{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "id": "view-in-github" }, "source": [ "\"Open " ] }, { "cell_type": "markdown", "metadata": { "id": "_b1K4JUNNREd" }, "source": [ "# Regression and FFTs\n", "\n", "Recall regression through the origin. If $y$ and $x$ are $n$-vectors of the same length, the minimizer of\n", "\n", "$$\n", "||y - \\beta x ||^2\n", "$$\n", "\n", "is $\\hat \\beta = / ||x||^2$. Note, if $||x|| = 1$ then the estimate is just $\\hat \\beta = $. Now consider a second variable, $w$, such that $ = 0$ and $||w|| = 1$. Consider now the least squares model\n", "\n", "$$\n", "||y - \\beta x - \\gamma w||^2.\n", "$$\n", "\n", "We argued that the best estimate for $\\beta$ now first gets rid of $w$ be regressing it out of $y$ and $x$. So, consider that\n", "\n", "$$\n", "||y - w - \\beta (x - w)||^2 =\n", "||y - w - \\beta x||^2. \n", "$$\n", "\n", "Thus, now the best estimate of $\\beta$ is\n", "\n", "$$\n", " w, x> = .\n", "$$\n", "\n", "Or, in other words, if $x$ and $w$ are orthogonal then the coefficient estimate for $x$ with $w$ included is the same as the coefficient of $x$ by itself. This extends to more than two regressors. \n", "\n", "If you have a collection of $n$ mutually orthogonal vectors of norm one, they are called an orthonormal basis. For an orthonomal basis, 1. the coefficients are just the inner products between the regressors and the outcome and 2. inclusion or exclusion of other elemenents of the basis doesn't change a basis elements estimated coefficients.\n", "\n", "It's important to note, that this works quite generally. For example, for complex numbers as well as real. So, for example, consider the possibility that $x$ is $e^{-2\\pi i m k / n}$ for $m=0,\\ldots, n-1$ for a particular value of $k$. Vectors like this are orthogonal for different values of $k$ and all have norm 1. We have already seen that the Fourier coefficient is \n", "\n", "$$\n", "f_k = = \\sum_{m=0}^{n-1} y_m e^{-2\\pi i m k / n} = \n", "\\sum_{m=0}^{n-1} y_m \\cos(-2\\pi m k / n) + i \\sum_{m=0}^{n-1} y_m \\sin(-2\\pi m k / n) \n", "$$\n", "\n", "where $y_m$ is element $m$ of $y$. Thus, the Fourier coefficients are exactly just least squares coefficients applied in the complex space. Thus we have that \n", "\n", "$$\n", "f_k = a_k + i b_k\n", "$$\n", "\n", "where $a_k$ and $b_k$ are the coefficients from linear models with just the sine and cosine terms. Of course, we don't actually fit Fourier transforms this way, since there's a much faster way to do, aptly named the fast Fourier transform (FFT). However, knowing how fast discrete Fourier transforms relate to linear models allows us to use them in creative ways, like putting them into models with other covariates, or in logistic regression models.\n", "\n", "Let's numerically look at FFTs and linear models using covid case counts in Italy as an example.\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "id": "EEsfBUm_Hnfa" }, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "from sklearn import linear_model\n", "import matplotlib.pyplot as plt\n", "import statsmodels.api as sm" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 244 }, "id": "oaCy9-V4YtNe", "outputId": "abc5f9c9-97d5-4923-a8e0-ce1bb0f25de1" }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " Province/State Country/Region Lat Long 1/22/20 1/23/20 \\\n", "0 NaN Afghanistan 33.93911 67.709953 0 0 \n", "1 NaN Albania 41.15330 20.168300 0 0 \n", "2 NaN Algeria 28.03390 1.659600 0 0 \n", "3 NaN Andorra 42.50630 1.521800 0 0 \n", "4 NaN Angola -11.20270 17.873900 0 0 \n", "\n", " 1/24/20 1/25/20 1/26/20 1/27/20 ... 2/28/23 3/1/23 3/2/23 3/3/23 \\\n", "0 0 0 0 0 ... 209322 209340 209358 209362 \n", "1 0 0 0 0 ... 334391 334408 334408 334427 \n", "2 0 0 0 0 ... 271441 271448 271463 271469 \n", "3 0 0 0 0 ... 47866 47875 47875 47875 \n", "4 0 0 0 0 ... 105255 105277 105277 105277 \n", "\n", " 3/4/23 3/5/23 3/6/23 3/7/23 3/8/23 3/9/23 \n", "0 209369 209390 209406 209436 209451 209451 \n", "1 334427 334427 334427 334427 334443 334457 \n", "2 271469 271477 271477 271490 271494 271496 \n", "3 47875 47875 47875 47875 47890 47890 \n", "4 105277 105277 105277 105277 105288 105288 \n", "\n", "[5 rows x 1147 columns]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dat = pd.read_csv('https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv')\n", "dat.head()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "id": "l73uf3IniLl6", "outputId": "884b3d4d-17db-4934-d918-6eaab05fd18f" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Get Italy, drop everyrthing except dates, convert to long (unstack converts to tuple)\n", "y=dat[dat['Country/Region'] == 'Italy'].drop([\"Province/State\", \"Country/Region\", \"Lat\", \"Long\"], axis=1).unstack()\n", "## convert from tuple to array\n", "y = np.asarray(y) \n", "## get case counts instead of cumulative counts\n", "y = y[1 : y.size] - y[0 : (y.size - 1)]\n", "## get the first non zero entry\n", "y = y[np.min(np.where(y != 0)) : y.size]\n", "plt.plot(y)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at a smoothed version of it and then take the residual. The residual is where we'd like to look at some oscillatory behavior." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 282 }, "id": "4flqXoIrwIkE", "outputId": "50c52dd4-6f41-41d2-df77-c340e7d699c8" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = y.size\n", "t = np.arange(0, n, 1)\n", "lowess = sm.nonparametric.lowess\n", "yhat = lowess(y, t, frac=.05,return_sorted=False)\n", "plt.plot(y)\n", "plt.plot(yhat)\n" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 286 }, "id": "t0pjkISLettX", "outputId": "a7a95f31-8cba-476a-9dcf-a411f634575e" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## We're interested in the residual\n", "e = y - yhat\n", "plt.plot(e)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's manually create our Fourier bases. We're just going to pick some periods to investigate. We'll pick a fast varying and slow varying." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "id": "lvD9JeJ1Lk5t" }, "outputs": [], "source": [ "\n", "## Create 4 elements\n", "## Orthonormal basis (note dividing by sqrt(n/2) makes them norm 1)\n", "c5 = np.cos(-2 * np.pi * t * 5 / n ) / np.sqrt(n /2)\n", "c20 = np.cos(-2 * np.pi * t * 20 / n ) / np.sqrt(n /2)\n", "s5 = np.sin(-2 * np.pi * t * 5 / n )/ np.sqrt(n /2)\n", "s20 = np.sin(-2 * np.pi * t * 20 / n ) / np.sqrt(n /2)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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17NixA3fddRd++ctfAgCampqwYsUK1xwzZ84EAM/nQWLFgg48sPNQw5AHwIneEJw5z3Iur0vK8aICaUj2voUzXZ+/Z74VbXi1AQgOKds8e+FMV3qDkIeXGuBaEzK7YkGHq5LmzHmE4NT/WpPS0rMWdCCVDOadaao/N1oy1puoKO0EeB2IKErBOk5ZeTN9DN25dR04zxb7eAxZk81N2ygjLnTkYTxfEqYodW1k11e6PpoRHHqufLGMUtnkVpuxxxBdQ3Y9ZMRFl1yx91muWEZzxhsp8UZwxETRTWb11keHALZmpxjBufTSSzEwMIAbb7wRR44cwYoVK7BlyxYsXrwYAHDkyBFXb4slS5Zgy5YtuOaaa/DjH/8Y8+fPx6233opLLrkkbFOlcCIP9Xd6r1ZsII6YYPk8izzsaoC3+j1HLf3KGT3uN/ozbYIzpNRUhA1CBAnpInjPfGtdXz8ygnLZdBGLqEEI9Vmea22t6+7eYeFDNSq8UenBceb84FJlU/250ZS2HIiswod9oxU5FPYYUkdBHUM2N+vARfe5J4IjIEOsc5wMIL1BjyuVTeRLZWRTXsfM2igkD6yNugRQRjI816bI1ZHozs2SMFlqTjeCw6avJgolLsFh5xoVzO2NPIptpM9TTrhJimqKERwAWL9+PdavX8/92d133+357Pzzz8fzzz+vfXzeMYIGCb0fHprEaK6IGQFfCD94q8/S37yLSQcQMnFkaBKD43nMbMl4vhsV3qg05noXo2F5d3cbkgkDJ8YLODI0ifkzm3lfjwRvVmw8fe4M1+endrYgnTQwUSjh0OBEXbVCeyoi4mUMUVzc2YqWTBLj+RL29o95ziFKEILzru5gbZjKz43mCsEplEwUS2VuZMsTwRE4CtaByBzKuGYEh40UTBRKXOeiOzd7LvIIjjsyI8IEG83IlbgEp1obpeSTmntcRjI4c3MJDme9+Ta6U1cyAugmOPoRHNHcHsItmNu73nopKp0IzoyppMGZTuhoSdvCtbfrWF1TKpt2N87T57gdSltT2taS7Kpj6sI0TbxZcXrvZpxeUzqJJV2WlkTV5TVMmKZpdyhlyUEqmcDSLuszWRfTKEC6o57GXOtkwrAJraoFetgg0TqWzJ7MIBEcAJgUdPVlS4VFDsUboeCPyxfLrtSBLJXFOhtRqoglAaJxuikq0zRdc8t0Huz6iOb2kgw9LZNsfeifydJo+ukxPXI1kWfuCU0b/eh/dNNjomuTK/qIMlFzSVOrlbl5IvtaEBMcHzh9ruWY36yjYz54fLwSqk1wox/vrjiZt/vrZ+PhoUmM5UtIJQwspoSxBEsrBGdvHcnDwFgeg+MFGIaXPAAO6XnzaP1sHJ4s2CX/S+d415HYvVfRIj5MjOWKdsdZlsyezMhSvYBEzsxLHkROr7pxsgiFrpPSJQWeKEGeT+pyDNmTOT3WftFYj0ZJuN5lrXGmabrslEVwxjkpKi0bJWJtGjIC6CY4eqk+QHxf6F4b7zrqCcDH80VhHyVyTF7qrBbEBMcHiEOpJ8EhvVmWzpnB1V0QQiHb4yVskH1RlnS1cpu+LSWOuY42kr1tTpnV7HrbJrAJTh2v9dsV4jK3LcsNe5NIWD3XkazPnLZsXVOijYZEwrC3X9B1ZqLITLXOUdZMjv0Z+11nLjaKouf0hE7UM6/ERpaEiQgO42BF0QzWJtH6sDaxJIYGe83E14ZZH82onui6mKbpsmuyUBZ2HvYQRU3CLbo2HmKuWcJfNuGKMLrnssaptizxi5jg+ABxevVsAEfmPo3zRg8AS7osvcje/vo10hNpWwhIBOftejpmkp7iRG8AR0+yp46N9AgJ40WYgMZYR0KuiC0xHKiExrrOnidk5R6PfQP3EcFhbXGOofv2r+dEPfMKHLg1F7M+IsesmSbykAzN61Iqm8LuyOx5ikgYe0xdkiq6J3LFMthgSK2RGXac6Np4SRjfxnLZ1J+7ckyexqoWxATHB4ijebuOKQEiMBY5PRLBUe0QHCbI5m68tAoALKl83sjrSHrOHDg+wf15FCBpRtE6nkoIzrHRum0rcaDSkXpxZ32bNjYimm2CI3gT1nRmbJRA9RZsf09CcHSdFOuQZA7XfXw951gomcLIg66zZwlN0CQMEK85O7doF3VvdE2TPIiIJ4coCOfWjK7pRnB0SSpvfVVrnq1xmxcWMcHxgUWVapp3TkzUzaHYb8zCCE6F4Bwfr9s+RcTpLZzFd3rkbf/w0ISvjfKCxIHj1jqeKog8LKo47P7RnDS/HSYICVuqIGHDk0XpPi9hgpBZntbqZAchOCpNCEnjqiI4pLeOyOmxx8sXy8JnAImGZO255foWe27BOHI8MrcfRyZyzJP2W718fUiqpq1SBaY6XqZS0aYiGbSNwjXXXZ+i+9qoSJjqupD1zSQTSFWkCipCklVeG2a9FfeZahxN/sj6qK4NTy5QC2KC4wPzZzbDMKwbRLYDb5h450SFPAhKl+d1NCGdNJAvlnFkWLxTb5gg+0wtEtg4uzWDtmwKpom67Un1zgkrMnPKLH6ZentT2u5Ge7BOUZyDlWtN0o4smjNJzK+0e6+XDodcv3pvu9GIyKpSVBXHQ3YeV5GMWRWNk8qRkfsW8EaJnM/LrrHiFBVjo0K3Qsap0iDttI2KiEK7Yn3IXGQLCRUJI8cTEs/K91uzKSV5IOTKvjZCUuBeRxXpta+LgvQ2pRNKMmRfm8r6qFJzZH2E947nusijTM3ppE1cdElYUIgJjg9kUgnMa7ccCnE+USJfLNvb1IsccyqZsJ1NPYTG5bJpkweR0zMMAwsq9r8zGD15ME21jYBD0OpNwhbMFNt4ih1VrI+NBxRk9mRGc1r+xuxxZgqS0aFw9DnmeACfaJimab9J6zqpmQpyRc5F5UTJ562ZpDryoLk+k571UZAwYqNCjJxNqcmDTa58zj0hJIr+yENLJmUTaZUoeGZzxvVdzziGIAvXmx0nJNFeEiZO4cUanIbAwjo6vd6hSZRN6xdvjmAzOcBJXeyrgw7n6Mgk8qUykgkD8wSbyQHAKbOcdF/UGBwv2KWTCySNBklPoQN1uNYjkwV7r5wFAjILAKdU7K/HOk4WSjbhXhwTHA9UImPdN2GHjMhTMOT7zemkNB1Bz0OclNBGTWdmR6MqREidBklKyQPpXOyem3/ehco40nxVRcJmEYKjWMemdFJKHkzTsdG5NoooiopkMKROde+4IjiK6FqHilx5oke1RZnIfZpJJag0rPp8gkRMcHyingSHvKUvmNUs3eKARHcO1yE6cqCiyVgws1m6LxGxsR6RB0IG5rRlpTlfcq3rQXBIb5mZLWlp12yyjofqcK3JtWvLpuw30xgOmpUpKj2HouvA6VJb0k+EJ3Cm7Wlvkh+zULQ0PG1NeuSKpGBUpdpN6YQ0bZHnkDDR+uRLbhvFjt5N1sQkgxPB4RyzVDbtSibltSFRJkUazSa9iutCiFWGsjFfUpErct7yBn7qaJR7XL5Y5mpSyX2bTuqTsDiCU2cQ4Ww9dBmObkT+tkwaAB4ZjF6Do5uycAhO/RzzQklkBKBF5XUgOAqNEAGJ7hyqwzoeoPQ39dxTrFHRRDbcVDhSZYSiQjJ0IxTZVBJNKfHc5PvJhGFvz6AkVwqHy6ZWdFIRWYng1h8Jsz4n5yKuMiOE0oky8RyzvY5peZSJ3plceW0YMqsqZVeTB+szizyIxefFktMfx44UitaHaHAq660SYdOpUN55ExsztI2Ka5ONIzj1BUlb1EODQxytyumR1FA93uoP2toWuY2EpNXDMR+011FOwgiZJZVCUcLR3+itYz0jYaprfbLCduAKQtKuiDx4SIZGBY5dScVxKO4IhVy/kdeNHlVstyM9Jb5jtudOJ6TpH5IaSyUMtGQ11ycrXx+WUArnJlEmxfrQa+sQQIXAudKwsyBw9GzaUjQ3IXXpZEJahUd/porCedOR8mgUuW+FNpY4NnKuYYEiYU1xBKe+sFNUdXQoyrf6ilM8PBQ9eSBpMbVjrmcER28d6VRf1G0BCDlVkTCyzofqYOORIStCOK8jJjg8EIJT0Az1i1MwxIGnXf/3Hs95C85IRJ1ujYk8daBLHsgxScdt0wSKnBJ1rgaHm0ajbFToN/SjTG4SRn+XayO9PtwIjvPd1oycPOSZuXVTffRnvLkzSbkQ2k1wFNE1TW0NIWFtTWmQwK2sd1A6ZWjbGEdw6gyS/jk6lIu8z8w7mk6P2Ng7NClsohUWejWdHomO9I/mIu+Fo5vqI+cwli9hRLInTBiw9VYKojhvZhMMw3IIA2PRti5wrrVYTH4yI13RoIne1tmyXLWI1tmhnPd7TY7XlEpK56YjFE0pef8WkmbQTVG1ZRXkgRbHpsVz51wVOPIok21jphqCI44yNSk0OHySoTe3kKSSKrNsCgld8pCWRXCcfjk24VY0ilSV5TsEWbE+VJRJtj40ac5IdJvVICY4PjG3LQvDsG6w4+PROhRdXcbctiySCQOFkon+0VwUptk4UokaqZxee3PKfhhGHcXRTfU1Z5K2eJY486igG2XKppKY22ZV1EWd7iPRup6Y4HBBHtY83YG/KiG3BgcQRWac9I9OBMcdoZDrW9qUAmcveeDNTdJ1bg2OOIJDjxNGR5gIjqiSiRCXlkzK3sePa6NNwpJSckW0Uemk4ZA1hcBZN4LjmptLrvQ0OM4WCOpS7UmGcAs7cHPWh0fYaBtl9yO5JzKpBBKc/RVrQUxwfCKddEq0o3R6xVLZJg+nKN7qU8kEetqj1+GYpmmnLVROzzAMzJtpjYmaPBDxNW83dhZkHY9EbCMhK7IScQI6TRUlSIm4zjqejEjbKSpvlIB+0JPUgSj9Q8bOaKLTFjxhLkUKkroaHHlnXZY8qKp/WqjIA5dc2QJeeWolX6QcsyRNBPipMnOOmZFEuOiuw1IbK1VLaY1+OZO2RkmeJnKVf2ukx9KKFNUkj/SqIjiq+5FTwSWLcKm0XmxX7SARE5wqQKITUTq9/tE8yqZV+dAp6YFDML9CHqIsFR/JFe3qAJ23+u4KeeiNsOPyWK5op5u629XraF/rCNdxslCy002qFBXgpNKiJIouMtseR3B4yNgkQ5xiAByxpipC0ZxOSiMPtMg4nbLG8Ry4izwo0z+M/keDPKRl5KpIkytJdMTlwBU2MtEjlTi2KZ1EOiluMligHbgkwpUv0lEUPfJAbBSliXjkgRdJ0U2P0ZtY2teFQ7jpeUhPH3F/G+q8JSQsr0nC6KhV0IgJThUgzrs3QhEvIQEk/aQCeauOkuAQB9vRnEZLRty7hYA4xqMREhwyV2smab9NydBTIQ9Rktm+YSutmE0lXBUfIsytELWjI9HZeHwsj3yxDMNwiGoMN2RheZdAVRF5cJy9IXdmnAiF0oFLjlcqmyhr93mh5padN52isgXOmgJVoRCapPD0SJjVeE68N5KbPMjSRHrjSmXTtlEVwbGb4yXl6TEyzronJNERzj0hImHkfOwIjlZ/Gx2SamilTIPW3wAxwakK8+rg9IhjnqvpTByCE52NR3yKTu0IToTrSIhit6aN8zqit5EQlZ6OJq3+MjZRjNBGcq27ZmTth1cMN5w0iMxJGMqOx/ZYRUdYXudYnkMhjfFSCecNnDc3TcLUVVQle25ZNMMhBXKyxheoeuemuwm3ZlWCaWp9kuIIl6MdMSBL4fEcuMzRA45QXEUyUvT6cOf26lukImPXPeE9Xrls2lVvLh2V5BqqCLf7GqqJUJyiahD01CFFRQhOj0ZaBYC9CWOUugwS0dIVnRKSEWWKikRHutv8EZwoNy4lZErXxp46rGNcQaWGPJKh56DosXQ6gpe2oNMbsioq2/FQb/VFXiqL2+dFHkWhUyFc7REhV0lqbk5FGPnMSoOInSP9XTpFJY88GFI9Sp5yzLJro5uCyXOidYWSKW3gl6HmLnDWhya98maE3tQhl3CXHRtJF2wAKErIuSs9JiFhGTqVpai2ChoxwakCjgYnOvJACI5uOoCM6xuJrorKbwSnHikqQgJ0SZgdrYuQKB71GWWaWyFChLxFAXLvx/obMWRaFNo52o5M8VZPvwnLqlZSCUWaiIqiOHNzHFmRdswOyZCRB9ox87RH9Lk4mhB5+kcn3QY4KSpRDx5e1IPXo8jVoI6QgrJ4vWktiiwtB8CVupdHRyhCokqjScgDVyfEPZ6zXq0Zeal/XjN6xCOAMj1aKhl8N/SY4FSBnjqkVo6SyIOmQyGprGN1eKvvaderqqnHOtrREc117KlHiooQnDa9aB0dwYmq2R8hs3EFlRg6JMNyZOJ0CUA7CoeQcFMmVGRG7sw4JEOZqqHe6iURhVTS0CIk6aQhjTLRGpNMRTDNizLRUSJCwkRz05EZMjevhJ9ELTKphLQSzh0JE+/95RBPw5WG4acPqfOWrY9rXFI4znVdNLRRgCX2tSvhuOvjnDdZxyKXADo6KnknY4cwBY2Y4FQBWoMTlUPxH8GxnGPfSHQNCX1rcDosG/tHc9yHVxjoGyHr6I88jOSKGJkshGYXDUJmtVN9lXMZj7AhYa9mO4CTGTLi4oqiVB7sZRPcBn68iII8dSAnD7RDkY/zzisayyMPMu1RRlHpxbMxzzkeccCG4Y6O8FMmXqIoj+Co1pETCZM5eupc6HOkQa5rmlofLvmkIjPydeRdF/G4hGFV6upcQxcJ4xFAzv2j6socNGKCUwVI1UquWMbgeFROz19JbtcMqyFhsWziREQNCf06va7WLFIJA2XTKoOPAr0+S5tnZFN2bj+qVFqvT0F5S4ayMaJIk18yezJCJyVAvwVbn4vHWtoaSfk3z6EonZ7e8dJU+oDvzLzaEel50+kfmRNV6YkoG5MJw448yHQ9GUXkyr2OeuuT0hpnIJkwpKX+tLPXIxkJpBMahFKRTiqU3VEUh7hI7kfNCCA9tyrSEzRiglMFmtJJzG61dqSNStjppFb0Ig/pZAKdFRuPRqTN0O1iTJBIGHYX3qjW0U71+XDMxMaoNC59PsksPTaqa+03ongyQqatEb3V89/W9d7CixxthNSJpvTfwOnWFNy0RdmbjqgtPUY7ep1IWMI+rnBuTmWW7rVRduqVrCOd8qJt1V0f6XlTpFfXRtk9Zq+jZH3oaJ2U2HHuW14PnimforrtttuwZMkSNDU1YeXKlXj88cel47dt24aVK1eiqakJS5cuxaZNm1w/v+OOO7B69WrMmjULs2bNwic+8Qk8/fTTYZ6CB6Sb8bEIRLwT+RKGJ63Ug+5bPQDMqYhPo+iPMlmozsbuCDUu5bJJpaj8EJyKnimCbS9M03RK2TXJLBB9JRVZiy6NppPVYqo/N2ydh6YGB+C/MdMRAFm6Rtc50iJRmSNzqrcMGIZYE2KaJt/ZK0qMZSJa3jmr0kmWreLKLKe3TkJBMrwRCmUURTPKBECzgktfg5PWSbelEraWSWpjihBFGWnyRgp1iaI0gjMVCc69996Lq6++Gtdddx127tyJ1atX46KLLsKBAwe44/fu3YuLL74Yq1evxs6dO/Htb38bV111Fe677z57zKOPPoovfvGLeOSRR7Bjxw4sWrQIa9aswaFDh8I+HRskTRUFwSFvy83ppGuLehWIgzwWwVs9WYdMKuHLxigrqY6P5+0H1VxNAS8AzIkwgjM8WbSFin5IWHeE6zhZKGGkQmbnhERwpsNzQ/rGTOk3DMNAKkGcjzzNQBwQV3BLR2YCiKLkBU6PdWa0zcroUZEmDxKHS2tMZBqcovvtX0rYeERRSgr0yEMmZWin+ui/VSk8m2Qox+mdMxEjq8TNtI1yHZWmVkexPlNag3PLLbfgiiuuwLp167B8+XJs3LgRCxcuxO23384dv2nTJixatAgbN27E8uXLsW7dOlx++eW4+eab7TE///nPsX79epx99tlYtmwZ7rjjDpTLZfz2t78N+3Rs2BGcCN7qj1Jv9DqN3whIH5UonB7Z1LOrNePPxgi3a+i1m9NlfL0tEDIU5bXuaE77al1OyGwU15psI5FJJuy27kFjOjw35GF+xjELnBTdTVitCaHKxGWOx5U60BOoys6H/r+rrFulb5GVqFcZHRGRAtc60mX0XNKkqcHRFVZXxpF0jk56zN3LSH4N5Vqmyn2mbB0g0OCoBOApNQmj7wnZvmxTrkw8n8/jueeew5o1a1yfr1mzBtu3b+d+Z8eOHZ7xF1xwAZ599lkUCnxB7/j4OAqFAmbPns39eS6Xw/DwsOtPrYjyrb63Sr3DXKqSKmwQkXCXj8gI4KRWohDHVpOeAuhrHb6NfsXkBFGW3A9UiF7nDH9kVheN8twAant26GotrL/5KQHawdCCW1WKSi+CYyicoyjyYHLHAZaT0ol6pKgoimo7CZ1UTSbltlFGwlzrGEgZvbyXEe3orfH8a013E04lDK1olFIwbZeyO1GUYtn0VNaKr7WcpOqV+uuvY9AIleD09/ejVCqhu7vb9Xl3dzd6e3u53+nt7eWOLxaL6O/v537nW9/6FhYsWIBPfOIT3J/fdNNN6OjosP8sXLiwirNxY06Eb/V9PnvgEMyNMG0xUKUmI8pIWO9Qpfy6SqIYjY2kgsrfOtrXOhIyG67+plGeG0Btzw6dCAV5axU5SNoh6OpR6BQVvwEbJ72haAho/c3XUdDnl0oYmqk5lU6I1piQPjiySIbbRnbN2XXUJSS60SNHY6ImDyLySZeYpzWJnYu4yMTfFAmjv2/PzayjqETd0lt5o0dSzZNK6zWVNTgAPG95pmlK3/x443mfA8APf/hD/PKXv8T999+Ppia+47r22msxNDRk/zl48KDfU/CgLm/1PktySWolWqeX8fU9EvGJUsvklzzMmRFdp2BCouZqbtNAQO7H/iiu9YgVrev0ea39ot7PDaC2Z4dOBIet/mFD+DTxSCc0t2Dw45ilglc2jSbS4DjnYhgq/Q9dHu+vf0u+5O2izOpbRFU97Dr6bYQo10Y5JAOApxcOq28RiYzpOWiNkrLjsZRIe0u1eccU6YRY4lsqmyCXwBU9UvUTSqivdSaEFFU4CfQKurq6kEwmPW9dfX19nrctgp6eHu74VCqFzs5O1+c333wzvve97+Hhhx/Ge9/7XqEd2WwW2Wywb5tRVtYQguJHGAs4EZ8ouhmTFFVnlRGcKPrgEBI2xyd5iDKCQ8hDV5s/8kBHwlREoFaEXUHVKM8NoLZnh5Q8lFjyIHd6qYSBRMKQV8KUvSkTpePxo8FRpKicKIreMaU6D47IGLAiBS4yIVhH9ph06ieR0BUFy9ebl6ohNmUpz1oUXWs2gkOTMFd0TbHthG6aKEHZyMwtspElTS5BeUqzEWJKTsJYchUkQo3gZDIZrFy5Elu3bnV9vnXrVpx33nnc76xatcoz/qGHHsI555yDdDptf/YP//AP+O53v4sHH3wQ55xzTvDGKzAnwsgDeSv361Ds/i0RdDOu1ukRR358LMft4hokbILjM/JAyMPgeEG4U3FQcMTaPtexYmO+WA69m3HYKarp8tygIzhs5IFu8w9oREcq41IJTQ2OTpqISoPwuih7S4fl+hYyTp9c6ZyLk/KSze2JhLEpKmZDR53dv9OphLPesoowtlkjS1yYayiK7JFx3m7C8gggqcCTXetU0k3sRFovYpuINNHfSyUUXZR5lXCyjWen4m7iGzZswJ133onNmzdj165duOaaa3DgwAFceeWVAKwQ8Je//GV7/JVXXon9+/djw4YN2LVrFzZv3oy77roL3/zmN+0xP/zhD/Gd73wHmzdvxqmnnore3l709vZidHQ07NOxQQjOyGSRuy9MkKjWocxpc7oZHw+5m7FDwvyRh87WLBKG9YAdGAuXLNpCaJ/rOLMlbT8Ywo40kTXwG8FpziQxo/LaGDbpdtYxvBTVdHhu0CkB75swo3kgWgaBdkQVoQDcOgp5zxN+dERIXBJElyFwekwqS04eKH2LRIys20WZLkUmx5WeC7Pesm0Q6BSMbP+tdNLdRVlECggREel/PN2ENZrtuUTdGlE4EbnKM+uoJXpXiNR515DXB4fWCQWN0AnOpZdeio0bN+LGG2/E2WefjcceewxbtmzB4sWLAQBHjhxx9bZYsmQJtmzZgkcffRRnn302vvvd7+LWW2/FJZdcYo+57bbbkM/n8YUvfAHz5s2z/9AloWGjvSll53HDdiikLNev00snE5jVYn2nP+T0CrHRb1+UZMKwu0KT9ExYsImiz1SfYRj2eYWtubJTVFVER6LS4QzYqb7wmvxNh+eGn8iD0OmxBIcQF+U2COKeJzyNCcDTZbClw/Iok02EtHVCeqmsZMIAybh6bCwK1keQ6sswUSblbuIazfHYCi4RKVCRDE83Yb/N9hRbaABikqqb6qOJomEYcqLIicKptExBI1QNDsH69euxfv167s/uvvtuz2fnn38+nn/+eeHx9u3bF5Bl1cMwDMxpy+KdExPoG8lh4eyWUOYplsr2XlLVOL2uGRkcH8tbjrMnaOscVEseAOu8+kfzoWtcqk31AcCc9iYcHpqMIDpSKcH2maICrGu9t38s9ChTLTb6wVR/brhEncUy6OXS1uBQ3YStv/mOxzRNbo8ZXQ2ONRff4bIpKjal5GzToE5R8boJqyqZiCPNF8vajlmU/iEpJ50UHl3Kruq2TI6ZK5a90bqiYH0UqT65wNl/oz/6vNnompdI88+7IOrfpLuvFneX94o+aipGcKYz7AZwIW6FcHwsD9O08rIkGuMHxAmFGcEplJxNR8n+V34QReRhIl/CWN5KJVaTWrEjOCHaWKJSiX6jdQCtCws5yjRavY0nE2RpC6+Alx8p8HYTrjiKMksyfFTgFFnywO+izDrHlMBJeVJUOg5Xd8dqkjIRVOFoa3DYVJbPMnG+TojfRZkt1/b2wVGkidhuwkryoBHpUZAmERESrmPl57K9qFwVcxLB/ZQvE5+uiEJoTKIas1uzrg3vdEEiKmESnIGKw0smjKpIWBS9cMj5Z1MJW6viB1FszUHIrGEAs6tYx64IKtJqjSiebBDpUZy3enlaR1TJJBKykmNqRVE00xGO8FSRomLSbawzY7syy9Ib3tSTrrZGXiauShOx56ObbqPnFpdg65WJ+yKKykom9zFF5fGe9VZocLw2yjtC16tMPCY4NSAKglOroJN8L0yn12+TsAwStZCwCIhi1wx/210QRBHBIQLjWS2ZqsK1UWwAW2tE8WSDPnng6yh0Iz3099JJqs+Lj7d6lQZHfS7ut39Zx2PtzR89UQ9+REHVyZhEuDxRFMYx092EVRte6kaPhARQVG3F6IlUBFBvywuFwLnKa62jwaEjYdJqvTiC01ggvXDCdHq16Ebo74UZwam1bDiSCM5I9RohIJoIjiMwrpLMRhCtqzWieLJBRDT0++Aw5EHgzOjmcikq/cPt/qspChaSDIUDFx3PT1dmlpAIq6OEe3rJUysOyXBXwLLdhGVl0J60l4hcCSIz7LVh96zSiczQ5KHE6aLsjcwo9D+6ImNFewP6swy1aSlvLPu7ECRiglMDoongVFd+TTAnEoJTq2O2vhdFJMxvDxwCJzoSnr6lVvFuVwREcSCCEvHpBMeJK0iBZgm22kHpVLe4+47YqSdBF2U2jcZqTDxkTXAutEN3d2WWpzfIefGOqe2Y2a0IhNEWVsvkjPP0MvKZPlSl0cSpQ3mJuqyLsjAC6Gn0p0ek/e3eTguhHRuF20RMxT440xlRakeqjY50zgi/TLz2CE6T6zhhoFYbnehI+Km+aqNMUYi1w27yN92gQ0jov1UOPCUS20p2J/dsbyDQtyibvwmiGcQ52vtqKc7F6SbszCsmDypC4k5Riedme8xobOmQ9HYolh0zpdTgqEiqngaHTaPJbBSl5rwRLvb+qZyLotpKFI1iz5vuosyOJVV4sQanwUAc0UCoTq+6XboJiCMK1cYqm/wRRBPBqZHgVKIqA2M5z8M4KASptwrPxtqu9ckGEXEhD3m2u61Qv8H2b1E4UXI8U6p5kKdCxGk0AclQjPN0E6YcM9tIj40yqdJeqgZ+Yk0PfxzpJhxEF2W/6R9VtZUnjUbbqBAPK/staXatVmlw2E05EwlDSM7JfZJKBE9HYoJTA0hJdP9omE4vmMjDQIhOz25EWKMG58R4gRvqDAK1OmZCwiYLZYznw+lcXfO1Jts1lMoYnghnu4Zqu0GfrFA7ZubtXyg8ZUuHVSkv735N3mNq6i2U2hq93igeYuWyUeHstRsh8tdHWIKtjLaIbRQRNlF0zdtkUN6VWRzVc6fR9NoRVEcA1fcE30Z2U07X3Ip+S0EiJjg1gKR/csWy3WMlaNT6Vk9IWLhOr6IdqdLpzWrJ2ILVsCJNziaW1dnYkkmhOW11hw3LxoEaSVhTOom2psp2DSGl+2oVa59sUL0xpxRC32rFyPRbPTvWK3pVpcfkfVlEDQFFjpmteLKOoag8UlSPsevDbgkgduD8yBFxyrIuyiLCpl5HvTSaaINKNo1G/y3crFVTy+RtKKlKZYnIGqW3UhI29/oEiZjg1ICWTAotGcvphaV7qPWtPgqnd6zGFFUiYdhELKw0VRDaEUJoQyMPAURHwha+h72T+HSDqLzZqx1RiWPdDkrowO1NOSWRB0E6Qm2jnoMS6ltsUue1UbwFAxt5UESjBGmQIpPyUu5ZVRlHC7aFGhxFEz19DY5mRIhJo7nHakbrBM0aWSKkEgSrUqa881bZGCRiglMjiNMLY6PIctnE8RrTP/R3wxLxBuGYw7YxCMfcaeuZwiVh1UbCgOiudWeswdGCqm+N7sPf4/QEb8yENBiGuIeLtgZHWMGlm/KSdxM2DMN/XxZV91+7/Ftho4CEscSK/o5wl3BFWqfoiaL40+Co0mj0eYsJmx4R8qb6qtPg0HaoopTstQ4SMcGpEWF2jz0xnrcFgrU4FBJZCSO1YpGw2jdfDDPyMFkoYWTSSs/53QyURlcrIbPBr6NpmoGUYIcdwbE32owjOFrQ13ooUk8ptwNXaSOsf3vLv+luwlXrW4RpEIXTK3ptVJEwVQM/XXGsUIysqBKiv6NaH+W5qNI/nqiVSJflTqPpjK02xVmtBocma6SxqqhxIY+wBYWY4NQI0rMkDPJASNPMlnRNFz/Mt/oT43n7gTm7in2oCMLs4ULOO5NMoL25+v1lu0KM4AxPFu1f9JpSVCFe63LZrFlQfrJBO4oi2CXctwaHEmryyr9pO/xqcIQl6toCVbFjpse6y6BVjlRTTyTcL0uuwaG/o06j8UmGh8wqdjzXjuqlvDaqxdp+yZqmBsejE3LK2FkbPQ0OGRIfJGKCUyOc6Eh4jrlWZxImwQmMhLWF16+HTqtUs00DQWeI216Q+2dGNoWmipi5GnSF2PdocKIQSETxZIJuWsfuJ6JoYy9sElf0hvl5Tk+mjVDaqIj0eLedYMaV3efimpuKMrnKoP1qcLQjD6J0kthGr2OuLs2ojB6p9C2yNFrVJep+G0q6x5XKpqsdAavzctvIj+zFZeINiDAb6QXVcyRcghMMCZsTYqqv1u0uCDojIIrBXeswIorWeddKZk8miLUMfIGqKq2jdmQ8p0dFcIpi8qAdPRLof7wRCkFnZM5bvctGugJHpUcRbEWgWh9HrO3e3oDVCQEaxI5cw4D2eWK30GBt5KfRvMe0etG404e6/ZZUm5ZmmMoodqzMRs89Xnb/LgSJ+ClVI0iKqj8EXcaxwBxzeJGHwElYCNqR4GwMT8sUhMAYCJnMjpCtJOLojS7EEReBY1aIOlOKcSrtCC1GtrURijdrfX2Ll6zRvbd4YlIeeeCVQWcEKTxvqk/TRnpvpLJ3fXjrSDtmbhpNkcLLKIS+0h48HBvpNBqvi7KMKCr7LenqsigbeASHm46k5nY3BIxTVA0Hp5FemG/1Dez0ArIxzGq0oFN9YdhYaw8cApvMhkAU4xJx/9CvZJJ3eWWdnmpbBfo7rvQPhwipyrq9UQ8REfL24ClyIg8unRDXMVv/psugbXLFbibJpnV8CoKtn+lGR3TTaLpRJoFOiNcnSNPGImccfb5ikirQKHkaJrq7DruuNTU3L43GW0deQ8AgEROcGmFX1oT4Vl9LdZL1/SjSaEGRsPDE2rU2pwszEnbM1gkFtI5jwXeuHghoHU8m+Ne3yFMHYsLkTkXQc/M0ODzHo6sTYp2eHclI8MgDb245eZCP45MCMidxvOy5sFtjuMhD0UuueETRPY4THRF0KCbr45ACOUnlRkeKnHWk02ic9XFtbqpqRqhJworM3MmEYZNQ/WstX8cgEROcGmH3RgkhRUXe6mtNCTjpnzD1LcHYeGI879mtuFYEFXkg6cgwbAxMy1QhH/liGSO5YDtX24Q7juBoIyxRZ9l07zHFfavnpBlYRx+Ejd4SbCq1woke0Q3+ZORBRTJ45y3SPLE2irY3IJEHmiiqtUzu9RE1YVSV+rObTorIA6/cnkdcyDkbPhoCpphrqBcpFKfHVKk+nug9SMQEp0aQt/pwnF5Q6R/r+xOFEsZCcnq12ji7NYOEYW0OeDxgshgUCZvVkoZRsfHEeCEI02w4/WVqs7EpncSMrFUKH3SaKt5o0z/E5d96+haRNoIdy3M8vHSNNAWjLG/W0+qItjfg7TnEJQ/cChxRCk8v1cd3uF7Cxh3H6d9Cjk+TEHGJOj895kn/cCvhdMmDV1tDX2tWb6UiLrqpLPdYisxyrjU/guNN9QWJmODUiFktlGMeD9gxE4dSY0qgNZNEU9q61EGn0oLqi5JMGHYfnaB74RAba408pJIJzGoJRyvUH1CKCnDvKh4k4o02/SMrrG7R1OB4ugmLqlZkDlye/lHpVtiKGZW+xb29gSIywyEPMv2GKI3mrTKTkwzrvDiOWZai4q4jx0aBbkW7ikpFHjRtZKuyXOMUDQHJ2ug0QpSR1Ay9PimxTiidNGpq4SFCTHBqBO2YgyQPQXW2BawHTliN9OzKmgDe6sPS4QRFFAGKPASc7hsIUMAb1pYSQVV6nUzgOWaesFK8BQMTRaF6hbgcLiP0pb/jSv9IyYNm5EGjOR7P6fFIAdGlKEW0ihJsb8fjKsvoJcRFl1CqK48UGhxOhCvP0+DongtH1K1bCSdqyscndnINDj/V59YnBY2Y4ASAMLoZD08E09mWIIxKKtM0A32rD6NTcKFUxmAlnRREebN9rUOK4ASR/gmr2V9Qqb6TCTzHTDtfe38iTtdhgCYu1s8TCYPbUVi3NwrPMacUxEW3xFhVos7uYq6ykR+hkJMw3VJ20fnIHLNrHOkHo0XC9NI/vKhHSjvNKG4JoIpaAY54mETryD2m1zFbb25uus1u/hh89AaICU4gCKPEmURaau1sS+CQhwBJGLW9QK2VXkA4TRNPVNJTCQN2eqkWhFFJNVkoYbSijQomRUWidcFGFPvjbRp8Q1bJZP1cbxuEjOKNWbf8W1aqzabR/O+CLU/X+LWR6xwV4mF1ybvCMTOl2oA+yVCl+uxmewKSIde3cKJwHH1LTrMizHsN+SkqVcoUcKKKqvvRiSjKWwcEiZjgBIDOEFIrQfVFIQjjrT6o7QUIwkhRkWPNbs0ikaj9LSGMKJNrr6ym6vfKIggjWjeSK9oPsCDI7MkCntOjixHSTD8RHccsa+qm0q1wIxS8aiuqQsuJPBge+91zqyIzPHIlSVHx0m2KUnZeysuyWVMc61eDQ9lI5qZJBt1NmCWK7PYG8s1IvQ0T3Y3+5PoW77nopai0qvXI3NyeR4pUH4cwBYmY4AQAkvoIlDwE/LYchtOj93gKAmF0MyZRtaCIYmcIequg9soi6Aqh2R85VlBk9mQBP5LhdBMmpNvPW31G6sz0SAa3VFvQJI5t4Kfa78h9PnLtSC36FnpndLbSS9ipV9E7RluDwy3V9l4XGVH0M3dRsY48Ik3uuZRrHfnROpFOSMtGqVBcnqIKcydxICKCc9ttt2HJkiVoamrCypUr8fjjj0vHb9u2DStXrkRTUxOWLl2KTZs2ecbcd999OPPMM5HNZnHmmWfigQceCMt8JcLYcNPugROUYw5hm4GgSsQJyDoGKYQeCJqEtYVAFAPakoPA6bgcDgmLCtPhuSEjGdUIVKs6Ji9toSrfpQiZhzwI3/5pxywurda1Ua0xcf7tiIwr48rubSJk6R+Vw81wIld8YbXcRl6nZ+U1lJSoV3NP8MTsPNG7ykbdRogqHRWPMAWJ0AnOvffei6uvvhrXXXcddu7cidWrV+Oiiy7CgQMHuOP37t2Liy++GKtXr8bOnTvx7W9/G1dddRXuu+8+e8yOHTtw6aWXYu3atXjxxRexdu1a/Mmf/AmeeuqpsE+HizD0LUGWDQMIpYoq6L4ozrYXwZMwIg6uFXa0LkDyEHSUKRQSFvE2DdPlucETnsoIgVCDk5K/MWs7XEmvFZFOKGVvlyBKUYk1Ie7eKHpz85woL2rFaxJHxplaqRVvjyJZKitfTcSMRxRd5EGPhOlXmfHSbd5SbbHonUfC9Gzkpah0++BM2QjOLbfcgiuuuALr1q3D8uXLsXHjRixcuBC33347d/ymTZuwaNEibNy4EcuXL8e6detw+eWX4+abb7bHbNy4EZ/85Cdx7bXXYtmyZbj22mvxR3/0R9i4cWPYp8OFrcEJ9I254lAC2tgwFO1IwJGHOSGm0YKyMYwS7LDIbKApqoib/E2X54bsrT7DKQcW78DNcSi6fVk0x3HFn0mnSRyxkdVlFGVv69zIjMJGzVJ22c7o1ny6ehS56FWfpIq1OoBDFIUdinnEJSEmJMoonM+oFf1zUadnv80aXSSVs5XFlCY4+Xwezz33HNasWeP6fM2aNdi+fTv3Ozt27PCMv+CCC/Dss8+iUChIx4iOmcvlMDw87PoTJDpDSVEFu+9PGM3fCKELyjE71Wh5lJlN9apF0Km+MHYUD2rXeAJi41i+hIl8KZBjRtnkr1GeG0Dtzw7u2z83kmH9mxWeyjQ4ysoa7lYNYsLET4N4HbhnblkqRJH+0XbMksgD3STOZWOZsz6B6YT8pYlookgfP1/0XhtetM6trdHT4FST6lP1t+HfF95zkUYpy/S5eMXxQSJUgtPf349SqYTu7m7X593d3ejt7eV+p7e3lzu+WCyiv79fOkZ0zJtuugkdHR32n4ULF1Z7Slx0tTqRh6A2OCRpi6BSK8QxDU0UPAK8akEiBLVuL0BAzrVUNjE4EcxWCI5YOygtU/DbXgRt44xsyn54BxUNizJF1SjPDaD2ZwcvksFz9PTeR7qOlEtIEnrkgbeXEHdeTpSAnZu3fxMvjcZL//D1Lby5/TlwgF1zvWgGl1xJoi2uKJyk5D3FOHDfERfNEmzuPaGIFBY5RJEey62OUqXRJCRelW4LEqGnqAB4KkNM05RWi/DGs5/7Oea1116LoaEh+8/Bgwd92a8CiQ5MFsoYD+iNOWhxbEdz2g6LBrXXU9BOL5NKoKM57Tp2rRgIWIMTxrYXQaf6DMMIPN1XjyZ/9X5uALU/O3SFlf5EnV7tiO0cXVVCYm2NqipLti+SaG7drQP4fVlqKNWmxlnbRBiesdrRDEl1lKsSrkYHziMasggXV9+iO7dyc1O+jfKomX9tDW9ue4PRqdgHp6urC8lk0vOG1NfX53mTIujp6eGOT6VS6OzslI4RHTObzaK9vd31J0i0ZlNorpTOBub0AtY8JBJG4OXs/QGn0YDg+/UEXf1jGIZNlvoDauzoiIzDWMfGJLMyNMpzA6j92aHfyE6hHVH0hJG+1fM0D640iJ6Gwh95kKR/6N4x0lSW/+aGormLMtKk2RxP20YFIRAdUzfVx9/TixcpFKf6dEq15aknvegaX2dGE8op3Acnk8lg5cqV2Lp1q+vzrVu34rzzzuN+Z9WqVZ7xDz30EM455xyk02npGNExo4Dd4TYAp5crljA8aaU/gnV6wVZSBbl/EkGQzf6srSTCIw/BkdngS7CD7nsUBpkVYTo9N3SFrLTwlDhjXpM4+nu1aEKq0eAAdCM9x0YSXdDf50kVRdHr30LGZQTpHy7R4PbBkTfws9No5erX22MjrxKOt/2Dpr6FXzFXfapPdT4qYsclgLx+OYL7LCiEnqLasGED7rzzTmzevBm7du3CNddcgwMHDuDKK68EYIWAv/zlL9vjr7zySuzfvx8bNmzArl27sHnzZtx111345je/aY/5xje+gYceegg/+MEP8Prrr+MHP/gBHn74YVx99dVhn44QnQGWipMUUiphoL0pXfPxCILshTORL2Gsko4L1DGTEucAKoDG8iW7q2iQNnYGSB6KpTJOjAcv4O0MuNlf1GXi0+W5wX342xsMso7Z7QBox6urHVHtjcTdi4qjMVG+1fNs5DjSPC+NpknWtDfvTMkdM2/bCfrfPGKX4miZeJEwro28KJPIRs760Hod3j5hsq0aXJonzj5PvEo4FVHkzs2NHnmbWVZDuINE7X3hFbj00ksxMDCAG2+8EUeOHMGKFSuwZcsWLF68GABw5MgRV2+LJUuWYMuWLbjmmmvw4x//GPPnz8ett96KSy65xB5z3nnn4Z577sF3vvMd/M3f/A1OO+003HvvvTj33HPDPh0hulqDq6QasLcXyASyvQBBkLoMe3uBVAJt2eBuo64A02jkWrRkkmjJBGhjgOTh+HgepgkYBuxd6YNAkM3+xvNFW1sWlQZnujw3/DzU08kEJgtl2znQ39EWBXMEvMoKHG4PFX7qgCUkYhtlaTTddJv/tJzrvCsOl9avuB0zbx11HTMv/eNN3/G0TJaN7vNRkTDVteal+mTaKDI2mUja86Y896O4wSFPuFxUVK3p6rKCROgEBwDWr1+P9evXc3929913ez47//zz8fzzz0uP+YUvfAFf+MIXgjAvEAS5UaTdnC7gt+Ugy9lJmmvOjGwg2wsQBJlaCav7bmeA5KF/pEJmWzJ2iiIIBJmOJIQ7m0pgRoBkVoXp8NyQvdWzwko2SiEq301xjuk4KXmPGV3xJy9K4B7rJWGqsm5++36ZvkWuHVGJY/OKdZSmlBQaJWeXd+q6JJx5iXjdiQjJq6h4WzpY/xaTMP44Xj8hPsHJl8poSieF6Ug2KuQmYZwy8SqicLyoVZAIPUV1siBI7YjTcyRYxxyojSFV1ThdeINYx2ArqAiCJA9hpX6CTPUdo2wMksyeDOC91Yscc4pJ6xCHkTDcb9f8DRglUQ/dbRA4GhNh2qLsttEw4CLotWhw+N2ExeXk4tRKheBwugm7bVSQAlmZeNLZl4125oSwiKN1bKqPImEKQbm02oqXbuOQEcC5L9QaHGvukoCEsaTXZSPnXFx6Is56B4mY4ASEIHUZYYh36eMFYmPATf4Iguy4PBAaUQwuRWVXULWFZGMQJKwOJeLTBfRbMClb5+38TY91IjiiChyeQJW81SepcXppC92SZXpuxzlWbExo2ChL//D0LZw0CK0dEaV/2PPmdROmx7ma7ZXFNnIjYZymfPTPRdE6XRImq3BTdYTmERdeJZx+RFGuCatKUB6yBicmOAEhyMoamzwEqMkA6DRaA0dwArQxLKIYqJZphFzrsMhskBHFaATG0wn0g1v1Vs8SDV5VDf09rqOgq3+kJepe50h3UVaXNzM2KlJZ9Nz8Pji8FJU3LUcfR6nBYUlGku0mrOmYOSXYSn1L5bzzAjLr0TJR0TP+Tu+8a62nE1LdP0KiyNw/vC0d6HNTa5QkGpyp2AfnZEKw2pFwNDhh2BhWlOlYAF2hnShTA2twQl7HIDpXR11BNZ2QkThmkeMpsg5cQB74e1HpRh6ccbwuykLyIBAZq6JR7rm9KRO10Nf5DpvWYdeHkKF8kSWU/FJtXmk1T9RNi2i53agpYkIIC09sS/+f1TJ5SBgvPVb0EhcemRVH4fgaJVFLgDyTymLHyqrRXOso2VdrypaJnywINP0TUmplTkWXcTyAvZ7Ceqsnx8sXyxipcSuE8DQ41nUZHC+4flmrga1vCThFNTPAztX9Idl4MsCteVBER5g+IaIeIbql1drVPzISluITF6+NciIkmpvXRZmQghTHOdI/z9tkhF9u7yFhwhQMTRT1+uXwiIthGEKhOEtmMyzJEOzJxO2iLCGzfKG4SuAsJ0Js5DGVMASRMIWWSbPpZZCICU5AIE7vRABOL6w3ZlKGHMReT06UKVin15xJojVj6Qhq1biEZeMsquKp1pTkQEhEMcjO1fa2IQETxZMByYQB4gtsUqB0PKo0kVffwhfm+iNC9Jwi8aeXPPjQCfHmlpI1Z30SCYPq16MS8GqmYCSRB34fHHmqj/6/TWY5mh7eeev29HGN1dTgeMkVYyMnIgR4o0KirsP8LsoSGzW6UQeFmOAEBNrp1frGHPQ+VATpZAIzW4LZ66mfKhMPGqQCqNYUUJjkYXZA5CHoLTlodAZU7eVEmWKC4xeWqJP/Vp9ihbkJ/jiVhqJcVnQT5lSt0GkpXhdl3S0G1CJaeeSBkBa9rQNYUqDqMeOOUAjXUbFVQ0qSRvOcN1uiLiy350eZ2Huiti7KckKiisKxhKTAaRyotFGx0adIJxQUYoITEGind6yGyINpms5O4iGQh6De6sNs3W+n+2qM4Di7dIdnY63kIUx9S1DC9zBJ2MkAYdrC4xzZN2ZN/QblWFzCUzvlpS5RF5UtK+fmNA50j7N+7t52Qi6i5UWjqrEx74n0yFNZrrHcFJV/Eiaa2yMo50StXOfC6RKs2ufJt40Kkqois677jBMV0o1GBYmY4ASIIJze8GTRvqGCrqICgqmuyRfLGKqkuMJ0zLWQMHoLhKAjYUAwpeLlshlalAkIrtqLnGMY0bqTAeK0jsiZsWkLkXN0H4/+GX08f5U1Kocr0gnJoyiiLR34XZT1dD1OBRdft+JodVRdmZ1uwvJOxjpdlP1F4VgBr06Kir9dgl7FHO+Y2uNUZfma/ZaKZdNpmSCIcAWFmOAEiCCcHiltbsum0JROKkb7RxAN4EiEKZkwMLM5uL2yCByiWD0JOzFesLdAmNUSPMGZEwBRHJ4s2KmFUEhYANc6XyyHsvHryQT2LVytHfGnwaEdC0/AqyPq9KZ/dN/+9QTTrgocjr6Fq8ERaJSKSg2OO2WijvSQVJa8F43OZqQsmRWl0XR1Qrz0mEzfUihR5EEQcfGW0YtIrzttqXtPCG2k7FDpqIJCTHACRBBOL6ztBQjsPbNq2PXc6d0S7F5ZBEFUpJHvBr0FAoHTcbl2G9ubUsimgiezQaQjyXdTCQMdIZDZkwHiN2b+27/SMQtKtRNMN2FpqbYoMkMiCsThCiqPCMkgzk+lExKXGPMcuNzZ5xXkQZT+UUVHaBu4ZeKuKIo8EqYks2w6UjMiRP+bV4IN0FVPCnE16dWjSIXWlOrjEG73eccanCmDIJzewGh4+huA1rfUQsIqKYuQRKfBRMJCJooB7Ot1bCTcBnpBpCNpjVAYZPZkgLd3jPyNmU1beMYl3A5c2XXY9VbPJy66JExYJq6oCFNv6eBN/3hE2EwqRGmjZx0V5eSubsJeG11dlAVzs5teikq1fWtwqO0SSKCJl6Jyze1bJ1TrPSHXCaU5BEe0jkEhJjgBIgjtSH9IXYwJnCZ1tTjmcBu/BbETti3UDqm0OWjyEAaCINz2tY574FQNsW5FQQpEAl7P27+AMElSAqK+LGzPE4/DFcytq8FJJ92N7AghcHdR5qeo/JIC7Wqropu0APxImPt8+FEhWRdlno1KwXSKRMw4kTAReVA2ONTT4LDnIhZ/u49HX0t6bDJhgCyrqslgUIgJToAIIrUyEHJJLiFhtehbjoUdwQkk/RNelRcQzN5jYTfQC2LbizDbAZws8GhrBMJKz9u/MsWgcrYSx6wQivqvElLYKNx2ghN5UFWPseSh2mo0gaNnuwnTJfUqx6xLrrzRKLneio14sHPTXZTZ5oHCPjia95k32sI2nuSTOutnomPK04dBISY4ASKI9I9dVRNSBCcI4WlUEZwgxNphRcKCiNaFWUEFOKTk+FjOtROwH4R9rU8GCAmJ0vHoaUeEkR5eSkARFcornJ44iiJ3zCpC4LJRU1wtrI4SOVGBA895rgtjI6eLsqoazatb0VwfRbdll6CcskvWRVl0/+RVKU6mi7JqHVnxN32envNhtF6xBmcKIEhxbGganFYnRVXtXk9RaXDG8iVM5EtVHSOs7S4IHPKQr5o8hJ2imlUhd2UTdsm8XxCCE9a1PhngbTynKBNXpDd0HTg/JaB6W1dFmdw6ITFh0tUJOf+3hcuKrQP86oTEVVmCSAZzzrwuykJhLlOiLkz/pATXMCG4JxhilUoYHk2cKNqjjB4JdELknFnRu7gPjttG63z0omaxBmcKgKQajo/nXYp7PwhdHFuxcbJQxliV5CHsxm8zsilkK78I1ZLFsIni7NYMDMMiD9V2rg5rKwmCdDKBWZXO1dU2+4t3Eq8dnl2ZFc6x6CEFqj4m4rdgYUpAKFxmyZXe3H40ODToLspsSsm7dYC/CIWTbtO1Uexs9SvhqiMFqsoxLRur3AhVSKQ9fYf8dbeWkTCVHi0oxAQnQMxusZyeaVokpxr0hyyObcmk0Jyuba+nsN/qDcOoORoWdnQklUzY/XWqtfFYBOSh1nWMIzi1QzdF5XEUQoei7/TolIBp8rd0ADgkzK8GR7Mqi3X0gHe7BieSIuqOrNeMUL9KSJ5ukx1TvBkpifRokgJBxIwlYTJC4C1RF2hwNIXinnJyoRiZIZQCAu8+77gPzpRDKpnAbOL0qtThROFQSBSn2koq8lYfpvC0VoFsX2Ud54a5jjXqcAZCJmH0sWslijHBqR7eh7qu+FORBmEjPSmO06PewkXdhOk51Dohfxoc7/G8NtLHNE1TXIJNIj1ld9TDs38Tm/5RRMzYVFaKZ6MnpaQrHvapwVFU1smIoici5bu/jZyEFUXXhWpHQI/nrqPnmN5y8iARE5yAMaeGCqDJQgkjla6xc9vDd3rHqiBhuWLJ3qYhVBJWg2Mul81IHLNdzl4FCTNNM5IKJZL+qnZ/tFhkXDt0UyG+35gVjoz+br5Udok/ReJYdZM4UaRH5Zj5ZARwkzBXN2GRfsOOFFgpdtY5kjnUFU/OuZimKYy2uM/HHaVIKUiBuARbFI1SaFakNrrTY7o7lOusj/W3ItJD1rEyPsuL1tk7mbttTIXUYysmOAGjFsdMnEk2lUBbNhWoXTQ6KaGxXxBnnk6G29m2lkqqoYmC/cvYqNGRsXwJkwXrlzssDQ5QW7+eyUIJIzmLcMcRnOqhSwrYMnHiRMWltnLH4x5rMtUtenoU4T5PCocr2jeKVw5Mr4/LRmUfHF0SJtfgmJUGfrJ0Cd1FmXbi6vSPKMKlp8HRFQ67jqnqg+OJMvGjKGzXahXhBiyCLCdhIvIZR3CmBGpJW/SNTAKwojd0H4agMaet+jSaLYxtDddGkkarbh2t78xqSYcW+gRq21yVELfmdBKtIZJZQkyq6bhMCHcmmUB7U3g2TnewD3W7YZqiSZzjRN3beOh2PKY/K5TK9vHYLR14x7TJlWduPQ0FHREqU+SB1cuwx3R3ExakvRgCyEYKhGJkgY1kbhL5kNpYdKf6VDtrC4mLpo1sF2UR6QXcBJnueKxKhaq6MqubEbp7GeVL/Mga/V1PujZOUU0N1PLGfCyiXZuDiDKF/UZv21hFhVJkNtZAFEn0LOwOwbUQbjrNFyaZne5wUisq3Yoo6qHoeKwhPKUdMz9CoXdMcaSHT0YASzMjizzQxyT6GsCbttAVLuuLkZ3v5UtlaYqKjh7ppPpUkSvvNhH8a51ykbCykGTQ5+eJhFWtwfEn1rbGOKk+FeEWdTwOEjHBCRi1NNJzhLFNgdrEorOGDTfDLhEn6KwhRUUiYaETnNZaiGI05ddBEO6wr/V0h4gUsCJMEXHR3ciSXzpMaXC0qlv00mN5RkMhb+BnKsiVo8ugyR9LqkU2yjQh9HiRAydjtMrEy2V7XoCj/2E0JkoNjt37p7I+nv233B2KZREcen3yMoKjvVUDPxXq1TyxERz1/eglYbEGZ0qglrRFdJGH6jsuRxfBqT7ycCwiolhLGi3sMnaCWraUsKvlYv1NTfDoKDS3DhClYBwxaSX9I9W3eCMP/Eomvo2iyIyu8BRwExeVLsPRb6grmXKaNuYFO6MbhsHV/0h1QkXHgdM9fGwbRVEmoaBcniZiuyjbAl7pOjr3BG07O47VUYkFznJND9tFWYeE5YvyKFNQCJXgnDhxAmvXrkVHRwc6Ojqwdu1aDA4OSr9jmiZuuOEGzJ8/H83NzfjoRz+KV1991f758ePH8Zd/+Zc444wz0NLSgkWLFuGqq67C0NBQmKeijVrKm/uGwy9tBhyRcX9VEZxoIg9zgkj1RZVGq0YnNFzRW0VEFAdG8747V9erB850e254IwrBlIkDVkRBr9Gf4s1aoK0RR4/kJdhsAz+RaJk9pqjyxxqnV3peVQO/IkUAORU9LhsF3ZvpcXlGY6LfB8d9TLqLcpEWQstaArjSkYYnEuZ3SxBV6wAyjzW3Kbx33OftRPVExwwCoRKcL33pS3jhhRfw4IMP4sEHH8QLL7yAtWvXSr/zwx/+ELfccgt+9KMf4ZlnnkFPTw8++clPYmRkBABw+PBhHD58GDfffDNefvll3H333XjwwQdxxRVXhHkq2qhJ3xJRzxFHZNy4NpJ1HJoouELCOuiLWMs0MJpH2ed2DcTG7vaQo0wVG/OlMoYrLQh0cWx00nWMqDDdnhu6KSXWOYoiFO5NNE2pBod29qLdoAFx9EhdwSVzZk56TNb8zanWcYgQr5w8xXRbFpUjsx2hdQTO+VJZKAgG3MJlUeqQ/q5KwKtbbeWysVh27glNDY5OtZWoVJstO5dVR9GCZFkEx9m13rGRFwkLCqGVRuzatQsPPvggnnzySZx77rkAgDvuuAOrVq3C7t27ccYZZ3i+Y5omNm7ciOuuuw6f//znAQA//elP0d3djV/84hf48z//c6xYsQL33Xef/Z3TTjsNf//3f48/+7M/Q7FYRCpV32oP4vjJHkV+Llxk2pGKwxqeLCJXLCGbSiq+4SCqvigdzWmkEgaKZRMDYznM62jW/q6dogqxlxDgrEGxbGJwooDZPjb2PBpRBKcpnURbNoWRXBH9ozlfpf0khRllBGc6PjcylMhY1k3YFvpqdjwmY6XEhYp6iES59Hc9FVyC9I+n1b4gMjNZKCs1OC6dkISMCEvPlRocvf42slQf3W1Zvo5u4lK0x+r1CRJdw4mCfvpHP1qnd5+pUlTiuXnjnPtRFgkLCqFFcHbs2IGOjg77IQUAH/7wh9HR0YHt27dzv7N371709vZizZo19mfZbBbnn3++8DsAMDQ0hPb2duFDKpfLYXh42PUnLHRW9igqVRyzH0SlHeloTts3ld8UUFSdbRMJw+4P47eR3rEIGugB1kOGCLYJYdFFVBEcwOmz4zdidywinRCNRnpuAME8O9w6D1k3YT0dDL2JZqGsKY5VRHrSVDrJNMWExM9mia7qKMk4JzJDp2DE5IHty6LWCclsdMY6m3wqHLgsiuKJHqmb49F/q66hnpZJMc5zDfniYboCT2UjvY56JExuY1AI7ci9vb2YO3eu5/O5c+eit7dX+B0A6O7udn3e3d0t/M7AwAC++93v4s///M+Fttx00012Pr+jowMLFy7UPQ3fSCUTtkMgmhodlMpmZKJOwzBsEuXbMQ9Hp8sgWiG/gm2ib4nCxrkVgtLrcx2PDkcTZQKqr6SKSghNo5GeG0Awzw6XiJYSVop3CZdHUehj0o6CO46zVYPM6eWLDhHiHZNt/qYTHaGjRyryoHU8BQkT7rauuT7cNBGlb9ES0SqIC33O1rn4JFeSuYuUWJsbCROVqHtsdEfrdEmT/jjxegcF30e+4YYbYBiG9M+zzz4LANzeGaZpKntqsD8XfWd4eBif+tSncOaZZ+L6668XHu/aa6/F0NCQ/efgwYM6p1o1eojTG9J3eiSlZRjhdrYl6K441qM+bBzNFTFa6WzbE0HkoZqS+8lCydaahB0JA4CedkJm9dexWCrb0b0obLS1Qj4iiqZp2vdvdwAkjPfc6OjoAAB0dHQ05HMDCObZ4Xbg4soRr4BXo59IUZ4SyNAkQ7NM3NXITiWOlWlHKJ2J9O2fUzqsslFGwtjIg5YGp2jq6YTK4r2yWBvdxIVPwkzTLR7mk1ReCk++jnKxthPpIce1PpeLtYsyAsgRYav2y4oiguM78fz1r38df/qnfyodc+qpp+Kll17C0aNHPT87duyY502LoKenB4D1RjZv3jz7876+Ps93RkZGcOGFF2LGjBl44IEHkE6LtQXZbBbZbHRvod3tTXj50JCvt3qSnprdkgn1ghOQ1IifCA4Z25ZNhdp9l6CaijS7+24qgfbm8G3stsmsPnnoH83DNK1UQ6cP3U616KpCVD40UbAFjUGk0XjPjdHRUXzwgx/EM888gxkzZjTccwMI5tlBRxSIMzG43YR9RHBSCSCnQwq8zlFWJl5k+7yI3up97hyt077fFY1SbMopJWHMJpoy8TCPfKrWUR5FcUhGqWyCFC56bWR68BQle3VRUTO96JFeKstLAPlE0e6irNBb2eciFUxT6yg5XlDw7QG6urrQ1dWlHLdq1SoMDQ3h6aefxoc+9CEAwFNPPYWhoSGcd9553O8sWbIEPT092Lp1K97//vcDAPL5PLZt24Yf/OAH9rjh4WFccMEFyGaz+NWvfoWmpvDfgv2gu4q3+qgExgS2Y/aRRiPRnu6OaNZ7ThUVabT+JoruuyRFdXTEP1GcMyOLREjVAzSc3kz6RJGQ85ktaTSl9UXoQhs4zw2iZ3n3u9+N9vZ2ANPzueFubiar1NHrl2N9Rjfw03PguvsY2RtJJgzP/elHeOqq4NLZBqEk7ybsigi5+rzwSZgqBUPbU1AQQHc5uUbH4yJTBi0QGZOxupVwOSl50CVrzjh6SweR3krnmL41OEVTKo4PCqEdefny5bjwwgvxta99DU8++SSefPJJfO1rX8OnP/1pVyXEsmXL8MADDwCwQsxXX301vve97+GBBx7AK6+8gq9+9atoaWnBl770JQDWG9iaNWswNjaGu+66C8PDw+jt7UVvby9KlT0w6o2eKnQZUfccIQTHDwkj5xNEykIHThm2D4IT8TqSa+0n1ecIjKOxkazFMV8kzLIxilQkjen43CD7OdFpIlWYHxB3MmbH6vUd0dO3KB2ZQKAqT4VoOlxKq8N2eXYdjxona7ZHIg+656O7ProaHFk3Ybok27U+qnUUNC0ERB2hedVogm7Cig7F0h3haYLs8z4LU4MTagz/5z//Oa666iq7uuGzn/0sfvSjH7nG7N6929Vs66//+q8xMTGB9evX48SJEzj33HPx0EMPoa2tDQDw3HPP4amnngIAnH766a5j7d27F6eeemqIZ6QHEuHwEx3pi9oxd1jz+CFhDsGJxukRAe5RP+sYUfk1ga1lqiaCE4H+BgDmVe7HIz5ImB2ti5jgANPvucHtlstxPKLNDXnN8XibaKq6/0ormSgbRf13ALiazrk30ZSka4pUZEZzN3F5tZW8kskVHaEdqSS1ki+ptDWcpoWaYlvLdn73X0JuZPoWmrjYG1nKokeqSBiHHNPnyI5jx/LWMaUZweH1E2ooDY4fzJ49Gz/72c+kY9juqoZh4IYbbsANN9zAHf/Rj37Ud0fWqFFNdIQ4vXkRpX+6q6ii6ov4rb6aSBhx4pGto61l8k9mo4rg9LRbPYT8iN7JmkcdwQGm33Mj7SIZ6p41RKAq2tEb4L+tq7r/inqyWHNoRig8XZSjK292Ig+mXJ9EfTevG5mh1kemMVFqcHjdm5PefbWsYxrIl/yklILV4NBrY9nuHkuiYyQK5qQuq4/MuFOrYmIeFMKjTicxanHMPT4a2tUCEmXy45h7I36rJ839jgxNaDsnYuO8mRGtY2Ut+kdzrrchGfoijoQRsjcwlsdkQS8dY0frIiKK0xn8aIv4Ddwkok7NVIh2akWrBFselfF0UZY4qQwnmqHW4Fjj2O7EonEyogiwVWaax1Q4cKkOhiazkn213GP1KuGUpey8NKNiHe2UIEdvRduTp/fBUlRHye5bd8+jKazBOZlBCM7geEHfoRDHHJHTI86VLv1WIeoUVXcljTZZKGNwvKD1nagjOJ2tGaQSBkxTXwzt7BofTQRnZkvafijp9mYiKap6RHCmG3hv/zIHTsaKOh7TY/1ocKSkwG5QV9aOjrj3PNLT4KS4pIk08HPSY7oEhzfOMJz9m1TRI15pdTYtTq0UqY0spXoZmlhxxrnHykvU09oCXl70SEKYqJ4+PM0TbU+RItxZTtEBL9Wn6ickK40PCjHBCQHtzSnfDsWJ4ETjUGZkU5hRKfXWTVORcVHZmE0l7VJxXf1I1KmVRMKwiYpuCuhoxETRMAxKhzOh9R17HTvincRrRdqlb6loKBTkYSznvBip+ono9G8plEx7bj558DpRHrFydVEuyZ1UmqPrkRGXfMmU6n/4KS+5Yy4oUiGuuQsyG73lzVLdkSLtRH+fXp8mDrlKu66hnmBaGq3jpPpE2/XwbJQRF5ogq3atF+2BFSRighMCDMOwSYBOmipXLNlv//MjSq0AtIhXbWO5bEauHQFAraPaMZumaTtwP3tX1Qq/6b6oU30AfN2PQPQkbDqDLo21nSj3Ldh50I/ni9TnMidFOQrZ3j+uqId37gwn8iB6syb25IpOlInnpGh9S04yt9NFWT5ONw1ize2ct3RujgOXj3MiOLpaJt7u5LSNBcW1cdanpCCUXht5ETM6skYyDDxS5xpbLCNHxnJJGC/KJIv0yNc7KMQEJyT4EfGSKE8mlcCsFv3NEGtFj49mf/1jOZTKJhJG+Hs80SAC2cODahuHJgqYrDiQKLZAIPBzrScLJQyMWf1oFkRIZh09k9rGfLFsN1eMU1S1g1c5IkqtEEdBp41VZeKENPH6FdEpAduhSFIwLiGrIvIwnneiTDzCluFEHnjnTT7LFUsKgbNeZ2T6+xP5kk3CpGmvol76MF8saZXvF6lzFvWRcpEHSXQt61NkrLrP6DUj11BEFMm9klOct7sJozpiVijJCVNQiAlOSHDe6tUOhdaNRNGcjsBPBdDRIWdfIt5bQViYP1N/2wuyjp2tmUCa0+mi20ck7PCgFWFqzSQj6bRMYEdwNNaRNJ1MJw3Magm/0/J0h/utVf7GTBzFSGW7kXRSJP6kIw+y1JN3HM9BkbfoHBUlEJEHQppGJh1dnDz1JHdmztx655Ir6ERwrM/HKKLIJXaa6cMMFWXSqTLLK45H2zhRKNnN9nhjaZIhF2s7gmBZuo2+/qOV+0x0P5LPJwtyguxcGwVJ1SS9QSEmOCGB7FGk55gnKt+J9m2ZOL0jg+r0T2/E+huCHh89XHoj1jERdPtI/5BI1PyZzZGSWT8anKN2L6GmSDotT3e4tCgSxwM4b/ujNsGREyF3WkehwSmIHRTtyFTkgSVhCUOQouJ0HualI5wIjjxtYY9TVI7Rn+tGwvIuh+udm1yXnLIqy0mNTUrSkYBDhmgb+edtfTZZkKcPsxQJm7SJojwVOpIrCsfRn4/miva2E+prI4n0pGhCGaeopixIdOSIhtMjjjlK/Q3gpEgOaRAcEnmImoT5ccyHbf1NtDbO7yBpNP11jPpa+9kAluyrFTVRnK7g7UUldigV8pCzoiPC1AGV1tHRjqg0D65UhOLNmowdmijYx+P3eeEIVGURCsXbPyEZqpQO/X1CwlIJg69HodOHkgiFQwDlNpK1NU0neiSO1nHSkbopPE5vJFckTEJmkwkD5HLZERxBmijLrKPofGwCqCDIdFdv1TUMAjHBCQmnzKqQhxNqpxd1BRUBsfEdDRsJCTplVkuoNrHw06SuXhGcatYxaoLjR4PzzolxAM55xagNxNGXyqaG5sFyACOKCA4ZN1nwL/7k62CSlXGmLTwVzd1UGWsTHIFz1Nfg0CkqtVYHcEiBcH0qY4cnC67/s+CSMG4Kz4kyyVJ4dBWUQwAVUSYqHcluO8HOLatQItdhslCSkgdL60WiR3IbyTGHJ5x0pHx9StIKLodIy0lYUIgJTkggREDH6R2pU+SBJmGqRnr1cnpEg3NkaFJp45E69W4h1/rI0KTdDVUEEsFZMLM