{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Using piecewise linear functions**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***piecewise_linear.ipynb***\n",
    "\n",
    "Example that uses [problem.addpwlcons()](https://www.fico.com/fico-xpress-optimization/docs/latest/solver/optimizer/python/HTML/problem.addpwlcons.html) and [xpress.pwl()](https://www.fico.com/fico-xpress-optimization/docs/latest/solver/optimizer/python/HTML/xpress.pwl.html) to approximate a nonlinear univariate function.\n",
    "\n",
    "&copy; Copyright 2025 Fair Isaac Corporation\n",
    "\n",
    "Licensed under the Apache License, Version 2.0 (the \"License\"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0.\n",
    " \n",
    "Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.\n",
    "\n",
    "This example uses FICO&reg; Xpress software. By running it, you agree to the Community License terms of the [Xpress Shrinkwrap License Agreement](https://www.fico.com/en/shrinkwrap-license-agreement-fico-xpress-optimization-suite-on-premises) with respect to the FICO&reg; Xpress software. See the [licensing options](https://www.fico.com/en/fico-xpress-trial-and-licensing-options) overview for additional details and information about obtaining a paid license."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install the xpress package\n",
    "%pip install -q xpress"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we approximate the nonlinear function $\\sin(5x),  \\forall x \\in [0, 2/\\pi]$ using $N$ points.\n",
    "\n",
    "As a simple approximation, we work with breakpoints lying on the curve of the original nonlinear function, which are determined by the function value for a sample of specified $x$.\n",
    "\n",
    "Start by importing the necessary packages and define a function that returns the breakpoints ($x$ values) and their corresponding $y$ values as lists for a specified $N$ and frequency value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import xpress as xp\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def create_segments(N, freq):\n",
    "    \"\"\"N: Number of breakpoints for an approximation with (N-1) segments\"\"\"\n",
    "     \n",
    "    step = (2 / math.pi) / (N - 1)                       # width of each segment = domain / (N-1)\n",
    "    breakpoints = np.array([i * step for i in range(N)]) # x value of each breakpoint\n",
    "    values = np.sin(freq * breakpoints)                  # value of the function at each breakpoint\n",
    "\n",
    "    return breakpoints, values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approximation using *problem.addpwlcons()*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [p.addpwlcons()](https://www.fico.com/fico-xpress-optimization/docs/latest/solver/optimizer/python/HTML/problem.addpwlcons.html) function can be used for creating and directly adding piecewise linear constraints to a problem by passing **the coordinates of each breakpoint**. \n",
    "\n",
    "Each piecewise linear constraint $y = f(x)$ consists of an (input) column $x$, a resultant (output column) $y$ and a piecewise linear function $f$. The piecewise linear function $f$ is described by a number of breakpoints, which are given as combinations of $x$ (breakpoints) and $y$ (values).\n",
    "\n",
    "An auxiliary variable $y$ is created to represent the approximated value for any given solution $x$. In our example, this variable is defined as the objective function **to be maximized**, but it could also be modeled via a transfer variable. The nonlinear function, as well as the approximated PWL function are then plotted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution: x =  0.28294212105225836\n",
      "Value of piecewise linear function: 0.987843334679394\n",
      "Objective function: 0.987843334679394\n"
     ]
    },
    {
     "data": {
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H5c+4bImIdANLyDZVQdxk5VGe55iW8TtyXMg4LjlW4v5IhT9bAR9blzkZrybHnVwEk/vYEpKEx5Yc93KbJPvSVfRRx/6jYpdjTo69Zzn+nmWfp8R3GFFK4BgnomQiV9AS6yufVkgLlrT4SFEDufo3btw4NfZD+tlXqFDhsY991JiSuImSJCRPc2JnO4mVFqC4JyNyEmQbnCzjzOSPfmLl4G2/S/4YP87vv/+uToTliquMpZETHHk98tpt49ie9rWmps8//1zFLwPL5cqxtLpI7DKw+1FjquQqs1wBl/dWxiJIIi+D9GVsgTyXnCylNEnWE7tC/jTkOLWdBMsJqpyEJcWj9uGT9q0jvG9JifNR5OQ2sfskLD4gnwFpNZX3Vy6myI8kpr169VIXGVIitpQgrSa2VuCEZJskv4m1RiXnMS3HhLyfUqAhMZIcCRnPIwm4JEwyHkgSS7mQI63ecqwlPLbktcmPtHpJ7wY9/zY97z5/lu8wopTCFicindiKIEirSUKyLW6RhKReKX/c80q3KbkK+ajiC0khf6ylW5T88ZKqUfKc8kctOchJ5pMqEMZl6+ZhO7GwkQHx0lVPBl/L8z1qnh7b77K1VjyKDGSW1pRFixapiTHliqd0y3zWyXNt77+cyCeU2LGQFE86PmQQtsxZJNWypPCBnMg/quy7kEHtJ0+eVPtWTsqk6468ZmntSYyctCXsdiOPFwkLhyT2uuW+TyowYnvvpKiCtCDFZeumFPfYPnTokDrBlJZJSexlioCUvkr9NO9bUj/TcnxL4p/YsSGvW07EE7aEPStpBYhbedMmsVZqadGTCylSTEAuIEh3MCmSkLBa5rOQ/SjPmfDEOjmeOy7pXifvryQWCSVW+OVRnueYlu9U6aYsLeVyrCT8kXmohFwMkvtJV2TprizFSuT2xLo3C0mqpICCtChJYQZprXqa2OWYs7V8pcbxl9zfYUQphYkTkU7kCqBcaZQv/7hdReTqrZz4y1gnG9tcH4md1CQkf0zlpOabb76Jd+IhleDkxDHu8yaVtNokTBTkD750mUqsm8uzkL720gqU8AQ8sTLK8kdTumFJ9znbVWMhVfokYZLWMUnwpIVIqlNJ5aeEZN4W+WP9pEl0bVdL476X8nt27tz5TK9T4pUTMrkyH/dEXrp5ShfPZ/Go40PGHthKD8c9AZGTncftt8ResyzHLTedkLzPce8r61J9S8YLxSUtlnHL7csJqryftopqjyNlnKX1I+7vEjKOTfal7TmMRqO6Qi0Ji8QsJ5tSsVJKWqekp3nfkvqZlueU6pFytT1u1y95PVJpTiq0SStEcpDPtJwMx/3MHTx4UFV2i0tO4OOS48lWkTM5vg/k4oQcI1LZ0Ea+f2bMmIHkJl3ZJMGI291sw4YNKnmQsvJJ8TzHtFSZk2NayoonJJ9d2/GR2LElF64kcX0U6dInrYLyd0ZaQhNrIZfvsbhjNeV9kGNNjjn5nal1/CX3dxhRSmFXPSKdyEmljBuSK+LSBUPK+9rKkcuVyrgnebbBu9JFQU4q5I+ZFKBIjFwhHDt2rCrfLVcaZYC1XC2UP7BS9vxZJpGVkwg5AZY/8lLAQPrqS+ELifdRcTwtSejkeaWYQNxJJ6X8rfzBl98vJ8Lyx1sGOsvg9LgnpHJiJYUA5AqrlCoX8h4sX75cvcfSGhB3sklJVOQq7+PKxQu5siutTTK2QGKUlipJduV9kDEIz0K6mchzyUmHjA+Rrl0yDkGKGTzLc8oJrwzYl7gkmZXXKYPT5aRXijTICaCMW5ATECl/LcePnDA+rvVPnlPKx8sJoZwYyXw3j+pKKVe3ZYyLvP/yeyX5lzFgb7/99kMtgjJORV63jEOTEx8plS37QPbzk0gLh8wFI2XG5TiQq/HS+ikndZIsS8zigw8+UF3J5ARY3g85qZdSx3LFWsoySwKWEp7mfXuaz7S8Hjle5X2T8UXyOZHPgLx/ic2B9KzkWJTy7RKPlHuX8TVyTMlxGbcAgLTeyTErJbelq5S0SMnxKxcEntSCmxTSeiXJsXwnSuuKXGyQrmy2gg1Jaa2Tx8tJuLRQCvkesI2HlLLWtvFpcoxKgQY5ruR3yedPSnvLybl8byTF8xzT8t0vr1e+E+SYlSRF/jZIS5DEJd9xcsxKgRFpXZLPmBwz8h7IZ/lJ3d2kK7Lt2JGLalLMIW4hCyk5Lvs7bjly23dnah5/yf0dRpRiUqRWH1E6YisBLOVUHyexUq1i3rx5WoUKFVQJ5KCgIK179+7xStsKKfsr5Z6zZMmiyhon5aMr5celfK+UopXS2YMGDVJltONKajnymzdvqvLJ8ny+vr5aQECAVrVqVe3PP/9MUjnyhKVkbWV8E5aebd26tdagQYN42+bMmaNK3sprd3Nz0zJnzqxK5e7bty/e/Wwll6UUcFxSalceJ6/fRsoyS3ndn376SXsSKes8efJkVY5Z9pHsKymDnrBEs+01JVayPWF5aVuZYCnTLs9ZsmRJbdGiRQ8959OUjZay5/I88lpt7+3Zs2dVyfRChQqpEsNyfNWvX1+Vzn+So0ePqrLWGTJkUO+5lDM+ePDgQ/tNYpZjQkoVS9l4KY0sx5u83rjlj+O+P1JuOk+ePOq1165dWz1vXLbnTExYWJja1zlz5lTHdpEiRdRz2spvy3Eh70Hc8ui2z1CVKlXU42yfg0eVI5djPa5H7dvEju+kvm+P+0wndrzs379fa9KkiXpeeY9lP+7YsSNJ30WP+u5JzO+//64VLFhQfT6kbP6aNWseOi4XLFig9rVMpyD3k+kBpCz21atXH/s745bJjiux416OXSlpL6W+5T0aNWqU+szIc+7ateuJr0Oez1ZuO+FP3PLx4r///rMfu4GBgeo7+Nq1a0/8Hcl1TIvp06er6Rjk9UqZ7zJlymhjxoxRZb9t/v77b61atWrqPnIcy+2yf5LyPkupfpkCQb5zbN/3tmNd9rl8jmzfb4kdJ0k5/p53nyf3dxhRSjDIPymXlhERJZ30XZdJFaW7UGLVnpKLXBGWK6XSkpWUqln0aNIlTsaBPamlTFqIpDiDXM2XFhmiZ/ncSku8tBw9apoHSjpptZJJexN2fSWiR+MYJyJyGDIniXRVSc7uRwnJ+BfpjiTdtpg0ETmmhPMnSVdc6R4mF1SYNBGRXjjGiYgcStxJTFOCjB+QuXaIyHG1b99ezUcl46akiIpMCyAt0Y8q201ElBqYOBEREZFDkYIFMumpJEpSdU6KscydOxedO3fWOzQiSsc4xomIiIiIiOgJOMaJiIiIiIjoCZg4ERERERERPUG6G+NksVjUhHgywVpSJtEjIiIiIqK0SUYthYWFIWfOnHBxeXybUrpLnCRpypMnj95hEBERERGRg7h06RJy58792Puku8RJWppsb46/v7/e4ag5ZdauXavmrpEyyeQcuN+cF/ed8+K+c07cb86L+855cd8lXWhoqGpUseUIj5PuEidb9zxJmhwlcfLx8VGx8MB2Htxvzov7znlx3zkn7jfnxX3nvLjvnl5ShvCwOAQREREREdETMHEiIiIiIiJ6AiZORERERERET8DEiYiIiIiI6AnSXXEIIiIiInoys9kMNzc3REVFqWVyruIQ3HdQhTFcXV2T7fmYOBERERFRvAlBr127hjt37iB79uxqCpekVBwjx9qH3HdWgYGB6r1IjveBiRMRERER2UnSdPfuXWTJkgUWi0XNb+PiwtEdzkT22/3795EhQ4Z0u+80TUNERARCQkLUeo4cOZ77OZk4EREREZEi3bokacqaNSsyZsyoJgf18vJKtyffzpw4xcTEpPt95+3trf6X5EmO6efttpd+30kiIiIiemhsjJDJU4nSAp8Hx7Lt2H4eTJyIiIiIKJ70Pi6G0g5DMh7LTJyIiIiIiIiegIkTERERERHREzBxIiIiIiJKQ13TJk6cCEfy3nvvpYnun0yciIiIiChd+eGHH9SJfNWqVfUOJc2IiIhQCdLmzZuRVumaOG3duhWtWrVCzpw51cG7ZMmSJz5GdkbFihXh6emJwoUL49dff02VWImIiIgobZg9ezby58+PPXv24PTp00hLIiMj8c477+iSOE2cODHRxOndd99VcTk7XROn8PBwlCtXDt9//32S7n/u3Dm0aNEC9evXx4EDBzB8+HD0798fa9asSfFYiYiIiMj5yfnkjh078MUXX6hJfiWJ0oPJZFJzLSU3mbvJzc2xpmp1c3NTcTk7XROnZs2a4YMPPkC7du2SdP+pU6eiQIEC+Pzzz1GiRAkMGTIEHTt2xJdffpnisRIRkQMxG4Gwa8C1/4CzW4D/FgJ7ZgBbPwM2vA+seQdYMQJYPBBY8DKwoB+wcACw6BXrtiWvAatGA+vfA7ZOAXb9COz/DTi+Cri8D7h7ETBG6f0qiSgFSKIkk/vKxXg5j0yYOJ0/f171hPrss8/UOWa+fPnURKp169bFf//9F+++ffr0QYYMGXD27Fk0adIEvr6+qifVpEmToGlaos/51VdfoVChQqr31NGjR9XtGzduRO3atdXjAwMD0aZNGxw7dsz++F9++UU9fubMmfF+/+TJk9X2VatWPXKMk2180cmTJ9GjRw8EBASohHHcuHEqxkuXLqnf5+/vj+zZs6vz7LgkuRs/fjwqVaqkHisxSqybNm2K9/rkOYX8bvl98iO/O24MCRPH999/3/5eSAvg22+/jejo6Hj3k+0tW7bE9u3b8cILL6gErGDBgvjf//6H1OZY6egT7Ny5Ew0bNoy3TQ5SaXl6FHnz4+4AmQHbNglWckyE9bxsMThCLJR03G/Oi/vOiUTeheHmceDmKRjuXoTh7gXUunAYrqffghZ2FQbEnpSkFM3TH/DPBS0wH7SM+YDA/NAy5ocWVFAtw+X5ZqFPD/iZcy6yn+Rk2mKx2E/8betphSRKctFeWkE6d+6MH3/8Ebt370aVKlXU7bbXKifmYWFhGDx4MKKiovDNN9/gxRdfxMGDB5EtWzb7e2M2m9G0aVM1XuqTTz7B6tWrMWHCBPVe2hIY23NKAiTPNWDAAJUsSJK0du1alcRJMiCPky5t3333HWrWrIm9e/eqxKF3795YuHAhRo4ciQYNGiBPnjw4fPiwev6XX35Z/f64+yjuvrMty2stXry4SrYk0ZLGC0kgp0+frnpzffTRR/jjjz/wxhtvqCSpTp066nF3797FTz/9hC5duqBfv364f/++SuDkHHzXrl0oX748MmXKpHqQvfbaa2jbtq29UaRs2bLxjqW4McpzyXvcoUMH9bpkH0gMkkwuWrQo3j6T7pSS5Mpr7dWrl3ofJWmtUKECSpUq9dj9bfv9sj9cXR/+zn6a7yanSpyuXbtmP1BtZF2SITnI5GpAQrIDEqssIgepI82KvW7dOr1DoGfA/ea8uO9Snlkz4+j9o7hjuoOMbhlRMkNJuBoSSTQ0C/yiriBjxFkERF6AX2Qw/KKC4WW699BdMyF1GaJDgRuhMNyIvfJrYzJ4IMw7F0K9ciPUO4/6uetTACZXx/nb4kj4mXMOkkxIq4OcHNu6kUnykFbIUI/jx4+r80M5f5QTe2khkjHzxYoVU/eR1247WZfERW4XtWrVUhfwJeH48MMP7SfdkghJ4iFJk+jevbtKMj799FN1ci9Jhe05pXVn//79yJw5sz0mSVQkgZGES/4XkhxJC5eMVZLETkhLUPXq1dG3b1/MnTtXJRBZs2ZVyZatYcAm7r6zNSDI8Bhp7RISn7x2+d3SmmRrhJCWHenVJcmUJERCkg153zw8POzPL0mYtP5Ii9y3336rtkkiJeR9bN26tf2+EpstBluckvRJ0iSv4euvv7a/b9KiJUnjypUrVauWLfE5ceKE2lajRg21TRLF0qVLqzil1epx5L2QPEFqK0grV2Jjs9Jk4vQsxo4dq7JYG9lhkqU3btxYNUnqTT5w8sekUaNGcHd31zscSiLuN+fFfZc6Fh9fjJHrRiI4LNi+LZdfLnzR6Au0y1sHhos7YQj+B4Yr/8Jw7SAMMeFJfm7NJzO0gDyAX3bAOwiab2br/z6ZAU8/wMMXcPOC5u4NyI+rh1x2lUeqJE0tW8wwGMMB+b0x99X/hugwIOIWEB4CQ/gN4L78HwKEBsNgfngcgpsWg4wR59SPPTYYgCzFoOWsBEuuytByVwEyFwUM6beILT9zzkWSADm5l+5n0iIiJ95+fn5o88MO3AyL34VKT5n9PLHstZpP/bilS5eqi+7SwmNrfZAkQlqhpEVJtslrF9J9TVpobCQ5klalDRs22JMF2zE9YsSIeOeVw4YNUxfppRVFnt/2nNK6Ii1LNlevXlVJxOjRo1WXQBtJECRJW79+vf155X9JKiTBkOJq8jgZ5587d+6HXqctyZF9J/tRDBo0KF6M0sIm74e0qMX9HZL4XL58OdHzZIvFolqgpLGicuXKquui7X62ZE1+X8LH2mKwbd+2bZv6f8yYMfHuK+ft8hqlwITsI+Hi4oKSJUuqZMnmSXEmPKYlXmlBS2ycVcKkM80kTnIF5Pr16/G2ybq8YYm1Ntl2lG1nxSUHuiN9gTtaPJQ03G/Oi/su5Sw6tghdFnWBlqAr3ZWwYHRZ1BkLNG+0xxPee59MQJYSKglBluJAUEEYM+TEml3/oUnLdqm77yxmIOwqcOc8cPsccOcccPMkcP0ocPusNSF7QHUfvHEchhvH4XJwduxryV8bKFgPKFgXyFhABiEgveFnzjlItzMZiyInq7YxKfL/zbAYXAt1nMRJPm0S49O+tnnz5qkE6MKFC/bt1apVU4UiZMyOXFi3PW/RokUf+h2y7c8//7Rvt71XUuk57n1tCdfFixfVdtttkjTFvZ8kqbb7J/xdkixI8iWtJTKuSHTr1g1z5sxRrS+vvPKKuiCR6LsTZ9/ZlqXLX9zfId0EJZGQVqu4pNXn1q1b8e47a9Ys1eIlrXVxu7ZJ7QHb/RK+J4nFY9tue18SvsfSuidx2W63yZs370PPKa1zksQ96TiwHcuP+g56mu8lp0qcpHky7uA3IVexZDsREenPbDFj2OphDyVNQrYYNGA4otAGbnCV1hnpFuOVA7cDSyM0qAwiMpeFMVNxuPplhbe7K7zcXa3/e7jADRbE4FTqvygZxxSQ2/qTv1b822IiAOnGJ0nU1YPA5X+Aa4cBzRx7H2nFOrrE+iMC8wKFXgSKNQcK1AXcnb/SFKV9WfwevgjtbPFIAQZp4ZFubvKTkLQ6SeKUkh51oT+pJKGR7oNCxgJJC1BSE8jExvcktk3ELWzx+++/qy6Hbdu2VS1jkmjJ46S745kzZ/A8kjopblLiTA26Jk7S3zNu7XwpDyl9KIOCglRmKc11wcHB9qoZAwcOVM130qwng8PkAyBZv2TdRESkI7MJOL8V2/ZMxeXQy4+8m2YALkHDaFMV3DPXxUFLYdyMCgDuSlkm273OPvhJjBvG/LNOJVTWHxeVWHl7uMLLTRIs+d9FrdsSL3vyJfeNcz/7trj3i/N4uZ+LyxP+qHv4ALkqWX/QMzaZunrAmkRd3AWc/xuIjjNeSyr27fvV+uPuE5tEFW0K+Kb2KC6ipFk+NMFFAyckiZGc9Cc2DY4UI1i8eLGq4Gxz6tTDF2qkMp203MQlyYtU1ZPWk7j3Ewnvm5Cte56M4UlIWndkLJSttUlI8QXpPilJi5wny5iluENSUsKCBQtUS9miRYviJToytupZkiDb65b3Td5jGVMVtyeZtCLF7bboSHRNnCRjluZSG9uOl8ohMkhPrgpIU13c5kBJkqQfqQwkkz6dUuXDNhiNiIiQul3YLuwAjiwCji4DIm7iKozSg+aJfrNUgq9Fko2nZ7JouB9tUj8pzUOSqMQSLFuS5e4Sf9uD+3q5Z4e3R1t4Fe0An5Iastw/hiw3diHo+k74huyDi/lBlydjBHB8hfVHxkFJC1SZTkCJloBXQIq/PqL0Qrq7yYl/p06dVHW2hKSLmFSUW7ZsmRrHJJYsWaIu4OfKlUuty2S5MmYpsWrOcmFfxkjZWkFkXbqASZGHx8mRI4cqwiBd4SQRkm5qQsYOSTc9KR8eN4GRrobye4YOHaqq+8nEslLQIW7SltxsrT2aptmTI3kfpNq1NHTY2IquSeLzJM2bN1elxyXxmzZtmn27dJkUtvFNjkbXxKlevXqPbWKT5Cmxx/z7778pHBkRET3S1UPAgTnWhOl+/HGnOZKSNQF4v1UtlMr0AiJjzIg0mhFttKj/o4zWdfu2B7fL9ogYE65cvwkfvwBEmSxqm7r/g/tYUqDHRozJon7uJcuE95IoVoIXolHb5TAauuxHA9f9yGx4MDBZClec3aR+YpYOwzG/6shTpyeCyrdmdz6i5yQJkbTUxK32FpeMc7JNhmtLnGTcklTSk6IKUhVOTvKlQp70fIpLxglJRTy58C+P/euvv9SFfkkMbHMbPc6UKVPU3KYy9ERKdEuSJ8UnZKyRbR6kkJAQFYc0OMg8pkKSMxmXJd3oZI6jpx3zlVSSmEnS2a5dO5XQSA8xaZmTMVi2aoG2boiyTZI7SeSkB5lUvpOfhKTCn7xfUhVPEi2pICiJqSSQ0iUwbsOKI3GqMU5ERKSTiNvWSWb3/w+4duihm6M0d2ywVMBy8wtw95gGo+F2vKIJNgYYkNs/Nwa80AKuTzkHkgxIlnGuzZtXe2gwr5qjw6w9SLhsyZY1GZPEKspkRpQ9CYtN0qLi3B4ZEycZs/8ff5vcN9r0fPPZRMET6yyV1Y+LyYLyhtNo7LoPzV12Ia/LDXUfDxhRLmwrsHIroteOgkeFrjBU6gNkK/lcv5sovZKESBKcRxVTkKRDkgK5n4wjElIqW7ZLwiSJi5TflmRFWokStshI4iSJjYwBkkp20o1NynwnhVTPs839JI+R7zdJJKS8ufS2ErbkzTYRrpAkThIPqf4nE+smTOiSiyRmMiXQtGnTVBU/SY5k3NP8+fNV9bu4pCeYtIZJ7zCpsievKbHEyXZf6QIoDSXSTVKKwEmrW8IugI7EoKX2qCqdSclByeDv3bvnMOXIrScCzVltyIlwvzkv7runIH8ezm8H9v0CHFsB2LqXPWAyuGOjqSxWmKtjvaUiIuCFRiWzoXLxUxj0V3frU8SrOGf9Y7/gpQVoX6K90+47i0VTyVPcFrLYJMySoNXs4SQuWiVp8ber+8WYUCD6GOobt6Kh+W9kNjw8jxVyVQYq9QZKtQc8reWNHZ2j7DdKGindLC0KcsIuJa3lvEnOl1KqNcMRnT9/Xr1+aQmSeY6elFRIF7q4LS+OQMYPpcd996Rj+lHlyJOaG7DFiYiI4pPiBof/BHZPB0KOPHTzrYBSmBZaHXMjqyIU1kHLBTL7YkKrkqhXTMraVlYVr6S6XtxCEdLS9FXTr54paXIkUjBCFZ/weLoWs6SpJ9eWce9+JKbNn40sZxejuctueBkelP8N3mv9Wf02ULEn8MIrQJD1ijQREaUsJk5ERBRb7W3PDGt3vKgEg3u9g3C9YFt8cLkill8Psm/28XDF0BeL4OVa+eHpFptISHLUplgbbLu4DVfDriKHXw7Uzlv7qbvnpVcBGbzxat/+2HSiNVot2InqERvQ1XUTSrg8KJgUEwbs+gHY9SNQvAVQbRCQr2a6nB+KiCi1MHEiIkrvrh8Btn9lHcMUd/4hkbsKQsu+jA/PFcG8fSHxbmpdLifebl4C2QMSL1wgSVK9/NKCQs+qfrGsqDSqOT5cUQDN9jZGWcNZdHXdiHau2x+0QmmxVfmylQFqDAVKdwBc+eediCi58ZuViCi9kjmGtn8JnFwdf7urhzr5NlUegP9dCMKXK08iLDo2aSqe3Q/vtS6FagU551Bq8Pdyxycdy6J52RwYu9AbY+8VwqemzqoFqr/negRZrAPZcf0wsPgVYPNkoNYIoFxXwM2xJi0lcgYy91JSSwBIYYPEqkBT2sTEiYgoPZGTASl5vWUKcHFH/Nu8g4CqA4HKL2PHdQPeW3AEJ69fs9/s5+WGUY2Koke1fHBzTd+DjfVQt2gWrBlRB5NXHccfey7iB3MbTI9ogTYee/FW4EZkCf3Pesc754Hlw4DNnwA1Xwcq9rZO1EtERM+FiRMRUXohk9Vu/AC48Hf87f65rF28KvbC1UgXfLjsGFYcuhrvLp0r58HopsWQOQNbMPTk5+WOj9qXQYsyOfDmwkMIvhuJhTHVsDCkGnrnDMZbvsvhfWmr9c5hV4DVbwFbPwNqj1IJMeeDIiJ6dkyciIjSusv7gE0fAGc2xt+euShQczhQphOi4Yqftp3DdxtPq/LYNuVyB2Bim9Ion8c6mz05hlpFMqvWp4//Oobfd1kLRsy6kgvz3Afj02qvoFXoHBhOrLLeOeImsGYssPN7oN6bQLluHANFRPQM2NeCiCitunEC+KMr8NOL8ZOmTIWBDj8Dg3cDFbpj0+m7aPLlVkxZc8KeNAX5euCTDmWweHBNJk0OKoOnGz5oWwZz+ldFniBvtU3mhXp9mws63R2KS13WW+d7spHS8MuGAj9UBf5bJBO96Bc8EZETYuJERJTWhN8EVo4CfqgO2FodRGBeoM0P1oSpTEdcuBOJ/rP+Qd9f/8H5WxHqLi4GoE+N/Ng0qh46V8mr5iwix1ajcGasHlYHvavns2/be+EOGv5+Ez9lHwfzK9uAIk1iH3DrNLCgLzCjvrX7JhERJQnb6omI0gpjFLB7KrDtcyA6NHa7Xw6gzmigQk/AzQORMWb8sOEEpm09ixhTbKvDCwWCMLF1KZTI8fiZ08nx+Hq6qS6VzcrkwJgFh3DxdgSiTRZ8sPIYVuUNxJROM1Go9n/AhkmxY9yuHgB+aQaUbAs0mghkzK/3yyAicmhMnIiI0kKlvKNLgHXjrZPY2rj7WstSV39NVVWT8rp/Hb6KD1YcxZV7Ufa7ZfP3VPMxybxMBk6g6tSkRPzq4bVVt8tfd5xXh8b+i3fR7OttqiJi/14r4HpuI7DuPWv5ciHHzom/gOqDrUUkPP30fhlERA6JiRMRkTO7cRJY9QZwbkvsNoMLUKEHUP8dwC+72nTqehjeW34Ef5++FZtXuRrQr1ZBDHmxsBovQ2mDj4cbJrQqhWalpfXpoOqGKS2LH/11HH/9dw1TOlZFkVe3AP/+Dmx8Hwi/AZijrXN6/Tvb2vokc0AxiSYiiodjnIiInFFMOLD+PeDHGvGTpoL1gVe3Aa2/VUlTWJRRtTBJi0PcpKlO0SxYPbwO3mpWnElTGiVdL/8aVgf9ahWw50AHLt1Fi2+244et52Aq3xMYut9aWVEmPRbhIcCSQcCvLYCQ47rGT5SWnD9/XrXoJ2Wy3FOnTqFx48YICAhQj1myZAkcUb169dRPesLEiYjImUjfq2PLge+rWlsILMbYwg9d/gB6Lgayl4bFomHhvsuo/9kW/LT9HEwWTd0td0ZvTO9ZCbP6VkGhLBn0fS2U4rw9XDGuZUksGFgdBTP7qm0xZgs+XX0C7X/cgRN3DdYWptf2ACVaxT5QxkFNrWlNzmOshUOInJ0kLZKI2H7c3NyQK1cu9OnTB8HBwXAUvXv3xuHDh/Hhhx/it99+Q+XKlXWL5ejRo3jvvfdU4kfsqkdE5DzuXQZWjAROrYndJi0FNYcBtUaqcUziv+B7mLDsCPZduGO/m6ebCwbXK4xX6xaEl7urHtGTjirlC8KqYbXx5bqTmLHtLCSPPnT5Hlp9ux2vN5DjohDcO/8OnF4PrHwDuHMOsJisyfnhhUDzT4FizfR+GUTJYtKkSShQoACioqKwa9culVBt374d//33H7y89J0kOjIyEjt37sQ777yDIUOGQG+SOE2cOFG1LOXPH7+AzNq1a5HeMHEiInJ0Mt/Ovl+AdROAmLDY7YVeBJpNATIXVqt3wmPw2doTmLPnomqYsmlSKhvebVESeYKsiRWlT5Iwj21eAk1KZ8fo+Qdx5ka4an36bO1JrD4iY5/KoUThhsDgndaESX7MMcC9i8AfXYBS7azHW4Yser8UoufSrFkzeytO//79kTlzZnzyySdYtmwZXnrpJV1ju3Hjhvo/MNDx58/z8HjQxTcdYVc9IiJHdusMMKsVsHJkbNKUITvQaRbQY5FKmswWDb/vuoD6n2/G7N2xSVPBLL7438svYFrPykyayK5i3oxY+XptDKxbSM3bJf4LDkXr77bjmw2nYHTxBOq/DQzaCRSoG/vAI4utk+ceXmDtMkqURtSuXVv9f+bMmXjbjx8/jo4dOyIoKEi1REmyJclVXLdv38Ybb7yBMmXKIEOGDPD391eJ2cGDB586DukSly+fdT620aNHq+6EtlYe6U6YsMXH9piE1VBlfejQoVi5ciXKli0LT09PlCpVCqtXr37o8dJFsV+/fsiZM6e6n7TEDRo0CDExMaolrlOnTup+9evXt3dx3Lx58yPHOIWEhKjny5Ytm3rPypUrh1mzZiU63uuzzz7D9OnTUahQIfW7q1Spgn/++QeOjC1ORESOyGwCdn0PbJoMmGJLh6u5mBp/AHhbr0buu3Ab45cewZErsfM2+Xq44vUGRdC3ZgF4uPH6GCXe+iSFQZo+aH06FXIfRrOGL9adxGqpvNepLErlLAz0Wgocng/8NQaIvANE3AIW9rMmUS0+t1dtJHJmtvE7GTNmtG87cuQIatasqcZAvfXWW/D19cWff/6Jtm3bYuHChWjXrp2639mzZ1XxBkkwJOm4fv06pk2bhrp166pubpKQJFX79u1VS9OIESPQtWtXNG/eXCVjz+Lvv//GokWLMHjwYJXMffPNN+jQoQMuXryITJkyqftcuXIFL7zwAu7evYtXXnkFxYsXV4nUggULEBERgTp16uD1119Xj3377bdRokQJ9Tjb/4l1M5RE6vTp06qbobwf8+fPV0mf/I5hw4bFu/+cOXMQFhaGV199VSVSn376qXoP5D11d3eHI2LiRETkaG6eBha/CgTvjd0WmA9o/Q1Q0Hp1LyQsCh//dRyL9scf0Ny2fE7VHSubv7799Mk5lM8TiBWv11ItTVO3nFWtl0evhqLNd39jcP3CGFK/MDzKvmQ97laOAo49uNp+fAVwfjvQ9GOgXBeWLk8PptUF7ofAYWTICkhZ/Wdw79493Lx5U41x2r17txrDIy0eLVu2tN9HTvLz5s2rWkDkNiFJSK1atfDmm2/aEydpaTp58iRcXGIvUvXs2VMlIT///DPGjRuX5LikdUiSHEmcKlasiB49euBZHTt2TI3fkhYfiU1ajGT5jz/+sI+dGjt2LK5du6beg7gFKGQMmMz7J0mctMZJ4tSoUaMnVtCT1iP5vb///ju6d++utg0cOFAlke+++y5efvll+PnFzhMnSZxUELQlrMWKFUObNm2wZs2aePvCkTBxIiJyFNL9ae9MYO27gNFWycwAVBsEvPgu4OELo9mCWTvO46v1p3A/2mR/aPHsfpjUprQqQU30NDzdXDG6SXE0LZUDb8w/iBPXw1QVRkmm1h65hs86lUPpXFmBzr8BR5ZYE6iIm0DUXWDJQODESqDVN4APj700TZKmsCtICxo2bBhvXbrAycl+7ty57d3vNm7cqBIIaRGRH5smTZpgwoQJqmVGWqNsSZUwm82qZUVaiSQJ2L9/P/TSoEED1eKTMCmT1hxhsVhUS1mrVq0Srdr3LJOhr1q1CtmzZ1etZTbSciStVrJty5Yt8RKizp07x2vls3WZtMXoiJg4ERE5grDrwNLXgNPrYrcFFQLaTQXyvKBW/z59U1XLOx1y334Xfy83vNGkGLq9kBduruyWR8+uTO4ALB9aC99tPIUfNp9RydPxa2Fo8/3fGFyvkJoo2bNUWyB/bWvXvf8WWB8o5fEv/QO0/QEo3EDvl0Ep2cKTRuL5/vvvUbRoUdXyNHPmTGzdujVeAiRdzaTFRVqLHtViJGN5JHGSBOTrr7/GDz/8gHPnzqnkycbWJU4P0lqWkCQpd+7csRehCA0NRenSpZPtd164cAFFihSJ1/oWt2uf3P64GG1JlC1GR8TEiYhIb0eXAcuHAZG3Y7dV7gc0fl+1MgXfjcSHK49i1eFr9pvlYmCXKnnwRuNiyJQh9g8+0fOQMXEjGxdD41LZMXrBIRy7Gqq673278TTWHrmuxj6VzZ0J6PgzULINsPx169in+9eA39sDVQcCDd8D3L31fimU3J6xW5wjknE9tlYWGbMk3e+6deuGEydOqNYiSYaEFH2QFqbEFC5srWY6efJklVxJN7T3339fFZKQxGH48OH250kOj2oBipuoxeXqmvi0E5IQOgpXJ4gxISZORER6iQm3Xrn/9/fYbb5ZgTbfA0UbI8poxk8bT+G7TacRZbTEG5cysXUplMvj+OVqyTmVzhWApa/VxA+bT+O7jadV65N04Wv3ww68WqcghjUsAs+SrYHcVYClg4EzG60P3D0VOLsF6DADyF5G75dBlKST948++kiNAfruu+9UIYiCBQvau5kl7NaXkBRSkMfKeKa4pMuelDlPLtIaI8+ZUMJWnKTKkiWL6ronc1c9ztN02cuXLx8OHTqkEsa4rU5SndB2u7Njvw4iIj1cPwpMrx8/aSreEhi8SyVNG45dR+Mvt6o5dmxJUyZfD3zasSwWDarBpIlSpfVpeMOiWDakFkrm8FfbpPVJuvG1/GY7Dly6C/jnALovBJp9Crg+aPm8cQyY8SKwezrLlpNTkKIH0gr11VdfqYIRWbNmVdukOt7Vq1cfOdeSLfFK2EIileRkDFRykpLd0rVQEhMbiW3x4sXP9HyS2Ehr2/Lly7F3b5xCRA/YXpNUExSJJW0JSRVAKTYxb948+zaTyYRvv/1WteRJkQhnxxYnIqLUJH+M9v/P2tJkKzPu7gs0nwKU74ZztyIw6c892HQizh9mFwN6Vc+nTmIDvB2zRCulXSVz+mPpkJqYuvkMvtl4SpUtl/Ll7X/4GwPqFMSIhkXhVfVVoEAdYOEA4Pph68S5f40Gzm8Dmn+l90sgeiKZN0lKisvcRVIJTsZBSRc+qZo3YMAA1QolpcZ37tyJy5cv2+dpkmIHUkSib9++qFGjBg4fPozZs2fbW62SS5cuXezV/KTYgpQL//HHH9VYrWctQiHdDNeuXasSGilHLmORJBmTxG/79u2qql758uVVcigTBN+7d0+NBXvxxRdVcpmQPIckm1J+fN++farohrTISWl0SUrjVtRzVkyciIhSS1QosGJE7KB6ka0M0OkXRPgXwPdrT2DG1nOIMcd2y6taIAgT25RC8ezWK/5EenB3dcHQBkXQqFQ2jJ5/CIeD78GiAdO2nMX6o9fxacdyqJSvBDBgA7D+PWDXD9YHHlsGt6uHEJCtr94vgeixZP4gadWRSVklUSpZsqRqiZFS5ZJM3bp1SyULFSpUwPjx4+2Pk/mNwsPD1ZxE0tIiZcRl4lnp8pecpNCEtC6NHDkSY8aMURXzpIuhlPN+1sRJiltIKXIZoyXJnhSLkG0yga+Pj3XSdKmSN3XqVPW7+vXrp8ZUbdq0KdHEydvbW02OK69dJr2V55Pqgr/88otKptICg+bII7BSgOzEgIAAlTVL3069GY1GVb5RmjcddbIvehj3m/PSbd9dPQjM7wPcjlNmtUp/aI0/wMpjd/DhymO4ei92otvs/l54p0UJtCyb45nKwqZF/Nw5BpPZgmlbz+Lr9afsSb4cov1rFcCoxsXU5Lo4vhJYMgiIuqduNxvcgEYfwLX6QM755OCkq5pUh5MTcw8PD3XeJOdLCSulkWOTcUbcdw8f015eXs+VG6Tvd5KIKDXs/w34qVFs0uTpD3T6FScrv4duvxzEkDn/2pMmd1cDBtUrhA2j6qJVuZxMmsjhSNn71+oXVhPnlssdoLbJJdgZ286h+dfbsPf8baB4C+DVbUCuSup2V80E17VvAX/2sra8EhE5ISZOREQpxRQNLB8OLBsCmKOt23JWQFjfjZh0thiafb0NO8/est+9XrEsWDO8Dt5sWhy+nuxJTY6taDY/LBxUA281K64KSYizN8PRadpOTFp+FJG+uYG+q2GuOij2QceWAT81AG6c1C9wIqJnxMSJiCgl3AsGfmkO7PvFvkmr3A8Ly/2M+j+dx8y/z6kKZSJPkDd+6lUZv/SpgoJZMugYNNHTtz4NrFsIq16vhQp5A+2tT3J8N/t6K3ZfDIOl4fvYXXA4NC9r6xRunrRW3ZPufEREToSJExFRcju3DZheFwh+UOLV1ROX6nyO9hc7YNTi47h5P0Zt9nJ3wchGRbFuRF00LJmN3fLIaRXO6ocFA2vgneYl4Pmg9en8rQh0nr4Lk1Yex4UMFWF6eT2QtZT1ATFhwNxuwMYPZTCGvsETESUREyciouQil9p3fg/8rw0Qbi0nbvbPg28L/IA663Lg34ux82A0K50d60fWxesNilgH0xM5OSmbL+XJVw2rjUr5Mtq3/7brIj456IrddwOA/uuA0h1iH7T1U+CPzkDkk+eIISLSGxMnIqLkGs+09DVgzduAZlabrmSqjvqhE/H5f972eUALZfHF7/2q4scelZA7o7XcK1FaUihLBvz5anWMa1lStaqKW9EG9Ji5F+NWnUN4y2lA4w8Aw4NTkFNrgen1gJDj+gZORPQETJyIiJ5X+E1rK9OB2fZNc71eQq3g13Axylr6NIOnm+rG9NewOqhVJLOOwRKlTutTv1oF1PFeOZ917JP4bdcFNPl6G3Zk7Qr0XAx4B1lvuHMO+LkRcHq9fkETET0BEycioudx/Sgwoz5wcadajTF4YnDM63jrbltYHnzFtq+QCxtH1VXdmGzVx4jSgwKZfTH75Spon98M7wetT5fvRKLbT7vxzsFMCO+7Eche1nrn6FBgdidg93R9gyYiegT+BScielYnVluvkt+9qFavaxnRIWocVlmqqfWSOfyxYGB1fNG5PLL6PzzpHlF64OJiQN0cGpYPqYGqBR60MAGYvfsiGs88h7/r/g4Ub2ndqFmAv0YDK0cBZqN+QRMRJYKJExHR05IBSzu+Bf7oAsTcV5sOWQqgdfT7OKwVRIC3O95vWxrLh9ZC5fyxJ4pE6Vm+IB/8MaAa3m9TCj4e1oIowXcj0X3Wf3jbfTSiqw+PvfM/PwGzO7JoBBE5FCZORERPw2wCVgwH1r4rGZTatMJcFS/FjEeIIQhdX8iLTW/UQ89q+dQ4DyKK3/rUs3p+NdFz9YKZ7Nvn/BOMevvr4FjVTwAXd+vGs5uBnxoCt87oFzARURxMnIiIkir6PsxzugD7frVv+srUHkONQ1EibzYse60WPmpfBkG+HrqGSeTo8gT5YHb/qvigbWn4Pmh9unovCs225MEP+b6ExftBUnXrlLU77OV9+gZMlIh69eqpn+R0/vx5Naffr7/G/p0hx8HEiYgoCbSw6wid2gSuZ9ap9RjNFa/HvIbfvbphSqcKWDiwBsrkDtA7TCKnan3qUS0f1oyog1qFYytNfnosCB1N7yPcv5B1Q8Qt4NcW1jGFRM/p8OHD6NixI/LlywcvLy/kypULjRo1wrfffpuqccyZMwdfffVVqv5Oen5MnIiIniD49EHc+LoO/O/8p9ZDNR/0Mb2NLDV6YOMb9dCxUm51EkhET0/mM/ut3wuqtVbK9ov9YYGoHvIWTvuUt97JFAnM7Qrs/UXfYMmp7dixA5UrV8bBgwcxYMAAfPfdd+jfvz9cXFzw9ddfO0TiJAldZGQkevbsmarxUNJYv6GIiChRVw5vgu/CHgiEtQhEsJYJX2WdjPc6tkDRbH56h0eUJkjXJBkfWKdoFoxddBhbT95AKHzR/PYIfOc9HY21v60V92R8YWgwUP8deZDeYZOT+fDDDxEQEIB//vkHgYGx84uJkJAQOMpnQVrCyDGxxYmI6BHC/l2EzAs72ZOmU4Z8ONZ8IT4d3JlJE1EKyBXojVl9q+DTDmXh5+mGGLjj1chBmG5qEXunrVOApa+xXLmTMVvM2Hx+M/44/If6X9ZT25kzZ1CqVKmHkiaRNWtW+7LJZML777+PQoUKwdPTE/nz58fbb7+N6Ojoxz6/jEuSxEfGKcW1efNmtV3+FzIuauXKlbhw4YLaLj/yOx43xmnjxo2oXbs2fH19Vfxt2rTBsWPH4t3nvffeU489ffo0+vbtq1qvMmbMqJYjIiKe4R2jhNjiRESUCOOemfBdNRIuDyrn7XMrj8JDFqNIIMuLE6UkOfF7qUoe1C6aGW8vOoxNJ25gsqk7rmpBGOf+u/UzeWA2EHYN6Pwb4OGrd8j0BIuOLcKw1cNwOfSyfVtu/9z4uunXaF+ifarFIYnEzp078d9//6F06dKPvJ9035s1a5YaCzVq1Cjs3r0bH330kUpUFi9e/NxxvPPOO7h37x4uX76ML7/8Um3LkCHDI++/fv16NGvWDAULFlTJkXTlkzFZNWvWxP79++1Jl81LL72kto0fP17F/PPPP6vE8JNPPnnu2NM7Jk5ERAlYtn0J9w3v2ddXGOqh4qDfEBDor2tcROlJjgBvzOxTBQv3B2Pi8iP4JaoZrmlB+Mr9B3gajMCZDcD/2gLd/wS8M+odLj0maer4Z0doDy5C2QSHBqvtC15akGrJ0xtvvKESkPLly+OFF15QLTgNGjRA/fr14e5uLYMv458kaZLkacaMGWrb4MGDVeLx2WefYdOmTer+z0OKUUhRijt37qBHjx5PvP/o0aMRFBSkkj75X7Rt2xYVKlTAhAkTVLxxyXaJPTQ0FP7+/rh9+7ZKnpg4PT921SMiijux7dpxcImTNP2stUL+frOQMxOTJiI9Wp+k+Mq6EXXRoHhW/GWpih4xY3FP87He4fIe4JcWQNh1vUOlREh3PGlpSpg0Cdu24auHp1q3PUlYJPlo3bq1SpA+/fRTNGnSRCUxy5YtU/dZtWqV+n/kyJHxHistT0K62KWmq1ev4sCBA+jTp489aRJly5ZVr8cWb1wDBw6Mty4J4q1bt1QiRc+HiRMRkZA/3MuGAju+sW/6xNQVBbt+gdK5H+4PT0SpJ3uAF37qXRlfdi6Hk15l0CVmHG5oD8r/hxyB+efGwJ3440pIf9subovXPS+x5OlS6CV1v9RSpUoVLFq0SLX27NmzB2PHjkVYWJjqlnf06FE17kiq7BUuXDje47Jnz67GFsntqcn2+4oVK/bQbSVKlMDNmzcRHh4eb3vevHnjrcs4JyGvmZ4PEyciIlM0ML8P8O9vatWiGTDW2A+5W41F/eKxA4aJSN/Wp3YVpPWpDnKXeAGdYsbjsmad/8n17nlETWsEhBzXO0yK42rY1WS9X3Ly8PBQSdTkyZPx448/wmg0Yv78+fGOt6f1qMeYzalbCMPV1TqpdEKa9Kqg58LEiYjSt+j7wJyXgGPL7BPbDjUORUCtV9C9aj69oyOiBLL6e2F6z0oY0bkZXnb5AKcsudR2r6gQ3J/aCHdO7dI7RHogh1+OZL1fSpG5nWzd4qSAhMViwalTp+Ld5/r167h79666/VFsLTtyv7gSa6VKamJm+30nTpx46Lbjx48jc+bMqtIepQ4mTkSUfkXdA35rB5y1loiN0DzR3/gGXMq0x5gmD3eLICLHICedbcrnwuyR7TG14Hc4ZCmgtmewhMJjdhuc2PXwuA9KfbXz1lbV8wxIPEmQ7Xn886j7pQYp7JBYq4ttnJB0h2vevLlaTjg57RdffKH+b9EiTmn8BKR8udi6dWu81qbp06c/dF9JdqSy3pPkyJFDFbOQAhBxEzKpDLh27Vp7vJQ6WFWPiNKnyLvA3JeAK/vVqgw27xszBq75qmJ6x7JwceHkmkSOLoufJz7rXR9r9v+JmOW9URlH4Yso5FvdGyFe/0PW8s30DjFdc3VxVSXHpXqeJElxi0TYkqmvmn6l7pcahg4dquYzateuHYoXL46YmBjs2LED8+bNU+W7Zb4jGcfUu3dvlexIolK3bl01FkoSF6lk97iKejJHVLVq1dS4KalkJ8Uc5s6dq+aFSqhSpUrq90oRCukyKOXIW7VqlejzTpkyRVUDrF69Ovr162cvRy6T+Up5cko9bHEionTHwxQGt9nt7EnTLc1PDTa/m6kCpvesDC/31PkjTkTJ0/rUtFJR5B/2F/Z5VlXbvBCDwCU9EXV0td7hpXtSalxKjufyt3aptJGWqNQsRS6knLgkPtLCJAmL/EhSJOXGZa4m28S4P/30EyZOnIh//vkHw4cPV5PPSjIkSdCTzJ49GzVq1MDHH3+sxk/J75PlhOR3duvWDb