz/slST9mjwPAADLUPjqKCcx8PT/lpo7OV40IlED4sI7IyoAAAC0V8N8r+Pkef/6fIdq3YbG9e2hcf16dlJgAADgaBS+OsoJBp5uzS/TovW5kngKCAAA4FMaHnC2kOfll1bpte/Nbq/bmO0FAIClKHx1hLoaKX+9edzCwNP/W7pdhiFdMCxBgxMiOjE4AAAAtJlhnHCw/b8+z1JNnUdj+0Qroz/dXgAAWInCV0fIXy+5a6TgHlJ06jEv7yg8pA/X5kiSfn0e3V4AAAA+ozRHOpQv2RxSwohjXi4sq9ar3+2WZO7kaLPZOjtCAABwBApfHSHniLkPzSQ7T362XR5DmjQkXsOSmh+ICgAAgC6oIc+LGyo5Q455+dkvs1RV61FaSpTOPCWmk4MDAABHa1Ph68knn1RqaqqCgoI0btw4fffdd8e9/vHHH9egQYMUHByslJQU3X777aqqqmpTwD4hu+XB9ruKyvVeptntdSvdXgAAoIshzzuBxsH26ce8tP9QtV5cYXZ73XbeALq9AADoAlpd+Hr99dc1Z84czZ07V6tWrVJaWpomT56sgoKCZq9/9dVXddddd2nu3LnatGmTnnvuOb3++uu655572h18l3WcgadPLdsut8fQOYNiNbJXVOfGBQAAcBzkeSfhOHnec8t3qrLWreHJETp3UFwnBwYAAJrT6sLXY489pp/97GeaNWuWhg4dqqefflohISGaN29es9d//fXXGj9+vKZNm6bU1FT96Ec/0nXXXXfCp4c+q6ZcKtxkHh818HTvgQq9vSpbkvTriezwAwAAuhbyvBMwjMOFr6PyvOKKGr3w9S5J0q0Tme0FAEBX0arCV01NjVauXKlJkyYd/gR2uyZNmqQVK1Y0+54zzjhDK1eubEyAsrKytGjRIl100UUtfp3q6mqVlpY2+fAZuWslwyOFJ0oRiU1eemrZDtV5DJ15SozG9Im2KEAAAIBjkeedhANZUlWx5HBJ8cOavDRv+U6V17g1JDFC5w+NtyY+AABwjIDWXFxUVCS32634+KZ/mcfHx2vz5s3NvmfatGkqKirShAkTZBiG6urqdMsttxy3Bf6RRx7RH/7wh9aE1nW0sL11TnGlFqzcK8nc4QcAAKArIc87CQ3dXgkjJEdg4+mSylr9p7Hbi9leAAB0JR2+q+OyZcv08MMP66mnntKqVav09ttva+HChXrwwQdbfM/dd9+tkpKSxo+9e/d2dJjek33Ejo5HePrzHap1Gzq9Xw+dmtrDgsAAAAC8q9vmeUfN93rh610qq6rTwPgwTR6WYEFgAACgJa3q+IqJiZHD4VB+fn6T8/n5+UpIaP4v+fvvv1/Tp0/XTTfdJEkaMWKEysvLdfPNN+vee++V3X5s7c3lcsnlcrUmtK6jceDp4cJXXkmV5n9HtxcAAOi6yPNOQs6xDzjLqmr13PKdkqRfTTxFdjvdXgAAdCWt6vhyOp0aM2aMlixZ0njO4/FoyZIlysjIaPY9FRUVxyQ9DodDkmQYRmvj7doqi6UDO8zjI5Y6/uuLHapxe3RqarQy+vW0JjYAAIDjIM87AY9byl1jHh+R5724YrdKKmvVLzZUF49IbOHNAADAKq3q+JKkOXPmaObMmRo7dqxOO+00Pf744yovL9esWbMkSTNmzFBycrIeeeQRSdKUKVP02GOPadSoURo3bpy2b9+u+++/X1OmTGlMjPxGQ7dXdKoUYi5nPFBeo1e/3SPJ7PZi5gMAAOiqyPOOo3CLVFshOcOkGLODv6rWrWe/zJIk/XriADno9gIAoMtpdeFr6tSpKiws1AMPPKC8vDylp6dr8eLFjYNQ9+zZ0+TJ33333Sebzab77rtP2dnZio2N1ZQpU/SnP/3Je99FV9HMYPv3MrNVXefRsKQITRgQY1FgAAAAJ0aedxwNeV5iumQ3i3qfbMzXwYpaJUcFa8rIJOtiAwAALbIZPtCHXlpaqsjISJWUlCgiIsLqcFo2/3pp84fS+Q9K42+VJF38jy+1IadUf7x0mGZkpFobHwAA3YjP5A/dnM/8nD6cI/3wnHTGr6UfPSRJmjnvO32+tVC3ThygOT8aZHGAAAB0H63JHzp8V8duJSfT/LV+p5+NOaXakFOqQIeNp4AAAAC+7KjO/rySKn25rVCSdMXoXlZFBQAAToDCl7ccKpBK90mySYlpkqS3Vu2TJE0aEq/oUKeFwQEAAKDN6qqlvPXmcf2Oju+szpbHkE5NjVZqTKiFwQEAgOOh8OUt2fVPAWMHSa5w1bo9end1tiTpqjE8BQQAAPBZ+RskT60U3EOKTpVhGFqwcq8k8jwAALo6Cl/eclT7+7IthdpfXqOYMJfOGhhrYWAAAABol8Y8b5Rksylzb7F2FJYrKNCui0YkWhsbAAA4Lgpf3tLQ8VU/36vhKeDlo5IU6OA2AwAA+Kzs1eav9XlewziLC4cnKjwo0KqoAADASaAi4w2G0eRJ4IHyGi3dXCBJupL2dwAAAN92RGd/Va1b72fmSGKZIwAAvoDClzeU7JUq9kv2ACl+uN7PzFat29CI5EgNTujC23IDAADg+GrKpcLN5nHSKH26KV+lVXVKigxSRr+e1sYGAABOiMKXNzQsc4wfJgUGaUF9+/uVo5MtDAoAAADtlrtWMjxSeKIUkagFK80874rRvWS32ywODgAAnAiFL284ov19U26p1meXKtBh0yXpFL4AAAB82hF5Xn5plb7YWiiJcRYAAPgKCl/ecMRg+7fqnwKeNzhePUKdFgYFAACAdmvM80bpndXZ8hjS2D7R6hsTam1cAADgpFD4ai+PR8pdI0mqjU/Tu5nZkhh2CgAA4BfqO76MpMMPOMnzAADwHRS+2uvADqm6VAoI1pfFMSo6VKOYMKfOHhRrdWQAAABoj8qD0oEsSdIG9de2gkMKCrTropGJFgcGAABOFoWv9mpof08cqTdX50mSLktPVqCDWwsAAODTclabv0an6vX1hyRJFwxLUERQoIVBAQCA1qA601717e9VcWn6dFO+JIadAgAA+IX6wpc7cZTeX5MjiTwPAABfQ+Grveo7vr6rSVWt29CwpAgNSYywOCgAAAC0W32et8Vxikoqa5UYGaQz+sdYHBQAAGgNCl/t4a6V8tZKkl7ZayZBDDsFAADwE/UdX+8VxEuSrhidLIfdZmVEAACglSh8tUfhZqmuSm5nuD7OC1Ggw6ZL05OtjgoAAADtVZYvlWbLsNn16t4ekqQrR/OAEwAAX0Phqz3q29/3uAbKkF0TB8epR6jT4qAAAADQbvVzXA+G9FWZx6UxfaLVLzbM4qAAAEBrUfhqj/qE6PNDKZKkq8akWBkNAAAAvKX+AecPNX0kMc4CAABfReGrPeoTom+qU9Uz1KlzBsVaHBAAAAC8on6+15cVveUKsOvikYkWBwQAANqCwldb1VZJBRslSWs9/XRperICHdxOAAAAn2cYjZ39az39NHlYgiKCAi0OCgAAtAWVmrbKWyd56rTfiFCOetL+DgAA4C+K90gV+1UrhzYZfcjzAADwYRS+2qq+/X2Np5+GJkZqaFKExQEBAADAK+q7vTZ5eqtHRLjGD4ixOCAAANBWFL7aqqH93ejHU0AAAAB/Uj/HdZ2nn64YnSyH3WZxQAAAoK0ofLVR9Z4fJEnrjf66ND3J4mgAAADgLTV7V0qS1hj9dCUPOAEA8GkUvtqiukzOg9slSZH9T1PPMJfFAQEAAMArPB4pZ40kqTY+Xf1jwywOCAAAtAeFrzZw71stmwxlGz31o3EjrQ4HAAAAXmLs3yan+5AqDadOPTXD6nAAAEA7Ufhqg53rlkuSNtsG6NxBcRZHAwAAAG/Zt/4rSdJG9dXF6b0tjgYAALQXha82KNn+rSTJSB4lZwC3EAAAwF/kbDQLX6U9RigyONDiaAAAQHtRtWml4ooaxZVtlCQNSD/L4mgAAADgLdV1bgUVmvO9EgazzBEAAH9A4auVPv5+g1JsBZKk1OHjLY4GAAAA3rJsY7YGGbskSQNHn21tMAAAwCsofLXSxlVfSJKKQ/pIwVHWBgMAAACv+eabrxRkq1WVI0yOnv2tDgcAAHgBha9W2JZfpvCitZKkoD5jLI4GAAAA3lJYVq3qPT9IkjyJ6ZKdNBkAAH/A3+itsGDVPo2075QkBfU+1eJoAAAA4C3vZWZruHZIkkJSyfMAAPAXFL5OUp3bo3dWZWuk3UyIlDza2oAAAADgFYZhaMHKfUqzZ5knksjzAADwFxS+TtKX24tkK8tVvK1Yhs0hJYy0OiQAAAB4wYacUu3M269Btr3miaRR1gYEAAC8hsLXSTKfAprdXra4IZIzxOKIAAAA4A0LVu7TUNtuBdg8UmisFNnL6pAAAICXUPg6CSUVtfpkQ75GNra/p1saDwAAALyjps6j9zKzj8jzRks2m7VBAQAAr6HwdRI+WJujGrdHGUF7zBPMfQAAAPALSzcX6GBFrcY5d5knmOMKAIBfofB1Ehas3CfJ0DDVPwkkIQIAAPALZp4nnebaZZ7gAScAAH6FwtcJbC8oU+beYvW1FyqorkRyOKW4YVaHBQAAgHYqOlStZVsKFKYK9axq6OxnsD0AAP6EwtcJLFiZLUm6NrnQPJEwQgpwWhgRAAAAvOG9zBzVeQxdGl8kmwwpMkUKi7U6LAAA4EUUvo7D7TH0zmqz/f1HUWYBjPZ3AAAA/9CwzPGKhHzzBN1eAAD4HQpfx/HltkLll1YrOiRQfaq3midJiAAAAHzehpwSbcotldNh1wjmuAIA4LcofB1Hw1PAy9ISZM9dY54kIQIAAPB5DXne+cPi5cxfbZ6ksx8AAL9D4asFJZW1+nij2fZ+Xb8qqbZcCgyVYgZaHBk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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "fig, axs = plt.subplots(1, 2, figsize=(15,6))\n",
        "fig.suptitle(\"Plots\", fontsize=20)\n",
        "axs[0].plot(x, func(x, *polytuple), label=\"Polynomial LSQ\")\n",
        "axs[0].plot(x, y, label=\"Original Data\")\n",
        "axs[1].plot(x, func(x, *chebytuple, basis=\"cheby\"), label=\"Chebyshev LSQ\")\n",
        "axs[1].plot(x, y, label=\"Original Data\")\n",
        "\n",
        "axs[0].legend()\n",
        "axs[1].legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 582
        },
        "id": "dk2D_KGf5CJ6",
        "outputId": "93c42c7b-bda3-4302-8e29-c70d8e048093"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1500x600 with 2 Axes>"
            ],
            "image/png": 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          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#3"
      ],
      "metadata": {
        "id": "Pe3e-GXB7Rh_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "YDpH3pT47W-6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Assuming the marks are normally distributed with a mean (μ) of 0 and a standard deviation (σ) of 1, you can use the properties of the standard normal distribution to estimate the proportion of students falling within each category.\n",
