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@fonnesbeck
Created July 23, 2014 22:43
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{
"metadata": {
"name": "",
"signature": "sha256:d83a937d41b362b5995819c3e5ec2082928fbea97d2c1845d6bc0f09b74a1d27"
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"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"<center><h1>Bayesian data analysis with PyMC3</h1><br>\n",
"<h2>Thomas Wiecki</h2><br>\n",
"<h2>Quantopian Inc.</h2><br>\n",
"<br>\n",
"First navigate **down** and then **right** to view all slides.\n",
"</center>\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "slide_end",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"# About me\n",
"\n",
"* PhD candidate at Brown studying decision making using Bayesian modeling.\n",
"* Quantitative Researcher at [Quantopian Inc](https://www.quantopian.com): Building the world's first algorithmic trading platform in the web browser."
]
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Why should you care about Bayesian Data Analysis?"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from IPython.display import Image\n",
"import prettyplotlib as ppl\n",
"from prettyplotlib import plt\n",
"import numpy as np\n",
"from matplotlib import rc\n",
"rc('font',**{'family':'sans-serif','sans-serif':['Helvetica'], 'size': 22})\n",
"rc('xtick', labelsize=14) \n",
"rc('ytick', labelsize=14)\n",
"## for Palatino and other serif fonts use:\n",
"#rc('font',**{'family':'serif','serif':['Palatino']})\n",
"rc('text', usetex=True)\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {
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"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Image('backbox_ml.png') "
],
"language": "python",
"metadata": {
"internals": {
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": "YmFja2JveF9tbC5wbmc=\n",
"prompt_number": 3,
"text": [
"<IPython.core.display.Image at 0x10bb71b10>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"* Blackbox models not good at conveying **what** they have learned."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Image('openbox_pp.png')"
],
"language": "python",
"metadata": {
"internals": {
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "subslide_end",
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"slide_type": "subslide"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": "b3BlbmJveF9wcC5wbmc=\n",
"prompt_number": 4,
"text": [
"<IPython.core.display.Image at 0x10bb71790>"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "slide_end",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"# Probabilistic Programming\n",
"\n",
"* Model **unknown causes** of a phenomenon as **random variables**.\n",
"* Write a **programmatic story** of how **unknown causes** result in **observable data**.\n",
"* Use **Bayes formula** to invert generative model to infer **unknown causes**."
]
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Random Variables as Probability Distributions\n",
"\n",
"* Represents our beliefs about an unknown state.\n",
"* Probability distribution assigns a probability to each possible state.\n",
"* **Not** a single number (e.g. most likely state)."
]
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"# Coin-flipping experiment.\n",
"\n",
"* Given multiple flips, what is probability of getting heads?\n",
"* Maximum Likelihood answer:\n",
"\n",
"$$\\frac{\\# \\text{heads}}{\\text{total throws}}$$\n",
"\n",
"* However: \n",
"\n",
"$$\\frac{50}{100} = \\frac{1}{2}$$\n",
"\n",
"* Clearly something is missing!\n",
"* **Quantification of uncertainty.**"
]
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Moreover...\n",
"\n",
"* Consider a single flip which comes up heads:\n",
"\n",
"$$ P(\\text{heads}) = \\frac{1}{1} = 1 $$\n",
"\n",
"* Again, this doesn't seem right.\n",
"* Incorporate **prior knowledge.**"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy import stats\n",
"# set every possibility to be equally possible\n",
"x_coin = np.linspace(0, 1, 101)"
],
"language": "python",
"metadata": {
"internals": {
"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## $$ \\text{Express probability of heads as random variable } \\theta$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import prettyplotlib as ppl\n",
"fig = plt.figure(figsize=(8, 6))\n",
"ax = fig.add_subplot(111, xlabel=r'Hypothesis for chance of heads', \n",
" ylabel=r'Probability of hypothesis', \n",
" title=r'Prior probability distribution after no coin tosses')\n",
"ppl.plot(ax, x_coin, stats.beta(2, 2).pdf(x_coin), linewidth=3.)\n",
"ax.set_xticklabels([r'0\\%', r'20\\%', r'40\\%', r'60\\%', r'80\\%', r'100\\%']);\n",
"# fig.savefig('coin1.png')"
],
"language": "python",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 4,
"text": [
"[<matplotlib.text.Text at 0x10f155590>,\n",
" <matplotlib.text.Text at 0x10f157f50>,\n",
" <matplotlib.text.Text at 0x10f16cad0>,\n",
" <matplotlib.text.Text at 0x10f1701d0>,\n",
" <matplotlib.text.Text at 0x10f170890>,\n",
" <matplotlib.text.Text at 0x10f170f50>]"
]
},
{
"metadata": {},
"output_type": "display_data",
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kYSJAA/bss8ATT+h1lwtIS5MXDxH1z/XX6/t/7NoFzJrFWQSJKOxEwO/3o729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\nf7TsSOkFXfvjAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x10f147990>"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"stats.beta(2,2).rvs(1)"
],
"language": "python",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 98,
"text": [
"array([ 0.37833632])"
]
}
],
"prompt_number": 98
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "-"
}
},
"outputs": []
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import random\n",
"import numpy as np\n",
"\n",
"def choose_coin():\n",
" return stats.beta(2, 2).rvs(1) # random.uniform(0,1) # np.random.normal(0,1) # \n",
"# pylab.hist([choose_coin() for dummy in range(100000)], normed=True, bins=100)\n",
"successes = []\n",
"returns = 0.\n",
"for i in range(10000):\n",
" prob_heads = choose_coin()\n",
" results = [random.uniform(0,1) < prob_heads for dummy in range(10)]\n",
" if results.count(True) == 9: \n",
" successes.append(prob_heads)\n",
" if random.uniform(0,1) < prob_heads:\n",
" returns += -1\n",
" else:\n",
" returns += 1\n",
"fig = plt.figure(figsize=(8, 6))\n",
"ax = fig.add_subplot(111)\n",
"r = ax.hist(np.array(successes), normed=True, bins=20)\n",
"print len(successes)\n",
"print \"Average return\", returns / len(successes)"
],
"language": "python",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"719\n",
"Average return -0.613351877608\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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"text": [
"<matplotlib.figure.Figure at 0x1116fb450>"
]
}
],
"prompt_number": 21
},
{
"cell_type": "markdown",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "-"
}
},
"source": [
"$$ \\theta \\sim \\text{Beta}(2, 2) $$\n",
"$$ P(\\theta) = \\text{Beta}(2, 2) $$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize=(8, 6))\n",
"ax = fig.add_subplot(111, xlabel='Hypothesis for chance of heads', \n",
" ylabel='Probability of hypothesis', \n",
" title='Posterior probability distribution after first heads')\n",
"ppl.plot(ax, x_coin, stats.beta(1, 1).pdf(x_coin)*stats.beta(90, 10).pdf(x_coin), linewidth=3.)\n",
"ax.set_xticklabels([r'0\\%', r'20\\%', r'40\\%', r'60\\%', r'80\\%', r'100\\%']);\n",
"plt.savefig('coin2.png')"
],
"language": "python",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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4Hx4YGJCUGuO3bduRgAAAyO3mr3DNuIo127K9JSd+Y0xmhv/y8rISiYRjQQEA\nWls9jO+nNdvM/pIT//r6ugYGBnTx4kXduHFDc3NzTsYFAGhhJH7nlDzGL6XG5m/evEnSBwA4isTv\nnJJb/Gtra/L5fJqcnJTP59Ply5edjAsA0MLqNfE3w+p9NV+rHwCAYuo18bdUi79aa/UDAFAMid85\nNV+rHwCAYkj8zqn5Wv0AABRD4ndO2Wv1AwDghE8/ld59N/v6scfci0VqvsRf8hh/NBqVx+ORx+NR\nd3e33njjDSfjAgC0qFu3Uslfkrq6Ug/KcVOzJf6SZ/XPzMwoHo+ro6NDtm1rfHxcGxsbTsYGAGhB\n9dTNL7Xwkr0ej0cdn/3Z4/V6mdUPAHBEvSX+lm3xd3R06JVXXlF/f79isRiz+gEAjqj3xG+M1Mjz\n20tu8c/Pz2tvb0+rq6uSpJWVFceCAgC0rnpL/KdPZx8L/Mkn0p077sZTqZJb/IFAIG/lPgAAnFBv\nid+yUq3+995Lvb59W3rgAXdjqkTJiX9oaEh+v1+BQEDGGFmWpQsXLjgZGwCgBdVb4pfyE38yWT9x\nleNYLf5AIMDCPQAAR9Vr4k9r9Al+JSf+sbExJ+MAAEASid9pRSf3LS8vq62tTSdOnOBRvAAAx5H4\nnVU08c/NzWl3d1c//OEP9fLLL9ciJgBAi9rbk37+8+xrEn/1Fe3q7+zsVEdHR2bxHgAAnLK7K927\nlyq3t6dupasHzZT4S76PHwAAp9VjN7/UXMv2Fm3xx2Ix+Xw+SZJt25myZVl68803nY0OANBS6jXx\nN1OLv2ji39nZqUUcAADopz/Nlkn8zihpjB8AgFr40Y+y5SeecC+O/XIT/+3b7sVRDYzxAwDqRm7i\nf/JJ9+LYr5la/CR+AEDdIPE7j8QPAKgbuYn/qafci2M/Ej8AAA6gxe88Ej8AoC589JH07rup8smT\n0uOPuxtPLhI/AABV9s472fIXviCdOOFeLPt97nPZeO7ckT7+2N14KkHiBwDUhXod35cky2qeVj+J\nHwBQF+p1fD+tWZbtJfEDAOrC229ny/WY+GnxAwBQRfXe4ifxAwBQRY2U+Bt52V7XE38wGHQ7BABA\nHajnyX0SLf6qiEQiWltbczMEAECdYIy/NlxL/MlkUh6Ph6f/AQCUTEq/+EWqfPq01N3tbjyFkPgr\nFIlENDAw4NbpAQB1ZP/4vmW5F8thSPwViEajCgQCbpwaAFCH6n18XyLxly0ej8vj8ag9dyUEAEBL\nq/fxfakE6PeWAAAUN0lEQVR5Ev/JWp8wFotpZ2dHGxsbkqREIqHXX39dQ0ND6u3trXU4AIA6UO+3\n8kkk/rKNjo7mvQ6FQnr++edrHQYAoI40QuJnyd4KJZNJzc/Py7IsvfLKK4rH426FAgBwGWP8tVPz\nFn9aR0eHpqenNT097VYIAIA60QgtflbuAwCgCoxpvMTfyC1+Ej8AwFXvvivdvZsqd3RIDz/sbjyH\neeih7PoCH3wg3bvnbjzlIvEDAFzVCK19SWpry5/g16jd/SR+AICrGmFiX1ozdPeT+AEArmqExXvS\nSPwAAFSoUbr6JRI/AAAVI/HXFokfAOCqRhrjb4bV+0j8AABXMcZfWyR+AIBr7t2TfvKT7OsnnnAv\nllKQ+AEAqMBf/qW0t5cqP/aYdP/97sZTTDMs20viBwC4ppHG9yVa/AAAVKSRZvRLJH4AACrSSBP7\nJBI/AAAVocVfeyR+AIBrGnmMP5FwL45KkPgBAK55661suRFa/I88ki2/+657cVSCxA8AcMXenvSD\nH2RfP/20e7GU6tFHs+X33kutQ9BoSPwAAFe884704Yepcnd3fmu6Xt13XypWSTImlfwbDYkfAOCK\n730vW/7KV9yL47g+//ls+Wc/cy+OcpH4AQCu+P73s+Uvf9m9OI7rscey5Z//3L04ykXiBwC4gha/\nO0j8AABXNGqLn8QPAEAZaPG7g8QPAKi5nZ3s+Pjp09Iv/ZK78RwHiR8AgGPK7eb/0pektgbKRiR+\nAACOqVG7+SUSPwAAx9aoE/skEj8AAMfWyC3+/ffx7+25F0s5SPwAgJpr5Bb/6dPZp/R9+mlqomIj\nIfEDAGrqzh0pHk+VLUv64hfdjaccjbx6H4kfAFBTb76Z7R7v7U21oBtNI4/zk/gBADXVyOP7aSR+\nAABK1Mjj+2kkfgAASkSL310kfgBATdHidxeJHwBQM3t70g9+kH1N4q89Ej8AoGbeflv66KNU+dFH\npe5ud+MpVyMn/pNunHRra0sbGxtKJBK6du2a5ubm1Nvb60YoAIAaaobxfYnEfyzJZFIbGxuamJiQ\nJEWjUQUCAd24caPWoQAAaix3fL+ZEr8xqcWIGkHNu/q3t7c1NzeXeT04OCjbtnX79u1ahwIAqLHc\nFn+jju9L0oMPSp/7XKr88cdSMuluPMdR88Q/MDCgSCSSeb2xsaGuri61t7fXOhQAQI01S1e/lN/q\nb6Rle12Z3NfT05MpLy0taXl52Y0wAAA11gy38qU16ji/q7P6l5eX9dxzz+ns2bNuhgEAqIH33kt9\nSalu8iefdDeeSjVq4ndlVr+UmtTX19enZ5991q0QAAA19N3vZstf+pLU1uA3lDdq4nel2mOxmDwe\nTybph8NhN8IAANTQn/1ZtvzMM+7FUS2Nmvhr3uK3bVt+vz9vW19fn8bGxmodCgCghv70T7Plv/k3\n3YujWkj8JfJ6vdpLP4gZANAS9vak//2/s69J/O5p8BEWAEAj+O53pUQiVf7856W+PnfjqQYSPwAA\nh/hf/ytb/rVfa5xV7o5C4gcA4BDNNr4vkfgBADhUbuL/tV9zL45qam+XTp1KlT/8UHr/fXfjKRWJ\nHwDgqLfekn70o1T5oYekX/5ld+OpFstqzGV7SfwAAEfltvZ/5Vekk64tHVd9jdjdT+IHADiqGbv5\n00j8AADss39GfzMh8QMAkGNnJ7tG/8mT0l//6+7GU20kfgAAcnz729nywID04IPuxeIEEj8AADma\nuZtfIvEDAJCnGRfuyUXiBwDgMx99JF27ln39q7/qXixOIfEDAPCZa9ekTz5Jlb/0JenRR92NxwmP\nPZYtk/gBAC2t2bv5JcnjkU6cSJVv35bu3HE3nlKQ+AEAjlhfz5abcWKfJLW15bf6G2HZXhI/AKDq\n3npLuno1VW5rkwIBV8NxVKON85P4AQBV95//c7YcCEhf+IJ7sTjt8cez5XfecS+OUpH4AQBVZYz0\nB3+Qff0P/6FrodTEV76SLW9uuhdHqUj8AICq+va3pRs3UuWODunv/T1343Fa7jLE/+f/uBdHqUj8\nAICq+k//KVs+d0564AHXQqmJv/bXsuVr16S9PfdiKQWJHwBQNR9+KK2sZF//9m+7F0ut9PRk1yhI\nJqUf/tDVcIoi8QMAqua//tfU/eyS9PTT0q/8irvx1IJl5bf6v/Md92IpBYkfAFA1uZP6fvu3U0mx\nFTTSOD+JHwBQFe+8k120x7Kk3/otd+OppdzET4sfANAS/vAPU7fySdKzz0pPPeVuPLV05ky2/Bd/\nUd9L95L4AQAVMyZ/Nn+z37u/X1eX9MUvpsqffCJtbbkbz1FI/ACAioXD0g9+kCo/9JD09/++u/G4\noVEm+JH4AQAVSSalf/pPs6+/8Q3pwQfdi8ctjTLBj8QPAKjIP/tn0l/+Zar8+OPSv/yX7sbjFlr8\nAICm953vSP/hP2Rf/9t/m1qmtxX98i9Lp06lytvb0nvvuRvPYUj8AICy3LsnhULZmfx/5+9IwaC7\nMbnp/vulZ57Jvr52zb1YjkLiBwCU5d/9O+n69VT5gQekf//vW2fBnsM0wjg/iR8AcGxvvSX983+e\nff0v/oXU2+tePPWiEcb5SfwAgGO5eVMKBFIP5JGkv/pXpW99y9WQ6sb+FfzSwyD1hMQPACjZ//2/\n0q/+qvTmm6nXbW3S4qJ0333uxlUvfL7UYj6SdOuWZNvuxlMIiR8AUJJvf1v6W39L+slPUq9PnZJW\nV6W/8Tfcjaue7H9SXz2O85P4AQBHMkZaW5OGh6Xd3dS2hx+W/sf/kM6edTe2epSb+P/8z92L4zCu\nJH7btrWwsKBoNKqFhQUlk0k3wgAAHMEY6cqVVNf+2Jj00Uep7Y8+Kl29Kv3tv+1qeHUrd5x/cVH6\n7//dvVgKOenGScfHx7WxsSFJ8vv9mpiY0MrKihuhAAD2uXtXikSkf/2vpT/7s/z3enpSfww8/bQr\noTWE4WHpy1+Wvv996eOPU88t+KM/Sk2IrAc1b/HHYjF5PJ7M646ODkUikVqHAQD4zJ070saGNDcn\njYykJqf9+q/nJ/1Tp6R//I9TY9Yk/aPdf3/qj6P07Y1370q/+ZvS//yf7saVVvMWv23b6uzszNvm\n8Xh0/fp1PZO75JGkvT3p009rGR0AOKOU27r2fyb92pj88t5e9t/078l797L/fvJJKpnfuZNKOh99\nJCUSqa/d3dS/77yTmnFu29KPf3x4TKdOSRMT0uys9MQT5V17K3rySemNN6SvflV6++3U9+LXfz3V\n9f/FL0oeT+rr4YcPLnp00uHMXPPEv7OzU/Jn/9W/Sn0BAGrL50slqm99K5XEcHw9Pdnk/+Mfp9Y9\n+K3fKr6f0/f+1zzxd3d3K5FI5G077I+Bf/NvOpVIvFSDqAAAhfzH/+h2BI3v+eeP9/mrV7+mr33t\na47EIrmQ+L1eb8FEv7+bX5J+53d+pxYhAQDQMmo+ua+/vz/vtW3bCtTLVEcAAJqcZUztVxLe2tpS\nJBKR1+vVtWvX9OKLL6q9vb3WYQAA0HJcWcCnv79f58+f15UrV7S0tKSBgQGtra3lfWZ+fl4+n08j\nIyOKx+N57/n9ft2+fbuWITe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"text": [
"<matplotlib.figure.Figure at 0x325e37a90>"
]
}
],
"prompt_number": 108
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "-"
}
},
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "-"
}
},
"source": [
"$$ P(\\theta | h=1) = \\text{Beta}(3, 2) $$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize=(8, 6))\n",
"ax = fig.add_subplot(111, xlabel='Hypothesis for chance of heads', \n",
" ylabel='Probability of hypothesis', \n",
" title='Posterior probability distribution after 1 head, 1 tail')\n",
"ppl.plot(ax, x_coin, stats.beta(3, 3).pdf(x_coin), linewidth=3.)\n",
"ax.set_xticklabels(['0\\%', '20\\%', '40\\%', '60\\%', '80\\%', '100\\%']);\n",
"fig.savefig('coin3.png')"
],
"language": "python",
"metadata": {
"internals": {
"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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FnQhUVlZy+iBJMX8+oHVAXXYZcM45cuMhGgjz5+vltWuBDz6QFwvFtl7tNbB6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\nmCAAAAUTBACgYIIAABTsCZMBPPXIIDpTAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x10bbaedd0>"
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Image('coin3.png')"
],
"language": "python",
"metadata": {
"internals": {
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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YPFnvz58vLvcSWcFA2QHaYrfbAQAOhwMKV5gjiQ4cAPLz9f6sWWJfJSKzWLhQ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\nRU5ErkJggg==\n",
"prompt_number": 11,
"text": [
"<IPython.core.display.Image at 0x10f773910>"
]
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "-"
}
},
"source": [
"$$ P(\\theta | [h=1, t=1]) = \\text{Beta}(3, 3) $$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize=(8, 6))\n",
"ax = fig.add_subplot(111, xlabel='Hypothesis for chance of heads', \n",
" ylabel='Probability of hypothesis', \n",
" title='Posterior probability distribution after 20 heads and 20 tails')\n",
"ppl.plot(ax, x_coin, stats.beta(22, 22).pdf(x_coin), linewidth=3.)\n",
"ax.set_xticklabels(['0\\%', '20\\%', '40\\%', '60\\%', '80\\%', '100\\%']);\n",
"fig.savefig('coin4.png')"
],
"language": "python",
"metadata": {
"internals": {
"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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EufGUG0WRZ++RiFyenGRyJ1qpgmaFczgccDgcqK+vx4EDB/L6XENDA3bt2oWG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\nyGKY3ImIiCzm/wNJZWk5n7HDSAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10f787bd0>"
]
}
],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Image('coin4.png')"
],
"language": "python",
"metadata": {
"internals": {
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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Mev0jBoAPeDoApZe9iEajsm1blmW5XRLgSc7RjUsukdatc6+WYsI8IMC/PB+A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\nkUhoenpa1ztWu926davuueeezO0Sfbw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"prompt_number": 13,
"text": [
"<IPython.core.display.Image at 0x10bb5c250>"
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_helper": "subslide_end"
},
"slide_helper": "slide_end",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"$$ P(\\theta | [h=20, t=20]) = \\text{Beta}(22, 22) $$"
]
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Bayes Formula\n",
"\n",
"$$P(\\theta| \\text{data}) \\propto P(\\theta) \\ast P(\\text{data} |\\theta)$$\n",
"$$\\text{posterior} \\propto \\text{prior} \\ast \\text{likelihood}$$\n",
"\n",
"$\\theta$: Parameters of model (chance of getting heads)).\n",
"\n",
"* Except in simple cases, **posterior impossible to compute** analytically.\n",
"* Blackbox **approximation** algorithm: Markov-Chain Monte Carlo (MCMC) instead draws **samples** from the posterior."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy import stats\n",
"fig = ppl.plt.figure(figsize=(14, 6))\n",
"ax1 = fig.add_subplot(121, title='What we want', ylim=(0, .5), xlabel=r'\\theta', ylabel=r'P(\\theta)')\n",
"ppl.plot(ax1, np.linspace(-4, 4, 100), stats.norm.pdf(np.linspace(-3, 3, 100)), linewidth=4.)\n",
"ax2 = fig.add_subplot(122, title='What we get', xlim=(-4, 4), ylim=(0, 1800), xlabel=r'\\theta', ylabel='\\# of samples')\n",
"ax2.hist(np.random.randn(10000), bins=20);"
],
"language": "python",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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JtIuLpSVL7MuTq5xOaelSax97DgEAgFyStmKooqLC0g6Hw/J4PJb28FLb/f39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\ngZi9jWIoT7//vbRsmdTZOfnc6tXSyZPSxo32xwX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"text": [
"<matplotlib.figure.Figure at 0x10bbe8510>"
]
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {
"internals": {
"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Approximating the posterior with MCMC sampling"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Image('wantget.png')"
],
"language": "python",
"metadata": {
"internals": {
"slide_helper": "subslide_end"
},
"slide_helper": "slide_end",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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AE6CABwAAAADABCjgAQDATUVHR6t8+fKqU6eOU/+cOXMUFBSk+++/XyNGjLD3T5kyRTVr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\nwHSUIpk4caK2bNmizZs3q2nTpkpKSjIdqVA9evRQRkaGNmzYoFOnTtl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"prompt_number": 15,
"text": [
"<IPython.core.display.Image at 0x10bb5c410>"
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "slide_end",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"PyMC3\n",
"=====\n",
"\n",
"* Probabilistic Programming framework written in Python.\n",
"* Allows for construction of probabilistic models using intuitive syntax.\n",
"* Features advanced MCMC samplers.\n",
"* Fast: Just-in-time compiled by Theano.\n",
"* **Extensible**: easily incorporates custom MCMC algorithms and unusual probability distributions."
