Experiments based on paper "Generalized distances between rankings" by Kumar and Vassilvitskii.

RankingDistances.ipynb

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  "name": "RankingDistances"
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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "# Distance measures between ranking lists\n\n- [http://math.stackexchange.com/questions/202390/measuring-orderedness](http://math.stackexchange.com/questions/202390/measuring-orderedness)\n- A [blog post about the symmetric group](http://cameroncounts.wordpress.com/2011/01/18/the-symmetric-group-9/)\n- Measures for evaluating the performance of information retrieval systems: [Mean Average Precision](http://en.wikipedia.org/wiki/Information_retrieval) and [Normalised Discounted Cumulative Gain](http://en.wikipedia.org/wiki/Discounted_cumulative_gain)\n- _comparing top $k$ lists_ by [Kumar](http://researcher.watson.ibm.com/researcher/files/us-fagin/sidma03.pdf)\n- _Generalized Distances between Rankings_ by Kumar [paper](http://theory.stanford.edu/~sergei/papers/www10-metrics.pdf) and [slides](http://theory.stanford.edu/~sergei/slides/www10-metrics.pdf)"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "$ D_n =  \\\\left\\\\{ 1, \\ldots, n \\\\right\\\\} $ a set of $n$ items.\n\nLet $S_n$ be the set of permutations on $D_n$ and for $\\sigma \\in S_n$, let $\\sigma(i)$ denote the rank of the element $i$. A permutation (or ranking) is an array of $n$ integers where each of the integers between 1 and $n$ appears exactly once.\n"
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## Kendall and spearman distances for the ideal case of rankings of $k=n$ items of $D_n$\n\n\n- [http://en.wikipedia.org/wiki/Kendall_tau_distance](http://en.wikipedia.org/wiki/Kendall_tau_distance) implemented in [`scipy.stats.kendalltau`](http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kendalltau.html).\n- [Spearman rank correlation]((http://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient)) measures the monotoniticy (ie the rank) between two data-sets implemented in [`scipy.stats.spearmanr`](http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.spearmanr.html)\n\n$$ K_(\\sigma) = \\sum\\limits_{(i;j):i>j} [\\sigma(i) < \\sigma(j) ] $$\n\n$$ F_(\\sigma) = \\sum\\limits_{i} | i - \\sigma(i) | $$\n\n`scipy` implementations calculates normalised versions of those distances.\n"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "from scipy import stats\nn = 8\nordered_perm = np.arange(start=1, stop=n)\n\n# brute force enumeration of all permutations, very slow for n=10\n#import itertools\n#sampled_scores = [stats.spearmanr(p, ordered_perm)[0] for p in itertools.permutations(ordered_perm)]\n\nn_samples = 10000\nspearman_scores = [stats.spearmanr(np.random.permutation(ordered_perm), ordered_perm)[0] for i in xrange(n_samples)]\nkendall_scores = [stats.kendalltau(np.random.permutation(ordered_perm), ordered_perm)[0] for i in xrange(n_samples)]\n",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "plt.figure(figsize=(16, 8))\n\nkd_hist = plt.hist(kendall_scores, bins=20, normed=True, histtype='stepfilled', ec=None, range=[-1.2, 1.2], color='b', alpha=.5, label=\"Kendall's Tau\")\nsp_hist = plt.hist(spearman_scores, bins=20, normed=True, histtype='stepfilled', range=[-1.2, 1.2], color='r', alpha=.5, label=\"Spearmann correlation\")\n\np_ordered = [1, 2, 3, 4, 5, 6, 7]\np_top_3_ordered = [1, 2, 3, 7, 6, 5, 4]\np_switch_3_4 = [1, 2, 4, 3, 5, 6, 7]\np_shift_5_to_3 = [1, 2, 5, 3, 4, 6, 7]\np_reversed = [7, 6, 5, 4, 3, 2, 1]\np_top_3_reversed = [3, 2, 1, 4, 5, 6, 7]\n\nillustrated_perms = np.array([p_ordered, p_top_3_ordered, p_switch_3_4, p_shift_5_to_3, p_reversed, p_top_3_reversed])\nillustrated_perms_labels = [\"\".join(map(str, p)) for p in illustrated_perms]\n\nillustrated_kd_measures = [stats.kendalltau(p, ordered_perm)[0] for p in illustrated_perms]\nmax_y = max(kd_hist[0] + sp_hist[0]) \nillustrated_kd_ys = max_y - np.arange(n - 1) % 2 / 10.0 - np.random.uniform(size=n-1) * .2\n\nillustrated_sp_measures = [stats.spearmanr(p, ordered_perm)[0] for p in illustrated_perms]\nillustrated_sp_ys = .1 + np.arange(n - 1) % 2 / 10.0 + np.random.uniform(size=n-1) * .2\n\nfor label, measure, y in zip(illustrated_perms_labels, illustrated_kd_measures, illustrated_kd_ys):\n    plt.text(measure, y, label, horizontalalignment='center', color='darkblue')\n    \nfor label, measure, y in zip(illustrated_perms_labels, illustrated_sp_measures, illustrated_sp_ys):\n    plt.text(measure, y, label, horizontalalignment='center', color='darkred')\n    \nfor x1, y1, x2, y2 in zip(illustrated_sp_measures, illustrated_sp_ys, illustrated_kd_measures, illustrated_kd_ys):\n    plt.plot([x1, x2], [y1, y2], color='k', lw=3, alpha=.25)\n    \nplt.legend();",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
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8Hq1fX641a8o0cODBP8xefPErjRvXT5s3b1ZVVZUGDhyosWMH6MUXv9LEiUO1\na1e1Vq8uU79++dq7d78CAZ8yM33atata77+/Rf/1Xydp0KAu2rr1x9Y9c3MfS7kwumtXtXw+j/Lz\ns1RTE9Y//rFe9957SrOf6wGHVkFvvHGEbrxxhKqrq7V69U6NHz9f8+ePkyRt21ZlbWkuK6vVUUcV\nKBSK6cQTi7R3736VlHSXx2Po3XfX64QTiqwtvXPnfqPcXH+jMCrJCqPhcFShUFRdux4Mvffcs0ST\nJ5+kBx9cbgXLpvpVD3WgX3XLlh2H3SK8ZMkSRSIRSdJpp50mn8+5P9MZEIlkQiAFAABpa/z4t7Ro\n0Ubt2lWj4uKnNHXqd3T//f9SKBTTOee8Kkk65ZSeeuKJ72rJks164IF/KSPDq4wMj55++lx16pRp\n3euVV1bp/vsHaM2aNZKknj176j/+o6/mz1+vIUNmyOs19NBDpSooyNIHH2zWjTf+Qx6PoVjM1F13\njdSgQV0arS8Vq2pbt1bp2mvnKhYzFYuZuvrqwTr77CM1cOCfmvxcJalPn6dVURFSKBTVG2+s1fz5\nl1qfx5dffqk1a3YpFAqpurpanTp10vTpH2n27LXy+Tzq0iWgBx8s1a23LpDX69FDD5Xq7LNfkWma\nVhj9/vfrKp1vvfWNamoiKimZpby8TP3616daA6gk6T/+41UtX75N55xzpM47r68k6aOPtmvz5kqN\nHt1PDz643Lq2fr/qt9+W67vfPVIPPDDKGtwkta1f1ev1WoE0Go06GkiBZMKxL0g5/KseACBZrVy5\nUjt37pQkDRo0SEVFRQleUeqr/5kOHjxY3bt3b3TNunXlGjPmb9bRPQf85jdL9dFH2/XaaxdJqpv6\nW1UVVkFBlj76aLvGjn1dK1dep9zcg4GxtjaiK654SxdfPEDXXDNEZ575Vz377Hk68sg8nXnmy3ro\noTN0/PFFevXVVfrBD+br44+vUXFxrq644i2NHt3XOg9Vks4//zX96EfDdPHFAw/7cy5btkzV1dWS\npJNOOknZ2YefyNxe/C0FJ3DsCwAAQILl5ORYX1dWViZwJe6RmXmwCr1///5Wf9+BftXnn/+e9Zzf\n77WO+TnuuEL175+vNWvKDnk/n8aNG6jly7epoiKklSt3qbT0ZfXt+7SWLt2qiy56XR99tF3FxZ00\nYkR39emTJ6/Xo7FjBzQYeLRrV7WWL9+m732v4TTh5ni9B7cRR6PRFq4E3IW9AAAAADapH0grKioS\nuBL3yMofWCbgAAAgAElEQVQ6eE5sbW1tC1ce1Fy/6q5d1SooyJLX69E33+zVmjVl6tcvT1VVYe3b\nV6sePXK0b1+lXn11pU47rVCRSJV27vyJ9f1nnvmyHn64VMcdV6hoNKa9e/dr165qde2arXffXa+T\nTuphXfvqq6s1Zky/JvtVm+LxHKwTxWKxVn0P4AYEUgAAAJvUD6RVVVUJXIl71A+kTVVI29IHvGjR\nJt177/vKyPDK4zH01FPnKj8/S9u3V+mii15XbW1U4XBYw4Zl6oQTYtq1a5c6d+7c5Lqa6lf94Q+H\nWa+//PIq3XXXyFb/nFRIka7oIUXKoe8BAJDM3n//fYXDYUnSyJEjFQgEDvMdaEllZaU+/PBDSVIw\nGNSJJ57o6Pvt3LlTK1eulCR169ZNQ4YMcfT9DqjfKztkyBB169bNsffibyk4gR5SAACAJJCbm2t9\nTR9px7W3h7S96k+3PfAPC/FAhRTpikAKAABgIwYb2SsjI8MKa9Fo1Doaxcn3O4BACjiPQAoAAGAj\nBhvZ73B9pHaqH0idDr/1MdQI6YpACgAAYCMqpPZLVCClQgo4j0AKAABgo0AgYIWLUCikUCiU4BWl\nvnj2kXo8HqtaGYvF4hYOCaRIVwRSAAAAGxmGQZXUZu05i7QjElElJZAiXRFIAQAAbEYgtVc8t+xK\niekjJZAiXRFIAQAAbMZgI3vF++gXKqRA/BBIAQAAbEaF1F7x3rKbiLNImbKLdEUgBQAAsFkwGJRh\nGJKkmpoaKl4d5Pf7rc8zFAo5HtiokALxQyAFAACwmcfjUTAYtB5TJe0YwzBcfxYpgRTpikAKAADg\nALbt2iuefaRUSIH4IZACAAA4gMFG9opnH2kiekgJpEhXBFIAAAAHUCG1V6K27DLUCHAWgRQAAMAB\n9QNpVVUVIaOD3B5IqZAiXRFIAQAAHODz+RQIBCRJpmmquro6wStKbYnqIY3XUCPDMKwqqWma/AMG\n0gaBFAAAwCFs27VPPHtIE1EhlaiSIj0RSAEAABzCYCP71K+Q1tbWyjRNx97L5/NZ555GIhFH36s+\nAinSEYEUAADAIVRI7ePxeKxQapqmKyft1h9sRCBFuiCQAgAAOIRAai+395HWr5DSQ4p0QSAFAABw\nSGZmpvx+v6S6ildNTU2CV5Ta3N5HypZdpCMCKQAAgIOoktonnke/JGLLLoEU6YhACgAA4CAGG9kn\nUVt2CaSAcwikAAAADqJCap9EbdlNRA8pgRTpgkAKAADgoNzcXOtrAmnHxHPLbiIqpPWn7DLUCOmC\nQAoAAOCgQCBgVb5CoZBCoVCCV5S66CEF3IdACgAA4DC27drD6/VaQTEWizka7ukhBeKDQAoAAOAw\nBhvZJ159pARSID4IpAAAAA6jQmqfeG3bZagREB8EUgAAAIcx2Mg+iQikiRhqRCBFuiCQAgAAOCw7\nO1uGYUiSampq4lZxc6N4nUWa6KFGTNlFumgxkG7cuFFnnnmmhgwZoqFDh2r69OlNXnfLLbdo4MCB\nGj58uFasWOHIQgEAAFKVx+NRMBi0HlMlbb949ZB6PB4rIJqmGZd/RGDLLtJRi4E0IyNDjzzyiFau\nXKmlS5fq97//vb788ssG18yZM0dr167VmjVr9PTTT+vHP/6xowsGAABIRfSR2iNRZ5ESSAFntBhI\ni4qKNGLECEl1/yd6zDHHaMuWLQ2umT17tq699lpJ0siRI7V3715t377doeUCAACkJgKpPRIVSOOx\nbZdAinTkO/wlddatW6cVK1Zo5MiRDZ7fvHmziouLrce9e/fWpk2bVFhY2OC6KVOmWF+XlpaqtLS0\nfSsGAABIQQw2skdGRoY8Ho9isZgikYgikUiDfk87xbuPlECKVLJw4UItXLiww/dp1f96Kysrdeml\nl+qxxx5r8K97B5im2eDxgab9+uoHUgAAgHRT/2+oqqoqxWKxBlNV0XpZWVmqrq6WVNdH6lQgjXeF\ntP7vA0ONkOwOLTJOnTq1Xfc57P8LhsNhjRs3ThMmTNDYsWMbvd6rVy9t3LjRerxp0yb16tWrXYsB\nAABwK6/Xq0AgIKnuH/OrqqoSvKLU5dazSKmQIh21GEhN09SkSZM0ePBg3XbbbU1ec+GFF2rWrFmS\npKVLlyo/P7/Rdl0AAADQR2qXeB39Qg8p4LwW9ze8//77+stf/qJhw4appKREknTfffdpw4YNkqQb\nbrhBo0eP1pw5czRgwAAFg0HNmDHD+VUDAACkoJycHO3cuVMSgbQj4nX0S6LOIj0QRqPRaIOQCrhR\ni4H0tNNOa9X+9ccff9y2BQEAALgVg43skYgtuwRSwBl00gMAAMTJoVt2Dx0MidZxaw+pxGAjpB8C\nKQAAQJz4/X75/X5JddWvmpqaBK8oNbm1h1SijxTph0AKAAAQRww26rjMzEzrmMFQKORYJTFRPaQH\nEEiRDgikAAAAcUQg7TjDMBpUSZ0abESFFHAegRQAACCOGGxkj3j0kfp8PqsSG41G49LTSSBFuiGQ\nAgAAxBEVUnskoo80HoONCKRINwRSAACAOAoEAlZvYigUcvQcTTeL11mk8d62y5RdpBsCKQAAQJwF\ng0Hra6qk7ROvo1/iPdiICinSDYEUAAAgzti223GJOIuUQArYj0AKAAAQZww26jh6SAF3IJACAADE\nGRXSjju0h9Q0TUfehwop4CwCKQAAQJwFg0FreE1NTU1cKm9u4/F45Pf7JUmmaSoUCjnyPvHuIWWo\nEdINgRQAACDODMNQdna29ZgqafvEY9suFVLAWQRSAACABKCPtOPicfQLPaSAswikAAAACUAfacfF\nY9IuFVLAWQRSAACABCCQdlw8AinnkALOIpACAAAkQP1AWlVVxQCbdnBjD2n9oUYEUqQDAikAAEAC\neL1eBQIBSXVTYquqqhK8otTj9h5S/pEC6YBACgAAkCAMNuqYeGzZNQzD2rZrmqbjoZQtu0g3BFIA\nAIAEoY+0Y3w+nxUWo9GoY1tq49lHSiBFuiGQAgAAJEj9QFpRUZHAlaQut/WRejweGYYhqW7Lrmma\njr4fkGgEUgAAgAQ5dLAR4aPt4t1HyqRdwF4EUgAAgATx+/3y+/2S6oJHTU1NgleUeuJ9Fmk8BhvV\nn7TLYCO4HYEUAAAggRhs1DHxDqRUSAF7EUgBAAASiMFGHROPHtJ4DjWSCKRILwRSAACABGKwUcfQ\nQwqkNgIpAABAAlEh7Rg39pASSJFOCKQAAAAJFAgErC2h4XDYsSqfW/n9fmsIUDgcdiTAxbtCWn+o\nEYEUbkcgBQAASDCqpB1Tv4/UiUCfyB5SpuzC7QikAAAACUYg7Rint+3SQwo4h0AKAACQYAw26ph4\nBlJ6SAF7EUgBAAASjAppxzh99IvX67X6OqPRqOPbaAmkSCcEUgAAgAQLBoNW4Nm/f39cqnBuEo+j\nX+LZR0ogRTohkAIAACSYYRgKBoPWY6qkbRPvo1+cDqT1p+wy1AhuRyAFAABIAmzbbT+3BVIqpEgn\nBFIAAIAkwGCj9svMzJRhGJKkUCgk0zRtf494DjYikCKdEEgBAACSABXS9jMMQ36/X5JkmqYjfaRU\nSAFnEEgBAACSQE5OjlXlq66upnewjZzetstQI8AZBFIAAIAk4PV6FQgEJNVV+aqqqhK8otTi9NEv\nDDUCnEEgBQAASBJs220/pyuk9JACziCQAgAAJAkGG7Wf02eR0kMKOINACgAAkCSokLYfPaRAaiKQ\nAgAAJIn6gbSqqsqR40vcyk09pARSpBMCKQAAQJLw+/1WsIpGo6qpqUnwilJHPLfsOt1DahiGNdjI\nNE0GG8HVCKQAAABJhG277eP1eq3QGIvFFAqFbL1//S27kUjE8eo1k3aRLgikAAAASYTBRu3nZB+p\nYRhWKDVNk0m7gE0IpAAAAEmECmn70UcKpB4CKQAAQBLJzc21viaQto2b+kgJpEgXBFIAAIAkkpWV\nZW0NDYfDjgQrt3L66BcqpID9CKQAAABJhm277eOms0gZaoR0QSAFAABIMgw2ah96SIHUQyAFAABI\nMlRI2yeePaQEUsAeBFIAAIAkw2Cj9snIyLCCXCQSsX3wEEONAPsRSAEAAJJMdna21UO4f/9+x6tx\nbuLktl0qpID9CKQAAABJxjAMBYNB6zFV0tZzcrBRooYaEUjhZgRSAACAJEQfafs42UeaqAopU3bh\nZgRSAACAJEQgbR8nK6T0kAL2I5ACAAAkIQYbtQ89pEBqIZACAAAkoWAwKMMwJEnV1dVs22wlJ7fs\nejweq7czFos5GhQJpEgXBFIAAIAk5PV6FQgEJEmmaVIlbSUnt+xK8auSEkiRLgikAAAASYo+0rbz\n+/1WZTkUCtleWY5XH2n9KbtUx+FmBFIAAIAkRSBtO8MwXNFHSoUU6cJ3+EsAAEAqW778I7311r8S\nvQxLMOjVT386QdnZ2YleStJjsFH7ZGVlWUG0trbW1t+1eJ1FSiBFuiCQAgDgclu37tA33wxQYeGw\nRC9FkrRhwwuqqakhkLbCoRVS0zSt7ahoXryOfiGQAh1HIAUAIA1kZuYqJ6cw0cuQJJWV8edHa2Vk\nZCgzM1O1tbWKxWKqrq5WMBhM9LKSnhvOIiWQIl3QQwoAAJDE6CNtOzf0kDLUCOmCQAoAAJDECKRt\n5+RZpPHqITUMwwqlpmkSSuFa7JkBALTL//7v+1q+fHWil2Hp3DlLkyZdSX8dXIfBRm3nhh5SqW7b\n7oEgGo1GG1RNAbcgkAIA2uWLL9bryy8HKC/viEQvRZL0xRczdf31DHyB+1Ahbbv6W3Zra2ttHQYV\n70B64D2i0WiD9wbcgkAKAGi3YLC78vOPTPQyJEl79yZ6BYAzsrKy5PP5FIlEFA6HtX///gYVQDTm\n8Xjk9/sVCoVkmqZqa2tt+8ziNdRIYrAR0gN1fwAAgCRHlbTtnOojjXeF9AACKdyKQAoAAJDk6CNt\nO6f6SH0+n7X9NxKJyDRN2+59KCbtIh0QSAEAAJIcFdK2c/Lol3hN2qVCinRAIAUAAEhyBNK2c/Lo\nl3j1kRJIkQ4IpAAAAEkuOzvb2r65f/9+x3sX3cANR78QSJEOCKQAAABJzjAMBYNB6zFV0sNzMpCy\nZRewD4EUAAAgBTDYqG0OPYvUTvGqkDLUCOmAQAoAAJAC6CNtG5/PZ1Uyo9GorcGRHlLAPgRSAACA\nFEAgbTuntu3SQwrYh0AKAACQAoLBoHX+ZXV1NVs4W8HJs0gPIJACHdNiIL3++utVWFioY489tsnX\nFy5cqLy8PJWUlKikpES//vWvHVkkAABAuvN6vQoEApIk0zSpkraCU2eRUiEF7NNiIL3uuus0b968\nFm9wxhlnaMWKFVqxYoV+8Ytf2Lo4AAAAHMRgo7Zx6ixSAilgnxYD6emnn66CgoIWb2Capq0LAgAA\nQNPoI22bePSQOjnUiCm7SAe+w1/SPMMw9MEHH2j48OHq1auXHnroIQ0ePLjJa6dMmWJ9XVpaqtLS\n0o68NQAAQNohkLYNW3YB5yxcuFALFy7s8H06FEiPO+44bdy4UdnZ2Zo7d67Gjh2r1atXN3lt/UAK\nAACAtjs0kJqmaQ06QmMMNQKcc2iRcerUqe26T4em7Obm5io7O1uSdP755yscDmvPnj0duSUAAACa\nkZGRYVX9YrGYqqurE7yi5Ob3+61tr5FIxLZQ5/F4rLBomqZj23YJpEgHHQqk27dvt3pIly1bJtM0\n1blzZ1sWBgAAgMYYbNQ2qdxHSiBFOmhxy+748eO1aNEi7dq1S8XFxZo6daq1LeGGG27Qq6++qj/8\n4Q/y+XzKzs7WSy+9FJdFAwAApKucnBzt2rVLUl0gLSwsTPCKkltmZqZVSd6/f7+CwaAt983IyLAC\nbjgcbhB87cJQI6SDFgPpiy++2OI3/+QnP9FPfvITWxcEAACA5tXvI62oqEjgSlKDU0e/xKOP9NAK\nKT3DcKMObdkFAABAfDFpt23isWU3XoONqJLCjQikAAAAKSQrK8sKQ5FIxNaQ5Uap3EMq0UcK9yOQ\nAgAApBiqpK3HWaRAciOQAgAApBgCaeulcg+p1HCwEYEUbkQgBQAASDEMNmq9zMxMaxBQbW2tbX2Y\n9JAC9iCQAgAApBgqpK1nGEaDbbt2VUnpIQXsQSAFAABIMdnZ2dZWztraWkcrdG7gRB8pPaSAPQik\nAAAAKcYwDKqkbeBEH2m8ekgJpHA7AikAAEAKIpC2nhNHv1AhBexBIAUAAEhBDDZqPSe27Pp8PmtY\nUjQadWzgUP0puww1ghsRSAEAAFIQFdLWc6JCKsVnsBEVUrgdgRQAACAF5eTkWBW6mpoawkoLnDqL\nNB7bdgmkcDsCKQAAQAryeDzKzs6WJJmmqaqqqgSvKHkdumXXNE1b7huPwUYEUrgdgRQAACBFsW23\ndbxer1XNNE1ToVDIlvtSIQU6jkAKAACQohhs1HpObNuNRw9p/aFGBFK4EYEUAAAgRVEhbb1UPfql\nfoWUKbtwIwIpAABAisrNzbW+rqqqsq030o2cCKT0kAIdRyAFAABIUT6fzwpasVhM1dXVCV5R8nLi\nLFJ6SIGOI5ACAACkMLbttk6q9pASSOF2BFIAAIAUxmCj1nFDDymBFG5EIAUAAEhhVEhbx4ktu/Ho\nIa0/ZZehRnAjAikAAEAKqz/YiEDavIyMDKvaGI1GbQmQVEiBjiOQAgAApLDMzEwrGEUiEduqf25k\ndx9pvM4hNQxDUl2FlEnKcBsCKQAAQIpj227r2N1HahiGtW3XNE0GGwHtQCAFAABIcQw2ap1U7SMl\nkMLNCKQAAAApjgpp66TqpF0GG8HNCKQAAAApjsFGreP0WaRUSIG2I5ACAACkuEAgYIWW2tpax4JR\nqnO6QkoPKdB2BFIAAIAUZxiGgsGg9Zg+0qY50UNKhRToGAIpAACAC9BHeniZmZlWP2Y4HLYl3DHU\nCOgYAikAAIALEEhbp36V1O6zSAmkQNsRSAEAAFyAwUatY3cfaTx6SJmyCzcjkAIAALhAMBiUYRiS\npJqaGippzbC7j5QKKdAxBFIAAAAX8Hg8ys7OliSZpkmVtBl2H/1CDynQMQRSAAAAl6CP9PCc3LJL\nIAXajkAKAADgEvSRHp6TW3Y5hxRoOwIpAACAS1AhPTy7K6Rer9caOhSNRh0ZOsRQI7gZgRQAAMAl\n6gfSqqoqmaaZwNUkp/oV0lAoZMtn5HQfKRVSuBmBFAAAwCV8Pp9VAYzFYqqqqkrwipKPx+OxQqlp\nmilxFimBFG5GIAUAAHARtu0eXqod/UIghZsRSAEAAFyEwUaH5+SkXScGGxFI4WYEUgAAABehQnp4\ndp9F6nSFtP5QIwIp3IZACgAA4CIE0sOzu0Iaz6FGTNmF2xBIAQAAXCQzM9Oq2EUiEdXU1CR4RcmH\nHlIgeRBIAQAAXIYqacuc3LJLDynQNgRSAAAAl2GwUcucHGrkRIXUMAyrj9Q0TbbtwlUIpAAAAC5D\nhbRlXq/XCpGxWEyhUKhD93O6h1SiSgr3IpACAAC4DIH08OzsI3W6Qio1nLRLhRRuQiAFAABwmUAg\nYFXUamtrO1wBdCM7+0id7iGVqJDCvQikAAAALmMYhoLBoPWYKmljdvaR1t+yG4lEZJpmh+7XFAIp\n3IpACgAA4EIMNmqZnVt2DcOwQqlpmkzaBdqAQAoAAOBC9JG2LNUm7RJI4VYEUgAAABcikLYs1c4i\nrT/UiEAKNyGQAgAAuFAwGJRhGJKk6upqQswhUrlCypRduAmBFAAAwIU8Ho+ys7Otx1RJG8rIyLBC\nXiQS6XBV0+mzSNmyC7cikAIAALgUg41alkpnkRJI4VYEUgAAAJeij7RlTp1FSiAFWo9ACgAA4FIE\n0pbZ2Ufq9FAjAincikAKAADgUvUDaVVVlUzTTOBqkk8qbdmtP2WXoUZwEwIpAACAS/l8PqsKGIvF\nVFVVleAVJRc7t+wy1AhoHwIpAACAizHYqHlObdklkAKtRyAFAABwMfpIm0cPKZB4BFIAAAAXqx9I\nKyoqEriS5OP3+2UYhiQpFAp1qDeTCinQPgRSAAAAFzt0sBEOMgyjwWCjjvSRejwea/BQLBazPTQy\n1AhuRSAFAABwsczMTPn9fkl1W0lramoSvKLkkip9pFRI4VYEUgAAAJejj7R5Th39YncfKYEUbkUg\nBQAAcDkCafOokAKJRSAFAABwOQYbNS9VziKt30NKIIWbEEgBAABcjgpp81KlQmoYBlVSuBKBFAAA\nwOUCgYAVZkKhkEKhUIJXlDxSpYdUYtIu3IlACgAA4HKGYVAlbcahW3ZN02z3vTiLFGg7AikAAEAa\nIJA2zePxWMfimKbZoeqxkz2kEoEU7kQgBQAASAMMNmqeXX2kVEiBtiOQAgAApAEqpM2zq4+UQAq0\nHYEUAAAgDQSDQRmGIUmqqakh0NRj19EvDDUC2o5ACgAAkAY8Ho+CwaD1mCrpQWzZBRLHd/hLAABA\nW+zYsUN/feIJmR2otNhp9dpvtde8WL17n5zopSDBcnJyrCBaWVmpvLy8BK8oOdgVSH0+nwzDkGma\nikQiMk3TqkrbgUAKNyKQAgBgs4qKCgXWrdNF3bsneimSpBd27dT6XIbYgMFGzbHzLFKfz2dVR8Ph\nsDXB1w4EUrgRgRQAAAf4fT51zc5O9DIkSVn1/ohFemOwUdPs6iGV6rbtHgikkUiEQAocBj2kAAAA\naaJ+IK2qqmIwzv/n8/msM0Sj0WiH+j+d7COtP9SIQAq3IJACAACkCZ/Pp0AgIEkyTVPV1dUJXlHy\nsGvb7oFgK9kfSOtXSPnHBLhFi4H0+uuvV2FhoY499thmr7nllls0cOBADR8+XCtWrLB9gQAAALAP\n23ablgqTdtmyCzdqMZBed911mjdvXrOvz5kzR2vXrtWaNWv09NNP68c//rHtCwQAAIB9GGzUtFQ4\ni5RACjdqcajR6aefrnXr1jX7+uzZs3XttddKkkaOHKm9e/dq+/btKiwsbHTtlClTrK9LS0tVWlra\nrgUDAACg/aiQNo0KKdA2Cxcu1MKFCzt8nw5N2d28ebOKi4utx71799amTZsOG0gBALCbaUrvvvu/\ntp75115btmxR+d5yqXfvRC8FaCQ3N9f6mkB6UKr1kBJIkWiHFhmnTp3arvt0+NgX0zQbPE6GPwQA\nAOknM/N7euGF5BjQsmNHhYbu3ikNTfRKgMb8fr/8fr9CoZCi0ahqamqsQUfpLBUqpPWn7DLUCG7R\noUDaq1cvbdy40Xq8adMm9erVq8OLAgCgrXr2PCHRS7DEYhFpd6JXATQvJydHe/bskVRXJSWQOtND\nSoUUOLwOHfty4YUXatasWZKkpUuXKj8/v8ntugAAAEgeDDZqzO/3WxXIcDjc7sDHUCOgbVqskI4f\nP16LFi3Srl27VFxcrKlTp1r/0nPDDTdo9OjRmjNnjgYMGKBgMKgZM2bEZdEAAABoPwYbNS0zM1M1\nNTWS6rbtBoPBNt+DCinQNi0G0hdffPGwN3j88cdtWwwAAG4Ri0VVVZ0cPa2RCH+4oiEGGzUtKyvL\nCqS1tbXtCqQMNQLapsNDjQAAQEN+f472lEX1zjufJ3opkqTNFdXK7NYp0ctAEgkEAvJ6vYpGowqF\nQgqFQvL7/YleVsLZMdjI4/FYn61pmopEIg1Cakd4PB4ZhiHTNBWLxWSaJgNFkfIIpAAA2CwQ6CJv\n7mDldUqOY19yzA3Kyzsi0ctAksnJyVF5ebmkuipp586dE7yixLPr6JeMjAyrgmlnIJXqQumBe8di\nsQZVUyAVdWioEQAAAFITg40aS4WjX9i2C7chkAIAAKQh+kgbs+voF/pIgdYjkAIAAKQhJu02RoUU\niD8CKQAAQBrKzs62BuLU1NTYfmZmKsrMzLQ+k1AoJNM023UfziIFWo9ACgAAkIY8Hk+DY02okkqG\nYVjThk3TbHeV1MkKqcdz8M/3WCxm672BRCCQAgAApCm27TZmRx8pPaRA6xFIAQAA0hSDjRqzo4+U\nHlKg9QikAAAAaYoKaWN2nEVKDynQegRSAACANFU/kFZVVdGTKCqkQLwRSAEAANKU1+tVIBCQVDfE\np6qqKsErSrxk7yFlqBHchkAKAACQxti22xAVUiC+CKQAAABpjMFGDdXvIe1IhfTAeabRaNTWSiaB\nFG5DIAUAAEhjVEgb8nq9VoUzFospFAq16z5ODTYikMJtCKQAAABp7NBAappmAleTHJJ52y6BFG5D\nIAUAAEhjfr9ffr9fUl3AqampSfCKEs+Oo1+cGmxEIIXbEEgBAADSHNt2G0rmCilTduE2BFIAAIA0\nx2Cjhuw4+oUeUqB1CKQAAABpjgppQ8lcISWQwm0IpAAAAGmOQNoQPaRA/BBIAQAA0lwgELACVCgU\navc2VbegQgrEj+/wlwAAANhn375d+vjjj5Wfn5/opUiS8vPz1b9//0QvI+GCwaDKy8sl1VVJ61cJ\n001GRoa8Xq+i0aii0agikUiDimdr73GAnT2kDDWC2xBIAQBAXO1bs1Rbnv5KVcFgopei2khEW3v3\n1i333ZfopSRcbm5ug0DapUuXBK8osbKyslRVVSWprkpaf1tzazg5ZdcwDJmmqVgsJtM0ZRiGbfcH\n4o1ACgAA4sqIxVRaWKjizp0TvRTtqanRX6gySaKP9FCZmZkdCqRO9ZBKddt2D1Rdo9Fom6u3QDKh\nhxQAAAAE0kN0tI/UqQqpRB8p3IVACgAAAAWDQas/saamxta+x1TU0bNIneohlQikcBfq+wCQIrZu\n3aql774rmWailyJJWrl8qUK+AYleBgCbGIah7OxsqzpaWVmZNIOnEqGjFVLDMOTz+RSJRGSaZrsG\nIzWn/mAjAilSHYEUAFLEpk2btO/NNzWioCDRS5EkZa38TOu6DZFpJscfQxkZARUVjUj0MoCUlpub\nSyD9/+w6i/RAdTQcDtsWSOtXSJm0i1RHIAWAFNIlGNTwoqJEL0OSNDL7G+V++46ytixP9FIkSf8y\npFG7z3IAACAASURBVMILn5Fh0I0CtBd9pAd1dMuuVLdt90CYDYfDCgQCtqyNLbtwEwIpAKBd+ubk\nKremp7Kzk+NoiGV71yV6CUDKI5Ae5Pf7reNVQqGQYrFYg62yreHUYCMCKdyEf0YGAACApLpAeuBM\ny6qqqrTeDmoYRoe37To12IhACjchkAIAAEBSXdA5sK3UNE3rHM50laxHvxBI4SYEUgAAAFjYtntQ\nR/tI6w8xsjOQ1t86nM5VbLgDgRQAAAAWAulBVEgB5xFIAQAAYKkfSCsqKhK4ksSjhxRwHoEUAAAA\nlvqBtKqqSqZpJnA1iUWFFHAegRQAAAAWv99vVQaj0ahqamoSvKLESdYeUgIp3IRACgAAgAboI61T\nf8tubW1tm6vFTlVI6w81IpAi1fkOfwkAAMnPiEX17VevSzISvRTV1parl5lcky/D4WrV1JQlehmS\nJFPpuwU0VeTk5Gj37t2S6gJp9+7dE7yixPB4PPL7/QqFQjJNU7W1tQ2qpocTjx5Spuwi1RFIAQCu\ncIE/R7Vr5iZ6GZbOmXmJXoIlz+OTPn1e2z59PtFLkSR1qypXVr0/qJF8GGx0UFZWlkKhkKS6PtK2\nBFKv1yuPx6NYLKZoNKpYLNagutlebNmFmxBIAQCu0C+nMNFLSFqDc3tqcKIXUU+5sVVBvz/Ry0AL\n2LJ7UFZWlvbt2yep/X2kBwJtOBxusA24vQikcBN6SAEAANBAIBCwBvKEw+F2BTG3SMZJuwRSuAmB\nFAAAAI1QJa1j51mkBFKgMQIpAAAAGiGQ1uno0S9ODDaq34fKUCOkOgIpAAAAGmGwUR227ALOIpAC\nAACgESqkdTq6ZfdAL65kXyA1DMOqkpqmSZUUKY1ACgAAgEaCwaAVevbv32/rOZqpxOfzWaEyFotZ\nE3Nby4kKqUSVFO5BIAUAAEAjhmEoGAxaj9O5StqRPlInekglAincg0AKAACAJrFtt05H+kidqpAy\n2AhuQSAFAABAkxhsVKcjfaRO9JBKVEjhHgRSAAAANIkKaZ1krJASSOEWBFIAAAA0KScnR4ZhSJKq\nq6vTdmsoPaSAcwikAAAAaJLX61UgEJBUd7xIVVVVgleUGB2pkNbfshuJRGSapi1rIpDCLQikAAAA\naBbbdjvWQ2oYhhVKTdO0rUpKIIVbEEgBAADQLAYbSX6/35pqG4lE2hwqnegjZcou3IJACgAAgGZR\nIa2TbH2kVEjhFgRSAAAANCs3N9f6uqqqyrYeyFSTbJN2CaRwCwIpAAAAmpWRkWH1UEajUdXU1CR4\nRYmRbGeREkjhFgRSAAAAtIhtu/Zt2SWQAg0RSAEAANAiBhsl35ZdhhrBLQikwP9r786jo6rv/48/\n78xkMtlIwhYwQSIETJAtlKVaQFoWRQWiaBWtYHHBpaLVLy71eFr8uvGt2m/Vn1b7VRBPi7ZYAcWA\noBJECkEBFUUSCEsCCRKSQPaZzNzfH0mmCWQnyWSS1+Mcz0lm7ty8J95zmVc+y1tEREQaVHMdaVcd\nIT2XKbva1EikfgqkIiIiItIgTdnteCOkCqTSWSiQioiIiEiDHA6Hd2Mel8vV7DWUnUFgYCCGYQDg\ndDqbNU1WmxqJ1E+BVEREREQa1dVHSQ3DqDVttzmhXCOkIvVTIBURERGRRmljo5avI9UaUpH6KZCK\niIiISKO0sVHL15Fql12R+tkaP0RERESk9ZgeSEs7iK3GCI+vnHKWkxkW7Osy/EJXn7ILLe9FarFY\nsFgseDwePB4Pbre71ghnS2iEVDoLBVIRERFpV4GOQWQead4upW2lwFnIgZAcX5fhF4KDg72hqqys\nDJfLVWvkrys41512q0Osy+VSIBWpokAqIiIi7SrIEQmOxo9rD87SQOBHX5fhFwzDICQkxLt+tKio\niMjISB9X1b7OtRdpdSBtzXWk1WG0NUZdRXxBgVRExE+cPn2anJwcDpumr0sBoKys1NcliEg7Cw0N\n7dKBtCP2IlUgFX+nQCoi4ieysrL4/vsCeh7r5etSqvSqtcmJiHR+YWFhZGdnA11zHemZa0hN0/T2\nJm1MW/Qi1cZG0hkokIqI+JGAgBAiIi7wdRkinYq7tJgVr77q6zK8RkyYwJChQ31dRp26+sZGFosF\nu92O0+nENE2cTmetabwNUS9SkbopkIqIiEiXFWZzcI0tgFHffefrUgBIO3mSQ336dNhAGhISgmEY\nmKZJSUkJHo+n1ihdVxAYGIjT6QQqp+22JJCqF6nIfyiQioiISJdlGAbRQSFc2LOnr0sBoKCsjJO+\nLqIBVquVoKAgSkpKME2ToqIiunXr5uuy2pXD4fCuo21O6xeNkIrUrWv9SUtEREREzklXn7bb0o2N\n2mINqQKpdAYKpCIiIiLSZDU3M+uKgbSlrV/aYoS05nRpBVLxV5qyKyJSj5KSEl757/+m4tQpX5cC\nQHZODt3oGC1fRKTr0ghpy0ZI23rKrnbZFX+lQCoiUg+n04nl+HHu69vX16UAcLSsjG9DmrZ5hohI\nWzkzkDan9UlncGbrl6bSpkYidVMgFRFpgAEE1fgQ4UtBNhuWLvShT0Q6poCAAAIDAykvL8fj8VBS\nUkJISIivy2o3HXWEVIFU/FWja0jXrVtHfHw8gwYNYsmSJWc9v2nTJsLDw0lMTCQxMZEnn3yyTQoV\nERERkY6hK0/btdls3iDodrubHC5tNpt3JLmiogLTPPclGAqk0hk0OELqdrv5zW9+w8aNG4mOjmbM\nmDHMnDmThISEWsddeumlrFmzpk0LFREREZGOISwsjJMnKxvUFBUVERUV5eOK2pfD4aC4uBioHCUN\naOJMGpvN5g2wLpcLu91+TnUokEpn0OAIaWpqKnFxccTGxhIQEMANN9zA6tWrzzquNf7CIyIiIiL+\noSuPkELHWUdac5ddbWok/qrBEdKjR4/Sr18/7/cxMTFs37691jGGYbB161ZGjBhBdHQ0zz33HEOG\nDDnrXH/4wx+8X0+aNIlJkyadW+UiIiIi4hMKpB1jHalGSMWXNm3axKZNm875PA0G0qbsmDZq1Cgy\nMzMJDg4mOTmZpKQk0tLSzjquZiAVEREREf/lcDiw2WxUVFTgcrkoKyurFdI6u5b2IrXZ/vPRW4FU\n/N2Zg4yLFy9u0XkanLIbHR1NZmam9/vMzExiYmJqHRMWFkZwcDAA06dPx+VykZeX16JiRERERMQ/\ndOVRUo2QirSeBgPp6NGjSU9P59ChQzidTt59911mzpxZ65jjx49715CmpqZimibdu3dvu4pFRERE\nxOfCwsK8X3flQOrLNaQKpNIZNDhl12az8fLLL3PZZZfhdru59dZbSUhI4LXXXgNgwYIFrFy5kldf\nfRWbzUZwcDDvvPNOuxQuIiIiIr7TlUdIWzplt7VHSGtuaqRAKv6qwUAKldNwp0+fXuuxBQsWeL++\n5557uOeee1q/MhERERHpsLp6ILVYLHg8HlwuF263u9ZoZX3acg2pdtkVf9XglF0RERERkboEBwd7\nR+jKyspaJWD5k5qjpE2dtqs1pCJnUyAVERERkWYzDKNLj5K2ZGMjBVKRsymQioiIiEiLdOVA2pJ1\npK29qZHFYvG2afR4PN6NRkX8SaNrSEVEuqrS0lJ27vyOdd9n+boUoOrDBn19XYaIiFdXDqQdYYQU\nKkdJq8Ot2+2utU5VxB/oihURqYfT6aSo2MQWNtrXpXgFBQU0fpCISCvJz88nPz+/3ucLCws5duwY\nAAUFBbVGDdtCYGAg0dHRbfozmqolrV9ae1MjqL3TrjY2En+kQCoi0gADA5vV7usyRER84qN33qHw\n3/8m2F73fdBjmqTl5GACBlDQpw+Wqimkrc00TQ4FBPD7v/ylTc7fXC0ZIbVYLFitVtxuN6ZpUlFR\ncc4jmlpHKv5OgVREOpStKSkcP3LE12UAUHDqFBZTf20Wka7LdLmYHB7OoB496j1mh8VCcdVo36je\nvenWRqOkpmmy+PDhNjl3S5xLL9Lq4KhAKqJAKiIdzK4NGxh+9ChhbTztqynKy8tx2YN8XYaItDG3\nx83JvDxflwHAqdOnKSkp8XUZzRJqt3sDaZHT2WaBtKNxOBwYhoFpmjidTkzT9G4w1JCAgABvgHW5\nXLVGWltCgVT8nQKpiHQ48T170iskxNdlUFZWRk5gtq/LEJE2ZLXYKSrqxhdbjvq6FAC+P5VD2cC9\nXOvrQpoh1G7neHExUBlIuwrDMLDb7ZSXl2OaJuXl5U0Kl629jlSBVPydAqmIiIh0WRaLlciIob4u\nwyug2E3Gnj289sQTvi4FgLxjx7i4nvWj1UJrPN+VAilUjpJWb2hUVlbWpEDa2jvtalMj8XcKpCIi\nIiIdxAXBPRhtyWPQqVO+LgUAIySEqBqtXepyZiBt6tTVzqAj9CLVCKn4OwVSERERkQ7CZljoHRTM\neWFhvi6lyQKsVhw2G2UVFXhMkxKXi5BGRlU7i47Qi1SBVPydAqlIF/fF5s18uny5r8vwMgsLCbjg\nAl+XISIizRBqt1NWNdpX5HR2yUDqq16kCqTi7xRIRbq44sJCfu7xcHFMjK9L8bLWWA8jIiIdX6jd\nTm7V7sBFTidRPq6nvZzrlF0FUhEFUhEBLIahECgi0gWtW72ajPR0gkNCuOWuuwBI2bCBA2lpWK1W\nIiIjuXzWLAIdDrKPHmXDhx8ClZvn/HTCBOKHDsVZXs6nK1ZQWjVC+nVJCcNHjuTnl10GwL7vvmNr\nSgoAvfv04cprrgHg+SeeoFdUZXTtFh5O0g031Krtk+Rk9uzezX2PPtr2v4gWOtcpu1pDKqJAKiIi\nItJlDR05ksSxY0letcr7WP8BA5g4ZQqGYbB540a2b9nCxClT6Nm7NzffcQeGYVBcVMSyV15h8JAh\n2AMDufH229mWlQXA3g8/ZFBCAgD5J0+yfcsWbpw/n0CHg5Kq9jAAtoAA5i5YUGddOceOUV5WRkff\nGqklU3a1y65IbQqkIiIiIl1UTP/+nCooqPVY7MCB3q/7RkeTtncvcMbInsuF3eHwhiGHzUaAxUJh\nfj6usjJ6nnceAN/s3Eni2LEEVgW34Cb0mPZ4PKRs2MBVs2eT/sMP5/YGW8m6+fPJWLuW4N69ueXb\nbwFIWbSIAx9+SJnLhf2884h96CGcTielx46xNCGB7vHxAJx38cVMeeUVAFZefjlF2dkUnT5NaEIC\ng3/3u1o/J+2991hz3XXc/OWXRI0aBcDpI0dYf9ttFGVlgWEwOzmZbuefzzsTJ+IsLMRVUUFRTg4h\n8fH0+etf2/G3ItI6FEhFREREpE7f7t5NwtD/9GnNPnqUdatXcyo/n6tmz651bKjdzuFDh4iMjaXI\n6cRhs5GflweGwYo338Rjmlxy6aVcEBcHgLuigrdffx2L1cq4n/2MuKoAtys1lbgLLySkkXYz7Wno\nr39N4r33kjx3rvex/tOmMXHJEr7auZMfXniBnL//nbKJEwGIiItj7q5dZ51n5sqVWBwOtmzZwoHf\n/57j69fD+PEAOAsL2fnnP3PeT3+KaZre1yTPnctPH3+c/pMn4yopgaqWOjds3gzAiRMnWHPttUSM\nH68pu+KXtGhMRERERM6ybfNmrFYrCcOGeR/rGx3Nr+++m5sXLODTdesor7FuMtRuJ+/gQXpccAFF\nTidQOdpZkJfH9bfcwlWzZ/PxBx94p7becf/93HzHHVx1zTV8un49Bfn5FBUWkrZ3L4ljx9YKZb4W\nM2ECjsjIWo/FTp2KYbHgcDgISUjAeeJEo+tI7aGh2Gw2TLcbT0UFlrAw7zTbLY8/zthHHsEaGOjt\n45r7/fd43G76T54MQEBwMAFBQbXO6S4p4fSuXQqk4rcUSEVERESklj27d5Oxf793A6Iz9ejZk4ju\n3StHQKs4CwowTZPgHj0orAqdYd26MXDwYCwWC+EREUT26EH+yZMAhFb1Wg2PjKRfbCw/ZmfzY04O\nBXl5/N9LL/HXF1+kwuXijZdeauN3e24cDge5ycmEjxvnDdunDh5keWIi706aRNaWLbWOX3nZZXx9\n9dVY7HbCx46loqKC4zt3UnT0KAOuuKLWsflpaQRGRLB69myWjxpFykMPYZ6xTjQzOZluP/kJ1qAg\nBVLxSwqkIiIiIuJ1cP9+dmzdStINN9TqmXmqoMA7mneqoID8kyeJ7NHD+/yx9HR6VPWRrh4hjbvw\nQjIPHQKgpKSE/JMniYiMpKyszLvDbElJCceOHKFH794MGDSIux58kDvuu4877rsPW0AAt957b3u8\n7RY78PrrGDYbPaZMoaysjNDzzmNBZiZzd+1i0gsvsPbGG3EWFnqPv3b9ei5OTsZ0uchdvx6n08mm\nBx7g0uee8x5TPTrsqajg6OefM+n55/nVjh2cyshgz7JltX5+xr/+Rfdf/KLyeG1qJH5Ia0hFRERE\nuqgP33uPzEOHKC0p4bU//YlLJk1i+5YteNxuVr79NgDnxcQw5corOXrkCNu3bMFqtWKxWJg2Y0at\nPpwZ+/Zx/qRJAJS73bjcbi6Ii+NwRgZLX3kFwzCYNG0ajqAgjmZmsuHDDzEMA9M0GTd+PD169jyr\nvo6+y+6eZcvI2bSJAU8+CVS2frHa7VjtdgCiRo0iYuBA8tPTvZsUAdiDg4mcOJGivXspycsj97vv\neLfqd1eSk8OqWbO4es0auvXrR++RIwmPjQUgLimJY9u2MWz+/Mpjc3M5sXMnQxYtAtT2RfyTAqmI\niIhIF3XmxkQAwxIT6zx2yPDhDBk+vN5z3b5wITuzsyl2Ogm123F5PARYrUyaNo1J06bVOja6Xz9v\n39OGLOzAPUgPrlvHjj/+kSvXruX7qlHgsrIySnJzcURGYrFaKcjIID89nfABA3AVF1N++jShffti\nNQwK/v1vuo0ZgxEUxD0nTnjP++7Pf86k558natQoPG43ZQUFlOTmEtyzJ4c/+YS+Y8d6j01buZIL\nrrgCS9UOyAqk4o8USEVERESkVQzr3ZsAq9XXZbS6D+fMITMlhdLcXF7r149LFi9m+zPP4HE6SU5K\noqi4mNCLLmLgf/0XWSkpfPH732MNCMCwWJj22ms4IiIoPn6cVbNm4S4vp6ysjODERHpOn+6dulwX\ni9XKpOee483Bgyk/fRp7WBiXVbV2SVm0iF2vvEJwVBSWQ4eIfeghbDYb2ampbKjq7+pxu/npY48R\nf/31tc6b/thjOLOzuejNN4HKkd6URYsIi4kBIPHee72jsI21nQEo+fFH+owdS9L777fuL166BAVS\nEREREWkVnTGMAly1YsVZj1UHNoDPP/8ct9tNRUUFA2bNYnAdI88hUVH8KjUVgIyMDI4cOQKAy+Wq\nddz1n31W6/v+U6aQtHo1AaGhJM+di6VqXW912xkMg7/ddBM5f/87/RYsoOewYdz81VcYFgvFOTks\nGzqUwddei6Xq/03av/6FNSjI2z4GAMMgfs4cJr/44ll1N9Z2BmDNtdcSl5RU/y9QpAHa1EhERERE\n5BzUXEvbWOsXgLCwMKKiooiJiSGsarfhhjTUdsYwDEKHDMF54gSmaVa2jbFUfsSvKC3FHh7uDaPO\noiK++tOf6HvzzVCzrY5p1v6+SlPazpSfPs2RTz9VIJUWUyAVERERETkHDofD+3VTAmmvXr1ISEgg\nLi6OyDOCZktUt52Byp12s1NTWXrRRSy96CJ+/sIL3uO+ePxxxvzXf2GpEaABMAzS3nuPZcOHs+a6\n6yjMygKa1nZm/6pVnD9lCvbQ0HN+H9I1KZCKiIiIiJyDmoG0uhdpe9n21FNY7XZ6TJkCVG5s1Hfs\nWH793XfcvHMnn953H+WnTvHj7t0UZGQQN2vWWecYOGMGdxw+zC3ffEP/qVNJnjcPaFrbmR9WrCBh\nzpw2f5/SeSmQioiIiIicg+ZO2W0te5YtI+Ojj0h44gnvYzV32u0RH+9tO3Ns2zaOf/klr19wAT8s\nXEhZVhb7HngAgKDu3bFW7dQ77NZbOf7VVwCExcR4285YrFbikpI4vnOn9/wlubnk7NjBgCuvbI+3\nK52UAqm0ubx9+1iemOj978XwcHZWLZrf+dJLvJmQwNKhQ0l5+GEATh06xP8GBXmP33j33WedM/2x\nx/iuxmYCu//yF5YNH87yxET+dvHF/Pj11wD8uHs3f7/kEpYOHcpbI0aw7x//8L5m18sv839xcTxn\nsVCal9eWvwIRERHpxJo7Zbc1VLedSVq9moDgYO/jBRkZeKp27j11+DD56elEDh7MyDvv5M6jR7nj\n4EHiX3wRR0wMF1ZN5y3OyfG+/sCaNfQYMgSAPmPGeNvOABz+5BN6XnSR99i0lSsZMGOGt++qSEto\nl11pc90vvJC5u3YBYHo8/CU6mrirr+bIZ59xYM0a5n3zDdaAAEpq9OCKiIvzvuZM+Zs3n7U73JCb\nbmLknXcCcOCDD9j04IP8cuNGAkJCuOLtt4kYOJCi7Gze/slPiL38cgK7dSN6/HgGzJjhbUQtIiIi\n0hJtPWW3obYzK6dOpbS0FEd8PP3vv59jW7ey/oYbsAYEYAkIYNrrrxPYrdvZJ63xOWrniy+yf80a\nLDYbQT16cHnVtNzqtjP/nDwZ0zTpM3o0w2+/3fu6fe++y7gO3CtW/IMCqbSrwxs3EhEXR7d+/dj0\n4IOMe/RR7xSR4F69Gn29s6iI4ytX0v/BB8lYvNj7uL3GDnXOoiKCevYEIHLQIO/joX37Ety7N6Un\nThDYrRu9R45srbclIiIifqairIx3Lr0Ud3k5HqeTgbNmMfGZZ0hZtIgDH36I1W4nYuBALl+6lMDw\ncErz8lgzezY5X37J0FtuYfJLL3nPVR1I0x97DFdODqMOHADatr9nzbYz33zzDXlVs70GXHsto++4\no8H3HtinDxe98Yb3+wlPP82Ep5+u89j+U6Ywr2rm2ZnObFEj0hIKpNKufnjnHeKrFr4XpKeTtXkz\nn//ud9gcDi597jn6jB4NwKmDB1memEhgeDg/e/JJYsaPByp3h4u6/vqzd4cDdr3yCl+98AKu4mJu\n3Lr1rOezU1PxuFxEDBzYhu9QzpXL5cLVQJPw9uRs540pRESk/dgcDq7/7DMCgoPxVFSwYvx4srZs\n8fb3NCwWNj/yCNufeYaJzz6LzeFg/JNPkrtnD7l79tQ6l91up+Dzz7EGBeGkcqdbi8XSbv09rTX6\nv9ZcQ1qfSZodJh2IAqm0G7fTyYEPPqhs4kzlzm1l+fnctG0b2Tt28MEvf8ntGRmEnnceCzIzcURG\ncnznTlYlJfHr776j4MABCjIyiJw1i/Iaax2qJd59N4l3383eFStYN39+rb/aFWVnkzx3LtOXL2+3\n9ysts23715w8WYFRs2G3D5lm4/3hRERai2EYHDx4nGNH831dCgBWm8Ho0UMIDQnxdSltonrtpdvp\nxHS7cXTvTs+q9ZMAfceNI+2997zHRv/sZ+Snp591HldxMT++9x79fvtbMhYvpqysjODg4Gb19zxT\ndX/Py8/Y1bYuzQ2kIh2JAqm0m4PJyUT95CfeqblhMTEMuuYaAPqOGYNhsVB68iRBPXp4F8dHjRpF\nxMCB5KWlkbNjB8e//JLMOXMw3W4qCgp49xe/4PpPP631c+Kvv54NVetJofKG/v5VVzH+6afpO3Zs\nO71baSmX0yQ4eDj2gLP/cRYR6exCQ/tSURHBGa0efaYwfx/l5eWdNpCaHg/LR42i4MABRt51V60w\nCvDtm2+e3dKkjj+YfvH441xwyy14qmZwlZeXVwbSqv6emSkpdL/wQn7+pz8RFhNTq7/nqYMH6T9l\nChOffRbD8p/9RpvT31OBVPyZdtmVdrN3xQrvdF2AuKQkjlSFyby0NNxOJ0E9elCSm4un6mZakJFB\nfno6EQMHeneHG75ihXd3uOowmr9/v/e8GWvX0mv4cKDyL56rr76aIXPnMrgq/Napjr9eioiItDfD\nMAgICO4w/xkWa+NF+zHDYmHe7t3cmZVF1ubNZG7a5H2uur9nwo03NniO6v6e/S6/3PtY9U677dXf\nU4FU/JkCqbQLV3ExRzZurBUKh86fz6mMDJYNG8baOXO4omo6bdbmzbw1YgTLExP54LrrmPbaazgi\nIs4+aY2/UO56+WWWDh3K8sREdr70EpcvXQrAvn/8g6zPP+e7Zcu8bWROfPMNULmj3Gv9+lF09Chv\nDR/Ox41sACAiIiKdU2B4OAOuvJKcL78E/tPf88q//a3R11b39/x06lRvf8+PZ88G2q+/p6XGyKoC\nqfgbTdmVdhEQEsI9VT2sqlkDArji7bfPOnbwNdc0PJrJ2bvD/eJ//7fO44b86lcM+dWv6nxu1MKF\njFq4sLHSRUREpBMqyc3FYrPhiIjAVVrK4Q0buPj3v/f297w+JQVbjXYuXmfMqhp5552MvPNOsrOz\n+SYlhf2/+x1jqz6jFOfkENKnD1B/f8/gnj05/MkntZYVNbe/Z80RUk9Hme8t0kQKpOJ3tDOciIiI\nnKvi7GyS583D9HgwPR6G3Hwz/SdP5v8GDfL29wQ47+KLmfLKKwC8HhuLs7AQt9PJ/tWrufbjj+kR\nHw/U6EVqGN5epO3V31NTdsWfKZCKdHElpaW4T53iZB07/PmC290xWr6IiEjn1mvYMObWmCZb7bY6\ndtGtdsehQ/U+53A4vDO4qteQtld/TwVS8WcKpCJd3Hff/QC7juLK6BgbO3k83Qjr1rQpSiIiIh1F\nYGAgvXv3xuFwEBQU1K4/W4FU/JkCqUgXZ5omAdYedOs2zNeliIiI+C2LxcKQM9rGtBcFUvFn2mVX\nRERERMSP1dxlV5saib/RCKmIiIiI1MnjsbBjxw+1Ao+vmKbJHmehr8vokDRCKv5MgVRERERE6hQe\nnoDH7fJ1GQB4MCkoWO/rMjokBVLxZwqkIiIiIlIni2HFYrM2fmA78JgdY/O9jkiBVPyZ7+dfiIiI\niIhIiymQij9TIBURERER8WPa1Ej8mQKpiIiIiIgfMwzDG0pN01QoFb+iNaQiIiIi4jc+//xzz9+C\nbwAADUBJREFUX5fgFR0dzYABA3xdBlA5bbc6iLrd7g6xM7JIUyiQirQz0zQpKCjA7CCbMzidLgJ8\nXYSIiEgTTDYMnG+84esyAMgrLeXI+PEMuPdeX5cCVAZSl6tyR2S3201AgP51F/+gQCrSzjIzM1n+\nxBOEdZDpNCVHjtLbFurrMkRERBpkGAYJIeFMjo31dSkApJ88Saqvi6hBGxuJv1IgFWlnbrebfsC8\n88/3dSkApJW72Jtn93UZIiIicg4USMVfaXK5iIiIiIif00674q8USEVERERE/JxGSMVfKZCKiIiI\niPg5BVLxV1pDKiIiIiLSztbNn0/G2rUE9+7NLd9+C0DKokUc+PBDrHY7EQMHcvnSpQSGh3tfc/rI\nEZYOGcIlixcz5sEHAVh5+eUU5+RQWlyMY9Agzn/gAdxuN3uWLSNl0SLCYmIASLz3XobNn+89z/rb\nbqMoKwsMg9nJyXQ7/3zemTgRZ2EhACU//kifsWNJev/99vy1SBekQCoiIiIi0s6G/vrXJN57L8lz\n53of6z9tGhOXLMGwWNj8yCNsf+YZJj77rPf5TQ88wIArr6x1npkrV2IPDWX//v2k3Hor+Z99hjs+\nHgyD+DlzmPzii2f97OS5c/np44/Tf/JkXCUlYBgA3LB5s/eYNddeS1xSUmu/bZGzaMquiIiIiEg7\ni5kwAUdkZK3HYqdOxajanKjvuHEUZmV5n0tftYrwAQPoMWRIrdfYQ6tat7ndeCoqsIWHV25qZJqV\n/50h9/vv8bjd9J88GYCA4GACgoJqHVN++jRHPv1UgVTahQKpiIiIiEgH8+2bbzLgiisAcBYVseN/\n/odL/vCHOo9dedllrB03DovdTvjYsZVrSA2DtPfeY9nw4ay57jpvuM1PSyMwIoLVs2ezfNQoUh56\nCPOMXXn3r1rF+VOm/CfsirQhBVIRERERkQ5k21NPYbXbSbjxRgC2/uEP/OS3vyUgOLjOUc9r168n\n6auvMF0uctevx+12M3DGDO44fJhbvvmG/lOnkjxvHgCeigqOfv45k55/nl/t2MGpjAz2LFtW63w/\nrFhBwpw5bf4+RUBrSEVEREREOow9y5aR8dFH/PKTT7yP5aSmkvbee6Q89BDlBQUYFgu2oCAS777b\ne4w9OJjIiRMp2rsXt9tNUPfu3ueG3Xormx96CICwmBh6jxxJeGwsAHFJSRzbts274VFJbi45O3aQ\ntHp1O7xbEQVSEREREZEO4eC6dez44x+5PiUFm8PhfbzmZkNbFy/GHhZG4t134youpvz0aUL79sUw\nTQr+/W+6jRmD2+2mOCeHkD59ADiwZo137WmfMWMoKyigJDeX4J49OfzJJ/QdO9Z7/rSVKxkwYwZW\nu72d3rV0dQqkIiIiIiLt7MM5c8hMSaE0N5fX+vXjksWL2f7MM3icTlZOnQrAeRdfzJRXXqn3HM6i\nIlbNmoW7vJyKigrsw4bRc/p03G43O198kf1r1mCx2Qjq0YPLq6blWqxWJj33HP+cPBnTNOkzejTD\nb7/de859777LuEcfbdP3LlKTYZp1TERv7R9iGLTDjxHxCwcPHmTzU08xr6ovmK+lpR9g71474d36\n+boUERGRepnAqYJNJCVN8nUpAKSfPEnq4MHcdO+9vi4FgPz8fL7++msMw6B79+4MGzbM1yVJF9PS\nzKcRUhERERERPxcREcHEiROxWLRnqfgXBVIRERERkRZwezyUlpb6ugwvR411pyL+QoFURERERKSZ\nggMCyE5N5c+7d/u6FABcwFULF5KYmOjrUkSaRYFUuoRvv/2WkpISX5cBwMmTJ31dgoiIiJyj6G7d\neLhbN1+X4fXRkSO4XC5flyHSbAqk0iWseuklRrlcWAzD16VgAKOCgnxdhoiIiIiIzymQStfg8XBZ\nv37YtNBfRERERKTD0KdzERERERER8QkFUhEREREREfEJBVIRERERERHxCQVSERERERER8QkFUhER\nEREREfEJ7bIrIiIiIn7B7TbY8eUeX5fhFRUVyfn9on1dhohfUyAVaWfl5eXs25eB2236uhQACouK\ngL6+LkNERKRBBhASMpITP1b4uhQAyp2FeDx5CqQi50iBVKSdlZSWsn9/EfbA/r4upUpPQkMifF2E\niIhIoxyOcF+X8B+GART6ugoRv6dAKn5p06ZNTJo0yddltJjNZic0pLevy5AquwsOMTIi1tdlSCei\na0pam64paW3+/llKOo9GA+m6deu4//77cbvd3HbbbTz88MNnHbNw4UKSk5MJDg5m2bJlJCYmtkmx\n4j/cbjdlZWVtdv4NGzYwZsyYNju/dC36oCetTdeUtDZdUx2T6fHgdLl8XQYAFRUVlJWVUVxc3KTj\n2/qzlNVqxeFwtNn5pfNoMJC63W5+85vfsHHjRqKjoxkzZgwzZ84kISHBe8xHH33E/v37SU9PZ/v2\n7dx1111s27atzQuXjm3V3/9O2saNWK3WNjl/6q5d/L/s7CYfX7Q/g29PFmIxjDappzmcznI8HWP5\nqIiIiLSQ1RrAsWPFHD+e6utSANhTlM/pU8+zrUePJh3f3M9SzVXmcPDbJUsICwtrs58hnUODgTQ1\nNZW4uDhiY2MBuOGGG1i9enWtQLpmzRrmzZsHwLhx4ygoKOD48eNERUW1XdXS4bmKi0kKDSWhV682\nOX9JRgYPnX9+k49fs/sQWSURGB2k01FQULCvSxAREZFzEGgPI7D7Jb4uw2so6YzuHUx0dNM2WWru\nZ6nm+nNmJhUVHWMDKunYGgykR48epV+/ft7vY2Ji2L59e6PHZGVlnRVIjQ4wMiWdy+KUlGa+4rM2\nqUM6h7cON/d6EmmYrilpbbqmpFG7m3d48z9LNc/9b77ZpueXzqHBQNrUEGmatecfnvm6M58XERER\nERERaXD+YnR0NJmZmd7vMzMziYmJafCYrKysJk8VEBERERERka6rwUA6evRo0tPTOXToEE6nk3ff\nfZeZM2fWOmbmzJksX74cgG3bthEREaH1oyIiIiIiItKoBqfs2mw2Xn75ZS677DLcbje33norCQkJ\nvPbaawAsWLCAK664go8++oi4uDhCQkJYunRpuxQuIiIiIiIi/q3RLUenT5/Ovn372L9/P48++ihQ\nGUQXLFjgPebll19m//79fP3114waNYp//vOfXHTRRVitVnbu3FnvuWNjYxk+fDiJiYmMHTu2Fd6O\ndFZNvabWrVtHfHw8gwYNYsmSJe1YofibvLw8pk6dyuDBg5k2bRoFBQV1Hqf7lDSkKfechQsXMmjQ\nIEaMGMGuXbvauULxN41dU5s2bSI8PJzExEQSExN58sknfVCl+Iv58+cTFRXFsGHD6j1G9yhpjsau\nqRbdo8w2sHfvXnPfvn3mpEmTzK+++qre42JjY82TJ0+2RQnSyTTlmqqoqDAHDhxoHjx40HQ6neaI\nESPM77//vp0rFX+xaNEic8mSJaZpmuazzz5rPvzww3Uep/uU1Kcp95y1a9ea06dPN03TNLdt22aO\nGzfOF6WKn2jKNfXZZ5+ZM2bM8FGF4m82b95s7ty50xw6dGidz+seJc3V2DXVkntUmzRljI+PZ/Dg\nwU061tQOvNIETbmmavbNDQgI8PbNFalLzR7K8+bNY9WqVfUeq/uU1KUp95z6enWL1KWp/47pniRN\nNWHCBCIjI+t9Xvcoaa7Grilo/j2qTQJpUxmGwZQpUxg9ejR//etffVmKdAJ19cQ9evSoDyuSjuz4\n8ePeDdiioqLq/QdY9ympT1PuOfX16hapS1OuKcMw2Lp1KyNGjOCKK67g+++/b+8ypRPRPUpaW0vu\nUQ1uatSQqVOnkpOTc9bjTz/9NDNmzGjSOb744gv69u3LiRMnmDp1KvHx8UyYMKGlJYmfO9drqql9\nc6XrqO+aeuqpp2p9bxhGvdeP7lNSn9bq1S1SrSnXxqhRo8jMzCQ4OJjk5GSSkpJIS0trh+qks9I9\nSlpTS+5RLQ6kGzZsaOlLvfr27QtAr169uPrqq0lNTdUHvS7sXK+ppvTNla6loWsqKiqKnJwc+vTp\nQ3Z2Nr17967zON2npD7q1S2trSnXVFhYmPfr6dOnc/fdd5OXl0f37t3brU7pPHSPktbWkntUm0/Z\nrW8OcUlJCYWFhQAUFxfz8ccfN7gDmEi1+q6ppvTNFak2c+ZM3nrrLQDeeustkpKSzjpG9ylpiHp1\nS2tryjV1/Phx77+DqampmKapMCotpnuUtLaW3KNaPELakPfff5+FCxeSm5vLlVdeSWJiIsnJyRw7\ndozbb7+dtWvXkpOTwzXXXANARUUFN910E9OmTWuLcqQTaMo1VV/fXJG6PPLII/zyl7/kjTfeIDY2\nln/84x8Auk9Jk6lXt7S2plxTK1eu5NVXX8VmsxEcHMw777zj46qlI5szZw4pKSnk5ubSr18/Fi9e\njMvlAnSPkpZp7JpqyT3KMLVVm4iIiIiIiPiAT3fZFRERERERka5LgVRERERERER8QoFURERERERE\nfEKBVERERERERHxCgVRERERERER8QoFUREREREREfOL/A7jgbV1u/9OsAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "### $\\sigma$ : the ranking definition\n\n$S_n$ the set of permutations of $\\\\{1, \\ldots, n \\\\}$.\n\n$\\sigma \\in S_n$, $\\sigma(i) = $ rank of element $i$ (and not the rank of the $i$th element!!!)\n\nExample :\n\n$ \\sigma([123]) = [231] $\n\nwith :\n\n$$\n\\\\left\\\\{ \\begin{array}{c}\n\\sigma(1) = 3\\\\\\\\\n\\sigma(2) = 1\\\\\\\\\n\\sigma(3) = 2\\\\\\\\\n\\end{array}\\\\right.\n$$"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "p = np.array([2, 3, 1])\n\nsigma = np.argsort(p)\n\nprint \"p = {}\".format(p)\nprint \"sigma = {}\".format(sigma)\nprint \"p[sigma] = {}\".format(p[sigma])\nprint \"sigma[p-1] + 1 = {}\".format(sigma[p-1] + 1)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "p = [2 3 1]\nsigma = [2 0 1]\np[sigma] = [1 2 3]\nsigma[p-1] + 1 = [1 2 3]\n"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## Weighted versions of $F$ and $K$\n\n### Element weights\n\n - \n\n$$ F_w(\\sigma) = \\sum\\limits_{i} w_i |  \\sum\\limits_{j:j \\leq i} w_j - \\sum\\limits_{j:\\sigma(j) \\leq \\sigma(i)} w_j | $$\n\n\n - $$ K_w(\\sigma) = \\sum\\limits_{(i;j):i>j} w_i w_j \\left( \\sigma(i) - \\sigma(j) \\right) $$\n\n \n"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import logging\nlogging.shutdown()\nreload(logging)\n\n_log = logging.getLogger(\"we7.notebook\")\n\nconsole_handler = logging.StreamHandler()\nconsole_handler.setLevel(logging.DEBUG)\nconsole_handler.setFormatter(logging.Formatter(\"%(levelname)s %(name)s - %(message)s\"))\n\nroot_logger = logging.getLogger('we7')\nroot_logger.addHandler(console_handler)\nroot_logger.setLevel(logging.DEBUG)",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "import itertools\n\ndef footrule_measure(p, weights, sigma=None):\n    _log.debug(\"footrule_measure\")\n    \n    n = len(p)\n    #sigma = p\n    #sigma = rankings(p) if sigma is None else sigma\n    sigma = np.argsort(p)\n    abs_sum = 0\n\n    for i in xrange(n):\n        all_w_sum = np.sum(weights[:(i+1)])\n        ordered_elements_mask = sigma <= sigma[i]\n        only_ordered_w_sum = np.sum(weights[ordered_elements_mask])\n        abs_sum += weights[i] * abs(all_w_sum - only_ordered_w_sum)\n        \n        _log.debug(\"all w_j / j<={} = {}\".format(i, weights[:(i+1)]))\n        _log.debug(\"all j / sigma(j) <= sigma({}) = {} : {}\".format(i, sigma[i], ordered_elements_mask))\n        _log.debug(\"all weights w_j / sigma(j) <= sigma({}) = {}\".format(i, weights[ordered_elements_mask]))\n        _log.debug(\"m = w_{} ({}) x abs diff of sum ({}) : {}\".format(i, weights[i], abs(all_w_sum - only_ordered_w_sum), weights[i] * abs(all_w_sum - only_ordered_w_sum)))\n        _log.debug(\"\")\n    \n    return abs_sum\n\ndef kendall_measure(p, weights, sigma=None):\n    _log.debug(\"kendall_measure\")\n    n = len(p)\n    #sigma = p\n    #sigma = rankings(p) if sigma is None else sigma \n    sigma = np.argsort(p)\n    \n    pairwise_inversion = np.array([(i,j) for i,j in itertools.product(xrange(n), xrange(n)) if i > j and sigma[i] < sigma[j]])\n    _log.debug(\"pairwise_inversions = [{}]\".format(\", \".join(str(r) for r in pairwise_inversion)))\n    _log.debug(\"\")\n    return 0 if len(pairwise_inversion) == 0 else np.sum(weights[pairwise_inversion[:,0]] * weights[pairwise_inversion[:,1]])",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def footrule_measure_wo_weights(p):\n    \"\"\" Making sure that the weighted version with equal weights matches the unweighted version.\n    \"\"\"\n    n = len(p)\n    sigma = np.argsort(p)\n    #sigma = rankings(permutation)\n    return np.sum(np.abs(np.arange(n) - sigma))\n\n_log.setLevel(logging.INFO)\nprint footrule_measure_wo_weights([7, 6, 5, 4, 3, 2, 1])\nprint footrule_measure([7, 6, 5, 4, 3, 2, 1], weights=np.ones(7))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "24\n24.0\n"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## Test example\n\nConsider the permutation :\n\n$ \\sigma([abc]) = [bca] $\n\nor alternatively :\n\n$ \\sigma([123]) = [231] $\n\nwith :\n\n$$\n\\\\left\\\\{ \\begin{array}{c}\n\\sigma(1) = 3\\\\\\\\\n\\sigma(2) = 1\\\\\\\\\n\\sigma(3) = 2\\\\\\\\\n\\end{array}\\\\right.\n$$\n\nWith $w_1 = 1$, $w_2 = 2$ and $w_3 = 3$ :\n\n$K_w(\\sigma) = 1 \\times 2 + 1 \\times 3 = 5 $\n\n$F_w(\\sigma) = 1 \\times (2 + 3) + 2 \\times 1 + 3 \\times 1 = 10 $"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "example_perm = np.array([2, 3, 1])\nweights = np.array([1, 2, 3])\n\n_log.setLevel(logging.DEBUG)\n\nprint \"weights = {}\".format(weights) \nprint \"footrule_measure = {}\".format(footrule_measure(example_perm, weights))\n\nprint \"kendall_measure = {}\".format(kendall_measure(example_perm, weights))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - footrule_measure\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all w_j / j<=0 = [1]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all j / sigma(j) <= sigma(0) = 2 : [ True  True  True]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all weights w_j / sigma(j) <= sigma(0) = [1 2 3]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - m = w_0 (1) x abs diff of sum (5) : 5\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all w_j / j<=1 = [1 2]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all j / sigma(j) <= sigma(1) = 0 : [False  True False]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all weights w_j / sigma(j) <= sigma(1) = [2]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - m = w_1 (2) x abs diff of sum (1) : 2\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all w_j / j<=2 = [1 2 3]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all j / sigma(j) <= sigma(2) = 1 : [False  True  True]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all weights w_j / sigma(j) <= sigma(2) = [2 3]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - m = w_2 (3) x abs diff of sum (1) : 3\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - kendall_measure\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - pairwise_inversions = [[1 0], [2 0]]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "weights = [1 2 3]\nfootrule_measure = 10\nkendall_measure = 5\n"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## Position weights\n\nLet $ \\delta_i$ be the cost of swapping an element at position $i-1$ with element at $i$. $\\delta_i=1$ for traditionnal versions.