{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "50ca8493-e877-4492-bea7-d62366feb273",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Basic MIMO Simulations\n",
    "In this notebook, you will learn how to setup simulations of MIMO transmissions over\n",
    "a flat-fading channel.\n",
    "\n",
    "Here is a schematic diagram of the system model with all required components:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a81e7722-9627-4dfe-8d95-5124bf834c1d",
   "metadata": {},
   "source": [
    "![System Model](data:image/png;base64,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)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa46d4da-d921-49d1-9e8f-2a67ab03c8b9",
   "metadata": {},
   "source": [
    "You will learn how to:\n",
    "\n",
    "* Use the FastFadingChannel class\n",
    "* Apply spatial antenna correlation\n",
    "* Implement LMMSE detection with perfect channel knowledge\n",
    "* Run BER/SER simulations\n",
    "\n",
    "We will first walk through the configuration of all components of the system model, before building an end-to-end model which will allow you to run efficiently simulations with different parameter settings."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da31eafd-c45b-43ec-824d-f1701810a132",
   "metadata": {},
   "source": [
    "## Table of Contents\n",
    "* [Configuration and Imports](#Configuration-and-Imports)\n",
    "* [Simple uncoded transmission](#Simple-uncoded-transmission)\n",
    "    * [Adding spatial correlation](#Adding-spatial-correlation)\n",
    "* [Extension to channel coding](#Extension-to-channel-coding)\n",
    "    * [BER simulations using a Sionna Block](#BER-simulations-using-a-Sionna-Block)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e79b7b0a-6beb-45d3-a95e-e22c3bea3527",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Configuration and Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e72fdc97-805a-466a-a098-113106f8a9b9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:42.219130Z",
     "iopub.status.busy": "2026-08-06T21:58:42.219004Z",
     "iopub.status.idle": "2026-08-06T21:58:45.423984Z",
     "shell.execute_reply": "2026-08-06T21:58:45.422868Z"
    }
   },
   "outputs": [],
   "source": [
    "import os\n",
    "\n",
    "# Import Sionna\n",
    "try:\n",
    "    import sionna.phy\n",
    "except ImportError as e:\n",
    "    import sys\n",
    "    if 'google.colab' in sys.modules:\n",
    "       # Install Sionna in Google Colab\n",
    "       print(\"Installing Sionna and restarting the runtime. Please run the cell again.\")\n",
    "       os.system(\"pip install sionna\")\n",
    "       os.kill(os.getpid(), 5)\n",
    "    else:\n",
    "       raise e\n",
    "\n",
    "# Set random seed for reproducibility\n",
    "sionna.phy.config.seed = 42"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6a999116-9ff6-4766-85f3-acaad6a7ad45",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:45.426576Z",
     "iopub.status.busy": "2026-08-06T21:58:45.426285Z",
     "iopub.status.idle": "2026-08-06T21:58:45.435705Z",
     "shell.execute_reply": "2026-08-06T21:58:45.434739Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import torch\n",
    "from sionna.phy import Block\n",
    "from sionna.phy.utils import ebnodb2no, compute_ser, compute_ber, PlotBER\n",
    "from sionna.phy.channel import FlatFadingChannel, KroneckerModel\n",
    "from sionna.phy.channel.utils import exp_corr_mat\n",
    "from sionna.phy.mimo import lmmse_equalizer\n",
    "from sionna.phy.mapping import SymbolDemapper, Mapper, Demapper, BinarySource, QAMSource\n",
    "from sionna.phy.fec.ldpc.encoding import LDPC5GEncoder\n",
    "from sionna.phy.fec.ldpc.decoding import LDPC5GDecoder"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "651c6928-5663-4c2b-89e8-877b94c14947",
   "metadata": {},
   "source": [
    "## Simple uncoded transmission\n",
    "\n",
    "We will consider point-to-point transmissions from a transmitter with `num_tx_ant` antennas to a receiver\n",
    "with `num_rx_ant` antennas. The transmitter applies no precoding and sends independent data stream from each antenna.\n",
    "\n",
    "Let us now generate a batch of random transmit vectors of random 16QAM symbols:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "63446495-cf9d-442a-8a6d-cfddee569eb7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:45.437716Z",
     "iopub.status.busy": "2026-08-06T21:58:45.437592Z",
     "iopub.status.idle": "2026-08-06T21:58:45.638065Z",
     "shell.execute_reply": "2026-08-06T21:58:45.637034Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1024, 4])\n"
     ]
    }
   ],
   "source": [
    "num_tx_ant = 4\n",
    "num_rx_ant = 16\n",
    "num_bits_per_symbol = 4\n",
    "batch_size = 1024\n",
    "qam_source = QAMSource(num_bits_per_symbol)\n",
    "x = qam_source([batch_size, num_tx_ant])\n",
    "print(x.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c536ec87-40bf-4590-88db-151ae7ac8de7",
   "metadata": {},
   "source": [
    "Next, we will create an instance of the `FlatFadingChannel` class to simulate transmissions over\n",
    "an i.i.d. Rayleigh fading channel. The channel will also add AWGN with variance `no`.\n",
    "As we will need knowledge of the channel realizations for detection, we activate the `return_channel` flag."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "35d7a3cd-e2ca-48bd-a77c-8bc8939f9624",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:45.640314Z",
     "iopub.status.busy": "2026-08-06T21:58:45.640171Z",
     "iopub.status.idle": "2026-08-06T21:58:45.699462Z",
     "shell.execute_reply": "2026-08-06T21:58:45.698437Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1024, 16])\n",
      "torch.Size([1024, 16, 4])\n"
     ]
    }
   ],
   "source": [
    "channel = FlatFadingChannel(num_tx_ant, num_rx_ant, add_awgn=True, return_channel=True)\n",
    "no = 0.2 # Noise variance of the channel\n",
    "\n",
    "# y and h are the channel output and channel realizations, respectively.\n",
    "y, h = channel(x, no)\n",
    "print(y.shape)\n",
    "print(h.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd565377-d54c-49a8-8fe1-6ca7cceedec7",
   "metadata": {},
   "source": [
    "Using the perfect channel knowledge, we can now implement an LMMSE equalizer to compute soft-symbols.\n",
    "The noise covariance matrix in this example is just a scaled identity matrix which we need to provide to the\n",
    "`lmmse_equalizer`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a05fce47-7361-4e68-a490-983f654c1dd1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:45.701778Z",
     "iopub.status.busy": "2026-08-06T21:58:45.701628Z",
     "iopub.status.idle": "2026-08-06T21:58:45.764918Z",
     "shell.execute_reply": "2026-08-06T21:58:45.763803Z"
    }
   },
   "outputs": [],
   "source": [
    "s = (no * torch.eye(num_rx_ant, num_rx_ant, dtype=y.dtype, device=y.device))\n",
    "x_hat, no_eff = lmmse_equalizer(y, h, s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85d71a4f-554f-4e19-905a-6b76e8306d7e",
   "metadata": {},
   "source": [
    "Let us know have a look at the transmitted and received constellations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6339a375-a4b1-45de-9cf6-c88e2e007ca8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:45.767156Z",
     "iopub.status.busy": "2026-08-06T21:58:45.767013Z",
     "iopub.status.idle": "2026-08-06T21:58:45.891146Z",
     "shell.execute_reply": "2026-08-06T21:58:45.890222Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UdICQ24HAinBmaFrrOVIVmt/Z2Yny8nJkZQWHBWdlZeHLL78UfJ3b7UZzc3PQPyMgta0DFzclkiacXZQf55VAskFIhU5X1bbpNTzqsNl85ZoAYPJLRZj75j48vrEEc9/ch8kvFanwZ4Tf2pLD4qmZcCUGr0VXYnRQQIfSpqpcq5q0xPAyOYbyxD+OUGlypEqYnTt3Dh6PB0lJSUG/T05OFhVQK1euRGJiov/f4MGDdR6pD1Lb+qpd/4fEmCi8Nm8c+ieIf5EuvjI8IO2mTKIYbPz8W7gSnKKbjCvBGRY9mrxe4PXPKvGQzLwoKSZelip9URjCrcNFuZnYsyQXGxbk4NU5Y7BhQQ72LMkN+v4F5tmRKJ+B5GWn+d8/d0Q/fR7GZFrd3fjTJ2QBNUZClTCLifE1lGtpaQn6fXNzM2JjYwVft3TpUjQ1Nfn/nTp1StdxcpCazvJ3V2Dum/vw9D+Pob0z2NfEV03MShuOmLFLTmI1qWIwd8Klgvf1Apg7YQh+e4s1En6VoiawJiejrz98vbcQug65iiGzxwzExIy+gkLpL3ePkzzF8RFht2FCegq+qm4RvMbqvLmnkrrTGVV5ZtHR0Rg0aBAqKyuDfl9ZWYlhw4YJvs7pdMLpNL56htwIJj7H+9lmd5Bv7UBlPQq/qlE8plcwD3c4fGYqrxfY3Ak8ifWK30+MO8cNxN6KOkEhJKebMqliMDQ1TrTr8KrC40hLjMbYwUk4fKqR6D3FMHI+5aA0By3CbsOLd4zCQyb4dsyaS6VdvfOy0/zfSRJ/ZWDgUm2LW/fgGTPXZqu727Qu3kKYLsy++OILHDt2DPfddx8AYNasWdi0aROWLVuGqKgoNDc3Y+vWrXjsscdMHmlPtIhg4pKmn9p8rEcSq1wqHPNgt/sWN8edduAOzzxkdGq7yG3wJdVyUYZqK4DIcbpPzOiLaVku5BeVY1Vhz0CZmqbzmmwkRs6nUpTkN+Vlp2HN3ePw7NYvUdN8MbfRleBE8/lOtHVoH2hj1lwuuiEDi6ddrjhghrTuo9E1GWlYm7Tl1ukqzE6fPo1t27b5fy4qKsK5c+cwcuRIXHfddQCA7du3Y/Xq1X5htmzZMmzbtg033XQTpk+fjs2bN6Nfv35UCrPACCY1RYK94E5tyttucIubD7vd93ctF/mDU9IRFem7oRbamZRiwBemvvFzfnOyFsYPo+dTKUrzm/hOHV3dHvz87QMaj9DcuZw0rJ/utUON7gNHy9qkLbdOV59ZS0sLSkpKUFJSgoULFyIqKgolJSVBPq2rrroK8+fP9/+clpaGw4cP49Zbb0VNTQ3uuece7N+/n6pWLoEI2daN5BVcXNyh6Xzcz3a77zotuOHyflg6Q1u/FKnTHfCFl6/adVw3Ldjo+VQCaWANH1yCP5dPdcvoAZiY0Rf7dSgua9ZcqpkfORidyE/L2jRibuXC+plpBGcv33uiFvm7jc3RqXDMQ0SE9HXd3dBEY1t0wzBMGpaqSyFhsTwzAIaYcoyeT7mo6TslNr+lp5uQv7tCw5GaM5dy5of73tY0+8rJpcRFwZUYQ7y2jW4US8vaDMw107s/HOtnZjCcbX1Cego+OPSdoZUACIurEF8nRf7uE8jffUKXQsJCTneuFqQRc2r0fMpFaUCDVIL/4zdmajfIC5gxl4mxDrx4xyjJ+RHzc5GubaP9RrStTZq6pjNhpjFa+dHkQHq21voMLlRBXC2hTnejTTlmzacYy2eORGq8U7Hm29HlwdMflop2bnj/i1OIi7KjVcMAEDPmskmiXBcg7eeqJlzbRvuNaFmbz20rg8cDPLqevLOA3lCVZxYuCPnRkmMdiI0isBHIZHOnb/EKLWDub5uVx5fwv++F/2pVSFgIo2symjWffHC+n3snpYvmRYlRUFqNnJWFQU1hQ+FC/Rdce5m6AYdgxlx6cbFYMh+kypEX0mvb6EaxtKzN6qbzWLZFWDkC9N8XQmHCTEMCK+cnxkThf5+8IajSwPO3jUJ7R7fm930S6+G5oEyHLnLuZ49HnxwUIzrTGm3KMXM+A9Gimzd3AqlvJdvd0vv10bTti1lz2dDWifwi/vqmcpQjqbVtdFduWtYmACLlyMiO1UyYaURBaXWPGnrXvbIbTe0dmD1mICakp2DFDv1MZRmdFxd5KB6P/oEKegocM0KAjZ7PGIcdySGVOUiqTYihxDx7SXw0fp03UtMqIWatzXV7q3hPBnLXqtT1fkuMQWXUzP6uy8FIRZQJMw2QKpBbUFptiKkso3M9Nrl9kUwej++/m9zGLG49BY7RphwOI+ezvdODhgBfT0pcFJbPVOdEl7PmAkPZD1TWS7aJkYsZa7OxvZP3ZCB3rYZez9e7MC87Db+9ZSRio4zZUs38rgNAShyZsmOkIsoCQFQiVSDXBp/t+D+nDTdkPE9iPZ40wJcTiN45J5wpx4wSTGbMJwA0tHbg0fWH8Be78pOZXK2YM2fqpU2bMZd7T/zQI2RcTuWe0LUtFL0368o0vP5ZJd9b6IZZaxMAfndrNp7/6CtZRQ70hp3MVEJaILfku0bDxmQkNqjz6TD40cKJTqoV942LCjJn0lbZQQ35uyt6tM4h9XOFrm0hC0x103nDBZnZ9I13Ku4soBdMmKmEXIsNv80+OdZhSPgtd/oVwgagj1P7KFGzUetEJzHPpsQ5ULz0xqDPcEJ6ClLiohTdk2YCzf5SvcfSQvyVRqeH0M73LedVdRbQA2ZmVAmpFtve0SV9kUWIi4rAg1Muw6LcTEM0L5LT7zm39lGitKDU7CeW88h9ai/cPspfYzPwdbeNGYC391Ypui+tBJr9p2W5ghL0pSqAGJ0eQjvcvie3s4CeMGGmEtICuf8q/8HooWmODcBjNw7DYzcON3Sx0lad22jUmP047TnUzyNVRWRalivshBnQs3UOaVX83r4GA3ElOIN8YaRzqDdMmKmERPudc/WlWFVIX2dWuTxwbToWT7vc8PuGkw9HDlo50ZVozw0iOUQ0EBsVgTYVOZtyhZMWa7CPMyIsLAhzJ1xKpY+c+cw0QMp2PDRVuEu2ldh+tNqU7rJmheYbid5OdJLuyhzdHi9W7BD2UZqJM9KOxVOH49iz07F4qvJaknKFk9o1mBzrwKHlN2H5zJEK34EehqbGmT0EXpgw04i87DTsWZKL9x64BotuGIZFN2TgD3deiWlZrrA5WRid0c9B0h7GqtgALJySTo0THaDbP+Tu8uByVx9E2G1YlJspO1FZaWsYtWtw5R0+32RqvFPWfWmE1v2MmRk1ZFdZTZBvIn93BdISo3HLaOM3JL3Ye+IHUxy8Yr6f5TNHYsUO4ZwXWklLjMbymVlIjovCCFcC6ls7kNLHCVeCeU50gH7/0FObjyHe6UBORl88O8tn4geki3qrPe1K+R8B9OgWH1pBnlZBQIIZuWNyYP3MNMLobrNmYlaLB0C4dxI3/4AxnQqUEuOw44XbR8GVGIOGVjdW7PiKivYZgRjdo0spYn3ukmMdAR3cg69XO7di/bukent1e7yY/FIR9YqXkP/fDGsB6X7OhJkGcAtUS9PM/ZOHYN3ekzDBRSWJmQtbDLH+VDSxeOpwXO7qI6r83D9pKKZmuUw5oVlpwwV865AvwAUAFSHjodCueOVd0R9HvmuiRsliwsxAYaaHJpuWGI2nZ4zELzYc1vR9tYIzOexZkkvFBsHR7fFi3zd1mL/uANzddC7tpBgHoh121DS7Ja81axOhfcPloHUdSkGz4vW3+ybAbreh+JtaAL7AoZzL5Lce0grS/ZwFgGiAHj6G6qbzSO3jxBqRKgVmYkaLBxIi7DZMGpaK3JH9zR6KII3tnUSCDAiuWmEkQhG6tEHrOpSCCxjbsCAHN2e7zB6On9ioCDz5wVHctXY/8ndXIH/3CfznP45gV1mN2UOThAkzDdDLqcuVjNmzJBd/mz9B8fs4I/X7mGkNFsjoR2f4sFzManQIXNxwF92QYeh9lUDrOhSDS5fIn2dc+xgp2jq6gwJYAPMUKrkwYaYBpDkocg/pnJCMsNsQGSH/o3Il+E52Zb/Lw9/mT8DtYwbgpqz++M2METj++5tFT319CWvz0RqdNfGyVLOHoBlmnj58J91+ht9XLrSuQxIi7DY8OysLNpibahIXxV/f1EyFSg4sNF8DSKqAPDglHVuPVBPZyPlCYOVqnounDsei3GF+O/e1w/vh2uHBm1JedhquG34JXthZhsraVsQ4InDTFS4MSo7F+CHJuO6V3VS1eJBDTkZfJMU6NO/LpRZu3rxeL842u2X5o8w6fchpmaIl3HdJrNoH7euQFKGw/9D9RE9aRSqqhJYBoxEmzDSCpAber/NG+qOrqmpbsaqwXFD4hebCyGnn8fzt2UQBAyt3luHNf1UGRUx+8vX3WHBtOiZm9JUU0DS3fomw2/DiHaNM6YEmBRdOzje3Yph1+hBT1vQkMH+LLxjFCutQDnxlx7q6Pfj52wdUvW9CdAQi7Pag5q+B2AAkxjjQ2C6t+NFszmXCTEOkauCFFuS83BVPVAC22+OFx+NFksSC49p5hFZB52PlzjLeHkweL/y/XzojS1GRWgY/dhuQP3esf9745pYPGk4fQspaH2ckzrm16wixeOpwDE2N7fHd6S3rMHSP6PZ4kZYYrSrqsfl8NxZPzcDqC/Vh+RSCG0dcgg8On5Z8r9Q4eiuYsNB8k5FKsiQJ4ZWb99XR5cGI5R+J5rDZbcDXK25GVKRdcow0olXuX5wzAvHOyKDow7QLVUd+t72MOCqRY8OCnB6b1YHKeuwqq8Hbe6uoSlblI3QtjB+SjGte2IWGNvUCbf6kofjtrVcQ39sK61ALhBRPObw6ZwyckXai5HIx3nvgGkwaZqw/mnQ/ZyczkxFrn0BaVUSuhvq34irJZGyP13fd/ddeRk2LBzloVV+w1d2NN35+Few2W49N1G63ya76Emqm4eZ2YkZfTEhPof70wbcWnr9tFB5Zrz4fclqWeIi6FdehWro9Xmw9oj6K8JL4aEzM6BtkOeJcHXKoPSdPeTMSJswohaSzbVKMA6/dNU52QuPJ+jZNr6MRLW37tefcmD1mYI/fc6a30Hp8Yoj5vaZluRAf7UBxRR0ALyZeloociQr3NDBj9AAs/K5R9PRgswFCNiAazKi0olYpC51bTiHgLBdyoTlqlAkzSiFZxI3tnbDbbD02OylzzOBkspY0Q1Ks27pGyy+d2HtxftL/98lxvPrJCdH36RsXhZqmdhRX1BGZkz84dJqqU5kYS2dk4cpByVi2pRT1Ab3QuAomHo+X9/QWbkEcWqNGKRObW7lC0goKBxNmlEK6iEOv49sUA0siFZRW461/VUi+r90G/HziUFljpgmtwsmTYh2SX+AIuw2Lp12O853doqeTutYOLP77EQA9PxM+cyWXrEqLv0yKGaPTMD1bOABqjd1GvRmVNtQoZWJzK0dIWkXhYMLMBEgc2aSLOPA6qU3xwSnpeOOzSqLNfcG16URRkbQilftHKuDu+1E68RdY6HTCB/eZvDZvLFbs+Ip3PN4LY31uWxmmZbmo3kg4xPxaSjpe93bkKGVpidGYc/WlvNGgocgRklZROFg0o8FInZw4pCqXhxZYJYnes9sgGfhht/kE2dIZWTKfjE6E5vuW0S68+a8q0dcmxTpwcNk02Zstp6zUNJ/Hiu1for5VOL8nOc4h+PdAQqMgGb0HoaLPnFI2f9JQTJPZYYGkM4JSn7zWsGhGCpFjTiKpKhJ47CexgZNUovnveyfg2svpL19EithpwG6ziZoFX7xjlKIvMXc6Ka6oExVUXoBIkAF0J6sy9IWkIINcSPaXF388yvAwfDUwYWYQYtGJQuYkOYtYq82uvl3cPGZFhExfUkELas0qWgogmqPIGPqjh4lWDyFpJkyYGYTUyYmrffb2nm9wSUK0f7GSLmKtNrvetmlKBS2ogXQuU+Ki0NDaYckamAzj0CPPLpz8mEyYGQSplv78zq/9/x94QpBaxCSOYvuFXB+2aQajVzKu1GfCzfnymVl4dL01a2AyrE+4JKNbN1zNYig58cjpI8TZwIGebSS41hILrk0X/DvANk2tkfpMAN+czxjN3wjTlRhtmbB8BsNsWDSjQZBED/Ehty08SZ4ZSTQlQzvkRLCGg7mHwdAS0v2cCTMDIa21yIec0GypTZFtmsbD5pzBUAYLzacQLnroqQ+OEfUOCkROZJyUDdxoGznbyMPHL8EwB/YdkoYJM4PJy05DfLQDd721X9brrBplyMyaDIY62HeIDBYAYgI5l/VFWmJ0j6AAPmzwLVwrRhlyZtXQlAQ5gS0MRm+GfYfIYcLMBMSi3AKxcpShVJI44EsS7yYpS8Jg9ELYd0geTJiZBOc/Cw3HDsTKodmkSeIHKuuNGxSDYSHYd0gezGdmIqHZ96l9nIAXqG11W97Jq7SFDYPB8MG+Q/JgwsxkwjXKTUkLG9phEWUMPRBaV+H4HdITJswYukBayskqgS0sokw+TPhLI7aupmW5wuo7pDcsaZqhG2J9mABYxh8olOxutecwEib8pSFZVwDC4jukBtL9nAWAGEi3x4viijpsKTmN4oq6sI9CEgpysVJgC4sokw8LJ5eGdF1Ny3JZ/jtkFMzMaBC9VVO1QosJMXMYaUTZql3HMWlYKnXPZjRK+vb1RuREKurxHQpHEzATZgYgp8N0OGJmkIvUl1ZKySCNFMvffQL5u0/0CgVFDDmbdDgGPgFkgkJupGLgd0itIApXxZoJM51hmqp5kHQQkFIy5EaK9RYFRYjeHk5OKiiURiqqFUThrFgzn5nOaJ342Nv8bkqR8tvsPHqGyGcxfkgycemx0Nf2xs+mN4eTy/EVctG+QuuKK2M3fkiy//v+auFxPKTCFxnu/l92MtMZLTXVcDUPaA3JaXjZllLUtwp3LuCUjIMnG/DMrVl4+N2enaClXhvOprRAAs1eqX2ccCU4cbbZ3avCyeVaYLiSdnzrihNwt4xOQ87KQtF1KvT+fIS7CZidzHRGK02VRYiRQ/KlldogOL5vOU9UekzoteFOQWk1Jr9UhLlv7sPjG0tw11v7cb7L499gA7FyrVEplFhgxKJ9p2Zdgjf/VUm8TkksPOFuAtb9ZObxePDpp5/i5MmTyMzMxOTJk0WvP3ToEA4cOBD0O6fTifvuu0/PYeqGFsnDcsJ4QzeJcIxakkLLLyOnZARGlO098QPyd1cQvzZcEfK/NLX5NuDEWAca2y5uxq4wtiIoFRR8kYp1LW4s2nhY83GEuwlYV2HW1taGvLw8VFVVYeLEiVi6dClycnKwadMmREby33rnzp3405/+hNtvv93/u9jYWD2HqSsk5gQpTVVK6wP4zQO91SxJ+mVMiYtCQ2sHsZLBRZRNSE/BB4dOSyoonL8jHBUJEgUrxhGB1+4fFxa1RqVQIyhCIxWvfr5Ql3FIKdYAkBTrsKwJWFdh9vLLL6OiogJHjhxBamoqKisrMXr0aKxduxYLFy4UfF16ejrWrFmj59AMhTMnhAoWUk21pplM6wu8LpyjlqQgPQ0vn5mFR9fLVzJIFJTxQ5Ix4fnCoI7igWWKrH5a3ldRR6Rg2e02zB4z0KBRmYdW5dsOVNajvrVD9v353j/UKjN+SDLmXH0pVhUeF3yfxrZO7CqrseTeoKsw27hxI372s58hNTUVgE9IzZw5Exs3bhQVZs3NzXjvvfcQHR2NcePGIT09Xc9hGoLSxMdujxeHTpJFOh46WQ+7DUiNc+LZrb03HYD0NDwty4VfTh2OdXsrg4SOK0DoCJ2shBSUpFgH3F0ebD/a04dZ03QeD717CEkh5jernZYLSqvx1AfHiK7dVVbDG0zAZ/4GfJt5TfN51J9zIynGgcb2TqT0ccKVQLfQ18ICAygzkfO9P59Vxm4DpAIVrbw36CbMOjs7UV5ejqysrKDfZ2VloaioSPS19fX12Lp1KxobG/Hpp5/iiSeewAsvvCB4vdvthtvt9v/c3NysbvA6ITd5mG9BivG3fd/ib/u+lbzO6lFLJEidhgFg8ktFQX+Lc0ZgSmYq7r5mKJraO3v8PSnGgfsmpWNR7jBE2G09FJSq2lasKiwXHBO3jwQKMsBap2WhE78QW0rO4DczsyQT1eOiImCz2XDO3SX4XrQLfbkWGD6BnhrnlH3f0PcX+oxIIu65veGdvZW4d1K6pQSaboWGGxoakJKSgn/84x+48847/b//05/+hCeffBLnz/Nv0IcOHcLIkSMRExMDAPj4449x8803Y8uWLbj11lt5X/Pss8/iueee6/F7KxcalrtpKOH+SUOx/NYrdLyD+fBtGLvKalTNbVKsAy/eMSpoc+r2eHsIPzlwZqI9S3Kp3UCUPuOGBTl+pUmLdb14aiYW5WZSPU9SFhg+gZ4U6wDQU9kRIyUuCr+fnY0Zo9P891azDgOhRXkwvdAwJ4xaWlp6DEwsoGPcuHH+1wLA9OnTMXbsWBQUFAi+ZunSpWhqavL/O3XqlMrRm4uYc11LPiw5rShB0kqJ29xpePaYgf4NVe3cNrZ14qGQdAiSIB0xrNA1WOkzcqYzrdb1qsJyTHqxiNp0lNA1xyfI+NJsGts6ZQkyAGho7cCj6y+uRbXrMBCrpf3oZmaMjo7GoEGDUFlZGfT7yspKDBs2TPZ7NTQ0CP7d6XTC6ZR/PKcVLRekGPWtnViy6QheuvNKYi3X6hGSWs7ts1u/RHy0A7Xn3Cg/2yL9AgLMzPGROlEoHVttixtbSk6jtsWt3UbbbB3TbCBaK6qhPnAt14/V/Ou6BoDMmjULmzZtwrJlyxAVFYXm5mZs3boVjz32mP+aL774AseOHfPnkVVUVCAjI8P/9+PHj+PgwYOYO3eunkOlCiM3tE2HTqPw6+97mM34CIcIycKyGs3eq6bZjbve2q/Z+wHm5fiQKClKxma3ASt2fKXZOEOxykbLoYeiGniqr6pt1e29afev6yrMli1bhm3btuGmm27C9OnTsXnzZvTr1y9ImG3fvh2rV6/2C7P58+dj4MCBGDt2LGpra/HWW2/huuuuwwMPPKDnUA1FSgM2ekNrbOvEw+8ewuM3ZqLL4wXgxcTLUpETYCKhoWCymgTwbo8X+UXlWLu3SpexqUWvMk+k/hsSJYUkTykUPS3QtG60YnOup6Ja03weGw5IB4ApwQpVQXQVZmlpaTh8+DDeeecdfPvtt7jnnntw7733ok+fPv5rrrrqKsyfP9//8+7du7Flyxbs378fcXFxeO+995CXl6fnMA2FRAOekJ6ClDgHcSkbLfACWP3JxUi8/N0VSIqJxD0/GopujxenG9pNreumxrxZUFqNZ7eWEefr6Y2a0G05kMyZXCUle2CCISZwOdC00fLNuSvBibkTLsXQ1DjUtrhFXq2OQyfrUdOsz/tfEh+Nji4P/lZchZP1bRiSEoufTxyKqEh6KiLqFs1oJqTRL0ZD0iad22RWbPuS2lOEGK/OGaN5kqyceeN77UMX2s7TwPxJQ/FRaY3uPkfSOSuuqMPcN/dJvt+GBTn49P/O4vXPKiWvNZrAaEkzIY3UJMn3kose7wlctBjcMjoNa/dUBt3DbgMWXJuOpTOyBF+vBaT7OauabxByNeCpWS5LCjOtTaRqzJvdHi+e2kyW3GsUN47oj9/MzJJlLpVrXpUzZ6SnmurGdrz5L/oEWVKsAx6PF1tKTptaTaXb48WzW78kMr/qIXT0Mud6AWQPTOD97D1e+JUbvQUaCUyYGYTc9gtK/BNmIuTzUVvoWE3bivyiE7JDnfXG4/XKSp5XYl6VM2ekysfhUw26+r+U0tTeibvWXgzCMSuyNr/ohG4mPjNJjIlE4Vffi17z5r8q8cRNI0w3OdJj8Axz5FTV5gTAzdkuywgyoKfPJ7Q9yNw392HyS/Lyg5RWI+/2eLFuL30niV9sOEz8/Erb/siZM6kmkYDPnPRtnbZRcloR6iQxIzeqoLRatN6hlWlq7+oxx6F4vMDfiqsMGY8YTJgZBKkGXFXb6hcAb1vEzJgY68Avpw7HtCyX/3da9V9TWo38QGV9UL1FWmhs79S9K7CcOeNqCorh8QL/W15H9J5mY3THZO5z6u2crG8zewhMmBkFSZv05FgHVhWWUxctJkSsw7d8Gts6sarwuP/UpWV7dtL28qHmTZoi3ELxQvr5lTR75JA7Z3nZaXht3jhYJFVLEiOrqRhV4IB2hqSY36aLCTOD4DRgofYQACxhUgykrdMT9DN36sovEhfIcjabwJMDaefiji4PvqiitywU4Hv+VbuOC5YDU9MVWMmc/d/ZFip9YmowQqGhWWkyCrsN+PnEoWYPgwkzo+GKiQYS54zE4zdmUhesIBduL1xHaB4l3QjE2suHhuWv3FmGEcs/IuoeYDb5u08I+hHVdgWWO2evfiJc7d+qGFF8wKpdmbVkwbXp/uAPM+u2smhGgxDLQTnn7sJrn54wfEx64AWIfVVyNgKSfnArd5ZRmQclBdfn7L5JQzEoKQYpcVG4JD4aroRonG1W3uyRZM52Hq225JyRsP+bOt1D9a0WdawEGwBnpB3uLk/QM4bmmZldt5UlTRuAlm0ZrEJsVATaOrp5/6a03YlYmH9Hlwcjln8UVqYyromnUMUQtbUwuz1eXP18oaLOxlYhMToS8yen69oyhjQxPynWgUevz8DzO7/WZRxGEeuIwIxRaXjhjlH+E5mawgZSmN4ChnGR3ugkFhJkgG9jllu6SSrM/2/FVWElyICLfa0SQ0zTfKZCJRyorA9rQQYATee7sKqwHON/v0u3cP287DQsnpopeV1jWyeyBiQiLdHapsn2zm58cOg7FH19FoC6yFstYcLMAHqbk1hKRiXHOoLC+KXgNF+xMH8aQoP1IjrSjvceuAavzhmDDQtysGdJLrEgE/Nh9KZ1yRXT1kugDU2NI7qu9pxbMhWCdkIFlJrIWy1hPjMD6C1OYs4cJqWANbR1EhckFitJFViaaf6kdLnDtQw1zW7YbTbZNS+lfBi9ZV1ycCkRenR2kBOwMzGjLxZPHW7pROtAAaUm8lZL2MnMADgncbjjSozG/ZOGEl1LurClSlJxX6oR/eOJ3s+qyN0ISJLWrbIuHRoKHj1OCN0eLzweL5JiekYqc4Tm9i3KHQZXgvUbCnP+axL0Vp7YycwAuLwfkoraankF83CHA7DZfKV+NncCT2K9zncFFk8djkW5w3Cgsp6oQDLJwpZTkqq+vQMzR7mw45h2zTcB8+YzFDkbgZxCw0atS0D5XM6ZMBjtHd3YdOi0JuPQ8oTAd/oNhRPFy0MKTP/2liw8sv6w4nvTsDa5QCyxiE69evWFwk5mBpGXnYYHp6TDpmOVhQrHPNzpBCIiALvd9987nb7f64kNwMbPfXldSit28CGnJNUl8dGYOrI/2YAJMWs+QyGdLw45PgwuH03vE5qaufzbvm/xvYZ9wLQ6IQidfkNxJUbjwSnp+N32sqAApt9t/woLp6QjNipC9r1pWJuuBKc/olhukr4eMGFmEAWl1Xjjs0rJop1KqXDMg13g07Tb9V3kgZujlgubVINOinGgobUDK3Z8RT5oCcycz0BsgH8+SZNRSeetpqkdxRV1cHd58IefXInHbxymxZB7oMVcflZeq8lYkmIdqk4IXEDNh4e+w9MfloqeaJNiHHjvgWuwfOZIvP5ZZY/msDXN5/H6Z5W4OZs8GAqgZ23OnXCp/3ssJ0lfL5iZ0QDEzD5a8AouLu7Qkx9ngrDbfdfpaYbgNtFpWS78cupwrNtbGXSycslMoCTVoCdnpuLR9dqZymiZTy5YAwAmvfhJUIsRV4ITz866gncuSedtxY6vgkLz9VCcaZlLjnsnDlV8QiAxKQbCrf2n/1kqet0HMsynNM1nXWsHiisuJqaTJOnrCRNmBqB3nhlnNxeC+9sdDuBJHStmVdW28X7hk2IcuG/SUNmJqyTVFZJiIvFFVYOmioIZ87l85kik9HGi/pwbKXFRcCXGYEJ6CnaV1fAm5NY0u/HQu4ewhkfrJa1KEZpjpkcaEC1rk2Pj599iRFq87JMCaRfpUP5dUatpmTqa5vOvxSfx1+KTQRGycnr1aQ0zM+oIZ5L4SOfeSqR+OD39dQDwzr8refPBmto7sbqwHLvK5AVniJksud/dNym9h/lGLWbMZ2q8E7ePHYj7r70Mt48b5N8QpDplP7X5WA+To9S8GQkta5PjbLNbdr6ZGsvK6YZ2Ba8Shrb5BMzpIccHE2Y6EVix4q/FJ3W9F6kfTu/CZQ0CGqiaKgBCtvi0C7Z40mRVOZgxn3ymwX0VdZJafWNbJ/ZV9Ow1JjRvKXHC4eN6QMva9N/nwn/lrEUllhUu0GlAkraBNbTNJ2B8DzkhmJlRB5SaJJSyuRO4U8CODlxc2JtNLMofGCQi1wwhZosv5tnI1WL0fApFKxZ/Qxb0UPxNLSZlpvb4Pd+81TSfx+L3S9QOmRga16bctSg3lD8w0Cne6cCfP/1G/iAFoHE+AXXfb61gJzON0TvYg48nsR6eC63FQjUy7mePx5z8qFCU5vhwtvjZYwZiYkZfv+9NKhVACUbPp3B0J+lTCV8XOm+uBGOTpGlem6RrUW4of2AEX05GX962T0qheT4Bc0ukMWGmMWYVFc7ovLjIQ/F4fH+nAa2rAOjlHzJqPhdOSRcMRiDVcOVownoIfyloXZuka5FkzlLiHFj1s561MyPsNrx4xygNRnsRWucTMLd0HxNmGkOqmfzHxCF49IYMTe+d0bkem9xAd7dvUXd3A5vcdAgyOcnSchHyD6nFiPnceqRa0M+Qc5m0Vp8c60DOZeTCzKzgENrWppx8M6ncSRuAF24fhdvHBlsNOPKy07Dm7nHoH69d+Sra5lPP7zfxGFg/M20prqjD3Df3SV63YUEOPF4v7nprvwGjMhet+m9J0e3x4tebjsjK26GBDQtyBE9XUr2y+ELzSZCbMxWOyJ07tc0n3/yswvK9zPjQ+/tNup+zABCNIa1T1tDqxu+2lxk9PFOQmywthliDzl1lNZYTZIBv3ELCjNPqn91aFpSCoLaDLxccsu+bOjz63iHismHhQmB9StLcR7VJwac0DtOnBS2/32pgwkxjAosKC3UInnVlGh5df9gybdavHJSII981KXrt8pkjce+kdE2qAIhpxtOyXHhumzWVgy0lZ/CbmcIlvvSqrBBht2HSsFS8+ONRePjC6c8qa1ItSqPv1CQFD0mJVfQ6Grlz3EBcO7yf4VU+xGA+Mx0Qq1P22rxx2Hqk2lKbRuYlfRS/NjXeqZkg4yvqWn0hYTO/6IRlTWZ1rR2SbUmEojm1QGi9UrA/6Y6R0Xda+sz0ItZBVvT42uH9dFmLamAnMx7ETFmkCGnTZkU7qmFnqfK2KlpEN0mlO3gBrPs3WasYWjG76zPfem1o7cCj68P7xGZU9F1BaTV+sbHEkHup4drMVHxcdlbyOhobuzJhFoJaJ28gfCYJszctJbR1dCt6nd0GjB+SrPr+JAqAlvXvzICGzYFvvf7FPi4sA0WM6rEFmJN7qhQpQWbkvMmFCbMAhCp3cLXHtIjWoWHTMgqPFzh4skF1RYCaJjLHeYzDjvZOgQQcikmJU9eWRE9CT2y1LW5NW+2YgZE9tgDzck+1xuh5kwvzmV1AqjsvoE3tMTOSVs1Ei5NoaHV3Iayg+fJx+5iBVG4OHIH+Or2beBqBkT22AGtaY/gwet7kwk5mF5DTnVfNSYOLdhTLHQontDiJpvQhc5yft+CpDABioiKC+kLRSrfHa9lT2S2j0zAtq7+u0XdCvnarW2Meuf4y9I1zIqWPE4kxUej2eKlcp0yYXYBUe9JCy8rLTsPiqZlYVViu+r1oRUvbutH1BI0mf3cF8ndXqM4d0xsrmsv6xkVhxexszBit75xKpY2Q9JejlfX7TwXlIdK6TpmZ8QKk2pNWWpYerUv0JCnW0UOocKWW+Er8ANrZ1jnTrBh946JU30cPYqN8oc4ks0BLXyghrGYuWz5zJA78ZqohgkwobeShdw/hhR1lmHP1YEsKMgA9EuppXafsZHYB0sodWjnqrWR6sAF48Y5RvKkGu8pqemikWlcECExEB/gT0VfMzsbvtpdp3qhTLe0XIkETYx2SEZdeKKtMYRRWWrOAdjmOYpBEKq7dWwXggvLn9aKxvUvXMekNreuUncwuIFVMFNA2isdKgSAPXqjszpe4m5edhj1LcrFhQQ5endOzarhW5GWn4bV545AccgJLiYvCa/PGYcboNMydcCnReyVr2JJDCu6LH+OIwHv3X4NFNwyTvJ7zzdKGldYsYIzwlWN6bWrrRFN7F24ROSna4OukQHugDY3rlAmzAMQqd2gdxUNTa3sxbBCv7A7oW52Co6C0Git2lPWIbKxr7cCKHWUoKK3G0FSyckFqKpoogfvi2+02ZPYnuzeNJj2rrFnAuArucj4n7ht08GQDpo7sx3vN1KxLsHRGll9BXPXTKxEdSe82TdM6pXeWTMKokwZ3Lz1al2gJDRqYkE+CgytpVVXbRvR+B6oatBweMZx5lgRaTXpCazYtMRpJsQ4qhJwNxuVCyf2cuO9T4Vc/8P59V9n3WLmzzK8guhJjcL6L3ihdmtYp85nxoKaYqFxCk1KratuwqvC4IfeWg1kamJzqCRs//xauBCdqmt26j0sJnJ/RSN+sHgiVattVVmN4yond5kvO5zA60k7q81TCm/+qxBM3jUBUpJ2qk08gNK5TJswoIFB40hYhxGGWBkbqk+A03ltHu7DtqPJaknrS0Oom6qpAa4WFQPgUPjNSTvLnjkVynFPTbgJyEPs8leLxAn8rrsL9115G1cmHg9Z1ysyMFNHt8eKpzcfMHkYQZneQlauZ0irIAGDZllJ8ePg0EmOi8Nq8sYb4Zo3GyJST+ZOGYsboAbr7a6XQw11wst5nMp+QnmJqnmUfZ2SP+9O6TtnJjCL2VdSZWjCXxpMCjZqpUupbO7H4/RIAPgVh+cwsJMdFmXaq0AMjP69pWS7D7iVFoOl1V1kN3t5bxft9Ij25cb3PIuw2zJ1wqWmuh5d/PBrTs7XvpacH7GRGEcXf1Jp6/9Cwdxo0MJKEaStS03Qej64/hKb2Dur6QqnBiM/LbGuBEJzp9be3XoE1AlHR+XPGSvaJs9uAn08c6v+ZNEpXaxZOSceM0fwpOTTCTmZUYe4iWT5zJFyJMVRpYIE+CbMqKERH2jWPKKM18ZQUoTqEetcepcFaQIJYd/BjZxrx+mfC/fcWXJuOqIBwfDWnXZ8FYCRW7PiKOEglJc6B38/OxozRAxTf1wyYMKOIiRl9kb/7hKLX2m3A/ZOHYvvRmqCAieRYB9o7uok2Y1dijGFRnHLgfBJCfbXSEqMx52r9TDEPTrkMre4ufFhyGvWt2pmBtSpebTRSPf+mZbnwyxsz8eon5ZorIFpXl9EToajopTN8uXpv/qsyKBLTbvMJMu7vHEojJhdPzcSi3ExE2G2w222iQUe/nDocQ1NjqVFilWDzer1WLRkmSHNzMxITE9HU1ISEhASzh0NMt8eL8b/fpdhvZgPw2rye0V3dHi/GrfgfnHPzN9nkwmz3LMmlehFzp4GapnbUt3YgpY8TroSL5qbJLxWJhrwnxjoQHRkRVPIqKSZSVnmhlLgo3DZmABJjHJpF7b06ZwxmjxmoyXvpjVDPP45bR7vweVWDJukRNgD9E5x45c4rsb+yHoAXEy9LRQ7Fpi45dHR58LfiKpysb8OQlFj8fOLQoBNZINy8A9J+N6H0BC0bDxsJ6X7OhBllFJRWKzbRiAklofflrjLbN6YFQl/4wGcMNf14vF7c9dZ+2ff687yxKP/+nCYCbcOCHEuczLo9Xkx+qciwyvk2+EqpbT1SbbkNWA/4hFFKnAOzrxyIQckxSImLgisxRvRkJWQephkmzCwqzADfon12a1nICcKBqSP7Y9Oh7yRfL7Q5ytXMrLjw5T7jlpLTeHxjiez72G3Aq3PG4vkdXykubmyVEzFHcUUd5r65T/Hrk2IdePT6YXh+p3RPtJQ4B34yfhDe+Kyyx0kknBQwuVjxO6kW0v2c+cwoRMh5vP3oGSJhJpSbJeaUDsWqJgk5zwgod657vMAvNhzGwinpeOOCM1+OVmiVQIZA1FajaGzrRFZagqT/p29cFPYsyUXuHz8V7PxupeAZLQWQkdWJrAYTZpTCt2i1qOtH8mUQ8otwfYxo14jlfOHVliPaeqQar80bixU7vpJlfrNSIAOHFjlkta1uyQooz9+ejZJTjYZ0ftcbqyqFVoTlmVkIqRYcWuTfiNVC5H733LYy0Sr6VkJtJfjqpvNIjnNiz5JcvHf/NUiKEW8vkxTrwHv3X6Nb8Wo90aIFzCXx0UTdKYzs/K4XQgWyaW1uaXWYMLMQRvRck6qFSEMVfa1RW47o+5bz/vDn0K68oTS2dcJ+IR/LagSuP7mEKlpS3Sms3l2gtymFNMCEmcXQu+daOGjESuA218VTMyVPV6FwG2pvmDv/+ktwEr9GSNESqyxhhBVCT3qjUmg2uvvMPB4PPv30U5w8eRKZmZmYPHmyLq/pTcgNcpCD1TViNewqq8HqQvJE39A2GL1l7rj1l190gihRXYl/0OrdBXqDYkMbugqztrY25OXloaqqChMnTsTSpUuRk5ODTZs2ITKS/9ZKXtMbURLVRBJVFQ79tpQgp28awL+h9qa5i7Db8PjUTFzu6sMb4DDn6ktVV5QQqvxiheCZ3qLY0ISu0uHll19GRUUFjhw5gtTUVFRWVmL06NFYu3YtFi5cqNlrGNKQRlVZXSNWCmnfNA6+DbU3zp3WVoJQhWtalks3K4Se9CbFhhZ0TZoeMWIEZsyYgf/6r//y/27OnDk4e/Ysdu/erdlrQrF60rTWCIXaiyWf9raQYtLk6f+YOAQ3Z6eJbqi9be6kIM2zCrd5I6lIY8XnMhrTk6Y7OztRXl6OrKzg6KesrCwUFRVp9hoAcLvdcLsv1oJrbm5WMXI6UZp4KRVVJZR8qqdfjkZIzT03Z6dJmnd729yJQSqgrJ7byIeVzaRWRDdhdu7cOXg8HiQlJQX9Pjk5WVDYKHkNAKxcuRLPPfec2iFTixqNVU5UVegm3ZuqDWhtFupNcycEqYBSqnBZAaMUm95Y5ioU3YRZTEwMAKClpSXo983NzYiN5W82p+Q1ALB06VL86le/Crp+8ODBisZNG2o1VhZVRUZv9HfpiRwBpUbhsgJ6KzZiym5vshDoJsyio6MxaNAgVFYGN6GrrKzEsGHDNHsNADidTjid5HkvVkELjZVFVZHDzELaIUdAMYVLOWLK7kPvHkJSrCOopZSVfZBS6Jo0PWvWLGzatAkdHR0AfCemrVu3YtasWf5rvvjiC6xbt07Wa3oLWiReWj351GikKlMwyJAjoJjCJY9ujxfFFXX48PBpPP3hMdEqI6G9EYVKaXHvuaXkNIor6ixZmUTX0Pxly5Zh27ZtuOmmmzB9+nRs3rwZ/fr1w2OPPea/Zvv27Vi9ejXuu+8+4tf0FrTQWJn5TD7M36UeOQKKhbGTw2dSlAOfRSdcokh1PZmlpaXh8OHDuPXWW1FTU4N77rkH+/fvDwqvvOqqqzB//nxZr+ktaKWx6l0Ci8EIRY5FwIiao+GAUOFiuQRadMKpGDJrzkkxXGdfKY2VtLkji3hiGIncPCu+E4IrwYm5Ey7F0NS4Xr1m9ejyveqnV+Llj/9P8D1paR5rep4ZQz1KTISBAis1zgnYgNpzbv9GwMxnPeET8gCY4BeBRDGSG1ATGsZeVduGDQe+xarCcv81VjR/aYHcCjUk1Ld2hFUUKRNmlCNnQ5Cyp/fWjUAMvjlLivVVze8tUWBykeNjkZtnxfkrC0qrsbrweFglUatBy0hO7sSV0ocsAtwqUaTMzGgRpDRhoRDdQFgZnWBI5oyDzZ0PJaXR5CJlUqPF/GUkxRV1mPvmPuLr45wRaHV3C1p0/nL3OCTGRBG954YFOaaezEj3c9bPzCJwGustowcAALYfPeMPoSWt+M6aAl5EbpV874V/T394DB8etm74shqMajjJeoH1RG6X73hnJP48b6xo0Fe4pe0wM6OFEDLvzLl6MLE9nc8ObsXAELVjVuqDqG/txOL3SwD0PtOjUZU6WBJ1TwL95yTUNLuRHOfEniW5gt8T7j0fEnhPL6wVRcqEmQko2YjFMv0DHeSkcBvBzqPVWLalFPWtHf6/0b5Ja5EXo8VGGM7+G741uqushui1e0/UqlKMWBI1P5z//KkPjqGxvVPy+u9bzveqnEkmzAyGbyNOiYvCbWMGYFqWi/fLT2Lekcsl8dFYubMMr39W2eNv1RRv0lpVV9diIxQrKWbF0y6HUFBMaDUJIfJ3n/D/P5+SITU3Vkyilvt5K10fedlpiHc6cNfa/ZLXSq1xbl8RwmprmwkzAxHaiOtbO/D23iq8vbeK98uvZVgutxHUtZznFWQcXtBXqVzL6upSGyYpfKY1K1dUEFqjpIIslFAlg2RurFa1Ru7nLed6PsGRk9FXE2GvxGxM89pmASAGQRpwwJ2KAjPvtfINcF/95TOz8NttX0peT5uTXcvAALGqE0rgPiMlFRX8tfYOfYe1//rGtACTbo8Xz279UpVwDyUwMGTnUfK5UVO1xsg6g3I/bznXF5RWY/JLRZj75j48vrEEc9/ch8kvFWFXWY0mFVNqmuX5JmmvFsJOZgYh93QVeMKoqm3VZAxcblpiTBTqW8k0bZqc7KRjqWlqR3FFnaQZRCiHLznWAS/knUaqatsUnRzFcgON1njzi06gptktfaFMOCVj2ZZSWXOTl52G3BH98bfiKpysb8OQlFj8fOJQREUK6+BGnhzkft5yrt9VViNpTudbuylxUVgxO1tS2OcXncAbn1UQPecl8dGW6DnHhJlByBEKgSeMCekp2HDgW1X3XnTDMEwalurf1LeUnCZ+LU1OdtKxrNjxFXFAi1BSLwDsq6jD3oof8N//rkJrh0f0nhs//xbjLk2SZbaRynMz0ndZUFqNVYXHdb1H4GcSCqlJ6609laLmOyO7Vcs105Fev++bOiLBsWdJLjwe74UALp/iVdfagRU7ymC3Q3COntp8jEhRCzRXWqHnHBNmBqFEKHzf4lscarTllDgHHrsxM0ibJR1LH2ckVU52Uj9X6KZZfaG305/njcP0bP5qFKFfQLnVyaubzuOh9w4SXft9y3lZeW56a7xSgQBGwpm+CkqreUPGhQSTGScHuSkEpNcXV9QRCY78onKsLiwXFN6vzRuL5DgnaprPo/6cG981tGHdv08SjSHUXGmFdAkmzAxCScDBJfHRqhdHfWsnrntld5A2O35Icg/HOh+REXQ42DnEAgNIeHTDISRER6Kpvcv/u8BTG+ds31VWg7f3VskeX6u7m+i6S+Kjic3ORmi8etT9U8qK7V/CGWHD0/8s5f27kGAy4+QgN4WAXKElW9nr9laJRjg/sv4w4f16khIXhedvv2iutEK6BAsAMQg5AQeBmfdaLI5QB+3Bkw1EX5fGtk7sq6hTfX8tEQoMSIlzSL7W60WQIAMuzs3KnWV+Z7sSQUZC4OcqV0khddYrgSa/aH1rJx5Zf1jUDMYX6GPGyUFuBY0J6Sn+up9CJMU6MPGyVKL7k+SaKWXZzJFBJ18rVAthwsxAhDbiULzwRRxG2G0YPySZaKOWej/gYqkh0uRXAHh0vflRSqHwdYNefssVit6LK1P1+meVhpxOOLONXCVlxfYvdfscaPKLymHviVp/pCLpM2gVTAWIK6hKUwhsAK4mEBxSQlEtofNphZ5zTJgZTOBGfP+koYKCasWOMjy/oww5Kz8hjjwU46Kd/YSsk0djeycVYbehcH6u2WMGYmJGX7gS6N6Qk2IdQX4eTtMlpb5Vv8+BpO4fXQZnH/m7T2DSi5+goLSauHbhqsJyyTmUE9ovJ4XgQGW9ZOBFQ1snPq+qx5yrLxXMIQOAeyYOFX0ftTzxjyM95on2Jr+sar7J7Dx6RpVtWy5JMQ7Z5onAKuUAnX2+Oro8GLH8I9Ba+/e9+6/BpEyf+YjzzRWW1WCtDMVCz2rxQgEXVmHN3eMAgKhzROgcBiYmcz3UAs26JKH9JFUxVmz7kujzFvuOJjgjMOXyS7CnvFZXMyPgmys+IWV0BRDWnNNAlH643R4vVuz4yoARXkTJFyAwemrj56eozP4/eLKBWkGWlhiNHJFwc7sNRGOnIfyZVp7afAwHl03DL6cOF00x4EuPkIpaJQntl6qBWFBaTay4iH1Hm93d2H7UOCsJXwQorfUemTBTiZokTZqiyEjgK2hMS7FdmoIYQpl1ZRoi7DbBPCjONjIlMxWflddKvp/Wz0pTaL5SuGCloamxRNd/33KeuJ+d2tB+q86v1ZQn5jNTgdryLjRvwKSEBpcYVUqo2+PF3hO1+MPH/4c/fPw1vtcx2k8tW49U49z5Ljy56ahoHtSXZ5qJ3k/rgA2rKVVCFH9TSzw3qXFO2f3slJZ3s/r8WmWfYiczhWiRpGnVKLJQjDJDBuaB/f2L73DO3SX9IgqobjqP7Gc/Fr3GC1/1hpQ4BxpaOw2tFl8oI7qVbmzEFfdhgyIBQ7Kxh7odapraZd+HJqyyTzFhphAtkjS5L56VtbZA9DRDyq3IYVVuHzMQb++tMqxafLfHiw9llDejmWsu+KpJKu7XnlNWVUdoYw9UtP5ZciaoCk1KXJSie9FASlwUPB4vtpScpirgiw9mZlSIFkmaEXYbls8cqdWQqCTUDKkEIXNuODI1y2Vo+POBynpNUj9o4MlNR1FQWk0UQi4330wsKTiwuv3be6t6lFNrEKlJSTvnO7tx19r9/qr9Vz9fiJ0GBqDIgZ3MFKJVeZfEGOtqbaSocSTLqWFoZQJNiBF2G2/xYz00Yqv4Q0g42xxsBRCaw26PV1bxbrFTMUkQiZXXbltHcIm2+tYOPLL+EBZ+l46lM7JMGhU/TJgpRKtuuMXfSEev0YycGolKNk6rO89J8QKYcaEIslDxYz2wij+EBG4d/ubDUuSO6I+oSDvvHMot3u0S8Pv2FkWLj9c/q8SVg5IwY/QAs4fih5kZFaJdeRc67c+kuBKjsXjqcKJrlXYO6C2s3Vvlb8BoVMUVknqBVqOutQM5KwsF55B0Tf3HxCHYsCAHe5bk8pp3e4uiJcSyLaWGN5AVgwkzFWhR3iWSUmeqFHHOCCyemok9S3KxKHeYbkVIw+nkQIqRnXt3ldXIakJqFcTKf5GuqZuz0zAxo6+gQtqbFC0+6ls7qepEz8yMKhGzzUvR7fFi4+enDBil9rS6u7G6sByXu+KRl51GFEGmxOejpHWO1TGqc69Vk3nlwDeHWrkIeqOiFQpNAp2dzDQgtOgt6eaTX1Sua2sPI+CiFPUqQiqndU44wQXNrNp1XLfk83A3kwklOmvlIpBbLDocoUmgs5OZSfja1PfMy7ISoVGKak6pYnCCsjfkmYWSv/sE8nef0KUGJk1atZ7wPafQmhIK9uDDl1qThUfWW7dAsxqSYh1UdaJnwswE9DTvvIJ5uMMB2Gy+mn+bO4EnsV6Xe3EEbhZ6ReFxgnLVruPI331C8/cXwoz55EOPGphGa9VmzaXQc2qhfCWbmBBt9tqkzVLCzIwmoJd5p8IxD3c6gYgIwG73/fdOp+/3emLUphhht2HSMLIuvFpg1nzyoUXyeSgkjV+1cteZNZfJEqcHpS4CDrNOtzSszYY2ugJAmDAzAT2+ABWOebALfJp2u36L3OhW6aRNGNVi1nyKoabYbSgFpdW47pXdgtU/uPnNu8Kl+l5mzqXeQUOkilwfp3ZGMJrWJk2maibMTKDi+3Oavt8ruLi4bSG7PPez3e67TmuMbpVuRECImfNJgtoNhKQ8WGxUBOKiIrCzVF0RYrPnslHn00NDq3TytSvBibioCE3uZ/Z8hkJTAAgTZgYQ2BblF+sP4v8Vaevz4ezmoYubg/vbHRrnxi6emmlKDzOhyEmtMGs+SVGzgZBWrWjt6EZrSCkjJdAwl3qdHkib6865+lKcbVFW2DgUGuYTUJc7qhcsAERnjKj2LrSwlV5HQlpiNBblZmr3hjIJdd7Xtrg169ptxnwS3Q/qW8AYHY5Pw1ym9nHq8r6kc9mlYVoFDfOpVwcHtbCTmY4YVe3dS/hdIb2OBNoWckObdpXJzZhPKbTaQIz2cdAwl0/8vUSXairkc6ndw9Ewn3p1cFALO5nphJFFSDd3AncK2NGBiwt7swZVixJjIvHSj0ebvpD1PPEaOZ+kyMl/EsNoHwcNc3m22a15WgNAPpeJMQ4kxTjQ2K7+Ic2cz/+YOAQ3Z6dR29PM5vUaqV8aQ3NzMxITE9HU1ISEhARTxlBcUYe5b+4z7H6BEU6Bi5z7dD0eIKNTfQ7Kew9co2l4fGhXXpIvCknbDbUYNZ8kLJ85EvdOStdkA+n2eDH5pSJDTY00zCVnot2zJFezjZibS7FSa3YboHXxFrPmc8OCHEM6OYRCup8zM6NOGG3OyehcD4+H/29aLm4ukEWLEkuBTQ255n9SFeONOvEaNZ8kpMY7VW/AXBDS9qNnMOfqSzUaGRk0zKWWaQ0cgZG1QuhRVN6M+aQt2IMPJsx0woyQ1YzO9djkBrq7fYu6uxvY5NZ2cefvPuEXPONX7MKrheWKhJqQP1GqYryRAQxGzCcJatdSQWk1Jr34iV9pWFV43PDqDbTMpdZKZl52Gh6ckq7pe5Jg9HzS5iPng5kZdYLEBBEuJMU68OIdo4j9EVKmLjGT0JaS03h8Y4nKEVsDLUxjBaXVeOjd3lk7kA+tTWVmmG2NJDnWgZUyvtt6wMyMJtObqr03tnXiIRn9t6ROV2ImIZqSNPVEi+jFbo8XT20+pt2gLIxeeVHh2nng5mwX3nvgGux/eioSY6KCXAuBebN6dXRQAotm1BGhytxpidEYnByDA1UNJo5Oe0j7b5Gaeviu4zojh2NDyUC0iF7cV1EX9vNEgp55UTSVc9IKG4CSU424dfQAXPfK7qC9i+tKHriu9OjooAQmzHRGqDL323u+CTthFtgORgzS01VvOYWF8psZIzB/8mWqN97ib2o1GpG10SqtgY9wXKOcZYSvtQ2fcqRHRwclMGFmAHxtUfSqSmA2JJqqmk6/Byrrw/60kTUgUaMTRLgbuMVJinXgtbnjkKOgGj4pvcVSIAZfZ3QlKTdqYcLMJFyJMWYPQRdINFXOn/jwu4dgQ3B9BCmTUE1TuybjpJnac9rU8ZuY0dfQ3m+00djWCbvdRn0UXjgQ6Oduau/gda3obYpkASAGEug49Xi8cCWEj4lCroNdqFiwWKmcgtJqzeov0oxWpqucy/r6fRy9lY9Kq3UNUugNlgI57CqrUZRyowXsZGYQfOWXwmWjUepgl9Pp14iqHzTQxxmJmqZ2FFfUqTbNRNhtePGOUb06NP+vxSfx1+KTSImLwu9nZ2PGaG1PBuEYAKKGf5ac4f2O8pkitYblmRmA0EbMmdisYnO3AYhzRiLCBjSd7/L/Xm8TQrjn8gih1bwWlFbj2a1lqGnuXfPHx8Ip6Vg6Q7xqhxyMLltHKzYAyXEOwWavgcjN9WN5ZpQgVn6J01aiI+1474FrsOiGYQaPTh5eAOfcXfjz3eOxYUEOXp0zBhsW5GDPklxdbeHhmssjhVammbzsNPzxJ1cSX8+ZjPPnjFF1Xxp5/bNK7Dx6RrP3M6rzOc1wz377mIFE1+t1mmXCTGdIEoRrmt2w22zI7N/HuIGpoPacGxMz+mL2mIGYqGOkGIcVTTlazAinAD23rUy1z6eWoCNyIM/cmoVbxgzEmrvHISUuStW9aWPZllLNfGjhXhwhzhncITsp1tHDPcL5uadmuYjeU690BuYz0xk5CcJWyVmpqm019H5WmZdAuK0yNFpTyfuQ5u+JQTqHfeOi8Pzt2f6Tdl52Gto7urH470cU35s26ls7Vc9nIELFEcKBSJuvU0btObffpw2A18/d7fEqTrnRAnYy0xk5CcIT0lPgSqA//2zDgW8NLWFjZVNOYow2+qLa0ynJHNoAPMfjowvHNBI9Cg7vWZKLDQtyqHcXyKHpfDe+qGoIssJwebOhlhmxU6oR3al1F2YejwdFRUVYt24d9uzZI3n9oUOHsGbNmqB/69at03uYuiG1iQSGtEfYbZhz9WAjh6eImma3pq00pCD5ktCK3W7H3+6bgKQYdZGrak+nJO1KvAB+sbFnV2ZuDYcTepz2uU1+8bThllW++Fj370pi5VVJyo1W6CrM2tracP311+Pee+9FQUEB7rzzTtx2223o6uoSfM3OnTvxzDPPoKSkxP/v2DHrFkuVq610CfQpog2j/VhiX5I/zxtH7eZR39qByEg7XvzxKNggX/hqWSA3LzsNr80bBynFONRHRyIItUbPz1Lv3lxmzJeeNLZ1ylJeA0+pRgWJATr7zF5++WVUVFTgyJEjSE1NRWVlJUaPHo21a9di4cKFgq9LT0/HmjVr9ByaoQjZ1PlrxlkjU8IMP5ZYXprdDt6KIjTwUWk1br4gSH63/UvUNJMFY+hhmkmOixJtGCnko5uW5cLiqZl4/bNv0NbRrclY+LhxRD988vUPsj5DOZ+5Dcb05uK+809/eIwoXJ125CqvfCX89EZXYbZx40b87Gc/Q2pqKgCfkJo5cyY2btwoKsyam5vx3nvvITo6GuPGjUN6uvHN77SGNEF44mWpyN9dYdIogV/emImNn3+Ls81uU5y4Ugh9ScQ6FMy6Mg1vfFYJwBxBxyXu8iXJp8RF4bYxA5AYE4UNB74NygXTo0Cuko4FfAn/WisNaYnRWD5zJHGFFy4HDwDvZ37LaBc+OHQ6SJAYXd09LzsN7Z0eLH6/xJD76YkVgrB0E2adnZ0oLy9HVlbwcTsrKwtFRUWir62vr8fWrVvR2NiITz/9FE888QReeOEFwevdbjfc7ovabnNzs7rB6wSJtpKT0de0JGobgPe/OIXf3pKFR9cfll030WzEFIaxlyb32PT6OCNwzq3fKSMUvs+0obUD6/ZW4S93j8Pep3J1L84qt2OB3pVXpl/RH/f+KB0T0lOI8wmXzxyJeyel++dG6DN/6uYsw4vdhkJasi6FMOHYaMxWXuUgS5h9/vnnOHjwoOg1s2bNwoABA3Du3Dl4PB4kJSUF/T05OVlU2MyYMQNPPPEEYmJ8EVQff/wxbr75ZkycOBG33nor72tWrlyJ5557Ts6jUIuZJYg4E1NynFOGWZQuxE5uoZteTVO76SHnnJB4avMxxDsdulZ4B+R1LJBK+NeC/ZX1+PNd4xFhtxGfGlPjnUFzJPSZm2HqCoV0vv/3yRtw8GQDvm85j/KzLaZaZwLHBtCrvIYiS5hVV1ejpKRE9Jrc3FwA8AujlpaWoL83NzcjNjZW8PXjxo0L+nn69OkYO3YsCgoKBIXZ0qVL8atf/SroHoMH0x8VKERedhrW3D0Oz24N9q/ERdnhhU1XnwXgMzHNHjOQuG6iVQjd3Ior6kwcTTCNbZ24a+1+3U1hcjoWFFfU6Z43xQUXTMzoq1mfOzPajwhBOt9RkXb/2iyuqKNCmFlBeQ1EljCbNWsWZs2aRXRtdHQ0Bg0ahMrKyqDfV1ZWYtgweXkY0dHRaGgQbmTpdDrhdNKfnyUHIZMZAOQXncCqwuO63ZvbLGjQbLWCb4ObkJ6CpBgHGtulzTuOCBs6u6XPIzdl9cf/lJ1VPE4jGh2SBiQZFbHK3Yc7xYgJUKlIRD7/ntmdkOUFgEmf5gDAGWlHZ7dHNJhHLpywnT9pKKZluSynvOoaADJr1ixs2rQJy5YtQ1RUFJqbm7F161Y89thj/mu++OILHDt2DPfddx8AoKKiAhkZGf6/Hz9+HAcPHsTcuXP1HCqV8AmTbo8XGz//Vpf7Wck+LgexDe7eHw3F6k/KJd+DRJABwPD+8aqEmRHVxQGygCQ1Tn8bgKhIO9wEuSaBytOsK9Pw+meVgtfOujJNcE6E/Hs0dEImDQDjlK4Z2S6s3Vsl+H4k8ypGH2ekr0ODzgFHRqKrMFu2bBm2bduGm266CdOnT8fmzZvRr1+/IGG2fft2rF692i/M5s+fj4EDB2Ls2LGora3FW2+9heuuuw4PPPCAnkO1DHoV3bWafZwUqQ3usRszNb3fxIy++ODQd6JatRRalbCSQurkTXJC4INbPat+eiWe/mepYDBTqPLU7fFi6xHxospbj1Tj13kjeYWAVEFvvRUEKaTmm0/pstsQdPpyJThxvsujOkDsDz8ZHXZuBF2TptPS0nD48GHceuutqKmpwT333IP9+/cHlfG/6qqrMH/+fP/Pu3fvxk9+8hPU1dUhLi4O7733Hj7++GNER9MfGmoEWpl+QitSGJGhbzQkAQz/XVyl2f36xkUh57K+mhWeNbvAslTCvw2+liqh1UG4tTRj9AC8eMco3nngU55IFDVOyIdCUtBb6LU0wCldoc/ANeiaP2koNizIwR9/OkaVIEuKdWDNhe+5UFkqq6J7oeG+ffviiSeeEPz7LbfcgltuucX/s91ux+23347bb79d76FRiZTzWqt8j9fuGge7zRY2WhkfJBsc6cZAEjq9YnY2Iuw2QR8Jl2dGek8acntI/D2/zhspuGbl+IuU5MBp8VqzITlVflRag9/MzMJ2wvY1ob7gpFgH7vtROhblDgu77zkHq5pPESTOa6Wmn0C4E0S4LmoO0o0rKcaBpvZO0dDp5TNH4tH1hwXnfOGU9KAuxmIBPPu+qcOj7x0SDDyhzXcp5e+RMp+R+ovURDNqFQlpBqSnynf2VqKBUBF6bd442O3hrayGwoQZJZA6r8VCfUmZPWZA2C9sgHzjum/SUKwuLBcNnc7LTsNf7LYeykZKnAO/n52NGaMH9HhfoU1+0rBUvPjjUXj4Qi6hFRLT1Ua2CgUzBQq48UOSFbcQkZM/RxukShdJdRTuOfXOV6QRJswoQK7zWm3/pGmETfSsDukGtyg3E5e74iVNYaQnDBLkhmuHG0JWCK70mNzqM3Ly52hDq9Mi7c+pNzav16vUWkUtzc3NSExMRFNTU1CwCa0UV9Rh7pv7JK/bsCAnSLsN1WzrWtx47P3DorknaYnR2LMkt9csdu7EC/BvcIFBL2Yk29KU4GsUQlYI7qkfnJKOrUeqFeWK0ZhnJkW3x4vJLxWpch0A9D+nUkj3c3YyowClzmt+048XizaW9Hhtb9Xa5JyAzEgSD6fEdBJIIkz/cfA7LJuRhYa2DqTERcGVGEMs5LU8PRuFWtfBohsyMGlYP+qfU2+YMKMArZzXBaXVeP6jr3n/1lvMV3xYcYMLV0jC7+tbO/Grf/hqZnKnDTmflRUVBDWug8z+8ZZ7Xj1gwowCtHBeS1U3Xz6zdwoyDitucOGI3NB4Gqp3GEWo0lXb4iYK+qAxQtMMdE2aZpAhtxt1KGKmG+49VuwoI259zmDohdyNl1uxod2vw5XAROZ7J6WLdlDXsgt5OMCEGSVwZgaXQDUFMa3U6tUPGL0Hzgohx8DbW9evWiW3t8HMjBSh1Ldj5eoHjN6FmmCH3rh+9UrhCMcoWibMKEOJb0duAEk4LeRwepbegtJgh97qG9I6gMmK6QskMGEWBsgJIAmnhazlszChaCyBG3RNUztW7PgKDa0dlqveQYIWa0urACaa2+SohSVNhwkkycEARJNVrbSQpRJv5TxLOAl4qyInud1K0LS2uORsodMwpzTQVlSBdD9nASBhglQAybQsl2SyqlUixkgSb0mfRaj1BqepFpSK99diaIOaAChaoW1thXugGDMzhhFitvXiijrihUx7PpacL6XYs1ihoWNvIpyS22lcW+EeKMaEWZghZFsPp4Ws1bNoJRQZ2hEuye00ri0rt8khgZkZewnhtJC1epZwEvAMuqBxbUnl+Fk9CZsJs15COC1krZ4lnAQ8gy5I10xtixtbSk6juKJOd391uCdhM2HWSwinhazVs4STgGeQ0+3xoriiTlchQlLpxG7zNdx8fGMJ5r65D5NfKiIKClEz/nAMtOFgofkWR24OC02hwmrR4lm0CAlnOWrWwcj1L7S2pFg8dTgW5Q7jXUNajd9Ka5Z0P2fCzMIoXdhWWshSaPEsajaIcFIOwh0tcxPl3DN0fdhtEG2gCwCuBCeenXVF0HjMGD8NMGEW5sJMquXLfT8agkHJsUjp44QrwdoCywjkCsVujxf5RSewqvB4j7+F++ZiRcxMGA5cW6RtXbgxcWvIqgnPWsA6TYcxUi1fAGDdv08G/azGFFHT1I761o6wFox8IeFCAq6gtBrPbv0SNc1u3vdiOWpkkCoQWpy+zQyVD1xbW0pOE7/OC+A3H5Yid0R/HDzZQF2oP20wYWZBSLr1hlIts/Yan3mEozeY0fiePyXOgbGDk/DJ1z9Ivp5tLuKQmme1MuPSEiovNzK2rrUDOSsLcfuYgUTX9+Y0EhbNaEHULFihMk+BEVKvFpbzluHh4ARjuJZ6EipDVN/aSSTIAunNm4sQpGWetCwHRUsahpJ+bvWtnVi7t4ro2t6cRsJOZhZE6YLlTgurdv0fJg3rh/FDknHwZAMKy2rwYclp1Ld2ynq/cDSjkZhw5dCbNpdujxf7vqlDcUUdAC8mXpaKnIy+QeuDtMxT7oj+mpaDktNZQk8C+7lpjd0GjB+SrOo9rBwcxoSZSahZNFJfTCnyd1cgf3cFUVSVEOFqRlNiwhXCleCkJkdN702qoLQaT20+hsa2iwpR/u4KJMU68OIdo/wmQVLf1fx3DmjqIxJrCmp0nmVedhp+OXU4b/CQGjxe4ODJBkxIT5H8rPnWw66yGktH5jJhZgJ8fgBXghNzJ1yKoalxkpuNmm69gWiRK6qVGc0IjVDsHtzfPtLQdHq+y4NdZTWmbwR6pw8UlFbjIYGTRmNbJx569xDWXPDVkq6XPSfqiK6Ts/706tpMSuD66+z26HKPwrIa/OrvJaKfNd96SIp1BCkiHFbqc8ZC8w1GKqSeg0S4iQVpGMWGBTmqT2ZG5GqJ3QOALvNIQ4i+3rlJ3R4vJr1YhJpm8blzJTix96kbcaCyHnPf3Kf4fqEoWX9mmNLM/q5yYf4Af09DqdeaGfbPQvMpRI4/pqbZjVWF5f6fU+KicNuYAZiW5fJ/+fKy0+DxAI+s197+TkJyrEO1Gc2Izrdi9xA6UWgBd79nt37Zw7dj1ElU7zYkByrrJQUZ4FvPByrrVZvIOdT4uIyuzE+qwKrBBsAm4jbwAnjqg6OIdkTKHodVXAosmtFA9n0j3lNMjPrWDry9tyqohlu3x4sVO8o0HiU5DW2d2FVWo/j1WjbZVHMPvalpdiO/6IT/54LSakx+qQhz39wnuy6fHIxoxijHzLf3hC8SVKiuJilWqiWqdUCREF5Iuw0a27uIFA8haI/MZcLMIHYePYP573yuyXtxofH5ReWmmhg5zV6psDFis9UyoEMNqwqPo6C0WjDcvPrCKVFLgWZEbpWcaM383RWY/FIRAPAWuyUlKdZhCR8OYMz6i4+OxLXD9D8x0R6Zy8yMBrByZxle/6xS0/f0AlhHmHuiF2rND0ZstjRpk89tK4PX6xXV0p/afEyzdAc5bUi6PV5Z9wysDpMSF4X61g6i13FC+/5JQ/GHn1wJeIH/Lq7C/5SdJb53VIQN8dEObCk5bUr4uBwTsRHrr+V8F/5FGDCjBKPSFtTChJnO7Dxarbkg42hsl5cXphdKv7BGJLLSpE2SaOiNbZ3ILzqBx6dmqr4fqX9qxY6v8NaeSsGAm9DNu6G1Ayt2qAtmWLu3Cmv3ViExxoGRrnhZrz3b0oG73trv/9nI8HG5wUo0rT8lWMmky8yMOtLt8WLZllKzh6E7Sr+wevYT4yqa1DSfR0qcQ9H4zOLtvd9o0mMrsO+bFEJVNfj8e4+sF64OI5em9k7sU2FGBpRVBFGCkookSip+mElSbPB3xUp9ztjJTEcOVNYTm1+siFrzg16JrGaHQaulqb1Ls8ixvOw0PDglXdI6wBfdaEQUnhaIRY1qhdLIUG6N6xk1qwVJMQ68cPsoJMY6RCu40Aw7mekITf4avVBrftC6862Q9mw1tExG33qE7MQS6APt6PLg6Q+PUS/IAgmNGtUSNcFKedlpuHW0S5dxacW9PxqCFTvKcNdb+5G/+wTyd1fgPzcdURWtbDTsZKYjSs1v0ZF2uLs81G8kD05J18T8kJedhmlZLtV5V0aFQRuBVr4WJdF0hWU1eHT9Idm1OmmAKxEl1KlZKXKClUJ9jOOHJONf5foFaKiljzMSqz/pqQRYqfoHwISZrkxIT4ErwSnY90qI8136lLrRmve/+A6/zhupyaahRSIrLWH4atGypqOSEx5phXZaWVV4HBsOnOzRqVkNpMpFVW1bjyaaKXFR1ARr8XHO3cX7e6v15WNmRh2JsNswd8KlZg9DNxrbOrGvgh6NM1zMus/OukKzjcPq0XRKqWl2axoUQhKslBTrwOrC4zytg6zrN9ci19MomDDTmaGpcWYPQVeKv6k1ewh+UmKjzB6CapJiHZiWpZ1/xWrRdFqjtoIMR2BkaOhcBgYvhYOJmw8rKIpMmOlMuGvGFT+0mj0EAL7Aj8c2HjZ7GKppbOvUVAsW24TDHa1PFWLBSounZvJWnQ8XlOxjgQ1/iyvqNFEqxGA+M52ZkJ4iq0KC1fiotAYFpdWmOoitEkJOitZasFDrk96ClvPJF6w0fkgy/t8n5dIvtihKmn4a0QkjFHYy05kIuw23jRlg9jB0ZenmY6q1LqVanBVDyKXQ4zSfl52GPUtysWFBDv5j4hDN359mtJ5PLlhp9piBaGrvwHWv7Eb+bn1SAmiAa/pJipLkci1gJzMDmJblwtsWjxATo6GtE/lF5Xh86nBFrxfT4sRC9gtKq/H0h6WWDCEXQmnFExICI0b/WnxSl3vQhN41BcPNIiBGTfN5FFfUSabOGNF2SAgmzAxAaYi+lVi3twqLcjMVVesQ6zUW2gE3sKFmOG4kRtTA06qnmBXQaz7DKaeRhBXbvwxSGoVMhnKSy7XujcbMjAYQYbfh2VlXmD0MXWlslx+4QNJrLNSpzpkqntocXqbFpJhIrDEoOVVOzUarkhSjb5uYcMlpJCXU+iFkMjSiE4YQTJgZRF52GtbcPQ5JMeF7GJa7QJVsCN4L/8ItcizaYey64IJC0hT2FKOdV382RlfFwAqh6noi1DzXiE4YQoTvzkohXCTUr/9Rgg8On9HlHq9gHu5w+Fqoe73A5k7gSazX5V6hyF2gVtgQjJrPs83Glw4KjMzbVVaDfx4+g/o2/aJujVybx78/h+tGXKLLewN0pNyY+V0H+E2GUiZsPf2Y7GRmMBF2G5J0Su6tcMzDnU4gIgKw233/vdPp+73eKAlcoGFDEMPI+RTSdPWGCwr57a1X4OHrL9PtPkavzVMNbbq8L4fZyehmftdDCVRKpZLLAf38mEyYGUxBabUute8qHPNgF/g07Xb9F3lWWjwOVNbL2ojN3hDEMGM+zS4ddKqhXZf3NWMuh6TE6pq0a2Yyutnf9VBClVKtO2GQwsyMBtLt8eKpzcc0f99XcHFx20K+WZwJwm73XaeXGeKTr3/AJ1//gLTEaCyfORLJcU7JMF6xfmZmYvZ8mmV+HZISq/l7mjGXNgCpfZy4+vnCoGIFWiftCiWj222+3Cw9MGo+ue9jUqwDTW2dsk2GWnXCkDVmr9dLyx6iGc3NzUhMTERTUxMSEhLMHo6fveW1uGvtfukLZVLhmIeICOnruruBjE7jbOocUpsIbc00zZ7P9x64BpOGpWr+vlJ0dHkwYvlHmm7EZsxlemoMKmv5T5k2QNPTQbfHi33f1AU1tGxq78Sj633NOLXeXI2az9AUGIC/ea4RPl7S/ZyZGQ1Er6K8oRqa2uu0RirzP7A6xX/95ErTzY5mz+cTfy/RrUoCH5w57qPSaswcpW0TSTPmUkiQAb4NWSu/ZEFpNSa/VNSjoaXdDl4zmxYYNZ8v3zEaedlpgibDxBgHfjk1U9Oi2GoxRJgdOHAAa9asQXk5Wf0yj8eDoqIirFu3Dnv27NF5dMah1xmY9H3NOoOTBDdwgQh3jB+EB6ekGzc4Hsyez7Maty8Rg9uQ5765D49vLMG2ozWIiyJQ/Qkxey750MIvKVWyCQD2LMnFohsyVN0nFKPms7jyouLNKZuLpw5HUowDgC+vdFVhOSa/VGSo4iWGrsJsz549GD9+PB555BE8/PDD2L9f2sTW1taG66+/Hvfeey8KCgpw55134rbbbkNXF38DOatQUFqN9fu/1eW9N3f6Fq/QAub+ttnE1Cw5wQ1LZ2Rh4ZR0hJrXjTpZmj2fRkU2Cm3IrR3dmt3D7LkUQo1fkiTZ/7ltZQCAScP6Kb4PH0bN55FTTUFrb1dZDVYXHu/RZFTveoty0P1k9sYbb+CLL74gvv7ll19GRUUFDh06hPfffx/FxcX45JNPsHbtWh1HqS87j57BQ+8eQoNO3WafxHp4LjSnDl3k3M8ej7E5KEKQbiJLZ2Th6xU3Y/nMkfiPiUOwfOZIlD2XZ0iSLw3zqXdko1HlmGiYSz7UpIXIKdmkdcSuUfO5t6IO41fswquF5ejo8hAJbyNTSvjQVZhNnjwZ48ePl/WajRs34mc/+xlSU30O8PT0dMycORMbN27UY4i6s+3IGTy6Qf8+WxmdFxd5KB6POYEffMjZRKIi7bh3Ujpuzk5DarwTJacasXzmSB1HdxFa5lOvyEYjyzHRMpccfeOiVCXtyinZpEfpMKPm02dKPI5xK3YRC28zoSoApLOzE+Xl5cjKCv7ws7Ky8OWXXwq+zu12o7m5OegfDazcWYZfbDhsmD8go3M9Nrl9kUwej++/m9x0CDIb5CdWh/pz5r65Dyt2fIUbR2hruhGChvnUK7Hc6PB/GuaSY8XsbFUh4nJLNuVlp+GXCjtKCGHkfJ5zk7l4zK7oIyvP7PPPP8fBgwdFr5k1axYGDFDWv+vcuXPweDxISkoK+n1ycrKogFq5ciWee+45RffUi51Hz+D1zyoNv++TWI8nKStbqCTzX6yavpEh/GbNp97tS8yovkLD2lw4JR0zRqsLJVdSsunSlBhV9+SDhvkMxOyKPrKEWXV1NUpKSkSvyc3NVTyYmBjfB97S0hL0++bmZsTGCid0Ll26FL/61a+Crh88eLDicail2+PFsi2lpt3fLBbdMAxZaQlYsSM4Z8wlM1mVpCeSTcfEVLPRu+wPcHFDpiW3T29S4hz4/exszBitvlGuWLK/0GdXey582z/prXiRIkuYzZo1C7NmzdJrLIiOjsagQYNQWRl8oqmsrMSwYcMEX+d0OuF0OnUbl1wOVNaHVcNIUiYNS8XEjL6Ynq0u85/Ewc6ZbmmqHCKHR6/PwHBXPKpq27DhwLeoaVYu/JXAbcgPXQgjD2eWzxyJeyela6oYCFX/CP3suj1e5BedwOufVWh2b5owQvEixfRyVl988QWOHTuG++67D4BPYG7atAnLli1DVFQUmpubsXXrVjz22GMmj5Qcs23HZpAU6/BrZoEdjZVAOn/3TxqKnaU1QZtJ37go1LXqV/ldKyZn9vPP0aLcYYaW/eHIy07D4qmZWFVIlv9pNbgTg9aCjEOqZFNBaTWe2nwsrNoVpcQ5ghR1IxQvUnQVZqdPn8a2bdv8PxcVFeHcuXMYOXIkrrvuOgDA9u3bsXr1ar8wW7ZsGbZt24abbroJ06dPx+bNm9GvXz9LCTOzbcdmMHlYqmYbBun8Tc1y4emZWUGbSU1TOxb//Ygm49ALuw1ouCBwuz1eUwQZx6LcTGw4cCroZBgOGHViEFLcCkqrw+7Ua7cBe5fciJJTjaatVzF0FWYtLS1+H9vChQsBACUlJejTp4//mquuugrz58/3/5yWlobDhw/jnXfewbfffot77rkH9957b9BraKe3+SMA4ODJBnR7vJosbDkO9tDNxFcjj248XuDR9Yfw4Hfp2HqkOmidaF0MVwpfF/Qs3vp7VuHm7P7YX9kQVFSYOzFMy3KhuKLO0M2X8/mGGx4vUHKqUZXVRU9YoWGdEIrGC2c2LMiRvdCFTibc/AHyCpx2e7yY/FKR5RWJP88bpzrqTg4FpdV4dmuZpU5onFKzZ4kv6Cx0He0qq+nh0zJCWSiuqMPcN/fp9v5m8uqcMZg9ZqCh92SFhk1GqC19SpwDN1+hXwdcM5HrK+TLI+NqvSnticQFNtBh+FDOog2HsPOoPt3I+cjLTsMff3KlYfdTS6gZkTuhzx4zEBMz+mJXWY1o7UQ9yy+Fs8+cZheK6QEg4YyQg3hfRR0++vJ7s4dHhA1AcojTVwg5C10sj+zhdw/5BZaSnkhCkWZWwuMFHll/GH+GDclxUYaYyWpbrRM+LhZ4QJLa8dy2MkzLcukylzRv+GpQ0k3eSJgw0xk+B3FORl8kxTosEeXkBfAfOUPwzr9P9igyyiE3z0TuZqPERs8Jwn0VdVjwty/QpmHxXCNZtOFQUD6dnmYy2jfhPs5I/PSqQZiW5RIV6nJqJ+rh/xk/JLlH1F84QEP4vRjMzGgQgS3cD1TW44XbRpk9JCJsAFZ/ckJUkAHyFrqczUYNEXYb7HabZQUZ0DMxXE8zmdZFcbWm1d2FdXur0NTeIbrW5NROVELgd7m4oi6owG5BaTWue2V32AmyxVOHUxF+LwY7mRkAXyfltMRoLJySjo2fn0JTO73tbaQCWJTkmei92Wj9HjShp5lMrLIFDZA+u9zaiXIQ+i4HdmWmbd7U0sdpx6Jc4aIVtMBOZjoj1sTvjc8qsfL2UVg8NdPf9M4qJMU68N7912DPklzZGpuem40e70GKkFgJ/T2nyChFzyrlQoE3tFiXSJ5d6oSppOg1IN2Q86nNx8JOkAHAC7NHU21e5GAnMx0h8Q2t2PGVryNtbibyi8otU42hsa0T9gtRZHJRUqhVKVL3Uku0w46Vd4yGKyEa44ck4/PKevy7ohZnGtsxIDkGP7osFVenp+DgyYYeQRxXDkru4ROTg16nTr7Am4ZWNx5df5iazVrs2ZXUTpSCpCGnFXzgSlj58deIirJTb2ZkJzMdkesb2vj5KYNGpg1KN9PAHk+h24nWlRvE7qUF5zs9OFnbiokZfREVacekzFQ8mTcCq+aMxZPTR2BSZiqiIu1BYePcc80YnYb8uWMV31vPU2doqPuM0QN8J7YEOmqgSj270tQOIfTo/8adEPPnjDH05Dt1ZD9Z3wWaukmLwU5mOiLHN2Rks0StULOZkhZq1QLuXnolBb+15xv84sZMRcJ3xugBWGO3yU4jMCNMmjux5RedwKrC44bem0POqV1pagcfWp+CA5W2xJgowzpALJySjqUzstDR5cF//7sSn1c1IC4qAjNHDcAv/34I59w9u34akc6gBUyY6Ygc35BZgQppidFYPnMkVuz4yvDNVMvNhgR3lz6BNufc3arCvAPnoaapHSt2fBVUmomP5TNHmrKpRNhteHxqJi539cGSD46aErwk59Sutug14DMx1rZom4MXqLRtKTmt6XvzEe2w479+MsZfVSbCbkP2wCRckhCNS+Kj4fF4eQUZh97pDFrAhJmOyPENGdVyfOYoF+ZdMwS159xBwsNutxFHYtmgrRlQ7y+HEaXF1Coj3DwUV9RJCjIASI4z19yXl52G+GgH7nprv2H3NLpuJcAfvciHDb6gqIa2Tl4/nRfA4qmZGJoa10NpMyJIKTE6EtOzXQD4n4k0AI3m6GAmzHREjiNaqjgxJ/h+dtVgrP5EOkgkJS4qaFPsGxeFFbOzBev9caY4qZYVybEOrLxjFPXOYA4xx72WpGokXIxMW1CLkQ0nF0/NxKJcZaZcpZAqQdyIVt7hyx2VazrXO0gJAM62dOBAZT2a2jt4n0kojzQUmhPrmTDTGVLfUITdhllXpuH1zyqF3spfBXzj58ItOzih979P3sAbQSc1Vp9PpBzr9lYFLfCkGAfumzTU0A1Fi/YoRvkiP6+qw6TMVNXvY2Taglq0HsOM7P7YF9LYNinWgft+lI5FucMMFWRylKDQ77Jc07lR+X01Te14+eP/U/T+tHSTFoMJMwMg8Q0VlFbjDRFBNnN0mt/5KtSyI/C0x0XQycXnExmORbmZpvbZEktO1SNBWy2rPzmBEWkJqk+sRqYtqKWh1Q27rWeVErlwz/SneeMBIEiZamzrxKrC49j4+beGmhhJlSC+LtZKTOdCSq+Wwq32nFuRYkdTN2kxWGi+QYSGOgcuChItcPvRakx68RNVFeW1Gq/eSCWnygkRNvIE89y2sqDSRkowMm1BDQWl1Xh0/WFNBBlw8Zl2ldVgdWF5D7OX0eHhpEpQarxTs88iLzsNe5bkYsOCHLw6ZwyWzxyp6Sktf3cF0XVxzoign7XcV/SEncwogFQLrGl2q64oTztaVzwn8UdEO+w43ykcyUWKVtFeRqYtKEGuH5IzFWZe0gcrdgg/k9nV7gMxy9wbeKrTOsqxidAv1uq+WMs0JS4Ky2eav+ZIYMKMAuSawtRWlKcZrSuekwTh/NdPrsTT/yzVpIKDVmZNmpUVUuVr0Q0ZmDSsX9C4p2cLP5PZ1e4DocHcS4NftKG1A4+uP4S/2Ok/mTEzIwXIWbR61uWjAT2i+aTMsjNGD8CLdwh3MbABuIWw67OWG5CZpl4xSOc+s398j3GLPRNNkZw0mHs5gUpKUowDT988QtMxcIJcCxO63rCTGQUoCc2lITRbD/Qy70iddPKy07CGx7THBZ1My3Lhi6p61DTzh6PTFJihN3p9RrRFcppt7iWJcAYuCtcXfzwK7i4yc3lSjIM4HN8KCdMAE2ZUQLpoA6HBBKEHepp3pMyyUgLv2VlXSEaR0nJ60hO9PiMaTHuhmGnu7fZ4sfWIdMBLoHAtrqgjeu/X7hoHu82G71vOo/xsC1FwCKdAa5EyowdMmFGAVFh+IOF+AtCj4rnc+wsJPLM1dVrQ6zMy+7MXG5cZJxJS3+Qf7rzSn+NIqhDkXHbRxFtcUUckzC6Jj9YsZUYPmM/MZOREhvWWE4ARqQdKCQ2f3rAgR1FPN6uj12dE82dvNKSuhNrWi6ZvJb4+0v5vDa1uzVJm9MDm9Xrp9uopoLm5GYmJiWhqakJCQoLZwxGluKIOc9/cR3QtLRqQUdBqzmBcRK/PiH325HvDhgU5PU6Ock9QXG4nwH8ifm3euB5pFQi5zpUYjT1LcjX/nEj3c2ZmNBlS7WvRDRlYPO3yXvWFDsfUg3BDr8+IffbqfIhyfX1SJvTEmChq0iaEYMLMZEgDOSYN69erBBmD0dtR60OUqxCICUDSBG4zo6yZMDMZGiO4GAyzYObFYIwOOhISgLSlTfDBhJnJ0BrBxWAYDc2RcmZCQzUYKyjdLJqRAlgEF6O3o2Vx6XDE7GowNFREkYJFM1IEM7EweiPdHi8mv1RkSqQcQx5mnJ5ZNKMFYRFcjN4ITQWGGeLQYPIUggkzBoNhKjQVGGZIQ6vSzXxmDAbDVKwQKcegHybMGAyGqZCWU2LpKQwxmDBjMBimYoVIOQb9MGHGYDBMh6WnMNTCAkAYDAYV0Bwpx6AfJswYDAY10Bopx6AfZmZkMBgMhuVhwozBYDAYlocJMwaDwWBYHibMGAwGg2F5mDBjMBgMhuVhwozBYDAYlocJMwaDwWBYHibMGAwGg2F5wjJpmus32tzcbPJIGAwGg6EGbh+X6iMdlsKspaUFADB48GCTR8JgMBgMLWhpaUFiYqLg321eKXFnQTweD86cOYP4+HjYbOFZ1625uRmDBw/GqVOnRFuJhztsHnywefDB5sFHOM2D1+tFS0sLBgwYALtd2DMWliczu92OQYMGmT0MQ0hISLD8YtUCNg8+2Dz4YPPgI1zmQexExsECQBgMBoNheZgwYzAYDIblYcLMojidTjzzzDNwOp1mD8VU2Dz4YPPgg82Dj944D2EZAMJgMBiM3gU7mTEYDAbD8jBhxmAwGAzLw4QZg8FgMCxPWOaZhTtutxv/8z//g4iICMyYMYPoNQ0NDfj3v/+NyMhITJ48GXFxcTqPUn/kPtPGjRt7/G78+PHIzMzUa4iaouQzZJ+79T93Idg+EAwLALEYS5YswbvvvovIyEjExMTg66+/lnzN9u3bMW/ePGRnZ6OtrQ3V1dXYvn07rr76agNGrA9Knslms+H6669H//79/b+bP38+brrpJiOGrAolz8s+dx9W/tyFYPsAD16GpfjDH/7g/eGHH7y/+c1vvJdffrnk9U1NTd7k5GTvM8884//d3Xff7R0+fLjX4/HoOFL9UPpMALy7du0yYITaouR52ed+Eat+7mKwfaAnTJhZFNJFvGHDBm9ERIS3rq7O/7tDhw55AXj37dun5xB1Q+kzAfD+8Y9/9P7zn//0HjlyxNvd3W3EcFWj5HnZ534Rq37uJPTmfSAUFgAS5hw7dgwDBgxASkqK/3ejRo2CzWbDsWPHTByZctQ80zvvvIM33ngDN954IyZOnIiqqiqdR6seJc/LPvdgrPi5a0k4rodQWACIiXg8Hvz9738XvcblcuH6669XfI+mpqagBQwAkZGRiI+PR2Njo+L31RK586D0mXbu3Imbb77Z/x433XQT7rnnHvzv//6vqvHrjZLntcLnLpfe9rlrSTiuh1CYMDOR7u5u/POf/xS9ZtSoUaqEmdPpxLlz54J+5/V60dbWhujoaMXvqyVy50HpM3EbGuCrwv2f//mf+OlPf4qmpiaiqtxmoeR5rfC5y6W3fe5aEo7rIRQmzEzE4XDwhg1rSUZGBqqrq9HZ2QmHwwEAOH36NLq6unDZZZfpem9S5M6DVs/Etcaora2lelNT8rxW+Nzl0ts+dy0Jx/UQCvOZhRlerxcbN25EeXk5ACAvLw/nz5/Hzp07/de8//776NOnD6ZMmWLWMFVB8kyh83D27Nkebdc3b96Mfv36YejQoYaNXQlKnpd97tb/3NXQG9ZDD0wJO2EoZteuXd4NGzZ4b7/9du+AAQO8GzZs8G7YsMHb3t7u9Xq93s7OTi8A75/+9Cf/a371q195U1JSvC+99JL3mWee8TqdzqC/WxGpZwqdh40bN3pzcnK8L7zwgveNN97w/uQnP/FGR0d733//fbMeQRZyn5fkNVakt33uQrB9oCcsadpiLF++3K9tBfL6668jMTERHo8H8+bN65EU+o9//AMff/wxIiMj8eMf/xjTpk0zcti6IPZMfPNw7NgxvP/++6ipqUF6ejruuusuS2nncp9X6jVWpbd97nywfaAnTJgxGAwGw/IwnxmDwWAwLA8TZgwGg8GwPEyYMRgMBsPyMGHGYDAYDMvDhBmDwWAwLA8TZgwGg8GwPEyYMRgMBsPyMGHGYDAYDMvDhBmDwWAwLA8TZgwGg8GwPEyYMRgMBsPyMGHGYDAYDMvz/wEBFmkrz+mALAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.axes().set_aspect(1.0)\n",
    "plt.scatter(np.real(x_hat.cpu()), np.imag(x_hat.cpu()));\n",
    "plt.scatter(np.real(x.cpu()), np.imag(x.cpu()));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f17acbe6-aaf2-470b-a436-e46a4c65f477",
   "metadata": {},
   "source": [
    "As expected, the soft symbols `x_hat` are scattered around the 16QAM constellation points.\n",
    "The equalizer output `no_eff` provides an estimate of the effective noise variance for each soft-symbol."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "402532df-487f-46f6-aa79-0356bc7fffff",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:45.893248Z",
     "iopub.status.busy": "2026-08-06T21:58:45.893105Z",
     "iopub.status.idle": "2026-08-06T21:58:45.896457Z",
     "shell.execute_reply": "2026-08-06T21:58:45.895588Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1024, 4])\n"
     ]
    }
   ],
   "source": [
    "print(no_eff.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3cf18ca7-ed1d-4b93-a26f-9afe93923a24",
   "metadata": {},
   "source": [
    "One can confirm that this estimate is correct by comparing the MSE between the transmitted and equalized symbols against the average estimated effective noise variance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "633d5bcc-fa6b-4997-a199-a897ee409581",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:45.898545Z",
     "iopub.status.busy": "2026-08-06T21:58:45.898421Z",
     "iopub.status.idle": "2026-08-06T21:58:45.902252Z",
     "shell.execute_reply": "2026-08-06T21:58:45.901425Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.016787495\n",
      "0.016619638\n"
     ]
    }
   ],
   "source": [
    "noise_var_eff = np.var((x-x_hat).cpu().numpy())\n",
    "noise_var_est = np.mean(no_eff.cpu().numpy())\n",
    "print(noise_var_eff)\n",
    "print(noise_var_est)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ac3d9e7-ac47-4135-9b6a-f08251fbb41d",
   "metadata": {},
   "source": [
    "The last step is to make hard decisions on the symbols and compute the SER:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5fce0538-545b-42fb-9d9d-7c3b84f6695f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:45.904328Z",
     "iopub.status.busy": "2026-08-06T21:58:45.904202Z",
     "iopub.status.idle": "2026-08-06T21:58:46.042149Z",
     "shell.execute_reply": "2026-08-06T21:58:46.041271Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.0032, device='cuda:0', dtype=torch.float64)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "symbol_demapper = SymbolDemapper(\"qam\", num_bits_per_symbol, hard_out=True)\n",
    "\n",
    "# Convert no to a tensor on the same device as x\n",
    "no_tensor = torch.tensor(no, device=x.device)\n",
    "\n",
    "# Get symbol indices for the transmitted symbols\n",
    "x_ind = symbol_demapper(x, no_tensor)\n",
    "\n",
    "# Get symbol indices for the received soft-symbols\n",
    "x_ind_hat = symbol_demapper(x_hat, no_tensor)\n",
    "\n",
    "compute_ser(x_ind, x_ind_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "400ab776-d452-4933-a1c1-70934b50e594",
   "metadata": {},
   "source": [
    "### Adding spatial correlation\n",
    "\n",
    "It is very easy add spatial correlation to the `FlatFadingChannel` using the `SpatialCorrelation` class.\n",
    "We can, e.g., easily setup a Kronecker (`KroneckerModel`) (or two-sided) correlation model using exponential correlation matrices (`exp_corr_mat`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "43b933a9-611a-4994-be08-eb0e5aff664e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:46.044482Z",
     "iopub.status.busy": "2026-08-06T21:58:46.044339Z",
     "iopub.status.idle": "2026-08-06T21:58:46.068812Z",
     "shell.execute_reply": "2026-08-06T21:58:46.067784Z"
    }
   },
   "outputs": [],
   "source": [
    "# Create transmit and receive correlation matrices\n",
    "r_tx = exp_corr_mat(0.4, num_tx_ant)\n",
    "r_rx = exp_corr_mat(0.9, num_rx_ant)\n",
    "\n",
    "# Add the spatial correlation model to the channel\n",
    "channel.spatial_corr = KroneckerModel(r_tx, r_rx)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8079d510-69de-48de-a2fc-4eb32d4bac0f",
   "metadata": {},
   "source": [
    "Next, we can validate that the channel model applies the desired spatial correlation by creating a large batch of channel realizations from which we compute the empirical transmit and receiver covariance matrices:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9b5c6273-0eb2-4065-82b2-64af71accff8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:46.071071Z",
     "iopub.status.busy": "2026-08-06T21:58:46.070929Z",
     "iopub.status.idle": "2026-08-06T21:58:46.110139Z",
     "shell.execute_reply": "2026-08-06T21:58:46.109383Z"
    }
   },
   "outputs": [],
   "source": [
    "h = channel.generate(1000000)\n",
    "\n",
    "# Compute empirical covariance matrices\n",
    "r_tx_hat = torch.mean(torch.matmul(h.mH, h), 0) / num_rx_ant\n",
    "r_rx_hat = torch.mean(torch.matmul(h, h.mH), 0) / num_tx_ant\n",
    "\n",
    "# Test that the empirical results match the theory\n",
    "assert(np.allclose(r_tx.cpu().numpy(), r_tx_hat.cpu().numpy(), atol=1e-2))\n",
    "assert(np.allclose(r_rx.cpu().numpy(), r_rx_hat.cpu().numpy(), atol=1e-2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5de3bbe1-06ba-4d84-9f38-c4e8f0c03d24",
   "metadata": {},
   "source": [
    "Now, we can transmit the same symbols `x` over the channel with spatial correlation and compute the SER:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "359d79ee-d3f4-48bc-aac6-fd9846515c0c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:46.112279Z",
     "iopub.status.busy": "2026-08-06T21:58:46.112156Z",
     "iopub.status.idle": "2026-08-06T21:58:46.118006Z",
     "shell.execute_reply": "2026-08-06T21:58:46.117164Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(0.1223, device='cuda:0', dtype=torch.float64)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y, h = channel(x, no)\n",
    "x_hat, no_eff = lmmse_equalizer(y, h, s)\n",
    "x_ind_hat = symbol_demapper(x_hat, no_tensor)\n",
    "compute_ser(x_ind, x_ind_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d76e543-6d2e-43b8-afb2-3f5d0b1dd54a",
   "metadata": {},
   "source": [
    "The result clearly shows the negative effect of spatial correlation in this setting.\n",
    "You can play around with the `a` parameter defining the exponential correlation matrices and see its impact on the SER. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3376816-8f98-409d-b0c5-c409baeef7aa",
   "metadata": {},
   "source": [
    "## Extension to channel coding\n",
    "So far, we have simulated uncoded symbol transmissions. With a few lines of additional code, we can extend what we have done to coded BER simulations. We need the following additional components:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "74723ddd-7e2e-4006-a4c2-6bc6c9d4bf38",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:46.120174Z",
     "iopub.status.busy": "2026-08-06T21:58:46.120052Z",
     "iopub.status.idle": "2026-08-06T21:58:46.155724Z",
     "shell.execute_reply": "2026-08-06T21:58:46.154934Z"
    }
   },
   "outputs": [],
   "source": [
    "n = 1024 # codeword length\n",
    "k = 512  # number of information bits per codeword\n",
    "coderate = k/n # coderate\n",
    "batch_size = 32\n",
    "\n",
    "binary_source = BinarySource()\n",
    "encoder = LDPC5GEncoder(k, n)\n",
    "decoder = LDPC5GDecoder(encoder, hard_out=True)\n",
    "mapper = Mapper(\"qam\", num_bits_per_symbol)\n",
    "demapper = Demapper(\"app\", \"qam\", num_bits_per_symbol)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1871330c-cb55-4ace-856b-9fe2d8375ea8",
   "metadata": {},
   "source": [
    "Next we need to generate random QAM symbols through mapping of coded bits.\n",
    "Reshaping is required to bring `x` into the needed shape."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ae31038f-a0a2-4e84-88f9-aa5bd28166c2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:46.157928Z",
     "iopub.status.busy": "2026-08-06T21:58:46.157789Z",
     "iopub.status.idle": "2026-08-06T21:58:46.194175Z",
     "shell.execute_reply": "2026-08-06T21:58:46.193154Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([8192, 4])\n"
     ]
    }
   ],
   "source": [
    "b = binary_source([batch_size, num_tx_ant, k])\n",
    "c = encoder(b)\n",
    "x = mapper(c)\n",
    "no_tensor = torch.tensor(no, device=x.device)\n",
    "x_ind = symbol_demapper(x, no_tensor) # Get symbol indices for SER computation later on\n",
    "shape = x.shape\n",
    "x = x.reshape(-1, num_tx_ant)\n",
    "print(x.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e925ebfa-fa9e-4a02-812d-40eb7e990f00",
   "metadata": {},
   "source": [
    "We will now transmit the symbols over the channel:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "8c5a0767-9896-4eab-88cc-8859273a8cc5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:46.196336Z",
     "iopub.status.busy": "2026-08-06T21:58:46.196195Z",
     "iopub.status.idle": "2026-08-06T21:58:46.200918Z",
     "shell.execute_reply": "2026-08-06T21:58:46.200220Z"
    }
   },
   "outputs": [],
   "source": [
    "y, h = channel(x, no)\n",
    "x_hat, no_eff = lmmse_equalizer(y, h, s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b849b3db-cace-4938-987c-57f1737a5a43",
   "metadata": {},
   "source": [
    "And then demap the symbols to LLRs prior to decoding them. Note that we need to bring `x_hat` and `no_eff` back to the desired shape for decoding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "85d3f599-b554-451e-ad73-765c997c1ba1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:46.203219Z",
     "iopub.status.busy": "2026-08-06T21:58:46.203098Z",
     "iopub.status.idle": "2026-08-06T21:58:46.206412Z",
     "shell.execute_reply": "2026-08-06T21:58:46.205647Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1024, 4])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_ind_hat.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2b988637-ba1c-4ca5-aabe-e400f600a807",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:46.208397Z",
