Koch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Curva de Koch\n",
    "\n",
    "La curva de Koch es un fractal que se forma de la siguiente manera. Primero, dibujamos una linea de longitud 1. Luego, separamos en tres partes, y al segmento del medio, lo dividimos al medio una vez mas, levantando ambos extremos hasta formar un triangulo equilatero. Obtenemos una poligonal de 4 lados. Luego, repetimos este proceso.\n",
    "\n",
    "\n",
    "\n",
    "Vamos a comenzar, importando librerias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import matplotlib.pyplot as pl\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Creemos ahora una funcion que cree el fractal. Para asegurarnos de que el triangulo se expande en la direccion correcta, crearemos un centro de la figura desde el cual el fractal siempre se expandira en la direccion contraria"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "pi = np.pi\n",
    "import math\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dist_lin(linea):\n",
    "    x_lin=linea[0]\n",
    "    y_lin=linea[1]\n",
    "    dist = math.sqrt(math.pow((x_lin[1]-x_lin[0]),2) + math.pow(y_lin[1]-y_lin[0],2))\n",
    "    return dist\n",
    "\n",
    "def dist_lin_x(linea):\n",
    "    return linea[2][1]-linea[2][0]\n",
    "def dist_lin_y(linea):\n",
    "    return linea[3][1]-linea[3][0]\n",
    "\n",
    "class Linea:\n",
    "    def __init__(self, f_angle, s_angle, x_s,y_s):\n",
    "        self.f_angle = f_angle\n",
    "        self.s_angle = s_angle\n",
    "        self.x_s = x_s # x points\n",
    "        self.y_s = y_s # y points\n",
    "    def dist_x(self):\n",
    "        return (self.x_s[1] - self.x_s[0])/3\n",
    "    def dist_y(self):\n",
    "        return (self.y_s[1] - self.y_s[0])/3\n",
    "    def dist(self):\n",
    "        return (math.sqrt(math.pow(self.dist_x()*3,2) + math.pow(self.dist_y()*3,2)))/3\n",
    "    def dividir(self):\n",
    "        if self.f_angle == 2*pi/3 and self.s_angle == 0:\n",
    "            prim_linea = Linea(self.f_angle, self.s_angle, [self.x_s[0], self.x_s[0]+self.dist_x()],[self.y_s[0], self.y_s[0]+self.dist_y()])\n",
    "            sec_linea = Linea(self.f_angle + pi/3, self.s_angle + pi/3, [prim_linea.x_s[1], prim_linea.x_s[1]+self.dist()*math.cos(self.f_angle)],[prim_linea.y_s[1], prim_linea.y_s[1]+self.dist()*math.sin(self.f_angle)])\n",
    "            ter_linea = Linea(self.s_angle + pi/3, self.s_angle - pi/3,[sec_linea.x_s[1],sec_linea.x_s[1] + self.dist()*math.cos(self.s_angle)],[sec_linea.y_s[1], sec_linea.y_s[1]+ self.dist()*math.sin(self.s_angle)])\n",
    "            cuar_linea = Linea(self.f_angle, self.s_angle, [ter_linea.x_s[1], self.x_s[1]], [ter_linea.y_s[1],self.y_s[1]])\n",
    "            return [prim_linea,sec_linea,ter_linea,cuar_linea]\n",
    "        if self.f_angle == 0 and self.s_angle == 4*pi/3:\n",
