{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "(lecture16:example-logistic-regression-with-one-variable)=\n", "# Example: Logistic regression with one variable (High melting explosives)\n", "\n", "\n", "[High Melting Explosives](https://en.wikipedia.org/wiki/HMX) (HMX) have applications as detonators of nuclear weapons and as solid rocket propellants.\n", "We will use logistic regression to build the probability that a specific HMX block explodes when dropped from a given height.\n", "To this end, we will use data from a 1987 Los Alamos Report\n", "(L. Smith, “Los Alamos National Laboratory explosives orientation course: Sensitivity and sensitivity tests to impact, friction, spark and shock,” Los Alamos National Lab, NM (USA), Tech. Rep., 1987).\n", "Let's download the raw data and load them.\n", "We will use the [Python Data Analysis Library](https://pandas.pydata.org/):" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "tags": [ "hide-input", "hide-output" ] }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "import seaborn as sns\n", "sns.set(rc={\"figure.dpi\":100, 'savefig.dpi':300})\n", "sns.set_context('notebook')\n", "sns.set_style(\"ticks\")\n", "from IPython.display import set_matplotlib_formats\n", "set_matplotlib_formats('retina', 'svg')\n", "import numpy as np\n", "import scipy.stats as st\n", "import pandas as pd\n", "import requests\n", "import os\n", "def download(url, local_filename=None):\n", " \"\"\"\n", " Downloads the file in the ``url`` and saves it in the current working directory.\n", " \"\"\"\n", " data = requests.get(url)\n", " if local_filename is None:\n", " local_filename = os.path.basename(url)\n", " with open(local_filename, 'wb') as fd:\n", " fd.write(data.content)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# Download the data file:\n", "url = 'https://raw.githubusercontent.com/PurdueMechanicalEngineering/me-297-intro-to-data-science/master/data/hmx_data.csv'\n", "download(url)\n", "data = pd.read_csv('hmx_data.csv')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each row of the data is a different experiment.\n", "There are two columns:\n", "\n", "+ First column is **Height**: From what height (in cm) was the specimen dropped from.\n", "+ Second column is **Result**: Did the specimen explode (E) or not (N)?\n", "\n", "Here is how to see the raw data:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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HeightResult
040.5E
140.5E
240.5E
340.5E
440.5E
540.5E
640.5E
740.5E
840.5E
940.5E
1036.0E
1136.0N
1236.0E
1336.0E
1436.0E
1536.0E
1636.0N
1736.0E
1836.0E
1936.0E
2032.0E
2132.0E
2232.0N
2332.0E
2432.0E
2532.0E
2632.0N
2732.0E
2832.0N
2932.0E
3028.5N
3128.5E
3228.5N
3328.5N
3428.5E
3528.5N
3628.5N
3728.5N
3828.5E
3928.5N
4025.5N
4125.5N
4225.5N
4325.5N
4425.5N
4525.5N
4625.5E
4725.5N
4825.5N
4925.5N
5022.5N
5122.5N
5222.5N
5322.5N
5422.5N
5522.5N
5622.5N
5722.5N
5822.5N
5922.5N
\n", "
" ], "text/plain": [ " Height Result\n", "0 40.5 E\n", "1 40.5 E\n", "2 40.5 E\n", "3 40.5 E\n", "4 40.5 E\n", "5 40.5 E\n", "6 40.5 E\n", "7 40.5 E\n", "8 40.5 E\n", "9 40.5 E\n", "10 36.0 E\n", "11 36.0 N\n", "12 36.0 E\n", "13 36.0 E\n", "14 36.0 E\n", "15 36.0 E\n", "16 36.0 N\n", "17 36.0 E\n", "18 36.0 E\n", "19 36.0 E\n", "20 32.0 E\n", "21 32.0 E\n", "22 32.0 N\n", "23 32.0 E\n", "24 32.0 E\n", "25 32.0 E\n", "26 32.0 N\n", "27 32.0 E\n", "28 32.0 N\n", "29 32.0 E\n", "30 28.5 N\n", "31 28.5 E\n", "32 28.5 N\n", "33 28.5 N\n", "34 28.5 E\n", "35 28.5 N\n", "36 28.5 N\n", "37 28.5 N\n", "38 28.5 E\n", "39 28.5 N\n", "40 25.5 N\n", "41 25.5 N\n", "42 25.5 N\n", "43 25.5 N\n", "44 25.5 N\n", "45 25.5 N\n", "46 25.5 E\n", "47 25.5 N\n", "48 25.5 N\n", "49 25.5 N\n", "50 22.5 N\n", "51 22.5 N\n", "52 22.5 N\n", "53 22.5 N\n", "54 22.5 N\n", "55 22.5 N\n", "56 22.5 N\n", "57 22.5 N\n", "58 22.5 N\n", "59 22.5 N" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's encode the labels as $1$ and and $0$ instead of E and N.\n", "Let's do this below:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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HeightResulty
040.5E1
140.5E1
240.5E1
340.5E1
440.5E1
540.5E1
640.5E1
740.5E1
840.5E1
940.5E1
1036.0E1
1136.0N0
1236.0E1
1336.0E1
1436.0E1
1536.0E1
1636.0N0
1736.0E1
1836.0E1
1936.0E1
2032.0E1
2132.0E1
2232.0N0
2332.0E1
2432.0E1
2532.0E1
2632.0N0
2732.0E1
2832.0N0
2932.0E1
3028.5N0
3128.5E1
3228.5N0
3328.5N0
3428.5E1
3528.5N0
3628.5N0
3728.5N0
3828.5E1
3928.5N0
4025.5N0
4125.5N0
4225.5N0
4325.5N0
4425.5N0
4525.5N0
4625.5E1
4725.5N0
4825.5N0
4925.5N0
5022.5N0
5122.5N0
5222.5N0
5322.5N0
5422.5N0
5522.5N0
5622.5N0
5722.5N0
5822.5N0
5922.5N0
\n", "
" ], "text/plain": [ " Height Result y\n", "0 40.5 E 1\n", "1 40.5 E 1\n", "2 40.5 E 1\n", "3 40.5 E 1\n", "4 40.5 E 1\n", "5 40.5 E 1\n", "6 40.5 E 1\n", "7 40.5 E 1\n", "8 40.5 E 1\n", "9 40.5 E 1\n", "10 36.0 E 1\n", "11 36.0 N 0\n", "12 36.0 E 1\n", "13 36.0 E 1\n", "14 36.0 E 1\n", "15 36.0 E 1\n", "16 36.0 N 0\n", "17 36.0 E 1\n", "18 36.0 E 1\n", "19 36.0 E 1\n", "20 32.0 E 1\n", "21 32.0 E 1\n", "22 32.0 N 0\n", "23 32.0 E 1\n", "24 32.0 E 1\n", "25 32.0 E 1\n", "26 32.0 N 0\n", "27 32.0 E 1\n", "28 32.0 N 0\n", "29 32.0 E 1\n", "30 28.5 N 0\n", "31 28.5 E 1\n", "32 28.5 N 0\n", "33 28.5 N 0\n", "34 28.5 E 1\n", "35 28.5 N 0\n", "36 28.5 N 0\n", "37 28.5 N 0\n", "38 28.5 E 1\n", "39 28.5 N 0\n", "40 25.5 N 0\n", "41 25.5 N 0\n", "42 25.5 N 0\n", "43 25.5 N 0\n", "44 25.5 N 0\n", "45 25.5 N 0\n", "46 25.5 E 1\n", "47 25.5 N 0\n", "48 25.5 N 0\n", "49 25.5 N 0\n", "50 22.5 N 0\n", "51 22.5 N 0\n", "52 22.5 N 0\n", "53 22.5 N 0\n", "54 22.5 N 0\n", "55 22.5 N 0\n", "56 22.5 N 0\n", "57 22.5 N 0\n", "58 22.5 N 0\n", "59 22.5 N 0" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Extract data for regression\n", "# Heights as a numpy array\n", "x = data['Height'].values\n", "# The labels must be 0 and 1\n", "# We will use a dictionary to indicate our labeling\n", "label_coding = {'E': 1, 'N': 0}\n", "y = np.array([label_coding[r] for r in data['Result']])\n", "data['y'] = y\n", "data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's visualize the data.\n", "Notice that lots of observations fall on top of each other." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "image/png": { "height": 372, "width": 542 } }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(x, y, 'o')\n", "ax.set_xlabel('$x$ (Height in cm)')\n", "ax.set_ylabel('Result ($0=N; 1=E$)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's train a logistic regression model with just a linear feature using scikit-learn:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from sklearn.linear_model import LogisticRegression\n", "# Make the design matrix\n", "X = np.hstack([np.ones((x.shape[0], 1)), x[:, None]])\n", "# Train the model (penalty = 'none' means that we do not add a prior on the weights)\n", "# we are effectively just maximizing the likelihood of the data\n", "model = LogisticRegression(penalty='none', fit_intercept=False).fit(X, y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is how you can get the trained weights of the model:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[-12.68785875, 0.41143587]])" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.coef_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here is how you can make predictions at some arbitrary heights:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "x_predict = np.array([10.0, 20.0, 30.0, 40.0, 50.0])\n", "X_predict = np.hstack([np.ones((x_predict.shape[0], 1)), x_predict[:, None]])\n", "predictions = model.predict_proba(X_predict)\n", "predictions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the model gave us back the probability of each class.\n", "If you wanted, you could ask for the class of maximum probability for each prediction input:" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "model.predict(X_predict)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To visualize the predictions of the model as a function of the height, we can do this:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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EVG+IJgMKEm6iIPYqCuKuQx9/A/rkKMB8733TICigdvKA2sUXalcfaFx8oHb1hdrZG0ob3b1fn4hqBIscRHWQUiHAw1kLD2ctuvu7S45l5ugRlZCF6MQsRCZkISo+CzfjM5GaWbn+H1m5Bpy9moSzV5MsMQedBm2aOMG/iRPa3PqytVFXy3MiIiIiuheiKMKYFo/82KuFRY2YqyhIuAGYjPd2YUEBtbMXNG5NoHFvArWrHzSuPlA7eUFQ8XUQUX3DIgdRPWNvq0GHFi7o0MJFEs/ILkBEXCZu3tqpJSIuEzfjs6A3VPyTjIxsPU6EJOBESAIAQBAAX3ddYeGjqTPaN3eGn7sdFGxuSkRERDXMbChAQexV5EddQX7UFRTEXYU5L/uerqnUOUPjXljM0Lg1vVXU8IVCxR0OiRoKFjmIGggHnRW6tHZDl9ZulpjJLCI+JQfh0Rm4HpOO69EZuBadjuw8Q4WuKYpAVEI2ohKysfdEFIDCZS7tm7ugfXMXdGjhjJa+jlBxO1siIiK6R6bczMKCRvTlW0WNcMBc9VkaamcvaDyaw8qzBTSezWHl0RxKW4dqzJiI6iIWOYgaMKVCgI+bDj5uOgzs5gOgcKpnYloerken43pMBq5Hp+NadHqFe31k5Rpw7FI8jl2KBwBYaZTwb+KEDi1c0LGlC9o2dYZGza7hREREVD5TTgbybl5EXsQF5EeGwJASU+VrqV28YeXVClZeLaHxbAErj2ZQWGmrMVsiqi9Y5CBqZAThdr+Pfp29ARQWPhJScxF6Mw1hkWkIvZmG6zEZFdrhpUBvwvlryTh/LRlA4Ta27Zu7oHNrV3Rp7YaWvo5QcnkLERFRo2fKz0H+zUvIu3kBeREXYUiKrNJ1lLYOsPJuffvLqyUbgRKRBYscRARBEODpYgtPF1vc190XAGAwmnAjNhNXbqYi9GYaLkekIikt767X0hvNxRqaXoatjRqdW7miSytXdG7tBl93HXdwISIiagREkwH5UVeQG34W+REXURAfDoh3/wBFQlBA49Ec1n5tYe3rDyuf1lDZu/G1BBGViUUOIiqVWqW07LCCgYWxxLRchISn4NKNVFwKT0FUQtZdr5OTZ8CRC3E4ciEOAODuZIMe7TzQs50HOrd0hbUVfw0RERE1FIaMRORdO4Pc8DPIi7gAUZ9fqfMFtRWsfNrA2rctrJu0g7V3GyisbGooWyJqiPjugogqzN1JC/ceWgzu4QegcEeXyxGFBY+L4Sm4Hp0OUSz/GolpefjrcAT+OhwBtUqBji1c0PNW0cPbjVNNiYiI6hPRaEBeZAjyws8g9/oZGJKjK3W+oLGGTZMOsG7aEdZN2sPKoxkEJd+iEFHV8TcIEVWZg84KfTp6oU9HLwBAdq4eF64n49zVZJwNS0JMUvnbvBmMZpwJS8KZsCQs3nwRXi626NneA306eqJDcxcouWsLERFRnWPKy0bu9dPIDT2O3OtnIBoqPltDUKph5dcWNk07wqZZJ1h5tWRRg4iqFX+jEFG10Wk16NvJG307FTY0TcnIw7mrSTh3NRnnriYhJaP8F0FxKTnY+m84tv4bDjutBr07eKJvJy90bePGHVuIiIhkZMxMRk7oceSGHUdeZAhgNlXwTAFWXi1h06JLYVHD1x8KlaZGcyWixo1FDiKqMS4ONhjaswmG9mwCURQRGZ+Fk5cTcOpKIkJupMBkLnttS1auHntORGLPiUhYa5To0dYDfTp5oVc7D9jaqGvxWRARETVO+uRo5Fw5ipzQ49DHX6/weQobO2hbdIVNy27QtugKpa1DDWZJRCTFIgcR1QpBENDUyx5Nvewxfmhr5OQZcPZqEk5dTsDJywlIyyoo89x8vQmHzsfi0PlYqJQCurZxx33dfNC7oxds2LiUiIio2hjS4pEdcgg5IYegT7xZwbMEWHm3grZld9i07AYrrxYQFJyBSUTy4LsDIpKFrY0a/Tt7o39nb5jNIm7EZuDE5QQcuRCH8JiMMs8zmkScvFUY0aiVCGjvgUHdfNGznTvUKr6gIiIiqixjZgqyLx9CzqVDKIi7VqFzBKUaNi26QNsmALate3K2BhHVGSxyEJHsFAoBLX0d0dLXEZMe8EdCai6OXIjD0YtxCLmRUuaOLXqDCQfPxeLguVjYWqvQr7M3BnXzQadWblAqhNp9EkRERPWIKTcL2SEHkRNyCPlRlyt0jsJaB23rHrBtEwCbFl2g0HBrVyKqe1jkIKI6x8NZi8D7WiLwvpZIzyrAsUvxOHoxDmfDkmA0mUs9JyffiN3HI7H7eCSc7KwwuIcfhvXyQxNP+1rOnoiIqG4SzSbkXj+D7PP/ICfsJGA23vUcpc4Jtm37wtY/ANZ+7bgTChHVefwtRUR1mqOdFYb3aYrhfZoiN9+AoxfjsP9MDM6GJcFcRuPStKwCbNx3DRv3XYN/UycM69UEA7v6sGEpERE1SvrESGRd+AfZFw7AlJN+1/EKrT1s2/aBrv0AWPu1ZX8NIqpXWOQgonpDa6227NaSkV2AQ+djceBMDC6Fp5R5TujNNITeTMPizRfRr7MXHghogo4tXKHgchYiImrATHlZyL50ENnn/0FB3N13RlFYaaH17wNdh/6wadaJhQ0iqrdY5CCieslBZ4WR/ZpjZL/mSE7Pw79nY7D/TDSuR5fetFRvMGHfqWjsOxUND2ctHghoggf7NIWTnXUtZ05ERFQzRFFEQew1ZJ4ORk7IIYhGfbnjBaUaWv8A6DoMhLZFVwgqzngkovqPRQ4iqvdcHW0wbnArjBvcClEJWdh7IhJ7T0YhvYxtaRNSc/H7zitYszsU/Tp7Y1T/5mjXzBmCwNkdRERU/5gNBci+9C8yTwVDHx9+1/FW3q1h13kIbNv3h9JGVwsZEhHVHhY5iKhB8fOwwxOjO2DqQ+1w+koi9pyIxPFL8TCV0r/DaBJx4EwMDpyJQXNve4zq3xz3dfOFtRV/