{ "cells": [ { "cell_type": "code", "execution_count": 224, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import numpy.linalg as la\n", "\n", "import scipy.optimize as sopt\n", "\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import axes3d" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "**Function optimization**\n", "\n", "Find the minimum of the following quadrating (convex) function:\n", "\n", "$f(x_1, x_2) = \\frac{1}{2}x_1^2 + \\frac{5}{2}x_2^2$" ] }, { "cell_type": "code", "execution_count": 214, "metadata": {}, "outputs": [], "source": [ "# function\n", "def f(x):\n", " return 0.5*x[0]**2 + 2.5*x[1]**2\n", "\n", "# gradient\n", "def grad_f(x):\n", " return np.array([x[0], 5*x[1]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "**Visualization:** 3D mesh plot" ] }, { "cell_type": "code", "execution_count": 215, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 215, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.gca(projection=\"3d\")\n", "\n", "xmesh, ymesh = np.mgrid[-2:2:50j,-2:2:50j]\n", "fmesh = f(np.array([xmesh, ymesh]))\n", "ax.plot_surface(xmesh, ymesh, fmesh)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "\n", "**Visualization:** 2D isocountours plot" ] }, { "cell_type": "code", "execution_count": 216, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 216, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAD8CAYAAAB+UHOxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAIABJREFUeJzsnXd4XMW5/z+zZ3vXqvfiKldcsE21gRhsakhCSCAFbgjJTeAm+SX3EhJukptGer9JgFQuJISE3nsxYOPeZNmy1Xtb7WpX2r7z+2MX2QZTLWul1XyeZ56zZXTOK+mc+b7vzLwzQkqJQqFQKKYfukwboFAoFIrMoARAoVAopilKABQKhWKaogRAoVAopilKABQKhWKaogRAoVAopinHLQBCiHIhxHNCiHohRJ0Q4gvHqCOEEL8SQhwSQuwWQiw93usqFAqF4vjQj8M54sCXpZTbhRAOYJsQ4ikp5b4j6qwHZqXLSuB36aNCoVAoMsRxRwBSym4p5fb06wBQD5S+rtolwO0yxSbALYQoPt5rKxQKheK9Mx4RwBhCiCpgCfDq674qBdqPeN+R/qz7GOe4FrgWwGazLZs7d+54mqg4LiTIGBBNH2Op45GvSR6urnOBVp4ZUxXvjXgLyOARH+hAGABD6njka4zpo8iEpYo3Ydu2bQNSyvx3UnfcBEAIYQfuAb4opRx+/dfH+JFjrkEhpbwVuBVg+fLlcuvWreNlouJtkDIJyT5ItEOiHRlvT7/uSJVk3xG1NUAPukrQSkArAl0RQisCXSFohaCVIbTCTP06iveATHRDohMSvZDsQSZ6IdEDyW5IdB9xDySBMBBJ/79LU2KvlSH05enXFaDLRwglEBOJEKL1ndYdFwEQQhhINf53SinvPUaVDuBIV7AM6BqPayveHVJKSA5AogXizchEC8RbIdEK8TZSD/Vr6EBXDPoyMJ2B0ErTD3op6EpAKyT1r1dkC0IrBu1w7+zrm24poylBSHRBoguZ6EgLRidEN0PyAeSRvp2wILUK0CpBX4nQqkBfDVo16DxKHDLMcQuASP0H/wjUSyl/9ibVHgSuE0LcRWrw1y+lfEP3j2L8kDIGiTaIN0G8ERlvgkQjxJtfF+IbUp6avhKMpyL0lan3WgVoxQhhzNjvoJh8CGEEfUWq8GYC0ZmKHOOtyER72rk4CJHnkMSOOJkTqa8G/QyEVgP6GaCvAa0CIbSJ+6WmMeMRAZwGfBzYI4TYmf7sa0AFgJTy98CjwPnAIWAUuHocrqvgNY++B2L7IX4AGT8I8YZUw3/kw6YrTD1clksQWnXaC6sCrUQ9bIpxIyUQ6fvLdLRASBlPRw7Nqegz3px6HXkJmTyy48CI1M8A/SyEfg4YZoN+LugKVMQwzojJvBy0GgM4GiljEG+E+D5krB7i+yF2AKTvcCVdSfqBmYXQz0x5VVoNQmfPnOEnGCmTRJMhYskQ0eQo0eQosWSYmAwTT4aIJsMkZIR4MkJcRseOCRkbK0kZIyHjJGWCJHGSMomUCSTJVJHJo7s2jkAgEEJLHdEhhIYmNAQamtCjExqaMKITejRhQBMG9DoTemFMFZ0JvTBh0Jkx6CwYhBm9zoxJZ8Ogs2DUWTHozAiRvXmbMjmcik7jjUc4MQdTzs1riBwwzAF9LcJQC/p5oK9BiHGdyzLlEUJsk1Iufyd11V9ukiJlFOIHIFaHjO2F2L7UQ0E0VUFYQD8bzOchDHNBPwf0cxA6R0btPh7iySjhxDChhH+shBPDhBMBwolhIokA4USASDKYKokRoskRosnRd3UdHXr0OuNYY6wJAzphSDXWaOiEhk7oEejQCUOqWdfpSPmzb+j0SAuERCKRMkFCRoknE2kxSZCQcRIySlLGSchYSnySUZIk3oXVAqPOgklnx6jZMOnsmDQ7Zp0Ds5YqJs2BRXNh0VyYNRcWzYlF70KbAuM0QucE42IwLj46akj6U/d9rB4ZP5Byekb/hiSSrmFCGmaDfj7CsAAMC0A/U3VdvkOUAEwCpIxD/BDE9iBjeyC2J93Yp7twhAsM88H2CYR+HhhqQauaEl03SZkglPARjA0wEvcykhhkND7ESDx1HE34GI37CCWG3rIhN+qs6UbPgVmz4zaUYjTZMGl2jDprqmjWtLdsxZj2og06CwadGb0wjXnduknyd0vKxBERSYRYMpSKXNLRSyw5SjQxmo5qUkIXSQSJJEeIJIIEYn0MJBoJJwPEkqE3vY5RZ8OqubHo3Vi1HKz6HGz6XGz6HKz6XGx6D3Z9HlbNPemiDKFzgfFkMJ48JgyprqQWiO1DxvZBfB+EH0GG7krXMCD1c8C4CKFfBIaF6UhhcvzfJxOqC2gSkBz8EMR2p94IR8qLMSxMeTT6+ampdZOw71NKSTg5zHCsl+FoD4F4H4FYH8F4P4FYPyPxVKMvj8wNSGPWnNg0DxZ9DlbNjVWfg0VzYdW7095ryoM1a05MmgNNhflvSULGCCeC6YjpcAQVivsYTfjGjqPxIUbjXsLJwBvOoUPDmhYDuyEfhz4fh6EAh6EQp6EQp6EIk84+ae9FEm0Q24uM10Fsb8qRkiOpCsZT0Hn+mlkjJwjVBTTFENargGTKU9EqJ5UXlpAxhmO9+KNd+GNd+KJdDMe68cd6CMR63+C1G4QZu6EAuz4Pj20Zdn0uNn0udn1e2uv0YNXnTIluiamEJgzY9DnY9DnvqH48GWU0kRKDkbiXYHyAYHyAkVjqOBBpoiX4KnEZOernjDorTkMxTkMhLkMJLmMxbkMJTmMxTkNRxoRaCJGayaavRHABkM5rSTSlhEBYM2LXZEcJwCRAWC7M6PWllATj/QxF29OlA1+0E1+0k+FYz1EevF6YcRmLcBqKKbeehMNQiMtQjMNQgNNQiEnnmJQeouJo9DojTl3Ks38zpJSEE8MMx3sJxHrTkV43w7FefNFOWke2kpDRsfoCHU5DMTnGUtzGMtzGUjzGCnKM5dj0uRN+XwihA/3MVFEcEyUA04ikTOCPdjEYbcUbacMbbcUbacUX7SAmDyeAGXQW3IZSCsyzmO1cg9tYhstQjNtYglVTyTvTBSEEFr0Li95FoXn2G76XMslI3DsWGfpjXWPOQ8fobuKvu6dyjOV4jBV4TJVjR5eheNKMyUxHlABkIVJKAvE+BiLNDEaaGYy0MBhpYSjaRkIezg1w6AvwmCootS4ix1ieLmUZ8dYUUw8hdNgNedgNeZRaFx31XSqqHDgiqmxnKNJOx+gu9g8/PVZPE0Y8xgpyTVXkmqrJNVWRZ6rBrs9T9+AEoARgiiNlEl+0k95wA/2RQ/SFDzEQPnTUIJ9dn0+uqZpK2zI8xsoxD8yoqX5RxYlBCIHDkI/DkE+F7ejtPyKJEYaibQxGWvBG2xiMNNM+uuMoYbBoLvJMMygwzyTfPItC82xchhIlCuOMEoAphJSS4Vg3PeED9IYO0Jdu9F8biNWEgVxTNTMdZ5BnnkGeqYY8UzUmLXuTwF4jKZOEEjGC8TAj8TCheJSRRIRQPEookSqRRIxwIkY4GSOSiBFNxo8qsWSChEwSTyaJy9TrpEySlOl0sDeZMacTAh0idRQ6NKFDLzT0utRrg07DqDNg1GkYdXqMOj1mzYBJZ8CsGTBrRsyaAavehEUzYtWMWPUmbHoTdr0Zi2bMqobPpNkostRSZKk96vNwYpjBSAsDkSb6wofoDx9ih/deksSB1HTWgrQYFJrnUGiZi0OvsoOPByUAk5hwYpie0H56QvX0hPfTGz5AOJFaaFUTRvJNNcx1vo8C82wKzLPxmCqm/HRJKSWhRJSh6Ei6BPFHR/HFRtPHEYZjIYZjIQKvlXiYkXjkTTN1X49AYNL0Y43xa0Wv01INt9Ch6XTohQ6DzoAOXbpxP3ZDk5QyLRIpwYjLBJFEjLhMEJdJYsk40WQifYwTScSJJGPHPNex0CFSYmCw4DRYcOjNOA0WnAYrbqMVl8GKy2jDZbDiMdrIMdrJMdqw6KdWMpRZc1JqXXRUd1JCxhiMtNAXPkhfuIG+8EF2Dt031pVp0dwUmueMCUqRec60cHjGi6ndWmQRUibxRtvoCu2le3QfPeF6hqKpLRQEOjymSmbYT6PQModC8xxyTdVTqrGXUuKPheiP+OkPD9MfCdAf9jMYCTIQCTAYCTAYDeKNBN+0cdQLDZfRmmr89BYKzC5mOIpw6M3YDeYxj9mmN2HVTFj1RqyaCYvehFkzYNGMmNKNfaa9Rikl0WR8LCIJx6OMJqKEEhFG41FG4hFG4mFGEhGCsTDBeKq8JnzNwT78sRD+2CgJ+cY8