9879HW04_Chen_Weiyi.ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# <font color=\"blue\"> Weiyi Chen"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# MTH9879 Homework 4\n",
      "\n",
      "Assigned: February 24, 2015.\n",
      "Due: March 10, 2015 by 6pm. \n",
      "\n",
      "Late homework **will not be accepted**.\n",
      "\n",
      "$$\n",
      "\\newcommand{\\supp}{\\mathrm{supp}}\n",
      "\\newcommand{\\E}{\\mathbb{E}}\n",
      "\\newcommand{\\Eof}[1]{\\mathbb{E}\\left[ #1 \\right]}\n",
      "\\def\\Cov{{ \\mbox{Cov} }}\n",
      "\\def\\Var{{ \\mbox{Var} }}\n",
      "\\newcommand{\\1}{\\mathbf{1} }\n",
      "\\newcommand{\\PP}{\\mathbb{P} }\n",
      "%\\newcommand{\\Pr}{\\mathrm{Pr} }\n",
      "\\newcommand{\\QQ}{\\mathbb{Q} }\n",
      "\\newcommand{\\RR}{\\mathbb{R} }\n",
      "\\newcommand{\\DD}{\\mathbb{D} }\n",
      "\\newcommand{\\HH}{\\mathbb{H} }\n",
      "\\newcommand{\\spn}{\\mathrm{span} }\n",
      "\\newcommand{\\cov}{\\mathrm{cov} }\n",
      "\\newcommand{\\sgn}{\\mathrm{sgn} }\n",
      "\\newcommand{\\HS}{\\mathcal{L}_{\\mathrm{HS}} }\n",
      "%\\newcommand{\\HS}{\\mathrm{HS} }\n",
      "\\newcommand{\\trace}{\\mathrm{trace} }\n",
      "\\newcommand{\\LL}{\\mathcal{L} }\n",
      "%\\newcommand{\\LL}{\\mathrm{L} }\n",
      "\\newcommand{\\s}{\\mathcal{S} }\n",
      "\\newcommand{\\ee}{\\mathcal{E} }\n",
      "\\newcommand{\\ff}{\\mathcal{F} }\n",
      "\\newcommand{\\hh}{\\mathcal{H} }\n",
      "\\newcommand{\\bb}{\\mathcal{B} }\n",
      "\\newcommand{\\dd}{\\mathcal{D} }\n",
      "\\newcommand{\\g}{\\mathcal{G} }\n",
      "\\newcommand{\\p}{\\partial}\n",
      "\\newcommand{\\half}{\\frac{1}{2} }\n",
      "\\newcommand{\\T}{\\mathcal{T} }\n",
      "\\newcommand{\\bi}{\\begin{itemize}}\n",
      "\\newcommand{\\ei}{\\end{itemize}}\n",
      "\\newcommand{\\beq}{\\begin{equation}}\n",
      "\\newcommand{\\eeq}{\\end{equation}}\n",
      "\\newcommand{\\beas}{\\begin{eqnarray*}}\n",
      "\\newcommand{\\eeas}{\\end{eqnarray*}}\n",
      "\\newcommand{\\cO}{\\mathcal{O}}\n",
      "\\newcommand{\\cF}{\\mathcal{F}}\n",
      "\\newcommand{\\cL}{\\mathcal{L}}\n",
      "\\newcommand{\\BS}{\\text{BS}}\n",
      "$$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<font color = \"red\">Homework is to be done by each student individually.  To receive full credit, you must email a completed copy of this iPython notebook to Yu Gan (yugan323@gmail.com), Fubo Shi (fubo.shi.baruch@gmail.com), and Tai-Ho Wang (tai-ho.wang@baruch.cuny.edu) by the due date and time.  All R-code must run correctly and solutions must be written up neatly in Markdown/LaTeX format.\n",
      "\n",
      "<font color=\"blue\">If you encounter problems with Markdown/LaTeX or iPython notebook, please contact your TAs Yu Gan and/or Fubo Shi.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 0. (0 points) \n",
      "Read Chapter 5 and 6 of Hasbrouck and Chapters 2 and 3 of Foucault, Pagano and R&ouml;ell. \n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Glosten and Milgrom"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 1. (8 points) \n",
      "\n",
      "(Adapted from Hasbrouck 5.2 but please note that the setup in (3) in the slides is different from Hasbrouck's in Figure 5.1 of his book.) Consider a variant of the Glosten and Milgrom model where there is informed trading only in the low state $V=\\underline V$.\n",
      "\n",
      "(a) Show that the learned probability after one step that the true price is $\\bar V$ is given by\n",
      "\n",
      "$$\n",
      "\\delta_1(Buy)=\\Pr(\\bar V|Buy)=\\frac{\\delta}{1-\\mu\\,(1-\\delta)};\\quad \\delta_1(Sell)=\\Pr(\\bar V|Sell)=\\frac{\\delta}{1+\\mu\\,(1-\\delta)}\n",
      "$$\n",
      "\n",
      "and that\n",
      "\n",
      "$$\n",
      "A=\\frac{\\underline V\\,{(1-\\delta)\\,(1-\\mu)}+\\bar V\\,{\\delta}}{{1-\\mu\\,(1-\\delta)}};\\quad B=\\frac{\\underline V\\,{(1-\\delta)\\,(1+\\mu)}+\\bar V\\,{\\delta}}{1+\\mu\\,(1-\\delta)}\n",
      "$$\n",
      "\n",
      "(b) Deduce an expression for the spread $s=A-B$.\n",
      "\n",
      "(c) Explain the sensitivities of the spread to the parameters of the model to a non-expert.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## <font color=\"blue\"> Solution \n",
      "\n",
      "<font color=\"blue\">\n",
      "#### (a) \n",
      "\n",
      "The learned probability after one step that the true price is $\\bar V$ is given by\n",
      "\n",
      "\\begin{equation}\n",
      "\\delta_1(\\text{Buy})=\\Pr(\\bar V|\\text{Buy})\n",
      "=\\frac{\\Pr(\\bar V \\cap \\text{Buy})}{\\Pr(\\text{Buy})}\n",
      "=\\frac{\\frac 12 \\delta}{\\frac 12[1-\\mu(1-\\delta)]}\n",
      "=\\frac{\\delta}{1-\\mu\\,(1-\\delta)}\n",
      "\\end{equation}\n",
      "\n",
      "\\begin{equation}\n",
      "\\delta_1(\\text{Sell})=\\Pr(\\bar V|\\text{Sell})\n",
      "=\\frac{\\Pr(\\bar V \\cap \\text{Sell})}{\\Pr(\\text{Sell})}\n",
      "=\\frac{\\frac 12 \\delta}{\\frac 12 [1+\\mu(1-\\delta)]} \n",
      "=\\frac{\\delta}{1+\\mu\\,(1-\\delta)}\n",
      "\\end{equation}\n",
      "\n",
      "and that\n",
      "\n",
      "\\begin{equation}\n",
      "A=\\E(V|\\text{Buy})\n",
      "=\\bar V \\Pr(\\bar V|\\text{Buy})+\\underline V \\Pr(\\underline V|\\text{Buy})\n",
      "=\\frac{\\underline V\\,{(1-\\delta)\\,(1-\\mu)}+\\bar V\\,{\\delta}}{{1-\\mu\\,(1-\\delta)}}\n",
      "\\end{equation}\n",
      "\n",
      "\\begin{equation}\n",
      "B=\\E(V|\\text{Sell})\n",
      "={\\bar V\\,\\Pr(\\bar V|\\text{Sell})+\\underline V\\,\\Pr(\\underline V|\\text{Sell})}\n",
      "=\\frac{\\underline V\\,{(1-\\delta)\\,(1+\\mu)}+\\bar V\\,{\\delta}}{1+\\mu\\,(1-\\delta)}\n",
      "\\end{equation}\n",
      "\n",
      "#### (b) \n",
      "The Spread:\n",
      "\\begin{equation}\n",
      "s=A-B\n",
      "=\\frac{2(\\bar V - \\underline V)\\mu\\delta(1-\\delta)}{1-\\mu^2(1-\\delta)^2}\n",
      "\\end{equation}\n",
      "\n",
      "#### (c) \n",
      "\n",
      "##### paramter $\\bar V - \\underline V$\n",
      "As the spread between the asset prices increases, the spread increases which implies a source of risk should be compensated by a larger bid-ask spread.  \n",
      "##### paramter $\\mu$\n",
      "As $\\mu$ increases, the spread increases which implies an increase of the impact in adverse selection should be compensated by a larger bid-ask spread.  \n",
      "##### paramter $\\delta$\n",
      "As $\\delta$ decreases, the spread increases, which implies adverse selection occurs in the case of a sell order."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Set up R environment for the next questions"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext rmagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "download.file(url=\"http://mfe.baruch.cuny.edu/wp-content/uploads/2015/02/tq.zip\", destfile=\"tq.zip\")\n",
      "unzip(zipfile=\"tq.zip\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "trying URL 'http://mfe.baruch.cuny.edu/wp-content/uploads/2015/02/tq.zip'\n",
        "Content type 'application/zip' length 695952 bytes (679 Kb)\n",
        "opened URL\n",
        "==================================================\n",
        "downloaded 679 Kb\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "load(\"tq.rData\")\n",
      "# install.packages(\"highfrequency\")\n",
      "# install.packages(\"quantmod\")\n",
      "library(highfrequency)\n",
      "library(quantmod)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "Loading required package: xts\n",
        "Loading required package: zoo\n",
        "\n",
        "Attaching package: \u2018zoo\u2019\n",
        "\n",
        "The following objects are masked from \u2018package:base\u2019:\n",
        "\n",
        "    as.Date, as.Date.numeric\n",
        "\n",
        "Loading required package: TTR\n",
        "Version 0.4-0 included new data defaults. See ?getSymbols.\n",
        "\n",
        "Attaching package: \u2018quantmod\u2019\n",
        "\n",
        "The following objects are masked from \u2018package:highfrequency\u2019:\n",
        "\n",
        "    getPrice, has.Qty\n",
        "\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The Lee and Ready tick test"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 2. (10 points) \n",
      "\n",
      "In the following use the trades and quotes object *tqBAC* in the loaded data *tq.rData*.  Denote trade prices by $p_t$ and mid-quotes by $m_t$.\n",
      "\n",
      "(a) Compute the time series of trade signs $\\epsilon_t$ according to $\\epsilon_t=+1$ if $p_t>m_t$ and  $\\epsilon_t=-1$ otherwise, using the Lee-Ready rule for trades at mid.  Name this series *tradeSigns*. (Note this was already done in the lecture.)\n",
      "\n",
      "(b) Compute the Lee-Ready trade-sign indicator time series (as if you didn't have quotes and so no mid-prices).\n",
      "\n",
      "(c) Compute the correlation of these two indicators.\n",
      "\n",
      "(d) Assume the rule in part (a) is 100% accurate.  What percentage of trades are correctly signed by the Lee-Ready test?\n",
      "\n",
      "(e) Explain the relationship between your answers in (c) and (d).\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## <font color='blue'> Solution:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# (a) Compute the time series of trade signs\n",
      "\n",
      "tradeSigns = getTradeDirection(tqBAC) \n",
      "\n",
      "# (b) Compute the Lee-Ready trade-sign indicator time series\n",
      "\n",
      "ts_price = as.numeric(tqBAC$PRICE)\n",
      "len_price = length(ts_price)\n",
      "ts_indicator = rep(0,length(ts_price)-1)\n",
      "ts_indicator[1] = 1\n",
      "\n",
      "for(i in 2:len_price){\n",
      "    if (ts_price[i] > ts_price[i-1])\n",
      "        ts_indicator[i-1] = 1\n",
      "    else if (ts_price[i] < ts_price[i-1])\n",
      "        ts_indicator[i-1] = -1\n",
      "    else\n",
      "        ts_indicator[i-1] = ts_indicator[i-2]   \n",
      "}\n",
      "            \n",
      "# (c) Compute the correlation of these two indicators\n",
      "            \n",
      "correlation = cor(ts_indicator, tradeSigns[-1])\n",
      "cat(\"(c) The correlation of these two indicators:\", correlation, \"\\n\")\n",
      "            \n",
      "# (d) What percentage of trades are correctly signed by the Lee-Ready test?\n",
      "            \n",
      "num_count = 0\n",
