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@fomightez
Created April 8, 2025 16:08
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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"id": "acbc9eb1",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "e89db0c3",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"from IPython.core.display import HTML\n",
"def css_styling():\n",
" styles = open(\"styles/custom.css\", \"r\").read()\n",
" return HTML(styles)\n",
"css_styling()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1be1fef2",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"import json\n",
"s = json.load( open(\"styles/bmh_matplotlibrc.json\") )\n",
"matplotlib.rcParams.update(s)"
]
},
{
"cell_type": "markdown",
"id": "cea7014c",
"metadata": {},
"source": [
"## Buffon's Needle "
]
},
{
"cell_type": "markdown",
"id": "88896972",
"metadata": {},
"source": [
"The problem is to randomly drop a needle on the unit square and count the number of times that the needle touches (or \"cuts\") the edge of the square. This is a well-studied problem, but instead of the usual tack of going directly for the analytical result (see appendix), we instead write a quick simulation that we'll later refine to obtain more precise results more efficiently. This methodology is common in Monte Carlo methods and we will work through this example in careful detail.\n",
"\n",
"Buffon's needle is a classic problem that is easy to understand, and complex enough to be characteristic of much more difficult problems encountered in practice. The overall idea is that when the problem is too complex to analyze analytically (at least in the general case), we write representative computer models that can drive a numerical solution and motivate analytical solutions, even if only on special cases. \n"
]
},
{
"cell_type": "markdown",
"id": "11930f44",
"metadata": {},
"source": [
"## Setting up the Simulation"
]
},
{
"cell_type": "markdown",
"id": "0e8cd236",
"metadata": {},
"source": [
"The following code-block sets up the random needle position and orientation and creates the corresponding matplotlib primitives to be drawn in the figure. As shown, the simulation chooses a random center point for the needle in the unit square and then chooses a random angle $\\theta \\in (0,\\pi)$ as the needle's orientation. Because the needle pivots at its center, we only need $\\theta$ in this range."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "58356657",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"tags": []
},
"outputs": [],
"source": [
"from __future__ import division\n",
"from matplotlib.lines import Line2D\n",
"from matplotlib.patches import Rectangle\n",
"from matplotlib.pylab import subplots\n",
"from numpy.random import rand\n",
"import numpy as np\n",
"from math import pi, cos, sin\n",
"\n",
"def needle_gen(L=0.5):\n",
" '''Drops needle on unit square. Return dictionary describing needle position and \n",
" orientation. The `cut` key in the dictionary is True when the needle intersects \n",
" an edge of the unit square and is False otherwise.\n",
" \n",
" L := length of needle (default = 0.5)\n",
" '''\n",
" assert 0<L<1\n",
" xc,yc = rand(2) # uniform random in [0,1] for each coordinate dimension\n",
" ang = rand()*pi # uniform random angle in [0,pi]\n",
" x0,y0 = xc-L/2*cos(ang),yc-L/2*sin(ang) # coordinates for one end of needle \n",
" xe,ye = xc+L/2*cos(ang),yc+L/2*sin(ang) # coordinates for the other end\n",
" not_cut = (0<x0<1) and (0<y0<1) and (0<xe<1) and (0<ye<1)\n",
" return dict(x0=x0,y0=y0,xc=xc,yc=yc,xe=xe,ye=ye,ang=ang,cut=( not not_cut ))\n",
"\n",
"\n",
"def draw_needle(ax,d):\n",
" '''\n",
" Draw needle symbol on given axis.\n",
" \n",
" If red, then the line cuts an edge of the unit square. If blue, then it does not. \n",
" One end of the needle is marked with a `o` symbol and the other end is unmarked. \n",
" \n",
" ax := matplotlib axes to draw needle symbol\n",
" d := dictionary output from needle_gen\n",
" '''\n",
" for i,j in d.iteritems(): exec('%s=%r'%(i,j)) # dump dictionary in local namespace\n",
" if cut: \n",
" line= [Line2D([x0,xe],[y0,ye],color='r',alpha=0.3), \n",
" Line2D([xc],[yc],marker='o',color='r')] \n",
" else: \n",
" line= [Line2D([x0,xe],[y0,ye],alpha=0.3), \n",
" Line2D([xc],[yc],marker='o',alpha=0.3)] \n",
" for i in line: \n",
" ax.add_line(i)"
]
},
{
"cell_type": "markdown",
"id": "ee164317",
"metadata": {},
"source": [
"Now, we can simulate the dropping event on the square (yellow background ). The red needles cut the edge of the square and the blue ones are completely contained therein. The circle marker shows the needle position."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "44777f4f",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"tags": []
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"L=0.5\n",
"\n",
"samples = [needle_gen() for i in range(500)]\n",
"\n",
"def draw_sim(samples,L=0.5):\n",
" 'Draw simulation results. Package this plot for reuse later'\n",
" fig,ax=subplots()\n",
" fig.set_size_inches(5,5)\n",
" \n",
" red_count=0\n",
" n=len(samples)\n",
" for k in samples:\n",
" red_count+=k['cut']\n",
" draw_needle(ax,k)\n",
" \n",
" ax.set_aspect(1) # set aspect ratio to 1\n",
" ax.add_patch(Rectangle((0,0),1,1,alpha=0.3,color='y')) # unit square background is light yellow\n",
" ax.set_xlabel('x-direction')\n",
" ax.set_ylabel('y-direction')\n",
" ax.axis([-.1,1.1,-.1,1.1]) # add some space around the unit square\n",
" ax.set_title(r'$\\mathbb{P}$ (cut)=%3.2f'% (red_count/n))\n",
" ax.grid()\n",
"\n",
"draw_sim(samples) "
]
},
{
"cell_type": "markdown",
"id": "aa8177e8",
"metadata": {},
"source": [
"The figure above is a good visual check of our simulation and helps motivate our reasoning. Now, we want to concentrate on counting the number of cuts and then use that to estimate the probability of a cut."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "4ace2946",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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MDOXds3U4HA7HjsFp3B2ONqYXynzuwdOUaxFjBSjXIj734GmmF8oXummOTTJXjhrPdnK44J6tw+FwOHYULnB3ONq498QCIwMBA3mf2QoMFwJGBgLuPbFwoZvm2CRPLiojAwH5wGN6scLwgHu2DofD4dg5OKmMw9HGXKnG5HCBxXKdpWpMOYwYKgTMrFQvdNMcm2SppgwVAmZXapxdrrJnpOCercOxQzn4jk+ct3Mdfd9rztu5HI5uuMDdcUnSTec8MZSnVA2JVAHQGErVkImh/IVssmMLGM1L8mxjs0Dds3U4HA7HzsFJZRyXHFbDvlIJ2T2cX6NzPrx/nOVKyHK5jqqyVA1ZroQc3j9+gVvu2CxXjUnybEPzbCt192wdDofDsWNwgbvjkuPeEwsMDwQcny8zX6ozMpBr0TlPjRe588Z95HyP1RAGAo87b9znnEcuAiaKPnfeuI984LFUqVNwz9bhcDgcOwgnlblIcBZ3vTNXqrFrMEcUK9XQSCbadc5T40VeeGiS+acf52XX72HvyMCFam4L7jn3R/v9Wi1HTI0Xef7Vuzmwe4jbD04wNpi70M10OBwOh6MnXMb9IiBtX+gs7tZnYijPSjUCIIxN4J6lc7brkn8uOO4590fW/br7bMT0QpkwNvULcVLH4HA4HA7HTsAF7hcB1r6wEPicXq6skX44Wjm8f5ylcki5FhFGynIHnXO0zYI7+5wRYa5Uc895He49scBwIWC5YvTsIwM5BgPh3hMLRHZQtk2ercPhcDgcvbDtAncReZWIPCwij4nIOzps80YReVBEHhCRP00tf6uIPJp83ppa/lwRuS855m+KiJyPazlfzJVqDBUCFst1Ti9WqUUxQ4WAuVLtQjdtWzI1XuSO6ycpBB6zK1WKeT9T57zdsrL2OZ9eLHNysYyquufchblSDQTOLFdZqYYADPhmeRiZZxptk2frcDgcDkcvbCuNu4j4wG8DdwIngK+JyMdV9cHUNtcCPwe8WFXnRWRvsnwC+A/AbYAC30j2nQd+B/jnwFeATwKvAj51/q7s3GLtC2OagWapGjmLuy7sGR3g1gO7GMz7vOiaycxtbHC3XaQyE0N5lst1SrUIVSiHEVGkO+45ny+d/sRQntNLpm4hSp5hJTLL7dsUF7c7HA6HYyex3TLuzwMeU9UnVLUGfBh4Xds2/xz47SQgR1XPJMu/G/icqs4l6z4HvEpEpoBRVf2yqirwQeD15+Nizhft9oWLq87ibj3iJHCrRZ2j8nCbySkO7x/n9HKV1WqEqnJ2ubrjnnNadz4xtNaKcys5vH+cpUrdSKLimOVKndVQObx/fNu9TbmUEZE/EJEzInJ/atkvisjTInJP8nn1hWyjw+FwbBe2W+B+OXA89fOJZFma64DrRORLIvJlEXnVOvtenvy/2zF3NNa+MJ8zFnd5Z3G3LjbjGkaKdgjetpvGfWq8yM37RynmPVaqIRqz456z1el7Ijw4vUQh558znf7UeJEXXb2bQuBxdtlIom7d4zM1Xkw92y0/raN/PoB5C9rOr6vqLcnnk+e5TQ6Hw7Et2VZSmR4JgGuBO4D9wN+LyM1bcWAR+THgxwD27dvHkSNH+j7GysrKhvbbCnLLMRO1mGDmLA+vPM7D5/BcF/I612OuHPHkorJUU0bzwlVjwkTRb9lmoRrz5GKSbT/lE3hryx6+dTakUq7w5a98lWPD22OM++BsxIQP40A4Aw/fc2xLnvP5ep53HaszVoBSHc6sxlTPehR8WKzCwMzW99hTpZhcKWZy0GNgxiOMynz+85/nnrPGVWj+qMeewe3xbC9VVPXvReTghW6Hw+Fw7AS2W+D+NHBF6uf9ybI0J4CvqGodeFJEHsEE8k9jgvn0vkeS5fvXOSYAqvp+4P0At912m95xxx1Zm3XlyJEjbGS/reD+pxc5tVjhhqkR9u8aPKfnupDX2Q0rxbh6X8BQIaCUzHr6wrbM9OmlCsMnFgF44aHdDBVavwqqSvjtM9x3/33cdvvtXLdv5LxeRxblWkT42AzXXzZCNYx5arbEd1y/Fz9j0NEv5+t5Vu6fplyLqEYxxbkyV00O4olQzPvccdPUlp/vsTPLHJ1Z5RnjRW58xihHjhzhxd/xUqKHzwJw7b5hDuwe2vLzOraEt4vIW4CvAz9t5ZFp0smWK6+88jw3b2McfMcnztu5jr7vNeftXA6H4/yw3VJNXwOuFZGrRCQP/CDw8bZt/pIkQBeRSYx05gngM8B3icguEdkFfBfwGVWdBpZE5AWJm8xbgL86L1dznrGSjugSfv+ftkxcroQdLRPT96ieoXMPU+u3i1RmtmQKLSeG8owWA1RhpRJe4Fb1R3s9xlIlPKc6/Xq09jsRtTzbc3Jax+b5HeAQcAswDfxq1kaq+n5VvU1Vb9uzZ8/5bJ/D4XBcELZV4K6qIfB2TBD+beCjqvqAiLxbRL4v2ewzwKyIPAh8Hvi3qjqrqnPAf8QE/18D3p0sA/hXwO8BjwGPcxE5yqSxAYkNVi5FGpaJSxVOLVUAMi0TWwP3tferJbjbJq4yc6UaAzmfoULA6ICZ7XOpUr/AreoPW4+RC5J6DP/c1mM0vhOph9gpiHdsH1T1tKpGqhoD/xNjXOBwOByXPNtNKkNShPTJtmW/kPq/Aj+VfNr3/QPgDzKWfx24acsb24F+7e62yh7PZdxT1pixdp0VNZ1E3+4Zd9s/7np8lit2DXJozxBT40Xygcdiud6iLdsJTI0XedGhSfaPD3J1ci3nCvts09+J9LPtVJjsuLCIyFTythTg+4H7u23vcDgclwrbKuN+MTBXjvqalj5tj7d7eHP2eDb+zApELxUaUoxqSBjFnWdF1e5SmSjaHoG77R+zKzWGCwG5QBr9Y7SY23EZd4v1yA/P8SCz+RYqO+N+CY9xtw0i8iHgLuB6ETkhIj8C/HIyad63gJcDP3lBG+lwOBzbBBe4bzFPLiojAwGxwoPTSwwVgq52d1aTfXalytPz5U1NY28Dkks5496QYvjCwmpna8woVkRApFPGvbnsQt5O2z+qYYTnCftGBxr9Y3QgYLUaEe7AgZodDJ3rQWaWxr312V6635Xtgqq+SVWnVDWnqvtV9fdV9c2qerOqPltVvy+VfXc4HI5Lmm0nldnpLNXMNPQzK1XCSKlHcePnLOZKNSaHCxyfL1OPYi4b6759N2wQEm4XUfYFYmq8yHOu3EUUKS+6ZjeD+bXdPFbF8wRfhFq4NnizmWBfLkxwZ+Uxn75/mqF8QM73OLR3mMDzGCoIMytVyrWQu5+a58mZFa6YGDxnM5CeC8KUj77lXMyoar8L6fM4jbvD4XA4diou477FjOaFUjVsTvATa6bG2mI12VGsqMJcqdp1+2644tQmVupSC7MHMVGseCLkfC9zoGMDy8CT866DTsunxgbznJivML1YoRCYr2upGiIoX3lynmoYU8z753QG0nNBZAPq5N/0NfciMeuVMPUWKm4bLAS+4BLuDofD4dhJuMB9i7lqzNgQLldCY3dXztZYW+y07CvJ9ifmyyxV6huyx4tccSpAi3Sk1kGKEavii5DzpavGPfCatQPnCyuPKeR8fBECX9g9lOfJmZWGZh+EXYM5xgZzVOvxpiRWF4JmPYa5z41rDnwWy/UtuR5VJYqUwDc+92GblCzve04q43A4HI4dhQvct5iJos+dN+4j7xu7u9w6dndT40XuuH4PhcAjVMVDuPXAro25ymQU4l2KpAseO719iGPwPMj5XgepjLmHwQWQylhLy4XVGoP5gJdfP8loMcf0YoVi3vQvxdhcDuR8KslbhSzby+1Ku4TFXvPMSpWnZldRdNPXY/vBQM7Mmpt+CyYCgQvcHQ6Hw7HDcBr3c8DUeJHnX72bg5NDXH/ZyLpB+OTwALce2MWzLh/lK0/M8oVHznLficW+dL5xIrURcRn3dDDWUSrTyLh7hPFaZ5YwVnxP8C5A4G7lU/XItOGysUGGCjluuXKcVyWzi9ptcp5Qrne2vdyuNINo0/bGNcdN+8ZyLdrU9USpwH2l0nrsC/Vsu3EuNP4Oh8PhuLhwGfdzRKTN7N56NLKOK1WemCkxu1JnZCDoS+drz5cPPFQv7eC9NePeWePue0I+yJbKhInEQoTzroO2lpYLqzVyvmRaWtptqmHU1fZyu5IuTlXVpo1nxcyouri6+euxz3UgZ37NRVFzsBB4Hp4n28YO8lxp/B0Oh8NxceEC93NEo/iuB9mKzQQ+fHqF/eODDBZ8Flb70/mmdbtwactl0g4inTLuqookGfc4XvucbGAvnP9BkLW0FBFK1aghj0lnX+02RlLT2fZyuxIn9xdMEG+vJ/ASidkWXE8j4x4YqczajLs05GUXGqvxX66Em7aFdTgcDsfFy6akMiJyHfAsYC+gwFngflV9dAvatqOxwWOn4sg0NsheLNe5fLzI6WWvEXD2ag1pX/kXcj7LlfASz7ibeyfS+f5HsVLIeQSNgY6SxHeNYwSeZ4K7HlLuWy1zmBov8uz9Y1w2NsANl4123OaVN+5jaqzY0fZyO2IdlAp5L/GhV3K+uZ5brthFpR5xy5XjTA4XNnUeW9+QpXEPfCuV2dy1bBXWFvb0UgU77tyoLazDYTn4jk+c1/Mdfd9rzuv5HI5Lkb7/0ovIM4EfB34AuMwuTv7VZJvTwEeB/6Gq396Cdu44opQUYD3sNnuHC0a37HuNYL5X3XJ7xr2X816sWHfHYs6nvq7G3XTdehxTpBm5R3HvUhkrcxgZCJhMnuHnHjy9qYxxGMWEkTayxZ3I2YFHqLAz5O2NgdVAzme1GrXce9vvt6L/NjXurd+Jloz7NtG4N2xhtVlkvpNqFhwOh8NxfuhZKiMih0TkY8D9wI8A3wJ+CXgL8GrgNcn/3w3cC/wocL+I/JmIXL3VDd/uNDXuvWfcn3Ol0fnWo4ha2J9u2Z6mkAQp9Ut4EqZGYJj313WVaUiL2gL8eqQEiVRmveDOyhwCXyjXoy2ROVTDZnDbDRu4V6Now+c63zT6arA2oG7ORbD5/tvUuJt7mNbVB9sscLca/5VKSKQ7r2bB4XA4HOeHfjLuDwL3AW8D/lxVS902FpEhTFb+Xyf7DmywjTuSsBGA9JBxjxXfF56xa5A7b9zHZx6Y5omZEtddNsILrt7dU9a2UZyaBHKXslTGXvtg3mdhNdtOMNbmBEyw9jmlnUc0yYJ6nmQdqiFzeHK2RBgp1+8b2bTMoVI3gbjNFnfCBr87adKtdMY9/XM6WN+KwD1MvYXyPWnUMTSerbd9pDJW4/+hrx5jvlTnhsv8nr/7DofD4bh06Cdw/8eq+vFeN04C+z8E/lBEXtd3y3Y41sGilwCkFsaNgHtqvMgrbriM/aeXeel1e8gHvb0UscFqI+O+zYtTz6X1XZgqSrSFp1bLbonUBG92cp72+9XUuJuf48RjP4uGzCHSRm3CZmUOlT4z7