Starcraft 0 - Multi-estágio.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import cvxpy as cvx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Um problema em T estados\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 231,
   "metadata": {},
   "outputs": [],
   "source": [
    "Buildings  = cvx.Variable(T)\n",
    "Gatherers  = cvx.Variable(T)\n",
    "Builders   = cvx.Variable(T)\n",
    "Army       = cvx.Variable(T)\n",
    "Resources  = cvx.Variable(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "metadata": {},
   "outputs": [],
   "source": [
    "custo_building      = 2 # buildings costs                         recurso/casinha\n",
    "custo_units         = 1 # units costs                             recurso/pessoinha\n",
    "supply_building     = 3 # supply per structure                    caminha/casinha\n",
    "army_building       = 2 # army trained per house                   pessoinhas/casinha\n",
    "building_builder    = 1 # buildings constructed per builder       casinhas/pessoinha1\n",
    "production_gatherer = 2 # resources gathered per gatherer          recursos/pessoinha2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [],
   "source": [
    "custo_building      = 2 # buildings costs                         recurso/casinha\n",
    "custo_units         = 3 # units costs                             recurso/pessoinha\n",
    "supply_building     = 2 # supply per structure                    caminha/casinha\n",
    "army_building       = 1 # army trained per house                   pessoinhas/casinha\n",
    "building_builder    = 1 # buildings constructed per builder       casinhas/pessoinha1\n",
    "production_gatherer = 1 # resources gathered per gatherer          recursos/pessoinha2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_Obj = cvx.Maximize(Army[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [],
   "source": [
    "B = cvx.Variable(T-1)\n",
    "G = cvx.Variable(T-1)\n",
    "Br = cvx.Variable(T-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [],
   "source": [
    "b0 = cvx.Parameter()\n",
    "g0 = cvx.Parameter()\n",
    "br0 = cvx.Parameter()\n",
    "r0 = cvx.Parameter()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [],
   "source": [
    "b0.value  = 1       # starting buildings\n",
    "g0.value  = 1       # starting gatherers\n",
    "br0.value = 0       # starting builders\n",
    "r0.value  = 1       # starting resources"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [],
   "source": [
    "Constraints = [Buildings[0] == b0,\n",
    "              Gatherers[0] == g0,\n",
    "              Builders[0]  == br0,\n",
    "              Army[0]      == g0 + br0,\n",
    "              Resources[0] == r0,\n",
    "              B >= 0,\n",
    "              G >= 0,\n",
    "              Br>= 0]\n",
    "\n",
    "for i in range(T-1):\n",
    "    \n",
    "    Constraints.append(B[i]  == Buildings[i+1] - Buildings[i])\n",
    "    Constraints.append(Br[i] == Builders[i+1]  - Builders[i])\n",
    "    Constraints.append(G[i]  == Gatherers[i+1] - Gatherers[i])\n",
    "    \n",
    "    Constraints.append(B[i] <= building_builder*Builders[i])\n",
    "    Constraints.append(Br[i] + G[i] <= army_building*Buildings[i])\n",
    "    \n",
    "    Constraints.append(Army[i+1]           == Builders[i+1] + Gatherers[i+1])\n",
    "    Constraints.append(Army[i+1]           <= Buildings[i+1]*supply_building)\n",
    "    \n",
    "    Constraints.append(Resources[i+1] == Resources[i]\n",
    "                       + production_gatherer*Gatherers[i]\n",
    "                       - custo_building*B[i] - custo_units*(G[i] + Br[i]))    \n",
    "#    Constraints.append(Resources[i+1] >= 0)\n",
    "    Constraints.append(Resources[i]   >= custo_building*B[i] + custo_units*(G[i] + Br[i]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [],
   "source": [
    "problem = cvx.Problem(F_Obj, Constraints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 102 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "5.956440843933209"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time problem.solve(solver = 'ECOS') #SCS #ECOS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Buildings.value,'--*', label='buildings')\n",
    "\n",
    "plt.plot(Gatherers.value,'o--', label='gatherers')\n",
    "plt.plot(Builders.value, label='builders')\n",
    "#plt.plot(Army.value, label='')\n",
    "plt.plot(Resources.value, label='resources')\n",
    "#plt.plot(Max_supply.value, label='')\n",
    "#plt.plot(B.value, label='')\n",
    "#plt.plot(G.value, label='')\n",
    "\n",
    "plt.yscale('symlog')\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.title(str(T) + ' Estágios')\n",
    "plt.savefig(\"figure.png\", bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gráficos bonitos\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "metadata": {},
   "outputs": [],
   "source": [
    "custo_building      = 2 # buildings costs                         recurso/casinha\n",
    "custo_units         = 3 # units costs                             recurso/pessoinha\n",
