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@joemilbourn
Created October 28, 2012 22:18
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Example ipython notebook file with a simple k-means algorithm
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{
"metadata": {
"name": "k-means-2d"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# k-means clustering in $d$ dimensions\n",
"\n",
"Given a set of observations $(x_1, x_2, \u2026, x_n)$, where each observation is a $d$-dimensional real vector, k-means clustering aims to partition the n observations into $k$ sets $(k \u2264 n)$, $S = {S_1, S_2, \u2026, S_k}\\;$ so as to minimize the within-cluster sum of squares (WCSS):\n",
"\n",
"$$\\text{arg min} \\; \\sum_{i=1}^{k} \\; \\sum_{x_j \\in S_i} \\; \\left|| x_j - \u03bc_i \\right||$$\n",
"\n",
"where $\u03bc_i$ is the mean of points in $S_i$.\n",
"\n",
"See [wikipedia](http://en.wikipedia.org/wiki/K-means_clustering) for a complete explaination.\n",
"\n",
"This notebook shows a simple example using k-means clustering to determine the centre of point clouds in a 2D space."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Set up the environment"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"from llib import coordinates\n",
"from llib import colours"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Build the point clouds\n",
"\n",
"Set up *nclusters* of points at random coordinates. Each cluster of *size* has *npoints* normally distributed about the centre."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"nclusters = 8\n",
"npoints = 500\n",
"stop_diff = 1\n",
"size = 1000\n",
"clusters = coordinates.random(0, size, nclusters, 2)\n",
"data = []\n",
"for cluster in clusters:\n",
" points = coordinates.random_cluster(cluster, size*0.1, npoints)\n",
" data.extend(points)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 36
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Show the cluster centres (red) and the points (gray):"
]
},
{
"cell_type": "code",
"collapsed": true,
"input": [
"scatter(*coordinates.to_xy(data), color=\"0.7\", label=\"points\", alpha='0.1')\n",
"scatter(*coordinates.to_xy(clusters), color='r', label=\"Cluster Centres\")\n",
"legend(loc='upper right', fancybox=True)\n",
"xlabel('x')\n",
"ylabel('y')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 37,
"text": [
"<matplotlib.text.Text at 0x7ff59a364cd0>"
]
},
{
"output_type": "display_data",
"png": 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qlVxfSzqddjWRRCLh6kelUsltH7CgTsXf7cwwCvdQbvl8vm0w5oTy0f/3/6Qj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\nYII=\n"
}
],
"prompt_number": 37
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Seed the k-means algorithm with *k* initial, random, guesses for the cluster centres."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k = 8\n",
"centroids = coordinates.random(*coordinates.extents(data), \n",
" size=k, dim=len(coordinates.to_xy(clusters)))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 38
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Show the cluster centres (red), cluster points (gray) and the inital centroid guesses (black, crosses)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"scatter(*coordinates.to_xy(data), color=\"0.8\", label=\"points\", alpha='0.2')\n",
"scatter(*coordinates.to_xy(clusters), color='r', label=\"Cluster Centres\")\n",
"scatter(*coordinates.to_xy(centroids), marker='+', color='0.1', label=\"Centroids\")\n",
"legend(loc=\"best\", fancybox=True)\n",
"xlabel('x')\n",
"ylabel('y')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 39,
"text": [
"<matplotlib.text.Text at 0x7ff59a5f8c50>"
]
},
{
"output_type": "display_data",
"png": 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231esAGKxdoLJZNp+/6//An7wg7bHNm4Epk5tO0Y6DRx+OLB2LVBc3Kv3tbGx\nEcW9fG5v4PV68cknn6CxsRElJSWYOHEigM7DW//5n/+JW265RYWjbrrpJtxxxx34+OOP8bWvfQ0A\ncPPNN8Pr9Xa59tLS0i7X8tlnn+Evf/kLXnjhBdjtdtjtdlx77bV48MEHcd111wEAxo4di4svvhgA\ncNFFF+Gqq65CXV0dysrKuly3XNOjjz6KK6+8Uo0s/vd//3fcfvvtijji8Tg+/PBDlJSU4MADD+z5\nBg4SdKWTRr/Bim2ZEsxQUnevoZGlEaU2wtAT6z4oSLOaPJ1OZ42tJekkk0m0trYqggmFQlmZTzTm\nDAcxVCQ1HqC94DA3O40gOVFsj8ViHToJU/uIRCKIx+MqnbinQVb0UqQ3xayupqYmpNNpuFyurGp6\n6YV1qRPcems7kQBtP//ud+2PNTS0kYdEPA7s3s03DJg+HaivB4LBtte9/z7wVWipNygpKUFTU1Ov\nn98THnnkEXz44Yc4/PDDccwxx+C5557r8rm1tbW49tprUVRUhKKiIuVhNDQ0qOcccMABXb6+tLQU\nu3kvujh+MpnEAQccoM5x5ZVXorW1VT1n9OjR6mdqibJjQWcbL7mm2tpaLF68WB2/qKgItbW1aGxs\nxLhx47B48WLceuutGDVqFM4777xhy3jVZKLRb+S2LeHPXe2SST5MpaXuQb2AhGQymVQasMvlgtfr\nhdvths/ng8fjycrIMpvNqqZDeioya4piPYVw6hQMKzFEBkAVXsrUXHoD8rpJbp3dE5KWTDPuDjIF\nWIa8GObjeeRURmaf8Zr8fn/nBxdGU7wRbcQAAOecA+TOfLHbgbPPbvu5rq7tn0QyCfzP/3R7TRLf\n/va3AaBDEbOE/AzJNHAAahgYcdhhh2HlypXYtWsXbr31VsycOROhUKhLo/zYY4+hublZ/QuHw5g8\neXKv1n7aaafhL3/5CxobGzv9++jRo+H1etHU1KSO39raig8++KBXx++NB3/AAQdg0aJFWdcQCoUw\ne/ZsAG31d2+99RZ27NgBh8OBn/zkJ706d76hyUSj35CCM9HdSFcKzVJQp2aQK3RTxGaXXZIBQz9S\n9Kbnwt2enMpH0RuA8nQYQpIiuKxW57lzjXhf0dvXyb5bcoJhKpVS8+x5jUwSoKbINXaZCnv66UBu\nNlBFBfBVJiUmTQIWLgScTsDvb/v/zjuBrwqF4fd3rpF0E/rJRUFBAW6//XZceumlePnllxWZr169\nGjfffDMjjUnjAAAgAElEQVSA7M/Q4YcfjlAohFWrViGTyeDee+/N0oVWrlypyMXn86nQZGFhIUwm\nU1aX4ssvvxx33303PvnkEwBAKBTq1pPJxamnnopTTz0V06dPV5pKMBjEf/zHf+Cxxx7DuHHjcNxx\nx2H+/PlqjZ999hneeuutXh0/d9xwZ7j00kvx+9//XoX7Y7EY1q5di1AohI8//hhvvvkmUqkU7Ha7\n+m4MBzSZaPQbZrNZZUzJnXRXQ5SodxC5AjdBAmAoJxqNoqmpCcFgUIWWKHSHw2FVnChng0jBW57T\n4/Go2DaArFAXDVpneslgw2azZYnsbNXS2tqq1sPKfcMw4PP54HQ61bjfLtvX/Pa3wNe/Dni9gM/X\nRiJ/+hMg7/lNNwGffw688grwxRfADTe0/83vB773PUCmervdQB/TSW+44Qbce++9mD9/PgoLCzFy\n5Ej85je/wVlnnQUgewNQVFSEJUuWYO7cuTjwwANhs9mysruef/55fP3rX4fH48GPfvQj/PGPf4TH\n40FBQQFuuOEGHHvssSgqKsL69esxZ84cXH755TjzzDPh9/tx2GGHZZFJbzyD//7v/8Ypp5yCc889\nFz6fD4ceeijeeustVWj9zDPP4PPPP8fYsWPh9/txzjnnYMeOHR2uq7NzXn311Vi+fDkKCgqUxpKL\n73znO/jVr36Fiy++GD6fD2PHjsXDDz8MoI1Yrr/+ehQVFaG0tBSff/45fvnLX/Z4TYMBPbZXY8Cg\nBsIspq6+oDLzCmgnDY/HkxXWkOEeeiXsm8VOv7JIkH+PRqPqdUwXZk0GPRi3262MM5snsp5kuD4/\nTCCg18bPMu8pr4FZXn6/X4XP5OyTsrKyzq/BMID33gOiUeCb3+zoqfSEdLqNlB59tI2Qbr4Z+Ld/\ny8/FawwZBntsryYTjSGDYRgIh8NZDQ5lwR7Q3iolGAyqMBezseQMD2Z6yVYi7LPl9/tVYSHQ5o3I\n9vByFgrTizuDXJesvu/quQD65c2wil1W88tzcU4KW+MXFxerzsH0CpPJJA499FD9HdDoEoNNJvtU\nOxWNPRscNCUzqqij0LAzM4lpuBTYWQBIYuHwKu7aSVCyIJAei8wek2I4q967ghzD210XZPbZYvPJ\nvoJaDkOFMo2Z62B4z+VyIRQKqcd5vj29Al5j34cmE40hBYvypOdgMpmU9sKWIrKOQxIAd+6cpEgh\nnwIkNRZmVeWOxpXoyQD3drdGo86sr756JxT95b/OwGulniK9M2pIiURijx/jqzH0iEajeW/Lkgst\nwGsMGN0ZwO5eA7RXfQPISt8lmTC7qbNuvMwKk6m49CIo0vO50nMZDMiGlH0FW7xw2mJuxb3sKsB+\nYLxmWfdy5JFH4le/+lXeZ8lo7L1IpVLYunUrZs2ahVNPPXVQz6U1E40BgXUZ1D9cLlevUhMzmYwq\nTmSIK5VKweVyqXG3bJLIwj+K+zTaLADjREQSCA0vs8p6UzSYFxgGXJs3w1FXh9BRRyHVi/TZvngy\nLpcra1YMi0SBtur5+vp6XHPNNdi0adOQZqJp7Lkwm80YOXIk5s2bh5///OdZqeeEFuBzoMlk6MER\nstw5M6zk8Xj69PpoNKrmctjtdtVmnWI9U2LZRZfV8QzzMNOLBpQGms8fCsNqSiQw7vrr4X3/fRhm\nM8zJJHZedx12X3DBwI/91WdbtnoB2smS9SdOp1OlC7P6nm3qKeI7HA7VaZn3L5PJwOfzAWjv/eX3\n+/sdFslti/PGG2/gySefxMaNG/HZZ5/h7LPPhslkwoIFCzo0dNQYemgyyYEmk6EHDbj0RFKplCok\n6w1yZ4dQFwCgJh4mk8msOesmkwkul0v1pJKNFodLiB7x9NMoe+ABWERrkozdjk3PP4/kiBH9Oib7\nnNH7y4Vspe9wOOB2u5VewmJPEojX64XNZlP3Uw73kpoPANWtOB9jBIhYLIa3334bF154IT788EM1\nSkBj+JEv26k1E40BITfrqK+gIM/KdjlMKhwOZ/XhYgiNBMJ0Wpl1NVwo+MtfsogEAAyrFd5+NimV\nUyK7a0/DTDCSCWtwrFYrfD6fqk1hvQq9vlQqBYvFAqfTqbwUt9utSER2ABgomGxBL4SdD3QG2r4F\nnc2l0W84HA7VE4nhF1aiDxTBYFBlZcmRuhS6WcDIavHBEtZ7i9iYMfC9+y7M0kAaBhLdNBHsDkyJ\nBrKzzqTGIkcAW61WVU/DTgQs4kyn0wgGg/B4PHC73aoTsdVqVcI/OxMzZEnSzsdcGq5x9OjR2LJl\nC4D2FO58HF9jz4D2TDT6DYZDGCphzH6gSCQSKhzDHTJbxXOYFetUnE6nWoPFYoHX64XT6eyypctg\nofGii2A4nTC+Mo5phwPRww5D+Mgju3xNd4aUIazclObclvipVCpLCwHaxxOTJNgAMxAIKI1J1tj4\nfL6sWSsksnx5Dp1tLmTWmsa+Ae2ZaAwIFMLzBc5k586VRo3eBycisnLeMAw1P4VV4fSUGAYbinBK\ndPRofLhiBUYvWwbn9u1oOfFENJx/fnYPrBz0FJbjfeXYXkkkFLcpuJN4OQ+eIjsz2ZgtFwqF4PF4\nlDGnRiVn0bPLQL7mynNEQSqVUuFIdnXW2HcwLAL8woUL8dRTT8FsNuPII4/EH//4R8RiMcycORP1\n9fU44IADsHLlShQWFgIA7rnnHixbtgwWiwWLFy/GtGnTOl6IFuD3WrC/VCKRQCwWUz28aOA4npaV\n5nyvKTw7nU4Eg0GV8SWNoM1mU0ayP58RW309Mg4H0l99FvOFntZCLQSA8iZyq/eZOUcPhqEuq9WK\nXbt2KSKR6dIc3MVBYBTpWZuSyWTg8XhUqKu3mXk9ge+BzMTTnsmegb02m+uTTz7BtGnT8NFHH8Fu\nt2PmzJmYNm0a/vGPf2DcuHG47rrrcP/992Pbtm1YsmQJNmzYgCuvvBJvv/02vvzyS5xwwgnYvHlz\nhypfTSZ7J5gCzFAMs7a4Q+YkQYZlSCIs5mP1N2eQ0OgyNdXr9aoW7kDv247Ya2tx6A03wFFbCxgG\nWo8/HtvuvBOGCOP1p9q9t6DXIKdEMm1XzlmhZ0YUFxfD6XQiGo2isbExi4Do6djtdhQVFSldhaHD\neDyuQoSZTAZer3dAXifDcPREhqs1ukb32GuzuYqLi2Gz2ZQBiUQiGDNmDFatWoW5c+cCaBv2UlNT\nAwCoqanBrFmzVFfUyspKrF+/fqiXrZFnZDIZtLS04PPPP0djY6NKM3a73Vlt7Lmr5i7Z5XIpkZ8N\nH0kyDH8B7RXzssK+1+Euw8Ch118P57ZtMCcSMCeTKPjrX1H2u991uIbBgpypImt42CGAREIjYBgG\nHA6H8vBSqRQKCgrgcDjgcrmU8A5AZX0xu4s1KoWFhbDb7YqEeyKS3NCbBBtrRqNRxGIxVaCqse9i\nWMjkxhtvxJgxY3DggQeisLAQU6dORUNDgxqpWVpail27dgEA6urqUF5erl5fXl4+bGMpNfKH1tZW\ntLS0qF03aymkDsAmji6XS3kaQPaceQrv1FdosKizsCiyL7qJrb4ejs8/h0ns1syJBIq7mRQ4WCBB\ncmcv7wMJ1Gazwev1ZhUrmkwmlerrcrkUoXAiIz1AFiwy7dpqtSqSlqD2RPKKx+MIBoPqX+79lckA\n1Lei0Wje7stA2tdoDA6GXIDfunUr7r//fmzfvh0FBQU4//zzsXz58rwce9GiRernKVOmYMqUKXk5\nrkZ+kUwmEQwGlcjOgjwSAgAVq3e73UilUmpmN5tEUhuRIa3O2qb0a0Ki0wl08rpM7njbQYYc2Uvi\nlOOIWVPidrvh8XhUF2aPx6M8O4bA6MHxeNRICgoKVFowwx3RaFRNowSgujaTSNj2n+vgIDOv16uO\nkTsITc5fGahWwvPxvWWNktZgeod169Zh3bp1eT/ukJPJ+vXrMXnyZOWFzJgxA2+99RZGjBiB3bt3\no7S0FA0NDRj51VjR8vJy7Ny5U72+tra2yxYMkkw0hhdsg5LJZNRAK0LOOadRZMU2w1escudUxOLi\nYoRCIWWouPNlqEe2Vxnw2gsL0Tp5Mgr+7/9g5lqdTnxx8cUDPnZfIGeppNNpNXKYdSQkU9kbTRIJ\n0G7ESeAMFzqdTkUsrH6nZsUQW0lJCcxmMyKRiPIAOZNGToZkZ2Y5ToCDvqhtUucaqMHn+WW2XiwW\nU16sRs/I3Wjf1sepmV1hyMNchx56KN5++22103nllVcwbtw4VFdXKw9l+fLlqK6uBgBUV1dj5cqV\nSKVSqK2txaZNmzBp0qShXrZGH8AUVO6Ew+Fwp+1AYrFYVnt4r9eLwsJClZEkZ5v4fD6UlpaqVFa3\n251VQ8GQDUMqPaEno7btrrvQ8P/+H5LFxYiXlWHnDTegcfr0ft+T/oCeG5tYAlBeWDQaVW3FfT6f\nMtokWtlBmanCbDfT2tqqUodZX8LWNXw/EokEQqGQChvynsoZMRKGYShvge8dkyLokeSjPUtuEgI9\ntq70mI8//hhlZWUDPq9Gzxhyz+S4447Deeedh6qqKpjNZkyYMAE/+tGPEIlEMHPmTCxduhSjR4/G\n008/DQCYOHEipk+frp7/8MMP6x3IHg5qH4ztc5ohDZ70QFixzUmCHJAlOwfLtiFAW4dczi9hMSM9\nFu6eu0Nuq3sZCmOYxnA6UXvjjai98cZBukvdg2I70K4PpFIpBAKBrDXHYjE0NzerokWGvujFAFDe\ni0wTZuYbq+aps1B/4nnlvaHnQe+For+833yvSe58P+WEy4Ggq2N09Xgsp8WNxuBBN3rUyDuCwSCA\n7MrnVCoFv9+vMvjYgp4hFY6kpcdBY8dwCnfVNFLUVij+yse6A8NnPA53tkPWpr4PkCnADDMxfMQQ\nD3UVemxsshmLxeDxeBCNRrPCQgxD2Ww2+P1+FBYWIhAIoKWlRYXPGF60Wq3w+/1K1KfHIosOTSaT\n6jDMDE2SCJ/LTQIAdeyBIBKJIJFIZH2+2AWB+O53v4t33323w2sXLFiAq666akDn39egx/Zq7LGw\n2+2q6BCAMnZy98hah1gspmodmKHFAkO5m2VhnqyaZmhDDs6SQ7K6WhubIjK7KLfQcajQU51KZ3/j\ndVJnYoaXbHxJggyHw0q0Z4U8a0o8Hg/sdjtaW1vVufgvHo+rtGGGDRk6Y3NI9tUiifH95aRH3n8a\nKq4tGo1m6S39AdclPdzc0OYDDzyAV199FR999BGWL1+OO++8EwBw/vnn9/u8Gt1DeyYaeQeNBj0F\nehw0nhSC+Xs6nVbtO7hrpoHMJQ8aEab98memtaZSKYTDYbWOXDidTrhcLhQUFKC5uVmF5Lhj7y/6\nU8DY3WdWZmvJWht6U7l/o5EnIQcCARWykp4bn+fz+WAYhsqq4zoo6peWlmLEiBHK8+Hc+VgspubE\nkKiYTZVMJtHU1KTWyvCcnJiZSqXg9XpVvzUSDSvy842NGzfijDPOQF1dXd6Pva9AeyYaeyxY40Cx\nVBKC2WxWXgGNodfrVaIyq6ZpBNk+hTtqt9utjGNRURECgQCam5vVbjmZTKoK7s7mvlNPYIt32fer\nr9fIdQF9S0GWxCMr3IlcfYH3j94HvTTeH14vs65kLy4mKNBzkAI6a1fYMJM6DUmIa8qdbc96Ht5z\n1qSwjT3fc2boUevi8bhWepQMfXq93j69B73BmDFj8n5Mjc6hyURj0NDVTpOFeAzJsCEhGxUC7Sm/\nNKrc/QLZ4nRBQYFqtc7XyQaJMnzFHVgikUBLSwucTqeK9dOb6cu1MbVZ1oP0BvSgZKhGrg+AIkyZ\nyJB7HSQi3g+SJB+npydDhzwn181kBmoQkUhEpdumUimMGjUKdrsdHo9H/Y2aGGta+B5R0JckQhIi\nOVGv4jXLBAqmgecTBQUF2isZImgy0RgWyOaDAJSxk39n3J7GtDPvwWKxYPTo0WhpaUE0GlXxfiC7\nCtvhcGT17qI4XFxcrDoV9wW5GWD9eS0NumxcmTtHhOulAC+9C0lgPAabNvJa5Zx4GY6ieM8OwsFg\nMKvrstVqRTAYVPeXRBAMBuHz+bIIOxKJqCFbXCffTyZUkPzogbLrAdeRTCZVo86h7OHFTYvuGzZw\naDLR2CPATCWCO3RqI8wgYmydu13uyouLixEOh5Wxyg1dSQ+Fu2DZkkNmTvVGjJc9sfoi3tOwUuPh\nuWUars1mU23l6XHwWujBce0AlBBvNpvR2tqqjsVwlAzJpdNp+P3+LMJi6JChJ4bESLLUYfh6V04n\ngObmZhXe4iZAFhS6XC7lVQJtSRBsccN7QC8mmUxmPTdfoPfD+wRAdanm48wo1OgfNJlo7BGw2Wyq\nHYiq9TAMJSRTcGYHYVkEyXRTtk+nmM4QjkxTpeGW7e0pwgPtRYHdha2kftAb8ZI1LSaTKSvRgNdA\nspDtTuhNyLns/BvJS+o1XH8ikVC9zJjZxmPQyLvdbuXBsY0/Ex/oWcg1kLx4/6ljAVDFjwyLxeNx\n+P1++Hy+rDVJ8mb/Nda+cH6K1GnyhdxkEADKW4pEIoo4c1vCaPQdmkw09ggw3i533axDYRW40+lU\n9Q6ssmYDQbmbpnEymUxK6KchZgaSnCvP+gm+noZHZpXlCubMqKLQ3J0RlEI2rzVXT2AIKFf05nOo\ns/D5nYVl+HpmXPE4mUxGeSOJREJ5ErKpI0mCBp4eGz0OriWdTqOlpSVrPj2JgCQUDAZVtTu9TavV\nmrUBoCcgCyXpfeYTLLSUSQD8vMj2Luztxs+WRt+h75rGHgOTyaQEWKYP05gnEglVF0LjFQ6HVaye\nhBEOh5VRYFiMBpLV2lLoZ6qsDHlw5yyJRta+0HvhDl32iZLhJ0ISEY/PwkMO9iKJklRk6q/UUSjc\n52aP5Z6bxpJkIj0+Nm60WCwIh8NZc+N5LpIuX897CCDrb8zA4/vGmpbW1la1FrfbjebmZtXtGUDW\ndfA6pT6WL0ixH0CW15uLXB1Po2/QZKKxR4K71GAwmFVRzR0xd8XJZFJ5KGazGT6fT7VHpyF2OBxZ\naajMIAKgYvc+nw9Op1O1cLHb7cpbAdq9CYfDofQMkg935QyxyWJIejE0YozdUyznjplGlIZdjrWl\nUM7r5jXk1rZIEmM6MMNTbD8j70Nzc7O6Rt5XEjDQpm2EQiEVEpNtbUiEJCZZC8OQHQmT2g0JnkTH\nnmuywDHfkLPu+bkC2jYkJFJJ1loz6T80mWjskeDkPxpgiswMxeRmDbF9CD0QhrJoKAyjrdssjSef\n09zcrAwjjR9JQBYIypYmJDFCtnsBkGUsGcKhoeSOnAZdkqV8TjAYRGFhofKApEjc0tKSdczOIMNH\nXAe9EoI/yywsroWtWPga1uQw3CiLF4G2FF+GHjmPhmFD2XgyGo2qEBi9w8H0BqjFySQJhva8Xq9q\noilTzzX6B00mGnskHA6HahhIYy9JhWThdrvhdDrR2tqaJYoz3u/3+1XPqNzWHjw+ACXS2u12uN1u\nuFwuFe+npyB30LkdinNTeGUYRabz0lMC2gxwbmsRagcU6NmaRrZMYRiPIbPOQjay+JOQ2Wuy4JK7\nd5IJdSCK6ww3MrxHr0c2lJREyjAd602A9jk01HSGyniTGGUrGRnizNeMew1NJhp7KGh0+WXnDpkG\nmzUMLpdLhaoYWmHoiMaSxi4ejysDKfUFhl+A9tkeDEHJ0BGNDxsfyhRYEpHP51PpzJzxwV06jTCP\nRSKSWU78n2thai1JQBr4zir8ee9o0FkUKY05PTbeRyk+y1Bgbu0L10oyovbD45Ag+FyLxaKSKPh3\n2ZCShDbYWoUkcI3BgyYTjT0WFMI5HwVo663FAkSzua3deTKZzDK4yWQSBQUFANrTZuVsDR6bP8uQ\nGABV7wBAicKy0I96B3WA3GwvEkZuBTp3xTwXSYHeEz0h6hey9oTr5PV01yFZajOdteVno0R2A6CG\nxPXx3DJdOrd1i6xdkfqNJFxeC/8xFOjz+dSIAZ6H2WUaey/0u6exx4K6iexHBbQXHdIYM0OIoZrc\nFiqhUCgrjMVQmUwLldoIQzrsBcbwErOWKI6HQiHV3p2730wmo+peWGzJ9TJjjOfiOUhUsr0MjS8f\n4+tlNlpXUyVlXQtDV7J4Ud5P3gOSIB9nOq3UXWTbexKKFK45h4YJDKlUKitcyfeD+pU8fjgcVu3z\nNfZOaDLR2GNBwT0UCinhl+3G4/E43G63IgeSCGPjbP/Bjrc0XCQnGi0acqC95xd36DJTjEaTHW9Z\npMdwEcM77EnFNFhWlzPExXCL1WpV7fc5bpdeFftX0dhT54nH4yr81B2YuUWiYuYbdQ56ddRUcivD\nZYNOSUgAVDiQmW1MaGBNDz01kh+HnpGQmGknm0XyvaNGpDOq9k4MyzagpaUF559/Po466igcfvjh\nePvtt9HU1ISpU6eiqqoKp59+OlpaWtTz77nnHhxxxBEYP3481q5dOxxL1hgGsIGjFOC5y6ahk8ae\nhYsulwsej0f1oQKQlcFFkuIo4MLCQtWxljqI1WpV2VQ0jsxCkqEd7uaZfhuJRBAIBNDU1KQ8C6fT\nqQZRlZaWoqSkBAUFBcow05BzxghJip4RRWsSXXeQoSkp7ssdP0mMayY50dAnEgml6dATokfjcrmU\nJ8jwXTweRzgcRiwWU4TH17MbAY/De8/3j6nYHENML1Jj78OwzDM5//zzMWPGDMyePRuZTAahUAgL\nFizAuHHjcN111+H+++/Htm3bsGTJEmzYsAFXXnkl3n77bXz55Zc44YQTsHnz5g7dRXvT1kJj7wE9\nCoZWwuGwCrUwVZY9nxj7lyEnVtRzljmF5FAohEQiAY/Ho9KBmZEkixM72yHTqIdCIQQCAUVuALK8\nCq/Xq9ZNL4fHkxlnu3fvVkI+iYKGnCEiEiU1H6ay5hYtStCbIDHJuTJ8rRS9ZXhN9jujlkQSYCGn\nzWZTacOJRCLrePS8fD5fp+1Z+B1lbQq9JknW7P810CFaGr1DvmznkIe5Ghsb8Y9//APPPPMMACgB\nctWqVVi/fj0AYM6cOfjWt76FJUuWoKamBrNmzYLFYkFZWRkqKyuxfv16nHDCCUO9dI0hRG5qrcPh\nUAYMgDLQ/LtsSQJA9VqiUWLxHjOKPB6P0hZoAHtqgU6jzkaMUkCWmgLDYyzoY0iJ4TZqQRyNKw05\n9RWGzVg/w0QDqVl0BkkS1FhIuFJYl0TC19GbkMV7fJweEb2JeDyuyJhiu+wQQFLk/QegBpfJECPv\nu2wmyZRimSlGcqRHo7HnYcjJ5OOPP8aIESNwwQUX4MMPP8QxxxyDhx56CA0NDSgpKQEAlJaWYteu\nXQCAuro6nHLKKer15eXlqK2tHeplawwxaDToUVBvYEFcrlHJbZvB3T0NGgdHsS6FGVV9idFTw5Dt\nThgmkh4T1yNneoTDYWVkaeQZamMLGJvNpgaFya7HMpVXGv/OdpMU8qUhVi1c6upQtHYtDKsVzaed\nhlRpadb9kl2MeSyGtpjRRU9EFnfKKn96WrJxJI8lPRh6kNRM+DxZREjSkqnOHo9HeTAaexaGnEwy\nmQzeffddLFmyBMcddxyuu+463HHHHXk59qJFi9TPU6ZMwZQpU/JyXI2hB9NFWa8BtKW0shdXLqRI\nDmR30qXxIgFxqFNnmUNSkJb1HgyBUZthk0Kuzev1qufI7CWGamQxID0VACguLkZRUZEiExp+dlCW\njRJlI8yewNfRy/C++SbG3ngjkE4DZjPKHnoIH//udwiPH5/1fJI1RXp6NTwWhXm+hh4Sr4ekyqFZ\nzNoKh8OIRCLqftDTANrDh0zJlplsPC8fSyQSqj2ORv+wbt06rFu3Lu/HHXIyqaioQFlZGY477jgA\nwHnnnYfbb78dI0eOxO7du1FaWoqGhgaMHDkSQJsnsnPnTvX62tpaVFRUdHpsSSYaez+sVit8Pp8i\nhu7SRp1OJ0KhUFalO4Vi2VUYaPcaZCEbW33I1u9utzur7T1DOpFIRIXEiouLVUaT2+1WHghrJqgH\nAFC1MrLdeigUgtvtVtlRgUBAERK9BBYU8hwUuXsDwzBgNplQvnAhzF8NCyPG3H03/vXUU+p3NtTM\nZDKKtGWXYpn1xXtIcqFXwwQJJgyEQqGs+yEHdTFMyF5gvFcsRJWQYTnZoVij78jdaN922215Oe6Q\nZ3NVVFSgtLQUW7ZsAQC88sorOPzww3HmmWdi+fLlAIDly5ejuroaAFBdXY2VK1cilUqhtrYWmzZt\nwqRJk4Z62RrDBBnL7w6sqmb6sNfrVcV/PA4hPQOC4SeGb0gu3KHTY6DWIivZuXunJlNUVKRmeshM\nL6B9ZC8JktlMTBVmRphsa89QnNvthsfjUc0YmUTQHTKZDDItLbA2N3f4m+vTT7N+J4lFo1EEAoGs\nqnaSscPhgM/nUxMaGa5j0SH1HHqUTFKgdkOyYbdhvo4dB2Q2m2xLL0Nk+SaS3OJQjf5hWOpMHn30\nUVx44YWIRCIYO3YsVqxYAcMwMHPmTCxduhSjR4/G008/DQCYOHEipk+fjqqqKpjNZjz88MN5n3mg\nsW+gs7YZuboBgKyW6QQLHglZtyJHCkuNRQrVNptNDVvKneooM84YqqEGwQypYDCoSEx2+5XzXbhb\nZ3YV03XZeLGre5LxeJD2+zsQSmzMmE6fz2ttbW1VayehUiPx+/3w+/2K9BjaY9djtlKRExf5M8Gp\nmRKy9Qw9EBI671U+Cxtl7Q4JWxdO9g/Dkho8GNCpwRpdQbaFB9qb/0mjwXbkJAfZC0w2ekwkEigo\nKFCftdz6jdyKfZIJP5/Nzc0qK43HZGGjTBqghyCbJsruv/QSKO73NDq46LXXcNDPfw5TMgnDZIJh\nteKTJUsQmjgx63kkSKlfsF6EhGsymeD3+2E2mxWZSE+KiQ28JhKQzBCT6d1+v18ViTIBgZ4ISZXv\nCbsg0IsZCJhhJ6ctmkym/W7aYr5spyYTjf0CrGeQQrwE61qk9yIJQablFhQUqMJFhrsYkqHXIWti\npKbb/L8AACAASURBVGFsbm5WO3iG29gShnoLjaQkQBka47GY5Ub9pLuUYQBwbduGojVrALsdu884\nA4mysg7fG3k97LLLcJasoqd+A2TPpZdpxPyd94MZXtKzY00JQ3ic+shz8jp5/VJfYQeE/oKhOOmR\nplIpRWj7C/baOhMNjeGAbBfSGdgqheEV1j0wG0nWSjC8RM8FgKq8589Ae10KwzPs1SX7ZfGYnEMv\nCwEZ8mFYK7edfC65dLebNplMiB58MKI/+EG7Af6K+GSdC0lONq6k1yE9C3oMDEkRMuWaZMTrZWU8\nj5E7AIxTJ0n4NPYej0elYMt1sFanv+jqfu1PXkk+oclEQ+MrsCaFoH5BY87dWzgcBpBtENl2npXw\nNMAkMRYo2mw2VZEvzwG0dwtmGxgaztw2+MyuomfCUFzuuGAJVtcDUDt87vYZcqJXBUD13ZK9wHI7\nENMbywVrZBgyIyEC7R4Wr0P2TKNHIiv1c2tuZKhtoKI5U6DpsXI9WjPpHzSZaAwJGHMH8hPvHgow\nlEMPhITBIjp2xGXaMgVm7q5ZU5FOp1WrF4/Hg1Ao1GGYVG4ICICqhAfaw3Q04E6nM8uToAGWHQKA\n9mLOXKMva0QYxgPaa0lkA0cJSVjdhUfkNEnen1xviucm0cp0Z/l3Gnd2H2DITX6G2C2AhMdiyO5A\nb5R6FGtsNPoHTSYag45EIqEqowGocM/eMLBIisWsnWDlN2so0ul0lnDMHTWNKEmAqbFMtZW7cJKR\nbEnvcDjgcrmyZpfQGHOHz/5ZFM2ZjUVDTwOeewyCQrv0PghJTJ0J/LlEImtRZOhNJgvQG6CXRCLk\nPHmmDZM0eL3sOEBylrPq2d9P3m+2tO8pZGWx6GmL+UKX/twDDzyA5k5y0zU0+grZRTZXNN5bwFAX\nwQI/Gs9kMpk1s569tDgtEWgnVe7GZZuQ0tJSNfudLURyZ67IGhgSgGwiSUNKw8/KcXo/bEcjK/e7\nClVJdJUpJod8dQZ6OLxO1tHY7XYUFhaqSZlMbZ4+fTq++93vqj5sbDMTCoUQj8dRVFSEwsJC+P1+\n1YEAaM+iY7t9ele9IUCN/KFLz6S+vh7HHXccjjnmGMybNw+nn366FqY0+gUZqsh9fG/5TNFoMnQj\n27zQiAPtrVtkRpMMJ9F4cxwvvRwSjGw3IkmJHo0Uu6lFcNcOtNVuSO+Ar5G6QHfaSl9Ag02y4HWw\n4JOaCQmWHoTdbkdBQYG6Vwz7bdu2DalUCrt371ZEzdY11JFkGIqt76lhOZ1ORCKRTlvuyBk09IT0\nZMf8otvU4Ewmg7Vr1+Lxxx/H3/72N1xwwQWYN28eDj300KFcY6+gU4P3XLCSnKEf7k6l2L2ng2Et\noG0n3NLSogY/cQdOw0fxXWZEsZ6EQjPDZ7wfZrM5qy07vQ2LxYJwOKx0mNxqen7u6bnwntK7YViI\nGolsmz9Q0ONhSI6CPcFQlPSE6CGRUJLJJI444ohOj//iiy8qYnY6ncozYd1LKBRSyQzpdFp5XqlU\nCm63W4W5qGPx/AxF9meyo5xvv69gSFKDzWYzRo8ejVGjRsFisaC5uRkXXHABpkyZgvvuu2/AJ9fY\nP8DdshTge2oD0hN4vNyBS4OF3NThoqIi9QXkDtvv92d5BgS9GArILPYDoNqH8Fi5nYg5g15qLzxn\nrhhOYy4zqXifejIYJKbuZsvnQpIIW8bT25QNN3k/ZEEkPYVoNIoHHngAu3btwp133gkAuOaaa1Bc\nXAygXYeR6dNA+waF94mtaXh8GQaT95PHpI7UW92OLWJk4oQ8h0Y3nsmSJUvwxz/+ESUlJbj00ksx\nffp0JYp94xvfwObNm4d6rd1Ceyb5B3fX3cXF+wI2AGTxW08ZN7IDb25oIhaLqU6zXOtgFpvJe0Gj\nLYVtk8mE4uJimM3mLJ2EXgoNKosZuTO22WxoaGiAxWJR0w8lkRQVFSEej6O+vr7HBo/yfeIxclOC\n5bXwuWazOasehAOxZBGibNcie2Sxk4AcBSzFdWbD0dtiZTybZcoCzFNOOQWpVAovvPBC1nVR+/F6\nvRg9ejTMZjMaGhpUl2bZNt/v98Pj8cDlcqm5KKzAl54wRwbLWS/dfc5zCxz3Ru+6Kwy6Z9LU1IRn\nn30WY8eO7XDiP//5zwM+scaeDeoC/JDxi9dXMATE3lIyFTYYDKpmiLlgRo7sZBsMBlFQUACn06mq\nz2