p0kQduRRl9ty7hXU9fQixvT+ueJ8TzwPMH3pDG4sc9WuthBduqf57LfTo0XueVKk2F/xQ37tuSYDofD4bi46Fkq0x60i8i7ReSqHvf9q34btpOxgYlIjxr32Ly6t9jguxr2Ln9oFKf6rYV425FzbX0XJW8w8l2y0XFsMu6dXHjSrjLQPTPbsDKshoRRzFyptmmZQ7kWIdIMbjvhJ0FpL0XQ24W0vzo0vyNbnXE3Pvjm/gW+NM67nqtMp/5577H5c9pv41iJYyMl0m0i4XE4HA7H9mIzNhQ/DzwEPLlFbblosK/+84FHtR53lVnA2oywDdY6WRlm0ShODUwmcTtLJ+49scDwQMCZlSpjUczkUKGxfCuyl1bDbLPRtai18NROVuV7gojJuqfvl3U9ySXOI9Bd596QOXztGPOlGoEv3Hnt5qwMK/WIQuAj0rnfWMzsrzsvcG/IfNqkMr4vW1acmkseYOB51OOYWJvPXpP/W2tQi61ZWKmFLFVCLk+e4yfvn+aGy0Y5u1KjUo/ZM7K1/TZdl2KLox0Ox/bAOfQ4tgvnzD9ORP4p8F5V7SkrfzFhA5Nizqdaj6nHMQWvs+ShFsUMF5qPopA4iVQ2ELh7nglKNppxPx+zN86VahQCj+VySOAJk0OFrprwftvUmFzJzx4A2SAkjaBvAAAgAElEQVTcBuX5lIsPpAJIz7jKpPfpxNR4kedcsYsoVm58xuim71k1jNbVt1vygXdBpFEb7StWBhN4HkEqSLfPaTDn93Q9652/HsUNr3ibcY/UWGAFnmBPESukY+SGNeNyhXqkXE6RoULA6aUKzz0wwZOzJVZrIZPD+S21bEx/ZyNVN621w+FwONbQ1wRMIvITIvJxEXlnsmioy+Y+cOWGW7aDaWYUrcVd96DP+FhvLuNuA0tfxGQXNxDIna/ZGyeG8pyYN8e0zeykCd9Im6yGuSmVaZPBNAJ3G9R5LVKTKBVY9iKVAZO1tfuV65t3eKnU43X17ZacL+c9476ZvmLvk5+8FbHPpx4ZTfpArrMbUD/nN1nrRCrjmRlybVLbSmVg7aCsUbMQt1oz7hsdYLkSJnUTykK5vqWWjWld/yVsCuVwOByOLvQ7c+oS8ALgPRjP9t8VkVMi8ikRea+IvEFErhIRH3ghMNNvg0TkVSLysIg8JiLvyFj/NhE5KyL3JJ8fTZa/PLXsHhGpiMjrk3UfEJEnU+tu6bdd/bDWP7r7X+Ewjht+4mCK6XKB15fGPR0MpfW8/WAlAiQ2eedq9sYbLhvhzHKVci0iiqKu1ne2TcMFM6tkL22yGfdch8LTdPAGJvCtZxRG9pNxTwdd5drmAndV7SvjboLf8yuNSltg1qO4r77SzLgbfb79uRaaAWzO99a1UbXn98Tsn3V+a+lpzuURxYo9auAbVxlYWw+StmYM46Y146tvmmJxtU65FqGqHJ8rballYxS1ZtwdDofD4Winr8BdVT+gqnuB6zBvnD8BfBkze+rPAX8GPAbUgH8BfKqf4ycB/28D3wPcCLxJRG7M2PQjqnpL8vm9pG2ft8uAVwCrwGdT+/zb1D739NOufmm4muTWz7hHSUFa4LU+ikKij++VWBXPA0kmFerFP76duVKNwbzPE2dXOJu8/h8qBMyVsi0VN0qkcHj/GOODOWZKdYp5v+NkRXOlGkOFgKVKnSdnSpTr4bptssW+ge/heZ2lMs3A3WsJvG0gZzTuSVZ2nYFQOvjbbMa9GprMcGGdyZcshQsglbHP5dhcmenFCtB7X4liRSQZoPpNm8ZaFCeBu6x7PXOlGoMFnydmSpxeyj5/GMcNnbiV5NjD+tJ8tu0xsq1ZyPnCwmqdQs70z8NX7uKl109SCMwbmjCCFx6a2DIpWbvG3eFwOByOdjYko1TVx0TkrzAzo34aQEQmgVuB5wBXA08Av9nnoZ8HPKaqTyTH/DDwOowPfD/8APApVV3tc78toR9rRrsuF2QE7n1p3JvSD9/zGj7g/TAxlGe5EqJKT7aG/WqcpxfK3HN8ga8+OcfekTyHrxgDhJdet6drm0rVEHsraqESRt3lCTbjDpD3/TWOKzababPp+aBVKmMHPb4njZHtenFUI4vsC6ubzLjbAVvvUhmvMXmR36UIeitpPpcYfx25Uzvpdgae1xjo1KOYfOAR+B5xTNfrmRjKM1eqEcXaeHbt5w/jpgQtSOo+Qm3KoOpi/p/1NsVaM8YxvOTaycazmBwucOuBXdy8f4wvPHKGv390hq8dnd+SepCoRSrjAneHw+FwrGXD9U+q+v1tP89gMtyfzd6jJy4Hjqd+PgE8P2O7N4jIS4FHgJ9U1eNt638Q+LW2Ze8VkV8A/hZ4h6quqSgTkR8Dfgxg3759HDlypO8LWFlZ4Ytf+geOLcfUT/o8NBcxd9Rj72D2y41yqDw0F7FyzOPRgeY2x5Yilmqw+lRvwZvdnmmfp5YiSnWoHOttX8tqOeIbpyJmKzEjOeH0oMdqqNy6x+fIzMMt2x6fWeFvPv4FBgNhwIejEXzxbrPtRHHteefKEXefjSCGhWpMOO/x7UdhTxHik52DvdVkv3oIpXrM3EkPzyezTZb7zoaMD3jMPOrx8FxEzoOz4802rdSURxciVk/4jOaFU6WY6VKMnvTxRJgtxxxbjommfVZXSzx6/32sHvcZLXQOiu0xR3LCcl0JT/gbDqLnKzFHl0z/KQbrHyPd3sIGnUhWVlb66u/2uZwtxQznhLmnO/eVdp5ailhO9dXlmumrD85GDAYwnBeOL8fE0z75DtezWo746tMRpXrMUE6YPdF6flXlnrMRpwY9Tg57nFmNeXolZsKr8OT991E/6VONlCcXs+9zrMq9Z5MBRWr9QjXmycWY048L/3AyJFLlmjGPoypd+38vnF2NObFiBiHr9TeHw+FwXJpsOHAXkXcBdwP3qOrTW9ekdfnfwIdUtSoi/wIzydMrUu2aAm4GPpPa5+eAU0AeeD/ws8C72w+squ9P1nPbbbfpHXfc0Xfjjhw5wuFnP4+xU2YCpdwjZ7lqzxCH9gxnbj9fqpF7ap5bD+xqyRY+dmaFp2ZLvOyGvT1ZAt7/9CJL5TovumaSh04tcWqxwh3X7+27/c8+s8yff+NpSrWQWw/t7phF/NUP/w3PvekGPBGmlyrcPDnESjWkmPe546apNdt/+v5pnrsv4sxKlb31mGdOjXB0psR8qc53vPT6rkHuCxfKfOaBUzx+doVr9450lNVY4odOc+XEINfsHWH02DxhpDzvqonG+tmVKgPHFrjt4C7GB/Mcn1vl4VPLvPi6SQqBz/G51cbz+5vP/x03X3cjz75ijL0jnSf/nUmOeWD3IE/NrnL71ROMDuQ6bt+Np2ZLjJxe4WXX72kpWu7E2eUq9x5f4ParJhgrbuycR44cod/+/ry5Vf70K8eohjG3XrWr54zzfScWWa7WedGhSR45vczTC2XuuH4v+vAZnjFWZHwwx30nFnnBod0tbkvt7Hn0DHc9NsdKrc6thyZbzl+PYqKHz3LdvhGu3D3IyYUyD55c4swTD3Dz1c/iJddOslINGT62wO0HJxgbbL1vtTAmfuQsAM89sItdyXfz5EKZ4ZNLrNZCXrQnZHqxwhUTg+weyrNcqXfs/71wdKbErjMrADx7/xh7Ry+pyaYdDofD0QObcRz7JUyBKiIyC9wDfNN+VLV72i2bp4ErUj/vT5Y1UNXZ1I+/B/xy2zHeCPyFqtZT+0wn/62KyP8CfmYDbeuZdPFdsI4ntdW15toyiwM5D1Wjd+5FMhGlvOJtId5G2DMywK0HdgF0DRyXatqwyFuphNRj7WqNN1eqsXs4z+psxMRQHkEYHshxbG41se3rfI1T40VecGg3+3cNcsXEYPegPakZsBPv5H2Pcq3esk3DVSa5X/OrNe5+ap7j86tMjQ2wa9AEaYGX8nFfR7Vk7/dIEqyXa9GGA/dKPcb3paegHVgzidRWWHr2cozJESMbyQUeL+sid2rHuv5AImGJjMwnitRIZZKbvl5RdyEIGn21fZbhRrF2SuMOUE8VHndylbFttKS15/a7vFius290gNPLFWpJEXmv1pCd7m1LncUlVJwqIn8AvBY4o6o3JcsmgI8AB4GjwBtVdf5CtdHhcDi2C/26yqQ5ALwB+E/A14HDwL8F/gR4UESWReRLfR7za8C1iTNNHiN5aZ+xNZ3O+j7g223HeBPwoax9xKSuXw/c32e7+iI91Xq7R3g7tnC1PUizQUivOvdI07phQXVjBW69FlmO5oVSNaSc6LGjOO6qcU5rkot5E6TXwoiRQq6nwsp2r++O26UGTbBWvw7NYkRPhOmFMv/w+AzVMGasmKNci/jiYzMsrFbxNuAqMzxgxsKbcZap1CMGeixMBcglMo5aGG+JpWevx7DXHPVZCJ3Wrtt+v1oLk5+lUe/RbTbYOFZWqnUG83bOg9b73agdSQ1mzXKSn7tPrpUOotPF5bUoRgT2jBQoVcOGqw30pvHvdm/DS7c49QPAq9qWvQP4W1W9lkTeeL4b5XA4HNuRDQfuqnpcVf9SVd+lqq9W1X3AtRgJShVTnDra5zFD4O0Ymcu3gY+q6gMi8m4R+b5ks58QkQdE5F7gJ4C32f1F5CAmY/93bYf+ExG5D7gPmMTYWZ4z0oWiwTqBu80qBm1SEeso0qslZBxr6pzZNoi90BK4dwk+rxoTlish86UaqspSOexqjXd4/zgzKzXKNWNzuFypU65HHJwc7GmWzHrDeaT7/UjbYkJSuBlpS7FfYxsR7j2xwFgxRzHvo4kF5kDgcWzOBKlNH/d1XGWi5mygucDbVIFqpd67FSS0ZtzTNo0btfS0xyjmfcq1qOMxrIVmHPdXTGldf6DZV21fy/seOc/aqHY+5nLV+KnvHTWzl7YXY7f3A3ueWtycMde+cclqetqaMWwrXPY9aVhGVusxUcoycj1ryPS9rYSt9zaMmrOlXko+7qr698Bc2+LXYWSQJP++/rw2yuFwOLYpm8m4r0FVH1fVXwK+E9jL2ixKL8f4pKpep6qHVPW9ybJfUNWPJ///OVV9lqoeVtWXq+pDqX2Pqurlqhq3HfMVqnqzqt6kqj+sqiubutB1aJEC+NKSvWunHhlrvMBf6yoDvU/C1O7UYZf1S3qfbsHnRNHnFTfsRYClSp2c73XVnk+NF7nlijGKeTNjajHv85037GViqNAiReiEvYfrvYGwWct0xh3InGDJ84yEZzTRhdtjF3Iepaq5djueWk+5UE+ddzDvb8oSstKjPMpibS/rUdywSXzsTInphf5sGi3W6nFmpcqjZ1ZYLNcyj9EiIemjr8Wpvmr/tX3NuMpYqUyXwL1i5E97krqDSq21X9gseXoCJtPm5rm7S2WyM+5hpOR9r2EZOVTwmVmpdbU0TZO+t4+fKaFo495GsTb666UklenAvpTE8RSw70I2xuFwOLYL52RWbVW9S0Q+idHB/+i5OMd2pkUK4HlU2jTWaepRvCZoBxO4ixi9c0/nVMVvy7j3ksnOOg4Yq8T15B6jg7mGxvimy8e4bKx7MV0hCHj5Dft4brJPpR7x1Gy5p8mDGhn3dQL3tRn3JNMaNYNhGxP5IkwM5SnXIgo5j5VqyN4RWKlGjCfFip5AzPqDoChWfN9kcos5n4XVzs+8E9MLZb55fIG7Hp/h2r0jjBdzPWvTc76xD50YyjNfqhPFSil5fv3O7pmeORTggZNL1MKIWE2RcUOTHa19i9ELYdv3A5qBe843GneR7lKZpXJILvAYK+bwPVkjlWnOfts6mI21uaybVCZqCdyb7ailvq9T40VedM0kUazcfnBizTGyaNpoasPCs1wzdR9hbAYFZYkuNalMV1RVRSTzhqSdwK688pKcqNtxkXLwHZ84r+c7+r7XnNfzOTbOlmbc27gHuCR7QktgEkijIC5z20jXFKaCmUgpH3g9Z9zjmMZMkI3ivg28b7cSgWLep1wPu267Wm0GS+vJcqwmeazYHCv2WoRottHGv91kGWFb4N6QkaTuY6M4VZqSB1+ElUrIUjKN/XX7jAtQr1KZMDVLZzHvU6lHfclHrPZ5qVxndCBHrNqXNt3Onnp4/zhnV8ystOVayOJqre/ZPe09Wa7UKFXrPHJ6maOzqzzrGaOtmux0JrqPvhZlSGWaGncPETujapfAvVJnNKknKOTWzltg+2NjAqaUFG1txn3t8dP7h20Z9yD1fc15/U1+1by3dVSVhdWmxCaMjAzH82Td/nYJcDpVmzQFnMnaSFXfr6q3qepte/b0XiDtcDgcO5UNB+4iclREPiYi7xSR704mYEpzGBjaXPN2JmkpQOB5XQPTehx3dA8pBH7PGvdINSXPSTTCG5HKJAHD6ECOcq17QLJSDRvFm+udy2qSR1JOK4Fv3ir0knFPz4LZLRPbnnHvJJWxM3daycPkcIH51RqxKrdcMc5lYybTLWKyv+vdyvRbFlsw2Y9cxmqf84EJXHcN5vvSpttB3tR4kedcMU4h8Fiq1EGkJwlHmubMoUbrf2D3INfuHaZUi1s02S2TVvX4dkdVWxyQmsWpESLNNyR53+t4zChWStWwIXEayPlr3kw1i5TN8T1PmgNbvy1wz3i4th8N5Pw2V5m4MRi0x+rnzZa9t4HnrZGYRcmEUb70d8yLlI8Db03+/1bgry5gWxwOh2PbsBmpzOMY//R/RNMW8gRmltMh4MW0eqlfMoSxUkyKC3O+cXgJO0hi6mHcYmOXphB4PQd/ZrBg/t/MuG9E424ccYp5n1OLFVP02sFjvZT4tlfq0brOIlaT3G6RuF7xLjQtHkcGAxZX610tMtsDtpmVKnc/Nc+3Ty1x7d5hDu8fJ9bWa5oaL/KPbr2cyZE8V+wa5MxytcVX3hNB18mA1lN1DUuJveQTMytcOTGYaaXYbgn45NkSh/YOc2J+Fd8TBnImgO/FXhBabS8LOZ+XXDfJajXiun0jG5rNc2q8yO1X7WZ2pcZtByc4uVhmvmSObzXa4QY07mslLE1HHDtoAdMvsgZo0wtl7npilm8em+emlTEGcz4Dgc9MpfU+2X6cfo72+Vir0PVcZUTMdzD91stIZVIZd3/tm4H1rDSnxovcfnCChdV6i1+7fVPnd8m4b4XV53ZDRD4E3AFMJn9D/gPwPuCjIvIjwFMYm1+Hw+G45NmMq8x3quoEcAj4J8B/wTjBPCv5fBr48a1o5E4jy+6uU2CTnpa9nULO68kOspHFlNZgqBcJSlZ7PJGessalashwIcD3vHWz5laTbK0gLTlv/eyizXgONmwku2TcG0WJxurxyENnqccxowNBQ+ZxarHcuFeWwDd66dlSzbiepIIzkfWLBaNkn+mFMl96fI5qGDNcCDKtFLMsAZ+aW+XYXImFcp3xwRy+5/WlTbe2l3GsLFfqTA4XGMj5Juu+QaJYGR/MUaqGxp0nVmLVRrvCpLDabtsL7VIm+9YFWi1RszLZ9r7NrdQYHcghSCIvqpkJk9oKSm2A3jhm22Chm1TGfodzvtdos/2eBanjBp7X4qrTr5Vm+vttJUSeSOb93Aqrz+2Iqr5JVadUNaeq+1X191V1Nvkbc62qvlJV211nHA6H45Jk0xp3VX1SVT+mqu9U1Vep6pWqultVX6Oqx7aikTuNtMZ9PXlHPeoulam3BSRZ2NXtwVAvEpR2bGBSTDLanZxlYlXK9YihQkDOyw400qQ1yWlygbeuq4wN4AbzZv+uUhlttXocGQgYHggaMp2RgYCHTy03CnnTTAwVWKmE5u1ImyZ6PQm31bjfe2KBXYM5hgcC6lG2HaNtl+8LgmnXdfuGuefYIqVKxMRQrmd7QYu1vVyuGEnS6ECO0WLAUnnjgXsYKTdcNtKwPVRVFkrNdtWiuGFb2qvG3WaS08FvU9bUvOdGKtN6THvfxIN8zmNiyMiJnpgpAa1e7lGsDQ93i33jZQP2ph3k2r5rv5e51BuhMFZUWSOVgWafTNtxeiIdrTRtn7bHjpNC1cD38D3JHCjaY1uf+41YfTocDodjZ7NhqYyIfC/wTOA3VLV3r7lLgDhVfNfNk1pV1xS7pUlPwtSeqU7TsDeU1mBzo3aQvieN87UX/VmqEeQUhgsBM550lbtYTfLk8NqSh8CT9SdVSu7dUC8Z99TkV3OlGpPDBVNnkNyLoULAY2dW8DLGSruH8zx+xrjOpLO1nqxfLGjvmz2ndXmx50xLXqwF5UPTy+waynFgYojLdxV5eHqZieEcpapxGXnB1bt7lkHYvjJTMucZLQZU6jnOLFW7Dg7Xu6Z9Y0WeOTXGFx6d4cmZFYJAuPM6o8k+Pl9mICkM7VWTbZ9D+v7nfI8wisj7zT4e+LJmgGbv7dMLFYo586urcW9HjANTMultMhtve+De6jRk29FJ4+6nZj6239X0cWCt9aqxe/R5+NQKh/YOM1IIMmdUtQMdO7iOGgMawe/QprlSjZzv8fj0MsMDAYcmh3qerdXRmfPt3uFwOBybYTMa958BUNVfbl8hIj5QPNd+6dsR+zq9PeOeJVuxQUwuK4oEFktGn310doX9u7K10tDMGLbreTc6AZPvCYXAx/ekY8a9Eio5jHwlSGQUWbRoki8fYyjvt1xDzl9/siKbkbce390Cd/O2w9xPa72XdigpVUOGB4LMjPtIIWC5UufR0ys8dGqJa/YOs1qOuEyaFpKdp6s3Gnd7znwgjWfeLnmZGMozu2LGuvOlOtX6EsfnypxaqnDLgXHuuG5v37plG4zOrtQIfGEwHzAyYO7rUrnO7uFCX8eD5nwEU+NFXnXzZUwM5Xn2FWPsTbzTwyhmtJhDpN67xj1am3FvDHKD1v4bxSZgtrp3e2/rUcxI8vamVA3ZlzEJk81ep7Hnaa9fyGq6nSSqMfCOtenVnw7c26xXJ4bynF4y/vn1MIbC2uefHgTYvmx/9hOpTHrQYvvcPccXmC/VOLB7EIAHpxdZSGo+0jadDofD4bh42YxU5ibgU1krVDUCviUi79rE8XckNvFoAxOb6cyyhGxMyx6sDSKNVnqWamiCo2561nYnFTABxWYy7mAtITsF7kb7PZQPCDzJlOV00iSnryHXQ3GqDWpyvkfe726RmbZltNZ79SiiHjZnt7x6cmhNNhbg1GKFh08vUw1jJkeMhvjusxHzpRqRavfp6iNtmVGzHsbUoihT8nJ4/zgLq3XKtYgwivjCI7OcWFjl0N4hCr6/Id2ylW8slesNtxX771Klu61nJ9J9wR4/q1Czn7c77Rp3aEpY0m8F8r5nirpTxz28f5yFcp2VSkjgSePePvdK46GeDtzrqX7QOI91XerhbYq1ZrTfzXoUNyxF01IZG9jboP7w/nGWKiHlWtTx+afvVa0hw2lO4JWWytg+t1IJGSsElOsRM8s1qrU6X358numlCs/eP37R6N0dDofD0Z3NBO5F4HSX9X+BcZy5pLB/k21s0AjcM4LNekb20WK00nmKeZ8o6q5nTfuSW4J1fLA70W5raP2126lESjHn4yVygqzArZMmOX0NaSlCJ+x1+J5QyHnUos4Z+nT7G7Nb5gNmS83ZLXcPFxpZ3Pb27hsZoJj3yXlGnzwYCE/OlohVm9cjwvRipfFMvnlsHjBZ78Y5BwLmOsyoOTVe5PlXTVAIPObLdXYNBRyaHOaqyWFGixvTLaediaxzT873GMz7G9K5R4meO+gQuNussZkwyduAxr3VmSV9DsieRGxqvMhLrtlNIfBYThyN7rxxH5dPDJIPvBZLSFssnMb+7PvtGfdsqYy9NjDf1YZjUZd2To0Xed5B82zPLmc//9ZZWePG+aCZcbe30/a5udU6xYGAV96wj11DOR46vcLu4YCp0QEGC77TuzscDsclwmakMk8Az+6y/mHgRzZx/B1JrGY01LSeM/7RWYGNlVJkTcBk9bwizX076Vnjtizm9EKZrx2dY65U4+xyta9X6OnJcVYqdb70+CxPni2xezjfyBree2KBu06GVMcWuGpyyGTNM67PXsP0YqVh39h+DWkpQtZ9gPaMu89ytXMgGsatmdap8SJ3XL+XJ86WeMUNe/E84djcKoXc2sHSXKnGvrFCo50AAz4sl81kOenrObtcZWpsgKFCwPRimcvHB1sGDK985j4eGh/kJddOZlpXjg3muO2qXZxarDBazDGzUmVypHnufnXL1vZyuVpnttSUJNXCiK88OccDJxdbpD3tkp/VcutgKD1YAhoDtFqqUBPM8/PbnIG6WRa2Z9ynF8p89Yk5nporMVuq8lJvD1PjxUZAXI9jijTv3/hggVsP7OL2qyYYKzatRQdyfqM4dXqhzJefmMETj+Nzq41+e9fjM9x3NmTqkbO87DpzHk/ILDy2Bea5lNStMSlT25staJ2AbNdQnlsP7GJqfIBnPWMs89h234ZUJjUoSGfcbZ87OrvKxFCe/eODPGNXkfnVGq+88TIeml5mtRoxmMvW0jscDofj4mIzGfePA/9cRA52WH9JTr5k45d2vXktzJLKNAPSdqye12TOzXad7AEb2TqRxqv1MI4Z6WBH2L39xg5yeqHM15+ap1KLGRs0Up2Pff04H7v7BKvViIJnzmmkMFWijKy5vYZqGFNIMsLt15CWInQiTHlyrzebbDrjbmmfhClS7eAqk6daj7liYrAx8KpEMFbMEWvzeqJGYWFMqRoyngSQ6Tcn6cLiLMw98ZkYylMPY/aPDzYGMf3YQAIN28taFLdIku49Ns89xxeNzGKwKbe699j8GsnP3Wejlj4SpYLL9DW1a7IDXxIv897sEKOUlttuW0/aXY+as8VmzXgLTTnMQNvAyxbJTi+U+eyDpyjXYnaPtPbbeqgMBube2/N0mqXUDmBtdr0eaeb3NT3wtNh71Kmf2gF7Mec3HWui5psI42LU1MyvVMOWAbXR9Q9Qqzf7s13eT79xOBwOx85jM4H7rwLLwP8RkRekV4jRIfxj4LFNHH9HohmBu/GCzpLKrC12s1itdCWMCaO4qz1gQyrjNV+tjwzkiOnfMs56mKelOmFiazi3WmNupUo+54EIu4cLjAwEPHam1Ni3/RrmV40mOed5mdeQliJ0wuiVzXb5wMyo2cki0xZUpmkEgQ3rPTJdZdLT0cdq/NBXQ+X6fSNEsabWh6gq88l09TdMjQKtz9xm2TvNfFsNIwqBl3nOfmwgIf3MzcyrVpL0yfun2TNSMJNkpWY9/eT904wMBBQCv2FZOBhISx/J0qKnJyNKF2qmNe62LYWc37C6TPe/LLvO0cEcIsL4YHPbTrP/VsMIz2uV1dj7Xa3H3HtigaF8kMidvJZ+awpphbGUHClLKmOtGdMZ93pkvoftkzrZGVnTxed2gNipT9trGswHqCbHTr3hSPu4p+shPGnq+l990xQr1ZBaGLfUb/TTbxwOh8Ox89jMBEyzwJ1ADviSiHxJRH5VRH4F+CbwfOD9W9PMnUNWxj3nZxdvdnOVsVrp4YLPzEo1UytrsWMCa0c4VAgawVQYxwwVAuZKvTl2xskETHOlGrsSbz0rQTBZx7gl6zlUCFhMJvlp17lPjRd5cYYmudVVZv3JotKWme3Z83ayMu65Nn12rLpmAibb3jtv3Ecx37znt+7x2TtaJFZtrM/5wlKlTuAJd964j8nEsSUt9Vism4kAACAASURBVLGBZbXeIeNeNxn3rHN2es6dsM+8EHgMF5o2iaeXKuwebn2GdrnvCw9OL7FSNTUMAz4tfSTL/aUQ+M3APVWomda4z5VqDOZ9Hj61zNlEtpHuf+12nUOFgJzv4Xkm22y3tdnl9jcxlXrMQOCvqVEYCHyiWDmzVG0MDnIt2fK44X+e85vn8WTtBExNa0av1VUmyp4sLWibgMzem05vkWx23Vqu1qO4ZUZZ23/jWBOp1ySFwGOxXG/0j8NX7uLOG/cxkPeYKWVr6R0Oh8Nx8bEZjTuqer+I3AS8E/gh4IXJqhrwm8D/3Fzzdh7txXdWbz5bqnF2udKiMf78w6c5OrNKGMeZOnRTjLeHcj3iBVfv7njOdHGqlXPsGsxzerHKXKlGMef39Ao9XZA4MZSnXIvwPaFcjWDIBqbCajVCMMHSSjVkMgkO61G8Rs89VjR63xcc2t0IKtOkg6tO1OOmD3kjIA7XnguabwzS2GA/7Zmd5SoD5p6nn8ORmYeRlB3k1HiRWw9MsFIJuXbfMFPjRc4k9n/t2WmRLlKZKGYykXu0n7Nf7DM/ONlUp1k5hX2GNli0yxdWzWCrEkYMFwIqES19JCvjng88qm0a94YmOyXtWCwbaUc5sflMSziy7Dp3DeYYLowSJG9lJobyHftFpR5RyHjui5Uadz81z9MLZVZr5tlYCZPttyOFgCtGPQqB3ziPl+GIk5YBeUkgHSZZ8axC8vbibNvmjlKZjJmAG4XqvteQcUWqeAi7hwe49cAuDl8xzp6Rpq3n1HiRF149yVDB59ku0+5wOByXBFsxc+qiqv6squ4HLgOuB3ap6k9qN6uQi5T0LKad9OZWY7xaDZkY6m712ItdYlo3nLYjHMp7HJ8rs1Sp9/QKPe1sYY+DKKWakXJMDOaZGC4wU6qQ82ClamQjNz9jtGX/NNZOspgRbEF2cV871moRUhn3jKBIVYmizhn39CyVWRn3TrTLKex1VtsLC1NBnYjR42dJZcIoJoq0ofvfLPZZZckplitGThGmrAlffdMUi2Ujv6jWo4YkKMuysNX9xczOGsXaUqiZ85sDAyOPqlGuRazW1tohZtl1tts7Ht4/3izqzsq4t+nbpxfK3JVYp44PBlTqEScXKsyWai39drlSJxBazmMcXNoC95Q1IzQngzITWa3tN+3F2bUoQsTcw6zvRHMm4CRwTzLu7a43dt9uReyd3uY5HA6H4+JkayKHBFU9o6qPquolayaclso0NLwDeWIlQ2MckPO7W7nlg+6zkppzNnXDaekF4iHA7Qd29ZTRTQfu9ji7innOLFUo5Hx+4LYreMNzLieOoa6k7PhMpjcrgFithRRyXscMd1ZxXzthFDe2K3SRymQFm2CCG5v9jpO3Cp3ak0W7T7l9HlYGk+Wjb9rqZ2bc7bJC0Hk23H7oJLexcopi3md2pVVm8aKrjYTpzHJTEtRqWdjqKmPa2xw02WedT2XcNZETWXnU2ZXKGglHlBo0rScTMoPW5n1XVaphtOZNy70nFphI6jHGBwum3w7m+NaJBYp5029/4Nb9FPM+i1VazpMplWl7nmZm125SmebAJYxi4rg5UM367oaxItKsgzBWk81svs2428Fip/4FJkPfTWbmcDgcjouLnqUyIvKdqvq3GzmJiLxSVf+mx21fBfy/gA/8nqq+r23924D/CjydLPotVf29ZF0E3JcsP6aq35csvwr4MLAb+AbwZlXtTfTdJzYICBIN7+RwgXI9IoqVWLWhMX7ugQlOLVUaWbZOVm6B5xHH2dptS5QEAl7KjnBqvEgcK194bIYOMuu1x2mbgXVqvMirnz3Ft44vcvvBCcYGc5SqIbdcsYur4pO86qYpwEghbDvaKdeijtl2oEWK0Im0/CVrIqD0dun2W0SMO0g9ihvBUB9xO15KKpOe9dJm08MOA4ZCkD0rbDNw37pxcye5jQmkJ1FVbjs40VhuLQvHB3PcdnCCIzMPt+yXFSym33bYCYo8TxoBp7X03DVkLBsBXnhod8NaE0wfS0uZusmE2v3hq2GMKmsCd/s9mxjKMVbMM1bMcdlYkZmVaqOP2nMNzDzMHallnsgaN6T2NyjGNSc2bwsGsjPu5ZqRHtmBxlAhYLUWUcuQj4WxuXfpvpz+ftsXN/YZ2MnbOg0aShuYaM3hcDgcO5N+NO6fFpEvAL8GfCqZHbUjIpIDXgv8G4z2fV2RtYj4wG9jil5PAF8TkY+r6oNtm35EVd+ecYiyqt6Ssfy/AL+uqh8Wkd/F+Mv/znrt2QiRmj+8ktKbN4ojk9kX940OUKqGxr4vMDrcTlZuuaAp8/A9EwC0+2SPDASNoD2N5wl5Hz77wCnuOT7PvtGBrp7uacmNxU7ms1SpMzaYYykpRB3MdfeytpTr0br6+rQ/eBZh3JQoNPzEMwL3qC3gSpNPAvesyarWQ1JSmfSbgYZUJmoWXKYp5DzmV9eOD23An+Ulfy7I+UKp2nq/7HVUOozqsgYjDYvLKDJOPxnSjpzfOqgq1cLWwL3LADTN9EKZu4/NsVSuc3KhzOH9441izoG2AY/9nl050arx76Wuw5OmZ3rj2lMadzD9qVyPWmot0gS+NIJr24+HCgFnl6vZA8wkc+95gu9L4iqTup/SvJ9m+7X+8ZZepHQOx/ni4Ds+caGb4HBc9PQTOTwHCDH+7SdF5E9E5F+LyGtF5EUi8mIR+V4R+SkR+ShwCvgYsApkBdNZPA94TFWfSDLiHwZe10cb15BYU74iaQvAHwKv38wxuxErjeI7q+GthbGxDyzVGhrjpUqdpdUQ36erlZsNWG1AkJ4C3fpkf+mxWRYyXGOmF8o8eHLFBGfCup7uacmNZSDnk08cLQCWyiG+JwykkohBB7lLFCvVesxgvvv40EoRMtsUK3G81iM9UzveRVKQD0ywn3bg6RXfE1QTDX3K3zydcc8aLBQCP9O60kps2i0NzxVZM5vagLIaRpmz1toAO+3eks4Q16OmtCOX3Et7/2th3Mgal6ptEztF2R76aRq1IYkNqe23T82uAmsz7pux1PS8tVKZdpmQedamLiEreA68plzF3tehQnepTKNmw/eSNxjNZfbfRsY9Mm/Ugoz+kpYpORwOh+Pip+fIQVXvV9XvAl4MfBb4XuDXgb8CvgD8PfCXwK8A35Usf4Gqfk9GxrwTlwPHUz+fSJa18wYR+ZaIfExErkgtHxCRr4vIl0XEBue7gQVVDdc55pYQa/OPu9XwjhYDlip1/MQ+8PCVu3jptXsoBB4rlairlVv7RDT3nlggH3gcnV2lXIsYGchRzHs8Nbe6Zt97TywwMZRj31iBpdVwXU/3RsDSVgQ3WsyZQlVM5n1kIGgJ6GwhYdQWHK5XmGqxUoQssrzu037iaTpp3M05PGopqUw/gbvdNF2UOVwIjNbfFhZmHK/QYRKmahjj+5IZiJ0Lcv7aOgkbZKtmO9+EGUW+6cA9/RbEbpcOXgcCn4Gc35BRWeIujj6WZm1IjjDWRr/91nHTb9sD981Yamb5uLf3o7zvNb5/WRn3nG8Gdun+Yd8y1DMmXgtTRa75wPTLMG7Wcdg3N1HjLU/csa+kz+1wOByOi5++7SD///bePEqO87zPfd6q6m16ZjAYDACBBMEVlEQ5V9wkkbIWho4cOXFoJ1G8XPtYyr2+ys29Ok5yoxtJ8YnPiewktq6vk+jEJ7EiO7YcW7ajeJFjxRJtEXGskJJIkCBBcMFGAAMMgBnM9Cw9vVZ9+aPq667u6Z7unulZuvE+5/SZ7lq/pbrnra9+3+81xjwNPB3JWh4C7gP2AwaYBU4Czxtjtur57R8CXzTGlETk7xCOoD8erbvdGHNZRO4iTAz1ErDY7YFF5KPARwEOHjzIsWPHei7cSr7ASy+eoDJdDy5GjWFf2UdmZ3mtcJ7XgJWyIbHsc5vrkp4TXpuD11ocr1A1vDrvs3zRYW/a4emLFTwxXC8YVq477EkJV1d8FkpwzLvSsO/TFyvsSUGuCAulgMpc+M9/sQTpubVnWygGvLEU4F9xSXn14OpqPmAmH5C/4HJyzmd/xmGPrDa0z8uzVS6nHabH6gFGrhRwfjGgdNklm2gfrJ1b9ClVYfn82gA/Xv8zaYf5gs8zMz65kuG/7XW5c48wmXEbzle+7DZIeQAuLQfkigG5cy6vLfisXHKYSHUOnFdWVvjWN7/J9EoAV12KVTid85nKOMwVAipXXGZWAioBlKcby79UNpzN+RSnXUaT9fKcX/QpVkFm+jM5tRPX8gFX8gHMnKpJhE4v+OQrBgMUp10o5xv6841Fn9UqBFcay/jKbJWZtEO+Yki6sPKGS75ieH3BZ/WSy3hKOL0Q3rA5ApUA5ibrx3hptspE2mHudPu2t9ftShlmCwGlWYeEA28sBRydcPGut/7ZSgO3ABRo+31aWVlpqOeVlYDrqwEyUz/mzErA1dUA91roF2+vf4Dliw5n041lv1EIuLgcEMy45EqGy9G1cnLO5/o5h1tGG7d/dd4n6YbX+7mcTzmAagDjSbhxxqVYNbwS+87bvjBX1l4v8XMnW7jOKIqiKMPFhnzcI/36dwITwDeNMa/0qTyXgfgI+mHqk1CBWuIny+eBz8TWXY7+nhORY4Tynv8MTIiIF426rzlmbP/PESWNevjhh81jjz3WcwXO/N6fcv8DDzRMBARInJ5jbzbB227ZA8DMYoH05SXefc++daUkpapP4vU53vymMW6bHKF4cobLCwUyqxX2ZZPcNjmCXMlxm+Pw2GNHG/YtnpyhUPapBIaLN1a599AYlWpAJuk2TNCzTC+sMjazzHuOTjWMas6tlHjhYo43v2kMri7zHbfu4dXnnyHePskzc4xnEnzHrXtqyy7eWGX02jLvu3d/TR/digNXlriRL/Heo/vXrMutlkm8scADRyYoR6nq70hXKVZ87pzKslys8mg0ujqzWGC0TZuenV3h/Gyeh27fS/JCeLx9o6k152vm2LFj3P/2d/Jq1C5LxQrpS4u8+U1jvHZ1mQeOTHB+Lo+I8FA0IdOyUqoycvYGf+HwHg6Op2vLR9+Yb7n9VjG9sMqrM8u8O9avybNzAKyW/Jb9+cKlHKWKz7ua8gekzt4gm3JZKlRr1/NKqUoqVs/k2TlGUx6ZhMulhVXe/+YDtSc0wavXODI5wj0HxtqW1163qYTLqStL3DqRIZ1wyCwVefDI3jVl6oVjx4411PPc7ArnZvO8/631Mr5+bZnLuQJ/8c0HALg0v8prV5cBuP/IRC3hluXaUpGXphd55O59zOQKTC2s8vhbDpI6Pcu+bIr7IrtUi3d6jomR8Luy/8oi8/ky1cBw60SGew+OUaz4eKfneOst49w6keH5iwuUq0HLel9fKvLi9CLvumuSsWg+iqIoijK89PysXkQOAk8CDxJOOP1REflPInJ0/T274tvAURG5U0SSwA8Raurj549HnE8Ar0TL94pIKno/RXhjcSrykn8K+FC0z4cJZTxbQjg5de3IVzrhNEwEtO/THSwB7eNz+wj+7YcnyEUe3IVKqOvNl3yOHhhds2/c090Yw42V8rra33b677F0GARfWgjlOOOZtTcarrNWjrFaqeK5sm7QDjT4gDcTT/RjJRR7RhIEJpSrxKU/9hitJp7GEze1quN61DJZxhxlrBSiVI0mFq4nlWmaAFqsBH11lOmElXfE5yBUfVObeGwz4cap+sGaRFYQSTuq1tM8PK7XQuOe8lxGIjmRlUwF0XwFt8V8gDj2ui1VfJKecHW5wHKxypHJkZZJtzaDU7NerC8L9fuN/vW1960SMMWkQuVYu7SbOFqNTXJNedGk6Zg0qVamoG4HmWhzvVgJTbvvj6IoijJcdDXiLiJ/2Rjz1ejjTxFmRn0LoR795wkD+F8Vkb+xGQ93Y0xVRD4GfJXQDvJXjDEvi8ingWeNMV8GfkJEniCcKDsPfCTa/a3AL4lIQHhD8rMxbf0ngN8SkZ8Bngd+eaNl7ERgWmus0wmXpWiCJ4QTRZOe0zLIj2NdVKzN3KGJDA8dmeBb5xe4tlTirv2jPHhkLwdiI7oWq/197sI8r16tcMtEhsffcqCt9rc58YwlFemVV0s+nistnxB4rrNGZ9vJCrJ53yAwa9rDBiQJt26vWctM6QcNNpr2/K10yPbmwQaRndo9Tjy4a06eU2qy8osTOoewZiJt2fdJJzqP9vcLr0mDDmFfpxMOnisU20z0bRUkpzyH3GolcpBpCtz90Ce/6huSnsNodJ2slKqMJL2Wk59bYa/bE9M5/CAsy3e95QCvz65sYeBucKlPCo1PNo4nPkp4a8tug+dKk9e7nVfRTPx6SbhO7YbZ3hQ0T04t+wGjXuuf6pqjU5s5IoqiKN2w3Y5Ab/zsX922cw1b3dYN3EXEAX4m2s4G7vcBfwkYI9SW/zQwCaSAHwN+aTMFMsZ8BfhK07Kfir3/FPCpFvv9D+AvtDnmOULHmi0naJPcJ51wuL4cOniIhMFSt0FI88jd+Eiy5pP9nqNTPH8x13YE+dBEhu+duJVsKsEt63hmh2U3NSvLZsrVKscv5PAxFCs+q4XGYM9zhNVy0+TUaPJsJ2zgV/YD0k5jm9h6u07dXjM+6bNcDZjMJpnJFTj22nXOza5QDYI1tpc2mLKjy73ZQYZ/A2NqAVLKc2rOMnErv2aakzBZZ5t+JV/qhkRT0qq4U0864ba0hAzaPEVIek6tDe16Nzbibs+R9BxGImeV1ZIPY3B5YZXjFxZ47doyd+/PrmtNav3dH75jkhcu5kh4YdbW5qypm8XG5/EJqs39GZ8Y2so9yAb21SC8Hu1NYspzGm7WIby5Maa+T/wm004Kr02GjiVganVeiCUw0xF3RVGUm4JO/wWfAt5GOGJtMcYY3xiTM8b8rjHmY8aY/xX4h8D7tqqgg4LfxjUj5bkEQT14Klb8roOQ5pG7YsWvBWP5UjUMuDsEopmkWxttbkdoU7e2TDO5Ai9OL1KqBtyyJ02h7HN81m+wlfTcxuyixhgKFZ9MsnMdbaDTKnuqXZZwnLqEosle89B4midPXWO17DMxkmxpe2kDJRt0dhr1jWPb1kSJsDw3tElMeS6lSoAfy3rZTKrJurLm4b6dUpmm4M7eDCU8G7i3HnFvaasZl41E70VCP3I/MLWblKTrkHAdUgmHlVI1tHh85TqlasD+sdZ91Iq9I0kcBy5H223ZiHvs3qX5CUrDiHuLGzQv1r4VP6i1UasR92bL0riMzN4IiYQuTVYqE/q+t75e7Q2GBu6Koig3B52ih/uBPzfdmQS/QOguc1OznlQG6tr2UmVtRsV2NGvAy9WAyZEwucxq2e8qqU0m4bJarq67TTuP7RPTOabG0mSSbqQrTzDiSYOtZMJ1Gh7XFyvhyGKmg4c7tJZy1MtUz9AZt9dcLlURBz5w30FmloqMpT3SCQfXlZa2lzZAsu3fQWbdQC0hjjGUq/UgPZUIE/OEo9frjLjHRrTrWVO3b8S9ObirBe6ORHMv1gbu7Swu44FmPJj0nPAatTaddrtsyiNfqnJiOocnQibpknCcjtakFtcR9mSS3FgJ8xR0mhPSK3GpjKWdxt11peXTKLttJdK427rb723cx7/aJOdqGHGPndMmhgoCE90sttG4O/XR/mFERN4QkZdE5AUReXany6MoirLTdIqqHgK+KCIvRxKWthhjjIhsyKVmWAiC0F6v1ai1HV0vVXzKCRc/MF0HIQnXYTVKqe5HGuLRtMeNvLBSqrYd5Y8zknS5kS/VpDoty9/mOPP5MgfGUmRTHqOR/CHthsstriP4fpgI5upikW+cmePEdI7FQoV3371vXYnO3EqJ4xcWODu7wu37RhokFPEMnVCXUOzJJMkkXQ5NZHjqtetMjaa4ulSsjWTHte9QH3W2eu6NjLgHxtRG3MHqvcu1+rcilXCYW2kRuG9T1lQIgzuR+tOeemZQh3SUJEqanpa0uxlsGCFuCjqrQVA7h+2HQrnK02dvcG42j8Fw51SW0Whib3MftcP3A45fWGC5VKFQqfLw7ZNdebR3QyupTLM0ZXapyPELC5SqAaWKv0bi4ziC64TZf/2Yxj0ZkyhZCVg1Jv2CxicY8ZsFm1ip0mbeicU+7Wj1tGqI+IvGmLmdLoSiKMpuYN3owRhzBngP8N7Y4nSU+OgLIvLjInLHFpZvoGiVJt4SH3G3weNGpDKl2L6j0WhmEHQnlQmC1sl24uVvFaxZbflYykOiCXxFn4aU8jYwvrSwypOnrrFYrDCeTuAHZl1JxEyuwH8/PUepGrAnk1gjoai2kaGMJF0KZb+hfMXYU4zmlPd2kq+/jvNMOyQW3MUTD1n5E7COxt2Jbrbsk5awzNuVNRXC4M5z69lTbTCYcKXWXvHpCfXruP0kX7t//b0TatxjUpmZXIHnLixQKAeAoVwx3MhXWFgNb0Kb+6gVM7kCL0znKFUDJkYSVPz1r6deaeUqE9e4z+QK/Mkr16kGhsns2uvT4rnCanQ91pIr1SatBg3Hhvr3pe2NkAhBEJ+c3f56STit3WsURVGU4aPjCLkxpkTjZNCSMeZDIpIFHgP+fpTw6AqhX/p+Y8zslpR2l2NH7Vo5liTcUMZRrPoUK1Zq0b1Uxo8euVvZRcpzyaY8ri0VMW0mxMax7i6FcvtJsUGbwP3thyd48tQ1oC59WK2aBltJO7HuxKXQsnG5WMV1hb3ZBCvFUFbTapT0xHSOiUyC3GoFY6hNZrXbV9roezOxJwhvPzzBf33pKivFKgfHU7WU9480+V4nXYeq7yOyMVcZY8InALYt4zr1tiPuXt19xnMdStWARBduQv0m4UhMKlMPBtMJu6y+rZ2r0JxBF5pHiBvr70eBu+eG0qYT0zn2ZVOUq4Y37cmwXKziOXB+bpmEO96yj5o5MZ1jajTFatnHFWE8nUCg7fXUK83Wi8aYBmtGa0E6lvZwXWfN9RlvC3sjWZfK1DPNWmwf2LZ1o9H6ZmmS44RSmfrTkfbXi7eOneoQYICviYgBfinKtVEjnjTvyJEjO1A8RVE2wnY7vQwTGxn2+7qI/AGhm0wA/GNjzBPR588C/1JEviIi/0xE3rvegYaN9UbcIdTnFsp+LfjuZcQdwpHSukbaIZv06oFAhxFka+G4us4E1XYj7q1Syj+43210bYn2m10ukU15FKs+SddFELIpr0FWE2c+X2Ys49WkBkDD9lbj3kwmUX+CcGgiwyN37SXlOeRL1bYp721A1WvQXNO4RzKlmlQm1n+t/L2BBgcc+3c7J6ZavNhTGzv67znxEfe1OuyWGne39Yh7XONu23k+X2YymyCbcnnbLeO84469jKUSzCwW2/ZRM/P5MqMpj6nRJBMjYdC83vXUK7aKQczBxdbHnj+b8tiTSbAn3f78CVfqgXuTVKbix9t2rfSlpqF3GtvTD0xbi9bmcw+rxh14jzHmQeB7gP9bRBoMEIwxnzPGPGyMeXj//pt+ipWiKDcBPWvSjTE/DSAidxLaQn5ORNLAceBrxphfjda/HfgN4Dv6VtpdzEyuwNPnbvDSbJU/e32W99wztSYosRMBixUfx+l+gmItcPdNTSqT9Byyqfr+nSZbphMOItSCi1a0swCEurbccmyuMaG8DTomRkLZymrZZzxK3LSeJGIym2S15JNJOLXJs/Ht437hcayPun2CMJYJLTLfe+9U23a1x+lFJgNr7SDryXPq52k1Og2wsBrq909fX2Yi43F+Lo/jhNr49ewQ+018VLbiG0TCYN51TKR/r29r5UStbpiuLRV5MZq7ELfdrGvc/dqNyWQ2dI85GsuSmnAd7j8ywQdbZO5thZVBvWm83k7dSGy6xd7E2fuWeMKv+PlvmVj//F7DDU3jiHuDVMZvvDGYyRV4/uIC15eLDe3p1AJ3s+b4zXiO09ExalCJZcO+LiK/R2jr+2c7WypFUZSdY8NDf8aY88aYf2+M+VHgbxH6vH+XiPy2iHwBeBfQeebZEDCTK/DkqWvkS1VGvPDReCsdbDrhUqwGoRa7B3cMO7JZqYYj7q4jJFynlr0TOktlRIRMwl03cK92oZVvhw0s7j04ykK+wnKhSjrh1mQr7bK1WovHwMBqucpSoXH7ShuP9IwN3KOAZaUUZmld72bIjoD2MjEVGi0Dfb9+c5NqYeUXJ67fr/g+3zq/wMtXlki5Ttd2iP0ilAlFGnc/qPWXtbWsBOuPCtv6PHnqGtXAsC/baOloNe6lSkDSDfvA9u1ysUJgTMdroRX9OMZ61GVQkfVi04h7t+ePt1XcVUakcV5JNajfNNn29E3A3iYbU1eiyal+5xF31xlOqYyIZEVkzL4Hvhs4ubOlUhRF2Vn68szehDxnjPk5Y8wPEmoOzwN/0o/j73asDnYk6SIijGW8llZ36YRLpRqQL1e71rdDPYFOJQgoVepSi3TCrWtluwhG08n1LSF90z6RUCdsYDE1muYdd4aylULZ7yiJsDKcyWyS3GoFERq2r/qtJ6emPRcRahMC86Vqza2kHbUR9x6ventTVPZt4qF6gp3mbeKcmM4xnk4wmvZ4ZWaZlZLPSDLB7EqpazvEfuG50uAqk4iVN51wGkfcg9Yj7vY63zOSIOE1WjpaV6FSzA6xlcSqG3lMnH4cYz3WJDtqetrQ7fnrnvaNfuxeU/K0ahCs0c/vSSfx3LXtabPQxo/fikRs4vGQcRD4cxE5AXwL+CNjzB/vcJkURVF2lC2xbzTGFIEno9fQM58vMzWaouIH7Ms4JF0Hx5M1VndW075SrHJoIt318ZNNUhmrrZ7JFXj5yiLXFossrJZbynPijCRdrjZlcozj+5sZca97WWeSLg/fuZfH7j3QlZ780ESGJ+6/hanRFG+9ZbxWh0vzeZ57Y4FTM4scPTDWIC1xIn12MTbifnB8/Ta17dj7iHv4146c2rpeXQxlIwurZSp+wP23NUpf7HVxx1SWi/N5RkfDzGEHdAAAG/VJREFUr5uN47q1Q+wHnhO62xgr9/Hq19Dxiws8e7XKbSdnePvhCUxsnzi2Poc9p7aNrYMNVn3fNDilNEusNkI/jtGOZleZVk8bujm/vSYSrtNgt5psDtxjdpG2PVMJl8nY/I65lRJHJrPh5NQgwHHWf6JmZVDrWb0OIlHG67fvdDkURVF2E9s/S24IsTrYlOeyJyV4jtNSBxuXx/SSAbKmlY2kMinPrT1mFwPj6QSlNvKcOCMJryFJTpzmSXm9YoM8PzAsFqpkk15Pk0BHkh6eK7UU8TO5Ak++HGbanBpNt5SWZJIuq2WfUtWn6huyHZI91aQyPdZRJPJBjwXutv0DY5gYSVCsrC1f3Ebz0HiGpOuS9BwmRjpr//tN0nUwJpRqVCO5T60OgSHlGFab2ri5neLXub2WbR3cFlKRQaDZVabd04ZOtLJ3DD9Lo6tMbAK4bc+k69Su3Xh7hlIZ0/