        "\n",
        "Here's how you can calculate the approximate number of students falling into five different mark categories based on standard deviations from the mean:\n",
        "\n",
        "Category (A): Below -2 Standard Deviations:\n",
        "\n",
        "Approximately 2.5% of students fall in this category. Number of students ≈ 2.5% of 600 ≈ 0.025 * 600 ≈ 15 students.\n",
        "\n",
        "Category (B): Between -2 and -1 Standard Deviation:\n",
        "\n",
        "Approximately 13.5% of students fall in this category. Number of students ≈ (13.5% - 2.5%) of 600 ≈ (0.135 - 0.025) * 600 ≈ 72 students. Category (C): Between -1 and 1 Standard Deviation (Central Category):\n",
        "\n",
        "Approximately 68% of students fall in this category. Number of students ≈ 68% of 600 ≈ 0.68 * 600 ≈ 408 students. Category (D): Between 1 and 2 Standard Deviations:\n",
        "\n",
        "Approximately 13.5% of students fall in this category. Number of students ≈ (13.5% - 2.5%) of 600 ≈ (0.135 - 0.025) * 600 ≈ 72 students.\n",
        "\n",
        "Category (E): Above 2 Standard Deviations:\n",
        "\n",
        "Approximately 2.5% of students fall in this category. Number of students ≈ 2.5% of 600 ≈ 0.025 * 600 ≈ 15 students.\n",
        "\n",
        "so according to our data we have A=77,B=150,c=210,D=125,c"
      ],
      "metadata": {
        "id": "Z2qtDfKK4lev"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Based on the given information and calculations, the distribution of students across different mark categories can be summarized as follows:\n",
        "\n",
        "Category (A): Below -2 Standard Deviations:\n",
        "Approximately 2.5% of students fall into this category. Thus, there are approximately 15 students in this category.\n",
        "\n",
        "Category (B): Between -2 and -1 Standard Deviation:\n",
        "Approximately 13.5% of students fall into this category. Therefore, there are roughly 72 students in this category.\n",
        "\n",
        "Category (C): Between -1 and 1 Standard Deviation (Central Category):\n",
        "Approximately 68% of students fall into this category. This translates to about 408 students.\n",
        "\n",
        "Category (D): Between 1 and 2 Standard Deviations:\n",
        "Approximately 13.5% of students fall into this category. So, there are around 72 students in this category.\n",
        "\n",
        "Category (E): Above 2 Standard Deviations:\n",
        "Approximately 2.5% of students fall into this category. Hence, there are approximately 15 students in this category.\n",
        "\n",
        "Therefore, based on the provided data, the distribution of students across the categories is estimated as:\n",
        "\n",
        "    Category A: 15 students\n",
        "    Category B: 72 students\n",
        "    Category C: 408 students\n",
        "    Category D: 72 students\n",
        "    Category E: 15 students."
