Ch18_Bonds3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bonds 3\n",
    "\n",
    "This notebook presents a yield curve model (a simplified Vasicek model) and then uses it to improve the duration hedging approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Packages and Extra Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Printf\n",
    "\n",
    "include(\"src/printmat.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots, LaTeXStrings\n",
    "default(size = (480,320),fmt = :png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predictions from an AR(1)\n",
    "\n",
    "Consider an AR(1) with mean $\\mu$\n",
    "\n",
    "$r_{t+1}-\\mu=\\rho\\left(  r_{t}-\\mu\\right)  +\\varepsilon_{t+1}$\n",
    "\n",
    "The forecast (based on information in $t$) for $t+s$ is\n",
    "\n",
    "$\\text{E}_{t}r_{t+s}=\\left(  1-\\rho^{s}\\right)  \\mu+\\rho ^{s}r_{t}.$\n",
    "\n",
    "In the the cells below, we code a function for these forecasts and then plot the results (for many forecasting horizons and also for several different starting values).\n",
    "\n",
    "### A Remark on the Code\n",
    "\n",
    "The line \n",
    "```\n",
    "xPred = [AR1Prediction(r,ρ,μ,s) for s in s_range,r in r₀]\n",
    "``` \n",
    "creates a matrix with results like `xPred[maturity,r₀ value]`. This could also be done with a traditional double loop\n",
    "```\n",
    "xPred = fill(NaN,sMax,length(r₀))          \n",
    "for s in s_range, j = 1:length(r₀)\n",
    "    xPred[s,j] = AR1Prediction(r₀[j],ρ,μ,s)\n",
    "end\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "    AR1Prediction(r0,ρ,μ,s)\n",
    "\n",
    "Calculate forecast from AR(1)\n",
    "\n",
    "# Input\n",
    "r0,ρ,μ,s: scalars\n",
    "\"\"\"\n",
    "AR1Prediction(r0,ρ,μ,s) = (1-ρ^s)*μ + ρ^s*r0;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction for t+50, assuming current r=0.07:      0.056\n"
     ]
    }
   ],
   "source": [
    "(μ,ρ) = (0.05,0.975)\n",
    "\n",
    "printlnPs(\"Prediction for t+50, assuming current r=0.07: \",AR1Prediction(0.07,ρ,μ,50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TGLJJfK/9N4BDv7tWt0mQkJC8L6Oi8fIyGj+/PkPHjyYOHFiUVHR/fv3P7yssbGxlJRUSkoK+RYWkJiY+PbtWw0NjXoH18J8+B34HEgrgo8bQpcuXWRkZKKioj7h+wP/PieBgYHvHaoT5OTk+vXrR6bFWCwW+WpBI92B58+fA3B1dRXWzq9fvxZ51Btqi/Tl6dOnnyPDlwlV0M2Kq6srgN27dws/ZNeuXYuNjdXX1xf5PBeBxWKRVfvVq1fX/acSLOV17tzZ1tY2JSWFrJjXi7q6ek1NjbBvh4KCgj/++EM4D7G3ExGAfO9XVlaSFLJbITMzU4zYBNLxgwcPki9rQkxMzLVr12RkZD52525FRUXd/1IycBbI9iHIyMgMHz6cy+Xu27dPOJ3M8ru6uoqfxwdAJuUzMjI+vNFPgNxnkVZkZGQmTpxYVVX1+++/1y3y3qVdMzMzGxubhISEY8eOiSletx5NTU0OhyO4z6qqqnJycllZWcKzxh8Lmc1LT08XTiSmNcIpWlpaHA6n7vM2ffp0Dodz6NChuh+XfD6/rKzskwVrcegUR7MyZcqUAwcOhISEfPfddz///LOWltb9+/fXrl3LYrF279793smytWvX3rlz5/Tp0zk5ObNnz+7cuXNZWVlKSsrdu3efPXsm8MJz8OBBR0fHH374ISYmZty4cWpqaqmpqXfv3tXU1CT/zH379o2IiBg7duyWLVsMDAyioqLWrl2rrKwsPJC8c+fOmjVrZs6caW1t3aFDh7KysuvXr//99986OjrEbAuAjY3NkSNHlixZ4ubmpqamxmKx5s6dW6/ktra2kydP9vLycnFx2bhxo4GBQURExKpVq3g83vr160Vm29/LixcvxowZM2PGjF69ehkYGFRXV9+/f//gwYMKCgof+5G7detWb2/vrVu3VldXjx8/vrq6+vjx456enurq6mvXrn1v8Xbt2mlra/v7+y9cuLBr165SUlJ2dnbEJq8RIW/udevWZWRkkPfQ1KlT5eTkduzY4efnt2/fvpSUlKlTpxoZGRUXFyclJd28eTMjI0NgkNMQR48edXBwmD9/fmho6NChQw0MDPLy8hISEi5cuKCrq0vs7aZPn15eXj5+/HgTExPyAbdz586amprx48cL6unRo8fjx48nTJjg6OgoKytrbGz8IZ5JhOnTpw+bzd63b5+2tvaAAQNKSkqOHj167tw5LS0t4QkoCQkJS0vL0NDQyZMn29vby8jImJqaOjo6GhkZbdq0ac2aNXZ2dr/88ou1tbWamlpaWlpYWNipU6f27dv33XfffZQ8XxAtZN73bfIhOwnz8/NFlEibNm1Etn6RdXmBSbJI8YkTJ4oYe8nKyk6fPl04W1BQkMhauYSExN69e8nV4uLivn37Cl8dMGCAj48PgAkTJpA8fn5+IhvQAXTt2pVMnhCqq6vnz58vWOMSv5OQ7FYXllxGRmbTpk0i+wg+xA46Jiam7kJrhw4d/Pz8BHmIHXRAQIBwwerqagAmJibCiU+fPhXZV2lubh4VFSWch+jcoqKiusL4+fl17txZUPYTdhKK7HaLjo7Gvzs2BaxZs0Z4QlywkzArK2vEiBEiI31FRUXhDZPkhSpiU0+IjIy0s7MTuZMaGhru7u4kw9KlS0W2MrLZbKK1BZXExMTY29sLftn37iTcunVr3UsHDx4U3kmopqZ29+5d4nSssLBQWOAePXoI+ivYScgwzJEjR+pOSZmbmws/sV8dLIZGVGk8KioqiB8AEa8XdYmNjSW+OPT09JycnETW3AoLC4uKijQ1NUXWEgVkZ2cHBATk5+crKiq2b9++R48eIpYAAPh8fmhoaExMTHV1tY6Ojr29vcjqeWho6MuXL1kslrm5uaWlZWVlZVZWloKCguAp5/P5L168SEpKys/Pb9OmjaGhoaWlZb1f/Xl5eWQmtGPHjuI7npGR8eTJk3fv3mlqajo5OampqYlkSElJYbPZZJOheGJiYhISEnJzc5WUlAwMDGxsbIQ/Qd68eVNaWtq2bVthYwOGYVJSUiQlJUV+oJqamoCAgPj4eA6HY2pqamtrK/IKzMzMrKqq0tfXb8gOmsvlvn79msfjtWnTRsRoT0BhYWFBQYG2trbAaCwrK6uyslKk2qqqqszMTDk5ubo+PciDAaBDhw7CnU1LSwsODi4sLFRWVtbT07O2thbudXZ2NpfL1dPTq3fXOICYmJjw8PDS0lLi2sLKykq48tLS0pCQkMzMTC6X27ZtW0tLy3qd6lVXV+fm5lZXVysqKjb0SVRcXEyepXpvUU5OTlBQ0Js3b9q3b0+M+eq9P+QWvX79urq6WklJSfiprqysDAoKSkpK4vP5Ojo6pqamwl5NvkaogqZQKJQvFLpISKFQKF8oVEFTKBTKFwpV0BQKhfKFQhU0hUKhfKFQBU2hUChfKFRBUygUyhcKVdAUCoXyhUIVNIVCoXyhUAVNoVAoXyhUQVMoFMoXShN6s6usrPTw8Hj58mW3bt3mzZsnElOdcPfu3Vu3bqmoqCxcuJDE3wsJCfHz8xPOs2jRIpGAN4WFhWfPniXhLEWoqalpyOHAt0pr6zKPx2Oz2e91BPot0dp+YgA8Hu+rjoTSWDThCHrmzJlXrlzp1avX5cuX6w1geu7cuZkzZ3bv3r20tNTe3p7EauJyuW//5Z9//tm3b1/dAGhpaWnHjx+vt9GKiopG78gXDpfLbWkRmpWqqqrPcT38NdLanmo+n/9Rfr2/ZZrIS15SUpK0tDTxo5ifny8tLZ2amiqSp3v37gI3m87Ozn/++adIhtGjR69YsaJu5eHh4ZaWlvW2W1xc/Lmif22UlJS0tAjNSnl5eU1NTUtL0ay0tqeax+OReBGUphpBBwYGmpubt2nTBoCamlq3bt0CAwOFM5SWlkZGRrq4uJDTfv36PXnyRDjDmzdvbt++PWPGjCaSkEKhUL5wmmpiKzc3V9hPq4aGhnCAJfwblFOQR0NDgwROFXD69GlbW9suXbrUrfzdu3epqaljx44lpywWa8aMGUTXV1RUtLapq/Ly8oacFH+TkHhXrepXbm1PNZ/Pbw0Td1JSUu9dWmgqBS0lJUWiVxCqqqpEgrSTNcPq6mpyUDeDp6fnzz//XG/l8vLyysrKwkF3unTpIi0tTeohB18UMTExZWVlNjY2ycnJcXFxjRt7uLq6WrjLN27csLS0fG/EgE/g+PHj48ePl5eXv337dqdOnUxMTABkZWU9ePBASkpq4sSJxcXFt27dKisrmzFjhnD0z8aFz+dLSUl9gsLy9vZu3769SKCZr4Iv86luOkiQnW++yx8yrmoqBa2rqysc2zEzM5OE1xSgra1N4j+S//PMzEzhMA2BgYHp6ekk0mhdJCQkVFVVJ0yYUPcSh8Mh/7r5+VBUxJfwE/P5/FmzZnl6enI4nIiIiCNHjnxsjFTxCLpM2LVr19q1a/X19RuxCcKPP/44ZMgQJSWlCxcujBo1ytTUtKSkxM7Ozs3NTV9fn8PhDBw40Nzc3NjYmM1mN+6Iz8fHx9/ff9OmTfi3v59Q/4kTJ/r379+tW7dGFKx5+LT+fr2wWKzW1uWGaKpP4/79+2dmZkZERAAIDw/PyckhUxBJSUkBAQEApKSkhg4dev78eQBcLvfatWujRo0SFPf09JwwYYKIdd2H8+YN9PRgZYW0tEboy2fi7e2tqKgooheqqqrq5qx35breFXzhrxPxdb631HsL8ng8Ho8nnHL27Nlx48YBiIuLU1JS2r59+4IFCyoqKkJDQw8dOrRy5UqBSWVDLZaXl3+UVNnZ2ZGRkWKErJdPswSoV57WZkdB+UJoqhG0kpLSli1bhgwZ0rdv34cPH27ZsoVo2ytXrty8edPf3x/Axo0bBw0aFBkZmZSU1KlTp2HDhpGyZWVlFy9evHfv3me0DhMTPH8OBwc8f47/huJrbs6ePTt69GjBKZfLHTt2bEhICMMwf/31F4k3vH79ek9PTzabzTDMzp07ycfBtWvXfvzxRw6HU15evnDhQhKQe//+/Xv27GEYRl1d3dPT09zcHMD58+eXLVsmKSnp6OhYr35JTEycOXNmSkoKj8dbunTpqlWrAKxbty4/P//ly5fx8fEKCgpXrlypG45648aNf/31l6ysrJubmyDRzc3tu+++09XVHTt2bH5+vqGh4ZgxYy5fvgygc+fONjY258+f9/f3X7x4cVFREYvF2rp1Kwnh6uTk5OLicvLkyXfv3hUUFNy8eXPlypWlpaWysrLu7u6DBw8mNcyaNevQoUNFRUXOzs4XL15MS0tbsWJFWVmZoaGhtrb2/fv3BZKsW7euvLx8165d5HTq1KmOjo4LFixwc3Pz8/NjsVgKCgqHDx/u3bu3cKf27NmTk5NDSmVmZjo4OKSlpQFISkqaN29eUlJSTU3N7NmzSYzXs2fPrl69WlJSsry8fMWKFT/99NMnPgeUT+XmzZsxMTEtLcWHIi8vv2DBgsayW29C6/clS5YMGTIkOjp606ZNgqjJs2bNIoMvABYWFnFxcU+ePFFTUxOOCgzg4cOHVlZWn9y0jAz++Qeurnj6FCUlLayg/f39v//+e8Hp06dPr1+/fuXKlYCAgCFDhiQmJmpoaIwbN27t2rUcDicmJsbZ2bl///5qamrLly/38vLq1asXn88nS6w3btzw8PAIDg7W1NS8evXqxIkTX758mZGRMW/ePH9//+7du3t5eZ07d05EAIZhpkyZMnTo0HXr1mVlZdnb23ft2nXEiBEVFRVEjI4dO65fv37t2rU3btwQLujr63v06NHIyEhtbe1Vq1YJhr2FhYXl5eX29vYXLlyYP38+iUL966+/qqqqJiQksNns3NzccePGXbt2zd7ePjU11cHBwcbGplOnTsXFxffv34+MjJSTk4uPj583b56fn1+XLl1evHgxaNCgqKgodXX1d+/ehYeHx8fHV1dX29nZXbt2zdXVdefOnVevXiXiCQ9mx40b5+zsvHnzZmlp6cLCwmvXru3evRvAzz//fPLkSQDe3t7Tpk1LTU0V7ldFRYWgEj6fT8Kw1tTUjBkzZunSpbNmzSouLu7fv3/37t1JyqNHj7p27crj8cjKNqWZWbduXffu3evGcf8y2bZt2/DhwxtrjrFptycZGRkZGRkJp6irqwtbd6iqqtadkJWXl/8c7UxQVoaPDyoqICeHlBTk58PG5jOr/BQYhsnOzhaOBm9iYkK63KtXr+7duz948GDixImdOnW6fPnyq1evysrKOBxOdHR0nz59NDU1Dx8+zDCMvb092WZ59uxZR0fHFy9eAFBSUsrOzs7IyHjw4IGTkxMZ/E6ePHnlypUiMuTk5ISFhT169AiArq6um5vb9evXiQxjxowhcbiHDRt29uxZkYI3btyYNm0aiS29YsWKHTt2fGCvb926paenV1paSka7nTt3fvjwIXlJf//99+Rb6tKlSxYWFllZWVlZWQC0tbUDAwOJVEuXLpWUlJSUlOzbt29sbKyYhszMzPT09O7cuTN69GgvLy8XFxcirZ6enqenZ3p6OpfLzcnJefPmjfBPUC9RUVHp6el6enpEZisrKx8fnzFjxmhpae3fv3/WrFk9evQQWUehNBtLliyxtLRsaSk+iAsXLjRibd/y/lEWC3JyAODqiogIbNuGOrqrGWRgSUpKCk87iFgf5ufn8/l8JycnExOT/v37y8jIXLlyhWyqvHr16r59++bNm/f69Wt3d/cpU6bk5ubm5+dfunSJFJ8wYQLDMIWFhcJ1qtf5XigoKFBUVBQYyWhpab18+ZIcq6iokANpaem6M7YFBQVEfQNQVVX98K+23Nzcd+/eCeTs1KkTecEAECjK3Nzc3NxcQR5bW1tiNQ9AWVmZHMjIyLx3HnnGjBknT54cPXr0yZMnydRNUVGRpaXl2LFjraysJCUlJSQkiouLG1LQzL9R7V+/fs1isQTyALCwsABw584dd3f3qVOnFhcXHzp0SHilhEJpar5lBS1gzhz88ANWrYKqKubNa+7WDQ0NMzIyOnfuTE4TEhB3WXIAACAASURBVBKqq6uJFVpMTMzs2bPT09Pj4+ODgoIAcLncBQsWkJw6Ojo7duzYsWPH33//vWjRoilTphgbG6uqqu7cuVO4/g4dOty+fZscV1RUpKSkiAigp6dXUlKSmZlJtGRUVJRA7YrHwMBAMPcXHx9fU1PzgV02NjaWk5M7dOiQGI8ZxsbGSUlJhw8f/pAKJSUlRRYqBUyZMmXNmjUPHz5MTk4ePnw4gODgYG1tbTLXkZmZKbwgSVBWVhb0KykpiRwYGRlVVVXt2rVLSUlJOHOHDh327NmzZ8+eEydOrFq1iipoSnPSKjY4LFyICxegrw9t7RZovX///k+fPhWccrncpUuXhoWFrVmzhmGYgQMHamhoAPD09AwLC5szZ45AEy1fvvzhw4cvX74MDg42NjYG8Msvv3h6erq7u4eFhfn6+hI78aFDh+bk5GzevDksLGzhwoWCIaEAZWXlmTNnzpw5MyAg4MiRIxcvXhS8A8QzZ86cK1eunDhxIigoaNmyZR8+giaLovPnzw8ODn7y5Mm2bdvqLvLMnDkzLi5u1apVz549e/z48e+//y6ylUmYLl26hIaGnjlz5tatWyKX1NTUBg0aNG3atMmTJxPLWQMDg9jY2Fu3bgUFBc2bN6+uOW2fPn1u3779999/e3t7b926lSQaGhqOHTt27NixDx8+fPbsmYeHx507d7hc7ooVKx49ehQVFRUaGkp+BQql2WgVI2gArq4gRtVZWThyBHPm4N9v7iZnzpw5rq6u69atY7FYhoaG69evb9Omzbp16/T09B4+fCghISEhIXHr1i13d/ebN29Onz7d3Ny8Q4cOALS1tQ8ePFhWVmZmZnbx4kUAxsbGz549++OPP7y9vdu0aUMsF2VlZf39/bds2bJ+/fqpU6d26dKl7i6VgwcP/vHHHzt37tTQ0Hj06BFRNHZ2doKFWTU1tcmTJ4uUMjAwuHv37v79+2/fvr1mzZpOnTrJy8sDGD58OPkg0NbWFiz5SklJzZs3jwyZJSUlnzx5sm/fvu3bt7NYrB49eujo6AAYO3asYBpXUVExLCxs7969mzdvlpGRsbOzU1VVBTB16lRyQCQkbwUrKysPD48nT55wOJx+/fqJyLl8+fKTJ08uXLiQnBobGx87duzo0aMyMjK//vprly5dyKB48ODBRGxzc3MPD49Tp06pqKi4u7t7eHiQgsePHz927Njhw4fLy8u7dOnSr18/CQkJFRWV/fv3c7lcCwuLjRs3fuJDQKF8Gi3kA+Sz+BxnSTt2MACjo8OEhDSBZA0wadKka9euNVHl1FnSN08rd5ZkaWkZHh7egvJ8FPr6+ikpKY1VW6uY4hBm/ny4uCAnBxMnNl+jR44ccXBwaL72KBTKN0FrmeIQoKyMe/eweTN0dJqvUXl5eTI5QKFQvnBiY2NDQkKKior09fWHDBlC1vMZhrl582ZeXt748eMFO5zPnj07ePBgNTW1phOm1Y2gAUhKYsMGLFgAHg+DB8PNDaWlLSBGbm7u4cOHibHB18Lly5fJtpQvEG9v77i4uJaWgvLVs2TJkocPH6alpW3atMne3p7sadqxY8eVK1fKysoEG56Dg4O9vLyaVDujdSpoAVVVCA3FqVNwcEBeXrM2zefze/XqlZycLLBEbimCgoKmTZv2gZlPnDgRHh7+Ca2Ul5f36NHjww31RPDw8Hjvm0xBQUGwTkihfDK+vr7Hjx//v//7v6dPn2ZlZT1+/BjA1atXN27cuGTJkoKCgjdv3vB4vGXLlrm7uze1MK1aQcvK4ulTmJjgxQsEBDRtW5WVlcLbVXJycvLy8nbs2DFnzpx68xcVFTF1DObqpbS0VLCbg8/nv337VlCwtL5Pg5qaGuH04uJiMQPPqqoq4QoFrZCtNHUlqbeG4uJiHo8XFhYmpkcMw7x9+5bEsmIYhmy/FkD2TIoU4XK5whrfwcHh7du3wcHBDTVBoXwURUVFlZWVxMumtLQ0MagvLy+XlpY+fPhwv379BB4smpDGWm1sTho35FVxMXPvHsPjMZWVzLNnny1cHfLz84cPH96+fXsdHZ0pU6aUlpampaWZmZlxOBxra+tly5YJZ+bz+Rs2bNDS0urcubOurm5AQADDMLq6utnZ2STDsmXL9u7dyzDM2bNnR44cOXjw4Hbt2h06dGjcuHHLli0zMjJq27ZtXl6ej4+PiYmJiYmJrq7usWPHSFknJ6e1a9caGxtraWn17Nnz7du3paWlRkZGcnJy1tbWNjY2wpLweLw5c+Zoa2ubm5vr6uo+ffqUYZhhw4YtXbrUzMxMV1e3a9euGRkZJPP+/fu1tbUNDQ27dOkSGBhIEvX09NatW9euXbuePXuS6ApWVlbW1tZRUVHCDc2aNWvJkiWdO3du165dUlLS77//3q5dO1NTU21tbQ8PD4ZhAgICdHR0NDU1ra2t58yZU15eHhsb6+DgQDq7dOlSHo9Hqlq/fv0PP/zQmD/elwG14hBYcaxcubLR4wVraWnFxsYKC7B161YHB4c2bdocPXqUpFy8eNHR0XHKlClz58598+aNlZVVeXl5Xl5eXYONxrXioAr6f6xZwwDMpElMaekn11EPs2bNmjBhQk1NDZfL7dev36+//sowTHJysrKyct3Mx48f79y5c05ODsMwZWVlJKijvLx8ZmYmybBgwYJt27YxDOPp6SkhIfHkyZOSkhI+nz9kyBBzc/PCwkKGYTIyMrS0tCIiIhiGycrK0tXVJc+fpaXlkCFDSESSAQMGEK943t7ePXr0qCtJSEgI2VzHMAyXyyUj+mHDhtna2r57945hmGnTpv3yyy8MwwQFBamqqiYnJzMMc/Lkyfbt21dUVDAMo6SkNHXq1JqaGsGIm9QmwoQJE4yMjN68ecMwDJ/PT0xMJAo3NTVVU1MzKyuLYZh169YtWbKE5C8pKenWrduJEycYhikvL3dycjp16hS5RIIVfMqP9GVDFbRAQS9ZsqRxtTMABQWFly9fCguQnJz89OnTrVu3amlpJSYmksSMjIyoqCg+nz9z5szr169funSpZ8+ew4cPX716tXBZambXVAwcCEVFnDuHf/deNA63b99etmwZh8ORlpZevHjxzZs3xWS+fPny4sWLiccfOTk5gXuKerG1tSXWe2RMMXPmTLLF4+7du/r6+vn5+ffv34+JiencuTPxlARg7ty5MjIyHA7HxcXl1atXYirX1NR8/fr19u3bo6KipKWlBf4xpk+fTvZ99O/fPz4+nnRwzJgxBgYGAKZNm1ZVVSXw3bx06VIOh/PeIc+0adPIdkoWi6Wjo3Pq1Knffvvt4MGDUlJSUVFRIpnj4+NTU1N1dXXv37//9OlT4nCKXNLS0iKulyjfKu7u7o2l+wSUlJR07dpVuBUDA4NevXqtXr3a3t7ey8uLJLZr187MzCwwMDA/P/+7777buXPnqVOnrl27duLEife6Yv9kWp2ZnRicnBAcjGnT0KFDo9XJMMzbt28FelZNTa2wsFBM/vz8fKKqGoLM0hJE/CIJTt+8eVNWVibwm9yjRw+BT0GBowkpKSnxTxXx63bs2LEhQ4YoKipevXqVxIesW0NhYaFgLZvFYgn3sa7npnoRZGMYpm/fvubm5oMGDVJRUbl9+3bdee03b95ISEgIeicrKyvwc1ZZWSkSOI1C+SgYhhGMJ/h8fmZm5sCBAwVXeTze8uXLid/HsrIyZWVlDocjKyvL5XIFQSoaF6qg/0OXLggNrT1euRKKili1Cp/jepvFYnXs2PHFixdkPSEyMlLE/2odAbqEhISM++8YXkVFpbCwkGySfvXqFRmr4t+Bc72VANi6deuHBD2TkpJqyLjCxsbGxsaGz+cvWLDgr7/++vPPP+vN1qlTJ0F0hXfv3qWkpNRdPCHGpDU1NeJjFebk5Lx8+TIoKIjFYlVWVr5+/bqukMbGxuXl5cuXL6/7JktLSxN/eykU8SQlJU2ePLl3796ysrIPHjyorKycOnWq4OqBAwcGDx4s8NC7ZcsWsnYi4mCrEaEKun4qK/Hnnygvh7c3rl3D5xg7/vLLLz///LOEhERFRcWmTZuOHTsmJvPKlSsdHR21tLTs7OwSEhIsLCwsLS1dXFx+++23JUuW+Pn5xcTEDBo0SHyL5PvLzc1t5syZPB7P399/3LhxDcXiMzY2Tk5OPnDggKampnAQyKdPnz569MjBwYHP50dGRs6aNauh5tzc3LZv375p0yZHR8d9+/YNGjSorpaUkZExMjLauHGjlZVVv379Gpq6UVdXl5eX37t3r42NzYEDBwSfC2ZmZsePHz958qSenp69vf3cuXNHjhy5evVqZWXliIiIdu3akUXIJ0+eDBgwQPzNoVDEYGBgsHPnzufPn1dVVa1cuXLYsGGCIQXDMFwuV+Bvfdu2bWfPnn337p1ImIvGhbN+/fqmq72JyM3NvXHjxvz58+teaqz4xxIScHaGtzeio2FkhM+JH2BpaWlgYPD333+npaWtX7+efDGRLylnZ2eRzOrq6qNHj3748KG3tzePx+vfv7+iomK/fv3i4+N9fHzs7e1dXV2NjIz09fV5PJ66unr37t2rqqrIbIO5uTnxScRms6dOnZqTk3Pr1i3iXNTZ2Zn4VraxsSHKsaamRkdHx9TUVFFR0cnJKSoqKjMzU9gPEZvNfvbs2d27d1+8eDFx4sRZs2axWCzhVng8nqqqqqWlpays7IQJEx4/fvzw4cOePXvu2rWLhPvkcrnOzs6ysrKkwqFDhyYlJaWkpFhYWAhmtAFUVVWZmpoSV6gcDqd///43b94MDAycMmWKnZ2dhYWFpqamsbFx27ZtY2Njq6qqLCwshg4dqqioePfu3adPnyooKAwdOlRFRaWqqur7778/cOCAgoLCp/9aXyStLao3wzDCH1uHDx8eOXKkTrPs/WWz2fr6+vb29g4ODp07dxYOXMtisRwcHAQ+Hdlsdvfu3e3s7ERm1dzd3WfMmNFY+xtYzIcZ235RREREzJ49u94dEyUlJZ8carYu+fm4cweurpCRQUgIrK0/a7qjiSgtLf32VJIYKioqpKSk6oZ8PnToUFJSkiA+4bdE4z7VXz58Pp/L5cqRcBuAlZXVsWPHvpaIKgYGBg8fPvw6Ql597airY/p0ADh5EjNmoGdPeHmhke48pZEZNWpUi2/LpFAaF6qgP4iePaGnh8BA2NsjIwNiF7ooLYN2i4RjoHxz+Pn5FRQUkGMVFRWyqsHn8y9cuFBYWDh16lTBBN2JEydGjx4tPF/X6FAF/UEYGyMiAosXo7j4S5zloFAojcXatWvZbDaZ8tbX1ycKesOGDXl5ed27dx86dCgJkPTo0aObN2/OmDGjSYWhyuZDadMGgrDXW7bg1i3s348ePVpUJgqF0gSsXLmSxLcUcPPmzVu3brVt29bd3T0vL09FRWXFihXCIYabCLqT8FOIjkZQEHr1wokTLS0KhUJpbJ4+fXrixImwsDBBipycHPFwUFpaKicn98cff4waNUpPT6+pJaEK+lM4fhw//YSaGnh7t7QoFEqrYulSsFgf96etjTdv6q/twgVISEBREUJeztu2bZuRkfHw4cPBgwfPnj2bJC5fvnzmzJkkrHBRUdH58+eXL1+ekZHR1C7I6RTHpyAtjT178P33tWFZDh+GnBymTkVju9miUCj/RVYWLBY+yjhYWhp1jDJrkZSEhASkpIQzCCYusrOzTU1Np0+f7uTkNHr0aEdHx5KSko4dO06aNGnr1q0XLlw4duyYurq6vr5+04XdoAr60zE0BAAuF99/Dx4PXl44exZivRtRKJTPY/t2bN/eaLWNGQMut6GLbdu27datW1xcnJOTEwANDQ0NDY0HDx7weLwBAwZYWlpeu3atXbt27du337Ztm3gfBp8MneL4XGRkcPEi1NRw7x5OnmxpaSgUymcg7IwsLy8vOjpa2LFMVVXV6tWr9+zZA4DL5SooKHA4HElJSeFYHI0LHUE3AmPGoFcvXLwI4lbl3j1YWIBa5VIoXx3JycmjR4/u3bs3m82+fv36gAEDXFxcBFf37t07btw44pZg1KhRv/32GwlSIdj02OhQBd04aGuDeBJ/8gRDhkBVFXv3ws2tpcWiUCgfQ4cOHf7888/o6GgWizV58uRevXoJX1VWVhYsG27ZsuXq1avFxcVXr15tOnmogm5krK0xciSuX8eMGejcGXZ2LS0QhUL5YCQlJZ2cnMikc10WLFggOGaz2cLeH5sIOgfdyMjK4to1eHlh7lyYmoJh8PIleLyWFotCoXyFUAXdJEyaBA8PKCrizBl06wY7O0REtLRMFArla4NOcTQttrbQ00NYGBwckJHxWY7/KRRKU1NcXHz+/HnhFEdHR1NT06qqqmPHjpWVlc2dO1fgHWn37t2LFi1quhVCUAXd1JiYIDoaGzciJwdKSuDzkZQEGpWJQvky4XK5gh3elZWVJ0+evH//vqmp6Y8//qimpqanpzdmzBgSpPjy5cuJiYlNqp1BFXQzoKCAnTtrj3fswKpVGD4c7u7o2LFFxaJQKHXQ1NQ8fPgwOb5w4cKjR4/69u0L4N69e1FRUfLy8ps2beJyuTweb+vWrYLIxU0HVdDNir09VFRw6xaCg5GdTT2XUigfzdu3ACAvDxJHu6YGJSUAoKwMEiS5ogJcLthsCBw1l5SgpgZSUpCX/08lcnIQE0rM09Nz5syZJPKykpJSYWGhpKRkTU2NlJTUmjVrFi1a1FBozUaELhI2K05OiI3FrFkYPhwSEqiuRmxsS8tEoXw9LFiANm3Qpg309VFaCoZB9+61Kd99BwApKdDSQps2UFGp3RN+5QpUVNCmDVRV8egRAPz0U22R9u1RWFh/Q5mZmQ8fPnT7dy/D6tWrx40bN3jw4KVLl8bHxwcEBMyaNSsmJiYyMrJJ+0uHcM2NtjYEcb1//RW7dmHQIPzxB4yNW1QsCuVrQFsbqqoA0LYtJCTAYqFdO+Tk1KYAkJWFtjYkJMBmQ0MDAFRUoKGBqirIyYFEdhRUoqNTOwyvy7Fjx1xcXDp06EBOJ0yYMHjw4OrqanV19YEDB+7bt2/fvn1+fn7y8vKdOnXasmVLU3WY+QoJDw+3tLSs91JxcXEzC/M5+PgwqqoMwGhqfnolJSUljSfRV0B5eXlNTU1LS9GsfF1P9efD4/HKysoEp5aWluHh4c0pAJ/PNzQ0vHDhQt1L58+fX7RoEcMw+vr67969q6ys1NLS4vP5ggz6+vopKSmNJcn7R9DV1dUJCQmJiYk2NjbNE/m89TBgAF69wqZNIFG5i4oQEICBA+ncNIXSkjx48ODt27cjR44USS8pKdmxYwex4iCT0RISEkSTsprG1/B75qBv3Lihp6fXtWvXkSNHEuuTR48esdnsrKysppCmFaKuDnd3kC+ktWsxbBi6d8c//7SwVBRKa8bT03Pq1KnSdRYQN2zYsGTJElVVVQCurq7Lly9fs2bNoEGDyEJiUyCu3vDwcFdXV0dHx3/++cfAwIAk9unTR19f//bt200kUGtm+nQYGiImBiNGtLQoFEorZuHChb/++qtIIp/Pt7S0FCwb/t///d+gQYN69Ojh6enZdJKI+5Y+evSolZXVhQsX2Gy2wB01i8Xq2rXrq1evmk6mVouNDWJicOwYiPF7YiLOnsWMGfh3oYJCoTQHvXv3rpvIZrOnTJkifPodMRxpSsSNoNPT03v16kVG78IzLPLy8u/evWtqyVonUlJYuLDWT+nBg1i/HiYm2LChpcWiUCgtgTgFra6unpKSIpLI5/MjIiKIy2pKk7JqFaZMQXU1tm5FVVVLS0OhUJodcQp65MiRN27cuHnzJv4dQfP5/A0bNiQkJIwePbqZBGzFaGjgzBlERiIgAFJS8PdHz55wdxcTRI1CoXxTiJuDHjVq1KRJk0aOHGllZZWVlbVjx46lS5cmJyevWbPG3Ny82URs5ZiZ1R68eoWgIAQF4a+/EBZWa3JPoVC+YcSNoFks1unTp0+cOKGsrKyoqJicnGxgYHDp0qUm3DZDaZjZs3HjBiwtUVpaGwEgNhZNFqySQqG0PO/ZEcFisaZPnz59+vRPqz0/P7+goMDIyKghO8GKioq0tLR27dopkK0a/1JVVZWcnKyioqJNY68KMWLE/yzwbt3CiBEwMMCqVRLz5rWoWBQKpWkQp6APHTqUm5u7fv16kfSJEyeOHz9+zJgx4qteuXLlsWPHtLW1q6ur796927GOe827d++6ubnp6uqmp6cfPHhw/PjxJP38+fPEGrykpGTevHl1BaAAMDeHqSliYjB/vkzXrnBwaGmBKJQmY/Pmzerq6i0txQdRUFDQiLsKxSno7OzsjIyMuunR0dH5+fni6w0JCfH09IyKitLR0Vm2bNmqVasuXrwonKGmpmbevHkHDhxwdXX9559/Ro8ePXz4cDk5uYiIiAULFvj4+Nja2gIobMjZVKtHTw9RUbhwAYGB1RYWklwuVq2CoSFmz0YT+xCnUJqVXbt2JSUltbQUH0rPnj0b0cjto50+VFZWZmVlaRA/UQ1z7ty5kSNHEt8dCxYsMDMzq6iokJWVFWR48uRJVVUVGYY7Oztra2vfvXt37Nixhw4dmjp1qq2tbWlpqYKCQjN4XP16YbMxaRJGjKiUl5eMjYW7OwBs2oSbN2k0ccq3Q79+/fr169fSUrQM9ShoLpc7YsQIAElJSVwud8CAAYJLlZWViYmJXC7X3t5efL2pqak2Njbk2NDQkMfjZWdnGxoaCjKkpaV17NhRMDdtaGiYlpYGIC4uTl9f39jYuKKiQkVFxcvLq1u3biKVMwxTUVEhiEwDoFOnToJAYa2TLl1w+zY2bUJQEBITYWeH168hKQn6gqNQvl4+bgStpKQ0cuTIGTNmvNetXVlZmYyMDDnmcDiSkpIlJOxBfRkAyMnJkQyFhYXp6ekhISHq6urr1q1zc3MLDw8XqZzkmTt3riBlyZIlrq6upNomciv1xVJWVkYO+vSBry8KC1lt2jAlJTAzky8pYU2YUL1qVVX79kzLCtmIVFRUSElJcTiclhak+WhtTzWfz+dyuXw+v6UFaVpkZGQk3ue4sp7LMjIyvr6+aHiR8EPQ0tJ6S6LKAGVlZcRrqnAGTU1NQQYAhYWFxGBDS0vLxcWFLAjMnj1706ZNJSUliv81+lVTUzMxMamruAEwDCNiENIaEO6y4HDMGBw7hlOnJKurJb28WkawpoDD4bQ2Bd3anmo+ny8hIdHU8Vi/CsTZQS9YsOCTLSgsLCyCgoLIcVBQkK6uroiCtrCwiIuLIz49qqurw8LCLC0tAVhbWwscfRQVFUlKSgoPtCkfzuHDiI/Hhg1YtgwA9u9Hv344fZruGqdQvhpYDPOej9+ysrLExMS8vDzhxC5duujq6oopRcyf161bZ2VltXjx4gkTJqxevRrAzJkzra2tf/jhBwDDhg1TUFD46aefiL1HYGAggJSUlB49eri7uxsbG69atcrAwOCYIELUv0RERMyePbveEXTd4fY3D1lNfW+2SZNw/jwA2Njg2bMml6rpaIVTHK3tqSZTHHQEjffOQW/evHnLli3cOt4fDh06NH/+fDEF1dTUHjx4sH379hs3bkybNu2nn34i6ebm5vr6+uT47Nmz69evX7NmjYmJyfXr10migYHBrVu39u7dW1xcPHDgwGVk+Ef5bE6cwKBBOHQIenoA8OYNPD3Rvz969GhpySgUSkOICYdF3CStXLny8OHDKioqgYGBR48e7dix46RJk968edNYQbc+gW8mJmGj8GkxCffsYQAGYBwcmLdvG12oJoTGJPzmEYlJ2JoRNwft4+Pj7Oy8fft2MzMzDodjb28/e/bsJ0+e+Pj4xMTENNcbhNIkzJqFn39GmzYIDKwNihwWhjrOZSkUSksiTkGnpaVZWVkBkJWVFRjJ6ejo9O3blwyuKV8vysrYtQuZmUhPR5cuyMiArS06dcLgwYiLa2nhKBQKAPEKuk2bNkVFRQB0dXWrqqoSExNJellZWUVFRXNIR2liZGVB1np1dDB3LqSl4e2NU6cAoKICr1+3rHQUSmtHnIK2srJ69uwZAE1NTRsbmwULFty+fXvHjh3e3t7EUQblm0FCAocOISsLly9jxQoAGD0aOjro1w++vi0tHIXSWnmPw/6XL1/m5eVpaGjs27dv5MiRw4cPBzB+/PipU6c2l4SU5kNVFWPH1h736wd/f/j54dUrEJdZJSU0SgCF0qyIU9Dt27c/fPgwOe7Vq1dOTs6rV6+UlJRoQMLWwC+/YN48XL5ca5Z37RrGjEHXrpg5E0uXojVZIVMoLYY4Bb18+fKqqqr9+/fXZpWQMDU1bRapKF8EysqYPbv2uF07aGri5UssXw4zMwwciNJSSEpCWrpFRaRQvmnEzUGnp6eXlpY2myiUL5kePZCRgRs3sH07+vQBjwdjY6ipYdo0vHzZ0sJRKN8o4hS0i4tLUFBQNQ17RwEASEpixAisXAkZGXA4sLFBeTnOnMGvvwJATQ2io/GtOyCjUJoVcQp66tSpenp648aNCw4OzsvLeytEZWVls4lI+TK5fh2JiXB3x6ZNALBhA8zMoK+PtWupmqZQGgdxCnrXrl0+Pj7Xr1+3t7fX1NRsI8SJEyeaS0LKl0vHjliyBObmAODkBH19ZGRg82akpwPA48cICcH7nHFRKJQGEbdI+N133zVksNG7d++mkYfytdK/P5KT8ewZioqgr4/sbDg7g2HQoQP++gvDhrW0fBTKV4g4Bd2jR48e1NcZ5YNhsf4XC1FbG6tW4fRppKXBzw/DhiEsDOfPo39/9O0LKakWFZRC+UoQN8VBoXwybDa2bkV6OqKjsX07ABw4gN27MXgwDA1BjYMolA/ho6N6UygfDosFgen81q1o3x7Xr4PHA5uN0lIMGgRZWYwYATc3qKi0qKAUyhcJVdCUZkJLC+vXQxBDahfpNQAAIABJREFULT8f0dF49w4PHiAhAX/+CS4XcXHo2hWSki0pJ4Xy5UCnOCgtg7o6UlPh5YVFizBtGgCsXAlLS6irw82NBk6kUACqoCktiIoKJk3CX3/VLi0OGwYzMxQXw8sLeXlgGKxahV9+gY8P6GYpSuvkPRFVLl26VDd93759wcHBTSYSpZUycCCiopCRgefPoauL4mLs2YPduzFoEBYtAgCGQXo63QVDaUWIU9BPnjy5c+dO3XRPT8/nz583mUiUVk27dujaFQCUlREYiNWr4egIR0cAcHdHhw7o0EFmxgw2tQOhtAY+ZZHw7du3ysrKjS4KhSKCtTWsrf93amkJAwOkpLDOnMHixbC1xdatSEpC794YPhzq6i0nKIXSNNSjoKuqqn7//XcA/v7+JSUlq1atEr6amJiYlZXVrVu3ZhKQQvkXJyckJ+PlS25xsZStLRvAX38hOxuenujVC0+fgs+Hry8MDdGpU0vLSqE0BvUo6Orq6h07dghOo6KiBMeysrIdOnTYu3dvV/IVSqE0O4aGjJRUrYOPgABcv47Hj+HsDADXrtVGhGnXDlevwsamxYSkUBqFehS0vLw8wzAAfv/994yMjOPHjze7VBTKB9GhA5YswZIltacODhg/Hv/8g6wsZGbCxgbLluHkSdjaYswYzJ3borJSKB+PuDno1atX8+mSOeXrQUsLFy4AQHExlJQAgMdDYSHu3YOvL9zcwGLhp5/AMLC3x6hRNMQi5UtHnBVHeXl5YGBg1b97Bvz9/SdPnjx//vy4uLhmkY1C+USIdgbg7o6sLFy6hHv3ICWFvDwcOoQDBzB9OpYvB4C8POzbh3v38PZtC8pLodSPuBH0iRMnDh069OrVKwDJycmDBg1SVFSUkJC4cuVKQkKCqqpqcwlJoXw6bdvC1fV/x6Gh8PHB8+cYPx4ADh7EunUAIC2NZ89gbo6MDGRkwNwcCgotJjOFQhCnoJ8/f+7s7MxisQCcPHlSRkYmLi5OWlra1NT0zJkzixcvbi4hKZRGw8ICFhb/O507F6WlCArC27e14+7BgxETAzYb48bh/HkAeP0acnJ0PoTSAoib4igqKtLQ0CDH3t7eQ4YMUVVVlZOT69OnDxlWUyhfOzo62LkTjx8jKgr6+gCweDGsrSEhgdRUAIiLg64uVFTQuTO8vWtL0W0ylOZBnIJWV1dPS0sDkJGRERIS0q9fP5JeUVHB0EBGlG+UBQsQGoqSEjx5AgCamnB0hIQE4uMRFAQAe/dCURE6OnB1RXExAPB41FsIpUkQp6AHDRp0+fLlDRs2LFiwQEpKavjw4SQ9JiZGT0+vWcSjUFoGKSlISABAmzb45x+UliIxEWvXAkD79lBRQW4url5FSgoAuLhAQQEWFti9u7Y4l9tCclO+LcQp6HHjxn3//fd79+4NCQk5fPiwpqYmgNDQ0JiYGBqTkNKqkJSEoSHYbABwdUVhIZKSEBGB7t0BQFcXNTWIjISHBwCkpEBDA8rKcHDA48e1NeTnt5DolK8ZcQqaw+Hs2bOnqKjozZs306dPJ4ndunUrLCy0E8Seo1BaHywWOnas1c4AvLxQXIzgYPj5AYCMDLS0UFyMgIDaaWt3d2hoQEkJffsiLw8A3r1DfDydGKG8hw9yllRdXZ2dna2hoSEnJyctLS0tLd3UYlEoXxfy8rC1rT3W0UFiIgoKkJgIS0sAMDSEtjZyc/HoETIzoaGBgQPx7BkkJTFyJIhP3ydPwOejc2doarZYLyhfGu9x2B8ZGdm7d285OTl9fX0/Pz8AQUFBNjY2b6lZP4UiFjU12NnVxi8fPhw5OcjPR1JSrcr+7jt07AgeD2TXV3Iy+vSBkxO0tLBxIwAUFOD//g+nTyMiouX6QGlpxCnolJQUZ2fnsrKy/fv36+jokMQePXpkZGTcvn27WcSjUL4d1NRgYFB7/OuvSEpCWRnCwwGgfXv8+CPs7KClBbID7ORJ/Pwzpk+HlRV8fSUAXLyIyZOxahXu3m2pHlCaG3FTHAcOHNDS0goICJCRkdm7d29tAQkJCwuL6OjoZhGPQvmWkZGpPZCUxJ49/7nk5oayMsTGoqQEXbrwARw/jnv3AGDXLhQXQ1oaffogNxcGBli4sHa3ZFwclJSgowMWq1k7QmkixCnouLi4QYMGycjIAGAJ/eBqamp5ZKWDQqE0DWpqtVZ9AEpK+ABOn4aPD5KToa0NeXlUVSE7G2lpSEmBhARcXeHri4EDAUBeHhcuYNgwJCXh8mVoa8PcvHZqhfJ1IU5BKygoFBQU1E0nirvJRKJQKPWgro7Jk/93KiWFhASkpCAzE2ZmAGBsDGdnxMYiP7/WEHvHDhw5AgAsFmJi0Lkzli9HQADatsXIkSCWWenpYBjo6NROl1O+KMQp6P79+y9evDgqKqpbt26CEbSXl1d4ePgeke8xCoXS7EhKwtgYxsa1px064OHD/2RYswba2khNBZsNsrfswQNERgJAcDCmT0daGoyMUF0NDgc7d2LZMmRnY88eKCnB2Bhjx0JSsnm7RPkv4hT09OnTPT097ezsXF1d8/Pzvby8Dh48eOfOnfHjxzs5OTWbiBQK5dPQ16+1CREQGIjnz5GVBRMTAFBXx5AhiIhAbi5qagDgyhX83//VZvbywqRJWL0ae/ZAWxt2djh7FpKSePQISUnQ1ESvXmjTpnm71MoQp6AlJSV9fX03btx46tSp/Pz8c+fO6erqbty4cfXq1c0mH4VCaURkZdGz5/9O5eVx/fp/MsyeDRkZpKairAwDBgAAm43qaqSnIz8fJSVQVcWQIaioAABbWwQHIzsbw4ahqgpt22L9ejg4oKQE165BRQUGBrXTL5RPQ5yCDgwMLC8v3759+/bt24uLiwEoCRyhUyiUbxE5OdHYYFu2YO1aZGdDRqZ2vHzkCO7fR14eyFJUcTHi4sDlIiYGNjZwcMC+ffj999riDx/C2Rnr1+P0aaipoWdP7NsHFgsPHiAtDWpq6N2bDsMbRJyC3rp1q7q6OnFiR1UzhdJqkZFBx47/O50yBVOm/O+0c2e8fo30dBQUwN4eACZNQmYmsrMB1M6lJCQgORnJyYiOxvbtYLMxaBB4PADo2xd+foiPh4MDWCxoaWHvXpaDA1JScOQIFBTQsSPGjwebXWu40qYNWo82EqegO3XqlJCQ0GyiUCiUrxQlpf9MZXTqhMOH/5PhzBls3YrcXKipQVYWAA4fxtOnKCjAmDEAwOOBx0NREfLz8eIFHBzg4YHt22uLa2rCxQVjxoDskOvWDRERYLOxaBFSU6GqiunTMXgw+Hz8/TcYBtrasLev9Uf4VfP/7d1nXFPX3wDwEyBhBTBhhSWCbBQQUYYLcW9FxYFCK1p9RP/ual111dqh1dpWtC7UWsGqiKi4AFmyh2wQlBX2zCCQcZ8XR29TCBEQCJLzfeHn3nNHfpfEX27OPUPcFfj6+jo6OoaGhs6cObPfAkIQZPAhEIChITA0/LfExwf4+Py7amUF6upAXR1gscDQoRiHA3bsADQaqK4GBML7enMXF5CVBerrgZwcIBBASwu4fh2wWAAAUFkJZs4ET5/+O73Z99+DPXvAxYtg/XqgqAiGDgWhoWDoUPDXX+D+fUChAEdHsGYNAAAkJoLiYkChgLFj38+bw+UOlOYr4hJ0dna2jY3NrFmzxowZY25urqSkhG/y9PScOHFi34eHIIi0kJEBmppAUxMIBAAAoKEBtmz5zw5794K9e/9dVVIC2dkgOxswGO9HqnJxATt2gOJiwGQCOL+IggIgkQCLBQoLQVMTAACcOwdiYgAA4PJlsHo1aGsDLi7vW7DMnAkePwZpacDFBbS0AE1NcOECWLgQxMaCw4eBkhLQ1wfHjwMVFZCWBsLDgbIycHAA9vYAAFBTA+rq3n8T9GI3TnEJurCwsKSkxNjYuK6uLjY2VniTq6trr4WAIAjSI0OHAuG5Q1RV/50zAVq1CqxaBRgMICsL4B3m7dsgKgo0NgITE0AkAiIRHDoEUlJAczNYuhQA8P5ZaHk5qK19P9f706fg6dP3J1yyBEyaBDZsAPHxAABAIgEGAwgEwMwMNDYCAMCyZe+nsuwVhM9x8qrU1FQfH58UOMzMfzEYDBUpm92TyWSSpWkC6paWFhKJJCsrK+lA+o+0faoFAgGHwxH+yS4RDMa/NR5xcaCmBigpAVjdGx0N7twBLBYwNQW7dgEMA15eICEBcLnA0xMcPdprMfRhLXpTU9Px48fT0tJGjBixb98+qqimNBcvXgwKClJTU9uxY4e9vT0AoL6+Xrid9aJFi1ANOIIg/Q//TiQSQbsppMaPB+PH/7tKIIDr1/skho+MB83j8S5evLh69epx48ZFRUUBALKzs3/88Uc+bCAj1qpVqwoLC7/55pvKysql8MfDf/3555/Hjx/ftGnT2LFjp0yZQqfTAQBMJtPf33/0BzQarUfXhSAI8vnDOsfhcKZMmSIrK+vs7KyiovLgwQMMw6qqqkgkUkREhJgDMQzLy8uTl5dvamrCMIzNZpPJ5PT09Hb7WFlZ3bp1Cy4vWrTo6NGjGIYVFxeTyWTxJ09JSRk1apTITc3NzeKPHXwYDIakQ+hXbDabx+NJOop+JW2faj6fz2KxJB3FgCCuiuPSpUuvXr2KiYlxdHQ0h83NAdDS0nJwcIiMjBQ/HEdKSsqIESNg9xZFRUV7e/vk5GQbGxt8h5aWluzs7HHjxsFV/A4dANDW1vbVV18RicQZM2bMnz+/h988WVmgoqJ7h4waBdTVRW+i00F2dvfOZmQEhg8XvYnFAnFxoFu1/xQKGD1a9CaBAERHd28eaSIRjBvXaTPRjAxQVdWNswEAHBzAkCGiN5WWgry87p3NxAQMGyZ6E4MhExlJIBLfT+DaFerqnQ61yeeDmBjQ1taN2EgkMG4c6KwGPC2t27PDOjqCzuqX370Db94AAGTZbNDFClkzs/88NRPW1AQSE7sXm5YWEPo/+x88HoiJ6d6kigoKwMWl0zcuORl8mKeJgGGybW1A/NR6BAJwcgLKyqK3wl4x3WJpCfT0RG+qrweinniJo6MDrK27d4go4hJ0eHi4h4cHnB9WeDxoQ0PD8vJy8eetqqqiwJkhAAAAqKurV/w3XVZVVQEA8IppKpVaWVkJAFBQUNiyZYutrW1FRcWGDRtSUlIOHTrU7uT19fX5+fmjhP7Xbd++feHChQAAJpMJACBUVpLt7N63neky3uTJLe0GJvhAefJkmfz8bp0NU1ZmlpaKTIIKW7YQr1zp1tkAAOzwcL6oHC24dg1s3tzds7V+912bqKNkiouV7ezeN3TqMt6cOS1//y1yk7KLi0xZWbfOhlEozHfvRDZWUli3Tj4goFtnAwQCKzZWIOp/C/HyZYWtW7t3NgA4p05x167tWC6Tm6vs6Ni9710AuEuWcC5fFrmJ7OBAqKsDAHT9YRmmp8fMyRG5SXH1arkHD7oVG5CRYaWmCvBpYISQfv9dvvtj8nD8/LjCQ6Z+IJuaqiR0w0cAoCvTnnK9vTlnz4rYwOeTbW0JTGa3YhOYmLA6ycKKHh5yL15062xATo6ZmYnp6orZRUFBgfix5tbiEnRbW5uyqC+ouro69c7uND8gk8kcoXs6Npvd7jE0bHjQ0tICn9W2tLTAHbS0tH788Ue4z6hRo+bPn3/w4EGZ/37rUigUAwODixcv4iXGxsb4+VVUVICCAvDyAiUl4oNsR87Ts9Nn5WvX/tvQpmsINjYqQl9R/7F0KSgr697/ZCpVyc5O5K0We+JEMG/e+9FruohIlJ89W17kxZqYgFWr3vfS7TJxf7r168HLl906G2HsWJXOOvMuXy6oqSEQCISutzXV1FQeMQKIbOgyfTqYMwe0tnYjOBJJYfp0BZEXa2UFVqwA1dXdOBsAxBUriJ396T405uLz+V1stUKYMKHTN8LTs3sfEgCAjo6yqen7nn/tzJoFIiO7ewet4OYm+k9nYwM8PEB9PVzDMEwgEHzkkgkEooeHuD9dWlo3YgNAZurUTv90Xl7dbttsYEA2MuqFMbbFVH/s27fP1NSUw+FgGGZubg7roIuLi5WUlK5cuSK+6uTJkyf6+voCgQCumpmZBQUFCe8gEAiUlJQSExPh6s6dO7/88st2JykuLgYAwIpsYagOWhiqgx70pO1TjeqgceIq8tavX19VVTVr1qznz5/zeLzKyspbt265ublpamp6eHiIz/uurq5cLjc0NBQAEBkZWVNTM336dADA69ev79y5AwAgEAhLly69dOkSTMG3b99etmwZAKCsrKytrQ0AIBAIfvvtN2trazROE4IgUkp8/o6OjjYU7j8PgIWFRWZmZldy/507d9TV1Z2dnalU6s2bN2HhL7/84ujoCJffvXtnZmY2atQoHR2dNWvWwNvtX375hUKh2NnZ6evrW1papqSkdDwzuoMWhu6gBz1p+1SjO2jcx3sScrnciIiI3NxcAICVlZWrq2vXO3ExGIw3b94MHz4cvwvmcrlcLhfvI8Tn83NyctTU1AwMDPCj6urqSktLYUWzjKhnvqgnoTDUk3DQk7ZP9QDpSShGU1MTm81ms9mNjY0sFovNZjMYjObmZrxQIBCsXr16xCfPVvCRsTg4HI61tfW0adOmwckVAAAAxMXFGRgY6HXWJEWIiorKqP+2cCISicIPLmVlZTteg7q6+kcfQiIIgnyi5g9gem1sbGxubmYymQwGg8FgwFUWi8VkMpubm5uamuAyg8Hoysnr6+v/hFP2fgJxCdrf37+0tPRKhwZhX331la+v7/r16z/xtREEQXoLj8draGho/EB4uampqampCS7AVNvc3Nzwodl1D6ioqCgrKyspKVEoFCUlJSUlJVVVVRUVFSUlJWVlZVVVVSUlpY8+qOuKnozFweFwFBQUPv21EQRBxGtqaqqvr6+rq6sX0tDQ0NDQABdgLm5oaGB2s+EzAIBMJqsKGTJkiIqKioqKCiyHq2QyWVlZWXhZTU2tL65UJBEJWiAQpKamAgAqKipqa2uTk5PxTbD7X1FRkZGotusIgiBdVFtbW1dXV1tbiy/U1NTUfVBTU9PY2FhfX8/rcnczOTk5CoUy5L/U1NTgv/iCqqoqvizyEdeAIiJBt7S0ODg44KshISHtdpgzZ8544aGcEARBhNTX11dXV9fU1FRXV1dVVdXU1NTW1sLl2g+6MuAaAEBVVZVKpcLnUlQqlUqlUigU+K8weIfb19fV/0R1RFZQePbsGQDg6tWrNTU1u3btEt40dOjQoZ119kcQRAo0NzfT6fTq6mr4b1VVFZ1Or6mpqaysrKysrKmpaevC8CZUKlXjA3V1dQ0NDU1NTZiIKRSKioqKrq6uurq63CCYWPATiLh4WVnZqVOnAgB0dHTYbPaYMWP6PSoEQSSpsbGxvLycTqdXVFSUl5dXVlbCZajlY13G1dTUaDSapqampqamtra2lpYWzL80Gg1PymIy78BvZtdvxH07WffGaEwIggxAGIZVVVWVlZWVl5eXlJSUl5eXl5eXlZVVVFSUlpay2WwxxyorK+vp6WlpadFoNB0dHU1NTV1dXZiIdXR0tLS05MUPRId02Ud+PiQkJJw5cyY/P7/+wzgm0LFjx1asWNGXgSEI0guam5tLSkrevXtX+kFxcTHMxWIqIpSVlQ0MDGg0mr6+Po1G09PTg/9qa2vr6emJHEMN6QviEnRERMTUqVM1NDQmTZoE56PCdaWXCoIg/aa+vv7du3fv3r0rLi7GF4qLixvhVKaiaGlp6enp6evrGxgY6OjowN5nurq6+vr6aACcAUJcgg4ICDAxMUlKSpKqnsQIMpC1tra+ffu2sLCwqKjorZDm5maR+ysrKxsaGsJn+wYGBvBfmJRRb4aBT1yCrqiomDx5MsrOCCIRcCibN2/eZGVllZWVFRYWFhYWlpWViRw/R1VVdZgQww80NDT6P3Kkt4hL0GPHjn3+/Hm/hYIgUqu1tbWgoCA/P7/gg/z8fDjHUDtEInHo0KHDhw83NjY2MjKC/w4bNgwNXzMoiUvQW7ZsuX///nfffbdr1y7Sp08NgCAIAACAysrKnJycvLy83NzcvLy8vLy84uJiQYdpxhQVFU1MTExMTAwMDCwtLYcPHz58+PChQ4dKedNgqSLunb5w4UJ5efn+/fsPHz6sp6cn3C0SteJAkK7AMKy4uDgnJycrKys3Nzc7OzsnJ6fjgzsikWhiYmJmZmZubm76gb6+PpzZS9qGG0Vw4hL08OHD58yZI3ITasWBICJVVFRkZmZmZGRkZ2dnZGTk5OR0HJ2SSqWam5tbWlqam5ubm5tbWFgYGxt/dP5QRAqJS9Dz58+fP39+v4WCIJ8dFouVmZmZnp6ekZGRmZn5+vXrdj0GAADa2trW1taWlpbW1tYWFhZWVlba2toSiRb57KDKLATphvLy8rS0tPT09LS0tLS0tMLCwnZ1x1QqdeTIkdbW1iNHjrSyshoxYgSVSpVUtMjnTkSCvnz5srKy8rJly5KTk+G4ox2NHz/ewsKij2NDEMkrLCxMSUlJSUlJTU1NTU2trq4W3kokEkeOHGljY4P/q6urK6lQkcFHRIJev369np7esmXLgoKCjh07JvIwPz8/lKCRQamoqCgpKSkpKSk5OTklJaXdAz0qlWpnZ2dnZ2dra2tra2tlZYXqjpG+IyJBV1VVwQYbe/fu3bp1q8jDUO8VZNCorq5O+CApKamurk54q46OzujRo+3t7UeNGjVq1Kh2k9wjSJ8SkaDxKjNFRUVFRcX+jQdB+lxra2tKSkp8fHx8fHxcXNy7d++Et2prazs4ODg4OIwePdrBwUFHR0dCYSIIekiISIeKiorY2NiYmJi4uLiUlJTW1lZ8k4qKioODg6Oj45gxYxwcHNB8FMjAgRI0MjhhGJadnR0dHR0TExMdHf327Vt8k4yMzMiRIx0dHZ2cnBwdHa2srAb+3HSIdEIJGhk8eDxecnJyVFRUVFRUdHS0cJNkVVVVJycnFxcXZ2dnJycnNJwm8llACRr5vPF4vMTExIiIiJcvX8bExDCZTHyTgYHBhAkTXFxcJkyYYG1tLSsrK8E4EaQHUIJGPj8CgSAtLS0sLCw8PDwqKko4KVtYWEyYMGHChAkTJ05ELS6Qz524BO3n51dZWXno0KF25cuXL/fw8HB3d+/DuBCkg4KCgufPnz958iQqKkq4+sLS0tLV1XXSpEmTJk2i0WgSjBBBepe4BE2n00tLSzuWZ2ZmTpkypc9CQpB/1dfXv3jx4unTp8+ePSsuLsbLjY2N3dzc3NzcXF1dUUs4ZLDqdhUHm80uLy/X0tLqi2gQBADA5/MTEhJCQ0OfPHmSlJTE5/NhuZaWlpub28SJE6dPnz58+HDJBokg/UBEgm5paZkwYQIAgE6nt7W1OTg44Jt4PF5xcTGXy3V2du6/GBHpUFNTExoa+vjx4ydPnuA1GPLy8pMmTZo+ffr06dPt7OwIBEJLSwuaPgKREiIStIyMjLGxMQCgpaWFzWbD5fd7y8lNnTrV29sb3UEjvSU1NfXhw4chISGJiYn4yHCmpqYzZsyYOXOmq6ursrKyZCNEEEkRkaDl5eUDAwMBAFevXq2pqdm1a1e/R4UMcq2treHh4cHBwSEhIfhzDgUFBVdX11mzZs2ePdvExESyESLIQCCuDvr169d49R+CfLrGxsZHjx7dv3//8ePH+Dwjenp6c+bMmTNnzpQpU9DNMoIIE5egy8rK0H8Y5NNVVVUFBQXdvXs3PDycy+XCwlGjRs2fP3/evHn29vZw5j0EQdoRl6CnTZv2888/t7W1oWcySA+UlZXdvXv3zp07MTEx8KeYnJzclClTFixYsGDBAjQmEYJ8lLgEvXLlyuDg4AULFuzZs8fMzExBQQHfpKSkJC8v3/fhIZ+f8vLyf/75JzAw8NWrVxiGAQAUFBTmzJmzaNGiefPmqaurSzpABPlsiEvQP/zwQ0hICAAgNDS03SY/P7/169f3YVzI56a6uvqff/4JCAiIjo6GjTGUlJRmz569ZMmS2bNnq6ioSDpABPn8fGRWb319fZGbYENpBGlubg4KCrp58+bz589hPYaiouLs2bOXLl06d+5c9AwDQT6FuAQN55Xot1CQzwiXy338+PFff/314MGDlpYWAACJRJo9e/ayZcsWLFiAZkRDkF7Rpa7etbW1cBgEU1NTNJCulEtISLh27dqtW7fg3H0yMjKurq6enp6LFy+mUCiSjg5BBpWPJOjc3FxfX9/w8HD4tEdGRmbevHlnz541MDDol/CQgYJOp1+7du3atWs5OTmwZOTIkatWrVq5cmVn9WAIgnwicQm6oqJi4sSJfD5/+/btI0aM4PP5aWlpV69enTRp0uvXr9HPWGnQ1tYWHBx89erV0NBQWMVMo9FWrlzp5eVla2sr6egQZJATl6B///13GRmZpKQk4SarGzZscHJyunbt2saNG/s+PERisrKyLl26dP369draWgCAvLy8u7u7t7f3jBkz5OTQPA8I0h/E/U/LyMhYuHBhuw4F1tbWbm5u6enpfRwYIhlsNjswMPDPP/+MjY2FJba2tmvWrPH09ERNmBGkn4lL0PLy8k1NTR3Lm5ubhw0b1lcRIRKSnZ3t5+d3/fr1xsZGAICamtqKFSt8fHxQSx4EkRRxs827urreuXMnKCgIL8Ew7MqVKy9fvpw8eXLfx4b0By6XGxAQ4Orqam1tffbs2cbGRicnp8uXL9Pp9HPnzqHsjCASJO4O2sfH58aNG4sWLbK1tbW2tubz+a9fv87JyZk3b96CBQv6LUSkj9Dp9AsXLly4cKGiogIAoKKismrVqg0bNtjY2Eg6NARBAPhoFUdYWNiZM2fu3r379OlTGRkZU1PTP/74Y926dWj4sc9aXFzcmTNn7ty5A8eWGzFixMaNG1etWoU6ZCPIgPKRx/EKCgq7d+8lr8hsAAAgAElEQVTevXt3D04tEAiSkpIYDIazs7OSkpLIfQoLCwsLCy0tLTs2rK6uruZwOGjMs17E5XJv3759+vTpxMREAACRSFy6dKmvr++kSZMkHRqCICL0VXspLpc7b968srIyPT29rKysiIiIjnNknD59+vvvv3d2do6JiTl16tTq1avxTVVVVSNGjCCTyW/fvu2jCKVKfX39hQsXfvvtt/LycgCAhobGunXrNm7ciPqYIMhA9pEEXVRU9NtvvxUUFHA4HOHyrVu3zpkzR8yBd+/eLS0tTU5OVlBQ2LZt29GjR/39/YV3aGho2LdvX1xc3MiRI8PDw5cvX+7h4YEPYerr6+vu7v706dMeXRTyr6KiotOnT1++fJnFYgEARowYsXXrVk9PT+HBYxEEGZjEteJISkqytra+cOFCY2PjkCFDKEI+Ohj03bt3ly5dCrPAqlWr7ty5026Hx48fm5mZjRw5EgAwefJkEokUFRUFNwUGBsrIyKDnkJ8oKSnJw8PDzMzs7NmzbDZ75syZT58+ff36tY+PD8rOCPJZEHcH7e/vr6WlFR8fT6PRunve0tLSGTNmwOWhQ4eyWKyGhgbhwXRKS0sNDQ3x1aFDh5aVlQEA6urqDhw4EBYWJqYvDI/Ha2xshDPbQmPHjoW11QKBAJ8ZWkp0vORnz579+OOPYWFhAAASibR69ept27aNGDECAIBhGBxW5fMFr1eqHlNL26da8IGkA+lbMjLi7o8hcQm6pKRk1qxZPcjOAIC2tjYikQiX4YxZLS0twgm6tbVVuMcwiUSCtSj/+9//vv76az09PTEJGqb7gIAAvIRIJGppacHT4q8rJTgcDvxLCgSCBw8e/PzzzykpKQAAFRWVtWvXbtq0Cb6D7SqpPl8cDkcgEMjKyko6kP4jbZ9qgUDA4XC6kr8+ayQS6aOjJojbbGNjk5yc3LPXptFocDhKAEBtba2srCxMoMI7hIeH46s1NTU6Ojp5eXlBQUH6+vp79uwpKipqaGjYs2fP3r17241xqqamZmRk1LHaBADA5/M7azEyWAkEAnl5+b///vv777/Pzs4GANBotK1bt27YsEFNTU3S0fU+AoFAIpGkKkFL26daIBDIyMhI1SV3Rtx31LZt296+fXv58uUe/Ch2dnaOiIiAyxEREWPHjm33XeHs7JyYmMhmswEAVVVVb968GTNmDIVCOXjwIJVKpVAoZDJZRkaGQqFI1Y/Z7uJyuTdu3LCwsFi9enV2dvawYcN+//33t2/f7t69e1BmZwSRLlgHjo6Ooz8wNTUFANBotNH/defOnY4HCquoqKBSqQcPHoQV2fj+Y8aM8fPzg8szZ86cO3cu7Gfs7e3d7gwPHz4cNmyYyJOnpKSMGjVK5Kbm5mbxgQ0abW1tFy9eNDIygu+jqanplStX2traJB1Xn2Oz2TweT9JR9Cvp+VRDfD6fxWJJOooBQUQVh5GRERz5F7Kzs+u4z0fnVaHRaK9evTp37tzLly+vXLkye/ZsWL5u3bpRo0bB5X/++efXX399+PDh/PnzfX19253BwsKiZx1kBj0ej3f9+vVjx44VFRUBAMzNzQ8cOLB8+XKp+tWPINKAgH2Gz/RTU1N9fHzgo7B2GAzGIO6vLBAIbt26dfjw4fz8fACAhYXFgQMH5s6dK1XzkLW0tEhbHfTg/lR3BB8SojpoIL4OGhlQ7t+/b2tr6+npmZ+fb2pqeuPGjczMzJUrVw76h91Iz0RERHxKR9y///67tbX1UwJ49OhRZWXlp5zh07W1tYnZymQyRbY1GDjEteLIzMz866+/Dh8+DNvJHTx48MyZM2Qy+ciRIz4+Pv0VIQLCw8P37t0bFxcHABg2bNiBAwe8vLzQtCaIGGVlZe/evXN1de3xGebNm+fn57dly5aeHZ6dnc3hcGATz7t377a2tvJ4PCqV2q4H8uvXryMiInR1dRsaGtatWwcA2Lp1K51OV1RUpFKpp06d6thGoKSkJCAgwNTUtLi4ePPmzcI3KEwm89SpUyNGjMjLy9uwYYOMjMyoUaMsLCzg/HxOTk6vXr2Sl5cnEolmZmbffPMNmUzW1dUNCwtzc3Pr2WX2OTH10998883EiRPhMuz1sGTJklWrVhEIhKysrP6oIe+E9DwkTEtLmzlzJnynaDTa2bNnW1tb2+3DYDAkEpukoIeEXbF79+6WlpZPfN0zZ868ffu2Z8du27aNz+djGFZbW7ts2TJYuGbNGjqdLrzbjBkzuFwuhmF//PFHcHAwhmE///zz5cuX792719m77OHhUVdXh2FYSEjI77//LrzJ19c3KCgIw7DY2NivvvoqLi7uypUrsbGxSUlJP/30U1ZW1qFDhy5duhQZGSkQCPCjtm7d2rNr7Afifh0XFhbiE4PCr6yAgIDr1687OTkN8N8Fg0BxcbGXl5e9vX1oaKiamtp333335s2bTZs2wV8zCCJGa2srg8EQ7tBfWFgIF5hMJtb5Y6fW1taEhAR8HqWZM2cKdwfruoaGBiKRCO9tnz9/rqurC8u1tbWFB9ih0+l1dXXwt6ChoSGcG0RTU9Pb23v69OkiHzO0tbXFx8dTqVThQ3BPnz6F/ZOHDx/++PFjGo3m7e3t7Oysr69vaGhoZWU1bNiwNWvWTJgwQfjG3MDAICsrqweX2Q/E/UzG6+kxDHv69Om8efPgX9zc3Bx2y0b6QlNT0/Hjx3/99VcOhyMvL79x48Z9+/ah+QCRrsvIyDA2NsZXmUzml19+GRkZCQBYtWqVn5+fyO7B7969u3Tp0v/+97/t27efPn1aRUXF1NQ0LS2t3W7R0dEde6WqqamNGTMGX42Li7O2tobLJSUlysrKcJlMJpeUlOC7CW9SUVEpLS0FAJSWlj569IjBYJSUlHRsx1VbW4vXaeCH4DQ1NWGlM5/Pp9Ppenp6MBFfvXr166+/BgDk5OQ8fvy4pqaGx+OtWbMGHmVnZxcbG4sHPKCIS9BDhw6Ni4vDMCw+Pv7t27fTp0+H5dXV1RYWFv0SnnThcrnnz58/fPhwbW0tgUDw9PT87rvvhEcsQZCuqKioEP5Gj42NdXZ2BgDw+fyysrLOBm/YvHlzQEAAvCdLTEx0c3MjEAgdnxOOHz/+owHQ6XT8VeCkEFC7E7bbBPP+5s2byWQyh8Px8PBwcnJqN1i5yENwBw8efPTo0dixY1+/fg0AgKN5JCUlycnJwUyNd0u2sbFxdXWFX2Pq6ur4SG0DjbgqDm9v7+joaAcHh0WLFhkaGk6ZMgUAwOVyk5OTzc3N+ytCafHo0SNbW9vNmzfX1ta6uromJCTcuHEDZWekB9pVYkRERMCnhampqXgvhHays7OHDBkCs3N6ejqeXsXUh3QxAE1NTQaDAZcZDIaGhga+SUNDo92mxsbGe/fuwRJ4g9juzB0PEd46Y8aMFStWPHjwQENDw9DQENYHXr16Fd4dv3v3Dh9eQldXV3gci55dZj8Ql6AdHBweP35saWk5e/bs0NBQWKWVmJior68PkzXSK3Jzc2fNmjVnzpycnBxTU9OgoKDw8HA0WyvSYzQarb6+Hl99+fIlzMsvXryYNGlSQkICg8Fo1wAuLCwMJvG8vDxVVVUrKysAAIZhHQcWjomJed4BnKMHp6Ojgwcwfvx44WF5XFxcmExmbW0tAMDMzAxvjFRbWztu3LiioqKMjAxYUl9fb25uzuPxhBsLKisrm5iYwPtoeAiGYcXFxfhVMJnMefPmFRcXr127FhZGR0cPGTIEAJCUlAQnrAAA1NXVmZmZ4ct4LflA85GmWtOmTZs2bZpwiYuLS1JSUl+GJEWam5uPHDny66+/crncIUOG7N+/f/PmzegxIPKJRowYce3aNbjMYrFycnIiIyO1tbWrq6s1NDSam5v9/f1DQ0NDQkLwQyIiIiZPnpyUlHTt2rWbN2/CwoKCgo4diceNG/fRAMaOHXvq1Cm4bGlpqaGhkZ+fLycnRyKRxo4d++uvv8J5JGRlZX18fIKCgtzc3KKjo3/88UdVVdX09PTi4uLMzEw1NbUFCxbEx8cvXry4tLQUr3reu3fvpUuXvvjii3v37m3btq2iomLChAnv3r2TkZHJzMzU0dEhkUgxMTHHjh2D+9fV1cFqjXnz5l2/fp1Op4eHh8+aNQtvAZGWlobX3w44Ems/8gkGQTM7gUBw9epV+ENSVlZ2/fr1NTU1PTsVamY36PXgU71z5044MMuzZ8/27NlTUVHR1NSEYRj+MXv+/Dm+s0AgGDNmjEAgKCsrE25/dvr06fz8/J7FvGXLFuFTZWVlJSQkCJfgysvLX758yeFw4Cqfz3/16lViYiK+Q3h4eLt3vKamJiIiQuSfJTk5OT4+HrbwgzIzM/HV1tbWmJiYN2/eCB/i6+vb7cvrLyhBS0Bqaip+GzJ+/PiUlJRPORtK0INeDz7VBQUFN27cwDBs3759T58+bbeVzWY/evQIX83IyFizZk27fVgs1vfff9/9YN9LSkp68OBBz45tN1jSR4dm+xRxcXEhISF9d/5PhHoJ96vm5uatW7c6ODjExMTQaLRr165FRkZ29twGQXrMxMSESqUWFRVZWlp2bHfBYrGEf9QLBIL169e32ycgIOB///tfjwMYPXo0h8P59K7era2tfdfNj8Fg5OXliZ9eVbLQYEn9JzAwcNu2bXQ6XU5OztfX9/Dhw70yZDOTyYQ9WaUEGixp0EODJeHQeA794e3btxs3bgwNDQUAODs7nzt3Dn9AgSAI0hlUxdG3eDzejz/+OGLEiNDQUCqVeuHChejoaJSdEQTpCnQH3YeSk5N9fHzg7Leenp6nTp1qNzEjgiCIGOgOuk+0tLR8/fXXTk5O6enpxsbGT548uXHjBsrOCIJ0C7qD7n1RUVFr1qx58+aNrKzsjh07jhw5gh53IAjSAyhB9yYWi7V3797ffvtNIBDY2NhcvHhReIgvBEGQbkEJutdERkauWbOmsLCQSCQeOHBg3759RCJR0kEhCPIZQwm6F7S0tOzbt+/MmTMCgcDOzu7q1auonQaCIJ8OJehPlZiY6OXllZubKycnt3///v3796MbZwRBegVK0D3H4/GOHz9+9OhRHo9nbW3t7+8/evRoSQeFIMjggRJ0DxUUFHh5ecXFxcnIyOzcufPo0aPCU8AhCIJ8OpSge+Ly5ctbtmxhMplDhw719/f/lMntEQRBOoM6qnRPQ0PD0qVLfXx8mEymp6fn69evUXZGEKSPoDvoboiKivL09CwtLVVVVf3jjz88PT0lHRGCIIMZuoPuEj6ff/ToUTc3t9LSUmdn57S0NJSdEQTpa+gO+uPodPqqVavCw8NlZGT27t17+PBhfKZLBEGQvoMSzUc8e/Zs1apV1dXVNBrt+vXrU6dOlXRECIJIC1TF0Sk+n3/w4MGZM2dWV1dPnTo1PT0dZWcEQfoTuoMWrbq6euXKlS9evJCVlT18+PD