{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Fisher Discriminant - Iris data set\n", "\n", "### Authors: \n", "- Christian Michelsen (Niels Bohr Institute)\n", "- Troels C. Petersen (Niels Bohr Institute)\n", "\n", "### Date: \n", "- 16-11-2018 (latest update)\n", "\n", "***\n", "\n", "Python macro for analysing the famous Anderson-Fisher Iris data set from Gaspe Peninsula. Edgar Anderson took 50 samples of three species (Setosa, Versicolor, and Virginica) of Iris at the Gaspe Peninsula, and measured four distinguishing features on each flower:\n", "\n", "- Sepal Length\n", "- Sepal Width\n", "- Petal Length\n", "- Petal Width\n", "\n", "Using these measurements, Ronald Fisher was able to make a classification scheme, for which he invented the Fisher Linear Discriminant.\n", "\n", "\n", "### References:\n", "- Glen Cowan, Statistical Data Analysis, pages 51-57\n", "- http://en.wikipedia.org/wiki/Iris_flower_data_set\n", "- http://en.wikipedia.org/wiki/Linear_discriminant_analysis\n", "\n", "***\n", "\n", "First, we import the modules we want to use:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# First, import the modules you want to use:\n", "import numpy as np # Matlab like syntax for linear algebra and functions\n", "import matplotlib.pyplot as plt # Plots and figures like you know them from Matlab\n", "from numpy.linalg import inv" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "r = np.random # Random generator\n", "r.seed(42) # Set a random seed (but a fixed one)\n", "save_plots = False # For now, don't save plots (once you trust your code, switch on)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Functions\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "def get_covariance_offdiag(X, Y):\n", " return np.cov(X, Y, ddof=1)[0, 1]\n", "\n", "\n", "def calc_separation(x, y):\n", " \n", " mean_x = np.mean(x)\n", " mean_y = np.mean(y)\n", " \n", " std_x = np.std(x, ddof=1)\n", " std_y = np.std(y, ddof=1)\n", " \n", " d = np.abs((mean_x - mean_y)) / np.sqrt(std_x**2 + std_y**2)\n", " \n", " return d" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Define parameters:\n", "\n", "Define path to datafile" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "filename = \"DataSet_AndersonFisherIris.txt\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set the variable and species names along with the number of variavles and number of species:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "var_name = [ \"Sepal Length\", \"Sepal Width\", \"Petal Length\", \"Petal Width\" ] #Variable name\n", "spec_name = [ \"Setosa\" , \"Versicolor\" , \"Virginica\" ] #Species name\n", "\n", "nvar = len(var_name) # Sepal Length, Sepal Width, Petal Length, Petal Width\n", "nspec = len(spec_name) # Setosa, Versicolor, Virginica" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set the range for the histograms to plot and the number of bins:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "xmin = [3.5, 1.7, 0.0, 0.0] #Range for different variables\n", "xmax = [8.5, 4.7, 7.5, 3.0]\n", "nbin = [ 25, 30, 25, 30] #Number of bins for different variables" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Set the colors and markers to use for each species:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "colors = ['Red', 'Green', 'Blue']\n", "markers = ['o', '^', 's']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Loop over and read data from input\n", "\n", "Now we open the file and save the data in the variable called `data`: " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Read data: 5.10 3.50 1.40 0.20 0 \n", "Read data: 4.90 3.00 1.40 0.20 0 \n", "Read data: 4.70 3.20 1.30 0.20 0 \n", "Read data: 4.60 3.10 1.50 0.20 0 \n", "Read data: 5.00 3.60 1.40 0.20 0 \n" ] } ], "source": [ "data = [] # Container for all variables\n", "with open(filename, 'r') as file:\n", " counter = 0\n", "\n", " for line in file:\n", "\n", " data.append(line.strip().split()) # Read line -> Convert to list\n", " for ivar in range(nvar): \n", " data[-1][ivar] = float(data[-1][ivar]) # First nvar values are floats\n", " \n", " data[-1][-1] = int(data[-1][4]) - 1 # Last one is an integer width species type: 1,2,3\n", " # Start counting at 0, to match your lists : 0,1,2\n", " #Print some numbers as a sanity check\n", " if counter < 5 : \n", " print(f\"Read data: {data[-1][0]:5.2f} {data[-1][1]:5.2f} {data[-1][2]:5.2f} {data[-1][3]:5.2f} {data[-1][4]:d} \")\n", " counter += 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we show the numpy version of the above cell:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "lines_to_next_cell": 2 }, "outputs": [], "source": [ "# Numpy version:\n", "data = np.loadtxt(filename)\n", "data[:, -1] -= 1 # Subtract one from all the last integers in the data:\n", " # Last one is an integer width species type: 1,2,3\n", " # Start counting at 0, to match your lists : 0,1,2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To introduce the notation that is very common in Machine Learning, we split the data up into the independent variable (input variables / features / columns) `X` and the dependent variable (output variable) `y`:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "# X is the independent variable / input variables / features / columns\n", "X = data[:, :-1]\n", "# y is the dependent variable / output variable \n", "y = data[:, -1].astype(int)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here the capital `X` refers to the fact that `X` is a matrix (2D-array) and `y` is a vector (1D-array)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Display data:\n", "\n", "Now we plot the data as histograms for each variable with each species colored according to: Setosa, Versicolor, and Virginica:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig_1D, ax_1D = plt.subplots(nrows=2, ncols=2, figsize=(10,8))\n", "ax_1D = ax_1D.flatten()\n", "\n", "mu = np.zeros((nspec, nvar))\n", "std = np.zeros((nspec, nvar))\n", "\n", "for ivar in range(nvar): # for each variable plot each species' corresponding histogram of that variable\n", " for ispec in range(nspec):\n", " \n", " data_spec = X[y == ispec] # extract the relevant species\n", " data_spec_var = data_spec[:, ivar] # extract the relevant variable\n", " \n", " ax_1D[ivar].hist(data_spec_var, nbin[ivar], range=(xmin[ivar], xmax[ivar]), histtype='step', color=colors[ispec], label=spec_name[ispec], lw=2)\n", " \n", " mu[ispec, ivar] = data_spec_var.mean()\n", " std[ispec, ivar] = data_spec_var.std(ddof=1)\n", " \n", " ax_1D[ivar].set(title=var_name[ivar], ylabel='Counts')\n", " ax_1D[ivar].legend()\n", " \n", "fig_1D.tight_layout()\n", "\n", "if save_plots:\n", " fig_1D.savefig('FisherInputHists.pdf', dpi=600)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below we plot the same data as 2D scatter plots:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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rPWSyg17GX5uQ2fWLl8eoR11KukB3q9dZNapE5IBKCSWq3VdLOZF0OfDvZubAV9x9abiAmc0F5gJM7dA5e4280Uz7Wrt2wfwfzOf2x25ncGiQ3u5ePnz6h7n1vbemeyGROsntza5BVWzXLhjYPcAbbn4De/fvZVzPOJ664imOnHDkqM/bCTT8T0QOqJRQotp9tZQTSdc73f2twNnA5WZ2ZriAuy919z5375s8eXLjI5RYSVKhD+we4I61dzA4NAjA4NAgd6y9oyT7oFKqiySz8IGF5DwHwJAPJUo4IwE1qkQaxMzGmtl/mdnjZrbezD4dUeYSM9uRn1S/1sw+3NAgoxJGVEoOEXVMWFcXnHAC9PQE44B6emD27NEnxEhyjHQ0d9+e//d54B7gjGwjan3hdNDP7BrgDV88vqpzJE2AEZWGPZxqufgmsGDIh7j6vquHU7vv2gXzvj+f3oUHwY1G78KDmP/9yzvmCbpIEkkeUEg8NapEGuc14N3u/hbgNOAsM5sZUe5b+Un1p7n7bQ2NMCphRKXkEOFjDj54ZJlcDlavhqGh4P3QUPB+tAkxKh3TYfQ0vpSZHWxmEwtfA38APJFtVK0t6rO08IGFbH5pc8NjKVj55Mrhm8CCwaFBVmxYMZzaXTeLIpXFPaBQb1UyiRpVZnaWmT1pZpvM7OqYMn9mZhvyT+D/Kd0wRVqfB17Ovx2TfzVffqv+/iChRC4X/JskUUTxMXv31nbdQkKMOOWSaAiQ7Kl+h3k98FMzexz4L+AH7v5vGcfUcsp9lgqNlfCNWCNtW7ANv8F5ZsEzvOF1b2DgqgGeWfAMQz5EznPcsfYOrll9TcXeLGkv7fCQae3AWsYsHMO659YlPmZg90DNn+m4BxTfe/J7VZ+rWKdkYqyYqMLMuoFbgfcA24CHzWylu28oKnMicA3wDnd/0cx+p14Bi7SyfH16BDgBuNXdH4oo9if5eR//D/hLd3864jzNO7G+0BtVi1oSYigBhsRw96eAt2QdRyuoNetX1JPtNNhBLwPVTd4v9Jgt/MlCHC+ZF7Jiw4rY3qxX97/Kwp8sVGKLNtMOD5Muuuci9uf2c+F3L+SJ+ck62YvrQbWf6W0LttUSZkWtlIlxNJL0VJ0BbHL3p9x9EPgmcG6ozEcIbhBfhOGx6yIS4u5D7n4aMAU4w8xOCRX5F2C6u58K3AvcGXOe5p1Y391d+7G1JMRotkalSAuqpZczPKSurBvLT6Aa+7fj4EZj3N+OZ2D3syOyoUU9fS/eVtxjtmztMpY9tqxkqF/OcwxcNYDf4MOvcG+WequkmawdWMv6HesBWL9jfaLequJ6oM904yVpVB0DFD8p35bfVuyNwBvN7EEz+7mZnZVWgCLtyN1fAu4Hzgptf8HdX8u/vQ14W6NjG7W5c2s7rpaEGJWOEZG6SbOXqlK2seKn71HbimMZHBpk39C+kuOjzqssZ9LMLrrnopL3F373worH6DOdrbQSVfQAJwLvAi4Avmpmh4YLmdlcM1tjZmt27NiR0qVFWoOZTS7UCzMbRzCk9pehMkcVvT0H2Ni4CPOSZNibP780k9/8+Qf2LV4MM2aUlp8xA2bNKt129NEHerW6u+Hii0fO3yq+zsUXw9vfXl0SjYTKjUGPGwve7mPDJRv1nHuQZK5FuEy5Y0bMv+iN6dYqbC+zP5xA4vFnH4/shSo8fS/pmXpsGXc8dqDHLOc5cpQ29sLzQpS4QppZcS9VQaXeKn2ms5ekUbUdOLbo/ZT8tmLbgJXuvs/df00wF+TE8ImaesiSSP0dBdxvZuuAh4F73f37ZnaTmZ2TL/PxfLKXx4GPA5c0NMIkGfbmz4clS0oz+S1ZcqBhNX8+bNhQet4NG+AnPynd9swzpee4887K11m9GubMqS6JRgJRT8ELko75brex4ZKNes49KPc5jytT7phCgojh12uTcIeTbz1lOG05Nxp88pDggE8eAjcar/vMYXR9upv53788SHN+Xen9wJAP0X93f2QvVOHpe7hnajBXOgSxt7uX+X3zS+Irni+iLGcHmNkyM3vezCIn7ZjZu8xsZ9FSH9c3OsZmU8sDimrO+7bjToAbfcTr9GlviD1m6usPZe+nXi0p/+qn9nDs7xxSduhsI7+/dpekUfUwcKKZHWdmvcD5wMpQmX8m6KXCzI4gGA74VIpxirQ8d1/n7qe7+6nufoq735Tffr27r8x/fY27n+zub3H333f3X5Y/a8qSZNhbujT62ML2uP3795e/drXXSYnGoEsniOvtCfdKFZd5/NnHq64bxU/Y4+Zavbj3xeFz3rPxnsgEEut3rI/shRocGhzZM0VuRAOpUsayemU5a1FfIzQUPcJ/FC31cVMDYmpqtTygqOa8udeik7REbS8cs//VcZHH7H91XNmhs7XGXs331w6ZGJOo2Khy9/3AR4EfEgxF+ra7rw89Xf8h8IKZbSCYJ/LX7v5CvYIWkTpJkmEvLrtfcY9SGtevdJ2UaAy6dIK43p5wr1Rxmf67+6uuG+F5IGFd1kVX/tZjyIf44zf/MX6DM69vHl3Wxfy++czrm0dvdy8Q3QsV1zN18uSTh88R7pkKG9HLFtGb1Snc/QHgt1nH0SqSPIir5WFdLcsTJD0mbuhsVGz1+P46ZbmPRHOq3H2Vu7/R3Y9390X5bcVP193dF7j7DHf/H+7+zXoGLSJ1kiTDXlx2v+L5UWlcv9J1UqAx6NIJoj7nhd6ecK9UcZn1O9ZXVTei5oGEFc93Kp4/FZe5L6oXKq5nqtC7pTpcF283s8fN7F/N7OS4Qp0wdz7Jg7haHtbVkvilmmOihs7WmsBFDyOjpZWoQkTaQZIMe3HZ/Qrb4/Z3Vfh1U+11UpDlvIpySS9E0hT1OS/u7Qn3SsWpVDfieqlOnnzycG9UoQeq+JzF147K3Bc1P6r4XIVeqsJ73eSl7lFgmru/BfgSwZSPSO0+dz7Jg7haHtZVtTxBjcdEDZ0Nx1av769TqFElIgf09wdzlspl2Fu8GObNK+2Zmjcv2A7wjncEGfuKRTWourrg8MNrv04KksyraLcx39Lc6jH3IOpzXtzbE+6VilNpztHG30QnKy1sj6tvxdeuNXNftb1qkpy773L3l/NfrwLG5OfPt624JAxJHsTV8rCumh6nwsO3oycdFSSm+LudiY6D6KGzQz7E1fdezfE3H881q6+Jjb3wM4krc/V9V3d84oqeykVEpKP091fOqrd4cXzj5tprRyalyEX8scjlYMIE+M1vartOCpLMnwiP+VZPktRTPeYYhD/n838wn9sfu72kgdPb3cuHT/8wnzrzU7zzjnfy4Ice5MgJR7J2YC3/87b/ySNzH+HU158aef6B3QO88453sn3Bdo6ccGTZOIqv3dvdy4mHncivfvurkli6rAs8aPgV4rr1vbcO709yA1q4ESw+TmpjZkcCz7m7m9kZBA/k23refPF8w+LPULkHcYVyScqERS5PMJhwHYVCubhjipYyyJEDDx0+NMiKjSt4df+rPPfyc7GxO87mlzbHllmxIThHJ9c7c/fKpeqgr6/P16xZk8m1RWplZo+4e1/WcRRrurrU1RXMQE3CLLrB1cTKNaqq+XWa1nlamepTNqZ8fgrbd4dXRoFjJh7DOSedw1ce+QqXve0ybn3vrZyy+BTW71jPyZNP5on5kRm3mf+D+SXHxBnYPcAbbn4De/fvrSrecT3jeOqKp4YbbHHxR30/nZJ4YjR1yczuIsjgfATwHHADMAbA3b9sZh8F5gH7gVeBBe7+n5XO26p1qfhzGv7sZalefzPC3+/PLv0ZM2+fWfL9u3vZn0mz/sxqVWt9Uk+ViKRr6tRgfaukZUWkoeIaGgO7Bzjui8cNJ4z4ozf90XDiicLCo5PHTy7pyQpnAbvu966LvZmK6mEK90RF9aKFe506paHUKO5+QYX9twC3NCiczEUlYWjnnpckWT8dL/sz6bSfWRzNqaqTE044ga6uruHXtcXr76Tgox/9KAcddFDi7Wk68cQD6zp/5zvfoatSAgJpLsuXw/TpQY/S9OmlC+5G7Z89O5gjZRb8W1jkN86iRdBbOhmdnh4YM6Z0WzgxRQPVa9HCcsknzGBSwtEc5c4xcWIuNvZJk0Z3XelsCx9YyL5ckCRicGiQP1vxZyX7L/zuhRXTsJebN5JkDqPWj5IsdVoShiTzE9NIbtEpdDdcB5/4xCf49a9/zXPPPUcul+M///M/OfPMM7MOKzWbNm3KOgSp1fLlQfa8LVuC8QJbtgTvCw2rqP2rV5euQbVkSeWGVXgsghl8+MPlE2A0UC2LMhbYQS/XfN3du2s+dNjLL3fFxh53/jSu28rMrNvMHjOz72cdSzNZO7CWMQvHsO65dQzsHmDZY8uGG0g5z/Hi3hdLyq/fsZ7bHrlteFHeqDTshRTp4UWFj7/5eNbMXVNxbSitHyVZyjIjbBaSzE+MS24R