{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A real-world case (Biomimetics: space technology)\n",
    "Here we use a some data produced by precisely modelling a nanostructured solar array inspired by the moth eye. We analyze the relations (found by **dcgpy** **symbolic_regression** using **mes**) between the cell efficiency and 12 different model parameters (thickness, etc..). \n",
    "\n",
    "* The data were generated in the context of the European Space Agency Ariadna study on bio-inspired solar cells (http://www.esa.int/gsp/ACT/projects/diatom/).\n",
    "\n",
    "* The fits were generated evolving 126 populations (size 8) via **dcgpy.mes(10000, max_mut=15)** on an AMD EPYC 7702 64-Core Processor (~20 minutes to complete)\n",
    "\n",
    "Data points are pickled into a file named *moth_data.pk* in the form of a tuple of two arrays Xs, Ys.\n",
    "\n",
    "The fitted expressions are pickled into a file named *result.pk* in a list: result[prob_id][0] = fitnesses result[prob_id][1] = chromosomes\n",
    "\n",
    "This tutorial is informative as it shows the wide diversity and quality of models produced by unconnected evolutions and their difference with respect to the fit error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Preliminaries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Core imports\n",
    "import dcgpy # This was compiled in bertha from github HEAD (v1.5 is unreleased)\n",
    "import pygmo as pg\n",
    "import numpy as np\n",
    "# Sympy is nice to have for basic symbolic manipulation.\n",
    "from sympy import init_printing\n",
    "from sympy.parsing.sympy_parser import *\n",
    "init_printing()\n",
    "# Plotting\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "# Pickling\n",
    "import pickle as pk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the data to fit\n",
    "with open(\"moth_data.pk\", \"rb\") as f:\n",
    "    Xs,Ys  = pk.load(f)\n",
    "# Load the best solutions found running dcgpy.mes(10000, max_mut=15) on 126 separate runs\n",
    "#with open(\"eph_3_r_1_c_16_lb_17_sum_diff_mul_diff_exp.pk\", \"rb\") as f:\n",
    "with open(\"eph_4_r_1_c_16_lb_15_sum_diff_mul_div_exp_gaussian.pk\", \"rb\") as f:\n",
    "    results = pk.load(f)\n",
    "kernel_list = [\"sum\", \"diff\", \"mul\", \"div\", \"exp\", \"gaussian\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We define the kernel set that was used to produce the runs\n",
    "ss = dcgpy.kernel_set_double(kernel_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Since we have not pickled all the objects used during the experiment, we need to reconstruct the \n",
    "# udp and the data in a good format.\n",
    "def reconstruct_udp(prob_id):\n",
    "    X = np.reshape(Xs[prob_id], (len(Xs[prob_id]),1))\n",
    "    Y = np.reshape(Ys[prob_id], (len(Ys[prob_id]),1))\n",
    "    udp = dcgpy.symbolic_regression(points = X, labels = Y, kernels=ss(), n_eph=4, rows =1, cols=16, levels_back=17, multi_objective=False)\n",
    "    return (udp, X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best  fit: prob-id  4 | Value:  3.359546731194255e-06\n",
      "Worst fit: prob-id  0 | Value:  2.3801558148325692e-05\n",
      "On average:  [1.0948612e-05]\n"
     ]
    }
   ],
   "source": [
    "# We also want to know (at a glance) if the experimental setup worked well in terms of MSEs\n",
    "mses = [min(a[0]) for a in results]\n",
    "print(\"Best  fit: prob-id \", np.argmin(mses), \"| Value: \", mses[np.argmin(mses)][0])\n",
    "print(\"Worst fit: prob-id \", np.argmax(mses), \"| Value: \", mses[np.argmax(mses)][0])\n",
    "print(\"On average: \", sum(mses)/len(mses))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The best fits found"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( 0.26, \\  0.34\\right)$"
      ],
      "text/plain": [
       "(0.26, 0.34)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 612x720 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The data and best fits at a glance\n",
    "fig, axes = plt.subplots(nrows = 4, ncols=3, sharex=True, sharey=True, figsize=(8.5,10))\n",
    "for i, ax in enumerate(np.reshape(axes,(12))[:12]):\n",
    "    udp, X, Y = reconstruct_udp(i)\n",
    "    ax.scatter(X, Y, s=2.0, alpha=0.5)\n",
    "    best_run = np.argmin(results[i][0])\n",
    "    best_dv = results[i][1][best_run]\n",
    "    Y_pred = udp.predict(X, best_dv)\n",
    "    ax.scatter(X, Y_pred, s=3.0, alpha=0.5, c = 'r')\n",
    "\n",
    "ax.set_xlim(0, 1.5)\n",
    "ax.set_ylim(0.26, 0.34)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'prob_id: 0, err: 2.3801558148325692e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} - \\frac{c_{2}}{x_{0}} + \\frac{c_{2}}{2 x_{0}^{2}} + c_{3} e^{- 4 x_{0}^{2}} - c_{4} x_{0} e^{- 4 x_{0}^{2}} + c_{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 1, err: 1.5481952594443556e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{1} - c_{2} e^{x_{0}} + x_{0} \\left(c_{2} e^{x_{0}} + c_{2} - c_{4} - x_{0} + \\left(- c_{1} + c_{2} e^{x_{0}} + c_{3}\\right) e^{x_{0}}\\right)}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 2, err: 4.866500757662433e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\left(c_{1} + c_{4} x_{0} + \\left(- c_{3} + \\left(c_{2} - x_{0}\\right) e^{\\left(x_{0}^{2} e^{x_{0}^{2}} - 1\\right) e^{- x_{0}^{2}}}\\right) e^{x_{0}^{2}}\\right) e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 3, err: 7.993101895616535e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} x_{0} e^{x_{0}^{2}} + c_{1} + c_{2} e^{x_{0}^{2}} + c_{3} - c_{4} x_{0} + e^{- e^{- 2 x_{0}^{2}}} - e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 4, err: 3.359546731194255e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} x_{0} - c_{2} + c_{3} e^{- x_{0}} + c_{4} - \\frac{c_{4}}{x_{0}} - e^{- e^{2 x_{0}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 5, err: 1.686027444316002e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} x_{0} + c_{1} e^{- x_{0}^{4}} + \\frac{c_{1}}{x_{0}^{2}} + c_{2} - 2 c_{3} - \\frac{c_{3}}{x_{0}^{3}} - 2 c_{4} x_{0} - \\frac{c_{4}}{x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 6, err: 9.922429392571683e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{2} - c_{3} e^{- x_{0}^{2}} + \\frac{2 c_{4}}{c_{1} + x_{0}} - e^{- \\left(c_{1} + x_{0}\\right)^{2}} + e^{- c_{4}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 7, err: 8.515167695863056e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} e^{e^{- x_{0}^{2}}} + c_{2} + c_{3} x_{0} - c_{4} e^{- x_{0}^{2}} + x_{0} e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 8, err: 5.7033656245193685e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{\\left(x_{0} \\left(c_{1} x_{0} - c_{3} + e^{c_{2}}\\right) e^{c_{1} x_{0} \\left(c_{3} - e^{c_{2}}\\right)} + \\left(- c_{2} x_{0} + c_{4}\\right) e^{x_{0}^{2}}\\right) e^{- x_{0} \\left(c_{1} \\left(c_{3} - e^{c_{2}}\\right) + x_{0}\\right)}}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 9, err: 4.523905989067585e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle 2 c_{1} + \\frac{c_{1}}{x_{0}^{2}} + c_{2} - c_{3} x_{0} + \\frac{4 c_{4}}{x_{0}} + \\frac{c_{4}}{x_{0}^{3}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 10, err: 1.9017543270061446e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{2} e^{\\frac{1}{x_{0}}} - c_{3} + x_{0} \\left(- c_{1} x_{0} + c_{4}\\right)}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 11, err: 1.1337997121125522e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{2} \\left(c_{4} - x_{0}^{4}\\right) - c_{3} x_{0} \\left(c_{4} - x_{0}^{4}\\right) + x_{0} \\left(- c_{1} x_{0}^{2} - c_{2} x_{0} + c_{4}\\right)}{x_{0} \\left(c_{4} - x_{0}^{4}\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Lets peek into the best fits functional forms. Each of the 12 problems is here\n",
    "## assigned an id\n",
    "from IPython.display import display, Math\n",
    "for prob_id in range(12):\n",
    "    udp, X, Y = reconstruct_udp(prob_id)\n",
    "    best_run= np.argmin(results[prob_id][0])\n",
    "    best_x = results[prob_id][1][best_run]\n",
    "    best_f = results[prob_id][0][best_run]\n",
    "    s = parse_expr(udp.prettier(best_x))[0].simplify()\n",
    "    display(\"prob_id: {}, err: {}\".format(prob_id, best_f[0]), Math(r'{}'.format(s._repr_latex_())))\n",
    "    \n",
    "# NOTE: selecting the fit with the best MSE may not be ideal as best formulas do get unnecessarily complex"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Looking for elegant forms\n",
    "Some of the best fits found seem to be unnecessarily complex, we here look in the results for more elegant forms with a marginally worse MSA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABDAAAALICAYAAACJhQBYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAgAElEQVR4nOzdeXxV9Z3/8dcnO0vY9002RRBEFLfiglo3BB3taLXqaLXa8Vdbne52Og+n08WOM3Vql7Hu1GplimIVS1Fra1FLEUGQTSoCQhIgQBYSkpDlfn5/nBN6udwkN5DkJve+n49HHuSe8z3f87nO9HD53O/38zF3R0RERERERESkM8tIdgAiIiIiIiIiIi1RAkNEREREREREOj0lMERERERERESk01MCQ0REREREREQ6PSUwRERERERERKTTUwJDRERERERERDo9JTBEYpiZm9n4BMd+y8wea+b8VjP7ZNtFJyIioGe1iEhXoGe1tDUlMCQlhA+0ajOrNLNdZvakmfVs7/u6+w/c/XNtMZcF/tPM9oY/95uZtcXcIiKdQYo8q88zsz+ZWbmZbW2LOUVEOpMUeVZ/zczWmlmFmW0xs6+1xbySfEpgSCqZ4+49gZOBU4Fvxw4ws6wOjypxtwP/AEwFTgRmA59PakQiIm2vqz+r9wNPAPowLCKprKs/qw34J6AvcAlwp5ldm9yQpC0ogSEpx90Lgd8Dk+Hg0rUvmNmHwIfhsdvMbJOZlZjZS2Y2LGaaWWa22cz2mNl/mVnc/62Y2b+b2dNRr280s4/DFRT/2srQbwJ+5O4F4Xv4EXBzK+cQEekSuuqz2t3fcfdfAZtbc52ISFfUhZ/V97v7Snevd/eNwIvAjNbMIZ2TEhiScsxsJDALeC/q8D8ApwOTzOx84D7gGmAo8DEwL2aaK4HpBFnnK4BbErjvJOAh4EZgGNAfGBF1/iwzK2tmihOA1VGvV4fHRERSThd+VouIpI1UeFaHW7LPBtYlMl46NyUwJJX8NnyQvQX8GfhB1Ln73L3E3auB64EnwqzsAeAe4EwzGx01/j/D8duAHwPXJXD/fwRedvcl4bz/BkQaT7r7W+7ep5nrewLlUa/LgZ6qgyEiKaarP6tFRNJBKj2r/53g371PJjheOrHOvG9JpLX+wd3/0MS57VG/DwNWNr5w90oz2wsMB7bGGf9xeE1LhkVf5+77w3kTVQn0inrdC6h0d2/FHCIinV1Xf1aLiKSDlHhWm9mdBLUwzg4TIdLFaQWGpIvoJEARcEzjCzPrQbAsrTBqzMio30eF17RkR/R1ZtY9nDdR6wgKeDaaipa6iUh66QrPahGRdNclntVmdgvwTeACdy9ozbXSeSmBIeno18BnzewkM8slWBK3zN23Ro35mpn1Dff93QX8XwLzPgfMDvfk5QD/Qev+N/YU8GUzGx4WP/oKMLcV14uIpJJO+aw2swwzywOyg5eWF84jIpKOOuuz+vowlgvdXUWXU4gSGJJ23P11gn10zxNkd8cBsW2VXgRWAKuA3wGPJzDvOuALBA/yHUApcDDba2Znm1llM1M8DCwE1gBrw/s+nNCbEhFJMZ34WX0OUA0sIvgmsRp4NaE3JSKSYjrxs/p7BCs2lptZZfjzi0Tfl3Repu31IiIiIiIiItLZaQWGiIiIiIiIiHR6SmCIiEinZGYzzexNM/uFmc1MdjwiIiIiklxKYIiIpAgze8LMis1sbTNj7jKztWa2zszujjq+1czWmNkqM3u3PeIws0vMbKOZbTKzbyYwlRO0F84jat+riIiIiKQn1cAQEUkRZnYOwT/4n3L3yXHOTwbmAacBtcBi4A53/9DMtgLT3X1PM/MPAqrdvSLq2Hh339RSHGaWCfwNuJAgGbEcuM7d15vZFOC+mNvdAuxx94iZDQYecPfrW/GfQ0RERERSTFayA+jsBgwY4KNHj052GCLSya1YsWKPuw9MZgzuvsTMRjczZCLwV3evAjCzPwNXAvcneItzgTvMbJa715jZbeH1sxKI4zRgU2MrMzObB1wBrHf3NcDsZu5bCuTGO2Fmc4A5+fn5tx133HEJvg0RSVed4VmdzvS5WkQS1dTzWgmMFowePZp33z2q1dQikgbM7ONkx5CAtcD3zaw/QevHWUDjA86BV83MgYfd/ZHYi919vpmNAeaZ2XyCVRIXJnjv4cD2qNcFwOnNXWBmVwEXA32An8Ub4+4LgYXTp0+/Tc9qEWlJF3lWpyx9rhaRRDX1vFYCQ0QkTbj7BjP7T+A1gi0eq4H68PQMdy8Kt4m8ZmYfuPuSOHPcH66eeAgY5+7N9WCPZvFCaiHeBcCCBOcXERERkRSnIp4iImnE3R9395Pd/RygBPgwPF4U/lkMvECw5eMwZnY2MDkcc28rbl0AjIx6PQIoavUbEBEREZG0pQSGiEgaCVdYYGajgKuAZ82sh5nlh8d7ABcRbDeJvXYa8ChB7YrPAv3M7HsJ3no5cKyZjTGzHOBa4KWjfT8iIiIikj6UwBARiaMh0vU6NJnZs8BSYIKZFZjZreHxRWY2LBz2vJmtBxYCX3D3UmAw8JaZrQbeAX7n7ovj3KI7cLW7f+TuEeAm4LD9ifHicPd64E7gFWAD8Bt3X9eGb19E0tCeygPJDkFERJrh7pTur22z+VQDQ0TS2rLNe5m/ooCS/bUHf0r31zJ2YA9evPOsZIfXKu5+XRPHZ0X9fnac85uBqQnM/3bM6zqCFRmJxrEIWNTSfUREWlJT18C9L67jTxuL+f1dZ9O/Z9xGRSIikmRvfriHz/9qBU9/7nROOabvUc+nBIaIpLX/emUj64r2MXZgD/r1yOGY/t3p2z2HMQN6JDs0ERGJY/PuSv7fMyv5YGcFd543nt7dspMdkoiIxBGJOPe/8gH9e+YweXivNplTCQwRSVtVtfWsLijj1rPG8s1Lj092OCIi0oKXVhdxz/Pvk5OVwdzPnsrMCYOSHZKIiDThd2t2sLZwHw9cM5XcrMw2mVMJDBFJW+9uLaWuwTlzXP9khyIiInFEIk5ZdR17Kw/wy6Vbefqv2zjlmL789LppDOvTLdnhiYhIE+oaIvzo1Y1MGJzPFScNb7N5lcAQkbS1dPNesjKM6W2wH09EJNXU1DVQUVOPe8tFjeONcIcGdxoaPPgz4tTUNbBrXw07ymvYUV7NjrIa9uyvpa4+QkPEqY9EwnER9u6vpWT/AaJrKt9+zli+dvEEsjNVh15EpDP7v+Xb2bq3isdvmk5mhrXZvEpgiEjaWvrRXqaO7EOPXD0KRSQ9VNXWs2xzCe9sLaGsqo7q2nqqahuormugqraB8uq6gz+19ZF2jSUzwxicn8vA/FxysjLIysggNzuLzAwjNyuDk4/py4CeOfTvkUP/nrmMHdiDE4b1bteYRETk6FXXNvDg6x9y6ui+nH98227106d2EUlLFTV1rCks5//NHJfsUKQJZjYT+C6wDpjn7m8kNSCRLmptYTlvbCzmzQ/3sHJbsHUuO9Po3S2H7jmZdM/JpFv456D8nvTulk3vbtn06pZNr7wsMhL85sw4fFxWhpGRYWRmQIYFiYnBvfIY2rsbA/Nz2/RbORER6RyeeHsLuysO8ND1J2PWts95JTBEJC0t31pCQ8Q5c2x61L8wsyeA2UCxu09uYsxdwG2AAY+6+4/b+n5mdgnwIJAJPObuP2xmGgcqgTyg4EhjEUlHkYjzhw27eHjJZlZ8XArACcN6cctZYzhr/ABOHd2PvOy2KagmIiLSqKyqll/8+SM+OXEQ00f3a/P5lcAQkbS09KO95GQGS5TTxFzgZ8BT8U6a2WSC5MVpQC2w2Mx+5+4fRo0ZBFS7e0XUsfHuvimR+5lZJvBz4EKChMRyM3vJ3deb2RTgvpg5bnH3S81sMPAAcH3r3rJI+jlQ38Bv3yvk4SWb2bx7PyP7deM7l5/A7BOH0r9nbrLDExGRFPfQGx9ReaCer148oV3mT8sEhpYli8jSzXuZNqpP2nwD6e5LzGx0M0MmAn919yoAM/szcCVwf9SYc4E7zGyWu9eY2W3hmFkJ3u80YJO7bw7vMQ+4Aljv7msIVmzEUwroX14izYhEnOdXFvDfr25k174DnDCsFz+9bhqXTh5ClgpeiohIB9hZXsPcv2zlymnDOX5Ir3a5x1ElMMxsJMG3a0OACPCIuz8YZ9xWoAJoAOrdffpR3FPLkkXkqJRX1bGuaB93XXBsskPpTNYC3zez/kA1QVLi3egB7j7fzMYA88xsPnALwWqKRA0Htke9LgBOb2qwmV0FXAz0IVjNEW/MHGDO+PHjWxGGSGp5d2sJ//Hyet4vKOekkX340dUnMWN8/zbfdywiItKcx9/aTH3E+ZdPHtdu9zjaFRj1wFfcfaWZ5QMrzOw1d18fZ+x57r4n3iRaliwiHWnZlr24kzb1LxLh7hvM7D+B1wgSvKsJnvGx4+4PV048BIxz98pW3Cbev6aa7M/o7guABS3EvRBYOH369NtaEYdISigqq+aHv/+Al1YXMbhXLv/z6alcMXV4wkU3RURE2sq+mjqefWc7l00Zysh+3dvtPkeVwHD3HcCO8PcKM9tA8A1bvARGczrdsmR9qyeSupZu3ktuVgYnjeqT7FA6FXd/HHgcwMx+QJwVamZ2NjAZeAG4F7izFbcoAEZGvR4BFB1pvCLpqK4hwhsbd/Pciu388YNiMsz40vnj+eeZ4+iek5Y7g0VEpBN4dtk2Kg/Uc/s5Y9v1Pm32N12YVJgGLItz2oFXzcyBh939kUNOdsJlyfpWTyR1Lf1oL9NH9yU3Kz3qXyTKzAa5e7GZjQKuAs6MOT8NeBS4DNgCPG1m33P3byd4i+XAseHzvhC4FvhMm70BkRT24a4Knn1nOy+uKmTv/loG9Mzhn84czWdnjGZE3/b7pktERKQltfURnnx7K58Y15/Jw3u3673aJIFhZj2B54G73X1fnCEz3L0o3Crympl94O5Logd0tmXJIpKa9lYe4IOdFXz1ovbbm9cZmdmzwExggJkVAPe6++Nmtgj4nLsXAc+HNTDqgC+4e2nMNN2Bq939o3DOm4CbW3m/O4FXCOoVPeHu69r4rYqknNr6CHN+9haRCFwwcRCfOnkE504YSLaKc4qISCewcHURO/fV8MNPTWn3ex11AsPMsgmSF8+EiYHDhB+MCb/Ze4Fgy8chCQwtSxaRjrBsSwkAZ44bkORIOpa7X9fE8VlRv5/dwhxvx7yuI1iR0Zr7LQIWtRSviPzdzvIaauoi/PCqKVx72qhkhyNyCDPLIOju1wt4191/meSQRKQDuTuPvrmZCYPzOfe4ge1+v6NK3VtQ3vpxYIO7P9DEmB5hgU/MrAdwEUG1++gxjcuSrwA+C/Qzs++1IpSDy5LNLIdgWfJLrX0/IpL6ln60l+45mZw4on2Xt4mItJXCsmqAdi2KJp2DmW01szVmtsrM3m1iTB8ze87MPjCzDWZ2ZrxxCd7vCTMrNrPYz+aXmNlGM9tkZt9sYZorCLZz16HufiJp589/280HOyu47ZyxHdL96mjXHs4AbgTODx+0q8xsFoCZLTKzYcBg4C0zWw28A/zO3RfHzHNwWbK7R4CbgI/j3TBclrwUmGBmBWZ2q7vXE6zYeAXYAPxGy5JFJJ6lm/dy6uh+WnotIl1GYwJjeJ9uSY5EOsh57n6Su09v4vyDwGJ3Px6YSvDZ9yAzG9T45WHUsaaq0s8FLokZ29jd71JgEnCdmU0Kz00xs5ejf4ApwFJ3/zJwR2veqIh0fY++uZnBvXK5fOqwDrnf0XYheYv49ScOWZZM8HBtbh4tSxaRdldcUcOm4kr+8ZQRyQ5FRCRhhaVBAmNon7wkRyLJZma9gHMI6w+5ey1QGzOsQ7v7mdkNUTE0NBG3uvuJpKC1heW8vWkv37z0eHKyOubLQX0FKSJp46+bw/oXY/snORIRkcQVllUxMD9XnZPSQ2PnvhVmdnuc82OB3cCTZvaemT0WbtH++wTu84HFBN39rifo7ndNK2KI191veDPjFwAXm9lPialxFxXTQne/vXdvbd8USSWPLNlMz9wsPnN6x9VnUgJDRNLGO1v2kp+bxQnDeiU7FBGRhBWV1Wj7SPqY4e4nE2zf+IKZnRNzPgs4GXjI3acB+4HDalS4+/1ADUF3v8vbubtflbvf6u5fdPeft+I+ItKFbSqu5HdrdnDtqSPplZfdYfdVAkNE0saWPfsZN6gnWap/ISJdSGFZNcP7KoGRDqI79xF05jstZkgBUODuy8LXzxEkNA4Rp7tfa6i7n4g0q6yqltufepfe3bK57ZyxHXpvfYoXkbSxraSKUari32WY2Uwze9PMfmFmM5Mdj0gyRCJOYVk1I7QCI+Ul0rnP3XcC281sQnjoAmB9zDzq7ici7aauIcIdT6+koLSah288hcG9OrY+kxIYIpIW6hsiFJXVpHwCo6mWeDFj/sXM1pnZWjN71szywuMttu872jha2ZrPgUogD7XmkzS1Z/8BausjDFMCIx002bkvqrsfwBeBZ8zsfeAk4Acx86i7n4i0C3fn3367lqWb9/LDT03h1NH9OjyGo+pCIiLSVewor6Eh4imfwCBoifcz4Kl4J81sOPAlYJK7V5vZbwi+XZsbDjnP3fc0ce0goNrdK6KOjXf3TYnEEdWa70KChMRyM3vJ3deb2RTgvpg5bnH3S81sMPAAcH1zb1wkFRWV1QBqoZoOwq4fcTv3RXf3c/dVQFMtVtXdT0TazeNvbWHe8u3ced54rjo5OV39lMAQkbSwraQKgJEpnsBooiVerCygm5nVEXxTl+je5g5tzRelFMiNd0Kt+STVNbZQVQ0MERFJpj+s38X3F21g1pQhfPnC45IWh7aQiEhaaExgjOqf2gmMlrh7IfDfwDZgB1Du7q82nqaZ9n0d3ZrPzK4ys4eBXxGs5oj3ftSaT1JaYVnw7NIWEhERSZa1heXcNe89pgzvzY+uPomMjHjNijqGVmCISFrYVlJFdqYxpIMLDXU2ZtaXYNXDGKAMmG9mN7j70wTt+4rCrSKvmdkH7r4k+np3vz9cOfEQMK6dW/MtABa0Yn6RlFNYWk1+bha9u3VcizoREZFGW/fs5+Yn36FP9xwe/afpdMvJTGo8abkCQ5XtRdLPtpIqRvTtTmYSM8adxCeBLe6+O9wXvQD4BCTUvk+t+UQ6WGFZjbaPiIhIUhTvq+HGJ5YRcXjq1tM6vONIPC0mMMxspJn9ycw2hFXr72pmbKaZvWdmL0cdi1vt/ki0UVV7UGV7kbSzvaQq5etfJGgbcIaZdTczI2jBtyGR9n1qzSfS8QrLqlXAU0REOty+mjpuenI5eytrefLmUxk3sGeyQwISW4FRD3zF3ScCZwBfMLNJTYy9i6DdEnBItfvp7j4ZyCT4wHoIMxvU+ME56li8imxzgUtixjVWtb8UmARc1xifmU0xs5djfgYBb7r7pcA3gO+0+F9ARLq8bSVVjOqX+v8IiNcSLzy+yMyGufsy4DlgJbCG4O+BR2imfV8UteYT6WCFpVWqfyEiIh2qpq6B2375Lh/uquAXN5zC1JF9kh3SQS3WwHD3HQSF3nD3CjPbQFB0bX30ODMbAVwGfB/4csw9Wqp2n1Bl+zauag+qbC+SFsqr6yirqkuHFqrNtcSLbsF3L4dv/2iyfV/UdWrNJ9KBKmrq2FdTry0kIiLSYSIR5+55q1i2pYQHrz2Jc44bmOyQDtGqGhhh8mAasCzO6R8DXwcijQdaqHZP1LijqWzfqqr24ftQZXuRNLK9sYVq39RPYIhI6igqqwHQFhIREekwr67fxeJ1O/nWrOO54qRm/1mdFAknMMysJ/A8cLe774s5NxsodvcVMcejq90PA3qY2Q3x5nf3+4Eagsr2l7eisn2rqtqH91rg7p9390+7+xsJ3kdEuqiC0jCBkQYrMEQkdTS2UNUKDBER6Shz/7KF4X26ccuMMckOJa6EEhhmlk2QvHgmbGsXawZwuZltBeYB55vZ0zRT7T7OPY60sr2q2otIs7aFKzBG9VcCQ0S6jsLSakArMEREpGNs2LGPv24u4Z/OPIaszM7ZsDSRLiQGPA5scPcH4o1x93vcfYS7jyYo0vlHd7+BJqrdx7nH0VS2V1V7EWnWtpIq+nTPpldedrJDERFJWEFZNTmZGQzsGbdcl4iISJv65V+2kpedwadPHdny4CRJJK0yA7iRYFXFqvBnFvy9qn1TFzZT7T5WQpXtVdVeRI7EtpLqtCjgKSKppaishqF98sjIiLdbVkREpO2U7q/lhfcKuXLaCPp0z0l2OE1KpAvJW8SvM3FIVfuoY28Ab0S9jlftPvaahCrbq6q9iByJ7SVVTBrWK9lhiIi0SmFplbaPiIhIh5i3fDsH6iPc/InRyQ6lWZ1zY4uISBtpiDgFpVVagdEFmdlMM3vTzH5hZjOTHY9IRyssq2aYEhgiItLO6hsi/GrpVj4xrj8ThuQnO5xmKYEhIilt574a6ho87RMYZvaEmRWb2dpmxvyLma0zs7Vm9qyZ5bX1vczsEjPbaGabzOybLUzlQCWQR1CwWSRt1NZHKK44oBUYIiLS7l5dv4ui8ppOv/oClMAQkRS3bW/YgSTNExjAXOCSpk6a2XDgS8B0d58MZBIURY4eM8jM8mOOjU/0XmaWCfwcuBSYBFxnZpPMbIqZvRzzMwh4090vBb4BfCfxtyrS9e0sr8FdLVRFRKT9zX17KyP7deOCiYOTHUqLlMAQkZS2vVQJDAB3XwKUtDAsC+hmZlkExZVjW1KfC7zYuDLDzG4DftKKe50GbHL3ze5eS9B2+wp3X+Pus2N+isOizgClQNw2DGY2x8weKS8vb+GtiXQtBWXBs2uEVmCIiEg7WltYzjtbS7jpzNFkdoGi0UpgiEhK215SRWaGMbT3Ee2GSBvuXgj8N0H76x1Aubu/GjNmPrAYmGdm1wO3ANe04jbDge1RrwvCY3GZ2VVm9jDwK+BnTcS90N1v7927dyvCEOn8CkurAVQDQ0RE2tUv/7KVbtmZXD2987ZOjdZiFxIRka5sW0kVw/rkkZWpfG1zzKwvcAUwBigD5pvZDe7+dPQ4d7/fzOYBDwHj3L2yNbeJc8ybGuzuC4AFrZhfJGUUlgUJjKF9lHyVzs3MMoDvAr2Ad939l0kOSURaUFPXwNLNe3l9wy5eXFXENaeOoHe37GSHlRAlMEQkpW0rUQeSBH0S2OLuuwHMbAHwCeCQBIaZnQ1MBl4gaJF9ZyvuUQBEp/dHcPg2FREBisqqGZSfS25WZrJDkQ5kZluBCqABqHf36U2MywTeBQrdffZR3O8JYDZQHNY/ajx+CfAgQT2kx9z9h81McwXBaroSVHBZpNNpiDg799WwbW8Vm/dU8ueNu3lr0x6qahvolp3J+ccP4kvnH5vsMBOmBIaIpLTtJVVcOKnzFyTqBLYBZ5hZd6AauIDgw/FBZjYNeBS4DNgCPG1m33P3byd4j+XAsWY2BigkKBL6mTaKXySlFJZVq4Bn+jrP3fe0MOYuYAPBqodDhEWQq929IurYeHffFGeeuQRb9J6KGttYcPlCgoTEcjN7yd3Xm9kU4L6YOd4Blrr7w2b2HPB6S29QRNrPvpo6Fq/dyavrdrKpuJLCsmrqGv6+4HVo7zyuOnk4F0wczJlj+5OX3bUS5UpgiEjK2n+gnj2VtYzUCgzM7FlgJjDAzAqAe939cTNbBHzO3ZeFHzxXAvXAe8AjMdN0B65294/COW8Cbk70Xu5eb2Z3Aq8QfKv3hLuva/t3K9L1FZZWc8Jw1XaRw5nZCIJE8veBL8cZci5wh5nNcveasODylcCs2IHuvsTMRsccPlhwObzfPIJVFuvdfQ3Bio3oeG4AasOXDUf6vkTkyNXUNfD6hmJeXFXIGxt3U9sQYWS/bkwd0YdLpwxlVL/ujOzbPfizXzfMOn+xzqakZQLDzGYS7NVbB8xz9zeSGpCItAt1IPk7d7+uieOzon6/l2BbSFNzvB3zuo5gRUZC9wrPLQIWJRCySNqKRJyishouPmFIskORjufAq2bmwMPuHptIBvgx8HUgP8453H1+uNJtnpnNJyi4fGErYohXcPn0ZsYvAH4abjFcEm+Amc0B5owfH6/ztogcjU3FlVz7yFL2VNYyMD+X688YxeVTh3HSyD5dOlHRlBYTGGY2kmBZ2RAgAjzi7g82Mfaw/Xhm1gd4jGDPtAO3uPvSIwm2jfbpEcZRCeShvXoiKWvbXiUwRKTr2bP/ALUNEW0hSU8z3L0o3Abympl9ELamBsDMGj8Hrwi/kIurgwsuVwG3Njehuy8EFk6fPv22VsQhIi0o3lfDTU+8A8DTt57OmeP6d4lWqEcjkbL89cBX3H0icAbwBTOb1MTYxv140R4EFrv78cDUOOcxs0Fmlh9zLF6Kdi5wScy4xn16lwKTgOsa4zOzKWb2cszPIOBNd78U+AbwnWbeu4h0YdtKlMAQka6nsYXqcLVQTTvuXhT+WUxQLPm0mCEzgMvDYp/zgPPN7OmYMfEKLreGCi6LdAEVNXXc/ORySqtqefLm0zjr2AEpn7yABBIY7r7D3VeGv1cQJCCGx46L2o/3WNSxXsA5wOPh9bXuXhbnNucCL5pZXnjdbcBP4sSyhKDCcbSD+/TcvZbgYX5FOH6Nu8+O+Sl290h4bSmQG+99m9kcM3ukvLw8/n8YEen0Ckqryc/L6jJtoURE4O8tVIcpgZFWzKxH4xd6ZtYDuAhYGz3G3e9x9xHuPpqgEPIf3f2GmHkaCy5fAXwW6Gdm32tFKAcLLptZTnifl47wbYlIO6itj3DH0yv5264K/vf6k5kyIn1qJiWyAuOgsMjPNGBZnNON+/EiUcfGAruBJ83sPTN7LHwgH8Ld5wOLCfbqXU+wV++aBMOKt0/vsARLzPu4ysweBn5FUHn5MO6+0N1v7907ff6fQSTVNLZQTcX9fyKSug6uwNAWknQzGHjLzFYTdPb4nbsvBjCzRWY2LMF5DhZcDr+0uwn4ON7AsOjyUmCCmRWY2a3uXk/QIvsVgi8uf6OCyyKdRyTifP251by1aQ/3XTWFmRMGJTukDpVwEU8z6wk8D9zt7vtizjW1Hy8LOBn4Yljh/kHgmw8BttoAACAASURBVMC/xc5/FHv1WrVPL7zXAoKCQyKSwraVVHHsoJ7JDkNEpFWKyoLVY73ytHosnYRdP6Y2cS5eB5E3gDfiHE+o4HJ4rqkCzyq4LNIJRSLOfb/fwG9XFfHVi47j6ukjW74oxSS0AsPMsgmSF8+E//iP1dR+vAKgwN0bV2w8R5DQiHePI92rp316InKYSMTZXlKlFqoi0uUUllWr/oWIiBxiR3k1//TEOzz65hZuOGMUXzgvPbv6tJjAsGDt9ePABnd/IN6YpvbjuftOYLuZTQiHXgCsj3OPo9mrp316InKY3ZUHOFAfUQKjCzOzmWb2ppn9orlq+yKppqBUCQwREfm7l1YXcfH/LGHFx6X84MopfPeKyWm7RTqRFRgzgBsJVlWsCn9mQcL78b4IPGNm7wMnAT+IMyahvXrapyciiUrXDiRm9oSZFZvZ2jjnJkQ9x1eZ2T4zuzvq/FYzWxOee7edYrjEzDaa2SYz+2YLU6nltaSdygP1QQJD9S9ERNJeeVUdX3r2Pb707HuMG9ST3991Np85fVTaJi8ggRoY7v4W8etMJLQfz91XAdNbuEdCe/W0T09EErVtb3omMAjaTf8MeCr2hLtvJEgkN7agLiTYthftPHffE2/isA11ddiRqvHYeHfflEgMUW2vLyRISCw3s5eATOC+mDluIWh5/WczGww8AFwf/y2LpAb3oDBbVW09c6YmWq9RRES6str6CEv+tpvfrdlBYWk1FQfqqTxQR2VNPRU19QB89aLj+Odzx5GV2aoeHCkp4SKeIiJdybaSKsxIu2XY7r4k7BjVkguAj9w9bmX6JpwL3GFms9y9Jmx5fSVwSDK7mRgOtr0GCAs3X+Hu9wGzm7lvsy2vgTnjx6fnPlBJLY++uZlFa3Zyz6XHc+rofskOR0RE2klDxHlnSwkvrS5k0ZqdlFfX0bd7NscP6cXwPt3Iz8unZ24WPfOyuGzKUCYPV2fMRkpgiEhK2lRcyci+3cnJUqa6CdcCz8Ycc+BVM3PgYXd/5JCT7vPNbAxBy+v5BKskLmzFPeO1vT69qcFmdhVwMdCHZlpeAwunT59+WyviEOl0/vLRHn74+w+4dPIQbj9nbLLDERGRdlDXEOGFlYX89E8fsr2kmu45mVx8whAunzqMs44dQLZWWLRICQwRSUnvF5Zx4og+yQ6jUwoLHl8O3BNzaoa7F4VbRV4zsw/cfUn0gKNoeQ2tbHutlteSLnaUV/PFX7/HmAE9+K+rp6b13mYRkVRU3xDht6uK+OkfP+TjvVWcOKI3X7v4eC6cOJhuOZnJDq9LUQJDRFJOyf5atpdUc8PpxyQ7lM7qUmClu++KPujuReGfxWb2AsGWj0MSGHFaXt/Zivuq7bVIjAP1Ddzx9Epq6hp4+MYz6Jmrj2YiIqnkTxuL+Y+F69myZz8nDOvF4zdN5/zjBylZfYS0RkVEUs6awnIArcBo2nXEbB8xsx5mlt/4O3ARsDZmzNG0vAa1vRY5xP4D9XxrwVpWbS/jv66eyvhB+ckOSURE2lBNXQNf+vV7mMHDN57Cy188iwsmDlby4igogSEiKef97WWYweThvZIdSoeL1246PL7IzIaZWXeCuhWxWzMGA2+Z2WrgHeB37r44ZswRt7wGUNtrkcCB+gaefHsL5/7Xn3h+ZQF3njeeWVOGJjssERFpY3/+224qDtTz73NO4OIThihx0Qa0TlFEUs77heWMHdCD/LzsZIfS4ZppNx3dKaR/nPObgaktzH1ULa/Dc2p7LWmrviHCC+8V8uM/fEhhWTVnjO3HwzcezynH9E12aCIi0g5efn8H/Xrk8Ilxh330kiOkBIaIpJz3C8r4xLgByQ5DRNLYnb9eyZK/7T7kWH3Eqapt4MQRvfnhp6Zw1vgB+jZORCRFVdXW84f1u7jy5OFkqbtIm1ECQ0RSyq59Nezad4Ap6pctIkni7ry+oZhjB/fk5FGHrq44Y2x/Lj5B+59FRFLdHz8oprqugTknDkt2KCklLRMYZjYT+C6wDpjn7m8kNSARaTPvFwQFPKeOVAJDRJKjZH8t1XUNXDltOJ+dMSbZ4YiISBK8vHoHA/NzOW1Mv2SHklJaXMtiZiPN7E9mtsHM1pnZXc2MzTSz98zs5USOt5aZPWFmxWYWWxn/EjPbaGabzOybCUzlQCWQR9DWT0RSxJqCMjIzjElDlcAQkeTYXloNwIi+3ZMciYiIJEPlgXr+tLGYy6YMJTNDK+7aUiKbceqBr7j7ROAM4AtmNqmJsXcRVJZP9DgAZjaosX1f1LHxcYbOBS6JGZcJ/By4FJgEXNcYn5lNMbOXY34GAW+6+6XAN4DvNBWXiHQ9qwvKOXZQT7rlZCY7FBFJUwWlVQCM7NctyZGIiEgy/GH9Lg7UR5h9ojpMtbUWExjuvsPdV4a/VxAkIobHjjOzEcBlwGOJHI9xLvCimeWF19wG/CROLEuAkpjDpwGb3H2zu9cC84ArwvFr3H12zE9x2P4PoBTIjReQmc0xs0fKy8ubCVtEOhN3Z01hOSeO0OoLEUmegnAFxvA+SmCIiKSjhauLGNY777A6SHL0WlUO1cxGA9OAZXFO/xj4OhBJ8PhB7j4fWAzMM7PrgVuAaxIMaziwPep1AXESLNHM7Cozexj4FfCzJmJa6O639+6tfwiJdBUFpdWU7K/lxBF9kh2KiKSxgtIq+nTPTstWziIi6a68qo4lH+7mshOHkqHtI20u4QSGmfUEngfudvd9MedmA8XuviKR4/G4+/1ADfAQcLm7VyYaWrzpWrjXAnf/vLt/WgU8RVLHmsJgxZRWYKQGM5tpZm+a2S/C4ssiXUJBaTUj+mr1hYhIOnpl/U7qGpzZ6j7SLhJKYJhZNkHy4hl3XxBnyAzgcjPbSrCF43wze7qZ4/HucTYwGXgBuLcV76EAGBn1egRQ1IrrRSRFrC4oIyczgwlD8lsenGaaKoIcnptgZquifvaZ2d1tfS8VXJZ0UVBazYg+KuApIpKOXn5/B6P6ddcXau0kkS4kBjwObHD3B+KNcfd73H2Eu48GrgX+6O43NHU8zj2mAY8S1K74LNDPzL6X4HtYDhxrZmPMLCe8z0sJXisiKWRNQTnHD80nN0sFPOOYS0wR5EbuvtHdT3L3k4BTgCqCZPIhVHBZpGXuTkFplVZgSNowswwz+76Z/dTMbkp2PCLJtLfyAG9v2sPsE4cS/DNa2loiKzBmADcSrJ5o/HZuFoCZLTKztlgb0x242t0/Cgts3gR8HDvIzJ4FlgITzKzAzG5193rgTuAVggKjv3H3dW0Qk4h0IZGIs6agnCnDle2Op4kiyPFcAHzk7oc9g1HBZZEW7d1fS01dRAkMOSJmttXM1oSft9+Nc36kmf3JzDaY2Tozu+so7tXcyrzWrJi7gqD+XB1aLSdpbvG6nTREtH2kPWW1NMDd3yJ+nQncfVacY28AbyR6PDz3dszrOoIVGbHjrmvi+kXAonjnRCQ9bN27n4oD9UxVAc+jdS3wbLwT7j7fzMYQFFyeT1Bw+cIE541XcPn05i4ws6uAi4E+NFNwGVg4ffr02xKMQ6RdNXYgGdFXW0jkiJ3n7nuaOFcPfMXdV4Yr4laY2Wvuvr5xQLiCrTrsHth4bLy7b4qZay7Bs/Wp6INRK+YuJHhWLzezl4BM4L6YOW4BJgBL3f1hM3sOeL11b1ckNZRX1fGrpR8zdmAPJg7Vdub20mICQ0SkK3i/IPgGfor2Gx6xcBve5cA9TY1x9/vNbB5BweVx7V1wGYhXd0mk0yoorQJgRD+twJC25+47gB3h7xVmtoEgQbw+ati5wB1mNsvda8LVclcCs2LmWhJ2GIx1cMUcQPjMv8Ld7wNmxw42swKgNnzZEC9uM5sDzBk/Pt6uQ5Gub+ue/dwydzkFpdX89DPTtH2kHbWqjaqISGf1fkE5edkZHDuoZ7JD6couBVa6+66mBqjgskjzGldgDO+jBIYcEQdeNbMVZnZ7cwPD5MM0YNkhE7jPBxYTrJa7nmCVxDWtiCHeirnhzYxfAFxsZj8FlsQb4O4L3f323r31JYOknuVbS7jyf9+mtKqWZ247nYtPGJLskFKaVmCISEp4v6CME4b1JitTedmjcB1NbB+BQwouXwZsAZ42s++5+7cTmPtgwWWgkGCrymeOPmSRzqWgtIo+3bPJz8tOdijSNc1w96JwG8hrZvZBWFfoEGbWk6BD4N3uvi/2/FGsloNWrphz9yrg1lbML5IyXnivgG88t4YR/brx5M2nckz/HskOKeUpgSEiXV59Q4R1Rfu49rSRLQ9OU2ER5JnAgHC5773u/riZLQI+B5QR7Hf+fDPTHCy4HM55E3BzK+7VWHA5E3hCBZclFRWUVquApxwxdy8K/yw2sxcItnMcksAws2yC5MUz4Va7w8RZLXdnK8LQijnp0nZXHOD5lQWsKWzfAt/VtQ388YNizhzbn1/ccAq9uytx3RGUwBCRLm/T7kqq6xrUb7sZzRRBjt4T3b+FOVRwWaQFBaXVjB+orWzSembWA8gIa1v0AC4C/iNmjAGPAxvc/YEm5jma1XKgFXPSBTVEnDc/3M28d7bzhw27qI84x/TvTlZG+9aiuPkTo/nWrInkZGkFcEdRAkNEOj13p7SqjuKKGor3HWBfTd0h59/dWgrAiepAIiJJ5O4UlFYx87iByQ5FuqbBwAth8b8s4NfuvhggarXcWOBGYI2ZrQqv+1aYIG50VKvl3L1eK+akq9hXU8evl23jV0s/prCsmn49cvjsjNF8+tRRjFddtJSkBIaIdFpP//VjHnrjI4oraqhraLZhBQN65jJG+w5FJIn27q+lpi6iLSRyRMKuH1ObONe4Wq6I+DUqosce1Wq58JxWzEmntrO8hiff3sIzy7ZReaCeT4zrzz2zjufCSYPJzcpMdnjSjpTAEJFOx935nz98yE9e/5DTRvfj8pOGMbBnLoN65TIoP48+3bMP+/Q2MD+XjHZeJigi0pzGDiQj+3VPciQiIp1bTV3cjruHqW2IULa/jpKqWkqraimrquUvm/by21WFNEScy04cxufPGcvk4dpGnC6UwBCRTqUh4vzbi2v59bJtXDN9BD+4coo6i4hIl1BQWgXAiL5KYIiIAEQizsclVawv2sf6HeWsK9rH+qJ9FFccOOI587Iz+Mxpo/jc2WOVME5DSmCISKdxoL6Bu+et4vdrd3LHzHF8/eIJhHuBRUQ6vcYVGMO1hURE0lAk4qwr2sfaovIwYbGPDTv2UVUbrLbIyjDGD+rJWccOYOyAHmRmtPwFVXam0btbNn2759C3RzZ9uucwpFcePXL1z9h0lZb/lzezmcB3gXXAPHd/I6kBiQiVB+q5/al3+ctHe/n2ZRP53Nljkx2SiEirFJRW0bd7Nj31wVpE0kjxvhrmryhg3vJtbC8JErk9c7OYNLQX10wfyaShvZg0rBfHDu6p+hRy1Fr8G9bMRgJPAUOACPCIuz/YxNhM4F2g0N1nt+baRJjZE8BsoNjdJ0cdvwR4kKBS8mPu/sMWpnKgEsgj6HUtIkn2yJ8/YunmvfzPp6dy5bQRyQ5HRKTVCkqrtX1ERNJCdW0Df928l3nLt/GHDcU0RJwzx/bnXz55HNOP6ceIvt1Um0zaRSJfEdQDX3H3lWaWD6wws9fcfX2csXcBG4BerbnWzAYB1e5eEXVsvLtvipl/LvAzgqRI47hM4OfAhQTJiOVm9pK7rzezKcB9MXPcArzp7n82s8HAA8D1Cfx3EJF24u68tLqIGeMGKHkhB2m1nHQ1BaXVHKu2fSKSYuobIqwuKOf9gjLWFJaztrCcTcWVRBz698jhc2eP4dpTRzFmgLrBSftrMYHh7juAHeHvFWa2ARgOxCYhRgCXAd8Hvtyaa4FzgTvMbJa715jZbcCVwKzoQe6+xMxGx1x7GrApbD2Fmc0DrgDWu/saghUbTSkFcuOdMLM5wJzx48c3c7mItIW1hfvYureKO2aOS3YoXVpTq9RixvQBHgMmE6xGu8Xdl5rZVqACaADq3X16W8eh1XKSytydgtIqzpswMNmhiIgctYaIs2zLXn73/g4Wr93J3v21QND1bcrw3lwyeSgnjezNWeMHkpOlYuvScVq1STNMHkwDlsU5/WPg60B+a6919/lmNgaYZ2bzCVZJXJhgWMOB7VGvC4DTm7vAzK4CLgb6EKzoOIy7LwQWTp8+/bYE4xCRI7Tw/SKyM42LTxiS7FC6urnErFKL40Fgsbv/o5nlANHr3c9z9z1NXajVciJN27u/lpq6iLaQiEiXVdcQYdnmEhavC5IWeypr6ZadyfkTB3Hp5CFMP6Yfg3vlqsC6JFXCCQwz6wk8D9zt7vtizjV+07YiXPKb8LWN3P3+cPXEQ8A4d69MNLR40zV3gbsvABYkOL+ItKNIxHl5dRHnHDuQPt1zkh1Ol9bEKrWDzKwXcA5wczi+FqhtxS20Wk6kCY0dSEaoA4mIdCFVtfUs+dtuXlm3i9c37GJfTX2QtDh+EJedOJTzJgyiW44Kb0rnkVACw8yyCRIQz4T/+I81A7jczGYRLPXtZWZPu/sNCVzbeI+zCZY0vwDcC9yZ4HsoAEZGvR4BFCV4rYgk2cptpRSV1/D1S45PdijpYCywG3jSzKYCK4C73H0/QeL3VTNz4GF3fyT2Yq2WE2laQWkVgFZgiEirbSqu5FsvrGFnec0hxx2nocGpbXDqGiLUNUSob3C8+e9qW6U+4rhDn+7ZXHTCEC6aNJizjx2opIV0Wol0ITHgcWCDuz8Qb4y73wPcE46fCXw1TF60eG14zTTgUYIaGluAp83se+7+7QTew3Lg2PBDdSFwLfCZBK4TkU5g4eoicrMy+OSkwckOJR1kAScDX3T3ZWb2IPBN4N+AGe5eFG4Tec3MPnD3JbETaLWcSHyNrQOHawWGiLTC79fs4KvzV5Obncm5xx1eQycrw8jOyiAnM4PsTCMzI4O2bO6RlZnBGWP7cdrofmRlqpaFdH6JrMCYAdwIrDGzVeGxb7n7IjNbBHzO3Zta8dDktTHjugNXu/tHAGZ2E+ES52hm9iwwExhgZgXAve7+uJndCbxCUBjuCXdfl8D7EpEkq2+I8Ls1O7hg4iB65raqJI8cmQKgwN0baxE9R5DAoPE57u7FZvYCwZaPwxIYWi0nEl9BaRV9u2frWSYiCalviHD/Kxt5ZMlmThrZh/+9/mSG9VECVKQliXQheYv435zh7rPiHHsDeKOla2OueTvmdR3BiozYcdc1cf0iIDYpIiKd3LItJeyprGXOicOSHUpacPedZrbdzCa4+0bgAmC9mfUAMsJuUT2Ai4D/iL1eq+VEmlZQWq3tIyKSkN0VB/jisyv56+YSbjzjGL49eyK5WdqyIZIIfU0gIkmzcHURPXIyOe/4QckOJSU0s0oterXcF4Fnwg4km4HPAoOBF8Kq4lnAr919cZxbaLWcSBMKSqs4bnDcRmwikoYiEWd7aRUbd1bw8d4qtpVUsb20iu0lVWwvrSbD4IFrpnLVySOSHapIl6IEhogkRW19hN+v3clFJwwhL1vfOrSFZlapzYr6fRUwPWZIKTA1gfm1Wk4kDnenoLSa85WMFUlb7s5Lq4t4e9MeNu6s4G+7Kqmuazh4Pj8vi1H9unPsoHwumDiYT508gglDlPQUaS0lMEQkKd7atJvy6jrmTB2a7FBERI7KnspaDtRHGNlPW0hE0tGO8mq+/tz7vPnhHvr3yGHCkHyuPW0kEwbnM2FIPmMH9KR39+xkhymSEpTAEJGkWLh6B727ZXPW+MMrbouIdCV/b6GqAnwi6cTdWbCykH9fuI76Bue7/zCZG04fRbglU0TagRIYItLhqmsbeHXdTuZMHUZOllp2iUjXVlAatFBVEU+R9FDXEGFneQ3ffXk9r67fxamj+/LfV0/lmP49kh2aSMpTAkNEjpq7s3JbGc+tKODND3fTEPFmx9c1RNhf28Ccqeo+IiJdX2MCY7haIIp0KcUVNRSWVlNRU09FTT37auqoqKmjsqaefeGxipo6Kg/UU15dR1lVHeXVwWuAnKwM/nXWRG45awyZGVp1IdIRlMAQkSO2s7yG51cW8PyKAjbv2U+37ExmThhIfl7Lj5aB+bmcMbZ/B0QpItK+Ckqr6Ncjhx65+lgl0lnVNURYW1jOe9vKWLmtlPe2lVFYVh13rBn0zM2iV142+XlZ9MzNYkivPCYMyadPtxz6dM+mT/dszho/gLEDe3bwOxFJb/qbVkRaxd356+YS5v5lC6+t30XE4bQx/fjnmeOYNWUoPfUBXkRSWEFpFX/bVXHIsbVF+1T/QqSTqm+I8PzKAh78w4cUldcAMKx3HtNG9eWzM0YzbmBP8vOyyA+TFfl5WfTIySJDKypEOiX9S0NEElJT18CLqwp58u2tfLCzgr7ds/nnc8fx6VNHas+niKSFhojzmUeXsa2k6rBzV508PAkRiSSfmWUA3wV6Ae+6+y+THBIQfOHy+7U7+e9XN7J5936mjuzDty6byPRj+jGkd16ywxORI5SWCQwzm0nwoF0HzHP3N5IakEgnt2p7GbfOXc7e/bUcPySf//zUFK44aTh52ZnJDk1EpMMs+dtutpVU8e3LJnLq6H6HnDt2sJaRS8cws61ABdAA1Lv79COc5wlgNlDs7pNjzl0CPAhkAo+5+w+bmeoKYDhQAhQcSSxtbW1hOfcsWMOawnKOHdSTh288hYsmDVZ3EJEUcFQJDDMbCTwFDAEiwCPu/mATYzOBd4FCd599FPeM+7Bt5YPWgUogj07yoBXprIrKqrntqXfpnpvJTz9zOmeO7a8PANIhlGyWzuZXf/2Ygfm53PSJ0WRnqoOSJNV57r4n3gkzGwRUu3tF1LHx7r4pZuhc4GcEn+Wjr88Efg5cSPA5ebmZvUTwGfu+mDluASYAS939YTN7Dnj9iN9VG/nac++zp/IAP7p6Kv8wbbgKbIqkkKP927ce+Iq7TwTOAL5gZpOaGHsXsCHeCTMbZGb5McfGNzHPXOCSmLGND9pLgUnAdY1xmNkUM3s5+gfY4O6XAt8AvpPA+xRJS1W19dz21LtU1zbw+E2n8olxA5S86KLM7AkzKzaztc2M6WNmz5nZB2a2wczObOv7mdklZrbRzDaZ2TdbmEbJZuk0tpdU8aeNxVx32iglL6SzOxd40czyAMzsNuAnsYPcfQnBqolYpwGb3H2zu9cC84Ar3H2Nu8+O+SkmeD6Xhtc2xAvIzOaY2SPl5eVH/+5asKm4gg079nHHueP41CkjlLwQSTFH9Tewu+9w95Xh7xUECYrDNoGa2QjgMuCxJqZK6EEb3ifewzbugzYc39TDFoKHbW7i71gkfUQizld+s5r1O/bxk+tO4rjB+S1fJJ3ZXGKSv3E8CCx29+OBqcQknZVslnT2zLJtZJhx3Wkjkx2KiAOvmtkKM7v9sJPu84HFwDwzu55glcQ1rZh/OLA96nUBcT7fR1kAXGxmPwWWxA3YfaG73967d+9WhHFkXlpVRIbB7BOHtvu9RKTjtVkNDDMbDUwDlsU5/WPg60DcfwG5+3wzG0PwoJ1P8KC9sBW3j/egPb2ZWK8CLgb6ECydizdmDjBn/PimPpuLpLYfv/4hv1+7k3+dNZHzjx+c7HDkKLn7kvA5HZeZ9QLOAW4Ox9cCtTHDzgXuMLNZ7l4TJpuvBGYleL+Dyebwno3J5vXuvoZge2A8TSab9ayWjlBT18D/Ld/GhRMHM7S3uo1I0s1w96Jwq8hrZvZB+AXfQe5+f/iMfQgY5+6VrZg/3pIFb2qwu1cBt7Zi/nbj7ry0uogzx/VnUC8V6hRJRW2yBtLMegLPA3e7+76Yc431KlY0N4e73w/UEDxoL2/nB+0Cd/+8u3+6qT3VHZkpFulsFq4u4ievf8jVp4zgc2ePSXY40jHGAruBJ83sPTN7zMwOaS/T0d/qmdlVZvYw8CuaSDbrWS0dYdGaHZRW1XHjmcckOxQR3L0o/LMYeIEgOXwIMzsbmByev7eVtygAopcajQCKjijYDramsJyte6u4fOqwZIciIu3kqFdgmFk2QfLiGXdfEGfIDOByM5tFsI+5l5k97e43xMwT+6C9sxVhdNkHrUi0ipo61hftY13488HOfVQeqCfiTiQStPCLeJO5uTZTsr+WU/8/e/cdXld15X38u9QtWS6Sey9ywRg3jOk9BDA2BiYQWkJPhoFkkkySSUhh3kACw2SYkEAIoQRIgh3TDTiUkNimGuOCG7g3uUm21fu9d71/3Gsiy5It2ZJu0e/zPPex7jn77LM24M3ROrsM6c7dl47VmhcdRwowCfiGuy80sweAHwA/qV+ond/qvUB4aLJIVP3xwy0M65nFKcNzox2KdHCRxHKSu5dFfv4i8LMGZSYCjxKevr0J+JOZ3e3uP27mbRYBIyKjo7cDVwJXt1Yb2tLLy3aQmmxccKymj4gkqqPdhcSAxwnPU76/sTLu/kPgh5HyZwHfbSR50WE7WhGAFfkl3PFieLuv/XpmpzOmbxfyenUm2QwzIzkJksxo65xCVloKt541nPQUbZPageQD+e6+fxrgc4QTGAdQslk6mpXbS1i6tZg7p49RQldiQW/gxch/iynAM+7+eoMymcDl7r4BwMyuIzI9sD4zmwmcBfQws3zgTnd/3N0DZnY78AbhnUeecPdVbdSeVhMMOa8u38GZI3vRNTM12uGISBs52hEYpwJfAVaY2bLIsTvcfa6ZzQVu3j/M7TCa1dFGzjXa2cZjRysSCIZ4eN4GHnh7HT06p/PdL47k2P5dObZfF3pla+6mtB9332Vm28xslLuvAc4FVtcvo2SzdER/+nALnVKTuWzSgGiHIkJkDaHxhynzXoPvdYT77oblrjpEHXOBuUcYZlR8tGkfu0tr+NFFmj4iksiOKoHh7u/S+JBg3L2xRd3mAfMaOd6sjjZyrtHOqymiiAAAIABJREFUNh47WunYNu+p4Duzl7FkazHTx/fj7hlj9cZA2swhkr/1k83fAP5sZmnARuCGBtUo2SwdSklVHS8t286lE/vTtZP6Z5FYNueTHWSmJfOFY3pFOxQRaUOttguJiDSPuzNr0TbuenU1KUnGA1dOYMaEQ+1OJnL0DpH8nVrv52XA5EPUoWSztDt3Z1dpNTuKqwmGnEAoRDDkn68JFAqFF1IJueOtvEbQhxv3UV0X4tqTtHinSCyrDYT468qdnDemN5lp+vVGJJHpb7hIOyqurOUHz6/g9VW7ODUvl//50nj6ddOWfCLSMYRCTll1gH2VtRRV1lJUUUt5TeCgcqVVdazZXcaaXeFPafXBZdrLlCE5HNtPu9yIxLJ31xdSXFmn3UdEOgAlMETayYcb9/LtvyxjT3kNd0wdzc2nDSMpSQvCiUjiCoWcFdtLmLemkPlrC1ieX0Ig1LxREtkZKYzuk83FE/oxqnc2A3MySU1OIjnJPv8kmZFk/1zc2Gj9RY4H5mS2boUi0upeXraDrp1SOX1Ez2iHIiJtTAkMkTYWCIb49dvrePAf6xmcm8Xzt57CuAHdoh2WiMghlVXXMX9tIaVVASprA1TVBqmoDVJdF2zW9fsqanl3/R72VdRiBuP6d+Wm04bSMzudnKw0umel0T0zjeyMlIMW08pMS6F3l3Tt+iEih1VVG+St1buZMaEfaSlJ0Q5HRNqYEhgiR6C6Lsi+iloqa4PUBUOff2oDzp7yGrYXV7GjuIrtRVWsKyhn675KvnT8AP7fxceSla6/diISu3YUV/Hk+5uZuXArZQ2md6QlJ5GemtT46t0NZKalcObInpw5sienj+hBbuf0tglYRDq0v326m8raIBeP13piIh2BfpMSaUJ5TYAV+SUszy/mk/xi8ouq2FsenrddWXv4N5BdMlLo3z2Tkb2z+f4Fo5g2TvMyRSQ21QZCfLarlD+8t5lXPtmBA1OP68t1Jw9mQPdMOqUlk5mWTGqy3m6KSGwoqarj8Xc38cS7m+jXNYMpQ3OiHZKItAMlMCQu7J9H/Y81BawrKCcUWX0+GAqvUN+a6867O/lFVawvLGf/gvaDcjIZ2iOLvJ6d6Z6VRk7kk5WeQlqykZKURGpKEqlJRm7ndPp1yyA7Q1vuiUjscHc2FFbwwca9LN1SxK7SagrLaigsr6G4sg6ArLRkrjtlCDecOoQB3bX2g4jEnvKaAH94dxOPvrOR0uoAF47tw3fPH0Wy1hUT6RCUwOjA6oIhtuytOGhBNffwJ7wlHTjO/iKtvUXd4eQXVfGPNQXMX1PI3sg86iG5WaREFnAzM5KTwgu3taZBOZlMG9eP8QO7Mm5AN3Ky0lq1fhGRtlQXDLGrpJptRZVs3lPJwk17+WDDXgrKagDolZ3OoJxMhvfszEnDcumZnU6frhmcf2wfunZS8lVEYtPLy7bzX3NWUVRZxxeO6cW3vjCSsf21S5BIR6IERgdSWl3Hki1FLN5SxMebi1i2rZiqZi7GFk1dO6Vy5sienDO6F2eM7KlkgohIA1W1QV5ZvoOXl21nU2EFu0qrqZ+b7tE5nZOH53LK8FxOHpbL4NxMLZApInHlpaXb+fbsZUwc2I0/TD+WCQO1ILpIR6QERgewq6SaX/99HbMXbSMQcpIMxvTrwpdPGMi4AV3plJp80DUW2Zrun3/WG+XQjs+83Tqlclz/rqRo3rVIh2NmZwF3AauAWe4+L6oBxaD1BWX8eeFWnl+cT2l1gOE9szhpeC4DumcyoFsnBnTvxIDumQzM6aSEhYjErdeW7+Q7s5dx4tAc/nD9FDqlHfzsKiIdQ4dMYHSUh+Kiiloenr+Bp97fTMidq6YM4oKxfZgwsJt2whBJQGb2BDANKHD3sU2U2QyUAUEg4O6TD3W8NeMwswuAB4Bk4DF3v/cwVTlQDmQA+UcaT1tyd7bsraSospZgyD//BEJOIBTemSgQ2r9LUYjymiClVXWUVtdRWhWgtLqOQDBEqN60vVAzp+qV1wRYnl9CarJx4di+XHPiIKYMzVGiQkQSyhurdvHNWUs5fnB3Hr/uBCUvRDq4w/4Wa2YDgaeBPkAI+L27P9CgTAawAEiP1Pmcu98ZOfdt4GbCD6IrgBvcvfpIgk20h+JgyCmqrKWoopZ9FbXUBPZvxxl+4A0ED36IdfzzNSqcegtYRh569z8E7yyp4un3t1BeG+DSif359hdGMjBHC7KJJLgngQcJ99mHcra772nBcQDMrBdQ5e5l9Y7lufv6w8VhZsnAQ8B5hPvdRWY2x91Xm9lxwD0N6rgReMfd55tZb+B+4JrDtKvVuDsVtUHqAqEDjociC2EujkzHW7K1iH0VtS2uPzs9hS6dUsnOSCEtJenz0W5JFh7r1pwcRKfUZL5/wSiumDyQHtqiVEQS0N8/283tzyzhuP5deeL6E/QCTkSaNQIjAPyHuy8xs2xgsZm95e6r65WpAc5x93IzSwXeNbO/AtuAbwJj3L3KzGYDVxJ+uP1cojwU/9ecVZRW1VFWE6Bi/6c2SDDkny9+6YQfgMuqA5RU1dGWa2J+cUxvvnv+KEb2zm67m4hIzHD3BWY2pA1vcSZwq5lNdfdqM7sFuBSY2ow4pgDr3X0jgJnNAmYAq919BeHkdFOKCCfID2Jm04HpeXl5zW7EI/M3sKGwnOq6ENV1QaoDIWrqglTUBj4fFVFaVUfoMP3zsB5ZnDO6F5MGdadv1wySk4yUJCMpsshwanISqclGWnISqclJpCQb2empdM5I0Wr5IiKHMX9tIf/6xyWM7tOFp26cot3dRARoRgLD3XcCOyM/l5nZp0B/YHW9MvtHNACkRj77H/1SgE5mVgdkAjsauU1CPBT//bMCQu50Tk8hKz2Frplp9O+eTEpSUqTOSN1Adkbq51txds9KIyczjYzUJFIiD7ypyUmkRHbZOCg2/rkmxf7TSUn13t4ZpCcn0zVTHb2IHMSBN83MgUfc/feHOf7PC92fNbOhwCwze5ZwQvi8Zt63P+Gk9n75wImHusDMLgPOB7oRTl4f3Bj3V4BXJk+efEsz4+CjTftYvbOUjNRk0lOSSE9NJiMlid7ZGYzolUqXjHqjIxpZf6d/90yOH9xdCwqLiLShhRv3MrxXZ/540xTtjiQin2vROKxI8mAisLCRc8nAYiAPeMjdF0aO/xLYClQBb7r7mw2vTZSH4gXfP7u5RUVEouVUd98RGfn2lpl95u4LDnH8AO5+XyRR/DAw3N3LG5ZpQmNDDg45xsHdXwBeaGb9zfb49Se0dpUiItLKvnf+KG47O0/TRkTkAM3e2sHMOgPPA99y99KG59096O4TgAHAFDMba2bdCY+GGAr0A7LM7NrG6nf3+4Bqwg/FF7f1Q7G7f93dv5yoC3iKiDTG3XdE/iwAXiQ8iq3J4w2Z2enA2EiZO1tw63xgYL3vA2h8RJ6IiAhmpuSFiBykWQmMyLoWzwN/jrwRa5K7FwPzgAuALwCb3L3Q3esIv0k7pYl76KFYRKQNmVlWZC0jzCwL+CKwsqnjjVw/EXiUcGL6BiDHzO5u5u0XASPMbKiZpRFeD2nO0bZJRERERDqOwyYwLLwIw+PAp+5+fxNleppZt8jPnQgnLj4jPHXkJDPLjNRzLvBpI9froVhE5CiZ2UzgA2CUmeWb2U2R43PNrB/Qm/Aiy58AHwGvufvrhzjeUCZwubtvcPcQcB2wpTlxuHsAuB14g/D/B2a7+6rW/ScgIiIiIomsOeOyTgW+Aqwws2WRY3e4+1wzm0t4i9QewFORdTCSCD+YvgpgZs8BSwjvZrIUOGhhOOo9FEeuuQ64vmGhyEPxWUAPM8sH7nT3x81s/0NxMvCEHopFpCNy96uaOF5/QeTxjZzf2NjxRsq91+B7HeHkc3PjmAvMPdx9REREREQa05xdSN6l8XUm6j8U7yC8uGdjZe7kMFNC9FAsIiIiIiIiIodi4R1QpSlmVkgjQ6QPoQewp43CaS+J0AZQO2JJIrQBDt2Owe7esz2DkX/qoH01JEY7EqENoHbEEvXVMUp9dVxLhDaA2hFLDteGRvtrJTBamZl97O6Tox3H0UiENoDaEUsSoQ2QOO2QxPl3mQjtSIQ2gNoRSxKhDRKWKP8uE6EdidAGUDtiyZG2odnbqIqIiIiIiIiIRIsSGCIiIiIiIiIS85TAaH2N7bISbxKhDaB2xJJEaAMkTjskcf5dJkI7EqENoHbEkkRog4Qlyr/LRGhHIrQB1I5YckRt0BoYIiIiIiIiIhLzNAJDRERERERERGKeEhgiIiIiIiIiEvOUwBARERERERGRmKcEhoiIiIiIiIjEPCUwRERERERERCTmKYEhIiIiIiIiIjFPCQwRERERERERiXlKYIiIiIiIiIhIzFMCQ0RERERERERinhIYIg2YmZtZXjPL3mFmjx3i/GYz+0LrRSciIqC+WkQkHqivltamBIYkhEiHVmVm5Wa228z+YGad2/q+7v4Ld7+5Neoys2+Z2UYzKzWzHWb2f2aW0hp1i4jEgkToq/czszQz+8zM8luzXhGRaEuEvtrM/svM6iJt2P8Z1hp1S3QpgSGJZLq7dwYmAScAP25YIMYTAq8Ak9y9CzAWGA98M7ohiYi0unjvq/f7HlAQ7SBERNpIIvTVf3H3zvU+G6MdkBw9JTAk4bj7duCvhJMA+4eu3WZm64B1kWO3mNl6M9tnZnPMrF+DaqZGRkPsMbP/MbNG/65Esrt/qvf9K2a2xcz2mtmPWhj3Bncv3l8VEAKaNeRORCTexGtfHbl+KHAtcE9LrxURiSfx3FdLYlICQxKOmQ0EpgJL6x2+BDgRGGNm5xB+6LwC6AtsAWY1qOZSYDLhrPMM4MZm3HcM8DDwFaAfkAsMqHf+NDMrbuLy/WWuNrNSYA/hERiPHO6+IiLxKJ77auA3wB1A1eHuJyISz+K8r54eSaqsMrNbD3dPiQ9KYEgieSnSkb0LzAd+Ue/cPe6+z92rgGuAJ9x9ibvXAD8ETjazIfXK/3ek/FbgV8BVzbj/l4BX3X1BpN6fEB5FAYC7v+vu3Q5Vgbs/E5lCMhL4HbC7GfcVEYkncd1Xm9mlQIq7v9icxoqIxKm47quB2cAxQE/gFuCnZtac+0qMi/V5SyItcYm7/62Jc9vq/dwPWLL/i7uXm9leoD+wuZHyWyLXHE6/+te5e0Wk3hZz93Vmtgr4LXDZkdQhIhKj4ravNrMs4D7CbyNFRBJZ3PbVkfKr631938weIJwUmdncOiQ2aQSGdBRe7+cdwOD9XyIPpLnA9nplBtb7eVDkmsPZWf86M8uM1HukUoDhR3G9iEi8ifW+egQwBHjHzHYBLwB9zWxXg7eNIiKJLNb76sY44TXmJM4pgSEd0TPADWY2wczSCQ+JW+jum+uV+Z6ZdY/M+/t34C/NqPc5YFpkTl4a8DNa8HfMzG42s16Rn8cQHoL3dnOvFxFJMLHYV68k/EA9IfK5mfBUvwkc+IZRRKSjiMW+GjObEbmnmdkUwjv7vdzc6yV2KYEhHY67v014Ht3zhLO7w4ErGxR7GVgMLANeAx5vRr2rgNsId+Q7gSIgf/95MzvdzMoPUcWpwAozqwDmRj53NK9VIiKJJRb7ancPuPuu/R9gHxCKfA+2sIkiInEvFvvqiCuB9UAZ8DThdTieal6rJJaZux++lIiIiIiIiIhIFGkEhoiIiIiIiIjEPCUwRERERERERCTmKYEhIiIiIiIiIjFPCQwRERERERERiXkp0Q4g1vXo0cOHDBkS7TBEJMYtXrx4j7v3jHYcicTMkoC7gC7Ax4daPVx9tYg0h/rq6FJfLSLN1VR/rQTGYQwZMoSPP/442mGISIwzsy3RjuFomdlmwtuNBYGAu08+wnqeAKYBBe4+tsG5C4AHgGTgMXe/9xBVzQD6E96qMv8Q5dRXi0izJEJfHc/UV4tIczXVXyuBISIi9Z3t7nsaO2FmvYAqdy+rdyzP3dc3KPok8CDhfdfrX58MPAScRzghscjM5hBOZtzToI4bgVHAB+7+iJk9B7x9xK0SERERkbinBIaIiDTXmcCtZjbV3avN7BbgUmBq/ULuvsDMhjRy/RRgvbtvBDCzWcAMd7+H8IiNA5hZPlAb+RpstVaIiIiISFzSIp4iIrKfA2+a2WIz+9pBJ92fBV4HZpnZNYRHSVzRgvr7A9vqfc+PHGvKC8D5ZvYbYEFjBcxsupn9vqSkpAVhiIiIiEg80ggMEZEG/rpiJztKqrnptKHRDqW9neruOyJTRd4ys8/c/YDEgbvfFxk58TAw3N3LW1C/NXLMmyrs7pXATYeq0N1fAV6ZPHnyLS2IQ0RimLuzvqCcwvIa9lXUfv4pqw40Wv4n08a0c4QiInI4oZCzcU8Fy7YVs3RrEd+/YDRdO6Uedb1KYIiIRNQFQ9z71894/N1NTB7cnetOHkxKcscZqObuOyJ/FpjZi4SnfByQwDCz04GxwIvAncDtLbhFPjCw3vcBwI6jiVlEEksgGOK7z37CS8sO7hqy0pIxOzgPqgSGiEhsqAuGePSdjXy4cR/LthZRGkk8Z6encOUJgzhuQNejvocSGCIiwM6SKm5/ZimLtxRx/SlDuGPqMR0qeWFmWUCSu5dFfv4i8LMGZSYCjwIXAZuAP5nZ3e7+42beZhEwwsyGAtuBK4GrW6sNIhLf6oIhvjVrGa+t2MltZw/ntLye5GSlkZOVRrfMVFI7UJ8sIhKPnlucz32vr2FU72wuGteXiQO7M3FQN4b37ExSUmMDcVtOCQwR6fDeWVfIv89aRk1dkAevnsi0cf2iHVI09AZejLzdTAGecffXG5TJBC539w0AZnYdcH3DisxsJnAW0COyEOed7v64uwfM7HbgDcI7jzzh7qvaqD0iEkdqAkFuf2Ypb63ezY8vOoabTx8W7ZBERKSF5q7YyeDcTF7/1umNjphrDUpgiEiH9szCrfzopRWM6NWZ315zPHm9Okc7pKiI7Awy/jBl3mvwvY7wiIyG5a46RB1zgblHGKaIJKDquiD/9ucl/P2zAn4241i+evKQaIckIiIttK+ilvc37OVrZwxrs+QFKIEhIh3Y7tJq7np1Nafl9eCRrxxPZpq6RBGRtrSrpJqy6jqq6oJU14Woqgvy2DsbeWfdHn5x6XFcfeKgaIcoIiJH4M1VuwiGnIuO69um99HTuoh0WPe9voZgyPn5JccpeSEi0sZeW76T255ZctBxM7jvS+O4YvLARq6SWGdmZwF3AauAWe4+L6oBiUhUvLZiJ4NyMjm2X5c2vY+e2EWkQ1qeX8zzS/L51zOHMyg3M9rhiIgkvFmLttK/Wyd+cOFoOqUm0yktmYzUZHp3SWdAd/XDAGb2BDANKHD3sU2U+TZwM+FtqFcAN7h7dWvey8wuAB4gvF7RY+5+7yGqcqAcyCC825SIdDBFkekjt5zettNHQAkMEemA3J2fvbKaHp3TuO3s4dEOR0Qk4e0qqebd9Xv4xjkjmD6+Qy6U3FxPAg8CTzd20sz6A98Exrh7lZnNJryj05P1yvQCqty9rN6xPHdf35x7mVky8BBwHuGExCIzm0M4mXFPgzpuBN5x9/lm1hu4H7imBe0VkQTw5ur2mT4CoP2oRKTDeXX5Tj7eUsR3vziK7IzUaIcjIpLwXlq2HXe4bGL/aIcS09x9AbDvMMVSgE5mlkJ4d6gdDc6fCbxsZhkAZnYL8OsW3GsKsN7dN7p7LTALmOHuK9x9WoNPgbuHItcVAenNbKqIJJDXVuxiYE4nxvZv2+kjoBEYItLBVNcFufevnzGmbxcu13xrEZE25+68sCSf4wd3Z0iPrGiHE9fcfbuZ/RLYClQBb7r7mw3KPGtmQ4FZZvYs4VES57XgNv2BbfW+5wMnNlXYzC4Dzge6ER7R0ViZ6cD0vLy8FoQhIvGguLKW99fv4abTh7b59BHQCAwR6WAee2cj24ur+Mm0MSQntX0nKyLS0a3aUcra3eVcqtEXR83MugMzgKFAPyDLzK5tWM7d7wOqgYeBi929vCW3aeSYN1XY3V9w96+7+5ebWsDT3V9x96917dq1BWGISDx4c9VuAu00fQSUwBCRDmR3aTW/nbeBC47tw8nDc6MdjohIh/DCku2kJScxbVz7PNwmuC8Am9y90N3rgBeAUxoWMrPTgbHAi8CdLbxHPlB/iOIADp6mIiIChHcfGdC9E8f1b58EpRIYItJh/Obv6wgEnR9OHR3tUEREOoS6YIg5n2zn3GN60S0zLdrhJIKtwElmlmnhsdrnAp/WL2BmE4FHCY/UuAHIMbO7W3CPRcAIMxtqZmmEFwmd0yrRi0hCKa6s5b31e7jouL7tMn0ElMAQkQ6ivCbAi0u2M2NCPwbnag62iEh7eGddIXvKa7ls0oBohxIXzGwm8AEwyszyzeymyPG5ZtbP3RcCzwFLCG+hmgT8vkE1mcDl7r4hssDmdcCW5t7L3QPA7cAbhJMjs919VRs0V0Ti3Jurw9NHprbT9BHQIp4i0kHMWbaDitogV584KNqhiIh0GC8s2U5OVhpnjuwZ7VDigrtf1cTxqfV+vpNDTAtx9/cafK8jPCKjWfeKnJsLzG1GyCLSgc2NTB8ZN6D91rfRCAwR6RCe+WgLo/tkM2Fgt2iHIiLSIZRU1fHm6t1MH9eXtBQ9coqIJJKSyjreW7+Hqe04fQSUwBCRDmBFfgkrt5dy9YmD2rWDFRHpyP66Yie1gZCmj4iIJKA3V++iLti+00dACQwR6QCe+WgLGalJXKIt/ERE2s0LS7YzvGdWuw4tFhGR9vHq8vD0kfHt3McrgSEiCa28JsDLy3YwfVw/umSkRjscEZEOYWNhOR9t3sdlkwZo5JuISIIpqojsPjKufaePgBIYIpLgXl62nUot3iki0m7WF5Rz7WMLyU5P4V80fUREJOG8sWoXgZAzfVy/dr+3diERkYQ286OtWrxTRKSdLN1axI1PLiI5KYmZXzuJPl0zoh2SiIi0stdW7GRIbibH9uvS7vfWCAwRSVjL84tZub2Ua7R4p4hIm5u/tpCrH11IdkYqz996MmP7a+0LEZFEs7e8hvc37I3K9BHQCAwRSWAzP9pKp9RkZmjxThGRNvXS0u1899lPGNk7mydvPIFe2Rp5ISKSiP66chfBkDMtCtNHQAkMEUlQZdV14cU7x/fV4p0iIm2kui7IL99Yw2PvbuKkYTn8/quT1eeKiCSw15bvZFjPLEb3yY7K/ZXAEJG4tm1fJa+t2MmqHaUHHC8oraayNshVU7R4p4hIW1i8pYjvPfsJG/dUcO1Jg/jxRWPISE2OdlgiItJGCsqqWbhpL7efMyJq07OVwBCRuLM/afHa8p2s2F4CwMCcTqQmHbisz/Tx/bR4p4hIK6uuC/J/b63l0Xc20rdrJ/5884mcmtcj2mGJiEgbe33lLkIO08b1jVoMSmCISNyoC4a4c84qnlm4FYDxA7txx9TRXDi2LwNzMqMcnYhIYqqqDbKuoIw1u8Kfv39WwMY9FVw1ZRB3TB1NtqaMdGhmdhZwF7AKmOXu86IakIi0mVc/2cnI3p0Z2Ts600dACQwRiROl1XXc9uclvLNuDzedNpTrTxmipIWISBv664qd3P/WWtYXluMePpaeksTovl14+sYpnDGyZ3QDjGNm9gQwDShw97ENzo0C/lLv0DDgp+7+q8j5bwM3Aw6sAG5w9+pWjuEC4AEgGXjM3e89RFUOlAMZQH5L4xCR+LCrpJpFW/bx7S+MjGocSmCISMzbXlzFjX9YxIbCcu77l3FcccLAaIckIpKwCkqr+enLq3h91S5G98nmm+eMYHSfbEb1yWZwbhbJSdqWuhU8CTwIPN3whLuvASYAmFkysB14MfK9P/BNYIy7V5nZbODKSH1EyvQCqty9rN6xPHdf35wYIvd8CDiPcEJikZnNIZzMuKdBHTcC77j7fDPrDdwPXNPcfwgiEj/mrtiJO1wUxekjoASGiMS4Ffkl3PTUIqpqgzx5wxROG6F51iIibcHdefbjfO5+bTXVgRD/ecFobj59KKnJSYe/WFrE3ReY2ZBmFD0X2ODuW+odSwE6mVkdkAnsaHDNmcCtZjbV3avN7BbgUmBqM2OYAqx3940AZjYLmOHu9xAesdGUIiC9sRNmNh2YnpeXd4jLRSSWvbp8B8f07cLwnp2jGkeHTGCYWRLhuXpdgI/d/akohyQijZjzyQ7+87nl5GSl8ad/OzGq8+1ERBJZ/Wl6U4bkcM+/HBf1h1QBwqMrZu7/4u7bzeyXwFagCnjT3d+sf4G7P2tmQ4FZZvYs4VES57Xgnv2BbfW+5wMnNlXYzC4Dzge6ER7RcRB3fwV4ZfLkybe0IA4RiRFb9lawZGsx3zt/VLRDoV1S6mb272a20sxWmdm3jqKeJ8yswMxWNnLuAjNbY2brzewHh6lqBuHOuQ7N1ROJOfsqarntmSV8c+ZSjumbzYu3naLkhYhIGwkEQ3zjmaV8sGEvd804lllfO0nJixhgZmnAxcCz9Y51J/wcOxToB2SZ2bUNr3X3+4Bq4GHgYncvb8mtGznmTRV29xfc/evu/mUt4CmSmH7+2qd0Sk3mXyYNiHYobZ/AMLOxwC2Eh6ONB6aZ2YgGZXqZWXaDY42NMXsSuKCRe+yfq3chMAa4yszGmNlxZvZqg08vYBTwgbt/B7j16FspIq3lb6t388X/W8Cbq3bxvfNHMfvrJ9MrOyPaYYmIJKxfzP2M+WsLueuSsXzl5CEkaY2LWHEhsMTdd9c79gVgk7sXunsd8AJwSsMLzex0YCzhtTPubOF984H6i00N4OBpKiLSQcxbU8Cbq3fzjXPz6NM1+s/k7TEC4xjgQ3evdPcAMJ/wPLz6zgReNrMMgMhcvV83rMjdFwD7GrnH53P13L0W2D9Xb4W7T2vwKSDcMRdFrg02FrSZTTez35eUlLS8xSLSYuU1Ab5LOz2mAAAgAElEQVT77Cfc/PTH9OicxpzbT+O2s/NI0dxrEZE2M+ujrTzx3iZuOHUIV00ZFO1w5EBXUW/6SMRW4CQzyzQzI7xGxqf1C5jZROBRwiM1bgByzOzuFtx3ETDCzIZGRoFcCcw5wjaISByrCQT5f6+sZmiPLG46bWi0wwHaJ4GxEjjDzHLNLJPwAkIHbCHg7s8CrxOeq3cN4bl6V7TgHo3N1et/iPIvAOeb2W+ABY0VcPdX3P1rXbt2bUEYInIkqmqD3PiHRbywJJ/bzh7OnNtP45i+XaIdlohIQvtw415+/NJKzhjZkx9NPSba4XQoZjYT+AAYZWb5ZnZT5PhcM+sXeWY+j/Az6+fcfSHwHLCE8BaqScDvG1SfCVzu7hvcPQRcB2xpUKbJGCIvHG8H3iCcHJnt7qtaqekiEkcef3cTm/ZU8F8XH0t6SnK0wwHaYRFPd//UzP4beIvwHtGfAIFGyt0XWeX4YWB4G8/VqwRuakH9ItJGagMh/u3Pi1m0ZR+/vnIi08f3i3ZIIiIJb+veSm7902IG5Wbym6smarRbO3P3q5o4Xn+nkNwmytzJIaaFuPt7Db7XER6R0awYIufmAnObOi8iiW9HcRW/eXs95x/bmzNH9ox2OJ9rl/9bufvj7j7J3c8gPAVkXcMymqsn0vEEQ853Zi/jH2sK+cWlxyl5ISLSDoora7npqUWEHB6/7gS6dkqNdkgiIhJjfv7ap4Tc+fFFY6IdygHaaxeSXpE/BwGX0WA+n+bqiXQ87s6PX1rJq8t38oMLR2vutYhIOyiprOPaxxeyZW8lD18ziaE9sqIdkoiIxJj31u/htRU7ue3sPAbmZEY7nAO0+RSSiOfNLJfwtqW3uXtRg/Ofz9UDMLPrgOsbVhKZq3cW0MPM8oE7I6M7Ama2f65eMvCE5uqJtL1gyHFvcrbWIf3yzbXM/Ggrt541nH89c3grRyYiIg2VVIWTF2t3lfPIV47nlLwe0Q5JRERiTF0wxJ1zVjEoJ5OvnTEs2uEcpF0SGO5++mHOa66eSBwpKKvm/95ax7MfbyMQOrIEBsA1Jw7i++ePasXIRESkMaXVdXz18YV8tquU3117PGeP7hXtkEREJAa9tXo36wvK+d21k8hIjY2FO+trrxEYIpIAKmsDPLpgE48s2EBtIMTlkwfQr2unI6qrZ3Y6V0weSHgXOBERaStl1XV89fGPWL2zlN9eczznHtM72iGJiEiMmv3xNvp2zeC8MX2iHUqjlMAQ6cDcnZXbSympqjts2c17K/j12+soKKth6nF9+P75oxmiudMiIjGjoibA/W+tpbCs5oDjn+0qZWNhBQ9dM4nzxih5ISIijdtZUsWCtYXcdnYeyUmx+ZJRCQyRDuy38zbwP2+saXb5iYO68fC1kzh+cE4bRiUiIi1VUlnH9U9+xPL8EgY1WHAtLTmJh66ZxPnHxubbNBERiQ3PL84n5PCl4wdEO5QmKYEh0kHN/Ggr//PGGmZM6Me1Jw0+bPmMlGTG9u+iKR8iIjFmT3kNX3n8IzYUlPPQ1ZO4YKwSFSIi0jKhkDP743xOGpbD4NzYHWWtBIZIB/T6yp386MUVnDWqJ7+8fDypye2yo7KIiLSyHcVVXPvYQnaUVPHYdZM5Y2TPaIckIiJxaOGmfWzdV8m3zxsR7VAOSQkMkQ7m/Q17+ObMZUwY2I3fXjNJyQsRkTi1eU8F1zy2kNKqOv5404mcMETT+0RE5Mg8+/E2stNTuODYvtEO5ZD0m4tIB7Jyewlfe3oxg3MzeeL6E8hMUw5TRCQeFZbV8OXff0BlbYCZXztJyQuJGjM7y8zeMbPfmdlZ0Y5HRFqutLqOuSt3cvGEfnRKi72tU+vTby8iCaikso7vPfcJO0uqCYackDvBkLOjuIpumWk8fdMUumWmRTtMERE5Au7OD55fTlFlHS/926mM6dcl2iFJC5nZE8A0oMDdxzY4Nwr4S71Dw4CfuvuvIue7AY8BYwEHbnT3D1o5hguAB4Bk4DF3v/cQVTlQDmQA+S2NQ0Si75VPdlBdF+KKyQOjHcphKYEhkoDuff1T/vbpbs4c2ZPkJCPJjOQk47gBXfnGOSPo27VTtEMUEZEjNGvRNt7+rICfTBuj5EX8ehJ4EHi64Ql3XwNMADCzZGA78GK9Ig8Ar7v7l8wsDThg2xkz6wVUuXtZvWN57r6+OTFE7vkQcB7hhMQiM5tDOJlxT4M6bgTecff5ZtYbuB+45nCNF5HYMvvjfEb1zmbcgK7RDuWwlMAQSTAfbdrHzI+2cfNpQ/nxtDHRDkdERFrR5j0V3PXqak7Ny+WGU4ZEOxw5Qu6+wMyGNKPoucAGd98CYGZdgDOA6yP11AK1Da45E7jVzKa6e7WZ3QJcCkxtZgxTgPXuvjFyz1nADHe/h/CIjaYUAemNnTCz6cD0vLy8Q1wuItGwZlcZn2wr5ifTxsTFboNaA0MkgdQEgtzx4gr6d+vEt88bGe1wRESkFQWCIb49exkpScYvLx9PUlLsP2jKUbsSmFnv+zCgEPiDmS01s8fM7ID9Dt39WeB1YJaZXUN4lMQVLbhnf2Bbve/5kWONMrPLzOwR4I+ER3QcxN1fcfevde0a+293RTqa2R9vIzXZuGRCv2iH0ixKYIgkkEfmb2R9QTl3XzKWrHQNsBIRSSQPz9vA0q3F3H3pcZoK2AFEpodcDDxb73AKMAl42N0nAhXADxpe6+73AdXAw8DF7l7ekls3csybKuzuL7j71939y+4+rwX3EZEoqw2EeHHpdr5wTG9yOzc6gCrmKIEhkiA2Fpbz4D/Wc9G4vpw9ule0wxERkVa0PL+YB95ex8Xj+3Hx+Ph4SyZH7UJgibvvrncsH8h394WR788RTmgcwMxOJ7zI54vAnS28bz5QfyW/AcCOFtYhInHgo0372FdRy6UTmxxkFXOUwBBJAO7Oj15cSXpKEndO17oXIiKJZEdxFf8+axk9s9O5a8bYw18gieIqDpw+grvvArZFdiqB8BoZq+uXMbOJwKPADOAGIMfM7m7BfRcBI8xsaGQUyJXAnCNrgojEsgXrCklLTuLUvB7RDqXZlMAQSQDPLc7ng417+cGFo+mVnRHtcEREpJWsyC/hkofeo7Cshl9fNZGumanRDklagZnNBD4ARplZvpndFDk+18z6mVkm4V1AXmjk8m8Afzaz5YR3K/lFg/OZwOXuvsHdQ8B1wJbmxuDuAeB24A3gU2C2u686+laLSKyZv6aQE4Z2j6up5/ETqYg0atHmfdz92qdMHtydq04YFO1wRESklby+chff+stScrPSef7WExnVJzvaIUkrcfermjhef6eQ3CbKLAMmH6Lu9xp8ryM8IqNZMUTOzQXmNnVeROLfzpIq1uwu41+OHx3tUFpECQyROBUKOb9bsIH/fXMtA7p34n+0Ir2ISEJwd36/YCP3vv4Z4wZ049GvHq/RdSIi0qoWrC0E4MyR8bV2nhIYInFob3kN35n9CfPXFnLRuL7ce9lxZGdoWLGISLypC4bYVVLNjuIqdpZUs6OkimVbi3lz9W4uOq4v/3vFeDJSk6MdpoiIJJj5awvp0yWDkb07RzuUFlECQyROhEJOSVUdy7eX8J/PLWdfZS13XzKWa04chJlGXoiIxJs95TVc9tv32bqv8oDjXTul8s1zR/Ctc0doZJ2IiLS6QDDEO+v2cOHYPnH3e4QSGCIxKhhyfvbKKhZvLaKwrIa95bUEQuFt2IfkZvLCracwtn/XKEcpIiJHIhAM8Y1nlrK7tJq7LhnLkNxM+nbtRN+uGXG1mJqIiMSfZduKKasOxN30EVACQyRmvblqF099sIUTh+YwZmQXenROp2d2Or2yMzhzVE866wFXRCRu/e9ba/lg415+efl4vnT8gGiHIyIiHciCtYUkGZwWR9un7qffgERikLvz8PwNDMnN5JlbTiJZQ4hFRBLGm6t28fC8DVw1ZZCSFyIi0u7mry1k4qDucbk1d1K0AxCRg723fi/L80v4+pnDlbwQEUkgm/ZU8B+zP2HcgK7cOX1MtMMREZEOZm95Dcu3l3DmyJ7RDuWIKIEhEoN+O289vbLTuWxS/2iHIiIiraSqNsitf1pMcrLx22smaXcRERFpd++u34M7cZvA0BQSkRizbFsx72/Yyx1TR5OeoodbEZF4t6O4ikWb9/Hc4nzW7C7jyRumMKB7ZrTDEhGRDmj+mkK6Z6bG7WYASmCIxJiH562nS0YKV584ONqhiIjIEXB3Xl+5i7dW7+ajzfvIL6oCoHN6Cj++aEzcvvUSEZH4Fgo5C9YVcvqInnE7TV0JDJEYsr6gjDdW7eYb5+RplxERkTi0vqCcn7y0kg827qVH5zROGJLDjacOZcrQHEb3ySYlWbN3RUQkOlbvLGVPeW1cJ9L1G5JIDPnd/I1kpCZx/SlDoh2KSNSZWRJwF9AF+Njdn4pySCJNqq4L8uDf1/PIgg10Sk3m55eO5aoTBpEUp2+4RJrLzM4i3FevAma5+7yoBiQiTZq/thCA00fG3/ap+ymBIRIjdhRX8dLS7Vx70mByO6dHOxzpoMwsGfgY2O7u046wjieAaUCBu49tcO4C4AEgGXjM3e89RFUzgP7APiD/SGIROVLuzrqCcrYXVzU4AcGQUxsMURcMURMIUVET4In3NrFtXxWXTezPD6ceQ89s9ePStMP0k6OAv9Q7NAz4qbv/ql6ZWOqrHSgHMlBfLRLT5q8t5Nh+XeiVnRHtUI6YEhgiMaC6Lshv560H4JYzhkU5Gung/h34lPCohwOYWS+gyt3L6h3Lc/f1DYo+CTwIPN3g+mTgIeA8wg+5i8xsDuEH5Hsa1HEjMAr4wN0fMbPngLePol0ih1VdF+TDjXv5+2cFvP1pwcHJi0MY1jOLZ245kVOGx+9bLWlXT9JIPwng7muACfB5v7kdeLFBsVjqq99x9/lm1hu4H7imqUaLSHSU1wSYuXArS7YU8bU4/11DCQyRVvT6yl18tqv0sOVCDoVl1WzeU8mWvRXsLK3GHb50/AD6d+vUDpGKHMzMBgAXAT8HvtNIkTOBW81sqrtXm9ktwKXA1PqF3H2BmQ1p5PopwHp33xi53yxghrvfQ/gtYMN48oHayNfgETVKpBncnf99cy2Pv7uJqrognVKTOW1ED75xTh4j+2TTcBJISlISqSlGWnISqclJpKUk0aNzetwuiCbt7xD9ZEPnAhvcfcv+A7HWV9dTBDQ69MjMpgPT8/LyDnG5iLS2wrIannx/E3/8YAul1QFOGpbDdXE+VV0JDJFW4O7c/9ZafvP3hi83mtajcxqDcjI5aVgug3OzGNIjk/OP7dOGUYoc1q+A7wPZjZ1092fNbCgwy8yeJfzm7bwW1N8f2Fbvez5w4iHKvwD8xsxOBxY0VkAPxdIannp/Mw/+Yz0Xju3DFScM5ORhuWSkahtriQlXAjMbHIupvtrMLgPOB7oRHtHRWEyvAK9Mnjz5lhbEIdIhhELOsvxi3v50N/sq6lqt3vKaAG+s2kVdMMT5Y/rwr2cNZ8LAbq1Wf7QogSFylALBED9+aSWzFm3jyhMGctclY0lpxls4M72pk9hhZvvnQS+OLMjWKHe/L/I27mFguLuXt+Q2jVV5iHtVAjcdqkI9FMvR+seaAn726mrOG9ObB6+epFEUEjPMLA24GPhhvWOx2Fe/QDjhLCLNVBsI8eHGvbyxKrzldkFZDSlJRvestFa7R5LBZRP7c8sZwxjes3Or1RttSmCIHIXquiDfnLmUN1eHtz79znkjlZiQeHUqcLGZTSW8EFsXM/uTu19bv1BkNMRYwvOx7wRub8E98oGB9b4PAHYcVdQiR2HNrjK+8cxSRvXpwq++PEHJC4k1FwJL3H13vWPqq0USwOWPfMAn24rJTEvmrFE9+eKYPpw9uhddO6VGO7SYp83IRY5QSVUdX338I976dDf/NX0M//HFUUpeSNxy9x+6+wB3H0J4yPLfG3kgngg8Snh3kBuAHDO7uwW3WQSMMLOhkTeLVwJzWqUBIi20p7yGm55aRKe0ZB6/bjJZ6XqnIzHnKhpMH1FfLRL/agJBVuQXc+UJA1nyk/P47TXHc8nE/kpeNJMSGCJHYNu+Sq743Qcs3VbEr6+cyPWnDo12SCLtIRO43N03uHsIuA7Y0rCQmc0EPgBGmVm+md0E4O4Bwm8B3yC8ev5sd1/VbtGLRNQEgvzrHxdTWFbDY1+dTD8tniztrKl+0szmmlk/M8skvG7FkUzNUF8tEsPyi6oIOZwwJEfrLR0BvW4QaaEPN+7l1j8tJuTw1A1TOCVPW+ZJYnH3ecC8Ro6/1+B7HeG3fA3LXXWIuucCc486SJFmmv3xNv7w3mbqgiHqgiECQaeiNkBxZR0PXj2R8QmwoJnEn6b6SXevv1NI7mHqmIf6apG4s2VvBQBDemRGOZL4pASGSAs8s3ArP315JYNzM3nsuhMY2iMr2iGJiEgTdpdW89OXVzIoJ5NRvbNJSTZSk5NITTZOGpbLtHH9oh2iiIh0MJv3VAIwJFe/RxwJJTBEmqEuGOLuV1fz1AdbOHNkT35z9US6ZGiemohILPvV39YRDDmPffUEBuXqTZeIiETflr0VZKenkNOKO450JEpgSMIoKK1mydYilmwtZsmWInaWVDdazt1xwJvcEOxgNYEgRZV13HL6UH5w4TFaqV5EJMatLyhn9sfb+MpJg5W8EBGRmLF5byWDe2Rq8f8jpASGxL0/vLeJx97ZxPbiKgDSkpMY278LJw7LwRrZytwsvMF5+M/mdxynj+yh4cYiInHil2+sISMlidvPyYt2KCIiIp/bvLeCsf27