]
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Linear Models\n",
"\n",
"* Assumes a linear relationship between two variables.\n",
"* E.g. stock price between Gold and Gold Miners."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"size = 200\n",
"true_intercept = 1\n",
"true_slope = 2\n",
"\n",
"x = np.linspace(0, 1, size)\n",
"# y = a + b*x\n",
"true_regression_line = true_intercept + true_slope * x\n",
"# add noise\n",
"y = true_regression_line + np.random.normal(scale=.5, size=size)\n",
"\n",
"data = dict(x=x, y=y)"
],
"language": "python",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize=(7, 7))\n",
"ax = fig.add_subplot(111, xlabel='Value of gold', ylabel='Value of gold miners', title='Synthetic data and underlying model')\n",
"ppl.scatter(ax, x, y, label='sampled data')\n",
"ppl.plot(ax, x, true_regression_line, label='true regression line', linewidth=4.)\n",
"ax.legend(loc=2);\n",
"fig.savefig('synth_data.png')"
],
"language": "python",
"metadata": {
"internals": {},
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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NWeWjW97XarXi+PHjcLlc0Ov1AOLLmC0vYG0ymVJSKRmNxsQC1J2dnTCZTNDr9Th16hQA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"text": [
"<matplotlib.figure.Figure at 0x10f7eda10>"
]
}
],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Image('synth_data.png')"
],
"language": "python",
"metadata": {
"internals": {
"frag_number": 37,
"slide_helper": "subslide_end"
},
"slide_helper": "slide_end",
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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7cAVkq2iQHSEk7w2OOjCjiiGo4TAtRPFw1JnrKsEfDOCLUScejbkQjoR37Dxf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\nctUitqqycljcUwiYkjHrwwmUF60kF0VRYNzm+fCXGvfim+lRhOVkcm+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"prompt_number": 18,
"text": [
"<IPython.core.display.Image at 0x10ffa6b50>"
]
}
],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Linear Regression\n",
"=================\n",
"\n",
"$$ y_i = \\alpha + \\beta \\ast x_i + \\epsilon $$\n",
"\n",
"with $$ \\epsilon \\sim \\mathcal{N}(0, \\sigma^2) $$\n",
"\n",
"Probabilistic Reformulation\n",
"---------------------------\n",
"\n",
"$$ y_i \\sim \\mathcal{N}(\\alpha + \\beta \\ast x_i, \\sigma^2) $$\n",
"\n",
"### Priors\n",
"\n",
"$$ \\alpha \\sim \\mathcal{N}(0, 20^2) $$\n",
"$$ \\beta \\sim \\mathcal{N}(0, 20^2) $$\n",
"$$ \\sigma \\sim \\mathcal{U}(0, 20) $$\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_type": "subslide"
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"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"## Constructing model in PyMC3"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import pymc as pm\n",
"\n",
"with pm.Model() as model: # model specifications in PyMC3 are wrapped in a with-statement\n",
" # Define priors\n",
" alpha = pm.Normal('alpha', mu=0, sd=20)\n",
" beta = pm.Normal('beta', mu=0, sd=20)\n",
" sigma = pm.Uniform('sigma', lower=0, upper=20)\n",
" \n",
" # Define linear regression\n",
" y_est = alpha + beta * x\n",
" \n",
" # Define likelihood\n",
" likelihood = pm.Normal('y', mu=y_est, sd=sigma, observed=y)\n",
" \n",
" # Inference!\n",
" start = pm.find_MAP() # Find starting value by optimization\n",
" step = pm.NUTS(state=start) # Instantiate MCMC sampling algorithm\n",
" trace = pm.sample(2000, step, start=start, progressbar=False) # draw 2000 posterior samples using NUTS sampling"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"output_type": "stream",
"stream": "stderr",
"text": [
"/Users/alexcoventry/Library/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/theano/scan_module/scan_perform_ext.py:85: RuntimeWarning: numpy.ndarray size changed, may indicate binary incompatibility\n",
" from scan_perform.scan_perform import *\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"# Covenience function glm()"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"with pm.Model() as model:\n",
" # specify glm and pass in data. The resulting linear model, its likelihood and \n",
" # and all its parameters are automatically added to our model.\n",
" pm.glm.glm('y ~ x', data)\n",
" step = pm.NUTS() # Instantiate MCMC sampling algorithm\n",
" trace = pm.sample(2000, step, progressbar=False) # draw 2000 posterior samples using NUTS sampling"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"prompt_number": 20
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"# Posterior"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = pm.traceplot(trace, lines={'alpha': 1, 'beta': 2, 'sigma': .5});"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37
},
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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nU36nvpbVkwvq61cYUEeOaE8yGF0vYpuyN1OEeE5Paxu209ORPcrmzKGczTlz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\nCIIgCIIgCEIQ/wMeLrx0a6olugAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x10ffab610>"
]
}
],
"prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize=(10, 10))\n",
"ax = fig.add_subplot(111, xlabel='Value of gold', ylabel='Value of gold miners', title='Posterior predictive regression lines')\n",
"ppl.scatter(ax, x, y, label='data')\n",
"from pymc import glm\n",
"glm.plot_posterior_predictive(trace, samples=100, \n",
" label='posterior predictive regression lines')\n",
"ppl.plot(ax, x, true_regression_line, label='true regression line', linewidth=5.)\n",
"ax.legend(loc=0);\n",
"fig.savefig('ppc1.png')"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37
},
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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SiIhoThBFEVEqVdATNADQyyMgSRIAQJIk6JSRQY6I5iP2pBER0YLV6+lFaY0N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\n3G73xx7jWG8nXdkIiiLTERxnTTp9TtPXmUyGdwd6iOZSuHQmlpRUiA/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YjIaoZO5u7GtK\nazg4cJJoNoVTa2LlHI0ECh+v099PczSIrNWQjU4R7U+wXEwvXzTyTtLsdjvf//73ZzoOfFqRxTNV\nWVk58+/HH3+cJ554Ys6OLZwZRVG4um4lPSMBVFQqawtFJfPzQFVVft/VTMw4nZblokmyqRSK0zr9\nOJXB5bYuZIgXpEQiwX/8x3/Q1dWF1Wqd2RBQWFjIgQMHMBgMOAsL8JWXoqpZWpuOYJmK8r+l09yT\nSGDPY5R4yGjkx3o9r5eW0viZz1AZDlNeXs63vvUtent7aW5uJhqNotPpuPLKKyktLT0Pr3z+6GSF\nD0726iTlE7/3bJiNJjbXrZzTY16OFjl9NI31g16Dmkyz2PXxv3cD0Ulk7fStXlFkBmOTzM3Eu3A+\n5J2kbdu2jYcffpht27ZRU1PDU089NefBPPHEE9xxxx3ccsstc35sIX8ajYba4ov7RnOxmZgMEdaq\nMyNnsllPhcZMOiORk1TKHAUUukSF9FMmJiZ45plnGBwcRK/X89ZbbyFJEj6fjyNHjjA0NERJSQnV\n1dX0h0Zp3tdEQTjC3ydTfCWVyquMxkmrlUdkmf3l5Vx/001Ud3XhcDj43ve+R0dHBwcPHmRychKT\nycQ111yDz3dptDivL6jggL+LpJTFLulYUVUx+5OE867I7WWz3kAoGsbhsmC3fvzsk1aSmd7ecurx\n3CbdwvzKvzgP8Nd//dfzFQe7du2ipqZmTjYjCMLFxmgwoqaz8F69LFVVsVus81IC4WI2MDDAa6+9\nNtP4fOfOnWSzWUpLS2lra2N4eBi3201tbS0ajYZdu3ZRHgrx41SKW1KpvC54R91uHshmOVFRwZdv\nvZXxY8dQVZWf/exntLW18fbbbxMKhbDb7dxwww0fWfqRyWRoGeolmctQaHZQNscL7+ebz+ni8w4n\nmUxGjKJf4OwWK3bLp4+wLy8o5Z2BDuKKij4LK4trz1N0wlzIO0lbu3btR/p11tTU8Nhjj502XXk2\nDh06hMvlmukN+vTTT5+X0h+CcKEwGgwstxXSPDFEToZCjZnaCjGaeUpbWxu///3vSSQSjI+Ps337\ndtLpNBUVFfT09HD8+HHMZjOrVq2aTs5ef52GcJhfJJNsSaVmPX4OeMfn43vpNMHKSm655RZyR44Q\nj8d57LHHaG1t5a233mJ8fBy3283NN9+M1frxN8e93W2Ma6c34AxODqKiXnQbPiRJEgnaJcJhtXH9\nkkZisRhGo/GsavMJC+eMkrTbbrttpnfn66+/zu233869997Ljh07zjqArq4u1q5de9r/1dTUiCRN\nuOwsKi6jxldMNptFp9MtdDgLTlVVDh06xKFDh9BoNAwODvKb3/yGZDJJTU0Nw8PDNDc3o9PpqK+v\nx2AwsGvnTq4Jh3k+mWRtOj3rOdKSxI7CQh5Ip8lUVvL5z3+e1tZWUqkUP/7xjzl58iS7d+9mbGyM\nwsJC7rjjDozGT58sDaaiaHTT36NoNQxHJy+6JE24tEiShNlsXugwhLOQd5LW1dXFli1bANi6dSsP\nP/wwDz744DkHUF1dTS6Xm/0bBeEyoCgKinJ5rxnJZDLs3buX1tZWTCYTg4ODvPLKK6TTaWpqagiH\nw7S0tABQX1+Poij8btcuvhSJ8GYySV0eZTTiGg3PFRTwg2wWU00NGzdsIBAIoNPp+N73vsfw8DB7\n9uxhbGyMsrIyvvrVr+Y9smSQNXwwAp18ef8850IsHiMUieCy2THk0d9UEC4VZ7y789RIGkyvIxMu\nHslUit5gAIBKb6EYrREuKNFolKamJjo7O3G5XAwMDPDiiy+Sy+VYtmwZU1NTtLW1kUwmWbt2LbIs\ns3/XLu6MRnkkHqc4jw97Ib2e//R6eRTwLVnCupoaUqkUJSUl/Mmf/AmRSITDhw8zNjZGdXU1X/zi\nF884aW4srOJQoJtELoNHa2LZBb7wPp1O8+5QD7FsGo/ezKLi8guqw8jg6AgH39vFKI8PsLGoZk46\nLAjCxUBS1fwrlZ4qaFtdXc19991HU1MTa9eunamfNt/uv/9+7r///vNyrktNOp3mzc7jJE3Tebkh\nluHq2pVi3YmAf3yU48F+0rkcpSY7q8przutNemRkhJaWFvr7+7Hb7ezfv58XXngBRVFYvnw50WiU\nrq4uIpEIDQ0NKIpCy29/y9ejUb4ej+PI4xLmN5n4N5eLJ41GimtqcDgc2Gw21q5dy9KlS1EUhYGB\nASYmJli8eDGbN28+5/fgTHocj0+GiCbieB1ODHrDOZ33TO3pfJdx7XSCm8vmWKJ3srjkwkksd544\nTMLwfqLsymj4TM2yBYxIEM6fM9rd+dBDD532+NT0p3DhGxoPziRoAAmTBv94kHJRffqyMBUJk0wm\ncTtdpy0czmazNA13g0kPKPRkI9hGhqjylcx7TD09PZw8eZKxsTHMZjMtLS288MILaLVa1q1bx9TU\nFC0tLYyPj7Nq1Sq0Wi0Dv/sd94bD/DKRyKuMRqfVyhNOJ7u9XorKyih7b7PB5s2bcTgcmM1mBgcH\nmZqaYsWKFdx6661zlqDme5z2oX5aY9PFRpVuPxtLanF8QjmF+TDdpml6ClFWZMaSsfN27nx8eHw0\nh+iAIlw+zihJEy5eGlkhl8vN3KBzuRyKWCtzWWgZ6OFEbAxZI2MJ9rO5ZsXMCGosHietSJwaT5UV\nmUhq9r6V56K5uRm/308sFkNRFPbv38/LL7+MXq9n06ZNhEIhjh8/TiAQYPHixZSVlRF75x3+NBzm\nS8lkXhetQ3Y7jzkctFdWUlhUhHlkhLKyMm666Sbi8TgOh4OBgQF6e3tZs2YNa9asmdfX/GnaJwPI\npukkKWvU0DHmZ915TNJMio7oaY8vrNtCldVDa2wUWaugpjJUOS6ukiaCcC4urL9GYd4UewooCI0y\nrEzvePPldBR7ChY4KmG+JZNJ2sIjaE3TU2gxI5wcHmRJaSUAFrMZc1bmVJGKXDqDxzX3CUI2m+Xw\n4cNMTEwgSRKJRIJdu3axfft2jEYjV111FZOTkzQ3N9PX10dlZSUrV6zAsH8/fxGJ5F1GY7fLxaM2\nG6nVq7HZbGS6uvB4PPzVX/0VfX19qKrK5OQkw8PDbNiwgZUrF77y/UKPC60prubgUBexbBqX1sjy\nisoFjuh0i4rLsI0ZmEzE8ThsuO1z1+1GEC50syZpP//5z7n77rt59tlnRSeAi5gkSVxZu4zxyela\ndy6744JaHCzMj3QmAx+qi5T9QFogSRKfqVhMy/AA6f+fvfuMj6u+877/OWd6H2nUe5dlG9uShRvY\ndMzChhB6EkICIRiyu4FsAiHXZvPivpNsIFnYTa47WVpI2HshAZKLbAiEDhtj3GTJclHvGpUZaUaj\nmdH0c871QEamWrItWS7n/chqc/4zHs389C+/ryKRb88kNz1j3q4fjUZpbm4mHA5jMBiIxWK89NJL\nvP3221itVs4//3xCoRDt7e10dXWRl5fHkqoq8vfs4e8jkTm30XgpPZ0n0tLIPf98bIrCgQMHyMvL\n49e//jVNTU0MDQ0RCoXw+Xycf/75VFVVzdt9PF4Vtkw6Yn5EnRYhlqQ898TuB3NYbVxYtfKEXvNo\n5bgyUZuYqM5EsxZpzz77LM899xwNDQ088sgjM58XBIFXX311QQenml+CIOBypi32MFQnkMVsJlsw\n4lOmm6uKsRSFBZkf+h6r2cKa0up5va7P56Ozs5NYLIbBYCAUCvH000+zbds27HY7mzZtIhKJ0NXV\nRUdHB2lpaSwpK2N5czN/NzVF5RwCzyMaDc+mpfFMZiZrPvc5iiYm2LVrF/X19bz88su8/vrr7Ny5\nk2g0iizLXHLJJXMKPZdlmY7hAWJKilxrOtlp6bP+zPGoKSgh3W9lKh4jKzMNq1ntZ/U+WZaJxWKY\nTCb1j0rVGWnWIu3111+np6eHBx98kPvuu4+jOAyqUqkWmSAIbKhcRs/IEElFJr/QhW0Bi4DBwUGG\nhoYQBAFFUfB6vbz00kvs2LEDp9PJueeeSzQapbe3l46ODiwWC9V5eZzb2sqWSITcORRnE3o9v7Hb\nebGggM/cfDOVnZ288sor1NfX88477/DKK6/wwgsvkEqlEEWRK664gry8uR+Q2dHdyrguhSAI9I9N\nskaRj3l2cSzgJxKPkelIw2z89KMO2fM4e3m6GJucYOdwN3ERLLLAhqJq7BbrYg9LpTqh5rQnrays\njEcffXShx6JSqRaAIAiU5y1sxFRbWxuBQACj0YgkSXR0dPD222+za9cubDYb69evJxaLMTQ0RFtb\nGzqdjiXp6Vze08MtHR045tDjbNBg4D8sZrZXVrHl7rupeucdnn76aerr63njjTfYunUr//mf/4kk\nSZhMJq655hoyMo6u+FEUBU8iPJMYIBp0DIX8x1Sktbn7aI9NTG949w2z2lVAXla2OiM0R/s8Ayhm\nPXogCRz0DLK+rGaxh6VSnVBzPjjw5ptvct111wHTL/rPP/+8GoauUp2h/JMBIrEow/2DyLKM0+kk\nmUzS0NDAjh072Lt3LxaLhbPPPptYLIbH46GtrQ1JklhmNnOD282NkQjGOczMt5pM/LvZxK6qMj5z\n+y1kv/EeDz/8MHV1dbzwwgu0trbyzDPPEI1GSUtL47rrrsNuP7bDD4IgoBM1H9rMf6yJAR3BMUSL\ngYnJACPhAANTfqonMtlYWnPCe6GdipKyxAffopKKmkyjOvPMuUh7v5Gtw+Ggp6eH66+/noaGhoUc\nm0qlOgk1drXyRtMu0Ahk29LIxcDWrVvZt28fzc3NmM1mVqxYQTQaZWJigpaWFqLRKBssFr7k9fK3\ng4NzeuFpsNv53yYT+6vKuPHuOxn845959t//g2XLl/Ob3/wGr9fLCy+8QDAYJC8vj1v9n94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Pn/vEj1HNtoPC6KPGm3U3ruuTz6gx/wy1/+kgcffJC/+Zu/4e6776a3t5ftf92K0WgkMzOTUCjE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\nYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x11b54fe10>"
]
}
],
"prompt_number": 22
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "-"
}
},
"outputs": [],
"prompt_number": 22
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Image('ppc1.png')"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "slide_end",
