{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Bayesian Test for Cointegration\n",
    "\n",
    "## R notebook implementation\n",
    "\n",
    "The code in this notebook is adapted from the original MATLAB implementation by Chris Bracegirdle for the paper [*Bayesian Conditional Cointegration*](http://icml.cc/2012/papers/570.pdf) presented at [*ICML 2012*](http://icml.cc/2012/)\n",
    "\n",
    "<a class=\"typeform-share button\" href=\"https://bayesiancointegration.typeform.com/to/gRS0pq\" data-mode=\"popup\" style=\"display:inline-block;text-decoration:none;background-color:#267DDD;color:white;cursor:pointer;font-family:Helvetica,Arial,sans-serif;font-size:20px;line-height:50px;text-align:center;margin:0;height:50px;padding:0px 33px;border-radius:25px;max-width:100%;white-space:nowrap;overflow:hidden;text-overflow:ellipsis;font-weight:bold;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;\" target=\"_blank\">Contact me</a><script>(function(){var qs,js,q,s,d=document,gi=d.getElementById,ce=d.createElement,gt=d.getElementsByTagName,id=\"typef_orm_share\",b=\"https://s3-eu-west-1.amazonaws.com/share.typeform.com/\";if(!gi.call(d,id)){js=ce.call(d,\"script\");js.id=id;js.src=b+\"share.js\";q=gt.call(d,\"script\")[0];q.parentNode.insertBefore(js,q)}})()</script>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "The downloaded binary packages are in\n",
      "\t/var/folders/bc/dnbc_47x6j7036ft8dp3bckh0000gn/T//Rtmp9bibIM/downloaded_packages\n",
      "\n",
      "\n",
      "Bayesian Cointegration \n",
      "Implementation of a Bayesian test for cointegration\n",
      "\n",
      "Written by Chris Bracegirdle\n",
      "(c) Chris Bracegirdle 2015. All rights reserved."
     ]
    }
   ],
   "source": [
    "install.packages(c(\"tseries\",\"pROC\"))\n",
    "options(repr.plot.width=4, repr.plot.height=4)\n",
    "\n",
    "cat(\"\n",
    "\n",
    "Bayesian Cointegration \n",
    "Implementation of a Bayesian test for cointegration\n",
    "\n",
    "Written by Chris Bracegirdle\n",
    "(c) Chris Bracegirdle 2015. All rights reserved.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a rather contrived function to randomly generate two time series, x and y, after making a random decision as to whether they are cointegrated, and generating according to the corresponding generating function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "GenerateData <- function(T) {\n",
    "    cointegrated <- runif(1) > 0.5\n",
    "    phi <- if(cointegrated) runif(1) * 2 - 1 else 1\n",
    "\n",
    "    std_eta <- exp(rnorm(1))\n",
    "    std_x <- exp(rnorm(1))\n",
    "    intercept <- exp(rnorm(1, sd=5))\n",
    "    slope <- exp(rnorm(1, mean=1, sd=5))\n",
    "\n",
    "    epsilon <- double(length=T)\n",
    "    x <- double(length=T)\n",
    "    y <- double(length=T)\n",
    "    epsilon[1] <- rnorm(1, sd=std_eta)\n",
    "    x[1] <- rnorm(1, sd=std_x)\n",
    "    y[1] <- intercept + slope * x[1] + epsilon[1]\n",
    "    for (t in 2:T){\n",
    "        epsilon[t] <- phi * epsilon[t-1] + rnorm(1, sd=std_eta)\n",
    "        x[t] <- x[t-1] + rnorm(1, sd=std_x)\n",
    "        y[t] <- intercept + slope * x[t] + epsilon[t]\n",
    "    }\n",
    "    return(list(\"cointegrated\" = cointegrated, \"x\" = x, \"y\" = y))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what some randomly-generated data look like. Give it a whirl!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>$cointegrated</strong> = FALSE"
      ],
      "text/latex": [
       "\\textbf{\\$cointegrated} = FALSE"
      ],
      "text/markdown": [
       "**$cointegrated** = FALSE"
      ],
      "text/plain": [
       "$cointegrated\n",
       "[1] FALSE\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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jUbTdp2ZdN2a3Wqjfj/hHsb+lN0IaqW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FQc3/Sw3hBjEdhAesKujwTnW4Sl6glppO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\nAAQgAAEIQAACEIAABCAAAQiUh8D/Az5CKMlmo7+3AAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gendata = GenerateData(1000)\n",
    "par(cex.axis=0.7, cex.lab=0.7, cex.main=0.7, cex.sub=0.7)\n",
    "plot(gendata$x, type='l', col='blue', ylim=range(gendata$x, gendata$y), ylab='')\n",
    "par(new=T); plot(gendata$y, type='l', col='green', axes=F, ylab=''); par(new=F)\n",
    "gendata[names(gendata)=='cointegrated']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "LinearRegression <- function(x,y) {\n",
    "    slope <- cor(x, y) * (sd(y) / sd(x))\n",
    "    intercept <- mean(y) - (slope * mean(x))\n",
    "    std_eta = sd( y - intercept - slope * x)\n",
    "    return(list(\"slope\"=slope, \"intercept\"=intercept, \"std_eta\"=std_eta))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$slope</dt>\n",
       "\t\t<dd>3.07897265732507</dd>\n",
       "\t<dt>$intercept</dt>\n",
       "\t\t<dd>-24.1198791434192</dd>\n",
       "\t<dt>$std_eta</dt>\n",
       "\t\t<dd>21.3009305364026</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$slope] 3.07897265732507\n",
       "\\item[\\$intercept] -24.1198791434192\n",
       "\\item[\\$std\\_eta] 21.3009305364026\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$slope\n",
       ":   3.07897265732507\n",
       "$intercept\n",
       ":   -24.1198791434192\n",
       "$std_eta\n",
       ":   21.3009305364026\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$slope\n",
       "[1] 3.078973\n",
       "\n",
       "$intercept\n",
       "[1] -24.11988\n",
       "\n",
       "$std_eta\n",
       "[1] 21.30093\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "LinearRegression(gendata$x,gendata$y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is an implementation of logSumExp with support for a vector of indices (b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mylogsumexp <- function(a,b) {\n",
    "    #LOGSUMEXP Compute log(sum(exp(a).*b)) valid for large a\n",
    "    # example: mylogsumexp(c(-1000,-1001,-998),c(1,2,0.5))\n",
    "    amax <- max(Re(a))\n",
    "    if (amax == -Inf) {\n",
    "        amax=0\n",
    "    }\n",
    "    return(amax + log(as.complex(sum(exp(a-amax)*b))))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a key result from the paper: calculating the moments and area as derived in the paper"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "CalcLogAreaLog <- function(logf,logF) {\n",