WBIAdJ9RfcAcv267nkYDKZlFfF58heX+w8LHUEDrqKRCIqU4mTHXkMkgSFeXpvLG70er3wer1o\naGjo1nugZ0BS4D9qM7JVCa+HBtUwDNW9mHpNLhEygQKAug4eLx6PK92ExMUUXuoV3NnzuthqJh6P\nY8aMGaqORHpdJLdkMonW1lbVHJOeCr00noszYmRrG248SGZcf+7n3OVydUgPpncnNRbWv+wLZJIv\n6HYqGh1Aw82MIhrZrgx/VzCMtnG7JJNYLAan0wmn06mMATv85hIVDbis40ilUmquh2xlwjWzr1J/\nwdCJ3N2zcp3ExXg7q7KZpmq1WlU7FBpeGi0aJ14PDT5303KKpCxgpCjP8ySTSezevVvt9HOr4nPX\nSA9I9siSoHFlhT89EepA3P1zaiSNNUnWMAz4fD54vV60tLSgpaVFeQoAskYWy+p3wzDU+0fS5TXR\nk2FXYd4nki6vj4WOQHtNCs/HUCM1Ov7PDQG9XLvdjmAwqDwfhgqZYSZDleyizMd4jT6fr9+ftz0F\nup2KxqCBRodfHO7+cvsY9QS566OBozHllzGTyahsHH6hgezMJ3lOGlAaR+oC7EobjUa71U943lzh\nlR6Q7NtFb0oW2UkDztoIDrFi6ANoL/5jNbwsepSEAwAjRoyAw+FAJBJR62ltbVWaBAmUJCRrMCSZ\nSC9IFgnyb7JPVm4lO7PIpMBPL4TXLw0uADULnu8Xj8HjUr/g3+S9pj7D95hGn14dr4NERkLhxoTv\nLz0h3hd6vAyLmUwmRUxsk+NyuZBOp9HY2Kjeb34G6YlxgBrJnZlivDbDMHR9Sg40mWh0QFc7ldx4\nMjUDhlFoTAjpfTCkINtzsHiNKaOFhYVqx0hDJQvvaFDYx4ndcrlDZeuTRCLRIVMnV0C12Wyq/xaQ\nPQudv/NfV3F0qduQeCQBk6B4zZzYSG1H1p/I2SfBYFCdl6E+pvbSU5JrBtoNPzPDSGq8vzS2NN4M\nz0kNisRDz0S+b9J7IFhg2NLSgsLCQgDI8oBIAvx8cCCWHGAmjTOJR3oQ0tOh0C8zAuk182d6sCQZ\n/s4sMvYa4/H5Pz/HfA6z60hIDD9SS2L9jkY79N3YTyGzbHKNJdNMKQZzJ5rbt4qGjrtVm82mMlxY\nAyDbdDBkQwPBOL4sAGS7EqvVCq/Xi0wmg1gspr688ovt8/my+ksRTIWVGWPcncqJfzQwQHsjSMby\naVxcLhcymYyqm6BRppbCNZnNZkQikawZIDSmPp9PkQOPy99l2qwM4fA6uCbqTYWFhXA4HKqgmORF\nAyjDhbL+hYaa7y3vJ9vzu91uZbzD4bAKZyUSiQ6pzvI+ExTUWTQp9RmmTZM4ctcks65ImtJwS9Kh\nB8P3iZ9hHit3AyA/H9LrlCE0ST4mk0m9pzy+/H7weLlZaxqaTPY7GEb2eFqTyaSm3REmU1sPqUAg\ngEAgAKBtJx8MBpW+wV2qnDhILyGRSCjNhV82kg0NaygUUl9kGkTODaHYabPZUFxcrAwwSUbOx5Bx\n7NzrlD9TbyEYMqHx5X1obW1VxMHr5Gt5DZJUpZAt18LdrlyH9N6YREARms8jeUjtQ2ZhUcehB8Yd\nPknW5XLBMAwEAoGssJ3M7iIZ81zMsuL9icfj6hpJdLJYsjPIzClCvrcMB5KIebxcT5D3Cciu6eDP\nkjB4fGpDAFSdCbsFUNOSNT3SC+JoZr63DF1yffSSczc6fWnZsr9gWMgknU7j2GOPRXl5Of7nf/4H\nTU1NmDlzJurr63HAAQdg5cqVym2+5557sGzZMlgsFixevBjTpk0bjiXvM+AXhTFshpi4M5W7YvbT\n4k6fIZPS0lL1xZd1Edz98zE5tY7iKOPMUh+QxkCGPfgzvQ6uVWYj0RNiGIw76NwQhDS68jwU+Jka\nK4sFgbYOwQwb0VuTQ6OkuM04OgnDZDIhEAgo4pV1IvTEmO6cTqdViC8ajaqMJV6r3JHLXlx8LQCl\nMwBQY3BJzswcI9nwvaE4LivxeS56O0DPs1Jy617k8yWhclOQ+x5L8DMkXyPfPxki4/vA959EIq+P\nnw+mSctMOb6uqKhIaXqye/IXX3yhOhVInYSbJ26ANIaJTJYsWYIjjjhCVaUuXLgQZ511Fq677jrc\nf//9WLhwIZYsWYINGzbg2WefxcaNG/Hll1/ihBNOwObNm3VnzwEgt8cUSYO7Ne685WhZSTDcqXPn\nzSwdhkdkS/ZAIKBmsfMLTvGTX2YAygDIXb1s086QSyAQULoEd9kM0bBGA0CHVhlMf5WaBo0rABWn\nZ3yc/6gJ8ZoZRmLcnimvDOfJ3TfPy6wjmWHFjCleB8NOQBux+nw+tdPnWmKxmPIYuXtmKAho97Qy\nmUzWpEDqNVK050TDgoICpFIpfPHFF6rgj5XzDFNyTT15JtLQ89oBdCAgGuzu0BlpdUY6svs0vQ6+\np6FQCBaLRaX6er3erEQGvp4gQVF/4aaBZMzPQ66Hq72Sdgx54/7a2lqsWrUKl156qXpTV61ahblz\n5wIA5syZg5qaGgBATU0NZs2aBYvFgrKyMlRWVmL9+vVDveR9CjLGSyNKEpEDnxhflztjhkoY16e3\nEovFEIlE1O5UNhHkLpsdcLmG4uJilSbMDBsSDg0gDS8bJDL8JD0EkiDrMHw+X4feTDJ7KhwOKw+K\nxCfDOxSm6QHI7LNkMonGxkY0NzejubkZwWBQpfvSkIVCIZUiaxhthZS8NnoLJAGXy6Vmx7e0tKj7\naBgGioqKslJrJbkxYyk3NdZqtcLv96vjyr5YUvMwm82qDoPeCvUlh8OR1VqfXlVPRlOG+aQ20RX4\nPH4ee6s/yKw6hqB4Pynyy/AY9Q9+JqLRqEo7ZwPJUCiEYDCoNhtSS6T2xdAwk0Jk63+NNgy5Z3L9\n9dfjV7/6lYrFA0BDQwNKSkoAAKWlpdi1axcAoK6uDqeccop6Xnl5OWpra4d2wfsY5EAghl1kVhN3\neDRkDB3QuDMMxIwc1nXIOovc1hr0bnheehWFhYUqI4jGjhXycnfPzBpmI/F8FHZlGEiCO01JIDRg\nbG0id7YU3FnHIjOceH9k3D8ajaK1tVVVifP+SmFeDn3ic6jVMFTDMA7vGYv/KGiTSEhuMrsLgJqh\nToIE2j0V3gNOJeR7kUql0NzcrF7LinE+VxYndlbTkgspfPMz1h2kF0P01ICSBML1M/zKn/1+f1Y/\nMNYDkTDoGdJ74XvD0BXFdZInPXGmHPNv3CR4PB7tmQgMKZm8+OKLGDlyJCZMmIB169bl/fiLFi1S\nP0+ZMgVTpkzJ+zn2dlBopgchDRDQvouX1c0MCTGmz7RWOUuDYSQaORoTfnkbGxtVIz5Zk8EdPXfB\nJC6/35+lb3AXGA6Hld7C4jMejyTF3SU7yjKFmOEyGi1qRTTiFOOpeZDAqCfwHDQ0zGYj+Bg9J6fT\nqXbCJDrpMVDUZagqEomoXlx8nLtjkjqLCHmdvH/8R6PHXTZDfszIIhnx/QKgigUl4cssNxI13yN+\njkgwuckOQBupMhyXO/SKhN5V8WXu51Wmg8tUY6C9oSUJTIr3rCVJp9vmxfPv9FhkGJGeOHUsTs3k\nZ5kenGym2Vnix96AdevWDYr9HVIy+etf/4oXXngBq1atQiwWQyAQwNy5czFixAjs3r0bpaWlaGho\nwMiRIwG0eSI7d+5Ur6+trUVFRUWXx5dksi9DjoWVO7HuwJCWNPI0XPLLLquB2UJFpq7yy0qSkIV9\njNU3NzcrgytbWnAdDFEByNq109CyfkPu3p1OJ5qamrJCNtQSuDYaW6/Xm9UHjIaQXhAAtfuXWTsU\n4q1Wq9rJ0zvhY7wXPLY8Lw0pDSN1DtnMkaTFlGspJNMzk8WhNIo0ejKzjQafhOLxeJRWxfc0Ho8r\nogiFQsow0iAzzEm9S+pFQFs6OEmTRCqvVRIJPzu8Xm5Ecj+HMnTK+0WDLo8lQ2fy3vJzKMN8JpNJ\n9c+itsEwLUOJJFp+PljtLonDarWiqKgILpdLdQCQmxkAWaS9NxJK7kb7tttuy8txh/RO3H333di5\ncye2bduG//qv/8Ipp5yCZcuWobq6GsuXLwcALF++HNXV1QCA6upqrFy5EqlUCrW1tdi0aRMmTZo0\nlEve48CwDdAeyqCB7A4snuOuTLY3oajrdrs7uO40sDSyQHsdRygUUloJ0BZvp2bB9cldPQ0vwzQ0\nNGxgSKPABpC5CQE8DtNjrVYrgsFg1m5TelySSGSKMu8DCxtlmEp6GyZTWydgGo/c9FSpD+UKxCQz\nAKrfFf85nU4UFBRkZTYFg0G0tLSgqalJETA9HBle4X1Lp9ta4nPnL+P6brc7q5sAdR0W5PHeyrCP\n3++HxdLWuJH1O/Rk+F7KOhUaaoLeKYtDZQIBPwe8Vl6LHFPcWciLXhHXyc0A38POsuRI4DILjSTJ\nxIJQKKQ2CbK9jcxYpHjPpBFJvFyvDnFlY1jrTPhm3HbbbZg5cyaWLl2K0aNH4+mnnwYATJw4EdOn\nT0dVVRXMZjMefvjh/T4NjztLWawmwwXdvU4Ko7IOgoarM0gBV6bLylYYbOVN70d++blGplFKYnA6\nnVk6AI2ow+FQhg1A1khWprYCyNJzpDArC/+kQZXZXkwpzc3M4fXa7XYVsmKrE4bDaEiZxitfS0jy\nlLtrehTM5qK3w3XmenPydbyv8vrokTB8FwgElAdhs9lUqiufx2PJYj3eC5nUQI/VZDKpwk3psdDY\nM6tMbhT4fvC9ATrP0LJarchEIih67jl43n8fkSOOQOM55yDzVRiJdTRsqcJjMdRHL0d6bjw3P3P0\n+Pie8DPE43ADwp8zmQwCgYAiEKvVqoR6AOq96ateQi1K1vXsa2SkGz3uZQiHw1npukDbB7WnQT98\nncxUyWQyHYqucmsxZOweaDfWFC+lbsKiLhmqkem3JAIK/H6/H4ZhqPALM57Y+ZUGMhgMwmazoaWl\nRYVneIxMJpPlPXAHTiGcr5FGjtoKRXyGnjwej4qvsyahtbVVnV8aLZPJlNXEsjNjSUNMjYDeEAnM\nbDarxo257yefw+wuis58HonNbrejtLQUFotFjbrlxoLfCd5z6YGROJjJxb5hUhvjMDBZsU5PmGRF\nnUveF14770ln98ZsNsOSyWDcnDlwbt8OSyyGtNOJxOjR+Nfy5TC+Ct3KjQM/RzINWV4riYFkKcNp\nJApm18maGqA9rCYJh9fNxJJMJqMy8jgpsjegF8m1kMDdbnevXj/YyJft1BXwexnkl1zWNfT0YTCZ\nTOoDDbR9OeUXgqKt3I3yyyVH0LKhIsEvN/UYhjpyM8C44+eOW2ZXybkUFPZp6ElcyWQSTqdT7RIZ\nVmGGkuw0y1Ag045pJGl8uMskkci261wn75nZbFbkEo1GVdsQGSKibsT7QUiDnk6n1fwSElDurp1E\nIUlDFuTx+EyCoMdBr4nvHcNThtFWZJebFcbf/X5/Vn0MSYeEwTAe10Kdi54jPYfcLDopqHdmcPl3\n/6uvwrljByzslRWLwV5fj+KXX0bjOedk3Ut+VmQhJH+X55KfZ5IcPyckaWYLkhxl4SkAdX8YEuO5\nZKqxTALoCXJgGa+/N9GEvQ2aTPYC8INNA8GdDkMmTMv1er2dfjgZiqJAyy+p9EAYRyY5RKPRTov/\n+EWQO1MptMpZHgRDcfRUuMsmQXCnyy9rIpHArl274HQ64ff74XA40NTUpMRUWU/BEEhra6sKW5lM\nJuWVyLAOjZ/MUPJ6vYqMGQYj2dAY8Z6zUSGzyWS/J+7upXED2tNZSVzhcFjdO1nhTmIiUbpcrqx6\nHWZgydAO193a2qp23iaTSWXh0RAy/Zs6GZ/jcrlUa3WuVaZE09jJ0CEz6JgMIL1P3lspTvN3Ca7T\nuX07zDl6nyUahXPr1i6/B3IXLUlEZpYxK0uK+CQNtgSil1xQUIDW1lZFDvRo+Xqun00vGWLrS4jq\n/7d37sFxlef9/2p1W0mri+UrlQymk0BsyTKuTRrAoc6A43KLuTixGy4p9OIkbSCQYeg/LdAWk4SG\nlGknBUJhaElb6JSUFhsHZhjRBogBO6