    "            prim_linea = Linea(self.f_angle, self.s_angle, [self.x_s[0], self.x_s[0]+self.dist_x()],[self.y_s[0], self.y_s[0]+self.dist_y()])\n",
    "            sec_linea = Linea(self.f_angle + pi/3, self.f_angle - pi/3, [prim_linea.x_s[1], prim_linea.x_s[1]+self.dist()*math.cos(self.f_angle)],[prim_linea.y_s[1], prim_linea.y_s[1]+self.dist()*math.sin(self.f_angle)])\n",
    "            ter_linea = Linea(self.s_angle + pi/3, self.s_angle - pi/3,[sec_linea.x_s[1],sec_linea.x_s[1] + self.dist()*math.cos(self.s_angle)],[sec_linea.y_s[1], sec_linea.y_s[1]+ self.dist()*math.sin(self.s_angle)])\n",
    "            cuar_linea = Linea(self.f_angle, self.s_angle, [ter_linea.x_s[1], self.x_s[1]], [ter_linea.y_s[1],self.y_s[1]])\n",
    "            return [prim_linea,sec_linea,ter_linea,cuar_linea]\n",
    "        if self.f_angle == 5*pi/3 and self.s_angle == pi/3:\n",
    "            prim_linea = Linea(self.f_angle, self.s_angle, [self.x_s[0], self.x_s[0]+self.dist_x()],[self.y_s[0], self.y_s[0]+self.dist_y()])\n",
    "            sec_linea = Linea(self.f_angle - pi/3, self.f_angle + pi/3, [prim_linea.x_s[1], prim_linea.x_s[1]+self.dist()*math.cos(self.f_angle)],[prim_linea.y_s[1], prim_linea.y_s[1]+self.dist()*math.sin(self.f_angle)])\n",
    "            ter_linea = Linea(self.s_angle - pi/3, self.s_angle + pi/3,[sec_linea.x_s[1],sec_linea.x_s[1] + self.dist()*math.cos(self.s_angle)],[sec_linea.y_s[1], sec_linea.y_s[1]+ self.dist()*math.sin(self.s_angle)])\n",
    "            cuar_linea = Linea(self.f_angle, self.s_angle, [ter_linea.x_s[1], self.x_s[1]], [ter_linea.y_s[1],self.y_s[1]])\n",
    "            return [prim_linea,sec_linea,ter_linea,cuar_linea]\n",
    "        if self.f_angle == pi/3 and self.s_angle == 5*pi/3:\n",
    "            prim_linea = Linea(self.f_angle, self.s_angle, [self.x_s[0], self.x_s[0]+self.dist_x()],[self.y_s[0], self.y_s[0]+self.dist_y()])\n",
    "            sec_linea = Linea(self.f_angle + pi/3, self.f_angle - pi/3, [prim_linea.x_s[1], prim_linea.x_s[1]+self.dist()*math.cos(self.f_angle)],[prim_linea.y_s[1], prim_linea.y_s[1]+self.dist()*math.sin(self.f_angle)])\n",
    "            ter_linea = Linea(self.s_angle+pi/3,self.s_angle -pi/3,[sec_linea.x_s[1],sec_linea.x_s[1] + self.dist()*math.cos(self.s_angle)],[sec_linea.y_s[1], sec_linea.y_s[1]+ self.dist()*math.sin(self.s_angle)])\n",
    "            cuar_linea = Linea(self.f_angle, self.s_angle, [ter_linea.x_s[1], self.x_s[1]], [ter_linea.y_s[1],self.y_s[1]])\n",
    "            return [prim_linea,sec_linea,ter_linea,cuar_linea]\n",
    "        prim_linea = Linea(self.f_angle, self.s_angle, [self.x_s[0], self.x_s[0]+self.dist_x()],[self.y_s[0], self.y_s[0]+self.dist_y()])\n",
    "        sec_linea = Linea(self.f_angle + pi/3, self.f_angle - pi/3, [prim_linea.x_s[1], prim_linea.x_s[1]+self.dist()*math.cos(self.f_angle)],[prim_linea.y_s[1], prim_linea.y_s[1]+self.dist()*math.sin(self.f_angle)])\n",
