{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7cafb758-b4f9-4afc-89a6-5901c14df143",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "# Inverse design optimization of a plasmonic nanoantenna metasurface\n",
    "\n",
    "In this notebook we perform inverse design of an antenna using a medium ranging between air and an experimentally measured gold from `tidy3d`'s material library.\n",
    "\n",
    "We use topology optimization to design the patterning on this sheet of gold to maximizes the intensity enhancement in a central location, while respecting fabrication penalties.\n",
    "\n",
    "<img src=\"img/adjoint_15.png\" width=400 alt=\"Schematic of the nanoantenna \">\n",
    "\n",
    "## Set up\n",
    "\n",
    "We start by importing the packages we need, including `autograd` and the `autograd` wrapper for `numpy`."
   ]
  },
  {
   "cell_type": "code",
   "id": "f63743b9-08dc-4a0c-af96-35ee416c66ef",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": [],
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:21.718674Z",
     "start_time": "2026-03-17T09:13:21.716684Z"
    }
   },
   "source": [
    "import autograd\n",
    "import autograd.numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "import tidy3d as td\n",
    "import tidy3d.web as web"
   ],
   "outputs": [],
   "execution_count": 55
  },
  {
   "cell_type": "markdown",
   "id": "d3540365-4e90-412b-8e45-28e3aecc2218",
   "metadata": {},
   "source": [
    "We'll set a few helper constants for the notebook."
   ]
  },
  {
   "cell_type": "code",
   "id": "3d005f0b-8f5e-4a4c-b1c9-3249bbc8d46d",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:21.763071Z",
     "start_time": "2026-03-17T09:13:21.761618Z"
    }
   },
   "source": [
    "# whether to run checks for setting up sim and normalization enhancement\n",
    "run_pre_sims = True\n",
    "\n",
    "um = 1e0\n",
    "nm = 1e-3"
   ],
   "outputs": [],
   "execution_count": 56
  },
  {
   "cell_type": "markdown",
   "id": "2f22ad10-d193-4419-b152-a58288a72cac",
   "metadata": {},
   "source": [
    "Then we define the parameters setting our source spectrum and FDTD spatial resolution."
   ]
  },
  {
   "cell_type": "code",
   "id": "1821d95b-eb37-416f-8f96-a73f4333dd71",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:21.808059Z",
     "start_time": "2026-03-17T09:13:21.806548Z"
    }
   },
   "source": [
    "wavelength = 0.910\n",
    "\n",
    "freq = td.C_0 / wavelength\n",
    "fwidth = freq / 10\n",
    "run_time = 20 / fwidth\n",
    "\n",
    "dl = 3 * nm\n",
    "\n",
    "# min_steps_per_wvl = 30"
   ],
   "outputs": [],
   "execution_count": 57
  },
  {
   "cell_type": "markdown",
   "id": "39c4a820-b6d5-4d00-b55a-34c48eecc1e1",
   "metadata": {},
   "source": [
    "Next we define our material parameters.\n",
    "\n",
    "We import the gold model from our material library, which is a `td.PoleResidue` medium from a fit to measured data."
   ]
  },
  {
   "cell_type": "code",
   "id": "6fd504c5-0ee9-45d5-9ced-0c5a8215fee1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:21.853178Z",
     "start_time": "2026-03-17T09:13:21.851507Z"
    }
   },
   "source": [
    "# select one of the material library variants\n",
    "print(tuple(td.material_library[\"Au\"].variants.keys()))"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Olmon2012crystal', 'Olmon2012stripped', 'Olmon2012evaporated', 'Olmon2012Drude', 'JohnsonChristy1972', 'RakicLorentzDrude1998')\n"
     ]
    }
   ],
   "execution_count": 58
  },
  {
   "cell_type": "code",
   "id": "0619b6e9-781c-495f-a13f-4f2ef26017d8",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:21.899447Z",
     "start_time": "2026-03-17T09:13:21.897559Z"
    }
   },
   "source": [
    "medium_SiO2 = td.Medium(permittivity=1.44**2)\n",
    "medium_gold = td.material_library[\"Au\"][\"JohnsonChristy1972\"]\n",
    "eps_background = 1.0"
   ],
   "outputs": [],
   "execution_count": 59
  },
  {
   "cell_type": "code",
   "id": "efc23f1f-0486-4d76-8469-46d0f2edee2f",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.004862Z",
     "start_time": "2026-03-17T09:13:21.943476Z"
    }
   },
   "source": [
    "wvls = np.linspace(0.5, 1.0, 101)\n",
    "freqs = td.C_0 / wvls\n",
    "eps_complex = medium_gold.eps_model(freqs)\n",
    "eps_real, sigma = medium_gold.eps_complex_to_eps_sigma(eps_complex, freq=freq)\n",
    "plt.plot(wvls, eps_real, label=\"permittivity (real)\")\n",
    "plt.plot(wvls, np.imag(eps_complex), label=\"permittivity (imag)\")\n",
    "plt.plot(wvls, sigma, label=\"conductivity\")\n",
    "plt.plot(wvls, np.ones_like(eps_real), label=\"1\", linestyle=\"--\")\n",
    "plt.plot(wvls, np.zeros_like(eps_real), label=\"0\", linestyle=\"--\")\n",
    "plt.xlabel(\"wavelength (um)\")\n",
    "plt.ylabel(\"relative permittivity\")\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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HM3r06Bfi4+PjiY9/9q4QERGBh4dHjo/xWea3kQGH30t3e1XHYAZWfnalyOcn3iVBm3ZdWtHhPiNqHAJ0L5whx9oSlZj2PWk8Cz3mq7qHdHOsoGLY0ZY8iLNNM7aEXSQzGx7k6Y4ZfbQpd6MLpRlbzDqG+U0P6JfHH2/EvxGOacYWskhgScu9qJ5O/jL5RH0uPU776icrdRIBrZ9d6jnrr9oE3ndOMxZgQ9vd+jefOaerczzENd3Y1W32Ym2ue3daeLYKB++4pxu7ovVBClslggqWnfdi13/pT664uNURXGzjAAi4WJ5tN0qnGzvvzROUcogGYP3lMvx0Jf1bgcxudooKTrqbNW6+VopVF8unGzulcSBVnZ8AsONmCZaeq5hu7LiG56nr+hCAvbdcWXCmcrqxI+r/TeMS9wE4cteZr0+mf0n94NqXaFlad2nzXyFFmXqserqxA2pcpW1Z3SX1F+47Mv5wrXRje1a5TqcKuvu+XXtciJEH66Yb29XrJt0q664mC4qw4/N96V/W37H8LXpWuQFAWIw1n+xplG5sG887DKhxBYDweAt672yabmxzj3sMrnUJgLgkM3y2v5lu7OtuoQyvd0G//P62VunG1nZ5wJcNzgK6D5WPdrQgXpP2QNHXijziq0an9ct9dzcjMiHt2z+UKxzOjDdOPN0vDNrfhPuxNmnGlrSP4psmR/TLww815k6UfZqxxaxjWdD8oH557NGG/BtROM3YQhYJLGmxV19ETT1Zn0uPi6YZa2WWxMpWu/WxX5+py7kH6f9Ru/qt3/Xff3euNqfC3NKNXdZ8B1Zq3af80n9qcDg4/d/7BW/swsEyAQWFVVeqse9u+r/LX7++m2I2saDAhhuvsfN2hXRjJ9fdSwk73e/91v8qse1WpXRjx9baT5lCTwDYebs8v9yslm7s8Kp/UtFR97u8/15Z1v2b/u/coMqHqeak+10+ElaaVdfrpRvbr+Ix6hS9A8DphyVZfjX9y9V9y52koYvuZtf9e7+HWp2znU4meXf2hIQETp8+zZgxY/TrzMzMaNWqFceOHUvzOTNmzGDSpEkGz02V5oxv2aOgkJSkSbki/VitQmyKKzq0GdS5Wq2WqOjYVMvpxioKEZHR+mVNBn9GKYpCePizOUSSNOk3BSgKPH4SoV9OzOgKAeDR42eTBSZkdFUO8PBRuP5NLT6jK22Ah4+ekGChi4mNzeDPZeDhwycQHQNATEzcS/drFaf7+aKji78030IJjwGIjEz7QyDZo8fhhGh1t+0IT+fDJWVsME9jw+0yjH38JJJg9YOn32d8iXZ4eCTBIQ+eHiPjt5bwiKhnseEZ/25EREYTEqqLfRiV8azIUdExhITqiroHMRm/HqKj4wgN08U+TOePgWQxsXGEPp3bJjIx4/tHxcUlEHZfF5teYZIsIT6B+/cfZxijj01I5P6DZ7EZ/c2amJSke10mx2bQfJKUpOHho2e/R5oMfu81Gk2q309NBlcRaRUtT8IjMxWrKArhESnfIzKIhdTvPUkveU1ExaSIzfj9JDomlqSn7xFJL9lvbFwc5pqETMXGxycSp0qOzfh2I4mJSfr3sozOWfJxk98jM3oPBt3/a3JMRp8Dydv1MQWrbQQoYC0+9+7do0SJEhw9epSGDZ9VnSNHjuTgwYOcOPHiZFS51eIDz5qbFUXRTWarmwIWRQEzlYKVuaJ/M4uKSxnz9DlPY1UouqZpRUF5GqsL0hVFT/8BCmaqp83jT/cTnZCiTnr6fFIs26Zs8k7V3Pzcy0QhRaxCbOKz34+0XlG2lop+W8rY1IdXnsY+WxeXmLrJ+/mXq41F+rHPs7F4tjE+SUGjffaB+/zTbCwUfakan8TT2Bd3rihgbaE7z6BrEk7SpP4gT3mWrS0U/cC6tGJTsjJXnjVjv+Qq0ZSxiRpIzGC/FuYK5pmMtUwRm6SFhKQM9qtWsFBnPVbzklhztYJlitj4TMZqFYhLVKXbnJ5WbHrUZkqq7qvYRFW6f8yozRSszFPHppQyHTMzBWvzZyuSu7if37UK3XtEyq6umITUfy2n2u8Lsen/bGZmqX+PYhNefKUnn0MVqbvFshSbZh36LC/bdGNfzP2F7qtUSSQPE3gaa5l+7POvDTuLFN1XSU+7r56LSV6yTRmrUZGkTXtCc0juvtJtTUzukkojWIVKF/v0dZlW95X+dff0vd08ra6uNHLWd3WpVLrf++ffT1I8xcpchblatypR86yrK63XfHJXl0qV3NWVIua5l7OlOViodUtWVhY53tVlki0+2WFlZYWVVdrdRDnt2S+r6rmvL8pKSoWzUJ9l3G4ghBBCZF/agyPylgJ1VVexYsVQq9WEhqa+4WRoaCiurumP/RBCCCGEaShQhY+lpSV16tRh795ng2O1Wi179+5N1fUlhBBCCNNU4Lq6hg4dSs+ePalbty7169dn3rx5REdH07t3b2OnJoQQQggjK3CFT9euXbl//z4TJkwgJCSEmjVrsnPnTooXz/gKGiGEEEIUfAXqqq6cIPfqEkIIIfIfuVeXEEIIIcRzpPARQgghhMmQwkcIIYQQJkMKHyGEEEKYDCl8hBBCCGEypPARQgghhMmQwkcIIYQQJkMKHyGEEEKYDCl8hBBCCGEyCtwtK/KqT5aPx8HWnndqt+T1CjUxV8upF0IIIXKbfPrmgvsRj9h2ei9aRcuqPzdTtJATbWs2o0PtFjT2qoPaTG3sFIUQQgiTIPfqeo4h7tWVqEni8OW/+PXMXnacPcjj6Aj9thJOxen+xjt0b9QBNyeXHDmeEEIIYWoy+/kthc9zDH2T0kRNEkevnObXM/v4PXC/vghSm6l5q1pjejV7j2aV66NSqXL82EIIIURBJYVPNuXm3dnjEuP5/cx+Vh/awvHrZ/Xrq3pUZJB3DzrUbiHdYEIIIUQmSOGTTblZ+KR05d5NVh/azNqjvxITHwtAGeeSDGz9EV1eb4uVhWWu5SKEEELkN1L4ZJOxCp9kj6LCWXngZ1bs/0nfDVayiCsj3xnAe/W9pQVICCGESIMUPtlk7MInWXRcDGuObOP73T8SGv4AAC/3sox55xO8azSRMUBCCCFEClL4ZFNeKXySxSTEsXL/zyzctZonMboWoLplqzHp/c+pU7aqkbMTQggh8gYpfLIprxU+ycJjIlm0+0eW7ttAbEIcAO/Wa83Yd/9HySKuRs5OCCGEMC4pfLIprxY+yULDHzBr2xLWHf0NRVGwtrDi45bd+KxNT+ysbY2dnhBCCGEUUvhkU14vfJJdCLrCxF/mc/TqGQBcCzszvvNAOtf3lvE/QgghTI4UPtmUXwofAEVR2HnuT7765TtuPbgLQL2y1ZjWbRjVS1UycnZCCCFE7pHCJ5vyU+GTLC4xnqV71zN3ux+xCXGoVCp8Gr/D6I6fUKyQk7HTE0IIIQxOCp9syo+FT7J7j8OYumkhm07tBqCwbSFGdOhPr6ad5W7wQgghCjQpfLIpPxc+yU5cP8vYDXP4+/ZVACq5l2Nq16G84VXHyJkJIYQQhiGFTzYVhMIHQKPVsObwNmZu/YFH0eEAtK/dggmdB1GqmLuRsxNCCCFylhQ+2VRQCp9kj6PD+frXZfgf3IRW0WJlbsn/WvswyNsXOysbY6cnhBBC5AgpfLKpoBU+yS7dvc64n+Zy5MppANwcnRn37kDerdcaMzMzI2cnhBBCvBopfLKpoBY+oLv8fcfZg3y18TuCHtwDoHaZKkzuMoS6ZasZOTshhBAi+6TwyaaCXPgki0uMZ8kf6/hu5yqi42MA6Fi3FePeHYhHUTcjZyeEEEJknRQ+2WQKhU+ysPCHzNz2g/72F1bmlgxo2Y3BbXxxsLE3dnpCCCFEpknhk02mVPgk+/v2VSb+Ml8//qeIvSPD2vXFt+m7WMj8P0IIIfIBKXyyyRQLH9CN/9l9/hBTN3/PtZBbAJR18WDsu/+jbc3mcv8vIYQQeZoUPtlkqoVPsiRNEmuObOPrX5fxIPIxAHXLVmN854E0KF/TuMkJIYQQ6ZDCJ5tMvfBJFhUXzfe7f+SHP9YRmxAHQOvqbzC200C83MsYOTshhBAiNSl8skkKn9RCwx/w7W8rWHNkGxqtBjOVGR80bMvw9v0oWcTV2OkJIYQQgBQ+2SaFT9quh9xixtbF/B54AABLcwt6N3uPz97uRVF7R6PmJoQQQkjhk01S+GTs9L9/M23LIo5ePQOAvbUtn7TqzietPsTe2s7I2QkhhDBVUvhkkxQ+L6coCgcvnWT6lkWcD7oC6C6B/7xNT3o264y1hZWRMxRCCGFqpPDJJil8Mk+r1fLrmX3M/nUpN0KDAHB3cmFo2z50bdRe5gASQgiRa6TwySYpfLIuSZPET8d38O1vy7n7OBSAMs4lGdGhP53qviU3QRVCCGFwUvhkkxQ+2ReXGM/qP7cwb6c/D5/OAVS5RDlGdfgY7xpNZBJEIYQQBiOFTzZJ4fPqouNiWLZvA4v2rCEiNgqAWp6vMfqdj2laub4UQEIIIXKcFD7ZJIVPznkSHcHiPWtYum+DfhLEhhVqMabjJ9QvX8PI2QkhhChIpPDJJil8ct79iId8t3MVAX9uIiEpEYAWVRoyuuPHVC9VycjZCSGEKAik8MkmKXwM5+6jUOZuX8m6o7+h0WoAaFfrTUZ2GCC3wRBCCPFKpPDJJil8DO9m2G2++W05m07tRlEUzFRmvNegDcPb9aW0cwljpyeEECIfksInm6TwyT2X7t7g61+Xsv3sQQDMzdR0f+Mdvni7N25OLkbOTgghRH4ihU82SeGT+87eusTMrT9w4J8TAFhbWNGr2XsMbuMr9wETQgiRKVL4ZJMUPsZz7FogM7f+wInr5wCws7Ll41Yf8mmr7hSykfuACSGESJ8UPtkkhY9xKYrCvovHmLn1By7cvgqAk50Dg7170rv5e9hYWhs5QyGEEHmRFD7ZJIVP3qDVavktcD+zty3leugtAFwLO/NFu950b/yO3AdMCCFEKlL4ZJMUPnlLkiaJn0/s5JvflnP3UQgAns4lGfXOADrWaSX3ARNCCAFI4ZNtUvjkTfGJCaw+tJl5O/x58PQ+YFVKVmB0x09oVbWR3AZDCCFMnBQ+2SSFT96WfB+w73f/SGRcNAANytfgy06f0qB8TeMmJ4QQwmik8MkmKXzyh0dR4SzctYqVB34hLjEegLeqNWZMx094rWQFI2cnhBAit0nhk01S+OQvwY/DmLN9JWuP/IpGq0GlUvFefW9GdBhA6WLuxk5PCCFELpHCJ5uk8MmfboQGMWvbErad3guAhdqcnk07M6Rtb4oVcjJydkIIIQxNCp9sksInfzt76xLTNy/iz8unALC3tuXTt3z4pOWH2FnbGjk7IYQQhiKFTzZJ4VMw/HnpJFM3L+J80GUAnB2KMKxdX3ze6ChzAAkhRAEkhU82SeFTcGi1Wrad2cvMrUv47/4dAMq6eDCm46e0r/2mXAIvhBAFiBQ+2SSFT8GTqEnix0Nb+Pb3Ffo5gGp5vsb4zoNoVLG2kbMTQgiREzL7+Z1vpr2dNm0ajRo1wtbWFkdHxzRjgoKCaNeuHba2tri4uDBixAiSkpJyN1GR51iozend/H2OT/mF4e37YWtlQ+B//9B5zv/o8f0wLt/719gpCiGEyCX5pvBJSEigS5cufPrpp2lu12g0tGvXjoSEBI4ePUpAQAD+/v5MmDAhlzMVeZW9tR3D2/fjxJRf6NXsPdRmavZcOEKLKR8xdPU0gh+HGTtFIYQQBpbvurr8/f0ZMmQIT548SbV+x44dtG/fnnv37lG8eHEAfvjhB0aNGsX9+/extLRMc3/x8fHEx8frlyMiIvDw8JCuLhNwPeQWM7Yu5vfAAwDYWFjxyVvdGdj6I+yt7YybnBBCiCwpcF1dL3Ps2DGqVaumL3oAvL29iYiI4OLFi+k+b8aMGRQuXFj/8PDwyI10RR5Q3rU0Kz6eya8jllKvbDViE+OZu92P18e/j//BjSRqpJtUCCEKmgJT+ISEhKQqegD9ckhISLrPGzNmDOHh4frH7du3DZqnyHvqlavOthFLWfHxDMq6ePAg8jGj133Nm5N92Hn2T/JZo6gQQogMZLnw8fPzIyYmJkcOPnr0aFQqVYaPy5cv58ix0mNlZYWDg0OqhzA9KpWKdrXe5ODEdUzvNpwi9o5cD71Frx9G0nnO/zh765KxUxRCCJEDslz4jB49GldXV/r27cvRo0df6eDDhg3j0qVLGT7Kli2bqX25uroSGhqaal3ysqur6yvlKUyHhdqcPs3f58SUjXzWpifWFlYcuxZImxm9GbhyIrcfBhs7RSGEEK8gy4XP3bt3CQgI4MGDBzRv3pxKlSoxa9asDLuT0uPs7EylSpUyfKQ3KPl5DRs25MKFC4SFPbsyZ8+ePTg4OPDaa69lOTdh2grZ2PFlp085PGkD7zd4G4CNJ3fxxsSuTNu8iMjYaCNnKIQQIjte6aqu0NBQfvzxRwICArh8+TJt2rShb9++dOjQATOznB0+FBQUxKNHj9i2bRtff/01hw4dAqB8+fLY29uj0WioWbMm7u7uzJ49m5CQEHr06EG/fv2YPn16po8jExiKtJy7dZlJG7/j6NUzABQt5MTIDv3xafwO5nILDCGEMLpcm7n5xIkTrFy5koCAANzc3Hj8+DFOTk74+fnRvHnzV9l1Kr169SIgIOCF9fv379cf59atW3z66accOHAAOzs7evbsycyZMzE3z/wHkxQ+Ij2KorD7/CEmb1rIjdAgACq6lWHie4NpWbWRkbMTQgjTZtDCJzQ0lNWrV+Pn58e///5Lp06d6Nu3L61atSI6OprJkyezfv16bt269Uo/hDFI4SNeJlGTxKo/N/Ptb8t5FB0OwJuvvc7E9z+jknvmxqQJIYTIWQYrfDp06MCuXbuoWLEi/fr1w9fXlyJFiqSKCQsLw9XVFa1Wm73sjUgKH5FZ4TGRzN3ux4r9P5GoScJMZcZHTToyssMAihVyMnZ6QghhUgxW+PTt25d+/frRsGHDdGMURSEoKIjSpUtnZdd5ghQ+Iqtuht1m6ubv9TNAF7K244u2fej7ZhesLDI3OF8IIcSrMdjMzc2aNaN27RfvaJ2QkMCqVasA3Zwo+bHoESI7yrh4sOLjmWwauojqpbyIjItm8qYFNJvcne2BB2QCRCGEyEOy3OKjVqsJDg7GxcUl1fqHDx/i4uKCRqPJ0QRzm7T4iFeh1Wr56fh2Zmz9gdDwBwA0qlibyV2GUNWjopGzE0KIgstgLT6KoqBSqV5Yf+fOHQoXLpzV3QlRoJiZmdGtUXuOTvqJL9r2xtrCiqNXz/DW9J4MWz2d+xEPjZ2iEEKYtEy3+NSqVQuVSsW5c+eoUqVKqkvENRoNN2/epE2bNvz0008GSzY3SIuPyEl3HoUwddP3bPlrDwD21rZ80bYP/d78QMb/CCFEDsrxwc2TJk3Sfx02bBj29vb6bZaWlnh6evLee+9leqblvEoKH2EIJ66fZfxP8zgfpLv3nKdzSSa9/xmtqzdJswVVCCFE1hjsqq6AgAC6du2KtbX1KyeZF0nhIwwlefzP9C2LCXva5dWscn0mdRki8/8IIcQryrWZmwsaKXyEoUXFRTN/RwBL9q4jISkRtZmank3fZUSH/jjZyTg5IYTIjhwtfIoUKcLVq1cpVqwYTk5OGTbNP3r0KHsZ5xFS+Ijc8t/9O0zeuIDtZw8C4GTnwMgOA+jRpJPc/0sIIbIoRwufgIAAunXrhpWVFf7+/hkWPj179sxexnmEFD4itx26fIrxP83j8r0bALxWojxTPviCxl51jJyZEELkH9LVlU1S+AhjSNIkEfDnZr7+dRlPYiIA6FC7JRPfH0zJIq5Gzk4IIfI+g83j06pVK/z9/YmIiHilBIUQz5irzen7ZheOTP6Jnk07Y6Yy49cze2kysSvf/r6C2IQ4Y6cohBAFQpYLnypVqjBmzBhcXV3p0qULW7duJTEx0RC5CWFyito7Mqv7SPaMDeD1CrWITYzn61+X0eSrbvweuF9ufyGEEK8oW11dWq2WP/74g7Vr17J582bUajXvv/8+Pj4+NGvWzBB55hrp6hJ5haIobD39B5M3LuDe4zAAmlSqy9QPhuHlXsbI2QkhRN6Sa2N84uLi+PXXX5k2bRoXLlyQe3UJkcOi42NZuGsVi3avIT4pAXMzNX3f7MKw9v1wsLF/+Q6EEMIEGGyMT0ohISH88MMPzJo1i/Pnz1OvXr1X2Z0QIg12VjaMeudj/py4jjY1mpKk1bBk73oaT/yA9Ud/Q6vVGjtFIYTIN7Lc4hMREcHGjRtZu3YtBw4coGzZsvj4+ODj40O5cuUMlWeukRYfkdftu3iM8T/N5UZoEAB1ylRlerfh1ChdyciZCSGE8Risq8vGxgYnJye6du2Kj48PdevWfeVk8xIpfER+kJCUyLJ9G5jz+0qi42NQqVT0eKMTozt+QhF7mf1ZCGF6DFb47Nmzh5YtW2Jm9kq9ZHmWFD4iPwl+HMaUTQvZdGo3oJv9eXTHT/jojY6ozdRGzk4IIXKPTGCYTVL4iPzo2LVAvlz/DZfu6mZ/rl7KixndRlCnbFUjZyaEELkjRwuf2rVrs3fvXpycnKhVq1aGt6w4c+ZM9jLOI6TwEflVkiYJ/4MbmbVtKZFx0QB82KgDX3b6FGeHIkbOTgghDCuzn9+ZuhNix44dsbKy0n+fUeEjhDAOc7U5/Vp0pWPdVkzZ9D0/Hd/OuqO/sv3sAUa/8zG+Td+V7i8hhMmTrq7nSIuPKChO3TjPmPXf8PftqwBU86jIjA9HULdsNSNnJoQQOc9g8/iULVuWhw8fvrD+yZMnlC1bNqu7E0IYSL1y1dk1xo/p3YbjYGPPhdtXaT+7P1+smsaDyMfGTk8IIYwiy4XPf//9l+bszPHx8dy5cydHkhJC5Ay1mZo+zd/nyKSf6NaoPQDrjv7KGxO7EvDnJjTa/D3TuhBCZFWmu7q2bdsGQKdOnQgICKBw4WdzhWg0Gvbu3cuePXu4cuWKYTLNJdLVJQqyUzfOM3rd11y8cw2AGqUrM/PDEdTyfM3ImQkhxKvJ8cvZM5q3x8LCAk9PT7799lvat2+f9WzzECl8REGXpEnC/89NzNq6hMi4aP3kh2M6fYKTnUx+KITInww2j0+ZMmU4deoUxYoVe+Uk8yIpfISpCAt/yORNC/nlxA4Aitg7MqHzID54vW2BnaBUCFFwGWxw86RJkyhUqNAL6xMSEli1alVWdyeEMBKXwkVZ2Hsim4YuoqJbGR5FPWHIqqm8O+dTLt29buz0hBDCILLc4qNWqwkODsbFxSXV+ocPH+Li4pLmwOf8RFp8hClK1CSxbO8Gvvl9OTHxsajN1PRr8QEj2vfD3trO2OkJIcRLGazFR1GUNCcwvHPnTqoBz0KI/MNCbc7/WvtwaOJ62tV6E41Ww5I/1tHkq278enofMt2XEKKgyHSLT/KtKs6dO0eVKlUwN3826bNGo+HmzZu0adOGn376yWDJ5gZp8REC9v59lC/Xf8utB3cBeLPK60zvOowyLh5GzkwIIdKWo7esAN1l7ABnz57F29sbe3t7/TZLS0s8PT157733sp+xECLPaFm1EQcm1GbBrtUs3LWK/ReP03yyD5+93ZNBrXtgZWFp7BSFECJbsjzGJyAggK5du2JtbW2onIxKWnyESO3f0CDGrP+Gg5dOAlDWxYOZH46gaeX6Rs5MCCGeMdjl7AWdFD5CvEhRFLae/oOJP88nNPwBAJ3qvsWkLp9TvHDBnNpCCJG/5GjhU6RIEa5evUqxYsVwcnLK8O7sjx49yl7GeYQUPkKkLyI2itnblrLywC9oFS2FrO34stOncud3IYTR5WjhExAQQLdu3bCysiIgICDD2J49e2Y92zxECh8hXu580GVGrJnFuVuXAKhZ+jVm+4ykeqlKRs5MCGGqpKsrm6TwESJzNFoNAX9uZsaWxUTGRWOmMqPvm10Y9c4AmftHCJHrDF74hIWFERYWhlarTbW+evXq2dldniGFjxBZExr+gIk/z2fLX3sAcHN0ZmrXobSt2TzDbnEhhMhJBit8Tp8+Tc+ePbl06dILk5qpVCqZuVkIE3XgnxOMXvc1/92/A8Bb1RozvdtwPIq6GTkzIYQpMFjhU6NGDcqVK8eoUaMoXrz4C3/RlS5dOnsZ5xFS+AiRfbEJcczf4c/3u38kUZOEjaU1I9r3p3/LrlioMz1tmBBCZJnBCp9ChQoRGBhI+fLlXznJvEgKHyFe3dXgm4xcO5vj1wIBqFKyAl/7jKJ2mapGzkwIUVAZ7F5dLVu25Ny5c6+UnBCiYKvoVobNQxcx13ccTnYOXLxzjXaz+zN63ddExEYZOz0hhAnLcovPgwcP6NmzJ/Xr16dq1apYWFik2v7OO+/kaIK5TVp8hMhZDyIfM2njAn4+vh2A4oWLMeWDL+hQu4UMfhZC5BiDdXX9+uuv9OjRg4iIiBd3JoObhRDpOHz5L0auncW/YbcBaFWtMTNk8LMQIocYrKtr8ODBfPTRRwQHB6PValM98nvRI4QwnDcq1WXf+B8Z2q4vFmpz/rhwhKaTPmTxnjUkaZKMnZ4QwkRka3Dz2bNnKVeunKFyMipp8RHC8K4G32Tkmlkcv34WgGoeFfn6ozHULF3ZuIkJIfItg7X4dO7cmf37979SckII01bRrQybhi5iTo8vcbR14MLtq7Sd2ZcJP80jOi7G2OkJIQqwLLf4TJs2jXnz5tGuXTuqVav2wuDmzz77LEcTzG3S4iNE7rof8ZCJP89n06ndAJRwKs6MD4fTunoTI2cmhMhPDDa4uUyZMunvTKXi33//zcru8hwpfIQwjv0XjzNq3WyCHtwDoEPtlkzt+gXFCxczcmZCiPzAIIWPoigEBQXh4uKCjY1NjiSa10jhI4TxxCTE8c2vy1iydz0arQYHG3vGdx6ET+N3MDPLcs+8EMKEGGSMj6IoVKhQgTt37rxygkII8TxbS2smvDeYXWP8qFG6MhGxUYxYM5N353zKtZD/jJ2eEKIAyFLhY2ZmRoUKFXj48KGh8hFCCKp6VGT7qOVM6fIFtlY2nLh+jpZTe/Dt7ytISEo0dnpCiHwsy23HM2fOZMSIEfz999+GyEcIIQBQm6np37IrByespWXVRiQkJfL1r8toNc2Xk9fltjlCiOzJ8uBmJycnYmJiSEpKwtLS8oWxPo8ePcrRBHObjPERIu9RFIWtf/3BuJ/m8CDyMQA9m3Zm3LsDKWRjZ+TshBB5gcGu6goICMhwe8+ePbOyuzxHCh8h8q7H0eFM2riA9Ud/A8DN0ZmZH47Au0ZTI2cmhDA2gxU+BZ0UPkLkfYcv/8XwNTP5777uQosOtVsyretQXAoXNXJmQghjMdjMzQA3btxg3LhxfPjhh4SFhQGwY8cOLl68mL1shRAiC96oVJf9439kkHcP1GZqfj2zlyaTurH2yK/I33JCiIxkufA5ePAg1apV48SJE2zatImoqCgAzp07x8SJE3M8QSGESIuNpTXj3h3IztErqV7Ki/CYSIaunkaXeYP1LUFCCPG8LBc+o0ePZurUqezZswdLS0v9+hYtWnD8+PEcTU4IIV6mWikvto9awYTOg7GxsOLwlb94c7IP3+/+Ue76LoR4QZYLnwsXLvDuu+++sN7FxYUHDx7kSFJCCJEV5mpz/tfah/0T1vCGV11iE+OZsmkhbWf14+/bV42dnhAiD8ly4ePo6EhwcPAL6wMDAylRokSOJPW8//77j759+1KmTBlsbGwoV64cEydOJCEhIVXc+fPnadKkCdbW1nh4eDB79myD5COEyJs8nUvy85AFzPUdR2HbQpwPuoz3jN5M37KYuMR4Y6cnhMgDslz4dOvWjVGjRhESEoJKpUKr1XLkyBGGDx+Or6+vIXLk8uXLaLValixZwsWLF5k7dy4//PADX375pT4mIiKC1q1bU7p0aU6fPs3XX3/NV199xdKlSw2SkxAib1KpVHzYqD2HJq6nfe0WaLQavtsZQMupPTh+7ayx0xNCGFmWL2dPSEhg4MCB+Pv7o9FoMDc3R6PR0L17d/z9/VGr1YbKNZWvv/6axYsX6+8Gv3jxYsaOHUtISIh+7NHo0aPZsmULly9fTnc/8fHxxMc/+0swIiICDw8PuZxdiAJie+ABxqz/htBwXVe8THwoRMFksMvZLS0tWbZsGTdu3OC3337jxx9/5PLly6xevTrXih6A8PBwihQpol8+duwYTZs2TTXg2tvbmytXrvD48eN09zNjxgwKFy6sf3h4eBg0byFE7mpbqzl/TlyHT+N3AAj4cxPNJn/IHxeOGjcxIYRRvNIEhslPValUOZZQZly/fp06derwzTff0L9/fwBat25NmTJlWLJkiT7un3/+oUqVKvzzzz9Urlw5zX1Ji48QpuPw5b8Y9uMMbj24C8B79b2Z/MEXFLV3NG5iQohXZtAJDFesWEHVqlWxtrbG2tqaqlWrsnz58izvZ/To0ahUqgwfz3dT3b17lzZt2tClSxd90fMqrKyscHBwSPUQQhRMb1Sqy77xP/Jxqw8xU5mx8eQumk76kC1/7ZGJD4UwEeZZfcKECROYM2cOgwcPpmHDhoCum+mLL74gKCiIyZMnZ3pfw4YNo1evXhnGlC1bVv/9vXv3ePPNN2nUqNELg5ZdXV0JDQ1NtS552dXVNdM5CSEKNjsrGya9/zkd67Tki9XTuXLvXz5ZPp4tp/Yw88MRuDo6GztFIYQBZbmry9nZme+++44PP/ww1fp169YxePBgg83lc/fuXd58803q1KnDjz/++MJ4ouTBzaGhoVhYWADw5ZdfsmnTpgwHNz9P7tUlhOlISEpk/g5/5u/wJ0mrwcHGnq/e/4wPG3XI9S58IcSrMVhXV2JiInXr1n1hfZ06dUhKMswsqXfv3qV58+aUKlWKb775hvv37xMSEkJISIg+pnv37lhaWtK3b18uXrzIhg0bmD9/PkOHDjVITkKI/M/S3IIRHfqzZ2wANUpXJiI2iqGrp9N1/mcEPbhn7PSEEAaQ5RafwYMHY2FhwZw5c1KtHz58OLGxsXz//fc5miCAv78/vXv3TnNbyvTPnz/PwIEDOXXqFMWKFWPw4MGMGjUqS8eSFh8hTFOSJokle9fz9a/LiEuMx9bKhrGd/kfvZu9hZpat4ZBCiFyU2c/vbBU+q1atwsPDg9dffx2AEydOEBQUhK+vr76bCXihOMoPpPARwrTdCA1i2OrpHL9+FoDXy9fk2x5fUq54KeMmJoTIkMEKnzfffDNTcSqVin379mVl13mCFD5CCK1Wi/+fm5i6+Xti4mOxtrBiZIcBfNyqG2qz3JuvTAiReQYrfAo6KXyEEMluPwxm+I8zOHjpJAC1PF9jru84KrmXfckzhRC5zaDz+AghhCnwKOrG+s/mM6fHWBxs7An87x9aT+/JvO1+JGoMczGHEMKwpPARQogMqFQqujfuwMEJa3mrWmMSkhKZuW0JbWf24eKda8ZOTwiRRVL4CCFEJrg5ubDqf9+wsPdEnOwcuHD7Kt7TezH712UkJCUaOz0hRCZJ4SOEEJmkUql4v8HbHJywjna1mpOk1TDn9xV4z+jFuVuZnyhVCGE8UvgIIUQWuRQuyvIBM1jSbypF7B25dPcGbWf1ZcaWxcQnJhg7PSFEBrJV+KxevZrGjRvj7u7OrVu3AJg3bx5bt27N0eSEECKvUqlUdKzbij8nrqNj3VZotBrm7wyg9YxenL11ydjpCSHSkeXCZ/HixQwdOpS2bdvy5MkTNBoNAI6OjsybNy+n8xNCiDytWCEnlvSbyvIB0ylWyIkr9/6l3ax+TNu8iLjEeGOnJ4R4TpYLnwULFrBs2TLGjh2b6kahdevW5cKFCzmanBBC5Bfta7fg4MR1vFuvNRqthgW7VtF6ei/O3Lxo7NSEEClkufC5efMmtWrVemG9lZUV0dHROZKUEELkR0XtHVncdzIrP56Js0MRrgbfpP3s/kzd/L20/giRR2S58ClTpgxnz559Yf3OnTupXLlyTuQkhBD5WttazTk4YR2d67VGq2hZuGs1b03ryZmbfxs7NSFMXpYLn6FDhzJw4EA2bNiAoiicPHmSadOmMWbMGEaOHGmIHIUQIt8pYl+YRX0n4/fJLJwdinAt5D/azx7AtM2L5MovIYwoW/fqWrNmDV999RU3btwAwN3dnUmTJtG3b98cTzC3yb26hBA57VFUOOM2fMumU7sB8HIvy/ye46lZWlrJhcgpuXKT0piYGKKionBxccnuLvIcKXyEEIayPfAAI9fO4kHkY9RmagZ79+CLtn2wsrA0dmpC5HsGu0np1KlTuXnzJgC2trYFqugRQghDalurOQcnrqNT3bfQaDXM2+FPm5m9uRB0xdipCWEyslz4/Pzzz5QvX55GjRqxaNEiHjx4YIi8hBCiQCpq78gP/aawfMB0ihZy4tLdG7w9sw/f/LZc7vguRC7IcuFz7tw5zp8/T/Pmzfnmm29wd3enXbt2rF27lpiYGEPkKIQQBU772i04MH4N7Wq9SZJWwze/LeftmX34R+74LoRBvdIYH4AjR46wdu1afv75Z+Li4oiIiMip3IxCxvgIIXKToihsPf0HY9Z9zePoCCzU5gxr15dB3j0wV5sbOz0h8g2DjfF5np2dHTY2NlhaWpKYmPiquxNCCJOiUqnoVPctDk5YR5saTUnUJDFz2xLazx7A1eCbxk5PiAInW4XPzZs3mTZtGlWqVKFu3boEBgYyadIkQkJCcjo/IYQwCS6Fi+L3ySwW9p5IYdtCnL31D29N68mi3WvQaDXGTk+IAiPLXV2vv/46p06donr16vj4+PDhhx9SokQJQ+WX66SrSwhhbMGPwxj643T2XzwOQL2y1fiu1wTKuHgYOTMh8i6DzeMzduxYfHx8eO211145ybxICh8hRF6gKArrjv7KhJ/nERUXg42lNeM7D6JX086Ymb3yKAUhCpxcmcCwIJLCRwiRl9x+GMyQVVM5cuU0AE0q1WWu7zhKFnE1cmZC5C05WvgMHTqUKVOmYGdnx9ChQzOMnTNnTtazzUOk8BFC5DVarRa/gxuZumkhsYnx2FvbMrnLF3zYqD0qlcrY6QmRJ2T28ztT10oGBgbqr9gKDAzMmQyFEEJkipmZGX3f7MKbrzXg84ApnPr3AkNXT2PH2QN889EYihcuZuwUhcg3pKvrOdLiI4TIyzRaDYv3rGX2r0tJSErEyc6BmR+OpGPdVsZOTQijMtg8Pn369CEyMvKF9dHR0fTp0yeruxNCCJEFajM1g7x7sGuMH1U9KvI4OoKPl4/jk+XjeRwdbuz0hMjzstzio1arCQ4OfuHmpA8ePMDV1ZWkpPx9rxlp8RFC5BcJSYnM3e7HdzsD0Gg1FC9cjDk9vqRl1UbGTk2IXJfjLT4RERGEh4ejKAqRkZFEREToH48fP2b79u1yp3YhhMhFluYWjHpnAL+OWEr54qUJDX+Az8KhjFgzk+g4uXeiEGnJdIuPmZlZhlcPqFQqJk2axNixY3MsOWOQFh8hRH4UmxDH9C2LWbZvAwClirmzoNcEGpSvadzEhMglOT6Pz8GDB1EUhRYtWrBx40aKFCmi32ZpaUnp0qVxd3d/9cyNTAofIUR+dvjKaT4PmMLdRyGoVCr+95YPIzsMwMrC0tipCWFQBpvA8NatW3h4eBTYmUOl8BFC5HcRsVGM/2kuG479DkDlEuVY2PsrqpSsYOTMhDAcg8/cHBMTQ1BQEAkJCanWV69ePTu7yzOk8BFCFBQ7zh5k+JqZPIx8jIXanBEd+jOw9UeozdTGTk2IHGewwuf+/fv07t2bHTt2pLldo8nfdxGWwkcIUZDcj3jEiDUz2XnuT0B3w9MFvSfi6VzSyJkJkbMMNo/PkCFDePLkCSdOnMDGxoadO3cSEBBAhQoV2LZt2yslLYQQImc5OxTB75NZzPMdh721Laf+vUCLqT1YfWgLMn+tMEVZbvFxc3Nj69at1K9fHwcHB/766y8qVqzItm3bmD17NocPHzZUrrlCWnyEEAXV7YfBfB4whaNXzwDQqlpj5nz0JS6Fixo5MyFencFafKKjo/Xz9Tg5OXH//n0AqlWrxpkzZ7KZrhBCCEPzKOrGL0MW8tX7n2FlbskfF47QfHJ3fg/cb+zUhMg1WS58vLy8uHLlCgA1atRgyZIl3L17lx9++AE3N7ccT1AIIUTOMTMz45NW3dn1pT9VPSryKDqcvkvG8Jn/ZCJio4ydnhAGl+Wurh9//JGkpCR69erF6dOnadOmDY8ePcLS0hJ/f3+6du1qqFxzhXR1CSFMRUJSIt/8tpyFu1ajVbSULOLKd70m0KhibWOnJkSWGfxy9mQxMTFcvnyZUqVKUaxYsVfZVZ4ghY8QwtScuH6Wwf6TCXpwD5VKxaetujPqnY9l0kORr+Ra4VPQSOEjhDBFUXHRjP9pHuuO/gpAlZIVWNj7KyqXKGfkzITInBwtfIYOHZrpA8+ZMyfTsXmRFD5CCFO24+xBhv04g0dRT7A0t+DLTp8yoEW3Ajtbvyg4crTwefPNNzN1UJVKxb59+zKfZR4khY8QwtTdj3jI0NXT2XPhCABveNVlfs/xlChS3MiZCZE+6erKJil8hBACFEXhx8NbmfDzPGIT4ihsW4hZH46kU723jJ2aEGky2Dw+ya5fv86uXbuIjY0FkBlAhRCiAFGpVPRo0om9Y1dRy/M1wmMi+WTFeP63YgLhMZHGTk+IbMty4fPw4UNatmxJxYoVadu2LcHBwQD07duXYcOG5XiCQgghjKds8VJsG7GUYe36ojZTs+nUblpM+YgjV04bOzUhsiXLhc8XX3yBhYUFQUFB2Nra6td37dqVnTt35mhyQgghjC/5zu7bhi/B07kkdx+H8v68QUzZtJD4xARjpydElmS58Nm9ezezZs2iZMnUd/atUKECt27dyrHEhBBC5C11ylZl79hV+DR+B0VR+H73j7Sb3Y8r924aOzUhMi1b9+pK2dKT7NGjR1hZWeVIUkIIIfImO2tbvu3xJX6fzKKIXWH+vn0V7xm9WLH/ZxnrKfKFLBc+TZo0YdWqVfpllUqFVqtl9uzZmb7sXQghRP72ds1m7J+whjervE5cYjxjN3yLz8KhhIU/NHZqQmQoy5ez//3337Rs2ZLatWuzb98+3nnnHS5evMijR484cuQI5crl71k+5XJ2IYTIPEVRWHHgZ6ZsXEh8UgJF7B2Z5zuW1tWbGDs1YWIMdjl71apVuXr1Km+88QYdO3YkOjqazp07ExgYmO+LHiGEEFmjUqno9+YH7PrSn9dKlOdR1BN8F41g5JpZRMfHGjs9IV6QpRafxMRE2rRpww8//ECFChUMmZfRSIuPEEJkT3xiAjO2/sAPf6wFoHzx0izqO4nqpSoZOTNhCgzS4mNhYcH58+dfOTkhhBAFj5WFJV+9/xk/ff4droWduR56i3az+rFw12q0Wq2x0xMCyEZX10cffcSKFSsMkYsQQogCoGnl+uwb/yNtazYjUZPE1M3f02X+YO49DjN2akJkfXDz4MGDWbVqFRUqVKBOnTrY2dml2m4Kd2fXaDQkJibmcmZC5CwLCwvUarWx0xAFmKIorDv6K2M3zCE2IQ5HWwe++Wg07Wu3MHZqogAy2E1KM7pkvaDfnV1RFEJCQnjy5IlxkhMihzk6OuLq6opKpTJ2KqIA+zc0iE9XTuTcrUsAdG/cgSldvsDO+sU54YTILrk7ezZldOKCg4N58uQJLi4u2NrayoeFyLcURSEmJoawsDAcHR1xc3MzdkqigEvUJPH1r8tYsGsViqJQ1sWDRX0nU7N0ZWOnJgoIKXyyKb0Tp9FouHr1Ki4uLhQtWtSIGQqRcx4+fEhYWBgVK1aUbi+RK45ePcMgv6+49zgMczM1o975mP+19kFtJq8/8WoMNo+PqUoe05PW7TqEyK+SX88yZk3klkYVa7Nv3I90qN2SJK2GaVsW8cH8z2Tgs8g1UvhkkXRviYJEXs/CGBztHFjafypzfcdha2XDkSunaTHlI34P3G/s1IQJyDeFzzvvvEOpUqWwtrbGzc2NHj16cO/evVQx58+fp0mTJlhbW+Ph4cHs2bONlK0QQoiMqFQqPmzUnj++DKBG6co8iYmg75IxjFgzU2Z8FgaVbwqfN998k59++okrV66wceNGbty4wfvvv6/fHhERQevWrSldujSnT5/m66+/5quvvmLp0qVGzFqkxd/fH0dHx2w996uvvqJmzZq5cqzM6NGjB9OnTzfY/pMdOHAAlUqlv6Jw586d1KxZUyaFE/le2eKl+HXEUgZ590ClUrH60BbazOjF37evGjs1UVAp+dTWrVsVlUqlJCQkKIqiKIsWLVKcnJyU+Ph4fcyoUaMULy+vDPcTFxenhIeH6x+3b99WACU8PDxVXGxsrPLPP/8osbGxOf/DmJiYmBglNDRUvzxx4kSlRo0aL8QByubNm1Oti4yMVB48eJDjx8qOs2fPKkWKFFEiIyNzZH8Z2b9/vwIojx8/1q+rW7eusmrVqlfar7yuRV7y56WTSo2R7ZXiHzdQPAa+oSz5Y52i0WiMnZbIJ8LDw9P8/H5evmnxSenRo0esWbOGRo0aYWFhAcCxY8do2rQplpaW+jhvb2+uXLnC48eP093XjBkzKFy4sP7h4eFh8PwLAo1Gk+3WBhsbG1xcXLL1XHt7+yxdVfcqx3qZBQsW0KVLF+zt7dONSUhIMMixAXr16sV3331nsP0LkduaVKrH3vGr8a7ehISkRCb8PA+f74dyP+KhsVMTBUi+KnxGjRqFnZ0dRYsWJSgoiK1bt+q3hYSEULx48VTxycshISHp7nPMmDGEh4frH7dv3zZM8kbUvHlzBg0axKBBgyhcuDDFihVj/PjxKClmMoiPj2f48OGUKFECOzs7GjRowIEDB/Tbk7uMtm3bxmuvvYaVlRVBQUF4enoydepUfH19sbe3p3Tp0mzbto379+/TsWNH7O3tqV69On/99dcL+0r+ftKkSZw7dw6VSoVKpcLf3x9PT08A3n33XVQqlX45ZVfX7t27sba2fmFCyc8//5wWLVpk+lh9+vShffv2qfaRmJiIi4tLurdn0Wg0/PLLL3To0CHVek9PT6ZMmYKvry8ODg4MGDAAgMOHD9OkSRNsbGzw8PDgs88+Izo6Wv+81atXU7duXQoVKoSrqyvdu3cnLCzjq1w6dOjAX3/9xY0bNzKMEyI/KWrviP+ns5nVfSTWFlbsv3icFlN7sP/icWOnJgoIoxY+o0eP1n8Apfe4fPmyPn7EiBEEBgaye/du1Go1vr6+qT68s8PKygoHB4dUj8xSFIXo+FijPLL6cwcEBGBubs7JkyeZP38+c+bMYfny5frtgwYN4tixY6xfv57z58/TpUsX2rRpw7Vr1/QxMTExzJo1i+XLl3Px4kV9S8rcuXNp3LgxgYGBtGvXjh49euDr68tHH33EmTNnKFeuXLr/V127dmXYsGFUqVKF4OBggoOD6dq1K6dOnQLAz8+P4OBg/XJKLVu2xNHRkY0bN+rXaTQaNmzYgI+PT6aP1a9fP3bu3ElwcLA+9rfffiMmJoauXbumeT7Pnz9PeHg4devWfWHbN998Q40aNQgMDGT8+PHcuHGDNm3a8N5773H+/Hk2bNjA4cOHGTRokP45iYmJTJkyhXPnzrFlyxb+++8/evXqleaxk5UqVYrixYtz6NChDOOEyG9UKhU9m3Zmx+iVVHIvx/2IR3y4YAgTf5lPfKLhWlGFaTA35sGHDRv20jf3smXL6r8vVqwYxYoVo2LFilSuXBkPDw+OHz9Ow4YNcXV1JTQ0NNVzk5ddXV1zPHeAmIQ4yn2e/i08DOnG/P3YWdlkOt7Dw4O5c+eiUqnw8vLiwoULzJ07l/79+xMUFISfnx9BQUG4u7sDMHz4cHbu3Imfn59+8G5iYiKLFi2iRo0aqfbdtm1bPv74YwAmTJjA4sWLqVevHl26dAF0LXUNGzYkNDT0hf8LGxsb7O3tMTc3T7XNxkb3syXfUiEtarWabt26sXbtWvr27QvA3r17efLkCe+9994L8ekdq1GjRnh5ebF69WpGjhwJ6AqujLqxbt26hVqtTrMbrUWLFgwbNky/3K9fP3x8fBgyZAgAFSpU4LvvvqNZs2YsXrwYa2tr+vTpo48vW7Ys3333HfXq1SMqKirDrjR3d3du3bqV7nYh8rPKJcqxY/QKJm9ciN/BX1jyxzqOXT3D4r5TKFe8lLHTE/mUUVt8nJ2dqVSpUoaPlGN2UkoeXxIfHw9Aw4YN+fPPP1NNxLZnzx68vLxwcnIy/A+Tx73++uup5mxp2LAh165dQ6PRcOHCBTQaDRUrVsTe3l7/OHjwYKpuFEtLS6pXr/7CvlOuS+5erFat2gvrXtZ1kx0+Pj4cOHBAP7XBmjVraNeuXZav5OrXrx9+fn6ArmDesWNHqmLkebGxsVhZWaU5D87zrUDnzp3D398/1bn19vZGq9Vy8+ZNAE6fPk2HDh0oVaoUhQoVolmzZgAEBQVlmLeNjQ0xMTFZ+lmFyE9sLK2Z8eFwAj6dTRG7wpwPusJb03uy/uhvr9ziL0yTUVt8MuvEiROcOnWKN954AycnJ27cuMH48eMpV64cDRs2BKB79+5MmjSJvn37MmrUKP7++2/mz5/P3LlzDZaXraU1N+YbZ8ItW0vrHNtXVFQUarWa06dPv3DbgpStDTY2Nml+0CcPMIdnE+Kltc4Ql17Xq1ePcuXKsX79ej799FM2b96Mv79/lvfj6+vL6NGjOXbsGEePHqVMmTI0adIk3fhixYoRExNDQkLCC8W5nZ1dquWoqCg+/vhjPvvssxf2U6pUKaKjo/H29sbb25s1a9bg7OxMUFAQ3t7eLx0c/ejRI5ydnbPwkwqRP3nXaMrecZUY5D+JI1dOM2TVVA5eOsns7qMoZGP38h0I8VS+KHxsbW3ZtGkTEydOJDo6Gjc3N9q0acO4ceOwsrICoHDhwuzevZuBAwdSp04dihUrxoQJE/SDSw1BpVJlqbvJmE6cOJFq+fjx41SoUAG1Wk2tWrXQaDSEhYVl+GFvKJaWlmg0mhfWW1hYpLn+eT4+PqxZs4aSJUtiZmZGu3btsnysokWL0qlTJ/z8/Dh27Bi9e/fO8JjJA6z/+eefl84rVLt2bf755x/Kly+f5vYLFy7w8OFDZs6cqb+qMOVg8PTExcVx48YNatWq9dJYIQoCNycXfvr8OxbuWs3sX5ex+dRuTt/8mx/6TqZ2marGTk/kE/niqq5q1aqxb98+Hj58SFxcHDdv3mTx4sWUKFEiVVz16tU5dOgQcXFx3Llzh1GjRhkp47wnKCiIoUOHcuXKFdatW8eCBQv4/PPPAahYsSI+Pj74+vqyadMmbt68ycmTJ5kxYwa///67wXPz9PTk5s2bnD17lgcPHui7Lz09Pdm7dy8hISEZTkng4+PDmTNnmDZtGu+//76+GM7KsUDX3RUQEMClS5fo2bNnhjk7OztTu3ZtDh8+/NKfb9SoURw9epRBgwZx9uxZrl27xtatW/WDm0uVKoWlpSULFizg33//Zdu2bUyZMuWl+z1+/DhWVlb6Vk8hTIHaTM3nb/di6/Af8CjqRtCDe7zz9ccs2LVKJvQUmZIvCh/x6nx9fYmNjaV+/foMHDiQzz//PFVrmJ+fH76+vgwbNgwvLy86derEqVOnKFXK8AMI33vvPdq0acObb76Js7Mz69atA+Dbb79lz549eHh4ZNiqUb58eerXr8/58+fTvJorM8cCaNWqFW5ubnh7e+sHeWekX79+rFmz5qVx1atX5+DBg1y9epUmTZpQq1YtJkyYoD+Gs7Mz/v7+/Pzzz7z22mvMnDmTb7755qX7XbduHT4+PnLjXGGS6patxt5xq3mnztObnW5exIcLhhAWLnP+iIypFBkdlkp6t7VPbmkqU6YM1tY5N74mNzRv3pyaNWsyb948Y6eSp0VFRVGiRAn8/Pzo3LnzS+NjY2Px8vJiw4YNud7q8uDBA7y8vPjrr78oU6ZMtveTn1/XQoBuWpF1R39l7PpviU2Mp1ghJxb0msibVV43dmoil6X3+f08afERJk+r1RIWFsaUKVNwdHTknXfeydTzbGxsWLVqFQ8ePDBwhi/677//WLRo0SsVPUIUBCqViu6N32HnGH8qlyjHg8jHfLhgCJM3LiAhKfHlOxAmJ18MbhbCkIKCgihTpgwlS5bE398fc/PM/1o0b97ccIlloG7dumlOniiEqfJyL8P2USuYtHEB/gc3smjPGo5eDWRJvymUdi7x8h0IkyFdXc8piF1dQqRHXteiINoeeIAvVk8jPCaSQtZ2fP3RaDrVfcvYaQkDk64uIYQQJqltreb8MXYV9cpWIzIumk+Wj2fY6unEJMQZOzWRB0jhI4QQosDxKOrG5mGLGfJ2L1QqFWuObKPNjN5cuis39TV1UvgIIYQokMzV5ozu+Ak/f74AF4eiXA2+ydsz+/DjoS1yuwsTJoWPEEKIAu2NSnXZO241b772OnGJ8QxfM5OPl48jIjbK2KkJI5DCRwghRIHn7FCENYPmML7zIMzN1Gw7vZe3pvXk7K1Lxk5N5DIpfIQQQpgEMzMzBrb+iK3Dl+BR1I1bD+7SYXZ/lvyxTrq+TIgUPiLX+fv74+jomK3nfvXVVy+9KWhOHSszevTowfTp0/XLnp6eeWKG7ISEBDw9PTN1s1MhTE2dslX5Y+wq2tV6k0RNEhN/mU/PxSN4FBVu7NRELpB5fJ4j8/gYXmxsLJGRkbi4uAC6YmbLli2cPXs2VZxKpWLz5s106tRJvy4qKor4+HiKFi2ao8fKjnPnztGiRQtu3bqFvb09APfv38fOzi5P3D9r4cKFbN68mb1796YbI69rYcoURcH/4EYm/jKfhKRE3J1cWNx3Mg3K1zR2aiIbZB4fYVAajSbbd0K2sbHRFyJZZW9vn+mi51WP9TILFiygS5cu+qIHdDcczQtFD+juWn/48GEuXrxo7FSEyJNUKhW9m7/P9lErKFe8FPceh9F5zkC+2xkgd3ovwKTwMQHNmzdn0KBBDBo0iMKFC1OsWDHGjx+fqk87Pj6e4cOHU6JECezs7GjQoAEHDhzQb0/uMtq2bRuvvfYaVlZWBAUF4enpydSpU/H19cXe3p7SpUuzbds27t+/T8eOHbG3t6d69eqpulxSdj/5+/szadIkzp07h0qlQqVS4e/vj6enJwDvvvsuKpVKv5yyq2v37t1YW1vz5MmTVD/v559/TosWLTJ9rD59+tC+fftU+0hMTMTFxYUVK1akeU41Gg2//PILHTp0SLX++a4ulUrFkiVLaN++Pba2tlSuXJljx45x/fp1mjdvjp2dHY0aNeLGjWdzi9y4cYOOHTtSvHhx7O3tqVevHn/88Ueq4wQHB9OuXTtsbGwoU6YMa9eufeHYTk5ONG7cmPXr16f5MwghdKp6VGTXGD/eq++NRqth+pbFdF/4Bfcj5E7vBZEUPq9CUSAh2jiPLPZQBgQEYG5uzsmTJ5k/fz5z5sxh+fLl+u2DBg3i2LFjrF+/nvPnz9OlSxfatGnDtWvX9DExMTHMmjWL5cuXc/HiRX1Lyty5c2ncuDGBgYG0a9eOHj164Ovry0cffcSZM2coV64cvr6+aQ4e7Nq1K8OGDaNKlSoEBwcTHBxM165dOXXqFAB+fn4EBwfrl1Nq2bIljo6ObNy4Ub9Oo9GwYcMGfHx8Mn2sfv36sXPnToKDg/Wxv/32GzExMXTt2jXN83n+/HnCw8Mzdb+sKVOm4Ovry9mzZ6lUqRLdu3fn448/ZsyYMfz1118oisKgQYP08VFRUbRt25a9e/cSGBhImzZt6NChA0FBQfoYX19f7t27x4EDB9i4cSNLly4lLCzshWPXr1+fQ4cOvTRHIUydvbUdC3t/xZweY7GxsOLAPydoOdWXw1dOGzs1kcPkJqWvIjEGJrsZ59gTgsHSLtPhHh4ezJ07F5VKhZeXFxcuXGDu3Ln079+foKAg/Pz8CAoKwt3dHYDhw4ezc+dO/Pz89IN3ExMTWbRoETVq1Ei177Zt2/Lxxx/r0powgcWLF1OvXj26dOkCwKhRo2jYsCGhoaG4urqmeq6NjQ329vaYm5un2mZjYwOAo6PjC89Jplar6datG2vXrqVv374A7N27lydPnvDee++9EJ/esRo1aoSXlxerV69m5MiRgK7ger4bK6Vbt26hVqsz1Y3Wu3dvPvjgg1TnYvz48Xh7ewO6FqrevXvr42vUqJHqHE+ZMoXNmzezbds2Bg0axOXLl/njjz84deqUvvBavnw5FSpUeOHY7u7u3Lp166U5CiGS7/TegdplqjBg2ViuBt/kg3mDGda+L0Pe7oXaTG3sFEUOkBYfE/H666+jUqn0yw0bNuTatWtoNBouXLiARqOhYsWK2Nvb6x8HDx5M1QVjaWlJ9erVX9h3ynXFixcHoFq1ai+sS6tF4lX5+Phw4MAB7t27B8CaNWto165dlq/k6tevH35+fgCEhoayY8cO+vTpk258bGwsVlZWqc5pejJzfuLi4oiIiAB0LT7Dhw+ncuXKODo6Ym9vz6VLl/QtPleuXMHc3JzatWvr91G+fHmcnJxeOLaNjQ0xMTEvzVEI8Uwl97LsHOPHh406oFW0fP3rMrrO/5ywcOn6KgikxedVWNjqWl6MdewcEhUVhVqt5vTp06jVqf+iSdniYWNjk+YHvYWFhf775O1prTPEYMF69epRrlw51q9fz6effsrmzZvx9/fP8n58fX0ZPXo0x44d4+jRo5QpU4YmTZqkG1+sWDFiYmJISEjA0tIyw31n9fwMHz6cPXv28M0331C+fHlsbGx4//33SUhIyPLP9ejRI5ydnbP8PCFMna2lNXN9x9KoYm1Grp3F4St/0XJaDxb1mUSTSvWMnZ54BVL4vAqVKkvdTcZ04sSJVMvHjx+nQoUKqNVqatWqhUajISwsLMMPe0OxtLREo9G8sN7CwiLN9c/z8fFhzZo1lCxZEjMzM9q1a5flYxUtWpROnTrh5+fHsWPHUnU9pSV5gPU///yTpXmFMuPIkSP06tWLd999F9AVpv/9959+u5eXF0lJSQQGBlKnTh0Arl+/zuPHj1/Y199//02tWrVyND8hTEmX19+mpmdl+i8dy+V7N/hg/mcMa9eXL9r2lq6vfEq6ukxEUFAQQ4cO5cqVK6xbt44FCxbw+eefA1CxYkV8fHzw9fVl06ZN3Lx5k5MnTzJjxgx+//13g+fm6enJzZs3OXv2LA8ePCA+Pl6/fu/evYSEhKT5oZ7Mx8eHM2fOMG3aNN5//32srKyyfCzQdXcFBARw6dIlevbsmWHOzs7O1K5dm8OHD2fxp325ChUqsGnTJs6ePcu5c+fo3r17qtaySpUq0apVKwYMGMDJkycJDAxkwIABabbIHTp0iNatW+d4jkKYkgqunuwYvQKfxu+gKArf/LZcur7yMSl8TISvry+xsbHUr1+fgQMH8vnnnzNgwAD9dj8/P3x9fRk2bBheXl506tSJU6dOUapUKYPn9t5779GmTRvefPNNnJ2dWbduHQDffvste/bswcPDI8NWi/Lly1O/fn3Onz+f5tVcmTkWQKtWrXBzc8Pb21s/yDsj/fr1Y82aNZn8KTNvzpw5ODk50ahRIzp06IC3t3eq8TwAq1atonjx4jRt2pR3332X/v37U6hQoVSTEB47dozw8HDef//9HM9RCFNjY2nNtz2+5PveX2FrZaPv+jp8WWZHz29k5ubnFMSZm5s3b07NmjXzxK0U8rKoqChKlCiBn58fnTt3fml8bGwsXl5ebNiwgYYNG+ZChum7c+cOHh4e/PHHH7Rs2RLQXb5fo0YNvvzyy3Sfl59f10IYy7WQ//RdXyqVSrq+8giZuVmITNJqtYSFhTFlyhQcHR155513MvU8GxsbVq1axYMHDwyc4Yv27dvHtm3buHnzJkePHqVbt254enrStGlTQHevrmrVqvHFF1/kem5CFHQVXD3Z/lzXV7fvPpcJD/MJGdwsTF5QUBBlypShZMmS+Pv7Y26e+V+L5s2bGy6xDCQmJvLll1/y77//UqhQIRo1asSaNWv0V4tZWloybtw4o+QmhCmwfdr11bBiLUasmcWhy3/Rcqovi/tOprFXHWOnJzIgXV3PKYhdXUKkR17XQry6K/du0n/Zl1wNvomZyowRHfrxeZtemJlJp0pukq4uIYQQIhd4uZdhx+iVfPB6W7SKllnbluKzcCgPo54YOzWRBil8hBBCiFdkZ2XDd70mMNd3HDYWVuz/5zitpvbg5PVzxk5NPEcKHyGEECKHfNioPdtHr6B88dIEP7nPu3P+x6Lda9K8SbMwDil8hBBCiBxUuUR5do5ZSae6b6HRapi8aQG9Fo/kSXSEsVMTSOEjhBBC5Dh7azsW953MzA9HYGluwa7zh2g9oxfnbl02dmomTwofIYQQwgBUKhW9mr3HryOWUaqYO0EP7tHh6/74H9woXV9GJIWPMBhPT0+Dzxb933//oVKpOHv2bKafo1Kp2LJli8FyEkKIlGqUrsTuMf60qdGUhKRERq/7mv+tnEh0XIyxUzNJUviIfKNXr1506tQp1ToPDw+Cg4OpWrVqpvcTHBzM22+/DWSvcBJCiKxytHPA75NZTHxvMGozNZtP7abNzD5cuXfT2KmZHCl8RL6mVqtxdXXN0mzLrq6uGd7BXQghDEGlUvHpWz5sGvo9roWduRbyH21m9mbTyV3GTs2kSOHzChRFITExySiPrPYPa7VaZs+eTfny5bGysqJUqVJMmzYNgAsXLtCiRQtsbGwoWrQoAwYMICoqSv/c5JaWb775Bjc3N4oWLcrAgQNJTEzUx4SFhdGhQwdsbGwoU6bMC3ctT6tl5cmTJ6hUKg4cOKBfd/HiRdq3b4+DgwOFChWiSZMm3Lhxg6+++oqAgAC2bt2KSqXSPy/lfrVaLSVLlmTx4sWpjh0YGIiZmRm3bt0CUnd1lSlTBoBatWqhUqlo3rw5f/75JxYWFoSEhKTaz5AhQ2jSpEmWzrsQQjyvQfma7BkbQJNKdYlNiON/Kycycu0s4hLjjZ2aSZB7db2CpCQNKwI2G+XYfXu+i4VF5v/7xowZw7Jly5g7dy5vvPEGwcHBXL58mejoaLy9vWnYsCGnTp0iLCyMfv36MWjQIPz9/fXP379/P25ubuzfv5/r16/TtWtXatasSf/+/QFdcXTv3j3279+PhYUFn332GWFhYVn6me7evUvTpk1p3rw5+/btw8HBgSNHjpCUlMTw4cO5dOkSERER+Pn5AVCkSBHu3bunf76ZmRkffvgha9eu5dNPP9WvX7NmDY0bN6Z06dIvHPPkyZPUr1+fP/74gypVqmBpaUmRIkUoW7Ysq1evZsSIEYDu3lhr1qxh9uzZWfqZhBAiLc4ORVj/2Xy++W0F83b4serPzZz97xLLB0ynVDF3Y6dXoEmLjwmIjIxk/vz5zJ49m549e1KuXDneeOMN+vXrx9q1a4mLi2PVqlVUrVqVFi1asHDhQlavXk1oaKh+H05OTixcuJBKlSrRvn172rVrx969ewG4evUqO3bsYNmyZbz++uvUqVOHFStWEBsbm6U8v//+ewoXLsz69eupW7cuFStWpHfv3nh5eWFvb4+NjQ1WVla4urri6uqKpaXlC/vw8fHhyJEjBAUFAbqWrvXr1+Pj45PmMZ2dnQEoWrQorq6uFClSBIC+ffvqCyyAX3/9lbi4OD744IMs/UxCCJEetZmaUe8MYM2gOTjZOXA+6DKtp/diz4Ujxk6tQJMWn1dgbq6mb893jXbszLp06RLx8fG0bNkyzW01atTAzs5Ov65x48ZotVquXLlC8eLFAahSpQpq9bNjurm5ceHCBf0+zM3NqVPn2R2JK1WqhKOjY5Z+prNnz9KkSRP9Hcazo2bNmlSuXJm1a9cyevRoDh48SFhYGF26dMnSfnr16sW4ceM4fvw4r7/+Ov7+/nzwwQepzpMQQuSEFlUasmfsKvov/ZLA//6hx/fDGPJ2L0Z06I/aLPPv9SJzpMXnFahUKiwszI3yUKlUmc7TxsbmlX/W54sRlUqFVqvN9POT71KccmxSyjFCkDN5gq7VZ+3atQCsXbuWNm3aULRo0Sztw8XFhQ4dOuDn50doaCg7duygT58+OZKfEEI8r2QRV7YOX0Kf5u8DMG+HP13nf879iEdGzqzgkcLHBFSoUAEbGxt911RKlStX5ty5c0RHR+vXHTlyBDMzM7y8vDK1/0qVKpGUlMTp06f1665cucKTJ0/0y8ldSsHBwfp1z19CXr16dQ4dOvRCQZTM0tISjUbz0ny6d+/O33//zenTp/nll1/S7eZK3ieQ5n779evHhg0bWLp0KeXKlaNx48YvPbYQQmSXpbkF07sN54e+U7C1suHwlb94a1pPudFpDpPCxwRYW1szatQoRo4cyapVq7hx4wbHjx9nxYoV+Pj4YG1tTc+ePfn777/Zv38/gwcPpkePHvpurpfx8vKiTZs2fPzxx5w4cYLTp0/Tr1+/VC04NjY2vP7668ycOZNLly5x8OBBxo0bl2o/gwYNIiIigm7duvHXX39x7do1Vq9ezZUrVwDdhIjnz5/nypUrPHjwIN0CydPTk0aNGtG3b180Gg3vvPNOurm7uLhgY2PDzp07CQ0NJTw8XL/N29sbBwcHpk6dSu/evTN1LoQQ4lV1qvcWO0evpIKrJyHh9+k8538s3bteZnvOIVL4mIjx48czbNgwJkyYQOXKlenatSthYWHY2tqya9cuHj16RL169Xj//fdp2bIlCxcuzNL+/fz8cHd3p1mzZnTu3JkBAwbg4uKSKmblypUkJSVRp04dhgwZwtSpU1NtL1q0KPv27SMqKopmzZpRp04dli1bpu9m69+/P15eXtStWxdnZ2eOHEl/AKCPjw/nzp3j3XffzbALzdzcnO+++44lS5bg7u5Ox44d9dvMzMzo1asXGo0GX1/fLJ0PIYR4FRXdyrBztO5Gp0laDRN+nseAZeOIiot++ZNFhlSKlJCpREREULhwYcLDw3FwcNCvj4uL4+bNm5QpUwZra2sjZihyU9++fbl//z7btm0zdioGIa9rIfI2RVFYceBnvvp5PklaDRVcS7N8wEy83MsYO7U8J73P7+dJi48QaQgPD+fw4cOsXbuWwYMHGzsdIYSJUqlU9HvzA7YM/wE3R2euhdzi7Vl92HJqj7FTy7ek8BEiDR07dqR169Z88sknvPXWW8ZORwhh4uqWrcbuLwN4w6suMfGxfLJiPOM2zCEhKe2xjiJ9UvgIkYYDBw4QExPD3LlzjZ2KEEIAutmeN3w+n8/b9ARg+f6feG/O/wh+nLVZ8k2dFD5CCCFEPqE2UzOm06es+t/XONjYc+rfC7w1vSdHrpx++ZMFIIWPEEIIke+0rt6EXWP8eK1EeR5EPuaD+Z/x/e4f5ZL3TJDCRwghhMiHyrh48Nuo5bzf4G00Wg1TNi2k39IxRMbKJe8ZkcJHCCGEyKdsLa1Z0GsCMz8cgYXanN8DD/D2zD5cuXfT2KnlWVL4CCGEEPmYSqWiV7P32DJMd8n79VDdJe/bTr94myIhhY8QQghRINQpW5XdXwbQ2KsOMfGxDFg2lq9++Y4kTZKxU8tTpPARQgghCghnhyJs+Gw+A1t/BMAPf6yly7zB3I94aOTM8g4pfEzAn3/+SYcOHXB3d0elUrFlyxZjpySEEMJAzNXmjO88iOUDpmNnZcuxa4G0nt6L0//+bezU8gQpfExAdHQ0NWrU4Pvvvzd2KkIIIXJJ+9ot2DF6BRVcSxP85D6dvv2EgD83mfwl7+bGTqAgUOLi099oZobK0iJzsSoVKivLl8aqrK2ylN/bb7/N22+/naXnCCGEyP8qupVhx+iVfB4wld8D9zNq7WzO3LzIzA9HYGNpmjcmlsInB8R0HZruNnWdKlhP+N+zWN/REJ+QZqxZ1QrYTBvyLLb/BIiIeiHObqu03AghhMgce2s7lg+Yzve7f2T6lsVsOPY7l+5eZ8XHM/Eo6mbs9HKddHUJIYQQBZxKpWKQdw82fD6fInaFOR90Be/pvfjz0kljp5brpMUnB9humJP+RrPUtaXtqpnpx6pUqWOXTX6VtIQQQohUmlSqx64v/em7ZAzngy7T7bshfNnpUwa2/gjVc59BBZW0+OQAlbVV+o8U43teGptifE9GsUIIIUR2eRR1Y9uIJXRr1B6tomXq5u/pt/RLouJM41YXUvgIIYQQJsbawoq5PcYyu/uop7e62E/bWf24ERpk7NQMLt8VPvHx8dSsWROVSsXZs2dTbTt//jxNmjTB2toaDw8PZs+ebZwk85ioqCjOnj2rP183b97k7NmzBAUV/Be4EEKItKlUKnybvsvmYYtxLezM1eCbtJnRm93nDxk7NYPKd4XPyJEjcXd3f2F9REQErVu3pnTp0pw+fZqvv/6ar776iqVLlxohy7zlr7/+olatWtSqVQuAoUOHUqtWLSZMmGDkzIQQQhhb3bLV2P2lPw3K1yAyLhrfRSOY/esytFqtsVMziHxV+OzYsYPdu3fzzTffvLBtzZo1JCQksHLlSqpUqUK3bt347LPPmDMng4HH6FqQIiIiUj0KmubNm6MoygsPf39/Y6cmhBAiD3ApXJSfhyykT/P3AZjz+wp6Lh5BeEykkTPLefmm8AkNDaV///6sXr0aW1vbF7YfO3aMpk2bYmn5bICwt7c3V65c4fHjx+nud8aMGRQuXFj/8PDwMEj+QgghRF5maW7B9G7Dmd9zPFbmluy5cIS3Z/bhyr2bxk4tR+WLwkdRFHr16sUnn3xC3bp104wJCQmhePHiqdYlL4eEhKS77zFjxhAeHq5/3L59O+cSF0IIIfKZrg3bsW3EUko4FeffsNu0ndWX3wP3GzutHGPUwmf06NGoVKoMH5cvX2bBggVERkYyZsyYHM/BysoKBweHVA8hhBDClNUoXYldX/rTqGJtouNj6LtkDDO3/oBGqzF2aq/MqBMYDhs2jF69emUYU7ZsWfbt28exY8ewsko9h03dunXx8fEhICAAV1dXQkNDU21PXnZ1dc3RvIUQQoiCrlghJ376/DumbFrIkr3rmbfDnwu3r7KozyQK2xYydnrZZtTCx9nZGWdn55fGfffdd0ydOlW/fO/ePby9vdmwYQMNGjQAoGHDhowdO5bExEQsLHSTBu7ZswcvLy+cnJwM8wMIIYQQBZi52pxJXYZQvVQlhv04g71/H+XtmX3w+2Q2Xu5ljJ1etuSLMT6lSpWiatWq+kfFihUBKFeuHCVLlgSge/fuWFpa0rdvXy5evMiGDRuYP38+Q4emfwNRIYQQQrzcew3asG3EEkoUcdWP+9keeMDYaWVLvih8MqNw4cLs3r2bmzdvUqdOHYYNG8aECRMYMGCAsVMTQggh8r3qpSqxa4wfjb3qEB0fQ58lo5m1bWm+m+9HpSiKYuwk8pKIiAgKFy5MeHh4qoHOcXFx3Lx5kzJlymBtbW3EDIXIOfK6FkJkVZImickbF7J033oA3qrWmO/7TMLBxt6oeaX3+f28AtPiI4QQQgjDM1ebM/mDISzoNVE/30/bmX25HnLL2KllihQ+QgghhMiyLq+/zdYRS3B3cuF66C3entknX9znSwofE/L999/j6emJtbU1DRo04OTJk8ZOSQghRD5Ws3Rldo3x4/XyNYmMi6bn4pHM3b6SvDyKRgofE7FhwwaGDh3KxIkTOXPmDDVq1MDb25uwsDBjpyaEECIfc3Yoyk9DFtCr2XsoisKsbUvpt/RLouNijJ1amqTwyQHR8ek/4hIzHxubkLnY7JgzZw79+/end+/evPbaa/zwww/Y2tqycuXK7O1QCCGEeMrS3IKZH47g24/GYKE25/fA/bT/uj+37t81dmovMOoEhgWF/f/S39a2Gvw+5NmyyxCISUg7tpkXHBj5bNlzJDyIejFOWZG1/BISEjh9+nSqW36YmZnRqlUrjh07lrWdCSGEEOnweaMjFd3K0HfJGC7dvYH3jN4s7T+VppXrGzs1PWnxMQEPHjxAo9GkeRPXjG7gKoQQQmRVvXLV2TXGj5qlX+NJTATdvhvC0r3r88y4H2nxyQFRi9Lfpn6utAybl36smSr18n+zs52SEEIIYTRuTi5sGb6YkWtm8dPx7Uz4eR5/377KbJ9RWFtYvXwHBiSFTw6wy8L/oaFiM1KsWDHUanWaN3GVG7gKIYQwBGsLK+b3HE9Vj4p89ct3/HR8O9dC/mPlxzNxc3IxWl7S1WUCLC0tqVOnDnv37tWv02q17N27l4YNGxoxMyGEEAWZSqViQMturP9sHo62DgT+9w/eM3pz5d5No+UkhY+JGDp0KMuWLSMgIIBLly7x6aefEh0dTe/evY2dmhBCiAKuaeX67ByzEi/3sjg7FKFkUeP1NkhXl4no2rUr9+/fZ8KECYSEhFCzZk127tz5woBnIYQQwhA8nUvy+8hlRMZGY2dlY7Q8pPAxIYMGDWLQoEHGTkMIIYSJsre2w97azqg5SFeXEEIIIUyGFD5CCCGEMBlS+AghhBDCZEjhI4QQQgiTIYVPFuWVKbeFyAnyehZCmBopfDLJwsICgJiYGCNnIkTOSX49J7++hRCioJPL2TNJrVbj6OhIWFgYALa2tqhUqpc8S4i8SVEUYmJiCAsLw9HREbVabeyUhBAiV0jhkwXJ97VKLn6EyO8cHR3lfm1CCJMihU8WqFQq3NzccHFxITEx0djpCPFKLCwspKVHCGFypPDJBrVaLR8YQgghRD4kg5uFEEIIYTKk8BFCCCGEyZDCRwghhBAmQ8b4PCd5QreIiAgjZyKEEEKIzEr+3H7ZxKxS+DwnMjISAA8PDyNnIoQQQoisioyMpHDhwuluVykyZ30qWq2We/fuUahQoRydoDAiIgIPDw9u376Ng4NDju1XpCbnOXfIec49cq5zh5zn3GHI86woCpGRkbi7u2Nmlv5IHmnxeY6ZmRklS5Y02P4dHBzklyoXyHnOHXKec4+c69wh5zl3GOo8Z9TSk0wGNwshhBDCZEjhI4QQQgiTIYVPLrGysmLixIlYWVkZO5UCTc5z7pDznHvkXOcOOc+5Iy+cZxncLIQQQgiTIS0+QgghhDAZUvgIIYQQwmRI4SOEEEIIkyGFjxBCCCFMhhQ+Oej777/H09MTa2trGjRowMmTJ9ON9ff3R6VSpXpYW1vnYrb5V1bOM8CTJ08YOHAgbm5uWFlZUbFiRbZv355L2eZfWTnPzZs3f+H1rFKpaNeuXS5mnD9l9fU8b948vLy8sLGxwcPDgy+++IK4uLhcyjZ/y8q5TkxMZPLkyZQrVw5ra2tq1KjBzp07czHb/OnPP/+kQ4cOuLu7o1Kp2LJly0ufc+DAAWrXro2VlRXly5fH39/fsEkqIkesX79esbS0VFauXKlcvHhR6d+/v+Lo6KiEhoamGe/n56c4ODgowcHB+kdISEguZ53/ZPU8x8fHK3Xr1lXatm2rHD58WLl586Zy4MAB5ezZs7mcef6S1fP88OHDVK/lv//+W1Gr1Yqfn1/uJp7PZPU8r1mzRrGyslLWrFmj3Lx5U9m1a5fi5uamfPHFF7mcef6T1XM9cuRIxd3dXfn999+VGzduKIsWLVKsra2VM2fO5HLm+cv27duVsWPHKps2bVIAZfPmzRnG//vvv4qtra0ydOhQ5Z9//lEWLFigqNVqZefOnQbLUQqfHFK/fn1l4MCB+mWNRqO4u7srM2bMSDPez89PKVy4cC5lV3Bk9TwvXrxYKVu2rJKQkJBbKRYIWT3Pz5s7d65SqFAhJSoqylApFghZPc8DBw5UWrRokWrd0KFDlcaNGxs0z4Igq+fazc1NWbhwYap1nTt3Vnx8fAyaZ0GSmcJn5MiRSpUqVVKt69q1q+Lt7W2wvKSrKwckJCRw+vRpWrVqpV9nZmZGq1atOHbsWLrPi4qKonTp0nh4eNCxY0cuXryYG+nmW9k5z9u2baNhw4YMHDiQ4sWLU7VqVaZPn45Go8mttPOd7L6eU1qxYgXdunXDzs7OUGnme9k5z40aNeL06dP6Lpp///2X7du307Zt21zJOb/KzrmOj49/YfiBjY0Nhw8fNmiupubYsWOp/l8AvL29M/1ekx1S+OSABw8eoNFoKF68eKr1xYsXJyQkJM3neHl5sXLlSrZu3cqPP/6IVqulUaNG3LlzJzdSzpeyc57//fdffvnlFzQaDdu3b2f8+PF8++23TJ06NTdSzpeyc55TOnnyJH///Tf9+vUzVIoFQnbOc/fu3Zk8eTJvvPEGFhYWlCtXjubNm/Pll1/mRsr5VnbOtbe3N3PmzOHatWtotVr27NnDpk2bCA4Ozo2UTUZISEia/y8RERHExsYa5JhS+BhJw4YN8fX1pWbNmjRr1oxNmzbh7OzMkiVLjJ1agaLVanFxcWHp0qXUqVOHrl27MnbsWH744Qdjp1ZgrVixgmrVqlG/fn1jp1LgHDhwgOnTp7No0SLOnDnDpk2b+P3335kyZYqxUytw5s+fT4UKFahUqRKWlpYMGjSI3r17Y2YmH5v5nbmxEygIihUrhlqtJjQ0NNX60NBQXF1dM7UPCwsLatWqxfXr1w2RYoGQnfPs5uaGhYUFarVav65y5cqEhISQkJCApaWlQXPOj17l9RwdHc369euZPHmyIVMsELJznsePH0+PHj30rWnVqlUjOjqaAQMGMHbsWPlQTkd2zrWzszNbtmwhLi6Ohw8f4u7uzujRoylbtmxupGwyXF1d0/x/cXBwwMbGxiDHlN+SHGBpaUmdOnXYu3evfp1Wq2Xv3r00bNgwU/vQaDRcuHABNzc3Q6WZ72XnPDdu3Jjr16+j1Wr1665evYqbm5sUPel4ldfzzz//THx8PB999JGh08z3snOeY2JiXihukot6RW67mK5XeU1bW1tTokQJkpKS2LhxIx07djR0uialYcOGqf5fAPbs2ZPpz85sMdiwaROzfv16xcrKSvH391f++ecfZcCAAYqjo6P+EvUePXooo0eP1sdPmjRJ2bVrl3Ljxg3l9OnTSrdu3RRra2vl4sWLxvoR8oWsnuegoCClUKFCyqBBg5QrV64ov/32m+Li4qJMnTrVWD9CvpDV85zsjTfeULp27Zrb6eZbWT3PEydOVAoVKqSsW7dO+ffff5Xdu3cr5cqVUz744ANj/Qj5RlbP9fHjx5WNGzcqN27cUP7880+lRYsWSpkyZZTHjx8b6SfIHyIjI5XAwEAlMDBQAZQ5c+YogYGByq1btxRFUZTRo0crPXr00McnX84+YsQI5dKlS8r3338vl7PnJwsWLFBKlSqlWFpaKvXr11eOHz+u39asWTOlZ8+e+uUhQ4boY4sXL660bdtW5ofIpKycZ0VRlKNHjyoNGjRQrKyslLJlyyrTpk1TkpKScjnr/Cer5/ny5csKoOzevTuXM83fsnKeExMTla+++kopV66cYm1trXh4eCj/+9//5MM4k7Jyrg8cOKBUrlxZsbKyUooWLar06NFDuXv3rhGyzl/279+vAC88ks9tz549lWbNmr3wnJo1ayqWlpZK2bJlDT7/l0pRpH1UCCGEEKZBxvgIIYQQwmRI4SOEEEIIkyGFjxBCCCFMhhQ+QgghhDAZUvgIIYQQwmRI4SOEEEIIkyGFjxBCCCFMhhQ+QgghhDAZUvgIIfIklUrFli1bjJ0GAF999RU1a9bM1nN79OjB9OnTczahNIwePZrBgwcb/DhC5HdS+AghRAo5WXCdO3eO7du389lnn+XI/jIyfPhwAgIC+Pfffw1+LCHyMyl8hBDCQBYsWECXLl2wt7c3+LGKFSuGt7c3ixcvNvixhMjPpPARwsT99ttvODo6otFoADh79iwqlYrRo0frY/r168dHH30EwMOHD/nwww8pUaIEtra2VKtWjXXr1uljly5diru7O1qtNtVxOnbsSJ8+ffTLW7dupXbt2lhbW1O2bFkmTZpEUlJSunnevn2bDz74AEdHR4oUKULHjh3577//9Nt79epFp06d+Oabb3Bzc6No0aIMHDiQxMREfUxwcDDt2rXDxsaGMmXKsHbtWjw9PZk3bx4Anp6eALz77ruoVCr9crLVq1fj6elJ4cKF6datG5GRkenmq9Fo+OWXX+jQoUOq9Wm1KDk6OuLv7w/Af//9h0ql4qeffqJJkybY2NhQr149rl69yqlTp6hbty729va8/fbb3L9/P9V+OnTowPr169PNSQghhY8QJq9JkyZERkYSGBgIwMGDBylWrBgHDhzQxxw8eJDmzZsDEBcXR506dfj999/5+++/GTBgAD169ODkyZMAdOnShYcPH7J//3798x89esTOnTvx8fEB4NChQ/j6+vL555/zzz//sGTJEvz9/Zk2bVqaOSYmJuLt7U2hQoU4dOgQR44cwd7enjZt2pCQkKCP279/Pzdu3GD//v0EBATg7++vLygAfH19uXfvHgcOHGDjxo0sXbqUsLAw/fZTp04B4OfnR3BwsH4Z4MaNG2zZsoXffvuN3377jYMHDzJz5sx0z+v58+cJDw+nbt26GZ3+dE2cOJFx48Zx5swZzM3N6d69OyNHjmT+/PkcOnSI69evM2HChFTPqV+/Pnfu3ElVEAohnmPQe78LIfKF2rVrK19//bWiKIrSqVMnZdq0aYqlpaUSGRmp3LlzRwGUq1evpvv8du3aKcOGDdMvd+zYUenTp49+ecmSJYq7u7ui0WgURVGUli1bKtOnT0+1j9WrVytubm76ZUDZvHmzfpuXl5ei1Wr12+Pj4xUbGxtl165diqIoSs+ePZXSpUsrSUlJ+pguXbooXbt2VRRFUS5duqQAyqlTp/Tbr127pgDK3Llz0zxusokTJyq2trZKRESEft2IESOUBg0apHtONm/erKjV6lQ5p7f/woULK35+foqiKMrNmzcVQFm+fLl++7p16xRA2bt3r37djBkzFC8vr1T7CQ8PVwDlwIED6eYlhKmTFh8hBM2aNePAgQMoisKhQ4fo3LkzlStX5vDhwxw8eBB3d3cqVKgA6LpwpkyZQrVq1ShSpAj29vbs2rWLoKAg/f58fHzYuHEj8fHxAKxZs4Zu3bphZqZ7yzl37hyTJ0/G3t5e/+jfvz/BwcHExMS8kN+5c+e4fv06hQoV0scXKVKEuLg4bty4oY+rUqUKarVav+zm5qZv0bly5Qrm5ubUrl1bv718+fI4OTll6hx5enpSqFChNPedltjYWKysrFCpVJna//OqV6+u/7548eIAVKtWLdW6549vY2MDkOY5FELomBs7ASGE8TVv3pyVK1dy7tw5LCwsqFSpEs2bN+fAgQM8fvyYZs2a6WO//vpr5s+fz7x586hWrRp2dnYMGTIkVZdThw4dUBSF33//nXr16nHo0CHmzp2r3x4VFcWkSZPo3LnzC7lYW1u/sC4qKoo6deqwZs2aF7Y5Ozvrv7ewsEi1TaVSvTDWKLuyuu9ixYoRExNDQkIClpaWqZ6nKEqq2JTjkNI6XnLx9Py654//6NEjIPU5EUKkJoWPEEI/zmfu3Ln6Iqd58+bMnDmTx48fM2zYMH3skSNH6Nixo36ws1ar5erVq7z22mv6GGtrazp37syaNWu4fv06Xl5eqVpaateuzZUrVyhfvnym8qtduzYbNmzAxcUFBweHbP2MXl5eJCUlERgYSJ06dQC4fv06jx8/ThVnYWGhH+j9KpLn/fnnn39SzQHk7OxMcHCwfvnatWs51kLz999/Y2FhQZUqVXJkf0IURNLVJYTAycmJ6tWrs2bNGv0g5qZNm3LmzBmuXr2aqsWnQoUK7Nmzh6NHj3Lp0iU+/vhjQkNDX9inj48Pv//+OytXrtQPak42YcIEVq1axaRJk7h48SKXLl1i/fr1jBs3Ls38fHx8KFasGB07duTQoUPcvHmTAwcO8Nlnn3Hnzp1M/YyVKlWiVatWDBgwgJMnTxIYGMiAAQOwsbFJ1R3l6enJ3r17CQkJeaEoygpnZ2dq167N4cOHU61v0aIFCxcuJDAwkL/++otPPvnkhdak7Dp06JD+SjAhRNqk8BFCALpxPhqNRl/4FClShNdeew1XV1e8vLz0cePGjaN27dp4e3vTvHlzXF1d6dSp0wv7a9GiBUWKFOHKlSt079491TZvb29+++03du/eTb169Xj99deZO3cupUuXTjM3W1tb/vzzT0qVKqUff9S3b1/i4uKy1AK0atUqihcvTtOmTXn33Xfp378/hQoVStW99u2337Jnzx48PDyoVatWpvedln79+r3QPfftt9/i4eFBkyZN6N69O8OHD8fW1vaVjpNs/fr19O/fP0f2JURBpVKe72wWQggTcefOHTw8PPjjjz9o2bJlju8/NjYWLy8vNmzYQMOGDXN8/ynt2LGDYcOGcf78eczNZRSDEOmR3w4hhMnYt28fUVFRVKtWjeDgYEaOHImnpydNmzY1yPFsbGxYtWoVDx48MMj+U4qOjsbPz0+KHiFeQlp8hBAmY9euXQwbNox///2XQoUK0ahRI+bNm5duF5sQouCRwkcIIYQQJkMGNwshhBDCZEjhI4QQQgiTIYWPEEIIIUyGFD5CCCGEMBlS+AghhBDCZEjhI4QQQgiTIYWPEEIIIUyGFD5CCCGEMBn/B5mFgqg/bcJXAAAAAElFTkSuQmCC"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 60
