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Created December 3, 2020 10:59
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CS146 - The Metropolis-Hastings Algorithm
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# The Metropolis-Hastings Algorithm"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy.stats as stats\n",
"import warnings\n",
"warnings.filterwarnings('ignore')\n",
"\n",
"p = lambda x: stats.norm.pdf(x, loc = -4, scale = 0.5) + stats.norm.pdf(x, loc = 4, scale = 1)\n",
"\n",
"xs = np.linspace(-6, 8, 100000)\n",
"ps = [p(xi) for xi in xs]\n",
"\n",
"figure = plt.figure(figsize = (8, 4))\n",
"plt.plot(xs, ps)\n",
"figure.show()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"q = lambda x0, eps: stats.norm(loc = x0, scale = eps)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"n_steps = 1000\n",
"\n",
"def mh(n_steps, eps):\n",
" d = []\n",
" acceptance_rate = 0\n",
" x = np.random.choice(xs)\n",
" \n",
" for i in range(n_steps):\n",
" y = q(x, eps).rvs()\n",
" a = min(1, p(y)*q(y, eps).pdf(x)/(p(x)*q(x, eps).pdf(y)))\n",
" if np.random.random() < a:\n",
" x = y\n",
" acceptance_rate += 1\n",
" d.append(x)\n",
" return d, acceptance_rate/n_steps"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"eps = np.array([0.5, 1, 2, 4])\n",
"samples = [[] for e in eps]\n",
"\n",
"for i in range(len(eps)):\n",
" samples[i] = mh(n_steps, eps[i])[0]"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"ys = np.linspace(0, 1, 1000)\n",
"\n",
"def plot_mh(eps):\n",
" samples = mh(n_steps, eps)\n",
" figure = plt.figure(figsize = (10, 5))\n",
" plt.plot(xs, ps, color = 'black', label = 'target distribution')\n",
" plt.plot(samples[0], ys, c = 'black', lw = 0.5, label = 'sample sequence')\n",
" plt.ylim([-0.05, 1])\n",
" plt.axhline(0, c = 'black')\n",
" plt.scatter(samples[0], np.random.uniform(-0.045, -0.005, size = 1000),\n",
" c = \"black\", alpha = 0.6, s = 0.7,\n",
" label = 'samples')\n",
" plt.title(fr'Metropolis-Hastings for $\\varepsilon$ = {eps}')\n",
" plt.legend()\n",
" figure.show()\n",
" print(f'Acceptance rate: {samples[1]}')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def plot_acf(x):\n",
" '''\n",
" Plot the autocorrelation function for a series x. This corresponds to the\n",
" acf() function in R. The series x is detrended by subtracting the mean of\n",
" the series before computing the autocorrelation.\n",
" The autocorrelation at lag = 0 is always 1 since the series is perfectly\n",
" correlated with itself. You can ignore this value. The autocorrelation at\n",
" all other values should be as small as possible, since independent samples\n",
" have no correlation.\n",
" '''\n",
" from scipy import signal\n",
" import matplotlib.pyplot as plt\n",
" plt.acorr(\n",
" x, maxlags=20, detrend=lambda x: signal.detrend(x, type='constant'))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Acceptance rate: 0.843\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_mh(eps[0])"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_acf(samples[0])"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Acceptance rate: 0.726\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_mh(eps[1])"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_acf(samples[1])"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Acceptance rate: 0.307\n"
]
},
{
"data": {
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q1XTv3p2vv/7anhg5yqy/bvpz2LYd92dnANWMPr+Np6cnAAaDAYvFkmV9WZFkSgghhMiGnLQg5RV/f3+io6Pt25GRkZQuXRqTycTmzZs5e/as0/e1b9+eUaNG8dprr2GxWFi9ejUjRoygWLFiVKtWjSVLlvDwww+jtebQoUM0btz4tnM5ateuHYsWLWLYsGH897//dVrm1KlTVK9enfHjx3Pq1Cl7vRnV6czu3bs5ffo0VapUYfHixYwcORKAMmXKcOzYMWrXrs3y5cvx9/d3en1s6tSpw5kzZzh58iQ1a9bkhx9+4N577812HDklyVQRVK5cOf773/9y9OjRXNdlNpvtS3BwMC1btiQgIECmoxFCiDxQsmRJ2rVrR4MGDXjggQd45ZVX6NOnDy1atKBJkybUqVPH6ftatmxJ3759ady4MVWqVKFFixYUL14cSG3dGj16NNOmTSM5OZlBgwbRuHFjBg0axIgRI5g9ezZLly6lRo0a9vpmzZrFkCFDmDVrFgMHDnR6zsWLF/Pjjz9iMpkoW7YskydPJjAwME38vXr1yvTztm3blldffZXDhw/TsWNHHnzwQQDee+89evfuTaVKlWjQoAExMTEAt8Vs4+Xlxfz583n44YexWCy0bNmSZ599NvsXPodkomNxx7TWJCcnk5SURGJiIr/99htXr17l5s2bJCcnU6FChXz9zyuEEPnt2LFj1K1b19Vh3JGYmBj8/PyIi4ujY8eOfPnllzRr1szVYRUKzv7dZaLju9Rvv/3G9evXsVqtpKSk2CcyvpNtq9UKZH1P3DH5zmxUdA8PD6pUqZIPn1oIIUR2jBw5kpCQEBISEhg+fLgkUvlIkqlC7JNPPsHf3x+DwYCHh4d9cRxg03Exm81OX20DcUJqUuTp6Um/fv1yPOCbEEII97FgwQJXh1BkSDJVSDz44IMYjUZKlSpFyZIl8fDwoHnz5vbjji1DtpYn2xIXF5dm29kC/9/q5O/vT58+fSSZEkIIIbJBkqlcOnnyJKdOnSImJibNkpCQYL91lhnH22SZiY+P5+zZs0RERDBixAimT5+eJ/ELIYQQInckmcql5cuXs379evz8/NIsnp6eGc5h55hA2VqUtNa39UFyLNumTRtat25tPzZ16lSn/ZVs70tOTqZz584FPtmjEEIIUdRIMpVLL730Ei+99JKrw7hNREQEc+bMoVq1ahgMBoxGIwaDIdN1ua0nhBBC5JwkU3epwMBA6tWrx/bt29m8eTMhISEkJiaSkJBAYmJimiUhISHLEWCDgoK4ePEiJpOpgD6BEEKIgtapUydmzJhBixZORwAQGZBkqpBLSkri559/Jj4+noSEBPuSmJhov+VnNptZunQpRqPRvthapWzr0iolhBBC3BlJpgoR2wSXAEajEQ8PD5KSkmjdujXt2rXDy8vLvphMpiw7tQshhHBvsbGxPPLII4SHh5OSksKkSZN49NFHefvtt/nll1+Ij4/nnnvu4YsvvkApRadOnWjatCn79u0jIiKC77//nunTp3P48GEeffRRpk2bxpkzZ+jRowetW7fmwIEDBAcH8/333+Pj45Pm3OvWrWPKlCkkJiZSo0YN5s+fj5+fX5oys2fP5vPPP8doNFKvXj0WLVpEbGws48aN4/Dhw1gsFqZOnUq/fv2Ij4/nySefJCQkhLp163LmzBnmzp1LixYt8PPzs49qvnTpUlatWsW3335LREQEzz77LOfOnQNSp/Rp164dU6dO5dy5c5w6dYpz584xYcIExo8fD8D333/PjBkzUErRqFEjfvjhhwzrySuSTLkR239+24CazoYwWLduHVFRUSQmJmKxWEhJSeGrr76yH0//PscnChcuXMigQYNc+AmFEELkxNq1aylfvjyrV68GUufmAxg7diyTJ08G4LHHHmPVqlX06dMHSL0b8fvvvzNr1iz69evHvn37CAwMpEaNGjz//PMAhIaGMm/ePNq1a8dTTz3Fp59+ysSJE+3nvXr1KtOmTWPDhg34+vry/vvv89FHH9nPafPee+9x+vRpPD09uXnzJgDvvvsuXbp04ZtvvuHmzZu0atWKrl278sUXX+Dj48OhQ4c4dOhQtgYRfe6553j++edp3749586do3v37hw7dgyA48ePs3nzZqKjo6lduzajR48mLCyMd999l23bthEUFMT169ezrCcvSDKVj44cOcLSpUszHDXc2XaPHj3sHcIdO4bb1pcsWZJmO/1xZ9vSQiWEEIVTw4YNmThxIq+88gq9e/emQ4cOAGzevJkPPviAuLg4rl+/