RjuMuKUEhsQtd+e+N9bw8LwNnDQshxtOHcLEQd0Z278L6Sla0VdEpKNasrWI11ft4ttfGEmPzunRDkdERAQIT0vPL6pi2ri+0Q4lbimBIXEpFHJ+Omclf/pwK1efOIi7ZozVtA4REcHduXfuZ/TonM7Np2uLaxERiR3bi6oIhpzBWsDziCmBIXGnLhjie89+wkvLdvD1M4fxgwtGaw6ZiIgA8I81BXy0eR93XTKWrHQ95oiISOzYvH8LVSUwjpj+zy5xIxAMUVJVx38+v4K/fbqb750/itvO1txmEREJC4ac//7rGobkZnLlCQOjHY6IiMgBtuyNbKHaQ4tLHyklMKTdBUNOflEl5TUBKmuDVNYGqaoNUFoVoLC8hsKyGgrKqiksq2FvRS1l1QHKqwNU1QU/r+OuGcfylZOHRK8RIiISc15cup01u8t46OpJpCYnRTscERGRA2zeW0FmWjI9tT7TEVMCQ9pNRU2A5xbn84f3NrE5kn1sTHZGCr2y0+mZnc4xfbrQpVMKndNTyM5IJTsjhWP7dWXK0Jx2jFxEROLBnE92MKxHFlOP6xPtUERERA6yZW8lg3OzNP39KCiBIW1uZ0kVT72/hWcWbqG0OsCEgd34+RnDyM1KJys9mcy0ZDqlppCdkULP7HQyUrWDiIiItEwo5CzdWsS0cf30YCgiIjFp854KRvXJjnYYcU0JDDlqO4qreH/DXt5fv4fVO0upDYSoDYYIBJ1AKERRZR3uzgVj+3DTacM4fnD3aIcsIiIJZkNhOWXVASYN6hbtUEQ6FDM7C7gLWAXMcvd5UQ1IJEYFgiG2FVXyxWM1SvBoKIEhjQoEQ5TXhNelKK2uo7SqjtLqAGXVdZRVByirDrCzpIoPN+79fDpITlYaEwd2o1NaMmnJSaQkG6nJSeRmpXH55IEMzNFiNSIi0jYWbykCYJKS5BIHzOwJYBpQ4O5jG5wbBfyl3qFhwE/d/VdmNhB4GugDhIDfu/sDbRDDBcADQDLwmLvfe4iqHCgHMoD8I4lFpCPYWVJNXdAZkqvfiY6GEhhCcWUtS7cW8/GWfSzeUsSqHaWUVQcOe13XTqmcMCSHr548hFPychnZK5ukJA3bFRGR9rdkaxHdMlMZ1kNb00lceBJ4kHAy4gDuvgaYAGBmycB24MXI6QDwH+6+xMyygcVm9pa7r95/vZn1AqrcvazesTx3X9+cGCL3fAg4j3BCYpGZzSGczLinQR03Au+4+3wz6w3cD1zT3H8IIh3J51uo6v9TR0UJjA6gNhDio037WLhpL0WV/9zVo6wmwJ7yGjYWhv8yJScZx/brwowJ/ejZOYPsjBS6dEqlS0Z4Ac0unVLoEllIMys9RSu8i4hIzFiytZhJg7pr/QuJC+6+wMyGNKPoucAGd98SuW4nsDPyc5mZfQr0B1bXu+ZM4FYzm+ru1WZ2C3ApMLWZMUwB1rv7RgAzmwXMcPd7CI/YaEoR0OjWCmY2HZiel5d3mOaKJK79o9aH5CqBcTSUwEhQBWXVzPuskLc/28276/ZQURskOcno1imVzhnhXT06p6cwoldnLpvYn+MH5zB+YFcy0/SfhIiIxJfiylrWF5RzyYR+0Q5FpLVdCcxs7EQk+TARWFj/uLs/a2ZDgVlm9izhURLnteCe/YFt9b7nAyc2VdjMLgPOB7oRHtFxEHd/BXhl8uTJt7QgDpGEsmVPBRmpSfTK1haqR0O/rSag+WsLufmpRdQFnb5dM5gxsT/njOrFKXm5SlCIiEjCWbqtGND6F5JYzCwNuBj4YSPnOgPPA99y99KG5939vsjIiYeB4e5e3pJbN3LMmyrs7i8AL7SgfpEOafPeSgbnZGnK/VHSb7MJZtu+Sr45cynDe3bm/748gdF9sjWcVkREEtrSLUUkGYwfoB1IJKFcCCxx9931D5pZKuHkxZ8jyYODmNnpwFjCa2fcCdzegvvmAwPrfR8A7GjB9SLSiM17K7ROUyvQIgYJpKo2yNf/uBh355GvHM8xfbsoeSEiIglv8dYiRvfpQla63stIQrmKBtNHLPxg9zjwqbvf39hFZjYReBSYAdwA5JjZ3S247yJghJkNjYwCuRKYcwTxi0hEMORs3VupBTxbgRIYCcLd+dGLK/h0VykPXDmRwVocRkREOoDg/2fvzuOrru78j78+2UgCWUjYw74IKMhSiitKXQZFrMvUVmutrVunra1dpp3a6dSZ1hlbp+NPu7lUqV1UKoqtWOpSreIu+76DCQmBANn35X5+f9yLxksSEkhy703ez8fjPsj9fs893883wMnN557zOQFnbV4pH9PyEYkhZvYE8DYw0czyzezG0PFlZjbMzFIJ1q0In2FxFnAdcJ6ZrQ095oe1SQWucvdd7h4Argdy2xuDuzcSnLHxArAFeNLdN3XSrYv0SvvLa6lvCqiAZyfQRxU9xB/eyWXJmgK+ecFJfGLSoEiHIyIi0i22H6igqr6JmaO0fERih7tf08rx5smI7BbOv0HLNSqat3kz7HkDwRkZ7YohdG4ZsKyt64hI++UeCm2hmp0a4Uhin2Zg9ACrcov50dLNnD9pEF87T9tTiYhI77EqtwSAmSM1A0NERKLTkS1UR2kJyQnTDIwYVd8YYE1eCW/uPMTj7+WR0z+Fez4zXVVtRUSkV1mdV8KAfkmMzNKnWiIiEp1yD1eRlBDH0PTkSIcS85TAiCH1jQEeezeXV7cd5L09xdQ0NBFnMH1EJj/551PJSEmMdIgiIiLdak1eKTNG9lfRahERiVrvH65iZFaqPmzuBEpgxIjdByv5+qI1bCwoZ/ygfnx61nDOGj+A08ZmK3EhIiK90uHKOvYcquIzHx9x7MYiIiIR8v6hatW/6CRKYEQ5d+epVfnc8ewmkhLieOi6j/FPpwyJdFgiIiIRtyavFFD9CxERiV6BgJNbXMWcCQMiHUqPoARGFCuvbeDfn9nI0nX7OH1sFv/vM9MZmpES6bBERESiwuq8EhLijFOHZ0Q6FBERkRYVVdRR2xBQAc9OogRGFAoEnKXr93H389vYX17Ld+ZN5F/OHUe81kyJiIh8YFVuCacMSyc5MT7SoYiIiLTo/cPaQrUzKYERRdyd17Yf5O7nt7G5sJxJQ9L4+TVn8LFRmhorIiLSXENTgPX5Zap/ISIiUS33gwSGZmB0BiUwosSavBJ+8retvLunmBFZKdz7mel8ctowVaoVERFpwdbCCmoampipJL+IiESx9w9XkxhvDM3QFqqdQQmMKPD2rsN87pF36Z+ayH998hSumT2SpIS4SIclIiIStVblFgNolqKIiES13MNVjOifSkK8fr/rDEpgRFhReS1fe2INo7JSeearZ2lLVBERkWPYkF/GvS/vYNzAvgzTJ1oiIhIFNu8r566/bWFnUeVHjh+urOes8dkRiqrnUQIjghqbAtz6xBqq6hp57KbTlLwQERE5hpXvF/PF364gIzWR335hNmZaaikSaWY2F/gxsAlY5O6vRjQgkW5UUlXP/720jcffzSMjJZHzJw8mvArAlTOHRya4HkgJjAj63xe38d6eYu759DQmDkmLdDgiIiJR7c2dh7jpdysZmpHMYzefpq3FpUcys4XAAqDI3aeEnZsI/KnZobHAD9393s68lpldBNwHxAMPu/tPjtGVA5VAMpB/PLGIxJqmgPP4e3n834vbqKht5PNnjOabF5xERqo+lO5KSmBEyIub9vPga7v57GkjlZETERE5hpe3HODLj61m7IC+/OHG0xiY1ifSIYl0lUeBXwK/Dz/h7tuA6QBmFg8UAM+EtzOzQUCNu1c0Ozbe3Xce61qhfn8FXEgwGbHCzJ51981mNhW4K6yPG4DX3f01MxsM3ANc25EbFukOB8pr2bq/AncHglk3gPKaBvJLakKPagpKaiivbTjq9QEPzqAPeDB50RRw6psCnD42i//85ClMGpLejXfTeymBEQF5h6v59uJ1TM3J4IcLTo50OCIiIt2ioSlA4MgbR//wuDs4HvoTqusa2VtSzd7iGvKKq8k9XM1f1hZwyrB0fnfDbDJTkyJzAyLdwN2Xm9nodjQ9H9jl7rktnDsX+LKZzXf3WjO7GbgCmN+Oa80Gdrr7bgAzWwRcBmx29ygppkwAACAASURBVA0EZ2y0pgRQdlGiRlPAWb79II+9m8crWw8Q8NbbZvdNYnhWKpOHpZORkkj4AkUzSIiLI86M+DiIizNmjOjPvFMGazljN1ICo5u4O9sPVPL6joM8/m4ecWb8+tqZJCfGRzo0ERGRTlVR28DmfeXsKKpkZ1ElO4oq2HGgkqKKuuPqb1BaH+adMoSf/PNU0pI1NVck5GrgiZZOuPtiMxsDLDKzxQRnSVzYzn5zgL3NnucDp7X1AjO7EpgHZBKc0RF+/lLg0vHjx7czBJGOcXdqGwKU1tRTVtNAaXUD7+0p5k8r9lJQWsOAfkl86dxxfGLiIOLjjCP5BgP69klgeP8UUpP0q3Es0N9SF3t9x0GeWV3AGzsPffDGbdzAvvzqszMZkZUa4ehERESOz5E3ixW1DRRV1LEuv5S1eaWsyy9lR1HlBzMs+ibFM35wGuecNDC0jdyHn1J9+AYy+GbSQseSE+MZ3j+FkVmpDO+fqmS/SBgzSwI+CdzeWht3vzs0e+J+YJy7V7bWNrz7lrpr6wXuvgRY0sb5pcDSWbNm3dzOGETaVFHbwIr3i3lndzFv7zrMtgMV1DcGjmo3Z8IA/v2SyVwweTBJCdrGtCdQAqML5ZdUc/3C98hISeSs8QM4Z8JAzp4wgGGZKjomIiKRV1PfREl1PcVVwce+0hr2ldaQX1pDQUkNRRV1NAUcb/a7SyAAlXWNVNY10hQ2F7d/aiLTRmQyf+pQpg3P5KQhaQzLSNbUWpHOdzGw2t0PtNbAzOYAUwjWyLgDuLWdfecDI5o9Hw7sO844RY6psSlAbWOA8poGCkI/f/JLqikoreFQZf1R7YvKa9m4r5ymgJMUH8eMkZlcf8Yosvr2ITM1kYyURDJTEhk1oC85+r2rx1ECowstei84++65r8/Rfx4REekS7k5xVT15xdXsLanhQFktRRW1FFXUUVRex6HKOhoDTsCDBcfcg7UoymoaqGvh06o4gyHpyeT0T+GUYekkxgc/sTqSgjAz+vWJp19yAv36JJKWnED/1CSm5KQzMitVyQqR7nENrSwfATCzGcBvgEuAPcAfzexOd/9BO/peAUwILUEpILhU5bMnHrJI0MtbDvAff95IRW0jtY1NNDS1PMFnQL8kBvTrc9TPlbTkBL4ydxxnjM1m5qj+mqXXyyiB0UUamgIsWrGX8yYNUvJCREQ61eZ95Ty4fBfbD1Syt7iayrrGj5xPToxjUFoyg9L6MG5gPxIT4og3iDMjLs6INyMjNZHM1ESyUpPITE0iq28SQzOSGZKR/EHSQkS6n5k9AcwFBphZPnCHuz9iZsuAm4BSgvUsvtRGN6nAVe6+K9Tn9cAXOnCtW4EXCG6jutDdN3XS7Ukvd7iyju88tZ6svknMmzKElMR4khPjSU6Mo1+fRHL6p5CTGXykJCkxIUdTAqOLvLT5AIcq67j2tFGRDkVERHqIwrIafvbCdpasySc9OZFZo/pz2pgsRmWnMjIrlRFZqQzJSCatT4JmQojEKHe/ppXjzXcQyT5GH2+GPW8gOCOjvddaBiw7ZrAiHfSfSzdTUdvAoltO56TBaZEOR2KQEhhd5LF3c8nJTOGckwZGOhQREYlxFbUN3P/qLh55Yw8O3DJnLF/5xHgyUrQjh4iIxIYXN+1n6bp9fPvCk5S8kOOmBEYX2H2wkjd3HuY78yYSH6dPwEREpH0amwK8srWIHUWVHxTU3FdaS15xNTUNTVw+fRj/Om8iw/trFysREYkdZdUN/ODPG5k8NJ1/mTsu0uFIDFMCows88V4eCXHGVbOGRzoUERGJAfWNAZ5Zk8+vX91F7uFqILijx7DMFEZmp3LGuGyunJnDqcMzIxypiIhIx935180crqpn4Rc+rjpLckKUwOhktQ1NLF6Vz7xThjAoLTnS4YiISBSra2ziyZX5PPDqLgpKa5iSk86D132MORMGkJqkH9EiIhL7Xtt+kMWr8vnqJ8YxJScj0uFIjNO7o072t42FlFY3cO1pIyMdioiIdKOymgbe3nWYN3Ye5K1dhymvafjIeXdwIOBOILSdaV1TgPrGADNGZnLn5VOYO3Ggim+KiMgJOVRZx8aCsha3yu5u7vDj5zYzbmBfvnbehEiHIz1Ar0xgmFkc8GMgHVjp7r/rrL4feyePsQP6csa4NotDi4hIDAkEnEOVdewtqaG4qp6K2gbKaxoor22krKaBNXklrMsvoyng9E2K57Sx2QzNOHoWXpwZcQZmhhnEmzF34iDOGp+txIWIiBxTIODUNDRRXd9ETX0T1Q2NlNc0smlfGWvySlmzt4S9xTWRDvMjEuONRbecQXKitkWVE9ctCQwz+ybBfasd2AB80d1rj6OfhcACoMjdp4Sduwi4j+B+1Q+7+0/a6OoyIAcoBvI7Gkdrtu2vYGVuCT+4ZLLeiIqIxAB3Z/ehKt7ceYh9pbXUNwZoaAo+6hsDHKqqJ7+kmoKSmlY/yUpJjOekIWl8Ze44zh4/gBkj+5OUoPW9IiKxrLahibKaBkqrGyitrqe6vom6xibqGgPUNQSoa2yiKeBA8BccCM42CLiHHtAUCM24C50LtvUPZuThH5478pqAO02BDx+lNQ0crqzjcGU9h6vqKK6qJ+BHxwswNCOZGSMz+fzpozl1eAb9kqPjs+oB/fowOF1L66VzdPm/ajPLAb4OnOzuNWb2JHA18GizNoOAGnevaHZsvLvvDOvuUeCXwO/DrhEP/Aq4kGBCYoWZPUswmXFXWB83ABOBt939QTN7Cnj5RO8T4PF3c0lKiOOfZ6p4p4hItCququfNnYd4Y8chXt9xkH1lwXx6UnwcSQnBR2K8kRgfR//UJCYNSeOCyYMZ3j+FnMwUBqb1IT05kfSURNKSE1SMTESkCxwor6Wkup5AIPhLffPkQLgPEwTeLFEQWroXShIQ9vxInyXV9ewtrmZvcQ17S6rZW1LNwYo6ahu6Z/mFWXB2nhH8Mz4u+IgzSIiPIyMlkay+SYzKTmXmqP5k902iX3ICqUnxpCYF/+zbJ4GJg9MY0sLMP5GeprvScglAipk1AKnAvrDz5wJfNrP57l5rZjcDVwDzmzdy9+VmNrqF/mcDO919N4CZLQIuc/e7CM7Y+AgzywfqQ0+bWgrYzC4FLh0/fny7brC6vpElqwu4ZOpQ+vdNatdrRESk+1378LtsKSwnPTmBs8YP4KvnDWDO+IGMzNbWpCIi0eKXr+zkD+/kdtv1BvTrw4isFGaM6M/g9D5kpiaRmZpI/9QkMlIS6dsngT4JccFHYjxJ8XEkxH044/rI5Gs7koQ4slQwzogLnbRmbTVbW+T4dHkCw90LzOxnQB5QA7zo7i+GtVlsZmOARWa2mOAsiQs7cJkcYG+z5/nAaW20XwL8wszmAMtbiXspsHTWrFk3tyeA5IR4fv25mdp5REQkyv37/Mn07RPPqcMziY/TG0gRkWj0mY+P4MxxwfpAcaFZCnFxYNiHmYBmjFB9IZolEwgmEexIA47UIvrweEZKIsP7p5KSpPoMIrGgO5aQ9CdYc2IMUAosNrPPufsfm7dz97tDMyfuB8a5e2VHLtPCsVZWh4G7VwM3dqD/Y4qLM+ZMGNiZXYqISBc4e8KASIcgIiLHMCUnQ1tuishRumPh7gXAHnc/6O4NBGc/nBneKDQbYgrwDHBHB6+RD4xo9nw4Ry9TEREREREREZEY1R0JjDzgdDNLteBir/OBLc0bmNkM4DcEZ2p8Ecgyszs7cI0VwAQzG2NmSQSLhD7bKdGLiIiIiIiISMR1eQLD3d8FngJWE9xCNQ54KKxZKnCVu+9y9wBwPXBU1R4zewJ4G5hoZvlmdmPoGo3ArcALBJMjT7r7pi66JRERERERERHpZt2yC4m730Eby0Lc/c2w5w0EZ2SEt7umjT6WActOIEwRERERERERiVLmLeylLB8ys4O0MBukDQOAQ10UTnfpCfcAuo9o0hPuAdq+j1Hurkq+EdJLx2roGffRE+4BdB/RRGN1lNJYHdN6wj2A7iOaHOseWhyvlcDoZGa20t1nRTqOE9ET7gF0H9GkJ9wD9Jz7kJ7zd9kT7qMn3APoPqJJT7gHCeopf5c94T56wj2A7iOaHO89dEcRTxERERERERGRE6IEhoiIiIiIiIhEPSUwOl/4DiuxqCfcA+g+oklPuAfoOfchPefvsifcR0+4B9B9RJOecA8S1FP+LnvCffSEewDdRzQ5rntQDQwRERERERERiXqagSEiIiIiIiIiUU8JDBERERERERGJekpgiIiIiIiIiEjUUwJDRERERERERKKeEhgiIiIiIiIiEvWUwBARERERERGRqKcEhoiIiIiIiIhEPSUwRERERERERCTqKYEhIiIiIiIiIlFPCQyRMGbmZja+nW2/b2YPt3H+fTO7oPOiExER0FgtIhILNFZLZ1MCQ3qE0IBWY2aVZnbAzH5rZv26+rru/j/uflNn9WdmM81sebP7uK2z+hYRibSeMFab2d9C8R951JvZhs7oW0QkGvSQsbqPmT0Qir/YzJaaWU5n9C2RpQSG9CSXuns/YCbwceAH4Q3MLKHbo2onMxsAPA88CGQD44EXIxqUiEjni+mx2t0vdvd+Rx7AW8DiSMclItLJYnqsBm4DzgBOBYYBpcAvIhqRdAolMKTHcfcC4G/AFPhg6tpXzWwHsCN07GYz2xnKyD5rZsPCuplvZrvN7JCZ/a+Ztfh/xcz+08z+2Oz5dWaWa2aHzezfOxj6t4AX3P0xd69z9wp339LBPkREYkIMj9XN+x0NzAH+cLx9iIhEsxgeq8cQfF99wN1rgUXAKR3sQ6KQEhjS45jZCGA+sKbZ4cuB04CTzew84C7g08BQIJfgoNbcFcAsglnny4Ab2nHdk4H7gesIZnqzgeHNzp9tZqVtdHE6UGxmb5lZUWiq28hjXVdEJBbF8Fjd3OeB1919Tzvbi4jElBgeqx8BzjKzYWaWClxLMBEjMU4JDOlJ/hwayN4AXgP+p9m5u9y92N1rCA5gC919tbvXAbcDZ4Q+STvip6H2ecC9wDXtuP6ngOfcfXmo3/8AAkdOuvsb7p7ZxuuHA9cTnPI2EtgDPNGO64qIxJJYH6ub+zzwaDvbiojEklgfq7cDeUABUA5MBn7UjutKlIvmdUsiHXW5u/+9lXN7m309DFh95Im7V5rZYSAHeL+F9rmh1xzLsOavc/eqUL/tVQM84+4rAMzsv4BDZpbh7mUd6EdEJJrF+lgNBD/9A4YAT3X0tSIiMSDWx+r7gWSCMzeqgO8SnIFxWgf6kCikGRjSW3izr/cBo448MbO+BAe3gmZtRjT7emToNcdS2Px1oelq2R2IcX1YnEe+tg70ISISy2JhrD7iemCJu1cex2tFRGJZLIzV04BHQzM/6ggW8JwdKpovMUwJDOmNHge+aGbTzawPwSlx77r7+83afMfM+ofW/d0G/Kkd/T4FLAityUsiOE2tI//HfgtcEYorkeBUuTfcvb1rsUVEepJoHasxsxTgKrR8REQkWsfqFcDnzSwj9L76K8A+dz/UgT4kCimBIb2Ou79MMDnwNMHs7jjg6rBmfwFWAWuBvxIsBHSsfjcBXyU4kBcCJUD+kfNmNsfMWv2kzt1fAb4ful4RwW1UP9ve+xIR6UmidawOuRwoA/7RnnsREemponis/legluBOKQcJFiK9ol03JVHN3P3YrUREREREREREIkgzMEREREREREQk6imBISIiUcnM5prZ62b2gJnNjXQ8IiIiIhJZSmCIiPQQZrbQzIrMbGMbbS4ys21mttPMvhc6NsLM/mFmW8xsk5nd1hVxtHTtY3CgkuA2aPnHaCsiIiIiPZxqYIiI9BBmdg7BX/h/7+5TWjgfD2wHLiSYEFgBXEOwMNZQd19tZmkEC21d7u6bw14/CKhx94pmx8a7+85jxdHatd19s5lNBe4KC/cG4JC7B8xsMHCPu197XN8YEREREekREiIdQLQbMGCAjx49OtJhiEiUW7Vq1SF3HxjJGNx9uZmNbqPJbGCnu+8GMLNFwGXufhfBCt+4e4WZbQFygM1hrz8X+LKZzXf3WjO7mWBF7/ntiKPFawOb3X0DsKCNuEuAPm2c11gtIu0SDWN1b6axWkTaq7XxWgmMYxg9ejQrV66MdBgiEuXMLDfSMbRDDrC32fN84LTmDUKJhxnAu+EvdvfFZjYGWGRmiwnOkriws64dzsyuBOYBmcAvW2lzKXDp+PHjNVaLyDHFyFjdY+l9tYi0V2vjtWpgiIj0HtbCsQ/WEZpZP4L7uH/D3ctb6sDd7ya4r/r9wCfdva092Nt97VautcTdv+Tun3H3V1tps9Tdb8nIyGhnGCIiIiISq5TAEBHpPfKBEc2eDwf2AZhZIsHkxWPuvqS1DsxsDjAFeAa4ozOuLSIiIiLSHkpgiIj0HiuACWY2xsySgKuBZ83MgEeALe5+T2svNrMZwG8I1q74IpBlZneeyLVP4F5EREREpJdRDQwRkTAVtQ2UVDUwMjs10qF0iJk9AcwFBphZPnCHuz9iZsuAm9x9n5ndCrwAxAML3X2TmZ0NXAdsMLO1oe6+7+7Lwi6RClzl7rtC17se+EIH4jjq2p15/yLSuQIB50BFLY1N0b1j3Yis2BqrRUR6E3dnc2E5pwzrnOW+SmCISK/VFHDW7i1h7d4ydh2sZPfBSnYdrOJgRR1TctJ57mtzIh1ih7j7Na0cn9/s62XAsrDzb9ByjYrwft4Me95AcEZGe+M46toiEj22H6hg7d5SNu8rDz4Ky6msa4x0WMf0/k8uiXQIIiISpqa+ib+sLeD3b+eyubCcpbeezdThJ57EUAJDRHqV0up6Xtt+kH9sLeK17QcpqW4AIDM1kXED+zH3pIGMHdiPSUPSIhypiEjXCwScl7cW8cBru1iVWwJASmI8k4emccWMHCYOSSM5MT7CUYqISKTVNjRR3xQ4Zrui8jqeeC+PxSv3Ul7byMTBadx5+RTGDuzbKXEogSEiPZq7s+tgFS9vOcDLW4pYmVtMwCGrbxKfmDiIT0waxBnjshnQr0+kQxUR6TZ1jU38Zc0+Hly+i10Hq8jJTOGHC07mnJMGMmZAX+LjjjkpS0REeondByu56N7X25XAAEiIMy6aMoTPnzGaj4/uT7DcWudQAkNEYl5BaQ0bC8poaAoEH41OfVOAPYeCiYv3D1cDMHloOl+ZO57zJg9i2vBMvUEXkR6tvjHAvtIa9pZUk19SQ0FJDQWlNeSXVLOzqJKS6gYmD03nvqunc8nUoSTEq7a7iIgc7c1dh6lvCvCtC08iNantWXl9EuOZd/JgBqUnd0ksvTKBYWZzgR8Dm4BF7v5qRAMSkQ7LPVzF3zbu528bClmXX9Zim6SEOM4cl82Nc8Zy3qRB5GSmdHOUIiLdpyng3Pv37ax4v5i9xTUUltUQaFZ/Mz7OGJKezPD+KZw/eTCfnDaMORMGdOonYyIi0vOsySthQL8kvnbe+Ij/zDjhBIaZLQQWAEXuPqWF8yOA3wNDgADwkLvf19nXMrOLgPsIVrd/2N1/0kZXDlQCyUD+8cQiIl3L3Xlr12Fe2VpEbUNTaHaFU98YnFmxubAcgGnDM/jexZM4Y2w2qUnxJMbHkZgQR2K8kZ6cqLXbItJrvLzlAL94ZSdTczKYPSaLEf1TGJGVyoisVIb3T2FIerJmWYiISIetyStlxsjOXQpyvDpjBsajwC8JJila0gh8291Xm1kasMrMXnL3zUcamNkgoMbdK5odG+/uO9tzLTOLB34FXEgwIbHCzJ4lmMy4K6yPG4DX3f01MxsM3ANc24H7FZEu5O68vuMQ9728g1W5JSQnxtE3KSGUmDCS4uPI7teHH1wymXmnDNH2eT2QZsmJHJ9H33qfYRnJPPOVM5WoEBGRTlFSVc+eQ1VcNWt4pEMBOiGB4e7LzWx0G+cLgcLQ1xVmtgXIATY3a3Yu8GUzm+/utWZ2M3AFMD+sr9auNRvY6e67AcxsEXCZu99FcMZGa0qAFiv3mdmlwKXjx49v4+UivVtVXSONTU6TOwF3AgHHj/2yVm3eV859L+9g7d5ShmYk8+PLTuGqWSM0iyKGtDZTTrPkRLrWtv0VvLXrMN+9aKKSFyIi0mnW7A3uUDVjRP8IRxLUrTUwQsmHGcC7zY+7+2IzGwMsMrPFBGdJXNiBrnOAvc2e5wOntRHHlcA8IJPgjI6juPtSYOmsWbNu7kAcIj1WbUMTm/aVsyavhLV7S1m7t5T8kppOv05OZgr/fcUUPvWx4fRJUOIiBj1K2Ew5zZIT6Xq/e/t9+iTEcfXHR0Y6FBER6UHW5JUSZzBtREakQwG6MYFhZv2Ap4FvuHt5+Hl3vzs0c+J+YJy7V3ak+xaOtfpBsLsvAZZ0oH+RHqmitoFn1hRQUdtIU8BpCgRnUtQ3BSiurOdgZR0HK4KPw1X1NIWqwQ3LSGb6yEyumT2SlMR44ixYHM7MMANr8b/ksWWmJnLB5MEkJejTw1jVyky5Tp8lF+rnFuAWgJEj9Uub9F5l1Q0sWZ3P5dNzyOqbFOlwRESkB1mdV8KkIemkJkXH/h/dEoWZJRJMXjwWSh601GYOMAV4BrgDuLUDl8gHRjR7PhzYd3zRivR8gYDzzJoC7vrbVg5V1n3knBkkxsWR1TeJgWl9GJyezJRhGQxO78PJwzKYMTKTwV20LZL0WJ0+Sw7A3R8CHgKYNWvWiaxeEolpf1qZR21DgOvPHB3pUEREpAdpCjjr9pZx+YxhkQ7lA12ewLBgqdJHgC3ufk8rbWYAvwEuAfYAfzSzO939B+28zApgQmgZSgFwNfDZEw5epAfaWFDGHc9uYlVuCdNHZPLw9bOYPDSNeLMPZlGIdDLNkhPpIk0B53dv5XLamCxOHpYe6XBERKQH2VFUQWVdY9TUv4DO2Ub1CWAuMMDM8oE73P0RM1sG3ASMBa4DNpjZ2tDLvu/uy5p1kwpc5e67Qn1eD3yhvddy90YzuxV4geCa6oXuvulE700klu0vq6WgtIbS6npKqhsora5n6/4Knl6dT1ZqEnd/6lQ+NXM4cXFKWEiX0yw5kS7y9y0HKCit4T8WTI50KCIi0sOsySsFYOaoHpTAcPdrWjl+ZAeRfbT86Vvztm+GPW8gOCOjXdcKnVsGLGvtvEhv4e78+tVd/OzFbXjYZ9xJ8XFcf8ZovnnhSWSkJEYmQOmNNEtOpIs8+ub75GSmcMHkwZEORUREepjVuSX0T01kdHZqpEP5QHRU4hCRTlFZ18h3Fq/jbxv3s+DUoXzqY8Ppn5pEZmoimalJpPVJ0IwL6VJtzMrTLDmRTrZ1fzlv7z7M9y6epK1TRUSk063ZW8qMkf2jaom5EhgiPcTug5V86Q+r2H2oih9cMpkbzx4TVYON9A5tzMrTLDmRTva7t3JJTozj6o+POHZjERGRDiirbmBnUSWXTYueAp6gBIZIzHN3Xtx8gH99ch2JCXH84cbZnDluQKTDEhGRLvTGjkMsWZ3PFTNyyEzV1qkiItK51uZHX/0LUAJDJGbll1Tz5zUFPLOmgF0Hq5iak8ED132MnMyUSIcmIiJd6Nl1+/j2k2sZO6Af3/qnkyIdjoiI9ECrc0swg1OHZ0Q6lI9QAkMkxjy7bh9/fCeX9/YUA/Dx0f258eyxXDkzh+TE+AhHJyIiXWnhG3v40XObmT0mi998fpYKMouISJdYs7eUiYPTSEuOrp8zSmCIxJCXNh/g60+sYcyAvnz7wpO4fEYOI7KipyqwiIh0DXfnp89v44HXdnHRKUO49+rpSlqLiEiXCAScNXklLDh1aKRDOYoSGCIxory2gR/8eQOThqTx7K1nk5SgivMiIj1NIOD84Z1c9hyqAoKJi4BDXnE1r20/yLWnjeRHl00hXjtKiYhIF9l9qJKK2kZmjIyu+hegBIZIzLhr2VYOVtTx0HWzlLyQXsHM4oAfA+nASnf/XYRDEulSTQHn+0s28KeVe0lLTiDODDOIMyM+zvjOvIl8Ze447TAlIiJdanVuqIDnyMwIR3I0JTBEYsBbuw7xxHt53HLOWKaNiL6BRKKfmd0G3AwY8Bt3v7eFNt8EbgIc2AB80d1rj+NaC4EFQJG7Twk7dxFwHxAPPOzuP2mjq8uAHKAYyO9oHCKxpLEpwHefWs+SNQV8/fwJfPOCCUpUiIhIRKzZW0J6cgJjB/SLdChH0ce4IlGupr6J25dsYFR2Kt+8QNXmpePMbArB5MVsYBqwwMwmhLXJAb4OzAolHeKBq8PaDDKztLBj41u45KPARS3EEQ/8CrgYOBm4xsxONrOpZvZc2GMQMBF4292/BXz5eO5dJBY0NAX4xp/WsmRNAd++8CS+deFJSl6IiEjErMkrZfrI/sRF4XJFJTBEotz/+/t2cg9Xc9eVU0lJUsE2OS6TgXfcvdrdG4HXgCtaaJcApJhZApAK7As7fy7wFzNLBjCzm4Gfh3fi7ssJzpoINxvY6e673b0eWARc5u4b3H1B2KOI4KyLktBrm1q6MTO71MweKisra/s7IBKl6hsD3Pr4ap5bX8jtF0/ia+dPOPaLREREukhZTQPbDlRE5fIRUAJDJKqt21vKw6/v5prZIzlz3IBIhyOxayNwjpllm1kqMB8Y0byBuxcAPwPygEKgzN1fDGuzGHgeWGRm1wI3AJ/uQBw5wN5mz/NDx1qzBJhnZr8AlrfUwN2XuvstGRnRtUe5SHtsKSznhkdX8MKmA/xwwcl86dxxkQ5JRER6scamAN/601oMmDtxUKTDaZFqYIhEqcamAP/29HoGpvXh9vmTIh2OxDB332JmPwVeAiqBdUBj8zZm1p9gzYkxQCmw2Mw+5+5/DOvrbjNbBNwPjHP3yg6E0tI8RG8j7mrgxg70LxITNuSX8fNXdvDS5gP065PAT66cytWzR0Y6LBER6cXcnR8+u4mXtxbx48tOYXqU1t1TsTREHQAAIABJREFUAkMkSi1ZXcDW/RX8+tqZpCcnRjociXHu/gjwCICZ/Q9HF8W8ANjj7gdDbZYAZwIfSWCY2RxgCvAMcAdwawfCyOejMz+Gc/QyFZEeqSngvLvnMA8t382r2w6SnpzANy6YwBfOHE1malKkwxMRkV7uV//YyePv5vHlueO47ozRkQ6nVUpgiEShusYm7v37dqYNz+DiKUMiHY70AGY2yN2LzGwkcCVwRliTPOD00BKTGuB8YGVYHzOA3wCXAHuAP5rZne7+g3aGsQKYYGZjgAKCRUI/e7z3JBLtahuaeGvXIV7YeIC/bznA4ap6svom8d2LJnLd6aNIU3JaRESiwFOr8vnZi9u5YkYO3503MdLhtEkJDJEo9Pi7eewrq+XuT01TJXrpLE+bWTbQAHzV3UsAzGwZcJO7v2tmTwGrCS4vWQM8FNZHKnCVu+8KvfZ64AvhFzKzJ4C5wAAzywfucPdH3L3RzG4FXiC4y8lCd9/U+bcq0j0CASe/pIbNheUUltVQUt1AaXU9pdUNFFfVsyavhKr6Jvr1SeATkwYx75TBnDdpEKlJevslIiLRYfn2g3zv6fWcNT6bn/7zqVH/u4d+gopEmaq6Rn71j52cMTabs8ZnRzoc6SHcfU4rx+c3+/oOgstCWuvjzbDnDQRnZIS3u6aNPpYBy9oRskhUWpVbwl/WFrClsJwthRVU1n1YTsYM0pMT6Z+aSGZqEp+cnsO8UwZzxrhs+iRoFynpmcwsDvgxkA6sdPffRTgkEWnFpn1lrNtbRu7hKnIPV/P+4Sp2Haxk/KB+3P+5j5GUEP17fPTKBIaZzSU40G4CFrn7qxENSKSZ3765h0OV9Tz0+YlRnwEVEelNSqrq+cLC9wi4M3loOlfOzGHy0HROHprOiKxUMlISiY/TuC1dx8wmAn9qdmgs8EN3v/c4+loILACK3H1K2LmLgPsIzpZ72N1/0kZXlxHcUaqYo+sriUiUWJVbzKceeBt3SIqPY0RWCqOz+zJnwgBunjM2ZmrutSuB0dYAd6w2ZvY+UAE0AY3uPut4g23jGh0ZZCFY9b4SSEYDrUSR0up6Hly+mwsmD2bmyP