KJU6tzD7mXu6IoioIG7n0hroM16+hgrS4b6vaM3RBmDg1Hs0vVcPKffcy+N5sM5Tnp1vKcOOlklBSnZYr7xsQwvWLLWA0ClosVxjOJno8xlk7UAvcT0zkyKYdM0iXZJhuqzQabL4X1iU/WbYWdK7CRUUlH6gFYwqm3/3gmidsmE2j8ujiyL0OuUGYhX+HIZLbvWu1OxLOnVvxwgq2tw0Q2CRI+wRhLe7x8ZSncp+laWE/vHQ8ut9OjfrPYKtr8S1brv540pRVubMQ9TtJ1axIlAD+WB2C99nSdKG+A337CuKU5M66iKIoyvAzOf9hdTFwHu1iivR2h69QcSnoZcQebPdUnCEI3E2tTN5b2SCfc0B6yg02etYRsNUHVSmQ3GriH+zosFatUfbOhwH1PxiNfDhNKzefLNTmGlXU0128kGWb9XIyC/WwHjftGR9yBhsyjniu19h+PbphalS9+XQQGHr59gnfcsZfAmL5rtTtRkzIFQS1wt3VIxfzGsymP+dVyS6/79fTe8bkRgzji3k7j3i12zkDzTUuiacQ9PoK+Xns6UQKmShCs6ygDjX2rKIqiDDdbonG/GbE62PTcazzWxuru2lKRE9M5FvJlVssV3nHHvq4Dt4Qbym8g9A+vyTDSCd7yptBub7lYWVd6kcuXOX4h1IzvH00CgiF8ZH/3/iywcakMhMFLbjUMXK0VZC+MpxMEASxHcoGXLi8ykvQYSbSWltinFnMrJdxYFtB23FgJrRlF4OpioSc7RteJjbi79fafGk0xRapl+WBr9dm9kIzJrawXfU36YrP6Vn2MMWGyoS5tQS3x62YnfOo3St0O0jCTK/DUa9c4c32lwZqxG+y15bkOl3OrtScpz5y7wdnrKxQrPm8/PIHflCuhXXvabUqVoCFfQCtqUhkdcVcURRl6Buc/7IBj9cQYw3g6QcWnJzvARCylespzerbJm8kV+Pqr1wkwVH2fb1/I8e035nEkTBzz9Vdnmc+XNpXRM3TCCF1bOjm8tMKO0i8VKty5L8tCvkI64bStn5UeLa5WOp5vJlfgv70+S6karJu6vh2OSE1O4Tmy5TaF/caO2lqZVMKpX0Olio9gmF8ps1yscvdUtqOuupkGjfsASWUgvF6vL1lLV3+NNWMnZnIF/vuZ0PZzaiy8tr707CW+dHwa3w+/78vFKk+eusa1xUJXMhz7JKBU9dsm97LUpTI64q4oijLsDNZ/2AGmbqWXJOk57Mn0ZgcY/2ef8tyebfJqeuaRBKev51kuVFku+jx/aYGxdIKRpMsbc6ubGnG3weFYOrEhHXk6EU7eXCpWqASGh26f4NB4um394vMEOk1MjVszum5rTfp62OqIhEHqVtsU9hvbr1YmlfAa61AOBDB84L6D7M2mepaK2EDfc2VTN387gSPCK1eXGUt7ZCKL1V6ujxPTOSYyyXA+hucylk4wv1pmfqXEnpHwu5D0HMbSHmdn8121rd0mnqm3HbbtKzo5VVEUZehRqcw2Ya3fkp5DJRv+g+3FDjAeuMd9srsNFO35DzkZTl1ZYnLEY7XsM78S6sPTCYflUmXDQddMrsC3z9/gcq7AnVNZDm9QIlKu+nzt5WssrJa4fV+Wd9/d3uJydrlUs2N888Fx9o4k2m4bt2a0mu5e2t+OgLqO1G5KdosMphsSTSPucZ31oYkM186d4q5IGjKzVOzZz392pcjxCwuU/KAmCxmUtnFEWMhXODwxwsxisSb16fb6sNeW44wwFj35qfgGMGRTHo4DudUKB8aSLBUrtcmp6xEP7jttb/vKV6mMoijK0KMj7ttE3ErPyjp6sQO0gZfnyoYmV9rzZ5MehydGSCdC+8VElKp+peQzlkpsaMS9nlEzYDwabd9IVtCZXIETlxdZKVYZSyXIJr22x7HnNIRShACz7jnj1oz2xqeX9rdt3qvbyG7Buv5YuVVzMJjxhFIlnLha9U1P19hMrsBTr1rrzt5lSDuNI8J42mOlWKVY9dvOqWiHvbYmIochCNs34ToknPDp2ny+zFIhvK67adt4PoVOsiX7ndXJqYqiKMPProtCROSDIvKaiJwRkU+2WP8REZkVkRei149Hy+8XkadF5GUReVFEfjC2z6+KyPnYPvdvZ51g86nbrW445fXmRtPq/NaasFDx2T+WZHa5xHKxwh1TIxtKwGRlOGPp0Jpy/1hqQ1lBT0znmMqmyCRDW8Kp0fbHqUt/wnOut21z/TfS/jbW2oyUaKdJuE59xL3pBiQVBfL5UpVqEPRUz7gMKem6254VdrM4AkcPjDKXL5Ev+qSTTk/XR6tra3IkyeRoiuVihb0jSVaKVaYXCtwxNdLVzV88uO/09CPM0Co6OVVRFOUmYFcF7iLiAr8IfA9wH/DDInJfi01/2xhzf/T6fLRsFfgxY8zbgA8C/0pE4v91/9/YPi9sZT1asVlNtP3n3clhopvzW2vCR+7aRwBg4NG79jGZTW0oMLW2gpmkSybZnTVlu+PsH0uS8IT9Y2EW1HbHqdlhphKR1/v659xs+1t5TCdrvt2M5zg1OUXziLs1AcqX/TXOJ52I97+15NxI/+8UjiPszaZ4+Pa9pDyH1ZLf0/XR6tr60MO38aEHD5NJhtl9xzMJ7pgaYbLL+QNuDyPuEN6UVXRyqqIoytCz2zTu7wTORKmuEZHfAr4PONVpR2PM67H3V0TkOrAf2DXDfpvRRM/nQ7s5x4XrS8UNaYhbnf9/nJljNO0xmvJYLFQ3JcOZHEkyORJKC1ZK61tTtjtOoezztkN7asvayRVq58wma+s7SRs20/42kOpGn7xbiZe92akk6QCOkC9V8YPO2Trj2L64Z/9obdl2ZoXdLI4IgTGkEx7vunsf7793f8/HaHdt2WXPvTHPn75yneVSjqVihUfvWt8KNt783cw3cB3RzKmKoig3AbstcL8VuBT7PA28q8V2f1NE3ge8DvwDY0x8H0TknUASOBtb/M9E5KeAPwU+aYxZM+tMRD4KfBTg4MGDHDt2rOcKrKysbGi/9Zgv+Hzzqs9CMeBAxuH4nPDnxw0P7neZzGxMOmN5Y9EnX4GJtDC7GuBd7+6SiNdzteBzfNZnxBPSLhR9WK2G5Ts291rXZenlOP06Z7f1fGPRZ6Fk2JcW5s9srs13inOLPoslgyOs6ed8Ps/lUy9x1oGVsuHKiMPMaHfB+3b1RT9o9f08veAjQNWA54C50t/+nS/4PHvN50YxICHw4vIMx0+y7ve3VDWcmg9lTaXLLtnE+sH76YVw29zZwbw2FUVRlO7YbYF7N/wh8EVjTElE/g7wa8DjdqWIHAJ+HfiwMcY+O/4UcJUwmP8c8Ang080HNsZ8LlrPww8/bB577LGeC3fs2DE2st96/PHJGR7cV+HSQoHDezNMRdrZTNJtm+ypWy7cyHP62goHxlMsrFa6Hm1sruejuQInpnPM58tMZpMbdhXp5Tj9Oud62HqevLzI1cUit+8b4ejBsb6eY7vYf2WRmVyRVMLhvUcb+/nYsWN859EHuJEvU6kG3HNglDumsl0fezv6oh+0+n6OX1ygXA3Il6rcvi/LPQdGW++8Qf745AzvOOiTK1S4sVLmvlvGKVX8db+/xYqPe3oOgEfv3tcxK/DeSzlWyz6P3r2vr2VXFEVRdhe7LXC/DNwW+3w4WlbDGHMj9vHzwGfsBxEZB/4I+EljzDOxfWaityUR+Q/Ax/tc7i3F2s0ZgYkoSVEvVobrMZ4Oj7ewWtnUxMt+WSP2cpzttGN0hkDjbidFtpscmU15XF0sAvQsmRoka8xmHAklQsbAeKb/P4n2+5uO5oAkXQfPkXW/v71MTrXbVNVVRlEUZejZbVHIt4GjInKniCSBHwK+HN8gGlG3PAG8Ei1PAr8HfMEY86VW+0g4w/D7gZNbVoMtwGqIp7Kpmva4XxrisWhWYqUabMhR5mbBBlKD7ioT/m1dh2yqLrPo1cd9kHGEWlZceyPbT+z3N+E4TGVTQOfvb3xyaqfMqRD2rbrKKIqiDD+7KnA3xlSBjwFfJQzIf8cY87KIfFpEnog2+4nI8vEE8BPAR6LlPwC8D/hIC9vH3xCRl4CXgCngZ7apSn1hs1aG6+FFbizh+5snWOuVmh3kALeRV7v5aP21H43JMTYySXlQsTesqYRDOtF/jfhGvr+OI4iEk1S7SYrmOYIfGAKdoKooijLU7DapDMaYrwBfaVr2U7H3nyLUrDfv9x+B/9jmmI+3Wj4oWLu5E9M55lZKTGaTPNLBlaIXxjMe+VJVR9zXoWYH2YPbym6jk1Qmk3BxHAiCwa5nr9jrfitG22Hj31/HkYaR9/WwfVoNDMmb6KZLURTlZmPXBe5Ka7ZSQ1ws+xy/sADA7PLGrCaHmZlcgW+cmeXM9ZWurPx2KzdWihy/sMBLlxe5OJ9f089XF4ucvLzE7HJxoOvZCzO5Ak+fm+ONuTz3HBjlwFhqS+rc6/d3Jlfg+QsL5Ms+q+Vqx++ktYu9tLDKoT1pcL2tuQtRFEVRdpSbZ1hNaclMrsCzFxYoVQMmBzBd/VYzXwjbo1wNGE8nKFeDgWyfmVyBPz9zg1I1YGosuaafbT1FzEDXsxdmcgWePHWNUiXsWxHZFXW25ar4hn3Zzt/J8MYy7NuJkXB7Jz22eR2doiiKsuvQwP0m58R0jv2jKUZSLq7jDFy6+q3m/KJhLO0xFgV245nBbJ8T0zkmMmGW2USLfrb13DuSHOh69sKJ6VzUtx4iwoGx1K6osy1XNuXhuZ2/kyemc+yJ+hYDY+kEBL6/zcVWFEVRtgGVytzkWKu62yZHyCTC+7h+WU0OA0tlQzblkUoYbjV0ZeW3G7H97BvDnpG1lqL1ero4IgNbz16wbZLwHBKeg+c4ZFM7X2dbrkN70rUJxet9J+fzZfaMhE9JapOnTaCBu6IoyhCiI+43OdaqbnIkSSYR3scNUrr6rWY8GXp8J12H/WPdWfntRmw/HxhL1+wF4/WI1/PAWHrN+mHEtknac7u2adzOcu3JJGqOT+uVazKbpFINopvvaCxGnKFIoSoiHxSR10TkjIh8cqfLoyiKstNo4H6Ts5VWk8PAnXtkKNqnUz8PSz17Ybde+72Wq9X2OO7AB+4i4gK/CHwPcB/wwyJy386WSlEUZWfRwP0mx1rVZZIucyslMkmXD9x3cOjdRLplMuMORft06udhqWcv7NZrv9dytdo+KC4Pw+SEdwJnjDHnjDFl4LeA79vhMimKouwoqnFXBjpd/XYwLO3TqR7DUs9e2K117rVca7b3q5UtKNZ2cytwKfZ5GnjXDpVFURRlV6CBexuee+65ORG5sIFdp4C5fpdnF6L1HC60nsPFm3e6ANuBiHwU+Gj0cUVEXtvC090s1w7cXHWFm6u+WtctRn5uw7ve3s1GGri3wRizfyP7icizxpiH+12e3YbWc7jQeg4XIvLsTpehD1wGbot9Phwtq2GM+Rzwue0ozM1y7cDNVVe4ueqrdR18VOOuKIqi7Ea+DRwVkTtFJAn8EPDlHS6ToijKjqIj7oqiKMquwxhTFZGPAV8FXOBXjDEv73CxFEVRdhQN3PvPtjy23QVoPYcLredwMRT1NMZ8BfjKTpcjYijatEtuprrCzVVfreuAI8aYnS6DoiiKoiiKoigdUI27oiiKoiiKogwAGrj3kWFNzy0it4nIUyJySkReFpG/Fy2fFJEnReR09HfvTpe1H4iIKyLPi8h/iT7fKSLfjPr1t6OJcgONiEyIyJdE5FUReUVEHh3G/hSRfxBdsydF5Isikh6G/hSRXxGR6yJyMrasZf9JyGej+r4oIg/uXMl3J51+u0XkIyIyKyIvRK8fj5bfLyJPR9fYiyLyg9tf+t7YaF1j68dFZFpE/s32lXpjbKauInJERL4W/T6eEpE7trPsvbLJun4muoZfiX4rZHtL3zvdxFsi8gOxuOU3Y8s/HP1OnhaRD29fqfuEMUZffXgRTp46C9wFJIETwH07Xa4+1e0Q8GD0fgx4nTAF+WeAT0bLPwn83E6XtU/1/X+A3wT+S/T5d4Afit7/O+Dv7nQZ+1DHXwN+PHqfBCaGrT8JE/icBzKxfvzIMPQn8D7gQeBkbFnL/gP+CvBfAQEeAb650+XfTa9ufruj6+bftNj3XuBo9P4WYAaY2Ok6bUVdY+v/dfT72Hab3fDabF2BY8AHovejwMhO12kr6gq8G/hGdAwXeBp4bKfr1If6HgWeB/ZGnw9EfyeBc9HfvdH7vTtdp15eOuLeP4Y2PbcxZsYYczx6vwy8QhgUfR9hAEj09/t3poT9Q0QOA38V+Hz0WYDHgS9Fmwx8PUVkD2Hg98sAxpiyMSbHEPYn4QT8jIh4wAhhYDXw/WmM+TNgvmlxu/77PuALJuQZYEJEDm1PSQeCDf92G2NeN8acjt5fAa4DG8oBsk1s6v+UiDwEHAS+tkXl6ycbrquI3Ad4xpgnAYwxK8aY1a0r6qbZTL8aIE0YAKeABHBtS0rZP7qp7/8B/KIxZgHAGHM9Wv6XgSeNMfPRuieBD25TufuCBu79o1V67lt3qCxbRvS48AHgm8BBY8xMtOoq4Q/6oPOvgH8EBNHnfUDOGFONPg9Dv94JzAL/IZIEfV5EsgxZfxpjLgM/D1wkDNgXgecYvv60tOu/m+K3aRN02z5/M5LDfElEbmteKSLvJAx+zm5NMfvChusqIg7w/wMf3/pi9oXN9Ou9QE5Efjf6jfz/RMTd6gJvgg3X1RjzNPAU4W/kDPBVY8wrW13gTdJNfe8F7hWRb4jIMyLywR723dVo4K50jYiMAv8Z+PvGmKX4OhM+gxpoiyIR+V7gujHmuZ0uyxbjEcos/q0x5gEgTyitqDEk/bmXcBTmTkIZQ5YBG1nZKMPQf7uMPwTuMMb8L4QjdL8WXxk9wfh14G8bY4IW+w8S7er6fwFfMcZM71jJ+k+7unrAewlvUt5BKMn4yE4UsI+0rKuI3AO8lTAz8a3A4yLy3h0rZf/wCOUyjwE/DPx7EZnY0RL1CQ3c+0fH9NyDjIgkCIP23zDG/G60+Jp95B79vd5u/wHhO4EnROQNwkdvjxPqOSciqQUMR79OA9PGmG9Gn79EGMgPW3/+JeC8MWbWGFMBfpewj4etPy3t+m+of5v6QMf2McbcMMaUoo+fBx6y60RkHPgj4CcjKdJuZjN1fRT4WPT7+PPAj4nIz25tcTfFZuo6DbwQSTGqwO8T/kbuVjZT178OPBPJgVYI58M8usXl3Szd/KZNA182xlSMMecJ5+Yd7XLfXY0G7v1jaNNzRzrvXwZeMcb8QmzVlwE7I/vDwB9sd9n6iTHmU8aYw8aYOwj77+vGmB8hfIz4oWizYajnVeCSiLw5WvRdwCmGrD8JJTKPiMhIdA3beg5Vf8Zo139fJgyyREQeARZjkhqli9/upjkBTxDO8yHa/vcI5xB8id3PhutqjPkRY8yR6Pfx44R13s3uaRuua7TvhIjY+QqPE/527FY2U9eLwPtFxIsG6N4fW7db6Sbe+n3C0XZEZIpQOnOOMBPzd4vI3uip7HdHywaHnZ4dO0wvQveG1wk1jj+50+XpY73eQ/jY/UXghej1Vwj1338KnAb+BJjc6bL2sc6PUXeVuQv4FnAG+E9AaqfL14f63Q88G/Xp7xPOrh+6/gT+KfAqcJJQypAahv4EvkioR60Qjiz97+36j9BN5hej36WXgId3uvy77dXqtxv4NPBE9P5fAC8Tulc8BbwlWv6jUR+8EHvdv9P12Yq6Nh3jI+xyV5nN1hX4QPT7+BLwq0Byp+uzFXUldGj5JcJg/RTwCztdlz7VV4BfiOr0EpGTWLTuf4t+/88Qytt2vD69vDRzqqIoiqIoiqIMACqVURRFURRFUZQBQAN3RVEURVEURRkANHBXFEVRFEVRlAFAA3dFURRFURRFGQA0cFcURVEURVGUAUADd0XZAUTkORF5cRP7PysiL/WzTIqiKIqi7G40cFeUTSAif1tE/l6P+ySA7yD0Ud/IOb1o/+c3sr+iKIqiKIOJBu6Ksjk+Q5ioo2uMMRVgD/DRDZ7zPsJEQhq4K4qiKMpNhLfTBVCUQUVE7gGmgGe63N4BPGNM2RhT3MSp74/+auCuKIqiKDcROuKuKBtARH6fMLU8wE+LiIlePxOt/7no81tE5LMichmoAg/F1u2LHW9SRD4tIs+IyKyIrIrIqyLyiSjgj/NA9PeFra6noiiKoii7Bx1xV5SN8TnABb4X+LvASrT86ejvA0AB+DLwOvAvgHHgJPBPgYvGmBux430A+FvAHwG/BiSBHwR+FjCEkhzL/cB5Y0yu77VSFEVRFGXXIsaYnS6DogwkIvIHwKPGmAMt1s0Symg+YYz5TIt13zDGfH9sWdYYk2/aLgG8CswYY94TW74APGWM+Rt9rZCiKIqiKLsaHXFXlI3zIC105iJymDBo/0aLoN2ua9jPBu0iIsAY4Yg7wHXCiah2/zuAiVbnVRRFURRluFGNu6JsABHZDxwGjrdYbTXoX1hnXUPgLSI/ICLHgDywCMxGr0eoa+nb7q8oiqIoyvCjgbuibIwHo7+tAne77uvrrKsF3iLyGeC3CYP2fwj8NULN+//ZvC0auCuKoijKTYtKZRRlY9gAut2I+yJwts26OWPMJahJZz4O/KYx5kfiG4rIYy3OcT8wa4y5vPGiK4qiKIoyiOiIu6JsjLuivxdbrHsAOG5az/x+gMbR8tsAIZyEWkNE3ksY0ENj4N68v6IoiqIoNwk64q4oG+Nc9PezIvI04AO/CewFjgC/07yDiExG634rtvgkMA98PPJrvw68E/iuaHnJGLMQ7b+PUFf/G1tRIUVRFEVRdjc64q4oG+OzwK8DHyL0Xf/n0Qh7JwkNxEbMjTHLhF7wrwCfAP4JUAYeJXSXaR5tB028pCiKoig3JerjriiKoiiKoigDgI64K4qiKIqiKMoAoIG7oiiKoiiKogwAGrgriqIoiqIoygCggbuiKIqiKIqiDAAauCuKoiiKoijKAKCBu6IoiqIoiqIMABq4K4qiKIqiKMoAoIG7oiiKoiiKogwAGrgriqIoiqIoygCggbuiKIqiKIqiDAD/EzQdOu7t5V1UAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 864x144 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,axs = subplots(1,2)\n",
"fig.set_size_inches((12,2))\n",
"ax=axs[0]\n",
"samples=np.array([[needle_gen(L)['cut'] for i in range(300)] for k in range(100)])\n",
"\n",
"ax.plot(np.mean(samples,axis=1),'o-',alpha=0.3)\n",
"ax.axis(xmax=samples.shape[0])\n",
"ax.set_xlabel(r'$trial$',fontsize=18)\n",
"ax.set_ylabel('$\\mathbb{\\hat{P}}(cut)$',fontsize=18)\n",
"ax.set_title('$\\overline{\\mathbb{\\hat{P}}}(cut) = %3.3f,\\hat{\\sigma}=%3.3f$'%\n",
" (samples.mean(),(samples.mean(1)).std()))\n",
"ax.grid()\n",
"\n",
"ax = axs[1]\n",
"ax.hist( samples.mean(1));\n",
"ax.set_title('Distribution of Mean Estimates');"
]
},
{
"cell_type": "markdown",
"id": "6f6177aa",
"metadata": {},
"source": [
"The figure above shows some statistical history of our Monte Carlo simulation. The `samples` array in the prior code-block is a 100x300 matrix of True/False values indicating cut or no-cut. The overall average of this array is our estimate of the probability of a cut. In other words, we count the number of cuts and divide by the total number of needle drops to obtain the estimated probability (approximately 55% in this case of $L=1/2$). The plot on the left shows the average across each of the 300 columns. Thus, there are 100 such column-wise averages (recall the `samples` matrix is 100x300). The title shows the estimated standard deviation across these 100 columnwise averages. \n",
"\n",
"The plot on the right shows a histogram of the column-wise averages. Why did we partition the simulated samples like this and compute column-wise instead of just using all the data at once? Because we want to get a sense of the spread of the estimates by computing the standard error. If we used all our samples at once, we would not be able to do this even though we'll still use our average of these averages to get our ultimate probability of a cut!\n",
"\n",
"Naturally, if we wanted to improve the standard deviation of our ensemble of columnwise means, we could simply run a larger simulation, but remember that the standard error only improves at the rate of $\\sqrt{N}$ (where $N$ is the number of samples) so we'd need a sample run *four* times as large to improve the standard error by a factor of *two*. Furthermore, we need to understand the mechanics of this problem better per unit of computing time."