CwCzZsBjtJNrcpBncpBrSr3ONznJNzkpMDvJMzlxGiwZ/3u8GZowUGCeRYF5FqnlxFKiMBBuojd8IB0N76dlZDOpFeYFHmMFRZZaii3zKbHMJ8dYPml/v0yjEsEmAU92/5imwMtEkqlVOi2ai2LLvLRHM49C8+xJ31+fkEkGwsN0hoboCg3RNeqlJ+yjN+ynJ+SjL+wnkoy/4edcButYw5RrTDVSOUZ7ypM12XEbrLiNNlxGKzbNpB7k1yGlZCQewR8bHYuafNERvNEgQ9GRlLCmxXUwEmA49saMYZPOQJHFRaHZTaHZRZHFTYklh1KrhxJLDnkmB7pJlJtyLCKJYEoQQvV0h+rpCe0bGwcz6xzMdp7NWUXXZ9jKiUElgk0xrJqbWY4zKbYuoNgyD7ehdFI2dPFkgp6wj9aRATpGBukIDdIx6qV9ZJCu0BBxeXhtG4Egz+Sg0OxijrOEMwtqKTC7yDc7KTClPM88swOjTt2Cx4MQArshFQGVWj1vWz+SiDEQCdAfGaY/PExfeJi+sJ/esJ++sJ+NAw0MRI7OEjbq9JRYciiz5qaLh3JrLhW2PIosbrRJIA4mzU6FbRkVtmVAKqIeinbQFaqjO1SHRe/KsIWTExUBKN5AMB6mNdhP80g/LcE+Wkb6aR8ZoH3Ue1Qjb9WMlNvyKLV4KEt7iyVWD6UWD0UWFwbVuE9Josk43SEfXaNeukJDdIa8dI16aR/10jE6SChxOPnLqNNTZvVQYcujypZPla2AKns+VbZ8rHpTBn+L6YuKABTviFA8SlOwl8ZgL03BPhoDvTQHe+mLHN7RUy80ym25VNrzOaOglkpbPuW2XCqseeQYbZMyUlEcH0adnkpbHpW2vDd8J6VkMBqkfWSAttFBWkf6aRsZoCXYz4a+/UeNRxSaXcywF1JjL6TGXkCNI3U0a1NrcDqbUQIwDZBS0hv2s3+4i4OBbg4FejgU6KFj1Ds2c8ak01NlL2BZbg019sKUN2cvoNSSg16nMjUVKYRIde3lmRws8VQf9V08maBjdDAdOfbTlHYstnqbiKbHf3QIym25zHQUMdNRxGxHMXOcJeSbnMqZyABKALKQgfAwdf4O9vk7qB/uZL+/E18slSsgEJRZPcxyFLG+5CRmOIqYYS+k1OqZFH25iqmLXqdRZS+gyl4ARywxFE8m6Bz10hjs5VCgh4OBHvb7u3imZ+9YHY/RTq2rlLnOEua5ypnnKiXXNHX3tpgqKAGY4oTiUeqHO9jja6fO384+X8dYF44mdFTbCzijoJZaVylznCXMtBdNufnhiqmNXqdRac+n0p7P2UULxj4fiUc4FOhh/3An+/1d7B/uZGN/A8l0VFpkdjPPVcYCdzkL3OXMdZZi1tQqsuPJuAiAEOJPwIVAn5RywTG+XwM8ADSnP7pXSvnt8bj2dKMn5GPnUAt7fG3s8bVxMNAz1u9aZvWwxFPNfFcZ81zlzHYWT6sHJppIMByJMBwJE4xGGYlGU8dY6hiOxxmNxRiNxwjHYkQSCSLx+NgxlkwQSySJJROpbOBkkoSUJJOpbODEm0yY0NJJYjqdDk0I9Dodep0Oo6aNHU2aPnXU6zFpGhaDAYvegNVgwGIwYDMYsBuN2AxG7CYTdqMRp9GEw2TCqGVnF5xNb2JxTiWLcyrHPgvFoxwIdFHn62Cfv529/g6e7U1FCnqhMdtZzEJ3OYvcqZ8rMKvZPcfDuMwCEkKcCQSB299CAL4ipXxX6x5P91lASZmkKdjHDm8zO4da2OVroy/sB8CiGZnvKmOBu4KF7goWustxG20Ztnj8iCeTDI6OMjA6wmAoxODoKIOhVPGFwwyFQ/hCYXzhEP5IBH8kTDj+xjyDY2HUNCx6A+Z0Y2zSpxrn1xpsg6ZhSC/joOleW94hnQn8xh0hx8QhKZMkkpKETBJNJImnhSSaSBBNi0w4ESccjxOOpbKD3wkWvR6nyYzLbCbHbMZttowdc61Wci0Wci1Wcq1W8qxWPBYrel32dOcNRgLs9bWzx9fGXl87df6OsWTBYrObRTmVnJRTxRJPFdU2tTTEhM8CklK+KISoGo9zTWeklDSP9LFloJEt3kZ2DrWMJe4UmJwszqlkUU4li92VzHQUTdnB2XA8RufwMJ2BAN3BAD3BAN2BAD3BIH2jI/SPBPGGQsdc2MGg0x3VAFbl5OBON45OkwmH0YQz7UHbjSZsRmPas0553BaDYdI0jvFkktFYjFAsxkgsykgsRjASYSQWJRCJEohGxiIafySCPy18TUPelACGw8STb8wC1gmBx2Ih32qjwGan2G6nyO6g2OGgyG6n1OGk1OHEpJ8aPcC5JgerC+exunAekBpTaAh0s2uolV1DrWz1NvFE9y4A3AYrSzzVLPfUsCJ3JhU2taroWzGRd8ApQohdQBepaKBuAq89qXmyexcv9zewZfDQWBJOqcXD6oJ5LPFUszSnmmKLe8rcyIlkkq5AgLZhH+1+P21+P+3DPjqGh+kYHmYw9Ma9f/OsVorsDsocTpYUFZNvtZFvs5FntY55t7kWCw5j9mQD63U6nKaUYL0XpJQMRyJjkdHgaIiB0RH6R0cYGB2lbyRIbzDI3r7eY/7N8602Sh1OylxOKpxuyl0uKpwuKlxuiux2tEkilK9Hr9OY5ypjnquMj1adhpSSjlEvO4aa2e5tZoe3med6U81LodnFityZnF4wl7MK52fY8snHRAnAdqBSShkUQpwP3A/MOlZFIcS1wLUAFRUVE2ReZrmvfQuNgR5W5M7k5LyZnOyZQYn1nW3tlymklAyERmnyemnyDdE05KXFN0SLz0eb30fsCM/UoNNR6nRR5nCytmYGpc6UB1ricFLicFBgs2dtP/eJRAiBy5yKfmpy3joLOBKP0zsSpDsQoDMwnCrDqeOe3l4eP3TwqGjCqGlUutxUud1UuXOocedQ4/FQ4/bgsUyutYOESE0tLbflcnFZquejY3SQzQOH2DzYyAt9+/DHRpUAHINxywROdwE9fKwxgGPUbQGWSykH3qredBkD8EVHcBosk3K9FSkl3cEABwcHOehNlUPeQRqHvAxHDu8Xa9br0w1GDpVuN9UuNxXpMpm9SUWKeDJJdzpqa/P7afEN0erzpUTd7yOaODxe4TabmZHjYaYnl1mvldxcCm2Tc8P4hEwSiIVxGyf3elrjxaTLBBZCFAG9UkophFgB6IDBibj2VGCyDN6GYjHqB/qpH+hnf7o0DA4SiB5u6HMtVmZ5crlo9lxm5HiYkeOhxuOh2O540+WSFZMfvU5HuctFucvFaeVHf5eUkq7AMI1eL41D6eL18mTjQf5Rt2esntNkYm5uPnPy8pibl8+8vHzm5uVnfKxBE7pp0/i/W8ZrGujfgTVAnhCiA/gmYACQUv4e+BDw70KIOBACPiIn8yJE04BIPM7+gX529fawp6+XPX29NHoHx6Y62o1G5ublc/GcuczOzWN22svzWNSDNN3QCUGZ00WZ08XqqqOzfwdGRzk4OMBB7yAHBgc4MNDPvfV1jMRSs3T0Oh2zPLksKChkYUEhiwqLmJuXr7r8JglqMbhpgJSSVr+PHd3d7OztZldvD/X9fWP99LkW69gDuqCggPn5hZQ4HJMynFdMfpJS0jk8TF1/H3v7etnb18uevh6GwqlN4o2axvz8AhYXFrG4qJilRSWUOdVSEOPFu+kCUgKQhUTicXb19rC1q5MdPV3s7OlmMJSaTmozGFhUWMSiwiIWFxazqLCQYrtq7BUnFiklnYFhdvf2sKu3h109Pezp6yGUzt3Is1pZWlTCkuJilpeUsiC/MONdR1OVSTcGoDixDEcibO3qZEtXB1u7OtnT2zuWZFSTk8OaqhqWFpewpKiYWZ5cNSCrmHDEEd1I58+aA6QGnhsGB9je3cWOnm62d3fxZNMhAEyansWFRSwvKeXkklKWlZRiN6olTMYbFQFMQcLxGFu6Onm5vY1X2tvY199HUkoMOh0LCwrTD00ZS4tLyLFYMm1uxkkkk4yGo4yEY4xGooxGYoyGo4RjccLRGJFonEgsTiSWIJZIEIsniMZSWbyJRCq7N5leEuJY6HSpPYM1nUDT0pnEeh0GvYZB0zAZNMxGAyaDHpNRj9mgx2o2YjUZsJmNWM1GbCYjOp2KwgZGR9nW3cnWrlSp6+8jnkyiCcHCgiJOLa/g1PIKlhWXqAjhTVBdQFmGlJIG7yAbWlvY0NbC5s5OIok4Bp2Ok4qKOaWsgpWlZSwpLsasz+61f2LxBN7AaKoMp45DwRD+kTC+YAjfSBj/SIjAaIRAKEJwNEIwHH37E78OIcCgaWhaehkIXWqtn2OsBJFaKyiZWg4ikUgSSyR4t4+VEGAzm3BYTDisqaPLZsZlN+O2WXDbLeTYLeQ4rOQ6rXgcVnLsFgz67B5MHY3F2N7dxaud7WzqaGdnTzcJKbHo9awsK+eMiirOqKhkRo5HdWOmUQKQBQSjUV5ub+X5lmZeaGmmZyS1X/DMHA+nV6Zu+pWl5VgN2dPgB0IRerwBeocC9AwF6BsK0usL0O8bYWB4hAFfEN9I+Jg/q9d0uG1m3HYLTpsZp9WMw2LCnm5Q7Ud42hazAZvJiNmoT5e0d27Q0Os1jHrtuLvJ4mkhiMcThGPxsSgjHI0TisbGopCRcCoiCYYiBEMRAmnB8o+EGR4J4xsJ4Q8ee8kHALfdQr7LRr7LTp7LRmGOncIcR6q47RR5HNgt2bMzVyASYXNnBxvaWnixrZUW3xAApQ4nq6uqOauymlPKK7LquXi3KAGYorT4hnimuYlnm5vY2tVBLJnEbjRyenklq6uqOaOikhKHM9Nmvmdi8QRdg8N09Pto7/fRMeCne3CYrnQJhCJH1dcJQZ7Llmrg3HbynDbyXLYxD9jjtJLrsJLjsGI1GbLWA5RSMhKO4g2EGAqMMpiOgAb9KWF8TSD7fEEGh0feEH24bGaKPU5KclOlNM9FWb6b8nw3xbkODFN4Sma738+GthZeaG3m5fY2RmMxjDqNlWVlnF1dwznVMyhzTq8VQ5UATDF+vullHj3YQOOQF4DZnlzWVNdwVmU1S4tLptwD6h0e5VDXAM09Xlp7h2jtG6K1d4geb4DkEfeb2ainNNdFcbphKvY4KfI4KEp7sHkuG3pNDVi/G2KJBP2+Efp8AXq9Qbq9w3R7D4ts9+Aw4djhVVM1naDY46SyMIeKghyqCnOoLvYwoySPHPvUGj+KxONs7e7k+ZZmnmtpomkoFR3Mzs3jkjlz+fflKzNs4cSgBGCKcd2jD+GPhDmnegbnVM+g3DU1PJZILE5j1yANHf0c7OznUNcghzoHGAqGxupYTQYqC3OoLMihvCDldZbluyjPd+NxWLPWa5+sSCkZGB6ho9+fisL6/bT1DdHW56O1b4hQJDZWN9dpZWZJHjNKcpldls/ssnxqijwYDVNj8LXZN8QzTY0829xEmcvJj963LtMmTQhKAKYYUspJ3xCOhKPsb++jvq2P+rZeGtr7aen1kkim7h+LycCM4tyxBmNmSS7Vxbnku9TG8VMFKSW9Q0Gae7w0dg1wsGuAxq5BmroGx6IGvU5HdbGHOWX5zK0oYF5lIXPKCrCYJnef+1R4xsYLJQCK4yIWT9DQ0c+elh7qWnqoa+2ltdc71rdc4LYzpzyfOWUFzC7LY3ZZAWV5LjWNMUtJJJN09Ps50NHHgfZ+DnYOsL+tl4Hh1BLTOiGoKsphfmURC6qKWFBdxMzSvCnXdZktKAFQvCv6fUF2N3Wzq6mLXU3d7G/vIxZPJZLlOa3MryqitqKQeZWF1FYUkOucHIvXKTJLvy/IvrZe6tv62NfaS11Lz1j3n8mgUVtRyKKaYhbXlLCopljdNxOEEgDFW9LvC7KloZ0tB9rZ1tBBx0Bqm0mjXmNeZSELq4tZWF3E/KoiinLUMhGKd4aUkm7vMHuae9jb0sOe5m7q2w47ExUFbpbPLufkOeUsn12mBOEEoQRAcRTBUIStDR1s3NfKloZ2WnpSs40cFhPLZ5exZFYZi2uKmVtekPWJRYqJJRqLU9/ex67GLrYd7GDHwc6xxLwZxbmsmFvOqtpKls0qw2pWSz2MB0oApjmJZJJ9rb28UtfCq/vb2NPcTSIpsZgMLJ1ZyslzUl7Y7LJ8tS6QYkKJJ5Lsb+9j64F2Nh9oZ+ehTsKxOHpNx6KaYlbVVnLqvCrmlheoMaX3iBKAachQMMQrdS28UtfCxn0t+EbCCAHzKgpZVVvJqtpKFtUUKw9fMamIxOLsbOzi1fpWNtW3sb+9D0hNQT2ltpLT5ldzyrxKnDZzhi2dOigBmCa09/t4dschXtjdyO6mbpJSkmO3cMq81IOzal7llEvmySSJeJJoNE4sFk8do4nUYnBHlNcjEOi01CJwrxWDUcNo1GMw6jEa9Wgqme0d4x0e5ZX6Fl7e28Km+lb8I2E0neCkGaWsXlTD2UtmUpI7NfJkMoUSgCymrc/Hk9sO8NS2Bg52prZUnltewBkLqzlzYQ21FYXTNnROJiXD/lGGvCMM+0fx+0IMD6eOwUCYYDDMSCDMyEiEYCBMKBQlHIoSDsUIhaLE48deb+d40et1WCxGzFYjFkuq2OwmbHYzdrsJu8OM3WHG5bLidFlwuq24XFZyPDYcTsu0/X8mkkn2tvSwYU8zL+5p4lD6fq+tKGDtstmcu2y2EoNjoAQgy+gaHObJbQd4cmvDWIi8qKaY9y2dzdknzZgWD0E0Eqev109vj5/+vmEG+gMMpI+DA0G83iC+oRGSiWPfz2azIdXgOlINr81uGmuMLRYjZosBk9mAMe21G43q+7yfAAAgAElEQVQa+vTicJqmQ6fp0HQitWznEcikPLwaaCJJPJ4gFk0QiyWIRlORRDgUIxyOEhqNEg7HCI1GGQlGCAYPi1IkEj+m3Zqmw51jw5NrIzfPQV6Bg7w8B3kFTvILHBQWu8kvcGI0To3s3OOhrc/HczsP8fT2BupaewFYUFXEuctmc+7yORS47Rm2cHKgBCALGAqGeHpbA49t2c/Oxi7g8M1+ztJZFHum7qJwx0JKiW9olM4OL92dQ2PH7k4fvT1+vIPBN/yMy20lL99Bbp4DT66NHI+dHI+NHI8Nl9uKy23FmfaqJ3sDGY3Ex6IVv38U/1AqkhkaCjI0OIJ3MMjgQICB/gDD/tBRPysEeHIdFBa5KC5xU1KWQ3FpDqVlHkrLPbjc2bePc+eAn6e2NfDktpRTJAQsm1XG+pPncs6SWdN6zGDCBUAI8SfgQqBPSrngGN8L4JfA+cAocJWUcvvbnXe6CUAkFufF3U08/Oo+Nta1Ek8mqSn2sP7kWtadPIfSvKnv6SeTkp6uIVqa+mltGaC9dYD2Ni8dbYMEA4eXetbpBAWFTopKcigqdlFY7KawyEVBkYuCAie5eQ6MpsndqJ8oIpEYg/0B+nqH6e3x09eTiox6un10dw7R3zd81IqgDqeF8opcyio8lFfmUVmdR1VNPkXF7qzI8WjtHeLxLft5bMt+2vp8GPQap8+v4oJV8zhjQfW0m/iQCQE4EwgCt7+JAJwPXE9KAFYCv5RSvu3SfNNFAJp7vNz70h4e3rQP/0iYAreddSfP4fwVtcwqzZuyD2k8nqC1eYCDB7pp2N9NY0MvzU19hEYPb9CSm+egvDI33UClGqmS0hwKi90YDNPrwR0votE4PV0pMeho99LeNkhH2yDtrYNHRVJWm4mamQXMmFXIrDnFzJ5bTEVlHpp+ag5aSympb+vlsS0HeHzLfgaHR8mxW7j41PlcetpCKgrcmTZxQshIF5AQogp4+E0E4BbgeSnl39PvDwBrpJTdb3XO6SAAUko++D9/paPfz1knzeD9py1kxdzyKTc/X0pJd+cQ+/d1Ub+3k/31XTQe7CEWTWWBWq1GZswqZMasIqpnFlA9o4CKqjxstuzZrGQqMBIM09o8QHNjH42Hemk61EvTocOibDLpmTG7iLnzSqidX8rc+aUUFrmmnBMSTyTZuK+F+1/ey4t7mphTXsAdX70i02ZNCJNRAB4GfiClfCn9/hngBinlG1p3IcS1wLUAFRUVy1pbW8fFvslMXUsPRR7HlEqNj0bjNOzvpm53O3t3t1O/txO/L7U4mNlsYNbclEf5Wikp80zb2SyTnUQiSUe7l4P7uzl4oJsD9V0c3N9DNJoamM7x2Ji3oIz5i8pZsLicmbOLplR01u8LMjA8Qm1FYaZNmRDejQBMVCfqsZ78YyqPlPJW4FZIRQAn0qjJwvyqokyb8LaEwzH27e1g9/ZWdu1o5UB915h3X1bhYeWpM6ldUErt/DKqqvOnbDfCdETTdFRW5VFZlcf71i0EUt13zY197K/ror6ug7o9Hbz84gEAjEY9c+eXsHhJJYuXVlI7v2xSj8fku+3kqxlCx0R1ASmOSTIpOdTQw+aNh9i2uYn9dZ3E40l0mmDW7GIWnlTBgkXlzFtYRo5n6kQuiveOdzA4FvHt2dlG48FekkmJwagxb0EZS0+uZuWps6iZWTDluoyyicnYBXQBcB2HB4F/JaVc8XbnVAIwsYRGo2zd3MSrLx9ky6ZGvINBhIBZc4o5aVkVi5dWMn9Rueq3VwAQDITZu7udXdtb2bmthUMNPQDk5TtYccpMVp42i6UnV2M2T+7NYrKNTMwC+juwBsgDeoFvAgYAKeXv09NAfwOsIzUN9Opj9f+/HiUAJx7vYJCNGxp4ZUMDO7Y1E4smsDvMLF9Rw4pTZ7J85Qzl4SveEYMDAbZsamTzK6mocXQ0ismkZ+nJNZx65mxWnTYLd466l040KhFM8Zb09fjZ8Px+Njxfz749HUgJRSVuTj1jNqeeMZsFiypUH77iuIjFEuzZ1cbGFxt4ecMB+nuH0ekECxaXc8ZZtZy+eg55+dmVzDhZUAKgeAP9fcM891QdLz5bz4H6VGZxzaxCTl89h9NXz6WqJl/12ypOCFJKGht6eXnDAV56bj8tzf0AzFtYxuqza1l9zjxy8xwZtjJ7UAKgAFLLC7yy4QCPP7yL7VuakBJmzS3mzLNqOeOsuZSWeTJtomIa0tYywIbn9/Pic/U0HexFpwlWrJrJuRcsZtVps6bUFNPJiBKAaU5LUz+PPLCdZx7fQyAQpqDQydrzF7F2/SLV6CsmFW0tAzz12G6eemwPgwMBXG4ra9cv4vyLl1BemZtp86YkSgCmIZFIjBefreeRB7ZTt7sDg0HjtDPnsP7ikzhpWbVKwlJMahLxJFs3N/H4wzvZuKGBRCLJ4qWVnH/xEk5fM3fSL+Y3mVACMI3o7hziofu28fjDuwgMhyir8HD+xUtZu36hmnGhmJJ4B4M88cguHn1wBz1dPtxuK+svXsKFly6loHDqL4h4olECMA2o29POP/5vI5tebkDoBKedOZeLP7CMxUsr1WDuW5CIJ/APDOPvH2bYGyQ4NEJgaITgUJBQIEwoGCI8EiE0EiYSihKPxolH48SicRKxBK9/XoQQ6I361N4BRj16ox6z1YTZasJiN2O2mbE6LdhzbDhy7Kmjx44734kzz4Gmqf7uNyOZlGzf0sRD925j08sHATht9Vwuv/IU5swrybB1kxclAFmKlJKd21q48y8vsWt7K06XhYsuXcaFly5VU+qAaCRGX2s/3U299LcP0t8xmDp2DuLtGsLX58c/EHhDI34kJosRsy3VeBstRgwmAwajHs2goTfoEbo3bggTj6VEIh5LEIvEiIxGCY+ECQXDRMOxN72WTidw5jlxFzjJLfGQX+ohvzyP/PJc8svzKK4poKAiD4NRJVL1dvt46L7tPHz/NkaCEZavrOHKq89gwaLyTJs26VACkGVIKdn6ahN3/HkD+/Z04Mmzc/mVp7D+4iVYLMZMmzehJOIJelr66DjQRdv+Ltr3d9J5qJvupl4GOrxHNe5CCDzFbvLL88gtduMucJNT6CKn0I0r34nDY8eR9sgdOTbMdvO4e+SJRIJQIExgKB1teIMEvEGG+vz4+vz4ev0M9fkZ7PLS3+FlqMd31O+g04kxMSidWUz53NJUmVNCQWXetIsgRkYiPHTvNu75+yZ8vlFOWlrJlVefoSLfI1ACkCVIKdm2uYm//uFF9td1kl/o5CMfO5V1F540qRffGi/8A8Mc2tFM0+42mve20ry7jdZ9HcQih71qd76T0tnFlMwoori6kKKaAoqrU56zpzgHvWFq/Z1i0Rjebh+9rf30NPfR3dRLd3Mv3Y29tB/oIuA9vJ6/0Wygcn45NQsrqVlUSdXCCmYuqcLpyf459aFQlEcf2MHdf9uIdyDIwsXlfPLaNSxeUplp0zKOEoAsYM/ONv50y3Ps3dVOQaGTK686nbXnL87aOdLh0Qj7Njaw/9WDNGxr5OC2JvraBsa+9xTnUL2wguoFFVTOL6dibgllc0qmRWN3JP6BYdr3d9J+oIvWunaa97bRvKeNoV7/WJ2i6gJmLath9tIaalfNpnbVLIzm7IwUo5E4jz60g7/f/jLegSBLlldx9WfOonZ+aaZNyxhKAKYwfT1+fv/rp9nwXD25eQ6u+ORprLvopKybBhcJRah7pYHdz9ex64U69r96kHgstbx06azisQZs5tJqahZV4spTYxxvxVCfn+bdrRzc3jwmoN1NqY3TDSYDtatmsXj1fBavmU/tKbMxmrJrXCESifHwfdu56/9ewTc0wjnnLeDTnz9nWmYYKwGYgkSjce6561Xu/PMGAD7yidO47IpVmLLkQZVS0lLXzrYnd7H1yV3seXEf0XAMnaZj9rIaFq2ez6LV85h/6hzsbjV9dTwY9gbY90oDu9Ii27ijmWRSYraaWLRmHsvPPYll5y6mfE5J1vSfh0aj3PV/L/PPv2/CoNf4xDWrueRDy9FPo32BlQBMMbZsauR/f/4Ene1eTl8zl89e/z4Ki6f+/qWRUISdz9Wx6aGtvPrIdvo7BgGoqC1l2drFLFu7iAVn1GJzWjNs6fQg6Bth94v72PbkLrY9tZvOg6ntOIqq8ll5wTJWXbScRavnZUV00Nnh5X9//gRbNjZSVZPP9V9ex6JpMj6gBGAKEYsl+LeP/g6dTnDd/1vHyatmZNqk4yIwFGTjg1t5+f7NbH9qN+HRCGabiWXnLmbF+qUsP3cRBRX5mTZTAXQ397Ltyd28+ug2djy9h0goisVuZvl5iznt/StZdeFSbK6pG41JKdm4oYHf