+/fvxWd8RBEH6B0rQIsTGxnp4eJSXl9NotJs3b06ePFnSESEIIo3QXWF7Z86ccXV1LS8vnzhxYkpKCsrOCIJICkrQ/2Kz2atWrdq6dSuPx9uxY8eLFy90dHQkHRSCINILVXG8V1RU5O7unp6erqKicvny5SVLlkg6IgRBpB1K0AAA8Pz582XLltXX15uZmd27d8/KykrSESEIgqAqDgBOnz49a9as+vr6efPmJSQkoOyMIMgAIdUJurW19Ysvvti2bRufz9+/f39QUJCampqkg0IQBHlPeqs4qqqqFi1a9OrVK2Vl5atXr6JKZwRBBhopTdDp6enz588vKSkxNDS8f/8+mkIQQZABSBqrOIKDg8ePH19SUuLi4hIfH4+yM4IgA5PUJehffvnF3d2dyWR6eXmFhYVpa2tLOiIEQRDRpChB8/n8zZs3b9++XSAQfPvtt/7+/vLy8pIOCkEQpFPSUgfNYDA8PDxCQ0MVFBT8/f09PDwkHRGCIMhHSEWCptPpc+bMSUtL09LSun//vpOTk6QjQhAE+bjBn6CzsrJmz55dUlIyfPjwR48emZmZSToiBEGQLhnkddBRUVETJkwoKSkZN25cfHw8ys4IgnxGBnOCvnv37vTp0xsaGpYsWfL8+XN1dXVJR4QgCNINfZigCwoKFi5caGVltXr16urq6o47cDic7du3W1tbT506NTo6GhZmZWUtXrzYxsZm9OjRW7dubWxs7Nmr+/n5eXh4cDicTZs2BQQEKCgo9PxKEARBJKGvErRAIJg7d66NjU1ISAiJRPLy8uq4z/79+9PS0u7du7d69eq5c+fW1dUBAGRkZFauXHnr1q3z589nZmZu2LChB69eXl6+ceNGgUBw/Pjxs2fPotmqEAT5LGF94+nTpzo6OgKBAMOwxsZGEon05s0b4R1aW1uHDBkSHx8PV6dNm3bq1Kl2JwkKCjIxMel48pSUlFGjRol83ebmZgzDeDzewYMHAwICPv1CBj4GgyHpEPoVm83m8XiSjqJfwU+19ODz+SwWS9JRDAh9dWuZmZlpb29PIBAAAGpqaiYmJpmZmcI7lJWVNTU12dvbw1UHBwd8Bz6fX1RUFBkZeebMGW9v72697qlTp1pbW+FMr9LQ2Lm8vPzatWuSjqJf3b9/v91nadA7ceIEhmGSjqL/5OXl3b59W9JRDAh91cyupqZmyJAh+CqFQmlXDV1TU0Mmk+Xk3gcwZMiQjIwMuNzU1OTh4VFXV6eioiJykLm6urrs7GwjIyO8ZPfu3Z6engCAc+fOrVy5kkaj9foVDUwpKSm3bt1avXq1pAPpP8HBwXV1dcbGxpIOpP/89NNPO3bsIBKJkg6kn8TFxd2/f9/d3V3SgfQtBQWFj76nfZWg1dTUWCwWvspgMCgUSrsd2Gy2QCCAFcRMJhPfgUqlJiUlAQB+/fXX2bNnFxYWwjtxnLq6uomJSXBwMFwlEAj6+vrwUgkEAplMVlFR6aPrGmiUlJRkZWWl53oBAEQiUUFBQaouGQCgoqIiPQlaUVGRSCRK21ssUl9VcRgZGeXn58Pltra2d+/eCd/wAgD09fVlZGSKiorgal5e3rBhw9qdZPHixW/fvm1ubu54fhKJZPyBkZGR9Hx2EQSRHn2VoOfOnVtRUfHkyRMAwKVLl/T19UePHg0ACA0N9ff3BwCQyeRFixadOnUKAJCXlxcaGrpq1SoAQHJyclNTEwCgra3tzJkzVlZWaJYTBEGkU19VcSgpKV27ds3b21tWVlZBQSEgIACWJyYm5uTkwEd/J0+edHd3p9Fora2t3333HezmFx0d7ebmpqCgwGQyx4wZI/JZAYvFyszMpFKpHTc1NTVZWVm1qxIZxHg8HofDEfmnGKzYbPadO3d27dol6UD6D4/Hk6pxcblcbltb26D/VG/YsOH48ePi9yH06dNhPp/f3Nzcrva5naamJkVFRRKJJFzY0NBAJpPFVFxUV1eL3Nra2iptg4hK2yW3tbURiUTp+Q4G0vcWYxjG5XLb5YTBR0lJ6aNva98maARBEKTHUBc7BEGQAQolaARBkAEKJWgEQZABavAM2I9h2N27dxMTE42Njb/44otB+YSBz+dHR0fHxMS0trY6OjrOnj0blufk5ERFReG7ubu7a2hoSCjGXpaRkfHq1St8ddmyZbDZJYZhd+7cSUpKGj58uLe396B5uwUCwcWLF4VLbG1tHR0dGxoahFs0jRs3ztraut+j601lZWVJSUnV1dUrVqwQ7pOSlpZ29+5dBQUFLy8vfX19WMjlcv39/d+8eWNvb7906VLpeUQ8eO6gv/322wMHDtBotFu3bonsID4IhIaGbty4sbm5mUQi+fr6btq0CZZHRUWdOHEi+YOWlhbJxtmLnj17dvLkSfzSWltbYfm+ffu+/fZbGo32119/LVu2TLJB9q5kIZs2bcrOzgYA0On0bdu24eU1NTWSDvOTlJeXW1lZnTx5cv369bW1tXh5bGzspEmTSCRSZWWlg4NDVVUVLPf09PT399fR0Tl27Nju3bslFLUkSHCgpl7U3Nysqqqanp6OYRiLxVJVVU1LS5N0UL0Pdo6Hy3FxcUQikcPhYBh2/vz5JUuWSDS0vnLy5MkvvviiXWFjYyOZTM7KysIwjMFgkMnkjIwMSUTXt2JjY8lkMhzKLjMzU0dHR9IR9Ro+n8/n8zkcDgCgqKgIL58/f/6xY8fgsru7+5EjRzAMy8nJUVJSamxsxDCsoKBASUmpvr5eImH3v0FyB52cnKysrGxjYwMAUFJSGj9+fHh4uKSD6n2Kior4jzsej0cikfDRpkpKSk6ePHnz5s0eT3EwYBUVFZ08efLWrVtMJhOWJCUlUSgUKysrAACZTHZxcRmUb/elS5eWL1+O//zncDhnz569dOnS27dvJRvYp5ORkRE5Snt4ePiMGTPg8vTp0yMiIgAAL1++dHR0hFVbJiYmOjo68fHx/RisJA2SBF1RUaGlpYWvamtrV1RUSDCevsblcnft2rV9+3ZZWVkAgKqqqrGxcVVV1ZUrVywsLAoKCiQdYK+hUChDhw6trKz08/OzsLAoKSkB0vF2s1iswMDANWvWwFU5OTlnZ+eSkpIXL17Y2Njcu3dPsuH1BRaLxWAwNDU14aq2tjadTgcA0On0dm83LJcGg+QhoZycnEAgwFd5PN4gHj6Jz+d7eXlRqdQDBw7AkuXLly9fvhwue3t7Hz58+MaNG5ILsDd9+eWXX375JVxevHjx8ePH/fz8pOHtDgwM1NXVdXJygqvm5uYPHz6EyxcuXNixY8eiRYskF12fkJOTIxAI+DuLv63t3m4ulzv43u7ODJI7aF1dXTqdjn3oFUmn03V0dCQbUh8RCARr166tra39559/RH5MJ06c+ObNm/4PrB9MnDixsLAQSMfbfenSpbVr14psrjBhwoTi4mIej9f/UfUpeXl5CoWC3x3T6XRdXV0AgJ6eXnl5Ob5bRUUFLJcGgyRBjxkzRk5ODtZYVVZWvnr1Cm+CNphgGObr6/vmzZt79+4JT4Pb1taG7/D48WNYOTs44JcmEAhCQ0PhpTk6OsIWhwAAOp2ekJAwyN7u/Pz8hIQEOL4jhP8dAACPHj0yNTXFHz8MJvPmzbtz5w740Gp27ty5AIAZM2akpKTA2q24uDg2m+3i4iLhQPvLIHmPSSTSsWPHVqxYsXDhwrCwMB8fn3bDTw8O9+7d8/Pzc3Z2xn/e+vv76+rqzpkzh0gk6ujopKSkMJnMsLAwycbZiyZPnkyhULS1tRMSEvh8PhyrVl5e/tixYx4eHgsWLHjx4sWGDRuGDh0q6Uh706VLl+bOnSs8MdC3334bHR1tampaWlqanJwcGBgowfB6xaJFi+BQ76tXr1ZUVAwJCZGXl9+zZ8/EiROrq6urq6vr6+vhsJd6enqbN2+ePHnytGnTgoODjxw5oqioKOnw+8mgGiwpKysrMTHR1NR03Lhxko6lT1RWVrabjm/cuHGKioqVlZWJiYl1dXUGBgYTJkwYNL02AADl5eVJSUkNDQ2GhoYTJkwQvm3MyMhITk42MzMbfPdTiYmJ2trawt86DAYjLi6uvLxcU1PTxcVF/AiRn4WIiAjhWprJkyfDJ961tbVPnz5VUlKaMWOGcCJ+9epVXl6evb09bKwlJQZVgkYQBBlMBkkdNIIgyOCDEjSCIMgAhRI0giDIAIUSNIIgyACFEjSCIMgAhRK0VMAwLD4+/vr161evXpV0LL0jLi7u2rVrvXjC169fS6p//PPnz+GYohLX2tp64cKFnJyc7h5YVlZ279491CSs90lsHD2kvwgEgvnz58vJyRkZGdna2ko6nI9raWk5f/58bm6umH127typrq7eiy96+PBhEonUiyfsorS0NBKJlJ2d3f8vnZmZef78+ba2Nrykvr4eAHDu3LnunqqxsZFKpd6+fbtXA0QGy3CjiBipqanBwcG3b98uKipKS0uTdDgfx2Aw1q9fD3ty95vJkycfPny4P18R2rNnj7u7u6WlZf+/dFhY2Pr16/E5ED6Fmprapk2b9uzZw+fzP/1sCA4l6MGvuLgYANBxhqS2trbKykox069wudzKykoul4uXMBiMyspK4aHFhDGZTJFb+Xx+dXV1Z/91ORxOVVWV8FgT3VVbWyscpDAWi1VZWSlmXCG4AwBgwoQJe/bs6fqL1tfXi5/WpLa29qMXVVhY+OTJky+++KLjJgzDqqurhc/A4/Hq6upEnofP51dWVuLjZYvcoaamButOFQSHw2loaBC5ic1mV1VVtfurrlmzpqio6PHjx11/CeTjJH0Lj/SthQsXKisrAwDU1NQoFMr+/fsxDONwOJs2bYLlcnJy8+fPLy8vxw8xNTXdt2/f3r174VDxISEhGIaFhYXZ29vDz4y2tna7X8EvX74cO3YsHHpNXl5++fLlsDwiIsLZ2Rn2z5aXl588ebJwxUVycjI+nCaBQBg1alRlZWV+fv6QIUMAAEpKShQKhUKhXLlypeN1wSqOmJgYCwsLAACJRFq2bBmbzcZ3yM3NdXNzg6PCDxky5MCBAzweD26Kjo6mUChBQUGzZs2SkZFRUFDAMOzUqVOGhoZwh61bt1I6CAwMhFsfPnwIXxQAYGRkFBAQgL/oDz/8oK2tnZSUNHLkSAAAkUhcsGABnBJFpP3796uqquKBYRj2f//3f2PHjg0ODobT8SkpKZ06dUogEBw/flxVVRUAoK+vHxERge/P5/OPHDlCpVLh33DixImZmZn41qlTp3p6ev75559wjkoVFZWjR4/CTSdOnFBSUoJ/HHiBjY2NsIrjzJkzGzZsgAMGGBoaPnnyBD/hkydP8Jt9OTk5FxcX4csZPXr0YJ3ZR1JQgh7kkpOT4bDR/v7+z549y8/PxzDM09NTTk7uxIkT6enpN27coFKplpaWLS0t8BBNTU0tLa3x48cHBwe/fPny7du3kZGRRCJx4cKFkZGR6enpe/fuJRAI165dg/tHRalORjgAAAoISURBVEURicQxY8aEhIRkZWU9fPhw8+bNcNOtW7eOHDkSGRmZk5MTFBRkYWFhbGwMKz0FAoGBgYGrq2tMTMybN2+ioqIOHDhAp9OZTOY///wDANixY8ezZ8+ePXtWVlbW8bp27typoKBgZmZ25cqVpKSkEydOEAiEH374AW6tra3V1dU1MDC4d+9eamrq7t27CQTCzp074VY46qG2tvaWLVsiIiKCg4Ox/9ZBZ2dnPxMye/ZsGRmZ6OhoeLGysrKTJ0+OjIyMiYmZO3cugUB48OABPPDQoUOysrIWFhYXLlxISkr65ZdfZGVl4ZeiSC4uLlOnThUu8fb2VlNTs7S0vHPnTnx8/IoVKwAA69atc3Nze/78+cuXL+3t7XV1dfE3C76527dvT0lJCQ4ONjIy0tTUrKyshFsdHR21tbVHjx4dEhISFxcHh8eLjY3FMKywsNDX1xcAEBwcDC+Ty+XCBE2j0by9vSMjI589e2ZjY0Oj0VgsFoZhdXV1ysrKHh4eSUlJ+fn5YWFhW7duFQ7e19dXXV2dz+eL/0wiXYcS9OAHRz4rKCiAqwUFBcLZCsOwu3fvAgCuXr0KVzU1NTU0NITv+5ydne3t7YVv9JYsWTJy5Ei4PG7cOF1dXSaT+dFIEhMTAQBRUVEYhsE5UPDbUmHV1dUAgIsXL4o51c6dOwEAoaGheMmUKVOcnJzg8g8//AAAiIuLw7euXLlSXl6+trYW+5Cgvby8hE/Y2UPCgIAAAoHwyy+/wNVZs2ZpaGjgF9vW1mZoaOjg4ABXDx06BAAQfla2cOFCa2vrzq6CTCZv3LhRuASO35aamgpXm5qaiESitrY2g8GAJc+ePQMAvHz5EsMwJpOppKS0ePFi/PDU1FQCgXDw4EG46ujoSCaT8Xzd0tKipqa2a9cuuPrrr78CAPAzYx8eEk6cOBEvgSMjvnjxAsOwmJgYAEBSUlJnlwNPWFpa2tkOSHehOmipA6fWFZ4Je8GCBQoKCi9fvsRLpk+fjk+F19TUFB8fb2lpGR4e/vwDbW3t3NxcLpfLZDJfvXq1fPlyWGHSUVFR0U8//bRly5b169f/8ccfAAA4n4Cmpqa+vv7u3bt//vnnns0wQCQSp0yZgq9aWVmVlpbC5bS0tGHDhjk6OuJbly1b1traKjyX3fz58z/6EtHR0V5eXmvXrt26dSt+5rlz5+IXSyQSFy9eDEd5hSUEAmHmzJkio2qnpaWFyWTC2glh2tradnZ2cFlVVVVHR2fcuHFkMhmWmJubAwDgOQsKCthstvBbaWdnZ25uHhkZiZfY29tra2vDZQUFBSMjo87iwQnHDys04CGmpqbKyspr1qw5d+6c8Aj6OHV1dQAA/H5FegVK0FIHPjMUnpNCRkaGRqMJP4DC/0sDAGpqagQCQVBQkIeQmzdvksnkurq6hoYGgUAAK0w7+uOPP8zMzAIDA1tbWykUCkxGTU1NAABZWdnHjx+bm5vv27fP1NTUxMTk999/79aFqKqqCo8+Ki8vjz9SKykpaTfHip6eHgBA+BqFR1sWqaioyN3d3c3NDX6vgA+PVdudWVdXVyAQ4M/TiEQinkwBACQSqbNHhXCGp47PTtsNJUoikYRLYNUwPCd8KzteaW1tLb7a7gtA+K/UGeGXk5eXBwDAlh6ampqPHj1SUVHZtGmTvr6+ra3t7du3hQ+Ej2qlZz6qfoAStNSBd3/tWiDU1NTAWZMh4RmX4bOp3bt313dAo9HU1NQIBEJVVZXI1zp06NDq1asTExP9/PxOnDixadMm4a0jRox4/PhxXV3do0ePbG1tN23aFBAQ0FvXKJykwIfbOuFrFDmbFK6urm7WrFna2tp///03/jVAJBJJJFK7M9fU1BAIBPhX6hYikUihUNqdrVtEvpXV1dXCl9m7Jk6cGB0dXVNTc+fOHQqFsmzZMuEfJfD7T/jbHflEKEFLHdhwAp+BFAAQFhbGYrGcnZ1F7q+lpWVpaXn37l2RjdVUVVXt7Ozu3bvXsaEbk8msqakZPXo0XvLo0aOOZyCTybNmzbp9+7aKikpcXBwsAQCIaf/3UU5OToWFhbm5uXhJSEiIrKzsmDFjunJ4W1vb0qVLmUzmo0eP2uV0R0fHJ0+e4BeLYdjDhw8tLS17lhPHjBmTkZHRgwMhe3t7Eokk/FYWFRVlZ2d39la2A2uxevB3plKp7u7usPlKQkICXv769ethw4YJz8CNfCKUoKWOra3tjBkzTpw4ERgY2NTUFBMTs27dOj09PU9Pz84O+f7779PT05cvX56RkdHS0lJSUhIYGIjPKX7kyJGCgoKlS5dmZWWx2ezc3Nyff/4ZAEAmk4cPH37x4kVYVRoYGPj999/j58zJydm5c2dycjKLxWKz2VevXmUwGDCbKyoqGhsb37x5Mzw8PDk5WXxzY5G++uorFRWVlStXpqenNzY2+vn5/fnnn6tXr+7i3LKbNm2Kjo4+e/Ysl8st+gDWMu/cubOkpMTHx6ekpIROp/v6+mZmZn799dfdjRCaNm1aamoqm83u2eFUKtXHx+fatWu//fZbQ0NDRkbG8uXLFRQUNm7c2JXDYdP4kydPvnr1Kjk5+aN9TMLDw48cOZKZmcnhcJqamvz8/AgEAt74EgAQGxs7derUnl0LIpqEH1Iifa9dKw4Mw+rq6ubPn4//xre1tRVuPKupqbljx452J7l9+7ahoSH+scGbVEN///23cJXupEmTYHlkZCRe2a2jowPv9U6fPo1hWH5+/vDhw/FDlJSUvvnmG4FAAA8MCwuzs7ODE+P6+fl1vKiOXb137typqamJr0ZHR5uYmMCTy8jIeHl5wbZi2IdWHDExMcKHC7fiEL7rx924cQNuPX/+PGypDQBQVlb+6aef8JMcOnSoXVOQQ4cOwXbWIlVXV8vLy9+8eRMv8fb2trCwEN7HxMTEx8cHX4Xdai5fvgxXORzO2rVr4WRRAAAjI6Pw8HB8Z0dHx4ULFwqfzdHR0d3dXTg8fX19eHhDQ0PHrt6w5Pz58xiGvXz5UvjRBZVKPXv2LL5nUlIS+G/LGeTToSmvpFdFRUVpaSmVSsUTmXgYhhUUFDQ2NmpoaAwdOrTdrNJ8Pj83N5fFYhkYGAjfqLa1teXm5hIIBEtLy44TUVdVVZWVlSkoKAwbNqyzdiA9hmFYXl5ec3OzsbEx7KkhfmcMw4Qr38VobW3Nycnh8/lWVlafOIHpmjVr3r1794nz/NbX179584ZMJltYWHTxEnqsrKyMTqerqKgMHz5cePbL//u//3v9+jVsiof0FpSgEUSS6HS6mZlZSEiIq6urpGPpudLSUlNT0xcvXgzW+ZolBSVoBJGwiooKeXn5jg2iPyMMBqO+vl64EgzpFShBIwiCDFCoFQeCIMgAhRI0giDIAIUSNIIgyACFEjSCIMgAhRI0giDIAPX//gFeTLMg508AAAAASUVORK5CYII=\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sMax    = 120                                #make forecasts for many horizons and initial values\n",
    "s_range = 1:sMax                             #different horizons, months\n",
    "r₀      = [0.03,0.05,0.07]\n",
    "\n",
    "xPred = [AR1Prediction(r,ρ,μ,s) for s in s_range,r in r₀]  #xPred[maturity,r₀ value]\n",
    "\n",
    "txt = text(L\"(\\mu,\\rho) = (%$μ,%$ρ)\",8,:left)   #laTeX string to plot, notice %$\n",
    "p1 = plot( s_range,xPred,\n",
    "           linecolor = [:black :red :blue],\n",
    "           linewidth = 2,\n",
    "           linestyle = [:solid :dash :dot],\n",
    "           label = [\"3%\" \"5%\" \"7%\"],\n",
    "           title = \"Forecast of short interest rate\",\n",
    "           xlabel = \"forecast horizon (months)\",\n",
    "           ylabel = \"short interest rate\",\n",
    "           annotation = [(80,0.038,txt),\n",
    "                    (15,0.068,text(\"(based on different values\\nof current short rate)\",8,:left))] )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Vasicek Model\n",
    "\n",
    "The simpified (because of no risk premia) Vasicek model implies that\n",
    "\n",
    "$\n",
    "y_{t}(n) =a(n)+b(n)r_{t} \\: \\textrm{, where }\n",
    "$\n",
    "\n",
    "$\n",
    "b(n)     =(1-\\rho^{n})/[(1-\\rho)n],\n",
    "$\n",
    "\n",
    "$\n",
    "a(n)     = \\mu\\left[  1-b(n)\\right].\n",
    "$\n",
    "\n",
    "In the example, $y_{t}(36)$ which corresponds to `y[36]` in the code, is the (annualized) continuously compounded interest rate for a bond maturing in 36 months (3 years).\n",
    "\n",
    "In the cells below, we code a function for this model and then plots the results for many different maturities (horizons) and several initial values of the short interest rate.\n",
    "\n",
    "### A Remark on the Code\n",
    "\n",
    "The code (used below)\n",
    "```b = ρ == 1.0 ? 1.0 : (1-ρ^n)/((1-ρ)*n)```\n",
    "is the same as \n",
    "```\n",
    "if p == 1.0\n",
    "    b = 1.0\n",
    "else\n",
    "    b = (1-ρ^n)/((1-ρ)*n)\n",
    "end\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Vasicek"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "    Vasicek(r,ρ,μ,n)\n",
    "\n",
    "Vasicek model: calculate interest rate and (a,b) coeffs\n",
    "\n",
    "# Input\n",
    "r,ρ,μ,n: scalars\n",
    "\n",
    "n is the maturity, but this could be measured in any unit (months, years, etc),\n",
    "but changing the units require recalibrating ρ\n",
    "\"\"\"\n",
    "function Vasicek(r,ρ,μ,n)\n",
    "    b = ρ == 1.0 ? 1.0 : (1-ρ^n)/((1-ρ)*n)   #if-else-end\n",
    "    a = μ*(1-b)\n",
    "    y = a + b*r\n",
    "    return y,a,b\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1ma and b for the first few horizons (months):\u001b[22m\u001b[39m\n",
      "horizon     a*100         b\n",
      "1           0.000     1.000\n",
      "2           0.062     0.988\n",
      "3           0.124     0.975\n",
      "4           0.184     0.963\n",
      "\n"
     ]
    }
   ],
   "source": [
    "y = fill(NaN,sMax,length(r₀))         #interest rates, different starting values in columns\n",
    "ab = fill(NaN,sMax,2)                 #a and b coefs\n",
    "for n in s_range, j = 1:length(r₀)\n",
    "    #local a, b                      #local/global is needed in script\n",
    "    (y[n,j],a,b) = Vasicek(r₀[j],ρ,μ,n)\n",
    "    if j == 1\n",
    "        ab[n,:] = [a b]                 #update ony if j==1, the same across r₀ values\n",
    "    end\n",
    "end\n",
    "\n",
    "printblue(\"a and b for the first few horizons (months):\")\n",
    "printmat([ab[1:4,1]*100 ab[1:4,2]];colNames=[\"a*100\",\"b\"],rowNames=string.(s_range[1:4]),cell00=\"horizon\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( s_range,ab,\n",
    "           linecolor = [:black :red],\n",
    "           linestyle = [:dot :solid],\n",
    "           linewidth = 2,\n",
    "           label = [L\"a(n)\" L\"b(n)\"],\n",
    "           title = \"Vasicek model: coefficients\",\n",
    "           xlabel = \"maturity (months)\",\n",
    "           annotation = [(80,0.2,txt),\n",
    "                    (25,0.95,text(L\"y(n) = a(n) + b(n)r\",8,:left))] )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p1 = plot( s_range,y,\n",
    "           linecolor = [:black :red :blue],\n",
    "           linewidth = 2,\n",
    "           linestyle = [:solid :dash :dot],\n",
    "           label = [\"3%\" \"5%\" \"7%\"],\n",
    "           title = \"Vasicek model: yield curves\",\n",
    "           xlabel = \"maturity (months)\",\n",
    "           ylabel = \"interest rate\",\n",
    "           annotation = [(80,0.038,txt),\n",
    "                    (25,0.069,text(\"for different current short rates\",8,:left))] )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hedging Using the Vasicek Model\n",
    "\n",
    "The change of the (value of the) overall portfolio is \n",
    "\n",
    "$\n",
    "\\Delta V=v\\Delta P_{H}-\\Delta P_{L}\n",
    "$\n",
    "\n",
    "The code below follows these steps:\n",
    "\n",
