{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "71cbf812",
   "metadata": {},
   "source": [
    "# Capítulo 7 — Consumo, ahorro e inversión\n",
    "## Diez problemas numéricos resueltos con Python\n",
    "\n",
    "Este notebook resuelve los diez problemas de `cap07_problemas_numericos.html`.\n",
    "Cada problema se resuelve **dos veces**:\n",
    "\n",
    "1. **Forma cerrada** — la solución analítica del apunte.\n",
    "2. **Optimización numérica** — planteando el problema de optimización tal como está\n",
    "   en el enunciado y resolviéndolo con **`scipy.optimize`** (`minimize_scalar`,\n",
    "   `minimize` con SLSQP y restricciones, `brentq` / `root_scalar`).\n",
    "\n",
    "Que ambos caminos coincidan hasta la última cifra es la verificación de que la\n",
    "derivación analítica está bien hecha. En los problemas con restricciones activas\n",
    "(P07) o con dinámica (P09, P10) el enfoque numérico además muestra cosas que la\n",
    "fórmula cerrada esconde: el multiplicador de Lagrange, la senda de transición y la\n",
    "diferencia entre la $q$ miope y la $q$ *forward-looking*.\n",
    "\n",
    "**Notación** — `y1, y2` ingresos; `r` tasa real; `beta` factor de descuento;\n",
    "`sigma` aversión relativa al riesgo (EIS $=1/\\sigma$); `W` riqueza;\n",
    "`K` capital; `phi` costo de ajuste; `b` deuda/PIB.\n",
    "\n",
    "*Fuente de enunciados y parámetros: Cap. 7, «Análisis macroeconómico intermedio»\n",
    "(M. Villena, UTFSM, 2025).*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "dcee60b7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:23.506946Z",
     "iopub.status.busy": "2026-08-04T12:30:23.506777Z",
     "iopub.status.idle": "2026-08-04T12:30:24.370131Z",
     "shell.execute_reply": "2026-08-04T12:30:24.368403Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "scipy, numpy, pandas listos.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import minimize_scalar, minimize, brentq, root_scalar, NonlinearConstraint\n",
    "\n",
    "pd.set_option(\"display.float_format\", lambda v: f\"{v:,.4f}\")\n",
    "plt.rcParams.update({\n",
    "    \"figure.figsize\": (7.2, 4.2), \"figure.dpi\": 110, \"font.size\": 10,\n",
    "    \"axes.grid\": True, \"grid.alpha\": .3, \"axes.spines.top\": False, \"axes.spines.right\": False,\n",
    "})\n",
    "\n",
    "REF = {}          # valores de referencia del HTML, para la verificación final\n",
    "def chk(nombre, calculado, esperado, tol=5e-3):\n",
    "    \"Registra una comparación contra el valor publicado en el HTML.\"\n",
    "    REF[nombre] = (calculado, esperado, abs(calculado - esperado) <= tol)\n",
    "    return calculado\n",
    "\n",
    "print(\"scipy, numpy, pandas listos.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ece22f89",
   "metadata": {},
   "source": [
    "---\n",
    "## Problema 01 — Restricción presupuestaria intertemporal y el precio del tiempo\n",
    "\n",
    "Un hogar vive dos períodos con dotación exógena $(y_1,y_2)$, presta o pide prestado\n",
    "libremente a la tasa real $r$ y no deja herencia.\n",
    "\n",
    "**Hogar A:** $y_1=100$, $y_2=126$, $r=5\\%$, mercado de capitales perfecto.\n",
    "\n",
    "De $s_1=y_1-c_1$ y $c_2=y_2+(1+r)s_1$ se obtiene la **restricción intertemporal**:\n",
    "\n",
    "$$c_1+\\frac{c_2}{1+r}=y_1+\\frac{y_2}{1+r}\\equiv W$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "42dc49d1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.373323Z",
     "iopub.status.busy": "2026-08-04T12:30:24.372857Z",
     "iopub.status.idle": "2026-08-04T12:30:24.383685Z",
     "shell.execute_reply": "2026-08-04T12:30:24.382094Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a) W = 220.00\n",
      "(b) c1_max = 220.00 | c2_max = 231.00 | pendiente = -1.05\n",
      "(c) s1 = -30.00  ->  c2 = 94.50   (deudor neto)\n",
      "    verificación VP:  130.00 + 94.50/1.05 = 220.00 = W  ✓\n",
      "(d) W' = 214.55   ΔW = -5.45 (-2.48%)  ->  el deudor PIERDE\n"
     ]
    }
   ],
   "source": [
    "y1, y2, r = 100.0, 126.0, 0.05\n",
    "\n",
    "# (a) riqueza\n",
    "W = y1 + y2/(1+r)\n",
    "chk(\"P01_W\", W, 220.0)\n",
    "\n",
    "# (b) interceptos de la recta presupuestaria\n",
    "c1_max, c2_max, pendiente = W, (1+r)*W, -(1+r)\n",
    "\n",
    "# (c) plan concreto c1 = 130\n",
    "c1 = 130.0\n",
    "s1 = y1 - c1\n",
    "c2 = y2 + (1+r)*s1\n",
    "chk(\"P01_c2\", c2, 94.5)\n",
    "\n",
    "# (d) alza de la tasa\n",
    "r_alto = 0.10\n",
    "W_alto  = y1 + y2/(1+r_alto)\n",
    "chk(\"P01_dW\", W_alto - W, -5.4545)\n",
    "\n",
    "print(f\"(a) W = {W:.2f}\")\n",
    "print(f\"(b) c1_max = {c1_max:.2f} | c2_max = {c2_max:.2f} | pendiente = {pendiente:.2f}\")\n",
    "print(f\"(c) s1 = {s1:+.2f}  ->  c2 = {c2:.2f}   ({'deudor' if s1<0 else 'acreedor'} neto)\")\n",
    "print(f\"    verificación VP:  {c1:.2f} + {c2:.2f}/{1+r:.2f} = {c1 + c2/(1+r):.2f} = W  ✓\")\n",
    "print(f\"(d) W' = {W_alto:.2f}   ΔW = {W_alto-W:+.2f} ({(W_alto/W-1)*100:+.2f}%)  ->  el deudor PIERDE\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "360e9e94",
   "metadata": {},
   "source": [
    "**Un uso de `brentq`.** Como $W(r)$ es monótona decreciente, se puede invertir\n",
    "numéricamente: ¿a qué tasa la riqueza de este hogar cae un 10%?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d6abe274",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.386466Z",
     "iopub.status.busy": "2026-08-04T12:30:24.386228Z",
     "iopub.status.idle": "2026-08-04T12:30:24.570078Z",
     "shell.execute_reply": "2026-08-04T12:30:24.568409Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W(r) = 0.90·W  cuando  r = 28.5714%   (comprobación: W = 198.00)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArkAAAHACAYAAACmm3AgAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjksIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvJkbTWQAAAAlwSFlzAAAQ6wAAEOsBUJTofAAArlNJREFUeJzs3XVYVNkbB/DvnQGG7lQpC7ATEQPbH2IHtmJ316qr4rq6dq6da62BjWBhY7vqWmAAEoJ058yc3x8uV8YBBQWGeD/PM886555773vvYWbfuffcczjGGAMhhBBCCCFliEDRARBCCCGEEFLYKMklhBBCCCFlDiW5hBBCCCGkzKEklxBCCCGElDmU5BJCCCGEkDKHklxCCCGEEFLmUJJLCCGEEELKHEpyCSGEEEJImUNJLiGEEEIIKXMoySWEEEIIIWUOJbmEEEIIIXnYsmUL1q5dC4lEouhQSAFRkksIISWUlZUVWrVqpegwwHEc3NzcFB1GidWqVStYWVkpOgyem5sbOI4r1n2WtHOQH/n5fK1YsQKzZ8+Gvb09hEJh8QRGCg0luUQhrl+/Do7j8Pvvvys6lCLx9OlTuLu7IygoSNGhkCLg7u6O06dPKzqMMmnfvn1Yv369osMgxez69etwd3dHfHy8okPhnTlzBr///js8PT3RvHlzRYdDfgAluYQUgadPn2Lx4sWU5JZRixcvLpYk19/fH5cuXSry/XxPWloadu7cWSz7oiS3fLp+/ToWL15crEnutz5fEokEb9++hZeXV4m4m0J+jJKiAyBEURITE6Gtra3oMBRGIpEgIyMD6urqig6F5JCZmQmpVApVVVWIRCJFhwMAUFVVVXQIZV55/z5ShG99voRCIWbOnFmM0ZCiQFdySYkmlUqxbNkytGrVCmZmZlBRUUHFihUxdOhQBAcH52sbQUFB4DgO7u7uOHHiBOzt7aGuro6uXbvydZ48eYLevXvD2NgYKioqqFy5Mn755RekpqbKbS8qKgrTp09HtWrVIBKJYGhoiBYtWuDIkSMAPveHGzZsGACgdevW4DhOpk9jYR+Th4cHGjRoADU1NZiZmWHq1KlITk6Wqe/u7g6O4/Dq1SvMnj0blpaWEIlEOHbsGACAMYadO3fC3t4eGhoa0NDQgKOjY65XKy9cuIA2bdrA2NgYqqqqqFSpEpydnXHr1i2+zrf6BObWDy77/Fy7dg3NmjWDhoYGDA0N4ebmhsjIyFyPJber5Hn1C8xv+4aGhmL06NGwtraGqqoqDA0N0bBhQyxbtgzAl242APDXX3/xbZvzWC9duoT+/fujSpUqUFNTg7a2Nlq2bIlz587JxZV9nmJiYjB69GiYmZlBTU0N9+7dy/NcFWT7eck+Tx8+fECvXr2gp6cHDQ0NtG/fHv/8849c/a//fi0sLFC9evVct3379m1wHIcFCxbwZVKpFBs3bkTdunX5mNu0aYPLly/L7efGjRv48OGDzLm9fv06AMDPzw8TJkxArVq1oKOjAzU1NdSuXRurV6/O90NBcXFxmDVrFqpVqwY1NTXo6emhdu3amDp1qlzdQ4cOoUmTJvxnwsHBgf+c5yY/57Owv4/yqzDOHQC8e/cOPXr0gI6ODrS0tNChQwc8e/Ysz/oXLlxA69atoa2tDTU1NdSrVw+bN28GY4yv06pVKyxevBgAYG1tzbe7u7s7ACApKQkLFiyAg4MDjIyMoKKiAisrK0ycOBGxsbG57vfs2bNo164d9PT0oKqqisqVK2PkyJGIjo7m6+TVJzc/MQNfPr+JiYmYNGkSzMzMIBKJ0KBBA1y8eDG/p5QUIbqSS0q0zMxMrFixAj179oSLiwt0dHTw77//Ys+ePfDx8cG///4LfX39fG3rzJkzWL9+PcaOHYtRo0bxX1gXLlxA9+7dYW5ujkmTJsHExATPnj3D2rVr4evri2vXrkFJ6fNHJTg4GM2aNUNYWBgGDBiAKVOmIDMzE0+ePIGnpyf69euHMWPGQCQSYceOHZg3bx7s7OwAAFWqVCn0Y/L09MTatWsxfvx4jBgxAj4+PtiwYQOePn0KHx8fuQclBg4cCCUlJUyYMAGampqwsbEBAAwbNgz79+9Ht27dMHDgQADAyZMn0aNHD2zduhVjx44FANy8eROdO3dGjRo1MGvWLBgYGCAiIgJ37tzBkydP0KJFi3zFnZsnT57Aw8MDw4YNw6BBg/DgwQP89ddfuH//Ph4+fAhNTc0f2m5+21csFqN9+/YICQnBuHHjYGtri+TkZPj5+eHq1at8Wx44cACDBw9GixYtMHr0aLn97du3D58+fcKgQYNQqVIlREVF4a+//kLXrl1x5MgR9O3bV26ddu3awcDAAL/88gukUilMTU3zPJ4f2X5uUlJS4OTkhPr16+P3339HSEgItmzZgpYtW8LX1xd169bNdT2BQIAhQ4Zg6dKl8PX1RbNmzeTiAyDzoJqbmxsOHDiAZs2aYdmyZUhOTsauXbvQsWNH7N+/H4MGDQIAHDhwAEuXLkV0dDTWrVvHr5/9Gbp+/TquXbuGzp07w9raGunp6fDy8sKsWbMQEBCALVu2fPe4XV1dce3aNYwePRr16tVDZmYm3r9/jytXrsjUW7hwIZYsWYLatWtj0aJFYIzh4MGD6N+/PwICAjBv3ryfOp+F8X1UEIVx7kJCQuDo6Ij4+HiMHTsWdnZ2uHfvHlq1agUDAwO5+rt378aoUaNgYWGBWbNmQVNTEx4eHpg4cSKePXuGHTt2AADmz58PfX19nDp1CuvWrYOhoSEAoE6dOgCAsLAw7NixAz179kTfvn2hqqqKBw8eYPv27bh9+zYePnwIZWVlfr/ZbVelShVMmjQJlSpVQnBwMM6dO4fQ0FB++7nJb8w5dezYEbq6upg7dy5SU1Oxfv16dO3aFW/fvoWFhcV3zyspQowQBbh27RoDwJYsWfLNelKplKWkpMiVX758mQFgK1eu/O6+AgMDGQCmpKTEnj9/LrMsLS2NmZqaMnt7e5aeni6zzMPDgwFg+/bt48tcXFwYAHbixAm5/UgkEv7fe/fuZQDYtWvXivSYOI5j9+/fl1k2efJkBoDt3buXL1u0aBEDwJo3b84yMzNl6p8+fZoBYGvXrpXbT5cuXZi2tjZLTExkjDE2bdo0BoBFRER8M76hQ4eyvL5eLC0tmZOTk0wZAAaAHT9+XKZ87dq1DABbtGiR3LEEBgbKbdvJyYlZWlry7wvSvs+ePWMA2PLly795bNnxDh06NNdlycnJcmUpKSmsWrVqrEaNGjLl2eepX79+TCqVyq2X27kqyPbz4uTkxACwCRMmyJQ/evSICQSCXNsn5/G+ffuWAWAjR46Ui0NbW5u1aNGCL/Px8WEAmLOzMxOLxXx5ZGQkMzY2Zrq6uiwpKUkmtpxtmFNux84YYwMGDGBCoZCFh4d/67BZfHw8A8DGjh37zXpv3rxhAoGA1a1bV+azmpyczGrVqsWEQqHM319Bzmdhfh/lJbfP38+eO8YYGzx4MAPATp06JVP+xx9/MAAy7RYfH880NTWZmZkZi4qK4suzsrJY+/btGQB269Ytvvxbn+uMjAy57y3GGNu5cycDwI4dO8aXPXjwgAFgDg4OuR5zzu/prz9fBY05+zyPHj1aZh93795lANjcuXPl9k+KF3VXICUax3F8n1GpVIr4+HhER0ejXr160NHRwf379/O9LRcXF9SqVUum7MqVK4iIiICbmxuSkpIQHR3Nv1q2bAl1dXX+tlNsbCy8vLzg5OSEnj17ym1fIMjfx6kwj6l9+/awt7eXKZs/fz4A4MSJE3L1Z8yYIXPFA/h89UxNTQ19+/aVOf7o6Gh0794diYmJuHv3LgBAV1cXAHD8+HFkZWXlO878qF69Onr37i1TNmHCBOjq6uZ6LPlRkPbV0dEBAFy7dg0RERE/fBwaGhr8v1NSUhATE4PU1FS0adMGr169QlJSktw6c+bMyfeQTz+y/bx8fTWyYcOG6NixI27cuCFzW/drVatWRfPmzXHs2DGkpaXx5SdPnkRiYqLMVdzstluwYIHMnQUjIyNMmDAB8fHx8PHxyVe8OY89IyMDsbGxiI6Oxv/+9z9IJBI8evTom+urqalBVVUV9+/fR0BAQJ71Tp8+DalUijlz5sj0WdfQ0MCsWbMgkUhw5swZufUKcj5/9vuooH723EmlUpw+fRo1atRA9+7dZZZNnTpV7k7LpUuXkJycjEmTJslcOVVSUsKvv/4KIPfvqNyoqKjw31tisZj/zmzTpg0AyHxnHjp0CADwxx9/yBxztm99T/9ozF/33XVwcICmpibevHmTr+MjRYeSXFLinT59Go6Ojnz/OSMjIxgZGSEhISHP/li5ya0P4evXrwEA48eP57eb/TI2NkZqaio+ffoE4HNfNMYYGjRoUGKOqUaNGnJlxsbGMDAwwLt37+SW5XUO0tLSULFiRblzMGLECADgz8HEiRPRqFEjTJo0CXp6emjfvj2WLl2KwMDAfMdckGNRUVFBlSpVcj2W/ChI+1paWmLRokW4fPkyKlSogLp162LChAly/Ua/JygoCIMHD4aBgQE0NTVhaGgIIyMjbN++HcDnPqFfy6t/a2FtPze6urqoUKGCXHl2O7x///6b6w8bNgyJiYk4efIkX7Zv3z6oq6ujT58+fFl2Mlm7dm25bWSXfW9f2VJTUzF37ly+z7SBgQGMjIwwZMgQAPjuZ0dFRQUbN27Eq1evUKVKFdjY2GDkyJE4efKkTL/UH4m5oOfzZ7+PCupnz11kZCSSkpJy/Zyqqqry3bGyFWa7A8DOnTtRv359me/M7H3mjD07sfyR7+kfjbly5cpyZQYGBoiJiSlwDKRwUZ9cUqKdOXMGPXr0QKNGjbB27VpYWFhATU0NANCvXz9IpdJ8byu3UQSy11+6dKncFdFsenp6PxB53grzmAoqr3Ogo6MDDw+PPNerWbMmAEBfXx/379/HnTt3cOXKFdy6dQuLFy/G4sWLceDAAb4/6LeuSorF4p86hoJsu6Dt6+7ujmHDhsHb2xu3bt3CiRMnsGXLFnTr1g2nTp367tXW5ORktGzZEgkJCZgyZQrq1KkDbW1tCAQC7NmzB3///Xeu7ZvfES5+dPtFoU+fPpg0aRL++usvDBw4ECEhIbh27RoGDRoELS2tItnnwIEDcebMGYwcORItW7aEoaEhlJSU8PjxY74/8/eMGjUKXbt2hbe3N27evIkrV65g9+7dsLe3x40bN4ptJIni/j4qjHOnKBs2bMDUqVPRrl07bNmyBRUqVIBIJIJYLIazs7PCY89rkgj21YNqpPhRkktKtL/++guqqqq4ceOGzP8UUlJS8n3F6luyr6aoqqqiXbt236xbtWpVcByHJ0+efHe730qGCvOYXr16JVcWGRmJmJgYNG3aNF/bqF69Ovz8/FC/fv1cHx75mkAgQPPmzfnB0UNCQtCgQQPMmTOHT3KzH5yLjY2VeYguLS0N4eHhqFq1ar6OJfuhoJz1c27765EUAgICoKKiInNsQP7aN5ulpSXGjh2LsWPHQiwWw83NDYcOHcKNGze+O17m1atXERISgt27d2P48OEyywpjnNnC3H58fDw+fvwod/Uxux2+vjL3NS0tLfTq1QuHDh1CaGgo9u/fD6lUKjczWvZ2Xr58iSZNmsgse/Hihdy+8vrsJCQk4MyZMxg0aJDcwz9v3779ZqxfMzExgZubG9zc3MAYw7x587B8+XIcOXIEbm5uMjF/3aUgt5iBnz+fwI/9veZHYZw7Y2NjaGlp5fo5TU9Px/v372W+P3Kew86dO8vUL0i7A5+/M62srHDx4kWZ7gbZV75zql69Ory9vfHkyRM4OTnl69h+NGZS8lF3BVKiCYVCcBwn90t9yZIlhfLrvWPHjjAxMcGqVaty7YcpFov5W2H6+vro1KkTrl+/nmt/vJzxZPdPy+0WYGEe0+XLl/HgwQOZsqVLlwJArv2Gc5N9u3L27Nm5XnnIeXs0KipKbrm5uTlMTExkbs1lj9rw9RPra9asyfMY37x5I3c1efPmzYiPj5c5lry2ffDgQYSHh8uUFaR9ExIS5PoZKykp8U/F5zw+TU3NPNsWkL+C8++//xbK5BGFvf3sodGyPX78GBcvXuSv9H3PsGHDIJVKsX//fj4R+fqHQHbbLVu2TKbto6OjsXnzZujq6qJt27Z8uaamJuLi4uSOMTu5+bo8KSkJa9eu/f7B4vMt+6+H4eI4jr+1nd3G3bt3h0AgwOrVq5Geni6z/qpVqyAUCtGtWze57f/s+SzI32tBFMa5EwgE6NatG169eiX3t7Z+/Xq5YQvbt28PTU1N/PnnnzI/3iUSCf8d1atXL778e9+ZgOx3LGMMv/32m1zd7NFh5s2bJ9NfPOd6eSlozKTkoyu5RKFu3LiR57L58+ejT58+8PDwgJOTE3/V5eLFi3j16lW+/qfxPerq6jhw4AC6desGOzs7DBs2DLa2tkhKSsL79+9x8uRJLF++nL86tXnzZjx58gQ9e/bEgAED0KRJE0gkEjx58gRisRgHDx4EADRu3BgCgQBLly5FXFwcNDQ0YG1tjSZNmhTqMdWvXx/t2rXD+PHjYWFhgStXruDUqVNo3rw5n7x+T69evTBq1Cjs3LkTz549Q/fu3WFqaoqPHz/i8ePH8PLy4pO/0aNHIzg4GB06dICVlRXEYjE8PT3x8uVLTJw4kd9m//79MX/+fIwaNQovX76EiYkJbty4gcePH+d5jLVr14abmxtu3rwJOzs7PHz4EPv27UP16tVlHuxo164datSogQULFiAyMhLVqlXDo0ePcPbsWVStWlUmUS1I+167dg2jRo1Cjx49YGNjA11dXbx69Qrbtm1DxYoVZa6sOTg44MqVK1ixYgUsLCzAcRz69euHZs2awczMDDNmzEBAQACsrKzw+vVr7Ny5E7Vr18bjx48L1L5fK8ztGxoawtPTE2FhYfzQaZs3b4aqqmq+ZxzLHm93xYoVSExMxKJFi+SuyLVp0waDBw/GgQMH0Lp1a/To0YMfQiwyMhL79++XeWjJwcEBnp6emDhxIhwdHSEUCvlxmf/3v//h0KFDEIlEaNKkCcLDw7F7926YmJjkK943b96gZcuW6N69O2rWrAkjIyMEBARg27Zt0NLS4hPyqlWrYv78+ViyZAkcHBwwcOBAfgix58+fY+nSpXJ3EQrjfBb0+yi/tLS0fvrcAcDvv/+OCxcuwNXVlR9m7969ezh79iyqVKki011IR0cH69evx6hRo9CoUSMMHz4cGhoa8PDwgK+vL0aNGiUzVa6DgwOAzw9hDhw4EKqqqqhVqxZq1aqFPn36YM6cOejYsSN69+6N1NRUnDp1CpmZmXIxNm7cGPPmzcOyZctQp04dDBgwAObm5ggNDcWZM2ewd+9e1KtXL9fjK2jMpBRQxJAOhGQPIfatV1ZWFmOMsd27d7NatWoxVVVVZmRkxAYMGMBCQkJyHV4pN9lD9uQchuprr1+/ZkOHDmWVKlViysrKzNDQkDVs2JDNnTuXBQcHy9QNDw9nEydOZJaWlnzdli1bygxjwxhj+/btY3Z2dkxZWVluCKbCPKZjx46xevXqMZFIxExMTNikSZP4Ib+yfWt4nmyHDx9mrVq1Yjo6OkxFRYWZm5szZ2dntnXrVr7OiRMnWLdu3Zi5uTkTiURMT0+P2dvbs23btskMzcMYYw8fPmQtW7ZkqqqqTE9Pj/Xr14+FhYXlOYTY0KFD2dWrV5mjoyNTU1Njenp6bPDgwbkOV/bu3TvWqVMnpqGhwbS0tFinTp3Y69ev8xx+Kj/tGxAQwMaOHctq1KjBtLW1mZqaGqtatSqbNGkSCwkJkdnemzdvWPv27ZmWlhb/95rt+fPnrFOnTkxPT4+pq6szBwcHdubMmVzb4FtDrTGW+xBiBdl+XrLPU2BgIOvZsyfT0dFh6urqrE2bNuzhw4dy9b/++80pe78cx7GAgIBc60gkErZ+/XpWu3ZtJhKJmKamJmvdujW7ePGiXN2UlBQ2fPhwZmxszAQCgcxQfDExMWzMmDGsYsWKTCQSMRsbG7Zy5Up25coVuWHzchMdHc2mTZvG6tevz/T09JhIJGKWlpbMzc2NvX79Wq7+gQMHmL29PVNTU2NqamqsSZMm7PDhw3L1CnI+C/v7KDe5/V397LnL5u/vz7p168a0tLSYpqYma9++PXvy5Emenz0vLy/m5OTENDU1mUgkYnXq1GGbNm3Kdci8FStWMGtra6akpCRzjiQSCVuxYgWrVq0aE4lErEKFCmzcuHEsNjY2z79NDw8P1rJlS6alpcVUVVVZ5cqV2ahRo1h0dDRfJ6/v2/zGXNChEknx4xijntGElDZBQUGwtrbGokWL+FmBSjOO4zB06FB+IgFStFq1aoWgoKBcZ40jhJCygvrkEkIIIYSQMoeSXEIIIYQQUuZQkksIIYQQQsoc6pNLCCGEEELKHLqSSwghhBBCyhxKcgkhhBBCSJlDSe43iMVihIaGygxwTQghhBBCSj5Kcr8hIiIC5ubmCAsLU3QoRAEkEgkiIiIgkUgUHQpRAGr/8o3av3yj9i8bKMklhBBCCCFlDiW5hBBCCCGkzKEklxBCCCGElDmU5OZD4ukzYFKposMghBBCCCH5REluPkRv3IgPAwYi4+1bRYdCCCGEEELyQUnRAZQWaU+fIqBnLxiOGgWDsWMgUFFRdEiEEEJ+EmMM0dHRSE9Pl3mSnjGG9PR0pKWlgeM4BUZIFIHav3gJBAIoKytDW1sbGhoahbfdQttSWZb9B56VhegtWxDYvQdSHz9WbEyEEEJ+CmMMYWFhiI6ORmZmpswyjuMgEokowSmnqP2Ll1gsRmJiIoKDgxEaGgppIXURpSu5+VBh4wYob92KjLfvAACZAQH4MHAQdPv1hfGMGRBqaSk4QkIIIQUVHR2NpKQkGBsbw8DAQGYZYwxisRhKSkqU6JRD1P7FTyqVIjo6GjExMYiPj4e+vv5Pb5Ou5OaDas2asD5xAkZTJoNTVubL448cRYBLZyRevqzA6AghhPyI9PR0qKioyCW4hJDiJxAIYGRkBGVlZSQnJxfONgtlK+UAp6ICw3HjYH3mNNQaNeTLxZGRCJs0GaGTJiHrU6QCIySEEFIQEokEQqFQ0WEQQv7DcRyUlJQKrbsCJbn5EJvypa+WqHJlWO7fD9PFiyHI0U0h6fIVBLi4IO7IERpujBBCCCFEwSjJzYcBu+7j4L0PkEgZAIATCKDX1xWVPT2h1b49X0+anIwI98X4MHgIMgICFBUuIYQQQki5R0luPiSlS/Dr6RfoucUXz0MT+HJlE2NU2rQRlf7cBCVjY7487fFjBHbrjqjNm8G+emKXEEIIIYQUPUpyC+BZaAK6br6NhWdeICEtiy/XatcOlc97Qrd/P76MZWUhetOfCOjZE6n/PFFEuIQQQggh5RYlufnQp2FFCP4bQYQxYP/dD2i75jpO/hMKxj53YRBqacFs0SJYHj4ElSpV+HUz373Hh4EDEfHbEkgK6WlBQgghRNHc3d3BcZzca9u2bTL1lixZAhMTE1hYWGDfvn1y2xk2bBimTJlS6PFFRkZCS0sLL168AAC0bNkSzZo1k6vXsGFDcByHwMBAmfINGzZAIBAgMrJoHyp/+PAhhg8fjqpVq0JdXR3VqlXD3LlzkZKSIlNv+/bt6NChA0xNTaGtrQ0HBwecOXNGbnuMMSxfvhwWFhZQU1ND06ZNce/evXzF4ufnh/bt20NDQwOmpqaYPXu2zBjSSUlJ0NfXh6+v788ddDGhJDcfprarhrMTm6O+hS5fFp2cienHnqHvjnt48ymJL1dv0ADWp07CcOJEIHu4McYQd/gwAlw6I+nq1WKOnhBCCCkaampquHv3rsyrZ8+e/PJLly5hzZo12LRpE8aNG4eRI0fC39+fX/7gwQN4eXlh8eLFhR7b0qVL0apVK9SqVQsA0KxZMzx+/BgZGRl8neTkZDx79gzq6uq4c+eOzPp37txBtWrVYJyjO2JROHr0KN6+fYvZs2fDy8sLU6dOxY4dO9ClSxe547G0tMTWrVtx4sQJ1KlTB927d8dff/0lU2/FihVYtGgRpk2bBk9PT5iZmaFDhw4I+M6zQnFxcWjTpg0yMzNx8uRJLFu2DDt27MD06dP5OlpaWpg0aRLmzZtXeCegKDGSp5CQEAaABQUFMcYYk0ik7O/7H1jdxReZ5RxP/lVl7nm2zOsVS07Pklk//e1bFtivP3tlYyvzCpk8hWVFRirikEgBiMViFh4ezsRisaJDIQpA7V/2BQYGssDAwFyXSaVSlpmZyaRSafEGVUikUilLT08v0n0sWrSIaWhofLPOzJkz2fjx4/n3tra2bPPmzXyM9vb2bMeOHYUeW1JSEtPQ0GAnT57kyzw9PRkA5uvry5dduXKFaWlpscGDB7Nx48bx5VKplJmamjI3N7dCj+1rkbnkA4cOHWIA2KNHj/iyqKgouXrt27dntWrV4t+npaUxbW1tNnfuXL4sIyODWVpayhxfbpYtW8Y0NDRYTEwMX7Z9+3YmFApZWFgYXxYUFMQAsKdPn+bvAAvoW5/LgqIruQUgEHDoZ2+BqzNaoW8jc75cLGXYfiMA7dbewIUX4XwXBlHVqrA8dBCmixZCkGMu5qSLF/HepTPijh/n6xJCCFE8xhgyxJL/XtIc/y7+V0H+/+Dm5oZatWrBy8sLdevWhUgkwrlz54rwTOVPRkYG1NTU+Pfq6ur8ldR9+/ZBIpFgxIgRhb5fDw8PAICzszNf5ujoCI7jZG61+/r6wt7eHs2bN5cpDwgIQERERK7dGwqbkZGRXFn9+vUBAB8/fuTLDA0Nc62Xs86dO3eQmJgIV1dXvkxFRQU9e/aEl5fXN+Pw9vZGu3btZGYac3V1hVQqxaVLl/gyS0tL2Nvb59r1pKShaX1/gL6GClb0rgPXxpXw6+mXeB2eCAAIT0jH2IP/oJWNERZ3rQlLA43Pw4317w/N1q0RseR3JPv4AACkiYmIWLAQiWfPwfS3xRBZWyvykAghhADIlEhh8+sFRYcBAPD//X8QKeV/soqPHz9i8uTJ+PXXX2FhYQELC4s864rF4u9uTygUfndK27S0NBgZGSEuLg7Vq1fHtGnTMGrUKH5548aNsWjRIkyYMAEBAQF4+vQpNmzYgMTERMybNw8nTpyAQFD419uuXLmCBg0aQFVVlS/T09NDjRo14Ovri1mzZgH4nOQ6OjrC0dER48aNQ2JiIrS1tfmEt3nz5t/cj0Ty/R8jHMcVeNKR27dvAwBsbW2/W8/Ozo5/7+fnl+t6dnZ2CA4ORlpamsyPjpz8/PwwfPhwmTJdXV2YmZnx283m6OiIy6Vgtle6kvsTGlrq49zEZljYuQY0RV9+L1z3j0L7dTex/sobpGdJAADKpqao9OcmVNywAUKjL7/GUh8+RGC37ojeto2GGyOEEPLD4uLicOjQIbi5uaFNmzaoWrVqrvWCgoKgrKz83dfXfT2/VrVqVaxYsQJHjhzBmTNnUL9+fYwePRqrV6/m6/Tv3x81a9ZE5cqV0a5dO4wbNw7NmzfH4sWL0a5dOzg6OhbqOcj28OFD1KlTR668efPmuHv3LgBAKpXi/v37cHR0RM2aNaGlpcU/oHXnzh0YGRnBxsbmm/tp27btd89j27ZtCxR7dHQ03N3d0a1bN1SrVi3PeocPH8adO3cwc+ZMviwuLg4ikUgmuQc+J/iMMcTFxeW5vbi4OOjq6sqV6+npITY2Vqasbt26ePXqFZKSkuTqlyR0JfcnKQkFGN7cGi51zPD7+dc49+zzbYNMsRTrr7zFqSdhWNy1JlrZGIPjOGh37ACNpg6IXL0G8ceOAQBYZiai1m9Aopc3zJb8BrW6dRV5SIQQQkohAwMDNGnS5Lv1KlSogIcPH363nvV37jAOGjRI5r2LiwsyMzPx+++/Y8qUKVBWVoaSkhLOnTuH4OBgiEQimJiYwM/PD/v27cOLFy8QERGB0aNH4/bt26hSpQq2bt2KRo0afTe27wkPD8+1G0Dz5s2xfft2vH37FmlpaUhMTETTpk3BcRyaNGkCX19fdOjQAXfu3IGDg8N397N9+/bvJnpaOWZH/Z6srCz06/d5ONKtW7fmWe/ff//F2LFjMWzYMHTv3j3f2y8shoaGYIzh06dPBTq+4kZJbiEx0VbFpv710a+xORaceYGAqM9Df3yISYXb3ofoVNsUCzrXgJmOGoTa2jD7bTF0unRG+IKFyAwKAgBkvHmDoH79oTdoEIymTIFQU+MbeySEEFLYVIQC+P/+PzDGIBZLoKT0/Vv2RRlLQZiYmORvuyoqqFev3nfrFfQWO/C5D6eHhwfevXsncxs9Z9eJqVOnYvbs2TAzM4OrqyuUlJQQEhKCP//8E7169cLbt2+hoqJS4H3nlJ6eDpFIJFee3cfW19cXaWlpqFGjBnR0dAB8vgV/69YtJCQk4OXLlxg4cOB391O1atV8dVfID8YYhg8fjgcPHuDWrVswMzPLtd6HDx/g7OwMe3t7bN++XWaZnp4eMjIykJ6eLnM1Ny4uDhzHQU9PL8/96+npISEhQa48Li5Opp8uAP7cpqWl5evYFIW6KxSyZlUN4T2lBWZ1tIGq8pfT6/U8Am3X3MCOm++RJZECANQbN4b1mdMwGDcWUPrv9wZjiDtwAAFduiDp+nUFHAEhhJRfHMdBpCT87yXI8e/ifxU0uc5v/cLqrvAjzpw5g4CAAEybNg3A576zw4cPh4aGBiZMmIDg4GC8efPmp/ejr6+P+Ph4uXJra2tUrFgRvr6+fH/cbE2bNsX9+/dx+/ZtSKXSfD10VpjdFWbOnIljx47h1KlTqJvHHd3o6Gh07NgRxsbGOHnyJJSzhyr9T3Zf3JzDtAGf+9tmj5ubF1tbW7m+twkJCQgPD5fr45t9bg0MDPJ1bIpCV3KLgEhJiAmtq6Jr3QpYfO4lrrz+PJB0aqYEy7z84PE4FL93rw17a30IRCIYT5kCbWdnRCxYiLRnzwAA4vBwhI4dB+1OnWAyby6UcnmqkhBCCCmowuqukJsjR45AV1c31/7AGRkZmD59OjZu3ChzpTY1NRUA+MkPCmPUIRsbG7nJHbI1a9YMd+7cQVpaGhYuXMiXOzg4IDU1FVu3boWamho/wsG3FFZ3heXLl2PdunU4dOhQnklxcnIynJ2dkZmZiWvXrkFbW1uujqOjI7S1tXH8+HE+Uc7KysLJkyfRqVOnb8bg7OyMZcuWIT4+nu+be/z4cQgEAnTo0EGmblBQEHR0dGBqavrdY1MkSnKLkLm+OnYNbYzLrz7B/exLhMV/vqz/5lMyXLffRa8GlTC3ky0MNUVQrV4dlocPIe7vI4hauxbS/z70iV5eSPb1hcns2dDp2UNht80IIYSUDSoqKoXS77Vhw4YYOnQobG1tkZaWhkOHDuHkyZNYv3693BVGAFi9ejVsbW3h4uLCl7Vp0wbLly+Hjo4O9u/fj0qVKn33Ya/8aNasGY7999xLbsuO/zeEZ84rudra2qhRowa8vLzQokWLfHWZKIxYDx8+jLlz52LQoEGwtraWmZ2sSpUqfN/inj174unTp9izZw8+fPiADx8+8PWy+w+rqqpi7ty5cHd3h5GREWrXro0tW7YgJiZG5gG1GzduoG3bttizZw+GDBkCABg7diw2bdqE7t27Y968eQgLC8OsWbMwduxYVKhQQSbmR48ewdHRsUhGxihUhTLabhn19WQQPyM1Q8xWXnjNqs47LzORRO1FF9j+u0FMLPky4Hjmx48seMxYuUkkgoa6sYxCiIXkD00GUL5R+5d9ZWkyiKFDh7KaNWsW6z5dXV2ZlZUVU1VVZWpqasze3p4dPHgw17ohISFMT0+PvXnzRqY8LCyMOTs7M01NTVanTh129+7dQont8ePHDIDc/nIuMzQ0lFs2evRoBoDNnTu32Np/6NChDECur7179/L18qrzdSonlUrZsmXLWKVKlZhIJGJNmjRhd+7ckalz7do1ue0zxtirV69Y27ZtmZqaGjM2NmYzZ85kGRkZMnUyMzOZvr4+2717d6Geh2yFORkExxjNRpCX0NBQmJubIygoCJaWloWyzXeRyVh45gXuvI+RKa9TSQe/d6+FOpV0AXy+XZN04QIifl8KScyXupxIBMOJE2Dg5gYul1/KpPBIJBJERUXByMjohx7AIKUbtX/ZF/TfQ79WVlZyyxhjEIvFUFJSojtopVTDhg3RrVs3mS4J+UXtn7fz589jwIABCAsLg6amZqFv/1ufy4Iq4deZy56qxpo4NLIJNvavDyOtL09+/huagG6bfbHg9AskpGZ9Hm7M2RlVzntCp9eXecBZRgai1qxFYB9XpD1/oYhDIIQQQkq8hQsXYtu2bfwMa6RwrFmzBjNmzCiSBLewUZKrABzHoWvdCvCZ4YRhzawg+O9HImPAgXsf0HbtdZx4HArGGIS6uqiwdCks9u2DsuWXIVgy/PwQ1LcvPv2xnO+/SwghhJDPunXrhunTpyMkJETRoZQZycnJcHJy4kfHKOmou8I3FEV3hdy8/JiABadf4J/geJlye2t9LOlWCzamn5/MlKanI3rLVsTs2QPkmJJRuWJFmLq7Q7PFt6cfJAVDt6vLN2r/so+6K5C8UPsrDnVXKGNqVtCBx1hHrOhVG7rqX/rZPgiMhcvGW/jD6zVSMsQQqKrCePo0WHsch2rt2ny9rLAwhIwahbBZsyH+auo9QgghhJDyiJLcEkIg4NC3sQWuzmiFfo3N+XKxlGH7zQC0W3sD3s/DwRiDqq0trI78DZO5v4BTV+frJp47h4BOLog/fbpQxhkkhBBCCCmtKMktYfQ1VLC8Vx2cGOeIGmZfBnoOT0jHuEP/wG3vQwRFp4ATCqE/dCiqnDsLjZYt+HqS+HiE/zIXISNGIpP6IRFCCCGknKIkt4RqaKmHsxObYVGXGtAUfZmz48abKHRYfxPrr7xBepYEyhUrwnz7dlRYvRrCHHNLp9y5g4AuXRGzew9Yjv67hBBCCCHlASW5JZiSUIBhzaxxdYYTutb9MttIpliK9VfeouP6m7juHwmO46DT2QWVz3tCp3t3vh5LT0fkqlUIcu2LtJcvFXAEhBBCCCGKQUluKWCsrYqN/evj8MgmqGykwZd/iEmF296HGHfwMT7Gp0FJTw8Vlv8Biz27oWz+pV9v+qtXCHLti08rV0GalqaIQyCEEEIIKVaU5JYijlUNcWFKS8zqaANV5S9N5/0iAu3W3sCOm++RJZFCw9ERlc+egf6I4UD20EcSCWL37EFA125IuXNHQUdACCGEEFI8KMktZVSUBJjQuiouT3NCOzsTvjw1U4JlXn5w2XgL9wNiIFBTg8msWbA+fgyqNWrw9bJCQhA8fAQ+zvkF4rg4RRwCIYSQYhIUFASO4/ixR4tSVFQUpkyZgiZNmkAkEn1zRqxz586hbt26UFVVRfXq1bF3716Z5WKxGJMmTYK+vj6qVasGb29vuW20adMG69atK/TjeP78ObS1tREVFQUAsLCwwMCBA2XqMMZgaGgIkUgkN6PalClToK2tDYlEUuix5XTlyhX069cPVlZWUFdXR40aNbBq1SpkZWXJ1Lt8+TIGDBiAKlWqgOM4TJw48bvbnjp1ar7ruru7g+M4ude2bdv4OkFBQdDQ0CiWv8OcKMktpcz11bFraCPsGtIIlfTU+PI3n5LRd8c9TD/2FFFJGVCtUQNWx47CePZscKqqfL2EM2cQ0MkFCec8abgxQgghPy0sLAxHjhyBsbExGjVqlGe927dvo0ePHmjatCm8vb3Rt29fjBgxAh4eHnydPXv24OzZs9i/fz9cXFzQr18/xOYYB/748eOIiIjApEmTCv04fv31VwwdOhRGRkYAgGbNmuHOV3dA/f39ERsbC4FAgEePHsks8/X1hYODQ5FPIrN9+3YkJSXht99+g5eXF4YMGYJFixZh9OjRMvUuXLiAZ8+ewcnJCbq6ut/d7vPnz7Fnzx5oa2t/t242NTU13L17V+bVs2dPfrmVlRV69+6NRYsW5XubhYKRPIWEhDAALCgoSNGhfFNqhpituuDHqs47zyznePKv2osusP13g5hYImWMMZYRHMw+DBvOXtnYyrw+jBzFMkJCFXwUJY9YLGbh4eFMLBYrOhSiANT+ZV9gYCALDAzMdZlUKmWZmZlMKpUWb1CFRCqVsvT0dBYYGMgA5HmchUkikfD/XrRoEdPQ0Mi1XocOHZijo6NMWf/+/ZmdnR3/vnfv3mzlypWMMcaysrKYpqYmO3/+PGOMsdTUVGZhYcEuXbpU2IfA3r9/zziOY48fP+bb/88//2QAWFhYGF9v165dzM7OjrVq1YqtWLGCL09OTmZKSkps8eLFhR7b16KiouTKli5dyjiOk1mWs10sLS3ZhAkTvrndli1bsoULF+arLmPfbuucbty4wZSVlVlkZOQ3633rc1lQdCW3DFBTEWJmRxtcmNoSzaoa8OWJ6WIsOP0CPbb44llIPFTMzWG+excqrFgOYY5fcym3biGgSxfE7NsHVsS3VwghpCRjjEGamQlpZibYf/9V1IsV4C6bm5sbatWqBS8vL9StWxcikQjnzp0rwjMlTyD4fkqRkZGBa9euoU+fPjLl/fr1w+vXr/nb2RkZGVBT+3yXUklJCSoqKny3gOXLl6NBgwZo37594R4AgP3796Ny5cqoX78+X9a8eXMAn6/QZvP19YWjoyOaNm0qU37//n2IxWI0a9as0GP7mqGhoVxZ/fr1wRhDeHg4X5afdsl26NAhBAYGYs6cOYUSY07NmzeHgYEBDh8+XOjbzovS96uQ0qKKkSYOjmgCz3/DscTzFSKTPn8h/BuagO5bfDGwiQVmdbCFTrdu0GjRAp+WL0fi2c9fgiwtDZHLVyDR8zzMfl8CVVtbRR4KIYQoBMvKgn+duooOAwBg8+8zcCoq+a7/8eNHTJ48Gb/++issLCxgYWEBKyurfCXLEonku/UEAkGBEqbcvH//HllZWbD96v8xdnZ2AAA/Pz9YWVmhcePGOHDgAPr06YOLFy8iISEB9evXx4cPH7Bp0yY8fvz4p+LIy5UrV+Do6ChTVrt2bWhra8PX15dPzn19fTFnzhwYGxtj586dfF1fX18oKSnBwcHhm/spqvN9+/ZtiEQiWFtbF2g9AEhKSsKsWbOwbt06qOeYTTU/0tLSYGRkhLi4OFSvXh3Tpk3DqFGjZOoIBAI4ODjg8uXLmDJlSoHj+xF0JbeM4TgOXepWgM8MJwxvZg0B97mcMeDgvWC0WXMdJx6HQqinh4orV8J8504oV6zIr5/+4gUCe/VG5Jq1kKanK+goCCGEFFRcXBwOHToENzc3tGnTBlWrVs33ulWqVIGysvI3X8OHDy+UGAHI9Q3V09MDAL7f7eTJk8FxHExNTeHm5oZly5bBysoK06dPx4QJE34oifsexhgePXqEOnXqyJQLBAI0bdqU75cbHR2NN2/e8Fdys98DwJ07d1CvXj1oaGjIbT+nojjfb9++xYYNGzB27NhvPvSXF3d3d1StWhV9+/Yt0HpVq1bFihUrcOTIEZw5cwb169fH6NGjsXr1arm6devWxf379wsc24+iK7lllJaqMhZ2qYFeDStiwekX+Cc4HgAQk5KJGcef4ejDECzpXgs2LZqj8rmziNq4CbH79wNSKSCRIGbnTiReugizxYuh8Z1fpIQQQhTPwMAATZo0+aF1z507JzdKwNdyuz1eVHR0dHD37l0EBgZCV1cX+vr68PHxwcOHD3HgwAG8efMGo0ePxrNnz1CvXj3s2rULVapU+al9xsXFISMjg3/gLKfmzZtj8eLFSE1NxZ07d2BgYAAbGxtwHIfq1avD19cXVatWxd27d+Hm5vbdfRX2+U5MTETPnj1hbW2NpUuX5nu9bC9fvsTmzZtx7969Aq87aNAgmfcuLi7IzMzE77//jilTpkBZWZlfZmhoiOjoaGRlZcmUFxVKcsu4mhV04DHWER6PQ/GH92vEpX4eWuRBUCw6bbyFEc2tMaVtNZj8MgfaLi4IX7gQGa9fAwCyPgQj2G0YdHr2hMnsWTL9eAkhpCzilJVh8+8zMMYgEYshVFICx3EKi6UgTExMvl8pDzVq1MjX7fOflX3FNiEhQaY8+wqvfo7p6TmOQ+XKlQF8HlJsypQpWLVqFdTV1TFo0CA4ODjAy8sLs2fPxqBBg3D37t2fii39v7uXIpFIblmzZs0gFovx4MEDfvSE7L8LR0dH+Pr6olGjRkhISOD78H5LYZ7vzMxM9OjRA3Fxcbh79+53ryLnZsaMGejTpw+srKwQHx8PAJBKpcjMzER8fDy0tbUL1P6urq7w8PDAu3fv+K4owJdzm56eXixJLnVXKAcEAg6ujc1xdUYr9Lf/MhOaRMqw42YA2q65Ae/n4VCtVRPWx47CeOYMcDk+5AknT+K9S2ckennRcGOEkDKN4zgIVFQgUFEB999/FfUqaHL9M8l4cXVXyN6Pn5+fTHn2+6/76mbbvHkzDA0N0bdvXyQmJuLhw4cYPXo01NXVMXbsWNy7dw/Jyck/FVt2gp2d5OXUpEkTKCsrw9fXl3/oLFv2w2fZD6DlJ8ktrPMtlUoxcOBAPH78GN7e3jDPMdtpQfj5+eHgwYPQ09PjXyEhIdi5cyf09PT47hg/Kz4+HioqKtDS0iqU7X0PXcktR/Q0VPBHzzro08gcv556gVfhiQCAiMR0jDv0D1pWN8JvXWvCauRIaLVvj/BF7kj979aFJCYGYdNnQPPMWZguWgjlChUUeSiEEEIKUXF1VxCJRGjdujU8PDxkHj46evQo7OzsYGVlJbdOVFQUlixZgqtXr8qUp6amAgBSUlIAfE74foaqqiosLCwQGBgot0xdXR3169fHtWvX8PjxY/z+++/8MkdHR4wdOxbnzp1D5cqVYWpq+t19Fdb5njBhAs6dO4eLFy+idu3a362flyNHjvBXsrP169cPTZs2xZQpU2BhYVHg7enq6sr1Cw8KCkL16tV/OM6CoiS3HGpgoYezE5vh4L0PWHPpDZIyxACAm2+i0GH9TYxzqoJxrarAYu8eJJw6jU8rVkD6362l5Bs3ENC5C4ymTYPegP7giniwa0IIIUXvZxKknLIndHj16hUkEgn/vnHjxrC0tAQALFiwAK1atcL48ePh6uqKa9eu4fDhwzh69Giu25w3bx769u3LPxCmra2Nhg0bYsGCBZg5cyZWrlyJxo0bF2jygrw0a9Ysz5EbmjVrhvXr10MoFMLe3p4vr1GjBrS1teHt7Y3Bgwfnaz+Fcb6XLVuGbdu2YdasWRCJRDL9abNjAoAPHz7g4cOHAD7/MHj//j3fLr179waAXEeDUFVVRcWKFdGqVSu+bP/+/Rg+fDh8fHzg5OQEAGjYsCGGDh0KW1tbpKWl4dChQzh58iTWr18v1yXh0aNHaNGixU8fe74Vymi7ZVRpmQziZ3xKSGOT//5HZhIJyzmerOXKq+yq3yfGGGNZ0dEsdPoMuUkkAlxdWZqfv4KPoOjQZADlG7V/2VeWJoMYOnQoq1mzpqLDYAByfe3du1em3pkzZ1jt2rWZiooKq1q1Ktu9e3eu23v06BEzMjJiMTExMuWvXr1izZo1YxoaGszR0ZH5+fkVSvwnTpxgqqqqLCEhQa79T5w4wQCwhg0byq3XoUMHBoDt2LGjUOLIDycnpzzP97Vr1/h6e/fuzbPet+Q2GUT2tnJu39XVlVlZWTFVVVWmpqbG7O3t2cGDB+W29+nTJyYUCpmPj88391uYk0FwjFEny7yEhobC3NwcQUFB/C/QsurOu2gsOPMC76NSZMr/V9MUC7vUQAVdNSTfuIHwxYsh/vhlkGkoKcFg5AgYjhsHQS6d9UsziUSCqKgoGBkZFfn0jKTkofYv+7InHsjtFjljDGKxGEoKfPCMFL+srCxYWFhg+fLlGDBgALV/Idq8eTPWrVuHt2/ffvOcfutzWVD04BkBADhWNYT3lJaY/T8bqCp/+bO48DIC7dbewPYb7yFq3gJVzp2D3pDBQPYfqFiMmG3bEditO1IePFBQ9IQQQsjPU1ZWxi+//IKNGzcqOpQyRSqVYsOGDVi4cGGx/migJJfwVJQEGN+qKq5Md0L7Gl+GoknNlOAPbz902nALDz+lw3TePFgd+RuiHJ3HM4OCEDxkKMIXLIQkMVER4RNCCCE/bezYsejWrRuio6MVHUqZ8fHjR7i5ucmNqVvUqLvCN5Sn7gq58Xn9CYvOvkRoXJpMec/6FTG3kx0MVQWI2b0H0Vu2gGVm8suFRoYwnf8rtDp2KNW3eeh2dflG7V/2UXcFkhdqf8Upk90Vjh8/jm7duqFSpUrQ0NBAvXr1sGfPHrlxWXfv3o3q1atDVVUVdevWhaenp9y2EhISMGLECOjr60NLSwu9e/dGeHi4XD3ybW3tTHB5mhMmtakKFeGXP5WTT8LQZs11HHwUBr3Ro2F95jTUczxpKomKRtjUqQidMBFZERGKCJ0QQr5LKBRCIpEoOgxCyH+yf1wUxsQjQAlKcteuXQt1dXWsWbMG586dg7OzM0aNGoXffvuNr3PkyBGMGjUKffv2hbe3N5o2bYoePXrITUPXt29fXLp0Cdu2bcOhQ4fg7+8PZ2dniMXi4j6sUk9NRYgZHWzgPbUFmlf9MmZfUroYC868RPfNvvBT0oPFX/tg9vsSCHIM4ZJ89SoCXDoj9vBhsJ8cv5AQQgqbqqoqMjMzERMTo+hQCCn3pFIpoqKikJWVBU1NzULZZonprhAdHS038PHo0aNx9OhRxMXFQSAQwMbGBg0bNsThw4f5Oo6OjtDV1YWXlxcA4O7du3B0dMTFixfRoUMHAIC/vz/s7Oxw5MgRuLq65jum8t5d4WuMMXj+G44lnq8QmfRlEGuOAwbYW2B2R1topMQjYukyJF24ILOuWv36MFvyG0RfDQxdktHt6vKN2r/sY4whLCwMSUlJUFFRkWtnqVRaaFeUSOlD7V98pFIpsrKyIJVKoaWlhQoVKhTKuS8xrZfbzB7169dHYmIiUlJSEBAQgDdv3sglqf369YOPjw8/c4i3tzd0dXXRvn17vo6NjQ3q1avHJ8Lkx3Achy51K8BnhhNGNLeGUPC5nxJjwKH7wWiz5jpOfUhHxXVrUWnLFijlmPUl7ckTBPToiahNf0Kao/8uIYQoCsdxqFixIgwNDaGioiKzjDGGjIwMmsq8nKL2L15KSkrQ1taGhYUFKlWqVGg/Lkr0jGe3b99GxYoVoaWlhVu3bgGQn9fazs4OmZmZCAwMhK2tLfz8/GBjYyPXUdzOzk5uruyvJSYmIjHHyADZ/XglEgn128pBXVmAec426FHPDAvPvsI/wfEAgJiUTMzy+BdHH4bgt671UfXMacRs2Ij4v//+nAlnZSF682YkenvDxN0dag0bKPZAvkMikUAqlVLbl1PU/uWHvr6+XJlEIuHvMNKV/PKH2l9xvvedW5D2KLFJ7u3bt3HkyBGsWbMGABAXFwcA0NXVlamnp6cHAIiNjeXrfV0nu152nbysXbsWixcvliuPjY2Furp6QQ+hzDNUAv7sURnnX8Xgz1uhSEj//If56EMcuvzpi771TTDCbTi0mjkiZdVqSP97YjIzIAAhQ4ZApWtXqI8eBa6Q+t4UNqlUioT/pjOmW1blD7V/+UbtX75R+5dcpjnuEn9PiUxyQ0ND0bdvX7Ru3RqTJ08utv1Onz4dI0eO5N+Hh4fD3t4e+vr6MDIyKrY4SpvhxsboYV8Fqy+9wdFHoWAMkDDg8D+fcPVdPOZ3ssP/Tp1E3O49iN2+HSwrCwCQefYsJPfuwXj+PGi1a6fgo5CX/WuSfsmXT9T+5Ru1f/lG7V82lLgkNz4+Hs7OzjAwMMCJEyf4X1DZV2wTEhJksvjsK7zZt5v09PQQEhIit924uLhcb0nlpK2tDe0cowNkEwqF9Ef+HYZaaljeqy5cG1tgwekXePnxc7ePiMQMTDryFC2qGeK3fm6w7uSM8IULkfboMQBAEhmJ8ClTkdy+HUx+XQBlE2NFHoYcgUBA7V+OUfuXb9T+5Ru1f+lXoq7Bp6WloXPnzkhISIC3tzd0dHT4Zdl9cb/uV+vn5wcVFRVUrlyZr+fv7y/XWdzPz0+uPy8pfA0s9HBmQjO4d6kBLdGX31C33kaj47qb2PxeDJPde2Hq7g5Bjm4KSZevIMDFBXFHjtJwY4QQQgj5aSUmyRWLxXB1dcXr169x4cIFVKxYUWZ55cqVUb16dRw/flym/OjRo2jbti3/ZKyzszPi4uLg4+PD13nz5g2ePHmCTp06Ff2BECgJBXBrZg2fmU7oXq8CX54pkWKjz1t03HAbT+u1RuXz56GVYxQMaXIyItzd8WHIEGQEBCgidEIIIYSUESVmnNzRo0dj586dWLNmDRwdHWWW1a9fHyKRCH///TcGDhyIBQsWoHXr1jh69Ch27dqFmzdvomnTpnz9//3vf3j16hXWrFkDVVVVzJ8/HwKBAI8ePYKSUv57aNA4uYXjzvtoLDj9Au+jUmTKO9Y0wcIuNaH9yBcRvy2BODKSX8YpK8Ng3FgYjhwJ7quhfYoLjZNavlH7l2/U/uUbtX/ZUGKSXCsrK3z48CHXZYGBgfwcxrt378by5csRHBwMGxsbLFu2DJ07d5apn5CQgOnTp+PkyZMQi8Xo0KEDNm3ahAoVKuSy9bxRklt4MsVS7L4diI0+b5GW9WV4EDVlIaa0q4ahdQwRv3E94v8+IrOeqFpVmP72G9Tr1y/ukOlLrpyj9i/fqP3LN2r/sqHEJLklESW5hS80LhW/nXuFS68+yZRXM9bEku61UCcuCOELFiIzZ3cFjoNe//4wmj4NwmIcboy+5Mo3av/yjdq/fKP2LxtKTJ9cUj5U0lPHjiGNsMetEcz11fjyt5HJ6LfjHua/E0LzwN8wnDABUFb+vJAxxB0+jIDOXZB09ZqCIieEEEJIaUJJLlGINrYmuDzNCZPbVIWK8Muf4aknYWi36S68G3WGpYcH1HJ0UxBHRCB0/HiETp0GcVSUIsImhBBCSClBSS5RGFVlIaZ3sMGFqS3QopohX56ULsbCMy/heukT4pf/CZOFCyDQ0Piy/MIFvHfpjLjjx2lecUIIIYTkipJconCVjTSxf7g9Ng9oABNtEV/+IiwRPbbdxWq12jD0OAXNtm35ZdLEREQsWIjgIUORERioiLAJIYQQUoJRkktKBI7j4FLHDD4zWmFkc2sIBRwAgDHg8P1gtD/oh3tus1Fh/XoIjb5c9U19+BCB3bojetuX6YIJIYQQQijJJSWKpkgJv3auAc9JzdHIUo8vj03JxKwTzzEySAuSPUeg26cPv4xlZiJq/XoE9uqNtGfPFBE2IYQQQkoYSnJJiWRnpo1jY5piVe860Nf4MhnEw6A4dN77DLub9IPR7j1Q+W/8ZADIePMGQf36I2LZMkhTUnLZKiGEEELKC0pySYklEHDo08gcV2c4YUATC3CfezBAImXYdTsQLjdS4P/7NhiMHQtkz2THGOL2H8D7Ll2QfOOG4oInhBBCiEJRkktKPF11FSzrURsnxzmiZgVtvvxTYgbGe7zADC0HKO86ANW6dfhl4o/hCBkzFmHTZ0AcE6OIsAkhhBCiQJTkklKjvoUezk5sjt+61YSWSIkvv/U2Gp3OhePUsEXQ/2UuBOrq/LJELy+87+SC+BMnabgxQgghpByhJJeUKkIBhyFNreAz0wk96lfkyzMlUmy8HojekZUQsWEfNJ2c+GXShASEz5+P4OHDkRkcrIiwCSGEEFLMKMklpZKxlirW9a2Hv0c5oKqxJl8eEpuGoeeDscRxBNSW/AGhgQG/LPXuPQR06YronTtpuDFCCCGkjKMkl5RqTasYwGtyC/zibAs1ZSFfful1JJz/VcWNeX9Cq0dPvpxlZCBqzVoE9nFF2vMXigiZEEIIIcWAklxS6qkoCTDWqQquzHBCx5omfHlalgRLb4XBzagDkpdthLKlBb8sw88PQX374tPyFZCmpioibEIIIYQUIUpySZlRUVcN2wc3wh63RjDXV+PL30Umo8+DTGwd9BvU3IYDwv+u+EqliN23DwFduiL51m0FRU0IIYSQokBJLilz2tia4PI0J0xuWw0qwi9/4ideRqNLWh08X7ARotq1+fKssDCEjBqFsFmzIY6NVUTIhBBCCClklOSSMklVWYjp7avj4rSWaFHNkC9PyhBj9tM0TG42AVljp4BT+3LFN/HcOQR0ckHCmTM03BghhBBSylGSS8o0a0MN7B9uj80DGsBUW5UvfxGRjG6fzOExcRVEjs34ckl8PD7O+QUhI0YiKzRUESETQgghpBBQkkvKPI7j4FLHDFdmOGFUC2sIBZ/nB2YM2PU2Hb2tXBE8/hcI9fT4dVLu3EFQt+5IP3IUTCxWVOiEEEII+UGU5JJyQ1OkhPkuNXB+cnM0svyS0MamZmHMR0Ms6eMOdHThy1l6OtK2bUNw/wFIf/VKARETQggh5EdRkkvKHVtTbRwb0xSreteBvoYKX34rMgudNdrg5uiFEFb8MptaxqtXCOzjik+rVkGalqaIkAkhhBBSQJTkknJJIODQp5E5rs5wwsAmFuA+92CARMrwR6Q2RjhNR2wXV0Dw30dEIkHs7j0I6NoNKXfuKC5wQgghhOQLJbmkXNNVV8HSHrVxanwz1KqozZeHpDIMFNpjq+tcoLoNX54VEoLg4SPw8Ze5EMfFKSJkQgghhOQDJbmEAKhnroszE5rjt241oaWqxJefTddDj5oj8Lq7GzjVL6MzJJw+jQCXzkg450nDjRFCCCElECW5hPxHKOAwpKkVrs5ohZ71v/TJTWcCTEctzO08F+l1G/HlkthYfJw1CyGjxyArLEwRIRNCCCEkD5TkEvIVIy0R1vath8Mj7WGt/+Xq7ROxBnpY9cWFLmPA6ejw5Sm3buF9l66I/esvMIlEESETQggh5CuU5BKShybW+tg/0A6zO1aHmrLwcyHHYYOwGoY4zUCEfSu+LktNxac/liOoX3+k+/kpJmBCCCGE8CjJJeQblIUCjGlZGVdmOOF/NU358kiBOoZV6IzN/5sEifGX8vTnzxHYuw8i16yFND1dESETQgghBJTkEpIvFXXVsG1wQ+x1awwLfXW+3FPVEr3sJ+FZ005fhhsTixGzcycCunVDyr37CoqYEEIIKd8oySWkAFrbGuPStJaY3LYaVISfPz4ZSiL8YtIGv7SdihTzynzdrA/BCHZzw8f58yGJj1dQxIQQQkj5REkuIQWkqizE9PbVcXFaS7SsbsSXP9OogL71x+C8Q08wlS8zqSWcOIn3Lp2R6O1Nw40RQgghxYSSXEJ+kLWhBv4a1hhbBjaAqfbnURgkAiH+NHXEiJbTEV65Fl9XEhODsGnTETpuPLLCwxUVMiGEEFJuUJJLyE/gOA6dapvhygwnjGphDaHg8/zA4ZqGGF57KLY5DIBYQ4uvn3z9OgJcOiP2wEEabowQQggpQpTkElIINEVKmO9SA+cnN0djK73PhRyHM6YNMLjFdPxb3Z6vK01NxaelSxE0YADS37xRUMSEEEJI2UZJLiGFyNZUG8fGNMXqPnVhoPG5X268qhbm1HCFu+NIpOoa8nXTn/2LwJ69ELl+PaQZGYoKmRBCCCmTKMklpJBxHIfeDSvh6oxWGORgAe5zDwbcN7bFoGZTccnWCSy7UCxGzLbtCOzWHakPHyouaEIIIaSMoSSXkCKio66M37vXxunxzVC74udpgNOUVbHOtgumtZiIT4aV+LqZQUH4MHgIwhcshCQxUVEhE0IIIWUGJbmEFLG65ro4PaEZlnSrCS1VJQCAv74lRjhOwoGazpAoKfN1448fx3sXFyRevETDjRFCCCE/gZJcQoqBUMBhcFMrXJ3RCj0bVATwebixw9XaYkyr6fA3rcbXlURFI2zKFIROnISsT58UFTIhhBBSqlGSS0gxMtISYa1rPRwZ7YBqxpoAgDBNI0xrMgrr6/VBuuqXKYOTfXwQ0MkFcX//DSaVKipkQgghpFSiJJcQBXCobACvKS0w19kWaspCME6Ai1ZNMLzVTPhWqsvXk6akIGLxb/gwaDAy3r1TYMSEEEJI6UJJLiEKoiwUYIxTFfjMcIJzLVMAQJyqNn5vNBjuTYYhTkOPr5v2zz8I6NETUZv+hDQzU1EhE0IIIaUGJbmEKFgFXTVsHdQQe4c1hqXB5+4K981qYmSrGThr7QiG/4Yby8pC9ObNCOzRE6n//KPAiAkhhJCSj5JcQkqI1jbGuDi1Jaa0rQYVJQFSlVWxtW5PTG85ASHapny9zPfv8WHAQIS7u0OSlKTAiAkhhJCSi5JcQkoQVWUhprWvjktTW6JldSMAgJ++Fca3mor9th0hFijxdeOPHEWAS2ckXbmiqHAJIYSQEouSXEJKICtDDfw1rDG2DmwAU21ViAVK+Nu2Pca1no4XBtZ8PXFkJEInTkLopMnI+hSpwIgJIYSQkoWSXEJKKI7j4FzbDD4znDCmZWUoCTiEahljdvNx2Fi3F1KVVfm6SZcvI6BzZ8QdPUbDjRFCCCGgJJeQEk9DpIS5nexwfnIL2Fvpg3ECeFs3xag2s3DbrDZfT5qUhIhFi/BhyBBkBAQoMGJCCCFE8SjJJaSUsDHVwtExDljTpy4MNFQQq6aDpU2GYon9UMSoavP10h49RmC37ojasgWMhhsjhBBSTlGSS0gpwnEcejWshKszWmGwgyU4DrhToTZGt52F81ZN+XosKwvRGzchsFcvpD55osCICSGEEMWgJJeQUkhHXRlLutfC6fHNUKeSDlKV1fBnvV6Y2WICgjWN+XoZb9/hw4CBiFjyOyTJKQqMmBBCCClelOQSUorVNdfFqfHNsKR7LWirKuGlgTUmtp6