{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# ECE 417\n", "### Fall 2018, Lecture 12: Hidden Markov Models\n", "Mark Hasegawa-Johnson,\n", "October 4, 2018,\n", "Distributed under a CC-BY license\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is an ipynb notebook, so the first thing I want to do is to load some libraries." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import requests\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now I'm going to download some data that I put on the course web page. These are temperature records (monthly high temperature, and monthly log temperature, in Fahrenheit) from two cities in the state of Illinois: Waukegan (in the far northeast corner), and Carbondale (in the far southern point of the state). The data originally came from here: https://www.isws.illinois.edu/data/climatedb/. I have extracted CSV files, which you might want to look at, for example, to see the dates over which they are collected: http://courses.engr.illinois.edu/ece417/fa2018/ps/carbondale_climate_edited.txt and http://courses.engr.illinois.edu/ece417/fa2018/ps/waukegan_climate_edited.txt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[['YearÂ\\xa0', 'MonthÂ\\xa0', 'High', 'LowÂ'], ['2005', 'Jan.', '45.6', '31'], ['2005', 'Feb.', '50.3', '33.1']]\n", "[['YearÂ\\xa0', 'MonthÂ\\xa0', 'High', 'LowÂ'], ['1923', 'Jan.', '35.1', '20.3'], ['1923', 'Feb.', '29.5', '10.8']]\n" ] } ], "source": [ "URLformat = 'http://courses.engr.illinois.edu/ece417/fa2018/ps/%s_climate_edited.txt'\n", "cities = ['carbondale','waukegan']\n", "rawdata = {}\n", "for city in [0,1]:\n", " r = requests.get(URLformat % cities[city])\n", " rawdata[city] = [ x.rstrip().split(',') for x in r.text.split('\\n') ]\n", " print(rawdata[city][0:3])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's separate it into training data and testing data. Actually, this time, we won't use the training data at all, we'll use that next time. But we can look at some plots of the data, to see what type of data we have." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "months = ['Jan.','Feb.','Mar.','Apr.','May','Jun.','Jul.','Aug.','Sep.','Oct.','Nov.','Dec.']\n", "train = [ np.zeros((0,2)), np.zeros((0,2)) ] # train[y] is a 0x2 matrix\n", "test = [ np.zeros((0,2)), np.zeros((0,2)) ] # test[y] is a 0x2 matrix\n", "\n", "for city in [0,1]:\n", " for a in rawdata[city]:\n", " if a[1] in months and a[2][0].isdigit() and float(a[2])>-99: # row gives one month, with temperature > -99\n", " if len(test[city]) < 12: # first twelve valid lines (first year's data) are the test data\n", " test[city] = np.vstack((test[city],[float(a[2]),float(a[3])]))\n", " elif len(train[city]) < 72: # next six years as training data\n", " train[city] = np.vstack((train[city],[float(a[2]),float(a[3])]))\n", " \n", "fig, axs = plt.subplots(2,2,figsize=(15,5))\n", "for city in [0,1]: \n", " axs[city,0].plot(train[city])\n", " axs[city,0].set_title('Train Data for %s'%cities[city])\n", " axs[city,1].plot(test[city])\n", " axs[city,1].set_title('Test Data for %s'%cities[city])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obviously, in any given season, Carbondale is warmer than Waukegan. Obviously, though, the two distributions overlap. If we have temperature measurements for a \"mystery city\" and want to know which city it is, then we need to know not just the average temperature --- we need to know the average temperature for each season. Suppose somebody gives us those averages, as follows:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "all_means = np.array([[[48,28],[78,56],[87,63],[58,35]],[[36,19],[65,43],[77,57],[46,29]]])\n", "fig, axs = plt.subplots(1,2,figsize=(15,5))\n", "for city in [0,1]:\n", " axs[city].scatter(all_means[city,:,0],all_means[city,:,1])\n", " axs[city].set_title('Seasonal Low vs High Temp, Averages for %s' % cities[city])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So that's not quite enough. It will be more useful if somebody gives us the covariances. Here they are." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "all_covariances = np.array([[[[1323,1093],[1093,956]],\n", " [[1111,1182],[1182,1319]],\n", " [[475,436],[436,523]],\n", " [[120,76],[76,55]]],\n", " [[[959,963],[963,1110]],\n", " [[1339,1089],[1089,948]],\n", " [[422,273],[273,280]],\n", " [[146,130],[130,119]]]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The only useful way to plot covariances is by plotting the principal components." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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AvwDcLWQRrOIoztBHG+BFwBtIArYBPQpoqhZ0vqqqa4A1AC1btiywjRBCVHfatDSi3p9I2qFDWA8ciNPUKYVuYh0Xfofdi+eQHBtD59eG06z7CzIfTQghngAGxsa89FEA38+bwd5lH6NoNPi0aVdp9cRHpXF4UyhR15Jw9LKk1yhfHDwsinWuVqdl01+bWHZuGRpFQ0DbAPrW6Sv9WQkUZ+jjs8AtVVXvASiK8j3gB1griqL/91c1NyCq/MoUQojHV87t24SPHEXOnTs4BfhjM3hwoW1Djh/ll8+WYmBsTP/pc3Cr36gCKxVCCFHZDI1NeHlSADvmBrD304Uo4ydRp1XbCq0hJyuP03tvc+FAOAYmejz9Sl0atHNB0RQvZN1MvknAsQDO3ztPB9cO+Lf1x8lMhu6XVHGCWhjwlKIoptwf+tgFOAP8DvTj/sqPw4Bd5VWkEEI8rtKOHiNywgQUjQaPdeswa9O6wHY6rZajm7/h9O4dONepS68Jk7Gwta/gakVJKYpiDawFGnF/ZMkbQAiwBfACbgMDVFVNrKQShRCPIUMTU16ePJMdc6fz45IF9H5/MrVatCn3+6qqyo2z9zi67RrpSdnUb+dM25dqYWJe8AiQ/y9Pl8fXl79m1flVGOsbM7f9XF6oKaNCSqvgdaD/RVXVk8B27i/Bf/Hvc9YAHwETFEW5DtgB68qxTiGEeKyoqkr8V18R/s47GDg54bV9W6EhLSMlmR1z/Tm9ewe+XXswIGC+hLTHx6fAz6qq1gN8gavAJOCAqqp1gAN//10IIUrEyNSUvlNm4ejlze7F87h59nS53i8pJoM9y//kly8uYWJhQN8PW/DMq/WLHdJCEkJ4Zd8rLD27lI5uHdnVZxe9avWSkPYIFFWtuGljLVu2VM+cOVNh9xNCiMqgy8khOmAGyT/8gEXXZ3GZPx+NWcGbWMfcvM6uxXPISE6iy5vvPXabnRZGUZRgVVVbVnYd5UlRFEvgT6Cm+q/OVFGUEOBpVVXvKoriDPyhqmrdh11L+kchRGGy0tPYPnsacWG3efGD6Xg3bVGm18/N0XL25zuc3X8HfX0NbV6sSaOOrmj0ivyec/98bS5fXPyCLy58gaWRJVPbTKWbV/Xoy8pLcftI2VlOCCHKUG5sLJGjx5D555