\n\n$$ p_1 = 1, p_i = 1 \\ \\text{ if $i = 1$ else } \\ \\sum\\limits_{j=1}^{i-1} \\delta_j $$ \n\n(as documented, but seems like a typo and actually sum up to $i$ instead of $i-1$)\n\n$$ \\bar{p}_i(\\sigma) = \\frac{p_i - p_{\\sigma(i)}}{i - \\sigma(i)}$$"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def get_position_weights(p, deltas, sigma=None):\n    _log.debug(\"get_position_weights\")\n    \n    n = len(p)\n    positive_weights = np.cumsum(np.concatenate(([1], deltas)))\n    \n    sigma = np.argsort(p)\n\n    # by default p_i = 1 if sigma_i = i\n    i_n = np.arange(n)\n    average_costs = np.ones(n)\n    differing_elements_mask = sigma != i_n\n    \n    average_costs_numerator = (positive_weights - positive_weights[sigma])\n    average_costs_denominator = i_n - sigma\n    if np.any(differing_elements_mask):\n        average_costs[differing_elements_mask] = average_costs_numerator[differing_elements_mask] / average_costs_denominator[differing_elements_mask]\n\n    _log.debug(\"p                         = {}\".format(np.array(p)))\n    _log.debug(\"sigma_i                   = {}\".format(sigma))\n    _log.debug(\"i_n                       = {}\".format(i_n))\n    _log.debug(\"differing_elements_mask   = {}\".format(differing_elements_mask))\n    _log.debug(\"positive_weights          = {}\".format(positive_weights))\n    _log.debug(\"positive_weights[sigma]   = {}\".format(positive_weights[sigma]))\n    _log.debug(\"average_costs_numerator   = {}\".format(average_costs_numerator))\n    _log.debug(\"average_costs_denominator = {}\".format(average_costs_denominator))\n    _log.debug(\"\")\n\n    return positive_weights, average_costs",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "## Test example\n\n$ \\delta_1 = 1, \\delta_2 = 0.5$\n\nthen \n\n$\\bar{p}_1 = 0.75, \\bar{p}_2 = 1$ and $\\bar{p}_3 = 0.5$\n\nand we get $K_\\delta(\\sigma) = 1.125$ and $F_\\delta(\\sigma) = 2.25$"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "example_perm = np.array([2, 3, 1])\ndeltas = [1, .5]\npositive_weights, average_costs = get_position_weights(example_perm, deltas)\n\nprint \"\\npositive_weights = {}\".format(positive_weights)\nprint \"average_costs = {}\".format(average_costs)\n\nprint \"\\n\"\nprint \"kendall_measure = {}\".format(kendall_measure(p=example_perm, weights=average_costs))\nprint \"footrule_measure = {}\".format(footrule_measure(p=example_perm, weights=average_costs))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - get_position_weights\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - p                         = [2 3 1]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - sigma_i                   = [2 0 1]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - i_n                       = [0 1 2]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - differing_elements_mask   = [ True  True  True]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - positive_weights          = [ 1.   2.   2.5]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - positive_weights[sigma]   = [ 2.5  1.   2. ]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - average_costs_numerator   = [-1.5  1.   0.5]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - average_costs_denominator = [-2  1  1]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - kendall_measure\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - pairwise_inversions = [[1 0], [2 0]]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - footrule_measure\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all w_j / j<=0 = [ 0.75]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all j / sigma(j) <= sigma(0) = 2 : [ True  True  True]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all weights w_j / sigma(j) <= sigma(0) = [ 0.75  1.    0.5 ]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - m = w_0 (0.75) x abs diff of sum (1.5) : 1.125\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all w_j / j<=1 = [ 0.75  1.  ]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all j / sigma(j) <= sigma(1) = 0 : [False  True False]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all weights w_j / sigma(j) <= sigma(1) = [ 1.]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - m = w_1 (1.0) x abs diff of sum (0.75) : 0.75\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all w_j / j<=2 = [ 0.75  1.    0.5 ]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all j / sigma(j) <= sigma(2) = 1 : [False  True  True]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - all weights w_j / sigma(j) <= sigma(2) = [ 1.   0.5]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - m = w_2 (0.5) x abs diff of sum (0.75) : 0.375\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\npositive_weights = [ 1.   2.   2.5]\naverage_costs = [ 0.75  1.    0.5 ]\n\n\nkendall_measure = 1.125\nfootrule_measure = 2.25\n"
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "### Illustrating the positionnal weights"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def plot_ranking_measures(ax, p, deltas):\n    positive_weights, average_costs = get_position_weights(p, deltas=deltas)\n    n = len(p)\n    i_n = np.arange(n)\n    ax.set_ylim((0, n+2))\n    ax.bar(np.arange(n) + .75, p, .5, color=\"grey\", alpha=.5)\n    \n    # showing permutations\n    sigma = np.argsort(p)\n    pairwise_inversions = ((i,j) for i,j in itertools.product(xrange(n), xrange(n)) if i > j and sigma[i] < sigma[j])\n    for i, j in pairwise_inversions:\n        ax.plot([i+1, j+1], [p[i], p[j]], 'k-', lw = 3, alpha=.2)\n        #ax.arrow(i+1, p[i], j-i, p[j] - p[i], length_includes_head=True, width=.1, color=\"gray\", ec=None)\n        ax.plot(j+1, p[j], 'ok', alpha=.2)\n    ax_measures = ax.twinx()\n    \n    ax_measures.plot(i_n[1:] + .5, deltas, \"xb-\", label=r\"$\\delta_i$\")\n    ax_measures.plot(i_n + 1, positive_weights, \"or-\", label=r\"$p_i$\")\n    ax_measures.plot(i_n + 1, average_costs, \"og-\", label=r\"$\\bar{p}_i(\\sigma)$\")\n    \n    text = \"$F_w(\\sigma) = {:.2f}$, $K_w(\\sigma) = {:.2f}$\\n$F(\\sigma) = {:.2f}$, $K(\\sigma) = {:.2f}$\".format(\n        footrule_measure(p, weights=average_costs),\n        kendall_measure(p, weights=average_costs),\n        footrule_measure(p, weights=np.ones(n)),\n        kendall_measure(p, weights=np.ones(n)))\n    ax_measures.text(0.5, ax_measures.get_ylim()[1], text, verticalalignment=\"top\", fontsize=12)\n\n    ax_measures.legend();",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Several weighting scheme possible:\n\n- DCG : $\\sigma_i = \\frac{1}{\\log(i+1)} - \\frac{1}{\\log(i+2)}$\n- TOPK : $\\sigma_i = 1 \\ \\text{ if  } \\ i \\ \\leq k \\ \\text{else} \\ 0$"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "# equal weights\ndeltas  = np.repeat(1.0 / 6, 6)\n\n# DCG weights\ni_n = np.arange(7)\ndeltas = 1 / np.log(i_n[1:] + 1) - 1 / np.log(i_n[1:] + 2)\n\n# linearly decreasing weights\ndeltas = np.array([6, 5, 4, 3, 2, 1], dtype=float)\ndeltas /= np.sum(deltas, dtype=float)\n\n# top-3 weights\ndeltas = np.array([1, 1, 1, 0, 0, 0], dtype=float)\n#deltas /= np.sum(deltas, dtype=float)\n\np_ordered = [1, 2, 3, 4, 5, 6, 7]\np_top_3_ordered = [1, 2, 3, 7, 6, 5, 4]\np_switch_3_4 = [1, 2, 4, 3, 5, 6, 7]\np_shift_5_to_3 = [1, 2, 5, 3, 4, 6, 7]\n\np_top_3_reversed = [3, 2, 1, 4, 5, 6, 7]\n\np_reversed = [7, 6, 5, 4, 3, 2, 1]\np_top_3_reversed = [7, 6, 5, 1, 2, 3, 4]\np_worse_than_reversed = [7, 6, 4, 3, 1, 2, 5]\n\nfig, ax_grid = plt.subplots(nrows=3, ncols=2, figsize=(24, 12))\n\n_log.setLevel(logging.INFO)\n\nplot_ranking_measures(ax_grid[0][0], p_ordered, deltas)\nplot_ranking_measures(ax_grid[0][1], p_top_3_ordered, deltas)\n\nplot_ranking_measures(ax_grid[1][0], p_switch_3_4, deltas)\nplot_ranking_measures(ax_grid[1][1], p_shift_5_to_3, deltas)\n\nplot_ranking_measures(ax_grid[2][0], p_reversed, deltas)\nplot_ranking_measures(ax_grid[2][1], p_worse_than_reversed, deltas)",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ZMHw4JCdDp05mVyQiTkRZ23xqyopI7bZtg1mzYNQoOHoU/PzMrkhEnMjnW7bw\n6dy5LElPtx5b+OPHtga9priGiIhIkysogCefhIQEWLUKxo41uyIRcTLK2o5B2xeISHX5+fDEE7Bn\nD7zxhqUpKyLSjGrLE4vGjuWF+PgaY/80dizPf/KJTddtimskJSVx8OBBjh8/zs0338zZs2dp164d\nkydPtun8a2X2W6rEXPo6i7QyhgHr18OcOXDffbBkCXh7m12ViLRidWUJR8jaZudsMD9ra6WsiFgY\nhmUvq3nzYNIkOHIEvLzMrkpEnJRbWVmtx10//dTmvfbqCjmupaU213HmzBkiIyP59NNPWbZsGRcv\nXiQmJsauYVFERFqB06chNhZSUmDdOrj5ZrMrEhEn5ghZWzkb2tT35PHjx4mJibH+8fHxYcWKFfaq\nTUTsJScH7r4bXngBNm6EV19VQ1ZETFXRrl2txyvHjrX8EsmGPxVjxtR+DQ8Pm+sYM2YM8fHx3HXX\nXQAcOnSIzp07A/DVV1/x5ZdfNvKVifyHsraIEzAMePNNGDgQoqPh8GE1ZEXEdI6QtZWzG1gpGxkZ\nyaFDhwCoqqoiKCiIX//613YpTETsoKoKVq+23PH18cctv7V3dze7KhERxsyZw8L09Gp7VC0IC+OO\n2bPteg2A7du3M336dADeeecdfv/73wNw0003Neo6Ij+nrC3SyqWnw4wZcP48bN8O/fubXVGzS05O\nJj4+nvLyctzd3RkzZgz9+vUzuywR+RlHydrOnrNt3r5g+/bthIWF0aNHj+asR0Ts5cQJeOQRKCmB\nnTtBYUlEHMhPNwf4U1wcrqWlVHp4cMfs2Y26aUBTXKOoqIiCggJ27NhBeXk5Q4cO5Z577iExMZEN\nGzawZMkS2rSp941HIjZR1hZpRSor4bXXYOlSmD8f5s4Ft9a/c2BycjJvv/02Pj4+AFy+fJm3336b\nqVOnqjEr4mAcIWsrZzeiKbt27Vruv//+5qxFROyhogJeeQVeesmyQnb2bHB1NbsqEZEaho8bd813\nbr3Wa+zYsYPx48czZcqUaseDgoIoKipq9UFR7EdZW6SVOHIEpk2zbAW2dy+Eh5tdkd3Ex8dbG7JJ\nSUl4eHjQqVMnPvnkEzVlRRyQ2VlbOdvGpmx5eTn/+te/WLZsWY3nFi9ebP145MiRjBw5sqlqE5Gm\ndviwJST6+cH+/dCrl9kViUgLtnjxYgoLC80uo9mkpKTwyiuvEB4ezvnz5+nYsaP1ufLyckJCQsjN\nzSUoKMhJuqi3AAAgAElEQVTEKqU1UNYWaQXKyuDFF+F//9fy3+nTbb5ZjqO41u/riYmJVFVVUVFR\nQV5envV4mzZt+Oyzz/D19cXX15f27ds36rq+vr7V/i0UkZZPOdvCpqbstm3bGDx4MAEBATWe0z+O\nIi1AaSk8/7xl/9hly2Dq1BYXEkXE8RQWFjJhwoRrvs7y5cuboJqmd/311/PFF1/U+ty5c+fw8vLC\nRf+WShNQ1hZp4b76yrLwISLCsgiihTYRrvX7+uXLl7l06RL5+flUVFRYj7u5uXHdddcBlmaLh4cH\ngYGB9OjRg27duuHawLv2Nm7ceNU1iYhjUs62sKkp+//+3/9j0qRJzV2LiFylz7dsIX7FCtzKyqho\n144xc+b85y0Eu3dbflPfty8kJUFgoLnFioi0AkOGDGHIkCFml1FNaWkpI0aMoKysjPLycu6++26W\nLl1aY9ycOXPYtm0bnp6evP3228TExJhQrVxJWVvEcdWbs4uLLduBffghrFgB997r1AsfBg8eTHx8\nPJ06daJt27acP3+e/Pz8Givdzp8/z/nz5zl+/Dht27ala9euBAYGEhwcjLe3t0nVi4ijcKac3WBT\n9uLFi2zfvp3Vq1dfffUi0mw+37KFT+fOrXbHw4Xp6XDpEsN37YINGyAuDiZONLFKERFpbh4eHuzc\nuRNPT08qKiq49dZb2b17N7feeqt1zNatW0lLS+PEiRPs27ePRx99lL1795pYtShriziuOnM2MLxt\nW5g5E4YPh+Rk6NTJrDIdRq9evRgzZgwHDx7E3d2dwMBA7r//fvz8/MjOziY3N5eCgoJqq2gvX75M\nTk4OOTk5JCYm4uvrS2BgIEFBQa3+bcsi0nI0V85usCnr5eVFfn7+tb8CEWkW8StWVAuKAEvS0/nT\n5MkMnzQJjh617CErIiKtnqenJ2B5e2hlZSX+/v7Vnt+0aZP1ZgpDhw6lsLCQM2fO0LVrV7vXKhbK\n2iKOq86cPWOGpSm7ahWMHWtSdY6pV69e9KrlvhV+fn7079+f8vJycnNzycnJ4cyZM1y8eLHauMLC\nQgoLC/n2229xd3ena9eu5OXlUVxcrFW0ImKq5sjZNm1fICKOy62srNbjrhER8NZbdq5GRESaQ0JC\nAgkJCQ2Oq6qqYtCgQaSnp/Poo48SFRVV7fnc3Fx69Ohhfdy9e3dycnLUlBURqUWdOdvFBY4cgQ4d\n7FxRy+fu7k5oaCihoaEAFBQUkJWVRV5eHvn5+VRVVVnHlpeXk52dTVZWFq+++ipdunQhJCSEiIgI\n6/kiIk3BlqzdHDlbTVmRFq6iXbtaj1dq71gRkVZj5MiRjBw50vr4ueeeq3VcmzZtOHz4MEVFRYwd\nO5aEhIRq5wEYhlHtsTPcREFE5GrUmbP79VNDton4+/tbV5v91IQ9ffo0eXl5XLp0qdrYs2fPcvbs\nWfbv30+7du3o2bMn4eHhREZGahWtiFwTW7J2c+RsNWVFWrgxkyaxcPdullwRWhaEhXHH7NkmViUi\nImby8fFh3LhxHDhwoFpYDAoKIjs72/o4JydHe/aJiNRhzOzZLDx0iCXnzlmPKWc3H3d3d8LCwggL\nCwMsd2D/ab9ZFxeXas2OsrIyUlNTSU1NZdu2bQQEBNCrVy8iIyMJDg426yWIiBNoypytpqxIS1VV\nBatXM3zRIrj7bv6Un49reTmVHh7cMXv2f+4KKyIiTiE/Px83Nzd8fX0pKSnhs88+49lnn602Zvz4\n8axcuZLf/va37N27F19fX21dICJSm/R0hr/6Kvj48KfevXFt21Y5284CAgIICAggKyuLp556irS0\nNFJTUzl58mS1VbSGYVhX0e7duxdPT0+Cg4Pp3bs3kZGRtG/f3sRXISKtQXPlbDVlRVqiEyfgkUeg\npAR27mR4v34MN7smEREx1XfffceUKVOoqqqiqqqKBx98kF/+8pesWrUKgJkzZ/KrX/2KrVu3Eh4e\njpeXF3//+99NrlpExMFUVsJrr8HSpTB/PsPnzmW4m35sNlv79u2Jjo4mOjoasOzdePz4cTIyMsjL\ny6u2ivbSpUukpKSQkpLC5s2b6datG7169SI8PFyraEXkqjRXznYxfr7hQSP8/C0EItLMKirglVfg\npZdg0SKYPRtcXc2uSkSc1Lx585gwYcI1X+cXv/iF8kQd6spaymDOQV9nETs7cgSmTQMvL1i9GsLD\nza7Irprq+3pT27hxI6+99lqdz5eUlHD8+HFOnDjBqVOnauxFeyVPT09CQkIICwvTKlpxCsoS9TM7\na+tXfiItxeHDlpDo5wf790OvXmZXJCIiIiLS8pWVwZIl8Prr8OKLMH066CaILUb79u0ZOHAgAwcO\nBODUqVMcP36crKysWlfRHjt2jGPHjrF582YCAwMJDQ0lMjJSe6yLiN2pKSvi6EpL4fnnLb+tX7YM\npk5VSBQRERERaQpffWVZ+BARYVkEocZcixccHGzdpqC4uNi6zUFmZiZlZWXWcYZhcPr0aU6fPs2e\nPXvw9vYmODiYiIgIIiMjcXd3N+sliIiTUFNWxJHt3m35TX3fvpCUBIGBZlckIiIiItLyFRfDwoXw\n0UewYgXce68WPrRC3t7eDB48mMGDBwOQmZlJWloaGRkZnD17ttrY4uJi6ypaFxcXAgMDCQ8PJzIy\nkm7duplRvoi0cmrKijiiCxdg/nzYsAHi4mDiRLMrEhERG2VmZhIaGlrvmO+++w4fHx88PT3tVJWI\niFjFx8PMmTB8OCQnQ6dOZlckdhIaGmr9Hv3TKtq0tDSysrLqXEX7+eef4+3tTUhICL179yYiIkKr\naEVM0tpytpqyIo5m61Z49FEYNQqOHrXsISsiIi1CRkYG+/btazAsBgQE8MILL7B48WL7FCYiIlBQ\nAE8+CQkJsGoVjB1rdkViotpW0aamppKRkUF+fn61scXFxSQnJ5OcnIybmxuBgYH06tWLiIgIraIV\nsZPWmLPVlBVxFPn58MQTsGcPrFljacqKiEiLsmrVKpYtW9bgODc3N8aNG8e7777L5MmT7VCZiIgT\nMwxYtw7mzoX77rOsjvX2NrsqcTBXrqItKiqyrqLNzs6mvLzcOq6iooLs7Gyys7PZtWsXHTt2JDQ0\n1Nqk1SpakebRGnO2mrIiZjMM+PBDmDcPJk2CI0fAy8vsqkRETLflsy2s+McKyowy2rm0Y879cxg3\nepxdr/H999/z5ptvVjs2Y8YM/Gp5F0NSUhLdu3e3+dpDhgwhLi7O4cOiiEiLdvo0xMZCSoqlMXvz\nzWZXJC2Aj48PN954IzfeeCOVlZWcPHmS48ePk5WVVWMV7fnz50lKSiIpKQk3NzeCgoIICQmhT58+\nBAQEmPQKRBpmdtZWzrahKVtYWMj06dM5evQoLi4uvPXWWwwbNswetYm0fjk5lq0KMjNh40bQ3y0R\nEcAS8Ob+dS7pMenWY+l/tXxsa9Brimt06tSJZ555xqaxmzdvZsKECTaN/UlAQABpaWmEh4c36jxp\nHZSzRZqRYVjefbZgAcyaBWvXQrt2ZlclLZCrqythYWGEhYUBllW03377LRkZGbWuos3KyiIrK4td\nu3bh4+NTbS9aV1dXs16GSDWOkLWVs21oys6dO5df/epXrFu3joqKCi5evGiPukRat6oqWL0aFi2C\nxx+H9etBb3MREbFa8Y8V1QIeQHpMOnFr42wOik1xjcZITExkwYIFjTpnwIABHDx40KHDojQf5WyR\nZpKeDjNmwPnzsH079O9vdkXSivj4+DBs2DCGDRtGZWUl6enppKWlkZmZSUFBQbWxRUVFNVbRhoWF\n0adPH/z9/Tl16hSJiYlcvnyZtm3bMmTIEIKDg016ZeJMWlrWbq05u96mbFFREV988QXvvPOOZbCb\nGz4+PnYpTKTVOnECHnkESkpg507o18/sikREHE6ZUVbr8U8zPsXlORfbLnISCKl5uLSy1OY6kpKS\nOHjwIMePH+fmm2/m7NmztGvXrta3Ql26dAkXl+q1paamsmjRIs6dO8eBAwcYOXIk48aNY9asWQD4\n+fmRmppqcz3SeihnizSDykp47TVYuhTmz7fsIeumHfuk+bi6uhIREUFERAQABQUFpKamWveiraio\nsI69chXtjh07qKys5Ny5c4SEhNClSxcqKirYsmUL48aNU2NWmp0jZG3l7AaaspmZmQQEBPDQQw+R\nlJTE4MGDWb58OZ6envaqT6T1qKiAV16Bl16yrJCdPRv09hURkVq1c6n9LaZje43lk2c/sekaY0+O\nJZ74Gsc9XD1sruPMmTNERkby6aefsmzZMi5evEhMTEytYbGysrLa44KCAmbNmsXWrVvx8PBgwoQJ\nvPPOO9Uab+3bt6/2tkdxHsrZIk3syBGYNs1yA699++DHt5qL2JO/v3+NVbSpqalkZmZSWFhYbWxK\nSgoVFRWcOXOG/Px8OnToQM+ePXF1dWXGjBkmvQJxFo6QtZWzG2jKVlRU8PXXX7Ny5UqGDBnCvHnz\n+POf/8x///d/W8csXrzY+vHIkSMZOXJkc9Uq0nIdPmwJif7+kJgIP97VU0Qcy+LFi2sEZkfg6+tb\n7futM5hz/xzS/5pe7S1RYV+HMfvx2Xa9xpgxY3j22We56667ADh06BCdO3cG4KuvvsIwDG7+8aYx\nbj9bjfXXv/6V2NhYPDwswbSsrKxGw62oqAh/f3+b65HWw5acDcraIg0qK4MlS+D11y0rZKdNAxcb\nV3mJXIPG5saSkhIKCgooKiqiuLiYs2fPAmAYBsXFxQDs37+fjRs3snr1avz8/OjUqROdOnWqkTHq\n44y5URrPEbK2cnYDTdnu3bvTvXt3hgwZAsC9997Ln//852pj9JddpB6lpfD885b9Y5ctg6lTFRJF\nHFhhYWGjN5C3h40bN5pdgt39tA9V3No4SitL8XD1YPbjsxu1P1VTXANg+/btTJ8+HYB33nmH3//+\n9wDcdNNN1cZ169aN4uJivL29Abhw4QJRUVEAHD16lL59+9K2bdtq53z33Xf06dOnUfVI62BLzgZl\nbZF6ffWVpQkbEWFZBBEUZHZF4kSuJTdWVlayceNG8vLyyMvLszZo27Rpg5eXF926dQOguLiY8vJy\nAgMDCQ4OJiIiAl9f33qv7Yy5URrPUbK2s+fsepuy3bp1o0ePHqSmphIREcH27dvp27evvWoTadl2\n74bp0y17xiYlQWCg2RWJiLQo40aPu+abBFzrNYqKiigoKGDHjh2Ul5czdOhQ7rnnHhITE9mwYQNL\nliyhTZs2AIwYMYL9+/dz++23A/Doo4+yadMmjh07Rk5OTq0Nt8OHD1uDqDgX5WyRa1BcDAsXwkcf\nwYoVcO+9WvggLYqrqyu33HIL+/fvp3fv3vzwww/k5ORw7ty5GvuLl5eXW/ei/eKLL/D39+e6664j\nPDycnj17NmoVrciVzM7aytkNNGUB4uLieOCBBygvLycsLIy///3v9qhLpOW6cMFyY4ENGyAuDiZO\nNLsiERG5Sjt27GD8+PFMmTKl2vGgoCCKioqsQRHgnnvu4S9/+Ys1LIaGhjJ37tw6r11aWkrHjh2t\nb7sS56OcLXIV4uNh5kwYMQKSk6FTJ7MrErkq3bp148YbbyQ1NZWAgAACAwOtK2HT09PJysoiOzvb\nurXBTwoKCigoKCA5ORl3d/dGraIVcSTK2TY0ZQcMGEBiYqI9ahFp+bZuhUcfhVGj4OhR8PMzuyIR\nEblKKSkpvPLKK4SHh3P+/Hk6duxofa68vJyQkBByc3MJ+vHtsr6+vnTu3Jn8/Hzrflj1Wbt2LTNn\nzmy2+sXxKWeLNEJBATz5JCQkwKpVMHas2RWJXLNu3bpZtyq4Ut++fa3vnsjLyyM9PZ2TJ09y9uxZ\nqqqqrONqW0Wbl5dnfTu3iKNSzrbQOneRppCfD088AXv2wJo1lqasiIi0aNdffz1ffPFFrc+dO3cO\nLy8vXH72dtm5c+fy5ptv8sgjj9R77ezsbPz8/IiMjGyyerOzs5k8eTJnz57FxcWFGTNmMGfOnGpj\nEhISuPvuu+nVqxcAEydOZNGiRU1Wg4hIkzMMWLcO5s6F++6zrI79cU9BEWfwU+P2lltuobS0lPT0\ndDIyMsjNzeXixYvVxhYUFHD69GlWrlxJu3btCAsLo2/fvgwaNEiraMWhKGdbqCkrci0MAz78EObN\ng/vvhyNHwMvL7KpERKSZDRkyxHqDpiu5uLg0GBQBevToQY8ePZq0prZt2/Lqq68ycOBAiouLGTx4\nMKNHj65xg4MRI0awadOmJv3cIiLN4vRpiI2FlBRLY/bHu3CLOCsPD48aq2hTU1PJysoiPz+/2ira\nsrIyjh07xrFjx/jnP/9Jt27diIyMJDo6WqtoxaE5U85WU1bkauXkWLYqyMyEjRth2DCzKxIRESd2\n5Vsgvb296dOnD6dPn64RFg3DMKM8ERHbGYbl3WcLFsCsWbB2LbRrZ3ZVIg7nyu/9paWlnDhxgo8/\n/pgOHTpw4cKFamPz8vLIy8tj165dtGvXjt69e9OnTx+tohWxQXPlbDVlRRqrqgpWr4ZFi+Dxx2H9\nenB3N7sqERFpxRISEkhISLB5/MmTJzl06BBDhw6tdtzFxYUvv/ySAQMGEBQUxF/+8heioqKauFoR\nkWuQng4zZsD587B9O/Tvb3ZFIi2Ch4cH0dHRpKen89JLL5GWlsbhw4c5fvw4ubm51ZpFZWVlJCcn\nk5yczLp167juuusIDw8nJiamSd/yLdJSNCZrN2XOVlNWpDFOnIBHHoGSEti5E/r1M7siERFxAiNH\njmTkyJHWx88991ydY4uLi7n33ntZvnw53j/bd3HQoEFkZ2fj6enJtm3bmDBhAqmpqc1VtoiI7Sor\n4bXXYOlSmD/fsoesm35cFbla4eHhhIeHA5Zs8PXXX3Ps2DFOnDjBpUuXrOMMwyA3N5fc3Fx27dqF\np6cnvXr1Ijo6mkGDBtXIEiKtka1Zu6lztr7LidiiogJeeQVeesmyQnb2bHB1NbsqERGRai5fvszE\niRP53e9+x4QJE2o836FDB+vHd955J4899hgFBQX4+/vbs0wRkeqOHIFp0yw38Nq3D8LCzK5IpFXx\n9vZm+PDhDB8+HIDjx49z5MgRUlJSOH36dLVVtJcuXbKuol27di3XXXcd119/PQMHDrQ2eUWcUXPk\nbDVlRRpy+LAlJPr7Q2IihIaaXZGIiEgNhmEwbdo0oqKimDdvXq1jzpw5Q5cuXXBxcWH//v0YhqGG\nrIiYp6wMliyB11+3rJCdNg1+drdtEWl6kZGR1m0KflpFe+TIETIyMupcRfvvf/8bT09PevfuTXR0\nNAMGDNAqWnEazZWz1ZQVqUtpKTz/vGX/2GXLYOpUhUQREXFYe/bs4f3336d///7ExMQA8OKLL3Lq\n1CkAZs6cybp163j99ddxc3PD09OTtWvXmlmyiDizr76yNGEjIiyLIIKCzK5IxCnVtor20KFDHD9+\nnDNnztRYRZuUlERSUhIffPABQUFBREVFER0drVW00qo1V85WU1akNrt3w/Tplj1jk5IgMNDsikRE\nWq2OHTviol961crPz8/msbfeeitVVVX1jomNjSU2NvZayxIRuXrFxbBwIXz0EaxYAffeq4UPIg7k\nylW0hYWFfP311xw9epT09HTKysqs4wzDICcnh5ycHOLj4+nQoQPh4eH07duXwYMH4+HhYdZLkCv4\n+fkpZ9fD1qzdXDlbTVmRK124YLmxwIYNEBcHEyeaXZGISKv3f//3f016vY0bN/Laa6816TVFRKQJ\nxMfDzJkwYgQkJ0OnTmZXJCL18PX15fbbb+f2228H4OjRoyQlJXHixAny8vKqjb1w4QKHDh3i0KFD\nfPDBB/Ts2ZOIiAhiYmIICQkxoXoBKCgoMLsEqYeasiI/2boVHn0URo2Co0ehEauTRERERESkDgUF\n8OSTkJAAq1bB2LFmVyQiV6Fv37707dsXsKyiTUxMJCUlpdZVtCdPnuTkyZPEx8fj4+NDr169iI6O\nJiYmRqtoRX6kpqxIfj488QTs2QNr1liasiIiIiIicm0MA9atg7lz4b77LKtjdWMgkVbB19eX0aNH\nM3r0aAC++eYbkpOTSUlJ4dy5c9XGFhUVWVfR/uMf/6B79+5cf/31DB48mO7du5tRvohDUFNWnJdh\nwIcfwrx5cP/9cOQIeHmZXZWIiIiISMt3+jTExkJKiqUxe/PNZlckIs2of//+9O/fH4D8/HwOHTrE\n0aNHyczMpLy83DquoqLCuor2k08+wcfHh969e1vPb9eunVkvQcTuGmzKhoSE0LFjR1xdXWnbti37\n9++3R10izSsnx7JVQWYmbNwIw4aZXZGIiIg4IWVtaXUMw/Lus/nzLXl77VpQk0XEqXTu3Nm6irai\nooJjx45x+PBhUlNT+f7776uNLSoq4sCBAxw4cAA3NzeCg4Pp06cPAwcO1CpaafUabMq6uLiQkJCA\nv7+/PeoRaV5VVbB6NSxaBI8/DuvXg7u72VWJiIiIk1LWllYlPR1mzIDz5+Hf/4YfV82JiPNyc3Or\nsYr2wIEDHD16lFOnTtVYRZuRkUFGRgZbtmzBz8+PiIgI+vbtS0xMDG5ubhQVFXHq1CkqKytxdXUl\nODgYHx8fs16eyDWxafsCwzCauw6R5nfiBDzyCJSWWm4y8OMG5SIiIiJmUtaWFq+iApYvh6VLLStk\n584FN+2UJyI1de7cmTvuuIM77riDiooKvvnmG7755hvS0tJqrKL94Ycf2LdvH/v27cPNzY2uXbvi\n7u7OgAED6Ny5M5WVlSQnJ9OvXz81ZqVFsmml7KhRo3B1dWXmzJk88sgj9qhLpOlUVMArr8BLL1lW\nyM6eDa6uZlclIiIioqwtLd+RIzBtmuUGXvv2QViY2RWJSAvh5ubGoEGDGDRoEAB5eXkcOHCA48eP\nc/LkSSoqKqxjf2rgVlVVsWPHDjw9PenZsyc33HADXl5eDBw40KyXIXLVGmzK7tmzh8DAQM6dO8fo\n0aO5/vrrue2226zPL1682PrxyJEjGTlyZHPUKXJ1Dh+2hER/f0hMhNBQsysSsavFixdTWFhodhk1\n+Pr6Vvv+ISLirJS1pcUqK4MlS+Bvf4MXX7RkbhcXs6sSEQfV2J9LDMOgoKCAgoICCgsLKS0tpaSk\nBMMwrFseJCYm8umnn+Lu7k7Xrl3x9fXF19eX9u3bN6o2/WwiZmmwKRsYGAhAQEAAv/71r9m/f3+d\nQVHEYZSWwvPPW/aPXbYMpk5VSBSnVFhYyIQJE8wuo4aNGzeaXYKIiENQ1pYW6csvYfp0iIiwLIK4\n7jqzKxIRB3etP5ecPXuWPXv2cPLkSXJzc6msrMTNzY1u3brh6uqKn58fAOXl5Xh4eBAYGEiPHj2s\nz9dHP5uIWeptyl66dInKyko6dOjAxYsXiY+P59lnn7VXbSJXZ/duS0js1w+SkuDHH3ZEREREHImy\ntrQ4xcWwcCF89BGsWAH33quFDyJiF126dGH06NGcPHkSFxcX0tPTOXfuHBcvXsTDw6Pa2PPnz3P+\n/HmOHz9O27Zt6dq1K4GBgQQHB+Pt7W3SKxCpqd6m7JkzZ/j1r38NWPbveOCBBxgzZoxdChNptAsX\nLDcW+PhjiIuDe+4xuyIRERGROilrS4sSHw8zZ8KIEZCcDJ06mV2RiDgZb29vQkJCOHv2LFFRUbRp\n04YuXbpw+fJlsrOzyc3NpaCgoNpetJcvXyYnJ4ecnBwSExPx9fUlMDCQoKAggoKCTHw1Ig00ZUND\nQzl8+LC9ahG5elu3wqOPwqhRlpD441sXRERERByVsra0CAUF8OSTkJAAq1bB2LFmVyQiTszb27vW\n1a5+fn7079+f8vJycnNzycnJ4cyZM1y8eLHauMLCQgoLC/n222+te9Hm5eVRXFysVbRidw3uKSvi\n0PLz4YknYM8eWLPG0pQVEREREZFrYxiwbh3MmQP/9V+WhQ9qWIiIg3N3dyc0NJTQH2/yXVBQQFZW\nFnl5eeTn51NVVWUdW15eTnZ2NllZWbz66qt06dKFkJAQIiIirOeLNCc1ZaVlMgz48ENLQ3bSJDhy\nBLy8zK5KRERERKTlO30aYmPh+HHYsAFuusnsikREroq/vz/+/v7Af5qwp0+fJi8vj0uXLlUbe/bs\nWc6ePcv+/ftp164dPXv2JDw8nMjISK2ilWahpqy0PDk5lq0KMjNh40YYOtTsikREREyXnZ3N5MmT\nOXv2LC4uLsyYMYM5c+bUGDdnzhy2bduGp6cnb7/9NjExMSZUKyIOyTAs7z6bP9+St9euhXbtzK5K\nRKRJuLu7ExYWRlhYGADnzp2z7jfr4uKCYRjWsWVlZaSmppKamsq2bdsICAigV69eREZGEhwcbNZL\nEJM0V85WU1Yc0udbthC/YgVuZWVUtGvHmDlzGH7nnbB6NSxaBI8/DuvXg7u72aWKiIg4hLZt2/Lq\nq68ycOBAiouLGTx4MKNHj6ZPnz7WMVu3biUtLY0TJ06wb98+Hn30Ufbu3Wti1SJib7Xm7HHjID0d\nHnnEcvPcf/8b+vc3u1QRkWYVEBBAQEAAWVlZPPXUU6SlpZGamsrJkyerraI1DMO6inbv3r14enoS\nHBxM7969iYyMpH379ia+CrGH5srZasqKw/l8yxY+nTuXJenp1mMLU1KgQweGe3tbbjLQt695BYqI\niDigbt260a1bN8ByE4w+ffpw+vTpamFx06ZNTJkyBYChQ4dSWFjImTNn6Nq1qyk1i4h91Zqz09Nh\nwwaG/9//WVbIzp0LbvoxUUScS/v27YmOjiY6OhqA3Nxcjh8/TkZGBnl5edVW0V66dImUlBRSUlLY\nvHkz3bp1o1evXoSHh2sVbSvVXDlb323F4cSvWFEtKAIsOXWKP11/PcP37AFXV5MqExERaRlOnjzJ\noUOHGPqzLX5yc3Pp0aOH9XH37t3JyclRU1bESdSas9PT+dMPPzB8/3748S29IiLOLigoiKCgIG6/\n/Y474qkAACAASURBVHZKSko4fvw4J06c4NSpUzVW0X733Xd899137NmzB09PT0JCQggLC9Mq2laq\nKXO2mrLicNzKymo97tq1qxqyIiLilBISEkhISLBpbHFxMffeey/Lly+v9aYUV670AHBxcWmKEkWk\nBagzZ0