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@megbedell
Created July 16, 2018 13:49
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thorium_fits
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### fitting lines to data with 2-dimensional uncertainties"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import emcee\n",
"import corner\n",
"import scipy.optimize as op"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"load up data and define some functions"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"data = np.genfromtxt('Table_solartwins_Th_fulldata.txt', names=True, dtype=None, encoding=None)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def vee(par):\n",
" # Hogg+2010 eqn 29\n",
" (m, b, lnjitter) = par\n",
" return 1./np.sqrt(1. + m**2) * np.asarray([-m, 1.])\n",
" \n",
"def ortho_displacement(par, ys, xs):\n",
" # Hogg+2010 eqn 30\n",
" (m, b, lnjitter) = par\n",
" disp = np.zeros_like(ys)\n",
" for i, (y, x) in enumerate(zip(ys, xs)):\n",
" z0 = np.asarray([0.0, b])\n",
" zi = np.asarray([x, y])\n",
" disp[i] = np.dot( vee(par), zi - z0 )\n",
" return disp\n",
" \n",
"def ortho_variance(par, dys, dxs):\n",
" # Hogg+2010 eqn 31\n",
" #(m, b, jitter) = par\n",
" var = np.zeros_like(dys)\n",
" for i, (dy, dx) in enumerate(zip(dys, dxs)):\n",
" cov = np.eye(2)\n",
" cov[0,0] = dx**2\n",
" cov[1,1] = dy**2 #+ jitter**2\n",
" var[i] = np.dot( np.dot(vee(par), cov), vee(par) )\n",
" return var\n",
"\n",
"def twodlike(par, y, dy, x, dx):\n",
" # log(likelihood) considering errors in both x and y\n",
" # Hogg+2010 eqn 31 with jitter\n",
" (m, b, lnjitter) = par\n",
" delta = ortho_displacement(par, y, x)\n",
" sigmasq = ortho_variance(par, dy, dx) + np.exp(2.*lnjitter)\n",
" return -0.5 * np.sum(delta**2/sigmasq + np.log(sigmasq))\n",
" \n",
"def lnprior(par):\n",
" (m, b, lnjitter) = par\n",
" if (-10. < m < 10.) and (-1. < b < 1.) and (-20. < lnjitter < 1.):\n",
" return -1.5 * np.log(1 + m*m) # from Vanderplas blog post\n",
" return -np.inf\n",
" #return 0.0 # flat prior\n",
"\n",
"def lnprob(par, y, dy, x, dx):\n",
" lp = lnprior(par)\n",
" if not np.isfinite(lp):\n",
" return -np.inf\n",
" return lp + twodlike(par, y, dy, x, dx)\n",
"\n",
"def bestfit(abund, err, age, age_err): \n",
" # fit\n",
" # parameters: (ys, y_errs, xs, x_errs)\n",
" nll = lambda *args: -lnprob(*args)\n",
" par0 = np.asarray([0.0, 0.0, 0.0])\n",
" result = op.minimize(nll, par0, args=(abund, err, age, age_err))\n",
" (m, b, lnjitter) = result['x'] \n",
" return m, b, lnjitter"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(the references mentioned above are [Hogg+2010](http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1008.4686) and [this Vanderplas blog post](https://jakevdp.github.io/blog/2014/06/14/frequentism-and-bayesianism-4-bayesian-in-python/#Prior-on-Slope-and-Intercept))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"remove the stars we won't use in fit"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"stars_to_mask = ['HIP28066', 'HIP30476', 'HIP73241', 'HIP74432', 'HIP64150', 'SunVesta'] # do not use when fitting\n",
"mask = ~np.isin(data['StarID'], stars_to_mask)\n",
"data = data[mask]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"find the best-fit parameters for [Th/H]_ZAMS vs [Fe/H] (top panel of Figure 3)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"args = (data['ThH_z'], data['error'], data['FeH'], data['eFeH'])\n",
"bf = bestfit(*args)\n",
"m,b,lnj = bf # slope, intercept, ln(jitter)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1120665f8>]"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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RyTR4KKU6nK+lmV0vPMWu5+eQf8TRlE+bh/vA/ildKzTH1rK12ywsZXqE7ozoZBo8lOoEGls9zF2+ntGD+1k6aJzs/uHGGJrfeZMdsx8EoOdtd1N4wqlJdVGFCs2xBfD4O/45Oas378rY3FaZwrm7oijViVnddRHc8S+RG3wygt+SEwlIbRu+YutvbmLbfb+i6w/OonzGc3Q58bSUA0fEHFuB6bp3/G2V5raymQYPpRwomZuyE8RKz+5PYDiFmhsvRgoKKK9aQLdLr8WVX9Cu94yZY8tYn2Mrk/Zr7wiZ8ZeplHKs8K6jqUvWUPX2WqaefxT9/7OMusem4OpSROnEyRQcfYJl7xsrx1Zzm8/yHFuZsF97R9KWh1IqZbHSs9/41L+pnT6JkvMuo/yReZYGDoidY6vA7bIlx1Y8nal1osFDKZWyWF1HXnHx8S0zKD73MiTX+m/qwwaURl9ZLrJnAWNHsmtsyYk0eCilUhaz60hyeeXrRtveO5hjqzg/l0K3/1YWXGF+11lHZOw6j0yhwUOpFHSm7olYDuheSGGUe3Sh28WZAxPa/y1l4Tm2rjrhIGDvinNlHw0eSqWgM3VPhAsGzl21tRy1sApX8+6Ix+W6XIwYGL6tT3LvkUhwDs2xNeSQXim9n0qeBg+lVFIadzdTO/8J6m68AFftBqYMP2ifriMrkhJ25uCcKXS+mVIqYc0fvkPr9EmcvXU77utvo88Z/48yEV4e5HX0HiTtFb6OJdvqlwpteSiV5WIt4EuUp3YTW++6jS0Tf4LruJMYf/xt5Jz0wz2rw63cg6Sx1cPTy7+Of2AEhW7rkwquqq5n5IylTF2yBvCvYzlz+lJWVddb9h6ZSIOHikoHhTNfe298vpZmdj4zi5obLsC0tlD+yDzco8fRnNu+1eGx7G718syKDSmd28Xilfnbd7dw3bMfRFzHMmHByn0CsRVBOpNo8FBRab+znx1BtCMCc6wFfOE3vnDGGHYve4OasRfS+Po/6PV/99D7d1NwH9DftvK2h11pzF9eVUOrd//tbQE8Ph+vfFYLdM7WiQYPpeKwI4h2RGCOmfvJFz33U9s3X7Hl1+PZfv8ddB1+NhVVz7Ur821HsCsX2L9i5MdqavOx8LOadgXpTKbBQ6kkZUr3RKwFfE1t3v1yP/l2N1D36BRqbrwIV5eulFc9T7dLrkHyOm9q8/+JsUo9uI5l8Zdb8KYQpDOdBg+lkhCve8JJ40Sxcj8VunP25H4yxtD4r39Qfd0ompa/Tenvp9L7l/eR26div/MyJXBaZdhhfaK+FlzHkmyQzhYaPJRKUIsnfveEk8aJYuZ+cvlzP7X+9ws233Y1O2bcR8moKyif9iwFg46PeE5n7NfPC6Q7KcrLibqOJdEgnW00eCiVoGVrt6c0htBRwls9kXI/BW98U0Z+i8aZ91H7kzHkVh5ExcwXKD53dNQEhh3Zrx96Lae0bp4aM3hPCpTxpxzKwnFDOaKiBPAH6Zw4QTobafBQKkHV9c2WdE/Y1fUTqdUTnvtp/MmH8PzBm+l5xxW0rv6MPvfNptdPf0tOz94Rr9nY6mFLQwsvfVK9Z7+OcB6fj79+XM22xpZ212FVdT2XP7F8z89Oad3k50ZfxxIrSLdnlb3T6QpzpRJUUVJAoTsnYgBJtHsi6sZJFwza803WasEFfH974VWGPDabpu2b6XbleLoOPxvJiX1jm7t8PbOXfRXzmKY2H5MWrQbgmAO6pTxdNti6aWgNXTvhoxkfExasZOG4oR16Iw4P8kNj5M0KBulsXmUfTlseSiVo6CG94o4hxJKuKZ3e7VtpnfZ77lw5E9e3v0f5rBcpGnFu3MABMHpwP14eO5TbTh9AgTvy7aLQ7eK20wfw8tihPDjqqJSny776eW3M1k1wTUVHiDS+c9kT78U8x8pV9plAg4dSCcrLdbWre6Kjb46mrY36F56k+rrzMFtquO24m3D/763kFHdL+Bpd83IpLcrnnCMrcLsi3y5yXS7OObKC0qL8dq2z8K+ZiPz7Ca6p6AjRgnywRdTqiVzGzkaDh1JJ2G8MIWzwNJaOvDk2vf9vasZfTMNfn6XH+F+SN/ERvirqm/L1OqJf/6jK6EGtI/YGCYq1uBJg6dptHVIOp9PgodLGSWsikpFq98SZA8tjdv205+YY7J/v2rabfz40lU133kbhCadRXvU8XU8bkdDq8HifR6TA+fw1J7B07dZ2f4bNbV6e+yB6PqucduwNkqxY6zYAanY1d0g5nE6Dh0obJ62J6AgjBpbF7PpJ9ebo759/m6mLPqcxt4AZ+d/j2tPuYuOIMbi6dE3oGsHAEe/zKHDn8P3+PQD4fv8eeH3Gks/w1c9r8Zjo3/YvPLqyw8YQYq3bACgvti8pZCbR4KFUDFZOq7Wj66ep1cP4Z1ewq8VLMzkgLprFza42X1KD8Mlksg1+K4/17TxZsbr0AD7auNOy94on1uLKvBwXP/hO9FXnnYltwUNExonIOhFpFpH3ReTkGMdWiMgzIvKFiHhFZI5d5VKJ6WxpKCKxY0V1e8ZMwrWtX8ff7pmEpyXy+orgwkX//hjrUy5zR7CzSy9ZsYL8rEuOoWeXvKjn2pXd14lsCR4ichEwBbgHOBpYBiwUkX5RTskHtgJ/BN61o0wqcZ0xDUW4eNNq2zPjpr1TOn27G9jxp4eoGX8xNQU9ac6NnLgwuHDR36r4JuXydgS7uvRSlWqQtyu7rxPZ1fK4BZhjjJltjPncGDMBqAbGRjrYGPOVMeYmY8wcYLtNZVIJ6KzppcPFm1b7xpebO7hEYHw+Ghf9neprR9G8Yhmlv5/KgLPPyYq8SpG+7YM/p1S6Vml3tnUbybI8eIhIHnAs8FrYS68BQ6x+P2WtVPeAyDbxptV29O+hdc0XbL7tGnZUTaLk/L0JDBNJfpgpwr/tAzw95njbVt6r9rGj5dEbyAHCVzzVApZ3XFZWViIi+zwmTpxo9dt0Gp01vXS4eH3wZxxetl/fth3jRN6ddWyfeje1Px1D7gH7JzAM/cYeLG9BlEH4S487wNK++FaPz/L6hn7bh71ZbZXzZHzH3MaNG+nbN/XFT2pfwWmK7cnflA1GDCxjyuI1NLN/68O/orrvPjfmZHNWxRtYNV4vDQtfpP6pGeSUV9Jn0p/I/873Ih4b/Mb+zIr1zHh7HVd9/yBGD+5Hfm7OPgGtsluXqK2UZAS7yW56/iO8gem1HZGjSzmLHWF9K+AFwke4yoCOyS+gUpZN3SDtkcy02lTGiWINrLasWkntzZdTP3cm3a6aQNmDc6IGjqACdw5DAon7hhzSi/zcHFsmPjS3efessG5s9XbqcbHOzvLgYYxpBd4Hhoe9NBz/rCvlYB2VXjoTpgInMuOmsdWTULryLQ0tcVdhe7dtYdukX7P5F9eTf8RRVCSRwDBcMgEt9LOA6LmbgsFo2pL/Rn3fzjQu1tnZ1aH4IHCliFwjIoeLyBSgL1AFICJPisiToSeIyCARGQSUAD0DPw+0qXwqBivXIkTilKnAiaRHiTfjZu7y9UxatDrm4PqkRasZOWMpc6OstTBtbdQ//wTV14/Cu7WWsoefpsfY/8NVnPrvO9GJD+GfBcBlT7y332cRGozavNFXgmfbuFhnWreRLFvGPIwx80WkF3AHUAF8Cow0xnwdOCTSeo8Pw34+C/ga6G9HGVVswZvmpEWrLZ2mGHoT2vtcevZsCKZHOfeoypTn5Y8e3I/uhXlMXbImYgApdLsYf8qhDBtQGvEG1LRiGXWz7sc0N9Fj/C/pcuoZCeWhiieRiQ+RPguAhlbvfp9FvGSBQdk2LhbsXlT7s20qgzFmujGmvzEm3xhzrDFmSchrpxljTgs7XiI8+ttVPpUeiaYltzNpYvDauy24dte83JTSlXuqN7D1zlvZeuctFA75H8pnvhA1gWEqv4tY+Zn8s7HcSXW3xUsWGGTluNilxx2o3/gdTOfBZZFMyFKbaFpyO5MmBq9tVW6mZMaJfM3N7HyqiuqxF2I8bZRPn0/3K8fjKuwSt7zJ/C5iTXxoDnSlJdPdFi9ZoDtHLB8Xu2xwv06xUjtTafDIIpmQpdaqHEaxAmU6gmi8cSJjDLuXLqLmhvNpXLyQ3rf/kd4Tp+CuPMiS929u87Ji/Q6APf+NFNCK8nOZPOrIuLsDFuTKnt0BRw/uFzMYAYw/+VuWjosp59PgoTqUVTmMYgXKdAXRaIPrbevXsuVXN7L9gd/QdcSPqZjxHIXfP8WSsQ3YO+g9c+k6AGYuXceZ05cC7BfQXhk3lKGH9I67O2CzxzCgT9c93W3RWldFgW6l4YeXafqOTkaDh+pQHTUV2Al8jQ3smP0gNeMvwVVcQnnVC3S7+BokL3Iiw1TEm5IrQtTZYvm5OTxw7pFRr33Li5/sM6U3Uuvq6THHW1YXlVk0eDhcJoxjJMvuqcDpJsaH982Xqb5uFM0fvkPpndPoffsfye1jfVrx9uQia2z18OWWhqhdV5H2VQ9vXdmRPkSnx2YGDR4OlwnjGKnI1oylvrVfcM+H02l7fDIF513B3y++C+/hR9v2fu3JRZbIGhUr91VPVGdKa57JNHiorBOcghtpKm7oauplgTQbVvDurGP7w3fT+qvr+KZLGflT5uM743xmvbvB1sAfaxZUvDUXowf3izlo3tGbMKnMosFDZZ1o26SGr6Z+/B3/mtXVm3el/F7G62HX35+j+tpzaVv3H/J+P4Pp37kA6dYj5WsmI5FcZNG6gRJZo9LRmzCpzKHBQ3UKEQeWAzmc7vjbqpRyazV/+kEggeEsul99M30emIPrsCMsLXc8iWyiFKsbKHh+UUhgydYJDMpaGjyU7Zww6L/4yy14owwse03sgeXwb+6erZvZdt+v2HL7WPK/e4w/geEZP0aifIO3W3s3UTqiooSnxgze83MyExh0cLvz0uChbOeEQf9YA8vNbb6YA8vBb+5dxEf9c3OouX4U3u1bKJs6lx433NauBIZWae8mSqEtjGQmMOjgdueln7jqFIIDy7sjBJB8tytuMr+mFUupm/kApqWZnjf/msKTh1u2yE+pTKTBQ3UKwwaUct/rqyO+5pLoyfw81RvYMesBmj94h+LzLqPkwqti5qHqDLSrSoF2W6kY0nWTaM9GUc1t3j1TcJet3bbn3EgDy8FZSmcevv+MIn8CwxlUj70QjKF8xnN0H3Nj1gaOLnk5XHrcAQkdq11VCjR4qBjsvklECk7t2SgqeG5wCu7j73y9z7nBgeVRg/a9Sf5jVc2e44wx7H7rdWpuGMXuN1+l9y/vpXTiZNx9D7Sq2rYJDbLJBt2ueblcNtiaJI2qc9Dg4WCZsFVre4QHp1T2Ag/a51zP3qm4kc79y0cbAfak9dhz3PwP2PjLG9n+0ESKzhxF+fT5FB5/si11t9qq6nouf2L5np/TtTuj6jw0eDiUU7ZqtVtjq4ctDS1saWhJeHOiLQ0tbGts2ef1RHM8vfp5bdTj2pp2s6R4ACXT5lNy0f9amsDQTsHA2dAaui95YkFXqVRpp6UDWbFVa2Orh7nL1zPa4RvqzF2+ntnLvop7XFPIBkaRJJrjaeFnNXtaJuGac/J5SI6kYV0L1/VNrPzhQrviOmpqciKBc4SmGVEW05aHA8XbqvWvH1fHXXDnhLUViRg9uB8vjx0ad3OiQrdrz+ZEf772BMaedDCwtzsv0RxPZw4spyDKGojCvBxuO30Aowf3S7k+6RhMbk9yRKVSpcHDgeJt1Tpp0WrmLl+f9HWdsNI7XNe8XEqL8uNuThTcC3zzrhaueHIFj7/rHxQPdueVl+THzfEEMLwynxxPS5Tj/O/hpJZaIuNe7UmOqFSqNHg4ULytWlP9duz01ki8jaKMIeqA+i0vfsID5x1JUV4O7kAQcbtkT46nPDHsemke28eez29rX8Hl85IfaIEU5Dozl1Oi416JJEdUymoaPBwo3latTvt2bKVYG0XF7s4zvL9+B4Sv+hah9b+fU3vTZdTPe5TuV9/M4LvuZcyJB3PZcf7pt1edcJDjNqNKZuZZZ9qdUTmHBg8H6uw3g2gbRcXuzvPy+Dtf09DioS0weNzmMzS0ePjpki3I9wbvSWBYVJDH/554sC274Fkl1iB4m8/H7S8lqA3/AAAXgklEQVR9uk/3Y7bvzqicx7n/ejo5vRnsL1Z3njtHgMg3W19BVz48ZTSuomIg8mLCEdOXcvcrnztmPCheIse3/rttv+7HbN2dUTmTBg8Ha8/NINZueh3JyoWOsbrzBKHVGzl4NHnNnhlH0RYTNrR4+Msn1dTtbku5fFaKNQgebbaYUh1J/wqzRPhNemez/yYY7dtrR7B6oWOs7rwxR3SnwES+8YfOOIrVHQTwxpebUypbuPYGzXiD4HbQhIcqGRo8skCkm/TYeSuBfZMDdoTgdODtu1tSTjUSy37deSf2Y363VZw+YwK5UbqtQmccxeoOAmJuCpUoK4JmrEB511n27FaoCQ9VMjR4ZLhos3Javf7/n710HSMeebvD0poEpwP/5aNNMRc6vvJZbcrvUeDO4bTDejN080pOfGQ8nrdfo+8v/8C0y4dQnJ+7p1sn0hTcWN1BQLuntbYnP1e4aONeA/oUt6uMSllBg0eGi9cN4zHQ0Opl3PwPaY2SlsMOM95eF3Oh48LPalK+dutXa2j7/QRu/GIBuT88L5DA8KQ9N9urTvBnh400BTdWdxDAsMP6pFwuiJcdIPZ2t5HoILhyKg0eGS5eN0zQ7jYv//wi9Rt2ssaedHDMhY5nppBrydewix2zHqB2wmjo3osJx99G7o8vR9x5e44pcOcw5JBeAAw5pNd+N9vQ7qDQFkpRoJ+/vdN3400n1lQhKlvYFjxEZJyIrBORZhF5X0Ri5rYWkVMDxzWLyFoRucGusmWTeN0wof7ySbXNpdnrjMPLYy50HDFw/w2YojE+Hw2v/ZXq686j5aPllN4znbybf8e2gu4plS1SC+XpMcendK1wsbMD2J8qRAe9VUexJXiIyEXAFOAe4GhgGbBQRCLm1BCRg4GXA8cdDfwBmCoio+woXzaJ1w0TSqL3blkuL9dlyUJH35rP2HzrVdT9aTIlF19N2cNPU/C9Y9tdvvAWilULBmNnB7A/VYgOequOYlfL4xZgjjFmtjHmc2PMBKAaGBvl+BuATcaYCYHjZwNPAD+zqXxZI7Qbxr9QLrpzjkwxz3iK2rPQ0ezcwbgvFtD66xtwH3wYFbNfpPjsi5EcZ98UO3t2ANV5WB48RCQPOBZ4Leyl14AhUU47McLxrwLHiYg71vtVVlYiIvs8Jk6cmELJM9fem/S3oh7TxZ1DXo7/4+7IXQmTHfA1Xg+7XppHy08upl9jLXl3zqTnTXeQ061HRxTXEpodQHUGdrQ8egM5QPhczFog2ihpeZTjcwPXi2rjxo0YY/Z5ZFPwSLQPu8Cdw/Dv+McRuoZllu0SGBOZsXQtYN+uhO1dGNf88QpqJ4ymfv5j5F5xE7cfMw7XoYcnXY7gGFCiY0F20FlSKtvpbCuHS6UP++kxg7lmSH8ArjzhIFzin21l5WK9cO1ZGOfZUsPWP97OljtuJH/Q8VTMepGSM87mmqGHpDTw2yXwu+qi/f5K2caO4LEV8ALh02nKgGhzRWuiHO8JXE8lIT9372BwrkuIkvIppXUHkcRbGBdtfYlpa6V+/mPUXH8+vvo6yqc+Q4/rbsXVtahDBn6DLROXiGX5t5TqLCz/l2mMaRWR94HhwIKQl4YDL0Q57d/AuWHPDQdWGBMlYZFKyOaGFtu3KI23be6rn+//naHpvbeom/UAxtNGz1smUjj0dCR8Lw6bBVsm1z/7AR7jj7BTl6yh6u21TL1gkI5RKBWDXV/rHgSeEpH3gKX4Z1P1BaoARORJAGPMFYHjq4DxIjIZmAkMBa4ELrGpfFkv+K06uA4kUgCxat1BvG1zZ7y9bs/PbZu+oW7WAzSvfI+SUZdTfMGVuArSs01qsIXREJLavLnNRzM+JixYycJxQ3WsQqkobBnzMMbMB34C3AGsBE4CRhpjvg4c0i/wCB6/DhgJnBI4/lfATcaYaC0VFUfwW/Www/rYvkVpvG1zx550MAWeFtqeraJm7IUgQsWM5+h2+VjLA0djq4enl38d/0D8qV2isapLT6lsZVuHsjFmOjA9ymunRXjuTeAYu8rT0RpbPcxdvp7Rg/uldcFWcLHehAUr8fh8NLX5KHS7yHW5LFt3MGJgGVMWr6GZ/VsfuS4XP6j7jGPeexBfrxJ6//p+Co8b2u73jGZ3q5dnVmxI6Ng310QfTtNUIkrFprOtbBLMLhu+21s62L3uIOrCOLfw+9qXkdl/5OUDhpA36UlbA0ey/t8RFWlNJZIKKzfXUqo9NHh0EnavOwgNUG5vK2P5ktn/uoPDu+eSP/lZ/txv2D4JDO126XEHxp3mm+5UIslavXmXpZtrKdUeGjyUZfJzhJO/+Tez3vkDJ/9nEZX3TKXXbXchPa2/CcdbPHlZAt2FmZZK5I6/rbJ8cy2lUqXBwwZO6Fro6OyqLV98Su0tV+KZO535/YeT98dHKfiufUNYVq0DyaRUItH2bdHBfZUOGjwsZvW+3anqqOyq3h3b2D75d2y+7WryDvk2+ZOf5ZXKIY5PYBgqU1KJNEdZbKmD+yodNHhYyMotSJ3OeDzs+sszVF93Hm3ffEXZg4/T86ZfISWZk8Aw0xRESRvv1MF9ld0y5+thBlj85Ra8cboWRqSwg57TNH+0nB0zJ+HbWUeP635Gl9N/hEQZeAbdoKi9uuTlcNUJ/Vjw4SaI0Ppw4uC+yn4aPCwUa0vYbOha8Gyuoe7RyTT9+w2KzrqIbpdeh6trUdzzgl1oKjVd83IZd/KhnHpoH1vX6yiVDO22slCsLWGT6VpobPUwa+laGls9VhYvZaa1hfp5j1Jzwyh8u+opn/YsPa69JWLg0FaGfTJpcF9lPw0eFho2oJQcC1KBOGWBoTGGpneXUD32Qhpe+TM9b/09pXc/grtf9FaEboNqr0wZ3FfZT/+FWyi4biAbuhbaNq73JzD8aDklo64IJDAsSHexlFIOocHDYsGuhZc+qWbSotWMP+VQzjmyImMCh69pN/XzH2PXn+dSeNwQKmY8R27FAekullLKYTR42CDYtTBp0eqM6VowxrD7zVfZ+djDSEEBvX/9AIXHRdtyXinV2Wnw6ESiDWa3rvuSuqpJtP73C0ouvpricy5F3O40lTJ14Sv7093i08kDKpvpgHknEj6Y7dtVz44Z91F702Xk9C6jYuYLlJw/JiMDh90r+1OZAaeTB1Q20+DRCRmvl4ZX/kz1defRsmolff5QRa/b7iSnV2YuNOuIlf1OmQGnlFPoVyKbOLXLouWLT9hRNQlv9QZKLh9L0ZnnITnOKmOy4u2h/spntZxzZN+Y13Dq56WUU2nwsInTVlV7d2yjbs40dv/rZbr+8Gy6/e5hcrp1T3exLBFvD/WFn9XEDR5O+7yUcjoNHlkk0rdn4/HQ8Lf57HxmFu5+36LsoSfIO/Q7aSyl9c4cWM6qmvqIAaTQ7eLMLMgnppTTaPDIIuHfnps/Ws6Oqkn46nfS44bb6DJsZMwEhpkq3h7qIwaWpaFUSmU3DR5ZyLO5hro/PUTTO4spPvsSSi69BleX+AkMM1U2rexXKlNk39fQDNeeXQhNaws75/3Jn8CwcRfl0+bR/ZqfZHXgCNKkgUp1LG15OMiq6nomLFi5Z+bQ1CVrqHp7LVMvGBTzJmiMofm9t9gx6wHw+eh5650UDhmGSOQkjdkqE1f2K5WpNHg4ROhahb3P+WjGx4QFK1k4bmjEm2Hbxq8DCQxXUHL+GIrPH6MJDJVSttNuK4dY/OUWPHF2IQzla9pN3eNTqRl3EeLOo6JqAd0uu14Dh1KqQ2jLwyES3YVwbwLDKUhhF0p/O5mCY07oyKIqpZQGD6cI7kIYKYAEdyHcJ4HhJddSfPbFtuWhamz1MHf5ekYP7qe5mZRS+9FuK4cYNqCU3Gi7EAocvfhJfwLD0kACw1GX25rAUHM5OZemUlFOoF8pHSLaWoUcr4fffPwYpouPPvfOJH/goHQXVaWZplJRTmB5y0NE8kVkqohsFZFGEXlJRGJuRScipwSO2ygiRkSutLpcmSB0rUKv5jpuqF7EYyvu47hRP6Zs8lMaOJRSjmFHt9VkYBRwCXAyUAL8XURitbGLgE+Bm4EmG8qUMdy7djD09ZlUvfNHTqvIp9/M5ygaeX7GZ75VSmUXS7utRKQbcDVwlTHmn4HnLge+Bn4AvBrpPGPMy8DLgePnWFmmTOFPYDiPnc/MhgMO4efHTuCRay4kpyg/3UVTSqn9WD3mcSzgBl4LPmGM+UZEPgeGECV4dHbNK9/zJzBsqKfH2J/TOPh01lUtS3exlFIqKqu7rcoBL7A17PnawGuWq6ysRET2eUycONGOt7KcZ3M1W+/5OVt+exOFg0+iYtYLdP2fH6U9rUh78mtlI/19KLW/hFoeInIX8Ks4hw1rf3GSt3HjRvr2jb3Rj9P4WprZ9cJT7Hp+DnkDB1E+bR7uA/unu1hA6vm1spX+PpSKLNFuq8nA03GOWQ+cAOQAvYHQfBplwFtJly7LGGNofudNdsx+CIyPnj+7i8ITT0t7SyMo1fxa2Up/H0pFl1DwMMZsZf+uqP2IyPtAGzAceCbw3AHA4UCn7sRv2/AVdTMfoOXTDyi+YAzFo67Ale+sPFSJ5Nca0Yl25dPfh1LRWTpgbozZKSKPAveJyGZgG/Ag8DHwevA4EfkCmGaMmRb4uQg4NPCyC+gnIoOA7caY9VaWsaP5djdSP+9Rdv31GQoHn0x51QJyy5zZzZZofi0ns3L1dTb8PpSyix0rzH8CeID5QCGwCLjCGBP6r/Db+Lu2go4D3gj5+XeBxxPAlTaU0XbGGHYvfoW6x6bg6lJE6cTJFBzt7ASGieTXcjorV19nw+9DKbtYHjyMMS3AhMAj2jES9vNiwBkd/xZoXbvan8Bw7WpKLr2W4rMusjUPlVWGDSjlvtdXR3wt1yUMG1DawSVKL/19KBWdJka0kHfXTnZMv5famy8np6yCilkvUHLeZRkROGBvfq3i/FwK3f4/jUK3i+L83E65F7j+PpSKThMjWsB4vTS+9ld2PvkIOaXl9Ll3FvkDj0p3sVISzK/10ifVTFq0mvGnHMo5R1Z02hul/j6UikxbHu3U8vnH1P50DDufeIRul4+l7KEn2x040p1yO7gXOKB7gaO/D6Ui0ZZHirzbt1I3Zyq733iFojPPo+TuR8gp7mbJtTXltlLK6TR4JGlPAsO5s3EffChlk58k71vfTnexlFKqQ2nwSELzh++yY+b9+Bp30ePGX9DltBGOWR2ulFIdSYNHAjybq6mb/SBN771F8TmXUHLxNbi6dE13sZRSKm00eMSwJ4Hhgjnkf/cYyh+Zh/uA/ukullJKpZ0GjwiMMTS98yZ1sx8EoOfP76bwhFM7VRdVumd8KaWcTYNHmLZvvqJu1v20fPohxRdcSfGoyx2XwLAj6IwvpVQsGjwCfLsbqX/2T+x66VkKv38K5TOfJ7dPRbqLpZRSjtTpg4cxht1vLKTu8YdxdS2mdOIUCo7+frqLpZRSjtapg0frf79gR9Uk2tatodvo6yg66yIkt1P/SpRSKiGd8k7pra9j51NVNL7yZ7oMO5Pet99LTs/e8U9USikFdNLg0fbVGlpXr6LPfbPJP/zIdBdHKaUyTqcMHgVHHkfZ5Cc71dRbpZSyUqfNqquBQymlUtdpg4dSSqnUafBQSimVNA0eSimlkqbBQ6kEaK4vpfbVKWdbKZUszfWl1L605aGUUippGjyUUkolrdMGj4kTJ6a7CJbLtjplW30g++qUbfWB7KuTXfURY4wtF7abiPQFNm7cuJG+ffumcj6ZWvdosq1O2VYfyL46ZVt9IPvqFF6fTZs2UVlZCVBpjNmU6nU7bctDKaVU6jR4KKWUSpoGD6WUUknL5HUeLoCampqUL7BpU8rdfY6VbXXKtvpA9tUp2+oD2Ven0PqE3DPb1XjI5AHzo4EP0l0OpZTKUMcYYz5M9eRMDh5u4LvAFsCX5uIopVSmcAGlwKfGmLZUL5KxwUMppVT66IC5UkqppGnwUEoplTQNHkoppZKmwUMppVTSNHgopZRKWlYGDxHJF5GpIrJVRBpF5CUROSDOOacEjtsoIkZEroxwzJzAa6GPd2yryL7vbVedREQmisgmEWkSkcUicoRtFdn7vknXJ3DeOBFZJyLNIvK+iJwc9vriCJ/RPJvqELMsEY4/NXBcs4isFZEb2ntNq1ldp8DfVvjnkfrK3iQlUx8RqRCRZ0TkCxHxisicKMeNEpHPRKQl8N9zbatA5Pe3tE4icmWEz8iISEGscmRl8AAmA6OAS4CTgRLg7yISaw/RIuBT4GagKcZxrwMVIY+RVhQ4AXbV6efArcAEYDCwGfiniBRbVO5okq6PiFwETAHuAY4GlgELRaRf2KGPs+9ndL3VhU+iLMHjDwZeDhx3NPAHYKqIjEr1mlazo04B/2Hfz+N7tlRg//Il+/vMB7YCfwTejXLNE4H5wFxgUOC/C0Tk+9aWPjI76hSwm30/owpjTHPMwhhjsuoBdANagdEhzx2IfyHhGQleowG4MsLzc4C/Z0udAAGqgV+FPFcI7AKud1p9An/8s8Oe+xL4Q8jPi4FpHfCZxC1L2Gv3Al+GPfcn4N+pXjND6jQR/2I028vf3vqEHfd3YE6E5+cD/wx77nXg2Qyu05VAQ7JlycaWx7GAG3gt+IQx5hvgc2CIBdc/SUQ2i8hqEZktIn0suGY8dtXpYKA87LpNwJJ2XjeepOsjInmB814Le+m1COdcHOgOWyUi91vdikqyLEEnRjj+VeA4EXGneE3L2FGnkOcOCXSLrhOReSJi+2bwNv4+o9XZqZ9RogpF5GsR2SAifxd/+qeYsjF4lANe/E21ULWB19rjFeAK4HT8XT3HA/8Skfx2Xjceu+oUPLfW4usm8r7J1qc3kEP8sj4DjAaGAXfi7xp7oZ3lTbUsocqjHJ8buF4q17SSHXUC/zflK4ERwLWBc5aJSK/2Fzkmu36f0ers1M8oEf8B/hc4B383cjOwVEQOi3VSxmTVFZG7gF/FOWyYnWUwxoQOvH4iIu8DXwM/Al5M9npOqJOVnFAfY8yskB8/EZG1wLsicowxRhNpdjBjzMLQn8U/wWQtMAZ4MC2FUvswxvwb+HfwZxFZBqzEPw56U7TzMiZ44B9gfTrOMeuBE/BH5974kyYGlQFvWVkgY8wmEdkAxIzQMaS7TsFZL2WB9wm9biozYuysz1b8rZWysOfjlXVF4LzDsC4LcyplqYlyvCdwPUnhmlayo077McY0iMgqUv83k6hU/17iiVZnp35GSTPGeEVkBXE+o4zptjLGbDXGfBHnsRt4H2gDhgfPFf8U0MPxz0ywjIj0BirxDzonzQF1Wof/jy70ugX4Zz8lfV0762OMaQ2cNzzspeFxyvo9/IEqpc/IwrL8O8rxK4wxbe2onyXsqFOkEwJ/X9/Bws8jEht/n9Hq7NTPKGkiIsCRxPuMOmKGQEc/gBnABuAH+KezvYG/GZYTcswXwPiQn4vwT70bhH/a2m8C/98v5PX78Q+Y9QdOw/+HtAEozsQ6BY75P2AncB7+FPfzgE121ynF+lyEf5bWNfgDzRT8s8gOCrz+rUAdjwt8RiPxD8J/EHpdi8ofryxPAk+GHH8w0Ii/dXZ44LxWYFSi1+yAvzE76nQ/cGrg2O/jn/FT3xF1SrY+geeC/16WAC8F/n9gyOtD8LesfoE/CN6O/4vQ9534GSVYp98CZwCHBF57LFCn42OWpSMq3NEP/HObpwLb8N80/wYcGHaMASaG/Hxa4Lnwx5zA64X4Z1VsDnx4X+OfuntgptYpcIzgn05ZjX+g7E3gu06sT+C5ccBXQAv+b2GnhLx2YKD82wKvrwn84+ppUx1ilWUxsDjs+FPxB7IW/K2+G5K5Zgf9nVlaJ/Z+GWkFNuKfvDDQ7nq0oz6R/r18FXbM+fi/2LTi/3JynsM/o5h1Ah7Cfz9rwX9/exU4MV45dD8PpZRSScuYMQ+llFLOocFDKaVU0jR4KKWUSpoGD6WUUknT4KGUUippGjyUUkolTYOHUkqppGnwUEoplbT/D7CaFi1Md4VxAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.errorbar(data['FeH'], data['ThH_z'], yerr=data['error'], xerr=data['eFeH'], fmt='o')\n",
"xs = np.arange(-0.15,0.15,0.01)\n",
"plt.plot(xs, m*xs+b)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"get errors with an MCMC"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 51.8 s, sys: 485 ms, total: 52.3 s\n",
"Wall time: 54.6 s\n"
]
}
],
"source": [
"%%time\n",
"ndim, nwalkers = 3, 20\n",
"spread = [1e-3, 1e-2, 1e-4]\n",
"pos = [bf + spread*np.random.randn(ndim) for j in range(nwalkers)] # randomize starting values\n",
"sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=args)\n",
"sampler.run_mcmc(pos, 1000);"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 547.2x547.2 with 9 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"samples = sampler.chain[:, 100:, :].reshape((-1, ndim))\n",
"samples[:,-1] = np.exp(samples[:,-1])\n",
"fig = corner.corner(samples, labels=[\"$m$\", \"$b$\", \"$j$\"]) \n",
"#fig.savefig('ThH_z_FeH_emcee.png')"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"slope = 1.564e+00 +2.116e-01 -1.759e-01\n"
]
}
],
"source": [
"m_16, m_50, m_84 = np.percentile(samples[:,0], [16,50,84])\n",
"m_errp = m_84 - m_50\n",
"m_errm = m_50 - m_16\n",
"print(\"slope = {0:.3e} +{1:.3e} -{2:.3e}\".format(m_50, m_errp, m_errm))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.lines.Line2D at 0x1125dec18>"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(samples[:,0])\n",
"plt.axvline(0.0, color='red')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"now let's do this for [Th/Fe]_ZAMS vs [Fe/H]"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"args = (data['ThFe_z'], data['error_1'], data['FeH'], data['eFeH'])"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"bf = bestfit(*args)\n",
"m,b,lnj = bf # slope, intercept, ln(jitter)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.12018648562053151, 0.07814959224878493, -2.9371141554777043)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"bf"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1128a54a8>]"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.errorbar(data['FeH'], data['ThFe_z'], yerr=data['error_1'], xerr=data['eFeH'], fmt='o')\n",
"xs = np.arange(-0.15,0.15,0.01)\n",
"plt.plot(xs, m*xs+b)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CPU times: user 56.2 s, sys: 552 ms, total: 56.7 s\n",
"Wall time: 58.1 s\n"
]
}
],
"source": [
"%%time\n",
"ndim, nwalkers = 3, 20\n",
"spread = [1e-5, 1e-3, 1e-4]\n",
"pos = [bf + spread*np.random.randn(ndim) for j in range(nwalkers)] # randomize starting values\n",
"sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=args)\n",
"sampler.run_mcmc(pos, 1000);"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 547.2x547.2 with 9 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"samples = sampler.chain[:, 100:, :].reshape((-1, ndim))\n",
"samples[:,-1] = np.exp(samples[:,-1])\n",
"fig = corner.corner(samples, labels=[\"$m$\", \"$b$\", \"$j$\"]) "
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"slope = 0.092 +0.688 -0.775\n"
]
}
],
"source": [
"m_16, m_50, m_84 = np.percentile(samples[:,0], [16,50,84])\n",
"m_errp = m_84 - m_50\n",
"m_errm = m_50 - m_16\n",
"print(\"slope = {0:.3f} +{1:.3f} -{2:.3f}\".format(m_50, m_errp, m_errm))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we've got a sense of how it works, we can do it faster for the fits in Figure 4 just by changing the args:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"args = (data['ThH_z'], data['error'], data['Age'], data['eAge']) #(ys, y_errors, xs, x_errors)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"slope = -0.018 +0.005 -0.005\n"
]
},
{
"data": {
"image/png": 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YxsZGKioqCAoKAqCsrIzw8HCKioq8wwsA/v7+PiFCRESkI3SpgADQKhyYVkMHTiACCGw+9wBwpTFmhLW24FC1peWD+qijjqKhoYHKykoWLVpEQ0MD/v7+pKen06dPH0JDQ+nZsyeBgYH06NGDvn37snnzZnbs2IG/vz9BQUH07duX9evXk5mZidvtZtu2baxbt464uDhcLheNjY3s2rULa613cygREZHO0qXmILS22zbOTiAcqDPG3APcBow/lOEAYMeOHRQXF/PNN98QFhZGTEwMmZmZ9O/fn6CgIDwej7c4EkB5eTnBwcH4+fnR0NCAMYaSkhIaGxupra1lw4YNfPvtt4SHh+N2u9m6dSvbtm2jsbGRgQMHkpycjNvtZvv27fz444/U1tb+RAtFREQOjU7rQWiuVWCstfWtjrVXAbGKph0cHwIuBUZZa5ce6jZGRUWxcOFC1qxZQ3BwMMccc4y3d6ChoQGXy+VdApmXl8eqVauoq6sjPDzcO68hOzub8vJy4uPjCQkJobi4mDfffJPhw4cTEhJCSUkJJSUlJCQkEBgYyIoVK6isrKShoQE/Pz8GDx58qL9MERERH50SEIwxGcB9QIIxJhv4t7X2leZdGfc06TAIOAZIA4631i7viHY6HA7GjRtHz549GT58OB6PhxUrVpCdnc2QIUPazNJOSkpi+PDhbN++nYyMDBITE0lISGDw4MFEREQwaNAgGhoaePbZZ/n+++8pLS1l0KBBrF69mpiYGAASExNpbGwkNDSU4uJi+vfv3xFfpkiXo30aRDpfhwcEY0x/YCHwPvAZTZUQhxpjTrfW/qZ5L4Uga23r/vUK4G3gLmvtuo5sb2hoKKeccgoARUVFlJaWUlNT06YyYnV1NQsXLqSurg4/Pz927NiBw+GgpKSEnj17EhUVRXl5OQsXLiQ3N9e7LXRRURHV1dUMHjyYsLAw/Pz8iI+Px+l0Eh8f79OWhoYGb12E1qspRA432qdBpPN16KeMafo/+3LgU2vt5OZjM4GrgauNMa9Za3/VEg6MMVNoWvK4zRgzyVpb15Ht3V1UVBQjRozA5XKRkpLiXd61ZMkSPvnkExoaGhgzZgwVFRWsWrWKwsJCSkpKqKuro0ePHhQVFREVFcWYMWM45ZRTKC4u5phjjmHgwIFUV1d76zA0NDSQnJzcpjiStZbS0lLy8vKorq6mb9++bX5Q6oemiIgcTB0aEKy11hiTCMS3OlbTvKeCC7jWGPOQtfYOY8yZwBzgbWPMb2iqj9Bh9vSBGxAQQJ8+fbDWUldXx5YtW0hKSmLEiBGsWbOG0tJSKisrWbBgAdu2bSM0NJSCggJ27dpFXFwcubm5pKSk0KtXL0pLS6mtrcUYg8PhwN/fn/z8fEpLS4mIiCAwMBCHw+HdACo/P5/evXsTGBiIv7+/txdDRETkUOiwgNC8bNECy4AMY0ymtXYVeEPCq8AAYIwxJsJa+7ExZhbwyoHurXAo5eXlsWnTJjweD/Hx8Zx//vl89dVXREdH43Q6iYmJYeDAgWzcuJG8vDy2bdvmrYmwefNm1q1bR3FxMVFRUezatYusrCxvr8OQIUPo0aMHbrcbj8dDSUkJOTk53nBRX1/v3XFSRETkUOiwgNBq2eKHwL3AbcaYG621O5vPVxhjHgGmAWOBN62193dU+/ZXUlISbrebwsJC/P39cTgc9OzZk9raWqKiosjIyMDpdJKSksKCBQvYsGED9fX1zJkzh5qaGlJSUkhKSmLBggUEBwdTUlJCeno6FRUV7Ny5k507d3oLLgUEBNCjRw+SkpK8qxvcbnebHgSPx0NNTQ0hISHaNVJERH62Dp/pZq3dZIy5GPgIcBljZlhrC5tP1wM/AGUd3a79FRgYiMfjITc3Fz8/P++2zr169SIqKorCwkLWrl1Leno6aWlpuN1uXn31Vd58801GjRpFr169AJg/fz5vvPEGs2fPpqqqitGjRxMbG8vOnTvp378/FRUVJCYmkpiYSHh4OIA3CLTWslU14K0GKSIicqA6ZSq8tfYLY8xFwOtAvDHmDZqCwWQgAdjUGe3aVy1bNrcscwwPD6ekpITQ0FBiYmKor69nw4YNLFu2jPXr1zNy5Eh27drF4MGDOfvss9tMPjzvvPM477zzaGho4Pvvv+eTTz7ho48+4pVXXmHMmDE8++yzFBUVERwcTGhoKP7+/nuce9B6HwkREZGfq9PWyllr3zPGnAA8CjxIU+9BPXCWtTa3s9q1L1rPP+jbty8BAQEEBwfTs2dPysrKWLFiBcnJyRQXF1NZWYnD4aCqqoqzzz673dd0OBwcf/zxnHTSSTzwwANs27aNSZMmcfrpp3PJJZcwYsQI79CBx+OhR48ehIWF4Xa7vcMKYWFheDweqqqqNNQgIiI/S6cuprfWLjPGTAB6AWFAobW2y+9t3LLrYs+ePb0rF1JSUli3bh1r1qxh8+bNJCYmct5551FaWkp5eTlff/0199xzDzt37my3hsHOnTu9wwNBQUG88sorTJ8+nSeeeIKbb76Z5ORktm/fTn5+PoMHDyYwMJCYmBiCgoJYt24dw4cP9y6VBPZ5lYOWSIqIyO46vdqOtbaCpkJI3UZgYCBpaWl4PB7y8vIoKCggNzeX7du3ExYWRlxcHJGRkVRVVZGUlMQHH3xAeHg4J5xwAhUVFe3+Zr/7trlBQUE8/vjjDBw4kAcffBCn00nv3r3xeDxs27aN8PBwXC4X9fX1/Oc//8HlcpGZmYnL5QLA7Xbz1VdfcdpppxEREQFAY2Ojt9hS66EOERGR1jo9IHRnfn5+DBw40Dv3YOnSpeTn5zN69Gjv0saWAHHGGWcc0AeyMYapU6fSr18/rr32Ws4991yOP/54amtr6dWrF06nk8jISACysrJwOByUlZVRWlrKunXr+OGHH7DWMmHCBEpLS2loaKC4uBhAW0mLiEi7NEj9MwUEBJCWlkZ4eDgOh4NNmzZRUFBAr169KC8vZ8WKFXz00Ud7nX+wL0477TS+/fZbvvvuO+bNm8fixYvx9/cnKSmJrVu3UlBQwLJly4iJiaFv37707duXCRMmcOqppzJmzBhKS0spKGja/DIhIYHo6OiD8eWLiMhhSgHhIIqKisJa6y2vHBcXR2VlJSEhIZSW/vypFUcffTTfffcdvXr14rXXXmP9+vX4+fkRGhpKamoqAwYMwOVyER4eTnx8PFFRUUycOJGIiAiio6PbDQZ1dXVs2rSJurpOrWQtIiJdSLcMCMYYP2OM/27HOn2mndvtxs/Pj/LycowxeDweKisrGTRoEM8++6zPHIMD0atXL959912mTZvGTTfdxHPPPUdJSQnHH3+8t35CUVERlZWVeDz/3Tnb39+f2NhYcnNz+ec//8mWLVu853Jzc8nOziY3t0svHhERkQ7U7QKCMeZo4GngX8aYB4wx54J3n4dODQkZGRmcffbZjB49mqOPPhpjDD179uSCCy5g06ZNfPnll/v8WjU1NVRWVu7xnJ+fH3feeSfz58/n0Ucf5dVXXyU2NhY/Pz88Hg9btmwhPz8fl8tFbW0tK1eupLa2aXPMtWvXsnHjRtauXet9veTkZNLT00lOTv55b4D4SExMxBjT5jFjxozObpaIyE8yB+O32o5ijBkIfEdTuWY30A9IBl601t7bfI2x+/BFGWMSgPz8/HwSEhL2qx2tfzNv0djYSElJCSEhIYSEhFBWVkZeXh5lZWW4XC5ef/11Ghsbefzxx9tdxbB582bvHgt33XUXn332GaNHj+ass84iKyuL1NRUn+fk5uZy3XXXYa3l0UcfJSkpiZ07d+J0OsnMzGTz5s2sXr2ajIwMBg0aRFVVFQsXLuSEE04gLCwMa+1e6yV0gY6ZLqmgoIDExESARGttwe7nf873V3dijDkoPWNd/Z4d7ae+v0Q6QrfpQWjuHbgG+ASYbK29kqbKi0/RtK/DTGiz58M+OZDf8Ha/3hhDWVkZGzduZMmSJdTU1BAdHU1ycjIBAQFs3LiRnj178vbbb1NXV0dkZGS7j/DwcPz8/FiwYAHTpk0jOjqaBx54gAsuuIC77rqLRYsW0djYiLUWay1JSUm88sorDB06lEmTJvHRRx/hcDioqKigqKiI0NBQ7yTKxsZGwsPDOeOMMwgPD/e2XUREZHfdJiA0f/CnAwEtIcBauw34C/B74CpjzLT9fd38/Hzvh23L40C6gKOjo4mIiPBWTXS73cTExDBy5EhGjhzJrbfeyoABA5g3b95PvtYXX3xBSEgIU6ZM4Q9/+AMLFy7k9ttvp6KigquvvprTTjuNZ555xtuT4XQ6mTdvHjNmzODee+/lgw8+wOVysWnTJjZtaqpanZ2dTVFR0V7v6/F4qK6u3mMPiYiIHFm6RUBoNbfgKyCheagBAGvtLuA14O/ARGNMXMe3sGkSYGZmJgMHDsThcLBkyRJKSkqorq5m1KhRlJSU0LdvX/7617/S2Ni419f64IMPOPPMM70VFwMDAxk9ejRPPPEE33zzDddddx1///vfufXWW6murgaaejWuv/56PvroI5599lleeeUVbyhobGzE5XJ5P/jdbjerVq3C7Xa3ue+OHTtYvHgxO3bsOATvkIiIdCfdIiC0GjZYDvQGLjPGxLQ6Xwy8BRwH9O34FjZpWSlQVFREbm4ua9euJT8/nx9++IHKykouv/xy3G43f/jDH/b6OuvXr2f48OF7PNejRw8uvPBCXnnlFdavX8/48eP5+uuvvedPOukkvvjiC5YvX8706dNZsWKFtzcjNzeXyspK/v3vf/Phhx/y9ddf09DQgMvl4vvvv2fjxo3k5uaSl5d3UN8XERHpfrpsQDDGJBpjzjbGXGGMyQSw1n4GPAZMB641xiS1eko2sHYPL9Xh+vfvz9ChQxk6dCgVFRV8/fXXfPjhh0RGRnL33XfzyCOP8NFHH7X7/IiICKqqqvZ6j9TUVN566y0mTJjAtddeyxVXXEFZWdMu2QMHDmT58uX8+c9/5uOPP+bss8/m1Vdf5T//+Q/ffvsthYWFFBcXs3PnTnJzc/nxxx9ZtmwZ9fX1DBs2jIEDB+713iIicvjrkgHBGDMY+Bq4A5gL/NkYcxmAtXYOcBtwC/C/xpjxxpiU5n9HATmd0uhWgoODyczMxO1243A4CAoKIjAwkM2bN1NaWsp9993HlVdeydatW/f4/MjISHbu3PmT9wkKCuLGG2/kjTfeYP369WRlZfHaa69hrcXf358LL7yQ//znP/zzn/9k8eLFTJ8+nfnz55Oens4vf/lL0tLSqK2tJSYmhmOOOYZhw4aRlpZGQECAd3nk7sMQIiJyZOhyezEYY44CPgBeBGYBocBzwLnNx7DWPm6MKQF+TdP8gy3N14231m7vjHa31jIiEhUVhcfjISEhgZycHJYuXUppaSmpqamMGjWKSZMm8emnn3qXNpaVleHn50dwcDAFBQXePRMAfvzxx3bv53A4ePDBB3n77be56qqrePrpp7n55pvp2bMnACeeeKJ3SOGee+7hq6++4sknnyQ6OpqtW7eSl5fHqaeeys6dO73ty83NZf369QAMHjx4j/fVCggRkcNXl+pBMMYEAVNp6j34I1Bprc0HHgdONsbEGWP8AKy1LwGXACNpWu440lq7vIPauU8Ph8NBXFwcMTExHHvssVx66aUkJSVx/PHHM2fOHMrLy5k3bx7BwcEEBwcTFxdHbGwscXFx1NXVERsb633s2LGD+vr6PT5KSkrweDxMmDCBuXPnUllZyTXXXMPixYupr6/3tvmkk07iww8/JCUlhcsuu4x///vf5Ofns3LlSpYtW0ZpaSllZWXU1NSQlpZGSkoK6enpHfGWiohIF9OlAgJggHrgc2tttbW2Zbp/KRAABFprPS2rGqy1ZdbaVdba5c0TFbucmpoaqqqq8PPzw+FwcPrppxMZGUl9fT1xcXG8++67Ps/Z1yGGPYmPj+fhhx/mnHPO4d577+X5559vs8dCaGgoL730EmeccQa33norGzZsYOjQoQwbNow+ffqQkpJCREQEubm51NXVaYhBROQI1aUCgrXWDTxurX0emvZcaD61HSgGapuvs8aYMZ3Tyv0TEhJCjx49vH9WV1cTHBzMO++8g9MW4dsxAAAgAElEQVTp5Ouvv6a8vLzNc35OQICm1RT/7//9Px5++GG+/PJLzjrrLDZv3uw973A4eOyxx7jpppv44x//6DMXYvv27WRnZ5OTk+Od+CgiIkeWLhUQAKy1JeAtmdxSsccJRACBzeceAF5sLmfbpRljCAkJoaamhvz8fOrq6igvL2fcuHFMnDiRpKQk5s6d2+Y5ycnJbNiwod1JjPsqMzOTp556iqSkJE488UQee+wxb2+CMYabb76ZOXPmcNddd/H66697d5zs1asXWVlZjBw5kpSUlJ/VBpGDLSUlpd1hvT2VIxeRA9PlAkKL3UomO4FwoM4Ycw9NqxjGd5ca5TU1NZSXl9PQ0EBKSgoZGRn07t2bqVOn8vjjj/OHP/yBdevWea8/7bTTOPHEE5k+ffrPrjkfHh7O3//+d/785z/z/PPPc9JJJ5GTk+M9/6tf/Yrp06cza9YsAGJiYvD39ycqKora2lo8Hg/WWqqrqw/7+vfSPeTk5PhUP215/NxQLSL/1WkBwRjjMMYE7HasvfZUAeuBh4C7gFHW2qWHuIkHTUhICPX19VRXV9OjRw+stXg8Hmpra5kwYQLnnnsu11xzjbfSoTGG++67j3Xr1vHee+/t171cLheffvopLpfLe8wYw7nnnsuiRYtIT0/nwgsv9PYWANxzzz3ExcUxY8YM76THlStXsnbtWjZs2EBVVRXbt2//ydoMIiJy+OiUgGCMyQBeBj43xvzNGDMJoHkCov8enhIEHAOcDxzfncIBNH1Ap6SkkJSURGRkJC6Xi9zcXO8ywcsvv5w1a9bwj3/8w/ucmJgYrr/+embOnOktp/xTXC4X99xzD7Nnz+bKK6/kvffe865igKbehOeee47evXtzySWXeF83ICCAefPm8fbbb3P11Vezfft2UlNTOfroo0lLS6OoqIiGhoaD+I6IiEhX1+HbPRtj+gPfA+/TVP3wdJpqGCyz1v6m+Zoga21tq+fE0bRr413W2nW+r3pA7eiU7XirqqpYvHgxubm5DB8+nMzMTCorK70rDpYvX06fPn0AqKurY/jw4UyYMIFTTjkFf/89ZSe49dZbcTgcZGdn09jYSL9+/di5cycFBQX4+fkxfvx4Bg0a5N3W2eVy8de//pWePXty9dVXc+211wLw+uuvc9VVV3HxxRcza9YsgoKCqK2tpbCwkMjISO98hJqaGkJCQo7obaK13XOTrrb1cldrz4HSds/SFXRoD0Lz8sTLgU+ttZOttTNoCgh/A0YaY14DaAkHxpgpxpg+1tpCYNLBCgedxePxeOsbDB48mH79+uHxeCgpKeHSSy/luOOO4/rrr/f+gAsMDOSRRx5h9uzZ5Ofnt/u6jY2N3nDQv39/AgICiImJITMzk+joaN5//32effZZsrOzsdbidDqZPHky27dv54033vDe76KLLmLu3Ln885//5Omnn6aiooLg4GB69OhBZGQk0BQOKisrqamp2Wt7CgsL1esgItKNdWhAaJ54mAjEtzpWQ9OWzU8AA4wxDwEYY84E5gB/MMY4aKqP0K1VVFSwfPlytm/fTkVFBR6Ph6KiIlwuF42Njdxyyy189dVXvPbaa97nnHHGGZxxxhn85S9/2eNrulwutm7d6u05aNkBEpqWO8bHx3PDDTfQt29fXnnlFV544QUqKyuJiIhg8uTJ/Pjjj/zxj3/0PufSSy/lySefZObMmcyfP5/s7GxeeuklvvzyS3bt2kVISAjh4eEEBwe3O3GxtLSUgoKCNvMcRESke+mwgNBqy+ZlgKNlAybwhoRXgc+AMcaYCGvtxzSVWn7AWttgD4N+w5qaGgICAti1a5e3gmFlZSU7duygoaGBjIwM7rnnHqZNm8aGDRu8z5s1axY//PADCxcu9HnNl156ifr6evr160dAQIDPeWgqjnTGGWd4eydee+01PB4PsbGx/OY3v+GRRx5h/vz53usvu+wyZs+ezfTp03n44Yf57rvvWLBgAeXl5fj5+REWFobb7aaiooKamhpcLheLFy/2ToyMjo4mISGB6Ojog/wOiohIR+mwgNDqA/5DIA24zRgT2ep8BfAIMAIY23zsfmvtxo5q46HWu3dv+vfvz5lnnsmQIUMYPHgw8fHx9O7dm5qaGtauXcv//M//MG7cOH75y1+yfXvTthJpaWlMmjSJJ598ksrKyjavmZWVRUNDwz6N+UdGRnLRRRdRVlbGkiVLAEhPT+fee+/lpptualMUacqUKfzpT3/ivffeIyoqiksvvZTAwECqqqpYtWoVgHffiBUrVrB06VJWrFgBNPVcxMXFtenNEBGR7qXDVzFYazcBFwO/Ah5unoDYoh74ATgsy/c5HA5iY2MJDQ0lMzMTp9NJaGgosbGx1NfXk5+fz7JlyzjzzDPp27cv119/vfe5F1xwAb169eLZZ59t85rHHnssgYGBlJSU7FMbQkNDGTduHJ999hkVFRUAXH/99SQnJzN9+vQ2115++eXMmzePN954g/fff59FixbxzDPPsHDhQlavXo3H48HtdpOVlcXw4cPJysr6me+QiIh0FZ2yzNFa+wVwETAFeMYYc1nzFs+3AQnAps5oV2dwuVzU1NQwcuRIBg0axJYtW1i4cCGDBg3i/fff9xZQcjgc3HzzzXzxxRfe3/6h6bf46OhoiouLvXUUfsoxxxxDXFwcH3/8sfe1586dyxtvvMGbb77Z5tpJkybx2muvMXPmTAoLC8nJycHlcpGWluYtIe10OvnFL36B0+k8SO+KiIh0tk7rA7bWvmeMOQF4FHiQpt6DeuAsa21uZ7XrUNt9KkXLh2pQUBButxuXy0VFRQUnn3wyGzZsYPbs2cydOxe32018fDznn38+jz/+OE888QQhISEABAcHY60lLy+PiIgIn3u+//77PsfCw8NZvXo1H3zwgfc3/9/97nf85je/YePGjZx88skEBAQwfPhwxo0bx0svvcSll17K7bffzgUXXIDT6SQgIIAtW7aQlJSEw+HA5XLhdDr3uvxRup/U1NR2KxSqFLfI4atTB4mttcuMMROAXkAYUGitPaynvu8+V8AYQ2hoKNXV1ZSVlZGbm0tCQgINDQ2MHz+eW2+9lQcffJDRo0djjGHkyJGMHTuWTz75xFse+ZxzzmH58uWsWrWK8ePH+3xAP/roo+2255tvvqGyshKn08mZZ56JtZaHHnqI+vp6xo4d623vOeecw/33389DDz3E6NGjOf7449m2bRsrV66kuLiYo48+2rv0MTQ09GC+ZdLJtm7deljUFhCR/dPpv+pZayustTnN2zYf1uFgbwIDAwkNDeWEE05g2LBhDB48mGOPPZZBgwYxZ86cNtc99thjvPDCC232bxgyZAjV1dVs2rR/ozN+fn68+OKL3n+fddZZ3HDDDcyaNYtPP/20zbU33HAD5513Htdccw2bNm0iKiqKgIAAduzYQVFREWFhYRpmEBE5THR6QJAmxcXFbNu2jaCgIPr164fT6SQzM5Ozzz6buXPnUlhY6L12xIgRnH322dx5553eUspBQUFkZWXx3XfftSmv/FP69+/P/PnzvSsQAMaNG8e0adOYNWsWL7/8sve4MYY//elPJCYmctNNN7F+/Xr8/Py8qxsADS+IiBwm9NO8i6mvr2fz5s3U1dWRl5dHeno6I0eOZPLkyW32ZHjwwQfZsmUL1157rXdy4siRI/F4PLzzzjs0Njbu0/0iIyOZNGkSM2bMYOPG/64oHTt2LL///e+59tpr+ec//+k9HhQUxLx581i8eDGPPPIICxYsIC8vj6CgoIP0DoiISFfQbQNCO5s6dVtxcXFkZmZ6A0JeXp733NSpU6mrq2Pq1KneD/6EhATefPNNvvvuOz7//HNvCeULL7yQ8vJy77F9MXnyZMaOHctdd93VZjLamDFjePLJJ7nmmmvaFFJKSEhg6tSpbNq0CZfLRX19PdZazT0QETmM7HdAMMZMNcYsM8Z8bYz5fXMZ5A5ljOkH/NYYc9hMoW6pUJicnExaWhrx8fGEhIQwZMgQsrKyePjhh1m6dCkzZszwPictLY0333yTzZs3ewNBWFgY5513HmvWrOGHH37Yp3sbY5g6dSq/+MUvuP3228nN/e8ikssuu4zHHnuMKVOm8NFHH3mP33zzzWzZsoXS0lJSUlLo37+/hhdERA4jB/IT/SqatlweTdNujH8+uE3aO2NMFk27QR4F+Dcf6/ZbB9bU1FBRUUFjYyN9+/aloqKCsrIyoqKigKZ5BzNmzGDevHk8//zzeDwePB4P/fr145e//CVr1qxhwYIF1NbWEhkZybhx41iwYAHZ2dk/ee/HHnuM2bNnA01LJq+77joeeOAB/vWvf7Fo0SIyMjK48sorueyyy3j11VdZtGgROTk5TJs2jaVLl9KrVy+stTQ0NNDQ0EB9fT1ut5sVK1bgdrux1rZ5iIhI17fPv/0bY0YAq4ElQBBQa619yxjzq0PVuD20IQF4HfiLtfb3rU6FAlUd1Y6fo70s01LTwOl0YowhOjoaj8dDZWUlJSUlNDY2cu6557J8+XLuvvtuMjMzOeusswB44oknmDJlChdffDHjxo3jpptuAvDWUBgzZgxhYWF7vO+///3vNns4WGtpbGxk4cKFGGM4/fTTAZg4cSKbNm3i3nvvZc6cOURGRnLjjTfy1FNP8eijj3L//feTmpqKMYa6ujo+/vhjb1nowYMHH5w3T0REOsz+9CBcDLwJHAesMMY8aIy5Hyjc+9MOqv5ACXCnMSbAGDPbGPMZ8J4x5t6Wi/anRyExMRFjTJtH6278juLn50doaKi3m94Yg5+fH0FBQZSUlPDDDz/wzjvvEBERwYMPPsgll1zC0qVLvc8fMWIEL7zwArNnz/aWY77xxhs59dRTWbRoEXV1dfvUDmMMTqcTf39/lixZ4l09YYzhhhtuICQkhP/7v//D4/EQHh7O9OnT+eabb9i+fTs5OTk0NjayefNmqqqqCA8Pp3///gf5nRIRkY6wzwHBWvt7a+3Z1tpjgOHApzTtmdCRM9MGAA5rbQNNmz4NAL6kachhujHm+ea27nM/dn5+vk8XeGcEhN25XC4aGhoIDg4mPT0day0RERFkZGQQGRnJlClTOOecc9rUPTjxxBN57rnneOCBB3jnnXcwxvD4448TEBDAkiVL9rkUc0tI6NGjB7fddhvl5eVA0wqG++67j3Xr1vHCCy8ATRMoAebMmcOWLVv47LPPcDgcZGVlMXr0aD7//HOfDaZERKTrO6BZZdbaMmvtF9baP1lrrzrYjdqLJUCcMeb3gAWmNu/4OJ2mzZ9+ZYy5qAPbc8g4nU4iIyOJiYlhwIAB3g2cjjrqKBITExk2bBijR49mwoQJ3k2XoGl54kMPPcT111/PV199hdPpZOTIkVRVVbF8+fJ9ngNgjCErK4uYmBieeuop7/HevXtz55138vLLL7NgwQKCg4OZOXMm7777Lh9//DE//PADy5cvJz4+niVLlvDNN9/wzTff4PF4qK6u3ueQIiIinavLTzs3xrRuYyHwI3A+0MNa27pA/Dc0TZpM7MDmHTKthxwCAgJITEwkOTmZxMREjj32WIYOHcrvfvc7nE4n1157bZu6B5MnT+aWW25hypQpLFu2DKfTyQknnEBxcTErV67c55Dg5+fHzTffzKJFi/j222+9x4cOHcoll1zCr3/9a0pLS7nooouYMWMGzz77LMYY+vXrR2BgoHcDquOOO867x4TL5Tro75WIiBx8XTYgGGOijDFOa62nJSRYa/OBF4B0YKQx5pyW6621O4EiwNX8/G6/sqG14OBgevbsSWpqKtHR0WRkZDBw4ECefPJJVq9ezf3339/m+htuuIHLLruMyZMnU1lZSVhYGMcffzy5ubls2LBhn++blJTE5MmTmTNnjrdaIsCUKVPo06cPV199NdZabr31Vq6++moeffRRVq5cyebNm9mxYwcZGRnU1dXhdrv56KOPcLvdeDweqqqq1JsgItKFdcmAYIw5GvgCeMAYE9ocEhwA1to3gf8BtgIPGmP+xxgz0hgzC8gC/t183WG5ns5aS319PRs2bKCuro6MjAweffRR5s2bx0svvURjYyONjY14PB7uvvtuxowZw8KFC6moqCA0NJRhw4axYcMGNm3a5C1wVFdXt8dHY2Mjb7/9NgEBARhjuPPOO3n77bd5++23WbhwIffffz9ffvkl9913Hxs3buTKK69k1KhR3H333Xz//ffk5OQQGRlJeHg4r732GkuXLuWzzz7zLumsqanxmf9xmP5nExHpdjp1N8c9Mcb0AV4GegInALcbYx621lYbYwKstfXW2jeNMRXAJOARYAtNcxLOstZu6bTG/0x76vTweDzU1NR4f+s2xpCfn8/KlSvp378/vXr1Iisri4kTJ3LHHXd45ya0eOGFFzj33HPZvHkzr7/+OlFRUXzwwQfccMMNXHfddZSUlOBw7PnboLy83DtBccSIEXzyySf07NmTPn36EBwcTEJCAjNmzOD2229n+PDhDBw4kP/93//1Ln88//zz8Xg81NfXExcXx65duxg5ciTBwcHAf5d2iohI19OlehCahwXOoWkp4wXAd8CZNIWEUGttvTEmAMBa+wlwNdCv+ZqTrbX7VjqwG6moqCA7Oxu3243L5SIwMBCn00loaCjGGD7++GMWLlzIoEGDuO2227jooovYvHmz9/kOh4Mnn3yS6Ohofv3rX1NZWck555zDfffdx4033thmguPeREZGcswxx7BkyZI2e0KcccYZTJgwgWnTplFaWkpAQACPPfYYkZGRfPbZZ95gk5CQwKhRo6isrMTtdhMSEuLtQRARka6nSwWE5mGBd4FnrLXfA7cBX/PfkBDWHBL8m69vBIqttQXNcxAOOzU1NVRVVVFQUEBFRQXl5eXEx8czcuRIKioq+OSTT9i2bRu9e/dm6NChnHzyyUycOJGdO//7dgQHB/Pcc8/R2NjI1Vdfjdvt5vLLL2fq1KlkZ2e3+cDfm/T0dGJiYvjuu+/afLDfcccdxMfH89vf/pbq6mqcTifvvPMOFRUVPPHEExQVFREfH89RRx1Fr169CA4ObjPMICIiXU+XCgjQNBHRWvtW8989wO3AVzSFhOnNPQmNxpjLW11z2Orduzfp6ekMHDiQ+Ph4oqKicDgcxMbG0qdPH4YMGUJGRgYTJ04kPT2dM888k7CwMEaNGsW6deu8r9OjRw9eeOEFiouLueSSSygrK2PatGlERUWxevXqNoGiPcYYUlJS2LlzJw0NDd7jQUFBPPHEE1RWVvLWW28B0KtXLz766CO+/vprPv/8c6qqqnA6nZSXl1NaWkp2djaBgYEaZhAR6aK6XEBozRjjZ62tA+7kvyHhdmPMM8Dzh9NmTe1xOBzExcURFBREbGxsm/kCycnJnHTSSRx99NHU19dz9NFHc+yxx3LbbbcxYsQIRo0axQcffOC9PiYmhrfeeouAgAAmTpxITk4Offr0ISEhgXXr1lFcXLzXtng8HlatWsWAAQPalGcGCAsL4/zzz+fdd9/1HktMTGTs2LG4XC42btxISUkJ1dXVrFq1ijVr1lBQUNBu6WkREelcXTogNK9e8LfW1gJ30BQSbgMuAUbuVgfhiONwODj66KOJj4+nV69e+Pv7069fPwYMGMCpp55KWloaF154IXPmzPEOCURGRvLiiy8yZMgQJk6cSFVVFUlJSRx11FFs2rSJlStXUlBQgMvl8pkfsGnTJurq6hg4cOAe2zN+/HjWrVvXZhnlL3/5S95//30KCwupqanB7XZzzDHHkJmZ2aYMs7WW6upq7z0bGhooLCxs01MhIiIdp9NWMTQvWzTW2vpWx/x2HzJoHk7ws9bWGWOcNNU5ONFau7qDm9wlORwOoqKiMMbg8Xi8H6rDhg3jqquuIi8vj7lz57JmzRpmzZpFaGgoQUFBzJ49m5kzZ/LMM8945wYMGTKEkpISSkpK2Lp1K4GBgZSXlxMdHU14eDgrV64kPT2dqqoqKioq9riddEZGBn/7298YN24cAGeeeSZ33HEHixYtIjY2lu3bt7Nt2zYuuugirLWsWrWK9PR0GhsbvRMmQ0NDKS0tpaCgAIDY2Fjv6xtjaGhooLS0lOjo6HZXYIiIyM/TKT9djTEZwH1AgjEmG/i3tfaVVj0Gja2vbz5+FTAVGH4khoO9dcW3dPdXV1cTEBBAjx49iIqKIjs727tq4ccff2TSpEm8/fbb9O3bF4Cnn36ao446ijvuuIMpU6YwdepU730KCgp47LHHWLVqFStXrqS2tpbExETuvvtu/P39ycnJ2eP8gdNOO40XX3yRxsZGb3h58sknufzyyxk7dixFRUVs2rSJxMREYmJivPMkMjIygKYS0wDR0dFt/mytdXiIi4s7oPdTRET2rsOHGIwx/YGFQD3wGU07NE43xvwVvD0GQbs/z1r7HHCUtXZ5R7a3OwkKCiIwMJA+ffqwevVq1qxZQ0VFBQ6Hg+uuu460tDRGjhzJhx9+6H3OFVdcwQsvvMAf//hH7rjjDm/J5oSEBE4++WRuueUW/vKXv3DXXXdxyy234O/vv9c2HHfccbjdbj777DPvsXPPPZeLL76YRx55hAEDBpCcnExQUBB1dXWkp6eTnp7us5ulv78/sbGxe7xfdHQ0CQkJewwPIiJycHRoQGiuc3A58Km1drK1dgZwOvA3mkonvwbQPOcAY8yvjTFJLc/vzkWQOkJtbS0ej4fa2lri4+Pp06cP1loqKipYu3Ytp5xyCjfffDPnnXceN910E7W1tUBTLYN3332Xd955h1NPPZV//etfbV43ICCAzMxM4uPjf7INTqeTUaNG8fLLL7c5PmvWLMrLy1m5ciW/+MUvKC8vp6ioiMjISAIDA/drI6eWiZsaXjh4UlNTfbY9b3mkpHSfucApKSntfh2pqamd3TyRbqVDf8Jaa60xJhGIb3WsxhjzF5rmFlxrjHnIWnuHMeZM4EngLWPMb3YfdhBfLd3zTqeT5ORkRo8ezYABAzDG4OfnR0REBBMmTCA6OpqHHnqItWvX8vzzzxMaGsrQoUNZuHAhTzzxBFdccQW//e1vGTJkyAG1Y+zYsdx3333k5+eTmNi0d1ZERATPPPMMEyZMICQkhNTUVCIiIvD396eystJbDyE0tCN3D5cWW7duPSyKVuXk5LR7TitmRPZPh/UgtNo8aRngMMZktpyz1tYAr9I05DDGGBNhrf0YmAX8QeFg37Tupm+pldC7d28mTpxInz59GDx4MMnJyfz617/m5ZdfJjc3l0svvdRbKKlnz57cd999vPXWWzz//PO8+OKLB7ShUmZmJsOGDeORRx5pc/zUU09l2rRp/PnPf6ampoawsDCys7MpLy+nrKzMO5xQW1vLypUrcblcbVY2iIhIx+mwgNBq86QPgTTgNmNMZKvzFTTtqzACGNt87H5r7caOauPhJjQ0lPj4eDIzMxk7diyZmZnU1dWxYcMG+vfvz9///nfKysr41a9+RWVlpfd5xx13HO+++y7/+c9/ePrpp/d7qaExhnvuuYe//e1v5OXltTl3zz330L9/f9544w0aGxsJDg6mrKyMtWvXkpubC8CGDRtYtWoVK1asULVFEZFO0uGTFK21m4CLgV8BDxtjWk9Drwd+AMo6ul2Ho5YeheDgYPr27UtgYCDZ2dmsXbuW/Px8MjIymDt3LlVVVVx00UVt9mXIysrizjvvZM2aNTz++OPU1dXt171POeUUjj32WGbOnNnmuMPh4B//+AcrV67k22+/9Q6LBAUFeTdx6t+/P5mZmWRlZdGjR49uXW0xMTHRZyx8xowZnd0sEZGfZDqr+9YYMx54HfgX8AZNwWAy8GvgWGtt7iG+fwKQn5+fT0JCwqG8Vadr2REyJCSkTQ+Cn58fmzdvZvXq1Tz00EP4+fnx8ccf07NnTwB27drFtm3bmDhxIklJSbz88suEhYUBsG3btnY/uIuLi+nduzeLFy/miiuu4JNPPvHORQDo06cPn3/+OePHj+epp55i5MiR7Ny5k2HDhhEcHOxTpbG1rjKOXFBQ0PI1JVprC3Y/392+v4wxh/1QTnf6Gn/q+0ukI3RaJUVr7Xs0befcA3gQmA//n703j2/ruu59vxsTMXMCR3ASRVEjJVuSJduRrSSy46lNGifO4KRt6pf09bq3ST4d7by0ceo0aZOm973ntHmfpO1N854bp0mTa7eWHY9J7cS2bGuiBouiSHAECYAzJoIA9vsDPEcgCY6iOGl/Px98IB0cnLNxzubZa6+91m/xATIlm6+qcXCtkV0YKS8vj6amJvLy8ujq6qK7u5v6+no+/vGPYzQaufXWW6csC9TU1HD06FEGBgbYu3cvX/ziFzl7dmEyFAcPHmTv3r18+9vfnvHZe9/7Xh5++GG++MUv8vzzzxMKheaVelYoFArFyrGqUstSyuNkjIJbJ98PKZ2D5cdut+d01Wu1HTZv3szHP/5xHnzwQWpqarj55ps5d+7clP2ef/55vvKVr3D27FluueUWPvaxj/H973+fwcHBOc/9+c9/nn//93/n1VdfnfHZww8/zO7du3nyySeRUi4ojVKhUCgUK8Oq12KQUo5KKX1SyjNSytBqt2cjIoTA4XDMcM93dXXR1dVFb28vTqeTsrIy7r77bm677TZuvfXWKZ4Cm83GRz7yEX76059y6tQpjhw5wve//30OHTrEY489NmuMwv79+/nEJz7BQw89NOMzo9HIv/zLv+Dz+XjyyScJBoMEAgHGx8fp7+/XRZsUCoVCsfIopZkNTnb8wVzr94lEgq6uLjo7O9m9ezcmk4l7772Xo0ePsnnz5in7VldX85nPfIbPfvazvPTSSzzyyCN861vfoqGhAY/Hg8PhoKqqiuLiYoqLi3n99de58847c563pKSE3//93+eJJ57gBz/4Abfccgvd3d26CJgSAPcAACAASURBVFJ2HQaFQqFQrBzKQNjgaPEHMFOEaPPmzeTl5eH1eunq6mJiYgKz2czAwABHjhxhcHCQ3/iN3+Do0aNUV1fPOLYQgiNHjvCud72LEydO0N3dzcDAAJ2dnQQCAc6fP08oFMJut/MHf/AHs7bxwx/+MF/4whf05Q2Xy4XdbqeoqIhIJDKvcaNQKBSK5UcZCBscLe5gevxBJBLh2LFj3HDDDVgsFrxeLwcOHKC6upqenh7sdjuPPvoof/RHf8QHP/hBnn766Vln81arlZtuukn/v5bFsFBqa2u56aabGBkZoaurC4fDQVlZGYlEYlbjRqFQKBRXl1WPQVBcXQwGg24cSCn117Fjx3jttdd4++23kVIyPj6O0WiktraWoaEhJiYm6Onp4cYbb8Tr9XLvvfcyODiofz+ZTDIxMZHzFYvF5nyNj4/PeN177734/X6KioooKCjAbrdjtVqxWq309fWRSCTWTYqaQqFQbATWnQdBCNEAfALYCfwceF6pLc5NLvf8gQMHANi7dy/RaJRwOMzY2Bg9PT0MDQ0RCoUIhUKcO3eOD33oQzzxxBO85z3v4Rvf+AYf+tCH2L59+6xuf4/Hg8VimbU9uXQO7rvvPv7sz/6MsbExrFYrUkqMRiPDw8P4fD4MBoMqtqNQKBQryLoyECbrNzwPHAPMwJeBHUKIzwMpqaaYC8bhcPCe97yHsbEx/H4/xcXFNDQ0sG3bNgwGAzfddBOpVIp0Os3dd9/N+9//fh5//HF+53d+h29/+9t8/etfp6mpadnaU1ZWxrvf/W7eeOMN6uvrCYVCeDwerFYrly5dYvfu3ct2LoVCoVDMz7pZYpgs+/xvwPellB+QUt4N/G+Tr61LNQ6UFG4GrbhTIpGgoqKCdDqN2Wzm4x//OFVVVVRXV3Po0CEeeOABysvLuemmm3jooYeIx+PL1ob3v//9PPXUU3R0dNDZ2ckvfvELjh49SktLCy+99NKSCkcpFAqFYmmsCw+CEMIA3AW8Azw2WRlSkPEmtAKepR57vUjhXi20gk5aTQS73Y7T6dTjBcrLy3G5XESjUWpra7nlllsIhUIYjUaefPJJXnzxRf75n/95WbwJL7zwAnv27OGdd96hpqaGjo4ObrjhBhwOB3v27CEWi+Fyua74PIprk9ra2jmzYWpra+csF61QXGusCw+ClDINtAEnpJTdMkMaGAfygKpVbeA6RhNRMhgyXcHlctHQ0MCmTZsoLy+nuLiYaDTK2NgYbreb7du3U1dXx+7du/nOd77D3r17OXToEF/5yleIxWJLbsexY8d45pln8Hq91NTUMDQ0RF9fH6dPn0ZKSWdn54zvJBIJLl26tOhCUoprE5/PNyVQd/qro6NjtZuoUKwp1rwHQQhhlFKmpJQvAi9ObhOTSwoSiAHprP0/BXRLKV9Yjfaud7QKkAClpaVIKUmn0/q2wsJChoeHqaiooLKykscee4yCggIef/xx/umf/ok//dM/5b777pszSDEXjzzyCPfffz/XX389o6OjFBQUUFBQQGdnJydOnNBlmI8cOaKLKHV1ddHa2gowQ8xJoVAoFFfGmjUQhBDFQFRKGdOMBO0zKaWcXHaQQBgYnvzOV4HPAntXo80bDSkl0WiUSCSiixcZDAa2bNnC+Pg4hYWF+P1+br31Vg4ePEhraytf//rX+eY3v8kf//Efc//99+fMWEgmk1P+/4tf/IJXX32V733ve4yMjDAyMkJ1dTWf+tSn6O3tpaurC6vVit1uJxAI6MaCJt5UXV2NlFKJKSkUCsUysiYNBCHEduCHwHNCiC9JKSNCCMPksgKQWXYQQpgAJ2ASQvwF8HngVilly+q0fG0y18A512eaN0EIoasZOp1OxsbG9JiFkpISKisr2bp1K/F4nJqaGn7605/y1a9+lccee4w///M/5/7778doNOrHzY4nlVLy6KOP8ulPf5pAIIDP52NsbIzKykra2tr0EtBFRUWMjY2RTqdJp9MYDAbMZjP19fXLcIUUCoVCMZ01ZyAIIWqAx4FCMuWgHxJC/HUuI4GMByEKfAOoJVMN8u0Vb/QGRotRyKa0tBSDwUBxcTEGg4GdO3cCGf2DQ4cO4XQ6+djHPsbzzz/PH/7hH/LlL3+ZgwcPsnPnTnbt2sX27dvZtGkTRqORo0ePcvr0aT796U9js9lIJpN4vV5SqRTHjh2jra2NWCzG9u3bKS4uJpFI0N/fj9PpnBI7oZifurq6WdfZa2trV7g1CoVirbOmDITJ7IR7gCDwe8BHgTsnP5tiJEzuawUcQBlwQErZvEpNv6YwGo2Ulpbq3geDwcDo6CgGg4F4PE4gEMDr9XLHHXdw44030tHRwdjYGC+//DJ///d/T39/Pzabje3bt9Pf38+DDz5IdXU1qVSK4eFhKisryc/Pp6uri1gsxujoKKlUCoPBQDgcJhaL0dHRwfbt28nPz1/lq7F+6OjoUGqUCoViwawpA2EytuApoF9KeUwI8Rbwt1w2Ev5GShnO8iREJuMOTkspz61i069pbDYbiUQCv99Pf38/kUiEvLw8qqqqkFLyvve9D4vFwo9//GPcbjfRaJSKigr6+vowGAyYTCYGBwf1ZYRTp05xyy230NDQgN/vJ5VKUVRURDQapbGxEb/fz8jICH6/n3Q6TTwep6SkJGe8g0KhUCiWxpoyEACklD3ATyb/nRZCPAR8jZmehE9JKb8npXxiFZu74UmlUrqqYXYcQTYGg4GhoSHa29spLy/n4MGDbN26lba2NqSUNDc3Y7PZOH/+PH6/n507d3L48GEuXrxINBqlqqqKiooKNm/ezNjYGB0dHbS0tLBp0yaklExMTPD2229jNBoZHx8nnU5jsViIRCJcuHBBj0koLy9f4aujUCgUG5c1ZyBkM+kpSAghvgB8lctGQinwgBDiZSmlSl6+ioRCIXp7ewFmreYIlzMKCgsL8Xg8dHZ2cu7cOWKxGFarlS1btnDbbbfhcrnYt28f9fX19Pb2Yjab2bJlC/39/QSDQUwmE3V1dVRUVCClZOfOnYTDYUZGRohGo3R0dDA6Osq2bdvIy8tj06ZNABQXF1/9i6FQKBTXEGvaQJj0IBillONCiIfJeBL+hIxA0gFlHFx9PB7PlPfZ0DIK0uk0JpOJ7du3YzabcTgchEIhTCYTTU1NVFZWYrPZiMViFBYW4na7mZiYwOfz0d7ejtvt5l3vehdlZWX09fXx2muvMTAwgMlkYteuXWzatImWlhZCoRA9PT0YjUb279+PwWCYc31dpUAqFArF4lg1A2EyRVFIKSeytk3PUkBKmcryJNjICCMdklKeXeEmX3MIITCZTDld97MNuJp2gsfjYc+ePUAmQv7SpUtEIhFisRgmkwmv18vg4CAWi4X29nYcDgcWi4XBwUESiQR5eXmcOnWK5uZm+vv72b59Ox6PB4PBQCgUIhAIYLPZsNvtRKNRvay1MgQUCoVieVgVA0EIsQP4ElAphGgFnpNS/iDLY5DK3n9y+6fJZDbsU8bB2iXXkkQikWBoaIhTp04hpdS9C/39/XR0dFBTU8MNN9xATU2Nntb4wx/+EKPRSG1tLaWlpZSUlCClJJlM6vUj9uzZg81m45VXXqGxsZGKiooZKZkKhUKhWBorbiAIIRqBXwH/SUY6+XbgeiHE7VLKByY9BnlSyvHs70kp/1EI8aKUsn2l26xYOLmWJOx2O42NjZhMJmw2G16vl3Q6zcsvv0woFMJgMLB3714KCgp0z8LExAQTExPcc889mM1mIpEIANFoFIvFQklJCRMTE7S3t9Pc3EwymSQSieixCQqFQqG4MlbUQJjULvgt4AUp5Scnt30d+AzwGSHED6WUH9WMAyHEbwMvSim7AZRxsPbRykZnI4TAarVSVVWF2+3GZrMxOjrK3XffzdGjRxkdHeX555+nsbFRH/itVitCCKLRKPv37ycSidDf34+UUpdchkwNBovFgtVq5cyZM8TjcQ4cOKCWGhQKheIKWVEDYVLnwAtUZG2LCiG+Sya24EEhxNeklA8LIe4EvgX8RAjxwPRlB8X6wm636zLJ4XCYgYEBjEYjn/jEJ3jmmWd48803dRnnrq4udu7cSU1NDdXV1aTTmbAUzfB46aWXkFLidrupqqqivr6eeDwOZFQeo9GoHpug4hIUCoViaayYgZBVgfE4sEMIsUtKeQZ0I+EJYCtwRAiRL6V8VgjxDeAHyjhY/wghdMVFh8NBSUkJAE6nk8rKSkwmEz6fjwcffJDz58+zZcsWnE4niUSCgYEBksmkvs/bb79NIpEgmUzS0NCgexAOHDgwxTgYHR0FUHEJCoVCsQRWTMheXs5BOwrUA38ihCjI+nyUjGrifuC2yW1/KaW8uFJtVCwcKeWcr1zY7XbcbjdOp1N/Adx4441UVVVhMBhobm7myJEjlJeXU1RUhNvtpqioCJPJRDKZpL6+nttvv53Dhw9TUlJCNBrVS1Ink0n6+/tJJpPYbDbcbjcmk4m2tjYSicSi2qpQKBTXOisepCilvCSE+AjwDBATQjwipeyb/HgCOAkMrHS7FMuHECKnW1+rBqkNytkqjb/7u7/Lc889x5YtW0gkEvqs32w269oK3d3deDwebr75ZgD9u9q5Ojo6OHfunF7wyWaz4fP5uHTpEoCq/KhQKBSLYFXSHKWULwsh7gN+BFQIIX5MxjD4JFAJXFqNdilWjlQqxblz5/TYgbKyMu69916i0ahe1bGrqwu/38+WLVu4dOkS77zzDjabjVtvvZXS0lL9WOPj47S0tFBQkHFIjY6OYrPZKCoq0hUetXeFQqFQLIxVE0qSUv6HEOJm4JvAX5HxHkwAd0kpu1arXYqVIRQKMT4+jtVq1VMihRB6UGFXVxf/+q//qldx3Lp1K2azWc9iCIVCdHZ2EggESCaTtLS06FoJHR0dJJNJysvLdYVHKSWRSEQFLSoUCsUCWVWpZSnlcSHEB4AiwAn0SSlDq9kmxcqQrZeQqwhUKBTCbDbj9XrZsmULLS0t7Nq1C8hUj3Q6nQQCAcbHxykpKWHHjh3U19fT09NDe3s7w8PDBAIBCgoKdGnn3t5eLl68yOHDh1XgokKhUMzDqtdimAxOHF3tdiiWRiwW4/Tp0+zevRubzbbg7xmNxhl6CZpMs81mo66ujv3797Nnzx5aW1s5fvw4AAcPHgQgnU5TU1NDNBqltLQUg8GAEIKGhgYcDgfBYBBAz2Sw2+1cvHiREydOYLPZeM973jOjTel0Ws+CMBhWLH5XoVAo1iSrbiAo1jenT5/mjTfeIBgMcsstt+B2u5fsws9OTSwsLOTgwYPYbDZ2794NoL9DxjCJRqO43W6MRqOewQAZLYSCggK9tkNeXh5CCA4fPozNZuPAgQPznl/LsFhP1NXV0dExe/2y2traFWzN+qO2tnbWvltbW4vP51vZBikUq4wyEBRXxO7duxkYGCAvLw+fz6fP4JeC3W4HMksIBoNBP47NZuPgwYNTUhKtVivhcBiDwUBbWxtms5kLFy4wPj6Ow+HgpptuIh6PMzY2hslkYmRkhOrq6pyeA414PM7TTz/NBz/4wXVpIHR0dKi0zStgLgNAxa0orkWUH1WxJLRURrvdzh133MGOHTuoq6tbUBCg9t3pL80oWIh7Px6Pk06naW1t1cs/b926FSklr732GqdPn9b37e7uprW1la6urpzn1fQQnnnmGX75y1/yzDPPKJ0EhUJxzbOuPQhZ6oyKVUQrCR2NRhf93UQiQVdXF9XV1Vgslnn31+IUrFYrAEVFRQC6oFJ5eTlnzpxBCKFXfTSZTLhcrnlTHe+5554p7wqFQnEtsy4NBCGEExCABSWqtCZY6vp9V1cXra2tQKbwUi40o2A2CeVdu3bpwY1NTU3k5eXR2Ng4ZZlitmNnU1hYyCc/+ckFt12hUCg2MuvOQBBC7CQjyVwD9Aoh/klK+cQqN+uaR4sf0N4XykKEjLKNglznydZPyMvLo6mpiXQ6TSQS0eMZYPHeCmCKfoLKbFAoFNcS6+qJJ4TYAbwKnAf+ARgGPiSEyBNLjCLyer0z1qQfeeSR5Wv0NYLBYMDpdC56ELVYLHrJ5tnQajhoRoDD4Zg3ziEWizE6OsrQ0BDNzc3E43HdW9HVlVuHSzMGsletNONkKcsnCoVCsZ5ZNx4EIYSdjOLiv0gp/3ByWwj4OBmRJZhcblhMbEJPTw+VlZVXocWK5UIzChYTbqJpMrS2tnL+/HkAtm3bBszurci1fLFUz4hiY6FSIBXXIuvGQCAjw1wNvJ21bTdwHZkS0r1CiGellF9WgYsbD63eghZboC0VmM3mnPtr8Qfbtm3DYDDQ2NioeytmY7bli7WU8jiX1oHSObh6qBRIxbXIujAQhBAGwAZ0ADcKIf53oA74LPAgMAY0AJ8VQpyWUv50tdqquDq0tLRw5swZIDO71wIb56vQqMUkzPUQz7YnNeMge9taGgCU1oFCoVgp1kUMgpQyPSnJ/D+BKHAb8AHg96WU/yKl/AnwOBAhYyhcFVYrNmE1zrta55xNI6GxsZFdu3bR2NhIdXU1DQ0NVFdX6zoG4XCYsbExpJQ5v7/Yc6bTaQKBAOl0Ouf3Ztu+1N+9GqjzbuzzKhRXilirsxEhxCbgCJn4gneklM9ObncDSeBXwF9rGQxCCDPwPPAjKeXfL+D4lUDPYmIQtMFopVmN866nc4bDYfx+PwAVFRWLWhLQjIHp9Pf309vbS2VlJeXl5TM+v3jxIo2NjQBeKWVvjuMuuH8t5ncv5325lvrz1TzvfMddynl7e3vxer0wS/9SKFaCNbnEIITYBfwCOAnsAIaFEA8B90gpR4UQDiAINAghqoAQ8H+Q8R4cXaVmK1YJu92uF37SlgiSySShUAiPx4PJtPhunl1tMheLKUy1WFScwfpivgBGhWK9suYMhMlshf8H+Dcp5X8TQhQC7wL+BnhDCHGblLJPCPEs8BfAJ8kYCLXAr0sp21er7YrVwWAw4Ha7p2wLhUL09mYmXrk8AHORHRCZqxS1ds6rhYozWF+oAEbFRmXNGQhAHuAGXgCQUg4JIY4Cl8jEGfwM2COl/KYQ4iKwDQgDzyjjQKExnwdgLrIDIpuampa1XRrTvQTZA4madSoUirXAWjQQRgEjmfiDf4dMkCJwXgjxaeCHQohvSyn/m5TyKeCpJZ7HANDX17eoL2mz0pVmNc67Ec4ZCAQWfU6n00lpaSlms5kXX3yR+vp6vfaDRla/mc2VMGf/6ujooKenB8iIdWn/nq1NV4trqT+vxnm1e5vLk+D1ejl27FjO7y2gfykUV501FaSoCRwJIb4E3A18RUr5H9mfA38JHAbullKGr+Bc15PRT1AoroS9UsoT0zeq/qVYJnL2L4ViJVhTHoQsgaP/F7gT+O9CiJiUUltukEKIM2TUE21klhaWyhlgL5lgx+XLWVNcKxiAEjL9KBeqfymuhPn6l0Jx1VlTHgSY4kVoAv4V6CWTuviPQog84KvADVyhB0GhUCgUCsXsrJqBIIQwTZ5/ImubQUqZznrfAXyFjJxyHplAxV3Ae6WUJ1el4QqFQqFQXAOsioEwOfB/CagEWoHnpJQ/mPzMKKVMZRkJHjKyyncCPcArUsrWFW+0QqFQKBTXECtuIAghGoFjwH+SMQ5uBxzAcSnlA5P75Ekpx1e0YQqFQqFQKHRW1ECYzEJ4FNgmpfzw5DY78JnJ11kp5Uez9v8U8IKUsnvFGqlQKBQKhWJlsxgmgw+9QEXWtqgQ4rtADHhQCPE1KeXDQog7gceAnwghHpBSppazLZO1G3ahoswVS0OPMs+Oo9FQ/Utxhczav1TfUlwhcz67slkxA0HLTiCTG75DCLFLSnkGdCPhCWArcEQIkS+lfFYI8Q3gB8ttHEyyC5Wnrrhy9gK58tRV/1IsB7n6l+pbiuVgtmeXzmrEIGwGXidTVOlzUsrhrM8qyAQi3iel/Per3I4qoOvtt99etFa/Ym5m61NSSmKxGDab7arWMlgJ+vr62LdvH0B1riWwa7F/pdPpDXN/V5u5+te12LcUy8d8z65sVlwoSUp5SQjxEeAZICaEeERKqemKTpCp4DiwAk1JQ6aQz0LLPSsWxnxG5wYrYDObi1f1L8VykKt/qb6lWA7mXZ5aFSVFKeXLQoj7gB8BFUKIH5MxDD5JJvXx0mq0S3F1kVISjUax2+1qhrmGSKfT6r4oFIoZrJrUspTyP4QQNwPfBP6KjPdgArhLStm1Wu1SXD2i0Sijo6NApiCSYm2g7otCocjFqtZikFIeF0J8ACgCnECflDK0mm1SXDnZnoLs5QS73T7lXbE2uFr3RXkmFIr1zaoXa5JSjpIp8azYIGTPSB0Oh749nU4TDoexWq1qwFhDZN+XXPEhS40ZUZ4JhWJ9s+oGgmLjMduMNBQK0dvbC6Cir9cQ2felrKxs2Y6rPEYKxfpGGQiKZUcIMcVzoOHxeKa8K9YGV+u+GAwG5TlQKNYxykBQrBhGo5GysrKNlua47tHui0KhUGSjFoIVCoVCoVDMYN15EIQQDcAngJ3Az4HnpZQXV7VRCoVCoVBsMNaVB0EIsQt4hYyGtBP4MvA5IYRJLNFv7fV6EUJMeT3yyCPL12jFNY3qXwqFYr2ybjwIk/rj/wZ8X0r5Z5Pb3g/8EPi2lPLsUo7b09Oj5EoVVw3VvxTXOnV1dXR0dOT8rLa2Fp/Pt7INUiyYdWEgCCEMwF3AO8Bjk94CATwPtAIqLH6JXI26CSoIcX1xJffrGqu7oVgCHR0ds/YT1T/WNuvCQJBSpoUQbcCJrOpTUggxDuQBVavXOoVCoVAoNh5r3kAQQhillCkp5YvAi5PbhMyYpBKIkVWVSgjxKaBbSvnCarRXoVAoFIqNwJoNUhRCFAshbFLKlBDCmP2ZlFJOLjsAhIHhye98FfgW0LmyrVUoFAqFYmOxJg0EIcR24GXgUSGEY9JImNJWKWUaMJLJZjAJIf4C+Dzwbilly4o3egMwNDTE448/ztDQ0Go3RbHOUH1Hodh4rDkDQQhRAzwOFAI3Aw9NGgnp6UYCmSWGKPAN4GHgFinlWyva4A3E0aNHefHFFzl69OiivqcV+0mn0/PvrNgQTL/nS+07iqWjUmgVV5s1FYMwmZ1wDxAEfg/4KHDn5Gd/LaWMCCEMk8aCAKyAAygDDkgpm1ep6RuCu+++e8r7QlFV+649plfsXGrfUSwdlUKruNqsKQNhMrbgKaBfSnlMCPEW8LdcNhL+RkoZ1owEIDIZd3BaSnluFZu+bslOP3I6ndx00004nc5509fgcorS9Kp9yWSSUCiEx+PBaDTO+r3lZCOl212N37KQ+zmdVCql30eTaeqjQrvXNpsNKSUFBQV85CMfoaurC6fTqe+/nq67QqGYyppbYpBS9kgpfzL57zTwEPBfZIyEP8tabvjU5D5PKONg6WS7J7u6umhtbaWrq0vfthC0qn0GQ6Y7aeWDQ6HQ1Wy64ioz133MvudX2n8UCsXaZE15EKYz6SlICCG+AHyVy56EUuABIcTLUsrcEl2KRVNdXT3lfamoss4bg8Xex+XqP4r1x3xqiYr1yZo2ECY9BUYp5bgQ4mHga8CfAONkYg6UcbCMmM1m6uvrr/g4a6l88MTEBF1dXVRXV2OxWFa7OVfESv+WxZbnXq7+o1h/zKWWqFi/rNoSw2SBJfO0bTPao6U4SikTgI2MMNLNUsoTK9TUDU8qlaK/v59UKrXaTVl2st3e65318ls2cn9SKK4lVsWDIITYAXwJqBRCtALPSSl/kOUxmPJkmdz+aTKZDfuWWphJkRttrRlY0Mx/ruC1tcZGcntf6W/Jvm+5gkeXi+z+VF5eftXOo1Aori4r/nQXQjQCvwL+k4x08u3A9UKI26WUD0x6DPKklOPZ35NS/qMQ4kUpZftKt3mjs9i15vU0AGhu740QMHelv2WxhuBSUTEoCsXGYEWXGCa1C34LeEFK+Ukp5SNkDIT/CRwQQvwQQDMOhBC/PVnmmcnt16xxIKWc9ZVOp+f8fD60tebps8rZvut2u0kkErjd7mX5bYqVwePx4PF4GBkZYWJi4qqdZ7b+tFDm6stX+lIoFAtnRQ2EyQJLXqAia1sU+C7wfwNbhRBfAxBC3EmmrsJfTa/FoFg+piuxTX/lwu/3MzIygt/vX+HWzs5Sfsda5Wr9FqPRyMTEBD6fb0Ycw1LPt5Guu2Llqa2tnbXv1NXVrXbzrnlWbIkhqwLjcWCHEGKXlPIMZIwEIcQTwFbgiBAiX0r5rBDiG8APpsckKFaXjbSuf62h7p1iLeHz+Wb9TBmYq8+KeRDkZf/eUaAe+BMhREHW56NkVBP3A7dNbvtLKeXFlWrjUliNOgTj4+M0NzczPj4lTGPFose1tfC5Uu2klEQiEeXWXQOk02n9Xmj3zmw2z//FNcBsfX0+rvRvQdUXUShWIc1RSnkJ+AiZOgt/LYTIjnKbAE4CAyvdrqWiadJHo9EVO2dLSwtnzpyhpWVq0cq1pGC4GtdFkZv1fC9m6+vzcaV/C+v5mikUy8Wq5KhJKV8WQtwH/AioEEL8mIxh8EmgEri0Gu1aCtPrEKwEjY2NU94BIpEIRUVFwNqIHl+N66LIzXq7F1JKotEodrs9Z19fCFeaSbHerplCcTVYNaEkKeV/kCnn7Ab+CvhfwAeAu6SUa1sJJovpdQhWgry8PJqamsjLywMuz3YSiQRlZWWk02na2tqWLVJ9KcsFQggcDoe+jqiWHFYPg8Ew5V7MRi63+mq42rNn79P7+mxMTExM6fNXmkmxGn/XCsVaY1VVbqSUx4UQHwCKACfQJ6Vcff/4GmSugdVms+nvUko6Ojo4d+4cyWQSr9eL3W6fc3CY7TPtnNmlfeebUWmzP5vNNuXhutCS0FdiQFwLQU1Xy8DS7lt2CWcpJYFAgGQyqW9bzvPNdr+0ZpA1ygAAIABJREFU/my323P+3uzvae3u6enh/PnzpNNpGhoa5jzvbFwL/UehWAyrbh5LKUellD4p5Zn1bhxczdnWfOlkDodDr6xXXFxMaWkpNpvtitZRtWPbbDbcbjc2mw0hBOl0mkAgMCMATEpJX18fPT09RCKRKZ/ZbDasVit+v59EIrHk66BYOvOlItrtdtxut24ERqNREokE4+PjWK1WPdhR69/TZ+3TWWqgYLbHY77USc2osdlslJaWUlxcvKhzTUcFJyoUl1nbOrnrjIXOkq82+fn5ult2fHz8itdRtQe2xmyKfNFolLGxMWKxmL4tnU4Ti8Ww2WwMDQ3R1taGwWBg8+bNS2pL9vq0mvFNvb5X6g7XDE0Nu91OOBzGYDAQjUaJRqNTvAldXV1cupQJF8pVpGkllBu1vm21WikqKrrivr5W/oYVirWAMhCWkSsJbEqn0/rAt9AHvZSS0dFRwuEwTqcTl8uFwWCYMqAbDAbC4TCQeeAtx6A6WwCY3W6noiKjgaWdPxaL6Q/c5cjBn+4Gv9bJvr7LfT2EEJSWlhKNRkmn0ySTSUwmk74EMN/9XEigoGbgaMZstlGbTqdn1I6YbiBmGzWL/f25jE0VnKhQXEYZCMuIFti0FJYyc4lGo/h8Pvr6+jCbzezbt4/8/Pwp+8RiMfr7+/X2LccgYjQaKS0tnWFsCCFwuVxT1pez4yOWQ59BPcCnkn19c3GlJaK1ATidTmMwGKZ4KuYr77yQst+agWMwGPRzaO79cDg8wwOxEANxoUWpch3rSv6GFYqNhjIQ1ghLGfjsdjt1dXVIKRkbGyMajc4wEGw2m/5wXcqgeqUVALONEp/PR2trK8CilhiyBzmz2aw8B1kYDAYsFgs+n0+/PtloJaJhcdc813mudEDOhWbY5PIgWK1WYKoHYiF/Jwtd2lDGpkIxN6sepKjIsJS0KiEE+fn5bNq0iWAwiNVqnRJEttTjZrNQwZmFpDFWV1fT0NCw6CUGbZCbXj9AkWGu67PUa57N9ODE6SxFlEjrL5CZvZtMJhwOB+Pj47z55ptEo9GcqYrT02dz4fF4qKysnHVpY/q5VSyLQpEbZSBcBZZaeTGZTNLX10cymVxUJbqTJ09y6dIl3njjDYaHhwkGg6RSKf17fX19PPXUU/T19S26rR6Ph9LSUuLxOD09Pfpxp383O3c913EikQhGo5FNmzZhNpsXVXHP6/VSUVGB1+ud0m6lq5Churqauro6zGbzjGWc5ZBW1pYBYrEYUkpSqRQ9PT309PQwMTGB1WqlvLx8URkEwWCQn/3sZ/T39xOJRPR+9cYbb/DLX/6S119/fUltlVLOq4GQSyVRSqmyFxSKaaglhjWA5kI3m836LGwxUd/79+9HSsm+ffv0SPN4PK67hE+ePMmpU6coKCjQgwgXghACKSWDg4P09PRgMpkwmUw525btrp0tFQ3mDyTLlcqWTCbxeDwkk0nd7RyJRK7JaPNcs12LxUJ+fj69vb1YLJZlzxiYfm9DoRDnzp0DMrUStDRYk2nhj5Nz585x9uxZTCYTdXV11NbWkp+fT11dHZ2dnXPGNiwV7e/M6/VOSecElb2gUORCGQhrAM1FXFdXR3l5OVardU4hmenY7Xbe/e53A5k13YGBgSnKc4cOHcJgMHDzzTfP+K42c4LcWQ6hUIjx8XHKysooLS2d1W2bTCbp7++fsg6ueRa0QX2pa7251orV+vFUrlRaeC6mpz8WFRVRW1uLzWajvLycRCIxJUhyesxILg4cOIDBYMDr9dLX10cwGMTlclFTU8Ndd91Ffn4+/f39FBcX62mWi8nwyUV2PMZ0A0T1J4ViJspAWAGyH5i5Zlna+nBFRQV+v19PJ1tsUFgymaSzsxOz2axXvxsYGKC4uJg77rgj57EikQhtbW3YbDa8Xu+Mc2YPPHMFoOV6+C5XSmKuyHIVbT6V2Tw7V4NEIoHL5dK9BtONgPb2dk6cOEEymZy1hoLdbufw4cMkk0kMBgNms5lYLIbD4aC0tJRAIIDf79czG5LJJKlUing8vqBgyLGxMV599VUOHTqEy+UC5k7LFEKo/qRQTEMZCCtA9uC5adOmGZ9r68T9/f0MDQ1RWFi4qCjtVCpFMBhkbGyMsbExXZQoPz+foaEh4vE4Y2NjNDQ06LP5bGw2Gy6Xa8Y54/E4p0+fZvfu3fM+kHM9fNWsbGMy33212WzY7fZZUy81YrEYzc3N7Ny5U/8eZPqdz+djdHSUiooK3WCORqN6ym5RUdGcXopXX32VV155BYC77roLmD8tU6FQTGVdGghCCAMgpJSprG1CrtGItYUKBGXP1ueL0tbe0+k0nZ2d9Pb2YrfbcblcdHZ2EggE2LFjh+6VaGlpIZlMUlFRQXFxMel0mp6eHj34T1tfzhaPOX36NMePHwfg4MGDc7Y918N3umtasTZZrDpl9n2d/ieneQT27t07r0ejubmZEydOAJklB422tjZeeuklxsbGcLvduoSyttTl8Xjo6OiYdbkAMstq2e8KhWLxrDsDQQixHfgc0CCEeA14U0r5lJRSrlUjIXvwnK15Ukri8XhOAaLpGI1GPB4PoVAIq9WK2WymvLycwsJCenp6sNlsVFZWsn37dvLy8sjPz9cDDF944QXe9a53IaXUZXI3bdqkZwVoWvQAu3fvnvKu2JgspzrlwMAAgUCAyspKDAYDkUhkVsOjqalpyrumqrhp0ya2b9/O+fPnOXHiBHv27AEycsoulwuj0Tiv0e1yubjrrrv02JiioiISiYSS6FYoFsG6SnMUQmwDfgW4gA7gMPB/CSH+EkAzElaxiUsilUrR3t7O4ODgggsracsM0WiUoqIi6uvrSSaTTExMkJ+fz6FDh/RARavVyq5duxgaGsLv9+Pz+RgaGsLr9eqpg9mDhBbhbbVaOXjwIDabbd5c+PnSDlOpFH6/n5GRkRn7TC/qk53uqZjJXAWF5rrOs6EVabJarYyMjOD3+5mYmNDv50JSSrWBuKCggMrKSoqLi/X0yNHR0ZxFm2w2GwcOHNCXFrT90+k0hw8fpry8XM9W8Xq9U5bBFpq+OTAwQG9vL11dXQwODtLe3r4sip4KxbXAuvEgTA78vws8D3xy0hioAT4CPCqEsEop/3SxHoTs3HqNL33pSzzyyCPL0OqFEQqF9NiD+dZtNbKXGaSUBINBCgoKACguLp4RDKmVwTUYDBiNRlpbW9mxY4f+gNVKRWdHimuXMjv4saioSC8FnG2LhcNhAoEAHo9H1+vPjjgPhUK0tbXhdDppaGjQ5Xu1QUHTaCgrK5tVCW8xmR3TWS27cSn9a74uPL38trY8AJnr3N7ejsPh0K/zQo7pcDiIRCL4fD4ikYheAEqrEaIZa3l5eXrga3YfCwaD+Hw+6urq9FRa7ZprBgLMnb6braoopeTuu++mvb2dPXv2YLFYsFgsJJNJgsFgzj6eC02bobCwkO7uboaGhnA4HCsW0KlQrGfWjYEwaRA0ACnNCJBSdgohvguMA18WQvillP9jMcft6emhsrLyKrR44WiDvZbStRCyde77+/vx+/3A7A9gbSamGQVWq5WGhgb9c4PBgNVqnfHwTSQSnDx5knQ6rZeQzkYb5LXZbLYHJNtdrcVLZAevZevwDw8P6xHvVzNlb6W5Gv0rO0hwurGgxZcsJEhwOlra4tmzZykpKdHrImQXaQoGg3pfKykp0RUJrVYrDodDL7IUi8UwmUyEw2EKCwsxGAwUFxeTTCYZGBigqKhoxuxfk3OORCKEw2Hcbjc33njjlH0GBgbm7evZZGd31NTU4HA4NkS/UihWgnVjIEzyX8B9QohtUsp3AKSUI0KIHwKbgA8KIX4gpZwpGbiG0Qb7pYRPpFIpkskkJSUlOZXstBngdPllm81GJBJhYmICh8OBwWDQZ4HxeJx0Ok1lZSU9PT26d6OmpkY3YNLptL6fVk2yqKhIT7/MHpy0fcvKyqYYQNo+586d49SpU7jdbvbt27egIj/acZer1PF6IjtIMLvccTQaxWazzSmGlS0WlEwmsdlsU7wrFy9e5PTp0xQUFLB3794ZRZqyZ+TBYFA38EpLS9m8eTN5eXkEg0GSySSJRIJgMAjAddddh8lkor+/n56eHqLRKLW1tTPuWzqdJp1O43Q6cxo42vnnUm3UjBC3243f76eqqgqLxbLgfqVQKDKs+afqZMaCxltAKfCbQogSbaOUMgD8BLiRjKGwbkkkErS1tZFIJPRtyWSSQCCQc+00FArpD+Tz588Ti8X0dEdtAB0bG9Mf4ul0mnPnzvHWW29x8uRJgsGgPuu32+04HA6GhoZoa2ujt7eXqqoqtmzZoj/gtfZ0dnYSCoUIh8P6IBUIBDh58iShUAiDwcDExARtbW2MjIzoUr3ZaDNGh8OB1WrNOSBMj0/IJlsC+FpFMxbi8fiMa6HFBWTHcmgpty0tLTP2j8VipFIp3ZsEl++RNpCbTCaKi4vp7u4mHo/jdDpxu920t7djNBqneIXKysoYHBwkGAzS1dVFJBKhsLCQwsJCTCaT7nnSYluSySQdHR0MDw8DGa+X1o81NI+AyWRifHyc5uZmXfNDQ/MyvPXWW7zwwgt6MK5CoVgca9aDIIQoBqJSypgQwiilTEkpfy6E+CbwfwIJIcQ/SSm7J7/SCpxftQZfAZrwkfbg1R5oWuZDMBikvb2dZDJJQUGBPptLp9NYrVZKSkro6Oigvb2dgYEBPYK8oqJCjy0wGAycPXtWdwF7PB4aGhooKirStxkMBl2nYWRkRHcza/ECXV1dxONxrFYrw8PDpFIp+vr62LVrF0ajkVAoRF5enj64aINRfX09FRUVejGp6TP+LVu2YLVac0akZ8cjlJaW6tvHx8dpbW2lqqpq0a70jYjdbicej9PS0kJNTQ2FhYV6gB5cvnbaNc72IGjYbDZ2796N1+ultrZ2yvE1zYKmpiZGR0cZHh6moKCA0tJSmpubefPNN0kkEkgp6enp4brrrmNkZISioiIgo1swOjqqB79qSyCxWIxQKMTIyIguNV5aWsr4+DiJRIKJiQnq6+t1saNsWlpaOHv2LHA5EwIuexfi8ThDQ0MEg0G2bt2qe0qutELptUpdXR0dHR05P5veXxQbgzVpIEymMv4QeE4I8SUpZUQIYZZSTkgpvyWEMANfBmqEEP8LOA38d6AY8K1aw+dhNgna7EGwqqoKyKgq+nw+uru7KS8v1wdxv99PWVkZLpeLWCxGNBrFYDCQn59PRUUF1dXV2O123UWrKQ6eOXOGtrY2PB4PAwMDXH/99Xi9XlKpFBcuXGBwcBCv14vRaOQnP/kJRUVFVFdX43A48Pv9+vJDLBZj9+7dFBQU0N3dTXt7O8XFxZSXl+uR5ZqLOzsVzWw2T6mfkB2fMJeAzfR4hPHxcVpaWojH41y6dGmK2/taRghBb28vx44d4+233+aDH/xgTnd89rXOy8ub0ieNRiMWi4X6+voZrv/m5mZdE2Pv3r36cQ0GA4WFhbjdbrq6uujo6CAcDmM0Grnuuuvwer04nU4cDgcWi4Xe3l6ef/557rzzTvLz8zEajZw8eZKzZ8/S1NSkqxkODw/rBnE22ctKWsxKVVUVr7/+Ops3b6aoqIiJiQk6Ojrwer00NTXh8XiIxWJTAjkXUg5aMZWOjg5VHO0aY80ZCJOZCY8DhcDNwENCiL+eZiT8DyFEEPhtMoZEO+AAfl1K6V+1xs/DbFrw2UGKJpOJ+vp6/H4/L7zwAj09PVx//fXs2rULu93O4OCg7nLVZn/JZJJIJMK+ffv0YLJUKoXP59MHZy0g8eLFi7z++utMTExQWlpKa2srb7/9NvF4nGQySXd3NydPnmTz5s382q/9mh40VlJSQiKRIC8vT890aGhoIBKJsGvXLl09r7i4WJ+VTR/4tfYuZsafvW4spdRnjQ0NDezcuVMfJDbSrHCpv6WxsZELFy4QCoXo7u6muLh4yrXLRVdXl+6xKisrm1UPQZuhb9++fUoWg5QSr9fLzp079XgDrS9EIhHy8vIYHR0lHo9TUlLChQsXuHjxInV1ddTV1dHa2kpbWxuBQIDe3l5uvPFG0uk0RqOR4uJifdlLQ1vC0NrY1NTEr371K1544QX27NnDbbfdRnNzM2+88QY33HADt9xyi94m7Tpo1SdVsOLapra2ds7so9raWnw+38o16BpkTRkIk6mM9wBB4PeAjwJ3Tn423Uj4/4QQzwLlgBnomYxFWLNkz6izH9hafEB2uWOr1cqWLVuoqalhy5YtmEwmhoeH9cFZS/mz2+0kk0k9R9xkMpFMJjlx4gR+vx8pJbW1tSSTSbZt20ZxcTGJRII9e/bQ0tKCwWBgx44dTExM4HK5qKio4Oabb2bTpk2YTCa9EE8wGGRiYoKCggIMBgMmk0nPbPD5fNTU1ODxeEgkErS0tFBfXz+lYBSgtxcuD1haAKPVatV/11wBh5pB0NjYiMVi0Y+1nmaF883C5votc6V6ms1mfv3Xf52WlhYaGxunnEfrW9rsWztGdXU1Qgi8Xi/pdJpQKITFYsFqtTIxMUFra6su0X3DDTcQCAT0lFSPx6MvGW3ZsoXi4mKEEHR2duJ0OsnLyyOdTnPhwgU2b95MNBrl1ltvxWq1sn//foLBIA6Hg1tvvRWfz4fFYqG/vx+Xy4UQQu/LY2NjOJ3OKbERJpOJtrY2qqqqqKiooK6ujsrKSkwmE263m82bN7Nly5Yp9RW03x+NRnG73Xp/WwhzDVRXMqteh7ItK8Z8g7+6dlefNWUgTKYyPgX0SymPCSHeAv6Wy0bC30gpw0IIk5QyKaUMAaHVbPNiMJvNbNq0ac6OrX1mMpnwer2UlZXhcDj02Zn20Ozr66OkpIR0Os3FixdxOp0MDw/j8/koKSkhHo9jsVgoKioiHo8zMjLC2NgY4+PjxGIxwuEwg4OD2O126urqiEajnD9/nmAwSDqdxufzUVFRQWNjI5FIBLfbzeDgIH19fWzZsgWz2czExASjo6O6RHNtbS0nT56kt7eX/v5+9u7di8vlmnXA1wakaDRKJBKhsbFxTuEbIQR5eXlT1ps1NlJq5JX8lmQyyc6dO/UYlWyDQEuJ1MqBFxcXYzabqaurAzISxxcuXGB0dJSGhgYCgQDvvPMOkDHIenp6dK+Gy+UiFAqRTCYRQmCz2XA6nbS1tfHOO+9QW1vLDTfcwFtvvYXf7ycQCHDzzTfj9Xo5dOgQZ86c0TU1vF4vpaWlDAwMYDAYOHnyJNu2baO1tVVfwti8eTMOhwOj0YjD4aCtrU33fNTU1HDjjTcSDodpb2/H5/NhtVpxu90z/tayvVjZnynXuUIxkzVlIABIKXvIZCQgpUwLIR4CvsZMT8JvSSm/v4pNzUkymVwWV7fD4dCDDA0GAx6Ph3g8TjQa5eWXX9ZzywcHBzl27Bh79uyhr6+PU6dO0dTURE1NDX6/n7y8PMxmM4lEgkQiwc9+9jOOHz+uexFcLpc+g6+qqqKwsJChoSHC4TBFRUUMDg7qmRCJRILu7m7dgzA8PKwL2dTW1hKNRjGZTKRSKdLpNB0dHfqDfXpKopYJYTQaCQaDunckVzEruLz2PJtUrhY1P33/9ZgCOV863my/bbr7Pfv/VqtVTx8Mh8MzhItSqRSJRAK3263LEufn59PQ0IDL5aKjo0PPXJFS8sorr9DQ0IAQguHhYZ577jkqKyvJz89nfHwct9vN6Oio3g8HBgZ46623GB8fp729neHhYerr66mrq6O/v5/Ozk5KS0u5ePEigUCAaDRKPB7nuuuu00tLZ6PF6lRVVWEymXSDRQiB3+8nHA5TXV3N1q1bp3xPC7pdLTbSUphi47PmDIRshBAGKWVCCPEF4KtcNhJKgQeEEL+QUuYOq10lZnMPa8F1dXV1BIPBWavQaRgMBiwWix5HoJV/vnTpEqOjo+Tn5+tZAfF4HICdO3cSj8dpamrC5/PR1tbG6Ogoe/fuZXR0lKKiIm6//XaklGzfvp2CggJdHVF7SJeXl+sz++7ubtxut56m6PV6yc/Px+Fw0NfXx+DgIIFAQJd3ttls+Hw+PB4PhYWFUx7skUiEQCCgiy298847RKNRPB4Pu3fvpqenh8LCwlld6NMHv/lY7P7ridl+2/QYD+3dYrHQ0dGh32vN85RMJkkmkxiNRgYGBhgYGMBisVBeXk4ikdCDBIeGhiguLqa+vp6ysjLefPNNAoHMal5tbS0vvvgi586do6amhrKyMsbHx+nr62Pr1q04nU7uueceTp8+jcVi0T1GHo9Hj1vQNArS6TT79u3D5XIRiUR4/fXXdW/F2NgY0WiUkpISTCaTHkwJ6MJQmzZtoqioiEgkQktLC5FIhEQiwdDQkK6JkP13p/1NZi9XLZXZApCns56WwhSKNW0gTHoQjFLKcSHEw2Q8CX9CRjnxwFozDmB297AWXNfV1aXrCcwWua/lhre1tenrvdrMurGxUU9hjEajeqGlgYEBIpEIDQ0NjIyM4HQ6KSgoIJlMcvbsWSwWC6WlpTQ2NlJWVsbAwIC+njs+Po7VaiUvL09/kIbDYdra2nS53ry8POrq6rBarYyNjXHp0iX279+Py+XS4wK0IMZ4PE5+fr4eSV5YWDgl3z0YDOoz0d27d+tBY6Ojo1gslpweB22wW2jpaG1/g8FAc3MzjY2NOUtdrybZA9T0eI25mG4AZF+rbINBu25tbW34/f4pHimTyYTf78dkMpGfn09fX5+uTwAZRczW1lbq6uooKSnRtQfS6TS7du3S02vT6TQ7d+6koKCAoqIiOjo6EELoA3NlZSWRSITi4mKGhoYoKyvDaDSyefNmhoeH6ejooLa2Vi/57HA4KC0t1ftHfX09586d040irUJpNiMjI7r6o8fj4cCBAxQUFOByueju7mZ0dJSOjg5GRkaAy3932WmSu3btWsot1JktAHk6y7kUthZk4hUbm1UzEIQQJjIlmyeythmklFMq0EgpU1meBBsQAw5JKc+ucJMXRLa0azbaIJrtQcjlKtYGUC0vvLKyUg9uTKfTpFIpduzYATBlwH399dcRQtDU1ITf7ycWi7Fr1y4CgQCFhYX6OvHExAQtLS2MjY2xbds2zGYzx48f5+mnn+b48ePcd999HDlyRDdCJiYmCIfDuk5/SUkJg4OD+Hw+hoeHee9734vL5SIcDmO1WvWBJBAIcPHiRQYGBti/f/+U4kJ2ux0pJSaTiZGRkSkiSdr72NiYru2fn5+/aNewtn9zc7M+CKy1qpQtLS2cOXMGIGdchUa2W9pgMMy4FnN5S2KxGMlkErPZrOtawOXUR6fTybPPPsvg4CD79u2jtraWsbExXnvtNS5cuEBrayvvf//7MRgMhMNhYrEYZ86c0Y2E4eFhpJS0tbXxne98h6amJvbv34/NZtPvod/vJz8/f4osd3t7OxUVFTidTpxO5xSdg1QqhdVq5dChQ/T19XHp0iVdOyGZTOqaHdrx+vr6OHHiBNXV1RQUFFBWVsaOHTuIxWKYzeYZHgSN7IDX6SWvF1sCe6El3ZdTzXEtyMQrNjarYiAIIXYAXwIqhRCtwHNSyh9keQymyOZNbv80mcyGfWvVOJgLLbgulUrpD3FNAREuP9i1B7rNZmN8fJza2lqMRqMul6wNtNqDXhMnKiws1Gd7muyultWgpT6OjY1x4cIFmpubuXDhAk8//TRPPvkknZ2d3HzzzRw+fJg///M/p6urizvuuEMXYkqn07S0tHDx4kXcbjcNDQ26i3p4eBiz2awr3rlcLlwuFyaTCaPRSCKR0AVr2tradMGkmpoafD6fng5nNpsJh8Pk5eXpg1EgEKCoqChn8SeYOXDmWt/NHgTWGrO1Lft3QEaKWltGyhaL0jCZTPT19ZFIJLBarfpv12SLKyoqqKio0GM/NPXEkpISzp49qwcbastLWhVPo9GI0WjkwoULWK1WEokEPp+PS5cu4XA4uHjxIi+99BI/+tGPcLlcfPSjH+W//uu/+O53v8tnP/tZ7rrrLj3t8pZbbqG2tpaJiQm9f7vdbl3nIJFIMDAwoGfpaLUYPB4PTqdT78fRaJRgMEhJSQmxWIzh4WFisRhVVVXU1NTowkzZRlRZWRnpdFoP3jUajRgMhikVISORCH6/H5fLRXl5+aJLYM+l5aFQrFdW3EAQQjSSKdn8n8CLwO3A9UKI26WUD0x6DPKklFP0U6WU/yiEeFFK2b7SbZ7OfBHP2uepVErPGdce2qFQCL/fr+eIa4OflFJ/OOfn5zM2Nsbg4CCDg4O6/PH4+LiucaDFCGgz7L1795JKpYhEIrq8rba2GgwG6ezs5MSJE5w5c4af/exnRCIRjhw5wuc+9znuueceSkoyytVHjhzhYx/7GD09PTz44IMMDg6yZcsW9u7dS0NDAyUlJbjdbqSUhMNhfTkgEAiQTqcpKiqioKBAd5n7fD49EHJoaEiPUWhra2NwcJB33nlHf6hrJYXLyspwOp2UlpZiMBj0B3WuCpHZSoG5VBctFose1b+ckeoLPVZ26ur071osFt21nb2P1kc0tFTT4uLinOft6emhpaUFl8uF1WrVf7vmWdD6WDgcJhqNEg6HgczA6fV6KSgoYPPmzXrsiebp2bx5s748UVxcTF1dHS6Xi+PHj/N3f/d3tLa2cuedd/K9732P973vfbouwpNPPsmjjz7KP/zDP3D//fdz22236ccPBALk5eURi8V48skneeONN/j5z39OKpXiN3/zN7n99tspLi6msLCQVCqFlJKhoSHq6uqw2+16X962bRt9fX3k5+czPDzM9u3b9eW2XNcoFovpqboWi4Xq6mri8ThjY2N6YPHY2Bhwudw5XPZ2LZUrqUCqUKw2K2ogTOoc/BbwgpTyk5Pbvg58BviMEOKHUsqPasaBEOK3gRc1OeW1YBxMJ9esVXsg+P1+Tp06xZ49e3TyzuubAAAgAElEQVTXozYYFhYWMjExoZfUDQaD2O12/SE/MjKCx+PR1eqCwSB9fX1YLBYaGxvp6uriwoULDA0NYbFYGB4epr+/n1deeYVoNMrbb7+NyWSiq6uLY8eOMTo6yrZt2zh48CDf+ta3uO2223A6nYyNjU0J0Lrhhht49tln+fCHP0woFOLd7343gUCA3bt36+vEg4ODunEzOjpKIBDg/PnzpFIpNm3aRDwe16V0i4uLqays1FMZtVmWJhldXV2tV/xzOBwUFRUhhMDlcun59/F4fEZaGkxdzxVCzPj/WmW+tuVSQMwWJpr+fa/Xq8saa1oEmr5Ed3c3ZWVl2Gw2XC4XeXl5ep/TUmS16onFxcVEo1EGBgYYHh6ms7OTVCrF/8/emcdHVZ7t/3sms2Qyk8lk3zeykYUlLFEMuFRcQEWp+morWqpUxL4uP5dq9a3r27rXSou2+qq1voIvKgUXBFsUZAcJaxZCEiD7Nklmkplklsz5/RHO00nIZEGK2Ob6fPIJzDlz5pwzT55zP/d93del0+lwOBw8/fTTLFu2jJSUFBYuXMhNN91EaGjoSaS8H/7wh1x99dWsWLGC3/zmN3z44Yf8/Oc/Jzo6mqKiIvbv388333yD2Wzm/PPP54477uDo0aM88cQTtLa2MmfOHJKTk1Gr1Rw8eJADBw7Q1tZGYmIiu3fvxmg0YrFYaGtrE9cy1P2BvuAyMjKS5uZm2tra8Hg8QnHU4XBgtVpF9iswMLCfIdZwAcJgc8BISYtjGMPZjDMaIJzQOYgHYn1ec5ywbO4G7pQk6RlZln8pSdLlwB+AVZIk3Tqw7HC2QFm1KrrxvhOC0paopIehLx2spEeVFXFLSwuVlZX09vYyefJkenp6aG1tJSYmRpDGFCGbjo4ONm7cyDnnnAP0kavq6urQarWsXbsWm83GW2+9hcFgYPr06Zxzzjn853/+J9OnTyc0NHRE15SRkcH69eu5/vrrWbNmDddccw1Go5Ho6GjR0x4TE0NSUhJut5vQ0FDR4uhwODhw4AChoaFkZ2eLHvuenh5SU1PR6/Vs376d+vp6GhsbiYmJEe2LDodDpJx9U8QDJ2pf7oZvPdfXFdNut59UP7bb7ezatYuCgoKzurNB4bHY7Xa++eYbpk2bhkqlwm639yshKPB4PCLb0t3dLVocKyoqaGpqErbL6enp9Pb2UllZKfw4lIDNaDTidrtpa2tDrVYLP4SysjK2bdvG8uXLiY+PZ+XKlVx22WXivvqaivkiICCAG2+8kR/96Ee88847/OY3v6G1tZWZM2dyzTXX8MILLzBlypR+13LFFVfws5/9jPXr13PvvfeSl5fH5MmTsdlsREVF0dnZKcaw0+kkLCyMhIQELBYLNTU1jBs3blDipsLb8JUfb29vp7W1lXHjxgnfCkVErKenZ1TjY7DOBH+kxbHAYQzfJ5yxAEGSJEnum+GLgBxJkvJkWT4EIkh4H8gCLpYkKUSW5XWSJL0ArDhbgwP4xyrWarUK5S9lQlD4AwkJCfT09FBRUSFSrUraXKPRYLPZ0Ov1OBwOWltbSUxMxOVyYbPZCA0NFW1gycnJFBcXs2/fPqCP2Ka0Pz7zzDOsXbuWrKws1q1bR2FhYb9a9GgRExPDJ598wsKFC/nLX/7Cz3/+c5xOJ01NTTQ0NLBv3z6qq6sB+OSTT5BlmUceeYS0tDT0ej0hISGYTCaCg4NxuVxihbZ//35KS0uprKwUTPWkpCQCAwOFmuJgtVzfVZriXDjQiliBv/rxrl272LFjBwAXXXTRqO+JL04l7Txa4ts333zDzp07AZg2bZrfmrhSPrDZbDgcjn622zqdDo/Hw5EjR8Rnbt26FafTSX5+PgUFBXg8HmpqaoRwVmhoKE1NTbz00ksUFRXR29vLCy+8wI9//ONR9+5rNBoWLVrEwoULRTYCEFwAXxQWFrJz504efvhh7rrrLh544AGuvfZaLrroIhwOBx6PB51Ox8aNG9m3b58wi8rIyAAgJCSEGTNmAH0lBSVTkJiYiEqlEkGs1+slPj5eZK7a29uFPbXJZBLtw/6+J6fTyZEjR8jIyECn0w3ameCPtDjSbocxjOFswBkLEOR/zKhrgceAByVJukeW5Y4T222SJL0I/D9gNvCRLMtPnanzO1Uoq1aFTOc7Ifj2ah86dIgDBw5gsViYOHGiWM0cO3ZMtHopx1CCg40bN1JYWEhwcLBIwefm5oo6fVVVFUuXLuWtt94iPj6e3/3ud9x4442nTRjIZDLx2Wef8eCDD/Lggw/y0EMP4XK5CAgIEI5/SUlJPPvssxw8eJAHHniASy65hLlz55Kfn4/BYKCrq4u///3vREREYDAYMJvNQqIZ+jIFAQEBog1xICtbCQxcLhfV1dWCvKh4Swx8aPb29grXwIEtkQUFBf1+D8RoHuCnYjE9FPFt4Gd7vV7Gjx+P1+sVq2jFCbG7u5sDBw4wceJEERyFhYXR1dWF2WympqZGcD+SkpJEOSctLQ3oK30dO3aM+vp6vv76awICApBlmba2NlauXMmGDRsoKytj8uTJ3HnnnSxevPhbO2YqJMPhEBwczO9//3uuvfZafvGLX/CHP/yBG264AYvFIroqXC4XoaGhZGZm0t3dzf/8z/9w3XXXcfHFFwP/IGcqgakSeHo8Htrb20XmKjw8XIiA1dXVCVEvxVTMNwBVxoPH4xEZMICcnBzhM+H7d6eQFgcGkiPtdhjDGM4GnHGSoizLlZIk/QfwOdAtSdITsiw3ntjsBvYBljN9Xt8WvilxhYCoPER0Oh3BwcH90o9KJkGj0ZCcnExycrJI/yqthPX19ZSXlxMUFERMTAwGg4EdO3ZQU1NDcXExH330EYWFhfz5z3/miiuu+KcoBup0OpYuXcp9991HTU0NSUlJxMfHI8vySSvAW2+9lV/96lfce++9HDhwgOuvv562tjbKy8uF02RycjKTJk2iq6uLuro6NBoNMTExZGZmDro6VdK3BoNBSPkqErzTp0/vp5Gg7N/Y2ChU/XxhMBiGzByMhrl+Kg9MX+LbUJ+t0+morq5Go9FQUFAglA9jY2MxmUwcOHBAOCsqpaa2tjY6Ojpoa2sjIiKClJQU4uPjUalU9PT0CHlsgAsuuIDQ0FD27NkD9Bl4bd68mY0bNzJ16lRuv/12rrnmGpKSkoC+oOtMY86cOVx22WWsWrWKjz76iLS0NObMmUNWVhYZGRn9eCYHDhzg0UcfpaCggNtvv50HHnhA2I4fPHiQ6OhoXC4XHR0dBAcHk5ycTGJiovB52LZtG5WVlZjNZgoLC8X345vp0+l0WCwWMW7Dw8PJyMgQnRRdXV0nBQlwcuA31u0whu8TvpM2R1mWv5Ik6XrgAyBWkqQP6QsMFgBxQOV3cV7fBsqDTAkOnE4nbrcbp9NJUFAQXV1djB8/HpfLRX19PQ6Hg46ODmpqakhNTUWr1VJeXs6+ffvQaDSEh4fj8XjYt28fTU1N7N+/X7S7JScnU1hYyJYtWygoKMDlcv3T5YQV9z0Fbrf7pH0yMjJ4//332bZtG7/85S9Zvnw5Dz74INHR0URGRlJZWYnH4yEkJISSkhLS09NRqVRMnTpVKOkp9V/leiIiIkTve3R0NOnp6ZhMJiZOnDioNsK3EaLxfYArmQtFdnhgVuFUSJBKm6ovj0B5gCgiTkFBQTQ2Ngo54ssvv/wk0mJeXp7QuVAQHh5OS0uL0BlITU1Fp9NRVlZGe3s7iYmJJCQk0N7ejtlsprS0lO3bt/Phhx8SHBzMj3/8Y373u999a8Gg0wmVSsV1113Hdddd1+/1gSWziRMn8sknn7Bx40Z++ctfMnHiRB544AEmTJjAl19+KcoMNpuN1tZWoeGg6IpkZGTQ09NDTEwMgCAoKsZher2epqYmjh49SldXF11dXeTm5goZ866uLtE+OpgOxb+qoucY/vUxbIAgSVK2LMulp/uDZVn+RJKk84CXgF/Tlz1wA3NkWa453Z83xHn4rSf7ewgMtr8yeSv+BV6vV6yyw8LCBEN6165dlJSUsHfvXvLz84Wiodlspre3F61Wy8aNG3n22WdpbGwkJyeHvLw8fvjDH/L0008L1ToFiunSUCtapX1rMLS1tfklLyrM+MHgdDoH7cmHf5Ac16xZw2OPPYbL5eLpp58Wuvl79+6lra0Nq9XKjBkz8Hq9uN1uGhoaRK1Yabvs7u5GpVIJl8GoqCimT58uHoTKd6RM5oMJ0QzHF1CO0dbWxurVq7nmmmvweDwi4FPu7bed4AeS2ZTuFUXSWGlnXbt2rVCeLCkpYdq0aeJeKw/HjIwMurq6hBBQeHg4mZmZIkjo6OjA7XaL1r7e3l5qa2vp7OwUwdu8efN47733hLARINQGB7s/g0EhyCr/VgS2AGETPhi6u7v9ji2bzTbkvfaniFlQUMDnn3/O+vXrefzxx+ns7GTWrFm8+uqrJCcnC02Fjo4OoqKiiIuLE2OmoKAAo9HIoUOHSE9PR6vVCpIjIGynY2JiiImJISsrS3RM+JKOB461oRRAhxqXY+ZRYzgbMJIMwgygVJKkrwAbcAg4eOKn7NsQCGVZLpIk6WogDDACjSccGs9qDDZhKsz5sLAwIiIi6O7uFnK2inVuXV0dNpuN2tpaWltbhbNebW0tBoMBvV7P/v37eeGFF1i8eDGPP/64mAwV0tRgUCY5fxhqm6+F7kB0dHT4fd9gJQbfY6pUKubPn8/cuXP59a9/zeLFi3nsscc4//zzSUxMxGAwiN55vV5Pa2srHR0dwgRKaaNUNAHi4uJEC+RwpYCBDHZJkpAkaVgG+erVq/n73/8OwE9+8hOAb51BUD4b/pHVUIJJxXq4paVFbPv888/ZunUrU6ZMoaCggJSUlH4W2MqKVlm11tXVYbFYaGhoEA/j9vZ2oC/rExERIVwTtVoty5YtY82aNezYsUO0rXZ0dAx5PUNxB5QA++233+a3v/0tbrebmJgY8vPzyc7O5gc/+AG5ubkn3e+AgAC//gcBAQFDns9wY/3aa69l3rx5rFixgpKSEoKCgmhtbaW0tJT29nba2tpob29nwoQJ3HPPPURERJCamkpTUxMHDx7EYrEwefJkHA4HgGg/VgSUJEkS914ZS/4CGkmS+llOj2EM3ycMGyDIsvzWid8XSZJkBPKACcBiYIIkSV/Ksvz0qZ6ALMs2+gKP7xwDyV+jQU1NjbCfTUxMxG634/F4sNlsgmGu9P07nU4qKipIT0/HYrFgMBioqanhV7/6FceOHeODDz4QhKvTjZaWFgICAjCbzSMuS/T09NDW1obZbB6xF4ICnU7HU089xYwZM1i8eDE7duxgwYIFQjFPr9cLJcWYmBgRMHV2dqJSqaiqqqK5uVlI8TY1NREWFobJZBr0O/J6vaIVc9y4cYKHIMsyZWVl1NXVAYMzyK+55hrx21cy+9sa+ShQq9XExMSI1aFy7e3t7dTV1TFu3DjmzJkD9NXgtVotzc3NHD16lNzcXOGwqcgmK2PMYrGwd+9eDAYDEyZMEAGpx+MRXSUej4eXXnqJ119/nXXr1ong4NuitbWVxx57jEOHDvHKK6+QnZ3N3r172bt3L59//jmvvPIKGo2GSZMmMWfOHBYsWHBGPDE0Gg233HJLv9fcbrfoorDZbMyePZvly5dz9913ExUVhdFopKWlRZAUw8LC+nl6KMqTtbW1wtUU/jndCL6t0WMYw3eFUXEQZFnuAnac+AFAkqSVp/ukvisMRv4aKXzZyXV1dWzbto2CggKhZdDS0iLMlfLy8hg/fjzR0dHU1dWxZcsW7rrrLs477zxWrFhxWoxcfNHa2srWrVtZuXKlaPNTqVSEhoYSEhJCVFQU4eHhhIWF4XQ6aWtrw2Kx0NzcTEdHB3a7Hejrlb/hhhu4/fbbR51unzNnDps3b+aWW27h0Ucf5ZxzzsHtdpOZmSlaz+x2O4mJiSKdXl1dLVolU1JSOHz4sJg4lZq7IpADfWS648ePY7FYsFqtxMTEiADB4XBgMpkA/wzy8PBwbrvttlHe3VOHSqUiMzOToKAgYV8cEhLC1VdfLR5MLS0tHD58mNraWkEajI6OFlkah8OB0+nEarUKdUutVktkZCSRkZGC2/Haa6/x1FNPsXr1ar9dHKPF+vXrWbx4Menp6Xz88ceihh8fH8+VV16J1WolJCSEffv2sXv3bl5//XX++Mc/ctdddzF37ly/5YczAZPJxOrVq7ngggtYtWoVaWlpeDweMjMzKS8v78dvUQI6lUrF+PHjAYSAV2JioshMRUZGcuzYsVGbbw2GkpKSb3eBYxjDacC3JinKsvwfp+NEzgYoZj6nYuqj0WiIjo5m69ateL1eGhsbaWxsJDg4WCgKejweYWlcV1cnpIlfeeUV7rzzTh566KHT4hHvcDjYsWMHmzZt4uuvvxZOd1dccQWPPfYYer1eyDhXV1cLqdn29nZ0Oh05OTmi5TI5OVlI3xYVFfHaa6+xatUqHnroIX72s5+NiqyXnJzMF198wSOPPMKKFSuYPHkyAQEBQiyppqYGq9XKuHHjhNRyWFgYISEhtLS04HQ6xT1T0urwD3Ea5RpCQkJISEjox5EICgoiIiKCpKSks0pl0bcVFk4mtU2aNAmHw4FWq0Wn0/Wr2yulBrPZTG5urshONTc3YzKZ8Hq9VFZW0t7ezpNPPsnSpUtPS2aqtbWVhx56iNWrV7N48WJ+/vOf+x23QUFBnHfeeZx33nksXryY9957j2XLlvHkk08yd+5cbrjhBi655BKRpWlubmb79u1UVFRQUlJCcXExFouFG2+8kUWLFp1Wi+S4uDjeeOMNLrvsMs477zzy8/MxGo0kJCQQFBTUz/NEgUajITc3t18Jq6qqisrKSg4fPiw4HEOZb40EiiHbGMbwXeKstns+09DpdOTl5Z1y9L9792527NjBlClTmDVrFgaDgbVr14oarMlkEja6NTU1REdHo9PpqK+v59JLL/3WDy6Px8Pvf/97fvvb36JWqyksLORHP/oRU6dOJSMjo9/xldWoxWLxO+k2Njb2k/u97LLLmD17Nu+++y5PPvkkGzZs4KWXXhKr35FAp9OxbNkyIiIiePLJJ4W4klqtJj09ndjYWLRaLZIkCfe+nTt3ihSwLMvYbDasVivh4eGEh4cLzoHRaBSM9YHlB1/p3LMZA10tdTodM2fOxGKxYDQaOXz4sJCgVqlUIvAMDAyktbWV9PR0oROwbds2iouLKSoqwu12c+ONN36rc/N4PLz//vv813/9F2lpaWzevJmgoKARB7WBgYHcdttt/PSnP2XLli2sX7+eO+64A5VKxYQJEygtLaWlpQWj0UhOTg45OTksXLiQwMBA3nzzTV577TWuu+467rvvPrGS/7ZQzl9xnlTcSAMCAlCr1YKj43uNA7tn4uPjsdvtJCUlUV1dfVqMwc42a/Ix/HtiLEDwwWAtSV6vV/Qx+1oyD7Rphj4fA+hTvTMYDGzYsIHKykpiYmIYP3483d3drFu3jri4OOLj44mMjKSrq6tfi9WporS0lLvvvpvGxkZeffVVLr/8ckEMG6qLYbQICAhg4cKFzJw5k2effZbzzjuPJ554goULF46Y0yBJEk899RTBwcE8/vjjhIaGMmPGDCIjIykqKiIjI4PAwEAsFgutra1s3LiR+Ph4LrzwQiRJora2lubmZhFYKDVjhfjZ0NDwveo1HzieBgYyCh/i4MGDlJWV4fV6BbfA6XTS09PD/v37hQBSamoqu3btorW1lZaWFnQ6HZdccskpix1ZLBbeeecd3njjDex2O48++iiLFi0iICBAqIeOBiqVinPOOYcrr7ySF154gXXr1nHkyBGWLFlCbm4uwcHBJ92DG264ga1bt7Js2TKmT5/O5Zdfzj333ENhYeG3CqwV8u/UqVPJz88XbahK2aqtrQ23201SUlI/sqbb7eb48eOEhobicrlExm1g5kD5bn3njzGM4fuCf/sAwbfN0Xf1pqQXfRnzer0eq9VKdXU1ZrOZiIiIfqS9oKAgLrjgAqHklpubi9VqJSsrS4i2KK1RKSkpbNmypZ/1bmdnp1/GeENDw6AEQY/Hw29+8xtWrlxJYWEh999/v2inVFBVVeX3+t1u95Ara39+8x6Ph+eee47PPvuMp556ig8//JAXXngBnU6H1+slOTnZ7zGVVr0777yT9vZ2Hn/8cd5++22h5nf06FGCgoJobm4WUswJCQlEREQI2WmTySQEm5TVlsLWT0xMHFWb2EjbIE8Fg7XR+rZnQv/AdCgSqCImFR0djc1mQ5Zl9Ho9ERERTJkyhaqqKnQ6ndBvcDgcRERE8MYbb/D444/7VX9ULMMHoqysjHfeeYc1a9YQFxfHj3/8Y+bMmYNer6esrAzo4+348xRwOp1+s1Pd3d39OAvx8fEAwpdksPfFxMTw9NNPc/fdd/P2229z1VVXkZ2dza9//WuhrOnxeESb5UAMpheiKFROmTJFKCZqNBo6Ojowm81CTKmuro7Ozk7S09PR6XTU1tZSVlaG0WgUolw6nU74ZSifM5QOwlib4xjOdvzbBwi+bWiDObip1Wqam5vRarV4vV7KysoEQz4xMbHfRK+I65jNZuHUOHnyZAwGA9XV1Zxzzjno9Xri4+MpKiqiurparC5CQkKGbFfUarUnsekrKip48MEHOXr0KPfff78gnw0UklHsfQfDsWPH/KZr7XY7qampg27r7u5Gq9Uyf/58CgsLWbRoEU888QTPPffcSeqGA+F7zx555BGKi4t55JFHWLp0KQ6Hg5SUFHQ6HZGRkRgMBtGuFxQUhMvlEmZCarUaSZIICAgQbYj+MgdnE+/Ad8xBf4Gmwc7TN8OQnZ2NLMt0dnbS2dkp0t86nY4pU6YIdUqVSkV6ejq7d++mpaWFuXPn+n2QGwwGESDIssz69et544032L59O7Nnz+bFF19k+vTpg55bR0eHX7KhxWLx+7BWtAgGgzK2/CE7O5vnn3+e++67T3hELF26lMLCQrxer9/3qlSqk7a5XC4MBgMajUbILiteHx6PB61WS0REBC0tLZSVlWG328nJySEqKkqYljU0NAj+x8BgYDAdBCX7EB4ejtlsHvS+nk3jdQz/vhjLeQ2Duro6jh8/Tnl5OQDjx48nNzeX8ePHn7QaUYRw6uvraW9vFw5xzc3NHD9+XHgIHD16FJvNhtFopLu7m9jY2FFNCL29vbz++utceeWVJCUl8etf//q0MdNPBVFRUbz66qvs27eP559/flSrH5VKxeuvv05vby9Lly7l/PPPF86EycnJREVFkZqaisFgoLa2VnRY2Gw2uru78Xg8NDU1nVY5YKfTycGDB7FarRw8ePBbtZzZbDYOHjyI0+n0u48SmPobA4rx0LFjx/B4PEI+ubm5maamJjo7O4V1cWZmJpGRkURHRxMXF4fH4xHSyiPB3/72N+644w5ycnLYunUrf/nLXygoKBh2fB47doxnn32W5557jlWrVnHo0KF/eqteTEwML774IosWLeL2229n5crRN1Qp5cOKigrUajXBwcFC0trr9dLa2oparSYzM5PY2FiR2Wpubkan03Hs2DGOHTtGRUUFer2eoKAgEVzA4N+tIpVeVlYmtBbGMIazEf/2GYThkJiYKPzmFQlgf1G/0p5oNpupra2lqamJoKAgMjIyUKlUQmglPT2duLg4ent7+dOf/jQqZrbD4eCee+5h3759vPzyy8yZM4dNmzYN+z5ZlqmoqODgwYNIkkRgYKBwkHQ4HGJyi4+PH5GpzkAkJCSwbNkybrvtNsLCwnj22WdH/N7g4GBWrFjBhRdeyGuvvcYDDzyASqXqt6JWWhdDQkKIjIykoaGB8PDwQbsZvi3Ky8spLi7myJEjws74VDpbALZs2SKEck6V2a7X63G73XR0dGAwGIiOjhbkUY/HQ3Nzs1DwjIuLIzExkba2No4cOcKaNWu46667RvxZf/rTn1iwYAFPPz0yaROXy8WKFSvYsGEDhYWFREREUF5ezt/+9jdcLhepqalkZ2eTnZ1NXl5ePxXQ0wFJkliyZAlJSUk89NBDVFVV8dvf/nbE9X673Y7BYKClpYXAwECio6NFt4zRaESr1QqxLEUa3Gg0otPpxN92VVUVmZmZInBrbGxEpVL5HY++c8podUXGMIYzibEAYRhoNBpR3/QHp9NJeXk5mZmZREdH43a7cTgcgjCmuPNt2bKFvLw88dquXbuEi9xwkGWZTz/9lGeffZagoCBWr14t6rYjwddff83mzZvJyclBo9Fgt9tpbW3FarVSWVlJd3c33d3dxMXFcdNNN/mVwR0KWVlZvPzyyyxevJhbb711VGzucePG8corr3Drrbdy7rnncvnllwP/IJGFhobicDiIjo6moqJCeFz4+hQMNMYZrb2yAuW8TwcrfebMmULvYSgovfTx8fF4PJ5+BFiVSkVSUhIGg0F8LwqZUavVolaraWtro6ysjI6ODlJTUykuLmbr1q2Ul5dz2WWXjehc3W43u3bt4o477hjx9X300UfU19fzi1/8ot819vb2snfvXlwuFyUlJbz55pu0t7eTlpbG1KlTSUpKIi0t7bS09QJcccUVxMXFsXjxYqKionjkkUdG9L6goCCOHz+OTqfDbDbT2dkpSgA9PT1UV1dTWFgogjylZGCxWDh27JgoN3g8HsrLyxk3bhxxcXH9umsGjr+RzCljGMPZgLEAYQCGk+MdDOXl5Rw8eBCHw8G0adOora1l//791NbWCoviDz/8kJaWFtrb25k9ezbR0dHs3r2bTZs2sW/fviGPv3fvXu677z7Ky8tZsmQJt91226haMQ8cOMCmTZtYsGDBSTV6Xw6Cw+Fg5cqVLF26lBtvvPGULGmnT59OXl4ef/3rX3nooYdG9d7Q0FCCgoJQq9VUVVXR1NSEVqslPT2dnp4e3G435R2dWCgAACAASURBVOXlWK1WQkNDRYtfS0sLISEhJ9WAfQmmo5G71el0YrU/YcKEb1UPNplMfomevjh+/DjFxcV0dnaK2rzBYMDpdHLkyBEyMjIEOfGzzz5Dp9ORlZVFcHAw1dXVhISEiHa9vXv3CqMwYMTBnkajYf78+bz77rtccsklw+5fVFTEgQMHeOKJJ05qdQ0ICCAuLo68vDyuvPJKZFmmpqaGoqIi9uzZw4cffsjrr7/O1KlTKSgoYOrUqSMug/hDfn4+L774InfccQeFhYVccMEFw77npptu4tVXX+XVV1/l+eefx2Aw0NTURFtbGzt37qS4uBiXy8XVV1/dz6119+7dVFRU0N7eTnR0NFarlcbGPlNaZewo3TUwvI/Hqcw7YxjDPxvf6wBBkiRJPs1035qaGioqKoDBJVQHa3FMT0+ntbWViIgIUbPMz88nPT2dCRMm0NLSQlpaGuHh4YSEhLBmzRr+9re/iYyAP2JdQ0MDTz31FCtXrmTevHm89tprfold/lBSUsLq1au56qqrhm39CwoK4pZbbmHTpk288847FBYWCqfF0eDiiy9mzZo1ow4QFE+CiooKGhoaaG1tJTIyUrDCa2trMZlM2Gw2ITV8/PhxSkpKsNvtjB8/HqPRKNK2gYGBom3tbIAii+yr/qggPDycqKgoEhISBCHW4/Gwf/9+IeGdl5fHjh07+OyzzzAYDAQFBREYGMjevXtJTEwkPz8fh8PBkSNHqKysFIGB0pUzEtx2221cfvnl2Gw2oTzp71peeuklzjvvvBHpYEiSRFJSEklJSVxzzTVUVFTQ2dnJrl27ePPNN3nuueeIj48nJyeHpKQkVCoV48aNG3Vr4IwZM7j//vu57bbb2Lp167BlJ61Wy9tvv82MGTOYOXMms2fPxmw2k52dTV1dHbIsi+9K+dvX6XRMnz6d8PBwcnJy6OrqIi4ujtDQUJFFUTqZfMfjUBhu3hnDGL4LfC8DhBOeEBKgBSyn89i+ksmDwZ9WQmZmJl6vF6vVSkREBDExMTidTjQajehj37JlC6+88gqNjY3ceOONbNu2jalTpw76Oe+99x6/+MUvmDhxIhs2bDippXIkqK+v57nnnqOwsJD8/PwRvUelUnHRRReRlJTEe++9x+OPP86DDz4oJItHgtmzZ/O73/1OlF1GipaWFiIjI9Hr9YSFhQkthG3btjFhwgThxwAI6+j4+Hh6enoIDAykpKSEnJwcseLv6ekRFtJng2GOxWLp5+boC7PZzMSJEwkKChKZD8XVUvHC6O7u5txzzxWy0ePGjaO+vp6IiAja29vxer2MGzeOo0eP4vV6sVgsSJKEVqsdMWEwJycHrVZLaWnpkHLjH330EW1tbdx8882ndC/0ej2TJk1i5syZIrtQUlJCSUkJ69at480338RoNDJhwgQKCgr40Y9+NGJuzMMPP8y2bdtYtGgRq1evHjbAzcvL48knn+S//uu/iI6OJi0tDUmSCA0NZeLEieTk5AjnTaU0N3HixH73p6mpiXHjxonMXnd3N11dXZhMphFloIabd8Ywhu8C37sAQZKkXOBFIAmolyTpTVmW3z9dx9doNIwbN84vE1+xdPW1dtXr9bhcLnbu3ElZWRmzZ88mISGBrq4u9u/fz/Lly1m1ahUpKSksXryYm2++WZC1FBIc9JUqtFotu3bt4p577uGRRx5h3rx5SJLEpk2b/LaTFRUVncRH6Orq4rXXXiMtLY3e3l7+9re/Dfrejo4OmpubB902ffp0KioquOOOO5g/f36/laIsy349IwICApgyZQofffQR991330nb/T2sLRaLyJDodDosFguHDh2iq6uL0NBQZs2aRVhYGM3NzXR2dhIcHExISAjTpk2jqqoKq9WKw+EQwYxSL1ar1VRWVpKYmDhoC9w/s6VsMDfHwe6bwnZXbK/Dw8MxmUyC9LZv3z50Oh0FBQXMmzePpqYmioqKaGlpEdbEHR0dhIWFMWPGDFQqFeXl5aK3fyhbc0XGGfru+/jx4ykvL+f8888HOGl8tLe386c//Ymf/exnfP7550O6jCrB9EA0NjaexOBXrJSVTMPx48c5evQof/7zn/niiy/4yU9+gk6nGzJwsdvtGI1GXnrpJa644grOP/98Fi5cyJVXXonb7fb7N3TLLbewdu1a3njjDd59910CAwPR6XRotVqMRqPgJtTV1dHU1IRerycmJobq6mpkWT6phKDMDyPNXinzzhjGcDbhe9XmKElSDrAFKAVeBTqAayVJ0klnqHHYl13f2dnJF198gdVqpaKiguLiYkpLS2lubqa9vZ3/+7//Y/78+bhcLj7++GP27dvH4sWLh2Ry19XV8fDDD3Pbbbdx9dVXn9LDy+128+677xIcHMz1119/yg/AwMBAbrrpJrKzs/nf//3fYbkSvpg3bx4ff/zxqD6vubmZyMhIwsLCGDduHJdddhmXXnopWVlZpKamEhwcLPwItFotTqcTp9OJSqUiMTERs9ncr96uEPnq6uqEvPV3CcXNcagVbU1NDVVVVbS3txMQEIDBYGDy5MlMmTJFdFJ0dXVRW1srbLEnTpzI5MmTiY+Pp6Ojg6qqKgwGA0aj8ZTUE3Nzczl06JDf7X/5y19ISkrioosuGvWxR4qgoCCys7OZO3cu9957Lx0dHSxbtmzEqqDR0dF89tlnXHjhhTzzzDPMmDGDl19+2e8YUKlUvPXWW2zZsoUVK1ZQV1dHYGCgkEevr6/HYrGQmpoqMlYbNmzgiy++YNeuXaLtUYHdbmfr1q1jbYxj+F7jexMgSJIUBPwaeEeW5ftkWV4GfAhoACMQ5rPviJ+ICQkJwhlP+Xnsscdobm7G4/Fgt9vZuHGjcDT0xfbt29m6dSsffPABvb29JCYmkpWVhcPh4IMPPuBXv/oVL730Eu+99x4XXHDBsA/q7u5u7r//fvLz81m0aNFIL6EfvF4vH3zwAXa7nZtvvvmUWhZ9ERAQwOzZs7nqqqtYt24dxcXFI3rflVdeSWlpqairjgQtLS10dXVRX19PS0sLKpWK7OxsJk6ciEqloqmpSQhQRUdHEx0dLR6AHR0deDweOjo6TjpuYmIi6enp30n6Nj4+XmQRlJ8nnnjC7/6DnatWqyUlJaVf9qO5uZmGhgYCAgLQ6/WMGzeOpqYmDhw4wNGjRwU59nQHCGVlZXz11VcsXrz4jEkHm81m7rrrLnQ6Ha+88sqIA73o6GgeeOABtm3bxmOPPcY333xDQUEBCxcuZNOmTSdlVJKTk3n55Zd5+OGHWb58ORs3bqSrq4vu7m62b9/Ozp07WbFiBV999RU7duxAlmXMZjOpqan09vZSVlaGy+XCarXy6aefsnnzZrZv3z7kHDKGMZzN+D6VGNxAIrDH57WJwGSgiL5ywzpZlp8cDXHx4Ycf5tJLL+XCCy8UrOPu7m7RW19aWioski+88MJ+RLMZM2bQ0dFBdHQ0RqORuXPnUlRUhFqt5u2332bhwoUsXrx4xBf45z//GY/Hw1NPPXVKk6/T6WTlypUcO3aMJUuWnFZzotzcXHp7e/nkk0+IjY0dlnGemJjI5MmT+fzzz0fUh9/T00NJSQmzZs0iNTWV8PBw9uzZw/jx48nMzKSmpgaLxYIsy8TGxgpNCgVKu6Nv+t6XUDqSVtJ/Burq6k7qYhhqePqmmpXzt9lsgiGvmFade+65xMTEEBQURFhYGMXFxezcuRNJksjKyiI3N5e///3vQyoS+kNqaqpfee6VK1cye/bsM34/9Xo9ixcvZvny5dxxxx288847I7ZF1+l0zJ8/n9mzZ1NfX89bb73FzTffzN13380DDzzQb99bbrmFVatWcfjwYRISErBarVxzzTUn3Y+ZM2eSlpaGwWAgKSlJZA3Ly8vxeDyEh4eTl5fHjBkzhIkb9M0hZytSUlI4fvy43+1Dyad/F0hOTva76EpOTj4ln5Ax9Mf3IkCQJEkF6IHjwLmSJC0GUoC7gTuBTiAduFuSpAOyLP91pMeeMmWKMFlSVlsRERG0tbURHh4utim/LRYLTU1NQN9kfe2112KxWAgNDRUtT6WlpUyaNAmLZXT8yZKSEubMmXNKD/aWlhbeffddVCoVd955Zz8XxtOFiRMnUlRURElJCYWFhcPuX1hYyDfffDOiYz/55JMA3HzzzWRnZ9Pe3s6xY8dITk4Wro4Gg4Hw8PCTSKK+OhS+6XtfQunZQFIcLZTzV6lUdHR0CMKnJEmEhYWh0WiEkqLD4SAsLAyTyUROTo6wth4sozIctm/f7pc863Q6R9S2+c+AWq1mwYIFLF++nKeffpqXX3551IH0pEmTeOWVV0QZZiAkSSInJ4eqqirCw8M5ePAgP/nJTzh48CBGoxGXy0VsbCyzZ88G+u6HyWQiISGB1tZWAgICcLvd5ObmEh0dTUBAAFOnTqW7u7vfPVVaJadPn37WuIweP378e+UBMVQAMCZVfXrwvSgxyLLslWXZBrwNOIDZwNXAz2VZfkeW5VXAe4CdvkBhxDjvvPPEH6hSs9ZoNELr32AwcOGFFwoCWXt7OzqdTqygAwICCA0Npby8nK6uLvbt20dlZSXBwcGsXr3aLwFwMBw9etSv98Fw7/vDH/5AbGzssMGB2+3+VpNAdnY2paWlI9p38uTJFBUVDft5mzZt4tVXXxXWv263G7fbTUhICGq1mvj4eLKysjjnnHMICQnBZDKh1WppamoSAjUlJSVCDluBXq/HZDKdsovhdw3l/BsbG2lqaqKqqore3l6am5uFtHRPTw91dXXo9XomTJjQz4/AbDYLN8KRQhHkuuKKKwbdrtVq+xFrzzSUEmB5eTnLly8/pWPIskxZWZlfD5LOzk6MRqNos5w0aRJz5szhkksuYebMmeTl5VFVVUVrayupqali3khMTKSrqwutVivGrnLOkydP7hfMKFkFxVStt7f3tEuGj2EM3xZnbQZBkqRU4GL6+AVlsiyvk2X5U0mSvgY8wDbAt3erGWigL4A4ZXi9XrEii4yM7FfDr6mpoby8nJiYGFwulxA0UXrxIyIiSEhIEKzm7du388477/Dggw8O+7mKx8BoUrder5dVq1axdu1aLr/8cmbNmuXX7KetrY36+npsNhtms1nYBY8W48ePZ8OGDbS2tg67b35+vqiV+1t1Wq1Wbr/9du69914MBgMul4uWlhays7PRaDQkJyej0WhISUlBlmUxGTc1NYmWQWVlPbClcjDr5O8TlPNXfD8yMzOxWCw0Njbi8XjweDzYbDZRktBoNBw8eFD4ACiEzZaWlhFLHG/evJnq6mrmzp076HaFHPpdIjIykkcffZRHHnmEKVOmkJOTM6r3NzQ0YLPZhgwQlBZlZaFw/PhxoqKiyMjIoKysjLq6Orq6uujt7UWtVuP1emlsbMTr9QqFy6amJsLCwvq5xCoYmJlUfFzg9EmGj2EM3xZnZYAgSVIesAnYB+QAHZIkPQxcIcuyTZIkA9ACpEuSlAC0Ao/Slz1YO5rPGtj+1d3dzbFjxwT72GQyCaGexMREIYOr2Bp3dnaK1qq4uDiOHj1KSkoKNTU1nHPOOfzP//wP99xzj0h92+32QVd0e/fuRa1W43Q6hTCOLyorK/vVQZ1OJ59//jl1dXVMnz6djo4OPvnkk37vcblcNDU1CcEXg8FAREQEXV1d7Nmzh+DgYGJiYgb9POibiLds2XLS6yaTiW+++cZvu1lAQAAtLS2i42DTpk0iJQv9ne3uv/9+wsLCiI+PR6fTYTQaiYqKwmq1iu9DCcQUq2z4B+fAZDJRV1fH+PHjUavVfrMV31XKcbD2Qt/rGAiXy0VtbS2JiYkiONVqteTl5QH/eOh7PB727dtHY2Mj7e3tXHzxxXR0dAhZb6UHH/oeiIpN9mBoamoiMDCQ9vZ2IZMty7IopfmOO5fLRWtrq3itq6vLb2dBaGgoRUVFg24LCAjg8OHDoo2zp6eHiIgIwsLCiI2NFRygwaBWq9Hr9RQWFvLwww/zi1/8Qjx8NRqNX96F0+kkMDCQoqIiTCYTBoOh37krWUGbzUZSUhKSJBEcHIxarRZBdXJyslCt9Hg8mM1ment76erqoqOjg9DQUBISEmhububw4cNkZWURHx/fTzNF4cX48hGGaoEdwxi+K5x1AcKJboU/AitlWV4iSVIoUAg8B+yUJGm2LMuNkiStAx4DFtAXICQDV8myfHSUn3eS9W5KSorQ8Petd2s0GuLj47HZbGIVdfz4cSHws2vXLkpKSoQr3Hnnncf777/Ptm3buPjii8XxB5uoq6qqSExM9LvSdrlc4uHQ3t7OihUr0Gg03H777fzpT3/qd8ze3l48Hg+9vb2iBx76JnNf62cluFFIlgNRVlY2qEyvTqejoqKCrKysQc/V4XAIUaP8/HzKy8uZP3++2K5M5hUVFaxYsYJHHnmEsLAwioqKiImJYeLEiXR2dtLV1UVPT49Y/fo+WBXxqaqqKo4cOYLdbic3N/eMMev/GfB6vZSXl1NXVwcMrqinXLfH42Hy5Ml88803dHR0UFlZSXp6OvHx8bhcLpxOJ2q1mtDQUCwWy6DuowqUgPexxx4jLi6Ohx56qJ/cr69vQHh4uLCShr4uIH+Ki6WlpX41EtavX3/Sa4ovSHBwMDk5OX4zXMpYvemmm/jv//5vli9fzl133YVKpcLpdPYT1PJFYGAgoaGh1NTUkJOT029sy7Is/oYU9c2uri4aGhpwOp2YzWZCQ0PR6XRERUUJu+be3l5MJhPh4eEEBASI+68oKUL/4NQfL0ZpgVUwVkMfw9mAsy5AAHSACfg7gCzL7ZIkrQUq6eMZrAcmybL8kiRJR4DxQBfw+WiDg8EgSZKocysyq74TlSKAEhQUhMvlEpOJy+UStcusrCzCwsIwGo1cddVVvP/++yJA8IeysrIRsYRlWeaTTz7BbDbzH//xH/0mclmWcbvdeDweAgIC0Ol0qFQquru7/R5Pq9XS2NhIUFAQkZGRI9KBDw4OpqWlZUSciUmTJgkG90CsXLmSadOmsXDhQurq6oToTGdnpyjvBAcHU1VVRWhoKCaT6aSHXGJiIna7HZPJRHd39/e6pNDd3U1wcDBxcXHEx8djt9uFpLey8gwMDCQgIAC1Wk1ycjLR0dGUl5cTGxsruAHKqtjhcBAVFSUyAUPhz3/+Mzt37mTt2rVDjgGNRnPKNs6yLAvr86HgdDrZuXOnyCyFhYUN+sDUaDTcddddPPHEE3z66afMmzdvROdRWlrqt7wA/7h/5eXllJeX09nZSXh4OJGRkRiNRhwOB11dXYSEhNDb20t4eDharZb4+Hj2798vtDwmTJhwEh9ICZjGXBzH8H3A2bjcsgEB9PEPAEFSLAUWAUGSJL124vWPZVl+XpblV09HcDAQSg3Y96Gk/HvLli0cOXKEtrY2ent7SU9PZ8qUKVx++eWMGzeO7OxsMjMzueiii/jrX/8q6sL+UFFRMaLao7LCvOqqq06ayJW6tE6nQ6fTERAQMOxKRK/Xk5SUhCzLHD9+fMhgQoFGoyE8PHxENtN5eXl+e+pXrVpFfn4+kZGRTJgwgYsvvhiDwUBrayudnZ0ilb1t2za2bNlCU1OTWJV5PB6ampqQJInc3FwiIiK+t2REBXq9noiICHJzcwW/QPk+7HY7DQ0N/YR3urq62LlzJ9HR0SI4MBqNqNVqDh06xJYtW4iKiqKlpWXIz21paeGZZ57hmWeeGVYrQqfTjWiMDITT6WTbtm0UFxcPy4eIjo5m6tSp6HQ6Dh48yO7du/2WjiIiIliyZAkff/yx39bMgSgpKSE7O9vv9s7OTuLi4tBoNMyaNYsZM2Zw6aWXijJYZGQkaWlpqNVqbDYb7e3tQF+Z8JNPPuHo0aMEBwcTHR19kg6JYhf9fc50jeHfB2fVKD1hvtQLrASmSpJ01YBd9gLvA7kn/BjOONxuN5999hnbt2+nqamJ8ePHk5aWhk6nIyUlhfT0dGJjY9Hr9QQGBpKZmYnVaqW2tnbI486aNYsNGzYMO/nW1dWRmpo6aFpXIfGN1lxJkZOVJGnEwkoj/ZwjR46QlJQ06LbW1lacTidffPGF0LLPysoiOTmZ6upqduzYQX19PSqVis7OTrGa83q9VFdXU1dXh8ViEeqWvpOuEkAMF5idCYyUoe4bkA7swFBcK5WslcfjYfPmzXz99dfs2LEDh8Mhvo/q6mo2bdokVD79pdwVKKZPI0FqaiqHDx8edSdMVVUVarWaWbNmjcifIzg4mNjYWCRJGrZFVQkQR9IxZLVaKS4upqCgwO8+yj222WxCPTEsLExwhJTSjcPhIDw8XGQJrFYrNpsNt9s9FgCM4V8CZ9Uo9hE4ehfwAv8pSdLsAdsPAXH06SKcUXi9XsrKyggICCAoKIipU6cSGxuLWq1GpVIRHByMyWTCaDQKsaXe3l6CgoKGFe1YsmQJWq2WFStWDLmfzWbza5ykpKJHO3m73W7Boxip1WxnZ6ffB78v1q5d67dlTgkyamtr2bFjBxUVFbhcLtRqNS0tLajVamJjY5k5cyYxMTFUVVVhsVjo7Oyko6MDo9F4UgrXarWyatUqKioqqKysHHb1fCagMNSVzg+Xy8WhQ4dwOp14vV7sdjterxen08mePXvYvXs3bre7X/ZKMZ7q6Oigvb2dsrIyYmJiiI6Oprm5mSNHjlBRUUFpaSm5ubnMnj2badOmcfz48WFLVwaDgZtuuok33nhj2LEzZcoU2traRiVCY7fbqaurIzMzc8Tjy2KxsG/fPuLj48nOzh42EzYU8dMXW7ZswWw2C9LnYFBKdMHBwUL7wOFwCOVKgNraWo4fP47b7RZB9cyZM5k/fz4zZ84c0TWOYQxnO86qAAFEFqEKuJ2+QOBBSZIWndimAwqAemD0ec5vie7ubkwmE8HBwaSnp9PW1ibamgIDA+ns7MRms6HRaFCpVMTExJCZmUlKSgpHjw5dAdHpdCxevJgVK1YI1bzBYLVa/ZLClMlrNAGCwlYPCgoadqWpoLe3l56enmEDhNraWvbv38+cOXMG3a5SqZg6dSqXXnop5557LuHh4bS3t/PFF19w6NAh0UIWGBhId3e3aPFzOBx0dnbS1tZ20rVu2LCBr776ip07dwpL5O8aERERxMXFCYb6kSNHKC4u5siRI4K01t3dzZEjR9iwYQNffvklZWVlInDo7e3F6/WSkpIiOmkUgZ4JEybQ3d1NXV2deFAZjUZuvPFGpk2bhtVqHRG3ZeHChZSUlIi+fH8ICQkhIyODPXv2DLmfLyorKwkPDx9WfVOB3W7n0KFDIiM3kgf/SAOEr7/+mlmzZg25wvd4PDQ2NvKDH/yA5ORkQkND2bt3L8XFxaIVMSEhgXHjxhEXFye+J1/NlDGM4V8B3xlJUZIkNSDJsuz2eU0ly7L3xO+DkiTdAPw38IgkSU/SR1TMA34gy3LX4Ec+fRj48FFqxBdccAENDQ2YzWbsdjvBwcFC+c9oNGI0GiktLWXixIn09vaSnJwsRG5sNpvf1Pz48ePJzc1l6dKlPPTQQ/22NTQ0UFNTQ0tLCxEREezfv7/fefq2To4mxel0Ounp6SEsLEy0Fvoed7AWNqXerTzUBkKtVpOYmMjq1avJysoiKiqqnw69kvZXFAIjIyMxmUy4XC727t0reBTx8fGYTCZCQ0M555xziI6OJi8vD41GI6SXa2pqSE1NFQ8IhQx60UUXodVqzwpeQkBAQD9+SUZGhvitrKj1ej0ZGRlcfPHFeL1eEhISBNu9q6uL5uZm4uLiUKvVJCQkEBgYSFBQELGxsfT09OByucTYa2xspLq6Wtzz+Ph4uru7/Y4Jq9WKXq9n7ty5vPrqqyfV5weSHMePH8/27duZNWsWNpvtpHGjwOl0UlZWRlNTE4mJicMGyQra2tqIj49Hr9cPmgEqKSk56TWXy0VdXR2xsbF+1SPdbjdfffUVt95660njWpZlESD39vZiNBopLi5GpVJht9tJS0sTpElZltFoNKSmpmK328WxTiUYHetWGMPZjO8kQDjhyvg4ECdJUgXwhSzLK04EBwGyLPeeCBJKJEm6nT5Z5cuBOmCzLMsjdwAa/lz8/pH6+i6o1WphySvLMqmpqUKxTq/Xo9frxYOvrKyMAwcO4HQ6iY6OJiwsjJqaGqHM6G+izsvL4/nnn2fOnDl0d3dz7rnnim1KN4XSL+6bRVCsgaGPo6AIvCjwZxLjdrtpbm4mPT3db//1YKnYI0eOsHfvXr8ZBJVKRWxsLBs3buS6664jNja233YlQAoICKCyspKNGzdywQUXUFNTQ0dHByqVioiICGJiYoRqYmRkJBEREeK7ys/Pp6amhsTExH5GSGazmWuvvXbQ8/ouMNj40ul0/e6rsuLU6XRMnTpVaBkorbYKPyAiIkIYiplMJmw2GyaTiSlTpnDs2DFMJhP19fV8/fXXOBwOLBaLYN4r7xsMsbGxBAYGct9993HhhRfS2dkpghjoU8T0RUBAALfddhtpaWmkpKT4XTGvWbOGzs5OwQ/xDWLT09P7tXHKsszhw4epq6sjJydHWE0PhsHGnUqlIjIykpiYmH5tmb44evQolZWVXHrppSdly3zbHBUvBYfDwZ49e3A4HOTm5pKbm4vb7UaSJNrb2wkPDxfOroqt9hjG8K+EM15ikCQpkz4VRDewAcgEHpIk6S2AE8GBTpZl74n/t8qy/I0sy/8ty/LbpzM4GA4Wi4WGhoZBPRXcbjfHjh1Dq9WKWrrZbEalUgmTlry8PCGyMtLVU2ZmJrfccgtPPvnkSaS27u5ukcr0h8DAwBG1ocmyTHt7O4GBgaMWZ7FarcOmi2tra9m9e/eQrWcqlQq1Wo3H4+Ho0aPIskxoaChRUVEijW4wGESd3jejo5gajbSm/X2DL9td6ZH3JZAqJEatVovD4SAlJQWj0UhKSgq5ubmEhITQ3Nw8tEdmugAAIABJREFUKoOd7OxsLrroIv74xz8OuV9OTg5Go3HYcoTL5eqnY+EPXq+XgwcP0tDQwLRp0wbV3hgJhntAb9++ncTExGFbc3t7e4mMjESv15OamkpKSgrBwcE0NjbS3NzMV199xbFjxwRBVhmjZ5oUO1qn0DGMYbQ4owHCCRvmW4C/y7K8QJblJ4BL6PNYKJAk6f8AZFl2nth/4QmlxO8E4eHhxMbGDuptUFNTQ2VlZT/rWWXSDg8PZ8qUKQQFBWG323E4HKMidd177700NDTwwQcf9HtdyQQMlTZXAgTFXa6rqwu32y3aAwFhi+zxeEZcF1YgyzItLS3Dvm/NmjXCidEflIegXq8nJSWF8PBw8YCbNGmSqK/7umz6wu12U1VVNSqvgX8F+KrxtbW1CSVChaSamprKueeei9frHbWx0pIlS1i5cuWQRmMBAQHMmDFj2DZXRcdhsM4YWZbp6Ojg6NGjbNu2DavVSkFBgV8C7nAYCe9m8+bNnH/++cMGEh6PB7VaTW9vLxqNhpiYGDweDzt37uTTTz+lpKQEu91OSEiICAosFgv19fWjNmj7NlAUUn1/xgKEMZxOnNEA4UQXQjwQ6/OaA3gDWApkSZL0DIAkSZcDvwd+LUnS6Pr2ThMU1brBJrjExETS0tKEoI3X60WlUhEYGIjFYkGr1Ype6JSUlBF5FygICQlhwoQJQlFPgcFgICAgQBClBoMieKT00StGP/X19eKnsbERl8sl1N9GCqUlsaWlxa+KIvRlXl588UUWLVrkd5/W1lYqKiqIiIggIiICjUZDSEiIeNDl5OTg9XpFHX4w06WamhoqKir6BWn/Duju7qajo4OWlhbCwsKIi4sTQaxerycqKor4+HjOP/981q9fz86dO0d87PPPP5+srCyee+65Ife77rrrWLdu3Ulj1BeKqJLiAWK322lvb6exsZGqqip2794tuBUzZsw4ZXKf1WrFarUSGRnpd58NGzawfv16FixYMOzxXC4XVVVVqFQqcnNzKSgoQKfTcfjwYUpLS+np6SEtLQ2r1Up9fb3IJMbExPxTXFTHMIbvCmeMg3CiO0EGioAcSZLyZFk+BH1BgiRJ7wNZwMWSJIXIsrxOkqQXgBUntBHOKHxXaSqVSmjkJyQkoNFoRIpbWd1C3wO8vr6eAwcOCD2E4OBg8vPzcblcI3Zqk2WZAwcOsHDhwn6vBwUFkZ2dzZ49e4iLixu0pixJEqGhof1W+J2dnUJ+GfoCn9Gm5pubm/nyyy/R6XTMnz/fr6iTLMssXbqUvLw8fvrTn/o93sqVK0lKSiI/Px+NRoPT6cRisWCxWOjp6elHMFS+g4GrREXUZzhxn3816PV6oYWgBHoWiwWz2YxGoyE4OBi9Xk9+fj5LlizhuuuuY+PGjcTHxw97bEmSeOaZZ5g3bx4LFixg4sSJg+6Xn5/PXXfdxbJly4iOjh505a+0oSoS3wr5VCH7jh8/ftSaHYNh//79REREnMR1UVBTU8O9997LPffcM6T+AfxDbKympoaSkhJ0Oh29vb1kZGSgVqux2+3CXwH61CqVsRsdHY3T6RyS7wF9mS+FP+PPN2IMYzgbcMYyCD4aB2uBcfS1L5p9ttuAF4Fp9Nk5I8vyU7Isn0yT/ydDEeL58ssvsVgseDweioqKOHDgANXV1f32HSho093djdVqFalGs9ksCIMjVaCrrq6mo6Nj0Mk5NzcXp9M5aPeAP6hUKjQajSBTjiY4sFgsfPHFF3z88cckJiYyb968IdshN2zYwL59+/jDH/4w5CT5v//7v8TExGA2m8nKyhJBTWpqKuHh4UImejBSp1JaAPrxEBSTIt9yytmIUymN+F6bQsgzm83o9XqR3m5vbxcGYk1NTRQVFdHb20tubi433XTTiCWSp0+fzvXXX8/DDz885L1csOD/s3fe8VFV6f9/n8kkmUnvPaRSUgklCARBsYECsiiCqyIWFuzoWgGlKH5d94vrV12Rn666664s6q4FUalSBQEBqUoPSSA9pE36nN8fd+51EtIzKcB8Xq95Qc69M8859z7nnOc89U6Cg4NZu3ZtkyWgHRwc8PT0JCQkhPDwcE2YMBqNNhEOQBEQUlJSGjUdVFVVMWvWLIYMGdKsRkuF+oxSU1Pp3bu3ZkqsqKggMTGRq6++mvDwcI0nDQYD7u7unD59mry8PM6fP9/iPL9cNV92XHzo8igGKeUJIcRtwLdAhRBigZRSDfyvQang2GWGvMaq7ZlMJg4cOMAvv/yCv78/UVFRVFZWaimGre8XQmjhTWp0gwpV06BWS1TLwza1cebl5VFeXs7mzZsJCgrSHJ/U76oLalxcHDt37iQzM5PevXtrHu9NobkFy2g0NhrKWFlZSUFBATt27CA8PJyxY8fi6emp/ZZOp9M0JyoKCwtZunQp06ZNIzAwsMkN6cyZM+zatYuXX34ZvV5PTk4ORqOR6upqXF1dqaurIyMjg9DQUGpqarRqmupzVxdYoN7zNplMjRbC6Wmw7n9jBZkag/XYGobTqWptLy8vKioqyM/PJzc3Fz8/P/r378/QoUOZO3cujz32GH/9618v2EjLy8svcK57/PHHueaaa/joo48YPHhwk/1KSkpi69atrF+/nmHDhtX7bbPZ3KQQpNfrmwyP1Ol0zdZrsBZQTSYTx44dY9iwYWRlZeHl5VWPLxctWkRRURHLli3T6ic0BimlVpURFG2g6pzo7u6Op6cn+fn59aq7lpeXk5uby9mzZzl69ChlZWXExMQQEBBwwRphjctV82XHxYduCXOUUn4vhJgMfAoECyE+QxEM7kRJjtR4/eHO6csFbQaDgaSkJHx8fOjfvz9OTk707dsXFxcXPDw8tAlvXUCnsrJSO517eHiQk5NDcXExAQEB2gJbVVWFj49PkwKCr68vRqOREydO0L9//3re3FOnTq3nDX7y5ElWrFjBli1biI6OZvz48YSFNe7P2VQ5Z1AEAeuyzWfPnuXrr7/m0KFDJCcn89ZbbzUaNlZWVlavXUrJ9OnTGThwIE8//XSTyZwA/u///o8rr7yS0NBQ9uzZg16vJzIyUivF26dPH6SU2uk1ICAAd3d3rTKlt7c30dHRWoijioulEI71BtHa0DjrsQkhMJlMnD9/npKSEq1EtslkYvfu3fTr14+wsDCklBQUFJCfn8/ChQt56KGHGDRoEI888ki93/b397/gNO/t7c3cuXN59dVX2bx5c5Pvc8aMGUyZMoWHHnoIDw8Pfv/732vXhg4d2uQm+PPPPzcZTbB169ZmN8/U1FTt/2vWrMHf359JkyZpnvyq+evTTz/lyy+/5JtvvqF3795UV1c3KSCYzWYcHBw0gUYNqw0MDMRoNFJRUYFer8fPz4+SkhKtemZAQAABAQF4eHjg6elJVVUVhYWF2vtQ35c1nerqaqKiouzpmO3o8ei2RElSypVCiOHAEmAxivagBhgrpewy3Vtjp+vKykqcnZ1JSUnRFmZrb3BVqFCz4KmqX1X9q9r/fXx8qKqq0iIYTCZTq0K4Dhw4wOjRo5u9Jzo6mueee4709HTefPNNXn/9deLi4rjuuutalQK5IfLy8vjqq6/YtWsXycnJzJkzh8DAwCZjyhvik08+Yffu3axevbrZTc9sNvPPf/6TSZMmaRUzk5OTCQ8PZ+3atezbt4+qqirS0tIwGAz8/PPPWvZKQKuk15idV42K6OlwcnIiJiamTd9Rx6aedNVTslqyu7q6mq+++oqMjAzKy8sZMGAAcXFx1NbWcu7cOaKjo6mtrWXmzJkkJCS0yF8A999/P//4xz9YsmQJCxcubPK+kJAQ5syZw7x588jPz2fAgAFN+i7YGtu3b79Ac6Hi1VdfZe7cuW3qi7oeVFRUUF1djZ+fH/n5+dTV1Wk+HpmZmezbtw9Q8jmUlJSQkpKCwWAgPz8fPz+/JrVZF4uWyw47oJvLPUsp9wghbgZ8ADcgW0rZend/G6CxkMHWnkTV7xoMBm3jMpvNeHh4aH4Hu3btYuXKlQDNmgFU1NbWcvDgQR577LFW9T8iIoLx48ej0+lYt24db7zxBr1792bEiBHExcW1eEqprKxk+fLlbN68mX79+vHss88SGRkJKBqP1uDMmTO8+OKLzJs3j7CwsGZjwTdv3kxeXh5Tp04lPT2drKwsEhMT8fHxYcyYMVoZ4/z8fGpra8nPz+fcuXOah7qLiws5OTkUFRXh6uraqgqYlxry8/PJzs4mKChIc8w7efIkDg4O2sk3PT2dmJgYAgMD8ff3Jzc3l4CAAObMmcPtt9/Ojh07WswHoNfr+fOf/8zEiRMZP358s6aG1NRUXnjhBdavX8/rr79OcXExwcHB9O/fn+HDhzdbXrm9OHbsGD///DNTpky54Fpubi6nT5/mhhtuaNNvqqHEsbGx+Pj4kJOTw7p160hOTiYwMBCz2YyXlxehoaGEhIRgNptxc3PTNAUqPza1hlwsWi477IBuFhBAc04safHGTkJjJw81Y2JL6l/ViQ6U0KhDhw7Ru3dvTSV55MgR9u7dy+nTp+nfvz+LFi3igw8+wNnZucnflFISGBjI4sWLefXVV4mPj2/VOAIDA7njjju4/vrr2bRpE//85z/x8fFh9OjReHh4XCAoSCk5fvw4W7ZsISAggNmzZzcbutgUdu3axQMPPEBaWhpTp05