/YjxqF/Yj3Ct3E+vKhA/z6xQpMLa0ZNGMBTrV9Krha8YhqAveALxVF8eX+ishjgRqqqt4F+DusORZ0sqyKLIQoDmMzc/pODWR74DR2LZpNnw+ml9l+mrcuxHFkSyip8Vn4tKmB38u1MbMyKvb5l+MuMz1oOtcSr/F8zef5qNVH2BjblEltQr6oCSFEmcm8eJGIUaPRpqTgMn8+ls8V/EZRm5fL71+v5c/9e/Fo1ITnx36EqaVVBVdbvp6QL2otgRNAO1VVTyqK8imQAoxWVdX6X+0SVVV96G8u0j8KIYqSmZrCtsCpJEZF0ucjfzwbNy31tVLiMjmy9Rq3L8Rh42xGp8E+uPoUP2Bl5WXx2Z+f8dXlr7A3tse/rT+d3KvWvm9VmXxRE0KICpS8Zw93p05D394er03fYVyvXoHt0hLi2bNkPlGhV2nZ62U6DB6GRk82/HxMRQARf8/lhvvzuScBMYqiOP9r6GNspVUohKg2TCws6TdtNtsCp7JzYSAvfRSAR6MmJbqGNlfHuV/DOPPTbRSNgt/LtWnSxQ29Yg5zBDgXew7/Y/7cTrlN3zp9mdByApaGliV9HFEMEtSEEOIRqFot95YsIX7tOkxbtcL106Xo29oW2Dbir8v8uGQ+2ZkZPD/2Q+r5dazgakVZUlU1WlGUcEVR6qqqGsL9VZGv/P1nGDAfWRVZCFGGTC2t6D99DltnTuaHhTPpO2kmbg2Kt41L+JUEDm8JJSkmg1rNHWjfvw7mNsbFvndGbgbLzi3ju6vf4WzmzOquq/Fz8Svto4hikKAmhBClpE1NJXLiRNIPHcZmyGBqTJ6MYmCQr52qqpzfv5c/vv4CSwdH+k0NxN7Dq+ILFuVhNLBRURRD4CbwOvdXR96qKMqb3N/ipn8l1ieEqGb+CWuzpvD9/Bm8PGUmbvUaFto+LTGLo9uuc+NsLFaOJvQa44tHA7sS3fPk3ZMEBAUQmRbJ4HqDGdd8HKYGpo/6KKIIEtSEEKIUsm/dImLESHLCw3GaMQObQQMLbJebk82Btau4fOgANZu3oseo9zE2M6/gakV5UVX1PFDQPIMuFV2LEOLJYWZtwwD/uWyZOZnv582g39RZuPjUf6CNVqvjwoEITu29hapTadPbm2ZdPdEzKP4wx9ScVD4J/oTtodvxtPTkq+5f0aJG2a46KQonQU0IIUoo7cgRIie8j6Kvj+eX6zFt1arAdsmxMexePJfY2zdo228wbfsOLnQFSCGEEKIkzKxtGDB9DltnTWbHXH/6TZ2Nc537O4FEXUvk0KZQEqLS8WpsR4eBPljam5To+ocjDjPr+CzuZd7j9YavM6LpCIz1iz9UUjw6CWpCCFFMqqqS8OVXxC5ahFGdOritXImhm2uBbe9cOM+PyxaiarX0+dCfWi0K3uxaCCGEKC1zWzv6+89l64zJbJ8znRfGB3D9LISejMHC1pie7zXG29ehRNdMzk5mwakF7Lm5h9rWtVny9BIaOzQupycQDyNBTQghikGXnU20vz/Ju3Zj8dxzuMybi8Y0//h8VVU5vXsHRzd9g62rGy9OnIqNc8FhTgghhHhUFrb29Js+h42TP+T7ef4YW/WnRc9WtOjhhYFhyVYV/u3Ob8w+MZvk7GSGNxnOO03ewVDPsJwqF0WRoCaEEEXIjYklYvRosi5cwH7MaOzfew9FUfK1y8nM4OfPlnLtZBA+bTvw3LtjMDQu2VATIYQQoiSibyZzaNNtdEof9A23o8v5gZq+rUsU0uIy45h3ch777+ynvm19Pu/6OfVsC95mRlQcCWpCCPEQmX/+eX8T6/R0XJcvw7Jr1wLbJURFsnvxHBIiI+g49A1avvBSgWFOCCGEKAtZabkc/+E6V47dxczaiO7v+mHv1oats6awbfY0Bkyfg4On90Ovoaoq+27tY/6p+aTnpjO2+ViGNRyGgSb/Csai4klQE0KIQiTt3Em0fwD6jo54rV2LcV2fAttdP3OSn1YsRk9fn37TAvFo5FvBlQohhHhSqDqVq0F3CfrhOjmZWpp29aDV814YGt//tX6A/zy2zJzEtsCpDPCfW+h2MDHpMQSeCORQxCGaODQh0C+QmtY1K/BJRFEkqAkhxP+jarXELlpMwpdfYtqmDa5Ll6BvY5OvnU6n5fj2TZzYsZkaNWvT+/0pWNo7VkLFQgghngT3wlI5tCmEmFspONe2otPguti5Prjli3UNJwb4z2XrjElsDZzKwIB52Ll5/HNcVVV+uP4DH5/+mDxdHh+0/IBX6r+CnqZk89lE+ZOgJoQQ/6JNSSHy/YmkHzmCzSuvUGPSRwVuYp2Vlsa+5R9z63wwDZ9+lmffHIG+oUy4FkIIUfayM3I5ufsWlw5FYGxuwLOv1cenjVOhQ+xtnFzo7z+PrbMms3XWFAYEzMPO1Z3ItEhmBM3gxN0TtKzRkpl+M/Gw9CjwGqLySVATQoi/Zd+8RcSIEeRERuI0ayY2AwYU2O7enVvsWjyH1Lg4nn1rBE2e7SHz0YQQQpQ5VVUJPRnNse9vkJWaQ6NObrTp7Y2RadFzyGxdXOk/fQ5bZ05mW+BUTF/xY0XYehQUpj81nX4+/dAosrdnVSZBTQghgLRDh4h8fyKKoSGeX32JaYsWBba7euwQ+1cvw8jUjIEz5uHiU7+CKxVCCPEkiI9M4/DmUKKuJVHD25Jeo3xx8LAo0TXsXN1pN34k++bPJfaLnbTp3YQp3QNxNncup6pFWZKgJoR4oqmqSsK6dcQu/gSjevVwX7kCAxeXfO20eXkc+e5LgvfuwrVeA3qNn4yZdf55a0IIIcSjyMnK4/Te21w4EI6BiR5Pv1KXBu1cUDQlG7mh1WnZcGUDK86vwN7PhOdO1KDGgTxM2gPmRZ4uqgAJakKIJ5YuK4u70/1J2bMHix7dcZkzp8BNrDOSk9izdD4RVy7RrHsvOr36Bnr6snSxEEKIsqOqKjfO3uPotmukJ2XToJ0zT71UCxPzks9/vp54Hf8gfy7GXaSze2emPzUduqexNXAqW2dNYeCMeVg5OpXDU4iyJEFNCPFEyo2JIWLkKLIuXcJh3Djshr9T4Dyzu9dD2P3JPLJSUugxcgINOj5TCdUKIYSozpJiMji8OYTwq4nYu5vT/Z1GONW0KvF1cnW5rL+4ns8vfI6FgQUfd/yY57yeu9+/eTrQf9psts2acj+sBczH0kFWKq7KJKgJIZ44mefPEz56NGp6Bm6rVmLxTMHh68KBXzi4/jPMbOwYFPgxNbxrVXClQgghqrPcHC3BP93m3K9h6Bvo0WGgD406uaIp4TBHgKvxV5l+bDohiSH08OrBpDaTsDW2faCNo1dN+k2bzbbZU9k6azIDAubJtjJVmAQ1IcQTJen7H4gOCEDfyQn39esxqlMnX5u83FwOfvk5Fw/8gmeTZjw/5gNMLCwroVohhBDV1a0LcRzZEkpqfBZ12zjh17c2ppYlH+aYrc1m9Z+rWX9pPTbGNiztvJQuHl0KbV+jZm36TZ3N9tnT2DZrKgMC5mFhZ/8ojyLKiQQ1IcQTQc3LI/bjRSR8/TWmbZ/C9ZNPCtzEOjU+jt2fzCX6eiit+/Sn3cChaGQTUCGEEGUkJS6TI1uvcftCHDbOZvSZ0AxXn9ItTvXnvT/xP+bPzeSb9Kndh4ktJ2JlVPSQSadadeg7dRbbZ09nW+AUBvjPw9zWrlQ1iPIjQU0IUe1pk5OJHD+B9KAgbF59lRoffYiin//HX/iVi/y4dAG52dn0njCFOm38KqFaIYQQVVriHchMAJdmJTpNm6vj3K93OPPTHRSNgt/LtWnSxQ09vZLvZZaZl8mKcyvYcGUDNcxq8Pmzn9POtV2JruFcuy59p8xk+xz/fzbFNrexLfpEUWEkqAkhKlTIyWiy0nJp0tmtxEsNl0b2jRuEjxhBbtRdnOfMxrpv33xtVFXl7L7dHPp2HdZOLgzwn4edm3u51yaEEOIxE34KNg8BExsYcQKKOeIi7Eo8hzeHkhybSa3mjrTvXxtzG+NSlXA6+jQBQQGEp4YzsO5AxjUfh7lh6dbbd/GpT9/JM9kx159tf4c12Xqm6pCgJoSoUHcuxXPtdAxhl+N5Zlh9zKyMyu1eqb//TtTED1CMjfH8+itMmzfP1yY3O4v9q5fz17FD1Gr5FD1GTsCogCX6hRBCPOEuboedI8DSBQZ9V6yQlpaYxdFt17lxNhYrRxN6jfHFo0Hphhim56azJHgJW0K24Gbuxvrn1tPKqVWprvVvrvUa8PKkGeyYH8C2wKkM8J+LqZX1I19XPDpFVdUKu1nLli3VM2fOVNj9hBBVj6qqXD4SxbFt19A31KPzq/Wo2dShzO8R/8Va7i1ZgnH9+ritXIGBs3O+dkkx0exeNJt74XdoN2Aobfr0R9GUfAiKyE9RlGBVVVtWdh2PC+kfhajCVBUOLYQ/5oJnOxj4LZg+fIigVqvjwoEITu29hapTadnDk2ZdPdEzKF0fcyzyGDOPzyQ6PZqhDYYyqukoTA3K9qVi+OULfD9/JtZOzvSfPgdTy5JvDyCKp7h9pAQ1IUSlSIxO59f1V7gXlkqDDi6071cHA6NHX7RDl5nJ3WnTSdm7F8uePXGeMxuNiUm+drfOB7N32UIUFHqO+QDvpi0e+d7ifySolYz0j0JUUblZsHs0XNwKvkOg11LQf/hIkMjQRA5vDiUhKh2vJvZ0GFAHS/v8/VBxJGcns+jMInZe34m3lTez/GbR1LFpqa5VHHcunmfnglnYuLjSf/ocWfG4nBS3j5Shj0KISmHjZEbfD1twas9Nzu4PIyo0ia5vNMDRs/SdQm509P1NrK9cwWHCBOzefivfJtaqTsfJnds4tvVbHDy86P3+VKxrOD3q4wghhKhu0uPuz0cLPwld/KH9BFAKn1udnpxN0PfXCT0Zg4WdMT1HNMG7SemXvT8YdpDAE4EkZiXyduO3Ge47HCO98psuAODZuCkvfjjC+R5xAAAgAElEQVSdnQtnceS7r+g2fEy53k88nAQ1IUSl0dPX0Pal2ng0sOO3r66wY0EwrXt706ybZ4k3+8w4e46IMWNQMzPvb2LduXO+NtkZ6fy0cgk3zpygXrtOdBs+GgOj0k3mFkIIUY3F/gXfDYC0GOj/NTTsU2hTnVbHpcORnNx1k7w8HS17etG8uycGhqUbJZKQlcD8k/P56fZP+Nj4sLLLShrYNSjtk5SYV5Nm9Js2GwcP7wq7pyiYBDUhRKVzrWvDwGmtOfRdCCd23iTscgJdXquPpV3xhook7djB3RkzMXBxxv2rLzGqXTtfm/iIcHYtmk1SzF06D3ubZj165/vaJoQQQnDjIGwdBgYm8Po+cC18aHz0zWQObQohLjwN9/o2dBxUF+sapZs7pqoqv9z+hbkn55Kam8rIpiN5s9GbGOgZlPZJSs2tXsMKv6fIT4KaEKJKMDYzoNtbDfFsbMfhzaFsmX2aTkN88GlV+LBENS+PmAULSdywATM/P1w/WYyedf6Vqq6dDOKnVUswMDKi//Q5uDdoXJ6PIoQQ4nF1eh3s+wAc68PgzWBd8FYtmWk5nPjhBleO3cXM2ojn3m5EreYOpX4BeC/jHoEnAvk9/Hca2TViVrtZ1LGp8yhPIqoBCWpCiCpDURTqPeWMS21rfl1/hV/XXeHOxXg6Dq6LkcmDP660SUlETphAetBxbIcNw/GDifk2sdbptBzbvIFTu7bjXLsuvSZMxsKu9PMFhBBCVFM6LeyfBidWQZ3noN86MLLI10zVqVw5FsXxnTfIzdTStKsHrZ73