Ch19_Options1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Options 1\n",
    "\n",
    "This notebook shows profit functions and pricing bounds for options."
   ]
  },
  {
   "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)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Profits of Options\n",
    "\n",
    "Let $K$ be the strike price, $S_m$ the price of the underlying at expiration ($m$ years ahead) of the option contract and\n",
    "$y$ the continously compounded interest rate.\n",
    "\n",
    "The call and put profits (at expiration) are\n",
    "\n",
    "$\\text{call profit}_{m}\\ = \\max\\left(  0,S_{m}-K\\right) - e^{my}C$\n",
    "\n",
    "$\\text{put profit}_{m}=\\max\\left(  0,K-S_{m}\\right)  - e^{my}P $,\n",
    "\n",
    "where $C$ and $P$ are the call and put option prices (paid today). In both cases the first term ($\\max()$) represents the payoff at expiration, while the second term ($e^{my}C$ or $e^{my}P$) subtracts the capitalised value of the option price (premium) paid at inception of the contract. \n",
    "\n",
    "The profit of a straddle is the sum of those of a call and a put.\n",
    "\n",
    "### A Remark on the Code\n",
    "- `Sₘ_range` is a vector (or range) of $S_m$ values. The idea is to show the payoff (or profit) at different possible outcomes of the final price of the underlying.\n",
    "- `Sₘ_range .> K` creates a vector of false/true. Notice that the dot (`.`) is needed to compare each element in `Sₘ_range` to the number `K`.\n",
    "- `ifelse.(Sₘ_range.>K,\"yes\",\"no\")` creates a vector of \"yes\" or \"no\" depending on whether `Sₘ_range.>K` or not. This is one of several possible ways of writing an `if` statement\n",
    "- To get LaTeX in the graphs use `L\"some text, $\\cos x$\"`   (Notice the `L` which indicates that this is a string with some LaTeX.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mPayoff and profit of a call option with strike price 5, price (premium) of 0.4 and interest rate 0:\u001b[22m\u001b[39m\n",
      "\n",
      "        Sₘ  Exercise    Payoff    Profit\n",
      "     4.500        no     0.000    -0.400\n",
      "     5.500       yes     0.500     0.100\n",
      "\n"
     ]
    }
   ],
   "source": [
    "Sₘ_range = [4.5,5.5]   #possible values of underlying at expiration\n",
    "K  = 5                 #strike price\n",
    "C  = 0.4               #call price (just a number that I made up)\n",
    "P  = 0.4               #put price\n",
    "(y,m) = (0,1)          #zero interest to keep it simple, 1 year to expiration\n",
    "\n",
    "CallPayoff = max.(0,Sₘ_range.-K)               #payoff at expiration\n",
    "CallProfit = CallPayoff .- exp(m*y)*C    #profit at expiration\n",
    "\n",
    "ExerciseIt  = ifelse.(Sₘ_range.>K,\"yes\",\"no\")  #\"yes\"/\"no\" for exercise\n",
    "\n",
    "printblue(\"Payoff and profit of a call option with strike price $K, price (premium) of $C and interest rate $y:\\n\")\n",
    "printmat(Sₘ_range,ExerciseIt,CallPayoff,CallProfit;colNames=[\"Sₘ\",\"Exercise\",\"Payoff\",\"Profit\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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q1ChtTXbv3r127VoNDY0RI0YYGRlR320BAQEPHjwQz6f1M2/evPPnz+vp6Y0YMUJPT09ZWRkAzp8///btW4nKqX+Jo2YIUL9h4b/GoX7yi6t9+krtJdXU1BQVFWX1jlerpveU2v0kNl3Tq6trhKK2kjhGXdN2JRqfanlS7JI7169f37Ztm7e3t4+Pj4+PDwAMGTLk77//rjrZo3ZUPRcuXLh48SLVtbKzs/v7779rn4MhIpqA8U3JycnFxcUWFhYSnTMAyM/PBwB/f/+q6UJTU7PaHCJSXFws8cuvWurq6lXfytoRBDF58uSgoCBq+Ksh5CtBq6urVzsZqxZUDqra0NQaiU5WQ/Tr1+/27dulpaXBwcH37t07ffr05s2bBQLB1q1bawksNzdXYn1lZWVeXh5BEHWNjfoRR00WrFZJScmmTZvatm0bGRkp3pdJTk5+8OBBnbZVVVRU1Pnz53v16hUcHCw+jYQalq2rmhpHmg9MTSULCwt5PJ5ozIRKTAKBQKJYaWlpXaMVEe1sXbt2FV9P9U8l3tCaXl1d33dqo58+fRIKhRIz4ard7jcpKytv27Zt27ZtsbGxDx488PHxefLkibOzc2xsrPRjDgCgoqKyffv27du3U/VcvHjx8ePHVD3UkUlZmTlzZocOHdatWzdkyJD79++Ln8lCNc7ly5ddXV3rWu21a9eoY0u1c3NzO3nyZF0rp747G7KzUeQrQdcD9XUtmkkqEhYWBgB17RRQg3e1dDZVVFScnZ2dnZ3nzp3bu3fvf/75p6YEbW5uThBEbGwsl8sVnwMUEREhEAi6d+9eU9e7JlZWVpcuXQoPD58zZ061BRISErhcrpOTk8QvzYiIiDptqFrUAMuoUaPEszOXy6WGmOqKel+qDotLH2pqampBQYF4QqGeK+q+6ejoUHPbJZ5YNeBvvuniYb98+fLVq1cDBw4UX1/tzlbTqxMVk3K7ysrKXbp0SUlJiY6OFh82KS4ujo+PJwii3vPczczMqGM8zs7OgYGBISEhI0aMaEg9jo6OQUFBoaGhVLqUvmG/ae3atQRBrF27dvDgwUFBQaJTE6ysrO7evRscHFyPBN2jR49qJ+BKoA711xX1edHX16/Hc8XJ10HCehg5cqSSkpKfn5/44GNBQQF18Hry5Ml1qq1NmzZqamrZ2dkSPS/qZ6Y4aqhBfJBXgo6Ojp2d3ZcvXzw9PcXX79ixox6BAcC0adPYbLaXlxd1SmS1WwQAapaeaOWNGzeqfnvVg6hy8ZX79u2racZr7caMGcNisc6dOyeeQOPj42/duiVlDTwe7++//xZfs3fvXgCYNGkS9ZDFYhkYGCQnJ1MnalJiYmKqzj2n3kpq1kftqMoPHjwofnWtkJCQR48eaWpqOjo6ihd+8uTJy5cvRQ8LCwtPnDhBEIRonJrqCb5//17K7e7cuVN85aFDh4qLix0dHev0o1M03VgcNZ1ZtDN/+fLl+PHj1NXEGlKP9A0rjTVr1hw9ejQ9Pd3e3j4pKYlaOWfOHCaTeezYsfT0dInyQqGQOgWpJtbW1oel8M2DhFV/zL17947aOUWn0dVfwyeCyES186AlUCeqVF1PpTx9ff3z589Tn0DqaMyUKVPEi0kzzY4kSWqi64QJEw4cOODp6RkUFESSpLOz86hRo86cORMcHJyQkODv708drFizZk0tAb98+ZLNZnM4HA8Pj6ioqODgYGrKc6dOncS3KOU0O9Er1dHR2b9/f0RExKtXry5evDhy5Mhnz56RJCkUCqmf3gsWLAgLC4uJidm7d6+qqmqXLl0A4MKFC6J66jHN7tOnT8rKygwGY/Pmza9fvw4PD//ll184HA51ar5oKpXoRBWJpx8+fBgA/vzzT9Ga1atXA0DPnj1v3ryZmJh4+fJlAwMD6rxEaabZ6enpKSoqbt68OTo6+uXLl9Sviu7du4tPgKMOHHXv3v3y5ctPnz7dt2+fpqYmNetZfJod1aqWlpY7d+709PQ8d+5cTZsWCoVUT23gwIH+/v4xMTEnTpygxlKPHDkiKkZNszMwMNDV1fX29qZ2GGr3W7BggXhtBgYGBEEsWrTo4MGDnp6e1LS8qtPsPn/+TCW7+fPnh4SEREZG/v7770wmU0FBITIyUlSMmmb36tUr8ZipX9kWFhbUw9u3b3fu3NnDw+POnTuxsbHh4eFbtmxhsVjik96o3p+Kikot74Kfn5+RkdHmzZtF9WzevJnJZOro6Ij2K+rsga5du27dutXT09PT05OavEzNZrl3717V5oVvnahy4sQJBoPRoUMH0WxF6ids+/bt9+zZ8/Dhw9evX/v5+W3cuLFz5843b96s5SXICpvNHj9+/J49ey5fvnz27Nnly5dTv5jt7OzEJ/7XT0tI0EKhcNu2beLDCAwGg7qIqHgxKRN0fHy8ra2taLCPmny6YMECiQMOTCZz0aJF5eXltb+ue/fuSQw4WFtbJycni5eRPkGTJHno0CGJgUJNTU1RfgwLCxM/uYvJZG7cuHHDhg0NT9AkSV67dk38nHIVFZXz58+PHz++fgm6srJy4cKF4ge+Jk2aRP3akPJMwlOnTokfZe3Vqxd1oodIaWkpNclMtFf8/vvvVedBl5WVzZw5UzTtpPYzCYuLi6dNmyYetqqqqsTJn1SC3r17t8QQ54wZMySuzvj06VPxQ2q1nEmYkJBA7cAihoaGDx48EC8jTYIOCQmpenSue/fu4ie8PHnyBADMzMxqaYdnz56JT5EU1RMWFiYqw+fzly1bJj4mJn4mYf0SNEmSPj4+LBarXbt2or3u+PHjVY/c9u7dOyoqqpaXICvUmUriOByOu7u7aF58QxCkfNxRJT09XSAQGBgYUKcqVIuaNNO5c+dq/5uXl/fkyZOcnBw1NbVBgwZJXCMCALKyssrLyw0NDcVT7fv373k8nrGxscThl8rKypycnIqKClVVVeq9LyoqCgsLo+au6enp9enTp+obU63y8vLg4OCkpCQ2m92rVy/qcgTiBb58+VJQUNCuXTuJc7hrUlpa+uzZs7S0NCUlJUNDQ1tbW/Hh7LKysuDg4LS0tDZt2tjZ2enq6ubn5+fn54vXn5GRUV5eLnrVJEkmJSUpKChUbTQJeXl5oaGhWVlZ7du3Hzp0qLq6ek5OTmlpqb6+PhWDUChMS0vjcDgSo29FRUWfP39u27atxOGj+Pj40NBQgiCsrKx69+5dXFz86dMnTU3NWn62JyQkmJqauri4+Pv7f/r0KSgoqLCw0MTEZMiQIdXuPCEhIdHR0UpKSnZ2doaGhgUFBV++fBE/p0Dk48ePZWVlTCZTdMWumqSkpISEhJSUlOjp6dnZ2Um8qEOHDi1fvpy6bmJsbGxYWBifz+/fv39NlzcrLy//+PGjQCCgXrhQKExOTlZUVJT4ahcKheHh4TExMZWVlSYmJgMHDpQ4jEG9Fx07dhT/3iJJMjU1VfwdEQqFMTExycnJubm5GhoaxsbGffr0Ed//t27dumHDBh8fH4kri0mg6klKSvr06ZOGhkbXrl2trKyqvaDH58+fqTlIRkZGBEFQD3V1dSXOzwaAd+/eiX6WAUBpaWlOTo66urrEl0F2djaPx1NRURFN3+LxeM+fP09JSREKhbq6uubm5jUlisaQmJgYGxtLHcg1MDDo379/1W+v+pGXBI2QlMQTNN2xVE88QdMdS304ODjk5OS8efOmHpdPQrLV7GdxIIRka8iQIQ4ODpid5QEmaITQ/7Nx40a6Q0BfMeXhTnQISY+6I9qwYcOkPGOt6bFYrC5dujTfm4Mg+YFj0AghJKdwmAkhhOQUJmiEEJJTsjlIePHiRdEZq9ra2tQdNBBCCDWEbBK0p6entrY2dRJtXa8BhBBCqFoym2Y3e/bscePGyao2hBBCMkvQt2/fjo6OtrCwGDNmDE5xRwihhpPNNLvly5erqKgwmcxr16517Njx3r17Ve9lMGbMGHV1ddEASKdOndasWSNRRiAQMBiMqneOQDXBFqsrbLG6wharK6FQSBDEN1uMw+HUcukhioznQRcVFXXr1u3kyZNVL4RqZGQ0Z84c0bXWDA0Nxa80RuFyuWw2+5tBIxEej8disbDFpMfj8ZhMpvhtVVHtsMXqSsoWk+ZrT8YfbDU1NTMzs2rv1aiiojJlypTaz/5i/ke2UbVg2GJ1hS1WV9hidSXDFpPBYHFlZWVFRQW1nJ6eHh4eXtNlFRFCCElPBj3o7Ozsfv36WVtbM5nMR48eff/993Z2dg2vFiGEWjkZJGhDQ8Pnz5+/ffsWAPbt20fdYAkhhFADyWYMukuXLpiXEUJItnDCMkIIySmcnoXkTnx8/I0bNxqpcj6fTxBEI81JYDKZs2bNkvJmlQh9EyZoJHeuXLkSEBAwaNAgugOps5s3b+rq6s6cOZPuQFALgQkayR2SJB0dHZvjvX4yMzPpDgG1KDgGjRBCcgoTNEIIySlM0AghJKcwQSOEkJzCBI0QQnJKjhI0SZIrAldsf7ZdtldARQihZkqOEjRPwPOO8d74eOOKeyvojgWhGr169YqaAigUCqdMmcLj8eiOCLVYcpSglVhKPuN8FFmKB18cDP8QTnc4CFUvKyvrwYMHACAUCq9evVpZWUl3RKjFkq8TVZyMnO5MvxOYGmjRDq8ojWiQm5sbFxenqqpqaWlJnQ6empqampqqra1tYWGBt31CNeLzwd8fhgwBNTUZ1ipfCRoABhsMHtplKADsDt7NZDBX2a6iOyLUWuzateuvv/4aMmRIfn5+7969d+/evWfPnuvXr3ft2jUuLk5DQ+Pu3bt4dzFUjcpKmDoVrl+H9eth2zYZViynextJktuebisqL8oqytrnso/ucBB9CgqgTx9ITa3DUwgCVqyAfTXsNmPGwM2bAAAsFhw+DO7u1OqwsLBdu3ZFR0d37NgRAAQCAQD89NNPv/zyCwCQJDl06FA/P78JEyY05NWgFqiyEqZNg+vXQUsLpk6Vbd1yNAYtjiCIixMvKjAV9j/f/yjtEd3hIPoIhVDXo3AkWdtTuNyvCwIBlJeLVj969MjFxYXKzgBAjW8UFRX99ttvo0aNcnZ2TklJSUxMrFskqMWjsrOvL2hqQmAg9Ool2+rltAcNACNNRt6accsnxqd3h950x4Loo6UF2dmyrDAwsNrVPB5PQUFBYuXMmTMtLCz27dvXtm3bVatW4YQN9P8IBDB3Lvj6goYG3LsHffrIfAty2oOmOHZxPDXmlKai5uW3l09GnKQ7HNSS9evX79GjR+VifWoACAsLW7x4cbdu3TQ0NF6+fElXbEge8fkwfTr4+ICmJty/D/36NcZG5LcHLW7lvZXZxdmJeYm7nXbTHQtqmVxdXa2tre3s7KZMmVJQUKChobFy5cphw4YtXrx47Nixt2/fpjtAJE+ovvPVq6CuDv7+0LdvI22neSTooyOPTr46eU/IHrvOdiNNRtIdDmqZLl26FBAQ8ObNm44dO44cORIAvL29fXx8cnJytm7dymKx2Gw2APTr18/DwwMAmEzmpUuXlJSUaI4bNTE+H2bOhCtXQEMDAgIaqe9MaR4Jekz3MdenXj/26hjOj0aNhyAIFxcXFxcX0RpFRcV58+ZJFNPT09PT06PKT5X1UXsk7wQC+P57uHLla9+5MbMzNJcEDQAjTEaMMBkBAE/Sn2QVZ03vOZ3uiBBCrQyfD7NmweXLoK4OAQHQv39jb7DZJGiRJbeXvP30NjonervDdrpjQQi1GgIBzJv3NTvfu9cE2RnkfBZHtbY5bGMz2Due7fgn9h+6Y0EItQ4CAcyeDd7eX7OztXXTbLb5Jeix3cdenXLVVt/WWMuY7lhQK7V58+Zly5bRHQVqQhs2gI8PqKmBv3+TZWdojgkaAMZ2HxviFmLVwSruc9ztdzj/CclAZmZmdnb2+/fvb968mZaWRq2srKyMjIwUlXn37l1+fn5RUdGHDx9yc3PDw8MTEhLoCRc1sXbtwMgI/P3BxqYpN9ssE7TIopuLRl0c9cfDP6OR1bcAACAASURBVOgOBDV7Bw4cmDJlyuTJk2/cuGFtbX3x4kUA+Pz584ABA0RllixZcv/+/bS0tKdPn0ZEROzatcvb25u+kFETWrECUlLA1raJN9u8E/TPNj+zGKwtT7Z4v8HPScv0hftF7089woMgPIgNDzcAwNOMp0rblAgPgrOFc+fdHQDYG7KX4cEgPAjt3dpZxVkAMO7SOOop1ietAaC4otjwgCG1ZlXAKgAIyw5T3a568MVB8W19/Pjx8ePHJ0+e9PX1/emnn2o6sbtXr15TpkxxdXW9cuXKli1bGrsFUGvWvBP0hB4TfCb6GKob6qjo0B0LahQMgqHIUhRfYDFYbAYbANhMNpvJBgAOk8MgGACgwFKgFpTYX08eUWIpUc9VYCpIVKLIUlRg/b+LbwwfPpy6HMfAgQNJkkxKSmq614lQdZrfNDsJk8wmTTKbBAAfSz4m5CXYGdrRHRGSJQ1FjZSfUsTX2OrbFv1aJL5mufXy5dbLxdf4TPTxmegjeqjCVklc9v8uRGfVwerzms8S22Iw/tdfYbPZfD6fIAjxO2TizVNQE5NlDzoqKmrXrl2ZmZkyrFN6P9z+wf6M/aZHm2jZOmoBHj9+TKXj2NjY0tJSExMTbW1tgUDw4cMHACguLo6OjqZKqqiocEWXLUWo0cisB83lcufNmxcfHz9gwAB9fX1ZVSu92b1m30q85fHYw0DdYL7V/KYPADV3AoFg1KhRtra2Xl5emzZtUlFRAYDp06ePHz/excXlyZMnWlpaVEl7e/udO3cKBIIePXqsWbOG1qiRTAmF8NtvkJ8Px47RHQqADBP0hg0bZs+evX07bWf3TegxwXuC90K/hdQoJEJ1NXbs2NGjR7948eL8+fMDBw6kVnp5eV2/fj0nJ+fcuXOpqaldunQBgL59+0ZFRUVHR1e9hDRqxoRCWLAATp8GdXU4dAjYbLoDklGCfvHiRXBw8LNnz2hM0AAw1XzqVPOpAFBaWZqYl2jVwYrGYFBzZG1tbf3/T0NgsViTJ0+mljt16iRa37FjR9HtV1BLQJKwZAmcPg3KynD9ujxkZ5BJgi4vL3d3dz99+jR1l6Ca5ObmrlixQu2/W9527ty56hQlLpfLZrMbfl/O5QHLvV57bRy8cY1NC//5yePxWCxWC7uTaWVlZdO/IhMTEw6H0/B6KioqysrKGl6P/ODxeEwmky0fCauxCIWcpUtZ586BigrP11dobQ0NeBOlbDEOh/PN/VwGH4MtW7aMHDnSyuob3dU2bdq4urqK+iDt27dXVFSUKEOSpEwS9IhuI86+Oevx1ENPXW+B1YIG1ibnWl6CpuXluP9399gGYrPZVXfs5q6FJ2ihkFi0iDh3DlRUhDdvcuxkMBNMmhYTnzVUExl8Em7cuFFQUHDp0iUAKCgomDZt2oYNGxYvXixRTElJydXV1dzcvJaqGP9pYEgTzSaeGXdmgd+CnNKchtcmz2TVYnJFYnJb80IQRAt7O1rkPvY/JAnLl38d2bh5kzF0aMOrlGGLySBB3717t6Kiglru27fvvn37xC95TpdZvWZN6DFBma0sJIUfSz7qtdGjOyKEkJwhSVi6FI4epbIzyCI7y5YMcry+vn6X/zCZTD09PQ0NjYZX23DKbGUA2Phoo/4+/V3Bu+gOByEkT0gS3N2/Zudbt2DYMLoDqoaMB/vCw8Pbt28v2zobqI9uH4Ig1t1fp66gvvg7yYEXhFBrRJKweDGcOCG3fWeKjBO0oaGhbCtsuPGm473Gei3wWxD1MYruWJBUCIIIDAys6VpF8iwyMnL48OF0R4G+hSThxx/h+HFQVgY/P/nsO1Na1NH/msztPXd41+FaSloAUFpZqsJWoTsiVJupU6c23gkg1BU2ap8SWm/z5s1zcHBojJqRzFDZ+cgRUFICPz+Q7/erVSRoAGin0g4Ajr06tvTO0t1Ou1fZrqI7IlSj7t27r127tpEqbxWzelEtliyBY8dASQlu3pTz7AzN/XKjddVRrSMArA5YfSTsCN2xIISa3Nu3X7Oz3PedKa0rQY/uNvrE6BMMghGQHEB3LAihJtejB+zbBw8fgqMj3aFIpbUMcYjMt5pv39leW1mb7kAQQk2OwYCff6Y7iDpoXT1oShfNLmoKan4JfirbVSRueoQQQvKjNSZoCpvJ5lZyV/ivwPFohJB8ar0JenjX4cdGHQMAvOEsQkg+tboxaHGL+i6y0rVqryJfpz4ihGTj3Tvo2hUIgu446q/19qAp/fT6GagbvMx6abDf4Oiro3SHgxCSBZKEn3+Gbt3g0CG6Q2mQ1p6gKUXlRZlFmUtvL8UcjVBLsHIlHDgACgrwrevUyzlM0AAAjl0cj4w8AgD7QvfRHQtCqGHWrYMDB4DDgatXYfBguqNpkFY9Bi1u8XeLTbVN1RXV6Q4EIdQAv/4Ku3Z9zc6jR9MdTUNhD/p/7DvbW3WwSs5P7nu8r1ekF93hIITqaPVq2LkTOBy4dg3GjKE7GhnABC0puzg78kPkAr8Fx8OP0x0LQkhq69fDn39+7TuPGkV3NLKBCVrSYIPBB4cfBID1QevpjgUhJJ3162HHDuBw4MqVltF3puAYdDV+7P+jkaYRi4GNg1Bz8Ntv/8vOY8fSHY0sYQ+6eiNNRroYu3wu+zzu0rjzb87THQ5CqAbr1sH27V9HNlpWdgbsQdcuvTDdL8HPL8GvnF++oM8CusNBCP1/v/8Ou3YBmw2XL7ekkQ0R7EHXpq9u3/2u+wFg6Z2lAlJAdzgIITG//grbtgGbDVeuwLhxdEfTKLAH/Q0/Wf+k10avpKKESTTKXewQQvWxZw/s3Pm179xCszNggpbGZLPJAMDlc3/2/3mY0bAp5lPojgihVi8pCRQV4cIFGD+e7lAaEQ5xSCu9IN0z3HP6temno07THQtCrd7Ro5CZCRMm0B1H48IELS1TbdO9znuFpHCh38LC8kK6w0GodWMwoG1buoNodDjEUQerbFfpKOukF6arcdTojgUh1PJhgq6bOb3nAICQFG5+vNmyg+XY7i1t3iVCSH7gEEd9ZBdnezzymHB5wtnXZ+mOBSHUYmGCrg99Nf2djjuFpNDthltWcRbd4SDUop06BceO0R0EPXCIo57WDFyjrqj+IvOFjrIO3bEg1HJ5eMCmTaCiAu7uzfrugvWDPej6c+/r7jXWi8PknIo85Z/kT3c4CLU4mzfDpk3AYsGpU60wO4OsetBHjhx59epVWVmZsbHxDz/8oK+vL5Nqm4WSipKFfgsZBOPMuDOzes2iOxyEWordu2HjRmAy4fRpmDqV7mjoIZsedFJSkp2d3bRp0zIzMwcMGFBSUiKTapsFVY7qNodtAlLw/b/fJ31JojschFqErVth7VpgMuH8eZjVevs9sulB79v39V6rY8eOVVdXj4mJsbGxkUnNzcKvg35VZivffXdXRwXHoxFqsD17YMMGYDLhzBmYPp3uaOgkyzHo8vJyX19fFRWVHj16yLDaZuEn65/8Z/mrK6j7J/k/SX9CdzgINVt79sCaNV9HNlpx35lCkCQpk4omTpx469YtFot18eLFsdVdNltbW9vY2FhFRYV6aGZmtnPnTokyXC6XzWazWM11bomQFOr8pSMQCk6OODnJdFITbJHH47FYrObbYk2Px+MxmUw2m013IM1GU7YYZ+9ejocHMJm8Y8f406Y1wRYbg5Qtpqio+M1PrswSNAAIhcKAgICpU6c+e/bMwsJC4r8mJiZr167t3Lkz9VBbW9vS0lKiTHNP0ACw9cnWDQ83sBisCPcIi3aSjSBzmKDrChN0XTVdi+3YAevXfx3ZaM59Zxm2mCw/2AwGw9XVtW/fvo8fP66aoBUUFGxtbc3NzWW4RTn0+5DfOUzOxeiLGooadMeCUPPx559fs7OXV7POzrIlgzHooqKi4uJiavn9+/dv3rwxNTVteLXN15qBa6IWR3VS6/Qm503Ehwi6w0FI7v35J6xeDQwGeHnBnDl0RyNHZJCgU1JSDAwMbGxsBg0a1LNnz3nz5jk6Oja82hbAxdvF+qT1lbdX6A4EITm2ezdm55rIYIjD0tLy/fv3sbGxJEmamJhoaWk1vM6W4Yfvftj4aONM35lGmkb99PrRHQ5C8ufNG1i7FhgMOHUK5s6lOxq5I5sxaFVV1f79+8ukqpbkD7s/GATj6KujHCaH7lgQkktdusD8+eDiAlPwTnLVkOUsjtr17Nnz8uXLtR8kbAGzOGqSWZRZWlnavW132VaLszjqCmdx1BW2WF3JsMXwYklNZPiF4RZHLHzjfOkOBCHUbGCCbiITe0ysFFZO+2daaGYo3bEghJoH/GncRDbZb+IL+XtC9pRUtKIrSSGEGgJ70E1n67CthesKnbo4FZUXZRZl0h0OQkjeYYJuUoosRQAYf3m88UHjGwk36A4HoSZ0+DCoqMAN3O3rABM0DewM7SoEFVOuTnma8ZTuWBBqEocOwfLlwOUCzjiqC0zQNPjD7o+1A9dWCCrSCtLojgWhxnf8OPz0EwDA4cMwciTd0TQn+G1Gj52OO1cNWKWjrMMX8ovKi7SU8PRL1EKdOAGLFwMAHDoES5bQHU0zgz1o2lC3A593Y57+Pv1bibfoDgehRnDkCLi7AwAcPgxLl9IdTfODCZpm3dp24/K5k65MepT2iO5YEJKpI0fgxx8BAA4fxr5z/WCCptmGIRtW2q4sF5S/yHpBdywIyc6JE7BsGQDAwYOYnesNx6Dp96fzn4v6LjLRMgEAHp9HTcVDqBk7eRIWLwaShL/++tqJRvWCPWi50L1tdwbB+DXoV509OneT7tIdDkIN4OkJixZ9zc5UJxrVFyZoOaKmoFZSUTLh8oSHaQ/pjgWhejl+HH74AQDgwAHMzg2HCVqOrBu4bln/ZTw+72bCTbpjQajuTp36X3ZevpzuaFoCHIOWIwRBHBx+cIbFDIv2jX47cIRk7Nw5WLQIhELYvx+zs6xgD1ru2OjbqLBVjr462ml/p4DkALrDQUg6V69+zc4rVtAdSsuBCVpOlVSUZBZljrs0DsejUfPg5QUREZidZQsTtJxabbt6Sb8lXD73dORpumNBSAo6OmBlRXcQLQ2OQcspgiAODz88pvsYyw6WdMeCEKIH9qDlF0EQLsYu7VXa+yX4WRy1eJD6gO6IEEJNChN0M5BakBqTGzPaZzRerwOhVgUTdDOwvP9y977uZZVle0L20B0LQgBPn0JwMN1BtAo4Bt0MEARxdOTRAZ0G9O/Yn+5YUKt37hzMmweamvD5M92htHzYg24eCIKY03uOqbbp88zndmfsHqc/pjsi1CqdPw/z54NQCOvW0R1Kq4AJupl5nfP6SfqTERdGYI5GTe3yZZg/HwQC2LoVVq+mO5pWARN0M7Owz8IFfRaUVZb9ev9XumNBrYm3N8ycCXw+bN8Ov/1GdzStBY5BNzMMguE5ytOqgxVerwM1GcY//8C8eSAQwJYt8Cv2DJoO9qCbHwbBWNJvyWCDwUlfkqb6Tg3NDKU7ItSSMS9fZs6eDXw+bN0Kv/9Odziti2wS9L///rtw4cIRI0YsXbo0ISFBJnWibwrNDPV75zfCZ8TTjKd0x4JaqCtX2AsWgEAAmzfjyEbTk02C3rdvn6Wl5fLly5WUlGxtbbOysmRSLardTIuZsy1ml1SU/HDrB7pjQS3RpUswYwbw+YKNG2HDBrqjaY1kMwb95MkTasHV1fXevXsPHjyYPXu2TGpGtWAQjGPDj5npmHXR6kJ3LKjFuXoVZs8GgYC/YQP5229MusNpnWQ8Bs3lcj98+NCpUyfZVotqwiAYq21XTzGf8qns06Kbi15mvaQ7ItQi/PMP1XeGTZv469fTHU3rRZAkKcPqFi1alJGR4e/vX/Vfbdu2bdeunaLi11tW9+zZ88iRIxJluFwum81msXBuibR4PB6LxWKxWLeSbs3wm6HKVvWd6GujZ0N3XPKLx+MxmUw2m013IPKL9e+/SvPnA59f/uuvFb/+ii1WV1K2mKKi4jfLyDJB//HHHzdu3Hj06JGmpmbV/3bv3n3r1q1dunz9Ma6urt61a1eJMpig60qUoIWk8Pt/vz//5ryBukH6inS645JfmG6+ISYGrKyAz4eNG2HTJsAWqzsZtpjMUuH27duvXbv28OHDarMzALDZbDMzM3Nzc1ltEYljEIzT404baRppKGrQHQtqzjQ0wNwcpk3Dk7nlgWwS9P79+8+cOfPo0aN27drJpEJUD0yC6WHvAQBcPndP8B682D+qD319iIqiOwj0lQwOEvL5/JUrV2ZlZfXs2VNLS0tLS+vAgQMNrxbVW8j7kI2PNtqdscNzWBBq1mTQg2axWF++fBFfo6Sk1PBqUb3Zd7afYTHjYvTFMT5jclfnEgRBd0QIofqQzRBHTePOiBZMgnlu/DldVV2+kI/ZGaHmC+dLtExMgrnXeS8ACEnhyYiTAw0Gmuvg4VmEmhm8WFILF/kx0v2W+8BTA/EcFiTp5k0YOBAiIuiOA9UIE3QLZ9XBaqr51MLywuEXhvP4PLrDQXLjxg2YNAlCQuDdO7pDQTXCIY4WjkEwvCd4ayhqZBZlspl4rgECAIC7d2HqVKiogJUrYepUuqNBNcIE3fKxGKxjo45RyzcTb5pqm5pomdAbEqLT3bswfjyUl8PKlfDnn3RHg2qDQxytSFpB2hifMdYnrMM/hNMdC6LJzZswbhyUl8Pq1Zid5R8m6FbEQN1gktmkfF6+83nnAl4B3eGgJnfrFkyaBBUVsGoV7NlDdzTo23CIoxVhEIyLEy+qsFWiPkbheHSr4+8PkydDRQX8/DPs3Ut3NEgqmKBbFzaDfWbcGWo5LDusvUp7A3UDWiNCTcLfH8aPBx4PVqyAffvojgZJC4c4Wql8Xv6AUwOsPK0iP0bSHQtqZLdvw7hxwOPBzz/D/v10R4PqABN0K6WhoDG62+gv3C9O55w+lX2iOxzUaO7cgYkTobwc+87NESboVoogiEuTLk01n8ogGAKhgO5wUOMICPianX/6CbNzc4Rj0K0Xh8m5NOkStZxakKrMVm6v0p7ekJAsBQTA2LHA48Hy5bB/P+Bls5oh7EEjqBRW9j7a2/xv89c5r+mOBcnOli3A48GyZXDgAGbnZgoTNAI2g+3YxTGPm+d4zjG7OJvucJCMHDgA58/DX39hdm6+MEEjAIBLky6NNx1fXF5cVF5EdyxIRvr2hVmzMDs3azgGjQAAOEyO71TfssoyZbZycUUxALThtKE7KIRaO+xBo/9RZisDQO+jvbse7BqdG013OAi1dpigkSQrXavc0lyHsw4ZhRl0x4JQq4YJGkm6OPHiSJORn8o+pRem0x0Lkk56OmTj0d0WCMegkSQFpoLfdL+PJR/12ujxhXwhKeQwOXQHhWr24AGMHg2dOkF8PN2hIBnDHjSqBoNg6LXRA4ChZ4ca/WUU+ymW7ohQDajsXFYGrq50h4JkDxM0qo2uqm52cfaws8NSC1LpjgVV8fQpjB0LZWXg5oZncrdImKBRbc6NP+di7JJTmhOejTdhkTOPHoGrK5SUwMKFcOIEMPCz3ALhGDSqjSJL8daMWxEfIvrp9aM7FiTm2bOvIxvz58OxY3g2SkuF37roG1gMVv+O/QmCmOU7y+gvo/jPeCSKbo8ff+07u7lh37llw7cWSUtICtMK0oadHZaSn0J3LK3Ys2cwahSUlsK8eXD8OGbnlg3fXSStU2NPOXVx+lDy4V7yPbpjaa2ePoXhw6GkBObPh5MnMTu3eDgGjaSlxFK6NeNWUGqQg5ED3bG0SsHBMHIklJTA99/jyEYrge8xqgMOkzO863AOk7Ph4YZeR3sl5iXSHVGr8ewZuLpCcTF8/z2cOoXZuZWQzdscGRm5d+/exYsXX716VSYVIjmXXpAenRs99OzQ5PxkumNpBUJCYMQIKCmBadNwZKNVkc07ffXq1fj4+MjIyNDQUJlUiOTcsVHHhhkNyy7Ovhh9ke5YWrp37772nefMgQsXgMmkOyDUdGQzBr19+3YAWLx4sUxqQ/JPma18a8ata7HXRnUbRXcsLV1JCZSXw7x5OO7cCuH7jepJiaU0q9csDUWN4+HHHc45JH1JojuiFsrKCgoKwMsL+86tUNPN4sjOzp40aZKSkhL1sFu3bidPnpQow+Vy2Ww2i4VzS6TF4/FYLBa9LRaaHvog9YH9GXv/qf6d1TvTGIk0eDwek8lks9l0B1JHJSV0bbm5thh9pGwxRUXFb35ym+6DraOjs3nz5i5dulAP27dvr6qqKlGGelWYoKXH+g+NMRwefTi1KPVx+uOT0ScPuB6gMRJpsFgsTDd1gi1WVzJssab7YLPZbDMzM3Nz8ybbImoaKmyV2zNve0V6je0+lu5YEGpRcAwayYAKW2VZ/2UG6ga3390ef3k8nguOkEzIJkFv3LiRIAhPT8/9+/cTBLFz506ZVIuanYDkgH/j/x16diheP7o+wsPBzQ1vXoVEZJOgPTw8SDHr1q2TSbWo2dk2bNsgg0EZhRmbH2+mO5bm5sULcHAALy94/JjuUJC8wMNxSJZUOap3Z9498PzAyG4j6Y6lWXn5ElxcoLAQpk6FKVPojgbJCxyDRjKmylH9fcjvVh2swrLD5t2Yl1aQRndEci8iAoYPh8JCmDQJvL1xvjMSwQSNGsu/8f+eiTpjf8Yec3RtwsLAwQG+fIEpU8DHB3COKRKDCRo1lnWD1g3oNCC9MH1VwCq6Y5FXr16BszMUFMDkyXDhAmZnJAF3CNRY2nDa+M/y/y3oNxyPrl5kJLi4QEEBTJyI2RlVC3vQqBG14bQ5OPygi7FLSn7KqoBV74ve0x2R3IiKAicn+PIFJk4EHx/A8/RQdTBBo6Zw5e2VfaH77E7bZRRm0B2LHIiIgGHDIC8PJkzA7IxqgQkaNYUl/ZZYd7ROLUhddHMR3bHQLSICnJwgPx8mTIBLlzA7o1rgsBdqCmoKavdm3/vp7k92ne3ojoVWUVHg7AxfvmB2RtLABI2aiLqC+plxZwDgC/fL0VdH51nO02ujR3dQTSsqChwdIS8Pxo/H7IykgUMcqKldirn0+4Pfh5weklmUSXcsTWvRIsjLg3Hj4PJlzM5IGpigUVOb2WtmP71+yfnJ069NpzuWprViBaxbh9kZSQ+HOFBTU1dQD5gdsMBvgUV7C7pjaVozZtAdAWpmMEEjGmgoavwz5R8A4PF5l99eHt51eDuVdnQHhZDcwSEORKd/4//9/t/vB3kNyi7GiyAjJAkTNKLTcJPhfXT7vPvybuwlvF0WQpIwQSM6qSuo359z37Wrq0W7ljUeXVEBAgHdQaBmDxM0opmmoubdmXe9xnqRJHnn3Z18Xj7dETVYTAwYGYGrK91xoGYPEzSSF4EpgSMvjhxwasCHkg90x9IAMTHg4ADZ2aCtTXcoqNnDBI3khbW+tWUHy/jP8cO9h9MdS329fQsODpCbC8OHw5kzdEeDmj1M0EheUOPRgwwGaShq0B1LvSQkgJMT5OaCszP4+oKCAt0BoWYP50EjOdJWqe3TeU+p5VfZr7prd2/DaUNvSNJKSIChQ+HDB3B2hhs3QFGR7oBQS4A9aCSPIj9G9jvRz+akTU5pDt2xSCEuDuzt4cMHcHHB7IxkCBM0kkddtbr2at8r9lOs0zknISmkO5xaJSSAoyN8/AhOTnD9OmZnJEOYoJE8asNpc3/O/T66fYrKiwSkHE8ojo8He3vIzgYnJ7hxA5SU6A4ItSg4Bo3klI6yzsuFLwVCAZvBTi9Mb6fSToklZ+kvMREcHL72nTE7o0aAPWgkv5gEk8PkZBRmmBw0sT5h/ansE90RiUlI+Np3dnTE7IwaCSZoJO+0lbW7a3ePzo12OOtQIaigOxwAAHj3DoYNgw8fYMgQ+PdfzM6okWCCRvJOma0cNCfIop1FemF6WWUZ3eEAvH//te/s4AD+/qCiQndAqMXCMWjUDLRTafdq0avSylINRY3C8kJltjKbQd9NSaKjITsbhg0DPz/sO6NGhT1o1DxwmBxNRc0CXoHhfkPrE9afyz7TFsqIERAdDffugbIybTGg1kE2CTozM3PGjBl9+/adM2fOx48fZVInQlUpsZU6qnWM/BjpdN6Jy+fSFkfPnsDCX5+o0ckmQU+YMEFbW9vb21tJSWnatGkyqROhqhSYCkFzgnpo94jJjflUKk+TOhBqBDLoBbx48SIxMfHZs2ccDufAgQPa2toxMTE9e/ZseM0IVdVBtUPYorDc0lwDdQO6Y0GoccmgBx0dHW1pacnhcABASUmpZ8+eb968aXi1CNVEha1ipGHEF/KNDxpbn7TO4+bRHRFCjUIGPejc3FwNjf9dH1JTUzMnp5oL3GRmZrq4uLDZXw++9+zZ08fHR6IMl8tls9ksHN2TGo/HY7FYrbPFhKSQw+C8zHo57MywgGkBKmypprvxeDwmkynaD2tHZGWxbt2qnDu3NV9ho04thkDqFlNUVPzmJ1cGH2x1dfWysv/NTi0pKRHP1yK6uroHDhwwMTGhHrZp00ZVVVWiDPWqWme6qR/Wf+gOhB4Pvn8w9MzQN7lvssuzrTStpHkKi8WSNt2kpICzM2RkKBgawqRJDY212apDiyEAkGmLyeCD3blz58TERGqZJMnk5OTOnTtXLcZkMvX19bt06dLwLSJE0VXVfbHwRcLnBKsOUmXnOkhNhaFDISMDBg+GESNkXDlC0pHBGLSTkxOXy71x4wYAXLlyhcPhDBkypOHVIiQNdQX1/h37A4DDOYehZ4fK5p6zGRng4AAZGTBgANy+jfOdEV1kkKA5HM7Zs2fd3d2NjY1Xrlx55swZJpPZ8GoRqpOckpxHaY+czjkVVxQ3qKKMDLC3h9RUGDAA/P2hTTO5pQtqiWQzdunq6pqZmZmbm9uuXbtWOx6K6HVv9r2hZ4aGfwh/nvncqYtTPWtJSwN7e0hPh4ED4e5dzM6IB/pVfgAAHhhJREFUXjJLpiwWS09PT1a1IVRXHdt0DHELeZT2yMHIoZ5VUCMb6elgawt37mB2RrTDa3GglkNbWXuS2SQGwVh4c+Goi6MKeAV1eHJGBgwdCikpYGsL/v6gptZoYSIkLUzQqAWK+BBx+91tF28Xacej09PB3h6zM5I3mKBRC/TvtH+NNY1fZr28lXjr26WpvnNqKtjYYHZGcgUP6KEWqJNap2fzn/nG+Y4zHfeNou/fw7BhkJoKffvCnTuYnZFcwR40apk6qHZY0m+JEktp29NtU/+ZWlheWE2h9+9h6FBIToa+fSEwEDQ1mzxMhGqDCRq1cHff3b3y9oqrt2s149FTpkByMlhbQ1AQZmckhzBBoxbuwsQLRhpGzzOfe7/xlvzf0KEwaRLcuwfq6nSEhtA34Bg0auEM1Q2fzHtyOur0ZLPJkv/bvp2OiBCSFvagUcunr6a/YcgGbWXtc6/P/XD3h4aeC45QU5GnBM3nK9jYsNhsIIg6/M2YUWOFixcDg1G32kxNobS0+trOngUFhbrVpqkJkZHV1xYdDVpadauNw4FTp6qvjccDc/O61cZgwIIFNTbd3Ll1q40goFcvqKiovrZjx4DDqVtt2toQG1t9bWFhoKFRt9oUFeHCBQA4/+b8mTdndP7UWXt/LQBE50Zr7dIiPAilbUq+cb4AcPb1WYWtCoQH0X5v+5T8FABYfGsxw4NBeBDfHf9OSAr5Qr6VpxXhQTA8GMvvLgeAxLxEnT06hAehuFXxQvQFALjy9oriVkXCg9DerR33OQ4AVt5bydzMJDyIXkd7VQgqSJK0OWlDVbLw5kIASC9M77C3A+FBcLZwTkWeAgC/BD/lbcqEB6G5SzPyYyQA/P7gd6oS08OmpZWlADD07FDCgyA8iBnXZgDAh5IP+vv0CQ+CvYV9+OVhAAhIDlDdrkp4EOo71UMzQwFg29NtrM0swoMwPmhMncgz8uJIqpJxl8YBQB43r/OBzoQHwdrM2hOyBwCCM4Pb7m1LeBBtdrR5mPYQAPY/38/ewiY8CIP9BrmluQAw+epkqhIXbxcAKK4oNjlkQlXi8dgDAMKywzR2ahAehMp2lbtJdwHg2KtjnC0cwoPQ+1MvqzgLAOb+O5eqZPDpwQDA5XPN/jYjPAjmZmbzer9e576u8ZNVR/KUoEmSELuutLRqyqcAUFYGJFm32mp5Snk58Pl1q628HCorq/9XZSWUl9etNj4feLzq/yUUQl2bjiRra7pa/lXLU2TYdDxejU+pR9NVVlJfHsdHHzfWNBaSQm4lFwAqBZXlgnJqoUJQAQDl/HK+kA8APD6PWiirLCOBBIDSylISSBLI0opSACCBLKssAwC+kM/j8wCgUvhfJYLySmGlRCVCUvj/Kqn8WglVm6gS0UKFoIKqpJxfXimoBAAun0tVUlZZRpIkAJRUlFCvj6pNSAqp5wqEAlElotdFVcLj8wSkAAC4lV9rq1oJdTdeAfm1ElErVQgqvkZSyaVelygk6lWIahO1sIAUSDS1KCRR44gWRJWUVpSSJEmSX1u4mb5fMkGQdU1h9dWzZ8/Lly+bm5vXUgbvqFJXrfmOKvWD9wepK2yxupJhi8lTDxohhJAYTNAIISSnMEEjhJCcwgSNEEJyChM0QgjJKUzQCCEkpzBBI4SQnMIEjRBCcgoTNEIIySlM0AghJKcwQSOEkJzCBI0QQnIKEzRCCMkpTNAIISSnMEEjhJCcwgSNEEJyChM0QgjJKflK0Hfu3Ims6SZ+qDp37tyJiIigO4rmxN/f/9WrV3RH0Zzcu3cvLCyM7iiak8DAwBcvXsikKtkk6IcPH/7yyy/Dhw8/duxYQ+q5d+/ey5cvZRJSKyHDXaGVuH///vPnz+mOojm5f/9+aGgo3VE0J0FBQSEhITKpSjYJ+uXLlxwOh8fjJSYmyqRChBBCsrnZ6Nq1awFg8eLFMqkNIYQQyNsYNEIIIRGCJElpykVFRWVlZUms1NLSsrW1FT1cvHixsrLyvn37qq1BQUGhsrJS9JDFYqmoqEiU4XK5TCaTw+FIFTvCFqs7bLG64vF4DAYDW0x6PB6PIAgFBYXai7m7u+/cubP2MtIOcQQFBT158kRipZmZmXiCrl16ejqXyxU9VFBQUFJSkihTWVnJZDIZDOzXSwtbrK6wxeoKW6yu+Hw+QRBMJrP2YsrKyt+sStoetDRq70EjhBCqE9kcJORyuTwer7y8nMFg5OfnKykpKSoqyqRmhBBqtWTzs+XAgQPGxsY3bty4dOmSsbFxA2dDI4QQAtkOcSCEEJIh2Qxx1ENBQYGXl9fnz5+dnJyGDh1atQBJklevXo2IiOjatevcuXPZbHbTByk/uFxuYGBgREQEi8VydXX97rvvqpa5evVqfn4+tayrqzt69OimjVG+vH///u7du6KHLi4uhoaGEmWEQuHFixdjYmLMzMxmzpz5zaM6LVtkZKTEKd1z5syRGKu8dOlSUVERtayvrz9ixIimi09upKamvnr1Kj8/383NTXyfCQkJuX37toaGxrx587S1tas+MSsr6+zZszweb8KECZaWltJsi54jsxUVFYMGDXr+/Hnbtm1nzJjh7e1dtcyaNWu2bt2qq6t77ty5mTNnNn2QcmX37t379u0jCKK0tNTR0dHLy6tqGQ8Pj9u3b4eHh4eHh+MpnW/fvt2wYUP4fwoKCqqWWbp06f79+3V1df/++++FCxc2fZBy5cOHD6LmOnfu3KZNm1gsyQ7cb7/95u/vT5V59+4dLXHS69WrV3369Nm/f7+7u7v4vOEbN26MGTNGXV09JibGxsamtLRU4om5ubl9+/bNzs5WUFCwt7cPDg6WanskHS5dumRubi4QCEiS/Oeff3r06CEUCsULfPnyRVlZOTExkSTJwsJCFRWVuLg4WkKVE6WlpaLlv//+28rKqmoZc3PzJ0+eNGFQcu3u3bv9+/evpQD1UcnMzCRJMjc3V1FRMT09vamik3djx45dt25d1fVdunQJCwtr+njkB5/PJ0kyNTUVALhcrmh9//79T506RS3b2tqeOHFC4ol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VnU+BovF0tLSys3NLS4urlOCproq1ChtTXbv3r127VoNDY0RI0YYGRlR320BAQEPHjwQz6f1M2/evPPnz+vp6Y0YMUJPT09ZWRkAzp8///btW4nKqX+Jo2YIUL9h4b/GoX7yi6t9+krtJdXU1BQVFWX1jlerpveU2v0kNl3Tq6trhKK2kjhGXdN2JRqfanlS7JI7169f37Ztm7e3t4+Pj4+PDwAMGTLk77//rjrZo3ZUPRcuXLh48SLVtbKzs/v7779rn4MhIpqA8U3JycnFxcUWFhYSnTMAyM/PBwB/f/+q6UJTU7PaHCJSXFws8cuvWurq6lXfytoRBDF58uSgoCBq+Ksh5CtBq6urVzsZqxZUDqra0NQaiU5WQ/Tr1+/27dulpaXBwcH37t07ffr05s2bBQLB1q1bawksNzdXYn1lZWVeXh5BEHWNjfoRR00WrFZJScmmTZvatm0bGRkp3pdJTk5+8OBBnbZVVVRU1Pnz53v16hUcHCw+jYQalq2rmhpHmg9MTSULCwt5PJ5ozIRKTAKBQKJYaWlpXaMVEe1sXbt2FV9P9U8l3tCaXl1d33dqo58+fRIKhRIz4ard7jcpKytv27Zt27ZtsbGxDx488PHxefLkibOzc2xsrPRjDgCgoqKyffv27du3U/VcvHjx8ePHVD3UkUlZmTlzZocOHdatWzdkyJD79++Ln8lCNc7ly5ddXV3rWu21a9eoY0u1c3NzO3nyZF0rp747G7KzUeQrQdcD9XUtmkkqEhYWBgB17RRQg3e1dDZVVFScnZ2dnZ3nzp3bu3fvf/75p6YEbW5uThBEbGwsl8sVnwMUEREhEAi6d+9eU9e7JlZWVpcuXQoPD58zZ061BRISErhcrpOTk8QvzYiIiDptqFrUAMuoUaPEszOXy6WGmOqKel+qDotLH2pqampBQYF4QqGeK+q+6ejoUHPbJZ5YNeBvvuniYb98+fLVq1cDBw4UX1/tzlbTqxMVk3K7ysrKXbp0SUlJiY6OFh82KS4ujo+PJwii3vPczczMqGM8zs7OgYGBISEhI0aMaEg9jo6OQUFBoaGhVLqUvmG/ae3atQRBrF27dvDgwUFBQaJTE6ysrO7evRscHFyPBN2jR49qJ+BKoA711xX1edHX16/Hc8XJ10HCehg5cqSSkpKfn5/44GNBQQF18Hry5Ml1qq1NmzZqamrZ2dkSPS/qZ6Y4aqhBfJBXgo6Ojp2d3ZcvXzw9PcXX79ixox6BAcC0adPYbLaXlxd1SmS1WwQAapaeaOWNGzeqfnvVg6hy8ZX79u2racZr7caMGcNisc6dOyeeQOPj42/duiVlDTwe7++//xZfs3fvXgCYNGkS9ZDFYhkYGCQnJ1MnalJiYmKqzj2n3kpq1kftqMoPHjwofnWtkJCQR48eaWpqOjo6ihd+8uTJy5cvRQ8LCwtPnDhBEIRonJrqCb5//17K7e7cuVN85aFDh4qLix0dHev0o1M03VgcNZ1ZtDN/+fLl+PHj1NXEGlKP9A0rjTVr1hw9ejQ9Pd3e3j4pKYlaOWfOHCaTeezYsfT0dInyQqGQOgWpJtbW1oel8M2DhFV/zL17947aOUWn0dVfwyeCyES186AlUCeqVF1PpTx9ff3z589Tn0DqaMyUKVPEi0kzzY4kSWqi64QJEw4cOODp6RkUFESSpLOz86hRo86cORMcHJyQkODv708drFizZk0tAb98+ZLNZnM4HA8Pj6ioqODgYGrKc6dOncS3KOU0O9Er1dHR2b9/f0RExKtXry5evDhy5Mhnz56RJCkUCqmf3gsWLAgLC4uJidm7d6+qqmqXLl0A4MKFC6J66jHN7tOnT8rKygwGY/Pmza9fvw4PD//ll184HA51ar5oKpXoRBWJpx8+fBgA/vzzT9Ga1atXA0DPnj1v3ryZmJh4+fJlAwMD6rxEaabZ6enpKSoqbt68OTo6+uXLl9Sviu7du4tPgKMOHHXv3v3y5ctPnz7dt2+fpqYmNetZfJod1aqWlpY7d+709PQ8d+5cTZsWCoVUT23gwIH+/v4xMTEnTpygxlKPHDkiKkZNszMwMNDV1fX29qZ2GGr3W7BggXhtBgYGBEEsWrTo4MGDnp6e1LS8qtPsPn/+TCW7+fPnh4SEREZG/v7770wmU0FBITIyUlSMmmb36tUr8ZipX9kWFhbUw9u3b3fu3NnDw+POnTuxsbHh4eFbtmxhsVjik96o3p+Kikot74Kfn5+RkdHmzZtF9WzevJnJZOro6Ij2K+rsga5du27dutXT09PT05OavEzNZrl3717V5oVvnahy4sQJBoPRoUMH0WxF6ids+/bt9+zZ8/Dhw9evX/v5+W3cuLFz5843b96s5SXICpvNHj9+/J49ey5fvnz27Nnly5dTv5jt7OzEJ/7XT0tI0EKhcNu2beLDCAwGg7qIqHgxKRN0fHy8ra2taLCPmny6YMECiQMOTCZz0aJF5eXltb+ue/fuSQw4WFtbJycni5eRPkGTJHno0CGJgUJNTU1RfgwLCxM/uYvJZG7cuHHDhg0NT9AkSV67dk38nHIVFZXz58+PHz++fgm6srJy4cKF4ge+Jk2aRP3akPJMwlOnTokfZe3Vqxd1oodIaWkpNclMtFf8/vvvVedBl5WVzZw5UzTtpPYzCYuLi6dNmyYetqqqqsTJn1SC3r17t8QQ54wZMySuzvj06VPxQ2q1nEmYkJBA7cAihoaGDx48EC8jTYIOCQmpenSue/fu4ie8PHnyBADMzMxqaYdnz56JT5EU1RMWFiYqw+fzly1bJj4mJn4mYf0SNEmSPj4+LBarXbt2or3u+PHjVY/c9u7dOyoqqpaXICvUmUriOByOu7u7aF58QxCkfNxRJT09XSAQGBgYUKcqVIuaNNO5c+dq/5uXl/fkyZOcnBw1NbVBgwZJXCMCALKyssrLyw0NDcVT7fv373k8nrGxscThl8rKypycnIqKClVVVeq9LyoqCgsLo+au6enp9enTp+obU63y8vLg4OCkpCQ2m92rVy/qcgTiBb58+VJQUNCuXTuJc7hrUlpa+uzZs7S0NCUlJUNDQ1tbW/Hh7LKysuDg4LS0tDZt2tjZ2enq6ubn5+fn54vXn5GRUV5eLnrVJEkmJSUpKChUbTQJeXl5oaGhWVlZ7du3Hzp0qLq6ek5OTmlpqb6+PhWDUChMS0vjcDgSo29FRUWfP39u27atxOGj+Pj40NBQgiCsrKx69+5dXFz86dMnTU3NWn62JyQkmJqauri4+Pv7f/r0KSgoqLCw0MTEZMiQIdXuPCEhIdHR0UpKSnZ2doaGhgUFBV++fBE/p0Dk48ePZWVlTCZTdMWumqSkpISEhJSUlOjp6dnZ2Um8qEOHDi1fvpy6bmJsbGxYWBifz+/fv39NlzcrLy//+PGjQCCgXrhQKExOTlZUVJT4ahcKheHh4TExMZWVlSYmJgMHDpQ4jEG9Fx07dhT/3iJJMjU1VfwdEQqFMTExycnJubm5GhoaxsbGffr0Ed//t27dumHDBh8fH4kri0mg6klKSvr06ZOGhkbXrl2trKyqvaDH58+fqTlIRkZGBEFQD3V1dSXOzwaAd+/eiX6WAUBpaWlOTo66urrEl0F2djaPx1NRURFN3+LxeM+fP09JSREKhbq6uubm5jUlisaQmJgYGxtLHcg1MDDo379/1W+v+pGXBI2QlMQTNN2xVE88QdMdS304ODjk5OS8efOmHpdPQrLV7GdxIIRka8iQIQ4ODpid5QEmaITQ/7Nx40a6Q0BfMeXhTnQISY+6I9qwYcOkPGOt6bFYrC5dujTfm4Mg+YFj0AghJKdwmAkhhOQUJmiEEJJTsjlIePHiRdEZq9ra2tQdNBBCCDWEbBK0p6entrY2dRJtXa8BhBBCqFoym2Y3e/bscePGyao2hBBCMkvQt2/fjo6OtrCwGDNmDE5xRwihhpPNNLvly5erqKgwmcxr16517Njx3r17Ve9lMGbMGHV1ddEASKdOndasWSNRRiAQMBiMqneOQDXBFqsrbLG6wharK6FQSBDEN1uMw+HUcukhioznQRcVFXXr1u3kyZNVL4RqZGQ0Z84c0bXWDA0Nxa80RuFyuWw2+5tBIxEej8disbDFpMfj8ZhMpvhtVVHtsMXqSsoWk+ZrT8YfbDU1NTMzs2rv1aiiojJlypTaz/5i/ke2UbVg2GJ1hS1WV9hidSXDFpPBYHFlZWVFRQW1nJ6eHh4eXtNlFRFCCElPBj3o7Ozsfv36WVtbM5nMR48eff/993Z2dg2vFiGEWjkZJGhDQ8Pnz5+/ffsWAPbt20fdYAkhhFADyWYMukuXLpiXEUJItnDCMkIIySmcnoXkTnx8/I0bNxqpcj6fTxBEI81JYDKZs2bNkvJmlQh9EyZoJHeuXLkSEBAwaNAgugOps5s3b+rq6s6cOZPuQFALgQkayR2SJB0dHZvjvX4yMzPpDgG1KDgGjRBCcgoTNEIIySlM0AghJKcwQSOEkJzCBI0QQnJKjhI0SZIrAldsf7ZdtldARQihZkqOEjRPwPOO8d74eOOKeyvojgWhGr169YqaAigUCqdMmcLj8eiOCLVYcpSglVhKPuN8FFmKB18cDP8QTnc4CFUvKyvrwYMHACAUCq9evVpZWUl3RKjFkq8TVZyMnO5MvxOYGmjRDq8ojWiQm5sbFxenqqpqaWlJnQ6empqampqqra1tYWGBt31CNeLzwd8fhgwBNTUZ1ipfCRoABhsMHtplKADsDt7NZDBX2a6iOyLUWuzateuvv/4aMmRIfn5+7969d+/evWfPnuvXr3ft2jUuLk5DQ+Pu3bt4dzFUjcpKmDoVrl+H9eth2zYZViynextJktuebisqL8oqytrnso/ucBB9CgqgTx9ITa3DUwgCVqyAfTXsNmPGwM2bAAAsFhw+DO7u1OqwsLBdu3ZFR0d37NgRAAQCAQD89NNPv/zyCwCQJDl06FA/P78JEyY05NWgFqiyEqZNg+vXQUsLpk6Vbd1yNAYtjiCIixMvKjAV9j/f/yjtEd3hIPoIhVDXo3AkWdtTuNyvCwIBlJeLVj969MjFxYXKzgBAjW8UFRX99ttvo0aNcnZ2TklJSUxMrFskqMWjsrOvL2hqQmAg9Ool2+rltAcNACNNRt6accsnxqd3h950x4Loo6UF2dmyrDAwsNrVPB5PQUFBYuXMmTMtLCz27dvXtm3bVatW4YQN9P8IBDB3Lvj6goYG3LsHffrIfAty2oOmOHZxPDXmlKai5uW3l09GnKQ7HNSS9evX79GjR+VifWoACAsLW7x4cbdu3TQ0NF6+fElXbEge8fkwfTr4+ICmJty/D/36NcZG5LcHLW7lvZXZxdmJeYm7nXbTHQtqmVxdXa2tre3s7KZMmVJQUKChobFy5cphw4YtXrx47Nixt2/fpjtAJE+ovvPVq6CuDv7+0LdvI22neSTooyOPTr46eU/IHrvOdiNNRtIdDmqZLl26FBAQ8ObNm44dO44cORIAvL29fXx8cnJytm7dymKx2Gw2APTr18/DwwMAmEzmpUuXlJSUaI4bNTE+H2bOhCtXQEMDAgIaqe9MaR4Jekz3MdenXj/26hjOj0aNhyAIFxcXFxcX0RpFRcV58+ZJFNPT09PT06PKT5X1UXsk7wQC+P57uHLla9+5MbMzNJcEDQAjTEaMMBkBAE/Sn2QVZ03vOZ3uiBBCrQyfD7NmweXLoK4OAQHQv39jb7DZJGiRJbeXvP30NjonervDdrpjQQi1GgIBzJv3NTvfu9cE2RnkfBZHtbY5bGMz2Due7fgn9h+6Y0EItQ4CAcyeDd7eX7OztXXTbLb5Jeix3cdenXLVVt/WWMuY7lhQK7V58+Zly5bRHQVqQhs2gI8PqKmBv3+TZWdojgkaAMZ2HxviFmLVwSruc9ztdzj/CclAZmZmdnb2+/fvb968mZaWRq2srKyMjIwUlXn37l1+fn5RUdGHDx9yc3PDw8MTEhLoCRc1sXbtwMgI/P3BxqYpN9ssE7TIopuLRl0c9cfDP6OR1bcAACAASURBVOgOBDV7Bw4cmDJlyuTJk2/cuGFtbX3x4kUA+Pz584ABA0RllixZcv/+/bS0tKdPn0ZEROzatcvb25u+kFETWrECUlLA1raJN9u8E/TPNj+zGKwtT7Z4v8HPScv0hftF7089woMgPIgNDzcAwNOMp0rblAgPgrOFc+fdHQDYG7KX4cEgPAjt3dpZxVkAMO7SOOop1ietAaC4otjwgCG1ZlXAKgAIyw5T3a568MVB8W19/Pjx8ePHJ0+e9PX1/emnn2o6sbtXr15TpkxxdXW9cuXKli1bGrsFUGvWvBP0hB4TfCb6GKob6qjo0B0LahQMgqHIUhRfYDFYbAYbANhMNpvJBgAOk8MgGACgwFKgFpTYX08eUWIpUc9VYCpIVKLIUlRg/b+LbwwfPpy6HMfAgQNJkkxKSmq614lQdZrfNDsJk8wmTTKbBAAfSz4m5CXYGdrRHRGSJQ1FjZSfUsTX2OrbFv1aJL5mufXy5dbLxdf4TPTxmegjeqjCVklc9v8uRGfVwerzms8S22Iw/tdfYbPZfD6fIAjxO2TizVNQE5NlDzoqKmrXrl2ZmZkyrFN6P9z+wf6M/aZHm2jZOmoBHj9+TKXj2NjY0tJSExMTbW1tgUDw4cMHACguLo6OjqZKqqiocEWXLUWo0cisB83lcufNmxcfHz9gwAB9fX1ZVSu92b1m30q85fHYw0DdYL7V/KYPADV3AoFg1KhRtra2Xl5emzZtUlFRAYDp06ePHz/excXlyZMnWlpaVEl7e/udO3cKBIIePXqsWbOG1qiRTAmF8NtvkJ8Px47RHQqADBP0hg0bZs+evX07bWf3TegxwXuC90K/hdQoJEJ1NXbs2NGjR7948eL8+fMDBw6kVnp5eV2/fj0nJ+fcuXOpqaldunQBgL59+0ZFRUVHR1e9hDRqxoRCWLAATp8GdXU4dAjYbLoDklGCfvHiRXBw8LNnz2hM0AAw1XzqVPOpAFBaWZqYl2jVwYrGYFBzZG1tbf3/T0NgsViTJ0+mljt16iRa37FjR9HtV1BLQJKwZAmcPg3KynD9ujxkZ5BJgi4vL3d3dz99+jR1l6Ca5ObmrlixQu2/W9527ty56hQlLpfLZrMbfl/O5QHLvV57bRy8cY1NC//5yePxWCxWC7uTaWVlZdO/IhMTEw6H0/B6KioqysrKGl6P/ODxeEwmky0fCauxCIWcpUtZ586BigrP11dobQ0NeBOlbDEOh/PN/VwGH4MtW7aMHDnSyuob3dU2bdq4urqK+iDt27dXVFSUKEOSpEwS9IhuI86+Oevx1ENPXW+B1YIG1ibnWl6CpuXluP9399gGYrPZVXfs5q6FJ2ihkFi0iDh3DlRUhDdvcuxkMBNMmhYTnzVUExl8Em7cuFFQUHDp0iUAKCgomDZt2oYNGxYvXixRTElJydXV1dzcvJaqGP9pYEgTzSaeGXdmgd+CnNKchtcmz2TVYnJFYnJb80IQRAt7O1rkPvY/JAnLl38d2bh5kzF0aMOrlGGLySBB3717t6Kiglru27fvvn37xC95TpdZvWZN6DFBma0sJIUfSz7qtdGjOyKEkJwhSVi6FI4epbIzyCI7y5YMcry+vn6X/zCZTD09PQ0NjYZX23DKbGUA2Phoo/4+/V3Bu+gOByEkT0gS3N2/Zudbt2DYMLoDqoaMB/vCw8Pbt28v2zobqI9uH4Ig1t1fp66gvvg7yYEXhFBrRJKweDGcOCG3fWeKjBO0oaGhbCtsuPGm473Gei3wWxD1MYruWJBUCIIIDAys6VpF8iwyMnL48OF0R4G+hSThxx/h+HFQVgY/P/nsO1Na1NH/msztPXd41+FaSloAUFpZqsJWoTsiVJupU6c23gkg1BU2ap8SWm/z5s1zcHBojJqRzFDZ+cgRUFICPz+Q7/erVSRoAGin0g4Ajr06tvTO0t1Ou1fZrqI7IlSj7t27r127tpEqbxWzelEtliyBY8dASQlu3pTz7AzN/XKjddVRrSMArA5YfSTsCN2xIISa3Nu3X7Oz3PedKa0rQY/uNvrE6BMMghGQHEB3LAihJtejB+zbBw8fgqMj3aFIpbUMcYjMt5pv39leW1mb7kAQQk2OwYCff6Y7iDpoXT1oShfNLmoKan4JfirbVSRueoQQQvKjNSZoCpvJ5lZyV/ivwPFohJB8ar0JenjX4cdGHQMAvOEsQkg+tboxaHGL+i6y0rVqryJfpz4ihGTj3Tvo2hUIgu446q/19qAp/fT6GagbvMx6abDf4Oiro3SHgxCSBZKEn3+Gbt3g0CG6Q2mQ1p6gKUXlRZlFmUtvL8UcjVBLsHIlHDgACgrwrevUyzlM0AAAjl0cj4w8AgD7QvfRHQtCqGHWrYMDB4DDgatXYfBguqNpkFY9Bi1u8XeLTbVN1RXV6Q4EIdQAv/4Ku3Z9zc6jR9MdTUNhD/p/7DvbW3WwSs5P7nu8r1ekF93hIITqaPVq2LkTOBy4dg3GjKE7GhnABC0puzg78kPkAr8Fx8OP0x0LQkhq69fDn39+7TuPGkV3NLKBCVrSYIPBB4cfBID1QevpjgUhJJ3162HHDuBw4MqVltF3puAYdDV+7P+jkaYRi4GNg1Bz8Ntv/8vOY8fSHY0sYQ+6eiNNRroYu3wu+zzu0rjzb87THQ5CqAbr1sH27V9HNlpWdgbsQdcuvTDdL8HPL8GvnF++oM8CusNBCP1/v/8Ou3YBmw2XL7ekkQ0R7EHXpq9u3/2u+wFg6Z2lAlJAdzgIITG//grbtgGbDVeuwLhxdEfTKLAH/Q0/Wf+k10avpKKESTTKXewQQvWxZw/s3Pm179xCszNggpbGZLPJAMDlc3/2/3mY0bAp5lPojgihVi8pCRQV4cIFGD+e7lAaEQ5xSCu9IN0z3HP6temno07THQtCrd7Ro5CZCRMm0B1H48IELS1TbdO9znuFpHCh38LC8kK6w0GodWMwoG1buoNodDjEUQerbFfpKOukF6arcdTojgUh1PJhgq6bOb3nAICQFG5+vNmyg+XY7i1t3iVCSH7gEEd9ZBdnezzymHB5wtnXZ+mOBSHUYmGCrg99Nf2djjuFpNDthltWcRbd4SDUop06BceO0R0EPXCIo57WDFyjrqj+IvOFjrIO3bEg1HJ5eMCmTaCiAu7uzfrugvWDPej6c+/r7jXWi8PknIo85Z/kT3c4CLU4mzfDpk3AYsGpU60wO4OsetBHjhx59epVWVmZsbHxDz/8oK+vL5Nqm4WSipKFfgsZBOPMuDOzes2iOxyEWordu2HjRmAy4fRpmDqV7mjoIZsedFJSkp2d3bRp0zIzMwcMGFBSUiKTapsFVY7qNodtAlLw/b/fJ31JojschFqErVth7VpgMuH8eZjVevs9sulB79v39V6rY8eOVVdXj4mJsbGxkUnNzcKvg35VZivffXdXRwXHoxFqsD17YMMGYDLhzBmYPp3uaOgkyzHo8vJyX19fFRWVHj16yLDaZuEn65/8Z/mrK6j7J/k/SX9CdzgINVt79sCaNV9HNlpx35lCkCQpk4omTpx469YtFot18eLFsdVdNltbW9vY2FhFRYV6aGZmtnPnTokyXC6XzWazWM11bomQFOr8pSMQCk6OODnJdFITbJHH47FYrObbYk2Px+MxmUw2m013IM1GU7YYZ+9ejocHMJm8Y8f406Y1wRYbg5Qtpqio+M1PrswSNAAIhcKAgICpU6c+e/bMwsJC4r8mJiZr167t3Lkz9VBbW9vS0lKiTHNP0ACw9cnWDQ83sBisCPcIi3aSjSBzmKDrChN0XTVdi+3YAevXfx3ZaM59Zxm2mCw/2AwGw9XVtW/fvo8fP66aoBUUFGxtbc3NzWW4RTn0+5DfOUzOxeiLGooadMeCUPPx559fs7OXV7POzrIlgzHooqKi4uJiavn9+/dv3rwxNTVteLXN15qBa6IWR3VS6/Qm503Ehwi6w0FI7v35J6xeDQwGeHnBnDl0RyNHZJCgU1JSDAwMbGxsBg0a1LNnz3nz5jk6Oja82hbAxdvF+qT1lbdX6A4EITm2ezdm55rIYIjD0tLy/fv3sbGxJEmamJhoaWk1vM6W4Yfvftj4aONM35lGmkb99PrRHQ5C8ufNG1i7FhgMOHUK5s6lOxq5I5sxaFVV1f79+8ukqpbkD7s/GATj6KujHCaH7lgQkktdusD8+eDiAlPwTnLVkOUsjtr17Nnz8uXLtR8kbAGzOGqSWZRZWlnavW132VaLszjqCmdx1BW2WF3JsMXwYklNZPiF4RZHLHzjfOkOBCHUbGCCbiITe0ysFFZO+2daaGYo3bEghJoH/GncRDbZb+IL+XtC9pRUtKIrSSGEGgJ70E1n67CthesKnbo4FZUXZRZl0h0OQkjeYYJuUoosRQAYf3m88UHjGwk36A4HoSZ0+DCoqMAN3O3rABM0DewM7SoEFVOuTnma8ZTuWBBqEocOwfLlwOUCzjiqC0zQNPjD7o+1A9dWCCrSCtLojgWhxnf8OPz0EwDA4cMwciTd0TQn+G1Gj52OO1cNWKWjrMMX8ovKi7SU8PRL1EKdOAGLFwMAHDoES5bQHU0zgz1o2lC3A593Y57+Pv1bibfoDgehRnDkCLi7AwAcPgxLl9IdTfODCZpm3dp24/K5k65MepT2iO5YEJKpI0fgxx8BAA4fxr5z/WCCptmGIRtW2q4sF5S/yHpBdywIyc6JE7BsGQDAwYOYnesNx6Dp96fzn4v6LjLRMgEAHp9HTcVDqBk7eRIWLwaShL/++tqJRvWCPWi50L1tdwbB+DXoV509OneT7tIdDkIN4OkJixZ9zc5UJxrVFyZoOaKmoFZSUTLh8oSHaQ/pjgWhejl+HH74AQDgwAHMzg2HCVqOrBu4bln/ZTw+72bCTbpjQajuTp36X3ZevpzuaFoCHIOWIwRBHBx+cIbFDIv2jX47cIRk7Nw5WLQIhELYvx+zs6xgD1ru2OjbqLBVjr462ml/p4DkALrDQUg6V69+zc4rVtAdSsuBCVpOlVSUZBZljrs0DsejUfPg5QUREZidZQsTtJxabbt6Sb8lXD73dORpumNBSAo6OmBlRXcQLQ2OQcspgiAODz88pvsYyw6WdMeCEKIH9qDlF0EQLsYu7VXa+yX4WRy1eJD6gO6IEEJNChN0M5BakBqTGzPaZzRerwOhVgUTdDOwvP9y977uZZVle0L20B0LQgBPn0JwMN1BtAo4Bt0MEARxdOTRAZ0G9O/Yn+5YUKt37hzMmweamvD5M92htHzYg24eCIKY03uOqbbp88zndmfsHqc/pjsi1CqdPw/z54NQCOvW0R1Kq4AJupl5nfP6SfqTERdGYI5GTe3yZZg/HwQC2LoVVq+mO5pWARN0M7Owz8IFfRaUVZb9ev9XumNBrYm3N8ycCXw+bN8Ov/1GdzStBY5BNzMMguE5ytOqgxVerwM1GcY//8C8eSAQwJYt8Cv2DJoO9qCbHwbBWNJvyWCDwUlfkqb6Tg3NDKU7ItSSMS9fZs6eDXw+bN0Kv/9Odziti2wS9L///rtw4cIRI0YsXbo0ISFBJnWibwrNDPV75zfCZ8TTjKd0x4JaqCtX2AsWgEAAmzfjyEbTk02C3rdvn6Wl5fLly5WUlGxtbbOysmRSLardTIuZsy1ml1SU/HDrB7pjQS3RpUswYwbw+YKNG2HDBrqjaY1kMwb95MkTasHV1fXevXsPHjyYPXu2TGpGtWAQjGPDj5npmHXR6kJ3LKjFuXoVZs8GgYC/YQP5229MusNpnWQ8Bs3lcj98+NCpUyfZVotqwiAYq21XTzGf8qns06Kbi15mvaQ7ItQi/PMP1XeGTZv469fTHU3rRZAkKcPqFi1alJGR4e/vX/Vfbdu2bdeunaLi11tW9+zZ88iRIxJluFwum81msXBuibR4PB6LxWKxWLeSbs3wm6HKVvWd6GujZ0N3XPKLx+MxmUw2m013IPKL9e+/SvPnA59f/uuvFb/+ii1WV1K2mKKi4jfLyDJB//HHHzdu3Hj06JGmpmbV/3bv3n3r1q1dunz9Ma6urt61a1eJMpig60qUoIWk8Pt/vz//5ryBukH6inS645JfmG6+ISYGrKyAz4eNG2HTJsAWqzsZtpjMUuH27duvXbv28OHDarMzALDZbDMzM3Nzc1ltEYljEIzT404baRppKGrQHQtqzjQ0wNwcpk3Dk7nlgWwS9P79+8+cOfPo0aN27drJpEJUD0yC6WHvAQBcPndP8B682D+qD319iIqiOwj0lQwOEvL5/JUrV2ZlZfXs2VNLS0tLS+vAgQMNrxbVW8j7kI2PNtqdscNzWBBq1mTQg2axWF++fBFfo6Sk1PBqUb3Zd7afYTHjYvTFMT5jclfnEgRBd0QIofqQzRBHTePOiBZMgnlu/DldVV2+kI/ZGaHmC+dLtExMgrnXeS8ACEnhyYiTAw0Gmuvg4VmEmhm8WFILF/kx0v2W+8BTA/EcFiTp5k0YOBAiIuiOA9UIE3QLZ9XBaqr51MLywuEXhvP4PLrDQXLjxg2YNAlCQuDdO7pDQTXCIY4WjkEwvCd4ayhqZBZlspl4rgECAIC7d2HqVKiogJUrYepUuqNBNcIE3fKxGKxjo45RyzcTb5pqm5pomdAbEqLT3bswfjyUl8PKlfDnn3RHg2qDQxytSFpB2hifMdYnrMM/hNMdC6LJzZswbhyUl8Pq1Zid5R8m6FbEQN1gktmkfF6+83nnAl4B3eGgJnfrFkyaBBUVsGoV7NlDdzTo23CIoxVhEIyLEy+qsFWiPkbheHSr4+8PkydDRQX8/DPs3Ut3NEgqmKBbFzaDfWbcGWo5LDusvUp7A3UDWiNCTcLfH8aPBx4PVqyAffvojgZJC4c4Wql8Xv6AUwOsPK0iP0bSHQtqZLdvw7hxwOPBzz/D/v10R4PqABN0K6WhoDG62+gv3C9O55w+lX2iOxzUaO7cgYkTobwc+87NESboVoogiEuTLk01n8ogGAKhgO5wUOMICPianX/6CbNzc4Rj0K0Xh8m5NOkStZxakKrMVm6v0p7ekJAsBQTA2LHA48Hy5bB/P+Bls5oh7EEjqBRW9j7a2/xv89c5r+mOBcnOli3A48GyZXDgAGbnZgoTNAI2g+3YxTGPm+d4zjG7OJvucJCMHDgA58/DX39hdm6+MEEjAIBLky6NNx1fXF5cVF5EdyxIRvr2hVmzMDs3azgGjQAAOEyO71TfssoyZbZycUUxALThtKE7KIRaO+xBo/9RZisDQO+jvbse7BqdG013OAi1dpigkSQrXavc0lyHsw4ZhRl0x4JQq4YJGkm6OPHiSJORn8o+pRem0x0Lkk56OmTj0d0WCMegkSQFpoLfdL+PJR/12ujxhXwhKeQwOXQHhWr24AGMHg2dOkF8PN2hIBnDHjSqBoNg6LXRA4ChZ4ca/WUU+ymW7ohQDajsXFYGrq50h4JkDxM0qo2uqm52cfaws8NSC1LpjgVV8fQpjB0LZWXg5oZncrdImKBRbc6NP+di7JJTmhOejTdhkTOPHoGrK5SUwMKFcOIEMPCz3ALhGDSqjSJL8daMWxEfIvrp9aM7FiTm2bOvIxvz58OxY3g2SkuF37roG1gMVv+O/QmCmOU7y+gvo/jPeCSKbo8ff+07u7lh37llw7cWSUtICtMK0oadHZaSn0J3LK3Ys2cwahSUlsK8eXD8OGbnlg3fXSStU2NPOXVx+lDy4V7yPbpjaa2ePoXhw6GkBObPh5MnMTu3eDgGjaSlxFK6NeNWUGqQg5ED3bG0SsHBMHIklJTA99/jyEYrge8xqgMOkzO863AOk7Ph4YZeR3sl5iXSHVGr8ewZuLpCcTF8/z2cOoXZuZWQzdscGRm5d+/exYsXX716VSYVIjmXXpAenRs99OzQ5PxkumNpBUJCYMQIKCmBadNwZKNVkc07ffXq1fj4+MjIyNDQUJlUiOTcsVHHhhkNyy7Ovhh9ke5YWrp37772nefMgQsXgMmkOyDUdGQzBr19+3YAWLx4sUxqQ/JPma18a8ata7HXRnUbRXcsLV1JCZSXw7x5OO7cCuH7jepJiaU0q9csDUWN4+HHHc45JH1JojuiFsrKCgoKwMsL+86tUNPN4sjOzp40aZKSkhL1sFu3bidPnpQow+Vy2Ww2i4VzS6TF4/FYLBa9LRaaHvog9YH9GXv/qf6d1TvTGIk0eDwek8lks9l0B1JHJSV0bbm5thh9pGwxRUXFb35ym+6DraOjs3nz5i5dulAP27dvr6qqKlGGelWYoKXH+g+NMRwefTi1KPVx+uOT0ScPuB6gMRJpsFgsTDd1gi1WVzJssab7YLPZbDMzM3Nz8ybbImoaKmyV2zNve0V6je0+lu5YEGpRcAwayYAKW2VZ/2UG6ga3390ef3k8nguOkEzIJkFv3LiRIAhPT8/9+/cTBLFz506ZVIuanYDkgH/j/x16diheP7o+wsPBzQ1vXoVEZJOgPTw8SDHr1q2TSbWo2dk2bNsgg0EZhRmbH2+mO5bm5sULcHAALy94/JjuUJC8wMNxSJZUOap3Z9498PzAyG4j6Y6lWXn5ElxcoLAQpk6FKVPojgbJCxyDRjKmylH9fcjvVh2swrLD5t2Yl1aQRndEci8iAoYPh8JCmDQJvL1xvjMSwQSNGsu/8f+eiTpjf8Yec3RtwsLAwQG+fIEpU8DHB3COKRKDCRo1lnWD1g3oNCC9MH1VwCq6Y5FXr16BszMUFMDkyXDhAmZnJAF3CNRY2nDa+M/y/y3oNxyPrl5kJLi4QEEBTJyI2RlVC3vQqBG14bQ5OPygi7FLSn7KqoBV74ve0x2R3IiKAicn+PIFJk4EHx/A8/RQdTBBo6Zw5e2VfaH77E7bZRRm0B2LHIiIgGHDIC8PJkzA7IxqgQkaNYUl/ZZYd7ROLUhddHMR3bHQLSICnJwgPx8mTIBLlzA7o1rgsBdqCmoKavdm3/vp7k92ne3ojoVWUVHg7AxfvmB2RtLABI2aiLqC+plxZwDgC/fL0VdH51nO02ujR3dQTSsqChwdIS8Pxo/H7IykgUMcqKldirn0+4Pfh5weklmUSXcsTWvRIsjLg3Hj4PJlzM5IGpigUVOb2WtmP71+yfnJ069NpzuWprViBaxbh9kZSQ+HOFBTU1dQD5gdsMBvgUV7C7pjaVozZtAdAWpmMEEjGmgoavwz5R8A4PF5l99eHt51eDuVdnQHhZDcwSEORKd/4//9/t/vB3kNyi7GiyAjJAkTNKLTcJPhfXT7vPvybuwlvF0WQpIwQSM6qSuo359z37Wrq0W7ljUeXVEBAgHdQaBmDxM0opmmoubdmXe9xnqRJHnn3Z18Xj7dETVYTAwYGYGrK91xoGYPEzSSF4EpgSMvjhxwasCHkg90x9IAMTHg4ADZ2aCtTXcoqNnDBI3khbW+tWUHy/jP8cO9h9MdS329fQsODpCbC8OHw5kzdEeDmj1M0EheUOPRgwwGaShq0B1LvSQkgJMT5OaCszP4+oKCAt0BoWYP50EjOdJWqe3TeU+p5VfZr7prd2/DaUNvSNJKSIChQ+HDB3B2hhs3QFGR7oBQS4A9aCSPIj9G9jvRz+akTU5pDt2xSCEuDuzt4cMHcHHB7IxkCBM0kkddtbr2at8r9lOs0zknISmkO5xaJSSAoyN8/AhOTnD9OmZnJEOYoJE8asNpc3/O/T66fYrKiwSkHE8ojo8He3vIzgYnJ7hxA5SU6A4ItSg4Bo3klI6yzsuFLwVCAZvBTi9Mb6fSToklZ+kvMREcHL72nTE7o0aAPWgkv5gEk8PkZBRmmBw0sT5h/ansE90RiUlI+Np3dnTE7IwaCSZoJO+0lbW7a3ePzo12OOtQIaigOxwAAHj3DoYNgw8fYMgQ+PdfzM6okWCCRvJOma0cNCfIop1FemF6WWUZ3eEAvH//te/s4AD+/qCiQndAqMXCMWjUDLRTafdq0avSylINRY3C8kJltjKbQd9NSaKjITsbhg0DPz/sO6NGhT1o1DxwmBxNRc0CXoHhfkPrE9afyz7TFsqIERAdDffugbIybTGg1kE2CTozM3PGjBl9+/adM2fOx48fZVInQlUpsZU6qnWM/BjpdN6Jy+fSFkfPnsDCX5+o0ckmQU+YMEFbW9vb21tJSWnatGkyqROhqhSYCkFzgnpo94jJjflUKk+TOhBqBDLoBbx48SIxMfHZs2ccDufAgQPa2toxMTE9e/ZseM0IVdVBtUPYorDc0lwDdQO6Y0GoccmgBx0dHW1pacnhcABASUmpZ8+eb968aXi1CNVEha1ipGHEF/KNDxpbn7TO4+bRHRFCjUIGPejc3FwNjf9dH1JTUzMnp5oL3GRmZrq4uLDZXw++9+zZ08fHR6IMl8tls9ksHN2TGo/HY7FYrbPFhKSQw+C8zHo57MywgGkBKmypprvxeDwmkynaD2tHZGWxbt2qnDu3NV9ho04thkDqFlNUVPzmJ1cGH2x1dfWysv/NTi0pKRHP1yK6uroHDhwwMTGhHrZp00ZVVVWiDPWqWme6qR/Wf+gOhB4Pvn8w9MzQN7lvssuzrTStpHkKi8WSNt2kpICzM2RkKBgawqRJDY212apDiyEAkGmLyeCD3blz58TERGqZJMnk5OTOnTtXLcZkMvX19bt06dLwLSJE0VXVfbHwRcLnBKsOUmXnOkhNhaFDISMDBg+GESNkXDlC0pHBGLSTkxOXy71x4wYAXLlyhcPhDBkypOHVIiQNdQX1/h37A4DDOYehZ4fK5p6zGRng4AAZGTBgANy+jfOdEV1kkKA5HM7Zs2fd3d2NjY1Xrlx55swZJpPZ8GoRqpOckpxHaY+czjkVVxQ3qKKMDLC3h9RUGDAA/P2hTTO5pQtqiWQzdunq6pqZmZmbm9uuXbtWOx6K6HVv9r2hZ4aGfwh/nvncqYtTPWtJSwN7e0hPh4ED4e5dzM6IB/pVfgAAHhhJREFUXjJLpiwWS09PT1a1IVRXHdt0DHELeZT2yMHIoZ5VUCMb6elgawt37mB2RrTDa3GglkNbWXuS2SQGwVh4c+Goi6MKeAV1eHJGBgwdCikpYGsL/v6gptZoYSIkLUzQqAWK+BBx+91tF28Xacej09PB3h6zM5I3mKBRC/TvtH+NNY1fZr28lXjr26WpvnNqKtjYYHZGcgUP6KEWqJNap2fzn/nG+Y4zHfeNou/fw7BhkJoKffvCnTuYnZFcwR40apk6qHZY0m+JEktp29NtU/+ZWlheWE2h9+9h6FBIToa+fSEwEDQ1mzxMhGqDCRq1cHff3b3y9oqrt2s149FTpkByMlhbQ1AQZmckhzBBoxbuwsQLRhpGzzOfe7/xlvzf0KEwaRLcuwfq6nSEhtA34Bg0auEM1Q2fzHtyOur0ZLPJkv/bvp2OiBCSFvagUcunr6a/YcgGbWXtc6/P/XD3h4aeC45QU5GnBM3nK9jYsNhsIIg6/M2YUWOFixcDg1G32kxNobS0+trOngUFhbrVpqkJkZHV1xYdDVpadauNw4FTp6qvjccDc/O61cZgwIIFNTbd3Ll1q40goFcvqKiovrZjx4DDqVtt2toQG1t9bWFhoKFRt9oUFeHCBQA4/+b8mTdndP7UWXt/LQBE50Zr7dIiPAilbUq+cb4AcPb1WYWtCoQH0X5v+5T8FABYfGsxw4NBeBDfHf9OSAr5Qr6VpxXhQTA8GMvvLgeAxLxEnT06hAehuFXxQvQFALjy9oriVkXCg9DerR33OQ4AVt5bydzMJDyIXkd7VQgqSJK0OWlDVbLw5kIASC9M77C3A+FBcLZwTkWeAgC/BD/lbcqEB6G5SzPyYyQA/P7gd6oS08OmpZWlADD07FDCgyA8iBnXZgDAh5IP+vv0CQ+CvYV9+OVhAAhIDlDdrkp4EOo71UMzQwFg29NtrM0swoMwPmhMncgz8uJIqpJxl8YBQB43r/OBzoQHwdrM2hOyBwCCM4Pb7m1LeBBtdrR5mPYQAPY/38/ewiY8CIP9BrmluQAw+epkqhIXbxcAKK4oNjlkQlXi8dgDAMKywzR2ahAehMp2lbtJdwHg2KtjnC0cwoPQ+1MvqzgLAOb+O5eqZPDpwQDA5XPN/jYjPAjmZmbzer9e576u8ZNVR/KUoEmSELuutLRqyqcAUFYGJFm32mp5Snk58Pl1q628HCorq/9XZSWUl9etNj4feLzq/yUUQl2bjiRra7pa/lXLU2TYdDxejU+pR9NVVlJfHsdHHzfWNBaSQm4lFwAqBZXlgnJqoUJQAQDl/HK+kA8APD6PWiirLCOBBIDSylISSBLI0opSACCBLKssAwC+kM/j8wCgUvhfJYLySmGlRCVCUvj/Kqn8WglVm6gS0UKFoIKqpJxfXimoBAAun0tVUlZZRpIkAJRUlFCvj6pNSAqp5wqEAlElotdFVcLj8wSkAAC4lV9rq1oJdTdeAfm1ElErVQgqvkZSyaVelygk6lWIahO1sIAUSDS1KCRR44gWRJWUVpSSJEmSX1u4mb5fMkGQdU1h9dWzZ8/Lly