t9t7KykqeffZZ7rjjDpKTk8nNzcXR0VHTyHh6ejJx4kTS09PJzs4mJCQET0/PeloMIQQRERG4urq2OcHTpQJ13H5+fpppQI0IiImJ0YoLWYfcpaenc/jwYXr37k1cXBzvvfceixcvbpFWWload999N7/73e8YP348TzzxRJNapbS0NNLS0rTS4atWrSIrK4uFCxdyzTXXMHXq1A6fmqWU7Nmzhy+//JJ9+/Zxww03XCB8mM1mnnnmGfr27duiEGSNDRs2MGPGDAYPHkx+fj79+vVj27ZtbNy4kZKSEqKjoykoKMDBwYGkpCQMBgNlZWX1zI4q1DWkIS4WLZcddkAPEBAuFWRmZpKZmYm/vz/h4eEcOHCAHTt24O/vT2pqKuPGjWPx4sU8/PDDLFu2rMmTvaOjI1988QWLFy9m0qRJ3HfffRfYjJuDv78/t956K2PHjmXr1q18/vnnODo6kpKSQr9+/dDr9ZSVlbF582YyMzMZOHAg99xzT7vsoR9//DHz58/nvvvu46mnnmpRoJo3bx6lpaW88sorlJaWYjQatY3s8OHDxMTE4OTkREREhBYi11gOioa1DS43NDZ+Z2dnEhIStLS/DW3tcXFx1NXV4erqSlRUVItJjqyxaNEiJk+ezJIlSxg9ejTPPPMMDz74YJPvWwhBZGQkI0aMIDw8nOPHj/P+++9z7733MnjwYIYMGdLq8tIqamtrOXDgAD/++CPFxcWMHj2at956q1FfhUWLFrFjxw6+/fbbVvl4lJWV8fzzz/P+++/zxz/+UQtdrq2tJSQkROPFkpISzp8/j5eXl6bRUkuN22HHpQi7gGAj9OvXD51Op2UOVFW7MTExxMTE8P333zNs2DDWr1/PnDlz+J//+Z8mFy93d3deeeUVxo0bx/PPP8/q1av5/e9/z7Bhw1rdH1dXV2644QZGjRrFqlWr2L17N7t378bb21sr7TxlyhQtnLAtqKmp4S9/+Qvr1q1jyZIlzaZTVrFq1Sree+891qxZg6+vr5Ze+dy5c/z3v//V/Cb69u1LVVUV/v7+dieuDqBhHg+DwUBqaiobNmzAz8+Pf//732zcuJGrrrqqVb+XlJTEhx9+yIYNG3jooYc4dOgQS5YsadV3Y2NjefHFFzly5Ag7d+5kxYoVFBYW0rdvXwYOHEhKSormm1NTU0N5eTnZ2dlUVFRQUVGhhWzqdDoGDx7M/fff36TT5KpVq/jwww/5/PPPNVNZc9i6dSuzZs3C0dGROXPmcOWVV1JeXo6bmxv5+fla6K2DgwM6nY7Q0FB8fX013rzYKjdGRkY2GSHSlrTcdlwesAsI7UBjkQ9OTk5aAR6z2UxoaCjx8fGcPXtWK2rj5ubGhAkTmDVrFt7e3jz55JP1fqO6urreifmKK67giy++4K233uKVV17h6quv5o477rhgUaqsrNTCsxpDeHg4ISEhWqx2//79iYqKora2FrPZ3GjFPFBOgo2FMi5atIi8vDw+/fRT4uPjL/A5qKmpqdeWlZXFzJkzmTNnjpZVsrS0lJtvvhkPDw+Cg4O1ctPqKU0tMmQNKeVlLzQ0l1LYZDJpIXiqAy0o9u66ujqEEAwePJi6ujoqKiqYO3cumzZtajEfg3WOgxEjRvDFF1/whz/8gQkTJjBz5swm1fglJSWcO3dO+9vX15exY8cyZswYfvjhB7Kzs1m7di0ff/wx7u7uVFZW1uuLk5MTBoMBDw8PRo4cqWnAHBwcGi1AtmfPHt59913eeecdUlJSLuDL2tpa7fmZTCYWLFjAsmXLeOSRRxg7diynT5+mvLyc+Ph4LSrJYDAwfPhwnJycNL+iM2fOEB4ers3Vi6lIU3p6epvKwdtxeeOyFxCaq+bY3HesUVdXp3kvOzg4aB9XV1fKysrIzMzUQvPi4+MpLCzkqaeeIjg4mFmzZmm/07dv30ZV6kuXLmXy5Mk89dRTPPvss5p2QUVMTEyzyYsOHTrU5LWCgoIm/Ryqqqrq2Xf37t3L7NmziY6OZvny5U36LKg57EFx+po5cyapqanMmDGDM2fOaAl94uPjSUxM5MiRIwQGBlJUVKQt4tXV1Zw6dYqwsDB7tjkrNMWrDTN6Go1GLbJGSqlVI1U1Cv379+cf//gH3377LWPHjm02aVFDgTQoKIht27Zx3333sXDhQt577z3S0tIu+J7BYGjyhO3n56eZB9LT00lPT9fyDTg5OZGamtqkr05j/HDgwAH++te/MmfOHKZNm9bo96SUODk5sWbNGh588EEcHBx48cUXue+++zCbzVrlzPXr1zNy5Ejc3d3R6XSaMF1dXU1OTo4WNqzmsLiYBAQ77GgLLu/jWAehZsRT87Hv3r273gkoKiqK1NRUhg0bRp8+fRg4cCBnzpzh6NGjDB48mMcff5w5c+aQm5vbIq3+/fuzZs0a/vCHP/DAAw8wdepUVq9e3WXV47788ksmTZrETTfdxPLly1sM18zIyGDOnDlERUWRlZXF7Nmz8fLyolevXqSkpODn54e/vz/BwcH069ePgQMHEhAQoFVzPH/+PL/++ivbt29vMkufHb9BzdFhHZWjhtRVVFRo6YO///57KioqiI6O5tFHH2XevHmtTgFuDQ8PD1asWMG0adOYMmUKf/vb39p9Mo2IiGDkyJEMGDCA6OhoLZNma5GVlcVdd93F5MmTmTlzZpP35eTkcOeddzJ+/HimTp3K7bffjpeXF8ePH8dsNhMWFsaqVatYuXIl//znPyktLUWn0+Hp6UlhYSF6vV6rwWJPcmTH5QC7gNABWKdhBSgqKqqXPlWt16BmZausrCQrK4vS0lJ8fX257bbbWLNmDbGxscyePZvMzMxm6Tk6OvLoo49qefUfeOABUlJSePPNN5vNPNdRrF+/nkcffZSXXnqJRYsWNarlULF7927uvvtuevfuzcaNG7niiisYNWoUhw4dIiMjg9OnT/Prr79SVVVFTk4OJpOJuro6Vq9ejdls1oo1hYeH4+LiQmZmJkuXLqWoqEijIaXUyj/X1dWRk5PTrk3uUoIQAkdHR06fPk1xcTGbN2/m/PnzVFVV4ezsTGFhIdu3b+f06dMYjUYSEhK02iHLly9vF02dTscf//hHli1bxksvvcTjjz/e6tBYW6G0tJS77rqLxMREXnrppUZP81JK3n//ffr37096ejqrV69m3rx5Ws4Q1WRRVFREQEAAfn5+BAQEkJGRQW1tLUePHtUqt17qZcYvFURERFxQClv9tMY3xQ4FdgGhHTCbzZSXlxMaGkpMTAxRUVEMHDiQPn361DtZWG9eqrOVwWBgyJAh3HbbbcyYMYMPP/yQp59+mn379jFo0CDefffdFk9iMTExLFmyhAMHDjBv3jz279/PuHHj+Pjjj21qX6yrq+PNN9/k3nvvZe7cudxxxx1N3msymZg9ezYjR47EbDYza9YspkyZwtVXX42Pjw/l5eX89NNPbNu2jZ9++ony8nJ8fHyora1lw4YNrF+/np07d2qFhpycnBg2bBj5+fns37+f7777DlAW+9zcXM6fP4/JZCI/P5+zZ8+2qVrmpYrMzExOnDjBhg0bOHz4MMePH6e2tlbL9hkbG8uAAQMYNmwYn3zyCatXr8bd3Z3HHnusQxqAm266iW+++YZt27bxwAMPdEktDJPJxBdffMGtt96Kg4MDy5Yta1JwfeONN3j66ae59957eeWVVwgNDUWv15OYmEhoaCjOzs6UlZXh6+vLNddcw/z58xk1ahSenp4UFBQghKC2thZPT09t7vf0eh+XO06fPn1BKWz105mHqUsNl70PQnugOoB5eHjUy6XfMK++unmBEn4YGBiIt7c3wcHB1NbW4uHhgclkYvTo0SQnJ7Ny5Urmzp3LypUrWbp0aYvV91xdXZk6dSrDhw9ny5YtzJs3jx9//JGXXnqpWZ+E1uDcuXMsXLiQs2fP8t5773Hdddc1ee/Ro0e55ZZbMJvN/PWvf2X48OEcPHiQsLAwfH19KS0tJTc3Vyth7e7uTkhICA4ODoSGhjJu3DgOHDjAiBEjyMvLIzQ0FCcnJ5ycnJg2bRrfffcdY8aMAZSNoba2Fr1er9mMgcs2J4KUUkvpq6ba9vX15ciRI/j7+1NXV6dl+Ozduzeurq7k5+eTnJxMRUUFTk5OZGZm8tRTT/Htt9/yzjvvtOtZxsXF8dlnn3HjjTeyaNEiFixYYOORKs64GzduZNWqVaxduxaj0ciECRN4+umnm/R1+Pnnn5k3bx7PPvssnp6eHD58GCcnJ3JycqisrMRgMBAQEKBVxVSFDDUKRBUegoKCNGHL2tfDDjsuZdgFhHbAugxxc/Dz89PKx0opcXd3p66uDr1ez5kzZ7TUyw4ODnh7ezNmzBhSUlL48ssvGTRoEG+88Qa33XZbq/p04403Eh8fz+zZs7n55ptZvHhxm8IiVUgpWbNmDUuWLCEpKYkNGzZoMd9N3f/II48QExPD9ddfT1RUFK6urhQWFuLn50dQUBDFxcUEBQXh4eFBWFiYVuimtLQUKSVGo5Hk5GQKCws5e/YsUkpN2PL29ub222/XaDWsSXC550RoWMRJfW5JSUmcP38evV6PTqfj/Pnz1NTUoNPpyMnJITw8HD8/P/r06cPZs2eJj4/ngw8+YNCgQbz99tuMGTOmzdUWIyIi+Oijj5g0aRK9evVi0KBBHR5fXV0dmzZtYuXKlaxZswadTse4ceP44IMPSEtLa9bcZTKZmDZtGnfeeSc33ngj27Ztw8nJSStOVVJSgpeXF66urhf4uVgnQbPOy6FG0bQ09+2w41KAXUBoB6wXj+bg4OCgCQOFhYVatICrq2u9egkGg0E7DQcGBvLkk0+yZ88eZsyYwfr163nttdda1a/IyEhWrFjB22+/zf3338+4ceN45plnWj2ukpIS/vd//5etW7dqoV/NCQcAK1euZMeOHbz//vv4+vpyxRVXsHnzZnbs2EF2djY1NTWcOnUKvV5fb8zqRl9aWsr+/fupqKggKSmJyMhIQkNDqa2tJS8vDxcXF/R6PYcOHSIpKQmj0XjZnNxMJhP79+8nOTm5yWQ8TaXubSjE5ubmkpmZyebNm5FS4uHhoQkWMTExpKamEh0dzebNm5k8eTIuLi4MHz6cESNGMHz4cAYNGtSqaJKBAwfy9ttvM2PGDJ5//nmuvfbado29rKyMTz75hPfff5/CwkKuv/563njjDa688spWZSI0m808/vjj1NbW8sgjj2jJwkpLSzXBx9HRkeDgYIqKirSqqY0Jmw2F0MuF/+yw46IVEIQQQnZTQG9LYU3W3fL19SU3N5eqqiry8/MJCAhACIGnpyeVlZUcPXoUT09Ptm3bhru7O4GBgSQnJ3PVVVcRFxfH888/T1paGn//+99JSUlplF6vXr3qnaRefvll7rjjDmbPns2NN97I3Llzue222xrtt8lkIisri48//pjPPvuMiIgINm/eTJ8+faiqqmrSVGE2m6mrq2POnDk88cQT9O/fH71ej7OzM7GxsYSFhREbG6uF1dXW1pKTk6MVsjEajVp8fq9evdi+fTt+fn74+PgghCAnJ4eTJ0/i5uZGYWEhR44cQUrJ0KFDW/OKLmqo/LN//35++ukngHoVN63foxBC2zCt+a6hEOvn58fevXs5f/487u7uREZGsmfPHu0eNzc3jh07ho+PD++++y65ubmkp6fzzTffsHDhQvR6PUOHDmXkyJHcdtttWvhrQEDABbkp7rzzTgoLC5k3bx5DhgxptFiSv79/vVTQKrKysli+fDnLly/H09OTBx98kGnTptXjw+ayMKolpqdPn87GjRsZOnQo69evJyIiQsvU6evry/Hjx3Fzc6O4uFjrR2P9UZ+xPZTRjssRF6WAIISIAQYLIdZJKQu6uz/NQa/XExcXR0FBQb0FyGw2c+DAAS0KIj09nYSEBK699lpKSkr4+uuvKSsr4+WXX2blypWMHDmSP/3pT8yaNatVi1VCQgLfffcdH374IQsXLuSzzz7jlVde0aoI5uTk8Pnnn/PJJ59w4sQJrr32Wv7yl79w0003tdpDe+nSpZSWlnLttdei0+nIyMhAr9fj7u7O6NGj0el0lJaW4uPjQ0BAANnZ2QQEBNRz8DKZTBw7doxTp06xadMmJk6ciBACPz8/LTY9NjYWFxeXLqsQ2FOgjrcj41Zt6a6urowaNYpjx47Ru3dvKisriYiIoKysTNski4uLOXjwIMHBwYwfP54BAwYAivPjr7/+qjmTLly4kLS0NO5AkTkZAAAgAElEQVS55x5+97vfNZrV8NFHH+XgwYPcfffdrFy5sslS5Cr27dvH0qVL+eKLL0hKSuKNN95g/PjxzZoQGkNeXh633XYbBQUFrFy5kl27dlFQUMCBAwe0EuJ5eXla5FF1dTWlpaUYDAbtOV3uybjssEPFRScgCCGSge+Bj4AfgILu1Ca0Bnq9XlNRWpeKVtX3AQEB/PTTT6SlpVFVVcWXX37Jtm3bMBgM+Pj48MgjjzBo0CCee+45NmzYwLJly1pVNtrBwYH77ruPq666igULFnD99dczbdo0Tp06xcaNG4mJiWHSpElMnz6doKCgNo2poKCAF198kYkTJ+Lo6EhtbS1HjhwhISEBb29vTVDYsmULpaWlpKenk5GRwc6dO5k+fXo9G+4111wDKEKNukg7ODholQqh/gn6coHRaGzXuMvLy9m5cydDhgwB0BxqXVxciIqKwsXFBW9vb2pqajQzmKenJ5MnT8bb25vY2Fh69+5NYWGhlhyof//+jBgxguLiYn788Ud2797N888/z+zZs5k8eTL33HMPQ4cOrSe8vvDCC5w9e5a77rqLL774ol59iLy8PDZt2sTWrVvZunUrp06d4qabbuLrr78mMTGxyVTKzeHo0aNMmDCBkJAQli1bRmJiIr/++it79+7VtCaZmZkMGzaMvLw83N3dyczM1OopGI1GgoOD7SYEO+yw4KISEIQQ4cCXwN+klE9bXdIBdZZ7erSwoMJoNOLv76/Z5f38/HB2diYvLw9HR0fc3Ny0hToiIgI/Pz9qamr417/+RUpKCq+88gq33357q7QJQUFBvPPOO6xbt44333yT5ORkvvrqK5KSkqisrGzRz6AhTp06xR/+8AciIyN57LHH8PPzY82aNezfv5/CwkIee+wxLS3tqFGjOH78OMHBwSxbtoyzZ8/y448/MmnSJOA3e+7EiRO12gF2dAw7d+5kx44dgPL8QVHLq7yimn0iIyM1T301IdAtt9xCeXk569ev15JZCSHYu3cvI0aMwNPTk7FjxxIeHk5ycjK//vorP//8M6NHj2bIkCEsW7ZMMz84ODjw1ltvMXnyZG655RYmTpzIqVOn2LlzJydPniQwMJArr7yShx9+mNGjR2taBvV031pIKfnoo4948sknue6667juuuvIyMjAaDQSHR1NdXU1iYmJODg4UF1dTV5eHomJidTW1mrpnHU6HTqdzs5/dthhBXER7KUahBA3Aw9LKa8TQjgCLwDJQDGwTUq5zHJfi0KCECIEyGrs2vz58zsUptUcaSmltlA3LKhjNpupqqri8OHDmM1mAgIC8Pf3JysriyNHjvDzzz/j7u7O/v37+eSTT7jppptYunQpZrO5WVVsY3nrVVhrMhqioQ9CXV0d77zzDgsWLGDUqFEsXryYhIQEKisrycjI4N///jcGg4GRI0c2mnq3pKREKxDUsNpgY8+nMfQUW/DZs2fVMNRQKeXZhtc7wl8tzcmmnoH6PWsNgiqANfdczWZzvWtbtmxh586dREREEBsbS2ZmJkePHiU1NZUrr7wSgOLiYlavXk1RUZFWzOjdd9/l66+/5s033+Tuu+/m3LlzODg4cP78eV5++WU2b97MsGHDGDJkCImJiQwePLjRPlVUVDSrQbD2QTh9+jQPPfQQO3bsYP78+YwZM0ZLqtWnTx+qq6u1OiU+Pj7k5OQQGxur/YY6Bw0GQ7NRG13Nd83xl8pbWVlZhISEtOl3hRCXfS2Gy/0ZtLR2WeOi0iAAKfyW3GkNUAP8CvgArwghIqSUc9qiQWjPJGsNrDf/iooKdu3aRd++fdm/fz/Dhw/H3d2d8vJycnNzCQgI0DZiNRwtIiKCoKAgjh8/zpYtW/D09CQiIoKoqChuvPFGZs2axf3338/w4cN57733tEJRnQEpJT/99BPPPPMMx44dY/LkyTzyyCMkJiZqp66wsDBmzJjB9u3btXjxhqcxDw8PJkyY0GM2+a5AZ/FXc3B1deXqq69u9/eTk5M1Z8a1a9dyxRVXkJSUREpKipYoSC1qdObMGby8vAgJCeH5558nNjaWRx55hE2bNjF37lzc3d3x8vLi1VdfrUejvLy8Q3xQXl7Oa6+9xpIlSxg5ciRbt24lPDyc8vJy3N3dcXJywsfHh/z8fPLy8qitrSUwMLBeQbWKigrMZrMmQJjNZrZt20ZaWho6nY5du3aRmpqqzWEXFxe7f4IdlxUuNgFhBzBBCPEoUAvcK6XMFEJ4ANOAJ4UQ30kpN3drL6FeQpVdu3axY8cOtm/fTmlpKWazmbFjx17wndraWsrKynB2dtY2VzWRi7+/P+7u7tTW1uLv74+/vz+LFy/ms88+Y8yYMbz22mutzpnQGtTU1LBlyxbWr1/PypUrOXfuHJMmTWLmzJn07dtXyzLn6+uLlJKCggKys7M5ePCglvZ3+PDhNuuPHZ0Ds9nM+fPnKSoqIiwsDLPZzP79+wkKCiI3N5fq6mqqq6uJi4sjIyNDE2jVDdjLywtQoiACAgKYPXs2AwYMYP78+YwfP57/9//+n1YC3Raoq6vjgw8+YMGCBbi6uvLEE08QEhLC+fPn8fHxwcXFBUdHR00r5+PjoyUmq6qq4scffyQ6OhqDwUBZWRlubm54eHhgMBhYtWoVq1evprq6Gg8PD3788UcAUlNTtbncmhBLO+y4VHCxCQh5gASmAEVSykwAKWWJEOJr4Bmg06uotEZBYR2HnpqaCkBoaCg//fQTKSkpWtKfoKAgDAYDUkqKioooKyvDy8sLNzc3pJQEBQXh5OSEq6urVghKr9ezcuVKsrOzmTZtGuHh4Tz22GNs376dl1566YIwsObqFFiXwC0rK2PDhg188803rF69mqqqKq677jqeeOIJAgMDCQsLo6ioCKPRiF6vJycnBwcHBy0rXV5eHkIInJ2dkVJqGQ9B8RY/e/Ys/v7+5ObmEh4e3mS0RHPP93LSPrQVTT03tVCTdYlitf2XX37R6hDodDpMJhO5ubl4eXnh5OTEyJEjGThwINnZ2Wzbto2ioiKuuOIKBg4cqGXI9PLyoqKigqqqKg4dOkRKSgpr167l0Ucf5cYbb+Tll1/m1ltvrdcnNcNjY6irq2uUZ9evX88LL7xAdnY2w4YNY/78+YSHh3PmzBl69+4NgLOzs1boSUqJg4OD5mvxyy+/sHv3bvLy8oiIiCAsLEzTCkgptRwckZGRWrSPqkGAC3NN2GHHpY4eKyAIIaKAawA34IiUcrWUco8Q4l1gKVAkhBgipdxp+UoGcAKo7J4e/wY1w5962nBzc+Pqq6/GbDYTEhKC0WiksrJSS4Kj2j7VFLd+fn4IITQ1fWBgYD0b8oEDB6iursbLy4uhQ4cyatQobr75Zn7/+98zYcIEVqxYQVRUlNafpuz9oCTQ+c9//sMXX3zBunXrcHNzY9y4cUyZMoVbbrmFfv36kZmZya5du7RKdrGxsRQVFVFeXk5mZiZlZWUYjUYiIiJwcnLizJkzmM1mCgsLteiNrKwsTpw4QXp6upa1Tl2E7aiP9gpBTX0vIyOD48ePA/XTgWdkZJCVlUVAQAB9+vQhNDRUKw+dnp7ODz/8QFxcHEOHDkWv12vaq7i4OBwcHHBxcdE0CY6OjuzevZs9e/ZQXV1NWloay5cv5/XXX+e5555j//79/OlPf9LyXNTV1TWprvf09Kx37cCBAzzzzDNs3LiRhx9+mLq6OsrKyjh//jyDBw+ul8RINR2omTZVuLm5kZCQoAmtp06d4vjx44wZMwaj0YgQgri4ONzc3AgPD8fJyamemcauObDjckSPFBCEEInAJmAfEA+cF0LkADdKKZdZJv6bwAIhxN8s980AegO7uqfXLcM6ec3+/fvZs2cPoITwVVVVcfToUfr06YMQQrObwoWZ21SVbZ8+fXB2dqaqqgpfX18+++wzFixYQGJiIv369SM+Pp64uDj69etHXFwcMTExODo6kp6ezldffcWXX37J1q1bCQsLY+LEiTzxxBMkJSWxdetW4uLiNAFArX4WHByMv78/x48fJzIykujoaMxmM1lZWdTU1JCfn6+dxsrLy+vlfQgLC6O6upqamhocHR2bLJdbV1dHfn4+fn5+bU71a0fjUJ91w2ceHBxMXl4ecXFx2im5trYWX19fysvLqaqqory8nFOnTpGZmYmHhweJiYm4uLhQUlKCm5sbUVFR6HQ6jh07hr+/P3369CEwMJATJ04QFRWFv78/w4cPZ/v27VpSJW9vb7y9vfHy8sLHxwdvb2+cnZ0pKSmhuLiY4uJiSkpKtL+rqqqYMmUKf//73xk6dCgHDx6krKxMCwE1mUwcOnSIfv36kZ+fr2lJGs4bg8HA0KFDqa6uJiMjg4yMDA4cOKCFgzo5OdmFVjvssEKPExCEEC7AO8AnUsoHhBDeQBrwJ+AnIcTVFiHBBNwJ/BM4BhiAcVLKM93V97agYRKco0ePcvjwYUA55aknncbCrpydnUlKSgLQNuiioiI8PT156623mDNnDvv378fX15dNmzbxzjvvcO7cORwdHQkJCSE9PZ34+HiioqJ48803GTZsGLGxsTg7O3P06FH8/PwoLS2lsLBQMwNER0dz7tw50tPTycnJ0arbVVZWaurl6upqBg0aRFlZGQkJCfXU2WrxpYyMDC2jXWOwLnB1OddYsCUcHR2Jioq6QMNQUlKCk5MTJSUlGp8VFBRw6tQp8vPzSUhI0MJwKysr8fLy0jZz1TlVCMGhQ4fYtWsXRqMRX19fNm7cSK9evQgKCmL8+PFIKenVqxe5ublaWOGZM2fIyMggJyeHiooKzp07R2VlJS4uLtx0002UlJSg1+upqKjAZDJxxRVXoNfrKSkpYfDgwdTW1mrjOXToEPv27aOwsJCAgAA8PT2bNQc4OTkxZswYDhw4oM0jOy4fqKWgm7p2+vTpru1QD0aPExAAZ8ADWAcgpSwSQnyDYj74F0r0QrKU8iNLuz9KZEOelDKvqzvb3hNvwyQ41loBdVNWHa2aQ0VFBY6Ojnh7e+Pp6UlRURELFixg27ZtDB06lF9//ZU9e/Zw4403sm7dOtLT0wkPD6esrIyamhr69etHZGQkjo6OHD16FJPJpJW1VW3aBoMBV1dXrQKlp6cnBoOBkydPEhYWxoABA9Dr9RQVFREcHIyLiwvZ2dlUVFQQGRmpCQNqnHtT2gOob2axo3OhPmNrTY+Hhwc6nY5BgwZRWVmpvauamhqqqqrIysrSaoao6bNdXFwYOHAgPj4+HD16VNMSmc1mPD09mT59OnV1dWRkZKDT6XBycmL48OFIKbVIgqysLFauXImPjw99+/bl4MGDnDx5UsvjMHz4cEwmE4GBgRw4cID4+HhNCEhISACgX79+mEwmzUTXHIxGo6Y5qK2tpaCgAD8/vzZnbuyJiIyMbLKkcURERBf3puehOQHA7uNUHz1xNpQADij+B/8BkFKagSNCiPuBFUKIt6WUD1rSLHdrqmVbnXidnZ1JTEysl8xG9UGQUpKfn6+Vo1UXNB8fH6qrq6mqqiIsLIyqqipAife+/fbbOXXqFOvXr+f06dNa+mOA3r17s3btWn755Rc8PDwwGo3s378fKSWurq5ER0eTn5+PlJKqqir27NnDwIED0ev15OXlERwcjJeXF87OzpqHuMFgwNfXFxcXF/Ly8ti3bx8VFRXo9XrN7u3k5ER0dHSzk/Byr87YlVCftbVz47lz5ygrK6Oqqqqeuj0+Pp7S0lJMJpMmUBQUFHDs2DHMZjMJCQkEBgZqJ3h3d3dN3a/WH1FNF2VlZZSWlmoZRk+cOMGWLVswGo0EBASQlpbG0aNHqaiooKysjIkTJ2qVFLdu3cru3buRUpKQkKDxXGpqKrW1tZhMpgvGqQrxavZI1SynCuAFBQWcO3cOoM0ZRXsi0tPTL+s4fztshx4lIFgSHNUJIT4BbhRCjJdSrrS6ZS/wb2CUEMJVStl0BqAuQmedeMvLy8nJySEwMBCTyaQtYL6+vhw5ckSzD5eWlmqqWVdXV/z9/bWTVVhYGJMmTWL79u2MGzcOV1dXfHx8NGdJddE+e/YsRUVFeHt706dPHwoLCyksLMTDw0NTNxcWFmqnD19fXxwcHIiKitIWe/jNkcvHx4eUlBQqKipazMFvR8+C+r4avjc106K1w6uvr68WPaAKDS4uLiQkJJCbm0thYaF2vaKigvLyclxdXXF1dSU/P5/i4mIKCwv54YcfyM/Pp1evXkycOBGj0ci9997Lxo0bSU1NrVdmecCAAZrJQp0TgYGBmM1mTp06RXp6OnFxcWoiGOA3Ib68vFwzpZSXlxMYGIi7u7vWd7vWyg476qNHCQhWCY4+AsYADwshKqSUqrlBCiEOArcDLkC3Cwi2PPE2JfVbq4ILCgqorq7G2dmZ8PBwTCaTtvCpSWLUTGF6vZ4rrriC5ORkzW5sNpv55ZdfOHnyJKGhofj7+2umkeDgYCoqKti7dy+xsbEEBwfj6elJVlYWoaGhODg44OfnR1lZmabKtQ7nVPvv4OBQb4ORUmrqZKPRaHc+7GFQ35uUkpqaGiIjI1uVbc5sNlNdXU1oaChCCEpKSqipqaGwsJDi4mLOnTtHRkYGvXv31kJvDQYDZrMZs9msVe90cnIiMzOTtLQ0DAYDJpMJNzc3xo8ff0EfXVxcGDlyJHV1dbi4uGh5OEwmk6b5aAh1/qgahNra2nrZRVVNhl29bIcd9dGjBATQtAgnhRB/AD4GnhJCREop3xNCOANDgLNA2xK227aPnfJda38DNzc3rYiMEEJbwKw1Fnq9HicnJzw9PZFS4uTkdEF4lxoL7ujoiE6n07QORUVFWnSCwWDQwiI3btzI1q1bqaqqoqysDCcnJ7y9vamrq0MIQWVlJadPn6a8vBydTkdgYKCmOaipqdHi7RvmODCZTK1KNmNfpNuP9qaoVvnO+h01VrCorq6O3NxcXFxctEJHJ0+eREpJYGAgubm5nDlzhrKyMm2jz8vLIyYmBr1er733w4cPs3XrVgYOHEhoaCgxMTH4+/uj1+uprq6mvLwcBweHZosmWRdAU/sbHR1NUFCQZtKwvlc1HTg7O2upyRvOFTvssDsw1ke35Q0VQugt9RSs23QWLYFOSnkAJSFSOTBHCJEFrAXuAR6VUpZ1dZ87Up+hrRBCYDAYyM3NZf78+Vq7utg1dKYSQuDq6qrFmOfk5FBXV6ct+moBHKPRSFJSEtdff70mIBw8eFA7eaWlpTFixAi++uortmzZwr59+6ipqamnKYiMjCQqKgofHx/Ky8u1hDcZGRmcOHGCjIyMC8bj4uKiVRRsCl35fLuTZk/pQ0O6Lb2j/Px8jh8/zuHDhykvLyc8PJzo6GjCw8O1fB39+/cnPj6etLQ04uPjcXJyoqCgvpvQ66+/Tl5eHrm5uVopZjVix2g0an2w5uOWIITQhOqWxqvT6Vq815boCTzWGOz9uhCnT5/WNJ4NP005fnY3OvN5dUuxJiFEPDAfCAGOA2uklMst1xwsfgg6KaVZCOEHRKKYHLKALVLK4zboQ5sLnnR2kY+Gv52Tk8PZs2cZNGjQBQV1WvO9kJAQAgICMJlMF0RElJeXU1JSQkZGBqdOnSIhIaFePQedTsfq1asJDQ2lb9++F5gFVLWuWkrY1dWViooKLflTc1XxmhpHdxRRaS/N1hZrag1/dVfxGJVuS7RVJz8vLy8yMjKora0lNDQUd3f3ZotAqeYG1blWhU6nY+3atcTGxnLu3Dn27t3LwIEDLyhtbc3HrTHjWd/fmLNhdz/ntqAjxZpaS6+nFi2y96ttaGu/enSxJiFEH+AH4GtgPXAdMEAIcZ2U8l6LcOAspawCkFLmA/nA7q7ua3ejvU5Tfn5+mM1mze5rHREBaKd+Nzc3kpKScHFx0ZzJrDF8+PBmQy11Oh1nzpzRcjk0Fldvx8UP60id6OjoRgtxWSf6UlMdW5sB1AyH6rUhQ4ZgNBo1U0Rjxcba6gBsD5G1o7PRnEnqUjRBdKmAIJSnOw1YJ6W809L2KkoWxBlCiBVSyimqcCCEmG65N7Mr+9lT0F4HSAcHBzw8PLRkM4BmWzabzZw8eRKj0UhoaCgGg6HJSpAt2WiPHz/OqVOncHFxISkpSfMGt46rVzUNdnvvxYHG3pf1xmudDdQaR48e5dChQwCNJh9Si5epwqZOp6Oqqori4mJ8fX0brcvQVv5X779c+Mw6UsMa9lwHnYfLrU5MlwoIFv+CUCDYqs1kqa9QATwohPgfKeVzQogxKOmU/yuEuFdK2bIh0g4Nqh3ZxcVFY2o10sFoNOLu7t7hU751cie40HEMWnZ8s6NnobH31ZqNuiEvNITKa6oGwWAwIITQypzb0XZ0RylxO5rGpejg2GUCgiU6QQJ7gHghRKKU8iBoQsK/gb7ANUIITynld0KIPwPLO0k40AFkZ2e36UuqqtVWUFWvatra5ui21gfBGsXFxfX+bzab0el01NXVkZ2d3awNuSWaah6Fhk5oDe9Ts+WpfWlpnF2N9tC04pumPN3axF/dMW6VrjX/NPa+moM1/zTkheZ4Kzs7GyGExo/FxcVaPo2OojGaqoYiMzOzy5wTrdHW99sCf7Vr7WoM3cV3LeFi7NcPP/zQ5LUhQ4bYXMMQGhrKzp07m+zXkCFDyMrKau4nWpwIXe6kKISIAXYA3wCPSSnPW10LRnFEnCyl/E8n92MAirBihx0dwUAp5d6GjXb+ssNGuIC/7Lxlh43Q6NpljS53UpRSnhBC3AZ8C1QIIRZIKVVRuAalMmNXpE8+CAwE8oDGC9PbYUfT0KHUATnYxHU7f9nRETTHX3besqMjaGnt0tAtYY4AQojxwKfAauAzFMHgTuBuIFVKeWEwvR122GGHHXbY0SXoNgEBQAgxEFgCxKBoD2qA21tSe9hhhx122GGHHZ2LbhUQAIQQHoAP4AZkW/Ie2GGHHXbYYYcd3YhuFxDssMMOO+yww46eh26rxWCHHXbYYYcddvRc2AUEO+xoBUQXp0nranrdDSHEZVcDvCe+457YJxU9uW+XKuwCgh12NAEhhJP6f9lFtjghhJsQwh3FL+eygBCiN/CAEKJLcwQLIXQNBZOu2ISEEEFCiEC1cm1n02stLDlqbhNC+LZ4cxeip86J7uKfrkSPYU47bAMhhEs3nHajhRCju5imTgjRaXk8hBAJwGdCiO+FEJuFEDcJIfw7i54VzU9REon9WwgxtTPpNaAdK4SYL4T4RAjxoGXT7gq6ycBOlEgmB0tbV2zSccDbwGohxItCiAmgpYPvNPoWIehX4D0hRC9LxdpuX4et3sMwwMXS1u2bXXfOiebQXfzTin7ZdB53O2NeihBChAshpgkhHhZC3NCFdONQJtKELqSZBGwGpgshLqyx2zk0+6JMzlVCiMVCCDcb/35vlIqj+Sh5OgqBd4B5nbVxCqUE+lbgCMrYzgO3CCGcO3vBEUIkAltQku+4AQuBx4QQ+k7eLENQFv93pZSPSylPWi51atEOIUQ/lPfrDqQDo4D/E0Isgk5f5GMACQjgVSshoTs3lXDgS+BvUsrZVjlodFb3dHn/unNOtNCv7uSf5vpl+3ms1oO3f2zzAZKA0yiMfRQoBmZ2Ee3XUTKrZQMTGrkubEwv2kLr1aZ+uxNoJqJkkPsEZdEwAfNtTGMxsKpB25Mo6W3fA6JsTM8F+Bx43aptCvAF4Av4duLzDAMOA3+yapuAUjwtwZa0GqF9lWWe6AFHC/+uB74HXuiMMaNszK9Z+EeN4upleb8VwKudPOY4Cx89h7LJrAACLNeMnUm7mT7dDKy1/N8ReBFFYPiH9dpla95roU/dNid6Mv80069Omcddnmr5UoYQIhr4GlgOLEBJZ3k/cKcQ4j9AgbS8uU7CLpTEU7Uo6rg7pJSfqxc7gfZVwCYp5dMWKfUJIArlxP2NlHKblIo0bQvaQghv4APgPSnlc5a2fBRJ3pZwBjyEEM5ArZSyTkr5v0KISmAmip12CVBno2daA4QDP1m1JQMpKJvJWSHEd1LKhbZ8hxbV9ljgF+BNyylDAGuB44CfrWg1gb6AXkpZK4RYi8K3m1A0CM8IISKklPfZcswWfozF6t1JKc8IpaJsFbBQCHFOSvkXW9FUYbFXlwElwF+BXGA6iiYhCNgrhJgnu75ybQq/aQvWoPDjryg2/1cs72FOJ69dDdEtc6IldCf/NIXOnMd2AcFGEEI4oggDPwELpZSVQIYQYgfwEODUBYxcBIxGsSMGAx8JIW4CbgKOSyn/n43pJaOcOAA2oPDTGeAG4GohxN+klH+z4bg9UDbvr63aQoE4IcQPwAHgAynljg7SyQN6A95SymwhhLOUskpK+ZYQIgzltPCBlDK3g3TUyW1EUVUOFULMBCKBR4EHgVIgFnhUCLHfWuDrKKSi2j4J7JVSZqrNQogqlOccZitaTWA38JwQ4mkUtfssKWU6gBBiC4qQ+52U8lNbELMSVDcDk4UQ/aSUvwBIKYuFECtQBNzfCSGWy99qxNgElo0/wyJoJkgp/yaEqEbRwHkDb0sp64QQOillV9ZY2AFMEEI8iiKk3SulzBRKErtpwJOW97C5KzrTnXOilegW/mkKnTmP7T4ItoMZxaSwSUpZYdW+C0XN49UFffgVqAbMUsrpwPvAOuAPKLYpWyMDqBZCjEEZ4wQp5VRgMHAWRXNiy9O9RFHRjhZCRAkhngd+j3LqXIEimCwQQnTIhi2l/BNKwbBPLX9XCSEMlstzUd71mI7QsKJlllKWoGhGTMC1KCrfh6SUf5dS/hf4F1COsijaBJbTLFLK9VLKFy1tqp1SorxPs9X904UQ19qArvWakw38DEwCPFThwIKtKKef0I7SVGElqO4FAoC7hJXjqUXg+y8wFGWhtymsbMEOQIKl+RqUzfAIcKsQIrKLhQNQBGKJosKvUjcZC19+belveIVsFWkAABAqSURBVFd1prvmRHNowLe76Qb+aaJfnTqP7RoEG8Ei+X8rpcyBeqcV9QWpJ22EECNtKY2rJw6pVMp0QPENOIpyKqkEnIAIlEXIlvge+BOK49VxLFU4pZSFQog/AqeA4SiOfh2GRZX3KPAWipZkFHCntJQGF0J8gyIkjUIpJ94ihOLweA/KCWUjsF9K+QOKKWGFEGIDcK1FIwTKM81DcWBsF4QQUSgbgxvwi5TyOynl10KIzSgnuB9Q3puKXOAcymLZIQglhM0kpawQQjhYq7Mt6lMdysJShuIUhhDiZZTT20Ab0VX5NUsI8Q9gGeAjhLhJSrnK0pfzQogclPljPZ/aSjcU6A8EAruklAellOuFEK8Bf0ERcP9mdfI6jg3mSQO6O6WUh6SUtZZrq4A6i1r6OmAkkAo8geIIO0u919ZowHtHpJSrpZR7LH1ZChQJIYZIKXdavpIBnKA+P3Z2v7p0TrTQrwvmi5Ryo8XE+DqdxD/t6Zd6zabzWHaDQ8Wl8gFCUOzwdzRoV51XHFBOQDlAX0vbYhSBIagDdH1R7LdpVm3OFnqbgCuBN1FO8QNQ7J1mYGwHaOob/K2z/PsUyiT9HvCyuh4M/IhSc7y9NINRFs4x1vQtzzTW8vvBljZHFLPAAWB4K38/HsUssxLFKesUSqjXTMv161EcTg+inGCuBl5COflGtHNMiSiC1HqUBe4IimDiarnuimI7nIeiGjSgOI1l0kHnSBTty37gf63o6Rp71ygn+/HAC5b3O9jGdK3f5y2WZ78PRTAbAvzZ8nzaPWYUh+GTKNqzShStxF1W1x9H8Qf4m2WsERa6mSpf2ZDuHVbXZ1nmYxYwyKr9HiCyI++4nbznYrk+E0UD+Y3lncQAr1j62asb+tXpc6IdfOvY2fzTzn51yjzulAFcDh/LInAExWGmGthGA29aFEeRYJQNJdzC4KUdXGwTUTbGX1Akw28aXH/FQiMDq80ZRdrt1wGaa4DejVwLA15GcSp6E2XT9UNx0jwOhLSTZjLK5vwLihR8GLgPi/cyipYkD7je6jsvoGgQWpycKALFhyihXdY0/8/y7B61tEUB36H4VpyyTMx2CT0ontlbgaWWv72BccAhFCEkyNL+R5Tol18s92cAAzrIr70svJqBchp7sanFBUXQ3G6hX4HVJmZjutaL7XUoJrFSyzP+GUjpAN0YyztbjGLeCwW+BT5tcN+dKJuPyfIeTnfkWbeGLopT7XMqHzV8/p3xaYH3jljx3l0oGr8Ky3s42lHe66lzwkZ8a1P+6WC/bD6PO5UpL9UP0A9FxfwiygbSD0WSvKGRe10tE+0bFC/XjggHfS10X0ZR3V+DInG/YnXP71E2tHYvrg1oRqJs9GbLQhJtaRdW9/ii+DmUWBbHgygORu2aKCj2vV8s44yx/P1vlE3jVSDQct/7lufxJUr4U05rx40ivG0G3mlkvK9aFsapDZ59JODXgWfpbeGFW6zadPwW+vazVfsE4GkUp6yOag4E8ADKwj8EJdJlV2OLi+VelWeLgKROpmu92DoAQSiaOa8O0HVGOcn9yzIWB0v79Siq6SCsFlML/yaiaNsCOpFusNW9+vbS6STe29/gefRDEfb9u7lfnTInbMy3frbgHxv1y6bzuMsY9FL5WBh6NbCkQftqFOn7IaAPYLC0R6FsrpVA/w7QdQc+A95q0P4a8FXDPtporAaUTfo/wAgUlekJGhESrMY6BuU0GNoBuv1RJPH+DdpfRnEwewFlM4kBZqOYCF6llRoSywKkQ/Fl+JwGmz6KMPBfy/N2sSHvOKCcMt5u5NpA4BiWk1Qn8G0oMMlq/K9ZLS5uarvV/VOB+C6i62D9bmzIt/c18oyLsKjLG/JvV9FtyBOd8b7byXsXXOsh/eqUOdFCv1rDt10q5LWhXzabx106uEvhgyKZPQZcYdU2D0XFvhnF9php9RJdgfmt3byaoesF/BMlBMm6/XbLBHPGIpTYeLx3AVMs/w9BUe9pQoLVfTZTkwKDUPwnrrT8bbC69hfLopFqTbs9i71l8lSgSOUNfSzGA3VYfEdswTeWf+ejmIjGN8JXL1p4yK0L+NiJxk8g07uJ7jQb0/G3+r96qgpGMUEFWl275lKga0Pec+2h/er0OdFCX7uEb23Yr+k2+f3uHNyl8EFxUjxt2VBUCW4dsMX6JdqAjg6Itf7b8u9UrNRwlrag9myYrexHGBdqEhxR7PfONqKhRzFTrLJqc7b6/x5geRt/MwolT8VsYIxV+2IU0890rDLZoahYD2EjAcHqd6NR7IKrUaIjrK9NQTHndLZaV+Ud5waLyzIUQTfiUqFLfVOYmvkz3PL3iyiCaLv8ZHoi3Z7OexdTv6z60C3zpSf0q1se+MX2ATxRTs++NFAJotilYy3/11v+nYviQNIhwcCaboN2aw/wKcABq7//jOIU1a60rU2NtQHNcH4TEvqhhEdtBTxtQNPR0jYcxafh3YZ9QAmt/LoNv9+Yl/QmfvPe/jOKtmARSgyzD4rJ4oQtFyZ+OzEloURbrAbut7Spk7yrNAiqfVw9gVSiOIF1moNVd9K10ExAiZ0PBJ630G63A2ZPp9tTee9i6Fcj/ew2vu3OfnXbwC6Wj4Vx96OcJossm+GoFr7zPooU1277Ykt0rSbWzShxw6DYPyuwMn/YmKa1bSsMJRTJbFn8Um1Ic6Tl2j2W3/67ZQKoEvO/gI9R7JfNakpo3kv6EL95ST+FEilx3tKfs+2dZFhqCzRo0zX4Nx7Fz+EkShjZZpQU1R1yLm2OdiP3qn152/Ls252z/SKhG4GifXqfDm7S3UW3J/PepdavRu61Gd9eLP3qlMFdKh+UTTAHJUQwDSXJxHoU9fctjdzvgKLiyaEDPgdtoQvcihJiuRBFVd7eELxW0eQ3wUQPfIRyMm+XE0wzNA9hsUeiaEjyUTbt/6IIBmVAYitpNOclvZf6XtJ9UZIstdvJ0rLIrUDRsHwA3G7NHyp9y79+KFkn56EIQ7HtodkW2o18534UIa8joX0XBV0U52EzihB40dHtybx3qfarM/j2YupXpwzwUvmgJAvZSX0nuSssL+0UVk41KJvKJyiSb0dj1ttC9y4LYxTQsRNRW2jqUJKE1HVwoW2K5ocofh1jLG3+wBsomoSltEEgoQu9pC0bwXkUZ9IFKILbPuB9q3ts4qdhS9p0LBnRRUMXxTfnP3RMeO8Wuj2Z9y63fnWEby+2fnXpS7nYPsBkFHtOnwbt/S0vcCO/ZUiMB/4HGzi1tYPuj3QgXr2tNC3tkxre20k04xtca3W0BF3ovW35rZeAz6zaXFAiXg4CKxrcPx0IsxGftpX23bagfRHRnc5voY3t9gvqLro9mfcuk37ZhG8vxn516oAv9g+KqusoSgrShvag61CSAk2warNJTHNb6KLY5jvswNPWsXbDOIX1v22k0yVe0ijalm0N2lxQkkjtA/7H0jYGJWPg323IM91C+yKi+w8Us1iHonu6i25PfQ/2fl3a/erUwV4KH5Q6BucbbiyWaz/SIBPfxUz3UqRJF3hJW9F4xNLnxAbXPSx0dmKJ9EBJ9nRB6uqLhbadbte9Y3u/7P3qtn515o9fzB/qe+z/ByXv/3h+C43ToaQ0fvZip3sp0KQHeEmjZHbMQ5HqvRpcC0bxFbnAufVipm2n23Xv2N4ve7+6ul9dOvie/qGRYkuWfx2A5Sgn3XdRCq28Zfm7w45H3UH3UqJJD/KSRqn4WAm8g1XFTgvdPcBVnci/3ULbTrfr3rG9X/Z+dWW/unzwPe3TcNNqqs3S/jhKpMJ+4Cs6Vluhy+leijTpgV7SKJqQSpQiUnehmDf+hFU2vUuNtp1u171je7/s/eqqfqgnuMsSQoh+KKl3vVDi8ZcBx6SUNUIInZTSrP5r9R1nFPW3lFJWXix0L0WaQgg1CqGflPJWS5sLMMPyOSSlnGJ1/3RgnZQys61jaSuEEANRbIYxKGlPa1A0G3svVdp2ul33ju39sverS/pwuQoIls1rJ0rdhAIUr/kiFK/jZVJKkxDCQUpZZ7k/Ukp5+mKkeynTFEJ8gBImmWbV5oJSp/1B4Fsp5XNCiDHApyg+CPeqdDsTQggPlLTNbkC2lDK/s2n+//buJ8SqMozj+Pc3DUaL/ggtwo1FCEHdiSJnEQQhTRD9JSUIJAqLXNTChbURF1EUJEEkLaSgTZsKsoSi3bSKQAYsNzVEVNAikCxKU0efFs+5eJvrlKPn3rd73t9n4+Uc4fdcZnGee857nrd0tnPH9zf+N65rdVzXCvk1NgiSpoF95Gz/x5pja5pjPWA/sCcijjfnXiP3BngmIg5OUm5XMyUpIkLSs2QzsC0iDg+cv4Kcf3AHMBcRv0naTW7ytHgh38vMrCZTpQsoISKWyA2CpgCaX7InyffxvwQeIp8B9X0ObAB+mbTcrmbG2c72E3LOwU5JVw2c/x3YQy5IvKs59oKbAzOz81Ndg6A0RQ6ZWA8QEaclrYmIE+RCuSPk9Cqa8x+RE9F+nKTcGjIj4jvgEXLg0SuSrhk4fYpcsHjkQr6LmVnNqnzEACBpA3AI2BsRzzXHLo2IE5KuJ+f3z5FTrc70b2lPYm4NmZLuJ9cYfAZ8QDYGW8lxpBsj4qeL+T5mZrWZLl1ACc3K+UVJO4A3JJ2MiF3NL1zICXs/AEf7K+xbag7GnltLZkQckHQ7uer3Jc6u+r3HzYGZ2epV2SCQj1bOkL84LwNelrSO3DHwKPAoucdB2ytGS+TWkklELEh6kP/hamQzs0lT3SOG/qt1kq4F7iMvYhvJbYQvAY43/z4cEQuTnFtLppmZta+qBkHSdEQsNRevb8hX3h5vzl1JbjN8Gvg+In6e5NxaMs3MbDSqaRCWXbwWgA+Bp5tj/5jmN+m5tWSamdnoVNEgnOPi9TG55e9S13JryTQzs9HqfIOw7Jn4OJuDsefWkmlmZqPX+UFJzcVrPfne/X5yJO/IL14lctvKlHRQ0l5J30p6QtLbkhYl3TuqTKuHpFclzZauw7pJ0pOSbixdRxdUcQeBXEE/BWwf18WrRG4bmZKuBr4AbgFuAN4BZoFbgc0RsaPtTKuLpE+BLRHxZ+lazGxlnW8QACStJYfyjPXLlsi92ExJm4BNEbFL0t3AbES8KOkB4LqIeL3tTKuLpEPknhy3AW9FxJuFS7IOkTQfEXeWrqMLOv+IASAifi1x8SqR20LmDNDfb/zmZZ+/GlGmVaK5Q7UWeJ7cwfOpshVZl0i6nNwHxlpQRYNgq9Ij9zGAbAoGP5+zQTBbhRng3aap/As4Vrog65SbgMP/+b/svNQ6atlWEBHbBj5vHfi8pUxF1jEz5LAsJG0GDpQtxzqmB3xduoiucINgZuPUA45Jeg/4A9heuB7rlh6wr3QRXVHFIkUzM+s+SfPAXEScKl1LF3gNgpmZTTxJ7wPzbg7a4zsIZmZmNsR3EMzMzGyIGwQzMzMb4gbBzMzMhrhBMDMzsyFuEMzMzGyIGwQzMzMb4gbBzMzMhrhBMDMzsyF/A+nIUFRLZYDiAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 547.2x547.2 with 9 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"bf = bestfit(*args)\n",
"m,b,lnj = bf # slope, intercept, ln(jitter)\n",
"ndim, nwalkers = 3, 20\n",
"spread = [1e-5, 1e-3, 1e-4]\n",
"pos = [bf + spread*np.random.randn(ndim) for j in range(nwalkers)] # randomize starting values\n",
"sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=args)\n",
"sampler.run_mcmc(pos, 1000)\n",
"samples = sampler.chain[:, 100:, :].reshape((-1, ndim))\n",
"samples[:,-1] = np.exp(samples[:,-1])\n",
"fig = corner.corner(samples, labels=[\"$m$\", \"$b$\", \"$j$\"]) \n",
"m_16, m_50, m_84 = np.percentile(samples[:,0], [16,50,84])\n",
"m_errp = m_84 - m_50\n",
"m_errm = m_50 - m_16\n",
"print(\"slope = {0:.3f} +{1:.3f} -{2:.3f}\".format(m_50, m_errp, m_errm))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
# coding: utf-8
# ### fitting lines to data with 2-dimensional uncertainties
# In[1]:
import numpy as np
import matplotlib.pyplot as plt
import emcee
import corner
import scipy.optimize as op
# load up data and define some functions
# In[2]:
data = np.genfromtxt('Table_solartwins_Th_fulldata.txt', names=True, dtype=None, encoding=None)
# In[3]:
def vee(par):
# Hogg+2010 eqn 29
(m, b, lnjitter) = par
return 1./np.sqrt(1. + m**2) * np.asarray([-m, 1.])
def ortho_displacement(par, ys, xs):
# Hogg+2010 eqn 30
(m, b, lnjitter) = par
disp = np.zeros_like(ys)
for i, (y, x) in enumerate(zip(ys, xs)):
z0 = np.asarray([0.0, b])
zi = np.asarray([x, y])
disp[i] = np.dot( vee(par), zi - z0 )
return disp
def ortho_variance(par, dys, dxs):
# Hogg+2010 eqn 31
#(m, b, jitter) = par
var = np.zeros_like(dys)
for i, (dy, dx) in enumerate(zip(dys, dxs)):
cov = np.eye(2)
cov[0,0] = dx**2
cov[1,1] = dy**2 #+ jitter**2
var[i] = np.dot( np.dot(vee(par), cov), vee(par) )
return var
def twodlike(par, y, dy, x, dx):
# log(likelihood) considering errors in both x and y
# Hogg+2010 eqn 31 with jitter
(m, b, lnjitter) = par
delta = ortho_displacement(par, y, x)
sigmasq = ortho_variance(par, dy, dx) + np.exp(2.*lnjitter)
return -0.5 * np.sum(delta**2/sigmasq + np.log(sigmasq))
def lnprior(par):
(m, b, lnjitter) = par
if (-10. < m < 10.) and (-1. < b < 1.) and (-20. < lnjitter < 1.):
return -1.5 * np.log(1 + m*m) # from Vanderplas blog post
return -np.inf
#return 0.0 # flat prior
def lnprob(par, y, dy, x, dx):
lp = lnprior(par)
if not np.isfinite(lp):
return -np.inf
return lp + twodlike(par, y, dy, x, dx)
def bestfit(abund, err, age, age_err):
# fit
# parameters: (ys, y_errs, xs, x_errs)
nll = lambda *args: -lnprob(*args)
par0 = np.asarray([0.0, 0.0, 0.0])
result = op.minimize(nll, par0, args=(abund, err, age, age_err))
(m, b, lnjitter) = result['x']
return m, b, lnjitter
# (the references mentioned above are [Hogg+2010](http://adsabs.harvard.edu/cgi-bin/bib_query?arXiv:1008.4686) and [this Vanderplas blog post](https://jakevdp.github.io/blog/2014/06/14/frequentism-and-bayesianism-4-bayesian-in-python/#Prior-on-Slope-and-Intercept))
# remove the stars we won't use in fit
# In[4]:
stars_to_mask = ['HIP28066', 'HIP30476', 'HIP73241', 'HIP74432', 'HIP64150', 'SunVesta'] # do not use when fitting
mask = ~np.isin(data['StarID'], stars_to_mask)
data = data[mask]
# find the best-fit parameters for [Th/H]_ZAMS vs [Fe/H] (top panel of Figure 3)
# In[5]:
args = (data['ThH_z'], data['error'], data['FeH'], data['eFeH'])
bf = bestfit(*args)
m,b,lnj = bf # slope, intercept, ln(jitter)
# In[6]:
plt.errorbar(data['FeH'], data['ThH_z'], yerr=data['error'], xerr=data['eFeH'], fmt='o')
xs = np.arange(-0.15,0.15,0.01)
plt.plot(xs, m*xs+b)
# get errors with an MCMC
# In[7]:
get_ipython().run_cell_magic('time', '', 'ndim, nwalkers = 3, 20\nspread = [1e-3, 1e-2, 1e-4]\npos = [bf + spread*np.random.randn(ndim) for j in range(nwalkers)] # randomize starting values\nsampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=args)\nsampler.run_mcmc(pos, 1000);')
# In[8]:
samples = sampler.chain[:, 100:, :].reshape((-1, ndim))
samples[:,-1] = np.exp(samples[:,-1])
fig = corner.corner(samples, labels=["$m$", "$b$", "$j$"])
#fig.savefig('ThH_z_FeH_emcee.png')
# In[9]:
m_16, m_50, m_84 = np.percentile(samples[:,0], [16,50,84])
m_errp = m_84 - m_50
m_errm = m_50 - m_16
print("slope = {0:.3e} +{1:.3e} -{2:.3e}".format(m_50, m_errp, m_errm))
# In[10]:
plt.hist(samples[:,0])
plt.axvline(0.0, color='red')
# now let's do this for [Th/Fe]_ZAMS vs [Fe/H]
# In[11]:
args = (data['ThFe_z'], data['error_1'], data['FeH'], data['eFeH'])
# In[12]:
bf = bestfit(*args)
m,b,lnj = bf # slope, intercept, ln(jitter)
# In[13]:
bf
# In[14]:
plt.errorbar(data['FeH'], data['ThFe_z'], yerr=data['error_1'], xerr=data['eFeH'], fmt='o')
xs = np.arange(-0.15,0.15,0.01)
plt.plot(xs, m*xs+b)
# In[15]:
get_ipython().run_cell_magic('time', '', 'ndim, nwalkers = 3, 20\nspread = [1e-5, 1e-3, 1e-4]\npos = [bf + spread*np.random.randn(ndim) for j in range(nwalkers)] # randomize starting values\nsampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=args)\nsampler.run_mcmc(pos, 1000);')
# In[16]:
samples = sampler.chain[:, 100:, :].reshape((-1, ndim))
samples[:,-1] = np.exp(samples[:,-1])
fig = corner.corner(samples, labels=["$m$", "$b$", "$j$"])
# In[17]:
m_16, m_50, m_84 = np.percentile(samples[:,0], [16,50,84])
m_errp = m_84 - m_50
m_errm = m_50 - m_16
print("slope = {0:.3f} +{1:.3f} -{2:.3f}".format(m_50, m_errp, m_errm))
# Now that we've got a sense of how it works, we can do it faster for the fits in Figure 4 just by changing the args:
# In[20]:
args = (data['ThH_z'], data['error'], data['Age'], data['eAge']) #(ys, y_errors, xs, x_errors)
# In[19]:
bf = bestfit(*args)
m,b,lnj = bf # slope, intercept, ln(jitter)
ndim, nwalkers = 3, 20
spread = [1e-5, 1e-3, 1e-4]
pos = [bf + spread*np.random.randn(ndim) for j in range(nwalkers)] # randomize starting values
sampler = emcee.EnsembleSampler(nwalkers, ndim, lnprob, args=args)
sampler.run_mcmc(pos, 1000)
samples = sampler.chain[:, 100:, :].reshape((-1, ndim))
samples[:,-1] = np.exp(samples[:,-1])
fig = corner.corner(samples, labels=["$m$", "$b$", "$j$"])
m_16, m_50, m_84 = np.percentile(samples[:,0], [16,50,84])
m_errp = m_84 - m_50
m_errm = m_50 - m_16
print("slope = {0:.3f} +{1:.3f} -{2:.3f}".format(m_50, m_errp, m_errm))
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