/88ov6X5K6R2nYsCFWr16NTJkyqbmZ5HVIgvb333+jQAFrayulDoOWzkaKSSlGydCleVRq2+tNBiPKB1iaWm1zCJDj435zXsa7VxAxtTECoi6pdanM1S3mHdz2KYhFg2sgXyb2FXdU/Nw5p9Tcb/fCwnHwq/aoY7aOczLCHa6d/weXEuzOlFRRUVE4d+6cOiGXAgq2uYCk0tzzkJLjUj1PCkHImCbpnpdaLU3pkYzTSq59l5aOaS8vr+fKDdL3O0lE6UvYNbj93saeNF3TMqJzzDhcdM2LGb0rM2kicnIBfr7INWAu1qCaWneHEdqfPYCj1uIvpB9Jkurlr4euZbqq/5k0kTNi4kRE6cO9YOCX5jDcPKlWg7VMKmk6h5z4uksFVMxrrYZERM6tUPaM8O7yK5aaa6p1V80Mi0w38N9CvUMjIifHxImI0r67l4BfmgG3z6jVS1oWdI4ZjwtadrzboiSals6ud4RElIzqFM+Bu02+wQJzHbXuopmhLewPHJynd2hE5MSYOBFR2m9pmtUSuGudR0OSpZeiZeLMLOhTIz9erplf7wiJKAX0qlkI+8t/gD9M1ipoBs0CbfGrTJ6I6JkxcSKitCvsGjCrFXDnvFq9YMiJTtHjcBWZ0LB4FoxrWfKZZocnIscnn+332pTB0tyj8ZupoXWbFMReMhD4b5He4RGRE2LiRERp0/0Qa9L0oHveFZcceCnybYQgI/L6aviiU1m4cq4mojTNw80FP/Ssghl+r8UmT9LyJN32ji3XOzwicjJMnIgo7Qm/CcxqDTwoBHHDNTs6RozFdQQhd0ZvDChuhrcHKzoRpQdBvh74qU8VfOraP063PTMwvy9wgvM8PUo6m62G0jAtGY9lJk5ElLZE3Ab+1wa4cUyt3nHPhnYRY3EFmRHg7Y6felaEv4feQRJRaiqazQ9fd62Id8z97AUjYDECf/YETq/XOzyHYptrKyIiQu9QiJKF7VhOjnnk3JIhHiIixxB5x5o0Xf9Prd73yIo2YW+pQhAeri6Y3rMSCmXxxQm94ySiVPdi8Wx4q1lJjFn1CtxgQlvXHYA5BpjbHeg2DyhYT+8QHYKrqysCAwMREhKiJlGVH5lANL1PoupsZL/FxMSk632naZpKmuRYlmNaju3nxcSJiNKGqFDgt/bAtUPWVa8saHnvTVzUsqn1KZ3KomrBTDAajToHSkR6GVC7IE5cu49R+wfBHSa0cN0DmKKAOV2AHguA/LX0DtEhZM9unaLhxo0biIyMhLe3NwvpOGHSwH1nJUmT7Zh+XkyciMj5GSOBP7oAV/ZbV70yoW3YWziv5VDro5sUQ5vyuXQOkoj0JieQk9uXxvlb4Rh2YQjc8TUau+4DTJHAnM5Ar2VA7kpI7+R9ypEjBzJmzIgNGzagTp06ydLNiVKPXCTcunVrut937u7uydLSZMPEiYicm1nGKfQGLvxtXfXKiC5Rb+O42Zo0damSB4PrFdI5SCJyFJ5urpjaoxLafv83htx9HVPxJV50PQDE3AdmdwD6/gVkLaF3mA5BTjhNJhO8vLzS9cm3M+K+Sxnps9MjEaUNFjMgE1qeWmNd9ciAV7W3sS/KmjTVKZoF77ctne67KRBRfFn8PDGjV2W4unthkHE4dppLxhkn2Ra4fU7vEInIATFxIiLnJOVFV44C/ltoXXXzwrve47D+nrVLXokc/vihe0W4u/JrjogeVjKnP77sXB7R8EB/4ygctBS03nD/GvBbW+sE2kREceh+RvH9998jf/78qimxatWq2LNnz2Pv/9VXX6FYsWJqsFuePHkwYsQIVTGEiNKZDROBfb+oRc3FDd9lHoc51/Oo9ez+XpjZpzIyeLI3MhE9WtPS2dUYyHB4o0/MGJzWcltvuHMe+K2ddXoDIiJHSJzmzZuHkSNHYsKECdi/fz/KlSuHJk2aqLKBiZkzZw7eeustdf9jx47h559/Vs/x9ttvp3rsRKSjbV8A2798sGLAonzv4vPzBdSaJEu/9K2CHAHeuoZIRM5BxkC2LpcTd+CP7tFv4Yohq/WGkKPA7E5A9H29QyQiB6Fr4vTFF19gwIAB6Nu3L0qWLImpU6fCx8cHM2fOTPT+O3bsQM2aNdGtWzfVStW4cWN07dr1ia1URJSG/POztbXpgb+Lv41Rx4qqZVcXg+qeJ930iIiSQsZAftqxLMrlDsB1BKFr1Fu445LRemPwXmBuN8DIni1EpGNVPZmUa9++fRg7dqx9m0zQ1bBhQ+zcuTPRx9SoUQO///67SpReeOEFnD17FqtWrULPnj0f+Xuio6PVj01oaKi9TKMjzOdii8ERYqGk437Th+HYUriuHAVbqYdjpUagx/5S9tvfb10S1QsEPna/cN85L+475+QM+02KFX/ftRw6TNuNC6HZ0TXyTSzy/gA+lvvAuS2wLHgZ5vYzAZfkK2vsDJxh31HiuO+S7mneI4MmM2Tp4MqVK8iVK5dqRapevbp9+5gxY7Blyxbs3r070cd98803eOONN9TEXlJmceDAgfjxxx8f+Xvee+89TJwYe3U6brc/ad0iIueQKewYqp+ZAlfNpNb3BrZA15BuMFqsaVTjXBa0yGvROUoicmaX7gNfH3FV3ysVDSfxh+dkeCJG3XYuU30cytNHmqj0DpOIklFERITqzXbv3j34+z++x4pTjZzevHkzJk+ejB9++EEVkjh9+jSGDRuG999/H+PGjUv0MdKiJeOo4rY4SVEJ6eb3pDcntbLcdevWoVGjRqyz70S431LZ9SNw++01GB4kTaHFO+OVkx1gtFjXW5fNgc86Jq3sOPed8+K+c07Ott/yHL6GYX8ewn6tKPrHjMIszylw0UwocGsT8paqCkvtN5BeONu+o1jcd0ln642WFLolTpkzZ1aTc12/fj3edlnPnj17oo+R5Ei65fXv31+tlylTBuHh4XjllVfwzjvvqK5+CXl6eqqfhOQgcqQDydHioaThfksFdy8CczsD0WFq1VioMdpf7ozbEdYxB9UKBmHKS+Xg4fZ0XWi475wX951zcpb91qZiHpy5FYlvNpzCNksZjLUMwieGb9Vtrls/hmtgLqBiL6QnzrLv6GHcd0/2NO+PbsUhPDw8UKlSJWzYsMG+zWKxqPW4XfcSNqUlTI4k+RI69TgkopQkpYB/72CdV0W+I3JWwsthg3H6pjVpKpw1A6b1qAzPp0yaiIgeZ3iDImhW2noRd150dfzg3if2xuXDgROr9QuOiNJnVT3pQjdjxgzMmjVLlRcfNGiQakGSKnuiV69e8YpHtGrVSo1nmjt3Ls6dO6eaIKUVSrbbEigiSiNiIoA5nYGbJ9Wqlqkw3vYeh20XI9R65gye+KVPFQT48EoaESUvFxcDPn+pHErltHbp/zSsEVb5trPeqJmB+X2AS//oGyQRpTpdxzh17twZN27cwPjx43Ht2jWUL18eq1evRrZs2dTtFy9ejNfC9O6776oxDPJ/cHAwsmTJopKmDz/8UMdXQUTJzmwCFvYDLj+YaiBDNkzLMwVzd1mTJm93VzXBbZ4gFnghopTh4+GGGb0qo/V3f+Pm/Wi8dqsDlmQLRbl7GwBTJDDnJaDfWiBzEb1DJaJUontxiCFDhqifRxWDiMvNzU1Nfis/RJRGSbfblSOBE6us6x5+WFXuO3y8IVKtuhiAb7pWQNncgfrGSURpXs5Ab0zvVQldpu9CjAnodL0XtuQIRY47/wCR0pW4PdBvHeCX+NhsIkpbdO2qR0T0kK1TgP2zrMsu7vi35vcYuslaPU9MaFUKjUpaW6WJiFJaxbwZ8UmHMmo5Bu5oen0g7gcWjy1eM7ujvXgNEaVtTJyIyHEc+hPYFNv19lK9L9FjgyfMFmvxl/61CqB3jfw6BkhE6VG7CrkxqF4htXzP4o02d4fD6JfbeuO1w8CCl61djIkoTWPiRESO4cIOYOlr9tV7tcah4/YcCI8xq3WpcPV28xI6BkhE6dnoxsXQsERWtXwmyh/9zWOheQZYbzy1Flj9prWrMRGlWUyciEh/N08Dc7sB5hi1GlO+N146VAXXQ6PVesW8gfiyc3lV6YqISA/y/fNVlwools1PrW+5nRGT/d+F5vKgsuc/PwG7ftQ3SCJKUUyciEhf4beAOZ2AyDtq1VKoAfrf6IITIffVer5MPqqylZc7pxwgIn1l8HTDT70rI8jXQ63PuJQLS/K8GXuHNW8Dx1fqFyARpSgmTkSkH2OUtaXp9lm1qmUtifHub2DrGWsSFejjruZqypTBU+dAiYisZBqEqT0qwd3V2gI+4kRJHC706oNbNWBhfyB4v64xElHKYOJERPqwWIClg4FLu6zrGbLjl/yf4vcD1qTJw80FP/WqjIJZMugbJxFRAi8UCMIHbUvb19sdq4sb+VtbV4wRwB9dgLuX9AuQiFIEEyci0odUz/tvoXXZ3QcbK36DSVtD7Td/+VJ5VM4fpF98RESP0blKXvSrVUAtmyxA8wtdEJXjBeuN969bJ8iNiv1OIyLnx8SJiFLfv78D2z57sGLAsZpf4dUN1up5Ymyz4mhRNodu4RERJYV8V9UtmkUt34gEuoW9DkvGgtYbQ44C83sDZqO+QRJRsmHiRESpX3Z8+XD7akjN9/DS5kAYzdYyvj2q5cUrdR6ceBAROTA3Vxd8260CCmXxVev7b7rgbe9x0LwftJaf2QisHqtvkESUbJg4EVHquXMBmNcDsFivwEaUfxnt9pVFWJR14sgXi2fFe61KwWBg2XEicg7+Xu74uXcVBHhby5LPPeuJ3/JPBlytlffwzwzgn5/1DZKIkgUTJyJKHdFhwB9dgYhbatWcvx66XmyL4LuRar10Ln9827WCuoJLRORM8mf2xY/dK8L1wVxz4//1x57S42Pv8NcY4NxW/QIkomTBMxQiSp0KeoteBUKOqFUtqDCGm4fh4BXrXE25Ar0xs3cV+Hq66RwoEdGzqVE4M95rXcq+3mNvYVwrNcC6YjEBf/ayT71ARM6JiRMRpbxNHwAnrJNCap7++CbrJCw/ZW1p8vNywy99qyCrv5fOQRIRPZ+e1fKhV/V8ajnGbEGrYw0Rmb+B9UaZ5HtOF1baI3JiTJyIKGUdmg9s+9y6bHDBX8U/xpcHrKtuLgZM61EJRbP56RoiEVFyGdeyJGoWzqSWb0SY0f3OK7BkKmq98eYJYGE/wBJbRZSInAcTJyJKOZf3AUtfs68eKfsWBu8OtK9/3KGs6t5CRJRWuLu64PtuFZE/k49a33/djHE+70Lzzmi9w6m1wPoJ+gZJRM+EiRMRpYzQK8DcboA5Wq3eKNoF7faVsd88vGERdKyUW8cAiYhSRqCPB37qXUV1RRazT7lhXoEPAJcH4zh3fAv8O1vfIInoqTFxIqLkFxNhTZruX1OrkTmrofmp1ogxWedqkoRpWIMiOgdJRJRyCmfNgO+6VcSDQnt4a39GHCzzduwdVgwHLu7SLT4ienpMnIgoeWkasHwYcOVftWoOyIsudwfhhrUWhOr7P7ldGc7VRERpXt2iWfBui5L29U77SuJGiV7WFXMMMK+ntXWeiJwCEyciSl67fgQO/6kWNXdfjHJ9EwdvWyeGLJbNDz/2qAQPN371EFH60LdmfnSpkkctx5gsaHWqBaLz1LLeGB5iTZ5M1i7NROTYePZCRMlHJnhc+659dUbmMVhyxTogOqufJ2b2rQJ/L2sSRUSUHkjr+qQ2pfFCgSC1fu2+GS/fHwxLgDWZQvBeYNVofYMkoiRh4kREyePuJWB+H0Czltn9O0dvTD5nHcfk4+GKmX2qqIluiYjSG2lln9qjEnJntH4H/n0V+MR/HDS3B/PX7Z8F7P1F3yCJ6ImYOBHR8zNGAvN6ABG31Gpw5proea6RWnZ1MajSvKVzBegcJBGRfoJ8PfBz7yrw9XBV69NOZcCagnGKRUir06U9+gVIRE/ExImInr8YxIoRwFXrrLYRvnnQIrg3LA++Xia1KYX6xbPqHCQRkf6KZffD110qwFYbZ+ChwjhXuLd1xWK0jncKs1YjJSLHw8SJiJ7PnhnAwT/UosXNG11CX8ddLYNaH1i3ELpXzadzgEREjqNhyWx4s2lx+3qrE41wP0d164pM4fBnL8AUo1+ARPRITJyI6Nmd/xtYM9a++rZlEA4Zc6nllmVzYEyTYjoGR0TkmF6tUxDtK1q/K+8bXfDSrQEw+1nXcWk3sPotfQMkokQxcSKiZ3MvGJjfG7CY1Oo8j/aYG1FZLVfJnxGfdSoHF9vMj0REFK/SnsxnVzFvoFo/GuqFMa6jobl6Wu+w92dg///0DZKIHsLEiYienjEK+LMnEH5DrR7yrIixoe3VcsHMvpjeszK83K0DoImI6GHyHTm1ZyXkDLBW1lt4LSv+yDoi9g4rRwGX9+kXIBE9hIkTET096UYSbP2Dfss9O3rde1UVg8jk64Ff+lZBRl8PvSMkInJ4Wf28MKN3ZXg/uND09rmyOJSrs/VGc4y1VT/itr5BEpEdEyciejoH5wL7rPONmFw80fP+67gLP3i6uagTgHyZfPWOkIjIaZTKGYAvO5ezr3c42wJ3MlW0rty7BCwaAFgs+gVIRHZMnIgo6a4fBZYPt6++Fd0HR7X8qrTu113Ko2LejLqGR0TkjJqWzoFRjYqqZaPmhnY3BsDkndl64+n1wNYp+gZIRAoTJyJKmqhQ67gmU6Ra/dNcHwvMddXyO81LqD/8RET0bIa8WBityuVUy+djAjDCNBSa4cFp2uaPgNMb9A2QiJg4EVESJ7ldNhS4dVqtHtPyY5zROmljnxr50a9WAZ0DJCJy/kp7UzqWRdncAWp9eVgR/OHb88GtGrCwP3Dvsq4xEqV3TJyI6Ml2TwWOLlGLYfDBqzHDEA0PNCqZDeNallR/8ImI6Pkr7c3oVRnZ/K1lyd+52QhHMzyYHDfyNvBnb06OS6QjJk5E9HiX9gBr37WvjowZiItaNpTLHYBvulSAK+dqIiJKNtn8vdSUDlJwR4MLut7sizAvaxc+BO+N931MRKmLiRMRPVr4TWB+H/skt1NNrbDOUhm5M3rjp95V4O3BuZqIiJJbuTyBmNLJWmnvHjKgR+hgWFzcrTfumQYcXqBvgETpFBMnIkqcxQws7AeEBqvV3ZbimGJ6Cf5ebvi1bxVk8Xswwz0RESW71uVyYuiLhdXyQUtBfGDuE3vjsteBGyf0C44onWLiRESJ2/IJcHazWryhBWBIzFC4urpjeq/KKJzVT+/oiIjSvBENi6JpqexqeWZ0Paxxq2e9wRgOzOsJRN/XN0CidIaJExE9TMrebvlULZo1A4bEvI4byIgpncqiWsFMekdHRJQuuLgY8EXnciiRw1/q7mHY/d646JbfeuPNE8CqN/QOkShdYeJERPGFXQMWvWItfwtgiqkzdmslMLpJMbQpn0vv6IiI0hUfDzf81LsyMmfwQBQ80Tt8KKJdvK03HvwDODBH7xCJ0g0mTkSUYFxTfyDiplrdYK6AaeaW6FIlDwbXK6R3dERE6VKuQG9M61kZHq4uOKflwOiol2NvXDmK452IUgkTJyKKtfUz4Pw2tXhVC8IbxldRu2g2vN+2NOdqIiLSUaV8GfFR+zJqeZmlJuaZ61tvMEZYq58aI/UNkCgdYOJERFbntkHb8rF9XNPrMUOQLXsufN+tAtxd+VVBRKS3DpVy49W6BdXyBGMvnEYe6w0hR4G/3tQ3OKJ0gGdDRKTma9IW9odBs6jVL00dccmvPH7pWwV+Xg/mDiEiIt2NaVIcDYpnVeOdBkYPRRQ8rDfsn8X5nYhSGBMnovTOYgEWvwrD/Wtqdbu5FP7n1kElTTkCHgxAJiIih+DqYsBXXcqjaLYMOK3lxjhjnPmdlg8Dbp3RMzyiNI2JE1F6t+Mb4PR6tXhD88co8xB8173yg/K3RETkaKQnwE+9qiCjjzvmm+tiobmW9YaY+9bxTqZovUMkSpOYOBGlZxd3w7Jhklq0aAYMN76Gke1qoU7RLHpHRkREj5E3kw+m9qgENxcXjDO+jDOWHNYbrh0C1o7TOzyiNImJE1F6FXEbMfP6wkUzq9XvzW1QoW47dK6SV+/IiIgoCaoWzIQP2pZGBLwwxPg6orUHY1L3TAOOLdc7PKI0h4kTUXqkaYiYPxAe4cFqdY+lGM6VGoJRjYvqHRkRET2FLi/kRd+a+XFMy4dJpp6xNyx9DbhzQc/QiNIcJk5E6VDE9h/gc26NWr6tZcCvOd7FR50qcq4mIiIn9E7zEqqL9WxzA6wwV7NujLoHLBoAmE16h0eUZjBxIkpnoi8fgtuGCfb1z31G4KPezeDp5qprXERE9GzcXF3wbdcKKJglA8Ya++Oi5cE41Uu7ga2f6h0eUZrBxIkoHbFER+D2/3rCA0a1PsfQAgMHDEaAD+dqIiJyZgHe7vi5dxW4eAdgmHEITNqDU7ytU4ALO/QOjyhNYOJElI4cmDkEOWLOq2XpD1+695fIE+Sjd1hERJQMCmT2xffdKuKQoaiayFyRic0XDgAi7+gdHpHTY+JElE4cWP8HKl5fqJYjNQ/cafojyubPpndYRESUjGoVyYwJrUriR3Nr7LYUt24MvQysGKEKAxHRs2PiRJQO3L9xEfm3j7av/1tyDGpUr6lrTERElDJ6Vc+PbtXyY3jMa7inPehVcGQxcGC23qEROTUmTkRpncWC6//ri0CEqdV93jVQvdMovaMiIqIUNKFVKeQvWBRvGQfYt2mrxgA3T+saF5EzY+JElMZdWjUFhcL2quXrWkZk7zEdBhd+9ImI0jJ3Vxf80L0ijmasjz9M9dU2gzEc2sJ+gClG7/CInBLPnojSsJhL+5F9r7UUrUUzYF+lj5ErVx69wyIiolSQ0dcDP/eujC9d++KMJYfaZrh6ANj4vt6hETklJk5EaVVMOO7P7g13WCc/XOzTAU1adtY7KiIiSkWFs/rhk27VMcw0FDHag/n6dnwDnNmkd2hEToeJE1EadW/xKARFXVTLhywFUaLbJ3B1MegdFhERpbL6xbKibbNm+MTUxb7NuPAVIPymrnERORsmTkRpkOXIEgQc+0Mth2ue2F3xE5TMk1nvsIiISCf9ahXA/fIDsNVcRq27R4QgauEglignegpMnIjSmtArMC4eal/93usV9GzRQNeQiIhIXwaDAZPalcVv2d/CTc1fbfM6uxYxe37ROzQip8HEiSgtsVgQtWAgPE2hanWFuRrqvDQcXu4P+rUTEVG65enmio97N8KnHkPs27TVY6HdOqNrXETOgokTURqi7ZkOr4tb1PJVLQj7yoxHtULsokdERFaZMnji5X6DMF+z9kTw1KJw7dc+gNlaSIiIHo2JE1FaceMELGvH21c/cBuC4a1e0DUkIiJyPMWz+yNT+89wXsum1nOEHcLJhZP0DovI4TFxIkoLTDEwLegPV0u0Wp1paopW7bohwNtd78iIiMgBvViuIPZV/BhmzVpttcCR73D6wFa9wyJyaEyciNKCrZ/C7fohtXjKkgv7Cr+OpqWtkx0SERElpn3rdlifpadadjeY4bF0IKIiwvQOi8hhMXEicnaX9kDb9rlaNGqueMcwFOPaVdI7KiIicoJKe3X7T8EptyJqPa8WjGP/G6F3WEQOi4kTkTOLvg/Loldg0Cxq9UtTB7Rp3hzZA7z0joyIiJyAl5cX3Dr+hEjNQ61XuDYfV/Yu1zssIofExInIma19By53zqnFvZai2J+7N7pWyat3VERE5EQKFC+Pvwu+bl/3WvU6LPdv6RoTkSPSPXH6/vvvkT9/fnXFo2rVqtizZ89j73/37l289tpryJEjBzw9PVG0aFGsWrUq1eIlchgnVgP7flWL4Zon3jQPxgcdysPFxTrQl4iIKKlqdR2L3S4V1HKQ5TaCfx8IaJreYRE5FF0Tp3nz5mHkyJGYMGEC9u/fj3LlyqFJkyYICQlJ9P4xMTFo1KgRzp8/jwULFuDEiROYMWMGcuXKleqxE+kq/Ca0ZbETGE4y9ULbF2uhcNYMuoZFRETOycvDDVrr73BHs/4dyXNtLcL3ztE7LCKHomvi9MUXX2DAgAHo27cvSpYsialTp8LHxwczZ85M9P6y/fbt21iyZAlq1qypWqrq1q2rEi6idEOuAC4fBkP4DbW6zlwRBzK1wqt1C+kdGRERObFq5Utjca437Oue69+Gd7T1bw0RAW56/WJpPdq3bx/Gjh1r3+bi4oKGDRti586diT5m2bJlqF69uuqqt3TpUmTJkgXdunXDm2++CVdX10QfEx0drX5sQkND1f9Go1H96M0WgyPEQs6x3wwH58Dt+Aq1fFPzx9umAfihbUkYNDOMRnOqx+Ns+JlzXtx3zon7zbk06zQAy77eiNbYCm9LOIqd/QnGmC56h0VPiZ+7pHua90i3xOnmzZswm83Ils06a7WNrB8/fjzRx5w9exYbN25E9+7d1bim06dPY/DgweoFS3e/xHz00UeYOHHiQ9vXrl2rWrccxbp16/QOgZxgv3nH3ET9Y2/b18ca+6NENj9cObwDVw6naihOj58558V955y435zH/uzdUfHqUeQ23ES+qGP4d/abuJitsd5h0TPg5+7JIiIi4PCJ07OwWCzImjUrpk+frlqYKlWqhODgYEyZMuWRiZO0aMk4qrgtTnny5EHjxo3h7+8PvUnSJwe1jN1yd3fXOxxy5P2mWeA6pwNcLFFqdZ6pHo741cLK/jWQwdOpPsq64mfOeXHfOSfuN+fT1KLhox9v4b271gt1pa/NR+k2Q4Egdgl3FvzcJZ2tN1pS6Ha2lTlzZpX8XL9+Pd52Wc+ePXuij5FKerLz43bLK1GiBK5du6a6/nl4WOcgiEsq78lPQvI8jnQgOVo85ID7bc8M4Pw2tRisZcL7ph74tn0ZZMzgnTq/P43hZ855cd85J+4359Ktay/8/t0m9HBdB3dLNCIXvwbvV9YCLokPjSDHxM/dkz3N+6NbcQhJcqTFaMOGDfFalGRdxjElRgpCSPc8uZ/NyZMnVUKVWNJElGbcPgusG29fHWN8BQ3KF0b9Yll1DYuIiNKmotn8EPLCWzhvsQ6p8L62F5Yd3+sdFlH6raonXeiknPisWbNw7NgxDBo0COHh4arKnujVq1e84hFyu1TVGzZsmEqYVq5cicmTJ6tiEURpllwoWPIaYLT2wf3N1BBHvCpiXMuSekdGRERp2IAGpfG+4VVYNOv8gNrG94GQxMehE6UHug6M6Ny5M27cuIHx48er7nbly5fH6tWr7QUjLl68qCrt2cjYpDVr1mDEiBEoW7asmr9JkiipqkeUZu3+Ebi4Qy1etGTBR6ZueL9dSWTO8HAXVCIiouTi5e6KogWL4OdTzTDAbRVcLTEwLhoI9wHrAVeOraX0R/ejfsiQIeonMZs3b35om3Tj27VrVypERuQAbp4CNkyyr442DkSlIrnRviInfSYiopRXPFDDluJDcfrkARR2uQL3a/8Cf38J1Bmtd2hE6aurHhE9hsUMLBkEmKxV9GaamuKQW2lMblcGBoO12wQREVFKG92iLCa4vAbzgy57ls2fANc4BwalP0yciBzVjm+Ay/+oxbOW7PjU1BkjGxVFniDHmX+MiIjSPuka3rJ5a0w1t1LrLhYjLIteBUwxeodGlKqYOBE5opBjwKbJalGu8L1hHIgiubKib838ekdGRETpUOfKebAtZz8cs+RR6y4hR4Ctn+odFlGqYuJE5GjMRmDxQMBsvZI3w9wCBw3F8HGHMnBz5UeWiIhSn4uLAZM6VMIY82AYNetcTtq2L4DgfXqHRpRqeBZG5Gi2fwlcPaAWT1ly4UtTR7xSpyBK5QzQOzIiIkrnczvVqfMivjW1U+sGzQxt8SDAaB2LS5TWMXEiciRXDwFbPlGLJs0Fo4wDkSNTIIY1KKJ3ZERERBj6YhEs9++CQ5YCat1w8wSw2dq1nCitY+JE5ChkkO2SwYDFpFZ/NLfGIa0QJrcvo+bSICIi0pv8PZrYrjxGGQchWrPOaqPt+JZd9ihdYOJE5Ci2fwFct5Z3PWbJi29M7dVg3BqFMusdGRERkV2dollQstwL+NrUXq0bNAuw5DXAFK13aEQpiokTkSO4LtWJpqhFGXQrVfQCMvji7eYl9I6MiIjoIe+2KIm57m1x2PKg2uuNY8DWz/QOiyhFMXEi0pvZBCx9LU4XvVY4ouXHxNalEODjrnd0RERED8ni54nRzctgjPHV2Cp70nNCxuoSpVFMnIj0tvM74Mq/avGkJRe+M7VDwxLZ0LxMdr0jIyIieiTpTu6btzx+MLdR6wbLgwuBMq0GURrExIlITzdPxZvoVq7ceXh64/22pWAwGPSOjoiI6LFzO0kBo6mWdjj+YGJcXDsE/P213qERpQgmTkR6sViApUMAs3Uw7UxzMxzQCuPNZsWRI8Bb7+iIiIiSNLfTy3WLYrTxVXUBUGgyrUbIMb1DI0p2TJyI9PLPDODSLrV43pINn5s6oXK+jOj+Ql69IyMiInqquZ3uZSyN6eaWat1gjnkwdtesd2hEyYqJE5Ee7pwH1r9nX33T+Aosrt74qH0Z1fWBiIjImeZ2+qBtaXxl6oAzlhzWjTKv064f9A6NKFkxcSJKbZoGLBsKGCPU6m+mhtitlcBr9QujSDY/vaMjIiJ6prmdmpbPjzFyIfBBlz1s/AC4eVrv0IiSDRMnotS2fxZwbqtavKxlxsemriiaLQMG1Sukd2RERETPNbfTKc9S+NXcxLrBFAUsG2Id00uUBjBxIkpN94KBtePsq28b+yHCIF30ysLDjR9HIiJy7rmdxjYvgSmml3DBktW68eJO4J+f9A6NKFnwTI0oNbvorRgORIeq1fmmOthqKYde1fKhUr6MekdHRESULHM7lcqXA2+ZBsRulDG9MraXyMkxcSJKLYf+BE6tVYshWiDeN/VAjgAvjG5aXO/IiIiIknVup39QGr+bGlg3GsOBZa9bLyASOTEmTkSp4X4IsPpN++o7xpcRigyqClEGTzddQyMiIkruuZ1erVtQjeEN1jJZN57bAhyYrXdoRM+FiRNRalj1BhB5Ry0uN1fDOktltCybAw1KZNM7MiIiohSZ2ykoKDPeMfaL3bjmHeuFRCInxcSJKKUdXwkcXaoWb2sZMMHYBwHe7pjQqpTekREREaXo3E6bLeWxxFzDujHqLvBXbO8LImfDxIkoJUWFAivfsK9ONPbCbfjj3RYlVPUhIiKitDy3U5vyOTFJ/vZpGawbjywCTvyld2hEz4SJE1FK2jARCLuiFreYy2KppSZqFs6EjpVy6x0ZERFRqsztZPIKwvvGnrEbV46yXlgkcjJMnIhSysXdwD8/q8UIzRPvmPqprguT25WBwfBgVnUiIqJ0MLfTYkstbDWXsW4MDQY2TNI7NKKnxsSJKCWYooHlr8vkTWr1c1MnXNayYETDosiXyVfv6IiIiFJ1bqfK+YLwtqmfupCoyKS4coGRyIkwcSJKCdu/Am4cV4sHLQXxi7kpSuX0R79aBfSOjIiISJe5na4ZsuFzU8cHWzVg2VDrhUYiJ8HEiSi53TgBbPtMLZo0F7xlHACDiys+6VAWbq78yBERUfqd2+lXc1N1QVG5eQLY/qXeoRElGc/iiJKTxQIsHwaYY9TqDHMLHNPyoX/tAiidK0Dv6IiIiHSd2ylXkJ+6oCgXFpWtnwEh1h4aRI6OiRNRctr3C3Bxp1o8b8mGr0wdkDfIB8MbFNU7MiIiIoeY20kuKE43t7RutBitY4LlwiORg2PiRJRcQq8A69+zr4419Uc0PPBR+zLw9nDVNTQiIiJHmtvpa1N7nLNks268tBvYa61CS+TImDgRJZdVo4Fo67wUf5rqYqelFDpVyo2ahTPrHRkREZFDze3k6eWDt039Yzeunwjcu6xnWERPxMSJKDkcWw4cX6EWb2j++NDUHZkzeOCdFiX0joyIiMgh53aSC4x/mOpbN8aEWSfG1azTeBA5IiZORM8r6h6w8g376iRjL9xDBkxoVQqBPh66hkZEROS4cztlxEemrrihPSiedHI1cGSx3qERPRITJ6LnJeOa7l9TixvN5bHcUh0NimdFy7I59I6MiIjIoed2inDxw3hjn9gb/noTiLyrZ2hEj8TEieg5GC7tAvbOVMvhmifeNb4MXw83vN+2NAwGg97hEREROfzcTn9ZXsA6cyXrxvAQYMNEvUMjShQTJ6JnZLCY4LpqpH19iqkzriAz3mxWHDkDvXWNjYiIyFnmdsob5IsJxt7qAqSy9xfg0h69QyN6CBMnomdUJGQVDDdPquUDlkL4n7kxKuYNRI+q+fQOjYiIyKnmdpILj1+YOj3YqgHLhwNmo87RET1n4tS7d29s3br1aR9GlLbcOYei15aqRZn9fKyxP1xdXfFxh7Kq3zYRERE93dxOv5qb4IjlwcXHkCPArh/0Do3o+RKne/fuoWHDhihSpAgmT56M4ODgp30KIuemaXBdPQaumvVK2ExzMzUL+uB6hVV/bSIiInr6uZ18vTzVhUiL9uAC5KaPgDsX9A6N6NkTpyVLlqhkadCgQZg3bx7y58+PZs2aYcGCBTAa2aRK6cB/C+FydpNaDNYy4StTBxTOmgGD6xfSOzIiIiKnntvpkFYIs8yNrRtNkcCqNzi3Ezn3GKcsWbJg5MiROHjwIHbv3o3ChQujZ8+eyJkzJ0aMGIFTp04lf6REjkBKpK4ea1+dYOyDCHjh4/Zl4OnmqmtoREREaWFup89NnXBNy2jdeGotcNTaNZ7IqYtDXL16FevWrVM/Mr6jefPmOHz4MEqWLIkvv/wy+aIkchQbJllLpQJYY66M9ZZK6FktHyrnD9I7MiIiojQxt1OUiy/eM/aOP7eTTDZP5GyJk3THW7hwIVq2bIl8+fJh/vz5GD58OK5cuYJZs2Zh/fr1+PPPPzFp0qSUiZhIL5f32udsuq95qS/1bP6eGNO0mN6RERERpam5nVZbqmC9uYJ1o0wyv/EDvUMjgtvTPiBHjhywWCzo2rUr9uzZg/Llyz90n/r16yMwMDC5YiTSn9lkLY0qJVIBfGnqiKvIhKktS8DPy13v6IiIiNLU3E7LD17FhNt9UMPlKHwM0cCeGUDZLkDuBxPlEjlDi5N0wZPWpe+//z7RpElI0nTu3LnkiI/IMez+Ebh+WC1KqVQpmVo+kwUNSmTVOzIiIqI0ObdTMLLgS1OHB1s1YMUw64VMImdJnKQIhJeXV8pEQ+SI7l4CNk1Wi1Ii9W1jP1UytUN+i96RERERpem5nX4xN8VR29xO1w4Du6fqHRqlY89VHIIoXfhrDGCMUIu/mxvioFYYbzUtBn8PvQMjIiJK23M7+Xh5qQuWsXM7fWi9oEmkAyZORI9zbAVwYpVaDNECMcXUGTUKZULHijn1joyIiChdzO10QCusLlwqciFz1WjO7US6YOJE9CjRYdbWpgcmGXsixi0DJrcrA4PhwZUvIiIiSvG5neTCpVzAVE7+BRxfoXdolA4xcSJ6lE0fAaHBanGLuSxWWKpheMOiyJ/ZV+/IiIiI0tXcTpEuvpho7BV7w6ox1gucRKmIiRNRYq4etFbSAxClueNdU1+UzBGA/rUL6B0ZERFRupzbaaWlKjaZy1k3hl0Btnyid2iUzjBxIkrIYrbO2aRZq+Z9Y2qHYGTDJx3Kwt2VHxkiIiI95nbKG+SL8aY+6oKmsvMH4PpRvUOjdIRngUQJ7Z0JXNmvFk9acmGGuSX61SqAMrkD9I6MiIgoXc/tdEnLhu9NbawbNTOwciQLRVCqYeJEFNf9G8DG9+2r7xpfRvYgP4xoVFTXsIiIiNI729xO080tcdaS3brx4k7g4B96h0bpBBMnorjWjQei7qnFBeY62KOVUFX0fDzc9I6MiIgo3ZO5nTy9fDDB1Cd249pxQOQdPcOidIKJE5HNhR3AwTlq8Z7mg4+MXdGhYm7ULpJF78iIiIgoztxO2yxlscJc1box4iawIba3CFFKYeJEJMxGYOUo+6rMFwHfLHi3RQldwyIiIqLE53Z639gT9zWv2PHJwfv0Do3SOCZORGL3NCDEWpnnkKUA5pgbYHyrksjo66F3ZERERJTI3E63XDLhS1OHB1s1YMVIa2VcohTCxIko9Aqw+SO1aNEMGGfsi7rFsqF1uZx6R0ZERESPmdtplrkJjlvyWDdePWBteSJKIUyciNa8A8TcV4t/mF/EKfdi+KBdGRgMBr0jIyIiosfM7ZQzyB/vGvvGbpSxTvdD9AyL0jAmTpS+nd0MHFmkFm9pfvjU1BmjmxRDrkBvvSMjIiKiJMzttFcrjvmmOtaN0fesFXKJUgATJ0q/TNHAyjfsqx+buqJAntzoVT2/rmERERHR083t9JGpG+5qvtaNMq/T+e16h0ZpEBMnSr92fgfcOqUW91mKYIlWF590KAtXF3bRIyIicqa5nUxeQfjU1CV2o1wYlYq5RMmIiROlT3cuQNsyRS2aHxSEGFSvCIpl99M7MiIiInqGuZ3mmuvjgKWgdeONY8CuH/UOjdIYJk6UPq0eC4MpUi3+z9wYUZlLYXD9wnpHRURERM84t1PFfJnwrvFlVSFX2fwxcO+y3qFRGsLEidKfk2uAEyvVYogWiC9MnfBx+7JqkCkRERE579xOxw2F8Ju5oXWjMVxdKCVKLkycKH0xRkJbNdq++qGxG1pXLY4XCgTpGhYRERElz9xOn5tewg3N37rx2DLg1Hq9Q6M0gokTpS/bv4Th7gW1uNNcErt8X8SbzYrrHRUREREl09xOgUFZMNnYPXbjqjcAY5SeYVEa4RCJ0/fff4/8+fPDy8sLVatWxZ49e5L0uLlz56pJStu2bZviMVIacOsMtO1fqUWj5opxpj54v20Z+Hu56x0ZERERJePcTosttbDLUsK68c45YOe3eodGaYDuidO8efMwcuRITJgwAfv370e5cuXQpEkThIQ8ftbn8+fP44033kDt2rVTLVZyYpoG/DUGBnO0Wv3Z3BxFSlVG41LZ9Y6MiIiIkn1up1yYYOwNk/bgVHfr58DdS3qHRk5O98Tpiy++wIABA9C3b1+ULFkSU6dOhY+PD2bOnPnIx5jNZnTv3h0TJ05EwYIPyk4SPc6x5cBpax/nK1oQZrp1wsTWpfSOioiIiFJobqerngVV5VxFKumufUfvsMjJuen5y2NiYrBv3z6MHRtb8cTFxQUNGzbEzp07H/m4SZMmIWvWrOjXrx+2bdv22N8RHR2tfmxCQ0PV/0ajUf3ozRaDI8SSZhkj4PrXW/arBJOMvTCsVVlk9HZ95ved+815cd85L+4758T95ryced8FerlgTJOi+GRpR7Ry3YEshlDg6FKYTq6HVqAu0jpn3nep7WneI10Tp5s3b6rWo2zZssXbLuvHjx9P9DHbt2/Hzz//jAMHDiTpd3z00UeqZSqhtWvXqpYtR7Fu3Tq9Q0izil9ZgGJhwWp5q7kMTvtWQtPrh7Bq1aHnfm7uN+fFfee8uO+cE/eb83LWfeerAZn9vPFxeDd87jFVbYtcOASbin8IzUXXU+BU46z7LjVFREQk+b5OddSEhYWhZ8+emDFjBjJnzpykx0hrloyhitvilCdPHjRu3Bj+/g9KVeqc5cpB3ahRI7i7s0hBsrtzDq5TV6vFGM0VH2p98WO/Osifyfe5npb7zXlx3zkv7jvnxP3mvNLCvitW+T7a/AB0s2xAJZdT8Iu+ihaZL8JSbQjSsrSw71KLrTeawydOkvy4urri+vXr8bbLevbsDw/aP3PmjCoK0apVK/s2i8Wi/ndzc8OJEydQqFCheI/x9PRUPwnJQeRIB5KjxZNWWNaNg4slRi3PNDdH6wZ1USR7YLI9P/eb8+K+c17cd86J+815OfO+K5k7I16pWxjjN/fBco934WLQ4LLtM7iW6wL450Ba58z7LrU8zfuja3EIDw8PVKpUCRs2bIiXCMl69erVH7p/8eLFcfjwYdVNz/bTunVr1K9fXy1LSxKR3cm1cDllbW26rgViTaYeeKUOi4kQERGlt7mdwjKWwmxzA7VuiLkPrBund1jkhHTvqifd6Hr37o3KlSvjhRdewFdffYXw8HBVZU/06tULuXLlUmOVZJ6n0qVLx3t8YKC19SDhdkrnTNEwrhwD2zWEj0zd8V7HanB31b2QJBEREekwt9PQmS+hhesuBBnuA4fnA5X6Avlr6h0eORHdzyI7d+6Mzz77DOPHj0f58uVVy9Hq1avtBSMuXryIq1ev6h0mORltx3dwv3dOLe+2FEemat1RLk/yddEjIiIi55rbqV75ophi6hy7cdVowGzSMyxyMrq3OIkhQ4aon8Rs3rz5sY/99ddfUygqclr3gmHeMkUd3GbNgB+9X8EPTYrpHRURERHpPLdTo+ON0NWyEWVdzgEhR4B/fgKqDdQ7NHISurc4ESW3qFVj4WaOVMu/mRuhb4fW8PFwiGsEREREpJMsfp54s3kpjDdah4MIbdMHwP0QXeMi58HEidKWc1vhdWKpWryl+eFUyddRt2gWvaMiIiIiB9C5ch645a2CeaZ6at0QHQasf3i+T6LEMHGitMNsRNiSUfbV7126Y1SbqrqGRERERI7DxcWAye3L4HNLF4RqPtaNB34HLv2jd2jkBJg4UZoRtWMa/O6dVMsHLAVRttUQBPl66B0WEREROZCi2fzQqW4FfG7qZN+mrRoFWMy6xkWOj4kTpQ3SP3nTZPvq0hzD0aZCbl1DIiIiIsed22mrf2scs+RV64arB4H9s/QOixwcEydKE24ueRtelnC1vFCrj35dOsFgMOgdFhERETno3E4T25XDeGMf+zbL+klAxG1d4yLHxsSJnF7M+V3IfHq+Wpb+ylF1xyF3xgf9lomIiIgeMbdTznIvYrHZOgmuS9QdYMMkvcMiB8bEiZybxYw784fbV+dl6Iku9SrqGhIRERE5z9xO37n2xH3NS61r+34Frvyrd1jkoJg4kVO7vmUGsoUfU8snLHlQq9tbcHVhFz0iIiJK2txO/ZvXxFemDmrdAA2WVWMATdM7NHJATJzIaZnDb8N764f29X9Lv4MSuYJ0jYmIiIicb26nw7m64Iwlh1p3ubwHOGwdAkAUFxMnclqn5r4Ffy1ULW90q4227V7SOyQiIiJywrmd3u9QAR+ae9m3mda8C0Tf1zUucjxMnMgphZzaiyIX/1TL4ZonAtt8rCrkEBERET3L3E4l6rTHenMFte4Wfh3ati/0DoscDBMncjqaxYK7C4bD1WDtf7wtRx9ULFNa77CIiIjIyed2+tn3FURrbmrdsuNb4PY5vcMiB8LEiZzO/tUzUTT6sFq+iByo3n283iERERGRk5OeK4PaN8JMczO17mqJQfSqsXqHRQ6EiRM5laiIMOTa85F9/UbNCQjwy6BrTERERJR25nY6V2IQrmuBat3z9F/AmY16h0UOgokTOZXD8yYhO26q5YNeVVCpYRe9QyIiIqI0ZHTryvjG0N2+HrFsNGA26hoTOQYmTuQ0bl85gzLnf1HLRs0V/m2mAAbO2URERETJO7dT6Wav4F9LYbXuc+80jLum6x0WOQAmTuQ0Lv85Gl4G6xWf3Vk6okAJa+UbIiIiouTUuUo+zMs8xL5u3jgZCLf2eKH0i4kTOYVL/65D2bsb1PItzR/FO3+gd0hERESUhud2erlzRyww11XrXub7uLeSxajSOyZO5PgsZlhWvWlfPVRsKDJnyaprSERERJT253YKeeFNhGneat3v6BxYgg/oHRbpiIkTObyTq39APuMZtXzCUADVOwzXOyQiIiJKB15uWg2/ebykll2g4daCEYBmnUeS0h8mTuTQzBF3kPWfT+3rITUnwsvTQ9eYiIiIKP3M7VSm/Zs4a8mu1rPc2Y/QffP0Dot0wsSJHNqpP8chUAtVy9s86qDmi631DomIiIjSkdolcmFd3tjeLpbV7wIx4brGRPpg4kQOKzz4CAqfn6OWIzUP+LeerAZrEhEREaWm9p1fxlZYq/kGmm7g0rIP9Q6JdMDEiRyTpiHkz5Fwg1mtbsjUFeVKl9E7KiIiIkqnczuF1pmEGM1VrWf7bzqib5zVOyxKZUycyCHd+ncZCtzbpZaDtcwo+9I4vUMiIiKidKx5vdr4y7etWvaAERf/GKl3SJTKmDiR4zHFwPLXWPvqrkLDkDd7Fl1DIiIiovRNhguU6voBbmgBar3I7U0I3r9a77AoFTFxIodzde0XyGIMVst7UQINOwzUOyQiIiIiFM6TE3sLD7Wvm1e9CYvJqGtMlHqYOJFD0cKuIeCfr9WyRTMguNoEBPiy/DgRERE5hvqdh+OYSxG1nNd0HgcWf6F3SJRKmDiRQwle+DZ8tAi1vNK9MZo1bKJ3SERERER2Xh7uiGo42b5e6MjXuHvzmq4xUepg4kQOw3hxH3KeX6SWQzUfZGj+HjzceIgSERGRY6lQozH2+DdWywEIx4l57+odEqUCnpWSY9A03F44HC7Q1OrigJ6oV6GE3lERERERJSp/508RoXmq5UohCxF88l+9Q6IUxsSJHEL43j+Q7d4htXzakhOVOo2BwcDJbomIiMgxZc1VAP/m7aOW3QwW3F0yRu+QKIUxcSL9Rd+HeW3sPE0b8o9A6TyZdQ2JiIiI6EnKdX4X12A9ZykVsQcnt1uHHFDaxMSJdHdn3RT4G2+q5Y1aJbTu0FPvkIiIiIieKEMGf5wpH9vS5L1pPCzGGF1jopTDxIn0dfciMuz7Xi3GaK44X3EscgR46x0VERERUZJUazUAR12Lq+U85ks4svxLvUOiFMLEiXR1a8lYuGvWiePmubZA56b19Q6JiIiIKMlcXV0Q2eBD+3q+Q98g6t4NXWOilMHEiXRjubALmc6vUMs3NX/4NnwLvp5ueodFRERE9FQq1WiIbT4N1bI/7uP0n+/oHRKlACZOpA+LBXcXj7KvzvHpgTbVSuoaEhEREdGzyt5+sr08efHg+bh74bDeIVEyY+JEuoj5dy6C7v6nlo9Z8qBi22FwdWH5cSIiInJORQoXw/ZsPdSyGyy4sfANvUOiZMbEiVJfTDhi1kywr67MMQS1imXXNSQiIiKi51Wu8zhc0TKp5SKhu3D1n6V6h0TJiIkTpbrwTV8gQ0yIWl5vqYi2HbrrHRIRERHRc8uWKSMOFB9pXzesfQcwW4tgkfNj4kSp614w3Hd9qxaNmisOl3wDhbP66R0VERERUbKo1/5VHDQUU8vZjZdwfvU3eodEyYSJE6WqeyvehYcWrZbnogl6trRWoCEiIiJKC3w83RFS4z37eqa9X8By/5auMVHyYOJEqUa7vBcBpxap5TtaBsTUGoPMGazVZ4iIiIjSihcbNMM69xfVsp92H+cXvqt3SJQMmDhR6tA0hC6JrS7zi3tXdK9XVteQiIiIiFKCVAr2bznJXp4877m5iL5yRO+w6DkxcaJUYT60AAE3/1XLpyy5UKTFUHi5u+odFhEREVGKqFquDP4K7GovT359/ih1IZmcFxMnSnnGSET9FdtEPTfjK2hZPq+uIRERERGltLIvvWMvT573zk7cO7xK75DoOTBxohQXve0b+EZdU8ubzeXQvH0vGAyc7JaIiIjStiK5smJLvqH29ZiVb7E8uRNj4kQpK/QqDNu/VIsmzQXbCg5HpXxBekdFRERElCoadByIf7WiajlL9EXc2Pid3iHRM2LiRCkqfPV78LBEquW5lobo06ap3iERERERpZqs/t44WeEd+7rPzs+AiNu6xkTPhokTpZwr/8L76Dy1eE/zwc3KI5EnyEfvqIiIiIhSVevmrbDSpZ5a9rXcx9Wl4/UOiZ4BEydKGZqG+0vHwAXW6jEzXDqhb+PKekdFRERElOq8PVyhNZhgL0+e9cRsWK4d1TssekpMnChFaEeXIsP1PWr5rCU7sjccigBvd73DIiIiItJF8+oVsMC7k1p2hQUhC0frHRI9JSZOlPyMUYhcGduXd6bvy+hcrZCuIRERERHpycXFgKJtxyL4QXny7De2I/r4Wr3DoqfAxImSnWnnj/CJuKyWt5tLoX6r3nB35aFGRERE6Vu14rmxIssr9vX7y94EzCZdY6Kk49ksJa/7IbBsmaIWzZoBy3MMwYslsukdFREREZFDaNBpEA5YrD1xMkWcReiumXqHREnExImSVdTaSfAwh6vleZb66NW2BSe7JSIiInqgcLYA7C46yr7usmkyEBWqa0yUNEycKPlcOwyPQ7PVYpjmjZMlh6FUzgC9oyIiIiJyKB3adsRqrZpazmC6g1trPtE7JEoCJk6UPDQNkcul/LhFrU7T2mFQC+sXAhERERHFypzBEzeqjkW05qbW/f+dBty9qHdY9ARMnCh5nFgF7+AdavGCJSs8a72GbP5eekdFRERE5JA6NaqN+W4t1bI7jAhZ/LbeIdETMHGi52eKQeTK2A/7jx690K9ecV1DIiIiInJkXu6uCGzyJm5rGdR61gvLYb5onQOTHBMTJ3puln9+hnfYebW821IclZr0ho+HtemZiIiIiBLXvHIJzMvQ075+Z/EbavgDOSYmTvR8Iu/AuPEj++qcwFfRoVIeXUMiIiIicpZJcSu0HY7TlpxqPfOdg4g+uFDvsOgRmDjRczFungJP4z21vNhcE53btFZfAkRERET0ZNWKZMfKHK/Z16P+GgcYo3SNiRLHxIme3e2zcNkzTS1Gae7Ymf811CiUWe+oiIiIiJxKyw69sd1SWi0HRF/B/a3f6x0SJYKJEz2zqL/Gw1UzqeWZlhZ4tXVdvUMiIiIicjqFsvrhYMnRsGjWXjtuf38OhN/UOyxKgIkTPZuLu+B1arlavKH5427F11Aoi7UqDBERERE9nS4tm2ER6qtlL0s47qyaqHdIlAATJ3p6moaIFW/ZV380dMbAxuV1DYmIiIjImWXK4In7Nd5CuOap1v2P/A6EHNc7LHK0xOn7779H/vz54eXlhapVq2LPnkfXsJ8xYwZq166NjBkzqp+GDRs+9v6U/LT/FsIn5F+1fNKSCznqDUCQr4feYRERERE5tS4vVsbv7h3UsissuLXkTb1DIkdKnObNm4eRI0diwoQJ2L9/P8qVK4cmTZogJCQk0ftv3rwZXbt2xaZNm7Bz507kyZMHjRs3RnBwcKrHni4Zo9TYJptp3i+jV63CuoZERERElFYmxc3Z7A0Ea5nUeqYrm2E+tUHvsMhREqcvvvgCAwYMQN++fVGyZElMnToVPj4+mDlzZqL3nz17NgYPHozy5cujePHi+Omnn2CxWLBhAw+q1GDe9SO8I6xJ6lZzGbzYojs83Vz1DouIiIgoTWhRoSDm+fW1r4ctHQNYzLrGRFZu0FFMTAz27duHsWPH2re5uLio7nfSmpQUERERMBqNCAoKSvT26Oho9WMTGhqq/pfHyI/ebDE4QixPFH4T2ubPIGmSWTNgUZaB+LR4JueIPT3vN4qH+855cd85J+4358V9p59qrQfgwO+LUN7lLALvn0bErplwr9InyY/nvku6p3mPDJqmadDJlStXkCtXLuzYsQPVq1e3bx8zZgy2bNmC3bt3P/E5pPVpzZo1OHLkiBojldB7772HiRMfrkoyZ84c1bJFSVfiwiwUvW1t2fvDVB8hxfsiv5/eURERERGlPTuOnsIn0e+r5VCDP7aVmQKTq7feYaU50gjTrVs33Lt3D/7+/o7b4vS8Pv74Y8ydO1eNe0osaRLSmiVjqOK2ONnGRT3pzUmtLHfdunVo1KgR3N3d4bBunoTrv5vVolR7OVTkNUzqXA/pldPsN3oI953z4r5zTtxvzov7Tl8lq4Zj9Q9r0NRlD/y1UNT2+A/eTSYk6bHcd0ln642WFLomTpkzZ4arqyuuX78eb7usZ8+e/bGP/eyzz1TitH79epQtW/aR9/P09FQ/CclB5EgHkqPFk1Dkmglwh7V/7QxLa7zWuqZDx5taHH2/0aNx3zkv7jvnxP3mvLjv9FEkeyBWlXkDL/7XFR4GM7z3TYN7rVeAwLxJfg7uuyd7mvdH1+IQHh4eqFSpUrzCDrZCD3G77iX06aef4v3338fq1atRuXLlVIo2HTu7Bd7n16nFq1oQzNWGIHdGdnMkIiIiSkm9mtfHHEMzteyuxeDuinF6h5Su6V5VT7rRydxMs2bNwrFjxzBo0CCEh4erKnuiV69e8YpHfPLJJxg3bpyquidzP127dk393L9/X8dXkYZZzPEnu3XphlcalNI1JCIiIqL0IKPMk1l7NG5rGdR64Okl0C7v1TusdEv3xKlz586q29348eNVifEDBw6olqRs2bKp2y9evIirV6/a7//jjz+qanwdO3ZEjhw57D/yHJT8tIN/wOf2UbV82JIfRRv3h58Xm3yJiIiIUkPXumXwq0dX+/q9JWMA/Wq7pWsOURxiyJAh6icxUvghrvPnz6dSVISYcEStmQhb/ZZfMwzAJy/k0zkoIiIiovRD5sss2nwozixegUIuVxF4cx/M/y2Ba5l2eoeW7uje4kSOy7j9G3hHhajldeZKaNnmJbi58pAhIiIiSk0tyufF3Iyv2NcjVr0DmGLnKaXUwbNgSlzoVWD7V2rRqLliba7BqFc0i95REREREaU7BoMBTdv1xnazdZy5X2QwondM1TusdIeJEyUqau0kuFui1PJsc0P0a9tYfWiJiIiIKPVVyp8JWwoMh0Wzno9pW6YAEbf1DitdYeJED7t2GB7//aEWQzUfXCwzBMWz6z9ZMBEREVF61qNNCyzW6qhlL3MY7q//WO+Q0hUmThSfpiFixVi4wFqtZZrWHgObv6B3VERERETpXr5MvrhUfiQiNQ+17rX/Z+D2Wb3DSjeYOFF8p9bB5/I2tXjRkgU+tQcjq5+X3lEREREREYA+TWvgN0MrtewGE+4tf1fvkNINJk4Uy2xSrU020z164eW6xXUNiYiIiIhiBfp4wLPuCNzQrMMoAs6thHZxt95hpQtMnMjOsm8WfEJPq+V9liKo2KwvvD1c9Q6LiIiIiOLoWrsU/ufZzb5+b+mbnBQ3FTBxIquoUMSs/8C++kfgQLStkFvXkIiIiIjoYR5uLijZYghOW3Kq9cBb/8L03xK9w0rzmDiRErPlM3jFWEtaLjdXQ6e27eDiwvLjRERERI6oadnc+DMo7qS44wBTjK4xpXVMnAi4exEuu35Ui9GaG3YWGIKqBTPpHRURERERPWFS3B3mkmrdP/ISonZO1zusNI2JEyFy9QS4adYrFLMsTTGg9Yt6h0RERERET1AxXxC2FhhmX9e2fAJE3tE1prSMiVN6F7wP3scXqcXbWgbcqfg6CmT21TsqIiIiIkqC7m1bY4mltlr2NoUibP0neoeUZjFxSs80DfeXx5Yfn2Z4Ca82qaBrSERERESUdHmCfHC5wihEae5q3Xv/T8DdC3qHlSYxcUrHtOMrkeGate7/GUsOZHtxkJobgIiIiIicR8+mtTDb0EItu2lGhK2aoHdIaRITp/TKbETEqtiZpn/x7o0eNQrrGhIRERERPb0Ab3d41huFW5qfWg86twKB98/oHVaaw8QpnTLt/RW+YefU8h5LMdRq2VvNCUBEREREzuelWqXxu2dX+3qBi39wUtxkxjPl9Cg6DMYNk+2rSzIPQpPSOXQNiYiIiIienVwAL97ydTX8QuSNPgnLsRV6h5WmMHFKh6I2fwnvB5PdrjBXQ5f27dRcAERERETkvBqXyY2FcSbFjVo9QQ3PoOTBxCm9Cb0C193fqcUYzRUHig5D2dyBekdFRERERM9JLoQ3ad8Xuy3F1XpA5EVE7vxJ77DSDCZO6UzYXxPhbolWy3O0xni5VX29QyIiIiKiZFIub0Zszf+6fV3b/BEQdU/XmNIKJk7pyfUj8D02Ty2Gaj64/8II5Az01jsqIiIiIkpGnVq1wlJzDbXsY7qH0HWf6h1SmsDEKR25u2wsXGCtrvKLawf0aVRJ75CIiIiIKJnlCvTG30GdEK25qXXv/dOAuxf1DsvpMXFKJyynNyEweItavqxlRvZGw5DB0/phIiIiIqK0pWLeTPjD0Fwtu2tG3F4+Tu+QnB4Tp/TAYkHo8rfsq7/79EbHqpzsloiIiCit8nYD3OuOwh0tg1oPOrMEWvB+vcNyakyc0oGYf/9A4L3javmwJT9qtH0Vri4sP05ERESUlrWrXgK/e3Wxr99ePIaT4j4HJk5pnTES0Wsn2ldXZH8NdYpl0zUkIiIiIkp57q4uKNFyOM5ZrOd+mW7+A+OxlXqH5bSYOKVx97d8B7/o62p5o7kCOnToqndIRERERJRKGpTOjUWZBtjXw1e8w0lxnxETp7Qs/CbcdnypFs2aAYdKjkTRbH56R0VEREREqTgpbuP2A/CPpahaD4w4j8hdM/UOyykxcUrD7vz1Abws4Wp5EV5E95ZN9A6JiIiIiFJZmTyB+LvgCPu6ZZNMihuqa0zOiIlTWnXrDPz++59aDNc8cb/6aGTx89Q7KiIiIiLSwUtt22Glpbpa9jXdwb31U/QOyekwcUqjbiwZCzeY1fJct7bo2uAFvUMiIiIiIp3kDPRGcKXRiNFc1br3vqnAvct6h+VUmDilQabzO5Dl0hq1HKIFIluzN+Dlbv2QEBEREVH61LVJHfzpYp0U10OLwa1lnBT3aTBxSms0DXeWxE52O9+vJ5pXLKJrSERERESkPz8vd3jUH4O7mq9az3hmMbQr/+odltNg4pTGRB5ajCx3D6rlU5ZcqNr+dbhwslsiIiIiAtC+Zmn88WBSXBdouLX4TU6Km0RMnNISUwyiVsU2ua7LNRiVC2bVNSQiIiIichxuri4o3noELlis54iZb+yG8fhqvcNyCkyc0pC726YhY7R1kN8uS0m06NBH75CIiIiIyMHUK5kbSzP3t6/fX/E2YDbpGpMzYOKUVkTehdv2T+2rR0qPRr7MGXQNiYiIiIgcc1LcBh1exb+Wwmo9Y/hZhO+ZpXdYDo+JUxoR8tfHyGC2TmS2ErXRsWUrvUMiIiIiIgdVKpdMijvcvm7ZOBmICdc1JkfHxCkN0O5eROChn9RytOaOiFpjEeDjrndYREREROTAOrbrhHVaFbXsZ7yJOxu+1Dskh8bEKQ24suhdeMColhd7tETb+tZZoYmIiIiIHiV7gBcuVxwDk2ZNCbz3fAfcD9E7LIfFxMnJGS8fQI6Ly9TyHS0DsrV4B+6u3K1ERERE9GSdmr6IxS6N1LKXFomQ5e/pHZLD4hm2M9M0hCwcrWrwi2UB3VGvnHWQHxERERHRk2TwdIPbi2/hvual1jOd+AOWkBN6h+WQmDg5sbD//kKuO3vU8gUtKyp3HK2qpBARERERJVWrGuWx0Ku9WnaFBdcXj9U7JIfExMlZWcyIWPmOfXVL7sEolTeLriERERERkXNOilug9Zu4rgWq9RxXNyD6zHa9w3I4TJyc1I1tM5Et6qxaPqAVRuNOA/UOiYiIiIicVO2S+bA8qK99/e6SN9WwEIrFxMkZxYTDfetH9tXjZd9E9kBvXUMiIiIiIuclwz1qdhyGE5bcaj1b2H+4v3++3mE5FCZOTujSqikINN9Sy5sML6BVS2ufVCIiIiKiZ1UiV0b8XeB1+3rMmgmAKVrXmBwJEycnYwm9hswHflTLUnM/qs44+Hq66R0WEREREaUBLdr3wk6ttFoOirmCm5ut553ExMnpnF84Dt6IUst/eTZF47q19Q6JiIiIiNKIbP9v726AoyjzPI7/Ju+8JQRiEggBBJb3QHgRFpQXT14UDmHPBeW20LModV280nNBcUEBeS1FxUILBRfhtDyB6KqLLPKiuGhQNIAGDLCGdxPCiwKBQBKSvuqHSgy7gSHIpLsz309Vm6fbnqr/8M9k5jfd/XRMLe3t8lj5elT6XOnsCUdrcguCk4ecy/lOTfenmXG+VUvxw6YoNITpxwEAAHDtjBgyVH/z9TXjuqX5ylk50+mSXIHg5CE5aY8pTKVmvDb2LvVMaet0SQAAAKhhakeEqaT/ZBVaFy4Hidvxukp/OqBgR3DyiJ92fKwWP24041yrgTqP/JPTJQEAAKCGuq1PD/01apgZR6hYh975+f6hwYrg5AWlpTq98uc7OG9q+nu1TIp3tCQAAADUXPblIEnDJuuEVcesNzn0VxUe3KpgRnDygEOfvankszvNeLfVVP1G/rfTJQEAAKCG69WxlVbFjjHjEFk68s5jQX1TXIKTy1nF5xTx6Yzy9d2dH1PD6NqO1gQAAIDg0H3kBB2wrjPj5BObdXL7agUrgpPLZX/4guJL8sx4c0hnDRj2n06XBAAAgCDROilOnzf7Q/n62Q//JJWWKBgRnFzs/OnjStg234xLLZ/O9p+qqPBQp8sCAABAELnltw8q02ppxonn9ihv4+sKRgQnF9udNlX1dMaMN9S6RX373Ox0SQAAAAgy8dG1tLvTzzfFjfj7LKmoQMGG4ORS+Ye/V6t9b5nxOStccbdPl8/HzW4BAABQ/YYMG6mNvu5mHFtyXPs/fFbBhuDkUgdXTFSEzpvxpw1HqlP79k6XBAAAgCBVKyJUBf2e0nnrQny47psFKs0/omBCcHKhvKx0tT++1oyPW9HqMHKq0yUBAAAgyA3s21drIgeZcW2d1d53nlIwITi5jWXp1AcTy1e/bn6/mjRKcLQkAAAAICTEp+uGTdUZK9KsN9u3XOdydylYEJxcJvvzFfrV2W/MeJ8aq9eoPzpdEgAAAGDckNJOa2PvNOMwleiHdx5XsCA4uYhVUqzIT54uX9+XOl7RdbjZLQAAANwjZeQkHbHqm3HLY5/op51/VzAgOLlI5l/nq0nJwQvj0Ha66d//y+mSAAAAgIu0TEpUevJ95eunPnjCXG5S0xGcXKLw9Ek12Tbv5/WbpyksjJvdAgAAwH1uGvU/yraSzLhZwXblbFqmmo7g5BI7/zJTDXTSjL+o1UfdbrwwYwkAAADgNnHRdZSVMr58PeTjadL5ItVkBCcXKCn4UR32v2nGRVaoGg6fxc1uAQAA4GoDbr9bW3wdzDjxfI6yV89XTUZwcoGGe/6iWr4LCf3LuN/oV207OV0SAAAAcFlREWE62efnezk1zJinkoITqqlcEZxefvllNW/eXFFRUerZs6c2b9582f1XrFihtm3bmv1TUlK0atUqedWhXRnqU3RhJpJTVm21GTXd6ZIAAACAK9Kv/2B9GtHPjOtbp7T73Zr7Wdbx4LRs2TI9+uijmjJlirZs2aLOnTtr8ODBOnLkSKX7p6ena/To0Ro7dqy2bt2qESNGmGX79u3yotMrJyvEd2EWkm+vH6v4hMZOlwQAAABc8U1x6w15WoVWmFm//vv/1dlj+1UTOR6cnn/+ed13332699571b59e73yyiuqXbu2Fi9eXOn+L774om699VZNmDBB7dq10/Tp09W1a1e99NJL8podG99XyrmvzDhXceo6aqLTJQEAAABV0jU1VZ/GjDDjKBVp7/JJqokuREOHFBUVKSMjQ0888UT5tpCQEA0YMECbNm2q9DH2dvsIVUX2Ear33nuv0v0LCwvNUubUqVPmZ3FxsVmcUlJSoqgNU8vX96Y8rBvCIx2tCVeurE/0y3vonXfRO2+ib95F77zLid5dP+JJnVz6N8X4zqht3krl7fpSDVp0ldtV5d/I0eB07NgxEyASEhIu2m6v79y5s9LHHD58uNL97e2VmT17tqZNm/Yv29esWWOObDnl3E+HNOR8ruSTdqm58kKSPX2tVrBau3at0yXgKtE776J33kTfvIveeVd19+7rWrdr9Ln/M5ehHF7+R33RaYLcrqCgwBvBqTrYR7MqHqGyjzglJydr0KBBio6OdrS2H48OU+Y7U3Qwoo2GDR6s8PBwR+tB1b6dsP8YDRw4kL55DL3zLnrnTfTNu+iddznVu+M33qQf5q9Tku+oOpdkKibeUlL3oXKzsrPRXB+c4uLiFBoaqry8vIu22+uJiYmVPsbeXpX9IyMjzfLP7F8ip/8IJDRuqga/X6ijq1a5oh5UHX3zLnrnXfTOm+ibd9E776ru3iXGNdS69o8oKevCNU6+j6cpvOcwKSRUblWVfx9HJ4eIiIhQt27dtH79+vJtpaWlZr1Xr16VPsbeXnF/m52oL7U/AAAAgOpx028e0E5fSzNuVrxHO9e8pprC8Vn17NPoFi1apKVLlyorK0sPPvigzpw5Y2bZs919990XTR7x8MMPa/Xq1XruuefMdVBTp07V119/rYceesjBZwEAAAAgKiJcx3tPLl9v+OUzKim88uuI3Mzx4HTnnXdq7ty5euqpp5Samqpt27aZYFQ2AcSBAweUm5tbvn/v3r311ltvaeHCheaeT2lpaWZGvY4dOzr4LAAAAADYet3yG30VfoMZX2cd0/Z356gmcMXkEPbRoksdMdqwYcO/bBs5cqRZAAAAALjvprhRt81Qyfu3KtRnqeWuRTrz0x9UJ7byOQm8wvEjTgAAAABqlpSuv1Z69G1mXFcF2r38KXkdwQkAAADANdfstzNVYF2Y3bpjTpqO7s+SlxGcAAAAAFxzTZu10OZGvzPjcF+Jct6ZKC8jOAEAAAAIiM53PqnjirkwPrVBe7Z+LK8iOAEAAAAIiNjYBvquzbjy9eK/TZZVWiovIjgBAAAACJgedzyi/b4kM25TtEPbP35LXkRwAgAAABAwkRGRyuvxRPl6bPpMnS8qlNcQnAAAAAAE1A2Df6cd4R3MuElpjra8N09eQ3ACAAAAEFC+kBCFDJ5Rvt7qu5eUf/JHeQnBCQAAAEDAtev+b8qo29+MG+iUti9/Wl5CcAIAAABQLRL/Y7aKrFCdtSLkC68tLwlzugAAAAAAwSGpRXt93eNZNU29Rb9Oai4vITgBAAAAqDbdh46VF3GqHgAAAAD4QXACAAAAAD8ITgAAAADgB8EJAAAAAPwgOAEAAACAHwQnAAAAAPCD4AQAAAAAfhCcAAAAAMAPghMAAAAA+EFwAgAAAAA/CE4AAAAA4AfBCQAAAAD8IDgBAAAAgB8EJwAAAADwg+AEAAAAAH4QnAAAAADAD4ITAAAAAPgRpiBjWZb5eerUKblBcXGxCgoKTD3h4eFOl4MrRN+8i955F73zJvrmXfTOu+jdlSvLBGUZ4XKCLjjl5+ebn8nJyU6XAgAAAMAlGSEmJuay+/isK4lXNUhpaalycnJUr149+Xw+V6RcO8QdPHhQ0dHRTpeDK0TfvIveeRe98yb65l30zrvo3ZWzo5Admho3bqyQkMtfxRR0R5zsf5AmTZrIbexfan6xvYe+eRe98y565030zbvonXfRuyvj70hTGSaHAAAAAAA/CE4AAAAA4AfByWGRkZGaMmWK+QnvoG/eRe+8i955E33zLnrnXfQuMIJucggAAAAAqCqOOAEAAACAHwQnAAAAAPCD4AQAAAAAfhCcAAAAAMAPglOAvfzyy2revLmioqLUs2dPbd68+bL7r1ixQm3btjX7p6SkaNWqVdVWK66+dzt27NAdd9xh9vf5fJo3b1611oqr792iRYvUp08fxcbGmmXAgAF+X6dwvm/vvvuuunfvrvr166tOnTpKTU3VG2+8Ua314urf68q8/fbb5m/miBEjAl4jfnnvlixZYvpVcbEfB/e/5k6cOKFx48apUaNGZqa91q1b8xnzKhCcAmjZsmV69NFHzXSQW7ZsUefOnTV48GAdOXKk0v3T09M1evRojR07Vlu3bjVvJPayffv2aq892FW1dwUFBWrRooXmzJmjxMTEaq8XV9+7DRs2mNfdJ598ok2bNik5OVmDBg3SDz/8UO21B7Oq9q1BgwaaNGmS6dm3336re++91ywfffRRtdce7KrauzL79u3T+PHjzRcX8E7voqOjlZubW77s37+/WmtG1ftWVFSkgQMHmtdcWlqadu3aZb40TEpKqvbaPc+ejhyB0aNHD2vcuHHl6yUlJVbjxo2t2bNnV7r/qFGjrKFDh160rWfPntYDDzwQ8Frxy3pXUbNmzawXXnghwBUiEL2znT9/3qpXr561dOnSAFaJa903W5cuXazJkycHqEJcy97Zr7PevXtbr732mnXPPfdYw4cPr6Zq8Ut69/rrr1sxMTHVWCGuRd8WLFhgtWjRwioqKqrGKmsmjjgFiJ3uMzIyzGk/ZUJCQsy6/Q1pZeztFfe32d8gXGp/uKd3qDm9s48eFhcXmyMa8Ebf7NsRrl+/3nyL2rdv3wBXi2vRu6efflrx8fHmDAt4q3enT59Ws2bNzNH54cOHm1PV4e6+ffDBB+rVq