/uJJLFYjt9x+7bTIiFcCMMVobx2ksNg1Zfv5o5EYrz68jSdvf54tj+0kEU+QX57LKRctZ9VFy1m8Zn5WeJXZTCQUYeeze9n40DY2PrQVb/cQBqOelRcuY+0nVrNi/ZIpN6PqNcLhGIMDgWmzDpYSAMWE0NHQxaO3Pc2Tf30e/0AAT3EO51xxOqs/fCqzl8/Imn7l6UYymaR+00FeuPsVnvv7S/j6h/EUuTnv6rNYf805FFdPj83VpypKABQnjFg0xsv3beaRW59i53N16DQdp15yMus/dQ7L1i5Cm0aDbdOBeCzO5sd28NgfnmHzo9uREpauXcQF167l1IuXq//3JEQJgGLcGer18citT/PQ75/E2z1EUVU+6695H+ddfRa5xTmZNk8xAfS1D/DEn57jsT8+Q3/HIPnluVz8uXWcf805OHOn33TLyUom9gReB/wS0IA/SCl/8LrvrwJ+DHSmP/qNlPIPb3deJQCZp3VfO3f98H5e+McrxKJxTl53Epdct56T152ETqe2jZyOJBIJNj20jft/8xg7n92L0Wzg7CvO4CNffT+lM4szbd60Z0IFQAihAQ3AWqAD2AJ8VEq574g6VwHLpZTXvZtzKwHIHH1t/dz+rX/y1O3PY7QYOe+qs7jkunWUz5m+GZaKN9K8t40Hfv0YT9/xIvFYgvWfOpuPfeMyFRVmkIkWgFOAb0kpz0u/vxFASnnzEXWuQgnAlGB4MMDfvn8vD/72CZCSiz+/jo/eeKnKxFW8Jd6eIe787j08cuvT6A0al37hAi7/r0tUUl8GeDcCMB4xfCnQfsT7jvRnr+eDQojdQoh/CSHedA1XIcS1QoitQoit/f3942Ce4p0QjcT4508e5BMzr+O+Xz7C2R89nb80/IrP/vSTqvFXvC2eohyu/801/Kn+F5x26Qru+sF9fGLmddz/68eIx+KZNk/xJoxHBHAZcJ6U8pr0+48DK6SU1x9RJxcISikjQojPAh+WUp79dudWEcCJR0rJS/e+ym033EF3Uy8rzl/CtT/6OJXz1DrrivfOoZ3N3Pqf/8eOZ/ZQPreUz/z446w4f6maGjwBTHQE0AEc2VqUAV1HVpBSDkopI+m3twHLxuG6iuNkoMvL1y+8mW9f9lNMFiM3P34T33v4a6rxVxw3M0+q5odP/jf/c/9/kUwkuemiH/Dty36Kr9//9j+smDDGQwC2ALOEENVCCCPwEeDBIysIIY6cGnAxUD8O11UcBxsf2spnFn+F3c/X8e8/v4rf7/gxy89dnGmzFFmEEIJTLz6Z2/b8lE/dfCWvPryNz5z0n2x/enemTVOkOW4BkFLGgeuAJ0g17HdLKeuEEN8WQlycrvYfQog6IcQu4D+Aq473uor3RiQU4dfX/YFvXPJD8stz+e22H/GBL1ygEnoUJwyD0cBHbng/v371ZuxuKzec+x1u+6//IxZ98+0yFRODSgSbRjTvbeP7V/yClr3tfPCLF/BvN1+p1uhRTCjh0Qi3fPmvPHzLU8xaVsPX7vwCZbPVBu/jyUSPASimAM/+bQPXrfgqvr5hvv/o1/jsz65Sjb9iwjFbTXzhd9fyzXu+Qk9zH59bfgMv378502ZNW5QATAMe/O0T3PyxXzFnxUxu2fljTl63JNMmKaY5p1+6klt2/oTKeWV8+0M/4anbX8i0SdMSJQBZzj9+9AC/vu4PrLpoGT94/CY8RSpDUzE5yC/L5UdPf4NFa+bzo6t+w0O/eyLTJk07lABkKVJK/vLfd/GHr97BmstP5Zv/+krWbgyumLpY7Ba+9/CNrLpoGb/6/B+4+8cPZNqkaYUSgCxESskfvnond37vHtb929l89Y7/mLKbeSiyH6PZyDf/9RXWXH4qt91wB3d+955MmzRtUK1CFvLAbx7n7h8/wEWfPZfr//calX2pmPToDfqUo2LU85dv3EV+eS7nfnJNps3KelQEkGUc2NrILV/5K6suXMZ1v/mUavwVUwZN0/jKnz7H4jXz+dXnbqOlrv3tf0hxXCgByCKCvhG+e/nPyCly859//rxar18x5dA0jRvv/AIWh4XvXv4zQiPhTJuU1agWIkuQUvLTa35Hf/sgN931JbVDk2LKklucw413/Adt9Z385vo/ZtqcrEYJQJbwyK1P89K9r/Kp71/BvFPmZNocheK4WPq+RVx50wd58i/P8+zfNmTanKxFCUAWEA1Huf1b/2DR6nl88P9dmGlzFIpx4WPf+BCzl8/gz/99F4l4ItPmZCVKALKAJ/78HEO9fj7+jctUv78ia9A0jSu//kF6mvt4/h+vZNqcrES1FlOcRDzB3T9+gNpVs1i8Zn6mzVEoxpVVFy2jan45d/3gPpLJZKbNyTqUAExxnrvrZXpa+vnojR9QUz4VWYdOp+MjX72Ulrp2Nj20LdPmZB1KAKY4j972NBW1pay8YGmmTVEoTghrLj+Vgoo8Hv3D05k2JetQAjCFiYaj7H/1ICvWL1V9/4qsRdNrLD93MXtf2k8ioQaDxxPVakxhDmxpJBaNs/CM2kybolCcUBacUcuIf5SWvSo7eDxRAjCF2bMhtbXygtPnZtgSheLEsujMecDhe14xPoyLAAgh1gkhDgghDgkhvnqM701CiH+kv39VCFE1Hted7tS9sp/KeWUq61eR9RRW5pNfnkvdy/szbUpWcdwCIITQgP8F1gPzgI8KIea9rtqngCEp5Uzg58APj/e6Cgh4g+SV5WbaDIViQsgvy2XYG8y0GVnFeEQAK4BDUsomKWUUuAu45HV1LgH+mn79L+AcoeYsKhQKRUYZDwEoBY4cmelIf3bMOlLKOOAHjum6CiGuFUJsFUJs7e/vHwfzFAqFQnEsxkMAjuXJy/dQJ/WhlLdKKZdLKZfn5+cft3EKhUKhODbjIQAdQPkR78uArjerI4TQAy7AOw7XntZY7GaGBwOZNkOhmBD8AwEsNlOmzcgqxkMAtgCzhBDVQggj8BHgwdfVeRD4ZPr1h4BnpZTHjAAU75zalbNp3NlCKBjKtCkKxQllqNdH58Fualeppc7Hk+MWgHSf/nXAE0A9cLeUsk4I8W0hxMXpan8EcoUQh4D/B7xhqqji3TP/9LkkE0n2bWzItCkKxQll70up6Z8Lz1A5L+PJuGwKL6V8FHj0dZ9944jXYeCy8biW4jDzTpmNTifYs6GeZWsXZ9ocheKEsWdDPSaLkVnLajJtSlahMoGnMDanlYVnzmPDPZsybYpCccKQUrLjmT3MXTkLg9GQaXOyCiUAU5xTLzmZtvpO6l45kGlTFIoTwtYnd9FS187ZV5yRaVOyDiUAU5z115yDM9fBXT+4L9OmKBQnhL/ffC/5Zbms/cSZmTYl61ACMMWx2Mx84AsXsOnhbTTuasm0OQrFuLL3pXr2vFjPZV+5WHX/nACUAGQBF3/+PKwOC3/7/r2ZNkWhGDeklPzt+/fiynOw/ppzMm1OVqIEIAtw5Nj5wBcv4MV/buSFu9Xm2Yrs4Ik/P8eWx3dy+Q2XYraqBLATgRKALOHKmz5I7apZ/OzTv6fzUHemzVEojovmPa38+ro/sOSchXzgi+dn2pysRQlAlqA36Lnpri+h6XV89/KfEw1HM22SQvGeCAVDfOfDP8PutnHjHf+BpmmZNilrUQKQRRRU5POff7mOQzua+f2Xb8+0OQrFu0ZKyS8/dxudB7u58c4vkFPozrRJWY0SgCzjlIuWc9mXL+Kh3z3Bvb98JNPmKBTvir99716euWMDH/vGZZx01oJMm5P1jMtSEIrJxb99/wq6m/v43Zf+Qjwa58P/+fr9eRSKyYWUktu/dTd3fOdfvO/jZ3LF1z+QaZOmBSoCyEL0Bj1f//sXWf3hU7jthjv46zf/gVp8VTFZkVJyy5f/yh3f+Rfrrj6Lr/zpc6rff4JQEUCWojfoufHOL2CxmbnjO/8iFAjxmZ9+ErUTp2IykUgk+OVnb+OxPz7D+69fz7///Cp0OuWXThRKALIYTdP40m2fxWw3c88vHiHgG+ELv/00RrMx06YpFIRGwvz0U7/lhbs3csXXPsBV3/mIclAmGCUAWY5Op+Nzv7gau9vGHd/5F4d2NPO1v32RytqyTJummMY07mrh+1f8gvb9XXz6hx9T41QZQsVa0wAhBJ/8n8v5zoNfZbDTy+eX38Ajtz6lxgUUE46Uknt/+QjXr7yRoG+UHzxxk2r8M4gSgGnEqguX8fudP2H+aXP4xWdv5duX/ZRhr9pTWDExDPX6+PqFN/O7L/2FZect5padP2bp+xZl2qxpjRKAaUZeiYebH7+JT//wY2x8cCufWfwVtj65K9NmKbKcVx7YwrWLv8LOZ/dy3a8/xbfvvwF3vivTZk17jksAhBAeIcRTQoiD6WPOm9RLCCF2psvrN4xXTDA6nY4P/+cl/Grj97A4LNy47rt86wM/UmsIKcad1voOvnbB9/nmpT/CU+zmfzffzCWfX6cGeycJ4nj6gYUQPwK8UsofCCG+CuRIKW84Rr2glNL+bs+/fPlyuXXr1vdsn+LtiYQi/OtnD3PXD+4jHo3z/uvP58qbPojdbcu0aYopjH9gmNu/dTcP3/IUFruZK2/6EO+/fp1a038CEEJsk1Iuf0d1j1MADgBrpJTdQohi4Hkp5Zxj1FMCMMkZ7B7iL/99F0/8+TnsbiuX33Ap779+HSaLWoZX8c4JBUPc8/NH+OdPHiQ8GuGCa9fyiW9dprp7JpCJFACflNJ9xPshKeUbuoGEEHFgJxAHfiClvP8tznktcC1ARUXFstbW1vdsn+Ld07irhT99/W9sfnQHuSU5fOKbH+a8q89C06vMTMWbE4vGeOTWp7nzu/fg6/Nz2qUruPq7H1XTjTPAuAqAEOJpoOgYX30d+Os7FIASKWWXEKIGeBY4R0rZ+HbGqQggc+x+cR9/vPFO9m1soGRmER/4wgWs/cRqrA5Lpk1TTCKCvhGe+PNz3P/rR+lp6Wfxmvl86uYrqV05K9OmTVsmXRfQ637mL8DDUsp/vd35lQBkFiklGx/cyp3fu4eGrY1YnRbWXX02F3/+PEpnFmfaPEUGaa3v4IHfPM5Ttz9PeCTCvFPn8LGbPsjy805SA7wZZiIF4MfA4BGDwB4p5X+9rk4OMCqljAgh8oCNwCVSyn1vd34lAJMDKSX1rx7k/l8/yov/3EQykWTZuYs4/9NrOeWiZegNKqF8OhCNxHjl/s08ctvT7Hx2LwajnjUfPY33X7ee2ctmZNo8RZqJFIBc4G6gAmgDLpNSeoUQy4HPSimvEUKcCtwCJElNO/2FlPKP7+T8SgAmHwNdXh699Wke++MzDHR68RS5Oe/qs1j/qXMorinMtHmKE0BHQxeP3vY0T/71efwDAQor81l/zTmc/+n3kVOgBncnGxMmACcaJQCTl0Q8webHdvDobU+z+dHtJJOShWfWsvbjqznt/Stw5joybaLiOPD1+3np3s08dfvz7NvYgE7TccrFy7ng2rUsW7tIrdg5iVECMMUIDIewO8xTtu+0r32Ap25/gaduf4HOg93oNB0nnTWfUy46mVUXLaOoqiDTJireAZ2Hutn00DY2PrSVPS/uI5mUVM4rY+0n1vC+