StdPCA.ipynb

{
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  "metadata": {
    "colab": {
      "name": "Q3a",
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "metadata": {
        "id": "XqxKcHMQYzFy",
        "outputId": "48c0455b-081b-475b-fe57-98e8886c2018",
        "colab": {
          "resources": {
            "http://localhost:8080/nbextensions/google.colab/files.js": {
              "data": 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              "ok": true,
              "headers": [
                [
                  "content-type",
                  "application/javascript"
                ]
              ],
              "status": 200,
              "status_text": ""
            }
          },
          "base_uri": "https://localhost:8080/",
          "height": 73
        }
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "from google.colab import files\n",
        "uploaded=files.upload()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-5a55d1be-33d2-4d55-ba9b-d6f9e4977e58\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-5a55d1be-33d2-4d55-ba9b-d6f9e4977e58\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script src=\"/nbextensions/google.colab/files.js\"></script> "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Saving Dataset3.csv to Dataset3.csv\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RNNvfO4JbcIm",
        "outputId": "a41ac9df-b5e1-4ccb-e75b-86c888ea5463",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        }
      },
      "source": [
        "import io\n",
        "data=pd.read_csv(io.BytesIO(uploaded['Dataset3.csv']),header=None)\n",
        "data"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.14300</td>\n",
              "      <td>0.98493</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>-0.30467</td>\n",
              "      <td>0.98562</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.46625</td>\n",
              "      <td>-0.84003</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.94847</td>\n",
              "      <td>0.37222</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-0.96871</td>\n",
              "      <td>-0.26697</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>995</th>\n",
              "      <td>4.48210</td>\n",
              "      <td>-7.40030</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>996</th>\n",
              "      <td>-3.49630</td>\n",
              "      <td>8.63860</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>997</th>\n",
              "      <td>6.10620</td>\n",
              "      <td>-5.98640</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>998</th>\n",
              "      <td>-7.40940</td>\n",
              "      <td>-5.52050</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>999</th>\n",
              "      <td>-0.12948</td>\n",
              "      <td>-8.80360</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1000 rows × 2 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "           0        1\n",
              "0    0.14300  0.98493\n",
              "1   -0.30467  0.98562\n",
              "2    0.46625 -0.84003\n",
              "3    0.94847  0.37222\n",
              "4   -0.96871 -0.26697\n",
              "..       ...      ...\n",
              "995  4.48210 -7.40030\n",
              "996 -3.49630  8.63860\n",
              "997  6.10620 -5.98640\n",
              "998 -7.40940 -5.52050\n",
              "999 -0.12948 -8.80360\n",
              "\n",
              "[1000 rows x 2 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "S596KArYVR3e",
        "outputId": "745f0648-b29d-4c1c-8470-3c83bb165631",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 141
        }
      },
      "source": [
        "df=data.values.tolist()\n",
        "#print(np.mean(data,axis=0))\n",
        "avg = np.full(data.shape,np.mean(data,axis=0))\n",
        "df=np.subtract(df,avg)\n",
        "sd = np.full(data.shape,np.std(df, axis = 0))\n",
        "df=np.divide(df,sd)\n",
        "df\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.03721355,  0.23990329],\n",
              "       [-0.07928601,  0.24007136],\n",
              "       [ 0.12133462, -0.20460953],\n",
              "       ...,\n",
              "       [ 1.58904894, -1.45813149],\n",
              "       [-1.92818785, -1.34465036],\n",
              "       [-0.03369538, -2.14432818]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Sy5PoywJX_4T",
        "outputId": "6988c3cd-5189-41d2-e2e7-4b4ea828cd63",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 514
        }
      },
      "source": [
        "plt.figure(figsize=(8,8))\n",
        "plt.scatter(*zip(*df))\n",
        "plt.title('Scatter plot')\n",