NRIRUd2nT45G5uldyD7/D8wFueWOVeqcoOt0H+w6D4HG1beWMiQiqn18JU9EDZJKqUBAB08EdPBEelYB9p2Owu7jkYiMzyp1/I3YTCz44xyWbr2E+wOaYFS/5vB246dbRERUt4iiGblXTyHjxHbkR1wof7BCBVv/XrDrPBQ2LbqwzwYRNQoschBRg+doZ4XA+1rh4UEtcTUqHX8djsCBM9HQG0tuR5uTb8SWA+HYciAcvdp7IGhwK3Ro4cKlLEREJCuzoQDZF/Yj49hWGFJjyx2rsneFXfcHYdflfqh0jrWTIBFRHcEiBxE1GoIgoE0TJ7Rp4oQZYzpgz/FI/HXkBuJTSp/ieyIkASdCEtCmiSOCBrdGn05eUHJXFiIiqkWmnAxknPwLmaeDYc7NLGekAJuWXWHffTi0rbpz1gYRNVoschBRo2Rvq0HQkFYIvK8lTocmYvuhGzh1JQFiydYdCItMxxfLT8DTRYvAQS1xf0ATWGv465OIiGqOPjkaGce2IvvCfogmQ5njFFp72HUZCvtuD0Dt5FmLGRIR1U18lU5EjZpCIaBnOw/0bOeB+JQc/HU4AruO3UR2XskXlPEpufhp4wWsDA7FqP7NMXpAczjorGTImoiIGqr8mKtIP/Qncq+eLHecxr0JHHqPha79AG79SkRUDIscRES3eLrYYsaYDpj0oD/2HI/EpgPXkZhacilLVq4ea3aHYsO+axjZrxmChrSCk521DBkTEVFDkR99BWn//om88DPljrNp0RUOvcfCpnln9osiIioFixxERHewsVJhzMAWGNmvGQ6fj8OGfVdxLTqjxDi9wYRN+69jx+EIFjuIiKhK8iIvIf3fP5BX3k4pChV0HQfCsfcYaNyb1l5yRET1EIscRERlUCoVGNjNBwO6euPC9WRs+OcaTl1JLDGuRLFjcCs42bPYQUREpRNFEfk3LyLt3z+QH3mpzHEKax3suz8I+54jobJzqsUMiYjqLxY5iIjuQhAEdG7lhs6t3HAzLhMb9l3DvtPRMJulXUpZ7CAiorvJi7iA1P1rUBB9pcwxSlsHOPQeC/sew6HQ2NRidkRE9R+LHEREldDUyx6vTu6OSQ/444+9Ydh7MqrsYsehGxgzsAUeGdoaOq1GpoyJiKguKIgPR+o/K5EXfrbMMUpbRzj2Gwe7bg9AoWZjayKiqmCRg4ioCrxcbfHSxG54dFgbrNtTRrHDaMb6f64h+OhNPDqsDUb1bw6NWilTxkREJAdDWjxS969GzqWDZY5R2rnAsW8g7Lrez+IGEdE9YpGDiOgeeLpIix1/n4yC6Y5iR3aeAUu2XsLWg+GYOqIdBnf3hULBjvhERA2ZMTsd6Yf+RObp3YDZWOoYlYMbHPsFwa7zEG4DS0RUTVjkICKqBsWLHX/svYq9JyJLFDuS0vLwzerT2LT/Gp4Y3QHd/d1lypaIiGqKuSAP6Uc3I+PYVoiG/FLHKHVOcBowAXZdh0JQsrhBRFSdWOQgIqpGni62mP1oV4wf0grLd1zGofOxJcbciM3EnJ+PoGtrNzw+uj1a+TrWfqJERFStRNGMrHN/I23fKphySm47DgCClRaOfQPh0GsUFBo2piYiqgkschAR1QBvNx3efrwXQm+mYum2EFwKTykx5uzVJJz7dj8eCGiK6SPbwUHHddhERPVRfvQVJAcvgT7+eqnHBaUa9j0fgmO/ICi1drWcHRFR48IiBxFRDfJv6ozPn++PE5cT8Nv2EETGZ0mOiyKw69hNHDofi6kj2uKhvs2gVCpkypaIiCrDmJmC1H9+R/bFA6UPEBTQdboPzoMmQuXgVrvJERE1UixyEBHVMEEQENDeEz3aeuDvE5FYGXwFKRnSddo5eQYs2ngBwUdv4tlxndCxpatM2RIR0d2YjXpkHNuG9EPry+y7oW3VA85Dp0Lj1qSWsyMiatxY5CAiqiVKhYAHejfFwG4+2HIgHH/sDUO+3iQZExGXiXd+OIRB3Xzw5JgOcHGwkSlbIiK6kyiKyL16Eim7l8KYnlDqGLWrL1wemAFti661mxwREQFgkYOIqNZZa1R4dFgb3N/LD0u2XsKBMzElxhw4E4Pjl+Ix8QF/PDyoBdQqpQyZEhFREUNGIpL/Woy866dLPa6w0sJp0ETY9xgBQcmX2EREcuFvYCIimbg42OCNqT0xom8z/LzxAiLiMiXH8/Um/LY9BH+fjMTsCd3QrrmzTJkSETVeotmEjBM7kLZ/NURDQSkjBNh1vR/Ogx+D0tah1vMjIiIpFjmIiGTWqaUrvn31Pvx1JAK/77yCnDyD5HhUQjbeWvgvRvVrjmkj20FrrZYpUyKixqUgPhxJ238qc9cUK19/uD74FKy8WtZyZkREVBYWOYiI6gClUoHRA1pgYFcfLN9xGbuP34Qo3j4uisC2Qzdw9FI8nh/fGb3ae8qXLBFRA2c2FCDtwFpkHNsKiOYSx5W2jnAZ9gRsOwyAIAgyZEhERGVhkYOIqA5x0Flh9qNdMbxPU/y4/hyuRWdIjien5+GTX49hUDcfzAzsBAedlUyZEhE1TLnhZ5H81yIY0xNLPW7X7UE4D50KpbVtLWdGREQVwSIHEVEd1KaJE/7z0iBsPhCOlcFXoDdId2E5cCYGZ0KT8PTDHTGkhy8/SSQiukem3Cyk7F6C7IsHSj2udvWF28hZsPZrV8uZERFRZbDIQURURymVCgQNaYW+nbyw4I+zOH8tWXI8K1ePb1afxv7T0XhxQle4OXG7WSKiqsi9dhpJ23+AKTut5EGlCk79x8Ox7zgIKvZEIiKq6xRyJ0BEROXzcrXF3Fn98PLErrC1KfkC+3RoImZ//Q/2n46WITsiovrLrM9D0o5FiF/7WakFDmu/dvB9+ms4DXyUBQ4ionqCMzmIiOoBQRAwLKAperT1wKJNF3DoXKzkeE6eAf9ZeQrHL8XjufGdodNqZMqUiKh+yI+6gsQt/4MxPaHEMYWVFs73T4dd1/shCPxMkIioPmGRg4ioHnGyt8bb03vh6MU4/Lj+PFIz8yXHD5yNwaUbKXhlUjd0beMuU5ZERHWXaDQg9cAaZBzZDEAscdymRTe4jX4eKjvn2k+OiIjuGYscRET1UJ+OXujY0hWLNpzHvjuWqaRk5OODRUcwdmALTB/VHlZqpUxZEhHVLQUJEUja8h30iZEljglqK7gMewJ23R5gM2cionqMRQ4ionpKZ6PG61N6IKC9JxauP4ecPIPk+JZ/w3EmLBGvPdYDrXwd5UmSiKgOEEUzMo5uQeq+1YDZWOK4la8/3MfMhtrZS4bsiIioOrHIQURUzw3s5oN2zZ3x3ZozOHs1SXIsKiEb//fdAUwZ0Rbjh7SGQsFPJ4mocTHlZCBxy/+QF3625EGlCs73TYZD7zEQFJz1RkTUELCTEhFRA+DqaIOPZ/bFzMBO0Kikv9pNZhHLd1zGx78eRUZ2gUwZEhHVvrybFxH9y+ulFjg07k3hM2M+HPsGssBBRNSAsMhBRNRAKBQCxgxsgW9evQ8tfR1KHD99JREv/3cfQm6kyJAdEVHtEc0mpB1Yh7iVH5eyNawAx35B8JkxH1YezeRIj4iIahCLHEREDUwTT3t8NXsQHh3WBneuTknJyMc7PxzC+r+vwmwuuasAEVF9Z8xKQ9yqT5D271pANEuOKXVO8JoyB85DpkBQqWXKkIiIahJ7chARNUBqlQLTHmqHLq1d8Z/fTyEt6/YyFbNZxLLtIbgYnoJXJ3eHva1GxkyJiKpPbvhZJG7+DubczBLHbFp0gfvYl6G0LTnTjYiIGg7O5CAiasA6t3LDd68PRpfWriWOnbycgJf/uw9XbqbKkBkRUfURzSak/rMS8as/LVngEBRwHjIFnpPeZ4GDiKgRYJGDiKiBc7Kzxscz++GxB/0h3LF8JTk9D28vOIiN+65BFLl8hYjqH1NuJuJWf4r0wxtKHFPaucB72idw7BcEQeDLXiKixoDLVYiIGgGlQsDk4W3Rrrkzvl55GunFdlkxmUUs2XoJoZFpeGViN1hb8U8DEdUPBfE3kPDnfBgzkkoc07bqAbcxs6HU2smQGRERyYUlbSKiRqRrG3d89/pgdGpZcvnKoXOxeOP7f5GQmitDZkRElZN96V/E/vZuyQKHQgnnYY/D49F3WOAgImqEWOQgImpknO2t8emzfTFxWJsSy1ci4jLx6jf7ceFasjzJERHdhWg2IWXvb0jc9C1Eo15yTKlzgve0T+HYeyyEO3/BERFRo8AiBxFRI6RUKjD1oXaY83Qf2NpIt1HMytXj/UWHsf1gOPt0EFGdYsrLQvyaz5BxdEuJY1a+/vB58itY+/rLkBkREdUVLHIQETViPdp64L8vD4Kfh04SN5tF/LTxAhb8cQ4Go0mm7IiIbitIiEDMkjeRd+NciWN23R6E99SPobJzkiEzIiKqS1jkICJq5LzddPjPS4MQ0N6zxLFdx27ivR8PIy0zX4bMiIgKZV8+XNh/Iz1RekChgutDz8Jt5LMQlOrSTyYiokaFRQ4iIoLWWo33ZgRg4rA2JY5djkjFq9/ux9WoNBkyI6LGTBRFpB1aj8QNX0M0FEiOKW0d4T3tY9h3f1Cm7IiIqC5ikYOIiAAACoWAqQ+1w1vTe8JKo5QcS8nIx9sLDuLIhViZsiOixkY0GZG8/Uek7VtV4piVd2v4PPUVrH3bypAZERHVZSxyEBGRxIAuPvhq9kC4O9lI4nqjGZ//dgJb/r0uU2ZE1FiY83MQv/YzZJ3bW+KYXZf74T3tU6jsnGXIjIiI6joWOYiIqITm3g747yv3oVNLV0lcFIHFmy7il80XYTZz5xUiqn6GjETELH8PeTfO33FEgPOwJ+A66jkIKvbfICKi0rHIQUREpXLQWeGTZ/viwd5NSxzbfOA6vlh+AgUG7rxCRNWnIO46Ype+A0NSlCQuqDTwGP8GHHuPgSAIMmVHRET1AYscRERUJpVSgRcndMHUh0quez9yIQ7v/3gIGdkFpZxJRFQ5OWEnELviA5hy0iVxpa0DvKZ+Atu2veVJjIiI6hUWOYiIqFyCIGDiMH+89lh3qJTST1Cv3EzDG9//i9jkbJmyI6KGIOPEDiT8+WWJHVTUrr7wfuJzWPu0likzIiKqb1jkICKiChnSww8fz+wLW2uVJB6XnIP/++5fXIlIlSkzIqqvRFFEyt7fkLLrV0A0S45ZN+0I7+mfQe3oIVN2RERUH7HIQUREFda5lRvmzx4Itzt2XsnK1eO9Hw/hyIU4mTIjovpGNJuQvP0HZBzdUuKYrvNgeE1+H0obnQyZERFRfcYiBxERVUpTT3t8NXsgWvg4SOJ6oxlfLD+Bv09GlXEmEVEhs1GPhA1fI+vc3yWOOQ2aBLfRL0JQcgcVIiKqPBY5iIio0lwcbPD58/3Rva27JG42i/hm9WlsOxguU2ZEVNeZC/IQv3YeckOPSQ8ICriNmQ2ngRO4gwoREVUZixxERFQlWms1Pnyyd6lbzC7aeAFr94RCFEUZMiOiusqUm4W4lR8hP+KCJC4o1fB45E3YdR4sT2JERNRgsMhBRERVpry1xWzQ4FYljv3+1xUs3RbCQgcRAQCMmSmIXfE+CuKuSeKCxgaekz+AbZteMmVGREQNCYscRER0TwRBwBOj22PaQ+1KHNu47xoW/HEOJjMLHUSNmSE1FrHL34MhOVoSV2jt4T31E9g07SBTZkRE1NCwyEFERPdMEAQ8OqwNZo3rVOLYrmM38Z/fT8JgNJdyJhE1dAXxNxC7/H0YM5IkcaW9K7ynz4WVVwuZMiMiooZIJXcCRETUcIwa0AI21mp8t/YMzMVmbxw8F4u8AiPefrwXrDX800PUWOTHhCF+9acwF+RK4moXH3g99iFU9q4yZUZERA0VZ3IQEVG1GtrTD29P7wWVUvon5tSVRHy0+Chy8w0yZUZEtSk/JgxxpRQ4NJ4t4T3tUxY4iIioRrDIQURE1a5vJy989HQfWGuUkvil8BQWOogagfzoUMSt+gTiHQUO66Yd4D31IyhtHWTKjIiIGjoWOYiIqEZ0aeOGT2f1g62NWhK/HJGKj39hoYOoocqPuoK41Z9A1OdJ4jYtusFz4ntQWGllyoyIiBoDFjmIiKjGtG3qjM+f7w8HnUYSD7lRWOjIKzDKlBkR1YT8qMuIW/MpRH2+JG7Tsjs8JrwJhdpKpsyIiKixYJGDiIhqVHNvB3w2i4UOooYuLzIEcavnlihwaFv1gOcjb0Kh0pRxJhERUfVhi/tizGYzNm7ciE2bNiE0NBS5ublwc3ND9+7dMWnSJPTq1eue73HkyBGsWbMGZ8+eRUpKCqysrNCkSRPcd999mDZtGlxcXKrhmRAR1S1Nvezx2az+ePfHQ8jM0Vvil8JT8PEvRzHn6T6wseKfJKL6Ki/yEuLXzINouKPA0bonPIL+D4JKXcaZRERE1YszOW7JysrC448/jnfffRfHjx9HRkYGDAYDYmNjsW3bNkybNg1ffPFFla9vNpvx/vvv44knnsDOnTsRHx8Pg8GA7OxshISE4Mcff8TIkSNx+PDhanxWRER1R1Mve3z2XH/Y20o/zS0qdORzRgdRvZR38xLi13xWssDRphc8xrPAQUREtYtFDgCiKOKVV17B8ePHAQADBgzAwoULsXbtWnz00Ufw8fGBKIpYunQpfv755yrd4+uvv8Yff/wBAHBycsJbb72FFStWYOHChQgMDAQApKen4/nnn0dYWFi1PC8iorqmWTmFjo9Y6CCqd/JuXkT82s8gGgokcW2bAHgEvQ5ByQIHERHVLhY5AGzduhUHDx4EAAQFBeHXX3/FsGHD0LVrV0yePBkbNmxAq1atAAALFixAfHx8pa6fkJCAZcuWAQCcnZ2xefNmPPnkkwgICMCwYcMwf/58fPbZZwCAvLw8fP3119X35IiI6phmXvaYO6sf7LSlzOj4lYUOovoiPyYM8Ws/L1ng8O/NAgcREcmGRQ4AS5cuBQDodDq89dZbJY47Ojri448/BgAUFBRg+fLllbr+v//+C6Ox8EX7U089BQ8PjxJjHnnkEbRt2xYAcOjQIRQUFJQYQ0TUUDT3dsBnz5UsdFy8noK5S49BbzDJlBkRVURBQgTi18wtsUTFtm0feIx7DYKSPXaIiEgejb7IERUVhZCQEADAkCFD4OjoWOq4nj17onnz5gCAnTt3VuoeKSkplsfNmjUrc1zR9Q0GA9LS0ip1DyKi+qasQse5q8n46veTMJnMMmVGROXRp8QifvUnMOfnSOK2bfvAPfBVFjiIiEhWjb7IcerUKcvjPn36lDs2ICAAABATE4PIyMgK38Pd3d3yODw8vMxxRcdUKhV3WSGiRuF2oUM6rf3oxXj8b91ZmM2iTJkRUWmMGUmIW/UxTDkZkrhNy25wD3yFBQ4iIpJdoy9yXLt2zfK4vFkWAODn52d5fPXq1QrfY8CAAbCysgIALFu2DMnJySXGbN68GaGhoQCABx98EGo117ESUePQ3NsBnzzbD1pr6Zujv09G4ZctFyGKLHQQ1QXG7DTErvwIpkzp6xjrJu3hMf4N9uAgIqI6odEXOYo3EfX29i53rJeXV6nn3Y2bmxveeustCIKAlJQUPPzww1i2bBmOHz+Offv2Yc6cOXj77bcBAE2bNi21LwgRUUPWytcRHzzZGxqV9M/S1n/DsXpXqExZEVERU14W4ld/AmOa9PWPlVdLeD76DhRqK5kyIyIikmr0cwozMm5Pt7S1tS13rFartTzOysqq1H2mTJkCPz8/fPPNNwgJCcHnn39eYsz06dPx/PPPw8nJqVLXBoDY2FjExsZW+jwAlhkkRERy6tjSFe88EYC5S47BVGyZyupdobC1UePhQS1lzI6o8TIX5CF+zWfQJ0qX6qrd/OA56QMorLRlnElERFT7Gn2RQ6/XWx5bW1uXO7b48eLnVUR2djZOnjxZ7gyQffv2oUOHDggMDKzUtQFg/fr1WLBgQaXPIyKqS3q288Brj3XHf1aeQvFVKr9svghbaxWGBTSVLzmiRshsKED8H1+gIFa6TFfl5AmvyXOg1NrJlBkREVHpGn2RQ6lUWh4LglDu2OLrwhWKiq/0SU1NxdNPP41Lly4BAB599FFMnToVzZs3R05ODo4cOYL//e9/uHHjBt566y1ERUVh9uzZlXwmREQNw6BuvsjJN+KHP89J4t+vOwuttRr9Ope/tJCIqodoMiJxw9fIv3lRElfaOcPrsTlQ2VV+5ikREVFNa/Q9OYovQcnPzy9nJFBQUGB5rNFoyhkp9dFHH1kKHO+99x4+/fRT+Pv7Q6PRwMnJCSNHjsSff/6JDh06AAAWLFiA/fv3V+ZpEBE1KA/1bYbpI9tJYmYR+Or3UzgblihTVkSNhyiKSNrxI3KvnZLEFVp7eD02B2pH9zLOJCIiklejn8lRvA9HXl4e7O3tyxybm5treezg4FCh6yckJGD37t0AgM6dO2P69OmljtPpdJg3bx4efvhhAMCKFStw3333VegeADB+/Hj07du3wuOLCw0NxSeffFKlc4mIasqE+9sgJ8+A9f/c3gXLaDJj7tLjmPdcf7Rpwk+RiWpK2v41yD6/TxJTWGnhNflDaFx95UmKiIioAhp9kcPHx8fyOC4uDh4eHmWOjYuLszwub1xxFy9ehNlsBgAMHTq03LFt27ZFkyZNEBkZiXPnzpU79k7e3t533R2GiKi+eXxUe+TkG7HzSIQlVqA34dNfj+GrlwbC06X8htFEVHmZp3ch/dCfkpig0sBz0nuw8mwuU1ZEREQV0+iXq7Ru3dryODIyspyRQFRUlOVxq1atKnT94rM/ypslUsTFxQVAYaNSIqLGThAEzArqjIFdfSTx9OwCfLT4CDJzKtcEmojKlxN2Ask7F0uDggLuQa/D2retPEkRERFVQqMvcnTt2tXScPTkyZPljj1+/DgAwMvLC76+FZuq6ezsbHl8tyIKULi85c7ziIgaM6VCwKuTu6NrazdJPCYpB3OXHEOBwSRTZkQNS35MGBI3/hcQzZK464hnYNu6p0xZERERVU6jL3J4eXmha9euAIDg4OAyZ1CcPHkSN27cAAAMHz68wtfv0qUL1Go1AGDnzp3lNjc9efIkYmNjAQA9e/LFBBFREbVKgXee6IVmXtIZcZcjUvH1ylMwmcUyziSiitCnxCJ+7TyIRunsKMcBj8C++4MyZUVERFR5jb7IAQDTpk0DAKSnp2POnDmWHhpFMjIyMGfOHACAWq3G1KlTK3xtnU6HoKAgAEB8fDw++OADGAyGEuMSEhLwzjvvWH4uq0EpEVFjpbVW46Nn+sDVwVoSP3IhDku2XCzjLCK6G2N2OuLXfApzXpYkrus8FE6DJsmUFRERUdWwyAFg1KhRGDBgAABg27ZtmDZtGoKDg3H27FmsXbsW48aNw7Vrhd39Z8+eDT8/P8n5x44dg7+/P/z9/S0Fk+Jee+01NGvWDACwZcsWBAUFYdWqVTh16hSOHz+OhQsXYuzYsZblLDNmzECPHj1q8BkTEdVPLg42mPNMX2itpX2zt/wbjk37r8uUFVH9ZdbnIX7tPBjTpVsz27ToBreRz1qW9BIREdUXjX53lSLfffcdZs2ahRMnTuDkyZOl9ud44oknMHPmzEpf29HREcuXL8fLL7+MM2fOICwsDB9//HGJcYIgYObMmXjllVeq8hSIiBqFZl72ePeJAHy0+AiMptvLVJZsvQg3Rxv078KdpogqQjQZkbD+a+jjpQVCjWdLeIx/HYKSLxOJiKj+4V+vW3Q6HZYvX45NmzZhy5YtuHLlCrKysuDk5IRu3bphypQp6NOnT5Wv7+HhgVWrViE4OBjbtm3DhQsXkJqaCrVaDW9vb/Tu3RuPPfZYhXdtISJqzLq0dsNLE7vhv6tOW2KiCHy96hQc7azQoYWLjNkR1X2iKCL5r5+RF35GElc5usNz4rtQaGxkyoyIiOjesMhRjEKhQFBQkKWHRkX17t0boaGhFbr+Qw89hIceeqiqKRIR0S1DevghKS0PK/66bIkZjGZ8tvQYvpw9EL7udjJmR1S3ZRzbgqxzeyUxhY0dPCd9AJXOUZ6kiIiIqgF7chARUb014f7WGNG3mSSWlWvAx78cRUZ2gTxJEdVxOWEnkLp3hSQmqDTwnPguNC5c7kVERPUbixxERFRvCYKAWeM6oVd7D0k8PiUXXyw/AYPRXMaZRI1TQUIEEjd9C0C67bL7w6/A2qeNLDkRERFVJxY5iIioXlMqFXhzak+08nOUxC9eT8GijechimLpJxI1MsbsdCSs+xyiIV8Sdx4yBbZte8uUFRERUfVikYOIiOo9aysV3p8RABcHa0k8+OhNbD0YLlNWRHWH2ahHwp/zYcxMlsR1nQbDoe84mbIiIiKqfixyEBFRg+DiYIP3Z/SGRq2UxH/dfBGnQxNlyopIfqIoInnbDyiICZPErXzbwm3kLAiCIFNmRERE1Y9FDiIiajBa+Tni1cndJDGzCHy5/ASiErJkyopIXumH1iP70r+SmMrBHZ6PvAlBpZYpKyIioprBIgcRETUoA7r4YPKD/pJYTr4Rny45hqxcvUxZEckj+/IRpO1fLYkJGht4PvoOlLYOMmVFRERUc1jkICKiBmfSA/7o30W6FWZccg7mLz8Bo4k7rlDjUBB3HUlb/icNCgp4jHsVGvcm8iRFRERUw1jkICKiBkehEPDKpG5o6Sv9pPrc1WQs3nRBpqyIao8xKxXx676AaJTOXnK+fzq0rXrIlBUREVHNY5GDiIgaJGuNCu/P6A1neytJfMfhCGw/dEOmrIhqnmg0IGH9f2DKTpXE7boOg0PAaJmyIiIiqh0schARUYPl6miD92b0hlol/XP386YLOH8tSaasiGpW8q4lKIgJlcSsm3aA64inuZMKERE1eCxyEBFRg9amiRNemnjHjitmEfOXn0RSWp5MWRHVjMyze5B1ZpckpnJ0h0fQGxCU3EmFiIgaPhY5iIiowRvc3RePDmsjiWXm6PH5b8ehN5hkyoqoeuXHXEXyzsWSmKDSwOORt6DU2smUFRERUe1ikYOIiBqFKcPbIqC9pyR2NSodP7MRKTUAxux0JKz/EjAZJXG30c/DyqOZPEkRERHJgEUOIiJqFBQKAa8+1h1erraSePDRmwg+elOmrIjunWgyInHj1zBlSRuNOvQeA12HgTJlRUREJA8WOYiIqNHQ2ajx7hMBsNIoJfGfNpxHWGSaTFkR3ZuUvb8hPzJEErNu2hHOQ6fJlBEREZF8WOQgIqJGpZmXPV56tKskZjSZ8flvJ5CRXSBPUkRVlHVhPzJP7JDElPau8Bj3GgSFsoyziIiIGi4WOYiIqNEZ1M0XDw9qKYklp+fhyxUnYTKZZcqKqHIK4sORvOMnSUxQquE5/g0obR1kyoqIiEheLHIQEVGj9MTo9ujY0kUSO38tGSv+uixTRkQVZ8rNRMKfX0I06iVx14dmwsq7lUxZERERyY9FDiIiapRUSgXenNYTLg7Wkvj6f67h0LlYmbIiujvRbELipm9hzEiSxO17jIBdl6EyZUVERFQ3sMhBRESNlpOdNd5+vBdUSkES/27taUTGZ8qUFVH50g+uR96Nc5KYlW9buDzwhDwJERER1SEschARUaPWtqkzZgZ2ksTyCkyYt+wEcvMNMmVFVLrcG+eQ9u86SUypc4JH0P9BUKplyoqIiKjuYJGDiIgavRF9m2FYryaSWExSNn748zxEUZQpKyIpY1YqkjZ/B6DY/yYFBTyCXofKzkm2vIiIiOoSFjmIiKjREwQBs8Z3Ritf6Y4U+89EY9exSJmyIrqtsA/HNzDlZEjizkOmwNqvnUxZERER1T0schAREQGwUivx1vResLVWSeI/bzyPG7EZZZxFVDvS9q9BfmSIJKZt1QMOfcbKlBEREVHdxCIHERHRLZ4utnhpYjdJTG80Y/5y9ucg+eReO430wxskMaW9K9zGzIYg8KUcERFRcfzLSEREVEy/zt4YM7CFJBaTlMP+HCQLY2YyErf8TxpUKOER9DqUWjt5kiIiIqrDWOQgIiK6w4zR7dHKz1ESY38Oqm2iyYiEjf+FOS9LEnceOg3WPm1kyoqIiKhuY5GDiIjoDmqVEm9N6wkt+3OQjFL3rURBdKgkpm0TAIeA0TJlREREVPexyEFERFQK9ucgOeWEnUDG0S2SmMrRHW6jX4AgCDJlRUREVPexyEFERFSG/p29MXpAc0mM/TmophnSE5G09XtpUKmCx7jXobTRyZMUERFRPcEiBxERUTmeHNMBrXwdJDH256CaIppNSNz0Lcz5OZK4y/2Pw8q7lUxZERER1R8schAREZVDrVLirem9Su3PERGXKVNW1FCl/bsOBTHSPhy27frCvudDMmVERERUv7DIQUREdBdl9ef4csVJFBhMMmVFDU1e5CWkH9ogiakcPeA26nn24SAiIqogFjmIiIgqoH9nb4zuL+3PEZWQhSVbLsqUETUkprxsJG76DhDNt4MKJdwDX4HCSitfYkRERPUMixxEREQV9OTYDmjhLe3PseNwBI5fipcpI2oIRFFE8o4fYcpKkcSdBk2CtU8bmbIiIiKqn1jkICIiqiC1Son/m9oDGrVSEv9u7RmkZubLlBXVd1ln9yDnylFJzLppRzj2fVimjIiIiOovFjmIiIgqwc/DDs883FESy8zR45vVp2E2c1tZqhx9cjRSdi2RxBQ2OriPfQmCQlnGWURERFQWFjmIiIgqaXifpujbyUsSOxuWhM0HrsuUEdVHotGAxE3fQjTqJXG3US9AZe8iU1ZERET1G4scRERElSQIAl6c0BXO9taS+PIdIbgenS5PUlTvpP7zO/QJNyQx++7DYesfIFNGRERE9R+LHERERFVgb6vBa491R/GdPY0mEf9ZeQr5BUb5EqN6Iff6GWQc3yaJqV194TzscZkyIiIiahhY5CAiIqqiLq3dEDS4lSQWnZiNX7itLJXDmJ2OpK3fS2KCUg2Pca9BobaSKSsiIqKGgUUOIiKiezBlRDu08pVuKxt89CaOXIiVKSOqy0RRRNLWBTDlZEjizvdPh8a9qUxZERERNRwschAREd0DtUqB/5vaE9Ya6U4Y3687i5SMPJmyoroq89RO5IWfkcS0rXvCvudDMmVERETUsLDIQUREdI983HSYGdhJEsvKNeC/q7itLN2mT4lB6t7lkphS5wS30S9AKN7chYiIiKqMRQ4iIqJqMCygCfp38ZbEzl9LxpZ/w2XKiOoS0WRE0ub/ldwudsyLUGrtZcqKiIio4WGRg4iIqBoIgoAXH+kCV0cbSXz5jhBExmfKlBXVFemHNqAg7pokZt/zIWhbdJUnISIiogaKRQ4iIqJqotNq8Nrk7pKYwWjGf1efhtFklikrklt+zFWkHfxDElO7eMN56DSZMiIiImq4WOQgIiKqRp1aueLhQS0lsevRGVi7O0ymjEhOZkMBkrb8DxCLFbkEBdzGvsztYomIiGoAixxERETVbNrIdvDz0Eli6/aGISwyTaaMSC6pe5fDkCrdTthpwARYe7eSKSMiIqKGjUUOIiKiamalVuK1yT2gVNzeMcNsFvHfVaeQrzfKmBnVptzws8g8tVMSs/JuDcf+QTJlRERE1PCxyEFERFQDWvk5YtKD/pJYTFIOftseIlNGVJtMeVlI2rpQEhNUGriNfQmCUiVTVkRERA0fixxEREQ1ZMLQ1mjTxFES23bwBs6GJcqTENWa5J2LYcpOlcSc758OjYt3GWcQERFRdWCRg4iIqIYolQq8Ork7NCrpn9vv1pxBdp5BpqyopmVf+hc5IYckMZsWXWHfY4RMGRERETUeLHIQERHVIF93OzwxuoMklpyRj583npcpI6pJxswUJO9cLIkprHVwG/0CBEEo4ywiIiKqLixyEBER1bBR/ZujS2tXSeyfU9E4dD62jDOoPhJFEUnbf4A5P0cSd31oJlR2zjJlRURE1LiwyEFERFTDFAoBL0/sDltracPJhX+cQ1pmvkxZUXXLOrsXeeFnJTFdh4HQte8vT0JERESNEIscREREtcDNyQbPBnWWxLJy9VjwxzmIoihTVlRdjBlJSNmzTBJT6pzhMvxpeRIiIiJqpFjkICIiqiWDu/uiX2cvSex4SDz2n46WKSOqDoXLVH6EqM+TxN1GzYLSRidTVkRERI0TixxERES1RBAEPD++Cxx1VpL4oo0XuGylHss6uwd5N85JYrrOQ6Bt1UOmjIiIiBovFjmIiIhqkYPOCs+Nly5byc4zYOGfXLZSHxUuU/lNElPaOcPlgRkyZURERNS4schBRERUy/p19sbArj6S2LFL8ThwJkamjKgqylymMvI5KK1tZcqKiIiocWORg4iISAbPjusEB51GElu08TzSsrhspb4ofZnKUGhbdZcpIyIiImKRg4iISAYOOis8F9RFEsvKNeDH9ee5bKUeKHuZyhPyJEREREQAWOQgIiKSTf8u3ujfxVsSO3IhDgfPxsqUEVUEl6kQERHVXSxyEBERyWjWuM6wt5UuW/lxw3mkZxXIlBHdTdaZ3VymQkREVEexyEFERCQjRzsrzAqS7raSlavHTxvOy5QRlceQkYiUvVymQkREVFexyEFERCSzAV280a+zlyR26HwsDp7jbit1iSiKSN7+I0S9tDksl6kQERHVHSxyEBERyUwQBMwK6gw77R3LVtafR0Y2l63UFVnn9iLvhnSGjV0XLlMhIiKqS1jkICIiqgOc7KwxK6iTJJaZw2UrdYUxKxWpJXZTcYHLsCfkSYiIiIhKxSIHERFRHTGwqw/6dpIuWzl4LhZHLnC3FTmJoojknYthLsiVxN1GPgsFl6kQERHVKSxyEBER1RGCIOC5oM6w06ol8Z82nEd2nkGmrCjnylHkhh2XxHQdB0HbqodMGREREVFZWOQgIiKqQ5zsrfFMoHTZSmpmAZZtuyRTRo2bKS8LKcGLJTGF1h4uD8yQKSMiIiIqD4scREREdczg7r7o0dZdEgs+ehMXriXLlFHjlbLnN5hyMiQx1wefglJrL1NGREREVB4WOYiIiOoYQRDw/PgusNYoJfHv/ziLAoNJpqwan9zws8g+/48kpm3dE7bt+8uUEREREd0NixxERER1kLuzFtNHtpfE4pJzsDr4ikwZNS5mfR6SdyySxASNDVxHzIQgCDJlRURERHfDIgcREVEdNbJ/c7Rt6iSJbdx/Hdei0+VJqBFJ3bcaxoxESczl/ulQ2bvIlBERERFVBIscREREdZRSIWD2o12hUt6eOWA2i/h+7VkYTWYZM2vY8mPCkHlihyRm3aQD7LoNkykjIiIiqigWOYiIiOqwJp72ePT+NpJYeGwGNu2/LlNGDZtoNCBp20IAoiUmqDRwGzULgsCXTURERHUd/1oTERHVcY/c3wZNPO0ksdXBVxCblC1TRg1X2qH1MCRHS2JOgyZC7ewtU0ZERERUGbVe5LhyhQ3TiIiIKkOtUmD2o11RvN+l3mjG93+chdksln0iVYo+8SbSD2+UxDSeLeDQe4xMGREREVFl1XqRIzAwEGPHjsWSJUuQkJBQ27cnIiKql9o2dcaYAS0ksYvXU7Dr2E2ZMmpYRLMJSdt/BMzG20FBAbdRz0NQKMs+kYiIiOoUWZarXL16FV999RWGDh2KJ598Eps3b0Zubq4cqRAREdUbUx9qB3cnG0ls6bZLSMnIkymjhiPzVDAKYq9KYo59A2Hl2VymjIiIiKgqar3IERAQAEEQIIoiTCYTjhw5grfffhv9+/fHG2+8gYMHD0IUOfWWiIjoTjZWKrzwSFdJLDffiEUbL8iTUANhzExB6r5Vkpja2RuOAyfIlBERERFVVa0XOZYvX459+/bhzTffRPv27SGKIkRRRF5eHrZt24ZnnnkGAwcOxPz589m/g4iI6A7d27pjSA9fSezIhTgcvRgnU0b1X/KuXyHqpbNhXEc+C4VKI1NGREREVFWyLFdxd3fHk08+iQ0bNmD79u149tln4evrayl4JCcnY9myZRg3bhzGjBmDX3/9lf07iIiIbnn64U5w0EnfgC/acB65+QaZMqq/ckKPIzf0mCSm6zwUNk07ypQRERER3QvZt5Bt2bIlXn31VezZswerV6/GY489BicnJ0vB49q1a/jPf/7D/h1ERES32Ntq8NRY6Zvw5Ix8rNzJGZCVYS7IRXLwYklMobWHy/3TZcqIiIiI7pXsRY7iunXrhg8//BAHDx7E4sWLMXnyZHh5eZXav+Ott97CkSNH5E6ZiIhIFoO7+6JLa1dJbNvBcFyNSpMpo/ondd9qmLJSJTGXYU9AqbWTKSMiIiK6Vyq5EyiNUqnEwIEDMXDgQBiNRqxcuRLff/89cnJyLP07tmzZgi1btsDX1xdTp07FpEmTYGVldU/3NZvN2LhxIzZt2oTQ0FDk5ubCzc0N3bt3x6RJk9CrV697fm55eXlYs2YNdu/ejRs3biArKwuOjo7o2rUrJk2ahAEDBtzzPYiIqOETBAHPP9IFs7/6B3qjGQBgFoEFf5zDf18eBKWyTn2OUefkx1xF5sm/JDGb5l2g6zhIpoyIiIioOtTJIkdeXh7++ecf7N27F//++y+ysrIAwLLrikqlgtFYuI99VFQUvvjiC6xcuRLz589Ht27dqnTPrKwsPP/88zh+/LgkHhsbi9jYWGzfvh1PPPEE3n777So/r/Pnz+Oll15CXJy0OVxSUhJ2796N3bt3Y+LEifj4448hCEKV70NERI2Dt6sOEx/wx4q/Llti4TEZ2HowHIH3tZIxs7pNNBmRvOMnALd3cxNUGrg+NJN/f4mIiOq5OlPkMBgMOHDgALZv345//vkH+fn5ACDZTrZbt24IDAzEyJEjkZGRgc2bN2P9+vWIjY1FZGQknnrqKaxatQpt27at1L1FUcQrr7xiKXAMGDAAkydPhqurKy5fvozFixcjJiYGS5cuhbOzM2bOnFnp5xcWFoYZM2YgOzsbgiBg9OjRGDVqFJycnHDhwgUsWrQISUlJWLt2Ldzd3fHiiy9W+h5ERNT4jBvcCvvPRCMyPssS+33nFfTr5A13Z62MmdVdGce3QZ8YIYk5DZwAtZOnPAkRERFRtRHE4lWEWiaKIo4ePYpt27Zh9+7dJWZsAICvry8efvhhBAYGws/Pr8Q1DAYD3nzzTfz1118QBAGDBw/Gjz/+WKk8tmzZgjfeeAMAEBQUhM8//1xyPD09HVOmTMG1a9dgZWWFXbt2wdOz4i+EzGYzJk6ciPPnz0MQBHz66aeYMGGCZExCQgIefvhhpKWlQaPR4MCBA3BycqrU86iqkydPYsqUKZafV65ciZ49e9bKvYmI6N6F3EjBWwsOSmK92nvggyd7c2bCHQzpCYhe9ApEo94S07g3gc+TX0FQ1pnPfoiIiBq8mnofKsuC3XPnzuGzzz7DwIEDLVvJZmZmWnZUsbOzwyOPPILff/8de/bswezZs0stcACAWq3GRx99BKVSCQA4ffp0pfNZunQpAECn0+Gtt94qcdzR0REff/wxAKCgoADLly+v1PX37t2L8+fPAwAmT55cosABAB4eHpYZInq9Hnv27KnUPYiIqPFq39wFI/o2k8ROhCTg8IW40k9opERRRPJfP0sKHIAA15HPscBBRETUQNT6X/Rhw4YhJibG8nPRrA2lUon+/fsjMDAQw4YNg0ajqfA1HRwc4OjoiNTUVBgMhkrlExUVhZCQEADAkCFD4OjoWOq4nj17onnz5rhx4wZ27tyJN998s8L32Lx5MwDA2toas2fPLnPc8OHDERoaCkdHR/j4+FT8SRARUaP3+Mh2OHoxDulZBZbYzxvPo2trN9jaqGXMrO7ICTmIvPCzkph9j+Gw9mkjT0JERERU7Wq9yBEdHQ1BECzFDX9/fwQGBmLMmDFwdXW9y9mlMxqNyMjIgCiK6Ny5c6XOPXXqlOVxnz59yh0bEBCAGzduICYmBpGRkWjSpMldr282m3HwYOEU4n79+sHZ2bnMsT4+Ppg/f34FMyciIrpNp9Vg5sOd8OXvJy2x1MwCLN8RgufGd5Exs7rBlJeNlN1LJTGlzhnOQ6aUcQYRERHVR7LMzXRxccGYMWMQGBgIf3//e76e2WzGhg0b4OnpCXt7+0qde+3aNcvjZs2alTu2+JKZq1evVqjIERERgby8PAAoUYDJyMhAcnIy7O3t4ebmVomsiYiIShrQ1Rt7T7rj1JVES+yvIxEY0tMPbZuWXWRvDFL/WQlTToYk5jr8KSis2JyViIioIan1IsfPP/+MAQMGQKGovnYgGo0GbdpUbappfHy85bG3t3e5Y728vEo9rzzFiyje3t4wm81Ys2YNVq9ejbCwMMsxPz8/TJkyBVOnToVaXflpxUVb3VZFaGholc4jIqK6RRAEzArqjBe++gd6gwkAIIrAwj/O4ZtX74NKKUsrLtnlR4ci68wuSUzbuhe0/r1lyoiIiIhqSq0XOVJTU7FlyxZ06tQJLVu2rNS5p06dQnBwMAwGA+bMmVMt+WRk3P5Ux9bWttyxWu3tT3uKdoK5m7S0NMtjKysrzJgxA0ePHi0xLioqCl988QX27t2LH3/8EXZ2dhW6fpH169djwYIFlTqHiIgaHk8XW0wZ7o+l20IssYi4TGw5EI6gIa1kzEweotmE5L8WSWKC2hquw5/izjNEREQNUK1/pPP222/jnXfewYEDByp97okTJ7B8+fJq3XlEr7/dYd3a2rrcscWPFz+vPDk5OZbHX375JY4ePYqOHTti8eLFOH36NE6fPo3Fixejffv2AAqf4+uvv16Zp0BERCQxdlBLNPeWLt9ctesKEtNyZcpIPhkntkOfeFMScxo0ESoHLhMlIiJqiOrVvNWi2RPFZ1/cq6KtZwHc9ROdomapACq83KaoHwcAxMTEoF+/fli9ejUGDRoEW1tb2NraYtCgQVi9ejW6dClsDLd//378/ffflXkaREREFiqlAi880gXF/6wV6E1YvOmCfEnJwJiZjLT9ayUxjXtTOPQaKVNGREREVNNqZLmKyWTCtm3bJEWBO128eBGbNm2q8PViYmKwcuVKAChzm9eqKL4EJT8/v9ytawsKbm/LV9EtbovP/lAqlZg7d26p51pbW+P999/HhAkTAACbNm3C0KFDK3QPABg/fjz69u1b4fHFhYaG4pNPPqnSuUREVDf5N3XG8D7NsPNIhCV29GI8jofEI6C9p3yJ1aLkXUsgGvIlMdeHZkJQytJ3nYiIiGpBjfyVVyqVOH36NNatW1fqcVEUsWPHDuzYsaNS1xVFEYIgoH///tWRJgBpH468vLxyd2fJzb09zdfBwaFC19fpdJbHHTp0gI+PT5ljO3fuDDc3NyQlJeHs2bMVun4Rb2/vuzZOJSKixuXxke1w5EIsMrJvL7FctOE8OrdyhbWmYb/Rz7l6ErmhxyQxu67DYO3bVqaMiIiIqDbU2HKV119/HU5OThBFUfJV5M54Rb6Awl1IXn311WrLs3jRIS4urtyxxY97eHhU6PrFt4b19Lz7J2dFY4o3LCUiIqoKnVaDJ8d0lMQS0/KwdndYGWc0DGZDAVKCf5XEFFp7OA+dKlNGREREVFtq7GMce3t7fPPNNzhx4oQkvmDBAgiCgH79+qFbt24VupZSqYROp4Ovry/69esHKyurasuzdevWlseRkZHo2rVrmWOjoqIsj1u1qliHen9/f8vj9PT0u44vamha3owSIiKiihrSwxd7jkfiwvVkS2zjvmsY0sMXTTwb5t+a9IN/wpiRKIm53P84lDaV27mMiIiI6p8anavau3dv9O4t3YO+aJvTAQMGYMaMGTV5+wrp2rUrBEGAKIo4efIkxo4dW+bY48ePAwC8vLzg6+tboev7+PjA3d0diYmJuHTpEgoKCsos0hgMBty8WdgBvqLXJyIiKo8gCHhufGe89PU/MJoKZ0WazCJ+3HAe857r3+C2UdUnRSL96GZJzLpJB+g63SdTRkRERFSban1BbmBgIARBkMygkJOXlxe6du2KM2fOIDg4GG+++aakj0aRkydP4saNGwCA4cOHV+oeo0ePxpIlS5CTk4P169fjscceK3Xcjh07kJ9f2CBt2LBhlXwmREREpfPzsMO4wa3wx96rltjF6yn451QUhvZsImNm1UsURST/9TNgNt0OKlSFzUYbWDGH6gez2Yzs7GxkZmZCr9fDZDLd/SQiojpOqVRCo9HA3t4eOp2uwjuP1pZaL3J88cUXtX3Lu5o2bRrOnDmD9PR0zJkzB1999ZXkHyojIwNz5swBAKjVakydWrk1vdOmTcOaNWuQm5uLr7/+Gh07dkTnzp0lYyIiIjB//nwAhc1QAwMD7+1JERERFfPosDbYfyYGiam3m2j/uuUSerX3hJ22YjuG1XXZ5/9BftRlScyxz1hoXDk7kmpfVlYWYmJiyt1tkIioPjIajSgoKEBWVhYEQYCPjw/s7OrOktCG3Vq9gkaNGoUNGzbg4MGD2LZtG+Lj4zF9+nR4eHggNDQUixYtQkxMDABg9uzZ8PPzk5x/7NgxTJ8+HQAQEBCAFStWSI57e3vj/fffx7vvvovs7GxMnToVjz76KAYPHgytVosTJ07gl19+QWZmJgDgvffekzQsJSIiulfWGhVmjeuET369veNIZo4ev20PwYsTusqXWDUx5WYhZe9ySUzl6A7HAY/IlBE1ZqUVOARBgFKplDErIqLqYTKZLL/fRFFETExMnSp01FiRo6j3BgC8+OKLpcbvRfFrVofvvvsOs2bNwokTJ3Dy5EmcPHmyxJgnnngCM2fOrNL1x48fD0EQ8OmnnyI3NxcrVqwoUQxRq9V45513MH78+Crdg4iIqDy92nuibycvHLlwe7ew4KM3MSygCdo2dZYxs3uX+s/vMOdlSWKuw5+GQl19zcqJKsJsNksKHDqdDs7OztBqtVw2RUQNgiiKyM3NRWpqKrKzsy2FjjZt2tSJpSs1WuQo+kV+Z5GjOn7BV3eRQ6fTYfny5di0aRO2bNmCK1euICsrC05OTujWrRumTJmCPn363NM9goKC0L9/f/z+++/Yv38/YmJiYDab4eXlhX79+uGxxx5DixYtqukZERERlfTMw51wJjQR+frbvQF++PMcvnnlPiiV8r8wqYr86FBknd0jidm27QNtqx4yZUSNWdELfgCW3QFZ3CCihkQQBNja2kKr1SI6Otryey87O7tO7BJao8tVRFEs9Zf6va5NrKk/FAqFAkFBQQgKCqrUeb1790ZoaGiFxnp4eOD111/H66+/XpUUiYiI7ombkw0mP9gWS7ddssRuxGZi68EbCLyvpYyZVY1oNiF552JJTNBYw+WBJ2XKiBq7ouXHAODs7MwCBxE1WIIgwNnZGdnZ2QAKf/816CLH559/Xqk4ERER1Y6xg1rg75ORuBl/e3nHquDLGNjVGy4ONjJmVnmZp4KhT7ghiTkNnAiVvYtMGVFjp9frARS++NdqtTJnQ0RUs4qW4omiaPn9J7caK3KMGzeuUnEiIiKqHSqlAs8/0gVvLThoieUVmLBkyyW8Ma2njJlVjjErDan7V0tiarcmcOg1UqaMiGDZJlapVHIWBxE1eEVNlY1GY53ZJrt+Lr4lIiKie9K+uQseCGgiiR04G4NzYUkyZVR5qX8vh1iQK4m5jngGgpKbxxERETVWLHIQERE1Uo+Pag+djVoS+2njeRiMZpkyqri8mxeRffGAJKbrNBg2TdrLlBERERHVBSxyEBERNVIOOitMH9lOEotOzMam/ddkyqhiRJOxRLNRhZUWzkOnyZQRERER1RU1Np+zXbt2dx9URYIgICQkpMauT0RE1Fg82KcZdh2PxLWodEts7Z4w3NfdF+5OdbNpYsbxbTAkR0tiToMfg0rnKE9CREREVGfU2EwOURRr9IuIiIjunVIh4PnxnVG8P2KB3oRfNl+UL6lyGDOTkfbvOklM49kC9t0flCkjIiIiqktqbCaHt7d3TV2aiIiIqlFrPyeM6NMMfx2JsMSOXIjDycsJ6NnOQ77ESpGyeylEQ0GxiFDYbFShlC0nIqrb3n77bWzcuLHcMUqlEjY2NnB1dUWnTp0wePBgPPTQQ1Aq5f3dcuzYMUyfPh0AMGvWLLz66qv1No/yrrFhwwa88847AIC5c+diwoQJlmPff/89FixYAABYunQp+vXrV+LaRqMRUVFRaN68eaXzqiuioqKwcOFCHDlyBCkpKdDpdHBzc8Pq1auh0+nuer6/v7/l8c8//4z77ruvQvf95ptv8NNPPwEAli9fjt69e1ftCdQhNVbk+Pvvv2vq0kRERFTNpo1sh0PnY5GZc3uP+583XkDnVq7