]
},
{
"cell_type": "markdown",
"id": "5346b653",
"metadata": {},
"source": [
"## Relative Errors and Using Weighting for Better Efficiency"
]
},
{
"cell_type": "markdown",
"id": "b5ddbac8",
"metadata": {},
"source": [
"There's nothing wrong with the way we have been using the simulation so far, but in the first figure all of those blue needles did not help us compute the probability we were after because they did not touch the edges of the square. Yes, we could reverse the reasoning and use the blue instead of the red for our estimation, but that does not escape the basic problem. For example, if the length of the needle were really short in comparison, then there would have been a lot of blue in our initial plot (try this using this IPython notebook!). In the extreme case, we could find ourselves in a situation where we run the simulation for a long time and not have a single cut! We want to use our valuable computer time to create samples that will improve our estimated solution.\n",
"\n",
"To recap, we computed a matrix of (100x300) cases of needle drops. Each of element of `samples` in the code above is a `True/False` value as to whether or not the needle touched the edge of the square. We averaged over the 300 columns to compute the estimated probability of a cut (the mean value of the boolean array in this case). The estimated standard deviation is taken over the ensemble of these estimated means. \n",
"\n",
"A common way to evaluate the quality of the simulated result is to compute the *relative error*, which is the ratio of the estimated standard deviation of the mean to the estimated mean using *all* of the samples ($R_e$). This is computed in the title of the figure below."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "d146c60b",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 864x144 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,ax=subplots()\n",
"fig.set_size_inches(12,2)\n",
"ax.plot(samples.mean(1))\n",
"ax.set_title(r'$\\hat{\\sigma}=%2.3f,R_e=%2.3f$'% (samples.mean(1).std(),samples.mean(1).std()/samples.mean()), fontsize=18)\n",
"ax.set_xlabel('sample history index',fontsize=16)\n",
"ax.set_ylabel('$\\mathbb{\\hat{P}}(cut)$',fontsize=18);"
]
},
{
"cell_type": "markdown",
"id": "54cb7ace",
"metadata": {},
"source": [
"So far, our relative error is pretty good (the rule of thumb is below 5%), but let's see how we do when the needle length is smaller? The code-block below draws the corresponding figure for the simulation for this case."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "bab74a92",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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hyBI9g266QCVio9N+9ncqdz1QAbpCsWKJSVzsWoC+rtaO3VKUdx36uCcIKL3jSkJf+m6tLqXWXrLsGXStSZGPVeVzM+hDbh/+kKptUCiMMuL247AU0VJlu+CKrD3+ELf+4BDv+dGhWGLoYkYF6ArFCsU55afYLKgoLQbAZBJsbanIe0fRMY82ETivAvQVg+6B3lplo8ZuWfYiUbc3hDcYnpNBb622ISUMTCgvdIXCKCNTPurLLbRWl15QGfRwRPJ/f3qUjkE3UsJx1RlbBegKxUpF90A3mURs29aWSjoG3XnNSo7PaBl0JXFZOeg37pYqWzSDvrwB+qwHenwGXfv/hRRkKBSLzYjbT71D6yXQfwFJxL7wwEke7hjmb15zCULAsb7FsQxeSagAXVGwfP9AF785NrDcwyhYnNNagB7P9tYKgmFJx+BUXl4jHJGMz8wWiSpWBn0uL7V2C6UlZmrtFsamA0Ty7O6TDYPRAH1VxdwMOqhCt3zxwye6+emhc8s9DMUiMzLlj2bQbYxOB5gJhDI+56muMT57f+G6Tt9zpI/vHuji1mvW8Bcv38CGOrvKoKMCdEUB84MnuvnJkz3LPYyCRW9SFE++O4pOeoNICQ5rEUNuHyHVGGNF0Dc+Q2u1lqGusVsIRSRuX3DZxjMYbVIUL3FpKLdSbBacUxn0vPDDP3bzud924PFnDtgUKxMpJcNuH/UOCy2xFajMiZN7j/RzxxPdy3oNSMVTXWN88r7nuW5jLf/yfzYD2krwsf6Ji75BngrQFQVJOCJxTvvpHJ666L+kqXBO+WMFojqryq3UOyx5C9BdUf355U0VhCOS4anldwNRZKZvfIbWKi1DXWsvAZbXC31wwofZJKh3zAboZpOgubJUWS3mgVA4wuCkjylfiF8dNdp8W7HScPu05nQN5dbZFSgDE9zTI9qK6rmxwpoM9455+NB/P8PqahvfvOVKisxaSLq9tYLR6cBFv2qrAvQVgssTYGjSl/BzoVY6j077CUckU77QHN9XhUYkIhnzBBIy6EKIWPYhH7iiDi5bog1vlA698AmFIwxM+GIZdH0S55xavmvFwKSXeocFc1y9BGgyl0wSl0hEFtzKTSQil1UyNJ/BSV+sQdmdB3sNJTWklMpBZwFEIjLvTeEy4YxaLNY5LKw2KBGLRCSnh6cB6C2gAH3SG+R9Pz4MwA9u3xkzO4D4leCLW4e+oEZFQoh24DKgHpCAE3hBSnk6D2NTRHny7Ci3fP/plI//8D07uOHShiUc0eIzNDnr7NA5PDVHu6qA8ZkA4YhMCNBByz483DGM2xek3Fqc5NnGiWXQm7UAXVktFj56sKZn0GuiAbruxrMcaE2KEr/DrdU2Xnh+MO1zv/JQJw+8OMRDH7seIUTafZeKT/7qBQYnvfz4vbuWeyjAbBb1jdub+NXRAQ51u7h6XU3a53zt4dPc9XQvT/zdDViLzUsxzAuKbzx6ht8cO88jH3/Zkr3mSDRZVe+wUlNWQmmxOaPE5fyEF29Qm4j1jHkWfYxG+fLvT9E7NsN/f+Bq2mrL5jx26apySswmjvdPcPPWxmUa4fKTdYAuhNgEfAh4K7BK3xz9V0b3GQbuAb4rpezIwzgvag53jyMEfOYNlydkoL704Cl+8ez5Cy5AH3bPDdCvb69bxtEUHvObFMWjZx+e75/kJRtqF/Q6sQx6NEC/2JccVwJ6sKYvgcckLssoTxqc9LG5qTxhe2uVjfGZINP+EHZL8tvRvucH6R71MDjpo6myNOk+S82RHlfM3agQ0LOoH7lhA3845WTvU71pA/Q+1wzf2X+WQCjCkZ5xXrpxYdeJi5H7jw9w1unBHwpjKVqaCc5wNIPeUG5BCKFZLWbIoHcOzxoG9BZQgP5U1xjXbazlmiTnaUmRic1N5RzNc0+PlYbhAF0IsR74D+BNgBd4HPgucBYYQwvSq4ENwDXAB4C/FEL8Evg7KWVXfod+8XBicJK2mjLefc2ahMdeHJjkF8+cZyYQwlayoAWRgkIP0EvMptjynGKWWJOiJAH61mYtQD/aN5GHAF17naZKK9VlJfQriUvB0xfngQ5QZSvBJFi2ZkVSSgYmvLzi0vqEx3QZTp9rhk2NiQH8ubEZuke1oOJY30RBBOjhiKR3bIZgJEIwHKHYvPxK0XOuGcwmQVtNGW/f0cKP/tjDsNtHQ3nylccvPngKgXZ93d85ogL0LDk/4eX0iHZfGnH7Y5PhxSaWQY9+rq1Vtowa9M7o/fOSBgc9BSJxmfaHOD0yzU1bUmfHt7VUcO8z/YQjMiExebGQzZXlBNAGvAdokFK+Vkr5aSnlXVLKB6SUv4v+/1NSytcCDcD7gPXR5ypy5MSgm81Jbl4AN21pxBsM84eTF1Zr3CG3VlS2vbWSzpH8WAZeSMzvIhpPha2YtbVlebGpcnmC2C1FWIrMNFeWKonLEhCJSH77/GDOuus+lxezSdAYdUwxmQTVZZZlk7hMzATxhyI0Jgmu9UlEqiBj/2ntuiYEHOs3pkcNhSPsOz64aBrx/vEZAuEIUmqWd4vFIx3DTBt0ZOlzeWmqtFJkNvHua9YQlpK7n05uufjcuXF+c2yAD163jl1rq1dEW3WXJ8CP/tjNHY93Jfzcc7hvyesBDsS9Z4t5DsxnZMqPrcQcW21qrbbRP+5NW3NweniKhnILW1oqCiaD/sL5SaScXe1NxrbWSmYCYc6MXLwJumwC9LdJKXdIKe+UUmb8lKWUHinlT6SUVwLvyH2IFzduX5A+lzfp8jDA1WtrqLWXsO/5C8svfGjST73DwqWNDs4MTysnl3mky6CDln3IR4GNy+OnukyTSDRVWpXEZQk4cNrJh+96lkdOjuT0/L7xGRorrHMyu7X2kmUrEtWbFDWl0KADKVuW7z/lpKWqlC3NFYadifY9P8hf3P0sT3WP5Tji9HQ5Z29/8bUy+aRn1MP7f3KEew73Gdo/3rVnTU0ZL2uv4+5D5wiE5k7ypJR8dl8HtXYLH3rZeva019E5PB3zqS9U7jzYy6f+9wSf3deR8PO3vzjO0SX2zD7Q6YxldfXCzaVAt1jUaakqZdofYiKN3KpzZIr2BgdtNTaG3X68geUvDNa/y9ta0gfoQN47Y68kDAfoUsrfxP8uhPi0EGKtwef+2ujrCCFuFEKcEkKcEUL8fZLHrxdCPCuECAkh3prk8XIhRL8Q4ptGX7OQORltOJMqg242CV57eSOPnhy5oPxv9eXZjQ0OpvyhmI+yQsM55ae02ExZCt3uttZKhty+OVr+XHDNBKmKBujNlTbOZ8jWKBbO090ugJwzR32u2WBNp9a+fBn0wQntHExW6F1lK6asxJw0gx4IRTh4dpQ97XVsb63k+fOThlwz9Pfv1NDirLyddc5+LiML/H6l4sUBN0BMRpGJPpd3zmd+2+42nFN+HnxxaM5+v3thiGd6x/n4q9uxW4pitT0HCjyLfsY5TXNlKcf/9dVzfn71Fy8BltY+MBiO8MTpUV5+ifbeLXUGvb7ceLOvSERyZmSajfUO1tRohZiF0HfgWP8ErdWlseRPMtbWlOGwFuXNMnglshDx3P8DdudrIABCCDPwLeC1wGbgXUKIzfN2O4cms7k7xWE+AxzI57iWkxMDWhY0mT5T5+atjfiCER7NMeNWiAy5fawqt9JebwfmFrootCLRVNlzyF/DIpfHT40eoFeV4g2GC6o47kLkcDTAjM/UZkPfuDem7daptZcsmw/6oFtvUpQocdEK3ZK3LH+mdxxPIMye9jq2tlQy7Q/R5cwcsOrvX+ci1a50jXooia5ODC1SgH5iULvuG/l7vYEwo9P+OZ/5nvY6Vlfb2HuwJ7bNHwrz+d+d5JIGB2/f0QpAe4OdVeXWgpe5dDmnWV9vp9xaPOfnkgYHYMwLPF8c7Ztgyh/iTVe0YDaJBSdBssE55Z+TQZ+ViCVfAekbn8EXjNDeYKctGqAXgpPLsb7JtNlz0KR5W1sqVAZ9MRBC3CKE6M7yabuAM1LKLillAPgp8Ib4HaSUPVLK40CCQFMIcRWa9v33OQ674Dgx6Ka6rISG8tTB2M62auocFvYdT29XtpIYnvTRUG6hPXoBNlIo+vhpJ//86xcWe2gFQbIuovFsbiynyCQWfHEb9wSpsukZdC0AUDr0xcMXDMc+s67R7ANMXzCMc8qfNIM+ukwSl8EJL0UmQW2SegmAlipb0gBjf6eTIpPg2g21bG/VXIQy6dBdnkAs63x6kSb1Xc5pLmvWbOAWLUCPZtC7RjMHU/rkJr5Q0WQS3HrNGg73jMeOtffJXs65ZvjkzZti8gwhBHva63ji9GjBec3rSCnpHvWwbp4VH0BpiZlauyWjk0k+0eUtL91YS629JFa4uRRoEpf4DHq0yDrF369PUjc2OFhdo50fRnToLk+AP917ZFG+Q84pP+cnvGxPoz/X2dZSycnBKXzB7GU5kYjkE/ce40iPK5dhFgRZBehCiL8SQvxGCPGP0U2J35hZzMDqLMfTDMSL7vqj24yMzQR8GfiEgX3/VAhxRAhxxOks7MxBx+AUmxvL0/r/mk2Cmy5fxR9OjRguKipkPP4QU/4QDRVWqspKqLVbDGXQ7zzYy96DvUmzcRcaybqIxmMtNtNWW7bgApsxj5/qMs1LXQ/QlZPL4nG0b4JgWNJcWUqX05O1nChZsAaaF7o3GGYmsPTXh8FJTa6WyolBt4qb/7fu73Ry1Zoq7JYi1tXasVsyL3cfjt6ML2lwLFoX4i6nh/V1durLLQwvkvTuxKAbIbTv+VSG9ux6cNYyb1L2th0tWItN3PlUD+OeAN949DR72usSLGuvb6/D7QsVbKZyyO1jJhBmfXQ1dT6t1aWG2t3ni/2dTq5oraSitJiGcuuSSVym/SFmAuE5yTqHtZhKW3FK2Yp+39zYYKeitJgqW7EhJ5c/nhnl9yeGed9PDjOW55U33bwgXYGozrbWSkIRyYlBd9avc37Cy8+f6eeLD57K+rmFQrYZdDeaheJn0TzP/0sIMSSE+J0Q4nNCiLcIIdZGpSq7gdE8jzcdHwZ+K6Xsz7SjlPJ70YLXHXV1heuvHQxHODU8lbJANJ6btzbhD0V4pGN4CUa2uOhLhquiWrv2BjudGQLNSETGbs6HV/CM2SijGSQuAKurk2cmjeINhPEFI1SXaa/TXKUF6KpQdPE41O1CCHjrVS1MeoNZdwrWP+9kEhdgWbLog5PepE2KdFqrbMwEwnP+1hG3j45BN3uiOl+jy92Hul1Yiky89aoW3L5Q3oOnKV+QkSk/6+rKWFVuXZQM+ti0n2G3n51rqoHMUqdUn3mlrYQ3bGvmV88N8Jl9J5j2h/jkzZsSnv/SDbWYhFaQW4jof//6JBl0iFoNLlFSZmzaz/PnJ9kTneTUOyxLJnHR6x3q562ma9f55H//6eEpGiussYZ1a2rKDGXQTwy6KTIJRtx+/uzOZ/LacfZY3wQmAZcZiGu2L0CqqdeKPN3t4uRQ9gF+IZBVgC6l/LGUsh5oR/M93wc8hdZN9B+Ae4EzQAD4M+B3WY7nPNAa93tLdJsRdgMfEUL0AF8CbhNCfD7L1y8oupweAqEImxodGffdsaaK+kWQuUQiS98OeighQHdwJkM27KxzOqaNPtQ9vviDXEYCoQjjM8GMAXprVeYmFunQiwr1DHqVrZjSYvOCJC7eQHjZikwLwb0gE4d7XFzS4OCK1dqNyYjEIZ75Hug6tdFzxbkMOvTBSV9Si0WdZE4uB05ruZ09cdneba2VdAy6016PDve42N5aGbv557t2RQ8W19XaaaiwMrwI8oaOqDGA3kExk9SpzzWDtdiUdEXt1t1r8AbD/PLZ87xz1+qYZDCeClsxV6yuYv/ppcynGUfX4a+rS51BH5z0LYlE54kzo0hJbOJY57DGHLWMsJB7qT7ZjJe4gPZdT7Wq2Tk8zca4z7ytxkbPaOZ7Qsegmw31dr7y9u0c6R3nH375fN6u28f6J2lvcBjq29JQbqWh3JJTgK5/V4vNgjsP9mb9/EIgJw26lPIM8Gvg21LKN0opVwP1wI3APwJ3RP/98ywPfRjYGM3ClwDvBH6T4Tn6mP5ESrlaStmGJnPZK6VMcIFZSeiFQpsbKzLuazIJbtrSyGMMV+GXAAAgAElEQVSdzoxLotnwzT+c4dVfPbCkPrN6RqIhmnXb2GDHEwinzdweimbN19eVcWiR7NUKBT1wzhigV9uY8oWYzLGoczzaRVTPoAshNKvFHCUuI1M+dn/+EX78ZE9Oz18IT3WNseVfH4zpcQuRUDjCM73j7FpbzfpoMGKkSDCePtcMliJTwrlRG/0M871cnQkppRagp8ugRzO/8cv0+zud1NotbFo1m2Xb1lJBMCxjAex8pv0hXhxws2ttdSwoyXehqB4sr9cz6JO+vE849ev+ay9fhdkkMmfQx2doqbIllUFe3lzBjjVVlJWY+dgr21Me4/qNdRzvn8h6xWYpOOv0UFZiTlmH1VplIxyRS+L0tf+Uk+qyEi5v0u7J9Q4LY54AQQOTgxcHJrn8Xx6c4wKUDfp9sX7ed7ulupTz496Ee3Q4IjnrnI4ZLYCWQR+c9GacKJwYcLO5qZybtzby169q55fPnuc7+8/mNO54pJQc658wpD/X2dZSyXGDPRDi6RqdptxaxBu3N3Pfc+dx5zEuWipyLhKVUr5JSvlA3O+jUsrfSyn/Q0r5Z9F/s7qTSylDwEeAB4EO4B4p5YtRS8fXAwghdgoh+oG3Ad8VQryY699Q6HQMTlFSZGJdXTqp/yyv29pIIBThkY78ubkc75+gd2wmZvu1FAxNakFEfAYd0heKHup2Ueew8JarWjjr9Cx5ILKUpGtSFI+uSc01iz4/gw7QXGXLWeLy1Yc6mZgJ8kzv0q9w3PF4N6GI5MmzhZklBM1abyYQZmdbNU2VpZQUmTibpZNLn8tLS1VpQrBW64hKXJa4m6jLEyAQimSUuMCsE0c4InnitJPr22sxxenWMzkTPds7Tjgi2bW2mlp7CVW24rwXuXU5PZgErK6xsarcijcYxu3Lr67/xICbxgor9eVWWqtKMwZ0msVi6hWKr7/rCu790LVpJ/R7LqlDSq3QvtDoGvWwtq4sZR1WbAVmkZ1cIhHJgdNOrts4e17qnVqNOCS9OOAmGJZ05mj/qV/368sTM+iBcITheX7s51wz+EOROasmbbU2IjJ9HZFzys/IlD9m7fyXN2zg9dua+MIDp3jghaGUzzPCOdcMEzNBQ/pznW2tlXSNerJONJ0d8bCuzs5tu9uYCYT5xTMZ1c8FR84BuhDin4QQNwshDBVxGkVK+VspZbuUcr2U8nPRbf+s+7BLKQ9LKVuklGVSyhop5WVJjvFjKeVH8jmu5eDEgJtLGhyGW0lfubqKVeVW7s+jzEXXNx5Ywgv3sNuHw1IU8/hur9ezYckvbFJKDnW72LW2mqvXarrNwz0XrsxFv1DXZsygz7ZRz4XxGS2Y0zPoQM7dRE8OuflZtOmKEUeefNLnmuHRk1pthtFulMuBXjuxa201ZpNgbU1Z9hn08Zmkbcdrop/hUlst6lnNxorUAWSZpYiaspJYgevz5ycZnwnOkbeANmGvd6Re7j7c48JsEly5ugohBBujhaL5pMvpobXahqXIHFvhy7cXesfgVMxWd12dPW0GXUpJn2uG1WlazTdVlmasY9rSXEGVrZgDnYU3gT07Ms262uTyFoib4C2yDv3EoJvR6cCc81LPZhuROukrj7nWRYxM+bEUmSi3zpWGzE5Q5l6X4wtEdXQv9HQ69I5oQaZ+zggh+MJbt7K9tZKP/ewoL5zP/Rp6NPrd3dqSWRWgo2fbj5/PTubSNTrNuroytrRUcMXqSu482LvkHWcXykJsFj+FJj85J4QYEUL8XgjxH0KIdwohLsnT+C5apNQql1M1KEqGLnM50OnMy3KOlDJ20VvKAqKhSV/s5geaRrLeYUm5XN0/7mVw0seutmq2NFdiKTJxqPvCLRTN1EVUJ1MTi0yMRbOt1bbZZhItVaWMeQJZ67k/t68Dh7WYd+5spWt02tCScL64K9ryfHtrZcxBoBB5utvFmhpbLCu3rq4say/0ZE2KAEqiN/alXlnSJ3PpMugALXEFzQc6nQgB122cG6ALIdjWWpmya+TT3S4ubyqfndg32Dmd5y7EZ53TMbs/fYUvn4WivmCYM87p2HV/XW0Z3aOelIHFpDfIlD+UdFKWDWaT4LqNdezvdBZUEOMLhhmY9KZdRW6stGISqb3A84XuFR9/XuoFm0YmafrK40iOnUeH3T7qyy0JKwn66sn8RMzpWIA+m0FfEz1P0unQdceU+NjDWmzme7ddRZWtmA/85EjOk9Lj/ZNYi01JayFSsSUazGejQ5/2hxh2+2NSwdt2r6Fr1MMfC3gFNRkLCdDXAG8B/g04AmwD/ga4CzghhJgSQvxx4UO8OBl2+3F5AoYKROO5eWsjgXCEh08s3M3F5QkwEwhTZSvmmXPjS6bhGnL7EvSG7Q0OTo8kz4bFZx5LikxcsbrygnZyiWXQ7am7sAGUW4upKC3O+cY1PhPAbBKUl85mbJoqtaAkG5nLY6dGePz0KH/1io3sbKsmGJaGnATygS8Y5meHz/GqzQ3cePkqesdmGC9AnW0kIjnS42JXW3Vs27q6Ms65ZgxPZia9Qdy+UIKbh06tw7LkEhc9eG2sTB+gxxc07+90srW5ImmXwW0tFXQ5PUx6516L/KEwR/sm2Bn3/rVHuxDnK4CORCQ9Y55YsaJ+jRrKo/b59PA04YiMZS/X1dnxhyIpv2/6d3u+xWIuXN9ex+i0n44CcrzoHvUgZeoCUYBis4mmyoUVxBthf6eTy5rK5yRG9Mm0kay4nkHPtbB4xO2nwZH4PWquKkWIxERM57DWfdUe1226uqwEh6UoYwa9qcJKpW3u96/eYeWO23finPZz51O5FV0e65vg8qYKw6oA0O5j6+rKslr97I4Vc2sTu5u2NFJTVsJPnlxZxaIL0aD3SSl/JaX8JynlTVLKBmAj8GnAD3QBxtO/ijnECkSbjC8FAVzRWklThTUvbi66q8LbdrQSjkiePLM0xZfDbl/swqezMZoNS5bdOdTtotxaFOsqt6utmhcHJvNaLFtIOKf9VJQWYykyZ9xX95jOBZcnQJWtZE7GprlSCwSMBuihcITP7eugrcbGrdesiWVOFqvL43zuPz7I+EyQ23a3xZZVC9Hv+UzUhWjn2rgAvdZOKCINt+bWM2ip5A61ZZYll7gMTPgoNotYkWoqWqttDEx4GfcEeO7ceIK8RUfXrs5fZj/eP0kgFJnz/m2sz++5NjDpxReMxLK5+jUqnzZ7s8YAeoCuvVYqN5+Ya0+KSVk2XL+xFqCgZC5d8wKtVLRWpbYazAdTviDP9iaelzVlJQhhLIM+MLlQiYsvwWIR0ORWDmtSiUu8vAW0Vag1tba0Xuh6gWgyNjeVs721kgM5dJ4NhiO8MDCZlf5cZ3tLJUf7JgyvhunF3PrEzlJk5p27Wnn05PCK6pOS106iUsqzUspPAa9g1tVFkQO6U8GlWWbQYzKX086ELFO26Be8129rwm4pWpJ20JGIZGTKH1s+1mlvcOANJndyOdTjYkdbdaxwZ+faaiISnj1XeIFYPsjURTSe1iqb4QBvPi5PgJp5WUzdC92oDv1nR/o4PTLN37/2UkqKTGyotyNE/u3vUnHnwR7W15Vx7foatjRXIITWZrrQ0CVZV6+dm0GHzD7YOv0pGtbo1DpKljxAH5r00lBunVPsmYzWKhvBsOQXz/YTkSQ009HZ2qzd3I/OW+7W37+5GXTt5pyvQtF4i0XQlv0rbcV5lbh0DE5RVmKOTbJmz4Hkkwz9Gr1QiQtoxYebG8vZ35k/k4GFMmuxmCFAry6dY9OZb548O0YoIhMC9CKziZoyS8agOxKRDE5o50mu8pARtz/BYlFnfiImFI7Q5fQklZKsqSlLeU/wBcOcjZNYJWNPex3Hz09m7fjTOTyFLxjJKUDf1lqJc8pv+Lt21