    "        ter_linea = Linea(self.s_angle - pi/3, self.s_angle + pi/3,[sec_linea.x_s[1],sec_linea.x_s[1] + self.dist()*math.cos(self.s_angle)],[sec_linea.y_s[1], sec_linea.y_s[1]+ self.dist()*math.sin(self.s_angle)])\n",
    "        cuar_linea = Linea(self.f_angle, self.s_angle, [ter_linea.x_s[1], self.x_s[1]], [ter_linea.y_s[1],self.y_s[1]])\n",
    "        return [prim_linea,sec_linea,ter_linea,cuar_linea]\n",
    "                                                                                         "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "primLinea = Linea(5*pi/3, pi/3, [1,2], [1,1])\n",
    "secLinea = Linea(2*pi/3, 0, [1,1.5], [1, 1+math.sqrt(0.75)])\n",
    "terLinea = Linea(0,4*pi/3, [1.5,2],[1+math.sqrt(0.75), 1])\n",
    "\n",
    "to_graph = []\n",
    "lineas = [primLinea, secLinea, terLinea]\n",
    "for item in lineas:\n",
    "        for linea in item.dividir():\n",
    "            to_graph.append(linea)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "depth=5;\n",
    "conjunto_lineas=[lineas]\n",
    "conjunto_iteracion =[]\n",
    "for i in range(depth): ##depth\n",
    "    for linea in conjunto_lineas[-1]: ##\n",
    "        for elem in linea.dividir():\n",
    "            conjunto_iteracion.append(elem)\n",
    "    conjunto_lineas.append(conjunto_iteracion)\n",
    "    conjunto_iteracion = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
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SHzLCc3VRaxE5KipbImKb8pJdjP/+arZtXwTAnG5fElT6E5v2rOPqfv9kQXM36eu/ZMP02WT87X/nuypauZVlj31NeX4BNR4Hy91XEdyllnEjfBn+wMX4Be5fkg7H11cOJeXqf5N8ynZCmncgtHlX6uvruXHSSh6YvATLstizbR1F2XkM/m4W/76iB6t9PmXIp1+TPCGGpU/976LWVeX5TPrhZtasm/jHNpKIHPe0G1FEGlxNRT5r3pxCZmkunw7uydol47l6g5tL6kvZODSI8nIPK8p9SazaRqajks5R6eTU1zLpi+WUZmwiPO0jyrq4mPbTKvpHhlARl86zCS1p45uNM8T3qHMFOB2U5G3gR78BuJw1FG3ZRsQ3H7Izv5j4rPU8nz+cyC1uWlbVsCN8PbuKFhNWV4ax+hPbez2L4tazcfoKgsvq2TEzn3HtTqLnkkWkfu9mVPc2pA5Nb8CtKCLHC5UtEWlQ13y5jJDcv9K5dgi+zhTS8rYSuPsLvlnuImFoS2a36E4H/2CuTYqm17n38a5nKWUZ+ZR0nsFT2QmcWV1DH6eHrwJHUVnjwPetl7gl/E6yd5fRr83gP3zMVK9e13HpD6fRujifb8rPIqCqhpMq1tN59QWElabwVfsEKgPWM9SvgqH97mVIrztZ+tJEtgd9zovZN3BK7fu0XbqRytCBpNUXkhT0CT6Ly/lp7UqKF2yk659H4fBzNtDWFJHjgXYjikiD2pWfxYjSeqYHZ1BV4GZIlysIro0gpHIb0SvP4MqMNtx76j0AJARH8dAV3zPo/gtxRCbh38bJ9y03MauomruaDaRPfTltXD7sqLSIKven/dX9GyRjv2teJqS2goj6IjqtHsWpntsJaNuSTaXLuDVsCwP7r+LcW18AwPj40uu+Cxh54af0CAnlpCoIM3HE1fXgjOow/EwCcX2WkXFeFZnNx2Cc+rUqIr9mvHXAZ69evayMjAyvrFtE7DN52tV8QTv6ZARy+VWXEpmcAK46PG4Ly+mLAzA++xcSl8sFDicutwenw4Ov05c6jwdTX43TNxDLAmdDFhlXHa46Dw5/PwyA24Xl44Onrh6Hn8Hh8NtvEcuyqLcsTH01DmcgTh8HuOoY+dkkllUEcU3MNzw08iUCAgIaLqeIHBOMMUsty+p1NMtqN6KINKhhg1+n7KE/k+4ejq9n3/FVPn44DvHbxsdn7wAfhxPYuxvOz+EA/2B7gvr44fPLTM69pcsRcPCD740x+Bnzq0yW05fbti6iOH83k1qsod5RTwAqWyLyP5rvFpEGNem7G5nlU82