6RDkdERJp54LVdVNY38vxt5zBxSFqkw5FeyN23AdMBzCyeYD2hZ5q3MbNBQI27VzQ7Nt7dd4Z19yjwS+D3Ya+PB34FXEjwffIKM3uW4Pvsu8L6uAGYCLzt7g+GliK+fCL3KCKdLxBwfvTcFgal9WHxl84kp39KzCbc2ztH5FHgohNo8wl3n95a8sLMBplZWtix8e25RrNB9mLgZOAaMzs5dG6qmT0X9hgEvO7uFwP/BvzXMe5LpNs8uHw3lXWN/Ou8kyIdioiINFNYVsOjb73PFdNzlLyQaHE+sMvdc8OOnwv8xcySAczsZuDn4S929+UEZ02Emw3sdPfd7l4PLAIuc/cN7r4g7FFEMMlREnptU0uBmtmlZvZQWVnZ8dyniJygpev3sW5vKd+ZN4mR2akxm7yAdiYw2hjgOtSmDScy0LY4yIbatzjQunsg9NoSoE9LAWmgle5WVFHLb9/cw2XThjFpSHqkwxERkWZ+/vIOAu5880IlmCVqXA08EX7Q3RcDzwOLzOxagrMkPt2BfnOAvc2e54eOtWYJMM/MfgEsb6mBuy9191syMjI6EIaIdIbahibufn4bU3LSuXJGW/+VY0N31MBw4EUzc+BBdw+vao+7Lw5tq7fIzBYTHGgvbGf/LQ2yp7X1AjO7EpgHZBKcOnd00O5LgaWzZs26uZ1xiJyQX76yk8YmvTkWEYk2uw9W8uTKfK47fRQjslIjHY4IZpYEfBK4vaXz7n63mS0C7gfGuXtlR7pvqcvWGrt7NXBjB/oXkW70yBt7KCit4WdXTSMuhmdeHNEdCYyz3H1faOnGS2a2NTST4iNOYKDt0CAbutYSgtlikajw9q7DPPZuHld/fASjsvtGOhyRqKDK9hIt/u+l7fRJiOOrn2hpdatIRFwMrHb3Ay2dNLM5wBSC9THuAG7tQN/5wIhmz4cD+44zThGJoIMVdfz6Hzu58OTgjlg9QZfvk+Lu+0J/FhEcRGe31K6Fgba9NMhKTCsoreGrj69mdHYq37t4UqTDkR7KzG4zs41mtsnMvtFKm0wze8rMtprZFjM74wSut9DMisxsY9jxi8xsm5ntNLPvHaObI5XtG1DBZYmQDfll/HV9ITedPYaBaS2uOhWJhGtoYfkIgJnNILjF9WXAF4EsM7uzA32vACaY2ZjQTI+rgWdPMF4RiYB7XtpOXWOA23vQ7xhdmsAws75HinOaWV/gn4CNLbQ7kYFWg6zErNqGJr70h5U0NAZ46POzSIuR7YsktpjZFOBmggnkacACM5vQQtP7gOfdfVKo3ZawftpbcBk6oegyMJVgZftvAV/uyD2LdJa7X9hK/9REbjpnbKRDEQHAzFIJLrVubTZxKnCVu+8K1X27Hggv9ImZPQG8DUw0s3wzuxHA3RsJzth4geDPgSfdfVPn34mIdKWt+8v504o8rjtjFGMH9ot0OJ2mvduoPgHMBQaYWT5wh7s/YmbLgJtCS0SOagP8A3jGzI5c63F3f76FS3ww0Iaudz3whQ7EcWSQjQcWapCVWODu3L5kA5v2lfPw52cxrgcNLBJ1JgPvhNYpY2avAVcAdx9pYGbpwDmExt5QUeT6sH7OBb5sZvPdvTZUcPkKYH74Bd19uZmNDjv8QdHl0DWPFF3e7O4bCG6T/QEz+1yzGFqtbA9cOn68pvZL53tr5yFe33GIH1wymXQlmCVKhMbyVueCu/ubYc8bCH5QGN7umjb6WAYsO4EwRaQbPb+xkPySmo8c++uGQtKSE7nt/JY+s4pd7UpgtDbAufv8Y7Uh+Cnesfo/oYFWg6zEooVvvs8zawr41oUncf7kwZEOR3q2jcB/m1k2UEMw4bAyrM1Y4CDwWzObBqwCbnP3qiMNTrDgMnS86PIS4BehJYatVrZHBZelizywfDdD0pP53OmjIh2KiIhIi3IPV/Evf1x91PE4g/++YiqZqUkRiKrrdEcRTxEJ89bOQ/zPsi3808mDuVVF4aSLufsWM/sp8BJQCawDGsOaJQAzga+5+7tmdh/wPeA/wvpSZXvpFdyddXtLmT91KMmJ8ZEOR0REpEV/3VAIwEvfPIfBGckfHE+IM1KTet6v+11exFNEPqq+McBtf1rLmAF9uecz03vEdkYS/dz9EXef6e7nAMXAjrAm+UC+u78bev4UwYTGR5xAweUj11DRZYkJhWW1lNU0cPLQtGM3FhERiZBlGwqZNiKTCYPTSE9O/ODRE5MXoASGSLdbvv0gByvquP3iSfTr0zMHFok+oa2sMbORwJWEVa939/3AXjObGDp0PrA5rA9VtpdeY0thOQCThqZHOBIREZGW5R2uZmNBOZdMHRLpULqNEhgi3eyZNQVk9U3inJMGRjoU6V2eNrPNwFLgq+5eAmBmy8xsWKjN14DHzGw9MB34n7A+2lXZPtTvUdXtVdleYskHCYwhmoEhIiLR6cjykYunDI1wJN1HH/+KdKPy2gZe2nKAaz4+gsR45Q+l+7j7nFaONy/GvBaY1UYf7Sq4HDqnossS07YUVjAiK0XbW4uISNRatqGQacMzGJGVGulQuo1+gxLpRs9v2E99Y4DLZ+REOhQREWnDlsJyJg/R8hEREYlOeYer2VBQxvypvWf2BSiBIdKtnllTwOjsVKaPyIx0KCIi0orq+kb2HK5isupfiIhIlFq2Mbh8RAkMEekS+0preGfPYS6fkYOZdh4REYlW2/ZX4I4SGCIiErWWbSjk1F62fASUwBDpNs+u24c7XKHlIyIiUW3r/goATlYCQ0REotDe4mrW5/e+5SOgBIZIt/nzmgJmjsxkVHbfSIciIiJt2FJYTr8+CQzvnxLpUERERI6yLLT7yCVKYIhIV9i8r5yt+ys0+0JEJAZsKSxn0pA04uK03E9ERKLPsg2FTM3pfctHQAkMkW7x57UFJMQZl5w6LNKhiMQMM4szs/82s1+Y2fWRjkd6B3dna2EFk4amRToUERGRo+wtrmZdL10+AkpgiHS5poDzl7UFzJ04kKy+SZEOR3opM7vNzDaa2SYz+0Yb7eLNbI2ZPXeC11toZkVmtjHs+EVmts3MdprZ947RzWVADtAA5J9IPCLtlV9SQ0Vdowp4iohIVPrbxt67fASUwBDpcu/sPsyB8jou1/IRiRAzmwLcDMwGpgELzGxCK81vA7a00s8gM0sLOza+lX4eBS4KaxsP/Aq4GDgZuMbMTg6dm2pmzzV/AFOBt939W8CXj32nIiduc2E5oB1IREQk+gQCznPrC5mSk87I7N63fASUwBDpcs+sKaBfnwQumDw40qFI7zUZeMfdq929EXgNuCK8kZkNBy4BHm6ln3OBv5hZcqj9zcDPW2ro7suB4rDDs4Gd7r7b3euBRQRnWeDuG9x9QfMHsBsoCb22qaXrmNmlZvZQWVlZa/cu0iFbCssxg0lDtIRERESiR2VdI//yx1Wszy/j07NGRDqciFECQ6QL7ThQwdJ1+7hk6lCSE+MjHY70XhuBc8ws28xSgflASz/57gW+CwRa6sTdFwPPA4vM7FrgBuDTHYgjB9jb7Hl+6FhrlgDzzOwXwPJWYlrq7rdkZGR0IAyR1m0pLGd0dl9SkxIiHYqIiAgAuYeruPLXb/Ly1iLuuPRkrjt9VKRDihj9dBbpInWNTXx90Vr69Ung2/NOinQ40ou5+xYz+ynwElAJrAMam7cxswVAkbuvMrO5bfR1t5ktAu4Hxrl7ZQdCaWlLB2/jWtXAjR3oX+SEbSmsYEqOlo+IiEh0eH3HQW59fA1m8PsbZnPW+AGRDimiNANDpIv87/Pb2FJYzt2fOpVBacmRDkd6OXd/xN1nuvs5BJd27AhrchbwSTN7n+DSjvPM7I/h/ZjZHGAK8AxwRwfDyOejMz+GA/s62IdIl6msaySvuJrJQ5TAEBGRyFv4xh6uX/geQzOSefarZ/f65AX00gSGmc01s9fN7IG2PmkUOV6v7zjIw2/s4brTR3G+al9IFDCzQaE/RwJXAk80P+/ut7v7cHcfDVwNvOLunwvrYwbwG4J1K74IZJnZnR0IYwUwwczGmFlS6DrPHuctiXS6bftVwFNERKLDH97J5UfPbebCkwfz9JfP7LVFO8OdcAKjta3yOtrmRK/Xwa35nOA06mS0NZ90suKqer795DrGD+rH9+dPjnQ4Ikc8bWabgaXAV929BMDMlpnZsHb2kQpc5e673D0AXA/kttTQzJ4A3gYmmlm+md0YKiB6K/ACwZ1OnnT3TSd2WyKdZ3NhBQCThymBISIikfPCpv3c8ZeNnDdpEL/67Ez69lHlhyM64zvxKPBL4PfH2yb0yWCNu1c0Ozbe3Xe2p69mW/NdSDAhscLMnnX3zWY2FbgrrI8b3P1iMxsM3ANc29YNirSXu/NvT6+npLqe337x46QkqXCnRAd3n9PK8fktHHsVeLWF42+GPW8gOCOjpX6vaeX4MmDZMQMWiYAtheWkJycwLEPL/kREJDJW5Rbz9SfWMHV4Jr/87AwS4nvloolWnfB3o5Wt8jraplu35nP3otDrSoA+LV1HW/PJ8Vi0Yi8vbT7Ad+dN4pRh2hVBRCSWbCksZ9LQdMxaqjcrIiLStXYWVXLj71YyNCOZhdfP0o5YLYiKdE53b81nZlea2YPAHwjO5mgpJm3NJx1S3xjgp89v5Yyx2dx49phIhyMiIh0QCDjb9ldwsupfiIhIBBSV13L9wvdIiDN+d8Nssvu1+Dl7rxc1KZ1u3ppvCbCkgyGKtOnNnYcorW7gxrPHEBenT+9ERGJJbnE11fVNTB6aFulQRESkB6trbOK5dYVsP1DB4ap6iqvqOVxVT97hKuoaAyy65XRGZfeNdJhRK2oSGC1szXdrB16urfkk4pau30dacgJzTtL2RiIisWZLoXYgERGRrlNe28Bj7+Sx8M09HKyoIykhjgF9k8jql0RW3z7MnTiIz542klOHZ0Y61KgWFQmMZlvzXQLsAf5oZne6+w/a2cUHW/MBBQS35vtslwQr0oLahiZe2nSAi6YMoU+CCneKiMSarYXlxBmcNFgzMERE5PiU1zZQUFLzkWONTc5z6/fx2Lt5VNY1MmfCAO79zHTOHJetmkvH4YQTGKGt8uYCA8wsH7jD3R8xs2XATe6+r7U2zbr5YGu+UJ/XA1/o4PWObM0XDyzU1nzSnZZvP0hFXSMLprV3N0oREYkWdY1NvLr9IGMH9iM5UUloERHpuBXvF3PL71dSUt1w1Lk4g0tOHcaXzhnLlBzVWDwRJ5zAaGOrvPnHatPsvLbmk5j23PpC+qcmcua47EiHItJjmFkc8GMgHVjp7r+LcEjSAwUCzreeXMf6/DLu/cz0SIcjIiIx6Jk1+fzbUxvI6Z/Cjy6bQmL8R2dWnDIsgxFZqRGKrmeJiiUkIrGspr6Jv285wGXTc0jUPs0SpczsNuBmgkWPf+Pu94adHwH8HhgCBICH3P2+47zWQmABUOTuU8LOXQTcR3C23MPu/pM2urqM4I5SxQRrHYl0KnfnR89t5q/rC7n94klcPqPVDcxERESO4u78v5e28/NXdnL62Cwe+NzHyExNinRYPZoSGCIn6B/biqiub+LSU4dGOhSRFpnZFILJi9lAPfC8mf3V3Xc0a9YIfNvdV5tZGrDKzF5y983N+hkE1Lh7RbNj4919Z9glHyW4RfXvw+KIB34FXEgwIbHCzJ4lmMy4K6yPG4CJwNvu/qCZPQW8fHzfAZGW/frVXTz61vvcdPYYbjlnbKTDERGRGFLb0MS/Ll7Hc+sL+fSs4dx5+VSSEvRhZlfTd1jkBD23fh8D+vXhtLFaPiJRazLwjrtXu3sj8BpwRfMG7l7o7qtDX1cAWwjOfmjuXOAvZpYMYGY3Az8Pv5i7Lyc4ayLcbGCnu+9293pgEXCZu29w9wVhjyKCSY6S0GubWroxM7vUzB4qKytrz/dB5ANPrtzL/76wjcunD+P78yerkJqIiLRbXWMTX/jte/x1QyHfu3gSP/3nU5W86Cb6LoucgKq6Rl7ZWsT8qUOIj9ObX4laG4FzzCzbzFKB+Xx06+mPMLPRwAzg3ebH3X0x8DywyMyuJThL4tMdiCMH2NvseT5HJ0maWwLMM7NfAMtbauDuS939lowMFcSS9ntl6wFuX7KBORMGcPenphGn8VtERNrJ3fn+ko28s7uYez49jX85d5yS4N1IS0hETsDftxygtiHAglO1+4hEL3ffYmY/BV4CKoF1BJeMHMXM+gFPA99w9/IW+rrbzBYB9wPj3L2yA6G09NPd24i7GrixA/2LHNOB8lq++ad1TBqSxgOf+5g+MRMRkQ554LXdPL06n29cMIErZgyPdDi9jn5qi5yA59YXMiQ9mVmj+kc6FJE2ufsj7j7T3c8huLxjR3gbM0skmLx4zN2XtNSPmc0BpgDPAHd0MIx8PjrzYziwr4N9iBw3d+e7T62nrrGJX1wzg7599DmOiIi03/Mb93P3C1u5dNowbjt/QqTD6ZWUwBA5TuW1Dby27SCXnDpU048l6oUKcGJmI4ErgSfCzhvwCLDF3e9ppY8ZBLe4vgz4IpBlZnd2IIwV/5+9O4+Psj73//+6shECCfsOsoMgCCiCS92qVotS1GrrWnf99VTter6n7ek59lRbe2yPp57WuuNecW+lUteq4M4iiqyGPSxJ2EL2ZGau3x8z4DBMlgmByUzez8cjj2Tu+3N/7utGublz3Z/P9QFGmtlQM8sBLgJeSvRaRFrqyY828M6qUn4+bQzDenVOdjgiIpJCPt9Uxg+fXsyEgV353QVHatpIkiiBIdJCry0tpi4Y4hytPiKp4XkzWwbMBr7n7jsBzGyOmfUHTgAuB75qZosjX9Ni+sgDLnT31e4eAq4A1seeyMyeAj4ARptZkZldAxApIHoj8CrhIqHPuPvSg3K1IjHWbavk1y8v58SRPbn82MHJDkdERFJI8e4arnl0Pt3ysrn/O0eTm52Z7JDaLY2dFGmhlz/bzMBuHZk4qGuyQxFpkruf2MD2PUmKzcSvURHd9r2Yz/WER2TEtru4kT7mAHOailekNQVDzo+eWUx2pnGH3pqJiEgz7K6p5+2Vpby+rJi3V5YQDDnPf/d4eufnJju0dk0JDJEWcHcWbdjFtPH99CAsItLG3fvOahZt2MVdF02kX5eOyQ5HRETasH+uKObh99bx4Zrt1AedHp1yOOuIvlx27GDG9CtIdnjtnhIYIi2wvbKOsup6RvbWHGoRkWg19UHWba9k865qvME1Zg6dsup6/vDGKs4e349vTNCKUSIiEp+78+C8tfx6znIGde/I1ScM5YyxfZh0WDcyVe+uzVACQ6QFCkvCK0eOUAJDRNq5nZV13Dt3NSu3lrOmtJKNO6vaROIiWp+CDtx27jiNmBMRkbiCIefWvy/jkffXMW18X+781kTVuWijlMAQaYHVpeEExnAlMESknfuPv33OPz7fyug++UwY1JXzJg1geO/ODOzWkaw28sZqcI9OdOmYnewwRESkDaquC/L9WZ/w2rJirjtxKD/7+hitMNiGKYEh0gKFJRXk5WTSr0BFfESk/fpg9Xb+/tkWbj5tJD86Y1SywxEREWlQTX1w7yjqPQIh55cvLeXTol38cvpYrjxhaJKik+ZSAkOkBVaXVjKsVydlZ0Wk3QoEQ/zX7KUM6NqR7548PNnhiIiINOrnLyzhhU827be9Q1YG9152NGce0TcJUUmilMAQaYHVJRUcM6RbssMQSWtmlgHcChQAC9z90SSHJFGe/GgDK7aWc8+lR9ExR/OERUSk7QoEQ7yxvJivHt6bi44ZtM++UX3yGdKzU5Iik0QpgSGSoKq6AJt2VXNx70FNNxZJIWb2feA6wIAH3P0PLexnJnAOUOLu42L2nQXcBWQCD7r7bxvpagYwANgBFLUkFjk4tlfU8j+vreSEET04a5zeWImISNv2ycZd7K4JcOHRA/maRlqktIxkByCSataUVgIwvJcKeEr6MLNxhJMXU4AJwDlmNjKmTW8zy4/ZNiJOd48AZ8U5RyZwN/B1YCxwsZmNNbPxZvb3mK/ewGjgA3f/EfDdA79KaS2/f20lVXVBfjn9CK3sISIibd5bK0rIyjBOGNkz2aHIAVICQyRBWkJV0tQY4EN3r3L3APAOcF5Mm5OBv5lZLoCZXQf8X2xH7j6X8KiJWFOAQndf4+51wCxghrsvcfdzYr5KCI+62Bk5NhgvaDObbmb3l5WVJX7F0iKfFe1i1vyNXHH8EEb2yW/6ABERkSR7a2Upk4d0oyBXK1KlOiUwRBK0urSCzAxjcA/NlZO08jlwkpn1MLM8YBqwzzwpd38WeAWYZWaXAlcD30rgHAOAjVGfiyLbGvICcKaZ/RGYG6+Bu8929+u7dOmSQBjSUjX1QX750lJ6dMrh+6ePbPoAERGRJNtaVsPyLbs5dXTvZIciraBd1sAws1MIF4ZbCsxy97eTGpCklMKSCgZ3zyMnS/k/SR/uvtzM/ht4HagAPgUCcdrdYWazgHuA4e5eEdumEfHmGngjMVUB1yTQv7SiL4rL+c2c5Wwpq6Gsup6dVXXU1IcAuOOCI/UWS0REUsLbK0sAOPVwJTDSQbMSGI0VZItqE7cwm5mtA8oJD/8NuPvklgbbUBwJFoWD8ANzBZCLCsNJglaXVjBM9S8kDbn7Q8BDAGb2G+LcH83sRGAc8CJwC3BjAqcoYt9RHQOBzS2NVw6ezbuq+c7Mj6mpD3L04O6MH5BN17xsuublMKxnJxXuFBGRlPHWyhIGdO3ISE3/TgvNHYHxCPAn4LF4O6MKs51B+AF1vpm95O7LIk1OdfdtDXUeKdZW7e7lUdtGuHthU3E0dm4zGw/cHtPH1cA8d3/HzPoAdwKXNnbxInsEgiHWbqvkq4f3SXYoIq3OzHq7e4mZHQacDxwXs38S8ABwNrAWeMLMbnP3XzTzFPOBkWY2FNgEXARc0moXIK1iV1Ud35n5MRU1AZ6+4TjG9i9IdkgiIiItUhcI8e4X2zh30gAVnU4TzRoD30hBtj3iFmZLII4DKQzX4LkbKgzn7qHIsTuBDvECUmE4iWfjzmrqg87wXqp/IWnpeTNbBswGvufuO2P25wEXuvvqyH30CmB9bCdm9hTwATDazIrM7BqASHHQG4FXgeXAM+6+9OBdjiSqui7INY8uYMP2Ku7/zmQlL0REJKUtWLeDyrqg6l+kkdaqgRGvMNvUyM8OvGZmDtzn7vfHHuzuz0beyM0ys2cJj5I4oxXOHZeZnQ+cCXQlPKJjP+4+G5g9efLk65oZh7QDWoFE0pm7n9jE/vdiPtcTHpER2+7iRvqYA8xpaYxy8ASCIW56ahGLNuzkz5ccxXHDeyQ7JBERkQPy1soScjIzOH6E/k1LF62VwGisMNsJ7r45Mk3kdTNbERlJsW/jlheGS6goXORcLxCubi+SkD0JjOFKYIhIGnF3fv7iEt5YXsKt547j6+P7JTskERGRA/bWylKmDutOXk67XLsiLbXWMgoNFmZz9z3fSwgXfZsSr4M4heEO+NwirW11aQW98zuo+r6IpI26QIh/fe4znllQxM2njeTyYwcnOyQREZEDtnFHFYUlFZo+kmZaK4GxtzCbmeUQLsz2kpl1MrN8ADPrBHwN+Dz24KjCcDOAq4DuZnbbgZz7gK9IJI7CkgqGawUSEUkTu2vqueqRj3luYRE/PH0UPzx9ZLJDEhERaRVvafnUtNSsBEZDBdnMbI6Z9W+kMFsf4F0z+xT4GHjZ3V+Jc4oWF4ZTUTg5VNyd1aUVqn8hImlh865qLrznAz5as4PfXziB758+UhXaRUQkbby1ooQhPfIY2lPF99NJsyYDNVSQzd2nRf28X2E2d18DTGhG/wdUGE79ljxgAAAgAElEQVRF4eRQKC2vpbwmoASGiKS8pZvLuPqR+VTVBnn06imcMKJnskMSERFpNTX1Qd5fvZ1Lph6W7FCklamaiUgzFZZGCnhqComIpKjtFbU8+v46Hnp3LQUds3n2u8dxeF8tlSoiIunlgzXbqQ2EVP8iDSmBIdJMq7WEqsghZWYZwK1AAbDA3R9Nckgpq2hnFQ/OW8us+RuoqQ/xtbF9+NWMcfTtkpvs0ERERA5ITX2QTzbsYlVx+d6vFVvK6ZidyZSh3ZMdnrQyJTBEmqmwpILOHbLoU9Ah2aGIJMzMfghcS3iZ6SXAVe5ek2ibZp5rJnAOUOLu42L2nQXcBWQCD7r7bxvpagYwANhBeMUpSdDOyjpufXkZf1u8mQyDcycO4IaThzGid36yQxORNKFksyRLeU09T3y4gYfeXcO2ijoACnKzGN03n29M7M9XD+9NbnZmkqOU1qYEhkgzrS6tZHivTipyJynHzAYANwNj3b3azJ4hvGLTIwm26Q1Uu3t51LYR7l4Yc8pHgD8Bj8XEkQncDZxBOCEx38xeIpzMuD2mj6uB0cAH7n6fmT0HvNmiP4B2auXWcq59bD7Fu2u56vghXHPiUPp16ZjssETkAJlZV+BBYBzhhPPV7v5BC/pRsllS0vaKWh55fx2PvL+O8poAJ47syRXHDWH8wC70zu+gZ/U0pwSGSDMVllRw/PAeyQ5DpKWygI5mVk945afNLWhzMvBdM5vm7jVmdh1wHjAtupG7zzWzIXH6nwIURgo8Y2azgBnufjvhh+h9mFkRUBf5GGzWVQoAry3dyg+fXkynDlk8ff2xTDqsW7JDEpHWcxfwirtfYGY5hO/XeynZLOlszpIt/PiZT6kJBDnriL78yykjGD+wS7LDkkNICQyRZqioDbB1dw3DVf9CUpC7bzKz3wMbgGrgNXd/rQVtnjWzocAsM3uW8IPrGQmEMgDYGPW5CJjaSPsXgD+a2YnA3HgNzGw6MH3EiBEJhJG+3J273yrk96+t4siBXbj/8smqcyGSRsysADgJuBLA3ev4MtG7h5LNkpaq64Lc8tJShvXqxF0XTdR0yHYqI9kBiKSCPQU8tQKJpCIz60Z4iO9QoD/QycwuS7QNgLvfAdQA9wDfcPeKREKJs80bauzuVe5+jbvf5O53N9Bmtrtf36WL3r7UBoLcPGsxv39tFTMm9ueZG45T8kIk/QwDSoGHzewTM3vQzDpFN3D3Z4FXCCebLyWcbP5WAueIl2we0Ej7F4AzzeyPNJJsNrP7y8rKEghDZF8Pv7+W0vJafvmNI5S8aMeUwBBphkKtQCKp7XRgrbuXuns94YfN41vQhshoiHHAi8AtCcZRBAyK+jyQ+FNZJEE19UFueHwhsz/dzP87azR/+PZEFS4TSU9ZwFHAPe4+CagEfhrbSMlmSTdlVfXc+/ZqTju8N8cM0coi7ZkSGCLNsLq0gqwMY3CPvKYbi7Q9G4BjzSzPwpWtTgOWJ9rGzCYBDxAeqXEV0N3MbksgjvnASDMbGpm3fRHwUouuSPaqqQ9y3WMLeHtlKbefP55/OWWECpiJpK8ioMjdP4p8fo5wQmMfSjZLuvnzO4WU1wb4yZmjkx2KJJlqYIjEWLZ5N4s37tpn23uF2xjcI4/sTOX8JPW4+0eRwmqLgADwCXA/gJnNAa5trE2UPOBCd18dOfYKIvOwo5nZU8ApQM/I3Ohb3P0hdw+Y2Y3Aq4SLwc1096Wtfb3tSXVdOHnx3upt3PHNI/nWMYOaPkhEUpa7bzWzjWY22t1XEk42L4tuE5VsPhtYCzxhZre5+y+aeZq9yWZgE+Fk8yWtdhEiCdpaVsMj763j3IkDGNOvINnhSJIpgSES5Z8rivn/nlhEXSC0374Ljh6YhIhEWoe730Kct3DuPq2pNlH734v5XE/4ITm23cWN9DEHmNO8qKUxVXUBrn10AR+s2c7vLpige5RI+3ET8GRkJNsawiPioinZLGnlrje/IOTOj84YlexQpA1QAkMk4h9LtnDzrE8Y3TefP118FB1z9p0/3rNzhyRFJiKyr+LdNdz01CcsWLeDO781gfMmKXkh0l64+2JgciP7lWyWtLGmtIJnFmzk8mMHM6i7pnKLEhgiAPxt8SZ+9MynTBjYhYevmkKXjtnJDklEZD/BkPP4B+v4/WurqA+G+N9vT2TGxMYWBxAREUld//P6KjpkZfC9U7VcuoQpgSHt3jPzN/JvL3zG1KHdeeiKY+jUQX8tRKTtWVJUxs9fXMKSTWWcOLInt507jsE9OjV9oIiISApasG4HL3+2hZu/OoJe+RoJLWH6TU3atcc+WMd//m0pJ43qxX2XHb3ftBERkUOprLqef64oZkdlPfXBEPWBEPXBEJt21fDiJ0X06NyBP148iXOO7KeVRkREJC0FgiHun7eGP7z+BX0KOnDtScOSHZK0IUpgSLv157cLueOVlZw+pg93XzqJDllKXojIoRcIhpj7RSnPL9rE68uK4xYR7pidyaVTB/OTM0dripuIiKStL4rL+cmzn/JpURlfH9eXW88dR0Gu/t2TLymBIe2Ou/O7V1fy57dXM2Nif35/4QQtjyoih9zyLbt5bmERf1u8iW0VdXTLy+biYwZx7qQBDOvZmZysDLIzjcwM02gLERFJW+7Ojso6nllQxP++vopOHTI12lAapASGtCuhkPNfs5fy6AfruXjKYdx27jgyM3RjFJFDY1dVHS99uplnFxSxZFMZ2ZnGVw/vzTePGsgpo3uTk6VkqoiIpKf6YIgVW8pZtGEnyzbvZtOuajbvqmbTrmpqI6MPzzoiPOpCNS+kIUpgSLsRCIb46QtLeG5hEdedOJSfTxujrK5IG2ZmGcCtQAGwwN0fTXJICSurrufzTWV8VlTGog07eWdlKXXBEGP6FXDL9LHMmDiA7p1ykh2miIhIq3N3Fm/cxWvLilm4fiefFe2ipj6cqOjZOYeB3fIY06+A08b0pn/Xjozum89xw3ro+VwapQSGtAv1wRA/mLWYl5ds4Yenj+Lm00bo5ijtipn9ELgWcGAJcJW718S06Qo8CIyLtLva3T9o4flmAucAJe4+Lmr7WcBdQCbwoLv/tpFuZgADgB1AUUviONTcnY/W7uD5hUXMX7eDddur9u47rHsel0w9jAuOHsi4AV2SGKWIiMjBU7Szir9+sokXFm1izbZKsjKMI/oXcPGUwzjqsG4cNbgb/bvk6llcWkQJDEl7dYEQNz21iFeXFvPv08ZwnSoZSztjZgOAm4Gx7l5tZs8AFwGPxDS9C3jF3S8wsxwgL6af3kC1u5dHbRvh7oVxTvsI8Cfgsai2mcDdwBmEExLzzewld19mZuOB22P6+Bj4wN3vM7PngDcTvPRDpmR3Dc8tKuLZBUWs3VZJfocsjh/RgwsnD+LIgV0YP6ALXfM00kJERNJXYUkFv/jrEj5cswOAqUO7c8PJw/j6+H4qxCmtpl0lMMzsFMLDkZcCs9z97aQGJAddbSDI955cxBvLS7hl+liuOmFoskMSSZYsoKOZ1RNOTGyO3mlmBcBJwJUA7l4H1MX0cTLwXTOb5u41ZnYdcB4wLfZk7j7XzIbEbJ4CFLr7msg5ZxEeZbHM3ZcQHrERHdNlUTEEE7nYQ2Xh+h3cP3cNbywvIRhypgztzo2njmDa+H5alllERNqNjTuquPTBDwkEnR+fMYpzJw1gUPe8pg8USVDKJDBaaTiyAxVALikyHFlarqY+yHefWMhbK0u5dcYRXH7ckGSHJJIU7r7JzH4PbACqgdfc/bWYZsOAUuBhM5sALAS+7+6VUf08a2ZDgVlm9ixwNeHRFM01ANgY9bkImNpI+xeAP5rZicDceA3MbDowfcSIEQmEcWBCIeefK0q4953VLFi/ky4ds7n2xKF8e/IghvXqfMjiEBERaQtKdtdw2UMfUVMf4pkbjmN03/xkhyRpLGUSGCQwHJlwMiN2KPLVwDx3f8fM+gB3Apcegrilhdx9b6GfRNUFQtz41CLmfbGN35w3nkumHtbK0YmkDjPrRnikw1BgF/CsmV3m7k9ENcsCjgJucvePzOwu4KfAf0T35e53REZO3AMMd/eKREKJs80bauzuVcA1jXXo7rOB2ZMnT74ugTha7OXPtvCHN1bxRUkFA7p25JbpY/nW5EF06pBK/5yKiIi0jl1VdVz+0MeUltfy5LVTlbyQgy5lnrgSGY7s7rcTMxQ5xk6gwbV5zOx64HqAww7TL76H2s7KOl78ZBNPz9/IyuLypg9ogBnc8c0j+dYxg1oxOpGUdDqw1t1LAczsBeB4IDqBUQQUuftHkc/PEU5g7CMyGmIc8CJwC3BjAnEUAdF/IQcSM5WlrQoEQ9z+jxU89O5aDu+bz10XTWTa+H5kZ2rZUxERaZ8qagNc8fB81m6r5OGrjmHSYd2SHZK0AymTwGhAQsORzex84EygK+HRHHG5+/3A/QCTJ09u8O2gtEww5GyvrN3vvesXJRXMmr+RVz/fSl0wxIRBXfnxGaPIzmrZLwhHDujC8SN6tkLEIilvA3CsmeURnkJyGrAguoG7bzWzjWY22t1XRtosi25jZpOAB4CzgbXAE2Z2m7v/oplxzAdGRqahbCJcSPSSA7iuQ6Ksup6bnvqEuatKueqEIfz7tDFkKXEhIiLtUG0gyNayGjbtquZP/yzk801l/PnSozhBz9xyiKR6AiPR4cgvEJ5TLRHuHvn+5bagO9X1QarrglTWBqiqC1Ib2L9+nnv4D9s93M/enwnv2PO5ojZAYUk5q4orWFVczpptldQF4k8NKcjN4pKph/HtYwYxpl9B61+wSDsUmRLyHLAICACfEEnSmtkc4Fp33wzcBDwZWYFkDXBVTFd5wIXuvjpy7BVEin7GMrOngFOAnmZWBNzi7g+Z2Y3Aq4Sn+s1096Wtea2tbe22Sq55dD4btldx+/njuXiKRuWJiEjrc2/dd6bu4Wf6YCj8FQg5oZATinlmd4fa+lD42b8+SE19+Pm/tLyWkvJainfX7P2+eVcN2ypq957DDH5/wQTOPKJvq8Yu0phUT2C0yeHIu6rqWLZlNyu2lLOquJyK2kA4qxK5UYRCX94wQpEdIYdAyKkPhAiEQtQFnUAwtPemEwz53ptQ+OYTvil51I0p+kYV7x745Tm/vHEdSgO6dmRUn86cPKoXA7t1JCNj3/xT97wcTj28N7nZqtwv0trc/RbCUz5it0+L+nkxMLmRPt6L+VxPeERGvLYXN7B9DjCneVEfGnWBELuq6thdE6CqLkBlbZCqugDFu2v571dWkGHwxLVTOXZYj2SHKiIirSwYcnZU1lFaXktpRS2l5bVU1gaoC4SoC4aoC4SoD4aoDYR/ya+pC1ITCL/oqwuGqI96Zq8PfvnMHop6do/lDoFQ+Ni6QGjvudqi7p1y6J3fgd4FuRzRv4B+XTrSv2tH+nfJZWivTvTr0jHZIUo7k+oJjDYzHLk+GOKGxxeyfMtutpTV7N3evVMOXTtmg4WHi2SYYQZG5LsZGRbOYGZlZJCdaWRlZNAxJ4PsDCMz9suMjL3fw/1lWHifGWTu/Tn8OVZGzLkN9razyIAWM8jLyaRjTiZ5OZnk5WSRm50Zd7jLPtcS7mSfz2ZGx+xMhvbqRGcVuRORNuCWv33O4o272FlVz87KOsprAw22HdWnMw9dcYyWghMROcRmvruW15ZtbVbbYCiSCAg6dYFwYiEY3D9xEIoZlRAKOZV1AeLkGPaRlWHkZmeSm51BbnYmHbMzyc3OJCcrg6wMIy8ni8wMIzvzy2f2Pc/nmXsfkveVnZFBTlYG2Znh7zmZtt/LvQOVlRHuMysqni9/FwEiv4fkZoWf+/dcX15OFr3yO9CrcwdyWjiVW+RgSZnfKNv6cOTszAzqgyGmDu3OmH4FHN6vgDH98umdn5uMcEREpAEhhy55OQzt2YlunXLonpdD1045FORm0Skni7wOmeHvOZkM6dlJhTpFRJLAocnEwh5ZGRnk5WWRnZlBh6xwQiAzw/bLG5ixT3Ihw4zOHbLoXRD+Zb1n5Jf2/NysL5MLmRmtnlgQkZZLmQRGKgxHfvyaBuuHiohIG3HrueOSHYKIiDThmq8M5ZqvDE12GCLSxui1koiIiIiIiIi0eUpgiIiIiIiIiEibpwSGiIiIiIiIiLR5SmCIiIiIiIiISJtn7s0s79tOmVkpsD6BQ3oC2w5SOIdKOlwD6DraknS4Bmj8Oga7e69DGYx8qZ3eqyE9riMdrgF0HW2J7tVtlO7VKS0drgF0HW1JU9cQ936tBEYrM7MF7j452XEciHS4BtB1tCXpcA2QPtch6fPfMh2uIx2uAXQdbUk6XIOEpct/y3S4jnS4BtB1tCUtvQZNIRERERERERGRNk8JDBERERERERFp85TAaH33JzuAVpAO1wC6jrYkHa4B0uc6JH3+W6bDdaTDNYCuoy1Jh2uQsHT5b5kO15EO1wC6jrakRdegGhgiIiIiIiIi0uZpBIaIiIiIiIiItHlKYIiIiIiIiIhIm6cEhoiIiIiIiIi0eUpgiIiIiIiIiEibpwSGiIiIiIiIiLR5SmCIiIiIiIiISJunBIaIiIiIiIiItHlKYIiIiIiIiIhIm6cEhoiIiIiIiIi0eUpgiMQwMzezEc1s+3Mze7CR/evM7PTWi05EpH3SvVlEJDXofi0HkxIYkhYiN7dqM6sws2Ize9jMOh/s87r7b9z92tboy8y6mtmjZlYS+fpla/QrIpIsaXJvPtXM3jKzMjNbF2f/kMj+KjNboQdtEUlF7eR+fauZLTGzgJ6zU5cSGJJOprt7Z+Ao4BjgF7ENzCzrkEfVfP8L5AFDgCnA5WZ2VVIjEhE5cKl+b64EZgL/2sD+p4BPgB7AvwPPmVmvQxSbiEhrSvf7dSHw/4CXD1lE0uqUwJC04+6bgH8A42DvMLbvmdkXwBeRbdeZWaGZ7TCzl8ysf0w308xsjZltM7PfmVncvytm9kszeyLq8+Vmtt7MtpvZvycY+nTgDnevcvd1wEPA1Qn2ISLSJqXqvdndP3b3x4E1cc4zivCD/i3uXu3uzwNLgG8mcg4RkbYkHe/Xkf2Puvs/gPJE+pW2RQkMSTtmNgiYRviN2B7nAlOBsWb2VeB24FtAP2A9MCumm/OAyYQfTGfQjESCmY0F7gEuB/oTfhs3MGr/V8xsV1PdxPw8rqnzioikghS/NzfkCGCNu0c/DH8a2S4ikpLS9H4taUIJDEknf43c1N4F3gF+E7Xvdnff4e7VwKXATHdf5O61wM+A48xsSFT7/4603wD8Abi4Gee/APi7u8+N9PsfQGjPTnd/1927NnL8K8BPzSzfwoWPriY8pUREJJWl+r25MZ2BsphtZUB+C/sTEUmmdL5fS5poy3OYRBJ1rru/0cC+jVE/9wcW7fng7hVmth0YAKyL03595Jim9I8+zt0rI/02183AHwkPzdtOeF51c272IiJtWarfmxtTARTEbCtAw5NFJDWl8/1a0oRGYEh74VE/bwYG7/lgZp0ID1HbFNVmUNTPh0WOacqW6OPMLC/Sb/MCDGepL3X3vu5+BOG/nx8393gRkRTU5u/NTVgKDDOz6BEXEyLbRUTSSarfryVNKIEh7dFfgKvMbKKZdSA8PO6jSOHMPf7VzLpF5gB+H3i6Gf0+B5wTmZ+XA/yKBP6OmdlwM+thZplm9nXgeuC25h4vIpLi2uq9OcPMcoHs8EfLjfSDu68CFgO3RLafBxwJPN/c/kVEUlDK3a8j+7Mj+zOArMj+zOb2L22DEhjS7rj7m4Tn1D1PONM7HLgoptnfgIWEH0xfJrwiSFP9LgW+R/imvgXYCRTt2W9mJ5pZRSNdHE24en054cJIl0b6FBFJe2343nwSUA3MIfwWsRp4LWr/RYQL1e0Efgtc4O6lTcUlIpKqUvh+/UBk28WEl72uJlwwVFKIuXvTrUREREREREREkkgjMERERERERESkzVMCQ0RERERERETaPCUwRERERERERKTNUwJDRERERERERNo8JTBERKRNMrNTzGyemd1rZqckOx4RERERSa6sZAfQ1vXs2dOHDBmS7DBEpI1buHDhNnfvdbDPE1lP/TGgLxAC7nf3u+K0Owu4C8gEHnT335rZaPZdh30Y8J/u/ofIMesIL+MbBALuPrmFMc4EzgFK3H1cU3E10pUDFUAuUcuoxaN7tYg0x6G6V0t8uleLSHM1dL9WAqMJQ4YMYcGCBckOQ0TaODNbf4hOFQB+7O6LzCwfWGhmr7v7sqhYMoG7gTMI/+I/38xeirSZGNVmE/BiTP+nuvu2eCc2s95AtbuXR20b4e6FMU0fAf5EONESfXzcuAgnM26P6eNqYJ67v2NmfYA7gUsb+kPRvVpEmuMQ3qslDt2rRaS5GrpfawqJiEgKcfct7r4o8nM5sBwYENNsClDo7mvcvQ6YBcyIaXMasNrdE3mYPxn4m5nlApjZdcD/xYlxLrAjzvFx43L3Je5+TsxXibuHIsftBDokEKeIiIiIpCGNwBARSVFmNgSYBHwUs2sAsDHqcxEwNabNRcBTMdsceM3MHLjP3e/fZ6f7s2Y2FJhlZs8SHiVxRgIhNyeuvczsfOBMoCvhER3x2kwHpo8YMSKBMEREREQkFbW7BIaZZQC3AgXAAnd/NMkhiYgkzMw6A88DP3D33bG74xziUcfmAN8AfhbT5gR33xyZKvK6ma2IjKb4shP3O8xsFnAPMNzdKxIJu7G49tvh/gLwQmMduvtsYPbkyZOvSyAOEREREUlBB5TAaE7BNzPrCjwIjCP8oHq1u3/QwvPFLQyXYFG4GYTfAu6giaJwItI21AaCbN5VQ9HOKop2VlOyu5aqugCVdQGq6oJU1QapDQRb9ZyDuufxqxnjmm6YBGaWTTh58WTkl/xYRcCgqM8Dgc1Rn78OLHL34uiD3H1z5HuJmb1IeMrHPgkMMzuR8P38ReAW4MYEQm8qLhERANyd4t21FJZUUFhSTmFpBVt21ezNeLp/mft8+KopyQlSREQaVVkbYPanm3l+UREPfucYuuRlH3CfrTECo8GCbxF3Aa+4+wWRt3550TsTKAoHcQrDNVaszszGs39huI+BD9z9PjN7DnizuRcqIgfPy59t4c7XVxII7ftCvrouSEl57X7tO2Rl0KlDFh2zM+nUIZMOWZlYvPf7LVTQ8cBvsAeDmRnwELDc3e9soNl8YGRkuscmwtNFLonafzEx00fMrBOQ4e7lkZ+/Bvwqps0k4AHgbGAt8ISZ3ebuv2hm+E3FJSLt3IbtVdw7dzWzP91MeU1g7/aC3CwGdssjK7MVb/TSKiLLXN8KLAVmufvbSQ1IRJJu2ebd/OXj9fz1k81U1AYY1aczm3ZVt5kERoPMrAA4CbgSIFK0rS6m2cnAd81smrvXRIrCnQdMi+3P3edG5nxH21sULnLOPcXqlrn7EsIjNqJjuiwqhgZf2Wpetcih88Hq7fzg6U8Y3qsz4wfk77OvQ1Ym/bt2ZGC3yFf3PPrkdyArs93WID4BuBxYYmaLI9t+7u5zzGwOcG1kGsiNwKuER6bNdPelAGaWRzjhe0NMv32AF8P5EbKAv7j7KzFt8oAL3X11pK8riNzfo5nZU8ApQE8zKwJucfeH3D3QUFwi0r6t2Lqbe94OJy6yMjKYPqE/Ewd1YXjvzozo3ZlenTtgrZmlPgQaW1K6qTaNjWBO5SWvRST9uDtbd9fw6cYyPivaxXurt/Ppxl3kZGVwzvh+XDL1MI4e3K3V7uEHmsBotOAbMAwoBR42swnAQuD77l65t4NDXBSO8HzqP0aGQc9tqJHmVYscGoUl5dzw+AIG9+jE09cf1yqZ2XTm7u8Sv5YE7j4t6uc5wJw4baqAHnG2rwEmNHHu92I+1xMekRHb7uJG+ogbl4i0P8GQ8/7qbTz6/nreWF5MXk4m1544jGu/MpTeBbnJDq81PEKcJaWb2abREcyk6JLXIpIa3J2y6nq2VdRSWl7H9spatlfUUVEboKI2QGXk+87KOj7fvJvSyGjpzAxjTL98fnH2GL551EC6dcpp9dgONIHRVMG3LOAo4CZ3/8jM7gJ+CvxHdCeHuChcFXBNAv2LyEFSUl7DFTPnk5OVycNXts68OBERadvWbqvkuYUbeWHRJraU1dA1L5sfnD6SK48fQte81n/YTZYGRg432aaZI5gb06zRzY3EF3d0s7vfTszI5hgNLnmtkc0iqeP5hUX8cvbSfabxRcvONDp1yKJTThb5uVmcOKInRw7swviBXTmifwG52ZkHNb4DSmA0o+BbEVDk7nuW+HuOcAJjHyoKJ9L+VNYGuOaRBeyorOPpG45lUPfYl0siIpIuAsEQryzdyiPvrWPB+p1kGJw0qhe/OHssp43pfdAfeFNMUyOYU27Ja41sFmn7quoC/OfflvLcwiKmDO3OWUf0pUfnHHp17kDP/A5075RDfm4WHbKSe79ucQKjOQXf3H2rmW00s9HuvhI4DVgW04+KwomkMXdnc1kN9YEQIXdCHt7223+sYOnmMh74zmSOHNg12WGKiMhBUF0X5LmFG3lg3lo27KhiSI88/u2swzn/qAH0SY9pIgdDUyOYU27JaxFp274oLudfnlxEYWkFN582ku+fNpLMjLZZd+hARmA0WPAtupAccBPwZGT+3hrgqph+mlUULrIvbmE4FYUTaXvqgyFe/mwL989dw7Itu+O2uXXGEZw2ps8hjkxERA4Gd2dXVT1bd9ewdXcNizfs4vEP17Ojso6Jg7ry82ljOGNsnzb7UNyGNDqCWUtei0hrKauu5+XPtnDr35fRqUMmj189la+M7JnssBrV4gRGYwXfYgrJLQYarI7c3KJwkX1xC8OpKJxI27G7pp6nP97IzPfWsqWshhG9O/Of54ylW6dsMiLVhzPM6FOQy5Sh3ZMcrYiIbC2r4b3CbSzcsJO6QOCpjlEAACAASURBVGiffSF3auqDVNYGqaoLUFUXpLo+uN/7+PpQiJLdtdTGHH/a4b254eThHDOk9SrQp7vGRjBryWsRSZS7U14boLS8luLdNSzbvJvPispYsqmMtdvCM9OOG9aDuy6amBIFlA/qMqoi0r4UlpRz3p/fp7wmwLHDuvOb88Zz8qheZOhtm4hIm1FdF2TeF6W8V7iNdwu3sbo0/ABbkJtFfu7+xZQ75mTSKSeTvJws+hZkk5uTuTchvUemQa/8DvTt0pG+Bbn07ZLLoG4dU+Jh+GBpZORw9JLXcdvQ8AhmLXktIo0KhpxXl27liQ/Xs357FaUVtfslp/t1yeXIgV244OiBHDmwC8cP75kyo+OUwBCRVvPm8hLKawI8/93jOHqwRleIiLQVu6rqeHN5Ca8u3crcL0qpqQ/RMTuTKUO7c9Exh3HCiJ4c3jdfCedW1MjI4WnNaBN3BLOWvBaRhtTUB3lh0SYemLeGtdsqGdwjj6nDuoeLcHbuQK/88NfIPp3pnZ+6yWUlMESk1awqrqB3fgclL0RE2gB3551VpTz07lreX72dYMjpW5DLtycP4mtH9OWYId3JycpIdpgiItJC7s7yLeW8sbyYxz9cT2l5LUcO7MKfLz2KM4/omzKjKhKhBIaItJpVxeWM7puf7DBERNq1YMiZs2QL97y9mmVbdtO3IJfrTxrGmUf05cgBXTTKQkQkhe2orGPuqlLmriplXuE2SstrAThxZE/u+vZEjhveI61rDimBISKtIhhyvigp59Kpg5MdiqQJMzsFuBVYCsxy97eTGpBIGxIMOa8vK2ZHZd0+28tr6vnLxxtYv72KYb06cccFR3LuxAEaaSEikuJ2VtZx91uFPPbheuoCIbrlZfOVkb04aWRPThrVq90sTa0Ehoi0io07qqipDzGqT+dkh9Iumdkg4DGgLxAC7nf3u+K0Owu4i3Bhtgfd/beR7euAciAIBNy9wdWjmhHLTOAcoMTdxzV17kY4UAHkEl7WT0SAeV+U8uuXl7Nia3nc/UcO7MK9lx3F18b21WgLEZEUV1kbYOa7a7l/7hoq6wJ886iBXHbsYMYN6JKWU0SaogSGiLSKVcXhB+lRfTSFJEkCwI/dfZGZ5QMLzex1d1+2p4GZZQJ3A2cQTgjMN7OXotqc6u7bGjqBmfUGqt29PGrbCHcvjGn6CPAnwgmVJs9tZuOB22P6uBqY5+7vmFkf4E7g0mb/aYikocKScn798nLeWlnKoO4dufuSo5g8pNs+bcygV+cOaT18WEQklQWCIT5cs4OS8pp9trtD0J36YIhAMPx9d3U9f/l4I9sqavna2D785MzR7f5ZWwkMEWkVexIYI9v5TTVZ3H0LsCXyc7mZLQcGAMuimk0BCiNV7DGzWcCMmDaNORn4rplNc/caM7sOOA+YFt3I3eea2ZCYYxs8t7svITxioyE7gQ7xdpjZdGD6iBEjmnkJIqmnsjbA715dyeMfricvO5OfTzucK44fQoeszGSHJiIizeDuLN28mxcWbeKlTzezraK22cdOHdqd+y4/mqMHd2u6cTugBIaItIqVxRUM6NqRzh10W0m2SPJgEvBRzK4BwMaoz0XA1MjPDrxmZg7c5+73x/br7s+a2VBglpk9S3iUxBnNDKuxczd0HecDZwJdCY/o2I+7zwZmT548+bpmxiGSUhas28GPnvmUjTuruGzqYH5w+kh6dI6bzxMRkTbor59s4k9vFVJYUkFOZgZfPbw3504awJh++7/0y8wwsjMzyM7MICvTyMnMIDdbyepo+k1DRFrFF1qBpE0ws87A88AP3H137O44h3jk+wnuvjkyTeR1M1vh7nP3a+x+R2T0xD3AcHevaG5ojZw7Lnd/AXihmf2LpJXaQJD/ff0L7pu7moHdOvL09ccxZaiWqBYRSSVFO6v4ybOfMrJPPr85bzxnj+9Hl7zsZIeV0pTAEJEDVh8Msbq0glNG9052KO2amWUTTl48GfnlP1YRMCjq80BgM4C77/leYmYvEp7ysV8Cw8xOBMYBLwK3ADc2M7wGzy0i+1q2eTc/emYxK7aWc/GUQfz72WM1uk1EJAXd+85qzOChKybTv2vHZIeTFtrdv4ZmlkF4Wb4CYIG7P5rkkERS3rptldQHndF9tQJJsli4Yt9DwHJ3v7OBZvOBkZFpIJuAi4BLzKwTkBGpndEJ+BrwqzjnmAQ8AJwNrAWeMLPb3P0XzQgx7rkTukiRNFeyu4b/feMLnlmwkW55Ocy8cjJfPbxPssMSEZEW2FpWwzPzi7jg6EFKXrSiA1oU3MzWmdkSM1tsZgsaaZdpZp+Y2d8P8HwzzazEzD6P2X6Wma00s0Iz+2kT3cwgPBe7Hi3LJ9IqVu4p4NlbU0iS6ATgcuCrkXvyYjObBmBmc8ysv7sHCI+YeBVYDjzj7kuBPsC7ZvYp8DHwsru/EuccecCF7r7a3UPAFcD62EZm9hTwATDazIrM7JpGzi3S7pXX1PM/r63k5N+9zbMLNnL5sYN57YcnKXkhKcPMTjGzeWZ2r5mdkux4RNqCe99ZTcidfzlleLJDSSutMQKj0WX3Ir5P+IG1IHZHAsvyQesszfcx8IG732dmzwFvNnWBItK4VcUVZBiM6K0RGMni7u8Sv84E7j4t6uc5wJyY/WuACc04x3sxn+sJj8iIbXdxA8fvd26R9sLdKS2vpbSilrKqenZV17Ozqo6tZTU8+dEGdlTWcc6R/fjXM0czuEenZIcrB5mZzSS8+lKJu49LpI2ZdQUeJDydz4Gr3f2D1ozDzM4C7gIygQfd/bdNdOVABZCLXhCKUFJew1Mfb+C8SQMY1D0v2eGklYM+hcTMBhIebvxr4EdxmjRrWT5onaX5zOwyoC7yMdjS6xKRL63aWs6QHp1UJVlEJOK9wm28sbyYjTuqWL+9io07q6ipD8Vte/zwHvzbWYczYVDXQxylJNEjxLyUS6DNXcAr7n6BmeUQHh23jwReEO53jha8HLwamOfu75hZH+BO4NJGrksk7T04by31wRDfO1XLvLe2A01gNLnsHvAH4P8BcceWH+CyfJD40nwvAH+MFKLbr0DdHmY2HZg+YoT+pxNpyqrickb10fQRERGANaUVXPnwx2RnZnBY9zyG9uzEKaN7Mah7Hr3zc+malx3+6phDl47ZdMxR8re9aeClXJNtzKwAOAm4MtKmji9fzEVr1gvC1ng5GGMnsN86v3qulvZke0Utj3+wnhkTBzCkp0bUtbYDTWA0uuyeme0ZkrawsflwB7AsHyS4NJ+7VwHXNNWpu88GZk+ePPm6BGIRaXdq6oOs217JOUf2S3YoIiJJ5+78cvYycrMy+edPTqFX/n6/y4kciGFAKfCwmU0AFgLfd/fK6EYH+IIw0ZeDmNn5wJlAV8IjOvah52ppTx56dy01gaBGXxwkB1TEM3rZPcJL6k2JaXIC8A0zWwfMIlxc7onYfuIsy5cILc0nkkSrSysIOYzqqxEYIiKvLi1m7qpSfnjGKCUv5GDIAo4C7nH3SUAlELeAvbvfAdQQfkH4jQReECb0cjByrhfc/QZ3/7a7v93M84iknV1VdTz6/jqmje+n2nAHSYtHYDRn2T13/xnws0j7U4CfuPtlMf0cyLJ8oKX5RJJqVWQFktGaQiIi7Vx1XZBb/76Mw/vm853jBic7HElPRUCRu38U+fwcDSQw4rwgvDGBc+jloLQLa7dV8m5hnPUo3PHwNzzyc3MsXL+TyrogN31Voy8OlgOZQtIHeNHM9vTzlz3L7pnZHODaPSM0mrB3Wb7IsVcQmdcXK7I03ylATzMrAm5x94fMbM/SfJnATC3NJ3LorCquIDvTNMdPRNq9e94uZNOuap6+/liyMg9okKtIXO6+1cw2mtlod18JnAYsi213gC8I9XJQ2o1/e+4zPl63o1X7nD6hP4f33W/xTWklLU5gNLbsXvSSfVHb3gbejrO9WcvyRfZpaT6RNmbV1nKG9exMth7WRaQdW7+9knvnruHcif2ZOqxHssORNq6Rl3J7XwI21Aa4CXgysgLJGuCqOKdo1gtCvRyU9mxHZR0L1u/ghpOGce2Jw/bbbxaeT2Vmke/N67cgN7tV45R9HfRlVEUkva0sLmfSYd2SHYaISFL91+xlZGcYP5s2JtmhSApo5KXctGa0WQxMbqL/Zr0g1MtBac/eWlFCyOHsI/upZlEK0StTEWmxytoARTurGd1HRYqk9ZnZKWY2z8zubWwlK5Fke2NZMf9cUcIPTh9Fn4LcZIcjIiLN8MbyYvoUdGBc/y7JDkUSoASGiLTYFyXhguYjVcDzkDGzQWb2lpktN7OlZvb9BtqdZWYrzazQzH7anGPNbJ2ZLTGzxWa24ABinGlmJWb2eXPiaoQDFUAu4aJyIm1O8e4afvHXzxnRuzNXnjAk2eGIiEgz1AaCzF1Vymlj+pCR0cy5IdImaAqJiLTYqq1agSQJAsCP3X2RmeUDC83sdXffW8TNzDKBu4EzCP/iP9/MXgJ2NnUscKq7xynHDWbWG6h29/KobSPcvTCm6SPAn4DHYo5vKK5M4PaYPq4G5rn7O2bWB7gTuLTJPx2RQ6iyNsDVj8ynvKaemVceo1pAIiIp4sM1O6isC3L6mN7JDkUSpH9pRaTFVhaXk5udwaDueckOpd1w9y3uvijyczmwHBgQ02wKUOjua9y9DpgFzGjmsY05GfibmeUCmNl1wP/FiXEuEK+kd0NxLXH3c2K+Stw9FDluJxB3cqqZTTez+8vKyhK4DJEDFww5Nz/1Ccu37OZPlx7F2P6qOC8ikireWFZMx+xMjh/eM9mhSIKUwBCRFltVXM7I3vlkauhdUpjZEGAS8FHMrgHAxqjPRcQkKho41oHXzGyhmV0fez53fxZ4BZhlZpcSHiXxrQRCbjKumBjPN7P7gMcJj+jYj7vPdvfru3TR/FU5tG79+zLeXFHCf80Yx6mj9QZPRCRVuDtvLi/mxJE9yc3OTHY4kiBNIRGRFltVXM4JI5S5TgYz6ww8D/zA3XfH7o5ziDfj2BMiS/f1Bl43sxWR0RRfduJ+h5nNAu4Bhrt7RSJhNxbXfjvcXwBeSKB/kUPi4ffW8sj767j2K0O5/NjByQ5HREQSsGzLbjaX1fCD00clOxRpAY3AEJEWKauqp3h3repfJIGZZRNOQDwZ+SU/VhEwKOrzQGBzU8e6++bI9xLgRcJTPmLPfSIwLrL/lgRDbzAukVRQXRfk6fkb+NXfl/G1sX20ZKqISAp6Y1kJZnDq4Ro9l4o0AkNEWmTplnDNgVF9lcA4lMzMgIeA5e5+ZwPN5gMjzWwosAm4CLiksWPNrBOQ4e7lkZ+/Bvwqps0k4AHgbGAt8ISZ3ebuv2hm+HHjauaxIoecu7O6tJJ3VpXy9soSPlq7g7pAiAmDuvKHiyZq+pyISAp6c0UxEwd1pVd+3PJa0sYpgSEiLfLA3DUU5GZx9OBuyQ6lvTkBuBxYYmaLI9t+7u5zzGwOcG1kGsiNwKuEV/iY6e5LzewrDR0L9AFeDOc4yAL+4u6vxJw7D7jQ3VcDmNkVwJWxAZrZU8ApQE8zKwJucfeH3D0QL67W+EMRaW019UGue2wB874IL8ozondnLj92MCeP6sWxw3qQk6VBrCIiqWZrWQ2fFZXxr2eOTnYo0kJKYIhIwj5YvZ23Vpbys68fTkFudrLDaVfc/V3i15LA3adF/TwHmJPAsWuACU2c+72Yz/WER2TEtru4kT72i0ukrQkEQ9z01Ce8W7iNfz1zNN+Y0F+rLYmIpIE3VxQDcMbYPkmORFpKrw9EJCHuzm//sZz+XXK54vghyQ5HRKRVuTs/f3EJry8r5pfTj+B7p45Q8kKkEWZ2ipnNM7N7zeyUZMcj0pg3l5cwqHtHRvbunOxQpIWUwBCRhPzj8618WlTGD88YpaWnRCTt/PaVFTyzoIibTxupJK0cEDObaWYlZvZ5om3MbJ2ZLTGzxWa2oLn7Wis+MzvLzFaaWaGZ/bSJrhyoAHIJF2sWaZOq6gK8W7iN08f0ITJlVlJQu0xgmFmGmf3azP4YmcMtIs1QHwzxu1dXMrpPPucfNTDZ4YiItKr7567mvnfWcPmxg/nh6SOTHY6kvkeAsw6gzanuPtHdJyeyz8x6m1l+zLYRzT23mWUCdwNfB8YCF5vZWDMbb2Z/j/nqDcxz968D/wb8V8OXKpJc877YRl0gxBljNH0klR1wDQwzWweUA0EgEHsjNbNBwGNAXyAE3O/ud7XwXDOBc4ASdx8Xs+8s4C7CheEedPffNtLVDGAAsANlikWabdb8jazdVsnMKyer+r6IpLyyqnrWbKtg3fZKPisq4+H31nHOkf345TeO0Ns5OWDuPtfMhhxomxY4GfiumU1z9xozuw44D5gW3aiRc08BCiO1kTCzWcAMd7+d8HN4Q3YCcZd1MLPpwPQRI+LlUUQOvq1lNdz9ViH5uVkcM7R7ssORA9BaRTxPdfdtDewLAD9290WRbPBCM3vd3ZftaRDJ3la7e3nUthHuXhjT1yPAnwgnRIhquydTfAbhhMR8M3uJcDLj9pg+rgZGAx+4+31m9hzwZmKXK9L+VNYGuOuNL5gytDunjta62SKSmkIh5/Z/LOf5RZvYUVm3d3uGwVlH9OXOb2l5VGkTHHjNzBy4z93vb+Y+3P3ZyHLVs8zsWcLPvmckcO4BwMaoz0XA1IYam9n5wJlAV8LP6ftfjPtsYPbkyZOvSyAOkVYx74tSfjBrMdX1Qf7/9u48vqrq3v//65OQBMI8I/MogiCgiFiqYquCOHDFWscW69DW1ntte6tX7/XWX+vst7Vaa60D1FnqgFdtKWJVBK0ooCizzBCCJIxJCBnP5/fH3ughZCQhZ8j7+XjkkZy919n7s0QWJ5+91mf97qIRpKU2yUUISeOI70Li7tuAbeHP+Wa2kmBgXBHVrFEzxeG2fgc+tZRXFrcyxSIHe2L+BnYUFPP490/Qk0kRSUhl5RFufPlzXv10K5OGd2Nkr3b069SKfp1a0qtDCzKaqa6PxI1x4ZbYXYC3zGyVu8+rxTkA3P2+8PPwI8AAdy+ow70r+0feq2rs7jOBmXW4vkijKI84f3h7DX94Zw2DurTiT5cfz8AurWt+o8S1hkhgVJsFjhYmH0YBHx10gUbOFBMMsg+Z2SnAvMoaKFMs8rXc/GIem7eOs4d1Y1Tv9rEOR0SkzorLyrnhhSXMXv4lN04YzE9P1wMKiV/unh1+zzGzVwke1s2r6dwB4WfcYcCrwG3A9XW4fRbQK+p1TyD78Hoi0nhKyiLs3V/K3v0l7NpXyh/eXsP7a3cw5fge3PFvw8hMP+LP7qURNMSfYo1ZYAAzawW8AvzM3fMqnm/kTHEhcHUdri/SpN32+jJKy50bJwyOdSgiInVWVFrOj55ZzHtf5PK/5w7l6m/2i3VIIlUys5ZASjhzuSVwFvCbms5FvX8U8DhwDrABeNbM7nD3W2sZwkJgUPhwcStwCXBZA3RN5Ih46l8b+X9vrqaguOyg4xnNUrj3wuF8d3QvzR5OIvVOYNQyC5xGkLx4LpxmdghlikXi098/38aspcETy/6dtWe2iBxZxWXl5BeVEXHHneCr6mcSNSotc2565TM+2rCLe6YM55IxvRswWpGqmdkLwHigU7h8+TZ3n2Zms4BrwgeAh7QB3gVeDX/hagY87+6zw8t2rebcAZnARe6+LoxjKnBlbeNz9zIzux54k6Ce3HR3X94Q/01EGtr63ALu/PtKRvRqyymDOtM+M422mem0a5HGwC6t6N6uRaxDlAZWrwRGLbPABkwDVrr7/VVcR5likTi0s6CYX722jOE92vKjU/vHOhxpYsxsPHA7sByY4e5zYxqQHLZIxPl44y4+XLeTorJySsoilJRFKC6LsL+knNyCYnYUFJObX0x+UVnNF6yj1BTjgYtHMnlkjwa/tkhV3P3SKo5PqqkNMKKK966v6lxUmw8qvC4l+Jxdq/jCc7OAWdXdRyTW3J1fvbacjGYpPHz58XRp3TzWIUkjqO8MjCqzwAeyy0B/4HvAUjNbEr7vv8OB8QBlikXi0G2vLyevqJTnLxpLM1VsTmpxuuW1AwVAc7TldULK2l3IK4u38sonWWzeVQhAerMUMlJTyEhLIT01hRbpqXRslcGQbm04ZWA6nVpl0DYzjRQzzMA48P3wDTmqDSN6tWuYTomISFx44/NtvL92B78+/1glL5qQeiUwqssCR2WXs6nhc4cyxSLxZ/aybfzt823855lHM7ibKjY3AfG45fV8d3/PzLoC9wOXN0A/5Qhwd3Lzi9m0q5CNO/axaWchizft5sP1OwH4xoCO/PzMQUw4tpuKqImISL3lFZVy+99WMLxHW64Y2yfW4Ugj0qcIETnE7n0l3Pp/yzi2ext+PH5ArMORRhCPW15H2Q1kVHZCW17HVml5hD+9u47H568/qHhaaorRr1NLfn7G0Vx4Qg96ts+MYZQiIpJs7p/zBTsKipk2dTSpKSrQ2ZQogSGSwIrLyikoKmNfcTkRP/widxX9ds5q9hSW8szVJ5GmpSNNTrxseW1mU4AJQDuCGR2H0JbXsbMiO49fvvQZK7blMfHYbpw8oCN9OmbSt2NLerRvobFDRESOiGVb9/L0hxu54qQ+HNdTywObGiUwROLc/pJylmfv5bOsvXyetYfl2Xns2ldCQVEZJeWRI3bfn59xNEOOanPEri/xKc62vJ4JVLpzlcTOgVkXD72zhnaZ6Tz6vROYcGy3WIclIiJNQHnE+Z9Xl9KhZQa/nDA41uFIDCiBIRIDP5vxKcuz83CCteMOlf4aVxZxsnYXEgnPdWvTnGE92jK2fwdaZaTRunkzWmU0IzM9lWapDTd9rnVGGqcf06XBrieJQVteS02ydhfyo2cWszw7j/NHdOfX5x9L+5bpsQ5LRESaiOnvb+CzrL08cPFI2rZIi3U4EgNKYIg0sg079vF/S7IZ2asd3ds1xwjK6xsQ7ujzFQMmj+zOcT3bMaJnW7q0UYVlOTK05bXUZGdBMd+f9jE7Cor58xUnMHGYZl1I02Fm3wQGuftfzKwz0MrdN8Q6LpGmZNbSbdz1j5WcNbQrk0d2j3U4EiNKYIg0srmrcwB48JKR9OnYMsbRiHxlHNryWqpQWFLGVU8tYuue/Tx7zUmc2LdDrEMSaTRmdhswGhgM/AVIA54lGDdFpBEsWL+Tn81YwvG92/PgJaMOeegnTYcSGCKNbO7qXPp1aqnkhcQVd38fbXktlSgtj3Dds5+wNGsPj35vtJIX0hRdQFDY+BMAd88Ot5sWkUaw6ss8rn16Eb07ZjJt6mhapKfGOiSJIZUIF2lERaXlLFi/k9OO7hzrUEREahSJOP/18ue890Uud10wnDOHdo11SCKxUOLuTlitysz0BKICMxtvZvPN7M9mNj7W8Ujy2LpnP1Onf0xmeipPXTWGdpmqu9TUaQaGSCP6cP1OissijB+sBIaIxL97Z69i5qdb+c8zj+aSMb1jHY5IrLxoZo8C7czsWoItpA+ZfVYXZjYdOBfIcfdhdWljZhuBfKAcKHP30Q0dh5lNBB4kWO73hLvfU8OlHCgAmhMUbJYkU1IWoaisnNKyCKXlTml5hOKyCCVlEYrLyikuC16XljXcDnlO8O9QYUk5L/34ZHq0a9Fg15bEpQSGSCN6b3UuGc1SGNu/Y6xDERGp1ouLtvDovPV8/+Q+XP+tgbEORyRm3P23ZnYmkEdQB+NX7v5WPS/7JPBH4OnDbHO6u++o6o1m1gXY7+75UccGuvvamu5hZqnAw8CZBMmIhWb2uruvMLPhwN0VrnEVMN/d3zOzrsD9wOXV9EsSzIL1O7nqyYUUlpQ3+r3Tm6Xw9FVjOKZbm0a/t8QnJTBEGtHc1TmcPKAjzdO0dk9E4te63AJue205J/fvyG3nHatiadKkhUtG3nH3t8xsMDDYzNLCOkCHxd3nmVnf+rapxmnAdWY2yd2LwpkjFwCTanGPMcBad18PYGYzgMnACndfSjBjoyq7gYzDjFniUCTi3PH3FbTPTOcXZ/YlvVkKaakHvoyMZqlkpKWQkZpCRlpw3KovqVUnXdtkaBc+OYgSGCKNZOOOfWzcWciV3+gb61BERKpUXFbODTM+pXlaCr+/eCSpKUpeSJM3DzjFzNoD/wQWARcTu1kGDswxMwcedffHDmng/lK4ZfUMM3uJYJbEmbW8fg9gS9TrLOCk6t5gZlOACUA7ghkdFc+fB5w3cKBmcyWaWcu2sWxrHvd/dwRTju8Z63BEVMRTpLEc2D51/OAuMY5ERKRqv31zNcu25nHvhcfRra2eeokA5u6FwBTgIXe/ABgaw3jGufvxwNnAT83s1Moauft9QBHwCHC+uxfU8vqVZS29uje4+0x3/5G7X+zucys5/4a7/7Bt27a1DEHiQWl5hN/N+YLBXVszeWSPWIcjAjTRBIaZpZjZnWb2kJlNjXU80jTM/SKXvh0z6dtJxctFJD7N+yKXx+dv4IqxvTnr2G6xDkckXpiZnUww4+Lv4bGYzWJ29+zwew7wKsGSj0OY2SnAsLDNbXW4RRbQK+p1TyD7sIKVhPbSoiw27NjHjRMGazaexI1GSWCY2UYzW2pmS8xsUT2uM93McsxsWSXnJprZajNba2Y313CpyQTT40pRpWRpBEWl5Xy4bqdmX4hI3NpRUMwvXvyMQV1aces5sXy4LBJ3bgBuBma6+/JwacY7sQjEzFqaWesDPwNnAZV9Lh5FsFPKZOAHQAczu6OWt1kIDDKzfmaWDlwCvN4Q8Uvi2F9SzoNvf8EJfdrz7SH6/CrxozGzx1VWS65PpeSwbaXVkgm2fqqsUvJg4EN3f9TMXgbePuxeidTCgnD71NO0fapIrZnZeOB2YDkwo7JpyVI1dyc3v5gtu/dTHql29jcAD7+7lryiUp69ZowKDYscrBCI6SbV1gAAIABJREFUAJea2RUESyxq/ktVDTN7ARgPdDKzLOA2d59mZrOAa9w9u7I2wLvAq2Fh3WbA8+4+u5JbZAIXufu68H5TgSvrEMf1wJsEn6Wnu/vy+vRXEs9TH25ke14xD116vAo5S1yJlyKe9amUDFVUS3b3u6mkUnI4QJeELyvdD0jFhqQhzQ23Tz1Z26dKAzCz6QRjW467D6uizQ3AtQQftB939wfC6vl/jWrWn2A7wAfC92wE8gnGxTJ3H93Q8ZnZROBBgg/FT7j7PdVcyoECoDmaLVej0vIIT8zfwOdZe9i4s5BNO/fVecu7X59/rLaqEznUc8AvCWY6RBrigu5+aRXHJ9XUBhhRi+t/UOF1KcGMjNrGMQuYVdN9JDntLSzlT++u5fTBnRnTr0OswxE5SGMlMKqtllzPSslQ92rJM4GHwrWB8yoN2P0N4I3Ro0dfW4c4RCr13he5jO2v7VOlwTxJJbPRDjCzYQTJizEEydrZZvZ3d18NjAzbpAJbCdZGR4un2XLz3f09M+sK3E/sKv4nhOcWbOLe2avo16kl/Tq1ZGz/DvTr1JJe7TNJb1bzitG2LdIY1kMF