     "iopub.status.busy": "2026-08-06T21:58:46.208274Z",
     "iopub.status.idle": "2026-08-06T21:58:46.288677Z",
     "shell.execute_reply": "2026-08-06T21:58:46.287669Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Uncoded SER : 0.121002197265625\n",
      "Coded BER : 0.0\n"
     ]
    }
   ],
   "source": [
    "x_hat = x_hat.reshape(shape)\n",
    "no_eff = no_eff.reshape(shape)\n",
    "\n",
    "llr = demapper(x_hat, no_eff)\n",
    "b_hat = decoder(llr)\n",
    "\n",
    "x_ind_hat = symbol_demapper(x_hat, no_tensor)\n",
    "ber = compute_ber(b, b_hat).item()\n",
    "print(\"Uncoded SER : {}\".format(compute_ser(x_ind, x_ind_hat)))\n",
    "print(\"Coded BER : {}\".format(compute_ber(b, b_hat)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26e4d3bd-d707-478e-924f-3473e1cc0b7c",
   "metadata": {},
   "source": [
    "Despite the fairly high SER, the BER is very low, thanks to the channel code."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b163543-2e72-49d3-9369-b851a6fb678e",
   "metadata": {},
   "source": [
    "### BER simulations using a Sionna Block"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54aaf845-81c7-4573-ae36-14892c258c5f",
   "metadata": {},
   "source": [
    "Next, we will wrap everything that we have done so far in a Sionna Block for convenient BER simulations and comparison of system parameters.\n",
    "Note that we use the `@torch.compile()` decorator which will speed-up the simulations tremendously. See [https://pytorch.org/tutorials/intermediate/torch_compile_tutorial.html](https://pytorch.org/tutorials/intermediate/torch_compile_tutorial.html) for further information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "07908bb6-6936-4d07-bb90-804f3a17a23b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:46.291002Z",
     "iopub.status.busy": "2026-08-06T21:58:46.290849Z",
     "iopub.status.idle": "2026-08-06T21:58:46.295958Z",
     "shell.execute_reply": "2026-08-06T21:58:46.295085Z"
    }
   },
   "outputs": [],
   "source": [
    "class Model(Block):\n",
    "    def __init__(self, spatial_corr=None):\n",
    "        super().__init__()\n",
    "        self.n = 1024\n",
    "        self.k = 512\n",
    "        self.coderate = self.k/self.n\n",
    "        self.num_bits_per_symbol = 4\n",
    "        self.num_tx_ant = 4\n",
    "        self.num_rx_ant = 16\n",
    "        self.binary_source = BinarySource()\n",
    "        self.encoder = LDPC5GEncoder(self.k, self.n)\n",
    "        self.mapper = Mapper(\"qam\", self.num_bits_per_symbol)\n",
    "        self.demapper = Demapper(\"app\", \"qam\", self.num_bits_per_symbol)\n",
    "        self.decoder = LDPC5GDecoder(self.encoder, hard_out=True)\n",
    "        self.channel = FlatFadingChannel(self.num_tx_ant,\n",
    "                                         self.num_rx_ant,\n",
    "                                         spatial_corr=spatial_corr,\n",
    "                                         add_awgn=True,\n",
    "                                         return_channel=True)\n",
    "\n",
    "    def call(self, batch_size, ebno_db):\n",
    "        b = self.binary_source([batch_size, self.num_tx_ant, self.k])\n",
    "        c = self.encoder(b)\n",
    "\n",
    "        x = self.mapper(c)\n",
    "        shape = x.shape\n",
    "        x = x.reshape(-1, self.num_tx_ant)\n",
    "\n",
    "        no = ebnodb2no(ebno_db, self.num_bits_per_symbol, self.coderate)\n",
    "        no *= np.sqrt(self.num_rx_ant)\n",
    "\n",
    "        y, h = self.channel(x, no)\n",
    "        s = no * torch.eye(self.num_rx_ant, self.num_rx_ant, dtype=y.dtype, device=y.device)\n",
    "\n",
    "        x_hat, no_eff = lmmse_equalizer(y, h, s)\n",
    "\n",
    "        x_hat = x_hat.reshape(shape)\n",
    "        no_eff = no_eff.reshape(shape)\n",
    "\n",
    "        llr = self.demapper(x_hat, no_eff)\n",
    "        b_hat = self.decoder(llr)\n",
    "\n",
    "        return b, b_hat"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78a7c2a1-2a12-4bd8-93a6-ae1f54b1717d",
   "metadata": {},
   "source": [
    "We can now instantiate different version of this model and use the `PlotBer` class for easy Monte-Carlo simulations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "71d23857-6ba5-40de-adfd-fb20969d9b96",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:46.297867Z",
     "iopub.status.busy": "2026-08-06T21:58:46.297743Z",
     "iopub.status.idle": "2026-08-06T21:58:46.300278Z",
     "shell.execute_reply": "2026-08-06T21:58:46.299450Z"
    }
   },
   "outputs": [],
   "source": [
    "ber_plot = PlotBER()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b9f84ad5-dd49-4d86-b732-e4c08c59ee26",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:58:46.302103Z",
     "iopub.status.busy": "2026-08-06T21:58:46.301980Z",
     "iopub.status.idle": "2026-08-06T21:59:28.678865Z",
     "shell.execute_reply": "2026-08-06T21:59:28.677740Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "EbNo [dB] |        BER |       BLER |  bit errors |    num bits | block errors |  num blocks | runtime [s] |    status\n",
      "---------------------------------------------------------------------------------------------------------------------------------------\n",
      "     -2.5 | 1.1086e-01 | 9.2010e-01 |      929929 |     8388608 |        15075 |       16384 |        17.0 |reached target block errors\n",
      "    -2.25 | 7.9898e-02 | 7.8961e-01 |      670235 |     8388608 |        12937 |       16384 |         3.4 |reached target block errors\n",
      "     -2.0 | 4.9461e-02 | 5.8514e-01 |      414907 |     8388608 |         9587 |       16384 |         0.2 |reached target block errors\n",
      "    -1.75 | 2.6604e-02 | 3.7183e-01 |      223171 |     8388608 |         6092 |       16384 |         0.2 |reached target block errors\n",
      "     -1.5 | 1.1831e-02 | 1.8707e-01 |       99243 |     8388608 |         3065 |       16384 |         0.2 |reached target block errors\n",
      "    -1.25 | 4.5459e-03 | 8.0383e-02 |       38134 |     8388608 |         1317 |       16384 |         0.2 |reached target block errors\n",
      "     -1.0 | 1.4158e-03 | 2.8870e-02 |       11877 |     8388608 |          473 |       16384 |         0.2 |reached target block errors\n",
      "    -0.75 | 3.2878e-04 | 7.7515e-03 |        2758 |     8388608 |          127 |       16384 |         0.2 |reached target block errors\n",
      "     -0.5 | 6.7443e-05 | 1.6174e-03 |        2263 |    33554432 |          106 |       65536 |         0.7 |reached target block errors\n",
      "    -0.25 | 1.7579e-05 | 4.0690e-04 |        2212 |   125829120 |          100 |      245760 |         2.7 |reached target block errors\n",
      "      0.0 | 2.4340e-06 | 6.7072e-05 |        1858 |   763363328 |          100 |     1490944 |        16.7 |reached target block errors\n"
     ]
    }
   ],
   "source": [
    "model1 = Model()\n",
    "\n",
    "ber_plot.simulate(model1,\n",
    "        np.arange(-2.5, 0.25, 0.25),\n",
    "        batch_size=4096,\n",
    "        max_mc_iter=1000,\n",
    "        num_target_block_errors=100,\n",
    "        compile_mode=\"reduce-overhead\",\n",
    "        legend=\"Uncorrelated\",\n",
    "        show_fig=False);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a2a4c2f1-fd81-4544-a85a-46807d76ffbc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-06T21:59:28.681245Z",
     "iopub.status.busy": "2026-08-06T21:59:28.680942Z",
     "iopub.status.idle": "2026-08-06T22:00:30.819942Z",
     "shell.execute_reply": "2026-08-06T22:00:30.819182Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "EbNo [dB] |        BER |       BLER |  bit errors |    num bits | block errors |  num blocks | runtime [s] |    status\n",
      "---------------------------------------------------------------------------------------------------------------------------------------\n",
      "      0.0 | 7.2127e-02 | 7.2009e-01 |      605049 |     8388608 |        11798 |       16384 |        12.9 |reached target block errors\n",
      "     0.25 | 4.6000e-02 | 5.3296e-01 |      385873 |     8388608 |         8732 |       16384 |         3.8 |reached target block errors\n",
      "      0.5 | 2.7557e-02 | 3.5443e-01 |      231165 |     8388608 |         5807 |       16384 |         0.2 |reached target block errors\n",
      "     0.75 | 1.3663e-02 | 1.9867e-01 |      114615 |     8388608 |         3255 |       16384 |         0.2 |reached target block errors\n",
      "      1.0 | 5.9122e-03 | 9.5276e-02 |       49595 |     8388608 |         1561 |       16384 |         0.2 |reached target block errors\n",
      "     1.25 | 2.2912e-03 | 4.2053e-02 |       19220 |     8388608 |          689 |       16384 |         0.2 |reached target block errors\n",
      "      1.5 | 6.1226e-04 | 1.3184e-02 |        5136 |     8388608 |          216 |       16384 |         0.2 |reached target block errors\n",
      "     1.75 | 2.1172e-04 | 4.4556e-03 |        5328 |    25165824 |          219 |       49152 |         0.6 |reached target block errors\n",
      "      2.0 | 6.7578e-05 | 1.3699e-03 |        5102 |    75497472 |          202 |      147456 |         1.7 |reached target block errors\n",
      "     2.25 | 1.5491e-05 | 3.3487e-04 |        4808 |   310378496 |          203 |      606208 |         7.2 |reached target block errors\n",
      "      2.5 | 3.0038e-06 | 7.0971e-05 |        4334 |  1442840576 |          200 |     2818048 |        34.6 |reached target block errors\n"
     ]
    },
    {
     "data": {
      "image/png": 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6dGl8fHyS9ZpN/D6GhIRkWcyJE6Tt2rVL93516tRxvL79Rw4RERFJm8ZkFRERkXwntV533t7elC5dmtatW/P000/TsmVLQkJCuHTpEk8//TRr1qy5x5H+J/F4rBlJsoIx53v16lXH6xo1aqRrnwIFClCxYkXHTOi3TwKW+NHtxJMBZYXEs9gXKVKEv/76i+bNm2fpMdKS0TFZ06NUqVIZ3sff3/+OvTUTX1uTyUS1atXSVXfi+8BqtRISEkJAQECq5e8m/ox69tln+eabbxzLsbGxnD9/ns2bN/Ptt99y+vRpIiIiGDp0KC4uLgwZMiTN+sxmMyNHjuS7777DbDZnKJas6skaHR2d5FH/oUOH8vzzzzuWEybnSvhv4tcJbQDg+vXrWRKPiIhIfqGerCIiIiIpqFatGu+//75jee3atezdu9eQWC5fvuzo1Vm3bt0Mj7GZHll9vuHh4Y7XXl5e6d7P29vb8TosLCzJtsRJqKweLiGx6OjoJPHnVnczhmx69kn83hQqVCjdQykkvraQ/PreTSyZ5erqmqRnadGiRalbty7Dhw/nwIEDScYJHj58OMeOHUuzvkcffZRvvvkmwwlWIN3j7N7JzZs3kyxHRkYSGhrq+BcWFkZYWFiSntERERFEREQkiTsiIiJL4hEREckvlGQVERERSUXnzp2TLK9bt86QOBYtWuToadazZ89sO05Wnm/C8AOQsWRN4rK3J2cTL2d1EnTUqFG0aNECsCdZe/TowZ9//pmlx8grEl/bqKioJD0i03L7fZCR5LsRChUqxLx58yhcuDBgP9eXXnop1fKzZs1K0uO8WrVqjB49mlWrVnH06FGuXLnCrVu3kiQ3s+M98PDwyJJ60ntdRURExE7DBYiIiIikolixYkmWg4ODDYnjbsdjzaisPN9ixYo5ep6eOnUqXftYLJYkY1/eHo+/v7+jl97Ro0fvOraU+Pj4sGLFCnr27MmaNWuIi4ujT58+TJkyhQEDBmTpsXK7xNfFarVy5syZdE2sdOLECcdrk8mEn59ftsSXlfz9/fnoo48ck4GtWrWKNWvWpDjO6dSpUx2vO3bsyOLFi9OcuCs+Pj5beov6+vpSsGBBx6P/K1euvKsJ0LJ70jEREZG8Rj1ZRURERFKReFxDyHzS4W5mJo+MjGTt2rUAlC5dmoYNG2YqhrRk5fkmjnPVqlXp2mfLli1ERUWlWAeQJFH0119/ZXlPu0KFCrF48WK6desG2JNgAwcO5JdffsnS4+R29erVw8Xlv74a6b2+ictVr149y3pcZrdhw4YlGTs28bAaiR0+fNjx+vXXX79j+9mxY0e67uG7+dxo2rSp4/WuXbuSTbiVnn+JJ6ETERGRO1OSVURERCQVq1evTrKc1iQ96ZE4qZQ4mZiWlStXEhMTA2RvL1bI2vNN3NNv+/btSWY7T82XX37peF24cGEaNGiQZHvXrl0dr//55x9mzJhx1/Glxs3NjT/++IPHHnsMsPfUfPbZZxk3blyWHyu3KlSoEE2aNHEsjxs3jri4uDT3CQoKYvbs2Y7ljMx4b7QCBQrwf//3f47lbdu2JWsrYP9BJEF6EsiJJ9xKy918bnTv3t3xevz48Vk2qZaIiIikTklWERERkRRcuHCB//3vf0nWderUKVN1Jn7M+p9//knXPvdqqICsPt8BAwY4xrIEGDRoEOfPn0+1/DfffMOSJUscy88991yS3pIADz/8cJKZ7J9//vkUk12Z5erqysyZMxk8eDBgH5vy1Vdf5bPPPsvyY+VWw4cPd7z+559/eOmll1LtlRkeHk7//v2Jjo4G7D0zE++fGzzzzDOULFnSsfzxxx8nK1OqVCnH6+nTp6dZ3yeffMKCBQvSdey7+dx47rnnHPtdvHiRHj16cP369XTtu2nTJgYNGpSusiIiIvIfJVlFRERE/mWxWDh27Bjffvst9evX58KFC45tDz/8MFWrVs1U/XXr1nW8XrRoEbNnz07S++12VqvVkXj08vKibdu2mTr+7bLzfAsVKpQkaXvmzBkaNmxIYGAgly5dAsBsNrN9+3b69evHG2+84ShbunTpJMsJnJyc+PHHH3F2dgbsEyl17tyZQYMGsXbtWsdkWHFxcZw/f54tW7bw8ccf06JFiyRjvaaHs7Mzv/32Gy+88IJj3TvvvMO7776boXryqsceeyzJI+k///wzbdu2ZeXKlY5k6s2bN5k5cyYNGzZk69atjrLPPfcc1atXv+cxZ0bBggV58803HcubNm1i/fr1Scoknjjup59+on///uzcudPR+zQ0NJTFixfTvn37VIccSEniz41ff/2VFStWOMZbTY2npyeBgYGOoQY2btxI1apVeffdd9m+fbtjLFibzUZoaCibN2/m888/p06dOrRq1YqNGzemOz4RERGx08RXIiIikq9ERkbi6emZbL3NZiM6OjrF3niVK1fmhx9+yPSxe/TogZubGzExMcTFxdG/f38A3N3dcXKy//bt6enJ5cuXAfsYpSEhIYC9V2mBAgUyfEwjz3f48OHs2LGDadOmAXD16lVefPFFXnzxRVxdXYmPj092fE9PT+bMmUPRokVTrLNNmzb8+OOPPP/881gsFiwWC9OmTXMco0CBAik+um6xWDIcv8lkIjAwkEKFCvHVV18BMHr0aCIjIxk7dmyG60tNatcoLb6+vmn2DM5uLi4uzJ49m5YtWzriWL9+vSPxmNp1aN68OWPGjLmXoWaZYcOG8fnnn3P16lXA3pv1wQcfdGx//fXXmTRpkmNyttmzZzuGSEjp/RgwYACLFy8mLCwszeP26dPH0XP2xo0bdO7cGZPJhLu7uyOJet9997Fz585k+124cIHXX38dq9XKjRs3GD16NKNHjwbsPbatVutdtQ0RERFJTj1ZRUREJN+JjIxM9i8qKirFhOPDDz/Mpk2bkjwqfLeKFi3KmDFjkk1kEx0d7Ygj8WzjixYtcrzu2bPnXR/XqPMFmDJlCu+//36yBLHZbE52/OrVq7Np0yZatGiRZp1Dhw5l2bJlVKhQIdm2O40Neje+/PJLPvroI8fyuHHjePbZZ7FarVl2jJSuUVr/smNW+owqV64c27dv54EHHki27fbrYDKZGDx4MKtXr8bNze1ehZil3N3def311x3L69atSzLWsL+/P4sXL6Z48eLJ9k38fphMJp577jkmT56crkmtatWqxciRI5Oss9lsREVFJWnPKXn11VdZsWIFVapUSbbNbDanmGBt06bNHYc7EBERkeSUZBURERH5l8lkwtfXl2bNmjFixAj27NnDggUL8Pf3z7JjDBs2jC1btjBw4EAqVqyYbNzRxBKSrM7OznTp0iXLYkhwL87XZDLx8ccfc/z4cd555x0aNmyIl5cXYO8NWbJkSR555BGmT5/OoUOHqFevXrrq7dChA8eOHWPq1Kk89thjBAQEOBK5Hh4elCtXjlatWvHhhx+ydetWKlasmKnz+PDDD/n6668dyxMnTmTQoEHEx8dnqt7crnTp0mzcuJFly5YxaNAgypUr57gO7u7u1KhRg5deeok9e/YwefJk3N3dDY44c1544YUkvaxHjRqVZHvz5s05dOgQ7733HrVr18bV1RWw35NVqlTh+eefZ9u2bUyYMMGxLT1Gjx7N0qVL6d27NwEBAY6e7+nRvn17jh49yh9//MGTTz5J1apVKVSoEGAfgsPPz4+2bdvy4YcfcvToUdauXUvLli3TXb+IiIjYmWypjVAvIiIikkfExcXdsYejyWTCw8MjXT3LbhcbG4vZbAbsjwVn9LH+mJgYR7LOZDJRqFAhjh49So0aNQB48MEHWbduXbrry+nnC/ZedC4uLnd1/LTExcWlO57o6GhHTz43N7c0E94JoqKikvRg9fDwyFDCK3Gcmel1m3Cf3O5uzik+Pp6YmBjAntDPikRoRq5DApvNlmSM4owOoZBeia9hVrXXtMTGxlKwYMEUt0VGRjp6dGf0Xkp8re/musXFxeHi4nJX96+IiIgkpzFZRUREJM+720RgehUsWDDVJEp6pPT49MKFCx2ve/TokaH6cvr5AhnqxZcRGTnvu0kmenh4ZHiflGTXNbqbc3JxccnyhObdnJvJZMq2xGpimb2GGR3uIK22cqcEbVoymwzPzs8IERGR/Eg/W4qIiIjkQFk1HquIiIiIiGQ/DRcgIiIikgMlPEacnseRRURERETEWEqyioiIiIiIiIiIiGSChgsQERERERERERERyQQlWUVEREREREREREQywcXoACR7WK1WLl68iJeXFyaTyehwREREREREREREchWbzUZ4eDilSpXCySntvqpKsuZRFy9eJCAgwOgwREREREREREREcrXg4GDKlCmTZhklWfMoLy8vwH4TeHt7GxyNSHJms5mVK1fSsWNHXF1djQ5HJF9SOxQxltqgiLHUBkWMp3YoOV1YWBgBAQGOPFtalGTNoxKGCPD29laSVXIks9mMh4cH3t7e+jIVMYjaoYix1AZFjKU2KGI8tUPJLdIzFKcmvhIRERERERERERHJBCVZRURERERERERERDJBSVYRERERERERERGRTFCSVURERERERERERCQTlGQVERERERERERERyQQlWUVEREREREREREQyQUlWERERERERERERkUxQklVEREREREREREQkE5RkFREREREREREREckEJVlFREREREREREREMsHF6ABEREREREREJONsNhvx8fFYLBajQxG5K2azGRcXF2JiYnQfS5ZzdnbGxcUFk8l0T46nJKuIiIiIiIhILmKz2bh58ya3bt0iNjbW6HBE7prNZsPf35/g4OB7lgiT/KVgwYL4+vpSuHDhbL/HlGQVERERERERyUWuXLnCzZs38fLyolixYve0p5ZIVrJarURERODp6YmTk0a0lKyT0NM/NDSUK1euEBcXh7+/f7YeU0lWERERERERkVwiNDSUmzdvUrJkSXx9fY0ORyRTrFYrcXFxuLm5Kckq2cLLy4ubN29y+fJl3N3d8fHxybZj6Q4WERERERERySXCwsLw8PBQglVEJJ0KFy6Mh4cHYWFh2XocJVlFREREREREcgGr1UpkZCSenp5GhyIikqt4enoSFRWF1WrNtmMoySoiIiIiIiKSC8THx2Oz2XBzczM6FBGRXMXNzQ2r1Up8fHy2HUNJVhEREREREZFcIKEHlsauFBHJmITPTfVkFREREREREREATCaT0SGIiOQq9+JzU0lWERERERERERERkUxQklVEREREREREREQkE5RkFREREREREREREckEF6MDEBERERERERERySpjxozh+vXr1KlTh8cee8zocO6pn376ieDgYCpXrsyQIUOMDidfUZJVREREREREROQ2o0aNwmw2U7p0aZ5//vk7lr916xZff/01QL5M7uUkgYGBnDp1ir59++a76/Dbb7+xY8cO2rVrpyTrPaYkq4iIiIiIiIjIbT777DNiY2Np2LBhupOsn376KUC+TO7lN1988QXh4eE0aNCARx55xOhwJAdQklVERERERERERCQDxowZw5UrVxg8eLCSrAJo4isRERERERERERGRTFGSNQcKDw/n5MmT3Lhxw+hQRERERERERERE5A40XEAOYTabmTt3LnPnzmX9+vWEhYXx4Ycf8tFHHxkdmoiIiIiIiIhkgYRZ72vVqkW/fv0AuHLlCsuXLyc4OBhPT0+aNGlCs2bNMJlM6arTbDazc+dO9u/fz40bNyhUqBBlypShUaNGVKhQIc19r1y5wrp16wgKCiIuLo4SJUrQrFkzatWqdVfnsXLlSoKDg4mKiuLtt9/G09OTgwcPMmfOHABefPFF/P39sdlsbNy4kYMHDxIUFETTpk1TfOQ+OjqaTZs2cfToUW7dukXhwoWpX78+zZo1w9nZOV3vT1pOnz7N/v37uXTpEiEhIXh4eFC+fHlatGhByZIlU9xn0qRJnDlzhoiICAD27t3Le++9l6RMyZIlGT58eIr7Z/acbDYb27Zt4++//yYiIoKAgAA6d+5M8eLFM3j2ktWUZM0hLl26xNKlS3nqqaf44IMPaNSokdEhiYiIiIiIiEgWSpj1vnfv3vTt25cPPviAL7/8kri4uCTlmjZtyu+//07p0qVTrctisfDNN9/w9ddfc+3atRTLNG3alOnTp1OpUqUk60NCQhgxYgQzZszAarUm269Ro0Z8//33NG3a9I7n8eijj/Lmm28SGBiI2Wx2lBk+fDienp4cPnzYMSHYo48+ysWLF+nfvz/Hjx93lH3yySeTJFnj4uL45JNPGDt2LOHh4cmOX6lSJX744Qc6duyY6vuTlu+++47x48dz4sSJFLc7OzvzyCOP8P3331OiRIkk26ZNm8aGDRscywcOHODAgQNJytStWzdZkjUrzmnfvn0MGTKE/fv3J1lfoEAB/u///o9Ro0aluq9kPyVZc4iyZcsyY8YMAA4dOmRwNDnfP5fCKO5VkKKeBY0ORURERERERCTDXnzxRX744QdatWpF06ZNcXZ2Zu3atezYsYPt27fTuXNndu/eTYECBZLtGxMTQ7du3VizZg0Avr6+dOrUiUqVKhETE0NwcDC7du1i+/btBAcHJ0myXrp0iQceeIBTp04BULt2bdq3b4+7uzsHDhxg2bJl7Nq1iwcffJB58+bRvXv3NM9jyJAhzJgxg1atWnH//fcTFRXFn3/+ic1mS1b2yJEjDB06FA8PD4YMGUKpUqXYtWtXkjIRERF06tSJrVu3AlC6dGkeeughSpYsyaVLl/jzzz85deoUXbt2ZebMmfTp0ydjbzywcuVKTpw4Qf369alatSolS5akUKFCXL58mW3btnHkyBHmzZvH/v372bFjB76+vo59n376adq3b88XX3xBREQE9evXT9YL19/fP8vPae/evbRp04bQ0FAA2rVrR+PGjYmPj2fdunX873//IzY2NsPvhWQhm+Q4Bw8etAG2Dz/88K7rCA0NtQG20NDQrAssB+nx/SZb5XeW2J6busu2+shlmzneYnRIkkFxcXG2P//80xYXF2d0KCL5ltqhiLHUBkWMlRvbYHR0tO3IkSO26Ohoo0PJFwoWLGgDbA0bNkxX+TNnztgAG2Dr27dvimUqVapkA2zFixe3eXp62pYvX56szBtvvOGo59dff02xnieffNJRZuDAgbZbt26lWG7r1q224ODgJOvat2/v2Pebb76xWa3WJNt37NhhK1q0qA2w+fj42M6fP5/qefj5+dnc3d1tixcvTrL9xo0btoiICJvNZrPNmjXLcTw/Pz/bQw895IjXYrHYbt68aTt79qxj38cee8xR/rXXXrPFxsYmqfvmzZu21q1b2wCbl5eX7dy5c6nGl9p1WL16dbL3JbFFixbZ3NzcbIDt//7v/1IsU6JECRtgGzx4cKr1ZNU5mc1mW40aNWyAzd3d3bZ06dJkxwgMDLQ5OzvbihQpYgNs7dq1u2Nc+cndfn5mJL+WZye+OnHiBJMnT2bo0KE0btyYevXq0aNHjwzVsWXLFl544QXatGlDixYt6N+/P7Nnz8ZisaS6z7lz5zh58uQd/124cCGzp5hvHb8Szv7zoZgtNpYfvszTU3bR7PO1fLb0H05eTd7lXkRERERERCQnuXr1KmPGjKFTp07Jtn366acULVoUgAULFiTbfujQISZPngxAhw4dmDJlCj4+Pikep1mzZpQpU8axvHnzZlavXg3Ye6COGDEi2divTZo0YdKkSQCEhoby7bffpnoeISEhfPLJJ3Tt2jXJ+sKFC1OoUKFk5Z2dnZk9e3ayeAMCAgDYsWMHc+fOBeDhhx/m22+/TdaT19fXl3nz5uHj40N4eDhjx45NNb7UtGvXLsn7crvu3bszbNgwAEc8dysrzmnBggX8888/gP3+eOihh5Id54UXXuDpp5/WJOoGypPDBZQpUybFJGbCoMR3YrPZeOGFF5gwYUKS9Vu3bmX27Nl89913/PXXX44PvcRat27NuXPn7niMFi1asHnz5nTFI0l5ubnwXKuK/LH3AtfC7V3hr4XH8tPG0/y08TT1Anzp06gM3euWwtvN1eBoRURERERE7r3u3292/L2UVxXzKshfL7U0Ooy74uvry+DBg1PcVqBAAVq3bs0ff/zBwYMHk22fPXu241H8jz/+ON0TZEHSpO3rr7+earmePXtSpUoVTpw4wR9//ME333yTYrmCBQsydOjQdB9/8ODBeHt7p7p9ypQpjtdpTQRerFgx+vfvz4QJE5g3b16aieC0REVFsW3bNsckVDExMY739ujRowCcOXOG6Oho3N3d7+oYWXFOCdfNw8ODZ599NtU6RowYwc8//3xXcUrm5ckk6/Xr16lSpQrNmzenRYsWLFmyhIULF6Z7//fee8+RYO3bty9PPfUUHh4erF69ms8++4xt27bx8MMPs3HjxmQfZuXLl8fF5c5va1q/mEjaSvq4M7JLDd7sVI0Nx68xb9d51hy9gtli/yDcF3yLfcG3+PivI3Su5U+fhgE0r1QUJ6f0f/GIiIiIiIjkZtfCY7kcFmN0GJKK+vXr4+qaeqeghAmvUuqVuH37dsCeqL3//vszdNw9e/YAULRoUWrVqpVm2datW3PixAnOnj3LjRs3KFKkSLIytWvXxsvLK93Hb968eZrbE8YsLVmyJHXr1k2zbNOmTZkwYQLnz5/n8uXLycZBTUtkZCQffPABP//8c7o65N28efOuk6xZcU4J161+/fop9hBOUK1aNYoXL87Vq1fvKlbJnDyZZD1//nySXqa7d+9O976nT5/m66+/BuxdrQMDAx3bWrZsSd26dXnkkUfYvHkzM2bM4Iknnkiy//r16zMXvKSbi7MT7WqUoF2NElyPiGXhvovM3RXM0cv2IQNi460s3HeRhfsuUtrXnd4NSvNowwDKFvUwOHIREREREZHsVcwr708SnN3nmNCpypbCBE4pSVzuTr1LCxcunOb2hMfJU5rIKCGBVqZMmQz1YgX74/0ApUqVumPZxJ3Drl27lmKSNSOJzfSUv3z5MgBOTk6OXp+J39eE1zabjRMnTjjWX716Nd2xWCwWunTpwsaNGwEoXrw4LVq0oHz58nh5eTmS33///TeLFi0CwGq1pqvu7DqnjFy3UqVKKclqkDyZZE3pMf70mjJlCnFxcXh4ePDJJ58k296rVy8eeOABNm3axM8//5wsySrGKOpZkKdaVuDJFuU5fDGMebuCWbj/IreizABcuBXNd2tP8t3akzStWIQ+DQN4qLY/HgXyZBMQEREREZF8Lrc+Rp+TeHh4EBMTQ2RkZLrKJ+4RmVZvQ7hzEjY90pv8vdt905M0LlgwY4nuO5VPmAPnwoULjBo1Kt31hoenf36WKVOmOBKsI0eOZNSoUSn2Kh4zZowjyZoZWXFOGUn4Z+a+kMxRhuk2S5cuBaBNmzap/rLUu3dvNm3axJYtWwgNDU11gGm590wmE7VK+1CrtA/vdK3B6iNXmbc7mI3Hr2H993Nm++kbbD99gw8XHaZr7ZL0aVSGhuUKZ8mXnIiIiIiIiOQNxYoV48aNG5w/fx6bzXbHvxmDgoIcr4sXL55tcZUoUYKDBw+mO67EihUrBsDFixfvWPb8+fPJ9stuJUqUICQkhCpVqjBo0KB071e2bNl0l01InJYvX55PP/001fcv8fXMjKw4Jz8/P0JCQtJ13dJTRrKHkqyJWK1WDh8+DECjRo1SLde4ceMk5e80pkh6nT17lvj4eIKDgwH72CsnT54E7N303dzcUt03NjY2yWMEYWFhAJjNZsxmc5bEl9s4AR1r+NGxhh+Xw2JYuO8S8/dc4Mz1KAAiYuOZsyuYObuCqVDUg0fql+Lh+qXw9079fZask3Bf5tf7UyQnUDsUMZbaoIixcmMbNJvN2Gw2rFZrph5flvRp1KgRx44dIzIykr1791KvXr00y2/ZssXxumHDhmleo4TrmNb2BLeXa9asGatXryY0NJQtW7ZkKCfRsGFD1q1bx40bN9i3bx916tRJteyGDRsAqFSpEj4+PinGe6fzuD3+2+/dxI/KW61WmjVrxuHDh4mNjWXkyJEZSiCnN76EJGSlSpWw2Wyp9vxcsWJFqnFD0t6lab0HWXFODRo04OjRo+zdu5ewsDA8PT1TLP/PP/9w7dq1ZPuL/b2w2WyYzWacnZ3TvV9GviOUZE3k2rVrREdHA2n/CpJ429mzZ7Msydq/f39HY6hUqRJLly519KydM2cODRs2THXfzz77LMVu5ytXrsTDQ2OQAgQAr1SBsyVhx1Un9lw3EWuxf7iduR7FN6tP8u3qE1T3tXF/MRu1i9hwcTI25vxg1apVRocgku+pHYoYS21QxFi5qQ26uLjg7+9PREQEcXFxRoeT53Xu3JkZM2YA9kfHv//++1TLRkREOGaR9/LyonHjxo7OT4klJL3i4+NT3J4g8fW9vVyPHj349NNPsVqtvPfeeyxYsCDdibtOnTo55qEZPXp0qjPR//XXX45OX127dk0WQ3rPA3DkWcA+4VRK5RMeje/duze//PILQUFB/Prrr/Tp0ydd53W7hPjMZnOy4yXkSI4dO0ZoaGiK7938+fP5559/ksR3ez0JE2HdunUrzfcgK86pc+fOzJw5k+joaMaNG8dLL72UYrkvvvjC8To91yY/iYuLIzo6mo0bNxIfH5/u/aKiotJdVknWRBKPd5HW7HiJt2Vk3I872bZt213vO3LkSEaMGOFYDgsLIyAggI4dO+Lt7Z0V4eUpw4GouHhWHrnK/D0X2H7mJgA2TPxzy8Q/t8DH3YXudUrSu35papby0nACWcxsNrNq1So6dOiQ5qyaIpJ91A5FjKU2KGKs3NgGY2JiCA4OxtPTM80nHSVr9OvXjzFjxrBnzx5mzJhBzZo1GTFiBC4uSVMpV69e5amnnnL0kHzzzTeTTBqVmJOTvSePi4tLmn+rJ0x8BSQr16BBA4YNG8YPP/zAhg0beOGFFxg/fnyyIQ+tVisbN26kYsWKjs5ibdu2pXPnzixfvpx58+ZRr1493nrrLUdcAFu3buXVV18FoEiRIrz11lvJYkjvecB/yUiwj1WbuLzNZiM8PBwvL/vf3B07dqRfv37Mnj2bV155BZPJxJAhQ5LEl3jfffv2cfXqVTp16pRifK6ursnia9u2LRs2bOD8+fP88MMPjBw5Msn2xYsX88orr+Dv7++YtMrLyytZPVWqVOHMmTPs27cPd3f3VD9HsuKc+vXrx1dffcXBgwcZPXo0tWvXpkePHkn2/f7775k1axZFixbl+vXr6bo2+UlMTAzu7u60atUqQ5+fGUlUK8maSOJMdlpdhxN/oGYk+52dChYsmOIA0q6urrnmfxjuNR9XV/o0LkefxuUIvhHFvN3nmb/7PBdu2X9lC42OZ/qOYKbvCKa6vxd9GgXwcL1SFPXM+7N03ku6R0WMp3YoYiy1QRFj5aY2aLFYMJlMODk5pZigkazl5OTE/PnzadOmDWfPnmXkyJGMHz+eNm3aULJkScxmMydOnGDt2rWO3pp9+vTh3XffveP1SbiOaW1PHMftxowZQ1BQEIsXL2b27NksWbKEdu3aUalSJUcyfteuXVy8eJF169ZRvnx5x75TpkyhVatWHDt2jHfffZepU6fSrl073N3dOXDgAGvWrMFqteLu7s7MmTMpXbr0XZ/H7fHffu8m9DhNXM9vv/3GzZs3WbFiBUOHDuX999+nVatWBAQEAPak9pUrVxzJyL59+/LQQw+lO77hw4fz008/cfHiRd577z3mz59Ps2bNcHV1ZceOHWzfvp26desyZMgQXnvttRTjBnjkkUdYuXIlQUFBNGnShLZt2zomPCtZsiTDhw93lM3sOTk5OTFjxgxat27NzZs36dWrFy1btqRx48bEx8ezfv16Dh48yLvvvsvq1au5fv16svc+v3NycsJkMmX4Mz8jZZVkTSTx7H9pdQdOvC21cTAkdwko4sGIDlV5tV0Vtp2+zrxdwSw7dJnYePsH/tHL4fxv8RE+W/oP7WoUp0/DAB6sVgwXZ31giYiIiIiI5FXly5dnz549vP/++0yePJkLFy4wffr0ZOUqVKjAW2+9xbBhw+5JXAUKFGDhwoV89913fP7551y5coU///wzSRknJyfatGlDuXLlkqwvXrw427Zt46233mLy5MkcO3aMY8eOJSnTokULxo0bl+awhdnFzc2NpUuX8uOPP/LVV19x7tw55s6dm6yck5MTDRs2pHPnzhmqv2jRoqxevZr+/fuzf/9+9u7dy969ewF7UvbRRx/ll19+YdasWWnW88wzz7B161amTp3KgQMHOHDggGNb3bp1kyRZs+KcateuzaZNm3jqqafYuXMnmzdvZvPmzY76P/74Y95//31Wr16dofdDso6SrIn4+flhMpmw2WyOLuEpuXTpkuP1vZphT+4NJycTLSr70aKyHx/HmFm8/xLzdgezN+gWAPFWGysOX2HF4Sv4eRbkkQal6dOwDFVKpD68hIiIiIiIiORehQsXZvz48Xz11Vfs3LmTY8eOcevWLVxdXSlatCgNGjSgZs2a6RpibsSIEdy4cYMaNWqkWe6hhx7C19c32dAEiTk5OfHqq6/y0ksv8ffff3Pw4EFu3ryJr68vpUuXpmHDhvj7+6d6ThMnTuSLL75gw4YNBAUFYTabKV68OM2aNaNKlSpZch4AderU4X//+x9g7+GZHk5OTgwfPpwXXniBgwcPsmfPHkJCQnB2dqZ48eKUKFGC+vXrU7Ro0TTjq1mzZorba9Sowd69e9m2bRt79uwhOjqakiVL0rJlS0ev3yZNmjji9vHxSVaHs7MzU6ZMYdSoUWzdupWLFy8SGxuLzWZL8X3P7DkB1KxZkx07drB7927+/vtvIiIiKFOmDB06dHDsN2zYMLp160aFChXSfI8l65lsqU2jlocMGzaMn376iUqVKjkGbk5NpUqVOH36NE899RSTJk1KscycOXPo168fYJ/46vZfhXKCsLAwfHx8CA0N1RgcWeDk1XDm7T7PH3sucC08Ntn2ugG+9GlYhu51S+HjnjseNTKa2Wxm6dKldOnSJdc8niWS16gdihhLbVDEWLmxDcbExHDmzBkqVKigMVklT7BarYSFheHt7a1H2yVb3e3nZ0bya+rJepsHHniA06dPs2bNGmw2W4q/RK1YsQKAsmXL5sgEa2Jmsxmz2Wx0GLleucJuvNG+Mq+2qcimk9eZv+cCa49dw2yx/0axP/gW+4Nv8b/FR+hQozi9G5SmecUiODlpsqzUJNyXuj9FjKN2KGIstUERY+XGNmg2m7HZbFitVsdYliK5WUK/v4T7WiS7WK1WbDYbZrM5zXmYbpeR7wglWW/Tt29fpkyZwrlz55g3bx6PPfZYku3nz59nzpw5jrI5TWBgIIGBgVgsFgBWrlyJh4eHwVHlPV18oFV92B1iYsdVJy5E2ZOpsfFWFh+8zOKDl/EtYKNJMRv3F7fipx+ZU7Vq1SqjQxDJ99QORYylNihirNzUBl1cXPD39yciIoK4uDijwxHJMuHh4UaHIHlcXFwc0dHRbNy4MUOT2Kc1Z9PtNFxAClq0aMHWrVspXLgws2bNolOnTgCcOnWKxx57jD179uDt7c3Jkydz7JisCd2ZQ0JCNFzAPXD4Yhjz917kr/2XuBWd/FeOJuUL07tBKTrXLIFHAf22AfZfg1atWkWHDh1yzeNZInmN2qGIsdQGRYyVG9tgwqzx5cuX13ABkifYbDbCw8Px8vJK15i2IncrJiaGs2fPEhAQkOHhAvz8/PLvcAEffPABixYtciyfP38egODgYOrVq+dYX6pUKZYuXZps/1mzZtG8eXMuXLhA586dKVmyJIUKFeL06dNYrVZcXV2ZPXt2jk2wJubq6ppr/ochN6tXrij1yhXlvW73seafq8zbFcyG49ew/vsTxs6zN9l59iYfLz5K1zol6dMogEblCutLBN2jIjmB2qGIsdQGRYyVm9qgxWLBZDLh5OSk8SslT0gYIiDhvhbJLk5OTphMpgx/5mekbJ5MsgYFBbF///5k6+Pi4pKsv3XrVor7ly1blr179zJy5Ejmzp3LpUuXAPvMcR07duTzzz+nfv362RK75G4FXZzpUrskXWqX5EpYDH/sucC83cGcvhYJQGSchbm7zjN313kq+BXi0YZleKRBaUr6uBscuYiIiIiIiIiI3K08mWT9+OOPefXVV+9YrkCBAqluK1asGL/88gs//vgjFy5cIC4ujlKlSuHp6ZmFkUpeVsLbjecfrMSw1hXZE3SL33cH89f+S0TE2sf+OBMSyVcrjvHNymO0rFKMPg3L0OG+Eri5pn8AZhERERERERERMV6eTLKWLVuWsmXLZkldrq6ulC9fPkvqkvzJZDLRsFxhGpYrzAfdarL88CXm7TrP1lPXAbDaYOPxa2w8fg0fd1d61C1Fn0ZlqF3aR8MJiIiIiIiIiIjkAnkyySqSU7kXcKZX/TL0ql+G4BtRzN9znt93n+f8zWgAQqPNTNt+jmnbz1GthBeDm5fnsUZlcHHW2DQiIiIiIiIiIjmVkqx5nNlsxmxOPtu9GM/fy5XhrSvw/APl2XH2BvP3XGTFkSvEmO0Dfx+7Es47Cw7yy6bT/F/nqrSp6penerYm3Je6P0WMo3YoYiy1QRFj5cY2aDabsdlsWK1Wx4RBIrmZzWZz/Ff3tGQnq9WKzWbDbDbj7Jz+YRoz8h1hsiXc0ZInBAYGEhgYiMVi4fjx48ycORMPDw+jw5J0io6HvddN7LjqxNmIpAnVKt5WepazEqBhgUVERERE8iUXFxf8/f0JCAhIc44RERFJKi4ujuDgYC5fvkx8fHy694uKimLAgAGEhobi7e2dZlklWfOosLAwfHx8CAkJueNNIDnT3uBbfL78OHuCbiVZ/3DdkozoUIWSPm7GBJZFzGYzq1atokOHDri6uhodjki+pHYoYiy1QRFj5cY2GBMTQ3BwMOXLl8fNLXf/PSAC9h6s4eHheHl55aknNyXniYmJ4ezZswQEBGTo8zMsLAw/P790JVk1XEAe5+rqmmv+h0GSalKxGPOf92P5oct8vvwo565HAfDn/kssO3yFZx6owLDWlfByy93XV/eoiPHUDkWMpTYoYqzc1AYtFgsmkwknJyecnDRvg+R+CUMEJNzXItnFyckJk8mU4c/8jJTVHSySg5lMJh6qXZJVr7Xm/W734ethb9yx8VYC153iwa/WM237OeItGrtGRERERERERMQoSrKK5AIFXJx4umUFNrzRhqEPVKCAs73pXo+M4/0/D9Fp7EZWH7mCRv8QERHJPUznd2KypX9MMBERERHJuZRkFclFfDxcebfrfawe0ZpudUo61p+6FskzU3cxYOIODl0INTBCERERSZdbwThPf5i2R97GdHAuWC1GRyQiIiIimaAkq0guVLaoB+MHNOCPF5rTqFxhx/ptp6/T7fvNjJizj4u3og2MUERERNK08UtMljg8467isugF+LEF/PMX6KkUERERkVxJE1/lcWazGbPZbHQYkk1ql/Rk5tONWHnkKl+tPMG5G/bJsf7Ye4ElBy/xZPNyPPtABbzccl5TT7gvdX+KGEftUMQ4pjoDMF0/g/O5TfYV1/6BOU9gLVkPa+t3sFVsA5plWSRb5cbvQbPZjM1mw2q1OiYMEsnNEoa8S7ivRbKL1WrFZrNhNptxdnZO934Z+Y4w2TSIY54SGBhIYGAgFouF48ePM3PmTDw8PIwOS+6BeCtsvmJixXknouL/+6PM08VG5wArzYvbcFbfdRERkRzFL/wINS7Oo0jUqSTrQzyr8U/JR7nhWc2gyEQkJ3JxccHf35+AgAAKFChgdDgiIrlGXFwcwcHBXL58mfj49I+JHxUVxYABAwgNDcXb2zvNskqy5lFhYWH4+PgQEhJyx5tA8pbQaDM/bjjN1O1BmC3/Ne+KfoV4q1MV2lYrhikH9Iwxm82sWrWKDh064OrqanQ4IvmS2qGIsRxtsH17Cpxbh/P60ZiuHk5SxlqpPZbWI6FkXWOCFMnDcuP3YExMDMHBwZQvXx43NzejwxHJNJvNRnh4OF5eXjni71TJu2JiYjh79iwBAQEZ+vwMCwvDz88vXUnWnPcMsWQpV1fXXPM/DJI1/Fxdeb97LYa0qMiXK47x1/6LAJwOiWTYjH00rViEd7vcR+0yPgZHaqd7VMR4aocixnItUACX+7pB9S5wZAGsGw3XTwLgdGo1TqdWQ40e0OZdKF7d4GhF8p7c9D1osVgwmUw4OTnh5KTH1CT3SxgiIOG+TmzixIl88803APz99994eXnd8/gkfTZv3swzzzwDwMyZM2nQoEGWH+Ovv/7izTffBGDZsmVUqFAhQ/s7OTlhMpky/JmfkbL6VBbJowKKePB9//osuG1yrO2nb9B9/GZem7OPC5ocS0REJOdwcoJaveGFHdBjPPgE/Lftn0XwYzNYMAxunDEuRhGRfOT111+nevXqVK9enStXrqRZdu/evdSvX5/q1atz3333sWjRonsUZd51/fp1jh07xrFjx7BYLEaHI2mIiIhwXKuoqKhsOUZoaKjjGLGxsdlyjMxSklUkj6tftjDzhjVjwhMNKF/0v/F5F+y9QJuv1/PF8qOExeSewf5FRETyPGcXaDAQXtoND30FhYrb19ussH8WjG8Ei0dA2CVj4xQRyeMuXLjgSOqkNfnNhg0bePDBB9m3bx+nTp3i7bffpkePHvcwUhHJCZRkFckHTCYTnWuVZOVrrfmw+334eti7u8fFW/lx/Ske/Go9U7edxWzRbI4iIiI5hktBuP9ZeGUftP8I3Hzt663xsGsSfFcPVrwLkdeNi1FEJJ9btGgRnTt3JiwsDDc3N/744w8GDRpkdFgiYgAlWUXykQIuTjzZogIb3mzDc60qUsDZ/hFwIzKODxYeptPYjaw6cgXNhyciIpKDFCgELV+DVw9A6/+DAp729fExsG08jKtjH8c1JtTYOEVE8pkpU6bQu3dvYmJi8PHxYcWKFXTv3t3osETEIEqyiuRDPu6ujOxSgzWvt6ZH3VKO9aevRTJ06i76/bydA+dvGRegiIiIJOfmA23egVf2Q7MXweXfmXHjImDDFzCuLmweC3HZMxaaiIj8Z8yYMTz55JPEx8dTokQJ1q9fT6tWrYwOS0QM5GJ0ACJinIAiHnzXvz5PtazAp0uO8PfZmwDsOHODHuO38HC9UrzRqRplCnvcoSYRERG5Zwr5QadPodlw2PgV7JlqH0Ig+ias/hC2/wAPvAENB9uHHBARkSz17rvvMnr0aAAqVKjAypUrqVy5cqrlO3XqxLlz5+jUqRPjxo0jMjKSGTNmsGTJEoKDg4mKimLz5s34+fkl2W/NmjX88ccfHDx4kFu3buHt7U2NGjXo0aMH3bp1w2QypXi8iRMn8s033wDw999/4+Xlxfbt25k4cSJHjhwhLi6OypUr07dvXx555JF0nfPZs2eZNWsWmzdv5vLly5hMJsqWLUunTp0YNGgQ7u7ud6wjKCiI2bNns2XLFi5fvozZbKZkyZKULVuWvn370rp161TPKTXXr19n8ODBnDx5EldXV8aOHUu7du2SHXfmzJmO2G02W5LYPTxS/nv3t99+44svvgBg+/bt+Pr6smXLFiZPnsyxY8e4du0aw4cP58UXX0x3vCnVuW7dOn777TeOHz+Os7Mz9erV44033qBChQqO/Ww2G0uXLmX69OmcOnUKk8lEw4YNefnll6levfodj7tu3Trmz5/PwYMHuXnzJt7e3lSvXp3u3bvTo0ePO77vZrOZadOmsWjRIoKCgvD09KROnToMGzaMWrVqpfv84e6vR26gJGseZzab0xygWwSgpn8hZjzViFX/XOXLFSc4d8PeA+bPfRdZeugyQ5qVZVirCni5uWbZMRPuS92fIsZROxQxVqbboHsx6PQlNHkB501fYTo4FxM2iLgCy97EtmUcllZvYav9GDjpf/tFbpcbvwfNZjM2mw2r1YrVqvkUslviYdSsVivx8fEMHz6cn3/+GYBatWqxbNkySpUqleb1OHXqFKdOnaJmzZocO3aMnj17cuzYsSRlYmNjHXVcv36d/v37s2bNmmR1bdmyhV9++YUmTZowd+5cAgICkpUJCQlx1G82mxk5ciSff/55kjJ79uxh7ty59OnThxkzZuDs7Jxi7BaLhffff59vv/02WVvZvXs3CxYsYPTo0cyfP58GDRqkWEd8fDzvvPMO3333XbI69u7dC8CECRN4+umnHe8tJH//b3+PT548Sbdu3Thx4gReXl7MmTOHNm3aOMpZrVY+/PBDvv76a+Li4pKd/59//sno0aOZN28ejRs3ThZ34vcxJiaGl156ifHjxycpc/Xq1Qy1xcR1xsbGpljn1q1bmTRpEosXL6Zt27ZER0czYMAAFi1alKTczp07+fXXX/n999/p0qVLise7ceMGAwYMYNWqVcm2bdmyhUmTJtGoUSPmzp1LuXLlUqwjODiYbt26cejQoSTrN23axIQJExg7diwVK1Z0rE/t8ymz1yNxnXfzGWi1WrHZbJjN5lTv95Rk5DtC/7eVxwQGBhIYGIjFYgFg5cqVufpXALn3Xq4CW6+YWH7eich4E3HxVn7edJYZ287wUICV5sVtOGfhQCMpfdiLyL2ldihirCxpgy5d8apej+qX/6DUrb8BMIWdx2Xxy4Sv+oyjJXtx0bcJmDRamMjtctP3oIuLC/7+/kRERCRLUkjWS5xcuXHjBq+++ioLFiwAoEmTJsyZMwdPT0/CwsLSrCchGRQeHk7Pnj2JiIjgiy++oGHDhkRHRzNjxgzCwsIoVKgQ0dHRtG/fniNHjgDQtWtXnnjiCcqUKcPVq1eZN28ec+bMYefOnbRs2ZINGzZQpEiRJMeLiYlxvP7ss88YO3YsTz/9NN26dcPPz49z587xzTffsHfvXubNm0fdunUZPnx4irEPHTqU33//HYAaNWrw3HPPUadOHUwmEzt27GDMmDEEBQXRtm1bNmzYkKT3ZcK5Dxw4kKVLlwJQuXJlnn76aerXr4+HhwcXL17kzJkzLFq0iIiIiCTvZeLzCA8Px8npv++w7du38/jjj3Pjxg1Kly7N7NmzqVWrVpL9hw0bxpw5cwCoXr06zz33HHXr1sXJyckRe3BwMB06dGDt2rXJeiMnPv6nn37Kjz/+yODBg+nZsydFihRh586dxMXF3fH6p1bn6NGjmThxIi+++CKdO3fG29ubvXv38sknn3Dt2jV69+7NgQMHeO2111i7di1vvvkmbdu2pVChQmzbto1PP/2UsLAwBg8ezK5duyhcuHCyY3Xs2JGDBw8C8NBDDzFw4EACAgK4du0av//+O7NmzWLXrl2Oe+n23tSRkZG0bduW06dPYzKZ6Nu3L3369KF48eIEBQXx22+/8fLLL/PCCy8k2Sel9ySz1yM6Otrx+vZ7JT3i4uKIjo5m48aNxMfHp3u/qKj0D8NksmmGmzwpLCwMHx8fQkJC8Pb2NjocyYXCos1M2HiGydvOYbb89zFRoagHb3WqSrvqxTL8KEdiZrOZVatW0aFDB1xds66HrIikn9qhiLGyrQ1e2ofz+s9wOp20B5SteC0sD47EVrkjZOI7XCSvyI3fgzExMQQHB1O+fHnc3NyMDifP69+/P3PnzgWgYcOG7N69G7A//v/777+nu0NT1apVOXXqFE5OTlSpUoWNGzcmS2ZZrVacnJwYOXIkX375JQDvvfceo0aNSlbfjz/+6HhEfeDAgUyePDnJ9i+++IJ33nkHsCfmFyxYkKynY2RkJA0aNODkyZOUKVOGs2fPJvv7btKkSTz77LMAPPzww8yaNYsCBQokKRMcHEyzZs24dOkS7dq1Y+XKlUm2f/fdd7z22msAPProo0ybNi1JHTabjfDwcLy8vIiNjU1yXyc+j+vXr+Pr6wvA7Nmzeeqpp4iNjaV+/fosWrSIUqX+m2sE7JOSPfXUUwB0796dOXPmULBg0iF0Lly4QPPmzTl//jytW7dm7dq1SbZ/8803vPXWWwA4OTkxc+ZM+vTpk6SMxWLJUK/IxHW6urqyZMmSZMMbbN++nRYtWgDQpk0btm/fzsaNG5P1FF6yZAk9evQA7GMEv/zyy0m2v//++45hLd5++20+/fTTZPFMnDiRYcOGAfb7ffr06Um2v/3223z11VcAjBs3LsWhEV588UV++uknx48JGzZsoGXLlknKZMX1mD59OoMHDwbg8OHD6RomIbGYmBjOnj1LQEBAhj4/w8LC8PPzIzQ09I75NSVZ86iEJGt6bgKRtATfiOKrFcdYtP9ikvVNKhThva41qFPG967qNZvNLF26lC5duuSa/6kVyWvUDkWMle1t8NxWWPM/CNqadH2ZJtDufaigCVokf8uN34MxMTGcOXOGChUq3DlJ8FNriLh6bwIzimdxeG5DtlXfr18/R8+7BCVKlOD06dMZemK0cuXKnDp1CoDly5fTqVOnFMvFxsZSokQJQkNDqVmzJgcOHEjSezOxtm3bsm7dOlxcXDh//jwlSpRwbPv8888ZOXIkAM888wwTJ05MsY5vv/2W119/HYCjR49SrVo1xzabzUbFihU5e/Ysfn5+nD59Gi8vrxTrmTZtGoMGDQLg4MGDjjE6LRYLZcqU4fLly5QtW5ajR48mG7vVarUSFhaGt7d3snNNfB43b97E19eXzz77jHfffRebzUa3bt2YPXs2hQoVShZTwntepEgRTp8+jY+PT4qxz5o1iwEDBgD2oQvq1avn2Pb111/z5ptvAvYkc0Iv5sxIXOfQoUOTDI+QWMOGDdmzZw9gT5Z+/PHHKZYrV64cQUFB9OzZkz///NOx3mw2U6JECW7evEn16tU5dOhQqsngjh07smrVKpydnQkKCnIkrOPi4ihRogS3bt2iefPmbNmyJcX9Y2JiqFy5MhcuXADswwjcnmTNiusxffp0Bg4cCMA///xzV0nWdH9+JpKR/JqeFxKRNCVMjvXn8BY0Kf/fYyg7/50c69XZezl/U7MYi4iI5DjlmsOTS+GJ+VCy3n/rz++EKd1hSg84v8uw8EQkm0VchfCLefvfPUwilylTBoArV67Qv3//uxquwc/Pj44dO6a6fefOnYSGhgIwaNCgVBOsgKNXYHx8POvXr0+1XELCKiWJx708efJkkm0HDhzg7NmzgL23bGoJVrD3UE34oSLx8Bu7d+/m8uXLjnjTMzlWauLj43nmmWd45513sNlsDB8+nD///DPFBOvhw4cdSe3HH3881YQewCOPPOLoUZnW0CFpvY9367HHHkt1W926ddNVrk6dOgCO802wa9cubt60T2w9cODANHvbJtxLFouFdevWOdbv3r2bW7duOepIjZubW5oxZsf1yKk0JquIpEu9AF/mPNeUlUeu8Pmyo5wJiQT+mxzrqRYVeKFNJbyzcHIsERERySSTCSq3h0rt4OhiWPsJXDtq33ZmA/zSDqp1gTbvgn/GZgcWkRzOs7jREWS/e3iOixYtYvDgwRw8eJBFixbxyCOPMH/+/GSPPKelVq1aaQ65lngyrNQmkUpp+9GjR1Mtl7h36u2KFi3qeH37+Jb79+93vG7evHmasbi7u1OhQgWOHz/uGP8TSDJRUtOmTdOs40569OjBtm3bcHJy4quvvmLEiBGpls1I7AULFqRSpUocOXIkSey3S0hmZqWqVaumui1haIQ7lUsYh/X265cV91LiOhL3KE1J/fr1U92WHdcjp1KSVUTSzWQy0ammP22rF2fmjiDGrj7OzSgzcfFWJmw4xdxdwbzSrgoD7i+La1bOjiUiIiKZYzJBje72hOrB32H9aLh51r7t2FI4tgxqPQIPvgN+ldOsSkRyiWx8jD4/KlasGOvWraN9+/bs27ePJUuWOB7RTu+jx4kTZylJ6MUKJJvE6HaJJ7tKvN/t0hrWIHFP2YTJsxNcv37d8fqtt97io48+AuzDCKT033PnzgH2CcISJPSkhKQJ3buxc+dOwD5cw8MPP5xm2cSxjxw5kk8++STN2BN67CaO/XZ3unZ3Iz3XxtnZOdk4uCmVu/36ZcW9lJE60tqeHdcjp1KSVUQyzNXZicHNy/Nw/dL8sP4kv205S1y8lRuRcXy46DBTtp7l7Yeq0+G+EpmaHEtERESymJMz1O1rT6junQ4bvrQ/cosNDs2Hw39CvQHQ+v/AN8DoaEVEcpSiRYuyZs0aOnTowJ49e1ixYgXdu3dn0aJF6XoU/k4TJCVOuiWeST0libdnZHzY9EqcOD5z5ky694uJiXG8Tvwof0ZmaE/JrFmzePLJJ7l06RIPPPAAq1at4r777kuxbOLYExJ26ZE49ttlZHKrnCAr7qXE93RG6rhddlyPnEpJVhG5az7urox8qAZP3F+Or1ceY+E+++RYp0MieXbabppUKMK7XWpQN8DX2EBFREQkKWdXaPQk1O0Hu36FTd9A1HWwWWDvNDgwBxo9BQ+8nj8eORYRSaciRYqwZs0aOnXqxM6dO1m9ejVdu3blr7/+SnF80IxIGPcV7I9q3z55UGKJH+VOvF9WKVeunOP1zJkz03wcPDFPT0/H6/LlyzteHz58mFat7n7CxQ4dOrBy5Uq6du3KxYsXadWqFStWrKBhw4Zpxj5t2jQaNWqUrmNk9vrlJLffSw8++GCqZVO7lwIC/vux9cSJE2kOGXD8+PFUt+Wn66Ekq4hkWkARD8b1q89TLSrw6ZJ/2HnW3q1/55kb9AzcQs96pXizUzXKFM76X1hFREQkE1zdodlwaDAItk+Ard9DbChY4mDHBNgzFe5/Dpq/DB5F7lyfiEg+4Ovry6pVq+jUqRPbt29n3bp1dOnShSVLliRJMmZU8+bNcXJywmq1snDhQp5++ulUyy5cuNDx+oEHHrjrY6amVatWFCxYkNjYWE6dOkX//v0zXEfLli0ddcyePZvnn38+UzE1b96cdevW0alTJ65evUrbtm1ZvHhxsvNv2bIlbm5uxMTEcPLkSZ544olMHTc3atasGc7OzlgsFhYuXMhzzz2XatnU7qX777/fUcfixYvp06dPqnX89ddfqW7LT9dDgyaKSJap++/kWD8PbEhFv/9+dVq47yJtv9nAZ8v+ISzGbGCEIiIikqKCXtD6TXhlH7QcAa7//jBqjoLNY2BcPdjwFcSGGxmliEiO4e3tzcqVKx29TTdu3EinTp0ID7/7z8miRYvSs2dPABYvXszatWtTLHfw4EF+/fVXwD6hVM2aNe/6mKnx9PTkmWeeAeDrr79Os6diWnUkzFy/ceNGR8yZUa9ePTZu3EhAQABhYWF06tSJ5cuXJynj4eHhSCqOGTMmzYnB8ipfX18eeeQRAJYtW8bKlStTLHfkyBF++eUXABo1akTdunUd24oUKUKPHj0A+3AN+/btS7GO+fPns2PHjlRjyU/XQ0lWEclSJpOJjjX9WfFaKz7uWZMiheyDdMfFW/lpw2laf7mOKVvPYrZYDY5UREREkvEoAu0/hJf3wf3DwPnfyTZiQ2HdJ/Zk67ZAMOe+cdJERLKal5cXy5Yto3Xr1gBs3bqVjh07pjkR1Z18/vnneHp6YrPZ6NWrF1OnTiUuLg7A0SuxY8eOxMXF4erqytixY7PiVFL0ySefUL16dUJDQ2nWrBnjxo3jypUrScrEx8dz9uxZfv31Vx577DGCg4OTbP/f//5HhQoVABg6dCivv/46QUFBju02m42goCDGjh3LF198ka64qlWrxqZNm6hcuTLR0dH07NmT33//PUmZUaNGcd999xEWFkbz5s0ZM2YMly9fTlLGYrFw7tw5fvvtN/r165eh8UJzg88++wxvb28AevfuzeTJkx33ktVq5a+//qJ9+/bExMTg4uLCuHHjktXx6aef4ubmhtlspnPnzixcuBCr1f63fGxsLBMnTmTgwIF3HAoiv1wPDReQx5nNZsxm9RwUY/RvVJputYozYeMZJm8LIi7eys0oMx8uOsyvm0/TvpiJ9v9+yIvIvZfw/aDvCRFj5Og26FYE2n8CjYfhvOkrTAdmY7JZICoEVryDbev3WFq+ga3uAPv4riK5UI5ug6kwm83YbDasVqsj0SHZJ2G2cyDV99zDw4PFixfTs2dP1q5dy/bt22nfvj3Lly9PNuN6wrVLS+XKlfnjjz/o06cPoaGhDB48mOeffx5/f3+uXbvm6Cnr5ubGlClTaNy4cbI60xN3wra0ynl7e7NixQr69evHtm3bePXVV3n11VcpVqwY3t7ehIaGcv369STH++STT5LUU7hwYVasWEGvXr04fPgw3377Ld9++y3FixfHw8ODS5cuERsbC8CAAQOS7JvWeQQEBLBhwwY6d+7MwYMH6devHz/99BNPPvkkYE+Ar1ixgv79+7N582ZGjBjBiBEj0oz9gw8+SPfx71Z667y9XHrrS6xChQosWLCA3r17c+vWLZ588kmGDx+Ov78/ISEhhIWFAfZ76ddff6Vp06bJ6qhWrRrTpk3j8ccf58qVKzz88MN4e3tTtGhRLl++THR0NB07duTFF19k48aNqZ5XVlyPO92vd2K1WrHZbJjN5gxNZJaR7wglWfOYwMBAAgMDsVgsAKxcuTJbZhoUyYiawMg6sDjIid0h9g70525EM+mGM3t/WMtjFa2469NIxDCrVq0yOgSRfC3Ht0GnThSqXofqlxdQ5uZ2AEzhl3BZ9joRa77gWMlenC/cDEx6SE5ypxzfBhNxcXHB39+fiIgIR480yT6Jkyvh4eGOpFRKpk+fzuOPP866devYtWsX7dq1Y8GCBRQuXNiRDIqPj0+zjgSNGzdm69atjB07lsWLF3Pp0iVOnz4NgJ+fH506dWLEiBFUrFgxxfoSz8oeHh6Ok1PKn88RERGO19HR0SnW5e3tzV9//cWCBQuYOXMmO3bs4Nq1a1y7dg0AV1dXAgICeOCBB2jTpg2+vr7J6ilWrBirV69m6tSpzJkzh/3793P16lUAnJycKFeuHN26dePxxx9Psu+dzsPDw4NFixbRp08fdu3axdChQwkJCXE8mu7p6cmff/7JwoULmTFjRoqxlylThlatWvHggw9StGjRNI9foECBFN/HjEhvnYnbd1r3TMI9arPZUizXoEGDJPfSxYsXHfdS0aJFHfdSpUqVUj1O+/btWbNmDZ9++ilr164lLCyMsLAw/P39GTFiBK+++irr1693lI+MjEyxrsxej+joaMfriIiIdLWlxOLi4oiOjmbjxo3Ex8ene7+oqKh0lzXZEqeJJc8ICwvDx8eHkJAQR/dwkZzg4IVQPlt+nL/P3nSsK+3rxjeP1qZhucJp7CkiWc1sNrNq1So6dOiAq6t6oonca7myDV45jPOGz3A6kXT8O1ux6lhajcRWrQuYTAYFJ5IxubENxsTEEBwcTPny5XFzczM6nDzv4sWLjkRO5cqVcXFJu2dIXFycI4EFULx4cYoUKcLp06eJi4vD29ubUqVKZTiO69evExoaipeXF35+fpju8Dl748YNRxKzatWqqSZZE8dbqlSpdOUOLBYLISEhREREULhwYYoUyfikiDExMVy7dg2TyUSJEiWIjo7Gy8sr2Xml9zyio6M5d+4cYB++rmrVqim+R7fHXrhw4TTfy8THr1KlSoZ6P2a2zmvXrnH9+nVMJhPVqlVLtb5Lly4RGhqKq6srlSpVStfxb926le576XaxsbFcvnyZQoUK4efn51gfGRnpGCqiXLlyuLu737GujF6PsLAwLl68CEDFihUznPSOiYnh7NmzBAQEZOjzMywsDD8/P0JDQ+/YRpRkzaMSkqzpuQlE7jWbzcafe4J5548DRFvsH6JOJni5XRVebFMZF2f1hBG5F8xmM0uXLqVLly655o9LkbwkV7fB87tg7f/g9Pqk60vVh7bvQaV2SrZKjpcb22BMTAxnzpyhQoUKSrJKnmC1WgkLC8Pb2zvVJKpIVrjbz8+M5Nd0B4vIPWcymehWpyRv1bXQqJwvAFYbjF19gn4/byf4Rvq744uIiIgByjSCQQth8F9Qpsl/6y/uhem9YXJXOLfNuPhERERE7jElWUXEMEUKwvSnGvN6h6o4O9l7u+w6d5Mu4zaxaP9Fg6MTERGRO6rQCp5eCQPmQona/60/twV+62xPuF45bFx8IiIiIveIkqwiYihnJxMvtavC3OeaUaawfdyW8Nh4Xp61l9fn7iciNv0DUouIiIgBTCao2gme2wiP/gZFq/y37eRqmPAALHsbom8ZFqKIiIhIdlOSVURyhIblCrP0lQd4uN5/A8HP33Oert9tYl/wLeMCExERkfRxcoJaj8AL26FnIPiUta+3WWDHjzC+EeydDv/Osi0iIiKSlyjJKiI5hrebK2P71WdM37p4FrTP3HnuehSP/riVH9afxGLVPH0iIiI5nrML1H8CXvwb2r4PLv/OMBx5DRYOh0kd4MIeY2MUERERyWJKsopIjtOrfhmWvvwA9QJ8AYi32vhy+TEe/2U7l0KjjQ1ORERE0sfVDVq9YU+23vfwf+sv7IKJbeGvVyDyumHhiYiIiGQlJVlFJEcqW9SDecOa8VLbypjsc2Kx/fQNOo/dxPJDl4wNTkRERNLPNwAemwKDFoJftX9X2mD3ZPi+AeycCFaLkRGKiIiIZJqSrCKSY7k6O/F6x2rMHtqUkj5uAIRGmxk2fQ8j/zhIVJwmxRIREck1Kj4Iz2+Bjp9CAS/7uphbsPQN+Lk1BG03MjoRERGRTFGSVURyvPsrFmX5K63oUtvfsW7WziC6fb+ZQxdCDYxMREREMsTZFZq/CC/tgrr9/1t/+SD82gn+eA7CLxsXn4iIiMhdUpJVRHIFHw9XAgc04MvedXB3dQbg9LVIev2whV82ncaqSbFERERyDy9/6DUBnloB/rX/W39gNnzfCLaOB4vZuPhEREREMkhJVhHJNUwmE481DmDxyy2pVdobALPFxidL/mHwbzu5Gh5jcIQiIiKSIWWbwrMboOs34OZrXxcXDivfhR9bwOn1RkYnkmPZbOpgICKSEffic9Ml248ghjKbzZjN6gUgOU/CfXk392dZ34LMeaYJY9ac5JfNZwHYdCKEzmM38nmvWrSpViwrQxXJszLTDkUk89QGE6k3GKp2w2n9pzjtnYYJG4Qcg6k9sdboiaXdKPApY3SUksfkxjZosViw2WzEx8djtVqNDkck0xISXzabTfe0ZKv4+HhsNhsWiyVDn/sZKWuy6SewPCUwMJDAwEAsFgvHjx9n5syZeHh4GB2WSLY5dsvE9JNOhJlNjnUP+FvpUdZKAWcDAxMREZG74ht1mtrB0ygSdcqxLt6pACdK9OBk8c5YnQoYGJ2I8UqWLEnJkiXx8vIyOhQRkVwjLCyMy5cvc+nSpQztFxUVxYABAwgNDcXb2zvNskqy5lFhYWH4+PgQEhJyx5tAxAhms5lVq1bRoUMHXF1dM1XXjcg43vnzMGuOXnOsq1rckzGP1aZqCf3Pp0hqsrIdikjGqQ2mwWbFdGAOzmtHYYoK+W914QpYOnyKrUpHA4OTvCK3tsGLFy9is9koW7as0aGIZJrNZiM8PBwvLy9MJtOddxC5S0FBQZhMJkqVKpWh/cLCwvDz80tXklXDBeRxrq6uuep/GCT/yYp7tISvK78Mbsz0HUF8svgIsfFWjl+NoNeEHbzbpQaDmpXTF7ZIGvRdIWIstcFUNBoENXvA+s9h589gs2C6eQaXuQOgamfo/BkUqWh0lJIH5LY26Ovry8WLFwkNDaVw4cJGhyOSKQlDBJhMJpycNG2QZI+bN28SHR1NqVKlMvx5n5HySrKKSJ5gMpkY2LQc91cowsuz9nL0cjhx8VY+XHSYjcev8eWjdSjqWdDoMEVERCQj3H3hoc+hwUBY+hac22xff3w5nFoLLV6BliOggIbHkvzDx8eH6OhoLl++TGRkJD4+Pri4uKhTgeRKVquVuLg4YmJilGSVLJUwfnVoaCjh4eEULlwYHx+fbD2mkqwikqdULeHFn8Nb8Pmyo0zeehaANUev0nncJr7pU5dWVTUploiISK5ToiYMWQyH5sPK9yD8EljiYONXsH82dPwE7usJSjJJPlGiRAkKFCjArVu3OH/+vNHhiNw1m81GdHQ07u7u+qFAskXBggUpUaLEPen5rySriOQ5bq7OfNSjJq2rFuPN3/cTEhHHtfBYBv26k2daVuDNztUo6KJZsURERHIVkwlqP2ofKmDjV7AtEKxmCA2GeYOhQmt46EsoXt3oSEWynclkokiRIhQuXJj4+HgsFovRIYncFbPZzMaNG2nVqlWuGrZDcgdnZ+d72tNfSVYRybPaVC/Oslda8ca8/Ww4bp8U65fNZ9h66jrf9a9P5eKeBkcoIiIiGVbQEzqMgvpPwLL/g1Nr7OvPbIAJLeD+YdD6/8BNk79K3mcymXLdmLIiiTk7OxMfH4+bm5vuY8n1NOCFiORpxbwK8tuQxrzf7T4KONs/8o5cCqPb95uYtTMIm81mcIQiIiJyV/yqwBPzod9M8P13lnVrPGwbD+Mbwf45oO95ERERuUeUZBWRPM/JycTTLSvw5/AWjt6rMWYrI/84yPPT93ArKs7gCEVEROSumExQvSsM3wkPjgQXN/v6iCuw4Fn4tTNcOmBsjCIiIpIvKMkqIvnGfaW8+evFljx+f1nHuuWHL9N57Ca2nbpuYGQiIiKSKa7u8ODbMHwHVO/23/rg7fBza1jyOkTdMC4+ERERyfOUZBWRfMW9gDOf9qrNTwMb4uthH/PnclgMA37ZzpfLj2K2WA2OUERERO5a4fLQb4Z9GIGile3rbFb4+xf4viHsngxWTRAkIiIiWU9JVhHJlzrV9Gf5K61oXqkoYB+y7Yf1p3h0wjbOhkQaHJ2IiIhkSuX28Pw2aD8KXAvZ10XfgL9egV/awfldxsYnIiIieY6SrCKSb/n7uDH96ft5+6HquDiZANgffIuu323i993nNSmWiIhIbuZSAFq+Ci/tglqP/rf+4l57onXhcIi4Zlh4IiIikrcoySoi+ZqTk4lhrSsx//nmlC/qAUBknIU35u3n5dn7CI02GxyhiIiIZIp3KXh0EgxZAsXv+2/93un2IQS2TwBLvHHxiYiISJ6gJKuICFA3wJclLz/AY43KONb9tf8iXcZtYtdZTZQhIiKS65VvCc9tgs5fQEEf+7rYUFj+f/BTKzi72dj4REREJFdTklVE5F+FCrrw5aN1GT+gPl5uLgBcuBXNYz9tY+zq48RrUiwREZHczdkFmg6Dl3ZDvSf+W3/1MEzuCr8/DWEXjYtPREREci0lWUVEbtOtTimWvfIAjcsXBsBqg7GrT9Dv5+0E34gyODoRERHJNM9i8HAgPL0aStb7b/2h3+H7RrB5LMTHGRWdiIiI5EJKsoqIpKBMYQ9mP9uMER2q4vzvpFi7zt2ky7hNLNqvHi4iIiJ5QkBjGLoWuo8D9yL2deZIWP0h/NgMTq42Nj4RERHJNVyMDkCyl9lsxmzWxD2S8yTclzn9/ny+VXmalvdlxLwDnL8VQ3hsPC/P2su6o1f4oGt1PAvqY1Ryr9zSDkXyKrXBHKTO41ClC04bPsNpz2RMNitcPwnTe2Ot2gVLh/+Bbzmjo5QspjYoYjy1Q8npMnJvmmw2my0bY5F7LDAwkMDAQCwWC8ePH2fmzJl4eHgYHZZIrhcdD/POOLE75L8HAPwK2hhUxUI5LwMDExERkSzlE3WW2uenUTTyhGOdxeTKiRLdOFGiK1anAgZGJyIiIvdSVFQUAwYMIDQ0FG9v7zTLKsmaR4WFheHj40NISMgdbwIRI5jNZlatWkWHDh1wdXU1Opx0W7jvIh8u/ofIWAsALk4mXmlbiaEPVHAMKyCSW+TWdiiSV6gN5mA2G6ZD83Be8xGmyKv/rfYpi6XDJ9iqPgQmfe/ndmqDIsZTO5ScLiwsDD8/v3QlWfWcax7n6uqqDyrJ0XLbPfpo43I0rujHK7P3sS/4FvFWG9+sPsmW0zcY07ceJX3cjQ5RJMNyWzsUyWvUBnOoBo/Dfd1hwxewYwJY4zGFBuHy+yCo3B46fwF+lY2OUrKA2qCI8dQOJafKyH2pia9ERDKoXNFCzBvWjBfbVHZ0Ytl++gadx25i+aFLxgYnIiIiWcfNGzp9CsO2QIXW/60/uRp+aAqrPoTYCOPiExERkRxDSVYRkbvg6uzEG52qMWtoU0r6uAEQGm1m2PQ9jPzjIFFx8QZHKCIiIlmmeHUYtBD6TAHvMvZ1VjNsGQs/Nocrhw0NT0RERIynJKuISCY0rViU5a+0okttf8e6WTuD6Pb9Zg5dCDUwMhEREclSJhPUfBhe3AkPvAHO/06Adesc/NIBjiw0NDwRERExlpKsIiKZ5OPhSuCABnzRuzburs4AnL4WSa8ftjBzR5DB0YmIiEiWKlAI2r0PL2yHkvXs68yRMHcQrP0UrFZDwxMRERFjKMkqIpIFTCYTfRuXZfHLLalV2j7joNli450FBwlcd9Lg6ERERCTLFa0ETy2H2o/9t27jlzDncYgJMy4uERERMYSSrCIiWahSMU/+eL4FT7Yo71j31YpjfL7sKDabzbjAREREJOu5usMjP0OH/4Hp3z+tji2FSR3g+iljYxMREZF7SklWEZEsVsDFiQ+71+StztUc6yZsOMW7fx7CYlWiVUREJE8xmaDFy/D4PHDzsa+7dhQmtoGTa4yNTURERO4ZJVlFRLLJCw9W5pOHa2Ey2Zdn7ghixNx9mC0aq01ERCTPqdwehq4Dv39/ZI0JhRmPwrZA0NMsIiIieZ6SrCIi2eiJpuUY27cezk72TOvCfRcZNm03MWaLwZGJiIhIlitaCZ5ZDVUfsi/brLDiHfjzeTDHGBubiIiIZCslWUVEslnPeqX56YmGFHCxf+SuOXqVIb/tJCI23uDIREREJMu5eUO/mdDqzf/W7Z8Fvz0EYReNi0tERESylZKsIiL3QPv7SjDlySYUKuAMwPbTN3h84nZuRsYZHJmIiIhkOScnaPse9JkMrh72dRf3wM8PQvBOIyMTERGRbKIkq4jIPdKsUlFmDG2Kr4crAPvPh/LYT9u4EqbHB0VERPKkmr3g6ZXgU9a+HHEFJneFPdOMjUtERESynJKsIiL3UL0AX+Y824ziXgUBOHE1gkcnbCXoepTBkYmIiEi28K8Nz66H8g/Yly1xsOhFWPoWWMyGhiYiIiJZR0lWEZF7rJq/F/OGNSOgiDsAwTei6fPTVk5cCTc4MhEREckWhYrCwAXQ5Nn/1u38Cab1gsjrxsUlIiIiWUZJVhERA5QrWoh5zzWnSnFPAK6ExfLYT9s4cP6WsYGJiIhI9nB2hS5fQffvwMk+dBBnN8HEB+HyIUNDExERkcxTklVExCD+Pm7Mea4Zdcr4AHAzysyAiTvYflo9WkRERPKshoNhyBIoVNy+fCsIJnWAw38aGpaIiIhkjpKsIiIGKlKoADOeuZ8mFYoAEBEbz+Bfd7L26BWDIxMREZFsU/Z++zitperbl81RMG8wrP0ErFZDQxMREZG7oySriIjBvNxcmfpUE9pUKwZAbLyVZ6fuZuG+CwZHJiIiItnGpzQ8uQzq9P1v3cavYM7jEBNmXFwiIiJyV5RkFRHJAdxcnflpYCO61SkJQLzVxqtz9jFzR5DBkYmIiEi2cXWHXj9Bx0/B9O+fZseW2ocPuH7K2NhEREQkQ5RkFRHJIQq4ODGuX336NykLgM0G7yw4yE8b9EeWiIhInmUyQfMX4fHfwc0+TjvXjsLENnByjbGxiYiISLopySoikoM4O5kY3asWz7Wq6Fj32bKjfLXiKDabzcDIREREJFtVbgdD14FfNftyTCjMeBS2jrf/8ioiIiI5mpKsIiI5jMlk4u2HqvNmp2qOdYHrTvHBwsNYrfojS0REJM8qWgmeWQ3VutiXbVZY+S4seA7M0cbGJiIiImlyMToAyV5msxmz2Wx0GCLJJNyXuj9T92zLcni4mhi1+CgA07afIyw6js961cTVWb+RSeapHYoYS21QUuTsDr0n47TxC5w3f2Nfd2AO1mvHsDw6FbxLGRtfHqI2KGI8tUPJ6TJyb5psev40TwkMDCQwMBCLxcLx48eZOXMmHh4eRoclIpnw9zUTM086YcUEQK3CVoZUteKqPKuIiEieVvLmThoE/YyLNQ6AGBcfdlZ4mZueVQyOTEREJH+IiopiwIABhIaG4u3tnWZZJVnzqLCwMHx8fAgJCbnjTSBiBLPZzKpVq+jQoQOurq5Gh5PjrTpylVfm7sdssX9kN6tYhB8H1KNQQT2QIHdP7VDEWGqDki5XDuMybyCm0CAAbE6uWB76Clu9JwwOLPdTGxQxntqh5HRhYWH4+fmlK8mqv87zOFdXV31QSY6mezR9utQtjU+hggyduouoOAvbTt9gyJQ9TH6yMb4eBYwOT3I5tUMRY6kNSprK1INn18O8wXB2EyarGZclr8K1I9BpNDjr3skstUER46kdSk6VkftSD5uKiOQSLSr7Mf2Z+/F2s/8+ti/4Fv1+3s7V8BiDIxMREZFsVagoDFwATZ77b93On2FaL4i8blxcIiIi4qAkq4hILtKgbGHmPNcMP8+CABy9HE6fCdsIvhFlcGQiIiKSrZxdocuX0ON7cPq3V83ZTTDxQbh80NDQRERERElWEZFcp0ZJb34f1ozSvu4AnLseRZ8J2zh5NdzgyERERCTbNRgEQ5ZAoeL25VtBMKkjHF5gbFwiIiL5nJKsIiK5UHm/Qswb1oyKxQoBcDkshsd+2s6hC6EGRyYiIiLZruz99nFaSzWwL5ujYN4QWPsJWK1GRiYiIpJvKckqIpJLlfJ1Z95zzahZyj7D4Y3IOPr/vJ2dZ24YHJmIiIhkO5/S8OQyqNPvv3Ubv4LZAyAmzLi4RERE8iklWUVEcrGingWZ9WxTGpcvDEB4bDyDft3B+mNXDY5MREREsp2rG/SaAJ1Gg+nfP+2OL4Nf2sP1U8bGJiIiks8oySoikst5u7ky9an7aV21GAAxZitDp+5iyYFLBkcmIiIi2c5kgmbD4Yn54OZrXxdyDCa2gZOrDQ1NREQkP1GSVUQkD3Av4MzEQY3oWrskAGaLjZdm7WHO30EGRyYiIiL3RKW2MHQtFKtuX44JhRl9YOv3YLMZG5uIiEg+oCSriEgeUcDFie/61+exRmUAsNrg/+Yf5JdNpw2OTERERO6JopXgmdVQrat92WaFle/BgufAHG1sbCIiInmckqwiInmIs5OJL3rX4emWFRzrPlnyD9+uPIZNvVhERETyvoJe0Hc6tP6//9YdmAO/dobQC8bFJSIikscpySoikseYTCbe61qDER2qOtZ9t/Yko/46gtWqRKuIiEie5+QEbd6Bx6aCayH7ukv74OcHIWi7kZGJiIjkWUqyiojkQSaTiZfbVeHD7vc51k3eepY3fz9AvMVqYGQiIiJyz9zXE55eCb5l7cuRV2FyN9g9xdi4RERE8iAlWUVE8rAnW1Tg6z51cTLZl+fvOc/wmXuIjbcYG5iIiIjcG/61YOh6KP+Afdlqhr9ehiVvgMVsaGgiIiJ5iZKsIiJ53KMNy/DD4w1wdbZnWlccvsIzU3YRFRdvcGQiIiJyTxQqCgMXwP3D/lv390SY1gsiQ4yLS0REJA9RklVEJB/oXKskkwY3xt3VGYBNJ0J44pcdhEapB4uIiEi+4OwKD30BPQPBuYB93dlN8HMbuHTA2NhERETyACVZRUTyiVZVizH9mSZ4ubkAsCfoFn1/3sa18FiDIxMREZF7pv4TMGQpeJawL4cGwa+d4PACY+MSERHJ5ZRkFRHJRxqWK8LsZ5vi52nvwXL0cjiP/bSNC7eiDY5MRERE7pmAxvDseijd0L5sjoJ5Q2DN/8CqCTJFRETuhpKsIiL5TM1SPsx9rhmlfNwAOBMSSZ8ft3LqWoTBkYmIiMg9413K3qO1bv//1m36GmYPgJgw4+ISERHJpZRkFRHJhyoW82Te882p4FcIgIuhMTw2YRuHL4YaHJmIiIjcM65u8PCP0OkzMP37p+HxZfBLe7h+ytjYREREchklWUVE8qnSvu7Mfa4ZNUp6A3A9Mo5+P29n19kbBkcmIiIi94zJBM1egCfmg5uvfV3IMZjYBk6uNjQ0ERGR3ERJVhGRfKyYV0FmD21Kg7K+AITHxDNw0k42Hr9mbGAiIiJyb1VqC8+ug2I17MsxoTCjD2wZBzabsbGJiIjkAkqyiojkcz4erkx/5n4eqOIHQLTZwtNT/mbZwUsGRyYiIiL3VJGK8MwqqN7NvmyzwqoPYPnbSrSKiIjcgZKsIiKCRwEXfhnciM41/QEwW2wMn7mHebuCDY5MRERE7qmCXvDYNGj99n/rdkyAxa+B1WpcXCIiIjmckqwiIgJAQRdnxg+oz6MNywBgtcGbvx/g181nDI5MRERE7iknJ2gzEnr+AJjs63b/BoteBKvF0NBERERyKiVZRUTEwcXZiS9712FI8/KOdR8vPsK41Sew6TFBERGR/KX+4/DIRDA525f3zYA/ngVLvLFxiYiI5EBKsoqISBJOTiY+7H4fL7er4lg3ZvVxPlnyjxKtIiIi+U2dPtDnN3BysS8f+h1+fxLi44yNS0REJIdRklVERJIxmUyM6FCV97rWcKybtPkM/zf/ABarEq0iIiL5yn09oe90cC5gX/5nEcwdBPGxxsYlIiKSgyjJKiIiqXrmgYp80bs2Tv8OxzZ313lemrWH2HiNxyYiIpKvVHsI+s8CFzf78vFlMKs/mKONjUtERCSHUJJVRETS1LdxWb7v3wBXZ3umdenBywydupvoOCVaRURE8pXK7eHxeeDqYV8+tQZm9IG4SGPjEhERyQGUZBURkTvqWqckEwc1ws3V/rWx8fg1Bv26g7AYs8GRiYiIyD1VoRU88QcU8LIvn90E03tDTJixcYmIiBhMSVYREUmXB6sVZ+pT9+NV0D7xxd9nb9L/5+2ERivRKiIikq+UawaDFoKbj305aBtMexiibxoaloiIiJGUZM1Bzp07x3fffcfw4cN58803mTZtGmazkhciknM0qVCEWc82pUgh+8QXhy+G8ezUXcSYNXSAiIhIvlKmIQxaBO5F7MsXdsOUHhB1w9i4REREDKIkaw7x9ttvU7FiRRYvXkzNmjUpWrQo77//PjVq1ODEiRNGhyci4lCrtA9zn/sv0brjzA1em7MPi9VmcGQiIiJyT5WqB0MWQ6Fi9uXLB2ByN4i4amhYIiIiRlCSNYcICgpi5syZrFy5khdeeIG3336bHTt2cPPmTZ577jmjwxMRSaJycS9+HdIYd1dnAJYdusyHiw5hsynRKiIikq+UqAlDloKnv3356mGY3BXCLhkbl4iIyD2mJGsOMX78ePr27ZtkXYkSJWjWrBkbN27EarUaFJmISMrqBfjy4xMNcHEyATB9exDfrz1pcFQiIiJyzxWrCk8uBe8y9uWQ4/DbQ3Ar2Ni4RERE7qE8n2S9cOECS5Ys4c8//2T16tUZ3v/y5cts2LCBVatWcezYsWyI0K5IkSIprj916hSenp44OeX5SyUiudCD1Yrz5aN1HMvfrjrOrJ1BBkYkIiIihihayZ5o9S1nX755BiZ3gZtnDQ1LRETkXnExOoDsMGHCBDZt2sSWLVs4d+6cY32lSpU4eTJ9vayOHz/Oiy++yOrVq5M8/lqtWjW+/fZbunTpkuJ+r732GteuXbtj/dWqVeP9999Ps8zUqVM5evQow4YNS1fMIiJGeKRBGUIiYhm99CgA7y44SNFCBehY09/gyEREROSeKlwOnlwGU7rDjVNwKwh+62KfIMuvstHRiYiIZKs8mWR99dVXiY2NBaB06dKAvUdreh08eJAHHniA0NBQnJycaNq0KR4eHvz9998cO3aMrl27MnnyZAYPHpxs3wULFiRJ7KamRYsWaSZZDxw4wPDhwylbtiyffvppumMXETHCs60qcTUsll82n8Fqg5dm7WXGM/fTqHzKvfRFREQkj/Ipbe/ROqUHhByDsAv2Hq2DFkHx6kZHJyIikm3yZJL1+eefp3HjxjRv3pzy5cszbNgwfvrpp3Tta7FYGDBgAKGhoQQEBLBs2TJq1qwJQFhYGH369GHlypUMGzaMBx98kHLlyiXZf+zYsURERNzxOMWLF0912/Hjx+nYsSMeHh4sX7481aEERERykne61CAkIpY/910kNt7KU5P/5vfnm1O1hJfRoYmIiMi95OUPQ5bAtIfhyiGIuPJvonUh+Nc2OjoREZFskSeTrGPGjLnrff/44w8OHToEwG+//eZIsAJ4e3sze/ZsKlWqxM2bN/nyyy8JDAxMsv/DDz9818cGOHPmDO3atcNisbB27Vpq1KiRqfpERO4VJycTXz5al+uRcWw6EUJYTDyDJu1k/gvNKe3rbnR4IiIici95FoPBf8G0XnBpH0Rdh8ndYOACKN3A6OhERESynGZTus3vv/8OQPXq1WnXrl2y7YULF+bxxx93lLVarVl27ODgYNq2bUt0dDRr1qyhdm39yisiuUsBFyd+fKIhtUv7AHA5LIbBv+7kVlScwZGJiIjIPedRxN57tUxj+3LMLZjaE4J3GhqWiIhIdsiTPVkzY9u2bQC0adMm1TLt2rVj/PjxXL16ldOnT1O5cuYHcb98+TLt2rUjPDycNWvWUKdOnTvvlEhsbKxjHFqwD20AYDabMZvNmY5PJKsl3Je6P/Oegk4w8Yl69J34N+duRHHyagRP/raTKUMa4V7A2ejwJBG1QxFjqQ1KvuBSCPrNxXlOf5yCt0NsGLZpD2PpOwtb2eaGhqY2KGI8tUPJ6TJybyrJmkhERATBwcEAVK1aNdVyibcdOXIkS5KszzzzDCdOnKBRo0Z89dVXybYHBgbi4+OT6v6fffYZo0aNSrZ+5cqVeHh4ZDo+keyyatUqo0OQbDKoHIwNdybcbGJvcCj9x6/i6WpWnE1GRya3UzsUMZbaoOQHzoWf5v6bYRSLOIIpLhKmP8rfFV/lmncto0NTGxTJAdQOJaeKiopKd1klWRO5ceOG43VaE1OVKFEixX0y4+WXX6Zfv36pbi9YsGCa+48cOZIRI0Y4lsPCwggICKBjx454e3tnSYwiWclsNrNq1So6dOiAq6ur0eFINmnYNIzHf/2byFgLh286sTUugNEP34fJpExrTqB2KGIstUHJd8ydsc5/EqdTq3GxxdHs7Dgsj07GVrmDMeGoDYoYTu1QcrqEJ8XTQ0nWRBJnp93c3FItl3hbRERElhy7Y8eOmdq/YMGCKSZiXV1d9UElOZru0bytXrmiTBzYiCG//U2cxcrvey7g7+POG52qGR2aJKJ2KGIstUHJN1xdof9MmPckHFuCyRKLy7xB8NgUqN7VwLDUBkWMpnYoOVVG7ktNfJVI4jcuPj4+1XKJx2O4Uw9TEZH8rnllP77tW5eEzqvj151k8pYzxgYlIiIixnApaE+q3vewfdlqhrmD4PACQ8MSERHJLCVZE0n8WH1oaGiq5RJ3Ffby8srWmERE8oJudUrxYbf7HMujFh9h8YGLBkYkIiIihnF2hd6ToE5f+7I1Hn5/CvbPMTYuERGRTFCSNZFixYo5kqZnz55NtdyZM//1wKpUqVJ2hyUikicMaVGB4W3sn5k2G4yYs5+tp0IMjkpEREQM4ewCD/8I9Qfal21WWPAc7JlmbFwiIiJ3SWOy3qZOnTps2bKFHTt2pFpm+/btgH14gfvuuy/VcjmB2WxOMryBSE6RcF/q/sxfXmlTkSuhMfy+5wJxFitDp+5i5tONua+kJugzgtqhiLHUBkWAh77ByckV592/AjZY9CKWuCisDZ/K9kOrDYoYT+1QcrqM3JtKst6me/fubNmyhY0bN3Lp0iVKliyZrMysWbMAaNu2LYUKFbrXIaYpMDCQwMBALBYLACtXrsTDw8PgqERSt2rVKqNDkHuseQH4p7ATh286ERlrYeDEbbxay0LR1OcblGymdihiLLVByfdsralZ7AKVr60AwHn5Wxw5uI/TxTvfk8OrDYoYT+1QcqqoqKh0lzXZbDZbNsaSIwwbNoyffvqJSpUqcfLkyTTLXr58mcqVKxMZGUnv3r2ZO3cuTk7/jaoQGBjIiy++CMCiRYvo3r17tsZ+t8LCwvDx8SEkJCTJWLMiOYXZbGbVqlV06NBBs0jmQ9FxFgZP3sXeYPv41+WKeDBnaGOKemoywXtJ7VDEWGqDIonYbDit/xTnrWMdqyxt3sfa/JVsO6TaoIjx1A4lpwsLC8PPz4/Q0NA75tfyZE/WPXv2EBQU5FhOGF81MjKSP//807Hew8ODjh07JtnX39+fTz75hNdee4358+fTqlUrBg0aRKFChVi1ahVTp04FoGfPnjk2wZqYq6urPqgkR9M9mj+5urry65Am9PlpGyevRnDuRhTPztjHrKFNKVQwT3415WhqhyLGUhsU+VeHj6CAB6wfDYDzuv/hbDXDg2+DyZRth1UbFDGe2qHkVBm5L/PkX7LfffcdU6ZMSbb+8uXL9OrVy7Fcrly5FCe4evXVV4mKiuKjjz5iy5YtbNmyJcn2Rx99NMX6RUQk/QoXKsCUp5rQ+4etXA6L4cD5UIZN382kwY0p4KJ5GUVERPIdkwke/D9wKQCrP7Kv2/A5WGKh3YfZmmgVERHJrDyZZG3QoAG3bt26Y7nixYunuu2dd96hf//+zJkzh6NHjxIXF0fZsmXp2bMnzZo1y8JoRUTyr9K+7kx9ugmP/riVsJh4Np0I4a3f9/PtY/VwctIfUiIiIvlSy9fAxQ2Wv21f3jwG4mOh02glWkVEJMfKk0nWl19+mZdffjnT9VSoUIG33347CyISEZHUVC3hxaQhjXnilx3Exlv5c99FinkV5N2u9xkdmoiIiBil6fPgXACWjLAvb//Bnmjt8jU46YkXERHJefTtJCIihmtcvgjf969PQufViZvOMHHjaWODEhEREWM1fhp6BgL//g/Crknw10tgtRgaloiISEryZE9W+Y/ZbMZsNhsdhkgyCfel7k9J0KZqUT7ucR/vLTwCwKdL/6GwuzM965UyOLK8S+1QxFhqgyLpUKsvJpxwXjQck80Ke6djNcdg6T4enDL356zaoIjx1A4lp8vIvWmy2Wy2bIxF7rHAwEACAwOxWCwcP36cmTNn4uHhYXRYIiLptjzYxLLzzgA4mWw8W81KjcL6qhIREcnPSt3cScOzP+KEvRfrBd/G7C7/PDaT+g2JiEj2iYqKYsCAAYSGhuLt7Z1mWSVZ86iwsDB8fHwICQm5400gYgSz2cyqVavo0KEDrq6uRocjOYjNZuOjxf8wc+d5ADwKODPtyUbUKeNjcGR5j9qhiLHUBkUyxnR8Gc5/PI3JEgeAtUpnLI9MApeCd1Wf2qCI8dQOJacLCwvDz88vXUlW/eyXx7m6uuqDSnI03aOSkv89XIebUfEsO3SZqDgLQ6fv5fdhzahYzNPo0PIktUMRY6kNiqRTzR5QYBbMeRziY3A6sRyn+YOh73Rwdb/ratUGRYyndig5VUbuS018JSIiOY6zk4kxfetxf4UiANyIjGPQrzu5GhZjcGQiIiJiqCrtYcAccP13SLSTq2HmYxAXaWxcIiKS7ynJKiIiOZKbqzM/D2pEdX8vAM7fjGbwb38TFqNB8UVERPK1ig/CE/OhwL9PuJzZCNN7Q0yYoWGJiEj+piSriIjkWD7urkx5qgmlfe2PAP5zKYxnp+4ixmwxODIRERExVLnmMPBPKPjvmO1B22BaL4i+ZWRUIiKSjynJKiIiOVoJbzemPt2Ewh72sXC2n77BiLn7sFg1b6OIiEi+FtAYBi8E98L25Qv/z96dh0dZnX0c/06SSSBAwhL2TXbcwV1xqwru+1Kl7lqttVZrF7Vardbd1qo16mvdF9xXXIm74q4oyBZAQUBEIpABAmQyM+8fowGLQAIJZ5J8P9fl1XMyz8z86HXuzMydZ87zMdx3EFTMD5tLktQk2WSVJGW8Pu1bcteJ29I8mg3AC+O+5dKR40mlbLRKktSkdRkMJzwH+UXp+ZzP4d4DYfG8sLkkSU1OTugAql/xeJx43P0LlXl+XJeuT9XUZp1b8p+jt+A3D35GVTLFfe/NoF1+lN/u3jt0tAbLOpTCsgalOtJuABz3LDkPHkpk8VyY+wWpe/ajaviT0KrTau9mDUrhWYfKdLVZm5GUpwE1KsXFxRQXF5NIJCgtLWXEiBHk5+eHjiVJdebDeREenJpdPT+6d4IdO/pSJklSU9di2bcMmXo1zePp7QIW53VkdN/zWZbbLnAySVJDVVFRwfDhwykvL6egoGCNx9pkbaRisRiFhYWUlZWtdRFIIcTjcUpKShg6dCjRaDR0HDUwt7/9FdeNmgJAVgRuGT6IPQd2CJyq4bEOpbCsQakeLJxBzgOHEin/GoBUYQ+qjn0KWvdc5VBrUArPOlSmi8ViFBUV1ajJ6nYBjVw0GvUXlTKaa1Tr4re/6Mf3S6q4a/RXJFNw9iNjGfHr7dm6Z9vQ0Rok61AKyxqU6lD7vnDyi+l9Wed/SaT8a6L3HwwnPAvt+vzsXaxBKTzrUJmqNuvSC19JkhqcSCTCRftvzEFbdgFgeVWSk+/5mNK5iwInkyRJwRV2g5NehKIB6XlsFty9H8ybHDaXJKlRs8kqSWqQsrIi/PPILdmlX/pqwuVL45xw14d8s3Bp4GSSJCm4Vp3gxOehw6bp+eJv043Wb78Im0uS1GjZZJUkNVi5OVnceuzWbN61EIA55cs44a4PWVhRGTiZJEkKrmV7OPE56Lxlel5RBvceAN98FjSWJKlxsskqSWrQWublcPdJ29KzXT4AU75bzKn3fsyyeCJwMkmSFFx+Wzj+Wei6TXq+dAHcexDM+jhsLklSo2OTVZLU4BW1zOO+k7ejqGUuAB/PWMDvRoyhKpEMnEySJAXXvDUc/zT02Ck9X14O9x1M5Ov3QqaSJDUyNlklSY1Cz3YtuOek7WiRmw3AKxPnctHTX5BKpQInkyRJweW1gmMfh167pueVi8l++JcULZoQNpckqdHICR1A9SsejxOPx0PHkFbx47p0faouDeiQzy3DB3Hq/Z8ST6R4+KOZtM2P8oe9+oaOlpGsQyksa1DawCK5cOSDZD9+IllfvkokXsEO0/5FvHQL6D8sdDqpSfK1UJmuNmszkvIUn0aluLiY4uJiEokEpaWljBgxgvz8/NCxJGmD+rQswn1TskgRAeCIXgl26eTLnSRJgqxknG2+upnOsTEAVEVyebffeSxo0S9wMklSpqmoqGD48OGUl5dTUFCwxmNtsjZSsViMwsJCysrK1roIpBDi8TglJSUMHTqUaDQaOo4aoXvfm8HlL0wGIBKBG4/agn036xQ4VWaxDqWwrEEpoEQlkSdPJaf0BQBSzVpTdfzz0H5A4GBS0+JroTJdLBajqKioRk1Wtwto5KLRqL+olNFco6ovp+7al+8rqrj1jWmkUvCnx7+gfUE+O/ZpFzpaxrEOpbCsQSmAaJT4of9lXvFQ2i+eQGTZQqIPHwWnjILCbqHTSU2Or4XKVLVZl174SpLUaP1l7wEcsXX6g1JlIslp933MhG9igVNJkqSMkJPHh73PJtlpy/Q8NhvuPxQq5ofNJUlqkGyySpIarUgkwlWHbc4eAzsAsGh5FSfc/SEz51cETiZJkjJBVXZzEkc/DG37pH9QVgoPHgmVS8IGkyQ1ODZZJUmNWjQ7i+LhWzG4R2sA5i1azvF3fcj3i5eHDSZJkjJDi/Zw3JPQsmN6PvtjePR4SHi1c0lSzdlklSQ1es1zs7nrhG3p074FAF+VLeHkez5iyfKqwMkkSVJGaLMRHPsk5BWm51Nfgad/C8lk0FiSpIbDJqskqUlo0yKX+07Zno4FeQB8PqucMx78lHjCD0+SJAnotBkMfxhymqXn4x6FURdCKhU2lySpQbDJKklqMrq2bs69J29Hq2Y5ALxVOo/zHh9LMumHJ0mSBPTcCY64GyI/fFR+/xZ4599hM0mSGgSbrJKkJmVgpwLuOH4bcnPSL4FPjpnNNS9NCpxKkiRljIH7wYE3rpi/eil8en+4PJKkBsEmqySpydm+dzv+c8xgsiLp+f+99SV3vP1l2FCSJClzbHU87HnJivnI38OkF8LlkSRlvJzQAVS/4vE48bhXxVTm+XFduj4Vyh7923HpgZvwt2cnAHD58xNp3TyHg7fsHDjZhmMdSmFZg1JYa63B7X9H1qJvyf7w/yCVJPX4SSSOeYxUjx03YEqpcfO1UJmuNmszkkq5i3djUlxcTHFxMYlEgtLSUkaMGEF+fn7oWJKUsV6cGeGlWdkAZEVSnD4wycDWvjRKkiQglWSrGbfTfcG7AMSz83mn31+JNe8ROJgkaUOoqKhg+PDhlJeXU1BQsMZjbbI2UrFYjMLCQsrKyta6CKQQ4vE4JSUlDB06lGg0GjqOmrBUKsXFIyfy8EezAMjPzeaBk7dh866FgZPVP+tQCssalMKqcQ0mKsl+9FiyvnwNgFTLjlSd8AK07rmBkkqNl6+FynSxWIyioqIaNVndLqCRi0aj/qJSRnONKhNccegWLKiI8/L4uVRUJvj1/WN4/Iyd6FXUInS0DcI6lMKyBqWw1lqD0Sgc/QDcexDM/pjI4rlEHzoKTn4ZWrbfcEGlRszXQmWq2qxLL3wlSWrysrMi3Hj0YLbbqC0A3y+p5Pi7PuC7RcsCJ5MkSRkhtwX86jEo6p+ez58GDx4ByxeFzSVJyhg2WSVJAppFs/nvCdswsFMrAGbOX8qJd33EomVuwi9JkoD8tnDsk1DQNT2f8xk8/CuoWh40liQpM9hklSTpB4XNo9x78nZ0bd0cgAlzYvzl8bG4fbkkSQKgdfd0o7VZ6/T8qzfhqdMhmQgaS5IUnk1WSZJW0rGgGfeevB2FzdN777z4xbc88P6MwKkkSVLG6DAwvXVATvqPsox/Cl48D/yjrCQ1aTZZJUn6H307tOSfR25ZPf/H8xMZ/015wESSJCmjdN8OjroPItnp+Uf/hbeuC5tJkhSUTVZJkn7G0E06ctKQjQCorEpy1ogxLFleFTaUJEnKHP2HwSG3rJi/fgV8fFe4PJKkoGyySpK0GufvO5DNuhYA8GXZEi56+gv3Z5UkSStseTQMu3zF/LlzYcIz4fJIkoKxySpJ0mrk5WRz8zFb0TIvB4Cnxszm8U9mBU4lSZIyyk5nwZCzf5ik4IlT4au3gkaSJG14NlklSVqDjYpacOVhm1fPL35mPFO/WxQwkSRJyjh7XQqDfpUeJyrhoeEw5/OwmSRJG5RNVkmS1uKgLbtwzHbdAVgaT3Dmg2NYFk8ETiVJkjJGJAIH3gT990nPKxfBA4fD99PC5pIkbTA5oQOofsXjceLxeOgY0ip+XJeuTzUUF+zdn4+nz2fKd0uYPHcRf3/2C/5x0CahY60X61AKyxqUwqqXGjzkdrJHHEnWrA9gyTxS9x9G1QnPQ8uOdfccUiPia6EyXW3WZiTlFTwaleLiYoqLi0kkEpSWljJixAjy8/NDx5KkRuHbCvjnuGziyQgAJ/ZLMLjIl1FJkrRCtGoJO0+5goJl6X3cy5v34J1+f6Uq289lktTQVFRUMHz4cMrLyykoKFjjsTZZG6lYLEZhYSFlZWVrXQRSCPF4nJKSEoYOHUo0Gg0dR6qxxz6ZzV+fHg9Ay7wcnv7tDvRs2zA/NFmHUljWoBRWvdZgbA459+1HpHwmAMkeO5E45lHIaVa3zyM1cL4WKtPFYjGKiopq1GR1u4BGLhqN+otKGc01qobmmO178uH0BTz92TcsXl7FHx4dx+Nn7EheTnboaOvMOpTCsgalsOqlBtv1gOOegrv2horvyfr6XbKe+Q0cdR9kNdz3DFJ98bVQmao269ILX0mSVAuRSITLD92cXkUtABg3u5xrXpwcOJUkSco4Rf3gV49BNP2egUnPwXN/AL9MKkmNkk1WSZJqqWVeDjcPH0xudvpl9K7RX1EyYW7gVJIkKeN03RqOfgCyfjgT6tN74fUrwmaSJNULm6ySJK2DTbsUctEBG1fP//z453yzcGnARJIkKSP12QMOvQ1IXziTt66DD/4vaCRJUt2zySpJ0jo6boee7L1pRwAWVsT5/UNjqEokA6eSJEkZZ/MjYN9rVsxfPA/GPR4ujySpztlklSRpHUUiEa49fEu6tm4OwMczFvDvV0oDp5IkSRlp+9Nh1z//MEnBU7+Baa8FjSRJqjs2WSVJWg+F+VH+M3wwOVnprwDe8sY03p4yL3AqSZKUkX5xIWx9YnqcjMPDx8LsT4JGkiTVDZuskiStp616tOHPew8A0hcM/sMjn/HdomWBU0mSpIwTicD+18PAA9Lz+BJ48EgomxI2lyRpvdlklSSpDvx6l97sPqA9AGWLK/nDI5+RSKYCp5IkSRknKxsOvxN67pyeV3wP9x8GsTlhc0mS1otNVkmS6kBWVoR/HbklHQvyABg99XtufWNq4FSSJCkjRZvBMSOg4+bpefnX8MBhsHRB2FySpHVmk1WSpDrSrmUeNx49mB+2Z+X6klI+/Gp+2FCSJCkzNSuEY5+ANhul599NgBFHQ2VF0FiSpHVjk1WSpDq0Q+92/H7PfgAkU3D2w2NYsKQycCpJkpSRWnWE456CFukth5j5Pjx+EiSqwuaSJNWaTVZJkurYWXv0Y4febQGYU76MPz32OamU+7NKkqSf0bZ3+ozW3FbpeelLMPLs9NU0JUkNhk1WSZLqWHZWhBuPHky7FrkAvDrpO+5856vAqSRJUsbqvGV6j9bs9HsHPnsAXvl70EiSpNqxySpJUj3oWNCMfx21ZfX8mpcm8fnMheECSZKkzNZrVzj8DuCHzd1H3wDv3hwykSSpFmyySpJUT3Yf0IHTd+sNQDyR4ncPfUpsWTxwKkmSlLE2ORgOuH7FfNSF8PnD4fJIkmosJ3QA1a94PE487gd6ZZ4f16XrU43d2b/ozQdffs9nM8uZOX8p5z32OTf+cgsikUjoaNahFJg1KIWVsTW45XFkxb4l+61rAEg9cyaJ3EJSffcKHEyqexlbh9IParM2IymvxNGoFBcXU1xcTCKRoLS0lBEjRpCfnx86liQ1afOXw7WfZ7M0kW6sHtU7wZCOvvxKkqTVSKXYfNb99C57BYCqSC7v9juPBS36BQ4mSU1LRUUFw4cPp7y8nIKCgjUea5O1kYrFYhQWFlJWVrbWRSCFEI/HKSkpYejQoUSj0dBxpHo3asJcznzocwByc7J44vTtGdipVdBM1qEUljUohZXxNZhMkP30aWRNfAaAVLPWVB3/PLQfEDiYVHcyvg7V5MViMYqKimrUZHW7gEYuGo36i0oZzTWqpmL/Lbvx4fSF3PveDCqrkpzz6Fie/d3OtMgL/1JsHUphWYNSWJlbg1E4/L/w4EL46k0iyxYSffgoOGUUFHYLHU6qU5lbh2rqarMuvfCVJEkbyAX7bcymXdJ//Zw2bwkXPzM+cCJJkpTRcvLg6Aeh86D0PDYb7j8UKuYHjSVJWpVNVkmSNpBm0WxuHr4VLXKzAXji01k88cmswKkkSVJGy2sFxz4Bbfuk52Wl8OCRULkkbC5J0k/YZJUkaQPqVdSCKw/bvHr+t2e+YNq8xQETSZKkjNeiCI57Clp2Ss9nfwyPHg8Jr8guSZnCJqskSRvYwYO68sttugNQUZngzAc/ZVk8ETiVJEnKaG16ps9ozStMz6e+Ak//FpLJsLkkSYBNVkmSgvj7QZvSr0NLACZ9u4jLn58QOJEkScp4nTaD4Q9DTrP0fNyjMOoiSKXC5pIk2WSVJCmE5rnZFP9qK5pF0y/FD7z/Nc+PnRM4lSRJyng9d4Ij7oZIeo933i+G0TcEjSRJsskqSVIw/Tu24u8Hblo9P/+JsXz9fUXARJIkqUEYuB8ceOOK+St/h0/vDxZHkmSTVZKkoH65bXcO2rILAIuWV3HWQ59SWeXeapIkaS22Og72vGTFfOTvYdIL4fJIUhNnk1WSpIAikQhXHLoZPdvlA/D5rHKue3lS4FSSJKlB2PkPsMOZ6XEqCY+fBDPeDZtJkpoom6ySJAXWqlmU4uFbkZudfln+79tf8dqkuYFTSZKkjBeJwLDLYYtfpudVy2DE0TB3fNhcktQE2WSVJCkDbNa1kL/uN7B6/sdHP2dO+dKAiSRJUoOQlQUHF0PfvdLz5eVw/2GwYEbYXJLUxNhklSQpQ5yw00YM26QjAAsq4pz90GdUJdyfVZIkrUV2FI66D7puk54v/hbuPxQWzwubS5KaEJuskiRliEgkwrVHbEHX1s0B+HD6fG56dUrgVJIkqUHIbQG/egyKBqTn86fBg0fA8kVhc0lSE2GTVZKkDNI6P5ebjhlEdlYEgP+8PpXRU8sCp5IkSQ1Cfls47kko6Jqez/kMHjkWElVBY0lSU2CTVZKkDLN1z7b8aVj6LJRUCs555DPmLVoeOJUkSWoQCrvBsU9C8zbp+ZdvwPvFQSNJUlNgk1WSpAx0+q692bV/ewDmLVrOuY9+RjKZCpxKkiQ1CB0GwtEjgPQ3Y3j9SiibGjSSJDV2NlklScpAWVkRrj9qS9q3ygPg7Sll3PrmtMCpJElSg9FzJ9jht+lx1TJ49neQ9IKaklRfbLJKkpShilrmceMvBxH54SSU60tK+Xj6/LChJElSw7HHRdCmV3r89Xvw0R1h80hSI2aTVZKkDLZT3yLO2qMfAIlkit8/NIaFFZWBU0mSpAYhNx8O+s+K+St/hwUzgsWRpMbMJqskSRnu93v0ZbtebQH4pnwZf3psLKmU+7NKkqQa6LULbHNyehxfAiN/n76ypiSpTtlklSQpw+VkZ3HT0YNpkx8F4JWJc7l79PSwoSRJUsOx16VQ0C09/vINGPNA0DiS1BjZZJUkqQHoVNiM648aVD2/6sWJjJ21MFgeSZLUgDQrgANvXDF/+UKIzQmXR5IaoZzQAVS/4vE48Xg8dAxpFT+uS9enVHM792nDKUN6cufoGcQTKX434lOePmNHWjVbt5dz61AKyxqUwmpyNbjRbmRvcTRZYx+G5eUkR55N4sgHqL7CphRAk6tDNTi1WZuRlJu6NSrFxcUUFxeTSCQoLS1lxIgR5Ofnh44lSaojVUm4aXw2MxanPxANbpfkhH5JPx9JkqS1ilYtZo+JF9CsqhyAj3uewey2OwZOJUmZq6KiguHDh1NeXk5BQcEaj7XJ2kjFYjEKCwspKytb6yKQQojH45SUlDB06FCi0WjoOFKDMmvBUg665T0WLasC4PKDN+GX23Sr9eNYh1JY1qAUVlOtwcik58l54gQAUs3bUnX6aGjRPnAqNVVNtQ7VcMRiMYqKimrUZHW7gEYuGo36i0oZzTUq1V6vDlGuPXwLznjwUwD+8fwktu1VxIBOrdbp8axDKSxrUAqrydXg5ofAxENgwtNEls4nWnIhHHl36FRq4ppcHarBqM269MJXkiQ1QPtu3pnjdugJwPKqJGeO+JSKyqrAqSRJUoOw33XQvG16PP5JmPhc2DyS1AjYZJUkqYG6cP+N2bhz+isrU79bzCXPjA+cSJIkNQgtO8C+16yYP38