+qb5jGg0JD9k2xgQnCNB9UFRv9ewbs0joy4/gyCMUUiErhzyohKfDmg5cKaKlU1QSskbr6lTrQ8YOjRMSJiqD9mpwZHPnFGJkq2ux9e9hKsLFA5tGE0b1NKMjfKIoL/92NDjyFBUhiplkgpu2dqJwZeQl2qMmO90mjzwGhZjghISFFafXP5rDRF7e7I/oMqIsbQaABTMtG0dyRQxPyJv9kUjUgogJDkn1TRRK9huRCAePExIWbZRpblsW6aTV0lylwyFptKgjOJ2tGWSSCZimOhpGSHnU6zhd4dI8qESdacahKLQ6E3nN0uqivMcMbY8qesRGcFRVQi69BWes++1fHEVJUT14bBuF68Om0VQkjO6DI7ZxslCS6n8Mw7DHqiJc5Ps2WdNIR8p6HjW5IjjivjrW90l6TJ4m8hBuxf04WZSvT5NmlCkoxAQnJLQ3p9BWaaR3aHBcOvZgJTqyaHa0DqU5k0Rna8ZlgwjE6UX9Vt+Udpr9qaJh5OcLZ0drYyJh2OuispEWGUeJRMKwo2/qax2nqIIE3frfjuAISIHfCA5dySRvEicnQqlkwhYKD6scri55SFFt/iVRD1q/IesTZBiGE5kh5EromJk0mk6KSlJazYuOiAkJa6MgilJZH2VUj0pHFjRtdPrbqKJH8ggXWW9VtM4mYQVnbt79SAum4yqqKQzDMOxox0GJ0xuaKNjbENTDodhpKolAdiLv9G5ZWIe3+oUV4kciNDwUSmU71VcPG0m0Q6a5Mk2zrumfUzTW0TRNKoITE5wgkEg4WwfY6R8FcSGplaaMwvG4SrXFFTN5RQqGnptOR/DHseRBngYZy8sFqrQuQ9a/hf58aMJ6HomiR8S5OhoceSWTqvybFkITB96sO7cigjOqmbak05F8EbY3gqPU//hMmaqq/yaLJYrg8KrRqHOx05FximpKgjjmdyQOhTibrhkZtGaj64tCoKMVIk55RjYVae8WAhLZOiBZx8ODEyib1i/gnIj2eKKhIzQeGMsjXyzDMOrTIXhRJbIlW8cT4wVbCBt1lGk6Q9ehEKcwSBy4ZgrGMHQaq6mqo9y6lRYBucp6yINeCsYaK6v+cdIWqugIeSlsFhFAbSF0JYqiIGGOA5dHKOix2iJjZak2IS5lTBByxTlvbgRHdN6aqScP6dWK4Fj3GY8AknusbKp/F4JATHBChI7TI+mAhRGnpwgWaFR70SmLKHu3EOgQHPKzhbNb6mKjc63FNu4fsH42r70p1A3mRFhkR3AkZLZyH8xpy0baLHG6g5CPEc2yXJUDt8WfE46T4N33vAoclSMl5EoYobDJg965kJSXiIS5RcaqPkHu9RGmqGwCKHei+iTMifSQFwDR74d93hNy4pJh1ke8jpXKulzB7kXDuzY04RpRioeJjaoqKnekUCVGHs87Oire+tDzDCnWJwjEBCdE6ERHbMdcJ0GnjmOul/6GQIfgEKe9sE5pFZ1rva9/DABwaldrJDaxIPeYbB1j/U04yDJaBlX6xyY4ijSIKk1kRx4KJe0mg0pyxVRRiTQm5PuD43l7XhkJUzWooz+39S1KAqjnmOkyaBkJo+cWXxu9CE6z5j3Bkjp6DreNzmf2tRGQJnJtToyr1ochayISxtyPgCCCk+JVmcURnCmJhRqiTuJsohYYExBHJnN6+wcsx7y4sz6OWYvg1DkSpiPgrfc66miZ9tepEm26g6R7Bu2UiZw8qCqUdEW0xJHR6Q2lvmVcPncTSx5ETpQhTKoyaEBH60GcPUnh1SaO9VwXIQlz5lFfG4Z8KtbnBCGAiggOuS7ppMGtUEonnSozFbFzro1DPmXnoqvLIscTHZOuMlPdP0EgJjgh4hSNN2YSeagXwVnSNQMAsG9gDOUyv8/M3krkYcmcOhGcTkfAK+ozc7DORJHMe3hwwtYRsNhbSVEt6aqTjZV1HBjLu/boobH3mHWtl9YpyjRdoetQiMMm+gSViNbWMQicBK2jUUV7nC7K8rnJXKo2/4RcqUgY/bm6Wsc65lherEWxbGdsVEQyVNeFJg9kzcVzu6+han3UBJC5LoJxFnlIusYqo0ea6TEVGSHrTa5LNsXvl2ONZW2MU1RTEku6WmEY1g08MMrf0JKQn1MiLm0mWDirGemkgclC2e7RwuLt/vo6ve42S7NSLJvCTryEhNWL4Mxpy6KtKYWy6WhtWNQ7gtPelMbMym71IhvJOi6tE5mdriBEQ7apIuB1IKo0iP09USRDsi2D53NmrEqD43xPTa5k89L9bcqS/Y54xxClYNjvqyIZznVRkwf2u+q5NddHgwAC4rQc4F0PFbFz5pCvt/K6MJ/L9Hvs+cQpqimK5kzS1q282Tfq+XmuWLKd3ulzZkRqG0EqmbAd7tuVt3caxVIZByrOsF7akUTCsIkLIVs0ymUTbx2z1vf0ufVZR8MwcFrlGr7FudamaTqRsDpGR4iNbx7z2ggAb/dbny/tqs86TlewDkVYocQ6M4WAV/R/gkTC8BxDFAHwkKuMHglTaXoIROkNLnlQaGvscYoIl8pG9jqIrgvAOW+FHkU1N2u7Kh0p+p5srIrYEaiqo+zvad63Mhs95DxOUU1dEIfLcyh7+8dQNoG2plRdSpsJTqu8rb/FsfGdExMolk1kUwnMq0NpM8G7Kuu45+iI52eHhyYwWSgjnTTqFsEBKPLAITgnxgsYmSzCMOoXZQLk6zg0UUD/qBWqP7VOabTpiuZ0Svp/Avbhrx/BET/KWzLM3NrkShTBYR29nhOVtcFgCYmIaHgjFHrrIzoXXeIJeImhdoRLc+5gyIMmuWLmalWk2whatNdbfD+y6yMi3EEgJjgh43SJ0yOfvWvujLqUNhMsrdjIi+DQUQdRTjUKvKu7DQCw56h4HU/tbOXuGBwVTpsrJorks/kdzXUtv5atI7nWc9uyaGtKR2rXdIdupIAlD7pOT0YeaIeYThrCt3UPERJqcPQcve7xAK/9uukf3QhOa1aPhInWm3dMlUbJnltwTA8BFIxj10aWomLXR3SfeYkd//5pZT5X9UaybfRBwsLs/xYTnJBhR3A4BIc4mXqlVQjs1ArHMb/ea73p19tGO/LQ5408kLWtt42n2+voJYqvHxkGAJzR0xapTSzIOr7BWUcS1Yn1N8GDdQwih9vCPOx1IxSyyAPtzGQkY0aTXqTHG5mpPYIzg/pZU1osUGXPUzetI3Lg7OesQxeNTSX4lUyANyKhO3eziGQw69ssi45oEhf22ojuHw/xFJ2LZsQM0CdhQSAmOCGDOF1edISkrd41t75Oj6So9nBI2GsVx3zm/PZIbWLxbirywO4qXm/9DcFpcx2iyFakvXbEIg/L59X3WpN13D8w7qn2evVw5VrP64jcrukObzpC741ZHB1h3/71IjgihwfA3juPQJQ6YJ2e6JhNGb1oFOAmODIbdSM9uqmnprTTl0VlI0005NEoTQKY0UvLZVNJV9RNRh5mUHPJonW6JLWtib3W/HGpZMIVVZStj+d3Id6qYeqCkJdDgxN2HwOCXRXy8K7u+jrmZT3tSBjAsZEcjjK7YRMbz5xXX4JzalcLkgkDI7mip5LqlUOWjct66mvj4tktaEonMJ4vYd+Am9CSday3jd3tWbRlUyiVHdEzASGz76kzmZ2O8LwxCx7q3rd1/jg22iJNUVEOpUXgyAA3yWC/J7OR/R5BJplAkorEiFIw1jGdY0ijTMzcIq0HS9ZEBNAwDIYA6tkoSxOx6yG6NqwOS7Y+bZrrQ5+n7J5gz1OkCfOSWb3zlmlw6Hu3JZMMVfoQKsE5ceIE1q5di46ODnR0dGDt2rUYHByUfsc0Tdxwww2YP38+mpub8dGPfhSvvvqqcOxFF10EwzDwr//6r8GfQADoaEljcaX/yIvvDNqfD08W7KjOe0+ZWQfLHDRnkvab/UvvDNmfTxZKeLsSHak3wcmmkjijYuOLBwftz/PFMnZX0mhnLahv5CGVTOA98y0b6GtdLpu2jcvrvI6GYWBZJYr0MnWty2UTuw43RrRuOj43PA5F4ChY5ygrg6arkmTERdeBs6RJFClgbRQd00seJCkqxumJoBvBYc8liPVprcKBA2JypRvVY48pJ4AUwZEcj722ogiOLum1jpHSGtemGa0LAqESnC996Ut44YUX8OCDD+LBBx/ECy+8gLVr10q/88Mf/hC33HILfvSjH+GZZ55BT08PPvnJT2JkxKsZ2LhxY13Fubo4e+FMAG7H/Mohy7mcMqsZs1szdbDKjRUVcvAy5Zh3HRlG2QQ6WzN1rfIieP+imQCAndQ6vnF0BPlSGR3NaSysUy8hGu89pUJwDjrk4a1jo5golNCUTuDUzvpXJ31g0SwAwPMHBu3PDp4Yx0iuiEwyUfdU33R8btDOK2HIypbdD3xRdARwOyW5doRy4II3det4esSFHSevjtIjD26np09w2pv5YnhPFEWWwnNplCTrQ42bkRWL8D0EUKS38lHBRduvSzJ0dVnWWP5566ao2LnbJUUKLhImIZ5BIDSCs2vXLjz44IO48847sWrVKqxatQp33HEH/uM//gO7d+/mfsc0TWzcuBHXXXcdPv/5z2PFihX46U9/ivHxcfziF79wjX3xxRdxyy23YPPmzWGdQmB4XyVC8wLlmMm/iUOsN2zHTL3VP733OADg/YtmNQSRfH/FMe88cML+jPz7rAUdDWGjTWYpovj0vso6LpxV1yovArKOz+931vHZfda/l89vF4ono8B0fW7QjqG9OS28V1nnOLNF/PKjG/WgnRkbXaDR5nr7TwrvA0/6RyoeTmqNo3/WITtnalwmlRBGmdoYAiIjBe5ro2fjTAGxYm0ExOlI1iYZmaWvG2nWqRqnu97W/0X6H3eacWaz7No4x+iQrY9mNCoIhPYk27FjBzo6OnDuuefan334wx9GR0cHtm/fzv3O3r170dvbizVr1tifZbNZnH/++a7vjI+P44tf/CJ+9KMfoaenR2lLLpfD8PCw60+UOLsSeXjuwAmUKuLTJ97sBwB86NTZkdoiAnmrf2bfceSL1nYIT1UIzoeXNoaNJILz0jtDtkD2iTcHADSOjYTgvHJoyG7V/kxlHT+4pDFs/MDimQCsSiqyx8yOt611XLW0s15mWXY00HMDCO7ZQT/wZ0kcOOtoZI6Cfqtn37Rp0PPpOkcZsWKdI6uLcc3dqjm3JnnQjRKw6yibW/fa0DZKrwujlxG91LRlUy7yIJu7zbU+ejbKCNNsaq5MKiEkGoZhuM9bso6ua6NJAGXXJQiERnB6e3sxd+5cz+dz585Fb2+v8DsA0N3d7fq8u7vb9Z1rrrkG5513Hv74j/9Yy5abbrrJzud3dHRg4cKFuqcRCM5a0IH2phQGxwvYeeAEJgslPFN5Y/7Dd82J1BYRzpzXjq4ZGYznS3h2/3HkiiXbMX+oQRzz0q5WdLdnkSuWsf2tAZTKpu2Y/+D0rjpbZ2HR7BYs7mxBoWTiiTf7USqb+H2FhJ3bIOs4t60JS7taYZrAtt3HYJomdrxVITin1ZfgNNJzAwju2TFb09GzjlPmSGkH3zVDnEKm554dgANno0WdreK5aaetO7dsfWjy0yGJtqSSCVcFkUwGoHtt6HORrQ9NNrvaxPMahuE65qxWPfIpIxnt1LjOGeK52esii37rkk/6ZzKCQ6+P7N4JAr4Jzg033ADDMKR/nn32WQDgLpppmspUAvtz+ju/+tWv8Lvf/Q4bN27Utvnaa6/F0NCQ/efgwYPa3w0C6WQCHz3Demg/9NpR/O71PuSLZSyY2WyXaNcbiYSBj1TI1kOvHsXjb/RjJFfE3LYsVsxvjDSaYRj45JmWE/vNK7144s1+DE0UMLMlXXeBMYFhGPgYudavHsWz+46jfzSHtqYUPtgg0ToAWPMeK4Lx4Cu9eOHgIA4NTqAlkwwtosh7bnR0WNeso6OjIZ8bQHDPjk7aiUoe/uzbvkzMOrfdcQ6dmgRnlsTRt2mmQazr5/xf5uxdjlR3bsnxuqlu6jMUzShpEbYsOjKbcrKyyBW93jKSQdsoizIB7usrWx9dkjGXmltGemkyJRNgA+5Ummx93OctJp+0njNs/alvCfPXv/51/Omf/ql0zKmnnoqXXnoJR48e9fzs2LFjnjctAhI27u3txbx58+zP+/r67O/87ne/w1tvvYWZM2e6vnvJJZdg9erVePTRRz3HzWazyGbrK5L91Hvn4VcvHsa9zxzEI6/3AQA+9/75DaEbIfjj9y/A/TsP4b7n38H2t6wU2qfeO6+uHYxZXLxiHn725AH82wuH7Yqvz7x3fkNoWwg+8755uHv7PvzHS4fxRqV53kUreoQ9KeqBT501D5u2vYWtrx3FOyesvcbWnNkt1SrUAt5zY3R0FB/84AfxzDPPYMaMGQ333ACCe3bQBMRPl2jZ82Feh+NQOiWOwhUlkDiong5HpJ9QPJdSCQOFkpVulz0fZlOOVObMFsxy5pZpcLqoqITqqdSUToDscSzTldHHnCUhLnOoayglTNTPSkw/LBlkehT6WstIag9FMmSFIbL0FQuXRklCXGhyJYvMzJ/pXGtZlCkI+CY4XV1d6OpSpwNWrVqFoaEhPP300/jQhz4EAHjqqacwNDSE8847j/udJUuWoKenB1u3bsX73/9+AEA+n8e2bdvwgx/8AADwrW99C+vWrXN976yzzsI//dM/4TOf+Yzf04kMn1jejaVdrXi7fwxDEwU0pRO47NzF9TbLhdWnd+GM7jbsPjqCkclRpJMGLv+DJfU2y4VVp3XirAUdePnQEF47MoxUwsD//Qen1tssFz6waBbev2gmdh4YxMuHhmAYwLrVS+ttlgtnndKBVUs7sePtAVtY/rWPhGcj77lB9Czvfve70d5ulaZP1+cG/dYtE/oCFhE4PpZXHpOu5JE5s1Mo8kD/23s8x66k4qWmszWLXqZnFnccRQp6OsR72Z1GbTYss5F+kZmrqOzsmpFF/2ge6aT8XOjIg2yfONp+mY004Vuo2HduwcxmvHNiAoCczJ5ONYOV2UgToe528frQc82TXBfAkgaQl0nZiyR9PWQ20gQn7Orc0F4ply9fjgsvvBBf+9rX8OSTT+LJJ5/E1772NXz605/GGWecYY9btmwZHnjgAQDWol999dX43ve+hwceeACvvPIKvvrVr6KlpQVf+tKXAFhvaytWrHD9AYBFixZhyZLGcsY0kgkDt37x/ZjblkVzOonv/ZezXBe6EZBIGPinS8/GvI4mNKUT+LvPrVD+gkYNwzCw8U/PxoKZzcikErj+s++x99JqFBiGgVv+5Gwsmt2CTDKBv/nUmXafoUbCD7/wXpw2pxWphIFrL1pm9/CpJ6brcyORMLD2w4vRNSOLK/5QPt/ffW4FDAP4x//rfdJxn//AAnS3Z/H59y+Qdrdd1tOGVUs7cea8dpxz6izpMf/8I0sxsyWNv77wDOm4v/8vK5BJJfDdz62QjvvUWfOwaHYLvrDyFGnkal5HEz546iy8u3uGUk/39Y+djkwqga9//HTpuP/+6TPR3pTCf7twmXTcJ5Z3Y06btY6yFMyi2S04d8lsLJzdbKfzRfhvFy5DczqJrylebL7xiXdhTlsW1128XDruw0tno7s9i0+e2e0iZCzmtGXx8WVz0dPehPPf7dWy0bj2omWY05bF1z/2Lum4L527GC2ZJK69SL6Oq9/VhQUzm3HeaZ3Slh3tTWl8/v0LMLcti08u50dlA4MZIgYGBszLLrvMbGtrM9va2szLLrvMPHHihGsMAPMnP/mJ/f9yuWxef/31Zk9Pj5nNZs2PfOQj5ssvvyydB4D5wAMPaNs1NDRkAjCHhoZ8nE0wKJfLZr5YinxePyiWymau0Ng2lkqNv47lctmcLBTrbYYU9VxH0e9hoz43ZDbrolwuBzquVNIb5we6xwx67nK5rHXMcrkc+DrqjvMztl7rUyrpr48udM8ljHVk4ed30DBNUz9JOE0wPDyMjo4ODA0N2aHxGDFiRIup+Hs4FW2OEWM6wc/vYOOoHmPEiBEjRowYMQJCTHBixIgRI0aMGNMOMcGJESNGjBgxYkw7xAQnRowYMWLEiDHtEO5e5Q0KoquOek+qGDFiOCC/f1OpziF+dsSIUV/4eW6clARnZMTqLhv1nlQxYsTwYmRkxN62odERPztixGgM6Dw3Tsoy8XK5jMOHD6OtrU25VcLw8DAWLlyIgwcPTpmy0NjmaBDbXBtM08TIyAjmz5+PRGJqZMt1nx2NtM66mIo2A1PT7tjm6uHnuXFSRnASiQROOeUUX99pb2+fMjciQWxzNIhtrh5TJXJD4PfZ0Sjr7AdT0WZgatod21wddJ8bU+O1KUaMGDFixIgRwwdighMjRowYMWLEmHaICY4C2WwW119/PbLZcHc9DRKxzdEgtjmGCFNxnaeizcDUtDu2ORqclCLjGDFixIgRI8b0RhzBiREjRowYMWJMO8QEJ0aMGDFixIgx7RATnBgxYsSIESPGtENMcGLEiBEjRowY0w4xwZHgtttuw5IlS9DU1ISVK1fi8ccfr5stN910Ez74wQ+ira0Nc+fOxec+9zns3r3bNearX/0qDMNw/fnwhz/sGpPL5fCXf/mX6OrqQmtrKz772c/inXfeCcXmG264wWNPT0+P/XPTNHHDDTdg/vz5aG5uxkc/+lG8+uqrdbMXAE499VSPzYZh4C/+4i8ANMYaP/bYY/jMZz6D+fPnwzAM/Ou//qvr50Gt64kTJ7B27Vp0dHSgo6MDa9euxeDgYGDnMZ3RKM+O+LkRzXMDiJ8dNBrm2WHG4OKee+4x0+m0eccdd5ivvfaa+Y1vfMNsbW019+/fXxd7LrjgAvMnP/mJ+corr5gvvPCC+alPfcpctGiROTo6ao/5yle+Yl544YXmkSNH7D8DAwOu41x55ZXmggULzK1bt5rPP/+8+bGPfcx83/veZxaLxcBtvv766833vOc9Lnv6+vrsn3//+98329razPvuu898+eWXzUsvvdScN2+eOTw8XBd7TdM0+/r6XPZu3brVBGA+8sgjpmk2xhpv2bLFvO6668z77rvPBGA+8MADrp8Hta4XXnihuWLFCnP79u3m9u3bzRUrVpif/vSnAzmH6YxGenbEz41onhumGT87GvHZERMcAT70oQ+ZV155peuzZcuWmd/61rfqZJEbfX19JgBz27Zt9mdf+cpXzD/+4z8WfmdwcNBMp9PmPffcY3926NAhM5FImA8++GDgNl5//fXm+973Pu7PyuWy2dPTY37/+9+3P5ucnDQ7OjrMTZs21cVeHr7xjW+Yp512mlkul03TbLw1Zh9SQa3ra6+9ZgIwn3zySXvMjh07TADm66+/Hvh5TCc08rMjfm5E89wwzfjZ0QjPjjhFxUE+n8dzzz2HNWvWuD5fs2YNtm/fXier3BgaGgIAzJ492/X5o48+irlz5+Ld7343vva1r6Gvr8/+2XPPPYdCoeA6r/nz52PFihWhndeePXswf/58LFmyBH/6p3+Kt99+GwCwd+9e9Pb2umzJZrM4//zzbVvqYS+NfD6Pn/3sZ7j88stdGys22hrTCGpdd+zYgY6ODpx77rn2mA9/+MPo6OhomN+BRkSjPzvi50Y01yB+djTGsyMmOBz09/ejVCqhu7vb9Xl3dzd6e3vrZJUD0zSxYcMG/OEf/iFWrFhhf37RRRfh5z//OX73u9/hH//xH/HMM8/g4x//OHK5HACgt7cXmUwGs2bNch0vrPM699xz8S//8i/4zW9+gzvuuAO9vb0477zzMDAwYM8nW+Oo7WXxr//6rxgcHMRXv/pV+7NGW2MWQa1rb28v5s6d6zn+3LlzG+J3oFHRyM+O+LkR3TWInx2N8ew4KXcT1wXNvAHrAcF+Vg98/etfx0svvYTf//73rs8vvfRS+98rVqzAOeecg8WLF+PXv/41Pv/5zwuPF9Z5XXTRRfa/zzrrLKxatQqnnXYafvrTn9riumrWOKrrcNddd+Giiy7C/Pnz7c8abY1FCGJdeeMb5Xeg0dGIz474uRHdNYifHY3x7IgjOBx0dXUhmUx62GZfX5+H3UaNv/zLv8SvfvUrPPLIIzjllFOkY+fNm4fFixdjz549AICenh7k83mcOHHCNS6q82ptbcVZZ52FPXv22FURsjWup7379+/Hww8/jHXr1knHNdoaB7WuPT09OHr0qOf4x44dq/vvQCOjUZ8d8XMjOnvjZ0fjPDtigsNBJpPBypUrsXXrVtfnW7duxXnnnVcXm0zTxNe//nXcf//9+N3vfoclS5YovzMwMICDBw9i3rx5AICVK1cinU67zuvIkSN45ZVXIjmvXC6HXbt2Yd68eViyZAl6enpctuTzeWzbts22pZ72/uQnP8HcuXPxqU99Sjqu0dY4qHVdtWoVhoaG8PTTT9tjnnrqKQwNDdXtd2AqoNGeHfFzI3p742dHAz07IpU0TyGQUs+77rrLfO2118yrr77abG1tNfft21cXe/7rf/2vZkdHh/noo4+6ygzHx8dN0zTNkZER86/+6q/M7du3m3v37jUfeeQRc9WqVeaCBQs8JX6nnHKK+fDDD5vPP/+8+fGPfzy08sm/+qu/Mh999FHz7bffNp988knz05/+tNnW1mav4fe//32zo6PDvP/++82XX37Z/OIXv8gtSYzKXoJSqWQuWrTI/G//7b+5Pm+UNR4ZGTF37txp7ty50wRg3nLLLebOnTvtMuSg1vXCCy803/ve95o7duwwd+zYYZ511llxmbgGGunZET83ontumGb87CBolGdHTHAk+PGPf2wuXrzYzGQy5gc+8AFXaWXUAMD985Of/MQ0TdMcHx8316xZY86ZM8dMp9PmokWLzK985SvmgQMHXMeZmJgwv/71r5uzZ882m5ubzU9/+tOeMUGB9FBIp9Pm/Pnzzc9//vPmq6++av+8XC6b119/vdnT02Nms1nzIx/5iPnyyy/XzV6C3/zmNyYAc/fu3a7PG2WNH3nkEe698JWvfMU0zeDWdWBgwLzsssvMtrY2s62tzbzsssvMEydOBHYe0xmN8uyInxvRPTdMM352EDTKs8MwTdOMKloUI0aMGDFixIgRBWINTowYMWLEiBFj2iEmODFixIgRI0aMaYeY4MSIESNGjBgxph1ighMjRowYMWLEmHaICU6MGDFixIgRY9ohJjgxYsSIESNGjGmHmODEiBEjRowYMaYdYoITI0aMGDFixJh2iAlOjBgxYsSIEWPaISY4MWLEiBEjRoxph1S9DagHyuUyDh8+jLa2NhiGUW9zYsQ4KWGaJkZGRjB//nwkElPjXSt+dsSIUV/4eW6clATn8OHDWLhwYb3NiBEjBoCDBw/ilFNOqbcZWoifHTFiNAZ0nhsnJcFpa2sDYC1Qe3t7na2JEePkxPDwMBYuXGj/Pk4FxM+OGDHqCz/PjZOS4JDQcnt7e/yQihGjzphKqZ742REjRmNA57kxNRLfMWLEiBEjRowYPhATnBgxYsSIESPGtENMcGLEiBEjRowY0w4xwWlQlMsmhsYL9TZDiqlgo2maGBzP19sMKUzTWkfTNOttihBTwcapBN11NE0T+WJZa9xEvqR1zFJZb+5CqaxlZ7FURq6oN7fOufhBoVRGsaQ+ZqlsoqAxDtC/NrrnnCuWtGwE/F0bHUwWSihrHLNQKmuN04Vpmpgs6K3PZKEU2nMlEoJz2223YcmSJWhqasLKlSvx+OOPS8dv27YNK1euRFNTE5YuXYpNmzYJx95zzz0wDAOf+9znAra6fjg+lsfFtz6O9934EDb8nxcCvfGCwtB4Af/ltifwvhsfwl/+cqf2L2aUGM0V8bnbtuPsG7fiv/7suYa18Yt3PIn33fgQ1v302cAdQBCYLJRw2Z1P4X03PoSv/uQZ7Qd7rZiuz413Tozjg3//W3ztX56VjjNNE5+7bTs+/o+PKkn6zQ/txoobfoOn3h6Qjtvx1gDO/O8PYuPDb0jHHR2exDl/9zCu+OmzUudjmia+dMdT+MMfPIJjIznpMX/0uz1Y/t8fxKO7+6Tjtr/VjxXX/wa3bJXb2D+aw4e/91tcdudTSgd5+d3PYOV3t6J3aFI67vZH38KK63+D3+46Kh33zL7jeM9//w3+8aHd0nGD43l89B8exedv3658jn/jnp04+8aHcPD4uJaNW1+T27jzwAmcdcNv8He/3iUdN5or4pO3bMNF/+NxJRG76pc78cG/fxhvHRuVjvvp9n04878