j59JbvEx8zwnPVJKRoIR7A5zpk2ZEJQATCESiSTXf/rPuFwWPv+l8yiryM20Se8ZKSUN25p46Z5NvHTfq3Q0pDKLqxaUs+rC5ay8YCm1K2epKaWThFg0xr6NDWx+ZDsbH95G+/5OACrnlXH6pSs5/YMrmbG4aso6JgDNjX385mePA/CT33x8Sv8u7xQlAFOIRCLJg/ds5S+3vUAsGudDH13FRz95GhbL1F+zv6Ohi00Pb2PTw9vYs6GeZCKJ1WlhyTkLWbZ2McvPXUxRdcG0eCgnA1JKOg92s/XJXWx7ahe7nqsjFAyj///tvXmQHNl95/d5lZl139XV9w00unEPBhhg7oPXcIYUKe0uHSvJa2llmdYfkuUIKyzbjPDS61BYG+vYWFnrQ6KkDWnNldZrmjtaDkUOh+TMYAZz4wa6gb7vq7qrquuuysznP7JQaGCAATBooLu68xPx4tWRnfWyq/L3/f3e8XuawqHn9vH4V4/x+FePbouxnFyuxL/587f4/r//AJ/PzX/+Wy/w0teO4HBs/9+aLQB1yOpKlu/87z/l9R9dIN4U5L/8nS/w7At7t41xzCSznPnpBT5+7RwfvXaOpakEAI2dDRx+fj+HntvP4ef30dxtC8JGIaVkbnSBc29c5vyblzj3xiUSs6sAtPQ2cexLhzn6pcM88rkD+ILeTW7txmCakp+9dpHv/B8/JbmS5eWvHeE3fusFgqHtcX13gy0AdcyFs1P8q3/xI8ZGlth3sJ1f/y+e48ixns1u1oYipWTm6hwf/+Q859+6zPk3LpFOWGmpY60R+o72sufRXfQd7aXvaC/R5rAtCndASklidpXh02Nc/WiU4dNjDH88RnIxDUCkKWQJ7bP7OPqlw7TuutXazvpFSsmH743yl995k6tD8/TvbeW3/5sXGdjXttlNe+jYAlDnGIbJj39wln/zFydJLGc4/GgXv/abz3Hwkc7NbtoDwTRNpgZnOffGJcwg4TAAACAASURBVIY+GObqR6NMD83VNqwJNQToOdhJ94FOeg910bWvnfb+VoLRnTnTKJ1YY/rKHJOXphm/MMX4xSnGz0+SSeYAcDgEnfva6Tvay94Tezj8/H46+lu3pYhKKTnz8QR/+advcvniDM0tIf6z33yOz794cEd099wKWwC2CeWSzquvnOav/+odkqs5Dj/axa/++tM8crS+B+buhkK2wOjZCYZPj9eM3MSFKYr5Uu2YcDxIx0AbbX0ttO5qpqW3kZbeJpp7GgnGAnX7P5JSkk6sMT+2xPzYolVGF5kZnmN6aI61leub+Hj8bnoOdtJzsIueg53sPtLDrke6cXu3dxK/ax7/d//121y+OEO8McCv/PrTvPiVR9C0nT3JwBaAbUaxWOGHr5zh3333FKuJLPsOtvOf/uNnOHait26N3GfBNE3mxxaZHppj+soc00OzTF+ZZebqPKml9A3Hur0uGtqjNLTHiHfEiLVEiTSGCDeFiDSFCDeGCER8BKL+h5LxVEpJqVAms5ols5oltZQmtZQmuWjViblVEjMrLE2vkJhZoVys3PD30eYwbXta6Oxvo2Ogjfb+Vjr3ttHUFd9Rc/JNU/LeO8N891+f5OrQPI1NQf7hP3qKF79yGKfLXpEOtgBsW8olnR/94Cx/83+fYnlxjd17mvnGrzzOMy/s3fFeTyFXZGHc8pgXxpZYmk6QmF1hedoqqwspDN245d9qLo1AxIc36MHtc+P2ufD43bi8LlSniuZUUVQFzakibupWMA0TvWKgV3T0ikGlVKGUL1HMlShkixRzJfJrebLJHJWyfsvPVzWFSHOYeEcDjR0x4u0xGtpjtPQ20bqriabuxm3v0d+Jcknn569f4v/96/eYGFumpTXML//aU3zhy4d2/G//ZmwB2OZUKgav/+g8//677zE9tUIk6uPlrx3hK7/4KPHG4GY3b0timibZVM7yuKtedyaZI5vM1up8tkgxW6SYK1LIFinly5ZhL+tUylZ98+0ihCUgqqagOlVUTcXtc1nF78btc+MLePBHfPgjfgLVOtwYJNIUJtIUwh/27ahI7l5YmE/xg++f5u/+4xnW0gW6e+P8J7/6BJ/74gEUdedEPveCLQA7BNOUfPzBGH/7vY94/9QwQghOPNnHV75+hGOP70JR7BvEpv7QdYP33hnmh6+c4aP3RxFC8OSz/Xzt7x3dEeNf94stADuQ+bkkP/zbM/z4B+dIruaINwV56auP8KWXD9HUEr7zCWxsNpm5mVV+/Oo5fvTqOVYTWRriAb78C4/w0i88QmOTnXTubrEFYAej6wbvnrzKq6+c4eMPxhACjhzr4cWvHOap5/pxuew9WW22DoVCmZM/H+THr57j/JkphIDjT+zm5a8/yokndtvdPJ8BWwBsAKv/9Cc/PM+PXz3H4kIar9fJE8/s4dkX9nL0RK8tBjabQqFQ5sN3Rzn5xiDvvTNMsVChtT3Ci185zBdfOmSPY90ntgDY3IBpSs6dnuBnr13knTevkMkUcXs0Hn+yj6dfGOCxE7vw+nb2LBObB0suW+T9UyO8/cYQH7w7QqmkEw57eeq5fj7/4kEOHO6w+/Y3CFsAbG6LrhucOz3JyZ8P8s6bV0il8miawiPHunnqmX4ef7qPWMPOXGFrs7EsL61x6uRVTr11hfNnJtF1k2jMz9PPD/DM8wMcPNxpd/E8AGwBsLkrDMPk4vlp3n3rKqdOXmF+LgVA/95Wjj+xi+NP7mbPQOuOXVJvc28YhsmVy3O8f2qYD94dZeTqAgAdnTGeeGYPTz67h7372+3f0wPGFgCbe0ZKycTYMqdOXuWDUyMMXppBSgiHvRx7fBeHH+3i8KNdNLfYidlsLKSUzM0mOXd6krMfT/DR+2Nk1go4FMH+A+0cf7KPJ5/ZQ2d3w2Y3dUfxMPcE/gbwbWAvcFxKeUtrLYT4MvBHgAL8mZTyD+/m/LYAbB7pVJ6P3h/l/VMjnP5wnHQqD0BjU5DDj3Zx4HAnBw510NEVswVhh2CakqmJBBfPT3Hx7DTnzkySWLbyEkWiPo4e7+XEk7s5eryXQNCzya3duTxMAdiLtdn7nwC/dysBEEIowFXgi8AM8CHwy1LKy3c6vy0AWwMpJZPjCc6dmeTc6UnOn5msCUIw5GH/wQ72H2pnYH8bewZatsVmNjaQz5W4OjTP4KVZLl+Y4dL5aTKZImAZ/MNHujj0aBeHj3TZjsAW4l4E4L6yJ0kpB6sf+GmHHQdGpJRj1WP/Bvg6cEcB2CksrGZoCPlQt+jKXSEE3b1xunvjfP3vH7Py+U+tcvH8FJfOz1jjCG9fBcChCLp7G9m7r5U9Ay3sGWilqzdu52vZ4pTLOuOjSwxfmefqoGX0J8eXa6kvOrpiPP38APsPdXDgcAetbZG6MfgV3SCZLdAY9m92U7YcDyN9Xhswve75DHDidgcLIb4JfBOgs3N75r+/mf/2Oz9gMZnhF586wNefPEBrbGvPgxZC0NEVo6Mrxku/cASwuoyGLs0yeHmWwYuzvPHTy7z6yhkANE2hZ1cju/c0s6uvid6+Jnp64/j8O2OT7q3G2lqBidElxkaWGB1ZZPTqAuOjS+i6CUAg6GFgXyvPvrCXgf1t9O9rJViHXTrTyyn+wzsXeeXUJfraGvg/f/fvb3aTthx37AISQrwO3Gr7oG9JKV+pHvMGt+8C+gbwopTyN6vP/xHWeMHv3KlxO6ELSErJm+fH+N7J85y6PIGUcGxPBy+fGODzR/oIPIRUxQ8C05TMzyUZHppn+MoCVwfnGB1erHUhADTEA7R3WkLS0RmjvTNGe2eUxsaQPT3wPtF1g6WFNDPTq8xMrTA9tcL0pFWvJrK140JhL7v6mujrb2HPQAt9A811PdCfzhV5/fRVXn1/kLOjcziE4JmDPfyDZw7x1IHttbPe7Xjos4DuIABPAN+WUr5Yff7fA0gp/5c7nXcnCMB65lbWePX9y/zgvUGml1M4VYWnD/Tw0vEBnj7Qg0ur73znUkqWl9YYG1liYmyZyfHlmnHKZa9v9KIoDppbw7S2RWhpi9DUHKKpJWTVzSHCETt7pmlKUskcC/MplhbSLC6kWZxPMzebZH42ycJCCtO4fm8HAm5LYLtidPdY3Xm9u5uINfjr/n9ZKFd46/wYP/pwiHcuTaAbJt3NUb56Yi9fObGXpsjOWtey1QRAxRoE/jwwizUI/CtSykt3Ou9OE4BrSCm5NLnI330wyI8/uspqJo/f7eT5w7v40rF+Tgx0oqnbp09dSsuYTU2uMDezytxskrkZy5DNzSZvEAewupRi8QAN1RJrCBCN+YlEfUSiPqIxP8GQl2DIg9NZX6JZLuuspfOkUwVWV7KkkjlWV7IkV3IkEhkSy2skljKsJDK1LptrBAJumtsitFWFs7U9Qlt7lI6uGKGwt+4N/XpKFZ13L0/y2kdXePPCGIVShXjIx5cfG+Cl4wP0t8e31fXeCw9zFtAvAX8MxIEUcFZK+aIQohVruufL1eNeBv4l1jTQv5BS/sHdnH+nCsB6dMPkwyvT/PijK/z87AiZQomg18ULj+zmC0f6eKy/A2edRwZ3IpctsriQZmE+zdJCmuWlNcsQLmdqxrBUuvVmK16vk2DIQyDowed34w+48ftd+Hxu3F4Nj8eJx+PE7dFwuTWcTrVWNKeCojhqxeFwfGJDGGlKDMPENE0Mw0TXTSplnUrFoFzWKZd1SsUKhUKFQr5MsVimkC+Ty5bIZovkMkVyuRJr6QJrawUK+fItr8Pt1m4QvYZ4kIbGAM0tYZqaQzQ2h/Bt83QepYrOe4OTvH56mDfPjZItlgn53HzuyG5ePNrP0T3tKDtod7TbYS8E26ZUdIN3B6tez/kxcsUyfreTpw/08OyhXp7c103Qt/MGVqWUFPJlVldzJFeyrK5mLYOayrO2ViCdypPNFKsGt0QuVySbLVEslD+xwcuDRgjweJz4/K6aIPl8LgJBD6GQl0DIQyhsPY5Uo5po1I/HuzOn1iazBd65NM7J82O8c2mCfKlCwGM5QF86tofH+jvQlO0TDW8EtgDsAEoVnQ+GpvjpmRFOXhgjmS2gOAQHe1p4cn83Tx/o2dFh8N1gmpJSqUKxUKGQL1EqWR77Ne+9UtIxrnn4huXh33y/CCGs6OBapOAQaC71hkjC6VTweF14vE5cLtX+Tj4F05QMTi3y9sVx3rk0waXJBaSEWNDLs4d6+fyRPh7b07GtukA3GlsAdhiGaXJxYoG3L1g3zdD0EgANQS8n9nbx+N4uTgx00hDybXJLbWw+yVIqy3uDk7x3eZL3h6ZIZgsIAfu7mmvOzL7OJjuH0F1iC8AOJ5HO8e7lCU5Vb6hUtgBAX1sDJwY6OdbfwaO72/DX6RRTm/omky/y8fAsH16Z4v2hKcbmVwHLyz8+0MlT+7t5Ym8XkYB3k1tan9gCYFPDNCVXZpZ4f3CKdwcnOTc6R1k3UByCvZ1NPFYVg0O9LQS8O2/8wObBk8oWOD8+z+nhGT68Ms2V6WVMKXFrKo/sbuXxapTa19Zgd49tALYA2NyWUkXn/Ng8H16Z5sMrU1yaWEQ3remEvS1RDve2crCnhQPdzfS