    "    lncdf <- pnorm(c(1, -1), mean = Re(exp(logf)), sd = Re(exp(0.5*logF)), log.p = TRUE)\n",
    "    logarea <- Re(mylogsumexp(lncdf, c(1, -1))-log(2))\n",
    "    return(logarea)\n",
    "}\n",
    "CalcMomentsLog <- function(logf,logF,logarea) {\n",
    "    lnpdf <- dnorm(c(1,-1), mean = Re(exp(logf)), sd = Re(exp(0.5*logF)), log = TRUE)\n",
    "    logmoment1 <- mylogsumexp(c(lnpdf[1]+logF-logarea, lnpdf[2]+logF-logarea, logf), c(-0.5, 0.5, 1))\n",
    "    logmoment2 <- mylogsumexp(c(logF+logf+lnpdf[1]-logarea, logF+logf+lnpdf[2]-logarea, \n",
    "                                logF+lnpdf[1]-logarea, logF+lnpdf[2]-logarea, 2*logf, logF),\n",
    "                              c(-0.5, 0.5, \n",
    "                                -0.5, -0.5, 1, 1))\n",
    "    return(list(\"moment1\"=Re(exp(logmoment1)), \"moment2\"=Re(exp(logmoment2))))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now inference: filtering and the EM update routine."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Filtering <- function(V,std_eta) {\n",
    "    T <- length(V)\n",
    "        \n",
    "    # DIRECT METHOD\n",
    "    logft <- log(as.complex(sum(V[2:T]*V[1:T-1])))-log(sum(V[1:T-1]^2))\n",
    "    logFt <- 2*log(std_eta) - log(sum(V[1:T-1]^2))\n",
    "    stopifnot(!is.nan(logft)) #logft must be real\n",
    "    stopifnot(!is.nan(logFt)) #logFt must be real\n",
    "    stopifnot(is.double(logFt)) #logFt must be real\n",
    "    logarea <- CalcLogAreaLog(logft,logFt)\n",
    "    loglik <- -0.5*log(sum(V[1:T-1]^2))-0.5*(T-2)*log(2*pi*std_eta^2)+logarea\n",
    "                        -(sum(V[2:T]^2)-sum(V[2:T]*V[1:T-1])^2/sum(V[1:T-1]^2))/(2*std_eta^2)\n",
    "\n",
    "    # calculate moments\n",
    "    moments <- CalcMomentsLog(logft,logFt,logarea)\n",
    "    \n",
    "    return(list(\"loglik\"=loglik, \"moment1\"=moments$moment1, \"moment2\"=moments$moment2))\n",
    "}\n",
    "\n",
    "EMUpdate <- function(x,y,moment1,moment2) {\n",
    "    T <- length(x)\n",
    "    xt <- x[2:T]\n",
    "    xtm1 <- x[1:T-1]\n",
    "    yt <- y[2:T]\n",
    "    ytm1 <- y[1:T-1]\n",
    "    \n",
    "    # find the coefficients\n",
    "    a <- 2 * (T-1) * moment1 - (T-1) * moment2 - (T-1)\n",
    "    b <- moment1 * sum(xt+xtm1) - moment2 * sum(xtm1) - sum(xt)\n",
    "    c <- moment2 * sum(ytm1) - moment1 * sum(yt + ytm1) + sum(yt)\n",
    "    d <- 2 * moment1 * sum(xt * xtm1) - moment2 * sum(xtm1 ^ 2) - sum(xt ^ 2)\n",
    "    e <- moment2 * sum(xtm1 * ytm1) - moment1 * sum(xtm1 * yt + xt * ytm1) + sum(xt * yt)\n",
    "        \n",
    "    # solve simultaneous equations\n",
    "    slope <- ((a * e) - (c * b)) / ((b ^ 2) - (a * d))\n",
    "    intercept <- (-slope * d / b) - (e / b)\n",
    "\n",
    "    # now find optimal sigma\n",
    "    eps <- y - intercept - slope * x\n",
    "    ept <- eps[2:T]\n",
    "    eptm1 <- eps[1:T-1]\n",
    "    std_eta <- sqrt( (sum(ept^2) - 2 * moment1 * sum( ept * eptm1)  + moment2 * sum(eptm1 ^ 2)) / (T-1) )\n",
    "\n",
    "    stopifnot(std_eta>0) #Standard deviation must be positive\n",
    "    stopifnot(is.double(std_eta)) #Standard deviation must be real\n",
    "    return(list(\"slope\"=slope,\"intercept\"=intercept,\"std_eta\"=std_eta))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the real meat of the routine, simple since the inference routines are given above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "CointInference <- function(epsilon,std_eta,x,y) {\n",
    "    filtering <- Filtering(epsilon,std_eta)\n",
    "    update <- EMUpdate(x,y,filtering$moment1,filtering$moment2)\n",
    "    #std_eta_with_old_regression <- sqrt( (sum(epsilon[1:]**2) \\\n",
    "    #                                      - 2 * sum(moment1 * epsilon[1:] * epsilon[:-1]) \\\n",
    "    #                                      + sum(moment2 * epsilon[:-1] ** 2)) / (x.size - 1) )\n",
    "    return(list(\"loglik\"=filtering$loglik,\n",
    "                \"slope\"=update$slope, \"intercept\"=update$intercept,\n",
    "                \"std_eta\"=update$std_eta#,\"std_eta_with_old_regression\"=std_eta_with_old_regression\n",
    "                                        #,\"moment1\"=filtering$moment1\n",
    "                ))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And finally, the function we'll expose to check for cointegration using the Bayesian method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "BayesianLearningTest <- function(x,y) {\n",
    "    T <- length(x)\n",
    "    ols <- LinearRegression(x,y)\n",
    "    slope <- ols$slope\n",
    "    intercept <- ols$intercept\n",
    "    std_eta_coint <- ols$std_eta\n",
    "\n",
    "    # cointegrated case - learn slope, intercept, std by ML\n",
    "    logliks <- c(-Inf)\n",
    "    for (i in 1:1000){\n",
    "        stopifnot(!is.nan(intercept)) #Intercept cannot be nan\n",
    "        stopifnot(!is.nan(slope)) #Slope cannot be nan\n",
    "        stopifnot(is.double(std_eta_coint)) #Standard deviation must be real\n",
    "        stopifnot(std_eta_coint > 0) #Standard deviation must be greater then 0\n",
    "\n",
    "        inference <- CointInference(y-intercept-slope*x,std_eta_coint,x,y)\n",
    "        slope <- inference$slope\n",
    "        intercept <- inference$intercept\n",
    "        std_eta_coint <- inference$std_eta\n",
    "        \n",
    "        if (inference$loglik-tail(logliks, n=1)<0.00001) {\n",
    "            break\n",
    "        }\n",
    "        logliks <- c(logliks,inference$loglik)\n",
    "    }\n",
    "        \n",
    "    # non-cointegrated case - use above slope, intercept, use ML std\n",
    "    epsilon <- y-intercept-slope*x\n",
    "    std_eta_p1 <- sqrt(mean((epsilon[2:T]-epsilon[1:T-1])^2))\n",
    "    loglik_p1 <- sum(dnorm(epsilon[2:T], mean = epsilon[1:T-1], sd = std_eta_p1, log = TRUE))\n",
    "\n",
    "    bayes_factor <- exp(loglik_p1 - inference$loglik)\n",
    "    cointegrated <- inference$loglik > loglik_p1\n",
    "    \n",
    "    return(loglik_p1 - inference$loglik)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bringing it all together\n",
    "Here we'll test the routine. First, generate some data to use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<strong>$cointegrated</strong> = TRUE"
      ],