wtC4dL9Sq6rKrhu7WHh6ITnaHN5v8T5DGwxFXyO/ogsJakKIKsjS3oSX3m9G8M93OL33NnevJ/PsGw1wqX3/a1n2tWuEjxxF3t27OM+di/XLL+W7RmZqCnuXfcydC+do0qU7nV8fjr5BxQ8fEUIIUcVlp8L2N+HaL/DUCOg2u8A90u6FpXJoUwgxt1JwqWNNx8E+2LmUbqNpgLtpd5l5fCbHoo7R3LE5M/1m4mXl9QgPIqobCWpCiCpJo6eh1fPeuNe35df1l9m5+CwtenhRz/Q20R9+gGJmisc3X2ParFm+c2Nu3WD34rmkJ8bT9Z3RNOnyXCU8gRBCiCovKRw2DYLYq/D8J9DqzXxNsjNyObn7FpcORWBsbsCzr9XHp41TqYc56lQd20O3s/jMYlRUJreezKB6g9Aoso+neJAENSFEleZU04qB01pzZEsoZ/bdJjTlNs1qN6PustkYOOWfv3bl8EF+XbMCY0tLBs5cgHPtupVQtRBCiKok9bffUIyMMO/Q4X//GBF8P6TlZcEr26B2lwfOUVWV0JPRHNtxnay0XBp1cqNNb2+MTEs/OiM8JZyA4wGcjj7NU85PMcNvBq7mrqW+nqjeJKgJIao8fTWXen+uRf9yNCEN/8Mxw6FobuioX0P9542mNi+PP75Zy/lffsS9QWNeGPcRplb5FxYRQgjxZFF1OuK/WEvmlSu4frwQy+7d4fJO+GE4mNeAYXvAsd4D58RHpnF4cyhR15Ko4W1Jr9FNcfDIP2etuLQ6LRuvbmT5ueXoa/SZ6TeTl2q/JKsPi4eSoCaEqNJyo6IIHzWK7Kt/0ej9CTR/uRMHvv6L3zf8xZ2L8XQeWg9tXhp7lswj8q8rtHi+Dx1feR2NXun2rxFCCFG9KBoN7l+sIfzd94ic8D66szuwztkK7m1g0Hdg9r9FpnKy8jj94y3+PBiBoYkenYfWo76fM0oJ9/b8t5tJN5keNJ0L9y7Qya0T05+aTg2zGmXxaKKaU1RVrbCbtWzZUj1z5kyF3U8I8XjLCA4mYsxY1OxsXBcvwrxTJ+D+qlvnD4RzYucN9PVjyUnbQ15uJs8NH0O9dp0quWoBoChKsKqqLSu7jseF9I9ClD9dahIRQ3qSfi0Rxx5e2C38AQyMgfvDHK8Hx3Js+3XSk7Jp0M6Zp16qhYm5Yanvl6vL5evLX7Pq/CpMDUyZ1HoSz3s/L1/RRLH7SPmiJoSokhK3biU6cDaGLi64bfgGo5o1/zmmaBSaPutOesIZTn6/EUVjQaNnxlC7dftKrFgIIUSVlR6PZttQ3JteJtLCj9ifbqP1Wo3DmDEkx2ZyeHMI4VcTsXc3p/s7jXCqafVItwtJCGH6selcTbhKN89uTG4zGXsT2R5GlIwENSFElaLm5hIzfwGJGzdi1r49rosXoWf1YIeZl5PDb+tWcfmP3/Bs0gJbtz5cPZ5IQnQwXd9s8EjLJQshhKhm4q7Bxv6QEoUyYB2uDV7ibkAAsavXcTHCmtBMD/QN9Ogw0IdGnVzRPMIwxxxtDmsurGHdxXVYGVnxydOf0NWzaxk+jHiSSFATQlQZeYmJRI4bT8bJk9i+/jqOE99H+X9zzVLiYtm9eC4xN6/zVN/B+PUbjKLRULN5HAe/ucq2uWdo+3ItmnR2k+ElQgjxpLt5CLa+ChoDeO1HcG+NAmT1G8vppHZkpBrhbhBBl+l9MbM1faRbXbx3Ef8gf64nXadXzV582OpDrI1lUStRehLUhBBVQlZIKBEjR5IXG4vz/HlY9+mTr82di+fZ++lCtHl5vPjBdGq3bPPPMa/G9gya3oaDG65ydOs1wi7H88x/6mNmZVSRjyGEEKKqCP4a9k4AuzowZAvYeJISl8mRLaHcvhiPrbMtbUyvoqxbQIJ6EpPFi9EYlbzPyMrLYtX5VXx95WscTBxY2WUlHd06lsMDiSeNBDUhRKVL/e03Ij/8CD0zMzw3fIOJr+8Dx1VV5cye7zny3dfYurrR+/0p2Lq45buOqaUhz49owuXDkRzdfp3Ngad45tV6ePs6VNSjCCGEqGw6LfwWAEHLoVYX6P8lWj0Lzu27xZmf7qBoFPxerk2TLm7o6bUhwUmfmDlzCH/3XdxXrEBjZlbsW52NOYt/kD93Uu7Qz6cfE1pMwMKw9Mv4C/FvxQpqiqJYA2uBRoAKvAGEAFsAL+A2MEBV1cRyqVIIUS2pqkrcZ58Rt2w5xk2a4LZ8OQY1HB9ok5OVyS+fLyP0+BF82rTjuffGYmhS+PAURVFo1MkNFx8bfl1/mX2fXaRhBxfa9auDgZEs2S+EENVaTjrseBtC9kKrt6H7fMJCkjm8+STJsZnUau5I+/61Mbcx/ucU21eHorEw5+7UaYS98Sbuqz9Hz/rhQxYzcjNYenYpm//ajIu5C190+4KnnJ8q76cTT5jiflH7FPhZVdV+iqIYAqbAFOCAqqrzFUWZBEwCPiqnOoUQ1YwuI4OoyVNI/eUXrF7sjdOsWfmGnCTejWTXojkkREbQYchrtOrdt9jzzmydzej3UUtO7r7JuV/DiAxNousbDXD0tCyPxxFCCFHZUqLgu4EQcwl6LCTNZxhH113lxtl7WDma0GuMLx4N7Ao81bpPH/TMzYkcP4E7/xmGx7q16DsUPBrjeNRxZh6fSVRaFEPqD2FMszGYGjza/DYhClLkPmqKolgCfwI11X81VhQlBHhaVdW7iqI4A3+oqlr3YdeSfWKEEAC5kZGEjxxFdmgojhMnYvv6a/kC2I3gU+xbvgiNvj4vjPkQzyZNS32/iJBEfvvyCpkpObTu7U2zbp6PtKqXKJrso1Yy0j8K8YiizsOmQZCdivalL/kzvC6n995G1am07OFFs64e6BloirxMelAQ4aNGo29vj8f69Ri6uf5zLDUnlcVnFrPj2g68LL2Y6TeT5jWal+dTiWqquH1kcYJaU2ANcAXwBYKBsUCkqqrW/2qXqKqqTQHnvwO8A+Dh4dHizp07JXkOIUQF2hqyFSM9I3rX6l1uKyZmnD5NxNhxqLm5uH6yGPMOHR44rup0HN+xiePbN+HoXYveE6Zg5Vjjke+blZ7LHxtDuHE2Fpc61jz7egMsbI2LPlGUigS1kpGgJsQjuPojfP82mNoR6beBQz/nkHg3Ha8m9nQYUAdLe5MSXS7j3DnCh7+LxsQEj/XrMKpVi0Phh5h1YhZxmXEMaziMEb4jMNaXPkSUTlkGtZbACaCdqqonFUX5FEgBRhcnqP2bdERCVF2qqvLub+8SFBXEM+7P4N/WHzuTgoeIlFbi5i1Ez56Nobs7bitXYlTT+4HjWelp/LRiMTfPnqZhpy50eWsEBoZlt2qjqqqEnIjm8OZQFI3C00PqUqfVo4dAkZ8EtZKR/lGIUlBVCFoGvwaQ7tiBIP0ZhJ5NxsLOmA4DffBuUvoNprNCQgh78y1UbR67RzblG+1RalvXJrBdII3sG5XdM4gnUlkGNSfghKqqXn//vQP356PVRoY+ClGtaHVaNlzZwLJzy7AwtMD/KX+6eHZ55OuqublEz51L0qbNmHXsgOuiRehZPjhXLC7sNrsWzSElLpbOw97Bt1tP7qVl42hR9m8sk+9l8Ov6K8TcSqFuGyc6DvLB0EQWwS1LEtRKRvpHIUooLwf2TkB3diOXrD7iZFhb8vJ0NO/mSfPunhgYPvriUQeDNmI4YS4mmTr+mvQyAwbMwEDPoAyKF0+64vaRRQ7WVVU1GghXFOW/IawL94dB7gaG/f1vw4BdpaxVCFFF6Gn0eK3Ra2x5YQs1TGsw7o9xTD06ldSc1FJfMy8xkbA33yJp02bs3noT988+yxfS/go6zMZp75ObncUA/3m4+HVh1KZzPLfkMPFp2Y/6WPlYOZjy8sTmtHrBm9DTMWyefYq715PK/D5CCCHKQWYifPsy0SdPsi37a46EtqZGTSsGT29Dm941HzmkxWXGMeGPCYy9Np+vRvpg6uRGi/l7yT4aVEYPIETxFPlFDf6Zp7YWMARuAq9zP+RtBTyAMKC/qqoJD7uOvDEU4vGRq81l9YXVrL24FgdTBwLbBZZ46eGskBAiRowk7949nGcHYtW79wPHdVoth7/7iuAff8ClbgOeH/sRe2+kM2/fVbLydIx5pjbvdKyFoX7RE8BLK/pmMr+uv0xqfBYtenjR8nkv9PTK735PCvmiVjLSPwpRTPE3yPzmNY6Hd+JqxjOYWRvRvn8dajV3eOS51aqq8uPNH1lwegGZuZm81/Q9Xmv4GiSlEP7W22SFhuK6cAGWPXuWzbOIJ1aZDX0sS9IRCfH4uXjvIlOOTuF2ym2G1BvCuBbjMNEvemJ2yv79RE2ajJ65OW4rV2DSuPEDxzNSkvlx6QLCL1+g6XPP4959MNP2XOXUrQSeqmnL3JcaU9PBvLwe6wE5WXkc2RLKX8ejcfSypOsbDbB2lKWWH4UEtZKR/lGIoqm3jnJl7RqOJ/YjF3OadPGg1fNeGBo/+tD16PRoAk8EcjjiML4OvsxqN4uaVjX/Oa5NTSX8vffIDD6L08wZ2AwY8Mj3FE8uCWpCiDKTmZfJsrPL+Pbqt3hZejGn/RyaODQpsK2q0xG3chVxK1di4uuL6/JlGDg+uIl19I1r7F48l8yUZDq98R6HdF6s/P06JoZ6TO1Zn/4t3cpt1cmHuR4cyx8b/8LM2ohB01qjyBL+pSZBrWSkfxSiCOe/I2LbanbFB+DiZUTH//hi5/LoL/NUVWXHtR0sPrMYraplTLMxDK43GD1N/uGTusxMIsaOJf3wERw/mIjdm28+8v3Fk0mCmhCizJ28e5Jpx6YRmxHLm43e5D3f9x6YWK1LTydq0mRSf/0Vq5dewmlGQL5NrC/+vp8D6z7DzNqGWoNHMfdkKtdj0+jt64J/rwbYm5fdKo+lkZaYRWZqLg4eFpVax+NOglrJSP8oRCF0OjgYCEc/Ae9OhDddgVsT9zJ5mReRGsGM4zM4efckrZ1aM8NvBu4W7g89R83JIWrSJFL2/YTd8OE4jBtbKS8WxeOtuH2kLHMmhCi2Ns5t+L739yw4tYAvLn7BkcgjzG0/lzo2dciJiCRi5Eiyr13DcdJH2A4b9kDnlZeby+9frebCbz/j0tCXSz69mLPnLq7WJnz5eis613V8yJ0rjrmNMeY2sjeOKD5FUfSAM9zfX/QFRVG8gc2ALXAWeFVV1ZzKrFGIx1JOBux8F67sghavQc9FuJfBqos6Vcemvzbx6dlP0Sga/Nv607dOXzRK0fOTFUNDXD7+GI2ZOfGrV6NLTaHGtGkoGpnbLMqeBDUhRIlYGFowu/1snvF4hpnHZzLwx4FMNXiRRkt/Bp0O9zVrMG/f7oFzUhPi2PPJPO5eC8HOrztLUn2I+zOetzt4M76rD6aG8qNIPNbGAleB/y5nugBYoqrqZkVRPgfeBD6rrOKEeCylRsOmwRB1DrrNgbYjoQy+XN1Ovo1/kD/nYs/R3rU9AW0DcDJzKtE1FD09nGbNRGNhQcL69WjT0nCZMwfFQJbuF2VLfjsSQpTKMx7P4Ovgy44Fb+OzdTOx9sZ4rPoM80YPrgwZcfUSe5bMJycrk4hm/Vl+156GLiase60Njd2sKql6IcqGoihuwPPAHGCCcv8z8jPAkL+bfA3MQIKaEMUXfRG+G3R/Gf5B30G9gldZzIlMQ5eVh3Et6yIvmafL45sr37Dy3EqM9Y2Z034OvWr2KvWwRUVRcPxgInqWltxbuhRdWjquSz7JN9xfiEchQU0IUSpqTg4585fTYctV0lvVI6DzXdL+HMNEg4n09+kPwLmf93BowzqwsGW7c08S0m2Z2tOH19t5oS9L4IvqYSnwIfDfSY12QJKqqnl//z0CcC3oREVR3gHeAfDw8CjnMoV4TIT8DDveBCNLeOMncPbN10TVqaQdiSB5/x0MnMwwGtX0oYErNDEU/2P+XI6/TBePLkx7ahr2JvaPXKqiKNi/OxyNpQUxswIJH/4ubitWoGdu9sjXFgIkqAkhSiEvIYGIMWPIPBOM3dtvU2/cWL7Luse0Y9MIPBHI77d+o1uIJzeDjhNnV4cd5h1oW9eN2X0a4W4ry96L6kFRlBeAWFVVgxVFefq//1xA0wJX7VJVdQ2wBu4vJlIuRQrxuFBVOPEZ7J8KTk1g8GawdM7XLC8pi8StoWTfTMakkR3WL9UpNKTlanNZe2ktay6swdLQkkWdFtHNs1uZL/5hO2QIeubmRE2eQtgbb+CxZjV61kV/5ROiKBLUhBAlknX1KuEjR6KNT8Bl0SKsXngeACczJ9Z0XcO3x9cS+uUObqREcsbJg2t2Pfi4d0N6+7rIyliiumkH9FYUpSdgzP05aksBa0VR9P/+quYGRFVijUJUfdpc+OlDOLMe6r0AL68Bw/xfpTL+jCXxh+ugA5t+Ppi2cCy0X7kcfxn/Y/6EJobS07snk1pPwsbYptwewap3bzRmZkSOG8+dV/+D+7q1+bamEaKkZOyREKLYUn7+mdtDXgGtDs9vv/0npP1X2IXzJKw5gFm6GfubqFxufpT27X6mUz0zCWmi2lFVdbKqqm6qqnoBg4CDqqq+AvwO9Pu72TBgVyWVKETVl5kEG/vfD2ntxsGADflCmi4rj4QtISRsCsHA0ZQaY5th1rJGgf1KtjabT89+yit7XyExK5FlnZexoOOCcg1p/2XRpQvua1aTExnJnVeGkhMRUe73FNWbBDUhRJFUnY57y5YROW48xnXr4r19GyaNG/3vuKryx9ZNbJ8bQEyeEUfqD2X6wC8Z3Ww0hyN/56XdL3E44nAlPoEQFeoj7i8scp37c9bWVXI9QlRNCbdgXTe4fQR6r4CuM+H/LXOffTuZmKVnyfgzFstnPXAY7ou+nUmBlzsfe57+e/qz9uJaetfqzc4+O+ns0bkinuQfZm3b4vnlerQpKdwZ8gp5CQkVen9RvcjQRyHEQ2nT0oma9BFpvx3Aqu/LOAUEoDE0/Od4Vno6X86fR0boea6b16b2S2/w/XMNMTbQowPv0MG1A1OOTmHkgZH0rdOXD1p9gJmBTLQW1Yuqqn8Af/z93zeB1pVZjxBVXtgJ2DwEdFp4dSd4d3jgsKrVkfJbGKl/hKNnY4zDcF+MPC0LvFRGbgbLzy1n49WNOJk5sfrZ1fi5+lXEUxTIxNcXzw3fkHbwIHo25f8lT1RfEtSEEIXKCQ8nYsRIsm/epMaUKdi8OvSBoSaXLl9j1+LZGKYncLtWF8aNfpN6zg92pPXt6rPlhS2sOL+Cry59xYm7J5jdbjYtnVpW9OMIIYSoCi5shV0jwcoNhmwD+9oPHM69l0HClhByI9IwbVED69410RgV/CvrqbunCAgKICItgkF1BzGuxbgq8TLQ2McHYx+fyi5DPOYkqAkhCpR+4gSRY8ehAh5frMHM739vJ/O0OlZ/s4uU/d+gKvrY9h3N+/26otEUPA/NUM+QCS0m8LTb00w9OpU3fnmD/zT4D6Obj8ZIT/acEUKIJ4Kqwh/z4NAC8GwPAzeAqe2/Dqukn44mec9N0Ndg+0p9TBsXvIx+Wk4aS4KXsDV0Kx4WHnz53JfyAlBUOxLUhBAPUFWVxI3fETNvHobeXrivXImhp+c/x8/fSWDtp5/hHXkcrZULgyf7U8vbrVjXbl6jOTt672DRmUV8feVrjkYe5dNnPsXT0rPok4UQQjy+crNg1wi4tAOavgIvLAX9/w2j16blkPj9dbKuxGNU2xrb/j7oWRX8Iu9IxBFmnZhFbEYswxoMY2SzkZjoFzxvTYjHmQQ1IcQ/1JwcogMDSdq2HfPOnXH5eCF65uYApGfnsXjPeeJ+XId3ZjjWzTowdsJ49P81X604TA1M8W/rT2f3znx+4XNsjW2LPkkIIcTjKy32/ny0iNPQJQDaj4d/DaPPCkkgYXsouow8rJ6viXk7F5QCRmgkZyez8PRCdt/YTS2rWmzosYEmDk0q8kmEqFAS1IQQAOTFxxMxZiyZwcHYvTschzFjUP5efevgXzEs+u4PWt7YiYcugw6vv0fr7s8//IJF6ODWgfau7WXZfiGEqM5irsB3AyH9Hgz4Bhq8+M8hNVdL8k+3SQuKQr+GKfZvNMbQueD5ZQfuHGD2ydkkZiXyTpN3GN5kOIZ6JXtRKMTjRoKaEIKsK1cIHzkKbWIirp8sxrJnTwBiU7OYuecK14IO8Wz8IUwsLOg7cQEuPvXK5L4S0oQQohq79htsew0MTeH1feDa/J9DOVFpJGwJIS8mA/N2Llh190YxyL9rVHxmPPNOzeOX279Qz7Yeq7qsor5d/Qp8CCEqjwQ1IZ5wKfv2ETVlKno2Nnhu/BaThg3R6VS2ngln3t5LNIs+ynNJF3Cp15De4ydhZi1LDQshhCjCqS/gpw/BsSEM2Xx/hUdA1amkHY0k+ZfbaEz1sX+jEcY++fsVVVX56dZPzDs1j/TcdEY3G83rjV7HQGNQ0U8iRKWRoCbEE+q/m1jHf74ak+bNcVv2Kfr29lyPTWPKDxe5eD2CASm/Y5kURvOeL9LxldfR05cfGUIIIR5Cmwe/TIFTq8GnO/RdB0b35zrnJWeTuDWE7BvJGDeww6ZvHfTM8gev2IxYAk8E8kf4HzSxb8KsdrOoZV2rop9EiEonv3UJ8QTSpqUR9eFHpB08iHX/fjhNn06ORo+Vv11j5e/Xcc+LZXjCfpScTLqNep/6HTpXdslCCCGquqwU2P4GXP8VnhoJ3QJBowdAxsV7JH5/HfJ02LxcB9NWNfINf1dVlZ3Xd/Lx6Y/J0eUwseVEhtYfit7f1xDiSSNBTYgnTE5YGOEjRpBz6zY1pk3D5pUhnLmTyOTvL3I9JpUhVlE4XNqHuZ0dvacH4uhVs7JLFkIIUdUlhd1fNOReCLywBFq+AYAuK4+kPTfJCI7BwN0C24F1MbDPv5R+VFoUM4JmcPzucVrUaMFMv5mydYt44klQE+IJkh4URMT4CSiAx7q15Pm2YNrOS2w8GYa7pQEzbC8Tf/YIHr7N6TnmA0zMLSq7ZCGEEFVdxBnYNBjysmHodqj1DADZd1JI2BKCNjELi2fcsezigaL34IIhOlXH1pCtLAleAsDUNlMZUHcAGiX/wiJCPGkkqAnxBFBVlcQN3xKzYAFGNb1xXbmSg8kGBHxyiLi0bN5uboPHuW3E3rxGm5cG4jdgCBoZaiKEEKIol76Hne+BeQ147UdwqIuqVUk5GEbqwTD0rI1wGN4EIy+rfKeGpYThH+RPcEwwfi5+BLQNwMXcpRIeQoiqSYKaENWcLifn/9q77/Aoqv2P4++z6T0EklASeu9VQMEKCoogUkTAi/3qxV4pV0AUxY6KV0QRLFTpCIpgA0FQlF6k91BDEtLLnt8fif5QKRFCZpN8Xs/jk+xmdvYz4yxnvzNnzuHQs8+SOGMmwe2uwTVwGP0X72bx5sPUKx/KK5cFsnHiOyRkZdL5icHUaNHa6cgiIuLprIUlr8K3z0NsK+g1EYLKkH0sjfipv5G57ySBTaMI71wNl/+fv27muHP4dPOnjF49Gh+XD8MvHc5N1W/SlC0if6FCTaQYyz56NHcS69Wribj/fr5oegOvvLcKt4VBHWvTOHEtP7w3gVLlKtDlicFElI9xOrKIiHi67AyY+xCsmwINb4HOb2O9fEn9+RAJ83aAy0VE79oENoz820t3JOxgyLIhrDu2jitjruSZ1s8QFRjlwEaIeD4VaiLFVNqGjex/4AFyEhNh6AvcGx/F2vlbuLxmJM92rM7GaR+wdPkSalxyKR3+8wi+AYFORxYREU+Xchym9oG9P8JVg+HyJ8lJzSZh5mbSNh7Hr2oYpXrWwjvc708vy3JnMX7DeMasHUOQTxAvtX2JjlU66iqayFmoUBMphhI/n0/c4MG4IiL4rv8IXl1vCQtI5c1ejWkbDfNee4bj+/fR5tZ+XNKluxpKERE5t6NbYVIPSIqD7h9C/W6kbztB/GdbcadkEdaxCsFtK2Bcf25TtsRv4Zllz7AlfgvXVb6OgZcMpHRAaYc2QqToUKEmUozYnByOjnqT4++/T1a9Rgxq1JsN2930aBbDoOvrcGLrWiYNfhVjXNw8cBiVGzV1OrKIiBQFO76Faf3A2xdun48t24zEeTtIXnYQ76gAytxeD9/ywX96SWZOJu+te48P139ImGxhuZAAACAASURBVF8Yo64cxTWVrnFoA0SKHhVqIsVETnIyBx9/guTvv2dz83Y8Vb4dMQEhTOrTgNZVIlgxayrLP5tEZKUqdHl8EGFRZZ2OLCIiRcGq8TD/cYisBbdOISujDPHvrCbrUCpBrcsRfn0VjM+fRwped3QdQ5YNYUfiDjpX68xTLZ4izO/vIz+KyJmpUBMpBjJ372Zf//5k7N7D+BY9mBXbivuuqMYDV1fHZKUz+9Xn2fnLT9RtexXt7umPj5+/05FFRMTTuXNg0RD4cTRUb4e9+UOSf00m8cvVuPy9KX1HPQJqRfzpJWnZabyz+h0+2fwJkQGR/O+a/9E2pq1DGyBStKlQEynikn9Yxr5HHyU12zKs1T14N2vO/JsbUqtsCMf27WHuayNIPHKYq+/4N42v66T70URE5NwykmHmPfDbArjkXnJaP0v85B1kbEvAv04EpbrVwCvY908vWXVoFUOXD2Xvyb30qNmDx5o9RrBv8BneQETORYWaSBFlreXY+AkcfeVV9oRG88rVd3N790vp07ISXi7Dbz/+wMJ3R+Hj70+PZ0YQU6e+05FFRKQoSDwAk2+Bwxuh4yukBd3MibfXYrPchHetTtAlZf900i8lK4VRv4xiym9TiAmOYdy147ik3CUOboBI8aBCTaQIcmdmsvnJQbgWzmdZuQas6fMQE3s0o1xYAO6cHJZM/Jif586gXM3adH50IMERGl1LRET+Lj4+np07d9K8efPcJw6uhkm9IDMFd49pJGyqROqqzfhUCCaiVy18Iv88lcvyg8t5dvmzxKXE0bdOXx5s8iCBPpruRaQgqFATKWKS9sex7s77KL13K7MadaTp4Ce4p2F5AFKTEpn/5svs3bCWRu2v56rb78HL28fhxCIi4qlWrlzJypUrOX78OO1j0nHN+jcERZJx/TTi52eSE3+YkCtjCW1XEePt+uN1SZlJvPrzq8zaPovKoZX5uOPHNI5q7OCWiBQ/KtREipCl877HNXQAQRkpLO3zOA882Y9Q/9xC7PDO7cx5bQSpiQlcd9/D1L+qvcNpRUTE01133XVYa/nxxx9JYBtdyzUiPfYNkqYdxyvUj8h7G+JX5c+jNX6791ueX/E8x9OPc1f9u7i/8f34efmd4R1E5HypUBMpAo6cTGfyC+9z5ZyxnAwMxb79Pvde3fKPv2/8/msWvT+awNBwej37MmWr1XAwrYiIFBUudzbXZ82nFBtZyBXEH72EdrviKN24AuE3Vcfl//9fFU+kn2DkTyNZsGsBNUvV5K1r3qJe6XoOphcp3lSoiXgwt9sy7afd7B75Kl22fMOJGvVpNu5dAqLKAJCTncW3H33A2q/mU7F+Q254+GkCQzVPjYiI5ENqPEz7F3bXUhpWf42c7aX5Nns98yPW0rddoz+KNGstC/cs5MWVL5KUmcR/Gv+Hu+vfjY+XutaLXEwq1EQ81PYjyTw7ZSXtZoymy+EtuLp2p/XwIRif3IYxOf44894YycGtm2l+4820vbUfLi+vc6xVREQEOL4DJvbAnXCCE1GfkbYxgJpVQom9vBFT501n3Lhx9OrVi6CoIJ5f8Txf7/2aeqXr8f6171OzVE2n04uUCCrURDxMRnYOY77byay5y/nvjx9SPvU40cOGEtGr1x/L7N+ykc/fGElmWhqdHnmaWq01maiIiOTTrqUwtS/pOfU5Yd4k54AhtEMlQi6PwbgMd0ffzcSJE5nw0QTWlF3D3oC9PNrsUf5V9194u/TVUaSw6NMm4kF+3h3PwJnrCVu/ilG/TsI/wI+KE8YT2KIFkNv9ZM1X8/nuo/cJjYyi++DnKFOxMu7ULNxp2XiXDnB4C0RExKOt/hQ79wkSvf5DcvJVeEcGEHVHLXxjQv5YJNMvk83VN8NaiAqJ4vXrX6dKWBUHQ4uUTCrURDxAYloWL3+5hYkr9nDHgeX0+HUO/jVrEjN6NL4xFQDIysxg8fvvsGnJN1Rt2oKODzyOD34kLtxN8vKD+MaGEHl3A4e3REREPJLbDV8/S9bSmcSbd8hKiyKoZVnCbqiKyze327y1lunbpvPaqtdwWzcPdX6I3nV64zKuc6xcRC4GFWoiDrLW8uWGQwydu5HExGTGHPiSSr98T8h111H+xRdwBeZOGpp45DBzX3uBI7t30Lp7by65rhspSw5y/Mc4bFYOAfXLEHJ1RYe3RkREPFJmKnbmvaRssCS438YV4EfpXjUJqFP6j0X2ndzHsOXD+OnQT7Qs25Jhlw4jJiTGwdAiokJNxCEHE9IYMmcjizcfpnWYm2e2foLZsokyDz1ImfvvxxgDwO51q5n/1ivYnBxueugZSidGcviVVdhsNwENIwm9Ohaf6CCHt0ZERDxSUhw5n9xN/IH2ZLib4V+rFKW618QrxBeAHHcOk7dM5q3Vb+EyLoa2Hkq3Gt3+aINExDn5LtSMMV7AKuCAtbaTMaYKMAWIAH4FbrPWZl6cmCLFR47b8smPu3ll4W+4LbxY29Bs3Cu4U1Io//ZbhLbPnajaWsvPc2fww+SPKRdTg6ta9CPny5MkZx8gsFEkIVdXxCcq0NmNERERzxW3jrQJL3Ai6T+4XSGEd6lGUKtyfxRhOxN3MnTZUNYcXUPbCm0Z0noIZYPKOhxaRH73T66oPQxsBkLzHr8EvGGtnWKMGQPcBbxbwPlEipXNcUkMmLmetfsSuLxmJMP8dpP50ghcUVFU/OAD/Gv9/5DHGSkpbPrqG66s24eozApkr00ksHEUIVfF4hOpAk1ERM7MveELEqeuICWrPz6RLiJva/LHyb1sdzYfbfyI/635H/7e/rzQ5gU6Ve2kq2giHiZfhZoxJga4ARgBPGZyP8lXA73zFvkIGIYKNZHTSs/K4a2vtzF2yU7CAnx4s2cDWi2aTPz4CQS2bEmFUW/gXarUH8tnJ2SQ9v0h2oX3hnRLYJMoQq+KxbuMRnUUEZGzsJbMLz4kfmkg2fZqgluXIuyGuhjv3AFBfov/jSHLh7Dp+CbaV2rPoJaDKBNQxuHQInI6+b2iNgp4Cvh97NbSQIK1Njvv8X6gwuleaIy5F7gXoGJFDXYgJc+y7ccYNGs9e46n0qNZDAPaViDlmUHEL11KqT59iB7w9B+TWGcnpHPy232krDoMFoKaRRNyZYyG3RcRkXOyWZmcfH8cSXtr4+WTTpm+tfGvFQ1AVk4W769/n/fXvU+oXyivXfEa11a+1uHEInI25yzUjDGdgCPW2l+MMVf+/vRpFrWne721diwwFqB58+anXUakODqRksnz8zcz49f9VC4dyKS7W9LMlcT+228j88AByg5/llI9ewKQHZ/Oye/2kfLLYQCCmkcTcmUs3qX8ndwEEREBsnPcrNpzglZVS597YYdkxx0hfuzXZKbVJyD6MKXu7YwrKHfAkI3HNvLM8mfYdmIbnap24ukWTxPuH+5wYhE5l/xcUbsM6GyMuR7wJ/cetVFAuDHGO++qWgxw8OLFFCk6rLXMXnOA5z7fTFJaFg9cVZ0Hrq5O9vIf2P34ExhfXypNGE9gs2ZkH08j6dt9pP56BAwEtSibW6CF+zm9GSIikmfST3sZMmcjt19amQEda+Pv4+V0pD9Ya0n9YSMJCw6CLUWplscIvCl31Mb07HTeXfsuEzZOoIx/GUZfPZorYq9wOrKI5NM5CzVr7UBgIEDeFbUnrLV9jDGfAd3JHfmxHzDnIuYUKRL2Hk9l8Oz1LN12jCYVwxl5c0NqRgcTP24cR157Hb86tYkdPRp8SxE/7TdS1xwBlyG4VTlCrojBK0wFmoiIp+nZPJZdx1IYv2w3K3Ye5+1bm1AjOuTcL7zI3GnZnJi4grTtFl/vvUT0rIV3ww4ArD6ymiHLhrA7aTfdanTjseaPEeobeo41iognuZB51J4GphhjngdWA+MKJpJI0ZOd42bcD7t4Y/FWvF0uhnepR5+WlTCZGRx86mmS5s0jpGMHIh97hpNLj5K6Zgd4uQhuXZ6QK2LxCvV1ehNEROQM/H28GHpjPdrWKMMTn63jxtE/MPTGevRqEevYSIkZOxOI/3Q1OakQGvIlIffeg4msTmpWKm+tfotJmydRPrg8Y9uPpXX51o5kFJEL848KNWvtd8B3eb/vBC4p+EgiRcu6/QkMmLGeTXFJtK8bzfAu9SgXFkDW4cPs7/8A6Rs2UPo/T+EV2Zqj/9uI8XYR3KYCIZfH/DHhqIiIeL6ra0fz5cNteWzaWgbOXM+SrUcZeXNDwgJ9Ci2DzXaT9NVuTi7Zj7c5TFSlxfj2exkCI1gRt4Jhy4dxIPkAvWv35uGmDxPoo+lcRIqqC7miJlKipWRk89pXW5mwfBdlgv0Y07cZHernThSatmYN+x58EEwYEf8eQ2acC3PsOMGXxxDStgJewSrQRESKoqhQfz6+8xLGLt3Jqwt/Y+2+Jbx5axNaVI646O+ddSSV+CmbyTqYSpDXQsKaJePq/D9OujN4/cdnmb51OpVCKzGhwwSaRTe76HlE5OJSoSZyFgcOHKB06dL4+/959MVvtxzhv7M3cDAxjb4tK/Fkh1qE+ueeUU2YOYsjr47Fr8FteJWqQ3aCFyFXlie4TQW8ggrvrKuIiFwcLpfhviuq0bpqaR6asppb3vuRh66pwQNXVcfby1Xg72etJWVFHInzd2LcyZT2eYOA6zrCZc+z5MBShv84nKNpR7mj3h38p/F/8PfWiMEixYEKNZEzSEtL4+OPP6Z8+fL06dMHb29vjpxMZ/i8TXy+Lo6a0cFMv681zSrlnkW12dkcHvkuaVstgZcPwvi5CL6sAiFtKuAqxG4xIiJSOBrFhjP/obYMmb2BUYu3sWz7MUb1akKF8IKb+zLnZCYnZmwjfUs8fr4bifAdhVePV0isejkv/TCYeTvnUT28OqOuGkX9MvUL7H1FxHkq1ETOICAggI4dOzJ79mzmzp1LRoVmvPjFFtKz3Dzevib/vqIavt65Z07TNsdxbOw3GL/G+JTPIuTqGELaxKhAExEp5oL9vHn9lsa0rVmG/87aQMdRS3ipW0M6Nih3wetO23ycEzO24U7LJNx/AkFByzF9JrM46zjPz+5CYkYi9zW6j3sa3IOvl7rUixQ3KtREzqJx48bsOniUtT8tY+2vR6kT25AXbm5AtchgADL2JpE4bwuZ+zLAlMa3QjJl7mmPy18fLRGRkqRrkxiaxJbi4SmruX/ir9x6SUWGdKpLgO8/n3PNnZlD4oJdpKyIwyc0nUjvx/EpG8qxrtN5cfN4vtrzFXUi6vBe+/eoFVHrImyNiHgCfZsUOYPMbDdjvt/B6GVZtPaJppF3HDc0bUq1yGAy9iSRtHgPGdsSsJnJZB34gejHbiaopW7eFhEpqSqXCeKz+y7l9UVbGfP9Dn7eHc9bvZpQt3z+5y/LPJBM/JQtZB9NI7jCdsKOPQG12jO/WQ9Gfns/KVkpPNz0YfrV64ePS702RIozFWoip7FqdzwDZ65n25FkOjcqz+Drr2Lx5zNZsGABrDhBuQMB4MomY+McXL6HiB39Bj7lLrybi4gUHcaYWOBjoCzgBsZaa980xkQAU4HKwG6gp7X2hFM5pXD5ersY0LE2baqX4dFpa7jpf8sY1LE2/S6tfNY516zbcnLJfpIW7cEr0JsylWfgf2g8h1vexXO+GXy/YhgNIxvy3KXPUTW8aiFukYg4peCHJhIpwhLTshg8az3dx/xIamYO4+9owVu3NiHsWAZXnqxD6ZxgFh5fyVG7mpNzHsG/hheVPh2vIk2kZMoGHrfW1gFaAf2NMXWBAcDX1toawNd5j6WEaVOjDF8+3JbLqpVm2LxN3PPxKuJTMk+7bHZCOkffX0/Sl7sJqO5PdMhA/I58wszL7uamhB9ZeegnnmrxFB93+FhFmkgJYqy1hfZmzZs3t6tWrSq09xPJL2stX244xNC5GzmWnMGdl1XhkXY18N6fTNLXe8nclYQrxAdb34/JKz8jy+2mZ8VKVL3/vrOeIRUpqYwxv1hrmzudozAZY+YAo/P+u9JaG2eMKQd8Z609641Eah+LL2st45ftZuQXWwgP9GHULY25tHqZP/6euuYIJ2ZvBzeEtzUErr6Ng2QxrFYLViT8RouyLRjWehgVQys6uBUiUpDy20aq66OUeAcT0hgyZyOLNx+mXvlQxv2rOTXSLEnjN5G5JwlXqC/hN1bF+BzmwGMPcYXLxdfXtmd+dhZ3paYSFBTk9CaIiMOMMZWBJsBKINpaGweQV6xFORhNHGaM4c42VWhZNYKHJq+mz7iV3HdFNR5pW5WUeTtJXXMU34ohRDTehevrfzO5TFlGhfhhkvfxTKtn6F6zOy6jDlAiJZEKNSmxctyWT1fs4eUvt5BjLYM61qJPZClS5u7m2L6TeIX5Et6lGkHNy5I4dxZxw57Fp3w5Gr7zDtG+vnz00UdMnjyZfv364eOjG7pFSipjTDAwA3jEWpuU36vsxph7gXsBKlbU1ZLirl75MOY92Ibh8zax7LvddFh6lAg3hLWrSIhrCnu+eZmhsZX51WRyWXQzhrYeSrlgdasXKclUqEmJtOVQEgNmrGfNvgQur1GGEQ1i8f3pMCf2x+EV7kd41+oENYsG3Bx+aSQnPvmEoEsvpcIbr+MVFkZFoFu3bkybNo0ZM2bQs2dPXC6d8RQpaYwxPuQWaROttTPznj5sjCl3StfHI6d7rbV2LDAWcrs+FkpgcVSAl4uBwaEkmUTi3G6e8k7hxd0DmZm0hNGxMfj6+vF8iyF0rtZZ3epFRIWalCzpWTm89fU2xi7ZSZi/DxPa1KDOzmSyZu7AHeFPqZtrENg0CuPtIichgQOPPUbK8h+J6NePqCefwHj//0embt26dOjQgVWrVpGamkpwcLCDWyYihc3kfpMeB2y21r5+yp/mAv2AkXk/5zgQTzxM1tFU4qf+Rtb+ZIKaR1OhmS93TuvJoJwE1pcuxeUVLmfYpUOIDIx0OqqIeAgValL4Ns2Bmh3B27dQ33bZ9mMMmrWevcdTebpqNJ1TDO4fDuMu7U+p7jUIbBKF8cq9KpaxbRv7+j9Adlwc5V54gfCbu552na1ataJp06b4+hbutoiIR7gMuA1Yb4xZk/fcIHILtGnGmLuAvUAPh/KJB7DWkvLTIRI/34nxcVG6bx28yxxi2uxuvBdt8TVhpB/oyoYjrThU25fIQKcTi4inUKEmhStuLUz7F1S9Enp+Av75nwT0fJ1IyeT5+ZuZ+et+egQHMb5UJL4703CVCSCsR00CG0dhvP6/i8nJb77h4BNPYoICqfjxRwQ2aXLW9atIEymZrLU/AGfqn3ZNYWYRz2TdluOfbiZ903H8qocT0aMmW3dP5ZnPR/JbgBcdo1sx4MqX2XbQ8sjUNdz87jKevK4Wd7episulro8iJZ0KNSlc5RrBTe/C3Adh/PXQ5zMIvTg3S1trmbPmIM/P20TTNMvngaUIS87BO9JFaK9aBDSMxJzSEFprOf7eexx98y3869UjZvTb+JQte1GyiYhI8WdcBp+oAPyqVsWnZWne+ep+Pjz6ExFe3rx5yX+5uk5PAFpWhS8ebsvTM9bxwoItLN12jNd6NiIqxN/hLRARJ6lQk8LXuDcER+deWfugHfSdAVG1C/Qt9h5P5ZlZ6/DdnsgY70DKWvAO8SO0S0UCGpT5U4EG4E5LI27wYJIWfEHojTdS7rnhuPzVQIqIyIUJ61CFtYdXM2Rqd3bmJHOTK5wnuk4lLKTCn5YLD/RlTN9mTPppL8PnbeL6N5fySo9GXFVLszuIlFQq1MQZ1a+BOxbAxB7w4bXQazJUvuyCV5ud4+bDJTtZv3gX97t9iSEQ7zKBhF5TkYB6fy/QALIOHmTfAw+QsXkLUU88TsRdd2m0LRERuWBp2WmMXvU6n/w2hejsbMaUvpTLOo8Fl9dplzfG0KdlJVpUzp1z7Y7xP3N3myo82aEWft6nf42IFF8q1MQ55RrB3Yvh027wyU3Q9T2of/N5r27dnhPMm7SBdolurscfogMo3b4y/nVLn7ZAA0j95Rf2P/gQNjOT2DHvEnzFFef9/iIiIr/7+dDPDP1hMPtS4rglKZlHWjxBcKv++XptzegQZve/jBcWbOaDH3bx487jvHVrE6pFanRhkZJEhZo4K7wi3LkQpvSG6XfAyThonb+G7HfJKZl8PmkD1XacpB8u0iICKN2pGv51Is56ZezEtGkceu55fCtUIOZ/7+BXteqFbo2IiJRwKVkpvPHLG0z9bSqxOZYPTyTTossHUL3dP1qPv48Xw7vUp031Mjw1Yx2d3vqBZ7vUo0ezGPX6ECkhVKiJ8wIj4LbZMPMeWDgIEvfDtSPgHBNI22w3qz/fjll5iDbWcCTIh4Au1anQIPKsjZjNyuLwyJc4MXEiQW3aUOH11/AKvfijT4qISPG27MAynv3xWQ6lHOJfJ1N5IDuQgNu+gKg6573Oa+uVpWFMOI9OXcNT09exdNsxRnStT6i/TwEmFxFPpEJNPIOPP/T4KLdQW/E/SDoAXcfmPv8XNsvNoR/2ceKbfURlWbZ7g9e1FWnStuI5zzJmnzjBgUceJXXlSiLuuIOoJx7HeKnfv4iInL/EjEReXfUqs7fPpqpPGJ8cjKNRZGPoNQmCL3wC67Jh/nx6d0vGfL+D1xdtZfXeE7zZqwnNKpUqgPQi4qlUqInncLmg40gIi4GvBkPykdxGLjACAJuVw8mVhzi6eA9+6TnsIYfEpmXo2rUOfj7nLrbSf9vK/v79yT5yhHIjXyT8ppsu9haJiEgx983eb3huxXOcSD/BPb4x/HvrcvzqdYcu75z2ZOP58nIZ+l9VndbVSvPQ5NX0fO9HHm1Xg/uvrI6X5lwTKZZUqInnufSB3LnVZt0HH3bAfcs0Urb4kPDdXkxKNpvIZkVZX+7s3ZhqUSH5WuXJxYs58NTTeAUFUemTjwlo1Ogib4SIiBRn8enxjFw5ki92f0GtsOr8L8WLOjuXw5UD4Yqn4SLdR9a0YikWPNyWwbM28OpXW/lh+zFG3dKEsmGaUkakuFGhJp6pfjfcflGkTJzIydc34LZhrCabqb45dLmxFs83z9/N1NZajr37Lsfeehv/hg2JefttfKI1J42IiJwfay0Ldy/khZUvcDLrJA/UvJU7f56GT+JB6DYOGnS/6BlC/X14q1djLq9RhqFzN9LhzSW83K0h19Yre9HfW0QKjwo18UjJyw6Q9I037vQ+GNcGgr1fYV+lPoy6pR+RIX75Woc7NZWDAwdxcuFCwrp0puzw4bj88vdaERGRvzqaepTnVjzHt/u+pX7p+gyv3IUanz8FLh/oNw8qtiy0LMYYejSPpVmlUjw0ZTX3fvILt7WqxOAb6uCfj9sBRMTzqVATj5R6Ip3d3jCCFLxDyjAxIJ3+BwfCjmBo3Pucr886cIB9/R8gY+tWop56iog7btdwxiIicl6stczZMYeXf36ZzJxMHm/2OH0zwHtmfyhdHXpPhVKVHclWNTKYGfdfyqsLf+P9pbv4aVc8b/duQs3o/N0aICKe6+zjn4sUMmstX6yPo/OaXfRNiqd1m4pMeqwrwfctgkqXwez7YckrYO0Z15H688/s6t6DrAMHiH1vDKXvvENFmoiInJe45DjuX3w/zyx7hhrhNZjeaRq3H9yB97yHocrlcNdXjhVpv/Pz9mLwDXWZcEcLjqdkcOPbP/Dpij3Ys7SVIuL5dEVNPMbBhDSGzNnI4s2HqVc+lPdvb0GDmLC8v4ZCn+kw9wH45vncudaufw28/nwIn5gylUPPP49vbCwx77yDX9Uqhb8hIiJS5Lmtm+lbp/PaqtewWAa1HMQtVTrhmnUfbPkcWtwNHV76WzvkpCtrRfHFw5fz+GdrGf75Ji6vEUnF0oFOxxKR8+Q5/7pIiZXjtny6Yg8vf7mFHGsZdH1t7rysCt5ef7ng6+0LXd+D0Arww+tw8hB0/xB8g7BZWRx64QUSJk8h6PK2VHjtNbxC1O1DRET+uX1J+xj641B+PvQzrcq1Ytilw6jgNjDhBji0PrdAa/nvizay44WIDPFjwu0t2BSXpCJNpIhToSaO2nIoiQEz1rNmXwKX14xkxE31iY04S8NiDLQbCmEVYMGT8NGNZHd8jwODnif1p58offddRD76qCaxFhGR87I3aS/d5nbD2+XNs5c+S9fqXTFxa2FyL8g4CbdOgZrXOR3zrFwuQ/0KYedeUEQ8mgo1cUR6Vg5vfb2NsUt2Ehbgw5u9GtO5Ufn830vW4m4IKUf6+/eyf2xnsjN8KP/yS4R17nxxg4uISLEWGxLLfY3uo1PVTkQHRcOW+TDjbgiIgDsXQtn6TkcUkRJChZoUumXbjzF41np2H0+le7MYBl9fh1JBvv94PUl7fTj4dSRernQqXZdCQNPyFyGtiIiUJMYY7mpwV+6gVcvegkVDoEJT6DUZQqKdjiciJYhGfZRCcyIlk8enraXPBysBmHR3S17t0egfF2nW7ebo26M58NDD+NeqTeVJHxMQEwwTOsGWBRcjuoiIlCQ5WTDvIVj0DNTtArfPV5EmIoVOV9TkorPWMmfNQYZ/vomktCz6X1WNB6+ucV4TcrpTUjg4YCAnFy0irGtXyg4bmjuJdcwimNQTpvaB61+FFnddhC0REZFiL+0ETPsX7FoCbZ+AqwaDS+e1RaTwqVCTi2rv8VQGz17P0m3HaBwbzshuDahdNvS81pW5fz/7+z9AxrZtRA14moh+/f7/nrbgqNwznp/dDvMfg6QDcPUzHjkil4iIeKjjO2DSLXBiN9w0Bhrf6nQiESnBVKjJRZGd42bcD7t4Y/FWvF0uhnepR5+WlfBynV/hlLLyJw48/DDW7SZ27FiC21z294V8g3LvIZj/GCx9Dawb2g27oO0QEZESYvey3F4ZGOg3Fypd6nQiESnhVKhJgVu3P4EBM9azKS6JdnWiee6mepQLCzjv9Z2YPJlDI17At1Il4/BdqAAAFqNJREFUYt8ZjW/lymde2MsbbnwTSleDWjec93uKiEgJsmYyzH0QSlWG3lNz2xAREYepUJMCk5KRzWtfbWXC8l2UCfZjTN+mXFevbP6H3P8Lm5nJoREvkDB1KsFXXEH5117FKzj43C80Bi57+LzeU0REShC3G759PrcXRpXLoefHEFDK6VQiIoAKNSkg3245wn9nb+BAQhp9W1XkqQ61CfX3Oe/1ZcfHs/+hh0hb9Qul77mHyEce1iTWIiJScDJTYfZ9sGkONO0HN7wGXuffbomIFDQVanJBjpxMZ/i8TXy+Lo4aUcFMv681zStHXNA60zdvZl///uQcj6f8q68S1kldGEVEpACdPAyTe8HB1XDt89D6AQ0+JSIeR4WanBdrLdNW7WPE/M2kZ7l5vH1N/n1FNXy9L2wI46Qvv+TgwEF4hYVRaeJEAurXK6DEIiIiwKENuSM7psVDr4lQWycDRcQzqVCTf2zH0WQGzVzPyl3xXFIlghdvbkC1yHzcO3YW1u3m2OjRHPvfuwQ0aULMW2/iHRlZQIlFRESArQth+p3gFwp3fgnlGjmdSETkjM5ZqBljYoGPgbKAGxhrrX3TGBMBTAUqA7uBntbaExcvqjgtM9vNmO93MPqb7fj7uHipWwN6NIvFdZ5D7v8uJzmFgwOeJnnx14R1u5myQ4fi8vUtoNQiIlLiWQsrx8DCQVC2Adw6BULLO51KROSs8nNFLRt43Fr7qzEmBPjFGLMIuB342lo70hgzABgAPH3xooqTVu2OZ+DM9Ww7ksyNjcozpFNdIkP8Lni9mfv2sf8//cnYuZPoQYModVvf8x4lUkRE5G9ysuGLp2DVOKjdCW4emzvvpoiIhztnoWatjQPi8n4/aYzZDFQAugBX5i32EfAdKtSKnaT0LF76YgsTV+6lQngA429vwVW1owpk3SkrVnDg4UewQMX3xxJ0qSYXFRGRApSeCJ/dDju+yZ225Zph4Lqwe6lFRArLP7pHzRhTGWgCrASi84o4rLVxxpjTfns3xtwL3AtQsWLFC8kqhchay8KNhxgyZyPHkjO4q00VHmtfkyC/grmtMemLLzjwxJP4VqlM7Dvv4FupUoGsV0REBIATu3MHDTm+HTq/DU3/5XQiEZF/JN/fuo0xwcAM4BFrbVJ+u6dZa8cCYwGaN29uzyekFK64xDSGzNnIok2HqVsulA/6NadhTHiBvkdAkyaE3dSF6IED8zeJtYiISH7tXQlTeoM7G26blTuZtYhIEZOvQs0Y40NukTbRWjsz7+nDxphyeVfTygFHLlZIKRw5bsunK/bw8pdbyLGWQdfX5s7LquDtVfDdRHzKlqX8iBEFvl4RESnh1n0Gc/pDWAXo/RmUqe50IhGR85KfUR8NMA7YbK19/ZQ/zQX6ASPzfs65KAmlUGw5lMSAGetZsy+By2tGMuKm+sRGBDodS0REJH+she9GwvcjodJlcMunEBjhdCoRkfOWnytqlwG3AeuNMWvynhtEboE2zRhzF7AX6HFxIsrFlJ6Vw1tfb2Pskp2EBfjwZq/GdG5UXiMviohI0ZGVnnsVbcN0aNwHOo0Cb03zIiJFW35GffwBONO39msKNo4UpuXbjzFo1np2H0+le7MYBl9fh1JBathERKQIST6aez/a/p/gmqHQ5lHQyUYRKQYKZgg/KVJOpGQyYsFmpv+yn8qlA5l0d0surV7G6VgiIiL/zJHNMKlnbrHW82Oo28XpRCIiBUaFWglirWXOmoMM/3wTSWlZ9L+qGg9eXQN/Hy+no4mIiPwz2xfDZ3eATwDcMR8qNHM6kYhIgVKhVkLsPZ7K4NnrWbrtGI1jwxnZrQG1y4Y6HUtEROSf++l9+OJpiKoLvadAWIzTiURECpwKtWIuO8fNuB928cbirXi7XAzvUo8+LSvh5VL/fRERKWLcObBwEKwcAzU7QLcPwC/E6VQiIheFCrVibN3+BAbMWM+muCTa1YnmuZvqUS4swOlYIiIi/1zGSZh+J2z7Clr1h2ufA5e67otI8aVCrRhKycjm9UVbGb9sF2WC/RjTtynX1SurIfdFRKRoStgHk26Bo1vghtehxV1OJxIRuehUqBUz3245wn9nb+BAQhp9W1XkqQ61CfX3cTqWiIjI+dn/C0zuBdkZ0Hc6VLva6UQiIoVChVoxceRkOsPnbeLzdXHUiApm+n2taV45wulYIiIi52/jLJh1HwRHQ795EFXb6UQiIoVGhVoRZ61l2qp9jJi/mfQsN4+3r8m/r6iGr7fL6WgiIiLnx1pY+ip88zzEtoJeEyFI832KSMmiQq0I23E0mUEz17NyVzyXVIngxZsbUC0y2OlYIiIi5y87A+Y9DGsnQ4Oe0Plt8PF3OpWISKFToVYEZWa7GfP9DkZ/sx1/HxcvdWtAj2axuDTkvoiIFGUpx2FqX9i7HK4aDJc/CRoIS0RKKBVqRcyq3fEMnLmebUeS6dSwHENurEtUiM40ioh4GmNMB+BNwAv4wFo70uFInu3oVpjUE5IOQrdx0KC704lERBylQq2ISErP4qUvtjBx5V4qhAcw/vYWXFU7yulYIiJyGsYYL+AdoD2wH/jZGDPXWrvJ2WQeaud3MO1f4OULt8+H2BZOJxIRcZwKNQ9nrWXhxkMMmbORY8kZ3NWmCo+1r0mQn/7XiYh4sEuA7dbanQDGmClAF0CF2l/9MgHmPw6la0DvqVCqktOJREQ8gr7te7C4xDSGzNnIok2HqVsulA/6NadhTLjTsURE5NwqAPtOebwfaHnqAsaYe4F7ASpWrFh4yTyFOwcWDYEfR0P1dtB9PPiHOp1KRMRjqFDzQDluy6cr9vDKwt/IdrsZdH1t7rysCt5eGnJfRKSION0IGPZPD6wdC4wFaN68uT3N8sVXRjLMvAd+WwCX3AvXvQhe+koiInIq/avoYbYcSmLAjPWs2ZdA2xpleKFrA2IjAp2OJSIi/8x+IPaUxzHAQYeyeJbEAzD5Fji8ETq+DC3/7XQiERGPpELNQ6Rn5fDW19sYu2QnoQE+jLqlMV0al8doWGIRkaLoZ6CGMaYKcADoBfR2NpIHOLgaJt+ae0Xt1qlQ81qnE4mIeCwVah5g+fZjDJq1nt3HU+neLIbB19ehVJCv07FEROQ8WWuzjTEPAAvJHZ7/Q2vtRodjOWvzPJh5LwSWhrsWQnQ9pxOJiHg0FWoOOpGSyYgFm5n+y34qlw5k0t0tubR6GadjiYhIAbDWLgAWOJ3DcdbCsjdh8TCo0Ax6TYKQaKdTiYh4PBVqDrDWMmfNQYZ/vomktCz6X1WNB6+ugb+Pl9PRRERECk52Jsx/FFZ/CvW6wk3vgk+A06lERIoEFWqFbO/xVAbPXs/SbcdoHBvOizc3oE45DUcsIiLFTGp87iTWu5fC5U/ClYPApdGLRUTyS4VaIcnOcTPuh128sXgrXsbwbOd69G1VCS+XBgsREZFi5vgOmNgDEvdB1/egUS+nE4mIFDkq1ArBuv0JDJixnk1xSbSrE83wLvUoH66uHyIiUgztWgpT+4Jxwb/mQqXWTicSESmSVKhdRCkZ2by+aCvjl+2iTLAfY/o25bp6ZTXkvoiIFE+rP4V5j0BEFeg9FSKqOp1IRKTIUqF2kXy75Qj/nb2BAwlp9G1Vkac61CbU38fpWCIiIgXP7Yavn4Vlo6DKFdDzYwgIdzqViEiRpkKtgB09mcHwzzcxb+1BqkcFM/2+1jSvHOF0LBERkYsjMxVm3Zs7T1qz2+H6V8FLJyZFRC6UCrUCYq1l2qp9jJi/mfQsN4+1r8m/r6iKn7eG3BcRkWIqKQ4m94K4tXDtCGjdH9S9X0SkQKhQKwA7jiYzaOZ6Vu6K55IqEbx4cwOqRQY7HUtEROTiiVuXW6SlJeROYl37eqcTiYgUKyrULkBmtpsx3+9g9Dfb8fdx8VK3BvRoFotLQ+6LiEhx9tsXMP0u8A+DO7+Ecg2dTiQiUuyoUDtPv+yJZ8CM9Ww7kkynhuUYcmNdokL8nY4lIiJy8VgLP74DX/0XyjWCW6dAaDmnU4mIFEsq1P6hpPQsXv5yC5+u2EuF8AA+vL05V9eOdjqWiIjIxZWTBQuegF8mQJ0bcyey9g1yOpWISLGlQi2frLUs3HiIIXM2ciw5g7vaVOGx9jUJ8tMuFBGRYi4tAT7rBzu/g8segWuGgsvldCoRkWJNVUY+xCWmMWTORhZtOkzdcqF80K85DWM0P4yIiJQA8Tth0i25P7u8A036Op1IRKREUKF2Fjluy6cr9vDKwt/IdrsZdH1t7rysCt5eOosoIiIlwJ4fYUpvsG64bTZUaet0IhGREkOF2hlsOZTEwJnrWb03gbY1yvBC1wbERgQ6HUtERKRwrJ0Kcx+AsFjoPQ3KVHc6kYhIiaJC7S/Ss3J4+5ttvPf9TkIDfBh1S2O6NC6P0QSeIiJSErjd8N0LsOQVqNQGbvkEAiOcTiUiUuKoUDvF8u3HGDRrPbuPp9K9WQyDr69DqSBfp2OJiIgUjqw0mH0/bJwFjftCpzfAW+2giIgTVKgBJ1IyGbFgM9N/2U+l0oFMvLsll1Uv43QsERGRwpN8BCbfCgdWQbthuaM7qjeJiIhjSnShZq1lzpqDDP98E0lpWfznymo8dE0N/H28nI4mIiJSeA5vzB3ZMeUY9PwE6nZ2OpGISIlXYgu1ffGpDJ69gSVbj9I4NpwXb25AnXKhTscSEREpXNsWwWd35E5efccCqNDU6UQiIkIJLNSyc9x8uGwXry/aipcxPNu5Hn1bVcLLpe4dIiJSwqx8D74cANH14NapEFbB6UQiIpKnRBVq6/YnMGDGejbFJdGuTjTDu9SjfHiA07FEREQKV052boH28/tQsyN0+wD8gp1OJSIip7igQs0Y0wF4E/ACPrDWjiyQVAUsJSOb1xdtZfyyXZQJ9uPdPk3pUL+shtwXEZGSJz0Jpt8B2xdD6weg/XBw6d5sERFPc96FmjHGC3gHaA/sB342xsy11m4qqHAF4dstR/jv7A0cSEijT8uKPNWhNmEBPk7HEhERKXwn9uQOGnJsK3QaBc3vcDqRiIicwYVcUbsE2G6t3QlgjJkCdAE8olA7ejKD4Z9vYt7ag1SPCmb6fa1pXlkTdoqISAm172eYcitkZ0LfGVDtKqcTiYjIWVxIoVYB2HfK4/1AywuLc+GstUxbtY8R8zeTnuXmsfY1+fcVVfHzVrcOEREpodZPh9n/gdBycPt8iKzldCIRETmHCynUTneDl/3bQsbcC9wLULFixQt4u3PbcTSZQTPXs3JXPJdUieDFmxtQLVI3R4uISAllLXz/Mnz3AlRsDbdMhKDSTqcSEZF8uJBCbT8Qe8rjGODgXxey1o4FxgI0b978b4VcQcjMdjPm+x2M/mY7/j4uRt7cgJ7NY3FpyH0RESmpstJh7oOwfho0vAU6vw3efk6nEhGRfLqQQu1noIYxpgpwAOgF9C6QVP/AL3viGTBjPduOJNOpYTmG3FiXqBD/wo4hIiLiOVKOwZQ+sG8FXPVfuPwJ0EjHIiJFynkXatbabGPMA8BCcofn/9Bau7HAkp1DUnoWL3+5hU9X7KVCeAAf3t6cq2tHF9bbi4iIeKYjW2BST0g+DN3HQ/2bnU4kIiLn4YLmUbPWLgAWFFCWfPtyQxxD5mzkWHIGd7WpwmPtaxLkV6Lm7hYREfm7Hd/AtNvB2zd30JCY5k4nEhGR81Skqpu4xDSGzNnIok2HqVsulA/6NadhTLjTsURERJz38zhY8GTuiI69p0L4xR3AS0RELq4iVagNmbORpduOMrBjbe5sUwUfL5fTkURERJx39DdY8ARUuwa6fwj+oU4nEhGRC1S0CrVOdbEWKpYOdDqKiIiI54isBf3mQWwr8CpSTbuIiJxBkfrXPDZCBZqIiMhpVW7jdAIRESlA6jsoIiIiIiLiYVSoiYiIiIiIeBgVaiIiIiIiIh5GhZqIiIiIiIiHUaEmIiIiIiLiYVSoiYiIiIiIeBgVaiIiIiIiIh5GhZqIiIiIiIiHUaEmIiIiIiLiYVSoiYiIiIiIeBhjrS28NzPmKLCn0N6w4JQBjjkdwsNon5ye9svpab/8XXHfJ5WstZFOhygqinD7eLEV98/JhdL+OTvtn7PT/jm3i7WP8tVGFmqhVlQZY1ZZa5s7ncOTaJ+cnvbL6Wm//J32ici56XNydto/Z6f9c3baP+fm9D5S10cREREREREPo0JNRERERETEw6hQy5+xTgfwQNonp6f9cnraL3+nfSJybvqcnJ32z9lp/5yd9s+5ObqPdI+aiIiIiIiIh9EVNREREREREQ+jQk1ERERERMTDqFA7hTEm1hjzrTFmszFmozHm4bznI4wxi4wx2/J+lnI6qxOMMV7GmNXGmM/zHlcxxqzM2y9TjTG+TmcsTMaYcGPMdGPMlrxjprWOFTDGPJr3+dlgjJlsjPEviceKMeZDY8wRY8yGU5477fFhcr1ljNlujFlnjGnqXHKRwqf2N3/UDp+Z2uRzU/v8Z0WhnVah9mfZwOPW2jpAK6C/MaYuMAD42lpbA/g673FJ9DCw+ZTHLwFv5O2XE8BdjqRyzpvAl9ba2kAjcvdNiT5WjDEVgIeA5tba+oAX0IuSeaxMADr85bkzHR8dgRp5/90LvFtIGUU8hdrf/FE7fGZqk89C7fNpTcDD22kVaqew1sZZa3/N+/0kuR/yCkAX4KO8xT4CbnImoXOMMTHADcAHeY8NcDUwPW+RErVfjDGhwOXAOABrbaa1NgEdKwDeQIAxxhsIBOIogceKtXYJEP+Xp890fHQBPra5VgDhxphyhZNUxHlqf89N7fCZqU3ON7XPpygK7bQKtTMwxlQGmgArgWhrbRzkNiZAlHPJHDMKeApw5z0uDSRYa7PzHu8nt1EtKaoCR4Hxed1QPjDGBFHCjxVr7QHgVWAvuQ1AIvALJftYOdWZjo8KwL5TlivJ+0hKOLW/Z6R2+MzUJp+D2ud886h2WoXaaRhjgoEZwCPW2iSn8zjNGNMJOGKt/eXUp0+zaEma68EbaAq8a61tAqRQgrtU/C6vL3cXoApQHggit7vAX5WkYyU/SvrnSQRQ+3smaofPSW3yOah9vmCOfN5UqP2FMcaH3EZiorV2Zt7Th3+/vJn384hT+RxyGdDZGLMbmELuZfJR5F729c5bJgY46Ew8R+wH9ltrV+Y9nk5uI1HSj5V2wC5r7VFrbRYwE7iUkn2snOpMx8d+IPaU5UryPpISSu3vWakdPju1yeem9jl/PKqdVqF2irz+3uOAzdba10/501ygX97v/YA5hZ3NSdbagdbaGGttZXJvPP3GWtsH+BbonrdYidov1tpDwD5jTK28p64BNlHCjxVyu1S0MsYE5n2eft8vJfZY+YszHR9zgX/ljSrVCkj8veuFSEmg9vfs1A6fndrkfFH7nD8e1U4ba3WF83fGmDbAUmA9/98HfBC5/eSnARXJPdB7WGv/evNhiWCMuRJ4wlrbyRhTldwzexHAaqCvtTbDyXyFyRjTmNybun2BncAd5J78KNHHijHmWeAWckdxWw3cTW4/7hJ1rBhjJgNXAmWAw8BQYDanOT7yGs3R5I4+lQrcYa1d5URuESeo/c0/tcOnpzb53NQ+/1lRaKdVqImIiIiIiHgYdX0UERERERHxMCrUREREREREPIwKNREREREREQ+jQk1ERERERMTDqFATERERERHxMCrUREREREREPIwKNREREREREQ/zf9gji+dMQ7RCAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Find