0RO1ZFTb3hG6YjM2vcGF8nosTC5wbm2diwfLwVcXBod4WHtvTwbH+Dg52N2/7GWybgS0ANndNoVThwvg858fnOT82z/mxOdby1rx7r0tjX1cT+7ub2dvZyL7OJtoaQraXZgNY0eVMIsXg5BKXpxa5OLHA4NQixbI1JTfsc3Oot5XDu1o41NPK/u5m3HW2LqMesQXA5jNjmpLp5RQXJua5OL7ApYkFrswsoxtWlBD0uhjoaKS/o5H+jjh72uJ0N0e3bCI7m42hYhiMz69ydWaZqzPLDE0vMTS1RLZorVtwqgp72uMc7GnmQHcL+7ub6YjbzsJmYAuAzYZSruiMzK0wOLXI4NQSg1OLjM6tUNYNwLr5e1ti7G6NsbutgV2tDexujdEYrv80AzsNKSULyQyjcyuMzCYYmUswMrfC+MIqler37dIUdrc2sLeziX1dTeztbKS3NWbPx98iPLR00DYbwx++8xbFSoXP9+zieFs7LnVrfS1OTWVfl3WzX6NiGEwuJLk6u8yV6WWGZxO8NzTFD94frB3jczvpaopYpTFCZ2OY9niYjniY0A5csLZVkFKSyhWZXkoxk0gxtZRiajHJxGKSqaUk+VKldmxTxM+ulgae2NdFf3ucPe1xOhsjdRHxlXSdUzNT/HR8jLjXy++eeHKzm7Tl2FqWZoeylM3ydyPD/NX5s/g1J093dvFCTy/PdXXT6NuaOcw1RWF3WwO72xp4+fje2uupbIHR+RVGq17j5OIqZ0fm+NGHQzesug14XLTHQ7TGgrTGQrTEgrREA7REgzRFAgS9Ljt6+IxIKUnniiwmMyysZphbWWNudY25lTXmV9aYWU7Vum7AWp3cGg3S2RThyO5Wepqj7GptYFdLrO5Wli9kM7w5Mc7PJsZ4e2qSgq7j1TR+cWDfZjdtS2J3AW0RCpUKp2am+Nn4GD8bH2MxZ6XsPRBv5LnuHp7r6uGR5hbUOp2VUyzrzCZSzCynmU6kmV5KMZtIM7e6xvxKmlLFuOF4t1OlORKgMewnHvYTD/loqJZY0Ec04CUW8BLYQUJhmpK1fJHVTJ5kpkBiLUcinWM5na3WORaTGZaSWYqVG3MjuZ0qrbEgLdEg7fEw7Q0h2uMhOuJh2hpCdZtptmwYnJmf443Jcd6cnGAosQxAayDA57p7+XzPLh5v79hyUfWDxB4DqHOklAwllvn5xDhvTo5zen4OQ0r8TidPdnTyTGc3z3Z20xEKbXZTNwQpJauZPLOJNRaTGctzTWZYSmVZWM3UDN21gej1qIqDsN9D2Ocm5PMQ9lt10Osi4HUR8LgIeNz4PE68Lg2f24nXbT12OzXcTvWhTXXVDZNSRadYrpArVsiXyuSKZfJFq87kS2QKVlnLF0lni6RyBdLZIulcgVS2WJuyux5NVWoC2RT20xQJVIuf5miQtliQsN+zLYRSSslEOsXJyQlOTk3w3sw0uUoF1eHgsdY2nuvq4fnuHvqiO3eLSlsAthnpYpF3pqc4OTXBW5MTzGetjbg7gyGe7OjkiY5OTrS1b9nuoo3ANCXpfJHlVJZkJs9qpsBKJk+y6g2ncwWS2QLpXJFUtkCmULqlYNwKTVVwaSouTUFTFDRVQVMdaIqCwyFQHA4cDoFDiE+kIzBNiSklpikxTBPDlOiGQVk3rMyghkGpYlAsV+6pPQGPqyZm18QtEvBYkU/QSyTgJRrwEg/5CPnc29rYzWcyvD87w7szU7wzPclcxvr9dwRDPNPVzTOdXTzR3knQZa9sB1sAtjVSSsZTSd6anODU9BTvzU6TLVv9ud3hCMdaWznW0sax1jZ6wvWzb+tGI6WkVDHIFIpk8iWyhTL5Upl8qVLzuC1vXK955WXdoKKbVHSDsq5T0U1MaRl2y8BL4Ob7RaA4xHWhEALnTULiVFXcTqu4NBW3U8Pr0vC6nfiqtd9TjVa8rrrtjtkIpJSMJlf5aG6Wj+Zm+XBulum1NAAhl5vH2zuqUXAX3eHIJrd2a2ILwA5CN00uLy/xwewMH87N8NHcLMmite1izOPhSHMrj7ZY5WBjEx5N2+QW29hcJ1cuc35xgdML85yen+Pswty636+XY61tPNbaxom2dgYa4vbK9LvAFoAdjCklY+s8qNML80ykkgCoDgcDsQYON7dwuKmZw00t7IpGcezQKMHm4WKYJsOrK5xbXOD84gLnFuYZWklgVm3QrkiUIy0tdgR7n9gCYHMDq4U8ZxbmOTM/z9nFec4vLtS6jfyak33xRg40NnGgsYlDTU10hyO2KNjcF4ZpMpZMcnFpkQvLi1xYXGAwsUy+Yq0xCLpcNSfk0ZZWHmluJuz2bHKrtwe2ANh8KqaUjCdXObe4wLnFBS4uLXJ5eZmSYU0d9Kgqe2IN9McaGGiI0x9roC/WQMyzPWaS2GwcUkqW8zmGV1e4kkgwtLLMlUSC4dUVivr139M1J+NwUzOHmppt7/4B8jD3BP4G8G1gL3D8VpvCV4+bADKAAeh32zhbAB4eejU8v7i0yODyEldWEgwllmv9sQARt5u+aAN9sRi7IlF2RaL0RqO0+AN2xLDNMaVkLrPG6Ooqo0mrDK+uMLyyQrp0/TcS83jpb7Cch33xRg42NrErYmeVfZg8zFQQF4G/B/zJXRz7gpQycZ+fty2RUm66N6Q6HOxtiLO3IV577Zp3d82jG1ldYXh1hf94dYi1Uql2nFtV6QlH6A5H6A6Ha3VXKEzc69v0a7O5O0wpWcplmUqnGU8lmUglmUilavW1CBGsGTl9sRgv9+2hLxqjLxZjT6yBuHdr7jq3Fe6xrch9CYCUchCw/7H3ye+f/S7JUo7jDbs5HtvN/lA7qmPzE2sJIWj0+Wn0+Xmmq7v2upSSRCHP2DpvcDyVZDCxzE/GRm5YrORWVTqCIauEQrQFgrQGgrQHg7QFgkTtbqWHhiklK4U8c2trzGbWmKnW02tpptNpptfSlI3rK7I1h4OOUIjuUIRnOrvojUTprUZ+W/17q5g6F1JTfLAyygeJETp9DXz70Dc2u1lbjoc14VgCrwkhJPAnUso/fUifWxcMBNt4a2mQPxv5Gd8Z+Sk+xcUj0W4ejfZwJNLDQLB1SwjCNYQQxL0+4l4fJ9o7bnivYhjMZtaYSKWYSqdqxmUyneKD2RmylfINxzsVhRZ/gBZ/gGa/nya/3zq3z1f9DC9Rj5eQ2213M90GU0pSxQKrhQLLuRzL+RzL+TzLuSyLuRzzmQwL2QwL2Sxl88aUGwGni/ZgkN3RGJ/r6a2JdU8kQmsgWDepRyqmzmB6ljPJCT5eHeNscoKiUUERDvaF2ukLtGx2E7ckdxwDEEK8DjTf4q1vSSlfqR7zBvB7nzIG0CqlnBNCNAI/AX5HSvnWbY79JvBNgM7OzqOTk5N3ey11T7qc5/TqGO+vjPDRyhhTeavHzKM4ORju5FC4k8ORLg6EO/Gp9bfqUUrJWqnEbGaN2ar3uZDNMFc1TvOZDMu53CeMFIAiBBGPh5jHS8TtIex2E/FYddjtJuhyE3S5CLpcBJwu/E4nAacLn9OJR1W3tLcK1v+moOtkyyWy5TLZcpm1Uom1UolMqchauUSyUCRVLJAsXq9X8nlSxQLGLe5jp6LQ6PNZAhsI0OwP0OL30x4I0VqNwOp19Wy2UuRCaopzqUnOJSe5mJqmZFozjHr8jRyL9nI8tpuj0V78Wn0ltLtfHvosoDsJwE3HfhvISin/1zsdu9MHgROlDGeTE5xZHedccpKRzAImEgeC3YFmDkU6ORDq5GC4k3ZvdMsbubtBSkm6VGQ5l696sjlWCwVW8nlWC3lWCnnLABauG8JbGb/1OITAq2l4NQ2Peq1WcakaLlXBpai4VAXNoaA5rBQQqsOB5nAghEARDhSHQCA+EYWYUiKxVgkb0lo5rJtWCgjdNKmYJhXToKQblAydkm6VvK5TqFTIVyoUdKs273AdqsNhCd81AXR7iHm9RKvCGPV4atFTo89HwLk9EuVJKZnKJbiQmuJCepoLySlGs4tIJIpw0Bdo4ZFIN0ei3TwS6SLi3L4pUe6GLSUAQggf4JBSZqqPfwL8Uynlj+503p0uADeT1YtcTE1zPjnJ2eQEl9Mz5A2rSyWsedkf7uBAqIN9oXb2hdoJOb2b3OIHj5TS8pbL17zlEulikVylXPOks+Uyeb1SM7jFqsEtGwYlw6BYNcoV06BimOimYRluw0TK64b9dneKwBIZRVg5g66Jx3UhUXCrKi5VxaVYguPRVDyahlfVcGsaPk3D73Ti05z4nS78Tu2GqCbocuPTtG1h0O9EspzlcnqWS6lpLqdnuJieZq1SAMCnujgQ6uBwpItDkS4OhDrw1mE0/CB5mNNAfwn4YyAOpICzUsoXhRCtwJ9JKV8WQvQC36/+iQr8WynlH9zN+W0B+HQMaTKWXeRiapoLqSkupaaZyCW4ZqravVEGgm0MBNvYG2qjP9hKULMX23xWbueh22MTn51UOc+VtVmG1uYYTM8yuDbLfMFauS4Q9Pob2Rdq52DYinR7/HEcoj7GJTYLeyHYDiarFxlKz3IpPcPl9AxD6Vnmi6na+y3uMLsDzTeUDm9sSw0y22w/dNNgMpdgNLvASGaB4WpZKqZrx7R5ogyEWtlfjWIHgq22d/8ZsLeE3MH4VTfHYrs4FttVey1VzjG0NseVtTmG1+YZzi5wKnEVQ1rTNTWh0OWP0+tvZJe/mR5/Iz2+OG3eqC0MNveEbhpM51eYyC4xlltiLLPIWHaJyVwCXVqD+4pw0ONr5NFID7sDzQwEW+kPtu6ILsuthh0B7FBKRoWJ3DLDmQXGsouMZ5cYzSyysC5aUIVChy9Gty9Ol6+BTm8Dnb44nb4GwvbNumORUpKq5JjKrTCZW2Yql2Ayl2Ayt8x0fqXmWAC0eiL0+pvo9TfS62+iL9hMty+O5rB9zweFHQHY3BGXotFf9bzWk9WLTOUSjGeXmMguM55bYiy7yFtLgzfc2EHNQ7s3Rrs3atWeKK3eCG2eKA3uIIrdT1vXGNJkqZhmLp9ktrDKbH6VmfwK09U6q19P/6AKhQ5vlG5/nOeb9tPjj9Pta6TL12B34WxxbAHYApxLvoIhK7R69hN370YRm5ez36+6a7OI1qObBnOFZM3bm8mvMJNf5VJqhtfnL2CumyOjCoUWT5hmT5gmd4hmd5hGd4gmd4i4O0jcFSSobe2VpNsZKSXpSp6l4hrLpTWWimkWi2kWC2kWiikWCikWiqkbBF8RDlo9Edq9MQ6GO2j3xqyo0NdAszu8JbsKdbPMUnGY+cJFXEqQA+GXNrtJWw5bALYAI5m3mcmfAUARTprc/bR49tHs2UuzewC/1rDJLQTVodBZveGfvum9iqmzUEgzV1hlrpCseY0LhRQfJEZYLmW4eRKly6HS4ArS4AoQc/mJuQLEXAGiTj9Rl5+I00fU6Sfs9OFVnLZY3AEpJTmjRLKUI1nOkSxnSZZzrJQzrJQyrJSyrJQyJKqlbN64abwDQYM7SJM7xP5QO19sOUjruqiuyR3akkZ+PZnKMguFQRaKg8wXLrFUHMaQ1uKwXv+TtgDcAnsMYIuQ01eYy19ivnCp+uMdwcS6Sf1