+bm5vXUgbvqFJXrfmOKvWD9wepK2yxupJhi8lTDxohhJAYTNAIISSnMEEjhJCcwgSNEEJyChM0QgjJKUzQCCEkpzBBI4SQnMIEjRBCcgoTNEIIySlM0AghJKcwQSOEkJzCBI0QQnIKEzRCCMkpTNAIISSnMEEjhJCcwgSNEEJyChM0QgjJKflK0Hfu3Ims6SZ+qDp37tyJiIigO4rmxN/f/9WrV3RH0Zzcu3cvLCyM7iiak8DAwBcvXsikKtkk6IcPH/7yyy/Dhw8/duxYQ+q5d+/ey5cvZRJSKyHDXaGVuH///vPnz+mOojm5f/9+aGgo3VE0J0FBQSEhITKpSjYJ+uXLlxwOh8fjJSYmyqRChBBCsrnZ6Nq1awFg8eLFMqkNIYQQyNsYNEIIIRGCJElpykVFRWVlZUms1NLSsrW1FT1cvHixsrLyvn37qq1BQUGhsrJS9JDFYqmoqEiU4XK5TCaTw+FIFTvCFqs7bLG64vF4DAYDW0x6PB6PIAgFBYXai7m7u+/cubP2MtIOcQQFBT158kRipZmZmXiCrl16ejqXyxU9VFBQUFJSkihTWVnJZDIZDOzXSwtbrK6wxeoKW6yu+Hw+QRBMJrP2YsrKyt+sStoetDRq70EjhBCqE9kcJORyuTwer7y8nMFg5OfnKykpKSoqyqRmhBBqtWTzs+XAgQPGxsY3bty4dOmSsbFxA2dDI4QQAtkOcSCEEJIh2Qxx1ENBQYGXl9fnz5+dnJyGDh1atQBJklevXo2IiOjatevcuXPZbHbTByk/uFxuYGBgREQEi8VydXX97rvvqpa5evVqfn4+tayrqzt69OimjVG+vH///u7du6KHLi4uhoaGEmWEQuHFixdjYmLMzMxmzpz5zaM6LVtkZKTEKd1z5syRGKu8dOlSUVERtayvrz9ixIimi09upKamvnr1Kj8/383NTXyfCQkJuX37toaGxrx587S1tas+MSsr6+zZszweb8KECZaWltJsi54jsxUVFYMGDXr+/Hnbtm1nzJjh7e1dtcyaNWu2bt2qq6t77ty5mTNnNn2QcmX37t379u0jCKK0tNTR0dHLy6tqGQ8Pj9u3b4eHh4eHh+MpnW/fvt2wYUP4fwoKCqqWWbp06f79+3V1df/++++FCxc2fZBy5cOHD6LmOnfu3KZNm1gsyQ7cb7/95u/vT5V59+4dLXHS69WrV3369Nm/f7+7u7v4vOEbN26MGTNGXV09JibGxsamtLRU4om5ubl9+/bNzs5WUFCwt7cPDg6WanskHS5dumRubi4QCEiS/Oeff3r06CEUCsULfPnyRVlZOTExkSTJwsJCFRWVuLg4WkKVE6WlpaLlv//+28rKqmoZc3PzJ0+eNGFQcu3u3bv9+/evpQD1UcnMzCRJMjc3V1FRMT09vamik3djx45dt25d1fVdunQJCwtr+njkB5/PJ0kyNTUVALhcrmh9//79T506RS3b2tqeOHFC4olbtmwZO3Ystbxjx47Ro0dLszl6etCPHj1ycnKiZla6uLjExcV9/PhRvMCLFy/at29vYmICAGpqatbW1o8ePaIlVDkhPmWSz+dXPceHcvPmzb/++uvp06dNFZdc+/Lly4EDB86ePSuxd1GCg4O7devWsWNHANDR0enVq1fVmf6tU05Ozp07d+bOnVvtf69fv37w4EFpO4AtTrXjYKWlpS9fvnRxcaEeOjs7V81Xjx49cnZ2ppZdXFwePnwozeboSdAfPnxo164dtayqqqqiopKdnV1TAQBo3779hw8fmjREeZWTk7Njx47Vq1dX/VfPnj3Ly8uTk5OnTJkyb968po9NrigqKlpYWHz48OH69eumpqZVE4rEPtauXTvcxyhnz561sbExNTWt+q/evXuXlpYmJiZOmDDhhx9+aPrY5BO15+jo6FAP27dvL5HQAODjx4+i/a19+/YlJSWi0fxa0HOQkMViCQQC0UM+ny9xDJDFYgmFQvECVYfDWqGCgoIRI0bMmzdv7NixVf976dIlamHt2rXdunVbsmRJv379mjZAOWJvb29vb08t//HHH+vWrZP4YYH7WE3OnDmzZs2aav/l6+tLLaxevdrU1HTJkiUWFhZNGJqcovYc0e5UNaEBAJPJFCU9Pp8PANJMfKCnB62npyf6hsnLyysvL9fT05MoIH7pj+zsbIkCrVBRUdHw4cMHDx68ffv22kt27NjR2Ng4OTm5aQKTf4MHD67aGriPVSs4OPj9+/eTJk2qvVjnzp0NDAxwH6Po6uoyGAzR7lTtviSe9LKzszU1Nate66IqehL0qFGjbt++TV2a49q1azY2NtSslNjY2PT0dAAYMGAAj8ejLhOemZkZERHh6upKS6hyoqysbMyYMT179ty/f7/4+qSkpKSkJACorKwk/5vS/u7du3fv3vXo0YOGQOVGRUWFaPnOnTtmZmbUcnR0dGZmJgDY29tnZWVFR0cDQGJi4rt37xwdHWkJVa6cOnVq+vTpqqqqojWJiYkpKSkAUFFRIdrHqI9qtcMgrZCCgoKjo+O1a9cAoLKy0s/Pb9SoUQDA5XKfPXtGdZxHjRrl6+tLNeC1a9eoAt/W0IOa9SIQCKjJvG5ubm3btr1//z61fuTIkevXr6eWDx8+rKuru3jxYmNj419++YWWOOXH+vXrmUymg4ODo6Ojo6PjuHHjqPXz5893c3MjSfLVq1ddunSZOXPm9OnTNTQ0Vq9eTWu89Js7d66Dg8P8+fMHDBigq6sbERFBrbezs9uxYwe1vHPnTn19fXd3dwMDg82bN9MXrLwoLi5u06ZNaGio+MoZ/9femUc1dbQNfAI3YKDIJpsaK0k0lkXRUIuisigibj0WWzieWFu1atVq3YBqq+IhikfccKlWj4j1iCweRSmKmAiKyCJQlkABgyBCDCARE0NY5/1jzne/+yaRIlLBt/P7696ZO3OfO0meO5l5liVL1q9fDyHMyMjgcDh8Pj8wMHDo0KE7duwYIDEHErVaPWvWLHd3dwCAt7c3aZiRmZlpYWHx7bffTp06dfr06ehlVlZWBgBobm6GECoUivHjx8+aNYvP51tZWZWWlvbmdgPmSdjV1SUUCqVSqZeX16hRo1BhaWmpsbEx6VBQVFSUn5/P5XJ7HzPvf5XKykr03wJBp9M9PDwAAGj6zOFwurq6CgsLy8rKCIJwcXHhcrkDJuvgoLm5OTs7WyaT2dnZTZs2jbR7KS4uNjc3HzlyJDrNz88vKipycnLS6fvzb0MulxcUFHh7e1MLKyoqCIJgsVidnZ0FBQUVFRV0On3ixInIyOrfRnd3t0gkIk8JgiC3Ourq6kQikaWlpY+PD1pfbm1tzcvLmzJlCrL9UKvVKSkpr1+/nj17tk5PFm2wqzcGg8EMUnCMVwwGgxmkYAWNwWAwgxSsoDH/OIcPH05OTh5oKd4fERERKSkp/dhheXn57t27m5qa+rFPzAcBVtAfAHPnzqXRaGFhYf/0jVJSUnbt2tXv3b5/BV1TUxMSEoICJrx/IiIibt261efm586dO336NLWkvLw8NDS0sbHxnUXrLaWlpWFhYXv37hUIBPX19QkJCUql8r3dHfP//FPWKJh+ora2Vl9f38zMjM1ma4SU6ne2b99uYmLS791evXr1PUfYQY7d6enp7/OmJFeuXMnLy+tz8zlz5nh4eFBLnj17dvHixZaWlneVrHfExMRs3ry5ra0NQqhSqdauXevo6Ph+bo3RAPu2Dnaio6P19fWPHz/O5/Pv3buHrOtIOjs7JRKJXC43NzfncDjUSC5NTU1Pnjyh0+lMJtPS0lKjlVgsbm1tHTdunJmZWd8Ek0gkTU1NXC5XZw8KhUIsFo8YMYLJZPr5+WmHmCkvL5fL5dbW1iwWi1re3d1dVlamUCjs7e1tbGx6luHFixfV1dVGRkZsNrtvaafVanVpaWlHR4eTk9ObQlC9ic7OzuLiYgjhhAkTqA84b9487edtb28Xi8UGBgaOjo4AgK6urqqqKrlcPnr0aGpIEJ3Y2dn5+/trZImWSqU1NTWmpqbjxo2j0WjarZ4/f15bW8vhcMzNzXv/UDU1NQcOHMjNzUWxzBgMxuLFi9Vqde97wPQnA/2GwPREd3c3h8Px9/fv6uoaOXLksmXLqLV3796lBqE3MzOrrKyEEHZ0dHz99ddkGmYajYYcDRDR0dFkVBc6nR4cHIzivq5evZr6xWAwGDpFIggiKCiIDNzFYDBOnjxJ1vL5fEdHx2PHjiE3VnRfJpO5bt068po7d+5wOBzyRvb29mQw1Zs3b44ePZoUe9myZdSIjlRevnzJ4/FIxcRgMMLCwlDV9evXNb7kQqFQZycHDx4cOnQousbIyCgiIgKVC4VCPT098hRCuGLFCmNjY7FYDCG8du0aAOD8+fNMJhO1ZbFYBQUF5MU2NjY//vgjOj5y5AgAIDExEb1s3NzcIIQnTpywsLAgxXNxcSkvL0fXa4RPcXd3hxAmJiYCAEjXhlevXi1evJh8di6Xm5OTQ96dzWYvX7583bp16CVBo9HeymspPDx86dKl1JLS0tILFy70vgdMP4IV9KAmPT0d/bwhhNu2bTM2Nqb+zx0xYsSCBQtqa2u7u7tRsoa6ujoI4alTpwwMDK5fv97W1qZSqXJycuLj41ETFOxmw4YNtbW1r169+u233wiCOHToEISwsbHx+++/NzY2lkgkEomkqqpKp0gEQRgZGa1evVomk0ml0qVLl9JoNJFIhGr5fL6RkZGTk1NaWppUKpVIJPC/FXReXp6hoeHUqVNzc3NVKpVEIomIiEAKOicnh06nBwQEPH78WKlUXrlyxcTEZMOGDTrFaG5uDg0NLSkpaW1tlUqlP/30EwDgxo0bEMLXr1/Hx8cDAGJiYtCzqFQq7R4iIyPRyr5MJmtubhYIBAAAcqBCQkIIgnjw4AGEMDY2FmlkVIUUtIWFxcWLF5VKZV5e3tixY5lMplKpRBdoK+jRo0fHxsZKpVKkZC9evJiYmFhfX69Wq+/fv8/lcidOnIjWr549ezZjxozJkycjydEHqqGgFy9ePGTIkPPnz7e0tDx69MjBwcHS0lImk6FaNpttYmISEBBQUVEhlUrXrFkDAMjOzn7DV0yTn3/+2dbWFr2KEHK5XC6X97I5pn/BCnpQ880331haWqLVQLFYDAAgA4ErFAoAwOnTp7Vbbdq0adSoUWherIGzs7OXlxe1ZPny5WPGjEHHvVmDJp3K0KlarbazsyMdXvl8Po1GKywspDahKmh/f38zM7OmpibtnhcsWDBmzBjkI4vYs2fPkCFDUJiRv8XFxeW7775Dx3+7Bt3R0WFlZaUxVUTZ18gLpk2bxmQys7Kyhg4dGhgYSF6GFPTmzZvJEhTbNzo6Gp1qK+hz5871IDma8pPpArTXoKkKurq6mkajBQUFkbWPHj0CAJD+62w2++OPP0bfGQjh69evDQwMBAJBDwJQKS4uNjIy0tPT4/F4O3bsQEkzMAMFXoMevCiVyoSEhOXLl6PVVQcHBx6PFxUVtXLlSgDARx995Orqum3btkePHi1atMjDw4MM6u/p6Xn48OGpU6cuWbJkzpw5Y8eOReUvXrwoLi4OCAiIj49vb29HWXlaW1urqqra2to0ljh7YPbs2eQaq6Ghobe3d3Z2NlmLgt+/qe39+/dnzpypsSaOSEtLc3V1vXbtWldXFwqV29DQoFarq6urqUsiJLW1tWfOnCkvL29ubgYA1NXV6exWJ6WlpY2NjSYmJvHx8eh/BgBAX18fxU4CABAEERMT4+LiMm3aNA6Hc/bsWY0e/Pz8yGMPDw8Gg4HeoDqZOXMm9bS7uzsxMTE5Obm+vr69vR0ZSFRVVZExD3qWHEI4b948soTH4w0fPjwrK4sscXNzI1fkjYyM7OzsqHH7esbJySknJ+fXX38VCoUCgeDo0aP5+fn/Tq/uwQBW0IOX2NhYpVJZV1cXEhKCSuh0emZm5l9//YWiiCUnJwsEgqtXr545c4bBYKxYseLgwYMGBgYLFy5MSEg4efLktm3bNm7c6OTkdOrUKXd3d5RSNisrC0XwIHFxcVEoFL1X0Bp60MrKipqypOcgAy9fvtS59dfZ2alQKMrKyvbv308t5/F4SHtqkJ2d7eXlxeVyP//8c0tLS0NDw8bGRu1EcG8C6fTU1FTqqwUAQC4rAwBGjBgxYcIEkUgUEBCgvX9IHQQajTZs2LAe4v1rjElgYGBSUlJgYKCnp6epqemzZ8+ysrJ6KTwaanIXAWFlZdXS0kKempiYUGsJgkABiHuJo6Pj8ePHAQDFxcU+Pj7R0dHvwcQToxOsoAcvUVFRZmZm1dXV1dXVZCGdTo+KikJazMrK6siRI0eOHKmsrDx//vzevXtZLNamTZsAAP7+/v7+/iqVSiQSBQUFLVq0qL6+3tLSkkaj8fn8d/y9aWSQqq+vJ2MPAQB0WhSQWFtbo2ifGhAEYWpqOnPmTJ0ZhLU5d+6cjY1NdnY2OVU8c+ZMbxoikHrdsmWLxtYolUOHDqWlpfn6+oaHhy9YsIDH41FrqYPQ1dUlk8moyl0D6pjIZLL4+PiTJ0+SGUneymga3UUqlVLDydbX1/fLJDcuLu6rr74iT52dnefOndvW1vbuPWP6BnZUGaRUVFRkZmYGBQU9+m/8/PwuXLigMSEaM2aMQCCws7ND4Q1JjIyM5s+fv379+sbGxhcvXpibm3/66aeXL1/WOScFAJiamqpUKmqyG5388ccf5I9WoVDcvn170qRJvXwuHx+f27dv19bWalf5+vomJyfrzB+ozfPnz21tbUntXF5e/ueff5K1yPIPLdPrxNHRceTIkdHR0dSkKlRyc3O3b98eHBx848aNSZMmBQQEUKeoAAAU/BeRlJTU3t7ey0FAE22q+Q3ahCQxNTXtQXJnZ2eCIOLi4sgSkUjU2NioYX/5JpB5n06nRJVKpZ0o7+nTp9TFHMz7ZqAXwTG6CQ4OptFo2qYUKK9VUlJSRUXFwoULY2NjCwsLxWJxWFgYjUaLiYmBEG7evDk0NDQ9Pb2ysjI1NdXZ2Zl0NMjIyDAwMHBzc0tMTBSLxWlpaeHh4SiiNIRQKBQCANauXXvp0qUrV67oFIwgiGHDhs2dO/fhw4cZGRleXl50Op00MkNmdhpNqJuEVVVV5ubmbDb78uXLJSUlQqFw7dq1CoUCQlhRUWFmZjZu3LiYmBixWHz//v3IyEhy+1GD/fv302i0w4cPl5WVXbt2jcPhWFtbIyM2CKFKpbK0tJw+fXp0dHRcXBxp4UAlISFBT09vzpw5t27dEovFd+7c2blzJ9p8k8vl9vb2kydPRjuWNTU1FhYWX375JWqINgmtra337NlTVFQUFxdnbW3t7OxMbm9qbxJSzUhUKpWVlRWPx3vw4EF+fv6WLVtsbW3RZ4ouOHDggL6+vkAgiI2NReYxGlYc69at09PT27VrV0FBQWxsrK2trb29/atXr1Atm81euXIl9UnZbPaqVavQMVqM/uGHH7QHJDU1lcViUUVNSUmh7o5CCJOSksLDw0tKSu7du7dz584nT56kp6fv27cPJUfH9DtYQQ9Guru73d3dyaj8VFQqlYODw8aNG58/f+7r60uujTKZzMjISHRNZGQkuTFIp9MXLlxIVfQPHz708PBAu3x6enrjx48/ceIEWYt2F1ksloODg07ZCILYuXPnmjVr0Jr1qFGjSM0CIdy0aZOvr69GEzc3t19++YU8FYvFPj4+SACCIGbPnk0aO5eVlc2fP5+cF48dO3b37t06xWhra1uxYgWKumtjY3P69Ok1a9Z88cUX5AV379719fXlcrksFiszM1NnJzdv3nR1dUXrDwRBTJ48+fLlyxDCrVu3Ojg4kGYVEML4+HgWi3X9+nX4fwr6xo0bKGo7jUbz9vZ++vQpeTGPxwsNDUXHUVFRLBZLw5o7LS0NbXvq6en5+vqKRCIWi0WaKqpUqq1bt7q6urJYLPRWSE1NZTKZyMgdQtjR0RESEoL+Jejr6/v5+T158oTs3NPTMyQkhHo7T09PMg9GUVERAODYsWPaoxEaGvr7779v2LDh7NmzycnJoaGhwcHBpDUIhFAqlT548MDb2xsZ4a1atSouLg5CeOrUqUuXLukcYcw7ghX0B09zczOagWrQ1tbW0NCg09gOQqhSqWQyWS8t2KgQBIGSj6jV6oaGhj57nyMBSHM9Kmq1WiaTUVXDm2hvb29oaOibACRKpVImk71poLRBChopqZaWlpcvX/btvnK5XKeBdi/p6OiQyWRv28PRo0eHDx+usxVp+/j48ePc3Fxt2+eurq7W1lZPT090OmPGDPTiWbZsWUlJyVs/AKYX4E3CD543OfIaGBho7PVTYTAYvclZ2QOGhoY99P+39CCAoaHh33o/I+h0+rvIgDA2Nn5bJ28S0hGxD/TZyR5BEEQvR4mKVCrdt2+fzpEn7VLYbLbOtnp6ellZWZ999hkAQKlUGhoaIiv18vJye3t7tCvwtvJgegYraAzmX8S+ffvepXl6ejrK8JSRkYFWeKqqqtzc3NLT0zVsvTH9Ak55hXk7hEIhi8Wyt7cfaEEGjMbGxsLCwilTpvR53v3hkpubO2HCBAMDA4lEglxgAABCofCTTz4ZPnz4QEv3PwhW0BgMBjNIwXbQGAwGM0jBChqDwWAGKVhBYzAYzCAFK2gMBoMZpGAFjcFgMIMUrKAxGAxmkIIVNAaDwQxS/gMb2Mk2qcbXwwAAAABJRU5ErkJggg==\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Sₘ_range = 0:0.1:10          #more possible outcomes, for plotting\n",
    "\n",
    "CallProfit = max.(0,Sₘ_range.-K) .- exp(m*y)*C\n",
    "PutProfit  = max.(0,K.-Sₘ_range) .- exp(m*y)*P\n",
    "\n",
    "p1 = plot( Sₘ_range,[CallProfit PutProfit],\n",
    "           linecolor = [:red :green],\n",
    "           linestyle = [:dash :dot],\n",
    "           linewidth = 2,\n",
    "           label = [\"call\" \"put\"],\n",
    "           ylim = (-1,5),\n",
    "           legend = :top,\n",
    "           title = \"Profits of call and put options, strike = $K\",\n",
    "           xlabel = L\"Asset price at expiration, $S_m$\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "StraddleProfit = CallProfit + PutProfit   #a straddle: 1 call and 1 put\n",
    "\n",
    "p1 = plot( Sₘ_range,StraddleProfit,\n",
    "           linecolor = :blue,\n",
    "           linewidth = 2,\n",
    "           label = \"call+put\",\n",
    "           ylim = (-1,5),\n",
    "           legend = :top,\n",
    "           title = \"Profit of a straddle, strike = $K\",\n",
    "           xlabel = L\"Asset price at expiration, $S_m$\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Put-Call Parity for European Options\n",
    "\n",
    "A no-arbitrage condition says that\n",
    "\n",
    "$\n",
    "C-P=e^{-my}(F-K)\n",
    "$\n",
    "\n",
    "must hold, where $F$ is the forward price (on a forward contract with the same time to expiration, $m$, as the option). This is the *put-call parity*.\n",
    "\n",
    "When the underlying asset has no dividends (until expiration of the option), then the forward-spot parity says that $F=e^{my}S$, which can be used in the put-call partity to substitute for $F$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\u001b[34m\u001b[1mPut-Call parity when (C,S,y,m)=(5.5,42,0.05,0.5):\u001b[22m\u001b[39m\n",
      "\n",
      "C               5.500\n",
      "exp(-m*y)       0.975\n",
      "F-K             5.063\n",
      "P (implied)     0.562\n",
      "\n"
     ]
    }
   ],
   "source": [
    "(S,K,m,y) = (42,38,0.5,0.05)    #current price of underlying etc\n",
    "\n",
    "C = 5.5                   #assume this is the price of a call option(K)\n",
    "\n",
    "F = exp(m*y)*S            #forward-spot parity\n",
    "P = C - exp(-m*y)*(F-K)   #put price implied by the parity\n",
    "\n",
    "printblue(\"Put-Call parity when (C,S,y,m)=($C,$S,$y,$m):\\n\")\n",
    "\n",
    "printmat([C,exp(-m*y),F-K,P],rowNames=[\"C\",\"exp(-m*y)\",\"F-K\",\"P (implied)\"])"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pricing Bounds\n",
    "\n",
    "The pricing bounds for (American and European) call options are\n",
    "\n",
    "$\n",
    "\\max[0,e^{-my}(F-K)] \\leq C \\leq e^{-my}F\n",
    "$\n",
    "\n",
    "We plot these bounds as functions of the strike price $K$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pricing bounds for European call option with strike 38:      4.938    42.000\n"
     ]
    }
   ],
   "source": [
    "(S,K,m,y) = (42,38,0.5,0.05)        #current price of underlying etc\n",
    "\n",
    "F = exp(m*y)*S\n",
    "\n",
    "C_Upper = exp(-m*y)*F\n",
    "C_Lower = max.(0,exp(-m*y)*(F-K))  #pricing bounds for a (single) strike price\n",
    "\n",
    "printlnPs(\"Pricing bounds for European call option with strike $K: \",C_Lower,C_Upper)"
   ]
  },
  {
   "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": [
    "K_range = 30:0.5:50             #pricing bounds for many strike prices\n",
    "n = length(K_range)\n",
    "\n",
    "C_Upper = exp(-m*y)*F\n",
    "C_Lower = max.(0,exp(-m*y)*(F.-K_range));\n",
    "\n",
    "p1 = plot( K_range,[C_Upper*ones(n) C_Lower],\n",
    "           linecolor = [:green :blue],\n",
    "           linewidth = 2,\n",
    "           linestyle = [:dash :dot],\n",
    "           label = [L\"C \\leq \\exp(-my)F \" L\"\\max[0,\\exp(-my)(F-K)] \\leq C\"],\n",
    "           ylim = (-1,S+1),\n",
    "           legend = :right,\n",
    "           title = \"Price bounds on European call options\",\n",
    "           xlabel = L\"Strike price, $K$\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The pricing bounds for (European) put options are\n",
    "\n",
    "$\n",
    "e^{-my}(K-F) \\leq P_{E}  \\leq e^{-my}K\\\\\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P_Upper = exp(-m*y)*K_range\n",
    "P_Lower = max.(0,exp(-m*y)*(K_range.-F))\n",
    "\n",
    "p1 = plot( K_range,[P_Upper P_Lower],\n",
    "           linecolor = [:green :blue],\n",
    "           linewidth = 2,\n",
    "           linestyle = [:dash :dot],\n",
    "           label = [L\" P \\leq \\exp(-my)K \" L\"\\max[0,\\exp(-my)(K-F)] \\leq P\"],\n",
    "           ylim = (-1,50),\n",
    "           legend = :right,\n",
    "           title = \"Price bounds on European put options\",\n",
    "           xlabel = L\"Strike price, $K$\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Julia 1.11.1",
   "language": "julia",
   "name": "julia-1.11"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.11.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}