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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8sZCIiIjmTHJsPJJjH+ylKETT4Qw0ERHRJHw+HzweT7jLIKIFhjPQREREE7jR\n3IDrve0IyBKSFZF4InMtJEkKd1lEtAAwQBMREd2hf6Af1wc6oYzSAgC6hA/2thaYk9PCXNncGfK4\nce12I7zCj9RoE5bFJ4a7JKIHBgM0ERHRHdweD2SVIvhakiR4Av4wVjS3hBD4g+0a3JFKQALaXC1Q\nKhRINsWFuzSiBwLXQBMREd3BZDAiaszSZ8ntRaohNnwFzTG3241e6fMfCBRqJToGesJYEdGDhTPQ\nREREd5BlGU9Z1qG2owUBIbAsJQ66qOhwlzVnNBoN1OLz14FAAJEqdfgKInrAMEATERFNQKNWY11a\nRrjLmBeyLCMvMR0XO5vgDfiRqtEhM8zruweHhnClrRHugA/JETqsTFkW1nqIpsIATUREtAQttEeH\nn26swZBWBmTAMdgJVYcS6QnJ4S6LaEJcA01ERERh5ff70eP/fNG5QqVE91B/GCsimhoDNBEREYWV\nQqFABD6/60kgEEC0UhPGioimxgBNREREYbcxdSWiPALKIR+WIRIPcQ00LWBcA01ERDSPGjrbcKWr\nGT4RQFqEHjnpD/GJhhMw6fXYol8f7jKIZoQz0ERERPPE4/GgursJgUg15CgtmsUg6ttbw10WEd0j\nzkATERHNk4GhQUD9+VetrFBgyOcNY0UjTyFsaG+FJ+BHqiEW0ZFRYa2H6EHEGWgiIqJ5YtDpETkm\nLwuPF4kxhvAVBOCc7TouDnXipteFj5pq0DvAu10QhYoBmoiIaJ7IsozNK1YjFVokCQ0ei1uBWH34\nArTH40GLdwCyPPL1L7RKNDg6wlYP0YOKSziIiIjmUaQ2AjkrHgp3GQBGAr0UCIzfxgsaiULGGWgi\nIqIHkBACrV0dsLe1wO1xz6iNSqXCal0ifMNeCCGgHfQhMyF1nislWnw4A01ERPQAqrLXoAVuyAoZ\nN+zteCZ9DSK1EdO2W5uWjtQ+E4aGPYhfZoJCoZi2DRGNxxloIiKiB4zb7UajtxeyYuRr3BehhL2r\nbcbt9TE6JMXGMzwTzRIDNBER0QNICK5dnorH4wl3CbSIcQkHERHRA0ar1cKsMaDR1w9ZqYB6yAdL\nRnK4y5qQo6cHF9sb4An4kByhw6PLLfP6JMaGhgY0NTVh+fLlWL58+bwdh5Y2BmgiIqIHUHbGSqR2\nd8Hj8yIhORYatTrcJd1FCIFzrbXwRaoAKFHv70NUWzMyk5fN+bGcTieuXbsGt9sNIcSc9080FgM0\nERHRAyryyVw2AAAgAElEQVQhNm7S99weD260N8ErAlgWY0KSafJ954vP58Og8EENFYCRJzH2emd2\nx5CZGh4eRmVlJfr7+6HRaOD1etHY2IikpKQ5PQ7RWAzQREREi4wQAp/Yr2MwYuRSp9auBjwpy4g3\nmGbcR1ePExfbGzEc8CNllksvVCoVYiQVRlcj+70+xOqiQ+pjMkIIWK1WdHR0ICoqCl6vF7dv34bT\n6YTX6+UaaJpXDNBERESLzNDQEFySD2qMLOuQNSq09blmHKCFEDjbUgsRpcHo0ovothZYktNCruXJ\nFatw+XYjhoUfKZHxWJFw72u1b968iYaGBsiyjCGPG9W1N9DR2QW1XyDeYMSyZctgMIT3kem0uDFA\nExERLTIajQYK/+dPHBRCQCPP/Ct/eHgYHllgdFW1rFCgzze7pRfRkVF4wrJmVm3v1NbWhpqaGvT3\n9wMYGVf5udMYkvwQQkAfa4IhIR6SJHEdNM0rBmgiIqJFRqFQIDd+BT7taIQPASRrY7Byxcwv3FOr\n1YiGEsOfvQ54fYjTx8xPsTMwMDCA6upqdHV1QalUQqvV4tNPPwUAeOBDREw09EYjAn4/rt+6iTRj\nHDIzM8NWLy1+DNBERESL0LL4RCyLT4QQIuS1y5Ik4cnlq3C1rQle4UdKlAlp8YnzVOnkAoEALly4\ngJaWFkRERCAmJgaffvopZFmGWq2GEALxsfFApBrd7R3weobxcGo6nnrsCeTk5Nz3emnpYIAmIiJa\nxGZ7z+WYyChsNK+e42pm7urVq6ipqUF0dDQiIiJgs9kQCASgVCrh9XqRnJwMpVIJX2MjrtXVIz41\nGZlrVuBrX/wKzp8/j/feew8vvvhi2OqnxY0BmoiIiBaMhoYGXLp0CUqlEkqlEvX19fD5fPD5fPB4\nPFixYgVkWUZ3dzccDgcyMzPx+GOP4aGHHkJtbS3+4i/+AvX19firv/qrcA+FFjEGaCIiIgo7h8OB\nqqoq9Pf3Q5ZldHR0YGBgAIFAAB6PBykpKcH9HA4HVq9ejTVr1iAtLQ0OhwPf+ta3UFtbC51Oh8jI\nSDQ0NIR5RLSYMUATEdGSN3rHhvl8xDRNbHh4GKdPn0ZraysiIyPh9XrR2dkJWZbh9/sRFRWF6Oho\nOBwO9Pf3IzMzE+vWrYNOp4MQAt/5zndw48YNREVFwWg0oq6uDrJaBU28EU2d7VgWhrXbtPgxQBMR\n0ZJW19aMK92tCEBgeYQBORkPMUjPA1dfLy62NWBY+JEcocPa1HRYrVZcvXoVOp0OWq0Wzc3NUCqV\nEEJAoVBArVZjcHAQg4ODyMjIQHZ2NiRJQv/QEL6/fz/qbt5ETEwM4uPjUVNTA61Wi0ce34CAVoE+\nVQDWnhZIQFgugKTFjQGaiIiWrIHBAVzpbYMcrYUMoNk/iLiO21iRmBLu0u7JwOAA3MPDMOkNC+KH\nASEEzjbfgjdSBUDGxzcv4/iv34U5deSBJ83NzVCr1cFaNRoNBgYG4PP5sGzZMqSnp8Pr9SIQCOBH\nb/0rPr1yCRq1BpH6KDQ1NEGtVuMrX/kKvF4vbI52aCO0CAT8kFVK3B7sQRoYoGluMUATEdGSNTg0\nBKg+/yqUFQoM+bxhrOje3WhuwPWBTkgqBWLaJDxtWQeVShXWmnw+HwaEH/0dLly7UA0hAohTRqC9\nvR1qtRqyLMPn8yEiIgIulwtCCMTFxeHhhx+G2+2Gy+XCu+++i6qqKvQOu2FMiENTjQ3dnZ34wgsv\nIEahRl9fHxITExHoaEVbQxOSVyyDEAJahSKsY6fFiQGaiIiWLJPBCG1HI4YjZQCAcHuRlGIMc1Wz\n5/V6ca2vHapILQBgMAKobW/BmrT0sNbl8Xhw6cM/oM/rhkqtRp+zF7FRMqQIFbxeL9RqNRwOB4aG\nhqDT6ZCVlYXh4WHYbDacO3cOZ8+ehSzLSExMREO1Fd2dnXjmy3+Egb5BdLZ1IGN9Frq7u3H58mV0\ntbZiCH74B9wweRVYk7YirGOnxYkBmoiIliyFQoGnzWtR094MvwggPWk5DDG6cJc1a16fD+KOFRv+\nMD7S2u/346OPPkJDQwMyYmJxvdEOv+RBoiIChsgYSJIEp9MJWZah1+uxfv16qFQqXLlyBVeuXMGZ\nM2cAACaTCTdv3kRzczO++OUv4nafC631zVhhToc+2oDz58/D4XBArVbD6/VCJUlYHZuCzSsfDtvY\naXFjgL5HVqsVTqcTLpcLJ0+exJ49e5CRkRHusoiIaIYiNFpkLV8cj32O0GqRJEeiW/hH1hMPeZGW\nGhuWWqqqqlBZWQmdTodAIAA5IGNlUhq8Xi+USiW6u7vh9/uRkJCAdevWwWg04uzZs6ipqcHZs2fh\n9/uh1+tRV1eHlpYWFBUVIRAIoL6+HmssFji10ai/XotbPb3QaDQYGhqCx+PBqlWr8Mwzz2Dnzp1h\nGTctDQzQ92jr1q2or6+HTqeDw+FAUVERKisrw10WEREtQZIk4YnMtahra4EvEEDqsljooqLvaw02\nmw2nTp2CSqWCUqnE8PAwZFnG8PAwlEolent7MTAwgGXLlmHt2rVISEjA73//e1y/fh1WqxVutxtG\noxE2mw3Nzc146aWXoNVqcePGDTzyyCMwm804f+4cBgYGoNVq4Xa74fP5sHbtWhQWFuKLX/wiPvjg\nA5w9exabNm26r2OnpYMB+h6NhmcAMBqNC+JqZyIiWrpkWcbKlGX3/bjd3d34n//5HwwNDUGpVEKW\nZajVarjdbmi1WnR2dqKjowOrVq3C5s2bkZSUhI8++gj/9V//hU8//RSDg4MwGo1obW3F7du38cIL\nLyAuLg4XL17E6tWrsWrVKlRUVGBwcBBRUVFwu90AgKysLLz44ot4+umnUV5ejgMHDqCtrQ0vPP88\nkJIC8LfCNA8YoO/RaHgGgNLSUuzfvz+M1RAR0b0IBAIIBAJQKvn1OFMejwe/+c1vUNtQj9ZBFxRq\nNfTqCKTFGIO3qGtubsajjz6KjRs3Ijk5GWfPnsU777yDGzduoL+/HzExMXA6nejs7MTWrVuRnJyM\nqqoqaDQarFmzBh9++CGGhoYQHR0Nr9cLr9eLDRs24Itf/CJyc3Pxu9/9Dv/0T/+E+vp6ePv68FR9\nPb5w/DgQHQ3U1AD8PGmO8b+oOWC321FWVobCwkJs2bIl3OUQEdEs3GxtwlVnKwKyhFRVNB63rOFv\nFacghMAHH3ww8uQ/WUaXfxBaow4etweeCAVq6m3o63IgJycHGzduDF4IWFZWhlu3bqGvry/4hMHu\n7m48++yzSEpKwqVLl6BSqbB+/Xp88MEHGBgYgMFggN8/sq77iSeewIsvvoi1a9fizJkzeOutt1BT\nUwOptxeFNhteampCnPezWxF2dABlZcCf/ml4TxYtOpIQYbw8d5E5duwYDh06hBMnTtz13r59+7Bv\n3777XxQREU2rf6AfJ5troNSO3C85EAjg0Yh4ZCSlhrmyueX1ejHs9SIyIuKefjiorKzE2bNnEQgE\noNfrodVqcepGNYwJcehsaUPjLRvWr16LP84vhFarRXt7O06cOIHa2loMDAwgIiICdXV1GBZ+rMlZ\nj9TEJLhaO5CYmIjY2FgcP348uKSjv78fRqMR69evR0FBAcxmMy5cuIDa2lpcunQJUb29eKG2Fl+5\nfRvRfv/dxa5fD1RXA/xhiOYQZ6Dvgc1mw7Fjx/Dqq68CAPLz81FUVIT6+nqkp6eHtzgiIpqxIbcb\nsvrzB27IsgyP3xfGiuZeXVszLjpaIGQZcZIamyzrQlqqctvRhQ+sZ3Du4z9A6fFj/crVSE1NRUND\nA6KioqD1SbB+fAaJy9Lw3FdexCPGZAwODuLo0aOora2F2+2GWq1GW1sb1Go1Mh5dC11iHNoam9HU\n1Y7lSYk4d/YchoaGYDAYoFQqodVq8eSTT+K5555DSkoKrFYrzp8/j8rKSsS7XPi/amvxYlcX1FPN\nBV68CJw4ATz//BycRaIRDND3wG63o7u7O/jaZrPBaDQyPBMRPWBijSZEdTZhKOKzDe5hJKeawlrT\nXPL5fLjkaIUqamSAPUKgtq0Zq2f4gBWXy4Xv/fM/oHegHzqjAfEr09Da0oHo6GhotVp88MEHiI2N\nxde274Affmh8Ek6+dxy3bt2Czzfyg0hLSws0Gg2eeuopREdHo6ruBkS3A6bEBFw9ewG33J8iPjYO\narUaMTExePrpp/Hss88iNjYWly9fxtmzZ3Hu3DmkOxz4m7o65DudkGdSfGEhEBueW/nR4sUAfQ/y\n8/Phcrlw+PBhmEwmnDx5EhUVFeEui4iIQiTLMjZnrMWtjhb4EcCK5BXQR8eEu6w54/V6IcY80VqS\nJHhFYNp2fr8fv/zlL3Hr1i0MB3xYk/0objc2o9fhQJJJj/LyckRHR+Mb3/gGJElCZ2cnPvnkE1y9\nehV+vx9erxeNjY2IiIjA008/jaioKPT29qK3txeGqGhcu3wFQ0NuaLRaREVHIzExEevXr8fmzZuh\n0+lw48YNnD59GmfPnMHa27fx3aYmPN7XN33dAG5lZWH1j38M5OTcw5kjmhgD9D3atm3bhH8nIqIH\ni1ajwSPLzOEuY15EREQgDlq4hIAkSRBuL1KTp56V/e///m9UV1cjMjISmzdvxsnK0+hsbUdcSiI+\n+e+TuK2Owv+zaxckSUJDQwOuXbuGixcvwuv1YmhoCM3NzYiKikJ+fj7UajWGhobQ09MDIQQuXryI\nvr4+SEoZhpgYLF+2DBuyc7F582ZotVrU1dXh97//Pc6fOYMNTU34p9ZWrBsamnacHknC/8TH43cb\nNiD/lVewmuGZ5gkDNBER0RKwKXMdbt1uhlf4kZYcC6NOP+F+Z8+exYcffgifz4ecnBwMDAygsbER\nW3I34u3/+AlqBgbxF1//OtKTU1FTU4OmpiZUV1djYGAAbrcbLS0tiIiIQEFBAZRKJXw+H/r6+jA4\nOIibN2+iv78fKpUKcXFxyMzMREZGBjZt2gStVgu73Y6bN2/Cevo0nrLb8W8dHVg+PDzt2HplGb9K\nTMTpDRugXrYMGRkZWLbs/t8Lm5YOBmgiIqIlQKFQYHXaiknfr62txbvvvou2tjbk5eUhOjoaDQ0N\nePjhh/Gb3/wG5eXl+FpREdLS0lBVVYVT12tw+fJlOBwOuN1uNDY2Ijo6GgUFBVCr1ejt70NLWwtc\nTgec7Z0QXj9kWUZCQgLWrFmDlJQUbNy4EVqtFk1NTbh06RIu/+EP+EJ9PX7udCLeN/1FnO1KJX6a\nlIDjax5CbEoannnsCdhsNtTW1mLz5s1zefqIxmGAJiIiWsJ6enrw05/+FLdu3UJubi4ee+wxXLp0\nCQkJCejs7MSPfvQjfOELX8DXv/714CO3b926haamJgwNDaGlpQVRUVF44YUXoNFoMDw8jL6+PlRf\nvwKnwwmPxw1JSEhJSsRjOXmIj4/Hhg0bEBUVhba2Npw7dw43f/c7vNTUhO/09CAmMP3a7HqNBj9O\njMfHa1YhJikBq1ZlwnGzHtXV1diyZQsSEhJgNi/O5Ti0MDBAExERLUE+nw//8R//gcrKSmRlZeGb\n3/wmTp8+jaGhIXi9XvzoRz/CE088ge9+97soLy/HsWPH0NXVhVu3bmFwcBBNTU2IiorC888/D6PR\niIGBAfT29uLWrVvo6upCV68LCqUCiampWLYyA0k6E57fUgCdTofu7m689957aP7wQ3y9rQ1v9PVN\nfSu6z1yJjMQ7K1bg5tq1iIozYU1yLBprbWi4dB0vPf8CVq18CMnJyQzPNO8YoImIiJYQIQTeffdd\nHD9+HKtWrcJf//Vf46OPPkJDQwM0Gg3efPNNrFmzBj/4wQ/w/vvv46c//Sk8Hg+uXr0Kl8uF1tZW\nREZGorCwEKmpqXA4HOjo6EBNTQ0cDgeGhoagVquRnpGBpIfSERkdjRUPrURW4nIEAgH8/Oc/R8+p\nU/hmVxe+MDAwo1vRnY6JwX8uX462NWuw7uGH8aTBgKtXr0LR2YcvPp2PdatWI2v9euj1E6/rJppr\nDNBERERLxB/+8Af86le/QmxsLP7yL/8SZ86cQXV1NRISEvCzn/0MaWlp+N73vocTJ06gtLQUGo0G\nly9fRkdHB27fvg2tVov8/HysXLkSbW1taGxsxNWrV9Hd3Y3h4WFoNBpkZ2fDYrFAo9FAl5oAbXQ0\nIoWM9379W0inTqGkpwebZ3BHDT+Ak3o9jmZkYHD1auTm5iJpeBg3b95ESkoK/uRP/gSJiYnIysqC\nLM/ojtBEc4YBmoiIaAHq6nHhSkcjvCKAZZHGKS8AnM6NGzfwk5/8BLIs48///M9x8+ZNnDt3Dmaz\nGf/2b/+GyMhI7N69Gx9//DHeeustGAwGNDU1ob6+Hm1tbdBoNNiyZQvWrVuH5uZm1NbW4uLFi+ju\n7obX60VkZCQ2bdqElJQUREdHY/Xq1TAajfD5fPjpT36CuI8/xp7eXjwygztqDMsy/kuvx68zM6Fc\ntQqbNm1CY2MjLl68iPT0dHzzm99EWloaMjIyZn0+iO4VAzQREdEC4/f7cba1FiJSDUDGDXc3Ijs1\nWB6fFFI/HR0d+Nd//Vd0dXXhq1/9Knp6elBZWYm1a9fi3//933Hq1Cl885vfxKVLl3D48GEkJCSg\nt7cX58+fR1NTEyIiIvDMM88gOzsbzc3NuHr1Ki5duoT29nb4/X7o9Xo899xzMBqNiIqKwsqVKxEb\nGwshBA796EdYde4cDvT3I30Gd9ToVyrxc70eJ1avhmnNGmzduBHV1dX4+OOPkZOTgy996UtYt24d\ndDrdLM8q0dxhgCYioiXB6/Wirr0FfggsM8ZDFxUd7pIm1T84AK9KCn5JK1RK9LqnX/YwamhoCG++\n+SauXbuGbdu2QafT4cqVK3jkkUdw8uRJvP/++/izP/szdHR04Be/+AUSExOhVqtx8uRJNDQ0IDIy\nEs899xxycnLQ3t6OS5cuobq6Gu3t7RBCwGQy4dlnn0VkZCSio6OxYsUKJCQkQAiBN3/4Qzxx8SJK\nBweR4PdPW2uXWo0f63T4ZN06mLOy8IV163D27FkcP34cX/rSl/DII49g/fr1XKZBCwoDNBERTaun\ntxcBEYBBp4ckSfNyDHt7K645bkMggIzoWKybw6cCBgIBfFx3BYMRI8+zbmhy4unlqxAdGTVnx5hL\n0ZFR0HgBv2rkdcDrh1E/fa1+vx8/+9nPcOrUKRQWFqKgoACnT5/GypUr0draivfffx8vvPACHn74\nYbz//vuIj49HfHw8PvzwQ9TW1iIqKioYnF0uFy5duoSqqiq0tbVBlmXEx8cjPz8fSqUSkZGRSE9P\nR0JCAvx+P0q/8x0UXL+OXw4NzehWdI0REXgrOhqfPvII8jZtQn5sLKxWK06ePIlvfOMbWLduHdLT\n0+/xTBLNDwZoIiKaUqXtBpr8g5BkIKFDgycy1855iO7t68OlnjbIkSOJ8ZbHBVNXJ5Lj4uek/26n\nA/0aKXjHB3+EEi3ObqxaoAFaoVDgidRMXO1shjcQwLLoOKTGJ0y6vxAC7733Ho4cOYLc3Fx8+9vf\nxu9+9zvY7XYMDAzgX/7lX7Bx40Z86UtfwpkzZ2AwGGCxWHD8+HFcu3YNkZGRyM/PDz558PLly7hw\n4QLa2tqgVCqRmpqKLVu2QJZlREZGYvny5UhKSkJPTw/+7fXX8Se1tSjzeGZ0K7pr0dH431FRsD36\nKJ7buhWbfT5cuXIFdrsdO3fuRHZ2NmJiYubydBLNOQZoIiKaVHtXF5rhhlI98nXRGfCiqaMNyxOT\n5/Q4fe5ByJrPv5IUKiX6h91z1r9GrUHA54esHonQQggIvx/XmusREALLTQtvSYdRp8fmSR63PVZl\nZSXefPNNrFixAt/+9rdx/vx5WK1W+P1+/PKXv0RGRgYKCwtRWVmJmJgYrFmzBsePH8enn34aDM55\neXnwer2orq6G1WrF7du3oVKpYDab8eyzz0IIAa1WC7PZjKSkJNTX1+Pn/+t/4U8bG1Hm8UAxg/Gc\n0enwv6Oi4MrOxh+98AJ0zc04f/48UlJS8Ld/+7fIzs7mMg16YDBAExHRpIYDPsjy57PNsizDL6b/\n9XyoYnUGKLqb4Y8YmYEWbi/iTXp0OrrhCwSQaIoNhqu6tubPlnoA6VFGPLoic9r+dTExeMhlRE1/\nNySFhLiAGk3CCXfkyNdgfbMTzyxbhZgFOiM9Ebvdjn/4h3+ARqPB7t27ce3aNZw/fx4+nw8nTpyA\nXq/Hxo0bcenSJfT29mL9+vU4efIkfvazn0Gr1WLLli14/PHH4fP5cPHiRVRWVqK1tRUajQarV6/G\nU089BSEEVCoVMjMzkZKSgqrKSpz+7nfx57dv4/+dwR01ApKE4zExOGwwADk5eO6553Dr1i0cP34c\njz32GN544405XabR6XRgcNiNBIMJERrtnPVLdCdJiBn8voXu2b59+7Bv375wl0FEFBKfz4ePai9j\n6LO1w+ohH57JWAetRjPnx+rp70NNZysEBDKMCWhwtKMFHsiyhBi3wDMPPYqBwUGcaq2BrBkJ2n6f\nH3m6FKTFJ87oGG63Gz6/D4NDbpzpax4347lSacDq1OVzPq651tnZiX/8x3+Ey+XCK6+8gra2NnR0\ndEClUuH3v/89fD4fzGYz7HY7ZFnGo48+io8++ggffvghVCoVNm3ahCeeeAK+z5ZOnD17NnirurVr\n12Ljxo3w+/1QKpVYtWoV0tLSUP7BB3D/4hf4v7u6sN7rnbZGr0KBo1FR+ElcHJI2bcLDDz+M2tpa\ntLS04I//+I/xta99bc6XaVxtsqHW44KsUkLh9mFz2kML7rcKtHhwBpqIiCalVCrxjOVh2DpuAwBW\nZCTMS3gGAH10DB6LXgUA6HR0owUeKBQjAbdPO3KRYYRSDUk9ZqmHUoEBr2fGx9BqR2YlA0JAOPyA\n5vMlHWrF/V0+EAgEUNfWAr8IIM0YN+0FjQMDA/jnf/5n1NXV4Wtf+xoUCgWqq6uhVqtx6dIldHd3\nIy0tDV1dXbDZbMjKysKZM2ewb98+yLKMJ598Es8++2xwqUZlZSVaWlqg0Wjw+OOPIysrC0IISJKE\nNWvWIC0tDb89cgS3fvMb7HK5kDGDO2oMaTT4sUaDdxISkPWFL+Dxz+4nff78eXz1q1/FSy+9NC8X\noQohcKuvC4qokc/Xr1WitqsVOVEPzfmxiAAGaCIimoZKpcKq+zwz6xcBjM1ZkiRBQCBOb4Cquxm+\niJGvL+H2ItFkCLl/XXQMVkXG4lpfByBJSFJEIGNF6lyVPy0hBE7XXoVDHYAkSbA1duOp5RMvIfH7\n/Xj77bfxySef4Ctf+Qq2bNmC69evAwAaGxvR0NAAg8EArVaL9vZ2ZGVloaqqCt/73vcQCASwYcMG\nFBQUYHh4GNXV1Th79mzwqYKbN2/GI488Ar/fD0mSsHr1aiQmJuK3P/0pOk6cwP/X24vEGdxRwxkR\ngX9RKvHb5GQUbt+OvMFBtLa2YnBwEC+//DI2b9485+eQKJwYoImIaMFJNMXB0NWKHs3IjKh60Idl\nySP3Kn5q+SrUdLQgAIH0xGUwxMzuwRpr0tJhGU6Bz+9HhFY7b7fnm0hffz86JS+U0sjXsD9CiSZH\nJ9aOCdBCCJSVleHdd9/Fk08+iW9961uoqanB5cuX4XQ6cePGDUiSBJVKhb6+Pjz66KO4cuUKvv/9\n78Pj8SArKwtf/vKXMTg4iAsXLuDChQtoaWlBZGQknnnmGaxduxaBQAB+vx9r1qxBTEwMjv+f/4O8\nTz7BG/390M1ghWdrTAzekCS8mxiPx7/0POKabuPy5ct46KGH8J3vfAerV6+et3M4liRJWBkTh9ph\nF2SlEoohHzKXpdyXY9PSxABNRIuO2+NBs6MDCknGioTkWV3ZP3p5yP0MVfQ5SZLw1MpHUN/eigAE\nliUnQqNWAxi5R3Ju+tz8al6tVkM9Jz2FRqlUQvj9GP0aFkJAgc//W6uoqMB//ud/IjMzE3/zN38D\nu92O8+fPw+/34+LFi+jt7YVOp0MgEMCqVatgs9nwxhtvYHBwEKtXr0ZxcTGGhobwh/+fvTsPj6s+\nE3z/PXVq3zeVqrRvlmRbXuQNL2CzmU46CZ1kgEmT7pB0BpLpvj19+5mnk87TM5Pc27kTSDrPPLd7\nuhOWG+gEtwkGmhBCQohDCHi3McbGsqx9V1WpSrXvdc79Q0ZAIFjGEpLl3+cvbEvnvHWQTr31O+/v\nfV95hRMnTjAxMTHbcaOtrQ1VVSmVSnR0dCDLMr956CFuPnmS76XTzKVAp9vh4LuyzGsNDTRsWUdN\nMEzfmS7aN67nTz59Ozdt2rYwF+59rK5twhuNkC3k8FW6MRtNH3oMwtVDJNCCICwruXyelwbeoGDS\noqoqwz1T7Gxde0mJ8KmhXvpTESRgpTPwoZcvCDM0Gg1NgZrLOkYsEadYKuF1uZfUhyGzyUSbxcP5\n7DQarQZ7QaK5pZojR46wd+9erFYrn//850kkEhw6dAhJkujq6mJkZGR2bHZTUxOTk5P88z//M/F4\nnIaGBj7/+c+TSqX49a9/zdmzZxkfH8doNHLzzTfT3Nw800WlXKa9vR1VVTnwj//Ip3p6eCiTmVMr\nuqNOJ9/Vahlva2Pb9u00DA4yOjDMto/czIbrt2N3OfFqFq+TSaXbs2jnFq4uIoEWBGFZGY2GKFyo\nj5UkiZheIRidwu+Z20COsakQA6UkWuvM6lVXJowv4cA1h368wtJyaqiX/kIcjazBGR7luhVrllSf\n4dW1TdSmkhSKRUITk3z961+nUCjwh3/4h+h0Ok6ePIksywwPD3P27FmsVitut5uGhgamp6d58MEH\nicfjVFVV8Vd/9VckEgmee+45BgcHGR0dnW1V19LSgqqqKIpCc3MzSrnMa//wD9w5MsKXchfvta1q\nNLxwYcW5vG7dzDGiUUKhEHfffTf6Sjcxq4xG1qDJFmmsnVtHFEG4kokEWhCEZUUjSbOdBABURUWW\n5jxF90QAACAASURBVJ40ZYt5ZO1ba3GyXkc6l1vUBLp3YpSeeBCAVmclzf7LW5VdKFPxGOemxlCB\nFmcFAc/vn5y30GKJOAOFBFr9TLu7uEZlIDhO82WuaM+3ZDzBj370I8bGxrjhhhuorKzk1KlTKIpC\nJBLh1VdfRa/X4/P5qKmpIZlM8qMf/YhYLEZFRQVf+tKXyGazPP300wSDQcbGxtDr9ezatYvm5mYk\nSUJRFOrr66Fcpv/b3+auyUn+cg49nMs6HU/abPyTwYBt/Xo8zpnNmhaLhbvuuovOzk5MppkPmqPh\nILlSgSqfF7NJlE4Iy59IoAVBWFYafFUMnZ8iaQRFUamWjFRcwmNdv8PNuZEQqnEm8dJmS1QEXAsV\n7kVF4jHOpELIFwaMnE6GcJmsuB2X3nliIWVyWY5M9qMYZ95WjkVH2Kkz4FykDx7FYhFJfqtkQ5Ik\nSgswAOaDisfj/Ou//ivnzp1j27ZtXHvttXR1dTExMUEymeTw4cMAeDweamtrSSQS7N27l3g8jsfj\n4c///M8pFos8/fTTxONxxsfHkWWZHTt2zK44S5KE3+9HUygQ+/a3+cLUFA2l0kVjy5tMPGIy8YDR\nSKCzkwq9HrvdzqpVq9i1axednZ3o9e+sHJ9rH25BWC5EAi0IwrKi0WjY1bqWUDSCrNFcUvIMMxvU\nrg200DcdQgJa66pmN68thkQ2jfz2vsd6LclcZskl0JFEfDZ5BpD0OqbSiUVLoL1uD/bwKEnjTCKp\nzRap8y/eivibcrkce/bs4fjx46xbt47bb7+dkZERXn/9dVKpFEeOHCGZTFJVVUVdXR2xWIzHH3+c\nRCKB0+nkzjvvRKfT8eyzz5JOpwmHwwBs2bKFFStWUC6XkWUZj8dDORpF+93v8rnpaXxz6OGctFr5\nZ72ePVYrDWvXElBVamtr2bFjB21tbWzYsAFZnkul9PyLxKbJFHJUONwL1odcEC6FSKAFQVh2NBoN\nfu/cap7fi9PuYOMSqXn22hwQn4QLK+JSroi3YmklzwAOswU1VkS6MCFQKZZwOBZvCpwkSexqXUvf\n5BiKqlLX6FvU0c6lUol9+/Zx+PBhmpubufXWW4nFYpw7d45kMsmrr75KKBSitraWjo4OotEoTz75\n5Gy3jY9//OPo9Xp+/etfk8vliMfjlEol1q1bR3t7O4VCYebn3u8n1dOD71//lT+Ox7HNoYdzyOXi\nu5LEMw4H9a2t1Mky7e3t3HTTTfh8Pjo7Oxd1A2bX6CDnc9NodDLa6DjX1bVfdOiMICw0kUALgiAs\nYTaLla2VTfREJ5CQWOGvw2I2L3ZY72K32uh01XAuOoGCSovDR4Vz8UpfYOaD1Iqq2gU7/nQizhvh\nUcqqSr3dQ4Mv8K6vURSFZ599lgMHDuDxeNi5cycA/f39ZDIZTp8+zcjICIFAgG3bthGJRHjyySdJ\nJpM4HA5uuOEGdDodBw4coFQqkUqlKBQKtLe3s3r1avL5PKqq0tDQQOTIEVp++EM+HY/PqTXfQEUF\n96kq+2026hobWelwsGnTJq699lpcLhcdHR2L3rlEVVXOxYOzm3pLJh09U+N01q1Y1LgEQSTQgiAI\nS1yF07Xoyehc1FZUUnuV1MKWSiUOjPWgmmdS1dfiExi1evwXSoZUVeXFF1/k