QqOtGASH3+hnkXDkqidl1vR/WPm1kyoiIGgqTyYTs7GxkZ2cjIiICW7duxaJFi/DTTz/Bx8dH7vSoHMeOHcMnn3yCESNGYPbs2XKnUyWJiYmYMGEC0tLSLLG0tDRoNJoKFTju9MEHH2D79u2ws7OrzjTrDe6xRkRERLDTajBjdHt8t/asJRaXkoP1/1zD5Af9yz6xlpiNeiQH/yKJKWzs4DxkqkwZEVF9NHfuXHTs2LFE3GQyIS8vD+Hh4ViyZAkiIiIQFhaGJ554Alu2bIGNjY0M2dLdxMXFWWaH1GcrVqywFDiGDh2KadOmQavVwmyu2m5nCQkJmDdvHj7//PPqTLPeYJGDiIiIAABDezbBrmORuByRaon9uTcMQ3r4wtPFVsbMgIwjm2FMi5fEnIdOhVLbOD+lIqKqadKkSbkbJPTq1QujRo3C5MmTERYWhsjISCxbtgzPPfdcLWbZMPXu3RuhoaGVPm/27NllztAwmUz3mladcPXqVQCASqXCf/7zH9ja3vvf3A0bNmDEiBEVXrbSkHALWSIiIgIAKBQCZgV1hqJYE1K90YxFGy/I2vTbkBaP9MMbJDErH3/YdRkqU0ZE1JDpdDq8+eablp83bdokXzLUKOTm5gIAXFxc7rnAoVarLY8/+OADZGZm3tP16qMam8lRNG1IEAT89ttvJeL34s5rEhERUfVo4eOAUQNaYOu/4ZbYycsJOHYpHn06esmSU8rupRCNt3uFQFAUNhsV+FkNEdWM/v37Q61Ww2AwICIiAvn5+bC2tpY7LWqgij5IUKnu/e15p06doNPpcODAASQkJODzzz9vdMtWaqzIcfz4cQjF96O7S7yiRFG8p/OJiIiofFOGt8XBszFIy7q9i8niTRfQtY0brDW1u9I15+pJ5F49KYnZ9xgBK8/620GfiOo+hUIBR0dHJCUlAQAyMzMtRY6i3T6USiVCQkKwevVqLF26FLGxsXB0dES7du3w7bffSj6Rv3nzJlatWoUjR44gOjoaBoMBLi4u6NKlC8aMGYNhw4ZVKC+9Xo/ffvsNW7duxc2bN2FlZYUWLVpgxIgRmDx5MqysrMo9/8iRI/jrr79w+vRpJCUlITs7G1qtFu7u7ujRowcmTZqE9u3b10geVd2hpbTdVaKjo3H//fdLxi1YsMAybvny5bhy5QrmzZsHoHCHnRkzZpR5j/z8fPTr1w85OTkYMmSIZbeRyggJCcGaNWtw4sQJxMfHw2w2w9XVFT179sT48eMREBAgGV/ac4iJiZHsklKV5T1AYe+ZUaNGISsrCxs2bMDw4cMxePDgKl2rPqrRVyplFSTknPJKRERE5bO1UePJMR3w9arTllhiWh7+2HsV0x4qey17dTMbCpCy61dJTGnrAKf7JtVaDkTUOBkMBmRkZAC4XfAozaJFi/Df//7X8nNSUhJ8fX0lBY6FCxfihx9+gNFolJwbFxeHuLg47Ny5EwEBAfj222/h4uJSZk4ZGRmYOHEiQkJCLLH8/HycOXMGZ86cwcqVK/HLL7+gadOmJc7NzMzEK6+8gkOHDpV6LDMzE9euXcO6devw1ltvlVsQuJc8atPYsWPx1VdfwWAwYPPmzeU+p127diEnJwcAEBQUVKn7GAwGzJs3D6tWrSpxLDo6GtHR0di0aRNGjBiBefPmVUu/jbvx8PDAO++8g3fffRfA7d1W7O3ta/zedUGNFTn27t1bqTgRERHVHfd198WuY5G4cD3ZEtvwzzXc39MP3m6V386uKjKObIYxPVEScx46HUpreZugElUnk1lEdq7+7gMbGJ1WA6Wi7s7OPnz4MPT6wn+XDh06QKPRlBhjMpnw7bffws/PDy+99BJ8fHxw/vx5+Pn5WcZ8/fXX+PnnnwEAtra2mDZtGvr06QNra2tcu3YNK1asQGhoKI4fP46pU6fijz/+KHPL0DVr1kAURfj7++PJJ59E8+bNERsbi1WrVuH48eOIjIzEjBkzsHXr1hJvpF999VVLgSMgIADjx4+Hj48PBEFAdHQ0NmzYgGPHjkEURXz11VcYNGgQWrZsWe15VBd3d3ds2rQJiYmJmDlzJgBg4sSJmDx5MoDCBrO2trYYOnQogoODcfnyZYSFhaFNm9K3HC/qu+Lk5IQhQ4ZUOA9RFPH2229j27ZtAABXV1c8/vjj6NatGxQKBS5duoTffvsN0dHR2LlzJ1JTU7F06VKoVCrLcwCA9957D5cuXYKbmxsWL15cxf8qUuPHj8fOnTtx4MABJCYmYt68efjiiy+q5dp1XY0VOcraT5r7TBMREdV9giDg2aBOePnrfTCZC2dgGk1m/LzpAuY83afGl44a0hOQfmSjJGbl2xa6To2vSzw1XAfPxWDRhgtIzy64++AGxlFnhWeDOmFAl7r33qDoDWGRiRMnljlWo9Fg+fLl8Pb2BgD06NHDcuz8+fOWAoenpyeWL18umd3QrVs3jBs3Dm+99Ra2bduG8PBwfPnll/jkk09KvZcoihg8eDC+//57S9GlS5cuGDFiBN59911s2LABMTExWLRoEV577TXLeUePHsXBgwcBAEOGDMEPP/wAheJ2T6OePXsiMDAQH374IdauXQuTyYTg4GA8//zz1ZpHddJoNGjXrh3s7G7vsOXm5lZi55zx48cjODgYALB582a88cYbJa6VkJCAI0eOAADGjBkjadx5N3/99ZelwOHv749ly5bB2dnZcrxHjx4YP348nnvuORw7dgzHjx/HkiVLMHPmTMtzAGApBhWPVYe5c+di9OjRyMzMxMaNGzF8+PBKFXHqK3bsIiIiolI19bTHmIEtJLFTVxJx7FJ8GWdUn5RdZTUbrbuf/BJV1oJ1ZxtlgQMA0rMLsGDd2Vq/b2RkJC5fvlzi69y5c9izZw/mz5+PMWPGICIiAkDhm9Rx48aVeb2hQ4daChx3Kv6J/Lx580pdvqFSqfDZZ59ZPgjesGEDUlJSSr2enZ0d5s+fX2JWiSAImDNnDtzc3AAA69atg8FgsBy/fv06fH19oVar8fLLL0sKHMWNHTvW8jguLq7UMfeShxwGDhwIDw8PAMDWrVthNptLjNm8ebMlPn78+Epd/5dffgFQuKTpm2++kRQ4itja2uLbb7+FVqsFACxZsqTE0qWa4uHhgbffftvy84cfftgodlupM0UOvV6PGzdu4Ny5c7h8+TJiYmLkTomIiKjRm/ygP5ztpQ3kFm+6gHx9zb1Ay716CrlXT0hi9j1GwMqjWY3dk4gah/fffx+BgYElvh599FG88MILWLJkCdLT0wEU7rCycOHCcne86NKlS6lxo9GIw4cPAwCaNm2K/v37l3kNa2trPPLIIwAK+zsUzSq404gRI8rsDWJtbY0RI0YAANLS0nDp0iXLsSlTpmDv3r04f/58ubMEiooTAFBQUHbxrap5yEGhUFiKVAkJCTh27FiJMRs3Fs4abN++Pdq2bVvha6ekpFj6kvTp06fM5T0A4OzsjJEjRwIo/O9y4cKFCt/nXo0fPx733Vc4CzIxMRGfffZZrd1bLrIWOXJzc7Fq1SpMnjwZPXr0wMiRIzFp0iQEBQVh2LBh6NmzJ5555hns3r2bzUqJiIhkoLVWY8aYjpJYYloe/vz7ao3cz2zUI5nNRqmRePHRrnDUlb8bRkPlqLPCi492lTsNC41GA2dnZ3Tq1AmTJ0/G77//jiVLlsDJyanc87y8St9aOy4uDtnZ2QCArl273vX+3bp1szwOCwsrdUxZBZUiHTp0sDwubVeO4jM4kpOTcebMGWzevBnffPMNnn76acmMldJmPFRXHrWteCPRzZs3S46dP38e4eHhJcZVRFhYmOU9anX9G9eUTz/91NJ0dNOmTfjnn39q9f61rXb3gStm//79+OCDDyzbMpVWxMjOzsbBgwdx8OBBdOjQAd98842kkQ8RERHVvPu6+SD4aAQuXr89hbqwCWkTeLlWb1O5jCObYExPkMSch05js1FqkAZ08UHfTt5sPFqLli9fjt69e1fb9cpqEpqWlmZ5XN6OKUVcXV0tj4tmktzpbtcpXpAp7Rq7d+/GunXrcPr0aUsBpriylrFUdx61rWnTpujVqxdOnDiB4OBgzJkzBzY2NgBuz+JQq9UYPXp0pa5b/N+4+L9fWSryb1xTinZbeeeddwDc3m3FwcGhVvOoLbIUOYKDg/H666/DZDJZihtKpRI+Pj6wt7eHKIrIyMhATEyM5fjFixcxadIkrFq1SvbtiIiIiBoTQRAwa1xnvPTffTDfakJqMN5uQlpdDOkJSD98Z7NRfzYbpQZNqRDg0EhnczQEZfUJKm8mxN3GV7X3UPEPjYv3y9Dr9Xj11VexZ88eyXgvLy+0aNECbdq0QZcuXdC0adNy+4/cax5yGj9+PE6cOIHc3Fzs3r0bY8eOhV6vx44dOwAU9la526ydO1V2pUF1/Bvfi6CgIOzcuRP79+9HUlISPvvsM3z55Ze1nkdtqPUiR2pqKj744ANLs5X27dvjueeew6BBg2BlJf0Fn52djT179uCHH35AZGQkUlJS8Pzzz2Pz5s3lro0jIiKi6tXUyx6jBzTHlgPhltjJywk4fikeAR08q+UepTYbHf4MBKHOtBAjIqqQ4j0rymokWlxy8u3tusvqd5GRkVHhaxR/w75w4UJLgaN9+/Z44YUXEBAQYFm+UKSiSyiqmoecRowYgU8//RQ5OTnYsWMHxo4di4MHD1pmVFS24Sgg/Xcq/pzLUhf+u3z66aeW3VY2b95s6Z/S0NT6q4bVq1cjMzMTgiBg1KhR+OOPP/DAAw+UKHAAhdO/AgMDsWXLFsu0svDwcPz555+1nTYREVGj99iDbeFkJ/17vWjTBRQYTPd87dxrpTUbHQ4rz+b3fG0iotrm5+dn2Rb03Llzdx1/5swZy+MWLVqUOuZuRYjizSzbt28PoHD2wKpVqwAU7ory22+/YdiwYSUKHED5O6rcax5ys7GxsTT+PHz4MHJycrB7924AhQ1XBwwYUOlr+vv7Wx6fPXv2ruOL/xs3by7P37aiZStFGupuK7Ve5Pj7778BAO7u7vjss8+gVCrveo61tTW++eYby5qh7du312iOREREVJKtjRozxnSQxBJTc7H+HpuQFjYbXSKJKbT2cLpv8j1dl4hILkqlEn379gUAREREWHZaKU1BQQE2bNhQ4rw7BQcHl7kla2ZmJnbu3AkA8PHxQevWrQEUziIpehPbpEmTUosbRYo35TSZyi5eVyWPmlLRPiLA7dkaBQUF2L9/P/bt2wcACAwMrNB70ju5urpadqs5evQobty4UebY1NRUBAcHAwDs7e3RuXPnSt+vugQFBVl2W0lKSsIff/whWy41pdaLHFFRURAEAQ888ACsra0rfJ6zszOGDx8OURRx9WrNdHQnIiKi8g3u7osOLaRN5/78+yriU3KqfM2MI5thTIuXxFzYbJSI6rkZM2ZYHr/33nuIiooqMcZkMuGDDz5ATEwMAODhhx+Gu7t7qdeLiYnB3LlzS/SCMBqNePfddy3LSB5//HFLzwc7OzvLMv9r164hOjq61Gv/+uuvkg+S9fqym+FWJY+aUrznR25ubrlju3XrZtnm9bvvvkNqaioA3FMfkieffBJA4YyZ1157TdKMtEheXh5ee+015OQU/p18/PHHZe9VUny3lbIKVvVZrTe2KPqPWJEOtHfy9vYGAOTn51drTkRERFQxgiDg2XGd8Mo3+yVNSBdvuogPnqr8jgWG9ESkH94giVn5+EPXeXB1pEtEJJuePXviySefxJIlSxAbG4tx48Zh6tSp6NOnD6ytrXH16lWsXLkSly9fBgA0a9YM7733XpnXs7GxwZo1axAREYHJkyfD29sbERERWLZsGS5dugQACAgIwNSpUy3nWFtbY+jQodi1axcKCgowbdo0PPXUU2jbti3MZjOuX7+OTZs2lVhukZWVVa151BRHR0eo1WoYDAZs27YN/fr1g729Pfz8/ODs7FxifFBQEL766itEREQAkBY+qmLs2LHYs2cPgoODERISgjFjxmD69Ono3r07FAoFQkJC8NtvvyEyMhIA0KNHD8yaNavK96suHh4eePfdd/H222/LnUqNqPUiR5MmTRAWFmbZj7gyitaJlbUfNREREdW85t4OGNW/Obb+e/tv+fGQeBwPiUdA+8o1IU3Zs6xks9ERT7PZKBE1CG+++Sasra2xaNEiZGVl4ccff8SPP/5YYtzAgQMxf/78MrekBYA33ngDy5Ytw9GjR3H06NFSr/Htt9+WWHrx/vvv48qVK4iMjERsbCw+/fTTEueqVCo899xz2LVrF0JDQ3H9+vVqz6MmqFQqDB06FMHBwUhMTMTTTz8NoHCmwqOPPlpifGBgIL755hvLJhhBQUH3nMN//vMfODg4YN26dUhKSsLXX39d6rjAwEB8+OGHdWYDjXHjxmHnzp2WZTsNSa3/Fx4+fDhCQ0Oxe/duxMXFVbhgkZ2djeDgYAiCgPvvv7+GsyQiIqLyPDa8Lf49G4P0rAJLbPGmC+ja2g0adcVe2OZeP4Pc0GOSmH33B2HlWXrTPSKi+kYQBLz88ssYM2YMVq1ahaNHjyI2NhZmsxkeHh7o2LEjgoKC0K9fv7su7fDw8MDGjRvx888/Izg4GLGxsdBqtejYsSPGjx9vaaxZ1nnLli3Dnj17cPPmTRQUFMDW1hZ+fn7o2bMnJk2ahBYtWiAvLw+hoaFITk7GkSNHSu0PUtU8asq8efPg4uKCvXv3IjU1FXZ2dpZdU+7k6uqKgIAAHD58GNbW1tWSq0ajwaeffooJEyZg3bp1OHHiBBITEyEIAry8vNCjRw+MHz8eXbp0ued7VbdPPvnEsttKQyKIld3g9x7l5eVh9OjRiImJgb+/P3799de7Ll3Jz8/Hyy+/jP3798PNzQ1btmypM9sRNQQnT57ElClTLD+vXLkSPXv2lDEjIiKqD/4+GYlvVp+RxKaMaItJD/iXccZtotGA6MWvwpB6u5u/QmsPv1nfQ2lT9ieZRHXd1atXYTQaoVKparzpIhFVjtFoxKBBg5CSkoKHH34YX375pdwpNQhV/b1XU+9Da2wuaGxsbKlfaWlpmDt3LhwcHBAWFoZRo0bhp59+KnVKVEJCAjZt2oSgoCDs378fHh4e+Pnnn1ngICIiqgOG9PBDu2bSNc9/7AlDQmr5zd8AIOP4VkmBAwCch0xhgYOIiGrM/v37kZKSAgClLmehhqHGlqsMHTq0Qt10MzIy8N133+G7776DWq22dHnNzs5GQUHhFFhRFCEIAjIzM/Hkk09CEIRyt2EiIiKimicIAmYFdcar3+zDrR6k0BvN+HXLRbz7RECZ5xkzk5F28E9JzMq7Ney6DK3JdImIqBFLTU3Ft99+CwBo27YtZ643YDXak6OiK2GKxun1eiQnJ5c5Ji8vD3l5eTW+FRERERFVTAsfBzzUrzm2H7phiR25EIfTVxLRvW3p2yCm7PkNoqGgWESA63A2GyUiouq1ceNG/Pvvv7CyssLBgweRmJgIAHjppZdkzoxqUo0VOXr16lVTlyYiIqI6ZOqIwiakmTm3d0lZtPE8FrwxBGqVtAlp3o3zyLksnY1p120YrLxb1UquRETUeIiiiO3bt0ti48eP50YWDVyNFTlWrFhRU5cmIiKiOkSn1eDxUe3x/bqzllhscg427b+OCfe3scREkxHJu36VnKuw0cF58GO1lSoRETUi/v7+8PX1RUJCAry9vTFhwgQ89dRTcqdFNaxubNJLRERE9dqwXk0QfDQCYZHpltjaPWEY0sMPro42AICMEztgSI6WnOd832NQau1rM1UiImokOnTogL1798qdBtUyLn4lIiKie6ZQFDYhLd42q0Bvwq9bLgIAjFlpSPt3reQcjWcL2HUbVptpEhERUQNX74ocCQkJ+OWXX+ROg4iIiO7Q2s8JD/ZuKokdPBeLc2FJSP17OUR9vuSY6/CnISikPTuIiIiI7oVsy1Xi4+OxefNmXLx4EVlZWTAajSV2YxFFEWazGUajEfn5+UhPT7fsa/z000/LkTYRERGVY9pD7XD4fCyycg2W2PYNOzHJdEAyTtd5CKx9/Ws7PSIiImrgZCly7N27F//3f/+H/Pz8uw9Gya1ouYUsERFR3eSgs8K0h9rhh/XnAQAKmDGoYJ/kFYfCSguXodPkSZCIiIgatFpfrpKamor/+7//Q15eHkRRrNBXUVFDoVDAz88PEydOrO20iYiIqIIe7NMMLX0dAAADrELhrUqXHHe6bzKUtg4yZEZEREQNXa3P5Fi9ejXy8vIgCAJcXFwwY8YM+Pv7IyIiAnPnzoVKpcIPP/wAURSRlpaGY8eOYevWrTAajVAoFPj888/Rs2fP2k6biIiIKkipEDBrXGd8smAXRtqclRzTuDeFfY/h8iRGREREDV6tz+Q4cuQIAECpVGLp0qV46qmnMGDAADz66KPQaDQwmUwQRRH33XcfAgMD8fnnn2PNmjVwdHSEyWTCW2+9Bb1eX9tpExERUSW0beaMmU1CYaMwSOKZHR9hs1EiIiKqMbVe5IiIiIAgCOjfvz9at25tiWs0GrRr1w4AcOLECck5HTt2xNy5cyGKImJjY7Fp06baTJmIiIgqKT86FE2yzktiJwua48dDBTCZzDJlRURERA1drRc5MjMzAQDt27cvcaxNmzYQRRGXLl0qcWzYsGFo3rw5AGD//v01myQRERFVmWg2ITlYut17vqjC5tweiIjLxI7DEfIkRkRERA1erRc5lMrCKaq2trYljjVr1gwAcO3atVLP7du3L0RRRFhYWI3lR0RERPcm68we6OPDJbGdeV2QKWoBACt3XkZaVsV2WCMiIiKqjFovcjg6OgIAsrKyShxr0qQJACA5ORnZ2dkljru7uwMAUlJSai5BIiIiqjJTbiZS962SxMz2Xtif387yc06+Eb9tD6nt1IiIiKgRqPUiR/PmzSGKIi5cuFDimJ+fn+VxSEjJFz9paWkAwMajREREdVTqvlUw50s/qPAZ8ywGdW8iie09EYUrEam1mRoRERE1ArVe5AgICAAAHD16FMePH5cca9GiBVSqwl1t//nnnxLnFu3MYm9vX8NZEhERUWUVxF5D1pk9kphtu36wadYJM8Z0gI2VdFeVnzaeh8ks1maKRERE1MDVepFj3LhxUKvVEEURTz/9NL788ktEREQAKNxhpWfPnhBFEatWrcKuXbsAFM7cmD9/PsLCwiAIgmUXFiIiIqobRNF8q9no7aKFoLaCy7AnAADO9taY/GBbyTnXozOw62hE7SVJREREDV6tFzk8PDzw9NNPQxRFGAwGLF26FL/99pvl+LRp0wAUFjZefvll9O7dGz169MCyZcssY8aMGVPbaRMREVE5ss79jYLYq5KY04BHoLJ3sfw8ZmAL+HnoJGOW77iMjOyCWsmRiIiIGj6VHDd9+eWXYTQasXTpUphMJvj6+lqO3X///Rg9ejS2bdsGQRCQkZEBABAEAQDQp08fBAYGypE2ERERlcKUl43Uf1ZKYmpnbzgESD+UUCkVeHZcZ7z/02FLLDvPgBV/XcaLE7rWRqpE1Ai9/fbb2LhxY7ljlEolbGxs4Orqik6dOmHw4MF46KGHLDtDyuXYsWOYPn06AGDWrFl49dVX620e5V1jw4YNeOeddwAAc+fOxYQJEyzHvv/+eyxYsAAAsHTpUvTr16/EtY1GI6KiotC8efNK51VXREVFYeHChThy5AhSUlKg0+ng5uaG1atXQ6fT3fV8f3//Kt+7bdu22Lx5c5XPr2tqfSZHkddffx3btm3D888/jy5dukiOzZ8/H7Nnz4adnZ0lplKpMHHiRPz444+1nSoRERGVI23/aphzMyUxlwefhKBSlxjbpbUbBnTxlsR2HbuJq1FpNZojEVF5TCYTsrOzERERga1bt+L1119HYGAgYmJi5E6N7uLYsWN4+OGHsW3bNrlTqbLExERMmDABGzduRHx8PAwGA9LS0pCRkVGhAgdJyTKTo0izZs0we/bsEnGlUokXXngBzzzzDMLDw6HX69GiRQv+AxMREdUxBfE3kHl6lySm9e8NbctuZZ7z5JiOOHE5AQV6EwBAFIGfNpzHV7MHQaEQajRfImrc5s6di44dO5aIm0wm5OXlITw8HEuWLEFERATCwsLwxBNPYMuWLbCxsZEhW7qbuLg4y+yQ+mzFihWWnUSHDh2KadOmQavVwmw2V/pabm5uWLx4caXOsbKyqvR96jJZixx3o9Fo0LZt27sPJCIiolonimJhs1Hx9oswQaWxNBsti5uTDSYOa4PlOy5bYmGR6dhzIhIP9m5aU+kSEaFJkyblbmLQq1cvjBo1CpMnT0ZYWBgiIyOxbNkyPPfcc7WYZcPUu3dvhIaGVvq82bNnl/rBOFBYnGoIrl4t7GmlUqnwn//8B7a2tlW+lkajafQbdci2XKU0er0eycnJyMzMhChySzkiIqK6LPvCfhREX5HEHPsFQe3oftdzA+9rCR836Yu437aHICtXX605EhFVlk6nw5tvvmn5edOmTfIlQ41Cbm4uAMDFxeWeChxUSPaZHPv378fWrVtx6tQpxMfHW+KCIKBly5bo0aMHHnnkkVKnlREREZE8TPk5SP17uSSmcvSAQ9+HK3S+WqXEzMDOmLP4iCWWmaPH739dxnPju5RzJhFRzevfvz/UajUMBgMiIiKQn58Pa2trudOiBqroA36VSva35w2CbP8VQ0JC8O6770qmLBWfvSGKIq5du4Zr165h7dq1GDZsGObOnQsHBwc50iUiIqJi0g6sgSknQxJzefBJKFSaCl+je1t39O3khSMX4iyxnUci8GDvpmjp61hdqRIRVZpCoYCjoyOSkpIAAJmZmZYiR9FuH0qlEiEhIVi9ejWWLl2K2NhYODo6ol27dvj2228ln8jfvHkTq1atwpEjRxAdHQ2DwQAXFxd06dIFY8aMwbBhwyqUl16vx2+//YatW7fi5s2bsLKyQosWLTBixAhMnjz5rr0Vjhw5gr/++gunT59GUlISsrOzodVq4e7ujh49emDSpElo3759jeRR1R1aSttdJTo6Gvfff79k3IIFCyzjli9fjitXrmDevHkACnfYmTFjRpn3yM/PR79+/ZCTk4MhQ4bgp59+qlBuxYWEhGDNmjU4ceIE4uPjYTab4erqip49e2L8+PEICAiQjC/tOcTExEh2SanK8h6Sqchx8uRJPPPMM8jPz5cUNlQqFezs7CCKIrKzs2E0Gi3H9uzZg7CwMKxatQouLi5ypE1EREQAChIikHlypySmbd0Ttq17VvpaT43tiFOXE6A3Fvb1MN9qQjr/xYFsQkqNgmg2wZyXLXcatU5ho4OgkHd71vIYDAZkZBQWcosKHqVZtGgR/vvf/1p+TkpKgq+vr6TAsXDhQvzwww+S9zZAYdPMuLg47Ny5EwEBAfj222/LfZ+TkZGBiRMnIiQkxBLLz8/HmTNncObMGaxcuRK//PILmjYt2dsoMzMTr7zyCg4dOlTqsczMTFy7dg3r1q3DW2+9VW5B4F7yqE1jx47FV199BYPBgM2bN5f7nHbt2oWcnBwAQFBQUKXuYzAYMG/ePKxatarEsejoaERHR2PTpk0YMWIE5s2bx+UotaDWixy5ubl47bXXkJeXBwDw9PTEE088gcGDB6Np06YQhMIXNGazGdevX0dwcDBWrFiBjIwM3Lx5Ey+++CJWr15d22kTERERCmdaptzZbFSphssDZb94LI+HsxYThrXByp23e3tcuZmGv09GYVhAk3vOl6guy758GCnBv5SYFdUYKG0d4DL8aeja9ZM7lVIdPnwYen1hj6AOHTpAoyk5S81kMuHbb7+Fn58fXnrpJfj4+OD8+fPw8/OzjPn666/x888/AwBsbW0xbdo09OnTB9bW1rh27RpWrFiB0NBQHD9+HFOnTsUff/xR5o6Sa9asgSiK8Pf3x5NPPonmzZsjNjYWq1atwvHjxxEZGYkZM2Zg69atJd5Iv/rqq5YCR0BAAMaPHw8fHx8IgoDo6Ghs2LABx44dgyiK+OqrrzBo0CC0bNmy2vOoLu7u7ti0aRMSExMxc+ZMAMDEiRMxefJkAIUNZm1tbTF06FAEBwfj8uXLCAsLQ5s2bUq9XlHfFScnJwwZMqTCeYiiiLffftuyfa2rqysef/xxdOvWDQqFApcuXcJvv/2G6Oho7Ny5E6mpqVi6dClUKpXlOQDAe++9h0uXLlVpZxQqqdaLHGvXrkViYiIEQUBAQAAWLlxY6v+RFQoFWrdujdatW+PRRx/F008/jbCwMJw9exbbt2/HqFGjajt1IiKiRi/74gHkR12WxBz6jYPaybPK1wwa3Ap/n4hCXEqOJbZs+yX06egJnbbiy1+I6pvk7T/CXJArdxqyMOVkIHn7j3WyyJGYmGhZ5gAUvnkui0ajwfLly+Ht7Q0A6NGjh+XY+fPnLQUOT09PLF++XDK7oVu3bhg3bhzeeustbNu2DeHh4fjyyy/xySeflHovURQxePBgfP/995aiS5cuXTBixAi8++672LBhA2JiYrBo0SK89tprlvOOHj2KgwcPAgCGDBmCH374AQrF7f0nevbsicDAQHz44YdYu3YtTCYTgoOD8fzzz1drHtWpaAcROzs7S8zNza3EriLjx49HcHAwAGDz5s144403SlwrISEBR44U9ocaM2YM1Gp1hfP466+/LAUOf39/LFu2DM7OzpbjPXr0wPjx4/Hcc8/h2LFjOH78OJYsWYKZM2dKdkEpKgZVx84oer0ely9fvvvAYhrabiy1vrvK7t27AQAODg743//+V2alsjh3d3f8+OOPlv2p2eGYiIio9pnzc5C6985mo+5w7Bt4T9fVqJWYOa6TJJaRrZfM7iAiqg6RkZG4fPlyia9z585hz549mD9/PsaMGYOIiAgAhW9Sx40bV+b1hg4dailw3Kn4J/Lz5s0rdfmGSqXCZ599Bh8fHwDAhg0bkJKSUur17OzsMH/+/BKzSgRBwJw5c+Dm5gYAWLduHQwGg+X49evX4evrC7VajZdffllS4Chu7NixlsdxcXGljrmXPOQwcOBAeHh4AAC2bt0Ks9lcYszmzZst8fHjx1fq+r/88guAwg/ov/nmG0mBo4itrS2+/fZbaLVaAMCSJUtKLF2qTklJSQgMDKzUV0NT60WO8PBwCIKABx98sFJNRH18fPDggw9CFEXJ+i8iIiKqHan/roMpJ10Sc3ngSSjU5Te6q4ie7TzQu4N0NsiOwzcQHtP4pvFT4+E66jkobRtnU32lrQNcRz1X6/d9//33S32T9+ijj+KFF17AkiVLkJ6eDqBwh5WFCxeWu+NFly6l7wZlNBpx+PBhAEDTpk3Rv3//Mq9hbW2NRx55BEBhf4eiWQV3GjFiRJm9QaytrTFixAgAQFpaGi5dumQ5NmXKFOzduxfnz58v9xP7ouIEABQUFJQ5rqp5yEGhUFiKVAkJCTh27FiJMRs3bgQAtG/fHm3btq3wtVNSUizvS/v06VPm8h4AcHZ2xsiRIwEU/ne5cOFChe9DlVfry1WKenEUVSsro3nz5gCArKysas2JiIiIyqdPvInMEzskMW2rHrBt06va7vH0wx1xJjSxRBPSL14YwCak1CDp2vWDrX9vNh6tAzQaDXQ6HXx8fNCxY0eMGjUKvXrd/febl5dXqfG4uDhkZxf+u3bt2vWu1+nWrZvlcVhYWKljyiqoFOnQoYPlcWhoaIn7Fp/BkZycjKioKERGRiI8PByXLl3C6dOnLcdLm/FQXXnUtqCgIMtuKZs3b0bfvn0tx86fP4/w8HDLuMoICwuzbKJR0X/jP//803Ju8X/z6uTj44O///67Rq5dX9R6kcPb2xsRERGIiYmp9LlFU7fc3d2rOy0iIiIqgyiKSC6t2eiDT1brfTxdbPHI/W2wKvj2MpXLEan451QU7u/FJqTUMAkKZaOdzSGH5cuXo3fv3tV2vbKW3qelpVkeV2RnSFdXV8vjopkkd7rbdZycnMq9xu7du7Fu3TqcPn3aUoAprqxlLNWdR21r2rQpevXqhRMnTiA4OBhz5syxtEEomsWhVqsxevToSl23+L9x8X+/slTk35iqR60vVxk6dChEUURwcLDkfxh3YzAYsHv3bgiCgEGDBtVghkRERFRczqWDyI+ULhV16PvwPTUbLcv4Ia3g6aKVxJZuu4TsPHnXdRMRlaZoZ8g7lTcT4m7jy7rm3RTNKgAg6Zeh1+vxwgsv4MUXX8SBAwcsBQ4vLy/0798fM2bMwLfffov169dX6b4VzUNORb02cnNzLT0i9Xo9duwonKE4dOhQSXGmIoo/z4qojn9jqphaL3I8/fTTcHJyQmZmJl599VXL8pXyiKKIjz76CPHx8bC1tcVTTz1VC5kSERGRuSAXKXt/k8RUDm5w7Fe5ab0VpVErMTOwtCaklesUT0Qkp+I9K8pqJFpccnJyqecWl5FRfo+i4tco/oZ94cKF2LNnD4DCvhMLFy7EiRMnsG/fPixZsgRvv/02HnrooXJ7j1RHHnIaMWKEZQeTosLGwYMHLTMqKttwFJD+OxV/zmWpi/9dGqpaL3I4OTlh0aJFsLe3x7Fjx/Dwww9j69atpRY7zGYzTpw4genTp2P9+vXQ6XT47rvvqtTPg4iIiCov7d91MGVLZ15WV7PRsvRq71myCemhG7gRyyakRFQ/+Pn5Wd5Un/v/9u47Popq///4e0t6DwkhdBAICALSUSwoggoqoqhIERuiP9v1fu16sV3FdtUr6rUgiooiIqhYUERQQKqgQCAUAwmk99529/dHYMmSQgJJJtm8no9HHjn7mTMzn9Vhsvlkzjl//nnC/lu3bnW2u3btWmWf6ubqOKriZJann366pPLfpxYsWCCpfFWUDz/8UKNGjVJgYGCl/WtaUeVU8zCaj4+Pc+LPdevWKT8/3/lER3h4uEaMGFHnY0ZFRTnb27ZtO2H/iv+Pj841iYbRYHNy1GatXYfDobi4OD3wwAMym81q3769syKWm5urhIQE58y+JpNJPj4+euWVV/Tqq69q0aJFDZU6AACQVJIap+yN37rEfE47U771ONlodaqahPStxX/p+TtH8JgvgCbPYrFo+PDhWrFihQ4cOKB169bprLPOqrJvcXGxvvzyS5f9qrJ8+XLdd9998vDwqLQtJydHP/zwg6TyiSe7d+8uqfwpkpycHElSx44dqyxuHPXVV1852zabrdp+J5NHQ6ntPCJS+dMaixYtUnFxsVavXq1Vq1ZJksaPHy+Lpe6T4IaFhalXr17atWuX1q9fr9jY2GqLFxkZGVq+fLkkKTAwUH379q3z+VB7DfYkh8PhqPFLKi9cmEwmORwO2Ww2HTx4UH/99ZdzltuioiKXsU5paWnasWOHduzY0VBpAwAAHZls9AfXyUZlsSps9M2NUmRo08pPV1/g+uH46CSkANAc3Hjjjc72o48+qvj4yvcvm82mxx9/3LkowxVXXFHtIguHDx/WM888U2kuiLKyMj3yyCPOYSQ33HCD8z4dEBDgHIayb98+HTp0qMpjz507V99+e6yoXVJSUu37Opk8GkrFOT8KCgpq7HvmmWc6l3l97bXXlJGRIUnOJWZPxk03lU/Abbfbdd9991U552RhYaHuu+8+5efnSyr/79JU5ipxVw32JEfbtm0b6tAAAKCB5e38TUVxO11iwcOukEdo1cslNoQJF3TXyi3xSko/9sF13jfRGtI7Uv4+lf+CCABNyaBBg3TTTTfp/fffV0JCgq688kpNmTJFw4YNk7e3t/bu3atPPvlEu3aVzznUuXNnPfroo9Uez8fHR5999pkOHDigSZMmOVet/OCDD7RzZ/n9esiQIZoyZYpzH29vb11wwQX68ccfVVxcrKlTp+rmm29Wz549ZbfbtX//fi1durTScIvc3Nx6zaOhBAcHy8PDQ6WlpVq2bJnOOussBQYGqkOHDgoNDa3Uf8KECXrxxRd14MABSa6Fj5Nx+eWXa8WKFVq+fLmio6N12WWXadq0aRowYIDMZrOio6P14YcfKi4uTpI0cOBAzZw586TPVxslJSXOa6ou2rdvr4CAgAbIqPE1WJGjpa/NCwBAc2UvylfGiiomGz277hOznQovD4tuHX+Gnp67wRnLyivWJz/s0m1X8qgvgKbvgQcekLe3t95++23l5ubqrbfe0ltvvVWp3znnnKPnn3++2iVpJen+++/XBx98oPXr12v9+vVVHuPVV1+tNPTiscce0+7duxUXF6eEhAQ9/fTTlfa1Wq26/fbb9eOPPyomJkb79++v9zwagtVq1QUXXKDly5crJSVFt9xyiyTp6aef1jXXXFOp//jx4/XKK6+orKxMUnnR41S99NJLCgoK0ueff67U1FS9/PLLVfYbP368/vWvf9V6gteTlZqaqvHjx9d5vzfeeEOjRo2q/4QM0LD/hQEAQLOT8etnsuVnucQaerLR6gw5vY2GnN5GG6OTnLHv1sZq1OCOOq19cKPnAwB1YTKZdM899+iyyy7TggULtH79eiUkJMhutysiIkJ9+vTRhAkTdNZZZ51waEdERISWLFmid955R8uXL1dCQoJ8fX3Vp08fXXXVVc6JNavb74MPPtCKFSt08OBBFRcXy8/PTx06dNCgQYN03XXXqWvXriosLFRMTIzS0tL0+++/Vzk/yMnm0VCeffZZtWrVSj///LMyMjIUEBDgXDXleGFhYRoyZIjWrVsnb2/vesnV09NTTz/9tCZOnKjPP/9cmzZtUkpKikwmkyIjIzVw4EBdddVV6tev3ymfC7VjctR1gV+4nc2bN2vy5MnO15988okGDRpkYEYAAKMUJ8Xq8PsPuMzF4dttoCKuediwCT+T0vP1/15Y6ZyEVJKiOoXohTvPkdnMJKRoWvbu3auysjJZrdYGn3QRQN2UlZXp3HPPVXp6uq644gq98MILRqfkFk72vtdQv4ca/iSH3W7X+vXrtXHjRsXHxys7O1tms1kBAQHq0KGDBgwYoOHDh1c5ey8AAKg/DoddacvfdSlwmKyeajX6JkNXNGnTyk8TR/XQJz/sdsZiDmZqxaY4jR7aybC8AADNy+rVq5Weni5JVQ5ngXswtMixbNkyvfrqq87ZhKsTGhqqBx98UJdffnkjZQYAQMuT99cqFR+KcYkFn3WlPELaGJTRMRPO76aVm+OVmJbvjH2wLFrD+kQq0I9Z6gEANcvIyNCrr74qSerZsydPrrsxw4oczzzzjD755BNJqrT80PHS09P14IMPatOmTVVOlAMAAE6NrTBX6Ss/colZQ9ooaPh4YxI6jqeHRTOv7KtZ7/7ujOUWlGj+d9G6c2J/4xIDADRZS5Ys0W+//SYvLy+tWbNGKSkpkqS7777b4MzQkAwpcrzzzjv6+OOPZTKZ5HA41LZtW40ZM0Y9e/ZUcHCw7Ha7MjMztWvXLq1YsUKJiYlyOBz64osv1L17d02bNs2ItAEAcFsZqxbIXpDjEgsbfbPM1qbzlMSAnq11Vt9Irfsr0Rn7ccNBXTSko6I6VV4qEADQsjkcDn377bcusauuukoXXnihQRmhMTR6kSMpKUlz5syRJFksFv3zn//U9OnTqx3r+8gjj+jDDz/Uiy++KJvNppdeekmjR49WmzbGPzoLAIA7KErYp9w/fnKJ+UYNlW+3AQZlVL1bLj9Df+xOUVGJTZLkcEhvffmXXr7nPFmYhBQAUEFUVJTat2+v5ORktW3bVhMnTtTNN99sdFpoYObGPuGnn36qkpISmUwmPfzww7rxxhtrnMzMZDJp+vTpeuyxxyRJpaWlWrhwYWOlCwCAW3PYbUr/4R1Jx4aOmjy8FHbRjcYlVYPwEB9NGh3lEtt/KFs/rIs1KCMAQFPVu3dv/fzzz9qxY4d+/PFH3XrrrTKbG/1XYDSyRv8/vHbtWklSt27dXJaLOZFJkyY5l6P57bffGiQ3AABamtytK1ScuN8lFjLialmDwg3K6MQuP/c0dYgIcIl99P0uZeYWGZQRAABoKhq9yHHo0CGZTCaNGDGizvuec845cjgcOnDgQP0nBgBAC2PLz1bGqgUuMY9W7RQ09DKDMqodq8Ws2yf0dYnlF5Xpg2XRBmUEAACaikYvcuTl5UmSQkJC6rxvUFCQJKm4uLhecwIAoCXK+OVj2YvyXGJhF98qk8XDoIxq74xuYTp/QHuX2MrN8dr5d7pBGQEAgKag0YscwcHBkqTDhw/Xed+EhARJx4odAADg5BTF71bunytdYn6nny2fzmcYlFHd3XRZb/l6u86h/tbiP1VmsxuUEQAAMFqjFzl69Oghh8OhlStX1umJjKKiIv38888ymUzq1q1bA2YIAIB7c9jKlPr92y4xk6e3Wl14g0EZnZyQQG9NubiXS+xgUq6++e1vgzICAABGa/Qix3nnnSdJSktL03PPPVfr/Z599lmlpaW5HAMAANRd9qZvVZoa5xILOfc6WQNbGZTRybv0rM7q2tb1Cc9Pf9yttKxCgzJCS2exWCRJNptNDofjBL0BoHlzOByy2cqXdT96/zNaoxc5rr76aueQlYULF+qee+7RoUOHqu0fHx+ve+65R4sWLZLJZFJQUJAmTpzYSNkCAOBeynLSlPnr5y4xz9adFTT4UoMyOjUWi1m3X+U6CWlhsU3vfrXdoIzQ0nl6ekoq/+BfUFBgcDYA0LAKCgqcBd2j9z+jWU/cpX75+fnpqaee0j333CNJ+vHHH/XTTz+pV69e6tWrl4KCgmQymZSZmandu3dr165dcjgccjgcMpvNevLJJ+Xv798gudntdi1ZskRLly5VTEyMCgoKFB4ergEDBui6667T4MGDG+S8s2bN0meffSZJ2rlzp6zWRv/fAgBoIdJ+fF+O0opLrZoUdultMpmbxl9fTkbPzqEaPbSTftxw0Blb91eiNu9K1qBeEQZmhpYoMDBQubm5kqSMjAz5+vrKZDIZnBUA1D+Hw6GMjAzn68DAQAOzOcaQ36ZHjx6t2bNn69FHH1VZWZkcDoeio6MVHV156beKVaHHH39cY8aMaZCccnNzdccdd2jjxo0u8YSEBCUkJOjbb7/V9OnT9dBDD9XredetW6eFCxfW6zEBAKhK/t7NKojZ4BILOHOUvNv1MCij+nPD2NO1fkeicvJLnLH/ffmX5tw/Ut6e/PEAjcff318mk0kOh0N5eXk6dOiQQkNDKXYAcBtHn1TLyMhwrp5qMpka7GGEujLsp/4VV1yhM844Q3PmzNGKFStUUlJSZT+r1aoxY8Zo5syZ6t69e4Pk4nA4dO+99zoLHCNGjNCkSZMUFhamXbt26d1339Xhw4c1b948hYaGasaMGfVy3ry8PD366KOM1wQANDh7abHSl891iZl9AxU6crJBGdWvQD9P3Tiut15buNUZS84o0Ocr9mjapacbmBlaGrPZrHbt2unw4cPOQkdeXp5MJlOTGa8OAKfi+DmHTCaT2rVrJ7O50WfDqJKhf9ro2rWr/vOf/6i4uFh//PGHDh06pKysLDkcDgUHB6tjx47q16+ffHx8GjSPb775RmvWrJEkTZgwwWVC1P79++uSSy7R5MmTtW/fPs2ZM0eXX3652rRpc8rnffbZZ53L4gIA0JCy1nyhsuwUl1irC2+QxSfAoIzq34WDO2jFpjjt/DvdGVuyap/OH9BeHds0jUdo0TIEBAS4FDqk8j+qlZWVGZwZANSvowWOgICm83mi0YscixYtUmxsrC6++GL17Vs+UZiXl5eGDx/e2Kk4zZs3T1L544UPPvhgpe3BwcF68sknNXnyZBUXF2v+/Pl64IEHTumcq1ev1uLFi52TqWZlZZ3S8QAAqE5J2iFlrf/aJebdsbf8z3Cv1cpMJpPuuKqv7n55lWz28l8sy2wOvfXlX3r29rMZKoBGFRAQoB49eigvL085OTkqKSlxrkAAAM2ZxWKRp6enAgMD5e/v32Se4Diq0Yscixcv1p9//ql58+bpgQce0I033tjYKbiIj493zgUycuRI58ovxxs0aJC6dOmi2NhY/fDDD6dU5MjJydFjjz0mSZo0aZL27dtXaS4QAADqg8PhUNoP70j2Cn9BNlsUdvGtbvlLf8c2gZowspsW/bzXGduxP12/bInXBYM6GpgZWiKz2azAwMAmMxkfALQEjV5yiY2NdT62d9FFFzX26SvZsmWLsz1s2LAa+w4ZMkSSdPjwYcXFxZ30OZ9++mmlpKSoXbt2+r//+7+TPg4AACeSt2O1ig7udIkFD7tcnuEdDMqo4V0zqodah/q6xOZ+vVO5BVXP/wUAANxHoxc5Ko5FDAsLa+zTV7Jv3z5nu3PnzjX27dDh2AfCvXv31tCzeitWrNDXX38tk8mkf//73/Lz8zup4wAAcCK2wlylr/jQJWYNaq3gERMNyqhxeHtaNfPKM1xiOfkl+vDbyqu4AQAA99LoRY6Kc2+sX7++sU9fSVJSkrPdtm3bGvtGRkZWuV9tZWRkaNasWZKk6667ztB5SAAA7i/jlwWyF+S4xFqNuVlmDy+DMmo8g09vo+FnRLrElq8/qF2xGQZlBAAAGkOjz8nx8MMPKzo6WgkJCXr88cf1xhtvOCcgNUJ2drazfaKnKnx9jz36mpubW+dzPfnkk0pLS1O7du10//3313n/miQkJJz0Si0xMTH1mgsAwHhFh/cod+tPLjHfHkPk132QQRk1vhnjz9C2PSkqLD422eObi//UK/84T1ZL05okDQAA1I9GL3J4e3vr3Xff1ezZs/Xbb7/p2muvVa9evXTmmWeqffv2CggIkNV64rTGjx9fL/mUlBwbn+vt7V1j34rbK+5XG999951++OGHBhumsnjxYs2ZM6dejwkAaJ4ctjKlffc/SRXWsPfwUtjom4xLygBhwT66fkxPzf362JwkBxJz9M1vf+vK87sZmBkAAGgojV7kGDFihLNtMpnkcDi0a9cu7dq1q9bHMJlM9VbksFgsLsetydEJUyXVaZmctLQ0Pfnkk5Kka6+9lmEqAIAGlb1xmUpSDrrEQs69VtagcIMyMs5lI7pq5eZ4xSYcG7azYPlund2vrVqH+NawJwAAaI4a/VlNh8Ph8lVVrDZf9aXiEJSioqIa+xYXFzvbnp6etT7HrFmzlJWV1SDDVAAAqKg0K1mZvy50iXm27qSgwWMNyshYFotZd1zdTxX/jlFUYtM7S7bX6+cJAADQNDT6kxx33nlnY5+yRhWHjRQWFta4jnlBQYGzHRQUVKvjL126VCtWrJAkPfPMM/L39z/JTGt21VVXnfQTIjExMXrqqafqOSMAQGNzOBxK+/5dOcoqDqk0KezSmTJZGv1HfpPRs1OoxgzrrB9+P+CMbdiZpN+3J+qsvjVPOg4AAJqXFl/kaNeunbOdmJioiIiIavsmJiY62zX1OyotLU3//ve/JZUP0wkJCalyWE5+fr6zvXv3blksFnl4eKhbt9qPF27btu0JV4cBALi3/F3rVPj3VpdY4MAx8m7Xw6CMmo4bLu2l9dsTlZV37KnMt5dsV7/u4fLz8TAwMwAAUJ9a7p91jujevbuzHRcXp/79+1fbNz4+3tmuTQFi//79yskpHwO8Zs0arVmz5oT7XHXVVZLKiy8rV648YX8AACTJVpin9B/fd4lZ/EMUev71BmXUtPj7euqWK/ropU+2OGMZOUX66PtdmjnBuFXeAABA/WqUIkd6erq++uorrVu3TsnJybJYLOrYsaPOOeccXXHFFXWa36K+9e/f3zkB6ubNm3X55ZdX23fjxo2SpMjISLVv376xUgQA4IQyfvlEtvwsl1irMTfL7F2/q3k1Z+ee2U4rN8frj5gUZ+y7dbE6f2B79ewUamBmAACgvjR4kWPhwoV64YUXXOazkMrngfjpp5/0xhtv6IUXXtCQIUMaOpUqRUZGqn///tq6dauWL1+uBx54oMp5MzZv3qzY2FhJ0pgxY2p17KFDhyomJuaE/aZOneosoOzcubNWS+gCAHBUUfxu5W790SXm222g/KKGGZRR02QymXT7VX31/178RSWlNkmSwyHN+XybXr3vfFktjT4fOwAAqGcN+tN8wYIFeuKJJ5Sfn1/tCilJSUm66aabtGHDhoZMpUZTp06VJGVlZWnWrFmy2+0u27OzszVr1ixJkoeHh6ZMmdLoOQIAUBWHrVSp373lEjN5eCvs4ltPuDR6S9SmlZ8mj4lyiR1MytWSVfsMyggAANSnBityZGRk6MUXX3S+9vf313XXXadHH31Ujz/+uK655hrnyiZlZWV64IEHVFZW1lDp1Gjs2LEaMWKEJGnZsmWaOnWqli9frm3btmnhwoW68sortW9f+Yefu+66Sx06dHDZf8OGDYqKilJUVJSzYAIAQGPIWv+1StMOucRCzrtW1qBwgzJq+i4/9zR1aeu6mtpnP8YoMS2/mj0AAEBz0WDjIr766isVFhbKZDJp6NChmjNnjgICAlz63H333ZoxY4aio6OVkpKi5cuXa+zYsQ2VUo1ee+01zZw5U5s2bdLmzZu1efPmSn2mT5+uGTNmGJAdAACVlWYkKuu3RS4xz4guChpszM/S5sJqMevOif31f//9VUceLFVJmV1vLv5TT80YzhMwAAA0Yw32JMfR4ScBAQF64403KhU4JCksLEyvvPKKzObyNNauXdtQ6ZyQv7+/5s+fr+eee07Dhw9XSEiIrFarwsPDNXr0aH344Yd6+OGH+eADAGgSHA6H0r5/Ww5b6bGgyazwS2fKZLYYl1gz0aNjiMae3cUltm1Pqlb9caiaPQAAQHPQYE9y7Nu3TyaTSaNGjapyIs+jOnXqpIEDB2rTpk2Kjo5uqHRqxWw2a8KECZowYUKd9qvtBKPV+eijj056XwBAy5S341cVHtjuEgscdIm82p54iXOUm3pJL63fnqi07CJn7L2vdmhgzwgF+hm38hsAADh5DTonhyS1bdv2hH179+4tSUpNTW2odAAAcBu2glylr/jAJWYJaKXQ8yYZk1Az5evtodsm9HWJ5eSXaN43Ow3KCAAAnKoGK3IUFxdLknx8fE7YNyQkRJKUl5fXUOkAAOA20lfMk70gxyUWNuYWmb1O/DMXrob1idTwMyJdYis2xWn7vjSDMgIAAKeiwYocNlv5+vNH59uoiYeHhySppKSkodIBAMAtFOzfqrztq11ivlFD5Rc1xKCMmr/brjxDPl6uI3jf+GKbSkptBmUEAABOVoMVOQAAQP2ylxQq7bv/ucRMXr4KG3OLQRm5h1ZBPpp2aS+X2OHUfH3208nPtwUAAIxBkQMAgGYiY9WnKstxHUbR6oKpsgaEGpSR+7jkrC6K6hjiElv8yz79fTjboIwAAMDJoMgBAEAzUHR4j3I2fecS8+7YWwFnjjIoI/diMZt01zX9ZbUcWyrebnfov59vlc1mNzAzAABQFxQ5AABo4hy2UqV++6YkhzNmsnoqfOxMmUz8KK8vnSIDdfUFPVxi+w9la+nq/QZlBAAA6opPRgAANHFZa5eoNDXeJRZyzjXyCD3xMu2om2tGdVeHiACX2ILlu5WQygpwAAA0B9YTdzk1n376qX755Zca+yQlJTnb06ZNO+ExTSaTPvzww1PODQCApq4kNV6Zaxe7xDwjuiho2OUGZeTePKwW3X1tfz3w+m9yHHlwpqTMrtcXbdO/Z54ts9lU8wEAAIChGrzIER8fr/j4+BP2M5nKPzRs2rSpxn4Oh8PZFwAAd+aw25T67VuSvexY0GRW+Ng7ZDJbjEvMzfXsFKrLRnTV17/97Yzt2J+u5RsO6pLhnY1LDAAAnFCDDldxOBz1/gUAQEuRs2W5ig+7LmMaNOxyeUV2NSijlmPKJb3UOtTXJTbvm51Kyyo0KCMAAFAbDfYkx3PPPddQhwYAwO2VZqco45dPXGLWkDYKOecagzJqWXy8rPp/V/fTrHd+d8YKi8v05uI/9fhNQ3mqFACAJqrBihxXXnllQx0aAAC35nA4lPbdO3KUFrnEw8feLrOHl0FZtTwDolrrwsEd9POmY8NuN0Un67dth3Xume0NzAwAAFSH1VUAAGhi8nb8qsK/t7rEAvqPkk+nPgZl1HLdfHkfBQe4FpbeXrJd2XnFBmUEAABqQpEDAIAmpCwvU+k/ve8Ss/iHKPTCE68+hvoX4OupmVf2dYnl5Jfova93GJQRAACoCUUOAACaCIfDobTv35G9MM8lHjbmVlm8/QzKCmf1jdTwMyJdYqu2HNLmXckGZQQAAKpDkQMAgCYiP3qtCvZsdIn59TpLfj2HGpQRpPJl7m+78gz5ebtOZTZn0TblF5YalBUAAKgKRQ4AAJqAsrwspS1/zyVm9g1U2JhbDMoIFbUK8tFNl7vOiZKeXaS5DFsBAKBJocgBAIDBHA6H0n54R/bCXJd42MW3yuIXZFBWON5FQzqqf/dwl9hPG+MYtgIAQBNCkQMAAIPl71qngpgNLjG/nsPl3+ssgzJCVUwmk+66pr98vCoPW8lj2AoAAE0CRQ4AAAxky8+uPEzFJ0BhF99qUEaoSetQX910WW+XWHp2keZ+xbAVAACaAoocAAAYKG35u7IX5LjEGKbStI0Z1kn9e7gOW1mxiWErAAA0BRQ5AAAwSN6udcrf9btLzDdqqPwYptKkMWwFAICmiyIHAAAGsOVnK+2Hd11iZh9/hV08QyaTyaCsUFutQ3x18+UMWwEAoKmhyAEAgAHSfpxbeZjKmFtk9Q82JiHU2eihDFsBAKCpocgBAEAjy9v9u/Kj17rEfHsMkd/pIwzKCCejumErr3/OsBUAAIxCkQMAgEZkK8hR+vHDVLz9FXYJw1Sao6qGrWTkFOm9r7YblBEAAC0bRQ4AABqJw+FQ6nf/ky0/2yXeaszNsvqHGJQVTtXooZ105nHDVn7eFK9N0UkGZQQAQMtFkQMAgEaSt+NXFcRscIn5dh8s/97nGJQR6oPJZNKdVa628qfyCkoMygoAgJaJIgcAAI2gLCdN6cvfc4mZfQIUdultDFNxA+XDVvq4xDJyivS/Lxm2AgBAY6LIAQBAA3M47Er9Zo7sxQUu8bBLb2OYihsZPbSjBkS1domt3npIv209bFBGAAC0PBQ5AABoYDmbf1DhAde/6PufcZ78ew43KCM0hKOrrfj5eLjE31z8p9KzCw3KCgCAloUiBwAADagk7ZAyVn7kErMEtFKr0TcblBEaUliwj26f0NcllldYqtc+2yqHw2FQVgAAtBwUOQAAaCAOu02pX78uR5nr5JPhl/0/Wbz9DMoKDe28Ae11Tv92LrGte1L13dpYgzICAKDloMgBAEADyVr7pYoT97nEAgddKt8u/QzKCI3l9qv6KjTQ2yX2/rJoHUrJNSgjAABaBoocAAA0gOLE/cpcs8gl5tGqrUIvmGJQRmhMAb6euue6M11iJaU2/WfBHyqz2Q3KCgAA90eRAwCAemYvLVbK1/+V7LZjQZNZ4ZfdLbOHl3GJoVENiGqtsWd3cYntjc/SohV7DMoIAAD3R5EDAIB6lrlqgUrTDrnEgs++St7tuhuUEYwyfdzpahfuOv/KZyv2aE9cpkEZAQDg3ihyAABQjwoP7lD2xmUuMc82XRUy4mqDMoKRvD2tuu/6gTKbTc6Y3e7QfxZsUVFJmYGZAQDgnihyAABQT2yFeUr56r8uMZPFQ60vv1smi9WgrGC0Hh1DdN2oHi6xw6n5+nBZtEEZAQDgvihyAABQDxwOh9K++59sueku8ZCRk+UZ3sGgrNBUTBzVQ907BLvElq2N1R8xKcYkBACAm6LIAQBAPcj9c6Xyd//uEvPu1EdBQ8YalBGaEqvFrPuuHyBPD4tL/LXP/lB2XrFBWQEA4H4ocgAAcIpK0hOU/uP7LjGzj3/5MBUTP2pRrn3rAN007nSXWEZOsf67cJscDodBWQEA4F745AUAwClw2EqVsvRVOUqLXOLhl94ha2Arg7JCU3Xp2V00oGdrl9jG6CR9uzbWoIwAAHAvFDkAADgFGas/U0nSfpdYwJkXya/nUIMyQlNmMpl073VnKtjfyyX+/jc7FZuQbVBWAAC4D4ocAACcpMID25X9+1cuMY9W7dRq1HRjEkKzEBLgrXsnnekSKy2z68WPt6i41GZQVgAAuAeKHAAAnARbQe6R5WIrzKVgtqr1+Htl9vQ2LC80DwN7RuiKc09zicUn52ru1zsMyggAAPdAkQMAgDpyOBxK/fZN2fIyXOKhIyfLq01Xg7JCc3PD2F7q2jbIJfb9ugP6fXuiQRkBAND8UeQAAKCOcrf+pII9G11iPl36KWjoOIMyQnPkYbXo/6YMrLSs7Oufb1V6dqFBWQEA0LxR5AAAoA5K0g4p/ad5LjGzb6DCL7uL5WJRZx0iAjRjfB+XWG5Bqf6z4A/Z7CwrCwBAXfFpDACAWnKUHVkutqzEJR4+9g5ZA0IMygrN3eihnXRW30iX2F/70vTlL3sNyggAgOaLIgcAALWU/vOHKkmOdYkFDrxYfj0GG5QR3IHJZNJdE/srLNjHJf7xD7sVczCjmr0AAEBVKHIAAFALebt+V87m711iHmHtFXrhNIMygjvx9/XUP68fILPpWMxud+jFj7eooKjUuMQAAGhmKHIAAHACpZlJSv32TZeYyeqpiCvvk9nDy6Cs4G76nBamiaN6uMSSMwr038+3yeFgfg4AAGqDIgcAADVwlJUq+cv/yFFc4BJvNfpmebbuZFBWcFeTLopSz06u87us/TNB366NrWYPAABQEUUOAABqkP7zfJUk7XeJ+fc5VwH9LzQoI7gzi8Ws+6cMkp+Ph0t87tc7tDc+06CsAABoPihyAABQjbzdvytn83cuMY9WbRV2yQyZTKZq9gJOTetQX/3jujNdYmU2h2bP36y8gpJq9gIAABJFDgAAqlSamaTUZZXn4Wh95T9l9vSpZi+gfgztE6krz+/mEkvJKNCrn21lfg4AAGpAkQMAgOM4ykqVsqTqeTi8IjobkxRanGmX9lKvzqEusQ07k/TVr38blBEAAE0fRQ4AAI6TvnK+ihOZhwPGslrMemDqIAX4errEP1i2U7sPZhiUFQAATRtFDgAAKsjfvV45m5iHA01DWLCP7rt+gEvMZnfo+fmblZPP/BwAAByPIgcAAEeUz8PxhkuMeThgtEG9IjTxwu4usbSsQr3y6R+y25mfAwCAiihyAAAgyV5arOQvX5adeTjQBE0e01N9TmvlEtu8K1lLVu0zKCMAAJomihwAgBbP4XAo7Yd3VZLkOqEj83CgqbBYzPq/yQMV7O/lEp///S7t/DvdoKwAAGh6KHIAAFq83D9+VN5fv7jEPFq1VdjFzMOBpqNVkI/+b/JAVbwk7XaHXvhokzJyioxLDACAJoQiBwCgRSs6vEdpP77vEjN5eiviqgdk9mIeDjQt/XqEa9JFUS6xjJxizf5wk0rL7AZlBQBA00GRAwDQYpXlZSn5ixcle5lLPHzcnfIM72BQVkDNrrkoSv17hLvEdh3I0HtfbTcoIwAAmg6KHACAFslhK1PKkv/IlpfhEg8aPl7+vYYblBVwYhazSfdPGaTWIa5PGn237oBWbIwzKCsAAJoGihwAgBYpY+VHKorb6RLz7nyGQs+/3qCMgNoL9PPUI9OHyNPq+lHuzcV/am98pkFZAQBgPIocAIAWJ2/nGmVvXOYSswSGKWL8P2QyWwzKCqib09oH685r+rvESsvsevaDTcrKLTYmKQAADEaRAwDQopSkHFTqt2+6Bi1WRVx1vyx+QcYkBZykkQM76LJzurrE0rIK9cJHm2WzMREpAKDlocgBAGgxbEX5SvriBTlKXf/KHXbxrfJu282grIBTc9NlvdW7ayuX2Pb9afrg22iDMgIAwDgUOQAALYLDYVfqV6+pLDPJJR7Qf5QC+48yKCvg1FktZj04bZBaBXm7xJeu3q9VfxwyKCsAAIxBkQMA0CJkrv5MBfu2uMS82nZX2JhbDMoIqD8hAd56ZPoQWS2uH+1e/3ybYhOyDcoKAIDGR5EDAOD28nb8pqy1i11iZt9ARVz1fzJZPQzKCqhfPTqG6Par+rrESkpt+ve8jcrJLzEoKwAAGhdFDgCAWys6vFepy95wDZrMirjyPlkDw4xJCmggo4d20sXDO7vEkjMKNPvDTSotYyJSAID7o8gBAHBbZTnpSl40Ww5bqUs8bMzN8ul8hkFZAQ1rxvg+6tkpxCW2fX+a3l7ylxwOh0FZAQDQOChyAADckr20WEmLZsuWn+USDxx4sQIHXmxMUkAj8LBa9NANgxUa6DoR6fL1B/XVr38blBUAAI2DIgcAwO04HHalfvO6SpJcf6Hz6XyGWl10o0FZAY2nVZCPHr9pqDw9LC7xed/s0KbopGr2AgCg+aPIAQBwO5m/LVL+rt9dYh6hkWo94f9kslgNygpoXN06BOu+SQNcYnaH9OLHW3QwMcegrAAAaFgUOQAAbiUveq2yfvvcJWb28lXExIdk8fE3KCvAGGf3a6spl/R0iRUWl+mp9zcoK7fYoKwAAGg4FDkAAG6jOHG/Ur+Z4xo0mdV6wj/lGdbemKQAg11zYQ+dP8D1+k/JKNCzH2xUaZnNoKwAAGgYFDkAAG6hLDdDSZ/PlqOsxCXe6qLp8u3a35ikgCbAZDLprmv6K+q4FVd2HcjQnEV/suIKAMCtUOQAADR79pIiJS+aLVtehks84MyLFDjoUoOyApoOTw+LHr1xiMJDfFziKzfH64uVew3KCgCA+keRAwDQrDnsNqUs+Y+KE/e7xL079VbYmFtkMpkMygxoWkICvPX4TUPl7em64sr873bp9+0JBmUFAED9osgBAGi2HA6H0n54VwX7trjErcERiphwPyupAMfp0jZI908ZpONrfy998od2H8yoeicAAJoRihwAgGYra92Xyt36k0vM7OOvNtc9KotvgEFZAU3bkN5tNH1sb5dYSalNT723QYdT8wzKCgCA+kGRAwDQLOVuX63MVQtcYiaLh9pMfFierdoZlBXQPFx5/mm6aEhHl1huQYlmvfO7MnOKDMoKAIBTx3O8Fdjtdi1ZskRLly5VTEyMCgoKFB4ergEDBui6667T4MGDT+n4NptNP/zwg5YtW6adO3cqMzNTHh4eioyM1NChQzVlyhR17dq1nt4NALivwgPblbrszeOiJoVfcY+8O/Q0JCegOTGZTLrj6n5KzynSH7tTnPHkjAI9NXe9nr1jhHy8+JgIAGh+eJLjiNzcXN1www165JFHtHHjRmVnZ6u0tFQJCQlatmyZpk6dqtmzZ5/08ZOTk3X99dfrvvvu08qVK5WcnKySkhLl5+dr3759+uSTTzRu3DjNnTu3Ht8VALifkpSDSvriBcle5hIPHXWD/HsNNygroPmxWsx6aNpgdWsf5BLfdyhbs+dvUpnNblBmAACcPIocKp+47t5779XGjRslSSNGjNAbb7yhhQsX6oknnlC7du3kcDg0b948vfPOO3U+fnFxsW655RZt27ZNkjRw4EC98MILWrRokT744APddttt8vX1lc1m0wsvvKBPP/20Pt8eALiNspx0JX72bzmKC1zigYPHKnjoZQZlBTRfPl5W/euWYWrTytcl/sfuFM1ZtE0Oh8OgzAAAODkUOSR98803WrNmjSRpwoQJmjt3rkaNGqX+/ftr0qRJ+vLLL9WtWzdJ0pw5c5SUlFSn43/44Yfas2ePJOnaa6/VJ598oiuuuEJ9+/bV8OHDdd999+mzzz5TYGCgJOnFF19URgYznANARfbiAiUt/Ldsuekucb+ew9Rq1A0GZQU0fyEB3nri1uEK8PV0if+8KV6fLN9tUFYAAJwcihyS5s2bJ0ny9/fXgw8+WGl7cHCwnnzySUnlT2XMnz+/TsdfvHixJCk0NFSPPvqoTMev2yYpKipKt99+uyQpPz9fP//8c53OAQDuzGErVfLiF1WSctAl7tU+SuGX3y2T2WJQZoB7aBfur3/dMlSeHq7/lhb+tEc//H7AmKQAADgJLb7IER8fr+joaEnSyJEjFRwcXGW/QYMGqUuXLpKkH374odbHT0tL04EDBySVD4Px8vKqtu/ZZ5/tbO/ezV9OAECSHHabUr5+XYWxf7nEPULbqs3Eh2X2qP6+CqD2enYK1YNTB8l83N9i3lr8pzburNtTrAAAGKXFFzm2bNnibA8bNqzGvkOGDJEkHT58WHFxcbU6vtls1j333KNJkybpnHPOqbFvxXGvxcXFtTo+ALgzh8OhtB/eVX70Wpe4xS9Iba57VBbfAIMyA9zTkN5tNPOqfi4xu0N6/qPN2hXLUFoAQNPX4tcG27dvn7PduXPnGvt26NDB2d67d686duxYQ+9yoaGhuuOOO2qVy4YNG5ztdu3a1WofAHBnGb98rNytP7nETB7eirjmEXmEtDEoK8C9XTK8s9KzCrVwxR5nrKTUpiff+13/vv1sndY+2LjkAAA4gRZf5Kg4iWjbtm1r7BsZGVnlfvWhqKhIH374ofP1ueeeW6f9ExISlJCQcFLnjomJOan9AKAhZa37Utm/L3UNWqyKmPiAvNt2MyQnoKWYfHFPpWUX6udN8c5YflGZZr37u567Y4Q6RPAUFQCgaWrxRY7s7Gxn28/Pr8a+vr7HllfLzc2t1zyeffZZHT58WJI0dOhQ9e7du077L168WHPmzKnXnADAKDlblivjl09cgyazIsb/Q75d+lW9E4B6YzKZdOfE/srJL9Gm6GRnPDuvRI+/vU7P33mOIkJ9azgCAADGaPFzcpSUlDjb3t7eNfatuL3ifqfqvffe08KFCyVJPj4+euyxx+rt2ADQ3OTt/E1pP7xbKR4+9nb59ax57iQA9cdqMevBaYPVt1uYSzw9u0iP/2+dMnKKDMoMAIDqtfgih8VybKm0qpZ2rajixKBmc/38p5s7d65efPFF5+snn3xSPXr0qJdjA0BzU7B3i1K+fl2SwyXe6qIbFdDvAmOSAlowLw+LHr1xiKI6hrjEE9Pz9fjb65STX39/9AEAoD60+OEqFYegFBUVydPTs9q+FVc8qalfbTgcDr388st6991jf618+OGHdcUVV5zU8a666ioNHz78pPaNiYnRU089dVL7AkB9KYzbqeQvX5LsNpd48DnXKGjIOIOyAuDr7aFZtw7TI2+u1YHEHGc8LilXs979Xf+eeZZ8vT0MzBAAgGNafJGj4jwchYWFCgwMrLZvQUGBsx0UFHTS5ywuLtaDDz6o77//XlL5EySPPvqopk6detLHbNu27QknTgWApqo48W8lfT5bjjLXvwoHDr5UIedcY1BWAI4K8PXUUzOG66E31ighLd8Z3xefpafmbtATtw6Tt2eL/1gJAGgCWvxwlYpLtSYmJtbYt+L2iIiIkzpfenq6pk2b5ixweHh46Pnnnz+lAgcANGfFyQeU+OmTchQXuMT9+56vVhfdeMKhhAAaR0igt56eeZbCgn1c4jv/TtfsDzeptMxuUGYAABzT4osc3bt3d7bj4uJq7Bsff2wZtW7d6r584aFDhzRp0iRt27ZNkuTv76+33377pIeoAEBzV5x8QImfzJK9MM8l7ttjiMLH3iGTqcX/mAKalNYhvnpm5lkK9vdyiW/ZnaKXPtmsMhuFDgCAsVr8p8f+/fs7/0q4efPmGvtu3LhRkhQZGan27dvX6TyJiYmaNm2aDh48KKn8SZAFCxbo7LPPPomsAaD5Ky9wPFGpwOHT+Qy1vvIfMpkt1ewJwEjtwv311G3D5efjOg/Hur8S9cJHFDoAAMZq8UWOyMhI9e/fX5K0fPly5eXlVdlv8+bNio2NlSSNGTOmTucoLi7WjBkzdPjwYUlSly5dtHDhQkVFRZ184gDQjB0rcOS6xL079VbExIdktp7a5M4AGlaXtkF68tZh8vZ0LUb+vr280MHQFQCAUVp8kUOScz6MrKwszZo1S3a76w/m7OxszZo1S1L5HBpTpkyp0/Ffeukl7dmzR1L5ExwfffSRIiMj6yFzAGh+SlIOKnHBk5ULHB17q801j8js6W1QZgDqIqpTqP518zB5VVnoYI4OAIAxmAZb0tixY/Xll19qzZo1WrZsmZKSkjRt2jRFREQoJiZGb7/9tvMpjLvuuksdOnRw2X/Dhg2aNm2aJGnIkCH66KOPnNsOHz6sTz/91Pl6xowZSktLU1paWo05+fr6qlOnTvX1FgGgSShJOaiET56QvSDHJe7d8XS1uZYCB9DcnNEtTLNuGaYn31uv4pJjyz+v35Gk5+dv0oPTBsvDyt/UAACNhyLHEa+99ppmzpypTZs2afPmzVXOzzF9+nTNmDGjTsf94osvVFpa6nz99NNP12q/44slANDc1VzgeJQCB9BMnXFamJ44UugoqlDo2LAzSbM/3KSHbhgkDytz7AAAGgel9SP8/f01f/58Pffccxo+fLhCQkJktVoVHh6u0aNH68MPP9TDDz9c56UMo6OjGyhjAGg+SlLiqi5wdOjFExyAG+hzWpieuHV4pTk6NkYn6dkPNqm0zFbNngAA1C+e5KjAbDZrwoQJmjBhQp32Gzp0qGJiYqrc9vbbb9dHagDQbBUnHyifg6OqAsd1j8rs6WNQZgDqU++urfTErcP15Hu/q7D4WFFj865kPfvBJj18w2B5evBEBwCgYfEkBwCgwRQd3qPEj/9FgQNoIXp3baUnbz1LPl6uf0fbvCtZ//5go4pLeaIDANCwKHIAABpEQeyfSvzkSdmL8l3iXu17HpmDgwIH4I56dQnVUzOGVyp0/LE7RU++u14FRaXV7AkAwKmjyAEAqHf5MRuUtPBZOUqLXOLeHXop8rrHZPaiwAG4s56dQ/XUbcPl6+1a6Ni+P02PvrVW2XnFBmUGAHB3FDkAAPUqd/sqJS9+SbKVucR9TjtTbSY9ToEDaCF6dgrV07edJb/jCh37DmXrwTlrlJpZaFBmAAB3RpEDAFBvsjd9p9SvX5ccdpe43+lnq83EB2X28DIoMwBG6NExRM/eMULB/q7/9g+n5umBOb/pUEquQZkBANwVRQ4AwClzOBzKXPOF0n+cW2lbQP9Ran3FPTJZPAzIDIDRurYL0vN3jlDrENenuNKyCvXgnDXadyjLmMQAAG6JIgcA4JQ4HA5lrPxImas/rbQtaNjlCrt0pkxmlo0EWrK24f564a5z1CEiwCWek1+iR95cq+370wzKDADgbihyAABOmsNuU9p3/1P2+q8qbQs5/3qFXjBNJpPJgMwANDWtgnw0+/+NUI+OwS7xwuIyzXrnd23YkWhMYgAAt0KRAwBwUuzFhUpa+Jxyt62otK3VmFsUcvZVFDgAuAj089TTt52lft3DXOKlZXY9++EmrdwcZ1BmAAB3QZEDAFBnZbkZSvjocRX+vdV1g8ms8MvvUtCgS4xJDECT5+vtoVm3DNPwMyJd4na7Q698ulWf/hgjh8NhUHYAgOaOIgcAoE5KUuN0+IOHVZIc6xI3WT0VcdX9CjjjfGMSA9BseFgtenDqIF00pGOlbQuW79arn21VaZm9ij0BAKiZ9cRdAAAoV3hgu5K/eEH24gKXuNk3UG0mPiTv9lEGZQagubFYzLrrmv7y9/XUklX7XLat3ByvtKxCPXzDYPn7ehqUIQCgOeJJDgBAreRuX63ET5+pVOCwhrRRuxuepcABoM5MJpNuuqy3Zow/Q+bjpvD5a1+a7n/9NyWl5xuTHACgWaLIAQCokcPhUOaaL5T69X8le5nLNq92UWo3/Tl5hEZWszcAnNhl53TVozcOlZen63LTh1LydP9/f1PMwQyDMgMANDcUOQAA1XLYypT27VvKXP1ppW1+PYcpcvIsWXwDDcgMgLsZ0ruNZt8xQiEBXi7xrLxiPfLmWq37K8GgzAAAzQlFDgBAlWz52Upc8JRy//y50ragoZep9YR/yuzhVcWeAHByunUI1kv3nKuObQJc4iVlds2ev0lLV+9j5RUAQI0ocgAAKilOitXheQ+qKG7ncVtMajX6JrUaNV0mEz9CANS/1iG+euHOc9S/R7hL3OGQ5n69U69/vk2lZTaDsgMANHV8QgUAuMjbtU4J8x9VWXaqS/zoErFBg8calBmAlsLPx0Ozbhmm0UM7Vdr208Y4PfzGWqVnFxqQGQCgqaPIAQCQJDkcdmWsWqCUL1+Wo7TYZZsloJXaTn1afj2HGpQdgJbGajHrzon9NO3SXpW2xcRl6h+vrFZ0bLoBmQEAmjKKHAAA2YsLlLzoeWWtXVxpm1f7KLW76Xl5te1mQGYAWjKTyaSJF/bQQ9MGV1p5JTO3WI++tVbf/37AmOQAAE2S1egEAADGKs1IUNKi51WadqjStoD+oxQ25haZrB4GZAYA5c7u11Ztw/3073kblZxR4IyX2Rx684s/tf9Qlm678gx5WC01HAUA0BLwJAcAtGAF+7fq8LyHKhc4zBa1GnOrwi6dSYEDQJPQpW2QXvnHeZUmJJWk5esP6pE31yojp8iAzAAATQlFDgBogRx2mzJWLVDSZ/+WvSjfZZvZN1CR1/9LQYMulslkMihDAKgswNdTT9wyTBPOrzx8bvfBTP3jlVXafSDDgMwAAE0FRQ4AaGHKcjOV+MmTR+bfcLhs82zdWe1ufF4+nfoYkxwAnIDFYtaNl/XW/VMGytPDdXhKRk6xHnpjjZas2ie73VHNEQAA7ow5OQCgBSmI/VOpX70mW352pW1+vYYrfNydMnt6G5AZANTNuWe2V/vWAfr3BxuVUmGeDpvdofe/2am/9qXpH5MGKNDP08AsAQCNjSc5AKAFcNhtyvh1oZIWPF25wGG2KHTUDWp95T8pcABoVrq2C9J/7jlXfbuFVdq2eVey7nn5F+38m2VmAaAlocgBAG6uLC9TiZ8+razfPtfxw1OsgWFqO+0ZBQ+9nPk3ADRLQf5eemrGcE28sLuOv42lZRfpkbfWatHPexi+AgAtBMNVAMCNFR7YrpSlr8qWn1Vpm2+3gQq//C5ZfAIaPzEAqEcWi1nTLj1dfU4L0ysL/lBWXrFzm93u0Pzvdmn7vjTdd/1ABQd4GZgpAKCh8SQHALghh61UGb98osQFT1UucJjMCr1gqiKueYgCBwC3MiCqtV775/lVDl/ZuidVd7/8i/7al2pAZgCAxkKRAwDcTElqvA7Pe1hZ676UHHaXbZaAULWd+rSCh4+XycSPAADuJzTQW0/ddpauH9NT5uOGr2TmFuux/63Th99Gq7TMZkyCAIAGxXAVAHATDoddOZu/V8bKj+UoK6m03afrmWp9xd2y+AYakB0ANB6L2aRJo6PUp2srvfTJZmXkHBu+4nBIX6zcq827knXf9QPUpW2QgZkCAOobf8YDADdQlpOupE+fVvqP71cucJgtCh05WW2ue4QCB4AW5YxuYXrtvpEa0LN1pW0HEnN036ur9cXKvbIxKSkAuA2KHADQzOXtXKND7/5DhbF/VdrmEdZe7W6creCzJjA8BUCLFBzgpVk3D9ON406X1eI6fqXM5tCH30br4TfWKCEtz6AMAQD1iU+8ANBM2QrzlLL0VaUsfUX2ovxK2wOHjFO7m16QV5uuBmQHAE2H2WzShJHd9Z97z1PnyMpPtO06kKG7X16l79fFyuHgqQ4AaM4ocgBAM5Qfs0GH3vmH8nb+VmmbJSBUba7/l8IuulFmD5ZKBICjurQN0n/uPVdXX9C90qSkxSU2vbn4Lz3x3nqlZxcakyAA4JQx8SgANCNleZlKXz5X+bt/r3K7X+8RChtzqyw+/o2cGQA0Dx5Wi24Ye7oGnx6hVz79Q0npBS7b/9idov/3wkpNH9dbo4d2kvn4aggAoEnjSQ4AaAYcDodytv2sQ2/fU2WBw+ztp9bj71XE+H9Q4ACAWji9Syv9958jdcnwzpW25ReV6Y0v/tTDb65RfHJu4ycHADhpPMkBAE1caWaSUr/7n4oObK9yu0/X/gofe7usgWGNnBkANG8+XlbdcXU/DendRq9/vtVlqVlJio4tn6vjmgu76+oLu8vDajEoUwBAbVHkAIAmymG3KXvDN8r8dWHlZWElmX0C1OqiG+Xf51yZTDxODQAna1CvCM25/wK9s3S7Vm055LKtzGbXgh9j9Ou2w7pzYn/17trKoCwBALVBkQMAmqCihH1K+/4dlSTtr3K7f+9z1OqiG2XxC2rkzADAPQX4euqf1w/UyIEd9OYXfyo5w3WujkMpeXrojTUaM6yTpo/rLX8fD4MyBQDUhCIHADQhtvxsZfzyiXL/XCmp8jKGlsAwhV8yQ77dBjZ+cgDQAgyIaq0594/UZz/GaMnq/bLbXe/Fy9cf1MadSbrpst46b0B7nqQDgCaGIgcANAEOu005W5Yr89fPZC/Kr6KHSYGDLlHo+dfL7OXT6PkBQEvi7WnV9HG9de6Z7fX6om3aF5/lsj0zt1gvL/hD3607oBnjz1C3DsGG5AkAqIwiBwAYrPDgTqX/+J5KUuKq3O4R1l7hY2+Xd/uejZwZALRsXdsF6aW7z9WyNX/r4+93qajE5rJ914EM3ffaal00pJOmXtJLwQFeBmUKADiKIgcAGKQsJ13pP3+o/Oi1VW43eXgr5JyJChoyViYLY78BwAgWs0lXnHuahveJ1Ftf/qXNu5Jdtjsc0o8bDmrtn4d13eieGjeii6wWs0HZAgAocgBAI7OXFit74zJlrf1SjtKiKvv49z5HoRdMlTWQWfwBoCloHeqrf908VJuik/XeVzuUmO46tDC/qExzv96h5esP6NbxZ2hAVGuDMgWAlo0iBwA0Eofdpty/flHm6oWy5WVU2cezdSe1GnOLfDqe3sjZAQBOxGQyaUjvNjozKlxLV+/X5yv2VBrCciglT7Pe+V2DT4/QDZeerk6RgQZlCwAtE0UOAGhgDodDBXs3K+OXj1WadqjKPmZvP4WcN0mBA0bLZLY0coYAgLrwsFo08cIeumBQB33wbbRWbal8b98UnazNu5I1cmAHTb64p1qH+BqQKQC0PBQ5AKABFR3eo4yf56soflc1PUwK6H+hQs+/Xha/oEbNDQBwaloF+eif1w/U2LO66O0lf2nfoWyX7Q6HtHJzvH7bdlhjz+6iiRf2UKCfp0HZAkDLQJEDABpASXqCMld9ovzd66vt49Olr0JHTpVXZNdGzAwAUN96dg7Vy/ecp583xWn+d7uUlVfssr20zK6lq/frxw0HNWFkN11xzmny9uJjOAA0BO6uAFCPSjOTlLX2S+VuXyXZbVX28YzootALpsi3a//GTA0A0IDMZpMuGtpJZ/drq6Wr92vp6n0qLHb9OVBQVKaPv9+tb9fEatLoKI0a0kkeVlZiAYD6RJEDAOpBeXFjsXL/WiU57FX2sQaFK+S8SfLvc45MJj7UAoA78vX20PVjeurSs7po4YoY/fD7AZXZHC59MnOL9ebiv7Ro5V5NvKC7Rg3pKA8r8zEBQH2gyAEAp6A0M0mZaxYrb/uqaosbZm9/BY+4SoEDL5bZylhsAGgJggO8dNuVfXXFuafp4+93a/XWypOTpmYW6s3Ff2nhij26amR3jR7WSV4eFDsA4FRQ5ACAk1Cb4obJ6qnAwZcq+KwJsnj7NWp+AICmoU0rP/3flIGaMLKbPvwuWn/sTqnUJz27SO8s3a5FP+/RhJHddfHwTvL25GM6AJwM7p4AUAclKQeVtf5r5e34tebixsCLFTTsCln9gxs3QQBAk9S1XZCevHW4/tqXqo+/361dBzIq9cnMLdbcr3do8cq9Gn/eabr07C7yYYJSAKgT7poAcAIOh0NFB3co6/evVPj31mr7UdwAAJxI327hev7OMG3fn6bPftyj7fvTKvXJyivWB99G64uVe3XJWZ01bkRXhQZ6G5AtADQ/FDkAoBoOu035u35X1vqvVJL0d7X9TFZPBQ66WEFDKW4AAE7MZDKpb7dw9e0Wrh3707Twpz3atje1Ur+8wlIt+nmvlqzap3PPbK8rz++mzpGBBmQMAM0HRQ4AOI69pFC5f65U9oZlKsuuPHb6KIobAIBT1ee0MPU5LUy7D2Tos59itKWKOTvKbA6t3ByvlZvjdWaPcI0/v5vO7BEuk8lkQMYA0LRR5ACAI0ozk5Tzx3Llblspe1Fetf3MPgEKHHSJggZeLItfUCNmCABwVz07h+qJW4drT1ymFv60Rxujk6rst3VPqrbuSVXnyEBdce5pOvfMdvJkRRYAcKLIAaBFc9htKty/TdlbflDh/q2SHNX2tYa0UdCQyxTQb6TMHl6NlyQAoMXo0TFEj988VPHJufrq1/1auTlepWWVJ7o+kJij1xZu1fvf7NTooR118fDOatOKlbwAgCIHgBbJVpCr3D9/Vs4fy1WWVf2QFEnyattdQcOvkF+PITKZ+WsZAKDhdYgI0J0T+2vKxb303bpYfbs2Vjn5JZX65RaUaPEv+/Tlqn06M6q1Lh3eWYNObyOLmaEsAFomihwAWgyHw6HihH3K+WO58qPXylFW+cNiRb7dBylo2BXy7tCLcc8AAEMEB3jp+jE9ddUF3fXL5ngtXb1Ph1PzK/VzOKQ/dqfoj90pCg/x0ZhhnTR6SCeFsCoLgBaGIgcAt1eWl6W8Hb8q96+VKk2Nr7Gv2dtPAX1HKnDgGHmEtm2kDAEAqJmXh0UXD++s0UM7afOuZH316379ta/y8rOSlJpZqI+/361Pl8doWJ9IjRrSUWf2CJfFYm7krAGg8VHkAOCWHLYyFezfqtw/V6pg3xbJbquxv2dEFwUOvFj+fc5hvg0AQJNlNps0pHcbDendRodScvX97wf088Y45ReVVeprszu09q8Erf0rQaGBXho5sIMuGNRBHduwDC0A90WRA4BbKUk7pNw/Vypv+2rZ8rNq7my2yr/XcAUOulhe7aIYkgIAaFbatw7QrVecoamX9NJvWw/ru3Wx2ncou8q+GTnFWvzLPi3+ZZ96dAzWhYM76tz+7eTv69nIWQNAw6LIAaDZK8tJU170WuXtXKOSpL9P2N8a3FoB/S5UQP9RsvoHN3yCAAA0IG9Pqy4a2kkXDe2kPXGZ+n7dAf269ZBKqliVRZL2xGVpT1yW3vtqh4b2bqPzB7TXgJ6t5WFlcm0AzR9FDgDNki0/W3m7fld+9BoVxe86YX+T1VN+vYYroN8F8u54ukwmxiUDANxPj44h6tExRDdf3lurtx7Wz5vitDc+q8q+pWV2rfkzQWv+TJCft1XDzojUuf3bq2/3MFmZvwNAM0WRA0CzYS8uUH7MBuXtXKPC2L8kR9V/oarIq12UAvqNlP/pZ8vs5dsIWQIAYDx/X0+NPbuLxp7dRQeTcrRyU7x+2RKvzNziKvvnF5Xp503x+nlTvAL9PHVW37Y6t387nd61FcvRAmhWKHIAaNLK8rJUsHeT8mM2qPDAdslWeWK141n8guV/xnkK6HeBPMPaN0KWAAA0XZ3aBOrGy3pr2qW99EdMin7eFK8NO5NUZqv6jwU5+SX64fcD+uH3AwoN9NJZZ7TVsDMi1btrK57wANDkUeQA0OSUZiUrP2aDCmI2qih+tyTHCfcxe/nKr+cw+fc+R96destkZlwxAAAVWSxmDT69jQaf3kY5+SX6bdth/bbtsHb+nV7tPhk5xVq2NlbL1sbK38dDg06P0LA+kRoQ1Vo+XvwqAaDp4c4EwHAOh10lSQdUsG+z8mM2qiQ5tlb7maye8u0xWP6nj5DvaWfKZPVo4EwBAHAPgX7HhrOkZRVqzZ8J+m3bIe2Jy6p2n7zCUq3ackirthySh9Ws/j3CNaxPpIac3kbBASy/DqBpoMgBwBD2onwVxP6lgn1/qHD/Hyde7vUos1W+XfvJv/c58u0xSGZPnwbNEwAAdxcW7KPx552m8eedpqT0fOcTHrEJOdXuU1pm16boZG2KTpbJJHXvEKyBPSM0sGdrdesQwjweAAxDkQNAo3A4HCpNjVPBvj9UsH9r+YootZg4VJJMHt7y7Xam/KKGyve0ATJ7+zVwtgAAtExtWvlp4oU9NPHCHopPztW67QlavyNJ+6pZoUWSHI5jy9J++mOMAnw9dWZUuAb2jNCAqNY85QGgUVHkANBgynLSVXjgLxUe2K7C2O2y5WXUel+zT4D8egyWb9RQ+XTpK7PVswEzBQAAx+sQEaBrI6J07agopWYWauPORK3fkaTt+9Nks1c/X1ZuQYl+3XpYv249LEnq1iFYA6Jaq2+3MPXsHCovD+bNAtBwKHIAqDe2wlwVHdx5pKjxl0ozEuq0vzWkjXy7DZBf1FB5d+jF5KEAADQR4SE+Gjuiq8aO6Kq8wlJt3pWs9TsS9cfuZBUW22rcd198lvbFZ+nzFXvkYTWrV+dQ9e0Wpr7dwtW9YzArtgCoVxQ5AJw0W0GOiuJ3qSh+lwoPRqsk6W/VZiWUo0wWD3l36i3fbgPke9qZ8ght23DJAgCAeuHv46HzB7TX+QPaq7TMpp1/p2vL7hRt2Z2i+OTcGvctLbPrr31p+mtfmqTd8vGyqHfXMJ1xWpj6nNZKXdsFUfQAcEoocgCotdLsFBXF7XIWNkrTDtX5GNagcPl2Gyjf0wbIu1NvmT29GyBTAADQGDysFvXv0Vr9e7TWzZdLKRkF2hKToj92J+vPvaknfMqjsNimzbuStXlXsiTJy9OiqI4h6tUlVL27tFJUpxD5erN6GoDao8gBoEqOslIVJ8eq+PAeFSXsVVH8btly0up8HLO3v7w79ZZP577y6XKGPELbymRixnUAANxR61BfXTK8sy4Z3lmlZXbtOpCuP3anaPv+NO2Lz1INU3lIkopLbBWe9JDMJqlLuyCd3qWVenUKVY9OIWod4sNnCQDVosgBQA6HQ2VZySo+vFdFCXtUfHivipNjJVtZnY9lsnrKu0Mv+XQ+Qz6dz5Bnmy7MrQEAQAvkYTWrb7dw9e0WLknKLyzVjv1pziLGgcTql6g9yu6Q9h/K1v5D2frmt78lScH+XureMVhRHUPUvWOIenQIlr8vE5QDKEeRA2hhHA6HyrJTVJz0t0oS/1ZxUqyKk/bLXnDiDxpVMXl4ybtdD3l3OF3eHXvJq30UK6EAAIBK/Hw8NLRPpIb2iZQkZeUWa/v+NP25N1XRsemKT86r1XGy8oq1KTpZm6KTnbF24X7q3jFE3doH67R2QeraLohhLkALRZEDcGMOu02lmUkqSYotL2oklRc17EW1+xBRFbNPgLw79CwvanToJa82XWSycCsBAAB1ExzgpXP6t9M5/dtJkrLzirX7QIaiYzMUHZuufYeyVGar3YTmh1PzdTg1X6u2HJsvLDLMT13bBem0dkE6rV2wurYLUnCAV4O8FwBNB7+ZAG7Clp+tkpSDKkmNU3HyQZWmHlRJarwcZSWncFSTPMLayattD3m36y7vDr3kEdZOJhOzngMAgPoV5O/l8qRHUUmZ9sZnKTo2XbtiM7QnLlO5BaW1Pl5iWr4S0/K19s9jS9qHBnqrU5sAdYoMVOfIQHWKDFSHiAB5eTC0FnAXFDmAZsZWkKOStEMqTTt07HvKQdnys0752GbfQHm36yGvtt3l1a67vCO7yeztd+pJAwAA1JG3p1VnnFa+vKxUPuQ2Kb1AMXGZ2huXqZi4TP19OFulZfZaHzMjp0gZOUXauifVGTObpMgwf3WKDFDnNoHq0CZAHVoHqG24nzysFD+A5oYiB9AEOew2leWkqTQ9QaXph1WSdlil6eVFjZOdO+N4Zp8AebXpKq/IrvJs01VebbrKGhzBbOUAAKBJMplMigzzU2SYn84f0F6SVFpm14HEbO05mKl9h7L19+FsHUzKke1Ey7hUYHdIh1PzdDg1T+v+SnTGzSYpopWfOrQOUPvW/uoQ4a/2EQFqH+7PRKdAE0aRAzCIw2GXLTdTpRkJKs1IPPaVmajSzKSTWtmkOha/YGchwyuy/LslMIyCBgAAaNY8rGZ17xCi7h1CnLHSMpsOJuVq/6Fs/X04S/sPZys2IUclpbY6HdvuODbkZWO067YAX0+1DS8vuLQN81fbMD+1DS9v+/kw4SlgJIocQAOylxSqLCtFpZnJKs1KVllWskozy7+XZaee4nwZlZmsnvIM7yDP1p2OfYV3lMUvqF7PAwAA0FR5WC3q1j5Y3doHS+okSbLZHUpIzdOBxBwdTMwp/56Uo6T0gpM6R25BiWIOlijmYGalbYF+nops5aeIUF9FtPJVRKif2hxphwX7yGphbjOgIVHkAE6Sw+GQvTBPZdmp5V855d9Ls1Nly0lTaXZqvQ0tqcRilWertvJo1V4eYe3lGd5Rnq07ySMkQiYzY0cBAAAqsphN6hARoA4RAc7VXCSpsLhM8cm5zuJHXFKu4lNylZ5ddNLnyskvUU5+iWLiKhdAzGaTwoJ91Ca0vOARHuKj1iG+Cj/SDgv2kbcnv6IBp4J/QUAVHA677AW5KstJV1luumy56UfaGeXt3HSV5WTIUXryPwBrw+zlK4/QtuWFjLAjBY2wduVzZ1DMAAAAOCU+Xlb16BiiHh1DXOIFRaU6lJKnQym5OpSSp/jkXMUn5ykxPV/2Osz3cTy73aGUjAKlZFT/BEmgn2d5wSPIR62CvNXK+f1Y29ebITFAdShyVGC327VkyRItXbpUMTExKigoUHh4uAYMGKDrrrtOgwcPPuVzREdH64MPPtCmTZuUmpoqf39/denSRePGjdPEiRPl6ckkRg3JYSuVLT9HtvwsleVlynbk61j7aDxLstffnBg1MVk95REaWV7MCI10aZt9A5k3AwAAoJH5entUWfwoLbMrJbNACal5SkzLV0JavhJS85SQlq/UzAKdQv3D6eiTIPsPZVfbx8fLqlZB3goJ8FZIoJdCA70VEuClkEBvhQZ4K/hIzN/Hg8+SaHEochyRm5urO+64Qxs3bnSJJyQkKCEhQd9++62mT5+uhx566KTPMW/ePL344ouy2Y5NepSZmanMzEz98ccf+vzzz/X222+rTZs2J32OlsZht8lemCdbYa5sBdmyF+TKVpAjW362bPlZshVkH2vn58helGdInhb/UFmDW8sjJELW4Ah5BEeUt4NayxIQIpOJsZkAAABNnYfVrHbh/moX7l9pW2mZXckZ5ROVJmcUKCm9QMkZx9qFxfX3B7TC4rIjT5rU/NnWajEpyN9LQf5eCvb3UpC/p4IDvBXs7+mMB/l7KtDPS4F+nvL2tFAUQbNHkUPlcyvce++9zgLHiBEjNGnSJIWFhWnXrl169913dfjwYc2bN0+hoaGaMWNGnc/xzTffaPbs2ZKk1q1ba+bMmerdu7cyMjL0+eef65dfftHu3bs1c+ZMLVy4UF5eXvX6Ht2BvbRY2Ru/VeH+P8oLGQU5shfmSaqHkvmpMJllCQiVR1C4rEHhsgaGuX4Pbi2zB/8/AQAA3JmH1az2rQPUvnVApW0Oh0O5BaVKzshXUnqBUjMLlJpZqNSswiPfC5RbUFrvOZXZHErPLqr1HCMeVrMC/TwV6OepoCOFjwA/T/n7eijA11MBvh7y9/VUoO+xmL+PhyxMpoomhCKHygsQa9askSRNmDBBzz33nHNb//79dckll2jy5Mnat2+f5syZo8svv7xOT1vk5eXp3//+t6TyAscXX3yhiIgI5/YLLrhAL7/8st555x3t2rVLH3/8sW6++eZ6enfuI2vtl8pa+0XjntRklsU/RNaAUFkDW8kS0ErWwFayBrSSJSBU1qAwWQNaMT8GAAAAqmUymZzFg4rL3VZUWFymtKxCpRwpgJQXJwqVnlOkjOwipWUVKq+w/gshFZWW2etUFDnKx8siP5/ygoefj0el734+HvL1ssrXx0N+3lb5envI19sqP28P+fp4yNNq5gkS1BuKHCofRiJJ/v7+evDBByttDw4O1pNPPqnJkyeruLhY8+fP1wMPPFDr43/55ZfKzCyfXfnuu+92KXAcde+99+qnn35SbGys5s2bpxtvvFFmMxXRikpSDtbfwUxmWfyCywsY/uXfy9shx9oBobL4B1PAAAAAQIPz8bI6V4CpTlFJmTJyyosQGdlFyswtVmZOkTJyi5SVU6yM3CJl5hQ1yFMhNSkstqmwuFBpWYUntb/VYpKPl1U+3uXFkPK21dn29fYoj3lZ5O1llbfnkbZn+fbyWPlrb0+LPD0sMpspmrRULb7IER8fr+joaEnSyJEjFRwcXGW/QYMGqUuXLoqNjdUPP/xQpyLH8uXLJUkeHh4aO3ZslX0sFosmTJigl19+Wampqdq8ebOGDBlStzfj5vz7nKOCvZuq3W7y8pXFN1AWn4Dy737BsvgFHflybZt9/JkHAwAAAM2Kt6dVbcP81Tas8pwgFZWW2ZSZW6zsvGJl55UoK7dIWXklys4rVlZusbLyjm4rVk5+icpsxg7/LrOVD+epz+KMl6dFXh4WeXta5OV5rAhyNO7pYZaXp1VeHpYKMYu8PMzydLbL+1V87WE1l38/0vawmCmoNDEtvsixZcsWZ3vYsGE19h0yZIhiY2N1+PBhxcXFqWPHjic8fllZmf78809JUr9+/eTr61tt34qrt6xbt44ix3H8Tz9bHqFtVZy4X2YvH1l8AmT2DSwvaPgGyGRhKS0AAADAw2pR6xBftQ6p/nePoxwOhwqLy5yrupR/lRc/svNKlFtQoryCUuf3nIIS5RWUqKjEdsJjG6m4xKbiEpty8hv+XFaLubwYYrXIw6O88OHpYZH1SBHEw1r++mhRxGo116pttRz5spplNZtcYxaTs22pou1hMcvbq2X+ut8y33UF+/btc7Y7d+5cY98OHTo423v37q1VkePgwYMqLS2t1fErHq9iXjjGq00XebXpYnQaAAAAgFswmUxH5sjwUJtWfrXer7TM5ix+5BeWKa+wRPmFpcorLK3ye0FRqQqKylRQVKb8olKVltkb8F01rjKbXWU2uwpUfyvo1IduHYL1wJRBigyr/f9Xd9DiixxJSUnOdtu2bWvsGxkZWeV+NUlOTq5y/6q0atVKnp6eKikpqfXxAQAAAKCxeVgtCgm0KCTQ+6T2Ly2zOQseBYVlKiwu/yooKj3y/cjr4jIVFpWpsKRMRcVlKiqxqbD4aLu8T1GJTQ6DF1xsivbFZ+nDb6P10A2DT9zZjbT4Ikd2draz7edXc4Wr4lCT3NzcWh0/KyvL2fb3r3ns3NFzlJSU1Pr4RyUkJCghIaFO+xwVExNzUvsBAAAAwMnwsFoU5G9RkL/XKR/LbneopNSmohKbikrKVHzke9GRISsV28WlNpWUHmtXjBWVlKmk1K6SsiN9Su0qObKtpNRm+NwlJ6PM5j5PzNRWiy9ylJSUONve3jVXIStur7hfbY/v5XXif8BH+9T2+EctXrxYc+bMqdM+AAAAANDcmc2m8hVWvKySTr1oUh2b3aHSUptKyuwqLbM5CyKlFb4Xl9lUWmZXaZldZRXaJUe+lx6JldnsVX8vs6vUVv69fBiMwzkcpjzmKN9us8t2ZHt1woK8NfWSXg3236OpavFFDovl2PKgJ1qb2VHhGajaLu9al+NXPAfrRAMAAABA02Exm2Txssq74eoodeZwOGSzO5wFEduRAojDIbUK8m6Rv1e2+CJHxSEoRUVF8vT0rLZvcXGxs11Tv5qOfyJHn+Co7fEBAAAAAC2TyWRyrrSCci2+yFFxHo7CwkIFBgZW27egoMDZDgoKOqnjn8jRcwQHB9fq+EddddVVGj58eJ32OSomJkZPPfXUSe0LAAAAAEBT0eKLHO3atXO2ExMTFRERUW3fxMREZ7umfjUdvybp6enOJzlat25dq+Mf1bZt2xOuDgMAAAAAgDtr8c+0dO/e3dmOi4ursW98fLyz3a1bt1odv3379s4hKxX3r0rF81fMCwAAAAAAnFiLL3L079/fORnL5s2ba+y7ceNGSVJkZKTat29fq+ObTCb169dPkrRt2zaVlpZW23fTpk3O9qBBg2p1fAAAAAAAUK7FFzkiIyPVv39/SdLy5cuVl5dXZb/NmzcrNjZWkjRmzJg6neOSSy6RVD7fxnfffVdlH5vNpsWLF0uSWrVqRZEDAAAAAIA6avFFDkmaOnWqJCkrK0uzZs2S3W532Z6dna1Zs2ZJkjw8PDRlypQ6Hf/SSy9VWFiYJOnFF1/UoUOHKvV57bXXdODAAUnStGnT5OHhUde3AQAAAABAi0aRQ9LYsWM1YsQISdKyZcs0depULV++XNu2bdPChQt15ZVXat++fZKku+66Sx06dHDZf8OGDYqKilJUVJSzYFJRQECAHn74YUlSamqqrr76as2bN09bt27VqlWrdMcdd+jtt9+WJPXs2VM33nhjQ75dAAAAAADcUotfXeWo1157TTNnztSmTZu0efPmKufnmD59umbMmHFSxx83bpxSU1P14osvKjMzU7Nnz67Up0ePHnrnnXfk5eV1UucAAAAAAKAlo8hxhL+/v+bPn6+lS5fq66+/1u7du5Wbm6uQkBCdeeaZmjx5soYNG3ZK57jxxhs1bNgwzZ8/Xxs2bFBqaqo8PDzUrVs3XXrppbr++uvl6elZT+8IAAAAAICWhSJHBWazWRMmTNCECRPqtN/QoUMVExNTq769evXSc889dzLpAQAAAACAGjAnBwAAAAAAcAsUOQAAAAAAgFugyAEAAAAAANwCRQ4AAAAAAOAWKHIAAAAAAAC3QJEDAAAAAAC4BYocAAAAAADALVDkAAAAAAAAboEiBwAAAAAAcAsUOQAAAAAAgFugyAEAAAAAANwCRQ4AAAAAAOAWrEYnAOMVFBS4vI6JiTEoEwAAAABAS3D8753H/156sihyQPHx8S6vn3rqKYMyAQAAAAC0RMf/XnqyGK4CAAAAAADcAkUOAAAAAADgFhiuAl1wwQUurzt27CgfHx+DsqleTEyMy1Caf/3rX4qKijIwI8AV1yiaOq5RNAdcp2jquEbR1DWXa7SwsFBxcXHO18f/XnqyKHJAkZGRmjx5stFp1FlUVJQGDRpkdBpAtbhG0dRxjaI54DpFU8c1iqaupV2jDFcBAAAAAABugSIHAAAAAABwCxQ5AAAAAACAW6DIAQAAAAAA3AJFDgAAAAAA4BYocgAAAAAAALdAkQMAAAAAALgFihwAAAAAAMAtUOQAAAAAAABugSIHAAAAAABwCxQ5AAAAAACAW6DIAQAAAAAA3AJFDgAAAAAA4BasRicA1Fbbtm115513urwGmhKuUTR1XKNoDrhO0dRxjaKpa+nXqMnhcDiMTgIAAAAAAOBUMVwFAAAAAAC4BYocAAAAAADALVDkAAAAAAAAboEiBwAAAAAAcAsUOQAAAAAAgFugyAEAAAAAANwCRQ4AAAAAAOAWrEYnAKSlpenTTz/VmjVrFBsbq4KCAvn7+6t79+668MILdc0118jX17fa/e12u5YsWaKlS5cqJiZGBQUFCg8P14ABA3Tddddp8ODBjfhu4I5O5RpdvXq1ZsyYUavzjBgxQnPnzq3P1NFCJCcn66OPPtLq1at16NAhSVJERIRGjBihiRMnKioqqsb9uY+ioZ3KNcp9FEbJycnR2LFjlZKSossuu0wvvfRStX25j8IItb1GW9p9lCIHDLVixQo99NBDys3NdYlnZmZq48aN2rhxo+bPn6833nhDvXr1qrR/bm6u7rjjDm3cuNElnpCQoISEBH377beaPn26HnrooQZ9H3Bfp3qN7t69u7FSRQu1YsUKPfjgg8rLy3OJx8bGKjY2Vp9++qlmzpypu+66q8r9uY+ioZ3qNcp9FEZ5+umnlZKScsJ+3EdhlNpeoy3tPkqRA4bZuHGj7r33XpWWlsrDw0PXXHONzj//fAUHBysxMVFLlizRL7/8osOHD+umm27Sl19+qcjISOf+DodD9957r/MHyogRIzRp0iSFhYVp165devfdd3X48GHNmzdPoaGhta5eAked6jUqSdHR0ZKksLAwvffeezWez9/fv8HeC9zT1q1bndeoxWLRNddco3PPPVf+/v6Kjo7Wu+++q7S0NM2ZM0d+fn666aabXPbnPoqGdqrXqMR9FMZYsWKFvv766xP24z4Ko9T2GpVa3n3U5HA4HEYngZbH4XBo3Lhx2rdvnzw8PDR37lwNHTq0Ur833nhD//3vfyVJ48aN08svv+zc9vXXX+v++++XJE2YMEHPPfecy75ZWVmaPHmy9u3bJy8vL/34449q06ZNA74ruJP6uEYlafTo0Tp48KDOPfdcvfvuu42SO1qOK6+80vnB5Y033tCoUaNctqenp+uKK65QamqqfH19tWrVKgUFBTm3cx9FQzvVa1TiPorGl5GRocsuu0xpaWnOWHVDAbiPwgh1uUallncfZeJRGGLbtm3at2+fJOm6666r8pdHSbrjjjvUo0cPSdKPP/6ogoIC57Z58+ZJKq82Pvjgg5X2DQ4O1pNPPilJKi4u1vz58+v1PcC91cc1mpeXp7i4OEnS6aef3sAZo6XZsWOH85fHMWPGVPrlUZJatWqlm2++WZJUUFCgVatWuWznPoqGVB/XKPdRGOHJJ59UWlqaQkNDT9iX+yiMUJdrtCXeRylywBCbNm1yti+88MJq+5lMJp199tmSpJKSEv3999+SpPj4eOcHp5EjRyo4OLjK/QcNGqQuXbpIkn744Yf6SB0txKleo1L5+MejD8tVNV8HcCpKSko0atQodezYURdddFG1/bp27epsJyYmOtvcR9HQTvUalbiPovF99913+uGHH2Q2m/XYY4/V2Jf7KIxQl2tUapn3UebkgCH69u2rmTNnKjk52XnTr07FEVXFxcWSpC1btjhjw4YNq3H/IUOGKDY2VocPH1ZcXJw6dux4CpmjpTjVa1Q6Nv5Rknr37l3/SaJFGzBggAYMGHDCfocPH3a2W7du7WxzH0VDO9VrVOI+isaVlpamp556SpI0ffp09evXr8b+3EfR2Op6jUot8z5KkQOGGDZs2Al/GBy1YcMGZ7tdu3aS5BxGIEmdO3eucf8OHTo423v37uWHCmrlVK9RSdq1a5ckKSAgQDabTc8995zWrFmj+Ph4Wa1WderUSRdeeKGmTZumwMDA+n0DgMrH7L7//vuSJF9fX40cOdK5jfsomoKarlGJ+yga16xZs5SZmakuXbro3nvvVWpqao39uY+isdX1GpVa5n2UIgeatNWrVzv/Yfbo0cM5UVNSUpKzT9u2bWs8RsXVLiruB9SH6q5R6VjlvLS0VOPGjVNpaalzW3FxsaKjoxUdHa2PP/5Yr7/+ugYPHty4ycMtFRcX69ChQ/r55581f/58paamymQy6fHHH1dISIizH/dRGKW216jEfRSNZ+nSpVqxYoXMZrOee+45eXl5nXAf7qNoTCdzjUot8z5KkQNNVkZGhmbNmuV8fXRiMknKzs52tv38/Go8jq+vr7Odm5tbjxmipavpGi0pKdH+/fslSUVFRQoICND06dM1dOhQBQYGKjY2VosXL9bGjRuVmZmpm2++WQsWLFCfPn0a/X3AfWzfvl1XX321S6xNmzZ64oknKv2FnPsojFCXa5T7KBpLcnKy/v3vf0sqHwJw5pln1mo/7qNoLCd7jbbU+yhFDjRJ+fn5uv32250TkA0ZMkSXX365c3tJSYmz7e3tXeOxKm6vuB9wKk50je7du9dZKe/cubPmzp2r9u3bO7f369dP48eP18svv6x33nlHxcXFeuCBB7Rs2TKZzcwJjZOTkJBQKZaamqqFCxcqPDzc5UML91EYoS7XKPdRNJbHHntMOTk56ty5s+65555a78d9FI3lZK/RlnofpciBJic3N1czZszQtm3bJJX/hec///mPyz80i8XibJtMphqPV3FSyOb8jxVNR22u0Z49e+qnn37SoUOH1LFjR5cfKBXdd9992rRpk7Zu3ar9+/dr1apVuuCCCxrjbcANde7cWW+//bZCQ0OVkpKib7/9Vt99951++eUXrV+/Xq+//rrOOeccSdxHYYy6XKPcR9EYFi1apF9//dU5BOBExYqKuI+iMZzKNdpS76P8C0OTkpKSoqlTp+qPP/6QJIWFhen9999XeHi4S7+Kj/wVFRXVeMyKq114enrWY7ZoiWp7jVosFnXs2FFnnXVWtT9QpPIPRddee63z9bp16xomcbQIUVFROv/889W3b1+NGjVKr7zyip599llJUmFhof7v//5PeXl5kriPwhh1uUa5j6KhJSQkaPbs2ZKkG264oVarAVXEfRQN7VSv0ZZ6H6XIgSZj9+7dmjhxonMSxzZt2mj+/Pk67bTTKvWtOO6xsLCwxuMWFBQ420FBQfWULVqiulyjdVFxzfKKSykC9eGqq67SmDFjJElZWVlavny5JO6jaDqqu0brgvso6srhcOjRRx9VXl6eOnfurHvvvbfOx+A+ioZUH9doXbjTfZThKmgSVq9erXvvvdf5A6Br16567733XJbjrKhiPDExUREREdUe++icCZJq7AfUpK7XaF0wThcNbfTo0c5fHI8W6biPoimp6hqtC+6jqKuFCxc6/1o9bdo0xcbGVuqTkpLibOfk5DivzbCwMIWHh3MfRYOqj2u0LtzpPkqRA4ZbsmSJHnvsMZWVlUmSBgwYoLfeekvBwcHV7tO9e3dnOy4uTv3796+2b3x8vLPdrVu3U84XLc/JXKPR0dE6dOiQ0tPTNX78ePn4+FTbNz093dkOCwurt7zh3nJzcxUXF6dDhw5p9OjRNY4Hr3itHp2AjPsoGtqpXqPcR9GQjs6rJUlPPfXUCfuvXr1aq1evliTdeeeduuuuu7iPokHVxzXaUu+jFDlgqC+//FKPPPKIczKmSy65RC+88MIJxyr2799fJpNJDodDmzdvdlnV4ngbN26UVL4+eU1j0YCqnOw1+u677+q7776TVD7R3vDhw6vtu2XLFme7b9++9ZA1WoKnnnpKX3/9tSRp6dKlLo+ZHi8uLs7ZbtOmjSTuo2h4p3qNch9FU8d9FE1dS72PMicHDLNp0yY99thjzl8ep0yZoldeeaVWkzFFRkY6q+XLly93TlJ2vM2bNzsf7To63heorVO5RocNG+ZsL126tNp+hYWF+uyzzyRJHh4eGj169KkljRZj8ODBzvYXX3xRbT+73e6yfcSIEZK4j6Lhneo1yn0UDWn27NmKiYmp8evnn3929r/sssuc8bvuuksS91E0rPq4RlvqfZQiBwyRl5en+++/XzabTVL5pGOPP/74CZffqmjq1KmSyicpmzVrlux2u8v27OxszZo1S1L5P9YpU6bUU/ZoCU71Gr300kudj19//fXXWrFiRaU+paWlevDBB52TO11//fV1Hj+JluvSSy9VSEiIpPJxu7///nulPg6HQ88++6x27twpSTr77LN1xhlnOLdzH0VDOtVrlPsomgPuo2jKWup91OSouGgz0Ej+97//6ZVXXpEkhYeHa86cOfLy8jrhfpGRkS7jdm+++WatWbNGkjRo0CBNmzZNERERiomJ0dtvv+38x3rffffptttuq/83ArdVH9fod999p/vuu08Oh0MWi0UTJ07U6NGj5e/vrz179mj+/Pnas2ePpPLHAufPn1/jWEngeMuXL9e9994ru90us9msiRMn6rzzzlNYWJhiY2P12WefaevWrZLKhwAsXLjQORTgKO6jaEineo1yH4WRDh06pAsvvFBS+V/JX3rppSr7cR+FUWpzjbbE+yhFDhji/PPPd5lluraee+45TZgwwfk6Ly9PM2fO1KZNm6rdZ/r06XrooYfq9JQIUF/X6NKlS/XEE0/UuLTciBEj9MorrygwMPCkckXLtmzZMj3++OMuyxMer0+fPnrttdeqHAfOfRQN7VSvUe6jMEptixzcR2GU2l6jLe0+ysSjaHQZGRkn9ctjVfz9/TV//nwtXbpUX3/9tXbv3q3c3FyFhITozDPP1OTJk13GogG1UZ/X6Pjx4zV06FB98sknWrNmjeLi4lRSUqKwsDD17dtXV1xxhfOHE3Ayxo0bp8GDB+uTTz7Rr7/+6rzGQkJC1LdvX40dO1YXX3yxzOaqR6hyH0VDO9VrlPsomjruo2jqWtp9lCc5AAAAAACAW2DiUQAAAAAA4BYocgAAAAAAALdAkQMAAAAAALgFihwAAAAAAMAtUOQAAAAAAABugSIHAAAAAABwCxQ5AAAAAACAW6DIAQAAAAAA3AJFDgAAAAAA4BYocgAAAAAAALdAkQMAAAAAALgFihwAAAAAAMAtUOQAAAAAAABugSIHAAAAAABwCxQ5AAAAAACAW6DIAQAAAAAA3AJFDgAAAAAA4BYocgAAAAAAALdAkQMAAAAAALgFihwAAADHefrppxUVFaUnn3zS6FRO2cyZMxUVFaX33nvP6FQAAGhwJofD4TA6CQAAgKbit99+06233qrAwEAtX75cISEhRqd0Sg4cOKBx48ZJkr744gv17NnT4IwAAGg4PMkBAABwREFBgR577DE5HA7NnDmz2Rc4JKlz586aNGmSSktL9fDDD8tmsxmdEgAADYYiBwAAwBFz5sxRUlKS2rRpoylTphidTr25/fbb5evrq+joaC1YsMDodAAAaDAUOQAAACQdOnRI8+fPlyTdeuut8vT0NDij+hMaGqrrr79ekvT6668rNzfX4IwAAGgYFDkAAECT8vnnnysqKkpRUVEaOHCgsrKyaux/4MABDRs2zLnP888/f1LnffPNN1VaWipfX1+NHz/+pI7RlE2aNEkmk0nZ2dn68MMPjU4HAIAGQZEDAAA0KVdddZW6dOkiScrLy9PcuXOr7ZuWlqZbbrlFmZmZkqRx48bpgQceqPM5U1JS9PXXX0uSLrnkEvn7+59wn+joaD311FMaO3as+vXrpz59+uj888/X3XffrV9++aXa/aZOnaqoqCjnZKCFhYX64IMPdPXVV2vw4MEaMGCAxo0bp//+97/O93XU8uXLdfPNN2vEiBHq06ePRo4cqYceekj79+8/Yb7t27fX8OHDJUnz589XUVHRCfcBAKC5ocgBAACaFIvFonvuucf5+uOPP1ZGRkalfvn5+ZoxY4bi4+MlSWeddZZmz54tk8lU53MuWrRIpaWlkuQsPlSnqKhIjzzyiK688kp98skn2rdvn4qKilRaWqrExEQtX75cM2fO1G233ab8/Pwaj7V//35deeWVeu6557R9+3bl5OQoPz9fe/fu1RtvvKFrr71WiYmJKiws1J133qm7775ba9asUWpqqkpLS5WQkKAlS5boqquu0u+//37C93n0vWVnZ+u7776r5X8dAACaD5aQBQAATY7D4dDVV1+tHTt2SJJuuukmPfjgg87tZWVlmjlzpn777TdJ0umnn66PPvqoVk9gVOWiiy5SXFycfH19tWHDhmrn47DZbLr11lu1du1aZ+zMM8/U4MGD5enpqV27dmnlypU6+vHq7LPP1ty5c10KL1OnTtXGjRsVEREhq9Wqw4cPKzQ0VKNHj1abNm0UFxenZcuWqaSkRJI0evRoORwO/fTTTwoICNDo0aPVsWNHJSYm6ttvv3XOr9G6dWv9/PPPNc4lkpycrHPPPVeSNGTIEH300Ucn9d8LAICmymp0AgAAAMczmUy67777dNNNN0mSFixYoJtuuknh4eGSpMcff9xZ4Gjfvr3efffdky5w7N27V3FxcZKkgQMH1lgk+OCDD5wFDl9fX7388su64IILXPps3bpVN910kwoKCrR27Vp98803uvzyyysdKzk5WZI0atQovfTSS/Lx8XFuu/zyyzV9+nRJ0o8//iipvJjy5ptvKjQ01NlvxowZuuaaa5SWlqaUlBT9+uuvGjVqVLX5R0RE6LTTTtP+/fu1ZcsWZWVlKTg4uIb/OgAANC8MVwEAAE3S2WefrWHDhkkqHyLyzjvvSJJeffVVffnll5LKVw2ZO3euwsLCTvo8GzZscLZ79uxZbT+73e4yP8js2bMrFTik8mLEY4895ny9cOHCao8ZGRmp//znPy4FDkkaPny4+vbt63zt4+Oj119/3aXAIUnt2rXT5MmTna+PPvlSk169ekkqfypl8+bNJ+wPAEBzQpEDAAA0Wf/85z+d7YULF2rOnDl66623JJU/SfH222+rc+fOp3SOv/76y9nu0aNHtf22bt2q9PR0Z78xY8ZU23fcuHHq1auXzjnnHJdixfGuu+46eXl5VbmtYsHlwgsvdD7FcryKOVc1d0lN/Su+dwAA3AHDVQAAQJPVt29fXXTRRfrpp59UXFys119/XZJktVr16quv1lhAqK3Y2Fhnu2vXrtX2qzgPx8iRI2s8ppeXl5YuXXrCc59xxhnVbmvVqpWzffrpp1fbz8/Pz9k+Oo9HTU477TRn+8CBAyfsDwBAc8KTHAAAoEn7xz/+IYvF4hJ75plndN5559XL8RMTE53toKCgavslJSU52926dauXc7du3brabRXfc2BgYLX9zOa6fZyr+B4TEhLqtC8AAE0dRQ4AANCk7dy5U3a73fm6V69euvLKK+vt+EdXJ5GkgICAavsdHaoi1VwMqQtvb+9a9Tu+yHMqKr7Hiu8dAAB3QJEDAAA0WWvXrtUjjzyiiive79q1S+vWrau3c1Qc4uHr61ttv7Kysno751EVl5ZtLBXfY2lpaaOfHwCAhkSRAwAANEnR0dG66667nL+I9+7d27nt5ZdfrrfzVHyaoqY5LSoOGcnJyam38ze24uJiZ7u6SU8BAGiuKHIAAIAmJz4+Xrfeeqvy8/MlSTfddJPmzZvnHGqxY8cOLV++vF7OVXHizqPnq0qHDh2c7b///vuEx507d66eeOIJvf/++0pJSTm1JOtRQUGBs+3v729gJgAA1D+KHAAAoEnJyMjQLbfcorS0NEnS2LFj9cADDygoKEjTp0939nv11Vdls9lO+Xzt27d3tpOTk6vtN2DAAGf7t99+O+FxFy5cqE8//VTPP/+8y5wiRqs40WrF9w4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" ] }, "metadata": { "image/png": { "height": 372, "width": 540 } }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "xx = np.linspace(20.0, 45.0, 100)\n", "XX = np.hstack([np.ones((xx.shape[0], 1)), xx[:, None]])\n", "predictions_xx = model.predict_proba(XX)\n", "ax.plot(xx, predictions_xx[:, 0], label='Probability of N')\n", "ax.plot(xx, predictions_xx[:, 1], label='Probability of E')\n", "ax.set_xlabel('$x$ (cm)')\n", "ax.set_ylabel('Probability')\n", "plt.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Questions\n", "\n", "+ What is the probability of explosition when the height becomes very small?\n", "+ What is the probability of explosition when the height becomes very large?\n", "+ At what height it is particularly difficult to predict what is going to happen?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Tags", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 4 }