ulBCFhTM/u9+JOr1wCzkseVQF4DdB0p5UHgt2g6dUUOnBhws7raFmswkA03b20kGJY8+OLCKq71L/za2jJesqGGA53OjDPY/vEZPvCTIznbdY16/IQjklUV8wN07aY4P7AbnfbT5fSwKy6wuXJ1FWaTuGDtFjN1EY2ntVrzyM1FVzruCVJVNvf8a3BYMJuEIavFKV+Qrz7Uya62al5z2SpAa83dWmVbcKHooyeH+dufH0vbAvpo3wTH+ie5bXcbQggc1mI21NkLUod+uMdFvcMyJ/u9LkurxXMZgrVa+9JLXAYmfTSlKRDV0TPAdz19Doe1KKUNW4WtmHW1ZQl61EPdLjbW2+fIYmrsFmrKSvI2GdQ/h/VxwaJmtZh50nNyyM2H73omY+3GiQE3lzaWxyY0dXYLDmtRykla3/gMFaXFOd0nknF9ex1HesYLpiN116iHxgprRs/s1iobzin/ovU62N/pxG4p4so1VQmPNZRnDtCd034C4QjFZpFTBt0bCDPlD6VMzLRW2eiPC7p7XTMEwhE2Jum+2lajrTYk840/NTRFRJK2qHhPe26OP7pV4rYsCkR1Mjk4zafLOU1LVSnW4tlV5qbKUl61uYGfHjqX9r5RSCxKgB7lKHDzIh7/gubEoDtr/bnO9tZK1taW8T+HFjZT7HN5qS4rocxSxJ72es5PeDNaft3xeDcPdwznbGc3HL3ZzZe4bEixXH04SeaszFLE5U3lHL5AGxYZ6SKq01pVSiAUyalBzZjHH3P/0Ckym1hVbjUkcfnOY2cZnQ7w/163aY5Mpr3BvqCgKRKRfPb+Du450p+2gcbegz2UlZh585WzRlNbWyo51m98qXQp0F2Idq6tnvM+VZQWU2u3GM6g97m8lFuLqChNHqzVlFmY9AYJhJauQHdw0ptRfw6zThzdox6u21hLURqN6vyOouGI5Nmof/x8NjbYOZ2hC7FRukY9OCxFCRpkIxKX3784zG+fH+LRk6mz05FIojGAEEJzcknRrKjP5c2LvEVnT3udZkd6pjBkLl3O6VihXzr0SeliyBeklBzodHLt+pqk2ul6hyVj4ad+vdzcVBGzHs0G/fjz74s6rdU2Bt2+mL+5vmp0yarkGfRQRDIwkThmvUB0U5oM+uVRx59sV9SP9U1QaStO6ziUik2NDorNwrAOvcvpSXre3L67jfGZYN4bOi4WC7FZ7BFC/FwI8Y9CiNcIIWrn7bINMGbgrZiDxx+iZ8xjqEFRMoQQvPuaNTx3bmJBlkiaI4R28b++Xft496fRJ077Q/w86jWaa0OY+V1EdSpKi1lVbk1Yrj7U48JabGJL89z3atfaao72TayYmXI2ZCNxaVmAR/D4TGIGHTSrxUwB+vkJLz94ops3bm9ia8vcbOjGBgfdo56cA8UnzozSNaqtmtz33Hm+/VhiA42xaT/3HxvkzVe24IjLLm5vrWB0OpCzl/tioLsQXZ0kwFxXV5axk6ROKotFHd0Lfama0UQikuFJf8JqWDKaKrVCNyCl/lxnW2slw25/rDizY9DNlD+UNEDXuhDnx8mly+lh3Tw/7lXlVkPL7nr2fd/zAyn36R/3Mu0PJWQv19emdvPpG0/u2pMrV0WbGi2lrW4qpJSx9zwTMUvZRQjQu0Y99I97Y91D51PvyNxRVl9xvCKaCc5WajbbRTRFBr3ahpTEgm49kbUhSQY95uSSpFC0Y9CN3VKU9pzSHX8OdI5mtTJ7tG+CbS2VKf3s02EpMrOpsdxQBj0SkXSPepJac+5eX8OGejt7D/ZkPYblYCEZ9LPADcBn0eQsw0KIXiHE74QQB4D3Ak/kYYwXHSeHppAZlpky8darWigtNi/oROwbn4kFeC1VNtbXlaWdNd/33Hmm/SEclqLYTDxbYgF6kpv6xgY7nfOcXA51u7iitYqSormn8s62agLhSE4dyAoZjz+EJxDOSoMO2d+4whHJ+ExgjsWiTnNVaUaJyxcfOAnA39x4acJj7Q1a8WOyG4QR9h7spdZewp3v38UbtzfxxQdP8bvn52ZEfnakj0A4wm2718zZPrtUWjjnRTL9tM76LKwWU1ks6tTal9YLfcwTIBCOGJK4lBSZaIxOylPpz3Vin2E0i57u/dsYdXLJR5fJLud0gptIQ4WV0Wl/xjbzepHnoydH8KSQj6TKXq6rK2Nw0sdMYO7zIhFJ/7g3L/pznZIiE7vX1/LYKSc9o56En3wVxPpD4YzdLJ3Tfqb8oYwFohDf7Cr/E2/dYvj6jSkC9HILY9OaNDMVekLgitXauZutzCXWRTRlN9W5Voudw1O0VpcmlQa11ab2Qj8xoK3cZ6oZ2ZOl489MIETn8FRO+nMdvaNopknBkNuHNxhOOrETQnDb7jUc659MqGMpRBbi4vIKKWU1sB54B/AfaN0/L4v+PAB8KB+DvNg4Ma9RQC5UlBbzpiub+fXRgZxs5cIRycCEd85y1J72ep7uGkualZZSsvfJHrY0V/CqyxpyzqAPT/owidlgIp72BgdnRmadXNy+IB2D7jnODTr6zfpCs1vUg6tk708yWmIX7uxuXJPeIFKS1OquubKUIbcvZVByZmSaXx0d4P0vXUtzZWJwtjFD46l09LlmeOTkMO/cuRpLkZnPv2UrV66u5GP3HOX56GQsHJHc9dQ5dq+rmeMBDHDpqnJKzKaC0qEf7pnrQhTPulo7Y54AEzPpv8NS6sFa6mBYt+VcqgB9cNKYB7rOujo7l65ypG1qBJrDSZFJxLJph3tctFSV0pTkXNPbnC9Uhz4TCDEw6UsIFleVW5GStBIyPRO8qbEcXzCSUuZyYtCNSZBwHszWIswNqJzTfgKhSNouornw8kvr6B/38rIvPZbwc/W/PcIPn+he8Gt86M5n+PB/P5t2n1hRrgGJS53DgqXIlHcnFykl/3t8gHV1ZSknQvXlViKStD0Gzo9r8jM9q5vtRGckmqFPZrMIiT0vTg9Pxxr8JYzXYcFabEpwcolEJB0Ge69cF1tRN7bS8uKAm4jMTX+us621kml/iDMZZLaz503yid2brmimrGRhyculYsEadCllt5Ty51LKf5RS3iilXB3t8HmzlHLllMsWECcG3FSUFtNk8MaWitt2r8EfinDvM31ZP3fI7SMYlnMycte31+IPRXg6SROgp7pcnB6Z5tbda7isqYKRKX/Mrzvb162LFiLOp73Bji8YiV2EnukdJyJJKg2oKiuhvcGedKwrGaNNinSsxWYayi1Z37hcHu11qpIE6E2VpYSjbjvJuP/4AELA7de2JX18Q70dk8jN/u6up88hgFuuXg1of993b91BTZmFD+w9zNCkj0c6hjk/4eX2a9ckPL+kyMSmpvKCyp4c6naxM86FKB79JnM2QxbdOeXHH4qkl7jEMuhLI3Ex0kU0ns+/ZQvfu3VHxv2sxWYubXTEagkOdc/1j49Hd7FYaFFyqmDRiBe6c8rPtD/E23e0UO+wpNS/nhhws67OTmnJXPvUVFaL+ne6JY8ZdNBWX791y5V89R3bEn5uuLSez+47wR/SaOkz4fYFefz0KAdOO9MWo2YKtOIRQtBSlX8v9AdeGOK5cxN84KXrUu5jpJvowISX5irbbGOjLO+NI1N+SswmKm3J60sayq0UmwV9Li/BcISu0emE5ISOEIK2mjJ65wXo51wzeAJhQ4nBekfU8cdgA8NjsQ6iuWfQd0QLdDMl3XRJYKraBYe1mC+8dRsfftn6nMeyVCxEg/5/hBB/K4RI3y1FkTV6gWguWq14Ll1Vzq611dz5VG/a5bdkzNp3zd5cr1lXg6XIlPRLufdgD5W2Yl6/rSlW3NqRg8xl2O1L0J/rbJznoX2420WRScSWDeezs62aZ3vHMy4/ryRiAbrBDDpEPYKzvHG5PJpF5/wiUZi1Wkyl4953fJCdbdUpC5qsxZqNXLb2d3rToVdvXjUnW1rnsHDH7TuY9oX4wN7D3PFEN40VVl65qSHpcba3VPD8+cmsvxOLgXPKH9PTJ8Ook0vMD7uAJC6DehdRA0WioMnoVtcYCzb15e6zzmnGPIGU719VWQm1dsuCM+h6cDw/WDTiha5PrjbU27lpSyN/ODWSNDBNlb1sqylDiMRzIObak0cNOmh635u3NvKmK1oSfr55yxVsaiznL//nOU4N5faePnlGsywMhiUHz6Z22upyTmMtNhmSSIGWRc6nxMUfCvP5B05ySYODt+9oSbmfHqCnKxQ9P+GlubI05pvuzDqDriWuUsUEZpOgOdqsqXfMQzAsY85nyVhTY0uQuBgpEI1nzyV1PNNrzPHnaN8EzZWlhhNLyVhTY6POYYkZQ6Ti7Mg0ZSXmlHp90JzuNqRYYSgk0nsXpecTAFLKL8x/QAhhBkqllEvTjeQCIhyRnBpyc8uuxOxfLty2ew0fufs59neOcMOlyQOWZPQlufhbi81cva4m6pO7ObZ9cNLL708M84GXrsVabI7dZDoG3Rn1pPMZdvtoq0meMdkYt1z9qs0NHO5xcXlzRUoLrl1rq7nr6XN0DE7F2gUvhFA4wm+ODRj2ANfZ0lKZsfDNKPpSejYXutZqW0yna5TZDHryIlHQlm13ts19rHN4itMj03z6DZelPf7GBkfWQdNs06HE78amxnL+851X8ME7jyAlfOLV7SmdQLa1VvKTg72cGZlO6nKQiae6xjiSIouzrbUyoUV9OvTjJJNpgaYtLTaLlI1qdPTAJJ3ExVZixlpsSrsUn08GJ32UmE0JXvr5YFtrJXc9fY6fHdZWB1O9fxB1DVqgk0uXcxohNMvZePRamXQZ9PimKdZiMz9+sodHOoZ5w/ZZd6HJmSDnJ7y8+5rEc9tabKa5sjRhFWW2i2h+JS7psJUUccftO3jDN//I+358mF9/5CWG5XY6B05rloWRqDvKqzYnvy91jXpoqynLqIfWaa2y8Uxv/py77jzYS+/YDD953660rkJGuomeH/dy9dpqiswmau2WrLuJjhgwBmit1qwW9QRWMg90nTU1ZfzhlJNIRMbe345BN2aTSPu8ePa01/Gdx87y5JlRXh210U3Fsf6JlNapRhFCsGttNYd70n/GXaNat9+FJjgLgYUE6JcDX0z2gJQyLIQ4LoT4kZTyMwt4jYuO7lEPvmBkQfrzeF5z2SrqHRZ+8mRvdgH6uBchSNB17mmv4zP3n6B/fCbWEOXup88RkTJ2c6m0ldBcWZpToejQpI9r1tUkfcxh1WQ/p4en8AXDHOub5D0vaUt5LD2rdqjHteAA/XCPi3/+9Ys5rQqUlZh55p9eNceTNVecU35MIrk2PBWtVaX8+qi29Gm0xXK6DHpTNCOaLIN+//FBhIAbL09/wW5vsPPoyRH8obChjqigrdJsqLeze33y8+OVmxv4l9dt5kdP9vCOnatTHie+yDCXAP3vfnE8YXlYx24p4ql/fMWc9trpeLrbRWmxmctTdAwuMptYXW3LnEF3pW9SBNoNbim90AcnfayqsC7KjVK/2f/0UB+19pK0hYTtDQ7uPdKHlDLnsXQ5PTRVlCZ8h6ttJRSbBUNpAq6zIx6sxVoRbGO5lYZyC/cfH5wToGeqO1pXZ084B/rGZ6J64oVfV7KhsaKUO27fwdu/e5A/u/MZ7vrA1YbHIKVk/ynNsjAiJY91jqT8XM46p1N+L5KxutrGlC/E5EyQihRSEKOMewJ8/ZHTXN9elzG5ok9QRlKcA25fkCl/KLbyaMSWcT4jU76EyeF8WqpsPDgwROfwFEKklniAlo0OhCIMuX2xe/yJATfr68oMf5ZXrtYcf/Z3OtMG6C5PgD6Xl1uTTD6zZVdbNfuOD86JP+bT5fSwoy3Rr34lspAAvRQYTvP4fcCbgawCdCHEjcB/AmbgDinl5+c9fj3wNWAr8E4p5c+j27cD3wHKgTDwOSnlz7J57UIgdqE2uMyUiWKziVuuXs3XHj5Nz6gnVsGdiX7XDI3l1gR3lD3ttXwGrR30LVevxh8K8z+HznHDJfVz9K+bGsuzLhT1BsK4faGU0gjQM6/THOubIBCOJHVu0GmsKKWlqpRD3WO8/6VrsxqLzojbx7//7iT3PXeepgor3/6TK3nlpgaM3uefPDvG7T88xGOnnBmDViM4p/zU2JNr9FPRUm0jImFwwmdYQpAug24rKaK6rCQhQJdSsu/4AFevrU7Z8U6nvcFBOGqHdemqzOf60b4JjvdP8uk3XJY2yHrPS9Zy+7VtafdZW1OGw1LEsb4J3r6jNeNrx+MNhDnnmuGvXrGRv7xhw5zHjvdP8pbvPMl9z/Zz6+42Q8c73OPiitWVCd+zeLTgLEMGfXyGOgPBWo3dsqRFokYLRLNlfZ0dW4mZKX+Il25clfbz3thgxxPQuhCnm8Cko2t0OqkW2mQSUZu99Bn0tbX2WKbypi2N3PXUOaZ8wZgFaKbr/rraMo70uOYEs32u9Laai8nWlkq+8vbtfPiuZ/mHXz7PV96+zdDk56zTw/kJL3/+svVEpOThjhF6xmYSgk9/KEyfa4bXb2syPKZ4q8UK28ISMl9/9DTT/hCfvGlTxn1LikxUl5UwnCLo1h2vmiu1z0oL0LPPoF+9NnliQqe1uhSXJ8DRvglWV9sSahni0Vepe8Y8swH6oDtpPVcqSopMXLuhlv3RBoapPn/dbWkh+nOdePOHZN9lb/R7/vba7K7rhcpCikS70ILkVJwCsoqKotKYbwGvRdNQvEsIsXnebueA9wB3z9s+A9wmpbwMuBH4mhBi4WfEEnNiwE2xWST1L82VW3atpsgkuPOpXsPPibdYjGd9nZ3mytJYO+gHXhhidDrAbfMKAjc3OjjrnM7KhzyVB3o87Q12zjqnOdilaRd3Zpgp60ti2fogB8MR7ni8ixu+vJ99xwf5yMs38PDH93DTlkZKikwUm439vGR9DdVlJex7Pj+NEUanjXcR1dFlSqnaOyfD5QlitxSlzG43VyZaLZ4anuKs08PNWzPfVDemaDyVir1P9mC3FPHmK1NrQXUyBQomk2Br69xmN0Y5MzKNlLBplSPhs75qTRVbWyr4ycFeQ+eb2xfkxKA7pX5aZ12dVgwGs60AACAASURBVNCVTjPf5/IaagBSZy9Zsgz6wIQvqbNKPjCbRKz3Qab3b6GFolJKulM0PgFN5pI2QJ/n5f26rY0EwhEe7pjNb50YcFPnsKSUMayvK2MmEJ7jud4/7s27g0s23LSlkY+/qj1lL4JkHIi6fuyJy0wfSOIEcm5shog0ViCq0xKzWlxYoWiXc5o7D/byjp2rDa+w1TssKTPosQA9+lk1lFuzCtB9wTATM8G0mmqYvc4fPDsWu76mYk00UaOvBLo8AQYnfVmv3O9p1xx/utNI8I71TWASJPQqyYVLVjkotxallGx2p6gVWaksJED/DfBBIURbisdzeYd2AWeklF1SygDwU+AN8TtIKXuklMeByLztnVLK09H/DwAjQH6Ev0vIiUE3G+odaTNq2VJfbuXGy1dx75G+BC/dVPS5vEmLj4QQXN9ex5NnxgiGI+w92EtbjY3rNsztU7W5qZyIJKtCIl3Hma6xycYGB/5QhPueO88lDQ4qk/h0x7OrrRqXJ5CxA2o8T54d5ab/fJzP7utgR1sVD37sej7xmksytptORpHZxI2Xr+KRjuG8tKHOpkmRTi5NPFwef9LsuU6yZkX7jg9iEnBjBj0iaBdQk8BQoejYtJ/7jw/y5iubDUtHMrGtpZKTg1NZN7LSdfOpHBJu293GmZHZCWQ6nu5yISUpHUh01tfaCYQjKbskSinpHfMYCtZqlyiDPukNagXfi5RBh1mZS7pVNCBmN5droeiw248nkNxXGdI3K/KHwvSPz7A+LkN8RWsVjRXWOW4umezt5lstBsMRBieNTcoWk4/csCHWi8CI5d7+TmfMsnBNTRltNbakz9P19smazaRivtVgrnz+dyexFJn461e1G35OfbkVZ6oMevQ6qUsD6x0WQ975OroxQLqVZZj9+/2hSNoCUdBWl0vMpliA3pFlgaiOPslK9dlLKXnyjDZhKMvDtdtsEuxoq04ZoM/We6gA/cvAFPCoEOKa+AeElsJ6G3Amy2M2A/GegP3RbVkhhNgFlKA1U0r2+J8KIY4IIY44ncvfMS0eoz6k2XL7tW24fSF+fTR1JzsdfyjM8JQvZcHZnvZapvwh/vupXp7pHefW3W0JhTx6F9RsNNt6FirdhUjPhvWOzWTMnEGcDr07c/HQ4KSXv7j7WW75/tP4QmG+f9sOfvSenRm1f5l43ZZGZgJhHjuVuzWZTi4BemNFKUUmkVVmyTUTpDqJ/lynqbKUgQlvLFOsyVsGuWZdjaHxWYvNtNWUGQqafno4edOhhbC1pZJQtLV6NnSOTFFiNtGWQir0uq2NVNmK2ftk+tWqSETyjUdPs6rcypVr0q8Cra+P2uylkLk8e26CgUlf2kJJnRp7CS5PIKsOgNkSCkf4yN2ax/WrUxQA5oN37Gzlz1+2PuP1ssJWTL3DkpOtJ8y6p6TKoNeXWxhOUSTaG8sEzz7XZBLctKWRA52jTHqDBEIRTo9MpQ2O1s9z8xmY8BKR+bdYzBYhBJ9/y1Zaqkr59h/S3+59wTBPdY3NafhzfXsdB8+OJTQtyiXQqigtptxatCAnl6e6xvj9iWE+/PINWV1n6x2pCz8HJryUFJmojV5P66Le+WMG+5Po2fa6FE2KdOIna5kKPc0mQWt1aczJJdcAvbXaxrrasqSrIADfePQMh3pcvC2NC0627FpbzVmnJ2miQb9GLvSeXSgspFHRGPAqoBj4oxDij0KILwshvgQ8B1wNfC8/wzSOEKIRuBN4r5Qy6RRVSvk9KeUOKeWOurrCSbKPTPlwTvnzViAaz441VVy6ysFeA8vv58e9SJnavuvaDbWYTYLP/+4kpcVm3npV4pevpao0646iQ7EAPfWFaGOc9MdIQLK2toxae0la71R/KMy3HzvDDV/az8MnhvnoKzfy0Mf28KrNDXkpcNu1tppaewn3L1DmIqXEOe3P2jXBbBI0VZbSl6H7Zzwuj5/qNIVWzVWlzAS0pVeAjsEpukY93Ly10fBrbGywZ5QdhMIR7n76HNeur8mrLdb2WEfR7GQup4c1LXIqVwdrsZl37FzNQx3Dad1+fnNsgOP9k/ztjZdk1I3rWcRUq0B7D/bgsBTxxu2Zcxm1dgvhiGTCG8y4b658+v4TPH56lM+96XKuWL14xVrr6uz83Y2XGnL5aG9wcHoktwz62QzL5qvKrXgCYaZ8ie9pquD+Zl3mcmKYMyPTBMMy7XW/odxCWYk5llmOufbk2WIxF6zFZm69Zg1Pd7s4maaz5KFuF/5QhD2XzN5z97TX4Q2GOTLPmaPL6aHeYYlp9I3SWp29paxOJCL53L4OmiqsWdcs6VnxZBPf/qjFon6exmwZDTq5jOhdRDNMGKpsxZRFdecbM2TQQXNy0ZsVnRhw01BuyfreAtFJVpIGhvcfH+ArD3Xy5iuac64BS4a+YpbMSavLOU1zZfIOqiuRBekopJQvoLm5fAlYA3wM+GvgUuDrwPezPOR5IF7d3xLdZgghRDmwD/iklPKpLF972ekY1G4gi5FBF0Jw+7VtdAy6OZLBikoP5FIVIJVbi7lqdRX+UIQ3XtFMRWniRdRkElkXig5N+igrMae9KJdZimI2f5mkAaD93Tvbqnm6a4wzI1MJPw+dGOa1X3ucLzxwius21vLwX+/ho69sz6szgi5zebRjxLDEKBmT3iDBsMzJS7a1ujSrDPq4J30GPWa1GA1C9z0/YFjeotPe4KBnzJNWZvLIyRHOT3i5zWDRpVFWVWhuGtkG6J3DUynlLTp/cvVqIlJy99PJ+7T5gmG+8MBJtjRXGAqqq8pKqLIVJ7VadE75+e3zg7zlqhZDS8iL7YW+92APew/28sHr1qZ10llq9MlgLisHXc5pbCXmlLUxuownmQ5dD6jXzgvur2itpLmylH3PDxoyBhBCsLauLHYOxHzv09hqLiVv39GKpcjEnQdTrxzt73RSUmTimrhix2vW1VBiNiVIJLqcyYtyM9FaZctZg/6ro+d5/vwkf2Ng0jyfhnIroYjElaTj7/lxb0zeou8LxruJ6hn0TIX3Qghaq22YMji46Ohe6FJqK4m5xh172uvwBSNzkmDH+ib4+D3H2LGmin9/y5a8Ojltaa7AWmxK2oRQs1i8MLLnkJ9OopNSyr+TUrYAq4BLgCop5cdktpV5cBjYKIRYG22A9E40rXtGovvfB+zVnV1WGvqMUG/0k2/esL0Jh7WIew6n7yyarEnRfF52qZYFSSc72NTooGPQbfimOOz20WBAs3pZUzlra8sM61t3r69hYNLHK79yIOHng3uPIIEfv3cn37ttx6K5Ity8pQlvMMwfTuYuqcq2i2g8rVW2lBrmZIx5/FSn0aC3xDUr0uUt166vpSaLDMzGBgcRmVq6AZoXsdZ0qN7wcY2yraWSY/2Thvf3+EP0j3tj7eNT0Vpt4xWXNvDTw+cSlu4BfvBENwOTPj558ybDHs/JbPYAfnroHMGw5FaD8p8au1azsRgB+oFOJ5/63xO84tJ6/v61md0vlpL2BgfeYDhlc610dDk9rK0tSxlk6AHX0GTyJfeGcktC7YQQgpu2rOLx006e6hrDWmzKuCy/rnb2HOhzzVBkEoa7tC42VWUlvH5bE/c9dx53kpUE0M6Pq9dWz3EXKbMUsaOtKqH5ne5lnS2t1aX0j3uzNgUIhSN8+fedbG2p4A3bslbVps2KD0Qz6P+/vTMPk6us8v/ndPW+L+nuLN1JZw9hCSELCVuQfRPUQQVFQEAc1HEfhXFGZxDH8aeio464KyAiiAiMIMgawAkkgSABknSSzr703um9eju/P+693ZXqqu7q6qruSvf5PE893XXr3qq36ta9de55v+d7Bq0bYaFoTUsnviSJqJ/A3OJs5rp++8NRUeQUHu9v7GBHTWvUM/enzikkNTmpX+Zy6EgHH7tnI8U5afz0I8sittGNlNTkJJaWFwyaFVdVpyB7gshbYHQ2i4NQ1Rqc4sxot+8RkU8BT+HYLP5KVd8WkduBjar6mIiswAnEC4B3i8h/uM4tHwDOAopE5Hr3Ka9X1TdG8ZbGjO7ePh7YsI81C4qHLXyMlszUZE6fO4VXdg1dwLavsZ1UXxKlQ1yx33D6bE6bO2VIzdri6bm0rXNs6SKxdxyqi2ggd7znBDpGUNz3geXllOSk0x2iKCctOYk1C4tjfhIJxpG5pPH45oMjkoEEEk0XUY/ywkzqWrto7+oZdvqvo6uXzu4+Cob4QZge0Kzo7YPN7K5v5+NrRtY62Stk2l7TEvLHYUdNKy/vqOOfL1w4ZKOQaFlSns9f36mO2Dd5h9vsZrgMOjgXrs9sqeYvmw/znqUDP/i1LX5+/PwOLlhcGtbvPxRzpmTxQlCWsae3j/te3cuZ86dElDGDge9OrJ1cdtS08Mn7Xmd+STb/ffXSEdmAjgXed62yumXEF+FVda2cXB5equOds0IVilbVtYYtdLz0pOn8/KVdPLLpAMfPyBv2M5tTnMX/vnmQzu5e9jV2MD0/I6E+52tXV/CH1/bzx9f289HTj5Y0HGjqYHtNKx9cMdj+bs2CYr75l60cdn3zG9q6aGrvjirQKi/MxN/TR22Ln5IIfks8vJm6f7ss8ovmQEpcWWZ1SyeLGTiX+Xt6qWnx91ssQoBveoRe6NXNjnNXJOP62uWLIzYj8Jxcnt1STU+fjlh/7pGZmsypswtZW1nL587v4aa7N9Le1ctvbzp1RAmbkbBidiE/em77UValtS1+Wv09UV3YJSoR/+qJyLnRvoiInBfpuqr6hKouUNW5qvoNd9lXVfUx9/8NqlqmqlmqWuQG56jqb1U1RVVPDrgdE8E5wF/frqamxR/TQrhQrJhdyL6GDg4dCZ9J2tfQzoyCjCFPCOkpvmE7g420ULS62R9RgF6Sm86sMN1GQ5Ge4uOiE6by7iXTB90uOH5q3INzcHTgl5w4lee21tAWQWvkUETTRdTDy3jvj0CHXu96oA+VsSnITCEjxceBpg4e33wIX5Jw4QjkLeDUB/iSJGyh6G9f2UOqLynkj3osWOL68r55IDKZizfO4RwSAM6YN4XZU7K4Z93uo5Z/75lK/D193HrxohGNdU5xNrUt/qN0zk+/U83h5s4RyX+84CCW3UQb2rq44TcbSUtJ4hfXLY+Z004smTdCW0+Pzm4nwzhUsBhO4tKf0Qsz5b6kLI8Z+Rn09GlE8oI5xdmoOt7VexvaE0be4nFiWR5LZ+Zz77o9g2ZNA+0Vg/E06d46wxXlDkU0lrIQOFMXXVGzJz+pDcqgH2pyvhMzAhyWUpOd7rqRdhOtafH3XwBEMo5Ifxs9L/S/vHUYGJ209qz5xVRWt3Ljbzay5VAzP/zQ0og7kkbDqbML6VOO6hy7o3ZiObjAyCQuT4rIcyJymetXPiQikiIi7xWRtcAT0Q9xcnD3ut2UF2Zw9sLYT+UHcmq/q0n4osl9DR0xkXrML83GlyQRFYr29WnEEpdjlUtPnEZndx/PbY1ukmk0Ehevwj8SfWaj20W0YIiZHBFhRoHjhe7IW4pG1N0UIC3ZR0VRZsigqdXfw0Ov7efSk6ZFVbgUCV532Uh16NtrWklNToroBzApSfjIqlm8vreJtw44Mppth1v4/fq9XLNq1oizPN6PTqAc6O51u5mRn8E5iyI/Z