5ZdfRpZlVq9ejdPp\nZGJiglgsRk9PD729vfh8PjZv3sz09DTPPPMMqVQKh8PB1q1bKZfLnDhxAlVVSafT5PN5mpubWbVq\nFdlsllKpRGtrK+Hnn6fzRz/iD1KpObWiO+X3c6+icNRioaGxka1VVbMTCV0uFytXrlzAK3dp1Pcc\n5rJ02hEKVy+RQAuCICwRyUya/sgkAM0e/7w9pk6kU/SExy4cN/CBJ/cJb4kl4pQNMm/2d5H1WqKZ\nJH63h+PHj7N//34KhQKBQIBAIEAoFKKrq4uBgQG6u7txOp1s2bKFqakpnn/+eVKpFG63m9bWVtLp\nNKdPn0aSJDKZDMVikdraWtrb28nlchQKBdatXUv4sce4bs8edmSzF41X1Wh42e/n26rKWaORhoYG\n/nD1am644Qb8fj8+n4+WlpaFvWgfgEajocnqYbCURKOVkXIlGqsWv5ZdEEQCLQiCsARk8zleHj5H\n+UK3jfHhc9zQuBrjZdbtZvM5Xhk5T/lCb+yJ8V5urFspWo1dJpvFihQsgXlmzVcplQiOjPDLJ54m\nkUjg8XgIBAIkEgnOnz9PT08P58+fx2w209nZSSwW45e//CXJZBKv10t9fT3T09N0dXUhyzK5XA5F\nUfD7/TQ3N5PL5SiXy2xYt47EI4/wkcceY80cW9E9W1HBP6gq40YjdXV1/OnOnezYsQObzUZVVdVM\ni7slbF19C76pMNliHr/PI352hSVBJNCCIAhLwOR0ZDZ5hplaz1AsSl1l1WUdNxyLzibPAKpRSzAe\npdFUfVnHvdoZDAau8TdxJjzK2Mgo/UdfQyqU8Hg8rFixglKpxODgIOfOnWNgYAC9Xs+aNWtIJBLs\n37+fdDpNRUUF1dXVTE5O0tfXh1arJZfLodPp8Pv9VFZWUigUkCSJHRs3kr3/fm7bu5fGObai+7Hb\nzf8ql0lbLNTV1fFfPvEJrrnmGgDq6+sJBN5ds71UBS5jU7AgLASRQAuCICwBJp0eJV1Go31rRdOo\nv/x2XWaDCSVZRqO7cNxiCbNt8bpRLCelTI7xI68zOjKCw2TGUenAYDAwMTHBuXPnGBoaQq/Xs2LF\nCpLJJC+99BKZTIaKigr8fj8TExPE43EMBgPpdBqbzUYgEMBms6EoCjabjc6mJrj/fj772GNzakWX\nttt50GbjfxcK6Gw2WltbufXWW9mwYQO5XI7m5mYqKkQyKgiXSyTQgiAIl0hVVSKxaTQazbz1Y/Z7\nKmhIxelLRQCVVrsPn+vSeli/F6/TRVsqzvlEGBWVFXYflZfYG/t3FYtFBsOTKKjUe3yXXWZypQmF\nQrz00kv09fUhyzJ2ux2n00kkEuHIkSMMDw+j1WppaGggkUjwyiuvUCwW8Xq9eL1exsfHiUQi2Gw2\nUqkUBoOB+vr62eEnlZWVrPF6cf7wh9wRiWB/z4107xTxevlHvZ6H8nlcTifXbd7MRz/6UVasWEEu\nl6OxsRGnc+m1PxSEK5VIoAVBEC6Bqqoc7HmDsLaIqqjURExsbpqfrgXr6lvoKDciSRIazdzHj19M\ne00DbepMnevltiUrl8v8tu8NMqaZ+AYHptjVuHpZDrd4+0h4gOnpaV555RW6urqIZVOUywq1/iok\nVeXQoUP09fVhMBgIBALE43EOHTpEuVymoqICRVGYmJiYTbjD4TBOp5PGxsbZns5tbW00qyotTz/N\nJ2Mx5nJFRwMB7lVV9hWLVPl83L5rFx//+MdxuVzk83laW1uxWETPZEGYbyKBFgRBuATDoQki+jKy\nJIMMY+U89dEpfG7vvBx/oSa9zVc/34lImLRRmm0kVjBpGZ8O0+SvedfXDoUn6YqOo6rQZPfSVlU3\nLzEstIHgOGciY5RRqTM5aa2o4tChQ5w5cwatVktfeBLFrENv1PPC4VdIjk3idDiprKwkFotx/Phx\nJEnC5/ORTCYZHR2deVrhdhMKhTAYDKxatYqhoSEAOjs7qQkG2fLEE9ySTM6pFV13fT1fz2T4TblM\nY1MTX7zhBm677TaKxSKKotDR0YFhGX6oEYSlQiTQgiAIl6CsKu9IRjUaiULp4rWpy4Ve1qIoKrI8\ncw0URUErvXu1PJFKcmp6HOnCeO9zmQiuacu8lKUspEw2y6nYBLLFgJIv8PPDL/NM/zgVTjflcplo\nbBqtx0pweIzzr53G6rBT5asgE0/S19eHRqOZbVvX39+PXq/H5XIRiUTQ6/Vs3ryZU6dOkc1m2bVz\nJ95Tp7hljq3oFEniSH0dX0+mOJ3Ps2rNGu7ZsYM/+7M/Y3JyklKpxMaNG9FqxVu7ICw08VsmCMKy\nl8vnGImEkZBorAxc1ipvtdtHT3+IwoXOFpacQlXd1bMpy+fxUhOfYqSYQdJIVJR01L7HBL5EJo1k\neOstRqOTSeQy+FjaCXQ6k0bRqPS8+joDXd2oioI5p6Apq1RXVxOJRvjNz5/H5nRS3VDH+MgoZ4bG\nMRuN+P1+RkdH6enpQa/X43A4SCQSWCwW1q1bx29+8xsSiQQfveUWPC+9xCd/8APW5PMXjamo1fLT\nQCX/dyrFSCZD54YN/OX113PPPffQ09NDJBJhy5Yt81r2IwjC+xMJtCAIy1oun+OlgbMUTFpUVWWk\nZ4pdrWs/cLJh0OvZ1bia4UgIjQT1Vf6rLnHZ1NROczyGoqq4Hc73LA/x2B1oYmMohpnWfGq+hNft\n+LBDvSSKotDX08vB3/ySZDFHMV8gORVlW/taCrkcjzzyCF6vl3Wr1vD62TOMD41g1GpprK1jcHCQ\naDSK2WzGYrGQSqUIBALs2rWLn/zkJ4RCIf7oD/6Ayuef547776ehWLxoPAWzmcdcLv4+kyKuKLRc\ns5k7tm/hTz55O5pUltHRUbZu3XrZ5Tm5fI6zk8MUFYUam4tq79ymSaqqymBwnHy5TJXTjd1ivaw4\n5up3a9MFYTGIBFoQhGVtNBqeXS2WJImkEULRCP7L6CtrNBhoraqdrxCvSK6LdB8xGU1s87fQPTWO\nCjR5q5bUBERVVVEUBVmWUVWVU6dO0dPTQzgcplJrYmpoFJfXQ0tjK08/9RRWq5WtW7dy7Nix2RXm\n1tp6BgYG6OnpwWKxoNFoyOfz1NXV8YlPfIK9e/cyNjbGp2+6iYZf/IL/eP/9c2pFl3E6+Z7BwPcU\nBa3VSmVHG5/8+C2s37GV0d4BsrE4N1+3a96uwysDXWRNMmhgIjqGRiMTmENN/9H+LiY1BTQaDb2j\nYa6tWrGg/48nImFOBIcoqCV8eivbmlYu2J4BQbgYkUALgrCsaZDesWKllBXkeVoxVlWVRCqJRpKw\nWW3zcszlxG13sM2+9Fade8ZHeCM2QVlVKY4EMeVVJicnKRaLjI6OYjKZuHbjFvbs2YNer+faa6/l\n4MGDPPfcc5jNZgKBAL29vcRiMRwOB+l0mmw2S21tLdu3b2fv3r0MDQ1x6+bNrP3Nb7jj4YexKcpF\n45r2+fiOqrJHo8FTVcWW9nbuuecevIFKXjx5lHxwmk9s28WqmsZ5uxb5fJ44RfQXti7KBi2hdPyi\nCXSxWGQ0n0JvmWlhqBp1DMXCC5ZAq6rKieAgqsWADj1RtUzX+BAdtU0Lcj5BuBiRQAuCsKw1VFYx\n2hNlWq+gKiq1kpmKy+yDDDNv6Id7zzJJHlSFep2dDY2t8xCxsJCS6RRvpEJMBicJjU0QHBmnSjYR\nC0cAWLNmDY8++iilUont27dz6NAh/v3f/x2bzYbf76evr4+pqSm8Xi+xWIx4PE5NbQ01K1v57S9e\noLevj0+0t7Pr6FE+9cQT6OfQw3k0EOCbxSLPabUEamrY2drK3/3d32E2mxkdHcWiN/KXn7lrQa6H\nXq9H97bcXlEUTFr9Rb9Po9Gg+Z3XpmHhyipUVSWvKrwZmSRJ5JWLT2QUhIUiEmhBEJaMqXiMwVgI\nDRLtvhrMJtNlH1Oj0XBd6xrC0QiyLONxuuYhUhgJTRLSFtFqZm6jw6U0NfPYzk5YGN3d3ZzpPkl4\nbIJSsURwaJjpXJmP3/IR9uzZw9GjR9mxYwdHjx7lySefxG63U11dPVveUVVVRTgcZmpqihUrVtDR\n0cHjP/l3zvf1coPXzR/39POxF16YUyu6M1VVfLNY5KjBQKCxkZtaW/n2t79NIpEgFAphtVrZvn37\ngl4PjUbD5spGXgsNU1QVqoxWVlS9uyXh75JlmVXOAGdTYTR6GXNOYUXTwo2H12g0VOhMxC/8uVwo\nEXCJwTDC4pFUdQ4fj4XL9o1vfINvfOMbix2GICxZsWSC3473IBlnNp3psyVualm7pFpylUolRqeC\naCSJYrnM2eL07L+pqsoGcyU1Pv8iRij8PmNjYwwMDDA4OMix/i7GQ0Fi4QhrNm2k5+UjTEen2b59\nO6dPn2ZgYACLxYLD4aCvrw+A+vp6xsfHKRQKtLW1sXr1al588UWmo1Fu1Gv5wtg4u/KFi8ahSBIH\nAgG+VS7T53Dg9/tZt24d9913H0NDQ0xPT9PU1ERl5dw28r1dLJngTGhkZjOgxcmKS6zTf+v7y1RZ\nnHPq251Mp8jlcnhc7gXfTFssFumaGCavzsRX7fUt6PkE4f0snXcmQRCuapOJ2GzyDJAzaIjEY1R6\nlsaKbrFYnJ3Ap6oqpkQRrV5D6cIGRVNOwV+zNGIV3hIKhejt7SUcDjM+Pk4wGCTaN8yqjpWcGA/z\n8r6fsGXzFjSShp/+9KcYDAb8fj8DAwNMTU3R1NTExMQEAwMDtLS0sGbNGo4cOcJPnnqKT6kqnw+F\nWFu4eOJc0mp5zufju5JExOnE5/Nx+/btfP3rX+fcuXOcPHmS9vZ22tvbSaRTHO4/RxmFGquL+vdo\nE/i7FEXh4GgPZfPM79DZbBhTWE9Nxdw7ahwcOU/ZMlMk0ZWZwhTWU1fx/h8IbRYrtg+p+4ZOp2Nt\nXfOHci5BuBiRQAuCsCSYdDqUvIJGvrCKVSxhNhoXN6i3GY2EZsdXS5JE1q6jQ+siL6loVGhsCiyp\n1fKr3fT0NF1dXSSTSQYHB5mcnKSnp4cNGzZgNpv55dM/pa2tDVO9npdeeglVVfF6vQwPD8+WZwSD\nQXp6emhsbOT666+nt7eXXzz9NLdlMtwdj9NYungNbs5o5DGXiweMRlJWKz6fjy9+7GP85V/+JadP\nn+b48eN0dHRgs81sQlUUhQPD3ZQuJMLh+AQGrQ7/RUqD0pkMOVnhzY+gGq2W6VyaixdjXIgzlyOr\neavGWNbNfP+VMTtSED584m4vCMKSUFfhJ5JOMpSaRpYkOtxVH9rK1ly9vZuHqqqYjCaaLqMdnjD/\nUqkUp06dolgs0tfXx8TEBF1dXbS2tuLz+XjyyScJBAI0NDTw+uuvk8lkcLlcTE5OEo1GWblyJVNT\nU5w/f362q0YoFOLAc8/xmViMuzOZObWiS1itPGS18pjDQdFkwufz8Z//5E/4zGc+w6lTpzh+/Djr\n1q3D9Dt1/sl0ipzurTdnWa9lKp28aAJtMZsxlCXe3A+olMo47OY5Xzej0YhJ1fDmKyuXyjisl78H\nQRCWq2WfQMfjcaLRKG63mwceeIDbb7+dhoaGxQ5LEITfIUkSGxpb6VyiQxLqfQEGzodJGWeSZ09B\nxr9EykuEmXZsJ06coFwuMzAwwPDwMOfPnycQCFBbW8v+/fux2Ww0NDTQ09NDPB7HZrNRKBRmyzMy\nmQznzp0jEAiwe/du0uk0rz//PJ+dmuIL+Tz2OWwZCjmd/G+TiZ+53UhGI16vl7/+67/m+uuv51cv\nvci//Pu/0dDeRmOF913JM4DFZEYuKLy5lFwuK1iNhoueV6PRsLWqhdOhEYpqmVqz66LlF28nSRJb\nq1dwOjhEQVWoMjlpqKya8/fPJ1VV6Z8YI6+UCNhduJZgK0RBWPabCO+44w6+9KUvsW/fPpqamti3\nbx/Hjh370OMQmwgF4cqUzmSQNRqMRiOKojA2FULWaAh4KpZkon+1KZVKHD9+HEVRGB4epqenh4GB\nAWw2G3q9npMnT86WZ4yNjREKhTAajaTTadLpNM3NzeRyOYLBIF6vl7Vr11IsFgkeOMCfBoPcWShw\n8fQVBr1e/tFs5td2O0aLhcrKSr7yla/Q2dnJqVOnkCSJcSvobDOrwuWyQqe18j3rmyeiU5wJj1BS\nFarNDtbWtczzVVvajvSdnR3QouaK7PA347nI4B5B+LAt+xXoWCzGTTfdxH333cf3v/99Hn/88cUO\nSRCEK4Cqqhzp62KslEYCmk0u1tW3UCu6bFyySDzGualxkKDJUUHAc/llL4qicOLECUqlEqFQiNdf\nf52+vj4sFgt2u53e3l6SySRer5doNMrrr7+ORqOhXC4TDoepr6/H7XYzODiIz+dj165dKIpC/MUX\nuWtykj8qlebUiu6U38+/WK0cMhpxOJ2sqq3lK1/5Ck1NTbzxxht0d3ezdetWpuMxJqODs98nyxrS\nhfx7HjPg9s5pEuBypCgKY7kkugvlI5JRx1A8LBJoYclZ9gm0qqp87WtfY8OGDZw8eZJYLLbYIQmC\ncAUYCU0QlAvodTPrjwPFBNXTUbwu9yJHdmXJ5rIcDvahGGZqEiLRYXbq9Dg/4GN5VVV57bXXyGaz\n5PN5Dhw4QG9vLzqdDovFMtttw263YzKZ6O7uplgsUiwWyeVyVFdX43a7GR0dpaKiguuuu45yqYTu\npZf43MQEN85hYqAiSRysquL7djtn9HpcLhfb29r4i7/4C6qqqjh//jxDQ0Ns3bp19imFw2bHMKlS\nulC1oRRKeCvemtr39tHiVzNJkpB/58mOVlrY9niC8EEs+wT6v/23/8bRo0e55557ePzxx9m3b99i\nhyQIwhWgqCjv6Gur0crkisVFjOjS5PMzq5sGw1wKEBZOJBGfTZ4BJL2OqXTiAyXQb7zxBolEAq1W\ny0svvcTZs2fR6/XIskyhUKCrqwudTofNZmNycpJkMkmpVKJQKODz+fB6vUxMTOD1ernmmmugXKby\nt7/lrmCQDXNInIuyzK9qanjQ4WBAo8Hj8fCHW7bw2c9+loqKCvr7+wmHw2zbtu1d3yvLMjtqWzkX\nGqOkKtQ5K/E5Zz6M9QfHOB0Zo4yKX2dlW8uqq7Y8SLqwgfh0bBL0Mpa8SusCDmgRhA9q2SfQX/zi\nF+nt7QXg7rvvXuRoBEG4UlS5vXT3B2f76s70eb78EeAfhpMDPfTnokhINBidizpi3GYyo8aKSBeS\n6HKxhP0SukMAnD9/nqmpKex2OwcOHODEiRPYbDYkSUKr1XLmzBlUVcXtdhMOhxkZGaFYLFIul/F6\nvWg0GoKhEG6Pm7Vr12JQVToOHuRPg0Fa5rANKGsw8NPaWh62WpkEfD4ff3zTTXz84x/HbrczMjKC\n0Whk69at73scu8XKlsa2d/xdPp/nVHQcrcWIBphSS/ROjF7yEJTlpNlfQ7XTSyaXxWl3LPiAFkH4\nIJZ9An3TTTexadMmbr75ZmDm0+23vvWtRY5KEISlzmQwcn3DKgYjQSQkmq6QPs/BSJghJYXePFMr\nMFzO4J8KU7VI7fYcNjvrc9V0RcdRVWizV+Bzze2DyMDAAJOTk3i9Xo4fP84rr7yC1+tFq9Wi1Wrp\n7+8nk8kQCARIJBJ0d3eTzWaRJAmn04ksy8RiMSx2O566GhySyrWHD/GF6Rj+OSTOCauVJ2pq+KHJ\nRFqWqays5D/feis7d+7EYDAwMTGB1Wp9zxXnucoV8qB7K0GUJImCcvH+0sud0WjEuIT6wAvC71r6\n7waXaffu3ezevXv2z1frYzFBEC6uf3KMvkQYSYWVniqqvT5W1TQsdliXJF8qImvfqqOVZQ2F0sUn\n5S2kugr/JbVUGx0dZXh4GL/fz+uvv87zzz+P3+9HlmVKpRLDw8NEIhHq6+vR6/X09vaSSqWQZRmH\nY2bFMplMUltbi8lswpjPcNu5c/zJdJy5FI6E3W72BAL8mywjm81UV1fzZ7feyrZt21BVlUgkQkND\nA9u3b//gF+UCu9WGfUwmc6HKRc0VCQREnb0gLHXLPoG+7bbbFjsEQRCuAOHYNK8ng8iGmdviq9FR\nHCYLVotlkSO7NJUuL7qBSYrGmdehy5bw+6+M0pNgMEhfXx+BQIC+vj6+853vUFVVhVarJZ/PEw6H\nOXnyJA0NDdTW1jI4OEg0GkWr1WI2m9FqteRyOerq6rBarVRns3yqt5dPxuNzakU3GgjwkMfDT2UZ\nk9XKyuZmPvGJT9DZ2Ukul5udUNjaOn8lMZIkcW3TKs4HR2dqo/1e3KLvsSAsecs+gT558iS33347\nLpeLO+64g+bmZj796U8vdliCICwxsUwKWf+2W6JBSyydvOISaINez66GVfSHJ1BVaGrwYzQs7Ufh\n09PTnD17Fp/PRzgc5rvf/S5utxudTkcsFiOTyfDaa69RU1NDS0sLo6OjBINBNBoNFosFnU5HuVym\nqqpqZuU5FOKzo6PcnEjMqRXd+cZGvm+38yJgdzjYtmYNu3fvZs2aNSSTScLhMCtXrsThWJjE1qDX\ns6a2aUGOLQjCwlj2CfTdd9/N8ePHueeee/ibv/kbNm3aJBJoQRDexWO1o0yG0VxYgZZyRVw++0W+\n652mE3H6poNIKqyoqMK+SKPITQYjq2saF+Xcl+LNsdsul4t8Ps/f/d3fYTKZ0Ol0JBIJisUiJ0+e\nJBAIsHLlSoLBIGfPnkWSJAwGA0ajEUmS8Pl8ZDMZVgwNcdfkJNvS6YueW5EkTq1YwfdsNo6Vy7jd\nbj6yZQs7duxg9erVRKNRgsEg69atw2y+tE2PgiAsf8s+gQZwOt9qwO52i9oyQRDezW13sDFfTV88\njAZoq2zEYpp74pTKpDkw0Ytq1IEEwZFubmxcveRXfxdDLpfj5MmTmM1m9Ho9f//3f0+ukEeWNGSz\nWcrlMmfOnMHpdNLe3k4mk+Ho0aMoioLRaMRgMKDX67Hb7SjFIpsGB/lCMEhH/r0Hk7xdSavlUHs7\n/2w0cr5cxut2c8cNN7B+/Xra29sJhUIEg0E2bNiAXq//EK6GIAhXomWfQG/cuJEvf/nLxGIx/vZv\n//YdybQgCMLb1VRUUlNR+YG+NxSfnkmeLyibdITj09S+x6jmq1WpVOLEiRPodDqcTif/83/+T1Kp\nFJlygUQ+R1lRCPYP4XE4aWxsRJZlTp48SS6Xw2g0YrPZsFgsyLKMQVW5ZXiYu0IhGubQnztvMvHC\nihU8YDAQlCS8Xi+f272bVatW0dLSQjAYJBwOs3Hjxiui24ogCItr2d8l7r//fh544AFUVaW5uZl7\n7713sUMSBGEZshiMlNMlZN3MbVUplrA4TYsc1dKgKAqvvvoqiqJQUVHBN7/5TYLBIFarlWKpyNYi\nSwAAIABJREFUxFQqSXh8HFmrxe734LW56erqIpFIYDQacblc2O12isUiDuCPxsb4bDiMr1y+6LnT\ndjtPNzbyA52OvMFAVVUVn9u1i9bWVpqamgiFQkxPT3PNNdeIfsOCIMzZsk+gAe65557FDkEQhGWu\n0u2lJZ2gLzkFKrS7/LgdV/cTrzfHbudyOaqqqvjOd75Df3//bBlGIpFgaGSYTLmIxW7DXeFl4Nx5\nhk53YzKZqKiowG63k0qlcOXz3BkKcdvUFPY59HCe9vl41O9nr1aLzmqlqamJbdu20dLSQk1NDZFI\nhHQ6/Y5x24IgCHO17BPoBx98kPvuu2/2z5Ik0dPTs4gRCYKwXHXUNrFandm8d7UnZWfOnCGRSOD3\n+3nsscc4c+YMsixjNBpJpVJEo1EKhQJWs4UKt5PBwQGGunvRyhr8fj9Op5NoNIovkeBr0Sgfi0SY\nSzX5ZE0ND3m9PA3YnE42rVnDunXraG5uxu/3E4vFKJfLlzX85PcJTkc5G77Qjs7qoq26ft7P8aap\n6Sj5UpFKl0eUnAjCIlj2v3X3338/J06cWLD2Q4IgCG93tSfO3d3dTE1N4fV62b9/P8eOHSOfz2O1\nWkkmk8TjcTKZDDqdjpUrVzIwMMBrh46gApXeCrweD1NTU9SGQvw/8Tg3xmJzakXX19zM9+x2fq2q\neCsq+MiWLbS2ttLQ0IDH4yGRSCDL8kXHbX9QxWKRo5P9YNYDGs7lIljDJqorfPN+rteHehkoJZBk\nGVNknJ1NqzG8z4bHYrFIT3CUoqpQY/fgucqfjAjCfFj2CfSmTZtE8iwIwjuMhIMz3TYkiXZPAJ9T\ndOe5HMHpKL85dYypUJjWymreOHmKF198kUQigd1uR1VVQqEQsVgMgNWrVzMxMcEvf/lLFEXB7/dj\ntVoJBYN0TE7y5Xica5LJi55XkSROt7XxL1YrJ1SVyspKbr/2Wmpqaqivr8fpdJJOp7FYLKxevXpB\nr0E8lUQxyLxZRa3RaonnM1TP83lyuRy9mSg688x6fM4k0xca/70TM1VV5UD/WZLGmQ92g5MxrqVZ\nJNGCcJmWfQIdiUTYtGkTN9988+zfiY2EgvDhUlWVVCqFTqfDaFzctm6RRIyTsTGkC0NTjgYHuNFg\nJJ3JoJFlPE7XosZ3pTnf08NPXj2AbDbQ39/Dnv/vYUqxJC6nC5PJRDKZJBKJUCwW6ejoIBqN8qtf\n/Yp8Po/f78dmszEVDPIHiQRfTiRYlclc9JwlrZbD7e38i8lEnyRRW1vLndu34/P5qK+vx2q1ks1m\n8Xg8rF279kO4CuC02dEGFRTTzHq5Uizhts1/H/CyooDmnU85VH5/TXgulyOiFtBfmMWoMeoYT0RF\nAi0Il2nZJ9Bf/vKXFzsEQbiqKYrCgZ4zhDVFKCu0W72sWsQhH9FUcjZ5BijrZX75xqtIbguqCjXR\nEJua2hYtvg9DJpulb2oCgEZPJVbzpU9bDAaD9Pf3E4xOMTk5yZEXXiQ4MoreaKLS7kSr1TI8PEyx\nWGTt2rVEo1FefvllkskklZWV2O12ouPjfDQW40vJJHVz6OGcMxrZ39bG/Xo9EZ2O5uZmPr9tG3a7\nnfr6eoxGI4VCgerqany++S+deD9arZZtVS2zNdD11kr8bu+8n8diNlMlWwgqBTQaDXK2RGO9//d+\nvU6nQ1beSrBVVUUvzaUoRhCE97NsE+jvfOc7/M3f/A0vvPDCu/7tpptuWoSIBOHq1Dc5xrRBRSfN\n9EjuzkSpSXmxW22LEo/TbKUcDiPrtYSmphiZnMDidRLIyTgsFkbLWeqjESrcnkWJb6Hl8nleGuqi\nZJq5/Y8Mx7ihcRWmOQ58iUajnDt3jkKhwPT0NI/v28fhV4+jMxrxBmYSudGBEcqlEmvXriWVSnHk\nyBEikQhut5vm5mZSY2N8Jhbji8kk3jn0cE7abDzT1MQPdDpKZjMdHR18evNmdDodDQ0NaLVaFEWh\nubkZl2vxniC47Q6utS98yeA1zSsZCU1QUMpU+yve9/+dVqtlnaeGU5FRypKKTzaxoq52wWMUhOVu\n2SbQTU1NwEwN9NW+qUcQFlNZVd7xO6jRaijMIWlaKBVOF2tzGU6O9pEo5fG6XOSMOiZzCYw6HXqd\njmK5tGjxLbRQLDqbPAOUTVompyM0+t+/WvfNsduZTIZcLsdzzz3HK6+8glarpaNtJVlJofvUadRy\nmY2dG8hms5w9e5bx8XEsFgvNzc2URkf5UjzO59JprHPo4Tzl8fBYTQ2P6XQY7HY2btxIZ2cnqqpS\nX1+PJElIksTq1auxWhdnbPpikCSJusqqOX99Y2UV9RV+SqWSmK4oCPNk2SbQ/+E//AcAmpub+fGP\nfzy7eeXt/yYIwsKrcXnpG55CMc2sQNsK0qLXGTf5qykrCvriNMVCkYHQOKrVSK5QwF2S8ddVLGp8\nC8mo01NOvjXwpVwqY7D8/qTqzbHb0WgUgBdffJGf//znSJLE+vXrsdls/OpXv6JQKLB65UoABgYG\n6O/vx2QyUV9fj2FkhL/u7eX2bBbDHHo4jwYCPOzz8XODAYfbzY2bN9PZ2Ukul6O2thZJkpBlmfXr\n179nTf1QeJKzkTHKqkqD1U1HbdMHuVTvkEqnKJZKOO2OK3JRRqPRiORZEObRsk2g33T33Xfzta99\nbbYTx5V44xOEK5nVbOG62jZGp6eQkWhuqV4Sv4deqx01GEKn19HoqyIeibDeX8HK2qZlPZHO5/bQ\nlJymNx1BBZpMbqq87/7A8ObY7YmJCQwGA0eOHGHfvn0oisKOHTuw2+08++yzFAoFVqxYgdFoJBwO\n09XVhVarpa6uDt/ICP+1r48/zOXm1Iquu76eB1wuDhmNVPr9fKSzk02bNpFIJKiomIlRr9fT2dmJ\nTqd7z2OkM2lei46hufCBra8QxxUOXVY7uTMj/ZzPRNFoNbgmZa5bsWZZ/4wIgnBxyz6BdrvdYsVZ\nEBaZ3WJllWVpPWJ32R1sLtbSH58CjZbrV12D+0OoX10K1ta3sKrUAPCuIRyKonDixAmGhoawWCx0\nd3fzgx/8AEVRuPHGG3G5XDz11FOk02kaGxtxuVwkEgkOHjyIqqpU+nysnpzkv/b1sbNQuGgsiiTx\nalMT37fb6TKZaGxs5BOrV7Np0yai0SgWiwWbzYbRaGTDhg0XTVyTmQyS4a3XpNHKJAu5S79IFyRS\nSXqy0+iMM6u3cVmlb3KMFVWijlgQrmbLPoHevXs3t9xyy2xNtCRJfO9731vkqARhaUmkUzMrxJJE\ni78GWb46dukHPD4Cng+3W8NS8buJ85tjt7u7u3E6nYyPj/NP//RPlMtlPvrRj+JwOHjqqadIJBLU\n1NSwcuVK0uk0r7zyCuVyGZfdzq5IhP86MsK6OdS4F2WZl5ubud9qJWS309LSwqfb21m/fj3RaBRZ\nlqmursZqtbJu3bo5P7Vw2x1ow8OUzTMr0Eq+SKXrg38wKpZKSNq3knZJkiirygc+niAIy8OyT6Dv\nv/9+7rvvPlHCIQi/RyKd4rej3ahGHaqqMtETY1fbWvG7chU5c+YMp0+fnh2f/d//+3+nUCjwR3/0\nRzidTp566ikikQi+Sh9tTR1kUhl++/LLlEslHAYDn8pm+etgkMbSxTdfZvV6ftHUxA+sVuIWM5X1\nNaxvbGTb+g3IZRVFUaiqqsLhcNDR0XHJr0Wv13NtXRvnQmMoKDR4q3BdxpMFt8OJY1IiaVRnaq9z\nJWpq5789nSAIV5Zln0Bv2LBBlHAIwvsYnZ5CNc6s1kmSxLS2RCKVxGGzL3JkwkLr7u7m+PHjOJ1O\nIpEI/+N//A9yuRyf+tSnsNlsPPfcc4yPjxMIBLhu5056J0Y4cegYhUIBtyzzxVyO/yOdplK5+Ips\n3Gzmyfp69tps6Dwe2traUHx2KhvrSMUSvBGZYFvdCurq6mhru7w+3HaLlS2N89PLW5Ikdq5YQ9/k\nzKbE2lrvB+qbLQjC8rLsE+jp6WluueUWNmzYAMzcDL/1rW8tclSCsHRoJQ2qqs6uOKslBYNO7NZf\nzvr6+jh48CAOh4OpqSm++c1vkk6n+djHPobVauW3v/0tAwMD+P1+br31VkZHR9m/fz+ZfA6/qvDn\n+QJfUhTsc+ioMelw8Kjfz8/cblx+P5va2li7di0avY5TkRHyuRxOnwdXhZfm5pVLsrZYlmVaq+sW\nOwxBEJaQZZ9Af/WrXwVE6YYg/D4tgRomeqaJaIpIZYVV1opFH7ctLIzTZ9/gqZ8/i8lmIR+K8dje\nvaRSKW688UZsNhuvvvoq3d3dVFRUcOedd9LV1cUzzzxDoVCgvljkL7JZ/lRRmMtPR7/Hw0MeDwd9\nPuoaG9leW8vmzZuxWq2k02kKxSIOu5OK+moqqvwoxRIOk3nBr8GVLJFOcTY4SlEtU2tz0+ALLHZI\ngnDVWvYJ9M0337zYIQjCkqbRaNjZupZkKoVepxPJ8zI0OTnJMz99hsFMnOGJEV5+8HlyqTQ7t+3A\n5/Nx+vRpurq68Hg8fP7zn+fUqVPs3buXYrFIRz7PX+VyfFJR5tSK7jWfj/udTrr8flatXs1Or5cd\nO3ag0WjI5/NkMhm8Xi9NTU1s12k4GxlHzZVptFXgcy3P6Y/zQVEUDo6cp3hhCE40MYFBqyOwAOPC\nBUG4uGWfQAuCcHGSJGG3Lc5obWHhRCIRnnnmGYxGI2fPneOZn/+MbDpDfXsLdrebwf5hXnnlFex2\nO//pP/0nDh8+zA9/+ENKxSLbczn+z3yem+ZQ36xIEi9XVvJ9u51QTQ1r167lBqeT66+/nlwuR7lc\nJpPJUFlZSWtrK17vW0lftbdyIS/BspFOp8nK6uybtkanJZJOigRaEBbJsk2gm5ubZ8s23pyg9ebf\nHzt2bLHCEgRBWHCJRIInnngCWZbp7+/nZz/7GYlkAmeVj/r2FUwMj3L+tTO47U7uuusuDh48yMMP\nP0y5UOCj2Sx/lc+zcQ71zUVZ5jmfjwftdmhpYdWqVXQ4HNx4440kEgmy2SzpdJpAIEBHRwd2u9iY\n+kGZzWa0JQUubE8olxWsRsPiBiUIV7Flm0D39fUBcMcdd/C1r32Nzs5OXn31Ve69995FjkwQBGFh\nZDIZ9u7dS6FQYHx8nJ/97GeUSiV8Ph8rVqzg3PnznOk5gcFo4JOf+iTdp8/yyCOPIBeL3JFO818K\nBVrmkDhn9Xr2ulw86nbj7ehgVUMDXq+X66+/nqmpKRKJBMlkkpqaGnbu3InZLGqbL5csy2zxN3E6\nNEJRVag322morFrssAThqrVsE+g3xWIxOjs7gZmWdrFYbJEjEgRBmF/5fJ49e/YQj8eJRCI8//zz\nKIqC3W7HZrMxOTnJ0NAQZrOZz97xHzl69Cg/+/dnsJRKfCmd5sv5PHPZjha3WHjIauVJr5dVW7ey\n2eOhurqa7du3EwwGiUajpNNp6urquOGGG9Dr37ubSyyZ4Fx4HCSVBocPv1vUPs9FpctDpagTF4Ql\nYdkn0Kqq8tBDD3HTTTfxq1/9arHDEQRBmDfFYpFHH32U8fFxkskkL774IhqNBotlpk9xJpMhHA5j\nMBi44YYbOHXqFHv27KGiXOZrmQxfyOeZy4iRkMvF/6vX8wuvl1233MJ1Oh2tra2sW7eOiYkJIpEI\nmUyGhoYGdu/e/b6TLHP5PAfH+ygbZ74mPDXEdTodTtF3XBCEK8iyT6CfeOIJvvWtb/H444+zYcMG\n9u3bt9ghCYIgXJZisci//du/0dfXRy6X4+WXX8ZkMqHX68nn82SzWfL5PCaTic7OTnp7e3niiSdo\nAb6bzXJHLjenVnTDlZXcq6ocqKjgU7fdxs3ZLBs3bqSxsZGJiQnC4TC5XI6qqipuueWWObUL7Rsd\nIqHkMatmJAkwaAkn4yKBFgThirJsE+i//du/fcef3xykcu+994pBKoIgXJGKxSJ79uzh/PnzFAoF\nDh48iMvlAiAcDmM2m1EUBZvNRnV1NePj4zz77LOsVxQeKRb5WC43p1Z0XbW1/H2hwJmKCv70c5/D\nEY1yzTXX4PF4mJiYIBQKUSqVaGhoYM2aNXPus3+sv4vezDTDmSiWjIE6jw+1VMZmNV3GVZmRy+Uo\nlUtYzBbR918QhAW3bBPoTZs2vesm+vZpa4IgCFeKQqHAo48+Sm9vL/l8nkOHDlFZWYmiKPT29uJ2\nu7FYLLhcLmRZJhgMcvLVV7muVOLeYpHri8WLnqMMHKuv55uFAmMeD5/5zGeoj8XYunUrer2eyclJ\nJiYmUBSFxsZGVq1adUmvIRyNMEYeq91KZblAOJ0kHppic1Uzfs/ltWI7M9LP+dQUkqzBJxnZ3rJ6\nwe710XiMQqmIz+VBo9EsyDkEQVj6lm0Cfdttt30o5zl58iTHjx8nFotx7Ngx7rvvPhobGz+Ucwvv\n1jsxwkQmgUGS6aiqx2y8/JUtQVgs+XyeH/7whwwMDJDP5zl8+DC1tbUoisKpU6eorKzE6/VSVVVF\nPB5ncnKS4YEBbi2VeKhQYN0cEueCRsP+2lq+oyjkqqr4yEc+Qi6XY/fu3eTzeYLBIKqqIssyq1at\noqWl5QO9lmK5hEYzk9R6XG48Ljer9G6aAzUf6HhviiXi9Oan0ZlnilIiapnB4DiN/urLOu57OTXU\ny0AxgSRrsIXH2NnSgVa7bN9GBUF4H8v+N3///v3cfvvtwMywiH379nHjjTfOy7Hj8TjHjx/n7rvv\nnj3X7t276e3tnZfjC5dmMDTBmXQYWacFyiQHu7mpff1ih3VVyuZzjEbCyJJEo79aPPm5RLlcjocf\nfpiRkRFKpRIHDhygpqYGVVU5cuQIgUCA6upqGhoaGBsb4+zZs0yNjvLHxSL/Z7FIQ6l00XOkZJmf\nVFfzz7KMuamJazZvRqvVcscddzA9Pc3w8DClUgmDwcDatWupr6+/rNfk91Rgi0yQNM7ci/XZEtX+\niss6JkCuWED6nU2L+Tm8/kuVSCXpL8TQXugskjKq9AfHaa2um/dzLXfxVJLXJ4YoqGX8Jjura8Wi\nk3DlWfYJ9Fe/+lUGBgZwOBz09/dzxx13cPz48Xk5dl9fH/fdd99sAr1x40b6+/tJJBJiYMAiiGST\nF5LnGbFyHkVRxGPWD1k2n+M3A2cpmbSoqsro+QjXta4VSfQcpNNpHn74YSYmJigUChw4cIC6ujo0\nGg1Hjx6lsrKS2tpa2tra6Onp4fDhwxSmpvhCLsefF4v4yuWLnmNKr+dRr5c9Viu1q1ezqaZmdoT3\n+Pg43d3d5PN5LBYLW7ZsoapqfnoNazQadq5Yw0BwAhWVWr8Po+HyB4H4XB4soVGyZghHpphKJsg5\nK0gXc2xoaJ23n7tyuYz0tnuJJEkoXLxntvBuh0d6KJi1gERPMY5pYpSmy3wSIQgftmWfQLvdbhyO\nmUZNTU1NuN3ueTv2hg0b3tEa7/jx47hcLpE8LxKrbEApZmYTZrNGK5LnD5F6YQDH0FSIkmnm1iJJ\nElFtiWg8hsfpWszwlrR4PM4jjzzC1NQUuVyOAwcOUFVVRUkt8+LLL+Fwu6nw+1i/bj09PT288MIL\nGKan+Yt8ni8Wi9jmMG572GTifrudX3i9rN6wgfUGA01NTdx1110MDg7y2muvkU6ncTqdbN++nYqK\ny18d/l2yLNNSNb+JkkajYWfzal4f7CGoqjRX16LX6RgtZ/GGJ6n3zaXD9cU57Q68QR1RWUGSJLTZ\nInUNvnk59tWkVCqRUkvoL6QfsqwhVsy+59dOTkc4OTlIXi3j01vY2rRS3NOFJWPZJ9AOh4N/+Id/\nmJ1E6HQ65/X4DQ0Ns//9wAMP8OCDD87r8YW5a62uIzWQI5hJoZdlNlR9sFpN4dKoqsqJgW5GsnFk\nScJe1qLa5NmVP7WsoJOX/a3mA5mcnOTHP/4xkUhkth2dz+fDaDRy9NgxdDYzFbXV1DQ1MDEyxk9/\n+lP8qRTfyOf543yeuazfnrVY+EeTieM1NWzcsoXV2Szr16/nzjvvZGBggGPHjpFIJKioqGDXrl3z\nfo/8MOj1emrcPsb1pdmfO42sITeHGvC5kiSJHSs6GJgco6yq1PgrMBnm0gxQeDutVotV0lK48Ody\nWcFhevdeFVVVOT7Rj2oxIKNjSi3RNTYkyj2EJWPZv6vt27ePb3/72+zbt4/m5mYef/zxBTnPgw8+\nyGc+8xk+/elPL8jxhYuTJImNTW2LHcZVZzA4zhhZtBdakUWSWawphbxVh1Iq02RwYrfZFjnKpaW3\nt5fnn3+eaDTK9PQ0Bw8exO1243Q6OX36NDabjaqaapwNVUTGJzmy/yVWZTL8X/kinygW59SK7rDd\nzv/S6xlpaeGarVtpDQZZu3Ytt912G319fRw6dIhYLEZ1dTU333zz7PCVK5XH4cQwNULhwtMPckUC\nNfP3xBFm7jGi1ODyba1dweuTwxSUEn6T/T03kqqqSl5VeHOWpSRJ5JT5r20XhA9q2SfQAF/5ylcW\n9Pj79++nubl53jYnCsKVJFcqoXnbJi6tWU+noxYFFb1Wh9tx5a1oLpRTp05x4MABUqkU4+PjHD58\nGLPZTEVFBefOnUOv11NXV0dbWxsDQ4Mc+vl+risUuS+f58Y5bIxTJIkXnE6+q9FQXreODRs2oBkd\nZcWKFXz1q/8/e/cdH+dZ53v/c09vmhm1Ue+ybEu23OQat/RKGk4BdkOWQ8I+HA5wdiEkD2f3ld19\nzm4IZWlbHFjgUDYJIT4QQkiIg1NcsC2ry5LVRm2kGWlmNL3P3M8fcrQ4CbFsy5atXO+/3HTfl0bW\n6DfX/K7v70sMDg5y+PBhPB4PVVVV3HLLLWjf0YecPL1rq1arL8pjcLGo1Wp2VK6kb8pBBpmKonLM\nRtNiL0t4DxZTFjtqG9733ygUCnJVOoKnf59OJCnMLrz4ixOEeVryBXRTUxM+n++MP6upqWHv3r1n\ntF+cr5aWFnJycli3bh0wO/nwUkXoCcLloNBspX/SjaSbLbh0CZm87BzRq3iaLMscOXKEzs5OYrEY\nfX19NDc3o9FosNls9Pf3A1BaWkpdXR0jIyP8at8+borFeCMWY+08CuekQsEvs7P5OpC7eTNr6usZ\nGxujrq6Ov/qrv8Jut3Pw4EF8Ph/Lli3jQx/60HvGr3WMDDAQ9iAjUaW3sr6qbqEfjovKoNOztly0\nbi0VW6tW0jM5SkJOUWQtoCRP9JwLl48PRAF9zz33cO2117J//37279/Pvffey8MPP8zvfve7C7r2\n0NAQTU1NZ/xZTU2NKKCFD5Rss4WtmSpG/G6UksSKqjJRPDOb2nDgwAGGhoYA6Ojo4OjRo6jVaoqL\nixkaGsLlclFYWMiqVavo7+/npX37uCcW41+iUWrmkagRUav5T6uVbwPLduxga3k5TqeT+vp6Pv/5\nzzMyMsLBgweZmZmhoaGBu++++09+baZmPAwlA6iNs604o+kIhe4pikXRIiwSrUbD2grxgki4PC35\nAnpoaIhrr70WgOuuu44nn3ySJ554YkGuXV1dTWYep98FYanLt+aQb13YftMrVSQS4fXXX2diYgKV\nSkVbWxuHDx9Gp9NRXV3N8PAwnZ2d5OXlsWvXLjo7O3n52Wf5i3icn0ajFMzjOWVGr+eHFgt7gXW7\ndrHbZsPj8bB+/Xp27NiBw+Hg4MGD+P1+1q5dy549e84a5xZPJM6IgVQqFcRTC3cITxAEYSlZ8gX0\n2ykcb+9Aw2zPsiAIwkJyu90cPXqU6elp1Go1J06c4NChQ+j1elatWsXo6Citra2YzWZuuukmuru7\nee1nP+MvYzE+Ho1ils+eKTxhMvGUxcJ/KpWs3byZ3dnZpFIptm7dyrp16/B6vRw6dIhIJEJTU9Nc\na9l82LJzUdsnSepOx4tFUxQW5p7343GpBEJB0uk0VrPlsssaD4RD9EyNk5IzVGTlUppfsNhLEgRh\ngUiyPI9n7Svc28NUqqureeyxx2hubqapqWkuH/pSePzxx3n88ccv2f2WktmYtD6m4iF0ShVrCyvJ\nMV+6r51w+YrFY4x5plEgUVVYvCitI6Ojo3R0dBAOh5FlmQMHDvDWW2+RlZVFfX09DocDu92OVqtl\nx44d9PT0EO3s5L9HItwbizGfILR+i4V/NZv5ncFA/erVGI1GjEYj1157LWVlZcRiMUZGRojFYmzd\nupWGhvc/oPWnROMxBqYmkJGpzi3EZLi8kznaRwYYSviQFApy0yq2L1t92RTR6XSa3/W3z2WiZxIp\ntuZXYhPv1AjCkvCBKKAvB6KAPn8943b6U4G5H4yaaIobV6xf5FUJiy0Wj3HgjyYemmOwa/mlm3jY\n29tLf38/siwTjUZ55ZVXOHz4MGazmbVr1zIxMTF3QHDHjh2cOnUKTVcXn4vFuDUWm1cU3fGcHP7d\nbKYtO5vyigo0Gg0VFRXs2rULg8GAUqlkaGiIVCrFrl27WLZs2cX9pN/BNeOlzzNBRpapsRZQmn/p\n+qW9fh9vTg2h1MwWqLIss1qXR1VhySVbw/txz3g5ODOC8o8SamqUZupLKxdvUYIgLJgl38IhXPlC\n6eQZRVE4nUCW5ctmp0m4eCa9bkb80yhQsMJWckYs2Zhn+oyJh35thmmvB1tu3kVbTyaToa2tjfHx\ncbRaLdFolBdeeIHjx4+TnZ3N1VdfjdPp5K233iKRSLB161YGBwbwPvcc/zsWY2cicdZ7pIEDeXl8\nz2pluqwMs9lMSSbD6tWrueqqq0gkEpjNZgYGBshkMlx33XVUVFRctM/5TwlHIxybssPp9JWWmTFM\nWi3WS/TuUCKVRFKdOVo7dRmdSckyGFG40qCfLaDT6Qwmgxi8IghLhSighctens7IRCiMQjX7g8iq\n1ovi+QNgJuDnuGcESTNboE2PnuL6mtVoNLOjFRRIZ7yQktOZM3b7FlI8Hqe1tZWpqSnMZjPxeJyf\n/OQntLW1kZ+fzzXXXIPb7eaNN94gGo2yceNGRu12NC+8wL/HYqyZx0S8hELBCzk5/J9putUHAAAg\nAElEQVS8PDT19aTTaZThMFu2bGHHjh2MjY2h1WoZGxtjenqam2++maKihRlTfT68Qf9c8QwgadW4\nw4FLVkDbsnMxTzsI6uS50dqlhQs/fvx8abVamvLK6fSMk8rIVBgtlOeLHGNBWCqWbAH9/e9/n09+\n8pPs27dPTAe8wlUVlJBKZ3BGA2gVKlYvwm6bcOm5gv654hkgrVfhDfopzJ0tkqoKixnv9+DTZJDT\nGcqURnKt2Qu6hpmZGXp7e/F6vVgsFhKJBN/4xjc4efIkhYWFXH311fj9ft566y2CwSCNjY14JyYo\nfeklnojHqZ5HhnNYpeI/rVaeLymhYvNmFE4nU1NT3H777dxwww20tbURCoUIBoPEYjHuvPNO8vIu\n3i77fFkMJmT/xNzXKJ1IYbVcusElCoWCHbWrGHJNkEGmvNJ22Y3WLs6ziRhAQViilmwP9PXXX48k\nSXMHBt8mSRKvvPLKJV+P6IEWhHPjmJ6iOeCYe+chE09yfdlKDHrD3L+RZZlprwelUrmgxbPD4WBs\nbIxwOIxOp8PhcPDDH/6Q/v5+SkpKWLZsGZFIhO7ubmZmZqirqyPl8XB1Xx//TzyObR4Zzh6tlh+Y\nzfyuqootN9xAR0cH09PT3HXXXezZs4fXX38dq9WKy+VCp9Nx9913Yzabz3rdt5/SL8W7NA63i16v\nkwwyteb8y6b/WBAE4WJbsjvQr776KkNDQ3zlK1/h0UcfZYm+ThCEJask38ZMLMRwyItSUlCfW3JG\n8QyzReJC9jz39fXh9XpJpVLIsszk5CQ//vGPGRoaory8nJ07d861c7hcLsrLy7FlMtx+5AgPRqNk\nzeN5Ztxg4F+NRk7U13PHvfdieOUVXnnlFe69914efPBBfvWrX3Ho0CFisRjBYJAHHngAg8Fw1usC\n9IwP0xeYQgaWZeXRUFZ9gY/I+yvJK6AkT0SzvVMsHqPXNU5azlBuyRMZ6YKwBC3ZHejLjdiBFoTL\nkyzLtLe3E4vFUCqVhMNhBgcHefbZZ7Hb7VRWVlJcXEwsFmN0dJTR0VHy8/MpjcW4d2SE++JxtPN4\nGu3NyuI7BgNjGzbw5w8+yE9/+lMmJibYs2cPn/nMZ3j66adJp9Ok02mysrK477775vq952Pa5+Ww\nexjF6WEomWSKLTkVFOSce5bzpHeaU14XsixTa7VRJvKL5y2TyfBaXzux04cH5XiK7YU1InpTEJaY\nJbsD/bbXXnuNe+65B5jdrXruuee45pprFnlVgiAstkQiQWtrK7IsYzQaCQaDnDp1il/+8peMj49T\nXl7Opk2bSCQS2O12hoaG0Ov1bNNq+fPeXm6Nx+cVRXfQnMU/a7W41zby5S98ie9+97s8+eSTc4Xz\nc889x1NPPYVGoyEvL489e/ac12HISDw2VzwDKNQqoonYOV8nGA7R7B4DrYpoNEpPXwsN7iLWlFZj\nzTp7C8kH3YzfR1jD3P8NSavCGZgRBbQgLDFLvoB+e4iKxWJhaGiIe++9l+bm5sVeliAIi2DCPUXn\n+DDD/QPU5BdRWljE0NAQR44c4Te/+Q0Oh4Py8nKampqIRCJMTEwwMDCAUqHgeoWCvxgbY2c8ftb7\npIH92dl8TasmsaWJ2//io/z8O0/xpcce4yP33cfHP/5xDhw4wHe+8x2MRiPl5eXcfffdF9S3bLPm\noLQ7SZ+O9lNEk9gKzr11YCYUBK2KZCLJiG8ayaRlJB0iNNnPLuWKy364ymIzGYzgTIHhdO9+JoNO\nu+R/1ArCB86S/67OycmZmzhYXV1NTo7oRROEK5Usy7i9HpQqFTkW6zl9bE/fKV5sO4Ih24wix8ir\nbUfJjsNr+19jYmKCsrIyNmzYQCgUwuVy0d/fTyoe525J4pNTUzTOI8M5Lkm8mJfHXpOJnG2bufm+\nO3j2u0/xH//wNZqu3sHDd9+P2znFD37wAzQaDfX19XzoQx9akAN/eq2O7WV1DLgnkJGoKanEoNOf\n83WsRhOyf5JgOIik1yKnM+j0WjJaNVP+GVFAn4VWq2VNTgkd7nEyyJTqzVQViMOVgrDULPkC2mKx\n8LWvfY1169bR0tKC1XpuP3QFYTGMT7sYD3lRoaShuPyyi+daDJlMhrf6O/FpZOR0hnKvifVVdWf9\nuIGBAaanp4kpZAw5Fk61dBAKBGh76whhp4eqqipWr15NMBhkamqKvr4+pHicj6XTfNLno2oeGc4B\nSeLZ3Fx+lptL4w038MSDD/KP//iP/OT/+zqrdm2lcdtmVDNhDrz6GkqlkvXr13PTTTctxMNyBrPR\nxHrj2R+T972GKYsNOaU0h/vxRiPkma3otVrSyRQGk3aBVrq0VRUUU2mbzegWmfWCsDR9IA4RPvnk\nkwwNDVFTU8MXv/jFRVmDOEQozJfT6+aoZxTF6RHF2kiK61es+8D/IB6aHKcr7pl7HNLJFDvzq99z\nJ1qWZTo7O4lEIlRXVzM1NcX//fULDPqn6T5+Ate4g7yCAipyC0gmk8Tjcfr6+tDF4/xFIsEnAoF5\nRdG5FAp+lJ3NS2VlbLvpJm699Va++93v4na7uemmm1i3bh0zAT9/OHIEo97Arl27rqgzGKcco/T6\nnMgS1Gblseoip3oIgiBcKZb8DjTAI488sthLEIR5mwoH5opngKAiQzQanXeU2VKVesf4dkmpIPmO\nQSWpVIqWlhbS6TSrV69mYGCA73//+2g0GlqOHaeru5ssWw6lZaXoZBXhcJienh6y43Eejcf5s1CI\nrHmMgx5SKvk3s5nWhgauveUW/t/16/nZz37GP/zDP3DDDTewatUqFAoFBw8eJBaLcfttH2Lnzp0L\n/phcbMtLyqkrLgPETqogCMIf+0AU0IJwJdEr1WRSGRQKBQDqtIxWK946L8/NZ9A+TUqvQpZlLHEJ\n2+mItnA4TEdHB0qlknXr1nHixAm+/vWvYzQaaWlpoauri7KyMuqWLUOWZRKJBKf6TlEWj/NENMqe\ncHheUXRtajX/YjIx3tTEh+68ky0FBfzmN7/h0KFDXHPNNaxYsYJkMklLSws+n4/bbruNHTt2LPhj\n4fb76PdMIkmwLKeI3HPsBz8XonAWBEF4tyVfQLe2tnLPPfeQnZ3NvffeS01NjRjtLVy2ZgJ+Yqkk\n8nQQ2aRFrVCxtqDyvGLNlhqdVsfVVfWMeqZRIFFdXsz09DRDQ0MYDAY2b97Ma6+9xt///d+TnZ1N\nT08PnZ2dFBcXU15ejiRJRCIRBgcHaYjF+NdQiFui0XlF0b2h1fIdg4HY1q18eM8e1Go1Bw8exOVy\nsX37du644w6m3NM0t5wgHAxxyy23sGvXrnddR5ZlHNNTKBQSRbn551WchiJh/uAcRNbNjtB2Owe5\nWr0S4wf8HQpBEIRLacn3QDc1NbF//34efvhhfv7zn9PU1LQoMXaiB1o4m5mAn4OTA6BTI8sy1rjE\nzuWNi7qmUCTMmNeNUlJQW1Qytyu+2Ox2Oy6Xi/z8fKqrq/nlL3/JiRMnKCgo4MiRI3R0dJCf/18F\naiKRYMLhYFssxkNeL7vmkaiRBl7S6/mu0Yhu2zbuvfdeQqEQJ0+exOVysW7dOhoaGnA6nbQPnmLc\n42LNVVu5bcfVNFWveNf13j4E6ddCIhYn7QvTWFpNta0I7TkMTBl2OuiMe874s0ZdHhUFxfO+hiAI\ngnBhlvwONHBG8oaIsRMuV+N+D5zeVZQkCTcxotEoev25R5EthGAkzJujvWT0swX9ZL+XnXWNi/qW\nfldXF8FgEAwaglYNv9r3DOEJNw0rVjA8PMyvfvUrcnNzycvLI5FIkE6n8Xu9XB8K8d3pada+o2f6\nvcSAX5hM/LvRiG3bNj5x331MTEzQ0dGBy+WitraWm266CbvdzqlTp+i3D2Lb0MAN1/w5AOPpGGVu\nNwV5Z44YH5924tdCKpli2DuFbNCQDk4wHvKyu2YVarV6Xo9Blt5IOuhCebpPPp1IYbKK3WdBEIRL\nackX0Bs2bOAv//Iv8fl8PProoyLGTrhsqSUF8h8flEvL8y6qLoZx7zQZ/X8V9F5lEn8ggNVyaSeq\npdNpjhw5wrh3mmV1deQXF/LPP/kPXBNOCipK6Rjo5fevvkp2djbZ2dmEw2EkSSIVCvGhmRn+fGqK\n2nkcDAxIEj/OyuJHWVlUbN7MZ+65h6GhIbq7u/F4PNhsNj7ykY8wODhIW1sbwWCQLVu2cMdH7qEn\n6Zu7jkIhkcy8u1B/+60+fzAARi0Ssy0dMYMS54ybstOxZ2eTa7HSEM6n3z8FQH12wUXtgRYEQRDe\nbckX0Hv37uWpp55ClmVqamp44oknFntJwhLWPWZnMupHIylZVVB+TuN7awtLcQ74mVEkIC3TmF2C\nSrV436KKdxX0mUta0EejUdra2kgmk/iytSR0Fv7j+aeZHBimZEUNrrExTrz+FlqdniyDgWAwiEaj\nwZROc8vYGH/u8VA4jw41pyTxA4uFZ61WVmzaxOduu42+vj4GBwcJhUKoVCpuvfVWhoaGOHToEGq1\nmsbGRm688UZ0Oh3xRILBITeJ0xMADdEMhaV577pPSa6N/n4XPkmanU6XkciyGEmnM2iU5/a4Lisu\nY9npdAxBEATh0lvyPdCXC9EDvfQNuyZoC0+hVM72CasiSW5asf6cWh5kWSYciaDVaBZ19xlmd37f\n6u/Cp04jpzLUGXJouAQ5wG63m76+PgwGA2vWrOF3h95k32u/JRwMYcnJpfnNt3CNjKPV60mlUqRi\ncQqsORQCt/b3c7/Px3xetgwoFOy1WNhfWEjjxo1s2rSJkZERcnNzyWQyhEIhNmzYgNPpZGRkhPz8\nfFauXMmWLVvIzc0941qxeIwR9xQKSaIyv/BPfu1SqRSj0066J4ZJZOmQZKhQZ7GhevmFP3CCIAjC\nJbPkd6CbmprO+L0kSRw/fnyRViMsZb5EZK54BohIaZLJJJpzOCAmSRIm4+UxKlmpVLJreSMzfh9a\njQbjRR7hPDo6isPhIDc3l61bt9La2sq3v/1tJj1TqLVq7Cf7mBwbQ6VQoJYlEuEIZrOZFRo9d/T0\ncHcoxHzmNbYolfy7xUJrRQUbt2zhw8WzaR6JRIKKigomJiaoq6sjkUhw6NAhKisrufrqq6mvr6e8\nvPw9r6nT6lhe8t5/98dUKhXVRaVUF5USCAaRJMgyZZ3jIyUIgiAstiVfQP9x4sb+/fvZv3//Iq5G\nWMqsWiMjwSAK1WwwmkFWLvou8oWSJIkca/ZFvUdPTw9+v5+ysjKampo4fvw4L774IgqFAr1eT393\nL529PchKiVgojEGjpbqiiqqZGW7r7p53FN1+hYLv5eTgXLmSpo0b2XU61i47O5vy8nIGBgaw2WzU\n1tbS3t5OTU0NN954I6WlpdTX1y/4523OEoXzuZryeemddpAGqix5c+OyBUEQLrUlX0D/seuuu44n\nn3xysZchXIG6x+w4owHUkoLGwgqsWeZ3/ZtKWxHxRIKJqB+1Qsmq0so/2b4xPu3CEZpBrVCwsrAc\nvXY+e6eXRiwWQ6m8uMV/JpOhtbWVZDLJihUrKCwspKuri2eeeQaNRkNaAS/85kWck5Po1RrSsThq\ntZqNjWuptg9z1xtvsHOeUXT7FAr+1Woh0FjP1Zu2keXxEggE2LhxIzabjY6ODiKRCLW1tbS1tVFd\nXc2dd96JXq9nw4YNl01039lkTh+UvFLWe66isSjHXPa5/Ov2wCRGjY78i/wCTxAE4b0s+QL6q1/9\n6tyvPR7P+/xLQXhvdqeD/qQfpVYByBwZ7/+Tvc3LSys4WzfrpNdN84wDpXb2289j7+G65WsXfeJb\nJpPh8EA3U3IUKQ311kKWF5+9LeFcxONxWltbAVi3bh0ul4v29nZaWlpQKBRYLBZ++cIL9Az2k8mk\niQQjxAx6rtq4kYqWFu596bfzjqL7sULBU9lWDNs2Ure2kb62TiYcDq6/9jpKS0s5fvw4LpeL8vJy\nurq6UCgU/Nmf/RnRaJQNGzag010+L2rOpmtsiP7ANAC1WXmsLq9Z5BUtvJlgYK54BlCoVXgjQVFA\nC4KwKJZ8AV1dXX3Grx977LFFXI1wJfIlomf0NodJnXNv8x+bCvvnimeAAClisdii5T2/bWDSgVeT\nQS3NFo4ng1NUxGwLUkjOzMzQ29uLVqtl48aN9Pb2cuTIEbq6uojH42RnZ/PrX/+a4eFhguEQgXAE\nszWLpm1NrD10lE889xw184ii8wN7lUr+My+PDbfeys3La9n/+/30tXRw07XXsX3DJo4fP87Q0BCl\npaWMjIzgcrl46KGH8Hg8VFRUvOuA4KUQioQZ8riQgJq8Igzn8H9hyuthMOFDZZr9mKGkH5vXQ0HO\npf88LqbsLDN4x+ey0tOJFNnmy+O8gCAIHzxLtoB+9NFH3/PPm5ub+ad/+qdLvBrhSpatNTASDs0V\n0SZUF9TeoFdoyKSCc2+1qzMyWq12QdY6X91jdsbCM6gkBattZRRk55KS02fugislYvH4BRXQDoeD\n0dFRrFYrGzdupLW1lTfffJP+/n58Ph95eXns37+fgYEBZFkmGAySnZPD6tUr2XTwCH/xixfmFUU3\nKUl8R6nk59nZ3PqRj/C/b7iBH/zgBwSbW/nLjzxAZWUlnZ2d/Pa3vyU/Px+dTkcgEODBBx/E7Xaj\n1+vZtm3beX+eFyIaj/Hm6CnSp2PwHCM97K5qQHP6/9jZWjKiyTiKP4o7VKhUxJLxi7fgRaLX6dmY\nX0GPe4IMMlXmAmzZS+tFgiAIV44lW0A3NTW96y3xMzJthSVDlmWOD/UylQijVShZV1hJnmXh3tat\nLCgmNp5gIhpAIylYVbrsgv4fLSsuxW8PMRkOoZYUrC2ouqR9q6PTTgYSPhR6FUng6OQQt2RZKLbk\nMDjhBt3szro1pcRifnev93z09/fj8XgoLi5m1apVdHV1cejQIQYGBpiamsJms3H48GH6+vrIZDLE\nYjEKCwu5ed06Vr7yCnva2+cVRdcvSXxDqeQ3OTk88NBD/OCGG/jWt77F3r17+djHPkZVVRWdnZ28\n+OKLmEymud3lu+++G6/XSyqVWrTC+W3OGc9c8QyQ1Ks42NtOUDX7wmGZOZ9V7xMfWGDNQWmfJH16\n6I0qlsJWuDQnrhbm5FGY8+6MbUEQhEttyRbQe/bsec8/f7v/Ulg6eh3DOJUJJIOGGHB8YoibLRsW\n9B4rSitZsUDXkiSJjdUrgdn84MkZDxPuKYrzbAt0h/cXiEXnkkIAMloloXAYq8XCjuI6xnxuVJKC\n2pqSc86wbm9vJxaLsWzZMgwGA2NjYzgcDrq7u3E6nRQWFvLWW28xNDSEJElEo1GKiorYVVLC2v37\nufPo0XlF0Z1QKHhSoeCtnBz+x+c/z3PXXMPXv/51WlpaePDBB6mpqWFgYIDnnnsOSZLm4ud27dpF\nIpEgFAqxdevWi/bCJZ5IMOp2AVBlK3rfgTg6lYZ0OI3y9NdkxuMloFFjPh1vN5jwYZvx/MndVp1W\nx/ay5Qx5nABUlxZeVodSBUEQlqIlW0C/7fnnn2fv3r1IkoQsy9jtdvr7+xd7WcICCqeTZxR6kUyK\nTCZz2acRhCMR3hjpIW1Q4xybRt2foTa/iFUF5e+Z8rFQcg0mBrxelJrZHUttUibLZALAmmU+53sn\nk0laWlqQZZk1a9YwMjJCX18fer2ejo4OXC4XBQUFvPbaa0xOTqJQKEgkEhQXF3Ot1cqmAwe46Q9/\nmFcU3WtKJU9KEu05OXzxkUf4q+3b+eY3v8mBAwf4xCc+QV1dHaOjozz99NPEYjHq6+vRaDSsWrWK\nrKwsfD7fRT8gmEgkeGOoi/jpXeXRATdX1635k/8fi/LyqQz5GQp7kGUoQEciyzD39wqVilji/Vsy\nzEYTa421C/dJCIIgCO9ryRfQe/fu5YknnuCpp55iz549Igd6CcrXZ+EIhub6QLNVusu+eAawe1yk\nDWpmfDPMKJLIahmLlHzflI+FUJSbz9p0itGgFyXQUFKJUjmf8vVMgUCA7u5uNBoN69evp6Ojg/b2\ndqxWKy0tLczMzJCTk8NLL72E1+tFo9EQjUYpLyvjVr2ebW+9xc742Xt108AvVSqeBEbz8nj00Uf5\n26Ymvv/97/Pyyy/zsY99jLVr1zI+Ps4zzzyDz+ejsbGR/Px8iouLKSgoYHp6msLCQhoaGs758zxX\nDu/0XPEMENYpmHBPUWor/JMfs7ayllWp2djDRCrJ7+3dZE63ZCijS7clQxAE4Uq15AtogPXr1wOz\nOdBPPfXUIq9GWGgVtiIymQyTkQAaScmqyoWNXrtYZGZ7XKOJJAqNknQyhSRBWMoQjUYxGAxnucL5\nq7QVnfcQCqfTid1ux2w209jYSEdHBy0tLeTk5PDyyy8TCAQwmUw8//zzxGIxjEYj0WgUW24uD+fm\nsvPQIdbMI4ouDvxUreZrskzAZuNLX/oSDQ0N/PKXv+TFF1/kzjvv5H/+z//J5OQkzz77LC6Xi3Xr\n1rF7925MJhMFBQW43W60Wi1XXXXVeX2u50N5+t2ut18AyRkZleLsT7Vvt3nolUp2lC1n0D0JEiwr\nL0YnWjIEQRAuK0u+gJZlmeeffx6A733ve/h8vkVekXAxVBWWUEXJYi/jnNTaipkYPolWrcaXiJCr\n0c8OMMmkz4i0k2WZZnsvE7EgKhSssZVRmldwydc7MDAwt5NbXFLM8fY2xlwTVJdW8Jvf/IZUajaO\n7xe/+AWJRAKLxYLX6yU/K4u/LSri6mPHqEmnz3qfgCTxfY2Gf06nkW02HnnkEWpqanjjjTd46aWX\n2LlzJw8//DBOp5NnnnmG8fFx1q9fz2233UYmkyEnJwe/308qlbqkhfPbymxFjPS58arTyEgUyxoK\nzjEaz2w0sc647CKtUFhsMwE/3dPjpOQM5aYcqguvrOcuQRBAkuV5ZERdgdra2li7di0Adrud7Oxs\nnnjiCe677z7WrVt3ydfz+OOP8/jjj1/y+wqXt3giwdSMh1G3i4ga1JKSRls5OZb/yqDonxjjZNwz\n15aSCce4bfmG82q7OFeyLNPZ2Uk4HKampga/38/E5ASDcT9RKc3x197AImlQxdO88sorAFitVkZH\nR6nJy+PBRIKbTp6kYB5PMy6lkn9Rq/nXdBpTcTGf/vSnqayspKuri/b2dtasWcNdd92F2+3m4MGD\nDA4OsnbtWq655hqSySQqlWpuGt9iTxCUZRm31wOSRP4Sy2MWLkw6neblvlYyhtm0m0wyzabsEopy\nL80hYkEQFsaS3YH+4he/iN1u55577uFTn/oUVquVJ554YrGXJQhn0Go0lBUUUVbwp9spYunkGcVg\nSqkgGothMl68IRKpVIrW1lbS6TSrVq2iv7+fwcFBamtr6Rrq58Brr6LVapkYGuHV5jYsOgN5ubkM\nDw9TolTyDa2WG9raMM+jcB5SqfiWRsMPUynyior49J/9GVVVVUxOTvL8889TVVXFF7/4RSKRCL/9\n7W/p7u6moaGBRx55BJVKhc/nw2QyEQwGL5sJgpIkkZ8r4taEd/MHAyQ1irlDswq1Em80zPk1VAmC\nsFiWbAH96quv4vP5+PnPfz4XaXf//ffz8MMPYz7PbFtBWAwFWVaGpmZQaGcPlZllJcaL1B8dDofp\n7OxEqVSycuVKurq66OrqYu3atXR2dvJv//Zv+GNhRgfsDHWcRKvTYcnNJjAxxTLgUVnmmo6OeUXR\ntanV/LNGwy9SKYqLi3no9tupqqoiFotx+PBhLBYLDz74IJIkcfjwYTo7O1m2bBlf+tKXyD1drGdl\nzUa9lZSULMoEQUE4V2ZTFsrJzNxP33QyheUinncQBOHiWLItHO/k9/vZs2cPv//970nPow9zoYkW\nDuFCTHqmGAt6UUlK6gvLFvxQ2dTUFENDQxiNRgoLCxkYGECn07F27VoOHjzIq6++CkBPTw9dXV1k\nVBIqvR7XuIOdWj2fi0TYPjU1ryi6N7Ravq5S8VomQ1l5Obt376aqqgqVSoXT6USSJBobG7FarfT1\n9dHe3k5JSQkf/ehHKS8vp7OzE5PJRDgcprS0dC7jGWZbYsY9U0jMDsC5EtJYLsSUz0u/14ksy9Tl\nFmGzirSOK8GUz0v31DgpMpQbslleWrHYSxIE4Rwt2R3ot7W2tvLss8/yi1/8gvXr1/O73/1usZck\nLBJZlukcHcQVC6FVKFldWEH2RcxbXkhFubaL0iNpt9txOp3k5+djs9lwuVz4fD62bt3Kq6++yqOP\nPgrAqVOn6OvrIysri/z8fEaGh7k6EOLTkRibJl1nvU8a+LVWyz+r1ZyQZSorK9mzYQOVlZWYzWbC\n4TDBYJCKigpKSkqw2+0cOHCA/Px8/vqv/5r6+nqOHz9OX18fkiShVqvfNUEwFo/zpv0kcb0SWZYZ\n7/eyo271kp0+GgyHODo1DNrZp/GjU8PsVmvIMpoWd2HCWdmsOeLFjiBc4ZZsAf3Vr36VvXv3YrVa\n+dSnPkVzczNWq3WxlyUsokHnOPZ0EIVOSQyZo+P93LRyYScWXim6u7sJBoOUl5djMBiYnp6mqqqK\nLVu28OKLL/Kd73wHnU5Hb28vQ0NDZGVlYbFYmJqc5E5Z5qmZGVaEQme9Twx4RqfjWyoVdqWSmpoa\nbqmpoby8HJvNhlarJRgMotfrqa2txeVy8fLLL2OxWPjMZz7DunXr6OjooLm5GYVCgSzLbNmy5T13\nlse9U8T1s3vgkiQxo8ng8ropzM1f6IfvsuAJ+ueKZwC0KjxB/5IooMemXZz0OpBlqDLnsbz4yoim\nFAThg2PJFtAej4dXX32VqqqqxV6KcJnwJ2Io/ii5IiynSKfTlyTN4nKQTqdpbW0llUpRW1tLKBRi\nZGSExsZG9Ho9zz//PK+88gpms5mxsTH6+/vJysrCZDLhnZjgI8kk/21mhrJY7Kz38gM/0uv5rlLJ\njFZLXV0d1xQWUlRURGlpKUVFRfh8PgKBAAUFBQSDQQ4fPoxOp+PBBx9k69at2DnVF2wAACAASURB\nVO12Dh06hEajIZ1On/WAoCS/O39ZKS3dFg6LwUQm6EKhmX0azyRSWLKv/OI5FAnT6htH0s32/PdG\nPFg8BgrFoUxBEC4jS7aAFokbwjvl6AyMhcMolbNFlVmh+UAUz9FolPb2dhQKBZWVlQwNDTEyMsLG\njRvJZDL85Cc/4cCBA2RnZ+PxeDh27BhGo3G2z3higgdiMR6cmSEvmTzrvSaBf9fr+Q+VirTRSF1d\nHcuzssjLy6O2tpaVK1cSDofninO9Xs+pU6cA2LNnD7t378bj8XDw4EE0mtmYr+rq6nkdEKwsKGK0\n301QB5mMTImkW9IRctlmC43RQvp8sy00yywFZJstZ/moy58/HEI6PWYeZlMqAvEof3qOoyAIwqW3\nZAtoQXinqoIS4uMpJqMBNAoFjeU1i72ki8rj8dDf349Op6OoqIjJyUm8Xi9btmwhHo/zzW9+k7a2\nNrKzs/H5fLS1taHX6zGZTCTHxngoEuGjfj+meRy67ZckvqXR8IxajSE7m1X19UiSRFZWFitXrmTb\ntm1EIhHa29tJJpOE00n6hyZIxGLcceOtfPwjHyWRSHDo0CGUSiWSJFFQUEBFxfwPVymVSnbVNeL0\nTKNSKLF9AHYsqwqKqSooXuxlLKhcsxXJ60DWzf54kuNJ8rOvjLMKgiB8cIgCWvhAWVFawYrFXsRF\nNjo6isPhIDs7G5PJRCgUQqVSsWXLFiKRCH/zN3/DyMgI+fn52EdHOXj0D2g0aizGLAwOB58KBLg7\nGEQzj4CeE5LE19VqXtJoyC8sZHtDA4lEAqVSyapVq7jllluIRCI0NzfjcrnIy8sjLUmMuCdZvmEt\n226+jkwsyeEjR8ik08iyjNVqpaGh4bw+d4VCQXH+pZ/SKCwcnVbLtqIaet0OZKA6t3BJ7KxfSWLx\nGD2TYyRJU2LKoSRPDHkRhHcSBbQgLBG9vb34fD4KCwtRKpXMzMzQ0NCA2Wxmenqaz3/+83i9XkpL\nSxkfH+dESwtRUmizjJQ6HPyPITu3RqLziqLbr1DwdZWKw1otZeXl3NjQQCgUIh6PU19fz/33308k\nEuHYsWOcOnWK3NxcampqcDqdZBfZePC/7UGhUDBhH2Fm2o2kz6e4oGDRJwgKl4ccs4VtomheFLIs\nc3Coh6hh9plgcmYcpUJBYc7Sf0dHEM6FKKAF4QqWyWRob28nHo9TVFTEzMwM09PTrF+/HpVKxSuv\nH+Dfv/8UkXCY1XUrsNvtdHR0oFar0eq0rBxz8dlAiJ3zOBiYBv6vUsnXFApO6nTU1tZye0MDbrcb\nj8dDQ0MDH//4x4lGo5w4cYKDBw9is9nYuHEjY2NjmEwm/u7v/o5gNMKL3cdxTk4gZ2RUiQzX3LRr\nbiiKIAiLJ5FIEFAkUZ9+Ka3QqHCF/aKAFoR3EAW0sKSdHLfjigbRSEpWF1VgXuSIr1g8xuSMB61K\nQ3He+cerxeNxWltbkSRpLr85FAqxZcsWJEni97//PT/8Pz/CEfZjteUyeqqXUyd7sFmyMen1rBse\n5uGZGVbH42dfM/BTlYpvSBITBgMrV67knvp6JicncTgcrFixgoceeohoNMrJkyd56aWXyMrK4sYb\nb8Rut5NKpfjCF76A2WwmEonQ29WNeSZKNK2iuraaLctXX3D0WiQaZcQ7hQKJalsRarX67B8kCMK7\nqNVqlKn/+r0sy+gU4vtJEN5JFNDCkjU4OU5fwo9SowDSHB3r5/oV6xZtPeFIhDdHe0jp1aQjGcqD\nM6yvqjuna/h8Pnp6etBoNJjNZgKBAEqlcu5g4L59+3jppZdQq9XIKgUTwyPYu3tRaTSYtBpuGBnh\nkz4flYnEWe8VkCSeUir5tiQRMBhobGxk+4oVTE1NMTg4SE1NDZ/5zGeIRqMMDg6yb98+VCoVd911\nF4ODg/h8Pj71qU9RUFBAJpPh2LFjRCIRVCoV61evOacDgu8nGo/xxshJUvrZH/Ljg16urmsUrSCC\ncB4UCgUbC6tonx4lkUlTqDVRV1G22MsShMuOKKCFJcuXiMxF1gEE0vFFzX22e1xzRZ5SqcAe8bE6\nmZzXbqnD4WBsbIysrCw0Gg3JZJLq6mrq6+txOp387Gc/4/XXX0er1aJSqWhvbycYCSErJawKiT3j\n4zzkD2KbR6KGS6HgWwoFe4G00UhTUxMrThfOAwMDlJSU8Nhjj5HJZBgfH+fZZ58lHo/z4Q9/GKfT\nyfj4OPfdd99cBvvJkyeZmpqa2y2vr6+/oMfxncY903OPK0BYJzE141myA1QE4WIrzs2nWHz/CML7\nEgW0sGSZ1XrGYxEUp4to0xWY+9zf34/H48FqtSLLMqFQiHXr1qFWqzl58iT79u2jubkZtVpNLBaj\nra0NAK1WS7EscffwGB/zB8jKZM56r0Glkq9LEj8BlEYjmzZtYtWqVbhcLnp6eigoKOB//a//hdFo\nZGZmhqeffhq/38+ePXuIRqM4HA5uvPFGVq1aBcwW/Xa7nVgshtVqZf369RdlV1gpnTlAJZNKo1GJ\nt5wFQRCEi0cU0MKSVVtUSnQsjisWQispaSytXdT1VOcXMjY8Q0qvIpNKU2vIec/dZ1mWaW9vJxaL\nYbFYkGWZeDzOli1bSCQStLS0cOLECU6dOoVCocDtdjMwMIBGo0Gn05Hj9fLnQ0N8aGYG7Tyi6NpU\nKv4JeEGS0BmNbNu0iTVr1jA5OUlPTw8Wi4XPfvazFBYW4vf7+d73vofL5eL222/HaDTicrnYvHkz\n27ZtAyAQCNDZ2Uk0GsVgMLB9+/b3nSB4oaoKS3D0eXErk5CRqdZaybFYL9r9BEEQBEGS5Xn8hBUu\n2OOPP87jjz++2MsQFlk8kcA140GnUr9r0EcymaS1tZVMJoPRaCQUClFQUEB1dTVOpxO73U5zc/Nc\n4TwyMsLY2BgGg4F0Ok2V18tfTE9zzczMvKLoXler+SdZ5g2FAoPRyIYNG9iyZQsjIyP4fD5MJhO3\n3XYbVVVVBAIB9u3bx+TkJLt376ayspLJyUlqa2u5/vrrUSgUpFIpmpubCQaDGAwGVqxYMa8JggtB\nlmV8AT9KpRKzSaR5CIIgCBeX2IEWhEtIq9FQXlB0xp8Fg0G6urpQqVQoFAoymQxFRUXk5uZy8uRJ\nDh06REdHB21tbajVavr6+vB6vZhMJiRglcvFJ6an2eT3n/X+aeBFrZZ/TKdpkySMJhNXrVvHzp07\nGRgY4OTJk5hMJm6++WZWr15NKBTixz/+MVNTU6xfv56bbroJt9sNwEMPPTQ3brujowOn04lOp6Ou\nrm7BDgjOlyRJZItdZ0EQBOESEQW0IAChSBin34tOpaH0Ek2yczqdDA8Po9FokCSJdDrN2rVrkSSJ\ntrY2ent76e7u5tixY6hUKvr6+ubaOpKxGJtnZvjE9DTLg8Gz3iuhUPC0RsNX0mnskoQ+K4utjY3c\ncMMNc/fJyclh1apVNDU1EYvFePrpp/F4PCxfvpxrr72WcDhMLBbj/vvvn8tsHh4enouqKykpOe8J\ngoIgCIJwJREFtPCB5wsGODgxgKxTkY5mcIV8bKhaftHuNzg4yNTU1NzurSRJbN68GafTOXcIsLW1\nlaNHjwIwMDAAgNlsxuNwcLvTyQPT05SEw2e9V1il4nsqFV9LJvEAOqORDQ0N3HXXXXR1ddHe3k5J\nSQlZWVk0NTUhyzL79u0jHA5TUlLC9u3bUSgUhEIhbrnlFmy22ZG+Ho+HkydPEggEsNlscxMEZwJ+\nRnzTKCUFy2wl6LTai/AICoIgCMLiEgW08IE37JtC1s1+KyiVCoZDPtYucNydLMt0dHTM5SDDbEFc\nW1tLd3c3R48exWAw8Ic//IG2tjai0ShjY2NotVpMJhPTAwN8dHycj7hcZM9jauCMTsc3JYnvJBLE\nJAltVhZrV6zg/vvvp7Ozk+bmZpYvX04ikaChoQGdTsfLL78MgMlkoqmpCZvNxuTkJNdff/1cS0Yi\nkeD48eN4vV5ycnK49tpr5w4I+oIBDk4OgE4NMjiHurl2+VqRxywIgiAsOaKAFj7wJFk64/cKmItE\nu1CpVIrW1laSyeTcNcvKyrBarbS3t3P06FHy8vL49a9/zalTp3C73XMH+DQaDfGRER5Op7ljchJD\nMnnW+zmzsvjHZJL/SCRAp0OTlcWqZct44IEH6Ozs5NixY6xfvx6Px0NBQQEWi4U333yTrKwscnNz\nKSgooL6+nv7+fiorK7n11luB2RcAra2tOBwOrFYr27Zte9cBwUn/zGzxfFpEK+H1+8jLzlmQx1IQ\nBEEQLheigBY+8OoKSnAOnySuVSKn0qy0FFzwrmk4HKajo4PM6fxlpVLJ6tWr8fv9DA8Po9PpyM3N\n5ac//SmDg4NMTEyQSCSw2WykUilSvb08kslw/cQE6nkMPxnKzeVvw2Gei0TQGgyotVpqa2t5+OGH\naW9v59ixY2zfvh2Hw0E6naampoZjx45hs9koLS1Fo9Fw1VVX0d3djU6n4/o7bmUkOMPBgS70wSTT\nLhdqtZrGxsY/eUBQq1KSSWbmHrtMMo1ee2Z8Xe/4MPaQF6Uk0ZBbQkme7YIeZ0EQBEFYDKKAFj7w\n9Fod11SvZsrnxaDVkW22nPe13h5z/fbEQ51Ox5o1a+jp6aGrq4uioiL0ej3PPPMMIyMjOBwOFAoF\nRUVF9PT0YBsf5xvJJFsmJlDMI2Gys7CQx/x+fuf3YzAa0Wk0VFVV8dnPfpbW1lb+8Ic/sHv3bsbG\nxhgfHyc7O5vu7m6qq6upra0lkUiwe/duenp6iEQifPKTn2TK5+WodxS/z8/YwCBxb5APX3UNa9as\ned+1VBWUMD0UwBENokBidXYRRoNh7u8d01P0xrwo9SpSQLN7hNwsi+iTXoIi0Sj97glkWaYy24Y1\ny3zB18xkMsiyfMUNQxIEYWkSBbQgAGq1mpILSN+w2+04nU6SySQajYa8vDwqKiro6OigubmZVatW\n0dLSwre//W2GhoZwu93o9XpKSkroaG+nZniYn8RirHI6z3qvjCTxh5ISHvF4aJ6ZQa/Xo1OpKC8v\n56//+q9pbW3lyJEjXH311Xg8Hrq7uzEajXPtF+vWrcPlcrF161ZGRkaYnp7mgQcemDvU6PBM09Pe\nQcDjJa+okJVN6yjJLTvruiRJYnNNPalUCoVC8a5d/EAiilL9X085kk6DPxQUBfQSE08keGOkh5R+\n9ms9PjHA7rLlmAzG877mqfERTvqdyECF3sr6qroFa7MSBEE4H6KAFoQL0N3dTSAQIBaLodfrqamp\nAWBsbIx4PM6mTZv49a9/zd/+7d9y6tQpAoEAubm52Gw2erq6WNPfzz8Gg1SezlZ+PymVileLi3nU\n7abP7cZoNKJJJCgpKeELX/jCXKvG1q1bUSgUnDhxYnbAiM9HaWkp5eXl2O12rrrqKqxWKy6Xiz17\n9mAymYDZHb7m5mbauruQDbBh9w40Oi1yOI7lHIaTvH1I8p3yjGb6pz1Imtm/V8VSZBdf+M6kcHmZ\n9nnnimcAWafC6fdSe54FtD8YoCfqRmXSAzCejpI/7aTcVnSWjxQEQbh4RAEtCOcok8nQ2tpKNBol\nmUyi0+lYv3793GTA4uJitmzZwo9+9CO+973v0dfXRzQapaysDIVCweDJk3w0leJfvF4K5jH8JK7T\n8X8LC/ny1BST09MYjUbU8Th5eXl84QtfoK+vj/b2dtasWYPNZuP111/H7XaTyWTYtGkTeXl5DA0N\nUV5ejlarxel0cvPNN5Ofnz93j97eXnp6esjJyeHDt9/BdDTEaNiLKi7TUFTzniPHz1W+NZv1yQTD\nAQ9KSWJlSeXcrrewdBi0OtKB1Ny7Del0Br36/L/O4VgMxR+9c6FQKoilUhe8TkEQhAshCmhhyctk\nMhwb6mEqEUGjULKuoIKC7HMfMR2NRmlvbycSiaBWq+f6m0+ePElPTw+rV69Gr9fz7W9/m9bWViYn\nJ4nH41RXVzM+Pk7f8eM8lMlwv9OJJRI56/3CZjP/JyeHf5iaIjg9jcFoRBGJkJOTw+c+9zmGh4cZ\nHBxk+fLl1NbW8vLLL/PCCy9gMpnYunUrJSUl2O12FAoFlZWVuN1ubrjhBsrK/qsdw+Fw0NHRgSzL\nrF+/fu6AYC65rGDhpwmW5hdcskE1wuLIsVhZHsyh1+9CBioN2ZTknf/XPN+ajdYzTuL0rrYUS1KU\nL5JdBEFYXJIsz+OkknDBHn/8cR5//PHFXsYH0slxOwOpwFzPpBROcOvKDfPuofR4PPT19REMBjGZ\nTJjNZiwWCxMTE+h0OhobG0kmk3zlK1+hvb2dUChEOp2mtLQUu92OPDnJf08m+ZDDgT6ROOv9ZvLz\n+VeDgW96PMQAg8FAKBSiuLiYT3/60zidTgwGA0VFRTQ2NvL73/+et956i5ycHHbu3EllZSWjo6Po\ndDo0Gg1+v5/t27dTX18/d49AIEBLSwtut5uVK1ee9wRBt9/HiG8KpaRgRUEpunekbggfXAt56C8a\nj9HnciCzcIcSBUEQLoTYgRaWvGg6dUaxnCBNJpM56w/20dFRHA4HPp8Pq9VKXV0dgUCAUCiExWJh\n8+bN+Hw+vvzlL9Pa2oosy2i1WvLz8xkYGGD6yBEei8W4Znx8XlF0kyUlfFWl4odeL5l4HJ3BQCYU\nIisri89//vP4/X5SqRQ1NTXU19fT1dXFl7/8ZXJycrjjjjuora3F7XbjcDjIysrC5/NRV1fH5s2b\n5+6RTqc5duwYw8PD1NbWsnPnzvOO7JsJBjjsHEQ6PThl2t7DtXVrzul649NTjATdKJBYmV8iCqNF\nMjrt5NSME2SotdqoKii+4Gsu5AAdvVbHmvKaBbueIAjChRIFtLDkFRjMjPmDcz2ZOUrd+xbPvb29\neDwefD4fOTk5NDY2Mj4+jsvlYvXq1RgMBoaHh/nc5z5HV1cXGo0Gi2U2+q6/v58V4TDfCIfZ7HDM\nK4pusLqav08keCEYRKVWozUY5na7H3roIWRZxmw2k5ubS1VVFYFAgL/5m7/BaDRy7733UlNTQyKR\nYGJiApVKRTKZJC8vj/vuu++MFw4dHR2cPHmSoqIi7rrrrrkJgufL6ffOFs+nRTSc0+AUj9/HiZkx\nFNrZaxx29HNd9WrRF32J+YMB2mYmkLSz3x8dASdmnYFci3WRVyYIgnD5EgW0sOSV5heQljM4w340\nCiUrK8vf9W8ymQxtbW34/X6SySQWi4UVK1YwPT2N2+1m06ZNSJJEc3Mze/fuxW63o9VqKSkpIRwO\n09bRweZYlKeCQTa4PWddk6xQ0FFXx5f9fo74fGg0mv+/vTuPjuq+7///ujMjjfZ9BUloQexmkYSN\nsWOwsbDhazuOMTZpErvxKYuTXxu3jb/GadOc9CSpwc1Jm9Ocb4C4rU8T+5jFaRI7TpAUY4MNDkJi\n34RGgBa0M6N9mZn7+wMjWwYDFyRGQs/HX8zMnXvf5zL36jWf+SxyhoSovb1dKSkp+trXvqbQ0FBl\nZmbKMAwlJiYqKipK3/ve92Sz2fTkk08qJydHISEhamxsVGdnp9rb25WWlqbly5cPGvR3+vRplZWV\nKSIiQoWFhZesIHi9QhxBgxZOMft8Cg8Nu8q7PtHU4RkIz5LkDXHofHubkuMThqQ+XBtPV+dAeJYk\nW7BDnu4OAjQAXAEBGmPChKRUTdCl01719vaqvLxcra2tioiIUFxcnEzTVE9Pj5xOp+bNmydJ+uMf\n/6hXX31VLS0tCgkJUUpKitrb23Xs8GHd29amH7U0a7L76jNqmE6ndk+apP/b2KjjF2fU8Pvl8XiU\nkpKiJ598UvHx8Zo8ebK6u7sVFRWlnJwc/d3f/Z16enq0YsUKTZo0SUlJSTp37pzq6urU1tampKQk\nLVu2TOHhn0wV1tLSoj//+c/q6elRfn7+564geL0yk8epuapNNR1tssnQzPjxCrXQqh3lDJWvu0X2\nIIe6u7p0vvW8alNCFBMZJSet0DdNXESU5DknXQzRfV7Fx1//YkIAMBYQoDEmud1uHTt2TA0NDUpK\nStKECRPU3t6unp6egW4apmnqV7/6lbZs2aL+/n6FhYUpLi5ObW1tqjp+XMs6O/UXdXVKaWu76vHM\nqChtz8nRt6ur1VBfr5iYGNk9HjU3NysxMVFf+tKXlJaWphkzZqjt4/3NnTtXzz//vJqamvTlL39Z\n06ZNU3Z2turr61VWVqaOjg7Fx8fry1/+shISLrTadnV3q6qhTofLy+Xt6tXs2bOve4Dg1RiGobnZ\nU1XwcTcVqwtbjEtI0qSeTp1orlNNe6uSExJU6+hVq+uI7rPYl3qs8Pv9qm1ukCSlJaYMyWIiEeHh\nuj0xUydb6mRKyo1LszTvNwCMRQRojGodXZ2q97QqNMip8QlJV92+trZWp0+fVn19vdLS0pSZmame\nnh75fD7dcccdMgxDXq9XP/7xj1VSUqLg4GCFhobKbrerra1NptutJ91uLauuVkx391WP509O1rYJ\nE/RCZaV66usVl5wso6lJ1dXVSkpK0he/+EVlZmYqPz9fTU1Nam9v17Rp07R+/XqtW7dOjz76qPLz\n8zVt2jSdP39eO3fulMfjUXR0tJYtW6a0tLSBY7V3dug/3/lfVZ2p0rjsTM0vmK3pky+E5yZ3q856\nWuQwbJqcnDakq//dSIiblpYlm2GXI/aTwNbpNNRyvlWJdOUYxO/36/2Th9T2cSO/62Sj7pk0c0hC\ndHJsnJKvse86AIAAjVHM3ebRzrpTUmiQfN1+NXe2adaEiZfdtqKiYmBGjZSUFKWlpck0TSUmJmr8\n+PGSpI6ODv3whz9UaWmpomNiZA8Nlsfdrvb2dkV1dWllU5OWnj2rsP7+q9bmy8nRf8XH63unTslW\nV6fkzEzV1NSosrJSiYmJWrFihaZMmaLbb79d9fX1qqmpUW5urn71q1/pJz/5iebPn6+nnnpKt912\nm3p7e7Vnzx41NDTI4XBo6dKlmjJlyqDjnTp1StveeUv98WH6wkMPKjjEqcaeXnV2damnv0+7G09f\n6OdqSk1VR7Vo8uwRsxRysM0mv/9Tfan7fXKyvPclapsa1BbyyRcWj9NUTVO90lmRDwBuOgI0Ri2X\nu1EKvTAIzW63ydXRoplmzkDAME1TBw4cUH19vSQpKipKSUkXWqlnzpyp0NALSwPX1dXpn//5n1VR\nUaHs7GzFxsXpZO1ZGYY0rqNLq5uataS+4ZqmouubNUs/DQ3VuhMnFNbfr8wpU1RZWakjR44oPj5e\njz/+uGbNmqV58+apvr5eJ0+e1Pjx43XgwAFt2LBBkyZN0ve+9z3l5+fLbrfro48+0unTp9Xf368F\nCxZo7ty5g47X0NCgDz74QEFBQbpn4QI1R31qdhHTlN1m07m284MGibXb/Wrv6FBU5Mj4mT4rZbwa\nTnlU5+uS4Tc1LSpJUXQhuMRl53NhFn8ACAgCNEatz7afXgzO/f39KisrU01NjeLj4xUaGqrg4GBF\nRERoxowZA9uVlZXpJz/5ic6dO6dZs2YpJSVFFRUV8hrSjJ4u/WVNve5tbJT9GkJK11136QderzZW\nVCg6JkbTZ87UyZMnVV5erujoaD366KOaN2+eCgoK1NLSoiNHjig6Olput1v/9V//pYSEBP3jP/6j\n5s6dq8jISO3evVtHjx5VR0eH5s+fr4ULFw5qMe7u7taOHTvU1tamO++8UxkZGert69P7riPqDrHJ\n9PqUGx6nkJAQOe0O+b2ftPAaXr+lwX7DzTAM3Zk7Xb29vbLb7XI4uC1dTlpisipPNqj94/+6yB5T\n4zNY1REAAoGVCG8SViIcep1dXdp59rj6Qx3y93uV5gtRb4tbp0+fVkZGhnp6ehQREaGMjAyNG3dh\nYQjTNPX222/r1VdfVUdHh2bPnq2qqirV1NQoKTFRtzU16eFjx1TQ2nrV45s2m9z3368Xz5/XVpdL\n8fHxmjBhgo4eParW1laFh4fr3nvv1YIFCzRr1iy1tbWptrZWpmmqr69PW7dulc1m05o1a7RgwQIl\nJCRoz549Ki0tlcfj0ezZs5U6daIavV0Kstl1W2K6kmPitHv3bp08eVK33377JQMEfT6fGlpbFBIc\nrLiPpyEzTVN/dh1TbU+bHIZNtyWkKSvpxhfKGEtM01RbR7tshqHIALaO+/1+1TRdHESYzEBLAAgQ\nAvRNQoAeHr19fTpy8oTO1dSo7bxbSUlJstlsCg8P18yZMwcWC/F6vXrllVf01ltvKSgoSFOnTtXJ\nkyd19uxZ5WRmam5NjR46ckS5nqtPRecLClLjkiX629palZw5MzCLx5EjR9TS0qLg4GAtWLBAS5Ys\n0ZQpU9Td3a3a2lp5PB45nU794Q9/UEtLi5555hk98sgjSkxM1IEDB7Rnzx7V1tZq6tSpeuSRR9TQ\ndl6Huptk+3jRl7MHjym4vk3Tp0/XvHnzLIcnv98vwzBGTN/n0cI0Te0+dVQN6pVMvyYERSkva1Kg\nywIABBC/lWLUqqysVGVlpdrb2+V0OpWRkaHo6GhNnz59ICS63W5t2LBBxcXFSklJ0W233abDhw+r\nqKhIt02apDV2uxa//bbGd3Ze9Xje8HCdXrJEf33qlPbt3q1x48bpzjvv1MGDB/Xee+/J6XRq0aJF\nWrZsmdLT0+X1enX69GnV1NQoMjJSBw8e1PHjx/XII49o1apVio+PV2VlpbZv364TJ04oPT1d3/rW\ntwYWOulobZDNblfzuQYd3rNXIaFh+tvHv6aE61wIhdbK61PdeE5Njn45bBdul9XeTqW3tigxbmgW\npAEAjD4EaIwqpmnq0KFDqqyslMPhUF9fn8aPHz+om4YknThxQq+99po+/PBD5eTkKD8/X+Xl5aqs\nrFT+xIl6qr5e923dqrje3qsesy8+XocLC/U3R46octcupaWl6c4779SBAwfkcrlkt9u1cOFCPfXU\nU4qLi5PNZlNtba1Onjw5MG/0b3/7W82fP1+///3vFRsbq8bGRv3mN7/Rp2oeXAAAIABJREFU3r17\nFRsbq1WrVg2akk6SQnyGdr39R8kwlLfwbiU4IxQfx1RjN1v/p2YIkSTDblOv1xvAigAAgUaAxqjg\n9XpVVlamkydPKjo6Wna7XUlJSZo1a9ZANw1Jeu+99/TWW2/p0KFDmjFjhmbMmKGysjLZbDbdlZOj\n+Xv3asHrryv8GgJQT3q69nzhC/r2gQOq37lTEyZM0O1ZWTp06JBOnDghwzA0b948PfvsswoJCVFI\nSIjOnTungwcPKjExUbGxsXrjjTeUm5urP/7xj4qOjlZXV5feffdd7dixQ3a7XU899ZQmTRrcHcDn\n8+lPf/qT6urq9Mi8hVJsuIIMu6Ylp9H9IgDGxyWooqpR/aEXbpehPX6lpNH6DABjGQEaI15dXZ22\nb9+u8PBwpaamKjk5eVA3Db/fr61btw6EzhkzZignJ0c7d+5UXFycHpk2TXP+9Cfd/f77Cvb7r3q8\nzqlTtT0vT98rL5dn1y5lZWVpdmamjh49qsOHD0uS8vPz9fd///cyDEORkZGqra3V3r17lZqaqmnT\npmnTpk1KSEjQ22+/rbi4OPn9fn300UcqLi5WR0eHHnvssUumpJOkffv2qbS0VPPmzVNhYeHQnkhc\nlxBniBZkTdPp5gbZZCgrO4WZQgBgjOOvAEa89vZ25eTkaOLEiUpN/WTRCI/Ho23btundd99VT0+P\nZsyYIZ/Pp3feeUcZGRlac/vtmvqb32juH/4g+xX2f5F77lxtycnRvx88qN6PPlJmZqbSgoJ08uRJ\ntbS0yO/367bbbtM//MM/qK+vTzExMQPhPjU1VXfffbd+/vOfy2az6b//+7+Vk5MjSTp8+LDefvtt\nnayq1IKFC/TVJ758SX/kqqoq/elPf1J2drZWrlxJf+URJtQZoqnjJwS6DADACMEsHDcJs3AMnYqK\nChUXF+vdd99VUFCQZsyYoWPHjunQoUOamJOjr44bp6zNmzWzoeGq+/IbhloWLtQv4uP1P0eOSJIy\nMjJkGIYqKyvV3Nys/v5+TZ06VT/4wQ/U2dmphIQENTQ06N1339W4ceN0++2362c/+5na29v1ox/9\nSHfccYck6cyZMyouLlbZgf0KTUvW3cuWyjAMjVOI5mZPlSS1tLToD3/4g8LDw/Xggw8O6o4CAABG\nJlqgMSqYpqldu3Zp37592r17t0JCQnTHHXfogw8+0NatW3XbtGl6+Y47lPXGG8pxu6+6P6/DofoH\nHtBPHA69c/KkQtxuZWZmyuv16syZM2publZvb69yc3P1ox/9SJ2dnQoNDVVHR4def/11paSkaMWK\nFdqwYYOKior03HPP6dFHH5V0IRTv2LFDO3fuVG5urp7+/9aowfnJKoZnu9o0taNDRUVF6urq0oMP\nPjgw88ZQqaqv1dmO83IYNk1PSlNMZNSQ7h8AgLGMAD0ECgsLVVRUFOgyblnHjh3Tr3/9ax0+fFjh\n4eGaN2+e3nnnHR0/flx35uXpuYgI5bz55jVNRdcbEqKz/+f/6KXubu12uRQTE6OJEyeqq6tLZ8+e\nVUNDg/r6+pSZman169erq6tLwcHB6uzs1Ouvv67ExEQ99dRTeuWVV/Td735XK1as0OrVq2UYhnp7\ne7Vjxw698847SkpK0ne/+13Fx8frSE2V5GuXdOGLwJGPytT8/n498MADyszMHPLzda6lUQc6GmQP\nckjy68OaCj04eQ7dQkagmqYGVbgbZRjS5LgUpcYlBrokAMA1IEDfgJKSElVWVqqkpCTQpdzSKioq\ndPbsWc2dO1dvvvmmjh49qiXz52vRqVOa/J//qbi+vqvuozMqShUPPaQfNjfryNGjSk5OVm5urtra\n2nTmzBnV1dUNBOcf/OAH8n882NDn82nbtm2KjY3V17/+db366qv6p3/6Jy1cuFA//elPFRoaKtM0\ntWfPHr355psKCgrSc889NygY5ySmqrbqvCqqT+vQ7lLdVzBPTyx9ZLhOl1q6Oj8Ozxf0OqT2zg5F\n0wo9orjbPCo7XyvDeeH/qrS5WguCQxQVwJUOAQDXhgB9AxYtWqRFixZpzZo1gS7llhYbG6v9+/fr\n+PHjemrxYs1+7z1N+8lPFO7zXfW97qQkHVmyRC/V1qrqwAGlpaVpypQpam1t1dmzZ1VTU6P+/n6l\np6frO9/5jqKjo+Xz+dTb26uSkhJFRkbq6aef1uuvv67vf//7mjt3rl544QWlp6dLko4ePaotW7ao\nra1NX/3qVzVnzpxLavC4Pap6b69iY2L0g7/+thJih3cu56iQUPnb3LI5LgyddHj9iggLH9Zj4sq8\nXq+qmxtkSMpISpXNZlNrV/tAeJYkOR1yd7YToAFgFCBAY8Q7d+6c1i5frgmbN2v6976n4GsY99qY\nkaG9ixbpp2fPqr68XBMmTNC0adPU0NCgpqamgeCclpamb37zm8rKylJbW5s8Ho8++ugjhYaG6itf\n+YrefPNNrVu3Trm5ufr+97+v/Px8SVJ1dbW2bdumiooKPfTQQ1qyZMklNXR3d2vbtm1yOBx6+umn\nb9oAwYzEFLX3dKu2yy2HYdOM1BzZ7dcyDwmGg9fr1XunDqsr1CbTNFV1skkLJs1UbFik/G2Nsl0M\n0X1eRccTngFgNCBAY0RrKinSnH9dr+y9+65pKrqzkydr51136T+rqnR+/35lZWVpWmKiampq1Nvb\nq7Nnz8rn8yk5OVlf//rXNXv2bDU0NKixsVH79u2T0+nUihUr9Nvf/lY/+9nPlJycrGeeeUZLly6V\ndGFp8N/97nf68MMPNX/+fH3rW9+6ZHETv9+vt99+W42NjfriF7+ohISEITsfXd3dqnM3K8hmV0ZS\n6ucurDI9PUvTh+youBE1zQ3qCr3Q/9wwDLWHSHXNjUpLSlFe73hVuBsk09TkuDRF0/oMAKMCARoj\n09696vm/zytxx3u62rAqn6TKOXP0zm236Xe1teo4ckTp6elKHTdOZ86cUU9Pj2pqauT3+5WQkKDH\nH39c9957r1wul6qrq3XkyBHZbDZ96UtfUlFRkV555RXFxcXpvvvu09e+9jXZ7Xb19/frrbfe0vbt\n2zVp0iT9+7//u4KDgy+pZc+ePdq/f7/uu+8+Pfzww0N6Sjq6OvX+2ePyhQbJ7/er3uXWHTnTLO3D\nNE11dnUpyOGQ0+kc0vpweYZhyDTNgS87pmkODOhMT0xWemJyIMsDAFwHAjRGppYWhex474qb9Nls\nOnb77dqWlaUPGxvlPXNGqampGjdunFwul/r6+lRXVyefz6eEhAQVFhbqscce05EjR3Tq1Cm5XC55\nvV49+OCD+uCDD7RlyxbFx8dr2rRpeuaZZxQdHS3TNFVSUqLf/va3SkxM1A9/+EPFxV3ah9nlcmn7\n9u2aOXPmsPWJP93SKF9okCTJZrOptq9D3d3dCg0Nvab3+/1+7ao4rGajT/L5NT0qRZPHZwxLrfhE\nemKKTlc0yeM0ZZqm4vvsSo1ntg0AGM0I0BiZHnhA3dOmKvTosUte6nQ4dPCuu/RaYqKOtLQoqKVF\nycnJcjqdqqioUHd3txoaGuT3+xUbG6v58+frmWeeUXl5uQ4ePKjGxkZ1dnZq4cKF2r9/v9555x0l\nJydr/PjxWr58+cAKguXl5Xr99dcVFBSkb37zm5o0adIltXg8Hm3dulXx8fFatWrVsE4VZ/tsbw2/\nYel4Feeq5XaaCjIutJwfbW9QZm8yLdHDzGaz6Z5JM1XX3CibYVNKfMLndr0BAIwOBOgbUF5erqKi\nIhmGobVr16qwsFCLFi0KdFm3BsNQ0NoXpaeeGniqJThYZQsW6Jfh4ar2eBTV36/U1FSFhYXp+PHj\n6u7uVmNjoyQpJiZGs2fP1je/+U2VlZVpz5496urqUltbmwoKCnTq1Cnt3LlTmZmZ8vl8uvvuu3Xn\nnXdKkk6fPq1XX31V58+f1xNPPKH58+dfUp7P59OWLVvU29urr3zlKzdlgGB24jjVVh1Vd4hNpten\n3Ig4S+HXa/oHBze7Xb19fQTom8AwDI2nqwYA3DJYyvsmYSnv6+D1SpMmqa27W8Vz5ug1m02tXV1K\nSEhQSEiIwsPDdeTIEbW1ten8+fOy2WyKiopSbm6unnvuOR0+fFhtbW0yDENut1vTpk1TTU2N2tvb\nlZubq9OnTysvL08PPfSQDMOQx+PRK6+8opMnT2rp0qV6+OGHL9tSuH37dlVVVenRRx9VcvLNDUVe\nr1eN51vkDApWfEyspfe629u0q65CZkiQTNNUVK+0YNJMWkMBALCIFmiMXA6HVFKiP+zZo/+3caPS\n0tKUFheniIgIHT16VG63W263Ww6HQ/Hx8Ro/fryee+45VVRUaMeOHQoPD1dXV5cmTJggwzBUUVGh\nKVOmqLKyUna7XWvXrpXT6ZTX69Wrr76qP//5z7rrrrv0N3/zN3I4Lr00Dhw4oA8//FBf+MIXtHjx\n4gCcEMnhcGjcdbZkxkRG6e5xuapxt8hh2DQxbTzhGQCA60CAxsiWlSXnwYPKyMhQZGSkjh8/rqam\nJrW1tSk4OFhJSUmKjY3VX//1X6u6ulrvv/++EhIu9DENCwuTz+dTdXW1pk+frjNnzsjtdmvVqlVK\nTEyUaZp68803VVRUpOnTp2vdunWKiYm5pIT6+nr95je/UW5urp599tkAnIShExMZpRhWJAQA4IYQ\noDHiRUZG6ty5cyovL1dHR4fCw8MH+j6vXLlSLS0t2rVrlyZMmKCIiAhJktPpVENDg2bPnq3Gxkad\nPXtWS5cu1ZQpUyRJ7733nn79618rOTlZa9eu1YQJEy45bm9vr375y18qMjJSK1euHNYBggAAYPQg\nQGPEKyoq0qlTpxQVFaX09HQZhqGvfe1r6unp0d69e5Wbm6uUlBT19PTINE21tbVp1qxZ6u3t1bFj\nxzRv3jwtWLBAknT48GG9/vrrMk1TTz/99GWX3r7YMn3+/Hn9xV/8hcLCwj63tmaPW7VtLQoybJqc\nmsGKfwAAjAEEaIx4mZmZyszMlNfr1fLly2UYhg4fPqxJkyZp0qRJcrvd8vv98vv9ysvLk2maOnz4\nsCZOnKhvf/vbstvtOnfunDZu3Kj29nYtWbJE995772VblN9//30dOXJEDz30kNLT069YV7PnvD5o\ncMnmvDAor/nUEd0zeeZwnQYAADBCEKAx4tlsNi1evFjh4eGqqKjQ5MmTNWfOHNXW1srv9ysoKEhz\n5syR0+lUWVmZEhMT9eyzzyoiIkJdXV36j//4D9XW1uree+/VAw88cNmFR06cOKGSkhLNnTv3mvs5\n17S1yOa8sLCJYRhq8nerr6/vsisUAgCAWwcBGiPerFmz9Mtf/lITJ07UPffco+PHj6uhoUGRkZGa\nOXOmIiIiVF5erqCgID355JMaP368/H6/Nm7cqEOHDmnevHn6y7/8SyUlJV2yb4/Ho9dee00ZGRn6\nxje+YamuYMM+aIlmu2lcdvYOAABwa+GvPUa8hIQELVmyROXl5SovL1dCQoLy8/OVkJCgY8eOqaKi\nQl/4whc0c+bMgf7L77//viZPnqznnntuYGXBT/P7/fqf//kf2Ww2rVq16rr6Lk9KSVez66iafD2y\nm9KshDQGGgIAMAYQoDHi1dTUaMeOHUpLS9OcOXOUmpoql8ul3bt3a9q0afrqV78qwzC0c+dO/e53\nv1N8fLyefvppzZ49+7LzHP/+979XTU2NVqxYoaio65/SzeFw6J5JM9XX1yeHw0F4BgBgjCBAY8SL\nj4/XPffco8zMTFVXV+uDDz5QSkqKVq9ereDgYB0/flyvvvqqnE6nHnnkEc2bN0+SVN/SpHBnqKIi\nIyVJe/fuVWlpqe6//34tXbp0yOqjzzMAAGMLARoj3rhx49TU1KQPPvhAYWFh+vKXv6y4uDjV1dVp\n06ZN6uvr0/3336+CggJFR0eru7dHO6uOqSfEJn+rTzHHenVs337ddttto34hFAAAEHgEaIx4dXV1\nOnXqlAoLC5WVlSW3260f//jHam5u1l133aXZs2crLS1tYPsTDTXqDbWrt7tHO958SxFhYXrpWy+w\nbDUAABgSBGiMeDk5OZo+fbp6enq0ceNGnT59WtOnT9fSpUs1derUS7b3mX69/9t31NvTq0XLH5H6\nfYNmywAAALgRBGiMeEFBQdq6datKS0s1adIkfelLX1J+fv5lB+2VlJRo/8GDmnXHHEWPT5Hf59d4\newQD/AAAwJAhQGPE+/DDD9XY2KiHH35YeXl5l10I5dChQ9q1a5fuvvtu/f3f/q3aOjt0zt2qkNAg\nZSSmBKDqW49pmio7fVLV3R45DJtmxI9XZlJqoMsCAOCmI0BjxJs8ebKmTJmixMTES15raGjQr3/9\na02cOHHQAMGo8AhFhUdccb9+v197XMfU2Ncpp82u2UkZSo279BjXo7+/X43uVoUGOxUXHTMk+wy0\n0w11qjG7ZA8PkSlpf2uNUqPj5HQ6A10aAAA3FQEaI97lVhDs7e3Va6+9ptDQUK1ateq6umgcrzuj\nZodX9qAQeSWVnjuth2ITbrivdE9vj97/eBYQ0+PXxLZoTU/PvqF9jgTd3n7ZPrXgjBHsUHtXJwEa\nADDmEKAxqpimqf/93/9VS0uLVqxYoYiIK7cyX0mP3zsoLPfZTPl8vhtejruisU69oXYZkowgu060\nN2uyN2NYlvk+UXNGNV1uOQxDM5IyFD+Mrd0pUbGqqG+RzRkkSQrt0y3Tug4AgBUEaIwau3bt0sGD\nB7V06VJlZmbe8P5SwqJ19ny77MEXLoMEe8iQhFzzU/9ubG7W+c4O7XYc08xxmYqOiLzh/V9U3dSg\nYz0tsjsv1Lyn7pSWROYN24DJuKho3eHNVHVbs+yGTVMyWbocADA2EaAx4p05c0Zvv/228vPz9Y1v\nfGPI9jsuIUkFpnSu87yCDLumZmYMyX4z45JUU+1WU2+7ms1eRUdFyO00tbv6pB6Ykjdk0+m5ezpl\nD/rkEu51SJ2dnYqMHLqQ/lkpcfFKiYsftv0DADAaEKAx4sXExOjZZ58dlnmc0xKTlJZ4aR/rGxEV\nHqGFE6Zqx4kDsocFKSrsQjeTTsOnvr6+IeszHBsSLlebW7aPW81DvIbCw8OHZN8AAODz8fsrRrzo\n6OhRtwhKWGiopqSkKSIkTBdLDzVtCg4OHrJjpCUma1pooiL6pJh+m+4cP5EuFQAA3AS0QAPDJDsl\nTV3Vfarr8ijIZtescblD/kUgd1y6cpU+pPsEAABXRoAGhtGM9GzNCHQRAABgSPF7LwCMYZ1dXers\n6gp0GQAwqtACjVGp1eNRXVurnHaHJqamjbo+0sBIUFZ1Uqf73DJNQxnBESrImsK1BADXgBZojDqN\n7lbtbDilKn+7jva26M+uY4EuCRh1GlqaddbfqaCQEAWHOlWnXtU2Nwa6LAAYFQjQGHWqPZ+shmez\n2VTX0y6/3x/gqoDRpc/bL7vjk6XZbXab+n3eAFYEAKMHARqjjsMY/LG1GzZ+dgYsSolLkLPHN/DY\n0e1VaiyL5ADAtaAPNEadyclpaqo6qna7X4bXr1kJ4wnQgEVBQUG6J3OqqpoaJJnKzEpRiDMk0GUB\nwKhAgMaoE+J0atHk2Wrv6FBoSIiCgoJueg1d3d06525RSFCQxick3/TjA0MhxBmiqWkTAl0GAIw6\nBGiMGn6/Xx+5jqmpr0tOm11zUjIVFRR50+to6+zQruqT8oU65Ov2q77drfysyTe9DgAAEBj0gcao\ncaz2tJocXhnhTvWFOlR6riogdVS1NsgXeuG7p91u0+kej7xeBl8BADBWEKAxanT7vYP6Ovf4+mWa\n5k2v47O9rQ2/SR9sAADGEAI0Ro3ksGj5+z9p6Y0PDgtIcM1NGq/gngt1+Pt9mhKdJLvdfpV3jW6m\nacrt8bBiHQAAog80RpH0xGT5TL/qO91y2hyaOiEjIHWEOkN0b9YMNbpbFRrtVHxMbEDquFl8Pp92\nnTqsVrtX8vk1KSxe09OzA10WAAABQ4DGqJKZlKpMpQa6DAUHBystKSXQZdwUlfW18jglhxEkBUkn\nu1qU2ZWi8LCwQJcGAEBAEKCBa2SapspOn1R9T7uCbXbNSp6gpJi4QJc17Hzm4D