9WAlan8nUaOqDp588kl6enoopBOdOXMmf/iHfwjAwoUL6enpoauri97eXu69916A4fKFnq3rrrsOgOuuu47u7m66urro7u7mq1/9ak0xlbvu0UcfTXd3N2bGlVdeCcDWrVsZP348ZsbYsWPp7u7m05/+NEcffTQAXV1dHHzwwQC4O4ceeihdXV2MGTOG7dsrj3WXjFx7LezZU7ptz55ge9z+KEuXlr/GvtKUyOzbB6tWwebNwRyqzZsza1DVsihjsdzeCSMWMKzFaM6htXiqdgXB4vVS5KJ7LmJ/bv9wD1Shl6qcfX6gJysqDXth+FC4N6vWhxgijTSantLihxQA9/73vdinjR/9+keR76vWG5PFpndX5EOMuPfFor7fsLh14Qo/E/UuH6BGVR38/d//Pfv27cPMOOyww/jYxz4GwM6dO7nxxhv5yU9+Qi6XY9asWZx33nnDx+3bt49cLsfHPvYxFuWHRV144YXs3LmTXC7Hhz70IT7+8Y9XHU+l6w4NDTE0NMSFF17IrbcGY2D/8A//kIMOOgh35zOf+Qy5fDKBZ555BoBcLscrr7wyfI5rrrmGXC7HmDFj+MAHPlB1jNIgW7eW3x63P6zQc1XLNTLWLosWtnLsjWRmU4D3ArdlHUs9VTuktXih3vU71vOd9d+pauHRHLnINOzhRXiLF/bVgwBpdqPpKS1+SAHw5yv+HIDzvn1e5Ptq+WuTcId5359P16e7mf/9y4P3d19d9iFGuYcahe93Xt88uqxrxHpw5V6Fn4l6lw9Qo6oOjj/+eF555RUuv/xyJk6cyC233MKZZ57JHXfcQS6X43//7/9NV1cXP/zhD9lT1Ctw/vnnA/DFL34Rd2fdunX86le/4ogjjqCrq4vbb7+dvXury5oEVLzu+9//fgA+8pGPsD+fCvvXv/41F1wQzF298sorsQp5pD/xiU8AcOyxx7J58+aqY5QGiUsMUdieNHFEYe2oWq6RoXYa+93KsTfYF4C/AWJbDGY218zWmNmaHTt2NC6yFFXbGxReqHfIh0YszFtJFyNvwooX5Y2b9C7SbsIPKb7y8FeGh8++uPdFPvfTz5W8r7W3KjzSIvzQotL7qL8Xox29IQeoUVUn48aN45ZbbmHLli28733v46GHHiKXy9HV1UUulxt+7SsaJhVO+NDV1cVFF13ESSedRC6X41vf+lZNsVS67sT8qpJjx46t6fzFDa6uri6GyvViSLYWLQoSRBQrThgRtT/K3Lm1XyND7Tb2u5VjbwQzex/wvLs/Uq6cuy919z537ysM224l1d4UFd8AFry498WKw4DCcuS4e+PdI+LQorzSacIPKeavKp13/Der/6bkfa29VZUy9VV6H/X3ol1GbzQDNarq4Ktf/Spf+9rXht+vXbuWCRMmcMkll5DL5YZ7dXbu3MmXvvSl4XJ33XUXAAsWLMDMOOWUUxgcHGT69OkA/PVf/3VN8VS6bpTjjjuOb37zmwDccssthNcz27kz+Qre0kT6+4P5UHEJI/r74eKLD/REdXfDjBml7+fNg3e8Iz5D4MUXw9vf3jRJKYrVb+x3sklR+ecXwMhMfbVcKxx78fnjrtth3gGcY2abgW8C7zazb2QbUvqqvSkK3wAWvG7s64Z7mXq7e0t6oQrDg4p1WRd//OY/joxTG3EkAAAgAElEQVQjjm7apN1EPaTIxXeMA7X1ViV5aFHpffihRjuN3mgGalTVwbPPPsull16KmdHV1cWOHTv4wQ9+wGGHHcZnPvMZ/v7v/56uri5e97rX8U//9E/DxxUSSXzhC18YTsF+xRVXsHLlyqp6gAYHBzGz4ddnP/vZsteNsmrVKl599VXMjL/6q7/CzJg2bRoARx11FIceeuhwogppMf398Qkjli+HO+8szfa3eXOwzR327w8aVJUyBK5eDXPmZJ6UIqx+Y7/jW0XFySh2Fc0zLpeRr3ziCouNfdeukQkwwtftJO5+jbtPcffpwPnAj9w9ukXRomq5Kdr4m+icHcW9VeHz3PPLe0Y0mHKe4+5fHuipSjLpvVMnsEv7intIUcl53z5vRHKLcpI8tKgk/FCj3UZvZM3CPRCN0qorbddLT08P1113HTfccEPWoQDw6quvsnPnTo488ki+8Y1v8P73v58XXniBww47LOvQMjWaVevrJdW6NH169MK906YFjaNyZcK6u4NGWAeoZaX7SsfUcs5W08j6ZGbvAv7K3d9Xrlyr/W2KWiw3vKBu3HG3PXob+3L7GNM1hjce/kZ+9dtfxZ6n1utIY7T936Ym1n1Td82NnZMnn8z6Hes5efLJPDH/ibJlp3x+Ctt3jz678jETjxl+GBd3zuIynajW+tRTj2Ck9T399NO8+c1vHh72d9FFF3V8g6ojJMncl0aGQJEGc/cfAz/OOIzUlRvSGtfYKfRuFVKo78vtGzF8KXyeWq4j0gmGrh9iYPcAb7j5Dezdv5dxPeN46oqnOHLCkcNlovY/u/tZTl96OhAkt1j33DpOff2psdfZtmBbxetUq5MbTvWgRlWT2N9kT/Tf+MY3KuFEJ5o6NboXqjhzX1yZsHIZAkUkFbXcFC18YCFDudLf72O6xvCRt36ET535Kd55xzt58EMPltys6eZLJF7UvMbihw1R+3+y5Scl57jwuxdW7K2qdB3JluZUiTSImY01s/8ys8fNbL2ZfTqizEFm9i0z22RmD5nZ9FFddPny0oQSy5dHbytIkrlv0aJkDaaxY6OvUaVK6++Ex6SXKx9ODlHNa9Kk2uIvPY8nWksoaeKKpN9PNbFX8zOq9Wci2Vr55MoRC/3uy+3je09+Twv1ilSp0rzGqP23P3b7iN7hQm9VrdeR7KlRJdI4rwHvdve3AKcBZ5nZzFCZS4EX3f0E4B+Az9Z8teXLRyaU+OAH4UMfKt02d+6BRk+l7IAADz6YbGjfK69EX6NKlW7ywgsulitfLjlEJeWOTZ5dz1K4YT0woSrp91PN912vsjI61S7uW87DH3mYsT2lS2iM6xnHDy78wYjU7GleV6RZjeZzHpfs4er7rub4m4/nmtXXjNj/2tBrkecq/B2r5jp6ANI81KgSaRAPvJx/Oyb/CqccOBe4M//1CmCWVVp5Oc6110LRIs8A7NsHg6HsXHv2BGULymUHhKCRVa3wNRKqtP5OeMHF1U+tzmQRw3DWvXIKsVWjNJtfbR8HaW1p9iDF3ZxFrWmjnivpBKP5nMfNN1yxYQWbX9rMig0rEq8BF5eZs9x1lE2zeWhOlUgDmVk38AhwAnCruz8UKnIM8DSAu+83s53A4cBvQueZC8wFmFo836lY0oQS1Zatda5dNdfIqzR+PJzK9k+/86ctMd58yDVfUZILP1y47veuG9Xk9Libs+LhSINDgyx7bBlAatcVaUajrV9RCSR+dunPmHn7THKeI+c5Bq4aGHXd0bzG5peop8rMzjKzJ/PzPK4uU+5PzMzNrKnSeoo0C3cfcvfTgCnAGWZ2So3nWerufe7eN3ny5OhCcY2t0ZatNQFFNdeg8vjxqAUXy62z00ySPrUUgeoX960kar22eX3zhhf+LRgcGmQwN5jadUWaURr1K3yOqF5faX8VG1X5J+u3AmcDM4ALzGxGRLmJwBVA+Mm7iIS4+0vA/cBZoV3bgWMBzKwHOAR4oaaLRCWdGDMGekId1L29pYkoKpk7t/pYwskuEqg0fjzJgotp/zE7/ubjmTgxF5u0oTAuvxkpwURrKXyWHn/28YZMTo/qvcqRG66DzfyQQqRWaSR/iDrH+h3rW+IBn6QrSU/VGcAmd3/K3QeBbxLM+whbSDCpfm+K8Ym0DTObbGaH5r8eB7wH+GWo2Erg4vzX5wE/8lpX6I5KOvHhD49MLVft6RcvhnnzDvRYdXfDrFml15k3r3yyiwQqjR8vN/Y8qjyAHfRymdIV9O5m80ubefnl6F+bu3cfGJc/cqpcQdH23l2JLlsuCUbyBBml0km6Ufv1pbLCZ6n4iXdBPZ58h3uvonqu9MRd2k0ayR+izhGmutMZkjSqhud45G3LbxtmZm8FjnX3H6QYm0i7OQq438zWAQ8D97r7983sJjM7J1/mduBwM9sELABih9smEk46sWpVkKyi2L591SeRWLwY9u8PGmT798N995VeZ/Hi8skuEogaouQ3+PC48qHrh3hmwTPDWczG9Yxj7V+sLXk/cNVAyTj03N4JoaQP8MyuAcb+7Ti40Rj3t+MZ2P3siG1rBx5n7PW/U/EPZ2Fc/ri/PZiB3c9GXGf8gdhe2DMilqjXrjJtr3CCjPCrFpXOmTQ2qV3xHI/iJ94FjZicrknxncXMlpnZ82YWuVCSBW7OTwNZl7/vawnhzH7Fy3Ck8TmPOkfY4NAgd2+8e0SGwUpZB5V9s7WMOvufmXUBnweuSlB2rpmtMbM1O3bsGO2lRVqKu69z99Pd/VR3P8Xdb8pvv97dV+a/3uvuf+ruJ7j7Ge7+VKpBxCWLqCGJRDNIYxx71Hj6cuctp9y1054XI+2r+LPS293LyZNPHu416u3uZX7f/LpPWq/0UEPaztcYORy92NnAifnXXGBJA2JKRTizX/EyHGl8zgvnmNc3jy7rYn7f/Mhz/tGb/2hEhsFKWQeVfbO1JGlUDc/xyJuS31YwETgF+LGZbQZmAiujklUkmlwvIvUTlyyiyiQSzSCNcexR51i2dhnLHlsWe95yqln8UWPsJYrmZ0gW3P0B4LdlipwLfD2/NMjPgUPN7KjGRFe7cGa/+/77vpJlOMottjua64TrZ9T+Wo6R5pakUfUwcKKZHWdmvcD5BPM+AHD3ne5+hLtPd/fpwM+Bc9x9TV0iFpHaRSWvqCGJRDNIYxx71DkGhwbZN7Qv5ojkiq+tRRslKc3PkCZVcSoINN+IpPAIgT9b8Wcl+8sttjua6yQZqVDLMdLcLMkceDObA3wB6AaWufsiM7sJWFMYtlRU9sfAX1VqVPX19fmaNWp3SWsxs0fcvamWDKi6Li1fHsyh2ro16KFatKimOU9Z6xr7Mv7ahJE7enfBJw8Jvv67nTA4MtXdxInBfKApn5/C9t3bR+wvEXOOZJw3fPEE9uzbE/mU8ZiJx4wYZjKwe4B33vFOHvzQg6Ne12TSpPJJKYoVfibVnKfcMUm0RX1KWaLPJNGfHelcadQlM5sOfN/dRyz1YWbfBz7j7j/Nv18NfKLcvV7Wdal47ahyHr/scU59/ampXmdczzieuuIpjpxwZOT+sT1jcXdeG3ot8THF+6W+aq1PiRb/dfdVwKrQtutjyr6r2iBEpIH6+1uyERUW2aCC4QbQyZNPZn1MY6jQQCh3U3rK4lOCYSI1N6gAjM0vbeayt12WeBHi4jH0o124OKrBE07+WFCu8RW3L2mDLStmNhZ4ADiI4O/dCne/IduoykvaUCpMYE+j8S2SQKWpIE0nSa8vBL1VT8yPzM9R83WKF5+PGxERThJb6ZhmXtBeAqNOVCEi0ozCCwNXI2ph4VpVMx5eY+hT9xrwbnd/C3AacJaZzcw4plRoArs02ErgA/ksgDOBne4+kHVQ5STJygfJlueo9jrFGQQj14DzHDlGNrTKHaPsm80vUU+ViEgnSbKwcDWSPmGMGkOvp5K1y6/xVlicbEz+VWOy+eYRbnxf93vXqbdKRsXM7gLeBRxhZtuAGwjqC+7+ZYLRSnOATcAe4IPZRJpco4bHVrpOLXFoaG9rUk+ViEiRNHupCmrNRKjeqtEzs24zWws8T7A23EMRZZpqcn0lmsAuaXP3C9z9KHcf4+5T3P12d/9yvkFFPuvf5e5+vLv/DyUjExlJjSoRyUyzLGxYHEfavVQFtWQi1A3z6Ln7kLufRjAH5AwzGzEJv5WW+1DjW0SkOalRJSKZGc28kIkTY3b0Vp+OrjiOEePrazhflErj4Rs1hj7u5xb786zxmGbj7i8B91N+gdOmp8a3iEhz0pwqEcnEaOeF7NpVmsq2NN1sMG3Gbqw+ju0LtpfGEcoVF5c9L47fkGwKT6PG0NeSAn00adOzZGaTgX3u/pKZjQPeA3w247BGpVzjW/PvRESyo54qEclEGvNCmuUc0rSOAu43s3UEC9nf6+7fzzimUdm2YBt+g494aWK7iEi21KgSkYZLY15Is5xDmpe7r3P30939VHc/xd1vyjomERFpT2pUiUjDjWZeSCGpxDWrr4k8x9X3XZ04+UVUHK/e9CxHTTwSM0pek0azBnCLmzSJET+PTv+ZiIiIFFOjSkQabjRJGQpJJVZsWBF5jhUbVhQlv4ibz+SxcTAY3VLYvTv4t5rkDK2UyKGcwveedLuIiEinUaIKEWm4Wud/FCeVyHmOgasGSpJKFBJXFJJODOy+DnePSWYRHUel5BatmrRBRERE6kc9VSLSMiollYjar0QUIiIiUm9qVIlIS6iUVCJq/7LHlnHHY0pEISIiIvWlRpVIg5jZsWZ2v5ltMLP1ZnZFRJl3mdlOM1ubf12fRazVqCaJQSHJRC2NmrjkFoXEFFNffyh7P/Uq3OjDr73Xvcrehc+NOGY0vVVpJW1Q8gcREZH2oUaVSOPsB65y9xnATOByM5sRUe4/3P20/KvpU0BXk8SgkGSilkZNXHKLQmKK/a+Oiz4wlHiiUkKMuOQShe1pJW1opeQPlX4mIiIinU6NKpEGcfcBd380//VuYCNwTLZRNU5xkolahuBtW7CNZxY8w9iesQCM6xnH2r9Yy5APjejBCqtmodRdu8B95KuTE1ToZyIibWH5cpg+Hbq6gn+XL886ImkjalSJZMDMpgOnAw9F7H67mT1uZv9qZifHHD/XzNaY2ZodO3bUMdL0pJEwInyO/rv7KzaoREREWL4c5s6FLVuCp0JbtgTv1bCSlKhRJdJgZjYB+C5wpbuHn/U/Ckxz97cAXwL+Oeoc7r7U3fvcvW/y5Mn1DTgFlZJM1HqO9TvWj1xnSkREJOzaa2HPntJte/YE20VSoEaVSAOZ2RiCBtVyd787vN/dd7n7y/mvVwFjzOyIBoeZurgkE9X0VkWdQ0REJJGtW6vbLlIlNapEGsTMDLgd2Ojun48pc2S+HGZ2BkEdfaFxUVYvSRKDuCQT5RJGhEWdo0Rv9ASftJMp2EEvV7U9jpI/iIg00NSp1W0XqVJP1gGIdJB3AO8HfmFma/PbPglMBXD3LwPnAfPMbD/wKnC+u3sWwSZVSFYw/wfz+cojX+Gyt13Gre+9taRMucQQSRXOccriU1i/Yz0nTz6ZJ+Y/caDADaO+RCK5vRNi9sRtj6YkDyLSLMzsLOCLQDdwm7t/JrT/EuBzwPb8plvc/baGBjlaixYFc6iKhwCOHx9sF0lBop4qMzvLzJ40s01mdnXE/gX5tXfWmdlqM5uWfqgirc3df+ru5u6nFqVMX+XuX843qHD3W9z9ZHd/i7vPdPf/zDruJEab2S+ptQNrWb9jPQDrd6xn3XPr6nIdaQ9J1oYT6XRm1g3cCpwNzAAuiFnu41tFf7taq0EF0N8PS5fCtGnBooDTpgXvQRkBJRUVG1UJK9tjQJ+7nwqsAP5P2oGKSPNKI7NfEhfdc1HJ+wu/e2FdriNtI+nacCKd7Axgk7s/5e6DwDeBczOOqT76+2HzZsjlgn9BGQElNUl6qipWNne/390L/ak/B6akG6aINKs0MvslUdxLVaDeKimnJdaGq2XdHK21I+k6Bni66P02ouvJn+RHJK0ws2MbE1qdKSOgpChJoyppZSu4FPjXqB2tuLaOSNsb5Q1aXGa/q++9muNvPj61xlW4l6ogq96qgd0DqX5/Ul/l1obL7G9TLevmaK0dyca/ANPzI5LuBe6MKtRy93nKCCgpSjX7n5ldBPQRTGYcodXW1hFpeyncoMVl9luxcQWbX9qc2lDAjb/ZWNX2elv4wMJUvz+pnwprw2X3t6mWp+R6si7p2w4U9zxN4UBCCgDc/QV3fy3/9jbgbVEnarn7PGUElBQlaVRVrGwAZjYbuBY4p6jiiUgzS+EGbduCbfgNXvJ6ZsEzDPlQqokrhq4f4pkFzzC2ZywA43rGMXDVAEPXD4363NVqVGIOGb1Ka8Nlqpan5HqyLul7GDjRzI4zs17gfGBlcQEzO6ro7TkEQ2lbT3hkxpw50N1dWqa7u3xGwNmzg0QXhdfs2dVfVz3LbSlJoypJZTsd+ApBg+r59MMUkbqo0w1avRJXNCohRqvEIeUlWRsuU7U8Ja/1yfr8+dDTE9wE9vQE7yvRjWBHcPf9wEeBHxI0lr7t7uvN7CYzOydf7OP5DJqPAx8HLskm2lGIGpmxdCkMhR7MDQ3Bgw9Gn2P2bFi9unTb6tXlG1YastsxKjaqEla2zxEs0vIdM1trZitjTicizaQOQx/qlbiiUQkxWiUOSaSwNty783+b1prZnKyDGrZoUbBOTrFK6+bMiQk/bjsEDaglSw7cPA4NBe/LNax0I9hR8st7vNHdj3f3Rflt17v7yvzX1xQt9/H77v7LbCOuQdTIjHCDqqCQaj0s3KCqtD3uuhqy25YSzalKUNlmu/vri9YvOKf8GUWkKdRyU1dBXOKK0fbm1OO8kyaVjuIovCZNGlm2kJjimtXX1OX7k/TFrQ2XdVzD4tbN6e+PP2ZVTPhx2yH+BjFuO+hGUNpPNSMw4hpbaV5XQ3bbTqqJKkSkxdRyU1dBXOKK7z35vVGFWo/z7t6dfHshMcWKDSvq8v1JhwgPqbvjDti2LegN2rYtethR8RyOLVuiz1vuBi3uBrHcjaNuBKXdVDMCIzzPqh7XVTKMttOTdQAikrH+/lE1osK2LdiW2rkacd4kihNT5DzHwFUDHDnhyMzikRZVGFJX6AHasqW0kVQYlgeweHHwb9QcjiiHHRa/r7s7ugFV7sZx6tToBpxuBKVRli8Peka3bg0+d3PmBD2yhfeLFo382xU+prjMokXwwQ/Cvn0HypsFDzTC5s6NjmnWrOj6OGtW/PcRdd0xY0Y1IkSak3qqREQqUGIKqVlxz9TFF48cUhdlyZIDSSWSNKgAXnihNAlF8XXHjYs+Ju7GEYIbvt7e0m29vboRlMaImtO3ZEn5OX5J5gGalV4n/L6S++4b2YCaNSvYXs5orystQY0qEZEylJhCaha+yatmnkatczoKvV2XXHLgui+/XNu5wk/wo57oi9RD1Jy+sPAcv0rzAK+9FgZLh26TK50fO6zcfMP77gvqQuFVqUEVdd3BQc1PbENqVImIlFGvxBvSBiqlHE9yY1gv+/dXLrNkSfnYi4crQfBeN4LSCEnn7hWXqzQPUIkqpM7UqBKRjmUHRT/BL95er8Qb0uKSDDWKSyrRTOJi142gZCnp3L3icpUSQihRhdSZGlUi0rFyeyeUjOIovHJ7JwyX2bZgG36Dj3hlmThDmkDcUKOLLz7Q+9NKwkOpdCMoWYpa7iMsvPxHpSVCovb3xORrKzffsFp1WLpEmpMaVSIiItWK64UaGjrQ+9NqimPWjaA0UvGyAWbBUgPh5T6OPrr0mN7e4CFGIUHLgw+OfJhRXObii0cOaZ0wYeR5x40Lrl047+zZpcN8Z88+kEimkBhm/vyR2wrili6B8sOHpeWoUSUiItJuDj/8wE1c0qFMxeWibgQvvjjozdJNoKQpatmA1auDhtXmzUEyiRNOgGeeKS3z0ksH5j4VErRs2FC+TLhR9dJLI8/76qulx6xeXTrMd/XqkdddsmTktnDDqvC9bN4cbKs0fFhajhpVIiIi7WT8ePjiFw/cxMVlOAsLT84vvhFctAjuvFM3gZK+uGUDircnXVqgmZTLIFgpU6G0JDWqRBrEzI41s/vNbIOZrTezKyLKmJndbGabzGydmb01i1jTMLB7gONvPl6px6U9Je39Ofjg6nqK5s0LXtUcM2vWyKFFxYuiJp0HNW1a/D7dBIpUp1wGQSWCaUtqVIk0zn7gKnefAcwELjezGaEyZwMn5l9zgSWNDTE9Cx9YyOaXNiv1uLSP4hTqY8dWLj9+PHzlK0F6c3f4xjei5yl94xvB/v37YfHi4FU4ppzCMffdVzq0qLhBBbVN+g/TTaBIdco9GFEimLakRpVIg7j7gLs/mv96N7AROCZU7Fzg6x74OXComR3V4FBHrbBgbs5zWihX2kM4hforrwSNq678n9EkPUZxE9bDjaBicb1H5XqVwqKuO29edXHoJlDSVPyAorc3usysWdFft4pyGQSVCKYtqVElkgEzmw6cDjwU2nUM8HTR+22MbHhhZnPNbI2ZrdmxY0e9wqxZ8YK5WihXsmRmy8zseTN7YlQnihr+lsvBsceW7zEKLxAM5XuVwtK6+QpPlF+8OJs4RMIPKAYHg8Z9sVmzgvpUcN99IxtWRx99oDeo8FAjfJ5Kjj66coPNLEj8UngAMWtW6XXDQ3YL2xYvjj9nLQ9YpOnFJOgXkXoxswnAd4Er3X1XLedw96XAUoC+vr4KY4Qaq9BLVVgwd3BokDvW3sF1v3cdR044MuPopAN9DbgF+PqozlLL8LfCzWOhMVZI7gDJb54K5a69NrjW1KlBQ6bRN1/NEoe0vqgHFO5Bw6KQGS9KcSMryvTplYfMQtDo2b8//hzh5RDcg9Trv/lN+fOWa0RF6e9X/Wkz6qkSaSAzG0PQoFru7ndHFNkOHFv0fkp+W8so7qUqUG+VZMXdHwB+O+oT1TL8La3kDuFepqxuxJolDmlt9Zqfl/R4JZCQOlGjSqRBzMyA24GN7v75mGIrgQ/kswDOBHa6+0DDgkzByidXDvdSFQwODfK9J7+XUUQi5SUaTlvL8DfdoImMVK/5eUmPVwIJqRM1qkQa5x3A+4F3m9na/GuOmV1mZpfly6wCngI2AV8F5secq2ltW7ANv8FHvLYt2JZ1aCKR3H2pu/e5e9/kyZOjC9UyB0I3aNIizOwsM3syv5zH1RH7DzKzb+X3P5SfF1ybes3PS5LlEpRAQupGc6pEGsTdfwqUnUXr7g5c3piIRKQq1c6BWLSodE4V6AZNmo6ZdQO3Au8hSI70sJmtdPcNRcUuBV509xPM7Hzgs8Cf13TBes3PizrvCSfAj38cDPnr7g7qY6UEEvWITTqCGlUiIiL1oBs0aQ1nAJvc/SkAM/smwfIexY2qc4Eb81+vAG4xM8s/CKxevZI0pHFeJZCQGiUa/tfQbmEREZGUmNldwM+Ak8xsm5ld2tAAlNxBml+SpTyGy7j7fmAncHj4RM2+3IdIPVVsVBV1C58NzAAuMLMZoWLD3cLAPxB0C4uIiGTK3S9w96PcfYy7T3H327OOSaRdJZqfKNKmkvRUDXcLu/sgUOgWLnYucGf+6xXArHymMxERERFpXkmW8hguY2Y9wCHACw2JTqRFJJlTFdUt/LtxZdx9v5kVuoVLVkozs7lAIe3Ka6Ne4T49RxCKNUOKZaRmiQPgpKwDCHvkkUd+Y2ZbKpfMRDP