ProblemSets_PartII/Math227C20Sp_P11_MCMC.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math 227C Problem Set 11: Markov Chain Monte Carlo!\n",
    "\n",
    "In the first part of this notebook, we simulate a chemical reaction\n",
    "\n",
    "$$\\frac{dx}{dt} = k_{\\rm on} - k_{\\rm off} x$$\n",
    "\n",
    "with some observational noise\n",
    "\n",
    "$$y = x + \\epsilon$$\n",
    "\n",
    "where $\\epsilon$ is Gaussian distributed with standard deviation $\\sigma$.\n",
    "\n",
    "Then we use MCMC to fit the simulated data to discover the values of paramaters ``kon``, ``koff`` and ``sigma``.\n",
    "\n",
    "To perform MCMC, we must choose priors. We make the simplest assumption and use flat priors, subject to non-negativity (we require kon>0, koff>0 and sigma>0). \n",
    "\n",
    "The Problem Set begins below the joint posteriors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(\"ggplot2\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Hhwhv2BA4UAAQIECBAgQGDCBHSQJqzB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\ndspGX560Xq1P2/19yXWSobwuIz2+/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L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\nXSaV26abGzYOdC730VeaN5Z5+e+lk7xyarbGfT/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JHTvWxvtj8IfB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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Let's simulate the reaction\n",
    "\n",
    "# solution to first-order kinetics\n",
    "\n",
    "NSample = 1000 # sample size\n",
    "sigma <- 1 # observation noise\n",
    "\n",
    "# parametrize by kon and koff\n",
    "\n",
    "kon <- 2.4\n",
    "koff <- 0.25\n",
    "\n",
    "\n",
    "tStart <- 0\n",
    "tStop <- 100\n",
    "times <- seq(from=tStart,to=tStop,by=(tStop-tStart)/(NSample-1))\n",
    "\n",
    "\n",
    "x <- kon/koff*(1-exp(-koff*times))\n",
    "soln <- data.frame( \"x\"=x, \"times\"=times)\n",
    "\n",
    "# add noise\n",
    "y <- x + rnorm(NSample,0,sigma)\n",
    "soln$observations = y\n",
    "\n",
    "par(mfrow = c(2,1))\n",
    "\n",
    "plot(x~times,data=soln,type='l')\n",
    "plot(observations~times,data=soln,type='o')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Markov Chain Monte Carlo\n",
    "\n",
    "We write from scratch an MCMC Metropolis-Hastings implementation. Note there are existing packages that do this, including STAN and ``mcmc``."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "-54874.4783432023"
      ],
      "text/latex": [
       "-54874.4783432023"
      ],
      "text/markdown": [
       "-54874.4783432023"
      ],
      "text/plain": [
       "[1] -54874.48"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "-55563.9673046161"
      ],
      "text/latex": [
       "-55563.9673046161"
      ],
      "text/markdown": [
       "-55563.9673046161"
      ],
      "text/plain": [
       "[1] -55563.97"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# define the likelihood function\n",
    "\n",
    "logLikelihood <- function(param,times,y){\n",
    "    kon = param[1]\n",
    "    koff = param[2]\n",
    "    sigma = param[3]\n",
    "    \n",
    "    pred = kon/koff*(1-exp(-koff*times))\n",
    "\n",
    "    singleLikelihoods = dnorm(y, mean=pred, sd=sigma, log=T) # really the log likelihood\n",
    "    sumLikelihood = sum(singleLikelihoods) # really the log of the product of likelihoods\n",
    "        \n",
    "    return(sumLikelihood)\n",
    "    \n",
    "}\n",
    "\n",
    "# Test it out\n",
    "logLikelihood(c(2.3, 0.25, 0.1),times,y)\n",
    "logLikelihood(c(2.5, 0.25, 0.1),times,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Here is the Metropolis algorithm!\n",
    "\n",
    "proposalGenerator <- function(currentParam){\n",
    "    \n",
    "    proposalParam = rnorm(3, mean=currentParam, sd = c(0.002,0.0002,0.0001)) \n",
    "    # play with these to make the acceptance rates around 30% for most efficient MCMC\n",
    "    proposalParam[proposalParam<0] <- 0 # Prevent negative values\n",
    "    return(proposalParam)\n",
    "}\n",
    "\n",
    "run_metropolis_MCMC <- function(startvalue, iterations){\n",
    "    chain = array(dim = c(iterations+1,3))\n",
    "    chain[1,] = startvalue\n",
    "    for (i in 1:iterations){\n",
    "        \n",
    "        proposal = proposalGenerator(chain[i,])\n",
    "         \n",
    "        # This is the Metropolis-Hastings (\"Boltzmann\") test\n",
    "        probab = exp(logLikelihood(proposal,times,y) - logLikelihood(chain[i,],times,y))    \n",
    "        if (runif(1) < probab){\n",
    "            chain[i+1,] = proposal\n",
    "        }\n",
    "        else{\n",
    "            chain[i+1,] = chain[i,]\n",
    "        }\n",
    "    }\n",
    "    return(chain)\n",
    "}\n",
    " \n",
    "startvalue = c(1,0.1,0.1)\n",
    "chain = run_metropolis_MCMC(startvalue, 100000)\n",
    " \n",
    "burnIn = 10000\n",
    "acceptance = 1-mean(duplicated(chain[-(1:burnIn),]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 6 × 3 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>1.000000</td><td>0.10000000</td><td>0.1000000</td></tr>\n",
       "\t<tr><td>1.000000</td><td>0.10000000</td><td>0.1000000</td></tr>\n",
       "\t<tr><td>1.000000</td><td>0.10000000</td><td>0.1000000</td></tr>\n",
       "\t<tr><td>1.000000</td><td>0.10000000</td><td>0.1000000</td></tr>\n",
       "\t<tr><td>1.000490</td><td>0.09973425</td><td>0.1001832</td></tr>\n",
       "\t<tr><td>1.001021</td><td>0.10011202</td><td>0.1003876</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 6 × 3 of type dbl\n",
       "\\begin{tabular}{lll}\n",
       "\t 1.000000 & 0.10000000 & 0.1000000\\\\\n",
       "\t 1.000000 & 0.10000000 & 0.1000000\\\\\n",
       "\t 1.000000 & 0.10000000 & 0.1000000\\\\\n",
       "\t 1.000000 & 0.10000000 & 0.1000000\\\\\n",
       "\t 1.000490 & 0.09973425 & 0.1001832\\\\\n",
       "\t 1.001021 & 0.10011202 & 0.1003876\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 6 × 3 of type dbl\n",
       "\n",
       "| 1.000000 | 0.10000000 | 0.1000000 |\n",
       "| 1.000000 | 0.10000000 | 0.1000000 |\n",
       "| 1.000000 | 0.10000000 | 0.1000000 |\n",
       "| 1.000000 | 0.10000000 | 0.1000000 |\n",
       "| 1.000490 | 0.09973425 | 0.1001832 |\n",
       "| 1.001021 | 0.10011202 | 0.1003876 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1]     [,2]       [,3]     \n",
       "[1,] 1.000000 0.10000000 0.1000000\n",
       "[2,] 1.000000 0.10000000 0.1000000\n",
       "[3,] 1.000000 0.10000000 0.1000000\n",
       "[4,] 1.000000 0.10000000 0.1000000\n",
       "[5,] 1.000490 0.09973425 0.1001832\n",
       "[6,] 1.001021 0.10011202 0.1003876"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 0.8448239\n"
     ]
    },
    {
     "data": {
      "image/png": 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jiSf1BcnC2uyBmSt7OzGOw0BRwXdSKS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\nBAgQIECAAAECBAgQ+GcCPwFuTXx8CtepfAAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “Histogram of chain[-(1:burnIn), 3]”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Explore the results.\n",
    "\n",
    "head(chain)\n",
    "print(acceptance) # Is it close to 30%?\n",
    "\n",
    "# Conditional posteriors\n",
    "par(mfrow = c(2,3))\n",
    "\n",
    "hist(chain[-(1:burnIn),1], xlab=\"Posterior of kon\")\n",
    "hist(chain[-(1:burnIn),2], xlab=\"Posterior of koff\")\n",
    "hist(chain[-(1:burnIn),3], xlab=\"Posterior of sigma\")\n",
    "\n",
    "plot(chain[,1])\n",
    "plot(chain[,2])\n",