    "supply_building     = 1 # supply per structure                    caminha/casinha\n",
    "army_building       = 1 # army trained per house                   pessoinhas/casinha\n",
    "building_builder    = 0.5 # buildings constructed per builder       casinhas/pessoinha1\n",
    "production_gatherer = 0.5 # resources gathered per gatherer          recursos/pessoinha2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Integer Problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {},
   "outputs": [],
   "source": [
    "Buildings  = cvx.Variable(T,integer=True)\n",
    "Gatherers  = cvx.Variable(T,integer=True)\n",
    "Builders   = cvx.Variable(T,integer=True)\n",
    "Army       = cvx.Variable(T,integer=True)\n",
    "Resources  = cvx.Variable(T,integer=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {},
   "outputs": [],
   "source": [
    "B = cvx.Variable(T-1,integer=True)\n",
    "G = cvx.Variable(T-1,integer=True)\n",
    "Br = cvx.Variable(T-1,integer=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [],
   "source": [
    "custo_building      = 2 # buildings costs                         recurso/casinha\n",
    "custo_units         = 1 # units costs                             recurso/pessoinha\n",
    "supply_building     = 3 # supply per structure                    caminha/casinha\n",
    "army_building       = 2 # army trained per house                   pessoinhas/casinha\n",
    "building_builder    = 1 # buildings constructed per builder       casinhas/pessoinha1\n",
    "production_gatherer = 2 # resources gathered per gatherer          recursos/pessoinha2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 278,
   "metadata": {},
   "outputs": [],
   "source": [
    "Constraints = [Buildings[0] == b0,\n",
    "              Gatherers[0] == g0,\n",
    "              Builders[0]  == br0,\n",
    "              Army[0]      == g0 + br0,\n",
    "              Resources[0] == r0,\n",
    "              B >= 0,\n",
    "              G >= 0,\n",
    "              Br>= 0]\n",
    "\n",
    "for i in range(T-1):\n",
    "    \n",
    "    Constraints.append(B[i]  == Buildings[i+1] - Buildings[i])\n",
    "    Constraints.append(Br[i] == Builders[i+1]  - Builders[i])\n",
    "    Constraints.append(G[i]  == Gatherers[i+1] - Gatherers[i])\n",
    "    \n",
    "    Constraints.append(B[i] <= building_builder*Builders[i])\n",
    "    Constraints.append(Br[i] + G[i] <= army_building*Buildings[i])\n",
    "    \n",
    "    Constraints.append(Army[i+1]           == Builders[i+1] + Gatherers[i+1])\n",
    "    Constraints.append(Army[i+1]           <= Buildings[i+1]*supply_building)\n",
    "    \n",
    "    Constraints.append(Resources[i+1] == Resources[i]\n",
    "                       + production_gatherer*Gatherers[i]\n",
    "                       - custo_building*B[i] - custo_units*(G[i] + Br[i]))    \n",
    "#    Constraints.append(Resources[i+1] >= 0)\n",
    "    Constraints.append(Resources[i]   >= custo_building*B[i] + custo_units*(G[i] + Br[i]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 279,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_Obj = cvx.Maximize(Army[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "metadata": {},
   "outputs": [],
   "source": [
    "int_problem = cvx.Problem(F_Obj,Constraints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 201 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "82.0"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time int_problem.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Buildings.value,'--*', label='buildings')\n",
    "\n",
    "plt.plot(Gatherers.value,'o--', label='gatherers')\n",
    "plt.plot(Builders.value, label='builders')\n",
    "#plt.plot(Army.value, label='')\n",
    "plt.plot(Resources.value, label='resources')\n",
    "#plt.plot(Max_supply.value, label='')\n",
    "#plt.plot(B.value, label='')\n",
    "#plt.plot(G.value, label='')\n",
    "\n",
    "plt.yscale('symlog')\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.title(str(T) + ' Estágios')\n",
    "plt.savefig(\"figure.png\", bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [],
   "source": [
    "custo_building      = 2 # buildings costs                         recurso/casinha\n",
    "custo_units         = 3 # units costs                             recurso/pessoinha\n",
    "supply_building     = 3 # supply per structure                    caminha/casinha\n",
    "army_building       = 1 # army trained per house                   pessoinhas/casinha\n",
    "building_builder    = 1 # buildings constructed per builder       casinhas/pessoinha1\n",
    "production_gatherer = 2 # resources gathered per gatherer          recursos/pessoinha2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [],
   "source": [
    "int_problem = cvx.Problem(F_Obj,Constraints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 203 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "82.0"
      ]
     },