931WiWOujXKzTGhlIEqpPqVGs9REX62jq0sPAiWZ2HEHj6XzgwlCZlcDFBENpzwN+VGk+lepSahRrfaT+t6mhiSrcfSmwFMDM1rh7XyOvH0exRGuWWJolDghiyTqGMHdv2jEWzfR/V4lirY9WihVUn9KiWOujHrHmH4Z/FPgh0A0sc/f1ZnYTsMbdVxKssfiPZraJYDHt8xOcV3UpBYq1PuoRa5JGVTXdwtvULSwiIiLSOtx9FcE6icXbri/6ei/wp42OS6SVJJlTNdwtbGa9BE8nVobKFLqFIWG3sIiIiIiISDuo2FNVr25h8sMAm4RiidYssTRLHNBcsbSCVvp5Kdb6aKVYm10r/SwVa320UqzNrJV+joq1PlKP1dShJCIiIiIiUrtEi/+KiIiIiIhINDWqRERERERERqHujSozO8vMnjSzTWZ2dcT+g8zsW/n9D5nZ9AxjWWBmG8xsnZmtNrO6raFSKZaicn9iZm5mdUlRmSQOM/uz/M9lvZn9Uz3iSBKLmU01s/vN7LH8/9GcOsWxzMyej1tHzQI35+NcZ2ZvrUccrc7MNpvZL8xsbTOmoi9mZoea2Qoz+6WZbTSzt2cdUxQzOyn/8yy8dpnZlVnHFcfM/jL/e+MJM7vLzMZmHVMrUl1Kn+pS51J9Sp/qU5671+1FkNjiv4E3AL3A48CMUJn5wJfzX58PfCvDWH4fGJ//el6WseTLTQQeAH4O9GX0MzkReAx4Xf7972T4/7MUmJf/egawuU6xnAm8FXgiZv8c4F8BA2YCD9UjjlZ/AZuBI7KOI2GsdwIfzn/dCxyadUwJYu4GngWmZR1LTHzHAL8GxuXffxu4JOu4WvGlulT3mFWXOuil+lT3mDu2PtW7p+oMYJO7P+Xug8A3gXNDZc7Nf2gAVgCzzMyyiMXd73f3Pfm3PydYk6sekvxcABYCnwX2ZhjHR4Bb3f1FAHd/PsNYHJiU//oQ4Jl6BOLuDxBksYxzLvB1D/wcONTMjqpHLFJ/ZnYIQUP6dgB3H3T3l7KNKpFZwH+7+5asAymjBxiXX79wPHWqs9IcVJfqSnWpw6g+1VVd6lO9G1XHAE8Xvd+W3xZZxt33AzuBwzOKpdilBL0R9VAxlvyQsmPd/Qd1iiFRHMAbgTea2YNm9nMzOyvDWG4ELjKzbQSLFH6sTrFUUu1nqVM58O9m9oiZzc06mGqI9scAACAASURBVDKOA3YAd+SHlt5mZgdnHVQC5wN3ZR1EHHffDvxfYCswAOx093/PNqqWpbpUX6pLnUX1qb46tj4pUUUEM7sI6AM+l9H1u4DPA1dlcf2QHoIhgO8CLgC+amaHZhTLBcDX3H0KwRC8f8z/rKQ5vdPd3wqcDVxuZmdmHVCMHoLhnkvc/XTgFSB2nmMzsGAh9nOA72QdSxwzex1Br+5xwNHAwfnfrVI91aU6UV3qSKpPddLp9aneN6TbgWOL3k/Jb4ssk++GOwR4IaNYMLPZwLXAOe7+Wh3iSBLLROAU4Mdmtplg3s5KSz9ZRZKfyTZgpbvvc/dfA/+PoJGVtiSxXEow9hV3/xkwFjiiDrFUkuiz1OnyT4MKQ0bvIRji2Yy2Advc/aH8+xUEf8ia2dnAo+7+XNaBlDEb+LW773D3fcDdwP/KOKaWpLpUV6pLHUb1qa46uj7Vu1H1MHCimR2Xb72eD6wMlVkJXJz/+jzgR56fOdboWMzsdOArBA2qes0dqhiLu+909yPcfbq7TyeY33WOu6edpSbJ/88/E/RSYWZHEAwHfCrlOJLGspVgrC5m9maCRtWOOsRSyUrgAxaYSdB1PJBBHE3LzA42s4mFr4E/ACKzKWbN3Z8Fnjazk/KbZgEbMgwpiQto4uEVeVuBmWY2Pj9PdhawMeOYWo7qUt2pLnUQ1ae66+j61JPGSeK4+34z+yjwQ4JsIMvcfb2Z3QSscfeVBBPw/tHMNhEkBzg/w1g+B0wAvpPPlbHV3c/JKJa6SxjHD4E/MLMNwBDw1+6eek9iwliuIhh++JcEY6IvqUcD3MzuImhIHpGfv3UDMCYf55cJ5nPNATYBe4APph1DG3g9cE++HvUA/+Tu/5ZtSGV9DFieb9A/RRP/n+ZvBN4D/EXWsZTj7g+Z2QrgUWA/QRbRpdlG1ZJUl+pEdakjqT7VieoTWH06hURERERERDqDJvmLiIiIiIiMghpVIiIiIiIio6BGlYiIiIiIyCioUSUiIiIiIjIKalSJiIiIiIiMghpVIiIiIiIio6BGlYiIiIiIyCioUSUiIiIiIjIKalSJiIiIiIiMghpVIiIiIiIio6BGlYiIiIiIyCioUSXSQGa2zMyeN7MnYvabmd1sZpvMbJ2ZvbXRMYqIiIhIddSoEmmsrwFnldl/NnBi/jUXWNKAmERERERkFNSoEmkgd38A+G2ZIucCX/fAz4FDzeyoxkQnIiIiIrVQo0qkuRwDPF30flt+m4iIiIg0qZ6sLnzEEUf49OnTs7q8SE0eeeSR37j75KzjMLO5BMMDOfjgg9/2pje9KeOIRKrXLPWpmP42SStSXRJJT631KbNG1fTp01mzZk1WlxepiZltqfMltgPHFr2fkt9Wwt2XAksB+vr6XHVJWlED6lPV9LdJWpHqkkh6aq1PqQ3/M7O/NLP1ZvaEmd1lZmPTOrdIB1kJfCCfBXAmsNPdB7IOSkRERETipdKoMrNjgI8Dfe5+CtANnJ/GuUXaiZndBfwMOMnMtpnZpWZ2mZldli+yCngK2AR8FZifUagiLc/MTjKztUWvXWZ2ZdZxiYhI+0lz+F8PMM7M9gHjgWdSPLdIW3D3Cyrsd+DyBoUj0tbc/UngNAAz6yYYSntPpkGJiEhbSqWnyt23A/8X2AoMEAxZ+vc0zi0iIpKCWcB/u3vTzT0REZHWl9bwv9cRrK9zHHA0cLCZXRRRbq6ZrTGzNTt27Ejj0tIiJk0Cs5GvSZOyjkxEOsT5wF1ZB1Ev+h0rtTKzY83sfjPbkJ8bf0VEmXeZ2c6iobTXZxGrxIuq/4VXtfT7pDZpJaqYDfza3Xe4+z7gbuB/hQu5+1J373P3vsmTmyrzp9TZ7t3VbRcRSYuZ9QLnAN+J2d/yD/z0O1ZGYT9wlbvPAGYCl5vZjIhy/+Hup+VfNzU2RGkk/T6pTVqNqq3ATDMbb2ZGMMxiY0rnFhERGY2zgUfd/bmonXrgJ53M3Qfc/dH817sJ7t+06LxIldKaU/UQsAJ4FPhF/rxL0zi3iIjIKF1AGw/9E0mLmU0HTgceitj9djN73Mz+1cxOjjm+5Xt9RWqV2jpV7n6Du7/J3U9x9/e7+2tpnVtERKQWZnYw8B6CYelSpNPnTXT69x9mZhOA7wJXuvuu0O5HgWnu/hbgS8A/R51Dvb7SyVJrVImIiDQbd3/F3Q93951Zx9JsOn3eRKd//8XMbAxBg2q5u494AOHuu9z95fzXq4AxZnZEg8Nsamk20tNu8OvhQWOoUSUNMXFiddtFRCS5Rv2OVe9O+8nPhb8d2Ojun48pc2S+HGZ2BsH94wuNi7L5pdlIb0SDv9y5dM9WmzQX/+0YkyZFfxgnToRd4Q7zGsrXeoyIiHSmRv1dUO9OW3oH8H7gF2a2Nr/tk8BUAHf/MnAeMM/M9gOvAufnF6uXJhH3v1FLSnXdZ9ZGjaoaVPtHpZY/Qu32h6vdvh8REZF24O4/Bcreerv7LcAtjYlIpDVp+J+IiIiIiMgoqFElIiLSgTp93kSnf/8iki41qkRERDrQrl3BPIzwS/MppNPVkpCl2kZ61PkLr3JqOUYaQ3OqREREJJGJE+OTKLUazfWVOLV8NvQwQtRTVYNqn0ZoiIF+BiIirSTuST2od0tEJIp6qmpQ7R8P/bHRz0BEpJWoF0dEpDrqqRIRERERERkFNapEREREREahluQW7aTTv39Qo6ppaQ6SiIjUU603Qc1641Tt96O/sxKnls9GmkNm0/wMNupzriHDmlPVEJMmxWdLiptrpDlIIiJST2neBDXDjVO134/+zkqcrD8baV4/6++lk6inqgHUehcRyYaZHWpmK8zsl2a20czennVMrUC9NSIi1VGjSqSBzOwsM3vSzDaZ2dUR+6ea2f1m9piZrTOzOVnEKdJGvgj8m7u/CXgLsDHjeFpC3MLAtYgblhf3aoahhCIi1VKjSqRBzKwbuBU4G5gBXGBmM0LFPgV8291PB84HFjc2SpH2YWaHAGcCtwO4+6C7v5RtVJ2n2lEZGsUhna6W+Y5KFJE9NaoypkrQUc4ANrn7U+4+CHwTODdUxoHC//4hwDMNjE+k3RwH7ADuyPf+3mZmB2cdlIhIObVMG8l6qokSv6hRlbmsK4E01DHA00Xvt+W3FbsRuMjMtgGrgI9FncjM5prZGjNbs2PHjnrEKtIOeoC3Akvyvb+vAFHDbjuyPrXbTVC7fT8irSRuyHAnJcpQo6oB9IteqnAB8DV3nwLMAf7RzEbUU3df6u597t43efLkhgcp0iK2Advc/aH8+xUEjawSrVSf0hzd0G43Qe32/YhIa1GjqgFq/UXfrONpNWSxZtuBY4veT8lvK3Yp8G0Ad/8ZMBY4oiHRibQZd38WeNrMTspvmgVsyDCkUdPoBhGR5qRGVYtphvG0+qNes4eBE83sODPrJUhEsTJUZivBjR9m9maCRlXnjEcSSd/HgOVmtg44Dfi7jOMRaSpmdmw+6+wGM1tvZldElDEzuzmfuXadmY3o8RXpdFr8V6RB3H2/mX0U+CHQDSxz9/VmdhOwxt1XAlcBXzWzvyRIWnGJe62JjEXE3f9/9u49PKry3hv+9zcTAgGCWKCKIEGsh6K1otlqXw89RPdW6qtXPbRo0N2n2myItrrx7cFNUSrleXef7trWCrSxQG1JPSHsZivdVlHLlqo1SEABaSkHjQxK1UIAISTze/5YM2EyWfeaWStr1loz8/1c11zJ3GvNve6E3Kx1n353G4DasMtBFGFdAO5Q1VdFpBrAGhF5WlUzR3UvA3BS6nUugAWpr0Vr2DD7zuDq6vCnjFZXmzuqRezPN30mqKUmUf59BoWNqpA5VRwqPaq6AlYAisy0uzK+3wjg/KDLRUTFz/SwZXqgsTs/83Nu702m63vBB7TgqGoCQCL1fYeIbIIVRCmzUXUlgF+lOvleSm2qPTr12aIU5Vk3butsR4f3feT8EuXfZ1A4/S9kfm6wSERElMnrA41fD0J+X7+cHtDCICLjAUwC8HLWoXyi1xKVNTaqiIiIigSjxlKhiMhQAI8DuF1VPY0Hluv2BEQAG1UlJajQ7QwRT0QUDs5uoEIQkQGwGlTNqrrM5pR8otcW1fYERH7zrVElIqeISFvGa6+I3O5X/pRb+ma7c28CE35yIhIduwqyRwf3AiEionyxwy3aREQALASwSVXvNZzWAuDGVBTA8wDsKeb1VF7ZbSeTfhH51qhS1c2qeqaqngngbAAHACz3K3/K35xVc7D979sx5w9zwi4KERGVOVNHnNOLAnU+gBsAfC6jY3yyiEwTkWmpc1YA2ApgC4AHADSGVNaS4WXWT5RnCkW5bEEpVPS/OgB/VdUdBcqfDBIdCSxuW4ykJrG4bTFmfXoWjh16bNjFIiKiAvI7nDIj05YPVX0BgONYSyrq3y3BlKg8eJndE+UZQVEuW1AKtaZqCoCHshO5gDF/Xlv8c1bNQVKTAIBu7eZoFRFRGXCalj1smP10pepq80iRn2u3TNcfNszf3wERUZh8H6kSkUoAVwC4M/uYqjYBaAKA2tpaDvA7cGrxm+fuKoD5qRfQmfruV0OT6OhgTBIionIUdnjysK9PRBSEQjxpXwbgVVV9pwB5kyP71ta+fWxQEREREYXBKcCFaRTX7fkUvkI8bV8Hm6l/RERERETkzO0oLkd9o8HXRpWIDAFwCQC7PQ7KXqIjgRPvOxG79u3KeS7noBMRUaFFNTw0I4kRUbHxtVGlqvtVdYSq7vEz31LhJtQ556ATEVG54n6IRFRsuNgmINmhzvMZrSIiov4Rke0i8lpq753WMMrg58wDbj5KRBRNbFQFxN9Q5wycSETkwmdTm9PXhnFxzjwgIip9bFQZ+NmzmB6l6uzuBAB0dnf2a7Squtp9lyR7N4mIiIi8c1rr5+d6P3Ne9p3qMnCffxcnz9ioMvCzZzFzlCqtP6NV7N0kIsqbAvi9iKwRkQa7E7gxPRHlw2mtn+lYrtf0JxoR+24cjU/cknPzbVWxTU8eHBr2r4bARlUgWja39IxSpXV2d+K3m38byPUZLYmIytgFqnoWrD0UbxGRi7JPUNUmVa1V1dpRo0YFX8IS5tSDz3sTlTuuty8tFWEXoBy0z2gP7FpqWG7FaX5EVI5U9e3U13dFZDmAcwCsCrdUpWnn3gQm3DcBB7sOoqqiCltv24pjhx7bczzRkcAFiy/A6q+s7pVOVK7s1tvP+/y8kEtFXnGkKiLc7GFFRES5icgQEalOfw/gHwG8HnQ5ymWkJldAJjfbihCVOr/X21P42KiKCN5siIh8dwyAF0RkHYA/AXhSVf876EL4uefSzr0JDPpeFTBbel5V3xuMREdhHsTcdPg5PSAmOhJYtHYRkprEorZFvfJjpyIVGz/+ZmuOORoHv/MhMFt7Xh9+5wDGfXR4QcrGelZ4bFQZBNmzaDen1hTJRQbuAyoNd2JTOkWGiFwqIptFZIuIfNtwzhdFZKOIbBCR3wRdRqJSoapbVfWTqddpqjo37DL1l9+Bj/K5Xr4dfk7lmrNqDg4nDwOwGlyZ+bFTkcLQn+c8P/5mD384yFV6vkxlYz0rPDaqDAqxm7upl8BuyoQeso/kooeGQg8Nsy1b9cBhxjDwTpFnKBgiEgcwD9aC+YkArhORiVnnnATgTgDnq+ppAG4PvKBEFFleAh957Qx0Gl2yYypXZj4AeuXHhfoUFq/PeVH+mzWVLcplLiVsVAXIrpfANKfWC24wGXnnANiS6j3vBPAwgCuzzvkqgHmq+gFgLa4PuIxEFGHtM9qhd2ufl1NAJNPDYy5Oo0t2ptdOR2W8EgBQGa9EY20j2me098onLZ1frnVYRFET5b9ZU9miXOZSwkZVQEy9BKapHFSSxgB4K+N9eyot08kAThaR1SLykohcapcR99UhKj5+rGnwc2N6GWjf4yYDO4yjS0OHJm0/M3Ro0rimavkby/vc55KaxNKNS3Mu1Oc6EIqSKAeXMJVt3a51kS1zqWGjKiCmXgLTVA4qWxUATgLwGQDXAXhARPqsWuW+OkTFx481DX7OSJj2+LcQ+268V9CL2HfjmP74t42jSzc+/DVMf6Kx12can7gFNzx8q3FN1RdO/ULPCFZaZbwSo4aMyrk+jOtACk9EFonIuyJiGxlTRD4jIntEpC31uivoMqb52amQ5qbh7rSmMVfZvHQQtCXaMGDOAKx/Z33OMpvKVr+sPtB1mOWMjSofmSqUiGLB5fPROesQMFvROesQ5l8+DyLaM5Vj54ydmHD0BCTuSEDvdp6XYboORd7bAI7PeD82lZapHUCLqh5W1W0A/gyrkUVERSyKaxpMI0jL3lhmPPbYxsewaO2iXukL1y7E8k3LjWuqTJ2Hm/62yXF9WBR/ZyXqlwBsZ0Vk+B9VPTP1uieAMtkqxDIHNw13pzWNucqWfZ18AmVMXT4VXckuXP/49TnL7LWekX/YqPKRuVKbWjxH0t1Uaq6RKlqvADhJRE4QkUoAUwC0ZJ3zn7BGqSAiI2FNB9waZCGJyH9Oaxr8nOLmJq8vnPoFxLIeA2KI4apTrzIe++iQj+JQ96Fe6Ye6D+Gqj19l20HYPqMd7TPabddbdd/V7bg+jOtAgqGqqwC8H3Y5wuC24e5lTaPpOnv3Ar/f8nSvUd+VW5/tCZTRlmjDht0bAAAbdm/oGa0yldlUtlz1jPzDRlUEsDeuPKhqF4BbATwFYBOAR1V1g4jcIyJXpE57CsB7IrIRwHMAvqGq74VTYiLyQ651GH5OcXOT1/JNy5FE1mgUkli2aZnx2MbdG23zWrppqfH6XtahRHntSpn6lIisE5HfichpppOKbb1vUA1303W+tPRLvc675tFrer6funxqr2Pp0Sp2NkRXWTWq3PTgFWLeruk6xw0b3bMB3IffOYDR1ceiutrfEOjmqYnB/JxkUdUVqnqyqp6Y3jNHVe9S1ZbU96qqM1R1oqp+QlUfDrfERNRfTusw/OxUc5vXFz5uv9bpqo9fZTw2fJD9xqSjBo9yHZDJ6WEw6P24yNGrAGpU9ZMAfgprRoWtYlrvG2TD3e46j7z2CD44+EGv8z44+AGe3fZsr1GqtA27N2Dl1pXsbIiwsmpU+THFzu+pd2Ffx6/ziYjIntM6DLe9zk7rMNzm5VQu07Hsh8C0TX/b5Dogk9OaDi+focJQ1b2qui/1/QoAA1LT04takA13u+vc+Nsbbc+95tFr+oxSpV372LXsbIgw0ZB2f62trdXW1tbArpfoSGDCfRNwsOsgqiqqsPW2rTh26LHG850CP5h+ZX4HiwjqOm6vX85EZI2q1oZdjkxB1yUiv5R7fcq8L6Xlc3/ymleiI4ELFl+A1V9ZnVf+bYk2TGqa1PN+3bR1GDV4lO11XrzpRZy38DxffhZyr791SUTGA3hCVU+3OXYsgHdUVUXkHABLYY1cOT4lFKIuxQbtgx4a2iddBu5D8mDfdCdj7x2LtzuyY0UBY6rHYO/sdtvO5epqa983u7pkKhsq9wL/dpSrssUk1qfx5GRM9RiukfKR1/pUNiNVpTQH1dRTCdj//yYD9xWsLERE5I2fPeX55OV27Zbdmg6GbS49IvIQgBcBnCIi7SJyk4hME5FpqVOuAfC6iKwDcB+AKbkaVIWSPDjUdlmE2wYV4Bx0wm0kv8yyTX+iEbHvxtH4xC1W+Q4Ng96tmF47HTGJobG2sdf1ThtlLVE7bdRpfYJLmD6Tnc4GVTSUZKMqe+1UqS143bvXtN5KfPvPhoiICsvPKW658srczHdR26KcG+ya1nQs3biUYZtLjKpep6qjVXWAqo5V1YWq+jNV/Vnq+P2qepqqflJVz1PVP4Zd5jA5rV00HTOlmyL8ecmLwleSjarsHgQueCUqDR/72McQi8V6XjNnzvQ1/1tvvRUDBw7skx6LxfD9738fALBv3z6ICOrq6nod/973vodrr70WJ598sm3ekpq3+9hjj+GSSy7pSb/oooswYsQIP38MKhJewzN7yStzM9/O7s6cI1imNR0fHfLRnp71tNNGncawzVQ2nGY+mY6Z0k0R/rzkReEruUaVXQveS2+gacqc01Q687Q8s3w2f/MDpwBSsfvWt76Fbdu24Z133kEymcQf//hHXHTRRYFc++ijj8ajjz4KAPjRj34EEcHatWsBANu2bYOq4o477sBjjz2GP//5z455/eEPf8CqVasKXmY6QkTiIrJWRJ4IsxymCLRe9qlyk1fmKBWAXqNVphGsTX/bZHvdjbs32o5gZfawE5Uy08wn06yodbvW2aY/89dnjHXJbV4crYqGkmtU2bXgvfQGOs3bNYUnB9yHQN+715p/WzlnIDBbUDlnIBqfuAWAv6HOTT8PUbHYvHkzKioqkA7Te9555+Gf/umfAABz5sxBRUUFYrEYKisr8fTTTwNAz/npka1Zs2YBAGbNmoV4PI5YLIZ4PI4HHnjA8dpnnXUWNm/eDAB4/PHH8Q//8A/Ys2cPAOAHP/gBKioqUFVV1WvU6ZFHHum5xvHHH9+T14IFC9DZ2YlYLIZPfOITAID9+/ejsrISIoLRo0f79SujI26DtTdcqExrmrzsU+Umr8xRqrT0aJVpBOtfzv4XVyHVM3vYicLUlmjDgDkD8m7ou+3UMM18crve8ItLv2ibP9cuFq+SalQFtXbKzzDopjIHFWqdqFj88Ic/xOHDhyEi+MhHPoKvfe1rAIA9e/Zg9uzZ+MMf/oBkMom6ujpcc82RDRQPHz6MZDKJr33ta5g7dy4A4Prrr8eePXuQTCbxla98BV//+tcdrz1t2jTs378fAPCXv/wFX/nKVxCLxfDnP/8Zv//9720bQjfeeCMuvPBCJJNJZO7XMn36dFRWViKZTOK1114DABw6dAivvvoqEokEdu3ahZaWlv79sqiHiIwF8HkAvwizHH6uj3Cb1/I3lvd5EEtqEo9tfMw4guUlpDpRFExdPhVdya68G/p2HRGm2UIycJ/rbQhM6w2d6pLbvLh2MRpKqlFVjGunTGUmot5OPPFE7N+/H7fccguqq6tx//3346KLLsLixYuRTCZx4YUXIhaL4amnnsKBAwd6PjdlyhQAwE9+8hOoKtavX4+//OUvGDlyJGKxGBYuXIiDBw+aLgsAuPrqqwEAzz77LD788EPcfPPNGDlyJH7wgx/grbfewmc/+9k+n+ns7MRvf2vd6Jqbmx3zP+qoo3D66afj2GOPxYABA/D888+7+dWQsx8D+CYAY3xiEWkQkVYRad29e3dBCuHn+gi3eX3hVPuNfD865KPGESzTDI/ptdNt85p29jQQhc0p8IMdU0eEKSBY8uBQ7JyxE4MqBgGwtg1I3JFA+4x2tM9ox++n/r5X/itvXInuu7ox/7L5vdKb/t8m6N1qm1f3Xd3G+se1i9FWUo2qqG4W6LRuylTmoAS1povID1VVVbj//vuxY8cOXH755Xj55ZeRTCYRi8WQTCZ7XocPH3lQjMV6/zcXi8UwdepUnHLKKUgmk3jkkUfyvvaMGTMwYMAAxONxnHvuuXjmmWfQ2dmJb3zjG7aficfjeeWdeZ6IoLMzuP8DSpmIXA7gXVVd43Seqjapaq2q1maOKvrFz/URXvJy6vW2G8Fa9sYy4/Wjep8lApwDP9jxs1MDAL609Eu9zr3mUWvWxK2/u7VX+rT/mub5+hRdvjWqRGS4iCwVkTdEZJOIfMqvvPO1d3Y7MFv7vPbODrYFnz0/d9XmNmC29Hm98Jf1eOWrr/T0UqRVVVQFVtZ0b8zOvQlM+MmJSHTsgqqVThQlDzzwAH75y1/2vG9ra8PQoUPx5S9/GclkEt/61rcAWNMBf/rTn/ac99BDDwEAZsyYARHB6aefjs7OTowfPx4AjA2ibCeeeCLWrVuHMWPGAABuueUWbN++vSfPbJWVlbjyyisBADfccENP+jHHHIPubo5GB+R8AFeIyHYADwP4nIgsCboQ/VkfkX0/8ZJX+4x2rG1Y2+vYumnrjOumrjr1KuPP4mfEQiI/mbYBMI1WeVky4vSZp//6dJ8pfR8c/AC3r7gdyayB8iSS+I/V/8GgEyXGz5GqnwD4b1U9FcAnEcKi4KisQ8qen2sKTeu0GDFoXhZKEwVp165duOmmmyAiiMVi2L17N5588kl85CMfwb//+7/jhz/8IWKxGI4++mj85je/6flcOoDFj3/8454Q7LfddhtaWloQi8XybuBcdZX1oJkOpZ4Oi37UUUfZnv+rX/0Kzz//PGKxGN55552e9K9//es9P0M6UAUVhqremdp3ZzyAKQCeVVX7/5ALqD/rI7L/b/aal10PPkedqJQ4PWvZyWfJSHbQC6fPZI9Spf3klZ/Ypn/jmW8U3ZIVciZ+bIotIkcBaAMwId9dtmtra7W1tbXf1+5dDvMxPyPdDRtm31CrrgY2v53AhPsm4GDXQVRVVGHrbVsx5t4xfSoOAMQkhtFDR+Ptjrf7ZjbbXGC/o/YlOvqW+dihx/p7kRIhImtUtTbscmQqRF0qFRUVFZg1axbuvvvusItCNoKsTyLyGQD/n6pe7nRelOpToiOBE35yAg51H8Kg+CBsu90K35/+/zot1//bbYk2TGqa1Cd93bR1OOOYMwpWfgoO701A/J648Vmr+66+nWdj7x1r+/w1pnpMz8jr6fNPx4bdG3DaqNPweuPrjp+xfZbzIPP6FA6v9anCp+ufAGA3gMUi8kkAawDcpqr7M08SkQYADQAwbtw4ny4dPKepcY1P9p0fa1eZe3+mEQvXLkRndycq45W4edLNmO/4CX/Zzemd9/l5AZaAiKiwVPV5AM+HXAxX5qyag8PdvcOdK9TYu236f9upB//1xtf9LTRRSHI9a2XL1XCxC3rRPqPdsSPabSc1O7VLi1/T/yoAnAVggapOArAfwLezTyr0YuCw+Tk/t7/lyHfPhaDC0BOFoauri6NUVJR6NuVNrcVIVjqlrgAAIABJREFUIolFaxdh+ablrqfsmcKd5xMG3cvGxESlwBT0wim4hNvAEwxUUVr8alS1A2hX1ZdT75fCamSVFS8h3QuxpsrN+qhiDENPRFTqMkep0jq7O3HVx69yHSjCFIY5n559rrelcmQKerFy60pjR7TbTmp2apceXxpVqroLwFsickoqqQ7ARj/ydkMG7nOV7jcvi379DqnudiNJLlQmInKv0CM4yzctt40YtmyTOdy53+XysjExUSkwTZm99rFrjR3Rbjup2aldevyM/vc1AM0ish7AmQD+t4955yV5cKhxs7ZCyL55vX2HfUj3t+9ohwj6vIYNM4en9crtUHKkw+M2NwPjxwOxmPU1xwaqRERBKfQIzhc+br9h71UfN4c797tcnJpEpcTU4ZAd4Q8wT4394OAHxo5ot53U7NQuPb5E//MiShGWvGp8shE/X/NzTDt7GuZ9fp5j9EET06/fSyTDzAWPaUW78LG5GWhoAA4cOJI2eDDQ1ATU14dWLEZYIvJPsdanIBaX5xOZrJDlKqn7SRko1roUpOxntrTsCH9EXuuTnyNVZSWK0yJKaih55szeDSrAep/aZ4iIKCxBjOB4mUXgZ7lK6n5CZc/0zGYX4Y/IKzaqPCr0TdXL+rCSGkp+80136UVCRC4Vkc0iskVE+kTIzDjvahFREYlUzyNRuYvq4nK/y1VS9xMqe6ZnNlOEPyIv2KgyGDas7xqo9DqoIMKgp9eH7dybwISfnIhEx66c68MivT4KcLdGyrSPWSH2Nwto7ZaIxAHMA3AZgIkArhORiTbnVQO4DcDL2ceIKFyFGMFxCi6Rb+AJv8sV+fsJUZ5Mz2zP/PUZ2wh/HK0ir9ioMujoMKcHGQa9ZMLZptdI7dhhLQrbscN6b2rAzJ1rraHKNHiwlR5mufrnHABbVHWrqnYCeBjAlTbnzQHwfQAHbY4RUYgKMYLj9P98vvcAjixRf4jIIhF5V0RsFxWJ5b7ULIv1IuLbtjleIla66YgwPbN9cekXbfPOHK0yXYf7t5EdNqo8MIdBNwX9sE+vrra+mub6RnHdlmdu10jV11tBKWpqrCHCmprCBKkIdu3WGABvZbxvT6X1SN2ojlfVJ50yEpEGEWkVkdbdu3f7X1IisuX3CI7T//Nu7gEcWaJ++iWASx2OXwbgpNSrAcACvy7spfPYTUeE6Zntg4Mf2OadGfmv5Du8yVdsVHnQPqMd02un94S7rYxXorG2EapiO2Wvuto5LKBpru+cVXPQnbRGwLqSXcVdeb2skaqvB7ZvB5JJ62shov5FaO2WiMQA3AvgjlznqmqTqtaqau2oUaMKXzgiKgin9bkMaU5BUdVVAN53OOVKAL9Sy0sAhovI6P5e10vnsduOiPYZ7VjbsLZXHuumrbPthMjcFLssOrzJV2xUeZBrQXB2D4bTVEJTXut2rcPitsU4nDwMADicPFzclTfINVJuBFuutwEcn/F+bCotrRrA6QCeF5HtAM4D0MJgFUSlyeleEtWAGFS2cs60ANzPovDSceClI8JLQAqnDm92dpAdNqo8cFoQ7LYHw5RX/bL6nlGqtKIerQpqjZRbwZbrFQAnicgJIlIJYAqAlvRBVd2jqiNVdbyqjgfwEoArVDU6G30QkW+c7iUMaU7FyM0sCi8dB146IrwEpMjV4c3ODrLDRpVBer2TXbrTgmC3PRimvDb9bVPPKFXa4eTh4l10HNQaqQiXS1W7ANwK4CkAmwA8qqobROQeEbnC9wsSlTkRGSQifxKRdSKyQUS+G3aZMjndS3IFnuBCeQpYrpkWrnnpOPDSEZFPQIp8r1O/rJ6dHWQkqqbgCoUVxk7biY4ELlh8AVZ/ZXWfHeHbEm34h1/8A9Y0rMEZx5yR127y2fmZPvPhd7ICIWTYudf+My1TWnDJkkv6nL9u2jqcccwZnn8HrjQ3WwEb3nzTmg43d274jaBcClxm7lpP5J9C1ycREQBDVHWfiAwA8AKA21JrQmwVS31qfLIRP1/zc0w7exrmfX5e2MWhkPlRl0RkPIAnVPV0m2Ofh9UpOBnAuQDuU9VznPLLVZfG3jsWb3f0bZeNqR5jDLDi9BkAtsdMYhLrWT+V73ViEuvTqMpVZio+XutTRSEKE1WZa52yb0JTl09FV7IL1z9+PV5vfN2xNyT92ez8vIRa99Kz8nqjbcRTf6VDjacj46VDjQPRbVgVY5mJqGDU6jVM75g+IPUKpyfRR9nTzGd9elafjkIiN0TkIQCfATBSRNoB3A2rvkBVfwZgBawG1RYABwD8r/5e00sjJKiGCxtI5EXZTP9zWuvUlmjrmW+bnmebz9SL7PxMn5GB+2DHaSphPqE+CyrYUOP+KMYyE1FBiUhcRNoAvAvgaVXts6l2sW1RwIXy5DdVvU5VR6vqAFUdq6oLVfVnqQYVUlH/blHVE1X1E1zrS9RX2TSqnG5CdlFhTGHT070XdvmZ9glJHhwKVfR57d1r3lsk/do5YycmHD0BiTsSvUJ9+qqxEaiosNYUVVRY772GGm9uBsaPB2Ix62s+m+jaXd+LCIVHJ6JoUNVuVT0T1hqQc0Skz9SmYtqigFEBiYiiqSwaVU43ocxRqrQNuzdg5daVkQh1W/AN5hobgQULgO5UY62723o/ZIj9+U6hxtPT73bssFqN6el3Tg0r0/W9NKyiGradiEKnqn8H8BycNziNPEYFJCKKprJoVDndhLJHqdKufeza0EPdBrLBXFOTffr+/e5DjXuZfme6vindSVTDthNRKERklIgMT31fBeASAG+EW6r+yTU1nYiIwlEWgSqcbkKJfQnbz9itacq8cZny8zMKk90UQ9+jPHUbphOqWg0bN5H0vEy/M13flO4kXbZii1hIRIUyGsCDIhKH1Yn4qKo+EXKZ+oUL6ImIoqksGlXFeBMyTTH0PcpTPG7fgInHrcaImwbJuHHWlD+7dC/X98JtmYmoZKnqegCTwi4HERGVvrKY/leMAps3nw45nm+6k8mT3aX7fX0iIiIiohCwURVRgc2bnz8fmD79yMhQPG69nz/ffV4rVrhL9/v6REREREQhKIvpf8Uo0CmL8+f704jxGtLcr+sTEREREYWAI1UFkOhI4MT7TiyefUNMe0u53XMqyJDmXvbDIiIiIiIqADaqCqDge0v5ybS3VGOj+z2nggpp7mU/LCIiIiKiAmGjymeB7C3lJ9PeUk1N7vecqq+3PldTA4hYX5ua/I/G52U/LCIiIiKiAmGjKge3U/ns9paKDLspc6b1TqZ9onKtj3Jy8cVWYyv9uvhib/l4XbtFRERERFQAbFTl4GYqn2lvqUiMVpmmzGVP18tlyBD312huthpQK1f2Pn/lSm8NqyDXbhERERGVKq5R9w0bVQ7cTuULbG8pL0xT5j780F0++/e7v8bMmX0bVGmmdCdBrd0iIiIiKlVco+4rXxtVIrJdRF4TkTYRafUz7zC4ncoX2N5SXpimxiWT9ukmqu6v4fe0vKDWbhERERGVKq5R91UhRqo+q6pnqmqtH5n5GZ7cTV5epvK1z2iH3q19Xp73nPIyJGv6jGlqXHrT3Xylz7e7TpDT8urrge3brUbh9u1sUBERERG5wTXqvor89D8/w5O7ySv0qXxehmSdPjN5sv1njjnGPr2qyj79lFPM15k82Twtr67OPj9TOhEREREVDteo+8rvRpUC+L2IrBGRhv5m5md4crd5hT6Vz8uQrNNnVqyw/8zOnfbpprVWmzebr7NihXla3jPP9G1A1dVZ6UREREQULK5R95XfjaoLVPUsAJcBuEVELso8KCINItIqIq27d+/OmZmf4clz5ZU9NXDv7HZgtvZ57Z3tcSqfW7mGZBsbgYoKq/FSUWG9d/qMX0O53d3O13GalvfMM9bIVvpVhg0qEblURDaLyBYR+bbN8RkislFE1ovIShGpCaOcRKVARI4XkedSdWqDiNwWdpmIoiiPe9OXRWR3as18m4jcHEY5KQe3y0a4Rt1XvjaqVPXt1Nd3ASwHcE7W8SZVrVXV2lGjRjnm5Wd48nzyyp4a2NFhn5cp3Xcf+Yg5vbERWLDgyF5S3d3We1O483Hj/BvKjcedy0ZGIhIHMA9Wp8NEANeJyMSs09YCqFXVMwAsBfB/gi0lUUnpAnCHqk4EcB6szr7sOkdU1vK8NwHAI6k182eq6i8CLSTl5jWSH9eo+8a3RpWIDBGR6vT3AP4RwOte8/NzTVOuvPycZhiIpib79P37zcO4piFe05qmiYbnjoZ+z+osZ+cA2KKqW1W1E8DDAK7MPEFVn1PV9NzKlwCMDbiMRCVDVROq+mrq+w4AmwCMCbdUlLcg9s/hHj1AHvcmKgKM5Bc6P0eqjgHwgoisA/AnAE+q6n97zczPNU258vJzmqFv3n/fnJ4eocqmah7GNQ3xPvMMMH36kah+8bj1fsMG+/T5853LRk7GAHgr4307nB/wbgLwO7sDbqfSEpU7ERkPYBKAl22OsT5FTRD753CPnrR8701Xp6amLxWR4+0yYl0KESP5hU7Uad+hAqqtrdXW1vC3skp0JDDhvgk42HWwJ62qogoffueA8TOB/MrGj7f+g89WUwO0t9s3rOJxoKvL/bUaG60GVne3lUdDg9V48lK27dvdX7+IiMgar9sFiMg1AC5V1ZtT728AcK6q3mpz7lQAtwL4tKoecso3KnWJyK3+1CeX1xkK4A8A5qrqMqdzWZ8iIoj7TAndywp9bxKREQD2qeohEfkXAF9S1c855cu6FLAS+nsOm9f6FPmQ6oVmmhoYuo99zJz+mc/YHzOlOzGtz2psNH+G0WK8ehtAZu/e2FRaLyJyMYCZAK7I1aAiImciMgDA4wCaczWoKEKC6HVnz35aznuTqr6XcT/6BYCzAyob5cvp2cwuuJlXTlNmTcf8vL7fZfZR2TeqTFMDZeA+2/Orq4MoFYDnnzenb9lif8yU7sS0PsuUDjBajHevADhJRE4QkUoAUwC0ZJ4gIpMA/BxWg+rdEMpIVDJERAAsBLBJVe8NuzzkQhD753CPnrR87k2jM95eAWt9IkWJ6dls9Wr3necmTlNmTccuvti/63sR5DRfVQ3ldfbZZys56B18vPdLxJw+fbpqPG69j8et916vQ30AaNV+/N0DmAzgzwD+CmBmKu0eWI0oAHgGwDsA2lKvllx5si5Rsepvfcr1AnABrP0T12fUqclOn2F9CtiSJao1Ndb9q6bGep9Or6zsfU+qrDxy3K9rO13DVLYICuDe9P8D2ABgHYDnAJyaK0/WpYhIPxNmv+Jx93nV1NjnVVNjPmZ6ebm+F05lNvBanyr8b6aRL+Jx87qpsWPt580OGWK1/tPSvQGAeY2U03XId6q6AsCKrLS7Mr6/OPBCEZUoVX0BgIRdDjJI9yCnI5ale5DTNGsBc/Z7P5iu4VS2EpyVkce96U4AdwZdLvKBKbiZKd2Jn1NmvVzfiwCn+Zb99L/IMoUub2gwz5vdv9/+M05T+ZyuQ0RElM20PsHtWgunENAzZwKHD/c+dviwle7X+ginazA8NZUKUye5l85zpymzbqfNBtV5H+A0X45URVV6ZMkpKt/MmVZLe9w4q6E1dap9Xk69Aflch4iICDCP4KxeDTz4oHnUye4z2Y2WtDffNI9KZX+2PyNIdjM+0uliGOAsvyAWVOwaGnrPYspMd2vu3L51NzNQmd2xT30KWLnSn+t7kavMPuJIVZTNn2+FSFe1vuZq6HjtjTj/fGtKoYj19fzzc5eNGyYSEZUf0whOU5PzqJPdMdO9KVcPspcRpIsvtu5x6dfFFzvfM732bvt5b+R91r1i+50FUd7584G6ut5pdXVHnindROZzClRWX281oDJ96lPm/VCD6rwPMrial4VYfry4gLEflixRHTy494K7wYNVJ060X4xXV+c+L6cFuV4+UyJQ4IX1Xl6sS1SsWJ+KkClQkpfgSul7h929xO01nIIr1dW5zyvse6PLvFiXtPieTYIqr9N1pk+3//vPFeTMjp95hcxrfSqfylZKTJFMTBFeHCKceImK4ukzJYI3LiL/sD5FnF30O7cRvtL3BlO6KWKt22ukI4nZ5ec1L7fR/5x+Tj/zssG6pMX3bBJUeZ2u42dkQD/zCpnX+iTWZ4PHnbb7IRaz/lTzJQIkk/bHTHn5/ZkS0Z9d6wuFdYmKFetThGWvnQKsdQjDhwM7d7rLa/p0+zUddXXAiy/2vUZTk3mNsJfreOHl2cjp3jx4sP3PaZqC5PI+y7qE4ns2Caq8Ttdx+jt3WwdM6xC95BUyr/WpfNZUFds8WyemOd1e5qd7mTfODROJiPwR1XuTaR2U2wYVAKxYYZ/+/PP+RthzinTrRk2N9dXtv43Tvdntz8n7rHvF9jsLqrxO1/EzMqCfeRWp8mhUBbmbchBMIdUbGuzTnSKcmPLy+zNERNRblO9NfkW5q6szR9kzRab1em23+95MnGi+l3n5tzHdG738nLzPuhfl35ldA33uXOt9pljsSHntgqsAwJgxvdPHjMl9HTvpqHh2GhrMASxM6V636HHbeRHVjiigTNZUFds823w47ULvdgf4oD5TAsB560S+Kfv6FOV7k5e1U9kBIdJBkryswTKtz8i1FsqUbiqb6V7m9d/GzTo0L3kZlH1dSovis4mX4GKm4CoDBtinH3ec+TpVVfafGT7cfJ3jjrNPN5V5+nTr+hUVvdMrKvwN7hJQcA+v9ak8Kpsp8pBIcGVwEnYDifLGGxeRf8q+PkX53mR6eHFq1Jg4fcZtVDKnl5/Rx5z+bdzeZwN4ECz7uhRlXjoovLyCuo7dKx4PJvBZQB1RbFQ5iXJvoOk/2+nTGeo8gnjjIvJP2denKN+bVP0bdYnF7D8Tizk3UOwi+eWKMGaKJuiW6eccMcLbfbbAHZ5lX5eizMs2BF5eQV3H7fWdOoncfiagjig2qpxEubERdnh0coU3LiL/lH19ivK9yWTJEtXKyt5lrqx0LvOQIfb3piFD3F8/qL1wTP82I0ZE8j5b9nUpyjhS5f53U6QjVeURqCLI3ZTdMi1U9bKw1XTMrwXHRETknyjfm5yoOr/Plh35Lle6k/nzrdDp6Yhi8bj1fv5893k5Mf3bvP++/fm8z5KJKYDGxIn259fVWS87AwbYpx93nPk6VVX2nxk+3Hyd446zTzeVuaHB/8BnpqAbUQ1GApTJSFWUcaSqqIC9gUS+CaI+AVgE4F0Ar+dzPutTDlHfML7Q64ojep/lvSni7P4unUZdlyzpO9UtvZ4vO4jEccc5X0fVCkqR+Znhw498xi6Ii1PQCacptn7FAnAaxQ8gdoDX+sTKFjbTH44pIovTFIdinEpSZHjjIvJPQI2qiwCcxUaVT7ysaQjq3hTEdSJ6n+W9qQg5rQ8Mu/Fe5tf3Wp/KY/pflJmmGGzZYn++aRNFp7yiPpWEiKhAVHUVAMOcLXLNy4alQd2bTBsWe91M2A7vs+QX0zKP7u7wl3OU+/U9YqMqCurrge3bgWTS+lpf7/0Pyi4vIiIyEpEGEWkVkdbdu3eHXZxo87qmIYh7U1APYrzPkh/S6wLt0r10Xvip3K/vERtVUVWkf1BERMVGVZtUtVZVa0eNGhV2caItyiM1vG96JiKXishmEdkiIt+2OT5QRB5JHX9ZRMYHX8oS09BgTg87IEO5X98jNqqiqkj/oIiIqMRFdaSG901PRCQOYB6AywBMBHCdiGSHebsJwAeq+jEAPwLw/WBLWYKcIlmG3XlR7tf3qCLsApBB+g9n5kxr6sK4cdaNIeJ/UERERKHgfdOrcwBsUdWtACAiDwO4EsDGjHOuBDA79f1SAPeLWNFJgixoyZk/37wdQH19uH+75X59DzhSFWVR7Q0kzzjFgihYIvIQgBcBnCIi7SJyU9hlogLifdOLMQDeynjfnkqzPUdVuwDsATAikNIRFQmOVBEFJGOKxSWwblqviEiLqmb2BvZMsRCRKbCmWHwp+NISlQZVvS7sMhCVCxFpANAAAOO4lo3KDEeqiILTM8VCVTsBpKdYZLoSwIOp75cCqBMRCbCMRERUXt4GcHzG+7GpNNtzRKQCwFEA3svOiEFfqJyFNlK1Zs2av4nIjjxPHwngb4UsT8Tx54/Oz1/Tj8/aTbE413SOqnaJSHqKRa+fP7M3EMAhEXm9H+XyU5T+rVgWe1EqyylhFyAb702u8OePzs/fn3vTKwBOEpETYDWepgC4PuucFgD/DGsq7TUAns21nop1yZVy//mBaP0OPNWn0BpVqpp3F4aItKpqbSHLE2X8+cv757ejqk0AmoBo/X5YFnssiz0RaQ27DNl4b8off/7S+PlTHXi3AngKQBzAIlXdICL3AGhV1RYACwH8WkS2wNpMe0oe+bIu5ancf36gNH4HXFNFFBw3UyzanaZYEBER+UVVVwBYkZV2V8b3BwFcG3S5iIoJ11QRBadnioWIVMLq6WvJOic9xQLIc4oFEREREYWrWEaqmsIuQMj485eAQk2xQLR+PyyLPZbFXpTK4kWxl7+/+POTX8r9d1nuPz9QAr8DYSc4ERERERGRd5z+R0RERERE1A9sVBEREREREfVDpBtVInK8iDwnIhtFZIOI3BZ2mYIkIoNE5E8isi7183837DKFQUTiIrJWRJ4IuyxhEpFLRWSziGwRkW/bHB8oIo+kjr8sIuNDLMuMVL1dLyIrRaQ/e6j0qywZ510tIioiBQvZmk9ZROSLGf+n/SassojIuNT/r2tT/06TC1SORSLyrmkvNbHclyrnehE5qxDl8Eu535cA3pvSeG/qv3KvT6xLlpKpS6oa2ReA0QDOSn1fDeDPACaGXa4Af34BMDT1/QAALwM4L+xyhfB7mAHgNwCeCLssIf4O4gD+CmACgEoA67LrAoBGAD9LfT8FwCMhluWzAAanvp8eZllS51UDWAXgJQC1If5eTgKwFsDRqfcfDbEsTQCmp76fCGB7gcpyEYCzALxuOD4ZwO9S/9+dB+DlQpTDx5+nrO9LqZ+b9yblvcmn32FZ1yfWpZ7fQ0nUpUiPVKlqQlVfTX3fAWATgDHhlio4atmXejsg9SqryCIiMhbA5wH8IuyyhOwcAFtUdauqdgJ4GMCVWedcCeDB1PdLAdSJiIRRFlV9TlUPpN6+BGtPrkLI5/cCAHMAfB/AwQKVI9+yfBXAPFX9AABU9d0Qy6IAhqW+PwrAzkIURFVXwYpkaXIlgF+l/r97CcBwERldiLL4odzvSwDvTQDvTX4p9/rEulRadSnSjapMqalMk2C14stGaki0DcC7AJ5W1bL6+QH8GMA3ASTDLkjIxgB4K+N9O/reeHrOUdUuAHsAjAipLJlugjUSUQg5y5KaTna8qj5ZoDLkXRYAJwM4WURWi8hLInJpiGWZDWCqiLTD2vTzawUqSy5u/54io1zvSwDvTeC9yXflWp9Yl0qnLhVFo0pEhgJ4HMDtqro37PIESVW7VfVMWD3954jI6WGXKSgicjmAd1V1TdhlIW9EZCqAWgA/COn6MQD3ArgjjOvbqIA1BfAzAK4D8ICIDA+pLNcB+KWqjoU1Be/Xqd8X5aGc70sA703gvclX5VyfWJdKpy5F/gYqIgNgVbRmVV0WdnnCoqp/B/AcgEL1bEfR+QCuEJHtsKYvfU5EloRbpNC8DeD4jPdjU2m254hIBawpXe+FVBaIyMUAZgK4QlUPFaAc+ZSlGsDpAJ5P/R2dB6ClQMEq8vm9tANoUdXDqroN1vqBk0Iqy00AHgUAVX0RwCAAIwtQllzy+nuKEt6XjuC9qezvTf3G+mRhXSr+uhTpRlVqPchCAJtU9d6wyxM0ERmV7sUWkSoAlwB4I9xSBUdV71TVsao6HlbghWdVdWrIxQrLKwBOEpETRKQS1u+jJeucFgD/nPr+Gli/r0LMzc5ZFhGZBODnsBpUhVo3lLMsqrpHVUeq6vjU39FLqTK1Bl2WlP+ENUoFERkJazrg1pDK8iaAulRZPg6rUbW7AGXJpQXAjakogOcB2KOqiRDKkZdyvy8BvDfx3uSfcq9PrEulVZcqwi5ADucDuAHAa6n5pgDwb6q6IsQyBWk0gAdFJA6rAfyoqhZ3uEnyRFW7RORWAE/Biuy2SFU3iMg9AFpVtQXWjenXIrIFVmCAKSGW5QcAhgJ4LBUr401VvSKksgQiz7I8BeAfRWQjgG4A31BV30cT8yzLHbCmH/4rrIXRXy5EI1xEHoLVkByZWr91N6zF2FDVn8FazzUZwBYABwD8L7/L4LNyvy8BvDeRf8q9PrEulRApTEc2ERERERFReYj09D8iIiIiIqKoY6OKiIiIiIioH9ioIiIiIiIi6gc2qoiIiIiIiPqBjSoiIiIiIqJ+YKOKiIiIiIioH9ioIiIiIiIi6gc2qoiIiIiIiPqBjSoiIiIiIqJ+YKOKiIiIiIioH9ioIiIiIiIi6gc2qoiIiIiIiPqBjSoiIio6IrJIRN4VkdcNx0VE7hORLSKyXkTOCrqMRERUPtioIiKiYvRLAJc6HL8MwEmpVwOABQGUiYiIyhQbVUQBE5G4iKwVkSdsjn1ZRHaLSFvqdXMYZSSKOlVdBeB9h1OuBPArtbwEYLiIjA6mdEREVG4qwrrwyJEjdfz48WFdnsiTNWvW/E1VR/Uzm9sAbAIwzHD8EVW9Nd/MWJeoWPlUn0zGAHgr4317Ki