9kQqkRt+LhRpEv48bx15RWXcOOGYWIcicojGSmCMC6fCdQHeMrNV7n5Q4sDd7wtnTjwCDKhDpWSoY7XksJL01XW4vshh27RzHxt27OP7J/eJdSiSJKqZjXbAEGBBONZhZu8RzGq7L6rNt4F17r6pDrdu1NlyUXYDGXWIs8nZu7+UB99ewzcGdOS5a07SdF+RhnWbmT1BsOS4+MBBd58Zu5BEGkZRaTlbdhWyOfzatLOQGQs3M3lkd4Z214w8iT+NksCIrpZsZgeqJR+UwKikUvL1dbiFqiVL3Jq7OhfQ9qnSqJYBd5pZR2A/QYKhYgHlS4AXKhyLq9lyZjYFmAC0I5jRUVkbLfcD/vTuWvbsL+V/zhmi5IVIw/sBcAyQxtdLSJxgRq9IQtq7v5SH3l7D0x9uoqT865VRmempDD2qDTdOGBzD6ESqdsQTGGGF5BR3z4+qlvybCm0OVEo+B9gAPGtmd7j7rbW8zVfVkgmmRF8CXNZQfRCpjR0FxSxYv5Pd+0oOOv7KJ1n06ZhJP22fKo3E3Vea2b3AWwQ1JD4Dyg6cD6vKnw/cUuGt8TZbbiY1/IKg5X6wZVchf/lgI1NG9eTY7loCInIEjHD34bEOQqQhlJVHeGHhFn7/1hfsLizhwuN7csqgTvTqkEmfDpl0aJmuRLjEtcaYgdGVmqsl16tSsruXqVqyNLb9JeV8vHEXH6zdwfw1O1i5La/KtteNH9CIkYmAu08DpgGY2V0cXATzbOATd99e4T2aLZeA7ntzNSkp8MsJR8c6FJFktcDMhrr7ilgHIlKdSMQpKiunsKSc/SXllJZHiLhTHoHyiJO1u5DfzlnNF9sLGNu/A/977lAlviXhHPEERrjWudpqyfWtlByeU7VkOeLcnaVb9/LCx1t447NsCorLSE9N4YQ+7blxwmC+MaAjvTpkHvQeAzq0TI9NwNJkmVmXMBHRG5gCnBx1+lIqLB/RbLnE9Onm3bzxWTb//q2BHNW2RazDEUlW3wSmmtkGghoYBri7HxfbsKSp2bWvhIUbd7F5ZyHZe/eTvWc/2/YW8eXeIgqKy2q181Sfjpk8+r0TOGtoV820kIQUL9uoisS1vKJSXvt0Ky98vIUV2/JonpbCOcO7c/7I7ozp24EW6dpdRBpPVbPRzGwWcE04k+KVsAZGKfBTd98dvjeToG7FjypcVrPlEoy7c+ffV9KpVQY/Ok2zvESOoImxDkCanrLyCHv2l/Lp5j38a90OPly3k1VffrUJGC3TUzmqXQuOatucY7q1pk3zNDIzmpGZnkpmeiot0lJJS00hJcVINSM1xchIS+EbAzqS0UyfWyVxKYEhUo3yiPPCx5v57ZzV7Cks5djubbj934Zx/ojutG2RFuvwpImqajaau0+K+vmUKtoUAh0rOa7ZcgnmzeVfsmjTbu66YDitMvTPuciRUsfdmkTqpLQ8wqyl2/jrwi1k79lPQXEZBcVlFJV+XVgzo1kKo/sGs33H9u/IwC6taNO8mWZQSJOkTzwiVVi8aRe/em05y7PzGNu/A7ecPYQRvdrFOiwREZZn7+WuWas4umsrvju6Z6zDERGROtpZUMwLH2/mmQWb2J5XTN+OmYzo1Y6WGc1oFfU1tHsbRvVup1kTIiElMEQqyMkv4p5/rGLmJ1vp1qY5D106inOPO0pZbhGJqUjEeXtVDtPeX8+C9bvITE9l2tQTaZaaEuvQRESklsojzu1/W8HzH2+mpCzCKYM6cfeU4Yw/ugspKfqsKVITJTBEQpGIM2PhFu7+x0qKSsu5bvwArj99IC01NVtEYqisPMKMhVuY9v4GNuzYR/e2zfnvScdw8Ym9tZRNRGLOzMYDtwPLgRnuPjemAcW5e/6xkif/tZGLTujJD0/tz6CurWMdkkhC0W9mIsC63AJumbmUjzfs4qR+HbhrynAGdG4V67BEpIlbnr2Xm19ZytKtexnRqx0PXTqKicO6kaZZFyJxz8ymA+cCOe4+rK5tzCwVWARsdfdzo45vBPKBcqDM3Uc3dHxmNhF4kKDg8hPufk81l3KgAGjOwVt2SwUzPt7M4/M3MPXkPvx6cqX/S4hIDZTAkCatpCzCo++t46F319K8WQr3Xjic747upeUiIhJTRaXl/OHtNTw6bz3tM9N4+LLjmTS8m8YmkcTyJPBH4OnDbHMDsBJoU8m50919R2UXNLMuwH53z486NtDd19bm3mHi5GGCHauygIVm9jpBMuPuCte4Cpjv7u+ZWVfgfuDyyuJq6v61bge3/t8yTj26M/977tBYhyOSsJTAkCZh7/5SnvlwI4s37WZ3YSl795eyu7CEvftLcYdzhh/FbecPpUvr5rEOVUSakD2FJeTkF1NW7kTcKY84OfnF3D1rJet37OM7J/Tk1nOG0C4zPdahikgdufs8M+t7OG3MrCdwDnAn8Is63vo04Dozm+TuRWZ2LXABMCm6UTXxjQHWhrtTYWYzgMnufjfBjI2q7AYy6hhrk7Bhxz6ue/YT+nZqyR8vG6XaRSL1oASGJLXd+0qY9v4GnvrXRvKLyzimW2s6t86gZ/sWtM9Mp31mGif07cBpR3eOdagi0sSsyM7jO3/+F4Ul5Yec69m+Bc9cPYZTBmlsEmmiHgBuAiorkODAHDNz4FF3f+ygk+4vmVk/YIaZvUQwS+LMOty7B7Al6nUWcFJVjc1sCjABaEcwo6OyNucB5w0cOLAOYSSHvYWlXP3kQlIMpk89kTbNVbtIpD6UwJCklJtfzBPz1/PMgk0UlpRz9rBuXP+tgRzbvW2sQxMRIa+olJ88t5hWGc2458LjSE81UsxITTHSUlMY3bc9men6J1qkKTKzA3UpFocFMisa5+7Z4VKRt8xslbvPi27g7veFMyceAQa4e0FdQqjkmFfV2N1nAjOru6C7vwG8MXr06GvrEEdCyS8q5fOsvWzdvZ8d+4rZkV/CjoJilmXvZcvuQp67Ziy9O2bGOkyRhKdPR5JU1uUW8MT89bzyyVbKyiOce1x3rv/WQI5WhWcRiRPuzi9f/Iys3fuZ8cOxjO7bIdYhiUh8GQecb2aTCApjtjGzZ939CgB3zw6/55jZqwRLPg5KYJjZKcAw4FXgNuD6Otw/C+gV9bonkH2YfUla2/OKmLs6h0837+GTzbtZk1OAR6V5Wqan0ql1Bp1aZXDThMGM6aexXqQhKIEhSWHxpl08+t563lq5nbTUFC48vifXntKP/tpJRETizGPz1jNnxXZuPWeIkhcicgh3vwW4Bb7aovSXB5IXZtYSSHH3/PDns4DfRL/fzEYBjxPU0NgAPGtmd7j7rbUMYSEwKFyGshW4BLis3h1LInlFpZz70Pvk5hfTtkUao3q345zh3RnZux39O7WkU6sMWqSnxjpMkaSkBIbEtbLyCLkFxWzbW8SX4df2vCJy84vJyS8Ovxexu7CUti3SuP70gXz/5L50bq0aUiKJLvzgfjuwHJjh7nNjGlADWLB+J/e9uZpJw7tx9Tf7xTocETmCzOwFYDzQycyygNvcfZqZzQKuCZeBVNqmmst2BV4NdyRqBjzv7rMrtMkELnL3dWEcU4Eraxufu5eZ2fXAmwQ7j0x39+WH9R8hST38zlpy84t57pqT+MaAjtohSqQRKYEhcamkLML/98Zy/rpwC+WRg5ddpqem0Ll1Bp1bZ9CnYyaj+7bnmKPaMGVUD1pm6H9pabrMbDpBhfgcd690g3kzuwG4lmCN8+Pu/kB4fCOQD5QDZe4+uqHjMLOJwIMEH4ifcPd7ariUAwUEU6izDjeeeJGTV8T1z39Knw6Z3HvhcfrAK5Lk3P3SKo5PqqlN1Pm5wNyo1+uBETW854MKr0sJZmTUKr7w3CxgVnX3aao27tjH9A828J0TejJuYKdYhyPS5DTJ3/bMLIXgqV4bYJG7PxXjkCTK7n0l/PjZxXy0YReXjunF8B7t6NY2g25tWtCtbXPaZ6bpg79I5Z4kqAD/dGUnzWwYQfJiDFACzDazv7v7mrDJ6e6+o6qLhwXj9rt7ftSxge6+tqY4zCwVeJigEn4WsNDMXnf3FWY2HLi7wjWuAua7+3tm1hW4H7i8us7Hsy+253Pjy5+zr7iM5645idaqQi8ikpDu/sdK0lJTuGnC4FiHItIkNUgCI/xgugjY6u6H7A9tZj8HriF4mrYU+IG7Fx3Gfap8uljHJ3uTCbaI2kUSPNVLJmtzCrj6qYVs21vEg5eMZPLIHrEOSSRhuPs8M+tbTZMhwAJ3LwQws/eAC4D7anmL04DrzGySuxeZ2bXh+ydFN6oijjHA2vDpIWF1/MnACndfSjC2V2U3UOm6sHjfmm/jjn088M8veO2zbFqmN+P+745gcDcVFRYRSUT/WreDN5dv58YJg+nSpnmswxFpkhpqBsYNwEqCGQ0HMbMewH8AQ919v5m9SFAM6MmoNof9VC9sW+mTPYJkRmVP9QYDH7r7o2b2MvB2XTssDW/+mlx+8twnZDRL4YVrx3JCn/axDkkk2SwD7jSzjsB+gsTDovCcA3PMzIFH3f2xim9295fCom4zzOwlgvH0zFreuwewJep1FnBSdW8wsynABKAdwdh/iHjdmi97z37+8PYaXlqcRVqq8cNT+/PjUwfQvmV6rEMTEZHDUB5xfvPGCnq0a6EaRiIxVO8Ehpn1JKhyfCfwi2ru08LMSgkKC1Xciqk+T/Wgiid77n43lTzVCwsVlYQvy6voV1w/1UsUJWURFm7cRXFZOWXlTlkk+CoqLWdHQbBH9s59xewoKGbB+l0M6tKKJ6aOpmd77ZMt0tDcfaWZ3Qu8RVBb4jOgLDw9Liwo1wV4y8xWufu8Sq5xXzjGPgIMcPeCWt6+snVfXsmx6HvNBGbW8vpxo7isnH97+AP2FJbyvbF9+MnpA+jSWk/qREQS2YuLtrDqy3wevux4mqdphxGRWGmIGRgPADcBlc6JdfetZvZbYDPBE7857j6nQpv6PNWDuj/Zmwk8FO6RfcgH9DCmuHyql0hKyyNc+/Qi3vsit8o2mempdGqVQcdW6VxyYi9umTSEVirEKXLEhNXtpwGY2V2Ey+jcPTv8nmNmrxIkhg8ZH8NxcxjwKnAbcH0tb50F9Ip63ZNDk9lJ4e2VOeTkF/OXK0/k9GO6xDocERGpp7yiUn775mpO7NueScO7xTockSatXr8pmtmBehSLw+3uKmvTnmCdcz9gD/CSmV3h7s9Gt6vHUz2o45O9cP331XW4vtSRu3PzK0t574tc/nvSMZzUryOpKUazVKNZipHRLJWOrdLJTFeyQqQxmVmXMEnRG5gCnGxmLYEUd88Pfz4L+E0l7x1FUMn+HGAD8KyZ3eHut9bi1guBQWGyeivBUsLLGqZX8eWVxVl0a9OcU4/uHOtQRESkHtyddbn7+OM7a9hVWMKT545RIXmRGKvvb4/jgPPNbBLBNndtzOxZd78iqs0ZwAZ3zwUws5nAN4CDEhj1eKoHTejJXqL43ZwveOWTLG749iB+eOqAWIcj0iSY2QvAeKBTuFTuNnefZmazgGvCWRavhDUwSoGfuvtuM+sPvBp+KGsGPO/usyu5RSZwkbuvC+83FbiyDnFcD7xJUJ9oursvb8Dux4Xc/GLmfpHLtaf0JzVFH3JFRBJNSVmEjzbs5J1VObyzKodNOwsBuGpcP4b3bBvj6ESkXgkMd78FuAUgnIHxywrJCwiWjow1s0yCJSTf5uuicYTvrc9TPWhCT/YSwTMLNvHHd9dy6Zhe/OyMQbEOR6TJcPdLqzg+KernUyo5vx4YUYvrf1DhdSnB2F3bOGYBs2q6TyJ7bclWyiPOd07QDkoiIolmX3EZF/35Q1ZsyyO9WQrjBnTkmlP6c/rgzqrPJhInjtj8/agnfh+FO318QlAs7lOgYnX7ej3Vc/eypvBkLxHMXvYlv3ptGWcM6cLtk4dpmp2INBnuzsuLsxjRqx0Du2irVBGRRBKJOL94cQmrvszj/33nOM457igtdRaJQw32t9Ld5wJzo15HP/G7jWBZSFXvrddTvfBc0j/Zq68tuwrZvKuQL/cW8WVeEV/uLSI3v5iyiOPuRNyJeA3bAtTgo/U7GdmrHQ9dejzNUlMaLHYRkXi3PDuPVV/mc/vkY2MdioiI1NEf3lnDm8u3c+s5Q7hodK+a3yAiMaG0YhNQUhbhrlkrefJfGw863rZFGp1bZ5CWmkJqCqSYYWaVVkStrfGDO3P3lONoka7tpUSkaXnlkyzSU1M4b0T3WIciItKowqXktwPLgRnhg82EMXvZlzzwzzVMOb4HV3+zX6zDEZFqKIGR5LbnFfGT5z5h8abdTD25DxOHHcVRbZvTtU1zJRlERBpIaXmE15dkc8bQLrTLTI91OCIS58xsOnBgN79hdW1jZqkENeW2uvu5DR2HmU0EHiRYmv2Eu99Tw6UcKCAo6p91uPHEwqov8/jFi0sY0asdd10wXMufReKcEhhJbMH6nVz//KcUlpTx0KWj9FRQROQImbs6l537Srjw+J6xDkVEEsOTwB+Bpw+zzQ3ASqBNZW80sy7AfnfPjzo20N3X1nSPMDnyMHAmQTJioZm97u4rzGw4cHeFa1wFzHf398ysK3A/cHk1/Yobu/eVcO3Ti2iV0YzHvncCzdP0cE8k3qlIQRJydx6ft57Ln/iINi2a8dpPxyl5ISJyBL28eAudWmVw6tGdYx2KiCQAd58H7DqcNmbWk2DnvieqeftpwGtm1jx8z7XAH2p5jzHAWndf7+4lwAxgcth+qbufW+Erx90j4Xt3AxnV9SteRCLOf8z4lO15xTz6vRPo2qZ5rEMSkVrQDIwk9Oi89dzzj1WcPawb933nOFo3T4t1SCIiSWv3vhLeWZXD1JP7kqbixSJy5D0A3ARUud2Ru79kZv2AGWb2EsEsiTNref0ewJao11nASdW9wcymABOAdgQzOiqePw84b+DAgbUM4ch75L11zF+zg3umDGdU7/axDkdEakmftJLMnOVfcu/sVZx73FH86fLjlbwQETnCXv8sm9Jy58ITtHxERI4sMztQr2JxTW3d/T6gCHgEON/dC2p7m8ouV8O9Zrr7j9z94soKeLr7G+7+w7Zt29YyhCPr4w27+N2c1Zw/ojsXn6gdR0QSiRIYSWRFdh4/++sSjuvRlt9eNEJFiEREjrDd+0p4ZsEmju3ehiFHVboUXUSkIY0DzjezjQRLO75lZs9W1tDMTgGGAa8Ct9XhHllA9G/1PYHsw4o2Du3aV8J/vPApvTtkcucFw/R5WSTBKIGRJHLyi7jmqYW0aZ7G498frSJEIpLwzGy8mc03sz+HW/TFldVf5jP54Q/YvLOQX5x5dKzDEZEmwN1vcfee7t4XuAR4x92vqNjOzEYBjxPUrvgB0MHM7qjlbRYCg8ysn5mlh/d5vUE6EGPuzi9f+oxd+0r442WaqSySiJTASAJFpeX86JnF7C4s5Ympo+miIkQiSc3MpptZjpktq6bNDWa2zMyWm9nPwmO9zOxdM1sZHr+hwns2mtlSM1tiZouORHxmNtHMVpvZWjO7uYZLxe22fLOXbeOCP31AUWk5f/3RWL49pGusQxKRBGJmLwAfAoPNLMvMrg6PzzKz7tW1qaVM4CJ3XxcW2JwKbKpNHO5eBlwPvEmw08mL7r788HsbP6a9v4F3VuXwP+cMYViP+FjOIiJ1oyKeCSoScXILisnaXcj0Dzby6eY9/PmK4zUYizQNT1LN9ntmNgy4lqCSfAkw28z+TpAM+E93/8TMWgOLzewtd18R9fbT3X1HFdc97G35wraVbs0HpJIg2/JFIs6Db6/hwbfXMLJXO1WuF5HD4u6XVnF8Uk1tos7PBeZWce6DCq9LCWZk1DaOWcCs6u6faJZs2cO9s1cx4diufP/kPrEOR0QOkxIYcc7d2byrkKVb97J0615WZOexZVch2XuKKCmPfNXuxgmDmTjsqBhGKiKNxd3nmVnfapoMARa4eyGAmb0HXBAWdNsWXiPfzFYSVJtfUeWVDnYacJ2ZTXL3onBbvguASdGNqonvq635wrhmAJPd/W7g3GruW+W2fI1Z2f7Alnt/+3wb3zmhJ3f82zAt1xMRSQD7S8r52YxP6dK6OfddqDpxIolMCYw4VVIW4caXP+PdVTnkFZUBkJZqDO7WmmE92jJx2FH0aN+Cnu1a0KdjJv07t4pxxCISR5YBd5pZR2A/QYLhoCUhYYJhFPBR1GEH5piZA4+6+2PR76nntnxQx635atqWL4zpDeCN0aNHX1uHOA7LH99dy98+38aNEwbzk/ED9AFYRCRB/HbOajbuLOT5a0+ibabqXogkMiUw4tS/1u3gtSXZnHPcUYwb0Injerbl6K6tSW+msiUiUj13X2lm9wJvESwb+QwoO3DezFoBrwA/c/e8qLeOc/fscKnIW2a2yt3nVbj2feHMiUeAAXXYlg/quDWfu88EZtbh+kfM3NU5/P6fX3DBqB5KXoiIJJCFG3cx/YMNfG9sH74xoFOswxGRelICI079c+V2MtNT+d1FIzRFWUTqzN2nAdMAzOwuwiKYZpZGkLx4LkwQRL8nO/yeY2avEiz5OCiBUcm2fNfXIayE3Jpvy65CbpixhMFdW3PXBcOVvBARSRD7S8q56eXP6dGuBTeffUyswxGRBqDH+XHI3Xl7ZQ6nDOqk5IWIHJZwFgVm1huYArxgwW/e04CV7n5/hfYtw8KemFlL4CyCpSjRbeqzLR8k4NZ8RaXlXPfcYiLu/PmKE2iRrjFZRCRR/G7Oajbs2Md9Fx5Hyww9txVJBk0ugWFmKWZ2p5k9ZGZTYx1PZZZn57FtbxFnaFs+EalEbbbfA14xsxXAG8BP3X03MA74HvCtcKvUJWZ2oABnV+B9M/sM+Bj4u7vPrnDrw96WDyARt+a77bXlLNuax++/O5K+nVrGOhwREamlxZt2Me2DDVwxtjffGKilIyLJot6pyHBbvEXAVnc/pIq8mbUDniCYcuzAVe7+4WHeazpBpfocdx8WdXwi8CDBVnxPuPs91VxmMkEhuV2EU6rjzT9XbscMTj+mS6xDEZE4VMvt906p5Pz7VF6HgnBnkBE13Lde2/KF5xJma77nP9rMXxdt4frTB3LGUCWURUQSRVFpOTe+9Dnd27bg5rOHxDocEWlADTGX6gaCJ2ltqjj/IDDb3b8TThnOjD4ZTnPe7+75UccGuvvaSq71JEEl+qej2qYCDxNUws8CFprZ6+6+wsyGA3dXuMbHwIfu/qiZvQy8XfuuNo63V+ZwfO/2dGpV6a6BIiJyBLk7T8zfwF3/WMkpgzrx8zOPjnVIIiJSC5t3FjJvTS5vfJbN+h37eO6ak2ilpSMiSaVef6PNrCdwDnAn8ItKzrcBTgWuBHD3EqCkQrPTgOvMbJK7F5nZtcAFBNv+HcTd54Vb/0UbA6wNnx4SVsefDKxw96UEMzaiY7oiKoby2va1sWzbu5+lW/fyXxNVaEhEpLGVlUf41evLef6jzUwa3o37vzuS1BQV7RQRiVcrsvN44ePNzF+Ty8adhQD0aNeC/5k0hHFaOiKSdOqbknwAuAloXcX5/kAu8BczGwEsBm5w930HGrj7S2bWD5hhZi8BVxHMpqitHsCWqNdZwEnVtJ8JPBRW0p9XVSMzOw84b+DAgXUIpf7eXpkDwBlDtHxERKQx5ReV8tPnP2XeF7n8+LQB3DRhMClKXoiIxK1/LN3Gz19cgmGcPKAjV36jL6cc3Zn+nVpqxyiRJHXYCQwzO1CLYrGZja/m+scD/+7uH5nZg8DNwP9GN3L3+8KZE48AA9y9oC6hVHLMq2rs7oXA1TVd1N3fAN4YPXr0tXWIpd7eXrmdPh0zGdilVWPeVkSkScvaXcjVTy5iXW4B90wZziVjesc6JBGRhBD+HnA7sByY4e5zj/Q93Z1H3lvHfbNXc3zvdjz2/dFaei3SRNRnF5JxwPlmthGYQVDV/tkKbbKALHf/KHz9MkFC4yDhbIhhwKvAbXWMIwvoFfW6J5Bdx2vEhcKSMj5Yt5NvH9NVWWMRkUaSV1TKZY9/RPbe/Tz5gzFKXohIgzCz6WaWY2bL6tLGzJqb2cdm9pmZLTezX1d4z0YzWxruJLXoSMRnZhPNbLWZrTWzm2u4lAMFQHMaoUB+SVmEm17+nPtmr+a8Ed15/tqxSl6INCGHncBw91vcvae79wUuAd5x9ysqtPkS2GJmg8ND3wZWRLcxs1EEVewnAz8AOpjZHXUIZSEwyMz6hUVCLwFeP5w+xdr8NTsoKYtwxlAtHxERaQzuzq2vLmPrnv385coT+eYgrZcWkQbzJDDxMNoUA99y9xHASGCimY2t0OZ0dx/p7qMrXtDMuphZ6wrHKlsTXWl8UQXyzwbLG9TWAAAL6klEQVSGApea2VAzG25mf6vw1QWY7+5nA/8F/Lri9RrSnsISvj/9I15anMV/fHsQf7hkJM3TUo/kLUUkztRnBkaVzGyWmXUPX/478JyZfU4wCN9VoXkmcJG7r3P3CDAV2FTFdV8APgQGm1mWmV3t7mXA9cCbBLuhvOjuyxu+V0feP1dsp03zZpzYt0OsQxERaRJe+WQrr3+Wzc++PYjRGntFpAG5+zxgV13beODAcuq08KvK5dGVOA14zcyaA4QF8v9Qh/i+KpAfFuCfAUx296Xufm6Fr5zw8zvAbuCITYXYUVDMxY8u4JNNe/j9xSP4xZlHa8aySBPUIPsKhWvd5ka9nhT18xLgkOxw1PkPKrwuJZiRUVnbS6s4PguYVZeY4015xHlnVQ7jB3chLfWI5JVERCTK+twCfvXaMk7q14GfnN64BZtFRKoTzoJYDAwEHo5ajg1BMmOOmTnwqLs/Fv3exi6Qb2ZTgAlAO+CPVbSpV3H83PxiLnt8AVt2F/KXH5yo3UVEmjD9phwnlmzZw859JZwxtGusQxERSXolZRFumLGE9GYpPHCJtkoVkfji7uXuPpKgttsYMxsWdXqcux9PsMTjp2Z2aiXvvw8oIiiQf/4RLpA/091/5O4XV1XA093fcPcftm3btg5hBHLyirjksQ/J2r2fv1w5RskLkSZOCYw48c+V22mWYpx2dOdYhyIikvR+O2c1S7fu5b4Lj+Ooti1iHY6ISKXcfQ/BLOeJUceyw+85BAXwx1R8X7IUyP9ybxGXPLaAbXuLePIHJ3LygI6xCENE4kiDLCGRwFsrtlMeieBROWoH3CHi/vVX5ND3/mPpNsb060DbFmmNFq+ISDw7UlvzvfdFLo/NW8/3xvbhrGO7NcQlRUQajJl1BkrdfY+ZtQDOAO4Nz7UEUtw9P/z5LOA3Fd5/oED+OcAG4Fkzu8Pdb61lCF8VyAe2EhTIv6wBulYn2/bu59LHFpCbX8xTV41RjTgRAZTAaFA3zPiUwpLyw37/Naf0b8BoRES+ZmbTgXOBHHcfVkWbG4BrCaYPP+7uDzT0/cxsIvAgkAo84e73VHOZBt+aLxJx7p61ksFdW/M/5wxpiEuKiFQqLD4/HuhkZlnAbe4+zcxmAde4e3ZlbQgSCE+FdTBSCArU/y28bFfg1bB4ZTPgeXefXeHWXxXID+OYClxZ2/jcvczMDhTITwWmx6JA/r3/WMWOghKevnoMJ/RR8kJEAuZel6LGTc/o0aN90aLabbG96su8r2ZfRBdFTjEjxcDMSDXDDKzC8sLUVKN72+aqpiySoMxscWXb2cWLcI10AfB0ZQmMcH31DIKpyCXAbOA6d18T1aYLsN/d86OODXT3tbW5X/hh/AuCYnJZBB/SL3X3FWY2HLi7wmWucvccM+sK3O/ul1fVv7qM1Tl5RewrKadfp5a1ai8iySPex+pkV5exOr+olE07CxnWo+51M0Qk8VU1XmsGRgM6plubWIcgIlIpd59nZn2raTIEWODuhQBm9h5wAXBfVJvTgOvMbJK7F4Vb810ATKp4sSru99XWfOE9ZgCTgRXuvpRgxkZlqtya73Aq23dp07zWbUVEJDZaN09T8kJEDqEiniIiArAMONXMOppZJkFSIrqIG+7+EsHMjBlmdjnB1nzfrcM9Ktuar0dVjc1sipk9CjxDFVvz1aeyvYiIiIgkFs3AEBER3H2lmd0LvEWw9OMzoKySdveFMyceAQYc6a35gJl1uL6IiIiIJDHNwBAREQDC4m3Hu/upwC5gTcU2ybI1n4iIiIgkHiUwREQE+KpIJ2bWG5gCvFDh/IGt+SYDPwA6mNkddbjFV1vzmVk6wdZ8rzdE7CIiIiKS/LQLSQ3MLBfYVIe3dAJ2HKFwGksy9AHUj3iSDH2A6vvRx907N2YwdRG9XR6wncq385sPdARKgV+4+9sVrjEOyAsLbmJmacCV7v54He43CXiAr7fmu7OB+tcUx2pIjn4kQx9A/YgnCTtWJzuN1QktGfoA6kc8qakPlY7XSmA0MDNblOjbcyVDH0D9iCfJ0AdInn5I8vxZJkM/kqEPoH7Ek2TogwSS5c8yGfqRDH0A9SOeHG4ftIREREREREREROKeEhgiIiIiIiIiEveUwGh4j8U6gAaQDH0A9SOeJEMfIHn6IcnzZ5kM/UiGPoD6EU+SoQ8SSJY/y2ToRzL0AdSPeHJYfVANDBERERERERGJe5qBISIiIiIiIiJxTwkMEREREREREYl7SmA0EDObaGarzWytmd0c63hqy8ymm1mOmS2LOtbBzN4yszXh9/axjLEmZtbLzN41s5VmttzMbgiPJ1o/mpvZx2b2WdiPX4fHE6ofAGaWamafmtnfwteJ2IeNZrbUzJaY2aLwWML1Qw6msTq2kmG8TqaxGjReS/zSeB07Gqvjj8bqrymB0QDMLBV4GDgbGApcamZDYxtVrT0JTKxw7GbgbXcfBLwdvo5nZcB/uvsQYCzw0/C/f6L1oxj4lruPAEYCE81sLInXD4AbgJVRrxOxDwCnu/vIqD2qE7UfgsbqOJEM43UyjdWg8VrikMbrmNNYHX80VoeUwGgYY4C17r7e3UuAGcDkGMdUK+4+D9hV4fBk4Knw56eAf2vUoOrI3be5+yfhz/kEf7l7kHj9cHcvCF+mhV9OgvXDzHoC5wBPRB1OqD5UI1n60VRprI6xZBivk2WsBo3XEtc0XseQxur4orH6YEpgNIwewJao11nhsUTV1d23QTCAAV1iHE+tmVlfYBTwEQnYj3B62BIgB3jL3ROxHw8ANwGRqGOJ1gcI/pGbY2aLzeyH4bFE7Id8TWN1HEnk8TpJxmrQeC3xS+N1nNBYHRc0VkdpdgQDbEqskmPan7aRmVkr4BXgZ+6eZ1bZH0t8c/dyYKSZtQNeNbNhsY6pLszsXCDH3Reb2fhYx1NP49w928y6AG+Z2apYByT1prE6TiT6eJ3oYzVovJa4p/E6Dmisjj2N1YfSDIyGkQX0inrdE8iOUSwNYbuZHQUQfs+JcTw1MrM0ggH2OXefGR5OuH4c4O57gLkEaygTqR/jgPPNbCPBdM9vmdmzJFYfAHD37PB7DvAqwXTWhOuHHERjdRxIpvE6gcdq0Hgt8U3jdYxprI4bGqsrUAKjYSwEBplZPzNLBy4BXo9xTPXxOjA1/Hkq8FoMY6mRBengacBKd78/6lSi9aNzmCHGzFoAZwCrSKB+uPst7t7T3fsS/D14x92vIIH6AGBmLc2s9YGfgbOAZSRYP+QQGqtjLBnG62QYq0HjtcQ9jdcxpLE6fmisruRa7pqN1RDMbBLB+qRUYLq73xnjkGrFzF4AxgOdgO3AbcD/AS8CvYHNwEXuXrEYUdwws28C84GlfL027L8J1uolUj+OIyhek0qQXHzR3X9jZh1JoH4cEE5z+6W7n5tofTCz/gSZYQiW2j3v7ncmWj/kUBqrYysZxutkG6tB47XEJ43XsaOxOj5prA6vpQSGiIiIiIiIiMQ7LSERERERERERkbinBIaIiIiIiIiIxD0lMEREREREREQk7imBISIiIiIiIiJxTwkMEREREREREYl7SmCIiIiIiIiISNxTAkNEREREREQahAX0e6YcEfofS0RERERERA6bmfU1s5Vm9ifgE6CXmRVEnf+OmT0Z/vykmf3BzP5lZuvN7DvVXO9xM1tuZnPMrEWjdUjilhIYIiIiIiIiUl+DgafdfZS7b6qh7VHAN4FzgXuqaDMIeNjdjwX2ABc2WKSSsJTAEBERERERkfra5O4Latn2/9w94u4rgK5VtNng7kvCnxcDfesboCQ+JTBERERERESkvvZVeO1RPzevcK446mer4nrRbcqBZocZlyQRJTBERERERESkoW03syFhQc8LYh2MJAdlsURERERERKSh3Qz8DdgCLANaNcRFzezHAO7+54a4niQWc/eaW4mIiIiIiIiIxJCWkIiIiIiIiIhI3FMCQ0RERERERETinhIYIiIiIiIiIhL3lMAQERERERERkbinBIaIiIiIiIiIxD0lMEREREREREQk7imBISIiIiIiIiJx7/8HTCB/l6Yfae8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x720 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Lets take for each problem the best 50 fits found and plot the corresponding final MSE\n",
    "fig, axes = plt.subplots(nrows = 4, ncols=3, sharex=True, figsize=(15,10))\n",
    "for i, ax in enumerate(np.reshape(axes,(12))[:12]):\n",
    "    a = results[i]\n",
    "    ax.semilogy(sorted(a[0])[:50])\n",
    "    ax.title.set_text(\"Prob id: \" + str(i))\n",
    "plt.xlabel(\"run n.\")\n",
    "plt.ylabel(\"mse\")\n",
    "plt.tight_layout()\n",
    "# Conclusion: there are many formulas with similar error that can be considered as equally good fits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Showing the best 5 fits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "Best five fits for id:  0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 0, err: 2.3801558148325692e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} - \\frac{c_{2}}{x_{0}} + \\frac{c_{2}}{2 x_{0}^{2}} + c_{3} e^{- 4 x_{0}^{2}} - c_{4} x_{0} e^{- 4 x_{0}^{2}} + c_{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 0, err: 2.380412125841117e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{2}}{x_{0}} + c_{3} + c_{4} \\left(\\frac{c_{2}}{x_{0}} - x_{0}\\right)^{2} - x_{0} \\left(c_{1} - \\frac{x_{0}}{\\frac{c_{2}}{x_{0}} - x_{0}}\\right) + \\frac{x_{0}}{\\frac{c_{2}}{x_{0}} - x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 0, err: 2.3804219347209996e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{4} + \\left(c_{4} + x_{0}^{2}\\right) \\left(- c_{1} + c_{2} x_{0} + c_{3} x_{0}^{2}\\right)}{c_{4} + x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 0, err: 2.3808190703491017e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{1} e^{- x_{0}^{2}}}{x_{0}} - \\frac{c_{2}}{x_{0}} - c_{3} - \\frac{c_{4}}{x_{0}^{2}} - 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 0, err: 2.3809219218852146e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} x_{0} - c_{2} x_{0}^{2} + \\frac{c_{3}}{x_{0}^{2}} - c_{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "---------------------------------------------------------\n",