      ],
      "metadata": {
        "id": "8C66-XDy7qBB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "O_i=np.array([77,150,210,125,38])\n",
        "E_i=np.array([15,72,408,72,15])\n",
        "\n",
        "\n",
        "def chi_square(x,y):\n",
        "  z=(x-y)**2/y\n",
        "  A=np.sum(z)\n",
        "  return A\n",
        "print(chi_square(O_i,E_i))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ens_v04l7SaI",
        "outputId": "d2c70135-f9d0-4bbb-eda5-81bb42cf3f2c"
      },
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "511.1354575163399\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Based on the significance levels of 5% and 10% with degrees of freedom (D.O.F) equal to 4 (5 - 1), the critical values from the table are 9.788 and 7.997, respectively. However, the calculated value of χ² is 511.13, which significantly exceeds these critical values. Consequently, we reject the null hypothesis that the distribution follows a standard normal distribution."
      ],
      "metadata": {
        "id": "gOF37fzF73QR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "np.random.seed(42)\n",
        "\n",
        "\n",
        "num_students = 600\n",
        "marks = np.random.normal(loc=0, scale=1, size=num_students)\n",
        "\n",
        "\n",
        "plt.hist(marks, bins=10, edgecolor='black')\n",
        "plt.xlabel('Marks')\n",
        "plt.ylabel('Frequency')\n",
        "plt.title('Distribution of Marks for 600 Students (Standard Normal)')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "75epgfmW7bPU",
        "outputId": "9f982bcc-34e5-4c9d-a22d-f5aee76a06f9"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#4"
      ],
      "metadata": {
        "id": "xE8h_g2g8YlL"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The necessary values for conducting a t-test have been provided, yielding a result of -0.1515 when substituted into the formula. However, with a significance level (alpha) of 0.05 and degrees of freedom (DOF) set to 20, the critical boundary values are ±2.086. Given that the calculated t-value falls within this interval, we cannot reject the hypothesis."
      ],
      "metadata": {
        "id": "ZjOdZc4O8Fg6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "# Define the arrays\n",
        "data_A = np.array([4.65, 4.84, 4.59, 4.75, 4.63, 4.75, 4.58, 4.82, 4.86, 4.6, 4.77, 4.65, 4.8])\n",
        "data_B = np.array([4.75, 4.79, 4.74, 4.74, 4.77, 4.58, 4.81])\n",
        "\n",
        "# Calculate means\n",
        "mean_A = np.mean(data_A)\n",
        "mean_B = np.mean(data_B)\n",
        "\n",
        "# Function to calculate sample variance\n",
        "def sample_variance(data):\n",
        "    n = len(data)\n",
        "    mean = sum(data) / n\n",
        "    variance = sum((x - mean) ** 2 for x in data) / (n - 1)\n",
        "    std_dev = np.sqrt(variance)\n",
        "    return std_dev\n",
        "\n",
        "# Calculate sample variances\n",
        "A_std_dev = sample_variance(data_A)\n",
        "B_std_dev = sample_variance(data_B)\n",
        "\n",
        "# Print results\n",
        "print(\"Mean of data A:\", mean_A)\n",
        "print(\"Mean of data B:\", mean_B)\n",
        "print(\"Standard deviation of data A:\", A_std_dev)\n",
        "print(\"Standard deviation of data B:\", B_std_dev)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TnrnQ43U8GaY",
        "outputId": "03a94578-7c5a-490e-f028-3939347865c4"
      },
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean of data A: 4.714615384615384\n",
            "Mean of data B: 4.74\n",
            "Standard deviation of data A: 0.1012929237916273\n",
            "Standard deviation of data B: 0.07527726527090799\n"
          ]
        }
      ]
    }
  ]
}