     "execution_count": 283,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time int_problem.solve()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEICAYAAACktLTqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nOzdeVxU1fvA8c9lG3YQEBVRcMEUFdxXzDXNJbXUMjUttcwy2yxN+6almaW/LJeyXMsttzTTzHKh3HIh930JEVFBlmEdYGbO748LiAqKCszCeb9evJK5d+59ZoJnDmd5jiKEQJIkSbIuNqYOQJIkSSp+MrlLkiRZIZncJUmSrJBM7pIkSVZIJndJkiQrJJO7JEmSFZLJXZIekqIo/RVF2a0oil0Rz6+qKEqqoii2JR2bJMnkLpktRVFGKYpySFGUTEVRlhRwvKOiKGcURUlXFGWnoigB97hWpKIoGTnJNfdrThFiEIqi1CzgcW9gAvCcEEJflNcjhIgSQrgKIQxFOV+SHoVM7pI5iwGmAIvuPKAoig/wM/A/wAs4BKy6z/WeykmuuV+jHiG2YOBlIcTVR7iGJJUYmdwlsyWE+FkIsQGIL+DwM8BJIcQaIYQOmASEKopS+0HvoyhKTUVR/lIURasoyk1FUVblPP53zilHc1r6zymKUk5RlE2oHyxbFEXZpCiKf75rVVMU5W9FUVIURdmmKMpcRVGW5RwLzPlLwC7nez9FUTYqipKgKMoFRVFeznedZjl/tSQrinJDUZQvH/R1SWWbTO6SpaoLHM39RgiRBlzMefxBTQb+AMoB/sDsnGs+nnM8NKelvwr1d2YJEABUBTKA/N07K4ADgDfqB84L97jvSiAa8AP6AlMVRemYc+xr4GshhDtQA1j9EK9LKsNkcpcslSugveMxLeB2j+dsUBQlKd9Xbks5GzVZ+wkhdEKI3YVdQAgRL4RYK4RIF0KkAJ8CbUEdMAWaAh8JIbJyrrOxoOsoilIFCAPG5tzzCLCAWx8G2UBNRVF8hBCpQoh/7vG6JOkuMrlLlioVcL/jMXcg5R7P6S2E8Mz3NT/n8fcBBTigKMpJRVGGFnYBRVEcFUX5WlGUs4qiXAE2AZ45M2D8gAQhRHq+p1wp5FK55+aP9zJQOeffw4BawBlFUQ4qitLjHq9Lku4ik7tkqU4CobnfKIrigtp9cfJBLySEuC6EeFkI4QeMAL4paIZMjneBekALIUQV4KncEIBrgJeiKM75zq9SyHVics7N/5dGVeBqTkznhRDPA77A58DanNcoSUUik7tkthRFsVMUxRGwBWxzWs25c8rXA/UURemTc85HwDEhxJmHuE+/fIOiiYAAcqcr3gCq5zvdE9ADOkVRvHLuC4AQ4jLqrJ1JiqI4KIrSklvJ/zZCiCvAXuCznNcVgtpaX54T0yBFUcoLIYxAUs7T5BRKqchkcpfM2YeoA5bjgEE5//4QQAgRB/RB7fNOBJoD/e9zvV/vmOe+PufxpsB+RVFSUfvI3xRC/JdzbBLwQ04f/bPATEADxAH/AL/fcY+BQEvUGT5TUKdnZhYSz/NAIGorfj0wUQjxZ86xJ4GTOTF9DfTPmRUkSUWiyM06JKnk5EyrPCOEmGjqWKSyRbbcJakYKYrSVFGUGoqi2CiK8iTQC9hg6riksqdINTEkSSqyiqgLnLxR57CPFEIcNm1IUlkku2UkSZKskOyWkSRJskJm0S3j4+MjAgMDH+q5aWlpuLjI6b+55PtxO/l+3CLfi9tZw/sRERFxUwhRvqBjZpHcAwMDOXTo0EM9Nzw8nHbt2hVvQBZMvh+3k+/HLfK9uJ01vB+Kolwu7JjslpEkSbJCMrlLkiRZIZncJUmSrJBZ9LkXJDs7m+joaHS6e6+49vDw4PTp06UUlfkr7P1wdHTE398fe3t7E0QlSVJpM9vkHh0djZubG4GBgSiKUuh5KSkpuLndq4R32VLQ+yGEID4+nujoaKpVq2aiyCRJKk1m2y2j0+nw9va+Z2KXikZRFLy9ve/7V5AkSaXo2GqYWQ8mear/PVa8m22ZbcsdkIm9GMn3UpLMyLHV8OtoyM5Qv9deUb8HCHm2WG5hti13SZIkq7X9k1uJPVd2hvp4MZHJ/R4iIyOpV69ekc/fuHEj06ZNA2DSpEnMmDHjntc8dOgQo0ePLp5gJUmyHNroB3v8IZh1t8yDik3WMWrlYeYMaIivm2Op379nz5707NmzyOc3adKEJk2alGBEkiQVxJiVhZKejjE9HcXODuztS6/r8uyWwo95+Bd+7AFZVXKftf08ByMTmLXtPFOerl8s19Tr9QwZMoTDhw9Tq1YtfvzxR4KDgzl06BA+Pj4cOnSIMWPGEB4ezpIlSzh06BBz5sy57RoREREMHToUZ2dnwsLC8h4PDw9nxowZbNq0iUmTJhEVFcWlS5eIiorirbfeymvVT548meXLl1OlShV8fHxo3LgxY8aMYdasWcybNw87OzuCg4P56aefiuU1S5K10icmkvDDDyQuXYZvWhpn8x+0tUWxtb2V7O3s1C9bW7C3Q7G79Rh2trd9rz5md/v39nYotvkfs4Wr+1Gu/IPi7IeiTwOyca2YicZDD/ZO0PGjQiJ/cBaT3J/7bt9dj/UIqUTvet489uEWMvXGvMeX7Y9i2f4o7GwULkztRkJaFiOXRdz23FUjWhbpvmfPnmXhwoW0bt2aoUOH8s033zxw7C+99BKzZ8+mbdu2vPfee4Wed+bMGXbu3ElKSgqPPfYYI0eO5OjRo6xbt47Dhw+j1+tp1KgRjRs3BmDatGn8999/aDQakpKSCr2uJJV1+sREEpb8QOLSpRgzMnDr0oUYN1dqBAYisvUIvR6hzwa9HqE35H0v9HrIPW4wqOfknZ/zpdPd/n3uOQZD3mNkZyOyMhEGPQg31G161X3U7VokoalaSU3sxTSYChaU3O/lj7cf55lv9pKYnoVRgI0C5ZwdeK19jUe+dpUqVWjdujUAgwYNYtasWQ/0fK1WS1JSEm3btgXghRdeYMuWgv8s6969OxqNBo1Gg6+vLzdu3GD37t306tULJycnAJ566tZ+yyEhIQwcOJDevXvTu3fvh3l5kmTV7kzq7l2fxGfkSDRBQVwID8e7NAqHGfRgawdZ6XDud0Rw75wPEfVLcXQEB4div63FJPfCWtopKSkEeLvwZL2KrDgQhcbOhiyDka71KjIsTN203svFocgt9Tvd2Q+nKAp2dnYYjepfCvebOy6EKHJfnkajyfu3ra0ter2ee22msnnzZv7++282btzI5MmTOXnyZJHuI0nWTp+YSMLiJSQuW3ZXUi81QsChhRCxBF76HTSuUO8ZFAAHB5QSSOj5Wc1smZupmQxsHsD611ozsHkAcamFbTj/YKKioti3T+0SWrlyJWFhYQQGBhIRoXbzrFu37p7P9/T0xMPDg927dwOwfPnyB7p/WFgYv/76KzqdjtTUVDZv3gyA0WjkypUrtG/fni+++IKkpCRSU1Mf9OVJklXRJyYS++VMLnbsRPz8+bi2a0v1jb9Q+csvSzexZ6XD+ldh87vgWhGM2aV37xwW03K/n+9euDXrZErvok9fvJ86derwww8/MGLECIKCghg5ciTNmjVj2LBhTJ06lebNm9/3GosXL84bUO3SpcsD3b9p06b07NmT0NBQAgICaNKkCR4eHhgMBgYNGoRWq0UIwdtvv42npycpKSkP+1IlyWLpExNJWLSYhOXLERkZuHftis9rI9HUrFn6wcRfhFUvQOwpaD8B2owBGxO0o4UQJv9q3LixuNOpU6fueqwgycnJRTrPkqWkpAghhEhLSxONGzcWERERhZ57r/ejqO+pNdm5c6epQzAb1vheZCckiBsz/k+cbthInKpdR0S//Y7QnT9fpOeW2PvxQ08hpgUIcf7Pkrl+PsAhUUhetZqWuzV75ZVXOHXqFDqdjiFDhtCoUSNThyRJJqVPSCBh8WISlq9QW+rduuEz8lXTtNRBHTTV69R+9Z5zQBihXIBpYskhk7sFWLFihalDkCSzUGBSf20kmhqPPjPuoaXGwbqhYO8Cz68EzyqmiyUfmdwlSTJ7dyX17t3VlropkzrAlQOweghkJED3L8GMCvTJ5C5JktnSJySQsGgRCStWmldSFwIOzIet48GjMgz7EyqFmDamO8jkLkmS2clL6stXIHQ680nquXRJ8Pd0qNkRnp4HTuVMHdFdZHKXJMls6OPjiV+0iMQVKxGZmbeSevXqpg5NlXhZLe7lVA6GbwOPKqaZ5lgE5hmVhdqwYQOnTp3K+75du3YcOnTIhBFJkmXQx8dzY/p0LnR6goTFS3Dr1Inqm36l8vQvzCexn9oI37aGXV+q35cLMNvEDtbUcj+2Wi10r41WP1mLuQhPUWzYsIEePXoQHBz8yNcyGAzY2toW+7mSZE708fHEL1xE4sqclnqP7vi8OhJNdTPa69egh+0fw95ZULkxhPY3dURFYr4fOw8id8sq7RVA3Nqyqhj2JJw8eTK1a9fmiSee4Pnnn2fGjBnMnz+fpk2bEhoaSp8+fUhPT2fv3r1s3LiR9957jwYNGnDx4kUA1qxZQ7NmzahVqxa7du0C1GT83nvv0bRpU0JCQvjuu+8AtQRw+/btGTBgAPXrqyWLly1bRrNmzWjQoAEjRozAYDAA4OrqykcffUTz5s3Zt28f48aNIzg4mJYtWzJmzJhHft2SVJL08fHc+CKnpb5kCW5PdKL6pk1U/uIL80rsqbGwtLea2JsMg5e2mM1Ux/uxnJb74u53P1a3N9TpD9s+LnjLqi1j1dZ7WjysHnz78Zc23/eWhw4dKrDc7jPPPMPLL78MwIcffsjChQt544036NmzJz169KBv375519Dr9Rw4cIDffvuNjz/+mG3btrFw4UI8PDw4ePAgmZmZtG7dms6dOwNw4MABTpw4QbVq1Th9+jSrVq1iz5492Nvb89prr7F8+XIGDx5MWloa9erV45NPPiEhIYFhw4Zx5swZUlNT8z4AJMnc6G/eJH7RYhJXrEBkZZlnSz0/7RW4fgye/s5iWuy5LCe530vy1YIfz0h4pMsWVm73xIkTfPjhh3nFuu5VL+aZZ54BoHHjxkRGRgLwxx9/cOzYMdauXQuoZYHPnz+Pg4MDzZo1o1o19Qd9+/btRERE0LRpU/XlZGTg6+sLqFUj+/TpA4C7uzuOjo4MHz6cDh060K9fv0d63ZJU3LKioohftAjt+g2I7Gw8nuqB96uvoqlmhkldCLi8FwJbq90wb50AR3dTR/XALCe5F9bSTklR+9i1V+4+5pHz55OLd5Fa6ncShZTbffHFF9mwYQOhoaEsWbKE8PDwQq+RW8Y3t4Rv7nVnz55914dCeHg4Li4ut91/yJAhfPbZZ3dd19HRMa+f3c7OjgMHDrB9+3aWLl3KwoUL2bFjxwO9VkkqCbpTp4hfsIDk37ei2Nri0bsXXkOHmmdSB8hMhY1vwMmf4cXf1ARvgYkdrKXPveNH6hZV+RXDllWFldtNSUmhUqVKZGdn31bC183NrUhVGbt06cK3335LdrZaBvTcuXOkpaXddV7Hjh1Zu3YtsbGxACQkJHD58uW7zktNTUWr1dKtWzemTZvGkSNHHur1SlJxEEKQtm8fUUOH8d8zfUj9exfeQ1+ixrZtVJo82XwTe9w5WNARTm2AjhOh6sPtAfEgYpN1PPvdPmJT7r0vxMOwnJb7veTOiinm2TKFldudPHkyzZs3JyAggPr16+cl9P79+/Pyyy8za9asvC6XggwfPpzIyEgaNWqEEILy5cuzYcOGu84LDg5mypQpdO7cGaPRiL29PXPnziUg4PaCRCkpKfTq1QudTofBYGDmzJmP9Lol6WEIg4GUP/8kfv4CdCdPYlveh/LvvkO5/v2xdXMzdXj3dmojbBgJdo7wwnqo3q5UblsS+z7nUgrreihNTZo0EXfOBz99+jR16tS573NTUlJwK8EfnNTUVFxdXUlPT+fxxx/n+++/N+uqjPd6P4r6nlqT8PBw2pXGVmoWoKTeC2NmJtr1G4hfvIjsy1E4BATgNWwoHr16YZNvdzFzc9v7cWSlumtSvx/UcgIl7M59n3Np7Gw4O6Vrka+jKEqEEKJJQceso+VegmS5XUkqmCE5mcSVP5GwdCmGmzdxrF8f36+/xq1TR5SC1l2YwVqU/HG01V6BAz7w5GfQ4Hk1FpvSWS8y4vHqzNpxARsFjAIc7W3oUrciE7oXX+NLJvf7kOV2Jel22TdukPDDjyStWoUxLQ2XsDC8hw/HuXmzwvcLzl2LkjtlWXsFfhkFcWeh8Yvq3PHsDLgacfdzvaqDu5862HmtgPEk7yBwqwA6LVw/fvfx8rXBxQfSE2DfXNg7GwyZ6l6m6Tdh42j1vBL8oBFCEH42Dm9XB0L8PXm+eVX2XYrn0OVENHY2ZOqNuGns8HVzLLZ7yuQuSVKRZF66RPzChWg3/goGA+5PPon38GE4FmVF9vZP7l6LYsiEXTPAwRnavAupN2BJAetZuk6H5q9AYmTBx3t/Cw0GQOyZgo8/uxSCe0LMv+r97qTPUOMrgeQuhGDb6VhmbT/P8ataejfw46v+Dank4YSXiwMDmwcwoFlVVhyIIq6YB1Vlcpck6Z4yjhzh5oIFpG7fgeLgQLl+ffF66SUcqhRhpeb142rNc210IScoUD9nXYZrBRjy692neOVUgiwXWPBxn1rqf31rF3zcN+fDx68RoJCmwGsVy3Pe3iHfSQJWtrr/63kAeoNAl23AKAQ2rgrl69pyQCi0Wplzgh2QAWGZHzGl95PFeu/cy0uSJN1GCEHa338TP38B6YcOYePhgferI/AaNAg7b+/7X+DKAfh7BpzfqlZQdPcreLGhhz94VlX/be8E1R4v/Joa13sfd/S493FnL/Dw53P7NI5oNPRNScU+dz6JxhXq9bzvy7qf3AkqiqJwLFrL+RsphFTxpIaPCzY2BXdZ+bv5P/J9CyKTuyRJeUR2NslbthC/YCGZ585hV7EivuPGUq5fP2zyLbArVOwZ+G0MRO4CJy9o/yE0exnO/3F7nzsUy1qUB/Vn436s/28tLydpGZ2ovRVHuy8eqVvGYBT8dvwas3ec5/X2NenVoDKZjQzYKgp2tqZZTiST+z1ERkbSo0cPTpw4UaTzN27cyKlTpxg3bhyTJk3C1dX1riJeD3pNSSoNxvR0ktb9TMLixWTHxOBQswaVPvsMj+7dUBwc7v1kISAjUW0ZO7ioNc87f6oOlGpc1XNKaC3Kg7iRdoNJV/+grnMlRiYIBMkojxiHwSj49WgMs3ec52JcGkG+rrg72QOgsTNtpVaZ3ItRz5496dnz0f+0y0+W85VKkj4xkcTlK0hctgxDUhJOjRpR4cMPcW3XFuV+tcqNBnU1564vwdVXXfzjWQXePFpwnfOQZ00z9REwCiMT9kwg25jNtM7fY+8RWCzz/kcsPcS207E8VsGNuQMa0bVexUK7X0qbdZQfKEF6vZ4hQ4YQEhJC3759SU9PJzAwkJs3bwJq5cjcH5AlS5YwatSou64RERFBaGgoLVu2ZO7cuXmPF7X0b1paGt27dyc0NJR69eqxatWqkn/hklXLvnqV659O5UKHjtycMwenhg0JWLGcwBXLcevQ/t6JXZ8F/y6FOU1h7VAwZEH9Z9UWPJjlBhZLTy1l/7X9vN/0fQI9Ah/6OtkGI2sjoknNVOtEDWwRwLxBjdjyZhu6h1Qym8QOFtJy//zA55xJOFPgsYdt2db2qs3YZmPve97Zs2dZuHAhrVu3ZujQoXzzzTcPfK+XXnqJ2bNn07ZtW9577728x4ta+nfdunX4+fnl1bbRarUPHIMkAejOniN+4QKSN/8GioJHjx54DxuKJiio6Bc5mLMxdMX66orOOk+V2uKfh3E24Sxf//s1Hap0oE9Qn4e6RpbeyM//RjM3/AJXEjLQG4z0b1aV9o/5FnO0xccikrspValShdatWwMwaNAgZs2a9UDP12q1JCUl0bZtWwBeeOEFtmzZAhS99G/9+vUZM2YMY8eOpUePHrRp06a4Xp5k5YQQ6GNiSD9yBM/FS/jvxAkUZ2e8Bg3C68Uh2FeqdP+LZKbAoUXqYqHa3aDhIPCuCUGdobBFS2ZCp9cx9u+xeGo8mdRqUuGLrAohhGD5/ii+Db/I1aQMQv09+LhnXbNO6rksIrnfq4Vd0rVl7vxhUBQFOzs7jEa1LoROd++FB0KIQn+gilr6t1atWkRERPDbb7/xwQcf0LlzZz76qHRnGUiWwZiRge7kSTKOHiXjyBEyjhxFHxcHgL2rKz6j38BrwABsPT3vf7H0BDjwPfzzLeiSoOnLanJ39IBahe9hYE6+jPiSi9qLfNfpO8o5livy84xGgY2NgqIobD52DV93DZ8+XY+2tco/8AeEqVhEcjelqKgo9u3bR8uWLVm5ciVhYWGkpKQQERFB165dWbdu3T2f7+npiYeHB7t37yYsLOy2EsG5pX87dOiAvb09586do3Llu4sWxcTE4OXlxaBBg3B1dWXJkiXF/TIlCySEIPvKFTWRHz5CxtGj6M6ehZx9A+yrVsW5ZQucQkNxatCA/devU7djx6Jd/J95sGMyZKXCY93UFaT+BdanMlu7onex8sxKBtUZRKvKRVugpMs2sPJAFIv3RLJ6REsqejjy3eDGuGnsLCap55LJ/T7q1KnDDz/8wIgRIwgKCmLkyJE0a9aMYcOGMXXqVJo3b37fayxevJihQ4fi7Ox8Wyu9qKV/jx8/znvvvYeNjQ329vZ8++23xfoaJctgTEsj4/iJW63yo0cxJKi7jSnOzjjVr4/3sGE5yTwUOy+v2y+Q04IvVNKVW9MZnTzV1nnYO1CxXgm9opITnxHP//b8j6ByQbzV+K37np+RZWD5/st89/cl4lIyaV7NixRdNhU9HHF3tC+FiIufLPlrZWTJ39tZaslfIQRZkZFkHDlKxlG1eyXz3DnI6Q50qFYtr0Xu1CAUTVBQwZUY8yn0vYi/CLu/hKM/QaePodXdM74siRCC0TtGszdmLyt7rKRWuVp3nRObrGPQtztZ9lp7XDV2tJ8Rzo3kTFrV8GZ0xyBaVC/CKlwzIEv+SpKZM6Smojt2jPScFrnuyFEMObOibFxdcQoJwe3VEWoyDwkpWp/5/dw4Cbv+D06uB1sHaDIUgns9+nVNbM25NYRHhzO26dgCEzvA//1xjnOJxrxNMoaHVadBVU+aBnoVeL4lksldkkqZMBrJunTptkHPzAsX8uaJO9SsgesTnXAKDcW5QQMcqle/b6v8nvLql0fD4XwrMn97Xy2h22o0tHxdXYhk4S5pLzH94HRa+bViQJ0Bdx2vNWELWYZbm2Qs2x/Fsv1RD7xJhiWQyV2SSphBqyXj2DG1i+XIETKOHcOYszWjjbs7TqGhuD3ZBafQBjiF1MfWvRg3ZM5XR10BtY76xjfUYz1nqUW9nK2jtZptyGbc3+NwtHNkSusp2Ci3FlNFJ6YzedMpsnMSe0lukmEuZHKXpBJiTEvjxvTpJK1arbbKbWzQBAXh3rVrXl+5Q2Dg/Zf5P4qC6qjrderjb1tXfaM5R+ZwOuE0X7X/ivLO5dFlG7im1VHNxwU3jT0nriYzsl0NYpIy+OVoDPY2lMgmGeZCJndJKgHp//5LzNhxZEdHU+7553Hr/ASO9epj61qEyorFxWhUW+oFKbS+umU6eP0gi08spk9QH+q4t+Lz38+w8kAU/uWc+HVUGB7O9ux6vz02Ngojlh5iYPMAatnc4JyxQrFvkmEuZHKXpGJkzMri5qxZxC9chL2fHwE//oBz06alHIRBLQdgYwP2LpCddvc5HiVTQ9wUtJlaxu8eTwWnyly/1IU2m3YihKBzcEVeah2Yd15u3ZfvXlAnl4SH32RwO8ub5llU5lfhR5IslO70aSL79iN+wUI8+/ah2i+/lG5iFwJOboDZjeHaUfWxp75S65XnZ4I66iUlI0vPx3snczP9Jt0rjmHfxRSGt6nG3++3Z94LjWle3dviFh8VF9lyLyIhBEIIbEqh4p0s82tZhF5P/IKFxM2di62nB/7zvsWttOfWxxyG38dD1F7wrQsGdZVq/jrqQhv9yPXLzcWNZB3L/rnM0uM/Y/DZyuiGoxkc3I5XWgicHWRaA9lyv6fIyEjq1KnDa6+9RqNGjVi6dCktW7akUaNG9OvXj9TUVADGjRtHcHAwISEheZtzXL58mY4dOxISEkLHjh2JiooC4MUXX8wrFAbg6qpuZnBnmV+AH3/8kZCQEEJDQ3nhhRcAiIuLo0+fPjRt2pSmTZuyZ88eAP766y8aNGhA69atadiwISk5szGkkpUVGcnlgYOI++or3Dp2pPrGjaWf2DePge/bw81z0OMreHUX+De+dTzkWXj7BH+126AOolpwYv83KpE3Vh6m9bQdzN19AHx+ppZHCEPrDUVjZysTez4W8U5cnzqVzNMFl/zVGwwkPEQrV1OnNhXHj7/veWfPnmXx4sV88sknPPPMM2zbtg0XFxc+//xzvvzyS0aNGsX69es5c+YMiqKQlJQEwKhRoxg8eDBDhgxh0aJFjB49usDSAvnlL/N78uRJPv30U/bs2YOPjw8JOcvM33zzTd5++23CwsKIioqiS5cunD59mhkzZjB37lxCQkJQFAVHR+sb/TcnwmgkceVKYqfPQNFo8JsxA/fu3UqvCyBbB3YatSqjW0Vo9QY8PkYt6mVlcot4AXy+5QynriUzuGUVTorlRKXaMbvTdGzNuOSwqVhEcjelgIAAWrRowaZNmzh16lRe+d+srCxatmyJu7s7jo6ODB8+nO7du9OjRw8A9u3bx88//wyoZX7ff//9+94rf5nfHTt20LdvX3x8fADwyqkTsm3bNk6dOpX3nOTkZFJSUmjdujXvvPMOffr0YcCAAfj7W8+AmbnJvnaNaxMmkLZ3Hy5hYVT6dAr2FSqUzs2FgBPrYNsk6PqFWqXx8TH3fZolik3RsWJ/FGsORbP+tVb4ujsyvW8o3q4OLD2zgDVHjjGtzTT8XP1MHapZsojkfq8WdknXlsktvSuE4IknnmDlypV3nXPgwAG2b9/OTz/9xJw5c9ixY8dd5+gtXfoAACAASURBVOS26PKXCxZCkJWVdde9co8V1Ao0Go3s27cPJ6fbB8nGjRtH9+7dWb9+PS1atGDbtm3Url37IV6xVBghBMkbN3J9yqcIvZ6Kkybh+dyzpddaj46ArR/Alf3qRhnOllH/5EEdvZLEkr2RbDoWQ7ZB0KG2L6mZenyBqt7OHIs7xryj8+hWrRvdq3c3dbhmS/a5F1GLFi3Ys2cPFy5cACA9PZ1z586RmpqKVqulW7dufPXVVxw5cgSAVq1a8dNPPwGwfPlywsLCAAgMDCQiIgKAX375hezs7ALv17FjR1avXk18fDxAXrdM586dmTNnTt55ufe7ePEi9evX5+2336ZJkyacOVNwN5b0cPQJCVwd/SYxY8ehCQqi+i8bKNf/udJL7H98CAs6QMJ/0HMOvPIXVL1/RVJLcyNZx9Pf7OHPUzcY1CKAnWPasejFplQvr45NpWenM27XOCo4V2BCiwkmjta8WUTL3RyUL1+eJUuW8Pzzz5OZmQnAlClTcHNzo1evXuh0OoQQzJw5E4BZs2YxdOhQpk+fTvny5Vm8eDEAL7/8Mr169aJZs2Z07NjxttZ6fnXr1mXChAm0bdsWW1tbGjZsyJIlS5g1axavv/46ISEh6PV6Hn/8cebNm8dXX33Fzp07URSFevXq0bWrddXJMKWUHTu49r+PMCYn4zvmXbxeeunRar0UVVY62NiBnQNUDFVrqoe9DRrLrYIam6xj1MrDzBnQEF83R+JTM1l5IIorCRl83jeECu6OzB/chGbVvHAroNTutAPTuJp6lUVdFuHuUIxlGqyQLPlrZWTJ39s9SslfQ0oKN6Z+hnb9ejS1a+P3+ec4PlZwlcFiZTTC8TWw/WNoOQpavlYslzWH8scfrj/O8gNRPFm3Ii4aOzYejSFLb6RtrfLMH9wEB7vCOxO2Xd7G2+Fv83L9lxndaPQjx2IO78ejkiV/JekBpf2zn5jxH6C/fgPvESMo//prKA4OJX/jqP1qv/rVCKjUACo3Kvl7loLHPtxCpv5WNcYtJ64DYKsobHunLTV9Xe/5/BtpN5i0bxJ1vesyssHIEo3VWhR7clcUpTowAfAQQvQt7utLUkky6nTEzZxJwg8/4hAQQOCK5Tg1aFA6N985Ff76HNwqQe95EPKcWkLAwqVm6nmtXQ32XYrnyJUkdNlG7GwUOtetwKSede9btMsojEzYM4EsQxbT2kzD3sYyd0YqbUVK7oqiLAJ6ALFCiHr5Hn8S+BqwBRYIIaYJIS4BwxRFWVvw1YruXptLSw/GHLrfzF3G8ePEjB1H1qVLlBs4EN9338HG2blkb5qZCsIIju5Qra061bH1m6C5d0vWElzTZrBkTyQrDkSRotMT5OtKpt6Ixs6GLIMRL2eHIlVjXHpqKfuv7Wdiy4kEegSWfOBWoqgt9yXAHODH3AcURbEF5gJPANHAQUVRNgohThV4hQfk6OhIfHw83t5ltzZEcRFCEB8fLxc2FUJkZ3Pz23nc/O477Hx8qLJwAa456xlKjNEIR1eqpXfr9oaun0Nga/XLCkzfeobv/rqEUQi61q/E8LBqzPvrIs2rezOgWVVWHIgqUjXGswln+frfr2lfpT19gvqUQuTWo8gDqoqiBAKbclvuiqK0BCYJIbrkfP8BgBDis5zv196rW0ZRlFeAVwAqVKjQOHfaYL7juLi43LfGimzd366w98NgMJCWllbmWvCpqal5JR4KYhtzDY8li7GPukJG8+akPPcsooRb6x5JJ6l5YSFuqRdJdqvFhZrDSPYo+TUJ93svHoVRCI7GGQj2skVjp7DnajZRyUY6BdhT3vnhupayjFlMvz6ddGM6H1T6AFfb4o29JN+P0tK+fftCB1TzCmLd7wsIBE7k+74valdM7vcvoLbuvYF5wEXgg6Jcu3HjxuJh7dy586Gfa43k+3G7wt4Po14vbi5cJE7XDxFnW7QU2q1bi//mR1cJ8WVdISZ6qP89ukqIPbOEmOguxP/VEeLoaiEMhuK/byFK4mcjPVMvlu6LFO2n7xQBYzeJlfsvF9u1p/4zVdRbUk/sid5TbNfMzxp+V4BDopC8+igDqgU1l4UQIh549RGuK0klKis6mmvjPiD90CFcO3Sg0icfY5dT5qHY5NveDlA3zfh1NLSfAO3Gq7VgHEq4P78E6Q1Gvt5+nmX/XCYxPZtQfw9mP9+QrvUqFsv1d1/dzYozKxhUZxCtKrcqlmuWNY+S3KOBKvm+9wdiHi0cSSo5Qgi069ZxY+pnoChUmjoVj6d7l0y33raJd29vl50B+7+z6O3tYlN0+Lo5Ymdrwz+X4mlWzYvhbarTJKBcsb2PCboEPtz9ITU9a/JW47eK5Zpl0aMk94NAkKIo1YCrQH/g7u3GJckM6OPiuPbh/0j96y+cmzfHb+qn2FeuXHw30CWrM14A1g2H5ELaORa4vZ0Qgr/P32TBrksc+C+BveM64O2qYfnwFvdcdPSw95q4ZyIpWSl83/l7NLaaYr1+WVLUqZArgXaAj6Io0cBEIcRCRVFGAVtRp0IuEkKcLLFIJekhJf/+O9cnfYwxI4MK4z+g3KBBj74pdWocXN4Nkbshcg8kRsK4y2oZ3mqPw7k/IFN79/MsaHu7TL2BXw7HsGD3Jc7dSKWCu4Y3OwXlJfTiTuwAa86tITw6nPebvk+tcqWwGtiKFSm5CyGeL+Tx34DfijUiSSomBq0W94WLuHrwII716+P3+TQ01as/3MVSY9WaLvZOcGA+/JZTZtfeBaq2UDfAMGSpyb3RYLBzvL3PHSxmezuRM+MqJknH2J+PUbuiO18+G0qPEL8SSei5LmkvMf3gdFr5tWJgnYEldp+yQpYfkKyOMSODpJ9/Jv6773G8eROf0W/g88orKHYP8OOecl1tlV/eo/735jl4fhU89iQEtIZOkyCwDVQKBdsCVkzm294ObbTaYjfz7e0uxKaycPd/pGXqmfV8Q6r5uLD5jTbUqeRW4tONsw3ZjPt7HI52jkxpPQUbxfJX5pqaTO6S1TAkJZGwYgWJS5dhSEzEKTSUG8OGEjxkyP2fnHwNjNngWRXizsLcZurjDm4Q0BIaDATfnLnoFYLVr/sJedaskzmorfR9l+JZsOs/dpyJxcHOhr6N/fN2Pwr2K53Ki3OPzOV0wmm+av8V5Z3Ll8o9rZ1M7pLFy752jYQlS0hcsxaRno5L28fxaV8Dp5gfCPjvd5g5/e5Wc3KM2lceuUttmSdchEZDoOcs8A6CLlOhakuoGAK2lv9rEpusY+r+DIIb625b8v/jvstM3HgSbxcH3uoUxKAWAfi4lu4g5sHrB1l0YhF9gvrQsWrHUr23NbP8n1qpzMo8f574BQvRbt4MQuDevRvew4bjmHnk7jnmG99Qu1Y6fKg+tqgLJEWBxgMCWkGTl6BGB/WYjQ20fN00L6qEzNp+nvOJRqb/fpbq5V0J9nOnba3ydKtfCY2dDb0bVsbRvvT3IdVmahm/ezxV3avyftP7b0UpFZ1M7pLFSY+IIH7+AlLDw1GcnCj3/PN4vzjk1tTGmc/cPcdcr4Nd/6cuIlIU6D4TXHzU7eqseHPlO0vtrolQp2LaKgoXP+tGeTcN/ZtVNUlsQgg+/edTbqbfZGm3pTjbW+6iLnMkk7tkEYTRSGp4OPHzF5Bx+DC2np74jBpFuYEDsCtX7vaTC5tLnr+uTlCnkgvWjOx6vz0vLj7AqWspANgq0KZWeb7oG2LiyGDTpU1sidzC6IajqedT7/5PkB6ITO6SWRNZWWg3bSZ+0UKyLlzE3s+PChMm4NnnmbvL8Ub9o24a7eGvdsXcycNfbbWXAVl6IzYK+Lo75m1XZ2cDBgH+nk5FKrVbkqJTopm6fyqNfBsxtN5Qk8ZirWRyl8ySITWNpDVrSPjhB/TXr6OpVQu/6V/g/uSTKPZ3TD2Mv6gu9z/9K4T0VwdPLXSO+aMSQvD7iet8/vsZhoVV44WWgXg62zOoRQC1bG5wzlihSKV2S5LeqGf87vEAfNbmM2ytuFvMlGRyl8yKPj6ehKVLSVz5E0atFuemTan0yce4tGlz91zrtHj4+ws4uABsNWp/esvXwSFn0/HtnyC00SgWMMe8OPwblcinm08TcTmRIF9Xqvmo5Wy/e0GtCBsefpPB7Uzf/bHw+EIOxx5mWptp+Ln6mTocqyWTu2QWsq5cIWHxYpLW/YzIysKtU0e8hw/HKTS08Cf98w0c+F6dwtjuA3CrcOtYzhzzv6xgE+SimLH1LHN2XsDHVcNnz9SnX2N/7GzNbyHQsbhjfHv0W7pV60b36t1NHY5Vk8ldMindqVPEL1hI8u+/g60tHr164j10GJrq1e4+2WiEE+vArSJUawOtR0P9frcWF5UxSelZ2NgouDva07KGNzY2CiMer46Lxrx+rYUQHLx+kDXn1rAtahu+zr5MaDHB1GFZPfP6KZDKBCEE6fv3Ez9/AWl79mDj4oLXSy/iNXgI9hV8C37Sf7vgjw/h2hGo/6ya3B091K8yJlNv4Me9l5m94zzPNa3ChO7BtK7pQ+uaxVyT/hEl6hL55cIvrD2/lsvJl3FzcKP/Y/0ZFDwId4fSWflalsnkLpUaYTCQ8uc24hcsQHfiBLY+PpR/5x3K9X8OW/dCftnjzqmDpWd/A/fK8PR3anIvg4QQbDp2jS+2nuFKQgZta5WnT2PzqjIphODQjUOsOau20rON2TT0bciIkBE8EfAEjnZyH9/SIpO7VOKMmZloN/xCwqJFZF2+jH1AVSp+/DEevXtho7nPUvfIXWqrveNEaDFSnfVSRk3bcobv/r5E7Ypu/Di0GY/XMp8aLIm6RDZe3Mjac2uJTI7Ezd6NfrX60bdWX4LKBZk6vDJJJnepxBhSUkhc+RMJP/6I4eZNHOvWpfJXM3F74gmUwjY+z0pXB0rdKkHDgepgaXAvdTVpGXQpLhUHOxv8yznTr4k/NXxd6dPIH1sb08/Xz22lrz23lj8v/0m2MZsG5RswpfUUOgd2xsmu7H4QmwOZ3K2IyMpCSU5GHx9v0jiMqakkrl5N0k+rMKal4dK6Nd4zpuPcvHnhpWONRji2CnZMhuSrak30hgPVol1lMLHHp2Yya/t5lu+PokdIJb7q35Cavm7U9HUzdWgk6ZLUVvr5tfyn/Q83ezf61upL31p95QYbZkQmdyuRef48USNG4BtzjfOmDgbAxgb3J5/Ee/gwHIPvUx73ygHY/A5cPw5+jeCZ+RDYunTiNDO6bAOL90Tyzc4LpGcb6N+0Cm91Mn3CFELwb+y/rDm3hj8j/yTLmEVI+RAmt55Ml8AuspVuhmRytwLp//7LlVdHYqPRkPxsP4Jqm3ZqoGJjg0urVjhUvU9BKiHUcgCZyZChhT4Loe4zalXGMmruzgvM3nGBTnV8Gde1tslb6tpMbV5f+iXtJVztXXkm6Bn61urLY16PmTQ26d5kcrdwKTt2cvXtt7GvVIkqCxZw9cJ5vMx90U7Kddj5KTj7QKeJULMTvBEBdg6mjswk9l68ibODHQ2qePJS62q0rOFNqxqm64oSQnA49jBrzq3hj8g/1Fa6TwiftPqELoFdZPVGCyGTuwVLWreOax9NxDE4mCrfzcPOywsumEWnTMGy0mDvbNgzS91vNH/N9DKY2C/EpjBtyxm2nY7lieAKzB/cBC8XB5Mldm2mlk2XNrHm7Bouai/iYu/C00FP069WP9lKt0AyuVsgIQTx388nbuZMXFq3xn/W19i4uJg6rHu7uAPWj4TU6+rsl44TwbuGqaMyibiUTL7ado6fDl7B2d6WsU/W5qXWgSaJRQjB0bijrDm3hq2RW8k0ZFLPux4ft/qYJwOflK10CyaTu4URRiM3PptG4tKluD/1FH6fTkFxMKNW77HVt28K3W4cNBykTm30qgbP/ghVm5s6ylITm6xj1MrDzBnQMK/M7sajMaw6eIUXWgTwRoeaeJfytnYAyVnJ/HrxV9aeW8uFpAu42LvQq0Yv+tbqSx3vOqUej1T8ZHK3ICIri5hxH5D82294DRmC79j3Ucxp8PHY6gK2txsNtg5qIa+hv5s2PhOYtf08ByMTeHPlEQa3DKBr/UoMalGV9o+Vp3p511KNRQjBkdgjeX3pOoOOut51mdRyEl2rdZWtdCsjk7uFMKSmcXX0G6Tt3YfvmHfxGjas8DnjprL9k7u3txMG9XErL7d7pzu3t9t3KZ59l+LR2NlwdkrXUkvsQgjOJZ5j19VdrLm2hpioGJztnHmqxlP0rdWXYO/7TFOVLJZM7hZAHx/PlVdGoDtzhkqffYbn071NHVLBCtverrDHrUym3oDGTl1526uBH6sP3Xrd9rYK3epVYkKPku/ySM5K5p+Yf9h9dTd7ru4hNiMWgKoOVfmo5Ud0q9YNF3szH6ORHplM7mYu68oVooYPR38jFv+5c3Az52mO7pUgOebuxz3Mq7hVcbocn0b42TjCz8ay71I8f7zVlqrezvQMrczF2DT+jUrEwc6GLIMRN0e7EtneTgjBmYQz7L66m91Xd3M07igGYcDN3o2Wfi0JqxxG68qtOXXgFO1qtSv2+0vmSSZ3M6Y7fZqoV16BrGyqLl6Ec8OGpg7pblH/wMGF8PQ86PRxmdne7lh0Em/+dIT/bqYBEOjtTP+mVfO2aA0L8mHpP5EMbBHAgGZVWXEgqli3t9Nmatl3bR+7o3ezJ2YPNzNuAlDHqw5D6w0lrHIYIeVDsLO59St+ilPFdn/J/MnkbqbS9h8g+vXXsXFzo+qSJWhqmNm0QX0m7JwKe2flbEgdfatfPf9sGSvY3u6/m2mEn40l/GwcTwRXYFCLACp7OhHg7cyQlgG0e8yXQJ+7uzlyt7cDmNL70ba3MwojpxNOsztabZ0fu3kMozDi7uBOK79Wea1zH6eyV4dHKphM7mYoeesfxIwZg31AVarOn499pUqmDul214/DzyMg9qRatbHLp6DJWSafs72dpRNCMHnTabafucHl+HQAqvu45LXMvV01LHmpWYnGoM3Usjdmb17febxOLQgX7B3M8PrDaVO5DfV86t3WOpekXPKnwswk/vQT1z/+BKcGDajy7TfYenqaOqTbGY2w7mVIj4cBq6FWF1NH9MiEEFy6qfadx6VkMq5rbRRF4XxsCjXLuzIsrBrtavlS1btkpwoahZHT8afZdXUXu6/u5vjN4xiFEQ+NB638WtGmchta+rWUrXOpSGRyNxNCCG7OmcvNuXNxbdeOyjO/xMbJjCrtxV9U9y51cIF+i8HFF1y8TR3VI4m4nMD6w1f561wcVxLUcYLaFd14r8tj2Noo/Di0WYlPN03UJea1zvfG7CVBl4CCQl3vurwS8gphlcOo510PW5tC6t9LUiFkcjcDwmDg+ieTSVq1Co9nnqHSJx+j2JnJ/xoh4OAC+PMjaDoMOk8BX8tYwRibrGPq/gyCG+so76rhYlwq4Wfj6NekCh5O9hz4L5Gf/71Kqxo+jHi8Bm1rlaeK163WeUkkdoPRwKn4U3kzW47fPI5AUE5TjlaV1b7zVn6t8HL0KvZ7S2WLmWSQssuYmUnMmPdI+fNPvF95hfJvv2U+i5O0V+GX1+HSTqjREVq8ZuqIHsiXf57jXKKRAfP3k5Fl4GqS2jqvUd6V9rV9GdwygKFhgXlz00tKgi6BPVf3sPvqbvbF7CMxMxEFhfo+9RkZOpKwymEEewfL1rlUrGRyNyFDcjLRr48i/eBBKoz/AK/Bg00d0i3nt8HaoWDMhh4zofFLYC4fOvcghOCx//1OVr7VoRdiUwGws1H46/32VPZUu7tcNCX/47/50mbG7x6PURjxcvQirHJYXuvc09HMxlMkqyKTu4lkx8Zy5eVXyLx0Cb8ZM/Do0d3UId3OqxpUbgTd/88iqjcmpmWx7t9oVh6Iov1j5dHY2/LHyevoso042tvQpW5FJnSvUyKLiAqjzdQy7cA06nrXZULzCdTxroONYka1gCSrJpO7CWRFRhI1bDj6xESqzPsW19ZmsqXc2S1wbqvaUveuAYM3mDqi+/o3KpEf90by24nrZOmNNKrqSbf6lTjwXwKZeiP2NpCpN+KmKZnVofcy+/BsUrJSmNhyoqyHLpU6mdxLWcbxE1wZMQKAgB9+wKn+oy1uKRa6ZPj9AziyDCrUB50WnMy3yyApPQs3R3tsbRS2nrjO9tOx9G9ahQHNq1K7ojsAvx2/xsDmAdSyucE5Y4ViXR1aFCfjT7L67GoG1hkoE7tkEjK5l6LUPXuIfmM0duXKUXXhAhwCA00dEvy3Cza8BsnR0OZdaDvOLHdFEkJwMDKRlQei2Hz8Gt+/0Jh2j/nyWruavNkpCGeH23+Uc1eHhoffZHC70v0ANQojU/+ZipejF681sKxBaMl6yOReSrSbNhPzwQdoqlenyvzvsff1NXVIag2YtUPV1aVDt0KVkl1x+TAy9QaW/xPFygNRnI9NxU1jx3NNqhDgrS7393C2N3GEd9twYQPHbh5jathU3BxMu8G1VHbJ5F4KEn78kRtTP8O5aVP8v5mLrZuJf+FvnITytdWiXoPWgndNdXGSmRBCcCM5k4oejtgqCt//fYkKHo583qc+T4X63dVKNyfaTC0zI2bSyLcRPar3MHU4Uhlmvr8lVkAIQdyXM4mfPx+3J57Ab8Z0bDSlv6VaHkM2/D0D/p6u1oNpMRIqhZounjto07P5+bA64yUxPZu94zpgb2vDb2+2wcvF/LqKCpI7iDq++XjzWa8glUkyuZcQoddz7aOJaH/+Gc/+z1Hxf/9DsTXhIpXYM7B+BFw7AiH9IfR508Vyh/M3Upj31yU2HYshU28k1N+DYZ2rIYR63FISuxxElcyJTO4lwJiRwdW33yE1PByfUaPwef0107bijqyEX98EjSs8uxSCe5oulhzajGz0BiPerhpuJGey9eR1+jb25/lmValX2cPU4T0wOYgqmRuZ3IuZISmJK6+OJOPoUSpOmki5/v1NHZI6Zz3oCXX+uqvpBnKFEBy+ksTK/VH8eiyGgc0D+F+PYFrV8Gb/+I6lsmK0pMhBVMncWO5vk7k4tjpvc4ps28pEhXuTHZtE5a++wr1L51KPo602Gg77Q4324OwDnSaqs2D6Ly+1UGKTdYxaeZg5AxrmLRxadTCKxXsiOXM9BRcHW55u6M/TDSsDYGOjWHRil4Ookjmy3N8oc3Bsdd62cplaO6LCszHqY6ky/iVcSjux58ShAGivwL8/gs9j0H482JbudMFZ289zMDKBjzeeYu7ARgDs/y8BO1uFqU/Xp2cDP1wtOJnfSQ6iSubIen7DTGH7J5CdQUa8PVf+8gYbQUCHOBwvfwP/5PQbe/hDnZzW3OFlkJl6+zW8qkOtnA+CQ4tAn3X78fK1oEYH9d/7vwdhvP14xXp5cdwlO61UE/tjH24hM1/Brs3Hr7F53GY0djYcndgZR3vrq3ooB1ElcyWT+6PQRpOdZsuVv7ywcTBStV08Dq4G0CXB72PVc2p0vJXcw6eprer8gnvdSu7bPlafm1+DgbeS+9YPwKi//XizEep+pQXGd/XhX9tD2PV