    "plot(chain[,3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FcYp1Xuvpcrblo48+kuuvv15+8IMfyPjx401W3XbPnj2ieD//+c/N\nOg2ULrvsMnPq3Xe+8x0zKuXU4ZSvr51T7px1+lvL3bp1a3iVXrukAVPdACucIeKJBnn6Rt9Q\nuRHZeBohoL7q5sU3YrOMfqrHmJ6a6oyQZjSGh53Xv3WdBVO/hXJOu/WwGVkQSAmBVH7v1A+R\netaIcwpNSoAnsJE62qafd/S9v6CgIIEtSa2qS0pKzPXofrY6Pz8/ph/c3dpeExrNqYxiRMet\nPC/pobFfL9lk06ZNMmXKlHBwpBvpRGk6gqSjbBrwvP/++2aAo6ECdWBFL8/RCdqc0Wb9rH7j\njTea9XpZTayWhAZIesqcRpGRi07NrTPY6QHV2KLXEenECxoETZw4MZytc+fO5rnOiOcsOg24\n/tNYu3atwdSpxPUPJHLROrt16xa5yjwfPXp0rXUa1S5btsxT0KMfxPRbHQKkWoTWF/rBVQMk\nzKxMtRJ19Eg/6PNhvxZLoy901MgJkDjOGmUiIUUFUvmY1vd+PV3e7cvRFO2amDdb3/udACmV\n+z3mMC4F6hexfntp0O98mHdpXkySdZy50uOITkwqDBVSbR/cDlejn6vrfrZ+8sknzfwCjpF+\n1tagX0/BKy4ulmOPPVbuu+8+0dPpnJhBnzuLfn7X/GvWrJGEBkibN282H/zrnhvoNDSa33pR\nlk7brcGEfguui55baCv7tddek1tuuUV+/etfG7zI+vr27WteaoSpU3zrou3VAMhJO/DAA00d\nei6js+j9kHSWOxYEEEAAAQQQQAABBFJXIE86dLyjXvP3lC6Q3Xtfrrc+mhU52V2lY7tf19sk\n4HEEqe6G999/vzmVTmec1kVPf9QgSCdQ08tlTj/9dHPrnxNPPNHcu1TT9EuUul8K68CKjk7F\ncol6BGn27NlmWm0NKpo7a8SIESPMtNw665zeq0h3/KWXXjIXXDk7qecg6rckGnHq6W533nmn\nDB8+3AQ8H374oZNNevfubSZf0DS9dkjvlaRBl7a3S5cucthhh5m8Ggj94Q9/MPdOGjRokPzr\nX/8yAZ9zcVi4QJ4ggAACCCCAAAIIIJBCAjXBSlm3+cZGWlx78rNGMjW6uqpmc4Nld2hznrRp\ndWaj2zWU8Mc//lHuuusu8zlcJ13QpW3btiYW0FEh50wyHRXSe5/qSJOeKdbQdde6TucwiOUS\ndYCkp5jpogFJcxfdeR0NUiQNknSI7KyzzpJhw4aFi543b565gawGSHPnzjWnx+iU3PqIXPR6\nJB0V0tkw7rjjDvnpT39qhut1NEqH5pxhe70O6dxzz5XLL7/cnLur6XruYqtWrSKL4zkCCCCA\nAAIIIIAAAiklYE6xk+YFQtHusNdrkLRcPZ32l7/8pQl49HN95GUxepqdjh5FLnqpjE7ooIMo\nRx55pAmQ6l5LprNMR04VHrl9U59HHSBpYKE7dNNNN5mZI+oOc0XbEL2Pkc6FrkNjGhnWndpb\nL+ZylgsuuED0YVs0gtSbxOp1BnrRp15zVHfRSRy0HD31Tq+DYkEAAQQQQAABBBBAINUFNECq\n8PsapChOsdMzxvTssIULF5r7kEZ66yDMOeecYyZt0JmjddHASOcR0OuOdJ1e06Wn5Dn3RNXr\nlHTSEr2EJpZL1AGSXgSlp6tNnTpV/vSnP5mRpI4dO9Zr03vvvVdvnW2Fc82QLU80aTpi5Iwa\nNbSdAhMcNSTDOgQQQAABBBBAAIFUFNAAqcrvAEkr9bA8/vjj8ve//93cokdv8qr3G3UWPXtM\nL33Rz+56VpjenkcvsdFrkTRG0LO/9GwvvbWPDp7o5A06i6MO2Fx00UXW+QucOqL5HXWApJMe\n6EVUQ4YMCdejw2UsCCCAAAIIIIAAAgggkDiB0GTZ/o8geQzIpk2bZqbz1vsY1V30tDkNgB58\n8EETBOklMDr1t15/9MYbb4QvhdHrls477zwzv4BemnPCCSeYQZu65TX3ddQB0qRJk0QfLAgg\ngAACCCCAAAIIIJA8AjqYU+lxRCdWra72WJCXs8v0/qWff/65mX9A5yqoe5aaXo6j8xPodUc6\nGVu87v8WdYDkGOjU3K+//rrZCZ09QkeU9NGuXTsnC78RQAABBJJUoDg439qyosBIa3qga/1T\nq60bNJBY1atLA2trr9rT3/5vKtC9qvYGdV994H4TzbKjSutuVev16ne613rd0Iv8FfYbJWZV\nlDe02f51u2vfn29/QuQzrx9DIrfhOQIIZJJAaNAlFCD5PEmDxxGkaPqhR48e1uwNzTFg3SDK\nRPt/nkYK0whw7Nix8sknn9TLoRMk/O53v6u3nhUIIIAAAggggAACCCAQP4F9I0j2L2xiXXs0\ns9jFuu54lRd1gKTXH+ndbXUESSdq0PnJ9ZxBnWXi0UcfNfcw0pntrrzyyni1mXIRQAABBBBA\nAAEEEECgjoAGSFVRzCpXZ/MmvUzHmQiiDpAeeeQRM0nDkiVL5OCDDw5DHnHEEeaOtxMnTjQ3\nfyVACtPwBAEEEEAAAQQQQACBuAuYSRp8DpD8DsjijhiqIOqTFD/88EMZPnx4reAosqE6M8WK\nFSvMxVWR63mOAAIIIIAAAggggAAC8RPQ0ZzKmixfH9VxuAYpfkLeSo56BCk7O1sqKioaLd1J\n05s2sSCAAAIIIIAAAggggIA/AvsmafD5GqQ0DJCiHkHS6fd0PvLFixfX62mdr/zuu+82N2Dt\n3bt3vXRWIIAAAggggAACCCCAQHwE9k3SsG+qb53u249HtVaaZkvUI0iXXHKJmZxBT7O79NJL\nzZ1sdQ5ynaThscceE702SSdrYEEAAQQQQAABBBBAAAH/BBJyo1j/ds+3mqIOkPSutQsXLpTx\n48eL3hE3cmnfvr1Mnz5dLr744sjVPEcAAQQQQAABBBBAAIE4C+hgTrXP90GqScNT7KIOkLRf\n9eZNc+fOlbVr18qyZctk69at0r9/fxk0aJCZ8jvOfU/xCCCAAAIIIIAAAgggUEdAA6RynwOW\ndJzFrkkBktMXvXr1En2wIIAAAgiklkBR4GR7gwsL7On5+fb0UGr54O7WPKXHut89o6p7qbWM\n9i3KreklFa2t6ZpY/V6hNU+bhSXWdE0M5uVZ8wS2bramBzfvsqZrYnHw/1zzkAEBBDJbQCdp\nqPI5QGIEKbOPOfYeAQQQQAABBBBAAIGkFdBrkCp9vg9SOs5b7TqCtH79evnhD38ow4YNk5kz\nZ5prjGbMmOF6YHzyySeueciAAAIIIIAAAggggAACsRHQcfnyGn+n+fZ7xCo2UvZSXAOkrKws\nc11RixYtTEl5odMIWrVqZS+VVAQQQAABBBBAAAEEEPBdoMrnGjNyBKlbt26yaNGiMPWZZ54p\nP/7xj6Vnz57hdTxBAAEEEEAAAQQQQACBxArUhK5BqvB5BCkd74MU9Y1iZ8+eLX369JHPP/88\nsUcAtSOAAAIIIIAAAggggEBYwFyDVJMllT4+qn2eFCK8s3F84nqKXd26dVpvXXr37l03idcI\nIIAAAggggAACCCCQQIGgz/dBira+r776Sp599lnJycmRU089Vfr161dLa8eOHfL888/L9u3b\nZdSoUTJw4MCo0mtlbuKLqEeQLr/8cunYsaPcdNNNUlZW1sRq2QwBBBBAAAEEEEAAAQRiKeDc\nKFZvFuvXIxjFCNLZZ58tRx55pCxZskTmzJkjhx56qLz00kthgqVLl4pe3vPnP/9Z/vvf/8rR\nRx8tL7/8suf0cMZmPol6BGnNmjVy2GGHydSpU+VPf/qTGUnSgKnu8t5779VdxWsEEEAAAQQQ\nQAABBBCIl0AoWKmp9ncWO73uycuiQdEzzzwjq1atCt9H9fzzz5ff/OY3Zn4DLWPcuHEyYcIE\neeCBByQQCMhtt90mkydPlhUrVpjXbule2uElT9QjSJs3bxYd+hoyZIgcccQR0r59e6mpqan3\n8FI5eWoT2c4AAEAASURBVBBAAAEEEEAAAQQQQCA2Ahqr6I1b/Xx4HUHatGmTTJkyJRwc6R6f\ndNJJsnr1agmG7nC7ceNGWbx4sUycONEEQ5o+fvx4WblypVnvlq75Y7VEPYI0adIk0QcLAggg\ngEByChQFfujasOLgfGueY3uOsaaHvhWzp4dS937HPvnrRaf917WMZVs7WfMEAvZ2LP7kUOv2\nmtju3XJrnqx1X1vTNTFYUWnNE9xrn3i3OLj/FBJrQSQigAACFoFA6NS6QW2G1suxpWyTfFO2\nod76aFbkZ7WQ/m0OqbdJm5wO9dY1tGL06NGij8jlySeflKKiIhMQ6ciSLv379ze/9YeebldQ\nUCB6BpsGUbo0ln7ccceZ9Fj8iDpAiqz0o48+kuXLl0vr1q3lRz/6kYkADzjggMgsPEcAAQQQ\nQAABBBBAAAEfBAISkDY57evVVJK1W4Khme2as2QFchssOyeQ16Ri77//flmwYEH4dkIaIBUW\nFopz71WnUD1bTUefqqqqrOlO/lj8blKA9Omnn5pRpDfffNO04ZxzzjEBkl50dcUVV8jvf/97\nyc/Pj0X7KAMBBBBAAAEEEEAAAQQ8CFRLjby1ad/n8/rZmxcglVSVNlj2iJzW9atyWfPHP/5R\n7rrrLvnXv/4lQ4fuG/HKy8uTysr6o/G6Tgdj3NJdqowqOeoAadeuXeZCKm3s1VdfLW+//bap\nsLq62kzFd8stt8i6detE75fEggACCCCAAAIIIIAAAj4JhK4/qvb5RrFer0FSAZ234Je//KXo\nqXVz586V73//+2GYHj16mACppKTEBEROwrZt28xU4Lm5udZ0J38sfkcdSs6cOVN27txppt67\n9957wxdaZWdnm5296qqr5K9//avs2bMnFu2jDAQQQAABBBBAAAEEEPAgoFfp6Kl0vj6imOb7\nwgsvNNN6L1y4sFZwpLs2YMAAM0q0aNGi8J4WFxeLDsIceOCBrunhjWLwJOoA6f3335fhw4dL\nnz59Gqz+3HPPNecIOhdaNZiJlQgggAACCCCAAAIIIBBbgVCEVBUKkPx86Ix5XpbHH39c/v73\nv8sf/vAHcxNYvVTHeWgQpLcNGjNmjJnpTgdj9u7da+67etFFF0nPnj1d0720wWueqE+x04un\n3n333UbL153RpaF7IzW6EQkIIIAAAggggAACCCDQLIFgaJKGmtBMdn4uXgOkadOmmZno9D5H\ndRc9ra5Vq1bmuqTzzjtPunTpYmavO+GEE8y9V538et2SLd3J19zfUQdIxx57rMyaNcvc6Okn\nP/lJrfr1+iS96ErPIdRp+VgQQAABBBBAAAEEEEDAP4Gaan8DpKDHa57ee+89V4TOnTvLvHnz\nRK87ysnJkTZt2tTaxi29VuZmvIg6QLr44otFr0M666yz5PjjjxcNinR+ch0S07vjlpaWylNP\nPdWMJrEpAggggAACCCCAAAIIRC0QOsXOa8ASddmNbeDxFLvGNm9ofYcO9nsruaU3VGY066IO\nkDSae+mll+T666+Xxx57zMxGoRXqaXfdu3c3wdPPf/7zaNpAXgQQQAABBBBAAAEEEGimgJ5i\nV+XzKXbVoTrTbYk6QFIAHd7Sabzvu+8+WbFihWzZssXMLqEzTOgUfCwIIIAAAokUqHGtvKjN\nGdY8VUPr3y09coNdA93f6/sNWhe5Sb3nn27tVG9d3RXrt3asu6rW6/XFnWu9rvsiZ437qSbZ\nG9fX3azW6+CuilqvG3xRU97gamdlcXCe85TfCCCAQNwEgqERpJpm3hA22sb5PmIVbQObkN/9\nP0edQnUK72uvvdasbdeunRQVFcno0aNl4MCBJjh69tln5YADDjCn2tXZlJcIIIAAAggggAAC\nCCAQN4FAaCKE0DTfPj4kU0eQNm/eLBUV+75B02m+Fy9ebG4GW7dvNY+efvf1119LWVmZuTap\nbh5eI4AAAggggAACCCCAQOwF9D5IVR4nTYhV7dVxuAYpVm1rajmeTrGbM2eOXHfddbXq6NWr\nV63XkS+GDBki7du3j1zFcwQQQAABBBBAAAEEEIingDnFzt9rgtLxFDtPAdKVV15pbv5aWVkp\nr732mqxevVrGjh1br3t1AgcNjM4+++x6aaxAAAEEEEAAAQQQQACB+AmY+yD5fQ1Spo4g6cQL\nN9xwg+nNQw45RD799FO5+eab49e7lIwAAggggAACCCCAAAJRCZhT7Hyexa4mU69BiuyZc845\nx7ysrq6W7Oxs87yqqkoWLFggGzZsMBM2xHtu8sj28BwBBBBAAAEEEEAAAQRCAuYUu6jnYGsW\nXY3P1zw1q7EeN26S4P333y89e/Y0EzFoPePHj5eTTz5ZLrjgAjOD3dKlSz1WTzYEEEAAAQQQ\nQAABBBCIjUBAakKnvPn50NP60m2JOkB688035eqrr5YuXbqYqbzfe+890am/TzzxRPnHP/4h\nffv2NYFSukGxPwgggAACCCCAAAIIJLOA3gWvMnQNkp+PjJ3FLvJA0Gm8u3fvLh988IFkZWWJ\n3vdIl3vvvdfcE0knctCRpJKSEmndunXkpjxHAAEEEEAAAQQQQACBeAmERo+qmaSh2bqeZrGL\nrGX58uUybNgwExzp+rlz50rnzp3lmGOOMdkOO+yw0M2pgrJq1SoZPHhw5KY8RwABBBBwESgK\njHDJocn20xkCffu4llE+qIs1z96Tqq3pY0YusKZr4rnttljzXPvxUdZ0TVy/yN7Ogk/0+9LG\nl5wNextP/DYluH67NU9x8CVret3ErVu3mnsHdu3aNfy/sm4eXiOAAALxENBJGvT0Oj8Xv+vz\nY9+iDpB0AoZ33nnHtE0nZViyZImcf/75Egjs64xXX33VpOkoEwsCCCCAAAIIIIAAAgj4J1Dl\n8wgSAVKob0eNGiWzZ8+Wyy+/XHQyBh0tGjNmjOisdjp5w5133inHHXecdOrUyb8jgZoQQAAB\nBBBAAAEEEMhwgdDH8tApdn6PIKUfetQjSD/5yU/kV7/6lUyfPt2cOnDNNdeYqb01QLrxxhvN\nbHYaKLEggAACCCCAAAIIIICAfwI6o1ylzwFSUwIyjRvuuOMOueyyyyTy9kA7duyQF198sR7Y\n2WefLXl5eWa95nn++edl+/btZuBm4MCB9fI3d0XUAZJOzPDAAw/Irbfeaup2JmLQeyItWrRI\nhgwZ0tw2sT0CCCCAAAIIIIAAAghEK6AXIfl8DZLbdbEN7YIOsOiAip6FFhkg6X1Vx44da24n\nFLndKaecYgIkPXtt6NChZp6D/v37yw033CBPP/20CZQi8zf3edQBklNhQUGBvP766/L555+L\nzlyngRHBkaPDbwQQQAABBBBAAAEEEiDgd4CkQZnHZc2aNTJp0iRx5iyou5nOkn388ceLBkoN\nLePGjZMJEyaYwRqd/+C2226TyZMny4oVK8LzITS0XbTror4Pklag9z466qijZOTIkaZRV155\npZx00knSvn17M1wWbSPIjwACCCCAAAIIIIAAAs0XCIQmIfX1EUWANH78eKmpqZF///vfDe7o\n+++/b0aIGkrcuHGjLF68WCZOnBgOhrS8lStXmvUNbdPUdVEHSHre3xlnnCGbN2+WqVOnysKF\nC+XDDz+U5557zqzXoS6uQWpqd7AdAggggAACCCCAAAJNFNBgpTo0SYOfjyiueZo1a5a5RVCv\nXr0a3EEdQdq0aZOJKXr06CFnnnmmCYA0s95CSBc9tc5ZunXrJnpWm45MxXKJ+hS7Rx55RDRI\n0um9Dz744HBbjjjiCDn99NNNVDdjxgzRUSUWBBBAAAEEEEAAAQQQ8EcgLztH7h5xTr3KXl/1\nmcxd8WG99dGs6NaqrVx5/Kh6mwRc7s0XuUGfPo3fp0/jCw2CDjjgANFrlDSumDZtmpx44ony\n6aefmrTCwkJp0aJFZJHmDDYNqmK5RB0g6WjR8OHDawVHkQ3S8wJnzpwp69evF438WBBAAAEE\nEEAAAQQQQCD+AhXVVXLd/z0Vl4o2luxssOwLjvyu/GTQMc2us23btiYI0lGh/Px8U57eOmjw\n4MHy5JNPSufOnc28B3Ur0rkQnEnj6qY19XXUAZLOVldRUdFofU6aTt/HggACCCBQW6AocHLt\nFXVftSysu6be64BLntIjutbbpu6K8qNq6q6q9friH/631uu6L67r7H46w5+2NHwKhVPW8nd7\nO08b/d3yXfv/ktxlXzW6rUmoqrKnh1IXB19yzUMGBBBAICUEdIKGKn/vgyT2t2nPbDrpgo4e\nRS6HH3646Ol4q0IjS0ceeaQJkEpKSmoFRNu2bZN+/fpFbtbs51Ffg3TMMcfIG2+80eDFUHrT\n2LvvvtvcJLZ3b/d/fM1uPQUggAACCCCAAAIIIIDAPgG9BsnvR4zsly1bJnrJjs5I5ywaGK1d\nu9ZcdzRgwAAz1bfeVshZiouLRQdlDjzwQGdVTH5HPYJ0ySWXmMkZ9DS7Sy+9VI499lhp06aN\niewee+wxc23So48+GpPGUQgCCCCAAAIIIIAAAghEIWA/QSCKgjxm1YAsBsugQYNErzG6/vrr\n5aGHHpI9e/aYa5G6du0q5557rrRq1crcN2nKlCkm/sjNzZWbbrpJLrroonr3TWpuc6IOkHSm\nCJ25TqfV0wunIhed5nv69Oly8cUXR67mOQIIIIAAAggggAACCPggEPD9PkixO6XvwQcfNEFQ\nz549Rc9M0+uP9Mw1DY50ueuuu+S8886TLl26mNnrTjjhBDNwE2vWqAMkbYBOvjB37lwz5KXD\nYVu3bjVDXxr5OTsQ64ZSHgIIIIAAAggggAACCFgEdDQnBUaQDjnkEBMA1d0TvZTn888/N5O9\n6UQNHTt2rJVFJ2qYN2+e6HVHOTk55iy2Whli9KJJAZJTt1401dg85k4efiOAAAIIIIAAAggg\ngIBPAnoPJD+XOARkbjNhd+jQIa576DlA0mEunYP83XffNcNaw4YNE52OjwUBBBBAAAEEEEAA\nAQSSRCBG1wR53hu/6/PcsKZn9BQg6XR6er7fiy++GK5Jh7hmz54tp512WngdTxBAAAEEEEAA\nAQQQQCBBAilyil2CdDxX62ma7xtvvNEER3oh1L333is/+9nPRO92q7NG6PVHLAgggAACCCCA\nAAIIIJAEAjpJg58P8fmUPh+IPY0g/e///q8UFRXJq6++ai6I0na98MILZvToqaeekssuu8yH\nplIFAggggAACCCCAAAIINCqgI0gxunFro3XUTYjDNUh1q/D7tWuApKfXbdmyRSZPnhwOjrSR\nP/7xj0XnH//qq6/8bjP1IYAAAkkrUBQ42d621i2t6YHsbGu6Jlb36WPNU36Q+7d5Bw9day1j\nV429HV9U2PdDC39u2aHWOgr/a002ibmffmnNFNy215ouNWX2dFIRQACBdBPwO2DJxGuQdu7c\naQ6bdu3a1Tp8srKyRK9DWrduXa31vEAAAQQQQAABBBBAAIEECHANUkzQXUeQqqv3jdNlN/Ct\npq6rqqqKSUMoBAEEEEAAAQQQQAABBJopkMI3im3mnsdsc9cAKWY1URACCCCAAAIIIIAAAgjE\nV4BT7Jrt6zlA2rRpkyxfvrxWhTp6pNco1V2vmQ4++OBaeXmBAAIIIIAAAggggAACcRTQ0aMa\n9+tQY9qCTLwGyQG89dZbRR91lw0bNsjAgQPrrha9sSwLAggggAACCCCAAAII+CcQZASp2diu\nI0itW7dmGu9mM1MAAggggAACCCCAAAI+CPg9RuF3fT4QugZIempdeXm53HLLLdK9e3epqKgQ\nnbihoKDAh+ZRBQIIIIAAAggggAACCHgS0GDF91PsfD6lzxNE8zJluW2u1xfNnj1bvvnmG5P1\ntttuM/dActuOdAQQQAABBBBAAAEEEPBZQCeg9vPh9yl9PnC6jiD179/fNOOee+6RCRMmiF5z\ntHv3blmyZIm1eUcffbQ1nUQEEEAAAQQQQAABBBCIoUBoBMnva5DScdoB1wDpsMMOkxNOOEH+\n9re/mYfThUOHDnWeNvibSRoaZGElAgiku0BWC+seBgoKrenBDp2s6ZpY2c3lrbuT+/3pvtPn\na2s9/1l2iDX9X18eZ03XxJav2E+7yPtkpWsZwdAp3talxn7ye3FwvnVzEhFAAIG0E/D9Pkhp\nJygu/2VFAoGAzJ8/X+bNmyfr1q2TZ555Rr744gu58sor00+DPUIAAQQQQAABBBBAIJUF7N8b\nJcWe6XwGd9xxh5kIrkOHDrXatGPHDnn++edl+/btMmrUqHqzZbul1yqsiS9cA6Rly5bJfffd\nZyZpGD16tOzZs0c6duwokyZNamKVbIYAAggggAACCCCAAAIxF9DgSK8/8nNpwjVI11xzjdx/\n//0yZswYiQyQli5dKnqW2uDBg0Uv87nhhhvk6aefNoGS7pJbeqx2O+pJGrZt2yZr1qyJVf2U\ngwACCCCAAAIIIIAAAjESCISCJL8fXpuuMcQpp5wiM2bMaHCTcePGmTkPFi9eLE8++aQJkCZP\nnhy+v6pbeoOFNmGla4AUOUnDggULak3SoBM1NPZoQlvYBAEEEEAAAQQQQAABBJoqoMFRaETH\nz4dEcUrf+PHjpaamRv7973/X28ONGzeKBkYTJ040l/hoBs2/cuVKs94tvV6BzVjheoodkzQ0\nQ5dNEUAAAQQQQAABBBDwSSAnO0suO3V4vdre/2K1/HfZl/XWR7OiQ+uWcu7wY+tt0rld63rr\nGlsxa9Ys6dOnj3z22Wf1sqxatcqscwZn9EW3bt3MvVd15MmZAK6x9OOOc588yFTg4YdrgMQk\nDfsVtWP0orLS0tL9Kxt5pvk0QvaSt5EiMm61eumCmfeu1+NMb97svGl43zIzc1ZWVpod198c\nZ5lxDCSin533srKysvC3oJmh3fS91L9J/md696uq2jdTpf5OxDHuvaXJlVP/V/rtpce2n/+j\na6pr5IW3P6gHX7K3TLKacK1QZEF7dpc1WPaPig6PzGZ9rsFRY4sGSIWFhdKiRe3ZYNu3by+b\nNm0SPd5t6Y2V25T1rgGSFpqbmys6QYMu5aEpV997772MnaRB38D1A6nbovm85nUrK1PSnTcQ\nL76ZYuK2nxog6ZcYjp1b/kxPVy9dnMAy0z0yYf8T8X6i7/26aN3698niLqB/k7yPuTs5OZxj\njM8Zjoj3336/J/h9bOs9idZu3O4dJIqclaG/04bKLi3b9+VjFEU1mDUvL0+cLzIjM+i61q1b\ni1t65DbNfe4pQIqs5PLLLzcvNYp7/fXX5fPPPzc7M2TIENFHu3btIrOn1XP9R6fBYtu2bV33\nS3127tzpKa9rYRmSQd+01M2Lb4aQuO6mTnWp37TU/bbFdcMMzaBf8OhDvfTNliX9BRLxfqLv\nY/p+1qZNG8nKcr3UN/07wcMelpSUSHZ2tvl22EP2jM+iHxh1hFI/MCbiGE/VDlAzv730/43f\n7wN6/ZGfi04IEYulR48eJqbQ94PI/9E6QVy/fv3MZ3A99htLj0UbnDKiDpB0Qx1BGjt2rHzy\nySdOOeHft99+u/zud78Lv+YJAggggAACCCCAAAIIxF9Ag5UsHUbycQnEqL4BAwaYoH/RokUy\ncuRIswfFxcXmrI8DDzzQfLmpXwo0lh7LXY46QNJvrM844wzzTf/UqVNFL4hq1aqV6HmDjz76\nqJmOT6NlbiQby26iLAQQ8EOgKDDCXk3ovc116d/bmqWij32Ufc9gDyMOveynM0wa+ba1DZo4\n/R37xayBdwutZbT9xP1U45z1m61lBEOjeW5LICfXmiUo7mVYCyARAQQQSDeBFLgPUkPkep9V\nvS/SlClT5NhjjzUjRjfddJNcdNFF0rNnT7OJW3pD5TZlnYf/xLWLfeSRR0SDJJ3yW4OgYcOG\nyRFHHCGnn366PPvss2bu8sbmNq9dEq8QQAABBBBAAAEEEEAgZgKhwSM/p/g2dcVwwOquu+6S\n/Px86dKli+gpd3ppiw7IOItbupOvub+jHkH68MMPZfjw4XLwwQc3WPeECRNk5syZsn79erNj\nDWZiJQIIIIAAAggggAACCMRcwO9rkKK5D5Kzs4ccckiDE7N07txZ5s2bJ3rdUU5OjrmW09lG\nf7ulR+ZtzvOoAyS9iNI2A4iT5swW1ZzGsS0CCCCAAAIIIIAAAgh4FQgN58TomiCvNTYlQHIr\nu0OHDtYsbunWjT0kRn2K3THHHCNvvPGGuaNt3fJ1is67775bOnXqJL1728/Dr7strxFAAAEE\nEEAAAQQQQKCZAnrKm5+PZjY3GTePegTpkksuMecC6ml2l156qbmISqcy1UkaHnvsMVmyZImZ\nrCEZd5Y2IYAAAggggAACCCCQtgKhwCjg8yQNvp/S50PnRR0gFRQUyMKFC2X8+PEybdq0Wk3U\nO91Onz5dLr744lrreYEAAggggAACCCCAAALxF4jVfYk8t1RHq9JsiTpA0v3XWSXmzp0ra9eu\nlWXLlsnWrVulf//+MmjQIDPlt55qx93D0+xIYXcQQAABBBBAAAEEkltAgxWfbxQbj2uQEo0c\ndYD01ltvmXsf6bR7vXr1Mo/Infjyyy/NCJJep8SCAAIIIIAAAggggAACPgr4PUlDGkZIUU/S\n8Morr8j5559v7mob2dU6avTggw+aeyJpEMWCAAIIIIAAAggggAAC/gno6XV6DZKvD79HrHzg\njHoEaejQoXLrrbfKL37xC3niiSckKytLvvrqKxk3bpy8/vrrcuihh8qsWbN8aDpVIIAAAt4F\nigIne8hsf0sMdGzvWkZFn3bWPCUH2uuQQXut22viyYM/seZ54+sDrOmamPtWgTVPqw9LremB\nqiprukncsd2ep8R9X4Np+M2kHYVUBBBAoJkCfl8T5Hd9zeTxsrnLf+r6RZx++uny+OOPy9ix\nY82dbnXa7+uuu07Ky8vlpptukhtvvFHy8vLqb8gaBBBAAAEEEEAAAQQQiK9Atc8RS43P9cVX\nz5QedYCkW11wwQWiN4y98MILZc6cOVJUVCSzZ8+WwYMH+9BkqkAAAQQQQAABBBBAAIF6AqFY\nxe9Z7AL1GpH6K5oUIOlun3feeSZIGjNmjAmQCI5S/2BgDxBAAAEEEEAAAQRSXMDvAR2/6/Oh\ne1wDpPXr18sPf/jDRpuSn58vf/nLX0Qnb4g8te6TT+znyDdaIAkIIIAAAggggAACCCDQNAG/\nJ03IxABJJ2Fo1apVox10+OGHN5pGAgIIIIAAAggggAACCPgkoKfY+X1NUCYGSN26dZNFixb5\n1KtUgwACCCCAAAIIIIAAAk0WYASpyXTOhq6n2DkZ+Y0AAggggAACCCCAAAJJLuD3iI7f9fnA\nT4DkAzJVIIAAAggggAACCCAQdwENVpJ4BOmjjz6Sjz/+uBaDnq128sn771W4Y8cOef7552X7\n9u0yatQoGThwYK38frwgQPJDmToQQAABBBBAAAEEEPBBwO9rkAJB70NI99xzjwl+2rfff+P1\nYcOGhQOkpUuXytChQ82tg/r37y833HCDPP300yZQ8oEuXAUBUpiCJwggkN4CWe6717qFNU9V\n7+7WdE3cMyjbmie7fZU1vabMvZ2vLrHfcy7wRb61Dk1sW7zLmierotyaHly50pquiUGxW7gW\nEMpQHJzvJRt5EEAAAQRUIMlHkN5//3259dZb5Ve/+lWD/TVu3DiZMGGCPPDAAxIIBOS2226T\nyZMny4oVK8zrBjeKw0r3/8RxqJQiEUAAAQQQQAABBBBAINYCoQhJZ7Hz8+FxAKmsrEw+++wz\nM0LU0F5v3LhRFi9eLBMnTgwHQ+PHj5eVoS/kdL2fCwGSn9rUhQACCCCAAAIIIIBAHAU6dWwp\ndR+FBbmh0aXQxUnNeGSHooa65errvFxvZwvoPVKrq6tl7ty5Jkg66KCD5PrrrxcNnHRZtWqV\n+a2n1jmLXp9UUFAga9ascVb58ptT7HxhphIEEEAAAQQQQAABBOIrkJOdLeeee0K9Spa8t1L+\nu/CzeuujWdGuXUGDZbdpW+ipmA8++MDkKy0tlXvvvVfmzZsnf/nLX2TTpk0yZ84cEyAVFhZK\nixa1T3fX65U0j58LAZKf2tSFAAIIIIAAAggggECcBKqqqmT6n56PS+nbtuxssOyzz6sfkDXU\ngAsuuEBGjBghffv2NcknnXSS5OTkyJQpU+S+++6TvLw8qaysrLeprmvdunW99fFcwSl28dSl\nbAQQQAABBBBAAAEE/BIwkzSETqWr8fPh7SIkHRlygiOHY/To0ebp6tWrpUePHiZAKikpcZLN\n723btkm/fv1qrYv3CwKkeAtTPgIIIIAAAggggAACPggEQtPY6bTbvj7M1HnuO/fnP/9ZTjvt\ntFoZ33zzTcnKyjKB04ABA8wo0qJFi8J5iouLzXVLBx54YHidH08IkPxQpg4EEEAAAQQQQAAB\nBPwQaMZEDE2bxMHbCNIpp5wiL7/8sjz88MNmpOjVV1+Vhx56SH7xi1+IXmfUsWNHGTNmjDnl\nbufOnbJ371656aab5KKLLpKePXv6IReugwApTMETBBBAAAEEEEAAAQRSWMCcYhf6kYTTfOso\nkF5rdPXVV0ubNm3MzV+HDx8uM2bMCIPfddddkp+fL126dDGn3OXm5srUqVPD6X49YZIGv6Sp\nBwEEEEAAAQQQQACBuAro6XXVca2hfuGh6508LldccYX88pe/NNN266iQBkORS+fOnc3sdnrd\nkU7goIFUIhYCpESoUycCCMRcoCgwylpmoHN7a7omVvc6wJqn5CQPg+4FVdYyuh28zZq+da/7\ndKkV77e0ltH6XXsbdOOsjeutZQTLy63pxcH51nQSEUAAAQQSJKCjR34uUdano0Ju1xR16NDB\nzz2oVxcBUj0SViCAAAIIIIAAAgggkIICoQkazAx2fjZd60yzhQApzTqU3UEAAQQQQAABBBDI\nYIE0DFj87k0CJL/FqQ8BBBBAAAEEEEAAgXgJVPt8DZLecynNFgKkNOtQdgcBBBBAAAEEEEAg\nQwU4xS4mHU+AFBNGCkEAAQQQQAABBBBAIAkE9D5Ifi5peEofAZKfBxB1IYAAAggggAACCCAQ\nN4HQhAm+ByxM0hC37qRgBBBAAAEEEEAAAQQQaIaAxipRTrvdjNr2bep3fc1usHsBjCC5G5ED\nAQQQQAABBBBAAIHUEKjxeZIG30es4t8NBEjxN6YGBBBAAAEEEEAAAQTiL5CQSRp8vuYp/opC\ngOQDMlUggIBdoCgwwp7BpGZZ8wTat7KmVw4+0JquidWFAWueQK77edbDTlxqLeOzdb2s6RUf\nt7Sma2LeN/YsOetcMoQ2D5aX2wvZW2lNLwqcbE3XxOLgfNc8ZEAAAQQQiLGA36e8uf9rjPEO\nxr84AqT4G1MDAggggAACCCCAAAL+CPh9ypvf9fmgSIDkAzJVIIAAAggggAACCCAQd4FQsBL0\n/RokTrGLe79SAQIIIIAAAggggAACCDRRoNrnc97SLz7iGqQmHnpshgACCCCAAAIIIIBAcgno\n6W7VPkcsnGKXXMcArUEAAQQQQAABBBBAAIFvBXTwqMLnEaQqn+vzobO5BskHZKpAAAEEEEAA\nAQQQQCDuAhqr+D2ik37xEafYxf1ApQIEEEAAAQQQQAABBHwR0GjF5xvFis+n9PngyAiSD8hU\ngQACCCCAAAIIIIBAvAXMAJL4O6QTmjcv3rvle/kESL6TUyECCCCAAAIIIIAAAvES8HtEhwAp\nXj1JuQggkNECHr6raZ1vFQp27GxN39s725quiTWHVVjz9Oy73ZquiTm5VdY8m1/vZE1vs9K+\nvW6cu+Rzaxni5S7qeyvtZbicolEcnO+yPckIIIAAAn4L9B3YW/70wu2+Vtujbzdf6/OjMg+f\nSvxoBnUggAACCCCAAAIIIIBAcwRatWsp3zvluOYUwbYhgSwUEEAAAQQQQAABBBBAAAEE9gkQ\nIHEkIIAAAv+/vTuBkqSoEwccPT33wcAMMByCgMiNAusswuoqh8olIoIXeKysxyqPXVl84OIf\nBRRRXH36xAVF0EVUBHfR3QcIw+J6IcyqIKIIcssxzMHczNVT//olVFnT051V1dPVXVX55Xs9\nXZURGRnxRU52/SojIwkQIECAAAECBJ4XECA5FAgQIECAAAECBAgQIPC8gADJoUCAAAECBAgQ\nIECAAIHnBQRIDgUCBAgQIECAAAECBAg8LyBAcigQIECAAAECBAgQIEDgeQEBkkOBAAECBAgQ\nIECAAAECzwsIkBwKBAgQIECAAAECBAgQeF7Ag2IdCgQItFxgds9Rufvo2WJybnqWOG16bp5n\n956Rm75+7zW56ZHYsyD/lPj4k1vXLeOp+bNy80x/KL8eYx+bn7t9JJYWP1snT1+d9Ej2/VgD\nSLIQIECAQAEF/IUsYKdrMgECBAgQIECAAAECAwsIkAZ2sZYAAQIECBAgQIAAgQIKCJAK2Oma\nTIAAAQIECBAgQIDAwAICpIFdrCVAgAABAgQIECBAoIACAqQCdromEyBAgAABAgQIECAwsIAA\naWAXawkQIECAAAECBAgQKKCAAKmAna7JBAgQIECAAAECBAgMLCBAGtjFWgIECBAgQIAAAQIE\nCiggQCpgp2syAQIECBAgQIAAAQIDC+Q/Nn7gbawlQKBAArN7Dstv7fiJ+enl1J6tp+XmKW0x\nMzc9Elfut3lunrX7rctNL00s5aZHYmnHNbl5pvzXuNz0SBz/wDO5eXoWzs9NLz2zNDe9kcS5\npTmNZGsoz/r169PChQvTVltt1VB+mQgQIECAQKcLuILU6T2o/gQIECBAgAABAgQIDJuAAGnY\nKBVEgAABAgQIECBAgECnCwiQOr0H1Z8AAQIECBAgQIAAgWETECANG6WCCBAgQIAAAQIECBDo\ndAEBUqf3oPoTIECAAAECBAgQIDBsAgKkYaNUEAECBAgQIECAAAECnS4gQOr0HlR/AgQIECBA\ngAABAgSGTaAtnoP06KOPpl/84hdpxowZ6eCDD05Tp07NbeDKlSuz/E888UTaZ5990gEHHFDN\nv2zZsnTbbbdV31deHHLIIWncuOeeYfLzn/88rVixopKU/d5zzz3TDjvssME6bwgQIECAAAEC\nBAgQKJbAqAdIV155ZbrsssvSq171qhQBT7z/0pe+lLbYYosBe+LGG29MF110Udp3333T5MmT\n0+WXX56OOeaYdMYZZ2T577rrrnTBBRekLbfccoPtDzrooCxA6uvrS+ecc06aNm1aGjv2L81/\n3/veJ0DaQMwbAgQIECBAgAABAsUT+EuEMAptjytHV1xxRfriF7+Y9ttvv7Ru3br0gQ98IF19\n9dXZ7/5Viie6f/Ob38zSTjzxxCz5Jz/5STr77LPTcccdl3bdddd0//33p7333jtdfPHF/TfP\n3j/22GNpzZo16etf/3qaOXPmgHmsJFAkgdk9r81v7pTJuek906fnpkdi31azcvMsO3V9bnok\n7jzz8dw8h77ogdz03y7YKjc9Em//j71y84xduCY3PUuc91RuntKyVbnpKW36yOe6fVquwdzS\nTXXqIZkAAQIECBRTYNP/Em+C2x133JG22267LDiKYuKKzhFHHJFuvvnmAUtdtGhRmj17dnrN\na15TTd9///2z13H1KZYIkHbffffs9UD/RHpcXRIcDaRjHQECBAgQIECAAIFiC4zqFaQnn3wy\nbb/99hv0QARMCxYsSHG1aMyYDeO3CGxOP/30DfLfcsstqbe3txoURQA0YcKEdNZZZ6V77703\nxb1Fp556anU/f/rTn7LhdZ///OdT3IsUQ/ne+c53pr/927/doNx4E1e4nn322er6p556KqvX\n2rVrq+sGexFD+aINjeQdrIyirS+VSlmTmTXe83GMxbHGrHEzOZ8TaPSYiWMs/m82mp9vyrzC\nIUZF9PT0IGlAIM5jsTjOGsAqZ4ljKxafMzKGhv8ZjXNZHNuVzzcNV1TGURcY1QApAo7NNtts\nA4S4Nyj+wy9ZsmTQ+5AqGzzwwAPp0ksvTSeddFKaNWtWigkaosxtttkmve1tb0uveMUr0rXX\nXps+9KEPpW9961vZ5A/33XdfiitRu+22WzYhxA033JAN0fvsZz+b4j6l2iWCsbvvvru66sUv\nfnEWaEUA1+jSTN5Gy+z2fMya6+HVq1c3t4HcBMoCzf4/azY/5JQWLlyIoUmB5cuXN7lFsbOv\nWrUqxY+lcYGRPpfFxGICpMb7p11yjmqAFLPKVb4FqYBU3scEDHnLb3/72+wq0aGHHppOOeWU\nLGvMfnfNNddks+GNHz8+W7fXXnuld73rXSmuNL3hDW9In/jEJ7IArDIJxMtf/vIUV5Xivqf+\nAVIM5YsrUJUlhgDOmzcvmxyism6w3xHkxb1OEydOHCyL9f0E4mpdnETq9X2/zQr9NoKjuIJa\nO+FIoUE0vmGBRv+fxf/J+AA2adKkhssuesbwir8BYeYKUmNHQ/y9jFEjzmWNecXxFcdZeFU+\n7zS2ZbFzRbDS6LlvuKQqMygPV3nKGRmBUQ2QYsjcww8/vEFLly5dml05imFygy0/+9nP0sc/\n/vH05je/Ob3//e+vZos/RHH1qHbZZZdd0lZbbZViOF8s0we4oTwCo5/+9Ke1m2Wva8