        "plt.xlabel('Variable_1')\n",
        "plt.ylabel('Variable_2')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oSKNvw8UigAV",
        "outputId": "c3cb8cc4-fef6-44b0-9191-4a8966aaface",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "df_trans=df.T\n",
        "cov=np.cov(df_trans)\n",
        "cov"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1.001001  , 0.05132212],\n",
              "       [0.05132212, 1.001001  ]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zBrmKqfVnTSS",
        "outputId": "cb8e03dc-fbba-4b9b-8006-723e5103da71",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        }
      },
      "source": [
        "w,v=np.linalg.eig(cov)\n",
        "id=np.argsort(w)[::-1]\n",
        "w=w[id]\n",
        "v=v[:,id]\n",
        "print('Eigen Values',w[:2])\n",
        "print('Eigen Vectors')\n",
        "print (v)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Eigen Values [1.05232312 0.94967888]\n",
            "Eigen Vectors\n",
            "[[-0.70710678 -0.70710678]\n",
            " [-0.70710678  0.70710678]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rIYcXew5qLsV",
        "outputId": "8e75dd08-4ad6-49f1-bb1a-74c8899d471a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        }
      },
      "source": [
        "prop_of_var=[]\n",
        "for i in range(0,len(w)):\n",
        " prop_of_var.append(w[i]/np.sum(w))\n",
        "print ('Proporion of variance explained:')\n",
        "for i in range(0,len(w)):\n",
        "  print ('Direction',i,':',prop_of_var[i])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Proporion of variance explained:\n",
            "Direction 0 : 0.5256353980349302\n",
            "Direction 1 : 0.47436460196506974\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gVaLlg1C6N_W",
        "outputId": "29e1e232-7d29-4d52-f763-270b53bd30f3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        }
      },
      "source": [
        "plt.figure(figsize=(8,8))\n",
        "plt.title('Priciple Components Direction')\n",
        "plt.quiver(*[0,0], *v[0], color=['r'],scale=10,label='PC_1')\n",
        "plt.quiver(*[0,0], *v[1], color=['b'], scale=10,label='PC_2')\n",
        "plt.text(-0.015,-0.015, 'PC_1', color='red', fontsize=10)\n",
        "plt.text(-0.015,0.010, 'PC_2', color='blue', fontsize=10)\n",
        "plt.xlabel('xaxis')\n",
        "plt.ylabel('yaxis')\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KtCWqwHIvm0B",
        "outputId": "de08bda1-85d2-483d-fd91-de0e834af84a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        }
      },
      "source": [
        "Z=np.matmul(v.T,df_trans)\n",
        "plt.figure(figsize=(8,8))\n",
        "plt.title('Projection onto top 1 component')\n",
        "plt.xlabel('Principle component 1')\n",
        "plt.ylabel('Principle component 2')\n",
        "plt.scatter(Z[0].T,[0]*len(Z[0]))\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XFlpElQ_O-TD",
        "outputId": "ff237a0d-0f56-4339-e9b3-170ce0963f76",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 513
        }
      },
      "source": [
        "plt.figure(figsize=(8,8))\n",
        "plt.title('Projection onto top 2 component')\n",
        "plt.xlabel('Principle component 1')\n",
        "plt.ylabel('Principle component 2')\n",
        "plt.scatter(Z[0].T,Z[1].T)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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rPRQdc6mgxgsOUbOB/m7bIjDmFkqukcdbmFPolwA8oJR6E4DVAH5HRN4UYnsoIuzW7aw4/UfkTaE3j13re7S1/J3WyCn6QhuBK6W+CeCbtf//roj8B4A8gK+E1SaKBlZQI2ofpxkqrpHHWySS2ERkGYBeAM+E2xKKAqcAzQpqRO2j+6yxkxwPoQdwEbkawOMAtiilvmNz/3tE5LiIHD9z5kzwDaTA2R2vCLCCGlG7OR1lymNKoy/ULHQRyaIavPcqpfbbPUYp9VEAHwWqp5EF2DwKCY/1JAqG7rMGgMltMRDacaIiIgD+FsBZpdQWL9/D40SJiPynO4o335XD0cHbQmhRejkdJxrmFPoaAL8E4DYRGat9vSPE9hAREZjcFhdhZqF/ATw0J/FYJIIofrwUgKHwhZ7ERslVLBkYeGwcxlQZCtV1tIHHxpkMQxRxTsltFB0M4OSLYsnAfY+OoTJdn2NRmVbYcXAypFYRkRduBWAoGlgLndrGnC43psoQVOvj2rHWNyeiaGKJ4uhjAKe2aKypzP1+RET+4hQ6tYVb/XKrrlzW59YQESUfAzi1hdftJdkOwdC65T63hogo+RjAqS28bC9Z1JnFyIYVXFcjImoDroHTnDTu7771pmvx+AmjbhrdTGTLc/83EVHbMYBTS4olAzsOTtZlkhtTZTx+wsCdt+Tx9HNnWLSFKOVYwCkYodVCnwvWQg9XsWTg/kfHMKN5y7BOMhE17kgxXbUwgw/+AveStyqqtdApZt63/1lt8AZYJ5mI9DtSzl+cZiXGNmMAJ88uVGYc72edZCJy6shXphVGDp8MsDXJxgBObcE6yUQEuHfkOVPXPgzg5Jk4nB3HOslEBFQPQnE6ZpIzde3DLHSyZZdFumnVEuw5drrpsZtXL2HwJiIA1Rrqx0+dtb1WZDPCmbo2YgCnOsWSgaEDk5gq128T27p/ArvW9wAAHnnmRUwrhYwI7ll1PXYWesJqLhFF0M5CD/qWLq67lizqzGL72uXs7LcRt5HRLN32DxO3iRERBctpGxlH4DTL7UASJp8QkV9Y/KV1DOA0yy1AM/mEiPywrTiBvcdOzx5DbC7bAWAQd8AsdJrlFKC5TYyI/FAsGXXB21SuTHPPuAsGcJo10N+NXDbTdPuiziy3iRGRL0YOn2wK3iYu2znjFHqK2a057Vrfw3UoIgqMU5Dmsp0zBvCUasw4t24VY6Y5EQXluq4cDJsgLgCX7VxwCj2l7DLOueZEREGzW7oTAJtYIMoVR+ApY06b2/V4Aa45EVGwzCDNpbvWMYCniFuhFoBrTkQUvEJvngF7DhjAU8StUAu3ipGOXYldAOjKZTG0rr48pjU5sqszi+9VplGuHUXbWE6TxTuI5o6lVBPOeoF0eqXzvHiSRrFkYGDfOCoz9u+gbIdgZMMKFHrznmZ5shnByF0rAMD2sQszgovT1d8lABT4/qT0ciqlygCeYF4upgBrnKeZlxHwmuEj2pwJk/ke8vJY8/EAPD3WZAZzEw/ToTRgLfSU2nFw0jV4c9o8+XRBWreVEKgvX+klsdF8jNckyLkkSzYONaaVmj2ycmehp2man6dfUdIxgCdUsWTg3IWK9n4BuOaYAG4jaKcg7bSV0PozdPt0rczkRy+PtT6+lRG4ziPPvIi+pYubpvnPXahgy+gYjp86i76li7nWTonDAJ5QTvu5OWWeDF5G0E5BWjcKbrx9oL/bdQ3cnMUZ6O/2tAZuPv6+0THH3AwvppXCyOGT2vbtOXZ6dqQOVJ+ngcfGAfCgDIo3FnJJKKcpSk6ZJ4OXYjxOQVq3ZbDx9kJvHiMbVqArl216bFcuO5vAZj521/oe5LtyEFSnsXPZy5eZRZ1ZjNy1Ynbb0KbVSyCe/lq9jEjLU/KVaYUdByfn+ZuJwsUReIJYp1M7RDBtk6DYlcty1JEQXkbQuiltcxq5cbSsy4loZZ9uK4/dWeipm97u6szi1co0LtS2nZmJa40JbFb3rLoeTz93puXp+HMXKlg2eAgA0CHAjGK2O8ULA3hCNE6n2gXvXDaDoXXLg24a+cQpOJucgnRUKmB5Cfh2FQStWehuW93cmN/Gc6jjo1gysOPg5Gyuj11NgqTjNrKYcyuNmhHBjFJM3Ekgu22CuWym6ejXtBRLqT4fz84WjZmPRZ1ZdC5ckPjnLK6KJQMDj42jMl0fv6w1CZKC+8ATyss+bwHwwvAdwTWKPLF2vKzTw61ufUpLcG5FYyW4l8sVzHFgPsuuY0Thcao3kLQkXe4DTyi30qgAa5tHzbbiBPYeO123nmv9/3MXKi1lSLOGdLPG56RxqtVpPV3HbnsdhccpaTFNBzIxCz3G3N6oLNISLduKE9jTELztVKYVj3Vto0JvHqX3345vDN+Bbwzfgd0bVyLb0XruuzFVxg2Dh7Bm+AiKJcOHlpJXTgOTDpHUvD4M4DHm9CbOd+U45Rcx1r3IbtI0igia3bY4M57nu3K22+VMCpcT3dISJKJooL8b2Yx9J2xaqdS8PpxCjzFdhjEDd/S0ejHh0oe/nJYevOSWcEo9XObzbl0asUrL68MAHmNR2QZE7lqZErdWKqPgNX6udEseL02VmUQYIrMTdsPgIdvXKA2zWAzgMaI7rCFJGZdx5nQx93ox4QEc0WAdoesynrs6s9pStgA71kHxUg8hqRjAY6JYMnD/6BisO1xbzVgmfzRmOQPNBUGcDvl4eONKvn4RpluqUgq2pWyHDkzi1Uszrqe8UXu0UlEwaZjEFhNDByZhV56CGcvhMtdLndbhgOpFJpfN1N0vADavXsKLesQ11nc3E0RfLtuf9jdVrrjWqKf20b0+afhccQQeE1OaiwWQjrWeqHLbi2++NsxXiDe7pDenCoh22nF0KtlLaz0EBvAESMNaT1S5dZ6sr01aLzJJZTd161QkRlCdseF7IBhpSDDkFHpMLOrU701Nw1pPVDl1ntKyDpdWdlO3TkV6FFrbjUBzZy5tGbVdBEndu88AHhPb1y63LVzANVR/FUsG1gwf0VbgslvbBqonI6VlHS7NCr15HB28DS8M34Gjg7ch7zIbxuWuYNgtbSUxD4FT6DHBNdTgNZ54ZEyVm7L++bqQld20uhWXu4Kh6yglrQPFAB4jXEMN1oNPTDQdV1iZVthxcLLudeDrQianCmF2SyppWKcNQ1r2hnMKnahBsWSg96GncP6i/SjKbssYkck8POXhjSsdtzYVSwYG9o3XrdMO7BtP3DptGOyWtpKYk8IROJGFlzrYRF64zcwMHZhEpeGg8sqMwtCBSY7C5yktS1sM4EQWXs5YdzqtisgrXW0Hp5oP5J1dByppSxYM4BGStDdXnJjPvZdiG0PrlgfQIiJqp8bZtSSUuOUaeERsK07gvtGxxO9bjCLrnlEnLH1K7aSr7eBU84HmTre1bOjAZEgtmj8G8AgolgzsOXa6qQhEEvcths1uX7fXafPdG1diZ6EnoJZS0tnVdshmBNvXcobHD7otZFPlSmwHSpxCj4AdB/U9wKTtWwyTbgrNKXjnuZRBPnFLtOKSWns5nQg4cvhkLJ9bUcqp+F+09PX1qePHj4fdjLbxsu6a78rxvO820Z3rnBHBtM3ngM89hcVuN4RZZ52dyrkplgxsGR2zvU8AvDB8R7AN8khETiil+uzu4xR6SLyuuyZt32IYzH3duud6WqlU7Bml+LBb1jG7mMyPmZtCb16bXxDXAi8M4CHxsu6ay3awlz1PZjlUp+IrZpGNNJ4nTNHktnTG/Ji52b52eaI661wDD0GxZLiOvLMdgl3rbw6oRcnjdVuY+eFlOVSKEqf1WpMxVcYNg4e4Pt6CpBV44Rp4wLxU+uIa1/y0Uk3t4Y0r+TxT5LRaEVAAbFq9hLskEshpDZwj8IANHZjUfihz2QynbtvAy/IEUO0o8bmmKLKOFI2p8mwCm44CsOfYaQBgEE8RBvAAFUuGY5lEBu/28FJNLdshsV33onSwLutYt5Q5BfK9x06jb+liXkdSgklsAXJKOuFosD2KJQPi8piuXBYjG1bw+abYKPTmcXTwNrwwfAfyDhnTCs7XGUoWjsAD5JRZytFge4wcPmk7QhEAu7neTQkw0N+N+0bHtCNxFn9KD47AA9Sl2YN41cIMA0ub6C5eCvE9sIDIqtCbx6bVS7T3x3VPM7WOATxAuoT/bIYvQ7voLl5O045EcbOz0IPNq5c0LRfFeU8ztY6RI0AvaxLYdLdT6wb6uxNVqIFIZ2ehB7s3rmwqQASg6cAeSiaugQdIV5yBU17tk7RCDUROGgsQJfHMa9JjAA/QQH93U3EGjg7bj1XVKK10Z17H9bStIMXx9DdOofuo8expAKy5TUS+0SVxMjPdmfVwKYX4HBjDEbhPdFNZu9b38IjKFsWxZ0wUBi7TzU1cZy44AveJ0xuCvItrz5goDEzinJu4zlwwgPtEV87TS5lPuowdISLvCr35pmW6O2/JY+TwSWalO9DNUER95oIB3AfbihPa+zLiVuiTrOLaMyYKi7Xs6kB/Nx4/YdTNYG0ZHUPvQ08xkFvEdeaCAbzNiiUDe2unAtmZjtHxrVEQ154xURToTuY7d6HCpSgLu5mLOCQYh5rEJiJ/DeCdAL6llPqxMNvSLrpa3CZWBGsNt94RzZ3TTFUckrSCFMftp2GPwD8B4G0ht6GtnD4wAh5a0qq49oyJosBtpopLUfEW6ghcKfUvIrIszDa0U7FkoENEO02+afUSBp45iGPPmCgK7GawrLgUFW9hj8ATo1gyMPDYuG3wFgCbVy/BzkJP8A0jotQyZ7C6cs0nIXIpKv5EhZxUVRuB/4NuDVxE3gPgPQCwZMmSW06dOhVc41rQ+9BTOHeh+VASEWD33TyHmojC1VgQadlrczj29XOYVgoZEdyz6noOMiJIRE4opfrs7ot8JTal1EcBfBQA+vr6IpvCbRe8geoRogzeRBQ261LUtuIE9lh2y0wrNftvBvH44BQ6RUJj3XhubyHyzyPPvNjS7RRNoQZwEXkEwBcBdIvIf4rIr4fZnvmwW2Nyup0uY7lUomDpEm1ZpyJeQg3gSql7lFI/qJTKKqXeoJT6eJjtmY+hdcuR7aivspbtEAytWx5Si+KD5VKJgqWrCMlKkfHCKfQ2KfTmMbJhRd1+5ZENK7j+7QHLpRIF655V17d0O0VT5JPYoo5HXc4fj0AkCpaZqPbIMy9iWil0CHDFgg7sPXYaTz93htcxG1G81oe+jawVfX196vjx42E3Y1bjmd9AdW8lK4W521acmL14iFT3ys9Y3op8HomCweuYuzCfI6dtZJxCnweu3c6NuYXFTJhRqhq8O7MdLJdKFDBex9xF9TniFPo8cO12bnRbVV69pPDC8B0Bt4Yo3XgdcxfV54gj8HngUZetK5YMbmEhihBex9xdo9kOrLs9KAzg8xDXQ+DDYq4j6XALC1HweB1zp7s0Xbxkf0hMUDiFPgfWbMRrcllcme3A1IVKZDITo8Z8vuwyza24hYUoeOb1KmoZ1lEypSmVfaEyg2LJCO25YgBvUWM24lS5glw2g90beWCJHbvsTTs8rY0oPI1H9pqljRnQq3RbXYFqxyes54ZT6C2KajZiVNk9X43yXTkGb6KIYGnjZk7LCW4zi35iAG9RVLMRo8rteeFaG1G0cJDSrNCb166DAwitc8MA3iJd1iEzNu11deqzNDMi3O9NFDG6TneYI80ocNokE1bnhgG8BcWSgfMXLzXdnu0QjiI1nN70M0oxeBNFjNNgZNPHvhhgS6Il7/C8hDUDywDegpHDJ1GZbo5IV1+5gIFI4+WyffYmwFkLoiga6O+Gbrb46PNnUxvEnZ6XsK5lDOAt0PWydFsMSP/GFjgnhhBROAq9eTiVVDr6/NlUJrQVevPYtHpJUxAPM4+HAbwFrFjUOrsiEQJg0+olnLUgiiin6WIgvDXfsO0s9GD3xpV1x0aHmcfDfeAebCtO4NPPnK47LcvELOp6dkfu7VrfwyIRRDEy0N+NLaNj2vvTvOumcc98mBjAXZgnZ9lZ1JnF9rXLI/Nihq2xaIu5f3TX+h4cHbwt5NaRE7uOF4DZCnoilxMSu3JZDK