uLF0QLo8kNQI2WSVJaqCaRbMpHj6Y/NxsAB77ZBZPjZkVOJUkSWoQNj8S+u+THi+eCy9fGDaPJDVwNlklSWrAerdvyRWHblY9v/CpL/hy3uKAiSRJUoMQicAB/4a8Hy7k8tmDMPWVsJkkqQGzySpJUgN36OBuHLF1NwAqKhP8bsQYlsUTgVNJkqSMV9AFhl2+Yj7yHFi+KFgcSWrIbLJKktQIXHbwpvRp3wKACXNiXPnCxMCJJElSg7DV8dBrt/S4fCa88vegcSSpobLJKklSI5Cfm0Pxr7YiLyf90n7fezN46Ys5gVNJkqSMF4nAQTdBND89/+gOmP5O2EyS1ADZZJUkqZEY2KmASw7ctHr+58fHMnN+RcBEkiSpQWizEex5yYr5s2dBpe8hJKk2bLJKktSIHLNddw7YojMAi5ZVcdZDY4gnkoFTSZKkjLfdadB9h/R4/pfw+hVh80hSA2OTVZKkRiQSiXDVYZvTo236K3+fzVzIP1+eHDiVJEnKeFlZcPDNkJ2Xnr9/C8z6OGwmSWpAbLJKktTItGoW5ebhg4lmRwD4v7e+5PXJ3wVOJUmSMl5RP/jFBelxKgnPnAlVy8NmkqQGwiarJEmN0BbdWnP+vhtXz//46Od8W74sYCJJktQg7HgWdB6UHs+bBG9dFzSOJDUUNlklSWqkTh6yEXtt3BGA+UsqOfvhMSSSqcCpJElSRsvOgYOLISsnPX/n3zBnbNhMktQA2GSVJKmRikQiXHfEFnQubAbAB1/N56ZXpwROJUmSMl6nzWCXP6XHyar0tgGJeNhMkpThbLJKktSItWmRy03HDCY7K70/602vTeHdaWWBU0mSpIy3yx+hwybp8bdj4d2bwuaRpAxnk1WSpEZu243acu7Q/gCkUnDOw59RttiLWEiSpDXIyYWDb4bID22DN66GeZPDZpKkDGaTVZKkJuCM3fqwS78iAL5btJxzH/2cpPuzSpKkNem6Nez4u/Q4UQnP/A6SibCZJClD2WSVJKkJyMqKcP1RgyhqmQfAW6XzuGP09LChJElS5vvFX6Ftn/R41ofwwf+FzSNJGcomqyRJTUT7VnncePQgIuntWbn+lal8tShsJkmSlOGizdPbBvzo1ctg/pfh8khShrLJKklSEzKkbxG/+0VfABLJFPdPyWZZ3K/9SZKkNei5E2x3WnpctRSe/X16o3dJUjWbrJIkNTFn79mPbXq2AeD75RHueGd62ECSJCnz7XkJFPZIj6e/DZ/cEzSOJGUam6ySJDUxOdlZXHnY5mRnpfcN+L+3v2LWgorAqSRJUkbLawkH3bhiPupvUD4rXB5JyjA2WSVJaoL6d2zFcdt3B2BZPMkVz08MnEiSJGW8PnvA4GPT48pFMPIctw2QpB/YZJUkqYn6/R59aBlNfzB68YtveWdKWeBEkiQp4w27Alp2So+nlsDYR8LmkaQMYZNVkqQmqlWzKAf1SFbP/z5yPPFEcg33kCRJTV7z1nDAv1fMXzwPFs0NFkeSMoVNVkmSmrBt26cY1L0QgKnfLebed6eHDSRJkjLfwP1gsyPS42UL4YU/BY0jSZnAJqskSU1YVgQu3n8gkfQ1sLjhlSl8t2hZ2FCSJCnz7Xst5BelxxOfhfFPB40jSaHZZJUkqYnbvGshR2+bvgjW4uVVXP3ipMCJJElSxmvRDva7dsX8hT9BxfxweSQpMJuskiSJP+89kMLmUQCe/HQ2n8zwQ5IkSVqLTQ+DgQekx0vmwUvnh80jSQHZZJUkSbRtkcsfh/Wvnl/8zHgSyVTARJIkKeNFIrD/v6BZen93xj4CpS+HzSRJgdhklSRJAAzfrgcbdy4AYPw3MR7+6OvAiSRJUsZr1Qn2vmrFfOQ5sKw8WBxJCsUma4aZOXMmL7zwAk899RSfffZZ6DiSpCYkJzuLSw/atHp+3cuTWbCkMmAiSZLUIAwaDn32TI8XfQMlF4fNI0kB2GTNEJMnT2bYsGHsvvvu3H777dx1113suuuubLHFFnz00Ueh40mSmojterXl4EFdAFhYEedfJZMDJ5IkSRkvEoEDb4Dclun5J/fAl2+GTCRJG5xN1gyxbNkyLrvsMqZNm8bTTz/NyJEjmTZtGosXL+bQQw+lqqoqdERJUhPx1/02pkVuNgAjPviaL2b7lT9JkrQWrXvAXn9fMX/2LKhcEiyOJG1oNlkzxJZbbskOO+zwk5+1b9+eAw44gNmzZzN79uxAySRJTU3HgmactWc/AJIp+Puz40mlvAiWJElai21OgZ5D0uOFM+DVf4TNI0kbUJNosi5btozFixdTUVGxTvdPpVLBziQdO3YsHTt2pEuXLkGeX5LUNJ08pBe9i1oA8PGMBTz9mX/skyRJa5GVBQf9B3Kapecf3AZfvx82kyRtIDmhA9SH0tJSRo8eXf3f5MmTSaVS9OnTh6lTp9boMSorK7nhhht44IEHmDx5MlVVVXTp0oWDDz6Yiy66iE6dOv3s/R5//HEWL1681sfv2LEj++677yo//+CDD5g4cSILFy7khRde4Ntvv+XJJ58kGo3WKLckSXUhNyeLSw7alBPu+hCAK1+YxF4bd6RVM1+PJEnSGrTrA3tcBKMuAlLwzO/gN+9AtFnoZJJUrxplk3WLLbZg+fLl1fNIJFKr+5eXl7PnnnvyySefVP8sOzubWbNmUVxczEMPPcRrr73Glltuucp9//SnPzFjxoy1PseQIUN+tsk6ZcoU3njjDb777js++ugjdt55Z9q1a1er/JIk1YXd+rdn2CYdGTVhLvMWLec/r03lr/ttHDqWJEnKdDv8FsY/BbM/ge+nwJtX/3S/VklqhBplk3XAgAFsvfXW7LTTTgwZMoQbbriB22+/vcb3P+mkk/jkk0/Iy8vjn//8JyeddBLNmjXj9ddf55RTTuHrr7/mwAMPZOLEibRo0eIn9z3iiCMoKytb63P079//Z39+7LHHcuyxxwLw/fffM3ToUHbeeWcmT55M27Zta/xvkCSpLvztgE14s3Qey6uS3PXOVxy1TTf6dmgVOpYkScpkWdlwcDHctgsk4zD6JtjkYOgyOHQySao3jbLJ+vnnn/9kXpszWd9//32eeuopAP71r39x5plnVt+211578fzzzzN48GBmzpzJTTfdxAUXXPCT+//zn/9cj+Q/1a5dO8477zyOPvpoXnzxRX71q1/V2WNLklQT3dvm85vd+nDjq1OoSqa4dOQE7jt5u1p/S0SSJDUxHTaG3c6D1y+HVCK9bcCvX4ec3NDJJKleNIkLX9XGAw88AECHDh047bTTVrl9s80245BDDgHg/vvvr/c8eXl5QHqPWEmSQjhj9z50bd0cgLenlPHy+LmBE0mSpAZh53Og4+bp8dwvYPQNIdNIUr2yyfo/XnvtNSB91urqLjZ1wAEHADBx4kTmzJlTJ8/7cxfkSqVS3HnnneTm5rLnnnvWyfNIklRbzaLZ/O2AFXux/uO5CSytTARMJEmSGoTsKBx8M0Sy0/M3r4W5E8JmkqR60ii3C1hXlZWVTJkyBUifsbo6K982fvx4OnfuvN7PffPNN/PBBx/wi1/8gh49elBWVsbjjz/OlClTuOuuu+jRo8ca7798+fKfXOwrFosBEI/Hicfj651Pqms/rkvXpxRObepwj/7tGNKnHaOnfc/shUu55fVSfr9H3/qOKDVqvhZKYVmDG0j7Tcna8Syy370BknGST/+WxIkvQpbtCFmHyny1WZv+VlvJvHnzqKqqAqBr166rPa5bt27V47o6k/WGG25gwoQJPP/883z22Wfk5uZyxhlncMghh9CxY8e13v+qq67i0ksvXeXno0aNIj8/v04ySvWhpKQkdASpyatpHe7WCt6LZJNMRbj1jWm0WVhKu2b1HE5qAnwtlMKyButfVnIzds/rTKvlc8iaM4YJ957DtI77hY6lDGIdKlNVVFTU+FibrCtZsmRJ9bhFixarPW7l2xYvXlxnz7/JJpuwySabrNN9L7jgAs4999zqeSwWo3v37gwbNoyCgoK6iijVmXg8TklJCUOHDl3t1hyS6te61OHcFpO5c/QMqlIR3lvWhVsOG1S/IaVGzNdCKSxrcMOKDOpK6t79iJBi0++eZsDBf4C2fULHUmDWoTLdj98UrwmbrKuRSqVWe1symaweZ8rVlfPy8qovkrWyaDTqLyplNNeoFF5t6vCcoQN4duy3zFu0nJKJ3/HuVwvZrX/7ek4oNW6+FkphWYMbSK+dYIcz4P1biFQtI/r8H+DE5yHLS8XIOlTmqs269LfZSlq2bFk9Xvms1v+18m0r30eSpMauVbMof91vYPX80mfHU1mVXMM9JEmSfrDHRdBmo/T463fh4zuDxpGkumSTdSUdOnQgNzcXgJkzZ672uJVvW3l/VkmSmoJDBnVlm55tAPiybAl3j/4qcCJJktQg5LaAA29aMS+5BBbMCJdHkuqQTdaV5OTkMGDAAAA+//zz1R638m2bbrppveeSJCmTRCIR/n7Qpvy4Y85Nr05hbmxZ2FCSJKlh6L0bbH1iehxfAiPPhjVs1ydJDYV7sv6PoUOHMm7cOF599VWWLl1K8+bNVznmmWeeAWDQoEG0b5/Z+9DF43Hi8XjoGNIqflyXrk8pnPWpwwEd8jlm226M+HAWSyoTXPHcBP515OZ1HVFq1HwtlMKyBgPa/WJySkcRWfQNfPk6VZ/cR2rL4aFTKQDrUJmuNmvTJuv/OO644/j3v//NggULuP7667nwwgt/cvt7773Hiy++CMCJJ54YIOGaFRcXU1xcTCKRAGDUqFHk5+cHTiWtXklJSegIUpO3rnW4WRLyc7KpqIrw7Ng5bJSYSZ+COg4nNQG+FkphWYNhdGh/DDsu+hcAqRfP57XpKZZF2wROpVCsQ2WqioqKGh8bSaUy47z8BQsWcMMNNzBo0CAOPfTQ9Xqs5cuX/6TTfM4553DnnXfSu3fvn3zVPysr62cbkCeccAL33XcfWVlZ/PWvf+Wkk06iRYsWlJSUcM455/D999/Tv39/xo4dS15e3nplrS+xWIzCwkLKysooKPATrzJPPB6npKSEoUOHehVJKZC6qMOHPprJxc9OBGBgx5Y8dcYO5GS7G5FUE74WSmFZg+FlP/tbssY9CkCy3z4kjryf6v2I1CRYh8p0sViMoqIiysvL19pfC34m6/fff8/111/PzTffTCwW4+67717vxzz99NO59957V/n5l19+SatWrarnPXv2ZPr06ascd9tttzF79mxeffVVLr/8ci6//PKf3N6jRw+ef/75jG2wriwajfqLShnNNSqFtz51+KsdevHoJ7P5YnaMSXMX89iYORy/40Z1G1Bq5HwtlMKyBgPa9xr48nVYMo+sKS+RNflZ2PyI0KkUgHWoTFWbdRnsVJN58+Zx3nnnsdFGG3HllVcSi8Xq7LGbNWtGixYtavTfz2nevDklJSXcfffd7LnnnnTt2pX27duz9dZbc9lllzFu3Dj69u1bZ3klSWqosrMiXHrQiotA/mtUKfOXVAZMJEmSGoz8trD/v1bMX/wLLCkLl0eS1sM6n8kaj8d57733+Pzzz/n+++/Jzs6mV69e7LHHHnTp0mW19ysrK+Pqq6/m1ltv/dl9Deriq+233XYbt91223o9RiQS4cQTT8zIfVclScokW/dsy2FbdeXJT2dTvjTOdS9P5qrDvAiWJEmqgU0Oho0PgonPQsX36UbrEXeFTiVJtbZOTdabb76Zyy67jHnz5q1yW1ZWFscddxw33ngjhYWF1T+Px+Nce+21XHPNNSxatOgn94lEIhx88MH87W9/Y6uttlqXSJIkKaDz9x3IqPFzWby8ioc/+ppjtuvOFt1ah44lSZIagv3+CdPfhqUL4IsnYLPDYeD+oVNJUq3Uusl66qmncuedd6729mQyyb333svnn3/O22+/TcuWLfnyyy856qij+OSTT35ybFZWFocffjh/+9vf2Hxzz3ipD/F4/CcXAZMyxY/r0vUphVOXddimWTZn/aI3V71USioFFz/zBY+cuh1ZWV68QlodXwulsKzBDNKsLZGhV5Dz7G8BSD33B6q6bg/NCtdyRzV01qEyXW3WZiSVSqVqevD999/P8ccfX+MHP/fcczn77LPZeeedmTlzZvXPs7OzOfroo7nwwgvZeOONa/x4Wrvi4mKKi4tJJBKUlpYyYsQI8vPzQ8eSJDUBiSRcMzabuUvTjdXhfRJs36HGbzMkSVJTlkqx/ZfX0yn2OQAz2u7KZz1PDRxKUlNXUVHB8OHDKS8vX+sWp7Vqsg4cOJDJkydXz4cPH87xxx9P3759qaysZMyYMVx//fXVZ6y2bNmSnXfemZdeeqn6PocffjhXXHEFAwYMqO2/S7UQi8UoLCykrKysTva5lepaPB6npKSEoUOHehVJKZD6qMPR077nxHvS7wPatcil5JwhtGpmjUs/x9dCKSxrMAPFviHn9iFElqe3GKw65jFSvX8ROJTqk3WoTBeLxSgqKqpRk7XG2wV89tlnP2mwXnfddfzpT3/6yTEbb7wxRx55JAcddBAvvfQSixcvrm6wFhQUcO+993LIIYfU4p+i9RWNRv1FpYzmGpXCq8s63H1gJ/bdrBMvfvEt3y+p5OY3pnPxgZvUyWNLjZWvhVJY1mAGadcThv4DnjsHgJwXzoXfvgd5rcLmUr2zDpWparMus2p64EcffVQ9HjhwIH/84x9X++S33XYb2dnZP/n5k08+aYNVkqQm4ML9N6ZZNP0W4973plM6d9Fa7iFJkvSDrU+EXrumx+Uz4ZVLg8aRpJqqcZN12rRp1eMDDzyQSGT1F7Lo2bMngwYNqp7vvPPO7LnnnuuWUJIkNSjd2uTz2937ApBIpvj7s+Opxe5EkiSpKYtE4MCbIPrDtUU++i9MHx02kyTVQI2brOXl5dXjXr16rfX4lY/Zfffda5dKkiQ1aKft2psebdMfjt6d9j0vjPs2cCJJktRgtO0Fe168Yv7s76CyIlweSaqBGjdZly1bVj1u3rz5Wo9v0aJF9bhbt261jCVJkhqyZtFs/nbAir1Yr3h+AhWVVQETSZKkBmW706Dbdunx/C/hjSvD5pGktahxk3V9vuaXl5e3zveVJEkN014bd2C3/u0B+KZ8Gbe8Pm0t95AkSfpBVjYcXAzZP/QT3iuGWZ+EzSRJa5ATOoDqVzweJx6Ph44hreLHden6lMLZEHV44b79eXdaGfFEiv97axqHbNmJnu3y6+35pIbE10IpLGuwAWjdi6xd/kz2G5dDKknqmd9SdfKrkOOJXI2FdahMV5u1aZO1kSkuLqa4uJhEIgHAqFGjyM/3w6wyV0lJSegIUpNX33W4a8csXv0mi3gixdn3vsVpA5P1+nxSQ+NroRSWNZjZIqne7Np8I1ovnU5k3iSm3XsmkzsfFjqW6ph1qExVUVHz/aDXqcn65JNPMnXq1DUeM2bMmFod/6PDDz+cwYMHr0ssAWeeeSZnnnkmsViMwsJChg0bRkFBQehY0iri8TglJSUMHTqUaDQaOo7UJG2oOtxteRV73ziauYuWM35BFvl9t2b3H7YRkJoyXwulsKzBBmSb3qTu2otIsooB3z1HnwPOgY6bhU6lOmAdKtPFYrEaH7tOTdaRI0cycuTIejm+b9++NlnrUDQa9ReVMpprVAqvvuuwdTTKX/ffmLMf/gyAK16YzK4DOpKXk11vzyk1JL4WSmFZgw1At8Gw87nw1rVEklVEnz8bTn0Nsv1ybmNhHSpT1WZd1vjCV5IkSevqoC27sF2vtgBM/76CO97+KnAiSZLUoOz6J2g/MD2e8zm8e1PYPJL0P2r8Z5/8/HwKCwvrMwsAubm59f4ckiRpw4pEIlx60Kbsf9PbJFNw82tTOWyrrnQubB46miRJaghy8uDgYrhzKKSS8MbVMPAAaN8/dDJJAmrRZL3lllu45ZZb6jOLJElqxDbuXMBxO/Tk3vdmsDSe4IrnJ3Lz8K1Cx5IkSQ1Ft21gxzPh3f9AYjk8cyac/BJkuQWRpPDcLkCSJG0w5w4dQNsW6W+tPDd2Du9N+z5wIkmS1KDs/ldo2zs9nvUhfHh72DyS9AObrJIkaYMpzI/yl70HVM///ux4qhLJgIkkSVKDkpsPB928Yv7qZTD/y3B5JOkHNlklSdIGddQ23dmyW3qf98lzF3H/+zMCJ5IkSQ3KRkNg21PT43gFPHo8VC4Jm0lSk1fjPVnVMMXjceLxeOgY0ip+XJeuTymckHV40X4DOPL2DwG4vqSUfTdpT7uWeRs8hxSSr4VSWNZgA7fbheRMfZXIgq/g23EknzqDxKF3QCQSOplqwTpUpqvN2oykUqlUTQ78+uuvmT9/PgA9evSgbdu265buZzz99NN89tlnABxyyCEMGjSozh67qSkuLqa4uJhEIkFpaSkjRowgPz8/dCxJklYxYmoWH8xLf6lm+/ZJhvd12wBJklRzrZbOZpfSS4kmlwEwofORTOl0YOBUkhqTiooKhg8fTnl5OQUFBWs8tsZN1hNPPJF7770XgLvvvpsTTzxxtcfeeuutvPnmmwCcccYZ7LbbbnX22KqZWCxGYWEhZWVla10EUgjxeJySkhKGDh1KNBoNHUdqkkLX4feLlzP0xtEsWlYFwOOnb1+9jYDUFISuQampswYbh0jpS2Q/dhwRUqSIkDjqAVL99g4dSzVkHSrTxWIxioqKatRkrZftAj744AMeeeQRAPbZZ5+1NllVf6LRqL+olNFco1J4oeqwU5sof9irP5c9NwGAfzw/iad+O4SsLL/mp6bF10IpLGuwgdv0QPj+QnjtciKkyHn6N/DrV6H9gLXfVxnDOlSmqs269MJXkiQpmON37MmAjq0A+HxWOY99MjNwIkmS1ODs8ifY5JD0uHIRPHQMLF0QNJKkpscmqyRJCiYnO4u/H7Rp9fyalyZTXuGFDyRJUi1EInDILdBx8/R8/jR4/BRIJsLmktSk2GSVJElB7dinHQds0RmA+Usq+fcrpYETSZKkBie3BRz9IOS3S8+nvQqv/D1oJElNi01WSZIU3IX7b0zzaDYA9703nYlzYoETSZKkBqdNTzjqPsj64fIz794EYx8Nm0lSk2GTVZIkBde5sDm/26MvAMkUXPLseFKpVOBUkiSpwdloZ9jn6hXzZ8+C2Z+GyyOpybDJKkmSMsKpu/Rio3b5AHz41XxGjp0TOJEkSWqQtj0Vtj4xPa5aBg//ChbNDRpJUuNnk1WSJGWEvJxsLj5wk+r5Fc9PYMnyqoCJJElSgxSJwL7XQfcd0vNF38Cjx0HV8rC5JDVqNlklSVLG2GNgR/Yc2AGAubHl3Pz61MCJJElSg5STC7+8Hwq6puczP4Dn/whuRySpnuSEDqD6FY/HicfjoWNIq/hxXbo+pXAytQ4v2Kc/b02ZRzyR4o63v+TQLTvRq6hF6FhSncvUGpSaCmuwCchrA0fcS859BxCpWgZj7ifRYTOS25wSOpl+YB0q09VmbdpkbWSKi4spLi4mkUgAMGrUKPLz8wOnklavpKQkdASpycvEOvxFpyxGzc4inkhx9r1vc/rAJJFI6FRS/cjEGpSaEmuw8eva9SS2mXErAJGXL+DDaQsoa7XJWu6lDck6VKaqqKio8bHr1GR98sknmTp19V/fGzNmTI2P/d/jtX7OPPNMzjzzTGKxGIWFhQwbNoyCgoLQsaRVxONxSkpKGDp0KNFoNHQcqUnK5DrcvbKKcTe9y5zyZUxcmEWz3lux58YdQseS6lQm16DUFFiDTcl+JF6Lkv3eTWSRZKfZt1N1cgm07hk6WJNnHSrTxWKxGh+7Tk3WkSNHMnLkyDo/VnUvGo36i0oZzTUqhZeJdVgYjXLR/ptw5ohPAbjypVJ237gTzaLZgZNJdS8Ta1BqSqzBJmLo32HeRJhaQmTpfKKPnwAnvwx5LUMnE9ahMldt1qUXvpIkSRlpv807sWPvdgB8Pb+C/771ZeBEkiSpwcrKhsPvgHZ90/O5X8DTZ3ghLEl1psZnsubn51NYWFifWQDIzc2t9+eQJEmZLxKJcOnBm7LvjW+TSKYofmMqh27VlW5t3GtckiStg+at4eiH4I49YXkMJj4Lb/0Tdvtz6GSSGoEaN1lvueUWbrnllvrMIkmS9BP9O7bihB034q7RX7EsnuTKFyZyy6+2Dh1LkiQ1VO37w+F3woijgBS8fjl03AQG7h86maQGzu0CJElSRjtnaD+KWqa/6fLCuG8ZPbUscCJJktSg9R8Ge12yYv7kafDdxHB5JDUKNlklSVJGK2gW5bx9BlbPL3l2PPFEMmAiSZLU4A05BzY7PD2uXAwPHQMV84NGktSw2WSVJEkZ7/CtujG4R2sApn63mHvfnR40jyRJauAiETjoZui0RXq+4Ct4/GRIVIXNJanBsskqSZIyXlZWhEsP2pRIJD2/4ZUpfLdoWdhQkiSpYcvNh6NHQIv26fmXr0PJxWEzSWqwNmiTNZVKMWfOHKZPn05FRcWGfGpJktTAbdGtNUdv2x2AxcuruObFyYETSZKkBq91dzjqfsiKpufvF8NnI8JmktQgrXeTdfHixZSXl5NKpVZ7TGlpKSeccAJt27alS5cu9OrVixYtWjBo0CBuuukmqqo8HV+SJK3dn/ceSGHz9IegJz6dxScz3DtNkiStp547wn7XrZiPPAdmfRwsjqSGaZ2arF988QXHHHMMbdu2pVWrVrRu3ZrCwkIOOuggRo8e/ZNjn3zySQYNGsR9993HwoULf3Lb559/ztlnn82uu+5KLBZb53+EJElqGtq2yOWPw/pXzy95djyJ5Or/0CtJklQj25wE25ySHieWw8O/gticsJkkNSg5tb3DAw88wEknnbTK2aeLFi1i5MiRPPfcc/z3v//llFNO4bPPPuOYY46hsrJyjY/53nvv8ctf/pIXX3yxtnG0FvF4nHg8HjqGtIof16XrUwqnodbhkYM7M+L9GUyau5gvZsd48P2vOOaHbQSkhqSh1qDUWFiDWsVe/yD7uwlkff0eLP6W5MO/InHcM5DTLHSyRss6VKarzdqMpNb0Pf//8dFHH7HjjjuSSCTWeFxubi6TJk3i17/+Na+++ioABQUF7LfffvTt25fKykrGjBnDq6++SjKZrL7fk08+yaGHHlrj8FpVcXExxcXFJBIJSktLGTFiBPn5+aFjSZJUp6bF4Kbx6b8V5+ekuGhQghbRwKEkSVKDlxuPsdvkS8iPfw/A1213YUyPU6m++qakJqWiooLhw4dTXl5OQUHBGo+tVZN111135e23366eDxkyhAMPPJC2bdvy9ddf89BDDzFt2jQATjrpJO6+++7q455++mmKiop+8ngff/wx+++/P9999x0Aw4YN4+WXX65pHK1BLBajsLCQsrKytS4CKYR4PE5JSQlDhw4lGrUzIoXQ0Ovw3MfGMnLstwAM364blx64SeBEUu009BqUGjprUKv17Thy7t2PSNVSABJDryC53emBQzVO1qEyXSwWo6ioqEZN1hpvF/Dll1/+pMF68cUXc+mll/7kmIsuuogDDzyQkpIS7r33XgCaN2/Oo48+ukqDFWCbbbahuLiYI488EoDXX3+d5cuXk5eXV9NYWotoNOovKmU016gUXkOtw4sO2JTXJs1jSWWChz+axa922IhNuxSGjiXVWkOtQamxsAa1iu5bwSG3wOMnAZD9ysVkd9oU+vwicLDGyzpUpqrNuqzxha/eeeed6nHfvn255JJLVjkmLy+P//u//yMSiVRvA7DvvvvSpUuX1T7uoYceWt2AjcfjfPHFFzUOL0mSmq6OBc04a89+ACRTcMkz46nFF3QkSZJWb7PDYJc/psepBDx2Isz/MmgkSZmtxk3WiRMnVo8POOAAsrJ+/q69evViiy22qJ5vs802a3zc7OxsBg0aVD2fM8er90mSpJo5eUgvehe1AODjGQt4+rPZgRNJkqRG4xcXQf990uNlC+Gh4bB8UdBIkjJXjZusCxcurB737dt3jceufPvPbRPwv9q3b189Li8vr2kkSZLUxOXmZHHJQZtWz698YRKLlnl1WkmSVAeysuCw26Gof3o+byI89RtY6QLekvSjGjdZly1bVj1u0aLFGo9d+faa7F2Qm5tbPY7H/WAkSZJqbrf+7Rm6SUcA5i1azn9emxo4kSRJajSaFcIxD6f/F2DSc/DmNWEzScpINW6y1maPs0gksk5hJEmS1sXFB2xCbk76bc1d73zF1O8WB04kSZIajXZ94Ii7IPJDC+XNq2HCs2EzSco4NW6ySpIkZarubfP5zW59AKhKprh0pBfBkiRJdajvXrDXpSvmT/0G5o4Pl0dSxrHJKkmSGoUzdutD19bNAXh7Shkvj58bOJEkSWpUdjoLNj8qPY4vgYeOgYr5YTNJyhg2WSVJUqPQPDebvx2wcfX8H89NYFk8ETCRJElqVCIROOgm6DI4PV84Ax47ARJeW0YS5KzLnZ588kmmTl39RSXGjBlT42P/93hJkqR1tfemndilXxFvTylj9sKl3PrGNP4wtH/oWJIkqbGINodfPgi37w5LvoOv3oJRF8G+XgxLaurWqck6cuRIRo4cWefHSpIkrY9IJMIlB27KPje8RVUyxW1vTuOIrbvRvW1+6GiSJKmxKOwKv3wA7tkfknH44DbouBlsdVzoZJICcrsASZLUqPTt0JKThmwEwPKqJNeXlIYNJEmSGp8e28MB16+YP38uzPwwXB5JwdX4TNb8/HwKCwvrMwsAubm59f4ckiSpcTtrz348/sksFlTEeWrMbE7ZuRebda3/9zGSJKkJ2ep4+HYcfHg7JCrhkWPhtDegoEvoZJICqHGT9ZZbbuGWW26pzyySJEl1oqBZlLP26Mdlz00A4JqXJnH/KdsHTiVJkhqdva+E7ybC9Ldh8Vx4eDic9GJ671ZJTYrbBUiSpEbpVzv0oHvb9Aect6eU8VbpvMCJJElSo5MdhSPvhdY90vNvxsDIsyGVCptL0gZnk1WSJDVKeTnZ/HnvgdXzq16cRDLpBx5JklTHWrSDox+C6A8X2hz7CLxXHDaTpA2uxtsFqGGKx+PE4/HQMaRV/LguXZ9SOE2hDvceWMRmXQr44psYE+fEeOKTrzlkkPukKTM0hRqUMpk1qDrVbgCRg4rJeeIkAFIlfyPRrj+p3r8IHCyzWYfKdLVZm5FUynPYG5Pi4mKKi4tJJBKUlpYyYsQI8vPzQ8eSJCmYKeURbp6QDUCb3BQXDk4Q9bs8kiSpHgyc8wQDvn0GgMrsfN7q/3eWNOsUOJWkdVVRUcHw4cMpLy+noKBgjcfaZG2kYrEYhYWFlJWVrXURSCHE43FKSkoYOnQo0Wg0dBypSWpKdXjqfZ/y5pQyAM7buz+n7rxR2EASTasGpUxkDapepJJkP34CWaUvpqdF/ak68WXIaxU4WGayDpXpYrEYRUVFNWqyul1AIxeNRv1FpYzmGpXCawp1eMH+G/PWjW+TSsGtb37JMdv3pHV+buhYEtA0alDKZNag6tzh/4U7hsK8iUTKSok++1s4egRk+VWa1bEOlalqsy6tcEmS1OgN7FTAEVt1AyC2rIpb3pgWOJEkSWq08lrBMSOgWev0vPRFeOPKoJEk1T+brJIkqUk4d1h/8nLSb33uGT2dmfMrAieSJEmNVtvecOTdEPmh7fLWdTD+qbCZJNUrm6ySJKlJ6FzYnJN37gVAZSLJ9SWlgRNJkqRGrc8eMOzyFfOnfwtzxobLI6le2WSVJElNxm9260Pr/PS+Sk9/NpsvZpcHTiRJkhq1HX4LWw5Pj+MV8PCvYElZ2EyS6oVNVkmS1GQUNo9y1h79AEil4JqXJgVOJEmSGrVIBA74N3TdOj0v/xoePQES8bC5JNU5m6ySJKlJOXaHHnRr0xyAt6eU8VbpvMCJJElSoxZtBr98EFp2Ss9nvAMvXRA2k6Q6Z5NVkiQ1KXk52fx57wHV86tenEQymQqYSJIkNXoFneGXD0B2bnr+0X/hk3uCRpJUt2yySpKkJufALbqweddCACbOifH0Z7MDJ5IkSY1e923hgBtWzJ//E8x4L1gcSXXLJqskSWpysrIiXLDvwOr5v0aVsiyeCJhIkiQ1CYN/lb4YFkAyDo8eB+WzwmaSVCdsskqSpCZpp75F7D6gPQCzFy7lvvemhw0kSZKahqH/gF67pcdL5sHDw6GyImwmSevNJqskSWqyzttnIJFIenzza1NZWFEZNpAkSWr8snPgyHugzUbp+ZzPYeTvIeUe8VJDZpNVkiQ1WRt3LuDwrboBEFtWxS1vTAucSJIkNQn5beHohyDaIj0f9xiMvjFsJknrxSarJElq0s4d2p+8nPRbonvenc6sBX5dT5IkbQAdN4HD/m/F/JW/Q+moYHEkrR+brJIkqUnr0ro5Jw3pBUBlVZLrR5UGTiRJkpqMjQ+E3f/6wyQFT5wKZVOCRpK0bmyySpKkJu+M3fvQOj8KwFOfzWb8N+WBE0mSpCZj1z+nm60Ay8vhoWNgme9FpIbGJqskSWryCptH+d0v+gLpa05c/eKkwIkkSVKTkZUFh9wGHTZJz7+fAk/8GpKJsLkk1YpNVkmSJOC4HXvSrU1zAN6eUsbbU+YFTiRJkpqMvJZw9Aho3iY9n/IyvPaPsJkk1YpNVkmSJCAvJ5s/7z2gen7VC5NIJlMBE0mSpCalbS848l6IZKfn7/wbxj0eNpOkGrPJKkmS9IMDt+jCZl0LAJgwJ8Yzn88OnEiSJDUpvXeDfa5aMX/md/DNZ8HiSKo5m6ySJEk/yMqKcMG+G1fP//lyKcvi7ocmSZI2oO1Og8HHpsdVS+GRY6FifthMktbKJqskSdJKhvQtYrf+7QGYvXAp9783I3AiSZLUpEQisP/10G279Lx8Jjx9BiSTYXNJWiObrJIkSf/j/H0HEomkxze/PpXyinjYQJIkqWnJyYMj74H8dul56Uvw3n+CRpK0ZjZZJUmS/sfGnQs4bHA3AMqXxrnljamBE0mSpCansCscejvww19+X7kUvn4/aCRJq5cTOoDqVzweJx737Btlnh/XpetTCsc6XLOz9+jNyLHfUFmV5O53pzN82650ad08dCw1ItagFJY1qAZho93IGvIHskdfD6kEqcdOpOqU16FFUehkdcI6VKarzdqMpFKpVD1m0QZWXFxMcXExiUSC0tJSRowYQX5+fuhYkiQ1SM/OyOLVb9Jf/Nm2fZJj+7oXmiRJ2rAiqQQ7Tr2W9osnAjC31ea83+ePEPHLyVJ9q6ioYPjw4ZSXl1NQULDGY22yNlKxWIzCwkLKysrWugikEOLxOCUlJQwdOpRoNBo6jtQkWYdrF1saZ89/v8PCpXEiEXjmjB3ZuHOr0LHUSFiDUljWoBqURd+Sc+ceRJZ8B0Bit7+S3PncwKHWn3WoTBeLxSgqKqpRk9XtAhq5aDTqLyplNNeoFJ51uHrtolF+t0dfLn9+IqkU/POVqdx38nahY6mRsQalsKxBNQhtu8Phd8D9h0AqSfZbV5O90Y7Qa9fQyeqEdahMVZt16bnlkiRJa3Dcjj3p1ia9F+tbpfN4e8q8wIkkSVKT1Hs32P2C9DiVhCdOhUVzw2aSVM0mqyRJ0hrk5WTz570HVM+vfnESyaS7LUmSpAB2+RP02SM9XjwXnjgFkomwmSQBNlklSZLW6sAturBZ1/QeTOO/ifHs598ETiRJkpqkrCw47L/QqnN6Pv1teOPqsJkkATZZJUmS1iorK8IF+25cPb/u5cksi3vWiCRJCqBFERxxF0Sy0/O3roOpr4bNJMkmqyRJUk0M6VvErv3bAzB74VIeeH9G4ESSJKnJ6rkT7Pm3HyYpePLXEPObNlJINlklSZJq6Px9BhKJpMf/eW0q5RXxsIEkSVLTtdPZ0G/v9Ljie3j8ZEhUhc0kNWE2WSVJkmpoky4FHDq4KwDlS+Pc8sbUwIkkSVKTlZUFh94Ghd3T86/fg9f+ETaT1ITZZJUkSaqFPw4bQG5O+i3U3e9OZ/bCpYETSZKkJiu/LRxxN2TlpOejb4DJLwWNJDVVNlklSZJqoWvr5pw0ZCMAKquS/GvU5LCBJElS09Z9Wxi60hmsT50OC78Ol0dqomyySpIk1dJvd+tLYfMoAE+Nmc2Eb2KBE0mSpCZthzNg4AHp8bKF8NhJUFUZNJLU1NhklSRJqqXC/Chn7dEXgFQKrn5pUuBEkiSpSYtE4OBiaN0zPZ/9MbxySdhMUhNjk1WSJGkdHLdjT7q2bg7AW6XzeGdKWeBEkiSpSWveGo66F7Jz0/P3b4GJI4NGkpoSm6ySJEnrIC8nmz/vPaB6ftWLE0kmUwETSZKkJq/LYNj7yhXzp8+E+V+FyyM1ITZZJUmS1tFBW3Zh0y4FAIz/Jsazn38TOJEkSWrytj0VNj0sPV5eDo+dAPFlYTNJTYBNVkmSpHWUlRXhgn03rp5f9/JkllclAiaSJElNXiQCB90E7dL7xzPncxh1YdhMUhNgk1WSJGk97NyviF37twdg9sKl3P/ejMCJJElSk5fXCo68F3Kapecf3QFfPBE2k9TI2WSVJElaT+fvM5BIJD3+z2tTKa+Ihw0kSZLUaTPY77oV82d/D2VTw+WRGjmbrJIkSetpky4FHDq4KwDlS+Pc8qYfYCRJUgYYfBxseUx6XLn4h/1Zl4bNJDVSNlklSZLqwB+HDSA3J/3W6u7R05m90A8wkiQpsEgE9v8XtB+Yns/9Al78S9hMUiNlk1WSJKkOdG3dnJN22giAyqok148qDRtIkiQJILdFen/WaH56/ul98NlDYTNJjZBNVkmSpDry2937Utg8CsCTY2Yx4ZtY4ESSJElAh4FwwL9XzJ8/F76bFC6P1AjZZJUkSaojhflRfveLvgCkUnDNS354kSRJGWLLo2Gr49PjeAU8ejxULgmbSWpEbLJKkiTVoeN27EnX1s0BeLN0HqOnlgVOJEmS9IN9r4WOm6XHZZPhuXPTfxmWtN5sskqSJNWhZtFs/rR3/+r5VS9OJJn0w4skScoA0ebp/VlzW6bnYx9O79Eqab3ZZJUkSapjB2/ZlU06FwDwxewYI8d+EziRJEnSD4r6wkE3rZi/+Bf4dly4PFIjYZNVkiSpjmVlRbhgv4HV8+tenszyqkTARJIkSSvZ7HDY9tfpcdUyePQEWOYFO6X1YZNVkiSpHuzSrz279CsCYNaCpdz/3ozAiSRJklay9xXQeVB6PH8ajDzb/Vml9WCTVZIkqZ6cv+9AIpH0+ObXp1K+NB42kCRJ0o9y8uDIeyCvMD0f/yR8dEfQSFJDZpNVkiSpnmzapZBDB3UFYGFFnFvfmBY4kSRJ0kra9oJDilfMX/4rfDMmXB6pAbPJKkmSVI/OHdaf3Jz0W667Rn/FNwuXBk4kSZK0ko0PhB3OTI8Tlen9WZcuDBpJaohssmaoRYsW8fDDD/Pwww9TWVkZOo4kSVpH3drkc+JOGwFQWZXk+pLSsIEkSZL+115/h27bpscLZ8AzZ7o/q1RLNlkz1DnnnMMxxxzDMcccQyzmFf4kSWrIzty9L4XNowA88eksJs7xtV2SJGWQnFw44m5o3iY9n/QcvH9L2ExSA2OTNQM9++yzPPDAAwwZMiR0FEmSVAcK86Oc+Ys+QPqkkGtemhQ4kSRJ0v9o3R0O/b8V85KLYeZH4fJIDYxN1gwzb948fv3rX3P++eez2WabhY4jSZLqyPE7bkTX1s0BeGPyPEZPLQucSJIk6X/03xt2/kN6nKyCx06EivlBI0kNRZNosiaTSaqqqkgkEqGjrNVpp51GUVERF154YegokiSpDjWLZvPHYf2r51e9OJFk0r3OJElShvnFRdBjp/Q4NgueOh2SybCZpAYgJ3SA+jBjxgzeffddRo8ezejRoxk3bhyJRII+ffowderUGj1GVVUVt9xyCw888AATJ06ksrKSHj16cPDBB3P++edTVFT0s/cbOXIkS5YsWevjt2/fnj333PMnP7vnnnt49tlnGT16NLm5uTXKKUmSGo5DBnXlv29/xcQ5Mb6YHWPk2G84eFDX0LEkSZJWyM6BI+6E23aBijKYMgrevXHFGa6SflajbLIOGDCA5cuXr/P9Fy9ezLBhw3jvvfd+8vOpU6fyr3/9i/vvv5/XXnuNTTfddJX7nnXWWcyYMWOtzzFkyJCfNFlnzJjB2WefzVlnncUOO+ywztklSVLmysqK8Nf9BnLcnR8CcN3Lk9lns07k5WQHTiZJkrSSgi5w+H/h/sOAFLz6D+i+PfTcKXQyKWM1yiZrz5492Xrrrdlpp50YMmQIt9xyC3fccUeN73/KKafw3nvvEY1GufLKKzn55JPJz8/nlVde4fTTT+ebb77hgAMOYMKECTRv3vwn9z3wwAOZN2/eWp9j4MCB1eNUKsWJJ55I27ZtueKKK2r+D5UkSQ3OLv3as0u/It6eUsasBUt54P2vOWXnXqFjSZIk/VSfPWC3v8Cb10AqAY+fDKe/DS3bh04mZaRG2WSdPHnyT+bZ2TU/O+Sjjz7i0UcfBeDaa6/lnHPOqb7tgAMO4LnnnmPbbbdl+vTp3Hzzzfz5z3/+yf3/85//1DrvuHHjeOONNzj99NMZOXJk9c+nTZsGwFNPPUXXrl3Zb7/9av3YkiQp85y3z0DemfoOqRT857UpHLF1NwqbR0PHkiRJ+qndzoOv34Ov3oJFc+DJX8OxT0CW38KR/leTuPBVbdx///0AFBUVccYZZ6xy++DBgzn44IMBuO++++rkOQsLC/nlL3/JwoULefrpp6v/++qrrwB48cUXefXVV+vkuSRJUnibdS3kkB/2Yl1YEefWN6YFTiRJkvQzsrLh8DuhZcf0/MvX4e1/hc0kZahGeSbr+vixmbnXXnuRl5f3s8cccMABPPnkk3zxxRd8++23dOrUab2es2fPnjz88MOr/Pw3v/kN06ZN4/bbb1/thbYkSVLD9Mdh/Xl+7BwqE0nuHv0Vx+/Yky6tm6/9jpIkSRtSyw7pRut9B0EqCa9fCd23g967h04mZRSbrCuJx+OUlpYCsPnmm6/2uJVvGz9+/Ho3WevC8uXLf3Kxr1gsBqT/TfF4PFQsabV+XJeuTykc6zCsji2jHLdDd+4cPYPlVUn++fIkrjlss9CxtAFZg1JY1qBUC912IGu3C8h+4wogReqJU6k65XVotX79EOtQma42a9Mm60rmzZtHVVUVAN26dVvtcSvfNmfOnHrLs+2227Jw4cLVnlG7squuuopLL710lZ+PGjWK/Pz8+ogn1YmSkpLQEaQmzzoMp08cmmdnszQR4akxs+mX+JouLUKn0oZmDUphWYNSDaX6sUOrLei4aCyRJfMov+sI3u17HqnI+u/Pah0qU1VUVNT4WJusK1m8eHH1uEWL1X/CadmyZfV40aJF9ZbnlFNO4ZRTTqnRsRdccAHnnntu9TwWi9G9e3eGDRtGQUFBfUWU1lk8HqekpIShQ4cSjXqxFykE6zAzlLebzjUvl5IiwvtLO3HHkVuFjqQNxBqUwrIGpXVQsSOpO3YnsmgORYsnsX+LcSR3/+s6P5x1qEz34zfFa8Im62qkUql1ui2UvLy8nz3jNRqN+otKGc01KoVnHYZ10s69eeCDmcxeuJQ3p5Tx0YxydurrXuxNiTUohWUNSrVQ2AmOvAfu3g9SCbJHX0/2RkOg317r9bDWoTJVbdZlVj3maHBWPkN1yZIlqz1u5dtatWpVr5kkSVLj1iyazR+H9a+eX/XiJJLJzPuDriRJEgA9doC9/r5i/uSvoXxWsDhSprDJupL27dtXd6hnzVr9L4iZM2dWj7t06VLvuSRJUuN2yKCubNw5vb3PuNnljBz7TeBEkiRJa7DTWdB/3/R46Xx4/GRIePEqNW02WVcSjUbp3z99JsnYsWNXe9zKt222mVcBliRJ6ycrK8IF+w6snv9z1GSWVyUCJpIkSVqDSAQOvRUKe6TnMz+AVy8Lm0kKzD1Z/8dee+3F+PHjeeWVV1i2bBnNmjVb5Zhnn30WgC222IIOHTps6Ii1Eo/Hicf9a5Iyz4/r0vUphWMdZpYde7Vmpz5teXfafGbOX8q9o7/ipJ16ho6lemQNSmFZg9J6ymlJ5NA7yL5vfyLJOLx7E1VdtyX14xmuNWAdKtPVZm3aZP0fxx13HDfeeCPz58/npptu4i9/+ctPbv/444957rnnADj++ONDRFyj4uJiiouLSSTSZ7+MGjWK/Pz8wKmk1SspKQkdQWryrMPMMaQFvPvD27MbSybRqmw8+b5ba/SsQSksa1BaP726/JItZj0AQPLJ03ljwD9Ymte+Vo9hHSpTVVRU1PjYRvm2PZlMkkwmq+ep1IqLR1RVVVWPI5EI2dnZP7nv1ltvzTHHHMNDDz3EhRdeSDwe56STTqJFixaUlJRw5plnkkwm6d27N2eeeWb9/2Nq6cwzz+TMM88kFotRWFjIsGHDKCgoCB1LWkU8HqekpIShQ4d6FUkpEOswM5VGxvHM53NYUhVherN+/GlYv9CRVE+sQSksa1CqI6l9ST4ZI2vSs+QmKthrwQMkTngesnPXelfrUJkuFovV+NhG2WQ9+eSTuffee1f5+bRp035StD179mT69OmrHPff//6XmTNn8s4773DRRRdx0UUX/eT2zp078/zzz//sVgKZJhqN+otKGc01KoVnHWaWP+09kBe/mEtlIsk9783gxJ170bmweehYqkfWoBSWNSjVgUNuhv8bBwu+ImvOGLJevwz2vabGd7cOlalqsy4b5YWvsrOza/RfTs7P95hbtGjBG2+8wa233sqQIUNo164drVq1YtNNN+Wvf/0r48ePZ+DAgT97X0mSpPXRvW0+J/ywF+vyqiTXjyoNnEiSJGktmhXCUfdCdl56/sFtMP7poJGkDa1RNlnvvPNOqqqq1vrf1KlTV/sY2dnZ/OY3v+Gdd96hrKyMWCzGF198wRVXXEGbNm024L9GkiQ1NWf+oi8FzdJ/DH7801lM+rbmX1OSJEkKovOWsO/VK+bPngXfTwuXR9rAGmWTVZIkqSFrnZ/Lmb/oC0AqBde8OClwIkmSpBrY+iTY/Mj0eHkMHjsB4svCZpI2kEa5J6tWiMfjxOPx0DGkVfy4Ll2fUjjWYWb71bZduefd6cwpX8brk+fx9uS57NC7behYqkPWoBSWNSjVk32uI+ebMUS+nwrfjiPx4nkk9/3nzx5qHSrT1WZtRlKpVKoes2gDKy4upri4mEQiQWlpKSNGjCA/Pz90LEmStA4+nBfhwanZAHRvkeLczRNkRQKHkiRJWotWS2ey6+RLyUlVAvBxz98wu+1OgVNJtVdRUcHw4cMpLy+noKBgjcfaZG2kYrEYhYWFlJWVrXURSCHE43FKSkoYOnSoV5GUArEOM18imeKQW99n0reLAPj3kZtzwBadA6dSXbEGpbCsQal+RT5/iJznzgIgFW1B1cmvQFG/nxxjHSrTxWIxioqKatRkdbuARi4ajfqLShnNNSqFZx1mrihwwX4bc8JdHwJw/atT2W/LruTlZIcNpjplDUphWYNSPdnmeJj1Pnz2IJH4EqJPnQKnvgq5q37b1jpUpqrNuvTCV5IkSRls135F7Ny3CICZ85fy4PtfB04kSZJUQ/v9Ezpskh5/NwFe+HPYPFI9sskqSZKUwSKRCOfvO7B6/p/XphBb5sUhJElSA5CbD0feC9EW6flnD8CYB8NmkuqJTVZJkqQMt1nXQg4Z1AWABRVxbntjWuBEkiRJNdS+Pxx444r583+EuRPC5ZHqiU1WSZKkBuCPwwaQm51+63bnO18xp3xp4ESSJEk1tMWRsPVJ6XHVUnjsBFi+OGwmqY7ZZJUkSWoAurfN5/gdewKwvCrJv0tKAyeSJEmqhX2uhk6bp8dlpfDcOZBKBY0k1aWc0AFUv+LxOPG4+7Yp8/y4Ll2fUjjWYcNz+i4b8ejHM4ktq+LxT2Zx/PbdGdCpVehYWkfWoBSWNShtaNlw6J3k3LkHkcrFMO4xkp23BTpZh8pYtVmbkVTKPxs0JsXFxRQXF5NIJCgtLWXEiBHk5+eHjiVJkurIq7MjPPt1NgCbtE5y+sbJwIkkSZJqrvOCD9lu+s0AJCJR3u7/N8rzNwobSlqNiooKhg8fTnl5OQUFBWs81iZrIxWLxSgsLKSsrGyti0AKIR6PU1JSwtChQ4lGo6HjSE2SddgwLYsnGHbjaOaULwPg/pO2YYfebQOn0rqwBqWwrEEpnKyXLyD74/8CsDi3A1lnjCbask3gVNKqYrEYRUVFNWqyul1AIxeNRn3DoIzmGpXCsw4blmg0yh+HDeBPj30OwGXPT+K53+9MXk524GRaV9agFJY1KAWwzxXwzSfwzae0rPyOxIf/IXvvf4ROJa2iNq8PXvhKkiSpgTl0cFe26FYIwJTvFnPrG9MCJ5IkSaqFnDw44k5S2XkAZH1wK3zv+xk1bDZZJUmSGpjsrAhXH7YF2VkRAIpfn0rp3EWBU0mSJNVC294kd/gdAJFkHF66IHAgaf3YZJUkSWqANulSwOm79gYgnkhx3hNjSSTdal+SJDUcyZ1+z9LoD3vLT3kZSl8OG0haDzZZJUmSGqjf79mP3kUtABjz9UIeeH9G4ESSJEm1kNuCL7oevWL+0gVQtTxcHmk92GSVJElqoJpFs7nqsM2r59e+NInZC5cGTCRJklQ737TenmSPHdOT+dPg/VvDBpLWkU1WSZKkBmz73u0Yvn0PAJZUJrjoqXGkUm4bIEmSGohIhMSwqyDyQ4vqresgNidsJmkd5IQOoPoVj8eJx+OhY0ir+HFduj6lcKzDxuNPe/Xh1QlzmbtoOa9PnseTn8zkoC07h46ltbAGpbCsQSm86jpsO4CsrU4k+5O7oHIxyZKLSRx0S+B0Uu1eIyIpT3VoVIqLiykuLiaRSFBaWsqIESPIz88PHUuSJNWzcfMj3DE5G4AWOSn+OihBy2jgUJIkSTUUrVrEXhP+Qm5iCQBv9fsbC1r2C5xKTV1FRQXDhw+nvLycgoKCNR5rk7WRisViFBYWUlZWttZFIIUQj8cpKSlh6NChRKN2AaQQrMPG56yHP+el8XMBOHjLzvzziM3Xcg+FZA1KYVmDUnj/W4dZn9xF9kt/ASDVaQuqTiqBrOzAKdWUxWIxioqKatRkdbuARi4ajfqGQRnNNSqFZx02HpcdshnvTvue2LIqnvl8Dodu1Y3dB3QIHUtrYQ1KYVmDUnjVdbjdqTDmfpg7jsi3Y4l+8TBsfWLoeGrCavP64IWvJEmSGokOrZpx0f6bVM8vfOoLliyvCphIkiSpFrKyYd9rVsxfvQyWLgiXR6oFm6ySJEmNyJHbdGOnPu0AmL1wKf8cNTlwIkmSpFrYaAhsdkR6XPE9vHF12DxSDdlklSRJakQikQhXHbY5eTnpt3n3vDudMV97BogkSWpAhl4G0R8u4v3hf2HuhLB5pBqwySpJktTI9GzXgnOH9gcglYLznxhHZVUycCpJkqQaKuwKu/wxPU4l4KXz0m9qpAxmk1WSJKkROmXnXmzWNX0F1MlzF3Hbm9MCJ5IkSaqFHX8HbTZKj796CyY+GzSOtDY2WSVJkhqhnOwsrjl8C7KzIgDc/NpUpn63KHAqSZKkGoo2g72vWjF/+UKorAiXR1oLm6ySJEmN1KZdCjlt194AVCaSnPfEOJJJv2onSZIaiAH7Qp890+PymfDuTWHzSGtgk1WSJKkRO3vPfmzULn3hiE9mLOCBD2YETiRJklRDkQjsczVk5aTn7/wbFvheRpkpJ3QA1a94PE48Hg8dQ1rFj+vS9SmFYx02DdnA5QdvwrF3fQzANS9OYvd+7ehc2CxsMFmDUmDWoBRejeqwdS+ytj2N7A9ugaplJF++kMThd2+ghGrqavMaEUmlvDxbY1JcXExxcTGJRILS0lJGjBhBfn5+6FiSJCmwh6dl8d536S8xbdI6yWkDk0QigUNJkiTVQE5iKXtO+AvNqsoBGN33PMpabRo4lZqCiooKhg8fTnl5OQUFBWs81iZrIxWLxSgsLKSsrGyti0AKIR6PU1JSwtChQ4lGo6HjSE2Sddi0xJbG2fc/7/LdouUA/PvIzTlgi86BUzVt1qAUljUohVebOox8/hA5z50FQKr9QKpOeR2yrV3Vr1gsRlFRUY2arG4X0MhFo1HfMCijuUal8KzDpqFdNMplB2/Gbx74BIDLX5jM7gM70aZFbuBksgalsKxBKbwa1eFWx8KYe2H2x0TmTSL62X2ww282TEA1WbV5ffDCV5IkSU3EPpt1Yp9NOwHw/ZJK/vH8hMCJJEmSaigrC/a7dsX89SthSVm4PNL/sMkqSZLUhFx28Ka0apb+MtOTn87mrdJ5gRNJkiTVUNetYfCx6fHycnj1srB5pJXYZJUkSWpCOhQ048L9Nq6e//WpcSxZXhUwkSRJUi3seQnk/bA35qf3wTdjwuaRfmCTVZIkqYn55bbd2aF3WwBmLVjK9SWlgRNJkiTVUMsOsPv5P0xS8MJfwGu6KwPYZJUkSWpiIpEIVx22BXk56beCd4/+is9mLgwbSpIkqaa2Ow2KBqTHsz6EsY+EzSNhk1WSJKlJ6lXUgnP26g9AMgXnPzGWyqpk4FSSJEk1kB2Ffa9eMS+5GJYvCpdHwiarJElSk/XrXXqxaZf0nmaTvl3E/705LXAiSZKkGuqzBww8ID1ePBfeui5sHjV5NlklSZKaqJzsLK45fAuysyIA/Oe1qUz9bnHgVJIkSTU07HLIzkuP37sFyqaGzaMmzSarJElSE7ZZ10JO3aUXAJWJJBc8OZZk0otHSJKkBqBtLxjy+/Q4GYeXLwibR02aTVZJkqQm7pw9+9OzXT4AH01fwIMffh04kSRJUg3t/Aco6JoeTxkFpS+HzaMmyyarJElSE9c8N5urDtu8en7Ni5OYU740YCJJkqQaym0Bw/6xYv7S+VC1PFweNVk5oQOofsXjceLxeOgY0ip+XJeuTykc61Ar27ZHIUdu3ZXHPpnN4uVVXPjkOG771SAikUjoaI2WNSiFZQ1K4dVZHfY/kOweO5H19bsw/0sSo28mudPv6yChmrrarM1IKpVy061GpLi4mOLiYhKJBKWlpYwYMYL8/PzQsSRJUgNQUQVXfZZNLJ5urJ7YL8HgIt8qSpKkzFew9Gt2n/Q3IqSoysrj1U2uZVm0TehYauAqKioYPnw45eXlFBQUrPFYm6yNVCwWo7CwkLKysrUuAimEeDxOSUkJQ4cOJRqNho4jNUnWoX7OS+PnctbDnwPQrkUuL/5+J9rk5wZO1ThZg1JY1qAUXl3XYdZL55H9yZ0AJDc7gsTBt633Y6ppi8ViFBUV1ajJ6nYBjVw0GvUNgzKaa1QKzzrUyg7Ysisjx37LqAlz+X5JJdeOmso/j9wydKxGzRqUwrIGpfDqrA73vAgmPAlLF5D1xeNkbfdr6LHD+j+umqzarEsvfCVJkqRqkUiEfxyyGa3y0n+Lf/yTWbw9ZV7gVJIkSTWQ3xb2+NuK+Qt/hmQiXB41KTZZJUmS9BMdC5pxwX4bV8//+tQ4KiqrAiaSJEmqoa1PhI6bp8ffjoVP7wsaR02HTVZJkiSt4uhtu7N9r7YAzJy/lOtHlQZOJEmSVANZ2bDftSvmr14GSxeEy6MmwyarJEmSVpGVFeGqwzYnNyf9dvGu0V/x+cyFYUNJkiTVRM+dYLMj0uOl8+H1q8LmUZNgk1WSJEk/q3f7lpyzVz8Akik474mxxBPJwKkkSZJqYOhlEM1Pjz+6A+aOD5tHjZ5NVkmSJK3Wr3fpzcadCwCY9O0ibn/ry8CJJEmSaqCwK+zyx/Q4lYAXz4NUKmwmNWo2WSVJkrRa0ewsrjl8c7Ii6fmNr05h2rzFYUNJkiTVxI6/gzYbpcfT34YJzwSNo8bNJqskSZLWaIturTl1l94AVFYlueCJcSSTngkiSZIyXLQZ7HP1ivmoi6CyIlweNWo2WSVJkrRWf9irPz3apvc1+3D6fB766OvAiSRJkmqg/z7Qd6/0uHwmjL4haBw1XjZZJUmStFbNc7O56rDNq+dXvzCJb8uXBUwkSZJUA5FI+mzWrJz0/J0bYMH0kInUSNlklSRJUo0M6VvEkVt3A2DR8iouevoLUl5AQpIkZbqifrDDGelxYnl62wCpjtlklSRJUo1duP/GFLXMA+CViXN5Ydy3gRNJkiTVwK5/gRYd0uOJI2Ha62HzqNGxySpJkqQaa52fy6UHbVo9v+TZL1hYURkwkSRJUg00K4Chl66Yv3Q+JOLh8qjRsckqSZKkWtlv807stXFHAMoWV3LF8xMDJ5IkSaqBLY6Grtukx/MmwUd3hM2jRiUndADVr3g8TjzuX2aUeX5cl65PKRzrUOvjkgMG8P6X37N4eRWPfTKL/TfvyJA+7ULHalCsQSksa1AKL0QdRoZdSc7dwwBIvX4lVQMPhhbtN9jzq2GpzdqMpLxaQaNSXFxMcXExiUSC0tJSRowYQX5+fuhYkiSpEXrn2wiPfZUNQLu8FOdvmSA3O3AoSZKktRg04w56zn8LgOntduPzHqcETqRMVVFRwfDhwykvL6egoGCNx9pkbaRisRiFhYWUlZWtdRFIIcTjcUpKShg6dCjRaDR0HKlJsg61vpLJFL+66yM+nrEQgFOG9OT8fQaEDdWAWINSWNagFF6wOlz8HTm3bU9k+SJSREicNIpUl8Eb7vnVYMRiMYqKimrUZHW7gEYuGo36hkEZzTUqhWcdan1cc8SW7Hvj21RWJbn73RkcMrg7m3crDB2rQbEGpbCsQSm8DV6HbbrC7hfAy38lQoqckr/CyaMgy0sX6adqsy5dPZIkSVpnfdq35Ow9+wGQTMFfnhhLPJEMnEqSJGkttjsNin74Bs6sj2DsI2HzqMGzySpJkqT1ctquvRnYqRUAE+fE+O/bXwZOJEmStBbZUdj36hXzVy6BZbFwedTg2WSVJEnSeolmZ3HN4VuQFUnPb3hlCl/OWxw2lCRJ0tr02QMGHpAeL54Lb10XNo8aNJuskiRJWm9bdm/NyUN6AVBZleSCJ8eRTHp9VUmSlOH2vgKy89Lj92+Fsilh86jBsskqSZKkOnHusP50b9scgA++ms/DH80MnEiSJGkt2mwEQ85Oj5NxeOl8SPmHYtWeTVZJkiTVifzcHK48dPPq+VUvTGRubFnARJIkSTWw8x+goFt6PPUVKH05bB41SDZZJUmSVGd26deew7dKf0hZtLyKi5/5InAiSZKktcjNh2H/WDF/6XyoWh4ujxokm6ySJEmqUxftvzFFLXMBeHn8XF4cNydwIkmSpLXY9FDouXN6vOAreO/msHnU4NhklSRJUp1q0yKXSw7ctHp+8bPjKa+IB0wkSZK0FpEI7HsNRH5olb31TyifHTaTGhSbrJIkSapzB2zRmb027gDAvEXLufKFiYETSZIkrUWnzWCbU9LjeAW8cknYPGpQbLJKkiSpzkUiEf5xyGa0zMsB4JGPZ/Lu1LLAqSRJktbiF3+F5m3T43GPwYz3wuZRg2GTVZIkSfWic2Fzztt3YPX8gqfGsbQyETCRJEnSWuS3hT3/tmL+4p8h6fsXrZ1NVkmSJNWbX23Xg216tgFgxvcV3PBqaeBEkiRJa7HVCdBp8/T423Hw6b1h86hBsMkqSZKkepOVFeHqw7cgNzv9tvOOt7/ii9nlgVNJkiStQVY27Hvdivmr/4CK+eHyqEGwySpJkqR61bdDS87aoy8AiWSKvzw+lngiGTiVJEnSGvTcETY/Mj1eOh/euCpsHmU8m6ySJEmqd6fv1ocBHVsBMGFOjDvf+SpwIkmSpLUYehlEW6THH90Bc8eHzaOMZpNVkiRJ9S43J4trjtiCSCQ9/3dJKV+VLQkbSpIkaU0KusCuf0yPU0l44S+QSoXNpIxlk1WSJEkbxKDurTlpp14ALK9KcsGTY0n5QUWSJGWyHc6ENun3L8x4B8Y/FTaPMpZNVkmSJG0wf9q7P93aNAfg/S/n88hHMwMnkiRJWoNoM9hnpf1YR/0NKv02jlZlk1WSJEkbTH5uDlccunn1/IoXJvJdbFnARJIkSWvRfx/ou1d6HJsF79wQNI4yk01WSZIkbVC79W/PYYO7ArBoWRUXP+NFJCRJUgaLRGCfqyErJz0ffSMsmB40kjKPTVZJkiRtcH87YBPatcgF4KXx3/LSF3MCJ5IkSVqDon6wwxnpcWI5vHxh2DzKODZZJUmStMG1aZHLxQduUj2/+JnxlC+NB0wkSZK0Frv+BVp2TI8nPQfTXgubRxklJ3QA1a94PE487gcWZZ4f16XrUwrHOlRo+27Snqf6F/FGaRnfLVrOlc+P5/KDNw0da4OxBqWwrEEpvAZXh9nNifziYnJGnglA6sXzqDr1TciOBg6m+lKbtRlJpVKpesyiDay4uJji4mISiQSlpaWMGDGC/Pz80LEkSZJ+1vzlcPVn2SxPRgD43SYJ+hX69lSSJGWoVJJdSv9B24ppAIzrOpwvO+wTOJTqS0VFBcOHD6e8vJyCgoI1HmuTtZGKxWIUFhZSVla21kUghRCPxykpKWHo0KFEo/7VTwrBOlSmeOCDr7n0uUkA9Gybz3O/25Fm0ezAqeqfNSiFZQ1K4TXUOox88ynZd+9NhBSpvFZU/eYDaNkhdCzVg1gsRlFRUY2arG4X0MhFo9EG9YtKTY9rVArPOlRoJ+zUm+fGzeWTGQuYMb+CW96aznn7DAwda4OxBqWwrEEpvAZXhz23h8HHwpj7iSxfRPStK+Hg4tCpVA9qsy698JUkSZKCysqKcPVhm5ObnX5revtbX/LF7PLAqSRJktZgz0sg74czG8c8ALM+CZtHwdlklSRJUnD9OrbizF/0BSCRTHH+k2OpSiQDp5IkSVqNlu1h9wtWzF/8CyR979KU2WSVJElSRjhj9z7079gSgC9mx7jzna8CJ5IkSVqD7X4NRQPS49kfw9iHw+ZRUDZZJUmSlBFyc7K4+vAtiETS8+tLSpletiRsKEmSpNXJjsK+V6+Yl1wCy2Lh8igom6ySJEnKGFv1aMMJO24EwPKqJBc+PS5sIEmSpDXpswcMPCA9XvIdvHVt2DwKxiarJEmSMsqf9x5A19bNARg99Xs+/XpB4ESSJElrsPcVkNMsPX7/VphXGjaPgrDJKkmSpIzSIi+Hs/fsVz2/e/T0cGEkSZLWps1GMOTs9DhZBS+dD6lU0Eja8GyySpIkKeMcNKgLbVvkAvDCuDnMKV8aOJEkSdIaDDkHCrqlx9NehckvBo2jDc8mqyRJkjJOs2g2x27fA4BEMsV9780InEiSJGkNcvNh78tXzF++AOLLwuXRBmeTVZIkSRnp2B16Es2OADDig69ZWpkInEiSJGkNNjkENtolPV4wHd67OWQabWA2WSVJkpSROhQ048AtugBQvjTOk2NmBU4kSZK0BpEI7HsNRH5ot739LyifHTaTNhibrJIkScpYJw3pVT2+e/R0Ul5EQpIkZbKOm8K2p6bH8QoouThsHm0wNlklSZKUsTbvVsi2G7UBYOp3i3l7SlngRJIkSWux+wXQvG16/MXjMH102DzaIGyySpIkKaOdvNLZrHeN/ipgEkmSpBrIbwt7/m3FvORv4LdxGj2brJIkScpoQzfpSNfWzQF4Y/I8pn63OHAiSZKktdjqBOiwaXo8+xOY9FzYPKp3NlklSZKU0XKyszhxp42q5/e869mskiQpw2Vlwx4XrZi/djkkE+HyqN7ZZJUkSVLGO2rb7uTnZgPwxCezWVhRGTiRJEnSWgzYF7ptlx7PmwRjHw2bR/XKJqskSZIyXmHzKEdu3Q2ApfEED380M3AiSZKktYhEYM+LV8zfuBKq/ENxY2WTVZIkSQ3CCSttGXDfu9OpSiTDhZEkSaqJXrtAnz3S44Vfwyf3BI2j+mOTVZIkSQ1C7/Yt2WNgBwC+KV/Gy+PnBk4kSZJUAyufzfrWdVC5JFwW1RubrJIkSWowTh7Sq3p812gvgCVJkhqALoNh44PS4yXfwQe3hc2jemGTVZIkSQ3GkL7t6N+xJQCfzFjAZzMXhg0kSZJUE3tcBJEf2nCjb4SlC8LmUZ2zySpJkqQGIxKJ/ORs1rs9m1WSJDUE7QfAlsPT42Xl6UarGhWbrJIkSWpQDhnclTb5UQCeHzuHubFlgRNJkiTVwO7nQ3Zuevz+bbDo27B5VKdsskqSJKlBaRbNZvj2PQCoSqa4/70ZgRNJkiTVQOvusM0p6XHVUnjrn2HzqE7ZZJUkSVKDc9wOG5GTFQHgwQ9msCyeCJxIkiSpBnb5I0RbpMef3AMLpodMozpkk1WSJEkNTqfCZuy/RWcAFlTEeXrM7MCJJEmSaqBle9jxt+lxMg6vXxU2j+qMTVZJkiQ1SCetdAGsu0Z/RSqVCphGkiSphnY6C5q3SY/HPgJzJ4TNozphk1WSJEkN0qDurdm6Z/oDSuncxYye+n3gRJIkSTXQrBB2/sMPkxS8dnnQOKobNlklSZLUYJ280tmsd4/+KmASSZKkWtjuNGiV3vqIyc/DrI/D5tF6s8maIRKJBGVlZT/737Jly0LHkyRJykh7b9qRLoXNAHh10nd8VbYkcCJJkqQaiDaHXf+8Yv7qpeGyqE7YZM0Q48aNo3379vTq1YuBAwf+5L9HHnkkdDxJkqSMlJOdxfE7bVQ9v8ezWSVJUkOx1fHQ5odv5Xz1Fkx7PWwerRebrBnm1ltvXeVM1hNOOCF0LEmSpIx19LbdaR7NBuCxT2ZRvjQeOJEkSVINZEfhFxeumL96GXghzwbLJqskSZIatNb5uRy+dVcAKioTPPrRzMCJJEmSamizw6HDpunxN5/CpOfC5tE6s8magWKxGMuXLw8dQ5IkqcE4cacVF8C6593pVCWSAdNIkiTVUFYW7Pm3FfPXLodkIlwerbOc0AHqy3fffce7777L6NGj+eyzz4jH43Tt2pUHH3ywxo8xbtw4HnroISZOnEhlZSU9evTg4IMPZp999lntfRYsWEAisfZiiEajFBYWrvLzU045hezsbJYuXcomm2zCOeecw69//esaZ5YkSWqK+nZoye4D2vPG5HnMXriUVybOZZ/NOoeOJUmStHb994Fu28GsD2HeJBj7CAwaHjqVaqlRNlk33XRTJkyYsMrP+/TpU+PHuOCCC7j22mtJJn96FsRtt93G3nvvzaOPPkpBQcEq9xs8eDAzZsxY6+MPGTKEd955p3qel5fHxRdfzKmnnkr37t2ZN28el19+Oaeddhpff/01//jHP2qcXZIkqSk6aUgv3pg8D4C73pluk1WSJDUMkQjsdQncs396/vpV6W0EcvLC5lKtNMrtAqZNm0aHDh04+OCDufbaa9l3331rdf+rrrqKq6++mmQyyT777MMjjzzCyJEjOfvss8nOzubll1/mqKOO+tn7tm3blnbt2q31v9atW//kfhtvvDGXXnop3bt3B6B9+/bceOON7LPPPlx99dXMmzdvnf6/kCRJaip27VdE3w4tAfhw+nzGzSoPnEiSJKmGNtoZ+uyZHpd/DZ/cEzSOaq9Rnsk6YcIEevfuXT2fNm1aje87a9YsLrvsMgCOP/547r333urbDjjgALbeemuOP/54Xn75ZR5//HGOOOKIn9z/008/Xc/0P7XPPvvw0ksvMWbMGIYNG1anjy1JktSYRCIRThqyERc+9QUAd4/+iut/OShsKEmSpJra828w7dX0+K3rYPCxkNsibCbVWKM8k3XlBmtt3XPPPSxbtoy8vDz++c9/rnL7cccdx3bbbQfArbfeus7PU1OVlZUA5OQ0yn64JElSnTpscDcKm0cBGDn2G76LLQucSJIkqYa6DIZNDk6Pl8yD9+u/76S60yibrOvj+eefB2D33Xenffv2P3vMj1sFvPnmmyxatKhOnjeVSq3ys2QyyeOPP06LFi3Ydttt6+R5JEmSGrPmudkM374HAPFEigc++DpwIkmSpFr4xUUQ+aFdN/omqJgfNo9qzNMjV5JKpRg3bhzAGpua22+/PQCJRIIJEyZUz9fHySefzEYbbcRee+1Fjx49mDFjBtdccw0fffQRt912G61atVrj/ZcvX87y5cur57FYDIB4PE48Hl/vfFJd+3Fduj6lcKxDNVbHbNOV29/6kkQyxQPvT+e0IT3Ii2aHjrUKa1AKyxqUwrMOf0brXmRvcQxZnz8Iy8tJvP1vkntcHDpVk1WbtWmTdSXz5s1jyZIlAPTs2XO1x61825dfflknTdZ///vf3H777VxwwQV8+eWXNG/enK233po333yTXXbZZa33v+qqq7j00ktX+fmoUaPIz89f73xSfSkpKQkdQWryrEM1Rlu0yWLM91nMXxLnigdHsUOHVb81lCmsQSksa1AKzzr8qeZVW7Nn5BGyU1Wk3r+NVxf1ZXm0dehYTVJFRUWNj7XJupKVv/pfUFCw2uNWPqu0rrYLaN26NX/5y1/4y1/+sk73v+CCCzj33HOr57FYjO7duzNs2LA1/lukUOLxOCUlJQwdOpRoNBo6jtQkWYdqzDpvvpCjbv8QgDGLC7n0hB2JRCKBU/2UNSiFZQ1K4VmHa9BiMnz4f+SkKhma9xnJfa4NnahJ+vGb4jVhk3UlK58CvKYLTa1c+JlySnteXh55eXmr/DwajfqLShnNNSqFZx2qMdqud3sGdW/NZzMXMmnuYj6eGWOnPkWhY/0sa1AKyxqUwrMOf8auf4YxD0B8Cdlj7iN7yO+hba/QqZqc2qxLL3y1khYtWlSPly5dutrjVr6tZcuW9ZpJkiRJ6+bknVd8ELnrnenhgkiSJNVWy/aw45npcbIK3rgqbB6tlU3WlbRr1676a2Rz585d7XHffvvtT+4jSZKkzLPvZp3oVNAMgFcnzWXG90sCJ5IkSaqFnX4Hzdukx2Mfhbnjw+bRGtlkXUl+fj49evQAYNKkSas9bvLkydXjTTbZpN5zSZIkqfai2Vkcv1P6gqWpFNzz7vSwgSRJkmqjWSHs/OP1d1Lw2uVB42jN3JP1fwwZMoQZM2bw2muvrfaYH69617lzZ3r1yuz9MOLxeMbsGyut7Md16fqUwrEO1RQcMbgzN706hWXxJI9+PJOzdu9Nq2aZ8RbYGpTCsgal8KzDGhh8IjnvFRNZ/C1MfoGq6e+R6rpN6FRNRm3WZma8w8wgRx55JCP+v707j46qytf//1RVioQACYQoGCBhEEEmAZUGQSNgkBYVGRw64oS2Y6utNkvbqdXWbrW9DmD0x22ndoh4rzI5oQFEJIB4RZTBECDMUwhgKhCSVKrq90d9c6hAhkqqkp3h/Vora+1TtXfVc/DsmHxyau/0dG3ZskWfffaZLr300nLP5+bmKj09XZJ01VVXNbhdatPS0pSWliaPxyNJ+vrrrxUdHW04FVC5sj9aADCHeYimbnA7u5bn2nW02KO/f5ChC0/zmY5UDnMQMIs5CJjHPKxaUruxGnjkHUnS4Y/v0/LTH5IaWD2qqSosLAy6r83n8zWsnzLrwO23366ZM2eqR48e2rx5c5V9fT6fzj77bP3000/q0KGD5s6dq6FDh0ryr9M6efJkLVu2TNHR0dq0aZMSEhLq4xRqzOVyKTY2Vnl5eYqJiTEdBziJ2+1WRkaGUlJS2EUSMIR5iOZiU+4RXTJjuSSpc7uWWvjnEXLYzf9iwhwEzGIOAuYxD4PkcSti5nmyHd4qSSr9w8fydb/QbKZmwuVyKT4+Xvn5+dXW15rknazPPvusFixYYB1nZ2dLknbv3q0LL7zQerxjx46aNWtWubE2m02zZs3S8OHDtX//fg0bNkxnnnmmWrVqpbVr16q4uFh2u13vvPNOgy2wBnI6nXyjQoPGNQqYxzxEU9enUzud3zNe323K067Dx7R08yGN6dvRdCwLcxAwizkImMc8rIbTKY16VPrkZklSxLfPSGdcxN2s9aAm12WTLLJmZWXp22+/PenxoqKico8nJSVVOP6MM87Qjz/+qPvvv1/z58/Xr7/+aj03ZMgQ/etf/9IFF1wQ/uAAAACoE1NHdNN3m/IkSW9lbm1QRVYAAIBq9Z0oLXtZ2r9W2vOT9OunUp/LTadCgCZZZH3ooYd04403VtsvKiqq0ucSExP18ccfy+VyKScnRyUlJUpMTFTHjvxADgAA0Ngk9zxF3U9ppZwDR7Uy55DW78lX34RY07EAAACCY7dLox+T0q/yHy9+Wuo9TrI7zOaCpUkWWXv37q3evXuH5bViYmI0cODAsLwWAAAAzLDbbbrpvK56bN56SdLbmdv0wpVnGU4FAABQAz3HSF1+J+38XsrbKP08Sxp0relU+H/spgMAAAAA9WHi4M6KifLfYzB/zR4dKCg2nAgAAKAGbDZp9N+OHy/5p1TKzzMNRZO8kxXHud1uud1u0zGAk5Rdl1yfgDnMQzQ3LezSVed01hvLtqnE49V7y7fq7lE9jOVhDgJmMQcB85iHtdBpiBzdR8ues0jK3ynPqjfkPfdW06marJpcmzafz+erwyyoZ2lpaUpLS5PH41F2drbS09MVHR1tOhYAAECDcKhY+vtqh7yyqY3TpycGexTBZ7sAAEAjElu4TRdufFySVBQRo4V9XpDHUfm+Q6i9wsJCpaamKj8/XzExMVX2pcjaRLlcLsXGxiovL6/aiwAwwe12KyMjQykpKXI6nabjAM0S8xDN1T2zftaX6/dLkp6f2E8TBiUYycEcBMxiDgLmMQ9rzzH7Ztl/nSdJ8iQ/LO+I+w0nappcLpfi4+ODKrKyXEAT53Q6+UaFBo1rFDCPeYjm5pYLultF1v+s3KErz02UzWYzloc5CJjFHATMYx7WwujHpKzPJJ9HjpVpcvzuj1J0nOlUTU5Nrks+HAUAAIBmZXBiOw3oHCtJWr/HpVVbDxlOBAAAUEPxPaWBqf52cb6U+bLROKDICgAAgGbGZrNp6vBu1vFbmVsNpgEAAKilCx+SHJH+9vczJddes3maOYqsAAAAaHYu6X+aTm3j/6Xk6w37tfNQoeFEAAAANRTbWTr3Fn+7tEha+i+zeZo5iqwAAABodlpE2HX9sCRJks8n/Wf5NrOBAAAAauP8+6UWrf3t1f+RDuWYzdOMsfFVE+d2u+V2u03HAE5SdvlpQR8AAC8jSURBVF1yfQLmMA/R3E0enKAZizeruNSrWT/s1F0XdlPryPr78Zg5CJjFHATMYx6GQYtY2YfcLseyFyRvqbyLn5Fn/P9nOlWTUZNr0+bz+Xx1mAX1LC0tTWlpafJ4PMrOzlZ6erqio6NNxwIAAGiQZm2xa0Wu/8Ndk7p6dMFp/GgMAAAalwjPMV20/gFFeo7IJ5u+6f20Clp2MR2rSSgsLFRqaqry8/MVExNTZV+KrE2Uy+VSbGys8vLyqr0IABPcbrcyMjKUkpIip9NpOg7QLDEPAWnjvgJdmrZCkpQY11IZ946Q3W6rl/dmDgJmMQcB85iH4WNfmSbHor9Jkrw9x8pz1fuGEzUNLpdL8fHxQRVZWS6giXM6nXyjQoPGNQqYxzxEc9avS5yGn95emZsPasehY/puy2Fd1KdDvWZgDgJmMQcB85iHYTD0NmnVTKlgj+ybFsi+7yepyxDTqRq9mlyXbHwFAACAZm3q8G5W++3lWw0mAQAAqCVnS+nCB48fL3rKv7sn6g1FVgAAADRrI3udqq7t/WvYZ24+qKx9LsOJAAAAamHgtVJcd39723fSlsVm8zQzFFkBAADQrNntNt0UeDfrsm3mwgAAANSWwymNfOT4MXez1iuKrAAAAGj2Jp/dWW2i/NsVzFmzWwePFBtOBAAAUAt9J0od+/vbe9dIv843Gqc5ocgKAACAZq9VZISuPqeLJKmk1Kv073cYTgQAAFALdrs06vHjx4ufljyl5vI0IxRZAQAAAEk3nNdVdpu//e7K7Sop9ZoNBAAAUBs9U6QuQ/3tvGzpl1lm8zQTFFkBAAAASV3iojWmT0dJ0oGCYn2xdq/hRAAAALVgs0kX/e348ZJnpVKWQqprEaYDoG653W653W7TMYCTlF2XXJ+AOcxD4GTXD+2iBev3SZLeXJajS/qeIpvNVifvxRwEzGIOAuYxD+tQwrly9LhI9i0Lpfyd8nz/b3mH3GY6VaNTk2vT5vOxzVhTkpaWprS0NHk8HmVnZys9PV3R0dGmYwEAADQKPp/0wlqHdh31F1bv7Vuq7jGGQwEAANRCbOE2XbjRvz5rcUQbZfT5L3kcUYZTNS6FhYVKTU1Vfn6+YmKq/qGQImsT5XK5FBsbq7y8vGovAsAEt9utjIwMpaSkyOl0mo4DNEvMQ6Bic9fs0bRP1kmSxvbtoBnXnFUn78McBMxiDgLmMQ/rnmPOLbJvmCtJ8iT/Vd4RD5gN1Mi4XC7Fx8cHVWRluYAmzul08o0KDRrXKGAe8xAo7/JBnfXcV5uUd6RYX2/Yr/1H3Orcru4+GcQcBMxiDgLmMQ/r0KjHpF8/lXweOVamyfG7W6XoONOpGo2aXJdsfAUAAAAEiIxw6LqhSZIkr096d8V2w4kAAABqKf50adC1/naxS1r2ktk8TRhFVgAAAOAE1w5NVAuH/0flWat26GhxqeFEAAAAtZT8kOSI9LdX/bfk2ms2TxNFkRUAAAA4QXzrSI0fmCBJchWVavbqXYYTAQAA1FJsJ2nIH/3t0iJp6fNm8zRRFFkBAACACtw0vJvVfjtzm7xe9osFAACN1Ij7pRat/e3V70qHcszmaYIosgIAAAAV6JMQo2Hd20uScvKO6tvsA4YTAQAA1FKr9tKwP/nb3lLpm3+YzdMEUWQFAAAAKnHT8K5W+63MreaCAAAAhGrYXVLLOH977cfSvnVm8zQxFFkBAACASow+s4MS46IlSd9tylP2/gLDiQAAAGopKkY6/4H/d+CTFj9tNE5TE2E6AOqW2+2W2+02HQM4Sdl1yfUJmMM8BIJz3dAueuaLjZKkN7/L0dPj+4TldZmDgFnMQcA85qEBg25QxIo02Qr2SNlfqnRrpnydh5hO1WDV5Nq0+Xw+VvBvQtLS0pSWliaPx6Ps7Gylp6crOjradCwAAIBGq6hUeny1Q8Uem5w2n54826NWTtOpAAAAaicxb4kG7XxLkpTXurcyT/+rZLMZTtUwFRYWKjU1Vfn5+YqJiamyL0XWJsrlcik2NlZ5eXnVXgSACW63WxkZGUpJSZHTyW+qgAnMQyB4z3yRpXdW7JAkPXDR6bo9uXvIr8kcBMxiDgLmMQ8N8ZYqYuZ5sh3KkSSVXvM/8vUYZThUw+RyuRQfHx9UkZXlApo4p9PJNyo0aFyjgHnMQ6B6U0f00H9W7pDPJ72/aqduH9lTTkd4tjdgDgJmMQcB85iH9c0pjXpU+niqJCni22ekM1IkO1s3nagm1yX/egAAAEA1EttH66IzO0iS9ruK9cXavYYTAQAAhKDPBKljf39778/Sr/PN5mkCKLICAAAAQZg6vJvVfjtzm7kgAAAAobLbpdF/O368+GnJU2ouTxNAkRUAAAAIwtDucTrzNP9aXGt2/qbVOw4bTgQAABCC0y+SEs/ztw9ukn7+0GyeRo4iKwAAABAEm82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",
      "text/plain": [
       "<Figure size 1600x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_tx = exp_corr_mat(0.4, num_tx_ant)\n",
    "r_rx = exp_corr_mat(0.7, num_rx_ant)\n",
    "model2 = Model(KroneckerModel(r_tx, r_rx))\n",
    "\n",
    "ber_plot.simulate(model2,\n",
    "        np.arange(0,2.6,0.25),\n",
    "        batch_size=4096,\n",
    "        max_mc_iter=1000,\n",
    "        num_target_block_errors=200,\n",
    "        compile_mode=\"reduce-overhead\",\n",
    "        legend=\"Kronecker model\");"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}