2RfaKINMAazcKQIUPOPvXUUwtUJKLCKHBd8oT3JipWXutTaI2q8ePHo7W1NazLE3kiIjv6+fmxAD4PYC6AGX6UiXWJilV/65NfVLUJQBMA1NbWKusTFZuo1KVMvDdRsfJanzj9jyhYPwbwTQBJh3OuTi2sXyoixwdULqJS8zaAzPozNpVGRETkO98aVSLyryKyQUReF5GHRGSQX3kTlQIRuRzAu6q6xuG0/wIwXlXPAPA0gAcNeTWISKuItO7evbsApSUqei0AbkzK4FV+AAAgAElEQVRFATwPwB5V7TP1j4iIyA++NKpEZAyArwOoVdXTAcQBTPEjb6IScj6AK0RkO4CHAXxORJZknqCq76nqodTbXwA42y4jVW1S1VpVrR01KlLT6IkCISIPAXgRwCki0i4iN4nINBGZljplBYCtALYAeABAY0hFJSKiMuDn9L8KAFUiUgFgMICdPuZNVPRU9U5VHauq42F1OjyrqlMzz8mKTnYFrIAWwWpuBsaPB2Ix62tzc+BFIMpFVa9T1dGqOiBVrxaq6s9U9Wep46qqt6jqiar6CVXl4g4iIioYXxpVqvo2gP8A8CasyEp7VPX32edxyhIVyrBhgEjf1zBTfL0IEZF7ROSK1Nuvp6bRroM1+vvlQAvT3Aw0NAA7dgCq1teGBjasiIhKlIgcLyLPicjG1P3nNptzPiMiezK2+7grjLJS8XF6PjMdK7bnuDS/pv8dDWtPkBMAHAdgiIhMzT6PU5aoUDo63KWHTVWfV9XLU9/fpaotqe/vVNXTVPWTqvpZVX0j0ILNnAkcONA77cABK52IiEpRF4A7VHUigPMA3CIiE23O+x9VPTP1uifYIlKxcno+y+cZLarPcXb8mv53MYBtqrpbVQ8DWAbg//EpbyIKyptvuksnIqKipqoJVX019X0HrGnnY8ItFVHx8atR9SaA80RksIgIgDqEsRaEiPpn3Dh36UREVDJEZDyASQBetjn8KRFZJyK/E5HTDJ/nMg8qW36tqXoZwFIArwJ4LZVvkx95E1GA5s4FBg/unTZ4sJVOREQlS0SGAngcwO2qujfr8KsAalT1kwB+CuA/7fLgMg8qZ75F/1PVu1X1VFU9XVVvyAgLTUTFor4eaGoCamqsFaI1Ndb7+vqwS0ZERAUiIgNgNaiaVXVZ9nFV3auq+1LfrwAwQERGBlxMokirCLsARH6orrZfzFhdHXxZil59PRtRRERlIrVsYyGATap6r+GcYwG8o6oqIufA6pR/L8BiUkiGDTM/X+3NHs9MEcmdb/r5LFcgimJ6jmOjikqCqWITERGRo/MB3ADgNRFpS6X9G4BxAJDa++0aANNFpAvAhwCmqKqGUVgKlt/RlUv5r4aNKioKXnpKMuXTa+I2TyIiomKnqi8AcLxLqur9AO4PpkRExcm3NVVEhRTkPlTFtCcCEREREYWPjSoiApqbgfHjgVjM+trcHHaJiIiIiIoGG1VUsoYNs6b9uZn6V5aam4GGBmDHDmuy844d1ns2rIiIiMgg/YyV/fLyGdNr2DDv5ct8DvQrTydsVFHJ4jS+PM2cCRw40DvtwAErnYiIiCgk/XmWC3LpCMBGFRG9+aa7dCIiIqIcSjnSnx02qqgomPYpKMT+BcW0J4Ivxo1zl05EREREvbBRRUVh716rxyP75TX0uV1e/c2zaM2dCwwe3DtNxFpbxaAVRERERDmxUUVU7urrgaYmoKbGei9yZMyeQSuIiIjIgyADhdkFpQgaG1VUsoKcMlj06uuB7duthlX2JGgGrSAiIipLYT8z5Xt9N8EnCvUzVRQmWyJ/DRtmX2Gqq83T9cpuGp8fGLSCiIiIUrw8S7kdJSp0QIugAmZwpIqKQtBhMcsWg1YQERERucZGFVHARCQuImtF5AmbYwNF5BER2SIiL4vIeN8L0NxsBaCIxfoGorALWjF4sJVOFDEicqmIbE7Vl2/bHB8nIs+l6tt6EZkcRjmJiKj0sVFFFLzbAGwyHLsJwAeq+jEAPwLwfV+v3NxsBZ7YscMaD88ORJEZtELE+trUZKUTRYiIxAHMA3AZgIkArhORiVmnfQfAo6o6CcAUAPODLSUREZULNqqo6GVHexk2LOwSmYnIWACfB/ALwylXAngw9f1SAHUiPsawmTnTCjyRKTsQRTpoRTJpfWWDiqLpHABbVHWrqnYCeBhW/cmkANL/IxwFYGeA5SMiKnl+RN3z+vyWeW2TIANtsFFFJSfi66x+DOCbAJKG42MAvAUAqtoFYA+AEdkniUiDiLSKSOvu3bvzvzoDUVDp6KkrKe2ptEyzAUwVkXYAKwB8zS4jz/WJiKjM+fnM5TYvp/PD2HuUjSoqCmGH9PSDiFwO4F1VXdPfvFS1SVVrVbV21KhR+X+QgSiovFwH4JeqOhbAZAC/FpE+9z3P9YmIiCiFjSqKBLvh48xXxEef8nU+gCtEZDusqUqfE5ElWee8DeB4ABCRClhTlt7zrQQMREGlo6eupIxNpWW6CcCjAKCqLwIYBGBkIKUjIqKywkYVRUKJNJocqeqdqjpWVcfDWjT/rKpOzTqtBcA/p76/JnWOfzssZAeiGDECqKoCbrihbyTATE4RA4nC8QqAk0TkBBGphFWnWrLOeRNAHQCIyMdhNao4v4+IiHzHRhVRyETkHhG5IvV2IYARIrIFwAwAfcJE91s6EMWvfw18+CHw3nv2kQDTckUMJApBas3hrQCeghVN81FV3ZBVn+4A8FURWQfgIQBf9rWTgqgEiMjxqa0HNorIBhG5zeYcEZH7UtsXrBeRs8IoKxVOrhlDpleY5XMSRvCyiuAuRRSMYlh/parPA3g+9f1dGekHAVwbSCGcIgFmRvzL9zyigKnqClgBKDLTMuvTRljTbonIrAvAHar6qohUA1gjIk+n6k/aZQBOSr3OBbAg9ZVKRBRmDDk9v3ktX5A/FxtVVPTY7+xRvpEAGTGQiKhkqWoCQCL1fYeIbIIVSTOzUXUlgF+lRnpfEpHhIjI69Vkqc2E/h6kGO2pmwul/ROUq30iAjBhIRFQWRGQ8gEkAXs46lM8WBtyegMoaG1UUCV6n7BXDVL/IMkUCnDz5SFCKkSOtNVfZBgywPs8AFiXHNK8+PS8913EiKk4iMhTA4wBuV1VPu/twewIqZ75N/xORUwA8kpE0AcBdqvpjv65BpStzczanIdywh5hLSno91MyZ1lS+ceOsBtWDDx5ZQ2XXoAKsf6TVq3ufmw5gkZk3FR3T/PN0eq7jRFR8RGQArAZVs6ouszklny0MqEyln9uqq71vtjtsmP19pD95Bs23kSpV3ayqZ6rqmQDOBnAAwHK/8qfgJToSOPG+E7Fr366wi0KFko4EmExaX1es6BuUwk5npxWa3RTAgoiIioKICKzIs5tU9V7DaS0AbkxFATwPwB6upyotfsz86U/nWq4OO1P50um5jgehUNP/6gD8VVV3FCh/CsCcVXOw/e/bMecPc8IuCgXFTfCJ7u7+50FERGE7H8ANsDakb0u9JovINBGZljpnBYCtALYAeABAY0hlpQLZu9eaDRTVGUGZ5ct8pUexch0PQqGi/02BtScIFalERwKL2xYjqUksbluMWZ+ehWOHHhvItaurzUPAVGDjxlnT+PIRj9s3rBjAgoioaKjqCwAcY6elov7dEkyJiIqT7yNVqZ3trwDwmM0xRoUpEnNWzUFSkwCAbu3uGa3KnhLotGjd64J3IPzehrI1d25+cUkHD7bWT9kFupg7tzBlIyIiIoqoQkz/uwzAq6r6TvYBRoUpDulRqs7uTgBAZ3cnFrctxq59u/pMCXSaA8sF70Vo8WLz2H88bn2tqbHWU82fb32tqbEaYul0BqkoasUwb52IiChqCjH97zpw6l9RyxylSuvWbnz76W/jkY2P9JoSCAQzJZACsnKl+VhXV9+0+no2okpMrhFhjhgTEZUOvzfNLcQmvNl5RjUioK8jVSIyBMAlAOzCcVKRaNnc0jNKldbZ3Ymlm5baTgkkIiIiovKSuUSjEHmbRHVGk68jVaq6H8AIP/Ok4LXPaO+T1pZow6SmST3v01MCgXmerpGrJ8PueFR7JoiIiIiovBUqpDqVmKnLp/ZJ61ZDSO0CiWrPREmpq3OXTkRERERsVFFuiY4ENuze0Ce9s7sTMnCf7Weqq7lwPRKam4Hx44FYzPra3Gx/XmMjUFFhv6aqrg545plClpIClCsqJxEREbnHRlUZyw6Pbjp+58o7URmvBABUxivRWNsIvVuxc8ZOnPB/PolEx64+Dah09L/q6uhuJFfymputsOc7dlj/CDt2WO+zG1aNjcCCBX33nJo+3focG1QlhVE3iYjKBzvSgsNGVRnLDo9ud3zbB9uwZP2SnOHV+aAWQTNnAgcO9E47cMBKz9TUZP95UzoREREVhdzPZ7l6vu2PF3I2UrFu4cFGVZlK70WVDo+ePVqVPq7QPmun0uHVMz9PEfTmm/mlZ49Q5UonIiKikqAqvaL4pV879yYw6HtVwOwYqr43GImOXb2OZwcOs8vD6yud9969zsejho2qMpW5F5VdeHS7varS7MKr5+JHr0JUeyYia9y4/NLTm/pmM6UTERFRScv1nEh9sVFVhtKjUHZT+hIdCdT8uAaL1y7utVdVVUUVEncketZSdWt3r8/nktnb4FbUeybyJSKDRORPIrJORDaIyHdtzvmyiOwWkbbU62bPF5w7Fxg8uHfa4MFWelpjI5C0bzyjuxsYOdJ65Qp0QURERCXB6TmRzNioKkN2o1DpXog5q+bgzT1vojPZaXvc9HnKyyEAn1PVTwI4E8ClInKezXmPqOqZqdcvPF+tvt5aF1VTY61Kramx3tfXW8fTASqcWrrvvWe9nAJdUFEptjnqRERUGKaAZXbPeV3JLpxy/ymeG1blEDCDjaoy1LK5pc/oUmd3J5a9saxnfVR2Zers7sRvN//W+HlU2g8j2T2ouXl4K6UHPbWkY9APSL0KGxuxvh7Yvt0ajdq+/UiDCvAWiMIu0AUVlWKbo+5ERC4Vkc0iskVEvm0454sisjE1OvyboMtIRBQmp440U8Ayu+e8w8nD2Htor+dpgOUQ0Kwi7AJQ8NpntKPxyUYsXLsQnd2dqIxX4uZJN0OhWLh2IQD0pM37/Dzbz6cNG5ZfhTCdV11tPczlm0+xE5E4gDUAPgZgnqq+bHPa1SJyEYA/A/hXVX3LJp8GAA0AMM60dioXr4EoTAEwiAKUqkvzAFwCoB3AKyLSoqobM845CcCdAM5X1Q9E5KPhlJaIKBx791ojUhPum4CDXQdRVVGFrbdthapiwn1HAo7N+vQsHDv0WAC9n/OA3p/PPpeO4EhVGbKbK7uobREWrV3kev5sroZQ+niuHopy6MEAAFXtVtUzAYwFcI6InJ51yn8BGK+qZwB4GsCDhnyaVLVWVWtHjRrlrTBeA1F4bcQR+escAFtUdauqdgJ4GMCVWed8FVbnxQcAoKrvBlxGIqLQ2QWdcBOIgkEr8sNGVRmymyvb2d2Jw92He6Wx4hSOqv4dwHMALs1Kf09VD6Xe/gLA2QUrREODt8/t23dkXVVzsxXAgoEseuTaVNsr03z0Up+j7mAMgMxR3PZUWqaTAZwsIqtF5CURuRQ2RKRBRFpFpHX37t0FKi4RUfD625HOoBX5Y6OqDNnNlU1qEkmY11FR/4nIKBEZnvq+Cta0pTeyzhmd8fYKAJsKVqD584Hp062ncDfee89qkDU2Wl937GAgiwy5NtX2ys2obamN8PZDBYCTAHwGwHUAHkjXwUy+jPwSFSkRWSQi74rI64bjnxGRPRlRae8KuozkXX870p2Cm1FvbFSVmURHAgMrBvaER0+/1jashaD3w3VVRRVaG1r7fc1cz+xun+mL2GgAz4nIegCvAHhaVZ8QkXtE5IrUOV9PLahfB+DrAL5c0BLNn2+NMrl14IAV6OLAgb7pZRzIItem2uSrtwEcn/F+bCotUzuAFlU9rKrbYK1TPCmg8hEVi18ia9aEjf/JiEp7TwBlIpdMsyTcdqS3JdogA/f2zHxYcPl8dM46BMzWnlfnrENYcPX3XZWvHCLPslFVZky96FOXT4VmBaJjT4S/VHW9qk5S1TNU9fT0jUlV71LVltT3d6rqaar6SVX9rKq+4ZyrD7wGrDB9rowDWXDeeaBeAXCSiJwgIpUApgBoyTrnP2GNUkFERsKaDrg1yEISRZ2qrgLwftjloP4xPd+1z2iH3q2IpR75Y4hheu10xCSG00adhpjE0FjbCL1b0T6jHVOXTwU6c88h10NDXZWvlCLPmrBRVUZMveiJjgQ27N7Q5/x8pv8VuoehlHowIstrwArT58o0kAXnnQdLVbsA3ArgKVjTZB9V1Q1ZI79PAXhPRDbCWsP4DVV9L5wSExW1T6U2rv+diJwWdmGot1yzJBb8aUHPyFQSSTzQ+gCSmsSG3Rt6faYt0Wb7PEj5YaOqjJh60eesmoPKeCUAK5R6usci3WvhxK7noT9KuQcjsrwErBg82Prc4MF90+fO9adcRYbzzoOnqitU9WRVPVFV56bSMkd+VVVnqOpEVf2Eqj4cbomJitKrAGpSG9f/FNYIsC0GfQlHrlkSt/7u1l7vu9DV6336M1OXTy1sQUscG1Vlwjb6y9pFOP5HxxsjwGTOz3UTecwv5bD7diTMnw/U1eV/fjwO/PM/W59ragJqaqx/mJoa633mBsNlxLSp9m83/9aXiIBuR22z6yTrExF5oap70xvXq+oKAANS02ntzmXQl4DlmiWROUpl0tndiYVrF3KUqp+4+W+ZMEV/ad/b3jPPNi3dY6HQnvm5HR19NwEutHLZuyp0zc3Aiy/2Ths8+EgDqbnZGpVKB6Xo7gYefBA4/3zreJk2orI5jeo2PtnYU5fsNtTOR65R21wdGqxPROSFiBwL4B1VVRE5B1aHPKfRBizRkcAFiy/A6q+s7rXxrtMsia+e9VU0/q4xr/wPdR/KfVKehg2zv7dUV5f2DCSOVJUJ2+gvGfNrM3V2d2LZpmW95udSCZs50zmKX67j5IgRAYkoykTkIQAvAjhFRNpF5CYRmSYi01KnXAPg9VRU2vsATFHt72R/cssUiMJploTn6XyVuVs+TrMnyrUTjyNVZSLdi57u6bhw3IV46PWH0Nndicp4Ja47/Tr8z5v/09MD0vhkIxauXQj87z34MI8oMHaqq0u/ApUEU7S+dHqu4+TIbq6719EqIiK/qep1OY7fD+D+gIpDNrI752Z9elbPaJVplkRbog2Tmib1vF83bR3OOOYMJDoSmHDfBBzsOtjr/IHxgTjUfQhVFVXY+t4BHDuUc8Pd4khVmZmzag62fbANS9Yv6TX/dsn6Jdj2wTbM+cOc3vNzPTaoADaoioYpWl86PddxMmJEQCIi6i8v23Vkj1Jd//j1ffLKlJ7+xwBL3rFRVUbSD3gKRbf23mOoW7uhUCxuW4w7V95pW+GoRDQ3A+PHW5v+Dh0K7NjR95zKSiuKX3MzsG9f3+NlHOUvl8ygFHY3r65kF065/5Q+DSs3wWDcBpcoow22KQ8iglgshlgshqqqKryZY9T5pJPy2y9ZRPDSSy/lne6Xq6++Gvfff2QgpaKiAt/97ncLdj2iIHnpnLMLjb5h9was3LqyV1522PnnHRtVZcTUO5GpW7uxdONSxwqXDz/2lyqH3bcDlw46sWOHFbN+/37781SB1autc9/LWo88YkRZR/nLJXPeu91c98PJw9h7aG+fnkA3I7scBab+SiaTSCaTiMVimDx5suO5W7ZsCahU3jz99NN46qmnwi4GUb+YosTaPbsd7j6M0T8cjabWJgyYMwDr31mPtkRbz/dXP3q17TUu+fUleXWac7TKGzaqSpBdxczu6QCAqooqtP1LGwZVDOpJ6+zuxIHDB7Bu2jqsbVib81rV1f7tkJ3dWCqH3bcDZxd0ws7hw1bDye7coUPZoDLInvfe2tCKnTN29tSxQfFBGBS3vmdPIEXBxIkTsXPnTgBAXV0d4vE4YrEYjj76aHz44Yc47rjjAACxWAxDhgwBAAwaNKhnpOvcc8/1dN1t27bhqKOO6rneNddcAwC46KKLMGjQIFRWVkJEMHr06J7PnH/++RARxONxDB8+HCNGjMA3v/lNdHR04IknnkAsFsOSJUsAAD//+c8Rj8chIrj99ts9/36IguImEEWXWvtMTX9yOrqSXbj+8esxdfnUnu+3/n2r7TUUmleneTrQhVfl2inORlUJsquYppCb9cvq+6QrtKeC5uJnjzl73wPgJrhEd7d9OgNUGNnNe89M6+zuRGeys9dxorDs27cPr732GiZMmIAFCxbghRdewPvvv49kMgkRwWWXXdbT4Eomk9ifGtlevXo1kskk3nrrLbzyyiv405/+5PraF154IWpra9Hd3Y22tjY8/vjj2LZtGwDg0KFDePXVV5FIJLBr1y60tLTgqaeewh//+Ee0trb+X/buPU7Our77/+szu5tkcyIRohyTgIKYUA66IohVamgLaLGKB2CDqGBuslLR8LA/vKNASdPeWm9baZOULYTSuh4wQI0cVEC4qVQOiSRICLQRk7BkkQRCDoRkszuf3x/XzGZ29rrmtNec38/HYx67c811XfPdzV655nt6f3n11VfZnRqW/M1vfpNJkybx4Q9/mGQyydy5wX1rcHCQwcFBLrroIpYsUTCM1LZcKbG9C3rxa33o8fO5Px96LZ3evG7ruqHhfmFrTY1rHcfYlrHB9xmNe+2t7fRd1Tfs/OlHrmVC8mnWRnFVqhpM1IUZFbm5ftv60FaLoQu0gFjNKI3eIlGXigmXaGkZ/TmaSOgC22uWD1tcO0lyWAVLvVVSLYlEgsmTJzNx4kR+/vOf093dTX9/P1OnTiWRSLB9+3Y2btwYeuz5559PIpHgqKOOwt258847i37/vr4+HnzwQRKJBCeffDIAP/3pTwE46KCDOOGEEzj00ENpa2vjoYceoru7m4kTJ/Kud72Lgw46iNmzZ+c8/8UXXwzA5z//eQYGBooun0glFRNE8akVnyr6/P2D/ewf3D/0vRr3yiO2SpWZTTGzFWb2rJmtN7PT4zq3FC7qwsxu6Ug/Bq8ZxK91npz3JIbRlmgr+j3Tk+cT43YP+4AY1VIhVbR4cRAyUYiwnqq2NgVUhOjb1cfxS45nMDn8d5Z5Iwsz6IMc94/HlVSxyg6vEClGek7Vtm3beNOb3oS7c/jhhw9td/fQStUVV1xBb28vGzduJJlM0tLSwq4Shhm4OzfeeOOw95s/fz4ALRkNOmZGf3/xc3wnpVr1xo0bl2dPkeoqJojivt/ex/a924t+j6Qnh61Nqsa98oizp+o7wE/d/XjgJGB9jOeWAowmvvlTKz6F4+xPZn0ALCJS3fdNVItHrevsDOZKzZgRfBKfMCFIASyUPr2HWvTwInbu2zni+sm8kYXpH+xnV/+uql436lEWgMsuu4wtW7bw8MMPA7B69Wpuv/32odd37NgBwEsvvURLSwvTp0/nxhtvZDBqmHAehx9+OFdfffXQ8X/7t3+bc/9LL72U3bt3s2bNGnbv3s26dQeGOI0ZM4bXXnutpHKIVFvU9Iyw+0IpvVT5qLcqPrFUqszsIOD9wM0A7t7v7vofrsKKuTAzrelbw3+/+t+xlEEtHnWgsxM2boRkMohLHxwsvBuxvz8Iu5Ah6cYMCB+fnhlUkfl65vb08VFK6eEN6yVuxjHuUpgrrriCs88+mzPPPJNEIsG73/1uVq1aBcBhhx3GlClTmDBhAsuWLcPdMTOuvPLKYb1KuZx++umYGWbGW97yFh577DGSySRtbW0kEgmuu+66nMefe+65nHrqqZxyyikcdNBBtLe3097eDsBnPvMZfvnLXw4LqhCpF1HTM7KDIvp29ZXUS5VP/2A/d6y/I/bzNqPWmM5zNLAVuMXMTgJWA1e6+7C8ZjObB8wDmK55GbHLdWEu+VD0RN1CAikKla7E5Xq/SZPCQynUYl4nFFQxTNiQ28y//6jXs7eLVIpH1NLvvffe0O3psIq0qOF4UeeN2r59+8gPiOmesrR9+/YNff+9732Pt771rezevZuDDz6Yd7/73QB861vf4lvf+tbQfumwCoDTTjst8v1FakGhgRCLHl5EwhJc/q7LcZwbV9/I5e+6fOh+03V3V0HbMqVf/9g7PhbfD9TELI7/bMysA3gUOMPdHzOz7wA73f3rUcd0dHR4uhVM4tG3q49jbjiGvQN7h7a1t7bz/JXP4+6875b38cjnHuHQiYcOvb6mbw2ndJ8y4lxrL1/LiW85seTRXhMnJtm1q/FyUMxstbt3VLscmWK9lgr5B58xI+jpkpzX3KETD418/VeX/orTbj5t2Haui/6/2L34kZf18Dmy4a8nidWhhx7Kyy+/jLtz8MEH8/vf/77gnrJGp2upsWXeS9LJfXsH9w77jJd+Pde2zM9/mecMe72ZlXo9xfWptxfodffHUs9XAO+M6dxSoFzD/6LWP4jqpbro9otGVZbduxuvQjVaZjbOzB43s7Vmts7M/ipkn7Fm9kMz22Bmj5nZzNgK0NMDM2cGc6hmzgyep7cVmnYwZkzTBlWk13+7/7f3Dy2wGLUo4+H/93Ce+v1TXH3/1QcqTn+zA65z3vjaHk4+7CT2fu2NoCKVfuRQSuNGdpBFvsfkHNMnJ08u/hiRuL300ktDoRbbtm1ThUqaRr6lOfIt5xE2FaSYxEEpTCzD/9z9JTN7wcze7u7PAXOAZ+I4txQuavjfHc/ewWt7XxuKWf/6B74+1Bqxflt4nkh6e9RQPSnJPuCD7r7bzNqAX5rZve7+aMY+lwLb3f1tZnYB8A1g9DNTe3pg3rwDi/lu2gSf/WzwybiYZK166P4ok3TDxCdXfHJogcXX9r4WuSjjRbdfxMbXNh54oYjQl2rIdZ1Hvab/G0REyis7hCxJElK34v7BfpY/uXzo+6Fta5bj7iOCy9Kf/6KCzTI/H0rx4uxO+Augx8yeAk4G/ibGc4e3ssuQvl19jG0dS99VfWxZsIVjph7Dmv+1hmOmHsOfvvVPI1sj0pHqYVHrEExin39XF2MWjYXrjDGLxtJ11xcUj14CD+xOPW1LPbJ/ix8Bbk19vwKYYxZD5N7ChQcqVGn79xdXoUof04RBFZnrv6UnCq/buo57Ou8ZFjiRXlwx/fpAMqhgtbe2V6ScuiZFRKojPZoh7rCuYSMeQpBk8B8AACAASURBVGT2XGVuy17OI/PzX6nBZpJbbJUqd1/j7h3ufqK7/7m7xxdRkm5l37Qp+NSwaVPwXBWrIZnD+9Lfd97Rye+2/47vPvXdkmLWYXQx7TKSmbWY2RrgZeC+jCGzaUcALwC4+wCwAzg45DzzzGyVma3aunVr/jeOM1yiCYMqwm5AEPRGZb62b3DfsNfTzxVEISLS2KKmWYzW7etvz/l65rpTQ9tClvPITBQsNHFQihNX+l95hbWy79kTbO/srE6ZakhmK3q6GzjpSdZtDdbxyP5AV0hCX1qu1oxCjpfh3H0QONnMpgB3mtkJ7v50CefpBrohmAyc94Dp04PGiDg0WXJndsNCpnVb17HhlQ0jWgmzhR0rIiKNIfNzWJzD6Pp29Y34DBdHqEShiYNSnPpIE4hqGW/CFvMwURMYoxTTGqHWjPJIreP2IHB21ksvAkcBmFkrcBDwyqjfcPFiGD9++La2tiB4IsqsWSOPGT++6YIqonqp0vYl90W+JuVlZmeb2XOpYJerc+x3vpl5KqlWRCRW5Qp90DC9+lIflaqolvHM7bmSzep0HlYh43PDJjCGfQAcmxhLa6KVtZevxa/1Ea0UUe/Vu6B3xHyrSf/XefGq3pLj1puVmU1L9VBhZu3AHwPPZu22Ergk9f3HgV94HOsedHZCd3cQh24WfL3lFli+PPg+26xZsG7dyGO6u+u+d7jYce9hDQslGVP+VXZHe01GJfxFrSFXzbXlzKwFWAKcA8wCLjSzWSH7TQKuBLKH2oqIjFq5pklEjZLQNIzaVR+VqrBW9swW87A5V5/9LHzuc3U9D6uQ8bn5WtHT9iX3DSWWlfpeaUr8KtlhwIOpMJcnCOZU3WVm15vZeal9bgYONrMNwAIgsvW9aJ2dwfpSyWTwtbMzeIRdXxs3BtdK2DF1rthx79kNC/M75pOwBF0dXcyeNhuA2dNmh76e/n72tNkkFk4dFvISxyOXuM61a1cQWBN2zM7y1xNzORXY4O7Pu3s/8AOCoJdsiwhSNKNneos0OTNbbmYvm1nocHQL3JDqFX7KzLRsTkqhvUlr+tYMLceRb3vfrj6OX3I8g8nw+biDPshx/3gca19aW5ZwDClNfVSqwlrZM1vMC002S8/DqgPZ43OjLphiW9HXbV034oIu9L1kdNz9KXc/JRXmcoK7X5/afo27r0x9v9fdP+Hub3P3U939+bIXLNecxQYz2r/1zONvfvLmoXmL6etq2PzGNctZ/uTyofmNur5iNxTqktKb2jYk9cHvKHe/O9eJig5+EWk8/8rI4eiZzgGOTT3mAcsqUKa6UOg0ibl3zg1t3A7bvujhRezct5P9yeEJfpnn39W/i847OssSjiGlqY9KFeRuMS9mblWdzMMqdHxu2PC8dGv5mJbw+TLZF3ScY4ELbUWXGtJEcxZH+7eeK+kvOwkwX6StlJeZJYBvA1fl29fdu1PptR3Tpk0rf+FEaoy7Pwy8mmOXjwD/lloa5FFgipkdVpnS1baoz2GZ0yzW9K0Z0QgXtT3dOAdBKEXfVX3Dzpu5jIca7GpL/VSqcikmjawOksvCxucuX7OcGf8wI/KiyZwnkiutDIZf0IWOBZ48+cAcC2kwhcxZbACjHfdeyHW1/NfLD8xvjIi01c0vNkOhLilHpralTQJOAB4ys43AacBKhVWIlCRvzzCo1zfK3DvnDnuebtwO256v8U/hFbWrMSpVhSab1UlyWdgF0z/Yz+YdmyMvmux1qvLNs0pf0IVenJpH1cDyzVlsEKXciDIbK/ItwAh5kgD/Zgdc57zxtT0cNunQ0FCIqEecMhtISnmPqOMnT463nAV4AjjWzI42szHABQRBLwC4+w53P8TdZ7r7TOBR4Dx3X1Xxkoo0CfX6jpTZG5W2bus6bnv6ttDty59cHtn4p/CK2tYYlap8yWZ1llwWNj43/WEw7KLJnidy57N35p1ntX7b+sj3KjUyvZpJYDIK+eYsNohS/tYzGyvyLcCYV3/lax1him0gyb6uo46vdMNLanHsK4CfAeuB29x9XVbwi4jEI1/PsETI7o1Ku/g/Lg7dnj20PLPxL1ejuXqrqq8+Fv/N1NMTTKDfvBne9KZg26uvBkOVFi8e+UGwDj8YZsedd93dxc1P3kz/YD+DPsjV913Nf77wn9zxyTv42G0f4w+n/+GwruI/nP6HrHhmBa2JVvYn95MgARZUzMa0jOGyUy5jyYeW0Lerj7GtY7nkpEv4/tPfp3+wf9jrhdL8qQaQTgJsYMUudhi2qDbkXnixb1cfx9xwDHsH9jKudRzuPuIGWcvq7Vp293uAe7K2XROx75mVKJNIg1oJXGFmPwDeA+xw974ql6kupBuxsxUaMpZu/FvyoSU5w8ky95PqqK9KVTo6PZ1U9krGmqjpyHRoqA+HYfNAvvub75L0JJ13dPK77b9j02ubhlbc7h/s50fP/AhgKDUmSRJSH5bSXcRf/8DXWfTwotDj41wNXKReZYdOkBoil24NDLtxjTimziopItKczOz7wJnAIWbWC1wLtAG4+z8TNF6cC2wA9gCfrU5J68/gNeGx6KUotnFQKqu+hv+FRT9nasAY6Kh5II6zbus6HB+qEBVq0Ae5+v6ruWXNLaHHqwtZml2uRbWjxq6POCYkqEJEpBa5+4Xufpi7t7n7ke5+s7v/c6pCRSr17wvu/lZ3/wPNTRQZqb4qVYVEPDdYDHSx61AVon+wnxXPrIgclxs2zyRqvpTmUUmjWdO3hiO+fUTkoosAbwy8wdX3D1+XudCFuEtRA6EQIiIikkN9VaoKiXh2h9ZW6OoKHq2twaeQ9LY6k7n+QebaBNnaW9u5b+59oa+tvXztiDUOBn1wWGVtXOs4ph80fWg9hOwu5p07h69BlX7s3BnfzypSC+beORfHIxddTFvxzIphz/M2gIyJ72IZTSjEaBtI1MAiIiIyUn3NqTr3XFhWwCLeg4Mj98vctnRp/GWrgHypL59c8cnQ1y66/SKe7no653kyI9s1yVGaVXb07drL13LiW04cFkCRlvQkL+1+aWjuYd6x7tce+DaumPRSgiVG2xCihhQREZGR6qun6p578u+TT3f36M9RJflSX7bv3R76WnbyTLGR7SLNImqBRi22KCIiIrnUV09VHPOlBuNLYam0uFJf8kW2q7dKmlHUAo0PPP9AzsUWlZQpIiIi9dVTVcicqnxaWkZ/jgYSFtmu3ippRlELNH7iR5/QYosiIiKSU31VqhYvhvHjh28bPx7GhYc3hEqvZSWAhjVJ8+jb1cdbb3hrZINB1AKN2/duz7vYYr5zZxttqEP6+MmTRyYDViMdsFbKISIiUi31Vanq7AzmRM2YEdyxZ8wInu/bF31MumeqpQXmz6/bkIpyCZtfFRapLlLvFj28iI2vbYxsMBi8ZnBYSqZf68zvmE/CEnR1dI14Lf3oXdCb99zZotI0C32kwyKiUgBHkw5Yiloph4iISLXUV6UKgorVxo2QTAY9VwsXRkdgzZgBAwPB6wMDDV2hKralPC0zsj37g6JIo0gPc016suDhrYUeU8q5RUREpLHUX6UqracnGMq3aVP0Pm97W+XKU2XFtpSLNJPMYa6FDm8t9JhSzi0iIiKNpX4rVQsXwp49ufd56KGKFKXa1FIuEq2UMJZCj1HQi4iIiEA9V6oKiVcfHIRDDoFEAmbODHq3enqC7zO3VUCpw/MKoZby+mBmR5nZg2b2jJmtM7MrQ/Y508x2mNma1OOaapS11hVzPRUbxtK3q4+3/9PbCzpm2Ln/Zgdc57zxtT0cNunQgsIazDw04CGOxYEVGiEiIlI59VupmjChsP1eeSWYU7VpE3z2s/C5zwXfp7fNm1eRilW5hueppbyuDABXufss4DTgC2Y2K2S//3T3k1OP6ytbxPpQzPVUbBjLoocXsat/V0HHDDt3f3itJXdYw+hqT8WkCJYzNCKqHKNNORQREakX9Vupev314o/Zvx/6s6KR9+wJhhKWUTmH5ykSvX64e5+7/zr1/S5gPXBEdUtVf4q9nooJY0mfG2BcyzjGtQTLNbS3ttN3Vd+IYzLPXcrPMVphKYLVEJVmmE4pFBGJVZVGHYnkUr+Vqjg/PRQylHAUyjk8T5Ho9cnMZgKnAI+FvHy6ma01s3vNbHbE8fPMbJWZrdq6dWsZS1p7ynk9ZZ67f7Cf/mR/Wd4n/V4iIlKkzKCyCo86Eskl1kqVmW00s9+k5oKsivPcQ60SZtDaGuupmT493vNlKGbCe/YckULmjSgSvf6Y2UTgduBL7p7dlv9rYIa7nwT8I/AfYedw925373D3jmnTppW3wDWknMNds8+dJDmsghVnL3Nmj5iIiBQhLKisAqOORPIpR0/VH6XmgnTEdsbs+PTBwdLO09YGY8YM3zZ+fLDeVZkUOjwvbI6IYtIbj5m1EVSoetz9juzX3X2nu+9OfX8P0GZmh1S4mDWr0Oup0CCLzP2uvv9q9g7sjdw3zt6qsJ9DREQKEDW6qMyjjkTyqY/hf4XEp+czYwbccgssXx58bxZ87e4OFhQuk0KG54XNEVFMeuMxMwNuBta7+7cj9jk0tR9mdirBNfpK5UpZ2wod7lpog0Tmfrevvz3nvvmG1RYT1nDg54h/EpRCI0SkoUWNLirjqCORQsQ8jg4Hfm5mDtzo7t2ZL5rZPGAewPRi/vjjaH3YuPHA92WsRGUrZBhe2BwRx0dsW/KhJWUtq5TdGcDFwG/MbE1q2/8GpgO4+z8DHwfmm9kA8AZwgXu14gdqTyHXU3aDxNc/8HUOnXhozv2Wr1lO+tfc3trO81c+H3pMLsWEMgz9HNcW9Raxl6PemdnZwHeAFuAmd/8/Wa8vAC4jSN7cCnzO3XOsGC/SnAq4lj4D/B3wYmrTP7n7TRUtZNrixcHopezG9t27g5FNFfyMJ5Ip7p6q97n7O4FzCOKi35/5YsnzQBq49SFsjsjyNctZ/uTyisSkT54cvkaO1rSJn7v/0t3N3U/MiEy/x93/OVWhwt3/yd1nu/tJ7n6au/9XtctdbwoNssgOpdg/uD/vMVI7zKwFWEJwv5kFXBiyRMGTQIe7nwisAL5Z2VKK1L4CryWAH2bcu6pToYKg0tTdDQcfPHz7K68osEKqKtZKlbu/mPr6MnAncGosJ168OJj7VKo5c2IpRjmEza3I/ICXVq4PelFr15RzTRuRcikmGGZYKIUnSVKeUAopm1OBDe7+vLv3Az8APpK5g7s/6O7p5uxHgSMrXEaRepD3Wqo5nZ0wceLI7QqskCqKrVJlZhPMbFL6e+BPgKdjOXm6VWLGjOB5S0vhx86ZA/ffH0sxyiFsjkjmB7w0xaSL5FdMMEyuoAj1VtWFI4AXMp73knvdt0uBe8NeaOYlCkQo/Fo638yeMrMVZnZU2Ikqei0psEJqTJw9VW8Bfmlma4HHgbvd/aexnb2zM5gX5Q4DA4Ufd9xxw5/X2IJxvQt6md8xnzEtQSrhmJYxdHV0KSZdKqPGrofRKjTIImy/sGNKSRGU2mNmc4EOgjkhIzTrEgUiRfgJMDM1lPY+4NawnSp6LSmwQmpMbJWqVLfxSanHbHcvX055MZYtg66u4PsaXDCunOvuiORUg9fDaKXXbZvfMZ+EJYYaKLIbJKLWd8tuxCglRVAq5kUgs7X8SA5Moh9iZmcBC4Hz3H1fhcomUk/yXkvu/krG9XMT8K6yliiswe+ss4ZP/n5xxOUeLJtz7rkN1Vgo9aM+ItXDBKnThelOhRDW4IJxhQ5XEoldDV4PcYhrOYJCz6PlD6rmCeBYMzvazMYAFwArM3cws1OAGwkqVC9XoYwi9aCQa+mwjKfnAevLVpqwBr+LL4YHHhi+X9iopYEBuPnmhmoslPpRv5WqYlKm04sF1+D420KHK5WL1rRpYjV4PcSh0PS/uM4T1/tJcdx9ALgC+BnBB7zb3H2dmV1vZueldvs7YCLwIzNbY2YrI04n0rQKvJa+aGbrUlM8vgh8pmwFCmvwK/QzXzIJ/VlDuxugsVDqg1VrCZyOjg5ftWpV8Qf29AQXx6YilhppaQlaL2bODD9uxozh61iJRDCz1e7eUe1yZCr5WmrA66FvVx/H3HAMewf2Dm0rZd2pQs8T1/s1q4a6nkSqqKGupUSiuIbzQpgFFS6RApR6PdVXT1Vml3Axzjwz+BoWzT5+fLBdpNk04PUQ13Da0aQIDvogx/3jcQUNA9Q6cSIiWcoRNKHwCqmA+qpUhXUJp7W0wIQJ4a9t2BB8zYxmNwu+dndr9W1pTg14PcQ1nHY0KYL9g/3s6t9VUEVO68SJiGQJa/ArdB59W1sQVpGpzhsLpX7U5vC/9BC/zZuD1oXFi4MPerm6hBOJ6K5ddftKTBpqiIXklDm0r9AhfcUek+tzQpX+a64oXU8i8Wi4a+mss0YGU2RrbR0eVtHSEoxmOuOM8M+QIgVqnOF/uWKec3Xf5qo0qdtXRIpUSgCFQitEREapqyt/hQqCxvS2tgPPBwfh1tTyWRs3Bp8LN25UhUoqpvYqVblinsO6hPNRt6+IFKmU9eO05pyISAzSy+Dk098P+/cP36akP6mi2qtU5Yp5zpwDUqg6nyMiIpVXSuCF1pwTEYlBehmcUtX5siBSv2qvUhU1VK+UIXwzZqhCJSJFKyXwopRjtE6ciEiWlpbRHa8pH1IlrdUuwAiLFwdzqDKHAKaH8KXnW0UlAGbSsD8RKVHvgt6KHLNzZ9GHiIjUv7BAskceCUYXjaanqq0Nzj03WIdRQRVSYbVXqUr/4Yclt8ycGV2hSiSgvT14XReRiIiISO3JbiDftAkuuWT0w/4gCKe4+eZgvlX63PPmBd/rM6GUWe0N/4PgDz8suSXXONmjjoIbb1Tai4iIiEitCgski6NClT5P//Bh2AqvkEqpzUpVlFzJf5nR6yI1yMyOMrMHzewZM1tnZleG7GNmdoOZbTCzp8zsndUoq4iISFlUI0hC4RVSAfVVqXrjjdyvqzVCatsAcJW7zwJOA75gZrOy9jkHODb1mAcsq2wRG1ffrj7eesNbFXEuIlJN1QiSUHiFVEB9VapyLfCbptYIqVHu3ufuv059vwtYDxyRtdtHgH/zwKPAFDM7rMJFbUiLHl7Extc2KuJcRKSawtYcHW3iX1pbG4wZM3ybgsukQmq7UtXTE4RTJBIHvuaj1gipA2Y2EzgFeCzrpSOAFzKe9zKy4iVFSi/Mm/SkFuQVEamm7DVHW1qCuVATJhT2OS/KjBlwyy2wfHnwvVnwVeuVSoXUbqUqnQ6zaRO4B1/zUWuE1AEzmwjcDnzJ3UsK1TazeWa2ysxWbd26Nd4CNqDMhXm1IK+ISJV1dh7osUqHVLz+OowbB9/9bvC5b/78/OeZPz/Y1/1ASFlU2JlImdVupSosHSaZDFoy0t3EiUTwXK0RUifMrI2gQtXj7neE7PIicFTG8yNT24Zx925373D3jmnTppWnsA0i3UuVXpi3f7BfvVUiItUW9jkvc258d3f+cxSyj0iF1G6lKmpu1J49MDAQtEoMDsLu3WqNkLpgZgbcDKx3929H7LYS+HQqBfA0YIe791WskA0os5cqTb1VIiJVFvU5L729kJj1uKLYRWJQu5WqqLlRmjMl9esM4GLgg2a2JvU418wuN7PLU/vcAzwPbAD+BeiqUlkbxsrnVg71UqX1D/bz4+d+XKUSiYhI3s95hYRXxBVwIRKD1moXINLixcNX3AbNmZK65u6/BCzPPg58oTIlag69C3qrXQQRkZpmZmcD3wFagJvc/f9kvT4W+DfgXcArwKfcfeOo3jTf57x582BZnlVF5s0bVRFE4lS7PVWZ6TCaMyUiIiISOzNrAZYQrJM4C7gwZA3FS4Ht7v424O+Bb4z6jfN9zlu6NAiiSPdGWUabZEtL8NrSpaMuhkhcardSBUpwERGRSGZ2tpk9Z2YbzOzqkNfHmtkPU68/llrKQESGOxXY4O7Pu3s/8AOCNRMzfQS4NfX9CmBOap7w6OT7nLd06YF59MnkgaS/gQFVqKTm1HalSkREJETVWtdFGk8h6yMO7ePuA8AO4ODsE2m5D2lmqlSJiEg9ql7ruoiE0nIf0sxUqRIRkXoUW+u6SJMrZH3EoX3MrBU4iCCwQkRSqpb+t3r16m1mtqla75/lEGBbtQsRs0b7mWrl55lR7QJk07VUdvqZyqcmriczmwekY8T2mdnT1SxPhlr5d4LaKUutlANqqyxvH8WxTwDHmtnRBJWnC4CLsvZZCVwC/Ar4OPCLVFptJN2byq7RfqZa+nlKujdVrVLl7jXTL2xmq9y9o9rliFOj/UyN9vPESddSeelnqlnFtK735mpdd/duoBtq63ejstRuOaD2ylLqse4+YGZXAD8jiFRf7u7rzOx6YJW7ryRYuP7fzWwD8CpBxSvfeXVvKqNG+5ka4eep3XWqREREopWldV2kGbn7PQSLz2duuybj+73AJypdLpF6okqViIjUnXK1rouIiJRClapAd7ULUAaN9jM12s/TqBrx30k/U40qU+t6Lf1uVJaRaqUcoLLUk0b8/TTaz1T3P49pJISIiIiIiEjpFKkuIiIiIiIyCk1bqTKzo8zsQTN7xszWmdmV1S5TXMysxcyeNLO7ql2WOJjZFDNbYWbPmtl6Mzu92mWS4Rr1etK11LjM7Gwze87MNpjZ1SGvjzWzH6Zef8zMZlapHAtS19VTZvaAmZUthj5fWTL2O9/M3MzKltRVSFnM7JMZ/+d8r1plMbPpqf//nkz9O51bpnIsN7OXoyL/LXBDqpxPmdk7y1GOeqJ7U31olHtT01aqgAHgKnefBZwGfMHMZlW5THG5Elhf7ULE6DvAT939eOAkGutnaxSNej3pWmpAZtYCLAHOAWYBF4b8vV4KbHf3twF/D3yjSuV4Euhw9xOBFcA34y5HEWXBzCYRXBePlaMchZbFzI4Fvgqc4e6zgS9VqyzA14Db3P0UgjCUpeUoC/CvwNk5Xj8HODb1mAcsK1M56onuTfWhIe5NTVupcvc+d/916vtdBP+AR1S3VKNnZkcCHwJuqnZZ4mBmBwHvJ0jxwt373f216pZKsjXi9aRrqaGdCmxw9+fdvR/4AfCRrH0+Atya+n4FMMfMrNLlcPcH3X1P6umjBOtxlUMhvxOARQQVzL1lKkehZfk8sMTdtwO4+8tVLIsDk1PfHwRsKUdB3P1hghTLKB8B/s0DjwJTzOywcpSlXujeVPsa6d7UtJWqTKlhHadQxpa3CvoH4C+BZLULEpOjga3ALamu7pvMbEK1CyXRGuh60rXUuI4AXsh43svID1pD+7j7ALADOLgK5ch0KXBvzGUouCyp4WRHufvdZSpDwWUBjgOOM7NHzOxRM8vVg1PuslwHzDWzXoI0yr8oU1nyKfbvqano3lSzGube1PSVKjObCNwOfMndd1a7PKNhZh8GXnb31dUuS4xagXcCy1JDK14HIsf6S3U1yvWka0lqjZnNBTqAv6vS+yeAbwNXVeP9Q7QSDHM7E7gQ+Bczm1KlslwI/Ku7HwmcS7A2WtN/vqolujfVtIa5NzX1RW9mbQQXWY+731Ht8sTgDOA8M9tIMEThg2b23eoWadR6gV53T7csrSC4+KTGNNj1pGupsb0IHJXx/MjUttB9zKyVYFjXK1UoB2Z2FrAQOM/d98VchkLLMgk4AXgodV2cBqwsU1hFIb+XXmClu+93998B/01QyapGWS4FbgNw918B44BDylCWfAr6e2o2ujfVvIa5NzVtpSo1Nv5mYL27f7va5YmDu3/V3Y9095kEk2V/4e5zq1ysUXH3l4AXzOztqU1zgGeqWCQJ0WjXk66lhvcEcKyZHW1mYwj+jVdm7bMSuCT1/ccJ/gbiXtgxbznM7BTgRoIKVbnmDeUti7vvcPdD3H1m6rp4NFWmVZUuS8p/EPRSYWaHEAwHfL5KZdlMcD1hZu8gqFRtLUNZ8lkJfDqVAngasMPd+6pQjpqhe1Pta6R7U2u1C1BFZwAXA78xszWpbf/b3e+pYpkk3F8APakb2vPAZ6tcHhlJ11N90LVEMEfKzK4Afga0AMvdfZ2ZXQ+scveVBB/E/t3MNhCEA1xQpXL8HTAR+FEqJ2Ozu59XpbJURIFl+RnwJ2b2DDAIfMXd4+5JLLQsVxEMP/wyQWjFZ8pQAcfMvk9QkTwkNX/rWqAtVc5/JpjPdS6wAdhDk17fWXRvqg8NcW+yMlz3IiIiIiIiTaNph/+JiIiIiIjEQZUqERERERGRUVClSkREREREZBRUqRIRERERERkFVapERERERERGQZUqERERERGRUVClSkREREREZBRUqRIRERERERkFVapERERERERGQZUqERERERGRUVClSkREREREZBRUqRIRERERERkFVapEREREmpiZLTezl83s6YjXzcxuMLMNZvaUmb2z0mUUqXWqVImIiIg0t38Fzs7x+jnAsanHPGBZBcokUldUqRIRERFpYu7+MPBqjl0+AvybBx4FppjZYZUpnUh9aK3WGx9yyCE+c+bMar29SElWr169zd2njeYcZtYCrAJedPcPZ732GeDvgBdTm/7J3W/KdT5dS1Kv4rie4qbrSepRBa6lI4AXMp73prb1Ze5kZvMIerKYMGHCu44//vgyFkmkPEq9nqpWqZo5cyarVq2q1tuLlMTMNsVwmiuB9cDkiNd/6O5XFHoyXUtSr2K6nmKl60nqUa1cS+7eDXQDdHR0uK4lqUelXk8a/idSQWZ2JPAhIGfvk4iISA15ETgq4/mRHBhRISLEWKkysy+b2Toze9rMvm9m4+I6t0gD+QfgL4Fkjn3OT6UrrTCzo8J2MLN5ZrbKzFZt3bq1LAUVERFJWQl8OpUCeBqww9378h0k0kxiqVSZ2RHAF4EOdz8BaAEuiOPcIo3CzD4MvOzuq3Ps9hNgprufCNwH3Bq2k7t3u3uH71xFvAAAIABJREFUu3dMm1ZTU1JEaoaZvd3M1mQ8dprZl6pdLpFaY2bfB34FvN3Mes3sUjO73MwuT+1yD/A8sAH4F6CrSkUVqVlxzqlqBdrNbD8wHtgS47lFGsEZwHlmdi4wDphsZt9197npHdz9lYz9bwK+WeEy5tbTAwsXwubNMH06LF4MnZ3VLpVIKHd/DjgZhgJiXgTurGqhRGqQu1+Y53UHvlCh4ojUpVh6qtz9ReBbwGaCJJgd7v7z7P00ZEmambt/1d2PdPeZBD25v8isUAFkRdSeRxBoURt6emDePNi0CdyDr/PmBdtFat8c4LfuXhMT+qU5TJ4MZiMfk6NiikSkbsU1/G8qwRoGRwOHAxPMbG72fhqyJJl0swmY2fVmdl7q6RdTcxPXEgyp/Uz1SpZl4ULYs2f4tj17gu0ite8C4PthL6jBT8pl167itotI/YorqOIs4HfuvtXd9wN3AO+N6dzSoJr5ZuPuD6XXqHL3a9x9Zer7r7r7bHc/yd3/yN2frW5JM2zeXNx2kRphZmMIen5/FPa6GvxERGS04qpUbQZOM7PxZmYEwyxqZ9iSiIze9OnFbRepHecAv3b331e7ICIi0pjimlP1GLAC+DXwm9R5u+M4t4jUiMWLYfz44dvGjw+2i9S2C4kY+