qnBbPXprc/TR5Bmh078HpqJ/pnLppVD1Ny9tcLq2RKGZYKqVrhmmllCGzrlthPZpQCDm9hDUfIaeHoOYloHkIqh4CmoeA5savuvGpLnyq9dirOvEoTnyqC5dj68+fl1JSNCrkjRIFo0xeL5HVi+SqdbZSJKMXyVQKrFUKZPQCa+UC6UqeVCVPupyvDbLeTFDzWALrtIQ27g7S6ArWorFGd4gGV2DLG/j1lIwcS8WrLBavsFAYYrE4RFa3Vs4rQqPR3UeLZz+tngM0e/bhU3fO9pH2NNBtgG6WWS6NsFAYZL5wmcXiFdYqCwAIHESdnTS699Do7qPJ00+DqxfNUd9L3otGhVQ5x2rVe73myabL141cqpKzDGC1lG7yZG+FQOBRNNyKhstRrRUNp0NFc6i4qrXmUFCFgiIcqA4HqlCsjeCFQOBAEdZq4PWYyOoiser+wdLEkCa6aaJLA0NaK4HLpk7Z1KlU66JRoWRUKJoVioZVbr/U7Douh0awKnpBzUvY6SWkXRNH7w2RU9TpI+z04VLqexvQsllguTjCUnGYpeJVlopXWS1Pc21/5pDWUo2W99Ls2UvcvWtTu1E3G1sAtil5PcVi8QqLhSGrLl6lYFizdq6JQty92yquXTS4e/EooU1u9YOlZFTI6EVylSI5o0S2UiSrF2tedL5aF40KpXXGtmRWaka5bFRXAUsd3awacGmgmwYmEiktI29g3rINCtZm8LW0EcISD9VhPdaEilOxBMbl0KyVE2z8mAAADElJREFUwevFyKFVIxZXLXLxKk58tcjGim6CmgfnNp89k9dTJEqjLBdHWK7W6429T43R6OqjyTNAs7ufRs+ebf8bv1dsAdghSCnJ6omqVzTMUnGY5dIIOX2ldoxXidLg6iHm6q6ViLMTl7I187bb7AxKRpbV8hQrpQlWShMkSuOslMZrDg1YXZ9x924aXbtp9PTT5O7Dp8Y2sdX1gT0NdIcghCCgxQlocXYFnqq9nteTLJdGSRTHrBusPMGF1A/Q5fVNXPxqnKirk6izi4izg6izg4irA6+yPZLK2Ww+Ukpy+grJ8jSr5SlS5RlWSpOslidvcFJU4Sbm6qLHf4KYq4cGVw9x1248qu3ZP2hsAdiGeNUIXeoxunzXnQBTGqQr86xWb8DV0hSr5Skupn6ILq8PvjodXsLOdsLONsJaOxFnG2FnGyGtFbcStMXB5gaklBSMFOnKPKnyLKnyTLWeJVmZoWIWasdqDg9RZyed3qM15yPq6iKkNSPsdSObgi0AOwSHUIg424k429nF9WhBSpOsnmC1PE2qPM1qaZpUeYaFwiBX196AdQOTToeXkNZKyNlKSGsmeENpQnXYi362IxWzyFplkbXKQq2ky/OkK/OsVeYpm/nasQIHQa2JsLONFu9+Is6OaoTZiU+N2Q7EFsMWgC2ALH8Iwg1qP0I4H+pnC+EgoDUS0Brp8h294T3dLJOuzJMuz5KqzFVv+jkSxVHGs+/W5lhfw6OErXOpcfxaHL/agE+N4Vcbao81h70AbKsgpaRs5snpK2T1BDk9QVZPkK2skNWXyFSWyehLFI21G/5OERpBrZmQ1kKb96DlFGgthJ1tBLVmVMfD/Q1/GlKWoTIImAjnkc1uzpbDFoAtgMz8M6icBzSkthe0QwjtAKgHQO1FiM35mlSHk5iri5ir6xPvSWmS01fXeYWLZCqLZPQlUuVZpvNnbvAMa+cUbnxqFK8asWolgkcN41UieNUwHiWMRwnirhaHqJ+56VsBUxoUjDWKxhpFI01eT5E3khT0FHkjRV5PkjeS5PVVcvrqDeNC13A6fAS0OH61kSbPAAG1kaDWRMjZQlBrwqtEtmSXjZQV0EegcglZuWjdU/oVoALOJxDRv9zsJm457FlAWwBpzELlPLJ8HioXQL8I8prxdIO2F7R9CHUfaPtB3f3QI4XPQtksWN5lxfIuc/oKOT1JzlixDJG+St5IfcLDXI/LEcCtBHApftxKALcjiEvx4XL4cVZrl+JDc3hxObxoDg9Ohw/N4UYTblSHq25ExJQGFbOILotUzCJlM18tBcpGjrKZo2RmKRk5SmaOspGlaGQomhlKRoaikaFkZm9zdoFHCeJRwnjVKL5q8SqRapQWw6c14K9GaVsdKUugX4XKZWRl0LpnKkNAdc9p4QPtIGgHEdohy6lSdsa+wPY00DpHSgOM8aoncwkqF0EfBJmrHqGBuhvUAYQ2AOoAaP0IR3RT2/1ZMaRe9VaTVe81TcFYo6CnKBhrlEzLuFllzTKERhaTW698vRlFONGEC9XhQhEuVIcTVThRhHZDcQgVh1BwUK2FgsCBQCCEUl0EdnP3lbUITEqz+shESgNTGpjoVi11dFnBlBWMatFlCd0sY8gyulmiIksYsnxX1+NAxaX4cTp8eJQALiVYFUc/HjWMWwniUUJ4lBBuJYhXjeBRQnUjhDcjjRXQh0AfQlaGqo9HobpSHuEHdR9oB6zIWdsPSteWjFIeBvY00DpHCKVq4HcjPF8HrC4XjCnL49EvW/2a5beRxe/X/k46GkHdA+oehLoH1F2g7kI4tvYeqYpQ8amxe5rjLaVElyVKRpaymbO8ZDNPxSxQNnNUTMuLrsgiFbOAbpYtoytLGNXHhtTRZZmSmcOQ5aqxtgy2ifUYJKY0LSN/m4VgAgcOHFWDI24SEateLzSaw4MqXCgODVW4UIULzeFCdbhxCg+qw43mcON0eHHWohpvLfJRxPbMjSTNjGXY9RGkftXy8PWrYCauH+RotBwe3wsIbZ9l+JX2HWvs7xdbAOoEIRygdoPajeDl2us3ekdXQB+G/HeRXO/blY4mUHut8QSlF9Qeqzha6vbGEUKgCXc1/cXmJ8uzuTus6HbOinD1CaQ+BsYY6GNgLq070m05Qa7nqs5MfUe5WxVbAOococRAeQpcT9U6J6ybbMoaENPHkPqodZMV/gOy1o0E4EKq3aB0gtqFUDpB6QK1ExzNViRiY3OPSKmDsWD9Bo0ppD4JxkT1NzlJrZ8eQASsSNX1NELZVXVUdoPSUbfOST1xXwIghPjnwC9gfaOjwD+WUqZucdyXgT8CFKzN4v/wfj7X5tOxupCqXj6sEwYJ5rJ1M+rjSH2i6omNQekNJOundWpIpQ2UDivEVtpAaQOl3aod9pzunYqUJpgrYMyCMQPGLNKYqT6etjx81ifpc1lOhdJpefRKjxXNKj3272iTua9BYCHEl4CfSSl1IcQ/A5BS/v5NxyjAVeCLwAzwIfDLUsrLdzr/Th0E3gykNMBcAH0CjBmkMW3dzPq0dWN/QtedoLSC0mLVjmaE0gxKMziarFqE7Ju7zpBSgkyCsWh58eYi0li0jLo5X+2+mQduXAOCCFeNfLvlvSsdlvOgdoOjyfbmHyIPbRBYSvnauqfvAf/gFocdB0aklGPVxv0N8HXgjgJg8/AQQql6+G3W85vel2a26vHNVgViHsyqMSidBHP5k+mM3S8hwn/0cC7AZkOQyd+E8smbXnVYg69KqzW10v0lhKOlauzbQWlFOOzkgvXIRo4B/Abw727xehswve75DHDidicRQnwT+Gb1aVYIcWXd2w1A4pN/Vfds0+saBv63bXpt2/U7u911XfnkS/XHTvnOPrly8zbcUQCEEK8Dzbd461tSyleqx3wLq9Pvu7c6xS1eu22/k5TyT4E/vU1bPrrb0Kae2K7XBdv32uzrqj+267Xdz3XdUQCklF+4w4f/GvBV4PPy1gMKM0DHuuftwNy9NNLGxsbGZuO5r5GZ6uye3we+JqX8ZOIXiw+BPiFEj7DyF/xD4G/v53NtbGxsbO6f+x2a/1dAAPiJEOKsEOL/AhBCtAohfgggpdSB3wZ+DAwC/4+U8tJn/Lxbdg1tA7brdcH2vTb7uuqP7Xptn/m6tnQuIBsbGxubB4c9OdfGxsZmh2ILgI2Njc0Ope4EQAjxPwshzlfHHF4TQrRudps2AiHEPxdCDFWv7ftCiPBmt2kjEEJ8QwhxSQhhCiHqfgqeEOLLQogrQogRIcR/t9nt2SiEEH8hhFgSQlzc7LZsJEKIDiHEz4UQg9Xf4e9udps2CiGEWwjxgRDiXPXa/qd7Pke9jQEIIYJSyrXq4/8K2Cel/K1NbtZ9czdpNeoRIcRewAT+BPg9KWXd5va4n7QmWx0hxLNAFvgrKeWBzW7PRiGEaAFapJSnhRAB4GPgF7fJdyYAn5QyK4TQgLeB35VSvne356i7COCa8a/i41MWldUTUsrXqjOmwEqr0b6Z7dkopJSDUsptsYyUdWlNpJRl4Fpak7pHSvkWsLrZ7dhopJTzUsrT1ccZrJmIbZvbqo1BWlzbAk6rlnuyh3UnAABCiD8QQkwDvwr8j5vdngfAbwB/t9mNsPkEt0prsi2MyU5ACNENHAHe39yWbBxCCEUIcRZYAn4ipbyna9uSAiCEeF0IcfEW5esAUspvSSk7sFJP/PbmtvbuudN1VY/5tLQaW5K7ua5twj2lNbHZOggh/MD3gP/6pl6EukZKaUgpH8HqMTguhLin7rstuSHMndJPrOPfAq8C/+QBNmfD2IC0GluSe/i+6h07rUkdUu0f/x7wXSnl/7fZ7XkQSClTQog3gC8Ddz2QvyUjgE9DCNG37unXgKHNastGcpdpNWw2FzutSZ1RHSj9c2BQSvkvNrs9G4kQIn5ttqAQwgN8gXu0h/U4C+h7QD/WzJJJ4LeklLOb26r7RwgxAriAlepL722T2U2/BPwxEAdSwFkp5Yub26rPjhDiZeBfYu1u9xdSyj/Y5CZtCEKIvwaex0otvAj8Eynln29qozYAIcTTwEngApbNAPgfpJQ/3LxWbQxCiEPAX2L9Fh1YaXb+6T2do94EwMbGxsZmY6i7LiAbGxsbm43BFgAbGxubHYotADY2NjY7FFsAbGxsbHYotgDY2NjY7FBsAbCxsbHZodgCYGNjY7ND+f8B2gwfUI4WQBUAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.axis(\"equal\")\n", "plt.contour(xmesh, ymesh, fmesh)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "Define the function of the **step size (1D optimization)**\n", "\n", "$\\alpha_k \\gets \\min_\\alpha f({\\bf x}_k + \\alpha \\nabla f({\\bf x}_k))$\n", "\n", "$f$ is `f_step_size()`" ] }, { "cell_type": "code", "execution_count": 217, "metadata": {}, "outputs": [], "source": [ "def f_step_size(alpha, x_vec, grad_vec, f):\n", " return f(x_vec + alpha * (grad_vec))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "**Initialize Gradient