5c5VS8hIUEdO3bUrFmzVFJSUo2V1wwEpwA5duyY+YW0f0ErstcPHz5c6WPs7VXZH+7pHWpO7x5//HE1btz4X77EgPv6dvLkSdWtW1cREREaOnSo5s+fb05Hgbt799lnn+nPf/6zOVUI3updmzZttHjxYr3//vt68803VVpaqt69e+vQoUPVVDWupm979uwxp+jZj7Ova3ryySf13HPPacaMGdVUdc0R5nQBAOAW9jVq9sXq9nVPXPDsfvXq1dO2bdvMN+D2ESf7nH/7WsP+/fs7XRouIT8/X2PGjDGhKS4uzulyUEX2UQt7KWOHpnbt2unVV1/V9OnTHa0Nl2YHXPsI78KFCxUaGqpu3bqZ63ifffZZc50UrhzBKUDsNwT7lzMvL++i7fb6pSYPsLdXZX+4p3fwfu/mzp1rgtO6devUqVOnAFeKa9E3+/SUVq1ambE9q15WVpZmz55NcHJx77Kzs80F6sOGDbvoQ50tLCzMnG7ZsmXLaqgc1+K9Ljw8XF26dNH3338foCpxLfpmz6Rn98p+XBk78NpHqOxT/+yj9rgynKoXIPYvoZ3o7W9BK7452OsVv62pyN5ecX/b2rVrL7k/3NM7eLt3zzzzjPm2dPXq1WaKa3jzNWc/prCwMEBV4lr0zr7dRmZmpjlSWLbcfvvtuvnmm83Yvm4G3nnd2ad+2f20P5jDvX278cYbTbgt+5LCtnv3btM3QlMVOT07RU329ttvW5GRkdaSJUus7777zrr//vut+vXrW4cPHzb/f8yYMdbEiRPL9//888+tsLAwa+7cuVZWVpY1ZcoUKzw83MrMzHTwWQSnqvausLDQ2rp1q1kaNWpkjR8/3oz/8Y9/OPgsglNVezdnzhwrIiLCSktLs3Jzc8uX/Px8B59F8Klq32bNmmWtWbPGys7ONvvbfzftv5+LFi1y8FkEp6r27p8xq553ejdt2jTro48+Mq+7jIwM66677rKioqKsHTt2OPgsgk9V+3bgwAEzW+xDDz1k7dq1y1q5cqUVHx9vzZgxw8Fn4U0EpwCbP3++1bRpU/PBzJ4+8osvvij/f/369TNvGBUtX77cat26tdm/Q4cO1ocffuhA1ahq7/bu3WvZ30P882LvB3f3zp4+vrLe2V9cwL19mzRpktWqVSvzoS02Ntbq1auX+TABb7zXVURw8k7vHnnkkfJ9ExISrCFDhlhbtmxxqPLgVtXXXHp6urnFjR247KnJZ86caW4LgKrx2f9x+qgXAAAAALgZ1zgBAAAAgB8EJwAAAADwg+AEAAAAAH4QnAAAAADAD4ITAAAAAPhBcAIAAAAAPwhOAAAAAOAHwQkAAAAA/CA4AQAAAIAfBCcAAAAA8IPgBAAAAAB+EJwAAEHj6NGjSkxM1KxZs8q3paenKyIiQuvXr3e0NgCAu/ksy7KcLgIAgOqyatUqjRgxwgSmNm3aKDU1VcOHD9fzzz/vdGkAABcjOAEAgs64ceO0bt06de/eXZmZmfrqq68UGRnpdFkAABcjOAEAgs7Zs2fVsWNHHTx4UBkZGUpJSXG6JACAy3GNEwAg6GRnZysnJ0elpaXat2+f0+UAADyAI04AgKBSVFSkHj16mGub7Guc5s2bZ07Xi4+Pd7o0AICLEZwAAEFlwoQJSktL0zfffKO6deuqX79+iomJ0cqVK50uDQDgYpyqBwAIGhs2bDBHmN544w1FR0crJCTEjDdu3KgFCxY4XR4AwMU44gQAAAAAfnDECQAAAAD8IDgBAAAAgB8EJwAAAADwg+AEAAAAAH4QnAAAAADAD4ITAAAAAPhBcAIAAAAAPwhOAAAAAOAHwQkAAAAA/CA4AQAAAIAfBCcAAAAA0OX9P4YE2R4aDLqjAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = xp.problem()\n",
    "\n",
    "x = p.addVariable()\n",
    "\n",
    "N = 10                                          # number of breakpoints\n",
    "freq = 5                                        # frequency\n",
    "breakpoints, values = create_segments(N, freq)  # breakpoints and values at breakpoints\n",
    "\n",
    "# Piecewise linear approximation using the p.addpwlcons() method\n",
    "pw = p.addVariable()  # auxiliary variable to represent the 'resultant' array and set as objective to maximize\n",
    "\n",
    "p.addPwlCons([x], [pw], [0], breakpoints, values) \n",
    "\n",
    "p.setObjective(pw, xp.maximize)\n",
    "\n",
    "p.controls.outputlog = 0 # Turn off output log for cleaner output\n",
    "\n",
    "p.optimize()\n",
    "\n",
    "print(\"Solution: x = \", p.getSolution(x))\n",
    "print(\"Value of piecewise linear function:\", xp.evaluate(pw, problem=p))\n",
    "print(\"Objective function:\", p.attributes.objval)\n",
    "\n",
    "# High-resolution plot of the function for comparison\n",
    "breakpoints_high, slopes_high = create_segments(10000, freq)\n",
    "\n",
    "# Plot the results\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(breakpoints, values, label='Approximation', linewidth=2)\n",
    "plt.plot(breakpoints_high, slopes_high, label='Real function', linewidth=2)\n",
    "plt.scatter(p.getSolution(x), p.getSolution(pw), color='green', zorder=5, label='Solution')  # Add the point to the plot\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title(f'Plot of sin({freq}x) and its approximation using {N} breakpoints')\n",
    "plt.legend(fontsize=12)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Approximation using *xpress.pwl()*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, you can use the [xpress.pwl()](https://www.fico.com/fico-xpress-optimization/docs/latest/solver/optimizer/python/HTML/xpress.pwl.html) method, which returns a piecewise linear function over variable $x$, by taking a Python dictionary as an argument containing as:\n",
    "  - keys: the intervals specified as two-elements tuples (must be pairwise disjoint, i.e., they must not overlap)\n",
    "  - values: linear expressions in a variable. \n",
    "\n",
    "A piecewise linear function must use only one variable in all of the dictionary's values. Besides, all values in the dictionary must be either constants or linear functions.\n",
    "\n",
    "In this case, besides the breakpoints and corresponding values, we calculate the values for the derivative of the initial function to **compute the slopes** to be used in the formulation of the function values for each interval.\n",
    "\n",
    "*Note: the method p.addpwlcons() is better suited for cases where only the coordinates are known, while the xp.pwl() method is more intuitive when the slopes are known*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original problem size\n",
      "   linear:    1 rows, 2 columns, 1 linear coefficients\n",
      "   nonlinear: 1 coefficients, 39 tokens\n",
      "              0 minmax          1 pwl         0 ufun\n",
      "Nonlinear presolve\n",
      "   converted 1 PWL to optimizer MIP constructs\n",
      "   linearizations will be solved as a MIP\n",
      "   converted 1 formulas to linear constraints\n",
      "   converted objective transfer row to linear objective\n",
      "   linear presolve removed 2 rows, 1 columns, 20 linear coefficients\n",
      "Presolved problem size\n",
      "   linear:    21 rows, 38 columns, 105 linear coefficients\n",
      "Problem is nonlinear presolved\n",
      "Maximizing problem using Xpress-Optimizer\n",
      "Problem is nonlinear postsolved\n",
      "Final MINLP objective (global optimum): 1.045444336715753e+00\n",
      "  Max validation error      (abs/rel) :      .000 /      .000\n",
      "  Observed primal integral            :  100.000%\n",
      "  Total time                          :     .017s\n",
      "*** Search completed ***\n",
      "Solution: x =  0.2829421210522584\n",
      "Value of piecewise linear function: 0.987843334679394\n",
      "Objective function: 1.0454443367157533\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = xp.problem()  # create a problem and add variable x\n",
    "\n",
    "x = p.addVariable(ub=4)\n",
    "\n",
    "N = 10       # number of breakpoints\n",
    "freq = 5     # frequency\n",
    "breakpoints, values = create_segments(N, freq)  # breakpoints and values of the function\n",
    "slopes = freq * np.cos(freq * breakpoints)      # derivatives\n",
    "\n",
    "# Piecewise linear, discontinuous function over N points: over the\n",
    "# i-th interval, the function is equal to v[i] + s[i] * (y - b[i])\n",
    "# where v, s, b are value, slope, and breakpoint.\n",
    "pw = xp.pwl({(breakpoints[i], breakpoints[i+1]):\n",
    "            values[i] + slopes[i] * (x - breakpoints[i]) for i in range(N - 1)})\n",
    "\n",
    "#p.addConstraint(1 >= pw)\n",
    "p.setObjective(pw, xp.maximize)\n",
    "\n",
    "p.controls.outputlog = 0 # Turn off output log for cleaner output\n",
    "\n",
    "p.optimize()\n",
    "\n",
    "print(\"Solution: x = \", p.getSolution(x))\n",
    "print(\"Value of piecewise linear function:\", xp.evaluate(pw, problem=p))\n",
    "print(\"Objective function:\", p.attributes.objval)\n",
    "\n",
    "# High-resolution plot of the function for comparison\n",
    "breakpoints1, slopes1 = create_segments(10000, freq)\n",
    "\n",
    "# Plot the results\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.plot(breakpoints, values, label='Approximation', linewidth=2)\n",
    "plt.plot(breakpoints1, slopes1, label='Real function', linewidth=2)\n",
    "plt.scatter(p.getSolution(x), p.getSolution(pw), color='green', zorder=5, label='Solution')  # Add the point to the plot\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.title(f'Plot of sin({freq}x) and its approximation using {N} breakpoints')\n",
    "plt.legend(fontsize=12)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "xpress9.8 (3.12.9)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