the principal component directions and variances of each Gaussia\n", "Lambda, V = np.linalg.eig(all_covariances)\n", "\n", "# Let's show the mean vectors plus/minus each variance-scaled principal component direction\n", "fig, axs = plt.subplots(1,2,figsize=(15,5))\n", "for c in [0,1]: # city\n", " for s in [0,1,2,3]: # pick out just two of the seasons: summer and winter\n", " for m in [0,1]: # principal component direction\n", " x0 = all_means[c,s,0]+np.sqrt(Lambda[c,s,m])*np.array([-V[c,s,0,m],V[c,s,0,m]])\n", " x1 = all_means[c,s,1]+np.sqrt(Lambda[c,s,m])*np.array([-V[c,s,1,m],V[c,s,1,m]])\n", " axs[c].plot(x0,x1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now somebody needs to give us the transition probabilities. We know that each year starts in Winter, then transitions (roughly) once every three months, and ends at the end of autumn (on December 21, which we'll call the end of the year). So the probability of transitioning out of a season is roughly 1/3, and the probability of staying in a season is roughly 2/3." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0.66666667, 0.33333333, 0. , 0. ],\n", " [0. , 0.66666667, 0.33333333, 0. ],\n", " [0. , 0. , 0.66666667, 0.33333333],\n", " [0. , 0. , 0. , 1. ]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = np.array([[2/3,1/3,0,0],[0,2/3,1/3,0],[0,0,2/3,1/3],[0,0,0,1]])\n", "A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, we know that every year starts in winter, so we can set the initial residence probabilities, pi, to be 1.0 for winter, and 0.0 for any other season." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 0, 0, 0])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pi = np.array([1,0,0,0])\n", "pi" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's define a function to calculate the Gaussian probability, given a mean and a covariance matrix." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def gaussian(x,m,S):\n", " det = np.linalg.det(S)\n", " mahalanobis_squared = (x-m).dot(np.linalg.inv(S).dot(x-m))\n", " return( np.exp(-0.5*mahalanobis_squared) / np.sqrt(det) )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For example, for each month in the test data, for Carbondale, let's calculate the log probability that the given month occurred in any given season." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "B = np.zeros((12,4)) # B[i,t] = log probability that month t, of the test data, occurred in season i\n", "for t in range(0,12):\n", " for i in range(0,4):\n", " B[t,i]=np.log(gaussian(test[0][t,:],all_means[0,i,:],all_covariances[0,i,:,:]))\n", "fig,axs=plt.subplots(1,1,figsize=(15,5))\n", "axs.plot(B)\n", "axs.legend(('Winter','Spring','Summer','Fall'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, the low covariance of autumn temperatures may cause some trouble later on... \n", "\n", "Let's write a function that will implement the forward algorithm. Given a full set of HMM parameters, it will compute the scaled alpha parameters, and the Gain terms, G." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "def compute_alpha_and_G(X, A, pi, means, covariances):\n", " T = len(X[:,0])\n", " N = len(pi)\n", " alpha = np.zeros((T,N))\n", " G = np.zeros((T))\n", " sum_of_log_G = np.zeros((T))\n", " #############################\n", " # First frame\n", " for i in range(0,N):\n", " alpha[0,i] = pi[i]*gaussian(X[0,:],means[i,:],covariances[i,:,:])\n", " G[0] = np.sum(alpha[0,:])\n", " alpha[0,:] /= G[0]\n", " sum_of_log_G[0] = np.log(G[0])\n", " ################################\n", " # All of the other frames\n", " for t in range(1,T):\n", " for j in range(0,N):\n", " for i in range(0,N):\n", " alpha[t][j] += alpha[t-1][i]*A[i,j]*gaussian(X[t,:],means[j,:],covariances[j,:,:])\n", " G[t] = np.sum(alpha[t,:])\n", " alpha[t,:] /= G[t]\n", " sum_of_log_G[t] = sum_of_log_G[t-1] + np.log(G[t])\n", " return alpha,G,sum_of_log_G" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's test it by finding the probabilities for the Carbondale, given the Carbondale model." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "alpha,G,sum_of_log_G = compute_alpha_and_G(test[0],A,pi,all_means[0],all_covariances[0])\n", "fig,axs=plt.subplots(2,1,figsize=(15,10))\n", "axs[0].plot(sum_of_log_G)\n", "axs[0].set_title('Total log prob of Carbondale data, according to Carbondale model, as a function of month')\n", "axs[1].plot(alpha)\n", "axs[1].set_title('Normalized probability of each season, for each month of Carbondale data')\n", "axs[1].legend(('Winter','Spring','Summer','Fall'))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Testing\n", "Now, for each of the two test tokens, let's find out how probable it is, according to each of the two possible city models." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "alphas = [0,0]\n", "G_scores = [0,0]\n", "prob_scores = [0,0]\n", "for ref in [0,1]: # reference label (the city the data really came from)\n", " alphas[ref]=[0,0]\n", " G_scores[ref]=[0,0]\n", " prob_scores[ref]=[0,0]\n", " X = test[ref]\n", " for hyp in [0,1]: # hypothesis (the model we are testing, to see how well it matches the data)\n", " means = all_means[hyp]\n", " covariances = all_covariances[hyp]\n", " alphas[ref][hyp],G_scores[ref][hyp],prob_scores[ref][hyp]=compute_alpha_and_G(X,A,pi,means,covariances)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig,axs=plt.subplots(2,1,figsize=(15,10))\n", "for ref in [0,1]:\n", " axs[ref].plot(np.linspace(0,11,12),prob_scores[ref][0],np.linspace(0,11,12),prob_scores[ref][1])\n", " axs[ref].set_title('Log Probabilities of the two Models, for Data from %s' % cities[ref])\n", " axs[ref].legend(('Carbondale Model','Waukegan Model'))\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }