3_9_Problems.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "3.9 Problems.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyN8OLdR3on+L77KmV82ES83",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/johanv26/analisis_numerico/blob/master/3_9_Problems.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D4rigi0MMVgY",
        "outputId": "7e02f3a6-1aa8-4287-cfcb-263b7fdbedd2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "#paquetes de trabajo\n",
        "!pip install sympy\n",
        "import numpy as np\n",
        "import sympy as sp\n",
        "from scipy import optimize\n",
        "import matplotlib.pyplot as plt\n",
        "from matplotlib.lines import Line2D"
      ],
      "execution_count": 257,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: sympy in /usr/local/lib/python3.6/dist-packages (1.1.1)\n",
            "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.6/dist-packages (from sympy) (1.1.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k2w-D4gsMjAm"
      },
      "source": [
        "Funciones de gradiente descente:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ilZrZ8oPMmlv"
      },
      "source": [
        "def descent_grad_optim_step(x, f, grad, epsi, max_iter): #Gradiente descendiente paso optimizado  \n",
        "  xs = np.zeros((1 + max_iter, len(x)))\n",
        "  xs[0,:] = x\n",
        "  for i in range(max_iter):\n",
        "    g = grad(*x)\n",
        "    def phi(s):\n",
        "      params=x-s*g.T\n",
        "      params=params[0,:]  #change into single array\n",
        "      #return f(x[0]-s*g[0],x[1]-s*g[1],x[2]-s*g[2])\n",
        "      return f(*params)\n",
        "    alpha = optimize.fminbound(phi, 0, 10)\n",
        "  \n",
        "    x = x - alpha * g.T\n",
        "    x=x[0,:]\n",
        " \n",
        "    xs[i+1,:] = x\n",
        "\n",
        "    tol = np.linalg.norm(g)\n",
        "    if tol < epsi:\n",
        "      \n",
        "      break\n",
        "  return xs,i+1"
      ],
      "execution_count": 258,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4m9Oi0l1MrIf"
      },
      "source": [
        "def descent_grad_fixed_step(x, grad, a, max_iter, epsi): #Gradiente desendiente paso fijo    \n",
        "  xs = np.zeros((1 + max_iter, len(x)))\n",
        "  xs[0,:] = x\n",
        "  \n",
        "  for i in range(max_iter):\n",
        "      g=grad(*x)\n",
        "      x = x - a * g.T\n",
        "      x=x[0,:]\n",
        "      xs[i+1,:] = x\n",
        "      tol = np.linalg.norm(grad(*x))\n",
        "      if tol < epsi:\n",
        "        break\n",
        "  return xs,i+1"
      ],
      "execution_count": 259,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2EDGAjsSWDn0"
      },
      "source": [
        "Funciones de gradiente y hessiano"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RqbKfI3FWD46"
      },
      "source": [
        "\n",
        "def gradient(f,*variables):\n",
        "  n=len(variables)\n",
        "  m=1\n",
        "  grad=sp.zeros(n,m)\n",
        "  i=0\n",
        "  for var in variables:\n",
        "    grad[i,0]=sp.diff(f,var)\n",
        "    i+=1\n",
        "  \n",
        "  return grad\n",
        "\n",
        "def hessian(f,*variables):\n",
        "  n=len(variables)\n",
        "  m=n\n",
        "  hess=sp.zeros(n,m)\n",
        "  \n",
        "  for i in range(0,n):\n",
        "    for j in range(0,n):\n",
        "  \n",
        "      first_diff=sp.diff(f,variables[j])\n",
        "      second_diff=sp.diff(first_diff,variables[i])\n",
        "      hess[i,j]=second_diff\n",
        "  \n",
        "  return hess"
      ],
      "execution_count": 260,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jwJsdfl_A3tD"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-EU_lCnGtAe5"
      },
      "source": [
        "#Solucion a)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KLTNwaQ6A1do",
        "outputId": "c1f4a576-ce0e-4441-9eba-c4a74acc51ed",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "sp.init_printing()\n",
        "x1=sp.Symbol('x_1')\n",
        "x2=sp.Symbol('x_2')\n",
        "x=sp.Matrix([x1,x2])\n",
        "a=sp.Matrix([[3,1],[1,2]])\n",
        "b=sp.Matrix([3,1])\n",
        "f=x.T*a*x +x.T*b + sp.Matrix([6])\n",
        "\n",
        "print('La funcion dada es : \\n',f)\n",
        "grad=gradient(f,x1,x2)\n",
        "print('El gradiente calculado es : \\n',grad)\n",
        "hess=hessian(f,x1,x2)\n",
        "print('El hessiano calculado es: \\n',hess)\n",
        "grad_val=sp.lambdify([x1,x2],grad)\n",
        "hess_val=sp.lambdify([x1,x2],hess)\n",
        "\n",
        "gradx0=grad_val(1,-1)\n",
        "print('El gradiente en el punto (1,-1) es : \\n',gradx0)\n",
        "hessx0=hess_val(1,-1)\n",
        "\n",
        "print('El hessiano en el punto (1,-1) es : \\n',hessx0)"
      ],
      "execution_count": 261,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "La funcion dada es : \n",
            " Matrix([[x_1*(3*x_1 + x_2) + 3*x_1 + x_2*(x_1 + 2*x_2) + x_2 + 6]])\n",
            "El gradiente calculado es : \n",
            " Matrix([[6*x_1 + 2*x_2 + 3], [2*x_1 + 4*x_2 + 1]])\n",
            "El hessiano calculado es: \n",
            " Matrix([[6, 2], [2, 4]])\n",
            "El gradiente en el punto (1,-1) es : \n",
            " [[ 7]\n",
            " [-1]]\n",
            "El hessiano en el punto (1,-1) es : \n",
            " [[6 2]\n",
            " [2 4]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dqmUrqzItE2C"
      },
      "source": [
        "#Solucion b)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uUK4mJXtsoX0"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QjejSL5Vs8fe",
        "outputId": "416a4434-1fc0-44cb-8774-b147d833e63a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "vector_max_increase_rate=grad_val(1,-1)\n",
        "\n",
        "#Procedo a normalizar\n",
        "vector_norm=vector_max_increase_rate/np.linalg.norm(vector_max_increase_rate)\n",
        "vector_norm\n",
        "print('El vector de maximo crecimiento, osea gradiente en (1,-1)es : \\n',\n",
        "      vector_max_increase_rate)\n",
        "print('El vector de maximo crecimiento normalizado  es : \\n',vector_norm)\n",
        "print('La norma del vector es ',np.linalg.norm(vector_norm))\n",
        "\n",
        "derivada_direccional=grad.T.dot(vector_norm)\n",
        "print('La expresion derivada direccional respecto a ese vector es : \\n',derivada_direccional)\n",
        "\n",
        "derivada_direccional_val==sp.lambdify([x1,x2],derivada_direccional)\n",
        "derivada_direccional_val2=grad_val(1,-1).T.dot(vector_norm)\n",
        "print('La expresion evaluada de derivada direccional respecto a ese vector es : \\n'\n",
        ",derivada_direccional_val2)\n"
      ],
      "execution_count": 262,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "El vector de maximo crecimiento, osea gradiente en (1,-1)es : \n",
            " [[ 7]\n",
            " [-1]]\n",
            "El vector de maximo crecimiento normalizado  es : \n",
            " [[ 0.98994949]\n",
            " [-0.14142136]]\n",
            "La norma del vector es  0.9999999999999999\n",
            "La expresion derivada direccional respecto a ese vector es : \n",
            " 5.65685424949238*x_1 + 1.41421356237309*x_2 + 2.82842712474619\n",
            "La expresion evaluada de derivada direccional respecto a ese vector es : \n",
            " [[7.07106781]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "40VQJh1LYCzd"
      },
      "source": [
        "#Solucion C)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b2clsEMjYDMA",
        "outputId": "4d21a77c-0793-40b4-98fa-5611835a46f3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "print('TEneindo en cuenta el termino del gradiente \\n',grad)\n",
        "\n",
        "raices_grad=sp.solve(grad)\n",
        "print('Hallamos las raices del gradiente como \\n',raices_grad)"
      ],
      "execution_count": 263,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "TEneindo en cuenta el termino del gradiente \n",
            " Matrix([[6*x_1 + 2*x_2 + 3], [2*x_1 + 4*x_2 + 1]])\n",
            "Hallamos las raices del gradiente como \n",
            " {x_1: -1/2, x_2: 0}\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ixX7cNyTeENy",
        "outputId": "124a4df1-94e9-4213-b8b7-71972be66a1a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "print('Teniendo en cuenta  el hessiano :,',hess)\n",
        "print('Consideramos los criterios para evaluar los criterios de optimos '\n",
        "' en ese punto(-1/2,0)')\n"
      ],
      "execution_count": 264,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Teniendo en cuenta  el hessiano :, Matrix([[6, 2], [2, 4]])\n",
            "Consideramos los criterios para evaluar los criterios de optimos  en ese punto(-1/2,0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qaADiP35srJs"
      },
      "source": [
        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ujpogIrxlX6o3j91OBzywyefk9MxMOrr6xMSEiDmlStXDkADw79V12eGnz9gPxgY6kzqGBgorDAwiouLhw8fDs1pyJAh4h5ZCOJwODIyMkJCQubNm5ecnGwymdLS0sS+j3N+8eLF4cOHh4eHr1692mq1jhw58sKFC5hifX19dHS06f/9rVy5sq2tDTcjzZo1C8ad+gkdO3bMYrH8vzhM+fn5ly9fjoyMBM2DgoJycnI4542NjbgDOzAw0Icdq7dv38a3u8fZdKfTGRERwRhT9ESK/fcpKSn622D08w4k79y5M23aNKvVmpaWZvn0px586BdEYWHhkCFDkGFmZubt27dHjx4N+Q0JCfnzzz+x1Djndrs9LS3NaDSCwIIFC86fP49wZLZIpaSkoLzOFNfvv/+OYrgWJFltvFJSh7NkciIffTcYGJzzkydPYu4YYzExMeIwS2Fg6GgoJqdfGTxG0tHRARuRZ82atWjRoiFDhkybNg2XQ/Wfcs4vX748YcKE2NjYtWvXwoqf1WoVRxgyMI8fPx4aGoq1MTQ09KeffuKcX7lyZcKECSaT6Ztvvrl48aKYa333P//8I3J2ZzBDJDabTXyX+7fhSLad3Nxcs9mMBE6cOME5z8/PF3NhNBpNJlNkZCTnXFMemfg9CxDztGnTGGOwvR7T8tZx8eJFyFRqaqpO2NevX1+/fl3RVT548ODu3bs4N2G32+vr64uLi8EyaWtrKy4uPnPmDMyAYOSSYijPOX/9+nVhYeHJkyerq6s1b1xoamoqKCg4d+7cw4cP3717p2kadXV1lZSU5OXl+bYsWVtbCxc/zJw5s6WlBQ/1wdT7oUOHQGGbzXbmzJnS0lJ3hv3jx49Pnz5dXl7ucDgqKytPnDiBAN0lIaKQcXd3d7d8+ktKSmKMnT9/vqWlxY+3AnDOi4uLJ0+efPLkSRl9PMq0trZCJUSMOkFCQ0MZY2lpaToyfn8EJ/fEfsnvSXDOdQyMmzdvpqSkwKb6UaNGie8przTp6uq6f//+pUuXFKFkWpAiiPhTXXXtdvu9e/fUo9aenp6GhgYMa7PZLly4oMiOOyUhVGNjY0FBQV5enuZWOpg86k1LR90kHV+kgZGYmBgTE5ORkYEz7iaTSZyscjqdcCZy+vTpAGLlypWMMfEA9LZt2xhjRqMRZkCbm5uDg4MZYxs3bkR2nZ2dZrMZmvfixYtnzpwZEBCA79GamhqZhMRTkkuWLBk7dmxGRsakSZMwnr/++mvMmDHp6enQ5YG/t2eV8BgltDTMgqYDbsxgjBUXF4sCRUVFqBU4AgICUlJSNCurTN5hCG4ymeBA/969eyFacVu/TEHcv38fFVu0aNHo0aO3bdsGrzQ4NHLr1i3IiNPphHtLGGOJiYnXr18/cuQIWFMQg4yB8c0332ByOputc3JyUIwx1tzcDDrIVBt5JT1y9picWMQe3WhgcM5hPz3mMTk5GUcGooHhUUNIVL8yyESyfPlyuGEJInz69GlkZOR3330HP/WfFhUVBQQEhIaG4nWZP/74I2RNXH2SgSnuaMJtwZzzN2/eMMawKnpEDQJbt25FwgaDAQl7DO7fhsM5l287Fy5cQJ3hRNzbt2/hxAL4b9q0qb6+/smTJ5ALtTz4+z0LCA0ujhs7diz6+OBwOp04o6S5O7SqqgonZcR9283NzQEBAVFRUZBoWVnZihUrgExRUdHx48enT58eHx9vMBgCAwOxq5cUw4y0t7enpqYuXLiwoqKitrY2Pj4+NjZWcWnpiRMngoODT58+fevWLVD1zJkzGAPnvLu7e8+ePfHx8QUFBbm5uYwxmYGsGEN5eXlSUhLMmsXGxiYlJWH3DvTg9VFSUhIREQEvUPUpyqamprlz565cubKioqKwsHDNmjVDhgzB4tNJQtRExn379u2kpCRYfDYYDEmf/latWiUTVlIGJi+GDBkiKa8v5nQ64TTggQMH9CU552BgfP67sMrKyiZNmoTX9njU0wcBHQNj8+bN//3vf+12+9q1a33bGPns2bP09HTgrBhBeWxB+nlRV92UlJRNmzYZDAbG2OvXr8XgmZmZ27dvR5/Dhw8zxpYtWwY+OkpyzpuamhITE9PT06urq+vr68PCwnbs2IFR+aWli7FJur9UAwPWIsRxpzgZf/ToUejNsac7fvw4+MDOnxs3bsDP77//HknNmTMHPMUtRmPGjAHPgICAQ4cOtbS0wJ2tJpPpw4cPHhPinD958gRiYIxNnz4djh7iXb2MscjISDiW7XQ6cbPEkiVLUDEZB4yWgoKCFFtZNMPC3mLFUXuQXLNmDWqLjoCAgKVLlyoWRjzmHS0rHKPjjODcuXMhOcmCePfuHSozfvx4mOW12WzouW3bNogwLy8PPM1mM86pZGdno6RHA6O7uxuFxeGsmqS4k4oxJn6eRb/aeKWkR86cc/3k1Jrr+IgGhjjAAia///47hBUNDBkNPVYGj5HgTN6RI0dQ/+vXr4OBof+Ucz5r1izIAk5Q/fXXX+ATHBwsTv16hNnZ2YkmaFRUFE6yXr9+fcqUKaibpEO8bFp+UOL3hsM5l6+WNTU12EZwsPjixQv0VKxSasr3RRaQ+aZNm0AZcUYQn8o73r59ixema66HdHd3GwwGk8kkninPzMxkjGG/B8lZLJbAwMB9+/ZhFwRi4eHhWIU455JiNTU1VqtVnA6DJpacnIy5A2tZvJjRarXevXsXBVpbWydNmhQXF/f+/Xs4I6tWG4X1HTDdIy6A2O12k8kUHh7ucrny8/M3btxos9lgjkkxxV5RUREWFiYOoDdu3KiY7OOcq5PQV0nnKUyxTZw4UUfG50fHjh0bMWLEzp07fY5BETA1NZUxtmjRIoW/4idskTIYDHDFvOJpX//Mzs4eNmyYWLv8m6JoYISHh9tstlevXlVWVqanpxsMhpUrV1qt1vT0dJw/8iF1GAFih8Y599iCJFNRV93vv/+eMSZuiG1sbDSZTHBaHaK12WwxMTGJiYliKmolYTNOWFgYXjbT0tLCGAsODsaAfmzpGKeM44s0MLAGfPz4EV9pYlcLexYZYziYwPENTER99913EFAMhfO1o0ePRnZjx44FSegoOectLS25ubn37t3jnHtMiHMOt2ZBJDg55HQ6cQ+POAmKZ7VjYmJQB4+O+/fvGwyGgICAc+fOeRTmnON0mvg+gIBOp3PPnj1gXiNbcIwZM0a0MTzmHW62FTdiNTY2ws5+5CBZEG1tbaiMuH8M7bH58+eD/iNGjABJ0XT06gyGaLcwxnbt2uUOKVYqSFHsLPSrjVdKeuTMOddPzp3+mv6igQEfQsHdaJBN2EYoGhgyGnqsDB4jgZO7jLGwsLCioiJU/tixY5xz/aecc5yKxktgcdGPMSZeQywDc+fOnVgh8UDU+vXrjx49iopJOsR1S9hTJBPQ7w2Hcy5fLRUbVkFhHQNDU74vsoDofv31Vygg9T4ElJF0NDY2Yj+DHReGra+vZ4zhFnDOucvlgmtDxbUCmFEKCQkR9cG713HxU1Ls4cOHJpMpLi5OtEzAxg4ICMCbal6+fMkYM5lMYD9wztPT03H/Umdn57hx4ywWC946uH//fsaYqCFmU9/x4cMHg8EwbNgwUay0tJQxlpqaWl5ejhMTcPU8bAwG4bq6OrPZrJhQgx0H+PrmnGsmISbnlRumnMS3v1fBP7Nwc3PzkCFDjEajuE1DrcPq1av1Z8TUQfzrc+jQIbhqUrGrxy+piAaG2WyGt9LkyZNnzZoVFBSUl5fXy31uTqfTYrEwxsQbrvVbkGS+NKvujh07GGN//fUXRrJq1SrG2A8//IA+nPPdu3eLE2qaSpaUlCi2g3Z2ds6dOxcvEPdjSxd1k3F/2QaG0+nE1/zPP/8MGQbrDfx37959+dMfztlPnDhRnA4XFxPFQQOetMbRBs4DIVaPCYGkpoHBOcdbUEUDAz7rBndaY0L6DpfLNW3atICAALS79OXFwZa75Y7Hjx8vWrRI3A8GPNG89pj35uZmLBrxZEtrayv2kvIF4c7AwNMscFKivb0dE920aRNycGdgnDx58tD//KupqXG5XPAlI4hKc9oSYsYFGZB8+PAhpqhTbbxS0iNnSFEnOVRJ0qEwMGAJDlbeIZshISG1tbVoYMho6LEyyETy6tUrLFzG2KRJk8S7rfSfcs7r6uqWL1+enp4Ogy2XywX3HECc4iZAGZhv3rzBQ/Bw+LK7uzsiIgJHb5K0RWufMRYSEiIT0O8NB67BRbwe246mweCVgdEXWRDRYYcvvp5FAa/c9+/fhyZgMBgUR0hhn6T4HsF5B3H/A6wOKRa4bt68CcxRUkasp6cHzHXFPRxg6oh7NTnnMA7DfSPiCZ8NGzYwxnCRv7q6Gj59K79JDxlClsUXGef8t99+Y4xlZWVt2rQJ44TlIJzYcjqdU6dOHTRokGJ0OH78eIPBIGqrmQQq4K0D1gTOnj3rbcD+ki8tLTUYDLNnz3anQEVFRUBAwJw5c0Sb052wR/+2trZnPv3l5OSYTKbhw4cfPny4ra3NY0LyAqKBAdfULlq0CG68WLBgQe9PvMAq66hRoxQq6bQghaS7n5pVF1o6ji7y8vJglKL4JGVKSoporamVbG9vj4yMDA0NFcUUmvixpSti9vjzKzQwYOIEOu64uLiV//Nv48aNt27dwlepuJQPJ9LgEd61h6MN9bdXPCYE9PvawMjJyfH28srJkydDNkVjXV1X6urqli1bJq5mGAwGGJ95zDu+OxljuHKnSEK+ICQNDLi0BLImbkB0Z2CMGjUKawI4YIYSC50xtn79eoXa+BP33cFhng8fPuAjjEFdbbxS0iNnSFEnOVRJ0qE2MDjn//zzj1gNRowYYTQaYZQgo6HHyiATCeccOkqxyODqBcia/lPM/r179zZu3Dhq1Cg8wcUY0zQw1GWHkXDOcWuT0WhsbW29fPnyjz/+KApIuvfs2SPmSHERhWYkfm84nHOvqmXvDYy+yILICg0M+WkXMbjaXVpaCvMOin01CxcuZIyh1eF0OsePHw+XIoiRwJQ8rLahP5x5CA0NxfG3jBhkTf11DjhBN2jQIHGXCN4uKH7viHMOB2bCw8PtdntHR0dWVlZ4eHhmZibczIYaSjrgy1+K+81gNT4lJQWveYRv7IrLdMeOHWOMrVixQkzo1atXBoNBYYxpJiGG8soNPb/+68+rCD+DMKy6aF7k2N3dPW7cOKvViruCe6kPHI4S+yUf3GazWVHreqOV2sB4/fr1yJEjW1tbW1paRowYgVa6b6nAfsUNGzYogrtrQQoxnZ+aVbesrAzPV7S2tq5bt45zPnjwYLF1FBcX4wEtiF+tJGwm3Lx5szsF/NvS3aXizv8rNzA0v7KMe39hfgXRwAIxNCRsGDpDN3FUpJkQxNynBkZ5eXlwcLDi1prGxkacIsLciQ78qpe4Qbm1tVWx2w+CPHjwACEwxuATGR7zjtN4jDFcqhN14JzLF4SkgSEmKm6B9dbAgOspoSbEx8cr1Maf0LZBTNwjIe5ZUg9SvVLSI2dQBgtInRxqK+nQNDA45+LJZsiy2sBw1wrELGtWBslsulyuY8eO4b0LWEAwaaf/lHNeWVkJNT85OfnNmzfiNVk+GBi4KYsxduDAgSVLluBeKUnUIIY3LkB28GC0TiR+bzhw9Q0owBjz2HZ6b2D0RRZEYjB9zhi7fPmy6C/pvn//vloSjZY3b97AU/jOg8lkQrPw9OnTMLDGRQOQjIyMNBgM4hZTzjmYE3ALmaSY0+mEzYRqwwm6I/EMBsQJe/AiIyPFBQE4kjRp0qR169alpqYeOnSoN2NT2O0mnvFtb2+HKQlxQAwzMng3ut1uh00pio37sHskIyMD9If/6iTEp165YROs4mNtXsXQX8KrV6+2WCyKWsQ537Vrl9lsFvd59lLDt2/fNvj0BysY4eHhWVlZaj17o5XawICrDmFz3V9//YXbpH1LBa4F0uwuNFuQfCqaVbexsZExBqOL1atXw1VDY8aMGTRoEMRssz8beRkAACAASURBVNlSU1Nx6gE8FUo6HA5oQTqfPvNvS5fPNUh+hQaGuN1CccwO8izupti7dy8iE6cSsa/UGbp5TAhi7jsDo6mpKSoqSjySDjuA58+fr/mCxJyuX78eBhPiuKq1tVX9CoQgTU1NuGsI5uo85l082u7uAm/5gpA0MHCTgGIrqjsDIzMzM/1//sFVMPX19ThhHxwc7G7RGW+CYoyJ+631DQyvlPTIGQpIp5ZioUs63BkYnHPYJIrDUDAwZDT0WBlkIkH9X758uWbNGiwgxV0F7p6ePn0aNjXFxMTAFG8vDQyxlEeOHGm1Wn2b/XW5XBMmTECq4q5czLLC4feGwzn3qlr23sDoiyyIlHCOQPNWVlFS0403t4hPHz9+DMWEd8vCjgXcuNLW1rZhwwY4hSle0Af1XzFV0draajKZgoODcZ+qjNijR49AB8UUEgzWDQaDOr8tLS1hYWHiRM/Hjx9h++u5c+fcdW5ixvXdcPZjzJgxohgsp0RHR4uNYsmSJYwxPON+9epV+MaOGLCrq2vIkCGMMfG9ppmEGMorN7wOFJcFeRXDZxbGK0zsdvukSZOWLl0qKlBfXx8YGIiTjNeuXRNPA4qSfe3OyckxGo0///yzaMr6K1FNA4NzPmfOHDirk5ycrLa6JVPv6OgIDAw0Go3iNgQMq25B+Mijw13VhSFNdHR0SUkJ2tIw/wX0fvrpJ8UnntRKwpKgYlekqJJ/W7oYs6R7QBgY4iU/6qMOkBPNV5rmGQy8rI0xprigAy7KEI8zijdU4n2R4iqV/tAN96a7S8jdIe/en8GAGwaSk5PxEMG+fft27NgRHx9vMpnEVXJ1VcDraHEnGOccWoK7M82w7h8QEIB9h37enU4nzjQbjUY02BTK4LlS/YKQNDC6u7vx6Lz4/nBnYCiUEX+Kt2lpftf8/fv3QUFB8LKfOHGi4j2tU228VVKfM+isk5yYKRn31atXFWMFDGW32/FqYMYYDnE8aihTGTxGUlhYKK6QNDQ04Li88NOfztOXL1+ihYyXBPTewBA/4IODAMQl7xA/heGuA4TYjh8/DktA/m04cImhfNvR7I29OoMh3wlLtn0FbVgcCA0NFQe4Chl3P10uV1hYmHixGEjCCWxxxgGO8eCi3E8//QRXwShGKrAVSjynAcc3GWPirQAyYrDWZzQaFerBjQXYi7a2tp4/fx4zCDsr4uLiwAfnvPB4N0r64CgoKFDf+ATLKXjAA2a+vvnmG6PRiCfOQSs0zyDprKysiIgIg8EgDvU0k/BBVQjyxx9/+HAbr8/J9T7glClT0Ga4efNmQECAuM6ZmpqK6+fd3d2JiYma0/C9V0M/htzc3KFDh+JeQX1hH566MzCeP38+atSo9vb2d+/eRUdHiych5VMBWxe/agDDIZ0WJB+zu6rrdDoDAgLMZvOUKVOwqsO224aGhsOHDyumLDnnaiVx5s7dAQz/tnT5XKPkgDAwoMHDWM3d7UniRYf//e9/IQMOhwNCKT4uIx7XFu8VLiwshMuFoNQVX8fEG83Fs194Z+XUqVORGjo8JqS4pvbgwYMYFg95iztQp0+fDjlyN8iD4J2dneL0OUIAh2KqDFNER2dnJwyOxR1+YGAEBQWpd6bih/nEAwke8y5uOUtKSsJdBPA9NfgpWRDikVCxQPGQ97x58yB3aBhYLBbc+4t7Gxhjp0+fRg46js7OTrz4SHMFBt6OjLEhQ4aoielXG6+U9MhZvKZWs5bqZFP96MKFC+Hh4Wp/8Hn9+jUyRwNDRkOPlcFjJAUFBVFRUeK46s6dO1Dh6+vr9Z9euXIF2wjuSMGbTBVnMPTLTiRjs9nQyFR8Z00Uk3Fv374dNRQHnRjW6XRmZmZGRETAtka/NxzOuXy11OyN4cYVyMWWLVtgDyS8JjXl+yILiAsuDdNsuSjjzgF3EqhnQ2GHj3iUGV4ZcNj68OHDhYWFsHEOdipmZ2fDxMrixYsVH0ipqakJCQmZP3++uAVCRgxGDEOHDhWV7+zstFqtkyZNwvujKisrly9fjjKwPIUX6+FFeYq9SeXl5T5s84PLi4qKijo6OvCbpzDlIXaMtbW1jDEgU1BQ8OjRo4yMDMXtq1euXDl37lxgYCB8PbOoqAhi0EwCc+etY8GCBbjX19uwMvIvXrzYu3cvdo8yQfRlpkyZYjQat27dWl1d3dnZabFYxC4iIiIiJyfn9evXZ8+ehXfW5zcwKioqJkyYIBa3fo58eHrjxg1seoo31OHDh+EMw+3bt8eOHevD4XKoirCfJTs72+l06rcgef11qi7MqYlFCac1du/ejVcWiQmplXQ4HLAs/+DBA1Hy1q1b0LT929LFJCTd/W9guFwuvEES7tTTnFYpLCzEFzCuKD18+BA9sfeErxWK53enTJmSnp4+b948q9WK22fhs1zBwcFwYdS7d++gvMWTml1dXTixOnToUBwiI9yuri6PCYmDG6w3b9++Rc1xYolzjneuh4WFKSbFMVGHw/HDDz9gcLVD58QPRgK2sjhYBwODMfbtt98qpgEOHTrEGBs1apR4SY7HvHd3d4sT3rGxsX/88cehQ4emTp0qHnaUKQjxgyd4oaHNZsN9MmiXvnr1Covs559/bmhoOHjwIF6BCl/fk+z6bTYbXFbNGMMXJwAsKyuDhj127FjxHAs89VhtvFLSI2ePyWGhyzhglKnziqqpqYFRNWL0qCFMkOtXBo+RwHh02bJluDoHA76EhASXy6X/FDa8QksJDAzcuHFjQkJCTEwMtp2MjAw4duUtTHh/KK7+kOGsltm7dy9sXDEYDL/99hsuFTqdzpKSkqlTp06YMAFvYOOc+7fhcM7lq6X44TycNe/p6YENwYyxwYMHr1q1avTo0bCzX1O+L7KAVIcNG6a4Zh4feXTA+ZBvvvlGXLp88uTJ8OHDLRYLvkGwuy4sLNy5cyes/cJqfFpaWl5eHhx6hnMajDHckt7U1BQeHp6amipay/JicMYDB3MOh2PRokVLly5F64Jzfu7cuaCgINxiAW9P8XJY2FYeHx8PJpDNZtuxY8fOnTvdvXR0oA0fPpwxdufOnc2bN8NcLOx4HDdunBgKPnSzbNmykpISMN7g6+9ms/nmzZs2my07O/vQoUNgi86dO/fYpz+IQZ2EGLO37vDwcLPZLML3NgZ9eWArXnavL+/xKV5eD/1VQECAeDmNyWRS3Peo03t7TMsHAZfLBafafAgrHyQ3NxemLTjn0dHR4rVjTqdz8uTJsB3jzJkzkyZNUnxu0mMqMFNQWFh48OBB2GTosQV5jBMEdKru8OHDR48eLS6x7tu3Dw5mqIeanHO1kpzzlJQUxtiPP/4ILdfpdObl5W3cuBFnLvzY0iWzLIr1s4GRkpIC363DNz1jzGw2JyYmip8ty83Nhc9s4xAhMzPzyZMneD05+KempmLe2tra4GOu2CYXLFiAXTyI5ebmhoSEjB49evv27RMmTAgLCxPHkfX19bgPASIZOXKkuOYLkegnBElAcMZYYGDgwYMHm5qacJYUHi1btsxutysWJSZPnqxQGFLE72FjtAqHuAKDQBSOxsZGo9GoWBM0Go3z58+PiIgICgpasGDBvn37jh07BhdJbdy4ERcEMCr9vMOwcvPmzXihJ2Ns3Lhx165dwxjAoV8QRUVFOHCB73b/5z//sdlsitLBZeLHjx+LeOfMmQMjhrCwsKlTpy5btmzfvn0KBdz9dDqdZ86cgZHonDlz9u/ff+TIkeXLl8Ol7wcOHBBf6hCJZLXxSkkdzpLJucug6H/8+PHo6GisSxMnTqyurhYF0H3u3DlxixTnXEdDDNXd3a1fGfQjKSgoGDFiREJCwrfffrtixYp169YFBwfPmTMH5iP0n8KlmfgaDg8Pz83N/fjxI37iHT6B7APMu3fvil96wcz65qitrU1OTob2EhgYOHny5IkTJw4ePDg8PHzXrl3qt45/Gw7nXKZa5ubm4uorY2zQoEHYKxYUFOBWtDFjxsARLx15zrnfswAftcUDlD4URE5Ozrx585KTky0Wy+LFi/fs2bNixYrQ0ND4+Hgc1kO0cIDSZDIhATCljEYjfjYORszBwcEZGRllZWX79+9PTEzEcwionqQY5/zp06fx8fHjx48/e/ZsXl5ecnKy+NqCCLOysqxWa0xMTE5OzunTp2NiYsS5JPia07Rp0xhjBoMhIiJi9uzZojWFWnl0OJ3OqKgoxpg4gX369GnGmOKYO5gTgYGBODi22+04t2ixWOD0EXAIDAxEpJpJeFTMnQBs5FMfhXcn74M/HDVR3ILlQzwYRGFgMMaQobjXGrvuz2xg9PT09PIGJ8yppiM/Px+O5ZjN5ohPf4MGDQoMDIyKisKt17W1tUOHDoWnBoPBbDbjlwY041R4wtKBxWJBdB5bkCIGzZ/6VXfMmDFXrlwRA/79998jRozQHPVxztVKwoeqoBGNGjVqwYIF8fHxJ06cEONsaWnxS0sX45R397OBIa+ob5Ktra3Xrl27evWq4sWAsXV1dd26dauwsPDJkydo8+FTeYfHhOSj+mySe/fuNRgMeGDx48ePeM/go0eP8vLy9u/ff+jQoYKCAnc1HlT1mHe73V5dXV1UVKRYGBFz6q+CgDidTueDBw8KCwthiNPe3l5XV+fD5Bxq+Pz587Nnzx4+fPjAgQN///33gwcPelNbfFPSI2fU9jM4CgoK1NfOyGjosTK4i6S5uRnqamdn5927dy9fvixuRNZ/CkAaGhouXrxYUVGBk5dtbW3FxcUPHz70uTThy0c+LMrrlFFHR8c///xz/PjxrKysvLy8srIyVFgdyr8Nh3Pey7bT0dFRUVHx6NEj+ebm9yzs27cPv9OiJubR5969e6C8w+Gora3Ny8s7e/ZsQ0ODupL09PRUVVUphjL19fVihwmzkrt3737//v3t27fdvYkkxVD5V69eVVRUPHnyRJMzrC729PQ8fPiwsrISjz1gcHC0tLRUVlbiFnDFU8mfra2tNTU1uK6oE+rp06fqzeLPnz+vqqoSZ68ePHigGLDKJ6GTOjwCC1C9/81jQHkBaEEyQOTjJMk+JWC326uqqsTKKdmCPGqlU3UVGxQ55y9fvnTXP3DO1Upi6s+fPy8vL29qalL3USDjl5aOyck7vnIDQx7Ev1DS5XKlpKSIW8v+hRAoy0TAWwKVlZXFxcUwsLt+/brmjUPexkny/iLQ1NQ0ePBg8XSZv2L2LR7YZnnr1i394JJi+pHQU48ENm/ePHjwYNGe8RiEBIgAEfCNABkYvnH7SkI5HI4VK1bs2rXLneH7leSTskEE/EQAD4Pl5uZyzufPnw9XG/speoqmVwRsNtv06dP7dH7aK/26u7uDgoKMRmNXV5dOQEkxnRjokQ6BxsZGXMOxWq14hlMnCD0iAkSg9wTIwOg9wy87BpfLdfToUbyf4cvODGlPBPqYAHwFjDG2cOHCgwcPan6bso9VoOi1CTx//jwhIWFA2XtwqyzciaSt9CdfSTGdGOiROwIdHR2DBg2Cr7AVFhbGxsbS8oU7VuRPBPxLgAwM//L8UmNT7Hn9UrNBehOBPibw7NkzvJQsJiZGZ8tsHytC0SsJvH37Vn3pglLoM/5+/PgxfDnLarXW19erz+iDLpJin1Hxryopl8s1fvz4iRMnXrlyZcaMGc3NzV9V9igzRGAAEyADYwAXDqlGBIjAwCPw4cOH0tLS+/fv65y9Hnhak0afm8ClS5fgE5Dw393VmZJin1v7ryi9rq6uG5/+qMF+RaVKWfkCCJCB8QUUEqlIBIgAESACRIAIEAEiQAS+FAJkYHwpJUV6EgEiQASIABEgAkSACBCBL4AAGRhfQCGRikSACBABIkAEiAARIAJE4EshQAbGl1JSpCcRIAJEgAgQASJABIgAEfgCCJCB8QUUEqlIBCQJpKWlRUZGxsTEJCUlTZ8+PTIyMjY2duHChVOnTo2MjJwzZ45kPCRGBIgAESACRIAIEAGfCZCB4TM6CkgEBhYBl8tltVovXLgAn02ELzYcOHAAtNy+ffumTZsGlsakDREgAkSACBABIvA1EiAD42ssVcrTv5LA/fv3jx49ilmfMmUKY+zhw4fgU15efuXKFXxKDiJABIgAESACRIAI9BEBMjD6CCxFSwQ+NwGbzeZ0OiHVtrY2g8EwbNgwVOLdu3cD6jNkqJjPju7u7nfv3vkcnAISASJABPqLAHVf/UWe0v1sBAaWgdHe3n7z5s3//ve/6enp4lysDg6Xy1VYWJiRkXHgwIG2tjaQ1PTUieRLfORwOO7evZufn79jx46NGzfqZOHVq1c3btzIzs5eu3atu4896QT/Qh99/PixoqLi4sWL+fn5165dG5gZ97bCP3/+fNv//Kurq9MsoPPnzzPGVq9erfmUc97Z2dnm5Z9X9sn79+9zcnK2bduWn5+PZo+mMqWlpZr+Hj337t07depUhZjNZquurlZ49u/Ply9f5uXl7dq1Ky8vr6WlxQdlBlSHptmfaHrq53SAZGqAdKTedgX6bP+FT+X7xgECR7P7GiC6kRpEwC8EBpaB8ezZs+PHjw8aNIgxdvz4ccxhWVnZ6NGj8/Pz0QccTqczOTk5IyOjs7MzIiIiNjaWc67pqQg4oH66y52+kh8/fjx79mxcXBxjbMmSJTrCJ0+eXLZsGWPMbDY7HA4dya/jUX19/cKFCwMDAxljAQEBISEh7NPfyJEj//rrL/3B7mcm4K7Cu1Ojp6envr5+6dKlkCPGWGFhoabw2rVrGWMFBQWaTznnpaWlGImk49q1a+5iU/g3NTVFR0eXlJRUVlYyxnbv3q0QgJ9dXV2bN2++ceOG5lN3no2NjTabjXN+9OjRpKQkzjmMEUHe5XJlZWXl5ua6C/6Z/ffv3x8WFvbnn3/W1tZmZ2eHhYUdPHjQKx0GWoem2Z9oeupksx8zpehvB0hH6q4rUGirg/QzPBpQyijyK983KgJ+5p/63ZcPyty5c2fDhg2hoaHmT3+VlZXuImlra7NarSCWkJBw8eJFd5LkTwT8QmBgGRiQpaioKMZYY2Mj5nDz5s2MsRkzZqAPODZs2BATE+N0Ol0uV3R09OTJkznnmp6KgAPqp7vcySiZkZHBGPvvf/+rL3zjxg3G2IIFC/TFvvSnnZ2daWlphk9/69atq6mpgUn35ubm/Pz8kSNHMsbGjh1bVlY2oHKqrvD66hUXF6NJ4M7AiIqKMhgMuKanGeG0adMYY6NGjaqqqrqr+5eWljZlyhTNSNSe79+/Hzdu3G+//cY5v3v3rslk+uOPP9Rib968iYuLu3v3rvqRvk9iYmJUVNTdu3dLS0s3btzY2tqakJBgNpvb29sx4IEDB7Zu3Yo/+8tx5MgRxtiJEydQgWPHjjHGjh07hj4eHQOwQ9PsTzQ93eWuHzOl2d8OkI5U3RVoauuOal/7DyhlNDMr0zdqBvxsnjLdlw/KLFiwAF4KOpNKMM8IfX5PT48PqVAQIuAVgQFnYDQ3NzPGRowYIWajrq4uJSVFMS588OCBOEfb09PjdDo1PcWo+t2t3meimTtJPeEgr2iMaQaEC4Wys7M1n34dng6HY/bs2Ywxi8VSW1urzlR3d3daWhpjbNCgQfKT8ep4/OujWeH1k7h27Zq+gfHkyRPGWFxcnH48//zzD8Rz69YtHcnu7u7IyMji4mIdGfHRrl27TCYTDvftdrv4FNwOhyMhIcGrcTZG8vHjx+PHj0+dOnXr1q3Lli2Lj4/fvXv3y5cvUQAcP/zwQ/+uY7x69SokJCQyMlJcNHM4HOHh4WazubW1VaGw5s+B2aFp9ieangMwU5r97UDoSDW7Ak1tNan2hafibdW/yshk0GPfKBOJjowCiI6ku0eS3Ze74O78o6OjoTPHawMVkgUFBWazGWR27NiheEo/iUBfEBhwBsaJEycYY+vWrfOY2yVLlgQGBn748EGU1PQUBfrR7XK51qxZc/PmTX/pAAd5IyMjPUYYHx/PGHO3X99j8C9CICsrizFmMBh09vQ7HI7ExETGWHh4OI6A+zd38hUe9fT4EoWJ8507d2IQd47JkyczxvS/j3H8+PHY2Fi4+tZdPOjf0dFhsVhg5xJ6qh1btmyZNm2a2l/ep6qqat68eaNHjy4oKNCcjXv06FFgYGB5ebl8nP6VPHToEGMsLS1NEe2aNWsYY0eOHFH4a/4cmB2aZn+i6flFZGqAdKQ+dAWaeP3i6fe3lV+08hiJx77RYwzuBPwLxGP35U4NTf+GhgaLxTJhwgTGmOZd5G/evBk6dOjPP/8MBsbt27c14yFPIuBfAgPOwID95RcuXNDPZ1tbm9FoVGya0vTUj+ezPe3p6Vm/fn1wcLDmhK5vasBB3p9++kk/eEdHh9FoHDp0qOQYUT+2gfnU5XKFh4czxhYvXqyvYV1dHXSy/Tu9jUpKVviurq6qqqpnz55xzj2+ROfPn88Yu3PnDqbiznH58mX9V47D4bBarfK7dU+fPs0YO3z4sLsUOec1NTXi2qOOpOaj4uLiCRMmJCQklJaW7t69e8uWLcOGDcvMzFQLz549e9asWWr/z+Mzc+ZMxlhOTo4iucOHDzPGEhMTFf7qnwOzQ9PsTzQ91TninA/ATA2QjlSyK9Ck6l/Pvnhb+VdDMTav+kYxoLzbj0Dkuy959bKzs5cuXbpo0SJ3b8AFCxakp6fD1EZYWNi/4SimPD2S7DsCA8LAeP78eX5+fmFhocPh+OabbxR7x7u6uu7fv3/p0iWg8Pr165aWluzsbMbYmjVrWj79vXjxQu2pGMp3dXWVlJTk5eXV19crgNrt9traWty8CPq8f/9eFHMX3GazlZWV4Z6clpaWU6dOKZKora2dOnUqY2zmzJktLS1wRBUiV+ROTJFz/vjx49OnT5eXlzscjsrKyhMnTojbLeAg75kzZ+BSoNLS0lOnTqm3S125coUxtmzZMkXkqIA7LJry4Pn69evCwsKTJ09WV1d3d3ejpMvlamxsPHPmjLg+YLfbCwoKNM8DuKPKOZcpFEy3tbUVBsqHDh1CT3eO0NBQzalld/IeC0KmDoiR61d4URI4pKWlGY1GyOCCBQtgPAQ/1Wcwenp6zGZzaGiozFvE5XLBvNfcuXMV6cLPU6dOjRs3Tqx1mmLd3d3QEpOSkhhj58+fb2lpefXqlabwqlWr1GuPO3bsCAoKMv2/P4vFkpGRwTlPSUkxm80mk2n48OGwNrVixYpt27Y5HI6ioiK4JqugoGDSpEnqK2tzc3MZY1VVVZpq9KmnzWYzGAyMsZKSEkVCYNQZjUbF6qsoptnLKTo0d20Q4vGq+YhJe6ztmv2JpqciWplM6XQIGJt+r8g5b2pqKigoOHfu3MOHD9+9e1dTU4NhNfvbfuxI9bsCTW0l+0aPJBsbGwsKCvLy8vDlBZTcva3cKQOh9GujfA+pU3ZYiOiw2+1e9Y0YUO3QqVTugIiR9EX3Jcav7547d+7Jkyc3btzIGFMflsvLyxs9enRnZ2dkZCRjLCUlxV1sOoUo2Z94rHXukuivkYMahU4NfP369fXr1x89eiSGevDgwd27d/EVabfb6+vri4uLodtpa2srLi4+c+YMTA5iQEkxlOecu0OHMjqao4zHAkJJvzj62cB49+7dsmXLkpOTr127VlRUBBY2tpBnz56lp6ebTCZsFQ6H44cffkhKSgoLC4O2lJSUNG/evFmzZik8k5KSsES7u7v37NkTHx9fUFAAYw4chnZ0dOzbt2/s2LGMsfj4eM751atXIcX09HRA7C54Xl7exIkTYZwH50POnj1rsVjAB99q5eXlSUlJ0LZjY2OTkpLgLIQ6d2KJNjU1zZ07d+XKlRUVFYWFhWvWrBkyZMjYsWNFmW+//ZYx9ubNmxs3blitVpjCNxqNijPfcDLvr7/+EsNyzt3lSyGm+Nne3p6amrpw4cKKiora2tr4+PjY2Fi4BPbRo0e//fYbFA1aa5zzkpISxhjc8YWx6aQuUygYDzicTieUmrsdqKI8GBjurjYSJWGwolMQknUA49Sv8CiGDqfTCTtPYM77+vXrR44ciYiIgDqmeYsUHHOcPXs2RqLvuHDhAsSmPm/tdDrHjBkDFqx+JLdv305KSoIzMAaDIenT36pVq9Sh3r17ZzKZFJUBxP744w/MlzjBHx8fn5iY2NHRoYht//79ijVMhUBFRQV2HYpHff0TVmkYY4q5Bs55bW0tZBO/gahQRrOXEzs0nTbIOfeh+aACMt2OZn+i6YnRwk1f6q5bzJROh4DxyKh34sSJ4ODg06dP37p1Kzk5mTEGFVinv+2XjlS/K3CnrUzheiTZ1NSUmJiYnp5eXV1dX18fFhaGm/I131bulIFy0a+NXvWQ7soOK4Do8KFvFIOjW79SaQLBsKLD792XGLmOu7Oz02QyNTc3HzhwAHb/isLNzc0Wi6WysrK+vh66HfF+TpTUKUSZKicznNBJoh9HDkgAHO5qYFVVFXQmjDHxMHBzc3NAQEBUVBQELysrW7FiBXAuKio6fvz49OnT4+PjDQZDYGAg3oMqKYa66aBDGXeao4DHbgEl/ejoTwOjvr5++PDhOI7nnMN4HTs7yOecOXMUt9ZyzocOHcoYa25uFlloera2tk6aNCkuLg5WJN6+fav+PkB+fj5j7Lfffrt9+/by5cthQgvU0A8OY4XBgwc7HI5jx47t27fPbrfDfQ6KPdawgqEebWjmrqKiIiwsTBwrw+SE+L2LxsZGGLWXlJRs2rQJDp/B7gvxiC3nPCYmhjH2/PlzkZV+vkRJ0V1TU2O1WkU1YDibnJyMYrC4tG3bNvTp6uqKj483Go04py6Tuk6hYMyiIzU1lTG2aNEi0VPthi1SBoPh8ePH6qcKH5mCkK8DkhVe1CEvLw96K7PZjDP0QBj8xRWM1tbWzMxMsDNDQkJyc3PVy1li5OB2Op3jxo1jjM2fP1/xtKCgDrFT4AAAIABJREFUIDo6GudmFE/VP+FS2okTJ6ofoc/Zs2fdrac5nU44awtZg+tri4qKxo4dqznZf/HiRbEqYhLoaGtrg9uZPWbhzp07uV7+nT9/HhNSO65evQq5UH+A5enTp/Do+vXr6oCij2aHJtMGOefeNh/OuUxtd9efaHYyYl7QrZkpmQ5BRr3Ozk6z2YzHe2CDn2g5q/vbfulIJbsCtbaAUadwPZK8ePFiWFhYXl4eRNXS0sIYCw4OxgLinGu+rTSVkamNkj2kx7ITNeSce9U3KsLiT5lK5Q4IRgIOv3dfivjd/bxy5cqYMWM45+fOnYOb2XFPgcvlSkxMhKVgfGuoeySZQtSpcpxzj7VOJon+GjkgWP0a2N3dbTAYTCZTV1cXBsnMzFSPJy0WS2Bg4L59+/DtDGLh4eHim0hSTAadvuYyBYQ58q+j3wyMFy9eDB06dM6cOeLBgNGjRzPGxDttnE4nrAk0NTVhzpuamhhjisPNmp6dnZ3jxo2zWCx4ycz+/fvV+7/h/pOCgoKlS5f29PS4XK6WlhaXy+Ux+KVLlxhjqamppaWluO88ISFBYeZ++PBB8VllyItm7urq6sxms+LTFitXrmSM4T4xzjksxfz444+ihfb+/XvYmIH771+/fq2+lctjvhC16Hj48KHJZIqLixMbCexNCggIwOs14HUizkBzzs+fPz9z5kyITTJ1d4UiqiS6m5ubhwwZYjQa9UfVq1evZoxt2bJFDKvpliwIyTogWeEVmowYMQIGo99//z0+8ngGAyUlHWfOnIFU7t27h0FcLtf48eNxIIL+Og54Q+gP+vfu3csY++WXXzTjqaurgw+YMMaioqJqamqioqKePHmiKSzjCb2HYlFbHXDbtm1AQP4/LrSqY+Ocgx3FGFN/WQ96KsaY/kkzzQ5Nsg1yzr1tPpK1XbM/0fTUxKKZKZkOQVK9ly9fMsZMJhNucE1PT8ctqZr97efvSCW7Ak1tgaq7wvVIEhaT4QppiKqzs3Pu3Ll79uzB8tJ8W2kqI1kbJXtI/bJD9dDR+75RslJpAkE1RIffuy8xcnfuDRs2wMHu27dvQ/eFg6Xc3NyxY8fC1sp58+bBLe2KeCQL0V2Vg+3Z+qMsyST6a+SAQPRrICwBJSQkoLzL5YK778VFfujiQkJCxE0cVVVVUDQ4Jy4pJolOX3OP3QLmyO+OfjMwEhMTDQaDOBa02+0GgyEkJATtbzwPOmrUKDHnsKlDMQTX9NywYQNjDK9nra6uNpvNK1euFK0azvnMmTONRuPPP/+sWGHwGBwWFrKzs1evXg1x9vT0hISEmEwmccM0TPOvXLlSzIVm7pxO59SpUwcNGqTYvz5+/HiDwSAebIAFu3Hjxon2dFdXF2zWxxEVTDysWbNGTNpjvkRhcPf09MTGxjLGKioqxKe48IotBwz9b7/9VhTbtGlTUVER+Eim7q5QxGgV7tLSUoPBoLM7qKKiIiAgYM6cOaKNpIgEfsoXhGQdkKzwojLt7e043hXvBvG7geF0OkeNGsUYW7hwISpw+fLlb7/9VvOCJpRROGAR6ezZswp/8Sdsg1SsUooCu3fvxlwbjUb563HFSNBttVoZYx6/5edwOOxe/ondFCaHDiwj9XwhTJkzxvQvlFN3aPJtUKdPQw1Fh3xt1+xPND3F+NGtzhR8uUi/l5ZXj3MOs1RowYp9JuxbU7xNPnNHyjmX7Ao0tQWS7vpG/a61vb09MjIyNDRUvdsQC4hzrvm2UisjXxsle0j9shM15Jz3vm+Ur1SaQBT64E//dl8YrY5j5MiRV65cgd280HPC1XlPnz4NDQ2trq6GQztBQUGMsc2bN4tRyReiuyrnsf3KJ9GPIwdkotN75OTkKD4aCxWDMfb69WuMARbWFNNPN2/ehKJBSRkxeXT6bUe/W0DN+8LRPwbG8ePHFaMZznl1dbX6Y3CwtLRhwwYx8zDdiGYDPFJ7Xr9+HbYk2u32jo6OrKys8PDwzMxM3KgDATs6OgIDAyMiIsSlAM65TPCxY8cGBgYuW7YMJ8nu3LnDGBPnmznnsEH51KlTYi445+rcwXe4VqxYIUq+evXKYDCIVdbhcMCd1rirD+Rhj4rZbEbzZtWqVYwxccwnky8xdXBDvzlhwgTFo6KiIviyhDgSjYyMNBgMOAJ78+YNjlwlU3dXKIrU1T9hEv3vv/9WP+ru7h43bpzVasW9RmoZ9JEsCM65TB2Qr/CoALYI6JjEETkOXjXPYIgxyLuhvwsICMATn1OmTPH2OxVgpeD8mWbqMJ77/fffNZ/CXl7YbwMZR7vUnby+/5gxY9QrlvpB/PIUZuM0z2DApy00H4lJqzs0+TbobfORr+3q/oRzrukp5gXd6kzJdAjy6nHOT506BTVHfbxe3d9+/o5UvitQawsY3RWuR5Iw0FcMMbFo0KH5tlIrI18bZXpISF2n7FA9cMBooTd9o3yl0gSi0Ad/dnd3+7H7wmjdORoaGgIDA8Fi7Onpgf0LZ8+ehQMquFRVWlqq2SgkC9FdlZMZJkkmARnsx5EDKKBTAxcuXMgYw3vPnU7n+PHjGWMxMTFi6cBmE8WrE5ZJQ0NDcWpbRswrdO4099gtiMr73d0PBobdbh88eLBiKxTnHE4+KI4uwFWPly9fFnMOe5DEnbWcc7XnrFmzGGOTJk1at25damrqoUOHNEeWcKmLwWBQnFLwGBx2rwYEBIiVac+ePYwx8fgE5/y7777T3CyhyJ3dbocdHYqsweok7KQEDrAYarFY0JAAf/gerXhx7fDhw+EgOAL0mC+URIfT6YSd/erzYfDSEs9gcM5hJz1uS0tLS8MDD5KpuysUVEnHsXr1aovFov6Q2a5du8xms8zHQOQLQqYOeFXhxXzhBAljTPyoRV8YGLBbnTH2448/wrn84cOHK2qXqJvabbPZGGMRERHqR6IPdKxiZRafghusdHgjDhs2TJyEVgvr+8CM1D///KMv5venHR0dcOuAOmmwyYOCgsS1R7UCig7NqzboVfORr+2cc3V/4s5TnSPfemmv1INE4SqzyMhIRc1R9Lec88/ckXrVFai1hdy5K1z9rtXhcMDLxeNqnubbSqGMfG2U6SHFquKu7EQZXGaBLsKHvtGrSqUJRKGP+NOP3ZcYraY7Oztb3LQzbNgwxtj+/fsPHDjw3Xff4RwfGPYmkwl3MnPO5QvRXZXjnOvXOvkkIHf9O3IAHTRroNPpHDx4sLgz5fTp06AtLpZCcLCRFMMPeOuJAzOPYt6i45xraq5fQJqVyo+e/WBgXLx4kTEWEhIiblNpa2uDJTxxvzXYzYr7HJ1OJ+xBwsYDTUXh+fHjx4CAAMbYuXPnxITU7P7zn//guAqfygQ/efIkY8xqtYqT99ARi6NYOKUAx7AwfrjsJTAwUMwdHAy1WCyiWFdX15AhQxhj4khl586d6o3sNpvNbDYPGjTo6dOnEMPjx48VFrZMvsTUwf3o0SPoyhVbyKCbNhgMeGUWyMMsNXheunQJvzghn7pmoagVE33wWLndbp80adLSpUvFp/X19YGBgfg9h2vXrul8j0++IGTqgHyFFxXmnOP2M8Whkb4wMDjnMLcaEBBQX18/ffp0xQqhQjf1T9BK5w5ECAI28H/+8x91DOizadMm/DAtY2zt2rX4yFsH3LjV0NCgH/DNmzf1Xv7hJXXuYobuXjFjwjmHy15wTU8zuLqX86oNetV85Gu7uj+BO20VnYxmjnzupeXVw3RbWlrgLjvxaIHm2+Qzd6TyXYGmtpBBzcL12LU+e/YM+nDcy4q4RIfm20qtjHxtlOkhRQU0y04UAHcv+0b5SqUJRK2P6OPH7kuMVtM9d+7cvXv34qO4uDjG2KxZs0JCQsQDdXAXuWJjhXwhalY5zrnHWiefBGShX0YOSA8cmjUQtgji7uu2trYNGzbAtQfiJt4nT57gfaQYbWtrq8lkCg4OxoGZjJi36Djnas09FhAq2UeOfjAwYD4e7oTFXG3ZskV9bht6genTp6MY5xxuAVJcT6n2bGhogP4U59HFSEQ3DGUUw02Z4EuWLGGM/fnnnxgbdMTDhw9HH855QUEBY0x98lWdO1iGxkoMkWRlZUVERBgMBvEinWnTpjHGYHslprV9+3bF4gkszMH2/e7ubqfTKZMvjBAdsMBqNBpFo45zDoeDt27dipLggIPUpaWlDQ0N4uhQPnXNQlGkovg5ZcoULMSbN28GBASIxmpqairO9HR3dycmJiqWxcTY5AtCpg7IV3hRB9gshJ+/EAfufWRgdHd3w2XKMTEx4eHh4lyXQjHNn3BLI14ArSnDOYcxluIOAFG4oKAgPj7+48eP8FKEVowlK0p6dMPlxQaDweNSDMzwQVqS/8Uti5qagMGmOP7EOYfZLP3T8+oOzas26FXzka/t6v4Eb5sQOxlNGppdt0yHIKlea2ureK8XhIqLi0Nl1P0t5/wzd6TyXYGmtpAXzcL1SBLGNIwx/QMYmm8rtTLytVGmh/RYdliI6Oju7u5N3yhZqXRe36iJwuHH7ksRs/onLJOKw4CUlBTovnbt2oXyb968AU9F5yxfiJpVjnPusdbJJwHa9svIAS5Z0u89YFYIJyx++umnxsZGk8kkThBjZ6i4AR92Oh09ehRLBDpSfTFJdPptx2MBoUp95OgHA2PTpk2MsXnz5mGWSkpK4KULF+dfunQJrAKY7AQDPTs7GxYiYEZEscVC7QkbNhhjiu1G5eXlV69exaRhXkdxfRjn3GNwuFXDYDC8efMGY4M7OiAXBw4cgAtkoM0UFRV1dHSI1og6d+AjXrR65cqVc+fOBQYGwncDioqKmpqa2tvbDQZDUFCQeJikoKAgICBg/fr1qAx8pIwxBiPpXbt2vX//3mO+xODohmo6dOhQ9IG7I6xW66RJk9Qj0fT0dMbYkSNHFi9eLL7PJFN3Vyhi6mr3lClTjEbj1q1bq6urOzs7LRaL2KQjIiJycnJev3599uxZOK2uY2BIFoRkHZCv8OpMwZFoxpjFYvn48SMIQIcF74zTp0+rQ/nsA+fYFGaqZGxwO3NlZaW+fGtr66BBgxRXwGGQhw8fhoeHwymO2tpaHENYrVbMPgp7dMCFsHPmzPEo2dDQcM3LP485ff/+ffinP9Es7+rqslgsw4YNE9uFWj11hybfBr1tPpK1XbM/ceepzhHnXJ0pmQ5BUr3Kysrly5djujDDLU7ZQjzi2+Tzd6TyXYFaW8iau8L1SNLhcAwaNIgx9uDBA6TEOb9165b4itR8W6mVkayNkj2kx7ITFUZ3b/pGyUrFOdcEgjooHP7qvmDZ3+O0yJkzZ4KDg8UNGnBcJDY2VtxV8ffff8PLQtFlSRaiuyonM0ySTAIx+n3k4HA49u3bd+DAAZESJocOjzUQllbghpvDhw8XFhaWl5czxmCmOzs7GwZ7ixcvVmz+r6mpCQkJmT9/Pp6+4JzLiEmi09fcY7eABPrI0Q8GBhwnDQ0Nra2t7erqOn78+B+f/hhj27dvP3XqFI4LoVALCwsPHjyIm3DS0tIU+4U455qesEUhPj4eyt5ms+3YsWPnzp1iVTt69ChjTDEuB9b6weE4tWJ1BUZ+e/fuPXHiBB7phl3Ld+7c2bx5s7gKoc4dXMZiNptv3rxps9mys7MPHToEa3Nz58499umPcw63/kVHR2OduHbtWnBwsMIg5pxHRUXB2Y+DBw/ixbX6+cI4RQfe8I3ndx0Ox6JFi5YuXaq2LjjnsPFg9OjR6js6ZVLXKRRRK4Vb/IQCXAeemZmJMiaTCbbMQVeLdhcKiA7JgpCsA/IVXtQB3K9evYLPAjLGfv7554aGhoMHD8J5GMhIYmKiYt+aOhJ5H7vdHhERYbFY9Ie/mhGGh4ebzWZxMK0pxjlfv349Y0z9Zffnz59HRUX9/PPPGHD58uVYXoqtriij44C7YsXLnXWE++LRpUuXDAaDWA937dplNBrh1hedFNUdmnwb9Lb5SNZ2d/2JZiejmTV1pnDfsE4vLaneuXPngoKC8BxdYWEhYywnJwc1Ufe3n78jle8K1NpCRnQK12PXCtPbP/74I7wBnU5nXl7exo0bxaGP5ttKrYxkbZTsIT2WHRai6OhN3yhZqfB8kfr1LWoCbn91X/idHPFspzo5p9M5ceJExUzNoUOHAgMD8aIO+MAlfNVEfQpUshB1qpzH9iuZBObO7yMHvL5J/DoeJocOjzUQbiMsLCzcuXMnrA7BdTJpaWl5eXkw2INzGowxPIDR1NQUHh6empoqvhblxWBIoz/o8qi5x24BIfSFox8MDLvdDnvXGGNhYWGw1RtKKzg4WDxGDOa4xWIRJ5tjY2MVZ5U455qeLS0tsAJuMBgiIiJmz56tsOA553AzgLimgZT1g4MtoTjMDVN0JpMJbSSn0wkv4AkTJmBFgSTUubPb7YmJiTCislgs8O1tMDACAwNxT3xbW9uSJUssFktubu5ff/2Vmpq6aNEisU/BLMyYMYMxNmbMGPH8hn6+MKzC8fTp0/j4+PHjx589ezYvLy85OVlcjVEIZ2VlRUZGam5Sl0ldp1AUCYk/FQYGY0wc2MGJWxyt6hsYkgUhWQfkK7yYHXQ/fvwYrkIC5efMmXPjxg1oO1OnTl22bNm+fftQuPeOw4cP//HHH97G8+LFC8aY4qy/u0iePXtmMBgUe4Sys7PBlDKbzWAq79+/H40ryDse5nEXs8J/yZIlI0aMECcUFAKf4WdxcfGIESPS0tJOnTq1du1aq9Xq0bpw16FJtkFvm49kbeeca/Ynmp6aYH3rpSXVy8rKslqtMTExOTk5p0+fjomJ2b59u6iGur/9/B2pfFeg1hbyolO4HrtWm80G75dRo0YtWLAgPj7+xIkTIiJ3bytNZWRqo2QP6bHsRCVFt899o2SlcgdE1AHcfuy+mpqa4DyqePejIsWqqiq4BAIu3sQPup0/fx57b6fTuXPnTnGjaUJCQmZmpjjYlSlEnSoH+/71R1kySWDu/D5yaG9vh3s+cEiGaYkOjzUQjkqbTCYchsGN20ajEQeBMFQLDg7OyMgoKyvbv39/YmIiFg0mJynGOZdB51Fzj90CKtYXjn4wMDjnLperoaHh9u3bOFHa3d1dUlKClwRDVu12e1VVFcpwzuE7D0lJSSILTU8UaGlpqaysFJcO8JGMw6vgLperrq5OcXVJa2trTU2NuGQJ6apzB/7Pnz+vqqoSN4Q8ePBAQQZOTD58+LCmpgY/KaXOjs1mq6ysFKNCGa/yhaFevXpVUVHx5MkT/UFbXV2deu0CI4FeqTeFIkbVd27JglAooFkHJCu8Iir86XQ6Hzx4UFhYCGZke3t7XV2dfhFg2M/jgN5WnB3QT3fNmjUezzDox+Dx6cuXL00mk2+HNzxG7pVAd3d3TU1NYWHhvXv3xLe7u0j0OzTJNugucnf+MrVdsz/R9FSnop8pj92RR/VgHa+np+fhw4eVlZXqXtFdf+t0Oj9nRyrZFbjTVg1W4SNDsry8vKmpSVy4wEg031Y6yvhQG9U9pMeyQ/XUjt70jR4rFezO13x9qzXxo8+7d+/wQLAfo3UXlQ+FqIjKY62TTKIvRg5lZWVGT5/f9VgDe3p6qqqq3r59K2a8vr4eFys45/v27YMPZbx///727duKCWUMKCmG8vroPGoO8XgsIEzOv47+MTB8zsOtW7fU+6M0PX1OggISASLgLYHNmzcPHjxY05TVjMput0+bNk08V6cp5rOny+WaP3/+/v37fY6hHwN+lR3aV5mpfqwklDQRIAIyBDIyMvy7yO8u0e+//15xAENTUlJMM+wX5/kFGBg2mw0322zevHnMmDEul0vT84ujTwoTgS+XQGNjI84TW61Wxb0LHvP19u3bKVOm9NFEXWZm5po1azTnaD0q1i8CX2WH9lVmql+qByVKBIiAtwScTuevv/6Km5q8De6VfHd3d1BQkNFo1P+6kaSYV0kPZOEvwMBISkoKDg7+8OHDu3fvIiMj4bS3pudABk26EYGviUBHR8egQYPmz5/POS8sLIyNjZVfvkAOra2tq1evxvsb0L+XjgMHDshv1uplWv4K/lV2aF9lpvxV4hQPESACfU3A3T4lv6cLt8rCbZ86kUuK6cTwZT36AgyMHTt2GAyGq1evLl68+MKFC8BX0/PLQk/aEoEvl4DL5Ro/fvzEiROvXLkyY8YM/a936WTT6XSqj8HpyHt89ObNG/ELUx7lB4jAV9mhfZWZGiAVhtQgAkRggBB4/PgxnLm3Wq319fXu7heWFBsgmfKLGl+AgeFyue7fv3/p0iXxPI2mp1+IUCREgAjIEOjq6rrx6U/m4LJMhP9mma+yQ/sqM/VvrqWUdyJABNQELl26VCj8vXjxQi0DHxgQpArdiWmG/UI9vwAD4wslS2oTASJABIgAESACRIAIEIF/IQEyMP6FhU5ZJgJEgAgQASJABIgAESACfUWADIy+IkvxEgEiQASIABEgAkSACBCBfyEBMjD+hYVOWSYCRIAIEAEiQASIABEgAn1FgAyMviJL8RIBIkAEiAARIAJEgAgQgX8hATIw/oWFTlkmAkSACBABIkAEiAARIAJ9RYAMjL4iS/ESASJABIgAESACRIAIEIF/IQEyMAZQoXd3d797924AKUSqEIGBSoAay0AtGdKLCBABIkAEiAAnA2MAVYK9e/dOnTp1AClEqhCBgUqAGstALRnSiwgQASJABIjAADMwXC7X8+fPi4uL9+3bt2rVqp6enr4uovLy8m1u/h4/fmyz2dw83JaXl+dOt9LSUnePNP0bGxttNhvn/OjRo0lJSZxzh8Nx9+5dELbZbNXV1ZoB+9Hz85dUP2b2i0va5XIVFhZmZGQcOHCgra1NXv/379/n5ORs27YtPz/f6XTKB/xskvqN5bOpQQkRASJABIgAESACOgQG1gpGR0fHiRMn4uPjGWOTJ0/W0dtfj2w226VLlyZMmMCEvxUrVpSWlnZ2djqdzjt37mzfvl14yMLDw/Pz85uamtQ6dHV1bd68+caNG+pHOj6JiYlRUVF3794tLS3duHFja2trQkKC2Wxub2/nnLtcrqysrNzcXJ0YdB6VlZWNHj06Pz9fR8aHR31dUleuXFm5cmVYWJj505/FYlm+fHllZSWoevv27Z9++ik0NBSejho1KjMz04dc+BCkj3j6oIm7IE6nMzk5OSMjo7OzMyIiIjY21p2kwr+pqSk6OrqkpKSyspIxtnv3boXAQPip31gGgoakAxEgAkSACBABIjCwDAwoj4MHDzLGfv31189WPOfPn0cTIiAgoKOjQ5H0iBEjUOD3339XPIWfb968iYuLw5UHTRlNz48fPx4/fnzq1Klbt25dtmxZfHz87t27X758KQofOHBg69atoo+ke/PmzYyxGTNmSMp7JdbXJbVo0SLAXlRUpFbs+++/Z4wZDIbGxkb10z7y6VOeftF5w4YNMTExTqfT5XJFR0dLGurv378fN27cb7/9xjm/e/euyWT6448//KKPfyORaSz+TZFiIwJEgAgQASJABLwlMCAMjM7OTlFvGFbevHlT9OylW5GEIrby8nK0H8xms+Ip53zatGkooLmY4HA4EhISjh07pg4r6VNVVTVv3rzRo0cXFBRo7g374YcfNJPWj7+uri4lJaWsrExfTOapmmFflJSoSVxcHGPsu+++Ez3RPXbsWMZYQkIC+nwGhx959oW2Dx48YIwVFBRA5D09PZI7nXbt2mUymWDRjHNut9v7Qj11FfItFY+NxbdoKRQRIAJEgAgQASLgFwL9bGC4XK41a9aItoTT6Rw8eHBQUJC/hjjqJNTgem9gbNmyZdq0aeqYZXyKi4snTJiQkJBQWlq6e/fuLVu2DBs2TL3n59GjR4GBgeXl5TJx+ldGk6HfS0qhs91uDwoKYoxt375d8YhzbrPZDAYDYywrK0v99F/rs2TJksDAwA8fPnhFoKOjw2KxwPkfrwLKC2tWIfngKCnZWFCeHESACBABIkAEiMDnJ9CfBkZPT8/69euDg4NFW6K6upoxNm/ePL+w0ExCHXMvDYyamhpx2lgdv77PihX/P3vf/tbUsfW/SEKUiFhBoabUC0eRFyitqBzFOypVOaJShYq3yqlYQdHSejkWKSBGBaoWFRUUK7UIeEPUqAhBuQSSzB/1fb6u5513zuxLJiEI1skPedaePbNmrc/suayZNTPrd+3a5XK5qqurN27cSAix2WxxcXHKI2sXLFgwf/58fW4Bf6uFYWBLSin2lStXcNVIdfnl3Llz+PbPP/9Upv04Q7q7u41Gox/ucOXl5QDw448/jhBuWp+QH9mJVxY/mMskEgGJgERAIiARkAgEBIFRMzCam5sTExMBYN68eXa7HY9RIoQUFhYCwJEjR1A9h8Nx+vTpuro6j8ejqvD9+/fLy8vr6+tdLldjY2NJSQn1CdHKQslnmAZGRkaGcto4Ly9v3Lhx5v/9hYWF7d69mxCSlpZmsVjMZvPUqVO586YOHTqkPzo8duwYANy+fVupgmrIwMDA3bt3a2pquLcdHR02m+3MmTP37t3r6upqamriItBHHQx9LamBgYHa2trS0tK2tjbKX4fYsWMHAISEhAwODiqjZWZmAsAnn3yi+mHo56Wvvs5bLTxRPJ1PEZdcrl+/3tzcjJHtdntZWZkgFFT9ly9fVlVVnTp16s6dOywsL1++tNvtxcXFAJCZmWl/92PtdsqBJQYHBzFmamoqAJw9e9Zut7948YKNI0jr6K7zCVHmI1FZKHNJSAQkAhIBiYBEQCLwnhEYHQOjvr4+NTU1MjISAGJjY1NTU4uLi1HzlJQUAMBxWG1tbURERFBQEACcPHmSg6ajo2PRokUbNmxoaGioqqrKzMycNGnSzJkzMZpOFhwfQshwDIyuri6z2ax6Vs8PP/xAd26kpKTQfJOSklJSUpRbyc+fP5+dnU2jKYmGhgYmfvIQAAAgAElEQVQASEtLU77iQtrb23Nzc81mszJ+SUnJ+PHjy8vLb9y4sXz5cgA4ffo0lxwf9TEUL6nBwcH9+/cnJSXZbDa0kagBqZovBsbExADAsmXLVOPgx/P1119zb73mpa++1lsdPAkh+p9iaWnp3Llz2dWYysrKsLAwDNGx7ljVenp61q1bt2LFioaGhubm5qSkpNjY2KdPn+KhxkuWLElNTQ0NDQWA+Pj41He/9vZ2loOSvnnzZmpq6oIFC3CvPKbKyMhQxtQJ0ddd/xNi2Qa8srDMJS0RkAhIBCQCEgGJwPtEYHQMDNQQVzDYSVyn02k2m8PDwz0eT0VFRXZ2tsPhOHDgAABkZWWxuDQ0NISGhhYVFdHA7OxsAOAG6MosaHyWYA0Mg8GwUvGjw0EA4HZaV1ZWAkB6ejrLEGm32x0fH09tDDy+trq6eubMmb56ySPD7u5uALBYLHSVRpkpG7Jw4ULONuvv77dYLHS7iMvlslqt+idfqWIoXlKdnZ1xcXEJCQlv3rwhhLx+/RoA0BOMFZWj7XY74paUlKS8imTr1q349tdff2UTes1LX339t4QQJZ6EEJFPsbm5GQAmTpzocrlOnDhx8OBBp9O5bNkyAPj5559ZFVTppqYmq9XKftsXLlwAgOXLl7PxJ0+eDADPnj1jA73SeCjt3LlzvcZURhDRnRCi+glx3AJeWTj+8lEiIBGQCEgEJAISgfeGwKgZGG/fvjUYDFOmTGFVraurA4B169bV19fT02A3b94MAEePHqUxW1paLBbLmjVraAghZMOGDQDAugOpZsEmoTRrYJhMJuWIdsqUKdRO4AwMtH++/fZbyo0lWlpaTCYTpo2KimpqaoqKinrw4AEbxycaTZ3W1lavqdxuN0Zmr+x4/vw5AJjNZhzuE0Jyc3Opf5qSpxaGgiXV398/a9assLAweuruoUOHRParnDp1CkHLzs5WFgeeLgUAdrudyiySl776+m9V8RT8FGtqavDDrquro1sdkpOTAUB1hwlVihBy7949s9mckJDAWpWdnZ0AEBQURM9l6ujoAIDIyEg2rQiNjlWs9SKSihAiqLvWJ6TMJeCVRZmFDJEISAQkAhIBiYBE4D0gMGoGBk7BbtiwgVVy7969eC5QTk4O9a23Wq0AQBc63G53YmJicHAw5yw+e/Zsg8FAz9kkhKhmwWZHadbA8PWYWtwMkJeXR7lxRH5+PjVOjEbjhQsXuAg+PSIaInf54dbzzz//nOM/ffp0AKAWEYsYF1MHQ5GSIoRs27YNAKj/2507dywWy4YNG2jhKnPEkNWrVwPAZ599phoBvbNiYmLYt4J56auv81aJp/iniMtrxcXFGzduRN2HhoZCQkLMZrP+TomhoaHY2FgAaGhoYJVta2vDj4quV+Cud87qZpNo0evWrQOAyspKrQiq4eK6i1dDQkhgK4uq5DJQIiARkAhIBCQCEoGRRmDUDAy8sKysrIzVEB2K0tLS+vr6MLy9vZ2blz1x4gQArF+/nk344sULg8EQHx/PBqpmwUag9HAMDNzGQNdbKE9KDA4O4nYCHBGq3hlHI3slZsyYIbICQAgpKCgAgG3btnE8y8rKUJLa2lrulfJRC0ORksJjoMLDw51OZ29vb2FhYXh4eEFBgcvlUmbEhtC1As4vDuMMDAzg3pLc3FyaSjwvffV13irxFP8UZ86caTKZ0tPT6WLRrVu3AOCf//wnVUGVwAH3nDlzuLfV1dUAEBwcTK9M2bVrF2vLcfF1Hj///HMAYJe5dCLTV+K6a31ClBVLBLaysJwlLRGQCEgEJAISAYnAe0Ng1AyMf/zjH5yLS09PD95swDrWnzx5EgA2bdqEiDidTnT74bYN5OXlAQAe00SxU2ZBX3HEcAwMdM3isub442gSh/VTpkzRXzTg0nKPOMX++++/c+HKx3nz5gHAb7/9pnyFpwZFRkZ6lUQVQ5GSIoTMnz8fAOLi4jZv3rxu3bojR44oD95VykYIwV0BAFBVVaWMUFtbi0hevnyZvvUpL331td5yeIp/irifJCgoiL2Hcf/+/QDAbiKiulDC7XaHh4dzu2jwLS6JsHsw0OGKqxeUlRbhcDgAICIiQiuCari47oQQ1U9IlS0GBrCy6OQiX0kEJAISAYmAREAiMHIIjI6BgR7kM2bMYBXDSdno6Gh2hnvNmjXsQPPSpUsAEBYWxiYcGBiYNGkSALDDbtUs2FQsPRwDY/fu3QCwdetWliFH5+TkREdH47CYtZe4aCKPERERAPDw4UP9yL29vSaTyWg0qu4mt9vteOLQ/v37dfhoYShSUn19fXj815kzZ9jNAzrZ0Vf79u3Dc43ofD99hZtGcBvJwMAAhvual776qm+VeIp/irifxGq10tUGQgiaKy0tLaxqHN3a2orfDPUPxAg4vjcYDPQEKrfbjQ5X7Nm1HDfVx8uXLyvPGVONyQaK6671CbHcODqAlYXjLB8lAhIBiYBEQCIgEXg/CIyOgWGz2ZQnPlE/daq5x+P55JNPjEYj3ZGMbioLFiygcfDqjIiICIPBwA6mVbNgU7H0cAyM8+fPAwB7Ci3LGW/NS0pK6uvrmzNnDrUxuBswuCRaj26322w2GwwGfcd9QggOAb/88kvKqrOz8+zZs/QRkUxISKAhSkILQ5GSevjwISpLt3cr+WuF4KFDnMMbjYz+ZizgInnpq6//VhVP8U8RjeSffvqJqoDmytSpU2mIKoE76Y1GI2c2nD59GgB27txJU7W0tACA/iUqNDJL4OGwIqcGs6nEddf6hFhuLG2z2QJVWVi2kpYISAQkAhIBiYBE4H0iMDoGxsaNGwGgurq6t7eXDrxmzpzJ+YLj4Z44bLLZbK2trbhcsHLlSorRxYsXz5w5YzKZ8CaK6upq9CZXzYKm4oirV6/Sob/ZbFZuQY6Li6MR6JZlZNLZ2RkcHKx1es+9e/fCw8NRpObmZqPRiHysVivdZ8IJo/P4+PFjAFi4cKFOHHyFQB04cIAQUlxc7Ha7Gxsb2VsjcJew/h4ALQxFSgp9bwCAc9qpr6+/dOmSjvzd3d3oKbd3715ltGfPniGArHORSF766uu/JYQo8RT8FHE/icFgePXqFVUHvbzwxomioiL2LCwahxCChtPkyZPZwP7+fqvVGhcXR8+PIoTgIom+nx7LhNJ4VG5jYyMNESEEdSeEaH1CqrkEpLLU1NQcO3bMqwWuKoAMlAhIBCQCEgGJgEQgIAiMjoExdepUALh169b27dtx2QH91GfNmsVqdfz4cbxiora2Fi/aq6iowIsgrl275nA4iouLjxw5gsf7LFq06MS7H3JQZsFy5ujvvvuO2g8AUF9fz0Z49uzZuHHjaISlS5dyPj9btmwBgO7ubjYVIeTJkydRUVHffPMNDf/6668pH3qOE33rlcA7N9ijeLWS4Nbzqqqqw4cPoyPNmTNnxo0b9+TJE0xSVVXFHf6rZKWKoWBJEUJwM0NSUhIOoB0OR15e3vfff8+hx+WLp6aqbjwghOTk5CCA7GqMSF766uu/JYQo8RT8FHE/CbuURM9KOnDgQElJCXfOAYsGvRqC7sB2uVwrV65cu3Yta10QQrKysjgXQZaPDh0eHm6xWLgVEp34+EpQd0KI6iekyj8glQUtcABgt7uoZicDJQISAYmAREAiIBEYOQRGwcBwu91RUVEAMGfOHDpyKi8vZ89ORYVxHGMymQoKCjDE6XTiEaW4E+OXX34hhKCBYTKZ6NqCahaqIFZVVeGd0HTcj9cLxMTENDU1vX79Oj4+nl5kQeNMnDiRPZe2vb3dYDCUlpayWRQXF0+YMAHNofz8fELIoUOHMITy4a7UYJOr0mvWrJk2bZr+AB0T4tE9YWFhdJN3YWGh1WqNiYk5evRoeXl5TEzMnj17VHPBQC0MBUuKEGK327/44gvcTREREbFgwQL9mfLOzs6srCw8IQoApk6dumfPHrov/OTJk7iPGdGbNm3a3r17qb3kNS999fXfEkKUeAp+ingMFLveQhcczGbz8ePHdYqAEPL48eOkpKTZs2dXVlaWlpYuX76crvixCWNjY81mM2d1sBFU6adPnypv61ONyQUK6q71CXHccJEtIJWlo6MD5wJ8PXVXKZIMkQhIBCQCEgGJgETAbwRGwcAghHR2djY1NbF7XrUUePz4cW9vL/f2yZMnt2/fZl2M/vrrr5cvX7LRxLNgU/lNZ2Zmau0Z8Jsnl/D58+dms1lw84bT6bx9+zYLHW4UHhoaunfvXmNjI93WwuXCPvqEoWpJoZnR2NjIbo9hswgsbbfbtfLSV1//LSFEiSdKLvIpKnX0eDwtLS1ej/CiCV+8eNHQ0PDgwQNV23JgYMBoNKamptL4ggRenYFrg4JJ2Ggiuvv0CbHM/aa7uroeP37sd3KZUCIgEZAISAQkAhKB4SMwOgbG8OUeaxycTucXX3zB+e0EUEiPx7N06dJDhw4FkKdk9fdA4MaNG/75R23fvn3ixImsof73AERqIRGQCEgEJAISAYnA6CIgDYyA4Y/+VCM0e1pQUJCZmancfR4w6SWjDwoBh8PR3t6OIm/fvn3GjBmC38ajR4/o4pXVavVjX/gHhZMUViIgEZAISAQkAhKBUUBAGhiBBL2zs3Pjxo30doJAsS4qKvLbjyVQMkg+YwqB1NTU8ePHv337tqurKzIyUvCT6+3tDQ4OXrp0KSGkqqoqNjZWLl+MqWKVwkgEJAISAYmARODvgYA0MAJcjm63W/X+ab+zefXq1Z9//ul3cpnwb4lAXl6ewWC4dOnSqlWrzp07J6ijx+OZPXv23LlzL168+NVXXz179kwwoYwmEZAISAQkAhIBiYBEQBwBaWCIYyVjSgTGCgIej+fu3bs1NTWdnZ0+yTQwMHD13c/Xo2l9ykVGlghIBCQCEgGJgETgY0ZAGhgfc+lL3SUCEgGJgERAIiARkAhIBCQCAUZAGhgBBlSykwhIBCQCEgGJgERAIiARkAh8zAhIA+NjLn2pu0RAIiARkAhIBCQCEgGJgEQgwAhIAyPAgEp2EgGJgERAIiARkAhIBCQCEoGPGQFpYHzMpS91lwhIBCQCEgGJgERAIiARkAgEGAFpYAQYUMlOIiARkAhIBCQCEgGJgERAIvAxIyANjI+59KXuEgGJgERAIiARkAhIBCQCEoEAIyANjAADKtlJBCQCEgGJgERAIiARkAhIBD5mBKSB8TGXvtRdIiARkAhIBCQCEgGJgERAIhBgBKSBEWBAJTuJgERAIiARkAhIBCQCEgGJwMeMgDQwPubSl7pLBCQCEgGJgERAIiARkAhIBAKMgDQwAgyoZCcRkAhIBCQCEgGJgERAIiAR+JgRkAbGx1z6UneJgERAIiARkAhIBCQCEgGJQIARkAZGgAGV7CQCEgGJgERAIiARkAhIBCQCHzMC0sD4mEtf6i4RkAhIBCQCEgGJgERAIiARCDAC0sAIMKCSnURAIiARkAhIBCQCEgGJgETgY0ZAGhgfc+lL3SUCEgGJgERAIiARkAhIBCQCAUZAGhgBBlSykwhIBCQCEgGJgERAIiARkAh8zAhIA+NjLn2pu0RAIiARkAhIBCQCEgGJgEQgwAhIAyPAgEp2EgGJgERAIiARkAhIBCQCEoGPGQFpYHzMpS91lwhIBCQCEgGJgERAIiARkAgEGAFpYAQYUMlOIiARkAhIBCQCEgGJgERAIvAxIyANjI+59KXuEgGJgERAIiARkAhIBCQCEoEAIyANjAADKtlJBCQCEgGJgERAIiARkAhIBD5mBKSB8TGXvtRdIiARkAhIBCQCEgGJgERAIhBgBKSBEWBAJTuJgERAIiARkAhIBCQCEgGJwMeMgDQwPubSl7pLBCQCEgGJgERAIiARkAhIBAKMgDQwAgyoZCcRkAhIBCQCEgGJgERAIiAR+JgRkAbGx1z6UneJgERAIiARkAhIBCQCEgGJQIARkAZGgAGV7CQCEgGJgERAIiARkAhIBCQCHzMC0sD4mEtf6i4RkAhIBCQCEgGJgERAIiARCDAC0sAIMKCSnURAIiARkAhIBCQCEgGJgETgY0ZAGhgfc+lL3SUCEgGJgERAIiARkAhIBCQCAUZAGhgBBlSykwhIBCQCEgGJgERAIiARkAh8zAhIA+NjLn2pu0RAIiARkAhIBCQCEgGJgEQgwAhIAyPAgEp2EgGJgERAIiARkAhIBCQCEoGPGQFpYHzMpS91lwhIBCQC7xuBrKysyMjImJiY1NTUL7/8MjIyMjY2dsWKFYmJiZGRkQsXLnzfAsn8JAISAYmARCDQCEgDI9CISn4SAYmAREAioIGAx+OxWq3nzp3zeDyEkLy8PAAoKirC6Hv27MnJydFIKoMlAhIBiYBE4INBQBoYH0xRSUElAhIBicCHjsDdu3ePHz9OtYiPjweAe/fuYUh9ff3FixfpW0lIBCQCEgGJwAeKgDQw3lPBDQ4OdnV1vafMZDYSAYmARGBMIuBwONxuN4rW3d1tMBimTJlCJe3q6urv76ePY4eQDfjYKQspiURAIvBBICANjPdUTAcOHEhMTHxPmclsJAISAYnAmEfg7NmzALBx48YxLymRDfjYLyMpoURAIjCmEBgrBobdbqfTWj4B9ODBA/8SiuTi8Xiqqqp2795dVFTU3d0tkoSL8+jRI4fDQQg5fvx4amoqIcTlcv3xxx9ctLH5+OLFi6tXrxYXF2/atOnp06ejJeQYEWO01P8g8h1OTXnz5s3Ro0d37dpVUVExcnX5/cPY19fX0NBw/vz5ioqKy5cvj1wN8ng8T548uXDhwsGDBzMyMoaGht6/smyOT5482fXfv5aWFjYCpTdt2gQANpuNhrBEfX39f7P5v6f79+87HI7/e/5vqrS0lOXD0XV1dVyIzqPXBtzhcNy5c0eHA/tKHBk21QjRz58/Ly0t3bdvX2lpqd1u9zWX4VR5X/PyGl+1j1AN1Gc1RpTCQUJFRUVeXl52draOzH7oqMONe9XT03Pt2rX//Oc/ubm5rFsjF00+aiEwpuq7lpAjGj4mDIz29vZNmzYNDg76oWptbW15ebkfCQkhTU1NmZmZEydOtLz7Wa3Wf//735SV2+1evnz57t27+/v7IyIiYmNj6StxIiUlJSoq6o8//qirq8vOzu7s7ExOTrZYLD09PSJMrl+/Pn369IqKCpHIAY9z6tSp9PR0ALBYLC6XK+D8BRm+BzGGifMwk3M4BJYbx3wkHodTUzo6OqKjo2traxsbGwEgPz9/JCR8zzzb2tpWrFhhMpkAICgoKCQkBN79Pvvss19++SXgRlRvb29JSUlSUhIA/M///M97VlaZ3dDQUFtb29q1a1FrAKiqqlJGI4RERUUZDAatuRuHw1FTUzNnzhzKBwDWr19fV1fX39/vdrtv3bq1Z88e9m14eHhFRUVHR4dqdgMDA9u3b7969arqW9VArw24x+MpLCw8duyYanIuUBwZLmHAHw8dOhQaGvrTTz81NzcXFxeHhoYePnxYPJfhVHnxXMRjqvYRqoE6PEdRKa7N7+vrq6ysTEhIAIA1a9boyOyrjjqslK/a29tPnjwZHBwMACdPnqQROGlp+KgQY0oYDoGxU985wd7b4+gbGI8fP05JSent7fVPZ5fLFRsbO5zh76pVq7CLunv3LivDtm3bYmJi3G63x+OJjo72r+fu6+s7efJkYmLizp0709PTk5KS8vPznz9/zmakQ2/fvh0AvvrqK504I/rq6tWrALBs2bIRzcUr85EWY5g4DzM5p35guXHMR+LR75ry5s2bWbNm7d27lxDyxx9/mM3mH374YSQkfG88+/v7s7KyDO9+mzdvbmpqwh0Fz549q6io+OyzzwBg5syZ169fD7hIhw8fBoDvvvsu4Jz9Y3jhwgU69Fc1MB48eAAACQkJ+vzRjQpZBQUFKXuKadOm0YzYGSKO7atXrxISEnxdPRZswIuKinbu3MnlqPXoFRmthIEK//nnnwGgpKSEMjxx4gQAnDhxgoboE35XeX22w3mr2keoBmrlMopKqbb5u3fvBoD//Oc/WgJjuE866rNSfRsVFQUAjx49om9VpaVv3zMxpoRR1X3U67uqVO8ncJQNjI6Ojk8//ZQeIeKfzosXL/7999/9S0sIwXmCOXPmsBz++usvdu1+aGhoOPOOt2/fXrx48fTp0202m08ODC0tLWlpaSMxHGGV1aHxEMni4mKdOO/h1UiLMUych5mcAzCw3DjmAX8cTk3Zt2+f2Wymq3lOpzPg4r1Phi6Xa8GCBQAQFhbW3NyszHpwcDArKwsAgoODL1++rIzgUwi3GXrlypUAcO3aNZ+YjFzky5cv03G/qoGBw9zvv/9eX4b6+nrKx2KxKCN/8cUXNILWSoLL5UpOThYfQHO5iDTgS5Ys0cqd4+YVGS6++IQUl1D18cWLFyEhIZGRkWyP5nK5wsPDLRZLZ2enaio2cDhVnuUTWFq1j1ANVM13dJVSbfPxgDV2ZK8qubiOqsn1A589ewYA06ZNY6OpSstGGFGaa/dGVxgRTX2t7yI8P5Q4o2lguN3upKQkfRdDERy3bt3q9zZBp9M5btw4ANizZw+b15o1a0wm09u3b9lAP+gLFy7MmTMnOTm5rq4uPz9/x44dU6ZMKSgo8IPVqCRBvwstF+r3JtIYEeO96fsBZeR3Tent7Q0LC8ONSR+QvjqiFhYWAoDBYNDx8ne5XCkpKQAQHh5OLSsdnqqvPB5PZmYma0u43e6JEyeOGzdu7BhpXrvVpUuXAsCtW7dUdaSBATEwduzY8cUXX1Ce4oR4A97a2moymerr670y94oMxyE2NjY+Pv7EiRN+fzAswyNHjgBAVlYWG0gIyczMBICff/6ZC1c++l3llawCGKLaR6gGqmY61pTCA9YiIyNVpWUDxXVkUwnSJSUlALB582bB+CMaTdnujWh2gWLua30PVL5jgc9oGhiFhYVGo9GP7WUccAcOHJg0aRIXKPh45coVnP26ceMGTdLd3W00GgPimLR+/fpdu3a5XK7q6mq0gmw2W1xc3AdxZG1vb6/RaJw8eTJeiUXxec/EGBHjPWv9QWQ3nJpSXl4OAD/++OMHoalXIT0eT3h4OACsWrVKP3JLSwu2OYIT3hy3oaGhLVu2jB8/nrUl7ty5AwCLFy/mIr/nx4GBgdu3b7e3txNC9LvVoaEhi8UyYcIEr96twzcwmpqa2OVonzDxqQFfsGDB/PnzVfmLI6NM3tnZefjw4ZiYGLPZvG7durq6uuE0yPPmzQOAo0ePchn9+OOPAJCSksKFc4/DqfIcqwA+qvYRqoGqmY5BpdAz8F//+peqwDRQXEeaxCcCd1KdO3fOp1QjEVm13RuJjALCczj1PSACjBEmo2ZgtLa2BgcHr169Wh+I+/fvl5eX19fXu1yuxsbGkpISdmEX0546dQoA/DNUduzYgZuYcYv5y5cv7XZ7cXExAGRmZtrf/diOHHPMy8sbN26c+X9/YWFhu3fvJoSkpaVZLBaz2Tx16lRuFvPQoUO+WiwDAwN3796tqanhIOro6LDZbGfOnLl3715XV1dTUxMXQetRBEw27cWLFwEgPT2dDaT0y5cvq6qqTp06defOHZ0N+o8ePbLZbKWlpapOI8hNXzB9Mag8hJDXr19fuXKFrinb7fby8nL29J7+/v4LFy5wkmjh7HA4rl+/TiPb7faysrK2tjY2R0KIanL/JFHl9vbtW/wO2f9Xr15xYmDa2tra0tJSTkin09nc3EzP6nny5ElFRcWbN2+UHJQhWqUsWFOUDAcHB1GR1NRUADh79qzdbn/x4oUypn6IlmAej+fRo0enT59mp3udTqfNZtPaTDwwMDB83Do7O9FsOHLkiL7khJAJEyaoziJ7Tdjc3JyYmAgA8+bNs9vteEIdIQQXT2jWDofj9OnTOiNRLZUJIYKfPSeq0+nMysoyGo0IwrJly9i9E0oXKfRLXrBgAcdH+Th8AyMjI4Nbjh6hBvzYsWMAcPv2bVYLX5Fh03L0nTt3srKyQkNDp02blp+fr7WXnUvFPjocDoPBAAC1tbVsOCHkt99+AwCj0ai1bi9Y5bUqJmbnd1vkRx8h0nGIKKVTWSiG+uIRQnR6bdUeBA9YO336NCGkv7+/rq6urKyMdm00X30dRSSnrCiBHURVVZXL5frkk0+4YxhUpSWEiJSsV3m0Rgta7Z6WMKiL/qco3tDplB0FjRIBrO+U54dLjJqBgQuyOpe2dnR0LFq0aMOGDQ0NDVVVVZmZmZMmTZo5c6YSa+yr/NuGERMTAwDLly/HA2SXLFmSmpoaGhoKAPHx8anvfjghx+X7ww8/YFfKzfokJSWp7lk/f/68uDNYe3t7bm6u2WwGgLS0NDbrkpKS8ePHl5eX37hxY/ny5QCAbRAbR0mLg8mmxe1Tv/zyCxtICOnp6Vm3bt2KFSsaGhqam5uTkpJiY2PZcTzG7+joSElJyc3NvXPnTltbW2hoaF5eHsdKRDAtMVhWJ06ciIuLwxLB4XVFRcXEiRPRIR5nSRsbG61WK8ZBs0EL59LS0rlz52JM3ABTWVkZFhaGIdSiU03unySEEFVuhJA1a9Zgvuz/tm3bWPUHBwf379+flJRks9lwlINjzd7e3oMHD86cORMAkpKSCCGXLl3C7yo3N5floKR1StnlconXFI7zzZs3U1NTca+CwWDAKpaRkcFF03nUEay1tXXv3r1Yf6lBRQipra0FAOVBcAHEze12I7BFRUU6wuMrNDB8PTKrvr4+NTU1MjISdUlNTaWbo9DtCr/q2traiIiIoKAg7uwXzFpLZUKI4Gev1A6dXfH7TElJuXLlys8//xwREUG/WNbA6OzsLCgowNWekJCQY8eOKYdNbBbDNDC6urrMZrOy6EeiAW9oaOBabJ+QYbXWoQcGBiorK1NSUgwGQ0pKSmVl5cDAgE589hUu5gAANwdBCGlubpRf11gAACAASURBVMbyUt0SKVLldSomIcTvtsjvPsJrx+FVKZ3KQlEVEU+r19Zq8wkhn376KQC8evXq6tWrVqsV64vRaOT2fGvpKCI5VYESXV1d6enpy5cvv3z5cnV1NQ7S4uPjMYKWtCIl61UendGCarunJQyKqv8p+tTQaZUdBY0lRqK+s/w/OHp0DIze3t6QkBCDwaA1WdLQ0BAaGsp21dnZ2QCgOkavqqrizsQQLAa73Y5NKuerMHnyZAB49uyZDh+32417sJADHn1YXV09c+ZMLaV0uKm+WrhwITdE6O/vt1gs1JnY5XJZrVav56L4BCYrCVpfT548YQObmpqsVitbEGjgoZFGY54/fz40NJQeSI9Qjx8/nkYghAgKpioGywdpPOcUnVaPHTtWUFAwMDCAJ2A8ffr0xo0bGzZseP36NY7XWatJiTPtbidOnOhyuU6cOHHw4EGn07ls2TKlm7Iyud+SEEI4bm6322q1btu2raio6Mi7X3Z2dkpKCutY0tnZGRcXl5CQgIsSr1+/5i4vq6ioAIC9e/fevHnz66+/xrkxpbHHQipYyiI1hWVLaYRo7ty5NESQEBEMVyB37dpFeQ4MDCQlJRmNxhHFbd26dQCwcuVKmq8qgS5SBoPh/v37qhH0A3EFgx0gOp1Os9kcHh7u8XgqKiqys7MdDseBAweUiyRePxUcZYp89qyQpaWl2AxaLBbq/ImlgOGsgcEmFKFZA8NgMKxU/KjlDwBcS04IqaysVF2GHYkGvLu7G9fD6TL7iCLz9OnT/fv3W63W0NDQb775hk586KB66dIlLBHlfNDjx4/x1ZUrV3Q4aFV5kYpJCPG1LRpOHyHYcRBCVJXyWlkEuzCvvTbX5hNCHj16hJMItbW1OTk5uK0ZfdjYUzEIIao6ikiuLOK2trapU6eyE084y8b1FEppkZVOyXqVR2S0oGz3lN0lSiLyKQo2dF7LjoNxROs7l9cH8Tg6BgbuHKKWMYdUS0uLxWLhjn/esGEDACj9hXDizT9nbvStAgB2jaKjowMARDZXtbS04FH3ABAVFdXU1BQVFfXgwQNOHf8e3W43dpzsOvjz588BwGw2U/+W3Nxc6iahmpGvYFImL1++VB4fce/ePbPZnJCQQHtQQgg6hwQFBdHjHXDCGI8fRYb9/f2LFi3av38/5S8omKoYlAlLYN3evHnzxYsXcZqHDrwePHjw7bffouMyNpr0bixVnAkhNTU1AIAez3SfQHJyMgCwh3qpJvdPEkKIkltzc3NlZSVVs7e3d82aNazzT39//6xZs8LCwuhRM4cOHeI8zvGYEZvNtnbt2qGhIY/HY7fbddy4BUtZvKZQ+SmBo0/WTKWvdAhBwbDz4LzJz549O2/ePMp8JHB79uzZpEmTjEaj/pT8xo0bAWDHjh1UGHHi7du3BoNhypQpbJK6ujr8Vuvr6+k5rZs3b+Zc7UVUFvzs2dwJIfSg2H/+85/0lf4eDBrNK8EaGCaT6b+v1Pv/T1OmTMGRsaqBgYbWt99+q8xoJBpwbLRbW1sxuxFFBrPweDw2m42uurP9hVJlNLdUPYqxOgOAjsO9VpUXrJiEEJ/aouH0EeIdh6pSIpVFUDz9XlvZ5hNCcBV69erV7HD/zZs36N5Gz0VQ1VFEcuWH8fTp08mTJy9cuJDtF6ZPnw4A7PZUVWmRm1bJepVHZLSg2u6pCiP4KQo2dPplp4TxPdR3ZaZjOWR0DIwtW7YAAO5b4NBxu92JiYnBwcGcW/bs2bMNBgM7tKIJ8/PzAcCPo5lWr14NANHR0ZQVIeTcuXNeb7eh8TFr7N6MRuOFCxfoq2ESuJb9+eefc3ywztP+UhUQmsQPMGlanJDIzMykIUNDQ7GxsQDQ0NBAAwkhbW1tiACu+fT09ERGRk6YMEF5Yj1NJS6YUgzKhCNw/rioqIgefHnjxg28mSs7Oxt3iaALMru1VAtnXDErLi7euHEjtrlDQ0MhISFms5ndk6Oa3D9J8OZHAFAWOmrqdrs3btz4+PFjVvFt27YBAHWVuXPnjsVi2bBhA9tPzJs3z2g0fvPNN+y0N8uEpQVL2deawmZBCEGIWNuJi6B8FBdscHDQYDB8+umnLJOcnJzq6moaEnDckHNdXZ3BYNDZWtDQ0BAUFLRw4ULWRKdSeSVwtXDDhg1szL179wJAYWFhTk4OLXf0BmRLXERlwc+ezb2np4eO73NycuirkTAw/DimFt08uFlYKmTAG3CEHRe0RxoZt9v9+++/p6WlmUymxMTEkydPel08p4WiXMHAWXP9k45VO0fxikkIEW+LhtlHiHccqkp5rSzi4hFCdHpt1R4EnZ9nzZrFOr8NDAzgHidqvqrq6FVy+vGzBHrcsTMjTqfTYDCEhISwGyxVpUU+WiWrL4/IaIEQotruKYUR/xTFGzqdsmMBRNfxEW0Juew+iMfRMTAWLVoEAKobMPDGn/Xr17PwvXjxwmAwaK14rF+/3qdLgpAzNX85d/Zdu3axIzZWDCU9ODiIa5T4YbEjGGVkn0IKCgoAgJONEFJWVoZ5KXfpKfn7ASZlkpGRAQDsEBA7Y+7CEEJIdXU1Hu2PV3xg1d2+fTtlpSTEBVOKoeRGCKFn+GRkZNAGEedU4uPjqZcXzlusWLGCMtHCeebMmSaTKT09nS4Q3bp1CwDYOVpCiDK535KocqNy4uQfO5lECMEz0MLDw51OZ29vb2FhYXh4eEFBAesI1NvbazKZIiIi2Mkwli1HC5YyIcSnmsLl8vnnnwOA/mwrl0RcMEJIZGSkwWCgX8KrV6/YQh8J3Ki0uDjz66+/0hBKDA4Ozpo1y2q1Uj8i+kqQQJfrsrIyNj76aqalpfX19WF4e3s7twwrojIhRPCzZ3PHA6ywUWLH8XQsq3OTN8tHi2ZXMPwwMHCsRhd2uFwC3oDPmDGDrh+OHDKPHj3au3fv1KlTw8PDd+3axZqRnILcI91ooUyCF0Gobs+gTFSrvHjF9KktGmYfIdhxqLZjIpVFXDz9XlvZg7hcLovFAgAVFRUUeUIIupVaLBY6w6XUUURylifSJ0+eBAC2hSSE4NfL3bGrlBY5aJWsV3lERguEENV2TymM+Kco3tCJj7hGrr4ri+xDCRkdAwONQuXwwul04hIzt68AR4qqKx6EEJw08nWTN1ZXAOCWHdANhhNApzhx3In965QpU/SXFHT4cK/wMMHffvuNCyeE4PE7kZGR+nn5BybNburUqbjJDEPcbjfuMzt58iSNgwS2EXSjPJYgzuFxMfHRJ8E4MVQZ0i0TnBMd3sC1ZcsWmurbb7/l/ChUccYdI0FBQezNXPv37wcAdl8QTsgBAFtMtAtn3flEJFHlRiUvKyujG1po4Pz58wEgLi5u8+bN69atO3LkiHLkiofDGAwGamXR5EpCsJQxoa81hWbncDgAICIigoZ4JXwSjBCCY27qNpaVlcVueAg4bpz8GzduDAsLU95Ztm/fPovFMpxbZf7xj39w/i09PT3oOMGaNDhi2LRpExVMRGXxz56ypZOL2ADSxUOvx9SyHPTpYRoY6Fur1XcQQgLbgGPXhp0RTrsGEJm+vr6ysrLk5GSTybR8+fLffvuNnUrQhxHf9vb24lEEyu4S54nGjRvHzppzPJVV3qeKKd4WDb+PEOw4CCFKpbxWFp/EQwy1em1lB3Tz5k08m4QaEsgBL/ZmD65V6uhVcq5A8fQnPA2Fm73CrXrcvShKaZGhVsnqy+NyubyOFpC/st1Tdpfin6KvDZ1W2XFgBry+c/w/xMfRMTAiIyONRqPSSQC3oIWFhbFQDgwMTJo0CQCUbSIh5OnTp9iCK4dWLBMlvW/fPgAwmUysJ4/b7UY3GDr3qUzIheTk5ERHR6MMAMB26lxM8UecD9A6MdBut6PHLbulQcncDzApk/v37wNATEwMDWltbUUduakvbGoNBgNuMcSpU/0t8uKCKcWg8nBEUVERAMyZM4e6iODAy2AwsBtsZs+ezW650cIZN+dYrVb22nVsW9nRoWpy/yTBU1ZMJpNqod+6dUs5BdvX14cnBZ05c0ZZlSg+W7duBQCv50FjfMFSxu0ivtYUKhLObXPHo9G3qoS4YJgc563xm6ypqWH3/o4Ebpgp3VbudDrj4uLWrl3L6tLW1mYymc6fP4+Bly9f5k6yZiOr0rjZacaMGexbHBdGR0ezY008yYBurRZUWfCzZ3NnPSS5jSVjZAUDh2Vbt27lxKaPgW3A8eyshw8fBhaZ27dvb9myxWKxzJo16/Dhw0rblarjlcDREjdwJIRgw8VNY7PcVDtHnyqmeFs0zD5CvONQKiVSWcTFowCq9tqqPcj3338PANQLGjk4HA6LxRIcHExdZJU6ikhO5aHE+fPnASAkJITtRLq7u/ECYnZPqaq0yEe1ZL3KIzJaoJs8uXZPKYz4p+hrQ6dadhRASlBf8RFqCWlGHxAxOgZGdHT05MmTlTDhmhfnwVxYWBgREaF15BRe18Vt6FRyVobgoQTcvUh4wIv4hRU2my0pKamvr2/OnDnUxvB13KCUDduvL7/8kr7q7Ow8e/YsfUSgEhISaIiS8ANMygQ3maFH9eDgoNvtxo2kRqORM71Onz4NADt37sS0Dx48QBxYs42yRUJcMKUYHCv6iEdbsHP8eLYYO4rt6uoKCgpit9wocUaGOD776aefKH9szqZOnUpD8MhXAGCLiZ5r4askWtzQhN6yZQvb+qMMDx8+RKjpPD0rG6XR+hX8JgVLmRDia02h8hBC8IRQemkD+0qLFhcMOeBG6rq6uocPH3I2/0jghpnGx8dTnK9duxYUFMR2z+vWrUtOTsaYg4ODKSkp7MKXluJsuM1mU56kR52JaUyPx/PJJ58YjUZ6FISgyoKfPc0IicHBQXr9BVvdxoiBgeMnrQ4isA04HlVsMBhw7jlQyCxZsmTChAlbtmzhbtjgCkLwEVe32M11mBCXetiGi2OoWuV9qpjibdEw+wjxjkOplEhlERTPa6+t2gHhcjc9hgRLYc+ePdz6uVJHEcm5MqXb7vEQc/oW7wfjjrpRlRaTqJasV3lERguEENV2TymM+Kco0tB5LTuKFSUCVd8pw78BMToGRnJyMrcFE6HE2Sb2nMeLFy+eOXPGZDLhQebV1dWcYxXu4ePcnLwWTHd3N/oV7Nmzh42Mpq3Oejob+d69e+Hh4ShPc3Mz7WWtVit1hmbji9OIw4EDBwghxcXFbre7sbHx66+/phzQVub2A9C3SPgBJuWQlpZGPX/27dv35s0bbCw4s7C/v99qtcbFxdHzo1wuV3BwMAD89ddflBsh5MaNG9TrTFwwpRgsT0r39/cHv/uxPmNZWVncHhI0OXBbS35+/uvXr5U406OcDAYDe5kdnnSB1zUUFRXhrY7K5H5LQghRcsNljYyMDNXPCR2NAIACi4DU19dfunQJaZwiCg8PV9onFD2WECxlQohPNYXNghCCp/02NjZy4TqP4oIhk9zcXDxQeNWqVZytOxK4Yabx8fFGo3Hnzp137tzp7+8PCws7fvw4VSoiIuLo0aMvX76srKzEwxLQwHC5XAcPHiwqKvJaRmg1VVdX9/b2UusXLzlhW0V00sNZEpvN1traKqIy7kkT+eypRpTARhj9Oui3iv7QaAOXl5fTyL4SV69epXM3ZrOZLlFSPvQCHNW9c52dncHBwdxQCdMGvAHHk14XLlxIZQsIMnV1dbSBpZz9Jt68eRP+7sdOFQ0MDISFhU2ZMoWrLGwuqlVevGL61BYNs48Q7DhU2zGRyiIontdeW9nm48L7uHHj2AVJm80WFBTE+vrirb5cHy0iOVugSOfk5ADA4sWL6ava2lq0NrG/q6mpwTkspbSYRKtkvcojMloghKi2e0phBD9FwYbOa9lRuFhCvL7jujrnBcey+nvQo2NgZGRkqLb4eCqCxWK5du2aw+EoLi4+cuQInhWwaNGiE+9+LO5DQ0Ph4eHR0dFe+2Y2FY7asdOix+9gBByVqvpicRyePHkSFRX1zTff0PCvv/6adoTc+iaNI0igg0dVVdXhw4fRzePMmTPjxo2jbvQ4Vj569KgOQ1/BZFnh9RF2u/3w4cN4KB49Np4OZVwu18qVK9euXct1fti4r169GgvF7XaXlpZmZ2fTkYG4YEoxWCEp/fvvvwNAamoqDcGdOdwVpLhD8cSJE8XFxTjTrMSZ7qXj1iVwtHTgwIGSkhK6xVaZ3G9JCCFKbm63e/ny5VarNT8/n47bWB3R2yEpKQkNHofDkZeX9/3339PqcPz4cQDgeiaWA0eLl7J4TeGyIISEh4dbLBZ2fKOMw4WIC4YJ0c1g+vTpiAzHLeC4IX/2YhwACAoKYo+2M5vN6NJGWwk0MK5du4Yh7PHHnMD4iC7Xt27d2r59O54XhM7Es2bNYuNjoaenp9fW1tIdU15Vxj1pIp89mxfSL168wKsDAeCbb755+PDh4cOHccsWqpaSksK5ViqZaIV89913FDEAqK+vZ2M+e/YMfTkwztKlS+nHT6PhoYXcPe4j0YDjIbDs5qsRRYYq6CtRU1NjMBjYj3Pfvn1Go1H12BXKXLXKi1dMn9qiYfYRgh0HIURVKa+VRVA8r722ss3HY0jYZfbLly+PHz9eeSmnqo5eJaelSQk8VH3ChAnNzc0DAwMnT5784d0PAPbs2VNWVkZnSZTSIhOdkvUqj9fRAiFE2e5pdZfYAusPUQQbOq9lRwFkCcH6Tu+cYTd5snz+NvToGBgnTpwICQlRguh0OvFKWpwMw9vQ0MAwmUycMUDXztgre5U8uZDOzs6srCzc6AYA4eHhu3fvptM2sbGxZrOZGzFzHNA+wQ7VYrFgzT906BDtYrGrY92+lRz0Q/DMhLCwMOpEUVhYaLVaY2Jijh49Wl5eHhMTw629KBn6CibL4auvvgKAGTNmsLbW48ePk5KSZs+eXVlZWVpaunz5cjqNyqZ1OBxYiJ9//vmyZcuSkpJKSkrYCOKCqYrBskIap6tpO0gvKoqLi2Mj466bTz75hK53KXEmhKAtwW3mxtk7s9nM5qJM7rck9KAMttB3796Nx4kAQGJiIn6l7e3tS5YsQVPTbrfjerrBYIiIiFiwYAG3LLBixQoAoAsaLBpatGApC9YUZS64aYq7llEZTRkiKBgmLCwsjIyMZLffsAxHAje6s5wdDbNjONrm0AhYu3t6enBnMPtpsdIi7Xa7cUgxZ84c2oOigyg3nYGjH5PJxObuVWXxz14pGyHk/v37eIASardw4UJceQgNDU1MTExPTz948KBqQp3AqqoqvLacIoZmW0xMTFNT0+vXr+Pj4+lNRDTOxIkT2cOsCCHt7e0Gg4F1/ikuLh6JBnzNmjXTpk3jLJyRQEYHNMFXFy5cmDZtWlZWVllZ2aZNm6xWq751QQjRqvKCFdOntmiYfYRgx6GllNfKIiie115b2YN0d3evWbMmLCzs2LFjv/zyy7p161auXNnc3KwsVlUdvUqu5ON0OtHBGABCQ0NxlIVH4Y0fP57OUKj2UMhNp2S9yuN1tKDa7mkJI/IpCjZ0XstOiSSGiNT3jo4OnBZhT+nUYvhBh4+OgYFratRFmEPwyZMnt2/fZqds//rrr5cvX3LRPB5PfHy80peUiyb+iOdMcxPh4skDGNPpdN6+fZuaPbhfkBAyNDR07969xsZGLeiUMgiCySV0OByNjY1sEdAIL168aGhoePDgAdeP0ghIPHnypL6+vqOjgy5cKCN4LWUdMThuIo9DQ0MtLS3sxLkSZy0+Ho+npaWFdcHC8ze4YtJKzoUrJVHlhm5m9+7dS09PDwoKSktL83g8OAHDzpLa7fbGxkavR+BzMug/6pfycGoKnjrP9lv6knBv9QWjkVtaWlTXLmgEQshI4MbyF6evX79u9HY9H252bGpqYg8e0Mri8ePHbOtBo/mqsupnT7lxhNvt/uuvv6qqqnA81NPT09LSot9KcBxG7jEzM1PrlPNAZfr8+XOz2Uw34bBsxyYyg4ODTU1NVVVVf/75J9sqspJT2muVF6yYlKEIIdJ5qfYRqoHKHPWV8lpZvIqHq3Y6vbZWB+R2u+/du9fU1KTT0evo6FVyDgqPx/Pw4cObN2/SRmNwcLC2tpYbdGlJy3FTPnqVR3+00NnZqWz3dITx41NUNnRey06pJg0Rqe9dXV10vz5N+PcjRsfAIITMmDGDW+z2Fdxff/11xowZqoNgX1lhfLyXjZ2z94+PTCURCDgCTU1NS5YsSUtLy8vL27p16+iO24ZTU7Zv3z5x4sQAVtuAQ/3+Ge7evduPCf73L+eHm6PT6fziiy/YczICq4vH41m6dOmhQ4cCy3bscBtOlR87WnCS/C2V4nSUjxKBUURg1AyMkydPDqc57ujoiI2NZS+e9A9Eh8NB/Si2b98+Y8YMrRl3//jLVBKBACIwODg4WtvChlNTHj16RKfirFar4CEKAcRtzLJyu93fffed0vlzzAr84QqGLlUjNGtYUFCQmZk5Qn3HypUrZwr/fHIY1i/N4VR5fc6j+PZvqdQo4imzlgjoIDBqBobT6WTPNNQRUfnq7du3q1evfvr0qfKVryGpqanjx49/+/ZtV1dXZGQk7qj2lYmMLxH42yPgd03p7e0NDg5eunQpIaSqqio2NlYuX7BfC91QwQZKeiQQ6Ozs3LhxY8Ab+aKiIr9d/kTULC8vPyL8U/XXF8lFGcfvKq9kNXZC/pZKjR14pSQSARaBUTMwCCFnz5716vrJykrpa9eucd6B9JWvRF5ensFguHTp0qpVq86dO+drchlfIvCRIOB3TfF4PLNnz547d+7Fixe/+uqrZ8+efSSISTXHIAJut5vePxgQ8V69evXnn38GhNVYY+J3lR9rirDy/C2VYhWUtERg7CAwmgbGWEDB4/HcvXu3pqZmOHejjgVFpAwSgRFFYDg1ZWBg4Oq7n38TCiOql2QuEZAIqCIwnCqvynAsBP4tlRoLwEoZJAJKBD52A0OJiAyRCEgEJAISAYmAREAiIBGQCEgE/EZAGhh+QycTSgQkAhIBiYBEQCIgEZAISAQkAjwC0sDgEZHPEgGJgERAIiARkAhIBCQCEgGJgN8ISAPDb+hkQomAREAiIBGQCEgEJAISAYmARIBHQBoYPCLyWSIgEZAISATeDwJZWVmRkZExMTGpqalffvllZGRkbGzsihUrEhMTIyMjFy5c+H7EkLlIBCQCEgGJQGARkAZGYPGU3CQCEgGJgERACAGPx2O1Ws+dO4dX1OXl5QFAUVERJt6zZ09OTo4QIxlJIiARkAhIBMYYAtLAGGMFIsWRCEgEJAIfBwJ37949fvw41TU+Ph4A7t27hyH19fUXL16kbyUhEZAISAQkAh8QAtLAeE+FNTg42NXV9Z4yk9lIBCQCEoExj4DD4XC73Shmd3e3wWCYMmUKlbqrq6u/v58+jilCtudjqjikMBIBicAYRGCsGBh2u532NC6X648//qioqMjLy8vOztZH7cGDBzShfkw/3no8nqqqqt27dxcVFXV3d/vBgSY5cOBAYmIiffwgiBcvXly9erW4uHjTpk1Pnz4dLZnHiBijpf4Hl+9was2bN2+OHj26a9euioqKkavX7x/Svr6+hoaG8+fPV1RUXL58eURrk8fjefLkyYULFw4ePJiRkTE0NPT+9WVzfPLkya7//rW0tLARkD579iwAbNy4UfkKQ+rr6/+bzf893b9/3+Fw/N/zf1OlpaVaPOvq6rRe6YertucOh+POnTv6Cdm3gsiwSUaIfv78eWlp6b59+0pLS+12ux+5DKfW+5GdThKt/kIrXIvVGNFIfDjkq4JaimuF9/T0XLt27T//+U9ubi678KgVX4azCIydys5KNdL0mDAw2tvbN23aRG/57evrq6ysTEhIAIA1a9boQ1BbW1teXq4fR+ttU1NTZmbmxIkTLe9+Vqv13//+N43sdruXL1++e/fu/v7+iIiI2NhY+kqcePTokcPhIIQcP348NTWVEILthSCH69evT58+vaKiQjB+YKOdOnUqPT0dACwWi8vlCixzcW5jRAxBgQNbZIHlJqjCcKINp9Z0dHRER0fX1tY2NjYCQH5+/nAkGSNp29raVqxYYTKZACAoKCgkJATe/T777LNffvllJIyo3t7ekpKSpKQkAPif//mfUcdhaGiora1t7dq1qDgAVFVVKaXatGkTANhsNuUrDHE4HDU1NXPmzKF8AGD9+vV1dXX9/f1ut/vWrVt79uxh34aHh1dUVHR0dCh5DgwMbN++/erVq8pXOiH67bnH4yksLDx27JgOB/aVIDJskpGgDx06FBoa+tNPPzU3NxcXF4eGhh4+fNinjIZT633KSCSyVn+hFa7KcxQ14tp88eGQTwqqaq0f2N7efvLkyeDgYAA4efIkjcwJTMPfPzF2JFHqPkYqu1KwEQ0ZfQPj8ePHKSkpvb29nJ67d+8GgP/85z9cOPfocrliY2OHM/xdtWoV9kl3795lmW/bti0mJsbtdns8nujoaP+66pSUlKioqD/++KOuri47O7uzszM5OdlisfT09LB5adHbt28HgK+++korwkiHX716FQCWLVs20hnp8x8jYugLiW8DW2SB5SYi/zDj+F1r3rx5M2vWrL179xJC/vjjD7PZ/MMPPwxTmNFN3t/fn5WVZXj327x5c1NTEzr8PHv2rKKi4rPPPgOAmTNnXr9+fSTkPHz4MAB89913I8HcD54XLlygQ39VAyMqKspgMHhdKMaFDmQVFBSk7DimTZtGM2InjFiZX716lZCQ8Mcff7CBIrRIe15UVLRz504RbhjHKzLirPyI+fPPPwNASUkJTXvixAkAOHHiBA3xSvhd671y9i+CVn+hFa7MZRQ1Um3zBYdD4goqVRYMiYqKAoBHjx7R+KoC07fvkxg7kmhpPbqVXUuqkQsfZQOjo6Pj008/pbv6WD1xwx/7HbNvWXrxb6hyZgAAIABJREFU4sW///47G+ITjUslc+bMYVP99ddf7HTa0NCQf3ONfX19J0+eTExM3LlzZ3p6elJSUn5+/vPnz9m8dOiWlpa0tLQRGoLo5Etf4bkuxcXFNGRUiDEihojugS2ywHITkX84cYZTa/bt22c2m6nh7XQ6hyPJqKd1uVwLFiwAgLCwsObmZqU8g4ODWVlZABAcHHz58mVlBJ9ClHsVVq5cCQDXrl3zic/IRb58+TId9ysNjAcPHgBAQkKCVwHq6+spH4vFooz/xRdf0Aiqiwkulys5OdmnATTNRbA9X7JkiWrWlA9L6CPDxvSJHhwc7Ozs1E/y4sWLkJCQyMhItndzuVzh4eEWi8VrcmQ+nFqvL57fb7X6C61wLqPR1Ui1zRccDgkqyOkr/vjs2TMAmDZtGptEVWA2wsjRXLs3ipII6jhClV0w9/cfbTQNDLfbnZSUpLrLAjf8RUZGiiCydetWHc9dfQ5Op3PcuHEAsGfPHjbmmjVrTCbT27dv2UC/6du3by9evHj69Ok2m23UXaJ90gIdLVR9pn3iM8zIY0SMYWrxt0/ud63p7e0NCwtDH8K/B0qFhYUAYDAYdLz8XS5XSkoKAISHh1PLylf1PR5PZmYmZ0i43e6JEyeOGzdu7Nhp+j0rzqN///33XtUfvoGxY8eOL774wmtGOhG8tuetra0mk6m+vl6HCX2ljwyNJk40Nzdv37590qRJrB+LavIjR44AQFZWFvc2MzMTAH7++WcuXPXR71qvyi0ggVr9hVY4l+lY00h8OCSoIKev+GNJSQkAbN68WTzJCMVUbfdGKK8Asg14ZQ+gbCPBajQNjMLCQqPRqLqlDNfB//Wvf4nofODAgUmTJonEVMa5cuUKTnfduHGDvu3u7jYajQFxTLpw4cKcOXOSk5Pr6ury8/N37NgxZcqUgoICmtdYJnp7e41G4+TJk/GU+tESdYyIMVrqfyj5DqfWlJeXA8CPP/74oSirL6fH4wkPDweAVatW6cdsaWnB9kd8wptlODQ0tGXLlvHjx3OGxJ07dwBg8eLFbOT3Tw8MDNy+fbu9vZ0Qot+zLl26FABu3brlVchhGhhNTU3s0rTX7LgI4u35ggUL5s+fzyWnj+LI0CReCYfDcezYsbi4OJPJlJaWdvHiRXZdQjX5vHnzAODo0aPc2x9//BEAUlJSuHDl43BqvZJbQEK0+gutcC7TMaiR4HBIUEFOX58ecSfVuXPnfEoV8Mha7V7AMwoIw5Go7AER7D0wGTUDo7W1NTg4ePXq1apK4oa/06dPE0L6+/vr6urKysq03KVOnToFAKqGiipzNnDHjh24iRm3mL98+dJutxcXFwNAZmam/d2P67wJIXl5eePGjTP/7y8sLGz37t2EkLS0NIvFYjabp06dijOX69ev37Vrl8vlqq6uxmUWm80WFxcncmTtwMDA3bt3a2pqWIEJIR0dHTab7cyZM/fu3evq6mpqauIiaD3ev3+/vLy8vr7e5XI1NjaWlJTo90AXL14EgPT0dFWGL1++rKqqOnXq1J07d+gGfWXMR48e2Wy20tJSVUcRjK8vmL4YbI6vX7++cuUK/U7sdnt5eTl7Yk9/f/+FCxe0JNEX49GjR5WVlewY6Pnz5xUVFazXuGqR+S2Vktvbt2/xm2T/X716xYKA9MDAQG1tbWlpaVtbG/fW6XQ2NzfT3bRPnjypqKh48+YNF035qFXigrVGyXBwcBAVSU1NBYCzZ8/a7fYXL14oY3oN0ZLN4/E8evTo9OnT7BKB0+m02WxswVH+AcGts7MTzYYjR45QzlrEhAkTVGeRteLT8Obm5sTERACYN2+e3W7HwyTwLa6f0NwdDsfp06fr6uq0Zgq0tHY4HNevX6f1xW63l5WVKb8oKhIlnE5nVlaW0WhEHJYtW8buneBcpIaGhiwWy4QJE0S20g3TwMjIyFAuTY9Ee37s2DEAuH37NsUECZ+Q4dKqPrrd7itXrqSnp5vN5jlz5hQXF4t0LoQQh8NhMBgAoLa2luP822+/AYDRaNRZwxep9Vq1kkLhX0NECNFpq7X6C61wqruIRoQQrcpC+ejIhnF0enBlm08IERwOeVXQq+RUBZbADqKqqsrlcn3yySfcRilVgUW6GBFhVAcPWu2eqiRUEf1PUbyh0yk7mhclAl7ZKecPhRg1AwMXYbXuUfr0008B4NWrV1evXrVarTgdaDQaVfd8474Z/7ZhxMTEAMDy5cvxfKclS5akpqaGhoYCQHx8fOq7H87AcSX6ww8/YN/JzfQkJSWp7lk/dOiQ+JJIe3t7bm6u2WwGgLS0NDbrkpKS8ePHl5eX37hxY/ny5QCAZhgbR0l3dHQsWrRow4YNDQ0NVVVVmZmZkyZNmjlzpjImG4Jbpn755Rc2kBDS09Ozbt26FStWNDQ0NDc3JyUlxcbGsuN4jN/R0ZGSkpKbm3vnzp22trbQ0NC8vDyOlYhgWmKwrE6cOBEXF4clggOgioqKiRMnohM8DlwaGxutVivGoWMmKqoOPh0dHfn5+Th5ExYWhgbn77//brFYAGDfvn2EENUi81sqVW6EkDVr1tCvjhLbtm1joRgcHNy/f39SUpLNZsNRDh1o9vb2Hjx4cObMmQCQlJRECLl06RJ+Zrm5uSwTjtYpcZfLJV5rOLY3b95MTU3FvQoGgwGrW0ZGBhdN/1FHttbW1r1792J1pgYVIaS2thYAuHPhAoib2+1GVOml1DoqoIHh65FZ9fX1qampkZGRqEhqaiq7UQo9r/Ajr62tjYiICAoK4s5+QZG0tC4tLZ07dy5+Y7gHrLKyMiwsDEP0JzXQ9xVjpqSkXLly5eeff46IiKBfLGdgYAO+YMECHZToq+EYGF1dXWazmSt35Bzw9ryhoUHZevuKDNValXjy5Mn3338fFRUVFhaWnZ3NHVKimoQNxMUcAFBajM3NzVhYqtsjRfpKnVpJCPG7IcL5NZ22mhCi1V9ohSMmIu2YVmWhqIp0Z1o9uFabTwgRHA7pKOhVcqoCS3R1daWnpy9fvvzy5cvV1dU4ZouPj8c4qgKLlKyIMFqDB9V2T1USqoj+p+hTQ6dVdjQvlghsZWc5f0D06BgYvb29ISEhBoNBdYLk0aNH2GvW1tbm5OTgPh5ctGW3gVKUq6qquHMw6Ct9wm63YzPK+SdMnjwZAJ49e6aT3O12474r5IDHHVZXV8+cOVNVqfPnz6vuNtHJYuHChdyYoL+/32KxUAdil8tltVq9noXS0NAQGhrKjnWys7MBwKs8aH09efKEFbKpqclqtbJpcXyARhqNef78+dDQUHoCPUI9fvx4GoEQIiiYqhgsH6TxbFPct3Ps2LGCgoKBgQE88uLp06c3btzYsGHD69evcYzOWk2CYhBCZsyYAQA3btxobm7esGFDR0dHZWUlu4CgLDK/pSKEcNzcbrfVat22bVtRUdGRd7/s7OyUlBR23rezszMuLi4hIQFXJF6/fq28W6CiogIA9u7de/Pmza+//hqnx5S2H0VYsMRFag3lyRII0dy5c9lAQVpENlyQ3LVrF+U5MDCQlJRkNBopdAHHbd26dQCwcuVKmqkqgS5SBoPh/v37qhH0A3EFgxsgOp1Os9kcHh7u8XgqKiqys7MdDseBAweU6yT6WuMoc+LEiS6X68SJEwcPHnQ6ncuWLfPqnV9aWoqtosViobPpWAoYTg2Mzs7OgoICnD8KCQk5duwYXX7UUpw1MAwGw0rFj1pBAMA17JWVlVpLsgFvz7u7u3FtnF0lFkdGS31c0q+oqFiwYIHRaExNTT179qxyjV0nOX116dIlLA7l3NDjx4/x1ZUrV2h8VUK11ovUSkKIrw2RYJeh1V9ohXN6qWpECNGvLIKyee3BuTafECI+HNJS0KvkHAL42NbWNnXqVHbiCWccuJ5CKbB+yYoI43XwoNruqUoi8ikKNnRey46DMSCVneP5wT2OjoGBW4WoKcyhhtOuq1evZj/uN2/e4Hou66OCCbEg/XDgRt8qAGDXKDo6OgBAZH95S0sLHm8PAFFRUU1NTVFRUQ8ePODU8e/R7XZjT8ke4v78+XMAMJvN1KElNzeXdY1Q5tXS0mKxWLjrRDZs2AAASucrNvnLly+V50Xcu3fPbDYnJCSwvSY6hAQFBdEjHXCGGI8cRZ79/f2LFi3av38/zUJQMFUxKBOWwM9g8+bNFy9exJUuOtJ68ODBt99+i/4h2ErS+7AExcCMcIooPz9/9erVVFkqg2qR+ScVIUTJrbm5ubKykmbX29u7Zs0a1vOnv79/1qxZYWFh9JiyQ4cOKT3O8aQRm822du3aoaEhj8djt9u1nGcES1y81lD5KYFDT9Zkpa/0CUHZsP/gHMrPnj07b9485D8SuD179mzSpElGo1F/xLxx40YA2LFjh76mqm/fvn3LXX2N0erq6gBg3bp19fX19JzWzZs3c972XrWuqalBPnV1dbR1TU5OBgD9c+3oQbH//Oc/qeT6ezBoNK8Ea2CYTKb/vlLv/z9NmTIFB8dKAwOtrG+//VY1l4C359iAt7a20uyGj0xpaSkuec2fP19/CoxmqkWguaXqXYzVGQD0ve1Va71grURPY2ydRBoiQohIW63VX2iFc+CoaoRGnX7TKiIbIUS/B1e2+YQQweGQloJeqzmHAD4+ffp08uTJCxcuZPuF6dOn4/waTaIqsE7JigjjdfCg2u6pSiL4KQo2dPplRzGhxPArO2X14RKjY2Bs2bIFAHDfghI79PyZNWvWwMAAfTswMIAevWx7jW/z8/MBwI+d06tXrwaA6Ohomgsh5Ny5cyIX/LFZY39mNBovXLjAshoOjevXn3/+OccEKzntI9nxJRcTB6mJiYnBwcGcX/vs2bMNBoN+WpxeyszMpGyHhoZiY2MBoKGhgQYSQtra2hAB7PB6enoiIyMnTJigPKKepnK73YKCKcWgTDgC54yLioroWTQ3btzAq7iys7Nxlwi6HVNvb3ExMC9sicaNG6d0rSaEqBaZH1JhXqrcqMput3vjxo2PHz+mIYSQbdu2AQB1lblz547FYtmwYQPbSRBC5s2bZzQav/nmG27mm2WFtGCJ+1pruIwQItZ24iKoPorLNjg4aDAYPv30U5ZPTk5OdXU1hgQcN2RbV1dnMBh0PH8aGhqCgoIWLlzImuuskPo0rhxu2LCBi7Z3714AKCwszMnJoUWPzoFsiXvVGtc5i4uLN27ciHyGhoZCQkLMZrPOlHlPTw8d3+fk5FDZRsLA8PWYWvTx4KZgqYSEEOxKAtWeI+b0Lr9AIdPa2pqbmzt58uTIyMh///vf7OwYq4tXmpaIcgUDZ829HnOs7CvFa6VPDZF4X6bVX2iFcygpNcII+pXFp35EpwdXbfMFh0NaCupLzqlPH1NSUgwGAzs54nQ6DQZDSEgIu99SVWCdkvUqjMjgQbXdU0oi/imKN3Q6ZUehQyJQlZ1j+8E9jo6BsWjRIgBQ3YDhcrnQtZ27vhr9KCwWi7JvW79+va8XA7EzxJwL+65du9hRmn6JDg4O4rok9kl0yKKfSuRtQUEBAHCyEULKysowL+XOPCVbvDJp/fr17KsXL14YDAat5SMaMyMjAwDYYR/2vtyFIYSQ6upqPM4fT+DF6rp9+3bKSkmIC6YUQ8mNEELP7cnIyKAtIE7Vx8fHUy8vtBBWrFiBTMTFwPhdXV0AMHXqVFUZlEXmn1TIXMmNzTQvL48994wQguehhYeHO53O3t7ewsLC8PDwgoIC6gWEyXt7e00mU0REBLs8yHJmacESJ4T4VGvYLAghn3/+OQCwK3VcBNVHcdkIIZGRkQaDgX4Yr169ot/ASOBGBcbFmV9//ZWGUGJwcHDWrFlWq5U6EdFXggSup5WVlXHx0XUzLS2tr68PX7W3t3OrsiJaz5w502Qypaen0zXSW7duAQC7LsFlTQjBA6ywjWKH8nQ4q3WTt5KVagi7guGrgYFjNbqqo+Qf2PYcPSrp5p/AIjM0NFRdXb1s2TKj0Th//vyKigrlmqpSQTaEbrRgzU6MgBdBqG7PYDkoa714rfSpISKECLbVWv2FVjirjlY75rWyCMqGeen04Mo2X3w4pKqgV8k59fHx5MmTAEBbSAzEr5e7clcpMG6wUe1iRIQRGTyotntKScQ/RfGGTqfsOCQDW9k55h/Q4+gYGGgIqg4pbt68iRtzOUMCb7JUPbgWJ4p83eSNFgsAcMsO6APgdWMDLWPsdLFDnTJliv6yAE3llcADBH/77TdlTDxyJzIyUj8vp9OJa/ScLjjs1lo+otlNnToV99ljiNvtRldp5dnq2CjQjfKYKZ23owwp4ZNgnBiUCUfQzpL1+8Irt7Zs2UIjf/vtt9RxwicxkIPT6UT/BNUrqJRF5odUVFQlN/qqrKyMbm6hgfPnzweAuLi4zZs3r1u37siRI6ojVzwfxmAwUKOLcuAIwRLHVL7WGpqXw+EAgIiICBoiQvgkGyEEx9zUcywrK4vueQg4bpz8GzduDAsLU34w+/bts1gsw7lh5h//+IfSv6WnpwddSVmrBkcMmzZtorJ51Ro3TQUFBbEX0u3fvx8A2N1clCElcH4R20O6luj1mFqa3CsxHAMDXUP1m74AtufYzdGOaYSQefny5aFDh2bMmDFhwoSsrCzq/OkVyd7eXjyKgEpIk+Cc0bhx41gnAvqWElyt96lWijdEhBDxtlqrv9AKp7ogwWmEgfqVRVw2mpdWD65s88WHQ6oK6ktO5WEJp9OJh6NwE1i4VY+7GkUpMCFEq2S9CuNyubwOHgghqu0eJ4n4p+hrQ6dVdiyGhJARquxcLmP/cXQMjMjISKPRqOoY8P333wMAdQFCBB0Oh8ViCQ4O5nxCCCFPnz7Fzkx1OKVTAPv27QMAk8nEevK43W70AaCTnToc8FVOTk50dDTKAABsL+41rVYEnN3ROiXQbrfjwTjslgYlK9zDFxYWxr4aGBiYNGkSACg7FTba/fv3ASAmJoYGtra2oo7cdBc2rwaDAQ+WwblS/S3y4oIpxaDycERRUREAzJkzh/qE4EjLYDCwLgSzZ8+mW27ExaB55ebm4qykcqlKtcj8kArzUuWGr27duqWcgu3r68Njgs6cOaNaragKW7duBQCt46FpNEKIYInjYqCvtYZmhBPb3FFp9K0WIS4bcsCpa/xEa2pq6N7fkcANc6R7yp1OZ1xc3Nq1a1ld2traTCbT+fPnMfDy5cs69/GxCSmNG59mzJhBQ5DAoWF0dDS7coUHG9Ct1SJa4/40q9XKXgyKvbi+UUQdJrm9JWNhBQNnqbZu3cqBxj4GsD3Hg7MePnyI/EcamcbGxk2bNlkslpiYmB9//FFp07JqIo2jJW7USAjBhoubw+aSK/tKn2qleEOEh93htCMrg7Iv0+ovtMJZblrtmNfK4kc/otqDq7b5gsMhVQW9Ss6pj4/nz58HgJCQELYf6e7uxvuI2S2mqgITQlRLVkQYkcGDarunlET8U/S1oVMtOyWSI13ZlTmOzZDRMTCio6MnT56sigjOOnPTMHv27NGaOcMrurgdnKqcuUA8iIC7CwkPdRE/T9ZmsyUlJfX19c2ZM4faGL6OFTjBaHv65Zdf0lednZ1nz56lj7ggmJCQQEOUBMbhXMALCwsjIiK0zu+iTHBjGbpQDw4Out1u3DlqNBo50+v06dMAsHPnTkz74MEDxIE12yhbJMQFU4rBsaKPeIIEO6+PZ4uxI9eurq6goCC65UZcDMylrq5u9+7d2B4p/Yuwm2GLjB4D5ZNUmJcqNzSnt2zZwjb9GP/hw4cIO52kp8hwBBrDIp+oYInj5ksAEK81rEh4PCg9SJd9pUOLy4ZMcC91XV3dw4cP2SmAkcANc4yPj6cgX7t2LSgoiO2b161bl5ycjDEHBwdTUlJU1yp1ELDZbKoHwVF/YprW4/F88sknRqORngwhojXaJD/99BPlg724ln8gjTY4OEivv2Br31gwMHDwpNNZBLA9x6OKDQYDXYofaWSwCPr6+srKypKTk4ODg6lJSUuHI3Bpi91ohxFwqYdtuLiEqrXep1op3hARQgTbaq3+QiucU0q19/daWQRl89qDq7b5gsMhVQW9Ss6pj4/o4ICHmNMIeF0Yd/KNqsCEENWSFRFGZPCg2u4pJRH/FEUaOq9lR4GixPup7DS7MUuMjoGRnJzM7blEgHDWedy4cez0m81mCwoKYh1dWDRx3x7n5sRGUKW7u7vRkWDPnj1sBBw+6q+h0/j37t0LDw9HR6/m5mbarVqtVur9TCP7ROBM24EDBwghxcXFbre7sbHx66+/pkzQPtZ3hkYm7EGZFy9ePHPmjMlkwpPgq6urVb3U8MZAAMBBz759+968eYMNBGcW9vf3W63WuLg46v7rcrmCg4MB4K+//qLSEkJu3LhBPbXEBUtLS+PEYHlSur+/P/jdj/UZy8rK4vaQoMmB21ry8/Nx0CmIT2dnZ1pamsvlwlmWuLg4QkhfX19JSQmKoSwy/6R6/fo1IUTJDX1bMzIyVD8tdDQCAAoySlVfX3/p0iUKFAofHh6uNFFoHEoIljghxKdaQ/kjgceeNjY2cuH6j+KyIZ/c3Fw8XHXVqlWs6TsSuGGO8fHxRqNx586dd+7c6e/vDwsLO378OFUqIiLi6NGjL1++rKysxIMTsK65XK6DBw8WFRV5LSD8equrq3t7e1kzAC85Yes1+umh+Wez2VpbW71qjUeyGAwG9ghmPN0FbykpKirSudgU22SccqafK7pEoxlcXl5OofCVuHr1Kp3KMZvNdMWS8qH34Si30nV2dgYHB3PjJJowsO05nvS6cOFCyp8QMqLIsBkRQh4/fsytNnMRCCFv3rwJf/djp40GBgbCwsKmTJnC1hRlWmWtF6+VPjVEtD302lZr9Rda4ZxSSo3wOkL83rSaVsHuzGsPrmzzxYdDqgp6reac+viYk5MDAIsXL6Zva2tr0eDEul9TU4PTWEqB8T4oAFB2MSLCiAweVNs9pSSCn6JgQ+e17ChWLOFTZcd1dToZwfL5oOnRMTAyMjJUW3ncg0vnmNFzd/z48Vq3UA0NDYWHh0dHR3vtj7lCooey0yN3MAKOSv9fe3f/EsW3B3B8tDKzjB6gh4XyJmUQJf1QEWVladYvGVgE/mIhFbdHQ7DEohSKaosehJvRg8JaKfRgWllZbRS01u75Q+5f0b3QBw6Hmd3Z0XW+uzlvfxpnz5w953X2nJnPzJkZ9+lDknJwcHDhwoX79u3TOe/atUvv+WxTvHQajwsyoyMcDjc1Ncm8jitXrkyfPl3Pm5dj5ZaWFpcM5bESRUVFXV1d0Wi0ubn5zJkz8rCFjRs3tv75S7W5vD5ieHi4qalJngusnxOvj11+/fpVWVm5c+dOHV1IbjLYVVVVSaPE4/GLFy8eOHBAHwp4L5izGEkLfPfuXcuyNm3aZH4aCoVs7xyVWxJbW1ubm5vv3bvnpRh3796tq6u7ceNGVVWVnnKwaNGivLy869ev19bW6pXOJhtfqaQKztzi8fjWrVtDodDRo0f1QZtZX5ntUF5eLkd+0Wi0sbHx8OHDZtc4d+6cZVmpYnUzN5kwILcupG1x773G9hVKqXnz5hUVFZnHN840zjXef42yrcw0WLp0qfOweMLd5BvNl+RYlpWXl2c+5q6goECmtOkRQwKMrq4uWeP+HFillEy5fvz4cX19vX7xjswnXrZsmSkmjV5TU9PZ2alvoHKvtdyfZrscJxHCsWPHLly44Lyz3PzG9+/fy61KlmXt27fv5cuXTU1NcgeX1G7Dhg1pj33NDM3lQ4cOaTTLsh48eGB++vbtW5nLIWkqKirM379SSh5g6HyJ+4SP5/IQWPOWMKWUrzKmg/flmzdv5ufnmz/OI0eOTJkyJekjWMxsnb3ee68c00Ck36uQdl+Wan+Rar1ZHaWUs0aSwL2zeNmPKKXS7sGdY773w6FUFXQvua368q88V33mzJnPnj378eNHW1vbv//8WZZ18ODB9vZ2faLEWWCllEvLeilM2oOHpOOesyQef4oeB7q0bZdU0ntn16+dMW94S5rnX7cyOwFGa2vrjBkznFhfvnyprq6ePXv22bNnz58/v3v37srKSttLl82t5HqZfkyH+VGq5ZGRkbq6Orm5TULthoYGfaqmrKysoKDAdsTszKq5uVn2oEVFRRL8nDp1Su9TZd+m53k7N0+7Rp6TMHv2bD1x4sSJE6FQqLS0tKWlpaOjo7S01HbtxZlnLBaTF/rKqUR5tZwEGFOnTrVFVrbN165da1lWSUmJGWsNDAyUl5cvX7788uXLFy9e3Lp1q3nqVOcQjUble5csWbJly5by8nJ9ml/SeC9Y0mLoL9ILcn5aD3z65URynUEnk7tu5syZI9e7vBRDcp47d675cGS5iFxcXGy+z9jZZOMrlZTWmVtDQ4M8Xc2yrNWrV8sv9vXr15s3b5awc3h4WK6n5+fnz58/f926dc7LAtu2bbMsy7ymoXGSLnhscY+9xvkVcgOV7RWNzmRJ13gsm2x74sSJBQsWmHfj6Dz9cNO3lZuHwuYxnB5/dALp6V+/fpU7g80fsy6qXojH43JIsWLFCh3+KaVkvqjt7IYcAE2dOtUsgHutJZaw3cwt53cLCgrcyyaFfP78udytJBVcv369XHmYNWvW6tWra2pqTp48qavjcSEcDsubyzWaRG6lpaWRSOTTp0+rVq3SLybSaYqLi82HWb1+/To/P982+ceP8by6unrx4sW28EYp5YeMR8BUyW7durV48eK6urr29va9e/eGQqG00YVSKmmv99grxzoQeRmrlVKp9hep1ttAktZIKeXeWTyWLe0e3Dnmez8cSlVB95Lbqi//xmIxmW9sWdasWbPkOEFOyBYWFuozFPqN6eZRilLKpWW9FMb94CHVuOekkyt4aQ9XPA50adsuqaT3zj40NCSnRcyHdqbK8++tcuuqAAAG40lEQVRan50AQ66Q6jnBNrJ4PN7X1xeJRFIlkPSJRGLVqlXO+aO23Lz/K6/asJ0I9775BKaMxWI9PT067JF3TSilfv782dfX193d7S5jlmRwcLCnp8c85/306dMPHz6YaZzL0Wi0u7vb3Eqnef/+/cOHD1+8eOHcd+o0SqnBwcEHDx4MDQ3pCxfmp5IgbcFcimHLzcu/P3/+7O/vt50sd/eJx+ORSEQ/plN/S29vr+2hAs4m04ndF5KWypmbTDnr6+urqanJy8vbsWNHIpGQEzDmWdLh4eHu7m59Stv9qz1+6t7imfQaeeq8udPyWCSdzL1sOll/f7/z2oX+VI4hJtzNzN/78v3796ekez2fvFc4EomYd2C7fMXAwIA5mOiUY/q1JBKJ/v5+cxaizifpQjwef/r0aTgcljNEX79+7e/vdx80kuYz4Stra2vTPqQ7wy999+5dQUGBvgnHllsOyoyOjkYikXA43NvbaxshbYWXf917vcdemTRnl5XuY7VMZ0q62/KyH3GvUdohIm3Z5JKdyx7cOeYLhZfDIfcKjqmbyzPfX758+ejRIz1ojI6OdnZ22g4bUhXYpQXTMsq2LgcPIyMjznHPpSTj+Ck6B7q0bedSZY+d/fPnz84nGLlk+7d8lJ0AQylVUlJiu7o9VrJLly6VlJQkPQgea1aSXt7LZp6zH18+bIWArwKRSGTz5s07duxobGzcv39/dg/aMuk19fX1xcXFE9iFfWX/ZzJvaGgYx9n9f6Zsk+NbYrHYmjVrzGdmTGy9EolERUXFqVOnJjbbnMotk16fUxXRhZl8NdJVYwGBbAlkLcBoa2vLZAgeGhoqKysz3zQ5PsFoNKonTtTX15eUlKQ64z6+/NkKAZ8ERkdHs3VPWCa95tWrV/r6WygU8vhABZ8McyrbeDx+6NAh97mLOVXgv7cwMp/Kp1OGx48fr62t9Wk/UllZ+S/Pf2OaPJy2NTPp9Wkzz0qCyVejrDDypQikEshagBGLxcyHGKYqX9L13759q6qqevPmTdJPx7Ry06ZNhYWF3759+/z584IFC8xZ9WPKh8QIBEdg3L3m+/fv06ZNq6ioUEqFw+GysjIuX5g/G/OGCnM9yxMuMDIysmfPngkf8E+fPp3JlL+01ezo6Djj+c/l9sW0X+RMMO5e78wqR9ZMvhrlCCzFQEAEshZgKKWuXr3qZbqns6m6urps0wGdaTyuaWxszM/Pv3Pnzvbt269du+ZxK5IhEGSBcfeaRCKxfPnylStX3r59e+3atW/fvg0yI3XPrkA8Hk/7pogxlfDjx4+9vb1j2uQvSjzuXp+zdZx8NcpZagoWTIFsBhi5IJ5IJJ48eXLz5k39vNFcKBVlQCCXBTLpNT9+/PjPn7/xnVzIZRbKhsAkFsik1+cmy+SrUW46U6rACgQ9wAhsw1NxBBBAAAEEEEAAAQT8ECDA8EOVPBFAAAEEEEAAAQQQCKgAAUZAG55qI4AAAggggAACCCDghwABhh+q5IkAAggggAACCCCAQEAFCDAC2vBUGwEEEEAAAQQQQAABPwQIMPxQJU8EEEAAAQQQQAABBAIqQIAR0Ian2ggggAACCCCAAAII+CFAgOGHKnkigAACCCCAAAIIIBBQAQKMgDY81UYAAQQQQAABBBBAwA8BAgw/VMkTAQQQQAABBBBAAIGAChBgBLThqTYCCCCAAAIIIIAAAn4IEGD4oUqeCCCAAAIIIIAAAggEVIAAI6ANT7URQAABBBBAAAEEEPBDgADDD1XyRAABBBBAAAEEEEAgoAIEGAFteKqNAAIIIIAAAggggIAfAgQYfqiSJwIIIIAAAggggAACARUgwAhow1NtBBBAAAEEEEAAAQT8ECDA8EOVPBFAAAEEEEAAAQQQCKgAAUZAG55qI4AAAggggAACCCDghwABhh+q5IkAAggggAACCCCAQEAFCDAC2vBUGwEEEEAAAQQQQAABPwQIMPxQJU8EEEAAAQQQQAABBAIqQIAR0Ian2ggggAACCCCAAAII+CFAgOGHKnkigAACCCCAAAIIIBBQAQKMgDY81UYAAQQQQAABBBBAwA8BAgw/VMkTAQQQQAABBBBAAIGAChBgBLThqTYCCCCAAAIIIIAAAn4IEGD4oUqeCCCAAAIIIIAAAggEVIAAI6ANT7URQAABBBBAAAEEEPBDgADDD1XyRAABBBBAAAEEEEAgoAIEGAFteKqNAAIIIIAAAggggIAfAskDjP/yhwACCCCAAAIIIIAAAgiMXeD379//M/4sY5lFBBBAAAEEEEAAAQQQQCAjAQKMjPjYGAEEEEAAAQQQQAABBEwBAgxTg2UEEEAAAQQQQAABBBDISOD/M/XTt1xsEeAAAAAASUVORK5CYII=)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wfJSYeBts1SH",
        "outputId": "bd16237f-8555-4bdf-83b0-5342b5839f11",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "d1=sp.Symbol('d_1')\n",
        "d2=sp.Symbol('d_2')\n",
        "d=sp.Matrix([d1,d2])\n",
        "\n",
        "condition=d.T*hess*d\n",
        "direction_pos=sp.solve(condition)\n",
        "print('Se entiende la expresion de posibles direcciones dada segun la ecuacion: \\n'\n",
        ",condition)\n",
        "print('Teniendo la expresion evaluamos si en todas las posibilidades la '\n",
        "' direccion del hessiano es positivo, no obstante  para asegurar se usa :')"
      ],
      "execution_count": 265,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Se entiende la expresion de posibles direcciones dada segun la ecuacion: \n",
            " Matrix([[d_1*(6*d_1 + 2*d_2) + d_2*(2*d_1 + 4*d_2)]])\n",
            "Teniendo la expresion evaluamos si en todas las posibilidades la  direccion del hessiano es positivo, no obstante  para asegurar se usa :\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0c6YegsutJM6"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RWA2_6hRtUlq",
        "outputId": "56ed6006-2bba-421d-aaeb-7e3c9add10eb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "eigenvalues=hess.eigenvals()\n",
        "print('Los eigenvalores de la matriz hessiana son: \\n',eigenvalues)\n",
        "print('Al ser positivos, la matrix hessiana se considera positiva en ese punto '\n",
        "'por lo que se le puede considerar minimo')"
      ],
      "execution_count": 266,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Los eigenvalores de la matriz hessiana son: \n",
            " {-sqrt(5) + 5: 1, sqrt(5) + 5: 1}\n",
            "Al ser positivos, la matrix hessiana se considera positiva en ese punto por lo que se le puede considerar minimo\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2VYzF77rBbd3"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oJfc9xHCO6xA"
      },
      "source": [
        "# Solucion a-)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "drGUASRPgQuZ"
      },
      "source": [
        "x1=sp.Symbol('x_1')\n",
        "x2=sp.Symbol('x_2')\n",
        "fx=(x1**2*x2) + (x2**3*x1)\n",
        "grad=gradient(f,x1,x2)\n",
        "grad_val=sp.lambdify([x1,x2],grad)\n",
        "grad_point=grad_val(2,1)\n",
        "vectord=np.array([[3],[4]])\n",
        "\n",
        "d_normalice=vectord/np.linalg.norm(vectord)\n"
      ],
      "execution_count": 267,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XBromQCXi294"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4c1YKKIEi-AK",
        "outputId": "6c93446f-5c7d-4298-f1a7-626e46bc079f",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "\n",
        "print('El vector director es   : \\n',vectord)\n",
        "print('El vector director normalizado es  : \\n',d_normalice)\n",
        "print('El gradiente  en el punto (2,1 )  es : \\n',grad_point)\n",
        "\n",
        "rate_direction_d=grad_point.T.dot(d_normalice) #Grad has to be transpose\n",
        "#* makes the point point multplicaiton, dot makes the matrix multiplication\n",
        "#z=grad_point*d.T, grad_point*d\n",
        "rate_direction_d\n",
        "print('La derivada direccional respecto a ese vector es : \\n'\n",
        "      ,rate_direction_d)\n"
      ],
      "execution_count": 268,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "El vector director es   : \n",
            " [[3]\n",
            " [4]]\n",
            "El vector director normalizado es  : \n",
            " [[0.6]\n",
            " [0.8]]\n",
            "El gradiente  en el punto (2,1 )  es : \n",
            " [[17]\n",
            " [ 9]]\n",
            "La derivada direccional respecto a ese vector es : \n",
            " [[17.4]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ijiM9D-hm-SU"
      },
      "source": [
        "#Solucion b-)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X3OmPSWlm99X",
        "outputId": "f4ff2ce7-8765-4be3-df9f-23f411f6cf24",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "min_vector_direction=-grad_point\n",
        "min_vector_direction_norm=min_vector_direction/np.linalg.norm(min_vector_direction)\n",
        "decrease_rate_min=grad_point.T.dot(min_vector_direction_norm)\n",
        "\n",
        "print('La menor tasa de cambio es en direccion del vector menos gradiente en ' \n",
        "'el punto(2,1). Este vector es : \\n'\n",
        "      ,min_vector_direction)\n",
        "print('El vector al ser normalizado se ve : \\n'\n",
        "      ,min_vector_direction_norm)\n",
        "\n",
        "print('La tasa de cambio en direccion de ese vector desde el punto(2,1)es  : \\n'\n",
        "      ,decrease_rate_min)"
      ],
      "execution_count": 269,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "La menor tasa de cambio es en direccion del vector menos gradiente en el punto(2,1). Este vector es : \n",
            " [[-17]\n",
            " [ -9]]\n",
            "El vector al ser normalizado se ve : \n",
            " [[-0.88378792]\n",
            " [-0.46788772]]\n",
            "La tasa de cambio en direccion de ese vector desde el punto(2,1)es  : \n",
            " [[-19.23538406]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BPAlYGEcBhXt"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "H0H_lH6MWMOj",
        "outputId": "c976d6b1-7174-428f-8947-c4e25ef973e5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "x1=sp.Symbol('x_1')\n",
        "x2=sp.Symbol('x_2')\n",
        "fx=(x1**2+x2**2-1)**2 + (x2**2-1)**2 \n",
        "grad=gradient(fx,x1,x2)\n",
        "fx_val=sp.lambdify([x1,x2],fx)\n",
        "grad_val=sp.lambdify([x1,x2],grad)\n",
        "##change the descent method into more variables\n",
        "x0 = np.array([4,8])\n",
        "epsi = 0.01;\n",
        "max_iter = 10000\n",
        "res1 = descent_grad_optim_step(x0, fx_val, grad_val, epsi, max_iter)\n",
        "xmin = res1[0]\n",
        "iter = res1[1]\n",
        "\n",
        "\n",
        "print(f'El minimo global se encuentra en x1={xmin[iter,0]},',\n",
        "      f'x2={xmin[iter,1]}')"
      ],
      "execution_count": 270,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "El minimo global se encuentra en x1=-0.10914710950071563, x2=0.9970633521654858\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9aDEPvS0YSF6",
        "outputId": "4cea1cfe-7009-4f7f-e58e-e891ef220b5e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "x1=sp.Symbol('x_1')\n",
        "x2=sp.Symbol('x_2')\n",
        "fx=(x1**2+x2**2-1)**2 + (x2**2-1)**2\n",
        "fx=-fx \n",
        "grad=gradient(fx,x1,x2)\n",
        "fx_val=sp.lambdify([x1,x2],fx)\n",
        "grad_val=sp.lambdify([x1,x2],grad)\n",
        "##change the descent method into more variables\n",
        "x0 = np.array([4,8])\n",
        "epsi = 0.01;\n",
        "max_iter = 1000\n",
        "res1 = descent_grad_optim_step(x0, fx_val, grad_val, epsi, max_iter)\n",
        "xmin = res1[0]\n",
        "iter = res1[1]\n",
        "\n",
        "\n",
        "print(f'El maximo global se encuentra en x1={xmin[iter,0]},',\n",
        "      f'x2={xmin[iter,1]}')"
      ],
      "execution_count": 271,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/numpy/__init__.py:1: RuntimeWarning: overflow encountered in double_scalars\n",
            "  \"\"\"\n",
            "/usr/local/lib/python3.6/dist-packages/scipy/optimize/optimize.py:1814: RuntimeWarning: invalid value encountered in double_scalars\n",
            "  r = (xf - nfc) * (fx - ffulc)\n",
            "/usr/local/lib/python3.6/dist-packages/scipy/optimize/optimize.py:1815: RuntimeWarning: invalid value encountered in double_scalars\n",
            "  q = (xf - fulc) * (fx - fnfc)\n",
            "/usr/local/lib/python3.6/dist-packages/numpy/__init__.py:1: RuntimeWarning: overflow encountered in double_scalars\n",
            "  \"\"\"\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "stream",
          "text": [
            "El maximo global se encuentra en x1=inf, x2=inf\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1H6uhJbtBn-d"
      },
      "source": [
        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XyQoKChgjH355Zc27TiMpF0mp0+frpHywoULjLGkpCSNNK9evWKMBQcHWyyW3NzcY8eOvXjx4uLFi4qXA9XV1RpG9F/SU1xjY+PNmzerqqoUPugvRaTUU9zr169v3Ljx5MkTjeJaWloYY4GBgdq3MOf84cOHeU4ely9fFg7bDLixHTnn7mpKm67ajCwrK5s9e7YYftPW8WrUT58+FQNb4peFMaa9eYNNT1yTYg756+lmbuzVNqvmMJIGZWnzN39//4MHD9rMouDv/fBp1orDP2J6bnObQESka53HI51fTOWVdfzp06cVOn7Xrl0Gg0H+u5eYmPjq1StRZZs/093d3Xq0EOc8NjaWMSamWDc3N9MG33/99ZcognN+7NixcePG/fLLL3Jk/4ed0/EBAQGRkZE0/8Tf33/69OkHDhyQ5RHnXGzSEhISQqN0jY2NeXl5jx494pxPmTKF/pzJo+9btmyhyIiICEIg63j5T97WrVvFX0OSI/Z0vBhIlp/YKC+9nampqRGmDh06ROVaLBZqZsaYLGhobQ1jTHuPjuLi4okTJ9KriT4aj09JSdm7d29mZmZGRsbmzZupt8k6nkYlZec557SSQR7hrqiooKkRos/9+OOPjDHFK8snT54QJW0RoK3j5aUF4i4Vg8pRUVEJCQkW6RCTeewt6iWfY2JiGGOK7TgmTJjAGDtz5oyoF+d82LBhjDF5tZ/LlDjnNvO63Rm6X6gWZrN51KhRio0y9HDr7Oyk5lP89ZHhiPCyZcsYY+I5QcRTH1u2bJmI6aWOp4dD+S+AsCwCv/zyC2Nsy5YtIsZmgF44XLx4UfHKlRJXVlYuWrRo1KhRNvO6EKlRnMVi+eGHH+gxkv5QyKMbLpTFOdcozmq1btu2LTAwkL7wMGnSpIaGBnulBAcHM8aeP39uLwHF0/Oz+KuoJ6DY+UBt3y3tyDl3e1OqXVXHtLW1TZ06Vd4HTFvHc851olaX5TDGNSmmh79GN+uLXu2wpooEFovl6NGjBw4c+O677+h1LmNMMRFXZOkj/n0H3423uYCgDrjgv6c6vxBmso4/f/68Qsdv2LBBsXrq5s2b8q1q82dapxbq6ury/3TI75m/++47xphigpwatUdinNPxU6ZMqa+vf/36tdlstifshI5XbzTx/v178dsg3lTSuxsRT5rPno6nj1pT4osXL9qbVyNmdNDHZa5/Ovbt20cZaSBQdBfGmNDx8iY8shSeM2cO5Z04caK9dmptbQ0PD5flV1+Mx6ul7YYNG2Qdv2vXLsVDCOecfuxlHS/0NLWj1WqlcSPFsmNFMnt119bx8lh7U1MTkaTBZhosHzNmzL/ftvrP/9prHKlRFDo+MjJSrePp3dH169eF/65Rouw287rdGeEq53zdunWMsdDQUPHwo5ObWMRSU1MjG1SHLRYLbT8lD2lQsuPHj9OIkcjVSx3//fffM8YuXLggDKoDycnJjLHMzEz1JTmGkk2cOFGx/oH+Mpw6dWr48OFu1PEaxe3atWvLli1VVVUlJSVUwYiICPmnSHZbZ1ijuNzc3Pz8fBonPnfuHGPM5vQkKoiEmsMPafX09HQ5edhcbijXrvft6EJTvn79us6Zw95v2dq1a0+ePClXx6GO14latqkIt7S02PR98+bNkZGRNi/JS0QU1vTw1+hmLvRqd8FXVIROnz9/ToS/+uormwl6yb//4XPONfg7dZvTLu82e4gLnccjnZ9zLoSZ/MdTreNppwSDwbBjxw4xai53CZs/03q0EOdcTNaQhyD37t3r2ps02as+Cjun4x2Ovsjj8XPmzFE4fe/ePdJwChwHDhwQ8bQIz56Ov379ukhJ7zJsjsfLkTNnzlzz34MGAkV3cZeOz8nJCQsLWy8da9euFd6GhoauX7/e5Zm79PvBGFPreMU6V5vd16GOpwlFRqNR0WRu1/HNzc3EhHQ8tZRDuabwik71S2d6thSTvDnnrlGicm3mdbszosriU1zy8lad3PTreHE7qHW8uJvevn1LXvVSx3/55Zfis2WimopAfHw8Y+ynn35SxCtO6X1ramqqIl6czpgxw4063l5xbW1tilUH9I3bXn5Vw15xFovl/Pnzoo6c8xkzZsTGxsoxcpgmfWk/Fcvp3Rh2VztSHXU2JT3Mi7+9DgPyQIOo+5UrV+Lj48UpBRzq+N6jdu9bET387XUz13q1W+ArsMunNCvPz89PvPeWr/aSf//D55zb4+/sbS4WHzrs8HICm6LOU51fv463Wq2JiYlUkVGjRqkXLtr8mdap4zs7O2lYkwaLqYPt2bOHMXbv3j25v3lJuF91vJgczxg7cOCAQJCdnS06FokVezpeXpxKA7FCZMgvWeRIuSBRotxd3KXjxXi/qIs6IEtJ2RmHYQ0dr8hrs/s61PGCmOLRtq91PE37dm0Rntuls0NKhNomYbc7Q2X9888/YWFhjDGFTNTJTb+Of/bsGXVXtfQUfaC+vp686o2ON5vNjDGHgoxWpSu+LKbo6pxz+pMiL/NQpImKinJYliKLxqm94kwmk/xKl3NObw7FpD4NmxqX7BWnzhIREaHxBQ96HyVWH6mz912Mu9qRc66/Kevr68UKbD0Bm+PxNM1M/TdcjpGn6hHD3qN+9+6dTZ83bdoUGRlp85LGlCo9/O11M9d6tVvga3dI2rpAcce5hX//w9fzR0zQ0L7NOefu8t9TnV8WZtrj8cQkPz+fdklhjK1evVosw7M3VKdTx3POjxw5QtMjSRF1d3dHRkYuWrRILJURjeINgX7V8W/evBF/BOWVAT///LOIp1eE9nT8mTNnREqayCsEqKzj5Xk169evtwlaDEBCx3POaY9hxphiEaTQcDZ/6gRY/fNqFOPxjx8/ZoyNGDFCXrAizMoLPUWkCLhdOnuhjk9NTaUZNYpVKDq56dfxHz9+pJUh6l2uKysrGWMBAQFismBvdPytW7f0bJ9CsxvFknHR6HKgq6trwYIFQUFBgwYNkv+Cy2n0iz85l82wnuJExhMnTjh85yAS2wzoL664uHjp0qUaU1xocYXDuVVNTU3VTh51dXU2nReR7mpHp3S8KL03gZycHLGtqgjMmDGDMRYeHk4x6nW3OlG74JgLU5zFYh6N+0h/N+Oc975Xu1BxdZYlS5b4+fkp/iRSsj7i30fwOef6+Tu8zdWgRIyz/nuw8wthpkfH094kCQkJJAtXr14tqmxzuE2/juecX7x40Wg0jhs3LjU1df78+RkZGerZm6I4zwYc63i6dQmTzVcwigqI+fHqeTWc83HjxpGp7du3i4zbt2+nSLF9jz0df+jQIUoZGBhIG5LY1PFiaSNjLCQkRKFBac6T6C7u0vH19fUl/z3kWUCzZs0qKSnRFqYCiDrQ1+PxHz58IBknryqmDSIIuIKhwkOh4+Vk4mlKfm2t0PFtbW1k/48//lDYNJvN69atU0TKpwNex9+9e5e2bVWMpN68eVMnN/06nnQSbRcrQ+ac00Zg8tYxvdHx+/fvV9xxiuLo9OrVq4yxuLg4m1cpcseOHX/99RcNHalHRimNG3W8nuKEt6tXr+7lJyP0FNfV1XXkyJGAgICEhAR5Kqdwg1bbG41Gg8Eg/y7KCUTYvZMKyKy72rH/dbzAIgfoNYvN77k6hVq2qTPsrBQjsw756+lmwsPe92phqjeBKVOm2FQXtMhHT1d3tvQ+gk8zYRz+EdNzm2vXyDX/FTb7p/MLYSb/vaKpR/IXxBVfoSGBNHToUDHY1Esdb7Vad+zYUVRU1NbW1tjYKMwqmHjJqWMdf/jwYVJajLFJkyY59JsmqCn2NBS5xOagy5cvF5E0h09e+ibreHny9NKlS8kZMXGW3glSpHoyE8Xv3LlTlFVQUEBbXoqlDIwxeR8rWu1Hr2lELtqNhDFmb3mNSCkHWltbBbpe/qjTNpGKTVfkskSYHorEptoUT6v45XWuQnmL90SLFy+m5Yzyw4Z4TKIt4UUpioDYr1NMoZY/5iXnFeJefP1nxYoVtHPO7du3hdmGhoa5c+fKi4bFJRGwuUUMzc5UPBVQn5QnNblMiXNuM6/bnWlvb6c1W4oXSlarlVZg6+EmdPyLFy8EN3uBv/76izE2aNAgReLk5GSDwSC/xb548SKNStozpRFPq/7Vs3cUWZqbmwcPHiwe7BVXOedFRUX0zEkvQGmj30ePHik2XNLW8dXV1fv371evOXG5OMr45s2bkSNHysQo3u3F/fbbb2lpabSBWGRkpLiXZf9pY0GxUa98SRGuqam55eTRb+3oEzpeP2oFeT2nrkkx7ftI501E7tnr1Xqcd2Ma+na44r0x2e87/n0BX/8fMT23uTZh1/xX2NTW8e6C39bWRrt+yYsJN27cSO+lhUtJSUmPHz8Wp5zz0E+HiLH5My12lNLWQpzz9PT0H3/8UVizF6ivr//ll18cvuq0l91d8Q50vNVqXbhwoRCjRqNRzJG16UFnZyft8ccYGzlypPxEJdLTvp5Dhw6lAaT3799TFnnncqHj/f39Z8+eTXnr6upoC885c+aId2pC4Cp2t+js7KTldOR8VFRUenr6t99+Gx4eTrLyxo0bol6bNm2iIt69eyciZ86cKXwmRcUYGz58uDzkLBLYDLhRx4tvYMlb09gslBZ/yF9i7+zspBtDXgvy559/Uk2Fan/x4gWt7Rg7duyVK1dqamrOnDkjHmDi4+M1PlrW3d1N09QyMjJMJtOuXbtaW1tpa0vGWGVlpXD1wYMHVO6TJ08osra2lpqVxl/T0tIWL148bNiw/Px8kctmgBpFXv9gtVppv1H52c9qtdJjzO+//y7suEyJc67OK/YOc5cznHPajHXMmDEfPnwQblsslqysLHp7qIebeL7S+HiKME5/vOjTy2KaU3l5+ZAhQxTPRVlZWbQluc0bXDaoDoeEhAQGBmpMAhFZ6Nsf8ssczvnPP//8008/Xbx4cePGjTRGQjP7v/zyy1u3bokbWRjR1vG0n+zw4cMVy0JEdmeLo4yJiYnyQ6Ow1kfFtbe3L1iwgDEmr4QWhdIO4r2cqS+suRBwSzv6hI7vU9QuSzE1f/f2ahe6hM4sSUlJI0aM2LNnj7g9GxsbZ82aZfPm4pz3HX83wnfhjxjh0r7NtZG67L9sVlvHuxH+zJkzGWMRERHnPh2LFi0SrwoPHjxIc/mSkpLi4uLE70hXV1dQUJA8YmvzZ1qnFqJnicGDB8fExCQmJqakpKSnp+/Zs+fSpUtCLxGZuLg4xti0adNkUP0f1tLxJ06cGD9+vNC1FBgyZMj8+fOFjJY9rq6uFtNmKPH48ePFZ5jklHl5eQEBARERETt37pw2bdrw4cMV8rShoWHIkCHHjx9/8eJFVFTUd999t3379rCwsMGDB2/ZskWIjPz8/CFDhggP/fz85GkhLS0t1JaUwM/P77vvvqNmIAdExkGDBh08eLC+vl68TKBLSUlJXV1d9K0lkXjGjBmKtpSrJofdouPPnDlDI+XkgNFo/P77723Ksvv376enp9MOuwaDYcOGDaWlpWVlZUuWLKG8EyZMoB028/LyREvNmzdPPJuaTCbql5R+4cKFDx488Pf3X7x48YULF2zuDyDqKx6oQkNDTSbThQsXxMYFU6dOpQ/Hnjx5kpYoMcamT59+48YNyv7y5UuxQz/dwNqrwu/evZuUlEROjho1au/evS0tLSUlJeJ1zbBhw9LT09+8eVNaWir6wNixY3Nycm7fvu0yJZuEe+NMcXGx2hnO+dOnT+nRa9SoUdH/HlOnTqUHErH6U5tbXl7e1KlTiVJoaGh6erqeYYPLly+Hh4dPnjx5586dycnJU6ZMEd2Dc/7o0aPdu3cHBQWR2ZiYmAMHDmhseye6BwXo+Vy9DYgiGZ3W1dUZDAbFJ4dpHeHcuXPlCfHU02bNmqX+u6St42nHN/GpabUbzhbHOT98+LC9R9C+KI58pnUsNv/YJiQkjBs3Tv/ogxpCL2Pc0o4+oeP7FLXLUkzN3729upfdQyO7UG8jR45MSkqKj4/ftm2bxl+bvilpYw0AACAASURBVOPvRviccxf4EyWN21wDI+fcZf9ls9o63o3wa2pqCBFjLCwsrKSkpKKiIiAgYNWqVZcuXaLNl5OSkiZMmBATE3Pw4MG8vLzY2Nj09HT6K2fzZ5pz7pQWOnDggJiaQT929O+wYcPkj7HQd17nzp0rg+r/sJaO71NvOjs77927V1BQ8PLlS/Xco46ODvmt9MuXLwsKCu7evav+nXboZHNz861bt4qKirTfJDi08/kkaGhoePjwIX3LtqOjw968WzWQurq6yspK8YisTqAdYzaby8rK5HbXTo+rRKAvuLW0tJSVlan3oOwl8ytXrjDG7MlctfHk5GTFmpx//vmnsrJSPMlTlq6urocPH9qcVaKt461Wa21t7fTp0+3t+OFscZcuXVIvFBb1cntxsmWj0Xj16lURQ4HXr18bjUb5SUyRoH9Oe9+OXqLjNXD1NereSDEFf/f2ag0mvb9UW1tbUFBQXFz86tUrmze4KKJP+bsRPufcWf6ijlar1eZtLhLYC/TGf3s25Xi3w7dYLI8fP3727Bk1ent7u2IYUWwjU1NTU15eLr+1lh1zOXz69OmDBw/W1tYWFxdfunTpzJkzx48fz8rKWrRokfwlcovF8uTJE+2e6bIP+jN6TMfrdxEpQQAEBgaBrVu3BgUF6V/139XVFR0dffnyZZerr63jOecfP37s5doV4VtRUZHia391dXWKr7q6sThRLu03ZzQa5dUpnHOr1bpkyZLs7Gw5pUfCvW9HL9fx/YC6N1KsN/z19GqPdCq50L7m7yn4ch3t3eaKNDZPe+O/TYNyZF/Dl8vqn3BOTk5kZKR6fJlK9/jouxoCdLyaCWJAAATcRqC2tla8RgsPDxeTgnQW8O7du6ioKJffDERERGisabFYLLt371bvHqjTNzlZaWlpRETEPulIT0+PiYmRJ7S4qzir1ZqTk/Pw4UPhQHp6umICEuc8KysrOTnZ3q+RyNs/gV62I81G0GjK/qmFvVL6AfX79+/tvTWy55Uc7xp/Pb1aLsVT4b7m7xH4Om9zPcx76b92EX0NX7t0t1998+aNwWCw93ns169fK77l4nYHXDAIHe8CNGQBARDQRaCtrW3w4MFLlizhnBcUFERGRuofjBcFNDc3u/At5AcPHmRkZNDGnRkZGTY3pqyqqnLLPK6nT5/SGnF5JqXiq9X0lQa3FNfe3k77ZC9ZsuTnn3/evXu3YmdSznlOTo7++UsCdZ8GXGtHzrmepuxTz7WNeyFqmw47y19nr7ZZVn9G+gR/Z+FzzvXc5v3J2WZZPgHfpuf2Iv/++2/aty03N1eermM2m3///feEhASdyyPt2e+LeOj4vqAKmyAAAv+PgNVqnTp1Kq1pnjNnzv/+9z/XuFgsFnubVLhm0NdzdXR0PHz4sKKigj6joahOU1OT9p6tivT9djrw2tFrUdtsU/C3iaV/Il2Ar32b94/bGqX4VufXqIjiUnZ2Nu0zYTAYQkJCIiIigoODR4wYkZmZqViapcjoqVPoeE+RR7kg8FkQ6OzsvPPpcHkB9GeBCZUEARAAARDwDgJv3rw5duzYli1b1q9fv2/fvmvXrnnz7xd0vHf0GngBAiAAAiAAAiAAAiAAAs4QgI53hhbSggAIgAAIgAAIgAAIgIB3EICO9452gBcgAAIgAAIgAAIgAAIg4AwB6HhnaCEtCIAACIAACIAACIAACHgHAeh472gHeAECIAACIAACIAACIAACzhCAjneGFtKCAAiAAAiAAAiAAAiAgHcQgI73jnaAFyAAAiAAAiAAAiAAAiDgDAHoeGdoIS0IgAAIgAAIgAAIgAAIeAcB6HjvaAd4AQIgAAIgAAIgAAIgAALOEICOd4YW0oIACIAACIAACIAACICAdxCAjveOdoAXIAACIAACIAACIAACIOAMAeh4Z2ghLQiAAAiAAAiAAAiAAAh4BwHoeO9oB3gBAiAAAiAAAiAAAiAAAs4QgI53hhbSggAIgAAIgAAIgAAIgIB3EICO9452gBcgAAIgAAIgAAIgAAIg4AwB6HhnaCEtCIAACIAACIAACIAACHgHAeh472gHeAECIAACIAACIAACIAACzhCAjneGFtKCAAiAAAiAAAiAAAiAgHcQgI73jnaAFyAAAiAAAiAAAiAAAiDgDAHoeGdoIS0IgAAIgAAIgAAIgAAIeAcB6HjvaAd4AQIgAAIgAAIgAAIgAALOEICOd4YW0oIACIAACIAACIAACICAdxCAjveOdoAXIAACIAACIAACIAACIOAMAeh4Z2ghLQiAAAiAAAiAAAiAAAh4BwHoeO9oB3gBAiAAAiAAAiAAAiAAAs4QgI53hhbSggAIgAAIgAAIgAAIgIB3EICO9452gBcgAAIgAAIgAAIgAAIg4AwB6HhnaCEtCIAACIAACIAACIAACHgHAeh472gHeAECIAACIAACIAACIAACzhCAjneGFtKCAAiAAAiAAAiAAAiAgHcQgI73jnaAFyAAAiAAAiAAAiAAAiDgDAHoeGdoIS0IgAAIgAAIgAAIgAAIeAcB6HjvaAd4AQIgAAIgAAIgAAIgAALOEICOd4YW0oIACIAACIAACIAACICAdxCAjveOdoAXIAACIAACIAACIAACIOAMAeh4Z2ghLQiAAAiAAAiAAAiAAAh4BwHoeO9oB3gBAiAAAiAAAiAAAiAAAs4QgI53hhbSggAIgAAIgAAIgAAIgIB3EICO9452gBcgAAIgAAIgAAIgAAIg4AwB6HhnaCEtCIAACIAACIAACIAACHgHAeh472gHeAECIAACIAACIAACIAACzhBwWseXlJTosf/hw4d79+7pSWkzTUtLi0n30dbWxjnv7u4uKSlJS0ujU5tmEdlHBDo6OgoLC1NTUy0WSx8V8dma7YeOjeb7bHsXKg4CIAACIODTBJzQ8W1tbT/88ENpaanOCmdlZe3du1dnYkWyo0ePsn+PgICAkJCQYcOGUURwcHBISIjRaPz3Ortz587p06fDwsIopqWlRWENp31KYM+ePV988QXBh453L+p+6NhoPvc2GayBAAiAAAiAQL8R0KvjGxsbIyMjTSaTU57l5uamp6c7lYUSZ2dn+/n5HTx48J9//qGY/Px8UoriQaK5uXnbtm2MscLCQs55eXk5dLwLqN2Spbi4GDreLSTVRvqhY6P51NgRAwIgAAIgAALeT0CXju/q6oqKijp16pQL9Vm6dGl+fr6zGfft25ecnCznUut4uhobG3vp0iXOeWNjo2d1fEZGhuywL4ZdrsLz5899Xce7XHe3N7TCk37o2AOg+dzeCjAIAiAAAiAAAt5PQJeOT05Ojo2Nda0yL1++NBqN5eXlTmXPyMi4c+eOnMWejs/Lyzt9+rTHdXxRUZGfn5/ssM+Fe1OF6upqn9bxvam7exta7Uk/6Hhfbz73NgGsgQAIgAAIgICvEHCs40tLSxljf/75p8tVWrBgwdy5c53KXl9f393dLWexp+NbW1ubmpo8q+NNJlNgYCBjjmHKNfKqcC+r4NNCsJd1d2M72vQEOt6NhGEKBEAABEAABAYSAcfSc/ny5Uajsb29XV3tzs7OAwcOLFu2bO3atdHR0atXr37z5o062fHjxxljt2/fVl/SH2NPxwsLstyprq5OSEgICwuLiIjYs2ePSCMC1dXV33//fcSnY+XKlc+ePROX7AXq6urWrVu3adOm1NTU1atXp6ent7a2cs7v3r0bFBREo9ErPx15eXnCiJ6CNNK8f//++PHjMTExr1+/NplMiYmJ4eHhM2bM2LNnz8ePH0UpFNCwQwlcq4KiFDp9+/ZtSkpKVFTUkiVLkpOTb9++bXM8Xtsle/6IEj98+LB79+7ExMQ5n45Dhw6pNyPSKKKhoSE3N3f27NnV1dUtLS1paWnjx4+PiIg4fPiwKEK7+UQyCjQ1NZ04cSIuLq64uNhiseTl5X399dehoaFJSUnNzc2cc7PZ/NNPP82YMSMiImLz5s3qu0bDW3ueONWx6+vrt2/fvmLFiujo6Li4uIyMDHJMURGdzafIhVMQAAEQAAEQAAGvIuBAxzc0NBgMhqioKLXT7e3t06ZNi4qKIkHZ2to6duzY8PBws9msSFxWVsYYc3ZIXmFEv44vKiqaNm1aWlpaamrqoEGDGGPZ2dmytaNHjy5cuLC6urq1tfXq1asBAQEGg0F7P83Gxsbhw4dfu3aN7BQWFvr5+TU2NnLOm5qarl27Riq25tNB7wc453oK0khz4sQJsQnPoUOHgoODlyxZMnPmTCprzpw5spTXsEM+u1YFmZsIV1ZWhoaGZmdnW61WznlFRUVISIhax2u7pOEPFXT79u0JEyacP3+eTtPT06kXyS9qNIooLi5etGgReXXx4sXo6OjU1NTk5GR/f3/GmFjsodF8or4UKC0tXbVqFRnMzc1dunRpWlpaTk7O9OnTGWOJiYmVlZVRUVEpKSlZWVmTJ09mjK1atUo2ouGtRkcSOt5hx75+/XpwcPBvv/1GhZaVlY0cOTI4OLigoEB2Q2fzyVkQBgEQAAEQAAEQ8EICDnT8H3/8wRhbs2aN2vVjx44xxlasWCEubdiwgTF29uxZEUMBs9nMGDMYDOrhSUVKjVP9On7NmjWdnZ1kKjc3lzE2btw4YfnRo0cjRoyQ96bcsWMHY2zs2LGyLBbpKbBr1y6DwSAryMTExFevXtFVk8lE8k7Opacgh2levnxJlpOSkkSlTp06RZFi4N+hHc65C1WQqyPCZrM5ODh45cqVIoZzTpwZY2LfSYcuaftDKv/IkSOilNraWj8/P8bYgwcPKNJhEd3d3aTa58+fL4alc3JyGGOzZs0Slm02n7iqCHz11VeMsZiYGPG82tzcbDAYGGNz5swRka9fv2aM+fv700sbzrlDbznnNj0ROl67Y7969Wrw4MGKW7W8vNzPz2/o0KF///03VURn8ylqjVMQAAEQAAEQAAEvJOBAx2dmZjLGtm3bpna9qKgoMDBQnqJAgnj37t3qxCNGjJAVmDqBwxj9Ov7du3fCmpi3LfavjIqKSkhIsEiHmBNSUVEhMioC9IhCG+PQpZs3b9bW1lLYpvzSU5DDNG1tbSTZRVlUYnx8PGNs/PjxdOrQDufchSqQccW/P/74I2Ps/v37cvyTJ0/IT6HjHbqk7U98fPyIESOENSorKytr5cqVYmqNwyI459Tx5JctFRUVjLFhw4YJ/202n7iqCMTExDDGxBMUXZ0wYQJj7MyZM3Ji+uKB2CZVj7c2PRE6XrtjL1u2jDF269Yt2QfOeWxsLGNs2bJlFK+z+RRGcAoCIAACIAACIOCFBBzo+KSkJMaYvc85yTLLZDKRxLG5YXx4eDhjTMxLcQGEfh0vj7U3NTWRvqThWBolHTNmTKStQ5bpCg/Pnj1LrxR27NghdKRIo5ZfegrSk6a9vZ38b2hoEMVxzgsKChhjfn5+nZ2deuxwzp2tglycCFutVlrR+/79exHJORfPS9Ql9Lik4c/79+8NBkNcXJxchCKspwjOOX2gStbxClftjYIrihOnc+bMUev4yMhItY6PiIhgjF2/fp1zrtNbdUeyt4Bb0bEtFgt9GU28IxIO0+qU4OBgzrnO5hN5EQABEAABEAABEPBmAg50/IIFCxhjP//8s706WCyWixcvrl279sSJExs3bmSM2dTxNBtBTEq2Z00j3jUd39zcLOv4kpISxlhmZqZGQTYvWa3WxMREMjVq1Khz587JydTyS09BetLY0/FijPbFixd67JCGc6oKcgVFuL6+njFmNBpFDAUU4liPSxpI7969Kw8hK8qiUz1FeFbHT5w4kTFGc9N1eqvuSPZ0vKJj19TUUOdU63gqmjH29u1bnc1nEzgiQQAEQAAEQAAEvI2AAx2/cuVKDeF7//79adOmZWRk0CgszauxqeNpbLL/x+MVcocWpMpz+p1qj/z8/KFDh5JgWr16tZiwrpZfegrSk8aejhfxZrNZjx1RTf1VEFnkgBCFipcSCh2v3yWb/ly/fp0xNm3aNLloRVhnER4cj5d1vE5v1R1Jp45/9uwZdcuysjIFKNE09fX1OptPYQGnIAACIAACIAAC3knAgY7ftGkTY2zLli1q70tKSoxGY2pqqrikoeNHjRrFGNOzvaOwpgi4ZTz+8ePHjLERI0bIK1ZFQWIppIhRB+rr6xMSEoSUpwRq+aWnID1phF5XzKuh8fgvvviCc67HjlwRnVWQs4hwVVUV1f3p06ciUj2vximX1P6Q9DQajWKRqFwWhXUW4SU6Xqe36o6kU8d//PiRVvQePXpUwaqyspIxFhAQYLVadTafwgJOQQAEQAAEQAAEvJOAAx1/8uRJxtjixYvV3kdHRzPGbt68KS5t377d5rwaMXlXMYgrMuoJnDhxghSkWDioyCWmmsjz4xXj8WLZ6B9//KHIbjab161bp4gUp4pN6PPy8hhjQ4cOpY0XhfwSCwb0FKQnjT0dTwOrmzdv5pzrscM5d7YKou5y4MOHD6QXs7Ky5Hgx6EsE9Lik4U9PT8/gwYMZY+o100+ePCGpqqcIZ+fViOaTq6YI658fL4/H6/RW3ZF06njOeVRUFGNs+fLlCocvXbrEGEtKSuKc62w+hQWcggAIgAAIgAAIeCcBBzq+rq7Oz88vPDxc4b3FYqGt2fft2ycuLVmyhDFG4lJEcs7r6uoUO/3JV3WGjx49Sjre3vekGhoaKIHYvl3WQOIDVStWrKDtSmQ7DQ0Nc+fOffTokT1nkpKSHj9+LF8N/XRQDE07pinIIo2eghymETpeMe9506ZN/v7+YpDeoR3OuQtVEHWRA4sXL2aMBQcHy68vxIQNAd+hS9r+rF+/njE2aNAgeWeY6urqWbNmdXR0kD8Oi+CcBwcHM8bkda5CK/f09JAdm80nV1kO29yvhta5Kh4OaU2I2Ltdj7c2PdHZsf/66y8i9uLFC9nh5ORkg8Eg9jvS2XxtbW379+/PzMyUn4plswiDAAiAAAiAAAh4nIADHU/6z2AwiH0bhceTJk1ijI0cOfLcuXPnz59fuXJlXFwcY+yrr766cOHCjRs3RMqLFy8yxi5evChiXAgkJyeTTM/JybGZnfYTZIxVVlaKBA8ePKBcT548ocja2tqAgACKjIuLS0tLW7x48bBhw/Lz80UudSApKSkuLk5sMN/V1RUUFLRz505K2d3dTfPmMzIyTCbTrl27Wltb9RTkMI3Q8cnJyaL0mzdvGo1GedGwQzvUjs5WQc2Bc/7ixQvasmbs2LFXrlypqak5c+YMqVvGWHx8PH1AwKFL2kjNZvPo0aOpmcaPH5+YmDhv3rygoCB5/rfDIjo7O2lnd3ld8p9//klmxXOIzeazWXfOOe28dODAAZHAarXSZ7Dk9dNWq5UeIX7//XdK6dBbzrlNT3R2bM45fSpr3rx5YtpYeXn5kCFD5AcMnc1Hu+wzxr799ltRUwRAAARAAARAAAS8ioBjHf/y5UuDwXDhwgWF3w8ePBg5ciRJotjY2NraWpPJRIP006dPf/v2rUiflJQ0evRooS1EvM5Adnb2woULqSD6ts6KFSuEPCIjFy5coDFRxtjUqVNJ4548eZI+q8kYmz59uni0ePnyJU1CIJsRERH37t3TdiYpKWnChAkxMTEHDx7My8uLjY1NT0+Xp2EI3RMaGmoymcianoK00wgdn5mZOWnSpDVr1ixYsCA0NJR2M5R91rZDOt6FKshFiLDJZKJnNgK4cOHCBw8e+Pv7L168+MKFC2K8XNslh0gbGxtpm3wqZdasWfITmkPCZWVl9IKIMTZhwoRDhw5xzvPy8saNG0cG582bJ8bpbTafqC8F7t69S9uwMsZGjRq1d+/elpaWkpKSpUuXksFhw4alp6e/efOmtLRUbA00duzYnJwcmlGmDYRKUXjiVMfmnF++fDk8PHzy5Mk7d+5MTk6eMmWKqKOojp7mKywspHt58ODB4sWFsIAACIAACIAACICANxBwrOM556mpqXPmzFG7297eXlFRUV9fLy41NTU9fvxYFriNjY1Go7E3O9UI4+4NmM3msrIyMd9A2zjpsO7u7pqamvLy8g8fPqjT19XVVVZWilFzkUBPQfbSCB3f0NDQ3t5eWVlZXV0t4xWlUMCeHZpGTyO+LlRBUQqdNjQ0PHz48PXr15zzjo4O+StFcnp7LulByjmn7GIGkWxZhO0VIRLoCdhrPj15nUrj0Nvee9LS0lJWVqaYi6Vw0mHzdXR0vHz5MiwsTJERpyAAAiAAAiAAAl5CQJeO7+rqmj17dmFhobNOW63W+Ph4xYpGZ418zullHf85c0DdPULg7Nmzv/zyi0eKRqEgAAIgAAIgAAIOCejS8Zzz5ubmqKgo7WFRdWG//vrrqlWrNMaP1VkQIxOAjpdpINyfBIqLi3Hz9idwlAUCIAACIAACzhLQq+Np75f4+Hgx+dthSQcPHjxy5IjDZEigQeDdu3c097qmpkYjGS6BgHsJWCyWvLw8PIG7lyqsgQAIgAAIgIB7CTih4znnXV1dV65c0ePBu3fvysvL9aREGg0C58+fJx1/7NgxjWS4BAIgAAIgAAIgAAIg8LkRcE7Hf250PFvfw4cPr5eOzMxMxR72nnUPpYMACIAACIAACIAACHiQAHS8B+GjaBAAARAAARAAARAAARBwkQB0vIvgkA0EQAAEQAAEQAAEQAAEPEgAOt6D8FE0CIAACIAACIAACIAACLhIADreRXDIBgIgAAIgAAIgAAIgAAIeJAAd70H4KBoEQAAEQAAEQAAEQAAEXCQAHe8iOGQDARAAARAAARAAARAAAQ8SgI73IHwUDQIgAAIgAAIgAAIgAAIuEoCOdxEcsoEACIAACIAACIAACICABwlAx3sQPooGARAAARAAARAAARAAARcJOKfjS0pKOOcdHR3Xr1/fvHmzRpkfPny4d++eRgLtSy0tLSbdR1tbG+e8u7u7pKQkLS2NTrXt4+rnSeD27dspKSl///23l1dfp58DuM+/fv361KlTe/fuPXXqVGNjowvtZTabr1y54kJGZAEBEAABEAABXyGgV8e3tbX98MMPpaWl+/btCw4OZowZjUbtSmZlZe3du1c7jb2rR48eZf8eAQEBISEhw4YNo4jg4OCQkBCj0fjvdXbnzp3Tp0+HhYVRTEtLiz2ziP/MCYwbN44xtnXrVi/noMfPAdzns7Ozhw8ffuTIEZPJlJubO3z48IMHD+pvsg8fPuzdu3fYsGFz5szRnwspQQAEQAAEQMDnCOjS8Y2NjZGRkSaTiap37do1PTqec56bm5uenu4ClOzsbD8/v4MHD/7zzz+UPT8/n2R6aWkpxTQ3N2/bto0xVlhYyDkvLy+HjncB9WeVJTc3d/r06Q8fPvTyWuv0c0D2eXqGP3nypGij48ePM8aOHz8uYuwFPn78mJeXl5KS8sUXXzDGoOPtgUI8CIAACIDAwCDgWMd3dXVFRUWdOnVKVLiqqkqnjuecL126ND8/X+TVGdi3b19ycrKcWK3j6WpsbOylS5c4542NjZ+bjs/IyJARuTfsLuPusuPe2vmoNQXMgdfn37x5ExAQEBoaarFYRBv19PSEhIQEBgY2NzeLSJuB7u7ujx8/cs4zMzOh420iQiQIgAAIgMBAIuBYxycnJ8fGxsp1fvTokX4d//LlS6PRWF5eLltwGM7IyLhz546czJ6Oz8vLO3369Geo44uKivz8/GREbgy7y7i77Lixar5rSg1z4On4Q4cOMcZSU1MVzZScnMwYO3r0qCLe3ml2djZ0vD04iAcBEAABEBgwBBzo+NLSUsbYn3/+KVfYKR3POV+wYMHcuXNlCw7D9fX13d3dcjJ7Or61tbWpqelz0/EmkykwMJAxB80nA9Qfdpdxd9nR7/kATmkT5sDT8XPnzmWMHTt2TNGUhw8fZozFxcUp4u2dQsfbI4N4EAABEACBgUTAgRBcvny50Whsb2+X6yzr+IKCgvnz548ZM2bGjBknTpyQk4kwTW+9ffu2iHEhYE/HC1Oypqmurk5ISAgLC4uIiNizZ49IIwLV1dXff/99xKdj5cqVz549E5c0Ah8+fNi9e3diYuKcT8ehQ4cUe+PU19dv3759xYoV0dHRcXFxGRkZipkADQ0Nubm5s2fPrq6ubmlpSUtLGz9+fERExOHDhxXl1tXVrVu3btOmTampqatXr05PT29tbaU0d+/eDQoKoklEKz8deXl5dKmzs/PAgQPLli1bu3ZtdHT06tWr37x5IyzrKV3DuLAjB+z5qW1Hm//79++PHz8eExPz+vVrk8mUmJgYHh4+Y8aMPXv20KwJ2QFF2J4/lKyysnLr1q07duyQc505c4Ywqv8tLi4WKbV9FskoUFZWlpCQQAa3bt3a3Nz8/v37LVu2iCJ++umnrq4uzrnZbE5LS1u5cmVycrLVaqXsCj/twXSqzys8FKeNjY0XLly4deuWojOXlpbKs+lE+r4LmM1mg8HAGJOxU3HXr19njPn7+4sFM9puQMdr88FVEAABEACBgUFAS8c3NDQYDIaoqChFVYWO37t379ChQ2fPnh0QEECy8scffxRaROQqKytjjDk7JC+yU0C/ji8qKpo2bVpaWlpqauqgQYMYY9nZ2bK1o0ePLly4sLq6urW19erVqwEBAQaDgbbUlJMpwrdv354wYcL58+cpPj09nSol3htcv349ODj4t99+owRlZWUjR44MDg4uKCigmOLi4kWLFhGoixcvRkdHp6amJicn+/v7M8ZkzdTY2Dh8+PBr165RxsLCQj8/P7H7XlNTEy01ZozVfDrojUR7e/u0adOioqJI7La2to4dOzY8PNxsNnPOdZZuzzh5ovhXw08NO9r8T5w4IbYeOnToUHBw8JIlS2bOnEnc5syZoyHlNfwpLy9ftmwZycQ1a9bIFUlLS0tJSXn+/HlTU1Pzp4OaKSwsTKhGbZ9layKclZVFgXLG8wAAIABJREFUPr969Yoi29raxo8fzxhbvHixSMY5//vvvxljtE+rTT/twRQ63mGfl4uTwwcOHAgODt69e/fBgwfDw8PLysro6suXLxljClByxr4I08Ibxlh1dbXCvslkIphPnz5VXLJ5Ch1vEwsiQQAEQAAEBhgBLR3/xx9/2PwtJx3v5+e3detWElVdXV3r16+nH9qbN28qGJnNZsaYwWBQjOsrkmmf6tfxa9as6ezsJGu5ubmMsXHjxgnjjx49GjFihLw35Y4dOxhjY8eOdSgQjxw5IuzU1tb6+fkxxh48eMA5f/Xq1eDBgxW6p7y83M/Pb+jQoWLD8u7ublLt8+fPF0P1OTk5jLFZs2YJ47t27TIYDOIJgXOemJgo5CDnXMgakYVzfuzYMcbYihUrROSGDRsYY2fPnqUYnaXbNC5sygFtP23a0cOfRCRjLCkpSTTlqVOnqIOJlw+yJxTW9odzvmrVKnWXTk1NFW3BORfPSLdu3SKzenxWO9Pa2jp06FAh0CkBvZtSLDgpKyubMWOGbEHtp02YQsdr93nZshxOSUkxGAziRdm1a9eCgoJoVJ50sHgElXPJ4YcPH+Y5eVy+fFm2IIeLioqoiRsaGuR4ur/okvBWkUBxCh2vAIJTEAABEACBAUlAS8fTng/btm1T1Jx0vMFgkF/Ed3d3T5w4kTE2b948RXrO+YgRI4TkVV/VE6Nfx797904YrK6upp9/MbAaFRWVkJBgkY7bt29TmoqKCpFREYiPjx8xYoS8hwbnPCsra+XKlQRh2bJljDGh/ET22NhYxtiyZctEDKGQh/8rKioYY8OGDRNpSH/TPjwUefPmzdraWpHApqorKioKDAyUp+jQI8ru3btFRj2l2zQuLMgBbT9t2tHDv62tjVpErjLnPD4+njE2fvx42Qc5rO0P5zwjI0Ot4x89eiSMmM3mUaNGMcY2btwoIvX4LBLLAXq4/eGHH0RkS0vLoEGD/Pz8xKMd5zwtLe33338XaWz6aROm0PHafV62LMI0UyUtLU3EWCyWoKCgI0eOWK3WiIiIoKAghw/e1MGosXT+q36/Jxy4cOECGRGvnsSl+vp6uqTz007Q8QIdAiAAAiAAAgOYgJaOT0pKYoypv+Uk5tUouNBEAqPRqJ5aEx4ezhgTE0UUGfWc6tfx8lh7U1MT/fzTgOvr168ZY2PGjIm0dci6WXbp/fv3BoNBY42dxWKh71LJQ+ZkgcZfg4ODhUHa2VrW8eJhQzwnnD17lt5g7NixQ35YEkZsqjrOubBAY/YxMTGMMXkLfz2l2zMuShcBbT/VdnTyb29vp1ZTjMsWFBQwxvz8/MQgvfCEAtr+cM537dql1vGykXXr1jHGQkNDxYOfTp9lIyJMM8qCg4NpKjznvLa2lub27Nu3j5K1t7eHhoYqWlntpxqmvbXdij4vnJEDPT09X331FWPsyZMncvycOXPi4+P//PNPxpjwUE6gCPf09HQ5eWi89bp165bNdidudOnu3bsKH2yeQsfbxIJIEAABEACBAUZAS8cvWLCAMfbzzz8r6mxPx//111/0W6seTiPRIE8BV9h0eOqajm9ubiaXSMeXlJQwxjIzMx0WJye4e/euYkxdvso5r6mpoVLUOp5KZIy9ffuWculR0larNTExkWyOGjXq3LlzihJtqjpKY7FYLl68uHbt2hMnTmzcuLFPdby2n2ondfK3p+PF8POLFy8UQOhU2x+HOr64uJiYy+ssdfps0x/O+eTJkxljYllFamrqihUrGGPh4eH0uHvy5En1Nou90fGKPm/Tsfv379PjiuLqihUrxo4dGxERMXz4cFpWoUjQp6eiw6jnxz958oSaRn3JpkvQ8TaxIBIEQAAEQGCAEdDS8StXrrSpeu3peDGtWTG4yDmPiIjwyHi8QtPQ1Gd5Brme5qQZCNOmTbOX+NmzZyQyxDJBkVKMtdfX11OkHh1PKfPz82mCNWNs9erV8iC0UDyiIArcv39/2rRpGRkZNDBP0x76bjxe20+1kzr529PxIl5bYmpwU+tjAfCff/6h9bWKD5Dp9FnYUQRohQZNiG9ubh45cuSHDx8iIyPFvPkZM2bIE3sou9pPNUx74/GKPq/wh05tTtPnnKemplJPVszzsWnE7ZFtbW30Xku9xoZeEQwZMkS+CzQcgI7XgINLIAACIAACA4aAlo7ftGkTY2zLli2K2trT8U+fPmWMhYWFKdJzzmnOsc7tHdXZOeduGY9//PgxY2zEiBHyElJRnLzYUURyzkmLG41GsfOjfJVz/vHjR1q9qv5OTWVlJWMsICBAzDXSr+M55/X19QkJCSStVq9eLcq1qepKSkqMRqM8uNs/Ot6en2ondfIXel0xr4bG47/44gvBwV7AHje1PhYWSMKGhoYqWlmnz8KOItDS0kLatK6ubs+ePbTlZV5eHmNs3bp1VVVV06dPV2Sx+d5ADbM3On7z5s20jFhR9NatWxljCxYsEN1VkUBx2tTUVO3kUVdXpzAin9JOQer7iNaCL126VE6sEYaO14CDSyAAAiAAAgOGgJaOP3nypHqPPM65PR1/9epVm/NwxPRx9Ti9fo4nTpwgOVtaWmozl5h0Ic+PV4xNigWUf/zxh8KI2Wxet26dIpJOe3p6Bg8ezBiTF4zSpSdPnpDmiIqKYowtX75cYeHSpUsKwaRHxyv2vCfZN3ToUKGuhKqTJ8RHR0czxuSxzO3bt/dmXo1sXFEvOtX2U+2kTv72dDxNcdm8ebNNZzjn2v7Y1Mdk6u7du7T7kEyPc37z5k2dPttzSWySs23bttGjR9N2/maz2Wg0BgQEJCQk5Ofnq/OqnzfUMHuj40mvK7prVVUVbSCrc+4K59y961zF47rilQjnfM2aNYq9WdXQ5BjoeJkGwiAAAiAAAgOVgJaOr6ur8/PzCw8PV1Teno5PSkoKCgpSDGdyzuvq6hT7KioM6jk9evQo6Xh7G881NDRQAtpMnWwKcS8+h0Szk4cNGybbaWhomDt3rnp6g3CMNh4ZNGiQvOlhdXX1rFmzOjo6OOe0NmDQoEGKqdvJyckGg0HedyU4OJgxJq9zFRKtp6eHSkxKSnr8+LEonXMe+ukQMWL7DjHt3mKx0Gb58vLEJUuWMMZk4aundLVxUa4ioO2nTTt6+Asdr1hvsGnTJn9/f8UgveyStj+cc3qwWbVqlZyrvb2d1mGvX79ejrdarbSRqB6f5YyKMK2v8PPzk/fAoZ0lAwICbD7cqv20CVNnn1f4wzmnLWXHjRsnHtVevXoVEhJCXaiqqorWSYuragsUU1NTc8vJQz33TDbe2toa8umQl8N2dnYGBwePHj1aZlVfX79//357r/hozf2cOXNk4xRua2vbv39/Zmam/MCvToYYEAABEAABEPB+Alo6nnOelJRkMBjE3h1Un9raWto2RP4my9mzZ41Go3rjRc75xYsXGWMXL17sDY7k5GSS6Tk5OTbt0O6NjLHKykqR4MGDB5RL7MtRW1srvloVFxeXlpa2ePHiYcOG2RwWFXbMZvPo0aPJ1Pjx4xMTE+fNmxcUFCSLEvoy1Lx588SknfLy8iFDhshj/52dnbRdibx0leb+MsbExJ6kpKS4uDghZbq6uoKCgnbu3Cn86e7upqnzGRkZJpNp165dra2tkyZNYoyNHDny3Llz58+fX7lyZVxcHGPsq6++unDhwo0bN3SWbtO4KFoOaPtp044e/kLHJycnCwg3b940Go3aS6W1/aFt+NVbo27ZsoV2Mfrw4YOoncViycrKorlMenwWGdUBq9X65ZdfKh7nSNzLyl7OSKuc5S1cbcLU2edlyxTu6OgYM2YM7Ub16tWr3377LSgoKCYm5vLly4yxc+fONTU1bdiwQZ2xH2KuXbtmMBiysrJEWXv37vX3979x44aI4ZxT3/7yyy/lSBFevXo1Y2zy5MkiRgRoig5j7NtvvxWRCIAACIAACICALxJwoONfvnxpMBguXLigqNvZs2cnT548ePDgb7/9dt26dZMmTVq8eLG91/FJSUmjR48W6lZhyuFpdnb2woULSUPTt9lXrFihWId34cIFWjvIGJs6dSqpvZMnT9JuIYyx6dOnCx3w8uVLmgZDNiMiIuhTmtqeNDY20v7llGvWrFnyAwPlvXz5cnh4+OTJk3fu3JmcnDxlyhR53L2srIwGyBljEyZMOHToEOc8Ly9v3LhxZHPevHmUPikpacKECTExMQcPHszLy4uNjU1PT1cMjgo5EhoaajKZOOcPHjwYOXIkmYqNja2trTWZTDTCOn369IKCAp2lc87Vxm3CceinTTsO+Qsdn5mZOWnSpDVr1ixYsCA0NPT69es23RCRGv7cv38/PT2daBgMhg0bNtAEradPn9KT1ahRo6L/PaZOnUovLjIyMsi4Q5+FDzYDhw8fTkhIkC9Zrdbx48erXwHZ81PdKE71ebloCldVVZGUZ4yFhIQcPny459MRGRkZGBgYHR0tv9dSZ+/TmMLCwnHjxqWmpp45c2bDhg3h4eHi5hXl0noGtRan/X9olhQtED927Jh4QuacFxYWUjcYPHiweAMmzCIAAiAAAiAAAj5EwIGOpy0sbL6e5pw3NTWVlZWZTCb1XBqBoLGx0Wg09mbneGHKvQGz2VxWVibPeNFjn3JpTO3gnLe0tJSVlSnmhOgxLtLQ/IHu7u6ampry8nJ5nFikoQlLlZWVYsSac97e3l5RUSH2xqE2evz4seIZQDZiL1xXV6cwrk6px097djT4Cx3f0NDQ3t5eWVlZXV2tpwp6/FHXQn+Mhs/aRjo7O9WyWHvFp02D9mDaTOwwsru7u6qqqra2Vmb78ePH2tpasRLDoZE+SvDx48eqqqqCgoJHjx7JPVwu7tmzZ7Ln8iXtcEdHx8uXL22uyNfOiKsgAAIgAAIg4FUEHOv4rq6u2bNnFxYWuuC31WqNj49XrD50wQ6yfFYEZB3/WVUcle03AmfPnv3ll1/6rTgUBAIgAAIgAAJ9QcCxjuecNzc3R0VFaQ9C23Tu119/XbVqlWtjZjYNIvJzIAAd/zm0sgfrWFxcjL9LHuSPokEABEAABNxFQJeOpx3u4uPjaR62zrIPHjx45MgRnYmRDAQEgXfv3tEs/5qaGhGJAAi4hYDFYsnLy8PggltgwggIgAAIgIBnCejV8Zzzrq6uK1eu6HT33bt35eXlOhMjGQjIBM6fP086/tixY3I8wiAAAiAAAiAAAiAAAoKAEzpe5EEABPqOwOHDh9dLR2ZmpmIr/b4rGpZBAARAAARAAARAwIcIQMf7UGPBVRAAARAAARAAARAAARD4/wSg49EVQAAEQAAEQAAEQAAEQMD3CEDH+16bwWMQAAEQAAEQAAEQAAEQgI5HHwABEAABEAABEAABEAAB3yMAHe97bQaPQQAEQAAEQAAEQAAEQAA6Hn0ABEAABEAABEAABEAABHyPAHS877UZPAYBEAABEAABEAABEAAB6Hj0ARAAARAAARAAARAAARDwPQLQ8b7XZvAYBEAABEAABEAABEAABKDj0QdAAARAAARAAARAAARAwPcIQMf7XpvBYxAAARAAARAAARAAARCAjkcfAAEQAAEQAAEQAAEQAAHfIwAd73ttBo9BAARAAARAAARAAARAADoefQAEQAAEQAAEQAAEQAAEfI8AdLzvtRk8BgEQAAEQAAEQAAEQAAHoePQBEAABEAABEAABEAABEPA9AtDxvtdm8BgEQAAEQAAEQAAEQAAEoOPRB0AABEAABEAABEAABEDA9whAx/tem8FjEAABEAABEAABEAABEICORx8AARAAARAAARAAARAAAd8jAB3ve20Gj0EABEAABEAABEAABEAAOh59AARAAARAAARAAARAAAR8jwB0vO+1GTwGARAAARAAARAAARAAAeh49AEQAAEQAAEQAAEQAAEQ8D0C0PG+12bwGARAAARAAARAAARAAASg49EHQAAEQAAEQAAEQAAEQMD3CEDH+16bwWMQAAEQAAEQAAEQAAEQgI5HHwABEAABEAABEAABEAAB3yMAHe97bQaPQQAEQAAEQAAEQAAEQAA6Hn0ABEAABEAABEAABEAABHyPAHS877UZPAYBEAABEAABEAABEAAB6Hj0ARAAARAAARAAARAAARDwPQLQ8b7XZvAYBEAABEAABEAABEAABKDj0QdAAARAAARAAARAAARAwPcIQMf7XpvBYxAAARAAARAAARAAARCAjkcfAAEQAAEQAAEQAAEQAAHfIwAd77E2s1qtJh2HxWLpBxe7u7sd+vLs2bN+8ARFgAAIgAAIgAAIgAAI6CEAHa+HUp+k6erqYjqO9vb2Pin+v0YbGxsd+hIYGPjfTDgDARAAARAAARAAARDwGAHoeI+hJx1vMBiiNY/Ozs5+cPHdu3caXsyaNYsxBh3fDw2BIkAABEAABEAABEBAJwHoeJ2g3J+MdHzfiePff//9ypUrbvHbYrFAx7uFJIyAAAiAAAiAAAiAgLsIQMe7i6TTdvpUx9++fdvPz2/jxo1Ou2UrA3S8LSqIAwEQAAEQAAEQAAFPEoCO9xj9vtPxLS0to0ePZoxBx3usdVEwCIAACIAACIAACPQxAej4PgZs33zf6fjly5fHxcVBx9tnjysgAAIgAAIgAAIg4PMEoOM91oR9pONPnjy5cePGvLw86HiPNS0KBgEQAAEQAAEQAIG+JwAd3/eM7ZTQFzr+1atXkZGRbW1t0PF2qCMaBEAABEAABEAABAYIAeh4jzWk23V8T0/P7Nmzy8vLOefQ8R5rVxQMAiAAAiAAAiAAAv1CADq+XzDbKsTtOn7Pnj379u2joqDjbSFHHAiAAAiAAAiAAAgMHALQ8R5rS/fq+LKystmzZ/f09FB9oOM91q4oGARAAARAAARAAAT6hQB0fL9gtlWIG3V8W1vb1KlTa2trRTnQ8QIFAiAAAiAAAiAAAiAwIAlAx3usWd2o49euXXvy5Em5JtDxMg2EQQAEQAAEQAAEQGDgEYCO91ibukvHX7lyJT4+XlEN6HgFEJyCAAiAAAiAAAiAwAAjAB3vsQZ1l45ftmwZc3SUlpb2pp4Wi4UxFhgY2BsjyAsCIAACIAACIAACIOBGAtDxboTpnCl36ficnJyVqmPGjBmMsfDwcLpSXV3tnHP/TQ0d/18eOAMBEAABEAABEAABzxOAjvdYG7hLx9uswB9//IHvudokg0gQAAEQAAEQAAEQGBgEoOM91o7Q8R5Dj4JBAARAAARAAARAwPcJQMd7rA2h4z2GHgWDAAiAAAiAAAiAgO8TgI73WBtCx3sMPQoGARAAARAAARAAAd8nAB3vsTbsUx3v3lphnat7ecIaCIAACIAACIAACPSeAHR87xm6aAE63kVwyAYCIAACIAACIAACIMA5dLzHegF0vMfQo2AQAAEQAAEQAAEQ8H0C0PEea0PoeI+hR8EgAAIgAAIgAAIg4PsEoOM91obQ8R5Dj4JBAARAAARAAARAwPcJQMd7rA2h4z2GHgWDAAiAAAiAAAiAgO8TgI73WBtCx3sMPQoGARAAARAAARAAAd8nAB3vsTaEjvcYehQMAiAAAiAAAiAAAr5PADreY20IHe8x9CgYBEAABEAABEAABHyfwGek481m8507d0pLS9vb272h4aDjvaEV4AMIgAAIgAAIgAAI+CiBz0XHX7p06euvv7558+bly5enTJlSWlrq8QaDjvd4E8ABEAABEAABEAABEPBdAp+Fjn/27NmQIUOEdj916tSoUaOam5s922zQ8Z7lj9JBAARAAARAAARAwKcJfBY6PjY2duLEiaKdOjs7g4KCNm7cKGI8EoCO9wh2FAoCIAACIAACIAACA4PAwNfxLS0tBoNhw4YNcoPNnz8/JCTEYrHIkf0cho7vZ+AoDgRAAARAAARAAAQGEoGBr+OvXLnCGDtw4IDcbBs3bmSMmUwmObKfw9Dx/QwcxYEACIAACIAACIDAQCLQhzr+9u3bKSkpf//9tzav7u7ukpKStLS0trY27ZSuXT18+DBj7OTJk3L23bt3M8Zu3LghR/ZzuC90fFVVVV5e3s8///znn3+6kafFYmGMBQYG9jMie8V1dHQUFhampqZ69o2KPfecjdd5pzhrtk/T95vP7i2otrZWvusLCgr+97//yaA6OjpanDw6OjpkCxrh1tbWY8eO7dix49y5c9pdt6SkRMOO4pLZbK6srFREqk8d1l2dpU9jXr9+ferUqb179546daqxsdGpsnTm1ZmMijabzVeuXHHKDSQGARAAAY8T6EMdP27cOMbY1q1bNSp5+vTpsLAw9uloaWnRSOnypT179jDGTp8+LVvYu3cvY+zcuXNyZD+H3avj379//9133xFJ+jc0NLS4uNgtlfIqHb9nz54vvviC6qgthtxS934woudO6Qc3nCqi33x2b0F5eXnh4eGipoGBgZcuXRKnnPOSkhL5JtITvnXrlmzBXri+vn7ChAnFxcVlZWWMsX379tlM2dnZuXXr1jt37ti8ajPSarUeOHAgLy/P5lUR6bDuImU/BLKzs4cPH37kyBGTyZSbmzt8+PCDBw/qLFdnXp3JOOcfPnzYu3fvsGHD5syZo9MHJAMBEAABLyHQhzo+Nzd3+vTpDx8+1K5qeXk5/Vj2kY7Pzc1ljOXn58tu7Nq1izFWVFQkR/Zz2I06vru7OzY2dsaMGfv27fv111+XL1/u7+/PGBs6dOiLFy96Xy+v0vGc8+Li4oGk43XeKb1vRzda6Def3VuQHi0bHR3NGPvyyy/Ly8srNI/U1NSoqCg9VFtbWydNmrR7927OeUVFhdFo3L9/vzpjU1PTzJkzKyoq1JccxuTk5Gzfvl0jmZ66a2R346WjR48q3pEeP36cMXb8+HGHpejMqzPZx48f8/LyUlJSaGgAOt4hfyQAARDwNgJ9qOPtVTUjI0O+1NjY2Kc6/urVq4yxX3/9VS40JSVlIM2Pz83NXbNmTU9Pj6jjnTt3hgwZwhhbuXKliHQ54G06/vnz527R8Yqu6DIfZBQEvBypHi178+ZN6l337t0T9VIHPn78GBoaWlhYqL6kjtm7d6/RaPzw4QNd6urqUqfp6emJjY3Vo2XVeSlm8eLFGqPyeupuz7Ib49+8eRMQEBAaGiq/TOvp6QkJCQkMDNTeDlhnXp3JOOfd3d0fP37knGdmZjLGoOPd2NAwBQIg0D8E+lvHFxUV+fn5yXXrax1vNpv9/f1TUlLkQr/55ptRo0ZZrVY5sp/DbhyPj4uLU7/NSEtLY4yFhYX1vl7epuOrq6t7r+PVXbH3oD5zC96PVKeWnTFjBmPsm2++0WjQ/Pz8yMhIPX9D2tragoODFy1apGGNc75t27bo6GjtNNpXnz9/PmjQIPGhDEVinXVX5HL76aFDhxhjqampCsvJycmMsaNHjyri5VOdeXUmky1nZ2dDx8tAEAYBEPAVAv2q400mU2BgIGP/KbSvdTznPC4ubvLkyaJJaP949Q+JSNA/AXfp+La2NsUqXvL/xo0bjLHhw4f3vjoDT8f/X3tn/xXFkb79mwFGgTAEVFREXI2MKyuCaIiLHNbwliCKEbOos1GzaLIuORAlAWOiWRMB3100flc3IAoqMawgQlBBGBHkxaH+qOcc7yd1Ot09QzUBBpKrf9Dq6rvePlU9XF1ddbfpUPz1oH7POcwKpIpa9uLFi/ygWF9fb9qnL1++jImJOXv2rOlVXeQ333xDREeOHNHFa0+bmpqISLdYX2ugGN6wYcP69etNjRXbbpp2EiPXrVtHRBUVFbo82SFBamqqLl57qphW0UybM3S8lgbCIAACs4jALyS1rt4NDQ3Z2dlZr449e/b09PT09vbu3r2bY7Kysg4cOMAviN1ud1FRUVZWVkFBgZygamxs3LNnz969eznba9euhYeH819HzoFfAWt1fEtLS3Z29sKFC+Pi4g4ePKirj+60uLh4zpw59p8Ph8PB7/QzMzNDQ0PtdvuCBQvY7cP9+/dDQ0PlW/ITJ05ER0f39vbqMpzm08nS8d6q/d133xHRunXrvBmox09Axw8NDX3yySebN2/Oz89PTEzMy8t7/PixtsTOzs7y8vK1a9e2tLT09fUVFRUtWbIkLi7OVO48efJkx44dCQkJ6enpBQUFV69eVZmPb29v37p1686dOwsLC/Py8lwuV39/vxDC21Dk6nV0dHzwwQeZmZmJiYmpqan79u3Tvevv7e394osvkpKSurq6mpubc3JyYmJiVq9effDgQX5Hz/komgkhdHcKJ7fEp6enx+VyZWZmOp3OlJSU8vLypqam3t7evr4+7WorLX8OP3v27O9//3tOTk7yq+Pw4cNaN0cDAwMnT5588803Hzx40NzcnJKSsnz58mvXrhnr7BupEKKlpeXdd9+Ne3VkZWXdu3dPVsZHKcaCONW4o0tmrgsoatmxsbH4+Hgi2rhxoy4HPj158uTy5cu1K0OMZiMjI49eHWlpaUR0+vTpR48e6e4CmSo/Pz8oKOj58+cyhhd7KP7EyVSVlZVEdPPmTRkjA4ptl/ZWA8PDw9XV1ToPv7pM3G63zWYjIuMWfH52CgwM1EGQOSimVTST2XIAOl4HBKcgAAKzhYAvHS+EKCkpYcH04MEDbtLAwMCSJUuIaNOmTdpGPnz4kIhYK9+8eXPz5s38e71lyxY26+7uvnDhAufW+uro7u4WQkgdX1tbGx8fX1RUVFhYGBQURESlpaXaIozhQ4cOcYZEpJ3IWbt2bWpqqlaRXLp0KSEhoaam5sSJE06nU8VNm7G4yY2Zah3PO73UvUD4aJ1VHT84OBgfH5+QkMC6tr+/f9GiRTExMW63m0u5cuUKixsiqq6uTkxMLCwsLCgo4O25X3/9tbYyjY2N0dHRpaWl/Ih469atqKiocXX8o0ePXnvttQsXLnBWly5dCggIYPd23oaiEOLixYsOh+Po0aMHlQUUAAAZ3klEQVScqqGhITIy0uFwnDt3jmOOHTsmPSwdPnzY4XCkp6f/6U9/4vokJydzkxXNTO8U3sirzqejoyMiIoL3TY6Ojr799ttcmddeey08PNzHRxKuXr0aGxt76tQpbprL5eIHv9HRUSHE0aNHY2JiOKuLFy86nU5+mbZixQr1u5tz/vzzzzdu3NjS0tLf33/27NmQkBCbzcbP2N5KKSgo8AZn3NHFhZr+q65l+bsTRGTcderxeJYtWya5mRYkhKivr09LS9uwYQMR2Wy2tFdHfn6+0b63t9dutzudTuMl9Z84TltXV0dEmZmZxqzU225M6zumqanp/fffDw8PX7hwoc6jgC4hv3YgopaWFt2l5uZmHmw//PCD7hKfKqZVNNMVAR2vA4JTEACB2UJgHB3f398/d+5cKdC5VexbICUlRdvIhoaG1atXa2PeeecdIpI6Xgghf6m1ZlLHb9myZWhoiC+xk5nFixdrLY1hj8eTkJDAv/5ExM7azp8//4c//ME4qfPixYvGxsa7d+9qJ02NecqYGzduVFo8Tp8+LZOPG5hqHb927dqoqKjBwcFxazKugVUdX1FRoRMT27dvJ6JvvvlGljU6OsqqfcOGDXLCu6ysjIjWrFkjzdxut8Ph0O3W5eFBRD4mRD/88EObzcaSlHPLycmRj6OmQ/HBgwfBwcHaESuEuHnzZkBAwNy5c+WXEO7fv89DLjc3V47Yr7/+miPlRkNFMyGE8U7hHXgqfIQQKSkpRCSfWnt6ekJCQojo+vXrEqMxwM85n332mbzU1tYWEBBARHIxSVtbGzcqIyPjxYsXPT09JSUlLLOMdTZFKoS4fft2RESEdv/G3r17iWjRokV8J/ooxRSOyuiSjdIF1LWsx+NZvnw5EaWnp+syqampiY2N9TH2tPbsZXLVqlXaSF24qqqKiHJzc3XxQghLP3FCiL6+Pv7Ug7F66m03VsM05unTp+Xl5W+88Ybdbs/Nzb169aqxUF3C2tpaHlGdnZ26Sw8ePOBLV69e1V3iU8W0ima6IqDjdUBwCgIgMFsIjKPjhRDbtm0jovfff182qa+vLygoKCAgQCobIURRUdFXX30lbYQQ+/bts6Tjnz59KpPLjYxGOS5tOHDv3j2evOc9nU1NTQsXLrx//77ObAKnrDb4T4viv4pO6LgyU6rjb926FRAQcPHixQk03JjEqo6vra0NDQ3VrpBhmOx3T+YfERFBRNpP3ty6dYuIwsLCpM2uXbuIqK6uTsYIIe7evcs94kM38JODdsHx5cuX29raOB9T0bl582YiMroDZ6G8efNmTjswMMCly9w4PiMjg4iWLFliycz0TuEcVPgMDw8HvjrkejYhBH9JoKysjPMx/TcjIyMiIkIHsKSkJCsrSz4SDA0NcUuNjwSKd7cQIiEhITs726M55LIonur2UYopHMXRZdpqS1r21KlT3Pzbt2/L3MbGxlauXKl7ZSSvGgP8zFlUVGS8JGP++c9/EtHu3btljDZg9SfO4XAQ0Y8//qjNRAhhqe26tNpTj8dTW1ubmZkZFBSUkJBw9OhR+Z5Na2Ya5icWIjJ++Kmjo4Npe/sYk2JaRTNd9aDjdUBwCgIgMFsIjK/jeT7J4XBIX2ltbW28ZkZ+ymRwcDA6Olr++efGs4927eymqXiS8/HaGbvu7m7+TZcztT6Afvzxx2xMRIGBgYqe4HxkyJdevnw5bPFQnOnn/Fm+zJ07d9yaWDXweDx//OMf9+/fbzWhN3vW8ZaqqhWIzc3NSUlJRORyubRFsM9mrY6Xz2+cfGxsjNdy6DYz6My0ecowby602Wx79+7VjUzTV0Mej8dutxORnLOXWfELKIfDwTGDg4M83nRziufOnSOigIAAnqRXNBNCGO8ULmhcPkIIOeuvfQzmz5yVlJTIJugCvb29NptNuxRNZ8Cn/KhJRK2trToDY51N7+6uri4iWrBggdPs4KcsH6V4g6MyunQV5lNLWtbj8SxdupSI/vKXv8jcLl68uGjRIu17HnnJNPDuu+8SUVVVlelVjmRXLcXFxd5sLP3E8Woo45ekLLXdtCatra379++fN29eZGSky+UyPiqYptJG8qYdItLdO0II+VqGN2BoU3FYMa2imS5/6HgdEJyCAAjMFgLj63ghxIoVK4hIrgctLCzMzMwkopiYGJ4FPH78uNH9i+JfelMd39PTo67jR0ZGuIac5Pz587OC/vPnz7nCk17b/fv35+fnaydof2URo6OjE6iqx+Oprq7Oz88/duzYe++9NwEdz1N0drtdV38VHT82NpaTk8PVnjdvnu7bvUbR2draysZGHS+/8fnkyRMhhDeBLkcyf3tL0cybVBVCqOj4oaEhftSprq6WlPgbxnJjt4yXgWvXrhGRfMMg43UBHwpb8e5mdD4UqhDCRyk+4Iw7unRt4VOrWpaXSwUEBMhtBgkJCZZcvPOTQEdHh2l9OJLf5Bw4cMCbjaWfuGXLlpm6vrHadlmZgYGBEydOrF27NjAwMCMj48KFC+qPMTITDsj7zrg+Xr5kM16ylHZiRUDH63oKpyAAArOFgJKO51fDvCC+p6cnMjLy2bNnTqdTrptfvXq19tUzN17xL71UP9r5eEs6Xghx48YNFmFENH/+fPm9lZncDSxfQkJCJreS3377bWZmpnbC8tfnz/PxlqpaV1cXHx+/b98+rgmvq7E6Hy8FtG5CXUXHc6u//PJL3uBBRHl5eXI5u/xjL+Hcu3ePh1BDQ4OM5IAsjtWYN4Eu43mZgTzVTT3KeLkawXincLkqOl4I8dlnnxHRihUrmNLo6KjT6UxLS/PhqYZ9g8THx+taqjv1obCNdTYiFULw1nbTbZeyLB+leNPxKqNL5q8NWNWy7F9Sfk/typUrCxYskG8mtTmbht1uNxHNmzfP9KqM3LJlCxH5/oSW+k9cXFwcEV2+fFnmzwGrbZfJu7q6iouLo6OjHQ6Hy+XS+hqSNoqBgYEBfutlrN758+eJaM6cOfIm1eWpmFbRTJc5dLwOCE5BAARmCwElHd/X18c/vu3t7QcPHmRXkuzgbOvWrU1NTaa7uBT/0k+Kjt+1a1dsbKyU8tu3b//1HdDd3d1i8Whvb1cvl+VLaGioepJxLS9fvpyRkWFpec+4efJmO948p2IshPjPf/5jt9u1r2gmpuOl6wmdCwsprFUeVzo6OrKzs3ls5OXlcROMonNkZIT3lRq/RNPY2EhEISEh/IpDCnGdQOeR/Prrr3MRimbepKrifDyXVV1dbbfbFy9eXFhYuGHDhn379vne38wA7XY7O+L01q0+FLbi3X3nzh0iioiIMJ3B5VVzPkoxhaM4ukwbNQEt++WXX/JyqZaWlqSkpPLyctOcTSN5jYfvxxi5B0C7B8mYm/pP3Lx580yXQk2g7dpqeDyeK1euZGdnBwcHJyQkHDt2zPfg0abVhtkRk/Eu4z3u2iVM2lQcVkyraKbNHzpeSwNhEACBWURAScdLrxF/+9vf5s+fzy6Q3W633W4PCQnJzs429TXm4y+9Vn79eh1fU1Ozdu1a9kYnpbx21fXE+mPW7XP9/vvv09LSjLNZLS0txrUilphY3eeamJiomxH84IMPJrCu5tmzZ6ytdUu9VXS87vsD/Ng5d+5c1uJSx2uHIvs+evvtt3VwampqtO5EvAl0fnvw17/+lZMrmplKVc5BcT5+bGxs7969tbW1AwMDjx49UllP9fLly+DgYCLS7TzmPcRSY/lQ2Ip3t9wTfOLECR1Vt9u9devWCayrURxduuL4dAJadmRkJDo6mt94REVFvXjxwjRn00j2Gnn48GHTqzLy7NmzOs+58hIH1H/ieJuHzWYzvjSYQNt11eDTvr6+zz//3Ol0zpkzZ8uWLf/9739VhpzMip+LCgoKZAwH+KWE7w3EimkVzbQVgI7X0kAYBEBgFhFQ1fG8oDYgIOC9996TzWPfcyEhIbplD2zA0u2dd96R9tIjAa8z5vjOzk4W3+xOniOluPf22RSZ5w8//BAVFcULHpqbm1n28dp931OSMgdvgdbW1u8sHsYlGd4yl/Jlsubjm5qadC7zeR69ubk5NTVVq1Z9VMnbJUs63uPxsAchuQ1aCJGenk5EUuNyQexYQ/vEJeW1XBOyadMmInI4HNodz3K9jXbM6Cqfm5t7584dbWT0q4NjTIfi9evXiSgoKIgXuMu0BQUFNptNeqeRAl33dLRz587AwEA5Sa9oJoQw3ilctAofIYTL5dq1a5esrWKA/VAFBQVJR5n8taY1a9ZIqSp1vA6IaZ1NkQoheC9NWFiY1p9gZ2fnunXreDGej1KMBamPLlMOE9Oy7OmSiHy7ADKWyI6Dxv1Z6OnpCQ4Ojo6ONuYghLD0E8feG998801jVhNruzEfGXPnzp2ioiKHwxEbG1tSUmJ0QSMttYH+/v6oV4f2teHQ0JDD4Zg/f772T0lHR8ehQ4e0y3gU0yqaaWvFX0pJTk7WRsrw9evXy8rKJvb+QWaCAAiAAAhMBQFVHT82NrZ06VKtmuHvYhKRVtlrq8i7DLUfCR8dHeXFyvv27Wtubv7www/7+/vZ1SARab/NVF9fz+L+7t272jx14YcPHy5cuHDnzp0ynh8tOK03P27S2L8Bli+TouN//PFHh8MRFBT088dt/////FSj1dMTa7IlHS+EYMfbkZGR33777alTp7KyslJTU4lo2bJlVVVV//73v4UQQ0ND7PVIuwOV18gSkVTt//vf/3gf56JFi86cOdPa2nry5En2fkNEGRkZWp/02tbl5uampqZKrTA8PBweHi59+JgORdbERLR+/Xq5DuTmzZtz5szRTidLgV5QUCDzv3z5st1u184mKpoJIYx3ijqfgYEBm80WHByclJSUk5OzY8cOl8t18ODBmpoayVCLRYbdbvf8+fP5TlmyZElOTs769evDw8O1olNKc6MPKGOdvSFta2tjf/Y85VxUVLRp06awsDD5Es9HKaZwVEaXbKYuMDEtOzw8PG/ePIfDoVWZupxNT6OiokJDQ+UgMbXhyB07dhCRdo8Qx1v9iWOvi/LzZ9oSJ9Z2bQ6m4eHh4ZqamrfeeisoKGjTpk1GPznGVBcuXLDZbNqXbB999FFgYCD/Mkh7/tFYunSpjOEdFyppFYuQOefl5fErFxkjA8+ePZszZ864GxikPQIgAAIgMJ0EVHW8EOLIkSPZ2dnayo2NjS1ZssS4w7Wurs7lcvGkrM1m2759+/fff88JeREkEUVHRzc3N1dVVfF+WSKSXpmPHz8u/c+sWrVK9+MuK1BeXh4WFsbrtlmqlpaWcgyrEyLSzjXKhDMkMFk6vqenh1fEylZrAzabraur61c22aqOr6+vj4yM5GqkpKS0tbU1NzfzeFi1atWTJ08aGhp4hp6IYmNjeeFBZWXl4sWLOdX69evlPD2/UpCN2rhxY319fWBg4KZNm6qqquTksa6Nubm5sbGxSUlJn376aWVlZUpKisvl0r6X0A1Fmfz06dMxMTErVqzYv39/QUHBG2+8IWvCNlKgFxcXL1++fMuWLW+99VZ0dLTOW7+Kmbc7xRKfTz75hLevSEQcCAsLM/p9l83kTymzpxS2X7NmjfZZurKycuXKlXwpOjra5XKx90lvdRZCeEN6//597ffa4uLipC8db6UIIbwVNO7o0rZRF56wlj1y5Ah/MVeXoY9TftOYkZHhw0Zeam9vt9ls2udAIcQEfuKys7MXL16sHeeyiAm3XebgO/DTTz/94x//8O0pX+Zw6dIl3s5x8uTJ7du3x8TEGH/nCwsLiejPf/6zTMUBlbRCCEUzdrbGX0Dj3fAVFRXaZ+Dnz5/zCjftg4euSjgFARAAAX8RsKDjh4aGjMsYLO3s5Ea2t7c3NjaqzFH5C8r0lDtZOn4aamtVx7Nzxlu3bmnd7XV3d9+5c8dUYag0obOz88aNG/xM8uLFC627dNPk0nlLa2vrzZs3TV0Y+RiKfX19DQ0NupUzXJAU6J2dnYODg42NjS0tLcZ2KZqZVt5S5L/+9a9PP/20ra3typUrNTU1J0+e/OKLL0pKStLS0kw3oOsyd7vdDQ0NcjmQ7qrVUx9IuSC5PMlqzlr7wcHBiY2uqday2kqeOXOGiORrB+0l03BBQYGlD8kZM+nq6rLb7brHTmk2nW2XhfoIjIyMNDU1nTt37vbt297+HNy7d894ZwkhVNKqm/moJF8aGBjw5g1z3LQwAAEQAIEpJWBBx09pPX6Hmf+2dfxvuEO1At1HMxXNfOSgcqmsrMzpdHrbaLhu3TqVTH4/NtOpZffs2RMeHq6+S2d4eDgxMfH06dMT646xsbH09PTS0lJvyaez7d7qgHgQAAEQAIHJJQAdP7k8LeQGHW8B1kwyVRToima/pmWPHz+22Wz5+fmmmXR1dRm9gpha/n4ip1rLtrW1yd2QMTExvl3CG7E/ffo0ISHB9C2Q0VgXU1JSUlBQ4O2JTggx1W3X1QenIAACIAAC00AAOn4aIJsXAR1vzmXGxz59+pRXjfN6cW/1VTTzllwl/uHDh+xgp7y8XLtwyO12f/XVV9nZ2dplvioZ/uZtplTLDgwMBAcHp6enCyHOnTvndDrVJ+Ml+Z6enm3btjU1NckYlUBZWdm4C3imtO0qlYQNCIAACIDApBOAjp90pKoZQserkpphdqdOnWIdX1FR4aNqimY+clC5VFpaym5/bDZbVFRUXFycw+GIiIgoLi6WLndU8vmd2NTW1mrfUWRlZdXV1U1W28fGxlauXMlb85OTk3/66aeJ5ezxeM6dO6eetru72+hswJh8SttuLA4xIAACIAAC00AAOn4aIJsXAR1vzmVmxx45cmSb5iguLtZ5qefqK5pNSlsfP35cUVGxe/fubdu2ffzxxxcuXPC2a3BSikMmPggMDQ3936sDXeCDEi6BAAiAAAhMFgHo+MkiaTkf6HjLyJAABEAABEAABEAABEDgZwLQ8T+TmPb/oeOnHTkKBAEQAAEQAAEQAIHfDgHoeL/1JXS839CjYBAAARAAARAAARCY/QSg4/3Wh9DxfkOPgkEABEAABEAABEBg9hOAjvdbH0LH+w09CgYBEAABEAABEACB2U8AOt5vfQgd7zf0KBgEQAAEQAAEQAAEZj8B6Hi/9SF0vN/Qo2AQAAEQAAEQAAEQmP0EoOP91ofQ8X5Dj4JBAARAAARAAARAYPYTgI73Wx/6S8e73e4zZ85YarbH4yGi0NBQS6lgDAIgAAIgAAIgAAIgMHUEoOOnju04OU+/jn/27NlHH30UFhaWnJw8TuV+eRk6/pc8cAYCIAACIAACIAAC/icAHe+3PphOHT8yMlJZWbljx47XX3+diKDj/dbrKBgEQAAEQAAEQAAEJokAdPwkgbSezXTq+NHR0ZGRESFEcXExdLz1vkIKEAABEAABEAABEJhxBKDj/dYl06njZSNLS0uh4yUNBEAABEAABEAABEBg9hKAjvdb30HH+w09CgYBEAABEAABEACB2U8AOt5vfQgd7zf0KBgEQAAEQAAEQAAEZj8B6Hi/9SF0vN/Qo2AQAAEQAAEQAAEQmP0EoOP91ofQ8X5Dj4JBAARAAARAAARAYPYTgI73Wx9Cx/sNPQoGARAAARAAARAAgdlPADreb31oScd3dXW1Wzk8Ho9pw+CvxhQLIkEABEAABEAABEBg1hGAjvdbl1nS8U6nk6wcfX19pg2DjjfFgkgQAAEQAAEQAAEQmHUEoOP91mWWdHxHR0erlQPz8X7rVxQMAiAAAiAAAiAAAtNCADp+WjCbFWJJx5tlMJE4zMdPhBrSgAAIgAAIgAAIgMDMIwAd77c+gY73G3oUDAIgAAIgAAIgAAKznwB0vN/60C86vqSkhIiSk5MtNdvj8RBRaGiopVQwBgEQAAEQAAEQAAEQmDoC0PFTx3acnP2i4/Py8ohoxYoV41Tul5eh43/JA2cgAAIgAAIgAAIg4H8C0PF+64Np1vHHjx8vLCwMCAhgtzd5eXkVFRU9PT0q7YeOV6EEGxAAARAAARAAARCYTgLQ8dNJ+xdlTbOO/0XZFk+g4y0CgzkIgAAIgAAIgAAITDkB6PgpR+ytAOh4b2QQDwIgAAIgAAIgAAIgMC4B6PhxEU2VAXT8VJFFviAAAiAAAiAAAiDwOyAAHe+3ToaO9xt6FAwCIAACIAACIAACs58AdLzf+hA63m/oUTAIgAAIgAAIgAAIzH4C0PF+60PW8cHBwYd9HqOjo9NQxYGBAR+1KCsrg//4aegFFAECIAACIAACIAAC6gSg49VZTbIl63j2Aunj38HBwUku2Cy7R48e+agDX8J3oMzIIQ4EQAAEQAAEQAAE/EMAOt4/3IUQL1++PKBwjIyMTEMVnz9/Pm5dDh06NA01QREgAAIgAAIgAAIgAAIqBKDjVSjBBgRAAARAAARAAARAAARmFgHo+JnVH6gNCIAACIAACIAACIAACKgQgI5XoQQbEAABEAABEAABEAABEJhZBKDjZ1Z/oDYgAAIgAAIgAAIgAAIgoEIAOl6FEmxAAARAAARAAARAAARAYGYRgI6fWf2B2oAACIAACIAACIAACICACgHoeBVKsAEBEAABEAABEAABEACBmUUAOn5m9QdqAwIgAAIgAAIgAAIgAAIqBKDjVSjBBgRAAARAAARAAARAAARmFgHo+JnVH6gNCIAACIAACIAACIAACKgQgI5XoQQbEAABEAABEAABEAABEJhZBKDjZ1Z/oDYgAAIgAAIgAAIgAAIgoEIAOl6FEmxAAARAAARAAARAAARAYGYRgI6fWf2B2oAACIAACIAACIAACICACgHoeBVKsAEBEAABEAABEAABEACBmUXg/wFeqqalhjJMHAAAAABJRU5ErkJggg==)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hf1q49XJVQ_w"
      },
      "source": [
        "#Solucion a-) Gradiente descendente\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8w9L80ojEB7R",
        "outputId": "892b1ce9-1494-4f6c-a4f8-fb9e5cdc710b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "x1=sp.Symbol('x_1')\n",
        "x2=sp.Symbol('x_2')\n",
        "x3=sp.Symbol('x_3')\n",
        "fx=(x1-4)**2 + (x2-3)**2 + (x3+4)**2\n",
        "grad=gradient(fx,x1,x2,x3)\n",
        "fx_val=sp.lambdify([x1,x2,x3],fx)\n",
        "grad_val=sp.lambdify([x1,x2,x3],grad)# Turn into a function with that name\n",
        "value=grad_val(1,2,3)\n",
        "grad\n",
        "#def f_values(fx_points)\n",
        "type(value)\n",
        "##change the descent method into more variables\n",
        "x0 = np.array([4,2,-1])\n",
        "epsi = 0.001;\n",
        "max_iter = 1000\n",
        "g=grad_val(4,2,-1)\n",
        "\n",
        "res1 = descent_grad_optim_step(x0, fx_val, grad_val, epsi, max_iter)\n",
        "xmin = res1[0]\n",
        "iter = res1[1]\n",
        "\n",
        "\n",
        "print(f'El minimo global se encuentra en x1={xmin[iter,0]},',\n",
        "      f'x2={xmin[iter,1]} y ',f'x3={xmin[iter,2]}.Luego de {iter} iteraciones')"
      ],
      "execution_count": 272,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "El minimo global se encuentra en x1=4.0, x2=3.0 y  x3=-4.0.Luego de 2 iteraciones\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kE37vXv1qSpi"
      },
      "source": [
        "# Solucion b-)gradiente descente con paso fijo\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ql_n4znuqUEY",
        "outputId": "498f7c4c-bc64-490a-b488-0cf1ca154fe6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "x1=sp.Symbol('x_1')\n",
        "x2=sp.Symbol('x_2')\n",
        "x3=sp.Symbol('x_3')\n",
        "fx=(x1-4)**2 + (x2-3)**2 + (x3+4)**2\n",
        "grad=gradient(fx,x1,x2,x3)\n",
        "fx_val=sp.lambdify([x1,x2,x3],fx)\n",
        "grad_val=sp.lambdify([x1,x2,x3],grad)# Turn into a function with that name\n",
        "value=grad_val(1,2,3)\n",
        "grad\n",
        "#def f_values(fx_points)\n",
        "type(value)\n",
        "##change the descent method into more variables\n",
        "x0 = np.array([4,3,-1])\n",
        "print(grad_val(*x0))\n",
        "print(x0-grad_val(*x0))#This could be subs point to point\n",
        "print(x0-grad_val(*x0).T)#This could be rest point to point\n",
        "\n",
        "epsi = 0.001;\n",
        "max_iter = 1000\n",
        "g=grad_val(4,2,-1)\n",
        "step=0.1\n",
        "res1 = descent_grad_fixed_step(x0, grad_val,step, max_iter,epsi)\n",
        "xmin = res1[0]\n",
        "iter = res1[1]\n",
        "\n",
        "\n",
        "print(f'El minimo global se encuentra en x1={xmin[iter,0]},',\n",
        "      f'x2={xmin[iter,1]} y ',f'x3={xmin[iter,2]}.Luego de {iter} iteraciones')\n"
      ],
      "execution_count": 273,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0]\n",
            " [0]\n",
            " [6]]\n",
            "[[ 4  3 -1]\n",
            " [ 4  3 -1]\n",
            " [-2 -3 -7]]\n",
            "[[ 4  3 -7]]\n",
            "El minimo global se encuentra en x1=4.0, x2=3.0 y  x3=-3.9995015395015807.Luego de 39 iteraciones\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0JSC3uDfB0kV"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Nh0Zk9eXB4sq",
        "outputId": "c943af83-11cf-4630-c79a-cb5d6da503ee",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "x1=sp.Symbol('x_1')\n",
        "x2=sp.Symbol('x_2')\n",
        "fx=(1-x1)**2 + 100*(x2-x1**2)**2 \n",
        "grad=gradient(fx,x1,x2)\n",
        "fx_val=sp.lambdify([x1,x2],fx)\n",
        "grad_val=sp.lambdify([x1,x2],grad)\n",
        "##change the descent method into more variables\n",
        "x0 = np.array([-1,1])\n",
        "epsi = 0.001;\n",
        "max_iter = 10000\n",
        "res1 = descent_grad_optim_step(x0, fx_val, grad_val, epsi, max_iter)\n",
        "xmin = res1[0]\n",
        "iter = res1[1]\n",
        "\n",
        "\n",
        "print(f'El minimo global se encuentra en x1={xmin[iter,0]},',\n",
        "      f'x2={xmin[iter,1]}.Luego de {iter} iteraciones')"
      ],
      "execution_count": 274,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "El minimo global se encuentra en x1=0.9999988283439782, x2=0.9999976539057863.Luego de 3 iteraciones\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}