      "Best five fits for id:  1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 1, err: 1.5481952594443556e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{1} - c_{2} e^{x_{0}} + x_{0} \\left(c_{2} e^{x_{0}} + c_{2} - c_{4} - x_{0} + \\left(- c_{1} + c_{2} e^{x_{0}} + c_{3}\\right) e^{x_{0}}\\right)}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 1, err: 1.5486489454637892e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{2} x_{0} \\left(1 - x_{0}\\right) + \\left(c_{1} + x_{0} \\left(- c_{2} x_{0} + c_{2} + c_{3} x_{0} + c_{4}\\right)\\right) e^{x_{0}^{2}}}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 1, err: 1.5494780218604477e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} x_{0} + c_{2} - \\frac{c_{2}}{x_{0}} - c_{3} + c_{4} e^{- e^{- 2 x_{0}^{2}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 1, err: 1.549478021860451e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - \\frac{c_{1}}{x_{0}} + c_{2} + c_{3} e^{- e^{- 2 x_{0}^{2}}} - c_{4} x_{0}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 1, err: 1.5524996126148153e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} + \\frac{c_{2} e^{x_{0}^{2}}}{x_{0}} + c_{3} x_{0} + c_{4} e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "---------------------------------------------------------\n",
      "Best five fits for id:  2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 2, err: 4.866500757662433e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\left(c_{1} + c_{4} x_{0} + \\left(- c_{3} + \\left(c_{2} - x_{0}\\right) e^{\\left(x_{0}^{2} e^{x_{0}^{2}} - 1\\right) e^{- x_{0}^{2}}}\\right) e^{x_{0}^{2}}\\right) e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 2, err: 4.8981961254319396e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} + c_{2} x_{0}^{3} + c_{3} e^{- x_{0}^{2}} - c_{4} x_{0}^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 2, err: 4.9140689166325595e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} x_{0} + c_{2} e^{2 x_{0}} + 2 c_{3} e^{- x_{0}} - c_{4} + 2 e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 2, err: 5.004121929538379e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\left(\\left(- c_{1} x_{0} + c_{2} x_{0} - c_{4} - x_{0}\\right) e^{x_{0}^{2}} + \\left(c_{2} x_{0} + c_{3} - c_{4} - x_{0}\\right) e^{2 x_{0}^{2}} + 1\\right) e^{- 2 x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 2, err: 5.0208570048206605e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{1}^{2} e^{- x_{0}}}{c_{3}} - c_{2} + c_{4} e^{- x_{0}^{2}} - e^{- \\frac{c_{1}^{2}}{x_{0}^{2}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "---------------------------------------------------------\n",
      "Best five fits for id:  3\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 3, err: 7.993101895616535e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} x_{0} e^{x_{0}^{2}} + c_{1} + c_{2} e^{x_{0}^{2}} + c_{3} - c_{4} x_{0} + e^{- e^{- 2 x_{0}^{2}}} - e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 3, err: 8.116838729621195e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} x_{0} + c_{2} e^{e^{2 x_{0}}} + c_{3} e^{x_{0}} + c_{4} + e^{- e^{2 x_{0}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 3, err: 8.13057337419324e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\left(c_{3} + \\left(c_{3} + \\left(c_{2} + e^{x_{0}}\\right) e^{x_{0}}\\right) \\left(e^{x_{0}} + e^{e^{x_{0}}}\\right) + \\left(- c_{1} e^{x_{0} + e^{x_{0}}} + c_{2} - c_{4} + e^{x_{0}}\\right) e^{x_{0}}\\right) e^{- x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 3, err: 8.19691765672383e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{2} + x_{0} \\left(c_{1} x_{0} - c_{3}\\right) - x_{0} + \\left(c_{2} - x_{0}\\right) e^{x_{0}} + \\left(- c_{2} - c_{4} + x_{0}\\right) e^{x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 3, err: 8.224153596665173e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} + 2 c_{4} x_{0} - \\left(c_{2} + c_{3} e^{x_{0}^{2}}\\right) e^{x_{0}^{2}} - e^{c_{2}} + e^{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "---------------------------------------------------------\n",
      "Best five fits for id:  4\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 4, err: 3.359546731194255e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} x_{0} - c_{2} + c_{3} e^{- x_{0}} + c_{4} - \\frac{c_{4}}{x_{0}} - e^{- e^{2 x_{0}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 4, err: 3.3734252967348888e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} - c_{2} x_{0} - \\frac{c_{3}}{x_{0}} - c_{4} e^{e^{- 2 x_{0}^{2}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 4, err: 3.3746957690291797e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{x_{0} \\left(c_{2} - c_{4} x_{0}\\right) + \\left(c_{1} + c_{3} x_{0}\\right) e^{e^{- 2 x_{0}^{2}}}}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 4, err: 3.3811044286786395e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} e^{x_{0}^{2}} + \\frac{c_{2}}{x_{0}} + c_{3} - c_{3} e^{- 2 x_{0}^{2}} - c_{4} e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 4, err: 3.3842683416733736e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{- c_{4} + x_{0} \\left(- c_{2} + c_{3} x_{0}\\right) + \\left(c_{1} x_{0} + c_{4}\\right) e^{x_{0} - e^{2 x_{0}}}}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "---------------------------------------------------------\n",
      "Best five fits for id:  5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 5, err: 1.686027444316002e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} x_{0} + c_{1} e^{- x_{0}^{4}} + \\frac{c_{1}}{x_{0}^{2}} + c_{2} - 2 c_{3} - \\frac{c_{3}}{x_{0}^{3}} - 2 c_{4} x_{0} - \\frac{c_{4}}{x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 5, err: 1.686067254813111e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{x_{0}^{3} \\left(- c_{2} + c_{4} e^{x_{0}}\\right) + \\left(- c_{1} x_{0} + c_{3}\\right) e^{x_{0}}}{x_{0}^{3}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 5, err: 1.686069307097475e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{2} x_{0}^{2} + c_{4} + x_{0}^{2} - x_{0} \\left(c_{1} + c_{3} x_{0}\\right) \\left(c_{4} + x_{0}^{2}\\right)}{x_{0} \\left(c_{4} + x_{0}^{2}\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 5, err: 1.6860856181522074e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{1}}{x_{0}^{3}} + c_{2} x_{0} - c_{3} - \\frac{c_{4}}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 5, err: 1.686098183474468e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} e^{x_{0}} + c_{2} + \\frac{c_{3}}{x_{0}^{2}} - \\frac{c_{4}}{x_{0}^{3}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "---------------------------------------------------------\n",
      "Best five fits for id:  6\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 6, err: 9.922429392571683e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{2} - c_{3} e^{- x_{0}^{2}} + \\frac{2 c_{4}}{c_{1} + x_{0}} - e^{- \\left(c_{1} + x_{0}\\right)^{2}} + e^{- c_{4}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 6, err: 9.936575700754542e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{2} + x_{0}^{2} \\left(c_{1} x_{0} \\left(c_{4} + x_{0}\\right) + c_{3}\\right) - x_{0} \\left(c_{1} x_{0} \\left(c_{4} + x_{0}\\right) + c_{4}\\right)}{x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 6, err: 9.936942645025763e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} e^{- e^{- 2 x_{0}^{2}}} + \\frac{c_{2} e^{- x_{0}^{2}}}{x_{0}} + c_{3} + c_{4} - \\frac{c_{4}}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 6, err: 9.937353947520078e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} + c_{2} e^{x_{0}} - \\frac{c_{3}}{x_{0}} + \\frac{c_{4} e^{- e^{2 x_{0}}}}{c_{2} + e^{x_{0}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 6, err: 9.938981126078224e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} + c_{2} e^{- x_{0}} - \\frac{c_{3} e^{- x_{0}^{2} - x_{0}}}{x_{0}} + \\frac{c_{4} e^{- x_{0}}}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "---------------------------------------------------------\n",
      "Best five fits for id:  7\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 7, err: 8.515167695863056e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} e^{e^{- x_{0}^{2}}} + c_{2} + c_{3} x_{0} - c_{4} e^{- x_{0}^{2}} + x_{0} e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 7, err: 8.519576231706857e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} e^{x_{0}} + c_{1} e^{- e^{2 x_{0}}} - c_{2} + c_{3} e^{x_{0} - e^{2 x_{0}}} - c_{3} e^{- 2 e^{2 x_{0}}} + c_{4} e^{e^{x_{0}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 7, err: 8.522266408037304e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} e^{- x_{0}^{2}} + c_{2} - c_{3} x_{0} - c_{4} x_{0} e^{- x_{0}^{2}} + e^{e^{- x_{0}^{2}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 7, err: 8.569811491073491e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} x_{0} + c_{2} e^{x_{0}} + c_{3} + c_{4} e^{- e^{2 x_{0}}} + e^{- e^{- 2 e^{2 x_{0}}}} - e^{- e^{2 x_{0}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 7, err: 8.596454393800356e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\left(- c_{1} + c_{2} x_{0} + \\left(- c_{3} + c_{4} e^{x_{0}^{2}} + x_{0}\\right) e^{x_{0}^{2}}\\right) e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "---------------------------------------------------------\n",
      "Best five fits for id:  8\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 8, err: 5.7033656245193685e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{\\left(x_{0} \\left(c_{1} x_{0} - c_{3} + e^{c_{2}}\\right) e^{c_{1} x_{0} \\left(c_{3} - e^{c_{2}}\\right)} + \\left(- c_{2} x_{0} + c_{4}\\right) e^{x_{0}^{2}}\\right) e^{- x_{0} \\left(c_{1} \\left(c_{3} - e^{c_{2}}\\right) + x_{0}\\right)}}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 8, err: 5.703378409998452e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} e^{- x_{0}^{2}} + c_{2} + c_{3} x_{0} e^{- x_{0}^{2}} + \\frac{c_{4}}{x_{0}} + x_{0} e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 8, err: 5.7033784099984615e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} e^{- x_{0}^{2}} + \\frac{c_{2}}{x_{0}} - c_{3} - c_{4} x_{0} e^{- x_{0}^{2}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 8, err: 5.705047245789752e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} - c_{2} c_{3} - c_{2} c_{4} e^{- x_{0}^{2}} + c_{2} + \\frac{c_{2}}{x_{0}} - c_{3} x_{0} - c_{4} x_{0} e^{- x_{0}^{2}} + x_{0} + 1$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 8, err: 5.705078353147797e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} x_{0} + \\frac{c_{2}}{x_{0}} - c_{3} + c_{4} x_{0} e^{- x_{0}^{2}} - x_{0}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "---------------------------------------------------------\n",
      "Best five fits for id:  9\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 9, err: 4.523905989067585e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle 2 c_{1} + \\frac{c_{1}}{x_{0}^{2}} + c_{2} - c_{3} x_{0} + \\frac{4 c_{4}}{x_{0}} + \\frac{c_{4}}{x_{0}^{3}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 9, err: 4.523956586681867e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} x_{0} - c_{2} - c_{3} - \\frac{c_{3}}{x_{0}^{2}} + \\frac{3 c_{4}}{x_{0}} + \\frac{c_{4}}{x_{0}^{3}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 9, err: 4.524279590137839e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{2} - c_{4} x_{0} + x_{0}^{3} \\left(c_{1} + c_{3} c_{4} x_{0}\\right) + x_{0}}{x_{0}^{3}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 9, err: 4.524279590138164e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{- c_{4} + x_{0}^{3} \\left(- c_{1} x_{0} + c_{2}\\right) + x_{0} \\left(c_{1} + c_{3}\\right)}{x_{0}^{3}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 9, err: 4.651129097622205e-06'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} x_{0} + \\frac{c_{2}}{x_{0}} + \\frac{c_{3}}{x_{0}^{2}} + \\frac{c_{4} e^{- x_{0}}}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "---------------------------------------------------------\n",
      "Best five fits for id:  10\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 10, err: 1.9017543270061446e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{2} e^{\\frac{1}{x_{0}}} - c_{3} + x_{0} \\left(- c_{1} x_{0} + c_{4}\\right)}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 10, err: 1.9104544589813626e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - \\frac{c_{1}}{\\frac{c_{4}}{x_{0}^{3}} - x_{0}} + c_{3} + \\frac{c_{4} e^{\\frac{1}{x_{0}}}}{x_{0}^{3}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 10, err: 1.9158737383062652e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle c_{1} x_{0}^{2} + c_{2} + \\frac{c_{3}^{2}}{x_{0}^{6}} - \\frac{c_{3}}{x_{0}} + \\frac{c_{3}}{x_{0}^{5}} - \\frac{c_{3}}{x_{0}^{6}} + c_{4} x_{0}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 10, err: 1.9240171327253178e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - 2 c_{1} + \\frac{c_{2}}{x_{0}^{3}} - \\frac{c_{3}}{x_{0}^{4}} - \\frac{c_{4}}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 10, err: 1.9291883990542647e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} x_{0} + c_{2} e^{x_{0}^{2}} - c_{3} + \\frac{c_{4}}{x_{0}^{4}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n",
      "---------------------------------------------------------\n",
      "Best five fits for id:  11\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 11, err: 1.1337997121125522e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\frac{c_{2} \\left(c_{4} - x_{0}^{4}\\right) - c_{3} x_{0} \\left(c_{4} - x_{0}^{4}\\right) + x_{0} \\left(- c_{1} x_{0}^{2} - c_{2} x_{0} + c_{4}\\right)}{x_{0} \\left(c_{4} - x_{0}^{4}\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 11, err: 1.135016956476325e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} - \\frac{c_{3}}{x_{0} - e^{c_{3}}} + \\frac{c_{2} + \\frac{c_{4}}{x_{0}} + e^{c_{4}}}{x_{0}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 11, err: 1.1360665073366816e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} + \\frac{c_{1}}{x_{0}^{4}} + c_{2} - \\frac{c_{3}}{x_{0}^{2}} - c_{4} x_{0} + \\frac{c_{4}}{x_{0}^{3}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 11, err: 1.1364062900679142e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle - c_{1} x_{0} + c_{2} x_{0}^{2} - c_{2} x_{0} e^{- e^{- 2 x_{0}^{2}}} + c_{3} e^{e^{- 2 x_{0}^{2}}} + c_{4}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'prob_id: 11, err: 1.138267448015574e-05'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\displaystyle \\left(- c_{2} e^{x_{0}^{2} + e^{- 2 x_{0}^{2}}} + \\left(c_{1} + \\left(c_{3} - c_{4} x_{0}\\right) e^{x_{0}^{2}}\\right) e^{x_{0}^{2}} - 1\\right) e^{- x_{0}^{2} - e^{- 2 x_{0}^{2}}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "for prob_id in range(12):\n",
    "    print(\"---------------------------------------------------------\")\n",
    "    print(\"Best five fits for id: \", prob_id)\n",
    "    a = results[prob_id]\n",
    "    fits = a[0]\n",
    "    best_idxs = sorted(range(126), key = lambda x: fits[x])\n",
    "    for best_isl in best_idxs[:5]:\n",
    "        best_x = a[1][best_isl]\n",
    "        best_f = a[0][best_isl]\n",
    "        udp, X, Y = reconstruct_udp(prob_id)\n",
    "        s = parse_expr(udp.prettier(best_x))[0].simplify()\n",
    "        display(\"prob_id: {}, err: {}\".format(prob_id, best_f[0]), Math(r'{}'.format(s._repr_latex_())))\n",
    "    print(\"---------------------------------------------------------\")\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}