      "text/latex": [
       "\\textbf{\\$cointegrated} = TRUE"
      ],
      "text/markdown": [
       "**$cointegrated** = TRUE"
      ],
      "text/plain": [
       "$cointegrated\n",
       "[1] TRUE\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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PcE+k2Arbw0UUZnVc578Vl1aXLWudvZ\nYeiMXL0E1ga3GIFdU3Thw1Pu2YMwL8HyZXyw32bXEOBoDU8Jp0MREAER6DsC/SbAVuX8d/gX\n4ukg5N6T+geytfbJl+PPxX8DL1cHgUODW5pzQ3+PsIY9bvwn5bfQ5msfOFRBe7OAtyTXvAS4\nHJL2RUAE+pZAvwmwCatVM/8j/n68VUk/HX8j3jpimTifj9+Il6uDwFI38DjE90LEdst2X1mb\nQI/ou9Blm5yDjxt/h0WHEDcswMNh8M3HBLeyjuwoiAiIgAh0DYF+HIZ0KU/n4/iH44/BW1vw\nPfhb8Vfj9+Pl6iaQi7NbUc08tSqfGHIwDcfhqdL3V9AIfCOzYb0eFR6iLjprCpg1JdR7mXe5\ntyxygzyb8atmDayLIiACItBFBPpRgO3xFPAmtnLzILA+DD6O219hUWDllk8/mcZa3IR4muW6\nMrjiJyZc7ktUubyeL54VNAhvTwPNumE8cTp2OKyYNaAuioAIiECXEei3KuguezydnV2qnd+C\nZXuq5ZJq6GkCvNGNX4sw35xc9/dPuLF7bZ+vvrrF9AA3lIbN1X2PpSEnAiIgAp1OQALc6U+o\nQ/O3PrjD6Nl8VpY9xHiaAKPKdHQLVEPHKcb20uhu7ewsVJhfbtv6XDAr21wD9yQ36K8IiIAI\ndDIBCXAnP50OzlvRDVnbeZmr1gZslrGnI1bc7mVnF52waAquvzoZYX9Mkkj995RlSrsiIAIi\n0LEEJMAd+2g6O2NFVzxkSg6nW8AEQHB3Wriim9iLGgeqqnezqduaJWxMByF+NJH1a5+FKah1\nKAIi0AsEJMC98BQXoAx0rjoMeR1DYAP+4xMu/Ff1bPg7k/Pehn3h/L3cW3d7Lm3INmzpq1jS\n56xzQyfGKPRHBERABHqAgAS4Bx7iQhSBH84fI6a3IpCvCa7wt5v8+LXV8xHi+N+cy22164j1\nPdxb96pICC+9qMMn8OPY0XHIU/V0dFYEREAEuouAqvS663l1TG6pGj4Y8f3qiC/8x+yZKt4R\nXK445gq/TcPdgwjXLcCERYCLO+i6xTwfHqtbTgREQAR6g4As4N54jm0vBeLLFJPJEKPZEqft\n95u0+/7JbT7OPEZQz6Qnvi4BPiq4AxHdAxFwxgwHqrLDobOl1a5rq8PQSe1KS+mIgAj0LgEJ\ncO8+25aWDGFcgghX7XhVnvCod/ds8AWbfSw6LGcEuL4q6EUuf77dVHQFm7RjN9bwEjteSLcu\nuMPzzv2KqTGPW8h8KG0REIHuJyAB7v5n2PYSID4HkKhZp7bYQkMO0d6FBbys1k2J9eteYuFI\nxAR4P+nZrFoL6si/lb3BscwLmmUlLgIi0KEEJMAd+mA6NVtMP/nIIZe/nergpVQv17SAp5Yj\nnbCjpiVLGg9GcH+HdL6VLPLg9xHX61aHhV3OkJ5gsd9ErgOs8alsdSwCItBdBCTA3fW8Fjy3\nRZc7CmFkGJFfzsIKDQswKySxaEM9VclJj2eqnb+eFnof6Xp+sAvaE5r0mZ6aZSac/5JZ6Qv+\nQJQBERCBriUgAe7aR7cwGc8mxrDUmWeyYQG2dmM6ZS2tlfsBl6yyhMWcriMc4ipV3g0eWuve\nZl4fDvnXrQ8Dz8ziHHBD6cgBv5ydKbOBZaG0FQEREIHaBCTAtRkpRAWB8MbscMKNb872691i\nxe5BVGtWQRPf8/BfHXEFWzrSXBRgqn6PTg7b9vdcemE/JkuN9OmDlbhBl1/wNuksL9qKgAh0\nHwEJcPc9swXOsWdmqjCOJTvC0KLUOq0/S9y3Fwt4GTNysJnVnUzYSwlFs2t0+6mOZtatZPWl\nWe+scXFNcEdi2e48NrijagS1TNLZLOl4ZWGx+ksCnIxRrhWDrouACIhAdQIS4OpcdHYGAoiR\nTT359o1u7IQZgsx6OmkDdkcxreRbZwqYtK36Q4sujJSFoQ3YjWNBbyg7N6fd4IZWEs/KITf0\ngToisF7PseezhaUKviTAzO4lC7gOgAoiAiJQnYAEuDoXnZ2ZwBCW6bVllunMIate8ffZaYTs\nL4fD0AuqBaGXUzrjVWHb5PXYC3qCtNM22Mkrje6R9qL0nqetC4NPmO1+LG7E1y/OwrCU0yAf\nIGzcRj4Qpi5IkQXTVgREQARqEpAA10SkACUCNIYiRtYL2IYEzckhaKkAe6p2w2OqR5KPM2WR\n2N1l1/chvkWs4CYIcNKT2eLGEj62LI1quwcguEdmPZ7JU548FDi3lfZgWcDViOmcCIhAXQQk\nwHVhUiAjQINptAQRrXRlo8a5sHBDFGC7E0EdrhYD4sY806G40blS2AlX/A7p3sX5JghwsI+I\nzM06KQgfCTbhyKMWucFX2g0cWxV0IcnLwk8MkhVCWxEQge4jIAHuvme2YDnG8ottofMRYHpU\nMRNWyR06HAb/2qqB6RT12uzsYLJYw32mdtk5Vlv6FuJ7e7MsYOKiP5W7kSRqrU0cPzoY97va\n8kLdc55MmQV8F3mRBZw9IG1FQAQaJjBva6LhFHVDNxOIArzfjc25Cpob78saYBFyG470JuzK\n3YiZCeJ7DU5wA2dwfJftlzvOWe/rgfJzc9s3C9iPEdcIteqzWsDEn3XAeuT6MPR2BPjniLbl\n426q04+bW/q6SwREQARsQh85EaiTAAKYdUaacxU06wraogqpgIflCNkS4j0C2S1ZogjcExG6\nj03NFmEnCDvvj0bitiroMdLZhZ9RgNeEwbMR6pgeaZ9Kvh9O+lRB+wL+Pu4t5XlqXnUsAiIg\nArUISIBrEZr7dZvtyToT1eMzK2vuqbXhTlYnYgrKqIANz4BVyh6qVXCF9QjuTxC1Q7CC0bTY\nHrx0Xci/Ot0/Aa39cemedIeAWJ65eQswRrQZ4YwrNivbWzX4422Vo6npDbrcK6yqOriJp3Dt\nE/ilHNML2iHARWuflgBPhaZjERCBuglIgOtG1VBAq5q0F7T14q3HX9xQ7AsUGOF5NP6WUZYY\nnE8WbvVu67gLr0d8S78/E2IE9k/XBrc4qZrObZuaBmkzDnj+FjDfAEOkMUb8tyD9Z3uX+4Z3\n+fdMTy8OM7p8o5/4MmlfQ9r2UZX2gvb3It4S4KnQdCwCIlA3gSZYE3Wn1U8Bf0thT8Zbj9l6\n3LMIdFE9ARcyDAL0VCzArzUjDwO0+06NB1FcmnNDx9v5iSoLPXDd2l7n/ZulHPZcaAMubsi5\ngawj1YOm5odjG+f7xfT8Ltp8lyHeZj0j3jacSlXQKRttREAE5kBg3i+zOaTZL7f8uoGC/m4D\nYRckqE3fiOiczXAgOk3N342zlvDUrxPE3dpjv046dE4Ym1bNnVjAoQmdsJxNJoIAmxWbucnJ\nNkpnmC2L9uKddpxzRQQ4t5yPgCdy722INwIsCzhjpa0IiEDjBEpVgI3fqjv6iQA/lFjdytTM\nG5tR7r1ubDOCi5ZZW3Ao2j7idrh5i59eWtMEGMu1WRYwnbDCWLacoqVPkhXt8MnEG+FIhPZW\nyw9iTYctb+35Tyf8b1itaQsCvGh9yGbtslByIiACIlA/AQlw/az6OmTR5eMKRtQbTxPGuYDZ\n4W08sL8JBb5kwoVziOPV5fHww5yWDmEZRjz/KmgE1NbxvX/CFWIaCCtiGrIe3jEbi13+JaQ3\nMObGr7MT97jxH3Efs3GFMOYK797txkbs/IQbPHVtyD/E9uVEQAREoBECqoJuhFYfh2XaRQTY\nux2sZtQsDPvc2FlbrZOadxNMxFGaoMNEjvNVhjqFpggwFcoHY03fTVfm3ck/QDAr96TKcvnX\nIsr3bvVJeZl1476Dgqf/mDtgi3e3WdglIdyLFf1Odi2aU+ycnAiIgAjUS0AWcL2k+jwc1iAC\nHPabWDYLBeK2I4uPKSq3I7xWFWxuL+dJcpprigATtU11eXeZlc3KipVV0JTVpqDke6Pchdu5\nL1q+dpbre/BYv3Wtb1wekfZFQAREQBNx9NVvgCmmhsPAs6xBs9FymwWMIk6rFm40npnCj3i3\niWvft+tk7pJq4UifiTj8I44J7uhq1+s9R/Gt5/NdmLGxPMTLLotMxMUmnEtXSKK8IXbAKot3\nM/u/zY7LeFRUX2fXtRUBERCB2QjIAp6NTo9dW+vc8d4NfBb1aljA0CazCFsmwClqG5trpu9l\n6XHFBmE26/tBrOP7mooLDR+YBeyt6ns/t34B8f2JRXEUM32tDe4I1vn9GmVlhi5/e3nUWOkX\n7HWFv548F9Lq+Mr248nr2hMBERCBmQlY25VcnxDIufxSKypfXTaWtSGH+Nm908buNhRJzcBx\ncgwTYJpnq7r0fFhd9WqNk8x49QYGONlsVow3LsY25w1+7BnrwtCDKZ9xWYwvTa5BD+j3lUeJ\nlX5H+TH3ZB8ksoDLwWhfBESgLgIS4Low9UYgFpBfygQYJjQMw2nMIVrWcemexu5qLDTxRwuY\nSTisrbeaS8/7ZdUu1j6XO9uqjUlnSZFxyJPhxxDWIVZ5yDPcOSzlenTk467JMNP3iGtvGlYC\nPB2PzoiACNQgIAGuAaiXLic9mc3SyyPAMxmZ1UtMb9+VVNvOKkjV76z/rFm+JmiDbqxq5qgS\njj2j6US1jF7TryT890d84ef1p+COp4J7NfflSKckwGbZrg/hBj5OPkEaD8jiy7lCKUx2rnxL\n2GgBs7UuY0N828QPiPIw2hcBERCBmQhIgGci04Pni24ACzh2cpqDBexWojItFWDEEQGL3ayr\nCnBwY2/HUrV24Ccheq9ia5N21C3A5P9Q4s9m0qoQVyL9Mz5Q6ASW2b9xr8pQKFJMHday9YKO\nR8P0ot6YWvDZdW1FQAREYDYC1EbK9QsBBCi2AbOtFOC6ekX7VViOLRbgxIJEfatWQW/07l5E\nbwOi92C2zN0cjqn72QUbq+tj+e2eopuoEOBRX/gBp39VHh+zcVWEKb+W7m/LzsFG1dAZDG1F\nQATqIiABrgtT9wcaDm41wvUcKwnqVhLg9WHwTcMu/7FZSxis01Z4AjodhwnNGnYeF7ElYxXu\nbPXj3hXj0CDKYqbnCfUmd1SyLGQpOPdPE1dE9NulAMnOtDDl1/kI2Fp2LAEug6FdERCB2gQk\nwLUZ9UiI/JNRrCdaYdgOZYVCVB+LGD2KNsysaja7VNquYYQOYRZTBXxd6WRrdqIAYwFXrYK2\nJDe6CYYNuU/bvuWbMcE2prem44d+UHkgqpyniSvtyX/Bh8bPsnCo66xV0NQkjCDCGMrcNW0i\njywWbUVABESgOgEJcHUuPXg2HJYVCuEoDUNCxE7g/LHrXf7u9SF/WhamfJtzg+hcCKPOoUmt\nc4hYFF4yV7UKOqaczMR1S5YLviRWZfszbY8I7tBFLn9u+XXGNd9bfpzt0/P5Xcipzcq1D4Un\nSzM7PgY+z3zSJ1qIbIjXzKF1RQREQAQqCUiAK3n05NFwGHonQvumssKhW5kL1pEJ55ex1OCx\nyf7Uv7kjsJp3IkjRQp16tXnHIY6zxaSc0QK2tBDH7VmaLBIxaQGnM1ll17LtEjeEZesvto8I\n/P3jrviIzX7shux6+XbUj30K1f0N52a1fuM91Idvcm7U4mWI15LyeLQvAiIgArUISIBrEeqB\n6xhytpZvqcc7s2FFAU6qb5mCMXXMADUpZtlJtty/jKrq0mIJZZeavBt+axFurSnAhU9MuIln\nmJgyoUbMM5Ns/OV6N/TZUoZip6vkCEF9WLLnr8RiPWmTH7+2FK7KDh8rrL0wvY24StAIh/N7\nsyFeVcPopAiIgAhUISABrgKl104hQFFkzVKzsiGo8RhFLlVL23muzyDANgtWaPEsWNYoO/Fd\n0nkfGZzVArZxu6N+4gsmlDRdp3n2p5B/+loljir1H6wL+VfbEeU9JDkbbt/k3UiyP/Nf4rHe\n3rUt4Mko9pCPUg/rydPaEwEREIGZCUiAZ2bTQ1d8bPNFff8dcbG2z1