      "for (i in 1:(len_price-1))\n",
      "    if (ts_indicator[i]==tradeSigns[i+1]) \n",
      "        num_count = num_count+1\n",
      "cat(\"(d) The percentage of trades correctly signed by the Lee-Ready test:\", num_count/(len_price-1)*100, '%\\n')\n",
      "\n",
      "# (e) The relationship between your answers in (c) and (d).\n",
      "        \n",
      "cat(\"(e) The larger the correlation, the larger the percentage number.\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "(c) The correlation of these two indicators: 0.6618357 \n",
        "(d) The percentage of trades correctly signed by the Lee-Ready test: 82.97026 %\n",
        "(e) The larger the correlation, the larger the percentage number."
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Realized spread by exchange"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 3. (8 points)\n",
      "\n",
      "(a) Reproduce Figure 6 from the lecture slides, making sure to get the aesthetics right.\n",
      "\n",
      "(b) Explain why the realized spread profile varies by exchange.\n",
      "\n",
      "(c) Redo the picture adjusting for the following (assumed) take fees:\n",
      "\n",
      "** Exchange ** | ** Take fee ** \n",
      "--- | --- \n",
      "| (**cents**)\n",
      "D | 0.10 \n",
      "B | -0.04\n",
      "Z | 0.29\n",
      "Y | 0.00\n",
      "P | 0.25\n",
      "\n",
      "(d) Based on your results, where would you advise sending a small market order?  How about a large one?\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# create a function to generate rsLags\n",
      "\n",
      "rsLag <- function(ex) {\n",
      "    set <- subset(tqBAC, tqBAC$EX==ex)\n",
      "    ts_mids <- (as.numeric(set$OFR) + as.numeric(set$BID))/2\n",
      "    ts_price <- as.numeric(set$PRICE)\n",
      "    len_price <- length(ts_price)\n",
      "    tradeSigns <- getTradeDirection(set)\n",
      "    rs <- function(lag){mean(tradeSigns[1:(len_price-lag)]*(ts_price[1:(len_price-lag)]-ts_mids[-(1:lag)]))}\n",
      "    rsLag <- sapply(1:50,rs)\n",
      "    return (rsLag)\n",
      "}\n",
      "\n",
      "# create rsLags for differen\n",
      "\n",
      "rsLagD <- rsLag('D')\n",
      "rsLagB <- rsLag('B')\n",
      "rsLagZ <- rsLag('Z')\n",
      "rsLagY <- rsLag('Y')\n",
      "rsLagP <- rsLag('P')\n",
      "\n",
      "# Reproduce Figure 6 from the lecture slides\n",
      "\n",
      "plot(x=1:50,y=rsLagD,col=\"red\",type=\"l\",xlab=expression(tau), ylab = \"Realized spread\", ylim=c(-0.003, 0.008))\n",
      "lines(x=1:50,y=rsLagB,col=\"blue\")\n",
      "lines(x=1:50,y=rsLagZ,col=\"orange\")\n",
      "lines(x=1:50,y=rsLagY,col=\"purple\")\n",
      "lines(x=1:50,y=rsLagP,col=\"green\")\n",
      "legend(\"topright\", \n",
      "       c(\"D...FINRA\",\"B...NASDAQ OMX BX Stock Ex\",\"Z...BATS Exchange\",\"Y...BATS Y-Exchange\",\"P...NYSE Arca SM\"),\n",
      "       lty = c(1,1,1,1,1), \n",
      "       col=c(\"red\",\"blue\",\"yellow\",\"purple\",\"green\"))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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       "png": 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YAa5j3LLsC6pSVFh78BMnUiUJ9znFGGIJheapWATpP/zHCAFjuN89CS+yQJEI\nT2DB8grQM1aqGVHfFgWPazr8OixmTwgs43N4rnHPexJ+PpY73MoPP/yw93Gec3MP2ouUImAKOKXw\nW+OGQOYggKsU6xf3q2d5JWN0rGOiuH799VdH0E+VIioKeQoPZYPLlrSigtilvCpJXjUe+tZke5Wk\nKVOmFKmrd9xxh3Mvs+bLmi51dNlQwp7FTilBj6oxkobRa5T1X8Y5depUZwVzr/A122jXYWGDtSde\nIQPeo4yxtPv27es+xouAlW7iLwQsCMtfz8N6YwikJQKsM+KOPeOMM9yap1eZhj0//kis6ke4ecOr\nJHGudz08zliYREOjVOKpUsT10QSFjVIsrEpS+LVevrDXH2/POVTXwQ2My5n1VaxhhNdYzQRR4U5m\nHTeaAnUnb/9v+fLlQsQ1dI1Y/JRB9AK0ws8Lf011JiYjRIRzTXiwF3V8qdQEtihyKkURpW7iLwRM\nAfvreVhvDIG0RAAFQrlAyu2Ruxu+sb6JEJg1adIk95pI3gcffNC9xuqLLPyOIuIeBDWhgFG8FFTA\n/YwrOlJowyulF/lZ+HvWRrGSqV1LitR+++3n2mb9NZpoJZ88Y/HGhWLDakWpVa9e3ZUmRBGjDL18\naPqOC5uJSWGR4Kzx3nLLLUKOMevErOt668PR+sUxxoGLmfVdraDk1o29msHdunVzeGHhs56M9Utx\nDxN/IWDVkPz1PKw3hkAuAlYNKReKpL8ojSpJ5A2zDu4pxcIGgaXKRMZzVxd2PilPrAN7EdbUIWZi\ng6fBEyLGkcjCCN7nthdHFIOHIHw9vbRwsTXg0kLa2jEEDAHfIFAaVZJIQUpEcFPHq3y5L4FZrPN6\nZQ8pgai1hvM0aYo3Dxy+e2MuaN89EuuQIWAIGAKFI4ALHbc/rm5ek2Z0/PHHF36hneEbBMwC9s2j\nsI4YAoaAIZAYAqyLR9J0JnYHOzuVCJgFnEr0rW1DwBBIGQLkBBOlbGIIpAoBU8CpQt7aNQQyCAGi\ngsnVhZAiXH7//XdHx/jtt9+GHy7w9eDBg6V8+fLuOhi1iOQlv9gjrfAuHjdunCPrIDLaE1KevKpF\nrH+y1uu9hyoSIXWIyODWrVtLo0aNXCR0eA6tdy9curQfGY1M5DHXewFO3vnsaQPWK69Nbz9o0KDw\n0+J+bRWU4oYqLU80BZyWj806bQj4CwHIJ0gXotoQRBcIeaxwFkMG4dEvxttrygwSRezRUJKqFM4H\nzX1QvFdeeWWe9CMUple1CEVLUJP3Hv5oijqQxjR06FBH50h+MaQXHp1jeP/oQ/fu3d0YyHNGIOy4\n+eabHdVjrAAnJhBem97eUoDCkbXXHgKmgD0kbG8IGALFQoBcXhQZa5Kk+QwcONBZiVTiKY7AfUzV\novCKSFjDWKh33XWXLFq0SLC04xH6ReUhLzUICxnrmvxlT8mG34eoYiodYcGSS4uyvvzyyx0PdPh5\n8bwmzYgcX6+aUXErKE2fPl06d+7suKEbN26cS7TBZIVCGFBbkrdMtSSP6Ys+UEQCbwXEJkwmmDAg\n1Es+5ZRTBIpMqjgl4rWIZ/x2Tn4ELAgrPyZ2xBAwBIqIAAUY2rRpI1AzQlIBw1VROKFRqJ7SI98V\nbmkUuicoX8gnIMGAfQsSDiooFSb0BcILFFeXLl1cNSMmDl4ubeT1kF2gMFFoKC8UOEq/IIHPmfPC\nBU8A90pmBSVyVyH5oNjD559/Lj169HD9ZHICJ/dtt93mvBH096abbnLn4UVAsUIYggLnHldccYXr\nKoQeeAxmzJjhqk1RQQl6UZOSQ8C3CpgvEQTlrAWZGAKGQMEIfHX5WlkxI/lcvy1Oqyh7XRJ/UQUs\nLmoA4+ZFAcA0VRShChKl+VB6VP7h/ezZsx1VI/fD/YxSQ1DA0D9iacfze4EChsYRdi0mCTBXYQWy\njyZYhW+99ZZTvN9//30uB3W0czkGD3S4tc4xlDwKOJkVlChDSDUkMGKdnLVnrFiEtefbb7/dvYaB\nDCsfGTZsmCth6FVWolQiAsXmyJEjncImpQlL/YUXXnCWc7t27dw59l/yEfCFAsYVwx8F6zm4UlhH\nouQYa0j8cZFg7rmMkg+B3dEQSH8EujxaVX+Ikz+OQBEWqU477TQ3efYUZFF6RaEBlJ4nWG5YaljC\nrNvCw4yr9dZbb3WncAyrGGVZkOBGJvKZ+7MRNMZ1TBio7YurO5qgxLDKUXjhglL1uK6p9YtcdNFF\nuQov/FzvdbIqKKFsDzvsMGex4mZmbJ7lDZWnJ6xVe+51mLPCx4AbmiIVcElDBIJXIFyg4jQFHI5I\ncl8X4c8ruR3gbsyUd911V9ljjz1cDVG+LARysG4BoblX4zL5LdsdDYHMQCBQJiBlyiZ/K6yIQGmh\nRx1b6vhi7VHoHot3xIgRrugBhQ+uvvrqPMFYsfpFqUTcz+FCsBXc0FiuiQqVjiZOnOg2rNt4JLyC\nEtHjiFdBybue+zLBQKI9AyxWrFRc2l5tYLBhi3UNx5l0UGvZEy/626szTJusqbPx+4tb2qTkEPCF\nAmZNAiWMCwVCc15TmouSZihfSo+ZGAKGQHojgLIJr3oUqzoSo8SF61UeYh2S9WCqBaGMcD+zdsmE\n3dv69esnX3zxhcybN69AkFjrxZLld4U8YKxGfnNY94xXgYY3QLASHMJsuH0Rgry8vnt7z0pOVgUl\n735MRFjXZlLCsl1hFZQo0kAJQ3BirdrjjcbDCDYsH2BFL1682K3lg4tJySHgCwWM28fL5evUqZNb\ni/CGTIABOXcmhoAhkN4IYF2FVz2KVR2JUWLdepWHsNpQaqQOETjERv3fcGGyznozJfgKEiKqUTpv\nv/22CzjCPcvaL5Yx7SVDyN31+u7tcceTN5ysCkp4DAkMYwKw7777uqApKikVFg3OxIXfWyYMeA0O\nOeSQ3OW9G2+80a2LQ23JZARXubmfk/GNiH0PX1RDYoYLhynh782bNxeqehBJSYoAeXRYyDvvvHPs\nUcTxCX9kzOqYKZoYAumAgFVDKtmnxFowSjGRAggl2yNxv3eJVFCi/3gFCJyKR8iNbtasmeOP5nzW\n61n3xYPgCWvLYBLN9e2dk0l7JiJMTLK2GhKzV2a1FKFmX69ePZenhuVLYES5cr6IFcuk75yNxRDI\negRY8mLzk3hu7Hj7FIsMJNb1eBLwQkCOguHDOq+Xl+xdw++vSekg4AvNxnoPgQmvvvqqLFiwwAUS\nMKPDFcIaCvloJoaAIWAIGALFQ4CAM9zX5AHj2ieKPFmu9+L1LDuv9oUCJr0A9zDrPrhHmNXhesYa\n7t+/vwsuuPTSS7PzCdmoDQFDwBBIIgKsG7OZpB4BXwRhEb1IgAUL/nC5svZAsARMN+TpkWZgYggY\nAoaAIWAIZBICvlDAbdu2FfLeoglR0LYmEQ0ZO2YIGAKFIUBaDstY6SpWMjFdn1x8/faFAoarlI01\nCbhNL774YiFFATcJOXrFJXOPDwo7yxAwBIqDAIx1BEwSSIQHi6wGvFiUDUxEyEWF4xmGvHAhT5Us\nBpirCisTyJIWAZxM3mF+onA91I2eFKVsIPmxrJ+yjlrSUlDJROJk8BLCghUpBFfxGcxgJv5HwBcK\nmD8QeF9JtoejtYnympJgTiUSGLGgpzQxBAwB/yNASgvxG1hu8DdTPYicXQgvEhHY8MiZjSbxlAmE\nzpbsimXLlslff/3lUhmJJ/nxxx9zb5lo2UAvcInfJJRgSQlBqYWVTCRFkyIVTDQ8AbNEJzvetbZP\nDQK+UMAMndw3KOL4g+UP78ILLxSIwrMlFy01j99aNQRKFgGsUBQylLKJCBbqkiVLHDFEtOsKKxPo\n5cd6KYyQT8CoB8NeUQWyILim8c7BJuUJdI69evUSWKagdKRtuAsguaDsHzm2sFQhL7/8srRu3dpZ\n8OSd/vDDD95tcvdY2oWVTOR3kYkIHkJPmCBEs4q9z23vPwR8EQVdUBoSXKfxpiHhYnrjjTeiokwl\nFdKaTAyBTERgvHwtKyXEK5zM8TWV3aW1FK0aDhzFlAiE3Q53dCJCJTRc2hD0HHPMMfnIMgorE3jd\nddc5bxquXCxwJgKwO4VP6AsqGxjZV5Tqp59+6qgaob9EEVPij/tB6EH5PwrKoGyZbMDTzNhpG+XM\nWOgDVYmYCODlg2iFayglGC7xlkyk9jJteBkiEBhBrEFtY5P0QMAXCjhZaUhUIWGLJh4TVrTP7Jgh\nkO4IrFb1u0JCpeiSOZb6khgDHcGUKFuKAmD5NmzYsMjsc1TqQaHgOkbBRUpBZQKJJ6F4AxPyd999\nN3d5CyXF+jJSUNnAyLaoznb44Ye7a4lNoewhFqdXRxilCZcBQhusOXuGw1NPPeVc4fXr1xfKGaLA\ncdHD9kchh2gST8lEPIZQXC5fvtytuTOhYP3cJH0Q8IUCJg1pwoQJ7kvrQReehkRdS2+W531ue0PA\nEPgfAl2l4DJ8/zuzZF/Bx0xKIQKdIRSy4VZnoq0TgIlbF+szmsQqE4iCo208aGxz586V7t27u7iS\nm2++2d2qsLKB4e3hfiZOxeOlZ+31ueeey1XA4a5tFDsTAE/4jI1JCRzUbExOoN31ygd657IvrGSi\nx37FJADvADzWTHTCeZ3D72ev/YuALxSwl4ZEBHSkWBpSJCL23hDwLwJYl8kk8Meafuihh1xcCBZk\nPEJ9W9ZeCZbylp1w+WItQr2YqFArFwMB13HFihXd5QRh4V72UpxwmXuCezzcrUzlIYK/ULpY41jT\n/OZRP5gCCJGCQr333nvzrA+z3uuVTAznLMYLwHo0kw1em6QXAr4IwrI0pPT60lhvDYGiIJBIOcLw\n+/fs2dNZi9EClsLP816jJLt27Sp9+vQRCtAjs2bNchXXwgvOF1Q20LsX+9dff12OOuooR9bvlT8k\nW4PX0OdGCq7hn3/+2bnA+eyBBx4QArVQ1ljQKF+sYRRntPKBiZRMZJzjx493PAr0ySS9EPCFArY0\npPT60lhvDYGiIJBIOcLI+7OOSs3aeIVoYyxRrEZ45XGNU4SAgChPYpUN9D739rifSQuKFCYGuKEj\nhbXdgQMHCmvYKFyUP3EunI81zRoyyps+UfieiUC4JFIykbFRJxmrmHVok/RCwBflCAuCjPUUvqAo\n6eKIF4Rl5QiLg6JdW5oIWDnC4qPNGivpTARFFWctuig9IS+X6GkUargQNFW7dm1XbjX8eLTXfiyZ\nGK2f6XwsleUIfWEBF/Twhg0blq9cVkHn22eGgCFgCHgIQFhR3EAw716J7slBjlS+3IPqQ/QrHqFc\nop/qFcfTZzsnfgR8EYRVUHcJxzcxBAwBQ8AQMAQyDYH4pmGlOGrcNgRrmBgChoAhYAgYApmMgC8U\nMExYsMo0atTIBVoQPEGuG9GCL774Yibjb2MzBAwBQ8AQyFIEfOGCThYTVpY+Qxu2IWAIGAKGQBoi\n4AsLGCYs2HNI4KfMGNGK4UxYH374YRpCa102BAwBQ8AQMARiI+ALBewxYUXrpjFhRUPFjhkChoAh\nYAikOwK+cEHDhEWS+pAhQ1wNTwp6w+UKmTpBWSNHjkx3nK3/hkDCCMCWBC/w2rVrE77WLjAEDIH4\nECAGKVXiCwXsMWHBtzpXSdMhOq9Xr54rwEAFktJOoE/Vw7B2DYFwBChCcOWVV0q8HMjh19prfyCw\nXCtUVdB/1SUvGYcfehcUrVilJSzXyzqpJXWlslTxQ7dKvQ9wdKdKfKGAGTw0anComhgChkAIgd69\newubSXoi8Lv8Ko/LPTJYXnJK2K+joJ9Pyn2yh+wt50o/qaSqOJuEalmpEl+sAadq8NauIWAIGAIl\nhcCr8pScKRf6Wvky9haqeu+TZ6SMlJXrtb/T5ZeSgsTuG4GAKeAIQOytIWAIGALFRWC8fO1ucbB0\nKe6tSuV6rN4+0l9664Y1/LoMlS36z6RkETAFXLL42t0NAUMgQxCIVyFtls3yljyn7txL027ke8n+\nMkielZWyQv6jKnmaTE67MaRTh00Bp9PTsr4aAoZAoQisVvVBYFGyZZyMklvkMiGwqiD5TN6XZtLK\nuXYLOs+vn1WVajrKG6WXXKGqeLA8IfdqsNZKv3Y3rftlCjitH5913hAwBMIRWCdr5W65Ri6SU2SI\n3Cnfy7dJcaXOkKnygbwm+8rBcpNconf9IrzZ3NdrZJWMkGFylq6lprtgDT8gL2p8dD21hi9Up/qI\ndB+S7/pvCth3j8Q6ZAgYAkVFgPXLA+Vwtdw+kPZykFMal8rpuqL5gLpTf5Yc/ZeocM1L8picoy7l\nk+VstYIHy6fynjwot6m6zVs4ZpieeZgcJfWlQaLN+PJ8UqgIJLtZ8WPScYf8n8yTP33Z13TslCng\ndHxq1mdDwBDIh8BoGanqcJkqyXNcTmtHOUYdqYNUXb4gu6pT+G3dt9BPvpCP8l1b0IGvZLjL4z1A\nVSvSSJrKAA1V4p43qK09Ub5xxxfK3zJJxrr23YEM+o8x3yGP6NTmaDlBLeN31DI2KT4CvskDLv5Q\n7A6GgCGQrQgslcUa+PS82qQPaTJN2Tww1JI6cqyc6rZL5DoZqMk2dWQH2U8OyXNetDe4tN+TV5wF\nGP45bZyuq6T7SgdNNhokP6ji3aD/TlLnM2uomSpd5DgZI787S7iqTkuOk9MydailMi6zgEsFZmvE\nEDAESgoBGJ1wPXeXntJQGhfYDJ9fp6vEz+kKMRZrYTJMLb2DpKOzeqOd20xaKtXG07JN3dQo5a66\n9pzpwoTmVp3osNb9i049TIqOgCngomNnVxoChoAPEEARQCKBlRuPNJHddSX3YreGu0HjpWMJa50E\ncZ0uF8Q6xR1nnbS/2t4Xq2oP6L9sEAKzrpLbnfW/UFeFTYqGgCngouFmVxkChoAPEEBJfqKru/3U\nrZyIECi1pzqQcR/HkpeUSPJUOS9ul3I1dclmk+wubdTncJGGZ92sSV9WMKQoz94UcFFQs2sMAUOg\nRBHYqOupL2jQT0H5p1tlq6rIgRpydYmmyuyYcH/gPSZt6APlfYoULN/1qlRY8zSJjQBBWaRmPaZh\naUWJMI995+z4xBRwdjxnG6UhkDYIkNrTX3mk5spsuVoDnSCC+F0ZiiPlXU35qa+rvlizRRHWbPur\nG5Uo58nqbPYEJqs3NHHpfLlcXdv2E+nhEmuPFSzqeoe+0iQxBOzblRhedrYhYAiUMALPy8NyhBwv\nd6ld9aj+rDfT5KGhcr8jwCDVaJP+o4LPN5pQ1FdXIosjNaW2ZrbeqqUIBmsc9QJ3q+Hq0m4urZXL\nas/i3DprrmWScqVmR092CVmfZ824kzFQU8DJQNHuYQgYAklBYIKMdoqQXF6kiq7AElz1oFq7Z6m6\nxVK9SDNtb1H3MSlFyaizy1rmaWrvPqTWMOlMn8uHurZ5cVLGky034Tldp/HgcGAzOSqq/KtEn9kk\nlgecTU/bxmoI+BgB1ntf0YSi/+gPeTn9FykETbHBxbxKiwWQApQsweKeIzM1oOgWpe842dEvJuve\n2XKfnWUX5Qq7Xr0WA5z3glzrRITnysTqDK3J1EmnXdkgZgFnw1O2MRoCaYDA8xp01Vm6KedSiwJ7\nSwpMMpWv19j5WnzgQnVpH6MZxSZFQ6Cd0puQj32nOvYLK1oR3sIC+UuV72UuoO5DXYHHkia/O9PF\nFHCmP2EbnyGQBghMUH6lRZpP6rmeU9Fl8nkpTp/JTFalgeuRSlbZTZ36d2sIXTwu5WWyRGlUbtSE\nr0uVm+wIR/M5S35zSwJEw2eymALO5KdrYzME0gABUoFwPbOmW17/maQ/Arjxj1JiTpQwtYVjCc/+\nXnVbnyA9lNSzszuNfOqbNOgOxq3b1CvBunymiingTH2yNi5DIE0QeFFXDTtqPmlJuJXTBIKM7CY8\n0azl3iPXRs3nxrq9T8tZHKzZ1kdHuP1JEeujSWJY07dpjDXlIDNRTAFn4lO1MRkCaYIAhBd/a/jT\nqRqFbJJ5CJyoxQyxbAeoEl6jatiTLVqlmYA3ItBhG4slR6sVfbnaw49oWNd3mrGdaZI/1DDTRmjj\nMQQMgSIjsE3LDEC4j6sQggzciUQgr9TX7P+rnz2naTtNNHM2UeGe0D1eoyE75npOFL30Of8UJVWB\n3OQ+dTXfpGq3siaXPaZ2cW11MUN2UpjsIXtrgtjDmql9i1KmvKOx1o2VfqXJ9n1j2UnfpSsHtyng\nwp6+fW4IZCECK7SuLqQXX2nNm101Lpn1OLZ6yj21u5JU1HTvaytd4zpX1GCIruJGSx0qCLqXVfni\neob0wiSzEThTHcrblDqU9d6G+o3arGQqEKDEqzhRstRgXizz9d9fus1VIpbP3Z7vagOtV3WJJrA1\nlt3SCkhTwGn1uKyzhkDJIjBNfpYv1c6YrrbtIbo2d4taLA30B7MgoTA9yvooObGg0/J8NlOmySxt\n5WL90TTJDgSoQAVdJeu7vXV9l30iUkltZypZsYUL1vUCVcg1dIqYbmIKON2emPXXEEgyAgTDhKzd\n4eoKruACXy5VxVhRKsXV0qnqYhyibmQCbuJ1Jb+q1syZmnUb7/lxdcRO8j0CKOFkC+ljheWOJ7vN\nZN3PFHCykLT7GAJpiMBU+Ul5kB/U7Ne9leLxOs2DbZPwKIhexvWHEidopjAZpzY29Xu9tJPCzrfP\nDYFMRcAUcKY+WRuXIVAAAhSif02r4eJyppB8W9mngLML/+g0jWQdrAkjMFkVZNXiLnxHCw1erjVk\nTQyBbEfAt2lIGzdulNWr/xe2nu0PysZvCCQLgSnyozqYL1QbtJyWo3+u2MqXfrEuR9Wi0Rq0VZB8\nKu+prdzaMU4VdJ59ZghkAwK+VcDvvfeeXH311dnwDGyMhkCpIEDE8rPqbn5eV2yJGO2tcagEtiRL\nSDf5SFl8sXKjCcUWRsq7WtXowmgf2zFDIOsQ8IULevfdd5dly5blAX/z5s2ydetWQRF3795dXnzx\nxTyf2xtDwBCIHwEijqlS014OclZvMhWv1wtygXfT9WCsYKgII2WYZv0erqvEO8rOkR/Ze0MgKxHw\nhQJGufbu3VvOOeccOf/8ECPOhx9+KBMmTJBBgwZJ1apVs/Lh2KANgWQggEV6rK7xvq9cQlSrKUmB\n1WiQ0i10luM0NrVCblNUu/lR2x8sNpHOBcVeZD0CvnBBH3roofLjjz/K7NmzndsZhbvDDjtItWrV\npHHjxu511j8pA8AQKCICX8onWmX1xhJXvnSPaGjoBb/SNsPldY21Pkmdz1ZpKBwVe53tCPhCAfMQ\natSoIa+88oqcccYZcvjhh8uXX36Z7c/Gxm8IFBsBqCRZdz1FK62WlpAX/InGOntrwURaU2qQ6jgm\nhoAh8D8EfKOAvS716NFDvvjiC7cmvNNOO3mHbW8IGAJFQGCCrshC01cUruYiNOcugRmLurpY3hRV\nf02eFggYEmU+Kmr7dp0hkC4I+GINOBwsAq9wQX/ySV4XVvg59toQMATiQwDy+p5KsVHaghV8r5aa\nq6T/qkg1XXk+pLS7YO0ZAr5HwBcWMBHPN910kzRq1EgqVKggderUcUq4bdu2Fv3s+6+QddCvCMBy\nhQVa0oFX0cbfSMkBWQuGZeucEqAfjNamHTME0g0BX1jAV1xxhSxevFhGjBghzZo1c8oXEo7p06dL\n//79BVKOSy+9NN2wtf4aAilFAOv3eOmRsj6geDtJV3VIt0xZH6xhQ8DPCPjCAmbNd+jQodKuXTsX\n+RwIBKRmzZrSoUMHeeSRR4SUJBNDwBCIH4G5MlsrxPwtB2tFo1RJPa3Uuo8cmKrmrV1DwPcI+EIB\n42oePXp0VLCGDx8u9erVi/qZHTQEDIHoCIxQ6/dYOdUCn6LDY0cNAV8g4AsX9F133SU9e/aUIUOG\nyG677eZSklatWiW//fabY8MaOXKkL8CyThgC6YDAcvlHflHaiz5yVTp01/poCGQtAr5QwPvss49M\nnjzZMV/98ccf8vfff8v+++/v1n3JCcYlbWIIGALxITBC8367aFWikqCbjK8HdpYhYAjEg4AvFDBR\n0FjBr776qixYsECCwaBUqVJFmjZtKtdcc41ccMEF8YxFxo4dK99//33Uc2HaMkrLqNDYwQxCYJ2s\nlbEySu7XKkcmhoAh4G8EfKGAkxUFzVpx69atoyI+btw42bZtW9TP7KAhkCkIQH6xn4Ze1Za6mTIk\nG4chkLEI+EIBEwVN4YVw5qvwKOjbb789rjSkVq1aCVs0gdqSVCcTQyBTEdgiW+Rz+VBLIQzK1CHa\nuAyBjEIgnwLu0qWLrFy5MuYgjzrqKFehKOYJRfjAi4I+66yz8l1tUdD5ILEDhkBUBMap6xn6i12U\neNLEEDAE/I9APgV8zz33uMjjWbNmyYABA6Rfv35y8MEHO1KMJ598UgiYSrZYFHSyEbX7ZSMCHyjr\n8qVK/2hiCBgC6YFAPgUM+QXy5ptvyp133innnnuue48SbtOmjaCgzzzzTHcsWf+FR0HPnTvXuYpZ\nz4X9yqKgk4Wy3SdTEdgqW+Ua6aX/b5PWSjxpYggYAumBQD4F7HW7evXqgjIMl2nTppVYbd5KlSpJ\n586dw5uz14aAIVAIAmtktQyRO9T13EL+T24t5Gz72BAwBPyEQEwF3Lt3b+natat89tlncsABB8hP\nP/0kc+bMEdZkS1Nmzpwp69evLxHXd2mOw9oyBJKNwCKZr+lGNynZY0c5U2k3TAwBQyC9EIhJRdmy\nZUuXU9urVy8pX768nHPOOTJp0iTheGnKsGHDhLVnE0PAEPgfAtOV6+ouZbo6WWsNmfL9Hy72yhBI\nJwRiWsDLli1zAVgEY5E/m5OTI/fdd58cdNBB8sYbb5TYGKkHvGbNGqldu7Zr45ZbbimxtuzGhkA6\nIjBGPpW35UW5Ul3Otuabjk/Q+mwIhBCIaQHDy4zrt2/fvrLLLrs4pqoaNWq4ur3JBs/qAScbUbtf\npiLwpjwrH8tbcruu/JryzdSnbOPKFgRiKmA4maGBxAUNPeRpp50mL774ojz44INJxwYmrF9//dXV\nA6YOMNb2woUL5dlnn5Wnn35annrqqaS3aTc0BNINgS+UZGOq/CR3yxNa6K9hunXf+msIGAIRCMRU\nwA0bNnRFEapVqyZYqMuXL5c6deq4YxH3KPZbqwdcbAjtBhmOwFJZLNdKb83yvU+qSrUMH60NzxDI\nDgRirgH36dNHyAlu3ry5nHjiiXL88cc7RXz66acnHRljwko6pHbDDEPgXXlZk40ekRpSK8NGZsMx\nBLIXgZgKGNINUoDKli3rFDGu4Fq1akmPHj2SjpYxYSUdUrthBiEwX+bKFK3vO0ReyaBR2VAMAUMg\npgIGGq84AkUMLrnkEilXrsDTi4ymMWEVGTq7MAsQeEcjnk/UZCOr75sFD9uGmFUIxNSoBEINHDhQ\n3nnnHVefd/DgwS4YisAoaCKTLcaElWxE7X6ZgMAsma727yy5QiwdLxOep43BEAhHIGYQ1jPPPCNf\nf/21vP/+++58qiQRmMVxE0PAECgdBN6S5+VUOV/K6z8TQ8AQyCwEYirgsWPHyrXXXisNGjRwI4YN\nq3///k4pZxYENhpDwJ8I/CI/KNPzSjlMjvJnB61XhoAhUCwEYirgRo0aCUo4XD766CPZeeedww/Z\na0PAECghBN6RF6SHXCBl9J+JIWAIZB4CMdeAr7rqKtl///1l1KhRsmjRIhcJTXWkL7/8MvNQsBEZ\nAj5DYKJ8IwFVvPvLoT7rmXXHEDAEkoVATAUM7eT06dPl7bffduQbHTt2FDbSkkwMAUOg5BDYpnV9\nh2nk8wVaYNDEEDAEMheBmAr4pptukvr168sNN9yQuaO3kRkCPkTgW/lc6sqO0lb28WHvrEuGgCGQ\nLARiLi41btxYpk6d6iohJasxu48hYAgUjMBm2SzvyatWYrBgmOxTQyAjEIhpAVeuXFmGDx8uuKIJ\nyPJcz8ccc4w89NBDGTF4G4Qh4DcEvpCPpLnWOWompVt32284WH8MgWxAIKYC7tq1q+y11175MKhb\nt26+Y3bAEDAEio/AelknI3T19xZ5oPg3szsYAoaA7xGIqYBxQbNRCemvv/6SJk2aCLnAJoaAIVAy\nCLwoj8rhmvPbUBqXTAN2V0PAEPAVAjHXgLds2SKXXXaZUI6wffv2bn/RRRcJx00MAUMguQhQbOF3\n+dWxXiX3znY3Q8AQ8CsCMRUwlJNz5syRKVOmyJo1a9yemsD33nuvX8di/TIE0hKBTbJRCSeHSF+5\nRiroPxNDwBDIDgRiKuBJkybJddddJ61atXJItGzZUm677Tb55ptvsgMZG6UhEAOBaTJZessJskQW\nxjgjscNUO2ote1naUWKw2dmGQNojEFMBH3XUUfLkk0/Kv//+6wa5ceNGefnllx0ZR9qP2gZgCBQR\nAQKlnpXBcp70kzukv6rgv4t4p9Blc2SmjJfRcrZcUqz72MWGgCGQfgjEDMJavXq1jBgxwpUe3GOP\nPWTWrFmyYcMGad68ubzxxhtupD/99JNUrVo1/UZtPTYEiojAC/KwtJcO0kmO1fpEFWSgXC+3q/u4\nnuyU8B1hvHpWHpJzVflWlxoJX28XGAKGQHojEFMBn3DCCY4LuqDhkStsYghkCwLj5Eu1d/+UAfKk\nG/IhcoSu3m7Q99eqEn5Y6sgOCUFBylEt5bw6WLokdJ2dbAgYApmBQEwFDPlGmTJlZMcddxTczy+8\n8ILsuuuucvLJJ2fGyG0UhkACCCyVxcpP9ZTm6A7OEyh1hByvSnijWsLXOSVcXWrGddfFssDl/N6z\nXZnHdZGdZAgYAhmFQEwFPH78eGEdeObMmXLXXXfJjz/+6HKCV6xYIX369MkoEGwwhkBBCORIjjwm\n98jJulLbSJrmO/U4OU1V8HpVwv+RW9WlXEUKX5Z5Tt3W3aWn2sz1893PDhgChkB2IBAzCOu1116T\n5557zhVkeOedd+SVV14Rjr377rvZgYyN0hDYjsAH8poq1WrSVU6JicmpGpZFJPP9cpOQVlSQfCOf\n6RkbCrxfQdfbZ4aAIZAZCMS0gFetWuUCsMaOHevc0G3btpXvv//ecUNnxtDjH0VQsQjUjM+1GP9d\n7cx0QOB3ma4rv8PlXnm60O4SGf2sPKi28nVyuvRSuzlHw6y2bf+fV1u11MImeUPPwpUd0H8mhoAh\nkL0IxFTAxx13nPTv399VQ+rVq5erDXz++efLzTffnHVofTVkiuw9b4TU6dFFAp07SaCCkSVkw5dg\ng7qVn1B12leu1mCpOnENGTKNnzSx6CN5U8ppnHQ5/VdGyrp/5fT/0fKpXKRBW7tquQUTQ8AQyG4E\nYirgnj11fWqHHWTlypVy2mmnOVasp556Sjp37px1iNU7+TDpe+Uecs3rw6TDE09L4OgjJXDi8RLQ\noDSTzEXgBXlE9pYDNe3ooIQGua/GNbNFk8vURW1iCBgChgAIxFTAfHj00Uezc0L+L1s2CkWhBjxZ\nRwYMuFi+37en9Cv/gVS46jqRhg0lcPKJEji4gwQqVsxGaDJyzHNltoxSG/ZPZWceKEMzcow2KEPA\nEEg90Px8bAAAQABJREFUAgUq4NR3zz89UC4STcUSeeSR6tJ37Hly64CzpcXyiZLzyQgJDnpQpFlT\nCey1pwTa7SmiW8AISvzz8OLoCcr2e/nWbZt1pbaaUmPcJY/nSTmK4zZ2iiFgCBgCcSNgCjhuqETg\nHbnhBlE+bJHrbywrp59+iJw96BAJUiFq+m8SnDJVct77QOTugSHrGIW8VzuRRrvo1kgCZcsm0Jqd\nWtIIzFMbF3KNifKNW6s9UDrK/8lt0kSy09NT0njb/Q0BQyAvAqaA8+IR17uOHUWwiAeqnv3lF5Hj\njisvtWu3kzqd20ntU86WKpW2icz8PaSQR30lMvcvkcVLRHbeSaTxrhLQTZo0loBazcrlGdLslSpJ\nwOotx4V/Mk5aJ2uls7RSFqsnNGzqLguKSgaodg9DwBBICIF8CrhLly4u8CrWXSDnGDRoUKyPs+a4\nxqfJQw+JvP22yNdfixatEFGOErffsqWs1KnT2m31lWfhoLNFDth3q9RaM0/k73kSRCF/N0Fy3tCL\n164VJdkW2bhJJCdHlXGlXIWsOV8i1atJgH2N6rrpXtOhAjVDe6m/o2iOmFnWRfjWDdMKRHfKo3Km\nXFiEq+0SQ8AQMASKj0A+BXzPPffI1q1bXfGFAQMGSL9+/eTggw92aUhUR9pnn32K32oG3eGMM/IP\nZvPmkDJGIS9eLPLttyKPPVZOvdBN5cADm0qHDiItz89/XXCbWs4oY29br681Cj2ohTFk9RoRzUeW\n2X9IDu+1RrMsXCSybLlILc1R3mknCaCQ2bzXO9UPvba0qTxgU0ZwgozRjN2X8hy3N4aAIWAIlCYC\n+RRwB7SDyptvvil33nmnnHvuue49SrhNmzaCgj7zzDPdsdL4b5sqJSYEFdMoyhh9pzrQbQqZqFNB\n86lFpk4VJTMRue8+p1dVGYt066YxW+1CSLo14mrVRNjCJBD2OvJlMBhUJbzMubiDS5aILPknpKS/\nHRtye/Me6xmljAscpdyggQR2rBdS1mqiZ5vr+x15QbopfSSBViaGgCFgCKQKgXwK2OtI9erVZe7c\nud5bt582bZrLDc5zMAlv5s2b5wg+3n//fbUOOwj5xl7K07Bhw4Tj0GGmsxB/tffeoe3ii1VPqq6c\nNElk8GARln5PUZZD9e5LosZqIKDquZ4qU90Ce7aNClFw6dKQgsYcX6TbtF8lh9co53/0s2q6Do2v\nXK3nAAq6jpJO1K0jgbp19XVtfV03Y6K6STH6TaYqGYamkZkYAoaAIZBCBGIq4N69e0vXrl3ls88+\nkwMOOECo/TtnzhwZPnx40rs7ZMgQ2XnnnV3BB2oNH3744TJmzBhp0aJF0tvyyw3Rd1rx0W0KrXyg\nwdPPPCNy7LEi3buHrOdk9TVQmILGV67K2FnQKGQsag0iy1m+XH3purjNfqua8PV04btWLefyDqCk\ncX3XVgVdu5YEOK57N5tgFuFt6rkIBgPKJa7r4AeIelGSNaqi3ecteU4Znc+RivqvIMGxwKYFwUwM\nAUPAECgRBGIq4JYtWzru548++kgmT54sZ511lpx00knqvWyQ9I6MHDnStUF9YSov4eo+5phjZNy4\ncUlvy4833HdfETaM0g8/FGUe05isjSJffBEyRku6z06ZqkINtG4Vs6ngJg0SQ1Ev1411aRSz7l1Q\n2S9TJMhr1qk5j0Vwt22RP1bWkQf+7iGNqq6Qz7c0l+o1A3LqQQul82FbpfwuOgtxvnp1g5cC1/Y0\nmSz/yCKNfu4Wc5x8sH69ZpLdrcPRpfarrxbZbbcCT7cPDQFDwBAoEgIxFXCORuQ+oyYZrl/WGVG+\nBGQ9++yzrkhDkVqLcREKl3KHhx12mDuDNeaFCxeqNXisXIy/NksEXXTJJSLqfFC3u0ivXiIPPKAB\nWy1TD4Bj+lIvhboqXGcKWpfmBFKjsXpxmFx0yzbpeuRWN8OYOGqtvD9iT3n6gbJyfOMpcmLNj6XO\nyjmhCHBPGbNWre3krlnDOIZFXUx5S4sgnCF9HC9zrFstWCBy442hCVGnTiLXXity5JGhZ0IeuIkh\nYAgYAslCIKYCRvl+rfk1rL+efPLJGkjURT7++GOnlJNdkOES1Tqnn366XHXVVXL99de7sV2tpsca\njfTlWHd8slkk6Bri3Jo0CRF/oITTiQWUYLP77w9ZjrCH1a6tC+Cq9qRxY+lwobhNl/31u9VUen95\nknNNn9xto+xRc75bow6yTj1vvuT88GNozZocata6vfQr3TuLmfe4wNXNLSyyl9Ovs9uHXrugNrSm\nKvTvG8zSzwLK7Hx4zG+SzgE1yFDkQu2j1iJxQkzi0KEi550ncsUVossjMS+3DwwBQ8AQSAiBgFq3\nutKVX84++2xh66RmwIEarjtVf1VnzZqlFtol8tVXX+W/oJhH1q1b59aYW7du7RRvbX5YVcaMGSN/\n/PGH9OnTp1gtoMgXq4+X6O50Erzw5Bs/+KBI06b+7jleZ81Uk+++E62kJXLIIYX3F3fvp5+GLGUN\ndndr4FCQk2cdLkF88qRhrVK/MC5w7zV+YtK2WKMm1JyNG+nm0rrUJb5t/t/ynwvGSJ/P20qbTa0l\noBa1I0VpqNHgWN2qoN8dVUveeks08l9EK2/mE40/dM+AtXvGxmUmhoAhkP4IXHPNNU7XtW/fvtQH\noyZDdGmk1InUAkYBe8J6MMFSyZbN+stNetOrr74qC9QHyJygSpUqqnCaCuAUV/kmu7+leb9DDw3p\nFIVBHn5YxG8FmNB9WLwEko0fH4ryfumlEMFXPDjpY5ZTTw1tv/0WUsa44FvpcjQBaYyfKPGAMoWJ\nbptq1Zd5ZUT+WqOb6t65cx0Xiex/UKhtjOFIGS2fSP3gztK2zVUhC5v8aV3ikLHfyaZ5S+Sh7w6Q\nP9bsKE8c9pnUe7Oa5Lh0LdWwWNhbVJmrUm+j2zPHbpNh3+0sFx3XSHoe+pcc3XaR1Kqqvnasc2+j\n8TLaQR1YLmGKZ7krkYqLWo/soL03BAyBrEQgpgW8RPNk9t9/fyVa2lF/5ObK7rvv7vZffvml0jDu\nkVSwWOfFOr1bI1+aNWum7IxVNQBmtSP/oCZxr1695NJLLy1Wm+lqAXuDVtjl6acpBuFopr3Dpb5n\nbffXX0WD5kR+/llTjmeHlCWTRzhaolmPiXYSSxrLH8v4999D6Vl//63xXrrBOLbLLs6b7SYjuOY5\n/sMPGrg9MxRlrV9b59bGY7BJ/10l58l/tK5vJMcz7WDNYtXe0H+DVFimSlnd30Fc3otUSa9T8xyX\ndu6milVf/7Ouqjz7XWuZ+Ec92XuX5dK17Xw5qOkS9XDnhEKnUcZr1v7PSnfWulrva9eFUr68NC/M\n/B3qhtK8iDAn7Yv8bCYbKHDuY2IIGAIlikAqLeCYCpgRr1WaxLeVa/Fv/YXrqATIbGX5MUqyYOlO\nmDBB3Xr5/XoTJ06U22+/XT7//PNitZruCpjBa0aYq8j06KMFu0DRHcl0VGDlohBHjw4pXhQbCpcN\nhZuE+KiYz5YUZlY8mjQJWf+MK5Zeop9MDFDG5FijYKue/YYsr/ynNBt5s4ssx5PtbSy+wGSmKy1F\nEtobMyY0UZg/PzRRYO04lpdi7dqgrJq/RpnN1kjDMqroSfeCyUwjy12uNhHmpHzhl4cFDdO/UsUQ\nNSlr2fCGV6zg3gd47zZV1uxR2krgEqheLURZyp7IcqzuaG6BIo3YLjIEMg+BVCrgcrHgJOCqmv5B\nh7t/WQf+QBNWb7vttliXFel4W/0VH62/7qQ6RQp5x/XIY02h/PnpZtn1iPJStkJqLRJNy3ZKBavt\nscdCv69//ikSvmmqthOWOYnmjTKniQtJsol0TuR4rnEvY90SDXzrraHf+7hukoSTePQFEa/9Lr8K\n1JI5sk1yKuv/B2+T1rq11CNLVmyR94NvyOV/Pys7awjBdi+226OTUMRYv0UV9B5ucjaip7HYNdSA\nWDMMWJfGxBI1G0Zw5coB1Yk1dHm6hv4NNZQ99HkWJEFmEGh5b9uk7zVWgvduTXyDDsD7jAbUcs9x\n6WA0qj56bXjLv5v0O1NB1lbYVeq33iIBV5lrl9y9Y0UjeM3EEDAESh2BmH95BD8N1fDPh3XhsW/f\nvq5jK/WPGzasZAu5vz179hQIOXbTpMsaOmtfpT8ov+miIDSU5AmnUlbNzZH/PrFR9r1Kf3FTLCee\nGFKqUFhi4GCNsqnn3lmk7FFa776r6T8XhdJn4g0ipxaEp3ShzPRoNAlM91t5442yQd6W5+W/Mkla\nyB4utSggZdy/svqujG5T6/ygjFe95Ji6ajZHkWSmHjPhIXqaWEF12rhYsO0GqKuhQR0Nz3k0fboo\n81vI/U1lrVjiUq9wL0TpqDcV3LoxKMumbpN//rtVVszbJlvUyt6sm7cvVykg5WsFpVJV5XdXpXxg\n4xlSYflfkqOlM2W+zhpwt+P+hkMc1wLKePvmosh5TR9wFzAAzmGN2+23n88AOOYdDz+P671r+JzP\nvHPL62ebt4SC5ljbIHgufM95Xn/wBrB5/eFaJiRcw0SF67yNY7RJv7nG27vX5UOsbtuXAYj2C3BP\nE0MgBQgU+M1DIT6mphbRz/dBYFxCQoEHyD5wQ8+dO9etB2P1su4LK1aq18LanFtRRp6zRnY/tYLU\n2FV/QFIsMEpB0sHvMr9R0QQyD1JoKJno6herEo1lDWM8jRgRYuNCkRxxhMj//V/Ikxnt3qk+9rNW\n8H1RKxm1k31loDwtlUXNTZ8Iv/vb6dRj9oiJDRSkeCigJO3RI+ap+T7Yuikoy6dtkyWTt8pSVbor\n/8iROi3LSr29y0rrcypK+SoBqVBdla56oCtUC0igjHZou0x5pqqMeq+uHHznUVK3Veh77CLFWbOA\nWAUFFh5FjiLjvdt0dsYMDUXs7TmOsOdY+MZ5KEY27sNn7rzt13vn8gVGmaIEPQWLa0GpcJ0S9a6n\nahj3ISiOfnJ9rnLWaz0li2uDzZ27XSnzBecalL3u8R4EYXzD3Y/bv4q2x3p8XSWj0ZgX10/6Hz5W\n2lNxeHHvPJuOn/c8/Kr6XWQpQDdH8co4eK187G4pINcNo330XtNfHXNx64W7vrF8gVfE7dVD4j1T\nbzzhewYE1vQZlw39JPYg1o8K55skFYECFTCsV7BRnaphqqfpLzpEHCUllfTL2LlzZ/0eb82ThlRS\n7SVyX37IWp9dUaYM3SSH3qNfVB/I9iytAnuCMn38cVEyFVFCk5B1hgXtCQFU772nwcBjRdf3Q0Ui\n/Mz6tEr+lVe0fu+fMksuleuljezlDSXt9uD8xBOhPG8Y0Mgx5vc7lqycs02mvbBJlvy0VWrvXlZ2\n3KestO1TSXbYQ+39OJdG2l1USeq2LSvjblwnbc6vJLt3rxD60SeqjS1CCuhOxJnp/daltLEez1o8\nbG8ID8PbUEj6GgXpjAFP8WPNe5MGXpfV83D9K39BkIA7Jg1sKHldOsjxlCOWuxeI4O29iQUTiQrb\nrXb3Wt+jqFHwkRMdbwLkliFU2fIeZYpSRaGyJ4YgcjzeuOgz/WRZw9uIPaBdCrjwuaewuYf3mj2Y\nsIVj4U2imFB55+Zet/163jMp5Nztkybn6QFHNmIcSCnMnbB5Ezfd67EgE4o8m+Ky3QNS5ur/k8Be\n7WghbaRABcwocAfjAr5I/ZnwQx900EFJHxxpSHfccUfMNKQLLrggrjYhD4FLOprMVm3TFF9tEWX3\nkyvIrPfXyj+/bJUd9yoUtiK2kvzL+Fsj0EiLWcm994asYeU8kdde0zoM/4iSrFD5KmRwJL/15N3x\nG/lM3lKXcydRdjSNaa6g/9JdWCpgLZ919VtuEV0XDhlv4eNarW7lX1/cpC7mbbLH+RWlw22V41a4\n4ffxXjc8uLzUfLKsfHfrenVdb5X9rq0s5XVtOpslROqi7iSdFSULiaLcx1EyoEwiNxQOf8goPJSi\np/y89ygyLFcUWBIk6FnQ9IN2EU9pe+9pm36FewK2qZLkGBMBFHC067zrCTLZrkhdrAOv8VB4kwo3\nodk+ViY2tKdKuwzHPWWdu9ffYzCI5eIL9cSX/8eMgh6hPknWY1uRkLldBqo/c6PO2FizTaakSxrS\n36O3yMy3NslRQ9VVk4bC34QGtTuiDJQyRBne30NJD4c120rqLE5EuOZnrdz7nXwtWL8XyTWyqzRL\n5BZpcS6/ObikCaZjpYe6FusW58ivL2+ShRO2SMszKsrup1SQchWL8rMeHYJtW4Ly8yMbZemUrXLo\n3VWkRmP9YTMxBLIQgVRGQcdUwKX5HJqqZZouaUijLl0rLU6rKI01KjpdhclmkibLcUEwXhXoq7pW\nW03/tZQ9pZVuLaWt1JOd8l2/VtbITzJeQ6vGatnAKc7NvI8SSHaR49Q6SZ4CytewDw7AnT3qoxzp\ntecmWTN5izRXr0vLHqF13ZLq3twvNst/n9wo+1xeSRofmf5ehZLCye6buQikUgHn86VCO3m/EvmO\nV1qjF198MR/qFEh4BDaIJIrf05DCh7rPZZVkwt0bZJfDy0nZ8umpEEpL+S6QvzRY6jG1Y9fJrfKg\nbFZSjN9lmrNq39DCCMQst1JFjFKuIBVV7X6t1Xpn6Lt95VA5Qq6QmxO2msOfVape52wLqqss8e/G\n6cfnyNLz/5X3Z1eRS1+oJm33VbdbCUuToyu4NeXvB26QuV9skf3VJV1lx5Jvt4SHZbc3BNICgXwK\nmHXUJk2aOPfz0ZDyRojH0RxxuFhv/Z6GFD64HdqWc1Gns97bLK3O3B7gEH6CvRZcx++rzfutfKG1\nd8+Vo+TEXOsVNqqjpbtDifzdGTLVKWWuOVJOUCfz3Wm/vrvm7xwpq+k/1XaOX5GtW5IjX12+Trp/\nUl3+qVtBbh0QWhemTGVJS82mZXVZparMeGuzfNF3rezRS13eJ9t3u6Rxz6b7E1MFYx08BcR7KbGi\nS51k6TabxRcuaB4Aa8uRaUjQXyYrDSmZTFhrFmyTr/qtk2NfrSYVa8T/I5sNX7SJ8o28LkPVrt1H\neuqqbXXR4JYskqUa2DS6/zqXCtR5SFVBuRUm5O1+2W+tKr0KuYoPuk8Cs4iO7tKlsDsk73OCvn64\nXyNqNWBg/+srS41Ghfc/ea3bnTIBAbhgyLDQGjpO4bJH+RIjBU8BOfEzZiiX+18hIpzmzV38GzFw\nbiM4sTTFVy5oFB6EG7EEq3gwESNJFi8NKfK2M5Xgd72G75Mr7Bep3rCsY8aa/somXTtLLLDIL2NI\ndj+2yla5T26QtbLauY4hx8g22bgyRybctUEOv6+qbFkflDFXr5NDBlTRVKF8jqZcaAiGGnvjetnl\n0PK5ypcPoVun+MZ114X4rylYURqCwj3isaoy+6PN8rVa5C10DbqNpuCZGAKFIaDZV5qFEmKEQ9Gy\n7b23yCmniGaghAKVw+9B8CGKGQXNRg109gQhkrVBkGhYDHD4pRnzOt8vA8p1C1E6MQR6ytKUYcOG\n6UzpL3n22WdLs9lC2yIl5NPz1rpAGRRytstATQ2qJjXkJrnfre1mGx6kkEzU2IBm3crLTvuH/qzI\nHx9303o58ObKsvMB+YP23DUDNkjVnQJCjm6kQGlJrjCVsEhP3U5IF3maSydTrhxXP4J87mRYEM1P\nqiANDi4nPw7eIF9N3KqkHpoFoulKuNbL6ZwThi0itTetDLpJRranMuV7KGlwgPrXLHEUNxOCrCX9\nmXacAp06iRBMiJVbmJBRhGJmg+bWE5jivvtOZNCgEI2rp4zpa3j8Cu166cvs4T2IQhrn3daX+5gu\n6GWamE7tX1iwtulUJUed+LiJyQOOlWvryxFu71QyXdDeOH97Y5OsmLlNDrlTk96zWAirGiqD5QHN\n00001ShTYJv24kZZpgxVHQfnrWK0fMY2p4SJMt61S14lPPnxDbJyTo50vL+KlCkXiAkFlgV0oC1b\nhvK2UbbhG+torKlRqILCFbj6DjsstKHEiyukQiFb1TO9Takvt27QTV+z37wmKIsnbZXOj1SVKvXK\nFLcpu76UEMBSpbgLPCCQ80BtCztnIoKd9uGHIauXCmTQNSSzCAx9oWqoxgO7YjCk6cEt4ild+Emg\nyPW2K68M/Y0kMgbO9ZUL2us8NJS4fuGBpiDChUp0O2DAALnpppu8U0pk70cmrFgDbXF6BWcFL/9t\nq9Rtnc+ZEOuyjDq+SUOuntUIZ3J0s1X5Lv5xq8wZuUWOfraqWhN5FSmUj52HVJEx166XTatyct3M\nM99RVquftzl3b0HKly8LbIb65+gIO6CvbNEipHDJ5eY1LjtPLr9cZMqU0A/Wf/4TIvagpjIWBlYJ\nyhorgj0WSDzSoEPeiUPkNb+/u8mte3d5tKpUrmtKOBIfP71H4ZJrDgnPU08pFfhiES3zLuefH7KG\nTzopVHglVp9xG3MNa7iUR8VFzHezSZNYVxTvuJIxKgtjaKOoCWRiOGFRuhF/asVrKEVXx7SAz9QS\nNChf0pI6KLktlZDga35Ua+FFS08qTv+TxYRVUB9KwgKmvTkjN8u8MVvUitFvRBbKy/K4JhdtVAV8\nbRaOXn8QlubIqIvXKb9yZam3Z+xJGFHO31y7TnNty0t15RP/5emNcsTjiVmNRJJCCJSIUE8ZqlE2\nLAePZAnrhR9TTyGzXgf/N4EwRZEZb2+SOcM3O0u4cp0EO1mUBu2ahBGgYheBfXCRU7ULNkhPcOeO\nGhVSxnxHUMSU1eQaNsptsqG4oc2GuZTCI3hl0l18aQE3VIc6dYCPUGZ+FORyJS6voz4KjiVbrtBQ\nz8U6rYJ9q5n+ElTV6c1qne5M18WA/lp7D9c3hRn8KE2OKe8Yi3BFQ4qfTUIpwEkyTld9n8umYeeO\nlXzf8XesV7KMCgUqXy6oWr+MdNHgpo+6r3GR0URIJ+qyTVT50i4WMhs/ltHEU8i4+a7VORSua6o6\nxbOGF36/VsrWFdQJAhHgXdQdXal2wUoY7Faoe76gALXw+9vr4iFAfWyoaJVNWE44If+9cO3iimYj\nAv+TT0SoiMa6KsqW9Vf2WKTxek7yt2JHIhEImwPl/aiP/sVi+TbXGPET9akcf/zxThGfDpFwkuUL\nLe0TyYRVU1fTaR/Sj9tvv923ChjChVZnVZTpr2qhBo14zRbZrLQaz+i67wUa81xVw6+yUSjOUamW\nkonEmQ/OuaeMrCGbVwc18KpgBVVaeGIBs5HyT9Qp3DvnnivSq1foxziRH9vW+ncQVKt6dP/10uXR\nKlKxZv4xUs0JS3nm25vl31nb5KBbKkuLUy3KuiSfN7zvrNXec0/I+i2sLSLw2UxKHoGYCriN+ilI\nASqrf4EowqfV4V9LF5t6JFI7Lc7+pxMTVrQhEfmKAl7157a48j6j3SPdjr0vr0hj2U32E/3VzkKZ\nP26LzB/Lum9ikw/KBbL5UVhXYw0ZK0hXmuTjj0N5yO3bx9/bNloSMWdrUEZftd6tfXtKeNPqHC1m\nsllmf7BZKzmVc5HTVeoF5PM+6zR+oqzUbRPzpyj+xu3MPAgsXRqaUOG0VH6lhIOs8tzM3pQIAgV+\n63faXl0C9zAR0eXCFw2S2J10YsKKNmzKweGGRAl3uC3zreC5Wg7wG/k8K1zPpAqtXxKUtQtyZI1u\n7FdpaUACr456upqruRvtO5HOx1j7I9WfVBD2rPNhEccbUd22VyW1hDfKmGvWS4fbK8sfmlM89/Mt\n0qhTeTniyaoSnra3/3UhatdjlHrTUpmK/61hjZb632PGhNZstcKryycvoZ/u4nc4y+8QUwGTdkT1\no3e0mCw/QuQHP6Vhc+Tj1ktGomEY8JBsEOAVyYTFum+ymLDCmiuRl+RNDj9zjayZv02q75K5a8Hb\nZJuWVXhACSYvzWiWq5nDNjlqRtzFlesqrWTDMrlbpdrlpH3/SnkUSYl8qVJ8U1zSBxwQIkggaAcu\nHKJlUdCFyZ5aq7hO6y3y7X/WS6OO5aXry9UkWnAWEdYLJ2x1lZkOvEEXIk0SRmDJkv8pXQKmWMcn\nJYjnlcgSQsIN2wXFRiCmAoYT+uuvv1Z2kve1ZuzJSofXRV1SH6sr4xm5+eabi91w5A1iMWFFnufX\n9xATsJY1/bXNksk/JB9rVd66sqMcrPWJMlXIe/3poY2OarRG4zJpW3QjGc+HlCXSnYiK/eAD0aDI\nUEAOipignIKE2sP125dzpB0Fnbe3FjiBg5psAqzkbBfyvqdNC20ERBHJjhCEh0Jl722s3xPdjtIl\n0A6ly2cm6YFATAU8VvMWrtWwyAaEvamU179EIpJxRZeEAk4PuAruJTVbh5+1RtYtqeiiXgs+23+f\nYt0+KgPkH1kodbRYYE2ppdxWtdTSZV9Tqmi41WdaZuFepd3IVPl39jaZNGiDdH2pmtRunrmejESf\nH6QHZ50l0r17SBGzVqwZii6qtn792HdjYlqYUOe4w61V1FrW9eA9yiYcHV7Y/f3++apVIt9+G8qt\nRfEqB5JLFWrbNhQQt+eeoZQx0sZIRfM23pNOxkqhKV2/P+Xo/YupgBs1aqS5g2OlU6dOuVd+pBnb\nOyeb6iT37un/onzVgOCKnqEMWftelX7utMfkHo1nrq61i66SVbJSK/OuVGZnXi2Xv+UPmS6/yCCl\n3ail6jkTZcPyHMdatd/VlUs0pSyYs1UCZWL+6eWBNrh2vsjKP0RWzZbgylkSqKJ0V7udLIEacfiB\n89wpOW9IV+nZM8TI9dZboR//L78UTVcs3v1r717W8U5/f88G6aTEJZGEJsW7u3+vhtDitttE9tsv\nRGoBbzI52ZlAMuFf1P3Ts5i/AhBX7K/8YqM0O3vRokUuEnru3LnyJX9tWSaT5XutbPuH7KCuV4rI\ns6+t/1PPNkf/sfekxWkVZOS5a6XNeRXTihXoKxnuLN+7lFhDnYbecEp8T3yBzP9aZLn62mo0Vpob\n9WtWbShSpX6p/giTHkNRhObdK2it5+S7QYMkyS6aIME5GlqsijRYQemtKiqFVYUaEqhQU1+z6fuK\ntUOfr5ytSlcVL8drNpdALd1276Gk0DMk+N31EqzZVAK7nSKB+vrLnQJBEbPOiOKlYhNKA07f4kir\nMyvI4u+3urV3UpoyXYgyf+GFEM2oJpqYZCECMX9p66tfCSKMt99+25FvdFSWdzbSkrJNaqvFB+nE\nL/KDLJMluv2jduG/qoTruPXQw+Qo6SzdHCykXTQ9Vq1gra26j65tpYPMl7kyTF6S2+Xh0lW+i7+X\n4PQXlZJHLZ5GXZR5/U8JLhyvi1oLRHkbJVhVrT1VyAGUcv39Rf2TqpT/N9lJFrauKIIWUsAKa92z\n8B/+4PLpysc3QfujPsI6bVSBqjKNIcGNK0TmfibBuSN0UrGTBJqdoIS5dykJrx7XMcpm3dx+te5X\nKgZ/6URElevOB6vi3U3vXS3vnXdsr8waqojnj5bgr89LcOpQCTQ/RaTRERIoqwuCpSwEZF12mcgd\nd4gGaIZyiovaBaxeCleMumit7LRfOfc8inovP18H+clDD4XWdp98MkRu4ef+Wt9KDoGYVJTRmuSH\n6ueff1ZWFKVFSTNJNhUl66UrZKluy+RVecq5bvsqH3JdtZE3rMiRz85fK91e03rBUcgIPOigcKyo\nDMqJykptlclARzkm0UvznQ+hxi3ST46XHnK4HJ3v85I4EFzxm1MeykghgTa9VdkclK+Z4Db9lVqr\nihgX7Jp5Elykinn9ErX4VBFz/o77SaB8clK+oIWElanjg1oUQYlVoklw1Z/OUg/OH6MThsoSaNhJ\ngsuniPw701mugdqtVBnrVru1kjM3V0tVlbRau8ElP0lgl45qIp6obuMm0W5drGPBpb9IcPZ7rh+B\npsdp+y21H61Vcdco1n0TvVgTJhyhB2xaxRWCsaa+sNHlWEPssWVdULZozWTqJnv7rUqd2Oy48jGf\nV3H7UFLXU1zg1ltDlJ9gRRCVSWoRSCUVZT4FTAGG23RRYppGA5yqRUgpwsDMdIYuVsANTVAWVnG6\nSbIVcPj4cUMPl3dkhNqRZ0ofZw3/9PAGKa/l6NpdmF/BLlcL+nP50OXS1lFXdkstX99S9pTW0i7q\n+irKfpauwP5XiR9/0W25Kv5m0kK26L++crU6xdVlW0R5QR6RDbJeLpMbi3iH+C8LokjVahN1rwZa\nn6f5LEcl5GYObtDolMUTJaiWsyyb6hReYOdDnBUq1RsVyQKcM2Kzeis2yZFP5c/pDa5bLDLvawku\nGEPpH1WknTX0t7ME1P3riXOhr/lbFaAu5uEe/vc3kQ3LVSmra1mVrjTSMSZpouC1GW0fZLLy1+du\nndj1Rd3aAbXO3aRAFbKzpkvAe+D1BZJ/KCyhOuzSxTta9D1K+L2uq13dbWIr+Ftij0OA13j0l0/f\nJu365q8yVfRWS/bKCeo0ocQeGEF2YuIPBHylgC+++GL54Ycf5Oyzz3YpR4899pisXLlSevXq5Sgp\noYbEPZ1uUpIK2MNiga4UP6VhStTFPfufq+SnvpWl2+vVc8kaflcl+pm8p87s/zpr80RV1//IIpkh\n02SmTNX9VEfriEJupQpZE2C00N9E/fRnVbINZC85wG3N9VPWnT/Ve30obzjrtZucpmcntjzwo3wn\nr2lW731KKllSlYyCOWrCLJ2sjO7fquKcKIEWZ+pi4QmqLMt7sBVpH9y2SUStS6eQV/4espYr1XXr\nyIHqupbMejJ7XNjl8k+CaHTRpC0y6d4NcsQT1aRagzK5/UCZBac+HZooNDg0pHTrqjKLU4LqUg6w\ndptCCa7+O2SF68QAj4Ns+Edd5nuqt6GDRk4dKIFKdZLeO4qpX311qMrO9uSJpLZBjitBS7/pcGjr\njMO3ytpRGwVnyV4XV8qtw5zURpNws3nzQmUiR44UueuuzC8ynwTISvUWvlLA7dq1k6FDh7qgq8+0\nYOT1Woj0H6VXeVIXK8gHTlcpDQUMNuHWcMvHz5ZOZbrKxn4TVVm+L2s1pvhYOUWV7zExFR5KHEXM\nJhJ0CredEj6SDhRNWJN+TtduV6lb+mKtSNREdo92Wr5jWOG3yOVyndyt1rS6LZMsQSxU1ikXjtOg\nqgYSQJE16VZi1qALclqr/j2s0dVz3T645i9VPEvFuWYJWNquFAm4+vGBDfLdrRvkghka0729iIZT\n6jPflOCfI3SicIZI81MTstCTDGFSbxfEZ4vnYJF6EJb8oJMTnZjspMpY3fmJuMbdhEoxlY3qjcDS\nX7dIFbuug+/QzvWXXGHqzD7xRN5qO4kOZu3aUFlFlK2ndClDR/m71mrQk4xBG0pVL9332iJLh290\nQY/tVBFTAjLVAiMVtZnZ1H7R39OQhyDdCsanGsfSaN9XChiWq3k6ZYMYY5ZW/YYTGpYq+JrTWUpL\nAXsYoUgf23if/Dl+rexYZQfp2fp06VDzYO/jpO/HyZfyuubnHipH6mpubymv/2IJk4S71XW9r/I4\nHy+nxzotoeNOAbJOOu9Lddl+q4tb6oJ1LtuOmjpTP6F7JfPkIIFNM16T4LzRLtBr3uLT5ZcXKssO\nbcu6VLEK6s5EggvGhgKadthTpG3fErEQkzmu4tzLKdHlOkFapFHZuuksQwK6dh0MblUggttvzV43\n3pMTs141Cgp3y2oRPA2V6ylGuq/WIDTJKqvr4s11gt6wk9x6W1lXNadfv8R6SUm8cTpfU/4fV9NY\nbQFHg+kp3UjlRQ4skcQUG9ivfVCOabpFfn9yg1TZMSDHv11dyC8uTfn33xAFJP2Hf1ljVl2UOOMA\nQhN/IuArBbyDFntcqJECFTQ64M8//9RC3kequ0f9PWkupa2AgQtFN33LFAm+2srx4VI1qcXpFUos\ncGSN2sGvyJOasztH9pEDXYQ2rFWkTbH3qha9Ky/LbLWxb1BKjaKIC5BaNSeUJqOpMkHSZVC+VTXK\nt8Fh6rLtJAFdky0NoQykxkRJDa2xW5CsnLlCJt8zSzYtXiLt+yyVet2Odn3EVRucoqYUAWF7XSYB\nIpuzTIKr54air3PXiFVbOI2xXWuUUWxxWavCjeW6Zl0+OPt9FzS3qcGJctHA4+Sy/tXkoINigxnc\nvFajGKopBW1I6f6kKwp77RVaQ4YGE/KPeIT152HDQlvHQ4NyUM5G2TBvmyuLuHFzQEub6vDCNqxr\n2KMo7u7tOcZ7WKj0J0+OOUZj6aI7nfJ1iX5j+U+ZIm68pGaR11u24K9kvvvYgdQgkEoFXC7akJcp\nFQsKeMWKFe5j3ntSsWJFqV69uvfW9gUgwDpt2/J7a9SFuNSkyY9tlDkj1kr7/6vs0iwKuLRIH1VX\ntiqCqQjWQgnPkz/da9zUBG4xIVivjvCm6qa+RR5MqA2XejP/K3GuZdyOur4a0DQZqdVMLUv9xSFl\nJsZaa0INFXLy+qU5skQLIVAMgX3lemU0PiooG/8NOldyHXU/4lJmT8m/rRuDMvW5jfLXl+Vkj177\nyG7HbpbA3OESHHudpjbt59yxgVY99QHpunSuAiqkExn2sXNB12hSrFEFWFfWjWjxShqV/fhJ58mw\nN7tIix2PlprlFsta/Q1Zt3yZZlotk21rl0mQpYEta+TTGcfLgmrnSscuFeU6fSS4mRMVFDUlFFkh\ne+ONgDz0eWXZZfp6ebvVRlnYsrKrbUx9YzZ+urCkyWOuUkVj1HRewZ5KUGwcpxbuOeeIUAXquONC\nfNiRFiwK+9NPQwXsaZ+2tWqqMgYm2ns7P5sRyBcFjQW8fPnymJhQD5gCDekmqbCAo2G06Pst8vOj\nG6Vms7Ly/+2dCXhV1fX235N5ImEKU4jMMggBtKAgIIOAQ79WUaygYtFWQUWhn3VAWqha/VttEQcQ\ntFLlU6v4WVoVB0SgIqDMDiBhRlAgzGSezn+tHTORm3CT3OSee8+7n+c89+ZMe+/fPrnv2XuvvVaf\ne6OqXKbk6Xoz1Ks9Fu2B6vrTcPnFMpv8esjfVmikp8vMPrV2VjFuiuaIFseSZ0vGsvZ7EV3ZEBIB\nq80IWf5zQZH4aq+ontKBVXklopt70hbdDDMvMPpZHNRel6joUiKzSa9YPwtzbUFioZn4I+7xm0gx\nTA4pKbHpxevyHZ2X9rPBVEmhguiLrn/e+cl/sPbdtcgNb4nc0KawopsiNLYpIhKaSmCGpohr3BAD\n4p9BVMbXMvpwlxFwXyDQny87T+b5H8pAu8vC0Xl05f8TleWnw+E6lPz++2JDmAZccQUkJrr8250s\n6u2uWAH0lxkldc0ps3RMAUzAnz3gCgJ8WsZgzNKKSoCqT+hofU0MsFQbAbYPrTPrK6tyuFAdHBov\n9TsJSJ4qEXdiW4bICpoQxCeHmk/9Htc6pGT+yj69X6w4tskyl9SiJSbqIUm9RMl6T1udOORlyCav\n4/qZK+NnOo+nnpV06ctPwmyFq1AXCXSJYKtQiwMM8ZQvm7SnzOGVfDeiK78+Mu9nJQ8pcvKga1v9\nkA6tz8cXYqmsfrZb9BXnDB29F35dj515qFDizXoc6PFDbdyX5Sl5YWoQL3PMP41meyJgp22CvfFp\n6ZrKaErKRBHqRE+nVXufjpYsmZBhgqO06FPzZ0Bm4owQL19eNKysgSm0Z3zmnHS1C8gLHEHAnwJc\n4ank8LLnZ8L+5FaxCPlpqLKWvb+QMAtdR3yHtvH/DxlpUTh9OAGnN8Vj78cNcTotQYbq4hEZm4Wk\nLlvR8+ovEdK4swz1nlvkHamRfKpgSvL0m2YMbGRoT7wWiCjLZ7E466fuU69LOoQsVrF2vkx65csE\nmlrI6lagnznSE+krDjJuBhJ7+3VYVkM7rn4kE4P/GouGHbwX3uIW1PB3nkLgFR/nZ90TiE/w9JSW\nz9dKlGmaS18S11D/hP3pHfJ/NkY8VVxV62dPR0cGPBKNz6ZmYuizseYlt3zO3v2lLjY1+IRuTCTg\nSwIVBNiXNw+Wexl/uwP/Klayc4Dd74qV7G01Hi5Tgxf7G/mxSf8e0X0nIVoMW5qW6x6IkwHbQmaa\nhfUv9Mbqz8bjomnRZw3pVsza0pcD41O4YfGuSj89/TSqgJt7VHpV/RwokOHjz/+YZRwt1ER866eU\nzMVXBExwii43mjXX9qZnxIx4iUzC/l/jA7s2eTTpFoaeE6KwUvx8X/pCRWcrtbk3ryWB2hIonRSr\n7Z2C/Hq16g3p/xisHhNEQF9E4aqpMM4OvKy3Gp3YG0TEVz4g4t0H1qUvG0f66lVJjWBKtzYISTgH\ncR2TMfCJhrKax8Knd2fICpBCL3Oq3WlOEF+twYZZ2eLRMUTcDdJXX+1aNLCutuKSEDLgCVgSeMJe\nNQ126ptVTol5U7t2l0WglcQmXv2nTPGgZXtzCc8hgXohQAGuJmb1RWwNFQf4avG58l7pFc8zlsGm\nZ6siq0O5ZZItQ7zGab4OrekyjhHzxUXhL73qZapf4r73RZsg5Z9MzMCJXQVl7hy8X/csyUXa1/nQ\nsIBM7iSgtgfW0OeNL237M/k/Ez/gtUk9J4jNgwz5bJqTU5vb8FoS8CkBDkHXAKfpJYqIovUwcfLw\nKuytrxQZQBmDKDFiU994xkJZDJ809qsGDhgmol1D938aoScuKQTLp4hBiUSLadk3eNc6nNpbgE3P\nZ2PI07FeD7vXoAl5SQAQUEcf1sC/wN7+NuzlkwAZfTJRs2pQdivEQv/pMVhye7rYE0jEMukVM5GA\nvwlQgGvRAiZUXModFYyhigyh1AhKNp1T9UHw9ORLwo2Hn5UPZeG8m210/GXw/YCoi0id9+05MQoJ\nbatvdFWLpuSlDiZgdbpWlr+dD3vt4+JO80ug1yRxaSovt9VMGsxh4BMxWDY50wR2aD0weF9kq4mG\np/uJAIeg6wC89pB1banOZ/lCfIuLqMtpLp0di9T/n4NvX8nGKfH2E0xp/d+yJORvKNqNDL6Xi2Bq\nJ3/UxdIlSkOeNyNL9qe3S9QpWZpXg9QgKRSDRIT1WdNgHEwk4E8CFGB/0q9B3urdabiEzju9vxDL\nf5eJxeNO46t52TjybX6tjVVqUByfXbJrca4sdS7EBZO99D/os5x5o0AhYIVGiMMOcRfa6x7YXzxS\nZAh59JtqF79h+1AMeCwGXzyWhbSvZN08Ewn4iQCHoP0EvjbZ6lDahVPF+b0sXzqWWoADK/PkjT7b\nuGNs1T9M5ojD0OrisDrzOV2bsnu69vDmfDPve+kLsQiN8LQ4ytNV3OdWAmoIieF/l8AfEm1r/VOw\nxcOWJWv0LRmm9jbpaFL/GTEy5ZEpPeLYkohY3l7P80jAFwQowL6g6Id7qPhqanyu+D2Wrcct4l/j\nYKER4x3/zsXW13KMwdbZghR4W3Rdl/vjl/loIMZgCe18Nz+7Rcr5wY3pJiygegNjIgFvCBiXq20v\nA9Q96v4VElBjDmzx6mZ1vkEc1lQRAaLMzZv1CkPfB8RRh6wRHvzXGJ8+12Wy4VcSqJQABbhSNIF3\nQIenz71WIi7Jtuv9XHw6KQNdxIK683UydFfO2Yd3dcs9beOH1Xki6hL4QFxC6vzscfGz3PlXkehy\nvdxTLEtrmnRdsw4BFso03MTDjUp8Otf0frzOnQRMAA1dsiSb/cMq2N8tgL1Flvp1G++VELe6KBzn\n3w2s+H0mhsyKkRdMvgS680nyT60pwP7hXue5qgMLDVbwpfhRVgHt+0CUVz8u6j93/woR3c/zZU62\nAM0vCEPSgDD0+X20CWygx798Qu+ZZ4bBG7Su/g+WivraJ7PR6eoIdL2xZi8HdQ6QGQQcAatVfwmH\n2V/WDq8TZzmyPl+CbVga21nct1aVkgeHm6hZalMx7LlYvgxWBYvHfEqAAuxTnM66WWzzELOedvs7\nOVh6R4aE44sU0ROHBGWS9nIPbcjHYdm0l6uuoVteGGZ6zSq+Z87Jqn/dwU/FQoe5l96ZgW7jpMd9\nTfl7lrl9ua86jL1pTrbEgc/HgEejoW4CmUjA1wSM61iN2rX3I9hrZgBNU4DzpEcsQUwqS7ou2BZn\nc7rWfpisNCgbOauya7ifBGpLgL+AtSUYANd3GhWJFiKqOuS7/7N89Lg1Ej9ID1cFV62pE1NCTU+3\n41Xez4PpOmSNMKORig7IPfs+GA0VfE8pL8MW39aF4gowyzhBGPlynARrqvnwtac8uI8EyhIwUy46\nRyxD01BHHsvulPnikcC5Y2DW75c9+afv7a+IwNFvC7Dl1Rz0vote2Dwg4i4fE3CcAOfniyhISMRG\njRr5uKruvp3Obenw2jYJg6iepjS0X6+7oqQXGlpja+m4ViEY+kwMtr2ViyW3pSPltihjCJaZZiNL\nBFdFN0u+a5z7qEaW6S23HcE1vu5+Euu39sZYq8sN0LjP0PnhT8RaseM1El2sk1gwdi2JLFZcKg3c\n8MGv09FmeAEto4uh8LPOCDhCgHNzczFjxgwsWLAABw4cMOtZY2Ji0K5dO2isxvHjx9cZADfdWHsF\nXa6XYWiJrXvm0HJNOZh7ilFWq4vC8K30HNSDVbNeITKPJnGjEy3ZQhAebUGHn32VZ03LyuvcS8CK\nkhf6XmJt1eFqYM/7sLe9LnG2t8OObQVLhFjFGI27IVzOU7/R6qjj0jmxtTI0dC9t1txbAo4Q4EmT\nJuHgwYMS9Pp9tG/fHrGxsTh16hS2bNmCyZMnIzs7GxMnTvS2TjzvLATqQgjj24Si3x9iKs25LvKs\nNDMeIIFKCGhUM+NTWo4bl7EndwLHtgBquLX1VYmJnYc2ve/Bng9TsP2dXLOioJJbcTcJ1JqA50m7\nWt+2ejf4+OOPMXfuXKSkpCAuLs4smUlISEC/fv0wa9YsLFq0qHo35NkkQAIkcBYCxmWsWEhbHa6C\n1edBhIxcAGuQhAz9ajbOv/xtGdHJNtMoZ7kND5NAjQk4QoC7d++OZcuWeazEe++9h8TERI/HuJME\nSIAEfEnA+G8fMkc6ArvRqftbWP/kEV/envcigXIEHDEE/fDDD2Ps2LGYOXMmOnTogPj4eJw8eRJb\nt26FGmUtXry4XKH5BwmQAAnUFQG1krYumoGujRbhozvWYv+iFmh9lSxrYiIBHxNwhAD37t0bGzdu\nxOrVq7Fnzx4zH6y9Xp33HTRoUI28OPmYE29HAiTgMgKhna/CBTN24ctpu9Gs5RyE9xGnHiGO+Ml0\nWUsEb3Ud8zRFRUVhyJAhpsfLZUjB+8CxZiQQSASaD2yP5pc1wTdvn0avrCnAz+6XMKOtA6kKLKuD\nCThiDliXIU2dOhXJycmIiIhA48aNjSW0zg3Pnz/fwfhYNBIggWAn0PPOBvh+5zCcsH8Je8UU8Tf9\nepEFdbBXnPWrcwKOEGBdhvTtt9+aZUi6/KiwsBA//PADXnzxRbzwwguYM2dOnYNgBiRAAiTgiYC6\npUy5XdYG/1OiLA2ZDfv4d7A/nQD72FZPp3MfCXhNwBECzGVIXrcXTyQBEvADgXYjIxDewMLOjxMQ\n0u9hWF3Hwf7iYdibn4Wdl+mHEjHLYCDgCAHmMqRgeJRYBxIIbgK974zClleykZsu7lWTBsK69CXx\n5mHDXvpbEwoxuGvP2tUFAUcYYXEZUl00Le9JAiTgSwIJ7UKRNDDcBGvodUcUrPDYIveWR7+BvXEm\n7O+Xwup5B6yoJr7MlvcKYgKOEOCyy5B27tyJffv2oU+fPlyGFMQPHqtGAoFIQCOJLb4pHR2vioAG\nI9FkNekODJ0LpL4pveEJgAxPW+3/TyBWz5TZPr0f2PYa7IJcWBpBqnkfLgWto9Z0hACrFbT2gmsb\njGHlypVYu3atR1Tr1683ltUeD3InCZAACXhBIDIhBF3GRJq41gMeKfV9btYHa9SlpEE/9YY/gdX7\nd7Di23hxV2ecYqcfkIhRIryH18HqeK2EbWwgQSteAzY+LaEcR5hwjlZsS2cUNkhK4QgB9lUwhiZN\nmhhPWp7apmHDhibKkqdj3EcCJEAC3hI499oIfCC94MOb89GsZ/mfUA32YA36G+w9i2F/di/Q7kqg\n81hYoc4Nw2lnHCzq8f64RvxiXw2r16SSMI1W28thn9oH7P1QlmDdA7tBG1gaZ7l5XyPQ3jLjeZ4J\nWLYkz4fqb6+GHVQvWC1atKiQ6Zo1azB9+nR89NFHFY5VZ8eUKVOMh6033nijOpfxXBIgARKoQOD7\n5XnY+loORrwYV+FY8Q47+xjw1RzYEvbQ6jsNVsOOxYcc8WlnHwe2viIGZJ/LkPkvJE7yqKJ57UpK\nZ6JHHVwDW8QYx6VO50+B1eLCSs4OnN0a8vaGG27A+eefX++FLv/6Vu/ZF2VYbAU9ZsyYCiVgMIYK\nSLiDBEjAzwSSB4cj9e0c7P4wF+0u89y7taIaA30fAg5+AXv1H2FbMmfcsAOsBBHihA5F32Oa12tN\n7BMSflHLc+gLIP0HWNJDt4bPl95s5S8SxQXU6FFodTEs2exTe6VO08y90ON26eFHFp/Gz2oQcIQA\n0wq6Gi3GU0mABBxBoNdd0fj8D5lQMQ6Lsiotk+kljvgHoD1ijT98Yof0Ij+Q3vEu2PnZIsQdYTXt\nIeImS5t8PGds7n9kc5HoivBChsKtFhfB6jYeaNy1xsJpyjlsHrD5OdjL7hAXnQ86rodfaYM46IAj\nBLisFTSDMTjo6WBRSIAEKiXQpEsomvUKxXdv5KD7+KhKz9MDZg44VqbYdNNe5E9n2zknRZC3AyKS\n9uqHYIfK8iYx5FJjLiu+7U9nVf/DzOtufwv2/hVFAi9DxdYAGWL2oR9rKywauOD3gORhr5oKdBot\nw9hivGUV16765XbbFY4QYIVeHIzBbQ3A+pIACQQugZTbovDRrelo//MIxCRW36+RFZkgBk0/M5t1\n3q3i5nIbcOC/IsZ/EDGW3morEePWl3gtxsaSedsbsKW3a7X7OayRr1Y5r+sL8paUD026wV73hPS0\nZRWKDLubevni5kF+D8cIcGWct23bhszMTGgvmYkESIAEnERARVfXBH/1YjYumlq6LKmmZbQadQZk\ns7qLd63jqUVirC4vc08DiT1lqLqnfPaCWluXTTonCxXetA1iUHUVLBnyNo5Cyp5Uh9+t6ERgwJOA\n9rqX3Qm07GfKiaYptJaugrvjBXjhwoXYu3evCcxQRT14iARIgAT8QqDr2Ei8f0M6jm0rQOPOYqjk\no2Q1OlfE+FwR49/AzjpihqmRJkPV2xcWOckQQYYMLasVM45+C6vTNbL2+J6SJUQ+KobXtzFDz+f+\nCmh2AZC2SZZiyTz3hqdgx7SApWVt2kt6yt29Mvg6M1P72HfyMiLD6fFtgXOGyzB39UcbzrynE/52\nnADn5+ejbDzgadPE0o6JBEiABBxKQA2wut0Ygc1zsjF4ZkydzIFa0U2B5GFm0xlWO/OQiJyIsS4h\nanJeUZxih6w1Nsut1LCs07VFYRtPSE/+yFewd/0bWPc/sGUeuujloqi3D11bfMa8sVnypMZjP35e\n5GdbnIJYrYfA3rfU9LLR9dfGH7dDHwmvi+UIAVZPWDNmzKi1Jyyva80TSYAESMCHBDpdHYkj3xRg\n1Yws9J8RXUFQfJiVuZWly5fEO5WlHqocnMzSJbG2NhbX0js2wqpGZydkrtv05t8Cso7CbthJRFkE\nWc/9YaXMYX8JqFMTNVgb+JQYjyUV1bvzGPHUtR72t/Nhi+tP67xbYDWr//W7vkLuCAH2lScsX0Hh\nfUiABEigugQunBqNFfdmYuOz2Tj/7ujqXu6K84sEuYsIrWztxTpcam3nposgSy9ZDNDsvR/JMinx\nsiVz4GYdtQcqlgxx62Yf+Az2V8/DjmpaJMQq4AGWHDGQznjAAfbUsLgkQAIVCISEWhjw5xikfVWA\nra/nVDjOHZ4JqBMQ7cVa0rs1sZbVeludmJwlmZCQw14sGppWQzV1MhJgyRECXOwJyxM7esLyRIX7\nSIAEnEggPMbCoL/EYOd/crFnSa4TixhUZVJjLPVNbQ3/B6DhIQMsOWIImp6wAuypYXFJgAQqJRDd\nOASDnozBsrszENUoBC1+5oif2UrLGwwHrNDwIicnAVYZRzwZ9IQVYHtqFzMAABazSURBVE8Ni0sC\nJFAlgfjkUDMc/dmDmbjkqVg06uS75UlVZuzCg4UFNlY/nIUGSSFQxyiBlBwhwAqMnrAC6bFhWUmA\nBM5GoEm3MPS5Pxr/fSATQ2fFoEFrivDZmNXk+JpHs8xlPX4bWZPL/XqNI+aA/UqAmZMACZBAHRFI\n6h+OHrdEYl7yCaT/WFhHubj3thuezULOcRsXTav7pV91QZkCXBdUeU8SIAES+IlA+ysjMOrDBlh6\nZwYOrc8nFx8RUEvztM0FZqg/NFwXNAVecswQdOChY4lJgARIwDsC7UZGIK5liJmr7PCLcJw3LrDm\nKr2rZf2dpXGYd76bi2HPx4rxc2CKr9JiD7j+nhnmRAIk4GICiSlhGPFiLA5vKMCK+zKQc4pD0jV5\nHH5Yk4ev5uWIcVsM1OI8kFNglz6QybPsJEACriOgy5IG/y0GjTqG4uPfZuDodwW1YrD/s7xa36NW\nBajni49uyceX/5OFgY+LUVtS4Bu1cQi6nh8gZkcCJOBuAlaIZZbLNO0RipUPZqDbuEioL+nqpFP7\nCrDp+WzpRdvIzwQKcmwkDw5Ha9madAl8YfLE4sTOAqx8KFMMrmJ8GnXKU171tY8CXF+kmQ8JkAAJ\nlCHQql84hs0Oxao/ZuLHNflIHioCOigc4dGVz2nmnrbxzfxs7Ps0D91uUuGOgAr6yd0F+H55Hr58\nPMuIcetLwpE8JDjEOO3rfHz9Ug42PpONG9cnoPn5wSNbwVOTMg82v5IACZBAIBBQw6xhs2NxYGU+\n9i3NMyLT8qIwtBkejhZ9wqD+pTWps4kdi3KxZUEOzhGhvmJBA0Q0KBXqhHah0K37eBSJ8Yo8vNH/\nJJIuDsNV/5ZQfiLSgZQK823sW5aH1IW5yM+2ce61kbhEvIuFRgRWPc7GnAJ8NkI8TgIkQAJ1SECX\n0JwjvVXdtIerwrP1tVwz16liq73idX/LMlbUQ5+JRfw5VQ8xl4jxr6Pw3/sz8PXfc5Dy28Cwus45\nWSh+tPOwXV42GrYPQY/fRKJlX3EzGaSJAhykDctqkQAJBB4B7dV2/EWE2TIOFmLvkjysfzobve+K\nqpEQaYjEj36TgeYXhDl66DbraCG+eyPH1FdfOIaIoVp8m6pfNAKvdSuWmAJckQn3kAAJkIDfCcS2\nCDHzvF1vlHleq2ZDr5EJIbjwwWh8IXPDI1+Khf7tpJSZVmhCN+rwe7vLI3D5gjhExjurjHXJiwJc\nl3R5bxIgARKoJYGaim9xtmq01HZE+E/Ld3wfsi833capvQWyFZpNDcJiEkPQsKNsHULNdqazjIxD\nIryv5RjDsQ4/j5A5bRFeh70cFPOry08KcF3S5b1JgARIwAEEuos/6qV3ZWD7OznoNKp6S57OLH5e\nlo3Nc7Jxep8IrmxqJJXQNgQNZG46vk0IOl8XifQfCnFSlg1pz/bEzkIRV0sEWcRYRDlPBHvPx3no\n+MsIXPlaeWOyM/MK9r8pwMHewqwfCZCA6wmoNXW/P8bgkwnpSOwVJgZONZ9fVUcYhbm2GR5vIIIb\n0/TsQ8anDxTgxI5CEeMChEZZuPJ1Ed64mg2rB1NjUoCDqTVZFxIgARKohIAueep9dzRWzcgUl5hx\nCIusvgD++GUejm8rwMj5cVWuVz6zCOq1SrdkWZ/MVErg7K8upefyGwmQAAmQQAATaDNMnHNInOKN\nz2ZXuxY617v2yWz0fSC6WuJb7YxcdAEF2EWNzaqSAAmQwPn3ROHwxnxs/1dOtWBslNi7rQeGoZkM\nYTP5hgAF2DcceRcSIAESCAgC6upy0F9i8J9R6TjyrXfxiQ+sysORbwqQcntgOPQIiIaQQlKAA6Wl\nWE4SIAES8BEBnY9Vv8orp2Yav9JV3VbDJq77a7ZZT1yTeeOq7u32YxRgtz8BrD8JkIArCej64CFP\nx0ps3Wx8/XLlc8IbxBNXm0vD0bQ7h559/aBQgH1NlPcjARIggQAhoH6jh8+NlTnhAnw+PRP5Etaw\nbPpegjoc31GAHrfWbu1w2XvyeykBCnApC34jARIgAdcRUA9UQ2bGIDzGwtI7M6DuITVlnyjEhqez\ncNFDwReFyCmNTAF2SkuwHCRAAiTgJwIhYRb63h9tXFYumZCBo98VYN1T2WgvbiIbd6650w4/VSdg\nsqUAB0xTsaAkQAIkULcE1I1k3/ui8Oagk9CYvOf9mkPPdUmcs+p1SZf3JgESIIEAI9DywnDcuC7h\nrHGHA6xajiwue8CObBYWigRIgAT8RyBeAisw1T0BxwtwQUEBcnKq57Gl7rExBxIgARIgARKoHQFH\nCPD333+PcePGIS4uDsOHD8eOHTtKarVw4ULcdNNNJX/zCwmQAAmQAAkEAwFHCPDMmTPRsmVLrFu3\nDv369cOgQYOQmpoaDHxZBxIgARIgARLwSMARRliLFy/Gxo0bER0djYcffhjdunXDyJEjsXLlSo+F\n5k4SIAESIAESCHQCjugBq+Bq77c4XX/99Zg0aRIuv/xyHD16tHg3P0mABEiABEggaAg4QoAnTJiA\n0aNH44knnigB+7vf/Q7XXHMNpkyZUrKPX0iABEiABEggWAg4Ygh6xIgR2LlzJ3bt2oX8/HycPn0a\njRo1wvTp03HJJZeYY8ECnPUgARIgARIgASXgiB5wbm4u/vznP+OKK65ARIS4PmvcGLGxsejevTt2\n796NW2+9la1FAiRAAiRAAkFFwBE9YJ3vPXjwIN5//320b9/eiO+pU6ewZcsWTJ48GdnZ2Zg4cWJQ\ngWdlSIAESIAE3E3AET3gjz/+GHPnzkVKSopZC2xZFhISEsySpFmzZmHRokXubiXWngRIgARIIOgI\nOEKAdah52bJlHuG+9957SExM9HiMO0mABEiABEggUAk4Ygha1/6OHTsW6pCjQ4cOiI+Px8mTJ7F1\n61ZjlKXrhJlIgARIgARIIJgIOEKAe/fubRxxrF69Gnv27DHzwdrr1Xlf9YqlQ9JMJEACJEACJBBM\nBBwhwAo0KioKQ4YMKbcMKZhAsy4kQAIkQAIkUJaAI+aAdRnS1KlTkZycXGEZ0vz588uWl99JgARI\ngARIICgIOKIHzGVIQfEssRIkQAIkQALVIOAIAdZlSDr/26JFi5Kil12GpB6xvFkHPG/ePLz++usl\n9yj7Rb1sde7cuewuficBEiABEiABvxFwhAAXL0MaM2ZMBRDVWYZ02223QTdP6c0338Tx48c9HeI+\nEiABEiABEqh3Ao4QYC5Dqvd2Z4YkQAIkQAJ+JuAIAeYyJD8/BcyeBEiABEig3gk4QoC11sXLkM4k\nsG3bNmRmZkJFmokESIAESIAEgoWAI5YhVQVz4cKFmD17dlWn8BgJkAAJkAAJBBwBx/SAKyM3bdq0\nyg5xPwmQAAmQAAkELAHH9YDz8/NprRywjxMLTgIkQAIk4C0BRwgwPWF521w8jwRIgARIIFgIOGII\nmp6wguVxYj1IgARIgAS8JeCIHrB6wpo7dy5SUlIQFxdnoh+V9YS1aNEib+vD80iABEiABEggIAg4\nQoCLPWF5IlYdT1ieruc+EiABEiABEnAiAUcMQdMTlhMfDZaJBEiABEigLgk4QoDpCasum5j3JgES\nIAEScCIBRwiwgjnTE5YGVbjuuuvMfLATwbFMJEACJEACJFAbAo6YA/ZUgVdffRXZ2dmeDnEfCZAA\nCZAACQQ8AccKcMCTZQVIgARIgARIoAoCjhXgm2++2QxLV1F2HiIBEiABEiCBgCXgmDngMwnqumAm\nEiABEiABEghWAo7tAQcrcNaLBEiABEiABJQABZjPAQmQAAmQAAn4gQAF2A/QmSUJkAAJkAAJUID5\nDJAACZAACZCAHwhQgP0AnVmSAAmQAAmQAAWYzwAJkAAJkAAJ+IEABdgP0JklCZAACZAACVCA+QyQ\nAAmQAAmQgB8IUID9AJ1ZkgAJkAAJkAAFmM8ACZAACZAACfiBAAXYD9CZJQmQAAmQAAlQgPkMkAAJ\nkAAJkIAfCFCA/QCdWZIACZAACZAABZjPAAmQAAmQAAn4gQAF2A/QmSUJkAAJkAAJUID5DJAACZAA\nCZCAHwhQgP0AnVmSAAmQAAmQAAWYzwAJkAAJkAAJ+IEABdgP0JklCZAACZAACVCA+QyQAAmQAAmQ\ngB8IUID9AJ1ZkgAJkAAJkAAFmM8ACZAACZAACfiBAAXYD9CZJQmQAAmQAAlYtiQ3YNi0aROuvPJK\n9O7du0J1Dxw4gNTUVERFRVU4xh2lBHJzc2FZFsLDw0t38lsFAllZWYiIiEBoaGiFY9xRSiAjIwOx\nsbGlO/jNIwFy8oil3M5iGevfv3+5/d78sWvXLixZsgRJSUnenO7Tc1wjwFVRW7FiBZYtW4YZM2ZU\ndZrrj82ePRuJiYkYPXq061lUBeDOO++Ebt26davqNNcfGzx4MJYvX+56DmcDQE5nIwQcPnwYkyZN\nwptvvnn2kx10BoegHdQYLAoJkAAJkIB7CFCA3dPWrCkJkAAJkICDCFCAHdQYLAoJkAAJkIB7CFCA\n3dPWrCkJkAAJkICDCFCAHdQYLAoJkAAJkIB7CFCA3dPWrCkJkAAJkICDCHAZkjRGdnY2dO1mo0aN\nHNQ0zivKqVOnzNpWrt2sum2OHj2K+Ph4rpeuGhN+/PFHtGzZ8ixn8TA5nf0ZKCwsxJEjR9CsWbOz\nn+ygMyjADmoMFoUESIAESMA9BDgE7Z62Zk1JgARIgAQcRIAC7KDGYFFIgARIgATcQ4AC7J62Zk1J\ngARIgAQcRIAC7KDGYFFIgARIgATcQ4AC7J62Zk1JgARIgAQcRIAC7KDGYFFIgARIgATcQ4AC7J62\nZk1JgARIgAQcRIAC7KDGcGJRNNB1QUGBE4vGMpEACZBAQBNwvQA//vjjSElJQbt27aDfmUoJqHeZ\n6667Dk8++WTpTvlGZqU43njjDQwdOhQ9e/bEjTfeiK1bt5YcJKciFPoCN2XKFPTu3RvdunXDzJkz\nSxgdP37cPGOdOnVCjx49sGrVqpJjbv5y22234fbbby9BQE4lKLBu3Tqcc8455bYDBw6YE5YvX44B\nAwaY3/Orr74ays3RSXo4rk1vvfWWffHFF9snTpywxd2bLT+i9uLFi13Lo2zF5SG35UG2xT2nLUJS\ncojMSlCYZ6Z58+b2wYMHzc6XX37ZHjFihPlOTqWcZs2aZY8aNcoWIbbT09PtVq1a2atXrzYnjB49\n2n7kkUdsedmzly1bZivPzMzM0otd+O29996zGzdubIsIl9SenEpQ2HPmzLFvueUWOyMjo2TT5yct\nLc0W16b25s2b7dzcXFte+uzx48eXXujAb67uAX/44Yem15KQkIAWLVpgzJgx+Ne//uXoF6b6Ktwr\nr7yCu+++2zApmyeZldLQEQIRWohomJ3aCy7uwZFTKSftyf3jH/9ASEiI2eTHsWRaQzndcccdsCwL\ngwcPRuvWrbFy5crSi132Tf2IP/roo5g0aVK5mpNTKY5NmzbhwgsvxOHDhyGii5iYGPP8aM+4a9eu\nZkQzPDzcMHznnXdKL3TgN1cL8L59+8o5g1cRPnTokAObqf6L9Mwzz0DeuitkTGalSKQnh0GDBpXs\nmDdvHq688krzNzmVYEFkZCQaNGiAf/7znxg4cKBh1K9fPzM8mJOTA+ntlZys/4P6w+rWNHHiRMyY\nMQNxcXElCHQYlZxKcEAF+KmnnoKMNqFt27a4//77zcEz/+f0xfjkyZOGXenVzvrmagHWt82ykX30\nTUqGNZzVQg4rDZl5bpCXXnoJ7777rvlh0DPIqSIn7eXqHLD2VHSu/ExGekV0dDRkmLrixS7Y8/rr\nr5v6jxw5slxtyakcDlxwwQX4+9//jtTUVGzYsAHPPvus6QmfyUmfJU0ypVH+Bg76y9UC3LRpU2iI\nveKk37VXw1Q5ATKryGbu3LmYNm0aPvnkEzOEqmeQU0VOv/rVr/Dqq69C7C7w3HPPVWCkV7j1f1DF\nY/LkycagT+aAzQvK3r17IXPl5HTGo/T888+bkRTdrYZ9+jzpUPOZ/3OnT59GVFSUo8PMulqAdb5J\nH/LitGfPHiQnJxf/yU8PBMisPBSdK9chQxVfnX8qTuRUTAIQ4zR88cUXJTvOO+88bN++HQ0bNjQ9\nvv3795cc0/9BtXB1WxJDUHTs2BH6MvfYY49h6dKlZqh1wYIF5FTmYdDY7X/6059MDPfi3drDTUxM\nNC+/+vwUp4D4PXegYVi9FemDDz6wZQmSLSbs9u7du235B7DXrl1bb/kHQkZiIFPOCprMSltt165d\ntkxh2LL0wZYeTMmmZ5BTKSe1WlXr8Ly8PFvmM20ZQjSWz3qGWrOKwZE59vbbb9tdunQxFqylV7vz\nmyz9K2cFTU6lz4HYXdgygmJ2rFmzxpahZlt6u7aIs92sWTNbXobN93HjxtkPPPBA6YUO/AYHlqne\niqSm62qmLm/ithh/2NOnT6+3vAMlozMFmMxKW+7ee++15W27wqbLI8iplJPyGDt2rHnB1Zfc++67\nz87KyjIn6Itv9+7dzdKkDh06mKVIpVe699uZAkxOpc/C559/bvfv39+WtePmt1vmzksO6vI/MWCz\nk5KS7CFDhhhhLjnowC+Wlqm4y+7WT513UktN3Zi8I0Bm5OQdgdKz1MBR/8fCwsJKd/70TZeT6DAi\nU9UEyKmUz7Fjx8zwvC5vK5vy8/Oh87/iw6Dsbkd+pwA7sllYKBIgARIggWAnUP7VIdhry/qRAAmQ\nAAmQgEMIUIAd0hAsBgmQAAmQgLsIUIDd1d6sLQmQAAmQgEMIUIAd0hAsBgmQAAmQgLsIUIDd1d6s\nLQmQAAmQgEMIUIAd0hAsBgmQAAmQgLsIUIDd1d6sLQmQAAmQgEMIUIAd0hAsBgmQAAmQgLsIUIDd\n1d6sLQmQAAmQgEMIUIAd0hAsBgmQAAmQgLsIUIDd1d6sLQmQAAmQgEMIUIAd0hAsBgmQAAmQgLsI\nUIDd1d6sLQmQAAmQgEMIUIAd0hAsBgmQAAmQgLsIUIDd1d6sLQmQAAmQgEMIUIAd0hAsBgmQAAmQ\ngLsIUIDd1d6sLQmQAAmQgEMIUIAd0hAsBgmQAAmQgLsIUIDd1d6sLQmQAAmQgEMIUIAd0hAsBgmQ\nAAmQgLsIUIDd1d6sLQmQAAmQgEMIUIAd0hAsBgnUB4FFixahefPmsCzLbKNGjaqPbJkHCZCABwJh\nHvZxFwmQQBASyMnJwY4dO7Bu3Tpcf/31WLhwIaKjo4OwpqwSCQQGAQpwYLQTS0kCtSaQl5eHe+65\nB/n5+YiJiUGrVq1qfU/egARIoOYEKMA1Z8crSSCgCMTFxZnypqWloWHDhgFVdhaWBIKRAOeAg7FV\nWScSqIJAYWEhUlNTkZWVhTVr1lRxJg+RAAnUJQEKcF3S5b1JwIEEkpKSkJ6ejq5duyI5OdmBJWSR\nSMAdBCxbkjuqylqSAAkUEzh27BjUKKtly5bFu/hJAiRQzwQowPUMnNmRAAmQAAmQgBLgEDSfAxIg\nARIgARLwAwEKsB+gM0sSIAESIAESoADzGSABEiABEiABPxCgAPsBOrMkARIgARIgAQownwESIAES\nIAES8AMBCrAfoDNLEiABEiABEqAA8xkgARIgARIgAT8QoAD7ATqzJAESIAESIAEKMJ8BEiABEiAB\nEvADAQqwH6AzSxIgARIgARKgAPMZIAESIAESIAE/EKAA+wE6syQBEiABEiABCjCfARIgARIgARLw\nAwEKsB+gM0sSIAESIAESoADzGSABEiABEiABPxCgAPsBOrMkARIgARIggf8FbqTRg7i7Mf8AAAAA\nSUVORK5CYII=\n"
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<font color='blue'>\n",
      "(b) As different exchanges have their own fee structures, and a market taker would choose his execution venue based on transaction costs, therefore the fee structure will decide where a market taker executes at."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<font color='blue'>\n",
      "(c) Below the R codes to new fees:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "plot(x=1:50,y=rsLagD+0.001*2,col=\"red\",type=\"l\",xlab=expression(tau), ylab = \"Realized spread\", ylim=c(-0.003, 0.012))\n",
      "lines(x=1:50,y=rsLagB-0.0004*2,col=\"blue\")\n",
      "lines(x=1:50,y=rsLagZ+0.0029*2,col=\"orange\")\n",
      "lines(x=1:50,y=rsLagY,col=\"purple\")\n",
      "lines(x=1:50,y=rsLagP+0.0025*2,col=\"green\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0Hjq5CIhAYhOQH3BiX/+Ea/0KLMVzeAx/M6/eNPunIgIiIAKRIiABjhR5nbfe\nCTBxwv3mpXui5R3qiC71fn6dUAREQATKEpAAl6Wh13FNgD3fNmZmNcLMr1REQAREINIEJMCRvgI6\nf70Q+B5fWSznL1wQjHo5oU4iAiIgAjsgIAHeASB9HfsEGFxjPO6xnEPXbpdIIfZbphaIgAjEMgEJ\ncCxfPdV9hwQ8i8L8oCU9GGV5inZG7x1urw1EQAREoL4IyA2pvkjrPEEJeAVbgOzlQGYb+NKbBN2u\nJl+8YTbPjNF8FE6qye5h3ccrLgBWzwA2LgTSGgGpltYwJdPWWf7XqXxtn5PFFluyl7m1x/dcCrOB\npFT42u0NtN8HaD0QviT9CYf1IulgIlCPBPTXW4+wdartCXhrfwF+ew/eyq+Ahh1NZFbAK8oFGrS0\npRV8bu1/jWY9gSY9THCStx5kOZZYnqIXsQorXdYhZhziP/Z6mYko21IibMA63Iun4LN/4Sie55mA\n/gqsmw007gI06mwPDcGzJHl564GVX/vbuOZHoOku8DW3njhF2ATVo6gWWfrCQnsICbxu0Np4tIcv\nqwPQvCd8nYbb+w7GoxW83NXAss/gzXsR+O5fQNvBJsYWe7rNnvAlp4WjiTqGCIhAPRGQANcTaJ3G\nT8DL3wj8Pgne4vftgyT4uhwKX7/z4Evz59l1vUSKTO4aIM8Wrjf/Dm+RbW+9QK9Jdyxs2xRvt12M\nuVlrcETyadgXB7teLkWWvd2A2P6B5eiDASFlMqrq+nibFrmeq7faBHTNz/Zw0AK+lrvBWzrV6rbE\nCb4T4oadnCCjaXdg/Vx4K6a5731t9oCvwzBg4BXWTuv1linVfSygCKPHn+CzxYn7ii/gLXwT+P5u\neK3tPHyQsYcC/9LJRFmxrMvg1ksRiCoCEuCouhzxWRnXq1070y+iNgTra78vfAMuh69FxTlZ14uz\n3h57fGULheqnoi/xdsFj+KPoWxy2ogPOX5CCtJR3TWx+gi/Teo0N2tgwtq1tKJtLj4xdyx4i5Nde\nSTGw/DNgxZfwVv/ghoh9rQbA1/EAoP8l8GU0c8cKiKd7qLCHBD4ouIeFP76Br/FO8O16BtBy9+16\n7SFXIoQNXT26HgGfLV7BZmDV9zZkvcR63F/Bm/+yvV4Kj71z9tIpyhxFaL6rsTI+KiIgAhEnIAGO\n+CWIvwp4RXkAh5dtyNVb8xPAHiSHXilge1gvMKVByI3mMDLTA75qw8hFKUU4KuU0DMVwJDe2oWjT\nE28L50mXAjl/2LLKDQ97fJ39hw3v2rAuh3I72hCunduX1a7K8zoRW2RD4gvfAmz419dlFHx9z3VD\nv1Xt6Oat03czsbXFSkCYq9on3N/5OKfc0XrZpYV1cMPlOStcLxzGybOha/w8znrs9i2FmEPhtkbT\nna2nnBrYNejajU7kbwAKNtliIxn5ts63IXaKOx9QykwPBD2IvhABEdhKQAK8FYVe1ISAE62A0RB7\nXOyFbVroF9yW/YA+Z2N6sw14O/kVGwr+Bp2w2pautnRBW4tHlWz/ypa19v08/GKi+7NbVuMP9LAE\n98fjLBtMHlx2U/faF6S3zC+94kITn0XA4g/gfTIGXlZb/1AwxTijudvfbbdpMbDgDROoT/y986G3\nwtek69bvY/WFz2dCm9Xev1gjOGzN4mWvtCHyOfaQZKMSSz92vWaPQ9slRe5724Lqve21z5wlKLxe\nCUAjuTQujW043dbG0Qn7t3cA7YYCHWw+mkPhMg4r5aeVCAQnIAEOzkbflCHghJZzoBsX+OdiA6LL\nH2v7kfdZTxM2B+rrfab1qnojP7kYU/G+/bsbzSyl/fEYjVzLtrvE0tx/hU/wCp7AGjOfamcizLCQ\njMv8C75Hvv1jasBe6Asmr+9izkOc161Jcb06692xh4d+F/gtkJdOhffRs/CamkHXTqPg/f6BPTAs\nhq/rkfAdPCHsVtg1qXdd7+OzBxFw4YOIncwrzvfPtfPEFG33KdelhQJMwU3JCHyy3dodI2+tDdt/\nbkPfr5hx2J2lxmH7up4x8tf5e8tbe87We2YPmvP7nQ+Cr82g7Y6nNyKQKAQkwDF0pd3cJIcUOexK\nAUy2H0QO53Ip+5ruLO59pv2elvkhrUZb3XAjh5FtztZbNcPOZ+e0Hq2PYmaWtz72rDi8W2o8FTj0\nGuuxfmCJ7JlxaDcMdEkPupucBspesB5SaSlAgZlJLcbvJsqF9vpwy8fb3vrGdVF8FBHrmbll978B\nf3zrDMF8nQ+2XpsJUQIPnzpDrXJz7tW9Br6MFkC3o+GzZatx2G9vAzPuM/G24XH2ltNLe83sRac3\nMyvyrvBmPg7vl/HWOz8O6HRgQl+H6jLX9rFPQAIcwjX0fnuH3QT7gTgYPopbmIr3x3elw35lh/wC\nB7fPOIdJC2DOcXKxeU3notPIepq0di0095XiXL/rDudd6cJj78EeDb8z9xbP/EYrFWj6k9JCNslc\nV+i+4hZ7n9zADI9McDlESbef1ja31+98M+DpVeWPI8X0YfwLs/ADDrCwF3dgnPV7bVizisJeL3u4\nXOqzuJ5x+71tuNn8aVXCTmA74zAzaKvq4cZnPWBOW3i/Ws951gSg+zFAl8MrWIuHvZI6oAhEAQEJ\ncCgXgb6W9pTuzXrKb+jCJ32zcq1J8fJsOI5zkmbsg0wbBnSCXqaXurXHas40DMpgPRNf5z5m6GI9\nQzMiqmxurczeFarkerIUZifOAZHm2kSaQs2lpMDWgSXXeiP/5+/tBhlyLH8Siu8lOBX9sRcesMAX\n6ah8qLL8fnof/wSqEt9A630MKGKLc/eyIWzvwzOBnWxkwu5D53YV2FBrEYgzAhLgEC6o+xEYdI35\npZp4mj+q98XV8CiM3Y60IAjmUsPhzSqKs0Zd9Z1fdG0eldbAvsE32nBu9yr2Cs9Xzq2HvdswR5gK\n1I6BLx6w1Pa7YxD+iisDH2stAtUm4GvcxVnJg/PJv74Ob4rN23caAexy0lbXr2ofVDuIQBQTkABX\n4+I4y9lep7ofBOcjutDmuH75rxn0dLfhXM7FBuZkbZjazc3aexsa9ha8bgLYFL4uh9kPzD+CGrNU\noypRs+kEy7BbaP/OxeVRUydVJLYJuPnkvn8Gdj4emPc8vMnn2rD0ofb+RA1Nx/alVe3LEZAAlwMS\nyls3rGbuFj5bPLqw0CiKc69uqJfDuzb/ymhOnJe1Ul+93VDqHs5tXsezWIi5+Cf+U8GdKJzn0bES\nk4Dzr97tPBuKNgOtuc/Bm3SWzREf7R+aroYveWLSU6tjgYAEuJZXyc0F13A+uJanjujun+JDTMV7\nuNlyDWXAev8qIlBHBFxM8P5muc4e8RxzIeMcsQ1LOzeqMv7cdXR6HVYE6oyABLjO0MbvgX/Cd3ge\n/8X11vNtYl6+KiJQHwRcJDOLpMb427BkFB7FmP7c5r7kbDHC6KFQH+3ROURAAqx7oFoEfrM4VXQ3\nutz6vgyioSIC9U3AR48ACjEjnTHT1NIpFmLzEXitzJqaRlv0U1ckrvq+LDpfDQhUEOARI0ZgwwYL\nOxekHHzwwbjzzjuDfKuPY5kA0/i9azGq5mGm9WybIgsNkemWLPc63Yaa/4f7nMGVktvH8pWOj7o7\nf+4O5oVgi0vryDSNjOPN4B+Mi81EFbSsVhGBKCVQQYBvu+02FBUVYf78+bj11ltxwQUXYO+998as\nWbPw8MMPY8CAAVHalLqrVhGKkGL/4rkwTOQd+IfJbgtLdjDM5dLNsf9zLBnCasu3uwWb8Stm4zbr\n/zbFtjjK8cxEbYsdAr7ULLOUtuQZtnh0Y6K74JfXwrPcyr6uh1u0s/3NU8Hc8VREIIoIVFCVoUOH\nuuo9//zzuOmmm3D66ae79xTh3r17gwJ90klmAJFAZSJew8t4woSnmfUMm7t5z8b2jvOfjdDY+cC2\nR+eYJZJnUZopvt2wi0Vsvjhm26GKiwAJODemXqdZtqxTbIj6G7hIdpYFCp1