/iF+/dEQ67pVDQ1j53a249v6XpeOqRegE595778XVV1+N6667Djt37sTq1atx0UUX4cCBA9zxe/fuxcUXX4zVq1dj586d+Pa3v42rrroK9913n2fs/v378c1vfhOrV68O+zQixd//ehde7x0BANz//CH86sXDdbbIix/85nW8+M4QAODfXzyM+55/p84WeXHzb3bjxYODAID/fKUXv3iaf8/VE//zd3vw5NvHAQC/fb0PP3tyf50t8uLHj7yJ7W9ZjnPbG8ew+ff7Qp9zOj83Hnr1KPpHc9j62lGcGBMTl2MjObx4cBDvnJjAtjeOSY/540feQqls4n/+7k3puO//5y7kimVsfHiPdNyju/swNFHA717vkxKXQ4MTeHrfcRwbySltvPmhN1Aqm7jj8bel425/9C2M5oq49bdyG3+/px8DY3k8tfc43jkxIRx3fCyPbW8cw/BkEY8oyNUPHnwdY/mScu5fPn0ARY31fvLtARwZmsRL7wzh7X4xKRjPF/FvLxzGyGQRv3m1V3rMW7buRq5YxvX/9op03D8/9jYKJRObn9grHffc/hPYNzCO3UdHsPvoiHDcaK6IX714GMdGckricsO/v4ayCXzrvpek437yxD6M5Uu455mDoURxQic4t9xyC6644gqsW7cOy5cvx8aNG7Fw4ULcfvvt3PGbNm3CokWLsHHjRixfvhzr1q3D5Zdfjptvvtk1rlQq4bLLLsPf/u3fYunSpWGfRmToG5nEv71wCADwsTPmALBu1EbC4Hge/++zBwEAH182FwBw5+NvN1T6YmiigHufcdv4k9/vbSgbJwsl/GyHRWj+iFrHRorYTRZK+On2fQCodXxir3bIvVpM5+fGsVGHMBweEjvmN6m35MOD4sgDfb+ooijHNdO1vUPOcQ5IIgpHh51xhyQkg/69O3hcPA4A+qhjyn4X+kacNZHZeIRaY9X6ENDnxQN9rrJUTB81n+y8Dw86PxuQkF4AKJSsNelXjnN+R4cmxFKCI9TcR4fF9xkd/TqumJtgJFeU/pyOBqvGVoNQCU4+n8dzzz2HNWvWuD5fs2YNtm/fzv3Ojh07POMvuOACPPvssygUnIt04403Ys6cObjiiiuCN7yO+M0rvSiWTbxv4Uzc8idnI5Uw8NqRYbytCAlGiYd39aFQMrGspw3/dOnZyKQSeOPoKHYdEbP/qPHo7j5MFEo4fe4M/M8vvh+tmSTe7h/Dy4eG6m2ajUd3H8NYvoQFM5vx48s+gLZsCoeHJvHcgRP1Ns3GjrcGMDxZRE97E2677AOY1ZJG30jOjjqFgen+3KCjNifGxI6HJjWDE2KHQjtEVWuQyYLj9GSanYExxzEPSnR2xyiScUJCnmgHm07KjTThkJrhSdncjo2yuWnH3D8qJi66GibAimYQyMgDTRhkxIWOQB0fFY+jXywSims9MunYKIsUHnGtj3gcvcaylKmfl0h67fo1yacfhEpw+vv7USqV0N3d7fq8u7sbvb38MFxvby93fLFYRH9/PwDgiSeewF133YU77rhDy45cLofh4WHXn0YFCfNe8J5uzGrNYNVpnQCA370uD61GCRJCveA9PehoTmP16V0AgMf3yEPUUYKs1yfP7EZrNoU/qNj4mCKMHiUeqqzjxWf1oCmdxB8ttyIk23Y3jo1bK1qET5w5F03pJD6+zPrdfPzN8GxslOcGEM6zg377lUVURinnLhPz0050LC9/C6ajDTSJYUE7Yxl5oEmGzNHTkYxRxZs67ZhlkQLaGevOLSM49HnmFRHKMeocZASQjgQNS2wcoM5FRoROUHMZkDMcOlKouz4DEoJD/+yE5JyHJ9zXV0Z46GidjFxVi0hExmzHQdM0pV0IeePJ5yMjI/izP/sz3HHHHejq6tKa/6abbkJHR4f9p1H3kimUyrbW4fx3W+kp4pif2hveG7MflMsmnq7Y8rFKyuK8io1PvCUXOEYF0zTx+B7LqX3sDMvGj1TW87E3+utmF4tn9lvruPpdlm1kHXcohKJR4ok3rfUi6anV77Js/P2e8Nex3s8NIJxnB+1Ij0sc7qimE6WdF+tcaJim6TqmjDwMjOpFcI5TESiZE2VJi8jpmabJkCsJKRijIwoyh0tFCSRO9PiYO0IhS4+5r434mLRdsvVxXxcZ8XR+NlEoSYsS6KiN7twDkvuRXR8dG4mdItAROtnc1SLUrRq6urqQTCY9b119fX2ety2Cnp4e7vhUKoXOzk68+uqr2LdvHz7zmc/YPy+XrYucSqWwe/dunHbaaa7vX3vttdiwYYP9f7KXRaNhd+8IxvMldDSnceY8qw38uUtmA7BU++WyiYQqLhky9g6MYWiigGwqYdv4B6dbUaZn9h5HsVRGKlnf7gMHj0/g+Fge6aSB9y3sAOAQxRfeGUS+WEYmVV8b+4YncfD4BAwDeP+imQCAVUutdXzx4CDG80W0ZOq7k8rxsTz2D1jahpWLrPuQrOOrh4cxPFlAe1M68Hkb5bkBhPPsoJ22zIGP5hzHIEtR0Q5qeLIgfE6M50ugeYWcFFDpDYkzoyNGuk60UDIxWSijOZP0jJsslF1OW5ZaoSNcsugIHW0ZnRQTQHo9yqa1ljNbMvy5aYKjObcs3aZ7PJbADk7kMbetSTC3c/9Irw1l14hsfSY0I49MhG5ooiB8ltFjVZG9ahDqUz6TyWDlypXYunWr6/OtW7fivPPO435n1apVnvEPPfQQzjnnHKTTaSxbtgwvv/wyXnjhBfvPZz/7WXzsYx/DCy+8wH34ZLNZe++YRt5D5qVKVdJ7T+mw30ZXLOhAUzqBwfEC9g6M1dM8AMDz+y19yHtP6bBJwrvntmFGNoWJQglvHau/jS+8MwgAOHNeO7Ip6yF6amcLOprTyBfLeENSKRAVnq/obM7obkNbhSQsnN2C7vYsimUTu47UP41KKtCWdrWio8WycU5bFgtmNgMAXj0Ujo2N8twAwnl2jFMP8nFJSmk0R7/9i8fRTtQ0gVHBMVkHMi7RnNCpLJljHtPUorDEQpRKY9dDlnKj7ZeRNZooytabnWtMsD6FUtmlZZKlD3UJIE0sZFogNhoiitjli2VXmk2XfMrWm7aLJk8s2J+Jro1pmq77R3Y/VovQX2M3bNiAO++8E5s3b8auXbtwzTXX4MCBA7jyyisBWG9IX/7yl+3xV155Jfbv348NGzZg165d2Lx5M+666y5885vfBAA0NTVhxYoVrj8zZ85EW1sbVqxYgUyGz7inAl4+NAgAOGtBh/1ZOpnAGT3WQ7URnN7OitN7/6JZ9meJhIEz51s2NoKI96WKje9bONP+zDAMvPcUa11frBCgeuL5A5YNH1g8y/U5iYq9drhxrvXZ1DoCsNeR3K9hYDo/N2gnJXuo06RAVqkzxhAXUTSDfTuXOXvaLpmN9NwjmkQIAMYFDpJ14NL10XTMNFEUkRbASywmBMdkz0WWgnFF1yQk1WWjJJLB2iQiQ+y1lUVm3ARQb32kRNFDpPljJwol0FlAlX6sGoROcC699FJs3LgRN954I84++2w89thj2LJlCxYvXgwAOHLkiKu3xZIlS7BlyxY8+uijOPvss/Hd734Xt956Ky655JKwTa07XjzoRHBonDnP2ha+EZzeqxUbWBtXzLf+/0ojEBw7EjbT9TmxuRFsJH2OyLoRvKfy/1cb4FqTdXofQ3DOqqwjWecwMJ2fG7rkgXY8srf6UYYsiMiQnwgO7ZR056ajGizYEmCRM2Pnkjl72n7Z3HREQUoeCuzceusoIzj0fDKSSpNZ2fHYayYiD6yN0rk1ydV4wb3eosap7LUVXRvWRtnc1SKSJP/69euxfv167s/uvvtuz2fnn38+nn/+ee3j844x1VAolbGnz3J672Gc3vJ5jRHBMU0Tb1bSO2d0t7l+tmJBJfLQADaSZlUkGkJAImF7jta/5H5PxcZ3d89wfU4iYfVeRwD2/XhGj/tak3UNO9U3HZ8b5bKJHKUxkT3Uacej60QBYCIvcCg+Iji6UaZqHLhsbvY8ZeRKe24mDSLSKHnIlSZ5kNtIkVRNGwslU6gT9BAcwTFZcjYp6T5OXxtp2pKNcBVKmJH1Ugj2GKL18aQtJWmvahHvRdUgOHh8HIWSieZ00tY4EJxpE5z6akcODU5gLF9COmng1K5W18/eNddygvXu19M/msfQRAGGASydw9pokYk9faN1bfg3Mlmwe0+QdSMg1/r13pHQm+nJMJEv2b05yLoRnF75/97+sbraOBXhceCaTk93HCB2ZroRikKpbDeTA+QOnCYquaJ4P6Pxgp4z03Xg1v5XVE8fPwRQMFaXXLGOWUSuTNN0kSQZCfOm5vjkij2GyEZPFEV6DakIl2baUmaj7nqz94CMcFeLmOA0CIg4d+mcVs/bBXmD7h2elAr+wsaePou8LOlqRZqplCJkon80X9fNLckeKafMakZT2l2lsaSrFQnDEtwdC6EkURdkHee2ZW3xLsGi2S3IpBLIF8s4NCjv+Bom3jo2CtMEZrWk0Tkj6/rZ/I5mNKeTKJRMaQfZGF54SYZMy+CMzRfFKQFdp8eO042isOTEZSMzl4hc5Zg0hXBu1okK1oedV0bCWJu002MigqPpwHPFsqtqTUbC2DSOaG4vyRCMY8iDaG7TdEcURdoowEs2RWNZ4iKa23td4gjOtAWJfCydM8Pzs7amNOa0WU5mX3/9qpRIWuVdTHoKAFqzKczvsMoVVRuxhYk3K+ThdM46NqWTWNxpEbF6pqmc9JR3HRMJA0sqNr5dx2tNruHpc73rmEgY9ueErMXQg8eBa4poAXEEgP1cd5xobj82eufmR/TYcaIIjq7IWPeceTaJHLM3tSKKUFRHKFmSJxsrmlvXRt3rkiuyxEpMZtkokPD+8Zy35v041crEY+iDOJTTmLQKwZJKSmhvHZ0eIQ9syoLgtMrnb9bR6TnryLeROOZ6looTcvWubr6NJBq2t44l9zZRFFzr0xvgWk9F+KkSYh2DLFJQ1TjNKIEsOlLt3Oz/RXOL1oclC7LoSI6JFIi6FOum8Njj1XpdeGPF5FNPKK59XQp61wXwRvJEUTjt9WHmVnWPrgYxwWkQkBSVyDEvbQCCQ5q+LenikzBie30JTmUdBY6ZkAdyLvUAicyIrnUjkVkVUaxntG4qgiULsk60uoTEQx40oyg5kaP3EcHxkDDdaIamTkgUmdF1otYx9NaHJQ8ih8uut9DGgt443s9E94UuQWbXRxjVY8lfsSzUJ7LXVjcqJBK9s3PLIlzVIiY4DYK3FZGHUxvA6RG9xcLZLdyfE/Kwr47k4S2FY15Usb2e2hEy96md8mjd2/31Iw97FSSMrOPBWIPjC57wvcDRs9oIwEeKSqSD0SRCE5U39WRFCygjYZO6zl4zgkNIBtl1o1aSAXhJmC65Eq2PbmSNvQ6ThZKQPHhImCLCZV8bwfqwx9MlYbK5CcFxrk1t0TU/0aNqEROcBsDQeMFu2S6KjtT7rX6yUEJvZVO/RQKCs3BWfZ1evljGkSFLmHtqF9/GehMc0zTt9Vk4u5k7huiw6pWiMk3TrqASkVmH4NRPCD0VQZxER7MlLhc91GnH1dZkleKqUiGkZFcVRSHHEzl64kRn2jbyHbNpmjb5aavMrSJh9tzCKErZPbciGuXMK67gIiSMzC2KPIx7ro18ve3rokijketSNiWETfPaTLDXRhhFca+PioSRea3vyqNHymtTZK+NYm7FuFoQE5wGwMETlsPrmpHl7s8C1J/gHBqcgGkCrZkkOlv5XV+Jw37nxERdyrB7hyZRNoFsKoE5TOUPAR15qIeNx0ZyyBXLSBjA/Jl8grO407LxyPCk9O05LAyOF2yB6ymz+DYS4tM7PBnKg2m6wnYSLXKCQzthMlZFXIhjVqUOVOTKdvSVecsmUOSQB/r7ZKxKZEz2LhOSq0r0aFZlDygVyaCrEHnnUy47JExFXCZ9Xhti44TC0ZN56e+y8FwbFQlr0SNhutdlRjYFUryrJL72tRGRNXZuOQFsV9yPtSAmOA0A8ra8QOBMAMfRjEwW61IqfmDASU+JdnQ+pRLBGc0VpXvDhIV3KkRxwaxmoY3zZzYjYVi/TMdGoi8VJ5Gj+TObPaX2BJ2tGTSlEzBN2BGpKEHuxzltWU+pPcGslrT9ZlrPcvapBtZJlMomt5cQcTKGAbRlKwRHEcGxiZAiiqKMHjHOVjQ2xyNhChtVc5NKHZXTy3HIA29uOmLikCs5eZipJFduIqRy4DOyKTulxBtbKpu2nbqRPeU6MmRNpd9qSiftfft45IpuUNmujHC5r40qeqQinrUgJjgNAOIgRG/LANCSSWF2JXJy6ET0DoU4ZlF6CrB+SUg5O4lKRQnimAnR4iGdTNiRk3qkqXTW0TAMu9njO3W41oQoyu5HwzDsn8e9cPRBHuLtipQAcTLZVAItlaiu6i1c5XA9URTBuELJnVoB+Docci4Jg0qPaZIrkY35SoNBJ1UjjxK0ZJLIVF4UeHPT8+imntoVaTSWrKnWuymdQFOlKzFvLG2PKsLFXhtRhNcmvc0ZLRuzqQSy6YRw7kKZJoqKa8MSbkUKr71ZfrxaEBOcBoCOQwFgO716EBxSdUTSJyIsrJxDPbQZuutYTx0OWZeFEhIGOCStHteakFOVjWQd34kJjjYKRS954BKcIiE4STuKphLwqp2Z26GInCNxotlUAumkUZmD55gdG5sVNrJzi5wZmZsQHJUDb0on0VRxzLyeMGRcMmGgNSuOUPDm1o0eqaJW2XTSlh7wSRhFHhTrk2fuHyFZ00wTkbmz6SSyNgnzzk13tta9NjPtFJ5mBCeuopqe0Ik8AKDe6uvgmE84KSoZbI1LXSM4jUtw7AiOgiiSc6jHtdZdx4UNUJE21UAcRVM6qSAPzps12ZNI6FBIdESVMvGkBERpEMvGdDIhTVuQ4zWlE7YDV5Ew1dxshEKll7EiD0nhMe0oSoo6F9HcPslDWyXaInb0lI0pcRSOjEsnDbRk5NEj7/rI556pJGF661OgPmvNqKJrrN5KodVRiNlrQUxwGgC2QxGITgmIw6mH5oFoQdh9slgsrGP5sC5RJDbWI/1zUDPKRM6hLjYq2gEQ1LsibSqCaCjSScN2KPz0D3mzTtgpGFHfmkmGPIhTWXpiW+LMLIKTcNnNO1425aSJlCSsWTc9pqoS0pubF6EQnTchdmRuVYSiXRHJIHPTUSYeAbTHpdQ2EoI8Q3NuQsLKJrhaL9pG2dzkuiQThk1mRddQd31Ywi0Ss9eCmOA0ALRTVLPqp8s4MmiViPdUtmMQ4ZQ62qi7jvMq59Bb2fAySpA5VUSxntdaN4JDtExH6rCOUxWFkpc8yDQ4Takk0pIIjqtUu+JQCsLeKHopAdpGEj2SRXCy6YQtmBf2ZSnqvdXni4RkyKMtvAgXnUbhjcumxSkY6/sVcqWZoiJRlGLZ5Jao03OT9eFdGzsa5SIZwURw6PJv3vrwNTjeY7qJudxGtuRdTHoJEaKrzIIVGscEp84YmihgpLI7rayKCqA0OBFHcCYLJQyMWRtozu9QkQfr50eHo3V6+WLZ7tOjcsyEpB2OuELJNE2b4OgTxWijI3QPHFUkjBDFmODog0twFOQhI3GOtJOxUyaKSI+qQonMk0kZ0rd6moTJ0milsmk7V1V5M0sy8iV+Z90cFZnRieC4qoQUc7cpyYObUBI75XPLbNRLt9E2KtNoTBRFNLduFVWBl7ZUrk/aZTMLm/QqqvVqQUxw6gwiIp3dmrHzryLUK21ByEo2lbCV8SLUy+np9MAhICSsd2gy0l44x8fyyJfKMAxgbpuC4FTIbO/wpPABEQZOjBfsfP38mXIbybXuH83VpV/PVARxFBkq8qAS8MrIA+2MlCkBJoKTL/Gb4/E0OFzHTJMwmY3U+elrcOROb5KnUeJ01uVFcFSRq1afGhxrbglJdUWZZCSDJr2CNBrRCSlTVNb3WzIpu/NwjrM+dKWXTooqo4g80sdso0gqDzZBTtO/CzHBmVYg0RhVyoIec3wsH2lzNUJW5nU0CfvLEJDIxNBEQbgZWxgg0RgdG4ljHs+XMDwRnY1kHbtmZO1faBG6ZmSRShgomxaBiAokwtTZmrGdmwizWzPIJK1+PX0jcRRHB8Qh0RoceRVVQvr2T5dqk0omkUNhq4REY7kpKkUpuyzKRNut6mTMRnCUc6edSi+S3qIxWaDXUbzepml69C2qLsGtyjJ6h6SSFBVXwGtHzNQpqrx2isqJzDjpMQ6ZLZK55cTFuW/lxJz+PrGxICJCNgFMKoldtYgJTp1B0iqqlAVglRASsVqUKaBem+CoSVhbk9MALkqNC1mP7nb1Ojalk5hViUQdGY4uGtZLEUUVEgkDcys9hRp1HQ3DsO/beuiZpiJcKSpJ3xE6bUEcOF+/oRfpsb7vFtECgnQER2QsizI1peVzE6ecMOBUCSmEvi1Ug0ntCJeErGUVAl5a3KpKUZE1b84kFddGL8LlREfkpNcaS66hXq+epnQCWUkKz5k7KZ3bvm9Tcg1OsVS211KVMi1UCGk2lbBbIcQRnGmGPkJwdB1Ke/QOhY6O6KAeTu+oD6IIOGQtylTaER/XGgC6K+cSKZn1uY6OnikmODrQ1+B4HbhM/JlRRFHoz5vTSWlbfpfDlQhPnfJmWmTsjRK49RsKES0voiDTKKUSyFQcMy9SoOuY6TWbodgPyjW3FnlIKKIo1PpISG+pbKJUZgiOMI1GXRtJesy1PmlxFMV1DdNirQ5vDzVVNErnvqgWMcGpM5w3ZrluhGBuxTkejXCbATvyoNBkENRDh3N02FoPncgDQNk4GGUkzCdRrAOZJXP5XcfeOmwpMRVha3BofQtPl1FxMhZxEY8rlr2pA1UDv4wiXeN2PLJxzrlIIxRFx9HL+sHQNqpK1PM2AUwgkxTvrJ3nRKN46f0Cld7S7RKcSSWkFW5Fjt4qLyGUKtLLI2E611pOwuj7USONpnldACpFpSDcaWp94iqqaYbeimOeq+lQiNM7GmXkwa78UaeoAMc59tYh8qDtmGdG75irX8foyOxRn1GmnriSyhe45baSqhXLiVbSIFzyQByUIY0SAI7zSbkiM16HYkcUKOcoSkeQcbIyaJ4jUzm9TMqQRgroiII8/eOMIzYWeVEUyh5VIzva2dvkgefsqWudkVwbcryUIkXlIjiKNBpJE1kRHAkB5OitZGlGd+sAzr1TGWcYsLcYUZEwen1416YWxASnzvCTogKo9E+E5IE0+ZvnNzoSIXno8xkJIymqKFMrfjQ4gHOt++qSotJcxzpEmaYybH2LooqqSDsUHSeaUlei0G/rdkqJI8zl6oS4aQvKQWk5R0MjjUYRl8rYSUXUQ3ZMXppIptXJJOX9YABRZEZBwjTnltvoXKtWqgdPiVMJR0fNpBEcKsIlJakccfykJGpFEyFRk0He/Rh0xWhMcOoMP6JOALbwtC4iY80UVT00OL0+iWI9mv0d0eyBQ0DIWqSRMJ8pqp46aJmmMmjHLIu4uIWnap2HykGxY/VIgSGN4LjSGxqOOZWgolECG3m6DN5bPU2udCqU0klDT4tCHa8kaOCX55FPFXkgURRJqs+6huL1cXUTVoiw7WOmDFujJL9/5OSTFzHjkxYvWaO/77LRRa7EUaZaEBOcOmKyUMKJ8QIA/chDT8TC01yxhP5Rq8mfThWVNS7atIVpmr41OFE3+zNN04mEaROc6KN1fsXapFdOlNG6qQzdt9a8dgqmkt5IyIlQuWxSaQvDdijFspw0ZSQkg055yYgLrQehSR2vB5UuYeP1E1KmVmzyIJmXqloD4NpF22sjFblSkCaZjoqO6qU11pueV3U+qQR93nopPCnhVlT18daGtp1royu9GhOcaYNjFaFwJpWwG2CpQJze0Yh0GX2VebKphF1arUJPe7Rv9YPjBfsXaK6uWLvSaO9YRGLtoYmCLazUJmER661owq2dMm131pH3RhfDDbeWQe0oUrqpFZUOhnLUtGaGl6LKc52egggl1Rs10tERgL/vEJ1a0dGOpBJyXQ/RKKVUhLLoPWdrrLwqTDY3fa2lOirtKIpzvFTC8HzOG6sSgLtslBJuXvRPXBGWqtgoazLIszEmONMItKBT1ZyOoId6q4+iC29fhQDMactq20iiUcfH8pF0uD1aaTI3qyWtbE5HQIjQyGQxkqaJhOzNaknbPR9UIFGUsXwJo7nwGxISMuuHcHfOyCJhWHn24+P5MM2bFuClQvil1VSaSOagipzUASe1QjsjVfTIFVHQeFvPKFIrPOcoPqaTWrFt1CQFqh4zaa1xDMFhxtKl2q7yeEX6UJ7C86fBySQTMAxD69rQ66iKMulE4dI+1tGyURYV4hBpDuGuBZEQnNtuuw1LlixBU1MTVq5ciccff1w6ftu2bVi5ciWampqwdOlSbNq0yfXzO+64A6tXr8asWbMwa9YsfOITn8DTTz8d5imEAietohd1ABzHnC+WMVh52w4TpItul2L7AxqzWjL2G8bAWPgREr+6EcBq5kWaJkYRxSFzqLZooNGSSdm9JKLQCvVWQbiTCQOzW617oy/gqOJ0fG64UyG60RFNB0WlVtixtKPW7Y3iIgWaugx1JRMVeWCcmWmagoiCPKUkjeBop7ycdUwmrD+8sfT/aXIl0yipoyP+NDjkWCJSQHdl1k1xuvsoiSNrftYRgLTJYN71uzBFNTj33nsvrr76alx33XXYuXMnVq9ejYsuuggHDhzgjt+7dy8uvvhirF69Gjt37sS3v/1tXHXVVbjvvvvsMY8++ii++MUv4pFHHsGOHTuwaNEirFmzBocOHQr7dAIFcSi6JeKA1fiLpIqORtAe3yE4Ge3vJBKGTYiiIA99PvU3gNU0cU5FsB3FNgOE6HW16a8jQKWpItDh+BVqExDh+7EAt5SYrs8Np6ybfmuVRTLkZITXBwfgEJzK/xOGRUrlugy/zkwuWi7ahCmBJJW2YG2kU1YqZ1+kohlyAkiVvKeI7kguHLb+5jtc1kbZTub2eaecKJxcCC2PZDiEwHDZql5HGXHhRKMU0SPdaB0AKbkqUmRoympwbrnlFlxxxRVYt24dli9fjo0bN2LhwoW4/fbbueM3bdqERYsWYePGjVi+fDnWrVuHyy+/HDfffLM95uc//znWr1+Ps88+G8uWLcMdd9yBcrmM3/72t2GfTqDwWyJO0B1haW7/iJV28BPBAeCQhwi0QtU7ZlKGHb6N1a5jlBVpROvTrSkwJiDX+liA6zhdnxtuUqBHMqSt9mnClBCnVgpUWoX+m5ce4wmcpZVMKc0y8ZTBpC3E0RFVusatb/FLHuTRFvpvlhR4ImHSCIWegLfIWUd5qbbbRlYozq6jrMkgN2KmrdXhnYtoHb2pPsLDaJI6pQhOPp/Hc889hzVr1rg+X7NmDbZv3879zo4dOzzjL7jgAjz77LMoFPgpmfHxcRQKBcyePZv781wuh+HhYdefRoDfLsYEUVZSVZOiAsJ5qxeh2nUku45HYSNZx85Wv+tIOleHf63JOnS31fdaN8pzAwj+2ZHnvLXKNDj6PWYSSCScNJUoRZVhHY+SFIhTB/RbvW6KirbBQ3CKdORB/lbPF+bKtUzS9aZ0R1IbmUhYVkIeeNVo/HGc/kSK9SbnZNnOkjD3Ourof+gUp1LTo1M5RtZRQD7dqT45aaoFoRKc/v5+lEoldHd3uz7v7u5Gb28v9zu9vb3c8cViEf39/dzvfOtb38KCBQvwiU98gvvzm266CR0dHfafhQsXVnE2wcNv912C7ggjD3ZqxUeKCqDe6iNIUdkEx2fkgeiZolhH4vz9pqjIOpIIUJgg16rLJ8FxonXBkLBGeW4AwT87XJUwMl0GL3Ug3WtJrsvwjtMp65aLRHlv9XKyJp+b7oJrpdEk0SOOuFo7QqHQHQFW6bJ1TL6NnhSMdgpPvo4pgfaHPR4AIdFg11Gr/FuRbuOR3kKp7Cl0scdVzkNEfPMswZH0CaoFkYiMWcGiaZpSESNvPO9zAPjhD3+IX/7yl7j//vvR1MR3cNdeey2GhobsPwcPHvR7CqGAOFY/wlPAcZL9UUQeSGqlWqcXQeTBFmv7XMc5EeqEBkZrS/VFGWWa0yDRuno/N4Dgnx2uLRg0U1SOE5U4HtahMGW5dOSIHFc4N09QKin/TrmiTPJyYHputkSdPmftKiFag6PZTVhHOyJOo7mjKI6NMmGuPApHr7eMZOheQ+eesNZRpv+xU0op/egROXfThKeLcl4zReVO9YWnwUkFejQGXV1dSCaTnreuvr4+z9sWQU9PD3d8KpVCZ2en6/Obb74Z3/ve9/Dwww/jve99r9CObDaLbNbfQzsKVJta6apDaqXqFFUE5MF2zH5TK+3RkbBqyQOJnPVHWOnln8wG21OoUZ4bQPDPDr4zU6RgNNIbHm2NhzxUp8HxSzLkHWv1HLOHCEkJiSGPPLia6Ok1vKNt8GhwNFMwlo26Al5v2pKUoyc5/W7IGFG0h61kkldw6UW48hzSC1iCZrozhyfVJyB2znpbuqwpqcHJZDJYuXIltm7d6vp869atOO+887jfWbVqlWf8Qw89hHPOOQfptNOb4x/+4R/w3e9+Fw8++CDOOeec4I0PGRP5Esby1gOr2uhIJGmLKqqogOhSVKZpOtER39qRSqovQhLWWe06Rkpm/dnoEMVgbJzOzw2uBkeyH5RyQ0fboRj2eN5YEXnQraLS1uDokAcBsfM4ZjKOsz68PY90++DwuigLS7DZ9A9D1uwOxQotk45GiY7q8eamS7rpv4XrqCAZbhv1I2Y0wRHfZ0yZuGBcKiEXddeK0FNUGzZswJ133onNmzdj165duOaaa3DgwAFceeWVAKwQ8Je//GV7/JVXXon9+/djw4YN2LVrFzZv3oy77roL3/zmN+0xP/zhD/Gd73wHmzdvxqmnnore3l709vZidHQ07NMJDMSZZFIJtGX9BdJINCXsFNVkoYSRyaJrTl3MiYg8DE8U7V+eztbGJGHlsll9iiqiNFqpbOL4WN41py7CsHG6Pjd4Td1UEQVdbQQAW/QqSgk4JEPdWVdto9fplTibP4r0Px7tSFEURZHphHxUW1GOWRSZIesi6qJcZKvRdLaoUETrxDay17C6aJ3OVg2uSibZBqwpd78lT7WeRyck11uxUaag++CEmqICgEsvvRQDAwO48cYbceTIEaxYsQJbtmzB4sWLAQBHjhxx9bZYsmQJtmzZgmuuuQY//vGPMX/+fNx666245JJL7DG33XYb8vk8vvCFL7jmuv7663HDDTeEfUqBgE5Z6DZVI4jKMQ9UHF46aWh3tiWgU1Qq7UQtIJGNtqaUdodgAmJj/2jOEw4OEsOTBfvBWG0EZ2iigFyxpN2p2S+Oj+VRNi1h4uwqieJ4pePyDJ+EnYfp+NygS2Pp9I9sP6gUVSXES1uQ+8qrbxE4lJSGBsflzCRCX06aiHyeTCS94yp2k7d2YfpHIUZ276ulF8Gh02jkc95eSZ4SbIWNshJ+R99CVbdplrJbn7P6FpYU8O8fNlqno/9JKUTvvC7KhZLJuYZ8kiqqoiK2ybayqAWhExwAWL9+PdavX8/92d133+357Pzzz8fzzz8vPN6+ffsCsqx+6Lff6P05E+s7lW0GctY2A34duy4GqNLmaklYrljGSK6I9iZ/BEkX1WpbAMuRG2SbgbG8bw2PLoiN7U0p3wSlozltP0wGRvOYP1Nvw1O/IDbObsnYDzpdtGZTaM0kMZYv4dhILhCCA0y/54arNDal98ZMv/0DlpNqziRd/wfUVT26Ghy6C641t4ZuJeUmD7li2fVM8gh47dSTwumJ0huUQ6cJoCo9Jk//+BPH2ikqAXlguzKLImv0Z3QX5VLZlKSoknIbS3o2AmzKVL33F70+hVJJOHdKMTcbjZqSGpwYYlQr3gUsR0luiDCjOP1VljYDQFM6aW8zEGYZdi3rmEom7L40YQqNj1VZiQZYFUBRpCRtgXEV6wg43biDKhWfjnCXxmpug5DS0zywUQ+vqFNPY0K/kbsra+QkTEoeis65WOP10haiiAK7r5aMhBUZ8iDqosyuj8jh6lZbiboJq5o1Elt5Yz3ERUCQ2VSfjsBZe38yRuBcrdarUBat4xTT4MTgg1TF+E1ZAO5tBsJ0etV23yWIIpXWP1I9CQPocvYISJjPJn8EUWx7UQuZBaJtmjhV4SqNTci3YHBXrRiez+1jMqkncdUKk7YQkAz6/yqn5+zo7a6E0SVXqigTsdGTJmK6CcuEvnQlk2zzR1YcKyYZfMF0TrGOMhF29SXqCgGvIkXFpkz1tF7u+8xLAPnr443gRKPBiQlOnUD0LdWSB7t8eDS8SqpjVIqqGkTh9PqrFO8SRFHOXjN5iILM1pDqA4A5ETZNnKogjiOVMFxdh1VpC1kZrcjpiap/UoxDkREc7TJxVjwsJFfs3GzkQZMIVd7+7X21NDfbtGzgp8fEJENEhJhxghSMNUZvB+4UG5lRrE9KQVLZ9RYRIcAdrZNt1cCmD4UNJYlGSVjpxUaZxPdZLYgJTp1wrIbUChBRdKRGxxxF2qKWFBUQzTpWW0FFQMhsuNe6xmhdHMFRQpwG4ZRBe8TD8rQOSRlkhREctvqHjOMLWQl5kDk9NrVi71vlEb1q6luE6Q1VTx+1gNeujhKRAiaNJoqueSJmilQW4O7KrEoT0ecl1tbI02giksFGwrwpU8m2HJppL6cPDkuuRFVr7nsnJjjTBP1VNlUjiEKXQZxe1W/1kURwaiM40axjMCQs1GhdjfdjlFtzTFUIS2MV1S2AxOEyjdVs5ygo1VY7Uf2GgEWBjkLWoRiAUDPDkgehGFm0r5a0m7BeWkdNHkgUjlwXfidjer3pbsL8ajSWXMn1Ld5KON2mjvx1BKyUqb9OzyR9WJ0GRxgx4wjua0FMcOqEapuqEUQTeWj86MixGqrR6O8NhEgeqm3yRxClBqdWMjsQR3CEEFUJyR0KS4Y0G9QpBaqCEmMBeeCVsvvtUOwhYYoUjEonxDay46+jKHqkqcFRirpVhMm9NsWyiTK7vYF2iToT1VMSRT0y66RMrXFlzhYMovPxrKNg13rV/RhrcKYZao2OTIXIA3HopIFcGAgqEkY2FQ0Dx2pN/0RBFGtcx84INGFTHd4wv16TOPpvlmiI+uCo3phTKsLE7qqts0u4Iq3j1eDoRo/kaTkZefBGj/ytj0hjkmGiKN5IBhOVoavMBH1rbGef4NuYExAh9XqrtnRwRwnlx1Rca0brpSSpsQZn+iFfLGNoogAA6GxogkPKm2uLjoRlo2maNUcebMcc4rYXtUbCIr3WVUaZOuMIjhK6Qla2usX6W6DBEXQoFvYdUbzVeyJHghQM/d0MKzJWVNao3ur9p9HU5MGjZVJVRynE2iodlSjSQx9DaKMqRaWY21PJJCBrosaBvPP2EjZ55Mpb6cVWwsV9cKYtSEQjmTAw02eHYIKw3+qLpTJOjNcWeSDVV2Glf0ZzRfutptr0j21jSBGcIEhY2Nfa2qahNhttMjuW9+zzE8OC501d2JSP0kawDkWYovK7kaXozdrteIjWJF8qu64r3U2YjaR4nL3f1BOb1lEIVGnyIN4cU1FR5NEy6a2PX8E038bq0jokSiIqwVbqt9h1TIht9KbRNNdHGTFz/y7wNEq1ICY4dYCtyWjNIFHl9gBhl4kfH8vDNK1qilktVUZw2hyCE4bTI+fekkmiJVNd91wSnTo+lvfknYPAWL6EyULZNZdfsJ2rg0Yt2zQQEKKYr3SujuGFLCxP/37QzsBLHnTfrFltBKvB0XPMdIdiunkdHSnxRIW0++CIIgruaJQuEWLnprsy+9fg8IlQ0TO3Ktpi/Zx0KJaej0KjpKvh0tW3sFGURMKoeYdy/Z4+elqmWhETnDqg1hJxwHmrH80VMZEP3ukRG2e3Zqreo4lsfpkvheP0atUIAdbWBIAlrBscD54sEo1Qc7p6EtbelLIfamFEcWrZpoGgOZNEa2ULgTAF21MZntLYylqbjKjT1U1Y9y1c5VCEZb7yaAuJfLDHZLsJ03+LIwVMdZTIxhQbPZJHPETkge0mLLOxascsilAw623922eHYsUxa47WMVVw9L+VaTSFRokVs7Nzk0iNysZaEROcOqBWYSwAzMim7P4GYWgzau3dAljbNZB9icJwevY6VpmeAqww7qwWK00YRjSMpL6qjd4Alc7VIZbcB0EUATpiF+tweBA5KICJjlQe8rTjVm1vkFKMEzpmzU05rWM4NtKiWpYMiTQ4dmm1z7SOSMjKJQ8uEub8W7vyiBHRenvH6OlbyPFSHPJAz03rrTxbNWhqcETVVkqdECMIpufW1T0JNTiK1KonWiewsVbEBKcOsAWdVaYDAPd2DWFsMxCU0+u0y7Ab2cbwHPOxGre7ICDkoT+Ea32sxu0uCEjELkwx9FSGLLVCOwq2/JoeK2qYpi4JZh2PrgaHH8FhGwK651ZUMmlqcHRTVKK5adLBdnBWNkL0WSauqmSy/s2xkUcUtVNPPm0UnDOdhhRt15DXvs/8kVlPT5+AdxOPCU4dYFfV1Lh7dZjVNbX26SEI0+nZ5dc1r6MjkA0agUVHWsPTXNUqgibotO/HOEXFg0iDA7gf7Ow4+t+iLQGcCIXqjVlPg0PmE20TwRICl42qFJXmW73onNlxovOhHb9SCC2wMah+Oe5j8m1URde81Vaa5EEhZlfZaGmZ/N4/inSkIKIYa3CmAYIiD2E2qau1dT9BmE5vKkRwgrvWYdoYUJQpgnL2qQzWQVmbP3rLsHlv1n7FmvrVP/KOx9ZYUlpNR0e844ROz2f/FqVOSEKu8hyiSLoJy2wUNdvTFUx7U4ccGzkpPPfGoayN8vSY+Brq6VtY0ksfk7axVDZBNPDqbTTckR5xtC7W4ExbTAWH4ux2HoyNYWpw5tRKHkKMMgWnbwnRxgA0YUA0XaGnMrhOjxsd8WojdNM1qgZsqqoVXnosxRnLs1EkovU4ZoXIWFUlVGRIhnVM7/rwU1maGhxVCobR6rCOvsg4etcxXSSMrI1hkzBhVEizlN3RZbnPhe1QzI/gePsE8UXvgnVkI4oCkirqJ8TrolwLYoJTBwTm9EIkOMeCjjKF0Gcm+AhOCCLjwMls8DYeCypF1RretZ4OYB0UwCcastSBKpqh0rc4nWj1NDj0v3mpFf44xtmXWWemSdZsEa085SWam40m0OO86RqWhOmVf5PxpbLJJQ8ZTnSEa6OvaJ1CTyTY8JI9JqvLEtnITaP5jSgKImGsNop3zFoQE5w6IDiCE95b/UBA+hbb6YWZRgtMy9S4abSuEKuoat2mgcARQscRHB7k4ljvG7OfFJWnakUoEpWLOnmkgEdIuERIET0i5yMq//ZocARdlHmRMK4Gh1eqbetb5Kk5v2Jtz9w8GznrIyeKCg2Oz3H0fICzBroRRfp8xWk0PgnTJUKsjbUiJjgRw+oaW1tbfIIo9C3BCU/DIGEBV3qFEmUK5lqHGa0bCOp+rDT7648jOFzw9C0Znr5FU2RMdxOuXjuiocHhpGGKjKOnvyOMCql2CRdqcPiNEFMJ7/rwImFaOiERAfSkVsSl/i5SwC1l14vWidJeovLvIrv/luee4IvZ+Roccbm9O40miB6xqT5FpJDV4LA21oqY4ESME+O1d40lCMvplcsm5fSCIQ9B2ziRL2Gs0uAwqDRaY2uZyJ5ZwV/r4wFd61iDIwfvrZ6nb2GjLYAgikJ3E/a5kWWKcmQ0eZAJT/mRB7lzNE2T0/NE1+k56+TqE0QiQinv3PxqNLUGR38rAnHkQZ164lxDW7NCaZ4SIi2TgACKUlSVn4vF7HrRI91ID+D05FERafb+EdlYK2KCEzGIE51VQ9dYgjlt4Ti9wYmCnU8OioQNBFyCTdYxm0rYzQSrRVhC6MlCye7gXGskjNg4PFn0PNBqwRB1ravdkoOA2Dg0UQjUxukCfaenp8HhiT+1xchC8qCbtpCMo6JRvG7CyrSFHUURdVH2rk+K40hlNuY8kQeBOFbRdVjURVk3HWkLgn2lI93ro7rWomNyI1yaabSUiCgyc9N7mdHgibBF510LYoITMfpHgkkHWMdwnF6uGNx2DYQ8dDSnXSHoakBsHBwvBHrj0toWEjatFiS6Mp4vYTwf3JYShNRlkgm0N9dGwjqa0/abXZCptCCvdUdz2n7YHw+hp9BUByv+BBTkgU7BcByPu8RYocERVFF55+akTHySMJF+gyUPLMmQ2kin8Mpe4sLv1SO2sSjYddyviNb6tzfiItUJcdORdMWcYG7PNhryVBZPPJzn3Wc8Iq3oy6S7i7ofMfsps5qxaHYLgty2MCY4ESMo0SnAOL0Aow9BbIFAMLM5DdIM9USATi8obQsAtGaS9rYXYaxj54xMzSQskTCcdF+AIl6yjtXuxk4jkTDsiF/cC8cL3Tdmu+pISYSsf/O7CftIrXAcLu0c7TRaFY6ZPrZnl3BWO8KsD91Fmdc7hksyeAQn5V1vensDt5ZJ1ejPnzC3Gg2OKFXjqfRK8K81WyYusjHPJdziVFY2JV9v+nueUn9F00IAeOia8/HYX38MizpbEBRighMx7J3EAyA4hmFQWyEE6PQC0mQAxOkFL4YOSmAMWOsYhp7Juda1kwcgHM2VvVdWAOsIxNs1yCDrg0OTBzaSAYg0OH66CUuEp1Q0I1f0EhdeKoRf/eN1euTfBkXCyFu9t/ybiJEd7YgsMsMvwVaN4xAhzs7oup163WO9ImwXeeARQA6h5J0LT8uk3leLo+HSFLMXuSSMcy4UcaFL5ZUaHM49HgZighMxgow8WMcJwTEHVDZMEEYvHJL+CY48BE8Ug+qBQxBGqfhAwPfjnLZw9EzTAbK3dTplIk8daHYTVrwxu0WdepEHbQ0OT8iaSHgqcHx1UXaRJln5t2KcRKtDzy0qUefbKF4f5bloap7oaJe2TijlXR9lBRdnfXRt5JWTqyrhaNIUBiIhOLfddhuWLFmCpqYmrFy5Eo8//rh0/LZt27By5Uo0NTVh6dKl2LRpk2fMfffdhzPPPBPZbBZnnnkmHnjggbDMDxRBRh7o4wTp9IIqEScIo5IqyEgYfZwgSdixgK91GOtI7kdS4l0rgmz2N92eG7WIP6VpEJcjIxEKUQt9ztyKt3peNIPbTZhDrmTn7N11nHNMjs7ELhNXOGZnt2xvus1lo0TLJC555625PMIl22xTFRFykYeUvBdNkUuuZCRVfm1k90SR09yQHisUs3PWMQyETnDuvfdeXH311bjuuuuwc+dOrF69GhdddBEOHDjAHb93715cfPHFWL16NXbu3Ilvf/vbuOqqq3DffffZY3bs2IFLL70Ua9euxYsvvoi1a9fiT/7kT/DUU0+FfTo1I6ieIwRhplaCtjGM6EhnjVVeBJ0hbGYZpN4KcAhnGOnIoCJhQfVmmo7PDV46QiY8TfFSAlwnKidMAD8lIBOe8p0jT6vDc8wKEuYj/SPXt+j1b8nwUjUKLZNqzypaH8QldrL1Vm2sytt2wqVlcpMwVjCt2zyQTyglUT2eaJk6F1rXxKbRhMdMTHGCc8stt+CKK67AunXrsHz5cmzcuBELFy7E7bffzh2/adMmLFq0CBs3bsTy5cuxbt06XH755bj55pvtMRs3bsQnP/lJXHvttVi2bBmuvfZa/NEf/RE2btwY9unUjKDfmMkeRYE6PVt4GtRbffAanKDJQxgNCadSOjKoax2UjdPxuSEL9avf/vW6CYscM3l7Vr3Vc0kTl1zx0kScSAb3nL09a6z/651PkRGyis5FV+hbTTfhaiIz3NSThFC6q7Kcfzs7oztpNFX6h3f/8KJwKY5wWaZl0hW9A26SxrvPwkCoBCefz+O5557DmjVrXJ+vWbMG27dv535nx44dnvEXXHABnn32WRQKBekY0TFzuRyGh4ddf3Twby8cwv+1aTv+52/3aI3XQZBVKwDQ1RpmBCfY1EqQO2EHr28JQ4MTcDoyhA037YhiQJGwPz57Pv71L/4A37pwWdXHaJTnBlD9s2PdT5/Ff7ntCRwYGLc/47+ti50e3zH7b9QmGist/+ZUzGiTB8GO3l4bBfoWxdz6EQrxOhY5Ghy+XsZNHmyiqCRXYgJYzbnQ62hrmSgb3Kk53fJv73nzuihLNU+cPavchElQCceJCoWBUI/e39+PUqmE7u5u1+fd3d3o7e3lfqe3t5c7vlgsor+/XzpGdMybbroJHR0d9p+FCxdq2T8wmscz+07g9aMjWuNVME0zcPIQitMLPPJAdBkBkoexcCqUwugxE7TeKsgycZuEBSQonz+zGWcvnIm57U1VH6NRnhtA9c+Ol94ZxM4DgxjNOX2VuG/1kiZx3CohbhqEX+Zbrjhj0zS5eouUxJEqIxTcuTlkrSweJ+6izHPMCp2QRKujXdLNKY0Xn7eXDOlqcLgpKi6p09PqCM9HQZCl3agV6TZ+OtJLmISVcEXv2DAQeooKgKcHiGma0r4gvPHs536Oee2112JoaMj+c/DgQS27OwNujz+WL9llmIGXDgfk9EzTDF4c20q0I8GsI72fV3DakfB6zBASWitCKRMPWMsUJOr93ACqf3b4Fw/rOXq1hoJyehVy4ep4zOtlUlRFM/S0I7oVOGLhaQAaHJcmhKMT4kVROGRNRB50dU9ycXUN58yJHGnZyKkyk+1u767q00v1iaIyvCgcu8N8WKitvaoCXV1dSCaTnjekvr4+z5sUQU9PD3d8KpVCZ2endIzomNlsFtmsf2c9J2CHQohSSyaJlkwwSx+00xvJOVsBzAnord6p/gmGPJD9vABgdo3bCxDYJCygCE6xVMaJ8WDTaGQdj4/nUSyVa97qg95KIigNThBolOcGUP2zg9/yXqJbcTkeb4UJzzHzUllux2wim3J/h0dcaGcWRPpHGU2gCEexZCKddOz12igW3FZjI28nc74Dl4tjlc0atXVCmtoozjknEwYSBlA2daqefLYE4DZ/pKN/YqJIp6WAyn2cLylJZRgIlT5lMhmsXLkSW7dudX2+detWnHfeedzvrFq1yjP+oYcewjnnnIN0Oi0dIzpmtSBh+6BSK0GnVehjHR/P202WagEhYTOyKTSRJ0+NoEmYGUAfbhJ1mNWSrtnJE5Aoy/GxYNbx+FgepmkJ7mrd44lgdksGhgGYpnW9awWJgqWTBtqbQn3X8YWp/twAqA0TlfoWCSngVOrwHDPPOdLz8cp3AUHnYe7bv55AVbebMP0dMpbXJI7+dy26FfU4L8lIJgyQwB5tI3k0cPeO4opoFXoi6ZYX8mstGlsLueKlk/xvO8G3kRcpDDuCE3qKasOGDbjzzjuxefNm7Nq1C9dccw0OHDiAK6+8EoAVAv7yl79sj7/yyiuxf/9+bNiwAbt27cLmzZtx11134Zvf/KY95hvf+AYeeugh/OAHP8Drr7+OH/zgB3j44Ydx9dVXB2o7CdsHtY9Sf8DCWIBxegEQsaArfwCHhOWKZXsH8FoQtHgXcCJBZRMYDIA8kHWc3ZqxKwpqRSqZsO0MQgzdT1X01bqVRNCYys8NQO6keKkQfqpG09FTb9bkrZ4ey+smTB+Tq2+hnWNC5nD1OvXSZI1+wyc/d5Ew7h5KVfSO4WlHZGXQjHaEFSS7iaJeibouoUxxz0VOPOnjk3N1bzuhp8Gh505pngtfb+UlVqrzqXX/OxVCf2279NJLMTAwgBtvvBFHjhzBihUrsGXLFixevBgAcOTIEVdviyVLlmDLli245ppr8OMf/xjz58/HrbfeiksuucQec9555+Gee+7Bd77zHfzN3/wNTjvtNNx7770499xzA7V9VkvGDgEeH8ujuwbhJEDrHYJzzMTpDYzl0T+aqzmtFHQDPQBoyaTQkkliPF/CwGiu5t2/g+7dAljrOKsljRPjBfSP5ms+/6AFxgRdM7L2ta4VAwFX9AWJqfzcAASaB0nEhVfdoo708N+C08kEcsWy7aR4b+rWOHH6h2tjFW/1eU40gXRRLpRMPsFRaEf4pdUyx+wldUWOo6eJIjl+vlgW2KgbPdIjlK5oi1QnJL+Grm0ngmooqbv3lyDtxNpIkzA2nRU0IolLr1+/HuvXr+f+7O677/Z8dv755+P555+XHvMLX/gCvvCFLwRhnhBkH6X+0RyOjeRqJjhBN9AjCNbphWNj54wMxo9PoH80j8WdrTUdayAEEgZY62gRnBzOQFtNxwqN4LRlsPtoMJqrsGwMClP1uQHo963RTa3wtmCw3/6ZZmmZCsEh8/EclJ+5bYerrP7Rc47k/4VSySZDLiF0gj5va26u6JWzFQFvqwYVWRPbyJAHTiM7+vjV6IS4O8dzSC8v5cU7H6GNmtdQ1tOHV9XHJYoqG6lrGXYEJ/QU1VRHV4Dt8R3HHDDBCbDZ37EQ0mhAsJVUtmMOuPInyK0QwiSzQDDVXkHv5xXDge3MynIHIOscm+HoYHipmixbtcKkQkTpDb7eQpb+4ZEr3VQNP7WSZ2xMJQwkFNojvxocrl5GMxIGOBEX8p1kwuCm+vidnhUaHBmZ5fTq8VYoucfytp0QnneRQ664vXo40Tpuuk2+jraNAhIWBmKCo0CQmwcGuUs3jc4Am/2Fl1oJrpJqIOBOywSOGLpxbQzyWoehZYphgdVGALTTU2hHdDU49l5LfOJCfq5+s9adW06udCNCvLHiFIwscqW7jpw+QYrUodxGtkrIWwmX59iY5ZECW3ium05irrWAzIpIWNAl6sWy029JSGaZ6JqIhIWBmOAo4OxRFGQEJxzHHMSGm0HvJE7g7EcVBAkLhygGWXIfdC8hAhKtC+JaN3IPnKkO3XQNr9qKOCH+ZpIab8zMWzivnNw6Ps/ZW2N5xIW3BYPLRs0uuNb5GC7blCJaznmrbORHUXg26mlHHMF0lak+DsngbaGRstNyThdlkSiXJWw8YiW0sSwmLmrCTQnFy+718YqM+etIb+kQFmKCo0CQTs92zAE7FLubcQBpC2cn8XDSP0GU3IdRbg840bogGjuGUY1mHS+4iOKxkAh3DFG1jqTlPacBWzV7LbnHyp2jU8GlJyjVdeB0yTevnJw+b48QmrWRu/Gkno2qvb9Y8qCrb9GrEpKUaiu0NfS/yXGUEa6yO/3DRqP423LolYnLNDh+bCTnKooohoGY4CjQFWCKKuwIThBN6oLeaJOApFaCjDwETx4C1OCEFAkLsvlkI1dRTXWwb+umaVax7xAntVLivNUrtDXiCIUkmuFqMigjV14b6Z/z0nKAE2Hw6oTUaTSejdw9vTjdcmlnTkgYrz8R/T2WKKoIpeuYSh2M3EZW4KxK4fHSScK5Oedjl4nTJExCFN1z62lweFVwYSEmOAqQ8H2tjtnqbGtt+he0Yw7W6YWVWgkyOhLsjuwEQe56TshmV8A2BhlRJDbOiSM4gYN1KHSfG/4bsyIlwNlYUSmOVTlHXhdlmS6DV94sjDwQcqVyeno6Ia5j5mlwuI3nvGJt6+fyqAcbXROVk3NTeDyxtrQHjyZR9ERmdHVCFRsVO3rrEiFa46MSs7PHFJGwMBATHAWCiuCQzrMJA5gZUGdbgqD2UZrIl+xGfI0aHRnPFzFObAxaJ9QWjE6oXDadKFNA+1AR0BVz5Ro6LpumGUdwQgSrjaAdhkpQKusxQ48Vv60zc9tiZDl5oDv1VtMHh5e2EEU9POJYgWNmdUK0jbpVQiIS5k2ZsJEwd4m6sJxcUoKt2neMRz55XZTFAl5DMK42nRCXcDP3GasfE19rNxESrXcYiAmOAkFFRwj5CLKzLQGdoqplKwRyjtlUouZmfCzmBFShRJxyNpVAayaYrSQI6EqvWtZxaKJgv7EHHWWaXYkoFssmhiYKVR9neKJo2zg7FhkHDs9bK/XmXIu+xXVMvxocRSrLRcJUNnLSOty3epUuoyiPRklt5G0cyo2iUCkYSRdlVXpMrG8RE0WR/kdmI91F2da3aF9rHxocjk7I1mUpUqbu89azMa9IZYWBmOAoQItja3ljtlMWIaQDiI2FUm1Oj678Cbp1PznvoYkCcsXqt2sYoErtw7IxXypjeLJY9XEIUexoTgfeyCqbStr7RtVCuvsr92NbUwrZVLBEMYbXOdJOzdU7hlN5xNOt0FswsG/MqtJhXeeYFxAcx+nJ0z/0//NFuY2iCiVvlZB4HaspbyZdlHlza+tbNAklO7c8iiIgD3YUTtUHx18ER7j3F6ffkjDN6InC6fbB4afbwkBMcBQgb+ClGt+Yw0wHuJ1e9RGSsISxgOXsyS9xLem+sJolAkBTOom2bO3k4ViINgKUnimIax3rb0KByPFkkgkXMed3weU7qRRLSBQORanBYccVBeRBIjJW9o7hlLzzx+k5ZpeNdMdjCVFMi0qmmeiRiFzpirVZ4smOlXWjFqYZ/WpwlDohLwlLqYiiotOzmszyryHbvykMxARHgUwqEcwbc0jCWIIgxKdhlbED1rYXQTSpc9YxZPJQgxiarGNY4t0grrXdxThOT4UCp8+LngBTpW+xjqkbUWD74OhpRxwiZLhIGM9GdUpJocFhokKqiBBbTSTqeMzr6SOMelS0NSJhLqsd0V1v0bYTTn8iqg+OcJ8wPmlSRcxEPY9YwbRa9C5PmdL/t8+bU7VmHVOkwYkjOA2BQN6YQxZ0BkNwKlU1IURwAKpfTxAkLCTyQBx+Lf16woyEAcHowuIuxuFC9MbsEWpqanCs/wscrsiBs2/W7Ft9xfkWPZ1o5fPKx4pSJnzxsFqgKiJCgmgCTRQ19+ASHZPs8cVeQ2+vHv7xxNtOOD14VJGroqa+RU0o+doodqzsfmTvH6ePEim3lxNKVUQxDMQERwOBvDGH7FCcZn81pFZGQiY4AeyjFNYWCARBXGuSogovghMcUYwrqMIBm9YRpZNk5c3ab/UJvuNxtDWiFJWbFOg6UZeNLGliqnqKmukfXsUT75zFFU/eyIPTB4dfHVUoqkiTT41J0d3wjk3B0N/zkkrNLsrCtKU8lSUidWw3YfpaOyTMZw8eYfTI3fwx1uA0CIJwKI44NtwITk2Rh5BJGHH4tfQUcsTaYaWoaieK/SETxc4giKLdDTqO4IQBmQZHNo7+t0hHoSYuovSGPG2hK7albVCNFZEmcTNCPccsIkxlk2rgJ0j/pDzrI6g8YlJ4fjU4onN2nY+ujqrIJ4qe9I+oDw4TUVStt3VMBQEUlKirNDginVAYiAmOBoJojz8VNDihR3Aqxz1Wk74lZAGvTcKqv9bhR3CCiCiGS7hPdoj23xFqKCo/N01TrG8R9Y7x7CbOiD8VTs8bRZHbSP+7Wg2OMLWiEtuKCEGKRx70Um7qTs/VaXC8ZNY5PivM1U89qciV5r2jKHkHqP4/mjaK7wn++sQpqgZBkA4lLMdMjnushrf6sCM4ga5jAxNFex0DbvJHEEyKKlzCfbLDjhIU9d6YHY0Jv1+O9X9+80Bl1YomGeFtgeAeR5MwuWZGSexYEqZKPSnXkSIPnkiBKvWkGMekk1SVTKK14TXwE5IrURdlRfpHqctS6reoPkHkmEX+eXuPWVtEMQzEBEcDnTU6FNM0pwR5CF+DQ0hY44qMAyEPI6SKqikQm1gEIXqPuxiHC92Hv4gQABoaHE4fE/p7bKl21aksJv1TKpsgfTCVNiq0Neqoh8hGvmDamlNBmrSFy2wKT9UPhiWK7nl5Dfy0RcF+U3hCrZc8lcUnYUQ8rGgU6XNPr1iD0yBwyEN1DmUsX0KucvEbtYpqPF8MbZsGAnu37iptLJdNHA9bg1NjOrJcNkOP4NBVVNV2XHYId0xwwoA3tSJ/+BfLJspl00VwVJtjqroEO5sb6qZW5FECMsYVZfLohPRKgunzBsQVT2xVj8jGRMKgNvA03d2EEyrSpNf917ZR1GPGkxL0uleWaKhE2L5tVEXMyD0hIMeGYdjrpRY4a/bBYaNRcR+cxkKt5IGITlsySbRkgt0CgWBOjY6ZRB2a0sFv00BQ63YNJ8bz9kNrVlh9cGq81mFu00BASHKuWMZozn/H5clCye7UPKctnCjTyQ5R2kKkbwGAQrlsOyiDqW6RHVM3MiNyPGwkQ2ZjvlR2aXF0IwreiiJRikov/cPrEE7P7SKKCl2PcosBzRJ1VTSKHVsum0Ki4U1dysmVQ3pV3YTVaSLdJoOxBmeagLzlVk0eIug5QqIFE4USxqpwemFu00BQ63YNfSNOk7+wfjlI+mc8X8J4vvp1nNkS/DYNBC2ZFFoq+3BVQxZJipBuYhkjWFRbtUI//Nnfw7Sg8ZyoVNvRbwicHvOm7rxZ88eRY9LkISUiYUV5OsJTWSOKjrDpH4EDtz5zxNCiLR14c4t1Qj7TP1rkwSGfpDEe30b3tSYZgJQgGqWvt2KjTN5nvbfFgT/yGWtwphiIY66WPBDHPDckbQtgOb3mNHF6/qMPYetvAGu7BvJArIYsRmFjayaJprT1a1FNGXZUWyDUEmki9+OcEMnsyQ4nOqInwAQq5EEg6KTHqjYtFDoeQSSD1Vqwc7PpH9rRe0iYILWiK3oVanAUuhrArWcSbengmlshzE2xG4eqSuM9ZJZDHqixckG5XuRKSMK0t52QRcJMJsqk12VaXycUp6gaAi2006vGoQxPAgjXMQO1dQqOIsqUSBjBOOYQ19EwnC0lqunXE3aJOIEthq5CsE2I4tz2uIIqLOjqW+hNNOnUiso5Av6727LRFtGbujL9U+Q7PN4x/VZwiUqr/URHCkXHKbPdhOljqoTQ2puWpvQjFEISpkiPia6NtgYn6RBUWSsC65iOjXQkTK0TEkQUPfdjnKJqKBiGUZPQmDi9MCM4QG1i6CiiI0BtJCw6G6snYcdC3qaBwL7WVTR2jIqEnczwOPCKg8pKyAOdWlE5HvpvbQ2OqPxb0dHX+syb/mEjHvQ4ZfqHjR4J2vx7tgMQECHa7nypLEyr0J8VGVIgdOBMubRMWG2aplA47BpLpfrYbsL03NoRLmVTPjYVKltH53zconf+MYvMPe6tFBTcEyGl8GnEBEcTNUUehskbc7iCzlpsjCKCQx+/mvRP34gVCZsbsjB2Tg2aq7A32iSoZVPQYxFFFE9msKkVWXSEJkOyt1thZZagDLrAkgdNHQyPhLkiD1okTN5NWNTnRajVUeiJrM+8jpmbyhKQT93tDUQaHLNSRk/OhY2YAc46Ksksq6MS3D+eUnbFliDkPESiZfq7+aJpzys7b23CrRCUh4FYYaiJWoTG0actGjiCU8N2DVHbWFsEJ9zy65pstCOKcQVVWBBrHgRpnZwVUdCpElJ1rdUu//ZEUTRSVEUTJmRVQowzE5Wys6XIwq7MzDkLxrlsLDml7DrrqGoe6HT01dBRlcRNEN02mkLyx54LPXe1JCztIThiopjirKNWqu9k0+CcOHECa9euRUdHBzo6OrB27VoMDg5Kv2OaJm644QbMn///t/etwW1VZ7uPZMmy44tycWzZuZpAEsCBck2cXkg5Q0hKCj3p9x1uzYRpy0DbcGmZaeEwZ5JzOi0pX0nzzaQ9nUlpSgcYzg8SvrS0hjAkKW0uhJCQKyaQEAyJbMexJSe2JUta54e0ttbe2usiR9pbcdYz4yFsrb3Xu98trffZ7201obKyEgsWLMDhw4eNz8+ePYtHHnkEs2bNwpgxYzB16lQ8+uijiEQixbyVgnhwJhY556EQHpyJRe6LMvECtmtwIgcHKJQeHSKzJUwUR4rRsG7klCILyUPWUChVtyTSeRTS7RLo5oacTSfzImFs9Y9SnpDlmpztJIw+OJlxAWWyJkkyFpAMa28dfn6LWY8qlXCmZyghYQmObthx1GMVUwz/8J4hm+sVl+iHzetRJb2sDNJyckElXKFR1Bnuu+8+7N+/H21tbWhra8P+/fuxbNky4TnPPvss1qxZg3Xr1mHPnj0IhUK47bbb0N/fDwA4deoUTp06hV//+tc4ePAg/vSnP6GtrQ3f+973inkrF2SYnfPgXPhbfUmTBweq0YDCkAfHcnBG4FF0iiiOFKNh3eAlBJeXlQnHqubgUGLAHrdeTzWJ1ppDIcwdSabEpdq8fAtOjokshEdlpl2UlXJwEkyYSIWEcUJz/PJmQS8j1nukmMArIooJy9z8RF9xRRg71uxlEusnnkzazmsdZ55brX+TtR1BMVC0ENXRo0fR1taGXbt2Ye7cuQCA9evXo7W1Fe3t7Zg1a1bOOYQQrF27Fk8//TSWLl0KAHjhhRfQ0NCAl19+GQ899BBaWlrw6quvGufMmDEDv/jFL/Cd73wHiUQCPl9xbonmz3Rm8hdUkUwR9NCQgEMenHzDaIQQI6xV/ByckW/X4JgHJ3N96nnLB855cC48jFZsojgSjJZ1gx9aEeWEpAyyIcsxoePsrplTHSXxPFi7KItDKyljmwY7A8Xmt5i6CcvyfxS8I7LQiikHR9RN2NJbR5aYSz/nJQ+nt2DwGMRBTFyyDQ7FlUwcL5NlrC+n63Dmml77ZxPLtCJQScIeThIhmc3N9eLpkdc48CIOUe3cuRPBYNBYpABg3rx5CAaD2LFjh+05J06cQDgcxsKFC41jgUAAt9xyC/ccAIhEIqitrS0auQGAhowx6MzTMPeciyFF0pnyxd7YcKSeh/PxJAaH6TYNxZVx4ggN80A8YXTtLbZhDmXIbFeezzqVIujJVDUV3xM2spwwdiuJUvTgjJZ1g9ct1xqCSY+lrn4mB0dWJSSqbuGFdax9XqxdlFXLxAUGyi6UZTc3N9GX46GwXlNGwkbSTTh3brWOx6a5E/nk4PCftbFZq9UDaNUjt0JJXMIvJIrMOF7yd/pc+xwc9V5GF7EHJxwOo76+Pud4fX09wuEw9xwAaGhoMB1vaGjAyZMnbc/p6enBz3/+czz00ENcWWKxGGKxrLGKRqNS+a1ooEYvTw+O0X23OpBTClhoTBhhAi+7lURVkbZpoJg4wo0iqdehmFtJUNBnHY4OgRCi3Azv7EAcyRSBxwOML9JWEhTUy3QulsDQcBIV/tzQhx36BoeNhajYZHYkKKV1Axj52pFTWSMiD76soeBt1AjYkwxA0E3Y6qHgjKNjxSTM3EeFlcdWxkSBugmbdrcWV/+U2+hHRoREfV64euReMyknYTZ9cGRhNLrBqZ2MOVVmQs8Mk+ulmIMjSnrPeo9kG4daw7UlnIOzatUqeDwe4d97770HALaGQcVgWD/nnRONRnHHHXfgqquuwsqVK7nXe+aZZ4yExWAwiClTpqjcqgkNzFt9iol/y+BkOIB6R/qH0kZPFZ0Olg2PdLuGrB4rit59l+ohnkghMjisfB7V44SqQNF/vDUBn7Ho5BPuo2PHFXErCTvYrRvBYBAAEAwGS3LdAEa+dlhDK6K3f9ZQCMMWTJIx+/bP7SZs7Xgs8I6YyIOUFIwgjJbTTVitgsvjsXZRVqjgUs0xYXJ17Mb6cvSolrciquCyz8GRhNsUiKKsD45ZRvb7I/LCEW5oDICp1F/c8dga6uPnCRUaec+wYsUKHD16VPjX0tKCUCiEzs7OnPO7u7tz3rQoQqEQAOS8qXV1deWc09/fj0WLFqG6uhqbNm2C3+/nyvzUU08hEokYfx0dHfneNuqqy+HxZHJq8miu5mTFSm2lz/gins1DRhp2ayhynx7AvEdTPjkuTibGVvjLMG5M+vvUmYeMlOCEgsWX0ePxoK4q/5CkWxVUduvGnj17AAB79uwpyXUDGPnaYQ2tqPXBkZGMjNFLSboJc5Jorde0dlGOiWS08TzYGSg2v8VIJrUpMfZZZaTeI0l4TEgKGIOrmqsj6vOS23dIlDycqQpjSIEwB0cSJiq3CROxx7PXs8/BUU9w5ofH2Fwd++8tQ8LYfbU4oT5rrpcTOTh5+/rr6upQV1cnHdfa2opIJIJ3330XN998MwBg9+7diEQimD9/vu05zc3NCIVC2LJlC6677joAQDwex/bt2/GrX/3KGBeNRnH77bcjEAhg8+bNqKgQG+ZAIIBA4MIWdF+ZF3XVAXT3x9AZHVI2ENnmdM4YvQnV5TgdGcKZczE0ja1UOq8zkjHMDhAcj8eDhtoAOs4OIhwdwpTxY5TOczoxtqG2Ar0Dw+iMDmFWqEbpHEqGGhzqL1NXE8CpyFBe4T76fXSa4NitGzTcM3PmTNTW1gIorXUDGPnaYQ2tqISozPkt4jdwUTdha14Gr0ycXjOWCSeJSUHW65Ei1IiKc3BE4ZKcLsqS0MrgsLWMXs3rIeuDw3oorJ4w1T292GPKeUIJYngypBVhgn21RrLR53CCSWaXVcwpeK3Y747d/Zi6KKfEHsBCo2gzXHnllVi0aBEefPBB7Nq1C7t27cKDDz6IJUuWmCohZs+ejU2bNgFIG7/HH38cv/zlL7Fp0yYcOnQIDzzwAMaMGYP77rsPQPoNbOHChTh//jyef/55RKNRhMNhhMNhJJP571CdDxoyVVDUSKjA6TfmkVTXhA3PgzOGmRKpcERdj04b5nomD0cV9H4aHNLjSJ41G+orRYyWdYNW1gDWslyRMUtJ3v5ZD4VaKIL9r/itniCeEJUEq+Vv2OUJ2ff0MTfR4yXRsscSktCTevhHUcac3JF8r6nojVLMt/KX2TTb82U9R2YZ+TqX5+AwMioknieSRLivljXXS0RSC42iZmu+9NJLePTRR43qhjvvvBPr1q0zjWlvbzc12/rpT3+KwcFB/PCHP0Rvby/mzp2LN998EzU16bfovXv3Yvfu3QCAyy+/3HStEydOYPr06UW7n4aaChxCNK+wRZfDBqWhNoCDX+QXWqFG3IkQFTtPPiX3TntwQpTM5iEjvR/HPDgj2HCz1HvgAKNn3fCXeTGcTJqMmSgEk0ipb4LISxxmz80pUeeFdYwuymqddXml3+ljrBdFoZuwUnKsWn6Lag5OOWOYxZ41nndELQdH3oxQHkZLpNRKuuPJVGYTTYGXKc8cHPWuzGr7agFycl5oFJXgjB8/Hi+++KJwDM3Ip/B4PFi1ahVWrVplO37BggU55ziFkfTC6XLaMGe8B6f7BpXPoSGqBod2lw6NQI+UsDllmLMkrDRzcABGxjw8ioa3ziEyOxKMlnWDJscqh2tY4iKptlIzZClzx2OJZ0Y1T0hEcNjQUzYHR+w5ovOzx+3uR7Z/k8ngGhVKYj3yOgSnj1lLsOU5OKrJw8peFDahXPCsgQxBFuQJmbxHmXG2+rHx4NjvT6Z2zzTXK0XkXrNCo/gUahSBEoC8vCMZ8lDsJn8UjcF03s3pPMI/Ths9SsLCI9Ajvb9iY0QhqqhzydoAo8d8nrWhx9IlOKMF5kRReV+WuGIfHNZAiYwjIdQrJPf2DMu8Gcw4I3dEtFFjHiEYQLbbesaQykJzPnacmqEXkYecLsoqnpSE6ji18BhLwkQhRno/2XwrRSIt0iPzDGUes4RA39b7EXmuCg1NcPJAvr1wUilivNU7ZZhDeRpmQohRzeR4iCoPw3w6kvZIOWWYG2ouIETlkB6bMt+pU32lmyd0KcNUjqxIHlSSOqWhA4ZQDA4nDY9LwCfaJkJWoZQlYcIycbtqK5txPqayRh72srtv1Ryc3HFsWb7Kc8m5pnIjRFXvSO5zYffLUultA5i/Z/IuyoIQlY1+lPOOOKXf5bbfcU1wSgqGB0cxJHDmXAyJFIHX41yIihIAVQ9O78Cw8YVz3POgSB7OxxKIDiVM5xYbdB5Vb10skTRK8533hKnpMWki3JrgFBvmt1aF8uYkW/6t+gbOJ0IAcC7zuwEke0zJKr2Uk2izhjkmMODsuQOxbJK3vEQ93z444tCKiqcnfU1Z0nRubo1dAz/W0Kt4Ztjr2Xm3yrwe0OIv5Uo4Zm7Rs2G9cFKyJgk7mfXD9wAWGprg5AGaKByOqBk9SjLqayoc2VgMyD9sQcdNqCp3rPFbyNIpWAZqwKsDPtRUiPuWFAqU7HWfixldREWgXrBynxdjxzgjIyUpZ8/HlRo79jCEu9h7ZWkwiaKyahQva3Dzq7ayM3psZ2O6vQl3blsSJvGOKOUTsUZUHFo5H8/KKEukVc3BoXPbdfg26VG4mWRWD0OMJ0yagyMkD0z+T+Y3G/CLSK/Yi5Ku1sslGrKkadpk1X5uJtRHCbcoL0vSdyh9POs9ig3z9VNoaIKTB6jR6zkfMxYDESjBaRzr3NsyJTjnYgn0D8m78DodVgGy+UjxRAp9A3IZ3cgbmVBVDq/HvFmqCFk9BoreaZkiWOlHZWYBVyG0bhDuSxl0sY9JCIl97xh+iEHmHfF4PIbxoQTHX+ax3SrGLjwmbrZHssZRUh2lklcDpPeZsztO4fPahGsk/VuyRlRN33akhe2ifJ7xMokSc+My/TDNCGMK+jaFkyThn8HhpPEyJiKV0uThzLhEimQJoCDMKOt4bLofCbkqNPQqlwcmVJXD5/WAELX2+E7njQDAmHIfgpVpD4KK0XO6Bw6QXpTpXk0q4ZVTmYowJ2X0lXmNii2VMJXTTf6A9AKcT0iSjnFSj5cyAhnyaU4oFRm9LMmw9Tz41EhGep608aEhKp7hse15UiYOWxjkwe7t3+RF4XtH2C7K/VRGX26zPfZ89poVklCWaG6qM1k+EXv8POMJs5ub7VFkkE+ZfoZFIcFcMssjONZnnb5HifdIoWt1LJFUIuZmj5C9V4Z+z4biTE6Yzfes0NAEJw94vR7D06FiUJyu/KHIx+gZSacOlw035JEM7VblT14yUg+OwzJm83DkbQHCLhDuSxkBw1Co5bfEk0khcSk3GRS+EQWyZIh6cHiGh54fSySZRFEbLwqTqyPyHrH5LTIvEz3eLyFhrDdjyCBXotCTOMeEHpM9l/Q10/cTzXjDy7weaWm1UD+KeTCsjLKyaiqPajhyOEGEYSLjezss2U7C7rlw9Zg+3s/IqD04JYhJme0PvlDoM3PKJcOcTx4OG1pxErSRnkol1WnDy+QsUQwZZFadPDjdXyaftgC0jF17cJwB9cLEEkkjHGFneCr8WYMyJDA8dm//vDwGv8Xo8QwPa8xUkl7jkvCGKZQlyDFhj7MeHDtk5xbn9diTDJG+k1KCQ59hdFCsRxOxG1YI4Un0GLDxopRznjXVD01JkIcjU0IizZIr1f3JpB5FX66XiUdoCwlNcPLEpHEZgtObzxtz6XpwKAlrcpo80BLnvDxhzhrmyePS+2R9rvCsKeGdpLj/V6FgPGuFUnHtwXEWdLEfGha/hZsNiiD5k03UlBgUIwdHQh7sPQU2Rs+ffVtXysFhEl55MlZk5j4Xyxpm23EMIRHPbUMybPQY8OfeM8/Y0vOjg8PCe2FzcIz7FjxDaRjN8KyxlUz2+qEyZUkYhwixfZkE3qMKO6+ejX7ouESKGJVwPE+hlXCXl3lztp0oBjTByRPUgH3eOyAdS/uTOP3GHKpNy6gStqD3MXmcs4aZzqeix9OuERx1MktJkNN6DI0oB8dZGS9VUMMzEE+ACPIOqKEYGk4qJcfKKpSArDGTenCYuUUeBUpGhoaTTHhM7GWShS1UPTh2HgW7ue364AhDMAkxyQCy9x0xCI7YgMu8a2avh4hkpI8Rks3/4eqHepmGZCRMLQcnYDxrcQiPlVs+t9r3sdAo6lYNoxGGB0cSokq52HOEzidrAEcIMYw39VY4BYPgnJWTBxoicpooTsqDhFE9TnKY4DSNVc/Bod/ZJu3BcQTUANC3f0BsKKQG3M44ct+YafWP+K2eHh9gkj9FHpyhYbFnhu2iPBCn3hbe3BnPgyQHhxLAwbha0ms8SeATkCv2mCwJ2/DgZAx4BS/nyS7JWFhaTZRCVECWAPISoalMEUUvkyyEZx8eE8som9ta1edE/g2gPTh5Q/WtvjvTc6TM63GsyR8FLUs/JSFh3ediiCVS8HqcJw9TxtPwj5g89A8NG6XkrpEwybMeiCfQk2ny57SM1FsnC1ElkinDg0N1r1FcGB6KmLgMOhvKShr9jGSbcorGsWP7ZW//PrMXhTc2S8IkYSImQZmGnvj5PzTJmIao1DwUgKTKTOKZYQkX1Y9dYjU7VubBoeEjNqQkLBOXhKjKy7xGAz9ZEjadx5BREiYaThBhKJQNj4k6Hnu92XYEdG6755KeW62qr9DQBCdPsEnGoiZ1n51NG+6msc73HJmaMWCfnR0QykhJWqi2wrEmfxSUPISjQ8Zbgh06Mh6e8VXlqA4463CkZKXnfNzUq8MKSiRrAtkSfadAPUYyGU9HhpBMEZT7vLrJn0Owkgevx76HSoXfxoMjKPMF5K5+IyQwJB5H5+4bjOccM4/LenBEIRiWpNDeMfy5rbkjvDCROQ+GN9a+T5D9uFzyYG+Yc7wjEg/OeVOVkKTcXiBjusosfZw+Gx55yCZCq3lR0rk1tF+OoIJrWBzKAvLPUZJV9RUamuDkiaYMwRmIJ4VN6j7rSROcqS68LTeNrYTXk14wRf16PncpPAWkO+kGfF6kiLhKqSPj4ZnicOgHSDfSq8mQKpE3rMOl8BSQlpF2Tqak2g4dZ7O5Vk4k92nkvv3zDBTrwVFJ4AVY4iKurDmvWEUVyaxl5WVe2wocKvtQgs3Byb0m20VZNbdGqh+/eZzXY56HwraMnluibvU8qMnIrxLK9dbJSFhcEmY05s48m8pyDsFRlZF6USRbYxhkNpH1KFZKyJU0R8lC9p3KwdEEJ09U+MtQl3kDFuXhUGPjBsHxl3kNItYhCAF97qJh9ng8SiEgapjdCqtQ3XQIZPzCpQRjCsNj1yMgOAZR1OEpp2B9+5cZiTjjwbEzuKxb30jq5PbBSRszWYgq68ERX89cTs4nYWwX5f4hsdHLkoy0h4JnwHNCML4y24aAbL8cWbdcq2HmPxurh0JMKKPKJEy8FxU7N302dg0Ggew9qpMMsSeM9eAMZgiOjJzLPFzZHBwxCSs0NMEZAVSST902zNSQid7q3aqgoqCeow4Fz4NbelQpFTeIosMl4hRTxsufNQ31uUG4L1VQQ9E3IA4xmKp6BOEfr5cJWwwohgQknp7s9TIkQ0LCYqwHR1KObLytS/rg0HtR9hJISItsawz2uHHfXHJF838SmTnsr0fPLyQJy/n+qHpwJCTDFDK1IWFskvFg3h4c1XCkDlGVLCgh6BBUALnpwWHn/aynlA2z3IND9eiW50GlnN1tEjZNgeAYehyvS8SdgpWM8IyjEf4ZTmJIYvSshlSWPCwzPNm3f2rAxYbMnIOj5h2R9cHpUwzhRSS5OmPKsxVhMhKWJQ/ixNzcCiX7cZV+xeeiWJbPHjeeDWdugzxIwj+qJIzqIkWyBFn92fD0kw71U7LmVBWVLhMfAZonVAEAjp85zx3jOsGZIDd6n/ak5Z9eV+WITFZkvSOi0Iq7ngdKcEThH/o9aHZJj1NVPDg6ROU4ApYQgywE0x9j+uUIDGkfhtFLDQVn3Jhys0GR93mReXCyhjmVEZJnpCjRkM1tkKsBMcExkmglIS86bnA4CQL+ppPs8T5JiEo1B4fOnX0uHN1kDH0iRZQTwGUhPNU8GOXnwhzvk+X/KPbgqSw369upKipNcEaAyyZmCE73OdvPB+NJdGWSe90yKNSbwMvBiSWShufhMpcN86cc8pBKEcY74o7nYUZ9NQDgeLc9mSWE4FO3CQ4ls6IcHJe9TJciqKGhb+oqOTjZc8Vv4bImenTc+bi4kR0lGbSqRpZsm0iRnGM5c/vNc8u8KLSsWlU/Mg8OINcP25lZNLd1nIzUDQk2IgXMRMF4NpwKLiq7/NlYZJQQpuxzkRMc+bNR1U+aahi9kXQfnNLFZRPTRu8Ex4ND36RrAj6jwsVp0LAFT8aOswNIEaA64DN2zXYaMzJ6/KTrnG05++noEGKJFHxej5E07TRm1GWfdTKVK2NnNIbB4STKvB7XyMNUhszaydg3EMeZc+m3NrdI2KUIqwGRufllx4BcQ8N9W7eMk3koZDLaGVcZuZKNsx6nb/mycbIcHBayCi753Gr6zr1nfn6SNe+lgje35T75JMwyt4RkyMZ5PJ4cvfG/u2r3bT1f98EpYVAj0dUfM2WkU3zclfbszKivto1xOgHqeejujxkuSRbUI9FcV+WajNPrxsDrSbvmu2zK2Y919mfGVXGbgBUbk8ZVotznRTyZsg2lUQI5ZVylazI2BisR8HkxnCS2Mn6S8TQ2BStQ5XAvoUsZ1kVd5qGgCPi83N9kDsGReBR4/5+d20oy1AwZwDdS1rm417TcCz/HRM2IlnlzDTM/tKJmwK3juJ4Zm2fIg1UmK/Ew5lYmn4qk1zqvn78WWCu2+PljFv0oEvNKzj0XGprgjADBSj/qqssB2HtIjnWlDfMVGZLhBqoDPiN5+FhXbijN7bwRIP1DnJ7JZ/rYRkZ6zE09lnk9RgjPLkx1ogT0WOb1GN6wjzr5epzhoh4vReR6KNQ8OKKmm7nGkWP0ckiGvUHJ8eAIyAPbaLDSX8btp2SVqYo798j0wzO21rl9TKfd3GuOzMMV4FzPKjvvnu3mkoXHKFQ9gDw9WucZE+BXMuWQzwv0AOZ+J3QVVUnjsjp+mIoSiisa3DUol9dTo9ef8xnNH3I7ZEGN7jEbGann4XKXDbMRSrPJuaLkobnOXRlnNvCf9ScZYkbvQ8MZVFeYjRzPkHkthjgf48gbaw1RXagHBzCTnyqBcbQaOd7c1ntR9VCo6qey3L5KCEBOV3RVT88Yjgc0H/LA6iPgs2+sCOSSTVUPII88qJJj61z+Mo90Hyxjbs59q34nCg1NcEYImmhs63nopJ6HGkdlsoIavWM2b/UfhtOGcFbIXRkpeflYQB7cJzjpZ21HcI6ejgIAZje6q8crGtLz2xFF7cFxBzUWY8gz4IDZ+IjIQ46R4oy1hj14BsUashR5R9i3el5YxW4uHnmwkgyefnJInSDMys4lMqJW8snzXOV4HhQJjpCEMZ+JZMx9NookjEd6rc9FEKJi5+bpxk4mLuFW9CgWGprgjBBXNtYCAA6fipqOJ5IpHD9TGoaZEiwaMqMYTqYMgnN1U63jcrG4PONVsBJFQogRbnHb80CJwdHTZj0SQnAkQ3CuanRXj1fU80NU7WH3Q6aXIlQNFGA29kIDnvMmzDG4OcaMQ3DK85FRjTzkkit7Ga33yZUxYL1nNc+DiGSoenCs11D1jog8YWNMJExAFAOKz9ByL1wvik9dj+yz5jUYTI9TmzsnhCcg8YWEJjgjRMuktEE7+EXEdPyjznMYThJTDoxboCGy9rC5Sul493nEEylUB3yu90Whno/Dp6JIMRVAn/cOIjI4DH+Zx/VQ3zWTxwJIe2vo7rpAegPLyOAwfF73ZaSeuI+7z5nKjc+ejxtbilzlMpm91KAaogLMC7747V/N6OUmGfNIhlqYCDDfj5BkKIZCcgw4p5rIqkcRAWTnEpEMVe9RrgHn5xOx0TBRjomyjDnk014/Vk8h71l7vR7T90WVpIq+t1b9cAm3Yt5RoVFUgtPb24tly5YhGAwiGAxi2bJl6OvrE55DCMGqVavQ1NSEyspKLFiwAIcPH+aOXbx4MTweD1577bXC34AAVzbWwutJVyl1RYeM4wc+7wMAzJkUdH1Tw9mhWvi8Hpw5FzPtm3XkdJqUXdlY47qMsxpqUOH3on8oYWqceODztIyzQ7WOtfXmYdr4Maip8CGWSJnCfTQ8NWNitesyTh0/BmPH+BFPpAyvEgAcyhDw5roq1Fa407IgX4yWdSPXO8Jfbs0eHDUPRaW/jJu/ketRsJ/bKqM1d4cvo5qXyevhV9aokoyAr8yU4CwyzBUj9ODwnk0OueJc0+OxkAdF/eQTouKG+nIIoBr5FHmPWP2IibmafnI9OKMgRHXfffdh//79aGtrQ1tbG/bv349ly5YJz3n22WexZs0arFu3Dnv27EEoFMJtt92G/v7c3IK1a9e6VuI8ptxnhE5YL84HGcN87ZSxbohlQmV5mfHWvvdkr3Gckge3wyoA4CvzYs6kIABgf0efcfzAF+l/z5kcdEEqM7xejyHjwYxcQFbeqye5r0ePx4PrMt+5fZ9lnzX9brZMcl+Pqhgt60aZ12N6k68REEx2wRcZnpG8gVuvz8Lr9ZiuExT07aoOZD8Tz202ojxdW68hIuCswbWSE941hd4RhhSU+7zcFxSr3kTJw6ZnIyAFrIyqJKzM6+Het6oXJUdGxWdYW8m/Xk2Fmn5U87IKjaIRnKNHj6KtrQ1/+MMf0NraitbWVqxfvx5//etf0d7ebnsOIQRr167F008/jaVLl6KlpQUvvPACBgYG8PLLL5vGfvDBB1izZg3++Mc/FusWpKAkZs+nWYPyfoZIXFsChhkAbpg2DgCw77M+49ju42cBADdOH++GSDn4UkaP+zuyetxzIi3jlzLhIbdBw1QmPWZkvLlE9Hj91PSzfp+RcdfxHgAwyE+pY7StG6whFTX9VPWOsATE+ubOwmpQxo0p545l5wtW8mVkjZnIMKtez2qYRWPZa4pDT9lr1Iruhbne2DxkFJErVn7Rs2ETbMdVqd1zbQWfKNYEzNdQJU2i76PqM2TnKi/zcqutrHpzyptcNIKzc+dOBINBzJ071zg2b948BINB7Nixw/acEydOIBwOY+HChcaxQCCAW265xXTOwMAA7r33Xqxbtw6hUEgqSywWQzQaNf0VAl++fAIA4F8fnwEAdEaH0N7ZD48HmHfZhILMcaGgBIca476BOI6G0/dfKjJSw7zjk7Qxjg4NG56wL19R55pcLOZdliYx//ioG4QQDA0nDQ/Ozc2lQXCuy+jx3RM9SKUI4okU9nyafu5fvrw09ChDKa0bwIWvHdWKhtRkzARvzCxRGV/FJy1W4yUkLqa51Yz9OMHcrIwiA271aIm9R8zcArI2nplvvOh6isTTSjZFhpnViejZjGPmC1byx7EyismfhcwKdM5+Nlagx1rT3Goyygg8G2YU6aeQKBrBCYfDqK+vzzleX1+PcDjMPQcAGhoaTMcbGhpM5/z4xz/G/PnzcddddynJ8swzzxjx/GAwiClTpqjehhBfnpE2GodORdDdH8P2j7oBANdMCgoXACfRetkEeD3pfJGOswPY/lE3CElX1Li1RYMVX7miDv4yD453n8cn3eew4+MzSKYILqurcj1Rm2LeZRMQ8HlxKjKEY13n8K+PzyCeSCFUW+F6LyGKG6ePQ1V5GTqjMRz4IoI9n57F0HAKddXlRsuAUkcprRvAha8d1YxBFBnwCdXZ9WJiNf93aSI4IkNv+UyUPFzHzCcy4CzxYuW1gv1MREashM+aVMuCvc4Ewdo6vip7L6I12Ew8Bd4ti7dIdN8scREZ8AmMvkWkoI6ZS0Q8fRavyYQq/veH/WycYG7WNojIlem5CL63Ho85xCb67hYSeROcVatWwePxCP/ee+89ALB1qRFCpPFv6+fsOZs3b8bbb7+NtWvXKsv81FNPIRKJGH8dHR3K54pQX1uBL00ZC0KAV9//HK/t+wIA8PXZuQu0W5hQHTA8NZs/OIVNGRkXtai9wTqBmgq/IeNfPjiFje+nZfxvV5aOHiv8ZZg/Iy3jpn1fmPToVh6YFRX+MizIfPdYPd52lfsy2q0bwWA6jBsMBkty3QAufO1gjYPojbmhpsL4t+jFg30DFxlRq9ETYWKtmjFrDGZfNuoERpSVS3TP1gIHUcFDYzCrnzqBfsYr6oclDCLyYP1OibZjUfWuscRF5NWrZ74TorATYN42QxTCU302qgQnxDwXazWXFawurbk7xULes6xYsQL33HOPcMz06dNx4MABdHZ25nzW3d2d86ZFQd3G4XAYjY2NxvGuri7jnLfffhuffPIJxo4dazr329/+Nr761a9i27ZtOdcNBAIIBIrjrbjv5qnY39GH1X//EEC6auDfbyyMh6hQ+O/XTcKOT3rwH2+kcxg8nvSxUsK/3zgF7xw7g7VvHTMdKyXcfdMUbG3vxv/d9olx7N9umOyiRLn4t+sn4/UDp/H8P09kj5WAjHbrxrlz53DTTTdhz549qK6uLrl1A7jwtYN19Ys8D6yhqBO8CbNv4KKk5XzAJsQ21PLnbhqblVHooWA+qy5QvxPWGIvJVYD5N19Gtj1Gymaj35GAJQKqXhTxs87K7ysTk3t/mQeZjbqFYL02dQJvFEtw6gXfCfb7HUuIBWA3AnaqejdvD05dXR1mz54t/KuoqEBraysikQjeffdd49zdu3cjEolg/vz5ttdubm5GKBTCli1bjGPxeBzbt283znnyySdx4MAB7N+/3/gDgN/85jfYsGFDvrdzwbjzS01Gp1sAWDZvWsmEVSi+dd0kU4jif9wwxdgRwpqEhgAAC/1JREFUvVTwjZaQ0VsIAJZeNwkzG9ztDmzFbVeFcN3Uscb/f2NOqOSqkxbMmmhKer7tqgYjD8tN2K0bM2fOBADMnDlz1K4bNzHPQhQmonuyAeLtU1gCMlvShfz2q9PkjuYK8tDMrF8i0nQZsx2JqO9TsNJvkItZkt8wle165ndlhynj02tqwOcV5iixOhHpp9znNQjJlZIu5FTGm6aLf0e0IeiY8jLUC7xMbANYUQd0lgTQ/Doebpk1EQDwVUnO4uXM85gs6IHGfh9F67DHk92jTBa5+Mac9MvHHCfXTFJELFq0iFxzzTVk586dZOfOnWTOnDlkyZIlpjGzZs0iGzduNP5/9erVJBgMko0bN5KDBw+Se++9lzQ2NpJoNMqdBwDZtGmTslyRSIQAIJFIJO97skPH2fPk6U0HyH++9REZGk4U5JqFRmdkkPyv1w6SNW+2k8F4icoYHSQr/+sQ+Y+2D8lArDRl7IoOkZX/dYj86u9HybmhYbfFsUXv+Rj5P385TJ7521ESHYy7LQ4XvN9hqa4bIpl5OB8bJqs2HyJ7T56Vjn3+nePkxV2fSse981E3+d3Wj8lwIikcd6yzn/z8L4fJqb4B4bjBeIL84vUj5J/HuqVzv/LuSfLCjhPScdvau8hvtrSTuETGz3rOk/+58QDpOHteKuNzb3xItn7YKZ371b0d5KVdJ6Xj/nWsm/zq70ela83pvvTa+XFXv1TG32/7WEmPL+8+Sf70rxPSce+e6CH/e/Nh6VrTGR0kv3z9CPnwNP/7Tggh8USSPPdmu5KM/2/PZ+T32z4mqVRKOO5ARx9ZtfkQiUjWmq7oEHnuzXbSHhbLKEM+v8GiEpyenh5y//33k5qaGlJTU0Puv/9+0tvbaxYAIBs2bDD+P5VKkZUrV5JQKEQCgQD52te+Rg4ePCicx22Co6GhkT94v8NSXTdEMmtoaDiDfH6DHkIKFIC8iBCNRhEMBhGJRFBb636TNg2NSxEX4+/wYpRZQ2M0IZ/foN6LSkNDQ0NDQ2PUQRMcDQ0NDQ0NjVEHTXA0NDQ0NDQ0Rh2c6bZTYqBpR4XaskFDQyN/0N/fxZQGqNcODQ13kc+6cUkSHLrDcKG2bNDQ0Bg5+vv7ja7GpQ69dmholAZU1o1LsooqlUrh1KlTqKmpkbZ/j0ajmDJlCjo6Oi6aqgktszPQMl8YCCHo7+9HU1MTvN6LI1quunaUkp5VcTHKDFyccmuZR4581o1L0oPj9XoxeXJ+7etra2svmi8ihZbZGWiZR46LxXNDke/aUSp6zgcXo8zAxSm3lnlkUF03Lo7XJg0NDQ0NDQ2NPKAJjoaGhoaGhsaogyY4EgQCAaxcubJou5EXA1pmZ6Bl1uDhYtTzxSgzcHHKrWV2BpdkkrGGhoaGhobG6Ib24GhoaGhoaGiMOmiCo6GhoaGhoTHqoAmOhoaGhoaGxqiDJjgaGhoaGhoaow6a4Ajwu9/9Ds3NzaioqMANN9yAd955xzVZnnnmGdx0002oqalBfX09vvWtb6G9vd005oEHHoDH4zH9zZs3zzQmFovhkUceQV1dHaqqqnDnnXfi888/L4rMq1atypEnFAoZnxNCsGrVKjQ1NaGyshILFizA4cOHXZMXAKZPn54js8fjwY9+9CMApaHjf/zjH/jmN7+JpqYmeDwevPbaa6bPC6XX3t5eLFu2DMFgEMFgEMuWLUNfX1/B7mM0o1TWDr1uOLNuAHrtYFEyawfRsMUrr7xC/H4/Wb9+PTly5Ah57LHHSFVVFTl58qQr8tx+++1kw4YN5NChQ2T//v3kjjvuIFOnTiXnzp0zxixfvpwsWrSInD592vjr6ekxXefhhx8mkyZNIlu2bCHvv/8++frXv06uvfZakkgkCi7zypUrydVXX22Sp6ury/h89erVpKamhrz66qvk4MGD5O677yaNjY0kGo26Ii8hhHR1dZnk3bJlCwFAtm7dSggpDR3/7W9/I08//TR59dVXCQCyadMm0+eF0uuiRYtIS0sL2bFjB9mxYwdpaWkhS5YsKcg9jGaU0tqh1w1n1g1C9NpRimuHJjgc3HzzzeThhx82HZs9ezZ58sknXZLIjK6uLgKAbN++3Ti2fPlyctddd3HP6evrI36/n7zyyivGsS+++IJ4vV7S1tZWcBlXrlxJrr32WtvPUqkUCYVCZPXq1caxoaEhEgwGye9//3tX5LXDY489RmbMmEFSqRQhpPR0bF2kCqXXI0eOEABk165dxpidO3cSAOTDDz8s+H2MJpTy2qHXDWfWDUL02lEKa4cOUdkgHo9j7969WLhwoen4woULsWPHDpekMiMSiQAAxo8fbzq+bds21NfXY+bMmXjwwQfR1dVlfLZ3714MDw+b7qupqQktLS1Fu69jx46hqakJzc3NuOeee3D8+HEAwIkTJxAOh02yBAIB3HLLLYYsbsjLIh6P48UXX8R3v/td08aKpaZjFoXS686dOxEMBjF37lxjzLx58xAMBkvmN1CKKPW1Q68bzjwDvXaUxtqhCY4Nzpw5g2QyiYaGBtPxhoYGhMNhl6TKghCCn/zkJ/jKV76ClpYW4/jixYvx0ksv4e2338Zzzz2HPXv24NZbb0UsFgMAhMNhlJeXY9y4cabrFeu+5s6diz//+c944403sH79eoTDYcyfPx89PT3GfCIdOy2vFa+99hr6+vrwwAMPGMdKTcdWFEqv4XAY9fX1Odevr68vid9AqaKU1w69bjj3DPTaURprxyW5m7gqWOYNpBcI6zE3sGLFChw4cAD//Oc/Tcfvvvtu498tLS248cYbMW3aNLz++utYunQp93rFuq/Fixcb/54zZw5aW1sxY8YMvPDCC0Zy3Uh07NRzeP7557F48WI0NTUZx0pNxzwUQq9240vlN1DqKMW1Q68bzj0DvXaUxtqhPTg2qKurQ1lZWQ7b7OrqymG3TuORRx7B5s2bsXXrVkyePFk4trGxEdOmTcOxY8cAAKFQCPF4HL29vaZxTt1XVVUV5syZg2PHjhlVESIduynvyZMn8dZbb+H73/++cFyp6bhQeg2FQujs7My5fnd3t+u/gVJGqa4det1wTl69dpTO2qEJjg3Ky8txww03YMuWLabjW7Zswfz5812RiRCCFStWYOPGjXj77bfR3NwsPaenpwcdHR1obGwEANxwww3w+/2m+zp9+jQOHTrkyH3FYjEcPXoUjY2NaG5uRigUMskSj8exfft2QxY35d2wYQPq6+txxx13CMeVmo4LpdfW1lZEIhG8++67xpjdu3cjEom49hu4GFBqa4deN5yXV68dJbR2OJrSfBGBlno+//zz5MiRI+Txxx8nVVVV5NNPP3VFnh/84AckGAySbdu2mcoMBwYGCCGE9Pf3kyeeeILs2LGDnDhxgmzdupW0traSSZMm5ZT4TZ48mbz11lvk/fffJ7feemvRyiefeOIJsm3bNnL8+HGya9cusmTJElJTU2PocPXq1SQYDJKNGzeSgwcPknvvvde2JNEpeSmSySSZOnUq+dnPfmY6Xio67u/vJ/v27SP79u0jAMiaNWvIvn37jDLkQul10aJF5JprriE7d+4kO3fuJHPmzNFl4goopbVDrxvOrRuE6LWDolTWDk1wBPjtb39Lpk2bRsrLy8n1119vKq10GgBs/zZs2EAIIWRgYIAsXLiQTJw4kfj9fjJ16lSyfPly8tlnn5muMzg4SFasWEHGjx9PKisryZIlS3LGFAq0h4Lf7ydNTU1k6dKl5PDhw8bnqVSKrFy5koRCIRIIBMjXvvY1cvDgQdfkpXjjjTcIANLe3m46Xio63rp1q+13Yfny5YSQwum1p6eH3H///aSmpobU1NSQ+++/n/T29hbsPkYzSmXt0OuGc+sGIXrtoCiVtcNDCCFOeYs0NDQ0NDQ0NJyAzsHR0NDQ0NDQGHXQBEdDQ0NDQ0Nj1EETHA0NDQ0NDY1RB01wNDQ0NDQ0NEYdNMHR0NDQ0NDQGHXQBEdDQ0NDQ0Nj1EETHA0NDQ0NDY1RB01wNDQ0NDQ0NEYdNMHR0NDQ0NDQGHXQBEdDQ0NDQ0Nj1EETHA0NDQ0NDY1RB01wNDQ0NDQ0NEYd/j8rk9S8X5rtIgAAAABJRU5ErkJggg==", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, axs = plt.subplots(2, 2)\n", "axs[0,0].plot(t, c5)\n", "axs[0,1].plot(t, c20)\n", "axs[1,0].plot(t, s5)\n", "axs[1,1].plot(t, s20)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's verify that they are indeed orthonormal. That is, we want to show that $ = I(i =j)$. We also show that they are all mean 0." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 228 }, "id": "TYnpYvOYNJ2a", "outputId": "4be183bb-0982-434a-96a6-0090c03dc4ca" }, "outputs": [ { "data": { "text/plain": [ "array([-0., 0., 0., -0., 1., 1., 1., 1., 0., 0., -0., -0.])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## Verify that they are orthonormal mean 0, round to 6 decimal places\n", "np.around( [\n", " np.sum(c5),\n", " np.sum(c20),\n", " np.sum(s5),\n", " np.sum(s20),\n", " np.sum(c5 * c5),\n", " np.sum(c20 * c20),\n", " np.sum(s5 * s5),\n", " np.sum(s20 * s20),\n", " np.sum(c5 * s5),\n", " np.sum(c5 * s20),\n", " np.sum(c5 * c20),\n", " np.sum(s5 * s20),\n", "], 6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take the FFT, the fast (discrete) Fourier transform th way one would normally do it. First, we use FFT in numpy. Then, there's a convenient method, `fftfreq`, which gives the associated frequencies with each element of the transform. Finally, we plot the spectral density, which is the sum of the real and complex Fourier coefficients. Sorting the elements first is necessary to connect the dots on the plot. Interestingly, once we remove the trend from the Italy data, there's some very noticeable spikes in the spectral density, which implies large coefficients on that specific frequency. This is possibly some reporting issue." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 294 }, "id": "ukCCrBakax2O", "outputId": "50f08370-19ee-4bf1-b39c-b66bd7d6aeed" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "f = np.fft.fft(e)\n", "w = np.fft.fftfreq(n)\n", "ind = w.argsort()\n", "f = f[ind] \n", "w = w[ind]\n", "plt.plot(w, f.real**2 + f.imag**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's manually find the coefficients using our constructed bases and the formula that the coefficients." ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 87 }, "id": "W0RDy2kcjGxw", "outputId": "5003fd1e-9a2b-4ca2-ff60-a99bc170b8c1" }, "outputs": [ { "data": { "text/plain": [ "[-42402.16539776623, -961069.7936856844, 62406.76098672958, 1902286.8621751775]" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[\n", " np.sum(c5 * e) * np.sqrt(n / 2),\n", " np.sum(c20 * e) * np.sqrt(n / 2),\n", " np.sum(s5 * e) * np.sqrt(n / 2),\n", " np.sum(s20 * e) * np.sqrt(n / 2),\n", "] " ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "id": "9VffVgrkJTaG", "outputId": "2bc28175-c9e0-4e18-d8df-6ee49cd561a1" }, "outputs": [ { "data": { "text/plain": [ "array([ 1222376.2412703 , -1286448.11961955, -4881386.48874237,\n", " 1827887.03044428])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sreg = linear_model.LinearRegression()\n", "x=np.c_[c5, c20, s5, s20]\n", "fit = sreg.fit(x, y)\n", "fit.coef_ * np.sqrt(n/2)\n" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "id": "XxYhZB_dNeJ_", "outputId": "7962bf96-2a0d-4756-ee70-eb7e52da7344" }, "outputs": [ { "data": { "text/plain": [ "array([ 1222376.2412703 , -4881386.48874237])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x=np.c_[c5, s5]\n", "fit = sreg.fit(x, y)\n", "fit.coef_ * np.sqrt(n/2)\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 87 }, "id": "XlLctyHMii7w", "outputId": "38efc131-3ecb-4252-b07c-0708ec8253d6" }, "outputs": [ { "data": { "text/plain": [ "[(array([], dtype=int64),),\n", " array([], dtype=float64),\n", " array([], dtype=float64),\n", " 0.004409171075837742]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "test = np.where( np.abs(f.real / np.sum(c5 * y) / np.sqrt(n / 2) - 1) < 1e-5) \n", "[test, f.real[test], w[test], 5 / n]" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 34 }, "id": "U5jQSTNVXfV9", "outputId": "562ddc9b-1a9d-4174-c56c-75ed01e5afb3" }, "outputs": [ { "data": { "text/plain": [ "array([], dtype=float64)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "f.imag[test]" ] } ], "metadata": { "colab": { "authorship_tag": "ABX9TyMfyrVnh6T8IJsageU7I0ur", "collapsed_sections": [], "include_colab_link": true, "name": "LinearModels and FFTs", "provenance": [] }, "interpreter": { "hash": "625a8f875bfb3f569e4f618df17e1f8389970b6b26ee2c84acb92c5fbebf95c3" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }