{ "metadata": { "name": "", "signature": "sha256:459e982258774b936e0470ae40c90105380bb7ab9dc6dd7fe1071b6b7a7797fe" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": true, "input": [ "from pylab import *\n", "%matplotlib inline\n", "import statsmodels.api as sm\n", "\n", "# nastavitve za izris grafov (http://matplotlib.org/1.3.1/users/customizing.html)\n", "rc('text', usetex=True)\n", "rc('font', size=12, family='serif', serif=['Computer Modern'])\n", "rc('xtick', labelsize='small')\n", "rc('ytick', labelsize='small')\n", "rc('legend', fontsize='medium')\n", "rc('figure', figsize=(5, 3))\n", "rc('lines', linewidth=2.0)\n", "rc('axes', color_cycle=['k'])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Linearna regresija" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linearna zveza $y=kx$ je najpreprostej\u0161a in najpogostej\u0161a zveza med dvema fizikalnima koli\u010dinama, zlasti \u0161e, ker lahko tudi druge funkcijske odvisnosti v ozkem intervalu aproksimiramo z linearno zvezo: $\\Delta y=k\\Delta x$. Vemo, da sorazmernostni koeficient $k$ za majhne $\\Delta x$ limitira k odvodu $\\mathrm{d}y/\\mathrm{d}x$.\n", "\n", "Kadar moramo dolo\u010diti koeficient v linearni zvezi dveh koli\u010din $x$ in $y$, je s stali\u0161\u010da merske tehnike koristno izmeriti ve\u010d kot en par $(x,y)$. \u010ce dolo\u010dimo vrednosti $y_i$, ki ustrezajo celi vrsti izbranih $x_i$, $i = 1, 2, ..., N,$ lahko z njimi dolo\u010dimo $k$ z ve\u010djo natan\u010dnostjo. Obenem preverimo, ali linearna zveza zares velja, pa tudi, ali na\u0161a merska naprava dobro deluje v \u0161ir\u0161em intervalu spremenljivk. Zlasti se lahko zgodi, da ima merilec te ali druge koli\u010dine premaknjeno ni\u010dlo. Tedaj se na\u0161a linearna zveza ne poka\u017ee kot premica skozi izhodi\u0161\u010de koordinatnega sistema, pa\u010d pa je nekoliko premaknjena. Zato velja, da iz vrste meritev $x_i$, $y_i$ nikoli ne ra\u010dunamo koeficienta kot povpre\u010dje kvocientov $y_i/x_i$, pa\u010d pa vedno kot naklon premice, ki jo potegnemo skozi izmerjene to\u010dke.\n", "\n", "Problem najbolj\u0161e premice skozi dane merske to\u010dke je mogo\u010de definirati na mnogo na\u010dinov, ki pa se vsi prevedejo na eno od dveh matemati\u010dnih oblik. \u010ce smo za meritve \u017ee dolo\u010dili korelacijski koeficient $R_{x,y}$, zado\u0161\u010da vedeti, da gre najbolj\u0161a premica vedno skozi te\u017ei\u0161\u010de oblaka to\u010dk $(\\bar x, \\bar y)$ in da ima naklon $R_{x,y}\\sigma_y/\\sigma_x$.\n", "\n", "Sicer pa lahko koeficienta $k$ in $n$ najbolj\u0161e premice $y = kx + n$ dolo\u010dimo tudi z elementarnim ra\u010dunom. Zahtevamo, naj bo vsota kvadratov razdalj to\u010dk od premice najmanj\u0161a (na\u010delo najmanj\u0161ih kvadratov \u2013 least squares principle):\n", "\n", "$$S=\\sum\\left(y_i-kx_i-n\\right)^2=\\mathrm{min}.$$\n", "\n", "V zaresni merilni tehniki se spodobi, da so meritve opremljene s statisti\u010dno napako, torej $y_i= y_i\\pm\\epsilon_i.$ Kadar se $\\epsilon_i$ od izmerka do izmerka znatno spreminja, je te\u017ea posameznih to\u010dk razli\u010dna. Statisti\u010dno neopore\u010den rezultat dobimo, \u010de sumande ute\u017eimo z $\\epsilon_i^{-2}$:\n", "\n", "$$S=\\sum\\left(\\frac{y_i-kx_i-n}{\\epsilon_i}\\right)^2=\\mathrm{min}.$$\n", "\n", "To je druga, popolnej\u0161a oblika za najbolj\u0161o premico. V njej vsoto $S$, ki smo jo minimizirali, obi\u010dajno ozna\u010dimo s $\\chi^2$ in jo lahko uporabljamo tudi za diagnozo kvalitete ujemanja. Za dobro ujemanje je pri\u010dakovana vrednost $\\chi^2/N=1\\pm\\sqrt{2/N}$. Govorimo o testu hi-kvadrat.\n", "\n", "Zgornji postopek lahko uporabimo tudi pri nekaterih nelinearnih zvezah med dvema koli\u010dinama. \u010ce bi npr. skozi to\u010dke radi potegnili najbolj\u0161o eksponentno funkcijo $y = Ae^{-\\lambda x}$, le-to najprej z logaritmiranjem pretvorimo v linearno zvezo: $\\ln{y}=\\ln{A}-\\lambda x.$ Vidimo, da lahko $A$ in $\\lambda$ dolo\u010dimo z obi\u010dajno linearno regresijo za spremenljivki $\\ln{y}$ in $x$.\n", "\n", "Druga posplo\u0161itev je, da poskusimo podatkom prilagoditi linearno kombinacijo poljubnih funkcij $f_i(x)$ s konstantnimi koeficienti $c_i,$\n", "\n", "$$y=c_1 f_1(x)+c_2 f_2(x)+c_3 f_3(x)\\ldots,$$\n", "\n", "tako da minimiziramo vsoto\n", "\n", "$$\\chi^2=\\sum\\left(\\frac{y_i-c_1 f_1(x_i)-c_2 f_2(x_i)-c_3 f_3(x_i)...}{\\epsilon_i}\\right)^2=\\mathrm{min}.$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Kot prvi primer bomo poiskali najbolj\u0161o premico za podatke, prikazane na naslednjih \u0161tirih grafih." ] }, { "cell_type": "code", "collapsed": false, "input": [ "podatki=loadtxt('anscombe.dat')\n", "fig, ((axa, axc), (axb, axd)) = subplots(2, 2, figsize=(10, 6), sharex='col', sharey='row')\n", "axa.set_xlim([3, 20])\n", "axc.set_xlim([3, 20])\n", "axa.set_ylim([2, 13])\n", "axb.set_ylim([2, 13])\n", "axa.set_ylabel(r'$y$')\n", "axb.set_ylabel(r'$y$')\n", "axb.set_xlabel(r'$x$')\n", "axd.set_xlabel(r'$x$')\n", "\n", "x1=podatki[:, 0]\n", "y1=podatki[:, 1]\n", "axa.plot(x1, y1, 'ko');\n", "axa.grid(alpha=0.5)\n", "axa.annotate('(a)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "x2=podatki[:, 2]\n", "y2=podatki[:, 3]\n", "axb.plot(x2, y2, 'ko');\n", "axb.grid(alpha=0.5)\n", "axb.annotate('(b)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "x3=podatki[:, 4]\n", "y3=podatki[:, 5]\n", "axc.plot(x3, y3, 'ko');\n", "axc.grid(alpha=0.5)\n", "axc.annotate('(c)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "x4=podatki[:, 6]\n", "y4=podatki[:, 7]\n", "axd.plot(x4, y4, 'ko');\n", "axd.grid(alpha=0.5)\n", "axd.annotate('(d)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "subplots_adjust(hspace=0.075, wspace=0.05)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podatki so namenoma pripravljeni tako, da je najbolj\u0161a premica za vse \u0161tiri sete enaka. Primerjava premice in podatkov na naslednjih \u0161tirih grafih poka\u017ee, da je opis podatkov s premico primeren le za podatke (a). Podatki (c) in (d) vsebujejo to\u010dko, ki mo\u010dno odstopa od obna\u0161anja ostalih to\u010dk (outlier). Posledi\u010dno je premica, ki jo dolo\u010dimo z linearno regresijo, zavajajo\u010da. Podatkov (b) pa s premico ne moremo opisati. Linearna regresija s polinomom druge stopnje pa te podatke opi\u0161e pravilno. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ((axa, axc), (axb, axd)) = subplots(2, 2, figsize=(10, 6), sharex='col', sharey='row')\n", "axa.set_xlim([3, 20])\n", "axc.set_xlim([3, 20])\n", "axa.set_ylim([2, 13])\n", "axb.set_ylim([2, 13])\n", "axa.set_ylabel(r'$y$')\n", "axb.set_ylabel(r'$y$')\n", "axb.set_xlabel(r'$x$')\n", "axd.set_xlabel(r'$x$')\n", "\n", "x=linspace(3, 20, 18)\n", "\n", "fit1=sm.OLS(y1, sm.add_constant(x1, prepend=True)).fit()\n", "f1=lambda x: fit1.params[0] + fit1.params[1] * x\n", "axa.plot(x, f1(x), 'r');\n", "axa.plot(x1, y1, 'ko');\n", "axa.grid(alpha=0.5)\n", "axa.annotate('(a)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "fit2=sm.OLS(y2, sm.add_constant(x2, prepend=True)).fit()\n", "f2=lambda x: fit2.params[0] + fit2.params[1] * x\n", "axb.plot(x, f2(x), 'r');\n", "fit2x=sm.OLS(y2, sm.add_constant(column_stack((x2, x2 ** 2)), prepend=True)).fit()\n", "f2x=lambda x: fit2x.params[0] + fit2x.params[1] * x + fit2x.params[2] * x ** 2\n", "axb.plot(x, f2x(x), 'b');\n", "axb.plot(x2, y2, 'ko');\n", "axb.grid(alpha=0.5)\n", "axb.annotate('(b)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "axb.legend([r'$y=kx+n$', r'$y=ax^2+kx+n$'], loc=8)\n", "\n", "fit3=sm.OLS(y3, sm.add_constant(x3, prepend=True)).fit()\n", "f3=lambda x: fit3.params[0] + fit3.params[1] * x\n", "axc.plot(x, f3(x), 'r');\n", "axc.plot(x3, y3, 'ko');\n", "axc.grid(alpha=0.5)\n", "axc.annotate('(c)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "fit4=sm.OLS(y4, sm.add_constant(x4, prepend=True)).fit()\n", "f4=lambda x: fit4.params[0] + fit4.params[1] * x\n", "axd.plot(x, f4(x), 'r');\n", "axd.plot(x4, y4, 'ko');\n", "axd.grid(alpha=0.5)\n", "axd.annotate('(d)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "subplots_adjust(hspace=0.075, wspace=0.05)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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IywMSEoAOHYAnnxTH6+KLJcZi+3aZ8fKx42Wo8YcQusdNfepXsGWLPNRFR0tow6FDQFwc\nkJEhMV133ulzx8tQ4w8CdMR8WQCsL39fCKCVhj4Q4nPsdjvS0tJQWFiIyLAwJDZsCNvXXzt3EF11\nlWzb5g4iQoivUQpYsULiuT79VNrq1QOGDxe707u31u6RqgTqL8BSAPHl72cAWAhZduwMYDKAm6qd\nz9gLElS4KuxtAZBarx5sI0fKNP8FF+jrYAjBmC8SUpw4ASxZIk7XmjXS1rgxcPfdwLhxgMWit38h\nghFjvqqTA4n1Qvm/BzX0gRDfUVKCtEmTqjhegPxHT7/sMtjefFNPvwgh5uXvv4HXX5fEqLnlkTyn\nnebcvHPaaXr7R2pFh/OVBWBQ+fvOkFmxk0hOTkZU+Q6MmJgYxMbGIjo6GoBzbbem49WrV6Ndu3Z1\nPt/Xx9QPEf1WrYDZs5E/ZQoK9+6FK4rMPH6D6M+fPx/Z2dkV9sIbaHeob3j9pk2BadOQn5oKFBQg\nGgAsFqweMgTtRo9GdLdu5h6/QfR9aXf8xY2Q2a1HAESWt02ABN6PruE7yhvy8vK8+r63UN/k+rt3\nK/Xoo0pFRiolkRYqvmlTBeCkl9Vq9W9fXGD6+38Kyu+9J3ilq3vc1De5/i+/KHX//UpFRFTYHdWn\nj1ILFypVWmr+8Rtc3127E+ahkfI35WMhxED89JOz/E9JibTFxQETJsBeVoakceNOKuydmpoanPUl\ngxjGfBFT8d13Es+1ZIm4XIBUvZgwQcqPhRn1z3hoEQwxX4QED47yPykpsk0bkB1EN94oxq9PHwCA\nrbzdFIW9CSF6KSuTHYspKVJiDAAaNgQcm3fOO09v/4hp8Wr6T/f0I/VNoF9aqtSiRTKt75jij4iQ\naf9ffvG/vheEuj647Ej9YNUvKlJq7lylunVz2p0WLSTMYfdu/+t7Qajru2t3OPNFSGVclf9p3dq5\ng+j00/X2jxBiPgoKgJkzJRv9nj3S1q4dkJwMjB4NtGiht3/E5xh1sbjckSQkQPz5p7P8z59/Slvn\nzs7yP02a6O0fqTOM+SJBw65dUm9x1izgyBFpu+ACCWm45RZZaiRBAWO+CHGH3FzJk/PaazLrBQC9\neonxGzoUaMBfEUKIj/nhB4nnmj8fKC2VtgEDgIkTgfh4BtGHAIGo7RhwHPk4qE/9Glm7Frj5ZuCc\nc4Bp08Txuvpq4Msvge+/B266yWPHKyjGb2J9XegeN/UNrq8UsHw5cOWVQPfusmu6rExmuNatk8+s\nVo8dL8OP3+T67sLHehI6KAV89pk8ca5YIW0NGwK33y47iP7xD63dI4SYkNJSYNEisTvry8saN2kC\n3HOPlP/p1Elv/4gWjDq3ydgL4juOHwfee09ydP34o7Q1bw6MHQskJQFt2+rtH/EpjPkihuDoUWDu\nXODllwHHrMwZZwAJCcD998tGHmIaGPNFiIPCQglkTU0Fdu+WtrPPlh1EY8YAkZG1f58QQtxl3z7g\nlVcknOGvv6Sta1fg4YeBUaOAiAi9/SOGgDFf1Deffna2BK526CD/7t4NnH++FKHNy5Ngej86XtrH\nH+L6utA9bupr1v/iC+C++4COHYFnnxXH65JLgA8+ALZulQc+Pzpe2scf4vruwpkvYh5+/FGWFt95\nx7mDqH9/cbauuoo7iAghvuebbySe68MP5TgsDLjuOrE7/frp7RsxLEb9a8TYCw3Y7XakpaWhuLgY\n4eHhSExMNH55HKWAlSvF+H36qbTVqwcMGybGr3dvvf0jAYcxX8TvlJUBn3widufrr6UtPFyWFR9+\nGDj33IB1JSjttglhzBfxCLvdjqSkpCqFoR3vDfmLfOKEFJp94QVJGwEAjRtLQtTx4wGLRW//CCHm\no6gImDdPKmD8/LO0RUUBDzwggfRt2gS0O0Fnt0kFjPmiPgAgLS2tyi8wIL/E6enpAdGvM3//LYGs\nXbtKLq61a4HTTgOefhrYuROYNg359ev7T78OBOPP30z6utA9bur7Uf/gQeC554DoaInd+vlniSmd\nOlWy1D/3HPKLivynXwO+tNveYuqfvx/gzBcBABQXF7tsL9JgUFyyf784Xa+8Ahw4IG2dO8sU/513\nsvwPIcT37NghqSLmzJHUEQBw0UUS0jB8uPbyP4a326RGTOl8RUdHU99NwsPDXbZHeLA7x6fj//VX\nKf/z+usy5Q9IHNfEicANNwAuZrmC8f5TP/jRPW7q+1B/wwaJ53r/fQlxAKTsz4QJwMCBLjfv6Bi/\nL+22t5jq5x8ATOl8EfdJTExETk5OlSlsi8WChIQEPR36/nsxfkuWSHArANhsYvwuv5w7FwkhvkUp\nYNkyiSNdvlza6tcHbrtNKmBcdJHe/rnAcHabBD3KG/Ly8rz6vrcEq35GRoayWq0qLi5OWa1WlZGR\nEVB9deKEUhkZSsXFKSWmUKmGDZW6806lfvzR//o+gvp69QF4umXRK13d46a+h/rHjys1b55S3bs7\n7U7TpkqNG6fUjh3+1/cSh93u27evV3bbW4L25+8j3LU7nPkiFdhsNj07ZIqLgXffhf2pp5C2axeK\nAYTXr4/E66+HLTWV5X8IIb7n8GFg9mxn0DwguxUTE6X0WMuWevtXRxx2Oz8/P+iW3kIZo67dlDuS\nxNQUFgIzZwKpqbD//juSAFTet2OxWJCamsot08QtmOeL1MqePUBaGjB9utggAIiJkaXFkSMlXxch\nbuKu3aHzRQLPb79JvcWZM+XpE4C1WTMsPXLkpFOtVisyMzMD3UMSxND5Ii7ZulUqYLz9NnD8uLRd\neqls3rHZJDkzIR7irt3R9b9tWPlrtD8urjvfB/Vr0N+8GbjjDqBTJzGChw8DV1wBfPopinv2dPkV\nT7ZMG3b81Dc1usdNfRf6SgGrVgFDhgDnnQe89hpQUgIMHQp8+618du21XjledrsdVqsVsbGxsFqt\nsNvtng/CCwx5/0NI3110xHz1AFAAYHn5+2EAFmvoB/ExjjIXhYWFiIyMlDIXV18NrFghOxc/+0xO\nrFdPEqROmAD06gUACJ861eU1dWyZJoQEOSdOAB99JDsXv/tO2iIiJCfg+PHAOef4RIYZ5kkw0QnA\nUgCREMcr2sU5+rYsEI/IyMhQFovFseNDAVCWM89UGRaLcwdR48ZKPfSQUjk5dfu+xaJt5w4JXqBp\ntyMxAH//rdT06Up16eK0O61aKfXkk0rt2+dzufj4+Co2y/GyWq0+1yLGxl27o2PmKw/A+vJ/nwdn\nvUyByzIX+/Yhfd8+2E47TeqePfCAlAJygeMpMT09HUVFRYiIiEBCQgKfHgkhp+bAAeDVV4H0dKmG\nAUh4w/jxUu+1aVO/yDLDPPEUHTFfUQAOABgO4DHI0qNP0b32G4r6xeWB89Up6tJFSnQ8+WSNjpcD\nm82GzMxMrFixApmZmR47XqF4/6mvH93jDkn9vDx5sGvfHvlPPimOV69ewIIFwPbtwEMP+c3xAoyV\nYT4kf/4G0ncXHTNfwwHMBHAIwMUAHgUwtvpJycnJiIqKAgDExMQgNja2IoeJ4ybXdPzbb7/V+rm/\nj0NK/9dfkf/UUyj79lu4IsJiQf4ff5h3/NTXrj9//nxkZ2dX2AtvoN0JEv21a5H/9NPAp58iunyH\n6m99+wLJyYi++WYgLKzO19uyZUtFrGqjRo3w6KOPVuTNOtX3b7755hozzJv6/lPfp3YnUEyAxHtV\nPq6O7uVbciqys5UaNkypsDClAJUBKEuTJozZItoBY77MSVmZUna7Uv37V62AcccdSm3e7NElfRFr\n6qvKICS4cdfuhHlopLxlAoBcAK0ALIDMglWmfCzEUJSVAZ9+KjsXv/pK2ho2BG6/HXj4Ydjz8hiz\nRbTDPF8m4/hx4L33JD3Njz9KW/PmwH33AUlJQLt2Hl/aarVi6dKlLtuZX5C4gxd2x1B45YHqrvFk\nOv2iIqXmzlWqWzfnE2dkpFKPPqrU7t3+13cTb2pbxsfHq7i4OBUfHx/42pY+ItT1wdqO5tAvKFDq\nhReUatvWaXfOPlvaCgp8oh8XF+dyt2JcXJzb1zLd/ae+W7hrd1jbkdRMQUFF+R/s2SNt7doB48YB\n994LtGiht38+hPl6CDEIjgoYs2YBh8oXRc4/X8r/jBgBNGrkMykjBcwTUhszANwLwN9/dbV6sCHP\nzp1KjR+vVPPmzifOCy5Q6q23lDp+XHfv/ALz9ZgHMOYrONm8WeK3GjZ02p3+/SXOq6ysxq95M2PN\n/ILEV7hrd9yd+ZoEYBCAOZCUETkA/gcg383rECOyebPEc733HlBaKm0DBkjts/h4ICzol7NrhPl6\nCNGAUq4rYAwfLhUweveu9evezlgzvyAJVsYAmAxggI+v65UHqnvtN6j0y8qUWr5cqSuvdD5t1qun\n1C23KLVunf/1/YAn+r6c+QrG8ZtJH4z5Mr5+SYlSCxYo1atX1QoYDz6o1K+/1vkyRpqxDqr7T32f\n467dcXfmazKAzpDlxy8gM1+zIGWCQh6XtQ2N+gRVWgosXiy1z9avl7YmTYB77pGYrk6d9PYvwCQm\nJtaYr4cQ4iOOHgVefx146SVJkApI8uWHHgIefPCUiZirwxlrEqy4u440EJIiYjhk+XFheXsupFC2\nryh3JIMHV9PfFosFqampxnLAjh4FXntNjJ8jI/AZZ0iW6PvvB1q31to9ndjtdi4/mACmmjAg+/cD\nr7wCTJsmpYAAwGIBHn4YuOMOefDzAKaKIEbB36kmInFyOaCBkGLZvkTr9KEnGGn62yX79in1xBNS\nZNYxzX/OOUrNnCnFaAkxCWDAvXH45Relxo5VKiLCaXf69lVq0SKlSkuVUgyYJ+bAC7tjKLy6CTrW\nfn2ZL8Zbqox/+3al7ruvqvGLjVVqyZIK4+dXfQ1QP7T1wZgv/frVKmAoQKlrr1Xqq6+q7Fz0ZYb5\nvn37as0wb6j7T/2A467dYZ4vH2GEfDFVYs4AJNarB1t2tpg+ABgyRHYQ9etn6p2LhBANlJUBGRkS\nR7pqlbQ1agSMHCnLi+edd9JX0tLSqoRqALJbMT09vc5L/jabraIWo6PuHiHEM7R6sJ6ge/rbpT6g\nMurXV+qee5T66aeA9IMQ3YDLjoGlpgoYkyYp9fvvtX7VSCsGhHiDu3aHM18+Qmu+mOJipD366MlP\nkADSL7sMtjlz/N8HQkhoUVAAzJgBpKU5K2C0b++sgNG8+SkvYYQVA0J0UE93B/xBvmMXX4Cx2WzI\nzMzEG2+8gczMTP87XgUFwOTJQHQ0irdscXlKkYbdW7ruP/WprxPd4w6Y/q5dsozYvj3w2GOw79kD\na7NmiO3cGdaYGNi7dq2T4wVIiheLxVKlzdMULyFz/6lvSH134cxXMLJrFzB1qtQ+O3IEABDerFnF\n+8rwCZIQ4hM2bQKmTAHmz6+ogGG/8EIk7d+PnD17xP7k5iInNxcAM8wTUhtGjbouX0IlVfjhBynD\nUcn4YdAgYMIE2I8fR1JysvHzjBHiZ5jny4coBSxfLnbHkU+rfn3gppuARx6B9bHHmGeLELhvdzjz\nZXSUAr74QnYQVTZ+t94qOxd7SNo1GwCEhfEJkhDiPaWlwMKF4nRt2CBtTZpILNe4cUD5rkJmmCfE\nMxjzZVT90lKZ4br4YpndWrpUjF9SEvDrr8C771Y4Xg4CHnNWA6a4/9QPWn1d6B63T/SPHAFSU4Eu\nXYARI8TxOuMM4NlnJdwhNbXC8QKMFTBvivtP/aDVdxfOfBmNo0eBuXOBl1+uWv4nMVHK/7RqpbV7\nhBBzYbfbkZaSguLcXITv2YPE0lKZSe/aVQLrR40CanCmWBOVEM9gzJdR2LfPWfvsr7+krQ7GjxBS\nFcZ81R37zJlImjABOYcPV7RZwsOR+sgjsP3nP0C9Uy+OsCYqIe7bHTpfutm+HXjxReDNNwFH/MQl\nlwATJ0pG+joYP0KIEzpfdeDrr4GUFFg/+ggnh8szYJ4Qd3HX7pjyL7vutd866X/7LTB0KBATIykj\niouB664DVq8GvvkGuP56jx2voBg/9alvMnSP+5T6ZWXAhx9KebFLLwU++gjFNZQZ8yRg3vDjpz71\nDYSumK+eAC4uf/8+gEJN/QgslWufff21tDVqJMuKDz8sjhghhPiSoiLgrbdkhn37dmlr2RJ44AGE\nr14NrFw7c5dcAAAgAElEQVR50leYH5AQ/6Jr2fF9ADcBGFZ+vLja5+aa/i8qAt5+W4zftm3SFhUF\nPPAAkJAAtGmjt3+EmIhQW3a02+1IS0tDcXExwsPDkZiYKDFXBw8C06cD6ekSUwoAHTtKqoh77gGa\nNYPdbkdSUhLzAxLiJcGQ5+tGAGvK31d3uszFX39J7bPUVKfx69DBafzqWIKDEEJc4cp5yvn5Z2Dm\nTNi++EJ2TwOSlmbCBGD4cKCB0+wzwzwhocPk8tfA8n9d4VV18by8PK++7y15q1crlZysVNOmSkma\nVKW6d1fqnXeUOn7c//q6x0996msEgKfTV17p6hh3fHy8Y7xVXlaH3bFalcrKUqqszO990f1zpz71\ndeKu3dEV86UALAcQBWACgBRN/fAtmzZJRuj33pP4LgAYPFieOAcNAmoIbiWEEE8oriEwvuiMMyQx\nc/fuAe4RIaQu6HC+ciq9LwTQ29VJycnJiIqKAgDExMQgNjYW0eWZlR27Gmo6drTV9XyvjpVC/jvv\nALNmIXrVKhGvVw/5Q4Yg+umngR495PwdOwLTn0CPn/rU16w/f/58ZGdnV9gLbwgau1NSgvxXXkHZ\n2rUuxxHRowfyIyOBAP4cAjp+6lM/yO1OmEff8o5OAO4DMAkS/xUNYEq1c8pn8QxMaSnw/vsy07Vx\no7Q1bQqMHg0kJ0tgKyEk4ARbwH2NAfOuOHwYmD0bmDoV2LULdgBJ9esj58SJilMYME9I4PHC7gSU\n0ZCdjoaK+crIyFDx8fEqLi5OxcfHq4yMjJNPOnxYqalTlerY0RnPdeaZSj33nFIHD3ql7yuoT/1Q\n1kcQxXxlZGQoi8VSJV7LYrGcbHt271bq0UeViox02p1u3ZSaO1dlLFmirFar6tu3r7Jara7tVgDQ\n/XOnPvV14q7d0RXzNbv8X8PsdnS5a6j8vc1mA/bulS3b06dXLf/zyCPA7bez/A8hxG3S0tKq2BxA\n7E56errYnZ9+AqZMkVQ1JSVywmWXSQWMq68G6tWDDYDthhuqLLkQQoyNUafIyh3JwGG1WrF06cmF\nNqyXXorMmBhJUnj8uDT26ydB9Ndey/I/hBiMYFp27N+/P1a6SHIa1707VrRvL0mZAdmsM3So2J2+\nfQPaR0LIqQmGPF+GpNhRV7EaRatXS8mfsDAp+TNhAvDPfwa4d4QQMxIeHu6yPWLTJtk9HREB3Hkn\nMH48cM45ge0cIcRvmHLaxrErwR1qNIJhYcCYMcDWrcAHH9TJ8fJE35dQn/qhrB9o7HY7rFYrYmNj\nYbVaYbfb6/zdxMREWDp3rtJmAZDQrBnw5JPAjh0S6lAHx0v3fac+9UNZ31048wUARUVIPOcc5Hz5\nJXIccRUALFFRSEhPB0aO1Ng5QohROWWsaG38+Sdsa9cC+/cjHUARgIjGjZEwahRsL74ou6cJIaYk\ntGO+qtU+swNIj4hAUdu2iOjUCQnJydyuTUiQEciYrxpjRa1WZGZmuv5Sbi7w0kvAa68Bx45JW69e\nEtIwdGiV8j+EkOCAMV91IT8fePllYO7cKrXPbBMmwFat9hkhhNREjbGirjLPr1kjeQEXL3ZWwLj6\nanG64uJYAYOQECK0Yr42bABGjAC6dAHS0sTxio8Hli0D1q0Dbr3VJ46X7rVn6lM/lPUDSY2xoo7U\nM0oBn34KXHEF0KcPsHAhUL8+cMcdwObNgN0O9O/vE8dL932nPvVDWd9dzD/Fo5Q4VykpQFaWtNWv\nD9x2m+Touugivf0jhAQtiYmJyMnJqRLzZbFYkDB2LPDGG5Kja8sW+aBFC+C++4CkJKBtWz0dJoQY\nAqPOc3sf81VSAixYIMZv0yZpa9pUdi4mJwMdOnjfS0KI4Qh0ni+73Y709HQUFRUhokEDJLRvD9uy\nZcDu3XJC27Zic0aPBiIjPegWIcTouGt3zOd8HT4MzJkjMV27dklbmzZAYiIwdizQsqXvekkIMRxa\nkqzu3i31FmfOFBsEAP/4h8yu33or0KiRZ9clhAQF7tod88R87d0LPP440KED8sePF8crJkYcsfx8\n4LHHAuZ46V57pj71Q1k/oGzeLPFb0dHInzJFHK8rrpA4rx9+kM8C5Hjpvu/Up34o67tL8Md8bdsm\nS4vz5jnL/1x8sSQovOaaoCr/Y7fbkZaWhuLiYoSHhyMxMZGpLggxGkoBK1ZIHOlnn0lbvXqAzQY8\n/bSkjSCEkFoI3mXHr78GXngB+PhjOa5c/ueSS/zfQx/jKlmjxWJBamoqHTBC3MBvy46lpZImIiVF\ndkcDQOPGwD33AOPGAdUy1RNCQgdzx3ydOCHOVkoK8O230hYe7qx91rVrQDvpSzxK1kgIOQmfO19H\njwKvvy6JUfPypO3004GEBOCBB4DWrb3oLSHEDJgz5uvYMQlk7dZNMkB/+63Eb/3731L7bMaMKo6X\n7rVfT/TdStboB31fQn3qm4I//pDwhQ4dxNHKy5McgdOni9154okqjpfucVOf+tQPHowd83XwIPDq\nq1L+548/pK1jR5nluvtuoFkzvf3zIadM1kgICQy//CKzXG+8ATgefvr2BSZOBK67TvIEEkKIFxh3\n2TEx8aTyP5g4EbjxRlOW/2HMFyG+watlx6FDgQ8+kKB6ALj2WokjvfRSlv8hhNSIeWK+HO+sVjF+\nAwaY3vhVSdYYEYGEhAQ6XoS4iVfOFyCpIUaOlBxd3br5tG+EEHNinpivkSOBjRuBzExg4EC3HC/d\na7+e6ttsNmRmZmLFihXIzMz02PEK1vFTn/ramTRJ8gLOneu246V73NSnPvWDB+Ou382b5/ZXHHmy\nCgsLERkZyTxZhBD3eP553T0ghIQARl3Hc7vMB2OmCCGApvJChJCQJtiWHSf76kJpaWlVHC8AyMnJ\nQXp6uq8kCCGEEEK8RqfzNaj85RN8mSfLW3SvPVOf+qGsrwvd46Y+9akfPOhyviIBHABw0FcXZJ4s\nQgghhAQDumK+hgFYDGApgHgXnzPmixDiEYz5IoQEGnftjo7djj0ArPf1RR0OFvNkEUIIIcTI6KiT\n0Q/AWQDOA3ATgB8B5FU75+mCggJkZ2djxYoV2Lt3L5o1a4aoqCgAsrZbUFBw0nGfPn0wcuRIdOnS\nBSNGjECfPn1qPd9fx6tXr0ZZWVnA9KhP/VDWnz9/PubMmVNhL1auXAkA/wf38cjuhOp9pz71Q1nf\nW7ujO9XEWgC9XLR7Nf2fn5+P6Ohoj7/vLdSnPvX16etadtQ9bupTn/r69IOpvNAYAM8DGA7gi2qf\nMfaCEOIRjPkihASaYHK+aoNGkBDiEXS+CCGBJtiSrPqF/Px86lOf+iGqrwvd46Y+9akfPJjS+SKE\nEEIIMSpcdiSEmAouOxJCAg2XHQkhhBBCDIwpnS/da7/Upz71Qw/d46Y+9akfPJjS+SKEEEIIMSqM\n+SKEmArGfBFCAg1jvgghhBBCDIwpnS/da7/Upz71Qw/d46Y+9akfPJjS+SKEEEIIMSqM+SKEmArG\nfBFCAg1jvgghhBBCDIwpnS/da7/Upz71Qw/d46Y+9akfPJjS+SKEEEIIMSqM+SKEmArGfBFCAg1j\nvgghhBBCDIwpnS/da7/Upz71Qw/d46Y+9akfPJjS+SKEEEIIMSqM+SKEmArGfBFCAg1jvgghhBBC\nDIwu52t0+WuGPy6ue+2X+tSnfuihe9zUpz71gwcdztdAAFkAZgMogDhhPiU7O9vXl6Q+9akfJPq6\n0D1u6lOf+sGDDuerM4BB5e9zAVh8LbBt2zZfX5L61Kd+kOjrQve4qU996gcPDTRozq70fhCA+Rr6\nQAghhBCiBZ0B950BHACwxNcXLigo8PUlqU996geJvi50j5v61Kd+8KAz1cRkAJNq+GwjgO4B7Ash\nxDzkAOjiwfdodwghnuKp3QkoYwBElr8fprMjhBBCCCFmZxCAMgAHy1/36u0OIYQQQgghhBBCCCGE\nEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghhBBCCCGEkDqhs7ZjjcTFxamV\nK1fq7gYhJDjZBOAid79Eu0MI8QK37E49P3bEY1auXAmllMevpKQkr77v7Yv61Ke+n3X27YN64gmo\nVq2gAHl16QI1fTrgYXFs2h3qU5/6tb5+/RXqgQegGjd22p3evaHef99tu9PAEyNldKKioqhPfeqb\nUf+XX4AXXwTefBMoKpK22FhgwgTguuuA+vWB++/3n34tmPq+U5/6oaz//fdASgqwZAlQViZtNpvY\nncsvB8LcX0Q0pfNFCDEZ2dnACy8AH34IKCVt114LTJwI9OvnkfEjhJAaKSsDPvtMnC5HOELDhsAd\ndwAPPwycf75Xlzel8xUTE0N96lM/2PXLyoCMDDF+q1dLW6NGwO23i/Hr1s03Oj7CNPed+tQPIX27\n3Y60tDQUFxcjPDwciWPHwlZQAEyZAvz0k5zUogUwdiyQmAi0bevDXhsP5Q15eXlefd9bqE996ntB\nUZFSc+YoFROjlMxzKRUZqdSkSUr9/vspvw4JxaDdoT71qV8rGRkZymKxVIRvAVCW+vVVhsPutG2r\n1JQpShUWnvJaXtgdQ3HKgebk5KisrCyllFLLli1TFoulxnMXLVpU958GIUQPf/2l1PPPK9WmjdPp\nat9eqZdeUurQoTpfBn50virbnertgwcPVuvXr69oo90hxNjEx8dXcbwcL2uzZkq9+aZSxcV1vpa7\ndseQux3rwuLFizFw4EAAwKBBg2oNtuvZsycWL14cqK4RQtxh505g/HigfXvgsceAvXuBCy8E5s0D\ncnKAceOA5s119xJAVbtTmc6dO6Nnz544ePBgRRvtDiEGZvNmFG/c6PKjop49gVGjJMzBTwSl85WV\nlYWLL764xs/z8/OrHHfq1Alr1qzxc69q1g801Kd+UOhv2iTxWxYL8PLLwJEjwMCBQGYmsHEjMHKk\nBLgahFPZncLCwirHtDvUp77B9JUCvvwSuOoq4MILEf7HHy5Pi2jc2Ledc0GgnK+Z1Y5Hl79meHKx\nRYsWYcCAASe1L1++HMuXL8fMmTORl5dX5bPWrVuf1EYICTBKAVlZgNUKXHQR8Pbb0nbrrcC6dc7P\nDLh70ZXdmT17doXd2blz50nfod0hxACUlgILFgC9ewMDBsgDXuPGSLTZYOnQocqpFosFCQkJfu9S\nIHY7jgFQeZ5+IIAsAHkALBAnbLYvhBzLAQMHDkSvXr2wdu3ais86d+6M3NxcdOrUyRdStRIdHe13\nDepTP6j0S0uBhQtl5+KGDdLWpAlw772yrKi5z56QlZWFgoKCCruzbNmyk86h3aE+9TXqHz0KvPaa\nzKw7HoJOPx1ISAAeeAC21q0Bux3p6ekoKipCREQEEhISYLPZ/N7fQDhfswDcWOm4c/lrNoBciAPm\nFpXjKmoiNze3ynFUVBQKCgrclSKEeMORI2L8XnoJ2LFD2s44Q7Zs338/0KqV3v65QXW7k5WVhd69\ne9f6HdodQjTwxx/AK68A06YBjt/bLl2ARx6RWK5Ky4o2my0gzlZ1dMR8zYZzpmsQgO/dvUCrUxjs\n/Px8WCxVfbqCgoKAZeANirVv6lPfn/r79gH//jfQoQOQlCSOV9euwMyZ8v5f/woqxws42e707t27\nSkzXrl27TvoO7Q71qR9A/V9+kXxcHTsCzzwjjldsLLB4MbBtG3DffVUcL53oDLjvDOAAgCXufjEq\nKuqk4NZBgwZh+fLl2LBhA9577z0sXLiwyudr1qw55VMqIcRLtm8HHn9cjN9zzwF//QVccgnwwQfA\n1q3AmDFARITuXnpEdbszbNgwtG7dusLu7Ny5E7NmzapyDu0OIQEgO1ucrnPPlQe8oiKpgLFqFfDN\nN8DQoVJ6zEAEKqp1KYD4am2TAUyq4fzytBmu2bBhA3JzczFs2LA6d2DSpEmYPHlync8nhLjBN99I\nPNdHHznL/1x3ndQ+69cvoF0Jk2B9T2wb7Q4hwUJZGWC3S9kxA1TAcNfu6CovNAbA8+XvhwE4KRlO\ncnJyxXR9TEwMYmNjKwLqWrZsie3bt1ec65judHxe/fidd97B5ZdfXufzecxjHtfhuEMH4JNPkP/M\nM8C6dYgGgEaNkH/DDcDo0YguD0T3d3/mz5+P7Oxsnyzv0e7wmMcGPz7rLODtt5H/3/8CublidyIj\nkX/rrcBddyG6T5+A9MeXdsdf3AjgIIBHAERC4rzKytsOArjXxXfqlFHWVaZppaqWGSgoKKjxPH8R\njGUWqE/9OnPsmFKzZil17rnOTPRRUUo9/rhSe/ZoHz/8XF6Idof61Negf4oKGLrH767dCcTM16Ly\nl4Ms+CjWzFWm6epERkbW6TxCyCn46y9g+nQgLU0C6gEJqB83DrjnHmcWes2Bt/6GdoeQALJzJzB1\nKjB7tuyeBqQCxsSJwE03ORMxHzigr48e4ElcRCAodyQJIdrZsUPy5MyZI3lzAEmQOmECMHy4obLQ\nA/6L+SKEBJBNm4ApU4D58yVPIAAMGiR2Z/BgwyViDpaYL0KI0dm4UYLoFywATpyQtsGDxfgNGmQ4\n40cICXKUApYvF7uzdKm01a8vFTAmTAB69NDbPx8SlLUdT0W+5mUP6lM/aPWVEqM3eLAYunfflfYR\nI4D1652f1eJ46R6/LnSPm/rUD1r90lKxNT17in1ZuhRo2lRyBP76q3x2CsdL9/jdhTNfhBCgpAR4\n/3154ty0SdqaNgVGjwaSkyVvFyGE+JIjR4C5cyWsIcgrYLiLUdcNGHtBSCA4fFhiuaZOlcBWADjz\nTKfxa9lSb/88gDFfhBicffuA9HTg1VdlIw8gFTAeeUTydAVhImbGfBFCTs3evbJrcfp0wFF78Nxz\nxfiNHBmUxo8QYnB+/hl48UXgrbeA4mJp++c/JZ5ryBCgnikjoVxiypHqXvulPvUNq79tmywlduwI\nPP+8OF79+gEffgj89BNw771eO166x68L3eOmPvUNq//NN8ANN0jW+dmzgePHgeuvB77+Wl7XX++1\n46V7/O7CmS9CQoGvv5YyHB9/LMdhYWIMJ0yQ2ouEEOJLysrE3qSkiPMFAOHhwKhRUv7n3HP19k8z\njPkixKycOOE0ft9+K23h4cAdd4jx69pVb//8BGO+CNFIUREwb54sL/78s7RFRQEPPAAkJABt2ujt\nn59gzBchoU5RkcRUTJkC/PKLtLVsCTz4IPDQQxJQTwghvuTgQYkhTU+vWgFj/HipgNGsmd7+GQzG\nfFGf+mbRP3gQePZZ5LdrB9x3nzheHTsCqamyk/GZZwLieOm+/7rQPW7qU18LO3YAyclid/79b3G8\nLroIeOcdydGVlBQQx0v3/XcXznwREuzk50uenLlzneV/evSQ2mc33gg04K85IcTHbNggIQ3vv1+1\nAsbEicDAgayAcQqMencYe0HIqVi/XozfwoVO42e1ShD9gAEha/wY80WIn1AKWLZM7E5WlrTVrw/c\ncoukqbnoIr390whjvggxM47yPykpUgMNkJmt228X43fhhXr7RwgxHyUlUuN1yhRWwPARjPmiPvWD\nQb+kBHj7bXmyvPJKcbyaNZNg1txcCbAvd7xMOf4gQPe4qU99n3P4sIQ0WCzygLdpk+xW/O9/gV27\n5LNyx8uU4/cjnPkixMgcPixJCadOFWMHiPFLSgLGjpUt3IQQ4kv27JEKGDNmOCtgxMQ4K2CEh+vt\nnwkwalAIYy9IaLNnj+xSnDEDKCyUtpgYiee67TYav1pgzBchHrJtmywtzpsnWegB4NJLxe5cc01I\nlf9xF8Z8ERLMbN0qxu/tt53G77LLxPjZbDR+hBDfopSzAsYnn0hbWBgwdKjYndhYvf0zKaa05LrX\nfqlPfbdQCli1SgrLnnce8NprEuM1dKhkpv/qK+Daa+vseAXd+E2C7nFTn/puceIEsGSJFLa+7DJx\nvMLDJUfgtm3A4sVuOV5BN37NcOaLEF2cOAF89JE8cX73nbSFhwN33inlf845R2v3CCEm5Ngx2aDz\n4ovOChitWkn5H1bACBiBivmaCeC+SsejAeQC6AxgtovzGXtBzMuxY8Cbb4rx+/VXaWvVyln+54wz\n9PYvyGHMFyEuOHAAePVVKf+zf7+0RUfLjum775bUEcRjjBjzNQbAwErHPQFEAVhe/u8wAIsD0A9C\n9FKT8Xv4YeCuu2j8CCG+Jy8PeOklCWf4+29p69lTMtEPG8YKGJoIRMzXLMgsl4OBlY5zAQz2taDu\ntV/qU78KeXlAQoIUmX3ySXG8Lr4YmD9fpv0fesinjpfhxh8i6B439alfhXXrJPN8ly7AK6+I4+XI\nEbh2LXDzzT51vAw3foOjw+W1AFhf/r4QQCsNfSDE/6xb5yz/U1YmbVdeKU+c/fuHbPkfQoifUArI\nzBS78+WX0taggaSnYQUMQxEo678UQHz5+xkAFkKWHTsDmAzgpmrnM/aCBCdKAZ9/LkH0lY3fiBFi\n/C64QG//QgDGfJGQ4/hxmUlPSQF+/FHamjcHxoyRhMzt2+vtXwhgxJiv6uRAYr1Q/u9BDX0gxLc4\njN+UKcDmzdLWvLls205KAtq109s/Qoj5OHQImDVLKmDs3i1tZ50l9RbHjGEFDAOjw/nKAjCo/H1n\nyKzYSSQnJyOq/D9OTEwMYmNjER0dDcC5tlvT8erVq9GuXbs6n+/rY+qHkP6hQ8j/3/+AuXMRvW+f\n6LdqhXajRyP6sceAyEg5Pz/fnOM3gP78+fORnZ1dYS+8gXaH+kGh//vvyP/Pf4B33kH0kSOi37Ej\n2j34IKITE4HwcDm/oMCc4zeAvi/tjr+4ETK79QiAyPK2CZDA+9E1fEd5Q15enlff9xbqh4D+7t1K\nTZyoVIsWSslio1LnnafU66+rvJ9/9r9+LYTE/a8FAJ6uHXqlq3vc1A8B/S1blLrrLqUaNnTancsv\nVyojQ+Xl5PhfvxZC4v7Xgrt2J8xDI+VvysdCiMH46Sdn+Z+SEmmLi5MyHFddxfI/BoAxX8RUKCVV\nLlJSALtd2urVc5b/6dNHb/8IgOCI+SIkuKjJ+N14I40fIcQ/nDgBfPCB2J3vv5e2iAjJCTh+vKSQ\nIEGLKR/THWuz1Ke+V5w4ASxaJPXN+vcXx6txYynDsX27pJBw4XiZZvxBqq8L3eOmvkn0jx0Dpk8H\nzj0XGD5cHK/WrYGnngJ27pREzS4cL9OMP0j13YUzX4RU5++/gTfekKzQOTnS1rq1JEN98EHg9NO1\ndo8QYkL+/BOYNk0Sov75p7R17iyzXHfdBTRpord/xKcw5osQBzR+poAxXySoyM11lv85dkzaeveW\nkIahQ4H69fX2j9QJxnwR4i45OWL8Xn+dxo8QEhjWrJF4rsWLnRUwbDaxO5dfzgoYJocxX9Q3jL7d\nbofVakX//v1htVphdwS3+0t/zRrgppuArl0ljuLYMeDqqyUz/XffSbyFB45XsN5/s+jrQve4qR8E\n+koBn34KXHGFxIsuXCg25s47JTlzRobsnvbA8QqK8ZtY310480UMgd1uR2JiEnJzcyracsrjrWw2\nm++ElAI++0zK/6xcKW0NGwKjRkn5n/PP950WIYQAUgHj3XclTc2WLdLWogUwdiyQmAi0bau3fyTg\nGHVek7EXQYjdbkdaWhqKi4sRHh6OxMTECsepqAj4/Xfgt9+AXbvk38qvH36w4vjxk4sdtGhhhdWa\niY4dgY4dgehoVLxv0aLu+jUaP0f5Hxo/08CYL2IYCgul/E9qqrP8T9u2zvI/1Y0YCVoY80W0YLfb\nkZSUVDFbBQCrV+egTRvg8GEb9u8/1RWKXbYeOlSEhQtdf6NlS6dDduKEHd98k4QDB6rNnB09CtuO\nHa6N3+jRQGSk64sTQoin/Pab2JyZM4HDh6XtH/+QeK5bbgEaNdLbP6IdU8585Veqo6eDUNIvKwNW\nrwZGjrRi1y5XZTqtADLRoAFw9tlSX9rxat/e+f7RR6346quTv9+3rxWJiZnYsQPIzwd27EDF+6Ki\n6jonf//yek2xsuyoHPzjH7K0eOutfjV+ofTzN6K+rpkv3eOmvgH0jxyR2fV333VWwLjiCnG6rrzS\nr0H0hhh/COtz5ov4HaUk79/8+cD778tyYk0zVz16FMFuB844o/bY9YkTE7F7d06VmTOLxYInnkiA\nq5AvpYD9+53O2KOPFiM39+TzvirrhbjIVIy4vT6GP30+WrU26vMGISQoUQpYsQL4v/9zxpHWqwfc\nfLM87PXqpbV7xJgY9S8RYy8MhlLAxo3AggXyqryxpGNHICzMivz8k2eerFYrMjMz66Rht9uRnp6O\noqIiREREICEhoW7B9krB2qcPlq5de9JHYWFWKCX6DRtK+cXbbgOuuYZpu8wKY74CS62xlmamtBRY\nskTSRThsT+PGwD33AOPGSY5AEjJ4YXcMRWDLkROllFIZGRkqPj5excXFqfj4eJWRkaG2bFHqiSeU\n6tpVKXHB5HX22UolJyuVna1UWZl812KxOCq7KwDKYrGojIwM/3W4pESpBQuU6tVLZQDKUknbob9g\nQYZ64w2l4uOVqlfP2f9mzZQaNUqpzz+Xy9Q0fhJ8lP/8aXcCgJbfe90cOaJUerpSnTo5Dcrppyv1\nf/+n1J9/6u4d0YQXdsdQeHUT8vLyfHM3Q0jflRFt1MiigIwq9uWBB5RauVKpEydcX8Nqtaq+ffsq\nq9XqPwPsyviddprKGDFCWa+4okb9PXuUmjpVqd69qzqSZ56p1LXXZqh27XzzRyQYf/5m0ocm50v3\nuHXox8fHV/mdcbysVmvA++L38f/xh1JPPqlU69ZO49Gli1LTpyv1998h+fOnvhN37Q5jvggAIC0t\nrUq8FQAcP56DBg3ScccdNtxyi9SWblDL/xibzQabzea/wMf9+6X0z7RpwIED0maxSFzFHXfA1rgx\nbKg58LJNG8kqkZQE/PKLxMS+8468/+STNABVx5+Tk4P09PTQWEIhxAOKi13HehZV3Q0T3Pz6K/Di\ni8A/JoYAACAASURBVFLv1TGuvn2BiROB665jBQxiKrR6sKHGvn1KtWkT5/IJ9rLL4nR3T6lfflFq\n7FilIiKcT5x9+ii1aJFSpaVeXbqsTKnvv1eqbVvX47/88jjfjIEEDHDZMWAYaebL52RnKzV0qFJh\nYU67c+21Sn31lRgOQirhrt0xZXkhUjeOH5dd0eecA+zdG+7ynCZNIgLcq0p89x1w441S/mfGDHnq\nvOYa2VGUnQ0MG+b1U2dYmJRxPP981+P/4YcIbNzolQQhpiUxMRFt2rSp0tamTRskJCRo6pGXlJUB\nn3witRVjYyWgvmFD4O67gZ9+Aj7+GLjsMtZdJF5jSudLd40no+srJTbk/PMl/cyhQ0CvXolo395S\n5TyLxeKREfVq/GVlUt/MYfwWL5a1zrvvlsz0DsNYi/HzRD8xMREWS9Xx16tnQUFBAi6+GLj/fudK\n56kw+s/f7Pq60D1u3fq68Wr8xcXAa69JLsAhQ4BVqyQB86RJsrV77lygWzf/6fsA6uvVdxfGfIUY\nP/4ou6CzsuQ4JgZ4+WXgyittsNvhWaoHX1BcLAFYU6YAW7dKW2Sks/bZ2Wf7Vd4xzsrjv+uuBHz3\nnQ1paTLxtmAB8OyzUhWkttg3QkKFtLQ07N27t0rb3r17gydWsqBAfrnT0oA9e6StfXsxkvfeCzRv\nrrd/hAQY3cu3pmP/ftmp6Ei3EBWlVGqqUsePa+7YX38pNXmyUmed5YyraNdOqSlTlCos1Nw5YcsW\npQYOdHbvwguVWrFCd69ITYAxXwEjLs51rGRcXJzurtXOzp1KjR8vOWcq/2LPm2cAo0iCEXftjimX\nHYmTkhIpMXbOOcCrr0rbAw/IDr/ERAln0MKuXcDDDwMdOsjU/p49wAUXAG+9BeTkyGcGKTp73nnA\nsmUS/hEdDfzwg+z8vOUWGQYhoUp4uOtYyYgIjbGitfHDD8Dtt0sC1JdeAo4cAQYOBD7/XLJIjxyp\n0SgS4n+Glb9G1/C5Vx6o7nwfuvQdSUL79u2r4uPj1VNPZaiYGOeD3aBBSm3e7P9+1Dr+TZuUuv12\npRo0cHZswAClPvvMZzuI/Hn///5bqf/8R6nGjaXrTZoo9eyzSh07Fhj9uhDq+mCer4BhpCSrNY6/\nrEyprCzJtOywOfXrK3XrrUqtW+d//QBBfb367todHZErPQAUAFhe/n4YgMUa+mEq7HY7kpKSquTq\nWrpU3nfpYsNLL8lGQS2bdJQCvvwSeOEFecIEpPbZLbdIjq6LL9bQKc9o3Bh44glg1CjZrLBwIfDv\nf0s87m232fH992koLCxEZGRk6JRZISFL5VjJgoICREVFBTZWtDZKS+UXNCUF2LBB2po0kViuceNk\nGpsQTej4U9wJwEwAwwEMArAOQH61c8odSVJXrFYrli49ubZi165WbN6ciUaNNHSqtFR2K77wArB+\nvbQ1aeKsfdapk4ZO+ZYvv5Tl2x9/tANIQuVErRaLBampqcb4QxRCsLZjiHPkiOxcfOklYMcOaTvj\nDPlFvf9+oFUrvf0jpsRdu6Nj5isPwPryf58HZ718wpEjrjNNn3VWUeAdr6NHncbPsf33jDOAhAQx\nfq1bB7hD/uOKK+Sh+oIL0rBtGzPkE6KNffuA9HQJbv3rL2nr2lXiR0eNAowah0ZCEh0B91EADkBm\nvh6DLD36FN35PgKt/8MPwPr1Bgh8/eMP4Mknkd+2rTxl5udLpP/MmfL+3/8OiOMV6PvfoAFw5pmu\nnd9jxwJfZiXU/v8bBd3j1qVvt9thtVoRGxsLq9UKu90e2A5s3w7cdx/yO3QAnntOHK9LLgE++EDS\n1owZExDHK1R//tT3DB0zX8Mhy46HAFwM4FEAY6uflJycjKioKABATEwMYmNjK+r1OW5yTce//fZb\nrZ/7+ziQ+osWAbffno+iopvRqFEOjh+vuuyVkJDg//F/+SUwZw6ilywBiorwGwD06IHoJ54AhgxB\n/q5dwL59prz/juOysjK4YsuWCGzalI/ISHP+/zOC/vz585GdnV1hL7yBdse94y+++AL//e9/q8Sa\nOt6ff/75/tVfvBiYORPRWVmAUmJ3Bg9G9FNPAf36yfk7d5r6/lPfHHYnUEwAEFntuDpady0EA6Wl\nSj3+uHPzzsiRSi1enKGsVquKi4tTVqvV/zuOvv1WqRtuqFr7bMgQpVat8q+uAXG166tePYsCMlSX\nLkr99JPuHoYOYJ6vgBHw2o4nTij14YdK9evntDmNGil1771Kbd3qH01C6oC7dkfHzFcKxOHKBdAK\nMgtG3KCwELjtNsBul9KGU6YASUlAWJgNQ4f6Ob7IUf4nJQVYvVraGjWSmIqHH5aU+SGIqwz5N9+c\ngLQ0GzZulEpJ770HXH215o4S4kOKi10vtxcV+Xi5vagImDcPePFF4OefpS0qSpIWJiQA1epLEkI8\nwysPVHe+D3/qb92qVNeu8sDXqpWkrwmIflGRUnPmqCqJw6KilHrsMaV+/93/+m5gJP0jR5QaPlxu\nV1iYJPP3UTqzOunrQLc+mOcrYPTo0cPlzFfPnj19I3DwoFLPPafUmWc67U6HDkq9/LJShw5VOTUU\n7z/1jaPvrt1hhbog4pNPZMbr8GHgwguBDz8MQLaGv/5y1j5z1HBj7bM607Sp1IS88ELJDzZpkmyQ\nmDNHcoYRYkaUtyk7duyQorNz5sjuaQC46CJJrjd8OLPQk6CnzjkpypkBYC2A9yEB8/5Cef3LayLK\nymQTz5NPyvHw4cDrr8sfdr+xcycwdSowe7bkzQGA7t3F+N10E42fB3z4oVQ2OXIE6NVLjtu21d0r\n88E8X4Gjf//+WLly5UntcXFxWLFihfsX3LhRQhoWLABOnJC2wYPF7gwapClLNCGnxl27426qiUmQ\n7PRzACwFMB1AtJvXIG5w+LA4W08+KXbn+efFLvnN8dq0Seqbde4sT55HjojR+/xzSWh12210vDzk\n+uuBb76R2cq1a8UBy87W3StCPMcntR2VApYuFSerRw/g3Xel/bbbxOY4PqPjRUgFYwBMBjDAx9f1\nau1V99qvr/R//VWp88+XMIfISKXsdj/pl5UptWyZ69pn69e73W+z3H9/6e/fr9QVVzg3ar3xRmD1\n/Y1ufTDmK2B4Vdvx+HGl5s1Tqnt3p91p2lSp5GSl8vPd7kso3n/qG0ffXbvjbszXZACdIcuPX0Bq\nqcyC1GckXmK325GWlobi4mIcORKOrVsT8fffNnTrJktUXbv6WLC0FHj/fZnm37hR2po2lViu5GSg\nPJ8J8S2nnSYTiePGAdOmAXfeKXFg//ufJGwlJFjwqLbj4cMSy/Xyy8CuXdJ25pnO8j8tWwag54To\nxd153IGQFBGOuowLy9tzIYWyfUW5Ixk6uCqMDVjQp08qli2zoUULH4odOSKVoF9+mbXPNDNrFvDg\ng+IHW62SjoJ/e7yDMV8GZc8e2bgzYwZQUCBt554LPPKIhDqw/A8JYty1O+4aqEjIzNeGSm0OhyzP\nzWvVRsgZwZoKY1utVmRmZvpGZO9eqX02fXrV2mePPCKR4DR+WvjqK2DYMODPP+XH8fHH8jeJeAad\nL4OxbZskI5w3Dzh+XNouvVSC6K+5Bqino8odIb7F3wH3hajqeAEy4+VLx8trHGUAgkm/qMh3yQpP\n0v/5Z6lvFh0N/Pe/4nj985/O2mejR/vU8QrG+69T//LLJQC/e3cpU9e3L7BmTeD0fY1ufV3oHrcu\nfZe1HZWSJMxDhgDduslMe0kJcMMNsutk1Sr5zIeOV6jef+obQ99dGGFiAJQC8vJ8sGuoOt98A7zw\ngkylKCW7ha6/Xp44//lPz69LfE7HjsDXX8vqy4cfAldeCaxYAVxwge6eEVIzrsIlcjZtAqKiYHNk\nog8Pl8DG8eP9ELhKSHBi1L27ITP9r5T4Qi++aAeQBNnDIFgsFqSmptYevFqdsjJxtlJSxPkCxPg5\nyv9wPcvQlJQAN94oP8Izz5QlSf69cg8uOwaOGsMlAGS2bCkBjQ89JP+ZCTEx7todznxp5sknpVxZ\nw4Y2PP44kJ3trA14yl1DlXFV+6xlS2ftMxq/oKBhQ8njdu21QFaWpFhbtUpmxggxGsWOBMzVKLJY\nJGegXzNBE0J8jVf5NnTn+6ir/nPPOVNqLVrkodiBA0o9+2yV2md5bdsqNXWqUocPe3hR7wiW+29k\n/SNHlOrXT36kFstJ5TP9ru8NuvXBPF/+JzdXqYQE1cNFXUcAqkePHoHrSzkhdf+pbzh9d+0OZ740\nMXUq8K9/SRjWW2/Jbje3cFX7rEcPWcPs3Rvo0sXnfSaBo2lTwG4HBgwA1q+XGbCVKyVHGCHaWLdO\nQhoWLpQQhxoIYzZ6QmrFqL8h5Y6kOZkxQ9JpAbIJ6O673fjyhg1i/N5/31n7LD5enK6BA1mCw2T8\n+SfQvz+wZQvQsyfwxRdAZKTuXhkbxnz5GKUkK3BKivwHBCQb8K23ov9PP2HlunUnfcXj2o6EBCn+\nTjVBvOTNN52O1yuv1NHxqlz7rGdPycQJOGufff45i86alNNOA5Ytk4nM9esBm8050UmIXykpkTjS\n7t2Bq64Sx6t5c9m4k5sLvPUWwlu3dvlVr3ZpExICmNL50p3voyb9BQuczlZKimwEqpWSEuDtt2U5\n0WqVCOymTaUuTW6ufHbRRXXWDxTU963+WWfJj759e0lHcf31sr8iUPruoltfF7rH7TP9Q4dk407n\nzrJLevNm+U/4v/8BO3dKwtT27QEAl1xyCRpUq4nVoEEDxMbG+qYvbmCa+0/9oNR3F8Z8BYiPPpKJ\nqrIy4D//kaTyNeKq9lmbNlL+Z+xY1p8JQTp2BJYvBy67TByxm24CFi+W3ZGE+ITff3eW/ykslLbz\nzhNjNWKEpKypxrfffovS0tIqbaWlpcjOzg5EjwkJWoy6TmWq2IvMTOC666SyxqRJkmTe5Qqhq9pn\nMTHO2mcujB8JLTZvlhiwgweBm28G3nkHqF9fd6+MBWO+3GTrVmf5n5ISabv8cmDiRFlurCULff/+\n/bFy5cqT2hnzRUIN5vkyGF9+KRU1jh8HkpJqcLxY+4zUkQsukBC/AQNkGbtpU2D2bP4XIW6ilCSQ\nS0kBMjKkrV49yfA7YQLQp0+dLhNewwMhY74IqR1Tmmzda78O/a+/lmSZRUVSWvHllys5Xn6sfWaU\n8VPfP/TqJWkoGjcGXntNQgArT9iYffxGRfe466R/4oSsV8fGAnFx4nhFRMguoJ9/lhQSdXS8ACAx\nMREWi6VKm8ViQUJCgpu9956guP/UN62+u3Dmy0+sXQtcfbXsTLv9dmD69HLH68QJCQBLSQH+v717\nj4+yuvM4/kEUwRUSAnWlYJtM1LJeWkOwunYVDQFU1m1FSNd212uDdLtctIQEtK1VWwIoSKBqE6u2\nVcQQ2lpNdSFDpd5ogURXrLxacmldEV40YYaqEBGe/eOXyY2EXGbmeebyfb9eeTHzZDK/M8PJmZPn\nnOf3C+2LUO0z6aNLL7UakNdcYyvVQ4fCffd53SqJWQcPwhNPwPLlsGuXHRsxwkr/fOtb8KlP9etp\nQxU4Vq1aRSAQIDU1tW+VOUSSlFd7vsYB2S23y4Fgp+/H5d6LyspKSkpKaGxs5s03T+aTT+YwY8ZU\n1qyBEw8ftGyqDzwAf/6z/UBaWlvts9NO87bxEpeefdYS9B45YkvaCxd63SLvac9XO3/7Gzz0EKxa\nZbfBrmK84w64+WY45RRv2yeSIPo67ng1+SoH8oBQXvf1nb4fd4NgZWUlc+fOpba2rTD2KadksuaR\ne/lywy4b/Pbts2+kp9vgd8stqn0mYVuzxq7HcBw7C+bBik9M0eQLS0WzfLmtSx88aMcuvND2c02b\npqs0RCIsjHHHNdOBgh4eE1aNJS9qPE2ePLnLGmdTTjihteaiM26c46xd6ziHD0e1LV7XuFJ89+OX\nlrZ1s6VL3Y/fntfvP8lc23HrVsfJy3Oc9uPO1Vc7zm9/6zhHj0Y/vocUX/G91Ndxx4s9X+Nb/p0I\nTAKKPGhDxB061Nz18aNH4cor7S/OK65QFnqJivx82194++1QWGhJySdP9rpV4grHgRdesASCv/+9\nHTvpJEuQOn8+nHuut+0TkWN4MRMoxmaIC7FlRx+wrNNjWiaSccJxyBg1gYa9Lx/zrSmXXMKLr77q\nQaMkGd11F/zgB7aXevt2S86abJJm2fHjj23N+f77rfgnwLBhcNttltdm9Ghv2yeSROIhz1dtu9tB\n4MKuHjRv3jxSU1MBGDt2LBdffDHp6elA2yWlnt8fPRrWruXhhS/RsPcmYHeHl5eZmcnsRYtip726\nn/D377kHXnmlgc2bYfr0dF5+GfbsiZ32ReP+2rVr2bJlS+t4EY64GHeGD4fSUhoeeAD27iUdYPRo\nGv7zP+H660n//Oddbc/bb79NSUkJwWCQQYMGUVhYyNSpU2Pn/dJ93Y/C/UiOO27JwM5+ge3/6qrQ\nTlhrr1Ff+z1wwHEeeMBxxoxx/shY51QOOOA43xh/nzMlJ8e56KKLnClTpjjPP/98dNvRDa/XvhXf\n2/g1NfVOerpt95k50/34Xr9+EnXP17vvOs78+Y4zdGjbfq7zznOcJ55wnOZmT973559/3snMzOyw\nzzUzM9OTsc/rfqf4yR2/r+OOF2e+6rHTQ9dh+7/iZ8/X++/DypWttc8OMJRrB23mg4+Hcn3eEUrX\n3smAAXfS0NDQOjsWcVtqquXRvOQSKC21fJo33+x1q6TfduywpcU1a9rK/1xxhe0jvfJKT/eRlpSU\ndLjCG6C2tpZVq1Yp15fIcXj3W3t8LRPJGBGqffbkk63lf5xLL+O6T9byy9dHcf758PrryhohseWx\nx+DWWy2B+WuvQVaW1y1yR0Ls+XIceOklS8b8wgt2rH35n/Hjj/vjblFtRxHT13EnIcsLRUSo9tk1\n18A559gn2eHDltFyyxaWXL2ZX74+ipQU+MUvNPGS2HPLLXYV5KFD1m2bmrxukfTok0+gvNxK/OTk\n2MRryBBLxvznP1tBzxiZeAEcOHCgT8dFxCTk5Cu0Ma5fQrXP/vmf4bLL2mqfzZpltc8qKth44CLu\nvNMe/uSTcOaZEYwfAYqv+CElJZCdDfX1Vubq6FF34yeTsF73hx/C6tVWXuyrX7X6ZCNHwve/D3/9\nq33P54te/Agb4MFSqNevX/GTO35fqbZjyMGD8NOfWvmfUO2ztLS22mct5X8aGuD66+1D7Hvfg3/9\nV++aLNKTwYPtb4lx4+A3v7H6j9/9rtetklb79tnE6kc/gsZGO5aZCd/+Ntx4Y8yX/xk2bFiXx4cO\nHepyS0Tii/Z8NTbawLd6dVv5n4yMttpn7dYTDx6Ef/kXqK62otnPPWfbMERi3YYNtjcbbBIWup2I\n4mLP165d9ofeE0/YujDYUuOCBfCVr8RN+Z8pU6awYcOGLo+/+OKLHrRIxBva89Vb9fVWBO+MM+wU\n1r59tj7zzDPwpz/ZGa92Ey/Hgf/6L5t4+Xy23KiJl8SLyZMtAbrjwNe+Zt1fPPD739um+bPPtqum\nDx2y0+ebN8OWLbY5L04mXgBz5szh9NNP73Ds9NNPZ3ayFxgV6UFCTh+Ou/a7bZvtqTjzTDvbdfAg\nXHUVbNoEW7dCXh6ceOxq7I9/bH+kDhkCv/wlDB/ez/guUHzF78qiRfY5v3+/ff6HTri4FT/Rdfu6\njx61vaOXXWZ5P9avtzHm5pstM/1zz9n3wtwnlazve4jXr1/xkzt+XyXk5OsYodpnOTlw4YV2NdHA\ngban4q23bB3mOHUXt2yBOXPsdlkZtCSQFokrJ5wAP/uZnbmtrraTuxJFzc12lfR559lV0y+/DCkp\nVnyzocG+d845XrcyLCUlJezZs6fDsT179rBq1SqPWiQSHxJ7z9fHH8PTT1uOrh077NjQoW21z8aM\n6fEp9u61zcq7d9sEbOXK8Jsl4qU33rCLeQ8dsj8mvvENr1sUWZ7v+QoE7FT5ypWWmBlsrLn9dnuz\nu9mkHo+U50vExENtx+g7cMBSez/4ILz3nh379Kdh3jyYOdP++uyFw4dthXL3brj0UpvDicS7Cy6w\nucGNN9rZrwsuiKnUUfHr3XdtzCkthQ8+sGPnn29JUf/93+Gkk7xtXxScfPLJXR4fPHiwyy0RiS+J\ntez43nuwYAENo0fbgPfee3DuufD447bDuKCg1xMvsNWBzZth1Chbqezt2On12rPiK35PbrjBUtc1\nN9v+r1CWA7fiJ5T//V+44QYaMjJg+XKbeOXkwIsvwptvWoI1FyZeXrzvc+bMITMzs8OxzMxMTzbc\ne93vFD+54/dVYpz5evttOy311FNttc8uv9wmW1dd1a+NrGvXwooVNmZWVECnC3o8kZaWxv79+71u\nhsSI4cOH0xRG2voHH7S9X3/4A3z961BZGVcX2nnLcewinWXL4H/+x44NGGBnuAoKbK9CEgjVb1y1\nahWBQIDU1FRmz56tuo4iPYjfPV+OY6elli2zDfNgO4qvu84Gvwsv7HPQyspKSkpKaGxspqbmZI4e\nncPq1VP51rf68QqiYMCAAcRM7TnxXCT6w7vv2jzhb3+D73zH0lHEu6ju+frkE/trbNkym7mCJUK9\n9Vbb05WR0Y+wIhLvEn/P15EjVkxx2TJLDQGW/+GWW2zw63QKvLcqKyuZO3cutbW1rcdOPbWWz34W\nQH/FSWI64ww7yzt5Mtx7r+X5VNWGLnz4IfzkJ3Y6PLS8cdpplivwm9+EESM8bZ6IxJf42fP10Ufw\n0EPwuc9ZLq6tW6322d13t9U+a5l49Wftt6SkpMPEC+CDD2pZvbrvl0zH29qzJJa+9r+JE63sENj2\npLo6d+PHtL177ZTgGWfYFdINDXDWWXbFQkMD3HVX68TL69et+Iqv+PEj9s987dtn5X9+9CNbG4Go\n1D5rbm7u8vihaGWiFIkhhYWWfP3ZZ2HaNHj9dTuhnLT+9Ccr//PTn9pVCWD5OQoK4N/+TZvjRCQs\nsbvna9cuu3Lo8cctCz3YPq4FC+DaayM++E2YMIXf/S62a5Rpz5e0F+n+EAxayoldu+zXbMmSiD21\nq8La8/Xaa7al4Ve/sn2lYJOtBQvgS1+KYCtFJJEkTm3Hs8+2ZcaDB2HqVHjppba6aBGeeDkOfPTR\nHCA2LpmWjgKBANnZ2WzatMnrpiS0lJS2mqX3329XQSadSy6x+mEnnWQJUd95x04HauIlIhEUu5Ov\ngQOt9tmOHVYXbcKEXqeM6Ova789/Dtu2TeWUU1Zy+eVTmDBhAlOmTGHlypX9umQ63taeY11qaioj\nRowgJycn7OcKBoMRaFFsC6f/XXQR3HGHlSO8+ea2FTe34nsuNRUWLrT9XGVlMHZsr3/U69et+Iqv\n+PEjdvd81dfD6NFRD7N7t+2jBXjooanceGMcX9kYZmHeDmJseTOcfFbtlZaWUlBQEJHnSlT33AO/\n/jX88Y92BWRoM35S+OtfrQSZiEgUxe6ZrzAmXunp6b16nONYmcdAwFY2b7ih3yH7FT+RBINB/H4/\nRUVFgC0Vzpo1KyLPXVVVRW5uLsFgkOrqavLy8gCoqalpjen3+1uP91d9fT1lZWWUlZVRU1NDTU0N\nZWVlkXgJrgq3/w0ZYjWfBwyA4uK2dFZuxfdUGBMvr1+34iu+4scPr898FQNFXgV/8klb0UxJsSvH\nI3niyBMenq2qq6vD5/NR15KnoKqqivGdCgYGg0HKy8u7fY7c3FwyukhSuXHjRkaOHElTUxPjxo1j\nyZIlBINBfD4fWVlZFBYWUlxcjM/nC/t1+Hw+1q1bR35+PoFAgMWLF5Ofnx/288abL33JUliVlNjy\n49atMGiQ160SEUkMXk43crHJV1clfXvONH0cDQ0NPc6C338fzjnHzno9/jjcdFO/w/Urfn/E+tWO\nS5cuZfz48eTk5JCXl8ejjz7KsGHDwn7e8ePHs2jRImpra49ZMqyrq2Pp0qU88sgjXf5s5wnfxo0b\nmTRpUuv9zhO+wsJCrr/+ei644AIqKipoaGhg/vz5Yb+GaOiuP0Sq/334IXz+85b36+674Xvf693P\nRav/91ZUM9wfh9evW/EVX/G9ix8vGe5TgEYgMht5+qj9cuPVV1u6MAlfVVUVCxYsAGzZsfPEqz9n\nvgKBAGlpaUybNo28vDzq6+sBq3PpOA7r168nOzsbsGXIrKysDj+fkpLS4cxVIBA47pksv9/PkpYc\nC+Xl5a1LkJ2fNxn8wz9YUvcrrrB9X9dea5MxEREJj1eTr1xgfbSevKfZ71NPwXPP2XJjaWnklxvj\nbe05UmbMmIHf76e2tpbMLso8dZ4I9cb27dtb93JNmjSpdXmztLSU1NRUfD4fTU1N+P3+Y5Y5+6N9\nu30+H9u2bYvI87opkv3v8sutes7DD1sFry1b4MQeRo1k7f9ev27FV3zFjx9eLDtmAQGgHtgATO7i\nMWGd/j+e99+Hc8+F/fsjv9wYbbG87Oj3+6mrqyM/P5+ioiJmzZoVk78MZWVlCbOHy63+8Pe/w/nn\nw1/+Aj/8oWViiGVeLTuKSPKKh2XH0K7ocS23c4BjsmfOmzeP1NRUAMaOHcvFF1/c+mEeyufR3f1X\nXnmFMWPGHPP9z342ndtug/37G5gwAW68sXfP19f73cUP934sC212X79+PZMnT47JiReQMBOv9qLd\n/xobG7j3XrjhhnTuvhvGj2/grLPc7//d3V+7di1btmxpHS/CEY1xx637iq/4ih8/444XZ77a24aL\nG+6fegr+4z9suXHHDhgzpt8h+hU/XLF85kvcF+0N953l58Ojj1oi1ldf7b7QRLTi95Y23Cu+4iu+\n2/o67ng5+ZoJLAZmcOyZr4if/m+/3PjYY3b5fLzR5Evac7s/BINw3nnwf/9n5Q9j9CJQLTuKiOvi\nafJ1PBEdBB0HvvIVy9p95ZXwm9/EZ04vTb6kPS/6wwsv2BXCgwfDm29aCdZYo8mXiLgtcQprAsBk\ncgAAC3dJREFUhyG0Nhvy9NM28Ro2zMq1RXvi1Tm+iJui2f+uuspSsxw6ZFc/HjnibvxY5vXrVnzF\nV/z4kZCTr/b27LFM3QArVkRvn5dIslixAkaNsn1fq1d73RoRkfgTq4tvETn97ziWGPLZZ2HKFFsy\nicflxhAtO0p7XvaHX/8avvxlqwP51lvQRVo3z2jZUUTcpj1f7Tz9NHzta7bcuGMHnHFGBFrmIU2+\neicYDLJt2zaqq6sZN24cEydO9LpJUeF1f/j612HNGpgwATZtghNi5Dy6Jl8i4jbt+cLWfvfsgf/+\nb7u/fLm7E694W3tONOXl5WRmZlJQUNBaKiiZuNX/SkrgtNNg82ZoX1ozWfu/169b8RVf8eNHQk6+\nHMdKojQ1weTJtjFYkkd+fj7p6elUV1d3WeaorwKBANnZ2WzadEwu4KQ2YgQ89JDdXrAA4mzsExHx\nTEItO1ZWVlJSUsK77zbzzjsnM2TIHHbunMpnPhOFFnrA62WmeFNUVMSiRYuOKfDdXjAYJCUlpcfn\nmjx5Mhs2bAi7Tb2N1xux0h/y8mDdOsjNhQ0bvN9XqWVHEXFb0i47VlZWMnfuXDZs2MA772wGNnDq\nqXN5661Kr5vmmgEDIvcV7yoqKli4cCGNjY3HfVxpaWmvnq+pqSkSzep1vHiyejWMHAlVVfCTn3jd\nGhGR2Jcwk6+SkhJqa2s7HNu3r5ZVq1a53pZ4W3uOhGAwiN/vp6ioCLClulmzZkXkuevq6igrK6Om\npoa8vDyCwSAANTU1rTH9fj95eXmATbyKioqYMWNGRCY7VVVV5ObmEgwGqa6ubo3TXfz+qq+vp6ys\nrPW11tTUUFZW1ufncbv/nXYahH7Nvv1teP11d+PHCq9/7xVf8RU/fnhRWDsqmpubuzx+6NAhl1vi\nHS9XTOrq6vD5fNTV1QE2YRk/vmPZzmAwSHl5ebfPkZubS0ZGxjHHZ82a1brkFwgESElJIRgM4vP5\nyMrKorCwkOLi4tbi3tOnT2f69OmRemls3LiRkSNH0tTUxLhx41iyZMlx44fD5/Oxbt068vPzCQQC\nLF68OC6KgX/1q7B2raV1WbgQfvvbxDiDKiISDQkz+Ro06OQujw8ePNjllrRVPU8mWVlZLF26tPVs\nV3l5OY8++miHx6SkpPR5IlFRUdG6aT4QCLRWkA/tm6qrq2ud5HU1ceu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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Na naslednjih treh grafih smo prilagodili najbolj\u0161o premico podatkom z napakami in izra\u010dunali $\\chi^2/N$. Na grafu (a) so napake tako majhne, da podatkov s premico ne moremo pravilno opisati. To nam potrdi vrednost $\\chi^2/N$, ki mo\u010dno presega $1+\\sqrt{2/N}$. Na grafu (c) je vrednost $\\chi^2/N$ premajhna, kar nakazuje, da smo mogo\u010de precenili napake meritev. Na grafu (b) je $\\chi^2/N$ v mejah med $1\\pm\\sqrt{2/N}$. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "def chi2(x, y, e, f):\n", " return sum(((y - f) / e) ** 2); \n", "\n", "fig, ((axa, axb, axc)) = subplots(3, 1, figsize=(5, 9), sharex='col', sharey='row')\n", "axa.set_xlim([3, 20])\n", "axa.set_ylim([2, 13])\n", "axb.set_ylim([2, 13])\n", "axc.set_ylim([2, 13])\n", "axa.set_ylabel(r'$y$')\n", "axb.set_ylabel(r'$y$')\n", "axc.set_ylabel(r'$y$')\n", "axc.set_xlabel(r'$x$')\n", "\n", "x=linspace(3, 20, 18)\n", "\n", "e1=[0.5 for i in x1]\n", "fit1=sm.WLS(y1, sm.add_constant(x1, prepend=True), [i ** -2 for i in e1]).fit()\n", "f1=lambda x: fit1.params[0] + fit1.params[1] * x\n", "axa.plot(x, f1(x), 'r');\n", "axa.errorbar(x1, y1, yerr=e1, fmt='ko');\n", "axa.grid(alpha=0.5)\n", "axa.annotate('(a)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "h1=chi2(x1, y1, e1, f1(x1)) / len(x1)\n", "axa.annotate(r'$\\chi^2/N=' + '%.2f' % h1 + r'$', xy=(0.4, 0.1), xycoords='axes fraction')\n", "\n", "e2=[1.0 for i in x1]\n", "fit2=sm.WLS(y1, sm.add_constant(x1, prepend=True), [i ** -2 for i in e2]).fit()\n", "f2=lambda x: fit2.params[0] + fit2.params[1] * x\n", "axb.plot(x, f2(x), 'r');\n", "axb.errorbar(x1, y1, yerr=e2, fmt='ko');\n", "axb.grid(alpha=0.5)\n", "axb.annotate('(b)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "h2=chi2(x1, y1, e2, f2(x1)) / len(x1)\n", "axb.annotate(r'$\\chi^2/N=' + '%.2f' % h2 + r'$ ($\\sqrt{2/N}=0.43$)', xy=(0.4, 0.1), xycoords='axes fraction')\n", "\n", "e3=[2.0 for i in x1]\n", "fit3=sm.WLS(y1, sm.add_constant(x1, prepend=True), [i ** -2 for i in e3]).fit()\n", "f3=lambda x: fit3.params[0] + fit3.params[1] * x\n", "axc.plot(x, f3(x), 'r');\n", "axc.errorbar(x1, y1, yerr=e3, fmt='ko');\n", "axc.grid(alpha=0.5)\n", "axc.annotate('(c)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "h3=chi2(x1, y1, e3, f2(x1)) / len(x1)\n", "axc.annotate(r'$\\chi^2/N=' + '%.2f' % h3 + r'$', xy=(0.4, 0.1), xycoords='axes fraction')\n", "\n", "subplots_adjust(hspace=0.075, wspace=0.05)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ENJCCHYwaNQqv1xvUYATD6/Uyso+6Q2lpaSQnJ+N2u7nggguCnhNsBBlIsBGk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\n", "text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Poglejmo si \u0161e, kako poi\u0161\u010demo najbolj\u0161o eksponentno funkcijo $y=Ae^{-\\lambda x}$ za podatke na grafu (a) spodaj. Vrednosti $y_i$ najprej logaritmiramo in poi\u0161\u010demo najbolj\u0161o premico $\\ln{y}=\\ln(A)-\\lambda x,$ graf (b). Iz koeficientov te premice preberemo $A$ in $\\lambda$ in nari\u0161emo ustrezno eksponentno funkcijo (c). " ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ((axa, axb, axc)) = subplots(3, 1, figsize=(5, 9), sharex='col', sharey='row')\n", "axa.set_xlim([0, 10])\n", "axa.set_ylim([0, 200])\n", "axb.set_ylim([1, 6])\n", "axc.set_ylim([0, 200])\n", "axa.set_ylabel(r'$y$')\n", "axb.set_ylabel(r'$\\ln{y}$')\n", "axc.set_ylabel(r'$y$')\n", "axc.set_xlabel(r'$x$')\n", "\n", "N=50\n", "x=linspace(0, 10, N)\n", "y=exp(log(200.0 * exp(-0.3 * x)) + np.random.normal(0, 0.05, N))\n", "\n", "axa.plot(x, y, 'ko')\n", "axa.legend(['podatki'])\n", "axa.annotate('(a)', xy=(0.03, 0.05), xycoords='axes fraction')\n", "\n", "axb.plot(x, log(y), 'ko')\n", "fit=sm.OLS(log(y), sm.add_constant(x, prepend=True)).fit()\n", "f=lambda x: fit.params[0] + fit.params[1] * x\n", "axb.plot(x, f(x), 'r')\n", "axb.legend(['podatki', r'$\\ln{y}=\\ln{A}-\\lambda x$'])\n", "axb.annotate('(b)', xy=(0.03, 0.05), xycoords='axes fraction')\n", "\n", "axc.plot(x, y, 'ko')\n", "axc.plot(x, exp(f(x)), 'r')\n", "axc.legend(['podatki', r'$y=Ae^{-\\lambda x}$'])\n", "axc.annotate('(c)', xy=(0.03, 0.05), xycoords='axes fraction')\n", "axc.annotate(r'$A=' + '%.3g' % exp(fit.params[0]) + r'$', xy=(0.75, 0.5), xycoords='axes fraction')\n", "axc.annotate(r'$\\lambda=' + '%.3g' % -fit.params[1] + r'$', xy=(0.75, 0.4), xycoords='axes fraction')\n", "\n", "subplots_adjust(hspace=0.075, wspace=0.05)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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WywXyhYWFlkEzWh5QQOtCc5iCpuSMaF35aFs0jx49OqXbfvDgQQCeffbZUJnWheYWdc8l\n50XbmVRUVMTIyMiM7qEufuZS91wkRrEmFLESbV2osjBlHwVNEWJLKGIl2rrQgoICjXVmGQVNkSis\nJo4WLVoERI5pOhwObr755iljmg6HgxtuuCHq3vj9+/crkGYgBU2RKKJ1263KrNaFBieZrM482rJl\nS8RCe00aZQ5NBIkkUHV1Nfv27ZvRtU6nMxRo1QJNHk0EiaSRaHvjrUy3Mwms14ZK8qmlKZJAVsuZ\nYj08zuoAuuA4qtW4qCaeYqOWpkgasRoXveGGGywnjaLtTHriiScYHx+PKIs2LqpF9omnlqZIClgd\n3dHe3m65N760tHRK0IxmukX2sYyX5lJrVS1NkQxgtS4UrA+PKyoqmnHQnC758kzHS9/0pjeptToN\ntTRF0ohVCxSY87hoLOOl0e6drVtC1dIUyWDRWqAws3HRaIvsYxkvtQqYMP2W0Fzqzmdd0PR6vYyO\njlJTUzPtdT09PTQ0NCSpViJzYxVMrRbTT7fI3iqTUyyibQmFqS1h7XpKD8ZMbNmyZUbXeb1eo7u7\ne0bXimS63t5ew+FwGJjHZhuA4XA4jIqKioiy4FdhYeGUa+++++4536O3t9fo7e016uvrjRUrVhj1\n9fVGb29vSn83gfrNWFa1NF0uF8uWLZvRteXl5ezYsUOtTckJ020JtUqLd/PNN/PLX/5yRltCS0tL\nLX+m1XlMd91115Qx1ExbwJ9VQbO7u5vt27dHlLlcLsrKynjooYdYt24d5eXlodfKysoYHR2NKBPJ\nVjMdLw128yeLJVVeNNHWnEYLptG6+NHGUHNpbHUmztnMXrdu3ZSyxsZGwzAMY3h4eMrr3d3dhsvl\nik8bXyTL1dfXW3bDKyoqpnTbJ3fNg1+lpaUxlccyTBCtPFr3PzhMQIzd86xactTU1MTOnTsjykZH\nRxkeHmZsbIyhoaGIlqjb7cbn86mLLjID0TLcb9u2DZjZ7H60bPjxWMA/3bKqhQsXnmvyKjeXHNls\ntojnLpcr1GUfHR1laGgoojvu8/koKSlJRVVFMs50xyWHvx5kNYsP1mOo8VjAH638d7/7XUSg9ng8\nFBUVTRmfnamsCpolJSX4/X6Ki4sB818eIPQLGxsbiwiaBw4c4FOf+lRqKiuSgaYbF43l2rks4I+W\nJT9a+eT1pdNNXs1EVnXPR0ZG8Hq9M+5ut7a2snnz5njUTUTmaPJuqFgX8FuVFxQUWC7KtxgOyM3u\neUVFBYODgzO61u128/73vz/BNRKRmZrrAn6r8sOHD1uOoS5ZsgSbzTarLnpWtTSD3G73tDuC/H4/\ng4OD59w1JCKZbSaTVz/5yU8ghliYTkGzGfACdqDL4vUZB00RkSCrJCjhLdpYE3akS9CsBGqArUBw\nQLJn0jVZHTQHBgaorq5OdTUSRp8vc2XzZ4PYg+a8xFUlJjWYrUwC3+tSWJeUGBgYSHUVEkqfL3Nl\n82ebjXQJmg7AF3jsB2zTXCsikjLpEjRFRDJCuoxp3onZLe/BHN9cC6yfdM0hzBapiEg8eYArZ3px\nuqzTdAG1gcd2YOrpUjF8KBGRRJmf6goEPAu8GSgEXg38Z2qrIyIiIiIiIiIiIiIikvnSZckRmEuN\ngqei7cRc5C4iIlEEz6lo4Oz+cxERsbAac4G7iEhaS5dtlFVAGWbiDqVSF5G0lS5BE8xjNN3AAdTq\nFJE0lS7bKMNzzvuB5ZMvcDgcxmxPjxMRmUZMe8/TpaXp4mwyjhLgkckXeDweDMPI2q+777475XXQ\n59Pny7XPZhgGxJgIKF2C5ihmtG/AHN/8UmqrIyJiLV2653D2XKDJx1yIiKSNdGlp5rxsPoMF9Pky\nWTZ/ttlIpx1B52IExh9EROIm1oPV0ql7LpI0NpuN8fHxVFdDkqi0tJSxsbE530ctTclJeXl56O8p\nt0T7b56pR/iKiGQEBU0RkRgoaIqIxEBBUySLeL1e6uvrGRkZifm9LpeLK6+03k0YrTwXKWiKhOnr\n68PpdFJdXY3T6aSvry8l95gtu91OZWXljGaJu7q6Ip7X1tZSUlJiee2hQ4fiUr9soCVHIgF9fX3c\ncccdhCeGCT5etWpV0u6RDD6fjx07dtDc3HzOa0dHRxkaGmL16tVJqFn6U0tTJKC9vZ3JmbQ8Hg8d\nHR1Ju4fL5cJms/Hwww8zMjJCa2sro6Ojode7urpwu9243W56enosy71e75R7Tr6X1+vF5/PR09Nj\n2ZV3uVxUVVXx8MMPY7PZaG1t5ejRozP+PWQztTRFAk6cOGFZPjExkbR71NbWYrfbWblyJWB2t2tq\nahgcHKS7uxuAmpoaAFpbW7Hb7Rw5cgSfzxcq7+/vj7hnZ2cnO3eap8m0tbWxfft2KisrKSkpoaFh\n6skyfr8fv9/P4OBgqMxut8+o/rlALU2RgPz8fMvygoKCpN4jXHFxcajl6HK5IoJXWVkZg4ODU8on\na2tro6enJyIIRmOz2XC5XOzYsWNW9c0FCpoiAS0tLTgckakVHQ4HGzZsSOo9wvl8vtD9li1bFtH1\n9ng8LF++nOXLl3PgwIGI9wS5XC7a2tpoaGigtrYWINRFt9lsALjd7oif2dDQQGNjI1u2bIko1w4q\nk7rnIgHBiZqOjg4mJiYoKChgw4YNMU3gxOMeALt376a8vByXy8WuXbsAaG5uZuvWrbjdbnw+H1VV\nVSxdupSlS5fi9Xpxu93YbDa8Xi+dnZ1UVVVRVlYGEBq3HBsbY3R0lPLychobG+nq6gq1UoeHhxkc\nHGT37t00NTVRWlrKvHnzqKmpwev1smvXLm655ZaYPkc20t5zyUnpvPe8qqpqRl1piU1O7j1P9po3\nkWQbHh7G6/Wye/fuVFdFosioliaY40Pbtm0DzOUdJ06cID8/n5aWlrRaByfpLZ1bmpIY8WppZtSY\n5nZgp8fDpk9/mvEXXkj7BcQikn0yqqUZ/DficF4e3YbBTuC/gTOBcqfTyZ49e1JTO8koamnmnpwc\n0/ws8EfgVYbBrcAA8CTQDtwEnDh+PKX7fkUk+2VUSxPAYbez7LzzuO4Pf6CJyBPeD593Hv91wQV0\n+f3sD7zB4XBw8803s3//fo1/SohamrknXi3NdAqaO4B1mGefuwD/pNcNp9MZWiQcTIpQCTQBH1yw\ngMtOnw5d/BdgF7ATOFhQwPGwbWzBySQFztyloJl7sjFojgFHgI2A1XqLiHWafX19kQuIb7+dH/7L\nv3DVyAhNwOVhb/xfzOC5EwiuftP4Z25T0Mw98Qqa6WRq5oBIxrnU19cbgJEHxvVg3AvGX8wJpNCX\nB4zNYDRXVhq9P/qRUV9fb6xYscKor683ent7DcMwjN7eXstyyR4z+XtKhaGhIcPhcKS6GnOux/j4\nuLFu3bo41sgwOjs7jc7Ozlm/P9p/cwJDf5noTqAG2Bzl9XP+Unp7ew2HwxH8JRiAcUFBgXEjGNvA\neGpSAH1iwQLj82BcF7jW4XAYd99995R7OBwOBc4sM5O/p1Spq6sz/H5/qqsxp3q0tbUlJPjP5Z7R\n/psTY9BMp9nzrYAb8ADnzoxqYdWqVWzbtg2n08mKFStwOp3cuXEjzzkc3AFcBrwV+I+iIp5fsIAr\nTp/mU8Cvgd8Df+/x4L7vvjnnVJQMl5cXv68cNDIyQl1d3ZS8nvFQW1s7JcFIsqXL4va1mOOZPcA4\nUGV10aZNm0KPq6urqa6unnLNqlWrpkzwLF++PGL807ZhA01btmD87Gc0YY4LXA3cBdzl9/M4Z8dA\nfxe4Ryw5FUXmyjAMXC4X69evD6Vp27VrF21tbRQXF4euC+a97O/vZ/Pmzfh8PlpbW9m+fXtS6xFu\ncHCQ5ubmqEdnzMW6dev44he/GModCmaQHhsbo7+/n7q6Onbs2BHKH2plYGCAgYGBWdchXYLmEcwZ\nc4By4BGri8KDZiysAml7ezt7Mdd6bgBWYM7Cr87L4/WGwSZgE/AYZvB8+uWXZ/WzJQOlwQRRXl5e\nKCGxw+FgyZIloSxE4QHD6/Vit9sjcm5WVUW2Ofx+/7RBpLa2lvLy8jnVI6irq4umpibATFwczKgU\nL4ZhMDw8jN/vp7i4GL/fj91up6Kigo0bN7J58+ZzJkye3OC65557YqpDugTNHswu+Rjm+ELCsxW0\ntLTg8XjweDy8DDwM/K/DwXMf+ADer3+dm555hvcBbwh88fOfw3XXQVOT+XXVVYA5i6898JJIwbyX\nEJkrE6CiooItW7awfv16AHbu3MkDDzwQcU1xcfGMzgKaSz3ADOAejweXyxVRZhU0u7q6LO8BsHbt\nWstWbLBbvm7dOnbu3Elzc3PoOq/XG/rHIp5B2kq6BE2ArnNfEj/T5T3su+EGOjo6+M6xY7zppZdY\nZ7OxaP9+zjt4EA4ehE9/Gr/DwTM33cSXfvpTBv7859B9w8dDFUxltoyw1m7wsRGlBexyufjEJz4B\nmMGsqKgo4vW5tDRjqYfb7Wbz5rPzuP39/Xi9XssWaaxB3OVyMTo6SnNzM1VVVdTU1NDc3Izf78cw\nDHp6eli2bBlgdtcrKipiun+2mvWs2Vz19vYar7PbjVVgfBMM/6RZ+EfA+DgYVwRm2ysqKjQDn+ZS\n+fc0neBSn66uLmN4eDj02OfzGXV1dcb69esNn88X8Z7Ozk7D5XIZO3bsMNavX5/0egwNDRl1dXVG\nV1dX6P1er9eoq6sz6uvrp9Q3Vl6v19i4cWNEWVNTk+H1eo0tW7YYnZ2dRnd3d+j3EO3nRftvToyz\n55k0vRf4fMnndDrZu3dv6Hk+UA98+PzzefvJk7wi7NpfAT8qLORbx4/zF4v7aEF9esiWxe3B0yeb\nm5tpbW1l/fr1LFmyJNXVSks5mRouVSafMHgC+BHw8wsv5PjJk7wDaATeBVwPXH/8OJ8D/gdzEqkb\neArNwEv8BSc9enp6qK+vV8BMAgXNGYh2wuCSJUs4arPxPY+H7wGFwEcuvpi/PXGCm3w+bgRuBO7D\nTGH36HPPwTPPwCWXJK3ukt3Ky8sTPvEhkdQ9n4G+vr5QgpCg8AzykyeTAFo3bOD1o6M0AX+DGVAB\nc8HzW99qzsA3NMDFFyf1s4gpW7rnMnPZmLDjXFIWNMEiQcg5ThgMv750wQL+pbKSij/9CX78Ywh2\n9+fNgxUrYM0aeN/7YOHCKffQDHxiKGjmHgXNDNTX18cD995L1dNPs/LIEa4fH2deMJ3d/PnwtreZ\nLdD3vpe+X/0qautWgXPuFDRzj4JmhrHq4i9dsoR/e+97efV//ze2oSEWBD7fmXnzGC4t5f4jR/g+\n5r7SIM3Ax4eCZu5R0Mwwk5ctBVVUVHD06FHGPB7ejbmVsxY4L/D6KaAfcxb++8DSFSu488471W2f\nI5vNxvj4+LkvlKxRWlrK2NjYlHItOUpTk5ctBT3xxBOh/3n/PfBlAz584YX8zUsvsRJzIulvgJPA\nL0dG+OFHPsL+w4d5IXAPncQZO6v/eURmIp1Sw2W1aMuWrIwBriVLuNXh4BLMM0DcwHzgrUeP8qXD\nhzkMfA/4APDcNKnrdNCcSHyppZkk4QlCghwOB0VFRZbdxMWLF7NhwwY6Ojr4w8QEWwsKOHPzzTz6\nmc9Q8ac/sQJ4T+DrOPDI0BA89BCsWgUXXQRYj6OqVSoyNxrTTCKrZUtATLPkwbHRRZh5QJswjy8O\ndhkm5s3jkYULufAf/oF7HnmEHz38sOU9NmzYoHFRETQRlJFiWQNqOQu/cCHvnJjgHS+8wI1h1x7L\ny+OHhsFO4MdAcBPnNddcw8TEhJYziaCgmRMmB9nDhw8zMjICwGLMffBNwA1h73kBc7/8Q8CgzcbT\nFhMhWs4kuUhBMwdVV1ezb9++KeV1V13FyiNHqBkbY3lY+Yvz5vG9M2d4CHM508lA+YoVKyyPAdDO\nJMlmWnKUg6LNzM+z27n2K1/hro4OSsfHqRsfp+HMGYo9Hj4MfBjwYa7/fAg44vPhdDojgiNMHXPV\nZJJIZphF+tLcYHV08XRJjx/escP4ks1m/HpSMuWxvDzjATDqwFgQuEdFRUXEfYNfTqczyZ9SJDGI\nMQmxWppZYLqjO6y8be1ajl16KRs7OnjV2Bi1Y2O86amnuGpigo8CHwWeB3Z7PPzXRRdxEJh8rJxy\ng0qu0piazSbYAAAgAElEQVSmAOa46F/37aMRWAO8Luy1w5gn3+0EfgacQZNGkj1iHdPUjiABzHHR\nx4F7gNcD1wKfA/43P59XAR8DfoqZgf5bRUXc/ba3gY41lhyklqYA0yRavu8+XjE6ytNf+QpveeYZ\nLg3rlk/YbOy56CJcNhuHFi5kwx13aHJIMo6WHMmsnXORvWHAyAjs3Mmxf/93LnjuudBLTwL9xcW8\n5tOf5s3/9E9mgmWRDJANQXMz0GpRrqCZRpz19Rzp72cN5kL6K8JeO1xQwE9f+Up+cemlOD/9aVa9\n850pqqXIuWV60KzFDJpVFq8paKaRyQvq/z/M4LkGc1dS0F8WLODku9+N45OfhMpK84wkkTSSyRNB\nxcARzMxokuYmL6h/BPg4cDnmCZzbMCeNLjt9GkdPD1RV8fSFF/Kfl1/OrW96E329vVHvrXR2IjPT\nEPg+Nb25KVVrX8WC1YL6goKCiOd5YNwExoM2m/Hc/PkRC+m9551n/HHNGsP4zW8M48yZae873UJ9\nkbkixsXt6dJXqsDc0TeKGTTrLa4JfD5JF9MlDglXVlbG+JEjvAUzmchqIOLg4quvNg+UW7MG5z/9\nk+WxIEpnJ4mSqWOaDWGP24C1wOREkMbdd98delJdXU11dXXiayYzFm3ZUmFhIY899liobD7wVuD/\nXnIJzpdeIv/o0dBrh/Lz+Y8TJ9gJ/D7s3kpnJ/EyMDAQkZjmnnvugQwMmuEG0URQxrJattTe3h71\nULmX/H4u93ppAt4HlIW9fhBzF9JOYKysjCNHjky5h3YmyVxlepajtUA5sJKpLU3JAKtWrbJs+Vkd\n9QHwR6+XPwIu4FbM//Afmj+fd738Mm8E3oi5M+l3L73Et4BdgCfsvtoDL8mWji3NaNTSzGBWLdCt\nW7da5gG95pprWPLqV/OGZ56hZmyMar+f8156KfT6EGdboFdP09JUHlCZiUwd05wJBc0sE+0s+Cld\n7hMnOPD5z/PUV77CyhdfpCjsWt9VV/HMW97CF/70J/4yb960eUA1BipWFDQlY0Td7x4lsPX19bH9\nvvu47plnqDlyhLf4fCwI657/ksBxHldcwUs2m+VMvsZAZTIFTckosRwqN8WxY3z2xht5zW9+wzuB\nC8Ne+tX8+Xz75ZfpBp4OK492pIfkrnQJmtsxZ8F3AkfPce1MKWjKFMHtnBcAqzC3cq4CCgOvnwF+\njvmH2A28uqKChQsXapxTQtJl9rwVcx/5A0AJ5oRnG/BEgn6e5Kjgds5jmDPruzBbnLcvWcLKv/6V\nt770Em/FXBfaDuz/7W/5j5Mn2Q38FSKGBjRpJDORrO75WsCOudtntkuJ1NKUKaYbFwX4+le+QuVT\nT1Fz5AjLnn+e8wN/Qy9jJlV+CPBcey1/PnZMk0Y5Kl2655sxg+R2zCBZA7gxd/70zPKeCppiaabj\nou+86SZsv/gFa4A64PxA+WnMP86dwPeA8UC5Jo1yQ7oEzRrAi7nVuBaz10SgzD3LeypoypyEL3Eq\nAd6DOQZaC5wXuOYU5lnwO4Hnb7yR3l/8IgU1lWRKl6BZjNnSDF/zEQyko7O8p4KmzEm0rvxlF1yA\n/dFHWYO5Iyk40H8qL4+xqiq+efw4+4qLOX3hhaE1oFbjn1pMn5nSJWgmgoKmzJlVVx7OLoR/JfBe\n4O8LC3nTxATzAn9zJ4A9wN7iYn6Sn4/n8OHQPR0OBzfffDMPPvigxkUzkIKmyCxYBdNvbt1K2b59\nrMGcfQ9m7J4A/guzC98LvISZ/k4JRTJTugbNYsA/x3soaEpShR/pcTHmLOYa4CbOBtBjQB/Qe8EF\ndB87xrFJ99Bi+vSXLsddFGOOYTYEvjYn6OeIJEz4kR7PAfcDK4DLgDswF81fgDnb+c1jxzgMfBcz\nxV1B4H0FBQVIdknkjqDg4E4e5gSlVTb2WKilKUllNXG0aNEiAJ599lnAPERufVkZf1dYyGVPPhm6\n7kXg4Ysu4tV33MFfly3jvu3bNUGUptKlex5clxmk7rlkpGgTR1brQh/+t3/Ds3kzNz3zDK974YXQ\nPV7My+N7hsFOzN0dlwUmjvbv369AmgbSKWh6ME+WzMPswTwwx3sqaErmGB2FXbv44+c/z2vCjvPw\nA98Hvn/++fSdPMmpQLlm2lMnXYLmIcw1mUF24Mo53lNBUzJOdXU1T+7bRxNmy6Ei7LVxzB1IOzG7\nZTWaaU+JdAmatZgnGARVELnQfTYUNCXjTE60fBXmLqQmzKM8go4A+xctYuFtt7Fp3z6OnzqlbnuS\npDpoBpNq53H2LGF1zyVnWU0mFRYWcvz4cV7L2QB6Tdh7/grsxmyBPmm3c297uwJnAqUyaE7ukodT\n91xy1uTJpBtuuGHK7qG3X3YZ7z11irc++yyvDXvvc8Ajl13GKz/2MT7z059y/ORJtUDjLJVBsxIY\nnsVrM6WgKVljuoPmrsVsfa7B7M4HPYOZSHkn8Kzdzn1RWqDaAx+bVHfPE0lBU7Ka1UFz12Hug//b\n48dxhJU/BexbuJAD5eX8uqCA8wsKdKDcLCloimSoaFmYCgsLeeyxx1iGOTmwBlgS9r6/YOZe/J9L\nL8W7cCEjv/71lHtrD3x0mRw012Ku7WwE1lu8rqApWc+q297e3j6lBbocM3g2YW7rDPrLvHl898wZ\ndmIe0hWkPfDRZWrQrMAMmh/D3ILZz9QM7wqakpOsWqAFBQVMTEyQB9yA2dJoxNzWGeTFHP/cCbyq\nvp4NLS0a67SQqUEz3F5gNVNPsVTQlJw1uQV6+PDhKee65wH/56qrWHH4MPV+P5eEvXbEZuOhM2fY\n4fNxMFB2rjPmcyXAxho000kxcCfQHOV1Q0RMvb29hsPhMDDXQxuA4XA4jN7eXqO3t9d4R3290XLd\ndcYPL7vMmCgpMQwIff0ejM+AcQ0Yzvr6mO6djTi7pnxG0jG6bscc1558llDg84kIzPxAOV5+mf9b\nWclrDx7kfcCrwl564oILOPnud7Plf/+XQ+edR35+Pn/961+ntGIheyeT0uXc81hVYkb7EWAIWIfF\nAWybNm0KPa6urqa6ujo5tRNJQ6tWrZpZl3n+fH63aBHbDh7kdqAacwKpAVhy7Bh85zs8ADyKOf75\n/fPPt7zNxMREnGqeWgMDA3OaFEuXluadmIvf3cAngDPAlyZdo5amyCxZTSZdbbdTk5dHpcfD+4DS\nsOt/zdlJpOA71NIMXJ+4qsSkGDPJhw2z1fkxi2sUNEXmYLpdSOdh/g/YhHm0cUnY+4YAt81G1ZYt\nrPzoR1NR9YTK1KA5EwqaInFmtQvpfGC93c7fHj/ODYcPc+HLL599saoKmprMryuuCBVn8mx7Js+e\nn0vqptdEstQ5Z8qPHzeM73/fMD74QcO46KKIWXjj+usN48tfNlz/9m8ZPdtOFsyeRxP4fCISTzOe\nhT9+nMHPfY4Xv/ENrj98mMIzZ0Iv/QJz/LMbeDpQVlFRwcKFC9O+9anuuYgkRPhkUiHwN8BHLryQ\ntx07RmHY/5v/DTwE9OXn88SJE6HydE0coqApIglhNf4JcLnNxg1jY6wB3gEUBsrPAD/DbIH2AIdJ\nzxn4dDn3XESyzImwVmO4V1xyCUMOBw2YC+c/CPxo3jxOYa4JvR+zy+4C6rxe+r/9bZxOJ9XV1Tid\nTvr6+pLzAeIkXRa3i0iay8/PtyxfvHgxGzZsCI2LjhUUcPfhw9w8MsK7MLMxOTGPqK350584/aEP\nAWYX/nvAHWFrRzN1Bj5dpXKCTSTnxbInffK1xWB8fOFC42dFRcbJsBn4U2D8GIxNl19uVCxZkpIZ\neDR7LiKJMuOZ9ijXbt26lYP79vFezFR2tZzt7p7EzAm5E/gB5hnxyRgD1USQiKStyZNJZcB7gQ8t\nWMBbTp9mfqD8BPAT4NHXvpZ//tWvoKho6s3iRBNBIpK2WlpacDjOnnZ0BPipw8E/XXstl2Ae2eDG\nbH3+LfDPv/89J0tL+fkrX8nmN76RPbt2AWYrNlWTSWppikhSWXXbIfJAuFcB/1BUZG7lPHUq1Lqb\nyMvD+9rXsn1sjK8/9xzHAuVzWQOq7rmIZKRo2ekXYR7l0AS8Jez6Y0Av5hjofwFvdTpDZyrFMgOv\noCkiWaG6upp9+/ZFlF0KfLiggHdNTHBjWPlLwM+KivhhYSH//txzBDN/zqQFqjFNEckKVutCnwK6\nLryQNwNXAP8P+BVwIfCOo0f52nPPcRh4EHgX8BePh46OjrjWS0FTRNLS5EkjMFuOt99+Ow6Hgz8D\n92Kexll9+eXce/HFDAKvAD4E/BBz6+Y//vrX0NcHJ0/GpV7qnotI2oq2LnS68+HtmGtAmzAzmoeU\nlMB73gNr1kBNDX1794afKa8xTRHJLVZHetRcdhmfvPJKyg8cwP7ii6Hyk694Bd8HHnjhBfrNIgVN\nEck9k1ugN9xwAw8++CAej4erMVufN593Hq85dSr0nryIb+emoCkiWStaOrs3FRVRf/Qoa4DXm0Wa\nPRcRiZbO7vfz53MPoYAZEwVNEcla0dLZLVmyZMrM/EwpaIpI1oq2bOmzn/0s27Ztw+l0xnxPjWmK\nSFY7Vzq7TN5G2Rz4vgwz2clkCpoiEneZuo2yBvMIkS7Ax9kAKiKSVtIlaNoxkzgDeIHZjdCKiCRY\nuhys1hX2uBb4bqoqIiIynXRpaQbZMZM57051RURErKRLSzNoLfCxaC9u2rQp9Li6uprq6urE10hE\nssrAwAADAwOzfn86zZ6vxTwK2Q80AD2TXtfsuYjEXabOntcC24FRYAwoTW11RESspVNL81zU0hSR\nuMvUlqaISEZQ0BQRiYGCpohIDBQ0RURioKApIhIDBU0RkRgoaIqIxEBBU0QkBgqaIiIxUNAUEYmB\ngqaISAwUNEVEYpB1QdPr9eJ2uwFwuVxceeWVUa/t6ZmcfU5EZHpZFzR7enqoqakBoLa2lpKSkqjX\nVlZWKnCKSEyyKmi6XC6WLVs24+vLy8s5cOBAAmskItkmq4Jmd3c3K1eunFLudrtxu91s3bqV0dHR\niNfKysqmlImIRJNuZwQlRLC7XlNTQ1VVFYODg6HX7HY7Xq+X8vLyVFVPRDJIVrU0x8bGznmN1+uN\neF5SUoLP50tUlUQky2RV0LTZbOe8xuFwRDz3+XzTThaJiITLqqBZUlKC3++PKKutrcXtdjMyMkJX\nVxe7du2KeP3AgQMsX748mdUUkQyWVQerjYyM4PV6aWhomPFNW1tb2bx581zrJiIZKqcPVquoqJjR\nuGaQ2+3m/e9/fwJrJCLZJt2C5o653qC5uTm0I2g6wW780qVL5/ojRSSHpFP3fC3wCSDavkedey4i\ncZfJ3fNOwHvOq7LUwMBAqquQUPp8mSubP9tspFPQzGnZ/oepz5e5svmzzYaCpohIDBQ0RURikE4T\nQQB7gfoorx0CHFFeExGZLQ/RJ6DT2mpgDPg4UJziuoiIiIiIiIiIiIiIiIiISC5JxpKj5sD3ZcD6\nsDIvYAe6pikTEUkr8xN8/xpgCHADNwHlgAG8Hngw8Pz1QIFF2e8SXDcRkZglekeQHagNPPZgLk6v\n5WxiDi9QF6VMRCTtJDpodnG2q10HHMAMnMGTzHyAbVKZP1AmIpJ2krX33A4cAXqS9PNERBIiWeee\nrwU+FnjsAYLHP5Zibp0MLysJlEVwOByGx+NJcDVFJAfFtPc8GS3NtcAXA48bABdmyxPMSZ+9k8rs\ngbIIHo8HwzCy9uvuu+9OeR30+fT5cu2zGYYBMSYCSnTQrAW2A6OYrcdSYCTwWg3m2OXuSWWlgTIR\nkbST6O65C+vAvDXw3X2OsghOp5OWlhZWrVoVp+qJiMQmWWOacbF3716C45rZFjirq6tTXYWE0ufL\nXNn82WYj3ZIQT8f4CPANzBbnnj17Ul0fEckCsZ5GmVEtzS8BvcDExESqqyIyKzabjfHx8VRXIyeV\nlpYyNjZlYU7MMipolgL3Ad8sKEh1VURmZXx8PDhjK0kWaFHOWUYFzZeADwCOG26gr6+P9vZ2Tpw4\nQX5+viaIRCQpMipo/ufVV7P2D3/gDfffzw0XXcSjo6Oh17J1gkhE0ktGTQQZp07B9dfD8DD3Av9v\n0gWaIJJ0l5eXp+55ikT73cc6EZRZ554vWABdXbwM3IGZoDOcJohEUsPr9VJfX8/IyMi5L57E5XJx\n5ZXWuxijladSZgVNgMpKvnfFFczHTJ8UPr5QoAkiyVB9fX04nU6qq6txOp309fWl5B6zZbfbqays\nnNHsdFdXZI7x2tpaSkpKLK89dOhQXOoXTxk1phl00Ze/zF/e/34qTp/mHzG3EjkcDjZs2JDqqonE\nrK+vjzvuuIPwhDSxjtHH4x7J4PP52LFjB83Nzee8dnR0lKGhIVavXp2EmmUnI9wv77nHMMCYmDfP\n+OhNNxm9vb2GSLqb/HdsGIZRX19vYJ5oEPHldDpnfN+53qO/v98oLS013G63MTw8bGzcuNHwer2h\n1zs7Ow2Xy2W4XC6ju7vbsryxsdFwuVwR95x8r6GhIcPhcBjd3d3G8PBw6Nply5aF3rNs2TLD7XYb\nPp/PcDgcht/vn/HvYTpWv/tgeSyBKCNbmgDX/8u/gNdL/je/yQOnT8Pb357qKonMyokTJyzLYxmj\nn+s9amtrsdvtrFy5EjC72zU1NQwODtLd3Q1ATU0NAK2trdjtdo4cOYLP5wuV9/f3R9yzs7OTnTt3\nAtDW1sb27duprKykpKSEhoaGKXXw+/34/X4GBwdDZXa7fcp1qZZ5Y5rh7rsPXv1q+OUv4ctfTnVt\nRGYlPz/fsjyWMfp43CNccXExXq95Ao3L5YoIXmVlZQwODk4pn6ytrY2enp6IIBiNzWbD5XKxY8eO\nWdU3mTI7aJaUwNe/bj6+6y54/PHU1kdkFlpaWnA4IlM6xjpGH497hPP5fKH7LVu2LBRAwRwrXb58\nOcuXL+fAgQMR7wlyuVy0tbXR0NBAba15TNhoYF21zWaeZuN2RyY0a2hooLGxkS1btkSUG2m2RCtj\nu+chb3873HILPPAA/P3fw/795tIkkQwRnKjp6OhgYmKCgoICNmzYENMETjzuAbB7927Ky8txuVzs\n2rULgObmZrZu3Yrb7cbn81FVVcXSpUtZunQpXq8Xt9uNzWbD6/XS2dlJVVUVZWVlAKElSGNjY4yO\njlJeXk5jYyNdXV2hVurw8DCDg4Ps3r2bpqYmSktLmTdvHjU1NXi9Xnbt2sUtt9wS0+dIpMxa3B7t\nX5yjR+ENb4C//AU+9zn4539Obs1EZiidF7dXVVXNqCudqXJzcXs0RUXwjW+Yj++5Bw4eTG19RDLM\n8PAwXq+X3bt1aMK5ZEdLM+jWW+FrX4OlS+FXv4Lzz09OzURmKJ1bmtlOLU0rW7Zw7OKL4de/5ltX\nXZX0XREikv2yasakb98+/nP+fB4EPvTnP9P15z9zh8fDgQMH2L9/v9LIicicZVX33Ol0snfvXr4A\nfBL4X+A64GRhIcePHw9d53A42LZtmwKnJJ2656mj7rmF4K6Iu4EDwBXA1yAiYIK5zqyjoyPZ1ROR\nLJBVQTO4K+IU8EHgRcxM7x+2uFZp5ERkNrIqaIbvijgEtATK/xWYvNlLaeREZDayaiJo8q6Ip/Pz\n+e2TT3LN44/zn8BbgNMojZxIphsZGcHlcnHnnXcm/Wdn1USQpfFxjr/mNRQ+/zzfuvxyvv26181q\ne5lIPGgiKH6amppCWZRmIl4TQdkfNAH27YO3vQ3y8sDthurquFZMZKYUNM3EHq2trWzfvn1O9+np\n6QHMRB+jo6N4vV727t3LK1/5Smpra6moqIi4XrPnsVixAj71KThzBj7wAXj22VTXSCRndXZ24nK5\n4nKvhx56CDAzJ9XU1OD3+7nzzjunBMx4yqoxzWlt2gQ//7nZ6vzgB6G/H+bPT3WtRM7Ki2PHL01b\nsyMjI9TV1dHa2nrOa4MtyaCSkpJQwuOuri5qa2vp7+/H7/cDZgu2pKQEv99PcXFx/CsfkBvd86Bn\nnoGKCnjuOfj0p+Gzn41PzURmaNrueQqDZjBjen9/P5s3b45bF3qyrq4umpubsdlsEYeweb1eenp6\nqKysBM5mibfS09NDaWkpK1euZGRkhMHBwVCOT6/Xi91ut8wMH6/uebJamjuAdRbPGwAX4AeaAS/m\n6qCuyTeIi0suge98B2przRRyb36zjsmQ9JHC1mEw2IRna6+qqoq4xu/3TzvxUltbS3l5edTXu7q6\naGpqAsxjLIL5NX0+H01NTaG0dF1dXdMGzfCAWFFRkdCuuJVkBM21wOTfQCOwEtiIGTArgRLAHfje\nAPSQCG97m5k+7q67OLlmDR9ZupQn8/K0J11yWkVFBVu2bGH9+vUA7Ny5kwceeCDimuLi4hmdImnF\n6/Xi8XgixjKDQdPlcuFwOBgZGWFsbGzWPyNZkhE0O4HJZ3A2ExkUazBbmQS+ryNRQRPgU5/i8Pe+\nx6uGh7n1Zz9jBeb6zfDjT9vb25XgQ3KKy+XiE5/4BGCODxYVFUW8PpeWptvtZvPmzaHn/f39eDwe\nVq5cyfj4eMRsd6LHJOcqVRNBdsxAWQe0Ag5gOPCaH7Al9KfPm8dtRUV8BbgR2Ax8HDNo3nXXXRw9\nejTtz48WibfGxkbcbjcej2fKeUMwu5bm8PAwra2toW45EFoeNDo6ypo1a0LHaQRbmjabLeld7lgk\nayJoL1BvUR78L7AM2IXZPbdjxrGmSdfOfSIoTHV1NSf37WMfcB7mHvXvAqWlpYyPj0+53ul0smfP\nnrj9fMlN6bpO0+124/V6aW5uprW1lfXr17NkyZJUVyuuMnmd5lrMMUuAMcxWpgdzLJPA9zGL98VV\nfn4++4F/DDz/OrB0muuV4EOymd1ux26309PTQ319fdYFzHhKRff8COaMOZitykeAUaA2rGyv1Rs3\nbdoUelxdXU31HHb2tLS04PF4+FePh0rgI0DvggV8+NJL+alFS1MJPiSblZeXTzvznU0GBgYYGBiY\n9fuT0T1fjTkZ9AXMpUTB5UVjQDnwpcB1d2KOa0ZbchTX7jlAX18fHR0dnDl2jG0HD/I6v58j117L\nm196iT+EnfOspMUSL+naPc8F2nseb08/DcuWwbPPMvqud/GxkyfndH60iBUFzdRR0EyE/fvNfeqn\nTplHAv/DPyT250nOUdBMHQXNRHngAWhuNo///dnP4PrrE/8zJWfYbDbL1RmSeKWlpRFbN4MUNOPh\nttvg/vvh4ovN89OvuCI5P1dEkk5BMx5OnTL3pD/8MLzhDWZ2pDTeoSAis5cJ6zTT33nnQU8PvO51\n8NhjsGYNnD6d6lqJSBpQ0IympAT6+mDhQvjJT+D229M2R6GIJI+C5nTKy+EHP4D8fNixA+69N9U1\nEpEU05jmTOzcaXbR8/Jg9254z3tSUw8RiTuNaSZCUxN84Qtm9/yDH4RHHkl1jUQkRdTSnPlPh1tu\nMRe9l5WZM+qvfW3q6iMicaElR4l06hS8973mBNHll8MvfgGLF6e2TiIyJwqaiXbsmHnG0P79cM01\n8N//DaWlqa6ViMySgmYyjI3BW94Cjz/O2Otfz/+55BKOnj6tozFEMlC6nkaZXWw2+MlPOF5Zie3x\nx2l+/HHeC7yMjsYQyXaaPZ+hvr4+nE4n1dXVOJ1O+n7zGzZcdRVHgHdhJgDNwwyaHR0dqa2siCSM\nWpoz0NfXxx133DHlsLXCwkJWYR5s9A/AS8AGzKMx+vr6dKKlSBZS0JyB9vb2iIAJZtAsKyvjCPAe\n4EfA7cBx4Dt+v2WQBXXbRTKduuczcOLECcvyRYsW4XA4cGGe6XEK88yO9c8+axlk1W0XyXwKmjOQ\nn59vWb548WK2bduG0+nkxRUr2HzddZyZN4+1zz7LJy2u14mWIplP3fMZCJ5cGd56dDgcobODIrrc\n3/42Zz70Ib6A2VW/L+w+OtFSJPMpaM5AMCh2dHSc+7C1D36QRx95hOu2beMrwEngfs4GWRHJbFrc\nniCP3nYb195/PwDbr76ay778ZU0CiaQhZTlKE9f+67/CV78KwPo//IFVv/1timskIvGgoJlIt90G\nnZ1mHs6NG+Fzn0t1jURkjtQ9T4ZvftM8Q90w4K674J57zEAqIimnhB3p6tvfhr/7O3j5ZbPV+cUv\nKnCKpAEFzXS2a5eZ+f30abj1VujogHkaIRFJJQXNdPeDH5jHZ5w8aZ479K1vwfnnp7pWIjlLQTMT\n/PSn8O53wwsvQH29ecb6RRelulaSg3w+H62trWzfvj1u9xweHmZoaIjm5uZQWXd3N3l5eYyNjWG3\n26mpqQmVl5aW4vP5GBsbi3hPssQaNDOJkVWGhgxj4ULDAMO4/nrDeP75VNdIclBbW5vhcDjidj+X\ny2U0NjYaW7ZsCZUNDQ0Z69atCz2vq6szDMMwxsfHQ48NwzDy8vLiVo9YADG1xjSgliqVlebhbFdc\nAb/6lZkJ/sknIy6ZksOzry9FlZVsNDIyQl1dHV6vN273rKmpoa6uLqLM5XLhcDim/OySkhL27t0L\nmK3TdevWxa0eiZSsbZQ7gPDfSDPgBeyY+XujlWW317zGPJzN6YTf/hZuvBH+67/gDW+ImsMTlF5O\n4mNwcJDm5mZKSkoS+nNKS0sj/o7HxsYYHx8PPR8ZGaGzs5O2traE1iNekhE01wI1Yc8rgRLM3L0l\nQANmsJxc1pOEuqXepZfCz34G73oX/M//wJvfDD09UXN4dnR0KGjKnHV1ddHU1ASA3W5ndHSU8vLy\niGv8fj87d+6Meo/a2top77HS1NQUMVbp8/kiXq+oqKCtrY1ly5Zx6NChWD5GSiQjaHZippsMqsEM\nkgS+rwM8FmW5ETTBPHPI5TLXcXZ3wzvewUq7nb0Wlyq9nMyV1+vF4/HgcrkiyiYHwOLi4rhMzBQX\nF9PW1obb7cZms2G326mqqmJ4eJjx8XFqamooLi4G4OGHH2blypVz/pmJFGvQ3A4MAjuBo7P8mQ5g\nOGqKz54AABZTSURBVPDYB9gCj4Nl/rCyrDLtERiFhfDQQ/DJT8KWLWz84x85Bdw16R5KLydz5Xa7\n2bx5c+h5f38/Xq83NKMdNNuWpjFplYvf72d4eJiGhgZ8Ph8Oh4OioiKGhoaw2SL/V7fb7bP5SEkV\na9BsBWqBBzC70R6gDXgivtXKPjMao5w3D9rawG7nzK238ukzZygHPoKZYk7p5WQuhoeHaW1tDXXL\nAUZHR/F6vYyOjtLU1BRq8cHsWpputxuXy4Xf76eysjLUivR6vbjdbrxeL1/72tcAaG5upqenh56e\nHrxeL1u2bGHJkiVx+ayJNNe1SWsxJ272Ag9Pc91eoD7w+E7MLngP5vjmWs52z8PL1k+6hzH5X7BM\n4nQ6QzOFk8v37Nkz9Q0//jGnGxpYcPw4jxYV8fnKSj788Y9rPFMkzhJ97vlmzCC5HTNIejDHLBti\nuIcLs7UKUI4ZUEfDyoJBeIpNmzaFHldXV1NdXR3Dj02taOcMTXdy5YL9++Gd7+TaJ5/ku4cOwaJF\nSa61SPYZGBhgYGBg1u+PtaUZnMRpxAxyuwLlXsyZbyurMQPrFzCXEvkxW5vDRC4vsioLl5UtzYqK\nCo4ePTrlKI1t27aZrcpnn4WGBnNmvaAAvvEN+oqKdDywSJwkekdQMVAxqawGs8WYaCnZLRAvvb29\nhsPhCO4+MADD4XAYFRUVEWXBL6fTefbNExOG8dGPmruHwNheUmLMm3Sf3t7e1H04kQxGgncE+YGR\nSWVuzO61TGPVqlWhkytXrFiB0+lk27ZtFBUVWV4fsbQoPx+6uuCrX+XlvDzW+Xz8EPNfMNDxwCLJ\npG2USbRq1Sr27NnDwMAAe/bsYdWqVVGPB56ytCgvD267jf/3xjfyPLAKGAKWBl7W+k2R5FDQTLGW\nlpYp+3KnW1r0u4svZjlmwHQA+zGXJBVECb4iEl86wjfFYjoeGDPI3uHx8GaPh22YW6e+Dvzl5Zfh\n2DG44IKI66ddUC8iMcukHHKBMVvp6+sLBdlVR47wT3/6E/NPnIBrrzW3Yb7mNaHrJi+oj5iZFxEl\nIc5Jjz4Kq1fDH/8Ir3gF3H8/3Hxz7AvqJSd0dZkr+uKd8Dc8oXBJScmUbZkAPT09lJSU0N/fz/Ll\ny2loaAi91ypJ8caNG1m/fj2lpaW43e7Q9fGkJMS5yu83jMbG0LIk4+abjXe8+c2Wy5lWrFiR6tpK\nisUz8bBhGIbH47FMNBxueHjYcLlcEXXw+XxRkxQHHzscDmP9+vVxrW84lIQ4RxUVmQk/urrMcc0H\nH+SB4WGWW1yqpB+yevVqenril0jM5XJF5OUsKSlhZCRydaLX66W/vz/imuCedKskxQDr1q3j0KFD\nof3q6UBBM0v09fXhfPvbqX7wQW6pqMBvt/Pq48f5BWaWleB/6ODMvLLC57Z169bx0EMPxe1+fr+f\nsrKy0HObzTYlI3xDQ0Mou5LP52N0dJSKigpKSko4cuRI6LrwJMVjY2OMjIyEEnukA82eZ4HJEz77\ngP+x2+l997ux/+AHfBFoKi7mvuuuo+kTnwBQVvgcNz4+zvDwMH6/PyKzEcQv+XBgrNBSa2srQ0ND\nwPRJioPlFRUVVFVVUVtbO6W+El3CxjQyXX19ffStmD/+sWG86lXmOOcrXmEYDzxg1NfVnXvrpmQt\nl8tluFwuY8uWLUZnZ2dc7tnZ2RlxmFpjY6MxMjJieW13d/eU17xer+FyuYzh4WGjrq7O8Pv9xq5d\nuyLuWVdXF/Wec0GMY5pqaWaB6TIo8fa3w2OPwcc+Zh4VfMstbLLZeBR4xup6yWoul4vR0VGam5up\nqqqipqZmyiz6bFqaTU1NbNy4MfTc5/OxdOnSyW/F5XJRWVlJeXk5Pp+P8fFxbDabZZJih8MRMdY5\nNjZmec9kU9DMAufcirlwIezaBd/5Dtx2G28aG+Mx4Dbgu1bXS1YaHR3F5XKFxhWLi4stzweaTfLh\n4uJiGhsbcbvNZGetra2h16qqqnj44Yc5dOgQ69evD00YjY6OhsYyrZIUV1RUhBIUB5MUS2zi3izP\nFtEyKFlmPnrqKeO5ZctCS5N2g/Hqc2RK6u3tNerr640VK1YY9fX1yqgkWYUYu+eZJNW/27TW29tr\nOJ1OY8WKFYbT6Zw+sJ05Y/ympcV4cf58wwDjxQULjIO33WYYL79sed8ZB2SRDESMQTOTVsEHPp/E\nzZNPwq23wo9+BMCRa67hEyUleBYsCO1Tb29v164iyWqJPu5CssnixfCDH0B3NxNr11L2299yP/BZ\nYCvmMqTCwkLLt2rSSHKVFrfnurw8aGzkQxUVPADkA58DDgLlHg/PPDN5jt2kSSPJVQqaAsCRM2do\nBlYCvwOuBvqBB0+d4s1XXBFxrY4Sllym7rkAZ5c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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Naloge" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
    \n", "
  1. V datoteki Maribor.zip so zbrani vremenski podatki z merilne postaje Maribor-letali\u0161\u010de za obdobje od 1. 1. 1977 do 31. 1. 2015. Poi\u0161\u010di premico, ki najbolje opi\u0161e odvisnost med vla\u017enostjo in obla\u010dnostjo v letu 2014.\n", "\n", "
  2. Teorija kemijske kinetike napove za sigmoidno krivuljo iz podatkov adrenalin.dat naslednjo odvisnost $F/F_\\textrm{max}=c/(a+c)$, kjer pomeni $a$ koncentracijo s polovi\u010dnim maksimalnim u\u010dinkom. Dolo\u010di koeficienta $F_\\textrm{max}$ in $a$. Pretvori v linearno zvezo \u2013 ena pot je uvedba recipro\u010dnih spremenljivk $1/F$ in $1/c$, druga pa je uvedba spremenljivke $c/F$.\n", "\n", "
  3. Iz povpre\u010dnih dnevnih temperatur v obdobju od 1. 1. 2000 do 31. 12. 2009 na merilni postaji Maribor-letali\u0161\u010de (Maribor.zip) oceni povpre\u010dno temperaturo za vsak mesec v letu (povpre\u010dna temperatura v januarjih v tem obdobju, ...). Oceni \u0161e napake teh povpre\u010dij.\n", "\n", "\u010casovno odvisnost mese\u010dnih povpre\u010dij modeliraj s funkcijama\n", "\n", "$$T(t)=T_0+T_1\\cos\\left(2\\pi\\frac{t}{t_0}\\right)$$ \n", "\n", "in\n", "\n", "$$T(t)=T_0+T_1\\cos\\left(2\\pi\\frac{t-t_1}{t_0}\\right),$$\n", "\n", "kjer je $t$ \u010das, merjen od za\u010detka zime, in $t_0$ eno leto. Dolo\u010di parametre $T_0$, $T_1$ in $t_1$ ter primerjaj vrednosti $\\chi^2$ za obe funkciji. \n", "
\n", "\n" ] } ], "metadata": {} } ] }