+RlpOBLkrASl8NHOnlkU8RlP3T39vGPv32Nw82d/Oza5VE3Aoo3eRkpTM1Nj8jWM5Dd9W3oMH7c6Sk+8jJSBgXoDW1dHOnoDruvRYTL3Nm0SOQF3kVCVW0b+xvaE6JANJhrV8+iqq6Nv+2sO2r5i5W1TMtLD9nfY2FpDqW5af06dO87HpUGPQpLWW+m7sOnzox6pq44J3RWPNhiMXD9cLaMwdQ0dw6rP4+GGQXODMz63Q1kpvpGlPQKxrvIWldVz79euph3xTmOWTozn+QkOUrmMvC9mYQZdGAp0IOjCT8oIveJyGfcgP00ETldRN4tIp8XkQeBw8BDOA2ETo790CcOWw83s35XA9ecOivuU5bHTcslOy280T84J7dYNMBIT/ExtzgrokLR+rYuevo0ogz6scryikJKctKO8j8eCbWtflKTk8hNH3mGsnwEAXp/Bj176IB7en4Gf9tRx96G9v5AY6QsKM0JGTT9adMBWv09EWuroyEvI4U5xVm8sS8yHXpldQtzi7MjPkb/YVkZGSm+/iz6fz6xhey0ZD5z7vwRj3WuF6C79nOV1S28UtXANatGds5IcrWsdS2hJS7f/MsWPvvAG2Ft04K575U9rN/VwH+970ROiaNjSyyYX5pN5QidXLwf/eGyuVNz0/v7OHjsjCDQvHJZGaW5aZw2d3i5k/c8mw8cob6ta9y6iA7FJSdOoygrlbsDbEa7e/t4eXsdaxYUh9TxiwhnzS/m5R119PT2sbOulVRfUlQXewPNiiKvNfBm6q5aGX1R88BF2tEXvl6AXpZ/9HspGUGzotoRZNBHQooviRn5GajCoqk5o4o95pdks6Qsj4+eXsFHT6+I3SDDkJmazPEz8o6KY6pq20hPSWLaBIohIg7QVfUtVb0AOB34K/Bu4HvAo8BLwIvAIziOLhe4y1ep6sWq+k6sBz6RuHfdHtKSk0bcdjwafEnCslmDCyw8Wjq7aWrvjtnJf/G03Igy6JF4oB/r+Fz/4+e31dAahcyltsXRIkZTEV+UlUpGii8iq8VG14lgqAw6OE4uLf4ekpOECxaPTN7iMb80hz0N7Uc5uagq9/zfbk6ckcfSYWRUo8UpFG2KqKhse3VrRPIWj7yMFN57ygwefeMgj75xgLWVtXz63PlDavvDMbPQkQN5AeM963aTmhyd/KcoO63/IiwQzxEG4BuPbxmycynAkfZu/vvZ7Zw+r4j3Lh15Yd1Ys6A0hx01I3Ny8eQWwxVwluSmDcqg90s1hmi2M780h1f/5byI5ByZqclMy0vvv3gqG8cuouFIS/Zx1cpyntta3Z8MeGNfEy3+npDyFo81C4s50tHN3/cfYWdNG7OKMqMKGNNTfJTkpEXs5NLq7+GPMZqpK81NG5xBb+xAZHDzvdIhOo8G0tXTR31b17AWi9Hi6dCj1Z97iAiPfuoMvvbu42Pq2DIUp84u5O/7jvT/dlTVtTJ7SnZUNQSJyojnc1R1nap+BKdIcxVwI3Ar8GXgBmAFUKiqN6jqhlgOdiLS3NnNnzYd4PIl06P64Y6GlbMLqaxupTFEo4RY++sunp7LoSOdIV8rEC/7NJQH+kTg0pOm4e/p49mANt+REk2TIg/HgisjIm1mvVtAWDSEzSIMBAinz5sS9Xd3Qamjq/UKMAFeqWpge00rH1k9K+4n+yVledS2+MN2gvRo9fdwoKljxLrKa1fPwt/Txxce/DszCzOjnhFITU6ivCCDqto2mju7efj1A7z7pOkjlhUBTMlOpTZEkajnCPPFCxawrbqFBzcO7fb0o+e309TRzVcuWTxmP8qjYUFpNp3dfSOSP1TVtjE1N31YC8tQ3USr6tpITU46Sn88WuYUZ/G2OyOZiBl0gA+f6nzH73NtRl+srMWXJJwW1G06kDPmTSFJHCvGqrroLBY9RuKF/qdNB2iJ0UxdSc7grPiBpg5KctIGdQYvyU2jttU/7EWwJ0WLh8QFBnTo8ei9Em9WVBTS1dvXL1Ecqt7jWCUqwZWIpABnAtOBV1X126r6HVW9W1VfC9cgyBjMH1/bT3tXL9edVjFmr+kZ/YfKosfaXzfSQlHvxy2ercETgWUzCyjNjU7mUtsy8iZFgUTqEdzY3oUvScgZRkrjWYdF60oDAx3vApvI3LNuN/mZKVy+ZHrUzxspS9wM/Rt7h9ahezKc+cNYLAazaGouK2cX0tOn3HbxolEVJM8pzmZnbSsPu+eMaAvKi7PTqAsKJAIdYT75rnksn1XAd/9aGXamZ299O3f/3x7ev6zsmPlx99x3HtiwL6I261W1razf3RDRj/7UvHRqW45u315V20pFlJngcAQ6wiSiBh0c6dv5i0t5YMNeOrt7WVtZy9Ly/JD9MjzyM1NZUp7Pc1ur2VvfPiodcXlBRkQSF1Xl3nWxm6krCZEVD7ZYHFg3nd4+pWGYxJUX8McrceVl0OPReyXerKhwJHUbdjfg7+llf2M7cyeQxSJEEaCLSCnwNHAKkApcIyJ/EJGRCysnOX19yr3r9rB0Zj4nzMgbs9c9qSyP1OSk0AG654Eeo5O/5+k+nMylurmTJInOQvBYwmvz/UJlbcjOg0NR1xp9Bh2czFIkHsENbV0UZKYOO1V49sJiPnbm7Kj15+BkcJKTpL9Q9NCRDv76TjUfXF4e02ZR4Th+eh6Zqb5BRW3BeB1Po3Em+Molx/GZc+dz0QnRyYA85kzJYlddG/e8socl5fn9FxcjpSg7lfo2/1HfA88R5iOrnFmLf71sMXWtfn66dmfI5/jWk1vxJQlfuGBhVGMYD06ckce5i0r48Qs7ufQHL/NKVWi72TZ/D996cisXfv9FjrR3c0OQZWAoSnPT6dOj7SsdT+bYFqx5FwsZKT6mDFMjMp5ct7qCxvZu7lm3m80Hjgwpb/FYs6CYtw4009Ono/KyLi/M5NCRjpC2uoG8UtVAZXXsZuqKc9OobTn6uDrQ1MGMEL+lXsA9nNVidX8X0fgkri47aTq3nD2XE8cw/ogV+ZmpLCzN4dVdDeypb6dPJ1aBKEQYoIvIhQF3vwp04XQLVRzN+aeAH4hI4oniEpi/7ayjqq4t7taKwaSn+Di5LD9koej+xg6y05LJj8AXOhKKstMozU0btlC0urmTKdlpcfG7TjQuO2kaXT19PLslcjeXnl5HiziaAL2sIINWfw9N7UNfGDS0dQ3ZpMgjPzOVr1y6eFRtlVOTnQYtXob6d6/upU+Va1aNzTGRmpzE6jlFrK2sHfLCpbK6hbTkpKhkBUvK8/nc+QtGHQTMLcnG39NHVW0b147i85mSnUZndx9tAX7J96zbw4z8DM51beZOLs/n8iXT+dmLVRwMau6zcXcDj28+xMfXzDmmakZSfI4N5E+uWUarv4erfvYKn75/U7+8TlX585sHOe/Otdz1wk4uXzKDZ7+4hvMWD2+9F+yF3t3bx96G9phPuXta9bKCjISWFa2eW8S8kmy+81Qlqk47+OEIXGfuCGeqAikvyKRPBywOw3HvK7GdqSvNSaert6///NrXpxxq6gyZQS92A+7hdOj9XUTjlEGfmpfOly9adMz+7q6YXcDrexr7EygTTeIy5C+riCQBd7jrPeUuXgycB+QA5wBfBwqBNOBa4KfxGuxE4+7/20NRViqXnBh9BjJaVs4u5K61O2nz9xylr9zX0B7zk38khaKHm/0TXt7isbS8gGl56fzx9f0sirBrbGNbN6rRWSx69Du5NLYPqRlvbOuOStscLQtKc3jr4BH8Pb3cv34v5ywsGVN97ZqFxTy7tYbd9e1hiwEra1qZVxK5g0s88LKKhVmpo5IVeTKpuhY/2WnJVFa3sK6qni9dtPCo9/elixby5NuH+c5T27jzg44Rl6pyx+NbKM1N4+az5ozi3YwPIsJFJ0xlzYJi7lq7k5+s3ckzW6q5+aw5rN/VwP/trGfxtFx+ePVSlrtSwEgI9kLf29DuZIJjnNHzApBE1Z97iAjXrp7FVx99m8Ks1IgytEvKHBnMkY7uIQtrh6MswGpxZlHoz+nQkQ6eeruam86YHbOZupL+rLifgqxUalv9dPX2MSN/8O9aSRhbxmBq3ZnlSLqITkZWzi7it6/s5c9vHgQmXgZ9uNTX80AT8J6AZaqqve7yh90bIrIU+CIWoEfEvoZ2nttazS1nzx2TRjnBrJhdyI+e38Hrexs5c/5A5mJfY/uo/FBDsXh6Li9tr8Pf0xv2vVYf6Qx7Mp1oJCUJl544jV+8vIuLvv/SiLYNdbKPlPIAC7KTysLLI+rb/CycGr8mE8HML83mibcO8cimA9S1dnHtGNZjwEDzlBcra8MG6NurW0bU+TMeeBcIV60YnfzHs8+sb/NTMSWLe9ftcRxhglykygoyufGM2dz1wk6uP72Ck8ry+d83D/HGvia+feVJo5o5GW8yUn18/vwF/MMpM/j6n9/h+89sJzc9ma9fcTwfisLu1ptJ8AL0AXvG2J5Lp+dlkJueHNJPPNF43yllfPvJbaxZUByRs4YvSTh7YTGvVjVE1Nk3HAPnufD1NvfHYabOk6FUN3eycGpOv8ViqCLhft/0YTLo1c1+iibJzHI0rHQvop9+p5rS3LSEbJI2GoZ7NycDd2gkHmTwBjD8PJYBDFS4exXvY82yWQUkCWzY1dAfoKsq+xo6OGNebHfjcdNy6elTtle3htXaH27uZOXsyDNWxzqfPX8ByysKI7L380hP8XHm/PBOCMMRaROPxvaxz6Crwref2kZFUSZnDuH2EA9mFWUxqyiTtZW1IYu1mzu7OXSkk/kjsFiMB0XZaTz6ydNH3aHPy6DXtnTR0tnNw6/v57KTpoVsy/2Js+fy4IZ93PH4Fu65YSXf+stWFk/L5R9OKRvVGBKFWUVZ/OK6FWw51MzU3PSo3YiKslJJTpJ+uUxVf1fD2H5nkpKERz55OlPiZLsXS7LTknnkU6dTOIxdayD/cfnxNA4jwRuOaXnp+JIk7Hmuq6eP363fF/OZutKADDo4FosAM/IHv0Z6io/8zJRhvdBrWjrjZrE4EZial87MwkxHThbjeo9EYLgAfRlwv4i8rapDdgNVVRWRiXX5Eic6u3t5YMNezl9cyvQQ+rSxIDstmeOn5/FqgA69vq2Lju7emLeQ9irE3znUHDJA7+zu5UhH96SRuIDz+Y+2aHCk5KSnkJ+ZMmRmqbdPaWzvGtGP6mjxvMXrWru45ex54+Jju2ZBMX/YuD/kLE9/gWjJ2M0qhCMWxeRe9q6+zc/Drx+grauX61ZXhFw3Jz2Fz56/gH975C0+ds9GDjR18O0rT5pQXsMweh/oh6PHuAAAGhNJREFUpCShJCetX4NeVdvGlOzUIZ1LouVYmsaPxN89kPzMVPJHee5J9iUxPT89rJPLX946RF2rP+YzdV4G3ZOthOsiOrD+YO/8YGpa/BagD8OKisK41HskAkPOm6jqDuAMHEtFj3QReUhE7hGRm0SkIo7jm5D8+c1DNLZ3h/1RHCtWzi7kjX1N+HucYrFYO7h4zCrKIjPVF7ZQ1Ms62Yko/pQXZA7ZrOhIh6N1HytPfnC+Hyk+ISPFx5XLxiczu2ZBMR3dvWzc3TjoMa+AdbSZ60TBmx2pbfFzz7rdwzrCXL2inHkl2by0vY7zjisZ0s96MlOal94fcO2sbZ2QGb1jBec8NzgR0dndy6/+tjsuM3UZqT5y0pL7ZSsHmzrITU8mJz30RVoo3/Rgalr8x1Qh9niwcrZjt3gsXbhGyrDCJlX1q+ptAYv8qnolcAtwCPisiDwmIj8B8kXEZC7D8NqeBuaVZLM6gvbO8WRFRSH+nj4273danXuBW6wLkHxJwqKpOWELRSeLB3oiUF6Ywf4hMugNbofJsZS4pPiSOHdRKTecURGXjGMkrJpTRIpPWBuixX1ldSsZKb6E7NwYDSm+JPIzU3j8zUPsjMARJtmXxO2XH8+8kmxuu+S4MRrlscfU3PQBiUvdxGuacizh9HwYSESoKn99+zDn3bmWv+9r4paz58ZlFqgkoJvogcbQFouB69YOEaAfae+mrtU/Yc478WLNghJmFmayas7Ek8hGU3nwnIg8iuPe0gf8i6pe7t7/AfA9EXlCRL4hImcO9UShEJGLRGSbiOwQkVtDPH6WiLwuIj0icmXQY9eJyHb3dl0U721M+Ob7TuKP/3jauNtkeUb/610/9P4MeowlLuBMIW852BxSc+1lnaZapiDueF7o4dqdN7Q5+s+xDNABfvKRZfzzhYvG9DUDyUpLZkVFIWu3DQ7Qt9e0MK9kYrWQLspKZXtNa8SOMKfNm8Izn18zYsnCZKI0N53qZj9N7V00tHVZgD6OzCzKpK7VT0dXL1W1rVz/6w3cfO9rZKb6uP9jq/jgiplxed2SnPT+DPqBME2Kjlq3pTNsHdLGPQ2owrJZEy/wjCVT89J58Uvv4vjpx56X+3CMOEBX1a+r6hXAD4Ey4Gci8hBwHfCWql6jqpcADwJ3jeS5RcQH/A9wMY6d49Uisjhotb3A9cDvgrYtBL4GnAqsBL4mIgUjfHtjxmiq1GNFUXYa80qy2bBrIECfkp0aF3eGxdNzafH3sD+EvMIL0Estgx53ygsy6ertozqMvdd4ZNAThTULitlW3dKfBfWorG4Z9wLRWOMVin5wlI4wxgBT89Jp9ffwpjsjaRKX8cPLOn/lT5u58Psv8vqeRv7tssU8/ukz4zpz7WTQB4pEh3LdKslJo7tXwxbFrt/VQIpPWDpz9F1OjWOTqL17VHWXqv5cVa8B3o/jk36uiDwgIvfgBMpDC6wGsxLYoapVqtoF/B64Iuh1d6vqmzjZ+0AuBJ5W1QZVbcTpdnrRyN/Z5GJFRSEbdzfS26fsa2ynLE7to71C0Xtf2UNXz9G77vARP5mufs+IL/1e6GEKqMYrg54InBVgt+hxpKOb6mb/hNGfe0zJSSNJ4MOnxieTOBnxZgDXuR1KLYM+fnjnuYc3HehvOHXjGbNJibNdoVf4eaSjmxZ/T0iLRQ9PWx7OC3397gZOKsu3C+hJTEy+rerwmqp+S1U/CNwM7AKeGeFTzQD2Bdzf7y6L6bYicrOIbBSRjbW1g6e0JxOnzi6kxd/D1sPN7GvoiFsDjBNn5HHJiVP52YtVXPTfL/LS9oHPvbq5k6m56eMu+ZkMlLs/GOGcXLwMesEYurgkCoum5lCSk8bagO/mQIHoxMqGXre6gjvec2LcLsgnI17AtW5nPclJkvDNhCYyJ83I45/OmcdD/7ia735gSb/DSrwpzU3H39PHtsPOeSOUxaKH19ioOoQXekdXL5v3H2HFCJplGROPuFxOqmqnqj6tql+Ox/OPFlX9maouV9XlxcWTu6Z1hes9vm5nPQebOvoDuFiT7Evixx9exq+vX0Fvn/KRX67nlt++xoGmDg43d1ql+hgxoyADkfBe6A1t3WSl+iZl1kZEWLOgmJe319HT68zyVLoWi/MTwGIxlqycXciHLHseUzwf7Df3NzGzKDPu2VojPMm+JL5wwcIRdYONBZ6F6aa9jhtUOItFCOgmGsJqcdPeRnr6lFMnUW8QYzCJdgY5AAS2sytzl8V720nLjPwMZuRn8L9/P0hPn8Y96/OuRSU89dmz+OcLF/L8thrO/e4LvHOw2Rxcxoi0ZB+lOeE9ghva/BRmT77suceahcUc6ejm766OuLK6hcxU35DFXoYBAy5UfWr688mKl6nftLcJCN1FNHjdUFaL63c3IAKnzErYMjpjDEi0AH0DMF9EZotIKnAV8FiE2z4FXCAiBW5x6AXuMmMYVs4u7A9IYu2BHor0FB+ffNc8nv3C2ZyzqISO7l5mFdl08FhRMSWTTfucuoNgGtq7x7RJUaJxxrwpJMmADn17TQvzJ5iDixEfMlOTyUl36mjmmv58UuLNory+t5HU5CSmZIXv7ZGR6iMnPTmk1eL6XQ0cNzV33GxnjcQgoQJ0Ve0BPoUTWG8BHlTVt0XkdhG5HEBEVojIfpzC1J+KyNvutg04Vo8b3Nvt7jJjGFYGTKPFw2IxHDPyM/jxh5fx9OfO4uaz5ozZ6052rl1dQVVtG3/YuG/QYw1t/klZIOqRn5nKkvL8fj/0yupW5k+wAlEjfniFomZHOTkpyR3Iis/Izxj2wj5UN9Gunj5e39t41O+yMTlJqAAdQFWfUNUFqjpXVb/hLvuqqj7m/r9BVctUNUtVi1T1+IBtf6Wq89zbr8frPRxreIUoSQLTx2Eqf35pTlysHY3QXHzCVJbPKuA7f62k1d9z1GONbd1j2kU0EVmzoJi/729iV10btS3+CVcgasQPT+ZiDi6Tk+y0ZDJTnfqdofTnHqG6ib518Aid3X0WoBuJF6AbY8/c4iyKslKZlpdhhU2TABHhK5ceR12rn5+u3XnUY/VtfoomeYB+1oJiVOFXL+8CsAy6ETFesftEbDtuRIb3HYikbqU0oPOoh9eXxBxcDIvGDESEK5eVce5xJeM9FGOMWDqzgMuXTOfnL1VxsMkpGO3o6qWzu2/SZ9CXlOWTl5HCQ6/tB5hwHuhG/DhtbhGnzyua1DKxyY7n5DKUxaJHidt9NrCb6IbdDcyZktX/PMbkxQJ0A4DbLjmO2684YbyHYYwhX7poIX0K33lqG+Bkz4FJXSQK4EsSzpw/hY7uXrLTkpluDkNGhLzvlDLuu2nVeA/DGEc8+8TIJC5pdPX00dzhSA37+pQNuxste24AFqAbxqSlrCCTG8+YzcObDrB5/xEaJ3EX0WC8rqLzSrKtgZZhGBHj2ScOZbHYv25QN9HKmhaOdHT39ycxJjcWoBvGJOYTZ8+lKCuVOx5/ZyCDbgE6a9wA3QpEDcMYCZ7VYlkkEhevWZFbKLre1Z9bgyIDwKwzDGMSk5OewmfPX8C/PfIWRW6DIgvQnUKv2684nuWz7IfSMIzIufzk6fSqRmRZ7AXontXi+l0NTM1NpyxOHb2NYwvLoBvGJOfqFeXMK8nmic2HAQvQPa5dXcHi6bnjPQzDMI4hpuVl8Imz50UkjQv0TVdV1u9qYOXsQpPVGYAF6IYx6Un2JfGVS44DnALJ3HTrXmcYhhFvstOSyUr1UdPsZ29DOzUtftOfG/1YgG4YBmcvLObM+VOYlpdube0NwzDGiJLcdKpbOk1/bgzCNOiGYSAi3HXNMhrbusZ7KIZhGJOG4pw0apv9rN/VQH5mCvOsyZXhYgG6YRiAM92anWanBMMwjLGiNDedzfubqGnpZPmsQpvBNPoxiYthGIZhGMY4UJKTxv7GDnbXt5u8xTgKC9ANwzAMwzDGgZKcNHr6FMAKRI2jSLgAXUQuEpFtIrJDRG4N8XiaiDzgPv6qiFS4y1NE5G4R2SwiW0TktrEeu2EYhmEYRqSUulaLmak+jjdbVyOAhArQRcQH/A9wMbAYuFpEFgetdiPQqKrzgO8B33KXvx9IU9UTgWXAx73g3TAMwzAMI9HwmhWdMrOAFF9ChWTGOJNo34aVwA5VrVLVLuD3wBVB61wB3O3+/xBwrjiu/gpkiUgykAF0Ac1jM2zDMAzDMIyR4TUrWmnyFiOIRAvQZwD7Au7vd5eFXEdVe4AjQBFOsN4GHAL2At9R1YZQLyIiN4vIRhHZWFtbG9t3YBiGYRiGEQFzpmTxzxcu5OqVM8d7KEaCkWgB+mhYCfQC04HZwBdEZE6oFVX1Z6q6XFWXFxcXj+UYDcMwDMMwAEhKEj75rnkUu1IXw/BItAD9AFAecL/MXRZyHVfOkgfUAx8CnlTVblWtAf4GLI/7iA3DMAzDMAwjhiRagL4BmC8is0UkFbgKeCxonceA69z/rwSeU1XFkbWcAyAiWcAqYOuYjNowDMMwDMMwYkRCBeiupvxTwFPAFuBBVX1bRG4Xkcvd1X4JFInIDuDzgGfF+D9Atoi8jRPo/1pV3xzbd2AYhmEYhmEYo0Oc5PPkRURqgT3j8NJTgLpxeF1j7LF9PXmwfT15sH09ebB9PXmI976epaoRFT9O+gB9vBCRjapqGvlJgO3ryYPt68mD7evJg+3ryUMi7euEkrgYhmEYhmEYxmTHAnTDMAzDMAzDSCAsQB8/fjbeAzDGDNvXkwfb15MH29eTB9vXk4eE2demQTcMwzAMwzCMBMIy6IZhGIZhGIaRQFiAbhiGYRiGYRgJhAXo44CIXCQi20Rkh4jcOvwWxrGCiJSLyPMi8o6IvC0in3GXF4rI0yKy3f1bMN5jNUaPiPhEZJOI/Nm9P1tEXnWP7QfcjsjGMY6I5IvIQyKyVUS2iMhqO6YnJiLyOffc/ZaI3C8i6XZcTxxE5FciUiMibwUsC3ksi8MP3P3+poicMpZjtQB9jBERH07X04uBxcDVIrJ4fEdlxJAe4AuquhhYBXzS3b+3As+q6nzgWQY64BrHNp/B6Xrs8S3ge6o6D2gEbhyXURmx5r+BJ1V1EbAEZ5/bMT3BEJEZwKeB5ap6AuADrsKO64nEb4CLgpaFO5YvBua7t5uBu8ZojIAF6OPBSmCHqlapahfwe+CKcR6TESNU9ZCqvu7+34LzQz4DZx/f7a52N/Ce8RmhEStEpAy4FPiFe1+Ac4CH3FVsP08ARCQPOAv4JYCqdqlqE3ZMT1SSgQwRSQYygUPYcT1hUNUXgYagxeGO5SuAe9ThFSBfRKaNzUgtQB8PZgD7Au7vd5cZEwwRqQCWAq8Cpap6yH3oMFA6TsMyYsf3gS8Bfe79IqBJVXvc+3ZsTwxmA7XAr1050y9EJAs7piccqnoA+A6wFycwPwK8hh3XE51wx/K4xmsWoBtGHBCRbOCPwGdVtTnwMXW8Tc3f9BhGRC4DalT1tfEeixF3koFTgLtUdSnQRpCcxY7piYGrPb4C56JsOpDFYDmEMYFJpGPZAvSx5wBQHnC/zF1mTBBEJAUnOL9PVR92F1d7U2Pu35rxGp8RE04HLheR3TgytXNwdMr57tQ42LE9UdgP7FfVV937D+EE7HZMTzzOA3apaq2qdgMP4xzrdlxPbMIdy+Mar1mAPvZsAOa7VeGpOAUoj43zmIwY4eqQfwlsUdU7Ax56DLjO/f864NGxHpsRO1T1NlUtU9UKnGP4OVX9MPA8cKW7mu3nCYCqHgb2ichCd9G5wDvYMT0R2QusEpFM91zu7Ws7ric24Y7lx4BrXTeXVcCRAClM3LFOouOAiFyCo1/1Ab9S1W+M85CMGCEiZwAvAZsZ0Cb/C44O/UFgJrAH+ICqBheqGMcgInI28EVVvUxE5uBk1AuBTcA1quofz/EZo0dETsYpBk4FqoCP4iS47JieYIjIfwAfxHHk2gTchKM7tuN6AiAi9wNnA1OAauBrwCOEOJbdi7Qf4cic2oGPqurGMRurBeiGYRiGYRiGkTiYxMUwDMMwDMMwEggL0A3DMAzDMAwjgbAA3TAMwzAMwzASCAvQDcMwDMMwDCOBsADdMAzDMAzDMBIIC9ANwzASEBH5dxGJmc2WiKiI3BHBei+IyAsjeN58d6ynjGqAMUZEfuM2korV81W4n+H1sXpOwzCMcCQPv4phGIYxifjECNfPx/ES3g+8HvvhRM3Xcbq7GoZhHHNYgG4YhmH0o6rvjPcYRMSH06ejJ9rnUNWdMRySYRjGmGISF8MwJgUiskBE/iQiNSLSKSJ7ReQPIpLsPp4uIt8TkbdEpFVEDovI/4rIoqDnud6VOpwmIg+KSIuIVIvIbe7jF4nIJhFpE5ENIrIsaPsXRORlEbnCfS2/iGwVkQ9E8B6SReQ2d32/iBwUke+KSPoIPodPi8gud9xrReT4EON7IeB+toj80P28/O7n94yILBKRCmCXu+rP3c+lXwbitsj+nIhsE5EuETkkIj8Skdyg11QR+YaI3Coiu4AuYIW7zWdCvId/F5F2ESkY4n0eJXEJkKh8XERud8fS5O7jsqBtM0XkxyJS734XHgPKgl/DXXeNiDzrfp5tIvKUiJwQ8PgJItIhIt8P2u4b7ueZUNIgwzASAwvQDcOYLDyO07L7FuBC4FbAz8B5MA3IAe4ALnXXSwfWicjUEM93N7AZeC9Oq+j/FJFvAd8GvoXTLjwLeEREUoO2nQf8APgu8D5gB/B7EXnXMO/ht8C/Ar9zx/hN4EbgvuHfPgDXuNt9Bqdd/UzgUe8iJQzfAz4A/AdwPvBx4A0cacshd/y4Y1nt3h53l30DuBN4Gng38P+A64HHRST49+d6d2xfdP9W4XyuNweu5GbXbwQeVNXGCN93ILfhfP434HwOq3E+10B+itPi/U73/W3D+cyPQkQuBZ4FWnE+2w/hfIdeEpFyAFV9C/gC8GkRudjd7hyc799tqppIsiDDMBIFVbWb3exmtwl9A6YAClw+gm18QCbQAnwuYPn17nN9NWBZMlADdAOzA5Zf7q67JmDZC+6yVUGvtRV4KWDZvzun6P77Z7rbXRs0zg+7y08e5v0osB1ICVh2pbv8tKDxvRBw/y3gziGet8J9jpuClhfiXAD9Jmj5NcH7wr1/EMgIWvds97EzQ3ymq4Z5v78BdocY5wtB633RXT7dvb8Q6AVuDVrvLne96wOW7QCeDVovF6gDvh+0/FGgGjgBOAA8iSPjGffjw252s1vi3SyDbhjGZKAeJyP7XyLyMRGZH2olEfmAiLwqIk1AD9AGZOMEbcH8xftHHa30DqBSVXcFrLPV/VsetO0+VX0lYPte4A/AyhCZZY+LcKQfD7lSl2Q38/1X9/GzwmwXyNOq2h1wf7P7d+YQ22wArheRfxGR5W4GOxJWAakMzk7/HuezXRO0/ElV7QhcoKovAO/gZO09Pg68Gfj5jZAngu4Hfwan4syqPBi03u8D77jfobnAfUH7ox1Yx+D9cQPOBdxGnAu661Q1Zi49hmFMLCxANwxjwuMGQufjBEffBCpFpEpEbvHWEZF3Aw8AW3CkCqcCK4BaHKlLMMHyiq4wywixfXWI56vGCWiLw7yNEvfxNpxAz7vVuI8XhdkukIag+/4w4wvkn3AkHzfgBOs1rlY/c5jXKnT/Hgpc6F7M1Ac8Tqj1ArgLuFJEikRkFs6Fyk+Gee2hGO4zmOb+Dd5HwfdL3L+/5Oj90Q1cRtD+UNV6HOlPGnC/qob6DhiGYQDm4mIYxiRBVauAa0VEgCXAp4Afi8huVf0LcBWwQ1Wv97YRkRQGB5KxoDTMsi6cC4JQ1AOdOFKXUByMwbgGoaqtOLrt29wA+Urgv3DG+uUhNvUC4anA295CN8tcxOBAOVw2+R6ci6rrgQKcDHWkmvto8C4USnFmXQi4H0i9+/c24JkQz9MVeEdEzgM+hnOR+AkR+a2qbhz9cA3DmIhYBt0wjEmFOrwBfN5d5DluZOJILwL5CI4+PNaUi8gq744rG3k/sF5V+8Js8yROljdPVTeGuMUlQA9EVfeo6ndxZCHe5+ZloDOCVn8FJ0i9Kmj5B3GSQy9E+JrNOAH5x3Gy+Pe7y+LFq0AfTmFsIMHvYxuwGzg+zP5401tRRKbgXGg8AZwGbAJ+JyLZ8XoThmEc21gG3TCMCY+InITTtOYBHK24Dycj2wM85672JPAeEfke8GdgOY68oykOQ6oGHhCRr+FkzG8BFrh/Q6KqL4jI/Tga9DuB9TiBZAVwCfBlVa2M9UBFZB3wGE5Q3oqjHV+C42LjvZd64CoReRNHgrNLVetF5Ls4mfc2nOD0OByXnJcZcHqJhB8zoEMfjbxlWFR1m4j8DrjdrQfYAFyA8xkHrqci8kkcF5xUHM16HU6m/TRgr6re6a7+K0CAj6pqt4h8CCdI/yGOm45hGMZRWIBuGMZk4DCwFydrXoYjFdkMXKaqr7nr/BynmPMGnGBwA4414J/iMJ4dOJaD/wnMx8nEXq2qzw+z3TU4Fw03AF/ByV7vBp4itK49FryIk02+Fec3owrH1eYHAKraJyI34byXZ9x1PorjovIVnAuQf8TpUFqPk0m+bYiZgkGo6psiUgk069jYEn4c52Lkizi6/+dw6hJeDhrXEyJyFs77/AXOLMJhnNmDBwBE5FM4mvQLVbXW3W6niHwCuFdEnlTVB8bgPRmGcQwhVkRuGIYxdrhNgJJV9YzxHsuxgogsxCne/Ziq/nK8x2MYhhFvLINuGIZhJCRuh895OE2SDhGiWZBhGMZExIpEDcMwjETlJhx5SSnwoWCfdMMwjImKSVwMwzAMwzAMI4GwDLphGIZhGIZhJBAWoBuGYRiGYRhGAmEBumEYhmEYhmEkEBagG4ZhGIZhGEYCYQG6YRiGYRiGYSQQ/x8iBr2heibF/wAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 864x144 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"L=0.1\n",