OQzbtkcUJP1diDHGHDiGgc2ckXb2m2IAJIYSQYkJJLiGlnFDAYbCDJa7ObIVeDSohS6iEg3YdMbH1NLzSt+TriSMiEDp+PEKnToM4KkqBERNCCCFFj5JcQsoIQ00R1rjWxdHRDqhuoolgbVPMbDEBf9bpgVQlEV8v6cIFvHfpjHgPDzDGFBgxIYQQUnQoySWkjGlS2QDnJ7fAvE62UBMp43zlZhjTdhbumtbk60gTExH+6wIED3VDZlCQ4oIlpdLevXthaGiIIPrbIYSUYJTkElIGKQsFGN2yCnxmOKFTbVNEq+nityZuWNp4MGJFWny91AcPENC1G6K37wDLylJgxOVXfHw8OI7Dvn378r3O9evXsWzZsiKLyc3NDbVq1cp1WVBQEGbOnIljx47BysqqyGIghJCfRUkuIWWYmY4atgxsiH3DGsPSUAO3K9bFmLaz4G3ZhK/DMjMRtW4dAnv3Qdq//yowWpJfRZ3kLliwAIcPH5Yrl0qlGDp0KBYuXIg2bdoU2f4JIaQwKCk6AEJI0WtlY4yLUw2w7cZ7bLn+Hhvr98E18waY/NQDlZI/P4SW4e+PoL79oDd4EIynTIFAQ0PBURNFqVKlSq7lAoEAN27cKOZoCCHkx9CVXELKCVVlIaa2q47L01rCqboRnhtWwfjW0/F39bYQc/99FTCGuP0H8L5LFyRTMlMkdu7cCSsrK6irq6Nt27Z49+6dzHKpVIrff/8dVlZWEIlEsLW1xfbt2/nl7u7uWLx4MVJSUsBxHDiOQ6tWrQAAfn5+6NevH8zNzaGuro4aNWpgzZo1kEqlMvvIyMjAr7/+isqVK0MkEqFSpUpwc3Pjl+fWXeH58+fo2LEjNDQ0oKOjg969eyM4OFimDsdxWLlyJdzd3WFiYgJDQ0MMGzYMKSk0RjMhpPjRlVxCyhlLAw3sG9YYF19GYPG5V9hfwxk3K9bDlKfHYRv3OWkRfwxHyJix0HZxgcm8uVAyMFBw1GWDp6cnRo8eDTc3N/Tr1w+PHz9Gnz59ZOrMmjULGzZswK+//gpHR0d4enpi7NixyMrKwsSJEzFy5EiEhobi8OHDuHr1KgBAW/vztM5hYWGwsbHBwIEDoaWlhadPn2LRokVITk7GokWL+H306tULV69exbx58+Dg4ICoqCicPHkyz7hDQkLQsmVLVKlSBQcPHkR6ejrmz58PJycn/Pvvv9DS+tLP+88//0SLFi3w119/4c2bN5g1axZMTEywfPnywjyVhBDyfYzkKSQkhAFgQUFBig6FKIBYLGbh4eFMLBYrOpQik5yexZadf8WqzD3PrGefZZN6z2GPa9Rhr2xs+Ze/fRMWd+Ikk0qlig63WBVF+zdp0oS1aNFCpmzBggUMANu7dy+LiopiysrK7JdffpGp079/f2ZkZMTHsmjRIqahofHNfUmlUpaVlcWWLl3KzMzM+PJLly4xAOzw4cN5rjt06FBWs2ZN/v20adOYhoYGi4mJ4ctev37NOI5jGzdu5MsAMHt7e7ltValS5ZuxlkTl4fNP8kbtXzaUmO4K7969w9ixY1GvXj0oKSnl+mRvq1at+NtzOV9+fn4y9RISEjBixAjo6+tDS0sLvXv3Rnh4eHEdCiGlhoZICXM72cFrSgs0qmyIs1VaYEzbWbhvYsfXkSQkIHzePAQPH47Mr25Pk/yTSCR4/PgxevToIVPeu3dv/t/3799HVlaW3NXdvn37IioqCm/evPnmPtLT07Fo0SJUrVoVIpEIysrKmD9/PsLDw5GcnAwA8PHxgbq6Ovr165fv2G/duoU2bdpAX1+fL7O1tUXdunVx+/Ztmbrt27eXeV+jRg2Ehobme1+EEFJYSkyS+/LlS5w/fx5Vq1ZFjRo18qzXrFkz3L17V+b19TA2ffv2xaVLl7Bt2zYcOnQI/v7+cHZ2hlgsLuKjIKR0qm6ihaOjHbDWtS6YsQncHYbjj0aDECfS5Ouk3r2HgC5dEbNrFxh9lgosKioKYrEYxsbGMuUmJib8v+Pi4uTKcr6PjY395j7mzJmDVatWYdSoUfDy8sLDhw/x66+/AvicAANATEwMzMzMwHFcvmOPi4uTiyk7rq9j0tXVlXmvoqKCjIyMfO+LEEIKS4npk9ulSxd069YNwOeHHh49epRrPV1dXTg4OOS5nbt37+LixYu4ePEiOnToAACwsbGBnZ0dTp48CVdX18IPnpAygOM49GxQCW1tTbD6kj8O3ufwj3F1jHzhiY7BDwAALCMDkavXIOG8F8yWLIFarZrf2SrJZmRkBCUlJURGRsqUf/r0if939pXSyMhIVKxYUa5OziupuTl+/DjGjBmDOXPm8GXnz5+XqWNgYIDw8HAwxvKd6Orr68vFnR1X9erV87UNQggpbiXmSq5AUDiheHt7Q1dXV+aWmY2NDerVqwcvL69C2QchZZmOujKWdK+FMxOaoXJlM6xv4Ipfmo3BR40vD59lvH6NIFdXfFq+AtLUVAVGW3oIhUI0aNAAp06dkin38PDg/21vbw9lZWUcP35cps6xY8dgbGzMJ5R5XR1NS0uDiooK/14ikeDIkSMyddq1a4fU1FQcO3Ys37E3b94cPj4+/JVmAPD398e///6L5s2b53s7hBBSnErMldz8unHjBjQ0NCCRSNCkSRMsWbIELVu25Jf7+fnBxsZG7gqFnZ2dXN/dryUmJiIxMZF/n92PVyKRQCKRFOJRkNJAIpFAKpWW27avaaYFjzEOOPowBKsuKWGc/kwM8LuM3u+uQ8ikgFSK2H37kHj5MkwWLYRGs2aKDrlQFUX7z507Fz169ICbmxtcXV3xzz//4MCBAwA+Dx2mp6eHCRMmYNWqVVBRUUGTJk1w4cIFHD58GBs2bODjsrGxgVgsxrp169C0aVNoa2vDxsYG7dq1w86dO2FrawsDAwNs27aNT4azv8dat24NZ2dnDB8+HG/fvoW9vT3i4uJw4sQJ/P333wAAxhi/DgBMnjwZe/fuRYcOHTB37lykp6dj4cKFsLCwwODBg2XO0dfnLHv4stL2OSrvn//yjtq/5BIKhfmuW6qSXCcnJwwZMgTVqlXDx48fsXr1arRr1w43btxA06ZNAXzuO/Z1nzAA0NPT+25/trVr12Lx4sVy5bGxsVBXVy+UYyClh1QqRUJCAoDCu9NQGrWvrIaGQ2rgz1th2CfshJsV62LK0+OoHv/5YSJxWBjCRo+BSvv2UJswAQJdHQVHXDiKov0dHBywYsUKbNiwAUePHkX9+vWxZcsWdOrUCUlJSYiKisKsWbOgrKyMXbt2YdmyZTA3N8eKFSvg6uqKqKjPE3c0adIEbm5u+OOPPxAdHQ0HBwecPHkSCxcuRHJyMiZPngw1NTX07dsXbdu2xcyZMxEdHc0nr1u2bMGaNWuwbds2/PbbbzAyMoKTkxO//fT0dIjFYv69qqoqTpw4gcWLF2PQoEEQCoVo2bIl3N3dkZ6ezvf3BYCUlBR+PQD8A285y0oD+vyXb9T+JZepqWm+63Is+1uvBMnuk/vixYtv1ktJSUHNmjVRo0YNvitC+/btIRQKceHCBZm6EydOxKVLl775dHJuV3Lt7e3x/v17WFpa/sQRkdJIIpEgOjoahoaGBfrlWJY9DIrFwrOv8C4iEV3f38bQ195QlWTxywW6ujCeMxtaXboU6MGmkojav3yj9i/fqP1LrjJ7JfdrGhoacHFxkenTpqenh5CQELm6cXFx331oQ1tbmx9UPSehUEh/5OWUQCCg9s/BoYoRzk9ugX2+QVh3RRl3zGph4rMTaBzpDwCQxscjYu48JHmeh+lid6hUqqTgiH8OtX/5Ru1fvlH7l35l7hq8ra0t/P398fUFaj8/P9ja2iooKkLKDmWhAKNaVobPDCc0cqiBhU1HYkXDAUhQ0eDrpPj6fh5ubM9eGm6MEEKIQpTqJDclJQWenp5o3LgxX+bs7Iy4uDj4+PjwZW/evMGTJ0/QqVMnRYRJSJlkpqOGLQMb4q8RTRBUrzlGt52NK+YN+eUsLQ2RK1ciqG8/pL96pcBICSGElEclprtCamoq36/2w4cPSExM5LshODk5wc/PD6tWrUKPHj1gZWWFjx8/Ys2aNYiIiJAZbqdp06bo2LEjhg8fjjVr1kBVVRXz589HnTp10LNnT4UcGyFlmVN1I1yY2hLbbwRgk4YWrpo3xKSnHjBL/fygZ/rLlwjs4wqDYW4wnDABAjU1BUdMCCGkPCgxD54FBQXB2to612XXrl1DpUqVMHHiRDx79gwxMTHQ0NCAo6MjFi1aBHt7e5n6CQkJmD59Ok6ePAmxWIwOHTpg06ZNqFChQoFiCg0Nhbm5OYKCgujBs3JIIpEgKioKRkZG1Ccrnz7EpGDR2Ze4+zIMA/0uoee7GxDiy1eMsrk5zBa7Q8PRUYFR5g+1f/lG7V++UfuXDSWmu4KVlRUYY7m+WrVqhapVq+LChQsIDw9HZmYm4uLicP78ebkEFwB0dHSwe/duxMXFISkpCSdOnChwgksIKThLAw3sdWuMDW5NcaFZb0xpNQXvdL7M3JUVEoLg4SPw8Ze5EOeYWKA8sbe3x+bNm/n3jx49wrBhw2BnZweBQIDOnTvnuh5jDMuXL4eFhQXU1NTQtGlT3Lt3T67ex48f0atXL2hpaUFfXx8jR46UGTWmILZs2YLOnTvDyMgIHMfJPOSb7cqVK+jXrx+srKygrq6OGjVqYNWqVcjKypKrmz2+rrW1NUQiESwsLDBr1ix+eVBQEDQ0NBAUFPRD8RJCSE4lJsklhJQNHMfhf7VMcXm6E9p1a4kZradgV83OSBcq83USTp9GgEtnJJzzlHtItCw7deoUgoKCMHz4cL7M19cXt27dQoMGDWBhYZHnuitWrMCiRYswbdo0eHp6wszMDB06dEBAQABfJysrCx07dsSbN29w+PBhbN26FRcvXsSAAQN+KN79+/cjOjr6m88zbN++HUlJSfjtt9/g5eWFIUOGYNGiRRg9erRMPalUim7duuHvv//GokWLcOnSJfz+++8yM7RZWVmhd+/eWLRo0Q/FSwghMhjJU0hICAPAgoKCFB0KUQCxWMzCw8OZWCxWdCilmn9EInPddoc1mfgXO9i8C3tlYyvz+jBqFMsMDVV0mHKKov1btmzJJk+eLFMmkUj4fzs5OTEXFxe59dLS0pi2tjabO3cuX5aRkcEsLS3ZuHHj+LLDhw8zjuOYn58fX3bx4kUGgN2/f7/A8WbHFhgYyACw48ePy9WJioqSK1u6dCnjOE5m2a5du5iOjg77+PHjN/d548YNpqyszCIjIwscb2Giz3/5Ru1fNtCVXEJIkapuooUjox0wZ3gbrOswEasb9EOCypcZBFNu3sL7zl0Q+9dfYGV4Cs3AwEDcunULvXv3linPz2xKd+7cQWJiIlxdXfkyFRUV9OzZk39gFwC8vb1Rp04d2NjY8GXt27eHvr6+TL38yk9shoaGcmX169cHY4yfGh0Adu7ciT59+sDMzOyb22vevDkMDAxw+PDhAsdLCCE5UZJLCClyHMehR/1K8JnZGhX79sKYdrNxtVIDfjlLS8OnP5YjqF9/pPv7KzDSouPj4wMlJaVcnyP4Hj8/PwCQG+vbzs4OwcHBSEtL4+t9XYfjONja2vLbKA63b9+GSCTiHybOysrCP//8A0tLSwwZMgQaGhrQ0tKCq6srIiIiZNYVCARwcHDA5cuXiy1eQkjZREkuIaTY6Kgp47dutXBw+v9wqfs4/Np0JD6p6fHL058/R2DPXohcuw7S9HQFRlr4Hj58iOrVq0MkEhV43bi4OIhEIqiqqsqU6+npgTGGuP8e4ouLi4Ourq7c+np6eoiNjf2huAvq7du32LBhA8aOHQtNTU0AQExMDLKysrBixQrExMTg1KlT2LZtG3x9fXMd2rFu3bq4f/9+scRLCCm7Ssw4uYSQ8qN2JR2cHN8MRx6aY/a56uj2xBPd3t/6PNyYRIKYHTuQcOECKvz2GzQcmig63EIRHh4OIyMjRYdRpBITE9GzZ09YW1tj6dKlfLlUKgUAaGlp4eTJk3yib2Jigvbt2+Pq1ato06YNX9/Q0BDR0dHIysqCsrIyCCHkR9CVXEKIQggFHAY2sYTXLx0Q5zYe050m4b32l6H+xMHBCHZzw8f58yFJSFBgpIUjPT39h67iAp+vxGZkZCD9q6vbcXFx4DgOenp6fL2EXM5VXFwc9PX1f2jf+ZWZmYkePXogLi4OXl5e0ND4Ms2zrq4uOI6Do6OjzDlo1aoVhEIhXr58KbOt7DpfHy8hhBQEJbmEEIUy1BRhdZ+6WDq3Lza7/oo9NTohQ/DlJlPCiZN46+yCRG/vUj3cmL6+PuLj439o3ex+tv5f9Vf28/Pjx83Nrvd131vGGPz9/eX66hYmqVSKgQMH4vHjx/D29oa5ubnMcnV1dVhZWeW5/tfJbHx8PFRUVKClpVUU4RJCyglKcgkhJUJjK32cneYEm2kTMKPjbDw1rMovY7ExCJs2HcFjxyErxxP7pYmNjQ0CAwN/aF1HR0doa2vLTGGelZWFkydPyoxh6+zsjGfPnuHt27d8mY+PD2JiYr451u3PmjBhAs6dO4czZ86gdu3audbp3LkzfH19ZRLaq1evQiKRoGHDhjJ1g4KCUL169SKLlxBSPlCSSwgpMZSFAoxsURkH3Xvj9lh3rK3viiRlNX556o0beNvJBbEHDpa64caaNWuGyMhIhIaGypRHRUXBw8MDHh4eiIqKQkREBP8+NTUVAKCqqoq5c+di9erV2LBhA65evYr+/fsjJiYGM2fO5LfVu3dv1KxZE7169YKnpyeOHTuG4cOHw8XFRWZUB3d3d3Ac992ZxR49egQPDw94e3sDAO7duwcPDw/cuHGDr7Ns2TJs27YNkydPhkgkwr179/hXzpnWZs2ahfT0dHTr1g1eXl7466+/MHToUDRv3hytW7eW22+LFi0KdoIJIeRrih2mt2SjySDKNxoMXPFu+EeyzotPsy1t+slNIuHfqw9L8/cvsn0XdvtnZGQwAwMDtmPHDpnya9euMQC5vgIDA/l6UqmULVu2jFWqVImJRCLWpEkTdufOHbn9hIaGsp49ezJNTU2mq6vLhg8fzhISEmTqzJw5k4lEIhYXF/fNmIcOHZprXE5OTnwdJyenPOO/du2azPaePHnCnJycmKqqKtPX12fDhw+Xi+HTp09MKBQyHx+fb8ZW1OjzX75R+5cNHGOluJNbEQsNDYW5uTmCgoJgaWmp6HBIMZNIJIiKioKRkRGEQqGiwym30rMk2HEzAPcOn8WYfzxgnBbPL5MKlWA4cgSMxo+D4Acf6spLUbT/jBkz8OTJE1y9erVQtvejWrRogdq1a2PLli0KjSM3mzdvxrp16/D27VtwHKewOOjzX75R+5cN1F2BEFKiqSoLMbltNSxfOQ6HxyzH6crNIcXn5EcgESN2+3a8dumK1IcPFRzp982cORP379/Hs2fPFBZDZmYmnj17hjlz5igshrxIpVJs2LABCxcuVGiCSwgpGyjJJYSUChYG6tg2piXqr1yCZZ1mIFD7y/SwgtBgfBg8BEHzfoUkRz/QksbMzAz79u1DVFSUwmJQUVFBYmJiibw79fHjR7i5uWHQoEGKDoUQUgZQd4VvoO4K5Rvdriq5UjPF2HTJD/F79qCf32WoSMX8sixdfVi6L4R2xw4/dTWQ2r98o/Yv36j9ywa6kksIKXXUVZQwp3MtDN+6GNuH/oZ/DSrzy5TjY/Fx6lS8HjEWWZ8+KTBKQgghikRJLiGk1KpmooXNs7tDtHEbdjXpj2QlVX4Zd+cmXnXshI/7D4L9N60sIYSQ8oOSXEJIqcZxHLo3NMfCbXNxZc5G3K5Qh1+mkp6KhGVL8U8PV6TnmCCBEEJI2UdJLiGkTNBRU8bcwS3Q9MAO/OUyEdGqOvwydf+XeNetB/yXr4E0M1OBURJCCCkulOQSQsqUWhV1sGzVeISt34uL1Vrww40JpRJI9+3Co/YuiL1f8ocbI4QQ8nMoySWElDkCAYd+reww+O9N8Brljg9aJvwyrU+h+DR0CB5MmQNxCR5ujBBCyM+hJJcQUmYZaIowa4YrDA8dgXejLsgSfBkKSOviWfzT5n8IOO0lt15sbCzOnj2L48eP4+zZs4iNjS3OsAkhhBQCSnIJIWVeo+qmmPTXcjx3/xOvDa35cq3kOGT8MgPX+41ASngE/P39MWzYMFSoUAE9e/bE5MmT0bNnT1SoUAHDhw+Hv7+/Ao+CEEJIQdBkEN9Ak0GUbzQYeNkUHpeKU79vhv3Fw9AQp/PltzLFmPoxBOmZmcjta5HjOGhoaMDT0xNOTk7FGTJRAPr8l2/U/mUDXcklhJQrZnrqGL9mFjJ2HcJTy3oAgMDMDEwNeo+MjIxcE1wAYIwhNTUVnTt3piu6hBBSClCSSwgpl5o51EDP8wfxbNRcbI5PQjpj+N6UEVKpFCkpKVi5cmWxxEgIIeTHUZJLCCm3REpCdBjWGVdSEpHffluMMRw6dIgeRiOEkBKOklxCSLl269YtZBZwgoiMjAzcunWriCIihBBSGCjJJYSUa4k/OFbuj65HCCGkeFCSSwgp17S1tYt1PUIIIcWDklxCSLnWokULiESiAq2jzHEIufkK8akF6+ZACCGk+FCSSwgp1/T19TFgwABwHJev+hyALtraaHt+P3yce+O81/08hx0jhBCiOD+V5GZlZWH16tWYPHkyLl26JLNsxowZPxUYIYQUlzlz5kBDQwMCwbe/EgUcB1WBACP09QEANT69RaWZI7F51AK8CYsrjlAJIYTk008luePHj8c///wDKysrTJ8+HdOnT+eXXbt27aeDI4SQ4mBjYwNPT0+oq6vneUWX4zioa2jg3Jmz0G7fjS9XkYrR9vYJvOvZC9u2nUVqpri4wiaEEPINP5XkPnjwAIcPH8b06dPx8OFDBAUFYdiwYWCM0e07Qkip4uTkhEePHsHNzU2uj65IJMKwYcPw6NEjtO3sgubb10F3+y4kGJjydawTwtF8/S/Y1XcyLj0KpO9AQghRMI79xDexnZ0dXr9+zb+XSqUYNmwYUlNT4efnh+fPnxdKkIoSGhoKc3NzBAUFwdLSUtHhkGJGc5eXX7Gxsbhx4wZCQ0NRqVIlODk5Qf+/Lgo5STMy8PyPdRAeOwCh9Mt8aZ/UdHHTZTjcpg2EhYF6cYZOCgl9/ss3av+y4aeu5FaqVAkPHz78sjGBAH/99RcMDQ3x6tWrnw6OEEIUQV9fH127dkWfPn3QtWvXXBNcABCIRKjr/gusT5xAknV1vtwkLR59PNbCu99IbD39EBliSXGFTggh5D8FTnITExMh/e+Kxd69e2Fubi5XZ+vWrTQbECGk3NCws0Vjz5NQmz4LWcpfujq0DHmCBgvGYtH4lbjpH6nACAkhpPwpcJI7ZMgQdOnSBcDnK7mmpqa51nN0dPy5yAghpBThhEJYjR4Ou4teyGzkwJdrZ6Vi6M39CBk5EnM3eSMiIV2BURJCSPlR4CT3zp07GDx4cK7LxowZg61bt/50UIQQUlopV6iAOgf2wHjlSmRq6fDlDaLewnXbHGwctQC7rr9FlkT6ja0QQgj5WQVOcpOTk2FkZJTrskaNGmHLli0/HRQhhJRmHMfBoGsX1Lp8AUouXflyVUkWBv/rCZM54zBu4SE8DIpVYJSEEFK2FTjJtbOzw71793JdVq1aNQQGBv50UIQQUhYIdXVRbc0KmO/dgyzTCnx51YQwTD3xBy5OnIdfDt1HTHKGAqMkhJCyqcBJ7siRI7FixQo8ffpUbllQUBC0tbULIy5CCCkzNJs2Ra0L56E9fDik/82qJgRDr3c30GHNdEyduR2H7n+AVEpj6xJCSGEpcJI7btw4dO7cGY6Ojpg+fTpu3bqFt2/f4syZM1i0aBGcnJyKIk5CCCnVBKqqqDh7Fqqc8ABna8eXm6XGYt71rYibPw8D117E89AEBUZJCCFlxw9PBrFp0yYsX74c4eHh4DgOjDHUq1cPZ8+eRaVKlQo7ToWgySDKNxoMvHwryvZnYjFiDxxExPoNEGR8GW0hQUUdO2t3Q8U+PTCjoy101JQLdb8k/+jzX75R+5cNPzXjGQC8fPkSERERMDU1hZ2dHQSCn5pfokShJLd8oy+58q042j8zNAyhCxci484dmfJHxjY47NgPo/s2R/d6FcFxXJHsn+SNPv/lG7V/2fDTGWnNmjXRtm1b1KxZs0wluIQQUtRUKlWE9e5dqLBqJZiOLl/eKNIfy84tw82lGzFgmy/efkpSXJCEEFJKUVZKCCEKxHEcdLp0QfULXtDu1o0vV5VkYfSLc+j312KMX3wEf3i/RkqGWIGREkJI6UJJLiGElABKenqouGI5zHftgrBiRb68enwo1l1bj6wtG+Gy8jIuvIjAT/YyI4SQcoGSXEIIKUE0mzdD1XNnoT98OFj2cGNMij5vr2PB6aXYtu4Ihu97iOCYVAVHSgghJRsluYQQUsII1NVhMnsWrI8fg8juy3BjFVJi8IfvdtT7exN6LPfChitvkZ4lUWCkhBBSclGSSwghJZRazZqwPn4MxrNmAiJVvrxD8CP8eXE5/tl3FP9bdwM330QpMEpCCCmZKMklhJASjFNSgsGIEajieRYajk35ct3MFPzy6BCGn9+EmX9ewIRD/yA8IU2BkRJCSMlCSS4hhJQCKubmMN+9G2bL/4BAR4cvb/zJD9t8VkPp9DG0X3UNO28GIEsiVWCkhBBSMlCSSwghpQTHcdDt3h1VvL2g3aULX64mycTY52ewxGc9Dv3tg84bb+NhUKwCIyWEEMWjJJcQQkoZJX19VFy1EuY7tkO5QgW+3DYuBJuur4fDtaMYuPkmZh5/hujkDAVGSgghikNJLiGElFKaLVui8rmz0B86FPhvuDElJkW/N1ex+eoa+F+4jjarr+PgvQ+QSGlsXUJI+UJJLiGElGICDQ2YzP0FVkePQGRjw5dXSonGSt9tGHb3MJYfe4CeW3zxPDRBgZESQkjxoiSXEELKALXatWHtcRxG06eDE4n48v99eIDtPqugff8Guv55CwvPvEBCWpYCIyWEkOJBSS4hhJQRnLIyDEePQuWzZ6DepAlfrp+RhHkPD2Lhvb3w8nmGtmuu4+Q/oTQ9MCGkTKMklxBCyhgVS0tY7NsLs6VLZYYbc4h4he1XV6Hpv1cx8+gT9N1xD28+JSkwUkIIKTolJsl99+4dxo4di3r16kFJSQm1atXKtd7u3btRvXp1qKqqom7duvD09JSrk5CQgBEjRkBfXx9aWlro3bs3wsPDi/oQCCGkxOA4Drq9eqLKeU9od3Lmy9XFGRj/72msvrkZEc9eodOGW/jD+zVSMsQKjJYQQgpfiUlyX758ifPnz6Nq1aqoUaNGrnWOHDmCUaNGoW/fvvD29kbTpk3Ro0cP3Lt3T6Ze3759cenSJWzbtg2HDh2Cv78/nJ2dIRbTlzghpHxRMjRExbVrUWnbViiZmfHldnEf8Oe1dej/0ht7rvqj3dobuPAinLowEELKDI6VkG80qVQKwX9D4Li5ueHRo0d48eKFTB0bGxs0bNgQhw8f5sscHR2hq6sLLy8vAMDdu3fh6OiIixcvokOHDgAAf39/2NnZ4ciRI3B1dc13TKGhoTA3N0dQUBAsLS1/9hBJKSORSBAVFQUjIyMIhUJFh0OKWVlsf0lyCqI2bEDcwYNAjq/+EE0jbKjXBy8NK6OVjREWd60JSwMNBUaqeGWx/Un+UfuXDSXmSm52gpuXgIAAvHnzRi5J7devH3x8fJCR8XnAc29vb+jq6qJ9+/Z8HRsbG9SrV49PhAkhpDwSamrAdP48WP19GKJq1fhy8+QorL69BZOeeuDh82C0X3cT66+8QXqWRIHREkLIz1FSdAD55efnBwCwtbWVKbezs0NmZiYCAwNha2sLPz8/2NjYgOM4uXrZ28hLYmIiEhMT+ffZ/XglEgkkEvqyL28kEgmkUim1fTlVlttfpXZtWBw7hti9exC7bTtYZiYAoFPQPTSJeIUtdXpg/RUpTv4TBvcudnCqbqTgiItfWW5/8n3U/iVXQa6sl5okNy4uDgCgq6srU66npwcAiI2N5et9XSe7XnadvKxduxaLFy+WK4+NjYW6uvoPRE1KM6lUioSEz4Pnf+9OAyl7ykX79+wJrUaNkLpmDcTP/gUAGKQnYsGDv3DHrBa21OmB4X+lok01XUxtaQ5jLRUFB1x8ykX7kzxR+5dcpqam+a5bapLc4jB9+nSMHDmSfx8eHg57e3vo6+vDyKj8Xcko77J/wRsaGlKfrHKo3LS/kRHYwYNIOHES0WvWQJr0eUgxx/AXqBv1DntrdoIXc8C9D0mY3KYq3BwtsfLRH3gb/7ZAu6mmWw3zm8wviiMoEuWm/UmuqP3LhlKT5GZfsU1ISJDJ4rOv8Orr6/P1QkJC5NaPi4vj6+RFW1sb2tracuVCoZD+yMspgUBA7V+OlZv2Fwph0K8vtNu0xqely5B08SIAQEOcjonPTqJ1yD/YUL8Pll+Q4OSTMGhY+eFd4vMC7YLjuFJ3HstN+5NcUfuXfqXmGnx2X9yv+9X6+flBRUUFlStX5uv5+/vLDYPj5+cn15+XEELIF8rGxqi0YT0qbdkMJRMTvrxmbBA2X1uLAX6XEPgxHn4Rid/YCiGElAylJsmtXLkyqlevjuPHj8uUHz16FG3btoWKyue+Ys7OzoiLi4OPjw9f582bN3jy5Ak6depUrDETQkhppNWmDSqf94TegP7Afw/xKkslGOx3CX9eXwv1rAwFR0gIId9XYrorpKam8kN8ffjwAYmJifDw8AAAODk5wcjICO7u7hg4cCCqVKmC1q1b4+jRo7h//z5u3rzJb6dp06bo2LEjhg8fjjVr1kBVVRXz589HnTp10LNnT4UcGyGElDZCTU2YLlwI7c5dEL5wATLfvQcAWCRFwjpRCH8d7jtbIIQQxSoxSW5kZCT69OkjU5b9/tq1a2jVqhX69++P1NRULF++HMuXL4eNjQ1OnTqFpk2byqx39OhRTJ8+HaNHj4ZYLEaHDh2wadMmKCmVmMMlhJBSQb1BfVifPImYnTsRs207WFaWokMihJB8KTEznpVENONZ+UYz3pRv1P7yMt6/R/iChZhZ4xn8zQt2Jbe+cX3sd95fRJEVPmr/8o3av2woNX1yCSGEKJaoShVYHjwAFQtzRYdCCCHfRUkuIYSQfOMEAijRuOGEkFKAklxCCCFFLi4lU25oR0IIKUqU5BJCCCly76KS4bb3IYKiUxQdCiGknKAklxBCSJETMiluvIlCh/U3sf7KG6RnSRQdEiGkjKMklxBCSJGrEh8G+4hXyBRLsf7KW3RcfxPX/SMVHRYhpAyjgWMJIYQUSDXdat+tI01LQ+aHYEhTPndPsIgSY9S9PbhRsR621e6GDzGA296HcK5ligWda6CCrlpRh00IKWcoySWEEFIgC5ouyFc9JpUi7u+/EbVmLaSpqQAAp7CnaBDpj121uuCSRWN4v4jAjTdRmNK2GoY3t4aykG4wEkIKB32bEEIIKRKcQAD9gQNR+bwnNFu35su1stIw7ckx/OG7DRWSo5CaKcEf3n5w2XgL9wNiFBgxIaQsoSSXEEJIkVI2M0OlLZtRcf06CA0N+fJ60e+x9dpauL7xgVAqwZtPyei74x6mH3uKqKQMBUZMCCkLKMklhBBS5DiOg/b//ocq5z2h26c3X64iycKwV97YdGM9qscFAwBO/hOGNmuu48DdIEikNLYuIeTHUJJLCCGk2Ah1dGC2ZAks/voLKpaWfLl1QjjW3dyE0c/PQFWcgaR0MRaceYnum33xLCRecQETQkotSnIJIYQUO40m9rA+ewYGY8YASp+fgRYwhh7vb2HHtTVo9Ok1AOB5WAK6b/HFr6efIyE1S5EhE0JKGUpyCSGEKIRAJILxtKmwPuEB1Tp1+HKjlFgsubsbcx4fgk5GEhgDDt4LRps11+HxOJSmByaE5AsluYQQQhRK1cYGVn8fhsm8eeDU1fnyViFPsOfaarQLfggwhpiUTMw8/gx9t9+Df0SSAiMmhJQGlOQSQghROE4ohP6Qwahy7iw0nFry5erpKZjxz1GsvL8TZinRAIAHQbHotPEWlnm9RkqGWFEhE0JKOEpyCSGElBjKFSvCfNs2VFizGkJ9fb68dsQb7Li+Fr3fXoNAKoFEyrDjZgDarrkBr+fh1IWBECKHklxCCCElCsdx0HFxQeXzntDp0YMv/5/fK4Rf3Y3td/5ElfhQAEBEYjrGH/oHQ/c+RFB0SqHHkp6eDnNzc5w/f54vu3z5MgYMGIAqVaqA4zhMnDhRbr2EhAT06tULVlZWUFNTg5GREZydnfHw4UO5uh8/fkSvXr2gpaUFfX19jBw5EomJiT8UL2MMK1euhLW1NUQiEWrVqoWjR49+c53169eD4zh07tz5u9vft28fOI6Te/3yyy98naSkJOjr68PX1/eHjoGQwkJJLiGEkBJJSU8PFf5YBou9e6BsYcGXV4oOwaYbGzH+9XmIxJ8njbj5Jgod1t/EustvkJ4lKbQYtm3bBj09Pbi4uPBlFy5cwLNnz+Dk5ARdXd1c18vIyICqqioWLFiA8+fPY8eOHUhNTUWbNm3w5s0bvl5WVhY6duyIN2/e4PDhw9i6dSsuXryIAQMG/FC8q1atwvz58+Hm5oZz586hVatW6N+/P86dO5dr/YiICCxevBjGxsYF2s+FCxdw9+5d/jVhwgR+mZaWFiZNmoR58+b90DEQUlg4Rvd48hQaGgpzc3MEBQXBMsd4jqR8kEgkiIqKgpGREYRCoaLDIcWM2r9kkaalwapiRbQAh19zJGSJukZYUaM7/jG24css9NWxuFtNtLYpWOKWk0QiQWRkJBwdHTF58mRMmzbtSyxSKQSCz9eIrKys0LlzZ/z555/f3WZycjIMDAywaNEiPgH8+++/MXDgQLx+/Ro2Np+P4dKlS+jYsSPu378Pe3v7fMecmZkJQ0NDjBo1CmvWrOHLu3TpguDgYDx79kxunSFDhoDjOHz48AGamprw9PT85j727duHYcOGISoqCoY5Zq/72ocPH2BlZYWnT5+ibt26+T6GkoI+/2UDXcklhBCiUG5ubqhVqxa8vb1Rq1YtqKqqomHDhrh37x5fR6CmBoG2NrSc/wfVWrUAAE/T0jD3xRPc3j8H4au749PuCUh+cRXBsakYtvchxh54DA/Pi+A4ju9ioKWlBUtLS6xcufK7cd29exdBQUHo3bu3THl2gltQGhoaUFVVRWZmJl/m7e2NOnXq8AkuALRv3x76+vrw8vIq0Pbfv3+PpKQkdOjQQaa8Y8eO+PfffxEcHCxTfvv2bZw+fRrLly//gaP5NktLS9jb22Pfvn2Fvm1C8ouSXEIIIQoXHh6O8ePHY9asWTh27BhEIhE6duyIyMhImXpKenqwOvI3jH+Zg48ch/pqavjN1BTbzMwwXEWMOO8NSH5+BQBw4WUEZhz7fPVy7NixqF69Ok6dOoUuXbpgzpw5uHDhwjdjunnzJszNzWFubv7DxyWVSiEWixEeHo4ZM2ZAIBBgyJAh/HI/Pz/Y2trKrMNxHGxtbeHn58eXubu7g+M4BAUF5bmv9PR0AIBIJJIpz37/+vVrvkwikWDixImYP38+zMzMCnxcNWvWhFAoROXKlfHHH39AIpHvIuLo6IjLly8XeNuEFBZKcgkhhChcbGwsdu/ejaFDh6Jr167w9vYGYwzr1q2Tq8spKcHAzQ2Tbt/ClG7d4KSpiSbq6hirqYleWlowvnMAximxAIAM8efkS2Jhj/8NmYR27dph06ZNsLKygoeHxzdjevr0KWrXrv1Tx7Vw4UIoKyujQoUKOHToELy8vFC5cmV+eVxcXK79evX09BAbG8u/FwgEEAqF4Dguz31lPwj34MEDmfLsK+I5t7dlyxakpKTIdMPIDzMzMyxevBj79++Ht7c3OnXqhF9//RVTpkyRq1u3bl28evUKSUk0pjFRDCVFB0AIIYTo6OigTZs2Mu/btWuH+/fv57lOioYGVqmp4nRsDMKjopB9LVFXKMTtm2vhUacTtkk/Ty6RZlIL/XbcQ8/6FTG3kx3s7OwQGhr6zZgiIyML1Cc2N+PHj0f37t0RHh6OXbt2oVOnTvDx8UGDBg0KtJ2FCxdi4cKF36yjra2NQYMGYcWKFahduzYcHBxw7tw5/P333wDAJ8iRkZFYuHAh9u/fDxUVlQLF0bFjR3Ts2JF/36FDB6ipqWHdunVyV4UNDQ3BGMOnT5+gpaVVoP0QUhjoSi4hhBCFMzIykiszMTFBeHh4nuu4ubnhyJEjmL1gAbxPn4bX4MHoqaODDKkUgox0uD48iQVvPz9IJRBpAABOPglDmzXX8SlZjLT/bu/nJSMjQ+7Wf0FVqFABjRo1QpcuXXDq1ClUrlxZJlnV09NDQkKC3HpxcXHQzzFOcH6tW7cODRs2RKdOnaCvr48ZM2ZgyZIlAMAnoAsXLkSdOnXQokULxMfHIz4+HmKxGGKxmP93Qbi6ukIikeDp06cy5dnnLi0trcDHQUhhoCSXEEKIwkVFRcmVffr0Kc/+ounp6fD09MSvv/6KSZMmoX23bnDevx9qjs3A5XgwTCMqDAAwMvohVCRZAICkdDFeRyThRVgCnobE5xmTrq4u4uPzXl5QAoEA9evXx7t37/iyr/veAp/HuvX395frq5sfBgYGuHTpEsLCwvD8+XOEhobCwsICKioq/NVjPz8/3Lx5E3p6evzL19cXFy9ehJ6eHq5cufJzB/qf7HNnYGBQKNsjpKAoySWEEKJwCQkJuHr1qsz7K1euoEmTJrnWz8jIgFQqlbndnpSUBO/798CpqkJ/+HAgR7Jb56UvPB5sQqvkIL4sJUOMHlt8Mf/UcySkZsnto0qVKggMDCyEo/tMLBbj/v37Mn1ynZ2d8ezZM7x9+5Yv8/HxQUxMDDp16vTD+6pQoQJq1aoFJSUlbN26FX379uW7DKxfvx7Xrl2TedWtWxcODg64du1agbtoHDlyBEKhEPXr15cpDwoKgo6ODkxNTX/4OAj5GdQnlxBCiMLp6+tjxIgRWLx4MXR1dbF8+XIwxjB16tRc6+vo6KBx48ZYvnw5jIyMoKSkhOXLl0NHRweRkZEwmT0L2p064cm4sUBICABA+dNHzPn0J/o2ao1+UjEyADAGHLofjAsvIvCLsy16N6zE911t3Lgxzp07h6ysLCgrK/P7/vDhAz9zWWpqKt6/f88/xJY93NiOHTvw4MEDtGvXDmZmZoiIiMD27dvh7++PLVu28Nvq3bs3li1bhl69emHZsmVITU3FzJkz4eLiIpNsuru7Y/HixQgMDISVlVWe5/HQoUNIS0tD1apV8fHjR2zfvh2BgYE4dOgQX6devXpy6+nq6kJTUxOtWrXiy27cuIG2bdtiz549/IgQHTt2RJs2bfgH8s6ePYsdO3ZgypQpcsnso0eP4Ojo+MNDrhHysyjJJYQQonBmZmZYsWIFZs2ahffv36NmzZq4ePEiTExM8lzn8OHDGDNmDIYOHQoDAwNMnjwZycnJWL16NQBArVZNmLm7A+3agVP50rfW6tE1NIr9hPfq+p+zXI5DTEomZnn8i2OPQrCkey1UM9LA//73P8ybNw/Xr19H+/bt+fWvXbuGYcOG8e8vXLjAD0eWPb9SzZo1cfLkSUyZMgXx8fEwNTVF48aN8fDhQ5nJEZSVlXHhwgVMnjwZ/fv3h5KSEnr27Ck3qkRKSgpEIlGeM6xlY4xhzZo1CAwMhKamJjp16oRDhw790DBhjDFIJBJIpVK+zNbWFrt370ZoaCikUimqV6+O9evXY9KkSTLrZmVl4cqVK1i1alWB90tIYaEZz76BZjwr32jGm/KN2r/4uLm54dGjR3jx4kWR7SMzOBgR7u5IuXNXpjyxrj3mWznjHffl6X+hgIOboyUG1NHFrKmToKuriz179hRZbPnRokUL1K5dW+YqcEl2/vx5DBgwAGFhYdDU1FR0OAVGn/+yge4hEEIIKfNULCxgvns3zJb/AaGODl+u/ewB/ry0EouzXkCIz1csJVKG3beD0G//Szj1HYujR4/i06dPigodmZmZePbsGebMmaOwGApqzZo1mDFjRqlMcEnZQUkuIYSQcoHjOOh2747KXueh3bkzX87S0mB/fh/Ovt6HtqJEvjwqOQvrnmShdu/JuPf8jSJCBgCoqKggMTGx1NxRTE5OhpOTU4EnmiCksFF3hW+g7grlG92uKt+o/cu+5Js3EeG+GFkfP34pVFLCx469MFOtEeLEX2YXUxEKMLZVFYxvVQWqyvT3UNbR579soCu5hBBCyiXNli1R+dxZ6A8d8mW4MbEYFc4fxZH7mzBCLZKvmymRYqPPW3RYdxPX/CLz2CIhpCShJJcQQki5JdDQgMncubA6egQiGxu+XBoSjN5/r8Sp1GuorfPlim5wbCqG7XuIMQceISyeZvIipCSjJJcQQki5p1a7Nqw9jsNo+nRwOabyVb10Hms8l2G1UTTUlL78L/Piy09ot+YGtt14j0yxNLdNEkIUjJJcQgghBACnrAzD0aNQ+cxpqOWYiEESE4OaO5fjbMRp9DL/Mrx8WpYEy7394LLxFu4FxCgiZELIN1CSSwghhOSgYmWFSnt2Q332LAi0tfly8e2bGL17Ho4Yh8BC78vV3reRyei34x6mHX2KyKR0RYRMCMkFJbmEEELIVziOg6hTJ1idOwvtTs58uTQ1FTo7NmDfP7swz04FKsIv/xs99SQMbdfcwP67QZBIaeAiQhSNklxCCCEkD0qGhqi4di0qbd0CJVNTvjzj2TO0WD0Dnlqv0Mr6y+QSSeliLDzzEt0238bTkHgFREwIyUZJLiGEEPIdWq1bo7KnJ/QGDQK4/0ZbyMqCZN8uLDi9DLvrK8FE+0sXhhdh/2/vzsOirPo3gN8zA8O+g4KgLAZi7poLbqi4Ibgb5pL9XCMtNE1ze1PKrFRcEnPJvTeDcEUQNbUQNdeyRcUNUFYFWUbZBmae3x/qg4S9UckMzNyf6+K64jvnmc7pMNPNw5lzFBj6xWnM3/cb8ouUWuo1kX5jyCUiIqoGmbkZHBcugNs3u2Dk6SnWlcnJaLBoBqKKTiK4XT3IpI9DsCAAu87dRa+weERdTIWaSxiINIohl4iI6G8wad0a7nt2w2F6CCSGhmK9cHcUhn8+CzGty/CKq41Yzy1UYvbuXzFy049IzFI87ymJqAYw5BIREf1NErkc9m+9BfcDB2D6yitivTw7G/hgLlZd+Qar/JxhayYXH7uQkoeAz09hScxVPCot10a3ifQKQy4REdE/ZOThjkY7d8Dxw1BILSzE+qNjx/DyvMk46HoPo9u7iMt4VWoBm08lwy/sB8T+mglB4BIGoprCkEtERPQvSKRS2AQFwSM2BhZ9+4p19aNHUCz9GFP2Lsf+AGc0d67Yc/eeohTTdv2EcVvPIyn7kTa6TaTzGHKJiIheAMN69eDy+Rq4rAuHQf36Yr340iUYvTUOW/ELPhrgCQvjilPTEm7moP/qBKw8eh0lZSptdJtIZzHkEhERvUAWfn7wiI2BzehRYk0oK8ODdevQedlMHO5thaFtnMXHlCo1Pj9xC31WxeP7xPva6DKRTmLIJSIiesFk5uZw/OADuO76GvLGjcW68tZtKCZPwPvXo/HNmBZ4qZ65+FhqbjHGb7+AKTsvIj2/WBvdJtIpDLlEREQ1xLRtW7jv2wv7t9+u2G5MEJC36xvYvz0OUc3LMNffGyaGMvGao1fvoXdYPNb/cBvKcrWWek5U9zHkEhER1SCpXA6Ht6fBff8+mLRtK9bL791DVsg7CNy7FkffeBn9mj2zjrdMhc8OJ2LA5wn48fYDbXSbqM5jyCUiItIAo8aN4frfr+C4eBGk5hXLFB4eOYKiUSPwqVESto1rh0a2puJjt+4/wqgvz2JGxM+4/7BEG90mqrMYcomIiDREIpXC5rXX4BEbA/PefmJd/fAhsj5YBI+lsxEzpCFC/Dwhl1X8L3r/5Qz4rYjHjjMpUPF4YKJqYcglIiLSMMP69dEwPBzOn6+BgYODWC+6eBEZI4Zj3O0TOPy2D7p52ouPPSwtx6LoKxgUfgo/383TRreJ6hSGXCIiIi2x7NsXHrExsB45UqwJSiWyV68BpozDxnZG+GJMWzhaGouPX8lQYNj6M5i39zfkFym10W2iOoEhl4iISItklpZwCl0M1692Qu7uLtZLb97EnVGj0fbAVhwNfgWTu7lDJn18PrAgAN+cv4teYfH49mIq1FzCQFQFQy4REVEtYNq+Pdz374P91LeAZ7cb++9/cW/4UISY3kNsSFe0d7MRr8ktVGLO7l8RtPFHXMtUaKnnRLUTQy4REVEtITUygkNICNz37IZJq1ZivTwzE2lvTYXFssXYNdwTK15tBVszufj4xTt5CFx7Ch/FXMWj0nJtdJ2o1mHIJSIiqmWMvbzguutr1F+4EFLTii3FFIfikBQ4EL1TzuH4zO4Y07ERJI9XMEClFrDlVDL8wn5AzK8ZEAQuYSD9xpBLRERUC0lkMtiOHfN4u7GePcW6uqAAmQsWQjEtGIvaWmL/1C5o4WwlPn5PUYq3d/2McVvPIyn7kTa6TlQrMOQSERHVYoZOTnD5Yh2cV6+CzL5iS7Gis2eRNGgwnOOisG9KB3w0uBksjA3ExxNu5qD/6gSEHb2OkjKVNrpOpFV1LuRu374dEomkytfcuXMrtduyZQu8vLxgbGyMVq1aISYmRks9JiIi+nckEgks+/dH49gYWI0YLtaF0lJkr1yJuyNHYoT5Q5yY1QPD2jiLjytVaqw9cQt9VsXj+LV72ug6kdbUuZD71OHDh/Hjjz+KX9OmTRMfi4iIwOTJkzFy5EjExcXBx8cHQ4cOxdmzZ7XYYyIion9HZmWFBkuWoNGOHZC7uor10sREpIx8DerwVVgR6ImIKZ3gWa/i6ODU3GJM3HERU3ZeRFpekTa6TqRxEqGOrUzfvn07xo8fj+zsbNg/82ebZzVp0gTt2rXDrl27xFrnzp1hbW2NQ4cOVfvflZaWhoYNGyIlJQWuz7yZkH5QqVTIzs6Gg4MDZDKZtrtDGsb51291Yf7VJSXIWb8BD7ZsAcordlQwbNAAjqGLYdS5C7aeSsbqYzdR/MxyBWNDKUL8PDGpqwfkBnX2XleNqgvzT39N5366k5KScOPGDQQFBVWqv/baazh+/DhKS0u11DMiIqIXR2psjHrvzoD7nt0wbtFCrJdlZCB18hTcf/99TGxhg2OzfNG/maP4eEmZGssOX4f/mpM4cztHG10n0giDv25SOzVr1gw5OTlwdXXF5MmTMWfOHMhkMiQmJgIAvL29K7Vv2rQplEolkpOTqzz2lEKhgEJRsZl2ZmYmgMe/0alUXLSvb1QqFdRqNedeT3H+9Vtdmn/Dl15Cw6//i/xdu5Cz5nMIxcUAAEVMDB4lJMBhzhyEjxqE+BvOCI25iru5jx+/nV2I0V+ew+BWTpjn7w0HCyNtDqNWqUvzr2/+zp31OhdynZycEBoaio4dO0IikSA6OhoLFy5Eeno6wsPDkZeXBwCwtraudJ2NzeMTYnJzc//0uVeuXInQ0NAq9dzcXJg+s08h6Qe1Wo2CggIAgFSqc3/0oL/A+ddvdXL++/eHRevWKFq9GuVnzwF4vN3YvQUL8GDvXnjPmomdo73x1YUs7LyYhTLV49WKB37JxLFr9/BmZ2cMa+kAgydHB+uzOjn/esLR0fGvGz1R59bkPs/s2bOxatUqpKam4sSJExg7diwyMzMr/Ye4ePEi2rdvj9OnT6Nz587PfZ7n3cnt0KEDbt++zTW5ekilUiEnJwf29vZck6WHOP/6rS7PvyAIeHgoDtmffgrVMzd2JMbGsJs2FTbjxiElvxShMdeQcLPycoVmTpYIHfQy2jSy1nCva5e6PP+6Tqfv5D5PUFAQVqxYgcuXL4t3bAsKCiqF3Kd3eG1tbf/0eSwtLWFpaVmlLpPJ+EOup6RSKedfj3H+9Vtdnn+bQQNh0a0r7i9bjoJ9+wAAQkkJcsJW4mFcHJw/+gg7J3RA3O9Z+PDgVWQpSgAAVzIVGLHxLEZ1aIg5/bxh88zRwfqmLs8/PaZz9+Cfrrd9ujb3qcTERMjlcnh4eGijW0RERBplYGODBp8sRaNtW2HYqJFYL716DSlBI3F/+Qr0f8kax2b5Ykp3D8ieWabwzflU9Ar7Ad9eSIVaXef/4Et6SidCbkREBGQyGdq0aQMPDw94eXkhKiqqUpvIyEj4+flBLtff30qJiEj/mPn4wOPAfthNngQ8vSupUiF361YkDRwEXDyH+QOaIjakK9q72YjX5RWVYc6eX/Hqxh9xNUPxJ89OVHvVueUK/fr1Q69evdDiyXYp0dHR2LRpE6ZPny4uT1i8eDHGjBmDxo0bo2fPnoiMjMS5c+dw8uRJbXadiIhIK6QmJqg3axYs/f2R+Z8PUHLlCgCgLC0NqRMnwWrwYLw09318+6YP9vyUjk8OXcODQiUA4NKdPAwMP4U3fNzwbh9PWBgbanMoRNVW5z54Nn36dMTFxSEtLQ1qtRpeXl6YNGkS3nnnHUgkFX9q2bJlCz799FPcvXsXTZo0wdKlSxEYGPi3/l08DEK/cTNw/cb512+6PP9CeTlyv/ovsj+v2G4MAGQ2Nqg/fx4sAwOhKC7H8qOJ+PrcXTybEupZGOE/gS8jsKVTpf/n6hpdnn99UudCriYx5Oo3vsnpN86/ftOH+VempSFr0WIUnj5dqW7WrRscFy2C3MUZv6TmY+H+3/FbekGlNl1fskfo4GZo7GAOXaQP868PdGJNLhEREf09chcXNNz8JRos+wyyZ/aWL0xIQNLAgXiwbTtaOplj/7Qu+GhIc1gYV6xwPHUrB/1Xn8SKI9dRrOSBCVQ7MeQSERHpKYlEAqtBg+ARdwhWgweJdaG4GPc/+wwpr41C2Y3reL2TK07M6oFhbZ3FNmUqAeHf30KfVfE4fu2eNrpP9D8x5BIREek5AxsbNPjsMzTcvBmGLi5iveT335E8fATuh4XBzlDAyqDWiJjSCZ71KpYppOUVY+KOi5i88yLS8oq00X2i52LIJSIiIgCAedcu8Ig+ANvx44Gnx9mqVHjw5WYkDRqMwrNn0cnDDoemd8P8Ad4wlVesV/3u6j30XhmPdd/fgrJcraUREFVgyCUiIiKR1NQU9d+fA7dvv4XRy03Fetndu7j7f+ORMX8BpA8VmNK9MY7N9IV/84rTRUvK1Fh+5Dr815zEmVs5z3t6Io1hyCUiIqIqTJo3g/u336Le7PcgMTIS6wV79+J2QCAKYmPhZGWM9WPbYdv49nC1MxXb3M4uxOjN5zA94mfcf3JkMJGmMeQSERHRc0kMDGA3cSI8DkbD1KeTWFc9eICMWe8hLfgtlGVkoGeTejgyoztm9PaE3KAiWhy4nAG/sHhsO52MchWXMJBmMeQSERHR/yRv1AiNtm6F0yefQGZlJdYfxcfjduBA5O78CkZSYEZvLxyd0R3dvRzENg9LyxF68CoGhZ/GT3fztNF90lMMuURERPSXJBIJrIcOgcehWFgGBIh1oagI95YuRcro0Si5fgNu9mbYMb491o9pC0dLY7Hd1UwFhn1xBnP3/Iq8J0cGE9UkhlwiIiKqNgM7OziHrUDDTRth0MBJrJf88iuShw/H/VWrISiV8G/hhOOzfPFmdw8YSCuOAI64kIpeYT8g8sJdqNU8dJVqDkMuERER/W3m3buj8cGDsH1jXMV2Y+XleLBxI5IHDUbh+fMwMzLAvAFNERvSDR3cbMVr84rK8P6e3zBiwxlczVBoaQSk6xhyiYiI6B+Rmpmh/rx5cIuMgFGTJmJdeecO7o57A5n/+Q9UBQVo4miByDc7IezVVrAzk4vtfrqbj8C1CQg9eAUPS8q0MQTSYQy5RERE9K+YtGgB991RcJg5ExJ5RYjNj9qN2wGBUBw+AgAY3s4FJ2b1wOudXCF5soJBLQDbTqfALywe0b9kQBC4hIFeDIZcIiIi+tckhoawnzIZHtEHYNqxo1hX5eQgfcYMpE17G2VZWbAyNcRHQ5rjwLQuaOlSsVPD/YelCPnmZ4zdcg63sx9pYwikYxhyiYiI6IWRu7mh0fZtcPp4CaSWlmL90YkTSAoIRO7XX0NQq9HSxRr7pnbBkiHNYWlsILY7fesB+q8+ieVHElGsVGljCKQjGHKJiIjohZJIJLAePhyNY2Ng4d9frKsLC3HvoyW4M3oMSm/ehEwqwdhOrjjxXg8Mb+sititTCVj3/W30XhmPY1fvaWMIpAMYcomIiKhGGDg4wGXVKris/wIGjo5ivfjyZSQNG47sz9dCrVTC3twIYUGtEDmlE7zqm4vt0vOLMWnnRUzacRGpuUXaGALVYQy5REREVKMsevaER0wMbMaOhfiJs7Iy5HzxBZKHDEXRpUsAgI4edogN6YYFA5rCVC4Trz927R76rIrHuu9vobScSxioehhyiYiIqMbJzM3guHAB3L7ZBSPPl8S6MikJd8aMReaixVA9fAhDmRSTu3vg+CxfDGhRcfe3pEyN5Ueuw39NAk7fytHGEKiOYcglIiIijTFp3Rrue/bAYXoIJIaGYj0/MhJJAwKg+O47AICTlQm+GNMOOyZ0gJudqdguKbsQYzafQ8g3P+O+okTj/ae6gyGXiIiINEoil8P+rbfgfuAATF95RayXZ2cj/Z0QpL3zDsru3QcA+Ho54PCM7ni3txfkBhWxJfqXDPQKi8fWU8koV6k1Pgaq/RhyiYiISCuMPNzRaOcOOH4YCqmFhVh/+N0xJAUEIC8iAoJaDWNDGab39sR373aHr5eD2O5RaTk+jLmKgeGncelOnjaGQLUYQy4RERFpjUQqhU1QEDxiY2DRt69YVz96hKzFobjz+jiUJiUBAFztzLB9fHtsGNsWTlbGYttrmQoMX38Gc/f8irxCpcbHQLUTQy4RERFpnWG9enD5fA1c1oXDoF49sV586RKSBw9B9rp1EJRKSCQS9G/uhGMzffGmrwcMpBKxbcSFVPQK+wER5+9CrebxwPqOIZeIiIhqDQs/P3jExsB61GtiTSgrQ87acCQNG4ain34GAJgZGWCef1Mcmt4NHdxtxbZ5RWWYu/c3DN9wBlcyCjTef6o9GHKJiIioVpFZWMBp0SK47voa8saNxbry1m3cGTMGWR9+BNWjRwAAr/oWiJzSCSuDWsHeXC62/fluPgauPYXQg1fwsKRM42Mg7WPIJSIiolrJtG1buO/bC/u33waebjcmCMjbtQtJAYF4eOIEgMfHCA9r64Ljs3pgnI+reN6EWgC2nU5Br7B4HLicDkHgEgZ9wpBLREREtZZULofD29PgsW8vTNq0Eevl9+4hbeo0pE2fgfLsbACAlYkhPhzcHAemdUErFyuxbfbDUkyPuIwxm8/h1v1HGh8DaQdDLhEREdV6Ri+9BNev/wvHRR9AamYm1h8eOYLbAYHIi4oS79S2dLHG3qldsGRIc1gaG4htz9x+AP81J7H8SCKKlTweWNcx5BIREVGdIJFKYTNqFDwOxcK8t59YVysUyPrPB7g77g2UJicDAGRSCcZ2csWJ93pgRDsXsW2ZSsC672+j98p4fHf1nsbHQJrDkEtERER1imH9+mgYHg7nz9dA5mAv1osuXEDy4CHI2bABgvLxfrn25kZY8WorfPumD5rUrzhwIj2/GJN3XsSkHReQmluk8TFQzWPIJSIiojrJsm9fNI6NhXVQkFgTlEpkr16D5OEjUPzLL2K9g7stYkK6YsGApjCTy8T6sWv30WdVPNZ9fwul5VzCoEsYcomIiKjOkllawunDULh+tRNyd3exXnrzJlJeG4Wsj5dC9agQAGAok2Jydw8cm+WLgBZOYtuSMjWWH7kO/9UJOHUzR+NjoJrBkEtERER1nmn79nDfvw92bwUDBk8+bCYIyPvqKyQNHIiHP/wgtnWyMsG6MW2xY0IHuNmZivWknEKM3XIO0yMvI/sRjweu6xhyiYiISCdIjYxQb/p0uO/dA5NWrcR6eWYm0oLfQvrMWSjPqbhT6+vlgMMzuuPd3l6QG1REophfszBy5xVsO5OCcpVao2OgF4chl4iIiHSKsZcXXHd9jfoLF0JqWnGnVnHoEG4HBCJ/z15xuzFjQxmm9/bEd+92R48mDmLbIqUaS2ITMTD8NC7dydX4GOjfY8glIiIinSORyWA7dgw8YmNg3qOHWFcXFCBzwQLcHT8Byjt3xLqrnRm2/V97bBjbDk5WxmL9WqYCw9f/iPd3/4rcQi5hqEsYcomIiEhnGTo5wWX9F3BetRIy+2e2Gzt7FkmDBiPnyy8hlJUBeHw8cP/mjjg6oytef6U+DKQSsX3kxVT0CvsBEefvQq3m8cB1AUMuERER6TSJRAJLf380jo2B1YjhYl0oLUV22EokvxqE4t9+F+umcgNM6+qCmHe6oKO7rVjPLyrD3L2/YfiGM/g9vUCjY6C/jyGXiIiI9ILMygoNlixBox07IHd1FeuliYlIGTkS9z75FOqiioMhPOuZI2JKJ6wa2Qr25nKx/vPdfAwKP4XF0VegKCnT6Bio+hhyiYiISK+YdewA9wP7YTdlSsV2Y2o1cnfsQFLgQBQmnBLbSiQSDG3jguOzeuANH1c8XcGgFoDtZ1LgFxaPA5fTxQ+yUe3BkEtERER6R2psjHoz34X7nt0wbtFCrJdlZCA9OBiFSz5GeW7FrgpWJoYIHdwcB6Z1RSsXK7Ge/bAU0yMuY/SX53Dr/kONjoH+N4ZcIiIi0lvGTZrALeIb1J8/D5JnthtTHjuGlIGDkL9/f6W7tC1crLB3ahd8PLQ5rEwMxfqPSQ/gvyYByw4nokhZrtEx0PMx5BIREZFek8hksB03Do0PRsOsezexrs7PR+bceUidOAnK1FSxLpNKMKajK07M8sWr7VzEeplKwBc/3EaflSdx9EqWRsdAVTHkEhEREQEwdHZGw40b4bhsGSTW1mK98MwZJA0chAdbtkIor7hLa2duhOWvtkJUsA+a1LcQ6+n5xZjy1SVM3H4BqblFIO1gyCUiIiJ6QiKRwDJgACx3bIflkCFiXSgpwf3ly5ESNBLFV65Uuqa9my1iQrpiYUBTmMllYv144n30XhmP8BM3UVqu0tQQ6AmGXCIiIqI/kFpZwfHjJWi0dQsMGzYU6yVXryIlaCTuLVsOdXGxWDeUSTGpmweOz+qBgJZOYr20XI0VR2/Af3UCTt3M0egY9B1DLhEREdGfMOvcGR7RB2A3aSIge3KXVqVC7tatSBo4CI9On67U3tHKGOtGt8XOCR3gZlfxQbaknEKM3XIOb+/6CfcUJZocgt5iyCUiIiL6H6QmJqj33ntwj/oWxs2aifWytDSkTpyEjPfnojwvr9I13b0ccHhGd8zs4wUjg4q4FfNrJvzC4rE5IQnlKrXGxqCPGHKJiIiIqsH45ZfhFhmBenPmQGJiItYLDhxA0oAAFBw8WGm7MWNDGUL8PPHdu77o2cRBrD8qLceS2GsIXHsKF1NyQTWDIZeIiIiomiQGBrCbMB4eB6Nh1qWLWFfl5SFj9hykTnkTyrT0Stc0sjPF1v9rj42vt0MDK2Oxnpj1ECM2/Ig5u39BbqFSY2PQFwy5RERERH+T3MUFDTd/iQbLPoPs2e3GEhKQNHAgHmzfDkFVsaOCRCJBv2aOODbLF8G+jWHw9HxgAN9eTEOvsB+w69xdqNU8HvhFYcglIiIi+gckEgmsBg2Cx6FYWA4aKNaF4mLc//QzpIx8DSWJiZWuMZUbYK6/N+Kmd0MnD1uxnl9Uhvn7fsOw9Wfwe3qBxsagyxhyiYiIiP4FA1tbOC9bhoZffglDZ2exXvL770gePgL3w1ZCXVJ5RwXP+hb4ZnInrB7ZGvbmRmL9cmo+BoWfwuLoK1CUlGlsDLqIIZeIiIjoBTDv1hUeB6NhO348IH0SsVQqPPjySyQNHozCs2crtZdIJBjSxhnHZ/niDR9XPF3BoBaA7WdS0GtFPPb/nF7pw2xUfQy5RERERC+I1NQU9d+fA7fISBg1bSrWy+7cxd3/G4+M+Qugys+vdI2ViSFCBzdH9Ntd0aqhtVjPeVSKGZGXMerLs7h1/6GGRqA7GHKJiIiIXjCTFs3h/m0k6r03CxKjiuUIBXv34nZAIApiY6vcoW3ubIV9b3XG0qEtYGViKNbPJuXCf00CPjuciCJlucbGUNcx5BIRERHVAImhIewmTYLHwWiY+nQS66oHD5Ax6z2kBb+FsoyMStdIpRKM7tgIJ2b54tV2LmK9TCVg/Q+30WflSRy5ksUlDNXAkEtERERUg+SNGqHR1q1wWroUMisrsf4oPh5JgQORu/OrStuNAYCduRGWv9oKu4N94O1oIdbT84vx5leXMHHHRdx9UKSxMdRFDLlERERENUwikcB62NDH240FBIh1dVER7i1dipTRo1Fy/UaV615xs0XMO12xMKApzOQysX4i8T76rIrH2uM3UVquqnIdMeQSERERaYyBnR2cw1ag4cYNMGjgJNZLfvkVycOH4/7q1VCXlla+RibFpG4eOD6rBwJaVlxTWq5G2Hc30H91AhJuZmtsDHWFzobcxMRE9OnTB2ZmZnB0dMScOXOgVPLIPCIiItI+c19fND54ELZvjAMkT/YOKy/Hgw0bkTx4CArPn69yjaOVMdaNbouvJnaAu72ZWE/OKcTrW85j2q6fkFVQUuU6faWTITcvLw+9evWCUqnE3r17sXTpUmzatAkzZ87UdteIiIiIAABSMzPUnzcPbpERMPLyEuvKlBTcHfcGMv/zAVQKRZXrunk64PCMbpjVxwtGBhVRLvbXTPiF/YDNCUkoV6k1MobaTCdD7oYNG6BQKLBv3z7069cPEyZMwLJly7BhwwZk/OFTjERERETaZNKyJdz37IbDu+9CIpeL9fyoKNwOCIDi8JEquykYGcjwjp8nvnvXF72864n1QqUKS2KvIXDtKVxMydXYGGojnQy5cXFx6N27N2xtK86EDgoKglqtxtGjR7XYMyIiIqKqJIaGsH9zCtwP7Idphw5iXZWdg/QZM5A27W2UZWVVua6RnSm2vPEKNr3eDs7WJmI9MeshRmz4EbOjfsGDR6VVrtMHBtruQE1ITEzEhAkTKtWsra3h5OSExMTEP71OoVBA8cyfBVJTUwEAaWlpNdNRqtVUKhVyc3NRVFQEmUz21xeQTuH86zfOv37T6vxLpRA+DEV5XBxyN26C+uGTk86OHEFSQgJsJ02CxaCBkEgr36dsYg5sGe6KHT/eQcSFNJSpHt/5/eb7HMT8+DuCfd0xqGUDSJ+eHVxHyWQyODo6wsDgryOsTobcvLw8WFtbV6nb2NggN/fPb92vXLkSoaGhVepdu3Z9kd0jIiIi+mdmTH/89XcvWwXMePG90YrU1FS4uLj8ZTudDLn/1MyZMzFp0iTx++TkZHTv3h1nzpxBw4YNtdgz0obMzEx06NAB58+fh5OT019fQDqF86/fOP/6jfNfuzk6OlarnU6GXBsbGxQUFFSp5+XlVVqn+0eWlpawtLSsUm/YsGG1fmMg3eTk5MT512Ocf/3G+ddvnP+6TSc/eObt7V1l7W1BQQEyMzPh7e2tpV4RERERkaboZMj19/fHsWPHkJ+fL9aioqIglUrRt29f7XWMiIiIiDRCJ0NucHAwLCwsMGTIEBw9ehTbtm3D7NmzERwcjAYNGlT7eSwtLbFo0aLnLmEg3cf512+cf/3G+ddvnH/dIBH+uLuwjrh27RreeecdnDlzBhYWFhg3bhw+/vhjyJ/ZZJmIiIiIdJPOhlwiIiIi0l86uVyBiIiIiPQbQy4RERER6RyGXCIiIiLSOQy5RERERKRzGHL/RGJiIvr06QMzMzM4Ojpizpw5UCqV2u4WvWDbt2+HRCKp8jV37txK7bZs2QIvLy8YGxujVatWiImJ0VKP6Z+6desWgoOD0bp1axgYGKB58+bPbVeduS4oKMDEiRNha2sLCwsLjBgxApmZmTU9BPoXqjP/PXr0eO77wfMOF+L81y1RUVEYPHgwXFxcYGZmhtatW2Pr1q3442fv+frXLTp5rO+/lZeXh169esHT0xN79+5Feno6Zs6ciaKiIoSHh2u7e1QDDh8+DCsrK/F7Z2dn8Z8jIiIwefJkLFiwAL169UJkZCSGDh2KhIQEdOrUSRvdpX/gypUriI2NRceOHaFWq6FWq6u0qe5cjxw5EleuXMGGDRtgbGyMBQsWwN/fHxcvXoSBAd9Wa6PqzD8AdOnSBStWrKhUc3Nzq/Q957/uWblyJdzc3BAWFgYHBwd89913mDx5MlJTU7Fo0SIAfP3rJIGqWLp0qWBmZiY8ePBArG3cuFGQyWRCenq6FntGL9q2bdsEAEJ2dvaftvHy8hJGjRpVqebj4yP4+/vXdPfoBVKpVOI/v/HGG0KzZs2qtKnOXJ85c0YAIBw5ckSsJSYmChKJRIiMjKyBntOLUJ359/X1FQICAv7n83D+66bnvcdPnjxZsLS0FH82+PrXPVyu8BxxcXHo3bs3bG1txVpQUBDUajWOHj2qxZ6RpiUlJeHGjRsICgqqVH/ttddw/PhxlJaWaqln9HdJpf/77a66cx0XFwdra2v06dNHbNOkSRO0bt0ahw4devEdpxfir+a/ujj/dZO9vX2VWps2baBQKFBYWMjXv45iyH2OxMREeHt7V6pZW1vDycmpytos0g3NmjWDTCaDh4cHPvnkE6hUKgAQ5/uPPw9NmzaFUqlEcnKyxvtKNaO6c52YmIgmTZpAIpFUacf3h7ovPj4eZmZmMDY2hq+vL06ePFnpcc6/7jh16hScnZ1hYWHB17+O4uKR58jLy4O1tXWVuo2NDXJzczXfIaoxTk5OCA0NRceOHSGRSBAdHY2FCxciPT0d4eHhyMvLA4AqPw82NjYAwJ8HHVLdueb7g+7y9fXFuHHj4OnpiYyMDKxYsQK9e/dGfHw8fHx8AHD+dcWpU6cQERGBsLAwAHz96yqGXNJr/fr1Q79+/cTv+/btCxMTE6xatQoLFizQYs+ISNNCQ0MrfR8YGIhmzZrho48+4p+idUhaWhpGjhyJnj17IiQkRNvdoRrE5QrPYWNjg4KCgir1vLy8Sut0STcFBQVBpVLh8uXL4m/xf/x5ePpbP38edEd155rvD/rDzMwMAQEBuHTpkljj/Ndt+fn58Pf3h52dHfbs2SOu1ebrXzcx5D6Ht7f3c/dFzMzMrLJeh3Tb0/n+489DYmIi5HI5PDw8tNEtqgHVnWtvb29cv369yv6az1vLT7qH8193FRcXIzAwEAUFBYiLi6u0bSRf/7qJIfc5/P39cezYMeTn54u1qKgoSKVS9O3bV3sdI42IiIiATCZDmzZt4OHhAS8vL0RFRVVqExkZCT8/P8jlci31kl606s61v78/8vLycPz4cbHNjRs38PPPP2PAgAEa7TPVrMLCQsTExKB9+/ZijfNfN5WXlyMoKAjXrl3D4cOHK+2FDvD1r6u4Jvc5goODsXbtWgwZMgTz589Heno6Zs+ejeDgYDRo0EDb3aMXqF+/fujVqxdatGgBAIiOjsamTZswffp0ODo6AgAWL16MMWPGoHHjxujZsyciIyNx7ty5Kp+6ptqtqKhIXFd5584dKBQK7N69G8DjDxw5ODhUa659fHzQr18/TJgwAWFhYeJm8C1btsSwYcO0Mjb6a381/4mJiVi+fDmGDh0KNzc3ZGRkICwsDFlZWZWCD+e/bpo6dSpiYmIQFhYGhUKBs2fPio+1adMGRkZGfP3rIi3v01trXb16VfDz8xNMTEyEevXqCe+9955QWlqq7W7RCxYSEiJ4enoKJiYmgpGRkdCiRQthzZo1glqtrtRu8+bNwksvvSTI5XKhRYsWwsGDB7XUY/qnkpOTBQDP/fr+++/FdtWZ6/z8fGHChAmCtbW1YG5uLgwbNowHxdRyfzX/N2/eFPr16yc4OjoKhoaGgrW1tTBgwADh3LlzVZ6L81/3uLq6/un8Jycni+34+tctEkH4w8ISIiIiIqI6jmtyiYiIiEjnMOQSERERkc5hyCUiIiIincOQS0REREQ6hyGXiIiIiHQOQy4RERER6RyGXCIiIiLSOQy5RERERKRzGHKJiIiISOcw5BIRERGRzmHIJSLSMYIgYP369Wjbti1MTEzg4OCAwYMHIz8/X9tdIyLSGIZcIiIdIggCxowZg9mzZ2PIkCGIjo7GmjVroFQqYW5uru3uERFpjEQQBEHbnSAiohdj7dq1mD17Nk6fPo127dppuztERFrDO7lERDpCEAR88sknePPNN/804M6fPx/u7u6QSCS4deuWhntIRKQ5DLlERDriypUryMzMxLBhw/60TWBgIE6ePAlXV1cN9oyISPMMtN0BIiJ6MbKysgAAjo6Of9qmc+fOmuoOEZFW8U4uEZGOeBpur169quWeEBFpH+/kEhHpiKZNm6J169YICQlBfn4+3NzccOvWLVy4cAGbNm3SdveIiDSKIZeISEfIZDIcOHAAs2fPxrx586BQKODu7o6pU6dqu2tERBrHkEtEpEMaNWqEyMhIbXeDiEjruCaXiEiPzJkzBy4uLkhLS0O3bt3g4+Oj7S4REdUIHgZBRERERDqHd3KJiIiISOcw5BIRERGRzmHIJSIiIiKdw5BLRERERDqHIZeIiIiIdA5DLhERERHpHIZcIiIiItI5DLlEREREpHMYcomIiIhI5zDkEhEREZHOYcglIiIiIp3DkEtEREREOuf/AUOm1tPm0kmyAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 792x462 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_star = brentq(lambda rr: (y1 + y2/(1+rr)) - 0.90*W, 0.0, 2.0)\n",
    "print(f\"W(r) = 0.90·W  cuando  r = {r_star:.4%}   (comprobación: W = {y1+y2/(1+r_star):.2f})\")\n",
    "\n",
    "# --- gráfico: pivote de la recta sobre la dotación\n",
    "fig, ax = plt.subplots()\n",
    "for rr, col, lab in [(r, \"tab:blue\", \"r = 5%\"), (r_alto, \"tab:red\", \"r' = 10%\")]:\n",
    "    Wr = y1 + y2/(1+rr)\n",
    "    ax.plot([0, Wr], [(1+rr)*Wr, 0], color=col, lw=2, label=f\"{lab}   (W = {Wr:.1f})\")\n",
    "ax.plot(y1, y2, \"ko\", ms=8, zorder=5)\n",
    "ax.annotate(\"dotación\\n(100, 126)\", (y1, y2), textcoords=\"offset points\", xytext=(12, 12))\n",
    "ax.plot(c1, c2, \"s\", color=\"tab:green\", ms=8, zorder=5)\n",
    "ax.annotate(f\"plan (130; {c2:.1f})\", (c1, c2), textcoords=\"offset points\", xytext=(8, -18))\n",
    "ax.set(xlabel=\"$c_1$\", ylabel=\"$c_2$\", title=\"La recta presupuestaria pivota sobre la dotación\",\n",
    "       xlim=(0, 240), ylim=(0, 240))\n",
    "ax.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4d28196",
   "metadata": {},
   "source": [
    "> **Lectura económica.** La tasa de interés es el precio relativo del consumo presente en\n",
    "> términos de consumo futuro. Como la dotación siempre es alcanzable, el signo del efecto\n",
    "> riqueza de un cambio en $r$ lo determina la **posición neta**: los deudores pierden, los\n",
    "> acreedores ganan."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "312d6e97",
   "metadata": {},
   "source": [
    "---\n",
    "## Problema 02 — Euler y la solución cerrada con utilidad logarítmica\n",
    "\n",
    "$$\\max_{c_1,c_2}\\; \\ln c_1+\\beta\\ln c_2 \\quad\\text{s.a.}\\quad c_1+\\frac{c_2}{1+r}=W$$\n",
    "\n",
    "con $\\beta=0{,}95$. La condición de primer orden es la **ecuación de Euler**\n",
    "$u'(c_1)=\\beta(1+r)u'(c_2)$, es decir $c_2/c_1=\\beta(1+r)$, y sustituyendo en la RPI\n",
    "se obtiene $c_1=W/(1+\\beta)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "76267ea1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.572973Z",
     "iopub.status.busy": "2026-08-04T12:30:24.572730Z",
     "iopub.status.idle": "2026-08-04T12:30:24.589152Z",
     "shell.execute_reply": "2026-08-04T12:30:24.587744Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>forma cerrada</th>\n",
       "      <th>scipy (minimize_scalar)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>riqueza W</th>\n",
       "      <td>220.0000</td>\n",
       "      <td>220.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>consumo c₁</th>\n",
       "      <td>112.8205</td>\n",
       "      <td>112.8205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>consumo c₂</th>\n",
       "      <td>112.5385</td>\n",
       "      <td>112.5385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ahorro s₁</th>\n",
       "      <td>-12.8205</td>\n",
       "      <td>-12.8205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>utilidad U</th>\n",
       "      <td>9.2129</td>\n",
       "      <td>9.2129</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            forma cerrada  scipy (minimize_scalar)\n",
       "riqueza W        220.0000                 220.0000\n",
       "consumo c₁       112.8205                 112.8205\n",
       "consumo c₂       112.5385                 112.5385\n",
       "ahorro s₁        -12.8205                 -12.8205\n",
       "utilidad U         9.2129                   9.2129"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1, y2, r, beta = 100.0, 126.0, 0.05, 0.95\n",
    "W = y1 + y2/(1+r)\n",
    "\n",
    "# ---------- 1) forma cerrada\n",
    "c1_cf = W/(1+beta)\n",
    "c2_cf = beta*(1+r)*c1_cf\n",
    "chk(\"P02_c1\", c1_cf, 112.82); chk(\"P02_c2\", c2_cf, 112.54)\n",
    "\n",
    "# ---------- 2) optimización numérica con scipy\n",
    "def U(c1, c2, beta=beta):\n",
    "    return np.log(c1) + beta*np.log(c2)\n",
    "\n",
    "def neg_U_de_c1(c1):\n",
    "    \"Sustituye la restricción: c2 = y2 + (1+r)(y1 - c1). Se minimiza -U.\"\n",
    "    c2 = y2 + (1+r)*(y1 - c1)\n",
    "    if c1 <= 0 or c2 <= 0:\n",
    "        return np.inf\n",
    "    return -U(c1, c2)\n",
    "\n",
    "res = minimize_scalar(neg_U_de_c1, bounds=(1e-6, W-1e-6), method=\"bounded\",\n",
    "                      options={\"xatol\": 1e-12})\n",
    "c1_num = res.x\n",
    "c2_num = y2 + (1+r)*(y1 - c1_num)\n",
    "\n",
    "pd.DataFrame({\n",
    "    \"forma cerrada\": [W, c1_cf, c2_cf, y1-c1_cf, U(c1_cf, c2_cf)],\n",
    "    \"scipy (minimize_scalar)\": [W, c1_num, c2_num, y1-c1_num, U(c1_num, c2_num)],\n",
    "}, index=[\"riqueza W\", \"consumo c₁\", \"consumo c₂\", \"ahorro s₁\", \"utilidad U\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "80b534ad",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.591872Z",
     "iopub.status.busy": "2026-08-04T12:30:24.591604Z",
     "iopub.status.idle": "2026-08-04T12:30:24.606898Z",
     "shell.execute_reply": "2026-08-04T12:30:24.606062Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Euler:  u'(c1) = 0.008864   vs   β(1+r)u'(c2) = 0.008864   (brecha 0.00e+00)\n",
      "β(1+r) = 0.9975 < 1  ->  perfil de consumo levemente DECRECIENTE\n",
      "Propensión a consumir de la riqueza  ∂c1/∂W = 1/(1+β) = 0.5128\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>r</th>\n",
       "      <th>W</th>\n",
       "      <th>c1</th>\n",
       "      <th>c2</th>\n",
       "      <th>s1</th>\n",
       "      <th>c1/W</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>226.0000</td>\n",
       "      <td>115.8974</td>\n",
       "      <td>110.1026</td>\n",
       "      <td>-15.8974</td>\n",
       "      <td>0.5128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0200</td>\n",
       "      <td>223.5294</td>\n",
       "      <td>114.6305</td>\n",
       "      <td>111.0769</td>\n",
       "      <td>-14.6305</td>\n",
       "      <td>0.5128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0500</td>\n",
       "      <td>220.0000</td>\n",
       "      <td>112.8205</td>\n",
       "      <td>112.5385</td>\n",
       "      <td>-12.8205</td>\n",
       "      <td>0.5128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0800</td>\n",
       "      <td>216.6667</td>\n",
       "      <td>111.1111</td>\n",
       "      <td>114.0000</td>\n",
       "      <td>-11.1111</td>\n",
       "      <td>0.5128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.1000</td>\n",
       "      <td>214.5455</td>\n",
       "      <td>110.0233</td>\n",
       "      <td>114.9744</td>\n",
       "      <td>-10.0233</td>\n",
       "      <td>0.5128</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.1500</td>\n",
       "      <td>209.5652</td>\n",
       "      <td>107.4693</td>\n",
       "      <td>117.4103</td>\n",
       "      <td>-7.4693</td>\n",
       "      <td>0.5128</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       r        W       c1       c2       s1   c1/W\n",
       "0 0.0000 226.0000 115.8974 110.1026 -15.8974 0.5128\n",
       "1 0.0200 223.5294 114.6305 111.0769 -14.6305 0.5128\n",
       "2 0.0500 220.0000 112.8205 112.5385 -12.8205 0.5128\n",
       "3 0.0800 216.6667 111.1111 114.0000 -11.1111 0.5128\n",
       "4 0.1000 214.5455 110.0233 114.9744 -10.0233 0.5128\n",
       "5 0.1500 209.5652 107.4693 117.4103  -7.4693 0.5128"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# verificación de la ecuación de Euler y de la propensión a consumir\n",
    "euler_izq = 1/c1_cf\n",
    "euler_der = beta*(1+r)/c2_cf\n",
    "print(f\"Euler:  u'(c1) = {euler_izq:.6f}   vs   β(1+r)u'(c2) = {euler_der:.6f}   (brecha {euler_izq-euler_der:.2e})\")\n",
    "print(f\"β(1+r) = {beta*(1+r):.4f} < 1  ->  perfil de consumo levemente DECRECIENTE\")\n",
    "print(f\"Propensión a consumir de la riqueza  ∂c1/∂W = 1/(1+β) = {1/(1+beta):.4f}\")\n",
    "\n",
    "# (c) c1/W no depende de r: se recalcula para una grilla de tasas\n",
    "grilla = pd.DataFrame({\"r\": [0.00, 0.02, 0.05, 0.08, 0.10, 0.15]})\n",
    "grilla[\"W\"]     = y1 + y2/(1+grilla.r)\n",
    "grilla[\"c1\"]    = grilla.W/(1+beta)\n",
    "grilla[\"c2\"]    = beta*(1+grilla.r)*grilla.c1\n",
    "grilla[\"s1\"]    = y1 - grilla.c1\n",
    "grilla[\"c1/W\"]  = grilla.c1/grilla.W\n",
    "grilla"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2fd5412a",
   "metadata": {},
   "source": [
    "> **Lectura económica.** La ecuación de Euler no dice *cuánto* se consume, sino *cómo se\n",
    "> inclina* el perfil de consumo. El nivel lo fija la riqueza; la pendiente, $\\beta(1+r)$.\n",
    "> Con $\\sigma=1$ la tasa de interés entra **solo a través de $W$**: no altera cómo se\n",
    "> reparte la riqueza, solo cuánta riqueza hay."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd0b8b4c",
   "metadata": {},
   "source": [
    "---\n",
    "## Problema 03 — CRRA: ¿sube el ahorro cuando sube la tasa de interés?\n",
    "\n",
    "Hogar B de ciclo de vida ($y_1=200$ trabajando, $y_2=21$ de pensión) con\n",
    "$u(c)=c^{1-\\sigma}/(1-\\sigma)$. La Euler CRRA da $c_2/c_1=[\\beta(1+r)]^{1/\\sigma}$ y\n",
    "\n",
    "$$c_1=\\frac{W}{1+\\beta^{1/\\sigma}(1+r)^{(1-\\sigma)/\\sigma}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "253f730c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.609265Z",
     "iopub.status.busy": "2026-08-04T12:30:24.609009Z",
     "iopub.status.idle": "2026-08-04T12:30:24.626513Z",
     "shell.execute_reply": "2026-08-04T12:30:24.624984Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>EIS = 1/σ</th>\n",
       "      <th>s₁ · r=5%</th>\n",
       "      <th>s₁ · r=10%</th>\n",
       "      <th>Δs₁</th>\n",
       "      <th>Var. %</th>\n",
       "      <th>s₁ · r=5% (scipy)</th>\n",
       "      <th>s₁ · r=10% (scipy)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>σ</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.5000</th>\n",
       "      <td>2.0000</td>\n",
       "      <td>87.0419</td>\n",
       "      <td>90.0560</td>\n",
       "      <td>3.0141</td>\n",
       "      <td>3.4628</td>\n",
       "      <td>87.0419</td>\n",
       "      <td>90.0560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0000</th>\n",
       "      <td>1.0000</td>\n",
       "      <td>87.1795</td>\n",
       "      <td>87.6457</td>\n",
       "      <td>0.4662</td>\n",
       "      <td>0.5348</td>\n",
       "      <td>87.1795</td>\n",
       "      <td>87.6457</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2.0000</th>\n",
       "      <td>0.5000</td>\n",
       "      <td>87.2483</td>\n",
       "      <td>86.4414</td>\n",
       "      <td>-0.8069</td>\n",
       "      <td>-0.9248</td>\n",
       "      <td>87.2483</td>\n",
       "      <td>86.4414</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        EIS = 1/σ  s₁ · r=5%  s₁ · r=10%     Δs₁  Var. %  s₁ · r=5% (scipy)  \\\n",
       "σ                                                                             \n",
       "0.5000     2.0000    87.0419     90.0560  3.0141  3.4628            87.0419   \n",
       "1.0000     1.0000    87.1795     87.6457  0.4662  0.5348            87.1795   \n",
       "2.0000     0.5000    87.2483     86.4414 -0.8069 -0.9248            87.2483   \n",
       "\n",
       "        s₁ · r=10% (scipy)  \n",
       "σ                           \n",
       "0.5000             90.0560  \n",
       "1.0000             87.6457  \n",
       "2.0000             86.4414  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1, y2, beta = 200.0, 21.0, 0.95\n",
    "\n",
    "def u_crra(c, sigma):\n",
    "    return np.log(c) if np.isclose(sigma, 1.0) else (c**(1-sigma) - 1)/(1-sigma)\n",
    "\n",
    "def c1_cerrada(sigma, r):\n",
    "    W = y1 + y2/(1+r)\n",
    "    return W / (1 + beta**(1/sigma) * (1+r)**((1-sigma)/sigma))\n",
    "\n",
    "def c1_numerica(sigma, r):\n",
    "    \"Maximiza u(c1) + β u(c2) sujeto a la RPI, con scipy.\"\n",
    "    W = y1 + y2/(1+r)\n",
    "    f = lambda c1: -(u_crra(c1, sigma) + beta*u_crra(y2 + (1+r)*(y1-c1), sigma)) \\\n",
    "                   if 0 < c1 < W else np.inf\n",
    "    return minimize_scalar(f, bounds=(1e-8, W-1e-8), method=\"bounded\",\n",
    "                           options={\"xatol\": 1e-13}).x\n",
    "\n",
    "filas = []\n",
    "for sigma in (0.5, 1.0, 2.0):\n",
    "    s0 = y1 - c1_cerrada(sigma, 0.05)\n",
    "    s1_ = y1 - c1_cerrada(sigma, 0.10)\n",
    "    filas.append({\"σ\": sigma, \"EIS = 1/σ\": 1/sigma,\n",
    "                  \"s₁ · r=5%\": s0, \"s₁ · r=10%\": s1_,\n",
    "                  \"Δs₁\": s1_-s0, \"Var. %\": (s1_/s0-1)*100,\n",
    "                  \"s₁ · r=5% (scipy)\": y1-c1_numerica(sigma, 0.05),\n",
    "                  \"s₁ · r=10% (scipy)\": y1-c1_numerica(sigma, 0.10)})\n",
    "tab3 = pd.DataFrame(filas).set_index(\"σ\")\n",
    "chk(\"P03_ds_sigma05\", tab3.loc[0.5, \"Δs₁\"],  3.01)\n",
    "chk(\"P03_ds_sigma1\",  tab3.loc[1.0, \"Δs₁\"],  0.47)\n",
    "chk(\"P03_ds_sigma2\",  tab3.loc[2.0, \"Δs₁\"], -0.81)\n",
    "tab3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "45331fa6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.628992Z",
     "iopub.status.busy": "2026-08-04T12:30:24.628792Z",
     "iopub.status.idle": "2026-08-04T12:30:24.744869Z",
     "shell.execute_reply": "2026-08-04T12:30:24.743228Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Δs₁ = 0  en  σ* = 1.2241   (EIS* = 0.8169)\n",
      "σ < σ*  ->  domina sustitución, el ahorro SUBE con r\n",
      "σ > σ*  ->  domina el efecto ingreso, el ahorro CAE con r\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAqUAAAHACAYAAACbCRFGAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjksIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvJkbTWQAAAAlwSFlzAAAQ6wAAEOsBUJTofAAAkg5JREFUeJzs3Xd4U+XbB/BvkrZJ994tLbNsKEhZCmXKFBREERRQ0SqggKKAA2QrwwmKE38M8WUqQ0S0KHtvKKsttKUt3TNpmuS8f5SGhq40pD1p+/1cVy6Ss3Ln7iG9+5zneY5EEAQBREREREQikoodABERERERi1IiIiIiEh2LUiIiIiISHYtSIiIiIhIdi1IiIiIiEh2LUiIiIiISHYtSIiIiIhIdi1IiIiIiEh2LUiIiIiISHYtSIiIiIhIdi1IikYWHhyM4ONhsx9u/fz8kEgnWrFljtmOKKTY2FhKJBHPnzhU7FItj7nPHGMHBwQgPD6/295k7dy4kEgliY2ON2r66cjF+/HhIJBKzH5eISmNRSmRmxUVhRY+oqCixw6RqcuDAAUgkEuzdu1fsUMiCrVmzptLvCZVKpd8+ODgYTZo0KXWcQ4cO4cknn0SjRo2gUCjg6emJdu3a4dVXX8WZM2dq8iMRPTQrsQMgqqtGjhyJYcOGlbnOz8+v2t63R48eUCqVsLa2rrb3qEvatWuHa9euQS6Xo2fPnli2bBmaNm1q8vG2bNkCV1dX9OrVS7/stddew4YNG1BYWIi2bdvio48+wuOPP26O8Ous999/HzNnzoRcLhc7lGr12muvoVu3bmWus7GxqXDf1atXIyIiAj4+PnjhhRfQpEkTZGZm4tq1a9i1axeaNm2K0NDQ6gibqFqwKCWqJu3atcPYsWNr/H2lUikUCkWNv29t1a1bN0yaNAkxMTH46quv8Nhjj+HixYvw8PAw6Xjbtm3DkCFDDP4oCAoKwqJFi5Cfn4+vv/4agwcPxr59+yq8DC4IAvLy8uDg4GBSHLWdlZUVrKzq/q+obt26mfQ9odFoMGvWLDg4OODEiRMICAgwWK/T6ZCWlmauMIlqBC/fE9UiR48exdChQ+Hn5we5XA5fX1/06tUL27dv129TXp/S7OxsTJ48GT4+PrC1tUXHjh2xbdu2MvvuFfejy87OxpQpU+Dr6wu5XI4OHTrgzz//LDO29evXo3PnzrC3t4e9vT26dOmCjRs3Vunz/fLLL2jXrh0UCgX8/f0xffp05Ofnl7mtIAj47rvvEBYWpn/Pbt26GeTCGF9//TVeeeUVLF68GBs3bkRycjI+/fRT/fr4+Hi88soraNiwIRQKBTw8PNCxY0csWrSo1LFOnDiB27dv46mnnjJYPnPmTEyaNAkzZszAoUOHYG9vj/fee0+/vvhS7r59+7B48WI0a9YMcrkcy5Ytq9JnKXbs2DEMGTIEbm5uUCgUaN68OebPnw+1Wm30MU6dOoW+ffvC3t4erq6uGDFiRIX9OyMjIzFw4EC4urpCLpejRYsW+Pjjj6HVakttGxMTg4kTJyIoKAhyuRze3t7o378//vrrL/025fUpvXHjBp588kk4OzvD0dER/fv3x7lz58qN68yZMxg5ciS8vLxgY2ODRo0aYebMmeWeV8aIiorCpEmT0Lp1azg7O8PW1hZt2rTBsmXLyvy81SE1NRUZGRkICQkpVZACRX+cenp61kgsROZS9/8MJRJJfn4+UlNTSy2XyWRwdXWt8vGuXbuGPn36wMvLC6+//jr8/PyQmpqKU6dO4ciRIxg+fHi5+2o0Gjz++OM4evQoRo4cifDwcMTHx2P8+PFo1qxZufs9/vjjcHFxwaxZs5Cfn4/PPvsMTzzxBK5fv44GDRrot/vwww8xf/58tGnTBnPmzIEgCFi3bh1Gjx6N6OhozJ49u9LP98033+C1115D06ZN8eGHH8LGxgbr16/Hf//9V+b2EyZMwP/+9z8MGzYMY8aMAQBs3boVTz75JL7++mtERERU+p4PGjx4MPz8/PDPP/8AKMpbv379EBcXh9deew3NmzdHbm4uoqKi8M8//5T6XFu3boW9vX2Fl+Z9fX0xZMgQbNy4EUqlEra2tvp1M2bMQH5+PsaNGwdPT08EBgZW+TPs2bMHTzzxBJycnPD666/Dx8cHu3fvxocffojDhw9j165dkEorbo84ffo0evToAZlMhilTpiAwMBB79+5FeHg48vLySm3/448/4uWXX0ZoaChmzpwJFxcXHDp0CLNmzcKZM2cM/jg5ffo0+vTpg/z8fIwfPx7t27dHTk4Ojh49in379qFfv37lxhUXF4du3bohMzMTERERaNGiBY4ePYrw8HC4u7uXmYvhw4cjMDAQU6ZMgbe3N86dO4cVK1bg0KFDiIyMNKk1dv/+/YiMjMSQIUPQsGFDqFQq7N69GzNmzEB0dDRWrVpl9LFyc3PL/J6wtraGs7Nzuft5e3vDwcEBly5dwuHDh8vtAkBUqwhEZFaRkZECgHIfQUFBBtv37Nmz1LKyfP755wIA4ejRo0a9/08//aRf9u233woAhBkzZhhse/LkSUEikQgAhJiYGP3ycePGCQCEV155xWD7I0eOCACEWbNm6Zddu3ZNkEqlQrt27YS8vDz98tzcXKF169aCTCYzOHZZMjMzBQcHB6FBgwZCZmamfnl+fr7Qvn17AYAwZ84c/fLt27cLAIQVK1aUOtbQoUMFJycnITs7u8L3LPkesbGxQmFhoSAIgtC1a1ehUaNGgiAIwrlz5wQAwpIlS4w6VrNmzYSRI0eWWq7RaITY2Fh9fmbNmiUAEG7fvi0IgiD89NNPAgChcePGQk5OjlHvJQilzx2NRiMEBwcLtra2wvXr1w22nTBhggBAWLt2baXHfeyxxwSpVCqcPHnSYPmrr74qABB69uypX5aYmCgoFAph+PDhgk6nM9h+2bJlAgBh//79giAIgk6nE1q3bi1YWVkJx44dK/W+Wq1W/3zOnDmlzsvnn39eACBs27bNYL/FixeX+r+lVCoFHx8fISwsTFCpVAbbb968WQAgrFmzptJcFP9fKCk3N7fMbZ977jlBJpMJiYmJlR63+Gde3qNkjgVBEIKCgoTGjRsbLCvOLwChTZs2QkREhPDDDz9U+v+NyFLx8j1RNRk/fjz++uuvUo/169ebdDwXFxcAwPbt26FUKqu077Zt2wAA7777rsHyjh07Vtgy9fbbbxu87tKlCxwcHHDt2jX9su3bt0On0+Hdd9+FnZ2dfrm9vT1mzJgBrVaL3377rcL49u7di9zcXEyePNmgdcjW1rZUDACwdu1a2Nra4plnnkFqaqrBY/jw4cjOzsaRI0cqfE8AWLlyJTw9PREcHAxfX19s3boVarVaH0Pxv5GRkUhKSqrwWBcvXsS1a9dKXbo/ePAggoODERwcDFdXV3zwwQf6y+gPtoRNnjz5ofqQnj59GrGxsXj++edLjdQunlJry5YtFR4jJSUFBw4cwIABA9CxY0eDdR988EGp7Tdv3gyVSoWXX34ZaWlpBj+LIUOGAIC+y8e5c+dw8eJFjBkzBmFhYaWOVVELrk6nw/bt29GyZctSVwWmTp1aKm/79u1DUlISxo8fj5ycHIO4evToATs7u3K7olTG3t5e/7ygoADp6elITU3FgAEDoNVqcfLkSaOPNXPmzDK/J5YvX17pvm+99RZ27tyJIUOG4NatW/jmm2/w0ksvoWHDhhg2bBhSUlJM+nxEYuHle6Jq0rhxY/Tt29dsx3v22Wfxyy+/YMmSJfj0008RFhaGHj164Nlnn0Xr1q0r3Dc6OhoeHh5lXuJs0aJFudMXNWrUqNQyd3d3gwEU0dHRAIA2bdqU2rZ42c2bNyuMr3h9y5YtS61r1apVqWVXrlyBUqmEv79/ucdMTk6u8D1PnjyJKVOmYPLkyVi0aBFOnz6NsWPHIisrCz169ABQNEBpzpw5mD9/Pvz8/NCmTRs8+uijGD58eKlifsuWLZDL5Rg8eLB+WX5+PkaMGIFmzZrh+PHjyMvLw/PPP4/o6Gg4ODjAycnJ4BgVdaUwRkU/iwYNGsDJyemhfhb+/v6lCukrV64AgL4ALUvxz6L4j5kOHTpUGENZ7t69i5ycnDLjUigUaNy4MTIzM0vF9frrr+P111+vMK6qys/Px/z587Fx48Yy+9mmp6cbfaxWrVo91PfE4MGDMXjwYOh0Oly9ehX79+/HypUr8fvvv2Ps2LEmF95EYmBRSlRL2NjY4I8//sDp06fx559/4uDBg/j000+xaNEiLF26FG+99ZbZ31Mmk5W5XBAEs79XVeh0Ojg7O2Pz5s3lblNWMVvS559/DhcXFyxduhRyuRw9evTAJ598gtGjR+ORRx7Rbzd37lxMmDABf/zxBw4cOIAtW7Zg1apVGDZsGLZt26afWH3r1q3o06ePQaH5yy+/4O7du9ixYwd8fX0BAP/3f/+HRo0a4dFHHy0VU8mW5upQHZPA63Q6AMD333+PoKCgMrepzinQylMc18KFC8tslQVgUt9uABgzZgx+++03vPzyy+jRowc8PDxgZWWFU6dOYebMmfr3rklSqRQtWrRAixYtMH78eLRq1Qp79+5FfHx8mQOhiCwRi1KiWqZDhw76lqaMjAx069YNs2fPxpQpU8qd17BRo0a4evUq0tLSSrWWFrcomapx48YAgEuXLpVqsb148aLBNpUd4/LlywYtjcXHfVCzZs0QFRWF0NDQMlt/jXHu3Dl07tzZYB7MxMREAMDQoUMNtg0KCkJERAQiIiKg0Wgwfvx4rF+/Hv/++y/Cw8Nx48YNnD9/Hm+++Wap97Czs0OnTp30y1JTU6HRaEq9hzmU/Fk8KC4uDllZWVX6WTwoISEBWVlZBsuKW3ddXV0rbfEr3taUSd29vLzg6OhYZlwqlQo3b940OBeK30uhUJj1ikVWVhZ+++03jB07Ft9++63BuuvXr5vtfR6Gra0tQkNDERMTg4SEBBalVGuwTylRLVHWCF1XV1c0atQIarUaOTk55e5b3Afv448/Nlh+6tQpg2l4TDF8+HBIpVIsW7bM4A40+fn5WLp0KWQyWbk3ESjWv39/2Nvb46uvvjIoelQqVZnTIr3wwgsAgHfeeafMVltjLstaWVkZjHzPzc3F559/ju7du+uL/qysLBQWFpbar127dgCg78awdevWMj+nlZUV5HK5QQvlwoUL4ezsjHHjxlUaY1WFhoYiODgYa9euxa1btwzWzZs3DwAwYsSICo/h6emJRx99FHv27MHp06cN1i1YsKDU9qNGjYJCocDcuXORm5tbar1SqdSfm+3atUPr1q2xbt26MvtdVtTCKJVKMWzYMFy+fLnUtF+fffZZqfd+/PHH4e3tjaVLl5bZH1ij0VTpMnvJOIDSVwtycnKwYsWKKh/PVCqVSj9LxIPu3r2LQ4cOwcrK6qFuBEFU09hSSlRNzp07h3Xr1pW5Ljw8vMqtFwsWLMCePXv009BYWVnh33//xe7duzFkyJAKWwwnTJiAH374AUuXLkVsbCzCw8MRFxeHVatW4ZFHHsGJEydMvrTbpEkTvPfee5g/fz66dOmCMWPG6KeEunDhAhYuXFjpPcmdnZ3x8ccfY/LkyejUqRMmTJgAGxsbrFu3rswuBCNGjMDEiRPx3Xff4dy5cxg+fDh8fHxw584dnDp1Crt37y5VTD5owIABWLlyJc6cOQNfX1+MHz8e6enp2Llzp36byMhITJw4EU8++SRCQkLg4uKCy5cv45tvvoG/v7++BW7Lli3o0aNHqZ/B448/jk8//RRr1qzBiBEjsHjxYmzZsgU///yzyS28FZHJZPj666/xxBNPoFOnToiIiICXlxf++OMP7N69G48//jiee+65So/z6aefokePHggPD8ekSZP0U0KdOXOm1E0F/P39sXr1arz44osICQnBuHHj0KhRI6SnpyMqKgpbt27F9u3bER4erp8/t3fv3ujevTtefPFFtGvXDnl5eTh69CgaNWpU6g+nkor/D4waNUo/RdfRo0fx+++/o3HjxtBoNPpt7ezssHbtWgwbNgwtWrTAhAkT0Lx5c+Tk5ODmzZvYunUrlixZgvHjx1cpx46OjhgwYADWr18PuVyOzp07IzExET/88AO8vb2rdCwAOHz4cLnrBg8eXG4XA5VKhT59+qB58+YYOHAgQkJCIJVKcfPmTaxduxbJycmYO3cu3NzcqhwTkWjEHfxPVPdUNiUUHpjSxtgpoSIjI4VnnnlGP+WPk5OT0LZtW+Hjjz8W8vPzS71/ySmhBEEQMjIyhNdee03w8vIS5HK50KFDB2Hr1q3C9OnTBQBCcnKyftuypsEpFhQUVGq6GkEQhLVr1wphYWGCra2tYGtrK3Tu3FnYsGFDpZ+rpHXr1glt2rQRbGxsBF9fX2HatGnCpUuXSk0JVWzDhg1CeHi44OzsLNjY2AiBgYHCwIEDha+//rrS91IqlcJzzz0nSKVSAYDQvn174cSJEwbbREdHCxEREULLli0FJycnwdbWVmjSpIkwZcoUIS4uThAEQYiLixMkEonw5Zdflvk+H3/8sWBvby8AEHx8fMqckql4eqDIyMjKk1RCeefOkSNHhEGDBgkuLi6CjY2N0KxZM2HevHlCQUGB0cc+fvy40KtXL8HOzk5wdnYWnnrqKSEmJqbcn//Ro0eFkSNHCt7e3oK1tbXg7e0tdO3aVZg/f76QlpZmsO3169eFcePGCb6+vvptH3/8cWHfvn36bcqaEkoQBOHq1avCsGHDBEdHR8HBwUHo16+fcObMmXJzceXKFWHcuHFCQECAYG1tLXh4eAgdO3YUZs2apZ+SqyJl/V9IS0sTXn31VcHf31+Qy+VCSEiI8Mknnwj79u0r8/9eWSqbEgqAcObMGf32D04JpdFohDVr1ghjxowRQkJCBCcnJ8HKykrw9vYWBg0aJGzfvr3SGIgsjUQQRB6xQESiGjx4MP79919kZ2dXOql6XaRSqZCTk2Py3W+++OILTJ06FXFxceXOBqDVapGSkgIvL696mWMiImPw25GonijrtoonT57Enj170Ldv33pbLCkUioe6HaOvry8+++yzCqenkslk8PHxqbc5JiIyBltKieqJcePGISMjA48++iicnZ1x8eJFfP/995DJZDhy5EiZc1sSERHVFBalRPXE+vXrsXLlSly9ehXZ2dlwc3NDjx49MGfOnEon3yciIqpuLEqJiIiISHTs4EREREREomNRSkRERESiq3NFqUajQXx8vMEkykRERERk2epcUZqUlITAwMAybytXX2i1WiQlJUGr1YodikVjnozDPBmPuTIO82Q85so4zJNxLD1Pda4oJSIiIqLah0UpkYgSZryDhBnviB0GERGR6KzEDoCoPitMSBA7BCIiIovAllIiIiIiEh2LUiIiIiISHYtSIiIiIhId+5QSicgmMFDsEKiOEQQBqampUKlUFjvtiyAIUKlUUCqVkEgkYodj0Zgr4zBPxjFnnmQyGRQKBTw8PMyWcxalRCLy+3iJ2CFQHSIIAhISEpCTkwMbGxvIZDKxQyqTRCKBXC5n8WAE5so4zJNxzJkntVqN3NxcFBQUwN/f3yzHZFFKRFRHpKamIicnB15eXnB3dxc7nHIJggCNRgMrKysWEZVgrozDPBnH3HlKS0vD3bt3kZqaCk9Pz4c+HvuUEokoadEiJC1aJHYYVEeoVCrY2NhYdEFKRHWHu7s7bGxsoFKpzHI8tpQSiUh18ZLYIVAdotVqLfaSPRHVTTKZzGz919lSSkRERESiY1FKRERERKJjUWoGao1O7BCIiIiIajWLKUp///13dO7cGY6OjvD19cWoUaMQHR0tdljliknNw6DPDyB03l70+/RfscOhWkrm6AiZo6PYYRDVesHBwTX6fidPnsSECRPQokULSKVSDBkyxKj9rl69ismTJ6Nly5aws7NDw4YN8dprryE1NdVgu02bNmHYsGEIDAyEi4sLQkND8eOPP0IQhHKPvX37dkgkErRu3fqhPltYWBhWrlz5UMcwN4lEgmXLllW4zb///gupVIqTJ09WSwxnz56FRCLB/v37q+X4JY0fP/6hf44Pa+LEiZg4cWKNvqdFFKX79+/Hk08+iZYtW2Lbtm347LPPcO7cOfTv3x9KpVLs8MpkZyPD5cRsZOQX4k6mEjpd+V8UROUJXP0NAld/I3YYRLXS2rVrcf78eYNlsbGxNVJQHTp0CAcOHECHDh3QoEEDo/f766+/cODAAbz66qvYvXs35s6di927d+Oxxx5DQUGBfrsVK1bAzs4Oy5Ytw7Zt2zBgwABMnDgR8+bNK/O4SqUS06ZNg7e390N9rm3btiE2NhYvvvjiQx1HDKGhoTh8+DBatGghdigP7YMPPsCGDRtEjeHdd9/F//73P1y/fr3G3tMiRt9v3LgRQUFB+PHHH/XzZnl5eaF37944efIkHnvsMZEjLM3DQQ4rqQQanYBCrYDUvAJ4OSrEDouIqN5o1qwZpk6ditDQUKjVaixatAi///475s6dW+3vPWXKFLz55psAgPDwcKP3Gz16NCZNmmQwR2TTpk3RvXt37Ny5EyNGjAAA7NixAx4eHvp5Jfv164f09HSsWLECH3zwAaRSwzalxYsXo0GDBmjYsOFDtRR+9tlnGD16NGxtbU0+hlicnJzQpUuXOjFPaePGjcUOAU2aNEH37t2xcuVKfPbZZzXynhbRUlpYWAhHR0eDE8nZ2RkAKrxUISaZVAIf5/tFaGKmeeboovolZeVKpFjYZTIiS7Fs2TI0bdoU1tbWkEgkBo/9+/ejc+fO+Oeff5CXl4fExEQcPnwYBw8exIABA6o9tgeLQmO5u7uXKppCQ0MBAHfu3NEv8/DwKLVvaGgosrOzkZeXZ7D85s2bWL58Ob744guTYioWExODAwcOYOTIkaXW7dq1C927d4ednR1cXV0RHh6OM2fOAADy8vIwefJkhISEwM7ODsHBwYiIiEBWVpbBMYKDgzF58mR89tlnCAwMhKOjI8aPH4+CggKcPXsW3bt3h729PcLCwnDhwoVSMWg0Grzzzjvw9PTU75uTk6NfX9ble5VKhenTp8PPzw8KhQLt27fHtm3bjMrHggUL4OPjAwcHBzz11FO4e/duqW0EQcCyZcvQrFkzyOVyNGrUCJ9++mmlx7506RIGDRoEd3d32NnZISQkBJ988ol+fVmX7w8ePIjQ0FAoFAq0bdsWf/31F9q3b4/x48eX2m///v0IDQ3V5/PUqVMGxzI2L08//TTWr18PjUZT6WcyB4toKR0/fjz+97//YdWqVRgzZgzS0tIwe/ZshIaGonv37hXum52djezsbP3rxMREAEXz9VX3fZ99nRWIzyjqXpCQkYfWfpbRN1Cr1UKn01nsfa8thSXkKffgIQCAW0SEaDFUxhLyVFuInStBECCRSCz2j/ligiDoH+VZuXIlZsyYgfHjx+PLL7/EjRs3MHv2bDg4OGDChAlo0KABTpw4gVmzZqFNmzbw9fVF165d0bNnT8ydOxd9+/Yt99jG/IKVyWRVbnEzNe8HDhwAADRv3rzUMUrm6uDBg/D394eDg4PBdm+++Saef/55tG3b9qFi2bdvH6ysrNCpUyeD/X/99Vc899xzGDZsGNavXw8bGxscOnQI8fHxaN++PfLy8qDRaLBgwQJ4enoiLi4OixYtwvDhw/HPP/8YvMdvv/2G1q1b45tvvkF0dDTeeustWFtb4+jRo/ruBzNnzsTTTz+NS5cuGRT/X375JTp06IA1a9YgJiYGs2bNgkqlwi+//GJwPpV8PmbMGOzZswcLFixA8+bNsXbtWowYMQLbtm3DE088UW4uvvrqK3zwwQd466230LdvX/z111946aWXSh3/jTfewA8//IDZs2ejc+fOOHz4MN59910oFApEVPC9PnToUHh7e+P777+Hs7Mzbty4gfj4+DJ//kBRbTNgwAB06NABv/76K7KysvDaa68hKysL7du3N9gvKSkJb7zxBt599104Oztj9uzZePLJJ3Hjxg1YWVlBEASMGTMGf/75Z6V56dq1K1JTU3HmzBk88sgj5X4eQRDK/d6rytzJFlGUPvbYY9i2bRuee+45TJo0CQDQvn177Nmzp9IPs2LFCnz00UellqelpUEul1dLvMVc5fe/sK7Gp6CDl2VMWq3T6fR/oZr613x9YAl5KiwsBACkpKSI8v7GsIQ81RZi50qlUkEul5dZdMW/MK7UMtsuneH++usAgMQpb0D7QMuWvHlzeM6eBQBI/uBDFN66ZbDeyscbPvdad1KXL4fqnGH/TolCAf9vV5d635K/wMor/D777DM89thj+PbbbwEAffr0gVwuR0REBJ5//nkEBgZi//79+Pjjj9G2bVts27YN77zzDp5++mn88ccf5V5Sj42NRbNmzcpcV9L333+PF154odLtij9P8WX2qlKpVHj77bfRvn179OzZs9QxinN16NAhbNy4EZ988onBNjt37sThw4dx6dIlaDQa6HQ6k2M5fvw4mjZtCplMpt9fEATMmDED/fr1w//93//pt+3fvz+AogLf1dUVX375pX6dRqNBgwYNEB4ejsuXL5fK9+bNm2FjYwMAiIyMxPfff48dO3bg8ccfB1D0vfjkk0/izJkzaNeunX4/uVyOTZs26esCuVyOV199Fe+99x5CQkKg0xXNhKPVaqHRaHD+/Hls3boVK1eu1A/Y6du3L2JiYvDRRx9h0KBBZeZBq9ViyZIlGDNmDBYvXgyg6PxLTk7G+vXr9ce/efMmVq5ciZUrV+Lll18GUNSVIzc3F/PmzcOLL75Y5vdAamoqYmJisHz5cv0AueJuisV5f/DnuHz5clhZWWH79u1wvDc4tkGDBujVqxd0Op3Bfunp6di3bx9atWoFAFAoFOjXrx8OHz6Mbt264ezZs9i2bZtReQkJCYFMJsORI0fQvn37MvOl0+lQUFBQ7u8xHx+fMpeXxSKK0sOHD+P555/HxIkTMWTIEKSlpWH+/PkYPHgwDhw4UGHflunTp+tPBqDor4mwsDC4u7ub5T6sFWnonQ5cTQcAZGmk1f5+xir+svfw8ODdXSpgCXlSWlsDgMWcO2WxhDzVFmLnSqlUQiKRwMqq9Fd7WcWfVCrVbyuRSkptI5HeP5a0rPUSaYn10jLWlx1LcatOefffzsrKws2bNzFp0iSD/UeNGoVXXnkFR44cQUhICCZMmGCwn5WVFZo2bYqmTZuWOmaxBg0a4Pjx4+WuL9awYcMyYy9LcZcCY7cvacqUKYiNjcWhQ4dgfe/7oCRBEBAfH4+xY8eiV69emDp1qr7QKS5o586dq//FX/xzMCWW5ORkeHl5GewbFRWF+Ph4LFu2rMJjrl27Fp9++imuX79u0L0gOjoaLVu21L/u2bMn7Ozs9K9DQkIglUrRr18//fGLByolJiaiY8eO+m2HDBli0NhUfD6cPn0arVq10udFJpPBysoKR44cAQA888wzBrE/88wzmD59OgoKCmBvb1/qsyQkJODOnTt46qmnDPYrvpRdfPziUfhPP/20wf79+/fHsmXLkJiYiKCgoFLH9/b2RlBQED744ANkZWWhT58+CAgIMNjmwZ/j6dOn0atXL7i6uhrk0s3NzeD/sVQqhZ+fn0Ex36ZNG30+q5oXKysruLi4IDk5udyfv1QqhUKhMMvvMYsoSt944w307t0by5cv1y/r0qULGjRogLVr1+KVV14pd18nJyc4OTmVWi6Tyar9l4K/6/3/WEnZKov6hS2VSmskB7Wd2Hkq/oVs6T8nsfNUm4iZq+LzqaxCL3jD+gr3DVy1qsL1fosWVbje+513KonOUMn+oQ/Kzc0FUDTg9cGxBgqFAklJSaX2i42NNep95XK5vg9nRUy5fF/V7d9//32sX78eO3fu1BcOD8rMzMQTTzwBd3d3bNmyxeC8+vzzzyGVSvHcc8/pW+jVarW+xd7Ozk7fImmM4pb2kp8jPb2o4cXf37/cz7dt2zaMGzcOr7zyChYuXAh3d3ckJibiySefREFBgcF+Li4uBq/lcjlsbW0Nis3i5w/u6+3tXeH5UPL8l0gkyMzMhLW1Ndzd3Q3i9fHxgSAIyMrKgoODQ6nPk5SUVOb7FRf+xcdPS0uDIAjlFmPx8fFlTlUmkUiwd+9evPfee5g8eTLy8vLQsWNHrFixAj169Ci1LVBUUDZt2rTUz8DLy8tgO6DsHAP381nVvMjlcqhUqgrPb4lEYpbvPIsoSi9fvoxhw4YZLAsICICHhwdu3rwpUlSV83W+34KbmMWBTkRE5lDc+lNcHBTLzMyESqUyaC2qqtjYWDRs2LDS7X766SeDASTm9uWXX2LRokVYs2aN/rL1g5RKJYYOHYrs7GwcPnxYPwC4WFRUFG7cuFFmUeTq6oqvv/66wn6ND3JzcytV3BcXLiUHYT1o06ZNaN++PVavvt9V499/zT9/94MDjbKzs6FSqeDr61vm9m5ubigsLERGRobBOZOcnAyJRAIXF5cy9ys+3oPvl5ycXOr4EokEBw8eLLP4DwkJKfezNGvWDJs2bUJhYSEOHz6M2bNnY+jQoUhISCizUPb19S3z8nhZg68qU9W8ZGZmlipgq4tFFKVBQUE4ffq0wbJbt24hNTW1xidErgrfEqPvk7IKKtiSqGxB//tZ7BCILI6dnR06deqETZs24a233tIv37hxIwA81DSBfn5+OHHiRKXbGVO4muqXX37Bm2++icWLF5fbb1Wj0WDUqFG4cuUK/vnnH/j7+5faZubMmaUK5yVLluDq1av46aefjOo7W1JISAgiIyNLLQsICMBPP/2EUaNGlbmfUqksVZStX19xy7wpduzYgRUrVuhb5DZv3gyJRIJOnTqVuf2jjz4KoKhoLnnFddOmTfqR6WUJCAiAr68vtm3bhieffFK/fPPmzQbb9enTB0DRGJahQ4ea9Jmsra3Rs2dPzJw5E0888QTu3LlT5s+tU6dOWL16NXJycvR9Sg8cOKBvya6Kbt26ATAuLykpKcjPz6+wwDYniyhKIyIiMHXqVLz55psYOnQo0tLSsGDBAnh5eZX7n8AS+LncbylNyVFDo9XBSsaBIGQ8iQn9vojqg7lz52Lw4MF47rnn8MILLyAqKgrvvfceRo0apR/AYQobG5sKRxEbKyUlRd8amJKSgtzcXH3RMmjQIH2/ySZNmiAoKAh///03gKIWxHHjxqF3797o2bMnjh49qj9mQECAvm/h66+/jp07d2LZsmXIycnB0aNH9ZdPQ0NDIZfL0bx5czRv3twgrjVr1iA+Pr5Kc6cW6969O+bNm4f4+Hh9HMV3Uho9ejRGjBiBF154AXK5HEeOHEGnTp0wZMgQ9OvXD5MmTcL8+fPRtWtX7N69W/95zamgoADDhw/H66+/jpiYGLz77rsYOXIkWrRoUeZsA23btsVTTz2F6dOnQ6lUIiQkBOvWrcPhw4fx22+/lfs+MpkMM2fOxJtvvglvb2/069cPe/fuLVWwN2vWDJMmTcLzzz+PGTNmoHPnzigsLMS1a9cQGRmJ7du3l3n88+fP46233sIzzzyDxo0bIysrC4sXL0ZwcHC585NOmzYNq1atwuDBgzFjxgxkZmbio48+goeHR5UHVVYlL8XTaxUX+NVOsAA6nU74+uuvhbZt2wr29vaCj4+P8OSTTwpXrlyp8rHi4uIEAEJcXFw1RGpIp9MJTd/bJQS9u1MIenenkJCRX+3vaQyNRiMkJiYKGo1G7FAsmiXkKW3dOiFt3TrR3t8YlpCn2kLsXMXExAgxMTGivHdV6HQ6Qa1WCzqdrsLttm/fLrRr106wsbERfHx8hOnTpwsqlaqGoqxYZGSkAKDMR8mfQVBQkNCzZ0/96zlz5pS735w5cwz2M+b4Dxo3bpzQqlUrkz5TQUGB4O7uLnz77bel1v3+++9C586dBYVCIbi4uAi9e/cWzpw5IwhC0Xn/1ltvCZ6enoKjo6MwcuRI4ejRowIAYdOmTQafadKkSQbHnTNnjmBvb2+wLCYmptS+AITFixcL06dPF9zc3AQHBwfh+eefF7KysgRBKDqn/vrrLwGAcOLECf1++fn5wtSpUwUfHx/BxsZGaNu2rbBly5ZKc6HT6YSPPvpI8PLyEuzs7IQnnnhC2LNnjwBAiIyMNNjuyy+/FFq3bi3Y2NgIbm5uQteuXYUVK1aUe+zk5GRh7NixQqNGjQS5XC54eXkJI0aMEK5du6bfpqyf43///Se0b99esLGxEVq0aCHs3LlTCA4OFqZOnVrhfhkZGQIA4aefftL/38vLyzMqL1OmTBEee+yxCnNlzu8diSBY+IR2VRQfH4/AwEDExcWVGs1WHR795C/Ep6sBAFte64qOQW7V/p6V0Wq1SElJgaenJwemVMAS8hT73BgAlQ9CEZMl5Km2EDtXxf0BLbnbEwD9VDfljb6n+2o6V2+99RbOnDlTan5RS1cfz6nr16+jefPm+PHHHzFuXOkp38pSlTwVT+21ZMmSCqdHM+f3Dq8dPiRvJxt9UXonU4mOpWd/ICIiqhXefvttNGnSBOfOnTOYVojEN2vWLLRt2xZ+fn6Ijo7GokWL4Ovrq781rblt2LABDg4OeO6556rl+GVhUfqQvJzuzysXn5kvYiREREQPx9fXF2vWrLHoG3rUV2q1Gu+++y6Sk5Nha2uL8PBwLF26tMzR+uYglUrx448/mjTnralYlD4kL8f7RekdFqVERFTLPTgZPFmG5cuXG8znXt3Gjh1bY+9VjEPFH5KX0/1pMO5kcq5SIiIiIlOwpfQhlbx8n8QJ9KmKAr78QuwQqA6RyWRQq9Vih0FE9YhWq63SncMqwpbSh+TtfP8HkcgJ9KmKrNzdYVVDd8qguk+hUECtViMtLU3sUIioHkhLS4NarYZCoah8YyOwpfQh+TjfbylNzyuEUq2FrQ2nzSHjZO3aBQBwHjxY5EioLvDw8EBBQQHu3r2LzMxMi57CS6fTVXnS7/qKuTIO82Qcc+VJq9VCrVbD0dERHh4eZoiMLaUPzc5GBifb+3N9JXCwE1VBxvoNyFi/QewwqI6QSCTw9/eHh4eH2S6nVQdBEFBQUFDmXXjIEHNlHObJOObMk42NDTw8PODv72+2uWHZUmoGnk4yZCs1AIC4DCWaeDmKHBER1VcSiQSenp5ih1EhsW8yUJswV8Zhnoxj6XliS6kZeDre/8HGpeWJGAkRERFR7cSi1Ay8nO4XpbczWJQSERERVRWLUjPwLFGUxmewTykRERFRVbFPqRl4GRSlShEjodrGd/48sUMgIiKyCCxKzaBkUXonk3OVkvHkjRuLHQIREZFF4OV7Myh5+b54rlIiY+QeOoTcQ4fEDoOIiEh0bCk1A1sbKZxsZchWFhWjCZlKNPFyEDkqqg1SV64CADh07y5yJEREROJiS6mZlLyzEwc7EREREVUNi1Iz8XG+f/eUuHROC0VERERUFSxKzaRkSynnKiUiIiKqGhalZlKyKI1L57RQRERERFXBgU5mYnD5nn1KyUheb00XOwQiIiKLwKLUTPxd7xel8ekqESOh2sSuY0exQyAiIrIIvHxvJj4u1pDce56l1CBLWShqPFQ7qC5fhuryZbHDICIiEh2LUjORW0nh4Xi/4fl2Gi/hU+WSFixE0oKFYodBREQkOhalZuRX4hJ+bBpH4BMREREZi0WpGfm7lCxKc0SMhIiIiKh2YVFqRmwpJSIiIjINi1Iz8ivRUso+pURERETG45RQZlSypZQT6JMx3F96UewQiIiILAKLUjMq2ac0OVuNAo0WciuZiBGRpXPs00fsEIiIiCwCL9+bkaOtDI6KoiJUAFtLqXKFd+6g8M4dscMgIiISHYtSM/NzsdY/v53OwU5UsYS3ZyDh7Rlih0FERCQ6FqVmVrJfaUxqroiREBEREdUeLErNzN9gWigWpURERETGYFFqZgZFaSqnhSIiIiIyBotSMwt0k+ufx6SyTykRERGRMTgllJkFuN1vKb2TWcBpoahCLiOeEjsEIiIii/DQLaVKpRLvvfcewsLC0KlTJ8yaNQt5efW3hdC5xLRQOgGIS+clfCqfy4gRcBkxQuwwiIiIRPfQLaWTJk3C5cuXMW7cOOTl5WHlypWIj4/H2rVrzRFfrSORSBDgZoMrd4rmKI1OyUMTL0eRoyJLpcsv+qNFamcnciRERETiMrooPXPmDEJDQ0st37lzJ27cuAEnJycAQKtWrTB27FjzRVgLBZYoSm+m5ADwETcgsli3X54IAAjesF7kSIiIiMRl9OX7AQMGICIiAmlpaQbLvby88NdffwEABEFAZGQkvL29zRtlLRNQYrBTUVFKRERERBUxuiiNioqCTCZDixYt8NVXX0Gn0wEAPv74Y4wfPx5eXl5wdXXF6tWrsWzZsmoLuDZo4FZyAv3627+WiIiIyFhGX753dXXFypUr8eqrr+LNN9/Et99+iy+++AKDBw9GdHQ0jh49CgDo3LkzvLy8qi3g2qBkS2lsqlLESIiIiIhqhyoPdGrbti0iIyPx66+/Yty4cQgLC8OKFSswdOjQ6oivVio5gX5aXiGyVYVwUliLGBERERGRZavylFBKpRJZWVl45plnEBUVhebNmyM0NBTz5s1DQUFBdcRY69jaSOHpeL/ej+UlfCqHY+9ecOzdS+wwiIiIRGd0URodHY0ePXrAwcEBbm5uaNasGY4dO4b58+fjxIkTOHv2LJo3b46tW7dWZ7y1Rsk7O0Wn5IoYCVky95dfhvvLL4sdBhERkeiMLkrHjRsHGxsbHDlyBGfPnkXv3r3x1FNPQa1Wo2HDhti6dSu+++47fPDBB+jbt291xlwrlLyz0/W7HIFPREREVBGji9Lz589j5syZCAsLQ5s2bbBkyRJkZmbi1q1b+m369u2L8+fPY8iQIdUSbG0S5H6/pZRFKZXn1oQJuDVhgthhEBERic7ogU7dunXD0qVL4ebmBoVCgZUrV8LHxweNGjUy2E4mk2Hq1KnmjrPWCfK4X5TeuMs+pVQ2oUAtdghEREQWweiW0p9//hnu7u4YMGAAunbtiqtXr2L37t2QyWTVGV+tVbIovZ2mRKFWJ2I0RERERJbN6JZSLy8vbNiwoTpjqVM8HKxgL5cir0AHjU7ArbR8NPFyEDssIiIiIotU5SmhihUUFCApKQlJSUmcCqoMEokEDdxLXsLnCHwiIiKi8lSpKI2NjcXkyZPRqFEj2Nvbw9/fH/7+/rC3t0ejRo0wZcoUxMbGVlOotU9wiUv4V5OzRIyELJVdh1DYdQgVOwwiIiLRGX35/tixY+jfvz/c3Nzw1FNPoUWLFnB1dQUAZGRkICoqClu3bsXatWuxd+9ehIWFVVvQtYXBCPxkjsCn0rzeflvsEIiIiCyC0UXptGnT0LdvX2zcuBHW1mXfMnPJkiV49tlnMXXqVBw+fNhsQdZWBiPwOYE+ERERUbmMvnx/9uxZTJ48udyCFACsrKwwadIknD171qRgfv75Z4SGhkKhUMDDwwMDBw6EUqk06ViWoOTl+5gUJXQ6QcRoyBLFT5uG+GnTxA6DiIhIdEYXpZ6enrhw4UKl2124cAGenp5VDmThwoWYMmUKnnnmGfz5559YvXo1GjZsCK1WW+VjWQpvZ2vIrSQAgAKNDgmZtbfApuqhSb4LTfJdscMgIiISndGX71977TW8++67SElJwdNPP43mzZvDxqboVppqtRpXr17Fpk2bsGzZMsyZM6dKQVy9ehVz587F77//joEDB+qXjxgxokrHsTTSeyPwryerABTd2SnQzU7kqIiIiIgsj9FF6cyZMwEU9RtdtGgRAEAuL7o8XTwllKOjI+bMmYN33323SkH89NNPaNiwoUFBWlcEedwvSq8kZqF3c2+RIyIiIiKyPEYXpUBRYTpt2jQcPnwYUVFRyMjIAAC4urqiefPm6Natm75QrYqjR4+iTZs2WLBgAb744gtkZmaiU6dOWLFiBTp37lzhvtnZ2cjOzta/TkxMBABotdoaufSv0+og6AToyrljU0MPG/3zy3eyaiQmrVYLnU5Xq7s+1ARLyJMgCPpYLJUl5Km2YK6MwzwZj7kyDvNkHDHyVJU7f1apKAWKWkd79eqFXr16VXXXciUlJeHUqVO4cOECVq1aBTs7OyxatAj9+/fH9evX4eXlVe6+K1aswEcffVRqeVpamkkFclVlK7OhUqmQoyx7yicfxf1i9cqdLKSkpFR7TDqdDllZRfOiSqUm3x+hzrOEPOl8fQGgRs4LU1lCnmoL5so4zJPxmCvjME/GESNPPj4+Rm9b5aK0MiqVCnfv3kWDBg2M3ken0yE3NxebN29G27ZtAQBdunRBcHAwvvrqK8ybN6/cfadPn46XX35Z/zoxMRFhYWFwd3c3acBVValz1FDlq+CocCxzfSuZAkAaAOB2hhoubu6wllXviVD8F5CHh0eV/kKpbywhT55LPxHlfavCEvJUWzBXxmGejMdcGYd5Mo6l58nsRemuXbswatSoKjUNu7q6wt3dXV+QAoCbmxtCQ0Nx6dKlCvd1cnKCk5NTqeUymaxGEi6VSSGRSiAtp9D0drGBvVyKvAIdNDoBtzNUaOZddgFr1rik0hrLQW3GPBmHeTIec2Uc5sl4zJVxmCfjWHKeLKKNu1WrVuWuU6lUNRiJ+UkkEjTyVOhfRyVmV7A11TeJc+cice5cscMgIiISndEtpU888YRR2yUlJVU5iCFDhuCnn37C2bNn0b59ewBFfUJPnz6NaXVgYvFGnnJciM8HUDQC/4n2/iJHRJai4Np1sUMgIiKyCEYXpbt27UJQUBCCgoIq3C4/P7/KQQwfPhydOnXCyJEjsXDhQtja2mLx4sWQy+V4/fXXq3w8S9OwREvplSS2lBIRERE9yOiiNCQkBB07dsTatWsr3G7z5s145plnqhSEVCrF7t27MW3aNLz66qtQq9V47LHH8N9//1Vp1JalauR1fxaAa8m5IkZCREREZJmMLko7d+6MQ4cOVbqdRCLRz71YFR4eHpUWvLVVQ4/7LaV3MguQW6CBg9zsY8yIiIiIai2jK6PJkycjNDS00u169uyJyMjIhwqqrnG0lcHT0QopORoAwNWkbHQMchM5KrIEMjdXsUMgIiKyCEYXpR07dkTHjh0r3c7DwwM9e/Z8qKDqoibeCqTkFF26v5iQxaKUAACBX30ldghEREQWwSKmhKoPmnrb6p9fTMgULxAiIiIiC8SitIY08b7fr/Qy5yqle+5+/jnufv652GEQERGJjqNtakjTEkXp9eQ8FGp11X67UbJ8+ceOix0CERGRRWBVVEN8nK1hLy9Kt1orIDolT+SIiIiIiCwHi9IaIpFIDC7hX0zIEjEaIiIiIsvCorQGNfEqUZTeyRAxEiIiIiLLYnKf0szMTGzevBnXrl2DSqUyWCeRSPA5B2+UUnIE/qU7HOxEgETKvwuJiIgAE4vS69evo1u3bigoKEBeXh48PT2Rnp4OjUYDV1dXODs7sygtQ8nL91cScyAIAiQSiYgRkdiC1tXNu5gRERFVlUnNNNOnT0fnzp2RnJwMQRCwe/duKJVKrFu3Do6Ojti0aZO546wTgj3ksJYVFaE5Ki3iM5QiR0RERERkGUwqSo8fP46IiAjI5XIAgFqthkwmw3PPPYfp06fjjTfeMGuQdYWVTILGJfqVno/nYKf6Lv3nn5H+889ih0FERCQ6k4rSgoICODk5QSqVws3NDXfu3NGva926Nc6ePWuu+OqcEJ/7RenZuHQRIyFLkP3nXmT/uVfsMIiIiERnUlHarFkz3Lp1CwAQGhqKVatWIScnB0qlEqtXr4afn59Zg6xLmvvdH+x0Pj5TvECIiIiILIhJA52effZZnD17Fs8//zzmz5+Pxx9/HK6urpBIJBAEAT/zcmS5QnxKjsDPgU4nQCrlYCciIiKq30wqSqdPn65/3qVLF1y8eBF79uyBUqlE79690bp1a7MFWNc08JBDbiVBgUZAboEWsWl5aOTpIHZYRERERKIyeZ7SkgIDAzFx4kRzHKrOs5JK0NTHFhfj8wEUXcJnUUpERET1nVmKUqqaEB+Fvig9G5+B4aEBIkdEYgn8epXYIRAREVkEFqUiCPG936/0AqeFqtdkzs5ih0BERGQReI9DEZQsSi/dyYFGqxMxGhJT1m+/Ieu338QOg4iISHQsSkUQ6GYDB0VR6lWFOkQl5YgcEYkl49f/Q8av/yd2GERERKJjUSoCqUSCFr52+tdnbmeIGA0RERGR+B66KFUqlXjvvfcQFhaGTp06YdasWcjLyzNHbHVaS//7l/BP3koTMRIiIiIi8T30QKdJkybh8uXLGDduHPLy8rBy5UrEx8dj7dq15oivzmpZ4s5OZ+M42ImIiIjqN6OL0jNnziA0NLTU8p07d+LGjRtwcnICALRq1Qpjx441X4R1VIsSRemtNCUy8tRwtbcRMSIiIiIi8Rh9+X7AgAGIiIhAWprhpWYvLy/89ddfAABBEBAZGQlvb2/zRlkHOdlaIdDtfhF6Nj5TvGBINH6LF8Fv8SKxwyAiIhKd0UVpVFQUZDIZWrRoga+++go6XdE0Rh9//DHGjx8PLy8vuLq6YvXq1Vi2bFm1BVyXtPS/P9jpVCz7ldZHNkFBsAkKEjsMIiIi0RldlLq6umLlypXYt28ftmzZgvbt22P//v0YPHgwoqOj8cMPP2Dt2rW4efMmhgwZUp0x1xmtSgx2OsUR+PVS7r//Ivfff8UOg4iISHRVHujUtm1bREZG4tdff8W4ceMQFhaGFStWYOjQodURX53WqkRL6bm4LGi0OljJOEtXfZK6+lsAgEPPniJHQkREJK4qV0BKpRJZWVl45plnEBUVhebNmyM0NBTz5s1DQUFBdcRYZwV7yGEvL/oR5Ks5iT4RERHVX0YXpdHR0ejRowccHBzg5uaGZs2a4dixY5g/fz5OnDiBs2fPonnz5ti6dWt1xlunyKQStC7RWno8hv1KiYiIqH4yuigdN24cbGxscOTIEZw9exa9e/fGU089BbVajYYNG2Lr1q347rvv8MEHH6Bv377VGXOd0iawRFHKwU5ERERUTxldlJ4/fx4zZ85EWFgY2rRpgyVLliAzMxO3bt3Sb9O3b1+cP3+eA52qoE1AyRH4GRAEQcRoiIiIiMRh9ECnbt26YenSpXBzc4NCocDKlSvh4+ODRo0aGWwnk8kwdepUc8dZZzX3tYWVVAKNTkBKbiHi0pVo4G5X+Y5UJ3i/+47YIRAREVkEo1tKf/75Z7i7u2PAgAHo2rUrrl69it27d0Mmk1VnfHWe3FqK5r4K/Wtewq9fbNu1g227dmKHQUREJDqjW0q9vLywYcOG6oyl3moTaIeLCUoAwLGYVIzsGChyRFRTlOfOAQALUyIiqvc4KaYFaBNgr39+LDpdxEiopiV//AmSP/5E7DCIiIhEZ3RRqlarSy2LjY3F5MmT0bVrV3Tt2hVvvvmmwcAnMk7bQDtIJUXPb6erkJilFDcgIiIiohpmdFFqa2uL48eP619fvHgRoaGhWLduHdzd3eHu7o6ff/4ZjzzyCK5fv14twdZVDgoZmnrf71fK1lIiIiKqb4wuSh+cqujdd9+Ft7c3oqKisHPnTuzcuROXL1+Gi4sL5syZY/ZA67r2Qfcv4R+8cVfESIiIiIhqnsl9Sv/77z+899578PHx0S/z8/PDzJkz8ffff5sluPqkfYMS/Upj2FJKRERE9YvRo+8fVFhYWGqOUgBo3LgxMjMzHyameqm4X6lOAOLSVbiTqYSfi63YYVE183j1FbFDICIisghVKkqXL18Ob29vAIC9vT1u376N7t27G2xz584duLi4mC3A+sJeLkMzH1tEJRYNcjoanYanOgSIHBVVN4eePcUOgYiIyCIYffm+QYMGOH78OHbs2IEdO3bAyckJx44dK7Xd7t270bp1a7MGWV+EBt2/k9N/19mvtD5Q37oFNWesICIiMr6lNDY21qjthgwZgoYNG5oaT73WMdgBvxwtuqPTweupEAQBEolE5KioOt2ZNRsAELxhvciREBERicvkPqXlefbZZ819yHqjTaAd5FYSFGgEpOYW4kpiDlr6OYkdFhEREVG14x2dLIjcSop2JUbh/3c9RcRoiIiIiGoOi1IL06mhg/75/qvJIkZCREREVHNYlFqYsEb3i9JTtzKRr9aIGA0RERFRzTB7n1J6OA3cbeDlZI272YUo1Ao4Fp2OXs29xA6LqonrM6PEDoGIiMgisKXUwkgkEjzS8H6/0v1XOTVUXeY8bBichw0TOwwiIiLRsSi1QGEl+pVysFPdps3KgjYrS+wwiIiIRGdyUarVaiGTyXDmzBn989OnT5sztnqrQ7A9pPemJ41JzUdCplLcgKjaxL32OuJee13sMIiIiET3UC2lgiBAEAT9czIPJ1srhPjev+/9f9fYWkpERER1m0Vevs/NzUVAQAAkEglOnjwpdjiiCOPUUERERFSPWGRROn/+fGg09XsqpE4lpoY6dCMNGq1OxGiIiIiIqpfFFaVRUVFYuXIlPvroI7FDEVVzP1vYy4t+PLkFWpyJyxQ3ICIiIqJqZHFF6ZQpUxAREYGQkBCxQxGVlVRicHenvZeSRIyGqovT4/3h9Hh/scMgIiISnUUVpZs3b8aFCxfw4Ycfih2KRXi0maP++Z+XEjmYrA5yGzcObuPGiR0GERGR6Czmjk75+fmYPn06Fi1aBCcnJ6P3y87ORnZ2tv51YmIigKIpq7RardnjfJBOq4OgE6Crhj6fYcH2kEkBrQ64na7C1aRsNPVyqHQ/rVYLnU5XI5+/NmOejMM8GY+5Mg7zZDzmyjjMk3HEyJNMJjN6W4spShcsWABvb29MmDChSvutWLGizP6naWlpkMvl5gqvXNnKbKhUKuQoc6rl+G185TibUAAA2HY8GhM6+1a6j06nQ9a9CdmlUotqDLcolpCnnDffBAA4fv65KO9vDEvIU23BXBmHeTIec2Uc5sk4YuTJx8fH6G1NLkqlUinmzJkDPz8/g+emuHXrFpYvX45t27bpk5Wbm6v/Nzc3Fw4OZbcQTp8+HS+//LL+dWJiIsLCwuDu7g5PT0+T4qkKdY4aqnwVHBWOlW9sgp4tC3E2oWhKqEO3cvDOkLaV7lP8F5CHh0eV/kKpbywhT0pp0fvWxLlqKkvIU23BXBmHeTIec2Uc5sk4lp4nk4tSiUSCOXPm6F+XfF5VMTExUKvVGDx4cKl1vXr1QufOnXH06NEy93Vycirzcr9MJquRhEtlUkikEkhl1fMXR/dmzvj8r6Ki9OKdHKTkFsLHWVF5XFJpjeWgNhM7TxJJ0a27LP3nJHaeahPmyjjMk/GYK+MwT8ax5DxZxOX79u3bIzIy0mDZ2bNnMW3aNHzzzTfo1KmTSJGJz8vJGs19bRGVWHSr0b+uJOP5LkEiR0VERERkXhZRlLq4uCA8PLzMdR07dkSHDh1qNiAL82gzR31RuufiHRalREREVOewN3AtUHJqqGPRGchSFooYDZmTXecw2HUOEzsMIiIi0VlES2lZwsPDOS/nPUHucgS42iA+Qw2NTsD+q3cxrL2/2GGRGXjdG31PRERU37GltBaQSCSlJtInIiIiqkuqXJSqVCo4Oztjx44d1REPlePRZvdnGNh/NQWqQk4QXBfETZ6MuMmTxQ6DiIhIdFUuShUKBezs7GBlZbFX/uukFn62cHcoynm+Wod/ou6KHBGZgzY9A9r0DLHDICIiEp1Jl+/HjRuH77//3tyxUAVkUgl6t3DWv952Jl7EaIiIiIjMy6TmTldXVxw9ehRt27bFgAED4O3trZ8EHCjqAzlt2jSzBUlF+rR0xqYTaQCKLuFnKQvhbGstclRERERED8+konTWrFkAim7pefHixVLrWZRWjxBfBfxdbZCQoUahVsCfl5Iw6pFAscMiIiIiemgmXb7X6XQVPorvrUrmJZFI0Lfl/Uv423kJv9aTN2sKebOmYodBREQkOo5WqmV6t3LGz4dSAABHo9NxN0cFL0eFyFGRqXznzhU7BCIiIovAeUprmSB3OZp6FxWhOgHYdZ5zlhIREVHtx6K0FurTkqPw64o777+PO++/L3YYREREomNRWgv1LlGUno/Pxu20fBGjoYehjo6BOjpG7DCIiIhEx6K0FvJyska7QDv96+1nE0SMhoiIiOjhsSitpUq2lm45HQdBEESMhoiIiOjhmFyUpqamYubMmejTpw+aNWuGS5cuAQA+//xzHD161GwBUtl6t3CGtazohgW30pQ4HpMuckREREREpjOpKD19+jSaNm2KjRs3IiAgADdv3kRBQQEAICEhAZ9++qlZg6TSHG1l6BnipH/9y4nbIkZDprLy9oKVt5fYYRAREYnOpKJ02rRp6Nq1K65fv44ffvjB4NJx586d2VJaQwa3d9U//+NCErKUhSJGQ6YI+PRTBPCPOCIiItOK0hMnTuCNN96AtbW1wT3vAcDT0xN37941S3BUsXYN7ODnYgMAKNDo8DsHPBEREVEtZVJRam9vj+zs7DLX3b59G+7u7g8VFBlHKpFgcDsX/etfjvMSfm1zd9ky3F22TOwwiIiIRGdSUfr4449jwYIFSEtL0y+TSCRQKpX4/PPPMWjQILMFSBV7vI0LpPcaqy8n5uBiQpa4AVGV5J8+g/zTZ8QOg4iISHQmFaUff/wxsrOz0bRpU4waNQoSiQTvv/8+WrZsibS0NCxYsMDccVI5PByt0aWxo/71L8dviRgNERERkWlMKkr9/f1x9uxZTJkyBYmJiWjcuDHS0tIwZswYnDx5El5eHE1ckwa3d9E//+3sHSjVWvGCISIiIjKBlak7uri44KOPPsJHH31kznjIBJ0bO8LdwQppuRrkFmix62IiegbKxQ6LiIiIyGi8o1MdYCWVYEAbF/3rNYdjeYenWkIit4FEbiN2GERERKIzuqW0YcOGpaZ/qkh0dLRJAZFphnVwwy9HU6ETgCuJuTh3Jw/92IvC4gX99JPYIRAREVkEo4vSYcOGGRSlmzdvRnZ2Nvr27Qtvb28kJydj3759cHZ2xsiRI6slWCqfl5M1eoQ4YX9U0VRdv55JQr/2DUWOioiIiMg4Rheln332mf750qVLERgYiD179sDJ6f6tLrOysjBw4EB4e3ubNUgyzohO7vqi9N+bWbiTqUSgu4PIUVFF0r7/HgDg/vLLIkdCREQkLpP6lH7xxReYNWuWQUEKAM7Ozpg5cya+/PJLswRHVdPa3xbNfBQAAJ0ArD3K6aEsXc4/kcj5J1LsMIiIiERnUlGanp6OrKyyJ2nPyspCRkbGQwVFppFIJBjxyP27aW08Ec/poYiIiKhWMKko7dOnD9599138+++/Bsv379+PmTNnok+fPmYJjqquVwsnuNrJAADZKg22nUkQOSIiIiKiyplUlK5evRp+fn7o3bs33NzcEBISAjc3N/Tp0we+vr745ptvzB0nGcnGSoqh7V31r384FM3poYiIiMjimTR5vq+vL06cOIE9e/bg+PHjSExMhK+vL8LCwjBgwABzx0hVNLS9CzYcTYVGB9y8m4f911LQK4TzQxEREZHlMvmOTgAwYMAAFqEWyN3BGj0a2+Gf6/kAgK/+uc6i1EI1+P47sUMgIiKyCLyjUx31VDtHFM8qe+pWJo7HpIsaD5VNamcHqZ2d2GEQERGJjkVpHRXoao3HmjnqX38VeU3EaKg8mVu2IHPLFrHDICIiEh2L0jrsuS73p4f671oaLiaUPY0XiSdzy1ZkbtkqdhhERESiY1FahzXzsUWnhvfv6LQy8rqI0RARERGVr8pFqUqlwhtvvIETJ05URzxkZmO7eeif77mYjBt3c0WMhoiIiKhsVS5KFQoFfvzxR+Tn51dHPGRmbQPt0DqgaCCNAGDVfraWEhERkeUx6fJ9t27dcPToUXPHQtVAIpFgbNf7raW/nbmDmylsLSUiIiLLYtI8pfPmzcOYMWMgk8kwaNAgeHt7QyKRGGzj5uZmlgDp4XVu7IAQHwWuJqmgFYAVe69i5ZiOYodFAPyXLRU7BCIiIotgcktpTEwM3nnnHbRp0wZeXl7w9PQ0eJDlkEgkmBjurX+960ISLt3hSHxLYO3nB2s/P7HDICIiEp1JLaU//vhjqZZRsmwdg+3RvoEdzt4u6gu87M+r+GlCmMhRUc7ffwMAHPv0ETkSIiIicZlUlI4fP97MYVB1k0gkeLmnNyavjQEARF5NwcnYdDwSzG4WYkr74UcALEqJiIg4T2k90jrADl0a35+39OM9URAEQcSIiIiIiIqY1FIKAP/99x++/fZbXLt2DSqVqtT68+fPP1RgVD1e6umFozeLRt+fiM3Af9dT0bMZ+wATERGRuExqKf3zzz/Ru3dvpKam4uTJkwgMDISHhweuXr2KvLw8PPLII+aOk8ykqbcterVw0r9etOsytDq2lhIREZG4TCpK58yZg6lTp2LXrl0AgPnz5+Off/7BtWvXYG1tjd69e5s1SDKvl3p4wereT/5qci42nrgtbkBERERU75lUlF65cgUDBw6EVCqFRCJBXl4eACAoKAhz587FggULzBokmVeAmxxPPeKuf73sz6vIVhWKGFH95fP+e/B5/z2xwyAiIhKdSUWpQqGATqeDRCKBr68vbt68qV/n6OiIuLg4swVI1eP57p5wtpUBADLyC/HF37z9qBgULVtC0bKl2GEQERGJzqSitF27drh69SoAoE+fPli4cCF27tyJP//8E++//z7atGlj1iDJ/BwVMrzYw0v/es3hWMSk5okYUf2Uf+oU8k+dEjsMIiIi0ZlUlE6dOlU/ef6iRYvg6OiIJ554AgMHDkRaWhpWrlxp1iCpegxu74qGnnIAgEYrYOGuyyJHVP/cXb4Cd5evEDsMIiIi0Zk0JdSgQYP0z/39/XHq1CncuHEDSqUSzZs3h42NjdkCpOpjJZVgcl8fvPXLLQDAvit38e+1FE4RRURERDXOLJPnSyQSNG3alAVpLdQx2AHdmzrqX7+//QJUhVoRIyIiIqL6yKSidO3atfjyyy/1ry9evIimTZvCzs4O4eHhuHv3rtkCpOo3ua8P5FZF3THi0pX48h8OeiIiIqKaZVJRunTpUkil93edMmUKbGxs8NlnnyExMRGzZ882W4BU/XxdbDDu0fuX7Ff/F43ryTkiRkRERET1jUlFaWxsLFrem8YmNTUVBw4cwPLlyzF58mTMmzcPf/75Z5WOt2nTJgwbNgwBAQGwt7dH+/bt8eOPP/K+7DVoVJiHwaCnWVsvQMc7PVU7j0mvw2PS62KHQUREJDqTilKpVAq1Wg0AiIyMhLW1NXr16gUA8PX1RVpaWpWOt2LFCtjZ2WH58uXYsWMHBg4ciIkTJ2LevHmmhEcmsJJJ8NYAP/3rk7cysOkU55utbg7du8Ohe3exwyAiIhKdSaPv27Vrh1WrViEgIABffPEFevfuDbm8qJXt9u3b8PLyquQIhnbs2AEPDw/96969eyMtLQ0rVqzABx98YNBVgKpP6wA7DG3vih1nMwAAC3dfQa8QL3g5KUSOrO4quHfjCXnjxiJHQkREJC6Tqr1Fixbhv//+Q9u2bXHhwgV89NFH+nXbtm1DWFhYlY5XsiAtFhoaiuzsbP0tTKlmvBLuDVe7ojs9ZSs1mLn1PLtRVKPEDz5E4gcfih0GERGR6ExqKe3evTtu376Na9euoXHjxnBxcdGve+mll9CkSZOHDuzgwYPw9/eHo6NjhdtlZ2cjOztb/zoxMREAoNVqodVW/9RGOq0Ogk6ATqur9vcylk6n0z+qyt5Ggjf7+2Du9gQAwD9RKfi/k7cxskOAucMUnVarhU6nq5HzpDzFBb+YMVTGEvJUWzBXxmGejMdcGYd5Mo4YeZLJZEZva1JRChTd475jx46llpecWN9UBw8exMaNG7F8+fJKt12xYoVBS22xtLQ0fZeC6pStzIZKpUKO0nJGqws6AapcFSSQQCKVVHn/UE8JejS2xX83lQCAeTsuo7mLBN6OdWsOWp1Oh6ysLAAQrYtIYWEhACAlJUWU9zeGJeSptmCujMM8GY+5Mg7zZBwx8uTj42P0thLBxGuzOp0O//zzD65duwaVSmV4UIkE06ZNM+WwiI+PR+fOndGiRQvs3bu30qSV1VIaFhaG2NhYBARUf+teQk4C7ubfhZvCrdrfy1g6nQ45GTlwdHU0+aTLVmrx0o83kZZX9NfUo03csWb8I/rby9YFWq0Wqamp8PDwqNJfcuZ0e+zzAIAG69aK8v7GsIQ81RbMlXGYJ+MxV8ZhnowjRp6qvaU0KSkJ4eHhuHbtGiQSif4SZMmCxZSiNDMzEwMHDoS7uzu2bNliVEHl5OQEJyenUstlMlmNJFwqk0IilUAqs6y/zKRSadHDxLhcHKSYMcgfMzfdBgAcvJGGjScTMLZLkDnDFJ1UKq2xc6Usxf9nLP1LVOw81SbMlXGYJ+MxV8ZhnoxjyXkyqWKZPn063N3dERcXB0EQcOzYMcTGxmL+/Plo2rQprl27VuVjKpVKDBkyBFlZWfjjjz/g7OxsSmhkRl2aOGJQWxf96wW7LnNSfTNzHfMcXMc8J3YYREREojOpKP3vv//w1ltvwdfXF0DRYI0GDRpg9uzZeP755zF58uQqHU+j0WDUqFG4cuUK9uzZA39/f1PComowqa8PvJ2sAQCqQh0m/3IaqkJ2JDcX58GD4Tx4sNhhEBERic6kojQrKwuenp6QSqVwcnIyuNd9165dcfDgwSod7/XXX8fOnTvx3nvvITs7G0ePHtU/CgoKTAmRzMReLsOHwwJQPF7qalIuFuy6LG5QdYgmLQ2aKt5sgoiIqC4yqU9pw4YN9VMvtWrVCmvXrsWQIUMAFM1T6uZWtUE/e/fuBQC89dZbpdbFxMQgODjYlDDJTFoF2OGlHl747t+iPz7WHb2NR5t4YEBrX5Ejq/3ip7wBAAjesF7kSIiIiMRlUkvp4MGD9YXk+++/j23btsHLywv+/v5YtWoVpkyZUqXjxcbGQhCEMh8sSC3D6K4e6BBsr3/9zubziM/IFzEiIiIiqktMaildvHix/vnAgQNx6NAhbNu2DSqVCv369cPAgQPNFiBZBqlEgveG+uOlH24iM1+LbJUGr607hU0R3aCwtrwRfERERFS7mDx5fkmdOnVCp06dzHEosmDuDtaYNcQf7/5f0TRRFxKy8eFvF/HxiLZ1av5SIiIiqnkPVZT+9ddfOHbsGBITE+Hr64suXbqgb9++5oqNLFDnxo4Y/6gn1hwsugPR/52MR/tAVzzXuYHIkREREVFtZvLk+SNGjMCRI0fg5uYGLy8v3L17F+np6ejSpQu2bt1apdtKUe3ywqOeuJqkxJEbuQCAOb9fRAtfR4Q2cBU5strHafDD35aXiIioLjBpoFNERASio6Px999/IzU1FZcvX0Zqair27duH2NhYvPbaa+aOkyyIVCLB7KEB8HMpmr+0UCsgYt0p3M1WVbInPchtzBi4jRkjdhhERESiM6ko/euvv/DJJ5+gV69eBst79+6NJUuW6EfmU93lqJBhwYgGUFgX9SVNzi7Ay/87CaWaE+tXhaDRQNBoxA6DiIhIdCYVpa6urnB1LftSraurK1xcXB4mJqolGnkp8O7g+3ffOh+fhen/dxY6nSBiVLXLrRfG4dYL48QOg4iISHQmFaVTp07FkiVLkJuba7A8JycHH3/8Md58802zBEeWr1cLZ7z4mKf+9R8Xk7Bs71URIyIiIqLayKSBTrdu3UJsbCwCAgLQq1cv/UCnyMhIODo6Ij4+Hm+8UXSnGolEgs8//9ysQZNleb67J+LS1fjrUhYAYNX+m2joYY+nHwkUOTIiIiKqLUwqSnfu3Alra2u4urri7Nmz+uXFl/R37NihX8aitO6TSCSYMcgPiVlqXIxXAgBmbb0AD0c5eoV4iRwdERER1QYmFaUxMTHmjoNqORsrKRaMaIDXfo5GYmYhNDoBr687hQ0Tu3CqKCIiIqqUSX1KicriYmeFpc8EwcWu6LajykIdJvx0Ajfu5ogcmeWy794N9t27iR0GERGR6FiUklkFuMnx8agg2NoUTRWVqSzE8z8cx51MpciRWSbPSZPgOWmS2GEQERGJjkUpmV2Iry0WjGgAa1lRYZqYpcKY749ycn0iIiIqF4tSqhYdgx3w3lB/SO69jknNx5jvjyE1t0DUuCxN3KsRiHs1QuwwiIiIRMeilKpNeAtnvD3IT//6+t1cjPn+GDLy1CJGZVm0OTnQ5rDPLREREYtSqlaD27li2uO++tdXk3Iw9odjyMxnYUpERET3GT0l1IoVK4w+qEQiwbRp00wKiOqeYR3cUKgV8NW+JADApTvZGP3dUax9qTM8HOQiR0dERESWwOii9O233zb6oCxK6UEjO7lDoxXwTWQyAOBKYg6e/fYI1r/cBd5OCpGjIyIiIrEZfflep9MZ/dBqtdUZM9VSz3bxwKQ+3vrXN+7mYdQ3RxCfkS9iVOJStG4FRetWYodBREQkOpPu6ERkqqfDPGBjJcWnfyYCAG6l5+Ppb45g7UthaOLlKHJ0Nc9n9myxQyAiIrIID1WUqlQqREdHQ6UqPf9khw4dHubQVIcN6+AGuZUUn+xOgE4omsd05NdH8MP4TugYxFuSEhER1UcmFaVqtRqvvfYa1q1bB41GU+Y2vIRPFRnQ1gUKawkW/B4Pja7ozk9jvj+KVWM6oHdz78oPUEfceXcmAMDv4yUiR0JERCQuk6aE+uijj7B3716sWbMGgiDgq6++wk8//YQ+ffogODgYO3bsMHecVAeFt3DGx88Ewc6m6DRUFeow8X+n8OuJ2yJHVnPUcXFQx8WJHQYREZHoTCpKN23ahLlz52LUqFEAgLCwMLzwwgvYu3cvHn30URalZLSOwQ74fEwwXO1lAACtTsC7Wy5g0e4r0OoEkaMjIiKimmJSURofH49mzZpBJpNBoVAgIyNDv27s2LHYtGmT2QKkuq+pjy1WPt8I/q7W+mXf/heNV/53ErkFZXcPISIiorrFpKLU19cXmZmZAICGDRti//79+nXXrl0zR1xUz/i52mDVC43QLtBOv+zvqLsYseoQ4tLr75RRRERE9YVJRWl4eDgOHDgAAJg4cSKWLFmCESNGYPTo0Xj77bcxbNgwswZJ9YOznRWWjQ7C4HYu+mVXk3MxbOUhnIxNFy+wamTt7w9rf3+xwyAiIhKdSaPvFy5ciNTUVADA1KlTIQgCNm/eDKVSiTfeeAMffvihWYOk+sNaJsXbA/0Q7CHH1/8kQycA6XlqjP7uKOY+0QrPhTWARCIRO0yz8V/6idghEBERWQSTilIfHx/4+PjoX0+bNo23FSWzkUgkeDrMA4Fucsz7LQ75agGFWgHvbbuIk7EZWPhka9jZ8L4PREREdYlJl++JakKXJo5Y+UIj+LncHwC17UwChn11CDfu5ooYmfkkL16C5MWco5SIiIhFKVm0hp4KfDuhMR5rdv8WpNfv5uKJrw7i93N3RIzMPJQXLkB54YLYYRAREYmORSlZPAeFDPOeCsTrfbwhvdedNF+txRu/nMH72y9Aqebdw4iIiGo7FqVUK0gkEowK88BnY4Lh7iDTL1939DaGfHkAFxOyRIyOiIiIHhaLUqpV2gba4/sXm6BjsL1+2c2UPAxfeQir9t/gXaCIiIhqKRalVOu42lth6bNBiOjtDat7Z7BGJ+CTPVcx+tujtWqyfam9PaT29pVvSEREVMexKKVaSSqR4NnOHvh6fCMEudvolx+PTcfAz//DryduQxAsv9W0wXffosF334odBhERkehYlFKt1tTbFt9OaIwRj7jpl+UWaPHulgsY+8Mx3E6rPa2mRERE9RmLUqr15NZSTOnni6XPBMHN/v4gqEM30vD4Z//h+wPRFtvXNPWbb5D6zTdih0FERCQ6FqVUZ3Rq5ICfJzbFoLYu+mXKQi0W7LqCEV8fxtWkHPGCK0fufweQ+98BscMgIiISXbUUpdOnT6+OwxJVytFWhncG+2PZs0Hwcb5/K9KzcZkY/MUBLN59BbkFGhEjJCIiorI8VFF6+/btMh/bt283U3hEpnmkoQN+erkpnu7kpp9wX6MTsPq/aPRZvh87zt2pFQOhiIiI6guryjcpX3BwMCQSSalf7hKJ5KGCIjIHWxspJvX1Ra8Wzlj2RwKiU9QAgOTsAkz55Qy6NnLDG9194OkpcqBERET0cC2lAQEBSElJgU6nM3g0atTIXPERPbSW/nb49sUmeKOfD+zl90/5I9HpGLv+MhbsuoLMfLWIERIREdFDFaURERFISUkptXzSpEkPc1gis7OSSvDUI+5Y+2pTPN7aWb9cqwN+OnwLPT6JxPcHolGg0dZoXEFrfkLQmp9q9D2JiIgs0UMVpbNnz0ZISEip5VOnTn2YwxJVGzd7K8waGoAvn2+IRp73J93PVmmwYNcV9FvxH3adT6yx/qYSGxtIbGwq35CIiKiOM6kozcnJQWpqqsGy9evX4/3330dkZKRZAiOqTm0C7LB6XCNMfswVriXmNr2dno9JG07jqa8P48jNtGqPI2PjRmRs3Fjt70NERGTpTCpKx44diw8++ED/et68eXj++efxzTffoF+/fvi///s/swVIVF1kUgn6NbfHuolNMP5RT8it7g/QO3M7E6O/O4ox3x/F6dsZ1RZD1u87kPX7jmo7PhERUW1hUlF64sQJ9O/fHwAgCAJWrlyJ2bNnIzU1FW+88QaWLl1q1iCJqpOtjRTjH/PC+oimGNTWGSXnjjh0Iw1PrTqMl9acwKU7WaLFSEREVNeZVJSmp6fDw8MDAHDq1CmkpqbixRdfBAA88cQTuHr1qvkiJKohHo7WeGdwAH58uTEea+ZosO7vqLsY/MVBRKw9hQvxLE6JiIjMzaSi1NvbG5cvXwYA7Nq1C8HBwfppoPLy8mBl9VDTnxKJqqGnAvNHNMDq8Y0Q1sjeYN2eS0kY+tVBPP/DMRyLTuME/ERERGZiUvU4atQovPPOO9i3bx92796Nd999V7/uzJkzaNq0qdkCJBJLiK8tPnkmGBfj8/H9v0k4e1upX3fgeioOXE9FxyBXTOrVGL1CvHjTCCIioodgUlG6ePFiODo64sSJE3j77bcxa9Ys/bpTp05h1KhRZguQSGytA+zw2ZhGOB+Xh7WH7+JEdL5+3albGXhxzUm08HXCa+GNMai1D6xkxl+A8P/s0+oImYiIqNYxqSi1srLChx9+WOa6bdu2ISYm5qGCIrJEbQPtsfSZhriepMTawyk4cDUHxRfvryRm441fzmCJswLjugXj2U4N4GxnXekxrb28qjdoIiKiWuKhJs8vKTU1FStXrkT37t15+Z7qtKY+tpj3VAP8/EoTDGjjjJINo3eyVFj8RxS6LP4b72+/gBt3cys8VvaePcjes6eaIyYiIrJ8D1WU5ufnY/369Rg8eDD8/f0xZcoUxMXFmTT4IyoqCv369YO9vT18fHzwzjvvQK3m/cjJcjVwl2PmkABsiGiKpzq6wtb6fp9SZaEW647eRt8V/2L8T8fx37WUMv9fpP9vLdL/t7YmwyYiIrJIVb58r9VqsWfPHmzYsAG///478vLy0Lp1a8ydOxfPPvsszp07hxEjRlTpmBkZGejduzeaNm2KrVu3IiEhAdOnT0d+fj6++uqrqoZIVKO8nW3wRn8/vNjDG7vPZWDLyTQkZ2v06/dfTcH+qylo6GGP0WGBGNkxEG72vLUoERFRSUYXpYcOHcKGDRuwadMmpKamolGjRnjzzTcxevRotGrVSr/d+fPnqxzEN998g+zsbGzbtg1ubm4AAI1Gg9dffx2zZ8+Gn59flY9JVNMcFDKM6uyBEZ3ccfhGDjYdT8H5OJV+fUxqHhbtjsKyP6/h8dY+eC6sAXxFjJeIiMiSGF2UPvbYY5BKpZg4cSJefPFFdOrUyWxB/PHHH+jbt6++IAWKpp2KiIjA3r17MX78eLO9F1F1k0kleKyZEx5r5oTryUpsPp6Gf65koVBbtF6t1WHHuTvYce4OvkrIgoeDHE55araeEhFRvWZ0UdqmTRtcuHAB69evR15eHp599ln079/fLBPlR0VF6e8IVczFxQW+vr6IioqqcN/s7GxkZ2frXycmJgIA4uPjodVqHzq2yiTlJuFu/l3kK/Ir37iG6HQ65Gflwy7XDlKp2cay1Tk1kScFgLHtgGEh9jhwNQf7LmchMfP+ealUFSBOVYDRMzeiayNXDGzljS7BrrCuwrRS1U2r0yE9IwN5OTmQ8XyqEHNlHObJeMyVcZgn4xTnKT8/HzKZrEbeMygoyOhtja4oz507h8uXL2PdunXYuHEj1q1bBzc3N4wcORKjR49Gz549TQoWKOpT6uLiUmq5q6sr0tPTK9x3xYoV+Oijj0ot79q1q8nxENWU2TZFraOxx/chFsAvokZDRERkXlUZ/F6lZs6WLVti0aJFWLRokb6P6ebNm/Hdd9/B19cXo0aNKrO4rE7Tp0/Hyy+/rH+dmJiIsLAwHDlyBL6+1d9jT61Vo0BbUO3vUxWCTkBmRiZcXF0gkfIuQ+URO0/ZKg32XU7DngtpUKYry9ymgaMM/QJt0SfAFl524ty+V6vTIaugAM5yOVsgKsFcGYd5Mh5zZRzmyThanQ6Z2dnwbNgQcgucJ9vk33Ldu3dH9+7d8cUXX+DPP//Ehg0b8P333yM3N7fKt1t0dXVFVlZWqeUZGRkG/UzL4uTkBCcnp1LLAwICEBAQUKU46gqtVouUlBR4enrWWPN8bWQJeWqXdxTTG9jhRkALbDl5GzvOJSJTdX/k/h0AP8cDP8cLCPW2wqDGThjQyAle9pVPzG8uWp0Oabm5cHdw4Jd9JZgr4zBPxmOujMM8GUer0+FufDx8AgKgqIGGu6p66KYXmUyGQYMGYdCgQVAqldi+fTt++aVqFyGbN29equ9oVlYWEhMT0bx584cNkchipXzxJQCg/Yb1aB/ogveHtkJkVAq2nryNf66lQqO7f9njTLISZ5KVWHQ4GZ387DCosRMeb+gEN1txWlCJiIjMyay/zWxtbTF69GiMHj26SvsNHDgQixYtQmZmpv7y/6ZNmyCVStG/f39zhkhk0eRWMgxo7YMBrX2QnqfGb2cT8PvpeJxJuD+YTwBw/E4+jt/Jx/yDSejib4++wY7oE+wI7xpsQSUiIjIni2hiiYiIwJdffonhw4dj9uzZSEhIwIwZMxAREcE5SqnecrO3wYTuDTGhe0PEpedj5/k72Hk2AZeS7t+6VCsAh+LzcCg+Dx8dTEJbLwX6BTuhT7AjGrvKRYyeiIioaiyiKHV1dcXff/+NKVOmYPjw4XB0dMTLL7+MhQsXih0akUUIdLPDa+FN8Fp4E8Sk5mHH2QTsPHcH11LyDLY7f1eF83dVWH78Lhq62KBvsCP6BTuijZctpFXs601ERFSTLKIoBYAWLVpg3759YodBZPEaetjjjb7N8EbfZrienIM/LyVh78VEnL+TY7BdTKYa351Nw3dn0+BpZ4UegQ7o2cAB3fzt4SjnADgiIrIsFlOUEtVHnlPffKj9m3o7oqm3Iyb3boo7mUr8dTkJey8k4titTINBUin5Gmy5moktVzNhJQVCve3QI9ABPRo4IMRNXuUZM4iIiMyNRSmRiOzDwsx2LD8XW4zr1hDjujVEVn4h/rmajD/P38G/N9KgLNTpt9PogBOJ+TiRmI/lx+/C294KjwU6oEegA7r628OJrahERCQCFqVEIlJdvQoAUISEmPW4znbWeDI0AE+GBkBVqMXR6DTsv5KEyKspuJWhMtg2OU+DzVGZ2ByVCakEaO2pQFc/e3QNcEAHb1tYcco/IiKqASxKiUSU9NE8AEDwhvXV9h4KaxnCQ7wQHuKFuQBiUvMQGZWMf68k4+itDBRo7l/m1wn3B0utPpsGuUyCUG9btPO0Qu+GMrTxtIOMdwkjIqJqwKKUqJ5p6GGPho82wouPNoJSXdSKGnklCf9eK92KWqAVcPROPo7eAVafy4aTjRSd/OzRydcOHX3s0NJDASsWqUREZAYsSonqMVsbGXo190Kv5kX3QE7IVOLQ9RQcupaCw9FpSMkrNNg+W63D37E5+Du2aKS/nbUUod626Ohjh06+dmjrZQsFr/cTEZEJWJQSkZ6/iy1GdWqAUZ0aQBAEXL+biwNXkxF5+Q7O3slHrlprsH1+oU4/eT8AWEuB1p626ORrh0d87dDB247TTxERkVFYlBJRmSQSCZp5O6Kxhx0GN3OAq5s7Lifl4lh0Gk5Ep+LErUxkFxgWqYU64EyyEmeSlfj2bBokAJq4ytHWyxbtvW3RzssWTVzl7JdKRESlsCglEpHb+HFih2A0K5kUoQ1cEdrAFRHhTaDTCbh2NwfHbhYVqcdvZeBuruHlfgHA9YwCXM8owJarmQCKLvm39VSgvbedvlh1t+VXERFRfcffBEQicurfX+wQTCaVStDcxwnNfZwwrntDCIKA2+n5OB6TjmM3UnA8NgO3M1Wl9ssv1N0bPJWvXxbgaI12XrZo7WmLVp4KtPJQwMGGl/2JiOoTFqVEIipMSgIAWPv4iBzJw5NIJAhyt0eQuz2efiQQAJCaW4CztzNxJjYNZ25n4NydbOSpdaX2jc8pRHxOIXbdzNYvC3a2QWtPBVp5FBWqLd0V7J9KRFSHsSglElHC9LcAVO88pWLycJCjb0tv9G3pDQDQ6gTcuJuL07fScSY2HWfiMnEjNR9CGfvGZqkRm6XGzhuGhWorDwVaeSrQwl2BEHcFL/0TEdUR/DYnohojk0oQ4uOIEB9HjO4cBADIURXifHwWzt5Kx4X4TFy8k434rIIy9y8uVEu2qHraWSHETY4QdwWauysQ4iZHIxc5rGUcTEVEVJuwKCUiUTkqrNG9iQe6N/HQL8vIU+PinSxcuJ2B83EZuJiYU26hmpKvQUq+BgfvTUsFFE1N1dhVfq9IVaC5e9FzN7aqEhFZLH5DE5HFcbW3wWNNPfFYU0/9spKF6sWETEQl5SI2QwldGdf+C3VAVFoBotIKAGTpl7spZGjiJkcTFzmauMrR2LXoX3dbGSQStqwSEYmJRSkR1QplFapKtRbXknNwJTELV+IzEZWUgyvJuaXmTy2WrtLi+J18HC8x8h8AXBQyNHEpLlJt0OReseppZ8VilYiohrAoJRKR87BhYodQq9nayNAu0AXtAl2AsKI+qoIgIDFLhaikbFyOz0TUnSxcSc5FTHrZraoAkKnS4mRSPk4mGRarTjZSNHSRo6GLDYKdbRDsXPQ8yMkGtta8nSoRkTmxKCUSkeszo8QOoc6RSCTwc7GFn4stejf31i9XFWoRnZKH68k5uJ6UhWtJObiRkodbGUpoyylWs9U6nLurxLm7ylLrfB2siopUZxsE3ytag5ysIS9zLgEiIqoMi1IiEelURZPLSxUKkSOp+xTWMrT0c0JLPycA/vrlBRotYlPzcS05G9cSs3EjOQfX7+YiNkMFTXlNqwASczVIzNXgSEKewXJrKRDoZINGLnI0cLJGoJMNAp1s0MDJBr4O1rDhrABERGViUUokotsvvgSg7s5TWhvIrWT6aarQ7n6xqtbocCstD9GpeYhOzkb03VzEpOYhJl2JtPzCco9XqAOiM9WIzlSXWieVAL4O1gh0tNYXqgFO1mhwr3B15s0BiKgeY1FKRFQGGyspmno7oqm3I9DK8I5bWcpCxKTmIfpuTtEjJRexqfmISVdCqSl9x6piOgFIyClEQk6hwW1WiznLpQhwtLlXpBYVrn4O1vBztIafgzUUVuzHSkR1F4tSIqIqcra1RvtAF7QPdDFYrtFocDnmDrIEBW6l5uF2Wh5upeXhdroStzOVZd5itaSsAh2yClS4lKoqc727rUxfpPo7WMPPsaho9b9XtDqxpZWIajEWpUREZiKRSODlaINWnu54rJmXwTpBEJCRX1hUpKbl4XZqLm6l5iEuIx+3MlRIzlFXOkQqTalFmlKLCyllF60ONtKiIrVE66qfozV87IsennZWvNMVEVksFqVERDVAIpHAzd4GbvY2CG3gWmq9qlCL+Awl4tLzcSs1p6hgTc9HQqYKCVmqcudeLSlXrcO19AJcSy/77lcSAB52VvCxtyoqVB2s4W1vBW97a/0yb3sryNlNgIhEwKKUSEQO4eFih0AWQmEtQxMvBzTxcgDgVWp9jqoQCZlKJGQoEZ+Wh4T0PMRnKnEnU4mErAKk5JU/+KqYgPu3ZS2vtRUAXBWye62rVvB2uPevvTW87Kzgee/hquBdsIjIvFiUEonI45WJYodAtYSjwhrNfazR3MepzPWqQi0Ss1RFRWt6UdGakKFEQqYSyTkFSMpRQ1XBIKySMlRaZKi0uJJW/jbW0qJW16Ii1VpfrJYsXD3trOBuawUrKYtXIqoci1IiojpAYS1DQw97NPSwB+BRar0gCMhSFiIxS4WkbBUS0/OQmKlEUpYSSVkqJGYXIDlXjRwjugkARVNfFc/VCpTf6ipB0QCtkoWrh60MdjItgl0FeNhZw8NOBneFFRxspGx9JarHWJQSiah4ntIGP/4gciRU10kkErjY2cDFzgYtfMtubQWA3AINkrJURYVqZh4SM4oK18QsFe7mFCAlV43U/MJyb9n6IAFAqlKLVGVZLa+ZBq+spRK428rgbmt17yGDm60VPGyt4KZfXvSvm4KDtojqGhalRCIqvqMTkaVwkFuV6NtausUVALQ6AWl5BbibXYCUnAIkZ+bjbraq6JFzv3i9m1eIwvLu4VqGQp2ApDwNkvI0Rm3vLJcaFq2Ke8WsnQyuiqJ+r0UPK7jIZSxiiSwci1IiIqoSmVQCL0cFvBwrvj1ucZeBuzlFBWxythJ3M5VIzspHXFoOctRAWn4h0vMKkaEyrhAtqWheVzViyrh7VlkcbKT6QtVFXrJolcFFUfo1C1mimsWilIiIqkXJLgPNvB31y7VaLVJSUuDp6QmZrGjC/0KtDhn5aqTmqJGWV4DUbBXSclRIySlAWm4B0vLU+kdqXiEKqtACWyxXrUOuWoe47MpnKijmeK+QdVEYtr66yGVwkt//11khg7NN0b+ONlJI2TeWqMpYlBIRkeisZVKjWl+BohbYPLUWabkFSM1VIzVHhdQcFdLuFbApuQXIyFMjU1mI9PxCZCg1UJtQxAJAjlqHHLUOt6tQyEoAOMmlRcVqycK1xMNJLi1zucJKwsFeVG+xKCUSkW379mKHQFTrSCQSOMit4CC3QpC7faXbC4KAfLUWGflqZOQVIj1fjfQcFTJyC5CRV4D0PDUy8tVIzytEprIQGcpCpCs1VeoPa/B+KO5aoEMcjC9mgaLBXi4KGZxspHC+96+NVICHXS6c5FZwtCkqdh1spHCyKWqVdZTL9M954wOqzViUEonI+50ZYodAVOdJJBLYy61gL7dCQOmbaZWpuDU2Q1+wqpGeW4CM3AKk5xUgM1+NzPxCZCuLCtkslQZZSg2yC7SV3i62IoU64d4NDh5cU2pBmWxkkqJC9V6RWl4B++Ayx3uv7dn1gETEopSIiOgBJVtjA93sjN5PpxOQo9IgS1mITGVR4ZqlL2LVyMpXIyu/qJDNVhYiU6Upeq7SQmnkzQ0qotYKSFNqkaY0br7ZsthbS2FvLYWDTdHD3loGB+vi51I43Cte7a2l95bLSqyTwsFaBntrKbsiUJWxKCUSUcL0twAA/iuWixwJEZmDVCqBs501nO2s0QDGF7MAUKDRIktZiKz8wqKiNr8QGblKJKZkQCuTI69Ag2xlIXJUGmSrNMgpKPFvgdbk7gYPyivUIa9Qh7vGNc6WSybB/aL2XtFq/2ARW1zklih67Uo87K2lsLOSwtZayjuD1QMsSolEVJiUJHYIRGQh5FYyeDnKDAZ7Fc1UoDCYqaA8qkItslX3itZ7xWtWfgFy7rXK5igLi9YrC4uKWZUG2QXF/2qRqza9dbUsWuF+31pzkMskpYrV4te2VhJIoYWbXT4crGUGha2dtRT2VpLSy6ylsJayNdeSsCglIiKqAxTWMiisZfByrHzbsmh1AvLUGuQVaJB7rwU2r0CDHGUhcpWFyFUVIregsGidqrBouwINcgq0yC3QIE+tRe694tbU2Q4qUqAVUKDVIkNVUfGcV6VjWklhUNzeL2KLWmdtrYoKXltrKRRWRYWw4l6BqyheZ3Vv3b0uC3b3XiusJOyfW0UsSomIiAgyqQROCms4KawB54c7llqj0xetxY+c4sL23iNHpUGeqvDeei1yCjTIV2uQr9YiT61FvlqH/EIt8gvN09JaFo0OyFbrkK2unvdQ3Ctai4tbRfFz6/vLiwpaiUHRe78gvl/42t4rekvuZy1FnWrpZVFKREREZmVjJYWNlQ1c7W0e+lg6nQBloRZ5ag3yC+79q9YiT6VBXkEh8gs0yFGqcTcjGxKZDZSF2vuF7b0W3Hy1FvmF95YV6pCn1kJn/sbcUlQaASqNFhkwb9eIYlIJilplZUXFqtzqgX/1y4uKWxuZBLr8ArhnJeH1wd6wklnWFGIsSolEZBMcLHYIREQWTSq9P6UXyumaUNZdwioiCAIKNLqi4rWguHX2XtFbUNQ1IU9VCKVaA6VaW/QoLHqer9ZCda/wVRbqoNLcW6bRIb9QB1WhDoU1UfEC0AlAfqEO+YUAqlL43riDyUPaV1NUpmNRSiQiv0ULxQ6BiKjekUgk+j64bmZozX1QoVYHZaG2REF7v5jNKyiESq1FfkHh/fX3it/8wvvbK4uL38Ki4lep/1f30NOHyWUSSC1wNgMWpURERERmZC2TwlomLeqfWw2KW3pVhUUFrKpQV1TEarRQ6YtaDVSFWqgKNPcL3IJCpOfkwc6+8juhiYFFKZGIkuYvAAD4fPC+yJEQEVFtUbKl16UK+5Xs5mCJWJQSiUh15YrYIRAREVkEyxp2RURERET1EotSIiIiIhIdi1IiIiIiEh37lBKJSObiInYIREREFoFFKZGIAletFDsEIiIii8DL90REREQkOhalRCJK+fIrpHz5ldhhEBERiY5FKZGI8o4cQd6RI2KHQUREJDoWpUREREQkOhalRERERCQ6FqVEREREJLo6NyWURqMBACQmJoociXi0Wi3S0tJQUFAAmUwmdjgWyxLylJifDwCwio8X5f2NYQl5qi2YK+MwT8ZjrozDPBlHrDz5+PjAyqryklMiCIJQA/HUmBMnTiAsLEzsMIiIiIgIQFxcHAICAirdrs4VpSqVChcuXICnp6dRVXldlJiYiLCwMBw/fhy+vr5ih2OxmCfjME/GY66MwzwZj7kyDvNkHLHyZGxLaZ2r2hQKBTp16iR2GBbB19fXqL9M6jvmyTjMk/GYK+MwT8ZjrozDPBnHUvPEgU5EREREJDoWpUREREQkOhaldZCTkxPmzJkDJycnsUOxaMyTcZgn4zFXxmGejMdcGYd5Mo6l56nODXQiIiIiotqHLaVEREREJDoWpUREREQkOhalRERERCQ6FqVEREREJDoWpUREREQkOhaltUxUVBT69esHe3t7+Pj44J133oFara50v+DgYEgkklIPlUpVA1HXvBs3biAiIgLt27eHlZUVWrdubdR+giBgyZIlaNCgAWxtbdG1a1ccPXq0mqMVj6l5qm/n06ZNmzBs2DAEBATA3t4e7du3x48//ojKJi+pb+eTqXmqb+cTAOzevRs9e/aEp6cn5HI5GjVqhOnTpyMrK6vSfX/44Qc0a9YMCoUC7dq1w86dO2sgYnGYmqfw8PAyz6moqKgailxcubm5CAgIgEQiwcmTJyvc1pK+p+rcbUbrsoyMDPTu3RtNmzbF1q1bkZCQgOnTpyM/Px9fffVVpfuPHDkSb731lsEyuVxeXeGK6tKlS9i1axc6d+4MnU4HnU5n1H4ff/wx5syZgyVLlqBt27ZYuXIl+vfvj7Nnz6JRo0bVHHXNMzVPQP06n1asWIHg4GAsX74cnp6e+OuvvzBx4kTExcVhzpw55e5X384nU/ME1K/zCQDS09PRuXNnvPHGG3B3d8fFixcxd+5cXLx4EXv37i13v40bN2LixIl477330Lt3b/z666948sknceDAAXTp0qUGP0HNMDVPANC9e3csW7bMYFlwcHA1Rms55s+fD41GY9S2FvU9JVCtsWjRIsHe3l5IS0vTL1u9erUgk8mEhISECvcNCgoSJk2aVN0hWgytVqt/Pm7cOKFVq1aV7qNUKgUnJydh1qxZ+mUFBQVCUFCQ8Nprr1VLnGIzJU+CUP/Op5SUlFLLJk6cKDg5ORnksKT6eD6ZkidBqH/nU3m+/fZbAUCF3+fNmjUTRo8ebbCsa9euwsCBA6s7PIthTJ569uwpDB48uAajshxXrlwR7O3thW+++UYAIJw4caLcbS3te4qX72uRP/74A3379oWbm5t+2ahRo6DT6Sr9i7G+kUqrfmofPnwY2dnZGDVqlH6ZjY0NnnrqKezevduc4VkMU/JUH3l4eJRaFhoaiuzsbOTl5ZW5T308n0zJE93n7u4OAOV2yYqOjsa1a9cMzikAePbZZ/H333+joKCg2mO0BJXlqb6bMmUKIiIiEBISUum2lvY9xd9ItUhUVBSaN29usMzFxQW+vr5G9ZNZv3495HI5HBwcMGjQIFy4cKG6Qq2VinP4YI5btGiB27dvQ6lUihGWxarv59PBgwfh7+8PR0fHMtfzfCpSWZ6K1dfzSavVQqVS4fTp05g3bx6eeOKJci8xV3ROqdVqxMTEVHe4oqlKnor9+++/sLe3h0KhQM+ePfHff//VTLAi2rx5My5cuIAPP/zQqO0t7XuKRWktkpGRARcXl1LLXV1dkZ6eXuG+TzzxBL766ivs27cPK1euxI0bN/Doo48iOjq6mqKtfTIyMiCXy6FQKAyWu7q6QhAEZGRkiBSZ5anv59PBgwexceNGvP322+Vuw/PJuDwB9ft8CgoKgq2tLTp27AhfX19s2LCh3G2Lz5kHfw+4uroCQKW/B2qzquQJAHr27InPP/8ce/bswc8//4z8/Hz07dsXR44cqaGIa15+fj6mT5+ORYsWGX1ve0v7nuJAp3riiy++0D9/7LHH0L9/fzRv3hzLli3DqlWrRIyMaqP6fD7Fx8fjmWeeQa9evfDGG2+IHY7Fqkqe6vP5tHv3buTl5eHSpUtYsGABhg4dir/++gsymUzs0CxKVfP00UcfGbweMmQIWrVqhfnz59fZ7jMLFiyAt7c3JkyYIHYoJmNRWou4urqWOQ1GRkaGQT9TY/j6+uLRRx/FqVOnzBVerefq6oqCggKoVCqDvxozMjIgkUj0rRFUWn05nzIzMzFw4EC4u7tjy5YtFfbJrc/nU1XyVJb6cj4BQNu2bQEAXbt2RadOndC+fXts27YNI0eOLLVt8TmTlZUFHx8f/fLi1qyq/h6oTaqSp7LY29tj8ODB2Lx5c3WGKZpbt25h+fLl2LZtm75OyM3N1f+bm5sLBweHUvtZ2vcUL9/XIs2bNy/VdzQrKwuJiYml+oNQ1RXn8OrVqwbLo6Ki9PO3Uf2lVCoxZMgQZGVl4Y8//oCzs3OF29fX86mqeaL72rZtC2tra9y4caPM9cXn1IO/B6KiomBjY1MnpxkrS2V5qo9iYmKgVqsxePBguLq6wtXVFUOHDgUA9OrVC3379i1zP0v7nmJRWosMHDgQ+/btQ2Zmpn7Zpk2bIJVK0b9//yod686dOzh48CA6depk5ihrr27dusHJyQmbNm3SLyssLMTWrVsxaNAgESOzfHX9fNJoNBg1ahSuXLmCPXv2wN/fv9J96uP5ZEqeylLXz6fyHDt2DIWFheUWl40aNUKzZs0MzikA+PXXX9GnTx/Y2NjURJiiqyxPZcnLy8POnTvr7DnVvn17REZGGjw+/fRTAMA333xTbjcYS/ue4uX7WiQiIgJffvklhg8fjtmzZyMhIQEzZsxAREQE/Pz89Nv16dMHt27d0v8V+csvv2Dnzp0YNGgQ/Pz8EB0djcWLF0Mmk5WarLquyM/P1/cbunXrFrKzs/WXbYrvDvJgnhQKBWbNmoW5c+fC09MTbdq0wapVq5CWllbpQI3aypQ81cfz6fXXX8fOnTuxfPlyZGdnG9ztJDQ0FHK5nOcTTMtTfTyfAOCpp57CI488grZt28LW1hbnzp3D0qVL0bZtWwwfPhwA8NJLL+Hnn382mAR97ty5GDNmDBo3boxevXrh119/xbFjx+rsyHJT8nTgwAEsXboUTz75JIKDg3Hnzh0sX74cSUlJpQr6usLFxQXh4eFlruvYsSM6dOgAoHR9YHHfUzU+Myo9lMuXLwt9+vQRbG1tBS8vL+Htt98WCgoKDLbp2bOnEBQUpH995MgRITw8XPDw8BCsrKwEDw8PYdSoUUJUVFQNR19zYmJiBABlPiIjIwVBKJ0nQRAEnU4nLFq0SAgICBDkcrnQuXNn4fDhwzX/AWqIKXmqj+dTUFBQuXmKiYkRBIHnkyCYlqf6eD4JgiAsXrxYaN++veDo6CjY29sLrVq1Ej744AMhKytLv824ceOEsn5Nf//990KTJk0EGxsboU2bNsKOHTtqMvQaZUqerl+/Ljz++OOCj4+PYG1tLbi4uAiDBg0Sjh07JsZHEE1kZGSpyfMt/XtKIgiV3JSYiIiIiKiasU8pEREREYmORSkRERERiY5FKRERERGJjkUpEREREYmORSkRERERiY5FKRERERGJjkUpEREREYmORSkRERERiY5FKRHVW4IgoHfv3nj66afFDoWIqN5jUUpEldq1axcCAgKgVqvFDqXKJBIJli1bVua6Tz/9FKmpqVizZk3NBlWONWvWQCKRIDU1tcr7bdiwodTy8PBwDBkyxFzhmUVwcDAmT55s0r6m5qcmLVy4EP369RM7DKJayUrsAIjIsgmCgPfeew/Tpk2DjY2N2OFU2ZEjRxAUFFRq+aVLl7B8+XIcPHgQ9vb2IkRmPmvWrIGDgwOee+45g+WrVq2CTCYTKSrzGzx4MI4cOQIXFxexQynXpEmT8MknnyAyMhK9evUSOxyiWoVFKRFVaP/+/bh48SJeeOEFsUMxoFQqYWtrW+l2Xbp0KXN5q1atkJCQYO6wSikoKIC1tTWk0pq/MNWyZcsaf8/qoNVqodPp4OnpCU9PT7HDqZCLiwtGjBiBzz//nEUpURXx8j1RHbRs2TI0bdoU1tbWkEgkBo/9+/dX6Vg///wzevbsaVAM5OXlYfLkyQgJCYGdnR2Cg4MRERGBrKws/Tbjx49H69atSx1v586dkEgkuHr1qn7ZmjVr0LZtWygUCvj7++O9996DVqs1WC+RSHDkyBH069cP9vb2mDFjBgDgxx9/RKtWrWBrawt3d3c8+uijOHHihH7fsi7fr169GiEhIZDL5QgODsaCBQug0+lKvd+ZM2cwcOBA2Nvbo2nTpvjf//5Xab6KL09/8sknCAoKgq2tLdLT0436nGWZOXMm2rRpAwcHB/j7+2P06NFITEzUrw8PD8e///6LXbt26X/Gc+fO1a8rvny/f/9+SCQSnDx50uD4Wq0WPj4+mDVrFgAgKioKzz77LAIDA2FnZ4eWLVti+fLlBvkpizHnhLGK4/7555/1P6dz586Vefm+oKAAs2fPRlBQEORyOVq0aFGqK8OlS5cwaNAguLu7w87ODiEhIfjkk08Mtlm9ejWCgoJgZ2eHfv364cyZM5BIJAZdO3Q6HRYsWIDg4GDI5XI0b94cq1evLhX/008/jV27dll0NwMiS8SWUqI6ZuXKlZgxYwbGjx+Pr776Cjdu3MCsWbPg4OCAF198scxL2RXZt28fXnzxRYNl+fn50Gq1WLhwITw9PREXF4eFCxdi+PDhiIyMBACMHj0aP//8My5evGhQnP7yyy/o0KEDQkJCAAArVqzAO++8g2nTpmH58uW4cuWKvlhbsmSJwfs+99xzeOWVVzB79mzY2dnhv//+w0svvYS3334bgwYNQn5+Po4fP47MzMxyP8+XX36JN954A1OmTMGQIUNw+PBhzJ07F5mZmaWK1zFjxmDixImYPn06vvvuO4wfPx6dOnVCixYtKszZli1b0LRpU3z++eeQyWSwt7ev0ucs6e7du5g9ezb8/PyQkpKC5cuXo2fPnrh8+TKsrKywatUqjB07FnZ2dvr4AwICSh2nR48e8PPzw8aNG/HII4/ol//zzz9ITk7WX/pPSEhASEgIxowZA0dHR5w9exZz5sxBbm4u5syZU26cxpwTVXHy5EnExsZi3rx5cHV1RWBgIC5evFhqu1GjRuHgwYOYM2cOWrRogd27d2Ps2LFwdXXFwIEDAQBDhw6Ft7c3fvjhBzg7O+PGjRuIj4/XH+P3339HREQEXn75ZYwcORJnz57FqFGjSr3XjBkz8Pnnn+P9999Ht27dsHPnTkRERKCwsNCgn2zXrl2h1Wqxf/9+jBw5ssqfnajeEoioTmncuLHQo0cPg2U//PCDIJVKhRs3blTpWHfu3BEACJs2bapwu8LCQuHgwYMCAOHq1av6ZZ6ensLs2bP12+Xl5QkODg7C0qVLBUEQhOzsbMHBwUGYNWuWwfG+/vprwdbWVkhNTRUEQRB++uknAYCwZMkSg+2WLl0quLm5VRgbAP37aTQawcPDQ3j22WcNtpk1a5ZgY2NT6v1Wrlyp3yY3N1ews7MT5s+fX+H7BQUFCe7u7kJubq5+WVU/Z0pKSpnH1mg0Qnx8vABA+PPPP/XLe/bsKQwePLjU9g8unzZtmhAQECDodDr9sgkTJgitWrUq8/10Op1QWFgoLFy4UPD19a3wcz+orHNCEIryM2nSpAr37dmzp2BtbS3cvn3bYPmD+fnnn39K5UIQBOGZZ54ROnXqJAiCIKSkpAgAhN9//73c9+vUqZPQu3dvg2Xz588XAAg//fST/jjW1tbCzJkzDbYbPXq04OnpKWg0GoPlQUFBwttvv13h5yQiQ7x8T1SHZGVl4ebNm3jyyScNlo8cORI6nQ4HDhyo0vGKLxOX1Y9v7dq1CA0NhYODA6ytrfHoo48CAK5duwYAsLKywtNPP41ff/1Vv8/OnTuRl5eHZ599FgBw+PBh5Obm4umnn4ZGo9E/+vbtC6VSWaplbPDgwQavO3TogPT0dIwfPx5//fUX8vPzK/w8UVFRSE1NLTUF1DPPPAO1Wo3jx48bLO/fv7/+ub29PYKCggxa2MoTHh5uMHiqqp+zpD/++APdunWDs7MzrKys9K2gxXmuitGjRyM+Ph4HDx4EAKjVamzbtg2jR4/Wb6NSqfD/7d1tSFPtHwfwr9nZlqCZbrOsqWlTNNAsZ0mYNu9VGD5ED2aYvUjphRipoOVDphIiIkhBFuYLHakoPtMKoRf5Ig0JoZBKUrEsrZktM5zpuv4vwv07bj6su/9/3N2/D+zFuc65Hs81/Hl5rmN+fj62bdsGoVAIjuOQk5ODsbExTE9PL1v+SnPCEv7+/pDJZMte09nZCScnJyiVSt64Lvz53WAwwNnZGe7u7rh06RKqq6tN7p/BYEBfXx+io6N56TExMbzjx48fY25uzuzc0Wq1Jn0Ui8W8xywIISujoJSQP8iXL18AmAaRDg4OEIlEFv+Q1Ov1AAChUMhLb2lpQWJiIoKDg9HQ0ICenh60tLTw8gA/gqDBwUFjsFdXV4fQ0FBjYLXwzN3OnTvBcZzxI5fLAQBv3rzh1evi4sI7ViqVUKvV6O/vx8GDByEWi5GYmGh8hnOxT58+mS1n4XhxvsW7vAUCAa9/S1lcvqX9XNDb24vo6Gi4urpCrVaju7sbPT09ALCqdiymUCjg5eWFuro6AD8CXp1OxwtKs7KyUFpaiuTkZGg0GvT29iI3N3fFOlc7J1Zr8RiaMzExgcnJSd6YchyHpKQkzM/PY2xsDDY2Nujs7ISvry9SUlIgk8kQFBSErq4uAIBWq8X8/LzJd0YqlfKOLZ07QqEQMzMzlnWakH85eqaUkD+Ik5MT1qxZg/HxcV66TqeDXq/Hhg0bLC5vIf/PGhsbsWPHDt4mj4cPH5rk37t3L2QyGerr6+Hj44N79+6hvLzcpPzm5mazq2Jbt27lHdvY2Jhck5CQgISEBExMTKCtrQ1paWngOA5VVVVL9ufDhw+89Pfv3/PO/12L22lpPxe0tLRg/fr1aGhoMO7eHxkZ+Vtti4+Px61bt3Dt2jXU19dj9+7d8PT0NJ5vbGzEuXPnkJWVZUy7e/fuiuWudk6slrl7vZiTkxMkEgk0Go3Z8wuBpbe3NxobGzE3N4dHjx4hOzsbUVFRePv2LSQSCdauXQutVsvLu3iO/Dx3Nm/ebExfau7odDps3759xT4QQv6LVkoJ+YPY2dlBoVCgsbGRl15fXw8ACA0Ntag8Dw8PCAQCDA8P89JnZmZM3ll6584dk/w2NjY4efIkGhoa0NTUBIPBwNv4ERISAjs7O4yOjiIoKMjk4+zsvOq2isVinD17FiqVCs+fPzd7jY+PDyQSicn4NDQ0QCAQIDg4eNX1WeJX+zkzM2N8g8ICc+O82hVc4EdQqtVq0d7ejvb2dt4q6UKdP99bg8FgnD/LWe2c+J3++usvaLVaCAQCs+O6uD0cxyEsLAwXL17E1NQU3r17B1tbWwQGBqKtrY13bWtrK+84ODgYHMeZnTtSqRTe3t7GtO/fv+P169fGzXyEkNWhlVJC/jBXrlzB4cOHcerUKSQmJuLFixfIycnBiRMnLF65EYlE2LVrF548ecJLV6lUSElJQVFREUJCQqDRaPDgwQOzZcTHx6O0tBR5eXk4cOAAxGKx8ZyjoyMKCwuRmZmJ0dFRhIeHw9bWFkNDQ2hra0NTUxPs7OyWbF9+fj4+fvyI8PBwSKVSPHv2DPfv30d6errZ621tbZGXl4fz589DKpUiMjISPT09KCkpwYULFywKgi3xq/1UqVQoLy9Hamoqjhw5gu7ubqjVapPrfH19UV1djY6ODmzatAmurq5wdXU12xY/Pz/4+/sjNTUVer0ecXFxJnVWVlbCz88PYrEYN27cwOzs7Ip9tGRO/C4qlQpRUVE4dOgQMjMz4e/vj69fv6K/vx+vXr3C7du38fTpU2RkZCAuLg5eXl74/PkziouL4eHhAS8vLwBAbm4uYmJikJycjOPHj6Ovrw/V1dUAYFyhFovFSE1NRWlpKUQiEfbs2QONRoPa2lpcv36d908KXr58ienpaYt/CSTkX8/aO60IIb9fa2srCwgIYAKBgG3cuJGlp6czvV7/S2WVlZWZ7Nien59nGRkZTCKRMHt7e3bs2DHW09Oz5E59Hx8fBoCp1WqzddTV1TGFQsHWrVvHHBwcWGBgIMvLy2Nzc3OMsaV3pXd0dLCIiAgmkUiYUChkXl5eLD8/35iPMf7u+wUVFRVMLpczjuOYm5sbKyoqYgaDwXh+qfoCAgLYmTNnlh2v5XaX/0o/S0pK2JYtW5idnR1TqVRsYGDApE+jo6MsMjKSOTo6MgAsPz+fMbb0rvzi4mIGgEVERJicGx8fZ7Gxscze3p65uLiwrKwsVllZuexbARhb/ZxY7e57c+02Nz6zs7OsoKCAyeVyJhAImEQiYfv372c1NTWMMcbev3/PEhISmKenJxMKhUwqlbKjR4+ygYEBXtkVFRVMJpMxkUjEwsLCWGdnJwPAWltbjdcYDAZWWFjI3NzcGMdxTC6Xs5s3b5q0s6ysjLm7u/O+M4SQldkwxphVomFCyD+CVquFTCZDZ2cn9u3bZ+3mEPJ/UVVVhaSkJAwPD8PDw8OivAqFAlFRUbh8+fL/pnGE/KEoKCWErCgtLQ0jIyNobm62dlMI+e0mJydRUFAApVIJe3t79Pb24urVq1AqlSbPlq6kq6sLsbGxGBoaMnl7AyFkefRMKSFkRdnZ2aioqMC3b99MNo8Q8k/HcRwGBwdRW1sLnU4HiUSC06dPo6SkxOKypqamUFNTQwEpIb+AVkoJIYQQQojV0SuhCCGEEEKI1VFQSgghhBBCrI6CUkIIIYQQYnUUlBJCCCGEEKujoJQQQgghhFgdBaWEEEIIIcTqKCglhBBCCCFWR0EpIYQQQgixOgpKCSGEEEKI1f0HcUafZ02yrIQAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 792x462 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ¿Para qué σ cambia el signo de Δs1?  ->  root_scalar\n",
    "dsahorro = lambda sg: (y1 - c1_cerrada(sg, 0.10)) - (y1 - c1_cerrada(sg, 0.05))\n",
    "sigma_star = brentq(dsahorro, 0.2, 5.0)\n",
    "print(f\"Δs₁ = 0  en  σ* = {sigma_star:.4f}   (EIS* = {1/sigma_star:.4f})\")\n",
    "print(\"σ < σ*  ->  domina sustitución, el ahorro SUBE con r\")\n",
    "print(\"σ > σ*  ->  domina el efecto ingreso, el ahorro CAE con r\")\n",
    "\n",
    "sg = np.linspace(0.25, 4.0, 300)\n",
    "ds = np.array([dsahorro(x) for x in sg])\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(sg, ds, lw=2, color=\"tab:blue\")\n",
    "ax.axhline(0, color=\"k\", lw=.8)\n",
    "ax.axvline(sigma_star, color=\"tab:red\", ls=\"--\", lw=1,\n",
    "           label=f\"σ* = {sigma_star:.3f}  (cambio de signo)\")\n",
    "ax.fill_between(sg, 0, ds, where=ds > 0, alpha=.15, color=\"tab:green\")\n",
    "ax.fill_between(sg, 0, ds, where=ds < 0, alpha=.15, color=\"tab:red\")\n",
    "ax.set(xlabel=\"σ  (aversión relativa al riesgo)\", ylabel=\"Δs₁  al pasar de r = 5% a 10%\",\n",
    "       title=\"El signo de ∂s/∂r lo decide la EIS\")\n",
    "ax.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc452f77",
   "metadata": {},
   "source": [
    "> **Lectura económica.** Un alza de $r$ mueve el ahorro de un acreedor por tres canales:\n",
    "> **sustitución** (+, proporcional a la EIS $=1/\\sigma$), **ingreso** (−, es prestamista neto)\n",
    "> y **riqueza vía descuento** (+, pequeño aquí). Con $\\sigma<1$ domina el primero; con\n",
    "> $\\sigma>1$, el segundo. Con $\\sigma=1$ los dos primeros se cancelan y solo sobrevive el\n",
    "> tercero. Por eso la elasticidad-interés del ahorro es empíricamente débil e inestable."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29d027d9",
   "metadata": {},
   "source": [
    "---\n",
    "## Problema 04 — Descomposición de Hicks de un alza de la tasa\n",
    "\n",
    "Hogar B con $\\sigma=1$ y $r:5\\%\\to10\\%$. La descomposición de Hicks mantiene la **utilidad\n",
    "inicial** constante: la canasta compensada $E^h$ es la **más barata a los precios nuevos**\n",
    "que entrega $U_0$. Esto es literalmente un problema de **minimización del gasto con\n",
    "restricción de desigualdad**, que aquí se resuelve con `scipy.optimize.minimize` (SLSQP)\n",
    "y se contrasta con la solución analítica."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b932dbe9",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.747551Z",
     "iopub.status.busy": "2026-08-04T12:30:24.747302Z",
     "iopub.status.idle": "2026-08-04T12:30:24.783814Z",
     "shell.execute_reply": "2026-08-04T12:30:24.782474Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>W</th>\n",
       "      <th>c₁</th>\n",
       "      <th>c₂</th>\n",
       "      <th>s₁</th>\n",
       "      <th>U</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>E₀ (r=5%)</th>\n",
       "      <td>220.0000</td>\n",
       "      <td>112.8205</td>\n",
       "      <td>112.5385</td>\n",
       "      <td>87.1795</td>\n",
       "      <td>9.2129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>E₁ (r=10%)</th>\n",
       "      <td>219.0909</td>\n",
       "      <td>112.3543</td>\n",
       "      <td>117.4103</td>\n",
       "      <td>87.6457</td>\n",
       "      <td>9.2490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Eʰ compensada (analítica)</th>\n",
       "      <td>215.0701</td>\n",
       "      <td>110.2924</td>\n",
       "      <td>115.2555</td>\n",
       "      <td>89.7076</td>\n",
       "      <td>9.2129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Eʰ compensada (SLSQP)</th>\n",
       "      <td>215.0701</td>\n",
       "      <td>110.2923</td>\n",
       "      <td>115.2556</td>\n",
       "      <td>89.7077</td>\n",
       "      <td>9.2129</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 W       c₁       c₂      s₁      U\n",
       "E₀ (r=5%)                 220.0000 112.8205 112.5385 87.1795 9.2129\n",
       "E₁ (r=10%)                219.0909 112.3543 117.4103 87.6457 9.2490\n",
       "Eʰ compensada (analítica) 215.0701 110.2924 115.2555 89.7076 9.2129\n",
       "Eʰ compensada (SLSQP)     215.0701 110.2923 115.2556 89.7077 9.2129"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1, y2, beta = 200.0, 21.0, 0.95\n",
    "r0, r1 = 0.05, 0.10\n",
    "\n",
    "def optimo_log(r):\n",
    "    W  = y1 + y2/(1+r)\n",
    "    c1 = W/(1+beta)\n",
    "    c2 = beta*(1+r)*c1\n",
    "    return dict(W=W, c1=c1, c2=c2, s1=y1-c1, U=np.log(c1)+beta*np.log(c2))\n",
    "\n",
    "E0, E1 = optimo_log(r0), optimo_log(r1)\n",
    "U0 = E0[\"U\"]\n",
    "chk(\"P04_U0\", U0, 9.2129)\n",
    "\n",
    "# ---------- canasta compensada: minimizar el gasto c1 + c2/(1+r1) s.a. U(c1,c2) >= U0\n",
    "gasto      = lambda x: x[0] + x[1]/(1+r1)\n",
    "restr_util = NonlinearConstraint(lambda x: np.log(x[0]) + beta*np.log(x[1]), U0, np.inf)\n",
    "sol = minimize(gasto, x0=[E1[\"c1\"], E1[\"c2\"]], constraints=[restr_util],\n",
    "               bounds=[(1e-6, None)]*2, method=\"SLSQP\", options={\"ftol\": 1e-14, \"maxiter\": 500})\n",
    "c1_h_num, c2_h_num = sol.x\n",
    "\n",
    "# ---------- solución analítica:  c2 = β(1+r1)c1  y  (1+β)ln c1 + β ln(β(1+r1)) = U0\n",
    "c1_h = np.exp((U0 - beta*np.log(beta*(1+r1)))/(1+beta))\n",
    "c2_h = beta*(1+r1)*c1_h\n",
    "W_h  = c1_h + c2_h/(1+r1)\n",
    "chk(\"P04_c1h\", c1_h, 110.29); chk(\"P04_Wh\", W_h, 215.07)\n",
    "\n",
    "pd.DataFrame({\n",
    "    \"W\": [E0[\"W\"], E1[\"W\"], W_h, gasto(sol.x)],\n",
    "    \"c₁\": [E0[\"c1\"], E1[\"c1\"], c1_h, c1_h_num],\n",
    "    \"c₂\": [E0[\"c2\"], E1[\"c2\"], c2_h, c2_h_num],\n",
    "    \"s₁\": [E0[\"s1\"], E1[\"s1\"], y1-c1_h, y1-c1_h_num],\n",
    "    \"U\":  [E0[\"U\"],  E1[\"U\"],  np.log(c1_h)+beta*np.log(c2_h),\n",
    "           np.log(c1_h_num)+beta*np.log(c2_h_num)],\n",
    "}, index=[\"E₀ (r=5%)\", \"E₁ (r=10%)\", \"Eʰ compensada (analítica)\", \"Eʰ compensada (SLSQP)\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "aac1d3cd",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.786266Z",
     "iopub.status.busy": "2026-08-04T12:30:24.786030Z",
     "iopub.status.idle": "2026-08-04T12:30:24.794590Z",
     "shell.execute_reply": "2026-08-04T12:30:24.793789Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                        Δc₁     Δs₁\n",
      "Sustitución (E₀→Eʰ) -2.5282  2.5282\n",
      "Ingreso (Eʰ→E₁)      2.0620 -2.0620\n",
      "Total (E₀→E₁)       -0.4662  0.4662\n",
      "\n",
      "Cancelación: |ingreso|/|sustitución| = 81.6%\n",
      "El residuo (+0.47 de ahorro) es la caída de riqueza: W pasa de 220.00 a 219.09 porque la pensión se descuenta a 10%.\n",
      "Wʰ = 215.07 < W₁ = 219.09: el hogar está 4.02 mejor en valor presente (es acreedor y subió r).\n"
     ]
    }
   ],
   "source": [
    "sust_c1 = c1_h - E0[\"c1\"]\n",
    "ingr_c1 = E1[\"c1\"] - c1_h\n",
    "chk(\"P04_sust\", sust_c1, -2.53); chk(\"P04_ingr\", ingr_c1, 2.06)\n",
    "\n",
    "efectos = pd.DataFrame({\n",
    "    \"Δc₁\": [sust_c1, ingr_c1, E1[\"c1\"]-E0[\"c1\"]],\n",
    "    \"Δs₁\": [-sust_c1, -ingr_c1, -(E1[\"c1\"]-E0[\"c1\"])],\n",
    "}, index=[\"Sustitución (E₀→Eʰ)\", \"Ingreso (Eʰ→E₁)\", \"Total (E₀→E₁)\"])\n",
    "print(efectos.to_string())\n",
    "print(f\"\\nCancelación: |ingreso|/|sustitución| = {abs(ingr_c1/sust_c1):.1%}\")\n",
    "print(f\"El residuo (+{-(E1['c1']-E0['c1']):.2f} de ahorro) es la caída de riqueza: \"\n",
    "      f\"W pasa de {E0['W']:.2f} a {E1['W']:.2f} porque la pensión se descuenta a 10%.\")\n",
    "print(f\"Wʰ = {W_h:.2f} < W₁ = {E1['W']:.2f}: el hogar está {E1['W']-W_h:.2f} mejor \"\n",
    "      f\"en valor presente (es acreedor y subió r).\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7915c3f5",
   "metadata": {},
   "source": [
    "> **Lectura económica.** Los dos efectos son de signo opuesto y magnitud casi idéntica:\n",
    "> con utilidad logarítmica el **ahorro es esencialmente insensible a la tasa de interés**.\n",
    "> Aplicada a un deudor, la misma descomposición daría efectos del *mismo* signo (ambos\n",
    "> reducen $c_1$), porque para él el alza de $r$ es un empobrecimiento."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3dfd5099",
   "metadata": {},
   "source": [
    "---\n",
    "## Problema 05 — Ingreso permanente: shocks transitorios, permanentes y anticipados\n",
    "\n",
    "Horizonte infinito, previsión perfecta y $\\beta(1+r)=1$, de modo que el consumo óptimo es\n",
    "constante: $c_t=\\frac{r}{1+r}W_t$ con $W_t=\\sum_{j\\ge0}y_{t+j}/(1+r)^j$.\n",
    "\n",
    "$r=4\\%$, $y=100$ por período."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3d0c0ada",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.796964Z",
     "iopub.status.busy": "2026-08-04T12:30:24.796767Z",
     "iopub.status.idle": "2026-08-04T12:30:24.810512Z",
     "shell.execute_reply": "2026-08-04T12:30:24.809559Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(a) W₀ = y(1+r)/r = 2,600.00   ->   c = [r/(1+r)]·W₀ = 100.00 = y  ✓\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>ΔW</th>\n",
       "      <th>Δy corriente</th>\n",
       "      <th>Δc</th>\n",
       "      <th>PMC</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>shock</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Transitorio&nbsp;&nbsp;(+100 hoy)</th>\n",
       "      <td>100.0000</td>\n",
       "      <td>100.0000</td>\n",
       "      <td>3.8462</td>\n",
       "      <td>0.0385</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Permanente&nbsp;&nbsp;(+10 siempre)</th>\n",
       "      <td>260.0000</td>\n",
       "      <td>10.0000</td>\n",
       "      <td>10.0000</td>\n",
       "      <td>1.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Anticipado&nbsp;&nbsp;(+100 en t=5)</th>\n",
       "      <td>82.1927</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>3.1613</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                ΔW  Δy corriente      Δc    PMC\n",
       "shock                                                          \n",
       "Transitorio  (+100 hoy)   100.0000      100.0000  3.8462 0.0385\n",
       "Permanente  (+10 siempre) 260.0000       10.0000 10.0000 1.0000\n",
       "Anticipado  (+100 en t=5)  82.1927        0.0000  3.1613    NaN"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r, y = 0.04, 100.0\n",
    "kappa = r/(1+r)                       # factor de anualidad\n",
    "W0 = y*(1+r)/r\n",
    "chk(\"P05_W0\", W0, 2600.0); chk(\"P05_c\", kappa*W0, 100.0)\n",
    "print(f\"(a) W₀ = y(1+r)/r = {W0:,.2f}   ->   c = [r/(1+r)]·W₀ = {kappa*W0:.2f} = y  ✓\")\n",
    "\n",
    "shocks = pd.DataFrame([\n",
    "    {\"shock\": \"Transitorio  (+100 hoy)\",     \"ΔW\": 100.0,                \"Δy corriente\": 100.0},\n",
    "    {\"shock\": \"Permanente  (+10 siempre)\",   \"ΔW\": 10*(1+r)/r,           \"Δy corriente\": 10.0},\n",
    "    {\"shock\": \"Anticipado  (+100 en t=5)\",   \"ΔW\": 100/(1+r)**5,         \"Δy corriente\": 0.0},\n",
    "])\n",
    "shocks[\"Δc\"]  = kappa*shocks[\"ΔW\"]\n",
    "shocks[\"PMC\"] = np.where(shocks[\"Δy corriente\"] > 0, shocks[\"Δc\"]/shocks[\"Δy corriente\"], np.nan)\n",
    "chk(\"P05_dc_trans\", shocks.loc[0, \"Δc\"], 3.85)\n",
    "chk(\"P05_dc_perm\",  shocks.loc[1, \"Δc\"], 10.0)\n",
    "chk(\"P05_dc_antic\", shocks.loc[2, \"Δc\"], 3.16)\n",
    "shocks.set_index(\"shock\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bdaebbee",
   "metadata": {},
   "source": [
    "**Validación numérica del PIH.** En vez de usar la fórmula de la anualidad, se resuelve el\n",
    "problema de optimización con horizonte finito largo $T$:\n",
    "\n",
    "$$\\max_{\\{c_t\\}}\\ \\sum_{t=0}^{T}\\beta^t\\ln c_t \\quad\\text{s.a.}\\quad\n",
    "\\sum_{t=0}^{T}\\frac{c_t}{(1+r)^t}=\\sum_{t=0}^{T}\\frac{y_t}{(1+r)^t}$$\n",
    "\n",
    "con `scipy.optimize.minimize` (SLSQP) y restricción de igualdad. Con $\\beta(1+r)=1$ la\n",
    "solución debe ser **plana**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a0b59f4d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.812664Z",
     "iopub.status.busy": "2026-08-04T12:30:24.812486Z",
     "iopub.status.idle": "2026-08-04T12:30:24.950172Z",
     "shell.execute_reply": "2026-08-04T12:30:24.948855Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Horizonte T = 40:  consumo óptimo plano = 100.0000 (desv. estándar 2.42e-10)\n",
      "Anualidad finita  W_T/Σ(1+r)^-t = 100.0000   ->  coincide  ✓\n",
      "\n",
      "Shock anticipado: el consumo salta HOY de 100.00 a 103.95 (+3.95) aunque y₀ no cambió.\n",
      "Fórmula de horizonte infinito: Δc = κ·ΔW = 3.16\n",
      "\n",
      "La diferencia es puro efecto de truncar el horizonte: con T finito el ingreso se\n",
      "reparte entre menos períodos, así que el factor de anualidad es mayor que r/(1+r).\n",
      "Al alargar T, el óptimo numérico converge a la fórmula del PIH:\n",
      "   T =   40:  factor de anualidad = 0.048094   Δc₀ = 3.9529\n",
      "   T =  120:  factor de anualidad = 0.038799   Δc₀ = 3.1890\n",
      "   T =  400:  factor de anualidad = 0.038462   Δc₀ = 3.1613\n",
      "   T = ∞   :  factor de anualidad = 0.038462   Δc₀ = 3.1613\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 792x462 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "T = 40\n",
    "beta_pih = 1/(1+r)\n",
    "desc = (1+r)**(-np.arange(T+1))\n",
    "\n",
    "def resolver_pih(y_path):\n",
    "    W = float(desc @ y_path)\n",
    "    obj = lambda c: -np.sum(beta_pih**np.arange(T+1) * np.log(c))\n",
    "    con = {\"type\": \"eq\", \"fun\": lambda c: desc @ c - W}\n",
    "    c0 = np.full(T+1, W/desc.sum())\n",
    "    s = minimize(obj, c0, constraints=[con], bounds=[(1e-6, None)]*(T+1),\n",
    "                 method=\"SLSQP\", options={\"ftol\": 1e-12, \"maxiter\": 800})\n",
    "    return s.x, W\n",
    "\n",
    "y_base = np.full(T+1, y)\n",
    "c_base, W_T = resolver_pih(y_base)\n",
    "print(f\"Horizonte T = {T}:  consumo óptimo plano = {c_base.mean():.4f} \"\n",
    "      f\"(desv. estándar {c_base.std():.2e})\")\n",
    "print(f\"Anualidad finita  W_T/Σ(1+r)^-t = {W_T/desc.sum():.4f}   ->  coincide  ✓\")\n",
    "\n",
    "# shock anticipado: +100 en t = 5\n",
    "y_ant = y_base.copy(); y_ant[5] += 100\n",
    "c_ant, _ = resolver_pih(y_ant)\n",
    "print(f\"\\nShock anticipado: el consumo salta HOY de {c_base[0]:.2f} a {c_ant[0]:.2f} \"\n",
    "      f\"(+{c_ant[0]-c_base[0]:.2f}) aunque y₀ no cambió.\")\n",
    "print(f\"Fórmula de horizonte infinito: Δc = κ·ΔW = {kappa*100/(1+r)**5:.2f}\")\n",
    "print(\"\\nLa diferencia es puro efecto de truncar el horizonte: con T finito el ingreso se\")\n",
    "print(\"reparte entre menos períodos, así que el factor de anualidad es mayor que r/(1+r).\")\n",
    "print(\"Al alargar T, el óptimo numérico converge a la fórmula del PIH:\")\n",
    "for Tv in (40, 120, 400):\n",
    "    d = (1+r)**(-np.arange(Tv+1))\n",
    "    print(f\"   T = {Tv:>4}:  factor de anualidad = {1/d.sum():.6f}   \"\n",
    "          f\"Δc₀ = {100/(1+r)**5/d.sum():.4f}\")\n",
    "print(f\"   T = ∞   :  factor de anualidad = {kappa:.6f}   Δc₀ = {kappa*100/(1+r)**5:.4f}\")\n",
    "\n",
    "activos = np.zeros(T+2)\n",
    "for t in range(T+1):\n",
    "    activos[t+1] = (1+r)*activos[t] + y_ant[t] - c_ant[t]\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "ax.step(range(T+1), y_ant, where=\"mid\", label=\"ingreso $y_t$\", color=\"tab:gray\")\n",
    "ax.plot(range(T+1), c_ant, lw=2, label=\"consumo $c_t$\", color=\"tab:blue\")\n",
    "ax.plot(range(T+1), activos[:T+1], lw=1.6, ls=\"--\", label=\"activos $a_t$\", color=\"tab:red\")\n",
    "ax.axvline(5, color=\"k\", lw=.8, ls=\":\")\n",
    "ax.set(xlabel=\"t\", ylabel=\"nivel\", xlim=(0, 15),\n",
    "       title=\"Shock anticipado: el consumo se mueve al anuncio, no al pago\")\n",
    "ax.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d24b34b",
   "metadata": {},
   "source": [
    "> **Lectura económica.** Bajo el PIH la PMC del ingreso corriente **no es un número**:\n",
    "> depende de cuánta información sobre la riqueza permanente contiene ese ingreso\n",
    "> ($3{,}8\\%$ si es transitorio, $100\\%$ si es permanente, indefinida si el ingreso no cambió).\n",
    "> De aquí salen dos predicciones testeables — el consumo sigue un paseo aleatorio (Hall) y\n",
    "> los cambios anticipados no deben moverlo cuando ocurren — que fallan parcialmente en los\n",
    "> datos. Ese es el puente al problema 07."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5124d8ed",
   "metadata": {},
   "source": [
    "---\n",
    "## Problema 06 — Equivalencia ricardiana\n",
    "\n",
    "El gobierno gasta $G_1,G_2$ y los financia con impuestos de suma alzada y deuda, sujeto a\n",
    "$T_1+\\frac{T_2}{1+r}=G_1+\\frac{G_2}{1+r}$. El hogar es el del P02 (log, $\\beta=0{,}95$),\n",
    "ahora con ingreso **disponible**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "20b2eac4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.952705Z",
     "iopub.status.busy": "2026-08-04T12:30:24.952390Z",
     "iopub.status.idle": "2026-08-04T12:30:24.969872Z",
     "shell.execute_reply": "2026-08-04T12:30:24.968605Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "VP del gasto = 39.0476\n",
      "Deuda emitida B = G₁ − T₁' = 20.00  ->  repago (1+r)B + G₂ = 41.00 = T₂' = 41.00  ✓\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>escenario</th>\n",
       "      <th>Antes (T₁=20)</th>\n",
       "      <th>Después (T₁=0)</th>\n",
       "      <th>Δ</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>W</th>\n",
       "      <td>160.9524</td>\n",
       "      <td>160.9524</td>\n",
       "      <td>-0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c₁</th>\n",
       "      <td>82.5397</td>\n",
       "      <td>82.5397</td>\n",
       "      <td>-0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c₁ (scipy)</th>\n",
       "      <td>82.5397</td>\n",
       "      <td>82.5397</td>\n",
       "      <td>-0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>c₂</th>\n",
       "      <td>82.3333</td>\n",
       "      <td>82.3333</td>\n",
       "      <td>-0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ahorro privado</th>\n",
       "      <td>-2.5397</td>\n",
       "      <td>17.4603</td>\n",
       "      <td>20.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ahorro público</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>-20.0000</td>\n",
       "      <td>-20.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ahorro nacional</th>\n",
       "      <td>-2.5397</td>\n",
       "      <td>-2.5397</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "escenario        Antes (T₁=20)  Después (T₁=0)        Δ\n",
       "W                     160.9524        160.9524  -0.0000\n",
       "c₁                     82.5397         82.5397  -0.0000\n",
       "c₁ (scipy)             82.5397         82.5397  -0.0000\n",
       "c₂                     82.3333         82.3333  -0.0000\n",
       "ahorro privado         -2.5397         17.4603  20.0000\n",
       "ahorro público          0.0000        -20.0000 -20.0000\n",
       "ahorro nacional        -2.5397         -2.5397   0.0000"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y1, y2, r, beta = 100.0, 105.0, 0.05, 0.95\n",
    "G1 = G2 = 20.0\n",
    "T1, T2 = 20.0, 20.0\n",
    "\n",
    "def escenario(T1, T2, etiqueta):\n",
    "    W  = (y1-T1) + (y2-T2)/(1+r)\n",
    "    c1 = W/(1+beta)                       # forma cerrada\n",
    "    # verificación numérica con scipy\n",
    "    f  = lambda c: -(np.log(c) + beta*np.log((y2-T2) + (1+r)*((y1-T1)-c)))\n",
    "    c1n = minimize_scalar(f, bounds=(1e-8, W-1e-8), method=\"bounded\",\n",
    "                          options={\"xatol\": 1e-13}).x\n",
    "    assert abs(c1-c1n) < 1e-4, \"la forma cerrada y scipy deben coincidir\"\n",
    "    c2 = beta*(1+r)*c1\n",
    "    return {\"escenario\": etiqueta, \"W\": W, \"c₁\": c1, \"c₁ (scipy)\": c1n, \"c₂\": c2,\n",
    "            \"ahorro privado\": (y1-T1)-c1, \"ahorro público\": T1-G1,\n",
    "            \"ahorro nacional\": (y1-T1)-c1 + T1-G1}\n",
    "\n",
    "# (b) el gobierno elimina T1 y se financia con deuda\n",
    "VP_G   = G1 + G2/(1+r)\n",
    "T1_new = 0.0\n",
    "T2_new = brentq(lambda T2v: T1_new + T2v/(1+r) - VP_G, 0.0, 500.0)   # root-finding\n",
    "chk(\"P06_T2new\", T2_new, 41.0)\n",
    "print(f\"VP del gasto = {VP_G:.4f}\")\n",
    "print(f\"Deuda emitida B = G₁ − T₁' = {G1-T1_new:.2f}  ->  repago (1+r)B + G₂ = \"\n",
    "      f\"{(1+r)*(G1-T1_new)+G2:.2f} = T₂' = {T2_new:.2f}  ✓\")\n",
    "\n",
    "comp = pd.DataFrame([escenario(T1, T2, \"Antes (T₁=20)\"),\n",
    "                     escenario(T1_new, T2_new, \"Después (T₁=0)\")]).set_index(\"escenario\").T\n",
    "comp[\"Δ\"] = comp.iloc[:, 1] - comp.iloc[:, 0]\n",
    "chk(\"P06_W\", comp.loc[\"W\"].iloc[0], 160.95)\n",
    "chk(\"P06_c1\", comp.loc[\"c₁\"].iloc[0], 82.54)\n",
    "comp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "edbd8d9b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.972125Z",
     "iopub.status.busy": "2026-08-04T12:30:24.971931Z",
     "iopub.status.idle": "2026-08-04T12:30:24.977284Z",
     "shell.execute_reply": "2026-08-04T12:30:24.976167Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ΔW = -2.84e-14  ->  la riqueza NO cambia: solo cambió el CALENDARIO de los impuestos, no su valor presente.\n",
      "El hogar ahorra íntegramente la rebaja: Δahorro privado = +20.00 = −Δahorro público = +20.00\n",
      "Δahorro nacional = 1.42e-14  ->  la deuda pública NO es riqueza neta.\n"
     ]
    }
   ],
   "source": [
    "dW = comp.loc[\"W\", \"Δ\"]\n",
    "print(f\"ΔW = {dW:.2e}  ->  la riqueza NO cambia: solo cambió el CALENDARIO de los impuestos, \"\n",
    "      f\"no su valor presente.\")\n",
    "print(f\"El hogar ahorra íntegramente la rebaja: Δahorro privado = {comp.loc['ahorro privado','Δ']:+.2f} \"\n",
    "      f\"= −Δahorro público = {-comp.loc['ahorro público','Δ']:+.2f}\")\n",
    "print(f\"Δahorro nacional = {comp.loc['ahorro nacional','Δ']:.2e}  ->  la deuda pública NO es riqueza neta.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a5942ce",
   "metadata": {},
   "source": [
    "> **Por qué falla en la práctica.** (i) *Horizonte finito sin altruismo*: si el hogar muere\n",
    "> antes de $t=2$, parte de $T_2$ la pagan otros; solo el legado altruista à la Barro\n",
    "> restaura la equivalencia. (ii) *Restricciones de liquidez* (P07): la rebaja es justamente\n",
    "> el préstamo que el mercado le negaba, y la consume (PMC $\\approx1$). (iii) *Impuestos\n",
    "> distorsionadores*, incertidumbre sobre quién pagará (ahorro precautorio) y miopía.\n",
    ">\n",
    "> En los datos la PMC de las rebajas transitorias se estima entre **0,2 y 0,5** — ni 0 ni 1."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a42679ee",
   "metadata": {},
   "source": [
    "---\n",
    "## Problema 07 — Restricción de liquidez y solución de esquina\n",
    "\n",
    "Vuelve el hogar A (ingreso creciente, quiere endeudarse) pero ahora **$s_1\\ge0$**:\n",
    "\n",
    "$$\\max_{c_1}\\ \\ln c_1+\\beta\\ln\\big(y_2+(1+r)(y_1-c_1)\\big)\\quad\\text{s.a.}\\quad y_1-c_1\\ge0$$\n",
    "\n",
    "Este es el caso donde el enfoque numérico paga: `scipy.optimize.minimize` con SLSQP entrega\n",
    "directamente la solución de esquina **y** el multiplicador de la restricción activa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ddbd3a7f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.979302Z",
     "iopub.status.busy": "2026-08-04T12:30:24.979112Z",
     "iopub.status.idle": "2026-08-04T12:30:24.988305Z",
     "shell.execute_reply": "2026-08-04T12:30:24.986867Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c₁* sin restricción = 112.82  vs  y₁ = 100.00\n",
      "Condición general:  y₂ = 126.00  >  β(1+r)y₁ = 99.75   ->  LA RESTRICCIÓN MUERDE\n",
      "Muerde cuando el ingreso crece rápido: jóvenes, estudiantes, inicio de carrera.\n",
      "\n",
      "SLSQP:  c₁ = 100.000000   s₁ = 0.00e+00   c₂ = 126.0000   (restricción ACTIVA)\n",
      "Desigualdad de Euler:  u'(c₁) = 0.01000  >  β(1+r)u'(c₂) = 0.00792\n",
      "Multiplicador de Lagrange μ = 0.00208  ->  precio sombra de un peso de crédito\n"
     ]
    }
   ],
   "source": [
    "y1, y2, r, beta = 100.0, 126.0, 0.05, 0.95\n",
    "W = y1 + y2/(1+r)\n",
    "\n",
    "# (a) ¿se activa la restricción?  c1* > y1  <=>  y2 > β(1+r)y1\n",
    "c1_libre = W/(1+beta)\n",
    "print(f\"c₁* sin restricción = {c1_libre:.2f}  vs  y₁ = {y1:.2f}\")\n",
    "print(f\"Condición general:  y₂ = {y2:.2f}  >  β(1+r)y₁ = {beta*(1+r)*y1:.2f}   ->  \"\n",
    "      f\"{'LA RESTRICCIÓN MUERDE' if y2 > beta*(1+r)*y1 else 'no muerde'}\")\n",
    "print(\"Muerde cuando el ingreso crece rápido: jóvenes, estudiantes, inicio de carrera.\\n\")\n",
    "\n",
    "# (b) optimización CON la restricción de no endeudamiento\n",
    "negU  = lambda c: -(np.log(c[0]) + beta*np.log(y2 + (1+r)*(y1-c[0])))\n",
    "restr = {\"type\": \"ineq\", \"fun\": lambda c: y1 - c[0]}        # s1 = y1 - c1 >= 0\n",
    "sol   = minimize(negU, x0=[90.0], constraints=[restr], bounds=[(1e-6, W)],\n",
    "                 method=\"SLSQP\", options={\"ftol\": 1e-14, \"maxiter\": 300})\n",
    "\n",
    "c1_c = sol.x[0]\n",
    "s1_c = y1 - c1_c\n",
    "c2_c = y2 + (1+r)*s1_c\n",
    "mu   = 1/c1_c - beta*(1+r)/c2_c            # multiplicador = brecha de Euler\n",
    "chk(\"P07_c1\", c1_c, 100.0); chk(\"P07_mu\", mu, 0.00208, tol=1e-5)\n",
    "\n",
    "print(f\"SLSQP:  c₁ = {c1_c:.6f}   s₁ = {s1_c:.2e}   c₂ = {c2_c:.4f}   (restricción ACTIVA)\")\n",
    "print(f\"Desigualdad de Euler:  u'(c₁) = {1/c1_c:.5f}  >  β(1+r)u'(c₂) = {beta*(1+r)/c2_c:.5f}\")\n",
    "print(f\"Multiplicador de Lagrange μ = {mu:.5f}  ->  precio sombra de un peso de crédito\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2ec51c8d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:24.992006Z",
     "iopub.status.busy": "2026-08-04T12:30:24.991801Z",
     "iopub.status.idle": "2026-08-04T12:30:25.104555Z",
     "shell.execute_reply": "2026-08-04T12:30:25.103266Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "U* = 9.21293   U^c = 9.19964   ΔU = 0.01329"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "λ = exp(ΔU/(1+β)) = 1.006839   ->  pérdida de 0.68% del consumo de por vida\n",
      "\n",
      "PMC del hogar restringido        = 1.0000\n",
      "PMC del hogar NO restringido     = 0.5128   (propensión a consumir de la riqueza)\n",
      "PMC del PIH de horizonte infinito= 0.0385   (problema 05)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 792x462 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (c) costo de bienestar en equivalente de consumo\n",
    "U_libre = np.log(c1_libre) + beta*np.log(beta*(1+r)*c1_libre)\n",
    "U_rest  = np.log(y1) + beta*np.log(y2)\n",
    "dU      = U_libre - U_rest\n",
    "lam     = np.exp(dU/(1+beta))              # ΔU = (1+β) ln λ\n",
    "chk(\"P07_dU\", dU, 0.01329, tol=1e-4); chk(\"P07_lambda\", lam, 1.00684, tol=1e-4)\n",
    "print(f\"U* = {U_libre:.5f}   U^c = {U_rest:.5f}   ΔU = {dU:.5f}\")\n",
    "print(f\"λ = exp(ΔU/(1+β)) = {lam:.6f}   ->  pérdida de {100*(lam-1):.2f}% del consumo de por vida\")\n",
    "\n",
    "# (d) PMC ante una transferencia transitoria de 5\n",
    "def consumo_restringido(y1v):\n",
    "    Wv  = y1v + y2/(1+r)\n",
    "    return min(Wv/(1+beta), y1v)           # esquina si el deseo excede el ingreso\n",
    "\n",
    "tau  = 5.0\n",
    "pmc  = (consumo_restringido(y1+tau) - consumo_restringido(y1))/tau\n",
    "chk(\"P07_pmc\", pmc, 1.0)\n",
    "print(f\"\\nPMC del hogar restringido        = {pmc:.4f}\")\n",
    "print(f\"PMC del hogar NO restringido     = {1/(1+beta):.4f}   (propensión a consumir de la riqueza)\")\n",
    "print(f\"PMC del PIH de horizonte infinito= {0.04/1.04:.4f}   (problema 05)\")\n",
    "\n",
    "# la PMC salta de 1 a 1/(1+β) cuando la transferencia libera la restricción\n",
    "taus = np.linspace(0, 40, 400)\n",
    "pmcs = [(consumo_restringido(y1+t+1e-4) - consumo_restringido(y1+t))/1e-4 for t in taus]\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(taus, pmcs, lw=2)\n",
    "ax.set(xlabel=\"tamaño de la transferencia τ\", ylabel=\"PMC marginal\",\n",
    "       title=\"La PMC cae de 1 a 1/(1+β) cuando la transferencia libera la restricción\",\n",
    "       ylim=(0, 1.1))\n",
    "ax.axhline(1/(1+beta), color=\"tab:red\", ls=\"--\", lw=1, label=f\"1/(1+β) = {1/(1+beta):.3f}\")\n",
    "ax.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84d4959d",
   "metadata": {},
   "source": [
    "> **Lectura económica.** Esta es la explicación estándar del *exceso de sensibilidad* del\n",
    "> consumo al ingreso corriente que rechaza el PIH en los datos, y reconcilia las estimaciones\n",
    "> de la PMC: los hogares restringidos gastan casi todo, los no restringidos casi nada, y la\n",
    "> PMC agregada es un promedio ponderado por la fracción restringida. De ahí que las\n",
    "> transferencias fiscales se focalicen en hogares de bajos ingresos y baja liquidez."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2818e5b",
   "metadata": {},
   "source": [
    "---\n",
    "## Problema 08 — Capital óptimo y costo de uso del capital\n",
    "\n",
    "Firma competitiva con $Y=AK^\\alpha$, $p_K=1$ y depreciación $\\delta$. Maximiza\n",
    "$AK^\\alpha-(r+\\delta)K$, de donde\n",
    "\n",
    "$$PMgK=\\alpha AK^{\\alpha-1}=r+\\delta\\equiv uc \\qquad\\Longrightarrow\\qquad\n",
    "K^*=\\Big[\\frac{\\alpha A}{r+\\delta}\\Big]^{1/(1-\\alpha)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "ce833e9d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:25.107440Z",
     "iopub.status.busy": "2026-08-04T12:30:25.107168Z",
     "iopub.status.idle": "2026-08-04T12:30:25.123173Z",
     "shell.execute_reply": "2026-08-04T12:30:25.122257Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>uc = r+δ</th>\n",
       "      <th>K* cerrada</th>\n",
       "      <th>K* scipy (max Π)</th>\n",
       "      <th>K* scipy (brentq)</th>\n",
       "      <th>PMgK en K*</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0500</th>\n",
       "      <td>0.1500</td>\n",
       "      <td>72.2128</td>\n",
       "      <td>72.2128</td>\n",
       "      <td>72.2128</td>\n",
       "      <td>0.1500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.1000</th>\n",
       "      <td>0.2000</td>\n",
       "      <td>47.8774</td>\n",
       "      <td>47.8774</td>\n",
       "      <td>47.8774</td>\n",
       "      <td>0.2000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        uc = r+δ  K* cerrada  K* scipy (max Π)  K* scipy (brentq)  PMgK en K*\n",
       "r                                                                            \n",
       "0.0500    0.1500     72.2128           72.2128            72.2128      0.1500\n",
       "0.1000    0.2000     47.8774           47.8774            47.8774      0.2000"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A, alpha, delta = 10.0, 0.30, 0.10\n",
    "\n",
    "f_prod  = lambda K: A*K**alpha\n",
    "PMgK    = lambda K: alpha*A*K**(alpha-1)\n",
    "K_cerr  = lambda r: (alpha*A/(r+delta))**(1/(1-alpha))\n",
    "\n",
    "def K_optimo_numerico(r, metodo=\"optim\"):\n",
    "    if metodo == \"optim\":     # maximizar el beneficio\n",
    "        return minimize_scalar(lambda K: -(f_prod(K) - (r+delta)*K),\n",
    "                               bounds=(1e-6, 1e5), method=\"bounded\",\n",
    "                               options={\"xatol\": 1e-10}).x\n",
    "    return brentq(lambda K: PMgK(K) - (r+delta), 1e-6, 1e6)   # raíz de la CPO\n",
    "\n",
    "tab8 = pd.DataFrame({\"r\": [0.05, 0.10]})\n",
    "tab8[\"uc = r+δ\"]        = tab8.r + delta\n",
    "tab8[\"K* cerrada\"]      = tab8.r.map(K_cerr)\n",
    "tab8[\"K* scipy (max Π)\"] = tab8.r.map(lambda x: K_optimo_numerico(x, \"optim\"))\n",
    "tab8[\"K* scipy (brentq)\"] = tab8.r.map(lambda x: K_optimo_numerico(x, \"raiz\"))\n",
    "tab8[\"PMgK en K*\"]      = tab8[\"K* cerrada\"].map(PMgK)\n",
    "chk(\"P08_K05\", tab8.loc[0, \"K* cerrada\"], 72.21)\n",
    "chk(\"P08_K10\", tab8.loc[1, \"K* cerrada\"], 47.88)\n",
    "tab8.set_index(\"r\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4ae96c76",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:25.125839Z",
     "iopub.status.busy": "2026-08-04T12:30:25.125639Z",
     "iopub.status.idle": "2026-08-04T12:30:25.245019Z",
     "shell.execute_reply": "2026-08-04T12:30:25.243499Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Caída de K* al pasar de 5% a 10%:  -33.70%\n",
      "Elasticidad  d ln K*/d ln(uc):  teórica = -1.4286   numérica = -1.4286  ✓\n",
      "\n",
      "I neta  = K* − K₀ = 12.21\n",
      "I bruta = I neta + δK₀ = 12.21 + 6.00 = 18.21\n",
      "De la inversión bruta, 32.9% solo repone el desgaste.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 792x462 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K0_, K1_ = tab8[\"K* cerrada\"]\n",
    "print(f\"Caída de K* al pasar de 5% a 10%:  {K1_/K0_-1:+.2%}\")\n",
    "elast_teorica = -1/(1-alpha)\n",
    "elast_num = (np.log(K1_)-np.log(K0_))/(np.log(0.10+delta)-np.log(0.05+delta))\n",
    "chk(\"P08_elast\", elast_num, -1.4286, tol=1e-3)\n",
    "print(f\"Elasticidad  d ln K*/d ln(uc):  teórica = {elast_teorica:.4f}   numérica = {elast_num:.4f}  ✓\")\n",
    "\n",
    "# (c) inversión neta y bruta desde K0 = 60\n",
    "K_ini = 60.0\n",
    "I_neta  = K0_ - K_ini\n",
    "I_bruta = I_neta + delta*K_ini\n",
    "chk(\"P08_Ineta\", I_neta, 12.21); chk(\"P08_Ibruta\", I_bruta, 18.21)\n",
    "print(f\"\\nI neta  = K* − K₀ = {I_neta:.2f}\")\n",