QY2oRJ7CD5BwFbsqXVrqTV7vn9IT6vnj3elXVZaVf2+53R\n2DraPec9t+f6fZ7nZIiYSF6ZlDywsrEYETwwZ2wPpXxjSHmZbW6EQkBeeutJ8JLSzt02BSRmjDdB\nchNhaSvLeclZm33h7XetwGK9hE9sVTPhKTwYaSwEYZOnfJ//E8bCosRS5Vg0lESgICjIZ+B5WOEv\nyYVD+vv73XVECCH4aL0CrRlFZimtNlyEx9XQ0JB1LrYtilW+KBRCNigclBtKJ5FIaHh4WE1NTVnT\nDrn2KHLOE/B3jodwxqCw/cHYD73DrHIJK5Ty8nIlV61SJhpVuVEo6ZoaDaxalfd9sN6JrYPBw7TH\n5Zrg7fK8McNk/vz5qqioUGNjo1OyeGMML6upqXHMP5uvsl6kHWyWK6fLuriOeEInklcieWVS8rCh\nCwSdbe1t48f5YEMkPMzJZNK1BkFJ2CRquOcW1lVtba1jfhHaseElvCBprEEfwt9aljbkQAIUoUAo\nBi8onU67ZDz7R8jRP6yystKxlqSxORdY2Fj8nKMkRxdFWA8NDbkZFlahsA4EDvtBQKOkOW9pTPGx\nDpSnDe8hqLieYcVgk/C1tbXq7e3NUsiEs6yRYAU3HpD1ykhK4x0i6CQ5A4GEO/tDgZKPQBFxH8jf\nWIo052fZfhaZTEZD552n+Lp1iv3whypLpxWUlyu+erWOnH9+zufYhpmsYLbPrQ1zcQ2sYrFjhHkv\nCNslEomsqZq27oRrRPKd64Vil0YNm5qammMMOhiJ7NfWqpxI8MqkxGETjPb//I3tKJtcgB4Jpdgm\nY8kD8ILhwsM84QUmlGVfXMIhhE8QcCCc2LPCVhrrG8WxLGxMmnyOndDIeSHga2pqsqx+aUx5Wkoq\n/x4+fNgdC48hlUq5XEtDQ4OrkrdhPIQmSoVzsnRhSU65sV+uu7VwEUQ2hAkzy/ZQq6ioyKqTsPeD\nbRRJsk7LwLP90xKJhLPS8VoqKysVj8fV19eX5aES9oI8YZUSnh1eDsYA98B60bYwlbV9+ICo+957\nVfXaa6p+800Nf+xj6l+9WsoTFrIECPJc3H+b+Lf1JdwTnkVLDkE5YjD19fU55cjYA64bHjq0dZ5f\ny6zkeoWVic3b4MGdiPBsrhKHHV1rZ3JYyihhHNul1yKVSqm3tzcrDNTY2JjVxpwaBQQC/9r4vQ2J\n8XtNTY1L3OeD3Z9VOLz4VgizHQWI5WwZRgh5SVlJfl7yeDyele/gx8bwraKU5AQr67V5DMgLtgYB\nAWWLOiVl/Z+/09IDoYuCQtjbY1IoahP/KCX6nEnZXZfDnoMkx0zjfK0nQr6AkJ99Dij8s/um1sLS\nsKPRqA4fPpwVSrLhTf7F47NC1Boztomi9VRzgRAgCt12oOa+WNoz1xACh/Voamtr1djY6DyG/v5+\nlwOyHjX3zw7NAigfm3vMxZAsdRRKdnrPpMQBO8r2CCL2S+iF7SQXbbX54OCgDh065OiIWG19fX2u\ncy95DksjlcYYMbYFiWUtIYAm2gXWhiHYR1j4sgabAEZoHD161CkJutyiqCgS5KW3SVS7PwQF37UJ\ndmt1IlTtNckVQrGhOUtjtVY5HY2td8M+bEjQMr3w/BCAttBUkgtHhdlwJJBRHH19fY4BhsXM/aqs\nHJt+ac/PrhFvhOsHAYLzs14lz5gNs9GnjX3Zv9lraL0wFE8uMoP1OtLptCMWQMRwyf0PmXyElHp6\netw5s57+/n4NDw9n3QObcCefRv+5MLhf1iA5EetHJgqvTEocWFHWkqVxoS204gUcHBx0whevhpAH\n4RzyBHYIkDSW+JbGePeEAGx4S9IxFdITxUQozDbBzTYS7dKxyskW9xEesoLZwgopBLSlxVq6KONr\nCedhhVvPyuaugPXgLCXX/j0XUAq2Wp992TwO99pSsS2xIZPJONaYZTVZVpc0FnajfQ3nBGwOhxwX\n15f929oOSBDhe23DsXzH9lDjGnHeUK8JCVoGoVXetl7Hekys3c6Rh9DAflFInHOYIAJxwk7rDCMa\njWblCGltdLLCK5M5AhsioOMyQg/qKQ0cpTHPAUFr8x0IGYRoLqqllF3IxbHDwrOQoUX2hQChHgXL\nPiyE+TxWfz4PyMKuneuDB0GoiO9bD9AKZgQOQi/XNbDX0lrj1nux58NnbHLdfpdQHgrMdn+24Umb\nkEZAc46EkIjtW68u1xphDNp1hicWxmKxrFY34ylNlAVC3VrxKAhrGHD9uR/2PhBCRNFy7jYhPjQ0\n5Jh6rM12Y4Byz7nwjuHxxGIxd11s9whgDT3u6ckMr0zmGGy/J6w6KMHW2gJYa7CpeGFt19kwjVPK\nTjRLYyGGsHVeaISL9VhLPmuev1k2D5Ys682nMPnBArXMufLycpcHQABbS5Zjcj3yIRwaA/xui+Xs\nOeX6zuDgoKugp8cXHgMhMdsix94r/g9LDiIDeRwUj01W2/Aq52K9AEsukOQS4rk8OJSwDf9RAGtD\nrPZZ5FpYD4jztbkTrhWhLhQFrDQ8Kmt8EColVMg9JkeC1815QMPPda9PdiUCvDKZYyApGO4rRB2F\nnWkOk4d28rTmsElj2+PIWonWKsYCxLKdiZgwAgVlh/UbDiFZoAxYu6205zxsKMV+D2vdHouwCYKE\nMAvfR4Hb6nwqq+3+bXhuPEUo5Z7hEf68De8QqoRhZJlaNhRnvQ7rCVhKLecart2wYR/7f+sZJQ/c\nvQAAIABJREFUWc8RL4JjYLRYRWDvlz3nTCbjyAL27+yDzyLo+Tv/8mzYolHuJ/eQMQOEdqFS267N\ndLymODEej2cZZoS9Jlr1fjLCX5kSAslAXspcyTyEGywc4rTz5s3LcsXp2oorD7MFD4WXywpMW4Bm\nXXfrJYTDM4WCtaC5DhPxfjhnSAQIUK6VjYNL2ZauPQ8bPkGQIUyxcBGoFPvZgjULvBjCKblghfZE\nr4s0Fmq0g6ysArY5DhtWgshgPVFpzFCAsMAxa2tr3d8kuaQ014wCPSjnfBb6OQrOXhN+t/cVb4Ru\nC1aJhEkN1dXVLlfDvqzHaGetcK2shxqmiNsiQzzRMCnEYqa88RMFXpmUCCiA4oHnwQ4n9Oi0K8lZ\nanV1dVntS9Lp0XYrfA5rkfACtQbUSZSXj84kJ2xjYVk3hBmwSvNROKcCa4HmSnbnAhY7P4R6EBwQ\nEQh9oAg4D66ZVdhWkdqeVDakY6nOdu12X7b+BNjQDawi1jQRQUUeR5ILQdl9W4WPUrEeGN4s3gRC\n04ZMJbkKfNbEc2aZYwBGIGGnWCzmui2zJsgQuc7R5gIxbsJGDvcEOjQGA54MzK7wftlGzQg0YIwJ\nDDJIJjC/bKeHcJ7LIz+8MikRhFvLY23zIoNIJOISg4Rcwt4LRXB8N5VKOSqwJGehYoFayzcMm+CV\n5F7CybK4csHSdkHYag3DvtwIwPD3ETIoY8Id1OlIY0l6LOZceRVqQmwoxeZIwjkDjmtbwFhkMhmV\nZTKqf+klNXR1aWjlSg2dc864igRBzLkhSG0rGmms03A4kW3PESXAOtlnNBp1tRGWCEAfLmpMUEZ4\nRTyDdXV1TnGTtGdNKG6b8LdgveSnwmuw/1plbBU9nhZKyJ43BAIMICrgOX9Co+QW2YZyQzGzH3Iw\nMxHqnevwyqREkCuRO56AD09HtJW91moj/m8TqTbRygvPCy3lLmKyQtoKpXxrjCSTiiSTGmluznvO\nWJ/hGP54wOuwrKdcn4Eea61+S6G2IaDx8jLkHCyLi7XaZDVCxxbN5diZzvjiF1Xzs58pMjysTGWl\n+s89VwP33KN0ntBh2OJmv3iUtpCO5yfcoJMOwPbcbX6IZDVtXRCafNcOX6uoqHCNHm0xJcWtKGDm\nqNj8Hmu094F7xXnYY+VSPJZ1ZhUpYT6rkGCy2cJJChDxlPDawvfftogPgsCFjTl2OBrgMcuTFiWp\nq6tL559/vlauXKkzzzxT3/zmNyVJPT092rBhgzo6OrRx40YdOXLEfefuu+/WihUrtHLlSj377LOz\nveRZgR3tKo1VZIcVDBMOSVLG43EdOXLEhR8QoDYJaVtO8D1bE4BA5UUkpCGNxaRramqy6g7y0m/T\naS39+te16oILtPKSS7Tis59V9YEDx3zMKqbJhssmkrMhjGMbRlpL11Jic4W72Ie1iq1g5d7YGg4+\nHxZMCL3m555TzU9/qvJEQmUjIypPJke9lL17J3X+kpzXYMOQWNd0xbXFq+Q0uNcIYJLKGCGEWsn5\nSGMNQsmt2GQ7fa34LBX81dXVTkHZxD9UXtZMaMmGknI9V+GcEM87zDQYjZyLJHduKFK+l0wm1dDQ\n4MYZW5ICzw21MLZ3me2BNpHppicbZl2ZVFVV6Tvf+Y7eeOMN7dmzRw899JB+8pOf6Pbbb9cll1yi\n//mf/9FFF12k22+/XZK0Z88ePfnkk3rjjTe0a9cubdu2Lasw6kQBLyYvOgI8DNg7/JCM5eVCYXCN\nrILic0xKtGGD8L9Y41TN8zLyQqJMwi/+wscf1/ynn1ZkeFiRVErRAwd0xh/9kZTDyixmQtN6I7kS\nw2EQ6rMEAUsPDns6uVD3k59kdciVpLJUStX79uWNx+fLM3BfGJPc0NCgefPmad68ee7e4JW6Yxn2\nG9cflpKdIWOfHbuucDcB+zdyFNXV1YrFYk5Yo1ws8OjwcmwNDM+TberI75y3VTjkZFDuNFpEmWJI\nWAaarZ1hO73HyP/YwVUYWvY6jOfNnqyYdWWyePFitbe3S5JisZg6Ojp08OBB7dy5U9dee60k6Zpr\nrtGOHTskSTt27NDWrVtVXl6ulpYWtbW16ZVXXpntZc84eBEaGhrcrI7BwUEdOXJEhw8f1pEjRxxz\nJyzArUCzyVdblJVKpVzowVI4EYyWmkmCmJfGzriwL1UuK3zhv/+7G3YkSWVBoPL+ftX87GcFvVaF\nwlQEAkI4X34nrBgQXIkzz1Q6RKgIKiuVOP30vN5WLpow1nMkEtH8+fPV1NTkrP50erQtDAIXC9uG\ngCxrK2y0WC8jnONAcBPy47lC6NuwD//H80NZoUDq6+vV2NjoJoTahL01UtgvCoxzsn24LJuLZ996\njpbswD7DYVXo8w0NDVkeH+cSvg75PKiTGUWlJxw4cECvvvqq1q1bpw8++EDz58+XJC1YsEDvv/++\nJOngwYNqbW1132ltbVV3d3dR1jsb4EWiHTb5Dkay4rlYWJoruRNCDZYqG06u4s3Y6mWbfLZUWQSY\nPXYuQZzJMU9FmYwyBWozgbIsFAqxr3CYLJ9i6LnoIg2fcopTKOmaGiXOPFN9n/jEMZ/NJ6gQlhT9\nvfvuuzpy5Iji8bgOHTrk+pdhYSNEbW7INsYMswUthZa/ESrMZEbbsdTX17uEvR0QZj0Q8gp0Yq6s\nrNT8+fO1ePFiNTQ0uJwLbXL4LsW0eBF4GXgktICvq6tTZWWlG9ls59eQA7LGFYrT5gt57tl3PnAd\nbLj0RGwhP10ULQEfj8e1efNm3XfffWpoaCjIPu+44w73//Xr12v9+vUF2e9swyoASVlzMQhv2Xh2\nc3Ozent71d/f714mFArCx7J3JGXFm/OxpmxtBcn58YRvWVmZ3vvCF7Tsjjucd5KpqNDg6adraNmy\ngtCJZ6LGZbrI5aFJxxIUgmhU//uP/6jmH/xAtf/3f4qfdZZ6L7hAypHI5Z5ZiqvdL7RuhCGCFA8U\n79MKfMI1hHTIy9lWNNaCR6AT9qKLcVlZmcvLWHoxngXtb2CAkVexeSyeK8gfJP9HRkbceGlLa6YN\nP96RzX/hfdCoEwo8eUjoy1CEm5qanPKweZB8KC8fnchJBIBznavo7OxUZ2dnwfdbFGWSSqV01VVX\n6eqrr9bll18uSVq4cKEOHTqkBQsW6IMPPtCiRYskjXoiXV1d7rvd3d1aunRpzv1aZXIiIBfDi3AY\nD3PYiqS5Iw0hbf2GNBav5sW3I2XDx+azExXgQRDoyIUXqmtgQKd897uq6O/XkXXr1HXrre7Y08Xx\nak+KgXzr4f6FFcrhTZt0eNOmnN+xCf0wVRbYXBef4x5ZthMGgK36Zq4GngSGCwll6jGobkcYS3Ks\nLJQNho0933g87v7G91EIqVTKzc7h+SLBXV5eroaGhmMmPeJhxWIxVVdXZzHTrMfAeGc8+1QqpZqa\nGh09etQxzCQ5T2eyygDldyIgbGjfeeedBdnvrKvXIAj0e7/3e1qxYoVuvvlmt/3iiy/WY489Jkl6\n7LHHdPHFF7vtjz/+uEZGRtTd3a19+/bp4x//+Gwve1aBO4+wsF4Jf7c1KWyjDgLmlTRWIGfzIXaf\n4TxIGCScJwKOeXjTJu17+mm9/sILOnDXXUo3NU31Uozt+1e/UsPLL6viw/DnTCJ8XS1DaCKwBoC9\nb8cDYSeEJF5mrhxMuELctlLnuKzf5hHIWeAtcIza2lrXUoTZHjYfgqeQ71lAkcTjcTffhtCSDT+R\ne4MZSP2JDUGh9Orr652xQ76PZ4zrxHnQvcEqYvZDbqaxsdEpNY/CY9Y9kxdffFGPPfaYOjo6tHr1\nakmj1N8777xTW7Zs0cMPP6wlS5boiSeekCStWbNGV1xxhTo6OhSJRPTAAw/knLN8ooFBVwhz4rr5\nBmBVVFRoYGDAufwkPqF6ZjIZF3KQ5JQO7VXyYSJJRl5cG2MvGIJALffdp0VPPKFMVZUiw8P61TXX\n6P99+ct5v2It6amExQiL4MGFWVHjwSaeJwuotNRE8MP1tfRVhHsQBFnFmGFgSECTZeyAZQRa2jge\ng01Q22cg3/NAHYYNw7ImOzeHZox4ORhBNK2UlGUoWUVOsS2Kk+/zvNvGpBRRsj+LcDKdvCRr8f23\npgY/abGEQcsMrNvxKm/T6bR6enoUj8edkMGqQ0DRKrysbGysKi8acXYUj7UWYYTlg61+hlpaKAsw\ntnevPnLTTVmU2nQ0qp/df78SH7ICc4HnYSrPRSwWU319vZvzYanWE8FUjokg436TVLaFkJbRRHId\nY8PWxFhhSY4EhhcV7Rgd/f39TnlZckdtba0L6+BFZDIZlzexCILATR20XYPJyxFW43ryN2pdmpub\n1dTU5EgFbCcHZJPxqVTK1VmRI0mlUorFYk5p2Vkp/f39WWHdkZERxWIxdw7xeNw975yjHTB3MqBQ\nstOr4BIFLBhJWdZWPqupvLxc8+bNkyQXt04mk6qqqlIsFnOeQzwed00kbTt7hBcvka1PsQVsuY6L\n8KJWhlBGIdDw0kuKhGozIsPDavjRj8ZVJuHamYkCWqid0QEraDK5o8m8oFxzjonwtAVz0hgllQFX\nGBkU/dF3yzZtlMZqaoIgcNRXQDdp5oAQZrJGB8YBDKpcsEWTeA6RSMQ9k1a5SHLhKXKAeFzs37Zv\nQUlZDzgejztKe01Njerq6o7xQMrKRtsFDQwMOM+psrLSVeyjQG0RJcrZs7UmD69MSgxBMNq6oa+v\nz7WZ4OVPJpOqr6/P+92Kigo3UQ4+PowWFEJFRYXzUiydEsuPNdjEvX3h7N8JtaB4YOoUEqlFi5SJ\nRrNqVzLV1UotXFjQ4wDbjdfSZCerlCbz+XBIzF5/kskoGBh4Nl8CqwplZ5lbtoX+kiVLstqfoPxh\nUWHB2+JEWIG0JLG9twCekt0vyuPdd991CoOiRtsZm0JJqwQp3oUsIMmRBKhab25udt/n2WS9PPv8\ny/6YR5JOp5VIJLzCKDC8MikxkGy0yUuG+GAl2n5MYcByCXswlZWVOnLkiLO2UTAITAQR1cS0+4Z6\niVKxCU4saizomehM0HPRRTrlu99V2ciIIiMjylRUKF1Xp94NGwp+LBBunV7o2pbjAaGIgrAtSAj9\ncB9s3oFmoQh3PoPSeP/9912Yic7AjY2N7pmhx1skMtYYkv3hRSSTyZxtfjgeITcMFpBMJl3H68bG\nRknZStMW3eJJUZ0vjXpQdPa1Fe9gaGjIefI8m3grtjGmdGxhJsYUYcSTISc7E/DKpMRAWAXrkpgw\nxV1QOCnkCgOL0OZDpFEhFIvF1N/f7wSkFRK2tsW2moBfj9WI1YoQC8e2CacUCun6ev3v976nJQ8/\nrLp9+xTv6NB7N9ygjGl3MZPIV0MyG8cFtgoc4YsHQNFpY2OjmpubNTAw4NhYtojSDkaTRsOo/f39\nrmcXQtV6I5y3nYyIQUHPLYtw+NQ+Z7ZGwxounJ+lQtuQna1NIv8Szh2m02n19va6fbHvoaEh543Y\n62mZbigpFCeDtCz5wWNi8MqkxGDDSjzk6XQ6q9iKUJi1ttiWSCScd0Poyg414sUiLAWjCyFik7wQ\nAGwC1Cbkc9XBzITgTS1apK4/+ZOC73eiyHdOM0X64JpiydPSJld7Eyxv7hGss3D/LEKc9vs0CrWh\ntLq6Oje+gOcwEolkVaoTKhvPQ5bGaMn2GSWHR46FfnF4C9bIIX+BsRKNRh1j0eZISPqj3Kxnx3W0\n830okmQNjOnlftpal/Ly0bb1KES2eSVzLLwyKTHAwCLcAKPKhq1svQiWWzwe19GjR7MqgnlZeJmT\nyaRL1mKFQou01q/9DnRiq8DCsyfwhKbCgCGEY2P+cwVUcI/HdJsKrADGuLAeib3WNh8B9ZZOCHwG\nxWJrVrjeQRA4a5xczMKFC511Ti6DAkM7/ZNOvWFQz0JuxLZ7h1VmryGKDCXAdaXNezwedwLf0txR\ntlCjUZ6RSMQZU1yzWCzmzi8ajR4TyrLnhHLj+UaRYjiggE4mxtdE4JVJiQF2DtYh1iRsFBt+QKng\njeDB2NYaAOVhab+2CtnOQAl3ROV3LFg+Yy1IgDKcyHmyD0Ifc0mZ2LBQoWAT33iOlonFfQP2XuIp\nsDbCnDD1EJC2WJUWJNShEDazHgc02lwV4Pmsc6rZbbgNunVYANtQKmvB20omk44QYem7XPuhoSE3\nNZI2LrY63yo63qvjAcVm8yvxeNyRELjuiURiXDLMyQivTEoQvAh2gBHWoXXdbe1BuEKeBCZ0Ylhc\n/I0iSEIWkrL2ZWHzODZcZvsgRSIRt2bmgo8Hy2CaanHhTOH+++/XpZdemtVgNIxCKz+uH0JSyi7+\ntAq8rq7OKQdCMJlMxlHCbViTe4xS4F7TYj1crR/eJo0ZCNxnW0iZDzCxMELGK37FoLCKsqysTEeO\nHHHPHc+zNNa9eHBw0D3b9u9VVVU5FddEYZ9/GwEAKLtcYd6TGV6ZlCBsYpuXl9wHL5flxvMd6gNQ\nCGFrEmGC8LEvOfsLh2ystyKNeRT82KQwgEFUWVl53PnmvJClpEx27typ1tbWcZUJQJDZmPpkYO/l\neO1K8EJp7ggFHBaXbQePl4n3iacQiURcU1UYTtRqSNm5hPCxUWB4LuFx0vnWPB1hS7gL4U0orqam\nxhlHtgaLa9fY2DjlnAYsRttZ2EYDpDGPkHCbfd5PZvgK+BKDpVVazrzl3IdBK28YV7YKGMuVcBjb\nbdVzEAQaGBhwL2ZfX5+ksXBJmCFmq61tmMv2A4N+Sv5nPFjGzkRR6Pt99OhR3X///RoZGdHu3bsl\nSZ/4xCe0bt06nX/++Vmfre7qUt1PfqKh1lYNrVmj6IckhunmTgg35jovngNpNPS0ZMkS18XgyJEj\nLpltY/tY07FYTI2NjVmKnzkmpSoQyQNaj4D8HV4VzESeW0JlufI4k4FlL5KzDBtF0WjU0aylMUUc\nbuk/F1Cod8l7JiWGRCLhwglYvRRq5QMeCx1VaRgYLiLkJSM0QNiMEIPtbRQe9UscnXg1L3Emk8my\n3GC6hIvXwnkYMNUajkIbDt3d3XrxxReztv3oRz9SX1+ffuu3fssdb8lDD+mURx5R8KHlm1y+XL+4\n/36NFIDdY+nVYWBpW++zsrLSsZQqKytVX1+vTCbj5ofgzZLkbmhoyKLFSmO5BJhT/f39kjSu8TIb\nsHUtPHeM+LVsN8J2JPgLseZcbeljsViWd877YUPL5DlP1tCX90xKCFhj9kEmqT5ViwchjpCKx+NZ\nTCx+CIugLN5///2svACfp6mebYRYVVXlwmfWk8Kyi8fjjhFjwWexplmnFaiENqbSOHGq+MxnPqMv\nf/nLuuyyy9y2VCqlqu5utW3Zoohp+piORvXuLbfoV1de6a7HdGpTuIZcX5vHoL6iqqpKCxcudDVI\n/f39LlxGwri+vj6r1frIyIibapgLjC7g73QSLpZCYa6JZbI1NjYe43XgbdmaqdlAPB4/pg7leNe4\nVFEo2Tm3zvokxXRutG0QScV0mNkViYz25bLWVlNTk2KxmEvUh7n11ipDyUCXpK/S4OCg4vG4o3uG\nvSuEnz0/lFpNTY0WLlyYs9o6F3LF+adD3aSOwSrj2OuvO48ElA8OqvHll7POI3w+UxFw5Ma4f7ZI\n1BbuDQwMuLBMIpFQIpFwBYXcL1sQmAt4JRAsaDB5vPDkTGJwcNB52HV1da4DRBgw1sZrgjoTwKgC\neOtzTZEUEj7MVUKwYSSEE9b9dIBHggVnk7MIKoQI9Mp58+YpkUiooqIii5Zsk48oKBQNHH0rkDiP\nsrIy1+aFamqSv2HqK3NZ+J5tvz7eOUpj4RF77Mkm97/73e9q0aJFWQWAkjSUIyGfqaxU/LTTnGAJ\ne1AInYl6VjwDlr7N+aG0yY/wrNjaoUgk4phMUGrJJYR7rGWdx4c1R+H7WizYgkup9BhUkAMII5Of\nPJnhlUkJoaxstMsple9WAE8HCHibILdWJ4VvCOJYLOaEWH19fVYFMaGTTCbjGgT29va6EA9hKcsk\nspMcIRhYYYEigepKS3G+T/HbRK8hIbmphpsWL16cc/vAqlVKLF+u2rfeUvngoDKVlcrU1ur9rVvz\n7sta0xMJJ0CttjM+COWgYLkm0hilWBqr/KY7Luw96kygiodDRdw72wsLpWKLH2cTdgKjJKcIS0GR\nSGPvqmVOlsraigWvTEoMVOuGqbvTAQ0ioY5i3WK1Ey4ZGBhwNQVYWbZ4js/iodTU1DgBBFXTCjzb\nmgUrDsVgKc1lZWWqr69336MYDcv7eNcApRT+XC7vZFrx4bIyvf23f6v5//mfanjpJQ3++q/r/S1b\nNLJggflI/v3nY2nhIeKFcY/wRJLJZFaiWdIxs0ZgxMF4YkSubXKI4LNV7IB7iAdFmKxYHgo1N7Yh\nYyl2+T2Zw1phzIkE/K5du3TrrbcqnU7rC1/4gm677bZjPnMiJOBnAngOtjcTAqu2ttblNWAA1dbW\nOiuY5Lg0FgbBeyCfwrCiIAic0IPWLI0xYyzllb8h0GidAVWVUBtWeb5pkDYsRtgML4siT0tlRige\nj8I73rM0nefMMuBsqJDcCIqatiUwhLgG7APvsLq6Oqs559DQkKLRqOt9xX2nUps6lUWLFh2jIEZG\nRjQwMJBlYafT6aImlK0R4C3/mcNJQw0eGhrSl770Jf3whz/U4sWLdc455+jTn/60G/nrMT6Ghoay\nKLoI/QULFmSNO0WgkfgcHBx0ExoJmTQ1NemFF15QZ2en7r33XkljSXRbPU9Oxjbuw/PAwrYCyyb3\nCQvZ3mFY6OwbS9x6JFiyWPeEe2x4DIWKBR5+gWzYLR8m+9LZrgEQFAjhoCBsnQ1rrK2tdX3TLCXV\nEijq6uqc11dbW+tCotbrs7mn8RLxMPDseOJwH63ZxnRJFB6zi5L30Xbv3q22tja1tLSooqJCW7Zs\n0Y4dO4q9rDkD4rnMq0Dg2yFQFGYhaAgx2RGvtEp56qmn9Pjjj7v9Ux0Ng6u6utoJzWg0qvr6es2f\nP1+NjY1qaGhQc3Ozi9tjjXMMBCGtP6xyQqhZdhfhIMJ4eCqEe3LBsqNsuIf8FOuaKnKF2riuVK/T\nrXnJkiXO+4OWjcCHSm2T4SidcCdn7g0xfMB9xWAIPuykkM/C537V1dWpvr5+2sV/HicXSt4z6e7u\n1tKlS93vra2t6uzsLN6C5hjoYZROp12reRQG2xFiJHURdngDw8PD2r59u1588UUdOHBAkrRu3TrF\nYjH967/+q5uZbce6VldXO5oqx7NdXFlHQ0ODi9fzN2uJY13blh8IX3o/IbDJFdi8jPVmOLdwjgVv\nwXbkpQB0sgjXmSDcKQK0xAIUmi1CxKsbHh7O6laLF1NfX+/WFY/H3XdQ/pZhhKLh8yjq8cJFJzu9\n1WPqKHllMpk46R133OH+v379eq1fv77wC5pjQOAePnw4awQriqSurs4VRkqjwpacCAI6k8lo7969\nTpFI0v79+yWN1gMgoGzTR2l0gFdNTY2jGCPkrdC2k/PS6dEBXmFFRxLdCl3WC6NMGhW0fX19rnml\nLdaUxpheNlQUZsrBNpuMImGNtq07sF6O9f7sZwjP2SI4wnCw22gtYpPzdiqiNBpGCzOM7L7CtUIe\nJyc6OztnxCAveWXS2tqqrq4u93tXV1eWp2JhlYnHKGz4hmp121Ie9ha9mWiSZ5Po0WhUzz77rCKR\niLZt26ann35aBw4cyGr/QcjINhqkuSCWNh6AZX0FQeBYZCT9afExMDDgYvkoCEI7CF/WQBiP/dgE\nPsATsDUrKLawIpzsNUahSMo6Nxums8OprPIgxCXJ5VK4J3TGpbkhcz2OHDniclDsF+ZW+BymSy33\nOLEQNrTvvPPOguy35M2Us88+W/v27dPBgweVSqX0xBNP6KKLLir2suYciH/bFiqW1VVTU6Pa2lrH\nqiKvUV1d7bwUSVq4cKGksR5iw8PDisfjTpkQYqmrq8tqAWPrSqgfoLYBr8MKdNtWBaXGMVAuVH3b\nUJjtMRYO2RAeI/9gQ1vQkMlrSBP3ihn6VF9f74Q554fiQkn09fWpv7/f5XnoqQUzC6KEpQnb+2eT\n6yjHVCql3t5e9fT0TGiWDNcimUyqr6/PVdF7TA4tLS168MEHi72MkkHJmyzRaFR/93d/p40bNyqT\nyejaa6/Vb/zGbxR7WXMOUH4RVPT7gn6JdQ9sHoWpdlVVVbrjjjt00003ZfVBSqfTbn4J4SdLLwY2\ndIRAh85LEVhPT49LyktyeZ6qqiqnOIaGhhwdmRCebWwYjUYdCyrMMqOAEqWF8kGp4S3kYnvlo1By\nLkz8Q6nyWRQaHhndlAnvEaqzIauKigolEgm39oqKCs2fPz/L26EGhc8kEgnXCud43gjGAPmrgYEB\nl/vy8JgK5kSdyUTg60yOD1hOtkcXAgUWEwIfIW7j7lBRczWjTCaT7u9so8cWNQyJRML9TZJTJoSy\notGoDh065PIiFDAGQeAYYsPDw+rp6ZEkpxwQrHyHWR98DmvdFmty3uFQGDkNvsPv5G1sF2auDWE3\nq0ispc93qRGxLWZgvxHSgsUGfZjrjMfI9evt7VUikXDMO657ZWWl5s+fr1gsNu5zkOsecr888uO5\n557T7/7u7+b828GDB2d3MQXCSVNn4lE4kIvIhUxmdFIflrxNrEujD9zQ0FDWZD+raGxPLNvJVRq1\nshsbGx0TiWp7aSzhTedh8h3M2SDf09DQoPLych09etQpCTwP28+MHmKEnCAX2DXZIkZeItZPrUY6\nnXa0adu7jHCaFeC0LyH/RLiO/I8k5xGSOyJkRyiOmg7b+oRQF0pHkmugac+dteBlce88Co8NGzbo\nzTffVCaT0cqVK3XjjTfqD/7gD/z1llcmHh8CKqyt6RgaGspSPoSjqqur1dvb64QZXgMCGMFdVVXl\nEsdS9rAtZm/U1NRkhZQaGxudt0H4xnYjtvMtGAZl+zbhdSBc8cI4Lol8iv1sIpyaD8IcDV1lAAAU\nBElEQVRfS5YscfTonp4eV9AHTddeL/YXZqCRz+H4HC+ZTGaNZoY6nEwmnQdFXgdFMzIy4phxdXV1\nWe3nydXYXFO+nA/rK3RD0ZMFTU1N7v/z5s1Tc3NzEVdTOvDKxENBELgchPVEKEKUxkbx4rXY3l0o\nhb6+vqx58OQ56uvrjxFslv3Ev7Y4z3aIJQ8zNDSUVR1u12qFN7UttjDR5k8I69GChWPbuhS+S7iJ\n4wCb/8Ez4v/QcG3BovWI+LudDcN1oC8bobKwBxQOaVlln0qlJpQvIT9lG4pape8xMVx66aW69NJL\ni72MkoF/ejyyai4QhoRuEK61tbWuVkTKrp8Idzi29QwkyyW5JHm4I2wmk3EFd7a1C3NQpLGZG4SP\nEPT9/f1ZXgesNBho7I+1EEKyVF2EuaUekwDHW6BbgFUo1iMgxEaoCaXBeVZVVam2ttbljaD72t5T\ngONZhpll1HHPJLm6Es4lnU5PaNofHqWtwfGYHB544IFiL6Gk4JWJhxNAtpdVEASKxWKTSsjCDELo\nEb9HSRECY/Qq4SyYYoR/SF7b2SaJRMKFw2wYjboYlBg0XWmUCZhIJNyALpLM0qhisc0n2QdeiTQq\nYI8ePeoaK9JePxqNuiS5VVhWcVkvz4bZwqE3FKy9FyhMYNvKky8hvIdSTSQSSqVSrp8a1+J48ErE\no1DwysQjq+4CQU4iPAyEoG3DggBGoOKpDA4OZvW6wrOh5xeKwrY3gdkkKUsp0eIFRhe/x2Ix10KF\n8BoKg/xBVVWVqqqqXONE1muHQXEuklyICQqvNJonsV11mRxpq9ptQabt+4UisJ/Fowi3eM/HquE6\nxWIxV6GPUibnATMM5ZsrvOjhMVPwysQjq5MtAjzXmF1pTOBjIdPQEcs7Fou5MM94lMPh4WEnzG2S\nWTp2RoTdB4qB6YH8Hg7XYLnDFEPBIZTJAaFcCClZKjAtSyQ54U1DSQQ4Xl06nVZTU5OSyaQGBgYc\nq8z2FZNGCQbxeNxVruNtoGgIp7Ffzsv2LrP5KsKIXEPuA56Yz4N4zBb8k+bhErC0WjleiISmjvn2\nZT0Da82z70wm4wrs8GYSiYSjV9peUgh2tnOMcEFkODlOWAyWGjkZihYRunZmC8CjQmlQGEgIDa8D\nL8AWQUajUXcMQn5cT8JPdh+sF2YaytWOSs6XHCdEiBcYVsLeK/GYTXhl4iFJx7TvKARgGxH6Iek8\nNDSU1erEhsdoM4Kwr6urc0Kd2pRIJKLGxsacnhMhHo4Pa4veVSgpOzkSVhUeCpY/3g9zVfBmyHvg\nhdmaGXJNAwMDbt8oHa4H3hCgtsQqcTxF24l5vOtsm1OyTl/N7jGb8MrEY0YBRVg6vqVM7gPhiQdD\nnobK9nDoyII8BEIZjwQFQ5U+1eU2GU4lPkWHklxoC8IACfL6+nqnfDOZjPr6+lyCH8IBTC5qc8i1\nsH7rcYU9JFvvA/LVjpBLYX3RaNTXjHjMOrwy8ZhxhAUgljTeB8KUnAUgh4DVbkNeQ0NDru7EWuA2\nZ2LDSFTfW+ozdOeKigpXI4NyoHCQuS6EkWiGSXhJGmtqifdSUVGhpqYmJRKJrPPEW6AjMp4SHpSt\n9bGV+YTBCKXlCnuFe6t5eMw2fG8uj6KALroIUzvH3dJrbZ6F7clkUqlUyrGZaLkCmEPPM0E+hoJL\nEtfRaNQ1wOzv73dsMNZHzQmgon8ygIxA7sQqO1usKI0qSBL+nBe1NHwOz6uYs9k9TiwUSnZ6ZeJR\nMqABoRW4FEJS+IiVXltb64oq8TwQrngesNNsroTiR9tLjDYptihTGm2VgSdjK/YLhVwFg3awFeE4\nQn2AXI4fq+tRCBRKdvowl0fJoLy8XPX19Y4NRf5BkssJDA4OutCTNCaIbbEkISXbDj8ejyuRSLh6\nDGowwh16mSxpOwIUGnhIJOLJK+XKk3h4zBV4ZeJRUsgX+yfXwNwQEJ4ZkgsoHOuNUMkOVZfEOrB1\nL4VGOJxH48mJFolK8gl2j5KDVyYecwqMAJ6M4Cd/QljItr2HokwlPR7JTBX70cTR7p+q/lzKJF+R\nqPdgPEoNs/pE3nLLLVqxYoVWrFihSy+9VIcPH3Z/u/vuu7VixQqtXLlSzz77rNu+Z88erV69Wm1t\nbbrppptmc7keJQiEK8OiYrHYcXMHYRqxzcnYbUyfnIwiIWcz0ZhzrmPb7blAkWhDQ4Nrx+/hUWqY\nVWVy2WWXad++fXrrrbfU3t6uv/zLv5Q0qjCefPJJvfHGG9q1a5e2bdvmEqHXX3+9Hn74Yb355pv6\n5S9/qe9///uzuWSPEoRtET8RwQrdF1AgSbJ7sqDinRnqfX196unp0cDAwHH3h9KyTSszmYxPpnvM\necyqMvnUpz7l3PPzzjvPjbncsWOHtm7dqvLycrW0tKitrU27d+/WO++8o0wmo9WrV0uSrrnmGu3Y\nsWM2l+wxTWzcuDFvgeFswfbzSiaTSiQSKisrUyKRmJACsBgZGVFfX5/6+/vd6Fza2h89elR9fX1Z\niisXotGoa3LpZ4l4nCgoWuD1wQcf1KZNmySNzk5ubW11f2ttbVV3d7cOHjyopUuXuu0tLS3q7u6e\n9bV6TB379u0rujKhS29tba3Lj1DpTr+uiYA+XeRZyHXYmfW0iz/eemCUxWKxnLkSD4+5hoKbQxs2\nbNB77713zPbt27frsssukyTdddddqqqq0tVXX13QY99xxx3u/+vXr9f69esLun+PieGVV17R9u3b\n3e9XXnmlKioqdOutt+q8884r2rqooLfJa+jBEwFhKcJmeBb2+9S1+LCVR6mis7NTnZ2dBd9vwZXJ\nc889N+7fH330Ue3YsUPPP/+829ba2qquri73e3d3t5YuXZpzu/VgwrDKxKN4eP311/Xqq6+633/8\n4x9Lkvbu3VtUZWKLGm0ifKLMKDt+13ZCpuU723zIyqOUETa077zzzoLsd1Yr4Hft2qWvfe1reuGF\nF7RgwQK3fc+ePfriF7+ol19+We+9957WrVunt99+W5WVlero6NCjjz6q1atX6/LLL9d1112nK6+8\n8tgT8RXwJYmWlhbt37+/ZEI5tmWJNMaUmmi79sHBQR09ejRr2iHFlYS66HTs4TEXMCcr4L/yla9o\neHhYGzZskCSdc845+s53vqM1a9boiiuuUEdHhyKRiB544AFXlPXII4/ohhtu0PDwsC644IKcisSj\ntFFKgpVcCe3nbb+siQDmlfVu2OdU9ufhcaLA9+bymFH09PSoubm52MsoCIIgUF9fX1YYixkm9fX1\nRVyZh8fUUSjZWTomo8cJiRNFkYDwizeZnIuHx4kM/xZ4eEwC5eXlbqohP5655eHhlYmHx4TAXJRU\nKpU1Fz4Wi3n2loeHfKNHD48JgeaSlZWVWXNUfJ8sD49ReM/Ew2MCoJ4E2DkqHh4eXpl4eEwITGkE\nuaYkeniczPBhLg+PCaCqqiprjkoQBKqpqfFMLg+PD+HrTDw8Jghaz9Ofy+dLPE4EFEp2emXi4eHh\ncRLDFy16eHh4eJQMvDLx8PDw8Jg2vDLx8PDw8Jg2vDLx8PDw8Jg2vDLx8PDw8Jg2vDLx8PDw8Jg2\nvDLx8PDw8Jg2iqJMvvWtbykSiainp8dtu/vuu7VixQqtXLlSzz77rNu+Z88erV69Wm1tbbrpppuK\nsdwpo7Ozs9hLOAZ+TRNHKa7Lr2li8Guafcy6Munq6tJzzz2n0047zW3bs2ePnnzySb3xxhvatWuX\ntm3bplQqJUm6/vrr9fDDD+vNN9/UL3/5S33/+9+f7SVPGaX48Pg1TRyluC6/ponBr2n2MevK5JZb\nbtE3v/nNrG07duzQ1q1bVV5erpaWFrW1tWn37t165513lMlktHr1aknSNddcox07dsz2kj08PDw8\njoNZVSZPPfWUWltb1dHRkbX94MGDam1tdb+3traqu7tbBw8e1NKlS932lpYWdXd3z9p6PTw8PDwm\niKDAuPDCC4P29vZjfp566qngN3/zN4OjR48GQRAEy5YtCw4dOhQEQRD84R/+YfAv//Ivbh/btm0L\n/vmf/zl46aWXgt/+7d9221966aVg48aNOY8ryf/4H//jf/zPFH4KgYK3oH/uuedybt+3b5/279+v\nVatWSZK6u7u1Zs0a7d69W62trerq6nKf7e7u1tKlS3Nutx6MReCbPHp4eHgUDbMW5mpvb9evfvUr\n7d+/X/v371dra6v27t2rxYsX6+KLL9bjjz+ukZERdXd3a9++ffr4xz+upUuXKhKJ6Mc//rEk6Xvf\n+54uvvji2Vqyh4eHh8cEUbThWHZC3Zo1a3TFFVeoo6NDkUhEDzzwgCorKyVJjzzyiG644QYNDw/r\nggsu0JVXXlmsJXt4eHh45ENBgmVFwF/91V8FZWVlweHDh9227du3B8uXLw/a29uDH/zgB277a6+9\nFpx11lnBihUrghtvvLHga7n55puD5cuXB8uXLw8uueQSlwsq5prCeOaZZ4L29vZg+fLlwde//vUZ\nPx545513gk9+8pNBe3t7cMYZZwTf+MY3giAIgsOHDwcXXnhhsHLlyuDTn/500Nvb676T75oVGiMj\nI8FZZ50VXHrppSWzpt7e3mDz5s1BR0dH8LGPfSx4+eWXi76uP/uzPws++tGPBmeeeWZw1VVXBQMD\nA7O+puuvvz5YtGhR0N7e7rZNZQ2FfO9yranYsiDXmsBMy8w5qUzeeeedYOPGjcGyZcvchXnttdeC\ntWvXBiMjI0F3d3ewbNmyYHh4OAiCIFi5cmWwd+/eIAiCYNOmTcGTTz5Z0PU8//zzQTqdDoIgCG67\n7bbgq1/9atHXZDE4OBgsW7Ys6O7uDlKpVLB27Vp37JnGe++9F7zxxhtBEARBf39/8NGPfjR4/fXX\ngz/+4z8Ovv3tbwdBEATf/va33QOb65oNDQ3NyNq+9a1vBZ///OeDyy67LAiCoCTWtHnz5uCf/umf\ngiAIgnQ6HRw9erSo63r77beD008/3e33c5/7XPDQQw/N+pr+67/+K9i7d2+WkJzMGmbivcu1pmLL\nglxrCoLZkZlzsp1KqdWqfOpTn3KzwM877zwdPHiw6Guy2L17t9ra2tTS0qKKigpt2bJl1up1Fi9e\nrPb2dklSLBZTR0eHDh48qJ07d+raa6+VlH3+ua7ZK6+8UvB1dXd3a+fOnfr93/99R94o9poOHz6s\n119/Xb/zO78jSYpEImpoaCjqupqbm1VZWamBgQGNjIwokUjo1FNPnfU1ffKTn9S8efOytk1mDTPx\n3uVaU7FlQa41SbMjM+ecMin1WpUHH3xQmzZtKqk1wY4Lr2O2ceDAAb366qtat26dPvjgA82fP1+S\ntGDBAr3//vuS8l+zQuPmm2/WPffc4158SUVf09tvv62FCxfqc5/7nNrb23Xdddepv7+/qOtqbm7W\n1772NZ166qn6tV/7NTU1NWnDhg1Fv1bS5O/XySoLZktmFi0BPx42bNig995775jtd911l+6+++6s\n3l3BLFGC861p+/btuuyyy9z6qqqqdPXVV8/KmiYKS3YoFuLxuDZv3qz77rtPDQ0NRV3L008/rUWL\nFmn16tUl1eIik8no1Vdf1X333aezzz5bX/3qV/UXf/EXRV3Tz3/+c/31X/+1Dhw4oMbGRn32s5/V\nY489VtQ1zQWUiixIJBLavn17VsnGTMnMklQmxapVmcqawKOPPqodO3bo+eefd9tmek0TRfh4XV1d\nWZbHTCOVSumqq67S1Vdfrcsvv1yStHDhQh06dEgLFizQBx98oEWLFuVca9irKgReeukl/cd//Id2\n7typwcFB9fX16dprry3qmiRp6dKlamlp0dlnny1J2rx5s/78z/9cixYtKtq6XnnlFZ177rnOA7jy\nyiv14osvFv1aSZN/hmbrvSslWfDzn/9cBw4cmB2ZOeVMTwkgVzIplUoFXV1dwWmnnZY3mfRv//Zv\nBV3HM888E6xYsSL44IMPsrYXc00WyWQyOO2004Lu7u5geHg4WLt2bbBnz54ZO55FJpMJrr32WpeI\nBDZ5eu+99wZf+cpXgiAY/5rNBDo7Ox2bqxTWtGbNmuCnP/1pEARBcPvttwc33nhjUdf1yiuvBG1t\nbUEikQgymUxw3XXXBffcc09R1rR///68CfiJrqHQ7114TaUgC8JrsphJmTmnlcnpp5+eRXO76667\nguXLlwdtbW3Brl273HZLc+OBKyQ+8pGPBKeeempw1llnBWeddVbwpS99qehrCmPnzp1BW1tbsHz5\n8mD79u0zfjzw3//930FZWVmwatUqd32eeeaZLFrnhg0bsmid+a7ZTKCzs9OxuUphTa+//nqwdu3a\nYMWKFcFFF10U9PT0FH1dt99+e/CRj3wkOOOMM4ItW7YEyWRy1te0devW4JRTTgkqKyuD1tbW4OGH\nH57SGgr53oXX9Pd///dFlwWsqaqqyl0ni5mUmWVB4PuQeHh4eHhMD3OOzeXh4eHhUXrwysTDw8PD\nY9rwysTDw8PDY9rwysTDw8PDY9rwysTDYwbw6quvatWqVRoaGtLAwIDa29v11ltvFXtZHh4zBs/m\n8vCYIfzpn/6pBgcHlUwmtXTpUt12223FXpKHx4zBKxMPjxlCKpXS2rVrVVNTo5dffrkk2tp4eMwU\nfJjLw2OGcOjQIQ0MDCgejyuZTBZ7OR4eMwrvmXh4zBA+85nP6POf/7x+8Ytf6N1339Xf/M3fFHtJ\nHh4zhpJs9OjhMdfxD//wD6qurtbWrVuVyWR07rnnqrOzU+vXry/20jw8ZgTeM/Hw8PDwmDZ8zsTD\nw8PDY9rwysTDw8PDY9rwysTDw8PDY9rwysTDw8PDY9rwysTDw8PDY9rwysTDw8PDY9r4/4Ne+OL9\nBl/JAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 39
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now define the k-means algorithm, looking for *k* clusters in points *data*. The algorithm starts from initial guess *centroids* and stops when the centroids move less than *stop\\_diff* between iterations."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def k_means (k, data, centroids, stop_diff):\n",
" centroid_paths = [[c] for c in centroids]\n",
" max_diffs = []\n",
" errors = []\n",
" while True:\n",
" regions = [[] for i in range(k)]\n",
" for point in data:\n",
" distances = [coordinates.distance(point, centroid) \n",
" for centroid in centroids]\n",
" regions[argmin(distances)].append(point)\n",
"\n",
" diffs = []\n",
" for i, region in enumerate(regions):\n",
" if len(region) == 0:\n",
" region.append(data[random_integers(0, len(data), 1)])\n",
" centroid = coordinates.mean(region)\n",
" diffs.append(coordinates.distance(centroid, centroids[i]))\n",
" centroids[i] = centroid\n",
" centroid_paths[i].append(centroid)\n",
" max_diffs.append(sum(diffs))\n",
"\n",
" for centroid in centroids:\n",
" errors.append(\n",
" mean([\n",
" min([coordinates.distance(centroid, cluster) \n",
" for cluster in clusters])\n",
" for centroid in centroids]))\n",
" if max(diffs) < stop_diff:\n",
" break\n",
" return centroids, regions, errors, centroid_paths"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 40
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Execute the *k-means* function and capture the results. The function returns the final *centroids*, *k* clusters of points, *error* vectors and *centroid* positions at each iteration."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"centroids, regions, errors, paths = k_means(k, data, centroids, stop_diff)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 41
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Generate a random colour palette, and plot the points, generated centroids, and correct cluster centres. Points are coloured by region."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k_colors = colours.light_palette(k)\n",
"\n",
"for i, region in enumerate(regions):\n",
" scatter(*coordinates.to_xy(region), \n",
" color=k_colors[i], label=\"Region %d\" % i, alpha='0.3')\n",
"scatter(*coordinates.to_xy(centroids), marker='+', color='0.1', label=\"Centroids\")\n",
"scatter(*coordinates.to_xy(clusters), color='r', label=\"Cluster Centres\")\n",
"for i, path in enumerate(paths):\n",
" plot(*coordinates.to_xy(path), color='0.5')\n",
"#legend(loc='best', fancybox=True)\n",
"xlabel('x')\n",
"ylabel('y')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 42,
"text": [
"<matplotlib.text.Text at 0x7ff59a834910>"
]
},
{
"output_type": "display_data",
"png": 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cUt448uI3F6vN6S3r8+/XO8ZUcHVSiEnBFcGOZooMg+QAwqUI529L17zxzPqH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\n"
}
],
"prompt_number": 42
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, plot the error between *centroids* and the known *cluster centres* for each iteration of the *k-mean* loop."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot(errors, '.-')\n",
"xlabel('Iteration')\n",
"ylabel('Max error')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 27,
"text": [
"<matplotlib.text.Text at 0x7ff5998a05d0>"
]
},
{
"output_type": "display_data",
"png": 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W82ck9FZrY2MjEhMTERAQgLFjxyI2NlZ3NQLAU089hWXLlsHD4+Z/Dz3WaTKZ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\nACZpHwAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 27
}
],
"metadata": {}
}
]
}
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