Tv369e3JVN++fe3vrV+/PuXKlQOgevXqnD9/noCAACpVqmRvmRk2bBizZ89Ok0zt3LmTkJAQe5mkpCTatm17W3yNGjVi6NCh9O/fn/79+wOpLVorV65kxowZACQkJHDu3Dl+//13e+tRo0aNaNSoUZaff8OGDYSEhNi3o6Ki7BMb9+rVC09PTzw9PSldujSXL19m06ZNPPTQQwQFBQGp/Yczq8c2YXJuSTKVj86ePUtiYiKenp5p9qdPbhy3f/vtN/u6rT9TlSpVGDJkSP4GK4QQIkvffvstZ86cybP6qlatyhNPPJHh8eDgYPbt28evv/7Ka6+9Rrdu3Xj55Zf517/+xd69e6lUqRJTp04lISHB/h7b7xwPD480v388PDzsDxtl9nsIUruV3H///SxcuDDT+FevXs3vv//OypUreeeddzh69Chaa37++Wdq1659W/mM/rh33O/4WaxWKzt27MDb2/u29zh+NoPBgMVisQ8zlF5m9eQFSabyUa9evbKcITsjWmtSUlKwWCz8/PPPTJkyJc3xzFqbbty4Qd26ddO0VNnK28a2clx3ts/ZuuO++vXrO/1BEUKIu1lmiU9+uHjxIoGBgQwbNgw/Pz++/fZbe7IRFBRETEwMS5cu5aGHHspRvefOnWPHjh20bduWhQsX0r59+zTH27Rpw5gxYzh58iQ1a9YkLi6O8PBwgoOD7WWsVivnz5+nc+fOtG/fngULFhATE0P37t355JNP+OSTT1BKceDAAZo2bUrHjh3573//S+fOnTly5AiHDh2y11WmTBmOHTtG7dq1Wb58ub3FqFu3bsyZM8c+BNHBgwdp0qRJhp/rvvvu48EHH+T555+nZMmSXL9+ncDAwBzXk1OSTLkppZT9abuhQ4fa97dp04Zdu3Zl+l6DwcDTTz+dpg+V7Vai42v6dWf7MnrPwIEDJZkSQoh8dvjwYV566SX7vKufffYZAQEBjBgxgoYNG1K1alVatmyZ43rr1q3Ld999x6hRo6hVqxajR49Oc7xUqVJ8++23DB48mMTERACmTZuWJplKSUlh2LBhREZGorXm+eefJyAggEmTJjFhwgQaNWqE1pqqVauyatUqRo8ezZNPPkmjRo1o0qQJrVq1stf13nvv0bt3bypVqkSDBg3sndFnz57NmDFjaNSoERaLhY4dO/L5559n+Lnq16/PG2+8wb333ovBYKBp06Z8++23Oa4np5Rjf52C1KJFC713716XnPtuN3bsWHr37k2JEiUoUaIE5cqVy7P7wkIIUZQcO3aMunXrujqMPHXmzBl69+7NkSNHXBqHO49p5ezfXSm1T2vtNFhpmXJzERERHD9+nH/++SfNrT+LxUJycrLT16SkJGbOnMmNGze4ceMGHTt2ZN68ea7+KEIIIcRdSVqm3NwLL7zA7t27KVOmjL3/k+32n8lkcvqa0RN84eHhDBo0CF9fX8xms/0piPTrXl5eGI2SZwshxN3YMiWyJi1Td5mPPvooV+8PCwvj/PnzJCYmUrlyZZYvX050dDTR0dH2R0Ojo6MJDQ0lICCApKQk2rdvn+apQiGEEEJkTJKpu9xbb71FTEwM3t7eeHl54e3tTVBQEJUqVcLb29u+2EZN9/DwwMPDg0WLFtnXHRdb61h2l9KlS1OlShVXXwYhhBAi30gyVUCuXbtmH0SsINiGMHAcAT0jnTt3pkqVKvan/7JaslvOarXywAMP8PbbbxfAJxZCCCFcQ5KpAlKyZEkKqn+a4zAHjomN47Zt/cqVK/z73//OVuvRqVOn0kxjk9EUNikpKcyfP586deoUwKcVQgghXEuSqbuQ42CbBoMh07IlSpTgu+++S7Mv/VODFouF06dP8/nnn/PAAw/YO7lntlSuXDnfPp8QQoi8585DFbg7SaaKiA0bNrBmzZpsjzdle2LQcXnttdeoWrVq/gYqhBBCFDKSTBURly9fpmHDhlSuXDnTSZEzm2TZYDBw9erV247bhmUQQgiRt2JjY3nkkUcIDw8nJSWFSZMmERoayi+//EJ8fDz33HMPX3zxBUopOnXqRNOmTdm3bx8RERF8//33TJ8+ncOHD/Poo48ybdo0zpw5Q48ePWjdujUHDhwgODiY77//Hh8fnzTnXbduHVOmTCExMZEaNWowf/58/Pz8ePXVV1m5ciVGo5Fu3brZJzMu6iSZugucPHmS8PDwTDuJWywWDh48yJ49e+wDfCYnJ5OUlGRfd9zOTpmoqCg8PT0JDg7mr7/+ynS+QCGEEDm3du1aypcvz+rVqwGIjIzk/vvvZ/LkyQA89thjrFq1ij59+gBgNpv5/fffmTVrFv369WPfvn0EBgZSo0YNnn/+eQBCQ0OZN28e7dq146mnnuLTTz9l4sSJ9nNevXqVadOmsWHDBnx9fXn//ff56KOPGDt2LMuXL+f48eMopbh582bBXgw3JslUIWbrZP7111/zxx9/OJ202PbqbHJj4LZJkD09PfH29nZaR/r3296rlOKRRx5h0KBBDBw4sOAugBBCuKHExET2799Ps2bN8PT0zFVdDRs2ZOLEibzyyiv07t2bDh068PPPP/PBBx8QFxfH9evXqV+/vj2Z6tu3r/199evXp1y5cgBUr16d8+fPExAQQKVKlWjXrh0Aw4YNY/bs2WmSqZ07dxISEmIvk5SURNu2bSlWrBheXl4888wz9OrVi969e+fqs91NJJlykZkzZ7JgwQJKlChBs2bN8PLyAuDmzZtYrVYCAwOzVY+Hhwe+vr488MAD9uQm/auzfZkdy255SDsJsjy9J4QQsH//fiZPnszbb79N27Ztc1VXcHAw+/bt49dff+W1116jW7duzJ07l71791KpUiWmTp1KQkKCvbwtefPw8EiTyHl4eGCxWID//+PYJv221pr777+fhQsX3hbP7t272bhxI4sWLWLOnDls2rQpV5/vbiHJlIsMGzaMdu3ace7cObZt22ZPpgICAjJ8z549ezh48GCaYQ8ch0HI7j5nZVw1rZDNrl270swgLoQQhVWzZs14++23adasWa7runjxIoGBgQwbNgw/Pz++/fZbAIKCgoiJiWHp0qU89NBDOarz3Llz7Nixg7Zt27Jw4ULat2+f5nibNm0YM2YMJ0+epGbNmsTFxREeHk758uWJi4ujZ8+etGnThpo1a+b6890tJJlykVKlSlGqVClatWqV7R+EiRMn0rlz5zSjkTt2BM9qX3aO30mrVVb7bOv+/v74+fnl85UVQgjX8vT0zHWLlM3hw4d56aWX8PDwwGQy8dlnn7FixQoaNmxI1apVadmyZY7rrFu3Lt999x2jRo2iVq1ajB49Os3xUqVK8e233zJ48GASExMBmDZtGv7+/vTr14+EhAS01sycOTNPPuPdQCY6LkRu3LjBlStX0rQuObYyOVvPzb68fs+mTZt48skn8fLyynTx9PSUzuxCCLdwt010fObMGXr37s2RI0dcHYpby5eJjpVSPYBZgAH4Wmv9XrrjxYEfgcq36pyhtZ6f8/CFTUhICGfPnnV6O87xtlxmx+90yY96AYoXL87cuXOJj493uiQmJpKQkGD/Syi9gIAA/vnnn1x36BRCCCHyUpbJlFLKAMwF7gfCgT1KqZVa6xCHYmOAEK11H6VUKSBUKfVfrXVSvkRdBCxfvpzff//dfpssKSmJ9u3bExQUhMlkytZiG//JthgMhjRP46VfgEyP3+mS3XqFEELkr6pVq0qrVD7ITstUK+Ck1voUgFJqEdAPcEymNOCvUn8j+gHXAUsex+pSO3bsSNP5G/7/STbH9fSdue90v8lkokuXLvbt2NhY/vzzT1JSUuzjPdmmekk/LpTjNDCOZbJzS/fFF19kypQpmQ6rkNF6RseEEEKIu1l2kqkKwHmH7XCgdboyc4CVwEXAH3hUa23NkwjdRHh4OIcOHQIyThacJRN5ud/2tJuzlpyc1pWSksLx48fRWlO3bl3MZjOQmsR98cUXxMXFERYWRkJCAklJSSQmJt62OO5PP/mx45KXfv/9dzp06JCndQohRGa01vKHYRFyJ33Js5NMOfsflP5M3YGDQBegBrBeKfWH1joqTUVKjQRGAoVuItyHH36Yhx9+2NVh5Inz589z//33ExoaCkCVKlVYv349tWrVspeZP38+ZcqUoWLFipjNZjw9PTGbzfbFcdt2S9H2ZGD6V/kSEkIUVl5eXly7do2SJUvKd1kRoLXm2rVr9uGKsis7yVQ4UMlhuyKpLVCOngTe06np3Eml1GmgDrA7XZBfAl9C6tN8OYpU5Ilr167Rs2dPwsPD+eSTTzAajbz66qt06dKFuXPn4uHhQVJSErt27eL1118vdEmvEELkpYoVKxIeHk5ERISrQxEFxMvLi4oVK+boPdlJpvYAtZRS1YALwCBgSLoy54D7gD+UUmWA2sCpHEUi8l1KSgp9+vThyJEjPPfcc5QtWxaz2cxrr73Gq6++ys8//8y4ceMwm800aNCASpUqZV2pEELcxUwmE9WqVXN1GMLNZZlMaa0tSqmxwG+kDo3wjdb6qFLq2VvHPwfeAb5VSh0m9bbgK1rrq/kYt8iGd955h8TERPvgmSkpKRw+fJgHHniAjz/+2F6ub9++/PXXX/z88898+OGHlC5d2nVBCyGEEIVMtsaZ0lr/Cvyabt/nDusXgW55G5rIrYYNG3L06FGsVitWq5Vdu3YRExND+fLlmTp1apqyAQEBxMbG0rJlSypUqEBKSgpWq5WUlBSnncttxzLaTn/ss88+49lnn3XNhRBCCCHykUwnU8iNGDGCH374IdNpXGzrN2/exGQysWrVqjT7lVIkJycTGBho71Nl61TuuDjbl939Hh4ebNmyJdM4mzdvjsFgcPUlFUIIIXJEppMp5GzjSmU1vcu+ffvo0aMHH374IUOHDnVa5tdff2XMmDHMmzePDh06ZDpVTHbXnR1LTk62j3qekJBAfHw8e/bsYcKECTRu3NjVl1QIIYS4Ta6nkxHuyza6eVZWr16Nl5cXI0eOpFixYk7LPPPMM7z++uv88ccfPPXUU3kW4/bt23nooYfw9PTEZDLh4+Njn/TY8TUyMpIDBw7YP1PVqlVl6hghhBBuT5KpIkBrzYoVK+jevXuGiRSA2WymT58+rFy5kuTk5GwlaVmxWq1UqFCBRYsWERcXR1xcHPHx8U7XFy9ebF+/evUqzzzzDIMHD851DEIIIUR+kmSqCPjrr784f/78bZ3OnRk4cCA//vgjW7dupWvXrrk+9x9//MGqVauoX7++vcXJ29ubYsWKZTiHoG27atWquT6/EEIIkd8kmSoCVq5ciVKK3r17Z1m2e/fueHl5sXr1arp27Wrv52R7Ms82/1/6+QAz2rdv3z569+7NvffeWwCfVAghhCh40gG9kNJaU6lSJS5cuGDf5+HhYX9CzvFJucTERAD8/PwyfNrP8fXq1atYrVbKly+Ph4dHmif00k8rk9VUM2azmZYtW+Lp6Wk/R/Xq1aXVSQghRKEiHdDvAlFRUYSEhNjHjLJarfz4449pWo1s40E5vkZHRzN69Gh69epF7969byvj7H3bt2+33+bz8vKyH7t69SpxcXEEBASkeUIvJSWFuLg4YmJinD69t2PHDvs+q9XKk08+KcmUEEKIu4YkU4XEkiVLMJvNlClTxt4CZWs1MpvNafY5Ln/88QdaawYOHEibNm0yLOe43H