SQB1PxCtG6ZY6sqgJs\nM2hRBd1yAd7m3fYNvvCaesGbUJq4MkPIcvK3Fh+rga3HN7J7GsfPs7iw3tOZs/yddcZ9N3HX\nLcB8COwmH6qCrhOugomACCQEJMD98UuIgnu/KzCRhaPnbiJUAy4cZEKDQG0xDIjIMdVwUDVt\nKyG1XICrpV3j3N3k+rUHuTzLBLpTKUcUQe+GPpje91DUl4+PsMKOKWssZ404LeR2/txXO1wS\ngngRYJeKfL13KZwIiEC/E5AA98UvIOn1zKwR9yAUWMA+ChJ9d1+E9YaIJZ2aELHhajgSC7jl\nKyFVS3rWc1YFTXmwfL2t1LQis0IRRCx51i7mzzo38HtsacMOf7nfFT46a4TpxX1u/N/GXOG5\n9YS1MKTNJFg2zaWcCIiACNRPoNQxp/5bFLILCSxCgGz5vYILHgFOLELKwRAazpcWnvdHVysb\nImcrCHWcBUyediJ+pSzzAZFVAx+ANWw9qjmVO9QEuuiKP9nqp4/9Ld1ctpOGmzZOuCzI1N0b\nSOjhU0/qWAREQARmIyALeDY6vXNtCLH6l6Q4sQ14BdI0gDCxLq77DpajVbniSsKcHKZ/kbiH\ncC32UK64sMAHiOzWJAtJ/k1oKRdTZLGN8zq7/ZRtlYVh9aOW9eJm2cJdMCJNOREQARGon4AE\nuH5W3RxyEaKUWXSxCnrYDVkHJcb9Fq9CnLLOScurFRKRNkv5umrXFvZc8lHAx8UfkccRywur\nLVh7NWLov0Se9zM0OPaAZvhRywSYtKy6O3Z0W1geSl0ERKCbCPS7ANv8vbyzy+oxu+np1ZlX\nxNc6YZlIWEekHfxlYYXikcmxp7NRMgEG4QaOClMsORSM80xD2ToL0vIxF1d0haspz8c3+vFv\nME3mkywOlJfOUIEq57jYglnAUYDzzrVQgN0Yoh87us2lHLpHBESgPwn0owCfzqP+DJ62zzjW\n06w/G3JyE/5ifC/2ZqUNOBNgfxvfG8fSs/lgymo1tghwyQJGRfIPZkrKT9oFu05vpji+FSt5\njx13krMxvRt94QWWp2Laa5lpM19g1cGpxY8A+1gFzddHywQYtswQlgz16iQ+yosIiEBnE+g3\nAT6Nx/FNvLV5vhB/Bv4k/Nn4i/DD+F/ie82aserRdBrJcCtWIcONrG3UrOHCpnvd2FfYP58w\nzGnsHoqYPJfeWLFDFl8jS5LzhY4TYMtX5qhfjwKL4P4T+c8jwlblThV0OARfrLcDVhZfg1tj\n22u/mQYRKLgIiECjBPpNgE1kzMp9Bf7L+B/hf42/Fv8p/FPxZgmfg+8hF6hqL8aJJXLO7zSB\nwsA9Gsvts6PebWMsz327XeHTSYGTTkuDbjAOq2HVoCjAhc4cB1x6RtudYzaqUESA0V7nWFRh\nD/smjMdxYncpYAt2YCoBbgFXRSkCvU6g3wTY2nz31Xiom7m+vkaYbrvMuF8bfmSTLBeiEGPx\nHpZUPydFucOXBMzaxFm9Pnd4ss3HKmjGq3W0BUyFeagU2sI95N+qoCmHVbO30k1Qwz25wlQr\nU1LcIiACvUOg3wT4czy6C/Bm6U4dA21C8xK89Q62auqecEmnKk8fpESAEakowAjTIdl+WUGt\nGjcKMIISe0QzW1a0gEdbbEWW5WHOu3xQMNdI4rDuTYBjtTuW8dbsfCu21gYMS1VBtwKu4hSB\nHibQbwJ8Bc/SBPgyvFnCNlnDBjxtoTZDlHs9/jy8VUv3hBtIF6JnDg4TJOtZFQUYUaJ/VVIt\nnRUUUTZL8QQ7ZvarKMBUQfNhwqxSfpY1erMIFni7z42dSl4/RNkC1Rg8T9b0xVHm0VZmDeFX\nFXQrAStuEehRAlOtwB4tZkWxLuHok3irZl6LPwxPE6K7DX89ng61veMQn4OsNGyjAPPFFQWY\nU1Ytne2nBQ4IsEfErDOWP8K21OzSD6vzhiBZ3qY662i1LrhfUcZdZJxviKTnNz24rV2/Zc4s\nYBjJAm4ZYUUsAr1JgHdVX7q9lNp6O38d/0X8/+F/iu8p8aU86NAgQhvNfLPw3ca0DRxr1yMc\nxqHkOC5V4XLnXw2H/MNYIcnWAm5pJ6ZSBpqz80PKcYVFhfDa892CRfzl5kRdPZZEgJ1jfeXY\nc7x6KJ0VAREQgUoC/SjAp4PgM/i+GAdMFfSBCBCdghNr0LYcpx8alRYw1c0Xlv88CGdTVVoV\ndBziU36tU/dHfOFHjA1+vuVvxI9dvsGPHTPqCz9sbX59rOpmDPW7W5uOYhcBEeglAv0mwKfx\n8KyDlVU598U4YESUSSkqLV3KnnbEmqiogt7rCjdzreS49wDEdxn3d5MFXMp/u3Y2uYLVpnye\nWgXa1eVEQAREoD4C/SbA54PlYvwr8FYt2fPjgHNuwOZGrqhqptyZoFYIMF8l0ZJDdOmUFsa9\nG0B8YxV011jAlK39LnZQK/6UD5aHHRt6bghb+3kqRRHoEwL9JsB9Nw6YnkhLaM+tEGAsNZt4\nBJezmoBJF4UkjBP+x7T73kYHrP/HxfOwgGP78WRA7U0lYO3kZgHn3dAZU6/pWAREQASqEeg3\nAe67ccA8dKtG3lP+8Pe7sVePubHjaCu9rvx8um9ibcvr7UVQWLLQHYllZ/Nly81CAE6RMdu3\nzhJMl0RABESgRKDfhiFdQckvwF+GZ3iNY1rGWB1rPYUPxtuY4PPwv8bP160jgnqHphw+38Rm\nuj9HGzDWWYUFjGm7ZabwVFdTLR1sSNY6BDgNJgGeiVd2HsZMfQm5OL46O6utCIiACMxMoN8E\n2Ehcgm/1OODjSOMWS2yhHasJLqEquUKAZ8+T9YwOtxKGbeIQl63ZvrbVCbD84Z4BR59zrQtc\nHZDOioAITCPQjwJsEEyQrOeqiaRZwnQ6wnhpnvstUa3CMwVkXe4FhPrnukI2HCgczy2b670N\nC+4iZs36Dsb779s9QPkyCzXYB4vcrARyt0OrQBDrZyAnAiIgAjUJ9FsbsAE5Hf8ZfKvHAVv1\n9rY6vU0B2Sp3MiL6s3ojZxztf2/0bjPVqb9I7/nVdl/qNV1vNH0XzsYa0+Ht8VTbU+s/bZ7x\nvuOhAouACNQm0G8C3HfjgOnRvJSfQcO9mOmo9V7uuy24ooYg1f4/iiEQ31htf6is4DqJKZgI\n9DeBfquCPp/HbeOAL6ry2LM1gb/KtXPwV1QJ04WnbCKOyhmv6imEddRaFyZe5d3Eb+oJrzB8\n6rhsRiy3CB7ZWGuhEQEREIGqBPrNArb2uXSyiao87KS1l9pCDT3hqEo+gA5CDXTCmiz2iJ/4\nItXRFbNjTV7V3lQCwY2xLrD1wso/d+o1HYuACIjAVAL9JsD9OA7YLOA5CfDUH4uOZyfAl136\ncefXzB5SV0VABERg+qL0vc7EqpXbNQ54wVmymtH7qBgdZBhSaUjRgmeqhzPAjCfRAqY3tFVB\ny4mACIjArAT6rQ3YYLRjHPCs0NtxcV0YeDaW76ssrXFZwO1Abt3q99lsLrh6J2BJQuuvCHQp\ngTXBPWiTdzd2afYXPNv9KMAG3apkf4W3scBT3YGcYIF1dKuLXc7lDsmyn3MFVUFnMFq4vYsp\nPA9ywab3lAXcQs6KujMIrA3ugTmXv+GoUFiz1TubvEeuQQL91gZseP4Ob2N0eV+6D+KX48ud\njZl9ZvmJbtxn7K99SGTunmxH2xYSoK6f2G38tCzgFmJW1J1CIL+CWjY/5IYe0Sk56rZ89JsA\nn8wDei3+Hfg34h+J/z6+59ZxZUarKMD0gP7DEe/uoIxy7SFg7cBPXh/y/96e5JSKCCwUAVsv\nnDXVnPudhcpBt6fbbwL8fB7YB/A27eP78Q/Db8Zb56wl+J5xVEGbAG/d7ya+3TOF6o6CjGEV\nHIwpfIZlFyH+MP687si6cikC9ROwhV6S0OFR1P2o2aV+dKWQ/SbAZunuKJU+WXDg2enxZ9j2\nTJs4FrB9nf6Ytpny8pYVXbutIeDTntD+IHqh22xizy06f1Jr0lKsIrCgBKIFzAfnWevdwLkL\nmpMuTbzfBNjGAb8c/7tlz8uG6DwZvxr/MXyvfMmxDGEjqyBRcrl5E8DytQ58zIoV1vBi+gv2\nlrGfWgrzjl4RiEDHEAhuIAqwZYhV19Z0TMa6KCP9JsDf4tlchf82/jH4zFmnrCfgH4jviR8S\nL/8jKYt6PwOhva6YWcDlHbEkwO19CEqtLQSSNmBLivfN0W1JsscS6TcBtqFFr8SbtWu9ncvd\nVg5Ow/8p/qbyC123z+co1u+TWcd3S9flvcszzD9UtIDLi8F0oD3Vv6C8bNrvXwL81ksWMBSO\n718Scy95z7R5NohgpnZRE2ibqKOr3THOHcQX6UBIll3s6rJ0W+Zp771/8qs27MY2WMqHkCzg\nbnuQym9NAnzk2zS3MRzvmgfXvEEBphGYfFdMu6QTXUmAtWgHXD5WoxfcmFWty7WRQM4VY60D\nL6dXsT6wDXez9mBZwG18BkqqPQSoaCt9WPIbX9WeVHsrFQlwrzzP4PIMd7lqvcu/f8C5b6bF\nsslG5NpIgJdSnBEIy+C7OedjTQvWwcPXhcEntjEbSkoEWk7APiz50LyO3/f/4kti3PKEeygB\nCXCPPExMXmqe/dn8I5zJy59xqGEfa/paD2+5NhLY4wo32gtptxsbwQJmLeXwE5Iv8kye1cZs\nKCkRaAcBq9nZMOGK7+b3PUBX6PKOh+1Iv+vTkAB3/SNMCpBzgwiwVXeWenHf2yNF66pi3OHd\nno1+7Fm2HfHj393gC6fzVL7DC+plq4NL12qYW5HWBrd2fRh63tzu1l0i0HQCJsB7qOmJoy2G\nKztlNT2xXoxQAtwDT/XQ4JbyT/DHSVH8snR7Xw8UrUeKEO62ggy6ofiRNNdCMfH927n3bQj5\niWvC4JlzjUf3iUAzCPBRSQdDt8e7Qqxpm1A1dMNYJcANI+u8G5a6gcdhZf1Zec5on9lVfqz9\nhSNArUQUYO8m5izAxwS3khfeCyjFIoT8bQMu98aFK5FSFgGbfCMs4Te5h4Hv0QIuSoAb/llI\ngBtG1ok35A6tkitZwFWgLMQpXkyMKw9jdNB66lzTz7v8scm9YTFbqrXDQXONS/eJQDMI2Pj2\n4IoMtUv6mgy6wa5fRa4ZXBqJQwLcCK0ODYu1W0WAvQS4Q57XiC+8DxG+AGvBZlubk/OumAqw\nW8zzPpKXnwR4TiR1UxMJHMDvcF+eamis4cACMO9eHYZOamL8PR+VBLjLH/G6kKfqOXe2FYN/\nglLHK/Y1BKmjnm0wK5jO6nN1AyuSO62N3/PO8+nxXOPTfSIwbwJDTDKzf9S7fXxc2mI29HOY\nKP3Gh4NbzYIk1NbIzURAAjwTmS44T69YrCF3Md7GmH6aDhGfn8y23za5r70OIEBHFYSTeui5\n5IUPqinjLIMEeC4gdU8TCXhbuCZOvZo0s/ALd/609WHwQkuEUUkv4d2kdbFnIT6nl8Es8elS\nGwnw8Fbzg09fzOEejktTbFJNeXsbs6KkahJIlik8yrnFTMrxV1gGH615S1kAXmRls2kFXnp+\nGR9gqoYuY6Td9hGg5u01fBTaAgz0wTLhzd43HvHNvQv1HeSc1dZkTSfty1wXpSQB7qKHNTWr\nTH5VegFj/e7lH2I7350F/A+YBOJnU8PreOEI8KEUh2rwD0ethX8agnpKI7kxCxi/L73nWvYn\nvBvU/LuNQFTYphHg9/scfscHMPwxWsBMQHMpkX8BwV1qiax2DvF1DFMKR5oY2zm56QQkwNOZ\ndNGZ8mpIv3fCjV9Or8TnM/nDmUwCcXUXFaQPsjoWxXPQ5Xk3+WNpO6vScW5mDHRwsYnvY7s+\nH1u2che1HbkjZr5DV0SglQT8qiT2iWgB28QzwU1clqXIdLjLEeml/GZza13eVpmTq0JAAlwF\nSvecmhRghHfPJu9GNvqJz3ZP/vsnp6hvFGAsBibTCMyIVa3n+sw8sCRs3t2sYx1b6+Uels98\nh66IQOsIUL0cPyD5GIwWsKXEu+dz/CZ32r53Q8v5yIzWMGJs66zLVSEgAa4CpXtO5aiCDuOW\nX74042D47sl7f+WUTipRgLEKnsyzsuUiD6AN18b01uW4z9r6owDzYruLF+AuvAS4LnoK1FQC\nwdlSp3xEmkv6NiT79jc8x/4ybA4LOEQB5tA6a8lVISABrgKlW07xUrZ2ll/yo7+PfQlwBz84\nvpKiAJdnEVEuX9C8/NK0fV54VOe5m7GCP8aMWj8igM10Zs9fTgTaRmA4DD5q2OVPtaplS7Tc\nArbjDX78