1bPns/O2bJU+jNY9/x0zj6/Fnb+znrGA3a8+u8IMkAACAASURBVMBFJAPgNwC8AcA/KaWOWu7bppTaGUwTLwvjPPAbtz6pPWQj35VjYLJYM3zEdqsJn6fwWcvZZkQwrRTyXTl0LuzAV791vunx2YxgekbZzjq5Ycc2OTZ97Iu2QfyqhRl88Be4BTQITueBO43A/xJAJ4AvAfjfIvJ5pdT9tfvWAwg8gIfB6YSsNE8j2WGRm3DpRtHv2/8sLlRmZh9nvqed9vXa7bbw6tyFCh7YN46t+59FufZ7O7MduCKb4ZkBMbP33jfbzkKevziNLaNjOH7qLKsohsgpgP+kUupmABCRPwXw5yKyH8A9gDabPnEE0GZkchrpsmLJQEdtZNeIz5P/Gi+yxlTZcQ3Tb9MzCmXL8P1CZWa2E2FMlTHw2DgAMIjHwNPPndHet/fYafQtXczXMSROAXyh+T9KqUsA3iMi7wdwBMDVfjcsCoolAx0d1anERh3gNihTsWTggX3jtsGbSX7+K5YMbZ5GVFWmFbaMjmHL6NhsJznPkXkkOc2gKYR7mEfaOW0jOy4ib7PeoJR6CMDfAFjmZ6OiYuTwSdvgLQA+wtPHZj34xIT2eWKp1PYyT4m6YfAQ1gwfQbFkYMfBybCbNS/mO8ecNXjrRz4XZnOogdsMGpfIwqMN4EqpzUqpf7K5/a+UUvoC1wni9MZkULrs/EX708YU+Dy1k+6UqHNtLiSU7age7xpWkYivfus8g3iEDPR3I9uhXzXlEll4uI3MQVdn1vbi6HRAB1G7WTPIG7kd1dqqNTcuxt573wwA6Fu6GEMHJjHVUA5XBFgggJkXd9XCDGaUmk1Yu2phBuWL05jB3H31W+exbPAQp9UjwHzurUmJJi6RhYsB3IEuAd3pgA6idimWDNsAOl9e15znU7CiXW03psq4j9nOoTPfC3Y7Hdi5Cg8DuAPdQRxOB3QQzce24gQeeeZFx+2LjbpyWXynXLEd8Ya1J9sa/M11+rlO9SsAe46dxqefOY13rVrCQB6iKFUhIw8BXET+WSn1s263JdF1XTnbaUuu+VzmdKhBRlKz27AtnKr+6eSymdmqaNYRb5SKqTRe9Oca0GdUNZDvOXaaU+tEcAjgInIlqoVcXicii3B57/f3AUjFp2agv7uuNCjANR8rM6lK555V1wfYmnjTVbxy0hjE4hLMGkfnc9mvbibwmT+PgsWp9GhwGoH/JoAtAK4DcAKXA/h3APypz+0KlfXNeU0uiyuzHawgZWPk8EltEtXm1Zzq9OqtH/mcbTlTnVw2k5jteebf8PuPjeNii9XfypVp7kEOge7MA4CdqaBpA7hS6o8B/LGI/J5S6k8CbFOoGt+cU+UKctkMdnPfdxNdKU4BGLw9mMtUcpSmxtvFHJHPZf2fe5CDZ9dxZ2cqHK5r4EqpPxGRn0K1eMsCy+2f9LFdoeGb05tiydCWmWWOgLttxQnsPXZaW6a3URrWfHcWemY7ftWOdPO2pUYKwLLBQ7NnzLPj6D+eeRAdXpLYPgXgRgBjAMzIpgAkMoDzzenNyOGTtsFHwBKzTrwGJlNalyLMUbnX5QUzUx3g7I/fdMm9aa2PEWY+gJdiS30A1iilflsp9Xu1r//b74aFRTd65Kiynq5Dw+presWSgYF9456Dd7aDwegz978Fb3z9VZ4fv+fY6dkSs+SPgf5uZDPNO0xe+d6l1D3vdtUR7xsdw7aiPrm3nbwE8H8H8AN+NyQqBvq7kctm6m5j5nkzXYcmz46O1tCBSVRaOGB7ZMNKH1sTH5+5/y3YvHqJ522JxlQZD+wbT10wCUqhN4+rFjZP3lZmFEYOnwyhReGxW3JVqJ7SFsT7z0sAfx2Ar4jIYRE5YH753bCwFHrz2LW+B/muHATVgJSUjN92YkfHm23FCdy49UksGzzkuSrZos4sHmbSZJ2dhR48v+sd+MbwHZ46idMz1dPOOBr3h66YVdqWGp1mIoPozHipxDbkdyOihtWG3JnPD/eC6rVamCWt692tGujvrh5f62E2g2eP+4NFrqp0zwMQTGfGSxb650VkKYA3KqU+KyKdADJu3xdHLE7QGnZ0ms21BjiDt3fme+7BJya0J+FZVaYVdhyc5Hu1jQb6uzHw2Dgqlr372YykbgZuoL8b942OhbYbx0sW+r0A3gNgMarZ6HkAfwEgUaVUWZyA5stMUmtlnbtDgI/czenyVlk7jzcMHnLdjtfuI1cJzXtIU3jIU6E3j+OnzjZtCQ1qOdHLGvjvAFiDagU2KKW+CuD1fjYqDE77v4m8GDl8sqXgnctmGLzbYNPqJWE3IXXs3utpTGIDqvkZuzeuDCVvyssa+KtKqYtSywAVkQVIYF+L+79pvnRrYXbSUJglKObSg1MVt65cOvco+4XXy8sal82MqTJ2HJwE4P/srZcA/nkReR+AnIi8FcBvAzjoa6tCwKQMmi8R97PiudbtD7OKm90yRrZDZk9so/bg9bJKt2x27kIlkORJL1PogwDOAJhA9YCTJwFs861FIeG2KGfFkoHeh57CssFDWDZ4CCt3PMXtORbFkuEavPNdOQZvnxV68xjZsKJuOnNkwwrOdLQZr5dVTstmlWn/lxS8ZKHPAPhY7SuxuC1Kr1gymrbtTJUrGNjH7TnmzgUv0+dpu7iFRbc7grtM2sd6vTSmysiI1OUMpeV5dVsy8HtJwUsW+hpU94IvrT1eACil1A/52rIQcFuUvR0HJ2333JpJK2l9zhp3LjjZvHpJap+nKOAuk/Yzn7c0P69O+8DN+/3kZQ384wDuQ/VMcPcrVQyxZ+7MaQtOGpNWTE7noZtEgN3MNA+dbpfJfaNjANIRbPyQ9tMbB/q7saX2HtLd7ycva+AvK6X+USn1LaXUt80vX1sVoGLJwMBj43XF6AceYx1lk9vzkLakFVOxZLhOm+eyGQbviHAqeTnAuulzpnteW9mREWdhf7a9BPCnRWRERN4sIj9ufvnesoDsODhZV00IuFy5idzr+aZxXdecjnXCGvrR4tTRrMwobN3/bICtSY5rHLbnpaVT5FSb3+8kNi8BfBWqR4p+CMCHa19/5GejgqSbHmblpiqnKfJctiN1AapYMvDAo+PaqfNcNoOHN67E0cHbUvfcRJlbR7NcmQnsCMgkcTogbuhAOgZBTu8tv5cYXQO4UupWm6/bfG0VRYbTyOV7Hs+1Tgpz5K0rFgKAo+6IKvTmsajTuZjLI8+8GFBrkmPKYaDT6nkAcVXozWsLBfm9xOgawEXkGhH5iIgcr319WESu8bVVAdI98azcVDXQ3w1dJztt699uSWsZEQbvCNu+djmyGf2Q0aljRvbSdg3QGVq3PJR98V6m0P8awHcB3F37+g6Av/GzUUEaWrcc2Y76DzUrN9XLZZvfJmks2uCWmMMAEG2F3jxG7lqhvT/jNB9MtpyuAVctTOShlbYKvXnsWt8TeD10L9vIblRK3Wn59w4R0efNxwwLuOhd3jtbP1XelctiaN3yVD1HxZJRLYDg8BinZBaKBvP0KLtz2u9ZdX0ILYq3Qm8eW/c/23SNAIBsxsv4MDnCqCPiJYCXReSnlVJfAGYLuyRij0Dj/u/dG7nlx0o3ZXzVFQtS9TyZiWtOwTuNMxJx1Xj4SUYE96y6nmVu50iXC/NyStbAgeYDTRZ1ZrF9rf+DHC8B/LcA/G1t3VsAnAXwK762KgCszOSOJw55S1zjyWLxYx5+QvOX9oNN7A40icxhJkqpMaXUCgA3A+hRSvUqpWK/aZLnf7vTfQDT8sEEqlthnBLX8l05bhmjVBvo77bNI0rLjJTuQJNIHGYiIq8FsB3ATwNQIvIFAA/FvRobR5fubr3pWuw9drpu6jhNU8XFkuG4FSZJz8W24kTTa23FWQZy1Jj/l6J8QKeYEfphJgD+DsC/ADAT2TYBGAXwc341Kghpn/ZxUywZePyEUXdBFwB33pKeA1+ces8ZkVjv+W7lFDWgusS0ZXSsru7zmhsXY++9b/ariYHbVpzguvgcjBw+aVvNMi310J0ONOlyqT0wX17SBH9QKfUBpdQLta+dAL7f11YFgOfZOrNbYlAAnn7uTDgNCoFT7/nDd8f3jOlVH/wMtoyOzbte9dHnz2LZ4CEsf/8/xb5s5rbiBPYcOz2b6zCtFPYcO83qbB7o3kdpmc10ihl+7yz1EsCfEpFfFJGO2tfdAA772yz/hbVvLy7SvsTgFJA6Y1ZCtlgy8Mb3HcKywerXf3/3Ylt//vmL09gyOoYfefDJ2AZyXRU2VmdzZm6vtJOW2Uyna4HfmfheptDvBbAFwJ7avzsAnBeR30T1XPDv86txfuP533q5bAcu2GwPcTq8ICnMzHNd5/mKbHwKVJgjyyBcnFbYMjqG46fOxm7qWbfLgMV5nI0cPqn9nNx607WBtiVM+ZCWZL1kob9GKdWhlFpQ++qo3faaOAdv0iuWDNvgDTgfXpAUbiVTneo/R0WxZOBHHnwysOBttefY6diNxjs072vd7VTlNCP3+AkjVu+B+dB1VvzuxHgqlSMiN4vIOhFZb3752ioKlVPyVhyC13y5LRNEeWqwWDKwcsdT2DI6hovT4Y0ezdF4XNaQr1hgfynU3U5VTp+FNG3LfeLf7Dsqh579pq+/18thJn+Naj30OwGsrX2909dWUaicAliUg1e7OP2NUU50NKf+23EKlMOZHy3Zc+w0Vu54KvIjMV01sbSduNcqu2RgqzTkzBRLBs5ftJ+x8/tYai9r4KuVUm/ytRUUKbptEQL3c