    "print(f\"I bruta = I neta + δK₀ = {I_neta:.2f} + {delta*K_ini:.2f} = {I_bruta:.2f}\")\n",
    "print(f\"De la inversión bruta, {delta*K_ini/I_bruta:.1%} solo repone el desgaste.\")\n",
    "\n",
    "rr = np.linspace(0.005, 0.25, 300)\n",
    "fig, ax = plt.subplots()\n",
    "ax.plot(rr, [K_cerr(x) for x in rr], lw=2)\n",
    "for x, col in [(0.05, \"tab:blue\"), (0.10, \"tab:red\")]:\n",
    "    ax.plot(x, K_cerr(x), \"o\", color=col, ms=7)\n",
    "    ax.annotate(f\"r={x:.0%}\\nK*={K_cerr(x):.1f}\", (x, K_cerr(x)),\n",
    "                textcoords=\"offset points\", xytext=(12, 8), color=col)\n",
    "ax.axhline(K_ini, color=\"k\", ls=\":\", lw=1, label=f\"K₀ = {K_ini:.0f}\")\n",
    "ax.set(xlabel=\"tasa real r\", ylabel=\"K*\", ylim=(0, 200),\n",
    "       title=\"Demanda de capital: la elasticidad −1/(1−α) está detrás de la pendiente de la IS\")\n",
    "ax.legend(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63976ff7",
   "metadata": {},
   "source": [
    "> **Lectura económica.** Este modelo entrega la demanda de inversión que está detrás de la\n",
    "> curva IS: $I$ decreciente en $r$, con elasticidad $-1/(1-\\alpha)$. Pero tiene un defecto\n",
    "> fatal: como no hay costo de mover el capital, la empresa **salta instantáneamente** a $K^*$\n",
    "> — inversión infinita en un instante y cero después. La inversión observada es suave y\n",
    "> persistente. El P09 arregla esto."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13cff966",
   "metadata": {},
   "source": [
    "---\n",
    "## Problema 09 — Costos de ajuste y la $q$ de Tobin\n",
    "\n",
    "Ahora instalar capital cuesta $\\Phi(I,K)=\\frac{\\phi}{2}(I/K)^2K$, con $\\phi=5$.\n",
    "Igualando costo marginal y beneficio marginal de instalar una unidad:\n",
    "\n",
    "$$1+\\phi\\frac{I}{K}=q \\qquad\\Longrightarrow\\qquad \\frac{I}{K}=\\frac{q-1}{\\phi},\n",
    "\\qquad q=\\frac{PMgK}{r+\\delta}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "b57a0503",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:25.247588Z",
     "iopub.status.busy": "2026-08-04T12:30:25.247390Z",
     "iopub.status.idle": "2026-08-04T12:30:25.263931Z",
     "shell.execute_reply": "2026-08-04T12:30:25.262701Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K* (donde q = 1, punto de quiebre exacto) = 72.2128\n",
      "Verificación con brentq:  72.2128\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PMgK</th>\n",
       "      <th>q</th>\n",
       "      <th>I/K</th>\n",
       "      <th>I</th>\n",
       "      <th>señal</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>K₀</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>60.0000</th>\n",
       "      <td>0.1708</td>\n",
       "      <td>1.1385</td>\n",
       "      <td>0.0277</td>\n",
       "      <td>1.6617</td>\n",
       "      <td>q&gt;1: invierte</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72.2128</th>\n",
       "      <td>0.1500</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>q=1: K = K*</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100.0000</th>\n",
       "      <td>0.1194</td>\n",
       "      <td>0.7962</td>\n",
       "      <td>-0.0408</td>\n",
       "      <td>-4.0757</td>\n",
       "      <td>q&lt;1: desinvierte</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           PMgK      q     I/K       I             señal\n",
       "K₀                                                      \n",
       "60.0000  0.1708 1.1385  0.0277  1.6617     q>1: invierte\n",
       "72.2128  0.1500 1.0000  0.0000  0.0000       q=1: K = K*\n",
       "100.0000 0.1194 0.7962 -0.0408 -4.0757  q<1: desinvierte"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A, alpha, delta, r, phi = 10.0, 0.30, 0.10, 0.05, 5.0\n",
    "PMgK  = lambda K: alpha*A*K**(alpha-1)\n",
    "q_de  = lambda K: PMgK(K)/(r+delta)\n",
    "IK    = lambda K: (q_de(K)-1)/phi\n",
    "K_est = (alpha*A/(r+delta))**(1/(1-alpha))\n",
    "\n",
    "tab9 = pd.DataFrame({\"K₀\": [60.0, K_est, 100.0]})\n",
    "tab9[\"PMgK\"]  = tab9[\"K₀\"].map(PMgK)\n",
    "tab9[\"q\"]     = tab9[\"K₀\"].map(q_de)\n",
    "tab9[\"I/K\"]   = tab9[\"K₀\"].map(IK)\n",
    "tab9[\"I\"]     = tab9[\"I/K\"]*tab9[\"K₀\"]\n",
    "tab9[\"señal\"] = np.where(tab9.q > 1+1e-9, \"q>1: invierte\",\n",
    "                  np.where(tab9.q < 1-1e-9, \"q<1: desinvierte\", \"q=1: K = K*\"))\n",
    "chk(\"P09_q60\", tab9.loc[0, \"q\"], 1.139); chk(\"P09_I60\", tab9.loc[0, \"I\"], 1.66)\n",
    "chk(\"P09_q100\", tab9.loc[2, \"q\"], 0.796); chk(\"P09_I100\", tab9.loc[2, \"I\"], -4.08)\n",
    "print(f\"K* (donde q = 1, punto de quiebre exacto) = {K_est:.4f}\")\n",
    "print(f\"Verificación con brentq:  {brentq(lambda K: q_de(K)-1, 1, 1000):.4f}\\n\")\n",
    "tab9.set_index(\"K₀\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa5362d3",
   "metadata": {},
   "source": [
    "**La regla $I/K=(q-1)/\\phi$ se anula exactamente en $q=1$, es decir en $K=K^*$: es la\n",
    "inversión *neta*.** La acumulación es entonces $K_{t+1}=K_t+I_t$ y el capital converge\n",
    "**gradualmente** a $K^*$, en vez del salto instantáneo del P08."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1b3d7eed",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:25.266257Z",
     "iopub.status.busy": "2026-08-04T12:30:25.266071Z",
     "iopub.status.idle": "2026-08-04T12:30:25.274709Z",
     "shell.execute_reply": "2026-08-04T12:30:25.274031Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " t     K_t  I_t neta  I_t bruta  brecha K*−K\n",
      " 0 60.0000    1.6617     7.6617      12.2128\n",
      " 5 66.3689    0.8077     7.4446       5.8439\n",
      "10 69.4422    0.3856     7.3298       2.7706\n",
      "20 71.5964    0.0862     7.2458       0.6164\n",
      "40 72.1826       NaN        NaN       0.0302\n",
      "\n",
      "P08 sin costos de ajuste: la empresa saltaría 12.21 de una vez, en un solo instante. Aquí la brecha se cierra gradualmente.\n"
     ]
    }
   ],
   "source": [
    "def senda_miope(K0, T=30):\n",
    "    K, I = [K0], []\n",
    "    for _ in range(T):\n",
    "        i = IK(K[-1])*K[-1]\n",
    "        I.append(i); K.append(K[-1] + i)\n",
    "    return np.array(K), np.array(I)\n",
    "\n",
    "K_path, I_path = senda_miope(60.0, T=40)\n",
    "resumen = pd.DataFrame({\"t\": [0, 5, 10, 20, 40]})\n",
    "resumen[\"K_t\"]          = resumen.t.map(lambda t: K_path[t])\n",
    "resumen[\"I_t neta\"]     = resumen.t.map(lambda t: I_path[t] if t < len(I_path) else np.nan)\n",
    "resumen[\"I_t bruta\"]    = resumen[\"I_t neta\"] + delta*resumen[\"K_t\"]\n",
    "resumen[\"brecha K*−K\"]  = K_est - resumen[\"K_t\"]\n",
    "print(resumen.to_string(index=False))\n",
    "print(f\"\\nP08 sin costos de ajuste: la empresa saltaría {K_est-60:.2f} de una vez, \"\n",
    "      f\"en un solo instante. Aquí la brecha se cierra gradualmente.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0bd28a3",
   "metadata": {},
   "source": [
    "### La regla de inversión como problema de optimización\n",
    "\n",
    "La regla $I/K=(q-1)/\\phi$ **es** la condición de primer orden de un problema de\n",
    "maximización: dado el valor sombra $q$ de una unidad instalada, la empresa elige cuánto\n",
    "instalar comparando ese beneficio con el costo total de instalación (precio de compra más\n",
    "costo de ajuste):\n",
    "\n",
    "$$\\max_{I}\\ \\underbrace{q\\,I}_{\\text{beneficio}}-\\underbrace{\\Big[I+\\tfrac{\\phi}{2}\\big(\\tfrac{I}{K}\\big)^2K\\Big]}_{\\text{costo de instalar}}\n",
    "\\qquad\\Longrightarrow\\qquad q=1+\\phi\\frac{I}{K}$$\n",
    "\n",
    "Resolviéndolo con `scipy.optimize.minimize_scalar` se recupera exactamente la regla:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "147f80e6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:25.277198Z",
     "iopub.status.busy": "2026-08-04T12:30:25.276926Z",
     "iopub.status.idle": "2026-08-04T12:30:25.289753Z",
     "shell.execute_reply": "2026-08-04T12:30:25.288841Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>I regla cerrada</th>\n",
       "      <th>I scipy</th>\n",
       "      <th>diferencia</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>K</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>60.0000</th>\n",
       "      <td>1.6617</td>\n",
       "      <td>1.6617</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72.2128</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100.0000</th>\n",
       "      <td>-4.0757</td>\n",
       "      <td>-4.0757</td>\n",
       "      <td>-0.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          I regla cerrada  I scipy  diferencia\n",
       "K                                             \n",
       "60.0000            1.6617   1.6617      0.0000\n",
       "72.2128            0.0000   0.0000      0.0000\n",
       "100.0000          -4.0757  -4.0757     -0.0000"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def I_optima_numerica(K):\n",
    "    \"Maximiza q·I − I − (φ/2)(I/K)²K con scipy; debe dar I = K(q−1)/φ.\"\n",
    "    q = q_de(K)\n",
    "    obj = lambda I: -(q*I - I - 0.5*phi*(I/K)**2 * K)\n",
    "    return minimize_scalar(obj, bounds=(-K, K), method=\"bounded\",\n",
    "                           options={\"xatol\": 1e-12}).x\n",
    "\n",
    "comp9 = pd.DataFrame({\"K\": [60.0, K_est, 100.0]})\n",
    "comp9[\"I regla cerrada\"] = comp9.K.map(lambda k: IK(k)*k)\n",
    "comp9[\"I scipy\"]         = comp9.K.map(I_optima_numerica)\n",
    "comp9[\"diferencia\"]      = comp9[\"I regla cerrada\"] - comp9[\"I scipy\"]\n",
    "comp9.set_index(\"K\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62fc8f32",
   "metadata": {},
   "source": [
    "### Velocidad de ajuste: qué hace $\\phi$\n",
    "\n",
    "$\\phi$ es lo único que gobierna cuán rápido se cierra la brecha con $K^*$. Con $\\phi\\to0$\n",
    "se recupera el salto instantáneo del P08; con $\\phi$ grande la inversión se vuelve casi\n",
    "imperceptible por período."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c5792493",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:25.292494Z",
     "iopub.status.busy": "2026-08-04T12:30:25.292245Z",
     "iopub.status.idle": "2026-08-04T12:30:25.689385Z",
     "shell.execute_reply": "2026-08-04T12:30:25.688197Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      φ  períodos para cerrar 50%  períodos para cerrar 90%\n",
      " 0.5000                         1                         1\n",
      " 1.0000                         1                         2\n",
      " 2.0000                         2                         6\n",
      " 5.0000                         5                        16\n",
      "10.0000                        10                        33\n",
      "25.0000                        25                        82\n",
      "\n",
      "Con φ = 5 (el del enunciado) la brecha de 12.21 unidades tarda 16 períodos en cerrarse al 90%.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1320x440 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def periodos_para_cerrar(fraccion, phi_, K0=60.0, T=4000):\n",
    "    \"Cuántos períodos toma cerrar 'fraccion' de la brecha inicial con K*.\"\n",
    "    K, brecha0 = K0, K_est - K0\n",
    "    for t in range(1, T+1):\n",
    "        K += K*((PMgK(K)/(r+delta)) - 1)/phi_\n",
    "        if (K - K0)/brecha0 >= fraccion:\n",
    "            return t\n",
    "    return np.nan\n",
    "\n",
    "vel = pd.DataFrame({\"φ\": [0.5, 1, 2, 5, 10, 25]})\n",
    "vel[\"períodos para cerrar 50%\"] = vel[\"φ\"].map(lambda f: periodos_para_cerrar(.50, f))\n",
    "vel[\"períodos para cerrar 90%\"] = vel[\"φ\"].map(lambda f: periodos_para_cerrar(.90, f))\n",
    "print(vel.to_string(index=False))\n",
    "print(f\"\\nCon φ = {phi:.0f} (el del enunciado) la brecha de {K_est-60:.2f} unidades tarda \"\n",
    "      f\"{periodos_para_cerrar(.90, phi)} períodos en cerrarse al 90%.\")\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(12, 4))\n",
    "for f, col in [(1.0, \"tab:green\"), (5.0, \"tab:blue\"), (20.0, \"tab:orange\")]:\n",
    "    K, serie = 60.0, [60.0]\n",
    "    for _ in range(40):\n",
    "        K += K*((PMgK(K)/(r+delta)) - 1)/f\n",
    "        serie.append(K)\n",
    "    ax[0].plot(serie, lw=2, color=col, label=f\"φ = {f:g}\")\n",
    "ax[0].axhline(K_est, color=\"k\", ls=\":\", lw=1.2, label=f\"$K^*$ = {K_est:.1f}\")\n",
    "ax[0].set(xlabel=\"t\", ylabel=\"K\", title=\"φ gobierna la velocidad de convergencia\")\n",
    "ax[0].legend(fontsize=8)\n",
    "\n",
    "Kg = np.linspace(35, 130, 300)\n",
    "ax[1].plot(Kg, [q_de(k) for k in Kg], lw=2, color=\"tab:purple\")\n",
    "ax[1].axhline(1, color=\"k\", lw=.9)\n",
    "ax[1].axvline(K_est, color=\"tab:red\", ls=\"--\", lw=1, label=f\"$K^*$ = {K_est:.1f}\")\n",
    "for k, col in [(60, \"tab:green\"), (100, \"tab:orange\")]:\n",
    "    ax[1].plot(k, q_de(k), \"o\", color=col, ms=7)\n",
    "    ax[1].annotate(f\"K={k}\\nq={q_de(k):.3f}\", (k, q_de(k)), textcoords=\"offset points\",\n",
    "                   xytext=(8, 8), fontsize=8, color=col)\n",
    "ax[1].set(xlabel=\"K\", ylabel=\"q\", title=\"q > 1 invierte · q < 1 desinvierte\")\n",
    "ax[1].legend(fontsize=8)\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39a81494",
   "metadata": {},
   "source": [
    "> **Lectura económica.** El aporte de Tobin es que toda la información relevante para\n",
    "> invertir —productividad, tasa de interés, depreciación, expectativas futuras— se comprime\n",
    "> en **un solo número observable**. Bajo competencia perfecta y rendimientos constantes a\n",
    "> escala, la $q$ marginal (no observable) coincide con la $q$ media (valor de mercado /\n",
    "> valor de reposición), que sí se mide en bolsa. Y el modelo entrega la inversión suave y\n",
    "> persistente que el P08 no podía generar."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51ed4df3",
   "metadata": {},
   "source": [
    "---\n",
    "## Problema 10 — Dinámica de la deuda pública y la carrera entre $r$ y $g$\n",
    "\n",
    "De $B_{t+1}=(1+r)B_t-SP_{t+1}$, dividiendo por $Y_{t+1}=(1+g)Y_t$:\n",
    "\n",
    "$$b_{t+1}=\\underbrace{\\frac{1+r}{1+g}}_{\\theta}\\,b_t-sp,\n",
    "\\qquad b^*=\\frac{sp}{\\theta-1},\n",
    "\\qquad b_t=\\theta^t(b_0-b^*)+b^*$$\n",
    "\n",
    "$b_0=60\\%$, $r=5\\%$, $g=3\\%$, $sp=1\\%$ del PIB."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9d0fe8a5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:25.691975Z",
     "iopub.status.busy": "2026-08-04T12:30:25.691779Z",
     "iopub.status.idle": "2026-08-04T12:30:25.708396Z",
     "shell.execute_reply": "2026-08-04T12:30:25.704651Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "θ = (1+r)/(1+g) = 1.019417   >  1   ->   punto fijo INESTABLE (umbral, no atractor)\n",
      "b* = sp/(θ−1) = 51.5000% del PIB     b₀ = 60% está POR ENCIMA -> la deuda explota\n",
      "Aproximación:  Δb ≈ (r−g)b − sp = +0.0020\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>b_t recursiva (% PIB)</th>\n",
       "      <th>b_t explícita&nbsp;&nbsp;(% PIB)</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>60.0000</td>\n",
       "      <td>60.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>60.1650</td>\n",
       "      <td>60.1650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>60.3333</td>\n",
       "      <td>60.3333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60.5048</td>\n",
       "      <td>60.5048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>60.6797</td>\n",
       "      <td>60.6797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>60.8579</td>\n",
       "      <td>60.8579</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   b_t recursiva (% PIB)  b_t explícita  (% PIB)\n",
       "t                                               \n",
       "0                60.0000                 60.0000\n",
       "1                60.1650                 60.1650\n",
       "2                60.3333                 60.3333\n",
       "3                60.5048                 60.5048\n",
       "4                60.6797                 60.6797\n",
       "5                60.8579                 60.8579"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b0, r, g, sp = 0.60, 0.05, 0.03, 0.01\n",
    "\n",
    "theta   = lambda g_: (1+r)/(1+g_)\n",
    "b_estac = lambda g_, sp_=sp: sp_/(theta(g_)-1)\n",
    "\n",
    "def senda(b0, g_, sp_=sp, T=25):\n",
    "    b = [b0]\n",
    "    for _ in range(T):\n",
    "        b.append(theta(g_)*b[-1] - sp_)\n",
    "    return np.array(b)\n",
    "\n",
    "th = theta(g)\n",
    "bs = b_estac(g)\n",
    "chk(\"P10_theta\", th, 1.019417, tol=1e-5); chk(\"P10_bstar\", bs, 0.515, tol=1e-4)\n",
    "print(f\"θ = (1+r)/(1+g) = {th:.6f}   >  1   ->   punto fijo INESTABLE (umbral, no atractor)\")\n",
    "print(f\"b* = sp/(θ−1) = {bs:.4%} del PIB     b₀ = {b0:.0%} está POR ENCIMA -> la deuda explota\")\n",
    "print(f\"Aproximación:  Δb ≈ (r−g)b − sp = {(r-g)*b0-sp:+.4f}\\n\")\n",
    "\n",
    "b_base = senda(b0, g)\n",
    "explic = np.array([th**t*(b0-bs)+bs for t in range(len(b_base))])\n",
    "tab10 = pd.DataFrame({\"t\": range(6),\n",
    "                      \"b_t recursiva (% PIB)\": b_base[:6]*100,\n",
    "                      \"b_t explícita  (% PIB)\": explic[:6]*100})\n",
    "chk(\"P10_b5\", b_base[5], 0.6086, tol=1e-3)\n",
    "tab10.set_index(\"t\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "ac910ee5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:25.710702Z",
     "iopub.status.busy": "2026-08-04T12:30:25.710508Z",
     "iopub.status.idle": "2026-08-04T12:30:25.844532Z",
     "shell.execute_reply": "2026-08-04T12:30:25.843222Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sp* = (θ−1)·b₀ = 1.1650% del PIB   (ajuste de +0.1650% respecto del 1% actual)\n",
      "Proporcional a la deuda heredada: con b₀ = 120% haría falta 2.3301%.\n",
      "\n",
      "g' = 6%  ->  θ' = 0.990566 < 1  ->  punto fijo ATRACTOR ESTABLE\n",
      "Con el mismo sp = 1%, la deuda cae de 60.0% a 52.3% en cinco años.\n",
      "Incluso con sp = 0 la deuda converge a 0% (23.25% tras 100 años, 9.01% tras 200): el crecimiento la licúa sin ajuste fiscal.\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAq4AAAG/CAYAAACZnVWlAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjksIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvJkbTWQAAAAlwSFlzAAAQ6wAAEOsBUJTofAAAwE9JREFUeJzs3XdYE9nXB/BvEnoJHUFBEJGiIFawxLoqYqPoz94rFqyvrrr2rquu69rrrt1VwQrWtbtrB0XFQlFQkN5rknn/AAYiSBNIAufzPDxw585MTnKT4eTOnTschmEYEEIIIYQQIuO40g6AEEIIIYSQsqDElRBCCCGEyAVKXAkhhBBCiFygxJUQQgghhMgFSlwJIYQQQohcoMSVEEIIIYTIBUpcCSGEEEKIXKDElRBCCCGEyAVKXAkhhBBCiFygxJUQQgghhMgFSlwJ+QGdO3eGubl5qctKwuFwMHr0aIll5ubm6Ny5c6XvtzKEhYWBw+Fg2bJlUt1HTVRVbfat0aNHg8PhlHn94t6PNVllP98///wTHA4Ht27dqrR9StOtW7fA4XDw559/SjsUUgtR4koqRXR0NObPnw97e3vw+XxoamrCwsIC7u7u2L9/f5U//pYtW+ggSgghhNRwCtIOgMi/T58+wdHREbGxsRgwYAAmTJgAJSUlhISE4N69e9iyZQvGjRtXpTFs2bIF5ubm1dJbVdjVq1fBMMwP7SMjIwM8Hq9aHosQANi7dy927dol7TBqjREjRmDw4MFQUlKSdiiEyD1KXMkP+/XXX/H161ds2bIFM2bMKFIfFRUlhaiqR2X8I1JRUam2xyIEABQVFaGoqCjtMGoNHo9Xpi+npHgpKSnQ1NSUdhhERtBQAfLD3r9/DwD46aefiq03MjIqsuzhw4fo06cPdHV1oaKiAhsbG6xcuRLZ2dkS6yUkJGDu3Llo1KgRVFVVoaOjA3t7e8ycORNAwVjJjx8/4vbt2+BwOOxPWFgYu5/g4GCMHj0adevWhZKSEkxMTDBlyhTExsZKPN6yZcvA4XDw7t07LFmyBGZmZlBWVoatrS2OHj1a5HmUNO7048eP6N+/P3R0dKCuro7u3bvj2bNnRdYr67jG7z3WtWvX0KZNG6iqqsLAwABjx44t8rzy7dy5E87OzjAxMYGSkhIMDQ3Rv39/BAYGFrv+8ePH4eDgABUVFdSrVw+zZ89Genp6set++vQJQUFByMnJKfW5fI9YLMbWrVvh4OAAVVVV8Pl8dO3aFdeuXSvXfrZu3Qpra2soKyujQYMGWLlyJa5fv15kXF5+exd+r+T73uv9/PlzDBgwAIaGhlBSUoKFhQXmz5//3delOOVpMwA4c+YMOnXqBD6fD1VVVTRv3hz79u0rdt0XL15gyJAh7Hu9Xr16cHV1xdOnT9l1vjfG9enTp+jWrRvU1dWho6OD/v37F/va5Lt58yZcXFygo6PDfk7Wr18PkUhU5teirK9nREQEJk6ciAYNGkBFRQX6+vpo2bIl1qxZU6bHYRgGe/fuhaOjI9TV1aGuro527drh7NmzZY61OJcvX0bXrl1haGgIFRUVmJiYwMXFBXfv3mXX+d4Y18jISIwYMQJ6enpQV1dHhw4dcOfOnWLbJ//9GBUVxW6jqqqKjh074smTJ0XiqsrPklAoLHbd7OxsbNiwAU2bNmUfs1u3brhz506ZHqvw2Nndu3ejadOmUFFRgZeXV7lirizv3r2Dq6sr+Hw++Hw+evbsicDAwHJfb0AqF/W4kh/WsGFDAMDBgwexfv16KCiU/La6fPky+vXrBz6fjylTpsDIyAi+vr5YsmQJHjx4gEuXLoHLzf1ONXDgQNy8eRMTJ05Es2bNkJ2djeDgYFy/fh0AYGBggMOHD2PWrFnQ19fHL7/8wj6OgYEBAMDf3x+dO3eGmpoaxo4dCzMzM7x//x47d+7EjRs38OjRI2hpaUnEOGrUKHA4HEyfPh1cLhc7duzA8OHD0bBhQ7Rp06bU1yQtLQ2dOnVC8+bNsWrVKoSHh2PHjh3o2LEj7t+/DwcHh7K/wCW4dOkSXF1dYWBggJ9//hm6urrw9vZGz549i11/w4YNcHJywtSpU6Gvr4/3799j3759uHbtGp4/f862JQDs2rULkydPRqNGjbBkyRIoKSnh6NGj3/0nNHLkSNy+fRuhoaEVPqiPHj0ahw8fRvv27bFmzRqkpqZi3759cHZ2xqFDhzB8+PBS9zF//nysX7+eTWqysrKwf/9+nDt3rkIxFXb58mW4ubnB1NQUXl5eqFOnDgICArB582bcv38fN2/eLPX9X942W7p0KVasWIEuXbpg6dKlUFVVxZUrVzBhwgR8+PAB69atY9f18/ODu7s7lJSUMG7cONjY2CAuLg63b9/GgwcP0LJly+/G9ezZM3Ts2BE8Hg9eXl4wNTXF1atX0blzZ6SlpRVZ/8CBAxg/fjyaN2+O+fPnQ1tbG/fv38eCBQvw/PlznDhxotJeT6FQiO7duyM8PByTJ0+GjY0NUlNTERQUhH/++QcLFy4s9bHGjBmDQ4cOwdXVFcOGDQMAeHt7w93dHTt37oSnp2ep+/jWnTt30KdPHzRu3Bhz586Fnp4eoqKi8ODBAzx//hwdOnT47rZJSUno0KEDQkJCMHbsWLRs2RJBQUHo3bu3xOewsLS0NHTo0AEtW7bEypUr8fXrV/z2229wcXFBSEiIRK9kdX+WhEIhevXqhdu3b2PIkCHw9PREeno6jhw5gq5du+Ls2bPo06dPGV5V4Pfff8fXr18xYcIEmJiYSKW39ePHj2jXrh1SU1Ph6ekJa2trPH78GJ06dYKurm61x0MKYQj5QcHBwYyWlhYDgDE0NGT69+/PrF+/nrl37x4jEokk1hUKhYy5uTmjqqrKvH//XqJuzJgxDADm8OHDDMMwTGJiIgOA8fT0LDUGMzMzplOnTsXWNWvWjGnQoAETFxcnsfzhw4cMj8djli1bxi5bunQpA4BxcXGRiP3Tp0+MoqIiM2TIEIl9dOrUiTEzMyuyDAAzdepUieVPnjxhuFxukTgBMKNGjSr1+Xz7WCKRiDE3N2c0NDSYT58+scuFQiHTq1evYvebmprKfCswMJBRVFRkpkyZwi5LTExkNDQ0mPr16zOJiYns8vT0dKZZs2YMAGbp0qXFPu/Q0NAij/Gt0NDQIvu4ceMG+9oLhUJ2eXR0NGNoaMhoa2szKSkpJe73/fv3DJfLZRwdHZnMzEx2eVxcHGNsbMwAYA4ePMguz2/v4mL+9vXOyMhgjIyMiuybYRjm9OnTDADmzz//LDG+8rbZs2fPGA6Hw0yfPr3IvqZNm8ZwuVwmODiYYRiGSUtLYwwMDBgtLS122bePnW/UqFHMt4f/Dh06MFwul3ny5InE8kmTJjEAJN6PkZGRjIqKCuPm5saIxWKJ9Tdu3MgAYG7dulXia1Ge1zMgIIABwKxbt67EfX7P2bNnGQDM5s2bi9T17duX4fP5THJyMruspONJYbNmzWIAMFFRUSWud/DgQQYAc/PmTXbZwoULGQDM9u3bJdb19vZmABRpn/zP15o1aySWHz9+nAHA7N69m10mjc/Sli1bGACMt7e3xH6ys7OZ5s2bMw0aNCjx8RiGYW7evMkAYLS1tZnIyMhS169KQ4cOZQAwly5dkli+efNmBkCR4z6pPjRUgPwwCwsLBAQEYPr06VBXV8eZM2fw888/QyAQwNLSElevXmXXffbsGcLCwjBixAhYWlpK7Cd/aqQzZ84AAFRVVaGiooKHDx8iJCSkQrEFBgbC398fgwcPhlgsRmxsLPtjYWEBS0tLXLlypch2s2bNYnt9AcDU1BTW1tZ49+5dmR/7216gli1bwtnZGbdv3y7xtHBZPX36FGFhYRg5ciRMTU3Z5Twe77s9UOrq6gByT5smJycjNjYWderUgbW1NR4+fMiud/XqVaSmpmLatGkSvdGqqqr4v//7v2L3fevWLTAMU+He1vx2X7x4scR4QAMDA0ydOhWJiYm4ceNGifvw8fGBWCzG//3f/0FZWZldrquri6lTp1YornzXr19HVFQURo8ejZSUFIn3UseOHaGmplbse6mw8rbZ0aNHwTAMxo0bJ/F4sbGx6NevH8RiMXv24erVq4iJicHMmTNhYWFRZF+F38/fiomJwd27d9GzZ88ivbKLFy8usv7p06eRmZmJ8ePHIy4uTiKu/F610l6L8rye+e/BmzdvVmjM/OHDh6GqqopBgwYVeR3d3NyQnJyMf//9t9z71dbWBgCcOnWq3ENkfHx8oKOjgwkTJkgsd3d3h7W1dbHbcLlczJo1S2JZ9+7dAUDi2CSNz9Lhw4dhbm6ODh06SLy+SUlJ6NevH0JDQ8t8/Bw1alSxQ8y+x9/fH8uWLSvzT2JiYon7E4vFOH/+POzs7NCrVy+JuilTptB4WymjoQKkUpiZmeH333/H77//jujoaPz777/4+++/cfz4cbi7uyMgIACWlpZsAmpvb19kH/Xr1wefz0dwcDCA3IuRtm7dCi8vLzRs2BBWVlbo0KEDevXqBVdX1zJd7PDmzRsAwNq1a7F27dpi1ynun3xxy/T09PDx48dSHxPI/YdWt27dIssbN24MPz8/BAcHQ19fv0z7+p7816lx48ZF6po0aVLsNnfu3MGKFSvw4MEDZGRkSNQ1aNDgh/b9o0p6b+Qvy4/re6oy7vz30pQpUzBlypRi1/n69Wulxpf/mCUNLcl/zPykoEWLFiXGUN646tWrV2QoTX5cJZ36Le21KM/raWZmhqVLl2LlypWoW7cu7O3tIRAI4ObmxiZupT1WRkYG6tWrV+F4izNt2jRcuHABXl5emD9/Ptq2bYvOnTtj6NChEp+n4oSEhMDe3r7Yi+RsbGzw9u3bIsvr1q1b5GJOPT09AEBcXJzEvoHq/Sy9efMG6enp7BCt4nz9+hVWVlYlPi6AMq1TmL+/P5YvX17m9UePHs1+6ShOdHQ0UlNTYWNjU6ROWVkZFhYWpSa/pOpQ4koqnaGhIVxdXeHq6or69etj3bp1OHHiBBYtWlTqtt9ekDBhwgT069cPfn5+uHPnDq5fv479+/fD0dERt2/fLvWKfLFYDADw8vJCv379il1HVVW1yLLvJcWMHE9H9fTpU/z000+wsLDA6tWrYWFhATU1NXA4HMyYMaPYcYw1XUmT8H97AUr+e2n16tVwdHQsdhsdHZ3KC67QY168eFGi16uw4r5kVbX8uPbt2wczM7Ni1ynui1tx+yjr67ls2TKMGTMGfn5+uHv3Ls6cOYMdO3bA1dUVPj4+JbalWCyGlpYWTp8+/d11KvLFRldXFw8fPsSDBw9w/fp13L17F8uXL8fy5ctx+PBhDBo0qNz7LElJX9alfWwSi8WwtrbGtm3bvruOnZ1dmfalpqZWrscePXp0tU+FSKSHEldSpdq1awcA+Pz5M4CCC7levXpVZN3w8HAkJSUVuTChTp067IGJYRgsXLiQTYbzD1bf+6dV+Jt7t27dfvj5lFViYiK+fPlS5J/369evAeC7F1+UR/4+8vdZWHGv79GjRyEUCuHn51ck2YmLi5P4ElB437179y5135Wh8HvDyclJoi5/1oPSXrfCcX+biBQXd/5FFvHx8UWGOISEhEhMQZb/XlJRUanwe6m8bWZlZYXLly/D2Ni41J7U/PieP3/+3S9pFYnr8+fPSEpKKvaxdHR0KvxaVOT1NDMzg6enJzw9PSEUCjF69GgcPXoUt2/fLvFOV1ZWVggKCkLz5s3ZHsrKwuVyIRAIIBAIAOQex1q0aIGff/65xMTVwsICwcHBEAqFRS7oCwoK+qGYpPFZsrKyQnh4ODp37lzqBYqyztDQEBoaGsW2Q3Z2NkJCQugCLSmiMa7kh926deu7UwH5+PgAKDjd1Lx5c5ibm+Pw4cNFTruvWLECANC/f38AQHp6epH9cjgc9h944VNjGhoaiI+PL/L4zZo1g729Pfbv38+emiyMYRjExMSU6XmW17fT9Dx9+hRXrlxBx44df3iYAJB7StjMzAyHDh1CeHg4u1wsFhc7RVB+b823PTO7du0qcpq0R48eUFdXx7Zt2ySSlszMTGzcuLHYeH50OiwPDw8Aua9bfm8cAMTGxmL79u3Q1tb+7pRr+dzc3MDhcLBx40ZkZWWxy+Pj47F9+/Yi6+ePJcwfJ5rvyJEjiIyMlFjm7OyMOnXq4Ndffy12nKVQKCz2PVhYedtsxIgRAIAFCxYU+7omJSWxz7NHjx4wMDDAli1bip3CqvBr+i0DAwMIBAJcvny5yJRtq1atKrL+wIEDoaKigmXLliE1NbVIfUZGBlJSUr77eED5Xs+kpKQiz19BQYEdQlH4WFCckSNHAgDmzZtXbM9kRYYJACj22GFqaoo6deqUGpObmxsSEhKwZ88eieU+Pj7FDhMoD2l8lkaOHImEhASsXr262P1V9DWWBi6Xi759+yIwMBC+vr4Sddu3by/1vU2qlnx/LSIyYcuWLbh58yb69OmDli1bQkdHB7Gxsbh06RJu374NOzs7jB07FkBu8rRz507069cPrVu3hqenJwwNDeHn5wdfX184Oztj6NChAHLH7HXs2BFubm5o0qQJDAwMEBISgl27dkFTU5M9OANAmzZtsH//fixevBi2trbsgUddXZ2djqVFixYYPXo07O3tkZOTg7CwMJw9exajRo1iLwyrLPr6+rh48SI+f/7MTuOzfft2qKioYMuWLZXyGDweD1u3boW7uzscHR3h6ekJHR0deHt7F5tMeHh4YPPmzXBxccHEiROhpqaGe/fu4cqVK2jYsKHEqXEtLS2sX78e06ZNQ+vWrTFmzBgoKSnhyJEj3z1d+aPTYXXt2hUjRozA4cOH0aVLF7i7u7NT+ERHR+PQoUPQ0NAocR+NGjXCnDlzsHHjRrRv3x5DhgxBdnY29u3bh7p16xZJRrt164bGjRtj8eLFiI6ORqNGjfDkyROcP38elpaWEsmSmpoaDh8+DFdXV9ja2mLMmDGwsbFBSkoKgoOD4e3tjXXr1pV4yrK8bdaqVSusWrUKixYtgp2dHYYMGQITExNER0fj5cuXOHfuHF6/fg1zc3Ooqanh4MGD8PDwgIODAzsdVkJCAm7fvg0XF5cS58P87bff0LFjR3Tu3BlTp05lp8N6/vx5kS9a9erVw+7duzF27FhYW1tj1KhRsLCwQHx8PIKCguDt7Y2zZ8+W2Atantfz5s2bmDBhAnvhkra2Nl6/fo1du3ahXr16pfbY9u/fHxMmTMDevXsREBAANzc3GBkZ4cuXL3j69Cl8fX0r9IVr4sSJ+PTpE3r06AFzc3MIhUJcvHgRr169wrRp00rcdt68eThx4gS8vLzw7NkztGrVCm/evMGBAwfg4OCAgICAcseTTxqfpRkzZuDGjRtYtmwZ7ty5gx49ekBXVxfh4eF48OABQkJCKnyRrTSsXr0aV65cgYeHBzw9PWFjY4NHjx7h3LlzsLS0/O5ctqQaSG0+A1Jj/Pfff8zcuXMZR0dHpk6dOoyCggKjqanJtGzZklmxYoXENDP5/v33X6ZXr16MtrY2o6SkxFhZWTErVqxgsrKy2HViY2OZWbNmMc2bN2d0dHQYZWVlxszMjBk9ejTz5s0bif19/fqV8fDwYHR0dBgOh1NkiqPw8HBm6tSpjIWFBaOkpMRoa2sz9vb2zIwZM5hXr16x65VneqTSloWGhjIeHh6MlpYWo6amxnTt2pV5/Phxkf2igtNh5bt8+TLj6OjIKCsrM/r6+szo0aOZmJiYYvd7/vx5plWrVoyamhqjo6PD9O3bl3n16tV3933kyBHG3t6eUVJSYoyNjZlZs2Yxr169qpLpsBgmd8qmLVu2MPb29oyysjKjoaHBdOnShbly5Uqp+8wnFouZ3377jbG0tGQUFRUZc3NzZsWKFcy1a9eKTOHDMAzz4cMHplevXoy6ujqjqanJ9OrVi3nz5s13X5M3b94wo0aNYkxMTBhFRUVGX1+fadmyJbNgwQKJKa5KUp42y1+/V69ejJ6eHqOoqMjUrVuX6dKlC7Np0yYmIyNDYt2nT58y/fv3ZwwMDNh13d3dmadPn7LrFDcdFsMwzKNHj5guXbowampqjJaWFuPh4cGEhoZ+d3qo//77jxkwYABTp04dRlFRkalTpw7Ttm1bZuXKlUWmn/uesryeISEhjKenJ9O4cWOGz+czqqqqjKWlJePl5cWEh4eX6XEYhmGOHTvGdO7cmdHS0mKUlJQYU1NTxsXFhdm5c6fEemWdDuvMmTOMq6srY2pqyigrKzM6OjqMo6Mjs2vXLonpx4qbDothGCYiIoIZNmwYo62tzaipqTECgYC5c+cO4+Hhwaiqqkqs+733I8MUfwyRxmdJKBQyO3bsYJycnBgNDQ1GRUWFMTc3Zzw8PJiTJ0+W+nj502F9u19pefPmDdOnTx9GQ0OD0dDQYJydnZmXL18yLVq0YGxtbaUdXq3FYRg5vtqEEELK6NatW+jSpQsOHjxIF3IQmdakSROIxeJihzcR6RIKhdDX10fbtm3h5+cn7XBqJRrjSgghhEhBcdcG+Pj44PXr13B2dpZCRKSw4trnjz/+QFJSErWPFNEYV0IIIUQK+vbtizp16qBVq1ZQVlbG06dPcejQIdSpUwc///yztMOr9Vq0aAGBQAAHBweIxWLcu3cPp0+fhq2tbZEbR5DqQ4krIYQQIgV9+/bFoUOH4Ofnh9TUVBgaGmLEiBFYvnw5jI2NpR1erefh4YHz58/j77//RmZmJurVq4fp06djyZIl7F0ISfWjMa6EEEIIIUQu0BhXQgghhBAiFyhxJYQQQgghcqFWJq5CoRARERE0gTAhhBBCiByplYlrVFQUTE1Ni73NYFUQiUSIioqCSCSqlscjlYvaT35R28k3aj/5RW0n32S5/Wpl4koIIYQQQuQPJa6EEEIIIUQuUOJKCCGEEELkAiWuhBBCCCFELlDiSgghhBBC5AIlroQQQgghRC5Q4koIIYQQQuQCJa6EEEIIIUQuUOJKCCGEEELkAiWuhBBCCCFELlDiSgghhBBC5AIlroQQQgghRC7IVOL6119/oXnz5lBRUYG+vj5cXFyQkZEBABg9ejQ4HE6Rn8uXL0s5akIIIYQQUh0UpB1AvtWrV2P9+vVYuHAh2rZti9jYWNy4cQMikYhdx8LCAkePHpXYztbWtrpDJYQQQgip8RiRCODxpB2GBJlIXN++fYtly5bh/PnzcHFxYZf3799fYj1VVVW0adOmusMjhBBCCKkRmJwcCOMTIIyJgTA2BqLYWAhjYyGMyfsdGwthTAxyoqPBGT0adWbOkHbIEmQicT148CAaNGggkbQSQgghhJDSMQwDcXJyQQIaE5OXhOYlpoWSUlFCAsAwZdqvKDa2iiMvP5lIXP/77z/Y29tj1apV2Lp1KxITE9G6dWts3rwZTk5O7HofPnyAlpYWMjIyYG9vj8WLF8PNzU16gRNCCCGEVBFxWhqEcXEFCWlcbEEimr88NgaimFgwOTmV/vhCSlyLFxUVhadPn+Lly5fYsWMH1NTUsGbNGvTo0QPv37+HoaEhmjdvjtatW6NJkyZITEzEzp074e7ujlOnTmHAgAEl7j85ORnJyclsOTIyEgAgEokkxtBWFZFIBLFYXC2PRSoftZ/8oraTb9R+8ova7vvEWVkQ5SWdotj837mJaP5p+/x6Ju8C9crGUVICT18fCgYG4OnrQUFfHwr6+rnL9PXB0dFBMpcH/UaW1daGvDKOpeUwTBn7i6uQlZUV3r9/j4CAADRt2hQAEB8fD3Nzc8ycORMrVqwoso1YLEa7du2QnJyM169fl7j/ZcuWYfny5UWWP336FHXr1q2cJ1ECsViMpKQkaGlpgcuVqYkcSBlQ+8kvajv5Ru0nv2pb2zHZ2WASEiBOSIA4PgFMfDzECQlgEvJ+x8ezy5m0tKoJgsMBR1sbXF0dcHR1wdXVy/ud+8Mp9JujoQ4Oh/PdXUmj/YyMjMq0nkz0uOro6EBPT49NWgFAV1cXzZs3x6tXr4rdhsvlon///pg3bx4yMjKgqqr63f3Pnj0b48ePZ8uRkZFwdHSEnp4eDAwMKu+JfEf+txV9ff0yf6MgsoPaT35R28k3aj/5VRParqBnNA6iuDiI4mLZv4VxhX7HxkKcklJlcXD5fCjo64Gnp1/otz54+nrg6elBwcAgt6yjA45C5aR1stx+MpG4NmnSBMHBwcXWZWZm/vD++Xw++Hx+keU8Hq/aGoTL5Vbr45HKRe0nv6jt5Bu1n/ySxbYTp6VBGB9f6HR8HITxcbmn7OPi8saQ5v5dpcmomhp4BvpQyEtC8xPR3L8NoJD3N09PD1xl5SqLo8QYZbD9ABlJXPv06YODBw/C398fzZo1AwDExcXh2bNnmDVrVrHbiMVinDp1Ck2aNCmxt5UQQgghNRN7NX3+mNH4+NxkND8BjY9nx48K4+KqbMwoAHDU1KCgpwcFPb2CJJTtJdXLTUgN9KGgpweumlqVxVHTyUTi6ubmhtatW2PAgAFYvXo1VFVVsXbtWigrK2PKlCn4+PEjRo0ahSFDhsDS0hIJCQnYuXMnnjx5gjNnzkg7fEIIIYRUkvx5RkXxcRDGxeeeoo+Lzy1/20MaHw9UwdX0+bhqarkXLOnpSSag+X/nJaYKenrgqqtXWRykgEwkrlwuF76+vpg1axYmTZqE7OxsdOjQAXfu3IGRkRHi4+OhpaWFVatWITo6GkpKSmjVqhX8/Pzg7Ows7fAJIYQQ8h0Mw0CclsaOCc0dHxqf2ysaF1/QKxofnzuWNCmpSuPhamoW9Irq6UNBT1ciCc1NTqlnVFbJROIK5A4APnz4cLF1urq6OHfuXDVHRAghhJDiiLOzc0/Lx8VBVLh3NO+3MC4WmV+jkZKcDFF8PJisrKoLhsMBT0enIBnV1Su4iElPDzw9XYmklKukVHWxkConM4krIYQQQqSDEYkgSkrK7RUtJhEtOG2fe3q+Ki9cAvLnGc1NQtnEU08XPF29gh7SvF5RnrZ2pV1NT2QftTQhhBBSwzBice5FS/lJaHx8bg9pfDxEcfEQJcTnJaR5yxISALG4SmPiamnljhXVzT81n5+U6rFlBV1d8PT1wVUveZ5RUntR4koIIYTIOIZhIE5JKUg04/MST4kENPe0vTA+DqKEREAorNKYOMrKbNLJ09XJPUWf1yvK1dFGKpcH3YYWUDIwhIKONjh0ip5UAkpcCSGEkGrGiMW5p+YTEgolowm5iWh87rLCfwsTEqr06nkAAI9XJAHNL+f3jLK9pbq64KipfbdXVCQSISsmBioGBjI3DyiRb5S4EkIIIT+IEQpzE9H4vGQzoVAyWqiXlE1GExOBqr4HfN5FS2zyqasLBV0dyYRUV4dNRnlaWuDUgtuzEvlGiSshhBDyDXFmZqEktFAimpCY1wOa30Oa1zuanAwwTNUGxeGAp6WV2+Opo1Nwil5HN7dHVDfv4iVdnYJElHo7SQ1DiSshhJAajb1QKSE/CU2QSEJFCbmn4kWFTstX5R2WWFwueNraBcmnrm7uKXod3YKe0MJ/09XzhFDiSgghRL6IMzLyks+8RDSxIOEsSEYTIEzMK1fHaXkAUFAAT0e7IAnV1clNPPN7Q3XyT9Xn1vP4fOoRJaScKHElhBAiNUx2NoSJibkJZn4SmpA7BjQnLh7pUZHISs+AODGR7TFlMjOrJTaOmlruKXldXYmElKejU5CAahf8zdXUpCmcCKlilLgSQgipFOwFSvmn4/N7QBMKekaFCQkQJRasI05NLXW/2ZURHIeTe1o+72IlnvY3PaN5SWjBKXodcFVUKuORCSGViBJXQgghRTA5ORAl5p5mF+b1gOafdhex5dzf+afkxcnJ1RYfV109LwnN6w3V1pEs6+SVdXLLdFqekJqBEldCCKnhxFlZbBJaJOn8NinNqytLT2hl4SgpFZyC19HO7fnU0QFHi48MBUVo1zeFop6eRCJK95snpHaixJUQQuQEwzAQp6UVJJ9sopmYOza00DJhobpquUI+n6IiFPJPyevo5J2e185LSvOX6RQkqTo64KiqFjs2VCQSISYmBpo0iT0hJA8lroQQIgVMTk7ueNDCCeg3ZaFEgppbV9W38SyMo6hYMC5U4rd23hjRvLK2NttjSveYJ4RUJUpcCSHkBzBiMcSpqZIJaKFE83tJqTgtrVrj5KioFEo+tQolnYWTUckElav+/Vt6EkKINFDiSgghyD8Nn56XZOYll0lJhRLOJMkENP93cnL1zBFaCFdTs6D3U1uroNfz217QQj9cVdVqjZEQQqoCJa6EkBqFYRgw6ekQJSUhOz4BOR/DkMLhgElOzk0+v008C/2uztPwAABFxdzeT21t8LS0wc1LQhUKJ53fJqJaWnT3JEJIrUVHP0KITGIYptAp+LyEMyk3wRQnJRVaVvQHOTkS+6ry6+M5HHD5fMneTy2tIgkn2yua95ujRqfiCSGkPChxJYRUKSYnB6KUlLxEMy/xLNz7mZQEUXLub7HEsuo/BQ8AXA0NyURTS6sgIc1bxtXSkkxMaY5QQgipFpS4EkJKxZ5+T07OSyyTJXs/k5Ilez2TC5LQ6r4IKR9XXR1cLS0w6upQ1teT7PnU+rYXNC8R5fPBUVSUSryEEEJKR4krIbWIODu74IKj/F7P5EI9oPmJaXISxPnJaHJybu/nN6ffqwuXz89LNgv9FOoBZXs/tYomoPnzgBrQPKCEEFIjUOJKiJxhcnLyEsxkiJOT2L8lEs68ZFMiSU1KApOZKZ2geTyJxJOrxS9INvMSTZ4WX6JXlJufgFLCSQghJA8lroRIAZOdnTvus6zJZ3JBmUlPl1rcHDW1QolmQe9nbq+odqHklF8oSaX5QAkhhFQOSlwJqQCGYcBkZrI9meK8JJQ97Z6cIpmApiRLJKPVegvOb3AUFXOnXeIXTkD5eT2cecvyk1F+3ml5Pj+395PuD08IIUSKKHEltRYjEuUmnPk9nymFEs7klNzezpRkCBOTkBEXh4zMzLykNBni5GQwUhrzCQBQUGCTSa4Wv1ASyi9IOAv1fHL5BX9zVFSo95MQQohcosSVyC32SveUFDaZFCWn5CagSXm9nPm9n/k9nikFiak4tXyze1b61PRlSj75khcn5fd80vyfhBBCaiFKXInUFJxuT2F7O3N/5/VqpqQUU1coSU1Jkco8n4VxVFXB09TMSzC1vv+3Fh88TU2Jvyn5JIQQQspHphLXv/76C1u2bMGbN2+goaGB1q1bw9vbG6p599i+cOECFi1ahLdv36J+/fpYsGABxowZI+Woa68iPZ55p93F35aT838nS/wWpaRIbYolVv4dj/h5iaUWHzxNPrh8zbweUE1w1DWQxgG0TUygqK3Nrs/l88GlMZ+EEEJItZGZxHX16tVYv349Fi5ciLZt2yI2NhY3btyAKK9H7d69e3B3d8f48eOxZcsW/PPPPxg3bhw0NTUxYMAAKUcvn9gxnqmpeclkam6vJvu7UNKZv7xw8pmaKvUeTyDvSndNTXA1NdjT7YUTTy4/NxnlafHB1eSDx9csSDzV1cHhckvcv0gkQk5MDNRpLlBCCCFEqjgMwzDSDuLt27ews7PD+fPn4eLiUuw6zs7OSE1Nxf3799llQ4cOhb+/P16/fl2ux4uIiICpqSnCw8NhYmLyQ7GXRVVMgs4wDJiMjNxkMjWvhzM1Na+nMzV3TGcxvwsnoGIpTqtUWP7pdi5fs6C3My/B5LK/CyWi+cv4fPA0NKr8Tkc0ib38oraTb9R+8ovaTr7JcvvJRI/rwYMH0aBBg+8mrVlZWbh58yY2bNggsXzw4ME4fvw4wsLCYG5uXg2RVkxkWiR4TEHDMwwDJisr71R6XuKZkiKZYKbm1RU+/Z6akpd85vaSQljplwtVSH6PJ5tUauYnmt8mnnxwNTTB09SQOD1PUywRQgghpCxkInH977//YG9vj1WrVmHr1q1ITExE69atsXnzZjg5OSE4OBg5OTmwsbGR2M7W1hYAEBQUJLOJ65dzf2NI9FpoxpqjT5Aq6kYJc3s6i0k6rRI+gYfcDnAROHinU7+YPXIBjhagqQUAsE34yNbkcHj4oF1yDzIHDGwSPrHlbJ4iQowbgaemCo6aOrhqqrn3eFdTBVdNHVx1NSipq8PeUDU3+dTURKaqBj5kK4Cjpg6eqiqgUPRtpKzAhV09LbacmiXE26gUyZVSAaSmAci9l72qIg+N6/LZ6qSMHHyILvnKf3VlHmyMCrZJTM9GcExaidvwVRTQqI4mW45LzUJY3Pd7n8ViEUQZmTAwKFgWk5KFT/El91jrqiuhgb