+e17+8RBHo7UA2NsqdA6uwMSeda0ysctBVMmcyeT+CIzOfkRvzUQIhSqP31QTO4B7ZXh1t/rv/C3nV3ff3fLOf/zNI+TN/8s7nm8a4Jjzdwdhp4Gzv939oQHqXw2lKDopg2M5iV1jZ0OWwUg5Z4dSL9hVWuQgqmTOZHJ/SMJo5PpBF3SJAv828WjccxK7vRN0mgTOBeykc79iXE7l7n28oGsCdPwor889j72T+ngpSkzLwkVjR7f6FXmxVTVWHIgq9YJdpUUOokrmTib3h5T0xZtoj6fi83hF3OrYql0jHv5qQg15tnSDyb3f9k8Q2mgUE8XRsU4Fjk3sjI2NOqg4pbcZVLwsIXIQVTJ3Mrk/hPStK7j+45+41HDDZ+5WsDeDFZQhz0LIs/wVHk67du1K9daf/XaayuWcGNwyMC+xWzM5iCpZArktzAPSx8VxddJM7F1tqLxoLYo5JHYT+uXIVb77+xL/3UwzdSilQg6iSpZCJvcHILKziX77bQwZevwXr8K2QoCpQzKp09eSGbvuGM0CvRjfrY6pwykVuYOo7zZ5Vw6iSmZNdss8gBtv9CXj0Dn8pk/HsW59U4djUknpWYxYGoGHkz1zBjbE3tb62wnaTC1fRXwlB1EliyCTexFp54wnMfwcXm1r4PGU/MX+61wc15N1/PRKC6ud6nin2Ydnk5yVLAdRJYsgk3sR6HZt5Nq3P+NcxQnfr1ebOhyz0KtBZZpV86KSh5OpQykVchBVsjTW/7f0IzJciyT6nbHYOipUXrASxdHZ1CGZ1I4zN9h3MR6gzCR2OYgqWSKZ3O9BGAxcfeNV9GkC/2kTsQuobeqQTOpiXCqjVx7hi61nEHeupLVichBVskQyud9D3OzZpJ24TIV3X8fpCTOoy25CqZl6Xl0agYOdDXMGNCozfc5yEFWyVLLPvRApS/+P+HkL8OzXl3LD3jB1OCYlhOD9tUe5GJfKsmHNqexZNrpjQA6iSpZLttwLkHloBzFfzMexkoYKH35o6nBMbuvJ6/x2/DrjutamVU0fU4dTanIHUZ+v/bwcRJUsjmy538GQcJ3oN0ah2IL/d4uw0WhMHZLJdQ6uyLxBjehSt6KpQyk1chBVsnSy5Z6PMBq5NuxpspKMVJ70Lva1Gpk6JJO6mpTBlYR0bGwUnqxXqUx1S8hBVMnSyeSeT/wno0g5nYTvs2G49H7Z1OGYlC7bwIilhxi4YD/ZBuP9n2BF5CCqZA1kcs+RunsPcav/wr1lHbwmfm/qcExKCMGE9Sc4cTWZiU8Fl4nSAvnJQVTJGpSt39pCZJ0+RMy776CpUYNKc5eh2JTtt2XZ/ijW/RvNmx2D6FingqnDKVW5g6j9a/eXg6iSRSvzA6rGlESiX3kRoTPiP+snbJzL9grUo1eS+OTXZGDEVQAAD5JJREFUk7R/rDxvdgwydTilSg6iStakTCd3YTRy/ZXeZMYZ8P/fyzhUq2bqkEwuqIIrg1sGMrpDUJnYeCO//Huiuju4mzocSXokZTq5J057A+3hWHx6NMBt4DumDseksvRG9EYjzg52/K9HsKnDKXVyEFWyNmW2czl9yzJuLN2Oa5AbPtOWmjock/t08ymenruX9Cy9qUMxCTmIKlmbMpncs2/EEj3lW+y9nPFbuA7Frkz/AcO6iGh+2HeZNkE+ODuUvfdCDqJK1qjM/SaLjHSuvvkmxgwdVX/6CVvfKqYOyaROXNUyfv1xWlT3YlzXslf1Ug6iStaqzCX3G6OeIePIZSr/33Qca9UydTgmlZimbpVXztmBOQMaYVfG5rODHESVrFeZSu5JX48lcc9lvDoE4d5dDpplZBuo4K7ho6fq4uNa9mroyEFUyZqVmeSeEb6e69//gnNVJ3xnyq3yhBD4eTqxbmSrMjuAKAdRJWtWJv4O10df5OqY8epWeYtWo2jKxobOhfn9xHVeXRZBaqa+zCY1OYgqWTurT+7CYCBm3Hj0GeA//RPs/MvWqss7XYhN5d3VR7ienIm9bdlM7HIQVSoLrD65x331NWmHjlFx0ic4dehn6nBMKkWXzYilh3C0t2XeoEZo7GxNHZJJ5C/nKwdRJWtl1X3uyQunED9/OZ7P9sOzX9lO7EajYMyao0TGp7N8eHMqeZSdrfLyk4OoUllhtS33zAN/cm3mMpwq2VNh3HumDsfkYrQZRFxOZHy3OrSo7m3qcExGDqJKZYVVttwNcVeJHv0mih1Unr8UG2e5k45/OWf+eLst5ZztTR2KyeQOog6oM0AOokpWz+pa7kKvJ2Z4H7K0Rvwnj8W+ZqipQzKpK//f3r1HR1nfeRx/f5OQhBAu6kIwCVe1EUEuGkWWoomg2N0i7p4eEC09h6Nlz1qWmyKX9dZVofQUCOy2WGrLFpFyENRaD5QeXQbiYiNQxHAnB0NICBIC5AK5z3f/SJBEwhJhkt/MM9/XX8zzzMzzOd+T+fLM7/fM8ztzgf/8+Ah1fuXGDtFhe7Zqk6gm3HiuuRdnzKf8UAkJEx4gbswk13Gcqqiu41/e2sVvMo/yVWml6zhO2SSqCTeeau7lmZkU/XYtnUY/yA0vLHcdx6n6pfKyOXCylKUThpDYJTwnUMEmUU148kxzr87eTsH0qcSkpHDzz34R9kvl/X57Lu/uLmDGqO+QntLNdRynbBLVhCNPTKj6S4rJ/9fJUFNL8sKfEtE+fM9SAYrLq1j450OM6pfAlPRbXcdxKq8qj3XHbBLVhJ+An96KSAcR+b2I/EZEngz0+3/ti3XULerPiC1jOTH+HqpO15I07xmiUwa22iGv5FRpJeN+/SmnytyOa58qrWR+VgV1qqz58VAWjx8UdkvlNeZXP++ceccmUU1YalFzF5HficgpEdn7je2PiMghEckRkTkNm/8ZWK+qPwYeDXDeel+sgz9NJbIsn5IjHSjLjaHrwAvE39G9VQ53Ncs+PsKO3DMs++iIk+NftOSjwxw+62fZR0cY0vMGOsWG72WPUD+Jmluda5OoJiy1dFjmv4H/AlZd3CAikcAvgYeAfGCHiHwAJAPZDU+rC1jSRgo2zCVJKrhwKpqvdnciPqmCm/qVkL9hLosPfIfkG9oz8+H6r+CL/3KI/LMVTV5/S7d4ftIwXLFg4wGKyqqa7L8jsRNPj+gLwMt/3EtZZdOl54b07MLEYb1JeWETVbX+r7evzspjdVYeURFCzvx/QFV5dt2ey/I/kNKVsYOTqKypY9672Zftf7h/dx4Z0J2SCzX89E/7Lts/ZnAi6SndOFVayc82HeT9zwvwK7Tr8ldibz7G+jxYvxQiIoTHBie1pKSetK1gG31j+tokqglLLWruqrpNRHp/Y/O9QI6qHgUQkbXAWOobfTLwOf/PNwMRmQxMBkhISMDn87U49ANSDEDluXZEd6wlceg5RCCRYjIPniC5YwR3RRcCsC27koJyf5PXnzgZQX/Jr9+/t4LTFdpk/+mir7i1Lg+AzP0VlFU33V925it6VOWy8LsxzP2kgopGvT8mEkYkReLz+VBVMg82/Y8FQMpP0fncESprm98fW1FE7OmDlFQ1v79zdRFS2I5TF/xkHqykSwxUtN9JVPf38dd0QjSK6EiIjxa25x27Wjk9q2NERx5t/yhbt251HSUolJeXf6vPmdd5vR6iqld/FtDQ3D9U1QENj38APKKqTzc8nggMBWZTf5ZfCXyiqm9f7b1TU1N1586dLU+9ZACUHAfAXwcRF+9/1bkHzNh75de1gn9/L5s1n+URHRlBdZ2fJ+/tyWv/dGebZthXvI8nPpxI9fle1OZPolYjneQIRj6fj7S0NNcxgoLVoikv1ENEdqlqanP7rudqmeZm6lRVzwOt++uhkS9R9d4UYrTq68ZeJTHEjHypVQ/bnNPlVTw5tBdP3NuTNZ/lUdTGk6pnKs8wY8sMoujEw91ncWdyBYf9CW2ewxgTXK6nuecDjVeXTgZOXF+cFho4jhiAj/8DLclHOifXN/aB49rk8I39euKl/zRfe2xAmx671l/L89uep7iimFXfX0X/m/rj8/n4UVrb5jDGBJ/rae47gNtEpA9QADwOPBGQVC0xcBwMHMdWD3y1ulbLdi8jqzCLV4e/Sv+b+ruOY4wJIi29FPIPwKdAiojki8hTqloLTAE2AweAdap6+aUdplVszt3Myr0rGZ8ynsdufcx1HGNMkGnp1TITrrB9I7AxoInMVeWczeHF/32RQV0HMfue2a7jGGOCUHjfgCUElVWXMd03nbioOBanLaZdZHj/UMkY0zxP3FsmXPjVz7xP5lFQVsCbo9+kW1x43xDMGHNlduYeQlZ8sQLfcR/P3fMcdyfc7TqOMSaIWXMPEdvyt/Grz3/FmL5jeOL2trsoyRgTmqy5h4DjpceZkzmHlBtTeHHYi3ZPcmPMVVlzD3IXai4wzTcNQViStoT2UeF9r3pjTMvYhGoQU1Ve+fQVcs7msHzUcpI7JruOZIwJEXbmHsRWH1jNpi83MfWuqQxPGu46jjEmhFhzD1I7Tu5g0c5FjOw5kqcGPOU6jjEmxFhzD0Inz5/kua3P0aNjD14b/ppNoBpjvjUbcw8y1XXVzPTNpLK2kpWjVxIfHe86kjEmBFlzDzILPltA9ulsMtIy6Nulr+s4xpgQZcMyQWTD4Q2sP7yep+98mpG9RrqOY4wJYdbcg0R2UTavZ73OsJuHMWXwFNdxjDEhzpp7ECiuKGaGbwbd4rrx8/t/TuTXi8IaY8y1sTF3x2r9tczaNotzVed463tv0SW2i+tIxhgPsObu2JJdS9hxcgfzvzuffjf1cx3HGOMRNizj0KYvN7Fq/yom3D6BMbeMcR3HGOMh1twdOXz2MC9vf5kh3YYwK3WW6zjGGI+x5u5AaXUp07dMJ75dPIseWGRL5RljAs7G3NuYX/3M2TaHwvOFrBy9kq5xXV1HMsZ4kJ25t7E39rxBZkEms++ZzeBug13HMcZ4lDX3NrT1+FaW71nO2FvGMj5lvOs4xhgPs+beRo6VHmNu5lz63diPF+57we70aIxpVdbc28CFmgtM3zKdyIhIMtIziI2KdR3JGONxNqHaylSVl7a/xNGSo7wx6g0S4xNdRzLGhAE7c29lq/avYnPuZqbdNY1hicNcxzHGhAlr7q0oqzCLxbsW81Cvh