5XjrFgysOPgpPZDF1R5xLlyKzqjI6hud5m6ULE9C8C65cytHrydqXIl8lUOua10bszX84FHx23zBdLw/IU5y+AlgH9RRN6klPqK762hSLAr4CIANq1eEtkL8HwVSwYe2DeOaZuKSnE4vGVbsfWR9+bVSzwlmzUmexZLBt77+LN49ZL30ak5nRrV53Cgv7uutDIQ7dmWKDFf07Q+f06zDH4fS+0lgH8S1SD+XwBeRfVarpRSN/vaMgqFXQEXAPjh118Vu8ziVuw4OGkbvIHoH95SLBktJat5Ddw61oBeLBn4/cfGPa23z3ffuZ+spxIaU2VkROrWcKP8+kdBmk91dCrk8s4VP+jr7xblsk1CRL4G4H4AEwBmu9xKqVO+tsxGX1+fOn78eNC/NlXWDB/Rvhnne+GPsmWDh7T3CYAXhu8IrjEtKJYM3Dc65mlaOyPAh+/258S9VR/8jKf95VFfhiiWDAw8Nt5UWSzJ732aH6fPoHlWwnyIyAmlVJ/dfV5SLM8opQ7UqrCdMr/m1SKKLKdRUlKLWrglWEV1Hc9r8M6IYPPqJXh+1x2+Bc5nHnyrp8S3cxeq6+FRTWp73/5nm4I3UE3Gi2qbKVyF3rz2M+h3Ep+XAF4SkU+LyD3cRpZsTlWVgOQWtXBLQonqOt7vP+Z8RjkAPLxxJZ7f9Y5ARo8fvnulp33TUd1e5FT/AKgmCRI1ctoq6Xfn38saeA7Vte/bLbcpAPt9aRGFxqmqElAdySWRUy95c0QT94olw3XdORdwyVfzd1kPPNGJ4vYit05FO7bnJZm5WyFta+BOM5N+d/5dA7hS6ld9bUFI0vpmc+J2Ub1n1fUBtSRYXZ1Z261jizqzkV339DIa3LU++DzTQm8e+46fxtHnzzo+bmEEC6REsVMRF43H0RpT5chvHWwXp5lJv/92L4Vc3iAiT4jIt2pfj4vIG3xtlc+KJQMD+8ZhTJWhUH2zDewbT/0al9t0T1SD2XwUSwZe+d6lptuzGcH2tctDaJE3bqPBMGcO9t77ZtcLSytb0ILi9v5nWVV7xZJhe5Z8VJdK2k03MRnEhKWXbvDfADgA4Lra18HabbE1dGASlYYtQ5UZlfo1roH+bu0aeD6iiVzzNXL4ZNN7AQCuWhjdrWNeypOG3dn6yMaVof7+uXB6/wOAZpdh6jktvaVhViOnmU3S3d5OXn7DtUqpv1FKXap9fQJArI+Z0Y1e0r7GVejN46duXNx0e5ILMuguMH4fAzgfe132fL/x9VcF1BK9qHZ+nDhlEwPJzQGZr7SXXi5rEh91t7eTlwD+bRHZLCKZ2tdmAN/2u2EUvGLJwL+dfrnp9h9fck0sL8hedHXaV0qK8oXHbSD4mfvfEkQzXMUx3DnNNCV1F8Z86T4rSS+9bNL9/UFcQ7wE8F8DcDeA/wLwTQB3AYh1YluYaxZRpjtG81+fP5vI/IBiydDWPV/22mgGcLfXYZGmQxKGTauXON4fxfeUU8DhCNye3YEmSS+9bBXWUaKAt/PATyml1imlrlVKvV4pVVBKBX/IcBvpOtJp72DrpsIUwi3Y7xenv+lfv+6cRR0WtzyNKCXe7Sz0OBZ3ieJ7yingcASuZz12dVFnFrs3rgw9DyMoTz93pqXb28lLFvrfikiX5d+LakeMzpuIvE1ETorI10RksB0/0wvdNFlSE7W8cprySWIyilPVuaheq53yNNbcuDhyIx6nrepRfU/prgN+H0wRR2bpWev78pVXm3d1JJnufRzE+9vLFPrNSqkp8x9KqXMAeuf7i0UkA+DPALwdwJsA3CMigRxbajflk+RELa+c/n7dWnGcJW1KdO+9bw67CS2Jap7BQH83sjZ7xs5fvBTJaf8w7Tg42VR6tjKtsONgenb0RH0NvENEFpn/EJHF8FbBzc1PAviaUurrSqmLAP4OwM+34ee6KvTmsWt9D/JdOQiqPe5d63siN3oJWqE3j1zW/i0R1RHpfDhNiS70Utg7YEkLHlHtMBd687j6yuZLXGVaRXLaP0y6HBLd7UkU5oDQSyD+MKrHie6r/XsDgA+24XfnAVhr0P0ngFVt+LmeNJ5xTFXf02x9iPK2qrlw20vdubAdfdT2et/+Z8NuQssyIrFcO57SBKCoTvtTuK5Y0DGbABzkiXtektg+CWA9gP+ufa1XSn3K74aZROQ9InJcRI6fOeN/UkDahTkdFCS3vdRR7LA4HbQRVT90baf2viiPZuO4vTAMuryAtOQLFEsGtu6fqMsB0A2C/OCpVIxS6itKqT+tfX2lTb/bAGAtrv2G2m2Nv/ujSqk+pVTftde2Ly2/WDKwZvgIbhg8hDXDRxI3PTlXYW6JCJLbmJAX6vb42pnz2vuiOpp12l6YtM/BfL1zxQ823dYBYGhddHZD+Mlu622QJWTDPFHgywDeKCI3iMhCAL+IaslW35m9Jmst9CifURykfxj/Zku3J1VU12fjxmn2PKqdpIF9+tPUgtgaFBfFkoHRL9mcxBW99BHf6HayBNU5DS2AK6UuAfhdAIcB/AeAR5VSgaQuht1rijKWma1ifsT8ueUZRLGTVCwZcJoBjeqsQRh05wjMKKQiC91pwHdNQEsInjJ1RGQpgDcqpT4rIjkAC5RS353vL1dKPQngyfn+nFaF3WuKqjTNQHRI/A6nyHflHPeuR83eZ5zzDKLYSXLrxEd11iAMTtfLNGShO71Xgtqh6qWQy70AHgPwl7Wb3gCg6Gej/FQsGdoZnrR/ONPQaza9a5W+zGeUypFauY1Yo9YBi2HyuWsnPoqzBmEJapQZVU7vFd0uhnbzMoX+OwDWAPgOACilvgrg9X42yk+6o+/SUnjfiVOvOapBba52Fnqg2fIe2cDjNmLdGqFtZlHrTHjl1omP4qxBWJxGmWnIQnd6rwQ1GPQSwF+tFVoBAIjIArgn8UaWU71vfjj1olRju10uadY6o7iFzItyZSYygfPBJ1z22et6TyGL6iE2UeQ0ykxDFvpAfzeyNgWfsh0S2GDQy6fo8yLyPgA5EXkrgH0ADvrbLP/oekZpr4MO6HvNuWxHIjs3uinAKE8NrrE5r93qgUf1GdRBKJYM9D70FM5fbD7VzupD628OqEWtOfq8/hAbXiPq6a6lizqzibxeNCr05jFy14q62cmuXBYjG1YE9vd7SWIbBPDrACYA/CaqSWd/5Wej/DTQ342t+yfqstBZB71qaN1yDOwbr8sszXYIdkX0YjtfFy/ZB5kol0jfe++bsWzwkPZ+p8ND/FYsGbhvdMx1ei6Kh654wWtEvVtvuhZ7bAoi3XFz897wpAq7oqeXSmwzSqmPKaU2KKXuqv1/bKfQC7153HlLfvYgi4wI7ryFZVWBWo9yw4q6GvFB9iaDVCwZ2spmQSWg+OWtH/lcKL/3vY8/62ltLW6HrpA9XW0I7pUPjnYELiITcFjrVkrFclhWLBl4/IQxW595Wik8fsJA39J4jgraLeweZVCctoDEfTfCV791HtuKE4Gex1wsGXhVl1RgEeHJDVcjh0+m4rPhRbFkaGtDpH07bpCcptDfGVgrAuRUxIUfzvRwushEfap0zY2LHddqAcxObQYRxM0zob3YtFq/fS/qGJguS3IHOE60U+hKqVPmF4BXAawAcDOqWemngmpgu4V5+DpFR5wTcPbe+2a88fVXuT5uz7HTvmelF0sGtoyONZ0JbWfNjYsDnRVoNwamy+LcAU4SL4VcfgPAl1A9kewuAMdE5Nf8bphf0nLa1nwl/bAX3Rm+cdku95n73+JpC4lTXe/52FacwLLBQ9gy6u3nb169JBZr3zmH7W0MTJfFuQOcJJ6uAQB6lVLvVkr9CoBbALzX32b5x+7CDQAXLl5KXJCaqzQc9lLozWPX+p66hL1d63tidfH5yMaVro+pzADLBg9h2eAhrNzxVFtew00f+6Jt9rFOXEbe24oTKGsSGzevXhKr94bfbr3p2qZ8hjh1gJPCyzaybwOw1j3/bu22WDI/hEMHJuuSMM5dqGDr/om6x6RVWvIE4p6wV+jNY2DfmOPhG1ZT5Qq2jI7h+Kmzcwqo24oTLQVuoFqwJQ4j72LJ0P5tizqzseiABMVMBLYumgjA3Twh8BLAvwbgGRH5e1Sz0n8ewLMicj8AKKU+4mP7fFHozWPk8MmmLMokBqm50B2YEaeDNLwqlgyMHD6Jl6bKuK4rh4H+7li9/iMbVnqexjbtOXa6LlhdsaADuWwGL5crs88BUO3Izfc1j2rBlkZO5wDEfVthu9l18BW4fSwMXgL487Uv09/X/vua9jcnOExm08uIzG6za7w9ScylAvNiZC4VAPGZhTHb2cpIvNGrl2Zmt4AZU+WWOwQ6cZp2djoHgPkx9dLUwY861wCulNoRREOCdp3maEZ+WGEbvJ1uj6ukLBWYSwE/8uCTuBhmKbYaAbB748rYPIdueQFMXqsnsC8QkrQOvk6UZu20SWwi8nDtvwdF5EDjV3BN9MdAfzeyHfVvuCCL0EeZ7uSxpJ1IppttietI4g/vWhF6oZQ1Ny7GC8N3xCZ4A857mpN6DsBcFUuGtrpX0jr4dqKW4Os0Av9U7b9/FERDQtF4tQv76hcRus/hK99L1lqgbhZGUP2gxu3Cbbb3ffuf1ZaJ9YsIsPvu+Iy6rZyWzZJ6DsBcOXV20nDYS9Rm7ZwKuZyo/e9xAP9HKfV5pdTnAXwBwJeDaJyfRg6fbCo+UZlWjm/QtNAdp1mZqWYiJ8VAf7dtn03B+UIVZYXePL7ygbfjG8N34OGNKwOZNclmJLbBG9CfPteV457mRmkv4BK13Ckv+8D/GUCn5d85AJ/1pznBidoLESVOeQCPPPNigC3xV6E3r50OTML7oNCbR+n9t+PhjStnR0ftnmRa1JnFyF3xPfCmWDJw/uKlpts7kI4zrVuV9gIuUSsE5iUL/Uql1CvmP5RSr4hIp9M3xEFXZ9Y287QrYeu8czHQ363NRE7aOlc+BcmMjfvd57Kf27SoM4vta5cn5mK94+CkbRnYYBcg4kN3HHNaCrhE7ThqLyPw8yLy4+Y/ROQWALEfnujiUMLi05wUevPaM7GTlmmqq8x37vyriao8Z7Wz0FM3KtfJiGDz6iX4xvAds1+l99+emOBdLBmO28fiuozipyRUMJyPqP39XkbgWwDsE5GXUJ2B+wEAG31tVQB067y629Nm06oltqO0e1ZdH0Jr/FPozeP4qbNNf+uFyszsCVtJvDjFvQpdO7gF6CQso/ghze+dbcUJPPLMi5hWChkR3HrTtaE+F64jcKXUlwHcBOC3APwvAD9qSXCLLd0UKafQq3YWerB59ZKmEffTz51J3MhUV0GqMq0wdEBfoYvizW27YJKWUWj+zKUncxlxWinsOXY61MReL1PoAPATqB4l+uMA7hGRX/avScEY6O9GpqN5OviV7/FQE9POQg8+fPeKuinmsPc9+sFppDVVriTqb6Uqt9c0zHVNiqZPP2OfNxJmYq+X40Q/hepe8J9GNZD/BIA+n9sViOmZ5gXvygy3klk57XtMCreRVpL+Vqrauv9Z7X2LOrOpWtd1k/Sjhb0olgzYhAsA4Sb2elkD7wPwJqWSld7ldFGOayUuPyStWpkdp6x7gGuhSbKtOIG9x05rtw8CQOn9twfWnqhLwnkB7RDVTryXKfR/RzVxLVGcLspJy7SeD6ecgKT0xAu9edispsziWmgymGuYiRqJ+CwNM3BeRLUT7yWAvw7AV0TkcJJqoTtdlJO213k+nJ6KJH2IddNjQDoqTKWBl7XKpNX7ny8WvKq6MqsPlWGWkPUyhT7kdyPCMNDfjftGx2x742mo6euV07a6JE2j645QFUnXVGGSeemYp6UgiVc8tbE6c1PWnC2QzYR7AJaXbWSft/sKonF+KvTmsWn1kqbSksw+ref0QU3SUoNuf/umVUsCbgn5xe3dGqfzy4NQLBm4YFNmNm3XSKeZm7DLCDsdJ/qF2n+/KyLfsXx9V0S+E1wT/bOz0IPdDQc+XLHA6866dHD6oCZpqaFx37tZhWxnoSfkllE7bCtOOK5987WuVywZGHhsvKlSXVcufRn6Tte5sJ8H7RS6Uuqna/99TXDNCccrr17uZU6VK4muwNWqQm8eOw5OaktOxvHYTZ2dhZ66i3ixZGDljqcwVVtGSFod8DRxGkU9vDG+J6n55cEnJmxrxKdxSUm3vBaFGUjH4aaIZETkuaAaEwa7wwwqiyiXLQAAIABJREFU0wo7DrICl8lpXfDBJ5JzvKhVsWRgYN/4bPAGgHMXqp27pGTfp0mUR1FRUz2hbdr2Pqfa8UmlW16LQllpxwCulJoGcFJEErsQqHtDpvGNquN0gTt/cTqRAW3k8ElU7Ar9sLxq7Di9P6MwioqaJO0uaYcoL695yUJfBGBSRL4E4Lx5o1JqnW+tolgZOjCZuFGMW3nVbcWJSHyAyZlZiEQnCqOoqHF673fl0rnNrnF5LSq8BPA/8L0VIerKZeumSa23kzd2z1/c6bbPmPYcO42+pYsT13FJimLJwHsffxavXtKf7B2VUVTUOL33h9Zxm12UOGWhXykiWwBsQPU0sqNJ2kZmGlq3HNmGMlzZDuEbNeUG+rub3heNmCcRTduKE9gyOuYYvAVg8NYY6O+uO8AIqD5f3GYXPU4j8L8FUAHwfwC8HcCbAPw/QTQqSOYbcujA5OxI8uorvUxMpMuizqw2LyCJ1avM94Wu2A/APIkoMsuluklTIZJWme/9kcMn8dJUGdd15TDQ383gHUFOkepNSqkeABCRjwP4UjBNCoe1t37uQiWVBfudbF+7HA/sG286wa1Dklu9qtCbr+vY2UnSNrq4K5YMT8E7bYVI5qLQm+f7OgacstBnr1pKqeZyPAnCgv3uCr15fHjDirrRdlcui4/cnew9tE6lZAHggUe5rSwqvO4OSFshEkoupxH4CkvFNQGQq/1bACil1Pf53rqAOB2ZyRHWZWnslbsls00rhS2jY9h3/DT23vvmAFtGjbwkU665kYmHlBzaEbhSKqOU+r7a12uUUgss/5+Y4A04r4dt3T/BEVaKeZ1qPfr8WWz62Bd9bg3Nx8KMsJNFicLC37DPujRxKl2vWDKwZvgIbhg8hDXDRxLZ0Sn05rF5tbc6RkefP5vI5yAunJIpc9kM/vCuFQG2huIqTtc1plvjcqLaltEx2/vTdvatF2aBDDN3wJgqJzbxb2ehB31LF7smtAHVfIqk/f1RVCwZda/Hos4s7rj5BzH65RebSiN35bIYWsca9uRuW3ECe4+dnt15EvXrGkfgNYXevPYccG45aaZL/EtqbfRCbx5j2293fZwxVcaNW5/EtmIyn4coKJYMbBkda6pTP/rlF7HxJ65HvisHAZDvyuHhjSsxtv32SF58wxankWYQiiWjLnibojwLyxG4xUB/d92oEuCWEx3drMT5i9OJLjPqtB/eNK3U7HampD4PYSmWDNynmSmrTCs8/dwZHB28LeBWxU+aZtC8Gjl8UlvzIaqzsByBWxR689i1vqeuB88tJ/acZiX2HDud2N789rXLkc14OwBj7zPue5LJOzPoOJ3rHdULbdRw62wzp/dOVGdhOQJvkMatUnMx0N+tzRkAgIF9yTxT3Vqlypgqa88KBgClgDXDR1jFqk3sgk6jqF5oo0YXrNLcAerSzK4JvO9GCRpH4DQnhd48nMahlRmV2N58oTePo4O34RvDd+D5Xe9wfKwxVcaW0TGs3PFUYmcl/NK4Ruu0H98U1Qtt1Og6OmntABVLhrZo06YI14BnAKc52+SyvSotvfnOrPvHaKpcYU2BFhRLBgb2jcOYKkMBnoI3i7R4Z7d1Ns35PjsOTmLGZiKtM9sR6TwWBnCas52FHsfg1ZXAQ07sfGj9zXA5uAwA1xi9MrPMK3ZXVBvmSVks0uId833q6RJTL1T0J9pFAdfAaV4+tP5m7Vq4Zmk4cRrXxZ0YU2WsGT7CU540zJG3F3k+f/PCfJ/44wic5sXpAuB2EEiSmOviXTnnWQcB6qaFOa1+WbFk4IFHxz2NvAXA0cHbGICoLXSfW7fPc9gYwGneWADnsqF1y5HVzKcLYFsk4n37n/W9XVFWLBn40T/4R2wZHdNm9DdK43trrliwxZ3d5zbbIRhaF+2jkhnAad7sEmLMkWbaLhiF3jxGNqyY7dRkpHpRyHfltPuXL1Rm8KN/8I+pep6AamDpfegpbBkdQ7mFtcY0J1u1ytw7z1kfZ9bPrZkTMLJhReRneETFaKGyr69PHT9+PNDfWSwZGDl8kmuWLsznyZgqN400c9lMqhNkTDdufdJ1hLmoM4vta5Nbt7tYMrDj4KRrNTsdrnu3Rrf9Lt+VY8U6xOP6LiInlFJ9tvcxgOs1lhsEGIzc8IKht2zwUEuPT9ohHMWSgYHHxpsOG3GT9E6Nn24YPGQ78yMAXhi+I+jmRErjwSVANK/vTgGcWegOnMoNRukFjhJWeNLLd+U87Wc2TZUrsa5o1zi6uXDxUkvBWwDs3rgyln97VFynec+lPYfA7eCSuLznuAbugMGodboLgwJStx7eaKC/GxkvG8YtKjMKDzw6HrsEJLu111anzaNcASuqzIS1ZYOHcOPWJ2eXtKyYQxDPg0vscATugL3X1tmd6GZK+4lH5t/84BMTOH/Ruaa3lblubpZl3br/Wexaf3Poz6F1hH1NLovK9ExLf5eTzauXRLoCVhQ1LvmZ7xuFyzsgmENQFceDS+wwgDuwC0YC4Nabrg2vURHnVtQkblNU7WYtnmEejdlqFkq5MoP7R8ew4+Akpi5U0NWZhVLVffdBJeKYBVfMPdtT89zz3yHAjGKAmY8dBye1h72YwTvteSgm3eAsygeX2GEAd1DozeP4qbN1ayUKwOMnDPQtZd1lHTNI6RJo4jRF5Sfz/WMNhF7N4HL5R+vUtDFVxn2jY9gyOoZ8Vw633nQtnn7uTNuzbIcOTLbcZqCamCdyuc1JS9QLS7FkuC5R8HN3mW5wFrdlGwZwF08/dyb2iQ5h4RKEu8YZC3MkCtgXfvHC/B5jqow9xy6fSW5MlTGwbxzHT52tC+rLXpvDsa+fw7RS6BDgigUd+F5lxjHgz2XEnctmGKx9MnRg0vUxaf/cNSZV3nlL3pfObZAYwF0wkW3u7Hq5TKBppqtJPdcpdieVGdUU1K2drBmF2aIq7cxZ4NS4f4olw7VDlfbPXWN+gDFVxuMnjMhtGWsVs9Bd8NzcueOJR/NT6M27HtnqN90Jaos8njSX7RA8vHEl65b7yO2EO37unLcExxlH4C44ipyfxtGluc0lztNWQdpZ6EHf0sXzql42X3azTdvXLnctysL1bf8VS4ZrbQEmriV3JpUB3IV1jZJBZ37sprHSvK3Mq8bMdd02Pb/YzTbxcxGuYsnA0IFJ16lz3UFDaZPUfByWUm1BHOrmRhnLrLaHte58RgTTSs1mnI9+6UXH7PBMh6AD8JxBHsXSkmlXLBm4f3QMbse/ZDskFgdyBCHOZbFZSrUNOHqcv6ROYwVNl/QGAH1LF9d1Mu22kQH1I+e5ZKFTeLbuf9Y1eHP5ol5SZ4wYwD3SJUE88Gh8a1UHLanTWFHiFNwbH0fx5Hb0Kme07Hn9bMQJs9A90o0Sp5XCfaNj2FacCLhF8WN3bng2Izj/6qXY1fomiiIm2F62rTiBG7c+OVsXPonXaAZwj5xGiQrAnmOnGXxcNG4rW9SZBVS1KIh54AU7Q0TOnM7DicOabhC2FSew59jp2Xrw06pa/yBp1xYGcI/sRo+Ndhx0r4aUdoXePI4O3oYXhu9A58IFTclUCsBedoaItN61yr42wOaYlQH10yPPvNjS7XHFAO6ROXp0EtY+3bjSLUsouBenIEqrnYUebF69BBmpDsUzIjy9rcG0ZneV7va4YhJbCwq9eWwZHQu7GYmhS2oDmJlO5GRnoYcB24G5vdLu9iThCLxFboUReh96itO/Hg30d0P3cerqzGLN8BEmt1EqmRUL+f6fm3tWXd/S7XHFAN6igf5uZDP6Xty5CxUMPDbOD5wHZq3vxmczmxG88r1LMKbKs8ltW/dP8DmlVDBrTvD9P3dpWWZgJbY5KJYM19rU3IvpXWOFu3PnX8UFm72uXbksxrbfHkILiYLDioVzk9RKmU6V2EIZgYvIBhGZFJEZEbFtWJQVevMovf927fQvwDXcVlgz0wf6u22DN1Ddbpa0bSBEjVixsHVpnbUIawr93wGsB/AvIf3+tnDaG87qYnPjln3OLWaUVOa6t25OlNcUvaQeF+omlACulPoPpVTsn9mB/m5kbaoqZDPCakhz5DbK4BYzSppiyUDvQ09hy+iYdlcGK6w5S+usBZPY5qHQm8fIhhXoymVnb1vUmcXIXTwBaK68jDKS/qGk9DCnft3yaVhhzZnuupH0WQvfAriIfFZE/t3m6+db/DnvEZHjInL8zJkzfjV3zgq9eYxtvx3fGL4Dm1cvwXfKl7BldCyxtXf9ppvVsEr6h5LSw27q10oAHB28jcHbhV2lzDTMWvhWyEUp9XNt+jkfBfBRoJqF3o6f6Qez9q7JrL0LIHFbF/xkXqiGDkxiqtw8KsllM7j1pmuxZvhI4rJNKfkaM6V1U+YmdladWZ/Prs4srljQgZfLldRcF1iJrU2cau8ygLfGeuxf4wXv1puuxeMnDJ7LTrFjTpdb37sCaJPW0jCCnI/G5/PchQpy2Qx2b1yZmmtBKAFcRH4BwJ8AuBbAIREZU0r1h9GWdklL7d2gNZ7hu2b4iDbbNC0fWoqfYsnAA4+ON10PFGAbxLtyWQytW873tAOnzPO0PG+hBHCl1BMAngjjd/slLbV3w5bWbFOKL3OkqOvMK1QT1bgk1BpeCziF3jb3rLq+bg3ceju1j27dkGuFFFVDByYdE9VYYa015rIa98tzG1nbpKX2btjSmm1K8VQsGbbJmCa+d1tjrbhmJ23PJ0fgbcQj/vxnTi3a1TxOai1kii+nokMZEe7vbpHTtrt8Cj/zDOAUO42JbYB9hi+z0ykM1o6kUwrrh+9mwScviiVDu63UZO6XTxtOoVMi6DJSt4yO8TxlCkzjoRo6izqzDN4eFEsGBvaNOwZvIF3r3lYM4JQITpmnxlQZW0bH8ENbD7E6HvnKrbIaUF2n3b52eUAtireRwydRmXHeipu2dW8rTqFTInipajWjwOp41Ba6fAunjqQAzM1okdtnOo3r3lYM4JQIA/3ddWvgTvYcO42+pYtT+6Gn+dlWnMDeY6dnp8it+Ra6jiS3is2Nrr4GwOcUYAAPTLFkYMfBydlTh1hpqb2s2eluvXYA2DI6hi2jY7hqYQYf/AVmApM3xZJRF7xNZgUwu45kmqd458upkiWfU66BB6JYMjDw2HjdkYFT5Qq2jI5xTbaNCr15HB28DQ9vXNm0V1zn/MVpPLBvnElu5IlTAZGXpsoo9Oaxa30P8l05CHgU6FwVSwbWDB/R3t+VYxIgwBF4IEYOn0Rl2v5jv5fTuW1nPpdb9z+LcmXG9fHTMwoPPDpe971EdpzWuM1MaLttjuRd45bQRrlsBkPrmAQIcAQeCKcPvYJzsQeam0JvHv/xgbdj8+olnh4/rRTu44wIudBtVxJwSrdd3Iq1cEbjMgbwALjtUUxT8f2g7Sz0eJ5SV6gmuG362Bf9bxhFkjl1e8PgIdv6AXalfAXAptVLGFTaRHc9NIu18Hm+jAE8AG4987QWIQiKuS551UJv6+JHnz/LkXgKNRZhMbPLrUHcbo1798aV3JbYRrrrIa+TzUTF6Lzqvr4+dfz48bCbMSfLBg9p73s4RQfQh61xC5BORgQfvnsFa6unyJrhI9wCFgF2a+C5bCa1U+cickIp1Wd3H0fgAclreo9XLcxg5PBJ7ZQdtdfOQg9eGL4DD29cCaeT2qeVch2NUbLwfOloYCa/dxyBB8SuV5nNCKBQVyowzT3NoG0rTtie4e4kI4IZpTgiT4DGamrnX71kW3ObI3AKk9MInNvIAmJ3DKbdBcMsCMHA4L+dhR68cOYVHH3+rOfvMQtLGFNl3Dc6huOnznL9MwYag/WtN12Lx08YdafXZTOCbIc0daiZXU5RxRF4iG4YPGS7FisAXhi+I+jmpNa24gQeeeZFTCuFjAjuWXU9nn7ujKeKbiYRYNOqJQzmEVMsGXjwiQmcv1i/LUkA28/eos4sOhcuYN4DRYbTCJwBPERMmokut2ISTtJ+wEJUzGWJhJ1n/+kOgiF7nEKPKNZNjq7GJY8Oh0MVGpnHl+44OInta1nv3m9mQDCmyrOHXyzqzNaVLvaKW5X81dgxth4Ew89J6xjAQ2S3Ls7eaHRYS2IWSwbuGx1z3X5mde5ChRcnn1iDtnU63OxkeQnejdPo7Dz7z67KGvN+5o5T6EQeed1D3oiZ6+0119fByqye9vRzZ9h5DoC1w2WHSxd6nEInaoOdhR70LV1cdyysF9bMdY7IW9N4DG+7bFrNhMOgeMkn4dLF3DCAE7XAnFYvlgy8b/+zuODhtDMrThfq2W31Gv3yi9qT/OYil+3ArvU38/kPkNupgFy6mDsGcKI5aDwyslgyMHRg0rYQSCNW9mpml9w032nybEZw1cIFeLlc4RR5SLYVJxyDN3dszA8DOFEbWEfmbpnrTtOFdclZApjf3iHAjIr/Ba+xo7OoM4vta5fbJjfNJ3jH/XlKikeeeVF7H7fLzh8DOFEbNWaut7JNsPHx1thvFgfzuo4+n722Tt+rC8CNnRfr9zklMJ27UMHAY+NtmSZnGeLocdp6yWnz+WMWOpGPWgmkusI+dpxGL3YFTLIZwchdK2x/t7WNV2Y7mqY8zcAIAAP7xutKjZo/e+NPXF9XmtT8vjtvyTfdbifTwj57u+/jiDs6rO8n3SvaIcDXdzHr3AtmoROFpHGt3Ekra+O6xxZLhm31scq0wo6Dk00j5a6Ggid265Vm4t35Vy81BW/zZ5ulaBu/z+52O9NKIZfN2HYADj37zbo2dgjwLpatjSSvFQzftWpJQC1KNgZwooi4rivneQSuW0cfOXxS+z3nLlSaLrBet2e5tUsXpL2Oqs0RtN1sBQN1fNjlMliZZw3wNW0PBvAYYi3hZLIrrWvHaR3dbRTvdoHVcZvi1t3vdWrcfA/zfRw/XqbMWajFHx1hN4BaY46gjNqHxUxqKpaMsJtG81TozWPX+h7ka6Nrkcv3ddT+P9+Vc0zUcspw78pl57yFzSkIZzPVUVUum6m7PZfN2N7eaPPqJQzcMbWtOIH7Rsdmr0c6LNTiD47AY4a1hJNtvqPQgf5u26zuDgBD65Y7lrPUyWU7sPiqK2y/r0MwmxzXt3Sx7cyQ9fauziyUAvdmJ0CxZHjaq89CLf5hFnrM6M4QB7j3laoay4925bIYWnd5q1crx6RmOwQjG1YAgO2WOG7bSi+3XRMCsJPWBsxCTxCnRCfW2ibAeRRvdwLestfmcOzr5zCtFESA3ILqVjK7iy9zL8jtYBKARVqCwhF4zHgZQfHDQ0R+8HL9EQC7N65k565NOAJPEOsIStcDZq1tIvKD2y4G85hWBu9gMAs9hgq9eRwdvG02W7kRMz6JyA9Og4N8Vw67N67kHu8AMYDH2EB/d9MWHUF1LXzN8BFuLSOittINDsxlO468g8Up9BhrnE4XXD7BiQltRDRfdme029W85zaxcHAEHnPW6fTGdERzfzgRUasai7QYU2U8fsLAnbfkke/KQeBeWIj8xRF4QujWppjQRkSt0hVpKVem8fRzZ7jLJSIYwBNCtz/8mlwWa4aPcO8uEXk2cviktmAUBwXRwQCeEHYHYWQ7BOcvXsJUuVqRi+viRKTj5VASgLtcooRr4AlhPQjDXJu6+soFTTWxuS5ORI0aD0nSEYAJaxHCEXiCNJbQvGHwkO3jOAVGREA1cA8dmJydpXPCIi3RwwCeYLp1cU6BEaVbq4Gb+TPRxACeYHbr4tyzSZRurZxIx3MVoo0BPMHsTp4ye9GNBRrYuyZKB7d65iZ29qOPp5GlkK4Hvqgzi+1rlzOQEyXYMk1uTKOHeaJYJPA0Mqqj64Gfu1DhNjOiBLLOuHnRlcvyGhAD3EaWQk4fYm4zI0oWr1vETNkOwdC65b63i+aPATyF3LLQuc2MKDm8rnkD1aS1kQ0rOPqOCU6hp5BddrpVVyfLrxIlhZcOeS6b4aEkMcQReAqZVdu6ctmm+7IZwcvlSt0JRAOPjfNscaKY0s24ZUR4oljMMQs95Rq3k507/youVGaaHreoM4vS+28PoYVENB92u0444o4PZqGTVmP5Vd0Wk3MX3Cs2EVH0ONWDoHhjACciiqFWijE1dtQpGRjAqU5XLmtbH9lcL2cFN6LwNU6L86jgdGISG9UZWrcc2Q6pu83cF9q4n9SYKmPL6Bh6H3qKSW5EAbLbGsYaDunDETjVcVovWzN8hBXciCJAtzWMNRzShQGcmujWy7xUcGMAJ2ovu2UrHhVMAKfQqQVuFwdjqowbBg9hzfARTqkTtYHdstXW/RO49aZrkctm6h7L08PShwGcPBvo7266aDTi2jhR++jWup9+7gx2re9BvivHYiwpxil08sy8OAwdmLTNVG/EtXGi1lmnzHVltl6aKnNrGHEETq0p9OYxtv12PLxx5Wzv3wkzY4m883pyGNe6CeAInObI2vvXVW8zGVNlHo5C5IGXk8O41k0mjsBp3hZ1Nh+K8v+3d++xctRlGMe/T08PcADjQSFBji3FIBgqUky5KF6gEgUVqAaDiBcUr1EEY4oSGsGIEVIjiWgkRBGEighqAW8Vba0XLFDpjYr1AgoUohgFLa329vrHzjbTPbOzu6e7Oztzns8/nDMzO+edH9t993dPE4wbhOO+cbPx8mZ6uK/bGrkGbrvt0tNmMu+21WzdPr7RTzCuKdBTzmyyarWSYbPpYWOjI/z6k3P6GaqVgGvgttvmHj3GgjOPYizplxtSrWd8bHSkaT9evVndNXGbLJpNCUv/G8ia6eEmc2vGNXDrimYjYk+4YklmjQK8frNNLnnLn9bf/945zDrhBG49Ne91h4/bizgtPUrdH1pWFVlN5e0uf+rpYdYuReRNVhgss2fPjhUrVhQdhnWo/mHWrCYOtWbCdJKv952POZlbycxftJaFyx/ZpftoZHiIPadOyVw/wf3blkfSbyNiduY5J3Drl2bN6UMS23Peh8NDYp89pvL05q2undtAaudL6n57D/PfrTt2+aI6MjzkUeWWKy+Buwnd+iarOb2x5p1l6/bYWXNxv7kNikUrN7S9KiHAU5u2ctVZs9xVZF3jBG5902yATquaSyNPQ7OiLVq5gXm3rmbrjvZbMA8aHXH/tnWVE7j1VbMPsLyBblm877EVacHi9R0lb4GnglnXFZLAJS0ATgO2AH8G3h0RTxURixUvXTPf8NTmzMVfGnktaOuHZguvdPIFUsA5x093zdu6rqga+F3AxRGxTdKVwMXAJwqKxQZAumae/tAc3XuYjf/dtkttxwtbWK/kvffS4y+arZhW51kU1g+Fj0KX9CbgzIg4p9W1HoU+ObVafrLT68zS0iPI22n9qSflZn3goyPDXHb6TL/3rCsGfRT6e4Bbig7CBlc7A3/qy1TW+9E9Wt3a0fi+aac6U9+LG9hlFPp+ew9z6WlO3NY/PUvgkn4KHJhx6pKIuD255hJgG7Aw5z7vB94PMH369B5EalXQzjKVZotWbuDTd67jX5tqSbedGnej+vgLjyi3ovUsgUfEyXnnJZ0LvBF4TeS040fEtcC1UGtC72aMVh3tLFPpJvbJbdHKDeN2zev0A8XjL2yQFDUK/RTgIuDVEbGpiBisWpoNKqrXltzEbgsWr8/c8jaPVwG0QVZUH/iXgD2Bu1TbenJ5RHywoFisApqt8lavLeU1sdfPu2ZebZ2uHTAkseDMo/xesIFVSAKPiEOL+LtWXa22YWz24V2vibtmXi7pkeP1tfRbTdlqNfUrzWuUWxkMwih0s67IG1TU7MN7SHLNvGQau0PqG+G0+vI173WHj+sDBxieIs46dhpLf/+k/19bqRQ+D7wTngduE9X4oQ+tN1LJOt84x9cD4/qnnR2/IH97zsZR6J6zbYPO24makZ1smyWEvC1O682rMH4N9+EpYt+9pvLUJg966qasL2DNCHj4ijf0PiizPhj0hVzM+qLdjVRa1czTTeyN123dETtrd+5P756sQYjNeJ18myycwG1Sm+gWp+2OaG62mEyZm94bYz/pRQf0vP+43fL2PG2bTJzAbdKbyBan9VpeO6OaG5PP7s5Jn79oLTff8yjbIxiSOPu4aVw+98id9+7lF4Os2G9a/sjO871qdcgbQd7uKHSzqnEfuFkTjQOe6vL6wLM0Dqo64Yolmckob/BV3fxFa3dJmHVvP762zHDWufq982rKWYkfOm+Z6ORZOtFsEKKnelnVuQ/cbALqNfNWtdr6uWePDPPMlm27TFPKatJtZ9nXZm6+59HM4wuXP5K7LGheTRkYV6ued+tqEDufpXG+fCudLprSSqt5/maTkRO4WQt588sbz7XThN1q2dc8zUbGT6QdrdVgvKzr80bnp/ViIJk3DzHblRO4WRe1k2RaLfuap90E2q5Oa8rbI9qaP++BZGa9N6XoAMwmm7lHj/G5Nx/J2OgIotZf3G5f7tnHTcs8vs8eQxOK5aDRkY5qy/VY07G//fjpE3oWM9s9HsRmVjJZo9BnH/yczGVC87RakCbdB56+3snZrH88iM2sQi6fe+TOaWON0qPmR4ansNfw0M5V4VrN125nFLqTt9ngcA3czMxsQOXVwN0HbmZmVkJO4GZmZiXkBG5mZlZCTuBmZmYl5ARuZmZWQk7gZmZmJeQEbmZmVkJO4GZmZiXkBG5mZlZCTuBmZmYl5ARuZmZWQk7gZmZmJeQEbmZmVkJO4GZmZiXkBG5mZlZCpdoPXNKTwF+LjiPH/sA/ig6i4lzGvecy7g+Xc+9VoYwPjogDsk6UKoEPOkkrmm28bt3hMu49l3F/uJx7r+pl7CZ0MzOzEnICNzMzKyEn8O66tugAJgGXce+5jPvD5dx7lS5j94GbmZmVkGvgZmZmJeQE3mWSFkj6vaQ1kr4nabTomKpG0lskrZO0Q1JlR5gWQdIpktZL+pOkTxYdT9VIuk7S3yU9UHQsVSVpmqSlkn6XfE5cUHRMveIrRoE9AAAFeElEQVQE3n13AS+OiJcAfwAuLjieKnoAeDPwi6IDqRJJQ8CXgVOBI4CzJR1RbFSVcz1wStFBVNw24OMRcQRwPPDhqr6PncC7LCJ+EhHbkl+XA88vMp4qiogHI2J90XFU0LHAnyLioYjYAnwLOKPgmColIn4B/LPoOKosIp6IiPuTn/8DPAiMFRtVbziB99Z7gB8VHYRZm8aAR1O/P0ZFP/hscpA0AzgauKfYSHpjatEBlJGknwIHZpy6JCJuT665hFpTzsJ+xlYV7ZSxmVkzkvYFvgNcGBH/LjqeXnACn4CIODnvvKRzgTcCrwnP05uQVmVsPbEBmJb6/fnJMbNSkTRMLXkvjIjvFh1Pr7gJvcsknQJcBJweEZuKjsesA/cBL5R0iKQ9gLcCdxQck1lHJAn4GvBgRHyh6Hh6yQm8+74EPAu4S9IqSdcUHVDVSHqTpMeAlwE/kLS46JiqIBl8+RFgMbWBP9+OiHXFRlUtkm4GfgMcLukxSecVHVMFnQC8A5iTfAavkvT6ooPqBa/EZmZmVkKugZuZmZWQE7iZmVkJOYGbmZmVkBO4mZlZCTmBm5mZlZATuFmXSNqeTFl5QNKtkvZuct3dE7z/bElfbHHNjMm+05WkC3PK/iPJTmshaf9+x2bWTU7gZt2zOSJmRcSLgS3AB9MnJU0FiIiXT+TmEbEiIj66+2FW3oVAZgIHfg2cDPy1f+GY9YYTuFlv/BI4VNKJkn4p6Q7gdwCSNib/PVHSzyXdluwhvzBZRQpJx0i6W9JqSfdKelZy/feT85dJulHSbyT9UdL7GgOQNJTsT39fsj/9B7IClfTO5PxqSTcmx2ZIWpIc/5mk6cnx6yV9RdJySQ8lMV0n6UFJ16fuuVHSVcl+zD+TdEByfFby2jWSvidpv+T4zyVdmTzrHyS9Mu8ZmpWdpI8CBwFLJS1tfNaIWBkRf5nI/1CzQeMEbtZlSU37VGBtcuilwAURcVjG5UdTqzEeAbwAOCFZxvSW5DVHUasxbs547UuAOdRWpPuUpIMazp8HPB0RxwDHAO+TdEhDrDOB+cCc5G9dkJy6Grgh2dd+IZBuut8v+Zsfo7bU6lXATOBISbOSa/YBVkTETGAZcGly/BvAJ5L7rk0dB5gaEccm5VE/nvcM48ouIr4IPA6cFBEnZZSZWWU4gZt1z4ikVcAK4BFq6zED3BsRDzd5zb0R8VhE7ABWATOAw4EnIuI+gIj4d2qP+bTbI2JzRPwDWEptP++01wLvTGK6B3gu8MKGa+YAtyb3ICLqe1W/DPhm8vONwCtSr7kz2aRnLfC3iFibxL8uiR9gB7UvIQA3Aa+Q9GxgNCKWJcdvAF6Vum9904nfpu6T9wxZZWc2aXg3MrPu2RwRs9IHkhbxZ3Je87/Uz9vp7N9k4zrIjb8LOD8iur1WfD3mHewa/w6ax9/Oms31e6XLIfMZJJ3I7pWdWem5Bm42eNYDz5N0DEDS/52VnM6QtJek5wInUttNLG0x8CHVtlZE0mGS9mm4ZgnwluQeSHpOcvxuaruRAZxDrU+/E1OAM5Of3wb8KiKeBv5V79+mtuHEsqwXd/gMjf5DbUMhs0rzN1azARMRWySdBVwtaYRa/3fW/uhrqDWd7w98JiIelzQjdf6r1JqV708Gxz0JzG34W+skfRZYJmk7sBI4Fzgf+Lqkecnr3t3hYzwDHCtpPvB34Kzk+LuAa5JpXg+1cd+Wz5DhWuDHkh5v7AdPBrldBBwIrJH0w4h4b/uPZTY4vBuZWQlJugzYGBGfLzqWLJI2RsS+RcdhVmVuQjczMysh18DNzMxKyDVwMzOzEnICNzMzKyEncDMzsxJyAjczMyshJ3AzM7MScgI3MzMrof8D4HD1OCdS6zEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}