Kn6jeyYSCzkKMGFeQJsL/Q/lphKQAE8l0kXHfGFSLWltL/5uvjlLY4C7qAh9k1Ua\nbKcJMP98dVsGvPBWmuW70RdeSFXfl9inCtp3hAW8Ngz+Hv6xffMw+7ig3uUu5bd4aYaA32Fs\nA86ObcuH4nX0WXgae7GTKOEfPegGNB64HFK6r95pVaB0yymGlDIXq9sz7sbO3OTcnd2S777M\nJzPWM1kQPdRtEo3E8ezqFmCsipXYG7EKOrk7TrpS6gWfxdnWLQM917n8iyjH80mXn6D7dlvT\nV2ILQCAOLRrOEp5qAdt5zl3Gb+Ld/GY94huD5twATSgs1yBXQUAWcAWO7jmwyfn5qT/MLGA6\nX93O71y/7g5/fFgL5/PMShYDr6a6BTizgLMicsxEK/6I7Hghtmtc/iQ6lX2EvDye9IcWIg9K\ns70EeN9YXwRENlnhK7hC6fc8mZPiHYSzcesrCMduDB/vmwyjPSMgAe7S38GQG3qSvfioht7T\npUXou2yzTvDHeBv9V1ZwDMi6OmEdHuxlFo7IuSI12Ymj1/vtnGtbuxrTCh7P5At/mqWf5qLU\nhs3HhAS4Ek7vHfEFSaGikLLzC37L/0TfhtGpBZ1gzDvvJhvvPkC42CuasBLgqaA47ncBtheg\ndae3H1ZXOWv/tQzzw5YAd9WTc/syq4BnWJcFfKAbfCRFXLTbTXxtsqg5BLidFnD+XKzdv51M\n3+b9Le/FHaclLL+s/R4jwNceiy9Qq5y4bXxQ/vVWP73zJ2HipDMWjPcTNTX2gk3eV/YxuTYM\nPN3OyfWnAFtngM/g6bgUl9G6M93exPZifFf0LOWHHQWY/wYJMA+tWxwvJ+uMdU+S3/oEmI4v\nqzA+dthkB1k5aXEgjslx4Nn51m0D1YmVVgwfEiULnmuygFsHvyNiptd+fOdYZphp7xczZYp3\nUkmA+b3floTLRQv4QNYup4PW52hCK9WezBRPP5zvt05YNiPLN/Efx78Qvx2/G78CzwxF8RzD\netwJ+DH8XJ19JZ6Br/eldHyjCY1vHF49uGbznt0fey75/+g53G/P0tLl/yRuGf/urMOP1XLY\nP47lxa6bt38QC2fnst+AHduYYjoKObvX9rO4zFKzl62FPxZv/0y34rMORZZG5rNzdq+dy9Ky\nfziL03x2ztqtLT+8v+PWjs1bHOYtH5m388fjf4O3Ht92j3mLz+IwZ2GyPFu57Lo9R8t3Fg+7\nMbzlx+6z8trW4rH7M2d5tzjM270Pxl+HtziNh91jYmr32TkTR4vL4sjaxSyMXbM8mR/f/6NH\nHpE/5Vf73OJ9E7suPf9U5z5kcViYLO0s35Z+fuDUn62auP0Zf+OX7ibczt9Pw+Xu/qc3PeDg\nC999gFu580x318rsXsunxWfpW9pZutl+lpbxML523u7N8m3nLV2Lx64dhrdrhcLNJ5+YX7+B\nj9PwSI4t/uLeL/7ByUue9iV2iWTHIYTdatfMZfmxbVYey4uV03gZK/MWj103Z9eMa5Zn+71l\nvxPLj+XLwpgv37fwNgTPnrOFs+t2zsJY3La1fGTnLJyFsQ9tu27ls7JaetlvwOKJZUyvWb4s\nnuw3aeHNGS+7x44tTovb7rP0LLwdU05PmGBhsvxYPBan/R/Z1pxdt/9Ty0/Gz+LMGFmerAzZ\nOXZjebPy2TYrv91jz9rCW/6y+yyNjIOla3FZGSxf9g60dI2DHZu38OYtT27PKz909JL3v8bt\n//Fpl9z5un+60blHPYHTVgaL0+61tMKOl/3XUYd98JUuFHP3j996zKL8ms3OB/+3yy/855v3\nfe2qBx74xG/kdr/rb//QuX+wd63dR9OK38q275xB7id3PoU1K/eiKoW+lnOfwn8Vfw7+Cvxc\n3TA3Xo1vGd89X3zKi4dOvHHJned99I1pJu2HbP9Q9o9oW/tnsH8c++ewF1n28rVr9k+T/WNZ\nOHN2n+XXXg4Wl/0zZ3HZiyR7sS9Nz29jG/8x2Vqc2T9hdi6714TO9i0PFr/5TPwsjXKX5cHS\ns3yZz+K1sOvxj8VbGpZ/C2/nLX1ztm/nzVkYu27lyeKycpmz8JYf29p1S8Pyld1vcdg5i8Pu\ntXjW4h+Kt3ssf3Y9e1nZdWNqcVkcdj7LE7uleAd3Xf6HA8uGCj5/wi1uz2ee8W92cTZ36Jvf\n7gaP3Obu//ajLdjn8ZZWcfcnnpNDgF0u+GssI612+655uMuvG7FkvpeltftTf+gWP/Iat+dz\nz3CLH/2909zQ2PfcmL3Pm+KMX/YsmxLhwkUSOyJ1fVn2ffdREeHWc7/wJ8Xth57HgT0j+5Cy\n32T2/5Pbe+Xvccg/zubVi/dd/cjH5F/0MZ5kGFz2zM//z+7Ln+0QYDf2/TMvjYGSP/bDGi47\n7pvdrv9RNPikPkL4jfh/nOW+D3PNqlf+fZYw9VxqhO2fEeGH8CZu9oOu6daFRRfnXFi9wY89\ns2ZgBegYAmtZwajoho5mXcLvTOxe9qrRZTu/TObst2IvMdua4Jsrrp844OKQm3gu1XhYa8W/\nY5KDtyeXqK4Jbjjvhjbsv/7UE2479QdbOG8vQ/vAsI8bs25Ml7MPCrtm+3be0rEPCPu4yM5n\nL087Z3HYvebtulmXYX3xwE84P/H0Hd97wsp7z/qShfNr7zn0BQMr7ns9HcI+RDX5O8NY/gXE\nvmbj8b96jxtdS5CYZgzLvqVr3tKyjxX7rZtaZ+W1spvlZmEsrwfjrarezlueLC+2b9ftnmzf\njrOPH8uznTdv+xYuK6OFs3PZF4L9n1neLD/m7APT0rXrlva9eIvHnOXL7s0+vLJ07NjuMWdh\n7QPMPr7snIUx3vY8LE4rg+XHztvW4jS2lm6WX7vX8mTxmrM8Z4zsPju2sFkZ7Jz5LL2Mi8WT\nPWsrX3ZfxsLykrG2tOw+s77vwFt+LA/Z74DdWC53zK3rTl50zNYf3O3GVjAV2312oZo7OrhD\nFruhHST2Ndp+N7G1iTuOYLs7jA9+Ojc4/ncTu5a9eHT5jv/lfss7eal7Jj8ru+X9Efhr8V3t\nsh9fVxeigcx/jrD/g7eqjyvx9sPLnL0Qno9/Hv492cl5bO3H3jJHj1hWx6lPrFuWCUXcMIFR\nb6Iydg/LEW7NLd11BC8eawKp7nL54xLxDTv2u/F/KQ/EW3OXve1zD/kZL6SKl1f28i4PPu/9\n4POMOfdu1aO+/stVYdEFfPh90q/I8/K0Nu1kRRw/VHgbCQ2vHln3qc0+fujOlK6Jm1yHE1gT\n3IMY4ngj2Yy/qcFj8oi/d8s5LhuQPq0U/C6ZHCiYgH+BLR+Pfhfb09kemxssHGRxDCy7jw8E\nm0ymv12/CbBVK1+AvwxvbUA78fYCtPYP++rdgD8P/2t8RzvE16Ym7PsfcEc/pFkyh5jxWwvH\nzRLETDd7xuauuM3HKvPkiL/bePbr2dqcu9lJhglRK+J+xmpY/y8718StWXLmjqYDzirbSXtx\nm8VkFom5YfuTdwMPwIDaaPty3UnArNhBN/RralpO3uzHbrBS8LztY8+NTlroVQs36t2+o0Nh\n7RbvbssC8MH5cn7v/8DxKXaO35C9f/ve9ZsA2wO/BP9JvL2/1uIPw2/H24/lerxV6XS84wV+\nEC/ozR2fUWWwKgGe3c1cOLXqRU7a3LmI7xq7Tlj7SKx0HtELYTfNEFEM7SLhz+BvSyxg4rZq\nzeiyISXki7GeNqzKjbEtOWZow7KfcIcGt3SZG7pgoxv7ezJHMLluIYDSWo2g1T2fspZ1BhHV\n3/CMOc3iL3z11SpHufhaWHrx7+TjcCW7j7VjmiwkwHDoRwG2529tL1YNbb4rHVU6WOzJbDRd\nWYC+z3T4Da+h582EAevjUVw71K7z8rL2ymnOhibZEKWkuc4u29y7k0ODpt0wrxM+s4CJJRlS\nwhZRjjN7VYg+L+qHrw+DR1MHeTX7b+ZL9/2Y+3fOK3nd3FYCKOyBCKZ9Nf1rzg39hG+sp3K0\niN9cxbOuN1NoOPcNlAWXBWwwjLFcVxKIS9rd3ZVZV6atCo45DMIRVPFZ08c0h2VbEjwMjukW\ncLwjIMD+SZM320dZ7HwzeapJe7yIy/KTTKpA1Aiw309/hF2VyfiX8qJ+A68XLOHYo6dkpVeG\n01GnEhh0eevYhqXqjkR4s30s4FIHsYayjvROFW5r9ut7JwHu2p9AOJgp3+jQI9eNBHixMQzK\nD/Giu6ha/hG8+NJLrnlrIqnmfkO4h2QXiBMLeLKqODvfpG2pCjrLW9Im6PZvcBOfH3fFx5Wn\nw4cBnbaK1syD3TN4SPk17XcDgYraGTpMWT3LgAlw1t7fUCGmW86+6odnQ5H2QGAJcNc+RP9j\nqol+1bXZ7/uMxxmxzMKwdrFpjiYGernHFY+swe1n0wJwgnu/wcZeirG91QQdXxJKO988V26R\nl2ZE4sVMFTRK7N34SJJW2JmlydSVD7Z9Zj66gOkHn5Gd17bzCfDbe2hZLhdRF52nVubVfFhN\ntWTLgs26WxJu4p7gJyMBBpcEeNbfTOdeZB7WJ2e9Ezs3l8rZzAQSAUYwS72Yy8Pyj2lVvvRR\nmDh31BV+WH5tcj+uxRqtEzo7rbPzWKctEWDEnvyEa0ni11gzmXVuaccX6yjLEdLO92SOSx+F\n5CXmiXNPQ4RpQ5TrBgLrwuBZ5PMxZXkdOsq5IxBf65cwJwEut4CJx1ZLkgADUwJc9ivTrgi0\ni4B3Y1RBm6s+nzM9iU3k7t/gJ640CzMGnfIn6dgShhji8V6CnJdcbmInLN6aa8Pg768L7gF8\nKCyacOFvsMa/TDo2aYO5kgBbHjf6CYb5ZR8WdtnTiSykL+zqHxoWSq7TCOSORCTLekz5RXzV\nZX0ASpZsI7nmB1wSbizgLdx7JL/qvtefvgfQyI9IYUWgWQT2JTMOWXQzdEYJtvKM9dafzdlL\nzUTw+YjdX6UB7bgpbr0bOmnA5a6kFyxtzeGO+9z4z5IOYSEOUTFR5sVa8UIuf9Eivodx/BHu\n/Q8yVNXSb0pGFUlTCVDVnNVwZPHynPNmFaOZ2QdVdqm+bdEVygX4C/y2D1/n8qfXd3fvhpIA\n9+6zVck6mACWJBpsbkbLkKn7wqwCjIG6n6phawPOLFKLsGlV0EVXLFUT8sK8Np1+cDdppgIc\n064QYK6l5aJkdMTi7728tplHJCxnBZyVNoWmZVKuMwkwmcuf8czebrnj9/cBPqBuYm85z/XD\naY5LQtpICRjvatNbWpz89HO3sLsV/0A7189OAtzPT19lXzACzIGaCtX0Kug1YfARiNfzeOlN\nGd5Tmd3E2vTMlZD1mA4/YL9pAmyiOZliuNX2ydduhH9JMlGITQIS26FLwTILiS3ZM1dkGkKb\nitAfMeTy/0iv7+xFnlzW304jcAoZYiIst/keV3gDfRDeyPHBPHefiGfx7+eSYX7sVDuHD6HD\nDxxxY58lrt/y+1o3l7h66R4JcC89TZWlawjsKAlwZdUsE1g8csB5692Mm3H4UXI5FT97OdqJ\novNXc0/TqqAZQFSqHueFGXs3I6R7SGwpC0EgpP5MUq2wgMlGtJAIEz8eTHwJdyfHa8nny7iO\naMt1KgEEIa1+DremNR7UsiS/L57h3qSdv/HcM+h9L1Okvmyjd7fwFcccLf5e4l3WeEy9dYcE\nuLeep0rTLQR8rJL7dRTMkAwlSrKeO5cXU9rhJdw5W3GwUirED4vCqvWaZgFjsZQJsL/L8lJ0\nE7s5zxzVwcYcm6vIQ3aM8N5tF3lp78Hi+Qz3fCo59ofYVq4zCfCbypozYidBnmP58007Ds4/\n7/x+9palNf8IuzQGCXCXPjhluycIPNdKsc4NxTY32kiP5vDEyZL5GgJcPiYzFMzS5N4mWsCT\nAsxHQRRgxvay0o1bgk+tl2kr2tycVFWGuFCIWcyoMPXR4XorF9uq454ny6y9hSTAc04F2Gdi\nWxJgnuWsfRIayTe/H6tJycS+kVt7KqwEuKcepwrTTQSCG4sihT79qeV7yA39O5tsworbuH7l\nbOUZdGOlDjHjLjyW9jqa2kITBTi3HMH8Ff6D1Cz/yPLCS3g7L2kbonKsHdMresS2maO360d5\nub6c49jGTW1jnMe66Mb/k7tviNZ9aOZHQpayts0gwLOOoshvMgowE6zcnsRrvZ+LH2hGGhaH\n1YzwW5IANwuo4hEBEWiMAB2xYjsporQy7dRU6nXMi3AL7WX0IJ7VReskuOKbN/nxawhpotdE\nAbZOWP6mjb7w8th2R+TBFe6wHJFnVuMKLPo6caMdZ26U9Y5HfIH24WT5RNqlowDbecr7Igu3\ndnJMqR3KdRCBzCrlI8o69NmizqM8Z2uzvXOjH39Xs7LqKw/QAAA2c0lEQVRq1nSWVrPi7MZ4\nZAF341NTnnuCwOZkVa5YlgGXZ4SOs+knv4tnqEaVJQinlJqX4xbCvnKjG39HcmlyZqwpQed6\nSBtwMh1mFsEoS3em+eOUfxHCyqlqLkTr3aqss6s0e6dWVTM/ErLYtW0GAX6DNC8U38BH13ti\nfDw0PrZu55nHNv1mpGFx2Hhy4jywWfF1azwS4G59csp39xNgTV9eQrzzbEo6P2wWAQef5hBL\n1sbP1nDU7/Ki/ABvM9p/o7MeqwOYqQy7nL8jLhuGVJmP2IPV3WOx8xJNqyerpZX7sp0dd4WS\nAFO2aLFTziZa6dXS1rm5EuCZH4B1Gnu8T8YRrNajqQJMGnTmqxwBMJle/+xJgPvnWauknUkg\ntpViab6Yl9KBiJN1TsFSjC+9BnOc9Fg9vEkCh2A+wD4Kpmci6XjFTILbp19LzjDVJvP9hrsZ\npMyIq8Rh1mcdeiTAGZTO29KLvnw6UWt28HcgzPGjq3nZLW7mt7WOaVRf17w4uy8mCXD3PTPl\nuIcI8BKiZ2mgedSfwBYL2KpsrQdq2NZ4MZMXJ6LXJIELWEPBLJUpLtzH+fs3urEbp1woHW7w\njjbDwkrbZiczAfZuqEn5y2LWtnkEbNUr68xX7sIt/B5pMWmeK7ocLSieGbb8vw6HmaZjbV56\nnRpTU6qqOrVwypcIdD6BKJqIVDBrk6rkCcZH5pgDwW9qPO9jWJhDrL/bLAH2RfL0yyr5oPc2\n+aOLbJVrM56iG+1+zCtcM3tqz5icLsyNwCKeeYUAb3QFs1I53UxX+I1zeX7vPk9i05s6mplU\nB8clC7iDH46y1vsEqOZFcMNPEVz+F/0ieg3v3ucKZzJr0KWNlj5rY+W+ROcajWBa+HDwhCtW\nqXq0Kug46ce0O2Y7QX11rIJmyJQs4NlALeA1fkNYwJVV0EgvFTO2LHXz3KiPIh8/7gbdkAlw\nXzoJcF8+dhW6cwjYeEvPmF8Xq5w91q9N2zeX/GFhxupiXmhV2m0bjDFZKs6GIVUR4HAP+b21\nwRiJyhX42ODWZlnoDedAN8xGgM57fAjaGO8KC3i2W+Z57ad2P9ouAZ4nSN0uAiIwNwIIcHzh\nxZfRuBsrdVpqNDpmu48CPO6K855jdz1zNvMyptpxugAXXOEiasvf3Gj+0vC2gpMs4DnCa+Vt\nh6Y1Jzx3+022wfmLqUlhmFP/9oZWG3AbfmZKQgRmIfBJlv27nnV37X/xXMzKOQswpsR+DMwC\n1VpLZ0mvzkv5c3k5bh91BearrnS3ereh8kxDR1RDqwq6IWJtCkznvdh0UZhaBd2i9Df4sV+t\nD/l7qPXpWwtYAtyiH5eiFYF6CNBT+L0Wbl0YWMaL6E5EtDS9ZD33Tw1D/e4umuzmbQEXXTiE\nscm3zjc/U/PHMQI8wIueyZXkOooAD+VgyxBToLarCtoal1lfOjThg7GjUNadGbUB141KAUWg\ndQRG3MSXxlzhQfNPwdbrzc3rhTYchk7hY+Dh5CXOVT3/PE3GQPXmfc34QJiMUXvNIzD4BxYX\nVlmVoWfNS6U8Jn4LtipS386IJQEu/zVoXwQWigBvotu8u2u+yRONzS+9bF0YPIvqvdPmEh9x\nvJ52uWfT/tt0Aca+uhd/0FzypXtaS4CPo6MRwytHvLOZr9riSG8vIrSuLYl1YCIS4A58KMqS\nCMydgL+Nf+o/4GX6LV5ur50xHur+1ofBCw8PVWe6ilXY9Fg2MW+qI0/0qs4xx7TcTASGw+Df\nrAn5U2e63qrz/CSO4ONopFXxV4uXDz1b3vJPql3rh3MS4H54yipj3xCg7fYmXmiPRoBtOMnq\nmQo+7AaejBC+a6nLP3BqGIQ3G8bUAgvY35tzk+sMT01bx0Yg95JBF85pP4twOALcNuvXyofo\nM/VqstZ0+8u78ClKgBf+GSgHItBEAuGzqfgSp1+9Lgy9kPl2/6UigTjGN/d5O4dgT2t/wyqJ\nbciteTEGLGB3UEV+dDCVgE2GcTwd85469UKLj6n5aEWzw8y55rdmE9HsmDlEb1+RAPf281Xp\n+ozAiBv/HnZF2okmMNdusHbgR5ZjWInAToq0zXxU6bCgowWMODe9OpJ0WdrOHV2Zoo7KCfDM\n7KPovJzLfbr8fKv3eTbLeDZNb3aYLd+Ir819vn22ML18TQLcy09XZes/AsmUgTdbwbEuGNrk\nzmDvcKypp2UwGG5SaoPlBVjFAvZpL+oQ48nua8YWUd/Ei35NM+Lq4Th4Jn4Iv4heUYe0q5z8\nFpbasKB2pWfp8Fv4Kh+M/9vONDspLY0D7qSnobyIQBMI8BJF5AKrK0UhPRMR5kWXu5yxt2iv\nTfY7VBLgnBvgZT91TG5YgSX0uhE/fnUTslMRBd8HW6gBP6riZBcerA02acXA7436iS80LfuB\nlTSsWdT50nt5kRuC1djOpqUxe0RLc26irQLMZByfnD1LvX1VFnBvP1+Vrg8JYMlciQh/rbLo\nfhGv9vj/zlSVpZmHCFuqgqat+HzGAI8iAFhdhc9V3t+cIxabsE43B1jvm+bEuDCxeDd41oAb\n+PyaMHj2fHOwOriDGTJ22bAb2rTWDVY0F7AYxqq1YeDpXP9+S5nx2+C52HKYba2Cni+7br9f\nAtztT1D5F4EpBEZ84cPMKf13U067Y9I5mFG+kgATpqwK2q/lGtXDYWyjd5un3t+MY2bXigtN\nkJdojTcjzoWJI+nJPehy9Byenxt0gyfx0fMiuB9Ou+9fWmx8GBXN0xt6Mef+luuPgFmcqWp+\nqVW/2/oF2BVbjat6CJ1tBQEJcCuoKk4RWGAC/GOXragUfmbZ4VwUPaqnaesL91PXeTuC+xLG\nnD40yW4yJSDn6RjTGoeVlU30X7K8W5NSa2PN5i+GY9kHzJzTTJ+Lt9UvjrNYmB/8WWzuo3GA\n9Xl9rLKnfnrVnFOocSPdn9OOcYXbawTV5SYSKLU1NDFORUXjEBCegrc2nXrcafUEUhgRqJcA\nk/nusa7MZkXx90Je4l/n5Z5anTlEI/Y8/Tnnnzrgio8l6E/xdot1jGmZAI+5sfuHkn+LrhZg\nMMV2dD5W5iXAVC1/GOKlNnmeFYsS+U+PuokvD7vcfqq5F/MMl/BMSHLoBetC2EwNx3/Zc6pw\n1B2vd/l/2+MKb93mXcO9ikln2D7KNqXLYlbErYOWEZAAtwbtsUT7H/h6BVjLs7XmOfRtrNuw\nntY7twX1fUrOjd9lP0XEIooer3ITWizk8FuTW2zjrEoaQ8hEu6VzAUcLmH+MeQmX5XNhXSKa\n1CYsOSa44/jguWOHb3wID6xPh/iaRGAj+5W0+36AxzLugo8rR6XPy57URfj7KPc0AU6qp/2r\nD3RDw2tC8R82+fFrGuFDE/A6mgdGSIQsybWLgKqgW0N6lGj5n3CH1ekvIJycCDSPAEsT0sP0\nmFFfuB6lzap9owWcWFSBzlDhS7zyd+CjBYYIpBawjc1sjUNAYl7o8NvlFnA2m1fuwEUuf/kK\nN/jyuRHzB8Odtt1QsPvZz/HBtDWNax9qyDPxQzyz9ybn/HJM1WkznPEiZxrJ+Dl1LtVvj07v\nr3vDcyFat7HuGxSwKQQkwE3BqEhEoHMJjDuHgWYv53wUYF7yGG1uzwY/fhXbr3ApWsAmzBbO\nrtm2FY4XTirAk72vW5FOq+OEUdohKjyTtE7Ggpxj+2wm5J5KC3NhJ4sh3JTu7+cjif5R0X2c\na2O2N+Hy08YGD7j8hUkwe37WxNCo84h62NToXQo/PwIS4Pnx090i0PEEMHGpyjQXFjPM6I8Q\n4L/AYxhHR5WmX8HqSU/ECnqMtQNyzaaLbIkb9Q6rLqBf3S3AMIrCyPYU+LGWvXv6uuAe0Ai0\nlSF++GTtv7vgMgYYmgtKDlZJOkVX4LrfYlcG0g+ltcEdtDbkz7BzVB9HCzjZn1PHMOsXsNvu\nl2sfAQlw+1grJRFYGALe8WIPE1RNHsgL/iGWCbaplRs2cPgIhOSkREj8S/a5sT9pcUbvZGjN\nkS1Oo2XRD4eBc4m8Qmz5eOE431DV7wqXfw7cudVcsI8kqx1IP5bsnNvPc4pCz4t6L9bwZjtZ\nTDvL5Vye6Sr9f9s5nm9piBL3NGwBE7c1CcSaEotPrj0EJMDt4axURGCBCfjNWFDreFWnHf4C\nlq9VZ/pvowBHIgRHmUgzfvjaLd61eualTcgIVZ7d55is5HRs0PfD7ARyn7XVxoJwbmkjJUL0\nbHgRHeHiMDETPxNfWgxKbh/P5VA7QnR5XuGNPKM9WMCZwK4ljnRhC38wwnuThZ2LAHMPAlyM\nzQMWh1x7CEiA28NZqYjAQhP4DdbSCYjEkGWEF3sUWe8KsSqaFztVmP4rm307OuJ4NN6n404n\nsawPdFoMrtNHZrwDhmss14jWD/m7n/mtL4UfQ7pKyzhOFmrWPX8EcfycIN/Hm9haG29s501u\n84hyoDNnGB917l7a7L9PmLuLbiC21fO8bLTFwTQrnJIIcbjS7uM5ZwJth/U6+gdYenLtJCAB\nbidtpSUCC0YgbEUkjiT5aAEHV0wFuNRDGgEO97Yne8EWYa8iEvmr1rn8ee3Jw5xTSS1OaLmJ\njwdXOJxxuS9GGLfR+akhCxjBO4xY7sC6/Tk8fnG/G3vCva7wrMmcxWX6TuDaXXwxsbE03V7W\nU44CzKl1xGEfLC/Ar+DDYCQNU4WtXZnN+QO4XxbwbIhacK3TvzZbUGRFKQL9SMAzTNX9DiIc\nO/lQHR0FmDfu3tScQoCtOrT1zl70CEma7GR65OkQRKVBEZu8vz17PhszbTOL0ZPcxY8WyrOb\nvE8r02x5goOtPnTLiB/7SPVw/g7CWM/1jZPXw14s7mXp8XHp9kSEeIjZs24k/PX4OQiwW8yH\ngCzgSdBt2ZMF3BbMSkQEFpYAqxDtRHwZKsOiDIz9RTB+YTmamLR6aI9sXe/nKaXnRe/jkKjK\n8wFxC1XOV4ZaqCMayQ9EZFdm6dN+nvUkxzINu2Ha0McD97Auc3GWIV9hW5rWDVmaiOt1WNu/\nd2iwtJKPAfL0CLuOmG/n76fIR8MCTBy0AZemCc2S07bFBCTALQas6EWgEwikFu+DeIH/Lvm5\nlAk6aL90NmdhrHbkpb4SMbi7HXklL5YmL/wyR9sveTDhSDuJlV3rkN3FTPWISJXG+9LWWhJg\nuCKk2TrKdWfYVh+acehPwRX+DzF9R3Bjb8pi5NjE+DAgxeFLiPj7STeOC865gq00ZXlqWIC5\nhw+fCVnAGeg2bSXAbQKtZERgIQnwot/Fy9mqSOm4Y1Mcps6bEZxM8MBKOG0RYFKmw1GlpUtP\no1i1yyIH1QWYBtZmLP2XFXtuW2uznXTjZQIMU6uKLlVPT4aaeY/nQRV0Nhxserhbvduw0Y/9\nLStT3ZxdtfD2HBlSlvIKo9k1HuRuqpEZrtR4Jyzi5WMgGfKUxadt6wlIgFvPWCmIwIITQGdL\nVZ10wJoUYHLGizdacljAd7Uno3G4S4UFTGeUKChYdFWroOmcdQpL/13FFF5Hk+HYk7s9eS1P\nJRnyQx6vsrMMr47ckhBFBDgbElR+z8z7JnqI5YwWcLU7sbqtqpsPqcG0M1ju1iwcC/lGC5jr\nDVnAa4NbTD5yfIC1pQ9All9t4wplwiACItDrBHi5lolFxWQPVvQv2R9ewm2ygL3NcVwhtEyl\nmE2v+DBboN7yU+lCtD5ZSenDwy5/MeNx/yKbBaoyXEuPsmrft1gqWC8lpgk7X+ohXU8uqAXA\n6pz8MKrnniLh7b4B5/8cwWeijuKO7D6+nvZwnTw1NssY9c5pp67cPVlc2raHgCzg9nBWKiKw\noASwnEoWMFJbNtY0Zusa+7vfjW9uUyatE1aFBYyQHG5pI2Rn5V3+OeX5YJrMs5g5673puXVs\nT8Wfz4QUTygP1/p9fxAfDptH3PgPsIJfNeLcnVmadMgyC/jwdHrJ7PTMW9oEiGspH0YYrvU7\ne47cZ00Jz2B7PfdHC5r9dwKPWmjPVKKNWcAHuPyTLAeDbqyhvNSfa4WciYAEeCYyOi8CPUSg\nsr2ycrwnL/G7EJTibYhLO4qMQEzvhOVyUYAtfcTkd8rzQbuwdUI6MTkXLeHTiePExsfdlsfa\n4H6wNb7DKizMP0foCht94f1syWricvQy5+NhxUFuoK6PAtq8bRUkVj7yDVX7I