iciIhKH2Napcvdr3f14dz/B3S92931xnVtEakBnJ3R3w4wZweS3GTOC50r/kxpmZhOAPyYYli6SUylzfTU/WEQg3kh1EWl0nZ2qREldcffXgYOrXQ6pD6XM9c11zKRJ4a9PmlR82USktsXWUyVSrKibim42IiJSa6J6pHLZuTNYgSL7sXNnZcosIpWjSpXUlaibWq6HiIjIaDVDMq2IlE6VKqmaOIdZiIiIiIhUiypVIs2qpwdmzoREIvja01PtEomIiIjUJQVVSE0KG7anuVYx6umBefNgz57g+aZNwXNQEIWISAx0zxJpLuqpkrqhoX8xWrjwQIUqbc+eYLuIiBRFYRQiokqVSDPavLm47SIiTU6JtSKSiypVUjWl3Ih084rJ9OnFbRcRqUNxLsyreHQRyUWVKqmaqBtUKcfkejS9sECKxYth/Pjh+40fH2wXEWkQpaTMioiUQpUqkUaWDqTYtCmoYWYGUnR3w4wZQbPtjBnBc4VUiIiIiBRN6X9ScyZNCm9F1NC/EuQKpNi4UZUoEZEMuv+ISKnUUyU1R+PWY6RAChGRUGFzrSDe+08pc7rinAcmIpWjSpWUlW4OVaZAChGRgsU916qUOV2aByZSn1SpkrLSzWEkM2sxsyfN7K6Q18aa2Q/NbIOZPWZmM0f1ZgqkkCZnZlPMbIWZPWtm683s9GqXSaTWmNnZZvZc6t5zdcjr083swdS96ykzO7ca5RSpZapUiVTelcD6iNcuBba7+9uAvwe+Map36uyMDqQISwUUaTzfAX7q7scDJxF97Yk0JTNrAZYA5wCzgAvNbFbWbl8DbnP3U4ALgKWVLaVI7VOlSmIRNcxPhjOzI4EPATdF7PIR4NbU9yuAOWaj/E12dgahFMnkgXCKqFRAVaykgZjZQcD7gZsB3L3f3V+rbqmkXjXwcPZTgQ3u/ry79wM/ILgXZXIg/ZMeBGypYPlE6oIqVRKLZh7OV6R/AP4SSEa8fgTwAoC7DwA7gINjL0WuVECRxnE0sBW4JTVs6SYzm5C9k5nNM7NVZrZq69atlS+l1IUGHs4+dN9J6U1ty3QdMNfMeoF7gL8IO5GuJWlmqlSJVIiZfRh42d1Xx3Cu0d24lAoozaEVeCewLDVs6XVgxHwRd+929w5375g2bVqlyyg1RNHpkS4E/tXdjwTOBf7dzEZ8htS1JM1MlSqpiia9cZ0BnGdmGwmGV3zQzL6btc+LwFEAZtZKMMzilewTjfrGpVRAaQ69QK+7P5Z6voKgkiV1KO7hd3FGp9f5sMCh+07KkaltmS4FbgNw918B44BDKlI6kTqhSpWMUMs3rjhVeny8u3/V3Y9095kEE31/4e5zs3ZbCVyS+v7jqX089sKUmgrY1QWtrcEvqrU1eC5So9z9JeAFM3t7atMc4JkqFklGod6G35VarqhGxzI2Rj4BHGtmR5vZGIL708qsfTYTXD+Y2TsIKlUa3yeSobXaBZDaU283rlLVys9pZtcDq9x9JcGE+n83sw3AqwQ3t/h1dgZfFy4MhvxNnx5UqNLbw3R1wbJlB54PDh54vlRBUFKz/gLoSX1YfB74bJXLI1JT3H3AzK4Afga0AMvdfV3Wvekq4F/M7MsEoRWfKUuDn0gds2pdEx0dHb5q1aqqvLfklitrLurPpZRjqq20n9NWu3tHeUpUmopdS62tQUUqW0sLDAyU//2l4TT19SRFq/a9Ke5E2zjLrGtJJD6lXk8a/ic1p4Fja+tbWIUq13YRkQj6fz7859dSJCL1S5UqqTm1MixPsrS0FLddRCSC/p8XkUajSpVIs+rpgZkzIZEIvmYu/BsWSDFvXvh5orZLxZTS6q+eAqk3VQhwEBEpmIIqZIRJk8JbC3PduEo5ptrqscyx6ekJKkPpBYA3bTpQOXrkkfBAijlzggpW5vyp1lY444zKlVtCldLqr54CqTe1kBorIhIltp4qM3u7ma3JeOw0sy/FdX4Znb5dfbz1hrfy0u6X8u67c2fxMeilHFNt9Vjm2CxceKBClbZnT7C9uzv8mAceGBlIMTAQHCMiIrFQj5xIfYqtUuXuz7n7ye5+MvAuYA9wZ1znl9FZ9PAiNr62kUX/b1G1iyK1YPPm6O3FBk9EnUtERIrW1A1+InWsXHOq5gC/dfdNZTq/FKFvVx+3rLmFpCe5Zc0tBfVWVZNa6Spg+vTo7cUGT0SdS0QkQi38P1/uOYW6Z4k0l3JVqi4Avp+90czmmdkqM1u1dasW4q6URQ8vIulJAAZ9cFhvVTHDAmtZVDSt4mkjLF4M48cP3zZ+fLA9KnhizpzoY0REilCrvTGlziks5WcJO6ZW13UUkfxir1SlVq0/D/hR9mvu3u3uHe7eMW3atLjfWkKke6n6B/sB6B/sH9ZbVYvDAjWBvgI6O+H004dvO/30YPvSpTB//oEeq5aW4Pn998MllwzffsklwTFSVaW0+tdCT4GIiEijKEdP1TnAr93992U4txQps5cqLd1bVW/DAiVGXV1B8ESmBx4ItkNQsRoYCJpNBwaC5z09cOutB+ZcDQ4GzzOj2KUqmiVcRqRYpfQGaakBESlFOSpVFxIy9E+qY+VzK4d6qdL6B/v58XM/zjksUBpcVMJf1HbInRgoItLAdu1S766I5BZrpcrMJgB/DNwR53mldL0LevFrnS0LtnDM1GPou6oPv9Z54vNP5BwWKA0uKuEvV/JfrsRAEZEYFLIodTFzgaPOV4q4e3fVIybSWGKtVLn76+5+sLvviPO8MnrZc6dyDQuUJhCV8Jcr+S9XYqCISAwKmVNbzFzgepuLW2/lFZEDypX+JzUkbO5UrmGB0mB6emDmTEgkgq89PdEJf1HbIXdioDS1QnoXqsXMNprZb1KL0q+qdnlkdHLNBW6UNFsRqU+t1S6AlF/Y3KneBb1VLpVURLoClZ4LtWlT8Dw7+a8Q6ZS/hQuDIX/TpwcVKqX/Nb06SOz8I3ffVu1CyOiF3c+WfGjJ0GvpHqz0NhGRSlFPVYPLF6leSste2DG13VIdXq5aLnNsosIlspP/0nIFVUBQgdq4EZLJ4KsqVCJSIbnuZ0qzFZFqU6WqweWbO1XKOlVhx9RBS/Uwu3bVX5lLUmyIRK6gCpH65MDPzWy1mYWOb9XC9PUh1/1MabYiUm2qVDW4XHOnSmnZU2tgnSk2RCJXUIVIfXqfu7+TYA3FL5jZ+7N30ML01VPMaImo+9kdz95Rs2m2xcatK55dpH6pUtVgsm9QvQt6md8xn7ZEGwBtiTa6OrroXdBbUsueWgNLZ2bjzOxxM1trZuvM7K9C9vmMmW1NTapfY2aXjepNo8Il5swJ3z8dVNHVBa2twXjI1tYDiwKXIiwoQ6RC3P3F1NeXgTuBU6tbIslUzGiJ9BIh2Y+PHv/Rmk2zjYphj3po8W2R+qVKVYPJvkGle5b2J/cDsD+5n1vW3MLal9YW3bKXb36W5LUP+KC7nwScDJxtZqeF7PdDdz859bhpVO/Y2RnMk5oxI6ggzZiRe97Uf/93UIFatuzAUMDBweB5KRWrdFDGpk3BJ4Z0UIYqVg2lVhdFNbMJZjYp/T3wJ8DT1S2VpIWNfBg/MXwIctR2yD0iQ0SkUlSpaiBhN6hFDy9iMDn8ZjSQHKDzjs6iW/a0ttXoeGB36mlb6uFlf+OwcImooIoHHoiudOULsQgTFZSxcGHx55KaFfeiqDF6C/BLM1sLPA7c7e4/rXKZGlaxwUeZ96eB5ACL/t8ijv7GSXCdjXgc/Y2TIt8nqgcrX8pt2N9sszKzs83sOTPbYGZXR+zzSTN7JjXS4nuVLqNIrVOlqoGEDc1b+dzKoV6qtP3J/azftr7olr1crYFxtlSXcq5Sxq1Xo3XdzFrMbA3wMnCfuz8Wstv5ZvaUma0ws6MizlO+ifVRYRWlhFhEBWUUG6AhUgJ3f97dT0o9Zru7FlUro2KG8kWNonhm6zOh+6/ftr6k9ylWrfa6lpOZtQBLCOYdzgIuNLNZWfscC3wVOMPdZwNfqnhBRWqcKlUNImpo3t0X3c241nHD9m1vbefFBS/i1zpbFmzhmKnH0HdVX96WvVJbA6OExZmbBel7Ua3eUTHoUPy49Wq0rrv7oLufDBwJnGpmJ2Tt8hNgprufCNwH3BpxnvJNrI8KqyglxCIqKKPYAA0RqWnFLsobNYpifsd8tizYwtiWsQCMax1H31V9DF4zmPd94lDDva7ldCqwIdUI0Q/8APhI1j6fB5a4+3YYmqMoIhlUqWoQUUPz8g3zi6vFr1Lx5I0Sg+7urwEPAmdnbX/F3felnt4EvKssBYgKqpgz50BYRbZ584oPsIgKyljcXB0GpawHVy251m9rirXdpCS5QozC7jNRoyh+/NyPWfTwoqHX+gf7R5yruLCkqDF9TTzWb6QjgBcynvemtmU6DjjOzB4xs0fN7GxEZBhVqhpE1NC8XMP8FI9eWWY2zcympL5vB/4YeDZrn8Mynp4HrKccVq+O3n7GGUFSX6ZEIgixKDbAIiooo8kWDS7ncKW45Wq4aJRGDYlXvkV5lz+5nKQnWb5m+dB95q4L7wo9161/fuvQ/sCw46LeZ9KkZGRl390iRixYBX4zDaUVOBY4E7gQ+Jf0/SyT1nyTZtZa7QJIPNJD8Pp29fG+W97HI597hEMnHprzmK67u0a0+C350JLYy2Yh965849PjPKaGhm0cBtyaGr+eAG5z97vM7HpglbuvBL5oZucBA8CrwGfKUpLXXovevnBhEGqRKZmMDrfo7oalS6Pfq7Oz6SpRmbIbL77+ga/nvTZF6kmuECPHR/Q6LfnQEubeOTf0XJ/40SdG9GClj3M89H3e2B3ePqzKfsFeBDLn7x6Z2papF3jM3fcDvzOz/yaoZD2RuZO7dwPdAB0dHeoOlKainqoGU2iLeLXj0Uu52VXqmHJx96fc/RR3P9HdT3D361Pbr0lVqHD3r6Ym1J/k7n/k7s/mPmsZFBsiUUqARRPR2m7S6HItyhvV6xQVSLF97/YRFaekJ7nj2Tsi30dG7QngWDM72szGABcAK7P2+Q+CXirM7BCC4YDPV7KQIrVOlaoGUsxwPsWjS6RiQyRKCbBoEtVuvBCphHSI0fyO+SQsQVdH19CivFG9Tpd3XM6YljHDXhvTMobZ02aHvsfHjv/Y0GL26ePGtIyhq2MUC5MLAO4+AFwB/IxgyPlt7r7OzK5PjZwg9dorZvYMwXzgr7j7K9UpsUhtUqWqgRTTIq7FEpvclBFD4Q9sjwqXiAq3iAq2EDVeSNMIa9S789k7i+51iurB6vlNT2QjhYyeu9/j7se5+1vTSw9kjaJwd1/g7rPc/Q/c/QfVLbFI7VGlqkEU2yK+49rNcJ2PeOy4dvOwc5YzsSwq7jxuSjILsX07tLcP39beHmyPCpe4/36YP/9Az1RLS/B86VLo6YGZM4NAi5kzg+dSE40Xxf6d51qnJ9e8xqglEqQ5hDXqffT4j5LI+piRIDHU65TdKzV72myM8D+aXft2RTZSiIjUAlWqGkSxLeK7Iyb2Zm6vp8SyYjV9kllPz8hPvGYHKkOdnbBxYxBQsXHjgaCJpUthYCCo/Q4MHKhQzZsHmzYF2zdtCp6rYhU5LKrUtd1KUezfea51eqJek+YW1ai3Yt0KkmT1VJHkjvV3sKZvDeu2rhv22rqt60bsn3lcVCOFjd0dekwjL9grIrVHlaoGEXeLeDXj1kttKZciLFwIe/YM37ZnT7C9mudqQFq6QBpdVKPemye+OXT/j73jY5Hpf7OnzQ5dmD7dGBG2AH1y78RmXLBXRGqMKlUNIj2Bty3RBkBboo2ujq6SW8SrmVhWSku5KltFikr4Kzb5L+5zNSCl/0mjK3Z+1I+e+RHrt4UvwZfe3sgjJUSkMalS1SDSreHppKX9yf0lt4rXY2JZUwzZi1NUwl+xyX9xn6vB1OO1JALFzantXdDLlgVbGNc6DoD21nb6rupj1rRZofu/ecKbGbxmMLTXafCaQfXuikhdUqWqQSx6eBGDyeETdgeSAyW18imxrAksXhw+p2rx4tLOFZYWWMq56kCuD5vZr5VyLZUSoBJn6EpU4IRCJ5pLsT1FYT2y+XqjijmXSK0zMxKJBIlEgvb2djbnGa1x7LHHFnzeRx99dNi2E088kWnTpg09nzp1Km1tbUPPTz75ZA455BAAWiKWPZk8eTJ/9md/BsAf/MEfDCuv6T/8kqhS1SBWPrdyxHog+5P7I+dURU3stbG7K5JYVu3hernmZ1W7bBXxl385MmHAPdherKi0wHS4RYPJ9WEz+7VSrqVSAlRyHdPUf+cpZtZiZk+a2V3VLks96NvVN7Rob3qx3nz7h/XI/qzzZ6H7P/m/niz6XOqtknqQTCZJJpMkEgnOPffcnPtu2LCh5Pc5//zzefXVV4ee79y5k2QyyRtvvAHA//zP/9DR0QHA4GD+hMynn36aLVu2lFweCahSVYfCWsqf+PwTQ0Mv0tpb29lx7ebQFucJbeMZ99ftcJ0NPdr/ejxbtu2OnAxc6vysak8gLnZ+VlNMbo76z7PU/1Sj0gIbTK5hSWGvxX0tlaISf+dRyyPUUDLglQSLmkoBFj28aKiRLr1Yb779w3pkP7nik6H7X3T7RUWfS71VUk9mzZo1VEmZM2cOLS0tJBIJpk6dyhtvvMHhhx8OQCKRYMKECQCMGzduqKfrPe95T87zX3XVVSSTSV588UWefvppEokEkyZN4oYbbgBgz549dHUFC2One50GBwc5+OCDMTPa2trYt28fACeddBIA733ve4f1dh155JEkEglaWlp46KGHYvrNNDZVqupQWEt51I0oV3S6blwixck1LElDlmqTmR0JfAi4qdplqQeZvVRAaG9VdsNeVI/s9r3bQ98jM8Ci0HNpYXqpF7t37+Y3v/kNxxxzDMuWLeOXv/wlr776KslkEjPjnHPOGapwJZNJXn/9dQAeeeQRkskkL7zwAk888QSPP/545HtMnDiR1tZWvvnNb/Ktb32LadOmMXv2bG677TbuueceAM4777xhx5x//vns3LmTPXv2cNddd9HfH1xna9euBeC//uu/2L//wIinM844g2QyyZvf/GYuvfTS+H5BDUyVqjoT1VIedSPKpZFuXBriJOWWa1iShizVtH8A/hIiFkACzGyema0ys1Vbt26tXMlqUGYvVVp2b1V2w146fTZhwUeK9Jps2Yv7pmUGWISdq9q9uyKlSiQSTJ48mYkTJ/Lzn/+c7u5u+vv7mTp1KolEgu3bt7Nx48bQY88//3wSiQRHHXUU7s6dd96Z873e8pa3cO+99/Lggw/y3ve+lwsvvJDnnnuOpUuX0t7ePmL/Rx55hPe85z20t7fzp3/6p4wdOzbn+b/3ve8Bwfysbdu2FfYLaHKxVarMbIqZrTCzZ81svZmdHte55YCo1vD0TW1MyxgAxrSMoaujK+e5GunG1dRD+fLp6YGZMyGRCL729EBq6MEIUdsl57CkWh6yFGeIRZznqgQz+zDwsruvzrWfu3e7e4e7d2RO/m5Gdz5754i/5aQnuePZO4Cs+VZPLh9qVAjr3YqKVE9vV8qfNJr0nKpt27bxpje9CXfn8MMPH9ru7qGVqiuuuILe3l42btxIMpmkpaWFXXlijT/wgQ+wadMmtmzZwhe/+EXmz5/Pnj17ePzxxwsOwcglHXDR2tqK19BY7loWZ0/Vd4CfuvvxwElo/HpBiomtLaWlPJd8H47W9K2hbVEbT/3+qdJ/QKmunh6YNw82bQpqmZs2Bc+nTAnf/x3vqGz56kiuYUnVHrKUq6e2lOCLKHGeq0LOAM4zs43AD4APmtl3q1uk2vbR4z861DiXNqZlDB87/mNAqidrcPh8q6jerbaWNsJMGTdl6FwaMiuN7LLLLmPLli08/PDDAKxevZrbb7996PUdO3YA8NJLL9HS0sL06dO58cYbCwqX+MpXvkJ/fz+Dg4O8//3vp6WlhdbWVrZu3crHP/7xEfufccYZPP7447zxxhvcd999Q3OqIJh3tWnTptH+uE0vlkqVmR0EvB+4GcDd+939tTjO3eiKia0tpaW8WJkfjubeOZeB5EDOScVS4xYuhD17hm/bsweeCW9B5oEHyl+mOhW1Fk/vgl56F/Ty5LzhiWZrL19bsZ5f9dSGc/evuvuR7j4TuAD4hbvPrXKxalquBoKhHqnUSMokQW/V7c/cHtq7FTUEffve7RoyK03hiiuu4Oyzz+bMM88kkUjw7ne/m1WrVgFw2GGHMWXKFCZMmMCyZctwd8yMK6+8MjIGPdPJJ5+MmTE+Y0mTdADGl7/85RH733777UyaNInx48dz7rnnMmbMgcaTE088kQsuuGBYUIUUrzWm8xwNbAVuMbOTgNXAle7+ekznb0jZQx++/oGvc+jEQyP3z9caHjqnasxO6C9+bM6avjWs27oOgHVb1/HU75/ixLecWPR5pMryrJMhxQlrWV/yoSVA0AiR6aLbL+LprqcrXkaR0Ug3BPTt6uN9t7yPRz73yNB9qevurqFeqrT+wX6mTZjGa/teG3YPGtMyhstOuWzo+sjWdXdXZCNh1DEitSxqiNy9994buj07wjwdHFHoeSEYbpgpbGhh+viWlhZeeeWV0POsWbMm8j1/8pOfRL6/DBfX8L9W4J3AMnc/BXgduDp7J00GHq7YoQ+5JvBGveb7JpcUcxz2AVHq0PTp1S5Bw8jVsp7ZCJGWboyQ2uDuD7n7h6tdjnoRNorizvV3DvVSpSVJsn7b+qKHv1Z7yKyISNziqlT1Ar3u/ljq+QqCStYwmgx8QC0PfdAHxAayeDFkDA0AguezZoXvP2dO+ctUp3INv81uhEhTY4TUo6gAiY++I3y+1eXvujxn8FHY3GGl/IlIo4mlUuXuLwEvmNnbU5vmABGTNgRqe4FDfUAsDzMbZ2aPm9laM1tnZn8Vss9YM/uhmW0ws8fMbOao3rSzE07PCuI8/XRYt25kWMWUKXD//cH3YYmBDSoqLKaY9XPWbwvP5Vn35f/KGwhTTFhNlFJT+cKOyUVLFzSHqFEUpfYuFTN3WESkXsWZ/vcXQI+ZPQWcDPxNjOduONUe+mBjd0duj/qAGLVdCrYP+KC7n0RwjZxtZqdl7XMpsN3d3wb8PfCNUb1jV9fI8IkHHoAjjoDXsrJkXnsNzjorOjGwQStWUR/4otbPSa+9M3va7KGW9cFrBvFrnanjpgIwddxU/FqPnM+YGQgTxwfOSqXyKRCj8eUaRVFK75Ji00WkWcRWqXL3NamhfSe6+5+7e/hS6qPVIC3o6ZvTlgVbOGbqMfRd1Vfw0Ic4os5f3LqLcX/dDtfZ0KP9r8ezZdvuoQ+I2Y/Ba4pPE4Tw1vB8LeJxqaV1dTyQrs22pR7ZM9w+Atya+n4FMMdsFL+t7u7w7VkTZIc88EB0YuDChSUXo1ZFfeCL2h4W4JJ232/vY/ve4L+97Xu384vf/aLk9xeplrhHUSg2XUSaRZw9VeXXgC3opbRSxxF1XsvDD+NUa+vqmFmLma0BXgbuy5iHmHYE8AKAuw8AO4CDQ85TWOhLAWtdjBCVGNiASYJRH/iitucKcPnUik8Ne+3jt41cJ6TQ9xepljhHUdTy3GERkbjVV6WqwVrQS2mlztVSXoy4hx9GDSeU4dx90N1PBo4ETjWzE0o8T2GhLwWsdTFCVGJggyUJRn3gW/vS2tDt9//2/sgAl8xeqrTs54W+v0g19S7oHRrimjZ72uySAiSapfGuEZjZ2Wb2XGo+74j05oz9zjczN7OOSpZPpB7UV6UqVwt6rmGBNTpkcNHDixhMBj0JA8mBgm40+aLO7/vtfdhfWd6hR3EnLyX3Tiw6ur2WhuZVWmpx7AeBs7NeehE4CsDMWoGDgPCFJQoxb1749tQCgSPMmROdGLh4ccnFqEVRH/g67+gM3f7JFZ8MPc9Ft180opdqNO8vUk1xpr9We+6wFMbMWoAlwDnALOBCMxsREWtmk4ArgewRFiJCfIv/Vsb06cGQv2xvelPw4THdi5UeFpgW9VpnZ3nLm0O6lXp/MlhIcX9yf94FgHPd7NIL86Y/3H38to/z6v/3ahl/gtGrtaF55WZm04D97v6ambUDf8zIIIqVwCXAr4CPA7/wXCv/5bN0afC1uzsYCtjSEvz9n3EGXHzx8JqvGXz2sweui4ULgwaL6dODClUVr5dyiPrAt37b+hGVnf7B/hH7poXtPyRi8e1Jk6LfvxSTJoVfN1HbRaLkSn8tdjFrxaPXjVOBDe7+PICZ/YBgfm92ivMignvWVypbPJH6UF9ezKxFAAAZnklEQVSVqsWLh1eQ4ECLeq5hgVGvVfFDYmYvVVq6typqNfl8N7uwifIfPPqD8RZcRuMw4NZUq2ACuM3d7zKz64FV7r4SuBn4dzPbALwKXDDqd1269EDlKm3mzJFdie4Hrov0o4Hl+sC37PFldN3bNfS8+8+6+fw7P0/frj6OueEY9g7spb21neevfH6oEST0tWtzdbuGv79dV/zPovQ9iYvSX5vS0FzelF7gPZk7mNk7gaPc/W4zU6VKJER9Df/r7Axa3GfMCFrVZ8wInr8a0SOzeXPNTrpf+dzKoV6qtP3J/TmHReS72ZUyUb7R1dK6Ou7+lLufkkrIPMHdr09tvyZVocLd97r7J9z9be5+arrlMHY1el3UiivuvWLY88t/cjmQO1hCoRPSCAavGQydU1Vq+qvUPzNLAN8Gripg38JClEQaUH1VqiCoWG3cCMlk8LWzM/fE+hqddP/E559gXOu4YdvaW9tZNW/V0PPsRUF7v9wbesyLC16MnCifb25VHAuP5hI2z6qQ+VZx0bo6EWr0uqgFyx5fRpLhw/mSJPnWI9+KTDJTypk0ijjnVEndGJrLm3JkalvaJOAE4CEz2wicBqwMC6soOERJpAHVX6UqTK6J9TU66b6QVKTsuPVcx0RNlM/XW6WV7ptUjV4X1ZDdsJDdS5X2lfu/Enn9zXjLVPZ+7Q24zoceb3xtD9PfPCXWskaFu+R6FHtMrqCYZg6XaRa5hplLw3oCONbMjjazMQTDzlemX3T3He5+iLvPdPeZwKPAee6+Kvx0Is2pMSpVUcMC0/NCol6ronypSGFx67mOiYpvzhXrrIVHm1iNXhfVkN2wkN1LlSnq+tv/xrjQ/aO2l6qU0Ilij8m1f7OFyzQjzalqPqk1Ea8AfgasJ5jvu87Mrjez86pbOpH6YaMJFhuNjo4OX7WqhEaOrq6RSWbZk/DrSN+uPt53y/t45HOPDEv967q7i5t+fRP7k/tpS7Tx+Xd+fijAIuqYN33jTcMqUVPHTc2ZANh1dxc3P3kz/YP9jGkZw2WnXBYZklEOZtGvVenPMi8zW+3uNbU+R8nXkkQGT9z32/v4k+/+ydB+D3z6AT549Acj94/zbznXuSolqsxxX7Plvp7MbBzwMDCWIJhphbtfm+sYXU/5Rd2DpHp0bxKJT6nXU331VHV1wbJlQYUKgq/LlgXb61TY8LuouPV0T1LYMcXOqdIcEJHocImo0BeFUdSdfcAH3f0k4GTgbDM7rcplqnsaNi4iMlJ9Vaq6u4vbXuOiht/liluPOqbYOVVa6V6aXVTDwg9/88PQBoofrfuRGiLqjAd2p562pR412g9eHzRsXEQkXH1VqgYjIl2jtte4qFbvXHHrUccUO6eqFla6r6W4c2k+UQ0Ln/7xp0P3n3vnXDVE1CEzazGzNcDLwH3u/ljIPoqBLpB6a0VEwtVXpaqlpbjtaWedNTyq6qyz4i9bkXINv4uKW7/7orsjj3ly3pOh77P28rWh23sX9OLXOlsWbOGYqcfQd1Uffq3nXBA1boo7l7gVs0RAVMNC9rZcr6UbImzs7tBj0tvLvXRBLsU2UuTavx4bQtx90N1PJoiJPtXMTgjZRzHQBdCwcRGRaPVVqXr724vbDkEF6oEHhm974IGqV6xyDb+Leq3zjs7IY0qNwdXYeGkkxfw9pxsW5nfM///bu/8gu8r6juPvb3aTEJKsVIkBSTYBRKfRRoM7FAanYhc7mD/IH9WKs6BW6g5Z7eCEqdMxig5MZrRO6Ug1yipUcbYq/t6psbSJYShOoARIMD/ESdMkLNlKRH6shBCz++0f59xwsznn/jh77j3n3PN5zdzZe557zrnfe/c+u/c5z/N8H2bZLIb6hvDP+Mlbo+Vj68aYOrYg8gLB1LEFTceVVNx6cHEXL2rtH6fIF0Lc/TlgK3BV1rEUlYaNi4jEK1aj6oknmiuH0xtU9crbpNbwu7jH9v52b+wxSdLgamy8dJIkn+e4Y5otTzsuSYeZLTKzs8L784B3Ab/KNqriysOwcRGRvOrOOoCmdNCcqnYOs4sTNTa+nSnVRdKU5PMcd0yz5WnHJak5F/immXURXES8x93/LeOYCisP/7dERPKqWD1VSedUyWk0Nl46SZLPc9wxO/9vZ1PlSZ5D9aw93P1xd1/l7ivd/c3ufkvWMYmISGcqVqPqiiuaKwfo72+uvCQ0Nl46SZLPc7NzFy9efiHHPvUSfNZP3l761FF6X3tWqnFlrafn1Lw+lVtPT9aRiYiI5FexGlX79jVXDrB58+kNqP7+oLzENDZeOkmSz3OzcxenXl4QeZ4/vHRGZHnSuLLOsDcx0Vy5iIiI5HVO1cgIrF8Phw5Bby9s2AADA8F2lLjyipI3oCAYhvT2f3k7v/jwLzhnwTkaGy8dZWzdGOMT41xw+wUcO3GMed3z2H/jfs5ZcE7NY3aM72DV8KqTZTtv2MnKxSsj97fPJourWUXIpCciIiKnyl9P1cgIDA7CwYNBrt6DB4PtkRGYPz/6mLhyOUmp06XTJVmUdPpSBPWWIBARERGJkr9G1fr1cPToqWVHjwblL74YfUxcuQBK6SydL0lCiB3jO9h9ZPcpZbuP7Obx3zze0lhFRESk8+SvUVVriJ979GNx5QIku4Iv6TOzpWa21cz2mNluM7sxYp8rzOx5M9sR3m7OItaiqZcQYsf4DmbfOvuUBlO9BbPHJ8a58PYLm7oI0cwxcQkh4m49PcmOERERkdbLX6Oqtze+vFZK9aEh6O4Ovkl0dwfbFXGPjYzA8uUwa1bwc2QkzVcyY0m+1EWdQymdc+MEcJO7rwAuBT5qZisi9vsvd39reFMK6AbUSwhx7Y+u5cTUiVOG99VbMHv6kNlGEkg0M8y22cQPExPJjmlW1okyREREiih/iSo2bAjmUFUPATzzzKD8E5+Aw4dPP2bOHPjKV17Znpw8dTvqsV//GrZte+V5KnO3IEiKkQPVX9CSLhZa6wq+FiBtL3cfB8bD+xNmthc4D9iTaWAdoFZCiOphfpXhfSsXr2Ty5vhFw6cPmf30Oz7NCy/EJ72IO6ZWooy8UqIMERGR5uWvp2pgAIaHYdmyoGdp2bJge2AgukEF8NJL0eXDw8EtypYt8XO3ciCteVBKnZ5PZrYcWAU8FPHwZWa208x+ZmZvijl+0My2m9n2I0eOtDDS4kuSjCLJkFkNsxURESmvVBtVZnbAzH4ZzgXZnvhEAwNw4ABMTQU/k/YcTU4Gt2ZU5nS1aWhg1FwPSO8L2ti6MfwzftpNKdWzY2YLgB8AH3f36f0CjwLL3P0twD8DP446h7sPu3ufu/ctWrSotQEXWJJkFEmGzGqYrYiISLm1oqfqneFckL4WnLs5ZkGjqBm9vbXTuqcsaq6HvqB1LjObTdCgGnH3H05/3N1fcPffh/c3AbPN7Ow2h9kx6iWjiFIv6UVax4iIiEjnyN/wvzTNnw/z5kU/NnduMFerWmXuVq207imKmusB+oLWqczMgDuBve5+W8w+54T7YWaXENTRZ9oXZbFN7/mtl4wiSpIhs0mOaTbxw8KFyY4RERGR1ks7UYUD/2FmDtzh7qdMaDKzQWAQoDcuy1+aaq1fdfw4fOtbQUPp0KGgh2rDhmCo4XXXRR8Tl+49oai5HruGdtX8gqbkEoV2OXAd8Esz2xGWfRLoBXD3rwLvAdaa2QngJeAad60Z0Kjqnt9dQ7tOJqMY+ukQdzxyBze87Ya6dSjJ0NgkxyghhIjkhZldBXwR6AK+7u6fm/b4OuBvCLLYHgE+7O4H2x6oSI6l3ah6u7s/ZWavBf7TzH7l7vdXHgwbWcMAfX198V8Uh4aCBBOTk0G69MFB2Lix+WgqDbeDEfW+tzdoQEXN1+rtjT8mJbXmeuR1vlNPT3SK5oUL9QWxEe7+AGB19vkS8KX2RNRZ4rL8dUpWPmmemS0F7gYWE1z0G3b3L2YblUi+mFkX8GXgXcAY8LCZjbp7dWbax4A+dz9qZmuBfwDe1/5oRfIr1eF/7v5U+PNp4EfAJU2fZGgoSHleSTBRSYE+NBQ/lG/27PihfBs2xD8WJ8kxTUoy1yNrcWveJFkLRyRtcVn+lJWv1BpdG06kzC4B9rn7fnc/DnwHWFO9g7tvdffKvIgHgSVtjlEk91JrVJnZfDNbWLkP/AWwq+kTxaVAHx4OhuxFmZqKT8NeK0V7nCTHNCnJXA8RiRbX87tl/xYlfSkxdx9390fD+xNAZW249DWbMTbni89LqZwHPFm1PUbtenI98LOWRiRSQGn2VC0GHjCzncB/Az91939v+ixxKdBrpUevlzY9SYr2tNK6x5i8eZK1fWuZ0zUHgDldcxjqG6q5IKlI2xTsC19cz+97v/fexElf4pY7kGKqtTbcjNd9azZjbBszzIqkycyuBfqAL8Q8rjUUpbRSa1SF3cZvCW9vcvdkY+XiUqDXS41esH9QSpsuuVXAL3xxPbzPHns28eLXUcsdSDHVWRtu5uu+NZsxtk0ZZkUa9BSwtGp7SVh2CjO7ElgPXO3uL0edSGsoSpnlL6V63LypuPKKgv2DUtp0ya0CfuGbvHmSw+sOc0b3GQDM657H+E3jkQtfN7L4ddxyB1I89daGS0VcZti0ykVa62HgIjM738zmANcAo9U7mNkq4A6CBtXTGcQoknv5a1RN/zJXr7yWHP+DSrKuTdbi1rzRWjgdpqBf+NJMSBGX9EKKpZG14VIRlxm2spj89KG0tfaHwg2/lWJz9xPAx4B7CeYd3uPuu83sFjO7OtztC8AC4HtmtsPMRmNOJ1JaaadUn7la6cyjyuudK6fymja9FqVNL4k2LCmQtrjhtEnSp9da7mDl4pWpxSxtEbk2nLtvSvVZVq8OstRO9/rXB0NnKxcFK0NpL7ssuo6tXv3K8Nvpx0Dqc3tFKsI6sWla2c1V969se1AiBZO/nqpa6cxf97roY846q+Up0EVKow1LCqQtzeG0SZY76OkJEoVOv/X0NP30kiJ3f8Ddzd1Xuvtbw1u6DSqATTGnvO++6KG0990Xf55aw2/VgyUiklv5a1TVSmf+m99EHzMx0fIU6CKl0YYlBdKW5nDaJMsdaA23kosbRdFsxtqDB+OH2VZ6rAqUQEZEpEzM3TN54r6+Pt++fXtzB5nFP5bR65ByMbNH3L0v6ziqJapLHWh8YpwLbr+AYyeOMa97Hvtv3N/00L+k9KcpmY6pT7U+AM3o6oIlS6IbaV1d0Y2xZcuCZT+k1DqmLonkQNL6lL+eqlq6uuLLNSxCpNTSTFQhEmloCLq7g0ZUd3ewXc/s2bW3q01Oxg+/jevdynkCGRGRsihWo2rx4ujyhQs1LEKkxLTum7Tc0FCQjKLSuJmcDLbrNaym92JVGmRR5s6NH367bFn0MTlOICMiUibFalQdPhxd/txzhVtXR0TSo3XfpOWGh5srrzh+/PTtEyei9305XE91YCAY0jc1FfwcGChkAhkRkTIpVqOqWRoWIVIKWa/7ZnN/31S5FFCzSSfSVsAEMiIiZZK/darS9OpXZx2BiLRB1uu+TR1bEPNIXLlIAgMDakSJiORUsXqq+vujy+PGp4uIiBTFihVZRyAiIgkVq1G1efPpDav+/vjhF7/7XetjEhGRzlcr+2xaXnwxvXOJiEhbFatRFScu+5GyIomISBoGB5srT0LzgEVECqtYjaorr4QtW04t27IF5s9XViTJPTNbamZbzWyPme02sxsj9jEzu93M9pnZ42Z2cRaxFtX4xDgX3n6hUqlL+jZujB4psXFjes+hC4EiIoVVrEbV9AZVxZ49yookRXACuMndVwCXAh81s+mTKN4NXBTeBoGvtDfEYrv1/ls58NwBpVKX9I2MwLZtp5Zt25ZsPcT+fl0IFBHpMPlsVI2MwPLlMGtW8LORf1pR63qI5Ii7j7v7o+H9CWAvcN603dYAd3vgQeAsMzu3zaEWUmUB4Cmf0sK/cpKZ3WVmT5vZrhmdaP36+PUQa823Wrv2lccr25s360KgiEiHyV+jamQkGKN+8CC4Bz8HB5NdDRTJKTNbDqwCHpr20HnAk1XbY5ze8MLMBs1su5ltP3LkSKvCLJTqBYC18K9U+QZw1YzPEjff6dCh2vOtNm4MFvt1D35WhgvqQqCISEfJX6Oq1tXAuJTqceUiOWRmC4AfAB939xeSnMPdh929z937Fi1alG6ABVTppaosAHx88rh6qwQAd78fmHkq2FoJkS6//PTeqq6uoFxEREohf42qWlcD41Kqb97c+rhEUmBmswkaVCPu/sOIXZ4CllZtLwnLpIbqXqoK9VZJqjZsiJ8HtX796Ut7TE4G5SIiUgr5a1TVS4++eXMwjKJyU4NKCsLMDLgT2Ovut8XsNgp8IMwCeCnwvLuPty3Ighp9YvRkL1XF8cnj/OSJn2QUkRRJQ8NpBwbi50HVuhgoIiKl0J11AKfZsCEYh149BFBZkaQzXA5cB/zSzHaEZZ8EegHc/avAJmA1sA84Cvx1BnEWzti6saxDkAJz92FgGKCvr89jdxwYiJ771NsbzP+NKhcRkVLIX6Oq8g9r/frgKl9vb9Cg0iReKTh3fwCwOvs48NH2RCQiqdDFQBGR0svf8D9QViQREUmFmX0b2Aa80czGzOz61J+k1tBAEREphfz1VImIiKTE3d/flieKGxooUgBmdhXwRaAL+Lq7f27a43OBu4G3Ac8A73P3A+2OUyTP8tlTJSIiIiItZ2ZdwJeBdwMrgPeb2Yppu10PPOvurwf+Cfh8e6MUyT81qkRERETK6xJgn7vvd/fjwHeANdP2WQN8M7z/faA/zGgrIqHMhv898sgjvzWzSrqks4HfZhVLDpT99UNx3oNlWQcwnerSacr+HhTp9as+5Ztef3Fe/0zq0nnAk1XbY8Cfxu3j7ifM7HngNUx7f8xsEBgMN182s10ziCtNefpdKpZoeYrljUkOyqxR5e6LKvfNbLu792UVS9bK/vpB78FMqC6dquzvQdlf/0ypPr1Cr7/crz+J6uUJ8vT+KZZoiiWamW1PcpyG/4mIiIiU11PA0qrtJWFZ5D5m1g28iiBhhYiE1KgSERERKa+HgYvM7HwzmwNcA4xO22cU+GB4/z3Az8N1FUUklJeU6sNZB5Cxsr9+0HuQFr2Peg/K/vrTVPb3Uq+/BMI5Uh8D7iVIqX6Xu+82s1uA7e4+CtwJfMvM9gG/I2h41ZOn90+xRFMs0RLFYrrQICIiIiIikpyG/4mIiIiIiMyAGlUiIiIiIiIzkGmjysyuMrMnzGyfmf19lrFkwczuMrOnc7SOQ1uZ2VIz22pme8xst5ndmHVMRab6pPqk+pQO1SXVJdWlxtWrL2Y218y+Gz7+kJktzzCWdeHv9XEz22JmLVsrr9G/I2b2l2bmZtaydOKNxGJmf1X1mf/XLOIws96w7j0W/o5WtyKO8Llq/p2zwO1hrI+b2cV1T+rumdwIJkP+D3ABMAfYCazIKp6M3oM/Ay4GdmUdS0av/1zg4vD+QuDXZfsMpPheqj6pPqk+pfM+qi6pLqkuNf5e1a0vwBDw1fD+NcB3M4zlncCZ4f21WcZS9fm6H3gQ6MvwfbkIeAz4o3D7tRnFMQysDe+vAA608LNb8+8csBr4GWDApcBD9c6ZZU/VJcA+d9/v7seB7wBrMoyn7dz9foIsOqXk7uPu/mh4fwLYS7BquzRP9Un1SfUpHapLqkuqS41rpL6sAb4Z3v8+0G9mlkUs7r7V3Y+Gmw8SrMnVCo3+HbkV+DxwrEVxNBrLR4Avu/uzAO7+dEZxONAT3n8VcLgFcQRPVP/v3Brgbg88CJxlZufWOmeWjarzgCertsfQH63SCocDrAIeyjaSwlJ9kpNUn2ZEdUlOUl2qq5H6cnIfdz8BPA+8JqNYql1P0BPRCnVjCYeTLXX3n7YohoZjAd4AvMHMfmFmD5rZVRnF8VngWjMbAzYBf9uCOBrV9P+CvKxTJSVmZguAHwAfd/cXso5HpMhUn0TSobrUuczsWqAPeEdGzz8LuA34UBbPH6GbYAjgFQS9d/eb2Z+4+3NtjuP9wDfc/R/N7DKCtdHe7O5TbY4jkSx7qp4CllZtLwnLpETMbDbBP60Rd/9h1vEUmOqTqD6lQ3VJVJca10h9ObmPmXUTDOt6JqNYMLMrgfXA1e7+cgviaCSWhcCbgfvM7ADBnJ3RFiWraOR9GQNG3f0P7v6/BPMIL8ogjuuBewDcfRtwBnB2ynE0qun/BVk2qh4GLjK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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Draw 2D histograms:\n", "fig_corr, ax_corr = plt.subplots(nrows=4, ncols=4, figsize=(12, 10))\n", "covariances = np.zeros((nvar, nvar, nspec))\n", "for ivar in range(nvar):\n", " for jvar in range(nvar):\n", " \n", " ax = ax_corr[ivar, jvar]\n", " \n", " for ispec in range(nspec):\n", " \n", " data_ispec = data[data[:, -1] == ispec] # extract the relevant species\n", " data_ispec_ivar = data_ispec[:, ivar]\n", " data_ispec_jvar = data_ispec[:, jvar]\n", " \n", " covariances[ivar, jvar, ispec] = get_covariance_offdiag(data_ispec_ivar, data_ispec_jvar)\n", "\n", " if ivar == jvar: # i.e. diagonal\n", " ax.text(0.5, 0.5, var_name[ivar], horizontalalignment='center', verticalalignment='center', transform=ax.transAxes)\n", " else:\n", " ax.scatter(data_ispec_ivar, data_ispec_jvar, marker = markers[ispec], color = colors[ispec])\n", " \n", " \n", "fig_corr.tight_layout()\n", "\n", "if save_plots:\n", " fig_corr.savefig('FisherInputHists_corr.pdf', dpi=600)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Make Fisher discriminant between species Versicolor (1) and Virginica (2): \n", "(i.e. not considering Setosa(0) for now).\n", "\n", "\n", "Put the (co-)variances into a matrix, and invert it to get the Fisher coefficients: __NOTE__: Fill this in yourself" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "covmat_Vers = np.ones((4,4)) # Covariance matrix for Versicolor, change this yourself!\n", "covmat_Virg = np.eye(4,4) # Covariance matrix for Verginica, change this yourself!" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Combined covariance matrix:\n", "[[2. 1. 1. 1.]\n", " [1. 2. 1. 1.]\n", " [1. 1. 2. 1.]\n", " [1. 1. 1. 2.]]\n", "\n", "Inverted combined covariance matrix:\n", "[[ 0.8 -0.2 -0.2 -0.2]\n", " [-0.2 0.8 -0.2 -0.2]\n", " [-0.2 -0.2 0.8 -0.2]\n", " [-0.2 -0.2 -0.2 0.8]]\n", "\n" ] } ], "source": [ "# This also requires the inverted COMBINED covariance matrices:\n", "print(\"Combined covariance matrix:\")\n", "covmat_comb = covmat_Vers + covmat_Virg\n", "print(covmat_comb)\n", "print(\"\")\n", "\n", "print(\"Inverted combined covariance matrix:\")\n", "covmat_comb_inv = inv(covmat_comb)\n", "print(covmat_comb_inv)\n", "print(\"\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calculate Fisher coefficients:\n", "\n", "Calculate the four Fisher coefficients:" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0 1 2 3]\n" ] } ], "source": [ "wf = np.array([0, 1, 2, 3])\n", "print(wf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Loop over the data (species Versicolor (1) and Virginica (2)), calculate their Fisher discriminant value, and see how well the separation works:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "\n", "\n", "\n", "\n", "\n", "# fill in yourself\n", "\n", "\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The separation between the samples is: 1234.00 <-- fill this in yourself\n" ] } ], "source": [ "print(f\"The separation between the samples is: {1234:5.2f} <-- fill this in yourself\") " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Questions\n", "\n", "As always, make sure that you know what the code is doing so far, and what the aim of the exercise is (i.e. which problem to solve, and how). Then start to expand on it.\n", "\n", "1. Look at the distributions of the four discriminating variables for the two species Versicolor (1) and Virginica (2), and see how well you can separate them by eye. It seems reasonably possible, but certainly not perfect...\n", "\n", "2. Calculate the mean, widths (RMS) and covariance of each discriminating variable (pair of variables for covariance) for each species, and put these into the matrices defined.\n", "\n", "3. From the inverted summed matrix, calculate the four Fisher coefficients, and given these, calculate the Fisher discriminant for the two species in question.\n", "\n", "4. What separation did you get, and is it notably better than what you obtain by eye? Possibly make two ROC curves to quantify this." ] } ], "metadata": { "executable": "/usr/bin/env python", "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": "3.6.7" }, "main_language": "python" }, "nbformat": 4, "nbformat_minor": 2 }