///XTp0oXmzZszdOjQNMc8PT1lsk8hhBDCgSRTbujcuXMsX76c6OhokpOTUUpx+vRpPvroI0qWLJmjun788Uc8PT0ZNGhQtmfBDgoKolSpUuzYsYPRo0ffyUcQQgghigxJptzQ0aNHOXz4MGXKlMFkMtn7GX3yyScZvkcpha3/m2NL0sKFCylfvjxz587NskXKNvp4586dadWqFVu3buX69esYDAb7ccdXWx8oIYQQoiiTZMoN3XvvvTRp0oSEhIQMF9uo5876KDn2l7p48SI9evTAw8MDi8WSaV8pi8VCeHg4b7/9NpGRkVy/fp169ephtVrt73VccvvwwtatW+nYsWMeXTUhhBDCNSSZckMvv/wyDRs2xMvL67YlMDAQT09PjEZjlk/mbd26FYAnnniCdu3aZVo2/fq+ffvo3LkzH330EQMHDnRaRlqlhBBCCEmm3FL16tW5ePEikPb2neO6TfrjNlprezJ14MABQkJCANK0XGXWSpWUlISHhwdTpkzhp59+SlPeYrEwbNgwnn766Xy/FkIIIYS7k2TKDb3wwgt5Uk/Pnj1p0KAB7733HpDaQlW9enW8vb0xGAwYjcZMX//66y9SUlJ44oknbjtWvXr1PIlRCCGEKOwkmbpLaa3ZvXs3/fr1s++rWrUqkydPznYdR44c4T//+Q/du3fH29s7P8IUQgghCj0PVwcg8sepU6e4du0arVu3tu+LjY0lPDyca9euERcXh9VqzbSOVq1akZyczKFDh/I7XCGEEKLQkpapu9Tu3bsB0iRT3bt3Z82aNcTHxxMfH09CQoK9v9Xff//NBx98QLly5ezlmzdvDsC+ffvS1COEEEKI/yfJ1F1q165d+Pj4UL9+ffu+rl27Zlh+xowZ9gTLZDJhMBioVKkSJUuWZN++fQURshBCCFEoyUTHd6l77rkHg8HAV199xY8//ojRmHnevGfPHv744w+SkpJITk7O8hbgc889x8cff5yHEQshhBDuSyY6LgI2b97Mli1bgNThD/bs2UPz5s35/PPPefbZZ6lTp84d1fv666/z4YcfEh0dne3paIQQQoiiRJKpQub06dOcOnWK2NjYNMuWLVtYvnw5AGFhYUybNo1Ro0bx5JNP5up8zZs3x2KxcPjwYVq2bJkXH0EIIYS4q0gy5UK//PILixcvtg+ImX5k8vSjjXt4eHDjxg0eeeQR/Pz8KFu2LH5+fvj5+TFw4EAiIiLw8PBg27ZtANSoUYOoqKhsj3zujGMndEmmhBBCiNtJMuVCVapUoUePHhiNRjw8UkepSD/PXvp1q9VKXFwcsbGxXLp0yenxX375BQ8PD3bu3MmePXvso57bRi93HAXdtt9qtaZZbPVaLBY8PT2ZOXMmO3futJ/DarUSHR3NypUrXXwVhRBCCNeSZMqFGjVqRKNGjTI8Hhsby6BBg6hbty4+Pj5pjmU0zYxSirNnz1KyZEni4+PRWqdpfTKZTLe1fjlrDXNc/+OPP0hOTubee+9Nsz8wMDD/Lo4QQghRSEgy5cbmzp3L/v372bBhAwkJCQB06NCB33//PdP3ff3113Tr1o0pU6bkSRxHjx5l3rx5DB8+3N6CJoQQQohUkky5sZCQEEaMGGHftrU+2ZIkZ/2cbKOcX7lyhbfffvu2/lGZLRmVu3r1KrGxsbz77ruULl06R3Xm9Pz33Xffba1wQgghhDuTZMqNffvtt5keT9+vSmvNpk2bmDFjBmPHjqVTp0639Ydytu24z9lxLy8vFixYgMFgoHbt2pnW56zOpKSkDN/jWPbMmTO89NJLLFu2jHr16hXMRRZCCCFySZKpQio6OprBgwfTsmXLNC0/27dvB1IH4Tx+/LjTlqGcblssFiD1ib7KlStnWd5oNGIymXJ8vhYtWvDwww9TsWJFV15aIYQQIkckmSqktNaYzWaKFSuWplP4tWvXKFasGJUqVcqwU3lOOqDbtsuVK8e1a9eoWLFilmWLFStGrVq1XH2JhBBCiAIhyVQhVaxYMb777jv7LTLbLb+vvvqKJk2a0Lt37zTDHKQf9iCj7YyO1ahRg9OnTwOQkpLCnj17CAsLIzExkYSEBBISEuzrV65cYffu3RgMBoxGIwaDQTquCyGEuGtJMlWI+fv7p9m2Wq2cPHmSkSNHUr58efu+zPpDpV8/fvw4Z8+eve2Yr68v58+fZ9euXXh4ePCf//yHy5cvZxhbmTJl0oxtlRmz2cylS5dkqAUhhBCFkiRTbsY2UGZSUhKrV69m9+7d+Pn5kdGE1I5jTEVGRhIXF8fJkyeZOnWq/bitZci2OG6nXzeZTHTt2vW2Y76+vvz222+0bduWZs2aMXbs2DR1ZjaKuhBCCHE3k2TKBebMmcPVq1czPG4ymTCbzXh5efHuu+/i6emZrXp//fVXZs2axauvvkq7du3yKlwA2rZtC6TODdixY8c8rVsIIYQozCSZcoGIiAimTp2a5y05ISEhANStWzdP6wWoVasWnp6eHD16NM/rFkIIIQozSaZc4N577+Wtt95Kc+vO8Xads32OiVdG+1auXImvry+zZ8/OtFx296VP9ooXL86KFSsyHFQzo1uRGfH29uaVV16R24NCCCEKNUmmXKBLly506dIlz+v97bffaN26tb2/VF65efMmb775JkFBQVy6dCnDchklhM5orUlKSnKatAkhhBCFiSRTdwmtNSEhIQwfPjzP646OjqZp06aULFmSadOm8eqrr+Ll5ZXn5xFCCCEKIxn85y5x4cIFoqOj820aluTkZOrWrYvVauXEiRP5cg4hhBCiMJJk6i5h63yeH8lUmTJliI+PZ9GiRQAcO3Ysz88hhBBCFFZym8/N7du3jxYtWmS7fKdOnZxO8ZJ+Hjxnr+n3pX+P1WoFYPHixaSkpGRYV/v27QkKCsqvSyKEEEK4FUmm3Fzz5s2z9ZTcyJEjWb58OVeuXEkzDUxevqakpNC5c2eio6MpX748CQkJxMfHp3k9d+4ccXFxDBkypACujhBCCOF6kkzdJUJCQqhXr559xPP8MGXKFPz8/Dh69ChHjx7F09PTvgQFBeHp6Um9evVo2rRpvpxfCCGEcEfZSqaUUj2AWYAB+Fpr/Z6TMp2AjwETcFVrfW+eRSmA1Hn2LBbLbUtycjJHjhyhZ8+ehIaG2vcvXrwYs9mcZ+f39/end+/ezJ07l1GjRuVb0iaEEEIUJlkmU0opAzAXuB8IB/YopVZqrUMcygQAnwI9tNbnlFKl8yneIuHvv//m2LFj9OnTJ8MyH3zwAV5eXhiNRuLi4oiMjMRgMLB//36MRiNGo5HBgwfTsGHDPI1t3rx5JCQkcPbsWapXr56ndQshhBCFUXZaploBJ7XWpwCUUouAfkCIQ5khwDKt9TkArfWVvA60KOnZsycNGzZk2LBheHt74+Pjg7e3N97e3vbJiGvVqmXvNG57kq9OnToEBQXZ91+/fp0//vjjts7o6ScodrbYylWqVAmj8f//m9imqjl27JgkU0IIIQTZS6YqAOcdtsOB1unKBAMmpdQWwB+YpbX+Pk8iLIL+/PNPYmJi0nQAz2zZuXMnkJpM+fj4pDlmsViyXU/6MqdPn6Zp06ZpWsjq1KkDpCZTvXr1csn1EUIIIdxJdpIpZ3N9pH+8zAg0B+4DvIEdSqmdWuuwNBUpNRIYCVC5cuWcR1tElCpVilKlSmW7/JIlSzCbzfTv3z9P+zEdOHCAc+fOpdkXGBhI6dKlOX78eJ6dRwghhCjMspNMhQOVHLYrAhedlLmqtY4FYpVSvwONgTTJlNb6S+BLgBYtWuRsVlyRobCwMGrWrHnHiVRERAQ7d+4kNjaWuLg4YmNjiY2N5ezZswwYMOC28nXr1pWBO4UQQohbspNM7QFqKaWqAReAQaT2kXL0P2COUsoImEm9DTgzLwMVGQsNDaV27dpOj82ePZvr16/bt51NKvzPP/8wbNgwatasia+vL76+vvj4+ODl5eW0fHBwMCtWrMiz+IUQQojCLMtkSmttUUqNBX4jdWiEb7TWR5VSz946/rnW+phSai1wCLCSOnzCkfwMXKRKSUnh5MmT9O3b1+nx48ePM2LECDw8PDAYDFl2PDcYDFgsFmJiYoiLi3Napnr16kRERHDt2jUCAwOdJlxCCCFEUZGtcaa01r8Cv6bb93m67Q+BD/MuNJEdZ8+eJTk5meDgYKfHH3nkEc6dO3dbZ/OUlBTCw8OJiIiwj1VlW9Jvpz925Urqw5pt2rTBaDSSkpKS4bJ161bq169fkJdECCGEKFAyAnohFxaW2i0to2SqU6dOGb73iSeeYN++fWlarIxGo9Ntg8GA2WzGw8MDLy8vTpw4QWBgINWqVbMft73PaDRiMpkwmUysXLmSVatWZTk8g22fl5cXw4YNk9YuIYQQhYYkU4VcVslUZr799ts7OmdSUhLe3t5069aNqVOn2lu6bK+2FiyLxcLff/9NSEgIiYmJJCYm2ufwS0xMJCEhwf4+23Lu3DkGDx6cZmwrIYQQwp3Jb6xCLiwsjOLFi+doKAWAVq1asWfPnlyde9q0abz77rsYDAZSUlKYMGEC5cuXT9NKBfDAAw9gNpsxmUy3vdrKCCGEEIWVJFOFXFhYGMHBwTm+LbZ79+5cnbdnz55cvnyZffv2AbBmzRoCAwNp3Tr9eK5CCCHE3U2aBQo5WzJV0GrVqkVYWBhapw4XVq9ePZYvX17gcQghhBCuJi1TWejfvz9//vkn8P9jNCml0iyOx5x1sratp3/N7FhGZZRSJCUlkZCQYJ9w+MaNG/Tp04fmzZvb47YlORm1WNmOZ6eMs+MnTpwgJiaGF198EX9/f5RS+Pr65ujaCiGEEHcDSaay8P3335OUlGRPLLTWaRbbPttr+jnu0u/LSRnH9R07dvDVV19RoUIFvL29KVGiBImJiYSEhNC0aVOeeeYZ+vXrV2DXZf369axZs4Z+/fpx7733Fth5hRBCCHcjyVQWihUr5uoQAKhUqRI3b97EbDYDqa1Fu3btAqBHjx5orVm7di2enp54eXnh6elJUlISJUuWpFatWnkej+3WYlhYmCRTQgghijRJpgqJatWqMX369DT7pk2bxtq1a7n//vsxGAwkJCRw+fJlunTpYi/j5eXFK6+8kicx1KpVi6FDhwKpyZ2np6d9aAYhhBCiqJJkqhA7deoU5cqVS9NXCtL2h8pLU6dOta97eHjYO6ELIYQQRZkkU4VYQT7J9/DDD3P27Fl8fHzsEyH7+Piwf/9+kpOTMZlMBRKHEEII4W4kmSrEwsLC6N+/f6ZltNaZzr3n7Nj+/fuJiIhIU0/9+vWpW7cuERERnD17lri4OKKiorhw4QIRERGUL18+Hz+pEEII4b4kmSpEkpKSmDdvHiaTiaSkJCIiIoiPj2fRokUkJSWRlJREYmIiSUlJxMfHExISQq1atTAajWnmyzOZTGm20x9r0aJFtgbf/Oabb3j66aeJj48vgE8vhBBCuCdJpgqR5ORk/vrrL5KTk7l06RIAf//9N/PmzcPHx4egoCDMZrP9ib6aNWtitVpJTk5GKYXBYKBVq1Z5Nkq54xN9NWrUyJM6hRBCiMJGkqlCxNfXl88//xyAH3/8kTVr1vDNN99Qp06dTN+ntWbp0qVs377dnoTlBVsydeLECR544IE8q1cIIYQoTCSZciNaa1577TW8vLwyLaeUYtOmTSilWLBgAQaDwf7+jMTHxzNz5sw8jbdUqVIUL15cnugTQghRpEky5Ua01hgMBl5++WV7PycPD+fTJx47dozq1avz9ttvF3CU/08pRXBwsCRTQgghijRJptyIUory5cszZ84cLBYLFovFPqWM7bjNli1b8Pf3TzP2E8DZs2f5+uuv7a1V+S04ONg+d6EQQghRFEky5UaUUowZMybLclprPvzwQwYNGnRbMvXuu+9itVoLNJlasGAB8fHxeHt7F8g5hRBCCHciyZQbOnr0KMuXL8disThtlYqKiiIuLo6wsDCmTJmS5lh4eHiGtwbzQ3BwMFpr/v77bxo0aFBg5xVCCCHchSRTbmjLli20a9eOMmXKYDQaMRgM9sXDw4OdO3cyc+ZMnnnmGe677740x2yvBcU2iXJYWJgkU0IIIYokSabcUL9+/di+fTv//PMPVquVlJSUNMuWLVsA2L9/P2FhYSQlJaUZxTw5OZmUlBSsVqv9/bb15ORkOnXqxIgRI/IkVsdkSgghhCiKJJlysTFjxvDpp5/ett9kMmE2m+2DcJrNZtq2bUudOnU4c+YMRqMRT09PrFYrZrMZb29vPDw80rROOds2GAy0a9cuz+IvVqwYZcuW5cSJE3lWpxBCCFGYSDLlYnPnzmXu3Llp9mmtSU5Otk8RY1uef/55tNZcv36dEiVK2J/4g9Q+VY7jTNm2HZMqpRQeHh78/PPPt+3LzXa1atWkZUoIIUSRpTIb6DE/tWjRQu/du9cl5y7s6tatS926dVm2bFmm5bTWaK3twyvYbvU527ZarSQlJdGuXTu6devm9Hj699kmUQbYtm0bly9fLoiPL4QQQhQ4pdQ+rXULZ8ekZaqQSUxM5MSJE9SuXZt58+YRFRXF4cOHqVixYo46njt7StBgMPD4448zderUNPuz8sEHH7B8+XJu3rxJQEBAtt8nhBBC3A0kmSpkQkNDSUlJITw8nG3btlG8eHEqVKiQ4yf4nCVLKSkpKKV46623slWH1hqlFMePHwfgpZdeonz58gB4e3tTrlw5KlasyL333ovRKP/VhBBC3J3kN1whY5uoeObMmXTo0MHF0aQKCQlh8eLFdOrUiaFDh6K1Jj4+nkuXLrFs2TI2bNhAtWrV7B3pPT098fT0BMBisZCcnAzAgAEDCnRYByGEECIvSDJVyNg6etuGJHAHNWrUQCllf6JPKYWPjw81atTgxRdf5Pr16yQlJZGYmEhsbCz9+/endu3aaK3tTy36+fnRp08fe5IlhBBCFBaSTBUyJ06csN9Cyw7bcAgGg+G2AUBtTw3axp5q2bLlHcdVvHhxfv75Z6fH0j9p+Pnnn9O1a9c7PpcQQgjhTiSZKmTCwsKoW7cu+/bty7Ks7ck7i8VCjx49uHDhQprhDTw9PfHx8cHHx4f+/fvTuXPnNONbBQYGZrsj+s6dO7l69eptcwUKIYQQdztJpgqZEydO0KpVq2yVVUrZW6G++eYbbty4YW+Jchw13ba+Y8cOEhISSEhIYP/+/bz44ovZniKmVq1abN++3d4pXQghhCgqJJnKhg0bNrBt2zacjcmV/hZWfkpJSeHUqVNUqFDhthYgZ0MdZLQ/fby2Y44DcgYHB1OpUqVsxxYcHEx0dDSXL1+mbNmy2X6fEEIIUdhJMpUNW7duxdvbG0hNOByX7O7LSdmM9v3zzz8A1KtXz97pO7d1Zhbn9u3bs/3++Ph4AJYsWULjxo2dlq1UqVKOEjQhhBCiMJBkKhumTp1qH+nbNqq4bcnuvuyUvXz5MhcvXnQ68rjVauX69esAlC1bNsMymS1a6zSTHufFYqszKioKgO+++44qVao4LVu9evXbps4RQgghCjtJprLB1u8ov3399dcsX77c3pLjOP+dUso+xtTatWsxmUxpytlu0WW1z/GpPmdP+jnuMxgM1K5dmx49eqRpZXKMybZorfntt99o06YNkydPdlrW1ronhBBC3E0kmXIjkydPZvLkyRkef/bZZ1m6dCk7d+50enzLli1s2rQpw4EvHefqy2qePq01SUlJWK1Watasma34a9asyYULFyhdunS2ygshhBB3A0mmCpGwsLBMB+s8ffo0FosFs9kMYB/+IP3Srl07qlatmufxBQcH2wcVFUIIIYoKSaYKkRMnTtClS5cMjz/55JNptlNSUkhMTCQxMZGEhAQSExO5efMmS5Ys4aWXXsrz+IKDg1mzZg0pKSkFcltUCCGEcAcyEVohERcXR3h4eI6mkTEYDPj4+FCiRAnKlStH1apV83UamuDgYJKSkjh37ly+nUMIIYRwN9Iy5eaWLl3K0aNH7Z3P//rrrwxHGXccPyqj8a+sVitNmzbNl1iDg4OB1Ba0atWq5cs5hBBCCHcjyZSbi4uLIyUlxT4sQmBgYIZlbU/t3bhxg1mzZhVIfI5syVRYWBjdunUr8PMLIYQQriDJlJt7/PHHAZg+fTpLlizhP//5D35+fpm+x1Xz45UpUwY/Pz/phC6EEKJIyVYypZTqAcwCDMDXWuv3MijXEtgJPKq1XppnUQpOnDhBuXLlskykANq0acNbb72V7WlutNZYLBYSExNJSkoiMTGR+Ph4oqOjiYqKIioqisjISNasWUONGjUyrEcpJU/0CSGEKHKyTKaUUgZgLnA/EA7sUUqt1FqHOCn3PvBbfgRa1IWFhdlvo2WlR48e9OjRw+mxdu3aER0dfdsAnl5eXnh7e+Pj44OPjw9+fn5UrlyZEiVKEBAQQIkSJUhMTOTkyZP299gWPz8/fH19gdRbfbt27cqzzy2EEEK4u+y0TLUCTmqtTwEopRYB/YCQdOXGAT8DLfM0QgGktkz17dsXSJ0rcOPGjWnmx3OUviO6o+rVqxMTE4PVaiUlJcW+WCwWYmJiiIyMvG2/47az/UOGDOHjjz8GUpOpn376icTERDw9PfPxigghCjOtNdeuXSMqKgqttb2bgBCFUXaSqQrAeYftcKC1YwGlVAXgQaALmSRTSqmRwEiAypUr5zTWIisyMpIrV67YW6a2bt3K1KlTMxzp3JWCg4OxWq2cOnWKunXrujocIYQbuXz5MkuWLGHVqlXs3buXa9eupTlevnx52rVrR79+/ejfv7+9xVsId5edZEo52Ze+M87HwCta65T0LSFp3qT1l8CXAC1atMhehx7BiRMnAPJ1jKi8YosxLCxMkikhBJD6Hfbuu++ycOFCkpKSqF27NgMGDKBu3br2J5QvXbrEoUOH2Lp1K0uWLMHf358xY8bw4osvEhQU5OJPIETmspNMhQOVHLYrAhfTlWkBLLqVSAUBPZVSFq31irwIsqgrrMmUEKJoi42N5a233uLjjz/GZDIxYsQIxowZk+kfWlarlT///JO5c+fy/vvv8+mnn/L+++8zcuRIt2yNFwKyl0ztAWoppaoBF4BBwBDHAlpr+wiNSqlvgVWSSOWdsLAwlFL2J+kqVarE22+/fUd1pe94blt8fX156qmnbutjlVMlSpSgVKlSkkwJUcTt37+fwYMHExYWxpNPPsm///1vypYtm+X7PDw86NixIx07dmTKlCmMHz+e0aNHs2jRIhYsWED58uULIHohcibLZEprbVFKjSX1KT0D8I3W+qhS6tlbxz/P5xiLvOPHj1OtWjW8vLyA2+fgyy6ttdOO5ykpKXzwwQdorXOdTIFMeCxEUTd//nxGjRpFqVKl2LhxY6ZzimamXr16rF+/nm+//ZaxY8fStGlTFi9eTKdOnfI2YCFyKVvjTGmtfwV+TbfPaRKltX4i92EJR6GhodSuXTvX9Sil7C1RWmtef/11+xN3KSkpeZJIwf9PeCyEKFqsViuTJk3i3//+N/fffz8LFy6kZMmSuapTKcWTTz5J69atGThwIN26deP7779n0KBBeRS1ELknI6C7OavVSmhoKDdv3qRNmzaYTCZMJhNGoxGz2WxfNxqN9mOOi9lsxtPT02mi1KZNG/r165fnMQcHBzN//nyio6Px9/fP8/qFEO7HarUycuRI5s2bx4gRI5g7dy4mkynP6q9Xrx47duygb9++DB48mIiICMaNG5dn9QuRG5JMubnw8HDi4uJ47LHH6NGjB8nJyVgsFpKTk+1L+m3HfQkJCSQmJt42Gnp4eHi+TTtj64R+4sQJmjVrli/nEEK4D6vVyqhRo5g3bx5vvPEG77zzTp61dDsKCAjgt99+Y8iQIYwfPx6DwcC//vWvPD+PEDklyZSbO378OAD33Xcfbdu2vaM6wsPD+eqrr9LsMxrz75/eccJjSaaEuLtprRk3bhxff/11viZSNt7e3vz000889NBDjBkzBm9v7zvuRypEXpFkys3Zkqnc9JkKDQ0lOjqa+vXr4+vra1/27NlDixYt8vyLr2bNmoAMjyBEUfDBBx/w6aef8tJLL+V7ImVjMplYvHgx/fr145lnnqF06dL06tUr388rREYkmXJzx48fJyAggNKlS99xHV26dKFp06bExsYSExNDbGwssbGxLFq0iFKlSlG1atW8C5jUvxwrV64syZQQd7nFixfz6quvMnjwYN57770CSaRsvLy8WLZsGffeey+DBg3izz//pHHjxgV2fiEcSTLl5kJDQ6lTp84dfUnduHGDK1eukJCQ4HSJiorKt0HwgoOD7YONCiHuPrt27WL48OF06NCB+fPnu2RATV9fX1auXEmrVq3o3bs3u3fvply5cgUehxCSTLm548eP061btzt67+TJk1m3bh1eXl63LZ6envj4+PDNN9/Yy3t4eNgXg8HgdN3Dw8PemV1rnWa9atWq9smYa9WqxcKFC/Ns7CohhPuIiIjgoYceonz58ixfvtylk5qXL1+eX375hQ4dOvDwww+zefPmPH2KUIjskGTKjX355ZdcvHiRc+fOMWXKlBy/PzAwMMuxWGzJkFIKi8ViH9TTarVmuK6UsidIjutms9leb+3atbl58yZXrlyhTJkyOY5dCOGeUlJSGDJkCBEREezYsSPX40jlhaZNm/LVV18xZMgQXn/9dT788ENXhySKGEmm3FhcXBwApUuXzrJ15+bNm3z88ccFEFX21KtXD4Bjx45JMiXEXWTq1Kls2LCBefPm0bRpU1eHYzd48GD++OMPZsyYQfv27fNlDD0hMiLJlBuz/cU3ZcoU6tSpk2nZ/Boz6k7ZJjINCQmRqR+EuEts2rSJadOm8dRTT/HUU0+5OpzbzJw5kz179jB8+HAOHjyY5w/XCJERSabc2PHjxzEajfYJjjPTqlWrXCdUFy5coE6dOmkmQM7ukn7iZA8PD3x8fNi8eTPdunWzD5cghCicbty4wfDhw6lduzaffPKJq8NxytPTk59++onGjRszfPhwNm3ahMFgcHVYogiQZMqNhYaGUqNGjWx1puzZsyc9e/bM1fkSExNJTExMMxHy9evXeeONN0hJSQH+f7Jk2zx/6SdOdlyUUvz2228YDAYWLVqUq9iEEK71r3/9i3/++YcdO3bg4+Pj6nAyVK1aNWbPns2TTz7JzJkzmThxoqtDEkWAJFNu6OrVqxw4cIA9e/ZQtmxZlixZQlJSkn2qGMd1W6dx+P9EJ7NX29N1zhYPD4/b+mbFxsaydevW2zqj26arcbR48WIeeeQR+/aTTz7J2rVrJZESopBbsGABixYt4p133qFFixauDidLw4cPZ+XKlbzxxht069aNRo0auTokcZdT6edsKygtWrTQe/fudcm53d2mTZt499132bx5MzVq1KBx48b2SY1tkxc7TnhsS4LSJ0XpX22LLanKaMkr27ZtY8OGDbz88st4e3tnWjY8PJxly5Zx48YNQkND7VPSCCFcKzw8nAYNGlC/fn22bt2ar1NR5aWIiAgaNmxI6dKl2bNnj0uHbxB3B6XUPq21078mJJlyUydPnqRWrVp88803hXbeqVWrVtGnTx+2bdvGPffck2nZr7/+mtatW9OgQQMZl0oIN6G1pm/fvmzcuJHDhw9nq/+mO1m9ejW9e/dmypQpbveQjih8MkumCsefGEVQSEgIQJZP8bma1WolKSmJlJQULBaL/dVisRAQEADAli1bCAwMtO93VjYkJIQePXpIIiWEG/npp59YtWoVM2bMKHSJFECvXr0YOnQo//73v3n44YepX7++q0MSdylJptzU0aNHAfL0h3/NmjXs27cPwOmtvfTr2Sm3f/9+7rnnHsxms30xmUz2J/pMJhN//PEH1atXtz/x5/hqW3/44YepUKFCnn1WIUTuXLt2jXHjxtGiRQuee+45V4dzx2bOnMnatWt5+umn2bZtmzzdJ/KFJFNu6ujRo1SqVIlixYrlWZ2JiYnEx8fbW38cO5w764SevoO6bR9AcnIyH3/8MQkJCfzxxx9pRkm3eemll+zJYFYjsQsh3MuLL77IjRs3WL9+faHpJ+VMqVKlmDVrFsOGDWPu3LmMHz/e1SGJu5D0mXJTTZs2pWzZsqxZs8bVoTj1zz//sHTpUsaMGZPprbmhQ4eybds2zpw5U3DBCSFyZf369XTr1o3XX3+dd99919Xh5JrWml69evH7779z9OhRqlSp4uqQRCGUWZ+pgp/mW2QpJSWFY8eOuf39faPRmGUfp3r16nH27FliYmIKKCohRG7Ex8czatQoateuzaRJk1wdTp5QSvHZZ58BMGbMmDx9alkIkNt8bunvv/8mMTGRBg0a5Gm9iYmJXLt2zWkncNtAmxkdS1/m2rVr2eosbptWJjQ0lObNm+fp5xFC5L0PP/yQ06dPs2nTJry8vFwdTp6pUqUKb731FhMnTuSXX36hb9++rg5J3EUkmXJD+dH5HOCjjz4iICAAs9nstDN4+qlhjEYjnp6eGZbNTlO5bcLjkJAQSaaEcHNnz55l+vTpPPzww3Tu3NnV4eS58ePHM3/+fMaPH0/Xrl3deiR3UbhIMuVGtNYkJiZy4MABAMqVK8e1a9dum7LlTrdDQ0P5+uuvC7QzqW06nGPHjhXYOYUQd2bixIkopZgxY4arQ8kXJpOJuXPn0qlTJ/79738zbdo0V4ck7hKSTLmRb775hr///ptff/2VEiVKsGTJEjw8PG6bVDj9vuyUMZlMjBs3rsCfyjGZTNSqVcve2iaEcE8bN25k6dKlvPPOO1SuXNnV4eSbe++9l6FDh/Lhhx/y+OOPy2wLIk9IMuVGWrRowblz57h48SJBQUFERkbeVsbWcdKxv9K1a9d48803KVOmTIHFmhMNGzZkz549rg5DCJGB5ORknnvuOapVq1YkJgaeMWMGv/zyC+PGjWPt2rUyWLDINUmm3Ejjxo2pV68e06dP56mnnsr29AeLFy/m+vXrbptMNWrUiMWLFxMdHY2/v7+rwxFCpPPpp59y9OhRVqxYcVd1Os9I2bJlefvtt5kwYQLLli1j4MCBrg5JFHIyNIKbOXnyJMnJyTnufH7hwgXOnTtHeHg4Fy9e5PLly0RERHD9+nVu3rxJVFQUsbGxxMfHk5SUhMViwWq15tOnSMs2Y/uRI0cK5HxCiOy7cuUKU6ZMoXv37kXqCbcxY8bQuHFjJkyYQGxsrKvDEYWctEy5mTt5kq9jx46sW7eOc+fOpRmJ3PE1o313klCFh4fz6KOPUqZMGapWrZrlKO22ZOrQoUO0bds2x+cTQuSf1157jbi4OGbNmlWkbncZjUbmzJlDhw4deP/993n77bddHZIoxGQEdDdy+fJlypYte9t+Dw8PjEYjJpPJPp+dyWQiJSWFiIgIe7latWoxZMiQfI/zn3/+4eTJk1y+fJlHH32UN998M9PyWmtKlCjB0KFDmTt3br7HJ4TInt27d9O6dWteeuklPvjgA1eH4xKDBw9mxYoVHDt2jKpVq7o6HOHGMhsBXZIpNzNgwACOHj1KaGgokJqI2AbKtC3JyclYLBY2b97M0KFDMZvNFCtWjNatW1OlShVGjRpFw4YN3eqvzA4dOgDwxx9/uDgSIQSA1Wqlbdu2nDt3jtDQ0DydB7QwOX/+PLVr16Znz54sXbrU1eEIN5ZZMiW3+dzMwYMHadmypX1bKWVvjUpvyJAht7VE/fPPP3z99dcsW7bsjmOIiorio48+uuP3O9OoUSN+/PFHtNZuleQJUVR999137N69m++//77IJlIAlSpV4rXXXmPy5Mls3rz5rhysVOQ/SabcSGRkJKdPn2bEiBEZlomLi+Pw4cNordP0e3JcWrVqlenxrI6tWbOG8uXLOy1naymzrXt5eXH27Nksn9Jr1KgRUVFRnDt3TiYZFcLFIiMjefXVV7nnnnsYNmyYq8NxuYkTJ/LNN98wfvx4Dhw4UODj8YnCT/7HuJFDhw4BqUMkZGTjxo188MEHBAUFYTab72jx8vLC19cXLy8v++Lt7Y2XlxdGo5GuXbvi4eFx26KUcro/O49SO3ZCl2RKCNd66623iIiIYM2aNdJSDHh7ezNjxgweeughvvjiC8aMGePqkEQhI8mUGzl48CAATZo0ybBMr169aNu27W39p9IvzvYnJyeTnJxMUlISMTExJCUlkZiYSFJSkn3d9nRfdHQ0jRs3Zvjw4Xny2WyTNh86dIg+ffrkSZ1CiJwLCQnhk08+YcSIETRr1szV4biNAQMG0LlzZyZNmsSgQYMoWbKkq0MShYgkU27kr7/+olSpUpQrVy7DMh4eHgQFBeVrHP/73//YsWMH7dq1y7M6/f39qV69ur31TQhR8LTWjB8/Hn9/f959911Xh+NWlFLMmjWLJk2aMHnyZHnyWOSIJFNu5ODBgzRu3DjPmt1XrlxJv3797NuOt/O8vLzw8/OjX79+eHikjt2qlEJrTXR0NFOmTKF48eJ5EodNo0aNJJkSwoWWLVvGxo0bmTNnTr7/UVYYNWzYkNGjR/PZZ5/x7LPP0rBhQ1eHJAoJGRrBTVgsFvz8/Bg3bhwffvhhntdvtVpJSEiwL/Hx8cyfP58JEyYU2JfqlClTmDZtGtHR0fj4+BTIOYUQqeLi4qhbty4BAQHs27dPOlln4Nq1a9SqVYsmTZqwceNG6VMm7DIbGkGmk3EToaGhJCYmZtr5PDc8PDzw8fEhMDCQ8uXLU6NGDacDhOanZs2aYbVa+euvvwr0vEII+OCDDzh37hyzZ8+WRCoTJUuW5J133mHz5s25GmJGFC2STLmJ7HQ+L+yaN28OwL59+1wciRBFy5kzZ3j//fcZNGgQ9957r6vDcXu2gY9ffPFF4uPjXR2OKATkzxM3cfDgQTw9Paldu3aBnbNixYp89NFHmM3mTMtprTNcILXVy2Aw3Paafp+Hhwf+/v4sWLAAb2/vLMtndSz9vqpVqxIQEFAAV06IwuXFF1/Ew8MjX7oQ3I2MRiOzZs2iS5cuzJgxg0mTJrk6JOHmJJlyE/v27aNhw4aYTKZc1dOrVy8OHjyIyWSyJxzpF6PRmGbbMTlxdtxoNBIcHGwfa+pOF0gdbfjMmTMkJSVl6z05OWfx4sUlmRIinfXr17Ns2TLeffddKlas6OpwCo3OnTszcOBApk+fzhNPPEGlSpVcHZJwY9IB3Q1YrVYCAgIYNmwYn376aa7qunbtGnFxcVgsFlJSUrJcslNu3bp1vPnmm1SvXj3Xn3Xy5Mm8++670gldiAKQlJRE48aNsVgsHDlyBE9PT1eHVKicOXOGunXr0r9/fxYuXOjqcISL5XpuPqVUD2AWYAC+1lq/l+74UOCVW5sxwGittfQyzqbQ0FCio6PTzMl3p0qWLJnjweaSkpJYsWIFcXFxxMfHEx8fT0JCAklJSUDq1BOVK1fOdWyQ2m/K1gm9bdu2eVKnEMK52bNnc/z4cVavXi2J1B2oWrUqL730Eu+88w7PPvus9DcTGcoymVJKGYC5wP1AOLBHKbVSax3iUOw0cK/W+oZS6gHgS6B1fgR8N9qzZw/AHSdTycnJJCYmOh0JPTvLuXPnuHr1Kg8//DDe3t72sajMZnOePxZs64S+d+9eSaaEyEcXL17krbfeok+fPvTs2dPV4RRar776Kt999x1jx45l//79ue6KIe5O2WmZagWc1FqfAlBKLQL6AfZkSmu93aH8TkBuzOfAnj178PX1pW7dunf0/ueee47q1atjNBpzvHh5eVGvXj0aNGiAn59fHn+y21WoUIEyZcrIE31C5LOXX36Z5ORkZs6c6epQCjUfHx9mzZrFgw8+yJw5c3j++eddHZJwQ9lJpioA5x22w8m81elpYE1ugipq9uzZQ7NmzTAYDHf0/kqVKhETE5OrGNauXZtm29aXztYy5di3ztZpvW/fvvYJjLNLKUXz5s2R/nJC5J/ff/+d//73v0yaNIkaNWq4OpxCr1+/fvTo0YMpU6YwaNCgTKf8EkVTdpIpZ/d5nPZaV0p1JjWZap/B8ZHASCDP+uAUdklJSRw8eJCxY8fa93399dfMmjWL1q1bp3n6Jn2Ck5/7HKXfZ+u0npCQkN2PmUbz5s1Zu3YtsbGx+Pr63lEdQgjnLBYL48aNo3Llyrz66quuDueuoJRi9uzZNGjQgJdeeokff/zR1SEJN5OdZCoccHwmtCJwMX0hpVQj4GvgAa31NWcVaa2/JLU/FS1atHDNY4Ru5siRIyQmJqbpLzVs2DBatmzJ4sWL05R11n8pO/t+++03du7cmUcR/79///vfuXr/m2++KbcghMhjn3/+OYcOHWLp0qXyxGweqlWrFi+//DLTpk1j5MiRdOzY0dUhCTeSnWRqD1BLKVUNuAAMAoY4FlBKVQaWAY9prcPyPMq7mLPO50lJSZQoUYKRI0ditVrtS0pKSprt7O6rV68eJ06cuG1/+u2bN28SFhZGQECAvTVKa43VarW/ZmfJrOzTTz/NU089RalSpShTpoxLrrkQd6uIiAgmTZpE165dGTBggKvDueu89tpr/PDDD4wZM0Y6o4s0skymtNYWpdRY4DdSh0b4Rmt9VCn17K3jnwOTgZLAp7daRSwZjcUg0tq1axclS5akWrVq9n1vvPEG8+fPJzY21r5vwoQJtGnTxj6SePqRxZ3tNxqNeHh44OfnR9WqVTMta1uqVKlSIPN21a5dm+3bt2ddUAiRbS+//DIxMTHMnj1bJujNBz4+Pnz88cfSGV3cRgbtdLHg4GDq1q3L//73vzT769evT1xcnD3Z6dSpE+XLl7cfd+zv5DhKuG3dlfsCAwNp165dpp/7qaeeYuXKlURERMiXvhB5YMuWLXTu3JnXXnst17fgRca01vTq1Ys///yT0NBQ6YxehOR60E6RP65cucKJEyd45plnbjt29OjRbNXheBsu/S05x31Wq5U//vjDPjp6VottdPSclktJSSEpKYl169ZlGnfbtm2ZP38+J06cIDg4+I6unxAiVWJiIqNGjaJ69eq8+eabrg7nrmbrjF6/fn1eeOEFGRldAJJMuZTtNldWrTiZUUpla0iF5ORkPv30Ux544AE8PT3x9PTE19fXvm5bvLy87K+O8/tlNAFx+tfstjLdc8899msgyZQQufPee+8RFhbG2rVrpdN5AahZsyavv/46U6dO5fHHH+eBBx5wdUjCxeQ2nwtNnDiROXPmEBkZme9TPWit2bRpE7GxsSQnJ2OxWEhOTs50PSUlBQAPDw8mT56cp/FYrVYCAwN59NFH+eKLL/K0biGKktDQUBo1asTAgQNZsGCBq8MpMhITE2natCmxsbEcPXq0QAY9Fq4lt/nc1LZt22jRokWBzJmllOK+++7L8LjVaiU5OZmkpCR7MmVbnz9/fp7H4+HhQdu2baUTuhC5oLVm9OjR+Pj48NFHH7k6nCLF09OTr7/+mvbt2/Pmm2/y8ccfuzok4UKSTLlIfHw8+/bt44UXXijQ886ZM4dr11KHAXPsxK6UwmQyYTabMZlM9sVsNvPII4/kSyz33HMPU6ZM4caNG5QoUSJfziHE3ez7779n8+bNfPHFF5QtW9bV4RQ599xzD6NHj2b27NkMHjyY1q1lStqiSpIpF9mzZw/Jycm56i91J65evcrUqVML9JwZuffee9Fa8/vvv9OvXz9XhyNEoXLp0iUmTJhAu3btnD7EIgrG9OnT+d///seIESPYt2+fjD1VREky5SJbtmxBKUW7du347rvvOH36dIGcNyoqqkDOkx2tW7fG29ubTZs2STIlRA5orRk1ahQJCQnMnz8fDw8PV4dUZBUrVoxPP/2Ufv368eGHH/L666+7OiThApJMucjGjRtp2rQpgYGBnD592m1aiwqSp6cn7du3Z9OmTa4ORYhC5ccff+SXX37ho48+olatWq4Op8jr27cvDz/8MG+99RZ9+/alQYMGrg5JFDB5ms8FYmNjKVGiBBMmTOCDDz5g0aJFHD9+HK01FovF3vE7KSmJxMTENNtJSUn8+uuvTickdjf33HMP27Zty7TM9OnTef3117l8+TKlS5cuoMiEKLwuXbpEvXr1qF+/Plu3bs3W0Cgi/0VERNCgQQPKly/Prl27MJvNrg5J5DF5ms/N/PnnnyQnJ9O1a1cABg0axLPPPss///yD0WhMM+ZTsWLFbhsLavTo0dSsWTPNCOTutOREly5dgNTbnvnV0V2Iu4Xj7b1vvvlGEik3UqpUKb788kv69+/PO++8wzvvvOPqkEQBkmTKBTZu3IjZbKZ9+/b2fY8//niBdEZv1qwZgYGB+ZZIOZv/L7MFwGQyMX36dA4ePGjfP2rUKCpUqJDv10OIwuTbb7+1396TwW7dT79+/XjiiSf497//Ta9evWjTpo2rQxIFRG7zuUDz5s3x9/dny5YtuaqnX79+nDp1yj6EgdFozHLE8kaNGqUp53gs/bq3tzdDhgzJ97nz+vTpw/Hjxzlx4kS+nkeIwuzEiRM0bdqUVq1asX79emmVclORkZE0atQILy8vDhw4ICPS30XkNp8buXr1KgcOHOCtt97KdV3pJ0fODts8fSkpKfbFarVy7do1pk2bhtlstu9XSjF48OB8T6a6devGqlWrOHnyJDVr1szXcwlRGCUlJTFkyBDMZjPff/+9JFJurHjx4syfP5/77ruPiRMn8umnn7o6JFEAJJkqYGvXrkVr7bK5nGy30YzG//+n11oTHh7Offfdx9ChQws8pl69ejF+/HhWr17Nc889V+DnF8LdTZ48mb179/Lzzz9TsWJFV4cjstClSxcmTpzIjBkz6NKlCw899JCrQxL5TG7zFbBHH32U33//nQsXLhTY2DArVqxg9+7dGT5dopTCbDbz6KOPUr169QKJKb26detSqVIl1q1b55LzC+GuNm3aRNeuXXnmmWf48ssvXR2OyKakpCQ6duzIsWPHOHDggMu+W0Xekdt8biI5OZm1a9fyyCOPFOgge5cuXcLf35/KlStTqlQpOnTogLe3d4GdPzt69erFJ598QkxMjEwYKsQtly5dYsiQIQQHBzNz5kxXhyNywGw2s2jRIpo0acKjjz7Kn3/+WSDzsArXkGSqAP3xxx9ERUXRu3fvAj3vqFGjuHnzJlevXmXbtm08//zz1K9fH6PRaF9MJlOm27Z9JUuWpEaNGnkeY69evfjPf/7Dhg0b6N+/f57XL0Rhk5yczCOPPEJ0dDQbN27E19fX1SGJHKpatSrz589nwIABvPLKKzIZ8l1MkqkCtGrVKjw9Pe3jS9mEhIRQv359F0WVcxMmTEgzaKjWOs221Wrl6aefpmnTptmus3379hQrVoxVq1ZJMiUE8Morr/Dnn3+yYMGCQvX9INJ68MEHGTduHLNmzaJ169YMHjzY1SGJfCB9pgqI1prq1atTt25dfv311zyp87fffmPNmjWUKFEiTTKjlMrWtm1cqPTjQ9me3svuq23dtq21pmfPnjme5mLIkCGsW7eOS5cuyWShokhbsmQJjzzyCOPGjWP27NmuDkfkUlJSEvfddx/79u3jzz//pFmzZq4OSdwB6TPlBnbv3s2ZM2eYMmVKntWZUSKcfn9G21prrFYrHh4e9nXAnlDFxcURExNjHz7B9pqd9T///JOUlBTef//9bCdVjz76KAsXLmTTpk107949p5dDiLvC/v37eeKJJ2jbti0zZsxwdTgiD5jNZpYuXUqLFi3o378/e/fulemz7jLSMlVAXnjhBebOncvly5cJCAhwdTh2tiTKarWitSYlJYXk5GSSk5N54YUXqF+/vn0wT8cBQLO73rVrV4oXL56tWBISEihTpgwDBw7km2++yedPLoT7uXDhAq1atcJgMLB7927Kli3r6pBEHtq3bx/t27enZcuWbNiwQebvK2Qya5mSZKoAWK1WKleuTPPmzXM80Ob8+fM5e/Zsrs5v+zd2Nvims2O2DufVqlXj0UcfzdW5c+rxxx/nl19+4fLly/JFI4qU2NhYOnTowIkTJ9i2bRuNGjVydUgiHyxYsIChQ4fy2GOP8d133+X7oMgi78htPhfbvn07Fy5c4IMPPsjxe8PDw9MkPBmtZyaz486OWSwWLBYLx44dY+rUqVnGGBERwZEjR0hISLhtiY+PJzExkV9//ZX77rsvy7oeffRRfvjhB9atW1fgTz0K4SoWi4WhQ4fy119/8csvv0gidRcbMmQIp06dYtKkSVSoUIHp06e7OiSRBySZKgDz58/H19eXvn375vi9kyZNyla5w4cPs2vXLvu2Yydxx87hmR1z7EDuePsvfb+o9Mv+/fuZNGkS/v7+eHl53bZ4enpme3yV+++/n6CgIObPny/JlCgStNaMGjWK//3vf3zyySf07NnT1SGJfPbGG28QHh7Oe++9R4UKFRg7dqyrQxK5JMlUPouKimLRokUMGTIkXwajjI+P5/jx4yxZsoTvvvuOmJgYYmJi7J3J89KhQ4coXbr0bX2jRo0alWdj4JjNZoYPH86sWbO4fPkyZcqUyZN6hXBHWmsmTpzIN998w+TJk+WXahGhlGLOnDlcunSJ8ePHU6pUqQLvUiHyliRT+WzhwoXExcXxzDPP5Ev9S5YsIT4+nvvuu4++ffvi5+eHn58fPj4+9r5PBoMhzVKQo6/fiWeeeYb//Oc/fPfdd7z88suuDkeIfPPuu+/y0UcfMW7cuGzdUhd3D6PRyMKFC+nRowdDhw7FYDDIHH6FmHRAz0daa1q2bElSUhJ//fVXjjsarl+/noMHD9qfrktKSiI5OZmUlBR769Dff//Nf/7zHypUqJBm3KjCrkOHDly+fJnQ0NC74vMI4UhrzbRp05g8eTKPP/448+fPd/s/ckT+iI6OpkePHuzevZuffvqJBx980NUhiQxIB3QX2b59O/v27WPOnDl3lBBcu3aNy5cvYzKZMJvN+Pj4YDKZ0owLFRAQwH//+980wxtkNK5UZh3Yc7pu+wK4//777+DKZG3UqFE89thjrFmzRvqQiLuK1po33niD6dOnM3z4cObNmyeJVBHm7+/PmjVr6N69O4888giLFi1i4MCBrg5L5JC0TOWj/v3788cff3Du3LkCm1fr6NGjnDt3LsvO4+n3ZaeM474rV64wd+5c+3k///xzRo0alWefIzk5merVq1OzZk02b96cZ/UK4UpWq5UXX3yRjz/+mJEjR/LZZ59JIiUAiIyM5IEHHmDXrl189tlnjBw50tUhiXSkZcoFQkNDWblyJW+88UaBTlA6Y8YMrly5ctskxY6TFRsMBqcTGtv22/Y5m+zYtr9Ro0Z069YtzTQ069atu21qGpPJRNu2bXPcMmcymZgwYQITJ05kz549tGzZMp+umBAFIz4+nuHDh7NkyRKee+45Zs6cKbewhV3x4sXZsGEDjzzyCKNGjeLy5cu8+eab8n+kkJCWqXzyxBNPsGjRIs6ePZvpE2nHjh2jY8eOmdblOH9edl4h7ZQxjsMcpKSkkJKSgsViSTNNTPolq/8X/fr1S1Nn+qEUbLccfXx8WL58OV5eXjm8gqlPQlauXJkuXbqwbNmyHL9fCHcRERFBv3792LFjBx9++CEvvvii/JIUTiUnJzNixAi+++47nnrqKT799NNsDy0j8pe0TBWwo0eP8sMPP/D8889n+Wh/cHAwISEhtyUvjn2UbIlKVq8nTpxg8uTJVK9ePc0xx75OjklXVouzch4eHlSpUoU33ngjfy6eg2LFivHCCy8wZcoUdu7cSZs2bfL9nELktQMHDjBw4EAuXbrEkiVL5IktkSmTycT8+fOpXLky77zzDiEhISxbtoxy5cq5OjSRCWmZygcPPvggmzZt4tSpU5QsWbLAznvkyBE+++wzWrZsmeZWW24Wx3n2srN4enpSsWLFPPtMMTEx1KhRgzp16rBlyxb5a14UKvPmzWPMmDEEBQWxdOlS+YNA5MjSpUsZPnw4xYsX56effqJ9+/auDqlIk7n5CtDGjRvp2rUr77zzDm+++WaBnltrTXh4eJYjludkWbhwIUeOHLFPguysbsdbfIGBgezatStPO9XOnTuXsWPHsmzZMnlsWBQKUVFRjB8/nu+++46uXbuyYMECSpUq5eqwRCF06NAhHnzwQc6cOcObb77JpEmTMBrlppIrSDJVQBISEmjYsCGQ+gPg7e3t4ohy7/vvv+fUqVP5fh6j0UiDBg2AtPMFKqWwWCy8+OKLREVF8dlnn+Hj45OmXPpXOZb9Y+4QgyuOpb+NndH6nbSEbty4kaeeeorw8HDeeOMNpkyZgsFgyHE9QthERUUxduxYfvjhB9q2bcv3339PzZo1XR1WkSPJVAF57bXXeO+991i/fj1du3Z1dTiFSlhYGHFxcWn6jjn2GTty5AhPPPEEAwYM4LXXXktzzPHV2T455vyYO8TgimOOi2O/QmfrOREfH8/GjRvZt28fgYGBPPjgg3l6y9uR1trtbnn//PPPHDlyJFtl0z84k52HaxzL2bofpP/3hNv/jZ0t2SmXk7pyIjf95hYuXMjo0aNJSEhg0qRJvPTSS5jN5juqS+ScJFMFYMOGDXTr1o2nn36ar776ytXh3JVefPFFPvroI37++WcGDBjg6nCEACAlJYV58+bx+uuvc+PGDcaPH8+7775rb0G9mzne4t+4cSN79+5N87SwxWKxL45PEjvuc7ad0attvVixYixatMjpgzOA0/13Ui6ndRWEixcv8vzzz/PTTz9Rt25dZs+eLX+8FxBJpvLZ+fPnadmyJSVLlmTPnj1F4kvUFZKSkujQoQPHjx9n79691KpVy9UhiSJMa83q1auZNGkSBw8epGPHjnzyySc0atTI1aHlqw8//JCZM2dSpkwZatSoQePGjfPsgZfsLuXLl6d+/fquvhQu9euvvzJmzBjOnDnD/fffz3vvvUezZs1cHdZdTZKpfHTz5k3at2/P+fPn2b59e5H/Ac9vZ8+epXnz5hQvXpxt27ZRtmxZV4ckihitNWvWrGHq1Kns2bOH6tWrM23aNAYNGuR2t97yg8Vi4fLly1y+fJmffvrJPoac4xAsjuvOFETZrORnWavVyrFjx5yOxZf+VnJWt5ozK2u1Wrl69SpXrlwhJSUFf39/SpYsiaenJ1arla5du/Lpp59mGbPInsySKXkkIBdu3LhBz549CQsLY+3atZJIFYAqVaqwevVq7rvvPrp378769espXbq0q8MSRUBMTAw//PADs2fP5vjx41SpUoWvv/6axx9/HJPJ5OrwCozRaKRChQpUqFBBWkIy8Pfff9OnTx+MRmOaPl9msxkvLy98fHyoWrUqAwYMuK1/WEbrjoMypz8eExPD999/z8KFCzlz5gwtW7bkiSeeoE+fPi6+EkWHtEzdofPnz9OrVy9CQ0NZtGiRPLJfwNavX0+/fv0oX748a9eulSdbRL6wWq1s27aNH3/8kcWLFxMZGUmLFi147rnneOSRR1zS+XfSpElcvnyZsmXLpvl/n1Hn6eysu9N73L11LzcxWiwWEhISSEhIIDAwkLfffjtPY4uOjubrr7/mo48+Ijw8nLJly/LEE0/w1FNPSbeIPCC3+fLY6tWrefzxx0lOTmbZsmXS+c9Fdu7cSe/evUlOTuaLL75g0KBBrg5J3AWSk5PZvn07q1evZsmSJZw5cwYfHx8GDBjAv/71L9q0aePSX/h//PEHISEhhISEcOrUKQICApx2lnbczs56bt6Tvk9T+ifwMlqcPamX0RAVGe3LrKyvry89evQoiH8Wt5KcnMyvv/7KvHnzWL16NVarlcaNGzNgwAAGDBhA/fr13T5pdUeSTOWR8+fPM3HiRH766ScaN27MkiVLJNt3sdOnTzN06FB27NhBv379+PDDD+XfROSI1WolJCSEP//8k82bN/Pbb78RGRmJyWSiS5cuDBs2jP79++Pn5+fqUN1W+v48zvr92JbFixfbh1DIqD9QduvLatvLy4sFCxa4+Oq41sWLF1m0aBHLli1j+/btaK2pUqUKXbp0oUuXLnTu3JkKFSq4OsxCIdfJlFKqBzALMABfa63fS3dc3TreE4gDntBa78+szsKSTGmtOXjwIJ988gk//vgjBoOB119/nZdeeumOJu8Vec9isfCf//yHadOmkZCQwCOPPML48eNp1aqV/PUl0rBYLJw8eZLDhw9z6NAh9u/fz/bt27l58yYAZcuW5YEHHqB379507dqVYsWKuTbgAhYdHc3evXvTDFdgsVhITk6+bV9GZaxWq/3nzlnHbaUUU6ZMccnnK+ouXbrE//73PzZs2MDmzZu5fv06AJUqVaJFixY0b96cFi1a0KBBA8qXLy/fn+nkKplSShmAMOB+IBzYAwzWWoc4lOkJjCM1mWoNzNJat86sXndOpqKioti+fTtbt25l+fLlhIaG4u3tzTPPPMOLL75IlSpVXB2icOKff/7h/fffZ968eURHR1O9enUefPBBunTpQps2bQgMDHR1iCKfWSwWrl69yuXLlzl37hynT5/m9OnTnDlzhtOnTxMaGkpCQgKQemuqTp063HPPPbRv35527dpRo0aNIv0LZMeOHbz22muYTCaMRuNtS0b7HZecTiWltS7woRWyc/uxTJkyVKtWLZ+utOtZrVYOHTrE5s2b2bNnD3v37uXEiRP2476+vgQHB1O7dm1q1apFpUqVqFChAhUrVqRChQoEBgYWuZ+V3CZTbYGpWuvut7ZfA9BaT3co8wWwRWu98NZ2KNBJa30po3oLKpnSWpOUlGTv9BcfH09CQgLR0dFERETYlwsXLhAaGkpoaChnzpzBarViNBrp0KEDgwYNYuDAgQU6abG4c1FRUfz0008sW7aMDRs2kJycDED16tWpVasWwcHBVK5cmVKlStkXf39/vL298fHxwdvbG29vb5kCJA84GzHaarWSlJREcnIySUlJ9iWj7ZiYGGJiYoiOjna6REREcOXKFSIiIrh27dptMfj4+FCtWjWqVq1KnTp1aNiwIY0aNaJu3brSuuwm1q5dy5dffpnhyOO2fbbX9CPUZ7Yvs/oyOp/Wmh49euR5B3F3FxkZyf79+zl27BhhYWFpfiemzxW8vLwICgqiRIkSBAYGpln8/f3x9fXFx8fHvjhum81me3JuWxy3HRN3d0rYcptMPQT00Fo/c2v7MaC11nqsQ5lVwHta6z9vbW8EXtFaZ5gt+fv76+bNm+f4w2RXTEwMBw4csP8wZcXDw8P+y9THx4fixYtTrFgx+YVayKWkpBAdHU1UVBQxMTHEx8cTHx9PSkpKtt6ffnRjZ51x80t+1p/+5z6vt/ObwWDAaDRiMBjsX8BmsznNq5eXF15eXkVq2ILCKjExkaioKMD5dEDp1/O6XH79f05JSaF48eIEBQXlSX2uYmuUSExMtC+2P3hst3cdX/Pr+yCj72OAcuXKUaNGjXw5r83WrVtzNc6Us2/09FcqO2VQSo0ERgJ4enpm49R3zmw2U6FChQybcdN/Cd9p0mS1WomJicHPz89p83ZGx9Pvt1qtREZGEhcXR9myZZ3GY7VaiYqKStMPwd/fn+joaACKFSuW5hwpKSn8888/9uTQdh7beYHbYnN23NfXl9jY2NvKRUVFYbVaiY2NBcDPz49ixYoRHR2dJsb0cWV1jbK6pjlhMBgICAggICAgzf6UlJQ0Xwa2qS7SD7IHt/8F6+y1MHH2aHdBbmc0fo6zfbafV1viZJuTTRRezn6+PT09KVWqlIsjy3uOrWOFmVIKT0/PbP/e1lrbv0+dvWb2kEH6/bb6nL06rru8f6OzD5KuObQt8JvD9mvAa+nKfEFqPyrbdihQLrN6mzdvru8GW7Zs0S1atNBbtmzJ9Pi6dev0li1b9JYtW3RCQoLevn277tq1q96+fbvWWuv169fr0qVLa7PZrEeOHKmfe+45vXz5cnt5rbVet26drly5si5XrpwOCAjQFSpU0P/61790cHCwDg4O1qtXr9YffvihHjdunF6xYoUeM2aMNpvNunjx4rpNmza6T58++tVXX9VBQUF6xIgR+sMPP9RNmzbVc+bM0ZGRkXr79u16y5YtumvXrnrFihW6Y8eOOigoSE+YMEH7+/vrqVOn6oSEBB0ZGanHjBmjg4KCdKlSpbTRaNQmk0mXLl1aDxw4UAcHB+vq1avrwMBA3ahRIz1jxgz9wgsv6CtXrujIyEj9xRdf6MjISPt12LJli+7YsaMeOnSovnLlit6+fbvu0qWL/uKLL+yfXWttL++4T4iixp1+Du4klvTffXdaT2FXEJ+5KF7X/ATs1RnlShkd0P+fGBmBU0A1wAz8BdRPV6YXsIbUFqo2wO6s6r3bkynbf+J169bpFi1a6Llz5+oWLVrYy27ZskWvX79eb9myRUdGRuoXXnhBm81mrZTSxYsX10opHRQUpKtUqaJXrFih586dq8eMGaN9fHy0j4+PBrSHh4cuWbKkDggI0GXLltWVK1fWJpNJK6V0qVKltK+vrya1hdC+eHh4aMB+ntKlS+umTZvq6dOn67Jly+qffvpJb9++Xffv39/+Htv5jEajHjhwoH722We1yWTSgPb19dWBgYHa399fe3h4aJPJpCtWrKiDg4O1h4eHbt68ua5YsaI2GAz65Zdf1l988YUODAzUc+fO1V988YXu0qWL3rJli/18I0eO1Fu2bNFz587VXbp0SfOF6+xLWIiixtU/B45/ENli2bJlS7Z/aTv7Be/qz5RfMktmCuIz363X1VVylUylvp+epD7R9zfwxq19zwLP3lpXwNxbxw8DLbKqszAlU5n9QGR0LP2XTGRkpF63bp2eO3euXrdune7atav+4osvdNeuXfXHH3+sa9Wqpdu3b6/NZrNu3bq1NhgMulWrVtpsNusOHTpoHx8fXa5cOd2hQwcdHBxsT3QMBoM90QF0uXLldKNGjXTLli1vS6ScLUFBQXrq1Km6QoUKGtDt2rXTc+bM0U8//bQ96TKbzWneExgYqH18fLS3t7cOCgrSzz77rG7SpIkePXq0/te//qVHjBihTSaT9vPz0/Xq1dMDBw7UTz31lB43bpw+cOCAHjp0qF6xYoXu1KmTfvnll3VkZKR+8MEHNaBr1aqlO3XqpNetW2f/wrZx/BIXoihKSEhI08LtCrY/iGw/i1988YVev359tpMqZ9+Zd2sLSvo/th0/p7RMFT6ZJVPZ6nygtf5Vax2sta6htX731r7Ptdaf31rXWusxt4431Jl0PC+Mdu7cyfjx49m5c+dtxzw9PWnbtu1t95KbNWvG888/z8qVK6lZsybFihXDz8+P5cuXk5ycTLNmzejZsydvvvkmp0+f5tKlS9StW5eAgAD7PfagoCA8PDwICQnBZDIRHR3Njh07CAsLs5/H1pHa09OTWrVqkZiYyOHDhwkNDbX3R7A9PeGsr0lUVBRffvklFy5cAGD//v289NJLGAwGqlevjtYai8WSZmThevXq2c8bGxuLwWBgxIgRPPjggxw/fpzIyEiMRiNPPPEEnTt35tdff2Xbtm189tlnvPLKK6xZs4bw8HAGDx7M3r17OXr0KA899BCenp6cP38es9lMXFwcX331FQcOHLDHevToUZYsWcLRo0dz888pRKG1f/9+pk2bhtlszpN+p4mJiezYsYPExESn284MGjSI6dOnM2jQIPvPpMlksj/5NnnyZPbvz3iYwf3792dZJruxZCUv6sjLOh0/e0a/O/JSQZxD3JJRlpXfS2FqmcqqX1RGXn75ZW00GvXLL7+stf7/vxI+/vhj7e/vr+fOnau3bNmimzVrpp977jk9duxY7enpab8V17dvX92lSxddtmxZ7e3trQFdvXp1rZRy2srUvXt3HRgYqJVSunXr1jooKEgbjUZdt27dLFuobOc0GAw6KChIBwUF6cDAQPvxGjVq6KCgIF2hQgU9ffp03aNHD+3h4aFbt26tK1asqGvUqKGfe+45/d577+nKlSvrypUr6127dukxY8Zoo9GozWazrl27tn7llVf0hAkT9Pnz5+1/YUdGRurnnntOe3t766ZNm2o/Pz89fvz42665tEyJoi6vWzbS3wbK6W2h9D+T2Ykpu7f58uIW1Z1+d2cmJ3Gl/6wF3TIl8ha5vc2XH0thSqbu9D/9lStX9Msvv6yvXLmSZv+6det0nTp19Lp16+zrts7gzzzzjL2vk+32muNttnLlyunixYunSYBsfZq8vLzsx/z9/fWbb76pu3Tpor28vJwmUKVLl9aA/T2291WvXl0bDAZdpUoV+/lLly6tS5QooWvVqqXvuece3aRJE3ty5+npqQMCArSPj4/u1KmTva5atWrp6tWr66CgIH3vvfdqb29v7enpqevUqWO/xbl9+3a9fft23bBhQx0YGKgnTZpk7yeWk34V8sUkipq8SDYy+2VfUDFkdN6MYslJjPmRTN1pwpie9GcqfCSZyqW8/kXtWN/69et17dq19dixY3Xz5s31iy++qIsVK5YmgfLy8tINGzbUgO7Vq5fu3bu3VkpppZT29