/RWzRzf22Ou\ncLZzhVGe3Tc3urG3WE7gggXsbe1J8luf4x46l8UpuCTA9SFrWigJcNNQKiIR6FwC5e2VEy7E\nKQuz3E64sasRlzfy9p5qGWdBmrrF2sVqqxzvi5YdmiWCwByV7duWa9m4Vzs04UJcbAGEivN2\nbc6O2aT+cV3I/+5MEaxzA0/m2gEDbuLaamE2uvFvo8YjVEyXPiSqhcvO0Ygdq9wR0TgeOztf\na8vEH9HqhsHXbvPu/lHvtvExcA6QYrs+go4AO7eqXiuY9nTiilXrfH1JgGs9gCZflwA3Gaii\nE4FOJEAnp1IV9KAbv6E8j/S23brRj7+z/Fwr95Me2Um74zpWEKLN16zZKEiWLhZdaT85nhxf\ni1hgsCWOnTPWh4FnZsfz2SLyr2KGqcfOFAdW+OO49g0m3ihVO1eE9W6cONCwyp7SFWHKDoou\nH8cTU4aGBHiTdyO0Gz+Fj6aXlUVX2mXVpFglTR11XWOSj41aHZnvQcTHSxFppy0E+L+UEwER\n6HUCG5y7Z9g5DKZwJPvbF7K8DJXZhaWWR2kXsUbxhbyEbIILhMPfihQwJaI/BFEezrmBB4/6\nic9zvtwCLsu6Pw2L83LWkBhCPErVwWUBZty1Re1ZV3fVJl/46bow9EICLqcqHsNxRkdeXY1O\nah5xTjqLzRhLemHAFWkuzu0zK7ZW2KnXN/qJL089lx0XGIpk47ioIqhLgIdc/ol2L7Nr/UEW\nh7btIyALuH2slZIILBwBqpcZZvQBxGxLo2LV7EwznGiXxUk9swkrnbH8CqxiLMLwBdo4X20W\n8KAbOm/ADfyvLdCAts4iJn6QumvrlNSQ827oNQj/v9pNtN+utS3pzCbANvSpYviW3VPpgvUi\nPqjyXPUjvhYO5EqsLq4eYm5nyWS0gPm4mIVZErfN7MXea+D+g1E//tW5pai75kNAAjwferpX\nBLqIAB2xvoG4vXuhs1xMe9tipdH2aFNShuWIHxahdUgq3kH+VtFOHNtjJ5gcArGqEFiO31Ve\nBi7WFJvy8LZvIk96R9h+MZ38wyxvO57B2VrKtdrI76M8y2e4f8rpARt727D1OyWSaYcbUwGm\nOr0mE8R6Nfl9KOW6cVpEOtEWAhLgtmBWIiKw8ASsupUOO/+50Dnhhc+QHZavd4PPoVoXC9gt\n5xyTUhT3jLtxamVj7+DHW5gBN/QQji1MySGet5QO2OElNkMVdXmoyv1EbMPhdhaxivETb1XR\nYszxKwn/PILOagFzPwJs81nXdoS1NJsuwJjxE8R9fz0CzBPIxmLXqFqvXR6FmBsBCfDcuOku\nERCBORIY9e4eROK7SN8jEKxHplYjYhDXo93CNfTYejlHh8UeYpV1lhzW8iYLg8dAtgUlale3\nZvdObsMqRPUgTOEhEosCzPEJ68Pg4ybDlPZOSvdqWMAeAa57OsoDyD/joZvv+KhhSsqBqh8T\n5amRflruWHVefkn7bSIgAW4TaCUjAiJQTsDfh1A8BaFdhqDSHOzW4/dbpySqhv8ZcfgfPFXS\njtkn/dV2J8dopY1XHWd65MIRdJqydXDNgq0pNhZuiotDb9YxrInz2fzTDM/1L50SjsO48L1t\nZ7WACVB3FTR5Nuuz+RYwkQJpG7UJw+zO6mgDTy1/v2PWgLrYMgL9LsD2T0AfDipu5ERABNpJ\noMz683msT+sQFAWO9XEvpKr8Rfxb7kwyVBq3HKtK+We934YDjfoxlt4LzPzU+HhgRN06VZmz\nTlNZVSziNX0hA+I/2gIibLNawLRb81FRbxV0FL+WCDBZvZphUw+3PM/mYGdW+P0bXeGS2cLp\nWusI9KMAnw7Oz+Dtn9n+ARg6ELc3sb0Y33B7EvfIiYAINESgWvVrrIIuiyWrGi1+H/n7CcJr\n/6M2xKa897D9D0dLruzGenajAAeXR4D9YoQojTPYh0CFQ5TT3tGVi1hUBOKAcFZVHt8fTJ/5\nxOpzWmd35cjz1PJm1+a3pSxbyc1hdcRCRzBYppN41BFeQZpMoN8E+DT4fRO/HW9j/87AW/vO\n2fiL8FZt80t89nXMrpwIiEALCJRV54Z0dqmJsnMxRdqK3U2Me/3sBl84veiSZfk2llXdYjkj\nwAMlC7befCI8aRtzXMHIeiRn1vU0AUbMrJbMOnvVsIBtJqk4DaTNLnXZoMv/8cz5CSZ+9vHQ\ndMcY6x2THw0zR89slfYR0JI8zJyqrpQT6DcBPp/Cm5X7CrwNZv8R/td4ewF8Cv9UvH1ln4OX\nEwERaB2BktgistenyZRVSyMNzt+D+JlVGR2CtdMEmQvlQkg8IWvDzYLWsQ3pR3YOC9jaYxNr\nm/gRpUlnY2XJR3pu9jbggXR8M/XVtGs7hjnFRSMmIyvb4zrDmkJLxI+q8O3EfwLTa76lLMkq\nu1YF3ZqPgCqJ6VQVAv0mwPalXPFPXoXJZs5ZhxA5ERCB1hGIAowIfYxZmC5PkpkqcOEehKQk\nwHtd4Z0YoU+ckiX7f27YAkZ4ogXMC/BtpGFCFC1gZL/CAqaj0hGWHvksEqZc+Kdkw8KMWS9o\nqs/y1plrEOGepRrYW+evNM1pUc3rBJOZpNZ8GK4W0drg1q4P+Q9Sdj4sWvMRUC1dnZtOgGfQ\nV+5zlPYCvFm6/G9VOOtJ+RL88/BWTS0nAiLQMgIlsb2OKYhvt2TGp3wcI8xWG/XbLAt07d1O\n9+fN2XGytbbk2KO48nTto9QCDschrFisWU/gcHT5UKScGzwW8SWIfzdjnn44W7Soc5yFiipg\n62OCm7lDFnHaRCA7k3DN/UtZYns28S+pFjNTfD6U8ryUQp3I9dIHTrWwOtdaAlNFqLWpLXzs\nV5AFE+DL8NZZwv4B7J9mBd6+SDfgz8NbtbScCIhAywgUEU4G47jiSIH/QatDHnQlUY6pjvjx\nf6kj+X0IScMWMFZvtIARK9blDYcTx+fowXwsx6eR5ovxV1narENsPaDv2OjH3mDHs7ktzLe9\n3gWK449Lw9k7ZiZ3COnZ+6fpLlsRiTJWFWB6SKf58labcEPTM6AI6ybQbwJsYC7BfxJv1czH\n44/Fj+Bvw1tbVBEvJwIi0FoC+61ad8xNfB+h2Mv+9QVXiJZwI8kinCbkjQkwpqFVEWOhmlia\nEK/C3zTuCpcOuPxvifPBk3koHkGYbZPHs+zZLFTBY6S7ByShqk9LSRWwdcA6hnHMLRl/O+bG\n7l8U+5GGs1l04gQydHN5rnnBLbOqT/KwDgZXl1/TfnsJ9KMAnw5i+5p9PJ4OGNFZe9Qm/Ffw\nb8KrWgYIciLQKgII7q+xNj+xxWfL8RVOnVta0WquLsCstnQ4hvUdfnIpxjSNtPrZ0cnLHUo+\nckU3sceW+mPxh49w7gWTecnRAzrYqIk6Xfg20pYKcPUq6OAGKas/BKG8ss5IGwqGsMYqaNJg\nlq/8Wc4VKgQYyxsLmFA4PjZa0g7dUIb7OHC/tQFb9dI38fYP9UL8GfiT8GfjL8IP43+Jz/5B\n2ZUTARFoNoERP/FFJtuw/8H5un3prFLT4hl2+Xctcfn/nHoBRY3VzxjCJfGh2taaoqxK/GtI\n09D6MPTu5L44BKkBAS5+KYnHoefVF4kYoGqYD5CJyY+PJKVm/SX+VIBNZv0J0+PNqqDjlU3T\nr+tMuwj0mwCfD9iL8a/AaxhSu35lSkcEWkYg9uJNhwlNS8SqltdNPUvgKMAIpDU9RUfP4T22\ngyjbdJJ5LMOn2DECZnHULcDBTdxi9yGwb+PuIYvQjssd11jzeFIky681Y3+0LG6s3ZVT40ws\n4OQs1f6fmnpdx+0j0G8CbFVV+2rg3cz19TXC6LIIiEAHEEAoaUf1GLXTHeJpvZuPmHoFCzHW\ncI27sdchlR+260VXiM1O6GXa/BRWM46WqujASk1xkYWp0VQ9HvHupglXfBL5usECrJ2cZ7oU\nngkwbGnDkpVautCsHcZJm4VN3reT92kCTNqloVYEsmp4uQUi0G8CrGFIC/RDU7Ii0BoC4Q7E\n5glrwnRLNxFPFnqgIbQ8bYYLxWM6I7Hr77RriHLskUzHqCjACDciFV6GWC3NuWIqyuWxzLzP\n4vbWlyR+6POCtQ7eFY4qc+Ju7QxUWNgfJ+/frGYBk5k0T6Gw1bfwQ6Ci1DqoRqDfBPgKIFyA\nvwxv/yB34DfgrTfivfjX48/D/xovJwIi0PEEPH2s/IGM1z2mSlbNAj5gvRs8y64Nh8Fz6BW8\nIrOAUeECtu99CHgYSQV40I2Via0/gvuXYkXurhL3rKeCK6QTjVQdItXSKmjLGFN3/jECfA15\nP3J6Rj0CHPj4SNZlnn5dZ9pFoB97QV8C3E/irZp5Lf4wvLXxaBgSEOREoJsIMHTo23mXD1gS\nFVaulQHxWY4lyHrB1pMZm5Ne1xjDF+adv86OUcg9ixKL914ujts5vsp30EZsH+XrsR6P4K57\nEbI5CHCyshPpT7OAiZdOWK23PGFyDeX4t3Uh/5KcK3zBVpCyMuJoivPfIg8/SA71d6EI9KMA\nG2trf/kl3jpM2KB0s4D5PcqJgAh0E4FbvdvA0KEx2jIrBZiGVoQO689TvRxWmBrzD057aFg9\n7sJvBpliYwvCOuwC7wH/pazMViW7KoydusINWWcs3g2BlZIaq4K2uKjejhYwu9MEOMSlArP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BBRGoaDNUo1mOmaXZpPb/M/uTr93ZZzVg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\nfgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gendata = GenerateData(1000)\n",
    "par(cex.axis=0.7, cex.lab=0.7, cex.main=0.7, cex.sub=0.7)\n",
    "plot(gendata$x, type='l', col='blue', ylim=range(gendata$x, gendata$y), ylab='')\n",
    "par(new=T); plot(gendata$y, type='l', col='green', axes=F, ylab=''); par(new=F)\n",
    "gendata[names(gendata)=='cointegrated']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And let's try the Bayesian routine to see if the result matches the truth given above when generating"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$test_result</dt>\n",
       "\t\t<dd>TRUE</dd>\n",
       "\t<dt>$comparison</dt>\n",
       "\t\t<dd>'Congratulations! The result of the routine matches the ground truth'</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$test\\_result] TRUE\n",
       "\\item[\\$comparison] 'Congratulations! The result of the routine matches the ground truth'\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$test_result\n",
       ":   TRUE\n",
       "$comparison\n",
       ":   'Congratulations! The result of the routine matches the ground truth'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$test_result\n",
       "[1] TRUE\n",
       "\n",
       "$comparison\n",
       "[1] \"Congratulations! The result of the routine matches the ground truth\"\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "BF <- BayesianLearningTest(gendata$x,gendata$y)\n",
    "test_result <- BF<0\n",
    "if (test_result == gendata$cointegrated) {\n",
    "    comparison <- \"Congratulations! The result of the routine matches the ground truth\"\n",
    "} else {\n",
    "    comparison <- \"Unfortunately the routine disagreed with the ground truth\"\n",
    "}\n",
    "list(\"test_result\"=test_result, \"comparison\"=comparison)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing with Dickey-Fuller\n",
    "\n",
    "For comparison purposes we now test for cointegration using the standard test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: tseries\n",
      "Warning message in adf.test(epsilon, k = 1):\n",
      "“p-value smaller than printed p-value”"
     ]
    },
    {
     "data": {
      "text/html": [
       "TRUE"
      ],
      "text/latex": [
       "TRUE"
      ],
      "text/markdown": [
       "TRUE"
      ],
      "text/plain": [
       "[1] TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "require(tseries)\n",
    "ols <- LinearRegression(gendata$x,gendata$y)\n",
    "epsilon <- gendata$y-ols$intercept-ols$slope*gendata$x\n",
    "adf <- adf.test(epsilon, k=1)\n",
    "pvalue <- adf$p.value\n",
    "cointegrated_adf <- pvalue<0.05\n",
    "cointegrated_adf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ROC curve: Bayesian test versus Dickey Fuller\n",
    "\n",
    "Both the Bayesian learning test and the Dickey-Fuller test do the job and provide a test statistic which we compare against a threshold. To compare which test is better, we look at the ROC curve, and in particular, the AUC of the ROC. To do that, we repeatedly generate time series and perform both tests, then plot the resulting ROC curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Experiment 250 of 5000\"\n",
      "[1] \"Experiment 500 of 5000\"\n",
      "[1] \"Experiment 750 of 5000\"\n",
      "[1] \"Experiment 1000 of 5000\"\n",
      "[1] \"Experiment 1250 of 5000\"\n",
      "[1] \"Experiment 1500 of 5000\"\n",
      "[1] \"Experiment 1750 of 5000\"\n",
      "[1] \"Experiment 2000 of 5000\"\n",
      "[1] \"Experiment 2250 of 5000\"\n",
      "[1] \"Experiment 2500 of 5000\"\n",
      "[1] \"Experiment 2750 of 5000\"\n",
      "[1] \"Experiment 3000 of 5000\"\n",
      "[1] \"Experiment 3250 of 5000\"\n",
      "[1] \"Experiment 3500 of 5000\"\n",
      "[1] \"Experiment 3750 of 5000\"\n",
      "[1] \"Experiment 4000 of 5000\"\n",
      "[1] \"Experiment 4250 of 5000\"\n",
      "[1] \"Experiment 4500 of 5000\"\n",
      "[1] \"Experiment 4750 of 5000\"\n",
      "[1] \"Experiment 5000 of 5000\"\n"
     ]
    }
   ],
   "source": [
    "T <- 20\n",
    "experiments <- 5000\n",
    "\n",
    "cointegratedActual <- logical(length=experiments)\n",
    "logBF <- double(length=experiments)\n",
    "pvalue <- double(length=experiments)\n",
    "\n",
    "for (expr in 1:experiments) {\n",
    "    gendata <- GenerateData(T)\n",
    "    cointegratedActual[expr] <- gendata$cointegrated\n",
    "\n",
    "    #classical test\n",
    "    ols <- LinearRegression(gendata$x,gendata$y)\n",
    "    epsilon <- gendata$y-ols$intercept-ols$slope*gendata$x\n",
    "    suppressWarnings(adf <- adf.test(epsilon, k=1))\n",
    "    pvalue[expr] <- adf$p.value\n",
    "\n",
    "    #bayesian test\n",
    "    logBF[expr] <- BayesianLearningTest(gendata$x,gendata$y)\n",
    "    if (expr %% (experiments/20) == 0) {\n",
    "        print(paste(\"Experiment\",expr,\"of\",experiments))\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: pROC\n",
      "Type 'citation(\"pROC\")' for a citation.\n",
      "\n",
      "Attaching package: ‘pROC’\n",
      "\n",
      "The following objects are masked from ‘package:stats’:\n",
      "\n",
      "    cov, smooth, var\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "$adf\n",
       "\n",
       "Call:\n",
       "roc.default(response = cointegratedActual, predictor = -pvalue)\n",
       "\n",
       "Data: -pvalue in 2539 controls (cointegratedActual FALSE) < 2461 cases (cointegratedActual TRUE).\n",
       "Area under the curve: 0.7822\n",
       "\n",
       "$bayes\n",
       "\n",
       "Call:\n",
       "roc.default(response = cointegratedActual, predictor = -logBF)\n",
       "\n",
       "Data: -logBF in 2539 controls (cointegratedActual FALSE) < 2461 cases (cointegratedActual TRUE).\n",
       "Area under the curve: 0.8976\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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27j/b3D6+Qz5COGZZfyhdDqEK/ljoFK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LAM5fTEW2+zzTaPzZ0710ydys+yQgREQAREYAgCW2Pd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\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "require(pROC)\n",
    "roc_adf <- roc(cointegratedActual, -pvalue)\n",
    "roc_bayes <- roc(cointegratedActual, -logBF)\n",
    "par(cex.axis=0.7, cex.lab=0.7, cex.main=0.7, cex.sub=0.7)\n",
    "plot.roc(roc_adf, col='blue')\n",
    "plot.roc(roc_bayes, add=TRUE, col='green')\n",
    "legend(\"bottomright\", legend=c(\"DF\", \"Bayes\"),\n",
    "       col=c(\"blue\",'green'), lwd=2, text.width = 0.15, cex=0.7)\n",
    "list(\"adf\"=roc_adf, \"bayes\"=roc_bayes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above curve shows the efficacy of the classification of the test between cointegrated and non-cointegrated. Perfect classification occurs in the top left of the chart.\n",
    "\n",
    "<a class=\"typeform-share button\" href=\"https://bayesiancointegration.typeform.com/to/gRS0pq\" data-mode=\"popup\" style=\"display:inline-block;text-decoration:none;background-color:#267DDD;color:white;cursor:pointer;font-family:Helvetica,Arial,sans-serif;font-size:20px;line-height:50px;text-align:center;margin:0;height:50px;padding:0px 33px;border-radius:25px;max-width:100%;white-space:nowrap;overflow:hidden;text-overflow:ellipsis;font-weight:bold;-webkit-font-smoothing:antialiased;-moz-osx-font-smoothing:grayscale;\" target=\"_blank\">Contact me</a><script>(function(){var qs,js,q,s,d=document,gi=d.getElementById,ce=d.createElement,gt=d.getElementsByTagName,id=\"typef_orm_share\",b=\"https://s3-eu-west-1.amazonaws.com/share.typeform.com/\";if(!gi.call(d,id)){js=ce.call(d,\"script\");js.id=id;js.src=b+\"share.js\";q=gt.call(d,\"script\")[0];q.parentNode.insertBefore(js,q)}})()</script>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.4.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}