46W/6anImIhJLnb9XXUIKZXsE2kUkZ+JJY8t2uDDWVYaqrxpYjEtLxNTmrxG2MtFRQT1uVLYfHpyM6peRt6mmrwkhLhS2HxaYhLi27xG1MdVRhyC/YJjgmFYnpJY9rNtNTg76GMlv+EJ2CpIySv6RZ6KtDR73gC9C7rylIyRRCLBYhMSEV2hkK4HIlew0sDTSgpVbQW/8mMhnp2SUPfWlURwN8lYJtAj8nIUsoLnEbGyNNqCsXfEZeRiQhW1TyNk3q8qGiWBCvf3giROKST47Z1eNDWaFgm2efElDa+TQHEy0o8HKHyojFDJ6HJ5a8AYDmptrgcnMvKhSKxAiISCpxfQ4HaFFfhy1nCUUI/Jxc4jY8LgfNTLXZcmaOCEERJW+jxOPC3qTgmJOWJUTQt8ecb3x7nErOzMH7ryUfc9SUeLA1LnScSs/Bh5iSt9FUUYBVoWNOQlo2QmJLPk5pqSrA0rBgm9jULHws4TgFANpqimhooMGWo5MzEV7KMUdPXQnmhY5TUUmZ+JxY8jbfHnM+J2YgKknyOPXtZ68OXxkmOgXblOWYU1dbBcZaBcepj3FpiE0t+ZhjoqOKOoWOOaGxaYgv5ThVX1cNBpqFjzmpSMoo+ThlrqcGvULHqfdfU5CcWfJxqqGBOrTVCo5TQVHJSMsq+ZhjaagBLdWCY87rL8nIyCl5G2sjTWgUOuaU5Thla6wJNaWCbV5EJMFYuYQNpEgmEteoqCg8ffoUL1++xI4dO6CmpoY1a9agR48eeP/+PRISEgAA2traEtvp6OQeDOPj40vcf3JyMpKTCw56kZGRAHK7wkVVPEbzz5hLSFQSIjxpPF4bAzD+/ro+FxaCJ8r9gOXwFDG7k1ep+7/s9wu4eT2c6doGmG02sMT1VXnA0+EW4GrknpqPyARm/Xav+JUzcn/0MpTwaGJXdnFYVAoG/XG/+G3ymOqo4tb/dWLLb74k4n+7H5a4jXUdDfhOF7DlgE/xGHnwSYnbNDfVwmnPtmz53+BYTD76vMRt2jXUw+Gxrdny7bfRmH3qRYnbdLDQwn7Lumz5SmAkFp17VeI2/RyM8dtAB7Z87nkE1vi9LXGbQa1MsMbdji2ffPQJW258KHGbse3N8EsvW7Z86EEY9twNLXGbqZ0bYnb3Rmx5z+1gHH74qYQtgHnOVpjU0YIt//HPe5x59rnEbZb2scXItmZseeOVIPgFfi1xm/UedhjQsuAL2MqLr3H7XWyJ2/wxuBl62Rux5UU+L/EoLKHEbfaNbIku1gXfRv7vVABefSk5OTo23hFODXTZ8vTjz0tNQM5OaQv7QsnRhEOPEVXKF4urMwUSCcjI/Q9L/ad4b15nGBf6YjFo97/IEZWcuT5b9BP7TzFbKEb/nQ9KXB8A3izvASWF3GQ3OSOn1G0UeRwErXBmyzHJmaVuw1dRwPPF3SASiSAWi/EpLq3UbYz4yrj/cxe2/P5rMvrv/LfEbSz01XFtVge2HBiRiKH7HpW4TZO6fJyf2o4tPw6Lw/hDT0vcxtFcB8cnOLHle+9j4HXCv8RtOlnp48CoVmz5xuso/OwdWOI2LnZ1sG1Ic7Z86cUXLL/4psRt+reohw397dmy97NwbLjyrsRtRjjVx7J+jdnysf8+Yvut4BK3mdihAX7uac2WD94PwYH7H0vYApj5kyW8ulqy5R03P+Dkk4gSt1noYo1xggZs+bdrb3E+ILLEbVa5NsEQR1O2vM7vDa6/iS5xm83/awrXZgX/E5aef4UHwXElbrNzWHP0aFyHLS848wLPw0v+4ndoTCu0t9Rny7NOPsfbUr5cnZrkJPFlcfKRp6V+gbnk1R42RgVflMYfeooL45pUeY5UWFmHJMhE4ioWi5GamorTp0+jadOmAIA2bdrA3Nwc27Ztg7Ozcyl7KNnmzZuxfPnyIsvj4uKgrFy1XykSOCX/gyqM18wBiuoq4KirQ6zGB8rwftG+cpn9OystB9hbcgLGcLhIzkv4kZGBhKTS4xMzYsTExLDl+FJ6GoGC8TH5EhNKnzNV+O02SSUnEQCQkyOU2Ca5DNtkZ2dLbpNS+jbCnBzExsaCm3chV2pqyT05AJCZmSXxOKlpJSc4udtkSmyTXoZxyOnpGRXYJk1im4zM0u/klZoquU1mZsk9wbnbpEpsk5VV+vstJSVFYpvs7JJ7S4DcL6cxMQUHvZwyzFaRnJSEQg8DYRmG3iQmJiImpuCDKRKVYZuEBMQoFTwHkbjkng8AiI9PAB8FbVKWSxHi4+KgkF3Qm1OWqxdiY2ORrZL7byCnlF7ggm1ioJjXS1taMp0fh8TxI6X09mQYBjExMRCLxUhKSkKCqPT3mkgs/uaYU/rnTSSSPH4kJpb+uRYKvz3mlJx4ALnvR4ltkst/nEpJKT22rKxvjjllmKv622NOamrpr1tG5rfHnNK3SU9P/2ab0o85325TpmNO2rfHqdKPOamp3xxzynCcSk5JRkxMQU9omY5TScmIiSm4GDgnpwzHj6QkxMQUfJiFZUgkExMSEaNasO+yJJ/x8fGI4RW8vvmfPQDs/72qZmRkVPpKkJGLs/KHA8TGSvaqdOrUCfr6+li5ciWaNGmCy5cvSySx79+/h5WVFfz8/NCzZ8/v7r+4HldHR0eEhYVV+cVZ2Z8+wT/gKlZHP0aISPJbn7ayNgZYDYCgrgAcDgcOJtrg5Z2CE4kZBEQklrr/wt+qsoViBH4p+SDK5UiegsvKEeFVZMkHUQUuF00LnYJLzy79FJwSr+hQgXdfS95GVVHyFFxyRumn4NSVFGBd6FtiYnrpp+A0VRTRyLCgNysuLRsf476/jVgkhigzFa2sTNhvhLGppQ8V0FErOlSgtFNweurKMNMrOJ0WmZSJyKTST9sVPgX3OSEDX1NKPsAb8VVQ95uhAjGppZy20/pmqEBc6afgTLQlhwqExKQisZRTcPV1vx0qkIrkzJK3aaCvDh01yaECqVlCiEViJCYlQVtLC1ye5MG3oYHkKbigqBSkZ5f8j6SRoQY0Cw0VePUlGVnCUk7b1flmqMDnpFKTxMbGkkMFAsITISrlUN2krhaUFQqe4/NPiWBQ8jZN60kOFfAvwzGnmYnkUIEXn0sZKgAOmtfXZstZQjFelXKc4nE4cDDVhkgkQmxsLDS0dPA2uuTPtSKPK9GznZYlxNtSjjnKCjw0KTQ8KSUzB+9LGZ6kpqQg0TOVlJGD4FKOUxrK3wwVSM9GaCnHKb6KIiwLHafKcszRVlWExTdDBSJKOeboqivBvNDwpKikTHwp5ZhjoCE5VOBLYgaikr8ZKvDNZ6+Opgrq6RQccyISSh8qYKylKnEW4WNcOuLSSh/S9O1QgYT00ocKFD7mBMeUPlTATE8deoWGJ72PTkVKKccpC33JoQJvo1KQVsoxx9JAA3xVySFNpQ0VsKpTdKhAacOTbIwkhwr4f4qHsXIO9PX1q+3irLI+jkwkrmPHjsX58+eLTVw1NDTg7e0NTU1N/Prrr5gxYwZbf+HCBfTr1w+hoaHlGuMqjVkFoqOjEZgZiN+e/4bwlHCJeltdW8xtPRetjVp/Zw9EmmT56kpSMmo7+UbtJ7+o7eSbLLdf9fT/lqJPnz6Ii4uDv78/uywuLg7Pnj1Dy5YtoaysjC5duuD06dMS2508eRK2trYye2FWYRwOB13rd8U513OY22ouNJUKvn2/iX+DsVfGYsY/M/AxueQxP4QQQgghtZVMJK5ubm5o3bo1BgwYgJMnT+L8+fPo06cPlJWVMWXKFADA4sWL8e+//2LKlCm4desWli5dimPHjhU7dlWWKfIUMbLJSPi6+2KozVDwOAXfZP4J/wdu59yw4fEGJGWVPm6KEEIIIaQ2kYnElcvlwtfXF23btsWkSZMwePBg8Pl83Llzhx2sKxAI4O3tjXv37sHZ2RnHjh3Dvn378L///U/K0VeMtoo2FjgtgLerNzqbdGaXC8VCHH59GL19euPom6PIEUv5lqiEEEIIITJCJsa4VjdZvHPWv1/+xcYnG/EuQXIaEnO+OWa3nI3Opp3B4XCqPFZSlCyP9SElo7aTb9R+8ovaTr7JcvvJRI8rAdrWbYu/+/yN5e2WQ09Fj10elhyG6TenY8LVCQiKD5JihIQQQggh0kWJqwzhcXnwaOSBSx6XMMF+ApR5BdNzPIx6iIEXBmLJ/SWISY8pYS+EEEIIITUTJa4ySF1RHdNbTMcFtwvobdGbXc6Agc8HH/T26Y3dAbuRISx9AmdCCCGEkJqCElcZZqxhjHUd1uFYr2NoblhwG78MYQa2+W9DX5++uBB8AWKmbHe8IYQQQgiRZ5S4ygF7A3v81fMvbOy0EfU06rHLv6Z/xcJ7CzH00lA8iXoixQgJIYQQQqoeJa5ygsPhwNncGefczmFWy1nQUCy4rd+ruFcYc2UMZt6cSTcwIIQQQkiNRYmrnFHmKWOs3VhcdL+IQdaDJG5gcOPTDbiddcO6R+uQmJkovSAJIYQQQqoAJa5ySk9VD4vaLMKZfmfQ0aQju1zICHH0zVH08umFv179hWxRthSjJIQQQgipPJS4yrmG2g2x/aft2NtjL6x1rNnlKdkp2PhkI1zPuuJK2BXUwvtMEEIIIaSGocS1hmhj3AYn+5zEinYrYKBqwC6PSI3A/93+P4z0G4mAmAApRkgIIYQQ8mMoca1BeFwe3Bu546L7RUxpNgWqCqpsnX+MP4b7Dsfc23MRkRIhxSgJIYQQQiqGEtcaSE1RDZMdJuOS+yV4NPIABxy27nLYZfQ72w+bn2xGcnayFKMkhBBCCCkfSlxrMAM1Ayxvtxyn+p5CW+O27PIccQ4OvjqI3t69cfTNUeSIc6QYJSGEEEJI2VDiWgtY61pjd/fd2PHTDjTUasguT8xKxLpH6+BxzgP/fPqHLuAihBBCiEyjxLWW4HA46GDSAaf7ncbiNouhq6LL1oUlh2HGzRkYd3UcXsW9kmKUhBBCCCHfR4lrLaPAVcBA64Hw9fDFBPsJUOYps3WPox5j8MXBWHh3IaLSoqQYJSGEEEJIUZS41lLqiuqY3mI6LrpfRF+LvhJ1F0IuoI9PH2x9thVpOWlSipAQQgghRBIlrrWckboR1nRYgxN9TqBVnVbs8ixRFva+3Ite3r1wMugkhGKhFKMkhBBCCKHEleRpotcEB5wP4Pcuv8Ocb84uj8+Mx6qHq+Bx3gM3P92kC7gIIYQQIjWUuBIWh8NB1/pd4e3qjYVOC6GjrMPWhSaFYvrN6RhzZQwCYwOlGCUhhBBCaitKXEkRilxFDLEZgkselzDObpzEBVxPvz7FkEtD8POdn/E59bMUoySEEEJIbUOJK/kuTSVNzGw5ExfcLhS5gMs31Bd9ffrSHbgIIYQQUm0ocSWlMtYwxpoOa3Cyz0k4GTmxy/PvwNXLuxeOvD6CHBHdgYsQQgghVYcSV1JmjfUaY2+Pvdj+03aJO3AlZSVh/eP1cD3niqthV+kCLkIIIYRUCUpcSblwOBx0NOmI0/1OY2nbpdBT0WPrwlPCMef2HIzwGwH/aH/pBUkIIYSQGokSV1IhClwFDLAaAF8PX3g6eEJVQZWtC4gJwAi/EZh9azY+JX+SYpSEEEIIqUkocSU/RE1RDVObTcVF94vwaOQBLqfgLXXt4zW4nnPFukfrkJCZIMUoCSGEEFITUOJKKoWhmiGWt1uOU31PoX299uxyoViIo2+Oord3bxwIPIAsUZYUoySEEEKIPJOJxPXPP/8Eh8Mp8jN//nx2nc6dOxe7TlBQkBQjJ9+y0rHCrm67sLv7bljrWLPLU3JS8NvT39DXpy8uhlyEmBFLMUpCCCGEyCMFaQdQ2OXLl6GlpcWW69WrJ1Hfvn17bNy4UWKZubl5dYRGyqld3XZw6uOEiyEXsfX5VkSnRwMAItMiseDuAhx6dQhzWs2Bk7FTKXsihBBCCMklU4lry5Ytoa+v/916bW1ttGnTphojIj+Cx+XB1dIVPcx74MjrI9j3ch/ShekAgDfxbzD+6ngI6gkwq+UsWOlYSTlaQgghhMg6mRgqQGo2VQVVTGg6Ab4evhhkPQg8Do+tu/f5Hv534X9Ycn8JvqZ9lWKUhBBCCJF1MtXj2qRJE8TGxsLMzAwTJkzAvHnzwOMVJDm3b9+Guro6RCIRnJycsHLlSnTs2LHU/SYnJyM5ueC2pJGRkQAAkUgEkUhU+U/kGyKRCGKxuFoeS5ZpK2ljQesFGGI1BH/4/4Eb4TcAAGJGDJ8PPvAL9cMw22EY3Xg0NJU0pRxtAWo/+UVtJ9+o/eQXtZ18k0b7Fc73SsJhZOA2R1euXMHDhw/h5OQEDoeD8+fPY+fOnZg8eTK2bdsGAFi6dCnMzMzQqFEjfPnyBRs3bkRAQABu376Ntm3blrj/ZcuWYfny5UWWP336FHXr1q2S51SYWCxGUlIStLS0wOVSJ3e+wIRA7H23F68TX0ss11LUwvCGw9HbtDcUuYpSiq4AtZ/8oraTb9R+8ovaTr5Jo/2MjIzKtJ5MJK7FmTt3Ln777TeEh4fD2Ni4SH1aWhqaNGmCxo0bw9fXt8R9Fdfj6ujoiLCwMJiYmFR67N8SiUSIjY2Fvr5+mb9R1BYMw+Cf8H/w+/Pf8SlF8mYFppqmmN5sOrrV7wYOhyOlCKn95Bm1nXyj9pNf1HbyTRrtV9bHkamhAoUNHDgQGzduhL+/f7GJq7q6Onr37o3Tp0+Xui8+nw8+n19kOY/Hq7YG4XK51fp48qRHgx7oYtYFp9+dxq6AXYjPjAeQewvZuXfnoql+U8xpNQct6rSQWozUfvKL2k6+UfvJL2o7+Sar7Uf990QmKHIVMcRmCC65X8LEphOhwlNh617EvsCoy6Mw/Z/pCEkKkWKUhBBCCJEmmU1cT5w4AR6Ph+bNmxdbn5aWhosXL6J169bVHBmpShpKGvBq7oWL7hfRv1F/iVvI3gy/CY9zHlj570rEZsRKMUpCCCGESINMDBVwdnZG165dYW9vDwA4f/489uzZgxkzZsDIyAh3797Fr7/+Cnd3d5ibm+PLly/YtGkToqKicOrUKSlHT6pCHfU6WNZuGYbZDsOWZ1twJ+IOAEDEiPD3u79xIeQCxjQZg1FNRkFNUU3K0RJCCCGkOshE4mpjY4P9+/cjIiICYrEYVlZW2LJlC7y8vAAAxsbGyM7OxsKFCxEXFwd1dXW0a9cOu3btgqOjo5SjJ1WpkU4jbP9pOx5FPsKmp5vwOi53BoIMYQZ2BOzA3+/+xpRmU+Bu6Q4Frky8nQkhhBBSRWR2VoGqFBERAVNTU4SHh1fbrAIxMTEwMDCQuUHO8kTMiHEl7Ap+f/Y7Pqd+lqhroNUAs1rMQmfTzpU+AwG1n/yitpNv1H7yi9pOvsly+8nsGFdCvsXlcOHSwAXn3c5jbqu54CsVzBQRmhSK6TenY/Tl0QiICZBilIQQQgipKpS4ErmjxFPCyCYj4evhizF2Y6DEVWLrnkU/w3Df4Zh1cxZCk0KlGCUhhBBCKhslrkRuaSlrYXbL2bjofhF9LfqCg4IhAtc/XYf7OXeagYAQQgipQShxJXLPWMMYazqswam+p9C+bnt2ef4MBL28e2G7/3ak5aRJMUpCCCGE/ChKXEmNYa1rjV3dd2Fvj72w1bVll2cIM7ArYBd6effCsTfHkCPKkWKUhBBCCKkoSlxJjdPGuA1O9DmB9R3Wo55GPXZ5fGY81j5aC9dzrrgcdhm1cEINQgghRK5R4kpqJC6Hi14WvXDe7Tx+bv0ztJW12brwlHDMvT0XQy8NxeOox9ILkhBCCCHlQokrqdGUeEoY3ng4fD18McF+AlR4KmxdYFwgxl4Zi8nXJ+NdwjspRkkIIYSQsqDEldQKmkqamN5iOi55XEL/Rv3B5RS89e99vocB5wfgl3u/IDI1UopREkIIIaQklLiSWsVQzRDL2i2DTz8fdDHtwi5nwOB88Hn08emDzU82IykrSYpREkIIIaQ4lLiSWslC2wJbu27FXz3/goOBA7s8W5yNg68Oopd3L/wZ+CeyRFlSjJIQQgghhVHiSmq1FnVa4LDLYWzpvAXmfHN2eXJ2MjY93YQ+Pn1wPvg8RIxIekESQgghBAAlroSAw+HgJ7Of4OPqgyVtl0BfVZ+ti0qLwpJ/l2Dyg8m4+/kuTaFFCCGESFGFEleRSIQLFy5g+vTpcHJyQv369WFgYAAbGxu4urpi48aNCA2l+8QT+aLAVcD/rP6HS+6XMK3ZNKgpqLF1oamh8LrphbFXxiIgJkCKURJCCCG1V7kS19TUVCxfvhz16tXDgAEDcO/ePTRu3BiDBg3CpEmT0K1bN4hEImzcuBGNGjVCt27dcP/+/aqKnZAqoaaohkkOk+Dr4YuhNkOhwFVg6558fYLhvsMx6+YshCSFSDFKQgghpPZRKH2VAg0aNICdnR1+/fVXuLm5QVNT87vrPnv2DMePH0ffvn2xatUqTJky5YeDJaQ66anqYYHTAgyxHoLNDzfjZtRNtu76p+u4GX4TbpZumOwwGXXU60gxUkIIIaR24DDlGLT34MEDtGvXrlwPkJKSgk+fPqFJkyblDq6qREREwNTUFOHh4TAxManyxxOJRIiJiYGBgQF4PF6VPx6pXPntF8uNxR8Bf+DBlwcS9co8ZQy3HY6x9mPBV+JLKUpSHPrsyTdqP/lFbSffZLn9yjVUoLxJKwBoamrKVNJKSEXZ6tlid/fd2NtjLxrrNWaXZ4mysD9wP1zOuNAUWoQQQkgVqrRZBYKCgrBjxw5s374dr1+/rqzdEiJz2hi3wfHex/Frp19RX7M+u7zwFFo+730gEtMUWoQQQkhlqpTE9ciRI2jWrBkOHjyI7du3w8HBAQcPHqyMXVepw4cPs393794dmzdvZsuurq5YvXo1Wx48eDAWLVrElseOHYvZs2ez5alTp2Ly5Mlsee7cuRg1ahRb3rBhAwYPHsyW161bhz59+rDl33//HV27dmXLe/bsgUAggFAoBJD7GgsEAqSkpAAAvL29IRAIEB0dDQC4fPkyBAIBwsLCAAC3b9+GQCDAmzdvAACPHz+GQCDA06dPAQCBgYEQCAS4d+8eACAkJAQCgQBXr14FAERGRkIgEODcuXMAgMTERAgEAhw/fhwAkJ2dDYFAgAMHDrAxd+rUCdu2bWPLLi4u2LBhA1v28PDA8uXL2fLw4cPx888/s+WJEydi+vTpbHnmzJkYP348W16wYAGGDRvGllesWAF3d3e2vHHjRvTs2ZMtb9++HZ06dWLLBw8ehEAgQFZWbo/oiRMnIBAIkJCQAAA4f/48BAIBPn/+DAC4du0aBAIBPnz4AAC4f/8+BAIBXrx4AS6HizoJdZC4ORGDVAZBT0UPWV+yELI6BB+efMCSB0vQ60Av2Le2x6VLlwAAMTExEAgEOHPmDAAgLS0NAoGAfR+KxWIIBALs2bOHjblbt27YsmULW+7bty/Wrl3LlgcNGoTFixez5dGjR2POnDlsefLkyRLvyzlz5mD06NFsefHixRg0aBBbXrt2Lfr27cuWt2zZgm7durHl/PelWCwGkPsZEggESEtLAwCcOXMGAoEAMTExAABfX18IBAJ8+vQJAHDz5k0IBAIEBQUBAB4+fAiBQIDnz58DAF68eAGBQMBe1PnhwwcIBAJcu3YNAPD582cIBAKcP38eAJCQkACBQIATJ04AALKysiAQCCSOP+7u7tixYwdb7tmzJzZu3ChRv2LFCrY8bNgwLFiwgC2PHz8eM2fOZMvTp0/HxIkT2fLPP/+M4cOHs+Xly5fDw8ODLW/YsAEuLi5sedu2bRLvywMHDkAgECA7OxsAcPz4cQgEAiQmJgIAzp07B4FAgMjI3NsRX716FQKBACEhuRcH3rt3DwKBAIGBgQCAp0+fQiAQ4PHjxwCAN2/eQCAQ4Pbt2wCAsLAwCAQCXL58GQAQHR0NgUAAb29vALnDuwQCAY4cOQIAEAqFRd6XXbt2xe+//86W+/Tpg3Xr1rHlgQMHYsmSJWx51KhRmDt3LluePHkypk6dypZnz56NsWPHsuVFixZJHC/XrFkDV1dXtrx582Z0796dLe/atQsCgYAt//XXXxAIBEhPTwcAnDp1CgKBALGxsQCAixcvQiAQIDw8HADwzz//QCAQ4O3btwCA//77DwKBAP7+/gAK3pcPHuQOE3r//j0EAgFu3LgBIHf4mUAgwIULFwAA8fHxEAgE+PvvvwEAGRkZEAgE+Ouvv9gYO3TogJ07d7LlHj16YNOmTWzZzc0NK1euZMtDhgzBwoUL2fK4ceMk3pdeXl6YNGkSW543bx5GjBjBlpctW4YBAwaw5fXr16N3795s+Y8//kCXLgV3E9y3b5/E/6Bjx45BIBAgOTkZAODj4wOBQICvX78CAK5cuQKBQMDOKHTnzh3069cPr169AlDwPyj/ffnq1SsIBALcuXMHABAaGgqBQIArV64AAL5+/QqBQAAfHx8AQHJyMgQCAY4dOwag4H25b98+NuYuXbrgjz/+YMu9e/fG+vXr2fKAAQOwbNkytjxixAjMmzePLU+aNAleXl5seebMmRg3bhxbXrhwIYYMGcKWV65cCTc3N7a8adMm9OjRgy3v3LkTHTp0YMv578uMjAwAwN9//w2BQID4+HgAwIULFyAQCBAREQEAuHHjBgQCAd6/fw8gd7hm/v8gAPD394dAIMB///0HAHj79i0EAgH++ecfAEB4eDgEAgEuXrwIAIiNjYVAIMCpU6cAAOnp6UXelwKBALt27WLLzs7OVZobLVmyBAMHDkR5VEriunz5cty4cQOPHz/G69evsXr1aokEhZCaigMOupt3h6+HL4bZDgOXU/CRCksOQ0hSCDY/3Yzn0c+lGCUhhBBSM5Tr4qxWrVph27ZtaNOmjcRyY2Nj+Pv7o06d3CurT58+jcmTJ7O9LrKGLs4i5VGe9kvITMCeF3tw8u1J5IhzJOo6m3bGjOYzYKljWZXhkkLosyffqP3kF7WdfJPl9itXj6uXlxf69++PESNGICoqil0+aNAgCAQCzJs3D9OmTcOkSZMkutMJqS10VHTws+PPuOB+AX0t+oIDDlt3K/wW+l/oj8X3FyMqLer7OyGEEEJIscqVuI4aNQpv376FkZER7OzssGHDBuTk5GDTpk2YNWsWgoODERkZiRUrVkiMiSCktqmnUQ9rOqzBqb6n0KFewRgnMSPG2Q9n0du7NzY92YSkrCQpRkkIIYTIl3INFSjs3bt3mDVrFt6/f48tW7agV69elR1blaGhAqQ8KqP9Hkc9xpanW/Ai9oXEck1FTYy1H4thtsOgqqBaGeGSQuizJ9+o/eQXtZ18k+X2q/DFWVZWVrh06RI2bdqEmTNnonfv3uzV14QQSa2NWuNIryPY0nkLzPnm7PKUnBT8/ux39Pbujb/f/l1kXCwhhBBCCpQrcWUYBgcOHMDgwYPh7u6OtWvXokuXLuzUSk5OTpg/fz47NQ4hpACHw8FPZj/Bx9UHS9suhaGqIVsXkxGDlf+thNtZN1wOvQwxI5ZipIQQQohsKlfiOmvWLMyePRu6urpo2LAh9uzZAxcXFygpKWHBggV4+fIlIiIiYG1tzc4BWBZ//vknOBxOkZ/58+dLrLd//35YWVlBRUUFDg4O7NxkhMgTBa4CBlgNwEWPi5jVchY0lTTZuk8pnzD3zlwMvjgY9z/fRwVH8hBCCCE1kkJ5Vj58+DD27dvHTmI8depUWFpaIiwsDObm5qhbty6OHDmC+/fvY/r06RKTcpfF5cuXoaWlxZbr1avH/n3ixAlMmDABv/zyC7p27YqTJ0/C3d0dd+/eLTI9FyHyQFVBFWPtxqJ/o/7489WfOPL6CDJFmQCAN/Fv4HndE62NWmNmi5loatBUytESQggh0leuxFVPT4+9MxMAfPz4EQCgra0tsV779u3x5MmTcgfTsmVL6OvrF1u3dOlSDB48mL2TSJcuXfDixQusWLECvr6+5X4sQmSFlrIWZrSYgSE2Q7A7YDfOvD8DEZN7u9jHUY8xzHcYfqr/E6Y3nw4LbQspR0sIIYRIT7mGCmzevBkrV66Evb09HB0d4eLigjVr1hRJXIHc8XyVJSQkBO/evStyW7DBgwfjxo0b7C08CZFnhmqGWNx2Mc65nUNP854SdTc+3YD7eXcsub+E5oAlhBBSa5Wrx7VPnz4IDQ3Ff//9h6ysLDRv3hzm5uaVFkyTJk0QGxsLMzMzTJgwAfPmzQOPx2Pva25jYyOxvq2tLbKzsxEaGlqkrrDk5GT2/soA2Ht+i0QiiESiSov/e0QiEcRicbU8Fql81d1+JuomWCdYh1G2o/CH/x94EJl7f3QxI4bPBx9cCrmEQdaDMM5uHLSVtaslJnlFnz35Ru0nv6jt5Js02q+s026VK3EFAF1d3Uqfs9XY2BjLly+Hk5MTOBwOzp8/j0WLFuHz58/Ytm0bEhISABQdkqCjowMAiI+PL3H/mzdvxvLly4ssj4uLg7KycuU8iRKIxWIkJeVONM/lVngGMiIl0mo/fehjedPl8K/nj/3v9yMoKfcLXLY4G4ffHMaZ92cw0HwgPMw8aA7Y76DPnnyj9pNf1HbyTRrtZ2RkVKb1ynUDAj8/P7i4uJQrkJiYGISHh6NFixbl2m7u3Ln47bffEB4ejn/++QfDhw9HZGSkxBN78uQJWrdujfv376Ndu3bf3VdxPa6Ojo4ICwurthsQxMbGQl9fX+Ym8iWlk4X2YxgGN8Nv4g//PxCaHCpRp6uii4n2E9Hfsj8UeYpSiU9WyULbkYqj9pNf1HbyTRrtVyU9rpMmTYKuri7Gjh2L/v37S1z1X5hIJMKtW7dw/PhxnDx5Elu2bCl34jpw4EBs3LgR/v7+bM9qUlKSROKa3xOrq6tb4r74fD74fH6R5Twer9oahMvlVuvjkcolC+3XvUF3dDHrggvBF7Ddfzu+pn8FAMRnxmPd43U4/OYwpjWfhl4NeoHLoR6OfLLQdqTiqP3kF7WdfJPV9itX4vr+/Xvs2LEDW7ZswaxZs2BqaoqmTZvCwMAAysrKSExMRGhoKF68eAGhUIi+ffvi3r17cHBw+KEg88evBgUFwdraml0eFBQEJSUlWFjQldakdlDgKsC9kTt6WfTCiaAT2PtyL5Kyck/nfE79jAV3F+Bg4EHMaDEDHep1qNSLJAkhhBBpK1e3jLKyMmbNmoWQkBDcuHEDI0aMQHZ2Np48eYIbN24gNDQU1tbW2LJlC8LDw3H69OkKJ60nTpwAj8dD8+bNYWFhASsrK5w6dUpinZMnT+Knn36CkpJShR6DEHmlzFPGqCaj4Ofhh4lNJ0qMcX2X8A5Tb0zF6Muj8ezrMylGSQghhFSucl+cla9z587o3LlzpQTh7OyMrl27wt7eHgBw/vx57NmzBzNmzGCHBixbtgzDhg1Dw4YN0aVLF5w8eRIPHz7EnTt3KiUGQuSRppImvJp7YYjNEOx5sQen3p2CUCwEADyLfoZRl0ehQ70OmN5iOmx0vz/zBiGEECIPKpy4ViYbGxvs378fEREREIvFsLKywpYtW+Dl5cWuM2TIEKSnp2PdunVYt24drK2t4ePjg7Zt20oxckJkg76qPhY6LcSIxiOw3X87fEN8wSD3usu7n+/i7ue7cDF3wdTmU2HGN5NytIQQQkjFlGtWgZoiIiICpqamCA8Pr7ZZBWJiYmBgYCBzg5xJ6eSx/d7Gv8W259twK+KWxHIehwf3Ru7wbOqJOup1pBNcNZLHtiMFqP3kF7WdfJPl9qNLjwmpgax1rfHHT3/gsMthtKrTil0uYkQ4/e40evv0xqYnm5CYmSi9IAkhhJByosSVkBqsmWEzHHA+gF3ddsFW15ZdniXKwp+v/oSLtwt2BexCWk6aFKMkhBBCyoYSV0JqOA6Hg/b12uNEnxPY2GkjzPnmbF1qTiq2+29HL+9eOPL6CLJF2dILlBBCCCkFJa6E1BJcDhfO5s7wcfXB8nbLUUetYIxrfGY81j9ejz4+feDz3oedmYAQQgiRJZS4ElLLKHAV4NHIA5c8LmFuq7nQUdZh6yLTIrHkwRJ4nPfA1bCrqIXXbhJCCJFhlLgSUksp85QxsslI+Hr4YorDFKgrqrN1oUmhmHN7DgZfGowHnx9QAksIIUQmUOJKSC2noaSByc0mw8/DDyMbj4QSt+BOdK/jXmPS9UkYd3UcAmICpBglIYQQQokrISSPjooO5raei0sel9C/UX/wOAVz9z2OeozhvsPh9Y8X3ie8l2KUhBBCajNKXAkhEozUjbCs3TL4uPrA2dxZou5W+C30P98f8+/OR3hyuHQCJIQQUmuVO3ENDQ3Frl278McffyAkJAQAcOPGDTg6OkJdXR1mZmZYv359pQdKCKleDbQaYGOnjTjZ5yTa12vPLmfA4FLIJfQ72w8r/l2Br2lfpRglIYSQ2qRcieu9e/dgb2+PqVOnYs6cObC3t8eZM2fQp08fZGdno2/fvuDz+Vi4cCH++uuvqoqZEFKNGus1xq5uu3DA+QCaGzZnlwsZIU69O4Ve3r3w6+NfEZ8ZL8UoCSGE1AblSlyXLl0KJycnxMXFITU1FaNHj8aoUaMwZMgQ+Pv748SJE3j58iWGDh2KP/74o6piJoRIQWuj1vir51/Y/tN22OjasMuzxdk49PoQXM64YLv/dqRkp0gxSkIIITVZuRLXgIAAzJo1C9ra2lBSUsKiRYuQnp6OoUOHSqw3bNgwfPjwoVIDJYRIH4fDQUeTjjjZ52SRu3ClC9OxK2AXXLxdcCDwADKEGdILlBBCSI1UrsQ1Pj4ehoaGbDn/b11dXYn1dHR0kJJCvS6E1FSF78K1ot0K1FWvy9YlZSXht6e/oZd3L5wIOoEcUY4UIyWEEFKT0KwChJAKU+AqwL2ROy64X8ACxwXQU9Fj62IzYrH64Wr0PdsX5z6cg0gskmKkhBBCagKF8m6wadMm1KmTe4/z/Lvp/PrrrzAwMGDX+fqVrjImpDZR4ilhqO1QuFm64XjQcRwIPIDk7GQAwOfUz1h0fxEOBB7A1GZT0c2sG7gc+s5MCCGk/DhMOe7laG5uDg6HU+adh4aGViioqhYREQFTU1OEh4fDxMSkyh9PJBIhJiYGBgYG4PF4pW9AZAq1X/klZyfjr1d/4fDrw0XGutrq2mJ6i+loX7d9uY4nFUFtJ9+o/eQXtZ18k+X2K1ePa1hYWBWFQQipSfhKfHg198JQm6HYH7gfJ4NOIlucDQB4E/8Gk69PRgvDFpjeYjpa1mkp5WgJIYTICzpfRwipMnqqepjXel6xt5F9Fv0Moy+Phud1T7yKeyXFKAkhhMiLcvW4xseXb4Lxb2cbIITUTvm3kR1rNxbb/bfDL9QPDHJHKd3/fB/3P99Hd7PumNpsKhpqN5RytIQQQmRVuRJXfX39co1JE4noKmJCSIH6/PpY33E9xtmPw7bn23Az/CZbd+3jNVz/eB29LXpjisMUmPJNpRgpIYQQWVSuxPXAgQNVfjEFIaTms9KxwtauW/Ei5gW2Pt+Kh5EPAQAMGFwMuQi/UD+4WbrB08ETRupGUo6WEEKIrChX4jp69OgqCoMQUhs1NWiKfT324VHkI2x9vhUBMQEAABEjwpn3Z3A++DwGWQ/COPtx0FfVl3K0hBBCpK3c87hGR0fjyJEjCA0NRb169dCvXz80bty4KmIjhNQSjsaOOGx0GHc/38W259vwJv4NACBHnIMjb47gzPszGGIzBGPtxkJLWUvK0RJCCJGWciWugYGB6Ny5s8RFWsuWLcOxY8fg4eFR6cERQmoPDoeDjiYdIagnwI1PN7D9+XYEJwUDADKEGTgQeAB/v/0bIxuPxIjGI6ChpCHliAkhhFS3ck2HtXDhQvD5fNy5cwfp6ekIDAyEo6MjZsyYUVXxEUJqGS6Hi+5m3XGm3xmsEayBqWbBRVqpOanYEbADPb174kDgAaTnpEsxUkIIIdWtXInrkydPsHLlSggEAqioqKBx48bYs2cPvnz5gqioqKqKkRBSC/G4PPRt2Bfn3M5hadulqKNWh61LykrCb09/Qy/vXjj65iiyRdlSjJQQQkh1KVfiGhUVBUtLS4lllpaWYBgGkZGRlRZUamoqTExMwOFw8OTJE3Z5586dweFwivwEBQVV2mMTQmSLIlcRA6wG4JLHJcx3nA89FT22Li4zDuserUNvn944/e40csQ5UoyUEEJIVSv3nbO4XMlNqmJ6rJUrV0IoFBZb1759e/z7778SP+bm5pUeAyFEtijzlDHMdhh8PXwxs8VM8JX4bF1UWhSW/7scrmddcSH4AkRimkOaEEJqonLPKjB06FCoqqoWWT5o0CCoqKiwZQ6Hg4CAgHIHFBQUhO3bt2PTpk3w9PQsUq+trY02bdqUe7+EkJpBTVEN4+zHYaD1QBx5fQR/vf4LaTlpAIDwlHAsvLcQ+1/ux9TmU9G5XmfpBksIIaRSlStxHTVqVLHLW7ZsWSnBAICXlxc8PT1hbW1dafskhNQ8mkqamNxsMobYDMHBVwdx7M0xZIoyAQDBScGYfWs2bHRsMLzBcPTW7y3laAkhhFSGciWuBw8erKo4AACnT5/Gy5cvcebMGTx79qzYdW7fvg11dXWIRCI4OTlh5cqV6NixY4n7TU5ORnJyMlvOH48rEomq5ba0IpEIYrGYboErp6j9ZJumoiamN5uOodZDsT9wP06/LxjrGpQQhEUJi/D3p78x1WEqHI0c6e5/coQ+e/KL2k6+SaP9eDxemdYr91CBqpKeno7Zs2djzZo14PP5xa7TqVMnjBw5Eo0aNcKXL1+wceNGdOvWDbdv30bbtm2/u+/Nmzdj+fLlRZbHxcVBWVm50p7D94jFYiQlJQEoOkaYyD5qP/kx1nws+tTpg6MhR3H582WIGTEA4EXsC0y6MQlNdZpidKPRsNexl3KkpCzosye/qO3kmzTaz8iobLf35jAMw1RxLGWycOFCXLt2DY8ePQKHw8GtW7fQpUsXPH78GK1atSp2m7S0NDRp0gSNGzeGr6/vd/ddXI+ro6MjwsLCYGJiUunP5VsikQixsbHQ19cv8zcKIjuo/eTTp5RP2Om/E5c/XgYDycNcG+M2mOowFfb6lMDKMvrsyS9qO/kmjfaTqx7Xjx8/YtOmTfDx8WEz/NTUVPZ3amoqNDSK3iVHXV0dvXv3xunTp0vcP5/PL7YXl8fjVVuDcLncan08Urmo/eRPA+0GWNthLfqb9MfJ8JO49ukaW/df5H/4L/I/dDLphKnNpsJWz1aKkZKS0GdPflHbyTdZbT+ZSFxDQ0ORnZ2N3r2LXkDRpUsXODk54b///pNCZIQQeWemYYZfO/6KD0kfsN1/O26G32Trbkfcxu2I2+hWvxumNJuCRjqNpBgpIYSQ0shE4tqsWTPcvHlTYpm/vz9mzZqFXbt2oXXr1sVul5aWhosXL363nhBC8lnrWmNr160IjA3ENv9tuP/5Plt3/dN13Ph0Az0b9MQUhykw1zKXXqCEEEK+q1yJq6WlJfr27Yu+ffuiY8eOUFConLxXW1sbnTt3LrauZcuWaNGiBe7evYtff/0V7u7uMDc3x5cvX7Bp0yZERUXh1KlTlRIHIaTms9O3w65uu+Af7Y9tz7fhYdRDAAADBn6hfrgSdgV9LPrA08ETppqmUo6WEEJIYeW6VGzevHkIDg5Gv379oK+vj4EDB+LQoUOIi4urqvhYxsbGyM7OxsKFC+Hs7Ixp06bB2NgYd+/ehaOjY5U/PiGkZmlm2Az7nPfhgPMBtDBswS4XM2KcDz6Pfj79sPzf5YhKi5JilIQQQgqr0KwCWVlZuH79Oi5evIhLly6xV+n36dMHffv2hZ2dXVXEWmkiIiJgamqK8PDwaptVICYmBgYGBjI3yJmUjtpPfpW17RiGwYMvD7Dt+TYExgVK1ClyFTHAagAm2E+AgZpBVYdMCqHPnvyitpNvstx+FZqcS1lZGb1798bOnTvx6dMnPH78GC4uLjh37hwcHBzQoEEDTJs2DVeuXKnseAkhpNJxOBy0r9cex3ofwx9d/4CNrg1blyPOwfGg43DxdsHGxxsRnxkvxUgJIaR2q/R5XKOjo3Hp0iVcvHgR169fZ6e3kiXU40rKg9pPflW07cSMGDc+3cAO/x34kPhBok5VQRXDbIdhdJPR0FLWquyQSSH02ZNf1HbyTZbbr9Jvh2BoaIgxY8bgzJkziI2NrezdE0JIleNyuOhu1h2n+57Gug7rYMY3Y+syhBnY93Ifep7piR3+O5CcnVzCngghhFSmKr2Pl6KiYlXunhBCqhSPy0Nvi94463oWK9uvRD2Nemxdak4qdgbsRM8zPbHnxR6k5aRJMVJCCKkd6AbChBBSCgWuAtws3XDB7QKWtF2COmp12LqU7BT88fwPOJ9xxr6X+5Ceky7FSAkhpGajxJUQQspIkaeI/1n9D5c8LmGB4wIYqBbMMpCUlYTfn/2Onmd64s/AP5EhzJBipIQQUjNR4koIIeWkzFPGUNuh8PXwxbzW86CrosvWJWQlYNPTTXA544LDrw8jU5gpxUgJIaRmocSVEEIqSEVBBSMaj4Cfhx/mtJwDHWUdti4uMw4bHm9AL+9eOPbmGLJF2VKMlBBCaoYfumdrYmIiTp8+jXfv3iEzU7JXgcPh4Pfff/+h4AghRB6oKaphtN1oDLQeiGNBx/Dnqz+RlJU7FWBMRgzWPlqLA4EHMLHpRLhbukORRxeuEkJIRVR4Htf379+jXbt2yMrKQlpaGgwMDBAfHw+hUAgdHR1oaWkhJCSksuOtFDSPKykPaj/5Ja22S81OZRPYlOwUiTpjdWNMajoJ/Sz7QZFLCWxJ6LMnv6jt5Jsst1+FhwrMnj0bTk5O+Pr1KxiGga+vLzIyMnDkyBFoamri1KlTlRknIYTIDQ0lDUxsOhGX+1/GZIfJ0FDUYOsi0yKx7N9l6OvTF2c/nIVQLJRipIQQIl8qnLg+evQInp6eUFZWBgBkZ2eDx+Nh6NChmD17NqZPn15pQRJCiDziK/ExpdkUXO5/GRObToSaghpb9zn1MxbfXwzXs664EHwBIrFIipESQoh8qHDimpWVBT6fDy6XC11dXXz58oWts7Ozg7+/f2XERwghck9LWQtezb1wuf9ljLMbB1UFVbbuU8onLLy3EG7n3OAX6kcJLCGElKDCiauVlRU+fvwIAGjevDl27NiBlJQUZGRkYPfu3ahbt26lBUkIITWBjooOZracCT8PP4xuMhoqPBW2Liw5DPPuzEP/8/1xJewKxIxYipESQohsqnDiOnjwYLZXdeXKlXj8+DF0dHTA5/Nx5swZLFu2rJJCJISQmkVPVQ9zWs2BX38/DLcdDiWuElsXnBSM/7v9fxhwYQCufbxGCSwhhBRS4VkFvhUeHg4/Pz9kZmaia9eusLOzq4zdVgmaVYCUB7Wf/JKXtotOj8a+l/tw+t1p5IhzJOqsdKww2WEyutbvCi6ndk29LS/tR4qitpNvstx+lZa4yhNKXEl5UPvJL3lru6i0KOx9sRfeH7yLzDZgrWONyc0mo6tpV3A4HClFWL3krf1IAWo7+SbL7VeuGxDcuXOnXDvv2LFjudYnhJDazEjdCIvbLsY4+3HY93IffD74sAns24S3mHlzJmx0bTDZYTK6mHapNQksIYTkK1fi2rlzZ3A4HOR30hY+aDIMU+QgKhLR1bGEEFJedTXqYknbJRhvPx57XuzBuQ/nIGRyE9ig+CDMuDkDtrq2mNJsCjqZdKIElhBSa5QrcX3+/Dn7d3R0NMaNG4cuXbpgwIABqFOnDr5+/YpTp07h1q1b2L9/f6UHSwghtUldjbpY1m4ZxtuPx76X+yQS2Dfxb+D1jxca6zXGFIcp6GjSkRJYQkiNV+ExrgMGDICFhQU2bNhQpG7u3LkIDg6Gt7f3DwdYFWiMKykPaj/5VdPaLjwlnE1gRYzkGS07PTtMbjYZHep1qDEJbE1rv9qE2k6+yXL7VfgS1StXrqB79+7F1vXo0QPXrl2rcFCEEEKKMtU0xfJ2y3HB/QLcLN3A4xT8QwmMC8TUG1MxzHcY7kbcRS287pYQUgtUOHHV0NDAjRs3iq27du0aNDQ0iq0jhBDyY0w1TbGy/UqcdzsP14auEgnsy9iXmHJjCob7Dsf9z/cpgSWE1CjlGuNa2NSpU7FkyRJ8/foVbm5uMDQ0RHR0NHx8fHD48GEsX768MuMkhBDyjfr8+lglWIWJTSdi94vduBhykb1hwYvYF/C87gkHAwdMcZiCtnXb1pghBISQ2uuH5nHdtm0b1q1bhy9fvrCzDRgbG2P+/Pnw8vKqzDgrFY1xJeVB7Se/alvbhSWFYc+LPbgUeqnIHbeaGTTDlGZT0Ma4jdwksLWt/WoSajv5Jsvt98M3IBCLxYiIiEBkZCSMjY1hYmICLle27+5CiSspD2o/+VVb2y40KRS7X+yGX6hfkQS2uWFzeDp4oq2x7PfA1tb2qwmo7eSbLLffD2eYXC4X9evXh5OTE+rXry/zSSshhNR0DbQaYF2HdfBx9UGvBr3AQUGC+jz6OSZdm4SRfiPx4PMDGgNLCJErFR7jumLFihLrORwOFi9eXKF9p6amwsbGBp8/f8bjx4/RqlUrtm7//v1Yv349Pn36BGtra6xevRp9+vSp0OMQQkhNZqFlgfUd12NS00nYFbALl8Mug0Fuouof449J1yfBwcABkx0mo13ddjLfA0sIIRVOXH/77bciy1JTUyESiaCqqgplZeUKJ64rV66EUCgssvzEiROYMGECfvnlF3Tt2hUnT56Eu7s77t69izZt2lTosQghpKaz0LbAhk4b4OngiV0vduFyaEECGxATAM/rnmhq0BSTHSajfd32lMASQmRWhc/rJyQkFPnJyMiAn58fLC0tcevWrQrtNygoCNu3by92VoKlS5di8ODBWLlyJbp06YJdu3ahdevWpfb+EkIIyUtgO27AWdez6NWgF7icgn8BL2JeYPL1yRjuOxz3Pt+jIQSEEJlUqQNSFRQU4OzsjBkzZmDy5MkV2oeXlxc8PT1hbW0tsTwkJATv3r3DwIEDJZYPHjwYN27cQFZWVoXjJoSQ2sRCO3cIgY+rD3pb9JZMYGNzE1i6kQEhRBZVeKhASUxMTODv71/u7U6fPo2XL1/izJkzePbsmURdUFAQAMDGxkZiua2tLbKzsxEaGlqkLl9ycjKSk5PZcmRkJIDcq+ZEIlGx21QmkUgEsVhcLY9FKh+1n/yitiuZmYYZVrdbjQlNJmBv4F74hRXMQpB/I4Mmek3g2dQTgrqCah9CQO0nv6jt5Js02q+ssxdUeuIaGhqK9evXo2HDhuXaLj09HbNnz8aaNWvA5/OL1CckJAAAtLW1JZbr6OgAAOLj47+7782bNxc79CAuLg7KysrlirMixGIxkpKSAIBmXZBD1H7yi9qubNShjplWMzGg3gAcDTmKf778AzFyE9hXca/gddMLVnwrjLQcCUd9x2pLYKn95Be1nXyTRvsZGRmVab0KJ66amppFDl45OTnIzs6GmpoavL29y7W/VatWoU6dOhgzZkxFQ/qu2bNnY/z48Ww5MjISjo6O0NPTg4GBQaU/3rfyv7Ho6+vL3HxopHTUfvKL2q58DAwM0Ny8OT4mf8TewL3wDfVle2DfJb/DomeL0Fi3MTybeqJDvQ5VnsBS+8kvajv5JsvtV+HEdc6cOUUOWioqKjAxMYGLiwt0dXXLvK+PHz9i06ZN8PHxYTP81NRU9ndqairbs5qUlCSRlef3xJb0eHw+v9heXB6PV20NwuVyq/XxSOWi9pNf1HblZ6FjgbUd1sLTwTP3TlwhlyBicv+RvY5/jem3pqOxXmNMdpiMTiadqjSBpfaTX9R28k1W26/CieuyZcsqLYjQ0FBkZ2ejd+/eReq6dOkCJycnHDt2DEDuWNfCF24FBQVBSUkJFhYWlRYPIYQQwIxvhtWC1ZjUdBL2vNiDiyEXCxLYuNfw+scLtrq2mOwwGZ1NO9M0WoSQKvfDY1wTEhIQGBiI8PBwuLi4QEdHB5mZmVBSUirzuIhmzZrh5s2bEsv8/f0xa9YsdsorCwsLWFlZ4dSpU3B1dWXXO3nyJH766ScoKSn96FMhhBBSjPr8+lglWJWbwL7cgwvBF9gE9k38G0y/OR02ujbwbOqJLvW7SMxSQAghlanCiatYLMaiRYuwdetWpKeng8Ph4PHjx9DR0YGHhwecnJywdOnSMu1LW1sbnTt3LrauZcuWaNGiBYDcXt5hw4ahYcOG6NKlC06ePImHDx/izp07FX0ahBBCysiUb4qV7Vdiov1E7H25F+eDz7MJbFB8EGbemgkrHStMajoJ3cy6UQJLCKl0FT6qLFmyBNu2bcOmTZvw7t07ibn++vXrhwsXLlRKgIUNGTIEe/fuxbFjx+Ds7Iz79+/Dx8cHbdu2rfTHIoQQUjxTvilWtF+BC+4X4NHIAwqcgj6QdwnvMOf2HHic84BfqB9EYpoOiRBSeThMBWeXNjExwfz58zFt2jSIRCIoKiriyZMnaNGiBa5du4aBAweyF07JmoiICJiamiI8PBwmJiZV/ngikQgxMTEwMDCQuUHOpHTUfvKL2q56RKREYH/gfpz9cBZCseTtuhtoNcDEphPR07wnFLjlO8lH7Se/qO3kmyy3X4V7XOPi4mBra1tsnUgkQk5OToWDIoQQIj9MNE2wtO1S+Lr7YpD1IChyFdm60KRQLLi7AG7n3HA++HyRxJYQQsqjwomrlZUVrl27VmzdrVu3YGdnV+GgCCGEyB9jDWMsarMIvh6+GGIzBErcgotmPyZ/xC/3fkFfn77wee+DHDF1bhBCyq/CieusWbOwadMmLF68GIGBgQByT8Fv374dW7duxezZsystSEIIIfLDSN0IC50Wwq+/H4bbDocyr+AOhRGpEVjyYAn6+vTF6XenkSOiBJYQUnYVHuMK5N5KddmyZUhLS2MvzlJXV8fy5ctlOnGlMa6kPKj95Be1nWyIzYjFn4F/4u93fyNDmCFRZ6RuhPF24+HeyB1KPMlpDan95Be1nXyT5fb7ocQVyL2z1YMHDxAbGwtdXV20bdsWWlpalRVflaDElZQHtZ/8oraTLXEZcTj0+hCOBx0vksAaqhlinN049Lfqz/bQUvvJL2o7+SbL7ffDias8osSVlAe1n/yitpNNCZkJOPz6MI4FHUNaTppEnYGqAcbajcUAqwFQ5ChS+8kp+uzJN1luv3LNTXLo0KFy7XzkyJHlWp8QQkjNp6Oig+ktpmNUk1E4/Powjr45itScVABATEYM1j9ej30v92FU41HorNNZqrESQmRLuXpcv72Fa/59qQvvovC9qkUi2Zx4mnpcSXlQ+8kvajv5kJydjKNvjuLw68NIyU6RqNNW0saoJqMwxHYI1BXVpRQhKS/67Mk3WW6/cs0qkJCQwP48fvwYZmZmWLRoEQICAhAVFYWAgAD88ssvMDMzw8OHD6sqZkIIITUIX4mPyQ6TcaX/FXg194KWcsF1EonZifj9+e9wPuOMXQG7kJydLMVICSHSVuExrt27d8dPP/2E+fPnF6lbu3Ytrl+/jhs3bvxwgFWBelxJeVD7yS9qO/mUlpOGE0En8Nerv5CQJXkHRg1FDQy1HYoRtiOgraItnQBJqeizJ99kuf0qPI/rgwcP0LJly2LrWrZsif/++6/CQRFCCKm91BXVMc5+HHzdfTHReiL0VPTYutScVOx5sQfOZ5yx+elmxGXESTFSQkh1q3DiamhoiJMnTxZbd+LECRgYGFQ4KEIIIURVQRX/M/8fLrldwnzH+TBUM2Tr0oXpOBh4ED3P9MSGxxsQkx4jxUgJIdWlXLMKFLZw4UJMmjQJwcHBcHNzg6GhIaKjo+Hj44M7d+5g9+7dlRknIYSQWkpFQQXDbIfhf1b/w9kPZ7H/5X58SfsCAMgUZeLw68M4GXQSHo08MM5+HIzUjaQcMSGkqlQ4cZ0wYQKMjY2xevVqzJ07F0KhEAoKCmjRogXOnTuHvn37VmachBBCajklnhIGWg+EeyN3XAy+iL0v9yI8JRwAkC3Oxom3J3D6/Wm4NnTFePvxMNGs+msYCCHVq1JuQCAWi9lBvN9OmSWL6OIsUh7UfvKL2k6+ldZ+QrEQfqF+2PtyL0KTQiXqeBweelv0xgT7CTDXMq+miEk++uzJN1luv0rJMrlcLurUqSMXSSshhJCaQYGrgL4N+8Knnw9+7fQrLLUt2ToRI8L54PNwPeeKn+/8jODEYClGSgipLJRpEkIIkWs8Lg89zXviTL8z2NJ5C2x1bdk6MSOGb6gv3M+5Y/at2Xgb/1aKkRJCfhQlroQQQmoELoeLn8x+wsk+J7H9p+1oqt+UrWPA4NrHaxhwYQC8/vHCq9hXUoyUEFJRlLgSQgipUTgcDjqadMSRXkewu/tutDBsIVF/K/wWBl8aDM/rnnge/Vw6QRJCKqTCswoQQgghsozD4aBd3XZoa9wWT74+we6A3XgYVXA78vuf7+P+5/tobdQaE5tOhJOREzgcjhQjJoSUhhJXQgghNRqHw0Fro9ZobdQa/tH+2PViF+5/vs/WP456jMdRj9HUoCkmNZ2EDvU6UAJLiIyioQKEEEJqjWaGzbCr2y6c6H0CXU27StS9iHmBqTemYuDFgbj28RrEjFhKURJCvocSV0IIIbVOE/0m+L3r7zjT7wxczF3A5RT8OwyKD8LsW7Phfs4dF4IvQCgWSjFSQkhhlLgSQgiptax0rLCh0waccz0H14au4HEKJlsPSQrBwnsL0e9sP3i/90aOKEeKkRJCAEpcCSGEEJhrmWOVYBUueVzCQKuBUOQqsnXhKeFY+mApevn0wrE3x5ApzJRipITUbpS4EkIIIXnqadTD4raL4efhhxGNR0CFp8LWRaVFYe2jteh5pif+DPwT6TnpUoyUkNqJEldCCCHkG3XU62Be63m43P8yxtuPh7qiOlsXlxmHTU83oceZHtgdsBvJ2clSjJSQ2kUmEldfX1906tQJBgYGUFZWhoWFBWbPno2kpCR2ndGjR4PD4RT5uXz5shQjJ4QQUpPpqephRosZuNL/CqY0mwK+Ep+tS8pKwjb/bXA+7Yytz7YiITNBipESUjvIxDyu8fHxcHJywvTp06Gnp4fAwEAsW7YMgYGBuHr1KruehYUFjh49KrGtra3tt7sjhBBCKpWWshYmO0zGyMYjcfLtSfz16i/EZ8YDAFJzUrH35V4ceXMEA60GYlSTUTBQM5ByxITUTDKRuA4fPlyi3LlzZygrK2PixIn48uUL6tatCwBQVVVFmzZtpBEiIYQQAnVFdYy1G4shNkPg/d4bBwIPIDo9GgCQIczAX6//wvGg43Bv5I4xdmNQT6OelCMmpGaRiaECxdHT0wMAZGdnSzkSQgghRJKqgiqG2Q6Dn4cflrRdIpGgZouzcfLtSfT27o1f7v2CkKQQKUZKSM0iU4mrSCRCZmYmnj17hhUrVqBfv34wNzdn6z98+AAtLS0oKSmhZcuWOHv2rNRiJYQQQpR4Svif1f9wwf0CVgtWo4FWA7ZOxIhwPvg83M66Yfat2XgT90aKkRJSM8jEUIF8ZmZm+Pz5MwCgZ8+eOHbsGFvXvHlztG7dGk2aNEFiYiJ27twJd3d3nDp1CgMGDChxv8nJyUhOLrjqMzIyEkBuoiwSiargmUgSiUQQi8XV8lik8lH7yS9qO/kmT+3HBRe9zXujZ/2e+Cf8H+wL3Ie3CW8BAAwYXPt4Ddc+XoOgrgDj7cejmUEz6QZcxeSp7UhR0mg/Ho9X+koAOAzDMFUcS5m9ePECaWlpePXqFVatWgULCwtcu3at2CcjFovRrl07JCcn4/Xr1yXud9myZVi+fHmR5U+fPmXHz1YlsViMpKQkaGlpgcuVqU5uUgbUfvKL2k6+yXP7MQyDR7GPcCzkGF4nFv0f1VSnKYZaDEULvRbgcDhSiLBqyXPbEem0n5GRUZnWk6nEtbCAgAA0a9asxB7VX3/9FfPmzUN6ejpUVVW/u6/ielwdHR0RFhYGExOTSo/9WyKRCLGxsdDX1y/zNwoiO6j95Be1nXyrCe3HMAyeRj/FvsB9+C/yvyL1TfSaYLzdeHQy6QQup+YkeDWh7WozabRfWR9HpoYKFNa0aVMoKiriw4cPP7wvPp8PPp9fZDmPx6u2BuFyudX6eKRyUfvJL2o7+VYT2s+prhOc6johMDYQe1/sxT/h/7B1r+JeYdbtWbDUtsR4+/FwNneGAldm/zWXS01ou9pMVttPZr/ePXz4EDk5ObCwsCi2XiwW49SpU2jSpEmJva2EEEKILLDTt8PvXX+Hdz9v9GrQS6KH9UPiB8y/Ox/9zvbDmXdnkCPKkWKkhMgumfha5+HhgVatWqFp06ZQVVVFQEAAfv31VzRt2hRubm74+PEjRo0ahSFDhsDS0hIJCQnYuXMnnjx5gjNnzkg7fEIIIaTMGuk0wvqO6zG12VQcCDyAc8HnIBQLAQDhKeFY9u8y7AzYidFNRqO/VX+oKlDnDCH5ZCJxdXR0xMmTJ7Fu3TqIxWKYm5tjwoQJ+L//+z8oKSlBU1MTWlpaWLVqFaKjo6GkpIRWrVrBz88Pzs7O0g6fEEIIKbf6/PpY1m4ZPB088derv3D63WlkijIBAF/Tv2L94/XY+3IvRjQegUHWg6CppCnliAmRPpm9OKsqRUREwNTUFOHh4dV2cVZMTAwMDAxkbqwIKR21n/yitpNvta394jLicOTNEZwIOoHUnFSJOk1FTQy2GYzhjYdDV0VXShGWXW1ru5pGlttPZse4EkIIIbWJnqoeZrSYgSsDrsCruRe0lbXZupScFOx9uRfOp52x/tF6RKVFSS9QQqSIEldCCCFEhvCV+JjYdCKu9L+Cua3mwlDVkK3LFGXiyJsjcPF2wZL7SxCWFCa9QAmRApkY4ypLhEIhYmNjkZ2dDbFYXCn7ZBgGmZmZyMjIqJETTdd01H4/jsvlQklJCfr6+lBQoMMOIWWhpqiGkU1GYrDNYJwLPoeDgQcRnhIOABCKhfD54IOzH86iu1l3jLcfD1s9WylHTEjVox7XQtLS0hASEoKEhAQIhcJK2y+Hw4GysjIlPXKK2u/HCYVCJCQkICQkBGlpadIOhxC5osRTwv+s/ofzbuexvsN6NNJpxNYxYHD141UMvDgQk69PxtOvT6UYKSFVj7o+CklISAAANGjQACoqKpW2X4ZhIBQKoaCgQMmPHKL2qxyZmZn49OkTEhISoK6uLu1wCJE7ClwF9LLoBZcGLrgTcQd7X+5FQEwAW3/v8z3c+3wPLQxbYLz9eAjqCeiYRWoc6nEtRCgUQklJqVKTVkJILhUVFSgpKVXq2QxCaiMOh4NOpp1w2OUwDjgfQLu67STqn0U/w5QbUzDw4kBcDrsMkVgkpUgJqXyUuBJCCCFyiMPhoLVRa+zuvhsn+pxAd7Pu4KCghzUoPghzb8+F6zlXeL/3prtxkRqBEldCCCFEzjXRa4LNnTfjrNtZuDZ0hQKnYCTgx+SPWPpgKVy8XXD49WGk56RLMVJCfgwlroQQQkgNYaFlgVWCVbjkcQlDbYZCmafM1n1N/4oNjzfA+YwzdgfsRlJWkhQjJaRiKHEllSYnJwd2dnYICwuTdigVNm3aNOzZs+eH9nHnzh00btwYmpqaGDBgAJKTkyspOkIIKZu6GnWxwGkBrvS/gvH246GhqMHWJWYlYpv/Njifccbmp5sRmxErxUgJKR9KXEmlOXjwIFq2bAlzc/NqfdyJEyeiXr164PP5MDc3x5o1a9i6pKQkODs7Q1tbG8OGDYNIVHCRwurVq7FlyxaJfc2fPx8rVqxATk7FxoKlpqbCzc0Nq1evRmxsLEQiEebMmVOhfZVk8eLFsLe3h4KCAubPn1/q+qdPn0bDhg2hpqaGn376CR8/fmTrbt68iS5dukBLSwtGRkZFtn3//j169OgBbW1tmJmZYf/+/cU+xq1bt8DhcMoUDyGkeuTfjevqgKuY0WKGxO1i03LScDDwIJxPO2PlvyvZOWIJkWWUuMoxsVgMhmGKLI+Kks6tAHfs2IERI0ZU++POnDkTHz58QHJyMu7evYsjR47g77//BgDs3r0bBgYG+Pr1K8LDw+Hj4wMACAkJga+vL7y8vCT2ZWJiAhsbG5w7d65CsZw8eRKWlpZwd3eHsrIy1q5di2PHjiElJeXHnuQ3LC0tsWHDBvTr16/Udd+8eYPRo0dj586diIuLQ9OmTTFw4EC2Xl1dHWPHjsXmzZuLbCsUCtGvXz906NABsbGx8Pb2xpw5c3D79m2J9bKzszF9+nQ4OTn9+JMjhFQ6TSVNjLcfj8v9L2OB4wIYqxuzddnibPz97m/08emDeXfm4W38WylGSkjJKHEtAcMwEGdnV8oPU9b1iklECzM3N8eGDRvQsmVLqKmpFZukjhkzBq1atcLWrVsRExNT5uf76dMndO3aFZqamhAIBFi4cCE6d+5cpm0jIiLw+vVrCAQCdllmZibGjx8PXV1dNGrUCNu3b6+SOQUbN24MVVVVtszlcvHhwwcAQGhoKDp27AhlZWW0b98eISEhAAAvLy9s2bIFPB6vyP66dOmCCxcuVCiW//77T+I1sLGxgaKiIl6+fFmh/X3PqFGj4OLiAj6fX+q6R44cQc+ePdGjRw+oqqpixYoVCAgIwKtXrwAAjo6OGDFiBBo2bFhk27dv3yIsLAwLFy6EgoICWrZsCXd3dxw4cEBivbVr16J3796wsbGpnCdICKkSqgqqGGo7FJc8LmFV+1Uw55uzdWJGDL9QPwy4MABTrk/Bs6/PpBcoId9BNyAoAZOTg7dNHar1Ma1fBICjpFTiOocOHcL58+dhampabCJ4/vx5XL58GYcPH8aiRYvQtWtXjBw5En369IFSCfseMmQImjdvDl9fXwQFBcHFxQXW1tZlivvFixcwNzeXmAN35cqVePXqFd6+zf323r9//xL30adPH9y7d6/Yuvr16+PFixff3XbBggXYunUr0tPTYW5ujuHDhwMA7OzscOvWLYwcORL379/Hzz//jL///hsNGjRA69ati92Xra0t22NbXpGRkbC3t5dYZmZmhsjIyGLXb9q0KT59+lRsnUAgwMWLFysUR2GBgYESz1VTUxMNGzZEYGAgmjRpUuK2DMMU+TLFMIxEW7x79w7Hjh3D8+fPMWXKlB+OlxBS9RS5inC1dEXfhn3xz6d/sO/lPryKe8XW3/18F3c/30Vzw+YYZzcOHU060s0MiEygHlc5NG3aNFhYWEBRUbHY+74rKiqib9+++Pvvv/Hp0yf07t0bW7ZsQb169TB79uxi9/np0yf8+++/WLNmDVRUVNCsWTMMGzaszDElJCQU6f07fvw4fvnlFxgYGMDAwADz5s0rcR8XL15EYmJisT8lJa1Abo9famoqHj16hKFDh0JHRwcAMG7cOGhoaMDR0RHt2rWDQCDAhg0bsHr1avzyyy/o0KEDpkyZguzsbHZfmpqa7F3Uyit/jKe2tjb78+rVq+8e8F+8ePHd51wZSSuQO+5WW1tbYpm2tnaZhi9YW1vDxMQEK1asQHZ2Nh4+fAgfHx+kpxdMpzN58mRs2LABampqlRIvIaT6cDlcdDPrhuO9j2Nvj71oY9xGov559HNM+2ca+l/oj4shFyEU0w1EiHRR4iqHzMzMyryutrY2mjZtCgcHBwiFQrx+/brY9b58+QItLS2J5NPU1LTMj6Ojo1Pk6vkvX75I7KM8+6sIDoeD1q1bQ0VFBUuXLgWQe7emPXv24MWLF1i3bh0WLVqEuXPn4v79+3j8+DHu3LmD7OxsiVPfKSkpbOJbXsbGxli1apVEAmpjYwNjY+PSN64iGhoaSEqSnPYmKSkJmpqapW6rqKiIc+fO4d69e6hbty5mz56N0aNHw8TEBEDuMARVVVW4urpWSeyEkOrB4XDQxrgN9vbYi+O9jxe5mcH7hPdYcHcB+vj0wYmgE8gUZkoxWlKb0VCBEnAUFWH9IqD0FUvBMAxEQiF4ZbjXPUdRsfS4ynC6Jjg4GEeOHMHRo0fBMAxGjBiB58+ff/eK/7p16yIpKQkpKSlsQhMeXvYrTJs2bYqwsDBkZWVBWVmZ3Wd4eDgcHBzKtD8XFxfcvXu32DozMzN2TGZphEIhgoODiyx/+vQpQkJC8Mcff2D9+vVo1aoVm+wGBBS085s3b9CsWbMyPda32rRpg0ePHrHlzMxMxMbGws7Ortj1mzRpInGFf2EdOnSAn59fheIozM7ODv7+/mw5NTUVwcHB342puBhv3LjBlgcPHow2bXJ7Za5fv4579+6xsxEkJSWBx+PhyZMnuH79+g/HTgipfnb6dtjceTNCk0JxMPAgLoRcYHtaP6d+xuqHq7EzYCdGNB6BQdaDoKlU+pdgQioL9biWgMPhgKukVCk/nLKuVwljiMaNG4fWrVsjMjISf/75J96/f48lS5aUOE1V/fr10aZNG/zyyy/IysrCixcvcOzYsTI/pomJCWxtbXH//n122aBBg7B27VrExsYiNjYWGzduLHEffn5+SE1NLfbne0lrQkICDh8+jOTkZIjFYty/fx87d+5Et27dJNYTi8WYNWsW/vjjDwBAgwYNcPfuXWRlZeH27duwsLBg17116xZ69+7NlseMGYNx48aV6XUYOHAgLl++jHv37iEzMxNLly5F3759v9u7+erVq+8+55KS1pycHGRmZkIkEkEkEiEzMxNCYfGn8IYPHw4/Pz9cv36djalp06bs+FaxWIzMzEx2uERmZiaysrLY7V+8eIH09HRkZWXhzz//xI0bN9ghJ7///juCgoLg7+8Pf39/9OvXD2PGjMHJkyfL9HoRQmRXA60GWNF+Bfw8/DCi8QioKhRcBBufGY/fn/2OHqd74Lenv9FcsKTaUOJaA02aNAmRkZHYtWsX2rVrV+btjh07hhcvXkBfXx+TJ0/GsGHD2N7TspgyZQoOHTrElpcsWQIrKys0atQIbdu2hZubW4kXh1UEh8PBwYMHYWZmBi0tLYwbNw5z5szBtGnTJNbbvn07nJ2d2QTVw8MD9erVg6GhIeLi4jBx4kQAwOfPn/HmzRu4ubmx24aHh5f5ddTQ0MChQ4cwYcIE6Onp4cOHD6Um7BUxYcIEqKqq4siRI9i4cSNUVVWxatUqALnjlTU0NNiLvmxtbXHw4EFMnDgRurq6eP78ucTFZ3fu3IGqqiqcnZ3x9etXqKqqSlyUd/z4cZiYmEBPTw9//vknrl27Bj09PQBg537N/1FVVYW6ujpbTwiRf0bqRpjXeh6u9r+KKQ5ToKWsxdal5qTiQOABmguWVBsOU9r8SzVQREQETE1NER4ezo7VA8De8amyJ9BnGAZCoRAKZRgqIEtmzJiBtLQ07Nu3r0zr5+TkoFmzZrh06VKxr6GPjw/mzp3LTlUli7y8vGBnZ4dJkyYByJ2f1MHBAU+fPoWqqqpctZ8sqqrP2PeIRCLExMTAwMCg2KnPiGyj9pNN6TnpOPP+DP569Re+pn+VqONyuHA2d8boxqOhK9SltpNTsvzZozGuhPX06VPw+XxYWlri/v37+Ouvv8o1XEBRUVHilH5UVBTevXsHgUCA8PBwrFy5Eh4eHlUReqXJH0qQT0lJCa9fv/7uaXhCCKlt1BTVMKLxCAy2HoyLIRdxIPAAwpLDABTMBesX6gdHfUd4tvBEK6NW9KWfVBpKXAnr69ev8PDwQExMDIyMjLBkyRL06tWrwvsTCoWYNm0aQkJCoKGhgX79+mHJkiWVGDEhhBBpUeQpwr2RO/o17Ieb4TeLzAX7KPYRHl19BAcDB4y1G4vOpp3B5dAIRfJjaKgADRUgpaD2qzw0VICUB7WffGEYBg+jHmLfy314GPmwSL2FlgXG2I1B7wa9ocgrfQYdIj2y/Nmjrz6EEEII+WH5c8Hu67EPR3oeQYc6HSTmgg1JCsHi+4vh4u2CQ68OIT0nvYS9EVI8SlwJIYQQUqns9O2wpNkSnO13Fv0b9Ycit6CH9Wv6V/z65Fd0P90dfzz/A/GZ8VKMlMgbSlwJIYQQUiXM+GZY1m4ZrvS/gjF2Y6CuqM7WJWcnY8+LPehxugdW/7caESkRUoyUyAtKXAkhhBBSpQzUDDC75WxcHXAVM1rMgJ5KwVzPWaIsnHh7An18+uDnOz/jbfxbKUZKZJ1MJK6+vr7o1KkTDAwMoKysDAsLC8yePbvI/dUvXLgABwcHqKiowMrKCgcPHpRSxIQQQggpL74SH+Ptx+PKgCtY0nYJTDVN2ToRI4JvqC8GXBgAz+ueeBz1GLXw+nFSCplIXOPj4+Hk5IRdu3bhypUrmD17Ng4dOoT//e9/7Dr37t2Du7s72rZtCz8/PwwaNAjjxo3D6dOnpRg5KWz58uVYvXq1tMOoFOnp6bCyskJsbPluY7h9+3YYGxtDT08PixcvrqLoCCFEvinzlPE/q//hgtsFbOy0Eba6thL19z/fx9grYzHcdzhufLwBMSOWUqRE5jAyas+ePQwA5vPnzwzDMEyPHj2Ydu3aSawzZMgQxtbWttz7Dg8PZwAw4eHhEstDQ0OZ0NDQCsf8PWKxmMnOzmbEYnGl77s6lfR2iYuLY+rUqcMkJyeXaV8HDx5kRo0aVUmRFcjIyGCmT5/OGBgYMJqamkyLFi3YmK5fv86YmZkxRkZGzPHjx9ltsrOzGUdHR+bTp08S+1