    "A. For an initial value of the short log interest rate $r$, use the Vasicek model to calculate all spot rates needed to discount the cash flows of the both the liability and hedge bond. Repeat for a somewhat different short rate.\n",
    "\n",
    "B. Calculate the prices of both the liability $P_L$ and the hedge bond $P_H$ at both yield curves and also the changes ($\\Delta P_{L}$ and $\\Delta P_{H}$).\n",
    "\n",
    "C. Calculate the $v$ value that makes $\\Delta V = 0$, that is, $v=\\Delta P_{L}/\\Delta P_{H}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bond Pricing Functions\n",
    "\n",
    "The next cell codes up functions for price of a zero coupon bond and a bond portfolio, based on continously compounded interest rates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "BondPrice3b"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "    BillPrice2(y,m)\n",
    "\n",
    "Zero coupon bond price as a function of (y,m). m is typically measured in terms of years.\n",
    "\"\"\"\n",
    "BillPrice2(y,m) = exp(-m*y)\n",
    "\n",
    "\n",
    "\"\"\"\n",
    "    BondPrice3b(y,cf,m)\n",
    "\n",
    "Calculate bond price from continously compounded interest rates, cash flows and time to cash flow.\n",
    "\n",
    "y:  scalar or K vector of continuously compounded interest rates\n",
    "cf: K vector of cash flows\n",
    "m:  K vector of times (years) of cash flows\n",
    "\"\"\"\n",
    "function BondPrice3b(y,cf,m)                #cf is a vector of all cash flows\n",
    "    if length(cf) != length(m)\n",
    "        error(\"BondPrice3b: cf and m must have the same lengths\")\n",
    "    end\n",
    "    cdisc = cf./exp.(m.*y)\n",
    "    P     = sum(cdisc)                      #price\n",
    "    return P\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Information about the Two Bonds\n",
    "\n",
    "In the example below, the liability pays 0.2 every 12 months for 10 years. The hedge bond is a 3-year zero coupon bond.\n",
    "\n",
    "### A Remark on the Code\n",
    "For the liability we define the periods (months) that we will consider as `1:120`, but the cash flows as `repeat([zeros(11);0.2],10)`, which means that the cash flows are zero in most periods, but 0.2 in period 12, 24,..., 120."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "nL  = 1:120                       #months, for the liability\n",
    "nH  = 1:36                        #same, but for hedge bond\n",
    "\n",
    "cfL = repeat([zeros(11);0.2],10)   #cash flow of liability\n",
    "cfH = [zeros(35);1];               #cash flow of hedge bond, 3-year zero-coupon bond"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A. Calculate Yield Curves\n",
    "\n",
    "at two different values of the current short rate: $r_0$ and $r_1$. This is similar to the previous figure on the Vasicek yield curves, but here for the horizons that we need in order to (later) calculate the prices of the liability and hedge bond."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[31m\u001b[1msimilar to the previous figure of yield curves. Plot y₀ and y₁ to verify that.\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "ρ = 0.975                         #experiment with this\n",
    "μ = 0.05\n",
    "\n",
    "r₀ = 0.05                         #initial (day 0) short interest rate\n",
    "r₁ = 0.03                         #another possible short rate\n",
    "\n",
    "nMax = maximum([nL;nH])           #calculate yield curves until the maximum maturity\n",
    "nM   = 1:nMax                     #time to maturity (months)\n",
    "\n",
    "y₀ = [Vasicek(r₀,ρ,μ,n)[1] for n in nM]    #yield curve starting at r₀\n",
    "y₁ = [Vasicek(r₁,ρ,μ,n)[1] for n in nM]    #yield curve starting at r₁\n",
    "\n",
    "printred(\"similar to the previous figure of yield curves. Plot y₀ and y₁ to verify that.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## B. Calculate the Prices of the Hedge Bond and the Liability\n",
    "\n",
    "With the two yield curves (based on different current short rates) from the Vasicek model, calculate theoretical prices of the hedge bond and the liability. In particular, the bond price $P$ is the present value of the future cash flows $cf_k$\n",
    "\n",
    "$P = \\sum_{k=1}^{K} \\frac{cf_{k}}{\\exp\\left[m_{k} y(m_{k})\\right]  }$,\n",
    "\n",
    "where $y(m_k)$ is the continuously compounded (annualized) interest rate on a bond maturing in $m_k$ years.\n",
    "\n",
    "The theoretical prices at `r₀` may deviate a bit from the actual (observed prices), but that is not crucial as long as the deviation is moderate. We are rather interested in a (reasonable) estimate of $\\Delta P_L$ and $\\Delta P_H$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mBond prices (according to the Vasicek model) at different r values\u001b[22m\u001b[39m\n",
      "               PL        PH\n",
      "at 0.05     1.535     0.861\n",
      "at 0.03     1.609     0.896\n",
      "Δ           0.074     0.035\n",
      "\n"
     ]
    }
   ],
   "source": [
    "PL₀ = BondPrice3b(y₀[nL],cfL,nL/12)       #liability, before, /12 to get years\n",
    "PL₁ = BondPrice3b(y₁[nL],cfL,nL/12)       #after\n",
    "ΔPL = PL₁ - PL₀\n",
    "\n",
    "PH₀ = BondPrice3b(y₀[nH],cfH,nH/12)       #hedge bond\n",
    "PH₁ = BondPrice3b(y₁[nH],cfH,nH/12)\n",
    "ΔPH = PH₁ - PH₀\n",
    "\n",
    "printblue(\"Bond prices (according to the Vasicek model) at different r values\")\n",
    "xy = [PL₀ PH₀;PL₁ PH₁;(PL₁-PL₀) (PH₁-PH₀)]\n",
    "printmat(xy;colNames=[\"PL\",\"PH\"],rowNames=[\"at $r₀\",\"at $r₁\",\"Δ\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## C. Calculate the Hedge Ratio\n",
    "\n",
    "The overall portfolio is\n",
    "\n",
    "$\n",
    "V=vP_{H}+M-P_{L}.\n",
    "$\n",
    "\n",
    "We calculate the hedge ratio ($v$) as\n",
    "\n",
    "$\n",
    "v = \\Delta P_L / \\Delta P_H.\n",
    "$\n",
    "\n",
    "This should (approximately) hedge against changes in the yield curve. That is, against such changes that can be accounted for by the Vasicek model. The value of $v P_H/ P_L$ (at the old interest rates) show the value invested into the hedge bond relative to the value of the liability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mHedge ratio from the Vasicek model\u001b[22m\u001b[39m\n",
      "v             2.106\n",
      "v*PH₀/PL₀     1.181\n",
      "\n",
      "\u001b[31m\u001b[1mNotice: ρ is important for the hedge ratio v.\u001b[22m\u001b[39m\n",
      "\u001b[31m\u001b[1mTry also ρ=1 (change in one of the first cells in the notebook) to see how it affects the hedge ratio v.\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "v = ΔPL/ΔPH                              #change PL/change PH\n",
    "\n",
    "printblue(\"Hedge ratio from the Vasicek model\")\n",
    "xy = [v;v*PH₀/PL₀]\n",
    "printmat(xy,rowNames=[\"v\",\"v*PH₀/PL₀\"])\n",
    "\n",
    "printred(\"Notice: ρ is important for the hedge ratio v.\n",
    "Try also ρ=1 (change in one of the first cells in the notebook) to see how it affects the hedge ratio v.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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