5jUf5LrOMaYMGLNvZUUlhcya+ssenfqzavDX7UJVGNMm7Lm3gqq6qqY4ZtBjb+GjPQMOrTr4DqSMSbM2IRqgKkqr//1dfYV72Np+lL6dO7jOpIxJgzZmXuAvXP4Hd7LeY/JAyfzYM8HXccxxoQpa+4BtKdoDws+W8DwpOE8M+gZ13GMMWHMmnuAnK44zcwtM+ke152FIxbaUnnGGKcC3txF5BEROSQiOSIyJ9DvH4xq/DU863uW0upSMtIz6BzT2XUkY0yYC+iEqohEAr8EHgLygR0i8oGq7g/kcS5ac2ANK0+sJOP9jNZ4+xarrKukoLyABSMWkHJjitMsxhgDIKoauDcTGQa8oqqjGx7PBVDVBc08dzIwGSAhIeHutWvXfuvj7Tq/i52lO4mKcn/Rz22xt3F/x/tdx6C8vJz4+HjXMYKG1eMSq0VTXqhHenr6LlVNbW5foLtiEnC80eN8YGhzT1TVFcAKgNTUVE1LS/vWB0sjDZ/Px7W81qusHk1ZPS6xWjTl9XoEesy9uZ9hBu6rgTHGmBYJdHPPB3o0epwMnAjwMYwxxlxFoJv7DuA2EekjItHA48AHAT6GMcaYqwjomLuq1orIFGAzEAn8TlX3BfIYxhhjri7gl5mo6kZgY6Df1xhjTMvZL1SNMcaDrLkbY4wHWXM3xhgPCugvVK85hEgRcOwaX/53wOkAxgl1Vo+mrB6XWC2a8kI9eqlq1+Z2BEVzvx4isvNKP78NR1aPpqwel1gtmvJ6PWxYxhhjPMiauzHGeJAXmvsK1wGCjNWjKavHJVaLpjxdj5AfczfGGHM5L5y5G2OM+QZr7sYY40Eh3dzDcb3W5ohIDxHZIiIHRGSfiExznSkYiEikiOwWkQ9dZ3FNRLqIyHoROdjwdzLMdSZXRGRGw+dkr4j8QURiXWdqDSHb3But1/o94A5ggojc4TaVM7XAs6raD7gP+EkY16KxacAB1yGCxFLgz6p6OzCIMK2LiCQBU4FUVR1A/d1rH3ebqnWEbHMH7gVyVPWoqlYDa4GxjjM5oaqFqvq3hn+XUf/BTXKbyi0RSQb+EXjTdRbXRKQTcD/wWwBVrVbVc25TORUFtBeRKCAOjy4oFMrNvbn1WsO6oQGISG9gCJDlNolzGcDzgN91kCDQFygCVjYMU70pIh1ch3JBVQuAXwB5QCFQoqp/cZuqdYRyc7f1Wr9BROKBDcB0VS11nccVEfk+cEpVd7nOEiSigLuA5ao6BDgPhOUclYjcQP03/D5AItBBRH7oNlXrCOXmbuu1NiIi7ahv7G+r6ruu8zg2HHhURHKpH657UERWu43kVD6Qr6oXv82tp77Zh6NRwJeqWqSqNcC7wN87ztQqQrm523qtDUREqB9PPaCqi13ncU1V56pqsqr2pv7v4n9U1ZNnZy2hqieB4yKS0rBpJLDfYSSX8oD7RCSu4XMzEo9OLgd8mb22Yuu1NjEcmAhki8jnDdvmNSx5aAzAvwFvN5wIHQUmOc7jhKpmich64G/UX2W2G4/ehsBuP2CMMR4UysMyxhhjrsCauzHGeJA1d2OM8SBr7sYY40HW3I0xxoOsuRtjjAdZczfGGA/6P96E11t+4z6+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Buildings.value,'--*', label='buildings')\n",
    "\n",
    "plt.plot(Gatherers.value,'o--', label='gatherers')\n",
    "plt.plot(Builders.value, label='builders')\n",
    "#plt.plot(Army.value, label='')\n",
    "plt.plot(Resources.value, label='resources')\n",
    "#plt.plot(Max_supply.value, label='')\n",
    "#plt.plot(B.value, label='')\n",
    "#plt.plot(G.value, label='')\n",
    "\n",
    "plt.yscale('symlog')\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.title(str(T) + ' Estágios')\n",
    "plt.savefig(\"figure.png\", bbox_inches = 'tight',\n",
    "    pad_inches = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Podemos pensar em penalizar a quantidade de recursos flutuantes ao longo do tempo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_Obj2 = cvx.Maximize(Army[-1] - cvx.norm1(Resources))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "problem2 = cvx.Problem(F_Obj2,Constraints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 142 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "-6.999999999988266"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time problem2.solve(solver='ECOS') #SCS #ECOS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Buildings.value,'--*', label='buildings')\n",
    "\n",
    "plt.plot(Gatherers.value,'o--', label='gath')\n",
    "plt.plot(Builders.value, label='builders')\n",
    "#plt.plot(Army.value, label='')\n",
    "plt.plot(Resources.value, label='resources')\n",
    "#plt.plot(Max_supply.value, label='')\n",
    "#plt.plot(B.value, label='')\n",
    "#plt.plot(G.value, label='')\n",
    "\n",
    "plt.yscale('symlog')\n",
    "plt.grid()\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.        ],\n",
       "        [ 2.        ],\n",
       "        [ 2.82985361],\n",
       "        [ 3.65190556],\n",
       "        [ 4.6945136 ],\n",
       "        [ 5.90114649],\n",
       "        [ 7.18539113],\n",
       "        [ 8.59790699],\n",
       "        [10.18007237],\n",
       "        [12.        ]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Army.value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "F_Obj3 = cvx.Maximize(Army[-1] - cvx.norm2(Resources))\n",
    "problem3 = cvx.Problem(F_Obj3,Constraints)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Wall time: 150 ms\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "15.397476770905984"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time problem3.solve(solver='ECOS') #SCS #ECOS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(Buildings.value,'--*', label='buildings')\n",
    "\n",
    "plt.plot(Gatherers.value,'o--', label='gath')\n",
    "plt.plot(Builders.value, label='builders')\n",
    "#plt.plot(Army.value, label='')\n",
    "plt.plot(Resources.value, label='resources')\n",
    "#plt.plot(Max_supply.value, label='')\n",
    "#plt.plot(B.value, label='')\n",
    "#plt.plot(G.value, label='')\n",
    "\n",
    "plt.yscale('symlog')\n",
    "plt.grid()\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 1.        ],\n",
       "        [ 2.        ],\n",
       "        [ 3.6       ],\n",
       "        [ 5.76      ],\n",
       "        [ 9.216     ],\n",
       "        [14.7456    ],\n",
       "        [21.57656691],\n",
       "        [31.6128801 ],\n",
       "        [43.66292576],\n",
       "        [58.53170789]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Army.value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}