"\n",
"samples_d=[needle_gen(L) for i in range(300*100)]\n",
"samples = np.array([k['cut'] for k in samples_d]).reshape(100,300)\n",
"\n",
"def draw_sample_history(samples):\n",
" fig,ax=subplots()\n",
" fig.set_size_inches(12,2)\n",
" mn = samples.mean(1)\n",
" ax.plot(mn)\n",
" ax.set_title(r'$\\hat{\\sigma}=%2.3f,R_e=%2.3f$'% (mn.std(),\n",
" mn.std()/mn.mean()), fontsize=18)\n",
" ax.set_xlabel('sample history index',fontsize=16)\n",
" ax.set_ylabel('$\\mathbb{\\hat{P}}(cut)$',fontsize=18);\n",
"\n",
"draw_sample_history(samples) "
]
},
{
"cell_type": "markdown",
"id": "16ba2af7",
"metadata": {},
"source": [
"The figure above shows that for shorter needles, we did *not* do so well for relative error. This situation is illustrated in the figure below."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "a1613e5a",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"draw_sim(samples_d[:500]) "
]
},
{
"cell_type": "markdown",
"id": "b904ac46",
"metadata": {},
"source": [
"The figure shows there are very few cuts in our simulation with the short needle (red needles). To remedy this, we can alter the code to bias for randomly generating x-coordinates that are within needle length of an edge instead of uniformly random in the unit interval. The code-block below makes this change for the x-coordinate."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "b57f38c2",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"tags": []
},
"outputs": [],
"source": [
"def needle_gen_b(L=0.5):\n",
" '''Drops needle on unit square using a biased strategy. Return dictionary describing \n",
" needle position and orientation. The `cut` key in the dictionary is True when the\n",
" needle intersects an edge of the unit square and is False otherwise.\n",
" \n",
" L := length of needle (default = 0.5)\n",
" '''\n",
" assert 0<L<1\n",
" yc = rand() # uniform on unit interval\n",
" r = L*rand()/2.\n",
" xc = r if rand()<0.5 else (1-r) # pick either edge 50/50\n",
" ang = rand()*pi # uniform random angle in [0,pi]\n",
" x0,y0 = xc-L/2*cos(ang),yc-L/2*sin(ang) # coordinates for one end of needle \n",
" xe,ye = xc+L/2*cos(ang),yc+L/2*sin(ang) # coordinates for the other end\n",
" not_cut = (0<x0<1) and (0<y0<1) and (0<xe<1) and (0<ye<1)\n",
" return dict(x0=x0,y0=y0,xc=xc,yc=yc,xe=xe,ye=ye,ang=ang,cut=( not not_cut ))"
]
},
{
"cell_type": "markdown",
"id": "8c08c380",
"metadata": {},
"source": [
"Now, we re-run this simulation using this biased method."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "d4e52848",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"samples_b=[needle_gen_b(L) for i in range(300*100) ] # create biased samples\n",
"draw_sim(samples_b[:500])"
]
},
{
"cell_type": "markdown",
"id": "5fa851f1",
"metadata": {},
"source": [
"The figure above shows that the samples are now clustered at both vertical edges, and, compared with the unbiased simulation, there are more red needles, indicating that we now have more relevent samples.\n",
"\n",
"The next figure shows the sample history and relative error which is now **much** better than before."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "49657827",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"tags": []
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x144 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"no_bias_samples = samples # save for later\n",
"samples = np.array([k['cut'] for k in samples_b]).reshape(100,300)\n",
"\n",
"draw_sample_history(samples);"
]
},
{
"cell_type": "markdown",
"id": "e2836beb",
"metadata": {},
"source": [
"Now, that we have a tighter result, we need to make sure we have not changed the result by correcting for the bias we introduced. The probability of being near the edges in the x-direction is $2 L$. We have to multiply our estimated probability by this *weighting* factor."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "36ce3c7b",
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
},
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/srv/conda/envs/kernel/lib/python2.7/site-packages/matplotlib/axes/_axes.py:6571: UserWarning: The 'normed' kwarg is deprecated, and has been replaced by the 'density' kwarg.\n",
" warnings.warn(\"The 'normed' kwarg is deprecated, and has been \"\n"
]
},
{
"data": {
"text/plain": [
"Text(0.5,1,'Biased samples more efficiently produce useful samples')"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 720x216 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig,ax=subplots()\n",
"fig.set_size_inches(10,3)\n",
"ax.hist(no_bias_samples.mean(1),alpha=0.3,normed=1,label='unbiased')\n",
"ax.hist(samples.mean(1)*2*L,alpha=0.3,normed=1,label='biased')\n",
"ax.legend(loc=0)\n",
"ax.set_title('Biased samples more efficiently produce useful samples')"
]
},
{
"cell_type": "markdown",
"id": "726641a6",
"metadata": {},
"source": [
"The histogram above shows the spread of the biased samples is much tighter than before, which is what the relative error we just computed is getting at. Still, it's good to back this up with a quick plot."
]
},
{
"cell_type": "markdown",
"id": "a84e5bb9",
"metadata": {},
"source": [
"## Summary"
]
},
{
"cell_type": "markdown",
"id": "cd144e04",
"metadata": {},
"source": [
"In this section, we illustrated some basic concepts of Monte Carlo methods by examing the famous problem of Buffon's needle. We showed how to code up a quick simulation that visually reveals the key issues and then how to boil this down into a simulation to compute the estimated solution. We also showed how to create biased samples to improve the overall efficiency and precision of our result.\n",
"\n",
"I carefully used the word [*precision*](https://en.wikipedia.org/wiki/Accuracy_and_precision) as opposed to *accuracy* because we have created a tighter estimate (as measured by relative error), but how do we know that this is the *correct* (i.e. accurate) answer? We don't! In this case, we can solve for the analytical solution (shown in the appendix), but in general, this is *way* too hard to do, otherwise we wouldn't bother with the simulation in the first place.\n",
"\n",
"The reality is that we have to do what we can using Monte Carlo methods and then carefully consider their computed results using as much domain knowledge as we can muster. In this section, we made the extra effort to generate some visual results along the way as a sanity-check and doing so is *always* worth the extra effort, when feasible. Furthermore, this kind of intermediate result can sometimes suggest a narrow special case for which we *can* generate a related analytical solution that we can use to further develop our simulation.\n",
"\n",
"As usual, the IPython Notebook corresponding to this section is available for download [here](http://github.com/unpingco/Pig-in-the-Python/blob/master/Buffons_Needle_Sim.ipynb). Play around with the various parameters as suggested above on your own to see what else you can discover about this famouse problem."
]
},
{
"cell_type": "markdown",
"id": "ff295896",
"metadata": {},
"source": [
"## Appendix: Analytical Results"
]
},
{
"cell_type": "markdown",
"id": "202ea6dc",
"metadata": {},
"source": [
"In this appendix, we carefully derive the analytical solution for our problem using excessive detail. Note that $x_c$ is the needle's center. The needle is entirely contained in the square (at least in the x-direction) when the following two conditions hold:\n",
"\n",
"$$ 0 < x_c - L/2 \\cos(\\theta) < 1 $$\n",
"\n",
"$$ 0 < x_c + L/2 \\cos(\\theta) < 1 $$\n",
"\n",
"combining these two into one big inequality gives:\n",
"\n",
"$$ \\max(-L/2 \\cos(\\theta) , L/2 \\cos(\\theta) ) < x_c < \\min(1-L/2 \\cos(\\theta) , 1+L/2 \\cos(\\theta) )$$\n",
"\n",
"In the case where $0< \\theta < \\pi/2 $, we additionally have the following:\n",
"\n",
"$$ L/2 \\cos(\\theta) < x_c < 1-L/2 \\cos(\\theta) $$\n",
"\n",
"Because $\\theta$ is uniformly distributed between $0$ and $\\pi$, for this domain of $\\theta$ and $x_c$, we have the probability of the needle being contained completely in the square (in the x-direction) as the following:\n",
"\n",
"$$ \\frac{1}{\\pi}\\int_0^{\\pi/2} \\int_{L/2 \\cos(\\theta)}^{1-L/2 \\cos(\\theta)} dx_c d\\theta = \\frac{1}{\\pi}\\int_0^{\\pi/2} 1-L \\cos(\\theta) d\\theta = \\frac{1}{2} - \\frac{L}{\\pi} $$ \n",
"\n",
"Now, we can consider the other half of the domain of $\\theta$, $ \\pi/2 < \\theta < \\pi $, where we have\n",
"\n",
"$$ -L/2 \\cos(\\theta) < x_c < 1+L/2 \\cos(\\theta)$$\n",
"\n",
"Then, following the same reasoning as before we obtain:\n",
"\n",
"$$ \\frac{1}{\\pi}\\int_{\\pi/2}^{\\pi} \\int_{-L/2 \\cos(\\theta)}^{1+L/2 \\cos(\\theta)} dx_c d\\theta = \\frac{1}{\\pi}\\int_{\\pi/2}^{\\pi} 1+L \\cos(\\theta) d\\theta = \\frac{1}{2} - \\frac{L}{\\pi} $$ \n",
"\n",
"Thus, combining these two results gives the probability of the needle **not** cutting the edge in the x-direction as the following:\n",
"\n",
"$$ \\mathbb{P}(\\text{no x-cut}) = 1 - \\frac{2 L}{\\pi}$$\n",
"Now, we can pursue exactly the same line of reasoning for the y-direction, or, just recognize that by symmetry it would be exactly the same as for the x-direction. Nonetheless, let's be thorough and reproduce the reasoning for the y-direction, just to be on the safe side.\n",
"\n",
"As before, the condition in the y-direction for the needle being entirely contained in the square in the y-direction is the following:\n",
"\n",
"$$ \\max(-L/2 \\sin(\\theta) , L/2 \\sin(\\theta) ) < y_c < \\min(1-L/2 \\sin(\\theta) , 1+L/2 \\sin(\\theta) )$$\n",
"\n",
"which can be combined into one big inequality, given the restrictions on $\\theta \\in (0,\\pi)$ as shown:\n",
"\n",
"$$ L/2 \\sin(\\theta) < y_c < 1-L/2 \\sin(\\theta) $$\n",
"\n",
"Then, integrating this out as before, we obtain\n",
"\n",
"$$ \\frac{1}{\\pi}\\int_0^{\\pi} \\int_{L/2 \\sin(\\theta)}^{1-L/2 \\sin(\\theta)} dy_c d\\theta = \\frac{1}{\\pi}\\int_0^{\\pi} 1-L \\sin(\\theta) d\\theta = 1 - \\frac{2 L}{\\pi} $$ \n",
"\n",
"$$ \\mathbb{P}(\\text{no y-cut}) = 1 - \\frac{2 L}{\\pi}$$\n",
"\n",
"which is exactly what we got for the x-direction. It's usually worth the extra work to check things like this instead of trying to be too clever too early.\n",
"\n",
"Then, combining the x-direction and y-direction results, we obtain,\n",
"\n",
"$$ \\mathbb{P}(\\text{no cut}) = \\left(1 - \\frac{2 L}{\\pi}\\right)^2$$\n",
"\n",
"so that\n",
"\n",
"$$ \\mathbb{P}(\\text{cut}) =1-\\mathbb{P}(\\text{no cut}) = 1-\\left(1 - \\frac{2 L}{\\pi}\\right)^2$$\n",
"\n",
"which we code next."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "d974d50d",
"metadata": {
"collapsed": false,
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},
"tags": []
},
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"source": [
"prob_cut= lambda l:(1-(1-2*l/pi)**2)"
]
},
{
"cell_type": "markdown",
"id": "01f3af4a",
"metadata": {},
"source": [
"We can use this result later to check or Monte Carlo estimates. Try it!"
]
}
],
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