7ehsOu/v7+AFYE\nAEBg0QcauEYVddWqUbf8YcHqCbHrz3WugAxivNnS4hJk674QmE3TVKzXruioqABXBQBA4NACjTGr\np6dHQUFB1zwAsNPXJ5vtk++cPYZP/f39Cg4OHq4SR4TIsHDdkzFFNa3NshuGJmakMesIAGBMI0Bj\nzOnv79cu11GdV69sPmlOYoYmJF69P3NiaKTOetplC7oQuKON4Fs+PF8UGRauqWHhgS4DAIARgQCN\nMedEQ7U6QgwFKUSStL/xrDISkq/aqpqWmKx+v1d1nR4FGXbNCNAsIAAAILAI0Bhz+vy+QY99him/\n339NXTmykscrS+OHqzQAADAKMIgQY05aVLzM3k8GxSUFhd/yC6EAAIChQws0xpykmDjNNwzVtrUq\nxHAoNyM90CUBAIBRhACNMSkhOlYJ0bf2CoIAAGB40IUDAAAAsIAADQAAAFhAgAYAAAAsIEADAAAA\nFhCgAQAAAAsI0AAAAIAFBGgAAADAAuaBBm4B9a3Nqm5rkcNm09TkdIU4QwJdEgAAtyxaoIFRrtlz\nXh81n1W90asas1s7q47JNM1AlwUAwC2LAA2McvVtbtmcn/yY1G73q6OzI4AVAQBwayNAA6Oc0+6Q\n3+8feGzr9yk0JDSAFQEAcGsjQAOj3MTUNKX6nfJ19kidvcpLzJDDwfAGAACGC39lgVHOMAzdnjNV\npmnKMIxAlwMAwC2PFmjgFkF4BgDg5iBAAwAAABYQoAEAAAALCNAAAACABQRoAAAAwAICNAAAAGAB\nARoAAACwgAANAAAAWECABgAAACwgQAMAAAAWEKABAAAACwjQAAAAgAUEaAAAAMACAjQAAABgAQEa\nAAAAsIAADQAAAFhAgAYAAAAsIEADAAAAFhCggVHK7/fLNM1AlwEAwJjjCHQBAKwxTVO7Tx1VfV+H\n7DI0KzFdmUmpgS4LAIAxgxZoYJSpqKtWc5BXQRGhskWEaH9ztbxeb6DLAgBgzCBAA6NMr98rwzAG\nHvsdNvX09gawIgAAxhYCNDDKpEbFyd/bP/A4xnQoPCwsgBUBADC20AcaGGUSomN0p5mlmrYWOQyb\nJmelD2qRBgAAw4sADYxCSTFxSoqJC3QZAACMSQToG+RyubRt2zbl5eWprKxMq1atUnR0dKDLAgAA\nwDAhQN+gJ554QqWlpZKkgoICrVy5Ups3bw5wVQAAABguDCK8AWVlZYqL++Rn9OjoaBUXFwewIgAA\nAAw3AvQNcLlciomJGfRcXFyc9u/fH6CKAAAAMNwI0DegtbU10CUAAADgJiNA34D4+Hi53e5BzxGq\nAQAAbm0E6BuQnZ192cA8e/bsAFQDAACAm4EAfQPmzJkz6LHL5VJhYWGAqgEAAMDNwDR2N2jTpk16\n+eWXlZ2drb1792rTpk2BLgkAAADDiAB9g+bMmTPQEr1s2bIAVwMAAIDhRoAGPmaapva6jquhr0PB\nNrtmJ01Qcmx8oMsCAAAjDH2ggY+drD2renufFOZUX4hDe8+5ZJpmoMsCAAAjDAEa+Finv0+GYQw8\n7pUpn88XwIoAAMBIRIAGPpYcFi1fv3fgcaw9WA4HvZwAAMBgpAPgY+MTkuT1+3Su060gw67pmRmB\nLgkAAIxABGjgUyYkpWqCUgNdBgAAGMHowgEAAABYQIAGAAAALCBAAwAAABYQoAEAAAALCNAAAACA\nBQRoAAAAwAICNAAAAGABARoAAACwgAANAAAAWECABgAAACxgKW/gCo5Uu3Suu03BNodmJmcoJjIq\n0CUBAIAAowUa+ByuczWq6G9Tt9MmT5Bfe2pPyTTNQJcFAAACjAANfA53f7fs9k8ukU6zX16vN4AV\nAQCAkYAADXyOOGe4fF7fwOMIBSkoKCiAFQEAgJGAPtDA58hMHqfu/r4LfaANm25Lzw10SQAAYAQg\nQANXMDUtU1MDXQQAABhR6MIBAAAAWECABgAAACwgQAMAAAAWEKABAAAACwjQAAAAgAUEaAAAAMAC\nAjQAAABgAQEaAAAAsIAADQAAAFhAgAYAAAAsIEADAAAAFhCgAQAAAAsI0AAAAIAFBGgAAADAAgI0\nAAAAYAEBGgAAALCAAA0AAABYQIAGAAAALCBAAwAAABYQoAEAAAALCNAAAACABQRoAAAAwAICNAAA\nAGABARoAAACwgAANAAAAWECABgAAACwgQAMAAAAWEKABAAAACwjQAAAAgAUEaAAAAMACAjQAAABg\nAQEaAAAAsIAADQAAAFhAgAYAAAAsIEADAAAAFhCgAQAAAAsI0AAAAIAFBGgAAADAAgI0AAAAYAEB\nGgAAALCAAA0AAABYQIAGAAAALCBAAwAAABYQoAEAAAALCNAAAACABQRoAAAAwAICNAAAAGABARoA\nAACwgAANAAAAWECABgAAACwgQAMAAAAWEKABAAAACwjQAAAAgAUEaAAAAMACAjQAAABgAQEaAAAA\nsIAADQAAAFhAgAYAAAAsIEADAAAAFhCgAQAAAAsI0AAAAIAFBGgAAADAAgL0ECgsLAx0CQAAALhJ\nHIEuYDQrKSlRZWWlSkpKAl0KAAAAbhJaoG/AokWLtGrVqkCXAQAAgJuIAA0AAABYQIAGAAAALDBM\n0zQDXcRIsmnTJlVWVn7u64WFhVq0aNGg52w2m/x+/xX3+2//9m9yu91DUiMAAMBwWrhwoRYuXBjo\nMkYsAvQQuJYADQAAgFsDXTgAAAAACwjQN6C8vFzr16+XYRhau3Yt09kBAACMAXThADCmuVwubdu2\nTXl5eSorK9OqVasUHR191fctX75cW7ZsuQkVAriSwsJCFRUVXXGb673Ob3XXcu7Ky8tVWloqt9ut\nvXv3at26dcrKyrpJFY5cBGiMCFZubtwIL2XlnHAzHKygoEClpaUOTyJbAAAJkElEQVSSJI/Ho5Ur\nV2rz5s1XfE9xcbEWL17M2AdZvx63bds26PGyZcuGu8QR7Xqu3bi4OLlcLj3++ONj+tq9uJjZmjVr\nrnotXs91fiu71nPn8Xi0efNmrVy5cuB9q1ev1qlTp25WqSOXiWFTWVlprl+/3iwuLjbXr19vut3u\nz922rKzM3Lhxo7l+/Xpz+fLlpsvluomVBl5+fv7Av91ut7l8+fIh2XasuNZz4na7zY0bNw48Li4u\nNnNycoa9vpFq3759ZmFh4aDnYmNjr/get9tt7tu376rbjRVWrsd169aZ27ZtG9j20+8dq6ycv/Xr\n1w96vHr16mGrazQxDOOKr1/PdT5WXMu5+/TfiPPnz5uGYZgej2e4Sxvx6AM9jJ544gk9//zzAysW\nXvwG91kej0elpaVauXKlnn/+ea1evVqFhYU3udrAKSsrU1xc3MDj6OhoFRcX3/C2Y4WVc1JZWal1\n69YNPM7Pz5fL5VJbW9uw1zkSuVwuxcTEDHouLi5O+/fv/9z3FBcXKy8vb7hLGxWsfPbcbrdeeukl\nPfbYYwPbXmwRHKus3s82bNggj8dzM0q7pVzPdY4L8vLyBn0mS0tLFRsbq6ioqABWNTIQoIcJoeba\nWbm5cSO8lJVzws1wsNbWVkvbl5SUjKkvt1dj5bNXWlqq7Oxsbdu2TSUlJXr55ZdVVVV1s0odkaze\nz1544QVlZWVp06ZN2rRpk9avX38zyhz1rF7nGCwzM3Pg3xs3btSmTZsCV8wI4gh0AbeqK90YZ8+e\nPej5sR5qrNzcuBFeyuo54Wb4ifj4+EsWOPq881lVVaW4uLgxc11eCyufPZfLpbKyMhUWFioqKkoF\nBQXKz88f030prV67K1euHGhwiYmJ0f3338/n8RpYuc7x+TZt2qQVK1YM/Io01tECPUwINdfOys2N\nG+GlrveccDOUsrOzL3uuPvslV7rwq1JpaelA65/b7dYvfvGLMd2KauWzl52drezs7IHAFx0dLZfL\npdOnTw93mSOWlfPndru1du1avfTSSzp16pSefPJJfg25Rlauc1xeSUmJcnJyxvTfi8+iBdqia13q\nOy4ujlBzjazc3LgRXup6zsnFm+F99903nKWNeHPmzBn02OVyDQolLpdL8fHxio6OvmS2iNWrV+uv\n/uqvbkqdI5XVa/ezPvsr3Vhj5fx9tvvQ888/r8rKSpWXl1/yOcbga/dq1zkG+/S5kz7pknrxPG7d\nulWPP/54IEscEQjQFn3eQMDPysnJIdRcIyshhhvhpaycP4mb4Wdt2rRJL7/8srKzs7V3795Bv/6s\nXbtWixcvHhSUPR6PNmzYIMMw9K//+q9atmzZmJ1KzMpnLzs7WzExMfJ4PIqOjpbb7VZOTs6gX9/G\nGqvnr7i4WIsWLRp4PSYmZkyH5/LychUVFQ0sZnaxAUu69Nq90nU+Fl3ruXO5XCooKBj03pycnDH9\nN+Mi5oEeRp+ed9LlcunFF1/UG2+8MfD4s6HGMIwxG2rKy8tVXFw8cHP7zne+M/BT7xNPPDHoRnil\nbceqaz1/LpdLEydOHPTenJwcVVRUBKJs3AKsXLtVVVXasGGD5s6dq71792rNmjVjOkBL1s7ftm3b\n1Nraqri4OLW2tmru3Llj+tc3IJAI0MOIUAMAAHDrIUADAAAAFjALBwAAAGABARoAAACwgAANAAAA\nWECABgAAACwgQAMAAAAWEKABAAAACwjQADBE1q5dq5dffnnQc4WFhdq/f/9lt9+6davWrl075HUU\nFhbqF7/4xQ3t4/Nqy8nJuaH9AsCtgAANAENk9erV2rBhw8Bjt9utqqqqz10tzjCMIa/B5XLJMIxB\ny49fj8+rbThqBoDRhgANAEMkKytLMTExKi8vlyRt3rxZy5cvl3ShVXjx4sVavHixtm3bNuh927Zt\nG9RyXVBQMPDv1atXq6CgQAUFBQP7vWj58uVavHixCgoKVFJSIklat26dSktL9eabb15S38Xt16xZ\nM+gYl9vPRR6PZ6D2J5544npOCwDccgjQADCEVq9erTfeeEOStHHjRq1evVpVVVVas2aNtm/frpde\nemlQK/WVbNy4UYZhqLS0VMXFxQNhXJLWr1+vO+64Q9u3b1dJScnAa2vXrlVBQYEee+yxQft64YUX\nBrZfvny53G73Ffdz0b/8y7/oySef1Pbt2/Xiiy+qtbX1us8NANwqHIEuAABuJcuXL1dBQYFefPFF\nSVJmZqbcbreKiopUVFQk6dq7Qezbt09VVVUDLb+xsbEDr7lcroGwGx0dPfC8aZqX3VdVVZVWrFgh\nSVq0aNFV93NRWVmZVq9eLUmaM2fONdUNALc6WqABYAjFxMQoLy9Pjz/++EBgfemll5Sfn6+f//zn\nevzxxwdC7qfDbktLiySpuLh44LmCggLl5eVp8+bN2rx586AuFDk5OSorK5P0Sb/nK8nOzh7Y96eP\n8Xn7uVhbXl7ewPYXtwOAsY4WaAAYYqtXrx7U1/nJJ5/UCy+8oKKiImVnZ6uqqkrl5eUyDEOGYej+\n++/Xhg0btHjxYuXl5Q2E2JUrV+qJJ57Q4sWL1draqu985zsDx3j++ecHvbZly5aB1y4Xpl988UUt\nX75cRUVFysvLu+p+Lta2du1aLV++XFu2bFFMTAyzcACAJMP8vN/7AAC3jIuDAxctWqSysjK9+OKL\n+uMf/xjgqgBgdCJAA8AY4PF4Bg0Q3LhxozIzMwNXEACMYgRoAAAAwAIGEQIAAAAWEKABAAAACwjQ\nAAAAgAUEaAAAAMACAjQAAABgAQEaAAAAsIAADQAAAFhAgAYAAAAsIEADAAAAFhCgAQAAAAsI0AAA\nAIAFBGgAAADAAgI0AAAAYAEBGgAAALCAAA0AAABYQIAGAAAALCBAAwAAABYQoAEAAAALCNAAAACA\nBQRoAAAAwAICNAAAAGABARoAAACwgAANAAAAWECABgAAACwgQAMAAAAWEKABAAAACwjQAAAAgAUE\naAAAAMACAjQAAABgAQEaAAAAsIAADQAAAFhAgAYAAAAsIEADAAAAFhCgAQAAAAsI0AAAAIAFBGgA\nAADAAgI0AAAAYAEBGgAAALCAAA0AAABYQIAGAAAALCBAAwAAABYQoAEAAAALCNAAAACABQRoAAAA\nwAICNAAAAGABARoAAACwgAANAAAAWECABgAAACwgQAMAAAAWEKABAAAACwjQAAAAgAUEaAAAAMAC\nAjQAAABgAQEaAAAAsIAADQAAAFhAgAYAAAAsIEADAAAAFhCgAQAAAAv+f0xHNsAwXixQAAAAAElF\nTkSuQmCC\n",
"prompt_number": 23,
"text": [
"<IPython.core.display.Image at 0x10bbab690>"
]
}
],
"prompt_number": 23
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Robust Regression"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Add outliers\n",
"x_out = np.append(x, [.1, .15, .2, .25, .25])\n",
"y_out = np.append(y, [8, 6, 9, 7, 9])\n",
"\n",
"data_out = dict(x=x_out, y=y_out)\n",
"fig = plt.figure(figsize=(7, 7))\n",
"ax = fig.add_subplot(111, xlabel='Value of gold', ylabel='Value of gold miners', title='Posterior predictive regression lines')\n",
"ppl.scatter(ax, x_out, y_out, label='data')"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 24,
"text": [
"<matplotlib.axes.AxesSubplot at 0x118ba0150>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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7h+bu2gZC8SjDYT8mReVgQ/uayyTZLFb21zYzk4pitFYwQoyZwYe8u/c7q15G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\nude/AAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x11a8dc3d0>"
]
}
],
"prompt_number": 24
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"with pm.Model() as model:\n",
" glm.glm('y ~ x', data_out)\n",
" trace = pm.sample(2000, pm.NUTS(), progressbar=False)"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"prompt_number": 25
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize=(10, 10))\n",
"ax = fig.add_subplot(111, xlabel='Value of gold', ylabel='Value of gold miners', title='Posterior predictive regression lines')\n",
"ppl.scatter(ax, x_out, y_out, label='data')\n",
"glm.plot_posterior_predictive(trace, samples=100, \n",
" label='posterior predictive regression lines')\n",
"ppl.plot(ax, x, true_regression_line, \n",
" label='true regression line', linewidth=5.)\n",
"\n",
"plt.legend(loc=0);\n",
"fig.savefig('ppc2.png')"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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iUiGGNCIiIiIVYkgjIiIiUiGGNCIiIiIVYkgjIiIiUiGGNCIiIiIVYkgjIiIi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URKmoxoELEajIgmIyHRgSY3bSRsNhuiKJLJNAem7Xa7PpMWjUbvCAeXJAmn06m3UFKpFKqq4vF4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\nAAAL+v9qVdnrEKJQrAAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x11cf42710>"
]
}
],
"prompt_number": 26
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Image('ppc2.png')"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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wvV6vpX0s9L7Ot3y5793c7WaWzfd/4lnbLudcZluv35vrnWGaFhtxsCynT5/W6dOnE10G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/FOG73MDT+8cKXZbN6XkGEymZibmxOLrTo6Os8m+gRa51vDveJZlmWRPNFPV+jzeaFtMBiEx/dp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\nUqlUz5ZhsbC7u8tvf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DU1pba2ttQypeFISCr2yuPLUl3BJm1ZYsh93PTMjOzOR78K7Hab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\nxIkT9LyQJBMrpquryzx9+rTZ1NRknj592gyFQgs+t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"prompt_number": 27,
"text": [
"<IPython.core.display.Image at 0x11da70310>"
]
}
],
"prompt_number": 27
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize=(8, 6))\n",
"ax = fig.add_subplot(111)\n",
"normal_dist = pm.Normal.dist(mu=0, sd=1)\n",
"t_dist = pm.T.dist(mu=0, lam=1, nu=1)\n",
"x_eval = np.linspace(-8, 8, 300)\n",
"ppl.plot(ax, x_eval, pm.theano.tensor.exp(normal_dist.logp(x_eval)).eval(), label='Normal', linewidth=2.)\n",
"ppl.plot(ax, x_eval, pm.theano.tensor.exp(t_dist.logp(x_eval)).eval(), label='Student T', linewidth=2.)\n",
"plt.xlabel('x')\n",
"plt.ylabel('Probability density')\n",
"plt.legend();\n",
"fig.savefig('t-dist.png')"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37
},
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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EwSPY59B35ulSuHxcLZF33LboS0pK8Prrr8NsNuP11193fm61Wl0GzRFR4F2/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\nEknGyliUn58fkmq7qakJOp2OqyAffP/xqKmpCSaTCRaLBVq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"text": [
"<matplotlib.figure.Figure at 0x11bb7d150>"
]
}
],
"prompt_number": 28
},
{
"cell_type": "markdown",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "-"
}
},
"source": [
"# Fit strongly biased by outliers\n",
"\n",
"* Normal distribution has very light tails.\n",
"* -> sensitive to outliers.\n",
"* Instead, use Student T distribution with heavier tails."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"Image('t-dist.png')"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_helper": "subslide_end",
"slide_type": "subslide"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"png": 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vXboUAFBeXg4ASElJwbp165ztjEYj8vLyBvVnIYpUDseNgODtEngpeoCSYpOQ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\n4+NFkhQTI6ZXz0+YIC61abWBlxu5NHe9zw2X51HwhV0ClJy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"prompt_number": 29,
"text": [
"<IPython.core.display.Image at 0x11dc34650>"
]
}
],
"prompt_number": 29
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"with pm.Model() as model_robust:\n",
" family = pm.glm.families.T()\n",
" pm.glm.glm('y ~ x', data_out, family=family)\n",
" \n",
" trace_robust = pm.sample(2000, pm.NUTS(), progressbar=False)"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_type": "subslide"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"prompt_number": 30
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig = plt.figure(figsize=(10, 10))\n",
"ax = fig.add_subplot(111, xlabel='Value of gold', ylabel='Value of gold miners', title='Posterior predictive regression lines')\n",
"ppl.scatter(ax, x_out, y_out)\n",
"glm.plot_posterior_predictive(trace_robust, samples=100,\n",
" label='posterior predictive regression lines')\n",
"ppl.plot(ax, x, true_regression_line, \n",
" label='true regression line', linewidth=5.)\n",
"plt.legend();\n",
"fig.savefig('ppc3.png')"
],
"language": "python",
"metadata": {
"internals": {
"frag_helper": "fragment_end",
"frag_number": 37,
"slide_helper": "subslide_end"
},
"slide_helper": "subslide_end",
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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AVsmCQ9qhQ4d0+PDh9Bg1wzD0t3/7txkrDAAA4Fm2qBUHLly4wOVOAACAVbDg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iZ/ue66bwKvqVQwVRie+blkOgWZIn8vliAIsNhssKnMuzqgAYDZaEL1ggq+XAYymQyKRAZ2By+R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\nTqy7n1VDQ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"text": [
"<ma
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