  },
  {
   "cell_type": "code",
   "id": "2006bd45-e462-49cf-931e-f6dcb3fc326b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.095081Z",
     "start_time": "2026-03-17T09:13:22.010536Z"
    }
   },
   "source": [
    "density_values = np.linspace(0, 1, 101)\n",
    "eps_complex = 0j * np.zeros_like(density_values)\n",
    "for i, d in enumerate(density_values):\n",
    "    new_eps_inf = 1.0 + d * (medium_gold.eps_inf - 1)\n",
    "    new_poles = [(a, c * d) for (a, c) in medium_gold.poles]\n",
    "    new_medium = medium_gold.updated_copy(eps_inf=new_eps_inf, poles=new_poles)\n",
    "    eps_complex[i] = new_medium.eps_model(freq)\n",
    "\n",
    "eps_real, sigma = medium_gold.eps_complex_to_eps_sigma(eps_complex, freq=freq)\n",
    "plt.plot(density_values, eps_real, label=\"permittivity (real)\")\n",
    "plt.plot(wvls, eps_complex.imag, label=\"permittivity (imag)\")\n",
    "plt.plot(density_values, sigma, label=\"conductivity\")\n",
    "plt.plot(density_values, np.ones_like(eps_real), label=\"1\", linestyle=\"--\")\n",
    "plt.plot(density_values, np.zeros_like(eps_real), label=\"0\", linestyle=\"--\")\n",
    "plt.xlabel(\"density value\")\n",
    "plt.ylabel(\"relative permittivity\")\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 61
  },
  {
   "cell_type": "markdown",
   "id": "d8543e97-047b-499b-9ed6-a1bb44d4d818",
   "metadata": {},
   "source": [
    "Next we define the geometric parameters describing our device.\n",
    "\n",
    "We have a rectangular metal slab sitting on top of a SiO2 substrate with air on top. \n",
    "\n",
    "The rectangular slab has a hole in the center, where we'll be measuring the field intensity enhancement."
   ]
  },
  {
   "cell_type": "code",
   "id": "efd2622a-2b11-4047-8576-49479ab4aea3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.101408Z",
     "start_time": "2026-03-17T09:13:22.099670Z"
    }
   },
   "source": [
    "size_design_x = 500 * nm\n",
    "size_design_y = 500 * nm\n",
    "thick_metal = 50 * nm\n",
    "thick_sub = 0.8 * wavelength\n",
    "thick_air = 0.8 * wavelength\n",
    "buffer_xy = 0.0 * wavelength\n",
    "\n",
    "hole_radius = 12 * nm"
   ],
   "outputs": [],
   "execution_count": 62
  },
  {
   "cell_type": "markdown",
   "id": "727bf15f-b121-4e66-bd71-34c23e62118b",
   "metadata": {},
   "source": [
    "We derive the total sizes needed for our simulation in all dimensions."
   ]
  },
  {
   "cell_type": "code",
   "id": "564b6050-8bd4-47a9-ba8d-9e147410db28",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.147129Z",
     "start_time": "2026-03-17T09:13:22.145450Z"
    }
   },
   "source": [
    "size_x = size_design_x + 2 * buffer_xy\n",
    "size_y = size_design_y + 2 * buffer_xy\n",
    "size_z = thick_sub + thick_metal + thick_air"
   ],
   "outputs": [],
   "execution_count": 63
  },
  {
   "cell_type": "markdown",
   "id": "84581acb-b824-484a-a059-399cd352fe51",
   "metadata": {},
   "source": [
    "As well as set some variables to help us keep track of location within the simulation."
   ]
  },
  {
   "cell_type": "code",
   "id": "fcab2178-fcea-4d51-83a8-3555c31b5c08",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.191680Z",
     "start_time": "2026-03-17T09:13:22.190036Z"
    }
   },
   "source": [
    "top_z = size_z / 2.0\n",
    "\n",
    "center_air_z = top_z - thick_air / 2.0\n",
    "center_metal_z = top_z - thick_air - thick_metal / 2.0\n",
    "center_sub_z = top_z - thick_air - thick_metal - thick_sub / 2.0"
   ],
   "outputs": [],
   "execution_count": 64
  },
  {
   "cell_type": "markdown",
   "id": "01369fa3-885e-44e0-ba0f-bdddfe07c23e",
   "metadata": {},
   "source": [
    "Next, we define our static components, such as the substrate, source, and monitors.\n",
    "\n",
    "We will include the pattern gold film later on, but we set the geometry as a `td.Box` here so we can use it later.\n",
    "\n",
    "All of these components will be combined into our base `td.Simulation`, which defines our setup without any gold film."
   ]
  },
  {
   "cell_type": "code",
   "id": "dd0ef553-b672-465a-869b-6c171fa13cd4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.243647Z",
     "start_time": "2026-03-17T09:13:22.234712Z"
    }
   },
   "source": [
    "design_region_geometry = td.Box(\n",
    "    center=(0, 0, center_metal_z),\n",
    "    size=(td.inf, td.inf, thick_metal),\n",
    ")\n",
    "\n",
    "substrate = td.Structure(\n",
    "    geometry=td.Box(\n",
    "        center=(0, 0, -size_z + thick_sub),\n",
    "        size=(td.inf, td.inf, size_z),\n",
    "    ),\n",
    "    medium=medium_SiO2,\n",
    ")\n",
    "\n",
    "plane_wave = td.PlaneWave(\n",
    "    center=(0, 0, center_air_z),\n",
    "    size=(td.inf, td.inf, 0),\n",
    "    source_time=td.GaussianPulse(freq0=freq, fwidth=fwidth),\n",
    "    pol_angle=0,\n",
    "    direction=\"-\",\n",
    ")\n",
    "\n",
    "point_monitor = td.FieldMonitor(\n",
    "    size=(0, 0, 0),\n",
    "    center=(0, 0, center_metal_z),\n",
    "    freqs=[freq],\n",
    "    name=\"point\",\n",
    ")\n",
    "\n",
    "field_monitor_xy = td.FieldMonitor(\n",
    "    center=(0, 0, center_metal_z),\n",
    "    size=(td.inf, td.inf, 0),\n",
    "    freqs=[freq],\n",
    "    name=\"field_xy\",\n",
    ")\n",
    "\n",
    "eps_monitor_xy = td.PermittivityMonitor(\n",
    "    center=(0, 0, center_metal_z),\n",
    "    size=(td.inf, td.inf, 0),\n",
    "    freqs=[freq],\n",
    "    name=\"eps_xy\",\n",
    ")\n",
    "\n",
    "field_monitor_xz = td.FieldMonitor(\n",
    "    center=(0, 0, 0),\n",
    "    size=(td.inf, 0, td.inf),\n",
    "    freqs=[freq],\n",
    "    name=\"field_xz\",\n",
    ")\n",
    "\n",
    "sim_no_antenna = td.Simulation(\n",
    "    size=(size_x, size_y, size_z),\n",
    "    run_time=run_time,\n",
    "    structures=[substrate],\n",
    "    sources=[plane_wave],\n",
    "    monitors=[point_monitor, field_monitor_xy, field_monitor_xz, eps_monitor_xy],\n",
    "    grid_spec=td.GridSpec.uniform(dl=dl),\n",
    "    boundary_spec=td.BoundarySpec.pml(x=False, y=False, z=True),\n",
    "    # grid_spec=td.GridSpec.auto(wavelength=wavelength, min_steps_per_wvl=min_steps_per_wvl),\n",
    ")"
   ],
   "outputs": [],
   "execution_count": 65
  },
  {
   "cell_type": "code",
   "id": "83ffebd8-197b-42a2-adf3-ad6d0e887dd1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.476872Z",
     "start_time": "2026-03-17T09:13:22.289571Z"
    }
   },
   "source": [
    "# shift the plot positions a little so the field monitors don't overlap plots\n",
    "shift_plot = 0.01\n",
    "\n",
    "f, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(10, 4), tight_layout=True)\n",
    "sim_no_antenna.plot(x=0.0 + shift_plot, ax=ax1)\n",
    "sim_no_antenna.plot(y=0.0 + shift_plot, ax=ax2)\n",
    "sim_no_antenna.plot(z=center_metal_z + shift_plot, ax=ax3)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 66
  },
  {
   "cell_type": "markdown",
   "id": "df0ab8c5-f286-4b21-9186-3f25008c7e17",
   "metadata": {},
   "source": [
    "## Antenna Parameterization\n",
    "\n",
    "Next, we'll define our antenna as a `td.Structure`, which we add to the simulation.\n",
    "\n",
    "We will be optimizing this pattern with respect to an array of parameters. So it makes sense to write our components from here on as functions so we can update them as they change.\n",
    "\n",
    "We start by defining some variables to define our design parameterization, such as the pixel size, feature size, and projection (binarization) strength."
   ]
  },
  {
   "cell_type": "code",
   "id": "61067dea-f204-4291-bd87-028300b33c4a",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.496537Z",
     "start_time": "2026-03-17T09:13:22.494783Z"
    }
   },
   "source": [
    "# resolution of the design region pixels\n",
    "# pixel_size = 10 * nm\n",
    "pixel_size = dl\n",
    "\n",
    "# radius of the circular filter (um) (higher = larger features)\n",
    "radius = 24 * nm\n",
    "\n",
    "# projection strengths (higher = more binarized)\n",
    "beta_project = 10\n",
    "beta_penalty = 10"
   ],
   "outputs": [],
   "execution_count": 67
  },
  {
   "cell_type": "markdown",
   "id": "629781cd-ec35-4348-acaa-6c6c2dcef1eb",
   "metadata": {},
   "source": [
    "Next, we write a function to get the density (between 0 and 1) of gold on our film as a function of our optimization parameters.\n",
    "\n",
    "> Note: there are many helper functions in `tidy3d.plugins.autograd` that are used for inverse design. These have very close analogues in the `adjoint` plugin, but are compatible with `autograd` and have extra features added."
   ]
  },
  {
   "cell_type": "code",
   "id": "82bc9aa3-6387-49e0-81dc-482b5f945c6b",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.541973Z",
     "start_time": "2026-03-17T09:13:22.540183Z"
    }
   },
   "source": [
    "from tidy3d.plugins.autograd import make_filter_and_project\n",
    "\n",
    "\n",
    "def get_density(params: np.ndarray, beta: float = beta_project) -> np.ndarray:\n",
    "    \"\"\"Generic function to get the etch density as a function of design parameters, using filter and projection.\"\"\"\n",
    "    filter_project = make_filter_and_project(radius, pixel_size, beta=beta)\n",
    "    return filter_project(params)"
   ],
   "outputs": [],
   "execution_count": 68
  },
  {
   "cell_type": "markdown",
   "id": "e4edf464-9ee5-4b49-b288-94f4e4867bb0",
   "metadata": {},
   "source": [
    "Next, we need to generate the `td.Structure` containing the gold film by modifying the material properties of the gold model from our material library.\n",
    "\n",
    "We use a `td.CustomPoleResidue` to define a spatially-varying dispersive medium. The relative permittivity at infinite frequency (`eps_inf`) is set between that of air (1) and that of the gold `eps_inf` linearly, depending on the density value at each point. The numerator of the `poles` are also multiplied by the density so that they interpolate between values of 0 for density of 0 and the values for gold when density is 1.\n",
    "\n",
    "We apply the mask over the central region to set it to air and combine everything together into a `td.Structure`."
   ]
  },
  {
   "cell_type": "code",
   "id": "ad55b6d0-efae-4c2f-a4ab-28e7fb726ea1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.586345Z",
     "start_time": "2026-03-17T09:13:22.583699Z"
    }
   },
   "source": [
    "def make_antenna_from_density(density: np.ndarray) -> td.Structure:\n",
    "    \"\"\"Make a `td.Structure` containing a `td.CustomPoleResidue` corresponding to a density array.\"\"\"\n",
    "\n",
    "    rmin, rmax = sim_no_antenna.bounds\n",
    "    coords = {}\n",
    "    for key, pt_min, pt_max, num_pts in zip(\"xyz\", rmin, rmax, density.shape):\n",
    "        coord_edges = np.linspace(pt_min, pt_max, num_pts + 1)\n",
    "        coord_centers = (coord_edges[1:] + coord_edges[:-1]) / 2.0\n",
    "        coords[key] = coord_centers\n",
    "\n",
    "    mask = td.ScalarFieldDataArray(\n",
    "        np.ones_like(density),\n",
    "        coords=coords,\n",
    "    )\n",
    "    is_in_hole = mask.x**2 + mask.y**2 >= hole_radius**2\n",
    "    mask = mask.where(is_in_hole, 0)\n",
    "\n",
    "    density_masked = density * mask.values\n",
    "\n",
    "    eps_inf_scaled_array = eps_background + density_masked * (medium_gold.eps_inf - eps_background)\n",
    "\n",
    "    poles_arrays_scaled = [\n",
    "        (a * np.ones_like(density_masked), c * density_masked) for (a, c) in medium_gold.poles\n",
    "    ]\n",
    "\n",
    "    eps_inf_scaled = td.ScalarFieldDataArray(\n",
    "        eps_inf_scaled_array,\n",
    "        coords=coords,\n",
    "    )\n",
    "\n",
    "    poles_scaled = []\n",
    "    for a_array, c_array in poles_arrays_scaled:\n",
    "        a_scaled = td.ScalarFieldDataArray(a_array, coords=coords)\n",
    "        c_scaled = td.ScalarFieldDataArray(c_array, coords=coords)\n",
    "        poles_scaled.append((a_scaled, c_scaled))\n",
    "\n",
    "    medium_gold_scaled = td.CustomPoleResidue(\n",
    "        eps_inf=eps_inf_scaled, poles=poles_scaled, interp_method=\"linear\"\n",
    "    )\n",
    "\n",
    "    return td.Structure(geometry=design_region_geometry, medium=medium_gold_scaled)"
   ],
   "outputs": [],
   "execution_count": 69
  },
  {
   "cell_type": "markdown",
   "id": "720bde9d-0906-4098-9ac4-d8c06aae9e51",
   "metadata": {},
   "source": [
    "Next we write a quick helper function to create the `td.Structure` as a function of the optimization parameters."
   ]
  },
  {
   "cell_type": "code",
   "id": "24c63879-5031-45ca-8ba1-34bb24b80e01",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.631223Z",
     "start_time": "2026-03-17T09:13:22.629771Z"
    }
   },
   "source": [
    "def make_antenna(params: np.ndarray, beta: float = beta_project) -> td.Structure:\n",
    "    \"\"\"Make the antenna structure.\"\"\"\n",
    "    density = get_density(params, beta=beta)\n",
    "    return make_antenna_from_density(density)"
   ],
   "outputs": [],
   "execution_count": 70
  },
  {
   "cell_type": "markdown",
   "id": "7ce00266-df6b-4aa6-a237-a49c637708e0",
   "metadata": {},
   "source": [
    "We also write a function that generates a `td.Simulation` with the structure added to our original simulation."
   ]
  },
  {
   "cell_type": "code",
   "id": "365091d4-a65c-4f71-af3f-8247337742d6",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.675441Z",
     "start_time": "2026-03-17T09:13:22.673818Z"
    }
   },
   "source": [
    "def make_sim_with_antenna(\n",
    "    params: np.ndarray, include_field_mnts: bool = True, beta: float = beta_project\n",
    ") -> td.Simulation:\n",
    "    \"\"\"Make a simulation as a function of the density parameters for the antenna regions.\"\"\"\n",
    "\n",
    "    antenna = make_antenna(params, beta=beta)\n",
    "\n",
    "    sim = sim_no_antenna.updated_copy(\n",
    "        structures=list(sim_no_antenna.structures) + [antenna],\n",
    "    )\n",
    "\n",
    "    if not include_field_mnts:\n",
    "        sim = sim.updated_copy(monitors=[point_monitor])\n",
    "\n",
    "    return sim"
   ],
   "outputs": [],
   "execution_count": 71
  },
  {
   "cell_type": "markdown",
   "id": "4967d886-0a65-4e78-90b2-4bbab0938c84",
   "metadata": {},
   "source": [
    "Let's test this out by generating a set of initial parameters for the optimization and calling our code."
   ]
  },
  {
   "cell_type": "code",
   "id": "62be700a-0e1c-4961-b995-6e362b35afea",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.719760Z",
     "start_time": "2026-03-17T09:13:22.717974Z"
    }
   },
   "source": [
    "# some variables we might need later\n",
    "\n",
    "nx = int(size_design_x // pixel_size)\n",
    "ny = int(size_design_y // pixel_size)\n",
    "\n",
    "\n",
    "# some initial parameters to test with\n",
    "def make_symmetric_x(arr: np.ndarray) -> np.ndarray:\n",
    "    \"\"\"make an array symmetric in x.\"\"\"\n",
    "    return (arr + np.flipud(arr)) / 2.0\n",
    "\n",
    "\n",
    "params0 = make_symmetric_x(0.5 * np.ones((nx, ny, 1)))"
   ],
   "outputs": [],
   "execution_count": 72
  },
  {
   "cell_type": "code",
   "id": "2ad4d7be-3a83-4b40-8be1-9c82a7d361b1",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:22.834245Z",
     "start_time": "2026-03-17T09:13:22.761915Z"
    }
   },
   "source": [
    "sim_antenna_params0 = make_sim_with_antenna(params0)"
   ],
   "outputs": [],
   "execution_count": 73
  },
  {
   "cell_type": "code",
   "id": "f26dd5fc-c64d-4275-8495-f16209b79823",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:23.009361Z",
     "start_time": "2026-03-17T09:13:22.838512Z"
    }
   },
   "source": [
    "f, axes = f, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(10, 4), tight_layout=True)\n",
    "sim_antenna_params0.plot(x=0.0 + shift_plot, monitor_alpha=0.0, ax=ax1)\n",
    "sim_antenna_params0.plot(y=0.0 + shift_plot, monitor_alpha=0.0, ax=ax2)\n",
    "sim_antenna_params0.plot(z=center_metal_z + shift_plot, monitor_alpha=0.0, ax=ax3)\n",
    "\n",
    "for ax in axes:\n",
    "    ax.set_aspect(\"equal\")\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 74
  },
  {
   "cell_type": "markdown",
   "id": "f161a440-094b-41b9-a4e2-13a81825561d",
   "metadata": {},
   "source": [
    "If we want, we can also visualize the initial fields."
   ]
  },
  {
   "cell_type": "code",
   "id": "c28c7d2a-843b-4d54-b951-76d67243c3be",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:40.915750Z",
     "start_time": "2026-03-17T09:13:23.018138Z"
    }
   },
   "source": [
    "if run_pre_sims:\n",
    "    sim_data = web.run(sim_antenna_params0, task_name=\"check fields\")\n",
    "    f, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4), tight_layout=True)\n",
    "    sim_data.plot_field(\"field_xy\", field_name=\"E\", val=\"abs^2\", ax=ax1)\n",
    "    sim_data.plot_field(\"field_xz\", field_name=\"E\", val=\"abs^2\", ax=ax2)\n",
    "    plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:13:23 CET\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'check fields'\u001b[0m with resource_id                       \n",
       "\u001b[2;36m             \u001b[0m\u001b[32m'fdve-f7c8770e-f0e6-467f-86f0-9a46c100c743'\u001b[0m and task_type \u001b[32m'FDTD'\u001b[0m.  \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:13:23 CET </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'check fields'</span> with resource_id                       \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-f7c8770e-f0e6-467f-86f0-9a46c100c743'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                          \n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=263426;https://tidy3d.simulation.cloud/workbench?taskId=fdve-f7c8770e-f0e6-467f-86f0-9a46c100c743\u001b\\\u001b[32m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=929138;https://tidy3d.simulation.cloud/workbench?taskId=fdve-f7c8770e-f0e6-467f-86f0-9a46c100c743\u001b\\\u001b[32mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=263426;https://tidy3d.simulation.cloud/workbench?taskId=fdve-f7c8770e-f0e6-467f-86f0-9a46c100c743\u001b\\\u001b[32m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=584899;https://tidy3d.simulation.cloud/workbench?taskId=fdve-f7c8770e-f0e6-467f-86f0-9a46c100c743\u001b\\\u001b[32mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=263426;https://tidy3d.simulation.cloud/workbench?taskId=fdve-f7c8770e-f0e6-467f-86f0-9a46c100c743\u001b\\\u001b[32m-f7c8770e-f0e\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=263426;https://tidy3d.simulation.cloud/workbench?taskId=fdve-f7c8770e-f0e6-467f-86f0-9a46c100c743\u001b\\\u001b[32m6-467f-86f0-9a46c100c743'\u001b[0m\u001b]8;;\u001b\\.                                         \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>View task using web UI at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-f7c8770e-f0e6-467f-86f0-9a46c100c743\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-f7c8770e-f0e</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-f7c8770e-f0e6-467f-86f0-9a46c100c743\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">6-467f-86f0-9a46c100c743'</span></a>.                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mTask folder: \u001b]8;id=432778;https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\u001b\\\u001b[32m'default'\u001b[0m\u001b]8;;\u001b\\.                                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "53718671b25c4149b766f2839721996d"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:13:34 CET\u001b[0m\u001b[2;36m \u001b[0mEstimated FlexCredit cost: \u001b[1;36m0.563\u001b[0m. Minimum cost depends on task     \n",
       "\u001b[2;36m             \u001b[0mexecution details. Use \u001b[32m'web.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to get the billed  \n",
       "\u001b[2;36m             \u001b[0mFlexCredit cost after a simulation run.                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:13:34 CET </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.563</span>. Minimum cost depends on task     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>execution details. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the billed  \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>FlexCredit cost after a simulation run.                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:13:35 CET\u001b[0m\u001b[2;36m \u001b[0mstatus = success                                                   \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:13:35 CET </span>status = success                                                   \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "1b9e5d970f8748d38e7ecc2f8c732bbb"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:13:40 CET\u001b[0m\u001b[2;36m \u001b[0mLoading results from simulation_data.hdf5                          \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:13:40 CET </span>Loading results from simulation_data.hdf5                          \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x400 with 4 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 75
  },
  {
   "cell_type": "markdown",
   "id": "0c6780fe-862a-43ac-b2ea-1c70166239fa",
   "metadata": {},
   "source": [
    "Next, we are ready to put everything together into an objective function to optimize.\n",
    "\n",
    "We start by writing functions to compute the intensity at our measurement point through a `tidy3d` simulation."
   ]
  },
  {
   "cell_type": "code",
   "id": "557b423f-490c-407c-9b33-ed98d62e3014",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:58.018928Z",
     "start_time": "2026-03-17T09:13:40.921845Z"
    }
   },
   "source": [
    "def extract_intensity(sim_data: td.SimulationData) -> float:\n",
    "    \"\"\"Grab the intensity from a simulation data.\"\"\"\n",
    "    return np.sum(sim_data.get_intensity(\"point\").values)\n",
    "\n",
    "\n",
    "def measure_intensity(\n",
    "    params: np.ndarray,\n",
    "    task_name: str = \"antenna_intensity\",\n",
    "    verbose=False,\n",
    "    beta: float = beta_project,\n",
    ") -> float:\n",
    "    \"\"\"Measure intensity as a function of design parameters.\"\"\"\n",
    "    sim = make_sim_with_antenna(params, beta=beta, include_field_mnts=False)\n",
    "    sim_data = web.run(sim, task_name=task_name, verbose=verbose)\n",
    "    return extract_intensity(sim_data)\n",
    "\n",
    "\n",
    "if run_pre_sims:\n",
    "    intensity0 = measure_intensity(\n",
    "        0 * np.ones_like(params0), task_name=\"antenna_normalize\", verbose=True\n",
    "    )\n",
    "else:\n",
    "    intensity0 = 2083.6917\n",
    "\n",
    "print(f\"Intensity without structure = {intensity0:.4f} (au)\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:13:41 CET\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'antenna_normalize'\u001b[0m with resource_id                  \n",
       "\u001b[2;36m             \u001b[0m\u001b[32m'fdve-d5a804e3-d652-4bf6-9da9-242f9e66f81a'\u001b[0m and task_type \u001b[32m'FDTD'\u001b[0m.  \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:13:41 CET </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'antenna_normalize'</span> with resource_id                  \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-d5a804e3-d652-4bf6-9da9-242f9e66f81a'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                          \n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=483497;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d5a804e3-d652-4bf6-9da9-242f9e66f81a\u001b\\\u001b[32m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=667608;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d5a804e3-d652-4bf6-9da9-242f9e66f81a\u001b\\\u001b[32mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=483497;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d5a804e3-d652-4bf6-9da9-242f9e66f81a\u001b\\\u001b[32m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=355885;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d5a804e3-d652-4bf6-9da9-242f9e66f81a\u001b\\\u001b[32mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=483497;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d5a804e3-d652-4bf6-9da9-242f9e66f81a\u001b\\\u001b[32m-d5a804e3-d65\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=483497;https://tidy3d.simulation.cloud/workbench?taskId=fdve-d5a804e3-d652-4bf6-9da9-242f9e66f81a\u001b\\\u001b[32m2-4bf6-9da9-242f9e66f81a'\u001b[0m\u001b]8;;\u001b\\.                                         \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>View task using web UI at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-d5a804e3-d652-4bf6-9da9-242f9e66f81a\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-d5a804e3-d65</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-d5a804e3-d652-4bf6-9da9-242f9e66f81a\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">2-4bf6-9da9-242f9e66f81a'</span></a>.                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mTask folder: \u001b]8;id=251619;https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\u001b\\\u001b[32m'default'\u001b[0m\u001b]8;;\u001b\\.                                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "0eb0080473614a509ce34bf043369744"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:13:53 CET\u001b[0m\u001b[2;36m \u001b[0mEstimated FlexCredit cost: \u001b[1;36m0.563\u001b[0m. Minimum cost depends on task     \n",
       "\u001b[2;36m             \u001b[0mexecution details. Use \u001b[32m'web.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to get the billed  \n",
       "\u001b[2;36m             \u001b[0mFlexCredit cost after a simulation run.                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:13:53 CET </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.563</span>. Minimum cost depends on task     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>execution details. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the billed  \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>FlexCredit cost after a simulation run.                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:13:55 CET\u001b[0m\u001b[2;36m \u001b[0mstatus = success                                                   \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:13:55 CET </span>status = success                                                   \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "f96803f7c7ba49dc8bb7637b9961b7f3"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:13:57 CET\u001b[0m\u001b[2;36m \u001b[0mLoading results from simulation_data.hdf5                          \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:13:57 CET </span>Loading results from simulation_data.hdf5                          \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intensity without structure = 2083.5806 (au)\n"
     ]
    }
   ],
   "execution_count": 76
  },
  {
   "cell_type": "markdown",
   "id": "6d566c7c-2afd-49cd-91ec-ca0e209f5547",
   "metadata": {},
   "source": [
    "We then define a penalty function to discourage density patterns that have small feature sizes below the `radius` we defined."
   ]
  },
  {
   "cell_type": "code",
   "id": "092b4059-bfd9-4faf-8d9e-c1b20678e9e3",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:58.027375Z",
     "start_time": "2026-03-17T09:13:58.025052Z"
    }
   },
   "source": [
    "from tidy3d.plugins.autograd import make_erosion_dilation_penalty\n",
    "\n",
    "penalty_fn = make_erosion_dilation_penalty(radius, pixel_size, beta=beta_penalty)\n",
    "\n",
    "\n",
    "def penalty(params: np.ndarray, beta: float = None) -> float:\n",
    "    \"\"\"Define the erosion dilation invariance penalty for Si density parameters.\"\"\"\n",
    "    beta_kwargs = {}\n",
    "    if beta is not None:\n",
    "        beta_kwargs[\"beta\"] = beta\n",
    "    density = get_density(params, **beta_kwargs)\n",
    "    pen_val = penalty_fn(density)\n",
    "    return pen_val"
   ],
   "outputs": [],
   "execution_count": 77
  },
  {
   "cell_type": "markdown",
   "id": "10f7c109-7e72-4088-9c5a-080139ade93d",
   "metadata": {},
   "source": [
    "## Objective Function\n",
    "\n",
    "Finally, we define our objective function as the ratio of our measured intensity compared to the intensity with no gold film minus the fabrication penalty, which is normalized between 0 and 1."
   ]
  },
  {
   "cell_type": "code",
   "id": "41761d3a-b478-4063-bb60-7fb3681f21dc",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:58.070735Z",
     "start_time": "2026-03-17T09:13:58.067933Z"
    }
   },
   "source": [
    "# let's us grab and print autograd values while they're in the objective function\n",
    "from autograd.tracer import getval\n",
    "\n",
    "\n",
    "def intensity_enhancement(\n",
    "    params: np.ndarray, task_name: str = \"antenna_intensity\", verbose=False\n",
    ") -> float:\n",
    "    intensity_with_params = measure_intensity(params, task_name=task_name, verbose=verbose)\n",
    "    return intensity_with_params / intensity0\n",
    "\n",
    "\n",
    "def objective(\n",
    "    params,\n",
    "    beta: float = beta_project,\n",
    "    verbose: bool = False,\n",
    "    penalty_only: bool = False,\n",
    ") -> float:\n",
    "    if penalty_only:\n",
    "        enhancement_factor = 0.0\n",
    "    else:\n",
    "        enhancement_factor = intensity_enhancement(params, verbose=verbose, task_name=\"antenna\")\n",
    "        print(f\"\\tenhancement = {getval(enhancement_factor):.2e}\")\n",
    "\n",
    "    # penalty_value = 0\n",
    "    penalty_value = penalty(params, beta=beta)\n",
    "    print(f\"\\tpenalty val = {getval(penalty_value):.2e}\")\n",
    "    objective_value = enhancement_factor * (1.0 - penalty_value)\n",
    "    print(f\"\\tobjective = {getval(objective_value):.2e}\")\n",
    "    return objective_value"
   ],
   "outputs": [],
   "execution_count": 78
  },
  {
   "cell_type": "markdown",
   "id": "d08899aa-88d0-46bc-ae1b-fdfb716be3d7",
   "metadata": {},
   "source": [
    "We can use `autograd` to simply compute a function that returns the value of our objective along with the gradient, to feed to our optimizer."
   ]
  },
  {
   "cell_type": "code",
   "id": "9814b547-421f-4ad2-b70c-c0638d4304b4",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:13:58.115029Z",
     "start_time": "2026-03-17T09:13:58.113539Z"
    }
   },
   "source": [
    "val_grad_fn = autograd.value_and_grad(objective)"
   ],
   "outputs": [],
   "execution_count": 79
  },
  {
   "cell_type": "markdown",
   "id": "2b2f58b6-28e8-42d8-ab1d-426789ae21aa",
   "metadata": {},
   "source": [
    "We can take this opportunity to run through the function to verify everything, see our initial objective function value, and visualize the gradients of our objective w.r.t. the initial parameters."
   ]
  },
  {
   "cell_type": "code",
   "id": "d5045ee2-a2ea-4da3-90cd-79fe6ef953ba",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T09:14:50.198529Z",
     "start_time": "2026-03-17T09:13:58.160360Z"
    }
   },
   "source": [
    "if run_pre_sims:\n",
    "    val, grad = val_grad_fn(params0, verbose=True)\n",
    "    print(f\"starting objective function value = {val}\")\n",
    "    vmag1 = np.max(abs(grad))\n",
    "    im1 = plt.imshow(np.flipud(np.squeeze(grad)).T, cmap=\"PiYG\", vmax=vmag1, vmin=-vmag1)\n",
    "    plt.colorbar(im1)\n",
    "    plt.title(\"gradient w.r.t. parameters\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:13:59 CET\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'antenna'\u001b[0m with resource_id                            \n",
       "\u001b[2;36m             \u001b[0m\u001b[32m'fdve-19430f29-8562-4c3c-a480-f40f917afbc9'\u001b[0m and task_type \u001b[32m'FDTD'\u001b[0m.  \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:13:59 CET </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'antenna'</span> with resource_id                            \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-19430f29-8562-4c3c-a480-f40f917afbc9'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                          \n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=549911;https://tidy3d.simulation.cloud/workbench?taskId=fdve-19430f29-8562-4c3c-a480-f40f917afbc9\u001b\\\u001b[32m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=463689;https://tidy3d.simulation.cloud/workbench?taskId=fdve-19430f29-8562-4c3c-a480-f40f917afbc9\u001b\\\u001b[32mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=549911;https://tidy3d.simulation.cloud/workbench?taskId=fdve-19430f29-8562-4c3c-a480-f40f917afbc9\u001b\\\u001b[32m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=755559;https://tidy3d.simulation.cloud/workbench?taskId=fdve-19430f29-8562-4c3c-a480-f40f917afbc9\u001b\\\u001b[32mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=549911;https://tidy3d.simulation.cloud/workbench?taskId=fdve-19430f29-8562-4c3c-a480-f40f917afbc9\u001b\\\u001b[32m-19430f29-856\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=549911;https://tidy3d.simulation.cloud/workbench?taskId=fdve-19430f29-8562-4c3c-a480-f40f917afbc9\u001b\\\u001b[32m2-4c3c-a480-f40f917afbc9'\u001b[0m\u001b]8;;\u001b\\.                                         \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>View task using web UI at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-19430f29-8562-4c3c-a480-f40f917afbc9\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-19430f29-856</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-19430f29-8562-4c3c-a480-f40f917afbc9\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">2-4c3c-a480-f40f917afbc9'</span></a>.                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mTask folder: \u001b]8;id=818721;https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\u001b\\\u001b[32m'default'\u001b[0m\u001b]8;;\u001b\\.                                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "e4090ead848f4e7e81900c598e595409"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "92b0e24bc92b464ca2229eeb62fce303"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:14:19 CET\u001b[0m\u001b[2;36m \u001b[0mEstimated FlexCredit cost: \u001b[1;36m0.563\u001b[0m. Minimum cost depends on task     \n",
       "\u001b[2;36m             \u001b[0mexecution details. Use \u001b[32m'web.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to get the billed  \n",
       "\u001b[2;36m             \u001b[0mFlexCredit cost after a simulation run.                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:14:19 CET </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.563</span>. Minimum cost depends on task     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>execution details. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the billed  \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>FlexCredit cost after a simulation run.                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:14:20 CET\u001b[0m\u001b[2;36m \u001b[0mstatus = success                                                   \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:14:20 CET </span>status = success                                                   \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "bc4a8d699cc945d5b9171847f6617f2e"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:14:23 CET\u001b[0m\u001b[2;36m \u001b[0mLoading results from simulation_data.hdf5                          \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:14:23 CET </span>Loading results from simulation_data.hdf5                          \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 1.20e+00\n",
      "\tpenalty val = 9.98e-01\n",
      "\tobjective = 2.17e-03\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mStarted working on Batch containing \u001b[1;36m1\u001b[0m tasks.                       \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Started working on Batch containing <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1</span> tasks.                       \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:14:43 CET\u001b[0m\u001b[2;36m \u001b[0mMaximum FlexCredit cost: \u001b[1;36m0.563\u001b[0m for the whole batch.                \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:14:43 CET </span>Maximum FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.563</span> for the whole batch.                \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mUse \u001b[32m'Batch.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to get the billed FlexCredit cost after    \n",
       "\u001b[2;36m             \u001b[0mcompletion.                                                        \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Use <span style=\"color: #008000; text-decoration-color: #008000\">'Batch.real_cost()'</span> to get the billed FlexCredit cost after    \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>completion.                                                        \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "23ba6ce9eb48469184e5c6ec08bf21bf"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m10:14:45 CET\u001b[0m\u001b[2;36m \u001b[0mBatch complete.                                                    \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">10:14:45 CET </span>Batch complete.                                                    \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "0758c9cacb374a3785474da540275721"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "starting objective function value = 0.0021721132071270124\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 80
  },
  {
   "cell_type": "markdown",
   "id": "7b606645-ade2-4814-9113-f74e3254917b",
   "metadata": {},
   "source": [
    "## Optimization\n",
    "\n",
    "Next, we will use Tidy3D's built-in Adam helper to optimize this objective function with respect to our parameter array.\n",
    "\n",
    "Note that the parameters are clipped between 0 and 1.\n",
    "\n",
    "We will also visualize the density of the gold regions as we go."
   ]
  },
  {
   "cell_type": "code",
   "id": "3da866ee-fdda-40a8-b179-e749219da972",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T10:03:19.819111Z",
     "start_time": "2026-03-17T09:14:50.207037Z"
    }
   },
   "source": [
    "from tidy3d.plugins.autograd import adam, apply_updates\n",
    "\n",
    "# hyperparameters\n",
    "num_steps = 20\n",
    "learning_rate = 0.01\n",
    "\n",
    "beta_min = 1.0\n",
    "beta_max = 55.0\n",
    "\n",
    "\n",
    "def plot_density(density: np.ndarray, ax=None) -> None:\n",
    "    \"\"\"Plot the density of the device.\"\"\"\n",
    "    if ax is None:\n",
    "        _, ax = plt.subplots(figsize=(2, 2))\n",
    "    arr = np.flipud(1 - density.squeeze().T)\n",
    "    plt.imshow(arr, cmap=\"gray\", vmin=0, vmax=1, interpolation=\"none\")\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "# initialize adam optimizer with starting parameters (all combined)\n",
    "params = np.array(params0)\n",
    "optimizer = adam(learning_rate=learning_rate)\n",
    "opt_state = optimizer.init(params)\n",
    "\n",
    "# store history\n",
    "objective_values_history = []\n",
    "params_history = [params.copy()]\n",
    "beta_history = []\n",
    "\n",
    "# optimization loop\n",
    "for i in range(num_steps):\n",
    "    print(f\"step = {i + 1}\")\n",
    "\n",
    "    beta = beta_min + i / num_steps * (beta_max - beta_min)\n",
    "    beta_history.append(beta)\n",
    "\n",
    "    # plot the densities, to monitor\n",
    "    plot_density(get_density(params, beta=beta))\n",
    "\n",
    "    val, grad = val_grad_fn(params, verbose=False, beta=beta)\n",
    "    gradient = np.array(grad)\n",
    "\n",
    "    # outputs\n",
    "    # print(f\"\\tobjective = {val:.4e}\")\n",
    "    print(f\"\\tbeta = {beta:.4e}\")\n",
    "    print(f\"\\tgrad_norm = {np.linalg.norm(gradient):.4e}\")\n",
    "\n",
    "    # compute and apply updates to the optimizer based on gradient (-1 sign to maximize obj_fn)\n",
    "    updates, opt_state = optimizer.update(-gradient, opt_state, params)\n",
    "    params[:] = apply_updates(params, updates)\n",
    "\n",
    "    # clip the parameters between 0 and 1\n",
    "    np.clip(params, 0.0, 1.0, out=params)\n",
    "\n",
    "    # save history\n",
    "    objective_values_history.append(val)\n",
    "    params_history.append(params.copy())"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step = 1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 1.20e+00\n",
      "\tpenalty val = 9.98e-01\n",
      "\tobjective = 2.17e-03\n",
      "\tbeta = 1.0000e+00\n",
      "\tgrad_norm = 1.0915e-02\n",
      "step = 2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 2.33e+00\n",
      "\tpenalty val = 9.98e-01\n",
      "\tobjective = 4.51e-03\n",
      "\tbeta = 3.7000e+00\n",
      "\tgrad_norm = 2.4471e-02\n",
      "step = 3\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK4AAACuCAYAAACvDDbuAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjgsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvwVt1zgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAClhJREFUeJztndtyo0oMRQUk/zufMv+bAZ+HU3K2FXVzCY6zxV5VrrGxubh7WahFkxlut9vNhCBjfPUBCHEEiSsokbiCEokrKJG4ghKJKyiRuIISiSsokbiCkretH/zz588TD2MbwzDYMAw2TZNN02TjONr7+7tN02Rvb28Py8dxtGEYXn3IL+V2u9myLLYsi83zbPM8279//2yeZ/v4+HhYfrvd7DdcRP379++mzyniCkokrqBE4gpKJK6gROIKSiSuoETiCkokrqBE4gpKJK6gROIKSiSuoETiCkokrqBE4gpKJK6gROIKSiSuoIRe3N9wuwkbFdqMXlxxTSSuoETiCkokrqBE4gpKJK6gROIKSiSuoIRW3ApF9FfD3Ia04oprU1Zc5mhyFpXboIy4y7K8+hB+PZXaiFJcjCT4d139eeVIs5fYJrF9WNuKUlyzrx0g9sHefrTiOuwd8NNUaS9KcVu5WpXT4Bm00qkIa95LKa5Znttm712ZXruwtxGtuA5GDOaOeDbYNqxRFqETN5MzRhLxyFqUZWwzOnGR2OAVIsmziG3DKCtCJW5r4KVabs6eGi5be1GJG5Ggx6jQbtTiOhWvDH2HqpUEhFZcz9kkbJuewGbcYwJacc2+dkCW012VVs4ff/CsUIqbRdllWe7/6XKlU+J38HbAtsHl/pwROnFjQ2NEyR7ZOpXJIm2rXeI6TNCJi2B0xedXldZpyRvbixlqcZ3YUVm6cAWBs8FYbIsq7UArbuyIVrG9SkftYa0tKkhMKe7WPLf1+cpkUbdafmtGKi7ip0J8vizL5dKFVpqQVRTY81szcnG3jqCvkjLsaQf29qAWF/FOmee5W9Nl77CM3qBsWRab57ncj5dWXOyEbOSclceqRBukd9bBNCorgzG3A624Tq/jMPpWlLdXr8UoW/G7v736AM5iWRYbhuH+7zAM904chsHMzMZxvD83+78D8fUZtKR49n5wMBYHqXGAVgFqcV08/BejLYqL75t9inSGvFsiGH7mzP1l0dZFjVEX12WPutTiIjGijONoHx8fNk3TvePGcXx4RIH2CnW08+OPZ+96MZfHxzzP90d8j11WhF7cGDE9wnrE8WibSYLLMXJv3e/Zx75lf60ImwmcDcjOOvZXQy8uginDsiw2juNDjhsZx/bYtCfUmR2/Jm8WZVvSYpTNqgqVKCFuFnXHcVyNNp4+xKjs8jtnD6zWyAZerVJXFDZWUipGW7Mi4iIusXdkfM9ZlsWmaTIzexAXozAO4J59zL3lWV0a04EoLz5+4vhfQRlxMeqivK3PuqD+WRysxZz4VRG3FWF7uW1P2koClxE3kl0l8mVYacC82GXGCIyDtmcLHMtWrXw2vsbIG0tiVSklbjbQcXkxmvpncRCHUse8N0byZ1xMaAmbpQW9CwytCw3VJC4lbgRThlhhyKSN6QOmEJmwZ11I6A2+Yg4b5c0+i9uuSjlxY9SN+a6L6kJGgc3sQeJpmr4IjOselbc18MKrXn4s/joK24qyWVWiGuXEzUDBYvSN8xpcapTXzB5SCLOvFy/2Hk+vtOXH2ZqamK2P274CJcXNIqF3aIy+KJ+LOs/zfQAXUwh/jgO5o8fYqw70RPb1twhbVeSS4vZoCRyrDGaPAmcC+HpHI27vyldMFVDaK0bYSFlx14TCDndJhmGweZ4f8ll/PU3TXWR/oOh75hxEQXFSTDaH+OiAq7LUZcU9QjaQyyoJ8dIwRvG17eMjXu3K5hrguuKT0uIePY2bfaYSPlDzZfjoTeBZ20fvCtgZZa3qotPfurPGdzq+VU/N3vvOdrOJMXu3G/dRndIRdy+xw+PtP/GCQVx3S6oQX8dtxspBPB7xP+Ujrtn+W2uyZa3nW/ezZZ21fRz9HhW5hLiiHpcQd8sptnVrz9rzrfvZss7aPo5+j4ooxwVasmBd15cdmXCT3VkRt+lVjO/Mg7gC5cU92vm+Xpxc45NuMqG3btfXdTn9Tgx/jSW4Izlr/IFUpLS4R6TFdVzMeFs7Lj+6D5zIgxclzL5OBDLbL3B1eUuLu5csymKkRXEx8m6NujEtwEjbKq9l5ThRWNw1kWJk9WUYTc3sQdgob+sPi6ztN0of50KcNcmmsuxlxW2RpQK+3EU0e5x/m8l6JL/FY8AfR+s9FNQvMd9ut4cpl0dTCXZKirtWSsruKcPTdxTW7KvIR6WNxxNv0PRlLmWcKxGnX64JXDXqlhQ30hpwxdM15q5bbt2J2957PPEysm/fl+EAziNuNuUxk7s65cRt1Vcz8VDYOAjLPhsHYt+NuFj+ilHU/41S+mus9eLgLRvIVZS5nLhIlDbLWaO8rdvTY0XgzOPD11FgvBCRpRBY741ltGqyIqXEzYTK6q6xOpDJ/Exhs+NG0bJcFiNrvNnT7Osfx4t/W6GayKXERXrVgN7FhOzvKDxL2OyYY6oQ77DA9/HhIqOwWEKrRhlxUS48tcYHpgJZWvDdgdczvkscwGH60DsTxJShUtQtI67Tkja7kLA2+IrbdM7u/Nb2YzUki8Cx1otUzndLiJt1GEZQFzW78tVKC14VbeO+Y3TFvLcnbTZhB7fBTglxHezgOOhak3aPsGd2/tr+eu9nV97MvlYYfDsVhHXoxe1F29bcgjjH4EiUPUOEI/uL0TfiEdnnPFSNuvTiOjG6DsNg7+/v99coccxjj6YFsRS1d72j+8PXsaaLy/w/b3EqVRmob93JIiZGW5S5Nfg6I5dtDer2fmbP/rLtxu8bZ6Hhuq/M4c+gTMRduyqGqYHzjM77yZpvvKzrOS/muFiJiCkDM9QR1yyPtjHHPToI++20vjumS1W/O624scYZO+ZZk2N+G70fbhyAYlTGdRmhFTeSRdkzB2K/mSznjTPezsqvfwvU4vaiTSvaVmZPO7C3B7W4Zo+332TTFKtHW6cVdbFN/L3WhQsmKL9Bq575zJIXC71SWXbmYW0bSnHN+jXc7PWVWGuLCukCrbhINnK+YtTtDdIqyIpQi7t2b5hZnY7aQ6++m5XFGKE7+q357VXl3VppydZhgk5cs6+dY5bfdn51spouLvfnjFCK66C0/rpCp5xBa2CGbcUMrbixA644GFsjG6zhcuY8l/fIgaz0g+9djZ6wVdqDWtxKHfGTVGg3KnFbkVQXHnJaFyLw/ew5A1TiRmJjM+dszya2DZuoEbqezhpclYQ+azkuY5vRiRupMjH62WDbVDgz0X6DtdxNEvfbhb2NKMVtRQyVwj7Z+kNmjb6cRw2wR46fpkp70YpbpQNeBXv7UYqrGu529tRymaAUN4M1V/tJKrVRnW8SYI0kZ1K5DcqKK2pDK27laPJTMLchrbji2khcQYnEFZRIXEGJxBWUSFxBicQVlEhcQQm9uMxF9FdRoc3oxRXXROIKSiSuoETiCkokrqBE4gpKJK6gROIKSiSuoETiCkokrqBE4gpKJK6gROIKSiSuoETiCkokrqBE4gpKhtvtdnv1QQixF0VcQYnEFZRIXEGJxBWUSFxBicQVlEhcQYnEFZRIXEHJf/7kg9DmDJYAAAAAAElFTkSuQmCC"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 4.20e+00\n",
      "\tpenalty val = 9.97e-01\n",
      "\tobjective = 1.36e-02\n",
      "\tbeta = 6.4000e+00\n",
      "\tgrad_norm = 7.9013e-02\n",
      "step = 4\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 7.29e+00\n",
      "\tpenalty val = 9.90e-01\n",
      "\tobjective = 7.31e-02\n",
      "\tbeta = 9.1000e+00\n",
      "\tgrad_norm = 4.4960e-01\n",
      "step = 5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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sQQAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 1.21e+01\n",
      "\tpenalty val = 9.61e-01\n",
      "\tobjective = 4.75e-01\n",
      "\tbeta = 1.1800e+01\n",
      "\tgrad_norm = 7.0505e+00\n",
      "step = 6\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 2.01e+01\n",
      "\tpenalty val = 8.40e-01\n",
      "\tobjective = 3.22e+00\n",
      "\tbeta = 1.4500e+01\n",
      "\tgrad_norm = 2.8487e+01\n",
      "step = 7\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 3.48e+01\n",
      "\tpenalty val = 5.08e-01\n",
      "\tobjective = 1.71e+01\n",
      "\tbeta = 1.7200e+01\n",
      "\tgrad_norm = 1.9941e+02\n",
      "step = 8\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 6.64e+01\n",
      "\tpenalty val = 2.80e-01\n",
      "\tobjective = 4.79e+01\n",
      "\tbeta = 1.9900e+01\n",
      "\tgrad_norm = 4.8410e+02\n",
      "step = 9\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 1.16e+02\n",
      "\tpenalty val = 1.81e-01\n",
      "\tobjective = 9.51e+01\n",
      "\tbeta = 2.2600e+01\n",
      "\tgrad_norm = 9.4315e+02\n",
      "step = 10\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 2.89e+02\n",
      "\tpenalty val = 1.09e-01\n",
      "\tobjective = 2.58e+02\n",
      "\tbeta = 2.5300e+01\n",
      "\tgrad_norm = 1.6785e+03\n",
      "step = 11\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 1.69e+02\n",
      "\tpenalty val = 6.00e-02\n",
      "\tobjective = 1.58e+02\n",
      "\tbeta = 2.8000e+01\n",
      "\tgrad_norm = 2.4872e+03\n",
      "step = 12\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 2.41e+02\n",
      "\tpenalty val = 3.40e-02\n",
      "\tobjective = 2.33e+02\n",
      "\tbeta = 3.0700e+01\n",
      "\tgrad_norm = 7.4299e+03\n",
      "step = 13\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 4.95e+02\n",
      "\tpenalty val = 2.07e-02\n",
      "\tobjective = 4.85e+02\n",
      "\tbeta = 3.3400e+01\n",
      "\tgrad_norm = 2.4180e+03\n",
      "step = 14\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 5.05e+02\n",
      "\tpenalty val = 1.48e-02\n",
      "\tobjective = 4.97e+02\n",
      "\tbeta = 3.6100e+01\n",
      "\tgrad_norm = 2.9640e+03\n",
      "step = 15\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 5.88e+02\n",
      "\tpenalty val = 1.29e-02\n",
      "\tobjective = 5.80e+02\n",
      "\tbeta = 3.8800e+01\n",
      "\tgrad_norm = 1.3945e+03\n",
      "step = 16\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK4AAACuCAYAAACvDDbuAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjgsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvwVt1zgAAAAlwSFlzAAAPYQAAD2EBqD+naQAAFC1JREFUeJztnelvE8cbx7++b9exY+KEXEihBEhQIEJQVIGanziqlleV+q7/YKW+Ka3KoUITVRSEQiKONpRU5I4bx4nr+IiP2L8XaJaJybFe78zOTvYjRa2QvZ7ju88+88wzz9rq9XodFhYmw250AywstGAJ18KUWMK1MCWWcC1MiSVcC1NiCdfClFjCtTAllnAtTIklXAtT4lT7QZvNxrIdmrDZbHA6nWhvb8fVq1fx7bff4vz584jFYnC73XA4HKqu08zmIauNxmbGV+1nd3Z2UC6XkU6nMTU1he+//x4TExNYX19HtVpl1pdWUNsmy+JamBJphCviE0E0ZBojaYQLvJ8YLZPD4jEt0u9rHReRkUq4FkcHaYTL06ro+Ts82yyT1VUdVTALZHLoiVKzUm3ms/Tnm/nOXt9l8R16DLT+nuhIY3GB/SeI9cSptWY8rJ5RY8AbKSxu46QYNUkiikOUsdEbqSzuQaidMBEn1sxtZ4U0wrXb7bpNnEgC0LNPdrs00y2PcNVgdLy2WczWXp4cKeECzYvBCEE0+7tHTbTAERQu0PxE8xSGyG0TCemEy2ohw9r6arn+UV60SREO00qzmw70d5r93mHX4vE9mTjSwiVoETD9vWa+24roLMF+QCrhtjqxNptNsxU1akeM1/dFQxofV8YYLkHmvmlFKourF3r6sXq0weJjLOEeAk8RW2JVj3TCZRm2YiFiUTLXzIZ0wiUYsVg6TMy8BSSjYAnSCpegdvL0sKA8hMKzPyIjjXD3migt+/2iTrgeu2qi9k0LUghXzwkRTcB6W3FR+tUqUggXAGq1GhMBA/wnm4XLUa/XUavVdL+uUZheuPV6/aM/vWkUkt6/wdo35jFGvDG1cMkE1Ot17OzscLMohwmtURgirO5rtRp2dnZ2jZmZMbVwCbVaDdVqFdVqVXeXQQsiCJVAXAR6fGTA9LkKZGIqlYpUE6MnRLiVSkWIG1sPpLG45XIZ5XJZmZiDJucgiyjqpGppMxmHxvGRAdMLt16vo1qtIpvNIpPJYHt7e8/J0fu0gEhbvgdFQGq1Gra3t5HJZJDNZoWti9ssmgs7i9T5nZ0dbG9vI5/P7+nnGl1hkSd0TjHt3+bzeWxvb2NnZ8fgFu5G6zhq9nFFmTgyOdvb28jlch89DkVpJ0/oPhM3IZfLKU8jUYxOK3PT0uJMFFHU63WUy2XFqog0OUZC39T5fB7lclmYcWlVOy1HFUQQb61WQ6lUwtbWForFojR+XKsQ/79YLGJrawulUkmIxZkemtElHGakeMnKuVKpYGtrC4VCgetmhMiQTYdCoYCtrS1UKhXDd8700opuUYVWDhq2ChFuNpvdNUFqEC1NUM/20Dd0NpttalxYoKeB0zUcZpR46ZBYNptV9Ug0e8UYNVlsxIUi42KkC6X3+Om+c2bUBO/s7CCXy+2K5e6XoyuaCFthv/7QC7NMJoNcLmdYKIzFeDPZ8uUtDJJkUywWkU6nlXiu0e3iyV59I/HbdDqNYrG4K8nGyHbpgelzFQi1Wk0RLvFzjzrEvyXClWnByky4PK0b/VhcX19HOp1GqVTatYKW2doSaL+3Xq+jVCohnU5jfX3dkPg2yzFnanF5i5e8tzaVSiGfzx/pWG69Xkc+n0cqlUI6nea++cB67pm7CrzESyzM0tISJicnsbCwwMynIwsivf70hvj8CwsLmJycxNLSkvIE4gGPOeeSHcYjTEbchUKhgJWVFSSTSVSrVTidzXXRCJdCzW82+4b3arWKZDKJlZUVFAoFbm4Cr/Hjtjjj0SHiLqRSKSwsLOxKnFZTrENkP1hN++j820qlgoWFBaRSKW5uAs/xkyaqAHywNJlMBnNzc6oWJKILtpHD2ksvVOfm5pDJZKTM3eAqXB6nWclGxPz8PHK53IGTZibBNrJf28nNS48Bj/gt77GUyuICHxZpyWQSa2trSvK00cklrCH9I0n1a2trSCaTXBdlPOEuXB5Wt1qtYnNzE4uLi4rVlSn4vh/ktEMul8Pi4iI2Nze5uAlGPLmktLi1Wg35fB4zMzNIpVJK0o2MlodA+l0qlZBKpTAzM4N8Pi9tv6UTLvDhuMrr16/x7t07JaVP1kmkIwnZbBbv3r3D69evpTrV24ghwuW1SJudncXLly+RTCYNSzLhAZ1klEwm8fLlS8zOzkq5KCNIaXGB91Y3mUxienoaMzMz2Nzc3FV3ARDrpHKzNJ7kLZfL2NzcxMzMDKanp5FMJqW1toCBdRVY76bV63XkcjnMzs7i2bNn6Orqgt/vh9PphM1m0/Vt60axl4vw7NkzzM7OIpfLSWttAQkKghxEuVzG2toapqam0N3djWg0Cq/XC7vdDpfLpdw8ZhMwbW2r1SoKhQJWV1cxOTmJqakprK2toVwuG9xKttjqKm9Lu52dV8HKMhDL6vF4kEgk8Nlnn+H27dsYHR3FsWPH4PP54HA4TLV7Rsdri8Ui1tbWMDk5iTt37uCPP/5QYrcsF6Isx0qteyO1xaX9v1QqhcnJSQQCAfh8PjidTrS3t8Pj8cDhcAAQfyeNFm2pVMLGxgb+/PNPPHz4EJOTk0pegqzRExohhMvS36Wt0+rqKh4/fgy32w273Y7h4WHEYjFTiLdRtOl0Gq9evcKDBw/w+PFjrK6ucomciDI+QgiXNWTCC4UCFhcXMTExoUxAo3hFmZhGGkX78uVL3L9/HxMTE1hcXFTqSchuaQnCCJdHlIEsZObn5/Ho0SOlpu65c+cQj8fh9XqF9HfpHIRUKoUXL17g3r17+P333xXRyrq1ux/CCBfgJ958Po/5+XlUKhUUi0UUi0VcuHABiUQCoVBIaYsIEBehUCggmUzi+fPnuHfvHp48eYKVlRVuGyuijAdBKOHygPZ5l5aWMD4+rlTAuXz5Mk6dOgWn0ylEnJcuEzo/P48nT57g7t27mJqaUnIwjpJ7QCOccHkd8yGP3n///RdPnz5FNptFOp1GR0cHwuGwsoAzSrx0RCSbzeLnn3/Gr7/+ir/++mvPXUCWGH0D74Wmws48Hku8xFsqlbC+vo7p6WlkMhkMDw9jaGgI7e3tymYFyxj2XtRqtV3H7V+9eoUffvgBc3Nz2Nra4pqmyUO0Wn5D9QYECRfR8BAXD2w2GxwOB3w+H7788kvcuHEDly5dwvHjxxEIBJRtYl7vIyN++PLyMp4+fYr79+/jl19+4Z4oxLq/e11fbZmollwF1paRVxE9Olw2MTGBZDKJpaUlfPHFFzh58iQikQhz14F2DTKZDN6+fYtHjx7h4cOH+Pvvv7me1AWMEW1T32/F4gLyWF2Cy+WC3+/H8ePHcenSJdy6dQsXLlxAR0cHvF4vHA6H7q4DqWNLfO7nz5/j7t27ePr0KZaXl1EoFLiXlDJKuFwsLmmADFaXQI6+vHv3Dv/99x9WVlawvLyMa9euob+/H8FgUDfXgXYNcrkc5ubmMD4+jnv37uHVq1fY2NgwJBlcdGsL6GBxaVjHYHlD+77Hjx/HtWvX8PXXX2NkZATRaBRut1vTbhtxTcrlMjY2NjA9PY2ffvoJ4+PjWF5eNjTpnaVo1Vybm8WVmcat4kePHinWT6t49xLtjz/+qIjWevmKOqSoSM4SusAGSdIJBoMIBAI4ffo0PvnkE8XnVVtphiR+v337Fg8fPlSSZGQWrd6W3DQW1+h3TBDxkm3Xvr4+JTnH7XZ/1NbG75P/1ut1pe7Bixcv8Pz5cySTSSFEK+JGw35Ie+ZMbxrTI9+8eYPV1dVdR8AbBbrXv5Gj8/Q1ZD7IyQpp3gHBA9rn3djYQCaTabpSDKm0k8lksLGxcSTSEU3zDggLC9boLlzZLYfD4YDf70c0GkUkEoHH42nKothsNng8HkQiEUSjUfj9fqET2PWAhSYsi6sSOqbb2dmJU6dOobOzE4FAQNkKJuLbq+I4+X+73Y5AILDrGvShTQt1mCaqYPRq2263w+v1IpFI4MKFCzh37hyOHTu269TEfsJr/Hev14tjx47h3LlzmJ+fx/r6OsrlMvd8hEbMdFRfV+HK6CbQou3s7MSVK1cwNjaGkydPIhwOK/UZ1Ew4+YzL5UI4HMbJkycxNjaGXC6HSqUi9QaE3jeFaSyuEbDY8iXXdLvdiEajGBkZAfC+boUIW75mQZdcBZkyxIiFJcIaGhrCzZs3DU+y4T0GRl1fba6CldbYgJXW+B7p0xplgVjaWCyGTz/9FGNjY9wSycl1yQ0TCASQSCTQ19enJJKnUikpfV+ttCRcWawt7ctevXrVkKM7dJ2zWCwGr9eLaDSK7u5uQ47usI4wtHp9TcLlNXA8sNvtcDqdCIVC6O/vx3fffWfYYUlyc9DtCQaD6OjowD///MP9sCQP8QLa3BLVwuX5iOJ15Joswtra2nD69Gn873//w8WLFw0/nk5+1+fzoaOjAz6fD998840hx9N5xHa19EE4H5eXaB0OBzweD+LxOM6fP49bt27h8uXLiEQiQhQEoW+sSCSCr776CrFYzJCCICJuTAgnXNbQ/mxXVxcuX76MmzdvKiWYmtlQ4NFWUoS6r68PHo8HoVAI4XCYewkm0RBKuDwKjTidTvj9fvT09ODzzz/HzZs3hS56R9ri9/vR1dUFl8sFn88Hn8/HteidaFZXGOHyFG1fXx+uXbuGGzdumKLMKHlKkByH8+fPw+l0wuVyYXx8HPPz80dOvMIIlyV0OmJPT48S8jKDaAm0Xx6LxTA8PAzgvZh+++03LC4uIp/PHxm3QQjhsq7LQKcjXrlyBdevX8fQ0NBHohVduAB2iXdoaEipfjMxMcElz0EUqyuEcFlBr8zj8ThGR0cxNjaGM2fOIBqNmka0hEbxRqNRnDlzBsViEfl8HuVymcvLS0TA0LfusB5Yl8uFYDCIU6dO4fbt27h+/TpOnDiBYDAIl8ul+li5aJBxI+84I5V3Hjx4gDt37uDNmzdKqiRLWIyb9dYdAG63W1nMjI6OorOzc9dL+gDziRb4cFSfXnB2dnZidHQUS0tLygYF78Qcnhh2dIdHFCEYDGJgYAAXL17EiRMnlMRvozcX9IKO84bDYZw4cQIXL17EwMAAgsGgkDteeiHtmTO73Y5EIoGRkREMDg6ira3to21cM4uX7gO9dT04OIiRkREkEgnuBal5YkjPeFhbh8OBgYEBDA8PI5FISH0gkY6cJBIJDA8PY2BggEt/jbK6Ut6SxAKdPXtWShehkb1chrNnzypPGBmRrlf0EfDBwUHE43F4PB5pRUug83nj8TgGBwd3HZ2XDe7C5bW129bWhp6eHuWMmKyWh4bkFgeDQfT09KCtrW1XBIUVRrgL0s0mqRSTSCSUugdm2mTQCukfndOQSCSarrRjFrgKl9eiLBgMoq+vb9eJXCPaw5L92k6eOPQYyLhIk8rikkmLRCLo7+9Xjt4cNGl0KVAzcFh76QIm/f39SmK8bFaXm3B5nWwgeQm9vb27IgmHTZzoAlbTPro+mcvlQm9vL+LxONxuNxfh8hw/LsLleYaMJFwnEglNlqaxKPNef3qj92+SJ08ikUBXVxf8fj+36AK3Q66sf4DnEXOPx4Pu7m6Mjo6it7eXmW+nRmjN/OkN8fV7e3sxOjqK7u5uros0HnPOVLi8ywa53W7EYjHE43EEAgHp/LpmsNlsCAQCiMfjiMVi3NwFAuu5ZyZcI+p9eb1etLe3KwnitG8rsv+qF3SdAvIEisViu2pEyCJeaaIKdrsdPp8PsVgMoVAILpfL6CYZjsvlQigUQiwWg8/nk2oThklPeFs3OskkFospZZOMbhdP9uqb0+lEIBBQhGtEkhGrMZfmHRBk4yESiRz4WBQ97NUs+/WHdp8ikYiyEWEELMZbiorkJPwTDocRDoeVpJqDaLZuFc/oiBrUtIck3ZBxMXIjQu9DlroJ10grZrPZlJQ+4t+KJki16NkeMi6k+k0z48ICPcWri6tgtGjpCSKvX5JpIaIVu92u1JOgb2ijxasHLc+uCBaLPBJDoRB8Pp+Ue/NaIC6Uz+dDKBRS5ULxQA/NtNQLEUQLfNh8CAQChsQrRYVeoAUCAe6bEAfRqnY0C1ck0ZLJCQaDHx1XEaWdPKH7TI4xBYNB4W7qVuZGyMLOzUKSp0n8tnFyWJQN0ms8WLaL3NQknkuS6kVC6ziaviAIHQqjY7iNNE7ofvC+QdX+ntY207Fco0NiemJ64QIfHod03QSRxKkHWtpM5+fS4yMDpu8FnTh9VA5FNgtxF2Q6oi+NxXU6nUK8uwH42Doa2R7az5Xpxja1cOkyRDw3HZp9bKs5csMashlBj5kZXSaCqYULfPDj6D+9YT3BrC00jzHijemFS9DbRTDSGqmNgDQDcRlkQQrhyiLYvWg2i+0wZLC2gARRBcJ+ubdqET1Pt9n27ZejKwtSWNyD4ClGHoswkW8unkgrXN4LKq3fYWkFZRa5dMJl+chnVQyEwLIGhGxIJ1y9McrVkMkfZYEl3D0QwUJZIj4YaaIKeolNBNE2InPftCKVxW11Ylr5vh7piYddvxXLK5NoAcmEqxWtk9pqZEFLJUkt35ORIy1cvUJaevx+M2K0BCyRj0tQKywtGV4sH7dars+qr2ZAOuGqgZVA9EDktonEkROuGfIX9MhLkJ0jJVyzicFs7eWJNMKt1WpSxjv17FOtVtPlWiIgjXAPw8wLGTO3nRVShMMaJ8yoCRThbFkjooyN3khlcfebFB4pjmp+g8diz6gx4I0UFpeGTBDrlble28PN1vFV83l6DBp/Txaksbg8Q1esds9YIlterjTCtThaSCVcrVbF6Hgp69+XzdoCEglXtolhgUxjJI1wLY4WtrpMt6HFkcGyuBamxBKuhSmxhGthSizhWpgSS7gWpsQSroUpsYRrYUos4VqYEku4Fqbk/2eSv7ELegQyAAAAAElFTkSuQmCC"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 6.60e+02\n",
      "\tpenalty val = 1.35e-02\n",
      "\tobjective = 6.51e+02\n",
      "\tbeta = 4.1500e+01\n",
      "\tgrad_norm = 3.1391e+03\n",
      "step = 17\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 6.67e+02\n",
      "\tpenalty val = 1.64e-02\n",
      "\tobjective = 6.56e+02\n",
      "\tbeta = 4.4200e+01\n",
      "\tgrad_norm = 2.5701e+03\n",
      "step = 18\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 6.17e+02\n",
      "\tpenalty val = 2.01e-02\n",
      "\tobjective = 6.04e+02\n",
      "\tbeta = 4.6900e+01\n",
      "\tgrad_norm = 3.9547e+03\n",
      "step = 19\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 6.23e+02\n",
      "\tpenalty val = 2.20e-02\n",
      "\tobjective = 6.09e+02\n",
      "\tbeta = 4.9600e+01\n",
      "\tgrad_norm = 3.3044e+03\n",
      "step = 20\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 200x200 with 1 Axes>"
      ],
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 6.63e+02\n",
      "\tpenalty val = 5.72e-02\n",
      "\tobjective = 6.25e+02\n",
      "\tbeta = 5.2300e+01\n",
      "\tgrad_norm = 4.3060e+03\n"
     ]
    }
   ],
   "execution_count": 81
  },
  {
   "cell_type": "markdown",
   "id": "3fdcd1d7-1557-449a-9740-d57655e770b3",
   "metadata": {},
   "source": [
    "## Analyze Results\n",
    "\n",
    "Let's grab and evaluate the final parameters, since we exited the loop without doing this."
   ]
  },
  {
   "cell_type": "code",
   "id": "5dd8b637-67d4-4100-af90-000bf7f04ae7",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T10:04:29.996084Z",
     "start_time": "2026-03-17T10:03:19.930268Z"
    }
   },
   "source": [
    "params_final = params_history[-1]\n",
    "beta_final = beta_history[-1]\n",
    "objective_value_final = objective(params_final, beta=beta_final)\n",
    "objective_values_history.append(objective_value_final)"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\tenhancement = 7.01e+02\n",
      "\tpenalty val = 1.31e-01\n",
      "\tobjective = 6.09e+02\n"
     ]
    }
   ],
   "execution_count": 82
  },
  {
   "cell_type": "code",
   "id": "458754a0-309d-4e32-bd24-3d8fd7f20f89",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T10:04:30.202645Z",
     "start_time": "2026-03-17T10:04:30.104567Z"
    }
   },
   "source": [
    "plt.plot(objective_values_history)\n",
    "plt.xlabel(\"iterations\")\n",
    "plt.ylabel(\"objective function\")\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 83
  },
  {
   "cell_type": "markdown",
   "id": "f520dfc5-4a66-49dd-a2d6-73e716247706",
   "metadata": {},
   "source": [
    "We can also generate a figure looking at the final fields and density pattern."
   ]
  },
  {
   "cell_type": "code",
   "id": "6ea5ebb2-6ff5-43f8-bc1f-c22ab99f5d94",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T10:05:49.904549Z",
     "start_time": "2026-03-17T10:04:30.219982Z"
    }
   },
   "source": [
    "sim_final = make_sim_with_antenna(params_final)\n",
    "sim_data_final = web.run(sim_final, task_name=\"antenna final\")"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:04:30 CET\u001b[0m\u001b[2;36m \u001b[0mCreated task \u001b[32m'antenna final'\u001b[0m with resource_id                      \n",
       "\u001b[2;36m             \u001b[0m\u001b[32m'fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7'\u001b[0m and task_type \u001b[32m'FDTD'\u001b[0m.  \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:04:30 CET </span>Created task <span style=\"color: #008000; text-decoration-color: #008000\">'antenna final'</span> with resource_id                      \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7'</span> and task_type <span style=\"color: #008000; text-decoration-color: #008000\">'FDTD'</span>.  \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mView task using web UI at                                          \n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=178026;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[32m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=768829;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[32mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=178026;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[32m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=964249;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[32mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=178026;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[32m-5b6169b6-ced\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=178026;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[32m5-4b20-bd73-84078b7f6bb7'\u001b[0m\u001b]8;;\u001b\\.                                         \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>View task using web UI at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">5-4b20-bd73-84078b7f6bb7'</span></a>.                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mTask folder: \u001b]8;id=857297;https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\u001b\\\u001b[32m'default'\u001b[0m\u001b]8;;\u001b\\.                                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Task folder: <a href=\"https://tidy3d.simulation.cloud/folders/folder-df61810d-cad6-4474-8ea9-e4f00d5dfcb0\" target=\"_blank\"><span style=\"color: #008000; text-decoration-color: #008000\">'default'</span></a>.                                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "ed2f18c4796f4c4581cd6fd08c8139a6"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:04:42 CET\u001b[0m\u001b[2;36m \u001b[0mEstimated FlexCredit cost: \u001b[1;36m0.563\u001b[0m. Minimum cost depends on task     \n",
       "\u001b[2;36m             \u001b[0mexecution details. Use \u001b[32m'web.real_cost\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m to get the billed  \n",
       "\u001b[2;36m             \u001b[0mFlexCredit cost after a simulation run.                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:04:42 CET </span>Estimated FlexCredit cost: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.563</span>. Minimum cost depends on task     \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>execution details. Use <span style=\"color: #008000; text-decoration-color: #008000\">'web.real_cost(task_id)'</span> to get the billed  \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>FlexCredit cost after a simulation run.                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:04:44 CET\u001b[0m\u001b[2;36m \u001b[0mstatus = queued                                                    \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:04:44 CET </span>status = queued                                                    \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mTo cancel the simulation, use \u001b[32m'web.abort\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or              \n",
       "\u001b[2;36m             \u001b[0m\u001b[32m'web.delete\u001b[0m\u001b[32m(\u001b[0m\u001b[32mtask_id\u001b[0m\u001b[32m)\u001b[0m\u001b[32m'\u001b[0m or abort/delete the task in the web UI.      \n",
       "\u001b[2;36m             \u001b[0mTerminating the Python script will not stop the job running on the \n",
       "\u001b[2;36m             \u001b[0mcloud.                                                             \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>To cancel the simulation, use <span style=\"color: #008000; text-decoration-color: #008000\">'web.abort(task_id)'</span> or              \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><span style=\"color: #008000; text-decoration-color: #008000\">'web.delete(task_id)'</span> or abort/delete the task in the web UI.      \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>Terminating the Python script will not stop the job running on the \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>cloud.                                                             \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "2d40cccb608e40c9851b2972b35b4233"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:05:01 CET\u001b[0m\u001b[2;36m \u001b[0mstarting up solver                                                 \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:05:01 CET </span>starting up solver                                                 \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m            \u001b[0m\u001b[2;36m \u001b[0mrunning solver                                                     \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span>running solver                                                     \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "0bf6ad17bbed479db9e9a7f2d688be0c"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:05:35 CET\u001b[0m\u001b[2;36m \u001b[0mearly shutoff detected at \u001b[1;36m20\u001b[0m%, exiting.                            \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:05:35 CET </span>early shutoff detected at <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">20</span>%, exiting.                            \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:05:36 CET\u001b[0m\u001b[2;36m \u001b[0mstatus = postprocess                                               \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:05:36 CET </span>status = postprocess                                               \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "f4fa97a8013541ddab56d07e0098ccc1"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:05:39 CET\u001b[0m\u001b[2;36m \u001b[0mstatus = success                                                   \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:05:39 CET </span>status = success                                                   \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:05:41 CET\u001b[0m\u001b[2;36m \u001b[0mView simulation result at                                          \n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=904903;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[4;34m'https://tidy3d.simulation.cloud/workbench?\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=688725;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[4;34mtaskId\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=904903;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[4;34m=\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=898402;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[4;34mfdve\u001b[0m\u001b]8;;\u001b\\\u001b]8;id=904903;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[4;34m-5b6169b6-ced\u001b[0m\u001b]8;;\u001b\\\n",
       "\u001b[2;36m             \u001b[0m\u001b]8;id=904903;https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\u001b\\\u001b[4;34m5-4b20-bd73-84078b7f6bb7'\u001b[0m\u001b]8;;\u001b\\\u001b[4;34m.\u001b[0m                                         \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:05:41 CET </span>View simulation result at                                          \n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">'https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced</span></a>\n",
       "<span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">             </span><a href=\"https://tidy3d.simulation.cloud/workbench?taskId=fdve-5b6169b6-ced5-4b20-bd73-84078b7f6bb7\" target=\"_blank\"><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">5-4b20-bd73-84078b7f6bb7'</span></a><span style=\"color: #000080; text-decoration-color: #000080; text-decoration: underline\">.</span>                                         \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Output()"
      ],
      "application/vnd.jupyter.widget-view+json": {
       "version_major": 2,
       "version_minor": 0,
       "model_id": "7721dbf8bd6240e8891e67163f679e47"
      }
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\u001b[2;36m11:05:49 CET\u001b[0m\u001b[2;36m \u001b[0mLoading results from simulation_data.hdf5                          \n"
      ],
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #7fbfbf; text-decoration-color: #7fbfbf\">11:05:49 CET </span>Loading results from simulation_data.hdf5                          \n",
       "</pre>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 84
  },
  {
   "cell_type": "code",
   "id": "1f8049fd-d992-4001-b6d9-a0f23f144f55",
   "metadata": {
    "ExecuteTime": {
     "end_time": "2026-03-17T10:05:54.508824Z",
     "start_time": "2026-03-17T10:05:49.913723Z"
    }
   },
   "source": [
    "f, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(12, 8), tight_layout=False)\n",
    "\n",
    "ax1.plot(objective_values_history)\n",
    "ax1.set_xlabel(\"iterations\")\n",
    "ax1.set_ylabel(\"objective function\")\n",
    "\n",
    "density = get_density(params_final, beta=beta)\n",
    "ax2.imshow(np.flipud(1 - density.squeeze().T), cmap=\"grey\")\n",
    "ax2.set_title(\"antenna density pattern\")\n",
    "\n",
    "sim_data_final.plot_field(\"field_xy\", field_name=\"E\", val=\"abs^2\", ax=ax3)\n",
    "sim_data_final.plot_field(\"field_xz\", field_name=\"E\", val=\"abs^2\", ax=ax4)\n",
    "ax3.set_title(\"intensity antenna (xy) plane\")\n",
    "ax4.set_title(\"intensity side (xz) plane\")\n",
    "\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x800 with 6 Axes>"
      ],
      "image/png": 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+CLPZjLlz57qESRMmTMCjjz6KjIwMDBw40K9xffzxx3jqqafw2GOPISQkBDNmzMALL7wg7u/evTs+++wzPPHEE3jooYeQkJCAadOmITY2FnfeeafLubx9XhISEvDmm29i0aJFmDJlCmw2G9atW4e4uDj84x//QFJSEp577jm88MILMJlM6NixIy666CJMnjzZr+dCRJ5JHOweRkRERERERE7OnTuHxMREPPXUU7VCMW/mzZuH+fPno6SkpMmqyIioZWDPJCIiIiIiInKxatUq2Gw23H777cEeChG1QJzmRkRERERERACAX3/9Fbm5uXj22Wdx/fXXiyuwERE5Y5hEREREREREAIAFCxZgw4YNGDp0qLgKGxGRO/ZMIiIiIiIiIiIin7FnEhERERG1W8uWLUOnTp2gUqkwaNAgbNmyJdhDIiIiavEYJhERERFRu/Txxx9j9uzZmDt3Lnbs2IELLrgAo0ePRnFxcbCHRkRE1KJxmhsAu92OgoIChIeHQyKRBHs4RERERC4cDgeqqqqQlJQEqZT/FxgogwYNwoABA/D6668DOP87YUpKCmbOnInHHnuszsfy90ciaqv4dw75gg24ARQUFCAlJSXYwyAiIiKq06lTp5CcnBzsYbQJZrMZ27dvx5w5c8RtUqkUo0aNwsaNG2sdbzKZYDKZxPtnzpxBVlZWs4yViCgY+HcO1YVhEoDw8HAA5/+waLXaII+GiIiIyJVOp0NKSor4Ows13rlz52Cz2RAfH++yPT4+HgcPHqx1/KJFizB//vzmGl67IJVKoVarkZCQgF69eqFnz57IyclBfHw8YmJioFAoEBISAqlUKlZ/CZMqHA6HeLPb7bDb7XA4HLDZbOJXu93u8lXYDkC8LzzO+eZ+HXfu2xwOh8fqNF8ngHh7fH3ncH5MXeeo6/H1PU44xv16wvfOX51vwnsmk8kAADKZTLwvlUpdvgrbhccJjxVuztcR3jOLxQKLxYJz586huLgYGzduxL59+7Bnzx4UFRXBYDDAbrf79XpQbfw7h+rCMAn/++Gk1WoZJhEREVGLxelUwTNnzhzMnj1bvC8EfNRwQlggk8kgl8uhUqkQGhqKsLAwhIeHQ6lUimGSu7rCJPcQyT1Mcv7akDCpru3+HtPQcwTiZ4Ev5/B2jD9hkvtX9zBJ+N7fMMlsNsNoNKKmpgYqlQpyuVy8Dn9WBgZfR6oLwyQiIiIianc6dOgAmUyGoqIil+1FRUVISEiodbxSqYRSqWyu4bUL/vxD1b0yKZBjCPQ5hWqfQIy5Kf4x39QBAQMIovaB3bSIiIiIqN1RKBTo168f1q5dK26z2+1Yu3YtcnJygjiy9sXX4KG+6V6NCTDcq18aq77z+BMuNeTY+h7TFOsvBeI1rOt99GfMrEwiah6sTCIiIiKidmn27NmYNGkS+vfvj4EDB2Lp0qWoqanB5MmTgz20dqm+EKChIYiv07n8DSwaOqaGVGT5c2x9j2nM9LZgnFfg6bV2/8wwRCJqPgyTiIiIiKhduuWWW1BSUoKnnnoKhYWF6NOnD3744YdaTbmpaTn32KnrGMD/8Ma5ybTzY5tq2hyd5ykYbGz1Ul2BH6uRiJofwyQiIiIiardmzJiBGTNmBHsYBNcmznUd48sKZ4EMFxrbV6m+4KohK7E1ZhzBPodwHl/P5ek492okhklEzY89k4iIiIiIKKi8VbHU95hAT3HyZxzujbZ9OXd9wUhT8LcXkb/jCfTr7utrygCJKLgYJhERERERUdA1tlqlvn2BDimCGWQEanpeQ0I852Mb+3o25H30dn6GS0TNi2ESEREREREFjXMI4O179+Mbez1fzuVP1VMgKpTcA6L6pvM5r95WV3Nq532N6TnUFK+bP+fy55xE1PQYJhERERERUVA0x0pcgVjdzJ/jBM5hj6/n99Qk3Nu5fe0P5ctrXN8YA1UxFsieS87ndA8hiajpMUwiIiIiIqKg8VSN5CkAaUhI4O2xnq7ha3WOv8GNtyokT+fy5TnW17Db39DGUwWTP+fy9p7VN7WtIWOs6/XlNDei5sXV3IiIiFogu92OCn0VinWlOKcrQ0lVGUp0ZdCbDLiu/yikx6UEe4hERAHVmP45nqp66guQmoun8EcYb12VQg3pM9QYdYVejTmnr6FZfdepq1k4QySi5scwiYiIqJnY7XaU63Uo0ZXhnK4MxbpSlDgFRWJwpCvHuaoyWO02j+dZ/stqrJq2GDld+zbzMyAiahqNDSwC1ZDa/ZzCuNzP7227p8f4Egr5+pi6xutpDL4+xtd9TT0tsb4xBfp9JqKGY5hEREQUAHa7HZuP7cbZ8mIxGBKCIl8CIm8iNVrEaqPQITwacRExOF6Uj72nDuOWV+7H65Pn4dp+I5voGRERtV3OwYSnqiYhkPE3vGjMVLxAaY4qnbqmDwpfAz0OBklELQvDJCIiokay2qyYtPwRrN23wafjo0K16BAejVjt+VucNgax2uha2zqER0ERInd5rMFsxPR35+K7Xetxz9tP4Gx5Me4ZdWtTPC0iohbDn2obf5pF11eB1FC+nLO+6W/u+93Dr/qmytV1jUBraANsf49loETUcjBMIiIiaqT5n7+Gtfs2QCVXol/nnogNdwqEtNHi/fOBUe2AyB9qhQorpi7Ek58swbu/fYa5n72CM2VFmHfj/ZBKua4GEZEz5549je3/4+91G3pMfVU/dR3TkHE0pfqaqxNR68UwiYiIqBH+88eXWPHrxwCAZXfOw5i+lzb5NWVSGZ695Z9IiorHM2uW4a1fP8LZihK8NvkpqOTKJr8+EVGgBaLixNfVxOo7h3vVT0N6J/lyjKfKo/qaYPvStNvb8YEIuJy/b0zza08hExG1LvwvTCIiogbacHgHHvvvCwCAR6+d2ixBkkAikWDG6Nvxxp3zIZeF4OsdazH+lQdQXlPZbGMgIgqk+gKZxgZOnsImT9OzAhGW+Dueuq7ja9NrT+Ntqn5MdX31VIHUVK+hw+EQb0TUvBgmERERNcDJkjO4699zYLXbcH3/yzDryslBGcfYgaPx3/tfQbgqFJuO7sK1L9yDU6VngzIWIqKGcA4DPIUDzREW+NtnqTHncNdcQYjza+zO2/PytwdVU/H2uajvGCJqOgyTiIiI/FRlqMHtbzyEsppK9EnLwpKJjwe1RH9Y93746uF/IzEyFkcKT+DqxXdj36nDQRsPEZGv6goHWpPG/B3gbWqbJ3UFQr5epy1MKfP0/Fvz54eoNWKYRERE5Aeb3YZ733kSh8/mITEyFqumPQ+1QhXsYSGzYxd8++g76JGUgaLKc7juxXuxPndzsIdFRFSvpq4maUh1jbfpW/Wds75paL42ofa3Obcv1/P2GvtSkeTLdMC6xuHpnIHEIImo+TFMIiIi8sOCL17H2n0boJYrsWraC0iIjA32kERJUXH4v4fexNDu/VBj0mPC67Pxyabvgj0sIiKfNEWoVFefJE8358d460FUX6gU7Klhvk7D82Xs3nof1dcrydtrWtf4GsLTFEkiah4Mk4iIiHy0+q+v8e9f/gsAWDrpSVyQ1iPII6otQhOO1TOW4IYBl8Nqt+H+VQuw9LuV/AWbiFo0Tz2Tmjpcqmu/r82xm3IsjT13U792/lYmBYq3zwoRNS+GSURERD7YdGQXHl39PADgn2Om4Lr+o4I8Iu+UcgWWTZ6H6ZffBgB47qt/49HVi2G1WYM8MiIi75orGPC1Qsn5WOF7T9vd99X32IaOyZfqn7rGVN80O18rkhpS7RVonhq0M1Aial4Mk4iIiOpx8lwB7vz3Y7DYrLjmwpH455gpwR5SvaRSKZ4cOwPP3vJPSCQSvP/HGkx+81HUmAzBHlqzKa4sxc4TuTBZzMEeChHVweFwwG63N1klTUODjfoCF1/3BbJyx5++R/7w93k15LX0Fq415n3nFDei4AkJ9gCIiIhasmpjDSa98TDKqivQO7UHXrnjSUilref/YqZcehMSI2Nx37tz8fPev3Djkul4/74XEauNDvbQAs5kMWPLsd34LXczfsvdjP2njwAA1AoVcrr2xSVZgzA8cxC6JXZq0uklRNQwgQoEhNDC4XDUO93L088CT48TjnPf57zd/Xzu13W/VmNWZAvEsb6ERHVVVtXVL8mX6waqeomBElFwMEwiIiLywma3Ydo7T+FgwTHER3TAe9MWQ9MCVm7z11V9L8Gns17DxDcews4Tubjmhan478wlSI9LCfbQGsXhcOBI4Qmsz92CdbmbsPHwDhgsJpdjIjVaVOh1+HX/Rvy6fyMAICEiFsOzBuKSrEG4qMcAdAiPCsbwiQiepyg1ZtqSt/DI21Q1b8cKoZEwnvqu0xQ9ipqbr32i6pq+5769Kae8uX9mnL9v7e8FUWvAMImIiMiLhV8ux897/4JKrsTKe59HYlRcsIfUYAMyeuPrh1fgH68/iBMlpzFm8d34z/QXcWF6z2APzS/lNZX4/cBWrD+wGetzt+BMeZHL/jhtDIZnDcKlTkHRgTNHsf7AFqw/sAWbjuxCYWUJPt74LT7e+C0AoHdqd1ycORCXZA7CgIzeUMoVwXhqRO2O+z/4fQkBAhUSuAdG7tfwFii5Vyi5P8bbfU9j9zVc8XYub2Pxxp9KpLru1xUYuW9vLE8VX+77WZlEFBwMk4iIiDz4eOO3WPbTfwAASyY+jgvTs4M8osbrkpCGbx5egduW/RN78g9i3MvT8eZdT2P0BRcHe2heWW1W7Mjbj3W5m/Fb7ibsOnnA5R8LyhAFBnW5AJdkDcYlWQOR2bFLrX90ZCV3RVZyV0y7bAIMZiO2HN0thkv7Tx/BnvxD2JN/CK//+AHUciUGd+uLSzIHYXjWIHRPTOeUOKJm4K3KxJfj6+OtkbRwHm9VRnVVKNVXmRTISiVfmmUH4rwNDZI8PcZbRZK//aF8DcwYIhE1P4ZJREREbrYe24OHP3wOAPDgVZNxw4DLgzyiwImLiMGa2W/g7hWP49f9GzH5zcew6NaHMOniscEemujkuQL8lrsJ63M344+D21BlrHHZ3y0xHZdmnQ97Bnft69fUQ7VCheF/PxY436T794NbsP7AVqzP3YxiXSnW7d+Edfs3ATg/Je7izAHilLi22GuKqCVwn9rmKRzwNzBw7p1U1zH+VCi572vofU8aG4g0pDrJn/v1TWGrryLJ/XH+8Pb+ePpKRM2DYRIREZGTU6Vnccebj8JstWBM30vx8NV3B3tIAReq0uC9+17AIx8+j/9u+BqPrl6MgrIiPHbdvUGpwqk21uCvQ9uxLncz1uduRl7JaZf9UaHa89PQsgZjeOZAJAVwumFcRAxuHHQlbhx0JRwOBw4WHMNvuZvx+4Gt2HhkJworS/DJpu/wyabvAAC9Urr9PZbzU+JUcmXAxkJE5wWqCbfzFClvFTV1Ndt23+9LNZOv94OhoUGSt0DJUyjkT9AUyGlwwX5tidojhklERER/qzHqMemNh1FaVY6eKd3w6h1PtaqV2/whl4Xg5dv/hY7R8Xjxm7fxyg/voaCiBC/dNgeKEHmTXNNoMaG0qgKl1eUorarA7pMH8NuBLdh2bA+sdpt4XIhUhv6de51ffS1rEHqndodMKmuSMTmTSCTI7NgFmR27YNplE2C0mLDl6PnV4X4/uBX7Th3G3r9vy376jzglbnjmQIzIzkG3xPQmHyNRW+RcleSpj5LA10DGUzWRt8d6OtbX/keBqkyqry+Qv+o6T2Omtrlvq69nUl3XbkxfJW+fEQZKRM0r6GHSmTNn8Oijj+L777+HXq9Hly5dsHLlSvTv3x/A+R8Kc+fOxYoVK1BRUYGhQ4di+fLl6Nq1q3iOsrIyzJw5E19//TWkUinGjRuHV155BWFhYcF6WkRE1MrY7XZMXzkPuWeOIlYbjfemvYBQpTrYw2pSEokED119F5Ki4vHwh8/h003foaiiBO/c8xzC1aH1Pt5kMaO0ugKlVeU4V1WO0uq/v/4dGP3v+wqcqypDtVHv9VydYpNxSdYgXJI5CEO79/Pp+k1NJVfi4syBuDhzIACgRFeK3w9sxW8HttSaErcjbz/euvvZII+YBIsWLcIXX3yBgwcPQq1WY8iQIXj++efRvXt38Rij0Yh//vOf+Oijj2AymTB69Gi88cYbiI+PD+LI27e6QoL6QgdPfY7cK4icAw+pVAqHwwG73e5yDU+VSM7naIoeSk3dX8nbvsb0SKrrq0QigVQqrbdvkrevdfE2tY2BElHzC2qYVF5ejqFDh+LSSy/F999/j9jYWBw5cgRRUf9bonfx4sV49dVX8d577yE9PR1PPvkkRo8ejdzcXKhU53skTJgwAWfPnsXPP/8Mi8WCyZMnY+rUqVi9enWwnhoREbUyz331b/yw+3coQxRYde9idIxuP/+g/MfQaxAfEYO7VzyO3w9uxfUv3YvHrrsXlXqdSxhUWlXxd2h0PkBy72XkixCpDB3CoxETHom0DknilLFOsclN8MwCK1Ybg3GDrsC4QVf8PSXuuLiq3GW9hgV7eORk/fr1mD59OgYMGACr1Yp//etfuPzyy5Gbm4vQ0PNB5YMPPohvv/0Wn376KSIiIjBjxgyMHTsWf/31V5BH3z7VFwb4Eyh52l6f+sIob0GTt/E1pGdSIPjyGvl6vyFBUkPH15jXxltVGxE1LYkjiH/qHnvsMfz111/4448/PO53OBxISkrCP//5Tzz00EMAgMrKSsTHx2PVqlUYP348Dhw4gKysLGzdulWsZvrhhx9w1VVX4fTp00hKSqp3HDqdDhEREaisrIRWqw3cEyQiolbhs83fY8bK+QCAZZPnYdygK4I8ouDYffIgbls2GyW6Mp8fEyKVISY8CjFhkegQHlXr+w5/3xe+16rDgtKXqbXj7yqNU1JSgri4OKxfvx4XX3wxKisrERsbi9WrV+PGG28EABw8eBCZmZnYuHEjBg8eXO85hfeEGk4mk0GtViMhIQE9e/bEBRdcgIsuuggJCQmIi4uDUqmEXC6HVCoVK4kE7svBCze73Q673e7xe+evnh4HwGW/+3U8ffW2zdP9+rbXt68u/lQkedteX48kb1+FSiQAHiuSnCuVnL96+t7blDnhq/CeWiwWmEwmFBcX4+zZs/jzzz+xe/du7N27F0VFRTAYDLDZ/jd9mhqGf+dQXYJamfTVV19h9OjRuOmmm7B+/Xp07NgR9913H+6++3yz07y8PBQWFmLUqFHiYyIiIjBo0CBs3LgR48ePx8aNGxEZGSkGSQAwatQoSKVSbN68GTfccEOzPy8iImo9th/fh39+sAgAcP8Vk9ptkAQAF6T1wDePvI3HVi9GYWXJ30HQ34FQeKTL9x3CoxETFokITTjDIWrxKisrAQDR0edX49u+fTssFovL75g9evRAamqqz2ESBZYv05Ua0jPJW0Difh5vFUfextrQn3tNVaHkb0WSp23eKozqm+5WV2WSp75KvvRX8sRTWOceKhJR8wlqmHT8+HEsX74cs2fPxr/+9S9s3boV999/PxQKBSZNmoTCwkIAqDV3PT4+XtxXWFiIuDjXVV1CQkIQHR0tHuPOZDLBZDKJ93U6XSCfFhERtRKnywpxx5uPwGQ144oLLsZj194T7CEFXVqHJPz3/qXBHgZRwNjtdsyaNQtDhw5Fz549AZz//VGhUCAyMtLlWOffMd3x98em46nKqK7jfFHXlLf6mmH7M53O25Q34Tj3cbtPffN07kBp6ook96/+Bkb+Pldv7ylDJKLgCGqYZLfb0b9/fyxcuBAA0LdvX+zbtw9vvvkmJk2a1GTXXbRoEebPn99k5yciopavxmTAHcsfQYmuDFkdu2DZ5HltduU2ovZs+vTp2LdvH/78889GnYe/PzYNXxsn+xoYOAcOdVXUeKpMAv7XmNtTYORrVZF76FHfNQMdhvgT3ngKkJy/97bN/bV1vu9+/rqCprrG68yXzwd7JxE1r6D+1pyYmIisrCyXbZmZmcjPzwcAJCQkAACKiopcjikqKhL3JSQkoLi42GW/1WpFWVmZeIy7OXPmoLKyUrydOnUqIM+HiIhaB7vdjvtXzce+U4fRITwK7933AkJVmmAPi4gCbMaMGfjmm2+wbt06JCf/r8l7QkICzGYzKioqXI53/h3THX9/bDqNnapUV5hR17G+BB3CY+p7rD/nbqk3X59jY1/P+l5bfzA8IgqeoIZJQ4cOxaFDh1y2HT58GGlpaQCA9PR0JCQkYO3ateJ+nU6HzZs3IycnBwCQk5ODiooKbN++XTzm119/hd1ux6BBgzxeV6lUQqvVutyIiKj9eOGbFfh2529QhMix8t7nkRKTGOwhEVEAORwOzJgxA2vWrMGvv/6K9PR0l/39+vWDXC53+R3z0KFDyM/PF3/HdMffH5uWr1PdfFFXOOJpm3uVjPPNvXG0e6jS0KDG03gDGQp5OndDxuv8GE+vRX2vX33vQ2ME8jNDRP4L6jS3Bx98EEOGDMHChQtx8803Y8uWLXjrrbfw1ltvATj/A2bWrFl45pln0LVrV6Snp+PJJ59EUlISrr/+egDnK5muuOIK3H333XjzzTdhsVgwY8YMjB8/3qeV3IiIqH1Zs/UnLPluJQDghQmPYUBG7yCPiIgCbfr06Vi9ejX+7//+D+Hh4WIfpIiICKjVakRERGDKlCmYPXs2oqOjodVqMXPmTOTk5LD5dhC5hwJNEQ5IJPVPV/PWB8n5sf400nY/tqmacHvjKWDyZZ/zffdQqK59/oZGDXktvAVJDJSImk9Qw6QBAwZgzZo1mDNnDhYsWID09HQsXboUEyZMEI955JFHUFNTg6lTp6KiogLDhg3DDz/8AJVKJR7z4YcfYsaMGRg5ciSkUinGjRuHV199NRhPiYiIWrAdefsx671nAAD3XTYBt+SMCfKIiKgpLF++HABwySWXuGxfuXIl7rjjDgDAkiVLxN8bTSYTRo8ejTfeeKOZR0oCfytL3IMdb8e4f19fKOQt6PH0GG9NuJ3vezpfXWN2PocvGhrU+BIo+fpV+N7fyq36xuxvyMQgiah5SRz8UwedToeIiAhUVlayZJmIqI0qKC/GFYsmo1hXist6DcWqaYshk8qCPSwin/B3lZZHeE+o4WQyGVQqFeLj45GVlYULLrgAQ4cORceOHREfHw+VSgWFQiFOqwJqN612b7ws3Ox2O4DzPfKE+96Ora/KxVNPJ2+VMPXd97bNn/3uGhIoNVVFkvt995vzVDkAHqfMebqW8+ttt9thNpthNBpRWFiIgoIC/Pnnn9i9ezdyc3NRXFwMo9EIm83my8tHdeDfOVSXoFYmERERNQe92Yg7lj+CYl0peiRlYPmUBQySiIhaCOewR7jvvK8h08Lcq46EVdrsdjskEonLV+E6zgFGXdVO3iqU6nus+3Uasr+u5+vP/kBVJnnb5hwWCV8D0TPJWwUbeyYRNT+GSURE1KY5HA7Mfv9Z7Mk/iOiwSLx/3wsIU4UGe1hEROSmsb1vvAU7ztt9meJWV6BT37S4xvRDamwvJV+mjvlz39M0NudjfalQcj+3tyCpvoCtru3u4SMRNQ+GSURE1KZ9suk7fLntZ4RIZXj3nueQ2oGLMxARtRSeVuJqSKBUX5BUX9AiVCp564dUXy8lT/cb06S7oXzpkeS+rb7KJE/bvAVHQiWSL1PXfA2UPFV7+TIFkYiaFsMkIiJqs06eK8DjH78EAHjk2qkY3LVPcAdERERe+TJVqb6G1u49dtz3uz/O+ZyNqVhqyLFNwZ8wyXm7P9VD9YVD7lVNdY3DUwWUvzwFSkTU9BgmERFRm2Sz2zBz5TxUG/UY1OUCTL/8tmAPiYiIvAjU6mWejm/ItDVPPZT86YfkrZqmqQOmQEx187Uyyf1rXT2UGtMryZfPBkMkoubHMImIiNqk13/8AFuO7UGYSoPX7pjLhttERC2Yt5XU/OEppKir6sjXZtgNqTYKZC8lf9R3jboCJV+noXmqQHIPjDzt9/RYT4/zNOa6mm5zehtRcDBMIiKiNmfXyQN44esVAICF4x9inyQiohbMU/+bQHEPg4RV3TyNwdv0ubp6KdV3XW/3m0ogK5M8bfPnq6+9khqL09uIgoNhEhERtSl6sxEz3p0Hq92Gqy8cgZsGXRnsIRERUT18DZLcQ5yG9kPyp0LJ/doNqTJqiZVJvoRJ7tvrC5F8Pc5TNZK369c3tVD4ylCJqHkxTCIiojZlweev4WjRSSRExGLxPx5tll/eiYiocRwOB+x2O+x2e52BgKef6c6hkKd9noIk9wolXyqHvPVO8uexTa2xlUm+9lHyZ8qbL5VJ9e2r67UTPjMMkoiaF8MkIiJqM37ZuwGr1n8OAHhl0hOIDosI8oiIiKg+zlUlvlaYeAqQPPUo8qUyqSHqun59QZO3qilnjRmfr8+vvmlt7g3F6/vqTwVTXRVKztevS0M+N0QUOAyTiIioTThXVY4HP3gGAHD3iFswPGtQkEdERET1aapAwJcgqa4+SYHga48iXx7r73UbWqHkLeTxNUTy92tjXwNPnxsGSkTNg2ESERG1eg6HAw/9ZxFKdGXontQZ/7p+WrCHRERE9XAOAWw2W4OmuHk7xlNgJJFIYLfbfQ6Y3B/raxPuhkyDC6TGTnVz/97bFDR/giSpVOr1XL6+r3Wt6Ga322Gz2VihRNSMGCYREVGr998NX+OH3b9DLgvBG3fOh1qhCvaQiIjIR84BQH2BkjfuU8z8qUzypWKpMdPkmqv5tsDX6W2ejvV2v74pcf5+9adKqz7OvbYYIhE1H4ZJRETUquUVn8ITnywBADx23b3ITu4a5BEREZGvnCuThOokXxpx+8Jb+OMtQKprjHVVKPk6jubSVJVJ3rY3ZMpbYzk3bBeqknypbiOiwGGYRERErZbVZsX0lfOgNxkwpNuFuHfUrcEeEhER+cjTsu6+TnVzrkByvu++raGVSHWN2d/HNLdAhUnO95uiIsnbFEFP9719Jpw/M3a73WU7ETUthklERNRqvfLDe9iRtx9adRheveMpyKSyYA+JiIj8IIQAVqsVVqvVpbrE27Sl+sImT6unBSJY8lShVNd1fRXIyiV/pri532+OKW8NGbP7a+MePtpstlqfHSJqegyTiIioVdqRtw8vf/suAOC5Wx9GcnRCkEdEREQN5T69zZ/qJPdt7qFQU1Yoebvvj0BXOTVFZZLz942Z/lbfOb0d4y1UdP7cMEgial4Mk4iIqNWpMeox/d15sNltuL7/ZRg7cHSwh0RERA3gXJlksVhgNptdVuXy9hghoPB2jL8VSu6P8aUZt6/36xPMyiRP2xoz1c3Tfm9jakyA5txry2w2i5VtDJSImg/DJCIianXmff4q8kpOIykqDs/d+nCwh0NERI1QV4WJp2DAU6jhvoqb8/fewiBvIVBj+iI112Pq0pApZb5Md/Nn2puv56zre2+vi3uvLWGqG4MkoubFMImIiFqVH3f/jg/++BISiQSv3jEXkaHaYA+JiIgaSAgDLBaLWJlUV4WJv4GPp95Gzufxdl73x/oa+HiqMvJ3jI3h6xgbet/XYMmXY/0dpzPnijaz2Sx+fhgoETUfhklERNRqlOhKMfs/iwAA94y8FcO69wvyiIiIqLGcK5Pqa8BdXxNo915Jzse433e+vi+VSr4+F3+nvDVnZZK3Y3ytInK+70+g5O816+KpATd7JhE1P4ZJRETUKjgcDjz4wUKUVpUjs2MG5lx3b7CHREREjeReYVJfZZI3/oYx9U2Hqy9g8nTfUyhUX9VRoIMk5+v6uy+QgVJ9Y/DE39DOvTLJarXWuQogEQUWwyQiImoV3v9jDX7Z+xcUIXK8ced8KOWKYA+JiIgawXkKmb9LvLtXGzlv91SB5E8I1JAgqa7n2BRhUX2ashG3+/2GhFC+nqeuJuyePjN2u93j8UQUeAyTiIioxTtaeBLzPn0FAPD49fchs2OXII+IiIgCwbnCRKgyaeyqXJ6qgTz1TvLUtNv5vj9BkqfpdcK5PD3nuvYHmj/BUiD6Kfl635exeVNfZRIRNT2GSURE1KJZbFZMXzkPBosJF/Xoj7tH3BLsIRERUQC5BwNCpYkvU5Y89T9y3+5LpZL7ORoaJNWnJVYqNSZAcr/f0ADJWx8rd86fCaEqKRABJBH5j2ESERG1aC9/+y52nzyACE04Xpn0FKRSabCHREREAeIcDFgsFphMJjEYaGg44GvDbU/3GxIceapscr6+p7F50tggpCF9o3w9R6ADJeftDXmdhM+H82fGl+mRRBQ4DJOIiKjF2npsD175fhUAYPE/HkVSVFxwB0RERAHnXmXibcpSQ1Yp80V9U96cx1lXryb37f4GR83diLu+4/wNhfy5ni/ndT/GuceWw+GA1WqFxWIRPzM2m83vaxNRw/G/d4mIqEWqNtZgxsr5sDvsuHHQFbiu/6hgD4mIWqnnnnsOEokEs2bNErcZjUZMnz4dMTExCAsLw7hx41BUVBS8QbZjnqa5eWumLJFIaoUXdYUcnvY7b3du/lzXzZdjfL0F8lxNeS1Pr2FDrlffe9iQ91f4fAifGVYlETU/hklERNQiPfnJUpw8dwYdoxOwcPxDwR4OEbVSW7duxb///W/07t3bZfuDDz6Ir7/+Gp9++inWr1+PgoICjB07NkijbN+EVbksFguMRqNYaRKocMDfPkW+VunUFVTVd35vQUxjNOS89YVt7ts9Pd7f8dXFl/dbCB+FqiThMyMESkTUPDjNjYiIWpxvd67Dfzd8DYlEgtcnz4VWHRbsIRFRK1RdXY0JEyZgxYoVeOaZZ8TtlZWVeOedd7B69WqMGDECALBy5UpkZmZi06ZNGDx4cLCG3O4I4YFQZSJMcRMacDsf48xb0OFpKppzxYynaztv97XPUn3bg6Eh46irQqix230JsgDvfaiEfc6cPxPC1EhhipsQPrI6iah5sDKJiIhalKLKc3j4P88BAKZffhtyuvYN8oiIqLWaPn06xowZg1GjXKfJbt++HRaLxWV7jx49kJqaio0bN3o8l8lkgk6nc7lRYDg34DYYDDCZTC4BgXCML5oq2GlIuOLvWAIxpc3fa/n7nJqCr+d1Dh6dG7YbDAaxMolBElHzYWUSERG1GA6HA7PeewZlNZXomdINj1wzNdhDIqJW6qOPPsKOHTuwdevWWvsKCwuhUCgQGRnpsj0+Ph6FhYUez7do0SLMnz+/KYba7rmv6OZLZZIvvFUSedtfV5VRa6hM8oevVUP+PM7ffQ157dwDJaEyif2SiJpfUCuT5s2bVytR79Gjh7jfl8aI+fn5GDNmDDQaDeLi4vDwww/DarU291MhIqIAePe3z7AudxNUciWWTZ4PRYg82EMiolbo1KlTeOCBB/Dhhx9CpVIF5Jxz5sxBZWWleDt16lRAzkuuPXAMBgMMBgOMRmOTrNAV6OCnIT2JgsnXPkqBvmYgryOESEajUfy8mM1mBkpEzSzolUnZ2dn45ZdfxPshIf8b0oMPPohvv/0Wn376KSIiIjBjxgyMHTsWf/31F4DzP0jGjBmDhIQEbNiwAWfPnsXEiRMhl8uxcOHCZn8uRETUcIfP5uHpL14HADwxdjq6J6UHeURE1Fpt374dxcXFuPDCC8VtNpsNv//+O15//XX8+OOPMJvNqKiocKlOKioqQkJCgsdzKpVKKJXKph56u+SpMklY0U3YH0i+9E7yZZ+wvyWFRfXxdayBCJya4nVx77HlXpnEMImo+QQ9TAoJCfH4l7YvjRF/+ukn5Obm4pdffkF8fDz69OmDp59+Go8++ijmzZsHhULR3E+HiIgawGy1YPq7c2G0mHBp1mDcOfzGYA+JiFqxkSNHYu/evS7bJk+ejB49euDRRx9FSkoK5HI51q5di3HjxgEADh06hPz8fOTk5ARjyO2ew+FwqUwyGAwu091ae0ggkUiC/hyaK/Rqquu4h47OnxWLxRL015eovQl6mHTkyBEkJSVBpVIhJycHixYtQmpqar2NEQcPHoyNGzeiV69eiI+PF48ZPXo0pk2bhv3796NvXzZtJSJqDV74egX2njqMqFAtlkx8HFIp14cgooYLDw9Hz549XbaFhoYiJiZG3D5lyhTMnj0b0dHR0Gq1mDlzJnJycriSW5A4T3Xz1DfJm7qCC/eqIW/n8mUlOE/nru/6DTm2OfgzjkBOifO3R5U3zp8V9kwiCp6ghkmDBg3CqlWr0L17d5w9exbz58/HRRddhH379vnUGLGwsNAlSBL2C/u8MZlMMJlM4n2uxkFEFDybjuzC6z99AAB48bY5SIiMDfKIiKg9WLJkCaRSKcaNGweTyYTRo0fjjTfeCPaw2iWh4sS5D45erxd7JvkbEgghRUNWOKOGach0P/egz9dgzmazwWw2i58Tob9WW6hgI2pNghomXXnlleL3vXv3xqBBg5CWloZPPvkEarW6ya7L1TiIiILHaDFh/6kj2JG3HztP7Me63E1wOBy4JWcMxvS9NNjDI6I26rfffnO5r1KpsGzZMixbtiw4AyIXQkggVJqYTCaxb5IQEjS2P5GnCiThvrdjPY2zrv0NPTYYmqpCqal6JQk3oV+SyWQSq5NYmUTU/II+zc1ZZGQkunXrhqNHj+Kyyy6rtzFiQkICtmzZ4nIOYbU3b80TgfOrccyePVu8r9PpkJKSEsBnQkREwPkGmXklp7Ejb//524n9yD19BBab66qbXRM64ZmbZ3s5CxERtXXCUu9msxl6vR7V1dW1AiVfNcVqZa2t0XZr4ut76xwkmc1mVFdXiyu52Ww2sWE7ETWPFhUmVVdX49ixY7j99tvRr1+/ehsj5uTk4Nlnn0VxcTHi4uIAAD///DO0Wi2ysrK8XoercRARNY1zVeV/VxzlYueJ818r9VW1josOi8SF6dm4sFM2LkzPxqAuF0CtCMzy3URE1LoIQY1zUCBMXXIPCerrs+NrxZCnShpPPZPcj6mv74/z41pT+NTQsXp77QJZ9eT8mjqHjgaDwSVwdD+WiJpWUMOkhx56CNdccw3S0tJQUFCAuXPnQiaT4dZbb0VERES9jREvv/xyZGVl4fbbb8fixYtRWFiIJ554AtOnT2dYRETUxAxmI/adOiyGRztO7Ef+uYJax6nkSvRK6YYL07PRt1M2+qZnIzUmsVX9kk1ERE3LvReOc2WSr9PcGrvsvbDimtBvyZdgoj3/XeZtapt7qORLuFTfMc6fAWGKW01NDYxGo1iZxCCJqHkFNUw6ffo0br31VpSWliI2NhbDhg3Dpk2bEBt7vvlqfY0RZTIZvvnmG0ybNg05OTkIDQ3FpEmTsGDBgmA9JSKiNslut+NYcb44XW3niVzknj4Cq91W69iuCWno+3fFUd9O2chK7gK5rEUVwhIRUQskVJ0YjUZxCpPJZGpwUOCtysiXx7h/766+leEaK5DT6hpzrkD0qHI/h6f3xZ/m2yaTSfyMGI1GTnEjCpKg/nb/0Ucf1bnfl8aIaWlp+O677wI9NCKids9kMWP5zx9iw+Ed2HXyAHSG6lrHdAiPcpmudkFaJiI04UEYLRERtWbuVSd6vV5ssOxLWNCYiiVfwib3Ztp1rUQWiAqZQFY8+dpDylPo1NhV2vw9rq7XTggbLRYLjEaj+Blxrl4joubD/yomIiKP1mz9Cc999W/xvlquRO+0HuenqnXKwoXp2UiOTmjXJf5ERBQ4QlhgMBig0+lQU1MDg8FQa1W3YP294y38aAt/D3p7Hi3hubmv4mYwGFBTUwOdTgeDwcDKJKIgYZhEREQebTyyEwBwzYUjcf8VE9GjYwanqxERUZMRAgOh8sRkMsFsNrsESU3Bl+lsdfVZqm9bXRU/zl+dH+9vnyFP4/T1uk1ZfRQozoGS2WwWp7o5fz6IqHnxXwVEROTR1mN7AAC35IxBr9TuQR4NERG1dUJYIFQmCTfnBsutKTSoK6Rxny7nra9QXeesr7+Tp+lr3r625Aor4X0X+iU5fzaMRiPDJKIgYZhERES1lOhKcbz4FACgf+eeQR4NERG1B85TmUwmk3hznubW3BrTb8lbUOTtPL4EO54qjwKxyp2vYVawCJ8NIVASbhaLhWESUZBIgz0AIiJqebYe2wsA6J7UGZGh2iCPhoiI2gMhMBBW6iovL0dpaSkMBgMsFkurq0zyh6+ryAm8VSi1RcL7brFYoNfrUVpaioqKClRXV8NkMjFMIgoSViYREVEtW/6e4jYo44Igj4SIiNoT575JJpNJDJKEaW4tTWOCnMY8n4ZUG7Vmziu5GQwGGI3GFv25IGoPWJlERES1bDm2GwAwIKN3kEdCRETthRAKmM1mGAwGlJWVoaSkBFVVVS6rulH74rzKX3V1NYqLi1FeXi4GjUDjgjkiahhWJhERkQuD2Yi9+YcAAAMZJhERUTNy7ptkNBpRU1NTqzdOS24W7Y+28ByamvMqbkK1ml6vh9FoDGovLSJqYJi0du1arF27FsXFxbX+d+Ddd98NyMCIiCg4dp08AIvNiviIDkjtkBTs4RARUTtjtVphNptRUVGB4uJiVFRUoKqqChaLBXK5vE0FSuSd8ypuFosFVVVV4meivLxcbM5ORMHhd5g0f/58LFiwAP3790diYiJ/iBMRtTFbjv5viht/xhMRUXNyDhCMRiP0ej30ej0MBgNsNlubq04i75yrkqxWKwwGg/h5cG68zcokouDwO0x68803sWrVKtx+++1NMR4iIgoyofk2p7gREVEwCD1yqqqqUFpairKyMpSXl8NoNEKpVDJAaCeE99lqtcJkMqGsrAylpaUoLS1FVVWVGC4SUXD43YDbbDZjyJAhTTEWIiIKMrvdjm3H9wIABnbhSm5ERNT8hBBB6I+j0+lQWVkpTmtigNB+OPdK0ul00Ol0YmUSQ0Wi4PI7TLrrrruwevXqphgLEREF2eHCE6jUV0GtUCE7uWuwh0NERO2QMLXJaDSK1Unnzp2DwWBwCREYJrRNzu+t3W6H2WyGXq/HuXPnxKokg8HA5ttEQeb3NDej0Yi33noLv/zyC3r37g25XO6y/+WXXw7Y4IiIqHkJ/ZIuTM+GXMYFP4mIKDgcDodYkVJWVgatVouqqiqEhobCZrNBKpVCJpMFe5jUhITpjgaDAVVVVSgpKXFpvM0giSi4/P6Xwp49e9CnTx8AwL59+1z2sQkeEVHrxn5JREQUbEJIIIRJFRUVOHfuHKqrq8VG3DKZTDxOIpGwIXcbILyfzlVJNpsNer0e1dXVOHfunBgmWSwWVqYRBZnfYdK6deuaYhxERNQCbBXDJPZLIiKi4HFeEr6srAwKhQLFxcVQqVRISEiAVCqFXC53CZAYKLVe7qGQe+Pt4uJiFBcXo7y8HGazGTabjUESUZD53TPJ2enTp3H69OlAjYWIiIKoqPIcTp47A4lEgn6dewZ7OERE1M4JS8JXV1ejsrISlZWV0Ol0sFgsYpjA6pS2xfk9FcJEoQF7ZWUlqquruYobUQvhd5hkt9uxYMECREREIC0tDWlpaYiMjMTTTz/NP9RERK3YlqPnq5IykzKgVYcFeTRERNTeCdOcdDodSktLkZ+fj/z8fFRWVkKv17uECgyUWj/hPRTe95qaGlRWVorve2lpKXQ6HcMkohbC72lujz/+ON555x0899xzGDp0KADgzz//xLx582A0GvHss88GfJBERNT0xCluXTjFjYiIgs95NS+DwYCKigpERETAaDTCZDLBbrdDKpW6TG/jVLfWxzkIdF/FzWAwoLy8HBUVFdDr9TCbzVzFjaiF8DtMeu+99/D222/j2muvFbf17t0bHTt2xH333ccwiYioldp87PxKbmy+TURELYEQKhgMBgDAiRMnYLVaUVBQALvdjsjISACATCZjgNRGOPdKOnfuHM6ePYvjx4/j1KlTYgN2hklELYPf09zKysrQo0ePWtt79OiBsrKygAyKiIiaV43JgH2nDgMABjBMIiKiFkTonVNVVSX2TaqurobVaoXNZgMA9k5q5ZzfP+H9rq6uFvslVVdXi72yiKhl8DtMuuCCC/D666/X2v7666/jggs4NYKIqDXaeSIXNrsNSVFxSI5OCPZwiIiIAPxvVTez2YyioiKcOnUKBw8exLFjxzz2TqLWS2i4rtfrUVlZiaNHj+LgwYM4deoUioqKuIobUQvjd5i0ePFivPvuu8jKysKUKVMwZcoUZGVlYdWqVXjhhReaYoxERNTEtv49xW1ARm9OFSCiNuHMmTO47bbbEBMTA7VajV69emHbtm3ifofDgaeeegqJiYlQq9UYNWoUjhw5EsQRkzfCdDej0Qi9Xo/S0lKUlZWhuroaRqOxVsDAKqXWwf19cp7WWFNTg/LycpSVlaGmpgZGo5HT24haGL/DpOHDh+Pw4cO44YYbUFFRgYqKCowdOxaHDh3CRRdd1BRjJCKiJias5MYpbkTUFpSXl2Po0KGQy+X4/vvvkZubi5deeglRUVHiMYsXL8arr76KN998E5s3b0ZoaChGjx4No9EYxJGTJ86re5WWluLgwYM4ePAg8vPzUVRUBKPRCIvFwhCplRLeN4vFAqPRiKKiIpw8eRIHDhzAwYMHxUCJFWhELYvfDbgBICkpiY22iYjaCJvdhm3H9wIABmVwujIRtX7PP/88UlJSsHLlSnFbenq6+L3D4cDSpUvxxBNP4LrrrgMAvP/++4iPj8eXX36J8ePHN/uYqW7CdDeLxYLKykqUlZWhuLgYCoUCRqMREokECoUCUun5/ytnlW3rIFQjORwOmM1mGI1GlJWVoaSkBOXl5aisrBR7JTEoJGpZfAqT9uzZg549e0IqlWLPnj11Htu7N/9Xm4ioNTlUcBxVxhqEKjXI7JgR7OEQETXaV199hdGjR+Omm27C+vXrxVWH7777bgBAXl4eCgsLMWrUKPExERERGDRoEDZu3OgxTDKZTDCZTOJ9nU7X9E+ERELlisPhwNmzZ2Gz2bBnzx4YDAYkJycjMjISKpUKMpkMISEN+v9yChKh8qy6uhoVFRU4fPgwjh07hhMnTqC4uBgGgwFWq5VhElEL49NP2j59+qCwsBBxcXHo06cPJBKJxz/MEomEHfaJiFqZzUfP90vql56NEBl/ASei1u/48eNYvnw5Zs+ejX/961/YunUr7r//figUCkyaNAmFhYUAgPj4eJfHxcfHi/vcLVq0CPPnz2/ysZN3QhWLyWRCdXU1zp49i9DQUBQVFQEAwsPDxeokoUIJYJVSSyP8O1J4P61WK8xmM8rLy1FcXIyzZ8/i7NmzqKqqgslkYq8kohbKp3815OXlITY2VvyeiIjajq3H2C+JiNoWu92O/v37Y+HChQCAvn37Yt++fXjzzTcxadKkBp1zzpw5mD17tnhfp9MhJSUlIOMl3wjhg16vh8PhwKFDh2Cz2dCpUyfYbDZER0cDAEJCQiCRSBgitXDC+2k2m1FTU4OCggLk5eXh0KFDOHbsGMrLy2EwGBgmEbVQPoVJaWlp4vcnT57EkCFDapWPWq1WbNiwweVYIiJq+bb8HSYN6sJ+SUTUNiQmJiIrK8tlW2ZmJj7//HMAQEJCAgCgqKgIiYmJ4jFFRUXo06ePx3MqlUoolcqmGTD5TOidZDabUVlZiaKiIhw6dAgAEBsbi5iYGISEhEAul4uhkoDhUnA5VyQ5HA5YrVaxB1ZpaSny8vJw+PBhFBUVobKyEmazmb2SiFowv1dzu/TSS1FWVlZre2VlJS699NKADIqIiJpHQXkxTpcVQiqR4sL07GAPh4goIIYOHSoGDILDhw+L/+mZnp6OhIQErF27Vtyv0+mwefNm5OTkNOtYyT/OYVJFRQXOnj2L3NxcHDt2DAUFBaioqGAI0QoI76PJZEJFRQUKCgpw7Ngx5Obm4uzZs3wfiVoBv5tjOBwOj6l+aWkpQkNDAzIoIiJqHluOne+XlJ3cBWEq/gwnorbhwQcfxJAhQ7Bw4ULcfPPN2LJlC9566y289dZbAM5XqMyaNQvPPPMMunbtivT0dDz55JNISkrC9ddfH9zBU72cp0fpdDqcOnUKKpUK4eHhMBqNkMvliImJQXh4OORyea0eShQ8drsddrsdFosFVVVVKC0txZEjR5Cbm4vDhw/j1KlTqKqqgtls5vQ2ohbO5zBp7NixAM7/5XvHHXe4lPkKqykMGTIk8CMkIqImI/RLGsgpbkTUhgwYMABr1qzBnDlzsGDBAqSnp2Pp0qWYMGGCeMwjjzyCmpoaTJ06FRUVFRg2bBh++OEHqFSqII6cfCUEEnq9HiUlJWKYpNVqER8fD7VaLa7uJgRJQjDB6W7Nyz0Qcn7vSktLcfr0aRw+fBinT59GSUkJ9Ho9LBYL7HZ7kEZMRL7wOUyKiIgAcP6HQXh4ONRqtbhPoVBg8ODB4nKrRETUOmz5eyU3Nt8morbm6quvxtVXX+11v0QiwYIFC7BgwYJmHBUFkhBK1NTUoLCwUAwtjEYj+vbti06dOqFDhw7QaDRQKBRsyh1EQjWZECKdO3cOeXl52LVrF/bt24f9+/ejqKgINTU1DJKIWgmfw6SVK1cCADp16oSHH34YGo0moAN57rnnMGfOHDzwwANYunQpgPN/Efzzn//ERx99BJPJhNGjR+ONN95wWcY1Pz8f06ZNw7p16xAWFoZJkyZh0aJFtRqEExGRq2pjDfafPgoAGJjByiQiImp9hICiuroaABAZGYnQ0FAkJSUhMjISYWFhYjNuqVQKiUTCCqVm4lyRJDTdtlgsMBqNKC8vR1FREfLy8nD69GkUFRWhurqaQRJRK+J34jJx4kScOXMGXbt2ddl+5MgRyOVydOrUye9BbN26Ff/+97/Ru7fr/4w/+OCD+Pbbb/Hpp58iIiICM2bMwNixY/HXX38BOD+9bsyYMUhISMCGDRtw9uxZTJw4EXK5XFwKloiIPNuRtx92hx3J0QlIiooL9nCIiIj8JjRyNhqNsNlsOHr0KMrLy2G1WnH69GkMHjwYHTt2RHx8PFQqFeRyOSuUmpEQIpnNZphMJhQVFeHMmTPYtGkTjh07hu3bt6O0tBSVlZWwWCxsuE3Uivjdie6OO+7Ahg0bam3fvHkz7rjjDr8HUF1djQkTJmDFihWIiooSt1dWVuKdd97Byy+/jBEjRqBfv35YuXIlNmzYgE2bNgEAfvrpJ+Tm5uI///kP+vTpgyuvvBJPP/00li1bBrPZ7PdYiIjaky1CvyROcSMiolbMeYW3qqoqlJSUoKCgAPn5+SguLkZZWRkMBkOtps5C0EGB5fy6uk9vKysrQ1FREfLz83HmzBmUlJSIDbcZJBG1Ln6HSTt37sTQoUNrbR88eDB27drl9wCmT5+OMWPGYNSoUS7bt2/fDovF4rK9R48eSE1NxcaNGwEAGzduRK9evVymvY0ePRo6nQ779+/3ek2TyQSdTudyIyJqb9gviYiI2gq73Q6bzSYGFnv37sUff/yBH3/8Ed9//z0OHjyIU6dOoaamhiuFNQPnFfdqampw6tQpHDx4EN9//z1++ukn/PHHH9i3bx/Kysqg1+ths9k4vY2olfF7mptEIkFVVVWt7ZWVlbDZbH6d66OPPsKOHTuwdevWWvsKCwuhUCgQGRnpsj0+Ph6FhYXiMc5BkrBf2OfNokWLMH/+fL/GSkTUllhtVmzPOx+6D+JKbkRE1AYIFUoOhwM1NTWw2+0oKCgAAJw5cwYOhwMRERGw2+3iKm8ymYw9lALEOZyz2+2w2+0wGAzQ6/UoLCxEQUEBTp06hYKCApSXl0Ov18NqtTLYI2ql/A6TLr74YixatAj//e9/IZPJAJzvXbRo0SIMGzbM5/OcOnUKDzzwAH7++edmX4J1zpw5mD17tnhfp9MhJSWlWcdARBRMB84cQ41Jj3BVKLondQ72cIiIiAJCCDGqqqqg1+uxe/duHD16FAaDAR07doTVakVsbCzS0tKgVCqhVCrFxtzUeEJFkslkgslkwsmTJ1FSUoIff/wRp0+fxrZt21BdXY2KigrYbDa/ixGIqOXwO0x6/vnncfHFF6N79+646KKLAAB//PEHdDodfv31V5/Ps337dhQXF+PCCy8Ut9lsNvz+++94/fXX8eOPP8JsNqOiosKlOqmoqAgJCQkAgISEBGzZssXlvEVFReI+b4S/OIiI2qvNx85PcevfuRdkUlmQR0NERBRYwpQpvV4vVijZbDYcP34cer0e4eHhCA0NRVRUFGQymfif5AKGS75xX7FNCIh0Oh1qampw8uRJFBYWIj8/H0VFRaiqqhKbpXNaG1Hr5neYlJWVhT179uD111/H7t27oVarMXHiRMyYMQPR0dE+n2fkyJHYu3evy7bJkyejR48eePTRR5GSkgK5XI61a9di3LhxAIBDhw4hPz8fOTk5AICcnBw8++yzKC4uRlzc+ZWIfv75Z2i1WmRlZfn71IiI2o2tQvPtLuyXREREbY8QbNTU1MBgMGDv3r04fvw4qqurkZycDLvdjoSEBMjlciiVSqjVakgkEkilfreUJUCcqmY0GmE0GnH8+HEUFRXh+++/x+nTp7F3717U1NSgurparB4jotbN7zAJAJKSkrBw4cJGXTg8PBw9e/Z02RYaGoqYmBhx+5QpUzB79mxER0dDq9Vi5syZyMnJweDBgwEAl19+ObKysnD77bdj8eLFKCwsxBNPPIHp06ez8oiIyAuHw+HUfJv9koiIqO1ynnYFAGfPnoXNZsPevXtRVlYGlUqFiIgIxMXFQS6XQy6Xu1QlsULJM/cV8SwWCywWC4qLi1FRUYHc3FwUFBTg5MmTKC4uRk1NDUwmE/sjEbUhDQqTKioqsGXLFhQXF9dKlSdOnBiQgQHAkiVLIJVKMW7cOJhMJowePRpvvPGGuF8mk+Gbb77BtGnTkJOTg9DQUEyaNAkLFiwI2BiIiNqa02WFOFtRAplUhr6dWMVJRERtlxB2GI1GmM1mHD16VGwA3alTJ9hsNrF/UmhoKKRSqdiYm+onVBnp9Xro9XocPnwY+fn5+Pnnn3Hy5EmcOHECBoMBRqORQRJRG+N3mPT1119jwoQJqK6uhlarrZXcNyZM+u2331zuq1QqLFu2DMuWLfP6mLS0NHz33XcNviYRUXsjTHHrmdINoUp1kEdDRETU9IQKJYvFAoPBgJKSEgDA1q1bUVJSApvNhsTERHTs2BEajQYqlUoMlgBWKAmEMEgIkYxGI/R6Pc6cOYOzZ89ix44dOHnypNh422g0wmKxMEgiaoP8DpP++c9/4s4778TChQuh0WiaYkxERNSEtvwdJg3iFDciImpHHA4HzGYzrFaruNBPeXk50tPTYTAYkJ2dDZVKBYfDAZlMJk55Y5DkyjmYq6mpQVlZGQ4ePIj9+/djy5YtyMvLE4Mkq9XK/khEbZTfYdKZM2dw//33M0giImqlhMqkARlsvk1ERO2P3W6H1WqF0WhEWVkZJBIJ7HY7zp07h6KiIvTo0QOpqamIjY1FaGgoFAqFS5US0H4qlZyriYRqJLPZjJqaGpSUlCA/Px8HDx7EgQMHcOzYMeTn56OsrAwmk4lBElEb53eYNHr0aGzbtg2dO3duivEQEVET0hmqkXvmKACu5EZERO2XEIoIoVJ5eTnKy8tRWloKh8MBqVQKhUIBmUwGmUwGiUQCh8MhhkhCyNJWQyX3KWlCNZLNZoPRaERlZSVOnz6N3NxcbNy4EcePH0d+fj70ej3MZjOntRG1A36HSWPGjMHDDz+M3Nxc9OrVC3K53GX/tddeG7DBERFRYG0/vg8OhwNpHToiPqJDsIdDREQUNO7TtU6fPg2dToeqqirs27cP/fv3R0pKCrp3746IiAhotVqEhISI4VJ74HA4YLPZYLVaodPpUFlZiYMHD+LUqVPYvn07zpw5g2PHjkGn06Gmpob9kYjaEb/DpLvvvhsAPK6YJpFIYLPZGj8qIiJqEls4xY2IiEjkcDhgtVphs9lgs9lQXV0Ni8WCoqIiaDQaGI1GREdHAwCUSqVYnSSRSCCVSl1Ck9YeMLkHQEIoZLFYYDabUVlZiZKSEhw5cgR5eXnYsWMHysvLUVJSAqvVCqvVyhCJqB3xO0zivFciotZry7HdAICBDJOIiIhEzqHSuXPnoNPpYDabsWPHDhw/fhyJiYkYMmQIYmJikJycDIVCAZVKJYZKwjlaa6Dk3hvJ4XDAaDTCbDbj9OnTOHfuHDZs2IDCwkLs2LEDFRUVKCgogNlshslkgsPhYJBE1M74HSYREVHrZLFZsSNvPwBgYBeu5EZERORMCESMRqMYkJSXlyM0NBSVlZVITk6GyWSCVquFRqNBSEgIpFKpGCC591VqLYQQSPhqs9lgt9uh1+tRU1ODgoICFBYW4tChQygsLEReXh4MBgOqq6vFqYJE1P74HSZ5mt7m7KmnnmrwYIiIqOnsP30EBrMREZpwdEvoFOzhEBERtUhCOFJdXQ29Xo+dO3dCrVYjPz8fcXFxuOiii5CYmIi+ffsiNDQUUVFRLo26WyOhN5LNZkN5eTlqamqwc+dOFBQU4I8//kBJSQmOHz8Og8EAnU4nNuMmovbL7zBpzZo1LvctFgvy8vIQEhKCjIwMhklERC3UlqPnp7j179zLZXljIiIiqk2o0KmqqoLRaMSpU6eg1+uRlJQEo9GI2NhYREdHQy6XQ6lUQqVSQSqV1vo7tqUFTJ56I9ntdrEiq6SkBGVlZTh+/DjOnDmDEydOoKysDOXl5bBYLOyNREQAGhAm7dy5s9Y2nU6HO+64AzfccENABkVERIEnNN8exCluREREPnE4HDCbzbBYLCgoKEBJSQmKi4sRHR2NvXv3IiMjA8OGDUN8fDw6duwIlUoFhULhMv2tpRKmqJnNZhiNRpw5cwZFRUX4888/cezYMezbtw+lpaViiGQ2mxkiEZEoID2TtFot5s+fj2uuuQa33357IE5JREQB5HA4sJUruRERETWIsKqZ3W5HRUUF7HY78vPzIZVKERcXB6PRiJCQEERFRSE8PBxyuRwymcxlxbdgh0vuTbZtNhssFgt0Oh0qKipw4sQJnDp1CsePH0d+fj5KSkpQVVUFk8kEm83GIImIXASsAXdlZSUqKysDdToiIgqg/HMFKKo8B7ksBH3SMoM9HCIiolZHmA5mtVqh1+tRUVGBo0ePIjc3F9nZ2ejfvz+ys7ORkZGBiIgIqNVqAGhxU8uFIMlgMKCyshLHjh3D/v37sXXrVuTm5qKgoAA6nQ5Go5EhEhF55XeY9Oqrr7rcdzgcOHv2LD744ANceeWVARsYEREFjjDFrVdqd6gVqiCPhoiIqPUSpoeZTCbU1NTg3LlzyM/PF1d4s9vtSEtLQ3R0tLhNJpMFrULJOQyy2WxiGFZWVoaTJ0/i8OHDyM3NRX5+Ps6dO4eamhqYTCbY7XYGSUTkld9h0pIlS1zuS6VSxMbGYtKkSZgzZ07ABkZERIEjTHEbmMF+SURERI0lVClVVVVBr9eLFT5nzpzB8ePHcfHFFyMjIwPx8fFQq9WQSCRBr1Cy2+2wWCwwGAwoKirC0aNH8ccff+DgwYPYvXs3dDodampqxMbjRER18SlM2rNnD3r27AmpVIq8vLymHhMREQXYFjFMYr8kIiKiQHE4HLDZbDAajZBIJDh9+jQcDgdiYmLEbVFRUYiIiEBISIhLoNTUFUpCVZFQSWW1WqHT6VBWVob9+/fj6NGjOHjwIE6fPo3q6mqxNxKDJCLyhU/xeN++fXHu3DkAQOfOnVFaWtqkgyIiosCpqNHhYMExAMCAjF5BHg0RUdOz2Wx48sknkZ6eDrVajYyMDDz99NMuU3YcDgeeeuopJCYmQq1WY9SoUThy5EgQR02tkRDUGI1GVFZW4ujRo9i6dSs2bNiAv/76CydPnkRZWRmMRiOsViscDkezTh0Trme1WmE0GlFaWoqTJ0/izz//xIYNG7B161YcO3YMlZWVMBqNDJKIyGc+VSZFRkYiLy8PcXFxOHHiBH/IEBG1ItuO7wMAdI5LQaw2JsijISJqes8//zyWL1+O9957D9nZ2di2bRsmT56MiIgI3H///QCAxYsX49VXX8V7772H9PR0PPnkkxg9ejRyc3OhUrG3HPlHCJXMZjMAID8/HyaTCcnJyaiqqoJCoYBWq4VWq4VMJmvSHkqeVm2rqqpCZWUlcnNzceLECRw4cABFRUXQ6/Uwm83sj0REfvMpTBo3bhyGDx+OxMRESCQS9O/fHzKZzOOxx48fD+gAiYiocbYe2w0AGMApbkTUTmzYsAHXXXcdxowZAwDo1KkT/vvf/2LLli0Azv9je+nSpXjiiSdw3XXXAQDef/99xMfH48svv8T48eODNnZqvRwOB8xmM6xWK06fPo2KigokJyfDYDAgNTUVMpkMGo1G7J8khEgOhyNggZJ79Z0wva26uhplZWU4ePAg8vLycPjwYbHfE4MkImoIn8Kkt956C2PHjsXRo0dx//334+6770Z4eHhTj42IiAJgM/slEVE7M2TIELz11ls4fPgwunXrht27d+PPP//Eyy+/DADIy8tDYWEhRo0aJT4mIiICgwYNwsaNGxkmUYMJwYxer4fNZhNDm/T0dOj1eqjVavEmlUrFHkqBCJTcK5KE6Xd6vR4nT57E6dOnsXfvXhQUFKCyslLskcQgiYgawufV3K644goAwPbt2/HAAw8wTCIiagXMVgt2ncgFAAzswpXciKh9eOyxx6DT6dCjRw/IZDLYbDY8++yzmDBhAgCgsLAQABAfH+/yuPj4eHGfO5PJBJPJJN7X6XRNNHpq7YQKJbvdjsLCQlitVpw9exYKhQKdOnWCTCaDUqmERCJxCZEaEyi5VyQ5T7szGo0oLi7G2bNncerUKZw7dw4Gg0Hs4URE1BA+h0mClStXNsU4iIioCew7dQhGiwnRoRHoEp8W7OEQETWLTz75BB9++CFWr16N7Oxs7Nq1C7NmzUJSUhImTZrUoHMuWrQI8+fPD/BIqa0SppdVVFTA4XDgyJEjMJvNSE9Ph81mg0qlgsPhgFwuBxC4vknODbetVisqKytRVlaGI0eOID8/H8XFxdDpdLBareyDS0SN4tNqbkRE1DptPnq+X1L/jF5NvgQxEVFL8fDDD+Oxxx7D+PHj0atXL9x+++148MEHsWjRIgBAQkICAKCoqMjlcUVFReI+d3PmzEFlZaV4O3XqVNM+CWrVhMogk8kEvV6P8vJylJWVQa/Xw2QyidPhnG+BuKbzzf365eXlMBgMLtcnImoohklERG3YVrFfEqe4EVH7odfrxV40AplMJlZipKenIyEhAWvXrhX363Q6bN68GTk5OR7PqVQqxdW4hBuRN84VQiaTCaWlpSgpKUFZWRl0Op3YqLspAh3humazGTqdDuXl5SguLkZpaSlMJpN4XYZJRNQYfk9zIyKi1sHhcGALm28TUTt0zTXX4Nlnn0Vqaiqys7Oxc+dOvPzyy7jzzjsBnJ9SNGvWLDzzzDPo2rUr0tPT8eSTTyIpKQnXX399cAdPbYpQIWSxWMQAqTnCHOeV3CwWi3hjRRIRBQrDJCKiNupEyWmcqyqHIkSO3mk9gj0cIqJm89prr+HJJ5/Efffdh+LiYiQlJeGee+7BU089JR7zyCOPoKamBlOnTkVFRQWGDRuGH374ASqVKogjJyIiah0aNM3tgw8+wNChQ5GUlISTJ08CAJYuXYr/+7//C+jgiIio4YR+SX3SMqGSK4M8GiKi5hMeHo6lS5fi5MmTMBgMOHbsGJ555hkoFArxGIlEggULFqCwsBBGoxG//PILunXrFsRRU1skkUgglUohl8uhUCggl8sREhICiUTSpL0MheuGhIS4XFsqlbKHIhEFhN9h0vLlyzF79mxcddVVqKiogM1mAwBERkZi6dKlgR4fERE1kNAvaQCnuBERETUrISwKCQmBUqlETEwMYmNjERUVBa1WC4VCIYZKTXHtkJAQKBQKaLVaREVFITY2FjExMVAqlc0SZhFR2+d3mPTaa69hxYoVePzxxyGTycTt/fv3x969ewM6OCIiajj2SyIiIgoOoTJIpVJBo9EgOjoa0dHR0Gg0UKlUkMlkYqATqGDH/XzC9UNDQxEdHY2oqChoNBoolUpWKBFRo/ndMykvLw99+/attV2pVKKmpiYggyIiosYpq67EkcITAID+DJOIiIialTDFLCIiArGxsejSpQvS0tLQoUMHhIWFISQkxCVQChThXEL1kVarhVQqRdeuXaFQKLB3715IJBJUVVXBarWKKxwSEfnL78qk9PR07Nq1q9b2H374AZmZmYEYExERNdK24+erkrompCEmLDK4gyEiImpHJBIJFAoFNBoNEhMTkZKSgsTERMTGxkKtVkOhUIiVQc5BUmNCJffzCJVJCoUCarUasbGxSExMRGpqKhISEsRxsDqJiBrK78qk2bNnY/r06TAajeeXnd6yBf/973+xaNEivP32200xRiIi8tMW9ksiIiJqdlKpFFKpFBqNBmFhYejatSvS09PRtWtXxMXFISwsDHK5XKxKEgRqmpvD4RDHIZFIxCl1nTp1gkajQc+ePREaGopTp06hqqoKZrMZdrudFUpE5De/w6S77roLarUaTzzxBPR6Pf7xj38gKSkJr7zyCsaPH98UYyQiIj9t+XsltwEZFwR5JERERO2DUJGkUCiQnJyMhIQEZGVlIS0tDTExMeL0Nvd+RYGe5iYESs4ruoWGhiImJgaZmZlQq9U4c+YMioqKYLFYYDabYTKZxMcREfnC72luADBhwgQcOXIE1dXVKCwsxOnTpzFlyhS/z7N8+XL07t0bWq0WWq0WOTk5+P7778X9RqMR06dPF3/4jhs3DkVFRS7nyM/Px5gxY6DRaBAXF4eHH34YVqu1IU+LiKhNMFnM2H3yIABgECuTiIiImpzztDKNRoPU1FT06NED2dnZyMrKqhUmCY9pqtXchPMKYVJ4eDhiYmKQlZWF7Oxs9OjRAykpKdBoNC7T7oiIfOV3ZdIzzzyDCRMmID09HRqNBhqNpsEXT05OxnPPPYeuXbvC4XDgvffew3XXXYedO3ciOzsbDz74IL799lt8+umniIiIwIwZMzB27Fj89ddfAACbzYYxY8YgISEBGzZswNmzZzFx4kTI5XIsXLiwweMiImrN9uQfhMlqRkx4FNLjUoI9HCIiojZLCG6USiXUajXS09PRsWNHDB06FBkZGUhLS0N0dDRUKpXYFLs5QxvnhtwqlQoxMTGQSCS46KKLkJiYCIlEgtOnT+PEiRMwGAxihRKrlIioPn6HSZ9++inmzp2LQYMG4bbbbsPNN9+MDh06NOji11xzjcv9Z599FsuXL8emTZuQnJyMd955B6tXr8aIESMAACtXrkRmZiY2bdqEwYMH46effkJubi5++eUXxMfHo0+fPnj66afx6KOPYt68eVAoFA0aFxFRayb0SxrYuTf/l5GIiKgJSSQSyGQyqFQqhIeHo2PHjujRoweysrLQpUsXxMXFQa1WQy6Xu1QkNdfYBEKPpvDwcISEhMDhcEChUKC0tBQOhwOlpaWw2+2wWq2w2WwMk4ioXn5Pc9u9ezf27NmDSy65BC+++CKSkpIwZswYrF69Gnq9vsEDsdls+Oijj1BTU4OcnBxs374dFosFo0aNEo/p0aMHUlNTsXHjRgDAxo0b0atXL8THx4vHjB49GjqdDvv37/d6LZPJBJ1O53IjImorhH5JA7twihsREVFTkEqlkMvlYoDUt29fXH311bjqqqtwxRVXIDMzE/Hx8dBoNC5BUksYs0ajEfs5XXnllbjqqqtw9dVXo2/fvujYsSPCw8NbzJiJqOVq0E+I7OxsLFy4EMePH8e6devQqVMnzJo1CwkJCX6fa+/evQgLC4NSqcS9996LNWvWICsrC4WFhVAoFIiMjHQ5Pj4+HoWFhQCAwsJClyBJ2C/s82bRokWIiIgQbykpnAZCRG2Dw+HA1uN7AQAD2XybiIgo4IRqJKVSibCwMMTGxiI1NRWZmZno1q0bMjIy0KFDB4SGhoortwmPC0bFsPN1ZTIZ5HI5QkND0aFDB2RkZKB79+7IzMxEamoqYmNjxX+bsY8SEdXF72lu7kJDQ6FWq6FQKFBVVeX347t3745du3ahsrISn332GSZNmoT169c3dlh1mjNnDmbPni3e1+l0DJSIqE04VpSPsuoKqORK9ErtHuzhEBERtRlSqRQymQxqtRparRYZGRno1KkTBg0ahNTUVGRkZCAyMhJarVas7GmJ1T3CmISqKYVCgcTERKSlpeHUqVPYtGkTTpw4gePHj0On08FgMMBms8Futwd55ETUkjQoTMrLy8Pq1auxevVqHDp0CMOHD8f8+fNx4403+n0uhUKBLl26AAD69euHrVu34pVXXsEtt9wCs9mMiooKl+qkoqIisQIqISEBW7ZscTmfsNpbXVVSSqUSSqXS77ESEbV0W46dn+LWp1MWFCHyII+GiIiobZBIJJDL5ZDL5YiMjERMTAxSU1ORnp6Obt26IT4+HnFxcVCpVLVWR2sp1T3COBwOhzg+iUQCrVYLhUIBi8UCtVqN4uJiOBwOVFVVQSqVwm63w2KxwGw2s5cSEYn8DpMGDx6MrVu3onfv3pg8eTJuvfVWdOzYMWADstvtMJlM6NevH+RyOdauXYtx48YBAA4dOoT8/Hzk5OQAAHJycvDss8+iuLgYcXFxAICff/4ZWq0WWVlZARsTEVFrITbfzmC/JCIiosZyDpHi4+MRHR2NoUOHomPHjhg0aBCioqKQlJQEhUIBlUrVYquRPHGerieXy9GpUyckJSUhLi4OZWVl2Lx5M86cOYMNGzagrKwMRUVFsFgssFgsDJWIyP8waeTIkXj33XcDEtbMmTMHV155JVJTU1FVVYXVq1fjt99+w48//oiIiAhMmTIFs2fPRnR0NLRaLWbOnImcnBwMHjwYAHD55ZcjKysLt99+OxYvXozCwkI88cQTmD59OiuPiKhd2vp3mDSAYRIREVGjyGQyyGQyaLVaqNVqpKSkIC4uDhkZGUhMTERSUhLCwsIQGhoqHhusvkj+cB+fUKWkUqkgl8vRoUMHqNVqdO7cGSqVCgUFBQgNDYXFYoFer4dOp4PdbofNZgvSMyCilsDvMOnZZ58N2MWLi4sxceJEnD17FhEREejduzd+/PFHXHbZZQCAJUuWQCqVYty4cTCZTBg9ejTeeOMN8fEymQzffPMNpk2bhpycHISGhmLSpElYsGBBwMZIRNRalOjKcKwoHwAwoHOvII+GiIiodRLClbCwMKjVavTq1QsJCQkYNWoU4uPj0aNHD7FvklQqRUhISIsPkOojkUgQEhICmUyGmJgYREVFQavVQq/Xo3v37igsLMQvv/yCwsJC7Nu3DwaDAdXV1XA4HOylRNRO+RQmzZ49G08//TRCQ0NdGld78vLLL/t88XfeeafO/SqVCsuWLcOyZcu8HpOWlobvvvvO52sSEbVV2/5exa17UmdEhmqDPBoiIqLWRagqEvoeJSUlITIyEt27d0diYiJSU1MRHR2N8PBwKJVKMURyDpJaY6gkkUjEaWvC1DepVIrQ0FCEhIQgMTERCoUCmZmZiIyMhF6vR0VFBQoKCmA2m2E0GuFwODj1jaid8SlM2rlzJywWi/g9ERG1POyXRERE1DBCZU5ISAg6dOiAqKgoDBs2DJ07d8bgwYMRGxuLuLg4KBQKcaU29+CoNQZJAudASej5pFaroVQq0bVrV6SlpSE5ORnFxcVIT0/H8ePH8eeff6K8vBwlJSWwWq2wWq0MlIjaEZ/CpHXr1nn8noiIWo4tR8+v5MZ+SURERL4RKnFCQkIQHh6OiIgIZGRkoGPHjsjOzkZKSgpiY2MREREBhUKBkJCQFrlSWyA4PxeHwwGJRCJO4wOAiIgIAEDXrl2hVqthMBhw5swZKBQKVFZWoqqqClarFTabjaESUTvgd8+kO++8E6+88grCw8NdttfU1GDmzJl49913AzY4IiLyjcFsxJ78gwCAQRkXBHk0RERELZ8Qlsjlcmg0GqSkpCA9PR1DhgxBdnY2MjIyEBUVJU738lSN1NY591KSy+XQarWIjo5GWVkZOnfujH379iEsLAzHjx9Hfn4+9Hq92EeJgRJR2+b3upXvvfceDAZDre0GgwHvv/9+QAZFRET+2X3yICw2K+K0MUjtkBTs4RAREbVYQjWSQqFAREQEkpOT0adPHwwYMADDhg1DVlYWUlJSEBERAZVKJfYQcu+N1JaDJU+9oKRSKWQyGVQqFSIiIpCSkoLs7GwMGzYMAwcORJ8+fZCcnCxWcclksiA+AyJqaj5XJul0OrGxWlVVFVQqlbjPZrPhu+++Q1xcXJMMkoiI6rb1735JAzJ6t+lfbomIiBpLCJNUKhWioqKQlpaGgQMHIjs7G3369EF0dDS0Wi3kcjlkMlmbD47q4ilAE4K4sLAwREdHIzU1FXFxcYiJiYFEIoHdbhf7J3G1N6K2y+cwKTIyUvwB0q1bt1r7JRIJ5s+fH9DBERGRbzYfO98vaVAXTnEjIiLyRCKRQC6XQ6FQICYmBnFxcbjgggvQqVMn9O3bF4mJiejQoQPUarXXJtvkOj0wNDQUUqkUPXr0QGRkJDQaDTp16oRdu3ahpKQEpaWlMJvNsFgsnPZG1Mb4HCatW7cODocDI0aMwOeff47o6Ghxn0KhQFpaGpKSOLWCiKi52e12bDu2FwCbbxMREXniHICo1WrExcUhLS0NAwYMQGpqKnr27InQ0FAxHBGmaDFMciW8HlKpFFKpVFzxTS6XIy4uDhKJBB06dEB5eTkkEonYQ8lms7GPElEb43OYNHz4cABAXl4eUlNT+YOViKiFOFJ4EhV6HdQKFXqm1K4cJSIiaq+EmRVKpRIqlQppaWmIi4vDsGHDkJSUhAsvvBARERGIiIhwmdZGvhGqt9RqNUJCQtC9e3fEx8cjJCQEBQUF+OOPP1BSUoITJ07AZDLBZDKJ09+IqHXzezW3X3/9FWFhYbjppptctn/66afQ6/WYNGlSwAZHRET12/L3FLcL07Mhl/n9Y52IiKjNEiqSVCoVQkNDkZiYiOTkZPTs2RPx8fFISUmBUqmEWq0WjxUeR96591KSy+UICQlBbGwstFotDAYDoqKikJ+fD5lMhpKSEgCAxWJhhRJRG+H3vzoWLVqEf//737W2x8XFYerUqQyTiIia2Za/m28P5BQ3IiIiAP8LkTQaDVQqFTIzMxEfH4+RI0ciISFBnNYWFhbmcbU28o9UKoXD4YBKpYJcLkdGRgYSEhIgk8lQWFiI8PBwFBYW4uDBgzAajdDr9QyViFo5qb8PyM/PR3p6eq3taWlpyM/PD8igiIiaypHCEzhe1LZ+Vjmv5EZE1B78/vvvuOaaa5CUlASJRIIvv/zSZb/D4cBTTz2FxMREqNVqjBo1CkeOHHE5pqysDBMmTIBWq0VkZCSmTJmC6urqZnwW1JRkMhlkMhk0Gg20Wi2SkpKQmpqK9PR0pKWlITo6GuHh4QgJCXFZsa09r9zWEO6vm0wmQ0hICMLDwxEVFSW+5ikpKUhKSoJWq4VGoxEDPCJqvfyuTIqLi8OePXvQqVMnl+27d+9GTExMoMZFRBRw56rKMXrRZADA+qdWIyUmMcgjarziylKcKDkNiUSC/p17BXs4RETNoqamBhdccAHuvPNOjB07ttb+xYsX49VXX8V7772H9PR0PPnkkxg9ejRyc3OhUqkAABMmTMDZs2fx888/w2KxYPLkyZg6dSpWr17d3E+HAkhoDB0WFga1Wo3evXsjKSkJI0eORFJSErp27QqNRlOr0TYFhhAoCU2509LSEBsbK/ZQUqvVKCgowN69e2EwGFBdXQ273Q673R7soRORn/wOk2699Vbcf//9CA8Px8UXXwwAWL9+PR544AGMHz8+4AMkIgqUr7avhd5kAAAs+Px1rJj6bJBH1HhCv6TMpAxo1WFBHg0RUfO48sorceWVV3rc53A4sHTpUjzxxBO47rrrAADvv/8+4uPj8eWXX2L8+PE4cOAAfvjhB2zduhX9+/cHALz22mu46qqr8OKLL3KF4lZKCDJkMhnCwsIQERGBpKQksSomPj4eYWFhUCqVLo22WYkUGMLr6HA4XBpzS6VSJCQkAABSU1MBAKdPn4ZMJoPRaITNZmNTbqJWyO8w6emnn8aJEycwcuRIhIScf7jdbsfEiROxcOHCgA+QiChQPt/8g/j91zvW4s+DN2BYj/5BHFHjcYobEZGrvLw8FBYWYtSoUeK2iIgIDBo0CBs3bsT48eOxceNGREZGikESAIwaNQpSqRSbN2/GDTfcUOu8wkpUAp1O17RPhPwiVCQJVUc9e/ZEp06dcMkllyA1NRWdOnVCaGioGG5wilXTEqa9KRQKhISEIDk5GVFRUVCr1Th58iRUKhVOnDiBPXv2oKamBjU1NaxQImpl/P4pqlAo8PHHH+PgwYP48MMP8cUXX+DYsWN49913oVAommKMRESNlld8Ctvz9kEqkeLafiMBAI9/8jIsNmuQR9Y4bL5NROSqsLAQABAfH++yPT4+XtxXWFiIuLg4l/0hISGIjo4Wj3G3aNEicQn5iIgIpKSkNMHoqSGEiiSFQgGtVou4uDh07NgRqampiIuLQ0xMDNRqNRQKhUujbfZHahrOr6vQCF2hUECtViM6Ohrx8fFITU1Fx44dxdXfFAqFS7UYEbV8DV5DulOnTnA4HMjIyBArlIiIWqrPt/wIABieORDP/+MR/HlwGw4VHMeq3z7H3SNvCfLoGkZvNmJv/iEAwMAuFwR5NEREbducOXMwe/Zs8b5Op2Og1AIIQZJKpUJYWBgyMjLQrVs3DB06FN27d0dycjLCw8NZkRQkQrAkl8shk8mQmJiIsLAwaDQaJCUlQSaT4fDhw7BaraiurobBYBCnvRFRy+b3T1O9Xo8pU6ZAo9EgOztbXMFt5syZeO655wI+QCKixnI4HOIUt3GDRiMqNAKPXXcvAOCFb1agRFcWzOE12M68/bDabUiMjEVydEKwh0NE1CIIvVmKiopcthcVFYn7EhISUFxc7LLfarWirKxMPMadUqmEVqt1uVHwCVUv4eHhiI+PR3JyMjp37oz4+HhxWpVcLmdFUhC4VygJoZJKpUJkZCQSEhLQuXNnJCcni/2shOoxImr5/P6TOmfOHOzevRu//fabuBoGcH6e+ccffxzQwRERBcLOE/uRV3IaaoUKV14wHAAwYdi16J3aHTpDNRb93/Igj7BhnPsl8ZdiIqLz0tPTkZCQgLVr14rbdDodNm/ejJycHABATk4OKioqsH37dvGYX3/9FXa7HYMGDWr2MVPDSKVSyOVyaDQaxMfHIzs7G/369cOQIUPQrVs3xMfHIzQ0tNb0Nmp+zlMRw8LCkJCQgG7dumHIkCHo168fsrOzkZCQAI1GI4Z/RNSy+f2n9Msvv8Trr7+OYcOGufxAzs7OxrFjxwI6OCKiQPjs76qkq/oMR6hKAwCQSWV49pZ/AgD+u+Eb7DyRG7TxNdTmv1dy4xQ3ImpvqqursWvXLuzatQvA+abbu3btQn5+PiQSCWbNmoVnnnkGX331Ffbu3YuJEyciKSkJ119/PQAgMzMTV1xxBe6++25s2bIFf/31F2bMmIHx48dzJbdWwjlIiouLQ0pKCrp3746UlBTExMS4hBKsSAou99fd+b2LiYlxee/i4uIYKBG1En43OyopKanVsBAAampq+MOZiFoci82KL7f9AgAYO3C0y74BGb1x46Ar8dnm7/Gvj17Et4+83Wp+cbHb7dh+fB8ANt8movZn27ZtuPTSS8X7Qi+jSZMmYdWqVXjkkUdQU1ODqVOnoqKiAsOGDcMPP/zgUlX/4YcfYsaMGRg5ciSkUinGjRuHV199tdmfC/nPuamzVqtFcnIyunXrhr59+yIlJQUJCQlQqVSsSGqBhPdDIpEgPDwccrkcFosFSqUSlZWVMBqNqKmpgcViEXsnsX8SUcvkd5jUv39/fPvtt5g5cyYAiD+c3377bbF0mIiopfgtdzPKqisQEx6F4ZkDa+1/cux0fL9rPXaeyMUnm77D+CFXB2GU/jt09jh0hmpolGpkdewS7OEQETWrSy65pM5/YEokEixYsAALFizwekx0dDRWr17dFMOjJiRMl1IqlYiMjERiYiKys7PRpUsXJCUlITIykiuDtQLO094iIyNhs9nQpUsX2O126HQ62O122Gw2mM1mNuQmaqH8DpMWLlyIK6+8Erm5ubBarXjllVeQm5uLDRs2YP369U0xRiKiBhMab9/Q/zKEyGr/yIuP6IDZY+7E01+8jmfWLMNVfS+BVh3WzKP03+aj56e49U/v6fF5ERERtUVCCCGXyxEZGYn4+Hh069YNnTp1cumRJJPJxGpjhkotg/P7IJFIEBISAolEgoiICISEhKBTp04AgOPHj6O6uhpVVVWw2Wyw2+0Mk4haIL/ncwwbNgy7du2C1WpFr1698NNPPyEuLg4bN25Ev379mmKMREQNUm2swY+7fwcAjBt0hdfj7h5xC7rEp+FcVTle+ubt5hpeg1XU6LD85/P/mz64a98gj4aIiKh5CNPbNBoNoqOj0b17d/To0QNdu3ZFUlISm223Ms7TFUNDQ9GxY0d07doVPXr0QPfu3REdHQ2NRsP3k6iFatB/Z2dkZGDFihWBHgsRUUB9t2s9DBYTMuJT0Sct0+txihA5nr75Qdz62iy8s+5T/GPodeielN6MI/Wd3W7Hfe/OxclzZ5DaIQmTLxkX7CERERE1CyF8UCqVCAsLQ2JiIhITExEXF4fIyEgolUqxIonNtlsu92bcQoVSZGQkACAxMRE1NTU4cuQI9Ho9ampqWJ1E1AL5FCbpdDpotVrx+7poNBqEhHDKBREFnzDFbdzAK+r9hfLS7MG44oKL8cPu3/HEJy/hkwdea5G/hL747Tv4df9GqORKvHvPc4gKjQj2kIiIiJqcRCKBXC6HSqVCUlISUlJS0Lt3byQnJyMmJgZqtRohISGtZiEN+h+hv1VYWBhkMhm6desGjUaD/Px8hISEwGAwwGg0wmw2M1AiakF8+mkbFRWF4uJiAEBkZCSioqK83lQqFTIzM7Fu3bomHTgRUV0KK0rwx8FtAIBxbqu4eTP/xgegDFHgj4Pb8N2u35pwdA3z054/8fK37wAAXpjwGHqmdAvyiIiIiJqHc8NmrVaLqKgoxMbGiv/+cJ7e1hL/M4g8E94vYbqbSqVCdHQ04uLiEBUVBa1WC7lczobqRC2QTyVEv/76K6KjowGg3pDIZDLhyy+/xLRp03Dw4MHGj5CIqAG+3PYz7A47BnTuhbTYjj49Ji22I+67fAKWfLcScz99BZdm50CjUNX/wGaQV3wKM1bOAwBMHn4jbhp8ZXAHRERE1EykUilkMhnCwsIQFRWFzMxMdOrUCWlpaYiMjIRKpRKnSjFwaH2E90wul0MikSA+Ph5KpRKZmZlQq9U4e/YsJBIJLBYLgPNT/oko+HwKk4YPH+7xe2/69OmDLVu2NHxURESNJE5xq6Pxticzr5iETzZ+h9NlhVj24wd4+Jq7m2J4fqkxGTD5zcegM1RjQOdemH/TA8EeEhERUbNx7pUkNN+OiopCaGgoVCpVraoVBkqtg/A+CVPXhOozlUqF0NBQREdHo6qqChqNBnq9HlKplEESUQvSoOZGNpsNa9aswYEDBwAAWVlZuO6668ReSXFxcdi2bVvgRklE5IeDBcex99RhhEhluLbfKL8eq1GoMPfG+zF1xeNY9tN/cEvOGKR2SGqikdbP4XDgof8swsGCY4jVRmPF1IVQhMiDNh4iIqLmJCwhr1AoEB8fj44dO6JHjx5ISkpCRESExzCJWidhmqKwgltGRgbUajX27t0LmUyGiooKOBwONuMmaiH87lC3f/9+dOvWDZMmTcKaNWuwZs0aTJo0CV27dsW+ffuaYoxERH75YsuPAICRPYcgOsz/BtXXXDgCQ7v3g9FiwvzPXw308Pzy9q+fYM3WnxAilWHF3QuREBkb1PEQERE1N5lMBrlcDq1Wi4iICGi1WoSFhSEkJAQymQwAOMWtlXN+/2QyGUJCQhAWFia+5+Hh4ZDL5VzoiagF8TtMuuuuu5CdnY3Tp09jx44d2LFjB06dOoXevXtj6tSpTTFGIiKf2e12fP53mOTvFDeBRCLBMzfPhkwqw7c7f8PvB4IzbXfjkZ1imDV33P0Y3LVPUMZBREQUDML0NpVKhfDwcKSlpaFz585ISkpChw4doFQqxV5J1DYIlWhKpRIdOnRAUlISMjIykJaWhvDwcKhUKrGCiYiCy+8wadeuXVi0aBGioqLEbVFRUXj22Wexc+fOgA6OiMhfm4/txpmyQoSrQnFZr6ENPk9mxwxMHj4OAPD4xy/DYrMGaog+KawowdQVj8Nqt2HsgMtx14ibm/X6REREwebcK0mtVourSqvVaiiVSo+rtzFkaH3c3z/n912lUiEyMhKRkZFQq9Uuq/YRUXD5HSZ169YNRUVFtbYXFxejS5cufp1r0aJFGDBgAMLDwxEXF4frr78ehw4dcjnGaDRi+vTpiImJQVhYGMaNG1fr+vn5+RgzZgw0Gg3i4uLw8MMPw2pt3n/4EVHLIDTeHnPhpVA3ciW2h6+5GzHhUThSeALvrPskEMPzidlqwV1v/QslujJkdszAC7fN4S9NRETU7giruIWHhyMmJgZpaWlITU2FVquFRqOBTCaDVHr+nzP8e7L1E95D4X3XaDSIiIhAamoqUlNTERMTA61W6/K+E1Hw+PSnUKfTibdFixbh/vvvx2effYbTp0/j9OnT+OyzzzBr1iw8//zzfl18/fr1mD59OjZt2oSff/4ZFosFl19+OWpqasRjHnzwQXz99df49NNPsX79ehQUFGDs2LHifpvNhjFjxsBsNmPDhg147733sGrVKjz11FN+jYWIWj+jxYSvtq8FANw4sGFT3JxFaMLx+PXTAAAvfvM2iitLG31OX8z99BVsO74XWnUY3r3nOYQq1c1yXSIiopZEKpWKvXMiIyNdeucITbfZK6ltcX5PnXtlCe+/0CuLYRJR8PnUwSwyMtLlh7TD4cDNN99caznHa665BjabzeeL//DDDy73V61ahbi4OGzfvh0XX3wxKisr8c4772D16tUYMWIEAGDlypXIzMzEpk2bMHjwYPz000/Izc3FL7/8gvj4ePTp0wdPP/00Hn30UcybNw8KhcLn8RBR67Z23wboDNVIjIxFTre+ATnn+Jyr8d7va7D75AE8++UbeGXSkwE5rzefbPoOK9d/BgB4ffI8pMelNOn1iIiIWiLnMCE6OhpxcXGIjY1FTEwMVCqVx15JDJVaL4lE4rJCm3PvpJiYGBgMBsTFxcFkMkEul8Nms9V6DBE1L5/CpHXr1jX1OAAAlZWVAIDo6GgAwPbt22GxWDBq1P+W9u7RowdSU1OxceNGDB48GBs3bkSvXr0QHx8vHjN69GhMmzYN+/fvR9++gfkHJRG1fMIqbjcMuBwyqSwg55RKpVg0/p+46vm78PHGbzHxohvQr3PPgJzb3d78Q3jkw/MVnrPHTMHlvYc1yXWIiIhaMqEyRS6XQ6lUIioqCh06dEBYWBjUarU4zcm5KolBUusnhEPu093UajXCwsLQoUMHVFdXQ6lUwmazwWQyAQADJaIg8SlMGj58eFOPA3a7HbNmzcLQoUPRs+f5f6gVFhZCoVAgMjLS5dj4+HgUFhaKxzgHScJ+YZ8nJpNJ/OEDnJ/GR0StW0WNDj/v/QsAcGMDV3Hz5sL0nrglZww+3vgt/vXxS/j+0XcCXl5dXlOJKW/NgdFiwsieQ/DQmCkBPT8REVFr4ilMCg8PdwmTqG1zDpPCw8MRGxsLnU4HpVIJs9nMyiSiIGvQT+GKigq89NJLuOuuu3DXXXdhyZIlYlVRQ02fPh379u3DRx991Kjz+GLRokWIiIgQbykpnEZC1Np9s+NXmK0WZHbMQFZy14Cf/4kb7kO4KhS7Tx7Afzd8HdBz2+w23PfOXOSfK0Bah45YNnkef0kmIqJ2S1jNS61WQ6vVIiYmBh06dIBGo4FSqXTpq8OKpLbH+b0VVnXTaDTo0KEDYmJixFCRq7oRBZff/1rZtm0bMjIysGTJEpSVlaGsrAwvv/wyMjIysGPHjgYNYsaMGfjmm2+wbt06JCcni9sTEhJgNptRUVHhcnxRURESEhLEY9xXdxPuC8e4mzNnDiorK8XbqVOnGjRuImo5Pvt7itu4ADTe9iRWG4OHrr4LAPDsl8tRqa8K2Llf/OZtrMvdBLVciXfvfQ6RodqAnZuIiKi1EYIEhUIhBkoRERFQKBRsvtzOCE3YlUoltFotwsPDa4WKRBQcfv8kfvDBB3HttdfixIkT+OKLL/DFF18gLy8PV199NWbNmuXXuRwOB2bMmIE1a9bg119/RXp6usv+fv36QS6XY+3ateK2Q4cOIT8/Hzk5OQCAnJwc7N27F8XFxeIxP//8M7RaLbKysjxeV/hh5HwjotbrVOlZbDqyExKJBDcMuLzJrnPnpTeha0InlFVX4IWvVwTknD/u/h1LvlsJAHjhtseQ3QRVVURERK2JML0pPDwcMTExiImJQVRUlEvjbYYIbZ/wPgthUnR0tPh5CA8P53RHoiBrUGXSo48+ipCQ/7VbCgkJwSOPPIJt27b5da7p06fjP//5D1avXo3w8HAUFhaisLAQBoMBABAREYEpU6Zg9uzZWLduHbZv347JkycjJycHgwcPBgBcfvnlyMrKwu23347du3fjxx9/xBNPPIHp06dDqVT6+/SIqBVas/UnAMCQbheiY3R8PUc3nFwWgmdvmQ0AWLn+cxw4c6xR5ztelI8ZK+cDAKZcehNuHHRlo8dIRETUmjkvC69SqRAaGgqNRuO18Ta1Xc5T3UJCQqBWq6HRaMTKJH4WiILL7zBJq9UiPz+/1vZTp04hPDzcr3MtX74clZWVuOSSS5CYmCjePv74Y/GYJUuW4Oqrr8a4ceNw8cUXIyEhAV988YW4XyaT4ZtvvoFMJkNOTg5uu+02TJw4EQsWLPD3qRFRK+RwOPDppu8BNN0UN2cXZw7EmL6XwGa34fGPX2pw48caox53/nsOqow1GJjRG3PH3R/YgRIREbVSISEh4iI8cXFxiIyMRHh4OORyOWQyGQOEdsI5WJTL5QgPDxc/E1FRUVAqlS4FDkTUvPz+03fLLbdgypQpePHFFzFkyBAAwF9//YWHH34Yt956q1/n8uUfYSqVCsuWLcOyZcu8HpOWlobvvvvOr2sTUduw79RhHCk8AWWIAldfeGmzXHPuuPuxdt9GbDi8A1/v+BXX9hvp1+MdDgdm/2chDhYcQ5w2BiumLoQiRN5EoyUiImo9nCtRVCoVNBoNFAoF5HJ5m6tEaeqVyNrC6+RcnSSs7hcaGipOeRQ+E1zVjaj5+R0mvfjii5BIJJg4cSKsVisAQC6XY9q0aXjuuecCPkAiorp8tuUHAMDlvS+CVh3WLNdM7ZCEGaNvx4vfvI35n72KkT2HIFSp9vnxb639CP+37ReESGVYMfVZxEd0aMLREhERtQ5C+KFQKKDRaBAdHY24uDhx9S42326fhB5aarUaYWFhiI2Nxblz56BWq2GxWACAgRJREPj901ihUOCVV15BeXk5du3ahV27dqGsrAxLlixhjyIialY2uw1rtpzvl3TjoNHNeu3pl9+G5OgEnCkvwus/vu/z4zYc3oEFX7wOAJh30wMY1KVPE42QiIio9RGmNQmVSSqVymV6W0vjcDgafHM/R0scW0shBEpyuRxqtbrFfy6I2oMGR/sajQa9evVCr169oNFoAjkmIiKf/HlwG4p1pYgK1eLS7JxmvbZaocL8mx4AALzx04c4WXKm3secLS/G1BWPw2a3YdzA0ZhyyU1NPUwiIqJWQ5jOpFQqERYWhsjISMTExECtVkMul7epKW7O2urzChTh9ZHL5dBoNIiJiUFkZCTCwsKgUqnEqW5E1LxYJ0pErdZnW34EAFzTb2RQeg5d1ecSXNxjAExWM+Z+9kqdx5osZtz11r9wrqocWR274IXb5vAXHyIiIifO/ZKUSqV4c+6N09yau4KnIecUHuPta0PO3dIql4TPhkwmazGfDaL2jmESEbVKerMR3+38DQBwYzOs4uaJRCLBM7fMRohUhh92/451+zd5PfapT5die94+RGjC8e69z0GjUDXjSImI2pbff/8d11xzDZKSkiCRSPDll1+K+ywWCx599FH06tULoaGhSEpKwsSJE1FQUOByjrKyMkyYMAFarRaRkZGYMmUKqqurm/mZkDMhMFCr1dBqteJNoVC0+FXc6gpYAhEQ1cX9NRHue9te1/VaIudV3ZRKpctng5VJRMHDMImIWqWfdv+BGpMeKTGJGJDRO2jj6JaYjikjbgYAPPHJyzBbLbWO+WjDN3jv9y8gkUiwbPJ8dIpNbu5hEhG1KTU1Nbjgggs8rvar1+uxY8cOPPnkk9ixYwe++OILHDp0CNdee63LcRMmTMD+/fvx888/45tvvsHvv/+OqVOnNtdTIA+cV+1Sq9VQKpVikNSUgUEgKnCcG0B7Ooc/vYo8ffXnsYHsj+Rtf3NXLTmv6qZQKMR+WgqFgmESUZD4vZobEVFLIKziduOgK4L+C8Q/x0zBF1t+xLGifKz49WNMv/w2cd+e/IN4dPVi8bhRvYYEa5hERG3GlVdeiSuvvNLjvoiICPz8888u215//XUMHDgQ+fn5SE1NxYEDB/DDDz9g69at6N+/PwDgtddew1VXXYUXX3wRSUlJTf4cqDbnVbvCw8MRGhoKtVrtUpUU7L/z69KSx1Yfb2NvCc/JOUgKCQmBWq2GRqOBVqsVPx9c5Y+o+fFPHRG1OueqysUpZWMHNu8qbp5o1WF4/Pr7AAAvf/suiirPAf/P3p3HN1GtfQD/TdKmLYW2lKWlsgrIJptFeqsiCJWyiKAoi1xARRClKuCCXJXNBQUuIovUDZAruOCCXlAQWUSlooBVBETgFvBVCipLaYEuyXn/aGaaSSbJZE/b39dPDJk5c+bMTJpMnz7nHACnC8/h7uzHUVxWgoz212Jyv7tD2Uwiomrr3LlzkCQJCQkJAICcnBwkJCQogSQAyMjIgMFgwM6dO0PUyupNDhjI4yXFxsaqZuxyFyzQM1uaL5k0WuMP6a3P2+wfb7fxtD5/ZxnpPd+e7s92Rrfo6GjUqFFDGTcp3AONRFURg0lEVOl8vOsLmC1mdGzSBi2Tm4a6OQCAIf/oh9RmV6Ko+AKe/nAJzBYz7l82Df93Oh9N6zXE4jun869mREQhcOnSJUyZMgXDhw9HXFwcACA/Px/169dXlYuIiEBiYiLy8/M16ykuLkZBQYHqQf4lZ55ER0crwaSoqCiPpn/XClbYv9Yb3HHVhczVtp52P3O33tNtvK1P7/HY78eTc2i7zL6sO7bjJkVHRyuzuTEziSg0+FNHRJXOB3IXtxANvK3FYDDg2WEPQ5IkvL/zM4x77Qls278TMZFRWHbvbCTExoW6iURE1U5paSmGDBkCIQSWLl3qU12zZ89GfHy88mjUqJGfWklARaBAHi+pZs2aDrN1+Zp54mxgavvAhu34R+4EaoygYPM2O8pd9zg93RNdXQ/bMvbZa3IwyXaAdiIKHgaTiKhS+d/J49iTtw9GgxGDrs4IdXNUOjVpgzuuGQAAWG+dae7fI/+Ftg1bhrBVRETVkxxIOnbsGDZt2qRkJQFAcnIyTp06pSpfVlaG06dPIzk5WbO+qVOn4ty5c8rjt99+C2j7qxM5CCBnJplMJsTExChd3GyDBO4CBvaBIK1/O1vmLtvGtpyejCVPs4OC/XB3bHqykDzJcnJVh+2/Xc1CJ3d1kwfhtg042pclosBiMImIKpUPvtsIALi+zdWoF1cnxK1x9PjA8YiLqQkAuOeGIWExphMRUXUjB5IOHTqEL774AnXqqL8v0tPTcfbsWezevVtZtmXLFlgsFqSlpWnWaT8luW1winxnGySoUaMGYmNjHTKTPCEHNuyDS/ZZMgw+6OfNNbB/rVWH3uthOwi3nJkUExOjmvGPiIKHs7kRUaUhhFCCSeHUxc1WvbhErLx/Hn44ug/39Bwa6uYQEVVJhYWFOHz4sPI6Ly8Pubm5SExMRIMGDXDbbbdhz549WLduHcxmszIOUmJiIkwmE9q0aYM+ffpg7NixyM7ORmlpKbKysjBs2DDO5BYicje3iIgIREZGanZxcxVokAMXWuVsX/ur+5on3cLCrSucfD70tMtdWa1r4iwzTE8wylXAyXZWN3nspMjISK8DjkTkGwaTiKjS2JO3D0f//D/UiIpBn07dQ90cp/7RshP+0bJTqJtBRFRl7dq1CzfccIPyevLkyQCA0aNHY8aMGfjkk08AAJ06dVJtt3XrVvTo0QMAsGrVKmRlZaFXr14wGAwYPHgwFi5cGJT2k5rtWDgxMTHK1O9a3dxc1SGzD0i4GtuHwoueboy2GWw1atRQukTK76NwC94RVVUMJhFRpfH+zvKBt/t16o7YqJgQt4aIiEKlR48ebse1cScxMRGrV6/2Z7PIB7ZdmORsEz2BJHezibkr58s6Peu9LRsIgchIcjZYtlYAz1/Hb/tekR/MTCIKPnYsJaJKodRcho93bQIADA7TLm5ERETkHUmSlJnc5IdtQKmyBwpCHUgKdhsCcb3k94HtrH/yQ85MIqLgYWYSEVUKW/d9i9NF51C3Vm10a90l1M0hIiIiP7EPEthnm/g7SKA3m8kf6zwpEy5cdRVzl5Gktc6f189+5j85ky1Q7xUico6ZSURUKXzwXXkXt1uu7o0II+PgREREVYXcbck22yQ6OloJEoQzPd3gwimQpKc94dReLfJA7dHR0cr7xWQysasbUZDxNzIiCnvnLxZh449fAQAGp7GLGxERUVWilZlkO16SsxnDvB1PydV6bzKQfM1aCjfOMpPcZSw5y0jyZCY4W66yn+QZ3ewzk4goeBhMIqKw92nuNlwqLUaLpCbo2Lh1qJtDREREfmQ7Q1dMTAyioqJgMplgNBqVzCT7QEGwAweeBpK8CSL5Gnjy5JzI+/IkUBfsWfHsA1T2gaTIyEhERUUpmUl6Z/4jIv9gMImIwt4H1lncBqdl8iaBiIioCtEKENjPzuUssGG7zpdxi/RmKPm6vTvhksXkSWaS1vnXM66Su/XuspnkAKScmSQHHuUst3A5l0RVGYNJRBTW8s/+ia8O7gIA3Hp1ZohbQ0RERP5mG0iKjo6GyWTya9clTzNq9ASHfMlIClSgw5vuZFoZSlqBIXm5fV2enFt//UHQdowtk8mkvGdsM9mIKPAYTCKisPbR959DCIGuzTugSb3LQt0cIiIi8jM5OBAREQGTyaRkJmkFBvRkJMkBDtt1zv6td703ZZyprFkzejJ+PBk7yXa5szLO9ie/P+T3jG1mEhEFB4NJRBTWPvhuIwAOvE1ERFRV2XZZkrOSIiIiHKZ6tw86OAsceBpQcBUk8iUjydOgUaDGTNKTseRsDCXb5XoylrwZV0muW08GlVxekiSli5v8njEajR7tl4h8w2ASEYWtA78fwc+//YpIYwQGXNUr1M0hIiIiP7OfyS0qKkqVmeRpwMjb8Y98CSjpDTi5W+crV3XrGXdKXqY12Ll9MMfZa3dlbffnLDjljpzJJnd1k98zttlJlTX7i6gyYTCJiMLWh9aspF5XXoPEmvEhbg0REREFglY3N3lmLvvsJHu+DJQdqACSu0BGsAMdngRXPAkcuavbWTaTnsG6XQ0CbhuAtO8ayW5uRMHDYBIRhSWLxaIEkwZ3ZRc3IiKiqsg2kBTIwIA3gSR/ZCSFKrCkd9Y02/XeBpL0dnnzdABvd4Eq2wCks66RRBQ4DCYRUVj69nAufj9zErWiY3Fjh2tD3RwiIiLyM9tp3m0DSnoGU9YK5LgadNvda38ElLwZlDsU3bG8GUjbVSDJ2y5vrsZZ0tM+eRZA2/cMZ3MjCh4Gk4goLH2wcwMAYEBqT0RHRoW4NURERBQItoEkeTBlbzKT/DHodiACSqGY3c1dsMjduEi+BpJ8GYxbL3eZSRw3iSjwGEwiorBzqbQY/92zBQBwK7u4ERERVWny+DdypokcSPKky5KnGUmeBo78Ob6Su/b7wh9ZR3q21RtgktcBjgN+uwpeuWuD/JDfM3qy2YjIvxhMIqKw88Xeb1BwsRAptevjmpadQ90cIiIiChB3mUmuZm3TEzhwFUhyFzjyJlMp1F3d3J0XrWCP3nNpu63tNnq7vOnZnyfl7DOTIiMjGVAiCiIGk4go7Hyws3zg7Vuu7s2+70RERFWc7VTvejNMnM0C5q77mqcBI0+6wzl77WyZJ+v18qZ7ly/beJup5Kw7nG3wyV3AyTY7SX4wkEQUPCH9LW379u0YMGAAUlJSIEkS1q5dq1ovhMC0adPQoEEDxMTEICMjA4cOHVKVOX36NEaMGIG4uDgkJCRgzJgxKCwsDOJREJE/nSk6h837dgAAbktjFzciIqKqzD4zKTIyEkaj0WkwwTag42m2j7NAkVyXxWLRzFySl9mv0/va3cN2v74+PK3Lm2Px9Ny5ux6eXEOZ/P4wGo2qMZMYUCIKnpAGk4qKitCxY0csWbJEc/2cOXOwcOFCZGdnY+fOnYiNjUVmZiYuXbqklBkxYgT27duHTZs2Yd26ddi+fTvGjRsXrEMgIj9bt2crSspK0fayFmhzWYtQN4eIiIgCTCu7RE83KFuuAh32y9w9+yMI40tAx5eHP9vhzfnw5Bw7W2a73BXb9438bwaSiIInpN3c+vbti759+2quE0JgwYIFePLJJzFw4EAAwMqVK5GUlIS1a9di2LBhOHDgADZs2IDvv/8eXbp0AQAsWrQI/fr1w7x585CSkhK0YyEi/5BncRvMrCQiIqIqTw4cRUREqKZ493QAbpmrDBhfn50t8+a13nWeEsL7GdTst7V97aornLMub66efWmz1gDc8vuHASWi4AnbwUjy8vKQn5+PjIwMZVl8fDzS0tKQk5MDAMjJyUFCQoISSAKAjIwMGAwG7Ny5M+htJiLfHP/rD3x7OBeSJOGWq3uHujlEREQUQPZj3+jJLtHKYNEK3Pg7E8lVNk1VffjzPLk6955eX/v3kFY2GwNKRIEXtgNw5+fnAwCSkpJUy5OSkpR1+fn5qF+/vmp9REQEEhMTlTJaiouLUVxcrLwuKCjwV7OJyAcfff85AODaK1KRUru+m9JERERU2dmOfSNnJflrMGVXARFn67We3a1z99pVMETPen/yJAtIK5tI72DdrrZ1lqHkCfuukbbvHwaSiIIjbDOTAmn27NmIj49XHo0aNQp1k4iqPSEE3t/5GQB2cSMiIqpOPMlMckYro8X+2ZusGXfbeJKlEw4Pb9rtzXnx5Nw7u356g2x6xtoiIv8L22BScnIyAODkyZOq5SdPnlTWJScn49SpU6r1ZWVlOH36tFJGy9SpU3Hu3Dnl8dtvv/m59UTkqdXffIJD+ccQHRmF/p17hLo5REREFGC2QSQ9WSV6M2L8FUiy/bc8W5nWrGX2D/sZ1fw5W5uvD71t8+TYPTmnrs611nvD3bW3HzvJ27G2iMhzYdvNrVmzZkhOTsbmzZvRqVMnAOXd0Xbu3In77rsPAJCeno6zZ89i9+7dSE1NBQBs2bIFFosFaWlpTuuOiopCVFRUwI+BiNwrNZdh5vsL8frW9wAA/7xuIOJiaoa4VURERBQMtr/8+3NGLn9lzbh7drZMz2u96zzhbqBs231pvRZCqOrQcy1st3HVpc3Zs6/Hax9AYiCJKDhCGkwqLCzE4cOHldd5eXnIzc1FYmIiGjdujIkTJ+KZZ55By5Yt0axZMzz11FNISUnBoEGDAABt2rRBnz59MHbsWGRnZ6O0tBRZWVkYNmwYZ3IjqgT+LjyLca89gW8O7gYAPHLTPZjc7+4Qt4qIiIiCSSsY4CwgYB/ssF/nbbaML8Ek27rsl7l6rXddMOkdE8mTutw925aX2Qe4nNWv9SCi4AhpMGnXrl244YYblNeTJ08GAIwePRorVqzAY489hqKiIowbNw5nz57Fddddhw0bNiA6OlrZZtWqVcjKykKvXr1gMBgwePBgLFy4MOjHQkSe2fd/h3Dn0sfw298nEBtVA4vvmo6+nbqHullEREQUArYDKrsKCGitc9ZVSl6n9WyxWFTb6g082S5ztg/75VrrnLUzkPRkAtmX8SWLSAgBg8GgOyNJKxtKz3nheElEoRHSMZN69Oih2Ud3xYoVAMo/SGbNmoX8/HxcunQJX3zxBa644gpVHYmJiVi9ejXOnz+Pc+fOYdmyZahZk11kiMLZ2l2bcNML9+C3v0+gab2GWD/ldQaSiIhIt+3bt2PAgAFISUmBJElYu3at07Ljx4+HJElYsGCBavnp06cxYsQIxMXFISEhAWPGjEFhYWFgG05OedJFSU+QxpsAkbuH1rZ6H95s4++HL+329Bx5cu5dXV93QSL7bDYGlIiCJ2wH4CaiqsdsMeO5tUsx/vWncLG0GD3apmHD48vQOuXyUDeNiIgqkaKiInTs2BFLlixxWe6jjz7Ct99+qzn8wYgRI7Bv3z5s2rQJ69atw/bt2zFu3LhANZlcsA8kuQsIeBIw0MpI0htosR94Ws/g2/bbOnsdioenbbI9Rlfnwt05sc0Cs332FwaRiEIjbAfgJqKq5dyF87h/2XRs/nkHAOD+G0fgiVvuh9FgDHHLiIiosunbty/69u3rsszvv/+OBx54ABs3bkT//v1V6w4cOIANGzbg+++/R5cuXQAAixYtQr9+/TBv3jyOvRkCngyi7CqjxV1mjW05rWV6Mmrs2+EsSOLutd51/qI1RpHe/bob78jVvvRu62lAiANvE4UWg0lEFHCH8o/izqWP4cjJ44iOjML8kf/CrV0zQ90sIiKqoiwWC0aOHIlHH30U7dq1c1ifk5ODhIQEJZAEABkZGTAYDNi5cyduueUWh22Ki4tRXFysvC4oKAhM46spTwIBngRBXGXM2JbRCiS5y6jRE2By1h53y/xN65zJgR1n67XKam3jSZDKm/GX9JwfBpKIgo/BJCIKqM9/+hoTlk3H+UtFuKx2Epbf9wI6NG4d6mYREVEV9sILLyAiIgIPPvig5vr8/HzUr19ftSwiIgKJiYnIz8/X3Gb27NmYOXOm39tKFbztrqQVGHK23n65pxlJegJHrgJKngSZAk1vlpGrsq6yjpwNsu1s1jat9XqPQ35mUIkoeBhMIqKAEEJgwWfLMee/r0EIgX+07IzXxj6LenGJoW4aERFVYbt378ZLL72EPXv2+PUXy6lTpyozDwPlmUmNGjXyW/3VldbAyd50W3IX0HE1NpAnASVPA1fB7OrmTbc1eb9aM7g520ZrW/nZYrG4HTBbK8vJ2X5dZTjZP7O7G1FwMZhERH5XdOkCHnzzaaz/YSsA4M7ug/H0kEmINPIjh4iIAuurr77CqVOn0LhxY2WZ2WzGww8/jAULFuDo0aNITk7GqVOnVNuVlZXh9OnTSE5O1qw3KioKUVFRAW17dedrQMCbbmiuAkneZCs525+z1+6OQS9PAknutvW225q7jCVAu7uc7XKt+uX1ztZpBSKJKPD4mx0R+dWxP3/HndmP4cDvRxBpjMDzwx/FiOsGhrpZRERUTYwcORIZGRmqZZmZmRg5ciTuuusuAEB6ejrOnj2L3bt3IzU1FQCwZcsWWCwWpKWlBb3N1Z0kSTAYDE6DA3qzVbTKyEEhT2Yu05OZpCeQ5Kyt/g4oeTIYtrP9aQV2nAV+nG1rux85Q8n+2WAwqMp6O+i23uVEFDgMJhGR32w/8B3uff1JnCkqQP24Onjj3tm4unmHUDeLiIiqmMLCQhw+fFh5nZeXh9zcXCQmJqJx48aoU6eOqnxkZCSSk5PRqlUrAECbNm3Qp08fjB07FtnZ2SgtLUVWVhaGDRvGmdxCzF1AwFXWj7xMz5hF7rrBuSur9ay3ja6Wu1vnKU/GQ7J/7cmYSu621QoIugoo6d2vbTdJBpOIgovBJCLymRACr25+BzM/WASLsKBTk7ZYPv55NKhd3/3GREREHtq1axduuOEG5bU8ltHo0aOxYsUKXXWsWrUKWVlZ6NWrFwwGAwYPHoyFCxcGormkg6fBAFcBI9syeoNEgcxI8rSrm6c8yToC1MEjV13a9GYoeRKMsi+n1UY9GVFaGEwiCi4Gk4jIJxdLLuGx1XOw5ttPAQBD/tEPc0ZMQXQkx5UgIqLA6NGjh0e/kB89etRhWWJiIlavXu3HVpGv7DNMAhEccJaJZBswsl1vv43Ws/2/vXkdKJ6Mf+RsW1cZSnq72Pn7WtoPvM3Bt4mCj8EkIvLaH2dO4a7sKfjx2AEYDUbMGPwg7uk5hF/kRERE5BFnwQFvOBsHyVUgyX5bZ9lKtuW0nrXKervcW/ZZPrbLvQ0kyXU5Cw45GyjbWWaSfXaUN/z5niEizzGYRERe+e7wjxjz6lT8WXAatWPj8OrYZ9Gt9dWhbhYRERFVMlrTu3tCKyikp6yrIJP9NrbP7pbZ/9vVMlfLg82bLCN3bdcbMNLq/qYHg0hEocNgEhF57D9frcW/3pmHUnMZ2l7WAsvvm4MmdTlgKREREXlGb/ckvVk17rKMnAWd5OUWi0VVjzdd3fR2aQtUEMlZAEdrud4uaO4ylWxnadPap9azszGTvMGBuImCj8EkItKtpKwUT743Hyu3fwQAGHBVLywY/SRio2JC3DIiIiKqrPR2V/Kkm5a7AI6eDCWt8lp1exJE0pvJ4ylnM6JprbcPKrkaB0lPoMfVdXG1zpMgkrO22q4jouBiMImIdPmz4G+MffUJfHs4F5Ik4fGb78WDfUbzC5yIiIh8Zp+h5C444oq7sZFcBXmclQ1WRlIgspU8CcJ5u62zsZScjZnkavwlT9rmaxdJIvIeg0lE5JIQApt/zsFjq5/HH2dOoVZ0LF4eMws3tr821E0jIiKiKsRdlzdfgiLOMpEsFovboJMnASW9r7Xa5wtXYxO5ylDSem1bl33QR+sZACwWCyRJUp7lbm/+Oj5XGEQiCg0Gk4jIqZ2Hc/Hc2qXYefhHAECLpCZYcd8ctEhuEuKWERERUVWiZ7wbbwMyesda8jSQ5GkAKdgZSfbsg3HuXtsu8+TZFWdl/JGhxKASUXAxmEREDn7+7VfM/jgbm3/eAQCIjozCXT1uw6R+dyEupmaIW0dERETVgW2mkn0mjD292UPOMpKc1eVsfbgGklwFZZxlIrl6DTgfQ0lPppKcoWS7nbOubnoCSs66Q+odyJ2I/IfBJCJS/O/kccz572tYu2sTAMBoMOKOawdgcr+70aB2/RC3joiIiKoiVzNxeRMk0NMNTausfWaSVqaSs/q9ee2sLd5yNUi1vN6TzCRXmUruXrvrbufLmEn+eI8Qke8YTCIi/HHmFOavfwNv71gHs8UMALjl6t549KZ7cHlS4xC3joiIiKoTf3SDcpaR5GpsJK3ytut9GSMpGN3Y3PEmM8nVGEoyV9s4y0LS2p83GEgiCh0Gk4iqsb8Lz2LRhpVYvu19FJeVAAAy2l+LqQPHo13DliFuHREREVUX9plJzrJPPKHVHU2rjG1ZV4EkXwNIegJK7gIs7rqxueLPzCRnXQ71ZCbJ59LTa6rVFq1nIgoOBpOIqqHCS0V4ZfM7WLppFQovXQAA/KNFJ0wdNB5pLTqFtnFERERU7dgGAvQESzyZ2c1VlpL9etvX/gwk6aV3zCB/8HUMJa3AkbPMJGd1uqIVUHTVhY+IgovBJKJq5FJpMd788kO8tOFNnC48CwC4stEVmDpwPHq2S+cXMREREQWNVrDA1b2IVmDDW95mJPnS1c12uSfBMG/Zn0tvxz+yrctdlzdndfnrGLTW22Ym8V6WKHgYTCKqBsrMZXjv20/x73Vv4PczJwEAl9dvhMduHoebr+qlzLRBREREFExaA2/7MtW7qwCOu4wk+zpcdZPzJRMpXAMe7jKTbJcD7ru0ucpQ8gdn2WwMKhEFB4NJRFWYxWLBuh+2Ys4nr+LwyWMAgAYJ9fBw/zEYes1NiDTyI4CIiIjCg7+CAHoCRvZl9XZ9c/Vvd/vzd0BFz/hKtlxlKmllHtnuw3651jpX+9Lar54xrfRgZhJRaPA3SaIqSAiBrfu/xfMfZ+On4wcBAImx8Xiw72jc2X0woiOjQtxCIiIionKSJMFgMPg9EKDVlc2b7d0tCwR3YxIBwctw0gpaeTqAtu21cJXR5CkGkohCh8Ekoirm+yM/4dm1S/HtoR8AALFRNTA+YzjGZ9yBWjGxIW4dERERkTZfurd5QisbSSs7SS7r7t9ar50tc9YeV8s97VKnd7Y3Z4NrO3vtagwlV20PxPX0V7dIIvIeg0lEVcT+/zuE2R9nY9PebwAAUREm3Nn9VjzQZzTq1qod4tYREREROWefYRKoAIGebm9a5QKRkRSoQIsvXLXJ1cxtnnS385Wz9woRBReDSUSV2KXSYuQePYCV2z/ER7s2QQgBo8GIYen9Mbn/GFyWmBTqJhIRERHpEujgkd6MJGfP9v/Weu1smbzc3QxrerZxx1lWkbtyWvt0laHkakY3V93a/Blc4mxuRKHDYBJRJVJwsRDfH/kJOw//iJ2Hc/HD0f0oKStV1t+c2guPDRiHFslNQthKIiIiIv0CHQTwZLwkPQElZ6+dDUbtaSDF1bhInmQH2QfBnI295GpbraCSs4CSq+ORn4PR7Y2IgoPBJKIwdvLcX0rgaOfhH7H//w7DIiyqMvXiEnHtFam4v/cIdGjcOkQtJSIiIvKcs+ndKxtXbff0uFwFaOyXeTsYd2U+14B2+yv7MRFVNgwmEYUJIQTyTv2Gb22CR0f//D+Hck3rNURai45Ia9EJ/2jREc3qN+KXJxEREVVaWl2VtAZYBgI3m5q3g2XrzUQK12CPVkaVq4G59dQVCK7a5Oq9Q0SBw2ASUYiYLWbs/7/D2Hk4F98e/hHfHf4Rpwr+VpWRJAntGrZE1+YdyoNHLTshKb5uiFpMREREFDjuukr5GiRwNX6S7Xp3Xdy02qwVjHHV9c12vbs26z1uvd3ObDnLdNK7D2djJznrBuhv3mZmEZHvqkwwacmSJZg7dy7y8/PRsWNHLFq0CF27dg11s4gU8mDZ5cGjXOw6shfnLxWpypgiItG5aVukteiEtBYdcXXzDoiLqRmiFhMREREFh7tggN7MGNt/e5PF5GlAyd1yZ4N4yxk07oIszgbOdtXNy9VsbLbrXQ2O7WoMJU/HTHLWFk/HUgpUVhoReadKBJPeffddTJ48GdnZ2UhLS8OCBQuQmZmJgwcPon79+qFuHlVhQggUl5Wg8NIFFBVfxIXi8uci6+ui4os4lH9Uc7BsAKgVHYsuzdvjHy06Ia1FJ3Rq2gbRkVEhOhoiIiKiqkUr+ygYQQlXM53pGSfKVXDFX1k4tsEnVwN0+8JZNpg3XGV5EVHwVYlg0vz58zF27FjcddddAIDs7GysX78ey5Ytw+OPPx7i1lU9LqdHhfN+5PYf/e7qEULAIgSEsEAIwCIs1of8RVT+b4vFAgHreoulfB3Kl1uEgMVme2GzvUUIXCq9ZA3+XERRsRwQqvh3xXNFgOiC3XKzxaz73NWPq1OeddSyI/7RohPaXNYcRoNR9/ZERERE1ZHe4IanM7f5EmTS05XL1YxqWstc3R+7ozeLSc84SN5kGsnbedLuQJUlosCr9MGkkpIS7N69G1OnTlWWGQwGZGRkICcnR3Ob4uJiFBcXK68LCgoC2sZD+UfRbcawgO6DQi/GFI3YqBjERtWwPscgNroGGiTUR9cWHfGPFh3RtF5D9ukmIiLy0fbt2zF37lzs3r0bJ06cwEcffYRBgwapyhw4cABTpkzBl19+ibKyMrRt2xYffPABGjduDAC4dOkSHn74YbzzzjsoLi5GZmYmXn75ZSQlJYXgiMgdf98/ufyjpo6xkuQ2ORu42ll5+/34O8tI73JfOevi5m6cKF8wM4kovFT6YNJff/0Fs9ns8MWflJSEX375RXOb2bNnY+bMmcFoHgWQJEkwSAZIKA8gGiSD0v/cYF1XvgyQJIOyTF4vSRKiI6OUAFCNqBjUjK7hEAyqYR8gslsfGxWDGFM0M4yIiIiCpKioCB07dsTdd9+NW2+91WH9kSNHcN1112HMmDGYOXMm4uLisG/fPkRHRytlJk2ahPXr12PNmjWIj49HVlYWbr31VnzzzTfBPBSy8iVIEIgAg7djJWmtcxZwcTVDnaeDc7sLarnLmtKbvaQ1dpI/BXJGOCLyr0ofTPLG1KlTMXnyZOV1QUEBGjVqFLD9NavXEHvnfBqw+u0F4wNY1dcb9rNA2JW1We9qxgj7egySBMlgDRZJBmvASIIETvtJRERUnfXt2xd9+/Z1uv6JJ55Av379MGfOHGVZ8+bNlX+fO3cOb7zxBlavXo2ePXsCAJYvX442bdrg22+/xT/+8Y/ANZ6c8mdASavbmq9j9njL0xnT/FlGT9lABYYAdVDOXXc+V23QO9A5EQVPpQ8m1a1bF0ajESdPnlQtP3nyJJKTkzW3iYqKQlRU8AY5jjBGoF5cYtD2R0RERFRdWSwWrF+/Ho899hgyMzPxww8/oFmzZpg6darSFW737t0oLS1FRkaGsl3r1q3RuHFj5OTkMJgUZFpjF/kydpB93Vp1aO1DT6DJVRaRJ2M1aZV3NauaJxlBesZE0irvbV1aGU566vS0nfb12tcTikAhUXVmCHUDfGUymZCamorNmzcryywWCzZv3oz09PQQtoyIiIiIgu3UqVMoLCzE888/jz59+uDzzz/HLbfcgltvvRVffvklACA/Px8mkwkJCQmqbZOSkpCfn69Zb3FxMQoKClQP8p2/gkZ69+HNendsZ0XTU6/e8Y1sA062WfneBon0HKev58JdEMlf11gr+MgsJaLgqvSZSQAwefJkjB49Gl26dEHXrl2xYMECFBUVKbO7EREREVH1YLFYAAADBw7EpEmTAACdOnXCjh07kJ2dje7du3tVL8fcDBxns6rJ/9YbpPFkf3rq8iTQpWdmN2/K+tr1TCsY5Wy/etpsm3nkqqyecvZ1u6tLT3kiCp5Kn5kEAEOHDsW8efMwbdo0dOrUCbm5udiwYQNn4yAiIiKqZurWrYuIiAi0bdtWtbxNmzY4fvw4ACA5ORklJSU4e/asqoyrYRKmTp2Kc+fOKY/ffvstIO2vzjzJXPFkAGxP6/dHBo2v4xn5c/yiQAaqfD2f3lxHZ/WzmxtRcFWJzCQAyMrKQlZWVqibQUREREQhZDKZcPXVV+PgwYOq5b/++iuaNGkCAEhNTUVkZCQ2b96MwYMHAwAOHjyI48ePOx0mIdhjblY33oyT5M+xlTytw9NxklzV7Y/Brz3JKnJXj96yevbtTR1628DgEVFoVZlgEhERERFVD4WFhTh8+LDyOi8vD7m5uUhMTETjxo3x6KOPYujQobj++utxww03YMOGDfjvf/+Lbdu2AQDi4+MxZswYTJ48GYmJiYiLi8MDDzyA9PR0Dr4dYs4CBHqDN/4ejNnTcY9st3M2GLXtsdh2P9PTPUxrsGtXdWtt60vgxx91yPXoHePIXVc3ZiURhQaDSURERERUqezatQs33HCD8nry5MkAgNGjR2PFihW45ZZbkJ2djdmzZ+PBBx9Eq1at8MEHH+C6665TtnnxxRdhMBgwePBgFBcXIzMzEy+//HLQj4XKgwEWi8VlMMDTLCDbum2fbZd7W5+eQIqrMs4G0rZ97WnXNNs6XQWUAP9kErnjLCDobJ2v+2EwiSj4GEwiIiIiokqlR48ebn9xvPvuu3H33Xc7XR8dHY0lS5ZgyZIl/m4eecldQMDXgJKvZeQ2eFLe2X60gj56gzzuspbczfrmSXc3veVdtctdGX8NMm7/byIKrCoxADcREREREVU+/uqK5ks9gciYcUZrVjV3wR+tOvTW7StPAkm2z97wZ9dEBpWIAo+ZSUREREREFHTh8Au/pwNoe5Id5a6cpxlCnm7rrs5ADbLtaTe6cHgfEJHnmJlERERERERhLRwCDp5mEFVGgQheuVOVzydRVcbMJFR8aBYUFIS4JURERESO5HuUcPiFmsrxWvhO7o5kNptRWlqKS5cuoaioCIWFhYiKikJxcTEiIiJgMBgcxiqyncHLYrEoA3ibzWbl2WKxqJ7l5QCU1/J29jOCueu25W6GNlfbenqOtPgjAGObZWVbn+0xOBvTSevZ9iFfM6PRCAAwGo3Ka4PBoHqWl8vbydvadtuzPacWiwWlpaUoLS1FYWEhioqKcOnSJZSWlirXlT+f/sHzSK5Igu8Q/N///R8aNWoU6mYQERERufTbb7+hYcOGoW4GgfePRFT18TuHXGEwCYDFYsEff/yBWrVqBSzNsqCgAI0aNcJvv/2GuLi4gOwjXPHYeew89uqDx85jr27HDgTn+IUQOH/+PFJSUmAwcJSCcGCxWHDw4EG0bdu2Ur73K/PPLdseGmx7aISi7fzOIT3YzQ2AwWAIWsQ1Li6u0n2A+QuPncde3fDYeezVTXU+diDwxx8fHx+wuslzBoMBl112GYDK/d5n20ODbQ8Ntl0/fueQOwwzEhERERERERGRbgwmERERERERERGRbgwmBUlUVBSmT5+OqKioUDcl6HjsPPbqhsfOY69uqvOxAzz+6qwyX3u2PTTY9tBg24n8jwNwExERERERERGRbsxMIiIiIiIiIiIi3RhMIiIiIiIiIiIi3RhMIiIiIiIiIiIi3RhMIiIiIiIiIiIi3RhM8qMlS5agadOmiI6ORlpaGr777juX5desWYPWrVsjOjoa7du3x6effhqklvrP7NmzcfXVV6NWrVqoX78+Bg0ahIMHD7rcZsWKFZAkSfWIjo4OUov9Z8aMGQ7H0bp1a5fbVIVrDgBNmzZ1OHZJkjBhwgTN8pX5mm/fvh0DBgxASkoKJEnC2rVrVeuFEJg2bRoaNGiAmJgYZGRk4NChQ27r9fTzIhRcHXtpaSmmTJmC9u3bIzY2FikpKRg1ahT++OMPl3V683MTKu6u/Z133ulwLH369HFbb2W/9gA0f/4lScLcuXOd1lkZrr2e77RLly5hwoQJqFOnDmrWrInBgwfj5MmTLuv19nOCwl+4/zzreU/36NHD4Wdz/PjxIWpxBXefGd78LAaLu/ukcDrn/rjPOX36NEaMGIG4uDgkJCRgzJgxKCwsDGnb9d6naF2r559/PqRtB/TdY4TqvBPJGEzyk3fffReTJ0/G9OnTsWfPHnTs2BGZmZk4deqUZvkdO3Zg+PDhGDNmDH744QcMGjQIgwYNws8//xzklvvmyy+/xIQJE/Dtt99i06ZNKC0tRe/evVFUVORyu7i4OJw4cUJ5HDt2LEgt9q927dqpjuPrr792WraqXHMA+P7771XHvWnTJgDA7bff7nSbynrNi4qK0LFjRyxZskRz/Zw5c7Bw4UJkZ2dj586diI2NRWZmJi5duuS0Tk8/L0LF1bFfuHABe/bswVNPPYU9e/bgww8/xMGDB3HzzTe7rdeTn5tQcnftAaBPnz6qY3n77bdd1lkVrj0A1TGfOHECy5YtgyRJGDx4sMt6w/3a6/lOmzRpEv773/9izZo1+PLLL/HHH3/g1ltvdVmvN58TFP4qw8+z3vu0sWPHqn4258yZE6IWq7n6zPDmZzFY9Nwnhcs598d9zogRI7Bv3z5s2rQJ69atw/bt2zFu3LiQtt2T+5RZs2aprsUDDzwQ0rbL3N1jhOq8EykE+UXXrl3FhAkTlNdms1mkpKSI2bNna5YfMmSI6N+/v2pZWlqauPfeewPazkA7deqUACC+/PJLp2WWL18u4uPjg9eoAJk+fbro2LGj7vJV9ZoLIcRDDz0kmjdvLiwWi+b6qnLNAYiPPvpIeW2xWERycrKYO3eusuzs2bMiKipKvP32207r8fTzIhzYH7uW7777TgAQx44dc1rG05+bcKF1/KNHjxYDBw70qJ6qeu0HDhwoevbs6bJMZbz29t9pZ8+eFZGRkWLNmjVKmQMHDggAIicnR7MObz8nKPxVxp9nrfu07t27i4ceeih0jXLC1WeGNz+LoWR/nxSu59yb+5z9+/cLAOL7779Xynz22WdCkiTx+++/h6ztWrTuU5o0aSJefPHFwDbODW/uMcLlvFP1xswkPygpKcHu3buRkZGhLDMYDMjIyEBOTo7mNjk5OaryAJCZmem0fGVx7tw5AEBiYqLLcoWFhWjSpAkaNWqEgQMHYt++fcFont8dOnQIKSkpuPzyyzFixAgcP37cadmqes1LSkrw1ltv4e6774YkSU7LVZVrbisvLw/5+fmq6xofH4+0tDSn19Wbz4vK4ty5c5AkCQkJCS7LefJzE+62bduG+vXro1WrVrjvvvvw999/Oy1bVa/9yZMnsX79eowZM8Zt2cp27e2/03bv3o3S0lLVNWzdujUaN27s9Bp68zlB4a+y/jw7u09btWoV6tatiyuvvBJTp07FhQsXQtE8B84+M7z5WQwVZ/dJ4XrOben5/MrJyUFCQgK6dOmilMnIyIDBYMDOnTuD3mZXnN2nPP/886hTpw46d+6MuXPnoqysLDQNtOPqHqMynXequiJC3YCq4K+//oLZbEZSUpJqeVJSEn755RfNbfLz8zXL5+fnB6ydgWaxWDBx4kRce+21uPLKK52Wa9WqFZYtW4YOHTrg3LlzmDdvHq655hrs27cPDRs2DGKLfZOWloYVK1agVatWOHHiBGbOnIlu3brh559/Rq1atRzKV8VrDgBr167F2bNnceeddzotU1WuuT352nlyXb35vKgMLl26hClTpmD48OGIi4tzWs7Tn5tw1qdPH9x6661o1qwZjhw5gn/961/o27cvcnJyYDQaHcpX1Wv/5ptvolatWm67l1S2a6/1nZafnw+TyeTwi4irn3lvPico/FXGn2dn92l33HEHmjRpgpSUFPz000+YMmUKDh48iA8//DCErXX9meHNz2KoaN0nhes5t6fn8ys/Px/169dXrY+IiEBiYmJYXQtn9ykPPvggrrrqKiQmJmLHjh2YOnUqTpw4gfnz54ewte7vMSrLeaeqjcEk8psJEybg559/djsGRnp6OtLT05XX11xzDdq0aYNXXnkFTz/9dKCb6Td9+/ZV/t2hQwekpaWhSZMmeO+993T9hb6qeOONN9C3b1+kpKQ4LVNVrjlpKy0txZAhQyCEwNKlS12WrUo/N8OGDVP+3b59e3To0AHNmzfHtm3b0KtXrxC2LLiWLVuGESNGuB1Uv7Jde73faUSVhbP3tO0YK+3bt0eDBg3Qq1cvHDlyBM2bNw92MxWuPjNiYmJC1i5Pad0nhes5r6pc3adMnjxZ+XeHDh1gMplw7733Yvbs2YiKigp2UxW8x6DKgN3c/KBu3bowGo0OM0icPHkSycnJmtskJyd7VD7cZWVlYd26ddi6davHmSaRkZHo3LkzDh8+HKDWBUdCQgKuuOIKp8dR1a45ABw7dgxffPEF7rnnHo+2qyrXXL52nlxXbz4vwpl8g3bs2DFs2rTJZVaSFnc/N5XJ5Zdfjrp16zo9lqp27QHgq6++wsGDBz3+DADC+9o7+05LTk5GSUkJzp49qyrv7vteLqN3Gwp/le3n2ZP7tLS0NAAIu59N288Mb34WQ0HvfVK4nnM9n1/JyckOg86XlZXh9OnTYXEtPL1PSUtLQ1lZGY4ePRqcBupkf48R7uedqgcGk/zAZDIhNTUVmzdvVpZZLBZs3rxZlY1hKz09XVUeADZt2uS0fLgSQiArKwsfffQRtmzZgmbNmnlch9lsxt69e9GgQYMAtDB4CgsLceTIEafHUVWuua3ly5ejfv366N+/v0fbVZVr3qxZMyQnJ6uua0FBAXbu3On0unrzeRGu5Bu0Q4cO4YsvvkCdOnU8rsPdz01l8n//93/4+++/nR5LVbr2sjfeeAOpqano2LGjx9uG47V3952WmpqKyMhI1TU8ePAgjh8/7vQaevM5QeGvsvw8e3OflpubCwBh9bMJqD8zvPlZDAW990nhes71fH6lp6fj7Nmz2L17t1Jmy5YtsFgsSpAsVLy5T8nNzYXBYHDoQhZq9vcY4XzeqRoJ6fDfVcg777wjoqKixIoVK8T+/fvFuHHjREJCgsjPzxdCCDFy5Ejx+OOPK+W/+eYbERERIebNmycOHDggpk+fLiIjI8XevXtDdQheue+++0R8fLzYtm2bOHHihPK4cOGCUsb+2GfOnCk2btwojhw5Inbv3i2GDRsmoqOjxb59+0JxCF57+OGHxbZt20ReXp745ptvREZGhqhbt644deqUEKLqXnOZ2WwWjRs3FlOmTHFYV5Wu+fnz58UPP/wgfvjhBwFAzJ8/X/zwww/KTCDPP/+8SEhIEB9//LH46aefxMCBA0WzZs3ExYsXlTp69uwpFi1apLx293kRLlwde0lJibj55ptFw4YNRW5ururnv7i4WKnD/tjd/dyEE1fHf/78efHII4+InJwckZeXJ7744gtx1VVXiZYtW4pLly4pdVTFay87d+6cqFGjhli6dKlmHZXx2uv5Ths/frxo3Lix2LJli9i1a5dIT08X6enpqnpatWolPvzwQ+W1ns8Jqnwqw8+zu/f04cOHxaxZs8SuXbtEXl6e+Pjjj8Xll18urr/++hC33P1nhp6fxVBydp8UbufcH/c5ffr0EZ07dxY7d+4UX3/9tWjZsqUYPnx4SNuu5z5lx44d4sUXXxS5ubniyJEj4q233hL16tUTo0aNCmnb9d5jhOq8E8kYTPKjRYsWicaNGwuTySS6du0qvv32W2Vd9+7dxejRo1Xl33vvPXHFFVcIk8kk2rVrJ9avXx/kFvsOgOZj+fLlShn7Y584caJynpKSkkS/fv3Enj17gt94Hw0dOlQ0aNBAmEwmcdlll4mhQ4eKw4cPK+ur6jWXbdy4UQAQBw8edFhXla751q1bNd/j8vFZLBbx1FNPiaSkJBEVFSV69erlcE6aNGkipk+frlrm6vMiXLg69ry8PKc//1u3blXqsD92dz834cTV8V+4cEH07t1b1KtXT0RGRoomTZqIsWPHOvwSWRWvveyVV14RMTEx4uzZs5p1VMZrr+c77eLFi+L+++8XtWvXFjVq1BC33HKLOHHihEM9ttvo+Zygyincf57dvaePHz8urr/+epGYmCiioqJEixYtxKOPPirOnTsX2oYL958Zen4WQ8nZfVK4nXN/3Of8/fffYvjw4aJmzZoiLi5O3HXXXeL8+fMhbbue+5Tdu3eLtLQ0ER8fL6Kjo0WbNm3Ec889pwrYhKLteu8xQnXeiWSSEEJ4mdRERERERERERETVDMdMIiIiIiIiIiIi3RhMIiIiIiIiIiIi3RhMIiIiIiIiIiIi3RhMIiIiIiIiIiIi3RhMIiIiIiIiIiIi3RhMIiIiIiIiIiIi3RhMIiIiIiIiIiIi3RhMIqIqqUePHpg4cWKom6EiSRLWrl0b6mYQERERERH5RBJCiFA3gojI306fPo3IyEjUqlULTZs2xcSJE4MWXJoxYwbWrl2L3Nxc1fL8/HzUrl0bUVFRQWkHERERERFRIESEugFERIGQmJjo9zpLSkpgMpm83j45OdmPrSEiIiIiIgoNdnMjoipJ7ubWo0cPHDt2DJMmTYIkSZAkSSnz9ddfo1u3boiJiUGjRo3w4IMPoqioSFnftGlTPP300xg1ahTi4uIwbtw4AMCUKVNwxRVXoEaNGrj88svx1FNPobS0FACwYsUKzJw5Ez/++KOyvxUrVgBw7Oa2d+9e9OzZEzExMahTpw7GjRuHwsJCZf2dd96JQYMGYd68eWjQoAHq1KmDCRMmKPsCgJdffhktW7ZEdHQ0kpKScNtttwXidBIRERERESkYTCKiKu3DDz9Ew4YNMWvWLJw4cQInTpwAABw5cgR9+vTB4MGD8dNPP+Hdd9/F119/jaysLNX28+bNQ8eOHfHDDz/gqaeeAgDUqlULK1aswP79+/HSSy/htddew4svvggAGDp0KB5++GG0a9dO2d/QoUMd2lVUVITMzEzUrl0b33//PdasWYMvvvjCYf9bt27FkSNHsHXrVrz55ptYsWKFEpzatWsXHnzwQcyaNQsHDx7Ehg0bcP311/v7FBIREREREamwmxsRVWmJiYkwGo2oVauWqpvZ7NmzMWLECGUcpZYtW2LhwoXo3r07li5diujoaABAz5498fDDD6vqfPLJJ5V/N23aFI888gjeeecdPPbYY4iJiUHNmjURERHhslvb6tWrcenSJaxcuRKxsbEAgMWLF2PAgAF44YUXkJSUBACoXbs2Fi9eDKPRiNatW6N///7YvHkzxo4di+PHjyM2NhY33XQTatWqhSZNmqBz585+OW9ERERERETOMJhERNXSjz/+iJ9++gmrVq1SlgkhYLFYkJeXhzZt2gAAunTp4rDtu+++i4ULF+LIkSMoLCxEWVkZ4uLiPNr/gQMH0LFjRyWQBADXXnstLBYLDh48qAST2rVrB6PRqJRp0KAB9u7dCwC48cYb0aRJE1x++eXo06cP+vTpg1tuuQU1atTwqC1ERERERESeYDc3IqqWCgsLce+99yI3N1d5/Pjjjzh06BCaN2+ulLMN9gBATk4ORowYgX79+mHdunX44Ycf8MQTT6CkpCQg7YyMjFS9liQJFosFQHl3uz179uDtt99GgwYNMG3aNHTs2BFnz54NSFuIiIiIiIgAZiYRUTVgMplgNptVy6666irs378fLVq08KiuHTt2oEmTJnjiiSeUZceOHXO7P3tt2rTBihUrUFRUpASsvvnmGxgMBrRq1Up3eyIiIpCRkYGMjAxMnz4dCQkJ2LJlC2699VYPjoqIiIiIiEg/ZiYRUZXXtGlTbN++Hb///jv++usvAOUzsu3YsQNZWVnIzc3FoUOH8PHHHzsMgG2vZcuWOH78ON555x0cOXIECxcuxEcffeSwv7y8POTm5uKvv/5CcXGxQz0jRoxAdHQ0Ro8ejZ9//hlbt27FAw88gJEjRypd3NxZt24dFi5ciNzcXBw7dgwrV66ExWLxKBhFRERERETkKQaTiKjKmzVrFo4ePYrmzZujXr16AIAOHTrgyy+/xK+//opu3bqhc+fOmDZtGlJSUlzWdfPNN2PSpEnIyspCp06dsGPHDmWWN9ngwYPRp08f3HDDDahXrx7efvtth3pq1KiBjRs34vTp07j66qtx2223oVevXli8eLHu40pISMCHH36Inj17ok2bNsjOzsbbb7+Ndu3a6a6DiIiIiIjIU5IQQoS6EUREREREREREVDkwM4mIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImIiIiIiIiIiHRjMImoklmxYgUkScLRo0dD3RSfbdu2DZIkYdu2baFuCtl47733kJiYiMLCwoDUv3//fkRERODnn3/2e91NmzbFnXfe6fd6iYiIqhLeT4a+LT169ECPHj383oZ+/fph7Nixfq8XAIYNG4YhQ4b4vd6q9H6sThhMIqpG9u/fjxkzZoT1B/Xq1auxYMGCUDfDrR07dmDGjBk4e/ZsqJviV2azGdOnT8cDDzyAmjVrBmQfbdu2Rf/+/TFt2rSA1E9ERESBw/vJ8PXNN9/g888/x5QpUwJS/5QpU/DBBx/gxx9/DEj9VLkwmERUyYwcORIXL15EkyZNPN52//79mDlzZth8+V9//fW4ePEirr/+emVZZfny37FjB2bOnFnlgkn//e9/cfDgQYwbNy6g+xk/fjw++ugjHDlyJKD7ISIiIke8nwxeW4Jp7ty56NWrF1q0aBGQ+jt37owuXbrg3//+d0Dqp8qFwSSiSsZoNCI6OhqSJIW6KT4zGAyIjo6GwcCPonCxfPlyXHvttbjssssCup+MjAzUrl0bb775ZkD3Q0RERI54P1n12nLq1CmsX78+IN3QbA0ZMgQffvhhwIZDoMoj9D9xROQRrT7FTZs2xU033YSvv/4aXbt2RXR0NC6//HKsXLlStd3tt98OALjhhhsgSZJDn+7PPvsM3bp1Q2xsLGrVqoX+/ftj3759qv3feeedqFmzJn7//XcMGjQINWvWRL169fDII4/AbDaryr7zzjtITU1FrVq1EBcXh/bt2+Oll15S1tv3K+/RowfWr1+PY8eOKe1r2rQpCgsLERsbi4ceesjhfPzf//0fjEYjZs+e7fK8zZs3D9dccw3q1KmDmJgYpKam4v3333coJ0kSsrKysHbtWlx55ZWIiopCu3btsGHDBqXMjBkz8OijjwIAmjVrprTV9pq89dZbSE1NRUxMDBITEzFs2DD89ttvqn316NEDV155Jfbv348bbrgBNWrUwGWXXYY5c+aoysnn6b333sOzzz6Lhg0bIjo6Gr169cLhw4dVZb/66ivcfvvtaNy4MaKiotCoUSNMmjQJFy9edHl+AODSpUvYsGEDMjIyVMuXL18OSZKwbNky1fLnnnsOkiTh008/hRACTZs2xcCBAzXrjY+Px7333qssi4yMRI8ePfDxxx+7bdeMGTMgSRJ++eUXDBkyBHFxcahTpw4eeughXLp0yeW2p0+fxiOPPIL27dujZs2aiIuLQ9++fR3Ssz05xwCwc+dO9OnTB/Hx8ahRowa6d++Ob775xu2xEBERhQPeT6rpvZ/0tC2yV199Fc2bN0dMTAy6du2Kr776SrP+4uJiTJ8+HS1atFDu4x577DEUFxe7bBcArF+/HmVlZar7OCEEbrjhBtSrVw+nTp1SlpeUlKB9+/Zo3rw5ioqKcPToUeVcaT1s3XjjjSgqKsKmTZvctkm+r161ahVatWqF6OhopKamYvv27W63/fjjj9G/f3+kpKQgKioKzZs3x9NPP+3w/tB7Pw34dn5JgyCiSmX58uUCgMjLy1OWNWnSRLRq1UokJSWJf/3rX2Lx4sXiqquuEpIkiZ9//lkIIcSRI0fEgw8+KACIf/3rX+I///mP+M9//iPy8/OFEEKsXLlSSJIk+vTpIxYtWiReeOEF0bRpU5GQkKDa1+jRo0V0dLRo166duPvuu8XSpUvF4MGDBQDx8ssvK+U+//xzAUD06tVLLFmyRCxZskRkZWWJ22+/XSmzdetWAUBs3bpV2aZTp06ibt26Svs++ugjIYQQI0aMEElJSaKsrEx1PubMmSMkSRLHjh1zed4aNmwo7r//frF48WIxf/580bVrVwFArFu3TlUOgOjYsaNo0KCBePrpp8WCBQvE5ZdfLmrUqCH++usvIYQQP/74oxg+fLgAIF588UWlrYWFhUIIIZ555hkhSZIYOnSoePnll8XMmTNF3bp1RdOmTcWZM2eUfXXv3l2kpKSIRo0aiYceeki8/PLLomfPngKA+PTTTx3OU+fOnUVqaqp48cUXxYwZM0SNGjVE165dVe1/4IEHRL9+/cRzzz0nXnnlFTFmzBhhNBrFbbfd5vL8CCHE119/LQCITz75xGHdTTfdJOLj48Xx48eFEEL89NNPwmQyiTFjxihlnnjiCREZGSn+/vtv1bbvvfeeACC2b9+uWv7MM88Ig8Egzp0757Jd06dPFwBE+/btxYABA8TixYvFP//5TwFAjBw5UlW2SZMmYvTo0crr77//XjRv3lw8/vjj4pVXXhGzZs0Sl112mYiPjxe///67Us6Tc7x582ZhMplEenq6+Pe//y1efPFF0aFDB2EymcTOnTtdHgsREVE44P2k5/eT3rRFCCFef/11AUBcc801YuHChWLixIkiISFBXH755aJ79+5KObPZLHr37i1q1KghJk6cKF555RWRlZUlIiIixMCBA11dTiGEEPfcc4+oU6eOw/L//e9/ombNmuKWW25Rlj3++ONCkiTx5ZdfCiGEKCwsVM6V/Fi2bJmIj48X9erVU9VXWloqYmJixMMPP+y2TQDElVdeKerWrStmzZolXnjhBdGkSRMRExMj9u7dq5TTej8OGjRIDBkyRMydO1csXbpU3H777QKAeOSRR1T70Hs/7ev5JUcMJhFVMs6+/O1/WT916pSIiopSfdCvWbPG4QtOCCHOnz8vEhISxNixY1XL8/PzRXx8vGr56NGjBQAxa9YsVVn5l3DZQw89JOLi4hy+rG1pfeH2799fNGnSxKHsxo0bBQDx2WefqZZ36NBB9UXszIULF1SvS0pKxJVXXil69uypWg5AmEwmcfjwYWXZjz/+KACIRYsWKcvmzp3rcB2EEOLo0aPCaDSKZ599VrV87969IiIiQrW8e/fuAoBYuXKlsqy4uFgkJyeLwYMHK8vk89SmTRtRXFysLH/ppZcEANWXsf1xCiHE7NmzdQXc5Jsd2/pkJ06cEImJieLGG28UxcXFonPnzqJx48aqQNDBgwcFALF06VLVtjfffLNo2rSpsFgsquWrV68WANwGYORg0s0336xafv/99wsA4scff1SW2QeTLl26JMxms2q7vLw8ERUVpXoP6z3HFotFtGzZUmRmZqqO58KFC6JZs2bixhtvdHksRERE4YD3k57fT3rTlpKSElG/fn3RqVMn1f3Fq6++KgCo9vmf//xHGAwG8dVXX6nqzM7OFgDEN99847J91113nerc2XrllVcEAPHWW2+Jb7/9VhiNRjFx4kSX9d1///3CaDSKLVu2OKy74oorRN++fV1uL0T5fTUAsWvXLmXZsWPHRHR0tCq4pfV+1Lqnvffee0WNGjXEpUuXlGV676d9Pb/kiN3ciKqItm3bolu3bsrrevXqoVWrVvjf//7ndttNmzbh7NmzGD58OP766y/lYTQakZaWhq1btzpsM378eNXrbt26qfaVkJCgOwVWj4yMDKSkpGDVqlXKsp9//hk//fQT/vnPf7rdPiYmRvn3mTNncO7cOXTr1g179uzR3Ffz5s2V1x06dEBcXJyuc/nhhx/CYrFgyJAhqnOZnJyMli1bOpzLmjVrqtpvMpnQtWtXzX3dddddMJlMymv5etuWtT3OoqIi/PXXX7jmmmsghMAPP/zgsu1///03AKB27doO65KTk7FkyRJs2rQJ3bp1Q25uLpYtW4a4uDilzBVXXIG0tDTVNTp9+jQ+++wzjBgxwiFNWt7PX3/95bJdsgkTJqheP/DAAwCATz/91Ok2UVFRyrgFZrMZf//9N2rWrIlWrVppXnt35zg3NxeHDh3CHXfcgb///lu5vkVFRejVqxe2b98Oi8Wi63iIiIjCDe8nnfOmLbt27cKpU6cwfvx41f3FnXfeifj4eFXZNWvWoE2bNmjdurXq/PXs2RMANM+frb///lvzHg4Axo0bh8zMTDzwwAMYOXIkmjdvjueee85pXStXrsTLL7+MOXPm4IYbbnBYX7t2bd33b+np6UhNTVVeN27cGAMHDsTGjRsduqzZsr2nPX/+PP766y9069YNFy5cwC+//KIqq+d+2tfzS44iQt0AIvKPxo0bOyyrXbs2zpw543bbQ4cOAYDyYWrPNmAAANHR0ahXr57Lfd1///1477330LdvX1x22WXo3bs3hgwZgj59+rhtjxaDwYARI0Zg6dKluHDhAmrUqIFVq1YhOjpa6bvvyrp16/DMM88gNzdX1S9aa+BJX8+lEAItW7bUXB8ZGal63bBhQ80gy08//eS2XfINg227jh8/jmnTpuGTTz5xaO+5c+fcth8o71+vZdiwYXjrrbewfv16jBs3Dr169XIoM2rUKGRlZeHYsWNo0qQJ1qxZg9LSUowcOdLpfvQO/ml/Tps3bw6DweByNhmLxYKXXnoJL7/8MvLy8lQ3LXXq1HEo7+4cyz8ro0ePdrrPc+fOOb2ZIyIiCme8n3TOm7YcO3YMgOM9TGRkJC6//HLVskOHDuHAgQMO50RmO+aRM87u4QDgjTfeQPPmzXHo0CHs2LFDFayxlZubi/Hjx2P48OGYPHmy0/14e/8GlP8B8sKFC/jzzz+RnJysud2+ffvw5JNPYsuWLSgoKFCts7+n1XM/7Y/zS2oMJhFVEUajUXO5qy8VmZxJ8Z///EfzAz0iQv1R4WxfturXr4/c3Fxs3LgRn332GT777DMsX74co0aN8noGr1GjRmHu3LlYu3Ythg8fjtWrV+Omm25y+MuOva+++go333wzrr/+erz88sto0KABIiMjsXz5cqxevdqhvK/nUpIkfPbZZ5r11KxZ0+t9uStrNptx44034vTp05gyZQpat26N2NhY/P7777jzzjvdZszIwZUzZ86gYcOGDuv//vtv7Nq1C0D5tMAWi8VhtpJhw4Zh0qRJWLVqFf71r3/hrbfeQpcuXdCqVSuH+uSbxbp167pslzN6bmKee+45PPXUU7j77rvx9NNPIzExEQaDARMnTtQ8H+7OsbzN3Llz0alTJ82y9teYiIiosuD9ZHDbYstisaB9+/aYP3++5vpGjRq53L5OnToug37btm1T/qC6d+9epKenO5Q5c+YMBg8ejCuuuAKvv/6607rOnDnj9A+n/nD27Fl0794dcXFxmDVrFpo3b47o6Gjs2bMHU6ZMcbiH0/O+9fX8kiMGk4iqEWe/fMtduurXr+8wk5cvTCYTBgwYgAEDBsBiseD+++/HK6+8gqeeegotWrTwqI0AcOWVV6Jz585YtWoVGjZsiOPHj2PRokVu2/HBBx8gOjoaGzduRFRUlLJ8+fLlnh+Um3Y2b94cQgg0a9YMV1xxhdf1e2Pv3r349ddf8eabb2LUqFHKcr3p2K1btwYA5OXloX379g7rJ0yYgPPnz2P27NmYOnUqFixY4PAXq8TERPTv3x+rVq3CiBEj8M0332DBggWa+8vLy4PBYNB9ng4dOoRmzZoprw8fPgyLxYKmTZs63eb999/HDTfcgDfeeEO1/OzZs14FseSflbi4OL/+rBAREVUW1fV+0pu2NGnSBED5PYxtxlZpaSny8vLQsWNHZVnz5s3x448/olevXrqzfmy1bt0aH3zwgea6EydO4IEHHkDv3r1hMpnwyCOPIDMzU2kfUB5sGTFiBM6ePYsvvvgCNWrU0KyrrKwMv/32G26++WZd7ZIz1mz9+uuvqFGjhtMsoW3btuHvv//Ghx9+iOuvv15ZnpeXp2ufWnw9v+SIYyYRVSOxsbEAyn+RtpWZmYm4uDg899xzKC0tddjuzz//9Hhf8vg7MoPBgA4dOgCAy+k3Y2NjXXbHGjlyJD7//HMsWLAAderUQd++fd22xWg0QpIkVReno0ePYu3atW63ddVOwPFc3nrrrTAajZg5c6bDX/GEEA7nxZ/kv8rY7lcIoZqy1pXU1FSYTCYl+8jW+++/j3fffRfPP/88Hn/8cQwbNgxPPvkkfv31V4eyI0eOxP79+/Hoo4/CaDRi2LBhmvvbvXs32rVr5/YvgbIlS5aoXss3fq7eA0aj0eE6rFmzBr///ruufdpLTU1F8+bNMW/ePBQWFjqs9+ZnhYiIqDKprveT3rSlS5cuqFevHrKzs1FSUqIsX7FihcP5GzJkCH7//Xe89tprDvVcvHgRRUVFLtuXnp6OM2fOaI5vNXbsWFgsFrzxxht49dVXERERgTFjxqjukWbOnImNGzfi7bffVv3xzt7+/ftx6dIlXHPNNS7bI8vJyVGNU/nbb7/h448/Ru/evZ1mFGnd05aUlODll1/WtU8tvp5fcsTMJKJqpFOnTjAajXjhhRdw7tw5REVFoWfPnqhfvz6WLl2KkSNH4qqrrsKwYcNQr149HD9+HOvXr8e1116LxYsXe7Sve+65B6dPn0bPnj3RsGFDHDt2DIsWLUKnTp3Qpk0bp9ulpqbi3XffxeTJk3H11VejZs2aGDBggLL+jjvuwGOPPYaPPvoI9913n8MYRFr69++P+fPno0+fPrjjjjtw6tQpLFmyBC1atNAcm0gPeSDBJ554AsOGDUNkZCQGDBiA5s2b45lnnsHUqVNx9OhRDBo0CLVq1UJeXh4++ugjjBs3Do888ohX+3SndevWaN68OR555BH8/vvviIuLwwcffKBrnAOgfOyC3r1744svvsCsWbOU5adOncJ9992HG264AVlZWQCAxYsXY+vWrbjzzjvx9ddfq7q79e/fH3Xq1MGaNWvQt29f1K9f32FfpaWl+PLLL3H//ffrPr68vDzcfPPN6NOnD3JycvDWW2/hjjvuUP1Vz95NN92EWbNm4a677sI111yDvXv3YtWqVQ7jFOhlMBjw+uuvo2/fvmjXrh3uuusuXHbZZfj999+xdetWxMXF4b///a9XdRMREVUG1fV+0pu2REZG4plnnsG9996Lnj17YujQocjLy8Py5csd7kVGjhyJ9957D+PHj8fWrVtx7bXXwmw245dffsF7772HjRs3okuXLk7b179/f0REROCLL77AuHHjlOXLly/H+vXrsWLFCmUYg0WLFuGf//wnli5divvvvx979+7F008/jeuvvx6nTp3CW2+9parbdnDrTZs2oUaNGrjxxhvdnjOgPBMsMzMTDz74IKKiopSA0MyZM51uc80116B27doYPXo0HnzwQUiShP/85z+6uls64+v5JQ3BnDqOiHznbCrX/v37O5Tt3r27wzSnr732mrj88suF0Wh0mEZ169atIjMzU8THx4vo6GjRvHlzceedd6qm8xw9erSIjY112Jc8fbvs/fffF7179xb169cXJpNJNG7cWNx7773ixIkTqv3Zt6GwsFDccccdIiEhQQDQnNa1X79+AoDYsWOHizOl9sYbb4iWLVuKqKgo0bp1a7F8+XKHNgtRPoXphAkTHLa3n3JeCCGefvppcdlllwmDweBwTT744ANx3XXXidjYWBEbGytat24tJkyYIA4ePKiU6d69u2jXrp3DvkaPHq06bvk8rVmzRlUuLy9PABDLly9Xlu3fv19kZGSImjVrirp164qxY8eKH3/80aGcMx9++KGQJEkcP35cWXbrrbeKWrVqiaNHj6rKfvzxxwKAeOGFFxzquf/++wUAsXr1as39fPbZZwKAOHTokNs2yddp//794rbbbhO1atUStWvXFllZWeLixYuqsvbX6dKlS+Lhhx8WDRo0EDExMeLaa68VOTk5Dj8bnpxjIYT44YcfxK233irq1KkjoqKiRJMmTcSQIUPE5s2b3R4PERFRqPF+0vP7SW/bIoQQL7/8smjWrJmIiooSXbp0Edu3b9c8ryUlJeKFF14Q7dq1E1FRUaJ27doiNTVVzJw5U5w7d85tG2+++WbRq1cv5fVvv/0m4uPjxYABAxzK3nLLLSI2Nlb873//U9rt7GErLS1N/POf/9Rxxiruq9966y3lPrxz584O50fr/fjNN9+If/zjHyImJkakpKSIxx57TGzcuNHh/Oq9nxbC9/NLapIQPoT3iIhC4JZbbsHevXtx+PDhUDelyjGbzWjbti2GDBmCp59+2ut6Jk2ahDfeeAP5+fmafe4HDRoESZLw0Ucfua1rxowZmDlzJv7880+vB+smIiIislUV7ye/+uor9OjRA7/88ktABsjOzc3FVVddhT179jidiMSWJEmYMGGCxxlpVDlwzCQiqlROnDiB9evXa041T74zGo2YNWsWlixZojkmkB6XLl3CW2+9hcGDB2sGkg4cOIB169b5FKwiIiIi8lZVvZ/s1q0bevfujTlz5gSk/ueffx633XabrkASVX0cM4mIKoW8vDx88803eP311xEZGYl777031E2qsoYOHYqhQ4d6vN2pU6fwxRdf4P3338fff/+Nhx56SLNcmzZtUFZW5msziYiIiDxSHe4nP/vss4DV/c477wSsbqp8GEwiokrhyy+/xF133YXGjRvjzTffRHJycqibRHb279+PESNGoH79+li4cCH/akVERERhhfeTRP7DMZOIiIiIiIiIiEg3jplERERERERERES6MZhERERERERERES6MZhERERERERERES6cQBuIjsWiwV//PEHatWqBUmSQt0cIiK/EULg/PnzSElJgcEQ2r8n/e9//8OmTS9j3Li5/KwlIiKP8H49fITTvcXhw4exZcsrGDt2Dt8XQcBgEpGdP/74A40aNQp1M4iIAua3335Dw4YNQ9qGBx/8J9avz0FKSncMGDAgpG0hIqLKhffr4Scc7i0mTLgDn3/+PRo16om+ffuGtC3VAWdzI7Jz7tw5JCQkQJIiQhLRVv9E6vvxrNjGVXl//qiXnxdJkmAwGAEAERHycyQAIDKyPFYdaX0dEVn+bDSWlzMYjMr5lc+yfBwCFtVr2K9XrRCaZSXVWjvOToVP1ztUf/3w4bpqffw7OQyt81lxutQbKdfVri75tQSD8m+5PvmaWixmAIDZXP5cVloKACgtsz6XlqHM+u+yMrNqm4r3hf/f667W6Xvb2J8jrxvkEyEEhCjD2bNnER8fH5pGANi2bRsGDrwJEyfdjvfe3YK9e48gIoJ/3yIiIn3k+/XyUVuYgRJaAoAl5PcWmzZtwpAhtyLrgVux9qOvkJt7SPm9gwKDwSQiOwUFBYiPj4fBEFklgkn6Ak2eqQgWuAomlT+bIp0FkyI8CCapA0bhGUwKVVqvxftNgxZMUr92HUwqA+AYTCqRg0qlpW6DSf79WpNcvC0qZzDJYinFuXPnEBcXF5I2WCwWdO3aBrfcej0efngoOna4GxMn3ob77psfkvYQEVHlI9+vA0YwmBRqAoA5pPcWZrMZqamtcMeIG/HAA7fiynZ34vHH78DYsXND0p7qggNwE5FPJEn7F2N5uYAHYSyp/CFZ/6OqRbmuHlxa+f2j9T5z9t6j8PbOO+/g5MkzeOih2xAZGYHnnhuLmTNX4Pz586FuGhERVToGSBIfoXyEQ0hh5concPZsISZMuAUmUySeffYeTJ++HEVFRaFuWpXGzCQiO8xMcs82M0nONJKf5cwkkylS9TpST2aSXaMtdt2WmJmkpfJkJhmU1CTJoT5nmUmlpXIWkjVDqaQiM0kuIz8zM8m9UGcmFRcXo1WrJpg+/U6MGt1HaVP37g+iZ8+r8PSsN4PeJiIiqnzk+/WaMVdAktiVKZSEMKPw4q8hu7e4ePEirriiCWbPHofhd2RY2yRw7bUT0L9/OqY99UbQ21RdcIACIgqoUGeOuAwqkVuhTvwJ9fuH/GvhoklISKiJEf+8UVkmSRLmzLkPmb0fxn3jZyMlJSWELSQiosok1lQPBom/0oaSRZSh8OKvIdv/iwseQlJSbQwd1lNZJt9b3NR/Cu4d9xySkpJC1r6qLPQ5aURULVh7sIUHvzYm1Om9ftp/WF2gsGsO+cHp06fx3LP/wfMvjHcYEPMf/2iLvn3TMH36uBC1joiIKiMJRj7C4BEqf/75J154fjWef2E8DAb1/fB117VHr16pmDGD9xaBwmASERERBdzTz4zH1Ve3xo03dtFc/8yzY/HWW5uwb9++ILeMiIiIKqNZs+7Fdde1xw03dNZc/9zssVixYgN++eWXILesemAwiShMCKE9hE14sc8X0ZM7ot5GkiSNsag8y0Nh16fw5NmA2NrX3PH9oee9ofW+DO83SeX4efefvLw8ZC/9GC/MGe+0TIsWl2Hs2Jvw2GP3BLFlREREVBkdPnwYr7++Hs+/cK/TMq1aNcadd/bB44+PDWLLqg8Gk4iIiCig/vWvezB0aE906NDcZbknnhyFb77Zi61btwapZURERFQZPf74PfjnP29E27ZNXZZ7atpobNmyB1999VVwGlaNcLQyIqLqmuokH3d1SpGhoNu1axc++WQH9h9Y6bZs3brxmPL4CDzyyL34/vtfHMY/ICIiIsrJycGGDTvxy8G33JZNSkrEI48OwyOP3otvc/aFZLbuqop3aURERBQQQgg8/Mg9ePChwWjYsJ6ubR544Fb8+ec5vP322wFuHREREVU25fcWYzH54aFo0KCOrm0mTbod//fbn1izZk2AW1e9MJhERAHlyeg1FWW9H/NGsv7n4Q69EOpZ3Oz50BYPzoFH51dzR55tHf6jH5Er69evx/59R/Hoo8N0bxMTE4VZs+7GE088jEuXLgWwdURERFTZrF27Fv878gcefnio7m1q1IjGjBl3YurUSSgpKQlg66qXcPpNiIiIiKoIs9mMxx7LwlPTRiM+vqZH2474542oXbsWFi2eHKDWERERUWVTVlaGxx9/CNOn34maNWM82nb0nX1Qo0YUXl76cIBaV/1wzCQi8it/dkOWc1gEfB/TRwJc1CI3urqNHeT8uP2ZDeR9JpNGXUxTqjQuXryIAweOYfjwXh5vazAYMHRYT+z6nlP5EhERUbnz58/j119/w/A7Mjze1mg0YsjQntj1/cEAtKx6YjCJiIiIAsYAABaL59tJEiSpvt/bQ0RERJWbAcLLewtAkpIC0KLqicEkIgpfHiQMeZf94k1P33DuHSy3zdMvV4PH20hucr3sClN1ZrF4dcMHS3XLFCQiIiJdvL234AzGfhXOvxURERFRZSff8Hn6EF7cJBIREVHVZxFe3lt4Fkzavn07BgwYgJSUFEiShLVr1yrrSktLMWXKFLRv3x6xsbFISUnBqFGj8Mcff6jqOH36NEaMGIG4uDgkJCRgzJgxKCwsVJX56aef0K1bN0RHR6NRo0aYM2eOQ1vWrFmD1q1bIzo6Gu3bt8enn37q0bEEAoNJRBT2XM0g5tvsYo61VY80Gv8cp7tz799rQ5WWEN49iIiIiLR4e2/h4f1FUVEROnbsiCVLljisu3DhAvbs2YOnnnoKe/bswYcffoiDBw/i5ptvVpUbMWIE9u3bh02bNmHdunXYvn07xo0bp6wvKChA79690aRJE+zevRtz587FjBkz8OqrryplduzYgeHDh2PMmDH44YcfMGjQIAwaNAg///yzhyfOv9jNjYj8yv4z2p+/EtoOyC3Z94HT0SVOf685rZKVKfburLub+8CO7tCPZPtP9fnyZwDJ/loxxkBEREREwdC3b1/07dtXc118fDw2bdqkWrZ48WJ07doVx48fR+PGjXHgwAFs2LAB33//Pbp06QIAWLRoEfr164d58+YhJSUFq1atQklJCZYtWwaTyYR27dohNzcX8+fPV4JOL730Evr06YNHH30UAPD0009j06ZNWLx4MbKzswN4BlyrTL8dERERUWXjdTc3Rg6JiIhIgw/3FmazGQUFBapHcXGxX5p17tw5SJKEhIQEAEBOTg4SEhKUQBIAZGRkwGAwYOfOnUqZ66+/HiaTSSmTmZmJgwcP4syZM0qZjAz1DHaZmZnIycnxS7u9xWASUZiQJE57rpe+zBdXXbkM0PfxJ9cRmI9KSTKoHv4nH6eebm3uzon7OtitTb9q9fPOYBIRERH5kw/3Fvv27UN8fLzqMXv2bJ+bdOnSJUyZMgXDhw9HXFwcACA/Px/166tnpo2IiEBiYiLy8/OVMklJ6hnm5NfuysjrQ4Xd3IiIiChwOOMKERER+ZMP9xbt2rXDV199pVocFRXlU3NKS0sxZMgQCCGwdOlSn+qqTBhMIqKgEtZfEEOZlSHvO1i/q+rNOtIqJ4I0o5Wkf0CpgBIMIFQ9wssbPgvfC0RERKTBh2CS0WhUMof8QQ4kHTt2DFu2bFHVnZycjFOnTqnKl5WV4fTp00hOTlbKnDx5UlVGfu2ujLw+VNjNjYiIiALH6+l7gxNIJSIiokomTLrQy4GkQ4cO4YsvvkCdOnVU69PT03H27Fns3r1bWbZlyxZYLBakpaUpZbZv347S0lKlzKZNm9CqVSvUrl1bKbN582ZV3Zs2bUJ6erpfj8dTDCYRUVAIuE960VPGJ5Kh/CG/dDtujZ6xhpxs6aexkPwzrpLr41CdA7tzFAh6rnHA3wsUNJKwePfgO4CIiIg0eH1v4WEwqbCwELm5ucjNzQUA5OXlITc3F8ePH0dpaSluu+027Nq1C6tWrYLZbEZ+fj7y8/NRUlICAGjTpg369OmDsWPH4rvvvsM333yDrKwsDBs2DCkpKQCAO+64AyaTCWPGjMG+ffvw7rvv4qWXXsLkyZOVdjz00EPYsGED/v3vf+OXX37BjBkzsGvXLmRlZfnnhHqJ3dyIiIgocDhmEhEREflTkO4tdu3ahRtuuEF5LQd4Ro8ejRkzZuCTTz4BAHTq1Em13datW9GjRw8AwKpVq5CVlYVevXrBYDBg8ODBWLhwoVI2Pj4en3/+OSZMmIDU1FTUrVsX06ZNw7hx45Qy11xzDVavXo0nn3wS//rXv9CyZUusXbsWV155pUfH428MJlFILVmyBHPnzkV+fj46duyIRYsWoWvXrpplX3vtNaxcuRI///wzACA1NRXPPfecqrwQAtOnT8drr72Gs2fP4tprr8XSpUvRsmXLoBwPadD1oe37L43Oh/yxrnGRguQ4hpLn2UiBmY3N/X48G1NJfZZcZmXJ+3Fy/Xwf8krnNWdAofKzCO/GP+KlJyIiIi3C23sLz7bp0aOHy/E89Yz1mZiYiNWrV7ss06FDB4dBwe3dfvvtuP32293uL5jYzY1C5t1338XkyZMxffp07NmzBx07dkRmZqbDIGWybdu2Yfjw4di6dStycnLQqFEj9O7dG7///rtSZs6cOVi4cCGys7Oxc+dOxMbGIjMzE5cuXQrWYRERka0wGdeAiIiIqgjeW4QFBpMoZObPn4+xY8firrvuQtu2bZGdnY0aNWpg2bJlmuVXrVqF+++/H506dULr1q3x+uuvw2KxKIORCSGwYMECPPnkkxg4cCA6dOiAlStX4o8//sDatWuDeGQElH9Wu/u89n5EIhe1+FCpJEnWh/7Z5vwxLpIvPNm/fFzycXq3Q9icX9+voN4a9LyfiIiIiIgoOBhMopAoKSnB7t27kZGRoSwzGAzIyMhATk6OrjouXLiA0tJSJCYmAigfEC0/P19VZ3x8PNLS0lzWWVxcjIKCAtWDiIj8xNu/HnqTvk5ERERVHzOTwgKDSRQSf/31F8xmM5KSklTLk5KSkJ+fr6uOKVOmICUlRQkeydt5Wufs2bMRHx+vPBo1auTJoQSYf3J3woK/U0v0nhpP0ow82DTUGUn2XLXFh1Ogb+NAvE2rTCpSFfoZ9pawePeAFwNrEhERUdXn7b1Flbi3DB/h85sQkQeef/55vPPOO/joo48QHR3tU11Tp07FuXPnlMdvv/3mp1YSERH/ekhERER+ZRG8twgDDCZRSNStWxdGoxEnT55ULT958iSSk5Ndbjtv3jw8//zz+Pzzz9GhQwdlubydp3VGRUUhLi5O9Qgln7JIqjodSR5KEclQMSOZWwa4+jisGGso/DKSbMltU7fX1Rauj1tdefn51JVnw2Qcp6rlz7c844qnD97vERGFhSVLlqBp06aIjo5GWloavvvuO5flz549iwkTJqBBgwaIiorCFVdcgU8//dSnOolUvLmv4L2F34Xnb0RU5ZlMJqSmpiqDZwNQBtNOT093ut2cOXPw9NNPY8OGDejSpYtqXbNmzZCcnKyqs6CgADt37nRZJ/mbgP8/qe2jE5LzeIVDEMlVZMM+mCLZPVyV9YTBh4cv+7Pn7Phc7cd+gHPHIF1FCcfrFID+b36ujwKOfz0kIqq0PJ19uaSkBDfeeCOOHj2K999/HwcPHsRrr72Gyy67zOs6iRww6zksMJhEITN58mS89tprePPNN3HgwAHcd999KCoqwl133QUAGDVqFKZOnaqUf+GFF/DUU09h2bJlaNq0KfLz85Gfn4/CwkIA5TNUTZw4Ec888ww++eQT7N27F6NGjUJKSgoGDRoUikMkIiLe8BERVVqezr68bNkynD59GmvXrsW1116Lpk2bonv37ujYsaPXdRI54L1FWIgIdQOo+ho6dCj+/PNPTJs2Dfn5+ejUqRM2bNigDKB9/PhxGAwV8c6lS5eipKQEt912m6qe6dOnY8aMGQCAxx57DEVFRRg3bhzOnj2L6667Dhs2bPB5XCWqBOyzZawJMdrfGfri6Frd2fR/B/krVm9fj/tBiSu6Uam3FS4bL5fVrt+ha5Zk4Bcy6SJZLJAsXgymzdnciIhCSp592faPu+5mX/7kk0+Qnp6OCRMm4OOPP0a9evVwxx13YMqUKTAajV7VCZTPvlxcXKy85uzL1ZvX9xa8d/UrBpMopLKyspCVlaW5btu2barXR48edVufJEmYNWsWZs2a5YfWERGRz7yemY83fEREoeRq9uVffvlFc5v//e9/2LJlC0aMGIFPP/0Uhw8fxv3334/S0lJMnz7dqzqB8tmXZ86c6ftBUdXAe4uwwG5uRBQgvo+d5HIEHnnsHjcDbVcMeCxB7zhEkiRBcjJKsv3g1pJkhCQZ4Z+xjvRQ70fev54Bt10dl2P95WfbZZ1OrkFgRk4KxFhcFBRBSkVfunQpOnTooEykkJ6ejs8++0xZf+nSJUyYMAF16tRBzZo1MXjwYIcJG44fP47+/fujRo0aqF+/Ph599FGUlZWpymzbtg1XXXUVoqKi0KJFC6xYscKhLRxYloiqK4vFgvr16+PVV19Famoqhg4diieeeALZ2dk+1cvZl0mF3dzCAoNJREREFDhBuuFr2LAhnn/+eezevRu7du1Cz549MXDgQOzbtw8AMGnSJPz3v//FmjVr8OWXX+KPP/7ArbfeqmxvNpvRv39/lJSUYMeOHXjzzTexYsUKTJs2TSmTl5eH/v3744YbbkBubi4mTpyIe+65Bxs3blTKcGBZIqoqvJl9uUGDBrjiiitgNBqVZW3atEF+fj5KSkq8ntE53GZfphBjMCksMJhERCHixYe5kgVTkeeid6p19xk55WMkaY2TpM1ofVTUH4qHuj366DlOPVlMDudeSY9ynS2mjZlH5JsBAwagX79+aNmyJa644go8++yzqFmzJr799lucO3cOb7zxBubPn4+ePXsiNTUVy5cvx44dO/Dtt98CAD7//HPs378fb731Fjp16oS+ffvi6aefxpIlS1BSUgIAyM7ORrNmzfDvf/8bbdq0QVZWFm677Ta8+OKLSjs4sCwRVRXezL587bXX4vDhw7DYjGfz66+/okGDBjCZTF7P6ExE4YfBJCIiIgoci/DuIQQsFgsKCgpUD9sBWJ0xm8145513UFRUhPT0dOzevRulpaXIyMhQyrRu3RqNGzdWBnzNyclB+/btVeN4ZGZmoqCgQMluysnJUdUhl5HrkAeWtS2jZ2BZIqJw5ensy/fddx9Onz6Nhx56CL/++ivWr1+P5557DhMmTNBdJ5FbPtxbkP9wAG6iMCVJ+j/vXM9cVokp2S32ByY5WaZVtqIOZ+fJMUvHPiNHwJPMH0e+jBjkyUW1b6PZ5f7l4xbCYrPMvpSzWd606rRbJldWRd+gejLivClb5QhrarnH2wns378f8fHxqsW2M3ja27t3L9LT03Hp0iXUrFkTH330Edq2bYvc3FyYTCYkJCSoyiclJSE/Px8AkJ+frzkgrLzOVZmCggJcvHgRZ86c8WpgWSKicOXp7MuNGjXCxo0bMWnSJHTo0AGXXXYZHnroIUyZMkV3nURueXtvwZli/YrBJCIiIgoci/c3fG3btsWOHTtUi6Oiopxu0qpVK+Tm5uLcuXN4//33MXr0aHz55Zee75uIiBSezL4MAOnp6UoXYm/qJHLL23uLKvaHzVBjMImoUnCWdVO1KEfpRRpHRfKLvK19HbbjLMnn0ZPxkfS2w98pKNr1CV1fhnK7XX/ZlmcoyWWctV+dJebVYVo3kqr4+7hcdU5FsiPg9c2bwWDwaJBVk8mEFi1aAABSU1Px/fff46WXXsLQoUNRUlKCs2fPqrKTbAd8TU5Odph1TR4g1raM1qCxcXFxiImJgdFo9GpgWSIiIvKAYJe1cMAxk4iIiChwvJ5xxYu/ODrs2oLi4mKkpqYiMjJSNeDrwYMHcfz4cWXA1/T0dOzdu1c169qmTZsQFxeHtm3bKmVs65DLyHVwYFkiIqIg4GxuYYGZSUTVRmXOblK3XXs8KYN1XfkKV98VFWMFOSuhP86uf/Y3wLNz724mNfV64fIXb/s2OpatOCeu21ixX8mhHsdspcqcnVOZ2x5m5EEvPeXhJlOnTkXfvn3RuHFjnD9/HqtXr8a2bduwceNGxMfHY8yYMZg8eTISExMRFxeHBx54AOnp6fjHP/4BAOjduzfatm2LkSNHYs6cOcjPz8eTTz6JCRMmKF3rxo8fj8WLF+Oxxx7D3XffjS1btuC9997D+vXrlXZMnjwZo0ePRpcuXdC1a1csWLCAA8sSERH5k9f3FpXx96DwxWASEYUPOTBj90GvPX6zs+5s2tuUB0u0661gtG7j/IvGs+CR3ELXbXVF6PyN2rZdrgNLgCTJ3d/MGuvUbZXr0u7W5myAdLkuZw0w+CXrhCqJII1rcOrUKYwaNQonTpxAfHw8OnTogI0bN+LGG28EALz44oswGAwYPHgwiouLkZmZiZdfflnZ3mg0Yt26dbjvvvuQnp6O2NhYjB49GrNmzVLKNGvWDOvXr8ekSZPw0ksvoWHDhnj99deRmZmplOHAskRERAFmERwzKQwwmERERESB48MA3J544403XK6Pjo7GkiVLsGTJEqdlmjRpgk8//dRlPT169MAPP/zgsgwHliUiIgogDsAdFhhMIqpSJAS7G1tgPpPdd8mTM2gc9y9pltNa56w7m+Mg2voziiQ/d49yVp+rjCXH7ClnZW0HFtf+Qq6oy/21cP/e8++5Cd39ALvAeYSp6ERERORPQepCT65xAG4iIiIiIiIiItKNmUlEYUx7rKDqzDH+7WzAbccBql3Xo39ba5kQx+K1MpaE0+wi++PRekPJx+NsUG05E0w4XeeYscM3rtNxo6oT4e3MbHz/EBERkQZv7y34S5VfMZhEREREgSOYik5ERER+xC70YYHBJCKnJKgzLfjh4ygw58QxI8tgXa6VhSRZ1zlLARFKnUK4y0hyNoaSgNNsJjcZUYHikF0kaWVLWSpW2hZVxpvS+ouOfK7t12mdZ3ezuKmznQJ3aviz6VwYpEZ5PUgmZ/wjIiIiDRyAOywwmERERESBw0EyiYiIyJ+YmRQWGEwi0i0cspT0zpoVPnS11ElGkGM2kJwdI5TvAvfjG1XMWOaYGeM6a0NyOhYQXLQ5OBwyoCRoZHKo22g/A5w6E8v+xBntXmuNpaQeR8lxDCX7dtjsQ963m+yTyvNOtxXKbKAwyESyZxHe/fXQm5tEIiIiqvoEM5PCAYNJREREFDj86yERERH5E7OewwKDSUReqXwZQoGjPZtaxWphU8ozzmezkzTGJlJnx2iNj1SRiaOuUMlycjpDm3A6npLwMNvJf+yyjACHbKmKMZGsGV12bROqsYzUWViO4ylpjaVkP46SuzGU9FNq0nhjVSziz1+FMMxIknE2NyIiIvInzuYWFhhMIiIiosDhXw+JiIhgcPpHS0cWcBIKl5j1HBYYTCLySXAylJxn6AR2W8+oM5Qc9idnKOlqiHYGkW1mkauxkcrLyruVM5Zsv8DtMnW0k5xsMm60sj4MTtc48GUaM6fnS6tO+3GN7DOVlBQs61PFMTgbT0nOUKo4F7bn2X5/+rKb7LfTbKPQzh4rfw7ejYC3ly5Ik/rJewvmzjzHGz4iIqqmPAkgOduOgSUN/ENVWGAwiYiIiIiIiMhPvA0iuaorHINKAmYImEPdDAoRBpOI/KK6jKEkH5+rTAhh9+yLitnb7JdXLCvPlLHPeJIza+Rytqslu8yniknIDFAtUFXpZuY3J+Mx+cxpiotW9o/9jYvdOTHY1WWzrXxOhN2NisFgUErY70+S5Cwls6qMY9P9kTnjyfuqqv8cysI8I0lm4YwrREQUGOXBDDnj3H4m2tDwZyDJvt5wCSiFPIDEe4uwwGASkV+FNqgkSeH3GelyXG6H34W1v3wrulzZLrXv1uasS5r9INEVjXI2qLbSDrmrnM1ROB+k28X+/MhZ0ExVBq4H3la6mdlsq90dsLw27f3ZLpevhXY3O8eujQaHss7et2H2dgYQ7C5smi0IdQM8I7xMRfdmGyIiqrZsAxyhCCwFKohkv49QBZRCHkCy5UsX+kp2GxXOAv+OJyIioupLvuHz9MFYEhEReSnYgY9gBJJs9xXM/QFhFkgCgnZvsX37dgwYMAApKSmQJAlr165VrRdCYNq0aWjQoAFiYmKQkZGBQ4cOqcqcPn0aI0aMQFxcHBISEjBmzBgUFhaqyvz000/o1q0boqOj0ahRI8yZM8ehLWvWrEHr1q0RHR2N9u3b49NPP/XsYAKAwSSigJAQ2LB3oOv3nRCiPCPF+hDw/HdDSTKoMmUkSc4KMTiUkSTJ+rCWg8HuYVPWUP6oOI8Gu4eaQdmHQdlEslmm9SjPB7Jvg/cPeccu92nXNoP14cj+eCXlnCj1KXu0a4t8fiUJ9tdHrq/iOmlfRz2U94v8/pHfT2GNP/ea5FR0Tx9hf72JiCichV0ApJIKy/MYpHuLoqIidLARCUAAANy8SURBVOzYEUuWLNFcP2fOHCxcuBDZ2dnYuXMnYmNjkZmZiUuXLillRowYgX379mHTpk1Yt24dtm/fjnHjxinrCwoK0Lt3bzRp0gS7d+/G3LlzMWPGDLz66qtKmR07dmD48OEYM2YMfvjhBwwaNAiDBg3Czz//7OGJ8y92cyMiIqLAkYPKnm/o96YQEVH1ImAOeJe3YGcJ2e43kF3ewjKIJBPw7t7Cw2369u2Lvn37OqlKYMGCBXjyyScxcOBAAMDKlSuRlJSEtWvXYtiwYThw4AA2bNiA77//Hl26dAEALFq0CP369cO8efOQkpKCVatWoaSkBMuWLYPJZEK7du2Qm5uL+fPnK0Gnl156CX369MGjjz4KAHj66aexadMmLF68GNnZ2Z6fBz9hZhKRE/bZFV7W4o+mVNSmq02hyV4QNtkjmhkkLn+hlLNuoHrYry8fm8foJCvGWoecyWN3GrSybWzSmNxmG8lZPm4zlGz+U+3by0fF0dn9p5GV5Kyt7jKZINlmUcmL7M6vfLyqTCn745OsY0UZrQ/JrpzttXXzPnXyfnH5Hgs4fT9b/h9Tyfefaf98nnmJ3dyIiCiEAhkUCVUgKVz2HzJhcG+Rl5eH/Px8ZGRkKMvi4+ORlpaGnJwcAEBOTg4SEhKUQBIAZGRkwGAwYOfOnUqZ66+/HiaTSSmTmZmJgwcP4syZM0oZ2/3IZeT9hAozk4iIiChwfBkkk4iIiIIurLOSAJ/uLcxmMwoKClSLo6KiEBUV5VFV+fn5AICkpCTV8qSkJGVdfn4+6tevr1ofERGBxMREVZlmzZo51CGvq127NvLz813uJ1QYTCJyQ+uv+Z79jhPaGd4CzeksXEJ+FnbLXZ0H9UxoFUXVf3Upz5gR6nV21RrkOlSnX7IrY9DaVHPGNjnTyOHtYP8G0XjDuJ8BzgWd2SSS0JrVTZ6hTbJbblG1S4LtdVHP1iYZ1MetzPoGyaZtFtW2Qqhfy+vVs7tpvw+cvV+cJbtVbZ6nErnLPgpJdpJFeDd9L2dzIyIiPwlEd7dwyQoK5QxvISOPgeQpIbBv3z7Ex8erFk+fPh0zZszwT9uqEQaTiIiIKHC8/uuh/5tCRETVlz8DSuESSJL5M6AU9llJQPlfFL3MTGrXrh2++uor1WJPs5IAIDk5GQBw8uRJNGjQQFl+8uRJdOrUSSlz6tQp1XZlZWU4ffq0sn1ycjJOnjypKiO/dldGXh8q4fVTQFRJhHT8EZ/5Pv6KzSRtgN08bRXj2dgth/PfDZ2dT/XMYepxkpyN8VMxbg/U5ZzMuAZI7scYcjOLWtg+nIyv5Djbm4vjU8ZIkq+JzbWoOIN2ZdTXQuv6uvsZcny/lC9RZy7Jy+zfk76onDOmhfVnknzD5/G4BowmERERBVOlCCQBPo2ZZDQaERcXp3p4E0xq1qwZkpOTsXnzZmVZQUEBdu7cifT0dABAeno6zp49i927dytltmzZAovFgrS0NKXM9u3bUVpaqpTZtGkTWrVqhdq1aytlbPcjl5H3EyoMJhEREREREVGV549gSbhlJVHgFBYWIjc3F7m5uQDKB93Ozc3F8ePHIUkSJk6ciGeeeQaffPIJ9u7di1GjRiElJQWDBg0CALRp0wZ9+vTB2LFj8d133+Gbb75BVlYWhg0bhpSUFADAHXfcAZPJhDFjxmDfvn1499138dJLL2Hy5MlKOx566CFs2LAB//73v/HLL79gxowZ2LVrF7KysoJ9SlT4k0DkA8+yASpnxoNe9jNsOczu5pA24m7sJNtZwaxLlcnXKrKKKrJgrNdCMpQ/UP5QZ9rIdWhn38j/VWQ7WTNrDM6zfyq2cXwYpEgYpEhIktHrh1KHs33I+9dqn8H6kI/DelwObdZxjuTzKZ9f2zL2M+k5/lxoz+5m9w5Svyes7xetWQJDN5tbsHj2WRG2GUkyr/96WJWvMRFR5bFkyRI0bdoU0dHRSEtLw3fffadru3feeQeSJCm/WMuEEJg2bRoaNGiAmJgYZGRk4NChQwFoefXia5Cr0mQlAUG7t9i1axc6d+6Mzp07AwAmT56Mzp07Y9q0aQCAxx57DA888ADGjRuHq6++GoWFhdiwYQOio6OVOlatWoXWrVujV69e6NevH6677jq8+uqryvr4+Hh8/vnnyMvLQ2pqKh5++GFMmzYN48aNU8pcc801WL16NV599VV07NgR77//PtauXYsrr7zSl7PoM46ZRERERAEjLAKCYyYREVVK7777LiZPnozs7GykpaVhwYIFyrTl9rNU2Tp69CgeeeQRdOvWzWHdnDlzsHDhQrz55pto1qwZnnrqKWRmZmL//v2qX8KJnAnWvUWPHj1c/gFTkiTMmjULs2bNclomMTERq1evdrmfDh06OIzjZO/222/H7bff7rrBQcbMJCI/qMjm0JMl4HuGUsV+Qp3t5PjhKicgyeP12JYUUGeV2I+LYzsmEjSXy9lIjsuUTCT5P2tWjn0d/n/IGUR2D0Oki20kNw+NDChDZPnDbj8VWUyBOT7l/MlZTsp1dZEdZrdc63ravy8q3j/WLCT794b1P+3vc1cjcgWD7fvSH3W5KeHR500YsB/USu+D0SQiopCbP38+xo4di7vuugtt27ZFdnY2atSogWXLljndxmw2Y8SIEZg5cyYuv/xy1TohBBYsWIAnn3wSAwcORIcOHbBy5Ur88ccfWLt2bYCPxtoGHzJw2MUtTPDeIizwp4EoAEL5S567waz9zXHQY3lQZNfd3NTbyN2onL0up+6W5aTLmt3g0hVdvWy7n9kNuG1bRjJUBGvk/zS6qhmkCBikCI39li83qP5Td04zShEuH9od2eS2ON+vsy5yFdvKASjH41bOiX3XN2sZ14OU210LuwG5ta+r+ho79oJ01s1NON/Gj7wZNDzQQr1/r3mbil7NZjkmIgo3JSUl2L17NzIyMpRlBoMBGRkZyMnJcbrdrFmzUL9+fYwZM8ZhXV5eHvLz81V1xsfHIy0tzWWd/lapunR5wNtgV6U7Hz4MwE3+w25uREREFDjyDZynOGYSEVFI/fXXXzCbzUhKSlItT0pKwi+//KK5zddff4033nhDGbDYXn5+vlKHfZ3yOi3FxcUoLi5WXhcUFOg5BKqqvL238GYbcorBJKIAkiRXvw/JKQaV/UPN2mXNehjKs7zWZtBkvSRr+oWkpGE4y3KxLWO33Hp+lbWSAZCEdZlBvU7+l/Jktz+bblkGu25IWt24bNa6WOdiK8067c+fuowQFWkcFrfvKXXKhyTZlJfU/5Dsq1IWWJQyQhhslsHhPMqXqOK94KZ5cHzfVLyfbLev7D87tpy/VyplNpItr4NJ/m8KEREFzvnz5zFy5Ei89tprqFu3rl/rnj17NmbOnOnXOkNNkiommRGikmUGhRrvLcICg0lEREQUOMxMIiKqlOrWrQuj0YiTJ0+qlp88eRLJyckO5Y8cOYKjR49iwIAByjKLpfwPTRERETh48KCy3cmTJ9GgQQNVnZ06dXLalqlTp6qmSi8oKECjRo28Oi5v+Tpekm3wyN06X4JLBhhg8aCveKXr4gbw3iJMMJhEFGAVWRlOS1if/f3hFuzMJ6F+dnLAFRlKjv2WHTMwNLKLrEsknZlJFXXLA0bb1m6fgaRer75p0JeRZFunUJZ5n1oiIGdT2S+3zy4yKNlJNn/nsq4sb5N8Y6G00XYMK/t1UGcE2e5Zq5W2ayTlPWCxLle/F1UZe3ZZRk4z2FQbBPtGIJCpQVU4I8nK2xlXeL9HRBRaJpMJqamp2Lx5MwYNGgSgPDi0efNmZGVlOZRv3bo19u7dq1r25JNP4vz583jppZfQqFEjREZGIjk5GZs3b1aCRwUFBdi5cyfuu+8+p22JiopCVFSUw/J4KQVGKdL7g7SySGE2UF+A7wEMwrfAmC0zSnHSfTG/4r1FeOAA3ERERBQ4wttBMj2745s9ezauvvpq1KpVC/Xr18egQYNw8OBBVZkePXo4zJ44fvx4VZnjx4+jf//+qFGjBurXr49HH30UZWVlqjLbtm3DVVddhaioKLRo0QIrVqxwaM+SJUvQtGlTREdHIy0tDd99951Hx0NEFA4mT56M1157DW+++SYOHDiA++67D0VFRbjrrrsAAKNGjcLUqVMBANHR0bjyyitVj4SEBNSqVQtXXnklTCYTJEnCxIkT8cwzz+CTTz7B3r17MWrUKKSkpCgBK09EwIQIRHn9MCISRkQiUkQF7WEUEZqPoLbBety+nLuKh8mfbzl9vB6Am9Ekf2JmElGQuM9Q8qXOUGUhOf7ZpGLsJKH5bF9OH7sMJes07Op18jhL1hi5PO6SkoUD1dhH5UXkcYHU2Tj2WUeSVDElvQSjwzp1SzVi9C7HVXJDaP+lzD4zSQihpEjL6cr2YxUZrW1TxleyFhCSBRB219JaRjIYVPuTbMY9UrKm5HGU7N6H9hlJLg9T2L/Wfv+4ft+EJmPJ3xlEVSUjKdi+/PJLTJgwAVdffTXKysrwr3/9C71798b+/fsRGxurlBs7dixmzZqlvK5Ro4byb7PZjP79+yM5ORk7duzAiRMnMGrUKERGRuK5554DUD4TUf/+/TF+/HisWrUKmzdvxj333IMGDRogMzMTAPDuu+9i8uTJyM7ORlpaGhYsWIDMzEwcPHgQ9evXD9IZISLy3dChQ/Hnn39i2rRpyM/PR6dOnbBhwwZlAO3jx4/DYPDsPuexxx5DUVERxo0bh7Nnz+K6667Dhg0bEB0d7XH7aohYvwUz3I85WXXYjwHqizLhe2YYVU6S8GRUXKJqoKCgAPHx8TAaTRpdqHzn/CfO+x9FrQGJnQ1S7M/Bi+W/7ANQbiQMhvKARmREeaw6MjJS/Wwq/8I3GiMRYSwvYzBGquqQO2rJQR3HLm0Gh8G5GUyy7bKmHUyqKCtvWxFMcvgqEOrBtJX9KUEdixJMkgferqhD/Voor+X9mpUxFCzmUgBAmbk888NsfV1aUlL+XFqqfi4rg8VSfnxyHd4M8u6cVoDIWdDIH8Ekx40DGUwSQsBsLsG5c+cQFxcXuB0BKCwsRK1atfDX0/9EQoxj1wR3/r1tL/bENsM777zj1f7//PNP1K9fH19++SWuv/56AOWZSZ06dcKCBQs0t/nss89w00034Y8//lB+UcrOzsaUKVPw559/wmQyYcqUKVi/fj1+/vlnZbthw4bh7Nmz2LBhAwAgLS0NV199NRYvXgyg/L3aqFEjPPDAA3j88ce9Oh4iIqog369fH/cgIiTPv2O8VRkCTv4MFOlRJoqxvWBhUO4tzpw5g8TERJx7dhRiozwPYj2/+Uf8Uqc1/vOf/wSgddUPM5OIwkaws4v8uz/7IFXF7FuuMpRc71sriFT+WiOYZBc8UsYpkox2dWgFnirW2NahLJUMDmUqXsnBJXlsI8fAkesZ31yzDxo5LpcDQraDJxqclLW+VsYFEEp5JeBjN86Skn2kJB8pUTWNyKg6e0iS9yPU2U1a2yivnGUk2ZQPzJ9Agp0OVI3Sj0I0SOa5c+cAAImJiarlq1atwltvvYXk5GQMGDAATz31lJKdlJOTg/bt26umrM7MzMR9992Hffv2oXPnzsjJyUFGRoaqzszMTEycOBEAUFJSgt27dyvdPoDyQHlGRgZycnJ8OiYiIlIzSUZEuhjY2l6gRkYKRZApUEEjT+9aDdB//v1GhObegtQYTCIiIqLAEV6OUSAELBYLCgoKVIudDcJqy2KxYOLEibj22mtx5ZVXKsvvuOMONGnSBCkpKfjpp58wZcoUHDx4EB9++CEAID8/XxVIAqC8zs/Pd1mmoKAAFy9exJkzZ2A2mzXL/PLLLx6cACIicifWEIlIQ3mGSjACOuEeiwhWV3nbQFapJQSDl3t7b0F+xWASUZAFa3Y3Z/sJxNhN1hrV9Tod86biuaIJ8pdQReZR+T/UjZZsM5PcdGtTMoSs6w2QbDKEnHRNk9cLdZaRbWaRs1nk5Awl28wrX6eQtW2q/RSv8v4rpnM1OnQrk1VkHVnHPZL/gicqllccY0U3tvL92r9RKuqW7K+5pC5bcYXV57N8uluLzRrX7xPbnZQ/Be7mQesmzL83Zq4rq4rjJQmL096abjYE9u/fj/j4eNXi6dOnY8aMGS43nTBhAn7++Wd8/fXXquXjxo1T/t2+fXs0aNAAvXr1wpEjR9C8eXMvGklERKEUHWGAycMxm7xVmWIXQQsqSUCJJfhzevlyb0H+w2ASERERBY7X3dyAtm3bYseOHarF7rKSsrKysG7dOmzfvh0NGzZ0WTYtLQ0AcPjwYTRv3hzJyckOs66dPFk+4XFycrLyLC+zLRMXF4eYmBgYjUYYjUbNMnIdRETkH1FGwGTwT+TEm6+qYNQFlAdtwrW+kMRnQtSFntQYTCIKkcBlCAWPbdsr/gLiPiNJKadOOnGoS0lMUrKB5PUGxzGSpAjrs3VAcKizkMqzmfRlJhnssnTK16v/6mKwz2ZS2u741xlf+rTLmUH2tVZkH1k/xoUFFsn+TzTW7B9JPb5SRZaTOmNJrtl2G0kZiNug2rY8s6zMtlqbC6keK0l5bfOet30bqPar531jt7vK/DMkq4oZSQoLvL7hMxgMugfzFELggQcewEcffYRt27ahWbNmbrfJzc0FADRo0AAAkJ6ejmeffRanTp1SZl3btGkT4uLi0LZtW6XMp59+qqpn06ZNSE9PBwCYTCakpqZi8+bNyjTXFosFmzdvRlZWlq5jISIifWIiJET5OdLi7/sKbzuBBSLfJxD3G0ZLCG5ivA0mhaBHXlXGYBIREREFjLep6J7ezE+YMAGrV6/Gxx9/jFq1ailjHMXHxyMmJgZHjhzB6tWr0a9fP9SpUwc//fQTJk2ahOuvvx4dOnQAAPTu3Rtt27bFyJEjMWfOHOTn5+PJJ5/EhAkTlIyo8ePHY/HixXjsscdw9913Y8uWLXjvvfewfv16pS2TJ0/G6NGj0aVLF3Tt2hULFixAUVER7rrrLs9PBBERORUbgGCSPVGJ+0ZJARqk21ZECIJJwbq3INcYTKKQWrJkCebOnYv8/Hx07NgRixYtQteuXTXL7tu3D9OmTcPu3btx7NgxvPjii8rsOd7WGQ6cZyhJ0Js4WlGH1jaBniVOzhyxjuGjZIu4m9XNcUwde/ZZPvJrSfVvdTaR/VhKSsYSJM1xlNTs6tTIPpKEkxnfXLz2ZTY3g9Ae/8jhtQQYlEwku/OpjH9kzTZStqmoSxkbSaizleS6hCiztgfKcov938yEdfwmeSY462tJea2RAWU37pKzWdxU7xu7bKbA0rpBkt9jvtZTxTOSZF7PuOJZ8aVLlwIAevTooVq+fPly3HnnnTCZTPjiiy+UwE6jRo0wePBgPPnkk0pZo9GIdevW4b777kN6ejpiY2MxevRozJo1SynTrFkzrF+/HpMmTcJLL72Ehg0b4vXXX0dmZqZSZujQofjzzz8xbdo05Ofno1OnTtiwYYPDoNxEROSbmhEC0Ub3Xxj+6nYW7rEIx9sK71rsSXwu0hyCs8JubmGBwSQKmXfffReTJ09GdnY20tLSsGDBAmRmZuLgwYNK9wJbFy5cwOWXX47bb78dkyZN8kudBPgv2KQdGHLebckMIZxNJSo5eenYZU0eTFoJJllf2w+eLUkRMAi5n5w6aFQRgLJuaxcwUgeG1GUrWiZvU7Fc2Z8v5AG4HQa3Nlufbbt9OS4DKrqs2QebbMtLdl3fLHZBJGH9upDrEsIMIR+r3QDcSpc0h7eWxi2OsGuL0+5tFUfu31u56hDNCTELvEsr9/AyO75X1Bo1aoQvv/zSbT1NmjRx6MZmr0ePHvjhhx9clsnKymK3NiKiAIs0lD/8zR/BJ3/FLfzxh6dAJm+FIpYUrHsLco3BJAqZ+fPnY+zYsUraf3Z2NtavX49ly5bh8ccfdyh/9dVX4+qrrwYAzfXe1ElERERERJVTzQiBGJvMJH8PfA34d5gdPQEmf2YtB2LcJfvAVIR9RjxVGwwmUUiUlJRg9+7dmDp1qrLMYDAgIyMDOTk5Qa2zuLgYxcXFyuuCggKv9u8r7e5uvmcNhWqgb3cDKQshVF2Xyp/tv67tu6xVPBvkzCCHddZMJcgZSxUDc1esq+j6Vv5sl6lkl30kQYIk7Lq+KQcqD/itnalkW683lG5s8jmyey9YIHctExVZTHYDb1d0JVNnLlWstyjLLFKZtc1yWXng7TL1/iAgKQOUy/uVX9sOXO6YMSKExXm3NrcDcAeX7zd01bh7m5WwCAgv7u5Ddc2JiKjyiDUKxBi1wz3+DQL5acY4N+v9GfyR/BTkcdcmQwjSfby9t2A3N/9iMIlC4q+//oLZbHYYPyIpKQm//PJLUOucPXs2Zs6c6dU+iYjIDaaiExFRgEQYBCINvn9huI1LOAnMiBB3l5e8/LL0Z7e30lAEaHhvERYYTKJqb+rUqZg8ebLyuqCgAI0aNbIO2Kz+pA3GbA6+ZBJJkv7tApWx5JBJoiMzCcp4OUbrs/XbQR7/Gurn8hG4y/9plNQZSBXPclaR9TUMymDcRuWjT1KXtf7VySis622yjuzfCxUDf1uzmIT9ANyS04wkx4G/1Swa7zNlQGwn4yGV5xbZDc5tPb+22UQAYLZmH8ljJ1mEuWKdkk1kzUSy1i+/X+RzZLsns91+5fstJa9Ofq9Z5PGWYHPN3WQiBSlDyZNMIV+yioKVkRSM2Vt083aYK97wERGRG7ERZtQwmt0X1OBttlG4zi7vbVaTrxlMkuTd+feJv4fQJK8wmEQhUbduXRiNRpw8eVK1/OTJk0hOTg5qnVFRUcqUz0RE5F/ep6L7vy1ERFS1xBrNiI1QBzP8OW6St5lH/h67yZdMIm+zl/S2Q0Lwg0nCAi+70AegMdUYg0kUEiaTCampqdi8eTMGDRoEALBYLNi8ebPXs98Eok57ochUkvcs79H7sv6atc3d3u3OkQdjJjmQM5Qk9UeVBIPmOEq2zwYp0vosZyMZbbKUKrKVAMAg7MdZkl9XZB3Zj68k//VHzkiyz0KyfeUsq8kZ2wwjxzGS7MqKivGRLMo2dmMl2WQvAYDR+qVvsWYHWSSzMs6SMs6R9TyalbKSqk4JNjPqyc/WcyGUmwolJcnxGD0cM0kmQQrSz53WXZsnd3LBzQwKq0wke0xFJyKiAIk0WBBp0Pcl40uAx+JpFpNdcU+DUr4GgAw+Zht5ErzSe/79ivcWYYHBJAqZyZMnY/To0ejSpQu6du2KBQsWoKioSJmJbdSoUbjsssswe/ZsAOUDbO/fv1/59++//47c3FzUrFkTLVq00FUnEREFV/lfD73Yjjd8RETkRnREGWIijO4LavD2e8bjwFIQeRNE8rULvtk6SUswCeHdvQWDSf7FYBKFzNChQ/Hnn39i2rRpyM/PR6dOnbBhwwZlAO3jx4/DYKjI4Pjjjz/QuXNn5fW8efMwb948dO/eHdu2bdNVp78FMlPJk/GP/LRH+PIJq2SaKGMxaWeYWKzj5lgsFo0yduPo2LdQzj6CVJFVJI93ZF1nlDORlIwkk7VchDJWUkUmkly2/LVRyOMsWesStvuTlH+rniV5XCWt9cK6zlMVN0UV35PqzCBl9jWb107XCXmspIrZ28pfl59vM8wVs7VZz4UZ8jhSZday6hYJWJRMropZ4tSz7ynjIlm3tL3Ort4X6rJ2z/DXz0WQM4cCsLuwzkayxb8eEhFRgMREliEmQv+dli+zsnkbRPJln96OZ+RtZpI3+5PH4gwqb+8twnXAq0qKwSQKqaysLKdd0OQAkaxp06a6Bt91VScREQUX/3pIRESBEuGim5tm8MfDYIltIMioc9tAxiu8GWTb1wG2AdfBqYgQdHNj1nN4YDCJyI/8nankOOOa+3GPnM3S5ulyfYRjm+SKrBUrmSeaYybJWSgW1aaA9uxuyvmUlP8pjPZjJNnN3BYBk5KlJGciRQh1plKEMh6SPP6SdXY3m/nXlLGSnGQmyU8GhxZ6lkniMGub9dlit8A2+6giI0m9jdluDCV5fKQy63m1SGaUWf+qJI+RZEBJeRmNjCQAMEKgTNiNjeSQlaa+vhXX1XGdQ6aSs9nbhNb0Hd7/nDnLGNJarj+7qKKgPzOSKk0mkj3+9ZCIiAIkKrIMUZGeh1i8zjKyeL6dLwEMb+4jJENws5lKKlNmEoNJfsVgEhEREREREVU6JlMZTDqCSb50NQMAi4dBJH9nwHgTVDJ4GVQq35/+bU2hCCZRWGAwiSiAgjfzlPbey3kyq5unM75J9olICoexbuQxcczW2cGMRlgs8kxh1jGM7MbPMbi4N5DH03KcxU09HlKEnI0EEyJFefaS8mw3q1uEXIf1PMivIVWMYiRnhxgN8thI0H62OR+OM2K4uyOoOP/2M48oY1PB8dlsUY+ZpEzUai2kZCJZFyivhQWl1mtQKpVqNlHOSDJYx1mywFxxzq3XwuxmZljb8ZAs8r7l94Dd+0M4GTtJ1SYPMvYquDv3vs7i5n+VNiPJqjwTzYvt/N8UIiKqYgxGAYNRzzeGdhm9mUa2gRmvvtM8DGZ52zUtmJlMMoMv0+R5ifcW4YHBJKIAk38R9CWo5E13t3CjNeByxaDLcsDJGkgwqLu32XexUpHUQR05iGSwdnszWgNHJkQi0hpYirSuM8nd3eyCRxHW6I9B6cIGGJXAllxW3Qw5YCTZtEe+bvKm8rG7+6IXQlLqUbqs2QeRlO5gFduVKf+2BpOsG8t1lFkM1m3UwaQyCEg2g41XHCVQItdlDSIZrF3bJJTYvDHt2g+762bflc1iVq65u4G3Kxf/dm+r7EEkmbfjGlSijzciIgoRY6QZEZFu/pqlk6cBH2+6vFXsy3GZL/cOngaE/DGOkswI/5x/T/DeIjwwmERERESBw3ENiIgoQCJMAhEm/V8YrgMQrutxDDY5L+9VoMMFycNhoXwJFnm6rwg/BqZ0471FWGAwiShIApOh5HlZV8v9kfnkMDSyk4GV1ZlJFd2tgIrsF2Gdlt5iHShbUr6ZKwbvruhWZlSOA6jo7maEPNh2JEwoz0iKsq6LtGZARVo3irR215K7sMnZRxGGiuwiOUPJYJd1pGQmKQNz22RLKfce6qwfZ2zPoZx5VJGRpH4tr7fY/NtsUWc1lVn/UaasL/9HqbVcqRCQJ+KQlPrtMpLk86scibGirM11sX1tUTKSyqzPZmW5w7VX3gOOA7Wrjh/eUp/1wAy87V15h+2rSEaSjDOuEBFRoBgiBQyR3n1heP7dJN+beLCJD9lLCg+yjry9B/E0gGTLEIIvbN5bhAcGk4iIiChgvB3XgH89JCIitwyo+Mueh1wGUFwEKhzyk1wFNXSN5+Q9j4JAPgSMQlKvC7y3CA8MJhEFmT8ylGxrg7U2z8v4Y1sNdp/sQpKP1/radhBmh+wUOSMpQrXcYE2bUbY1WJyePwnyYN7WgbKFPBB3BEyG8n9HWr95o43lZU0GOTMJ1mf16wgDYJTkbKXy/crZRkZlrKTyZ9tMJbthlmCwa7PjoOUV/7bIG9lkHgG2mUiSahuzqFhXZj12szw2knXjUrvnCIs1e8tm4CWhbGsdT0nIg5TLWVVG2BN2GUkV11h7PCSLxex8rCT5tVK30jD1syYv3q9uy/iyreeqWlYSgPK/ynrzl1ne8BERkRsGY/nD7+zqdHX7YfsN5+/ubQ778iBw44/xG/UIyPl3xwLeW4QBBpOIiIgoYJiKTkREgSIZASlAv9Hafne5DVvIwwUEM7DiSWApgNlDUvDH3+a9RZgIQVIaEQHlGQjeZiFIkv6/Njgrq7Xceb2S3cMDch6q9SGsD3nMpPJHGSyWMpjNFpjNFljMZeUPi/wohcVSCiHKIEQZLKIMQljUD1hUs71JMJQ/pPKHEUZESAZESAaYDOpHdISE6AgJNSINqBFpQM1ICTUjJcRGArGRQFwkEG8SiDcJJJiABBNQ2yRUj7omC+qaLKhjfdQ1mVEnqvxRz/qoa30or03qh205+d9yHXKZivrLH7ZtkNsmtzXO2nb5OOTjko9TPm7bcyGfI6P1P/n8yedTuaywOFwDi3JtrNfJet2U62i9rmazxebaWlQP+f1h/77xjPP3qyc/D/Jy3Xv14OfSYVsfPg/CnYAEITx/wMNZdYiIqBoy+PhwQTK4fnjUjkAcm852ugwk+Xr+fDk+H3hzX1Gefe/ZvYXZbMZTTz2FZs2aISYmBs2bN8fTTz+tmnVYCIFp06ahQYMGiImJQUZGBg4dOqSq5/Tp0xgxYgTi4uKQkJCAMWPGoLCwUFXmp59+Qrdu3RAdHY1GjRphzpw5Xp+fYGEwiYiIiALHUvEXRI8e/OshEREFmg8BFD1BHCWQ42WAJqD1V+JIgFf3FV5kM73wwgtYunQpFi9ejAMHDuCFF17AnDlzsGjRIqXMnDlzsHDhQmRnZ2Pnzp2IjY1FZmYmLl26pJQZMWIE9u3bh02bNmHdunXYvn07xo0bp6wvKChA79690aRJE+zevRtz587FjBkz8Oqrr/p8rgKJ3dyIQsw/Yyj5d+wkb2aNc8dhVjeb2dzMZuuMYQb5tXWmNoNc1jqrmyHSur4MBqkEAGC0LrPIM4ZJ6mnJ5BnHDJAqxj2yDnhksqYiR1sHPoqxTt8Wbd1vlFF+bYHJusxk/eKNsLbVZN1fhEEeS6n8OUISkKzn1CCvs76W3FxrAUkZE8likZRlQMV4SBbrc5l1fYkwoMxS3rgS6ykosa67ZF1ebE1DNlrUs8pZhFDqNVqfK8ZIspLsZ2orU8652VJ+LcxmefY9eTwk62vrmEzydbVYLMo1dzp2ko43n3/ep6EdK6mqZiPZYio6EREFitvMGy/p+t6y3a+rAbsDFbTxsN5AtSOQXeicEcLL8ak8vLfYsWMHBg4ciP79+wMAmjZtirfffhvfffedtR0CCxYswJNPPomBAwcCAFauXImkpCSsXbsWw4YNw4EDB7BhwwZ8//336NKlCwBg0aJF6NevH+bNm4eUlBSsWrUKJSUlWLZsGUwmE9q1a4fc3FzMnz9fFXQKN5U4HklERERERESBtGTJEjRt2hTR0dFIS0tTfpHW8tprr6Fbt26oXbs2ateujYyMDIfyeroF6eWvDBT7+oLB17Z6sz9ftvX3ua4MrrnmGmzevBm//vorAODHH3/E119/jb59+wIA8vLykJ+fj4yMDGWb+Ph4pKWlIScnBwCQk5ODhIQEJZAEABkZGTAYDNi5c6dS5vrrr4fJZFLKZGZm4uDBgzhz5kzAj9NbzEwiChPeZCg5ZmZI8Oc0BZ5kfthzmIVLeVkxa5d9VkpFhpI1O8ZcHu+2GOQsnRJruww2WTGlAACjwfoa5WUskGcFs+7fJgHEYJehJM/eJmckxUSUP8ca5dcWRFszkWKM5fsxWV9HGcvbHGm0ZihZXxuNFhitZQzWeuTzKclZU5L9uZGUZ/m0WczW2dWs2UVm6zkpM5enVZWa5awjI0qsZS6ayz/a5YykyDL1ccP6uswgnwebdTJlMjlrdpj1fCrnV5Qp516+Fsqz9TrJs/NZzPK1sj6bNWZzc5KZpDzDe/6fzcRxHCbPa6j6GUmyinEKiIiosnn33XcxefJkZGdnIy0tDQsWLFB+ya1fv75D+W3btmH48OG45pprEB0djRdeeAG9e/fGvn37cNlllwGo6Bb05ptvolmzZnjqqaeQmZmJ/fv3Izo62m9tD1iQQ2e9nuzfVVmnmT/22+hIE6kqgR9v7y0EJJjNZhQUFKiWR0VFISoqyqH8448/joKCArRu3RpGoxFmsxnPPvssRowYAQDIz88HACQlJam2S0pKUtbl5+c7/KxEREQgMTFRVaZZs2YOdcjrateu7fGxBgMzk4iIiChgyv9qKXn+YACKiCjk5s+fj7Fjx+Kuu+5C27ZtkZ2djRo1amDZsmWa5VetWoX7778fnTp1QuvWrfH666/DYrFg8+bNABy7BXXo0AErV67EH3/8gbVr13rcPlHm/FE+fbz/H7rH5vHX/sqCuz/N/bt5BJtX9xUWCRDAvn37EB8fr3rMnj1bcz/vvfceVq1ahdWrV2PPnj148803MW/ePLz55ptBPuLwxMwkomrCWZZRxXLnWU2eZF7ImSxK0o3dxrYZJ/YZSZJUnumiZCZZ5xqVDAbrennu0VIYrH+mMVjngzVbrM+G8vTQMuuYSmbrNhabP8XIWTjW3ShjJ8ljJNWwZhLViCjfpmZEGWpa03tqRJS3MSaq/NkUVb48MtqaVRVlHR8pCjBEWscdso7FBGv9yrSxBrsTax1bSJgFYLb+u8yaGVRqfS62Fi0u37b0UnllJcURuFhcPn7UhbLydheWlp8TyfpRL2C07kYeZ6m8rotmx8wkJRPJev7KrBlJZmF9thTbjJUkP5dan81unksdxkxyO1aSkqHkuN67zCPJ5bb+z2aqvryakA/wZ5IlERF5oaSkBLt378bUqVOVZQaDARkZGUoXHncuXLiA0tJSJCYmAnDfLWjYsGGa9RQXF6O4uFh5rWSWCFRk6NilSQQtC0fHfrz5HlTdizjbh80xh+x4Q/B97e29hRBAuyvb4auvvlIt18pKAoBHH30Ujz/+uPK+bN++PY4dO4bZs2dj9OjRSE5OBgCcPHkSDRo0ULY7efIkOnXqBABITk7GqVOnVPWWlZXh9OnTyvbJyck4efKkqoz8Wi4TjpiZRERERAHj7fS9HICbiCi0/vrrL5jNZpddeNyZMmUKUlJSlOCRnm5BWmbPnq3KJGnUqBEAwGK2eZQ6PoQ5CA9rYEPVFruHKovIVZaPTTmX9Vn3GYzjczivGu0JNm/vLQAJRqMRcXFxqoezYNKFCxdgMKhDJkajUfljaLNmzZCcnKxk3gHlgc6dO3ciPT0dAJCeno6zZ89i9+7dSpktW7bAYrEgLS1NKbN9+3aUlpYqZTZt2oRWrVqFbRc3gJlJRGHH97GT3M3spr1ekrzMHtDJPuNECKGMk2OR5DGR7DOVyqzPkt2zQRlDCOZLyjIAMBjKs2+MUnmGUqlU3vf+/9l79zgpqjP//3OquucCMwwXgYGoiAlG8BINKqKuUWEZDbkQWTcakxBlJXHBBNiNLomiEhOiWQWNKKtJMNmFH4nfXc2qCUpQMEZERU1EIxsVg1FmUC4zzK27qs75/XHOqa6qrurpe/cwz9tXWV1Vp06dqi66zjz1OZ/HQj3sNP8df8Yy083ippRJyv+oscbGkFr5NmzQIKnCqRsi22Y2qn2HqJ/TQVIdxAbVAPXKRK9GbauJ6wOpw0e8QnM4kFQPk6TSDvfI44puOUe3UkZ1yO11hxzUdCj/pm6uroks6mZ+E8pTieuscvrMmXu/6WtkwVFzeX0t0S3nXM2dXljq2rveSa4nklIo2XLZ1p5JHjVStl5JpSL37G7p28grKTtcaXnOOw68a0UQBHE48cMf/hDr16/H5s2bC/ZCWrJkCRYvXuwud3R04KijjpLBDdeTMn2/bHsT+WYky0YNlFOXxhOYydTPcAcAFCANydukPHA+3AovV0ry7Vvk2r387Gc/i+9///s4+uijccIJJ+Dll1/GHXfcgSuvvBKA/Ntk4cKFuOWWWzBhwgTXA2zs2LGYNWsWAGDixIm48MILcdVVV2H16tWwLAsLFizApZdeirFjxwIAvvSlL+Hmm2/G3Llzcd1112HHjh248847sWLFipzPsZxQMIkgqhTm+QM/632yCAj5h7UB/sdsX4Go3HEfdsH1nmFuulGpIFIweIS09akHrBruxfRQOD38TQZyYqac17JBsIV862BxbSqt26iGvanWxtQYvTo1zG1Q3HKDSPXDZWAkdoQMWhkj6mUlwxvkfIiaNzVCNKjPgwbJeW0OHamEDNSgWwZvWGennLcfkus75HJsv5wb+3rAYv5B6zZPmXMDQLcaOqf7Hfq8OYR7TWzVs0gyGTxLQNafVEGkpN0DQAaTUsPbAnM3iKSHvdmBeYgBd8SNW/yQUlTHI/OwN19JCiLlRN5S9OI3hSAIgsiBI444AqZphg6/6Wvozb//+7/jhz/8IX73u9/h5JNPdtdnMywojCiDZG4Z4H1EVIIJT0LLFGG8TnaBpb77A7q9mVqt2yvyVAXlZA7eR5u5Vf7BTuUaQv/jH/8YN9xwA/75n/8Ze/fuxdixY/H1r38dS5cudctce+216Orqwrx583Dw4EGcc8452LBhgy+AunbtWixYsADTpk2DYRiYPXs27rrrLnd7U1MTnnjiCcyfPx+TJ0/GEUccgaVLl2LevHl5nGT5oGASQRAEQRAlI+9sbqRMIgiCqCg1NTWYPHkyNm3a5KostJn2ggULIve77bbb8P3vfx+PP/64Lx064B8WpINHeljQ1VdfnXMbuQPwEANob3BIZHihU2hQJhN5K39C2psmZi9ie7MKgmUoU4lhbiggm1suNDY2YuXKlVi5cmVkGcYYli1bhmXLlkWWGT58ONatW5fxWCeffHKal1O1Q8Ekgqhi8hny5t0bau+s98ioWioOYQqU4HA3rVDytEz9PyxdhN4mn7JWwJibKbdr06xFDeQwszpHbrMcWdYWWqGjawwolOI2ahqUImm43MdsVqqjZmkoKUaPlPORKvVnTLts54l+m6HmQhlXwlbqrQ+kkR8b/IFsT3w/wKVqqUYNjatLqDYn9LA2vyJLeXvDcgQSjlzbzaTyqIu1AwB6HFln0u5SZdXQNjvpKpFsW83VOG9bK5NUW23bb8zNOa/A8LbslUdR++a3JwVEOGfgZZCiEwRBEMVn8eLFmDNnDk477TScccYZWLlyJbq6unDFFVcAAL761a/iIx/5iJsN69Zbb8XSpUuxbt06HHPMMa4PUkNDAxoaGrIaFpQLjmXCRnifqy9FUqY+ATPyewhlM/Qq6vmWlTo6z3YBmduW6ZnbV9DGsQrs8+YB9S2qAwomEQRBEARRMgRomBtBEER/5Ytf/CI++OADLF26FK2trTjllFOwYcMG10B79+7dPoPie++9F8lkEv/wD//gq+fGG2/ETTfdBCC7YUHZkkyYSHIzq0CMERKIiQo4FSOrazEDF4W2JzpZbnjFfQVqvPUlKxBMokyx1QEFkwjiMMNvxp1NuXQVUvo2pJXJGt2QwFNQeLZxXYZHaWjD9Mv6Q/g47YClEkxmIqZ8lGq4HHNfb8t9k47yXeJaoaTVTkqhFOOIDVZHG6Y6OqNkZgVx1EfkfMSIiLYXGaV4EtpnoEaeE+MCRo9UAMUOSX+jWLsy4nYVSf7zTCoPpR6bo5NLddEhJlPt9vADAICELZeTtvROsi2pTLKdXldxlJrL78kKLGtFks+AO6hIijrfgnpiqXuuL8PtUnklEQRBEER/Z8GCBZHD2jZv3uxbfuedd/qsL5thQdnCuQHOI/qCgUCRDpD410f3A8KCT7m1rTgdB8MQBXWHwtoRVl9UYKlPz6SI608c/tA3TxAEQRBEycg3fW+uXgjLly/H6aefjsbGRowaNQqzZs3Czp07fWV6e3sxf/58jBgxAg0NDZg9e3aasezu3bsxc+ZMDBo0CKNGjcK3v/1tNzCq2bx5Mz75yU+itrYWH/vYx/DAAw+ktWfVqlU45phjUFdXhylTpuD555/P6XwIgiCIvklYMSSS4VNvIo7eRDxtfbKPybJNWLbp28eyzNwnuzhTPsf3td1Tl3uOVvp5R13DqOvrTlb59Sl59y3IfqCokDKJIKJgLP01RYUG2ubjnZSt/5G/nAjdpsnlj7tgFre0rG5CQLi565VnUta1hxwoegUAwIABFpeqnhiT3kk1tlQT1assFI1xrdwxVE3qbZUhYNarbHFDpURJjJL7lk2RFIF7/J4esHbpa2R+INVDely9gP+8epUlVaclt7fbFtrZQblOfCjLWNIzKWlJRZLlKpKkp5Jt27CthPsZCFMkpXsl6bnrmeSeiP97C36LHt1c1KVII7OSKFtFEstLkVRxr6QqklHlbcCdI1u2bMH8+fNx+umnw7ZtfOc738GMGTPw+uuvY/Bg+e920aJFeOyxx/Dggw+iqakJCxYswMUXX4w//OEPAOS9OnPmTDQ3N+PZZ5/Fnj178NWvfhXxeBw/+MEPAAC7du3CzJkz8Y1vfANr167Fpk2b8E//9E8YM2YMWlpaAAC//OUvsXjxYqxevRpTpkzBypUr0dLSgp07d2LUqFElvxYEQRADhV4rhpiIp60PG75msGA/N7VsRKwP2y/TMYAslDwZtkcdK99jBo+lywX73MH9o/YLo9fO02m8APLtW5BnUnGhYBJBEARBECWDC5ax4xxFrp3EDRs2+JYfeOABjBo1Ctu3b8e5556L9vZ2/PSnP8W6detwwQUXAADWrFmDiRMn4rnnnsOZZ56JJ554Aq+//jp+97vfYfTo0TjllFPwve99D9dddx1uuukm1NTUYPXq1Rg/fjxuv/12AMDEiRPxzDPPYMWKFW4w6Y477sBVV13lGtSuXr0ajz32GH72s5/h3/7t33K+FgRBEEQ4Fjfcl2VejLQXpAKO50WPwYLb9HrhZhPVgRtHsKIN5+kr7FKsY2UKFnmfyf714eVlfdHP5LDrX2ry7ltU+mXfYQYFkwgiFyqsVCpldjfGslcxhZHtpfAplLRfTs4KJeGpyT8Xojb0iF4TYFYjj2eqjG81CZkprT4m32xphVLCMd0qWI16UA4ZJFcp48lCCKpX8vte1b6jR4O1SVURqzmgKwSQOo8OWx7voLRHwn6V7W0/2tEuZLaV7uR+AECv8kqyLaVEUlncLJWxzbETGRRJfq8kryIJkNn7slUkZaKQzGzZKJLypSKqpCpSIqXBWVbZbYIIIe+Zjo4O3/ra2lrU1gb/nafT3i7VdcNVJsTt27fDsixMnz7dLXP88cfj6KOPxtatW3HmmWdi69atOOmkk1xjWQBoaWnB1Vdfjddeew2nnnoqtm7d6qtDl1m4cCEAIJlMYvv27ViyZIm73TAMTJ8+HVu3bs3tIhAEQRAZ6bVjMCP+pGWeXoVX8eN9ZBohZfR277ZwpVN2beR5du+yrT/sGL4gEbzBI12eRW7zbne3Zejb9NrBLMylR+TZt8hvGAQRBQWTCIIgCIIoGYVkXHn99dfR1NTkW+3NCBQF5xwLFy7E2WefjRNPPBEA0NraipqaGgwdOtRXdvTo0W7q6tbWVl8gSW/X2zKV6ejoQE9PDw4cOADHcULLvPHGG32fN0EQBJE1nVYMQqT+pA0bJuZTIakAkV6XWg5f790WFmTKdNx8lDNhRA19C9afKWikg0E8Yr13W9i6TMftqkQwKc++BY1yKy4UTCKIQqgST6VMpGd3i1YfZeuzlOk4QVw1UFCBwjz6jSiFUnAfTwYwvSk1F75l/erB3e7+z/Mhrtsuj1vTIxUMg0z50zg8LudjEnE0CekPhHqZzY3Fa8JP2EuOfYiMipa+vop4jds2fdK9CdnGA0l5Hvt6Zf0f9EjlUJvK2LZf/A1dlvZKOgQAsGztjaS8kmzlj2SlMrhZSokU5ZGkvxMeWPZm8ks7vYj1hQtv8lMkVbPgp7obl6IQKfqkSZPw7LPP+tZno0qaP38+duzYgWeeeSbn4xIEQRD9BxsMlvcZoz57B175VEnqOZ8KHqn+gYgOMjmCyfVCrncCdQByeBrgfzQX688CR7A+680UHOIB42ku0oNLqXLpdbrLEe2zK6DILtcQeiIzFEwiCIIgCKJkFGKSaRgGhgwZktN+CxYswKOPPoqnn34aRx55pLu+ubkZyWQSBw8e9KmT2tra0Nzc7JYJZl3T2d68ZYIZ4Nra2jBkyBDU19fDNE2YphlaRtdBEARBFIcu24QQpm9dcHhYtBpJlUdqGJsOQhksFX4xmIjcl/WhUiqGOilTfX0FiVJBJu/QNr8RdyZFUnB4W5hSqdsx01eWmHIl9yAyQ8Ekgigm6TKg0hymoOxuuZQN/kjnfl7um5S09Fye1gfeCgWLamULM1LvmbwqJe+cR6yXaib9TiVwBOWHZNgq21vXUABAg1Imjeyqx4gD3bKoakvZX8JkczzVNvuAnH/QVQ8A2NMrz+O9Lrn+PVt6yezDewCALutD9FrSlyZpyfN0lUgBRZLXHymoSArzRgLSvwsgWokUpDDxTWrnXOup6gxu/USRpCmXSaYQAtdccw0eeughbN68GePHj/dtnzx5MuLxODZt2oTZs2cDAHbu3Indu3dj6tSpAICpU6fi+9//Pvbu3etmXdu4cSOGDBmCSZMmuWV+85vf+OreuHGjW0dNTQ0mT56MTZs2YdasWQDkv4lNmzZhwYIFuV0EgiAIIiNdtgEu/AbQ3mCS3pIeLFLrPcEhg8ll7zaDpQeb3GFvbl3+AFM23eWwoEykR1KgbJSaiAvmqoeE53MwyCTAwEV6wIgL+PZ3j9FHu3ucfmTATQGookLBJIIoBaXQuBaJXAJF6aP48g8uucOVQjcGgkiByJe7L+eeXYLBIj2UikfMRWQAyg1yqJFrRlI+FGsPSa+Whlg9Rv1NBmaa9+yThU7u44ThCS4U8txyH/RZXGvVtv2qrW93yvk7h+Q1eDcpA0YfYDcAoDMplRO9VkeGIJJ06w6abNu2lWaw7Qb0Astp328W/yYy3i+R5DNErR8Ma6vKRmVPudL3zp8/H+vWrcOvf/1rNDY2uh5HTU1NqK+vR1NTE+bOnYvFixdj+PDhGDJkCK655hpMnToVZ555JgBgxowZmDRpEr7yla/gtttuQ2trK66//nrMnz/fHV73jW98A3fffTeuvfZaXHnllXjyySfxq1/9Co899pjblsWLF2POnDk47bTTcMYZZ2DlypXo6upys7sRBEEQxSHJAZPpYWdqpbZYUIu+DG26nNBBIlVG6GCSN7AEOHq9mgvoYWfCDUylgjmpdgV9jrIJfOSyf7YBJO88uD5aoZR+TP/wN3+7kxUwtRbIs29RgrYMZCiYRBAEQRBEv+fee+8FAJx33nm+9WvWrMHXvvY1AMCKFStgGAZmz56NRCKBlpYW3HPPPW5Z0zTx6KOP4uqrr8bUqVMxePBgzJkzB8uWLXPLjB8/Ho899hgWLVqEO++8E0ceeSR+8pOfoKWlxS3zxS9+ER988AGWLl2K1tZWnHLKKdiwYUOaKTdBEARRGN0OS0tbnwoiqXnAN9GA8HxmniCSAFPLWo1kwK9YSn1mKRWTYGnqJadABUzU/mEBIK+ySO/n+wz/ehFYTgWjUibewrPeGzwKC8b0Ov37pReRPxRMIohSU8Khb/kMd3P3TWuWek2TxT4a+TDL7tjB42V87AQVSe7q1FA2PeRNBK5rSh2TPk8pZvpQ0ih/X7P7WABA3GjEkNhQAMDQl/fIIpOlYTWOOCL8fMGKMxROi5tEH9/1hx+i9+UDAIDXPxwDANgpR7NhV7c01W5j7wAADiWkYqMnKQtYdo9rtG1Z0cPaAP+QtqDRdnBYmya4nAn3O8/p2vk7ibns4y4V8F2VbHhbP1ckaTjyy8Sb669aNvdZXV0dVq1ahVWrVkWWGTduXNowtiDnnXceXn755YxlFixYQMPaCIIgSkynzWBxljFjm1znDy4xFlAiQSZk0YEmA1LxpL2TYuqZbDJvIInB9Axx085Bqb5M6rnkHQgW9UzMVCYsgBQcsibAYIuUQslRh3eEV4mklqG3eRRJgQBSmOIqzFcpwcvfXylX34LIDAWTCIIgCIIoGfmbZB4ewTSCIAiidHTZArYRHjzyrtOKI19QicENBpk6gGQwd9l0g0xATO1r6s9M/iHNha5PAJDBJY5ANjnvZ8/wuCi4UjoBAb8i+ANJjmC+QJFclvs7wh9MsoU24U4FkESgvmAASb/A9K4HRNowt0SYkVKJybtvQZ5JRYWCSUQku3btwu9//3v89a9/RXd3N0aOHIlTTz0VU6dORV1dXaWb1/8okzl3rvjtnXLzRGIsfx8lAZG1oiNMcaBVMCyg3oj2ReLgQhtEB1VL4YoloRRKRudHUWs2AACa/k8qkT65ebvcOFsNbQmeSoZT6+u8Q9VHAR8AT2HJ5u14TbXtTwflu7E3OzsBAO/hbQDAoV6pqupJHgQAJK0eANIfyVUk2Uk114okqT4KM9mO9EbK4x5PnXM298Rh6o2kqerG5Q6ZZBIEQZQGzjm2bNkS2l+fPn06jjrqqEo3seRYjvQz8j46vVnaACgVkoyI6GCSDi7Zas5VxjbO5X6cyclgTCmOdBCIqc9yHmMMXEiVkreT5vVU8maGywaTeXqCHhWRJhgAcjxKJB1ccoLrVSW22hYMIOngkXcZ8KuV4FmvtwGAVQHPpPyTexDFhIJJRBpr167FnXfeiRdffBGjR4/G2LFjUV9fj/379+Ott95CXV0dLr/8clx33XUYN25cpZtLEARBVDF5G3CXoC0EQRCHAz09Pbj99ttx7733Yv/+/TjllFPc/vqbb76Jhx9+GFdddRVmzJiBpUuXukkGDke6bAErQpnkqpJYSuljMh14Eq7CyFAqJAYm1UhKsaRVSKYhh7yZDOBKgSRUQIlDloNaq72TYkyoIXEpvyXmebIFDbaBoOE1U75GAjZncOAO6ncVR4AM9GjVkcWVMgkMFldBIwFYgSCTnMuAlcM9iifPULiUj1JKieRtsTeolOxHyiR6UVVcKJhE+Dj11FNRU1ODr33ta/jv//7vtDcaiUQCW7duxfr163HaaafhnnvuwSWXXFKh1vZT0o2HKtOOEPLJ3laI4Eq/dwkqdYJVpbVCpL8W4YFtwTnnsbTU9Zw7gWXurdLd971aE2a79E+qNQYBAIY/JT2Gxp+wU5ad+PHgyaU1PE2RFHF5meqkhG0Lwt6Qx9/1lInn90nF4BvtMjPbe+IdAEBH4n0AKY+kRLILQCpjm2X1epRIfkUS57aaB6+RSHkkuW0Mb2Sm7zMfvy+3nj77A6kCVS/2qfoG5o83/XAuVNFPI0EQRFVx3HHHYerUqbj//vvx93//94jH42ll/vrXv2LdunW49NJL8d3vfhdXXXVVBVpaerptAcuQ/RHv8DHpe6Q9FYVPjaSHu5kGc4exycCRgGnIbXFDBo9sBsSEQNyQSiUY0ldJqCFt2ieJqeBU3OAwmUDcEIgbHAwCpiEQY1y1SaSMuj2P/pQSSBqKO1wPYWOwmOEOabO4Ac70EDZZgUBqiJulgkY2TwWRbA7YKiikh7/pIJIMOKUUSbbqULsqJaEDaKnnclCIZFUkmJRn36L4TRnQUDCJ8PHDH/7Ql5EmSG1tLc477zycd955+P73v4933nmnfI0jCIIg+h8izzeB9PaQIAgilCeeeAITJ07MWGbcuHFYsmQJ/vVf/xW7d+8uU8vKT5KnWzHrDG2AkKokAddUO2W8zVRISC4LxtzHDmNwzZC4AJgBxATgQM45g2cIm1fJJINIJhOoMRwZWFJBJdPgYK5aSb1M9aiT9HPS4YYM8nADtmOAg8FwBCxuwBAGuBDKDFzAYcwXHeFIqY9sTyBJB5C4gKtY0kEkvd5VK6n6HCFC1Uk8EI6Ryqfyj3PLX5lUgsYMYCiYRPjIFEgKMmLECIwYMaKErRkgFMFLqZCsbhnrjVQqZVIoRZeJItIvJ0RWq4uxQMa3oIdSmEIpLdObE65U0s9EXU4IgNXJd0/xA+MBAI3xJgDAEev/DAAYfNNx/uOHeEKlKbEiLlHY9xhcp8+lUx3/D20fwesHpFrqXfFXAMCB3ncBAN2JgwCAZFIqlixbzT2Z22xHZ2vrW5HkzoNZ29I+BPCddr73KstakVRqsU9RsrgdxookDUd62ubs9iMIgiDC6CuQ5CUej+OjH/1oCVtTWXq4DUuY7rLrkwSmfIxkcMl0s7EpI27GYPLUsjbcdoTsZ8QN2fcyGQAus7qZkEGamOdYOohUawjUmQ4GxWzEDY7amIP6uAXTEKipsVFTa8MwBcy4gGEKwBBpfwIIm8GxZJDETppIJk3YtomEFUOvbcLmBkwWA+wYTMHgCOGqr3Q9OlBkCz3UTcDi/iCSzQVsLs/P4anAkcMFOISrRtJz7va5/aMB5GcBW1hF+z6zJd++RW7uVURfUDCJ6JO9e/di79697h+TmpNPPrlCLSIIgiD6CwL0JpAgCKKU9Pb24k9/+lNof/1zn/tchVpVHjpFL2IqyKEDK4YMJQFCqZTAlG8Sg6mCTDrApINJMYMhbsihYiZLvRzlTCqTtH+R9/WnO5yNyUBSY9xCQ20SNaaDwYOSqG+0YNZwxJsAs8kEqzHABtcAtTGwmAHEVOhLSYNEwobotgDLgdNhwWlPwkkAiUMxdHfVIGmZiCVqYDAg4eihbwIJnnq9JdyAkRx+5ggg6aghb1wGlmwu4Ag52WouBGALLoe3QQeTZHAptTalTPIqlGyRKOE3HE7IO02iAlAwiYhk+/btmDNnDv785z+7agTGGISQklGtYCAGDtmojwoTWulXM314NQnPmwU9C2YSM+QD2quo4a7iSK0LZHNLm7vZ3QAGqfL5a4382azbdwwAYPj/NQMALvyfJ2TZi2eoZqV8j9IyzuWi2nJfVwX2Vcf7vTr+H/fZ+Ksj23ggKeddvQcBAImkzOpmWemKJECqkbQyKXW9HN/x3bmnk5quRMpKkiTTruRJZiFPeRRJRG5QNjeCIIjSsWHDBnz1q1/Fhx9+mLZtIPTXbWZDMNnncz2ShF42UsEkIT9zZiAmpKE1lOMRB8AEU0PbAEBmcHM4AEP7BzHXaFujh7fFDY5ak6Mu5qA+bqOmxkZ9o4XaERxGPYM5ohbGiEFAfQ3QNBgYXA/EYkA8JvurjgPYDlhPL9ihbqA3Cba/C8agHpjdDphhQwjATMRgOyaS6jtNcg6TM8RcD6UU0kfJ65Ek1Geh1EoySCQ/p8JFjuC+AJL+zFUwSTCeNtTNgV2EbzI3qG9RHVAwiYjkyiuvxHHHHYef/vSnGD16dNofxARBEATRF/lL0QmCIIi+uOaaa3DJJZdg6dKlGD16dKWbU3a6WSdMVgMA0DnbDBVciomYuz4GUwaUhIGYCjFZgiPOpI7JEQJxtZ8OvxkyfRscI+UrxABltC1QY3AMMh3UmQ6G1CQxrKEbQ4b3It4gEP9IHObRI4Bhg4FxHwEfNw6or8/6vFhrK8xdf4XZ0YnYOx8i/m4XnEM24nsdmO0cPVZceSAZSBoyENTLmZuZzTXbVgqlJJdD2iwVPLK5gC04HAhYwpGBJTiw1dk7zHFDSZxxN5ik13mx0JPHN1cY1LeoDiiYRETy9ttv47//+7/xsY99rNJNqQgMkcm2SnTAwr2TyoVfodSHGiWPqxaV5S1YKmSWapxW2DCtVmGu0aFQY+tdDyWhlUi+XcF5SlGjOyiMyYwpu4TsEDTuk8qgcb+V64//TFLuE6+JbHlfgVlvtro0ZZIl639DHe/FfXL9rkQb9tl/AwB09R4AACQSUpGUSMqHvKtIsrUiKaVM6kuRpO/LlAipkO81HzLt1Q8VSSVubH+6FARBEET+tLW1YfHixQMykAQAPeiAAdknMpjs3zEYMGC6uiQDJkzEACYDTKYKJ8VFHLaQS4ILJYw3YBqAKaTPkDbh1rhqJCZQZ3IMjtkYFLMxdHAPmkb1oH6cCWNEPdjHx0KceDzEESPzOi/R3AzRLPuYxo7XEH9jF2L7usBqOsGYQG13DRzOkOQmerkBLmS7tDpLZ2PTyqTUkDcOS3AkhAMhBCzYsMHhMBs2HDjMBlf/OVD9RGaDqyCTO9xNpBRvHOX3TCKqAwomEZFMmzYNf/zjHwdsMIkgCIIonHx9Dao/rE4QBFF5/uEf/gGbN28+rE22M2EjAQMcBgxwYakBaiqgxEw3mMSFAwOmfNsiAK4CTRoGBlMN6TIE4HAGYcghcK6DAtOm2zJwE2MCtaaD2riNunoL8SGAMXIQ2BGNEEeNzTuQFIR/9FgY7YfATBOxA72oPehACAu1vTZiSY4Y47CZ4cswx9WzVyuV5LNYD23j7nA2GxwWs2TwiNmwYUOoQJJUJDlSnSQcN5Ak4LhKJaAywSTqW1QHFEwiIvnJT36COXPmYMeOHTjxxBMRj8d92w93Q78w8tfa5HKQ/BVKXp+ecsA8BoXZXpXcTi+fp0QwV1iqfSnvL73Vr1ASbva29DxSQiuT1D4f1Evl0dsdgwEAz7Q1AgCOvetRAEB88aw0ZVXWWfdEqkxQIWSp+p9p+4g6/iHZHv5XdPVImVKPUiQlXUVSr5pLZZJjq8xtOnud4KlMdsEMbSL4IR+y3zc3wU5lFEkFZXEbgIok8jUgCIIoHXfffTcuueQS/P73v8dJJ52U1l//5je/WaGWlYck74LB1HA2luqrSb8keS1MxN3gkok44qgFg6FCR3HYwgFEjQwvcQahgkVcMNUvSj2PtCqp1hQYHLPRUGOhYVAvBo+0UHPsYLCTx0McOQbiI0cW7yTr68HPPhPsvb/BxKuoS7bC/NBCMtGLHiuOHseEAEPcETANBkuJhmQgTPh8kiwulUlSkeTAYhYslnSVSBZLuMEjLqyUa5LQw95SfUcNF5XwTAL1LaoACiYRkWzduhV/+MMf8Nvf/jZt20Aw9MtEWYJK/YSo4FAxRu15M2bkX4l+i+IduOg33naDS+5MBX1EUs0N1xTcUMEk05CBmz11cmjZ6/vlG8Et26XMfPrbb0Mce2zgfLIZvhcxzO3tt331v75ftm2PkMfvTOxDrw4iJaTRdlINibPUXP+b5XruGdKWClqlWhtYkTfF+HcSFoPpV8PaSkw1XwoBllcqXvp9JQiC6Jv/7//7//DEE0+grq4Omzdv9g2lZ4wd9sEki3eBMTOlSGLKcpuZMEQCjBmwYcJkcTBhwEQcnEmVklDDuUzEYAgDhpDZ3gDD5z0E6OFtcqo1lV9SzEbj4F4Mbkqi5sg42IRm8FNOBmprS3Ku4iNHgp3QjdihHrC6TjR0JtHVk8ShZBy2YIgz022joV0flIJHZ22zIANJFrNUMCkJCwk4zIYDC7bolVfFDSQ5cISdskEAdwNJqcBS+f8mzLdvQRQXCiYRkVxzzTX48pe/jBtuuGHAjsMmCIIgCsPbGc8FCiYRBEH0zXe/+13cfPPN+Ld/+zcYhtH3DocZltMrg0kslcGNMTVBrjdYHAKOHMjGeMoLUw95Y3KYXEwYcGACgsPhBoSZUiV5h7jVGBz1JsegGguDGpOoHcZhHjkMYsL4kgWSNPy442C0fgAzZqC2bR8GHUiirrcOtjAQN4QMJAX3UVnbbDW8LQkbFizYzIaFBJKsB1w4sJFwg0hcWHCE5QaPuJBD2YSQATivMqkSwSTqW1QHA+8Xh8iaffv2YdGiRRRIykCYSXfxKi93tJ1lMWWzf/ER6r9i1KSHu8lJPSC5kJNw5OTY4I4Nx7HgOBZsOwnLtmDZFhLJHiSSPehNdKI30YkOqw0dVht223ux296LbR8Y2PaBgXd+9CY4575JH7e2tjbjJIRI2/edH72Jd370plu/Pp4+fm+i022bbqttJ2HbSfc89Hm556nOW14HrU7SUzGudrG+tyDZ3muF3tNFhLGS/Zuu9vdyephbrtNAlqK/9NJLWLJkCQ4ckGb6119/fYVbRBBEtZJMJvHFL35xQAaSADnEigsLnFsQgsMRNhxhg3NbevsISwVGbDdA4sBSqiRHTfo/kZb2XsMgwNTwNz3FDQ6zlsOoZ0BjPcTQoeU56SENQGM9jHqGeNyR7WBSq2OodnpV8F6ROYeAYKkMbQ6zXT8k1ytJXSf32qrrl7q2lhz2prZVZpgb9S1yoVT9ioH5q0NkxcUXX4ynnnqq0s0gCIIg+jXMlaPnMg1k5s2bh4aGBnzhC19Ae3s7nnzyyUo3iSCIKmXOnDn45S9/WelmVAyHJ93Jdnrg8AQcnoDNE7CcXtg8mVonEm4AxIZc1sO7dDYzIeSLMG9QialhYwYDYgwqk5uNulppum2OqAFGDQeamspyzmLsGGDUcJgjalA7yEZdzEadaSNuCLetafsI/ZJPG2+r83YHviVgi17Y6jo5Ql/HpO8ayikJm/f6rn25yadfIaeBSan6FTTMjYjkuOOOw5IlS/DMM88MSEO/gUMuf7T1Y7coIdKUIUFDbq4Vu4b6wGV5x7HBmJT3mob82Uxa0ty6O9EOANhnvA8AePOQNOTe3NqEr77wkjzO6Z8EAAwaNCirptbX16Orq0suqDo2tzap+tXx+Pu+4yetHjiObKNtW2675XnpNK5q7uqC/ebePorglVQ5Bsg93U8gKXru1NXV4bvf/S5mzJiBuXPnhv8bJQiCgPRDvO222/D444/j5JNPTuuv33HHHRVqWXngPOkOcfPjX+eac7sm3allr8+Sqcy8DScGw5LG3SaLI8ZqwZiJOOpRi0EwEUedGISGLc2IMxNN5iEMrd2CI+oYGmLAuEEOThzagebhhzD60mHgs2fmdmJdXbBvWY8Db9bilfdG4c3OWrRbDG09wIEER6/D0e4cgU7Rg16jBxY6kGDdsEQ3HNiwRa/rdaQVRt4hat5haykPpODwtWBCmvQENeHlSg/1LXKjVP0KCiYRkfzkJz9BQ0MDtmzZgi1btvi2FcvQb9WqVfjRj36E1tZWfOITn8CPf/xjnHHGGZHlH3zwQdxwww145513MGHCBNx666349Kc/7W4XQuDGG2/E/fffj4MHD+Lss8/GvffeiwkTJhTcVoIgCCJ38jfgHrjqpPr6egDA6aefjosuughXX311hVtEEES18uqrr+LUU08FAOzYsaMkx6jm/rphOp4svV5SPj6+AElgHjW6P/XHNnOX3ZeQWuEi4DE8N+QWT9AqZsZhMBODtwzDhH85hMnDRuK6J85CTU0NhgwZknbMAwcOoOu2X+HOx8fg0Q+ex/6ud2HZCdhOElwFfYTgyutJQAd3hBCqmV41FfO0TfiM2TPiKSZH6Pc9kEkIDpR5pBv1LXKjVP0KCiYRkezatauk9f/yl7/E4sWLsXr1akyZMgUrV65ES0sLdu7ciVGjRqWVf/bZZ3HZZZdh+fLl+MxnPoN169Zh1qxZeOmll3DiiScCAG677Tbcdddd+PnPf47x48fjhhtuQEtLC15//XXU1dWV7FxKpm3IKyVatq3pfz+m2WZDy7ledalSz1y/Ykf6FsmnpFb72EoFZDm9AIAe+yAAoK12DwDg3c4h4J88BQDQOHhwzm0arPY5pOp4t/NFWT/b4zuePr7tWB4lkl+R5HaIAvdRqcQOpfFJKjXZ/LvJ474rofdZf/kXnPfbw/54GxWJW265BbZtIxaLYe7cuRgxYkSlm0QQRJVSakuKau+vc25lHyjx79lniVSmW+b57A/YyK6WR/UkZD+VMQMWHJiGiYTdgT14Ey92CfTe8r+oWfYPkcdcsfFovNT1HrrsvUg4neDcgcOTqk+n3Ci5t+0cjAGCa7W9vhZMifJTJuJ9kx44yuZZXAn1LPUtcqNU/QryTCJyZs+ePbjtttsKrueOO+7AVVddhSuuuAKTJk3C6tWrMWjQIPzsZz8LLX/nnXfiwgsvxLe//W1MnDgR3/ve9/DJT34Sd999NwD5Q7Zy5Upcf/31+PznP4+TTz4Zv/jFL/D+++/j4YcfLri9BEEQBFEOpkyZglgs9b5v1qxZlWsMQRD9kr/+9a9YsGBBwfVUf3/dmzyEy0k4WUwCEFxNImTinrlnP6Q+C7UshAUhbHCelHNtSq3Mqh2eQI+1H632Tlz6VHvkmXxh2jps7t6OVnsnLKcHgjvg3FKJU/RQNdszWfL43PK00Q7M9TXJdJ56WxbXDTxwzYuXuIUoHaXqV5AyiYjkyiuvDF3/17/+Fc8//zyuvfbavOtOJpPYvn07lixZ4q4zDAPTp0/H1q1bQ/fZunUrFi9e7FvX0tLiPnh27dqF1tZWTJ8+3d3e1NSEKVOmYOvWrbj00kvzbu9AJS9hVHotal6ZB43vqCL41iZQVr91Um1mriw6JW1O+Q45vrnDlacSl14FVx6/pygKHV3HlcdLRdLzL8R9x/O2Q7ct9YZIK5L0egS2hxwvYlvlVDCFH5mxgfsmqhrQGVRyZaBK0Z9++um89jvmmGNw9NFHF7k1BEFUO+eff35ov2bPnj3Ys2ePG8TJh/7RX+dw+wrZqGhCC4WvE555ar/UJ+brXBhym0gNDRP6ScYMOQFgMCPbdiQ/Bq/jg/SW6ICQ+1kfl6e6eqlWpZ2PXJO+Pni+smwfz14hgLRhheXvZIl8+xYDsD9Yyn4FBZOISHTqQI3jOHj77bfx5z//Gffcc09BdX/44YdwHAejR4/2rR89ejTeeOON0H1aW1tDy7e2trrb9bqoMmEkEgkkEgl3uaOjI/sTIQiCIDKS7zvLAdjfAyAzM+UKYwwLFy6kxBgEMQA55ZRTfMu6v/7mm2/igQceKKju/txfz+2FXtSQN+/LORFYb7jBplQd2l+JgzFTDXczETPqMSg2HE2xUfj8sImRrfjxU2fhyrO70Rp7H92xTvQaveCcgzEDQjieoFIwsOV9cRsMKvX1Utc/UCnTdSu2zUQhlFMP9d577+G6667Db3/7W3R3d+NjH/sY1qxZg9NOO022JQsPsP379+Oaa67BI488AsMwMHv2bNx5551oaGhwy/zpT3/C/Pnz8cILL2DkyJG45pprChJvaErZr6BgEhHJQw89FLr++9//Ph5++GF8/etfL3OLSsPy5ctx8803V7oZBEEQhyV5K5MGaDSp1H6FBEEcXqxYsSJ0/U9+8hPcfffduPzyy8vcotKQa39dmmT39SApJAuZ3tfzfHONsFULWBwxsw71saE4Wnwc4+JDccrQnsgajd88hXOPaMAb+8ejK9aFXrMbEAyc2+DQQ8yCBANI+ZxH38431RRIAsqnej5w4ADOPvtsnH/++fjtb3+LkSNH4i9/+QuGDRvmlsnGA+zyyy/Hnj17sHHjRliWhSuuuALz5s3DunXrAMjg6IwZMzB9+nSsXr0ar776Kq688koMHToU8+bNy/k8vZSyX0GeSUTOXHbZZdi8eXNBdRxxxBEwTRNtbW2+9W1tbWhubg7dp7m5OWN5Pc+lTgBYsmQJ2tvb3endd9/N+XwIgiCIcHie0wCNJREEQRSFadOm4ZVXXimojv7eX2fqv2iK+aew15jbAIMBg5lgLIZaYwhG1wzChCbgE+fsj65i6GCcNeogJjQBQ8VwmEYtGIvBZ/AdcrzCiL4GzPNftVGuvsWtt96Ko446CmvWrMEZZ5yB8ePHY8aMGfjoRz8KIDsPsD//+c/YsGEDfvKTn2DKlCk455xz8OMf/xjr16/H+++/DwBYu3Ytkskkfvazn+GEE07ApZdeim9+85u44447CrpOpYaCSUTO/PGPf3RTkOZLTU0NJk+ejE2bNrnrOOfYtGkTpk6dGrrP1KlTfeUBYOPGjW758ePHo7m52Vemo6MD27Zti6wTAGprazFkyBDfREi0N1+BtaCSfxYy7+RLkxpSVm2XqVDhGePO3G0GM+RkmL7JNOIwjTgcw4JjWPjZG2OK8gDWdfzsjTH42Rtj3Pr18XztUG1Lnaea1Hno88p0HdxrELh2laPw+2egKlyqBZkFJ/cJebxxPFz41a9+hWQy6S7/7W9/c7MzAkB3d3dREmEQBHH48uSTT+L8888vqI7+0V831WTA09HxTWH/pTACU77ozqNaYgyGEUfcqMcwMRp/N4rjsi8dAPvaZyJr4GedgXF3X4DLvnQAx9QMRZ05FHGjXg6ZY8G2FfKMDD/ftGsUcT1T+5qeqbzk27fItU/4v//7vzjttNNwySWXYNSoUTj11FNx//33u9v78gADpI/Y0KFD3WFxADB9+nQYhoFt27a5Zc4991zU1NS4ZXTWxKD1TD6Uql9Bw9yISILmeYB8a/DrX/8aM2fO9G3PJ2q6ePFizJkzB6eddhrOOOMMrFy5El1dXbjiiisAAF/96lfxkY98BMuXLwcAfOtb38KnPvUp3H777Zg5cybWr1+PF198Effddx+A1NjOW265BRMmTHBlhmPHjqVMOARBEBUiZRuaGwM5BnjZZZdhz549btrtSZMm4ZVXXsGxxx4LADh06BCWLFlSFC8FgiD6NxdffHHaura2Nmzbtg3nn3++b/v//M//5Fx/tffX0wMt6U8c4VsnP7sBJeHxOlJeSHovuT63J5hsi5wYM2EwE0MwCBdM3wvx+VlZ1SE+Pw3Nq59FvLNOqpvAwGBAuEEcx3tE9P3E9L8a9AfThGsOLgkEmNKCWOllChsumB+F9C0cx0nz3KqtrUVtbW1a+bfffhv33nsvFi9ejO985zt44YUX8M1vfhM1NTWYM2dOVh5gra2t7vNcE4vFMHz4cF+Z8ePHp9Wht3mH1eVDqfoVFEwiInn55ZdD159++unYu3cv9u7dCyA6M1ZffPGLX8QHH3yApUuXorW1Faeccgo2bNjg/sPZvXs3DCP1Y3XWWWdh3bp1uP766/Gd73wHEyZMwMMPP4wTTzzRLXPttdeiq6sL8+bNw8GDB3HOOedgw4YN7njVUlGyP3ryklRku08h46srQ6lktmm3sFqh723DMGAY8ufSNOU8ZsqsanFT3lv1saEAgNFiDADgqAYG46VXAABdp38SADB48OCs29TV1SWPreo4qkG25e1OWX9vrBMAkDTl2HvL7IWj2mY4am7IzoZQCg8RSM9XnGx96TBfp6y/kE1b8/g3oy9unr+TRW5NRRAC4HncCuXvmlYPwayKmTIwEgQxsGlqagpdd9xxxxWl/mrvrxsqmJTqc6TaIlQ2WxkQ0QEY0/Obyn2BFG+SMn92NAZ/AMd7nL5/n+sNE2zOzD7LeWmuy/QUNOB/Soa1JRhAgm851S/RSiO9Omp9elAp1d8rf0+E59m3EABee+21tH83N954I2666ab043CO0047DT/4wQ8AAKeeeip27NiB1atX52VsXSlK1a+gYBIRyVNPPVXyYyxYsAALFiwI3Rbmy3TJJZfgkksuiayPMYZly5Zh2bJlxWriACCXP0n78R80IX/M+x+YgGGouXpg6s6RacYQi8XVZzmvidcDAAbVyofRCHMsAOBjDXL5vOZ24PTpvuP09MjAT319fcam9vT0uPsIFYg6r/l3AID3umT9nZ3yeFZtNwDAdhKwHSlfjcVsua9wfHM3sGHIuVa3MsbSHyqlijSVhQFyT/cTBFhFOpoEQRADgTVr1pT8GNXcXz/hxE8gHquBYcQRM2phMBMxYxBqjMGoRyPiqMNgPhgNRi1qDQMNcRNDahhqDaCpBhgad1BvcgyLJzG8vhdDmnpQM5gjPsqA2dwANNQBY0aCjx0LDB5UcHszMXz4cPfzv7x4Gf6lgLpYWyvYe21AZzdEawfs1l443UDnvhoc6KzH/kQtermJA0kT7ZaBXgc4ZAEdSY4k5+h0bHSiG0mWRA87hF7eAUdYsHk3bJ4A5xa4yjBnOxa2b3+y8AuQA/n3LRhOOOEE/P73v/etDVMlAcCYMWMwadIk37qJEyfiv//7vwH4PcDGjBnjlmlra3MzLTY3N7siDI1t29i/f7/PSyzMR8x7jGqEPJMIgiAIgigZ+u1hrlO/jGMSBEGUAVIrehFSgSQ4uLDBhQMOG0LYcJgNG0nYzIYtOGwhYHGBpAMkOZB0gITD0OswJLiJHiuGRG8MiU4TziEO3t4LtPcABw+BHdgP1t5e6ZPtGy7A2tvB9h8E2ruA9h447UlYh4BEp4neRBw9dgy93ESvw5DkTF4LDlhcwBZ6cmAzCzaScEQCQtjgUNdXTVL5JVCRYW4F9C1M00zz34oKJp199tnYuXOnb93//d//Ydy4cQCy8wCbOnUqDh48iO3bt7tlnnzySXDOMWXKFLfM008/Dcuy3DIbN27Exz/+8YKHuJUSUiYRPi688ELcdNNNOPPMMzOWO3ToEO655x40NDRg/vz5ZWpd9VHSR3nZOwqFHq907S3e8DY9fE0tMZ0dQyuSpIGgYQaGtMVqEFfKpNoaqSqqq20AAAyJS5n30TE5BnnKSPlAPebbHwMMf/2aRCKRuZUeg2zdYTzm2x+T9d8g31Ls75XH68YhAECythsOT6p9tDKJ++auUkcrtd1hcCm5dOq2K/z7TMmfi022yqMq6myXeLgb6X4OPx5//HFXhq8Nb3fs2AEAOHjwYAVbRhBEpTnhhBOwdOlSXHzxxT7D3iB/+ctfcMcdd2DcuHH4t3/7tzK2sJzIgIYAl5MKLDnMlsElZsIRDmzBYXDA4QYsLmAwhgQHElwO5+p2TNTYcdT2OuDcRqydw6i1AJvDqImB1caBpAVRVwdEBB6qAbbvQ7BDncD+DoiDXRCdSTjtHMmuGBKJGLqtOHocGUjqdQwVSAMsDiS4DLZZ3IENOXEmA0cObECkrq8OJIm83Yv6B4sWLcJZZ52FH/zgB/jHf/xHPP/887jvvvty8gCbOHEiLrzwQlx11VVYvXo1LMvCggULcOmll2LsWDnS4Etf+hJuvvlmzJ07F9dddx127NiBO++8EytWrCjauZSiX0HBJMLHJZdcgtmzZ6OpqQmf/exncdppp2Hs2LGoq6vDgQMH8Prrr+OZZ57Bb37zG8ycORM/+tGPKt1kgiAIoorJV4o+0IfGBb0Yvv71r/uW8/UrJAii//PjH/8Y1113Hf75n/8Zf//3fx/ZX3/ttdewYMECXH311ZVucskRQsiJyaASBAdnNjhiKiDCwWHAEQKOAGwBOBywBUNMABZnsIWBpGPCsDnspIF4jwOYHKzXAuvuBUwTrKsbolqDSY4D1t0D9PQCvQmIbhu8l8NJALZlwLINJLkBSxiwuAFHMNhKsWMLaX/AhQwPOUwqvDikAkl4A3YhhublJv++RW6cfvrpeOihh7BkyRIsW7YM48ePx8qVK3H55Ze7ZbLxAFu7di0WLFiAadOmwTAMzJ49G3fddZe7vampCU888QTmz5+PyZMn44gjjsDSpUsxb968nM8xilL0KyiYRPiYO3cuvvzlL+PBBx/EL3/5S9x3331oV5JOxhgmTZqElpYWvPDCC5g4cWKFW1s5qkjvUHGiBFTFEFYV5U8lV33kWeUx1pbLyhvJkMokMybn8XiNO6+pkePktSKpoXYEAGAMOxIAMGm4LPupye/Jgxw71T2OO9dn1MeJMbA082qhsi18avKfAAB/7foIAKD9A3n83toOV5nEtfSIaaNt+aC3LLns6LrV818IDu66GPpVP+6DWuTfWdCnW8gtESbsKaHYp99RzWbchZhk5sLTTz+NH/3oR9i+fTv27NmDhx56yJcZ6Gtf+xp+/vOf+/ZpaWnBhg0b3OX9+/fjmmuuwSOPPOJ29u688040NDS4Zf70pz9h/vz5eOGFFzBy5Ehcc801adlPHnzwQdxwww145513MGHCBNx666349Kc/nfW5eNP1EgRBBJk2bRpefPFFPPPMM/jlL3+JtWvX4q9//St6enpwxBFH4NRTT8VXv/pVXH755VU9RKY46OARk4oZxsC5DceUgRAubNhwYMEGEwyWMGFx2btJmgy9DgAw1DgGum0TcRYDFwzxHg6zQyBmc7B4D8y4ASQssJgJEYsBQxorfN7psNY24MN9QGcvxL5u8IMW7G6BRGcc3b016LVj6LFj6LEN9HI1xM2Rw/0sR8DiHLZwYAkHNrNVEM52VUmc20r9JeCqwVQQr9yUq28BAJ/5zGfwmc98JnJ7Nh5gw4cPx7p16zIe5+STT07zcioWpepXUDCJSKO2thZf/vKX8eUvfxkA0N7ejp6eHowYMQLxeLzCrSMIgiD6E3l3+HLcp6urC5/4xCdw5ZVXhqbKBuRQbq9ZbdAj4fLLL8eePXuwceNGWJaFK664AvPmzXM7gB0dHZgxYwamT5+O1atX49VXX8WVV16JoUOHum8Pn332WVx22WVYvnw5PvOZz2DdunWYNWsWXnrpJV82I4IgiEI555xzcM4551S6GRVFBjI4AEMFlQwIJnU0jrABZsBBEjargSEMWNyBxeVLxKTDkFRvYeIGQ9xhMpgEBrO3BqbBEbccMMMBWDeMbguMAQYYRFcnhMdwuaJ0doIdOgTW9gHwQbsc2rY/geQBwOo10dMTR7cVR69joss20a2GtyU5kBRAwhFIcgFbAEnBYcOBw+TQNhuW60cloNRfggeGtwUz3ZWecvUtiMxQMInok6amptC0owORsvz+FPArV+5U7LKpuR0zt9PLQ9PiqoD8VXh9iJj2RnKztSlFksrUpjO3xeNSnlpbU+8qkgbXS0XSyJg03ju2Qb6ZOme0zKpW883PqGMYvmP7m5hZPyIg0nyi9LKu/5ydfwAAtCXk8Ts7x8GuV55J6qHOIqTHrleUI03+HMeBq0RyM8BFKZX06ly+yOy/x9zURkLt4/fCKjX631leXl4lllNVo0KpXNncLrroIlx00UUZy9TW1kZmRfnzn/+MDRs24IUXXsBpp50GQA4l+fSnP41///d/x9ixY7F27Vokk0n87Gc/Q01NDU444QS88soruOOOO9xg0p133okLL7wQ3/72twEA3/ve97Bx40bcfffdWL16dZ/nMX78+Lyk5gsXLsQ3v/nNnPcjCII4rPD6+jAZ8BBMBkE4uAyBeIa62QBMATicweIGLCFgcgGLm0ha8k/leK8Ds8eBMADWnQC6usEAiMGHqkKhxNo7wDq7ZOa2ziREjwWnS8BOGLASJpKOiYRjwuIGbMHgCAZHQF4DLoMyjhDgQg9m48rE3AHAwd3+Fg9Rqpc/kATQEPpcKGW/goJJBEEQBEGUjHzfHpZCkL1582aMGjUKw4YNwwUXXIBbbrkFI0bIAPHWrVsxdOhQN5AEANOnT4dhGNi2bRu+8IUvYOvWrTj33HN9hrctLS249dZbceDAAQwbNgxbt27F4sWLfcdtaWnBww8/nFUbH3jggbzO7ZhjjslrP4IgiP6NAyFiAFPDr5jH10dwaSPNbFjMAgODJRxYXL5EtByBXsYgTMBkgGkwxBwZcDGY1DrVOiZYBwAkYXbZiDmdMB0B1B2CYVkQo0dCDBlSGVPuRALGnj1A2z6gswdiXxecDxNwegQSBw10ddYhaZvoTMTRaceQ5Aa6bAPdjhzep7O4JTiHzQWSwkESFmxmu6okx5PFLeWXJNVg+sXj4T7Mrb9Tyn4FBZMIIoKy/9j0I91ldhm/8j+f7BQfLGyW2hrIpCaVSX5FUszN2ibXx+JakVSr5jJzW21NAwbXSc+BEXHpUTS+RmZxO03+HYqJF6lUnuqPTAYWqUzq88wylVf16+Od9v/k6kPWaCRZDwBACLnNNUhU1RmGUHO5bKsmG8yA7cgMcJyHK5TcjoIec80Y0m+DzN85y0GhlE4mzU1lFEoFUSaFUrbrS0m+eV4E5Bj/jo4O3/ra2trIFL6ZuPDCC3HxxRdj/PjxeOutt/Cd73wHF110EbZu3QrTNNHa2opRo0b59onFYhg+fDhaW1sBAK2trRg/fryvzOjRo91tw4YNQ2trq7vOW0bX0Ref+tSncj43giAIQmcYk8PdtG+SCQOOSICjFjYzYAsHSeEA3ESCc8S4AYAhxoAYYzBhwDaEyvBbg6RjQ0AKcmI1DupsB8LqhFFvwkhYYD0JsEF1EKOOgBg5sjyn2tMD1tkJtvdD4MODEB92SjXSfgvJgwxWwkRPdy0O9dYg6Rg4ZMXRbRtIcAM93FBZ7KRXUsIRsHUWN+WVJCcLQnkkabWXCAkgVSKQBOhwVn77DTRK2a+gYBJBEARBECVDgLmBvtx2ZHj99dfThlnfeOONuOmmm3Ku7tJLL3U/n3TSSTj55JPx0Y9+FJs3b8a0adNybx9BEARRJTjw/lkrFUpqWLrg4Ey4Gd0c5shhbuDgwoAjAEMPeVMT40z5KTEAMdTYHEkrBgEg1iNgdHLAEoDZCyPeCSSSYAYDDANCqV1LRk8PjL0fAN3dwIEOiINd4IcSEN0cdqf0SLIsAwnbRNIxkOAxJIWBpGAyYx0HLEcOb3NEasif42Zsk8Pc9EtFiJTSyw0gVdArSSNEvn2L4rdlIEPBJIIgsiYbRVJhLygCMiMRWO9ZTHt8BDOnBTK2GYYBwwgokZQyKU2RFJOZ23QGt0G1QzGs7igAwDgm558YIff9u+NU9raLP+87bvCzv/l9eyYF6wj69IiLZ8jj/+nXAID91kfQu1e2zamz1T7KO0krk1jqWnjntmXJThC0f1JKgKSzP7hZINQ+QggwV12j2+1+CMdnZJXfjSJEJjFPP1QoDQAKeXs4adIkPPvss771+aiSwjj22GNxxBFH4M0338S0adPQ3NyMvXv3+srYto39+/e7PkvNzc1oa2vzldHLfZWJ8moiCIIg8sevjBFKnQRw4cAUHA6zYQo51I2BwUYcNhxAAEnOEXMYhABMpoa2MalS0v6ScS4gRA1sbqAm6cC2LdQnkzBjHDXdSZidB2HUGWD7OsE+OAA2vAmorYEYPqx4gaWeHrB9+8B6eoGDh4CDnRDdSYiOXjjtNqx2wEkY6O2Jo7u3FpZjoMuSQ9ssztDlyOFtSc7Q4wC9XCuSgKTDpSm54LAghwM6SELacMspZbgN9/pWmkJUz0TxoGASEcmcOXMwd+5cnHvuuZVuCkEQBNFPKcTXwDAMDBkypOhtAoC//e1v2LdvH8aobDxTp07FwYMHsX37dkyePBkA8OSTT4JzjilTprhlvvvd78KyLDe76caNG/Hxj3/cTb89depUbNq0CQsXLnSPtXHjRkydOrUk50EQxMDmggsuwKc+9SnceOONvvUHDhzA7Nmz8eSTT1aoZeVF+yUxmK75Nhc2DGZIQ2lhw2EMFixYQv5+W1yqjzgYDMeAwRgMAHEDAAwIwRA3BBzBYHOGmBGTZta2iZjhoK7HRm2HDbPGQWxwJ4yGbhhD2sFqTLCGPWANdUBNDBhUDwwaBBGLAXW1EPEawDQBpWYCly7YzEoASQuwbLDeXqCrG7AsoLMX6OyFSNoQnUnwDgc8KWB3MSS7Y0gkYrBsAz3JOLrtOCxuoMcx0eUYsDlDt8PQ4zBYHOh1gIQDJLga3iYELJXBTQeSHCY9kqRPkgD3qJQkHH5VUvkDTNJIPff9KJhUXCiYRETS3t6O6dOnY9y4cbjiiiswZ84cfOQjH6l0sw4/ijDWuFRZ3NKblo0iKfe2BJU6QUFSqMAkkLUt6JEUVN8YRgyxmFIkxcKztsViUvFQWzMYAFBfI4fXDK09Ckcxmb1t0jBZ9uzRBwEAjZdOlG0OZmwLaXXaumARkSoX/E5dRZJWKKnj6eOfffe7OGQNBQBYB2RbRV1AmaTURyypl7WHVC8MW6mUlJGSbWt1j+07nlYoCSEg9GfdxoBSKXBagdP2n0/2iCyUR36FUuay+VNQVje3ktJ6J1UDAoW5ZGVLZ2cn3nzzTXd5165deOWVVzB8+HAMHz4cN998M2bPno3m5ma89dZbuPbaa/Gxj30MLS0tAICJEyfiwgsvxFVXXYXVq1fDsiwsWLAAl156KcaOHQsA+NKXvoSbb74Zc+fOxXXXXYcdO3bgzjvvxIoVK9zjfutb38KnPvUp3H777Zg5cybWr1+PF198Effdd18eV4EgCCIzmzdvxquvvoqXX34Za9euxeDBsg+TTCaxZcuWCreuEgjPMCy4gSUBB1wwAByccTiCw4Ec6sW4gG2khrmBAzEDSAgGwaVqyWQG4hAwHBOGJWAyAxDSPzJmCXDHQczmiCWTQIzB6LLAOnrBakygrhOorwEzDaAmBhaLyee+NrHU6m/bASxbLvdaQCIJWBy8OwnRY0MkBHg3h90NcNuA1WsikYih11LBJDuGXseALQwkuBzWZnGGJJeBJD3ZXIBzwOECjhry50BdJybAhVYjOW4ASQh9XasjHFOuvgWRGQomEZE8/PDD+OCDD/Cf//mf+PnPf44bb7wR06dPx9y5c/H5z3/efStL5EgVG23nEjyK3id7ov4I7+vPasZY2rC29OCRnJumDhyZniCSNLHWw9p0EKlGGW7X1wwFADTWSsXCR3AMjm+SQ97OGNELADjmfGVQffzHo04ujbTgQ8S1Cw2wRHhX6+Mfc/47OOM3sm0JLtvqtB8DAOBuUMkfhEn6hgAm3M9yroNKctlxLF8dnPNUVy1wEwTNGDN9n8EgWS70HYdJ1RkcV191sRvvNau6xvUPXnzxRZx//vnuss6oNmfOHNx7773405/+hJ///Oc4ePAgxo4dixkzZuB73/ueb9jc2rVrsWDBAkybNg2GYWD27Nm466673O1NTU144oknMH/+fEyePBlHHHEEli5dinnz5rllzjrrLKxbtw7XX389vvOd72DChAl4+OGHceKJJ5bhKhAEMRD53e9+h69//es488wz8cgjj1B2R0B5/GiFkgPOZF/IZhZsqD6OMJHkgDBMmA6HgZQZNyCVL0nGYAuZ4S3GBJJK9RNjHHV2HLVWDUxw1MYc1MQdxOMODEPAjDmI1dpghgCLA0YMgAEwE8pfKaTRDiAcASEAYQPCkrEcxzJgJxkEN2FZcSQtE5xLX6QEN5FwYnLIGjfR6zDYgqHXMdCjPJISSpFkqeFtSS6Q5By2EEhyNZiNqextsN0hbtpBSQjuUSURRAoKJhEZGTlyJBYvXozFixfjpZdewpo1a/CVr3wFDQ0N+PKXv4x//ud/xoQJEyrdTIIgCKJKkcPccg+Q5RqoPu+88zJmlXn88cf7rGP48OFYt25dxjInn3wyfv/732csc8kll+CSSy7p83gEQRDFYMyYMdiyZQuuuOIKnH766XjwwQcxceLESjerbAghfO9hhBByYgKc2zBMB46wAQY35T0YkBQGmGDgXGfh5YBtwDEAgLm23raQARqDAb2OQI3JEGMGahwgbnOYEIgbAnGDI25wGEzAZBwxU4AxAQMCBhMAEzBS70PBWLqSWuih4YLBEQYEANsxwAUDV8PtktwEV4baSWHA4gyOAJJcKpJswZB0gCSXRtu9XH52uECvI5B0OBKcw1bD25IsCc4c2MwCFza4UiQJYYPrjG5If1lYqUxuANzrkSt5mXYTkVAwiciKPXv2YOPGjdi4cSNM08SnP/1pvPrqq5g0aRJuu+02LFq0qNJNrH6qVJHkb1ZubZT75ndeuQwNChpZM8bShrVpU+10RZL8mYvH4mlG27FYndqmFUlyWFtjrTTKHSuOBQB8rKEBJw+Vb7ROOO5D2YjzztEnEo6I3pbXsMS+TK3Pm4wT3nwGANBuSUVVwmkAAPBOeR7v16ldXIWSV5mkFV5qzvT19SuSggolwJMeloe/tcqms5FSKGVDsDOTjeF2+D7u8aupb3GYDX0jKTpBEETp0M/j2tparFu3DrfccgsuvPBCXHfddRVuWSXgqvsl+4RCcIAZEMKBkLbbMCHT3kMABjNhChNCCBgcAGKA4LAFc1+EGAywIYfDGUwqlWq4CYMJxBkQMwwwADFDIMYETAYwyLmhgkWGSlGig0deDBbu/SPUEDoOOXeENAp3VNscyMCSHJon1yXVsiOApCMTztkqkGQ5QiqRHI4kVz5JwkGSWbCZ7THcTsIRXuNt4WZzA7TiK9jgMJlVacm3b0EUFwomEZFYloX//d//xZo1a/DEE0/g5JNPxsKFC/GlL33JNUR96KGHcOWVV1IwiSAIggilEANugiAIIjPBP+yvv/56TJw4EXPmzKlQi8pPaPZcNcSNwdDJ7mFAeSfBgQMGzhw4ylzagQkuBBzlmWQzBoMLmAaDobymTQDCkM8nkzFwFWhiAGJuRjgVzlJBJUCGWnJ9P6S/VulSJANJHDLI5AjZBq2YstW7vKTyROJCBpKSjtzH5jKQ5HChgk+O8oySV4KDq+CR42Zuy+bFJ2OsYuqkfPsWNFivuFAwiYhkzJgx4Jzjsssuw/PPP49TTjklrcz555+PoUOHlr1t/YoS/sgWYrxdHH+k7I8f4c0cTsBcO8wfKeiVpJVJKV+klCIJAGLxGtcbKeWRJL2F6uIyONpQMxoAMBrHAADGD2oEAHy8CZh0xEFZ9lSZsUkccUTm84UA0+qXQgQmIlVfRo44wm3bpLaDAIAOW6aktbg8D6fnGFlWWcToa9jruZ5etZKc+xVL2phbG3UDHlPuEJNuIMTuKcO/CRYokl3nK10m3ve+rm14HscL1lQEI+7Qig8PhRKl7yUIgigdu3btwsiRI33rZs+ejeOPPx4vvvhihVpVWaQiyUz5JgkOwRxAyAASV0PebGGBqWxvhu5DcFOqhcClMokDjgGYQmZ6ixlyMiFVRSZjYGpuqHUao0iPb2/QhIuUKsdRARWH6+CS/KzVSRYXas5hq89JbiMpOCzY0ieJ2Z4MbjY4lD+S8Fw7PWywinyTqG9RHVAwiYhkxYoVuOSSS1BXVxdZZujQodi1a1cZW0UQBEH0J4TIM6ZOPT6CIIg+GTduXOj6E044ASeccEKZW1M9CHAweANKDhwGMGEDzIApBGxmAkq5xMDc544pAC5MNcyNweEMpgE3mGQwpoaxqQFe6rMcyibriEjYm95OEf3OyLvau79QASWtztHBJhlMEuACrhKJQwaVbMHBBXcDSa5PEpI+ryShh7ghNcStGs23qW9RHVAwiYjkK1/5SqWb0H+pUn8kwNu00iqRgmR8ORNUIrmr/Yok5ss+Fu6NlK5I0ttrIxVJg2tGAQBG4mgAwFFq/TGN8hjHNnRh+JE9slFjPpLN6QLwqInKdTuMkUqk4UfK9OjHdso2d9oyTXDCkefFLXmeXoVS2rVOmxtpc8ZsACkfJR7wTNIeSmmKJMb6VCnl9zIv2hcpm4xv3n2qSgwUvEZV1bi+4WDgeXyjothKL4IgCOKwI3SImyLNmFsHRzzD3QAOG4ABBw5MGIJDgMknlzBSbkAc4AzgnMFkAjYgh8AxSP8lVSxKjZTPkKywunwqJWjDbuEGlRzIbHCOGtrGAWm0LbgsBw6HOSqQ5KhgmwMBOcRNh5C0Kqlayb9vQRQTCiYRBEEQBFEy8n17WMUxeYIgCKKf4FXYMAHlEqQyuwkLNjPBBIOtXpZxwWHCBBcmHC5gAHCYCUsPZ4Mc0gYGGI5cl1IjpQc3vDYFweeadzkYE/MuZ6pXmnIL1XYVWIKc21yeuy2k/TiHgM1sWCwJG5bMbOdRJUlFks7kpr2T0gNK0isp9bkS5N23KH5TBjQUTCKIYlKmv37y8UrKpWm5qJeyrSvtUcNCHo0BhZLri6T8kLyZ29KztWllUroiSc7r3KxtdXHpITQ4Ln2PRkCqjT4Sa5LzwfJ4Y+qk8mbk4B7Ehsl1UG3J6tIU8/mazfG0b5Rq68jBUpk0pldeg87B8hrZnfI8ua1UVnFvRyGoRApXKhkhaiatUHKbrD2UHCftVFjADyhKqVSYbZC3A5eb4iif45bMOyntQP3LS0l5mea1H0EQBEHkjvT4Ycp2W4CDcxuGEZMKHJhw1HA3JhIwWAxMJMEZV2EnDkc44CIGBgZbCBiuJ5IBAyqIpOYZWxLifRnVJ48KIGU6hhzy5g0syXNw4P3MYTNbBpaYBRuWDCJB+kc5wlIeUY5SKXFPncIdKuh/MpsAHNW+8vdHyDOpOqBgEkEQBEEQJYOyuREEQRCVRKprTGXELVSmNwAqaMKFDc5MGMKAYFxmdGMyGOMGdYQBDsAAl9nZhHqpph5WRuBFEvcEY2QbhGdbOIZXqeQLJrGsj+GoZa6CYlqN5MgBcLCVAskNJMFWpbjaG+7wtjBVUrWQd9+COhdFhYJJBFEI/eAXKRffo0IUSZFvWdwPLHy9Z5urSDKCGcX8GdtMM5bujaSWTaVEimtlkikN5GPxetTFtEeS8hZiRwIARjOZBW1kvaxjRJ08mWE1UplUV2ul2t/TK8/XSkIdKPzEgT4vY1DBUkh2PlgWmGqbbmtdrVQK6fMYUSevX7cjzzPZpTLTCQHUpFoVMvN8fYa7nFImITDXSiW/Isn1VOLcVS3pG8fN4ha8T4TwFvNvy+lFmK6nL4WSPlAqy1vVCoAy6eMJgiAIYsBg9llCQLhZyhxmgwnTHe5mwIStAkhccBjMgIMYHDhgYDBhwhRKJS+YVCYpw+4oNbKr7FFzjvSgUhje+nTwSGcHzuZYqUF9HJxxNZf+SHKQX2pom1CG20KrklRgLXu/pJQ6iRiYUDCJIAiCIIiSIZCfyqj6Q/UEQRBE5fFbIXjRPkmCMRkcYQa4sGEwA4ADIZhU8oADTGZDM1gMhjLi5swAYCAGE7YKIWlL7kxD2lMBJO5bBgDBUkEaHWAKKo6Y8B/DYwPe53H1MTlzXHWSDiIJJqQSSWds08ok14BbBZJ0WEooFVfGl+cmADvD9tJB/YTKQ8EkgsiFCiuRClKu9LGvPLVsyhRGYYqklAopqEiKxWv9y6b0R4rHpTKpLj4E9fHhAIAm1gwAGA7pHTS8Vu4zVKlzhsTkidaajttokVQP/45uuaqtDQAgjjwytwvgobDv0w9ra3Pb5raVyeumz0Of19AaecV7bKVQ6m2CozKziRqlFFJfSm/qCP7jMQYgEdgWnIfDAUBneotSKGWswbdLJOFinfwUSrkgIErvm5R20OrN+EZSdIIgCKI8GH0XAdQwN0M5KslwC9MKGwE5FE5laXOzvbFU4EcHewB/cCcsaMQDgaWwQW7+NQbAHPXJcI8JIOvjeoNIeslRnkneQBKHVGoJNQQuf/pWhhUbGkJfHVAwiSAIgiCIkpFvxhWCIAiCyBchOJh6qSaEkMEdAQgwCKYyuzEbENIHyQE8b7TkEDDGTKVGcjxDzQw1NC49cMU9YSEB5c/kblN+RFmEM1KKpNTQOiCVHEVuiz6+9jpyXxTq4Wsqo5tWJEEoxRK0AkmpklQmN2QY6iYzulXu4U6ZYqsDCiYRRBRV9GtTWPa2bNVG6eVy8VsKElRmZMrmlosiCZA+SbG4zt6mFUl+jyStSKqJNwAA6uJNaGAye1uTGCrnyu+oIa48htSLlbjBVZuVioUzOD1ynXGwS27bu08WrpcKKDFiRKbLUTLYvn1ue4Rqm26r4PIa6fPQ51Vnyuurz7vJjiNpDQUA2Ez6LIm47PTwkDdokpRmKR8Rjltrlgql1HL296BWHwFhQp3sFUq5ZoJTe8l9yq1QchsQcZ0q8LtGGVcIgiCIUpIpm5gAB1MZ3eSyAc5tMGbAQAyCOXAAmALukDemVUvCBoOptElwg1Nhz/ZU9rOUh1DKGNtxFUqSSAtuzycdvPIfU7chrB3+jHFO4PiyXY7PI8lRwaOUT5IOJKX2rc6AEvUtqgMKJhHEYUa2v+nZBZGKMa4t/AHP4E8zD4QFkVSq+xCzbTd4FAsabasgUkwGkWqV6Xa9MQyNQn5uMOR4tvqYPF6NKY+vgy2Ga2Qo19u2AVvGaWAekEEUs/6APA9DnV9SGnKLkaOgGpTxsuSNrdKwfrBXzts+kOv3HgBXbdNttW3Ddx76vOIqXUiNCirVxww0OPKaJNU1sg15Pk4sJfv2zALwTBsR+rhXNxkPBJHSqghszw1vpyoqIJRtUCnVhCoaQdYvoGFuBEEQRKnIGEgSQmVc4+7Qf59iSeVnY2C+IW+GSr4h87ZptyQTQqigUqZgEvTLOH/wyGtoHfWizqs24q4Kye+rxDwPx+zbkTq+VhwJd1ifd5vIGDzytjS/UE7xoGFu1QEFkwiCIAiCKBlkwE0QBEFUGiEEwFLqpNQQLhuAIYekeYe8wVB22wYcAIz1nbVMB2WCw83grvc/2XRAR6uPvEcwBAOY1yNJ+yfprLqZ/aGCwSsdRJID2ZzU0DZvoEn4251NYIkxljGgVyqob1EdUDCJIKqYUhpuh+5RTEVSBKl08qmHT3CYW0qRpNVHfoVSLB5HLFajyqq5Wo6bWpk0GABQbzQCAAaLJgwSckharVIkxZUiKaaegal3QEqRpNQqvVYMNZ3y2OZ+lbHC6JQzSz36u3rkuXy4Xy43NUI0SHUUBg2S89q6LK6QIqGGkXUrw+9OeTy0H5LzDrks9ss539cDe7986CdVW3utmO88Ugol+M47bjLUKpXSIEteo6QyJ3cMabItlEKJq7dy7nh6VXMYqe1x/3ohXFk0i5CfFF82nb0CKWrffM245Z4DV85Ebw8JgiD6J0II3Hjjjbj//vtx8OBBnH322bj33nsxYcKEyH2WL1+O//mf/8Ebb7yB+vp6nHXWWbj11lvx8Y9/3C3T29uLf/mXf8H69euRSCTQ0tKCe+65B6NHjy6gtToDWnSQRSqVdB/GM6iMwfVQEq4CyPR4KRl9P5QCASPhCQ3pwI2vuC9QY6W1natjssBwN90+CPiCTdm2yRtEAgDObZ9PkjeLWxjeIYOVhFTP1UGWlvcEQRAEQRC5I8DynAiCIIhKctttt+Guu+7C6tWrsW3bNgwePBgtLS3o7e2N3GfLli2YP38+nnvuOWzcuBGWZWHGjBno6upyyyxatAiPPPIIHnzwQWzZsgXvv/8+Lr744gJamjmA5DWT1gET+VkGUTi3pUG1sJXXkAMOaVLtwIYjknBEElw4vkmvd0QSNizYsMBFUk1WauJJmUWNJ92JcxsOt9xJLnu3q8mtR9arj2PD8h0/tG2q/VxN8txsV43kDSS51yYQbZEvAMOCR0bG615q8u1b5GX0SURCyiSCqFIKM93OpkxY4eL/+Rb1k80Yy2C4HfPNY8qA24zp9TUpRZIZVCRJZU2NIdVAtZDqoBpRi5h6gxM3/Aod/WerK3jWiiTlOdRtxRHr9j9I62yp0DG7pDLIPKg6VoPaZZ2DasDqZdtQo35qa5RCR6mA0t4o6Ye1w4GkfEuFpFJC9ShPpm45R7fc7nTI7c4hoLdDHqe7u8Ztt/c89HnpM9HnbXiuib5GNUIam9cyef20hxKPqXYI7/h/rfpRS9r/SESvF6mVsl5txB24iYNG3IUTpTIqrXfSQFYoCXp7SBAE0e8QQmDlypW4/vrr8fnPfx4A8Itf/AKjR4/Gww8/jEsvvTR0vw0bNviWH3jgAYwaNQrbt2/Hueeei/b2dvz0pz/FunXrcMEFFwAA1qxZg4kTJ+K5557DmWeemWNL8wtoyAATACYdkdw+jXpMMwGIQD9NKCPu9Mr8WdwAz5Axjx+RWyYkOCPgH7omhOO2izGpBmJMDs/TCiYBuH3JyLZ52udtW7AN1aA2ygVSJlUHFEwiCIIgCIIgCIIgXHbt2oXW1lZMnz7dXdfU1IQpU6Zg69atkcGkIO3t8iXb8OHDAQDbt2+HZVm+eo8//ngcffTR2Lp1a2QwKZFIIJFIuMsdHR05n5Mc3mW43klynSeQo4IsbvAmi0CVNygjh4qlB428gZqMQRv9sio4ZE84qn2OJ6ub4e6Ti3+St40ioNbyDm8LUymFU1mFElFZKJhEEFVG4YqkPgd1Z1FH8fF6Jel50CspzTNJK5RcRVJclYvBNORnrUhy50qRFGdqDrUeJmL62G6r/FnbHC7nCUfOu1W2DyMp3OtjKZVPMiGVQTVKGRTfJ+dGraXm3TDi6njanEh5NLlZXY2ASkW9YhEOAEd9tpVyx1Jz1Y/iCbmv1Wuq9sTQk5DXpNuW807lmdTtmL7z0ufp6e6410Rfo7iQ+7jXT11PRyuUTCfVOdFj8lU2PNP0q4xScz0+33G/66B3UtDEsVQpZ6PVRZn8kfzbSKGUHeSZRBAE0f9obW0FgDQfo9GjR7vb+oJzjoULF+Lss8/GiSee6NZbU1ODoUOH5lTv8uXLcfPNN2c8XjD44waGlPk2U8bbQpeLCCp5VUGZyBQ48gWQvH2ZPuoEIM3AAQBOqt8sIgJMAFg2dfbR1lL1t0oF9S2qAwojEgRBEARRMkSeE0EQBFE+1q5di4aGBneyLKvgOufPn48dO3Zg/fr1Bde1ZMkStLe3u9O7776bcx1hqqBg8Mc7LK3P/5SSyWde7VH5uMP6BXentHIhk6+8riesrHvsvv9zzzdTIClESVWt5Nu3oP5FcSFlEkEMEKJeOGSTwS3Ty4qgKsNVXETINbzKpHSvpHhgOWoeT3kmGXouPX5MJpdjUOuVwsbwZsjQPj3KHyepEm4k1JsgLRhKjUmPweLys/YfqknKttZ2y53jSo0TMx3VRg5TKXUMU6tu9DUQvrlG+/UIwdxrzl01kTyu4yj/I6U2stRywjGRVGV6HJXNTS9r7yd9nkr1lFR1y7c7/rbo66WvX0xdV319TaMWpiHVWNxUc/fNmKPOQ2UeUX5IXC1zHk9XLaky+v5Ie0PmvplLV+/19TIt/FbM7JGUj+qICId8DQiCIKqfz33uc5gyZYq7rIeUtbW1YcyYMe76trY2nHLKKX3Wt2DBAjz66KN4+umnceSRR7rrm5ubkUwmcfDgQZ86qa2tDc3NzZH11dbWora2Noczkmh1kn+lDpoYYIylBU90wCVsmFtaWTcI5Q/IhG7z1B2FHGLnqM8sVZ9SJglP35EpZZVWLUW1OZd2B9cH/TH1MSodcKK+RXVAwSSCIAiCIEpG8K1o9vsRBEEQ5aKxsRGNjY3ushACzc3N2LRpkxs86ujowLZt23D11VdH1iOEwDXXXIOHHnoImzdvxvjx433bJ0+ejHg8jk2bNmH27NkAgJ07d2L37t2YOnVq3u3vy99ICOEGjlJDxTxD3gD/sDdkVuiEDV0LDm3zB44ibCYC3kxCOLoxnhdbMsCkg0vuy05lIO4NPmUb5Omr/dVOvn0L6l0UFwomEUSVUJzsbcX9gSwkeq8FHWFeSQDADCM6m5shf5oM5ZlkGEpdpFRIBovBYMpHSXknuctKkWS45oWqJZ5z0SocW73SsNSzs1d5CemEGFq5ZHGgV8mVulVbYkp1VKM6HjFDq5rkPMZSyc0NvQ3aLyfzhRVg4Krd3PU3knM3I5ua22p7UhiwlRIpqc4nqbZphVLC8Z+nxVPXIahMgtuB0Znv1HeE1Hegr73DY+46ABD6ezLkAbUyy9QKJVOAc/93zw097j/cO0nfjHl1G0SxFUbknZQL5GtAEATR/2CMYeHChbjlllswYcIEjB8/HjfccAPGjh2LWbNmueWmTZuGL3zhC1iwYAEAObRt3bp1+PWvf43GxkbXB6mpqQn19fVoamrC3LlzsXjxYgwfPhxDhgzBNddcg6lTp+aRyS03ogJKbkY0T18oKw/HDCqkqEBSpqF27rFhwNvX8Hk/AW7QS3tAyQUjY/uzOYdgub5UVJWE+hbVAQWTCIIgCIIoGfl6FFCHjyAIorJce+216Orqwrx583Dw4EGcc8452LBhA+rq6twyb731Fj788EN3+d577wUAnHfeeb661qxZg6997WsAgBUrVsAwDMyePRuJRAItLS2455578m5n36qk1FA3b0DJ3TcsoBKxXm4LN9cODgnzB4myD8zI/fxD14KKJZ9aCfAplmRbPBWy7M4leD6ZSFlBVCbgRH2L6oCCSQRRYfKTaKbXkn+Z9PW5KJKyVWUElUmGR5mkFUmpZa1a0WW18kVvj7leSVoNo+epN03+jGUcAk5AkaS9krSaSJdVNkRIqHIJgyGm2hJ3E7MxNdeeQlpporcL95qkPJj8ZaKQD8iUnxGQus5O4Ly0UskRqW0q8Rts7j8PrWJyz8tJXQd9TfQ14vBfE3099fX1q8Pkd6G9k4RQme3092ZoHynl+8QN9zvnSq3kZnfryzvJe52Kcp/6VUZ9r8+1TB/tGgAKJfI1IAiC6J8wxrBs2TIsW7Ysssw777zjW84mGFFXV4dVq1Zh1apVhTYR0fmkBKKez8Kjgg4LhqSyvkUEYPIIIIVfF8fz2Uzb5vaFPMGl1BA3B97AkiznhCqSfEPjsjgn/3llpq9AXqkQFehb/PCHP8SSJUvwrW99CytXrgQA9Pb24l/+5V+wfv16X2DUmwVx9+7duPrqq/HUU0+hoaEBc+bMwfLlyxGLpUIxmzdvxuLFi/Haa6/hqKOOwvXXX+8GX6sZCiYRRIUoJIiUzx/R2ayPrje4IYc/fFOu02qWHkzSQQc3iOQOb9PzuNo3FThy06Ey/8M11WJ/Vg4HDmxlAK2HgRm6bbY2uVbD3nTgSAeVjFTwKOaadOtgkj49PRxM1+3p3uigUuA6Rpk+A3CHueld9COdB5ZTQabUtlSASQeR5HrLHdbnH96X5AJJFcSxPddL1q+uY8BHgMFI+w7cgJ7+nrQBuQomCXe4mwPO/YEmd7hb4H5x5zk9/aPv16igUqb12Q5fK8S0+3AOKgnk2XmjYBJBEARRJMKMuLVKKa1s2FC0jMGW6EBSehDJQTjpgSVv0AsqoOT3WJIBM9cw3DPULW2YXrb+T3lR/oCSEOV96fTCCy/gP/7jP3DyySf71i9atAiPPfYYHnzwQTQ1NWHBggW4+OKL8Yc//AEA4DgOZs6ciebmZjz77LPYs2cPvvrVryIej+MHP/gBAGDXrl2YOXMmvvGNb2Dt2rXYtGkT/umf/gljxoxBS0tL+U4yDyoTSiQIgiAIYkDA85wolkQQBEEUEyF4muJGGmX3PXn3l3UIdxLQKqbU5N1PBorklN2xHM8Ez3pVt2fytcPTvmzPKyxIlq5Kqr4ncr59i3wG5XV2duLyyy/H/fffj2HDhrnr29vb8dOf/hR33HEHLrjgAkyePBlr1qzBs88+i+eeew4A8MQTT+D111/Hf/3Xf+GUU07BRRddhO9973tYtWoVkskkAGD16tUYP348br/9dkycOBELFizAP/zDP2DFihX5XZwyQsokgigzxRnWlqot/zLF2DdERRFUIgVKMm20zFiaAbc22vaql+SyEdjXiFRw6IwWXCmIHOWmbQsbSa7390uJHTX8y1b1J1WYPaYOETNSqiIlnnKHrnmVSPI8U6nmWWCbXpPNMDeNO8xNb3OXhW8793zWCiv9wNTKJDuw3VJqJEsIWFxet6Qak28zed0cNdfXMzVmP0XqnAPfkwiYbHP9vZoe1VLqfvDtq4e76fP2vmGLfBWVaX22Vz1suFu+++aOgDgs1UkEQRAEUX7Cn8/eYElQrRRWJr0+veTqxtU+3u2p/lK68idTSCNopK3rMT2qI6/xtyrnM+0Ob39u5xo8wsBl/vz5mDlzJqZPn45bbrnFXb99+3ZYloXp06e7644//ngcffTR2Lp1K84880xs3boVJ510km/YW0tLC66++mq89tprOPXUU7F161ZfHbrMwoULS35uhULBJIIgCIIgSkbevgbFbwpBEAQxIMnkn9SXViUqgASEeyJFBZGy1cR4y3mHrXnr9b585b5W+ofAwV0r98tVl1O9T+JC/Bgdx0FHR4dvfW1tLWpra9PKr1+/Hi+99BJeeOGFtG2tra2oqanB0KFDfetHjx7tZjFsbW31BZL0dr0tU5mOjg709PSgvr4+t5MsIxRMIogyUQxFUqm8ktLX59/WNCVS0Csp1DNJe+74lUMpjyS/QglgHrNB3X7Ht8zVw9zRShtYruJDn6sSv8BR67UJtTbbNjw+SKb7Mkd7J/nP21UmsVQp14DbbaPwlYlC+vQoA27POv/5+pVJQEp5pEs5aueUQknvo7yUVKfChnAVSRYstU7O9fXjrtRaH99JdVw834t3WX9v3PVSUv5IzAlRpel91HkH7hvmNbtEPvjfTubinZSrF1IuPkuh+x9m/kn5+hqQATdBEARRPLJRGgfLe5eCgZhc1EiBfTM94HwdiJTxdpi/k39dylMJCHqJ5qOgru6HcCGeSa+99hqampp862688UbcdNNNvnXvvvsuvvWtb2Hjxo2+DIZECgomEQRBEARRMvL1KKjubixBEATR/8j9yRIVRALCA0mRQaRsIx9pb7B0HWEqJe/QN+Yv6zl2uFqpf1NI3+KEE07A73//e9/6MFXS9u3bsXfvXnzyk5901zmOg6effhp33303Hn/8cSSTSRw8eNCnTmpra0NzczMAoLm5Gc8//7yv3ra2Nnebnut13jJDhgypalUSQAbcBFFyhPqvoDrSou/abK//wBjzTVqZJCcGw2Bghiknt5zOGCYnpiYf6uLoK8Jhy0lY4MKCAzklYSGp/xNySnALCW6hh9u+qcuWU4/toMd20OU46LLk1K2mLpujy+boVlOXpaakIyfLQWdSTZac9D6dlsg4yTJqP1WHPn6qfnk89/g2T7VNT46c9Hn0OLacAueb4JZ7TVL/yWumr5++nvr6Cs+1T/uu3e9JfW9MT+p7NUz3O/ffB0bafdK/SP27LEaWkWL8dlQD+lrkPOV4nKeffhqf/exnMXbsWDDG8PDDDwfaIbB06VKMGTMG9fX1mD59Ov7yl7/4yuzfvx+XX345hgwZgqFDh2Lu3Lno7Oz0lfnTn/6Ev/u7v0NdXR2OOuoo3HbbbWltefDBB3H88cejrq4OJ510En7zm9/keDYEQRBEpfAbXGtS4Ytwc21vIMkT6gjpEIgM/6UKicC+/uOHHTv0+JHn07/Ju28hANM0MWTIEN8UFkyaNm0aXn31VbzyyivudNppp+Hyyy93P8fjcWzatMndZ+fOndi9ezemTp0KAJg6dSpeffVV7N271y2zceNGDBkyBJMmTXLLeOvQZXQd1QwFkwiCIAiCKBnlyubW1dWFT3ziE1i1alXo9ttuuw133XUXVq9ejW3btmHw4MFoaWlBb2+vW+byyy/Ha6+9ho0bN+LRRx/F008/jXnz5rnbOzo6MGPGDIwbNw7bt2/Hj370I9x0002477773DLPPvssLrvsMsydOxcvv/wyZs2ahVmzZmHHjh05nhFBEARRTqIDLpnVSP71mdVIfb0kyvYlUrqpdxjp53K4BJTK0bdobGzEiSee6JsGDx6MESNG4MQTT0RTUxPmzp2LxYsX46mnnsL27dtxxRVXYOrUqTjzzDMBADNmzMCkSZPwla98BX/84x/x+OOP4/rrr8f8+fPdANY3vvENvP3227j22mvxxhtv4J577sGvfvUrLFq0qCjXqpTQMDeCKCGVVRVEHTtTm3Jtb/r4bU3QK0ln6TJM6YcklSjqs+uJ5M/ilgmus30Z+i2NnHM3m5vK4oakp1FqX5UFQ/sBGcrIMKazj0FnI5M7mDBSmdl0VU7AC0qX8PgkBa9MLh44wXsnrYuifZ9cJUzqjRYP7OO45ox6u/ZKUteMOansbdprSl03ff24yorHtTeVJ3Ws/i76wpvVTX/n7j1gqO9C3R9uNjc9Z9rrKHVd9K2XXYdK05dvQNj2fLwGikd/91AKSz2c5Y45Fb/oootw0UUXRbZh5cqVuP766/H5z38eAPCLX/wCo0ePxsMPP4xLL70Uf/7zn7Fhwwa88MILOO200wAAP/7xj/HpT38a//7v/46xY8di7dq1SCaT+NnPfoaamhqccMIJeOWVV3DHHXe4Qac777wTF154Ib797W8DAL73ve9h48aNuPvuu7F69ercrwNBEASRAX8AKE3B3geZgyu5BJH85cPUSNm3KfDc95kxhvkoRQ1787YpdV2C51z4NSt/gCrvvkWRWbFiBQzDwOzZs5FIJNDS0oJ77rnH3W6aJh599FFcffXVmDp1KgYPHow5c+Zg2bJlbpnx48fjsccew6JFi3DnnXfiyCOPxE9+8hO0tLRU4pRygoJJBEEQBEGUjLwzrhSxDbt27UJra6sv9W5TUxOmTJmCrVu34tJLL8XWrVsxdOhQN5AEANOnT4dhGNi2bRu+8IUvYOvWrTj33HNRU1PjlmlpacGtt96KAwcOYNiwYdi6dSsWL17sO35LS0vasDuCIAii+BSuvAlR85QskOTP3JZ2XAh/QAlQQSW/j1IqcOQAMN22sTQz76jj9D+1UiHZ3Aph8+bNvuW6ujqsWrUqUhUNAOPGjetzuPt5552Hl19+ubDGVQAKJhFEESm2Ein9B6/v+gvL4pYrLP1zQKkUzOLmVSyxQJa21K5mYL2auw9UAMzfcEdYvjKO+7BUb29YSpHjKCWSrX4CTZU9ztapVtU+pkgdVyuPWHAu/Mok/3bhaUF+eN+1Aal7LKUySi1n2gYADtMKJXUdmFYhOeBCKY/cdVqJZIcvq+sNVaN35l6DtCx8+nu1Qr778Kx/PKh8Y0x+md4DIricPaXJ6ibcNuWaCS5zrf7z6y9KpXwd3gSk6i3b9L2Z0Ol3w1LvelPzjho1yrc9Foth+PDhvjLjx49Pq0NvGzZsWGSKX10HQRAE0X/IWf2SVSAp01A6f6/RF1CKPGR0QAlASFCp/zvdFNK3IIpH/7+TCIIgCIKoWvTbw1wnIYDXX38dTU1Nvmn58uWVPiWCIAjisCM9P1i6Iqlvs2vf/lkHkjJvTzPmDikbpZ5K36b3639qJC959y0q3fDDDAomERUhm6w6QfrK1JNvvYUQmYGhGHWX/deusAMypiaoKZCVKyyLW/p2U01qGQHnGuXTIyDA9X/CAReOu80Rtm+ykYSNJByRgKUnN1dZLyz0IinklICckkggiQQSrFdO7ha5VZZQ/4kkEiKJXmGhV1joEUn0iCR6RQK9IolekUSPsHxTr3AyTv6ySTUl0CsSnvrl8fTxE5626ba6/6nzcM9Ln4k6b3kd1DVR18hRU+r6+a+rEKlrr78L91+Cx08JCLsnzIz3Rfi94bknWDGUPvm+08rzaKL4/6ZL9dtTbArp8E2aNAnt7e2+acmSJTm3QaffDUu9603N6822AgC2bWP//v19pu/1HiOqjN5OEARBVAtea+YU6X48/uBMJJ590p/NuQRw+iiXZ0DpcAoqFfKiiigeFEwiKkI2WXWC9JWpJ996CYIgiOrEMIys0vf2xfjx49Hc3OxLvdvR0YFt27b50vcePHgQ27dvd8s8+eST4JxjypQpbpmnn34alpUa5rlx40Z8/OMfx7Bhw9wy/TXFL0EQxMAhQk3UR7Qh0iepxOT34ijLIFg/DioRlYU8k4iyk01WnTAyZeoppN6c2l4xBUAux40qW562p/m6hHgl6Xnqc0RlrtdOcPx5Svmi/X+Ccw75x55+6As4YMozyNSeQdD+PMrLR2dvE/qnUfshmWnj1bWvkusFJYzAdhaZHcPoY+w7D/muUucXuBaMu/sEDRRd7yThuGsAwFGZ2wTzblfblDeS0B5K7nH1+lT2PO9nbxu9LQDg+R5T6O880/3hnQfPqfQE/Zii1uWyf+modj+lfL63XPfo7OzEm2++6S7v2rULr7zyCoYPH46jjz4aCxcuxC233IIJEyZg/PjxuOGGGzB27FjMmjULADBx4kRceOGFuOqqq7B69WpYloUFCxbg0ksvxdixYwEAX/rSl3DzzTdj7ty5uO6667Bjxw7ceeedWLFihXvcb33rW/jUpz6F22+/HTNnzsT69evx4osv4r777sv5GhAEQRDFJjpoEh5IKoYqKR/SvY3SDLkzZnjTpDyUwrcHj4m041Yj+SuzSZpUTCiYRJSdbLLqlLPeRCKBRCLhLmuz10oFjgqRX+ayb6lknmlBgCyCSdDBHHcX9RBTbdR+y+6f5562O0EZr56rEzT0voyBBYIe+oHMXaNtQ9WpzLx1u8DcYJERfMCKVMDJdx08f8znmnLVfz7hASKNGyjyXBQ3AMT8ASghUmP95Tx1PVKm3SpoBH9Z16DbXW/D0cd2L3roYiqm5DVad79zR80jgkgh60uRCjYXo+xCTLWLacid8TgRv1+V+F0rV8aVF198Eeeff767rDOqzZkzBw888ACuvfZadHV1Yd68eTh48CDOOeccbNiwAXV1de4+a9euxYIFCzBt2jQ31e9dd93lbm9qasITTzyB+fPnY/LkyTjiiCOwdOlSzJs3zy1z1llnYd26dbj++uvxne98BxMmTMDDDz+ME088MfeLQBAEQRSBvlU3fQWSwoeIFe/4hVOsgJKuS1OdgSWO/PoWpL8qLhRMIspONll1ylnv8uXLcfPNN+d9XIIgCCKaUvhFhXHeeedlDDQyxrBs2TIsW7Yssszw4cOxbt26jMc5+eST8fvf/z5jmUsuuQSXXHJJ5gYTBEEQJSa70EHuiqRAvUVXJWWJT52U666ynZmDSkDVqpXyNdMmYVJRoWASUXLWrl2Lr3/96+7yY489VsHWpLNkyRL3DTYglUlHHXVU2dsR/jdQ4b94lTKay2b4UnCYG0sbDpWuoJFz5ipkUknhvSlRU0PFUiqkGAxVD9dqGGhFkm6Hf7gbCyiWwsrqw7rrPW9+DFE8+Qln/i/SVQ557hFXeRSQCKUNBWQirbyrgHKvkS4TGN6G1NC21DA3x18mMA/ex4wZfSqS+hruVi4K6KfpGtQ8MFyvTAqlaoAr7VuuVLuxOEEQBFFN5Kc5ySaQlFERXdKOdvpQt2wJVycBCCjp+1YpedsSpHIBpvz7FkQxoWASUXI+97nPuealANwhZW1tbRgzZoy7vq2tDaecckrex/Fm68ml3tra2rwMXQmCIIi+yVeZRBlXCIIgiL7J3zy6II+kCuHzTUrDH3zKNlCUfUAp7HjeefkQeSqTqGtRXCiYRJScxsZGNDY2ustCCDerjg7y6Kw6V199dd7H8WbrKWa9hz/F+lllgblailSamBkeXCJ8kXmUSnpftY1rZZAr29Wqophab0G4D1jtfxQ4fkCJ5PojeRRTQdWSux7Ry+mKq+xx1T0BlZG73ZsSNqA8Sm3QJt1BxVBqX/ftTpqpdpRCSXiUTRFKpLRbK/1e894Pcm4H1gfvEQavHq1wymuUPRDJt5tPHT6CIAiiFEQrjdIDSYV5JZWBPiTUffknecsBlVOC5wr1LaoDCiYRZYcx1mdWHQCYNm0avvCFL2DBggUA+s7Uk229BEEQRPkQQuRlmk7KJIIgCKLYlCKJR+ko1TCy8IBSf0KIPLO59avvv/qhYBJREbLJqvPWW2/hww8/dJf7ytSTbb3VRvRvWvY/dqk6wvYp9Y9m0PdIz5lna5gyyZvxLPwtiFa6aGWPq3xhhqug0WjVja7f0OIYYbl1uGohpS7SNbCAAkkrkrRaR6qQ/A/0MNWSry5v2QK8k6LGgwcVShDcvQapXXigrD5vvz+Svy6/11RQbZRSN4kQLysE9glf9raFpd0/gfsEwfUeUZoopkIpCoH0+1Ortfxt77sepNU1ELyT8s7mVvymEARBEAOUvoNI2aiS+gP5+ywB/UehxAUpk6oBCiYRFSGbrDrvvPOOb7mvTD3Z1ksQBEGUDzLgJgiCICpFdgGhbH2SorO4ZcZI37ekZOOdFG7I7d1HU42BJTLgrg4omEQQFaJfvuwI4FWJeNaqbX1l5WKpTGhB66I0EYdW0pipZa1Kca2TlAJJeRmJoNpIcI93UcDXKeClxPVbGZ3tzeuZpNaJgGeTzuLmffimFE6FwwO16OsoPB0gfew0X6WgAsltewZlkuuzJELLCnD3i0r3V0KgLHzrvU1IfRU53DfBOkLq728MBIUSQRAEQZSTQgJJlVclVS5TWpD8DbqJwx0KJhEEQRAEUTLyzeZGrw8JgiCIbCl98KfQV4PFUSdFZ3LLTHRAKDv/pOD1rXRwKe9sbtS3KCoUTCKIMtP3j1hxfuWijlO6H9GAf0wfChPGvI9D/9sX1yvJXR+iuNHKHFcZFO5ro+Fgrrom5dOjVUxa+aR9evzr/T5I4YokwE4r6zoVFSObW+T6dIVS8NyjPYxE2rrg0CJ32c3clvouUh2LlI9SaP2uf5W3HTpznjqLvhRJzHt/lc4rKUwhVFzVUObscX0kZemXCJKiEwRBECUi3yQPknKrknR/MFNQqXSKpEIDSsG6wj6XCxpCXx1QMIkgCIIgiJKRrzKJunsEQRBE6cjWJ6kURKmUKjm0rX9leMtXmUSdi+JCwSSCqBrK/etW3OOlXnT0lcXN+0YkswQjpRjS3kVaAROyb9BDSR/PVcUgJPOaUh4JvwIqqCRiYB4FlP9Bq9uUKhvWESigcxClTErzRfK8IVIdpFTWsyilklI1MZ7+VsnNnBc4nkd9lHq741cmpSmVMr6BC/hXRSmUPOVT55Wh2pzJrBgqPuU+XuWgt4cEQRBE9ZA5iFSoyoaBZfn8KnXgKJ+sbv0noEQG3NVB9Th7EcRhTt6+IVnVKVDen0eGqD+CtSk3Yyx08pbLHnl+wvMpeO5CPVa4kJPgcuLcBue2Gpbl+CddRthyUv85woYjbBkwERycO6nPwgIXFgQcCDipfUMmXQ/nVt6TW0cfk2yLapun3d62u3Xp//S+POTa6Oupr597rdT1BU9de6HfEOn/UgMTs70vg2buUfdP5vsm+r4sDf7zL1qtJfitqCRciLymw+kaEARB9EeEEFi6dCnGjBmD+vp6TJ8+HX/5y1+y3v+HP/whGGNYuHChb31vby/mz5+PESNGoKGhAbNnz0ZbW1uRWx9GkdVIEZ2SfH2N+jxcEertO1jmoLKqrezIt2+RTwCKiIaCSQRBEARBlAxRwH8EQRBE5bjttttw1113YfXq1di2bRsGDx6MlpYW9Pb29rnvCy+8gP/4j//AySefnLZt0aJFeOSRR/Dggw9iy5YteP/993HxxReX4hQ89B0gqXwGt2hKFaCKproDStSvqA5omBtBlJhyGW6Xr94oAqnbo97WeFO8R6R2T+2q9S3+VPZSQhw8blR7/DXJLQHj7TRTbbnd0ds9w94MPTRMtyUwJM4/pEubYxdOXw9Ar7l12luXoAF32rAzEbLNf83T25Fanza8La2twWF2noXg8Mgo6ZH3vil7h6qUQ9Ki6y6u8Xfl4Mgvfw11+QiCICqHEAIrV67E9ddfj89//vMAgF/84hcYPXo0Hn74YVx66aWR+3Z2duLyyy/H/fffj1tuucW3rb29HT/96U+xbt06XHDBBQCANWvWYOLEiXjuuedw5plnFvEsKhcQyX64W3Z1FZNoI+4g+vpV39A36ltUB6RMIgiCIAiiZGhfg1wneoNIEARROXbt2oXW1lZMnz7dXdfU1IQpU6Zg69atGfedP38+Zs6c6dtXs337dliW5dt2/PHH4+ijj+6z3uxwkM9QrcyqpHzCFjIIVGggqM/9y/LGyUG+17VUCOpbVAWkTCKIEpJZlXS4/Jh5U7Z75nprqPF2ZlIp5rUhtq7T8FSuTZ51TFzXr9VEflUQE/BIPeDfxgIrMnw3+hHKIpQ74Qbc/vqCaqa00iJd3ZReY3rHJvIBKZzwch6Dbn0U99ju9ePeooHOVrpKybtauN9R7p2wKANuv7eS26qc668+Dl+FkvQ4Oxy+I4IgiIFDa2srAGD06NG+9aNHj3a3hbF+/Xq89NJLeOGFFyLrrampwdChQ3OqN5FIIJFIuMsdHR3qk4NClcMFPaMY63MYQj4qpVIPa0v1sfM5TjCgVP4AkxD5BYaoO1JcSJlEEARBEARBEAQxgFm7di0aGhrcybKsnOt499138a1vfQtr165FXV1dUdu3fPlyNDU1udNRRx1VlHrL9bIjF5VS+f2RCCI/SJlEECWgklHvqGOXqk3pLzTCU7sHC/oXtXLFiFiWpNLTs5CyQY+koPwotZB2LUSYv5KnkYKnKY5S1Ua0MZP6SNjR21KNDbbGbUtolaFKpaBiKFiXnnnf7XivcUpVJFLSpOi2RXomBepO+xxyHwWVST7PJP8+pbi3w9RAlVYIVfr4+ZJ/+l56fUgQBFEuPve5z2HKlCnuslYBtbW1YcyYMe76trY2nHLKKaF1bN++HXv37sUnP/lJd53jOHj66adx9913I5FIoLm5GclkEgcPHvSpk9ra2tDc3BzZviVLlmDx4sXuckdHR9ECSgWThTrJLVrMQFEROgTZ+ydVFxzC56CaLdS3KC4UTCIIgiAIomTkG0zKz6GCIAiCyIfGxkY0Nja6y0IINDc3Y9OmTW7wqKOjA9u2bcPVV18dWse0adPw6quv+tZdccUVOP7443HdddfBNE1MnjwZ8XgcmzZtwuzZswEAO3fuxO7duzF16tTI9tXW1qK2trbAs/RDQ7Al/TGglH8wiSgmFEwiiCKQ27Oo8J+x1PEq/ZOY/uBJ2Q+J0JLeh1Vw78gMae56rZZh0H9qpuoLZH7jeiy44akj6npllxEuHG+eOO9qB4zlm/0ivZ1ChI9HT519yD59KZNC941QenHuW+19gKd1xpgIX++WT7UrXZDEQtfrNob3dSrtnaTP1+8fln9dmStIu9xV3//jocq5vqn07xtBEMTAhTGGhQsX4pZbbsGECRMwfvx43HDDDRg7dixmzZrllps2bRq+8IUvYMGCBWhsbMSJJ57oq2fw4MEYMWKEu76pqQlz587F4sWLMXz4cAwZMgTXXHMNpk6dWuRMbpkpeiApB3VS0Y5XRPpbQEkoC+589iSKBwWTCIIgCIIoGTTMjSAIon9y7bXXoqurC/PmzcPBgwdxzjnnYMOGDT4/pLfeegsffvhhTvWuWLEChmFg9uzZSCQSaGlpwT333FPs5odSUjVSuQJKJQr69KeAEg1zqw4omEQQBVBuRVI1E3z49OWZlFl9oa+VVuNIhU/qenN3zHmqUxD0UEJgH+8xA28ygpnfdF16ZyEimysyPHRdRVUBuQ76euuSEqmFqZn8mdmCdYZnaNMEj6u9lPSMpZURqY0BssnyEbiOkZ5J+WYe6U9EZ3YLLS2qW52UfzCJIAiCqCSMMSxbtgzLli2LLPPOO+9krGPz5s1p6+rq6rBq1SqsWrWqwBZmT9mGtJU6oFTiB35hWd7KBwWTqgMKJhEEQRAEUTJkMCl3KTp1+AiCIIhiUHZvpFIFlMoY4Kn2oBIHB6O+RcWhYBJB5EH/9usrvPF+sVG4IiltfaYWRWSpSveGSvkgpRQ7WkUUzA6m1UZeRU14W3k2X2hEFrVs1SP5kvV48DBlEkToNl2nV/+S3tESqY0IUzF51Vp+nyURca3CMqNFEeLGpepgIesC51fQLZ6bKqhaqOZMbwIcguXT4SMLboIgCCJ3qsJYu5gpZyv4cA9ey2oJLgmWZ9+CVcG9cRhBwSSCIAiCIEoGDXMjCIIgSoUQojqCR1Hk8iYtar8qIuxaV+L6Uza36oCCSQTRB4X/Ph7eP1tRz7qUeilKuRRGMAtY0AfJm5kt3P9Ieym5aiNXscFSC6oeHlQz6fqDdTLmqnyC3yYTAT+ksBumgP5AlMonygcp7HCRWdU8CiUWcT2FyoonggoliJBbO8JnyW1H32+Qor23wsrqevustp+Su0oq6lpU8lpx9V+ukBSdIAiCOKzoK7BUpQGkaoSGuVUHFEwiiAiK80dXcX+wsmtTZX4kw4ySAwUy7O1PrZ6+i9+QWwjDXceY4SuTGtrlD/IIwQEWCE65lyowJC698elBpIjAk79M5mFfuZD28Asd1pY+fE0W7eueEOmyX+EfuuZeVp+kOPz8WJrsWJfzHzMjEfcLY6yCEuvsgjvFN8QufOhdJQNuQmmTct+POnwEQRDEYQoFjgqC+hbVQf4phgiCIAiCIAiCIAjisIb+ZCaIMOhfBkGUBIHSKoRKXX/huAoSNTHkrqsQgvtUL0JohQVPK6PHzOsywnVqSTm2uGW5nFLXkQcmP9w9Bnd3EZ51YZN89xFsQ/6TPnDGYwbaxtWUTvB8hXtN3PrcIwbaoq+vEAh+P7q+1PcU/j1mg3u/6PunooqkbKF/92FwxvOayCSTIAiCIIgw8u5b5NiPWr58OU4//XQ0NjZi1KhRmDVrFnbu3Okr09vbi/nz52PEiBFoaGjA7Nmz0dbW5iuze/duzJw5E4MGDcKoUaPw7W9/G7Zt+8ps3rwZn/zkJ1FbW4uPfexjeOCBB/K6NuWEgkkEQRAEQZQM4bom5fYfSdEJgiAIIl8O7z/z8+tZ5N632LJlC+bPn4/nnnsOGzduhGVZmDFjBrq6utwyixYtwiOPPIIHH3wQW7Zswfvvv4+LL77Y3e44DmbOnIlkMolnn30WP//5z/HAAw9g6dKlbpldu3Zh5syZOP/88/HKK69g4cKF+Kd/+ic8/vjjhV+sEkKeSQRRVCr7x081GhFHaUnCRSZ+o21NStXiXe+ouanKeFLWI8RLyXNxmM/I29uoKE8luZdcFZX2Pvp4pSEbP6aAj1SaM3c2/kfR21NKIcdXxq0+6Lvkkt7mSKut8NUVRX+1lRNKFe6hVE7yN8ks3GuMIAiCIIqDgbD+C1EZ9Iuq3PfLrX++YcMG3/IDDzyAUaNGYfv27Tj33HPR3t6On/70p1i3bh0uuOACAMCaNWswceJEPPfcczjzzDPxxBNP4PXXX8fvfvc7jB49Gqeccgq+973v4brrrsNNN92EmpoarF69GuPHj8ftt98OAJg4cSKeeeYZrFixAi0tLTmfZ7k4vEOWBEEQBEFUFJHnkM9KB+cJgiAIwk9/+dO5v7Qzfwqzjcif9vZ2AMDw4cMBANu3b4dlWZg+fbpb5vjjj8fRRx+NrVu3AgC2bt2Kk046CaNHj3bLtLS0oKOjA6+99ppbxluHLqPrqFYO/zuNIMpC//QyyZ1snI9YYCoE7ROUngks5d3jQAgnfU/tG8Tl5N/bnwHC9QeK9FTq21cp3bvJMwVqymkKqy/UrwghbfTXFuWLFHZN3BrV9Qs7nr72qe/H/+8gan1+5HJPFePe6w/0j98dDifPKbdzu+mmm1xvLT0df/zx7vaB7GlAEARBDBQGxp/3UpeUe99CgMNxHHR0dPimRCLR9zE5x8KFC3H22WfjxBNPBAC0traipqYGQ4cO9ZUdPXo0Wltb3TLeQJLerrdlKtPR0YGenp68rlE5GBh3G0EQBEEQFaGcbw9POOEE7Nmzx52eeeYZd9tA9jQgCIIgikU1//lczW0rLvkntRF47bXX0NTU5JuWL1/e5zHnz5+PHTt2YP369WU4w/4BeSYRREGURxVQiP1O+XyUpBJE+8ik+ckwvT0bxUi4144I8fhJ4VcnCZHuu5Tma+T6G+kag/ukdDupff1tTL+8IedXki/BX2fYVY30LBJ6xkM2h3sn6WvBWPR3EPStSqfvse0s4gbyry6f6kiI/LyRyuurJFDNSizOeOC+yY58DLhjsRiam5vT1g90TwOCIAiimAQ8NivOwAkiaTjjQD59CyZwwgkn4Pe//71vfW1tbcb9FixYgEcffRRPP/00jjzySHd9c3MzkskkDh486FMntbW1uf2R5uZmPP/88776tDLaWyaolm5ra8OQIUNQX1+f20mWkYF35xEEQRAEUTbyHeYmIIdY5iJF/8tf/oKxY8fi2GOPxeWXX47du3cDIE8DgiAIohQYqPyf05U+fmUopG9hmiaGDBnim6KCSUIILFiwAA899BCefPJJjB8/3rd98uTJiMfj2LRpk7tu586d2L17N6ZOnQoAmDp1Kl599VXs3bvXLbNx40YMGTIEkyZNcst469BldB3VysC8+wiiYPqHV0l5kP40jEWoMNSGfFxs0r2S3C0eD58on550b6N0XyN//eHDbERg34DfULrJUZkm/3FFSBu9ZyZ1HsHz816zTF5Mqevpv2ba0yr8u+j7e4zGvV9CbqzUqoHijZQN1fubVIgU/fXXX89aij5lyhQ88MAD2LBhA+69917s2rULf/d3f4dDhw4NeE8DgiAIopQYIVN/Pk71U0jfIhfmz5+P//qv/8K6devQ2NiI1tZWtLa2us/8pqYmzJ07F4sXL8ZTTz2F7du344orrsDUqVNx5plnAgBmzJiBSZMm4Stf+Qr++Mc/4vHHH8f111+P+fPnu0Gsb3zjG3j77bdx7bXX4o033sA999yDX/3qV1i0aFFxL1yRoWFuBEEQBEFUJZMmTcKzzz7rWxf19vCiiy5yP5988smYMmUKxo0bh1/96ldVLREnCIIgDkcGbqDncOLee+8FAJx33nm+9WvWrMHXvvY1AMCKFStgGAZmz56NRCKBlpYW3HPPPW5Z0zTx6KOP4uqrr8bUqVMxePBgzJkzB8uWLXPLjB8/Ho899hgWLVqEO++8E0ceeSR+8pOfVP0QegomEUTWVMNb/2poQ25kpRvRSpgIX6LUA9nvcSQ/64WoI6W8lII+Smm+Q4Hjp95eCKR1CnSbA19Jdp5QhSOykvpEeCa5dUSPNU/3uAn6IwHBk0/5BAW/k5B2ZDh29FH7C5X0MAreF5W/glw4YCEZF/tCgMMwDAwZMiSv4w4dOhTHHXcc3nzzTfz93//9gPY0IAiCIIjDCS4c5NPHya7/nFv5uro6rFq1CqtWrYosM27cOPzmN7/JWM95552Hl19+Oaf2VRoKmRJEJMHxS0Q6pflDNX1YVNgQK7c0vEOtMg1/Cxv65j9ucF9dd8gQsojbIjVcrLRT+oFDhuIJb9DHez5RQ9kyXev069z3sDb/9c5nuFt20HC3aNLGYVagBelDLEuVzc1LZ2cn3nrrLYwZM2bAexoQBEEQxOFEOTPFEtGQMokgCIIgiJIh4EDk8e5KZAj8hvGv//qv+OxnP4tx48bh/fffx4033gjTNHHZZZf5PA2GDx+OIUOG4Jprron0NLjtttvQ2toa6mlw991349prr8WVV16JJ598Er/61a/w2GOP5Xx+BEEQRDHI/KJQQvqJ/MnmWVz+rHayb5GHMqlqMvAdHlAwiSCqmNKoOPoz6Wnpo65R5uFvweFzUfv6j+UrE/EwYmVSyORiIJjbkLjgvqkjRm1LDWurviFWlSZ1jSrbjkoiwMHz6LzlapL5t7/9DZdddhn27duHkSNH4pxzzsFzzz2HkSNHAhjYngYEQRADGw4KKOVKdQddeFZBxHRy7VsQmaFgEkEQBEEQJSOYPTD7/XLr8K1fvz7j9oHsaUAQBEF4n0MUWIqmuoNImnz7FjTMrbhQMIkgDivK/wNZGsVF3+cRrTwKmkLLZWmuHaw3aApsBupOrzNo0p3WrpC2F6JWyucNSiZjbcBrEp7JFFkrv7jaJ3y7LCMiyqS1LG3fQqic2qe453G4I4QTYn6f1Y7FbwxBEARBkFIpgv4RSAKUT2jGfmzEfv3oHPsDFEwiCIIgCKJkkBSdIAiCqD4ooJSi/wVYZN8iH88k6lsUEwomEQRRPbiKmrA09GmFA3N/hyC4j1eto5U56fXqNxzRnYug6qcvpZJsYZSnUCZye0D2pUbyl01/k6NVPilVVlDh5S8nCR4z/HtLUxDl0Fai/yOl6PT2kCAIgqg2KKDUX5EG3PntSRQPCiYRBEEQBFEyBHhOwU7vngRBEARBlJL++eJGDnPLQ5lEQ+iLCgWTCGLA0J9/PMNVMn54YFv0Ayb1h23U26jggzUXpVKxfHQyf1+5PQz77iiICFVY1HFTGdy821QNbhX92VuoP7edIAiCIAiCIEoLBZMIgiAIgigZ5JlEEARBVC801K0/IsDByTOp4lAwiSD6BQPjh889y0iznQz7pnYOzI3AsreszlTWVyfCgc701nc7wr6rQtQthXz32qemL7WR108qeDy9rz8YIATLPZuaujaCDQS9DymbNEI4eUrR+6f0niAIgiCI0hLm/5kd1LcoJhRMIgiCIAiiZEgDblImEQRBEARRHARlc6sKSNNHEFVKLpY4QuRWvt8guJqCJxh2siJifWqITdR1EiJoECwCEyBVPt4pF4L15TLlQlQbw+tMP++waxQ1RCmL70BXpr/Hw4xc/t0dtv9Gs0DfZ7lOA0WRSRAEUa0IIbB06VKMGTMG9fX1mD59Ov7yl7/0ud97772HL3/5yxgxYgTq6+tx0kkn4cUXXyy43tJx+PVRsqP/nnfefYuB2hkrERRMIgiCIAiiZMj0vflM/beTSxAEcThw22234a677sLq1auxbds2DB48GC0tLejt7Y3c58CBAzj77LMRj8fx29/+Fq+//jpuv/12DBs2rKB6CcIL9S2qAxrmRhBEhcjDS0arWwRcP6XslSGiz2NqlU52Gdm08sf01F9+Um3NXi2VjRdNKmtbpjLwl3GvQT5+QeQtdLgihMiv80ZvDwmCICqGEAIrV67E9ddfj89//vMAgF/84hcYPXo0Hn74YVx66aWh+91666046qijsGbNGnfd+PHjC66XILzIviwNc6s0pEwiCKJEMBQaIAgO9PItu0PgMg+hSg0vEogeshXcR0QGh9yRW+7kKBNAHphKhf84+vjeNkWR6bzS65dXO2OdEd9Bxu8tbwq/n4jKkK8UnTp8BEEQlWPXrl1obW3F9OnT3XVNTU2YMmUKtm7dGrnf//7v/+K0007DJZdcglGjRuHUU0/F/fffX3C9iUQCHR0dvokYuMg+LQ1zqzQUTCIIgiAIomTI9L25/0fBJIIgiMrR2toKABg9erRv/ejRo91tYbz99tu49957MWHCBDz++OO4+uqr8c1vfhM///nPC6p3+fLlaGpqcqejjjoqr/MiDg/y61lQ36LYUDCJIIjDg6A6JqNKJ1uFkvdtRq4vM4qlUspd8ZRSKQUNjbM5TuY6UytozDmRHWSSSRAEUf2sXbsWDQ0N7mRZVl71cM7xyU9+Ej/4wQ9w6qmnYt68ebjqqquwevXqgtq3ZMkStLe3u9O7775bUH1E/4ZUz9UBBZOIipBPFofly5fj9NNPR2NjI0aNGoVZs2Zh586dvjK9vb2YP38+RowYgYaGBsyePRttbW2lPBWCIAiCIAiC6Nd87nOfwyuvvOJORxxxBACk9aPb2trQ3NwcWc+YMWMwadIk37qJEydi9+7dAODum2u9tbW1GDJkiG8iCKKyUDCJqAj5ZHHYsmUL5s+fj+eeew4bN26EZVmYMWMGurq63DKLFi3CI488ggcffBBbtmzB+++/j4svvrgcp0S4lMLbJt2FJ9KHJ81DKZNjT1CNIwJTprK5EFQX5TIVcrwgUeeX6TiBsiEeVakSpXFL8kO+Sf2NlK9XrhOp3wiCIMpFY2MjPvaxj7nTpEmT0NzcjE2bNrllOjo6sG3bNkydOjWynrPPPjvtZe///d//Ydy4cQCkGXc+9RKEl3z7FqR6Li6UzY0oO/lmcdiwYYNv+YEHHsCoUaOwfft2nHvuuWhvb8dPf/pTrFu3DhdccAEAYM2aNZg4cSKee+45nHnmmaU9MYIgCCINmcktnyAgdfgIgiAqBWMMCxcuxC233IIJEyZg/PjxuOGGGzB27FjMmjXLLTdt2jR84QtfwIIFCwDIF7tnnXUWfvCDH+Af//Ef8fzzz+O+++7Dfffdl1O9BJGJvLLEFrAfEQ4Fk4iy01cWh2xTgra3twMAhg8fDgDYvn07LMvy1Xv88cfj6KOPxtatW/tNMIkC5hnI4tr4sr0BmXPbu+gHS3hZ/3fCVbXVJ+yMUnJEX4IcHqiqbqHqynhV9fUiEVEa+l7K6rY8TKD0vQRBEP2Ta6+9Fl1dXZg3bx4OHjyIc845Bxs2bEBdXZ1b5q233sKHH37oLp9++ul46KGHsGTJEixbtgzjx4/HypUrcfnll+dUL0FkIn/1MvUtigkFk4iyk28WBy+ccyxcuBBnn302TjzxRLfempoaDB06NKd6E4kEEomEu0ypRgmCIIpH3sEkiqwTBEFUFMYYli1bhmXLlkWWeeedd9LWfeYzn8FnPvOZguoliEzkG0yivkVxqb5X68RhR7GyQ3iZP38+duzYgfXr1xdcV3WnGi2F50yFYKy4coxsL03uadiy2jW7DGnlI1NbCrgE2e1cEmukIt8vFeMw+jecJwICAjznaaBfN4IgCIIgwsmnX0F9i+JDwSSi5BQrO4RmwYIFePTRR/HUU0/hyCOPdNc3NzcjmUzi4MGDOdVLqUYJgiBKB6XvJQiCIAiimFDfojqgYW5EyWlsbERjY6O7LIRwsziccsopAFJZHK6++urIeoQQuOaaa/DQQw9h8+bNGD9+vG/75MmTEY/HsWnTJsyePRsAsHPnTuzevTtjdoja2lrU1tYWcIZEGNmISopjrSMyLuZUk8i9RVoRVCkPpVzUUSmBkfyQl/DHd4kK/waz/boOC5HSACVvBR9J0QmCIAiCCIH6FtUBBZOIspNvdoj58+dj3bp1+PWvf43GxkbXB6mpqQn19fVoamrC3LlzsXjxYgwfPhxDhgzBNddcg6lTp/Yb822CIIjDDzLJJAiCIAiimFDfohqgYBJREfLJDnHvvfcCAM477zxfXWvWrMHXvvY1AMCKFStgGAZmz56NRCKBlpYW3HPPPSU/HyIDWUlKdJn8f+Cj91RbhAAi1EPpLynyVyhpSqVUKsynyX+iGTOLpR3HX0ikrcmVLL9zkiT1e/I2yaQOH0EQBFEWBqrzi4H8gzKVRY4myL3t1LcoLhRMIipCPtkhsnHfr6urw6pVq7Bq1apCm0gQBEEUAZF3R7V/dnAJgiAIgigtsm9RiF8DUQwomEQQRFkojz6pD7RCQqmG+o5P5u8J5FVjFKJSKk7GuMwnKoRHAFSGDHW53AsEQRAEQRAEQVQfFEwiCKKssCoYtlRu772ogFAwyFScwFF+uEPeKtYCdfwquD+I4pL3MDcyySQIgiAIIgTZt8jnZS/1LYoJBZMIgiAIgighHPnpDanDRxAEQZSageqX1N9xkN8rUBpCX0womEQQVQIFyrNHZGX/nOmC6gdJXx0I4ZkXv7NReiVSZhPtzGWD9D3kT5sasorrm6qfjObnhxn5vj2kYBJBEARBEGFQ36I6oGASQRAEQRAlhDp8BEEQBEEUE+pbVAMUTCIIoqgElRbFFF5403mmVDDuiiz2z/5I6WSrZqoGolRG2aiL+irhKcj0R/93UUyFUrCGgaDkOezI9+1hBT3ECIIgCGJgYKBfDv3Ku29BwaRiQsEkgiAIgiBKhsjzLSB19wiCIAiCCIP6FtUBBZMIgqh6Mj0wRPZamqyONDAozjXr69qThxIhISk6QRAEQRDFhPoW1QAFkwiCIAiCKCEiz74bdfgIgiCIUtIfrAuIcKhvUQ1QMIkgiOolh9/7/FQw+fggVbN3Ur5j3nPfT0Bkf6WLKR4j+iH5itEJgiAIgiDCoL5FNVCNfw0RBEEQBNHPMU2zwBoEfvnLXxWlLQRBEARBRNF/QgKxWKFaGIH/+q+1RWkL0Z/uHIIg+gVCFC9RglD/FaeuvrYOxPcb0eddzCtS1O9xIH5N/ZT6+npIOVo+ijl5B27b9lxxG0UQBEEQAOjP4CD943o0Njai0L7Fiy++UNxGDWD6x11DEARBEES/4/3330N+oUlprHnGGWcUv1EEQRAEQfRb3n13NwrpW0yePLn4jRqgkGcSQRAlJZefeRHyKffjae+kHA6Yl5dPtXkn5euXBHkdsrwGhSmMhPp/9s5WJETq34wZMwby5nIAmMjuRpMdxLfeequUTSMIgiAGLNXSdyPy4cgjj0RKnWQgl77FO++8U8KWDTzoXxJBEEQxx+b1JwbqeRNl5dChDvUp23tNvjk89thjS9QigiAIgiDS6T+hgYMHDyB7dZKA7luMGzeupO0aaPSfO4YgCIIgiH5HQ0MDVq9eDdmR66vTJ8t8+OEHpW8YQRAEQRD9kqamJvz4xz9Gdn0LGXQ6cGB/6Rs2wKBgEkFUCYzJqboJvgHI9m2AZwCbEBBpapjcxj2TmKY6yU3oFP6dp98f2dwbYfdldd8k/ePfe/GYO3eu+pTpe9FvDg2MGDGi9I0iCIIgBiD05+/hwrx589Sn7PoWQ4cOLXmbBhr0r4kgCIIgiJISi8Xw61//GpnfIMr1PT1d5WoWQRAEQRA++k94oKamBv/v//0/ZNO36O3tLlezBhRkwE0QRFmoKp1IURtTaSPuAoy3vRRkRl58qup+IYrCZz/7WfWJQ5pxe5FvDv/zP/8TdXV15W0YQRAEQRD9kosvvlh9CssmI/sW69evR21tbXkbNkDoP6FHgiAIgiD6LYwxbNu2DeHDEOXyl770pXI3iyAIghhQcJr6nPoPjDH84Q9/QLg6SS7/4z/+Y7mbNWAgZRJBECWl0v5GpHApjEoLlip9/xDF5YwzzkAqna9WJ8k3h5s2bYJh0DsugiAIInuE4BCifwVADjcqff3POussRPUttmzZAjaQTCrLDAWTCIIgCIIoG2+99SY++tGPIiVJl+l6L7jggso2jCAIguh3yGCSU+lmDGgqHUwCgP/7v5047rjjEOxbnHvuuZVt2GEOBZMIgiiIKOWIXp/TuwChZyRHORzR3ysTLOsbQxcLu89ItdQ/OfbYY5Hq6BkABF599dXKNoogCIIgiH7LhAkTEOxb/PnPf65sowYApCcnCIIgCKKs7Nv3IWT02AHAcOKJJ1a4RQRBEARB9Gf27m2Dt29x/PHHV7hFhz+kTCKIAELJHUSFZA/hh83cltQ+2bS58PPytlFLWzlnau74lh1Hxqy1F0pq3LLjfnbVJ26d4d+BXvSvF75tmmCd/opCTwsoaEx1pWQyBRw37GaLuARh1zN1ufw7ud9roK7UegHmqtB0U+QnztX95Mj7yHH0/WSrueOW0fde+v1SjO8idcaF/RRkvBPLTqV/3zTDhw+HfJ/F8d57f6toWwiCIIj+h36O6X4CUTn0d1DpvsXIkSOh+xZ79rxf0bYMFCiYRBABDh06BAAQwqZhNH0gBKCf4XqeTFauPQRRCfL5naj0b8uhQ4fQ1NRU0TaQxwVBEASRL/v27QMA7NjxSmUbQrjs27eP+hYDDAomEUSAsWPH4t1330VjY2PZ3f87Ojpw1FFH4d1338WQIUPKeuxKMlDPGxi45z5Qzxuo7LkLIXDo0CGMHTu2rMclCIIgiGIiFa7A7t27Kx7AyJfDpS/U3t6Oo48+2v1OiIEDBZMIIoBhGDjyyCMr2oYhQ4b064dKvgzU8wYG7rkP1PMGKnfu/bXTTRAEQRAabZ/Q1NTU7/sRh0tfSH8nxMCBvnGCIAiCIAiCIAiCIAgiayiYRBAEQRAEQRAEQRAEQWQNBZMIooqora3FjTfeiNra2ko3pawM1PMGBu65D9TzBgb2uRMEQRBEMTgcnqWHwzkAh895ELnDRKVz+BEEQRAEQRAEQRAEQRD9BlImEQRBEARBEARBEARBEFlDwSSCIAiCIAiCIAiCIAgiayiYRBAEQRAEQRAEQRAEQWQNBZMIosQIIbB06VKMGTMG9fX1mD59Ov7yl79k3Gf58uU4/fTT0djYiFGjRmHWrFnYuXOnr0xvby/mz5+PESNGoKGhAbNnz0ZbW1spTyUn8jnvp59+Gp/97GcxduxYMMbw8MMPF6XecrJq1Socc8wxqKurw5QpU/D8889nLP/ggw/i+OOPR11dHU466ST85je/8W2v9vP1ksu5v/baa5g9ezaOOeYYMMawcuXKguusFLm08f7778ff/d3fYdiwYRg2bBimT5+eVr4/fecEQRAEUSxK1Wc+77zzwBjzTd/4xjdKcg6HQz+w2P2ar33ta2nX/8ILLyzpORDlgYJJBFFibrvtNtx1111YvXo1tm3bhsGDB6OlpQW9vb2R+2zZsgXz58/Hc889h40bN8KyLMyYMQNdXV1umUWLFuGRRx7Bgw8+iC1btuD999/HxRdfXI5Tyop8zrurqwuf+MQnsGrVqqLWWy5++ctfYvHixbjxxhvx0ksv4ROf+ARaWlqwd+/e0PLPPvssLrvsMsydOxcvv/wyZs2ahVmzZmHHjh1umWo+Xy+5nnt3dzeOPfZY/PCHP0Rzc3NR6qwEubZx8+bNuOyyy/DUU09h69atOOqoozBjxgy89957bpn+8p0TBEEQRDEpVZ8ZAK666irs2bPHnW677bb/v737j6myfv84/lI755ihkkH8WOOEKDYSZmoyxiYunFrMqDarpaCrFE22/MNG1oyWlUxZOt3sr36NMVg6HS2bq1BKCmvHcNYglifEVeKvAtmAUM77+0ffzofzAfRwuG/A83k+trOd8z7v+3pfF/fYrl0cwPL8w6EPtKOvkaRly5YFfP0rKipsyR8jzACwjc/nM7GxsWbnzp3+tba2NuNyuUxFRUXQcS5evGgkma+++sofw+FwmP379/v3NDY2Gkmmrq7OugJCZEXdksyhQ4csj2unBQsWmI0bN/pf9/b2mvj4eLN9+/YB9z/55JMmJycnYC09Pd0UFBQYY8Z+vX0Ntfa+3G632bVrl6UxR8pwc7x+/bqZPHmy+eijj4wxt9Y9BwDAKnb1zMYYk5WVZV588UUr0x1QOPSBVvc1xhizevVqk5uba3WqGAP4ZBJgo+bmZrW2tmrx4sX+talTpyo9PV11dXVBx2lvb5ckTZs2TZJ08uRJXbt2LSDufffdp4SEhCHFtYtVdY9UXCv09PTo5MmTAbmNHz9eixcvHjS3urq6gP2StHTpUv/+sVxvX6HUPhoxrWZFjp2dnbp27Zr/e/tWuecAAFjJrp75X+Xl5YqKitLs2bO1ZcsWdXZ2WpP4/wuHPtCOvuZfNTU1uvvuuzVr1ixt2LBBV65csTR3jI7bRjsBIJy1trZKkmJiYgLWY2Ji/O/djM/n06ZNm5SZmanZs2f74zqdTkVGRoYc105W1D2Sca1w+fJl9fb2Dpjbzz//POA1ra2tN6xlLNfbVyi1j0ZMq1mRY1FRkeLj4/2N261yzwEAsJJdPbMkPfPMM3K73YqPj9fp06dVVFSkpqYmHTx40LL8w6EPtKOvkf75FbcnnnhCiYmJ8nq9euWVV/Twww+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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 85
  }
 ],
 "metadata": {
  "applications": [
   "Metamaterials, gratings, and other periodic structures",
   "Plasmonics"
  ],
  "description": "This notebook demonstrates the inverse design of a plasmonic nanoantenna metasurface with permittivity binarization and minimum feature size control.",
  "feature_image": "./img/adjoint_15.png",
  "features": [
   "Adjoint inverse design"
  ],
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "keywords": "inverse design, plasmonics, nanoantenna, metasurface, design optimization, adjoint, Tidy3D, FDTD",
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.13.5"
  },
  "title": "Inverse Design of a Plasmonic Nanoantenna Metasurface in Tidy3D | Flexcompute"
 },
 "nbformat": 4,
 "nbformat_minor": 5
}