dHqyErIlKH9u3bM3DgQAYOHAjAqVOnOH78OFlZWbWuoj127BjHjh1j8+bNBAYGEhoaSmRk\nJEFBQWa9BGmArVm7qXO2mrLicCratq31eKWHh50rERERcQwjR45k5MiR1sfPPfdcreMuX77MxIkT\n+d3vfseECRNqPB8UFER2drb1cU5Ojn5AEHEiFXXctEs5W0TEdsHBwdZtCoqLi63bHGRmZlJ2xS+/\nDMPg9OnTnD59mj179uDt7U1wcDARERFERkbirnvkOAxbsnZz5Gw1ZcWx7N7NmG+/ZaGXF0suXrQe\nXhAWxh2zZ5tYmIiIiGMzDINp06YRFRXFvHnzah0zfvx4Vq5cyW9/+1v27t2Lr6+vti4QcRbFxYxp\n146Frq4sqay0HlbOFhG5et7e3gwePJjBgwcDkJmZSVpaGhkZGZw9e7ba2OLiYusqWhcXFwIDAwkP\nDycyMtK6X6k4pubK2WrKimO4cMFyY4GPP2Z4XBy0a8ef4uJwLS2l0sODO2bPttwVVkRERGq1Z88e\n3n//ffr3709MTAwAL774IqdOnQJg5syZ/OpXv2Lr1q2Eh4fj5eXF3//+dzNLFhF7iY+HmTMZPmIE\nvPcef3rnHeVsEZFmEBoaSmhoKPCfVbRpaWlkZWXVuYr2888/x9vbm5CQEHr37k1ERIRW0TqY5srZ\nasqK+bZuhUcfhVGjIDkZ/PwYDgqHIiIijXDrrbdSVVXV4LiVK1faoRoRcQgFBfDkk5CQAKtWwdix\nlpw9aZLZlYmItHq1raJNTU0lIyOD/Pz8amOLi4tJTk4mOTkZNzc3AgMD6dWrFxEREVpF6wCaK2er\nKSvmyc+HJ56APXtgzRpLU1ZERERERK6NYcC6dTBnDvzXf1kWPtRyQxIREbGfK1fRFhUVWVfRZmdn\nU15ebh1XUVFBdnY22dnZ7Nq1i44dOxIaGmpt0moVbeuhpqzYn2HAhx9aGrKTJsGRI+DlZXZVIiIi\nIiIt3+nTEBvL/2fv3uNzrv8/jj+uHRyGbCunRojkzBwi0VbEFz9nfSM5TkZyqtRX9I2+OauIklPK\nV6ESiZEcJoecN6eUYdPmFM2whp0+vz+ur2U223XtcH2ubc/77eaWfa7DnnvJrqf3Ptf7w2+/wbff\nwuOPm51IRETuUrJkSR577DEee+wxkpKSiIiI4LfffuPMmTNpzqK9du0ahw4d4tChQ7i5ueHj40Ol\nSpWoUaMGpUqVMukrkJxg06JsUlISjRo1onz58nz//fe5nUnys6go61YF4eGwejU0aWJ2IhERERHT\nqGdLjjEM67vPxoyx9u3ly6FwYbNTiYhIJlxdXalSpQpVqlQBrGfRHj9+nNOnT6d7Fu2ZM2c4c+YM\n27Ztw9PTk4oVK6bsRevq6mrWlyFZYNOi7KxZs6hZsybXr1/P7TySXyUnw4IFMG4cvPwyrFwJOuVe\nRERECjj1bMkRp07Biy9aL567eTPUrWt2IhERyaKSJUvStGlTmjZtSlJSEqdOneLkyZOEh4cTHR2d\n6r4xMTHExMSkOou2SpUq1KhRA29vb5O+ArFVpouyUVFRBAUFMXbsWN5//31HZJL8JizMWhJv3rRe\nZKBWLbMTiYiIiJhOPVuyLTERZs2CyZOtZ8iOGAFu2qFORCS/cHV1pVq1alSrVg2A6OhoTpw4kbIX\nbWJiYsp97zyLdsuWLXh6elK5cmWqVatGlSpVdBatE8r0FXvUqFFMnz6da9euOSKP5CeJifD++zBt\nmvUM2WHDQN8ERERERAD1bMmmw4chIABKlIA9e+B/b3sVEZH8y9vbO81ZtCdOnCA8PJyYmJhU942J\niSEkJISQkBAKFSqEj48PTz75JA899JBJ6eVuGS7Krl27ltKlS+Pr60twcHC69xk/fnzK7/39/fH3\n98/BeJJnhYZaS6K3N+zbB/+7wqBIdo0fPz7Ni40z8PT0TPX9UEREJCO29GxQ15Z03LoFEyfC3LnW\nM2QDAsBiMTuViIjkMHv/7Xvjxg2io6O5evUqsbGxGIaR5j5btmzhvvvuy1Yu/ds352S4KLtr1y7W\nrFlDUFAQN2/e5Nq1a/Tp04clS5ak3Ed/EJLKzZvwn/9Y94+dOhX69VNJlBwVExND586dzY6RxurV\nq82OICIieYgtPRvUteUuu3bBwIFQrRocOgQPPmh2IhERySXZ+bdvUlISUVFRREVFceHCBWJjYylS\npAjPPfdctnPp3745J8NF2UmTJjFp0iQAtm3bxowZM9IURZEUO3ZYS2Lt2taSWK6c2YlEREREnJJ6\nttglNhbGjoWvvoIPP4Tu3XXig4iI3JOrqysVK1akYsWKAFy5ckXbJTkhu3aBt+iFX9Jz/br1wgKr\nVsHs2dC1q9mJRERERPIU9Wy5p40bITAQ/Pzg6FG4/36zE4mISB7j5eWFl5eX2THkLjYvyvr5+eHn\n55ebWSQvCgqCIUOgVStrSdRfchERERG7qGdLuqKj4ZVXIDgY5s2DNm3MTiQiIiI5yMXsAJJHXb4M\nvXvDyy/DokXWX1qQFRERERHJHsOAr7+GWrWgZEnriQ9akBUREcl37Nq+QATDgBUrYORIeP55OHIE\nihUzO5WIiIiISN537hwMHQq//gorV0KzZmYnEhERkVyiRVmxXVSUdauC8HBYvRqaNjU7kYiIiIhI\n3mcY1neejRlj7dvLl0PhwmanEhERkVykRVnJXHIyLFgA48ZZtytYuRIKFTI7lYiIiIhI3nfqFLz4\novXiuZs3Q926ZicSERERB9CirGQsLMxaEm/etF5koFYtsxOJiIiIiOR9iYkwaxZMnmw9Q3bECHDT\nP89EREQKCl3oS9KXmAjTpsHjj0PnzrBzpxZkRUREnNiAAQMoU6YMderUSff24OBgSpYsia+vL76+\nvrz77rsOTigiKQ4ftvbsdetgzx549VUtyIqIiDip3OrZeuWXtEJDISAAvL1h3z6oXNnsRCIiIpKJ\n/v37M2zYMPr06XPP+/j5+bFmzRoHphKRVG7dgokTYe5c6xmyAQFgsZidSkRERDKQWz1bZ8rK327e\nhLFjoXVr696xGzdqQVZERCSPaNGiBV5eXhnexzAMB6URkTR27QJfX+tZsqGhMHCgFmRFRETygNzq\n2TpTVqx27LAWw9q14dAhKFfO7EQiIiLyP8HBwQQHB2frOSwWC7t27aJevXr4+PgwY8YMatasmTMB\nReTeYmOtJz589RV8+CF0767FWBERESeS3a6d1Z6tRdmC7vp164UFvv0WZs+Gbt3MTiQiIiJ38ff3\nx9/fP+XjCRMm2P0cDRo0IDIyEg8PD9avX0/nzp05ceJEDqYUkTQ2boTAQPDzg6NH4f77zU4kIiIi\nd8lu185qz9b2BQVZUJD1zNgbN+DYMS3IioiI5GMlSpTAw8MDgLZt25KQkEB0dLTJqUTyqeho6NcP\nBg2CTz6Bzz7TgqyIiEg+ldWerUXZgujyZejd27pv7KJF1l+Z7I0hIiIiedvFixdT9rrau3cvhmHg\n7e1tciqRfMYw4OuvoVYtKFnSenZsmzZmpxIREZFclNWere0LChLDgBUrYORIeP55OHIEihUzO5WI\niIjkgJ49e7Jt2zYuX75MhQoVmDBhAgkJCQAEBgbyzTffMHfuXNzc3PDw8GD58uUmJxbJZ86dg6FD\n4ddfYeVKaNbM7EQiIiKSA3KrZ2e4KHvz5k38/Py4desW8fHxdOrUicmTJ2f/qxHHi4qCIUMgPBxW\nr4amTc1OJCIiIjlo2bJlGd4+dOhQhg4d6qA0Ygt17XzCMKzvPBszxtq3ly+HwoXNTiUiIiI5JLd6\ndoaLskWKFGHr1q14eHiQmJhI8+bN2bFjB82bN7f7E4lJkpNhwQIYN866XcHKlVCokNmpRERERAo8\nde184NQpePFF68VzN2+GunXNTiQiIiJ5RKbbF9zeqDY+Pp6kpCTtPZaXhIVZS+KNG7B1q/WiXiIi\nIiLiNNS186jERJg1CyZPtp4hO2IEuGlnOBEREbFdps0hOTmZBg0acOrUKYYMGULNmjVT3T5+/PiU\n3/v7++Pv75/TGcVeiYnw/vswbZr1DNlhw8DV1exUcg/jx48nJibG7BhpeHp6pvr7LSIiIjlPXTsP\nOnwYAgKgRAnYsweqVDE7kdyDeraIiDizTBdlXVxcCA0N5erVq7Rp04bg4OBUZVAvJk4mNNRaEr29\nYd8+qFzZ7ESSiZiYGDp37mx2jDRWr15tdgQREZF8T107D7l1CyZOhLlzrWfIBgSAxWJ2KsmAeraI\niDgzF1vvWLJkSdq3b8/+/ftzM49k1c2bMHYstG5t3Tt240YtyIqIiIjkEeraTm7XLvD1tZ4lGxoK\nAwdqQVZERESyJcNF2cuXL6e83ePGjRv8+OOP+Pr6OiSY2GHHDqhfH379FQ4dgv79VRJFREREnJy6\ndh4QG2vdL7ZbN5gwAVatAh8fs1OJiIhIPpDh9gXnz5+nb9++JCcnk5ycTO/evWnZsqWjsklmrl+3\nXljg229h9mxrWRQRERGRPEFd28lt3AiBgfDkk3D0KNx/v9mJREREJB/JcFG2Tp06HDx40FFZxB5B\nQTBkCLRqBceOgZeX2YlERERExA7q2k4qOhpeeQWCg2HePGjTxuxEIiIikg/ZvKesOInLl6F3b+u+\nsYsWWX9pQVZEREREJHsMA77+GmrVgpIlrWfHakFWREREckmGZ8qKEzEMWLECRo6Enj3hyBEoVszs\nVCIiIiIied+5czB0qPUaDStXQrNmZicSERGRfE6LsnlBVJR1q4LwcFi9Gpo2NTuRiIiIiEjeZxjW\nd56NGWPt28uXQ+HCZqcSERGRAkCLss4sORkWLIBx46zbFaxcCYUKmZ1KRERERCTvO3UKXnzRevHc\nzZuhbl2zE4mIiEgBokVZZxUWZi2JN27A1q1Qu7bZiURERERE8r7ERJg1CyZPtp4hO2IEuOmfRSIi\nIuJYutCXs0lMhGnT4PHHoXNn2LVLC7IiIiIiIjnh8GFrz167Fnbvhldf1YKsiIiImEINxJmEhkJA\nAHh5wd698PDDZicSEREREcn7bt2CiRNh7lyYNAkGDgSLxexUIiIiUoDpTFlncPMmjB0LrVtb9479\n8UctyIqIiIhdBgwYQJkyZahTp8497zN8+HAeeeQR6tWrR0hIiAPTiZho1y7w9bWeJRsaat0iTAuy\nIiIiYqPc6tk6U9ZBpk4az7zlc0h2ScQl2Y3AHi/zxpvjYccO60/qa9WCQ4egXDmHZVq3Dp54Ajw9\n/z4WEwM7d0L79g6Lka51P67jwy8/5JZxi8KWwgx/fjjtnzE3lDPP6+cDP/Pt9m9JIAF33OnaoiuP\nN3zc1EyaV/6hedlH87KP5pVz+vfvz7Bhw+jTp0+6twcFBXHy5EnCwsLYs2cPQ4YMYffu3Q5OKZLz\n7tmzY2OtJz589RV8+CF07+6wxVhn7kHq2fZxxtcpZ56XiEh+lFs9W4uyDjB10nimfD2RmG6JKcem\nfD0RgoJ443QUzJ4N3bo5PNcTT1h76sSJ1hf0mJi/PzbTuh/XMeKjEZzyPZVy7NRH1t+bWRiddV4/\nH/iZORvncK7ZuZRj5zZaf29mYdS88gfNyz6al300r5zVokULIiIi7nn7mjVr6Nu3LwBNmjQhJiaG\nixcvUqZMGQclFMl59+zZJ0/yxtad8OSTcPQo3H+/Q3M5aw9Sz7aPs75OOeu8RETyq9zq2dq+wAHm\nLZ9DTOfEVMdiOicy/9xhOHbMlAVZsL6AT5xofQGPiEj9wm6mD7/8MFVRBDjle4rZy2eblMjKWef1\n7fZvUxVFgHPNzrFqxyqTEllpXvmD5mUfzcs+mpdjnT17lgoVKqR8XL58eaKiokxMJJJ99+zZP34J\nn3wCn3/u8AVZcN4epJ5tH2d9nXLWeYmIFFRZ7dk6U9YBkl0S0z1+uuItLB96OzhNOkrDx5//77+z\nzA4DRACV0h7+4fQPWCY4wf5fOT0vL5i1LRtPdDX9w/ti9vHUtqey/rxeMGtCDnyBmpe5NC/7aF72\nyaV5xRvxWX/OfCo4OJjg4OBsP49hGKk+tmhfTcnj7tWz/6jgzuCEVbDW3MWz682h8jCoWhW2TjI1\nCgBnTh1Jt2dvDztMzdcHOzzP3RIKwcc5OK+LVy6w+ptPs/z4C5ci0z1+OtKN99+vluXnjYh4lsE5\nMO7r16FyZRg1Ctzds/98IiIFVU507az0bC3KOoBLcvpjfjj6AU69fcnBaVK7/VaXRx6B1auhY0fw\n8DA1Eh+6teE4G9Mcr+nWhmFlNpiQ6G9xcbBmDTzzjPV6bDkxr6+++or69etn+fHf3grgDDvSHK8Y\n34KuVxdm+XlDQ0P55z//meXHw9/zat4cZs60nhQ+a1b2foo/cuRIOnfunOXHjw4ZzX72pzne2LMx\n0/ymZfl5V69ezcyZM7P8+NyiedlH87JPbs2rkKVQdmLlS/7+/vj7+6d8PGHCBLufw8fHh8jIvxcY\noqKi8PHxyYl4Iqa5V88ukuBO/bJZ71c5IS4OvtsKw/8J69dDzbpQyORvb1fcfiKO82mO3+fmZfq8\n4uOt12Lr+BgcP54z8zpw9gAVipfP8uOvW4pzi4tpjrsV+YuqVWOz/LyxsWfJRv0H/u7Z775rPSF8\n5Ur49FNo2TJ7zysiUhBlt2tntWdnuCgbGRlJnz59+OOPP7BYLAwaNIjhw4fbFUwgsMfL1r2u7nhr\nlecqNwY9N9TEVKn3HvL0hH79nOOtLxWqDGfER6dSvbWqysEqTHt9GO2fMS/X7XmtXm2dz9ChOTOv\nX3/dRceOpbP8+FI+7Ziz8XSqt1Y9uPNBAru25fGG5zJ4ZMaSk3cxeHDWF2XvntegQdCuHdSsCXPn\nQqdOWX7qbOnaoivnNp5LM68ubbqYE8jJaV720bzso3k5VseOHZkzZw49evRg9+7deHp6aj9Zk6lr\nZ9+9evZr/3yNwY3MO/Pzdg/67n89cUIH5+jZ6+pUSLOnbJWDVZg1Zpqpe8rentfej9PukZrtH+b/\nwy/Lj/+5VKE0e8p6/eRFXI1wTtd4nRcrv0gxt2J2P29O9+yhQ+GFF6BvX2jTBmbMAC+vLD+9iIjY\nKas9O8NFWXd3dz744APq169PbGwsDRs25JlnnqFGjRo5Frw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dBCEi+Z8WZUVE7NCs2Z98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44FPet7ch3rNbUEeXl5zJs3j0cffdSj80tLS3nwwQeZP3++lyvzXHl5OYmJiezbtw9rE39Rt4bx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\nWrlXbOlH9bV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uv/9+NBoNra2tcnJBEg6H5RTtT37yE9xuNwsWLODGG28UKVpB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\ndOG1p0iE43Eyh216HILBYKCwsBC1Wp0h1qZcs+lu0RTRaBSv15shBisUiqz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Tmpoa9Ho9\nzz333DBXLBC99qkj+uyxwXAdryPdR9jg2sCGtg10hDuYbZ7N98Z9j+mm6SjlSjgDJhsmH7dvHC56\nOl4PPZTc/t3vJlepvfQSPPooDOW5t9Rx6el47fHs4aGDD/FO6zvcOeFOijSD6M4QDChKpRK/309L\nSwuRSASLxSLdptfrMZvNyGSyLJdtLBYjHA5LIm3KdZsaOhaPx+ns7MTtduN2u6XBvOlCbSq71mg0\nUlFRgcViwefzYTKZpBVtHo+H6upqcnNzMRqNVFdXD/owMcHpx2D12ScUZS0Wi/SBMxgMTJ48GYfD\nIRrFfnDmzJnD3hweS08NjskkGsXjIY5X3zje8brqquTlm9+EG29MumaffBLSMrH7RDAWZGvnVja0\nbWBLxxbG6ccxxzyHRZWLsGgtPd5n5oyZJ2ymFTIF00zTmGaaxpLxS9jftZ+Nro38Yt8viCViSQet\neS5T8qYgl4kv/LHMzJkzJQes3+/nySefZP369T26aD0eD1u3bmXbtm289NJL5OXlMWXKFK688kry\n8vI466yzhuMlCE4j/vznP590n5UrVw5BJYLeInrtgUH02aOfoTpeiUSCQ75DbHBtYKNrI4FYgDnm\nOSytWcqZxjNRyBRZ9zlZ3zgcnOx47doF990H06Ylxdp/+7eBM0GcjOMdr6nGqfz3jP/mpYaXWLx9\nMTeOu5GFpQtFLz3CCQaDkvCZjlarxWazndB0EIlEeoxE8Pl8+P1+gsEgRqNRGijm9/slkdbj8RAO\nh6VtTU1N7N27l87OThQKBRqNBoDCwkKmTp1KS0sL48ePzxi0JBAMJIPVZ/c6U/bIkSPs2LFDWuKZ\n4r777pN+PjaDQSAQCI7H5z8P27bBf/0XTJ+ezMK69dbeDQPrjnbzUcdHbGjbwPbO7UzKncTcornc\nWn0rhZrCAa1TJpMxOW8yk/Mms7hqMXXddWxwbeDhgw/TFe1itnk2c81ziRMf0OcVDA/33Xcfbrf7\nhPtUV1dTXV3N0aNHqa2tpaWlBb/fTyKRIB5Pvg8SiQSdnZ0cPXqUtWvXUlBQgNVqlZZfqfuYdWgy\nmTK+bwUCwdhD9NoCweAQT8TZ590nCbEyZMwtmsuPJ/2YM3LPGJOiYE5Osse+5pp/mSCeegoqK4e3\nLrVczffGfY955nk8dPAh3m19l7sn3S1mOYxAYrEYDoeDtra2jOFFCoWCsrIyioqKTrp6MDU4LJUN\nm95nx2KxjEtKwA2Hw0SjUUmkDQaDhMNhIpEIsVgMv99PNBrNWL02adIkioqK2Lx5c79fr+i1BcNF\nr0RZn8/H17/+dVasWJEVtizeuAKBoL+o1XDvvXD11cllVn/5Czz9NEyalL1vR6CDNw68wRv6N3j6\no6c5y3gWc81zuWviXUM2NEAmkzHeMJ7xhvF8b9z3aPA3sNG1kafqnqLR2Ij/DT9XT76ai6ovQq0Y\n/gEjgr7jdru54oor+nw/l8vFu+++y8aNG2lubiYYDEq36XQ6DAYD4XCY+vp67HY7ZWVlTJgwgRkz\nZmQsATser732Wp9rEggEowfRawsEA0s0HmXj0Y28l/MeL330EgalgblFc/nF1F8wXj/+tImimjED\ntm5NumVnzICf/xyWLOmdCWIwqTZUs3L6SlbZV3H7J7fz7Ypv83Xb13t0KguGnra2tqzYLplMhtls\npqysDKWyf/Pie9tnR6NRwuEwHo+HtrY2Ojo6aG1tpb29Hbvdjt/vx+/3A0mReOHChRQVFVFdXd2v\nukD02oLh46SfpkgkwtVXX813vvOdfv2hKhAIBCdjyhTYuBEeewxmzYK774Yf/hDaQ828tv81Vu1b\nxcdNH/Ol6i8xMTyRRy98FIOy99M4B4sKXQXXVVzHdRXX8fwbzzOlaAoPbHyA6165joUTF3LVGVfx\nlZqvkKMSUz/HOmazmWuuuYYFCxZw5MgRDhw4wJYtW2hsbESr1WYMGohEIhw9epSjR4/yzjvvkJ+f\nT1VVFVOnTuXcc88dxlchEAiGA9FrCwQDQzgW5t36d1m1bxWv73+dcmM5hoSBh89+mApdxXCXN2yo\nVPDTnybjw1ImiGeegeFOSVHIFFxTfg2zzLN4+ODDvNv6LvdMuocaQ83wFnYa09XVRWNjI4FAIGN7\nbm4u5eXl5OQM7t80sViM7u5u6RKLxdBoNJSWllJaWirVePjwYdxuN21tbZhMJnJyciguLh7U2gSC\nweKEomwikeDGG29kypQp3HnnnUNVk0AgOA1RKOCOO2DGFxu4cfmr/OquVchLP+NrZyzgts/dxmvf\nfA29Ws+dH945IgTZY8mL53HXzLu4a+ZdOLucvLr/VVZuXcl3X/8uF4+/mKsnX83CCQvJ1fR/oq1g\n5GMwGBg3bhw6nY6zzz4buVyOTqfj0KFD7N27l4aGBunMforOzk46Ozv55JNP+J//+R+sVis1NTVc\ncMEFFBQUDNMrEQgEQ4HotQWCUyMQCbDm8BpW7VvF6oOrmVw0masnX81Pb/opVflV3Hnnnae1IJvO\nGWfAhg3JWQ5z5sCdd8KPf5wUbYcTa46Vh6c9zD+b/8ndu+7mstLL+E7ld1DLxaqzoSIUCmG327Mi\nvDQaDTabDVNqotwgEAwGJRE2GAxmRCWkI5PJyMnJoaioiKqqKjweD7FYDIVCQXFxcdYqE4FgtHBC\nUXbTpk28+OKLTJs2jenTpwPw4IMP8pWvfGVIihMIBKcHtR21rNq7ilX7VlHXWcdlV16GyfFjXvzF\nlyi/XsOll0LOKOrLSnNLuf3zt3P752/H5Xfx+v7XeWHXC9z895uZN24eV0++mssmXUZBjhDcxiIG\ngyGrMbRYLMyZMweA2tpaduzYQV1dHS0tLRnNZyrioL6+nrfffpvCwkIqKyuzhisIBIKxgei1B4bN\n2zfzysZXiBBBhYqr5lw14gYzCQaOrlAXqw+tZtW+Vaw9vJYZpTO4evLV/NeX/ouy3LLhLm9EI5fD\n7bfDV7+anOXwuc/Bs88m/x1OZDIZC0oXcF7Beaw4tILF2xdz98S7OcsohqQOJvF4HKfTmdWPKhQK\nLBYLJSUlAx71kcqFTQmx6REJx6JUKtHr9RgMBnJyclAo/hVvUVg4sHNEBILh4oSi7OzZs6WhJQKB\nQDBQJBIJ9rTt4ZV9r7Bq3ypau1u58owrefCiB5lbOReVInnK/sdXwdKlcPbZyWVWc+cOc+H9wKwz\nc+O5N3LjuTfiCXr4x8F/sGrfKn7w1g8433o+V0++mivOuIISQ8lwlyoYImpqaqipSS7N8/l8bNu2\njQMHDvToom1vb6e9vR2Xy8WCBQuYMGECn/vc5/jyl7/cqyxagUAwshG99qmzeftmVq5dieMLDmmb\nY23yZyHMjh06A528ceANVu1bxfoj65ldMZurJ1/N4wsep0hfNNzljToqKmD1anjpJVi4EBYtgvvv\nH+6qwKwx84upv2CDawP3772feUXzuKnqpuEua0zicrlwOBxEIpGM7ancWNUAWqj9fj9er5fOzk4O\nHz58QjesVqvFYDCg1+vRaDQDVoNAMFLpX0KzQCAQ9JFEIsEnzk9YtS/piA1Gg1w1+SoeW/AYM20z\nUcizg/1LSuCvf4XXXoNvfxu+9jWA0fvlbNT+//buPC7qcv3/+GvYHRAQ2ZTVlUVFREhRQXPXzFRc\nMktTUMq0zOVUv+qcdistszypWdkxO+r3HNQ0l9TSwIVcoNQkWRRlF0Q22Yf5/cGRIhcYBD4s1/Px\nmIfycZY3t8zMxTX3574tmOE1gxleM7hZepP98fsJiwnjxR9epJdtL4I8gpjkMQknCyelo4pGYmZm\nVm039YsXL3L27Fni4+Nv2+22pKSE8+fPc/78ef71r39hb29Pz549GTx4MP7+0ngQQrRO2yO2V2vI\nAqQOSGXH0R3SlG3mMgoy2Pn7Trb/vp3I5EiGdhrK1B5T2TRxE5YmDXc6dWuhUsHjj8PIkfDcc+Dl\nBb17K7+eq0qlYrDNYPpY9mFtwlpmn5pNf4P+SsdqMQoKCkhKSrptIoCZmRlOTk6o1er7fgyNRkNe\nXh55eXnk5uZWNX5LS0tva8jemg1ramqKWq2uNhtWiNZAmrJCiAZToa3gRNIJwmLC2B6zHSN9I4I8\ng/hm0jf07dC31qfDTJgAQ4bAsmWwbduLODsn4+9/vWHDNzBTI1OCPIMI8gyiuLyYQ5cOERYTxpvh\nb9LFqktVg7arlfLFsWg8bm5uuLm5AZCdnc3Zs2eJiYm5bY0vrVZLWloaaWlpHDx4ELVaXbUO7YgR\nI2QtWiFEq1FG2R2P3yi7QW5ZLhaGFo2cSNyP5LzkqjOpfk3/lTHdxjDXZy7bp27H1MhU6Xgtkq0t\nbNkCu3fDY4/NoLS0iNDQS5iZ3f208sZgbmjOC+4vcCr7FG8VvsXMHTNZNWoV7dVy2npdlJaWkpyc\nzI0bN6odNzIywtHRkXbt2t3X/RcVFZGbm0teXh4FBQU1zoa91Yg1MTG5r8cVormTpqwQol6VV5QT\nfiWcsJgwdsTswFptzSSPSeyevpuetj3rvC6RpSVs2ADZ2f9mzZo5/PCDLQsWxGNpeedfxpoTEwMT\nxnUfx7ju4yjTlPHTlZ8Iiwlj0JeDsDOzI8gjiCCPIDxtPOt9XSfRdFlZWVXNou3QoQOPP/44R44c\n4dy5c6SkpFQrdgsLCzl79ixnz55lw4YNODg40KtXLwYNGkT//jK7RAjRchly51Ns04rSmPHzDAz0\nDHBVu+KsdsZF7YKLqQsuahesjazlPbWJSMhOqDqTKj47nvFu41nqv5QRXUZgYiANm8by8MPw+OPv\nkZLyLLNn+7FoUSwDByo/CcLPyo8ZeTMwamNEz7U9WT16NVM8p8jzt5YqKipIT08nIyOj2nI5enp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6EsqbNFbbQxbIO3vTfe9t78XPwzE3pMACo3GUstTiXxZiJXC69y5sYZtqdsJ6kwCTMDM1xN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\nAxAVpXQqIYQQQ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      }
     ],
     "prompt_number": 136
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "### Two counter-intuitive examples which show that something in wrong in the implementation/the paper.\n\n - $1243567$ has $K = 1$ and $K_w = 1$ but $1253467$ has one more permutation but $K_w = .5$ (doesn't satisfy the triangular inequality?? it is however proven in the paper)\n - the rotation permutation has not the worst distance."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "p_switch_3_4 = [1, 2, 4, 3, 5, 6, 7]\np_shift_5_to_3 = [1, 2, 5, 3, 4, 6, 7]\n\n# top-3 weights\ndeltas = np.array([1, 1, 1, 0, 0, 0], dtype=float)\n\n_log.setLevel(logging.DEBUG)\n\npositive_weights, average_costs = get_position_weights(p_switch_3_4, deltas)\n\nprint \"\\npositive_weights = {}\".format(positive_weights)\nprint \"average_costs    = {}\".format(average_costs)\n\nprint \"\\n\"\nprint \"kendall_measure(p_switch_3_4) = {}\".format(kendall_measure(p_switch_3_4, weights=average_costs))\n\npositive_weights, average_costs = get_position_weights(p_shift_5_to_3, deltas)\n\nprint \"\\npositive_weights = {}\".format(positive_weights)\nprint \"average_costs    = {}\".format(average_costs)\n\nprint \"\\n\"\nprint \"kendall_measure(p_shift_5_to_3) = {}\".format(kendall_measure(p_shift_5_to_3, weights=average_costs))\n#print \"footrule_measure = {}\".format(footrule_measure(permutation=p_switch_3_4, weights=average_costs))",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - get_position_weights\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - p                         = [1 2 4 3 5 6 7]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - sigma_i                   = [0 1 3 2 4 5 6]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - i_n                       = [0 1 2 3 4 5 6]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - differing_elements_mask   = [False False  True  True False False False]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - positive_weights          = [ 1.  2.  3.  4.  4.  4.  4.]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - positive_weights[sigma]   = [ 1.  2.  4.  3.  4.  4.  4.]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - average_costs_numerator   = [ 0.  0. -1.  1.  0.  0.  0.]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - average_costs_denominator = [ 0  0 -1  1  0  0  0]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - kendall_measure\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - pairwise_inversions = [[3 2]]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - get_position_weights\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - p                         = [1 2 5 3 4 6 7]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - sigma_i                   = [0 1 3 4 2 5 6]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - i_n                       = [0 1 2 3 4 5 6]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - differing_elements_mask   = [False False  True  True  True False False]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - positive_weights          = [ 1.  2.  3.  4.  4.  4.  4.]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - positive_weights[sigma]   = [ 1.  2.  4.  4.  3.  4.  4.]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - average_costs_numerator   = [ 0.  0. -1.  0.  1.  0.  0.]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - average_costs_denominator = [ 0  0 -1 -1  2  0  0]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - kendall_measure\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - pairwise_inversions = [[4 2], [4 3]]\n"
      },
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": "DEBUG we7.notebook - \n"
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "\npositive_weights = [ 1.  2.  3.  4.  4.  4.  4.]\naverage_costs    = [ 1.  1.  1.  1.  1.  1.  1.]\n\n\nkendall_measure(p_switch_3_4) = 1.0\n\npositive_weights = [ 1.  2.  3.  4.  4.  4.  4.]\naverage_costs    = [ 1.   1.   1.  -0.   0.5  1.   1. ]\n\n\nkendall_measure(p_shift_5_to_3) = 0.5\n"
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "### Getting a feeling of the positional weighted measures"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "_log.setLevel(logging.WARN)\n\ndef get_measures(p, deltas):\n    sigma = np.argsort(p)\n    positive_weights, average_costs = get_position_weights(p, deltas=deltas, sigma=sigma)\n    k_measure = kendall_measure(p, weights=average_costs, sigma=sigma)\n    f_measure = footrule_measure(p, weights=average_costs, sigma=sigma)\n    return k_measure, f_measure \n\nn = 7\nn_samples = 1000\n\n# top-3 weights\ndeltas = np.array([1, 1, 1, 0, 0, 0], dtype=float)\n\nordered_perm = np.arange(start=1, stop=n+1)\nsampled_measures = np.array([get_measures(np.random.permutation(ordered_perm), deltas=deltas) for i in xrange(n_samples)])\n\n# Normalising by maximums for each measure\nmax_kd_measure = np.max(sampled_measures[:,0])\nmax_sp_measure = np.max(sampled_measures[:,1])\nsampled_measures[:,0] /= max_kd_measure\nsampled_measures[:,1] /= max_sp_measure",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 190
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "plt.figure(figsize=(16, 8))\n\nkd_hist = plt.hist(sampled_measures[:,0], bins=20, normed=True, histtype='stepfilled', ec=None, color='b', alpha=.5, label=\"$K_w$\")\nsp_hist = plt.hist(sampled_measures[:,1], bins=20, normed=True, histtype='stepfilled', color='r', alpha=.5, label=\"$F_w$\")\n\nn_illustrated = len(illustrated_perms)\nillustrated_perms_labels = [\"\".join(map(str, p)) for p in illustrated_perms]\n\nillustrated_kd_measures, illustrated_sp_measures = zip(*[get_measures(p, deltas=deltas) for p in illustrated_perms])\nillustrated_kd_measures = np.array(illustrated_kd_measures) / max_kd_measure\nillustrated_sp_measures = np.array(illustrated_sp_measures) / max_sp_measure\n\nmax_y = max(kd_hist[0] + sp_hist[0])\nillustrated_kd_ys = max_y - np.arange(n_illustrated) % 2 / 10.0 - np.random.uniform(size=n_illustrated) * .1\n\nillustrated_sp_ys = .02 + np.arange(n_illustrated) % 2 / 10.0 + np.random.uniform(size=n_illustrated) * .1\n\nfor label, measure, y in zip(illustrated_perms_labels, illustrated_kd_measures, illustrated_kd_ys):\n    plt.text(measure, y, label, horizontalalignment='center', color='darkblue')\n    \nfor label, measure, y in zip(illustrated_perms_labels, illustrated_sp_measures, illustrated_sp_ys):\n    plt.text(measure, y, label, horizontalalignment='center', color='darkred')\n    \nfor x1, y1, x2, y2 in zip(illustrated_sp_measures, illustrated_sp_ys, illustrated_kd_measures, illustrated_kd_ys):\n    plt.plot([x1, x2], [y1, y2], color='k', lw=3, alpha=.25)\n\nplt.xlim([-0.2, 1.2])\nplt.legend();",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
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fuuKaSCQy2m+dgH2eQHYQPAFnyVXwpOIJJ7jtnnvsXkKGUaNGadSoUfrlL3/Z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\nfTcFqwAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 208
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}