PTUDzzwgL2sn5+ffb1jx472vkuZtUpVrFhRBwQE2PtIZdWKdd999+n7779fA7p9+/a6WLFiukWLFtrPz09XrVpV+/v7a6WULlu2rK5QoYIOCAjQb775ph47dqyePn26Xr9+vb3zakJCgr5y5Yo96evVq5cuU6aMXrFiRY7+HeSLSWTH3ZR058dnyWmdrrieOUmQXPXvnZ3vo7vp/2JRkVkyJQO2ZEN27/HbJCYmsnXrVjZs2MDWrVtv648QFRXF4cOHiYqKIiwsjJSUFFasWEGTJk04duwYTZo0oUSJEvb6Bg8eTJs2bQDYtm0bISEh+Pr6UqxYMbTW7N692142JiYGAG9vb5KSkrBYLAAYjWmHFPP397f3oSpfvrx9jI5SpUplOsBc9erV6dq1K7///jsABw8eJCoqin379hETE0Pz5s154403qFChAv3796dp06bcvHmTmTNnsm7dOpo3b46vr2+ae/nLly9n9+7dmEwmdu/eTUREhL1+R5nd/2/WrBlvv/02zZo1y+JfRxRlOf1Zdmf50R8mO9fHsc/QncSQH/2YMpKba5SbOOvXr8/DDz9MzZo1M6xD+jPdXSSZyoTth6lmzZo8/PDD1K9fP1vv279/PxMnTmTcuHFMnDjR/sVk+6KaMWMGr732GjNmzODnn3+mcePGXL58mR9++IFff/2V7du32wft9PLyomvXrvbO30ajkYYNG2KxWGjYsCE+Pj7cuHEDSJ1LSSlF7dq1SUlJYf/+/fj6+mKxWGjatGmaGNu3b28fyLJLly40bdoUk8lE//79efbZZ9MM42+bcwugXbt2NGrUiO7du1OyZEnat2+Pj48PBoOB4sWLU6ZMGerUqYPBYGDnzp32CWTj4uK4efMmf/31F+PHj+f3339n69atbN26lQcffJBRo0ZRrVo1XnjhBSZMmMDzzz9/25dQZl9u8sUksuNuSrrzIymxJQGZfdflNiHN7fubNm3KiBEjbvtOy2uZPXiUFVvH/OXLl2f4WQsyqRQFIKMmq/xeCsNtPltT7dy5c3WzZs303Llzsz2Oyrp16/SsWbP0unXrbuuPcPLkST106FB98uRJvWXLFj127FhtNpvtt/bKli2b5rZav379dMmSJTWgS5QooWvUqKEDAwPtg2baOpjbbtHZhkkwm826d+/eevTo0bpatWr2saG41c/K19dXK6X0yJEjdYUKFbTZbNZjx47VTZo00X5+ftpoNN7W36pmzZq6SZMmukKFCvb+Vbbbea1bt9be3t66f//+umLFinrEiBE6KCjIPqZVpUqV9IwZMzIcd8vWGd1x8FAZZ0oI5/Lj56Egbk85e5Akv/pB5SbW3PS3sn1G2yDE0jXh7oDc5rsztr9ia9WqRVxcHN988022/pry9PTEz8+PX375BT8/P3tria31ZOPGjaxZs4aNGzdiNps5cuQIAwYMoFatWgwePJgWLVKn/vHy8qJUqVKUL1/ePm9VTEwMf//9NzExMdy8eZPIyEguXrwI/P+w+rZbeyaTiS1btuDt7c3NmzdJTk62T+yanJxMYmKifTodb29vypYtS48ePbjvvvuwWCwEBgby2GOPUaFCBXr27Im/vz8XL16kTp06JCcnEx0dTdWqVYmNjeXChQvs2bMHb29v9u7dy/Xr14mMjCQ2NpZSpUrx2GOPUapUKRo1asTs2bMZNmwYM2bMYMaMGQD2x72PHj3K5MmTAW5rQbibWhWEyK38+HnITp25bQV2NsRJft1+zU29bdq0Yfbs2fYuFjlh+4wnT56UrglFRJYTHeeXFi1a6L17C8dwVImJifam3jZt2mTrSyQxMZH9+/fTrFmz28pHRUWxaNEiBg0ahKenJ/v376d+/focPXqUZs2aERERwcsvv8yAAQMoVaoU9erV4/vvv+f06dM0bdqUBQsWMHz4cCIiItBaU6VKFX7//XeCgoL4559/KFu2LFevXuXee+/l8uXLPPLII2zbto2ffvqJZ555hldeeYVnn32WmzdvYjQaGTJkCCEhIfbPl5iYyI8//kitWrVo3bo1R48epX79+uzevZvQ0FAeeeQR9uzZw8aNG3n++efZuXMnc+bMoXPnzrRo0QKlFGfOnKFv376sXLkyTT3OrofjtQIyvG5CiMLP2XdjZt+X2Xl/XpTNS646r8hfSqkMJzp2WTKllIoAzhbAqYKAqwVwnsJKrk/m5PpkTa5R5uT6ZE2uUebk+mStIK5RFa210xm5XZZMFRSl1N6MMkkh1ycrcn2yJtcoc3J9sibXKHNyfbLm6mskfaaEEEIIIXJBkikhhBBCiFwoCsnUl64OwM3J9cmcXJ+syTXKnFyfrMk1ypxcn6y59Brd9X2mhBBCCCHyU1FomRJCCCGEyDdFIplSSo1TSoUqpY4qpT5wdTzuSik18dYEyhlPzlcEKaU+VEodV0odUkotV0oFuDomd6CU6nHr5+qkUupVV8fjbpRSlZRSm5VSx2599zzn6pjckVLKoJQ6oJRa5epY3JFSKkAptfTWd9AxpVRbV8fkTpRSz9/6+TqilFqolPJyRRx3fTKllOoM9AMaaa3rAzNcHJJbUkpVAu4Hzrk6Fje0HmigtW4EhAGvuTgel1NKGYC5wANAPWCwUqqea6NyOxbgRa11XaANMEaukVPPAcdcHYQbmwWs1VrXARoj18pOKVUBGA+00Fo3AAzAIFfEctcnU8Bo4D2tdSKA1vqKi+NxVzOBl0mdg0840Fqv01pbbm3uBCq6Mh430Qo4qbU+pbVOAhaR+keLuEVrfUlrvf/WejSpvwQruDYq96KUqgj0Ar52dSzuSClVDOgIzAPQWidprW+6NCj3YwS8lVJGwAe46IogikIyFQx0UErtUkptVUq1dHVA7kYp1Re4oLX+y9WxFAJPAWtcHYQbqACcd9gORxKFDCmlqgJNgV0uDsXdfEzqH3FWF8fhrqoDEcD8W7dCv1ZK+bo6KHehtb5A6t2mc8AlIFJrvc4VsRhdcdK8ppTaAJR1cugNUj9jCVKb2VsCPymlqusi9hhjFtfodaBbwUbkXjK7Plrr/90q8wapt27+W5CxuSnlZF+R+pnKLqWUH/AzMEFrHeXqeNyFUqo3cEVrvU8p1cnF4bgrI9AMGKe13qWUmgW8CkxybVjuQSlVgtQW8WrATWCJUmqY1vrHgo7lrkimtNZdMzqmlBoNLLuVPO1WSllJncMnoqDicwcZXSOlVENS/yP+pZSC1FtY+5VSrbTW/xRgiC6V2f8hAKXUcKA3cF9RS8QzEA5UctiuiIua192ZUspEaiL1X631MlfH42baAX2VUj0BL6CYUupHrfUwF8flTsKBcK21rUVzKanJlEjVFTittY4AUEotA+4BCjyZKgq3+VYAXQCUUsGAGZkw0k5rfVhrXVprXVVrXZXUH95mRSmRyopSqgfwCtBXax3n6njcxB6gllKqmlLKTGqnz5UujsmtqNS/TuYBx7TWH7k6HnejtX5Na13x1vfOIGCTJFJp3foePq+Uqn1r131AiAtDcjfngDZKKZ9bP2/34aIO+ndFy1QWvgG+UUodAZKA4dKyIHJoDuAJrL/VerdTa/2sa0NyLa21RSk1FviN1CdovtFaH3VxWO6mHfAYcFgpdfDWvte11r+6LiRRCI0D/nvrj5ZTwJMujsdt3Lr1uRTYT2oXjAO4aCR0GQFdCCGEECIXisJtPiGEEEKIfCPJlBBCCCFELkgyJYQQQgiRC5JMCSGEEELkgiRTQgghhBC5IMmUEEIIIUQuSDIlhBBCCJELkkwJIYQQQuTC/wGTngP5ZUkMwgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_mh(eps[2])"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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EUFXfurA8yWMryUNYLPN3V9VN3eZV2Wfr6pJLkt3A9cDvVdUPeoaOA9ckeWiSHcBO4D8mkbFXkpkkG7rlJ7CY68xkUwFTtL+6g/mC5wF3LDV3DYzygehrLslPJXnYhWUWXxwwyf3U7zjwkm75JcBS/zJcU9NwbGXxVPwfgDur6u96hlZnn03yN8AX8RvjeRavcd7afR3uGXs1i69QOA3sWeNcz2Px7O4+4FvAzd32PwBOsfhqic8BvzsNuSa9v/oyvgu4HbitO8g3T/gY28viKxG+wuJlq4ll6cn0hO4Y+nx3PE0sF/AeFi8l/m93bL0UeDTwceDL3fdHTUmuiR9bwK+xeMnntp7e2rta+8y3/ktSI9bVJRdJ0tIsdElqhIUuSY2w0CWpERa6JDXCQpekRljoktSI/wPs+TUh9DGc+QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_acf(samples[2])"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Acceptance rate: 0.23\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_mh(eps[3])"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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q7k6yFbhn0oEAquqbF6cnuW8leQiLZf6uqrqxW7wq22xdnXJJshe4Dvjdqvp+z6qTwNVJHppkF7Ab+I9JZOyVZCbJpm76iSzmunOyqYAp2l7dznzR84Dblxq7Bkb5QPQ1l+Qnkjz84jSLFwdMcjv1Owm8pJt+CbDU/wzX1DTsW1k8FP8H4I6q+tueVauzzSb5E+BL+InxPIvnOG/pvo72rHs1i1conAX2rXGu57F4dHcf8E3gpm757wNnWLxa4rPA70xDrklvr76M7wRuA27tdvKtE97H9rN4JcKXWTxtNbEsPZme2O1Dn+v2p4nlAt7N4qnE/+32rZcCjwE+Bnyp+/7oKck18X0L+BUWT/nc2tNb+1drm3nrvyQ1Yl2dcpEkLc1Cl6RGWOiS1AgLXZIaYaFLUiMsdElqhIUuSY34P6s5NSGPxvGDAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plot_acf(samples[3])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see from the plots above that the values of $\\varepsilon$ present a trade-off between autocorrelation and proper sampling of the distribution. Using $\\varepsilon = 4$ provided a low acceptance rate and high autocorrelation, but high-fidelity samples."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.8"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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