trriL9YobaepEd0p0\nEKggwIFqNWrUCIsWLQq8detffvkFLVu23O6zRHhzhMUoHoljsBHrsMGWTfb/Rqy3ZQOYvecWmxHt\nbTJ8jEWDYqafUMsqrLD+ZutqufCwN77Y+qKLbNnPasVwjrUpEt/a0NO+0UzABchpNwQ+W1yKSvaK\nP7vCsmJZRDnGvmYaRXowcE450z7bGoUumlulusUTgaACfPbZZ2PUqFGYOHEi9tprL0yfPh0LFy7E\nO++8E0/tD7ktFLpWlkCPS/nCTD+T8DZut14k50b/hNPQxZLoVVZWYKkl5fsM39riF/INaGMpCDqb\ncHeyPigzA/F14DzLnNzOsXQF80xy59jei1zCgg7YyWZrn8KhdraDcZTNzlY/RnVAfFlX9Xwru1r6\nLF4I+DLbAL1HA71sRI9xzhlb3Xz4vYU/mVX1YsvWtNGi21nPmOJswXZ8TbrFS9PVjigmEFSAe/bs\nia+//hpvvvmmmw8+7bTTcMQRR6BZM7mdlL+ejH18hCXcG4mj8bGZMf3bQlPshO5OiJkJiL3Vb/G5\nWzivOgj74hQL3MheM3u0FFmm6aO4TrH9l1h4iy32j/PODW2Qm8fg8PDeONAJe6DXy/3exosWh/k0\njMBhJsb/54bFy9evsvcU3ztxtavnWZazSEUEEoGAC6LTwmKrc7HiK220x6A5lvgEm36zULMWdrbN\nnibYZyoWdSkfreqGgM/iFHuVHXrNmjU477zznPgWFxejpKQEeXl5GDJkCJ577rnKdonqzy699FKs\nXLkSnNuu68LQjJ9gIt4yb9kGZj/MVHtMw7cn9rG+5q4hnZ5CzTjLFOAdlbWWV/cdm6X+HB+ZAdUB\nbii8OYJPFeQjzxyJrnK97XMwZkeH1/cikFAEPEa0m/+y9Y7fBo26FAIzvi//5ZdfjlNPPRUDBw6s\n94YG7QHfe++9yMnJwbnnnuuGnf/85z87q+hrrrGnQ5UqCaQiFQfhSAy3XukCGzbeBf6n7Sp3Kvdl\npgl3qIXzyGfiQtfjnojXcS3OdxmJAoZija1f3NgMxrhuZMskezTobH1qiW+ohLVdIhHwMczlrmc4\nNybMfhreR+dY5K0T4fIdJ3De6ES6B+qrrUEFeMGCBeCTweDBgzFu3Dgcd9xx6N69O+655x5MmDCh\nvuoX0+dJNvOqmohvTRtNceV89FE42ZmHcY45sNBgbJW5E31m8ntBae+3pufRfiKQCARc8pUBl1js\n6T/Bm/lf4DdLvrLLyZah6cAqcxwnAhu1MTwEggpwhw4d8Pvvv+PAAw9EQUEB1q5di+bNm7vPwnNq\nHaWuCKRb/5eGXVxUREAEakeAkbd8Q26Ct/YXF/4Ss590CSGYocn1lmt3eO2dwASCCvA555wD+gT3\n6NEDRx11lDPAohAff7wFRFcRAREQgQQj4GvRF7597oC3YYHNEVss6rlmT8IgH92PgS+9aYLRUHPD\nQSCoADPoxty5c5GcnOyE+NFHH0XTpk1xwgknhOO8OoYIiIAIxCQBn+X/xiCzhcleAfz6iqVJtDli\nhr7c+QT4siq6KcZkI1XpeiEQVIB59rZt/TcTrYdpEZ2SUuXm9VJhnUQEREAEooGAy860u0WO62UG\nWwvegPeJufO16u+3mqZIx2hxLlkrvrBkFwXOHcvXoFWMtiT6q50UrIp0O2Is6H79+oEJGCZPnoxj\njjkGq1evDraLPhcBERCBhCPgS28CH32GRz4FNOsF76vrUfLF1fBWz4gpFt7qH+FN/ze8iafAs8QW\nWPMTvCkXoGTyX+D9/Bi8Vd/DKymKqTZFe2WDdmkfe+wxTJkyBa+99hqOPfZYMEvSW2+9BX5+7bXX\nRnu7VD8REAERqFcCvpQMZzFNdyUsmQzvx4fhJafDt4sNTVsyiGgsXvZy4PeP4P0+CUhtCF/ng+Hr\n++dtc9oME7FhHvDHd/DMJcsFKmnZDz4GKulymNI+1vKiBhXgzz77DFdccQXat/db0qampmLMmDFu\nKFoCXEvq2l0ERCBuCbhoWzuNhM8Wj/mK55nB1pxn4GvW00Jd2u8pl4b+tcviVI8kXKaotbMtHOds\neOvnuehfvk7D4Rt8I9zcdrm6uPjYrLctDNHpFWwBVk0Hln9u7XrJ/KUttCdF2xd0MLXcEfW2LIGg\nAtypUydQhA844ICt2zMsZbt27ba+r8sXHOpm2EvNO9clZR1bBESgLgn42g4GF2/tLH+oS+txestt\neHeL9Tz5mikSTZBd7GmGx2TvMkxzrl5JMbBupontPHjrKLoWA5vzus13hY9Lz5PsfP2r5dPsS2vo\nNzij0dm6OfBmWUwIe8Bg4BJfxwPqEmVcHjuoADN046BBgzBp0iSsWLHCWUIzO9JHH30UdhBnnHEG\nGGGrV69ezvL6sssuc3PODRs2dKkPGZWLPXAVERABEYhFAr4WvS3+tC1WAvGn+drLW++EGBsXwlsx\nDbC0iV5yBnwmxDC3J7TczZ+5iRuHWJzYLpli87if+sW92c7wtd8X4NCyJZsIV/E17wXfvne6uW5v\n1hPWI37B5sLPcg8c4TpHvB8nqAA3btwYs2bNwosvvuiCbwwbNgxc6JYU7sI0h9nZ2e6wd9xxhxPi\np59+GoxHTTHmZ9dff324T6vjiYAIiEBECfgyLLkNF+v9+rod6eribV4CrP3ZjKDMKMqGrj37h8Zd\n/UPETbrb6242hN1hu/SJ3pZlNu9somtzz0hKsd7oCPiGja0XtyhfqwF2rgH+4XbrEXu/vmZzxIMA\nZpSy+tJITaVyAkEFmD3SNm3a4Kqrrqp8zzr69IMPPsC8efPAfMSMvEVLbIqwBLiOgOuwIiACUUWA\nkbdcjmIaOVnNvJxVYA8ZGxfAWzrV1o9b+sT18Bp3cUPJrsdr2/hsWNi317Um1DtHpD1bh9tZRxvu\n9lZ+46+zGaJRjN0cMx8e+BDBtI8hxNV2Vtecq143C55ZZbu0koxAFifpIoMK8E477YRvv/0WzIRU\nF73e8nfIl19+6Qy+mG2JYS8pwCw///wzBgwYUH5zvRcBERCBhCDgy2wNcGk3ZOvwtcvYZILM+V3f\nrtbbZC80Sgyh3FywzQcHhtq3e4DgsPicp2zY/Q94bBPDfDa0Bw7mYnYPHjv5560Z9pPz5ht/te9s\nG44Q2AMJ39PNy0trau8tU1VHMyBLDT1xTbTdMEEFuEGDBi4LEoeiaZAVEOFDDjkE//nPf8LaDqaC\nevvtt3HLLbdg48aNyMjIcGkDb7zxRjz00ENuPjisJ9TBREAERCCGCbgY1Jwj5hLlpdIHCBqI0QWK\nw+1bOORugrv4fXu/1IzEzOK6uQnurqeZ9bUZi9G9K1D4ENLrNOeTjMUTLUmGjQa0HQKYGLt588B2\nMbIOKsCjRo3C7rvvXqEZLVq0qPBZbT9g1iUuLMuWLcOmTZvca9aBrlA0xlIRAREQARGIDwJu+Dkw\n1F7apECPOZQW+lpb7l4uBZtt7tv8mH98CNj9wpgT4aACzCFoLkzAsHjxYnTp0qVeLJE575yZmemu\nAYejVURABERABESgMgK+NJuq7H4sfLbEYkkKVunCwkJceOGFrvc5cOBAt/7LX/4Cfh7uQpGn0ReH\nutPS0pzxVVZWFvr27avcw+GGreOJgAiIgAhEBYGgAsyQkwsXLsRPP/2EzZs3uzWNo+gSFO5y8cUX\nY+bMmXj33Xfd8DPjUC9fvhzjx48HszA98sgj4T6ljicCIiACIiACESUQVIC/+eYbXHnllc4nlzXs\n2bOncwX65JNPwl7hDz/8EOPGjXOJHzjfy/BnTZo0ccE/xo4dizfeeCPs59QBRUAEREAERCCSBIIK\nMDMgPfzww1i/3iK1WMnLy8OTTz7pgnGEu8Icav74448rPew777yDVq1aVfqdPhQBERABERCBWCUQ\n1AiLlsgcEqb49enTB/Pnz0dubi569OiB5557zrV3+vTp4FxtbcvNN9+MU045BQw52b17d9D1ie5I\ns2fPRlFREd57773ankL7i4AIiIAIiEBUEQgqwEceeaSLBV1VbekrHI7CQBszZszAtGnTwHjTK1eu\ndMJ//vnnY//9998u5Fo4zqdjiIAIiIAIiECkCQQVYFokJyUloXXr1m74+fHHH0fnzp1dbuC6qDSD\nbwwfPtz1eGn0xUxI1S3sMf/6q0VOqaQsWGBh3JjbUkUEREAEREAEooBAUAFmaEjOA8+dOxccIv7u\nu++cT/C6detwzjnnhLXqdENi1CsmYGAgDgolfYG7du3qAnScddZZIZ2PVtocKq+sbNiwYat/cWXf\n6zMREAEREAERqE8CQQX4mWeewX//+1+XkOGll17C559/7nqnV199ddgFmG5IHHbmnHO3bt3cvDLn\noJmNacyYMa4HzuHoHZV9990XXCorS5Ysceeo7Dt9JgIiIAIiIAL1TSCoFTSNoGiA9dlnn7lhaFoq\n5+fnOwOpcFdSbkjhJqrjiYAIiIAIRDuBoAJ8+OGHu94no2GNHj3a9UbPPPNMHHHEEWFvk9yQwo5U\nBxQBERABEYhyAkGHoOkW1LJlS3Du9LjjjnNRsRiRioZS4S7R7obk2WiAzwKDqIiACIiACIhAuAgE\nFWCeYOTIkVvPQ/9fLnVRot0NyZsyFSUvvATfUEuFNWQvYKDl3rSY1SoiIAIiIAIiUFMCVQpwTQ9a\nk/0Cbkjl96UVdk5ODijSkSpJxx4Nb48B8KZ97YQYN90G9O/nF+R997bclc0jVTWdVwREQAREIEYJ\nRI0AB+P38ssvu3SITMwQyeIzH2guOPF4eNnZ8L75FqAgP/4EwIAk3bvB17WLf92tK9CxI3zmR60i\nAiIgAiIgApURiHoBvu666yqrd0Q/81n4Td/wAwAuVjzzXcaChfAW/gYOV3vjHwfWrgN2MtGmGLdp\nbcmjW8PHdds2/tepqW5f/ScCIiACIpCYBCoI8IgRI5zhVTAcDM5x5513Bvu61p8z9nNNI2HV+uQ1\nPICvQwfAFt/++209gmfJK/DbIniLFwMr/wB+mYmSyVP8r1evARpaDO327YF0m0vmfLItbl45PX3b\nZxaMxPWube3Lstd8z9jbmdbjtqxRFi4MvuTkrefUCxEQAREQgdghUEGAb7vtNhdwgxGlbr31Vlxw\nwQXYe++9nRsSsyPVxVxsuCJhRRN2n4XWxK694LOlsuJZRDH8sQqW4QIWYgzmZA2P64JC99p9xvd/\nmHjn5KLEhr1tMhzItoVrLuxlN7DzMGxncxNjrps2BVrYnDTF2T4D56dL1xLryq6EPhMBERCByBCo\nIMBDhw51NXn++edx00034fTTT3fvKcK9e/cGBfqkk04Ka23DFQkrrJWq44M5w61yxlu+GpzTs7jZ\nljMSWLceHtcbNtqyAZg1GyUUefscXK+3z9iLLhVkH4W6GRcTaYo1XwfEu1Ej+MKUaKMGTdIuIiAC\nIpAQBCoIcKDVjexHmJmJypZffvnF+QaX/SwcrxkJi5mQ2rZtu/VwTczvlg8DY8eOxQ033IBQQlFu\n3TmBXvjsOoELjcR20G76MzsxNpF2PXCKMkV72XKUlBVvirhNBaCRDXPT/5nHb2yibGki3Wcc/naL\nzYVzze85pM41h8RT7LbiYvPc6nXv4KLoaxEQgYQlEFSAzz77bIwaNQoTJ07EXnvtBeb+XbhwId55\n552wwwpEwjr55JMrHJvnY0hMldoTcMFESgOK7FCsKcAWj9stm7e4tbfF1hvtM65/X+LWJXy9xYbH\nueZwug2lo9CG0YtLStfFToiRYsLMcwd64GWHxjlE3qKFv0duax/FW0UEREAE4pxA0F+6nj174uuv\nv8abb77pcvVSHI8++mizGzLDoTCXaI+EFebmxsThnAg6kbQ55NKyI9EObFd+7VGQS0yQywyJe4Gh\n8Xnz/UPl7I1bNis3ZM557YBQU5hb2hIwQLNhdFqhO2M0rtlLp2Cz582Frl+Btb1WwJTyV0PvRUAE\nooVAUAEusR/Mxx57DMyExPSAFF8aZNEfN9w90miPhBUtFytW6+ELuFy1awdwsVKVmHvseZeKtUdR\n5pA457rp7mVGaK7XHTBIo3Eae90U+GLrbW9dW+5nvmcO6CY2dE4hN+M0X+maAu9rbSMrnPcu7YFr\nuDxW7zDVWwRik0BQAab4TpkyBa+99hqOPfZY0D3prbfecqJ87bXXhr21wSJhhf1EOmDUE3BzzZxv\n7tKlSqEOpSF8eHQ9a1qMm5h7pWv8ugAlDKayhr1u+4498rJGauyBs4e9naibyFPguVjxbO3z2aME\nl0AJvKcVPI+3tbdepudeOqduqcVk7BbgprUIJCCBoALMNIRXXHHF1iHnVOvFMDfveeedh7oQ4ARk\nrybXAwEnkJZUxKwH3dnKSGWFs281UqNFOUU539zAWDisnWR7lh3attc+E3cn8BR5lsCa29NdjL1z\nLitW+HvugffmVuaM3zifToFnD53z4zR0o1U6Rwycb7it6RfO11xT1N13ZtxW9nP3vW3D70t9x2XF\n7r8k+l8EoplAUAHu1KmTywV8wAEHbK0/54PblQ4hbv1QL0QgTghsNVLr2jXknndVgh4KFjc/Tut0\nLptsmN2G310QF4q/8wsvXfP7NWvM0M0CvNjnJYHvOPwe8B0PGM5R4Pk5A7awBx6YP7ehdjfsTqPG\nVi3hK13bnJKs1UO5WNpGBMJMIKgAX3rppRg0aBAmTZpkD/ArnEsQ3ZI++uijMFdBhxOBxCXg5sfL\n9NBJoraizmO4njl73IGgLRTu1avhrVrt1pg7DyWrTdDts60BXbgje/mBhT15vg7M4fN7fhYYZg98\nz89ZAt9xtIDblP2e73mswOe2pqGfx4cGLhwJ2LrYED8/4/7uGKX1oLFdqcEdubmHl7L7u9eldgCs\nj9vezhnYz9bOuJAPJHSb4zQHpwFs5CEwAuFsAlgPFo5olF34Gc8RsDOgpT+3Dbzn9xyFoBEh/ehL\nFzcKw+9URKAcgaAC3KZNGxf96sUXX8Tvv/+OYcOGuSWZf0QqIiACUU3A/egH/LUDNd3VIrMFXpdZ\nO7GmC9lWASwVw4CwBNYBMeJ7lpLSoXfuV/Y7vuY2XLMERCrwWZm1S1gSEPxScXVCzdcsZQWWx+H7\n0uO5fQP7cB1Y+MDAbZw7XOk+pcdxgs/RA1rd07DPotGVuNEHmw7gCAQ/Y735oFB+CTwQBB4sAvXe\n+t4eFDj1QJZbF3vw4RQB7QFYLy5uesE+c6+3vXcPB2wDP3fr0jbxPZkFuLFtAcZkVDoC4nHUw42I\nWPs4gsJwuKWstl6LsvtxX9aFDwoZNsVh0xpu6sJNZdhnbBe35xIo7r29Kf+QFWDBNeteYZ8yx+E2\nPHbgerm1fz/3YFW2zq6tdj62nYXXNHAPBO6N0ve+USP9CXP8W8bE/0aq8kKDq4b2B3zOOeds3eDn\nn3/G66+/juuvv37rZ3ohAiIQ2wScWLNXmAClsgeQum62E8ayPvJu+sCEhGISmEowoXHbOYEpfXgI\nCAxFiIWiFRhBCLwOCJ7FlE8qaxfA14E48/69K3+gYL3yTLgp1ra46Q++p5CzLjwfS9l14DXrVX4J\ntImfB7bjOvCax2Ld2W5uy1GEQDtt7QXaynZxH24bWALCnVxOvPkQQRHnOsZKUAGeOnUqxo0bh/vu\nuw/nnnuua9YGC3HIaFgqIiACIiACoRFwBnMUxB2USDwclK9SNNShfJ3i+b09SgQv9957Lx544AH8\n/e9/txGA0iGA4JvrGxEQAREQAREQgRAJVCnAjHr1+eefu0hYxx13nI1K2LCEigiIgAiIgAiIQK0J\nVCnAPHpjsxJ87733zEiwCRgfWkUEREAEREAERKD2BILOAR944IHo3r27OwODcEyYMAG33367zdPb\nZL2KCIiACIiACIhArQgEFeDDDz+8woGvueaaCp/pAxEQAREQAREQgeoTqCDAgwcPxl133YUvv/zS\n9XrLH/LQQw91OXrLf673IiACIiACIiACoROoIMBMwtClSxc3/Dxy5MgKR2rGWLUqIiACIiACIiAC\ntSJQQYB33313d0AaXXXs2LFWB9fOIiACIiACIiAClROoIMD7778/GHAjWGGv+N///newr/W5CIiA\nCIiACIhACAQqCDDFtZAhwoIUhqdUEQEREAEREAERqB2BCgK81157uSOusdRnzP07f/58C/dZ7CJh\n0QVpyJAheO6552p3Vu0tAiIgAiIgAglOIGggDoahzLFUZowDzbngm2++2QXlkCtSgt8xar4IiIAI\niEBYCAQV4AULFuDyyy/H6NGjsWzZMjAUJYNx3HPPPWE5sQ4iAiIgAiIgAolMIKgAd+jQweUB5pxv\ngaWOWrt2LZo3b+4+S2RgarsIiIAIiIAIhINAhTngwEGZB3jo0KHo0aMHjjrqKBxxxBFOiI8//vjA\nJlqLgAiIgAiIgAjUkEBQAe7duzfmzp2LZEuCTCF+9NFH0bRpU5xwwgk1PJV2EwEREAEREAERCBAI\nKsDcoG3btm67lStXOovolJQqNw8cU2sREAEREAEREIEdEAg6B1xSUoJbb70V/fr1w8EHH4zJkyfj\nmGOOwerVq3dwSH0tAiIgAiIgAiKwIwJBBZgxoadMmYLXXnvNHWPEiBGgYRY/VxEBERABERABEagd\ngaAC/Nlnn+GKK65A+/bt3RmYE3jMmDFOlGt3Su0tAiIgAiIgAiIQVIA7deoEinDZ8uabb6Jdu3Zl\nP9JrERABERABERCBGhAIalV16aWXYtCgQZg0aRJWrFjhLKEXLVqEjz76qAan0S4iIAIiIAIiIAJl\nCQQV4DZt2mDWrFl48cUXXfCNYcOGgQvdklREQAREQAREQARqRyCoAPOwjILFgByB4nkepk+fjj32\n2CPwkdYiIAIiIAIiIAI1IFBhDpgJGGh8NWrUKIwfPx4UXZY5c+aAuYLvuuuuGpxGu4iACIiACIiA\nCJQlUKEHzLnfb7/9FqeeeiqYG3innXbChg0bXFIGhqQcO3Zs2f31WgREQAREQAREoAYEKgjwtGnT\nMG7cOGd01adPH1x55ZVYtWoVnn32WRx77LE1OIV2EQEREAEREAERKE+gggDT4nnAgAFuu+7duztD\nrBkzZqBv377l99V7ERABERABERCBGhKoMAfMOd+kJP/HjP3cuXNniW8N4Wo3ERABERABEQhGoEIP\nmBuuWbMGaWlpWLdunduP7wMlPT0djRo1CrzVWgREQAREQAREoAYEKhVgxnwuW1q1arX1LfMBv/TS\nS1vf64UIiIAIiIAIiED1CVQQ4N9++22r61Flh2NMaBUREAEREAEREIHaEaggwBperh1Q7S0CIiAC\nIiACoRCoYIQVyk7aRgREQAREQAREoHYEJMC146e9RUAEREAERKBGBCTANcKmnURABERABESgdgQk\nwLXjp71FQAREQAREoEYEJMA1wqadREAEREAERKB2BCpYQdfucPG59+LJheiwTwpSMnzx2UC1Ki4I\nlBR5KMqFLVx7KAy8zvGQu9ZD5xGpSGuoezguLrYaERcEJMAhXMb89SX4+NJsHPhgFpKS9QMWAjJt\nUscEVgjYugAALltJREFUsleWYP2vxdi4oNjWJW5NkU1OB1Ia+EoX/+vUTB/SGvkwc0Ieep+Rju5H\npek+ruPro8OLQCgEJMAhUNrluHSs+qEYPz6ajwEXZoSwhzYRgfAS2LK8BL9NLMDqH4uxwYQ3NcuH\npt2T0LRHMnY6KBVN/2ohYjsmV3nSjYvS8MPDeZj/agH6233cfqiC6lQJTF+KQB0TkACHCHivqxrg\nw3O3oNXuyei4r364QsSmzWpBoCjPw5JPCrHo/UJsWlyMLqPS0Gd0OpqZ6LJHW93SpEsyht2VhZXf\nFeGHh/Iw9+UC90DZtHvVwl3d82h7ERCB0AhIgEPg9OGHQLt2Pux9YyY+/Ue2+wHMaiv7tRDQaZNq\nEijK97BhfjF+M9Fd+mkhWvVLwc7HpVlvNSVsw8Zt90zBIf/LwsJ3C/HJlTloNyQF/f6Sjoymuqer\nebm0uQjUioAEOAR8O+8MXH01LDVjMg47KB1f3pCDAx+y+eCU6vdCQjidNolxAiXFltKzBrYC7OV+\nfm0OfHZfdT00FYc+1RAZzepGFH1JPnQ/Mg2dbfh69jP5mHjmFnQclopeJ6ejYbu6OWeMX1ZVXwTC\nTkB/aSEg7doVePZZYL/9gIc+ScfXs5Iw+Za8EPbUJolGwCvxMO2mXPw+pbBaTV/+VSGmXJKNARdn\n4NAnGqLXidYjrSPxLVuxVDPY6neunfPphkhv6sNH523BV7flYOOi4rKb6bUIiEAdEJAAhwg12abJ\njjwSeO45oOf5DTD58SLcenYhVq4M8QDaLO4JsOf71a25fovjp/LxhY2U5G8s2WG757yYj+/uycN+\nd2Si3eDI2BekN07Cbmdn4PAXGqFJt2RMvSwHn1+Xg7Wzi3ZYf20gAiJQMwIagq4mN2ZjPP4UH/br\nl4lXRmfjktFJyGyXjEaNsHVp2HDb6xYtgF69gDZtqnkibR5TBOiD++WNufBMbwdfm+HWMyfY0O5Z\n2djjsoxKDfeKCz0nvBsXFuOgh7OQ2Sryz8PsEe9qw9C7/F+am4dmb75J1yRzb/IhKc3cmkrXyWk+\nJNt7zwO6jEzdoQV2TF1MVVYE6omABLiGoNv2Tcaof2ag2xu56Hl1FnLyfdi8GVuXLVuAZcuAX34B\nHngAKLEf5l139Ytx797Wi+4JUKhVYp9AcYHneov0v937pgb++V8bMen3lwx02DfFhnRzsdSsmQde\n0mBrIIy8DSX4wnqYDVomOf9yClo0Fdanx9Fp6HZEKpZ/UeSElu0szrd7mesC2GLqa/f15Av9Q+c7\nHWSKrCICIhAyAQlwyKgqbsgfqDUzi7DpwzwMuKhBxQ3KfLJ6NTB7NjBnDvD008C8eUCrVsBeewH7\n7GM/1v2ApMh3gMrUWC9DIVBoEadoONWghQ+Dr24AGjeVLS16p2DUhIb46bE86w1vwaArM9CwfRKm\nXp6Dboelos+Z0e1XTmOyjvtXPSzeyYy3ONy+akYxBvwtw/WSyzLQaxEQgcoJSIAr5xLypwMvbuB+\nWDsNL0LLPsFxUmy57L+//9Aculu8GPjsM+CRR+DmkocOBfbd1y/KaXHWmfj2W2CXXYAmTUJGG/Ub\nFmZ7+PSqHDTunGTCGvwBjL1JPqB12K8I39yRa9bzQP8LMkDhiofSpGsyRj7WENPvzcWkv2ZjHxsF\naLyTDQFUUbasKHG+ze2HxAeDKpqqr0QgKIHgihF0F31RlgADIgwck4Fv7szFIf9taPNi2/eAym5b\n9rXPNuvSxb+cfjrAHvLnnwOvvw7cfjswcCBw1FF+MS67X6y9/vpr4JlngEIzCl66FOjWzf+QQYvy\ndu2iszV//OGfNsjJsfn+4wE+GJUv9Nedenk2WvRJBh/CQimtdzf/W+sNr5tTjDYD4utPj3HSB1+d\nid8+KMCUv2Vj9/MyzJVq+6fInNUlWPJxobMQz1nF4WwPzXoWYP9/ZYb8dxMKZ20jArFCIL5+BSJE\nnZGxlpjbycwn8t28X02qwd7xscf6F84ff/UVcO+9wEEHAWedFVvD05zvnjrV77rFB41TTwWGD7ck\nAWZQ+/33/geNCy8EmjXbJsY9etSEWnj34UPCCy8Ar7wCnHAC0KGDhyefAB6718MRwz3s0asEhRst\nscGaEqybbSI6kAEsqjeETCOneBPfsleh6yFpaLFrsvnK5+KP74sw8G8NsPijAhPdImz+vdhGAVId\ns9b9k91w/df/ynVD+PveJhEuy1GvE4OAz7OSCE299NJLbZh3JZ5//vk6aS7dTWjxSleS5j2rHn4L\ntQKbNgG33AIUmMHL9dcDtKiO5lJsrqPvvQdj7B9up/Byjruywrtu1iy/GHMYnuK8557AoEHAHnvU\nv4Eae+pjxwIMunLBBR5WvJqP3623lreuBPk2Of/7Wh9W5ySh1x4+7DksCY2b25C6xQhXqZwADbS+\nvz8Py78sQttByS4TUxuLwFU+QAl/fr66Jddlb9rn1swK31d+dH0qAuEjcPnll1sn4VQbdbRhx3ou\nEuAwAmfwhVlP52Pk+PBGyeIQLoemr7nGL05hrHKtDrVxI/Drr8D8+f71zJn+IfXTTgP69KneoTk8\n/c03AOeKf/zRP1RNMeZCq/E8i3uyahXA4eGya/phN23qtyqnZTmXrKzQz839H3zQPx8/Zgywe1+/\nLy/nd4dc18CCYfjgYzfeypIlwEsv+Xv3I0f6HxgGDAAyqtcJDr1ycbBlrj3ANGhetXUh/afpwuWz\nzYZeX2pFHgdtVxNig4AEuB6uU133gANN+PyfOc5vkkENwlkoSuwNH3YYMHp01UPS7IkycEg4S3Y2\n8PPP/l5rQHRzLd8se4xcOIRMI6suXWp/VvaGf/rJL8YU5DVr/ALcurXfn7rsun17//z53LkAF1qX\nt2y5TZC7dwc4l8tRhMDCoWa+5nlefhk46ST/kHPhphJ8fo0ZVVnSAlorl++tBVrGB4933wWmT/db\nttO9jD19PixwjntHhb3/Uk3f0aYJ8z1FmNbkzPLEB5/AQ0/CAFBDI0ZAAlwP6OtLgPMsdzDdTYb9\nO8slbQhn0/jDTxGmwP7rX0B+PrBihd+Cmj05vg4s/fv7515rGgCEgksR/OEH/8Le3267+X2ZKbZc\n2rYNZ+uCH4tD8Y0bB/++7DcUN1qXBwSZ9WYPlQFUaFledqEA08iK8+8MvfiZWTR3OzwNvU9PL3vI\nKl+zZz5jxrbeOx9KaGCWkuIXfnLkA0DZNS3BGVucDwcq2wgwMAmvQWbrJOz1j9AM27btrVciUDMC\nEuCacavWXvUlwKzUokkFmPtiAQ4eZ0PRNQjKX1XDKDD0I371VX9wD1oSc6EYcuHrTp2AiROBN9/0\niwHnYtlTrKrwuAwa8uWXfkMpCheHfinkXNjLC3evuqr61Od3f0wvshCSORaHuYGbq6zNufkARAM6\nPiRxKDwzs+KaDwf33AMceqh/NCPeXM5qw49zx59cwVGIJOx52TYR5lxxkT3IMEVjkfleMxBIUwuZ\nqSICtSUQSQG253SVcBPocnCas4qe81xBtXpTodSDQ5dnnAEcfHDVbjznnAOceKLfovf884EhQwC6\nO3XsuO0sHIb97ju/IdQXXwAc2qWf8sUXx7fgbiMALHyvAD//Nx9735yJVrvV/s+BD0C0Zq+qsMfd\nt6/f1YkW7lde6X/IqWqfRPmObnzD7snE7GfzMa7jerTZI9kE1x42LdRnSqYPdHdKKdXl1IaW0emI\nNHQakQpal6uIQKwRqP0vTqy1uJ7qu8flDfDuyVtcKEIGKgh34Q/9jgpDXY4e7Z/ffO014KKL/IZD\nHCKdPNk/h0mjJQb/4HYU4EQp+Tbfu+AtS3Y/sQAjHshEow7hv0ZVsaTh2D//6e8t33GH/7rwQUnh\nSW2kJdWHvqMtzOthaRaD2obzTVwr869f8U0hFr5TiB8eyXNBTRg2s8Wu+kmr6r7Td9FFQHdrHV2P\nTIvxO9DC8k06Lxv9L8xAl0NSIxaij8OgtEz+v/8D3njD7yp04IH+nheTSCRS2WCJD+a/WuCS3bcd\nlIIDLQkCMwFFqnBk4okngPHj/Q9BHH0YNixStYmu83IuuKrSbq9UcKHdxW8TC10mKgp1r1OsV2xR\nxioT7aqOp+9EoL4JSIDrkHh3S3jeeKckzHuFw5x57ol+5z+lOSOTOjxt0EM3sKG7k0/2L0E3iqEv\nNllgh3Vzi90PLcNBNuxgWXsqiUTG+cNlllCAwrt5aQl6HJOGw55piLTG21yMItlsXpe//c0fdIVz\nw1OmAOa27tyrIlmvWDk38yYzgxOXVT8W4TebVljwZoH55Ge51JCx0g7VM/EISIDr+Jq36pcCLtl/\nlGD+awX44M9b0NrCEO5yXFpY5hzruPpRcfjctSUo2Oxh/bzi0qUE6+cXI6O5Dy16J7sMPZuXlGDL\nshL3WSMT40YdbemUhCQbzpz9TL5lHfJh5/9Lt8QCFYNBREUjrRI0envsMWDCBH/0M/aGR4yIltrF\nRj0Y7pPLT+Pz8NGF5o1wVxay2lbdk46NlsVuLekZQOPE5cv9Hht836GDf6FxaKKNwpW9khLgsjTq\n8HVWmyT0Pz8Dfc9Kd8Nl396Va0EeLKKSWXsyD2yD1j7/upWtbeiNeVdVzMf35yLnH5rexIdmuyS7\npf0+qWhur+kzWrawp5u90sPmJcW2MNi/Cfcmz1IEhi86Wdnz1cVrWpr/+c9+YzjODU+dClx2mXrD\n1WXd79wMNLC/q8kX+6PTNetRv3P81a1vvGzPmPbvv+93BQyILl31aLNCseWaU2KMfkdBZspWFn4X\nWOhxwUA+zZv7v4vn/yXA9Xx1acW5sw2BcqERCQUj14LUr/q+GDmr/a8ZqJ7GJ232SDHXGPsh2UEk\noXpuQr2dbtUPRZh2Uw4OfCgLjTvt+AeUwRsatuOSZHOD9VbNOjkRg5pwXvjJJ3fcG6afNH/I1q3z\np7VM5B5F2YvBvzGOfHxyRTaG/jPT/T2V/T7RX//2G9C1a+0p0J+eiWQYhpYudocc4k9gEhBcxnyv\nqjCPOsU40EPmce6+2+++RyEOLIw9UDZlK89LcWePmmuG6qW4x1KRAEfwatGAJFihle6vb9iQtQX1\n6HtOBnoclRZs07j8fOV3ft/cfcw9KBTxjUcIDOZBdzJarbM3TFcxRtyi2JZd2HYO6fEHiNsF3Jzo\n6sTgKfwhTNTCRCkZTX344vpc7H5+OugimOiFyV7+9z+/zz9FbO+9/QtjsFfHJ33hQr/oTprkD8xz\n+OHArbdW7xi8FnxgDISR5XvaqbAwFgHD23J5+21/CFoG1QmILsWY77nQjuIf/6h+CFz/mSL3v2JB\nR459SGemodG3d+fBK/Ew6IoGFuZyxz3BkA4cxRstn1YIDtEzQw4T2qv4w2Y+8YT/RygwfxZYl40S\nxkxU/GFk2FAGVuGaP7KMM8/eAYe4KeyMDBZ4zfc8Fn3Ay/Yw4ok7/44+/XsOuh+d5oy14qltobaF\nwXYoZLQxOOAA4Lzz/GFep03zi/GcORYLfXd/73WfffxDwOvX+0O9MhxsYOEwMx8AGZOdwWS41DTi\nXqh153aMJkfxDYgu799wlEgG4pAAh+MK1sMxFrxjltRmWNLNAg/0OTO9UmvfeqhGnZ9i6WeFltg9\nL6xZpeq80lF+Av5QUogZEpNizChdjIcdeM01f3wZwvOYY4AjjgAYLjPeCo35Pv1HDpgKcXezxwh3\nlLpo5sXrz2xf9DO/5JLKh54pcEyIQkFmDHYODfPhjiMqjK8eWPieMQOYiCQeYppHUoDVvYjmv5oy\ndWPEnw77pmDGA3mYOHoLBl/TAM17JSMpZXtDpDK7xNxLZpOa8WAeht2diabdw/R4G3MUwl9h/ljS\n73tHhT1nhjhl6FIOe9NvnPNu8VIatEjCiPuz8PUduZhixlk0zqMBZDwXxo+//37/A9gFF/h7vsHa\ny9CpzNvNhb1ljqaEq5cZ7JyJ/rkEOIbugIymSc6YZOW3Rfj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ERCC2CFBw6T9LAfzyRksS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\nAAIIIIBAHARIwHFA55AIIIAAAgj8Bc8DvU08Olj6AAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<font color='blue'>\n",
      "\n",
      "(d) \n",
      "\n",
      "For a small one, take care about the fees, while for a larger one, take care about liquidity, because liquidity will be larger for a market order, and the cost for the order is comparably small. In conclude, it's a tradeoff between liquidity and fees."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Predicting trade signs"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 4. (6 points) \n",
      "\n",
      "The following require the *tradeSigns* series from Problem 2.\n",
      "\n",
      "(a) Denote the probability of a sign reversal by $\\pi$.  Derive an expression in terms of $\\pi$ for the conditional expectation $\\E[\\epsilon_t|\\epsilon_{t-1}]$.\n",
      "\n",
      "(b) Assume zero expectation of the trading signs, fit an AR(1) model to the series *tradeSigns*.  What is the coefficient returned by this model?  Explain how  this coefficient relates to $\\pi$?\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## <font color='blue'> Solution:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### <font color='blue'>(a)\n",
      "\n",
      "<font color='blue'>\n",
      "The expression in terms of $\\pi$ for the conditional expectation $\\E[\\epsilon_t|\\epsilon_{t-1}]$:\n",
      "\n",
      "\\begin{equation}\n",
      "    \\E[\\epsilon_{t}|\\epsilon_{t-1}] = \\epsilon_{t-1}(1-2\\pi)\n",
      "\\end{equation}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#### <font color='blue'> (b) \n",
      "\n",
      "<font color='blue'>\n",
      "Fit an AR(1) model to the series *tradeSigns*:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "\n",
      "# same process of problem 2\n",
      "\n",
      "tradeSigns <- getTradeDirection(tqBAC) \n",
      "\n",
      "# create epsilon_t and epsilon_{t-1}\n",
      "\n",
      "epsilon_t = tradeSigns[1:(length(tradeSigns)-1)]\n",
      "epsilon_t_1 = tradeSigns[2:length(tradeSigns)]\n",
      "\n",
      "# calculate coefficient\n",
      "\n",
      "df_tradeSigns = data.frame(epsilon_t, epsilon_t_1)\n",
      "df_tradeSigns.lm = lm(epsilon_t ~ epsilon_t_1, data=df_tradeSigns)\n",
      "cat(\"(b) The coefficient returned by this model:\", coefficients(df_tradeSigns.lm)[2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "(b) The coefficient returned by this model: 0.08153492"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<font color='blue'>\n",
      "The coefficient is close to 0, which implies the two *tradeSigns* are almost independent. \n",
      "\n",
      "In addition, given $\\epsilon_t=\\rho\\epsilon_{t-1}+\\eta_t$ we have \n",
      "\n",
      "\\begin{equation}\n",
      "\\E[\\epsilon_t|\\epsilon_{t-1}]=\\rho\\epsilon_{t-1}\n",
      "\\end{equation}\n",
      "\n",
      "Therefore we could conclude that\n",
      "\n",
      "\\begin{equation}\n",
      "\\rho\\approx (1-2\\pi)\n",
      "\\end{equation}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The MRR model"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 5. (6 points)\n",
      "Using the estimate of $\\rho$ (the coefficient obtained from fitting to an AR(1) model) from Problem 4 and equation (11) from the lecture slides:\n",
      "\n",
      "$$\n",
      "\\Delta p_t=(\\phi+\\lambda)\\,\\epsilon_t-(\\phi+\\rho\\,\\lambda)\\,\\epsilon_{t-1}+e_t+\\Delta \\xi_t\n",
      "$$\n",
      "\n",
      "estimate by linear regression the MRR parameters $\\phi$ (transaction cost) and $\\lambda$ (adverse selection or \"Kyle lambda\") from  *tqBAC*.  This amounts to ignoring the autocorrelation of the $\\Delta \\xi_t$.\n",
      "<br>\n",
      "\n",
      "Hint: Use the R function *lm*  to perform the linear regressions."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## <font color='blue'> Solution:\n",
      "\n",
      "<font color='blue'>\n",
      "Below are the R code to perform linear regression:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "ts_change = ts_price[2:len_price]-ts_price[1:(len_price-1)]\n",
      "df_tradeSigns = data.frame(epsilon_t, epsilon_t_1, ts_change)\n",
      "df_tradeSigns.lm = lm(ts_change ~ epsilon_t+epsilon_t_1, data=df_tradeSigns)\n",
      "cat(\"The coefficients of the model:\", coefficients(df_tradeSigns.lm)[2], coefficients(df_tradeSigns.lm)[3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "The coefficients of the model: -0.002336749 0.002876938"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<font color='blue'>\n",
      "Given\n",
      "\n",
      "\\begin{equation}\n",
      "\\phi+\\lambda=-0.002336749, -(\\phi+\\rho\\lambda)=0.002876938\n",
      "\\end{equation}\n",
      "\n",
      "We are able to derive\n",
      "\n",
      "\\begin{equation}\n",
      "\\phi=-0.00292489, \\lambda=0.00058814\n",
      "\\end{equation}"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}