uOFXfe\neWc2qcRAZfTfOAK9uArWSN7+2xb1ffyBDDdmjR8BixcvzoJwgXjjZnI+J9Do/7P4IBbDnhrN\nz/e54U9xPosREv2HivMZWCBGgMSXPSP94XXg2rT/2vg/GQFSBEf+bzbeX2E20l7x99l5oPE+\napecG97kM8K12nnnnbP7hCpXjWL399xzT/V+oYGqc+utt2bTdJ922mkbBEeRN4KtuFoUM9VV\nlgiM5s+fXy3zzDPPzIbdVdLjd0wNHvc+WQgQIECAAAECBAgQKLbAqAZIhx9+eKZ/1VVXZcMR\nHnzwwXT99dend7zjHdVeiWm84z6hWGI894UXXphe/epXp5122ikLbCK4iZ+4ryjWRaR+ySWX\npGeeeSa7avSVr3wluyJ12GGHZWXErHfxrKWYzCGGJ33/+9/PgrS4GmUhQIAAAQIECBAgQKDY\nAqM6xC6G0Z1//vnp3HPPTREkxXjt448/Pps8odItc+bMyR4ge+SRR2aBUowfjWnA+08FHrPW\nHX300enDH/5wOu+889Ib3/jGrIgYYvflL3+5etk+7kOK+5fe8573ZJemow7xHKX+9x9V9u83\nAQIECBAgQIAAAQLFERjVACmY44rOddddl01+EPcK9R+nGcFOZTn55JNT/OQte+yxR/r2t7+d\nzdAUN8b1H2saQdgFF1yQVqxYkc16F7PfuYk2T1QaAQIECBAgQIAAgeIIjHqAVKGOQGU4l5gA\nIm+ZMmVKih8LgXYVmN3z3LDQTavf4JOdVMudlj87Wc/mm1ezDvSib0b+/7XYZuVe+bM5lhbW\nf7bYgS97aKDdV9fNnrSi+nqgF5c+8NcDrd5g3eR5zz2La4OVNW96n5pX827gl6XypAb5S29+\nclpTJz2luaU5dfPIQIAAAQIECAxNYFTvQRpalW1FgAABAgQIECBAgACB1ggIkFrjqlQCBAgQ\nIECAAAECBDpQQIDUgZ2mygQIECBAgAABAgQItEZAgNQaV6USIECAAAECBAgQINCBAgKkDuw0\nVSZAgAABAgQIECBAoDUCAqTWuCqVAAECBAgQIECAAIEOFBAgdWCnqTIBAgQIECBAgAABAq0R\nECC1xlWpBAgQIECAAAECBAh0oIAAqQM7TZUJECBAgAABAgQIEGiNwNjWFKtUAgQ2VWBu6Za6\nRczuObxOnrV10lPqmbZFbp6+GVvmpi/92wm56ZG466GP5eZ57Yv+lJseiXMe2iU3zy0rJ+em\nT/7RxNz0SJz8y/x6pt7eumWktevr58nJMbc0JydVEgECBAgQINBqAVeQWi2sfAIECBAgQIAA\nAQIEOkZAgNQxXaWiBAgQIECAAAECBAi0WkCA1Gph5RMgQIAAAQIECBAg0DECAqSO6SoVJUCA\nAAECBAgQIECg1QICpFYLK58AAQIECBAgQIAAgY4RECB1TFepKAECBAgQIECAAAECrRYQILVa\nWPkECBAgQIAAAQIECHSMgACpY7pKRQkQIECAAAECBAgQaLWAAKnVwsonQIAAAQIECBAgQKBj\nBMZ2TE1VlEDBBGb3HNZAi8fn5umZMSU3PUucOCk3z9JDJ+Smp23X5qeXU6dNXpmb5/r7d8tN\nj8RH7t06N0/v78blpk/97cLc9EgsPT6vTp6eOulZKXXyrK+TLpkAAQIECBAYTQFXkEZT374J\nECBAgAABAgQIEGgrAQFSW3WHyhAgQIAAAQIECBAgMJoCAqTR1LdvAgQIECBAgAABAgTaSkCA\n1FbdoTIECBAgQIAAAQIECIymgABpNPXtmwABAgQIECBAgACBthIQILVVd6gMAQIECBAgQIAA\nAQKjKSBAGk19+yZAgAABAgQIECBAoK0EBEht1R0qQ4AAAQIECBAgQIDAaAoIkEZT374JECBA\ngAABAgQIEGgrgbFtVRuVIVAggdk9h296a6eNyy2jb+edc9MjcfHLJuTm6dlxVW76ttssyU2P\nxHse3z43z9o/TM5Nj8Sxj/Tk5pn6q6dz01NfX356pG4+JTdPafGy3PRInFuaUzePDAQIECBA\ngED7CriC1L59o2YECBAgQIAAAQIECIywgABphMHtjgABAgQIECBAgACB9hUQILVv36gZAQIE\nCBAgQIAAAQIjLCBAGmFwuyNAgAABAgQIECBAoH0FBEjt2zdqRoAAAQIECBAgQIDACAsIkEYY\n3O4IECBAgAABAgQIEGhfAQFS+/aNmhEgQIAAAQIECBAgMMICAqQRBrc7AgQIECBAgAABAgTa\nV8CDYtu3b9Ss6wV681s4Of8hsLHx+hftllvGupl19pEVkltEGrM0v4ynHtg6v4Byas/E9bl5\npvxffnpsPGZJnTyLFubuI/XU/z6otHh5bhkeApvLI5EAAQIECHSFQP1PDF3RTI0gQIAAAQIE\nCBAgQIBAfQEBUn0jOQgQIECAAAECBAgQKIiAAKkgHa2ZBAgQIECAAAECBAjUFxAg1TeSgwAB\nAgQIECBAgACBgggIkArS0ZpJgAABAgQIECBAgEB9AQFSfSM5CBAgQIAAAQIECBAoiIAAqSAd\nrZkECBAgQIAAAQIECNQXECDVN5KDAAECBAgQIECAAIGCCAiQCtLRmkmAAAECBAgQIECAQH2B\nsfWzyEGAQCsEejafnF/s+An56eXU9dN6c/OMebaUmx6JvdPW5+Yp9eQmp97F+emROvnBvtxM\nvQuX56ZHYs+iBbl5SitW56anNevy08upc0s3180jAwECBAgQINDdAq4gdXf/ah0BAgQIECBA\ngAABAk0ICJCawJKVAAECBAgQIECAAIHuFhAgdXf/ah0BAgQIECBAgAABAk0ICJCawJKVAAEC\nBAgQIECAAIHuFhAgdXf/ah0BAgQIECBAgAABAk0ICJCawJKVAAECBAgQIECAAIHuFhAgdXf/\nah0BAgQIECBAgAABAk0ICJCawJKVAAECBAgQIECAAIHuFhAgdXf/ah0BAgQIECBAgAABAk0I\njG0ir6wECDQhMLvnqNzcPTttk5veN3Nmbnokrt26NzdPqZGvQKb35ZYx7nf5+5jym4W520di\nz+pVuXlKjz6emx6JpZRfj5TW1ymjVCddMgECBAgQIEAgpUY+PnEiQIAAAQIECBAgQIBAIQQE\nSIXoZo0kQIAAAQIECBAgQKARAQFSI0ryECBAgAABAgQIECBQCAEBUiG6WSMJECBAgAABAgQI\nEGhEQIDUiJI8BAgQIECAAAECBAgUQkCAVIhu1kgCBAgQIECAAAECBBoRECA1oiQPAQIECBAg\nQIAAAQKFEBAgFaKbNZIAAQIECBAgQIAAgUYEBEiNKMlDgAABAgQIECBAgEAhBMYWopUaSWA0\nBKaNy9/runW56eun1v/+Yv24ntwy0vpSfno5te/x/HpOeXptbhk96/LTY+PSo3/OLSOlOu3I\nts7fz9zSLXX2kdLq1avTokWL0tSpU9O0adPq5peBAAECBAgQKJ5A/U9gxTPRYgIECBAgQIAA\nAQIECiogQCpox2s2AQIECBAgQIAAAQIbCwiQNjaxhgABAgQIECBAgACBggoIkAra8ZpNgAAB\nAgQIECBAgMDGAgKkjU2sIUCAAAECBAgQIECgoAICpIJ2vGYTIECAAAECBAgQILCxgABpYxNr\nCBAgQIAAAQIECBAoqIAAqaAdr9kECBAgQIAAAQIECGwsIEDa2MQaAgQIECBAgAABAgQKKjC2\noO0eUrNLpVKKn3Xr1tXdPvI0mrduYQXJEF6xNOK7qSQHjXtdnSLqfHcwZnyd7VPq2XxSbp6+\nLbfOTX92+/r/PXt6cotIExauz89QTp34eP7x3LtwZW4ZpYeeyE3PEsdMyM1z2+of5KY3ktjI\ncdPX15cVtX79+hE5zhqpd7vnCSvnsuZ6qXIui+Mt/Cz1BcKpp3xCa+T/cf3Suj+Hc9nQ+3ik\nj7HKOXToNbblaAjU/wQ2GrVq432uXbs2LVmypG4NKx8oGslbt7CCZKh8kGBWkA6vaeZI9Xnl\nGFu1apUPYjX+eS/jXBZuI9VHeXXplLTKB7Awiw/9lvoCYRZWq1evrp9ZjmrgvWbNGv83mzge\nRuNcFn9vKl+aNFFVWUdZQIDURAfEyXv8+PFp5syZdbeKk338cWwkb93CCpJh/vz52YdWZgXp\n8JpmjlSfx4evRYsWpcmTJ6dp06bV1MDLwQTiA8XChQudywYDGmB9eMUH1xkzZqQxY+pcjR5g\n+yKuWrZsWert7c3+bxax/c22Ob6sXbBgQZo4cWKaPn16s5sXNv+8efNG/FwWf2+cBzrvkHPm\n7rw+U2MCBAgQIECAAAECBFokIEBqEaxiCRAgQIAAAQIECBDoPAEBUuf1mRoTIECAAAECBAgQ\nINAiAQFSi2AVS4AAAQIECBAgQIBA5wkIkDqvz9SYAAECBAgQIECAAIEWCQiQWgSrWAIECBAg\nQIAAAQIEOk9AgNR5fabGBAgQIECAAAECBAi0SMBzkFoEq9ihCRy73Tvqbji3NKdunvoZ6h36\ndR7uWG/zcgX6tt8htxprdhyXmz5+6frc9Egcs6qUm2fcI4tz0yOxZ/nS3DylefUejFy/nml9\nX+4+JBIgQIAAAQIE2kXAFaR26Qn1IECAAAECBAgQIEBg1AUESKPeBSpAgAABAgQIECBAgEC7\nCAiQ2qUn1IMAAQIECBAgQIAAgVEXECCNeheoAAECBAgQIECAAAEC7SIgQGqXnlAPAgQIECBA\ngAABAgRGXUCANOpdoAIECBAgQIAAAQIECLSLgACpXXpCPQgQIECAAAECBAgQGHUBAdKod4EK\nECBAgAABAgQIECDQLgICpHbpCfUgQIAAAQIECBAgQGDUBcaOeg1UgECTArN7jmxyiwGyT5sw\nwMq/rOqZkJ/et/2Of8k82KvxvYOlZOt7V5by0xf35aZHYu/CRfl5Svn7yDZetSq/jEl1vkdZ\nUX8fc0s35e9DKgECBAgQIECgTQTqfPJpk1qqBgECBAgQIECAAAECBEZAQIA0Ash2QYAAAQIE\nCBAgQIBAZwgIkDqjn9SSAAECBAgQIECAAIEREBAgjQCyXRAgQIAAAQIECBAg0BkCAqTO6Ce1\nJECAAAECBAgQIEBgBAQESCOAbBcECBAgQIAAAQIECHSGgACpM/pJLQkQIECAAAECBAgQGAEB\nAdIIINsFAQIECBAgQIAAAQKdISBA6ox+UksCBAgQIECAAAECBEZAYOwI7MMuCDQhUD9m79li\nUn55U6flp5dT+7baOjdP79PzctNLE3pz0yOxd9GS3Dxjlo3LTe9Zlr99bFxaujS3jLRsdX56\nlrq2Tp6e3PS5pTm56RIJECBAgAABAp0kUP/TaCe1Rl0JECBAgAABAgQIECCwCQICpE3AsykB\nAgQIECBAgAABAt0lIEDqrv7UGgIECBAgQIAAAQIENkFAgLQJeDYlQIAAAQIECBAgQKC7BARI\n3dWfWkOAAAECBAgQIECAwCYICJA2Ac+mBAgQIECAAAECBAh0l4AAqbv6U2sIECBAgAABAgQI\nENgEAQHSJuDZlAABAgQIECBAgACB7hIQIHVXf2oNAQIECBAgQIAAAQKbIDB2E7a1KYGNBGZP\nOHqjdc2s6Nl8St3sfTu9KD9PqZSfXk4tTerJzbNux21y03vW1N9Hz5rVuWWkNWvy01euyE+P\n1GX5Zcwt3Vi/DDkIECBAgAABAgSqAq4gVSm8IECAAAECBAgQIECg6AICpKIfAdpPgAABAgQI\nECBAgEBVQIBUpfCCAAECBAgQIECAAIGiCwiQin4EaD8BAgQIECBAgAABAlUBAVKVwgsCBAgQ\nIECAAAECBIouIEAq+hGg/QQIECBAgAABAgQIVAUESFUKLwgQIECAAAECBAgQKLqAAKnoR4D2\nEyBAgAABAgQIECBQFRAgVSm8IECAAAECBAgQIECg6AJjiw6g/Y0LzO55bQOZe+vk6clP326L\n/PRyamlinTJ66qTHHtbW2U29/xnrSnUKKCcvXZKbp7R0TW56Wl+vkind/Mz30sSJE7Of/MKk\nEiBAgAABAgQINCLgClIjSvIQIECAAAECBAgQIFAIAQFSIbpZIwkQIECAAAECBAgQaERAgNSI\nkjwECBAgQIAAAQIECBRCQIBUiG7WSAIECBAgQIAAAQIEGhEQIDWiJA8BAgQIECBAgAABAoUQ\nECAVops1kgABAgQIECBAgACBRgQESI0oyUOAAAECBAgQIECAQCEEBEiF6GaNJECAAAECBAgQ\nIECgEQEBUiNK8hAgQIAAAQIECBAgUAiBsYVopUYOk0Cpfjnj82PunikTcsvom75Fbnok9m2e\nv48Vu/TWLWPqvX25eXoXrM1Pf/LPuemRWFq6Jj/P+nX56Wl9nXTJBAgQIECAAAECwy2Q/0lz\nuPemPAIECBAgQIAAAQIECLSxgACpjTtH1QgQIECAAAECBAgQGFkBAdLIetsbAQIECBAgQIAA\nAQJtLCBAauPOUTUCBAgQIECAAAECBEZWQIA0st72RoAAAQIECBAgQIBAGwsIkNq4c1SNAAEC\nBAgQIECAAIGRFRAgjay3vREgQIAAAQIECBAg0MYCAqQ27hxVI0CAAAECBAgQIEBgZAUESCPr\nbW8ECBAgQIAAAQIECLSxwNg2rpuqtZnA3NLNdWs0e7Nj8/PM2DI/vbd+zP7srN7cMiY9vj43\nPRJ7n+nLzdO7fGluemnFytz0LHF9/j7mln5Uv4w6ORYvXlwnh2QCBAgQIECAAIFmBOp/Gm2m\nNHkJECBAgAABAgQIECDQwQICpA7uPFUnQIAAAQIECBAgQGB4BQRIw+upNAIECBAgQIAAAQIE\nOlhAgNTBnafqBAgQIECAAAECBAgMr4AAaXg9lUaAAAECBAgQIECAQAcLCJA6uPNUnQABAgQI\nECBAgACB4RUQIA2vp9IIECBAgAABAgQIEOhgAQFSB3eeqhMgQIAAAQIECBAgMLwCAqTh9VQa\nAQIECBAgQIAAAQIdLDC2g+uu6sMsMLvnNXVKrH+49Gy7RX4Zq1flp/dNy08vp05+rC83T+/i\n/PTYuGf1mtwy0vLl+ekrVuenl1Pnlm6qm0cGAgQIECBAgACB9hJwBam9+kNtCBAgQIAAAQIE\nCBAYRQEB0iji2zUBAgQIECBAgAABAu0lUH/M1AjU99FHH02/+MUv0owZM9LBBx+cpk6dmrvX\nlStXZvmfeOKJtM8++6QDDjigmn/ZsmXptttuq76vvDjkkEPSuHHjsrd9fX3pzjvvTL///e/T\nHnvskWbPnl3J5jcBAgQIECBAgAABAgUWGPUA6corr0yXXXZZetWrXpUi4In3X/rSl9IWWwx8\nL8uNN96YLrroorTvvvumyZMnp8svvzwdc8wx6Ywzzsi68a677kou1mTCAAAkVElEQVQXXHBB\n2nLLLTfo1oMOOigLkCI4+sAHPpCefPLJ9IpXvCJ973vfSxE8nX766Rvk94YAAQIECBAgQIAA\ngeIJjGqAFFeOrrjiivTFL34x7bfffmndunVZ8HL11Vdnv/t3x/r169M3v/nNLO3EE0/Mkn/y\nk5+ks88+Ox133HFp1113Tffff3/ae++908UXX9x/8+x9BETLyzfgxz6mTJmSHnnkkfSOd7wj\nHX300Wn33XcfcBsrCRAgQIAAAQIECBAohsCoBkh33HFH2m677bLgKLjHjh2bjjjiiPSd73xn\nwABp0aJF2XC417zmL7Ot7b///llPxdWnSoCUF+j87Gc/S7F9BEexvPCFL8yG6d18880DBkil\nUinLV/vPQOtq0+N15Kn89E/zvhgCjRwnmypROcZGYl+bWtd22L7iVHFrhzq1ex0qVhW7dq9v\nO9WvYtdOdWrXulSsHGeN9VDFqeLW2FZyjYZXpa/od5bAqAZIMcxt++2330AsAqYFCxakuFo0\nZsyGc0jEsLn+Q+FuueWW1NvbWw1u4grShAkT0llnnZXuvffetOeee6ZTTz21up/YZ+yjdon3\nTz/9dO2q7PUJJ5yQ7r777ur6F7/4xVk5Tz31VHVdvRfN5K1XlvTOEhipvl+1qs7U6Z3FNiK1\nXbFiRYofS+MCI3U8N16j9s850N+V9q/16NZw6dKlo1uBDtv7s88+m+LH0rjASJ/LYtRSfKa1\ndJbAqAZIcZButtlmG4hNmzYtO5CWLFky6H1IlQ0eeOCBdOmll6aTTjopzZo1K8UEDVHmNtts\nk972trdl9xhde+216UMf+lD61re+lSZOnJgFX/33Ge/vu+++SrHV33ElKq5qVZaYRCIO8spk\nD5X1A/2Obwzifqfa7QfKZ133CjRynGxq6+MY6+np2ejLhE0tt1u3j/+/YRZfvsQXK5bGBNau\nXdvQea+x0ro/VwwXj78Bcf6P/5+W+gLOZfWNanPE8RXHmXNZrUr916NxLvO3pn6/tGOOv3z6\nH4XaxQfI+A9eu1TexwQMectvf/vb7CrRoYcemk455ZQsa8x+d80112Sz4Y0fPz5bt9dee6V3\nvetdKa40HXvssdnJpLKPSvnxvjLkrrIufn/qU5+qfZvNfBf3TPWfAGKDTM+/iTIjyJs5c+ZA\nydYVQKCR42RTGRYvXpwF/hH8W+oLrF69OsVQ3Ti/xJcxlvoCEVQuXLiwofNe/dKKkSO81qxZ\nk53/+4+EKIZA862MLzjjg2S9v/3Nl9ydW8QH/RhtE+f+6dOnd2cjW9CqefPmjfi5LI5p54EW\ndGaLixzVACk+QD788MMbNDEur8cMdjFMbrAl7iP6+Mc/nt785jen97///dVs8U1dXD2qXXbZ\nZZe01VZbZbPWRXpcBYoTce0S++y/XW16UV7PLd2c29TZPUfmpmeJq1bn5+ldm5s+ZlX9oQK9\nDy7OLaM0YVJuepa4Lr8epSUbHiP9C5xbuqn/Ku8JECBAgAABAgS6QGDDm3xGuEE777xzdp9Q\n7RWde+65p3q/0EDVufXWW9M555yTTjvttA2Co8gbwVZcLXrssceqm8Y9R/Pnz6+WGQFT7KN2\niech9b8XqjbdawIECBAgQIAAAQIEiiEwqgHS4YcfnilfddVV2b09Dz74YLr++uuzabcr/DGN\n9w033JC9jWELF154YXr1q1+ddtpppxTPPKr8xLCZWBeXmy+55JL0zDPPZFeNvvKVr2RXpA47\n7LCsjJh4Yc6cOdlDYmMM7/e///1sKMRRRx1V2aXfBAgQIECAAAECBAgUVGBUh9jFMLrzzz8/\nnXvuuSmCpEmTJqXjjz8+HXzwwdXuiGAmpvA+8sgjs0Bp5cqVKabkjp/aJWati2cZffjDH07n\nnXdeeuMb35glxxWjL3/5y9VxzS9/+cvTW9/61mzihrgHKq4cfexjH0tx/5KFAAECBAgQIECA\nAIFiC4xqgBT08Ryj6667LsWNc3GvUP8b2SLYqSwnn3xyip+8ZY899kjf/va3s5sXIwAa6ObF\n97znPVk5ce/RSNxIn1dfaQQIECBAgAABAgQItI/AqAdIFYqYpns4l3qBT8xyVy/PcNZHWQQI\nECBAgAABAgQItL/AqN6D1P48akiAAAECBAgQIECAQJEEBEhF6m1tJUCAAAECBAgQIEAgV0CA\nlMsjkQABAgQIECBAgACBIgkIkIrU29pKgAABAgQIECBAgECuQNtM0pBbS4kjIjC753X5+5k8\nLj89UidPzs1Tenx+bnrafEZ+eqSuXp2f55Gn8tMjdf2aOnn816gDJJkAAQIECBAg0JUCriB1\nZbdqFAECBAgQIECAAAECQxEQIA1FzTYECBAgQIAAAQIECHSlgACpK7tVowgQIECAAAECBAgQ\nGIqAAGkoarYhQIAAAQIECBAgQKArBQRIXdmtGkWAAAECBAgQIECAwFAEBEhDUbMNAQIECBAg\nQIAAAQJdKSBA6spu1SgCBAgQIECAAAECBIYiIEAaipptCBAgQIAAAQIECBDoSgEBUld2q0YR\nIECAAAECBAgQIDAUgbFD2cg2nScwu+eo+pWeOC43T8+E8bnpWeLKFbl5eraenpueFi/KTy+n\nlhbk76NuAVmG9bnZ5pZuyE2XSIAAAQIECBAg0J0CriB1Z79qFQECBAgQIECAAAECQxAQIA0B\nzSYECBAgQIAAAQIECHSngACpO/tVqwgQIECAAAECBAgQGIKAAGkIaDYhQIAAAQIECBAgQKA7\nBQRI3dmvWkWAAAECBAgQIECAwBAEBEhDQLMJAQIECBAgQIAAAQLdKSBA6s5+1SoCBAgQIECA\nAAECBIYgIEAaAppNCBAgQIAAAQIECBDoTgEBUnf2q1YRIECAAAECBAgQIDAEgbFD2MYmbSgw\nu+fwOrUaXye9nLxqXW6e0vpSbnqWuKavTp6eOunr66SXkyeOy80z99n/zk2XSIAAAQIECBAg\nQGAwAVeQBpOxngABAgQIECBAgACBwgkIkArX5RpMgAABAgQIECBAgMBgAgKkwWSsJ0CAAAEC\nBAgQIECgcAICpMJ1uQYTIECAAAECBAgQIDCYgABpMBnrCRAgQIAAAQIECBAonIAAqXBdrsEE\nCBAgQIAAAQIECAwmIEAaTMZ6AgQIECBAgAABAgQKJyBAKlyXazABAgQIECBAgAABAoMJCJAG\nk7GeAAECBAgQIECAAIHCCYwtXIs7tMGzew6rU/MJ+ekTG4iFV/Xll7FmTX56ljquTp56ZZTq\nbF9OXrWufh45CBAgQIAAAQIECAxBoIFPzUMo1SYECBAgQIAAAQIECBDoQAEBUgd2mioTIECA\nAAECBAgQINAaAQFSa1yVSoAAAQIECBAgQIBABwoIkDqw01SZA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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8ADBBBAAAEE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\nWl+eTSMqkBIGzc3N3s1hE8/1qJJOe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s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\nQIAAAQIECEymwLQmSNGxQw89NF155ZUpLuyPCzaHX8gWN5Adb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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
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9wie++9t/zg\nBz/wLvO7+uqrRa9fHI6ZsgICCCCAAAIIIIAAAggUokD8JiRNWIL8kjSm+daTIjrj9bJly+Sj\nH/3okBHYc889vbNEiUvuNNja2ip61Zo+b9UWH1LZGN+kfYmd7tTUqVPl+eefl5KSEu+5R9qH\na6+91rvJSk+D6ZkkTVj0dJhp0ZkoNBvUWe900Uke9IFQP//5z+Wcc84Zsem7774rf/3rX+Wn\nP/3pQExvyNIka/j1igMFeIEAAggggAACCCCAQBEIuOJIJOBpvqPxNv0sP/7xj73f8X/0ox95\nV4vpSZfEorfYTJgwQU455RTvpMm8efNE50C49NJL5bTTThu4ncYWT9Q31u9pJ0grV6707hPS\n5EgXPT02ceJEOeCAA7z3++yzjzfLhN5o9f73v99bl+ofvWdp+P1DmjBt3LhR9BRcoo3E9jqD\nhd73pDeDfe973/Nm09MHTOmMeoo4eOnq6vISp8HrtD2dItB0tkmzVN12tDecDW6vkF8nnovV\n3d3t3TRXyPs61n3TY0rv0zMdd4k2Plb3qcTLFN/tH0JOY12KbXeujv8hwrrEp9u0LnX15iLx\nfbYt86Z/zlgkVm9/XEBsnvlzRhvo3nPo58PwRks7YsNXjXgf6rSXKWnf8by4ERvvXBGqrEoV\nGljvVpv/sORUbx8om+pF/6ypqUID653t5jEu2d47UDbVi9LVbalCO9b7Oda22I8T2Tb0covh\njZauaB++asT7Uut/4PafLVfsF1083PmrEW0PXuHnc2Bw+SBf6zS7+nmVy30M0sPUln6m66JW\n/L5gkhLvOZrqpcdWMS69vb0Ds68Fsf/633cs6FnsfF5id9NNN3kW+pyj4Yv+LOkcBHpf0skn\nn+xdqaaz1+lcA3o5XmKxxRPlxvrdx29KQ5vQiRT0LI4umnDoQ5/0IU+JD4iHH37Yi+lZJtuy\nbt06qasb+sucnnXS5Kijo2PEs5Q0cdIzRRdeeKGXkOlNXb/73e+8s1l6ed7ghGrbtm2iT+Ed\nvGgSp/dNacy0aILE4k9Af/D1i8UuYDvu7DVQAgEEcl2gEH7OC2EfgjpO+H3Bv3Sx/q6gf1DW\nPz4Et8Qvrwv4DJJY/wC1Y+/1thzboiddlixZ4t13pFeWDc8TbHFb/X7jaSdIegnc4sWL5dxz\nzxWdjEEHXU936V8GdPKGa665RvSyt+bmZmsf9KxP4q8wicKJ9zrN3/BFY/phpE/RPfHEE72w\nJj1f/vKXvaTtoIMOGthEpwS89dZbB97ri6VLl0p1dfWIxGtwIZ0ZTzPYwcnW4Divdwhooqln\nj9RTZxVhSS2gx6162WZnTF0DEQQQyBeBfH5Iuv5xUpOj4b+Q5It9kP3Uv3brZ3tDQ8PAH4iD\nbD+f2tq+fbt39Y/eY16Mi54FSZxECGL/NRWL+Dyjk6n+RNO4B8lvm7YZsW1xv+2kKpd2gvSp\nT31KzjvvPFm0aJGXROjZHH3okyZI+qRbnc1OEyU/iyZReine4EUTFP0PJtkPkmaNugy+qet9\n73uf92G+Zs2awdV4v7QPLqdBvdFLkzLT/Ur6n4O2nZjCfEilvBkQ0PHWBMnmObBBEb/Qvx7p\nvXmm466Iedh1BApKIJ9/zvVzXX+Zzed9COpgSpw5Uqsgf/kNav8y2Y7+H6hnAor1uNJ9D/QY\n8S6xs18ynMkxTmcWu0y2m8260k6Q9MyKzjp35ZVXev1KTMSgCYXOOpGYcMFPp3fffXd58MEH\nvb/C6AGki56VGn5fUqIunSFPF700b/Lkyd7rDRs2eM9DSsS8lfyDAAIIIIAAAggggECRCegk\nDYHfg5SFM0jjPWz2O05T9FATo0RylCiSTnKk2xx++OHepjornZ7af+ONN7yp/3QKwMSiD6DV\niSB00QkcDjnkEC9B27Rpk3efkl7up1OO6+QQLAgggAACCCCAAAIIFKuAd4ld/B4knckuqK+Y\nz3uQ8mlM0j6DlNg5vfb2kUce8R7WqpcPaXKkX3o9rt9FL2W74oorRJ+mq0mSXqd5/PHHe7Pk\nJerQG7V0em+9jE+Xiy66SP7rv/5LPv3pT3uXwenZpuuuu06S3bOUqIPvCCCAAAIIIIAAAggU\nvIB3id2oz3+MiicW8D1Po+pkmhuNKkHSWSh0au2XXnppRHP64NZvfOMbI9anWrHffvt5z1Ja\nv369N1348MkR9AGygxc9a6Vt6HXSeuN7tm/SGtw2rxFAAAEEEEAAAQQQyF2B+CV2AV/yppf1\nFdqSdoK0ZcsWOe6447z7hnRecp2xTmfn0skW7rjjDrn44ou9G/HOP//8tKwS9xT53UjPGHHW\nyK8W5RBAAAEEEEAAAQQKXUCf2Ncf8HOQsjGL3XiPU9oJ0m233SaaJOnzj/baa6+B/n/gAx+Q\nT37yk3L22WfLLbfcIukmSAMV8QIBBBBAAAEEEEAAAQTSF4ifPYoGnCC5AZ+xSh8l/S3STpBe\neOEFb6KEwcnR4Gb16bj6/CG9b0gnVWBBAAH/Aq3uEv+FC7BkW1ub92y1dM8oFxJFi3OkcXfc\nilJjXIOlMR9PrC8JGeuJ1Tca414wbOlLt4+Hbscvl7Yt7rY+SxEf/5XZ3Hr8PPDa7tpSc6yl\nrz7CXd0+CtmKWMYmvrmz6xRzJT4ebtn7vqnGOsLv2MZOJNTRbqxDg+6a9cYyrf1/MMY1aPvZ\nslagBeIz9toWp7neXKTMPjbSudVcR9jej/jc0uY6NBqfIMu4lPp4zmHIcr+L5bPGa9/HsSbx\nZ0+ZFtdmFt+41V1qqqIgYjpJQ9CX2AXdXhAD5eN/laHd0Om8dU77VEsips9TYEEAAQQQQAAB\nBBBAAIHgBCIBn0EqxATJkvaPHMwDDjhAHn30UVm+fPmIoBv/C8B3v/td0QfA7rLLLiPirEAA\nAQQQQAABBBBAAIHsCOjJuGh8Vrkgv2J62qrAlrTPIJ1xxhmikzPo84jOPPNMmTdvntTV1XmT\nNNx1113evUk6WQMLAggggAACCCCAAAIIBCegM8r1BzzttiZjhbaknSDps4qWLVsmp59+utx0\n001DPBobG2XRokXyxS9+cch63iCAAAIIIIAAAggggECWBfRsTuCTJpAgeaOqky888MADsmbN\nGnnllVdk06ZNMmvWLNl77729Kb+zPPRUjwACCCCAAAIIIIAAAskEgk6QivkSO72/6OWXX5an\nn35aJk2aJPPnz5cZM2Z4X8nGhnUIIIAAAggggAACCCAQrIAT8DxpTrEmSFvjUyuefPLJ8oc/\n/HMazYkTJ8rixYvl2GMzMKVpsMcNrSGAAAIIIIAAAgggUHgCmqxEA77krQDvQfI1i90ll1zi\nJUcf+chH5Nprr5XPfOYz3sNiTzvtNO/yusI7utgjBBBAAAEEEEAAAQTyT0DP6AT9lX9K5h77\nmqThZz/7mbS0tMjDDz8s4fCOTe677z7v7NE999wjX/7yl82tEEUAAQQQQAABBBBAAIHsCxTg\nJW/ZRxvagjVB0svrNm7cKAsXLhxIjrSKY445RkpLS+XNN98cWiPvEEAAAQRGLdDq/tHXtu3t\n7VJdXS1lZT6edO+rxsIs1NPTI2pVW1vLJEKWIdYHvKuVPsuwMJeIZbesvxKJlPm68MbYTmTa\nFGNcg06TZQxKQtY6ok32Mk6/+Tfp0hdfs7bjtncbyyztuMf7/bGqqspYjmCGBHSChkjAl9gF\nfM9ThqSM1Vg/DTo6OrwKGhoahlRUUlIieh/SO++8M2Q9bxBAAAEEEEAAAQQQQGAcBDTnNee9\n49Cp/GvSmiDpX5R0CYVG/iVC10Uitr/I5B8KPUYAAQQQQAABBBBAIC8FYgH3ugATMmuCFDAx\nzSGAAAIIIIAAAggggMAoBZzAn4MU8CV9o3RJZzPfCdL69etl5cqVQ+rWs0d6j9Lw9Vpor732\nGlKWNwgggAACCCCAAAIIIJBFAT2bwxmkMQP7TpCuvPJK0a/hy9q1a+U973nP8NWiD5ZlQQAB\nBBBAAAEEEEAAgQAFAn8OUoD7FlBT1gRJZ/5hGu+ARoNmEEAAAQQQQAABBBAYi0DQ5yiCbm8s\nNj63tSZITU1NsmjRIp/VUQwBBBBAAAEEEEAAAQTGRYBL7DLCPvYJ/Yd1Qy+t+8tf/jJsLW8R\nQAABBBBAAAEEEEAg6wI6SUOQX1LEkzQMHsw77rjDO6vU1tYm/f39XkgTo8SkDbqOe5AGi/Ea\nAQQQQAABBBBAAIEsC+gZpKAf3Br0pBBZJtTqrZfYDe+Dnh0644wzvOciHXjggbJs2TLZf//9\nRZ9W/tprr4k+QPaWW24ZvhnvEUAAAQQQQACBEQItzuEj1o1cYfl1ZfauIzcZtsbZZfqwNUPf\nRhsmDF0x2ndl5r6GN26x17y1w1zGsV8AVPJcu7kOjVaY+yp11dY6nEZzkcPqTzQXiEdb3Qet\nZSiQhkDQCUsB3oNk/wkbNh733XeflwS9+eab8vjjj8t73/teOfHEE+Wll16SFStWyOTJk5M+\nVHZYNbxFAAEEEEAAAQQQQACBTAok7kHSJCmoLxIkkddff10OOuggmTFjhjec++23nzz11FPe\n69mzZ8t3vvMdueSSSzI51NSFAAIIIIAAAggggAACfgSCvP8o0ZaffuVRmbTPIDU2NkplZeXA\nLuozkJ577rmB9/Pnzxe9N2nNmjUD63iBAAIIIIAAAggggAACAQgEdeYo0Q5nkETmzJkjTz75\npKxfv94bYb3EbtWqVfL222977/UyO70PqbS0NIAjgCYQQAABBBBAAAEEEEDAE9AzOrGAv0iQ\nRD7/+c97Z5D23HNPefTRR+VjH/uYVFdXy6c//Wm5+uqrZeHChd4leHovEgsCCCCAAAIIIIAA\nAggEJ+DGz+wE+SUkSCITJ06U3/72t6L3HunMdXrJnc5a9/zzz8s3v/lNWb16tXz1q18N7iig\nJQQQQAABBBBAAAEEENghoAlL0F8FZm+Z3zH53n7oQx/yzh4lnnV06qmnyoIFC7x7kfbZZx/Z\nZZddkm/IWgQQQAABBBBAAAEEEMiOgCZGeoldkIte1ldgy6gSpITB5s2bvYfDJt7rWSVd9P4k\nLrFLqPAdAQQQQAABBBBAAIGABHhQ7Jih006Q9KzRV77yFbnzzjulq6srZQcSZ5dSFiCAAAII\nIIAAAggggAACmROIn0HS+4+CXOKpQcEtaSdIy5Ytk5tvvln2339/0Uvt6urqCg6FHUIAAQQQ\nQGC8BFqcwyxN+/ivu7rMUoeIU19vLONWVRvjGow2mutwIvbfnJz47Li2JdZUZS7i4y/mJVvL\njXWU9PcZ4xp02tZZy7hNzcYykaYGY1yDJeUVxjIlbWuNcQ06E2qsZdxe8z67bZutdex4Gmnq\nYks7fivhcFiqqixjmLoKIukKBH3Jm/3HPN09GPfyPj5lh/bxZz/7mey+++7eVN9M5T3UhncI\nIIAAAggggAACCIyrQAEmLEF7pp0gVVRUSENDA885CnqkaA8BBBBAAAEEEEAAAZOAJkc+zqia\nqkg7FvAlfWn3bxQblKS7zQknnCAvvviiPP300+luSnkEEEAAAQQQQAABBBDIooATT5KC/kp3\nd6LRqFx55ZWiE74NX7Zs2SJ333233HjjjfLqq68OD4stPmKDUaxI+wzSQQcdJLfeeqv3gNiT\nTjpJdtttN+/a0uFtf+1rXxu+ivcIIIAAAggggAACCCCQLQFNjoI+ozOKS/ouvPBCueGGG+SU\nU06RpqamAY0VK1Z48xy8//3vl1mzZsnFF18sv/71r+Woo47yytjiAxWN8UXaCZI+CPa6666T\nrVu3yu23356yeRKklDQEEEAAAQQQQAABBBDIjkAOTyunecQ555wjDz/8cNJ9/9KXviRnnXWW\nd/bIcRy56qqrZOHChfLaa6+JvrfFk1Y6ipVpX2L3P//zP6LZ2yWXXCJPPPGE12Ht9PCvUfSF\nTRBAAAEEEEAAAQQQQGCUAvrI1pL4GaQgv9I5Y3X66adLLBaT3//+9yP2cN26dbJ8+XI5++yz\nvWRIC2j5119/3Vtvi4+ocAwr0j6D9MILL4ie9rriiivG0CybIoAAAggggAACCCCAQCYFSuJn\nWQ79wMip899av0neeHfDmJqqriiTeXvvMaKOifW1I9alWqFXn82cOVP+/ve/jyiyatUqb51e\nWpdYpkyZIpWVlaJnnhLPWE0VP/DAAxObjfl72gnSBz/4QWltbR1zw1SAAAIIIIAAAggggAAC\nmRPQM0ilJSMvEAuLM+Z7k5z485WS1R2K1+130eQo1aIJkj4vS2fMHrw0NjbK+vXrJRKJGOOD\ntxnr67QTpM9//vPywx/+UPTmKj2LNHwnxtohtkcAAQQQQAABBBBAAIH0BWJRV5YuX5F0w5Fp\nU9JiKVd2b+9JWvekBv9nkFJWHg+UlZVJf3//iCK6rra21hofseEYVqSdID3++OMybdo0ufba\na73JGvS1zj6hN04NXvRSPBYEEEAAAQQQSE+g1V2a3gajLN1Se5xxS2fYX3GTFi5NunZgpbO1\ne+B1qhfR5upUoYH1pW+tHXid9EVJKOnqISvjf302Lt3bjWEvGPbxa9M/3jbWExI/U4yZ+7o8\noGPEuCM+g52dnT5LUixjAnn6HCTNKTQZ0ongNCFKLDoV+O677+49g9UUT5TPxHcfP+lDm9FO\n9vX1SUtLy9AA7xBAAAEEEEAAAQQQQGD8BMZhmm995lImlj333NM7S/TUU0/JEUcc4VWpt/Xo\nM5P22GMP76o1PcuUKp6JPiTqSDtB0qn39IsFAQQQQAABBBBAAAEEcksgnVnlMtLzDCVIEyZM\n8J6LdPnll8u8efO8M0aXXnqpnHbaaTJ9+nSvq/rcJFM8I/sTr2SslyNmqh/UgwACCCCAAAII\nIIAAAmMSiGcr+hykQL/G1OEhG3/nO9+R8vJymTRpkndLT2lpqVx//fUDZWzxgYJjfJH2GaQx\ntsfmCCCAAAIIIIAAAgggkC2BDJ3RyVb3tN45c+YMTNs9uJ2JEyfKkiVLRG/pCcfv+aurqxsc\nFlt8SOExvEn7DFJi5jqdvS7Zl85V3tzc7O34mWee6e3gGPrHpggggAACCCCAAAIIIOBHIJ4c\nOfFJGgL98jPviJ++DyqjE8ANT44Ghb0J4kzxwWVH8zrtM0gf+tCHZN999/WeaDt37lzR5yJp\nUvTGG2/IQw895F0vePDBB3uJ0eLFi71nJmkmqEkTCwIIIIAAAggggAACCGRPIFOTJvjuYR6c\nsfK9LzsLpp0gaUb34osvyo9+9KMRkzXoU3E1OTryyCPl7LPPFp0S/JhjjpEf//jHcsEFF6Tb\nN8ojgAACCCCAAAIIIICAXwFNVrJwRsfYfAEmSGlfYvfTn/7UO2uUbCY7vZ7w/PPPl5tvvtlz\n/PCHPyyHHnqoPPnkk0ZXgggggAACCCCAAAIIIJABgUAnaNDsqPAypLTPIK1bt854uVxDQ4Os\nXr16YHR1TnM9k8SCAAIIIIAAAggggAAC2RPQy+v0/qMgl8CnFQ9g59JOkA477DA577zzZOXK\nlbLXXnsN6aI+3fauu+7y7lFKBB599FHRbVgQQAABBBAYLtDiLBi+asR7p6F6xLrBK9ye/sFv\nk752ykuTrk+sdLv6Ei9Tf4/4KGN9eoaPCzfCljKRSOo+7ow49VXWMta/+nZssdYRjlmu5fHT\n11WrrO1InfkYkLB5fL0Gurcb23E7e4xxLxi17G+8UKv7oL0eSiCQTYGgT+gE3V427XbWnXaC\n9PGPf1wuu+wy+Zd/+RcvUdKJGvSptjpJg96XpPch/eEPf5BY/EPz6KOPlqefflq+973vBbAr\nNIEAAggggAACCCCAQJELRAPOWGIBtxfA8KadIOn845r0fPazn/WeZDu4j7vttpv84he/8CZp\nWBX/i9CyZcu8yRl04gYWBBBAAAEEEEAAAQQQyKJAPFcJehY7J4u7M15Vp50gaUc1SVq6dKls\n3LhRnnvuOWlra5PZs2fLfvvt551N0jK77LKLbN26VRynENl0D1kQQAABBBBAAAEEEMgxgaBP\n6ATdXgDco0qQEv3SZxsdccQRibdDvodCoSHveYMAAggggAACCCCAAAJZFrDfKpfZDhRjgvTu\nu+/KggULZP78+XLrrbfKokWL5JZbbrHCvvTSS9YyFEAAAQQQQAABBBBAAIEMCegldkHfE1SM\nCVJJSYnU1NRIRUWFN3I6IYO+Z0EAAQQQQAABBBBAAIEcE+AM0pgHxHqJ3ZQpU+Spp54aaOjM\nM88U/WJBAAEEEEAAAQQQQACBHBMI+oxO0O0FwG1NkFL1IRqNSuI+o0j8OQePPfaYrF271pva\nu6mpKdVmrEcAAQQQQAABBBBAAIFsCGiywhmkMctankaXvP4bbrhBpk+fLj09Ox6qdvrpp3sP\ng/3c5z4nu+66q6xYsSL5hqxFAAEEEEAAAQQQQACBrAnoPUiBfrmFdwop7TNIf/nLX7xnG73v\nfe+T7u5uLxm6++67RZ91tHDhQu/ZSJoo6fTfLAgggAACuSnQ4iywdMzHf3g1VcY6YrNmG+Ma\njByzv7XM9inmWVFj5rBX/4QH3za307XJHNdoTaW9zLZ+Sxkff9qN9BnraHWXGuOjDeqVIe3t\n7aIz1LKYBTZt2iR9fX2ityHwOBOzFdGABTiDlBHwtBOk+++/X6ZOnSrPP/+86AQO9957r9eR\na6+9VlpaWqS/v180QdJnINXW1makk1SCAAIIIIAAAggggAACNoF4hsQsdjYkazztS+xWrlzp\nTfmtyZEuDzzwgPfg2AMOOMB7v88++4gbP9W2atUq7z3/IIAAAggggAACCCCAQEACbvxMdaBf\nPq44CGjXM9VM2gmSTsDw6quveu3rpAzPPvus95ykxCnmhx9+2IvpWSYWBBBAAAEEEEAAAQQQ\nCEggnqsEev+Rnq3iHiSRo446ShYvXiznnnuud/+Rni065ZRTRK9d1skbrrnmGjnwwAO5hjmg\nnwOaQQABBBBAAAEEEEBgh4BeYhcNFkPPVhXYkvY9SJ/61KfkvPPOk0WLFnn3IF144YXe1N6a\nIF1yySXebHaaKLEggAACCCCAAAIIIIBAgAJ6tVss4IQl6HueAuBMO0HSe49uvPFGufLKK73u\nJSZi0Gci6QNl586dG0C3aQIBBBBAAAEEEEAAAQQGCzgSn+I74EvetM1CW9JOkBIAicQo8V6/\nkxwN1uA1AggggAACCCCAAAIBCwR9yVvACVkQmqNOkILoHG0ggAACCCCAAAIIIICATwHvEruA\nz+gE3JxPiTEVI0EaEx8bI4AAAggggAACCCCQKwJ6iV3AkzRIwPc8BUBNghQAMk0ggAACuSbQ\n6v4pJ7rU4hxm7UdZqNxYxtltujGuwWjDBGOZUCRijGvQbdtiLSPSbyzjNNYZ416wtMxYZl79\nvxrjGnS7+qxlJGruq4ifJ4FY3Cxj53WyImTvq3V/7L+gtboP2duhBAKFIBD0pAlBtxfAGJEg\nBYBMEwgggAACCCCAAAIIZF1A7wcKehY77kHK+rDSAAIIIIAAAggggAACCIxWoAATltFSjHY7\nziCNVo7tEEAAAQQQQAABBBDINYH4s0kDXYI+YxXAzpEgBYBMEwgggAACCCCAAAIIZF2AS+wy\nQkyClBFGKkEAAQQQQAABBBBAIAcEeA7SmAeBBGnMhFSAAAIIIIAAAggggEAuCMQnaQj8HqTC\nexASCVIuHMv0AQEEEEAAAQQQQACBsQporhL0tNtBtzdWIx/bkyD5QKIIAggggAACCCCAAAJ5\nIRALeJKGwM9YZX8USJCyb0wLCCCAAAIIIIAAAghkX2BcJmmwP6g5+zue2RZIkDLrSW0IIIAA\nAmkItLpL0yidftGenh5pb2+X2tpaqampSb+CHNyixTnM2iunqcFaxu0rNZZxJjYb417QNp1w\nJGKtI7LbNGsZycAtDvt95GvGdkrfeMcY94I+bn53124211Ph41ev+HFrWlrdJaYwsWIXCPqS\ntwz8fObakPn4Kc21LtMfBBBAAAEEEEAAAQQQSCoQ9CVvQbeXdKczu5IEKbOe1IYAAggggAAC\nCCCAwPgIxJMVN/B7kLjEbnwGm1YRQAABBBBAAAEEEEDALhAN+Jq3wsuPhDNI9sOMEggggAAC\nCCCAAAII5L6AXu4WDThj4RK73D8u6CECCCCAAAIIIIAAAkUpoCeP+gI+gxQJuL0ABpYzSAEg\n0wQCCCCAAAIIIIAAAlkX0Fwl6DM6hZcfcYld1g9UGkAAAQQQQAABBBBAIBABzVYCflCsBHxJ\nXwCOnEEKAJkmEEAAAQQQQAABBBDItoB3AikTDw5Lo6PxefPSKJ0fRYsqQYrFYtLb2yvbt29P\nOTpapru7W0pKSlKWIRC/vLWvz2NQTzfoU7l5NgCR+IMS9ct03OXZLmWtu/rzpwtWduJo/AGd\n+hBUPbZYUgv09/d7Qf3OcZXaiUh+CeTTsayfUYnP9vxSzkxv9bMn+N+Tgj6jQ4KUmaNlHGvR\nH1LTLxR6EGucBMk8SIkPO5unuZbiiOovsonjqjj2eOx7afoZHXvthVGD/uzpscViFkgY6XfT\ncXVY/fHmiuJRp7HOWsZt7zKWcSY3GeNe0DX/cuNMm2Kvw0fi7NQ3GOtxS8uMcQ06HW3GMu7m\nbca4BkPvbvj/7d0JmCVVeTDgc+menn2GgYEZQRGICqJGEAYVIURAZVFBjQtxjcadx7hL1PgE\n3GLcgnFBo6ICypZIorIJSQSXyOAaUSMqm7IMMwyzMWtP/fcr/9v2NlW3p7vvVm89z0zfW+fU\nqXPeU11dXy2nSvNcs+bi0jytzBAnUuN3cM6cOalWq7Vy1fm6irblllemZIWN44VuqnNJkyaU\n3Gj/hBaaROZ9D3hQ+qevv28SJUx80b32bWKfNPFi27pEpa4gRdAze/bstGDBjv/IxZWR+fPn\np76+vrZ2TKevfMOGDflVpPCMf6YdC8Q2FV5F292Ol65WSlwRiWCSVXm/xwH/3Llz08BA+UFs\neWm9myO2qbjSPWvWrDRv3rzebWiPt6zT9glxVSD27VGvdgRI3dTda9euTf39/Xkw2U31nqq6\nzpw5s6XbyLxd56YjT3rsVFW/suW4j6yyXa/hBAgQIECAAAECBAiMFhAgjRbxnQABAgQIECBA\ngACBygoIkCrb9RpOgAABAgQIECBAgMBoAQHSaBHfCRAgQIAAAQIECBCorIAAqbJdr+EECBAg\nQIAAAQIECIwWECCNFvGdAAECBAgQIECAAIHKCgiQKtv1Gk6AAAECBAgQIECAwGgBAdJoEd8J\nECBAgAABAgQIEKisQKVeFFvZXtZwAgQIdKjAstoJpTWr7TG/ME92z9rC9EisLZhVnGdu+Quv\ns62DxWXEevYpeaP8fWtKy6i/0bY4z7ZtxemRunlLaZ7s/pXFeTZuLU6vp2a1Wkme7SXpKS3P\nvlmaRwYCBAi0UsAVpFZqWxcBAgQIECBAgAABAh0tIEDq6O5ROQIECBAgQIAAAQIEWikgQGql\ntnURIECAAAECBAgQINDRAgKkju4elSNAgAABAgQIECBAoJUCAqRWalsXAQIECBAgQIAAAQId\nLSBA6ujuUTkCBAgQIECAAAECBFopIEBqpbZ1ESBAgAABAgQIECDQ0QICpI7uHpUjQIAAAQIE\nCBAgQKCVAgKkVmpbFwECBAgQIECAAAECHS3Q39G1UzkCBAgQmLDAstpx5cv0DRTmqS1ZVJie\nJw7MLM6TZcXp9dTaXruV5km79BXmyQ7cszA9EgcXzSnMk82oFaZH4vZ55ecUt5f8Ve3b8IDS\n9Qz87NbCPNmqtYXpkbh822WleUZnGBwcTKtXr06LFy8eneQ7AQIEKiVQvrevFIfGEiBAgAAB\nAgQIECBQZQEBUpV7X9sJECBAgAABAgQIEBghIEAaweELAQIECBAgQIAAAQJVFhAgVbn3tZ0A\nAQIECBAgQIAAgRECAqQRHL4QIECAAAECBAgQIFBlAQFSlXtf2wkQIECAAAECBAgQGCEgQBrB\n4QsBAgQIECBAgAABAlUWECBVufe1nQABAgQIECBAgACBEQICpBEcvhAgQIAAAQIECBAgUGWB\nknd+V5lG2wkQIDAxgWWzn1q4QG3JHoXpeeLgYGGebN78wvQ88cADSvPU1q8rzVOWIbvnnsIs\ntb6+wvRIzEramxewYUthOTdkX9ph+qZNm9Lq1avT/Pnz07x583aYTwIBAgQIEGgIuILUkPCT\nAAECBAgQIECAAIHKCwiQKr8JACBAgAABAgQIECBAoCEgQGpI+EmAAAECBAgQIECAQOUFBEiV\n3wQAECBAgAABAgQIECDQEBAgNST8JECAAAECBAgQIECg8gICpMpvAgAIECBAgAABAgQIEGgI\nCJAaEn4SIECAAAECBAgQIFB5AQFS5TcBAAQIECBAgAABAgQINAQESA0JPwkQIECAAAECBAgQ\nqLxAf+UFABAgMEbg8EXPGDNvzIy+vjGzhs/INm0e/nXcz7WZA+POH5q5aPehjzv6sH3W7B0l\nDc3f/JA5Q5/H+zDjjsHxZo+Yl82sjfg+3pe+/fcfb/Yf523d8sfPO/iUzZy1g5Q/zN5l7X2F\n6XniurXleWYU22f3bywvY1Ox2/XbvlZehhwECBAgQKDDBFxB6rAOUR0CBAgQIECAAAECBNon\nIEBqn701EyBAgAABAgQIECDQYQICpA7rENUhQIAAAQIECBAgQKB9AgKk9tlbMwECBAgQIECA\nAAECHSYgQOqwDlEdAgQIECBAgAABAgTaJyBAap+9NRMgQIAAAQIECBAg0GECAqQO6xDVIUCA\nAAECBAgQIECgfQICpPbZWzMBAgQIECBAgAABAh0mIEDqsA5RHQIECBAgQIAAAQIE2ifQ375V\nWzMBAtMhsKz25OJi+5r4tZ9Rfu6ktvu84vUs3rM4vZ6a/e72wjzLf/2ZwvRIXFY7tjTPrFtL\n6lpaQj3DtsHSXLUFxevJ7l1XWsYNW79RmicyrF69Os2dOzcNDAw0lV8mAgQIECBAoDmB8qOg\n5sqRiwABAgQIECBAgAABAl0vIEDq+i7UAAIECBAgQIAAAQIEpkpAgDRVksohQIAAAQIECBAg\nQKDrBQRIXd+FGkCAAAECBAgQIECAwFQJCJCmSlI5BAgQIECAAAECBAh0vYAAqeu7UAMIECBA\ngAABAgQIEJgqAQHSVEkqhwABAgQIECBAgACBrhcQIHV9F2oAAQIECBAgQIAAAQJTJSBAmipJ\n5RAgQIAAAQIECBAg0PUC/V3fAg0gQGCEwPLsqhHfu+nLihUrUpZlacmSJU1Xe3l2TdN5J5Nx\nWe3Y0sWzTdsK89R2nV2YHomHL3lucZ5txeuIhQcf+ODiMuqp2czJ7/77711duJ7s93cWpueJ\ntfIsaePGwkyt2gYKKyGRAAECBHpGwBWknulKDSFAgAABAgQIECBAYLICAqTJClqeAAECBAgQ\nIECAAIGeERAg9UxXaggBAgQIECBAgAABApMVECBNVtDyBAgQIECAAAECBAj0jIAAqWe6UkMI\nECBAgAABAgQIEJisgABpsoKWJ0CAAAECBAgQIECgZwQESD3TlRpCgAABAgQIECBAgMBkBQRI\nkxW0PAECBAgQIECAAAECPSMgQOqZrtQQAgQIECBAgAABAgQmKzD5V6lPtgaWJ0CAQDcIzJpd\nXstNW4vzDMwsTq+nZrvtXphn257zCtMjcZc1JfWo5+lfdW9xOevXF6fXU6+/+4LSPDIQIECA\nAIFuE3AFqdt6TH0JECBAgAABAgQIEJg2AQHStNEqmAABAgQIECBAgACBbhMQIHVbj6kvAQIE\nCBAgQIAAAQLTJiBAmjZaBRMgQIAAAQIECBAg0G0CAqRu6zH1JUCAAAECBAgQIEBg2gQESNNG\nq2ACBAgQIECAAAECBLpNQIDUbT2mvgQIECBAgAABAgQITJuAAGnaaBVMgAABAgQIECBAgEC3\nCXhRbLf1mPoSINAWgeUbvz7p9S6rHVtexor7CvPMuHdhYXokbnvwg0vzbN2n+IW0Gx+4pLSM\nQ458a2GeGbfeVZgeidnq1aV50oZNhXmWZ98sTJdIgAABAgQmIuAK0kS05CVAgAABAgQIECBA\noKcFBEg93b0aR4AAAQIECBAgQIDARAQESBPRkpcAAQIECBAgQIAAgZ4WECD1dPdqHAECBAgQ\nIECAAAECExEQIE1ES14CBAgQIECAAAECBHpaQIDU092rcQQIECBAgAABAgQITERAgDQRLXkJ\nECBAgAABAgQIEOhpAQFST3evxhEgQIAAAQIECBAgMBEBAdJEtOQlQIAAAQIECBAgQKCnBfp7\nunUaR4AAgQ4SWJ5dM+naLKsdW1pG34qVpXnK6nL4wlNKy0i1WnGegRnF6ZG6abA8T0mOZbWn\nlOSoJ88qqcvW7eVlzCg/p1grW8+8+aXr2T5/YWGeWlZe1+0zZxWWEYnbFxUfAsy48ebSMlKW\nFebJ7ru/MD1P3LapNE/Z9lpagAwECBCYgED53n4ChclKgAABAgQIECBAgACBbhYQIHVz76k7\nAQIECBAgQIAAAQJTKiBAmlJOhREgQIAAAQIECBAg0M0CAqRu7j11J0CAAAECBAgQIEBgSgWK\nn9Cc0lXtuLDbbrstffe730277bZbOuKII9K8efN2mHndunXpe9/73pj0Jz7xiWnGjJKHcMcs\nZQYBAgQIECBAgAABAgT+KND2AOncc89Nn/3sZ9PRRx+d7rjjjhTfP/axj6VFixb9sZbDPv3k\nJz9J73vf+9LixYuHzU3p8Y9/vABphIgvBAgQIECAAAECBAhMVKCtAVJcOTrnnHPSWWedlQ4+\n+OC0bdu29KpXvSpdeOGF+c/xGnPTTTelRzziEekTn/jEeMnmESBAgAABAgQIECBAYKcF2hog\nXX/99WmvvfbKg6NoQX9/fzr++OPTV77ylcIA6YADDiht8ODgYLrrrrtG5Nu8eXOK+RGI7WjK\n6u90iDzx07RjgTCKqcxzxyVUJ6WxPRVtd9XRKG5p4/eOVbHTVKQyngpFZbRKoNO21+H7qlrZ\n+8BahdSh69m+fXuKf53Wh63iirY3tpdWrdN6Ji/Q1gDpzjvvTHvvvfeIVkTAtHLlyvyXaZdd\nxo4hEVeQZs6cmU4//fT0y1/+Mj384Q9Pp5122phyooxjjjlmRNmHHXZY2meffdI999wzYv7o\nL6tWrRo9y/cdCMQzYfHPVC5Qtt2Vl1CdHKymv68ZT7+xNUydQKdur3GsYWpOoKrHChs2bBAg\nNbeJdFSutgZIcYVnwYIFI0Dmz5+fB0dr1qwZ8xxS/HLFMkuXLk2nnnpqOvLII9Mll1ySXvva\n16bzzjtvxOAOs2bNSieeeOKIsrds2ZI/pxRpO5riKtPAwED9BfElb4jfUQEVmR9nguJfDIzR\n19dXkVbvXDMbZ85iuzIVC2zatCnPUPQ7WlxC76dede8leSNjfxZX3cc7kTQVClfecs5UFNP2\nMuIK7tatW3Or8Gr39OTdnldahVp/yUm6GeV/n/pmlLe1747ifVJ27/rSuqYZY09kjlhoVnk9\n0rbZIxYZ78vJy9463uw/ztv8h33HH2eM/ZStLDmZN6/YIy9x/daxBY+Zs+O7VCLrVfdeNGaJ\nXp4Rv3+xn6rqsUIn7Hd6efuarrY1seearlWn/OB69CXXxvc5c+aMWXGMbnfxxRfno901DjYP\nOuig9OIXvzhdc8016eSTTx5aZuHChemjH/3o0Pf48KEPfSjNnTt3TOA1PFOcDYplq/qLPNyi\n6HOcEVm7dm3uOXt2+R+3orJ6PS0OZMNrRwOP9Hr7J9K+FStW5GfaWJWrrV69Ov/9a+wLy5eo\nZo4IusMq9lNFI6RWU0er2yFQtf1bHCtEkDDecV07/Fu9ztj3TNeJrFa3pUrrKzn1M70UMRLd\n6Euu8YsUO4+4jW70FFd14urR8AOC/fffP+2xxx4pbtczESBAgAABAgQIECBAYDICbQ2Q9ttv\nv/w5osZVo2jIjTfeOOZ5okYDb7nllvxq0e23396YlQdGcW/y6GeZhjL4QIAAAQIECBAgQIAA\ngSYF2hogHXfccXk1zz///Py5o9/+9rfpsssuSy984QuHqn/ttdemyy+/PP++7777png24eyz\nz85vmYirRp/85CfzK07HHnvs0DI+ECBAgAABAgQIECBAYGcE2voMUtxG9+53vzudccYZKYKk\nuE/zmc98ZjriiCOG2nL11VfnL5A94YQT8nlveMMb0plnnpme8Yxn5N/jFruPf/zjlb23dQjK\nBwIECBAgQIAAAQIEJi3Q1gApan/IIYekSy+9NN199935s0SjH2SLYGj4dOCBB6Yvf/nL+VDg\nMYJaDKhgIkCAAAECBAgQIECAwFQItD1AajRiyZIljY9N/YwBHkwECBAgQIAAAQIECBCYSoG2\nPoM0lQ1RFgECBAgQIECAAAECBCYrIECarKDlCRAgQIAAAQIECBDoGYGOucWuZ0Q1hAABAgQI\n7EBgeXblDlLaP3twcDAfIbZxC/uyGSeVV6pWnKW2cEFxhnpqtmZtaZ60eVNxnoGB4vR6am3P\nXYvzNPPS8zn3F5dRT81WrCzNIwMBAp0t4ApSZ/eP2hEgQIAAAQIECBAg0EIBAVILsa2KAAEC\nBAgQIECAAIHOFhAgdXb/qB0BAgQIECBAgAABAi0UECC1ENuqCBAgQIAAAQIECBDobAEBUmf3\nj9oRIECAAAECBAgQINBCAQFSC7GtigABAgQIECBAgACBzhYQIHV2/6gdAQIECBAgQIAAAQIt\nFBAgtRDbqggQIECAAAECBAgQ6GwBAVJn94/aESBAgAABAgQIECDQQoH+Fq7LqggQIECAAIEu\nEVi+9RulNV1WO64wT3bXqsL0PHFwsDRPtnFrYZ7a3OL0WDhbu6mwjNS/rji9nlrbc1Fpnuyg\nRxTmOXzv5xem54mbNxfmyVatL0yPxOXZFaV5ZCBAYHwBV5DGdzGXAAECBAgQIECAAIEKCgiQ\nKtjpmkyAAAECBAgQIECAwPgCAqTxXcwlQIAAAQIECBAgQKCCAgKkCna6JhMgQIAAAQIECBAg\nML6AAGl8F3MJECBAgAABAgQIEKiggACpgp2uyQQIECBAgAABAgQIjC8gQBrfxVwCBAgQIECA\nAAECBCooIECqYKdrMgECBAgQIECAAAEC4wsIkMZ3MZcAAQIECBAgQIAAgQoK9FewzZpMgAAB\nAgQIlAgsqx1XkqOePHtWYZ7a7rsVpkfi1v0fUJonm1krzDNw4+2F6ZFYW7CgOM/mTcXp9dTs\njrtL89zw+/NK88hAgEBnC7iC1Nn9o3YECBAgQIAAAQIECLRQQIDUQmyrIkCAAAECBAgQIECg\nswUESJ3dP2pHgAABAgQIECBAgEALBQRILcS2KgIECBAgQIAAAQIEOltAgNTZ/aN2BAgQIECA\nAAECBAi0UECA1EJsqyJAgAABAgQIECBAoLMFBEid3T9qR4AAAQIECBAgQIBACwUESC3EtioC\nBAgQIECAAAECBDpbQIDU2f2jdgQIECBAgAABAgQItFCgv4XrsioCBAgQINCRAstqTymvV3/5\nn8zanBmF5WT3by1Mj8Takt2K8+xSK07PCynPk82ZV1zOQx9SnN5EanbTb0tz/ej2L5Xm6bQM\nq1atSlu2bElLly5NtVq5dafVX30IECgWcAWp2EcqAQIECBAgQIAAAQIVEhAgVaizNZUAAQIE\nCBAgQIAAgWIBAVKxj1QCBAgQIECAAAECBCokIECqUGdrKgECBAgQIECAAAECxQICpGIfqQQI\nECBAgAABAgQIVEhAgFShztZUAgQIECBAgAABAgSKBQRIxT5SCRAgQIAAAQIECBCokIAAqUKd\nrakECBAgQIAAAQIECBQLCJCKfaQSIECAAAECBAgQIFAhgfLXglcIQ1MJECBAoJoCy7MrO6bh\ny2rHFdelb6A4vZ5amz+zPM+6dYV5sq2DhemRWFu0sDDP4KGPLkyPxEOOfGtpnl3WbyvM03f7\nrYXpkZit3VScZ1vxOmLhTtpOihsjlQCByQi4gjQZPcsSIECAAAECBAgQINBTAgKknupOjSFA\ngAABAgQIECBAYDICAqTJ6FmWAAECBAgQIECAAIGeEhAg9VR3agwBAgQIECBAgAABApMRECBN\nRs+yBAgQIECAAAECBAj0lIAAqae6U2MIECBAgAABAgQIEJiMgABpMnqWJUCAAAECBAgQIECg\npwQESD3VnRpDgAABAgQIECBAgMBkBARIk9GzLAECBAgQIECAAAECPSXQ31Ot0RgCBAgQINDl\nAsuzqwtbsKx2bGF6nrh9oDRPtmRJYZ7BXRcUpkfi4O7F51lnLv91aRm7rFpXmmd5dmVpHhkI\nECAwVQLFe7apWotyCBAgQIAAAQIECBAg0AUCAqQu6CRVJECAAAECBAgQIECgNQICpNY4WwsB\nAgQIECBAgAABAl0gIEDqgk5SRQIECBAgQIAAAQIEWiMgQGqNs7UQIECAAAECBAgQINAFAgKk\nLugkVSRAgAABAgQIECBAoDUCAqTWOFsLAQIECBAgQIAAAQJdICBA6oJOUkUCBAgQIECAAAEC\nBFojIEBqjbO1ECBAgAABAgQIECDQBQL9XVBHVSRAgAABAgT+v8Dy7JpSi2W140rzpPtvL8zT\n118rTI/Evv6S86wzB0rLqO3/oNI8h+/9/MI82fyFhemRWLv7zsI82X3rCtMjcXl2dWkeGQgQ\n6H6Bkj1b9zdQCwgQIECAAAECBAgQINCsgACpWSn5CBAgQIAAAQIECBDoeQEBUs93sQYSIECA\nAAECBAgQINCsgACpWSn5CBAgQIAAAQIECBDoeQEBUs93sQYSIECAAAECBAgQINCsgACpWSn5\nCBAgQIAAAQIECBDoeQEBUs93sQYSIECAAAECBAgQINCsgACpWSn5CBAgQIAAAQIECBDoeQEB\nUs93sQYSIECAAAECBAgQINCsQH+zGeUjQIAAAQIEekegtmBWcWPmzStOj9TB7cV5tg8Wp0fq\nurWlebKNmwvz1LZuLUzPE/v6ivP0DRSn11OX9Z9Ymqc2t7ic69dcWlqGDAQItFfAFaT2+ls7\nAQIECBAgQIAAAQIdJCBA6qDOUBUCBAgQIECAAAECBNorIEBqr7+1EyBAgAABAgQIECDQQQIC\npA7qDFUhQIAAAQIECBAgQKC9AgKk9vpbOwECBAgQIECAAAECHSQgQOqgzlAVAgQIECBAgAAB\nAgTaKyBAaq+/tRMgQIAAAQIECBAg0EECAqQO6gxVIUCAAAECBAgQIECgvQICpPb6WzsBAgQI\nECBAgAABAh0k0N9BdVEVAgQIECBAYAoElmdXT7iUwcHBtHr16rR48eIJL9sNCyyrHVtczXnz\nitPrqbUlS0rzbNl3t8I8Bz/p9ML0SOy7Z0txnu1ZcXqUsW5NaZ7slt+X5NlWkp7S8uya0jwy\nEOg2AVeQuq3H1JcAAQIECBAgQIAAgWkTECBNG62CCRAgQIAAAQIECBDoNgEBUrf1mPoSIECA\nAAECBAgQIDBtAgKkaaNVMAECBAgQIECAAAEC3SYgQOq2HlNfAgQIECBAgAABAgSmTUCANG20\nCiZAgAABAgQIECBAoNsEBEjd1mPqS4AAAQIECBAgQIDAtAlU6j1I8Y6HNWvWpLvvvnuHoNu3\nb0/33HNPqtVqO8wjIaUs+8M7GMJz7dq1SAoEwir+FW13BYtXKil+/2JiVd7tYbV582b7qhKq\nxr5q/fr1acOGDSW5q51sX1Xt/t/Z1pftr2NfFcdU69at29lVdPVyse9p/G3r6oZUrPKVCpD6\n+vrSwoUL05KCF72tXLkyLVq0KEVe044F4kAjAqPwnD179o4zSklbtmzJD8xiuzIVC6xYsSIP\nJot+R4tLqE5qvNBz7ty5aWBgoDqN3omWbtq0KX/56bz6S0Djn2nHAr3+otgdt1zKZATK9tdx\nrNDf35/mzJkzmdV07bKx39llFzdsdVsHVipA6rbOUV8CBAgQIDBdAstqx5UU3cSJwrnFAXpt\n991L1lG/I2HO3NI8adu24jx33VWcHqmzSk7mbdxaWkb2m9+W5vnxrz9TmkcGAgQ6W0BI29n9\no3YECBAgQIAAAQIECLRQQIDUQmyrIkCAAAECBAgQIECgswUESJ3dP2pHgAABAgQIECBAgEAL\nBQRILcS2KgIECBAgQIAAAQIEOltAgNTZ/aN2BAgQIECAAAECBAi0UECA1EJsqyJAgAABAgQI\nECBAoLMFBEid3T9qR4AAAQIECBAgQIBACwUESC3EtioCBAgQIECAAAECBDpbQIDU2f2jdgQI\nECBAgAABAgQItFCgv4XrsioCBAgQIEBgkgKHLzyltITBhz20NM/2ow4tztPEEcKM//1tYRnZ\nbXcUpv8hMSvP0z9QnGfbtuL0PHV7SZ7yeizPrs7LWLVqVdqyZUtaunRpqtVqJeVKJkCg2wRc\nQeq2HlNfAgQIECBAgAABAgSmTUCANG20CiZAgAABAgQIECBAoNsEBEjd1mPqS4AAAQIECBAg\nQIDAtAkIkKaNVsEECBAgQIAAAQIECHSbgACp23pMfQkQIECAAAECBAgQmDYBAdK00SqYAAEC\nBAgQIECAAIFuExAgdVuPqS8BAgQIECBAgAABAtMmIECaNloFEyBAgAABAgQIECDQbQICpG7r\nMfUlQIAAAQIECBAgQGDaBJp4T/a0rVvBBAgQIECgJQJPnH9yyXoGStJTqi2YWZonzZpVnKe/\niT+7W7cUlpEtWVqYniduGSzNM+Puu4vzrF1XnF5PzdasLcyzPLumMF0iAQIEOlHAFaRO7BV1\nIkCAAAECBAgQIECgLQICpLawWykBAgQIECBAgAABAp0oIEDqxF5RJwIECBAgQIAAAQIE2iIg\nQGoLu5USIECAAAECBAgQINCJAgKkTuwVdSJAgAABAgQIECBAoC0CAqS2sFspAQIECBAgQIAA\nAQKdKCBA6sReUScCBAgQIECAAAECBNoiIEBqC7uVEiBAgAABAgR/fvatAAAigElEQVQIECDQ\niQICpE7sFXUiQIAAAQIECBAgQKAtAk280rst9bJSAgQIVFJgWe3Y4nb3zSxOr6fWFi8szZM2\nbizMk61dV5j+h8S+kjy1kvRIzsrzzJtdmKe2cEFheiRmBz2iMM8ud/6uMD1PHNxemifbsKEw\nz/L1XytMb2fi4OBgWr16dVq8eHE7q2HdBAgQaLuAK0ht7wIVIECAAAECBAgQIECgUwQESJ3S\nE+pBgAABAgQIECBAgEDbBQRIbe8CFSBAgAABAgQIECBAoFMEBEid0hPqQYAAAQIECBAgQIBA\n2wUESG3vAhUgQIAAAQIECBAgQKBTBARIndIT6kGAAAECBAgQIECAQNsFBEht7wIVIECAAAEC\nBAgQIECgUwQESJ3SE+pBgAABAgQIECBAgEDbBQRIbe8CFSBAgAABAgQIECBAoFME+julIupB\ngACBbhdY1n9iYRNqC2cXpkdibcmexXlmDhSnR+r69eV5Fi0qzrN2c3F6nrqlMM/y7JrC9FYk\nbtq0Ka1evTrNnz8/zZs3rxWrtA4CBAgQ6HIBV5C6vANVnwABAgQIECBAgACBqRMQIE2dpZII\nECBAgAABAgQIEOhyAQFSl3eg6hMgQIAAAQIECBAgMHUCAqSps1QSAQIECBAgQIAAAQJdLiBA\n6vIOVH0CBAgQIECAAAECBKZOQIA0dZZKIkCAAAECBAgQIECgywUESF3egapPgAABAgQIECBA\ngMDUCQiQps5SSQQIECBAgAABAgQIdLmAAKnLO1D1CRAgQIAAAQIECBCYOoH+qStKSQQIEOhd\ngWW1J5U3bt6cwjzZvfcVpkdibcmexXl26StOr6dmW7aV5km33lmYp7bX7oXpeWL/jMI8h+/6\njML0SLz+vq+W5pGBAAECBAi0UsAVpFZqWxcBAgQIECBAgAABAh0tIEDq6O5ROQIECBAgQIAA\nAQIEWikgQGqltnURIECAAAECBAgQINDRAgKkju4elSNAgAABAgQIECBAoJUCAqRWalsXAQIE\nCBAgQIAAAQIdLSBA6ujuUTkCBAgQIECAAAECBFopIEBqpbZ1ESBAgAABAgQIECDQ0QICpI7u\nHpUjQIAAAQIECBAgQKCVAgKkVmpbFwECBAgQIECAAAECHS3Q39G1UzkCBAh0iMDy7Jstqcmy\n2vGF66kt2FiYHom1mTNK82TrNxXmye5YWZgeicuzK0vzyECAAAECBLpNwBWkbusx9SVAgAAB\nAgQIECBAYNoEBEjTRqtgAgQIECBAgAABAgS6TUCA1G09pr4ECBAgQIAAAQIECEybgABp2mgV\nTIAAAQIECBAgQIBAtwkIkLqtx9SXAAECBAgQIECAAIFpExAgTRutggkQIECAAAECBAgQ6DYB\nAVK39Zj6EiBAgAABAgQIECAwbQICpGmjVTABAgQIECBAgAABAt0mIEDqth5TXwIECBAgQIAA\nAQIEpk2gf9pKVjABAgQITFhgeXZFU8usXr06zZ07Nw0MDDSVXyYCBAgQIECgOQFXkJpzkosA\nAQIECBAgQIAAgQoICJAq0MmaSIAAAQIECBAgQIBAcwICpOac5CJAgAABAgQIECBAoAICAqQK\ndLImEiBAgAABAgQIECDQnIAAqTknuQgQIECAAAECBAgQqICAAKkCnayJBAgQIECAAAECBAg0\nJyBAas5JLgIECBAgQIAAAQIEKiAgQKpAJ2siAQIECBAgQIAAAQLNCQiQmnOSiwABAgQIECBA\ngACBCggIkCrQyZpIgAABAgQIECBAgEBzAgKk5pzkIkCAAAECBAgQIECgAgICpAp0siYSIECA\nAAECBAgQINCcgACpOSe5CBAgQIAAAQIECBCogIAAqQKdrIkECBAgQIAAAQIECDQnIEBqzkku\nAgQIECBAgAABAgQqICBAqkAnayIBAgQIECBAgAABAs0JCJCac5KLAAECBAgQIECAAIEKCAiQ\nKtDJmkiAAAECBAgQIECAQHMCAqTmnOQiQIAAAQIECBAgQKACAgKkCnSyJhIgQIAAAQIECBAg\n0JyAAKk5J7kIECBAgAABAgQIEKiAQEcESLfddlu64IIL0lVXXZXWr1/fNPvKlSvT5z//+TQ4\nONj0MjISIECAAAECBAgQIEBgRwJtD5DOPffc9MIXvjD9/Oc/TxdddFF69atfnVavXr2j+g7N\nz7Isvf/970/nnHOOAGlIxQcCBAgQIECAAAECBCYj0NYAKa4cRYBz1llnpTPPPDOdffbZaebM\nmenCCy8sbdMll1ySB1WlGWUgQIAAAQIECBAgQIBAkwJtDZCuv/76tNdee6WDDz44r25/f386\n/vjj0ze/+c3C6t98883pi1/8Yn61qTCjRAIECBAgQIAAAQIECExAoH8Ceac865133pn23nvv\nEeVGwBTPFm3fvj3tssvY+G3r1q3pjDPOSK94xSvGLDu8oLhN77TTThs+K82dOzdfZtWqVSPm\nD/+ybdu2/Ba/Wq02fLbPowQaz32tW7cu3X///aNSfR0uENtyeBVtd8PzV/lzY7tiVb4VxL4w\n9lfj7SfLl65Ojvj9iyn2U5s3b65Ow3eipXHremxTfv/K8eL3L6awcrxQ7BXbVBht3LixOGOP\npsa+p7Ef6tEm9mSz2hog3XXXXWnBggUjYOfPn59vSGvWrEmLFi0akRZf/uVf/iXtueee6elP\nf3r6wQ9+MCa9MWPLli3phhtuaHzNfx522GH5zj/SiqbGjq8oj7Q/CMQBbeOglkmxQNl2V7x0\ntVJZNdffceBhak7Avqo5p8jl9695K8cLzVtV9Vihqu1ufsvozJxtDZBmzJiRByzDaRp/8OfM\nmTN8dv75hz/8Ybr88svz2+vGJI6asWTJkvSzn/1sxNyPfvSjaeHChWnp0qUj5g//ElevIjDr\n6+sbPtvnUQIbNmxIcfUoPGfPnj0q1dfhAnGwEV7jBfzD8/mc0ooVK3KGOAliKhaIq+RxVXxg\nYKA4Y8VTN23alO677740b968/F/FOQqbHwdysV0tXry4MJ/EP1w5iuAojjVcQSreItauXZvi\nEYrxjuuKl+yN1Nj3uNLffX3Z1gApdsK33HLLCLX4RYoDyRisYfT06U9/Ov8F+8AHPpAnxVWm\nmN75znempz3taemoo47Kvzf+iwBs+BQbaOzIinZmjfSiPMPLrOrnhk/Dq6oOzbS7YdQwa2aZ\nquYJo7jNh1X5FmC7KjeKHI1tqeHV3FLVzNUwaphVU6G5VjeMGmbNLVXNXA2jhlnVFKra7m7v\n57YGSPvtt1+64oor8qtIcXYhphtvvHGHzxaddNJJI4YAv+OOO/L8Bx54YNptt926vS/UnwAB\nAgQIECBAgACBNgu0NUA67rjj0qc+9al0/vnn5+9CiqtJl112WXr7298+xHLttdfmtyedcMIJ\n+XNHQwn1D/EMUuR/wQte4DaT4TA+EyBAgAABAgQIECCwUwJtDZDiNrp3v/vd+ah0ESTFsyzP\nfOYz0xFHHDHUmKuvvjrFlaIIkEwECBAgQIAAAQIECBCYToG2BkjRsEMOOSRdeuml6e677057\n7LHHmAfZ4gWyO5oOPfTQdN111+0o2XwCBAgQIECAAAECBAhMSKDtAVKjtjESTCumT3ziE+kr\nX/nKDlcVo9LE81AeqtshUZ7QGDI3Rvsz4l+xVbz/IP41nrMrzl3t1MbwwkZmK98OYsTPGHjG\n6EjFVvG7F1b2VcVOkdp4D9LoAY7Kl6xejjhWCK+wcrxQ3P/x+xdGVT1WiLugRr+Xs1hMaicI\n1Oq/4FknVKQVdYhhqWOUvKIpOOzsioT+kBbDrX/pS19Kr3vd69LjH//48gUqnsN21dwGENtT\n/DH95Cc/2dwCFc5lm2qu8+N9eB/+8IfTqaeeOuY51uZKqFYu21Vz/R2PB/z85z9P5557rpNf\nJWSxTcVU5WOrGEjMK1FKNpQOS+6YK0itcImX0MY/0+QF4mpI3BYZ7zXYe++9J1+gEgjUBe69\n994UZ2ZtUzaHqRKIg9jYV8U+y3Y1VarKWb9+fb5dPeABDzBIlM2BQA8K7NKDbdIkAgQIECBA\ngAABAgQI7JSAAGmn2CxEgAABAgQIECBAgEAvClTqFrte7MB2tWmfffZJxxxzTGrV4Brtaqf1\ntlbgCU94Qv4MUmvXam29LLDnnnvm+6p99923l5upbS0WeMxjHpPfsm+QlBbDWx2BFglUapCG\nFplaDQECBAgQIECAAAECXSrgFrsu7TjVJkCAAAECBAgQIEBg6gUESFNvqkQCBAgQIECAAAEC\nBLpUwDNIXdpxU1HteC/Ud77znRQ/H/vYx6Z4rqhouv/++9N3v/vdFC89e+QjH5niHuzhU5S1\nYcOG4bPSwx/+8PSgBz0onxcvl/3xj3+cvzviwAMPTMuWLRuR15fuF9iZPo7t6brrrstfInjE\nEUekvfbaawgits3vfe97Q98bH574xCfmL2gsS2/k97O7BSa6r4qXw/7v//5vvr+J5yRje5k5\nc+YQQqTHdvWb3/wmPepRj0qPfvSjx7xw97bbbsv3d/H+ktgu582bN7S8D70hMNE+LvsbeN99\n9+XbTLxv8aijjhoxrLx9VW9sM1pRHQHPIFWnr0e09Oabb04ve9nL0v7775/vxCO4ec973pMe\n97jHjcjX+HLFFVekD37wg/nBRLz7KAKlpz71qenNb35zniUOjJ/85CfnD63G+0Ya0yte8Yp8\nfqS/6lWvSnfeeWc68sgj88AsDlre+MY3NrL62eUCO9PHf/d3f5e+//3v5wcTsU3eeuut+XbY\nePnwt7/97fTOd74zLV68eITOOeeck29rZekjFvKlKwUmuq9auXJl+uu//us8IIrAJwKhCG4+\n/elPpwULFuTv2frbv/3bFOXGSZr/+Z//Sbvuumv6/Oc/PxQkxcs/P/vZz6ajjz46PyG0efPm\n9LGPfSwtWrSoKw1VeqzARPu47G9gBNvx9zDeixRB+be+9a30whe+MP3VX/1VvnL7qrF9YA6B\njhaov+HYVEGBl7/85dlHP/rRrH4mNW/9F77whew5z3nO0PfhJPUD3+x5z3tedtFFFw3Nru/8\ns3qgk9100035vPrBRv69fnAylGf4hy9/+ct5GfWX6+Wzb7nllqx+hi375S9/OTybz10sMNE+\njr7/sz/7s6z+Es+hVv/93/99vp00ZtQPWrPXvOY1ja9jfpalj1nAjK4TmMi+Khr3qU99Knv1\nq1891M76Wf/s+OOPzz7zmc/k877+9a9n9ZM72T333JN/37RpU/79qquuyr/Xg/SsfvIm+9GP\nfpR/r7+4OKufTMrLzWf4r+sFJtrHzfwNfNOb3pTVA+8hm3pgntVPGmb1q0n5PPuqIRofCHSF\ngGeQOjp8nZ7KrVq1Kv3iF79IJ598cqrVavlK4mpQ3OoUb50fPd177735mdYnPelJQ0mHHHJI\n/jmWiakeKOVn+Xfffff8++j/4uxZLD937tw86cEPfnB+m943v/nN0Vl971KBifbx6tWr86uY\nMQxzY4rt6q677kr1vWc+K7arAw44oJE85mdZ+pgFzOgqgYnuq6JxcYX7RS960VA7Z8+eneKW\n3sa+6qtf/Wr6i7/4i6GrknHrXVyRbFy1vP766/PbPA8++OC8jLgiXg+wkn3VEGnXf5hoH5f9\nDYxtK66Ex10SjSluW4/tatasWfks+6qGjJ8EukPgj/dCdUd91XIKBOIANKbhz3pEYDMwMJBW\nrFiRHvGIR4xYS9zeNPpWuGuuuSZ/ZqRx8PrrX/86v+XpIx/5SH77XNyKEgcp9SsEeVlxa93w\n9TXWH+sz9YbARPs4buccfUtnbFfx3FojcI+DijiAPf3001P9ilOedtpppw3d21+W3huy1W3F\nRPdVITU8OIrvcXBbvxqUXvva18bXFM+dxL7oi1/8YvrhD3+Y3zb3ghe8ID3kIQ/J02M73nvv\nvfPPjf8if9y6F88uee9NQ6V7f060j8v+BtbviMj/HsZ+K25Fj1uFDzrooPSSl7wkf1YypOyr\nund7UfNqCriCVMF+jz8OcdA5/KHlYJg/f36Ks/plU9xrHffzP//5zx96UeyvfvWr/EDkYQ97\nWHrLW96SH2C84x3vyO//37ZtW35wEff/D5/iexy8mLpfYCr6+MILL0w/+clP0t/8zd/kIPFQ\ncxwgx4Hp05/+9Py5kth240C3fqtmPrhIUXr3q2rBZPdVW7ZsSfXbNlNcsT7llFNSPGS/cePG\nPDiKAWPiecjYhl75ylemOMiNKb6P3lfFvjGCozVr1uR5/NfdApPt49F/A2MfFVeK4m9fBEmH\nHnpoqt+ymV7/+tfn203Zvqy7NdWeQG8KuILUm/1a2KoZM2akOKAdPcVD9nF7StH005/+ND+b\nf8wxx+S3RzXyxkFIHEA0HmKOKwNxVSkOeuNznHUdvc743rjlrlGOn90p0NfXN6k+jgfkzz//\n/PTe97536Ja6eLD+4osvTjGKWFzdjCnOyr74xS9OcaUpgqai9LiF1NTdApPZV8VIYjEYQ/ys\nP2+Zn8mvP2+Ug8S2FfNiitvtnvWsZ6X6M3Tp7W9/e55vvH1V5C3bP0YeU+cLjLddNfq8rI/H\n+xsYy8YIri996UtT/VneHOCwww5L9ecn81vv4m+gfVXnbxdqSGC4gCtIwzUq8jluF4hgKM6m\nDp/iQCJG4NnRFM+YvOENb8ifXYozZcNvNVm4cOFQcNRYPu7pjzPAcUYtDnLjLNrwKda3dOnS\n4bN87lKBne3jCKrjlpQIpD/0oQ+lJzzhCUMCUWZsH43gKBJi1MU99thjaLsqSh8qyIeuFdjZ\nfVWc0Y+D0zhw/fjHPz70vFFcCYor53/+538+ZBLbWeyrfve73+XzYp3j7avi5M/oq+5DhfjQ\nVQI728c7+hsY+6SYYtTDxhSvwogrkbFdle3LGsv4SYBA5wgIkDqnL1pWkwc+8IEpHjy+8cYb\nh9YZgzbEwero54QaGf7rv/4rvetd70qve93r8ttRGvMbP9/2trelSy65pPE1/xm3SzXKiwPb\n4euLDDEgxOh7/UcU4EtXCexMH7/73e/Ob8OsjzyWGgN/NBodtzzF1aLbb7+9MSsPjOqjj+Xb\nTVn60EI+dK3Azuyr6qMi5sFRvH8thuaOkzfDp/322y+/jW74vN/+9rf5bXgxL9LjebfGFYWY\nF/su+6qQ6I1pZ/q46G/gvvvum8PErXuNKfZTcRIw0uyrGip+EugeAQFS9/TVlNU0DhjinUUx\nwk48yxG3ncQ7P2KkpsaZsGuvvTZdfvnl+TpjJKl/+Id/yM+6xs4+Ap/Gv8YzRHFwG++ViAdR\n450h//qv/5ofZDRuN4jbWK6++uo8KIoRyiI9ng848cQTp6xdCmqvQDN9HLfRNQLl2L5im4gH\nmeOMfWObip9xhTO2tbiv/+yzz86fjYurkZ/85CfzK5XHHntsaXp7Nax9KgSa2VfFA/GxXTWu\n+nz4wx/Ot59nP/vZ+T6osV3Fe49iOvXUU9PXvva1dMMNN+T54lmROFkTtw3HdNxxx+U/o8w4\naRTB02WXXZa/0yZP8F/XCzTTx8P3VWV/A+NEYFyVPOuss1LkjWfVPve5z6UYoTMGPSrbl3U9\nqAYQ6EEBL4rtwU5tpkkxGMMZZ5yRH5TGbSPxQsUYVKHxcHJcLYqhSyNwOu+88/JBGcYrN0YX\nO+mkk/IHn+NqwHXXXZffEhVlxtWmCLoaUzxnEkFU3P8dZ2PjYfu4T9vUOwJlfRxvl4+hcGOA\nj3hRcQzuMd505ZVX5s97xJn8M888c2iI5rhKFc+77bPPPvliZenjlW1edwmU7asaZ/bjNs2Y\nnvvc547bwBh2OW7jjOmCCy7ID2DjZE0MAx4vlh3+zFqMehf7x7gNOdIjLZ4vMfWOQFkfD99X\nNfM3MAL097///flL1OOZzPgbF/uuCI5isq/KGfxHoGsEBEhd01XTU9G4BSB25lM1WEI8qBp/\nKOJN4nHf9egprhrFOuMecFNvCkxHH8czJRFYj75dqiFYlt7I52f3Ckz1viquUsZ2E2f5x9tX\nhVTcrhdX1Yc/b9m9gmo+nsBU93EE1XFXRjx3O95kXzWeinkEOk9AgNR5faJGBAgQIECAAAEC\nBAi0ScAzSG2Ct1oCBAgQIECAAAECBDpPQIDUeX2iRgQIECBAgAABAgQItElAgNQmeKslQIAA\nAQIECBAgQKDzBARIndcnakSAAAECBAgQIECAQJsEBEhtgrdaAgQIECBAgAABAgQ6T6C/86qk\nRgQIEOgNgRjutzGM8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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# joint posterior\n",
    "\n",
    "dfChain <- data.frame(konPosterior=chain[-(1:burnIn),1], \n",
    "                      koffPosterior=chain[-(1:burnIn),2],\n",
    "                      sigmaPosterior=chain[-(1:burnIn),3] )\n",
    "\n",
    "\n",
    "ggplot(dfChain, aes(x=konPosterior, y=koffPosterior) ) +\n",
    "  geom_bin2d(bins = 70) +\n",
    "  scale_fill_continuous(type = \"viridis\") +\n",
    "  theme_bw()\n",
    "\n",
    "ggplot(dfChain, aes(x=konPosterior, y=sigmaPosterior) ) +\n",
    "  geom_bin2d(bins = 70) +\n",
    "  scale_fill_continuous(type = \"viridis\") +\n",
    "  theme_bw()\n",
    "\n",
    "ggplot(dfChain, aes(x=koffPosterior, y=sigmaPosterior) ) +\n",
    "  geom_bin2d(bins = 70) +\n",
    "  scale_fill_continuous(type = \"viridis\") +\n",
    "  theme_bw()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem set\n",
    "\n",
    "The chemical reaction we simulated is mathematically identical to \n",
    "\n",
    "$$\\frac{dx}{dt} = \\frac{1}{\\tau}\\left( K_D -  x \\right)$$\n",
    "\n",
    "where $\\tau$ is the timescale of the reaction and $K_D$ is the equilibrium constant. \n",
    "\n",
    "In this problem, we will MCMC to fit the simulated data to discover the values of paramaters ``KD``, ``tau`` and ``sigma`` (the same as above, the standard deviation of the observational noise).\n",
    "\n",
    "To perform MCMC, we must choose priors. We make the simplest assumption and use flat priors, subject to non-negativity (we require KD>0, tau>0 and sigma>0). \n",
    "\n",
    "## 1. Change of variables\n",
    "\n",
    "Show that the chemical reaction with $K_D$ and $\\tau$ is identical to the first one with $k_{\\rm on}$ and $k_{\\rm off}$. What is the relationship between the two sets of parameters?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Flat priors in KD and Tau\n",
    "\n",
    "Modify the code above to perform MCMC on the same data, but with $K_D$ and $\\tau$ (as well as $\\sigma$) as the parameters to infer. \n",
    "\n",
    "You may use a separate notebook if that is easier to organize."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Comparison\n",
    "\n",
    "Take the chain representing the posterior (minus the burn-in period) and convert it to $k_{\\rm on}$ and $k_{\\rm off}$ using the equations you found in Part 1. Plot the joint posterior distributions.\n",
    "\n",
    "How does this compare to the posteriors of $k_{\\rm on}$ and $k_{\\rm off}$ that resulted from assuming flat priors in $k_{\\rm on}$ and $k_{\\rm off}$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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   "language": "R",
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   "mimetype": "text/x-r-source",
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