q9ejUzZ86cMrff3bt3GX19febdu3fMly9fGAsLC+bIkSOV/hxv3brFNGnShFFVVWVatWrF+Pv7f3fd5ORkZvz48YyhoSGjo6PDTJ8+ncnJyWHr3717x3Tv3p3R0tJi6tevz+zbt09i+5cvXzJOTk6MqqoqY2try9y4cUOiPi4ujhk5ciSjra3N8Pl8pmvXriXGXlWfse8RCoVMZGQkIxQKq+0xSeWh9pNf5W07sVjMPPj8gBl/ZTxj96ddkZ++Pn0Z73feTJYwq4ojJwwj2589mehxLU7+vc6zs7ORlZWFmzdvSvTAAsDgwYPx5s0bdm7I2kYsFpf7NEpUVFSVxHLo0CF069YNmpqaVbL/svL09MSXL1/w8uVLJCYm4sCBA1BSUgKQezvXvXv34vr16//f3n2HRXG1fwP/Lr2uIL0sYMGGFFFQAUVRQWzYu4L6mFgSjS0RNPYSC8T2M+qToKJiwS6KIeZRoonRiFFQxEoXFZAiZYHdPe8fvExc6Qrubrw/17WXzJyzM/fMYeTes2fOYNasWRCLxQCATZs2YezYsRAIBFLbmjRpEvbt24fS0tJ67Xv37t2YMmUKbG1tYWZmhkWLFmHXrl2Nenw5OTnw8/PD119/jdzcXIwbNw5DhgypMcb58+fjxYsXePz4MRISEnDt2jWsW7cOQMUDIoYMGYIePXogOzsbJ0+exIIFCxATEwOg4hG+gwcPxpAhQ5Cbm4vly5dj2LBhePXqFbf94cOHo1mzZkhKSkJOTg42bNjQqMdLCPk08Hg8dDfvjv96/xdHBh2Bt7W31MMKkvKTsOyPZfA94Yt99/ahqLxIhtESmZJ15vw2kUjESkpKWGxsLHN0dGRDhgxhjDF2//59BoBFRUVJ1X/06FG16+tS3x5XiUTCSkWlH/wSlgtZYUkhE5YL66xbV6+etbU127BhA3N2dmbq6urs+fPndR5vUVERO3DgAOvbty8zNzevsV5KSgrr3bs309HRYe7u7iwwMJB5enpy5bX9uvTp04f99NNPUuvCw8NZixYtmJ6eHluwYAHr2rUr27t3L2OsaXpcExMTmY6ODsvNza22XENDg5WWVnxaNzU1ZS9fvmTPnj1jbm5uNX6qbN26Nfv111/r1ePaunVrdubMGW759u3bTE1N7f0OpgZ79uxhnTt35pYlEgmztLRkkZGR1dY3NDRkv//+O7e8b98+ZmVlxRhj7N69e0xDQ0Pq2AMCAtjkyZMZY4xFR0czY2NjJhaLuXI3Nze2Y8cOxhhjv/zyC7OysmrQJ3LqcSUNQe2nuBqj7VLyU9jKP1Yy5zDnKj2w3Q91Z1tit7Cs4qxGjJpUkudrT64e+WptbY2MjAwAQP/+/REeHg4AyM3NBQDo6elJ1dfX1wdQMUa2NgUFBSgoKOCWMzMzAVQ8GaKy1w2oeOoHj8fjejHLxGXocqjLBxxRw92acAtqymq11gkLC8OZM2cgEAik4n0bYwwxMTEICwvDqVOn4OLigokTJ2L48OE19tKOGzcOTk5OOH/+PBITEzFgwAC0bduWq19bD29cXBxWrlzJlScmJmLatGk4d+4cevTogZCQEMTGxoIxBsYY/P394e/vX+32UlNT4ejoWOPxf/PNN1i8eHGV9Tdu3ICNjQ1WrVqFAwcOwNDQEAsWLMC0adMAAB07dsSlS5cgEAigpKQEAwMDTJs2DSEhIVBSUqo2lvbt2+POnTvw8PCos3c7MzMT1tbWXD1ra2uUlZUhOzub+wbhQ48xPj4ejo6OUrE4ODggPj6+2sfzMsak2k0ikSA1NRV5eXnc+spXZf24uDgwxhAfHw97e3up3zFHR0fEx8eDMYY//vgD7dq1w5QpU3D+/HkIBAKsWrUKgwcPrvU8McakrrumJBaLIZFIPtr+SOOi9lNcjdF2FtoWWOK6BJ/bf47wxHAce3QMheWFAIA35W/wY/yPCLsfhsEtB2Nyh8mw5ls3VvifPFlce/V9QpdcJa4XLlxAUVER7t+/jzVr1mDw4MH45ZdfPni7ISEhWLlyZZX1OTk5UFdX55aFQiHU1dUhEokAACKx6IP33VAikQhKdYzgmDlzJqysrKTe87YffvgBISEh0NXVxYQJE3D37l2Ym5vXWB+oSKSuX7+Os2fPQkVFBR07dsS4ceMQGxtbbf135ebmQktLi6t75MgR9O/fHz179gQAzJs3DyEhIZBIJHVuz9zcHFlZWbXWqW4bKSkpuHfvHgYOHIikpCTEx8fD19cXLVq0QM+ePbFz504sWLAAQqEQoaGhiIiIgKWlJQwNDTFkyBDk5+dj5syZGDlyJLdNbW1t5OTkcBdvbY985fF46NGjB5SUpNtPLBZXifd9j/HNmzfQ19eXKuPz+cjPz6+2vq+vL9auXYv9+/ejuLgY27ZtA1DxYa5Vq1awtLTEihUrEBgYiDt37uDUqVMwMTGBSCRCQUEB+Hx+lX2lpqZCJBIhNTUV0dHR2LFjB3bt2oVff/0VY8aMwa1bt2Bra1vtMUkkEpSWltZ57I1FIpFws5O82y5E/lH7Ka7GbrtxluMwxGQIItMjcTL5JF6XVXRYlUnKcOLJCZx8chLuxu4Y3WI02uu1r2NrpC6yuPZMTU3rVU+uElcHBwcAQPfu3eHi4gInJyecOnUKHTp0AIAq02NV9sQ2b9681u3Onz8f//nPf7jlzMxMuLq6wsDAAEZGRtz6kpIS8Hg8qKhUnBYJ7+PfxaiiogIV5dqbpUWLFlyM1UlJSUF2djZ69OgBJycnWFhY1PlJ5tWrV2jWrJnUubSyssLt27dr3VclfX19FBcXc3VfvHgBKysrqfdaWFhASUmpXtt7Hzo6OlBWVsbKlSuhpqaGbt26YeTIkYiKioKXlxe6dOnCjd988+YNvLy8cOnSJXz22WcYM2YMBg0aBHt7e3h7e3PnoaioCAYGBlBWVoaKikqtiauZmRkOHz4MZ2dnAEB2djYEAgGMjY0b7Rh1dXVRUFAgdQ7fvHmDZs2aVXtet27dinnz5sHR0RE6OjqYNm0a7t+/z7XF6dOnMXfuXFhbW6Nt27bw9/fH/fv3oaKiAj6fjzdv3lTZF5/Ph4qKCrS1tWFpaYlZs2YBAAYNGgR3d3f873//Q/v21f/hUFJSgoaGhtR115QqP3AYGhrK3fO2Sd2o/RRXU7SdEYzwhfkX+KzzZzifdB77E/YjuSAZAMDAcO3VNVx7dQ2djTsjwC4AHuYetf6fTWomz9eeXCWub3NwcICqqiqePHmCwYMHQ1VVFYmJifDx8eHqJCYmAgDatWtX67b4fD74fH6V9crKylINUvkLXvmvmrIaYifGfvCxMMYgEonqTHwAQFVJtc46SkpKtdYJDg5GYGAgDh8+jG+//RZTpkzB2LFjMXHiRHTu3Lna91hYWCA/Px+FhYXcDVbp6RVPManPhe/g4ICHDx/C3d2d215cXBz3XolEgoyMDPB4vDq3l5qayn1YqU5QUBCCgoKqrK/86v3tfVT+/O4+v/32WyxcuBB6enqIj4/HmjVroKenB0tLSzx9+pT7av/Bgwf46quvatzO27p164bHjx9z5/jRo0dwdXWt9j3ve4z29vbYs2cPt83Kr/ZnzpxZ7X6aN2+O/fv3c8u7du2Ci4sL93vfsWNH/Prrr1z52LFj0a1bN/B4PNjb22Pjxo1gjHGfuO/evYtx48aBx+PB0dERp06dqrLfus4Tj8f7qP8RKikpVbnWieKg9lNcTdV2msqaGNl2JIa3GY4raVcQei8Ud7PucuWxr2IR+yoWrfVaY0rHKfBt4Sv1yFlSP3J77X2cobQNd/36dQaAHT16lDFWMR2Wh4eHVJ0JEyZ8ctNhWVtbN/hmtAcPHrDFixczgUDAnJ2da6zXvXt39uWXXzKhUMju3r3LzMzMpG7Oqk1ISAibNGkSt5yQkMA0NTXZ5cuXWXl5Odu4cSNTUVHhbs5qCuXl5czW1pYtW7aMlZeXs9u3bzM9PT0WExMjVS82Npb5+vpyy76+vuyHH35gL168YAYGBiwzM5MxVvF70rx5c1ZSUsK1HwB2+fLlavd/9epV5uDgwNLS0lhOTg7r3bt3o0+HlZ2dzZo1a8YOHDjASktL2ffff88EAgETCoXV1n/69Cl79eoVE4vF7OrVq8zc3JxdunSJK7979y4rKipiQqGQ7d27lxkaGrLs7GzGWMU0YTY2Nmz9+vVMKBSyY8eOMT6fz16+fMkYY+z169esefPm7L///S8TiUQsOjqaaWtrs8ePH9cYP92cRRqC2k9xfey2i30Ry7649EW1U2n1jejL9t/bzwrLCj9KLP8G8nztyUXiOmzYMLZ27Vp27tw5dunSJRYcHMxMTU2Zg4MDdxf41atXmbKyMps5cya7fPkyW7ZsGePxeOzYsWMN3t+nlrhWqkxeapKUlMQ8PT2Zjo4Oc3NzYwsXLmTe3t712nZ187gePHiQ2djYcLMKODs7s/Dw8PeKvb4ePHjAPDw8mJaWFmvdujULDQ2VKheLxaxnz57syZMn3Lo7d+6w9u3bMwMDAxYcHMytX79+PZs/fz7XfikpKUxXV5dL7Kqzfft2ZmJiwvT19dmSJUsa/wAZY5cvX2Z2dnZMQ0ODdenShf39999c2cGDB1mHDh245ePHjzNzc3OmqanJOnTowH0QrLR48WKmr6/PtLW1maenp9S2GGMsLi6Oubq6Mg0NDdauXTuppJcxxn7//Xfm5OTEtLS0WMeOHWuc3aASJa6kIaj9FJes2u5J7hO29NpS5hTmVHUmgvDubGvsVpqJoB7k+drjMSb756l99913OHr0KJ4+fQqJRAIbGxsMHz4cCxculPqK/+zZs1i6dCkePnwIKysrBAYGYurUqQ3eX3p6OgQCAdLS0mBpacmtr5wP1sbG5kMPSQprwFABeTJ37lwUFRXhxx9/rFf9FStWQFVVFUuWLKlSJhKJYGpqitOnT8PDw6OxQ210xcXFcHJywu+//w5DQ0OIRCIcOXIECQkJWL9+vazDU1hNdY3VRCwWIysrC0ZGRvL3dRepE7Wf4pJ1270seolDDw7h2KNjVeZ8VVNSg19rP/jb+dNMBDWQdfvVRi4S14+NEtfqxcbGgs/no3Xr1vj9998xaNAghIeHVzvNUn2cO3cOvXv3hoqKClavXo2wsDA8ffqUeyCAolCU9lMElLiShqD2U1zy0nYFZQWIeBiBgw8OIrtE+hHePPDQ17ovpthNgb2RvYwilE/y0n7VoflFCOfly5fo27cvtLW1MXnyZCxbtuy9k1agYnqzyrvqr1y5gtOnTytc0koIIURx8dX4mGY/DT+P+Bkr3VbChm/DlTEw/JLyC8ZfGI+pP0/F1fSrDX4aJfn4qMeVelxJHaj9Gg/1uJKGoPZTXPLadhImweW0ywi9F4q4rLgq5bb6tgiwC4CvjS9UlT/dmQjktf0A6nElhBBCyCdCiaeEPlZ9cND3IPb3349elr2kyh/nPsaSa0vQ/2R/7Lu3D4VlhbIJlNSIEldCCCGEfFJ4PB6cTZyxvc92nPY7Db9WflBR+mdq+1fFrxAcG4x+x/shJDYEr4pfyTBa8jZKXAkhhBDyyWql1wprPNbg4vCLmGI3BTqqOlxZYXkh9t7bC58TPlh6bSme5D6RYaQEoMSVEEIIIQQm2iaY32U+okdGY0HnBTDW+udx3SKJCGeensGws8Mw69Is/PXiL7qRS0YocSWEEEII+f901XQR0DEAF4dfxBr3NWit11qq/GrGVUz9eSrGnR+Hi8kXIZKIZBTpp4kSV0IIIYSQd6gqq8KvtR9ODjmJnX12wtXUVar8fs59LIpZhEGnBiH8QTiKy4tlFOmnhRJX8q+2b98+XLlypUm2/e2338Le3h4qKipYvHhxrXUzMzMxZMgQmJubg8fjITExsUqduLg4eHl5QUdHB0ZGRggKCuLKAgICoKamBh0dHe6VmpoKoOKpZGPHjoWenh769++PgoIC7n2HDh3CV1991TgHTAghnyAej4celj3wk89PODLoCPrb9IcS75/0KaMwA+tvrofPCR/8353/w2vhaxlG++9HiasCk0gk1Y6xefHihQyikS/btm3DuXPnuOXQ0FCEh4c36j5at26NjRs3YsiQIXXWVVJSQv/+/XH69Olqy1+/fo1+/frB398f2dnZSElJwdixY6XqzJ8/H4WFhdzLysoKAHDy5Em8ePECr169QvPmzbFnzx4AQF5eHkJCQrB69eoPO1BCCCEAADsDO2zy3ITzw85jfLvx0FTR5MrySvOw6+4ueB/3xurrq5FSkCLDSP+9KHGth9iU3DpfYsk/CaRYwqTKbqfk4u/UPNx+5z3vw8bGBhs3bkTnzp2hpaVVbZI6ZcoUdOnSBdu2bUNWVla9t52amgovLy/o6urCw8MDQUFB6NWrV431b968iZ49e0JfXx+mpqZYv349gIoJ+zdu3IiWLVvCwMAAQ4cOxfPnz6WOITg4GJ07dwafz8eAAQOQm1v9+cjJyYGfnx/09fWhr6+Prl27Iju74rF9vXr1QmBgINzc3KCrq4s+ffogLS0NAPD5558jISEBW7duRVBQEMrLy6skgh/K398fvr6+4PP5ddY1MTHBrFmz4OrqWm15SEgI+vbtC39/f2hoaEBLSwsODg71iiMpKQlubm5QU1ODp6cnnj17BgBYvHgxgoKCoKurW/+DIoQQUidLXUsEdg1E9IhofOH0BZprNOfKSsWlOPboGAafGox5l+fhbtZdGUb676NSdxUy4oc/6qyTsMoHWmoVp7NUJK7Xe5K/G/he8YSFheHs2bMQCATVPsnp7NmzuHjxIg4cOIClS5fCy8sLkydPxqBBg2p95Oq4cePQqVMnXLhwAYmJifD19UXbtm2rrZueno5+/fph69atGD9+PIRCIR48eAAA2L9/P3bu3ImLFy/C2toa8+fPx+jRo3Ht2jXu/QcPHsSZM2fQvHlzeHt74/vvv8eqVauq7Gfz5s2QSCTIyMiAuro67ty5Aw0NDa48NDQUUVFR6NChA+bOnYuJEyciJiYGPB5P6tzU9uQPBwcH7mv3d3l4eEj13DaV69evo2PHjvDw8EBiYiI6deqEbdu2oX379lydPXv2YM+ePRAIBJg7dy6mTp0KAOjYsSM2bNgAoVCImJgYuLu748aNG3j+/DlGjBjR5LETQsinSk9DD587fg5/O3+ce3YOYffDkFyQDKDikbKXUi/hUuolOBs7I8AuAJ4CT6lhBqTh6OwpoC+++AItW7aEqqoqVFSqfvZQVVXF4MGDcezYMaSmpmLgwIHYsmULLCwsMH/+/Gq3mZqaiuvXr2PdunXQ0NCAk5MTJkyYUGMMBw8eRI8ePbixl3w+H127duXK5s2bh3bt2kFTUxObNm3CjRs38PTpU+79c+fOhZWVFXR0dDBy5Ejcvn272v2oqakhJycHT548gbKyMjp37gwdnX/m2Js4cSKcnZ2hoaGBDRs24OrVq0hPT8euXbvQvn17zJ07F+vWrQOPx8PRo0er3UdcXBzy8vKqfUVGRtZ4DhpTWloa9u7di82bN+P58+dwd3eHn58fRKKKu1XnzJmDR48e4dWrV9iyZQu+/vprnDhxAgAwYMAAuLm5wdXVFTo6OggICMD8+fOxbds2bNu2DT179sSECROQl5f3UY6FEEI+NRoqGhjVZhTODD2DLb23wNHIUar89qvbmHN5DvxO+yHiUQSEIqGMIlV81ONaDydmutVZR11FWepnqfcwBrFYXNHr1wjPure2tq53XT09PTg4OMDR0RHx8fFISEiott7z58/RrFkzqa+9BQIBbt26VW391NRUtG7dutqyjIwMqWfR6+jowMDAABkZGWjVqhUAwNTUlCvX0tJCYWH1j9VbtGgRSkpKMGLECBQVFWHixIlYu3YtVFUrniFdOc6z8lj5fD4yMjIwZ84cABU3ZwHAtGnTqt2+vNDS0oKfnx+6desGoOLGr++++w4PHz6EnZ0dnJ2dubq9e/fG7NmzERERgREjRoDH4+G7777Dd999BwAIDg7GkCFDUFRUhD179uD27dvYuHGjVB1CCCGNr/KRsn2s+uDvV39j7729uJJ2BQwVwwmTC5Kx6voq7Ph7B8a2G4uxbcdCX0NftkErGEpc66GzdcN+qZSVeFLvYYxBJBJBRUWl2q/2G6o+23j69CkOHjyIQ4cOgTGGSZMm4e+//5ZKKN9mbm6O/Px8vHnzhhsTWTletDpWVlZSX/2/zcLCAsnJydxyYWEhcnJyYGFhUWfc79LR0cHGjRuxceNGPH36lBu+UJmIvv0Vf15eHgoKCqT2ExAQUOc+7OzskJJS/SD6Hj164MKFCw2Ou6HqO561kpKSUrU35qWlpeH48eP47bffcPLkSTg4OEBNTQ0uLi7YunVrY4VLCCGkDp2MO6GTVyck5SchLCEMZ5+cRZmkDADwWvgaO+/sRGh8KPxa+2FSh0mw5te/U+pTRkMF/oWmTZsGFxcXZGZmYt++fXj8+DGWLVtWY9IKVCSi3bp1w5IlS1BaWoq4uLha78KfMGECfvvtNxw4cADl5eUoKCjAjRs3uLItW7bg0aNHEAqF+Oabb+Dq6sr1tjZEZGQkHj16BIlEAj6fD1VVVanxqocOHcKdO3cgFAoRGBgId3d3WFpaNmgf9+/fl7pb/+1XVFRUje8rLy+HUCiEWCyGWCyGUCjkvtqvjlAohFBY8fVQWVkZhEIhl3xOmzYNZ86cwa1btyASibBu3TrY2NhwY4yPHTuGN2/eQCKR4Nq1a9ixYweGDRtWZR9fffUVNm/eDFVVVbRo0QJ//fUX3rx5gytXrqBly5YNOi+EEEI+XItmLbC8+3JEj4zGDMcZ0FPX48qEYiGOPjyKwacG46vLX+HOqzsyi1NRUOL6L/T5558jMzMTu3btgptb3cMcKoWHhyMuLg6GhoaYOXMmJkyYAHV19WrrCgQCXLx4Ebt27YKRkRHatm3LzZfq7++Pzz77DD4+PjA3N0daWlqN40vr8uTJE/Tv3x+6urpwcHCAt7c3Jk2axJUHBARg1qxZMDIywsOHD3Ho0KH32s/7mD59OjQ1NXHw4EFs3rwZmpqaWLNmDYCKnuC351oFAE1NTWhqVkyd4ujoCE1NTa6n19PTE8HBwRg+fDgMDAxw5coVnD59mhvDvGPHDggEAjRr1gyff/451qxZU2WWhMjISBgYGMDd3R0A4OrqioEDB8LKygqXL1+uc65ZQgghTcdA0wCznWYjemQ0lnZdCivdf4a6MTD8mvorJkVNwsQLE3Ep5RLEErEMo5VfPPYJPmw3PT0dAoEAaWlpUr1zlV9v19Yz+T4ae6jAxzJ37lwUFRXhxx9/lHUo1erVqxfGjh2LGTNmNOl+FLX95FFTXWM1EYvFyMrKgpGRUa0zSxD5RO2nuKjt6iaWiHEl7Qr23d+HO1l3qpQLdAWY3GEy/Fr7Sc0X+1Fik+P2ox5XwomNjcXjx4/BGMO1a9ewf/9+DB8+XNZhEUIIIf86ykrK6GPdBwcGHMAB3wPoa9UXPPzTOZL2Jg1rb6yF93Fv7Ph7B7JLsmUYrfygm7MI5+XLlxg+fDiysrJgamqKZcuWYcCAAbIOixBCCPlXczJ2gpOxE1ILUhGWEIYzT85AKK64JyKvNA+743Zj7729GNxqMCbbTUbLZp/uPQs0VICGCpA6UPs1HhoqQBqC2k9xUdt9mFxhLo4+PIrDiYfxWvi6Snkvy17wt/NHZ5POTfJ3SZ7bj4YKEEIIIYTIEX0NfcxwnIHokdFY3n05bPg2UuVX0q9gys9TMP78eFxMugiRpOYZbf5tKHElhBBCCJFD6srqGNlmJM4MPYPtXtvR2aSzVPm9nHtY9NsiDDw5EGH3w1BUXiSjSD8eSlwJIYQQQuSYEk8JvQS9sK//PoQPCIePjQ+UeP+kcM+LnmPTrU3oG9EXwbeC8aLohQyjbVqUuBJCCCGEKAh7I3ts9tyM88POY2L7iVJTZRWWF2Lf/X3wPeGLb377Bgk51T/mXZFR4koIIYQQomAsdS3xjes3uDTqEuZ1ngdjLWOuTMREuJB0AWMix2Dqz1MRkxYDCZPIMNrGQ4nrJyw5ORk8Ho97DGlj6NWrF3bt2lVt2YoVK6o87YkQQggh74+vxsfUjlNxcfhFrPNYh3bN20mV//XiL3zxvy/gd9oPxx4eg1DUeH/zZYESVyJXkpOTsWLFiibZ9ooVK6CqqgodHR3udfXqVa58x44d6NKlC9TV1euVYPN4PGhra3Pb8vX15cru3r2LDh06wMjICCEhIVLv8/X1RWxsbOMdGCGEkE+eqrIqBrcajGODjuFH7x/Rw6KHVHlyQTJW/7ka3se98X93/g85JTkyivTDyEXiGhERAT8/P1haWkJbWxtOTk4IDQ3F21PM9urVCzwer8orMTFRhpF/WkSipptu4/Lly9i4cSPE4opnM//xxx9YtmxZo+9nxIgRKCws5F49evxzYZubm2Pp0qWYPn16vbcXGxvLbSsqKopbHxgYiHnz5iE+Ph7r1q3DixcVA+XDw8PRpk0bdO7cuaZNEkIIIe+Nx+Ohq1lX7Oy7E2f8zmCE7QioKalx5bmludh1dxe8j3tjxR8r8CzvmQyjbTi5SFxDQkKgpaWF4OBgnDt3Dr6+vpg+fTpWrVolVc/d3R3Xr1+Xen2siczlxbvJ+uLFixEQEADgn6/+9+/fDxsbG/D5fKxevRpJSUnw8PAAn8/HgAEDUFBQILXNgwcPQiAQwMjICEFBQZBIKsbB7Nu3D926dcM333wDY2NjzJ49GwUFBRg8eDCMjY2hr6+PAQMGIDU1td7xl5WVYeLEidDV1YWdnR1iYmIAAL1790arVq0wY8YMHDlyBGfOnMHChQs/8Gw1zPDhwzF06FAYGhp+8LaSkpLg6ekJU1NT2NraIjU1Ffn5+QgODsaaNWsaIVpCCCGkdi31WmKF2wpEj4zGTMeZ0FfX58rKJGU48fgE/M74YdalWbiReQOK8EwquUhcz507h8OHD2PMmDHw8vLC+vXrMW3aNISEhHBJFADo6emhW7duUi8NDY0mj8/Dw0Nq3Ga/fv2kvv718/PD2rVrueWxY8di6dKl3PLUqVOxaNEibnn27NmYOXMmt/x2WWOIiYlBQkICYmJisGrVKkybNg179+5FZmYmcnJysGPHDqn6UVFRSEhIwJ9//okjR45g3759XNmtW7dgaGiIjIwMbNmyBRKJBP7+/khOTkZaWhr4fD5mzZpV79jOnj0LHx8f5Obm4uuvv4afnx9yc3MBgOtFBwAlJaUanwYya9Ys6Onp1fiqTVRUFAwMDNC+fXts2LBB6vfrfXh5ecHExAQDBw7E/fv3ufUdO3bE//73P2RmZiI5ORmtWrVCYGAgAgMDoaur+0H7JIQQQhrCQNMAs5xmIXpkNJZ1X1blgQZXM67iP9H/wejI0Tj39BzKxeWyCbQe5CJxra6Hq1OnTigoKEBR0b9/Mt3GtmzZMmhpaaFTp05o3749vL29YWtrC21tbfj5+eH27dtS9VesWAFdXV20atUKc+fORXh4OFdmbGyMhQsXQlVVFZqamtDT08PIkSOhpaUFHR0dBAYGcr2m9eHo6IhJkyZBRUUF/v7+aNGiBc6fP4/Lly/j8ePH2LlzJ8aOHYtBgwZh8+bN1W5j586dyMvLq/FVk1GjRiEhIQFZWVk4ePAg/vvf/+L777+vd+zvunLlCpKTk/HkyRN06tQJ3t7eXG/25s2bcfbsWQwcOBAhISF4+vQp0tLS0KdPH4wfPx49e/as8gGCEEIIaUoaKhoY1WYUzgw9gx1eO+Bi6iJVnvg6EUHXgjDwzEAceXYEBWUFNWxJdlRkHUBNrl27BgsLC6neqZiYGGhra0MsFqNr165YvXo1evbsWee2CgoKpL4ez8zMBFDxLN7KMZVAxTPpeTxela7yyht4KtdHR0dLLZ8+fVpq+fDhw1LLP/30E0QiEbdcmbBULm/cuLFB3fOMMa7+2/9W/mxiYsL9rKWlJbWsqamJwsJCqfoCgYD72crKChkZGVy5QCCQ2k9xcTHmzZuHn3/+mespLSwshFAohLq6epVY3o3byspKqsza2hrp6emYMGECevXqheTkZDDG4ObmBjc3t0b92qJDhw7cz87OzggKCsKePXswf/78KnG++291x1T5u6eqqorVq1fjwIED+P3339G/f39YWVnh/PnzACp+zzw9PXHgwAGsW7cOHTp0wN69e9G5c2d4eXmhffv2jXaMioAxJnXdNSWxWAyJRPLR9kcaF7Wf4qK2k38e5h7wMPfAg5wHCHsQhuiUaIhZRXu9Kn6Fnx7/hHPp53Bh2AWoKDV9uqisrFyvenKZuF67dg1HjhxBcHAwt87T0xOTJ0+Gra0tnj9/js2bN6Nv376IiYlB9+7da91eSEgIVq5cWWV9Tk4Ol2wB4JKvxr4J6e0/1DV9/V1f2traePPmDRdjZRIuEom4dW//zBiDRCLhliUSCRhjUnWePXsGe3t7ABXjZM3NzSESibiv0d8+H5s2bUJCQgKuXr0KMzMz3L17Fy4uLigvL4eysnKV/b1NIpEgJSVFqiwlJQVDhw7l1llaWmLp0qW1tsHs2bOleoXfVZlQ16WmWCUSidT6+rafkpKS1HmttHXrVgwYMAACgQDx8fGYM2cOlJSUYGdnhzt37sDW1rZe8f4bSCQSlJaWIisr66PtLz8/H0BF+xDFQu2nuKjtFIchDDG/7XxMtJqIM6lnEJkeiWJRMQCgp3FP5ObU72/qhzI1Na1XPblLXNPT0zFmzBj07t0bc+bM4da/m3gOGjQIdnZ2WL16NS5cuFDrNufPn4///Oc/3HJmZiZcXV1hYGAAIyMjbn1JSQl4PB5UVBr3tFT21KmoqHxw4tqpUyeEh4fD2dkZN27cwLlz5+Dn5wcVFRUu7rd/5vF4UFJS4pYrx46+XWfdunUIDQ1FVlYWduzYgcDAQKioqEjVrVRUVAQtLS0YGhrizZs3+O6776T2+e7+3qakpIS4uDgcO3YMo0ePxuHDh/Hs2TMMHjy4Qed89+7d2L17d4PP3enTp9GzZ080b94ccXFx2LBhA6ZMmcLtuzLpfDthV1ZWljqvle13//59lJaWwsHBAWVlZdi4cSNKSkrg4eEhdSwZGRk4ceIEYmJioKKighYtWiAmJgY9evTA7du3sXDhwkb/fZNnSkpK0NDQkLrumlLlBw5DQ8N6f5on8oPaT3FR2ykeIxjBzsoOc8vn4uSjkziceBhTHKfAiP9x/r+uL7n6i5mXlwdfX18YGBjgxIkTtX5K09bWxsCBA3H8+PE6t8vn88Hn86usV1ZWlrqgKpOSD00uq/P2FF4fYtu2bfD394e+vj68vb0xbtw4FBcXS2373f28W/buuv79+8POzg5CoRDTpk3D1KlTq30PAMybNw/jx4+HsbExzM3NsWDBApw4caLW/b8dx5AhQxAVFYUZM2ZAIBDg1KlTMDAw+KBzUl8RERGYPn06SkpKYGZmhilTpuDrr7/mYl27dq3UB6SIiAj4+/tj79694PF44PP5iIqKQo8ePZCVlYWZM2ciLS0Nmpqa6NKlC37++Wfo6+tL7XPevHnYtGkT1NQqpiIJCgrCyJEjsWfPHkyZMgUuLtLjiz4FPB7vo/4hU1JSqnKtE8VB7ae4qO0UE1+Zj0l2k+Bj5ANjvrHctR+PycncByUlJejXrx9SU1Nx/fp1WFhY1Pme2bNn4/jx43j58mWD9pWeng6BQIC0tDRYWlpy65OTkwGg0afYqvxqvjF6XMnHR+3XeJrqGquJWCxGVlYWjIyM5O4/X1I3aj/FRW2n2OS5/eSix1UkEmH06NF48OABrl69Wq+ktaioCJGRkZ9kjxUhhBBCyKdILhLXWbNmITIyEsHBwSgoKMCff/7JlXXq1Ak3b97Epk2bMGzYMNjY2OD58+cIDg7GixcvEBERIcPICSGEEELIxyIXiWvl9FILFiyoUpaUlAQzMzOUlZUhKCgIOTk50NbWhpubG3bt2gVXV9ePHS4hhBBCCJEBuUhcK8e91ebixYtNHwghhBBCCJFbNLnaW1RUVFBWVgahUCjrUAj51xEKhSgrK/ukpv8ihBDSuOgvyFv09fVRXFyMpKQkqKurN+qkyRKJhCZhVmDUfh+m8sEDysrKVaYMI4QQQuqLEte3aGtro2XLlsjOzkZZWRk3Ef2HYoyhtLQUGhoaNJ2SAqL2+3AqKircgyuox5UQQsj7or8g71BRUan3Y8fqS57nQyN1o/YjhBBC5AN990kIIYQQQhQCJa6EEEIIIUQhUOJKCCGEEEIUwic5xlUkEgEAMjMzP8r+xGIxcnJyuLuqiWKh9lNc1HaKjdpPcVHbKTZZtZ+pqWmdN/B+kolrVlYWANBTtwghhBBC5ERaWhosLS1rrcNjjLGPFI/cEAqFiI+Ph5GR0UeZmiczMxOurq64efMmzMzMmnx/pHFR+ykuajvFRu2nuKjtFJus2o96XGugoaEBFxeXj75fMzOzOj9JEPlF7ae4qO0UG7Wf4qK2U2zy2H50cxYhhBBCCFEIlLgSQgghhBCFQInrR8Dn87F8+XLw+XxZh0LeA7Wf4qK2U2zUfoqL2k6xyXP7fZI3ZxFCCCGEEMVDPa6EEEIIIUQhUOJKCCGEEEIUAiWuhBBCCCFEIVDiSgghhBBCFAIlroQQQgghRCFQ4tqEEhMT0a9fP2hra8PU1BRff/01ysrKZB0WqYd9+/aBx+NVeS1evFjWoZF3PHnyBDNmzICTkxNUVFTQsWPHauv99NNPaNOmDTQ0NODo6IjIyMiPHCmpTn3ar1evXtVej4mJiTKImFSKiIiAn58fLC0toa2tDScnJ4SGhuLdyYro2pNP9Wk/ebz2PslHvn4Mubm58PLygq2tLU6ePImMjAzMnz8fxcXF2LFjh6zDI/V08eJFNGvWjFu2sLCQYTSkOvfv38f58+fRtWtXSCQSSCSSKnWOHDmC6dOnY8mSJfDy8sLRo0cxbNgwXL16Fd26dZNB1KRSfdoPANzd3bF582apdTY2Nh8hQlKTkJAQ2NjYIDg4GEZGRvjll18wffp0pKWlYfny5QDo2pNn9Wk/QA6vPUaaxLp165i2tjbLycnh1u3evZspKyuzjIwMGUZG6mPv3r0MAMvKypJ1KKQOYrGY+9nf35/Z2dlVqdOmTRs2btw4qXXdu3dnvr6+TR4fqV192s/T05MNHDjwY4ZF6qG6/x+nT5/O+Hw+16507cmv+rSfPF57NFSgiURFRaFv375o3rw5t2706NGQSCSIjo6WYWSE/LsoKdX+39izZ8/w6NEjjB49Wmr92LFj8euvv6K0tLQpwyN1qKv9iPwyNDSssq5Tp04oKChAUVERXXtyrq72k1f0P0YTSUxMRLt27aTW6enpwczMjMZlKRA7OzsoKyujZcuWWL9+PcRisaxDIg1Ueb29ez22b98eZWVlSEpKkkVYpIFiYmKgra0NDQ0NeHp64rfffpN1SKQa165dg4WFBXR1denaU0Bvt18lebv2KHFtIrm5udDT06uyXl9fH69fv/74AZEGMTMzw8qVKxEWFoaoqCgMGDAAS5cuxdy5c2UdGmmg3NxcAKhyPerr6wMAXY8KwNPTE1u3bsXFixexf/9+FBcXo2/fvrh+/bqsQyNvuXbtGo4cOYKFCxcCoGtP0bzbfoB8Xnt0cxYh1fDx8YGPjw+37O3tDU1NTXz//fdYsmQJzMzMZBgdIZ+WlStXSi0PGjQIdnZ2WL16NS5cuCCjqMjb0tPTMWbMGPTu3Rtz5syRdTikgWpqP3m89qjHtYno6+sjPz+/yvrc3Fypca9EcYwePRpisRh37tyRdSikASp7d969Hit7g+h6VDza2toYOHAgYmNjZR0KAZCXlwdfX18YGBjgxIkT3LhluvYUQ03tVx15uPYocW0i7dq1qzKWNT8/H5mZmVXG+xBCmk7l9fbu9ZiYmAg1NTW0bNlSFmER8q9QUlKCQYMGIT8/H1FRUVLTB9K1J/9qaz95RYlrE/H19cWlS5eQl5fHrYuIiICSkhK8vb1lFxh5b0eOHIGysjI6deok61BIA7Rs2RJt2rRBRESE1PqjR4+iT58+UFNTk1Fk5H0VFRUhMjISLi4usg7lkyYSiTB69Gg8ePAAFy9erDLPNV178q2u9quOPFx7NMa1icyYMQPbt2/H0KFDERQUhIyMDCxatAgzZsyAubm5rMMjdfDx8YGXlxfs7e0BAGfPnsWePXswd+5cmJqayjg68rbi4mJurFVKSgoKCgpw/PhxABU3FhgZGWHFihWYMGECWrVqhd69e+Po0aO4ceOGzO+OJXW3X2JiIjZt2oRhw4bBxsYGz58/R3BwMF68eFElISIf16xZsxAZGYng4GAUFBTgzz//5Mo6deoEdXV1uvbkWF3td/PmTfm89mQ9key/WUJCAuvTpw/T1NRkxsbGbOHChay0tFTWYZF6mDNnDrO1tWWamppMXV2d2dvbs61btzKJRCLr0Mg7kpKSGIBqX5cvX+bq/fjjj6x169ZMTU2N2dvbs3PnzskuaMKpq/0eP37MfHx8mKmpKVNVVWV6enpswIAB7MaNG7IO/ZNnbW1dY9slJSVx9ejak091tZ+8Xns8xt55qDAhhBBCCCFyiMa4EkIIIYQQhUCJKyGEEEIIUQiUuBJCCCGEEIVAiSshhBBCCFEIlLgSQgghhBCFQIkrIYQQQghRCJS4EkIIIYQQhUCJKyGEEEIIUQiUuBJCSCM6ffo0du7cWe/6QqEQAoEA58+fb/C+SkpK0LlzZ1hbWyM6OhpffPEFdu3a1eDt1GXt2rXo169fo2+XEEIaihJXQghpRA1NXH/44Qfo6+tj4MCBDd7XtWvXoK6ujuXLl+Ozzz5DVFQU/Pz8GrydusyePRs3b97E5cuXG33bhBDSEPTIV0IIaUQBAQG4desW7t27V2ddxhhatmyJOXPmYN68eR8huvc3depUvH79GqdPn5Z1KISQTxj1uBJCSCMJCAjA/v37cf/+ffB4PPB4PAQEBNRYPyYmBsnJyRg5cqTU+rCwMHh4eKB58+bQ19dHr169cPPmTak6K1asgI6ODuLj4+Hh4QEtLS107NgRP//8s1Q9iUSCNWvWwMbGBurq6mjXrh12794tVSc9PR2jR4+GiYkJNDQ00KJFiyqJ9KhRo3D+/HlkZ2e/x5khhJDGoSLrAAgh5N/i22+/RVZWFhITE3Ho0CEAgJGRUY31L126BIFAAIFAILU+OTkZkydPRqtWrVBWVobDhw+jZ8+eiIuLQ5s2bbh65eXlmDBhAubMmYNvv/0WGzZswIgRI5CSkgIDAwMAwKJFi7B161YsXboUbm5uiIyMxIwZM1BeXo4vvvgCADB58mQ8f/4c27Ztg4mJCVJTU3Hr1i2pmLp37w6xWIwrV65USbQJIeRjoaEChBDSiBoyVMDHxweqqqqIjIyssY5EIoFEIkHHjh0xfPhwrFu3DkBFj+vKlStx/vx5DBgwAEBFwtuiRQscOHAAEydORHZ2NszNzbFgwQKsX7+e2+b48eNx6dIlZGZmQllZGTo6Oli/fj2+/PLLWuO1sbHBqFGjsGnTpvqcCkIIaXQ0VIAQQmQkMzOz2h7ZBw8eYNiwYTAxMYGysjJUVVXx8OFDPHr0SKqekpIS+vbtyy3b2NhAU1MT6enpAIAbN26gvLwco0aNknrfmDFjkJWVxW3P2dkZmzdvxg8//IAnT57UGK+hoSEyMzPf+3gJIeRDUeJKCCEyIhQKoa6uLrXuzZs38Pb2RkpKCkJCQnD16lX89ddfcHR0hFAolKqrqakJNTU1qXVqampcvdzcXACAiYmJVJ3K5devXwMAjh49ij59+mDJkiWwtbVFu3btcPLkySrxqquro6Sk5AOOmBBCPgwlroQQIiPNmzdHXl6e1Lrr168jPT0de/fuxYQJE+Dh4YEuXbogPz//vbYPAK9evZJa//LlS6lyMzMzhIaGIjs7Gzdv3kTbtm0xZswYPHv2TOp9eXl53NhZQgiRBUpcCSGkEb3d41mXtm3bIikpSWpdZY/m2z2pf/zxB5KTkxsci6urK1RVVRERESG1/tixYzA2Npa60QuoGHrg4uKCNWvWQCQSSQ0bkEgkSE1NRdu2bRscByGENBaaVYAQQhpR+/btERoaisOHD8PW1haGhoawsbGptq67uzuOHTuG8vJyqKqqAgC6desGHR0dzJ49G4sXL0ZGRgaWL18OCwuLBsdiaGiIL7/8Eps2bYKGhga6deuGCxcuIDw8HNu3b4eysjLy8/Ph4+ODSZMmoW3btigrK8P27duhp6cHZ2dnblsPHz5EYWEhevTo8V7nhRBCGgP1uBJCSCOaNm0aRo0ahS+//BIuLi5YsWJFjXX9/PwgEolw5coVbp2JiQkiIiLw6tUr+Pn5YcuWLdi9ezdat279XvFs2rQJy5Ytw08//YRBgwbhwoUL2LVrFzcVloaGBuzt7bF9+3YMGTIEkyZNgkQiQXR0NAwNDbntREVFwdraGi4uLu8VByGENAaaDosQQmRoxIgRaNasGUJDQ2UdSq1cXFwwePBgLFu2TNahEEI+YZS4EkKIDN25cwfu7u549uxZlbv/5cVvv/2GoUOH4tmzZ9DT05N1OISQTxgNFSCEEBlycnLCli1bkJaWJutQalRQUICwsDBKWgkhMkc9roQQQgghRCFQjyshhBBCCFEIlLgSQgghhBCFQIkrIYQQQghRCJS4EkIIIYQQhUCJKyGEEEIIUQiUuBJCCCGEEIVAiSshhBBCCFEIlLgSQgghhBCFQIkrIYQQQghRCP8PyX0kZ9AxIqYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 792x462 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# (c) superávit que estabiliza la deuda -> root-finding sobre sp\n",
    "sp_star = brentq(lambda s: theta(g)*b0 - s - b0, -1.0, 1.0)\n",
    "chk(\"P10_spstar\", sp_star, 0.011650, tol=1e-5)\n",
    "print(f\"sp* = (θ−1)·b₀ = {sp_star:.4%} del PIB   (ajuste de {sp_star-sp:+.4%} respecto del 1% actual)\")\n",
    "print(f\"Proporcional a la deuda heredada: con b₀ = 120% haría falta {2*sp_star:.4%}.\")\n",
    "\n",
    "# (d) crecimiento alto: g' = 6%\n",
    "g2 = 0.06\n",
    "b_alto = senda(b0, g2)\n",
    "chk(\"P10_theta2\", theta(g2), 0.990566, tol=1e-5); chk(\"P10_b5_alto\", b_alto[5], 0.523, tol=2e-3)\n",
    "print(f\"\\ng' = {g2:.0%}  ->  θ' = {theta(g2):.6f} < 1  ->  punto fijo ATRACTOR ESTABLE\")\n",
    "print(f\"Con el mismo sp = 1%, la deuda cae de {b0:.1%} a {b_alto[5]:.1%} en cinco años.\")\n",
    "print(f\"Incluso con sp = 0 la deuda converge a 0% ({senda(b0, g2, 0.0, 100)[-1]:.2%} tras \"\n",
    "      f\"100 años, {senda(b0, g2, 0.0, 200)[-1]:.2%} tras 200): el crecimiento la licúa sin ajuste fiscal.\")\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "T = 25\n",
    "ax.plot(b_base[:T+1]*100, lw=2, color=\"tab:red\", label=f\"r > g  (g = {g:.0%}),  θ = {th:.4f}\")\n",
    "ax.plot(b_alto[:T+1]*100, lw=2, color=\"tab:green\", label=f\"r < g' (g' = {g2:.0%}), θ = {theta(g2):.4f}\")\n",
    "ax.plot(senda(b0, g, sp_star)[:T+1]*100, lw=1.6, ls=\"--\", color=\"tab:blue\",\n",
    "        label=f\"r > g con sp* = {sp_star:.3%}\")\n",
    "ax.axhline(bs*100, color=\"k\", ls=\":\", lw=1, label=f\"umbral b* = {bs:.1%}\")\n",
    "ax.set(xlabel=\"t (años)\", ylabel=\"deuda / PIB  (%)\",\n",
    "       title=\"Sostenibilidad: lo que decide es el signo de r − g\")\n",
    "ax.legend(fontsize=8); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42d24243",
   "metadata": {},
   "source": [
    "> **Lectura económica.** La sostenibilidad fiscal no depende del nivel de deuda *per se*\n",
    "> sino del **signo de $r-g$**. Con $r<g$ un país puede correr déficits primarios permanentes\n",
    "> sin que la deuda explote; con $r>g$ ni siquiera un superávit sostenido garantiza\n",
    "> estabilidad si es menor a $sp^*$. El punto delicado: $r$ **no es exógeno** — si los\n",
    "> mercados dudan de la solvencia el spread sube, $r$ sube, y una trayectoria que era\n",
    "> sostenible deja de serlo. Ese es el mecanismo de equilibrios múltiples y profecías\n",
    "> autocumplidas detrás de las crisis de deuda soberana."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9d8f6c8",
   "metadata": {},
   "source": [
    "---\n",
    "## Verificación final\n",
    "\n",
    "Se contrastan todos los resultados calculados aquí contra los valores publicados en\n",
    "`cap07_problemas_numericos.html`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "830e9707",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-04T12:30:25.847057Z",
     "iopub.status.busy": "2026-08-04T12:30:25.846860Z",
     "iopub.status.idle": "2026-08-04T12:30:25.860738Z",
     "shell.execute_reply": "2026-08-04T12:30:25.859521Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "41 de 41 verificaciones coinciden con el HTML.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>calculado (Python)</th>\n",
       "      <th>publicado (HTML)</th>\n",
       "      <th>coincide</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>magnitud</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>P01_W</th>\n",
       "      <td>220.0000</td>\n",
       "      <td>220.0000</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P01_c2</th>\n",
       "      <td>94.5000</td>\n",
       "      <td>94.5000</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P01_dW</th>\n",
       "      <td>-5.4545</td>\n",
       "      <td>-5.4545</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P02_c1</th>\n",
       "      <td>112.8205</td>\n",
       "      <td>112.8200</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P02_c2</th>\n",
       "      <td>112.5385</td>\n",
       "      <td>112.5400</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P03_ds_sigma05</th>\n",
       "      <td>3.0141</td>\n",
       "      <td>3.0100</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P03_ds_sigma1</th>\n",
       "      <td>0.4662</td>\n",
       "      <td>0.4700</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P03_ds_sigma2</th>\n",
       "      <td>-0.8069</td>\n",
       "      <td>-0.8100</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P04_U0</th>\n",
       "      <td>9.2129</td>\n",
       "      <td>9.2129</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P04_c1h</th>\n",
       "      <td>110.2924</td>\n",
       "      <td>110.2900</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P04_Wh</th>\n",
       "      <td>215.0701</td>\n",
       "      <td>215.0700</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P04_sust</th>\n",
       "      <td>-2.5282</td>\n",
       "      <td>-2.5300</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P04_ingr</th>\n",
       "      <td>2.0620</td>\n",
       "      <td>2.0600</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P05_W0</th>\n",
       "      <td>2,600.0000</td>\n",
       "      <td>2,600.0000</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P05_c</th>\n",
       "      <td>100.0000</td>\n",
       "      <td>100.0000</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P05_dc_trans</th>\n",
       "      <td>3.8462</td>\n",
       "      <td>3.8500</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P05_dc_perm</th>\n",
       "      <td>10.0000</td>\n",
       "      <td>10.0000</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P05_dc_antic</th>\n",
       "      <td>3.1613</td>\n",
       "      <td>3.1600</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P06_T2new</th>\n",
       "      <td>41.0000</td>\n",
       "      <td>41.0000</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P06_W</th>\n",
       "      <td>160.9524</td>\n",
       "      <td>160.9500</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P06_c1</th>\n",
       "      <td>82.5397</td>\n",
       "      <td>82.5400</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P07_c1</th>\n",
       "      <td>100.0000</td>\n",
       "      <td>100.0000</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P07_mu</th>\n",
       "      <td>0.0021</td>\n",
       "      <td>0.0021</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P07_dU</th>\n",
       "      <td>0.0133</td>\n",
       "      <td>0.0133</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P07_lambda</th>\n",
       "      <td>1.0068</td>\n",
       "      <td>1.0068</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P07_pmc</th>\n",
       "      <td>1.0000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P08_K05</th>\n",
       "      <td>72.2128</td>\n",
       "      <td>72.2100</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P08_K10</th>\n",
       "      <td>47.8774</td>\n",
       "      <td>47.8800</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P08_elast</th>\n",
       "      <td>-1.4286</td>\n",
       "      <td>-1.4286</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P08_Ineta</th>\n",
       "      <td>12.2128</td>\n",
       "      <td>12.2100</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P08_Ibruta</th>\n",
       "      <td>18.2128</td>\n",
       "      <td>18.2100</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P09_q60</th>\n",
       "      <td>1.1385</td>\n",
       "      <td>1.1390</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P09_I60</th>\n",
       "      <td>1.6617</td>\n",
       "      <td>1.6600</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P09_q100</th>\n",
       "      <td>0.7962</td>\n",
       "      <td>0.7960</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P09_I100</th>\n",
       "      <td>-4.0757</td>\n",
       "      <td>-4.0800</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P10_theta</th>\n",
       "      <td>1.0194</td>\n",
       "      <td>1.0194</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P10_bstar</th>\n",
       "      <td>0.5150</td>\n",
       "      <td>0.5150</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P10_b5</th>\n",
       "      <td>0.6086</td>\n",
       "      <td>0.6086</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P10_spstar</th>\n",
       "      <td>0.0117</td>\n",
       "      <td>0.0117</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P10_theta2</th>\n",
       "      <td>0.9906</td>\n",
       "      <td>0.9906</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>P10_b5_alto</th>\n",
       "      <td>0.5232</td>\n",
       "      <td>0.5230</td>\n",
       "      <td>✓</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                calculado (Python)  publicado (HTML) coincide\n",
       "magnitud                                                     \n",
       "P01_W                     220.0000          220.0000        ✓\n",
       "P01_c2                     94.5000           94.5000        ✓\n",
       "P01_dW                     -5.4545           -5.4545        ✓\n",
       "P02_c1                    112.8205          112.8200        ✓\n",
       "P02_c2                    112.5385          112.5400        ✓\n",
       "P03_ds_sigma05              3.0141            3.0100        ✓\n",
       "P03_ds_sigma1               0.4662            0.4700        ✓\n",
       "P03_ds_sigma2              -0.8069           -0.8100        ✓\n",
       "P04_U0                      9.2129            9.2129        ✓\n",
       "P04_c1h                   110.2924          110.2900        ✓\n",
       "P04_Wh                    215.0701          215.0700        ✓\n",
       "P04_sust                   -2.5282           -2.5300        ✓\n",
       "P04_ingr                    2.0620            2.0600        ✓\n",
       "P05_W0                  2,600.0000        2,600.0000        ✓\n",
       "P05_c                     100.0000          100.0000        ✓\n",
       "P05_dc_trans                3.8462            3.8500        ✓\n",
       "P05_dc_perm                10.0000           10.0000        ✓\n",
       "P05_dc_antic                3.1613            3.1600        ✓\n",
       "P06_T2new                  41.0000           41.0000        ✓\n",
       "P06_W                     160.9524          160.9500        ✓\n",
       "P06_c1                     82.5397           82.5400        ✓\n",
       "P07_c1                    100.0000          100.0000        ✓\n",
       "P07_mu                      0.0021            0.0021        ✓\n",
       "P07_dU                      0.0133            0.0133        ✓\n",
       "P07_lambda                  1.0068            1.0068        ✓\n",
       "P07_pmc                     1.0000            1.0000        ✓\n",
       "P08_K05                    72.2128           72.2100        ✓\n",
       "P08_K10                    47.8774           47.8800        ✓\n",
       "P08_elast                  -1.4286           -1.4286        ✓\n",
       "P08_Ineta                  12.2128           12.2100        ✓\n",
       "P08_Ibruta                 18.2128           18.2100        ✓\n",
       "P09_q60                     1.1385            1.1390        ✓\n",
       "P09_I60                     1.6617            1.6600        ✓\n",
       "P09_q100                    0.7962            0.7960        ✓\n",
       "P09_I100                   -4.0757           -4.0800        ✓\n",
       "P10_theta                   1.0194            1.0194        ✓\n",
       "P10_bstar                   0.5150            0.5150        ✓\n",
       "P10_b5                      0.6086            0.6086        ✓\n",
       "P10_spstar                  0.0117            0.0117        ✓\n",
       "P10_theta2                  0.9906            0.9906        ✓\n",
       "P10_b5_alto                 0.5232            0.5230        ✓"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ver = pd.DataFrame(\n",
    "    [(k, v[0], v[1], \"✓\" if v[2] else \"✗\") for k, v in REF.items()],\n",
    "    columns=[\"magnitud\", \"calculado (Python)\", \"publicado (HTML)\", \"coincide\"]\n",
    ").set_index(\"magnitud\")\n",
    "\n",
    "n_ok = (ver[\"coincide\"] == \"✓\").sum()\n",
    "print(f\"{n_ok} de {len(ver)} verificaciones coinciden con el HTML.\")\n",
    "assert n_ok == len(ver), ver[ver[\"coincide\"] == \"✗\"]\n",
    "ver"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "16099712",
   "metadata": {},
   "source": [
    "---\n",
    "**Métodos de `scipy.optimize` usados en este notebook**\n",
    "\n",
    "| Problema | Método | Para qué |\n",
    "|---|---|---|\n",
    "| P01, P06, P09, P10 | `brentq` | invertir $W(r)$; despejar $T_2'$; localizar $q=1$; hallar $sp^*$ |\n",
    "| P02, P03, P06, P08 | `minimize_scalar` (`bounded`) | maximizar utilidad / beneficio en una variable |\n",
    "| P03 | `brentq` | encontrar el $\\sigma^*$ donde $\\partial s/\\partial r$ cambia de signo |\n",
    "| P04 | `minimize` + `NonlinearConstraint` (SLSQP) | **minimizar el gasto** sujeto a $U\\ge U_0$ (canasta compensada de Hicks) |\n",
    "| P05 | `minimize` con restricción de igualdad (SLSQP) | maximizar $\\sum\\beta^t\\ln c_t$ sujeto a la RPI de $T+1$ períodos |\n",
    "| P07 | `minimize` con restricción de desigualdad (SLSQP) | solución de esquina con $s_1\\ge0$ y su multiplicador |\n",
    "| P09 | `minimize_scalar` (`bounded`) | maximizar $qI-I-\\tfrac{\\phi}{2}(I/K)^2K$: recupera la regla de inversión |"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}