Descent:** \n", "- starting point (guess)\n", "- max number of iterations (or add tolerance)\n", "- preference for setting the step size\n", "- list with all visited values" ] }, { "cell_type": "code", "execution_count": 221, "metadata": {}, "outputs": [], "source": [ "max_steps = 6 # max iterations\n", "\n", "x_start = np.array([2, 2./5]) # starting point\n", "\n", "# list of visited points during the descent\n", "x_vals = []\n", "x_vals.append(x_start)\n", "\n", "constant_step_size = 0.5\n", "constant_step = False #True\n", "correct_step = True #False" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "**Run GD** and record visited states" ] }, { "cell_type": "code", "execution_count": 222, "metadata": {}, "outputs": [], "source": [ "for i in range(max_steps):\n", " x_current = x_vals[-1]\n", " #print(\"Iteration:\", i, \"x_vec:\", x_current)\n", " grad_current = -grad_f(x_current)\n", " if constant_step:\n", " step_size = constant_step_size\n", " elif correct_step:\n", " step_size = sopt.golden(f_step_size, (x_current, grad_current, f))\n", " else:\n", " pass\n", " x_new = x_current + step_size * grad_current\n", " x_vals.append(x_new)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "**Plot** what happened on the 2D isocontours" ] }, { "cell_type": "code", "execution_count": 223, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 223, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.axis(\"equal\")\n", "plt.contour(xmesh, ymesh, fmesh, 50)\n", "it_array = np.array(x_vals)\n", "plt.plot(it_array.T[0], it_array.T[1], \"x-\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "**Generate linearly separated 1D random data**\n", "\n", "Data are are separated in two classes ($y=0$ and $y=1$) by the equation $w_1\\cdot x + w_0 = 0$" ] }, { "cell_type": "code", "execution_count": 225, "metadata": {}, "outputs": [], "source": [ "import random\n", "import numpy as np\n", "import math\n", "\n", "def generate_1D_linearly_sep(n, w0, w1, interval):\n", " dataset = []\n", " for i in range(n):\n", " x = random.uniform(interval[0], interval[1])\n", " if (w1 * x + w0) <= 0:\n", " y = 0\n", " else:\n", " y = 1\n", " dataset.append((y, x))\n", " return dataset" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "Function to plot the data (on the $x$ axis are the feature values, the $y$ axis is the class)" ] }, { "cell_type": "code", "execution_count": 226, "metadata": {}, "outputs": [], "source": [ "def plot_1d_linearly_sep(dataset, w0, w1):\n", "\n", " plt.figure(figsize=(7,7))\n", " \n", " negative_samples = []\n", " positive_samples = []\n", " \n", " for i in range(len(dataset)):\n", " if dataset[i][0] == 1:\n", " positive_samples.append(dataset[i][1])\n", " else:\n", " negative_samples.append(dataset[i][1])\n", " \n", " yplus = [1] * len(positive_samples)\n", " yminus = [0] * len(negative_samples)\n", " \n", " plt.scatter(positive_samples, yplus, color='red', marker= '.')\n", " plt.scatter(negative_samples, yminus, color='blue', marker= 'x')\n", " \n", " plt.xlabel('$x$', fontsize=14)\n", " plt.ylabel('$y$', fontsize=14)\n", " plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "Function computing the **log-likeloihood function of logistic regression**" ] }, { "cell_type": "code", "execution_count": 207, "metadata": {}, "outputs": [], "source": [ "def univariate_logistic_regression_log_likelihood(bias, w, D):\n", " lg_sum = 0\n", " for n in range(len(D)):\n", " dot_product = w * D[n][1]\n", " lg_sum += D[n][0] * (bias + dot_product) \n", " lg_sum -= math.log2(1 + np.exp(bias + dot_product))\n", " return lg_sum " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "- set a linear separator (in 1D)\n", "- set limits for the values of the $x$ features\n", "- generate the linearly separated data\n", "- plot the data" ] }, { "cell_type": "code", "execution_count": 227, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "w0 = 2\n", "w1 = -2.5\n", "xinf = -4\n", "xsup = 4\n", "D = generate_1D_linearly_sep(200, w0, w1, (xinf, xsup))\n", "\n", "plot_1d_linearly_sep(D, w0, w1)\n", "\n", "#univariate_logistic_regression_fun(w0, w1, D)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "- call the univariate log-likelihood function of LR\n", "- compute the values for a range of values of the $w_1$ parameter\n", "- plot the log-liklihood function, which is expeted to be **concave**" ] }, { "cell_type": "code", "execution_count": 228, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "450 \n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7,7))\n", "\n", "#figure.suptitle('Example with only one row of subplots', fontsize=22)\n", "\n", "w = list(np.arange(-4 * abs(w1), 5 * abs(w1), 0.05))\n", "print(len(w), type(w), type(w[0]))\n", "\n", "lr_list = []\n", "for i in range(len(w)):\n", " lr_list.append(univariate_logistic_regression_fun(w[i], w0, D))\n", " \n", "plt.plot(w, lr_list, color='red', linestyle='-', linewidth=1)\n", " \n", "plt.xlabel('$w$', fontsize=14)\n", "plt.ylabel('$LR(w)$', fontsize=14)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "Use `ScyPy` to find the maximum of the LL function (as a function of $w_1$ only)" ] }, { "cell_type": "code", "execution_count": 212, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimization terminated successfully.\n", " Current function value: 927.059586\n", " Iterations: 27\n", " Function evaluations: 54\n", "[-2.3381875]\n" ] } ], "source": [ "max_x = sopt.fmin(lambda x: -univariate_logistic_regression_fun(x, w0, D), 0)\n", "print(max_x)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.2" } }, "nbformat": 4, "nbformat_minor": 2 }