PpXn8/btZlBQWezuSrd6bdgclKZm4w/tx9rKzCPGxqRyKSJOlsiUiDcoCKlusIihuCXlVJXz14ofejmSbf73zAuuWhPJB0akU1OUQEBaBp6rK27FE5Bij3Ygi0qBGn/8ZXYsqeejT2dy8u4IdxYVs/OgH2l11mrejNaiiilyW8h6nkciaiNP5033X43Do9auI7E+/GUSkwbWJCubLO8+kdM9/CCgKoiJvhrcjNbgIhw9nzg6men0Xri6dwLwF/6Ku3uXtWCJyDNLMlojY4vONeyhK9GO9+w380rrQ09uBGpgjKJpmscOwaqN4q2092zYGYM2fydy7hhAWcPQnXhWR44/Klog0PMsiqbCIv8beTlrr7YwOX+HtRLY4+R9/ZdWbUwjc8jR3z7UISk8jLGC4t2OJyDFGZUtEGtzD31xL66+yueXMTiS7N2Byo70dqUFZloedmz+n9j/B+MYEMHhpX9xBEFKtM8eLyP5UtkSkQdXVluLZtZitzQzxP6bRMvYSPCkeygsqCfRU4hNoQWi8t2MeFY/bQ+b6Wfwr48+Y2J5E9OxL24nLqK8u48O+F/FkaTWeGheOAP1qFZH/0W8EEWlQs2Y/QIvoZvyQcxYtdv/A5A7/odjVjNpH6ti9cwr5A3dwx31L8Pfb/wztx7rv73uWbWXRtK8LwtExn0+Dw2lfWU6k73Kuc7tZ3jWUgeZc/PWrVUR+Qe9GFJEG5fF0J7QulgtMMO09Fn1m51AZnkVRl28oDUvBFVTCc2Of93bMI1ZSUsSaiF3UeObRwuNgjd9pDE1ph+8ltQT186F5VCnt44N+PhO+iMh/6beCiDSoESNuwVN/I3mrNrO1eRYpu3LI9FxHdOo8vqs/k4qaNgTHVlJSkk1ERLK34x62nxbeTkL6LubXjuK6e57h/Li4fbd86dVcInLsU9kSkQbn8HWS0LM9kd0e5qaJo3jtpFZ0jLma2k2vsak+k2abKtjRM5Ru3g56mFwF1fjPORmfTBfdUjOo8Qv1diQRaUK0G1FEbOPvdPLhed3oGLO3nGQt20H81jCSNnRlwsQXmL97lZcTHlpVVTVfvfoxobUxlNWt45I9P5Bk5Xo7log0ISpbIseh6qwcds5a4+0Y+xmSmkhE0RaWFb7MhLh2vLt4IR63x9uxfteT8z7lmR6JrOr2NYnNfAm/6SkIT/F2rF+pLt7B8o3jvR1DRA5CuxFFjiO1tTW8MP1WYsa0ocJdxMjgK2jZu5u3Y/2s7SP3klRXTd5bD3FnxaeErD6LbfVzaX3hyd6OdkClNfW0nj+NK4M244r0cMYTH+AIDvB2rJ/VVVVz/YR1BObfTo+5pcQ8EErz3sO8HUtEfkMzWyLHicwP5nP9zNfZs2U9nXx88G8ZwaLFn3o71q+sWfswl3/6GZvW9KDm6xY49uwm7dwB3o51UOEBvrQIsGj205m0Wn0nG58YT272dG/HAmDGS3P48sn32LZnM6ctOxXLOYhFHy72diwROQCVLZHjQGVJMYtWLKCmzp9lVbdAlA/b0h0s71DNrl3Hzh/g9Zt3sjqkFWPS1lDrnEHzM5rh9Du2ryPY6daXcPs5yKvcwFc99/DyxrFUV2d6NZOroIA9M8dS4yrj1rSP2ZLYEqtlN0LDU8lftdWr2URkfypbIk3UttIqHpq1Ccuy8PUPZU9xOf2nLOVh1wzGD90FGz/E58cArK3xWB7LKxk9lodJM/9GWfluABLXnMUF21ZyenkK3Z56kz7n3+SVXEciISKR8x67lPTRaQzY8TwFRe2ocCZiWRZr35tC8bbGOVi+pGQ3SzJexbIsasICyImcQfSayfTO68iubq2YFOLDO5Fz2LS7Bo+Xvt8icmA6ZkukianNzWfhukd4eFN/Htv1NkuKryam/Wn4EEHCrkXklO4hulUi3Wa1oKLDmcybPpWggtaMGn1Ko2X0eNzc/skSyvMm0XrjN9R9/hOnPvMlO6oXMjgzlm3VefTkgkbL80cFdOjA58tuZY1Pd4asb0NFmxl4vnuLGRsH4rPwR0Y+/ygul4MWkUENvu76st1s+XAVa4I+4/3Uwdy8fALdnK2p6uOktqiGJYWZbPT34z7zMq87OrP400/I29SO8/50TYNnEZGjo7Il0oQ8NeUWgj/xI3bIdpr5bSRz28kEZtezZdkPzOjuwx1V28ho+X88OHoka8q+YYN5hx+adWZ2bmvSi6tobUMZ+K3Z7y2jfvVa3MGxtHcX03tdMD5dzuSORR/hn7SM8zLKCW/XidCUuEPf2THk9tPfZeMjU3G1nMO/dzt5YOtykiL6UdlzPTNeupYgx07WtWvHiPM/whjTIOu87oulDJxwNe1Cr+XF1FF0rXqKeYXRbN/aA98z+/N4wnk8lbKa77r344u5V3LFTDfupBAKA6ZSUjKMiIhmDZJDRP4Y7UYUaSrqawheMpuwshySVl1EeFkUhXH+FFatwzIFnJQ+i5m9buLei0eDjz/pt1xM+4GtGbl6AZ9v+yvPzt/YKDErVq9kW95s7opcT80QF0HDB1ER4KSyKpQVVbeye0BnLnmi6V2uJzm6FVEJzdheGkp2VTzPxV1KaEgsJb7x1Pn6ULegltnzVlJRX9Eg66txe8gvWEXb+mo2VFQTXlhOlrMZXTdsJ8Tj4uSVw3lqfRbndL8Hf4eDq0/+C0M7jaK8bQ1ftBzB8lXvN0gOEfnjNLMl0kTU4Ms2LuLC1lOZOCCQl0/+EJ/YQKo3bqTS40tws8vwC4rE8YtZlZaJD7Bp4T/Z7f6W1D7PAZ/YnnNdtzF0+M9O1sfUcPcNfyNmREcKs3bR2+Eh8JR6SurPISA82PYcDc0YQ+cHz6BZbjfOcRRQMaAVrePD6VF0Dgte/5G6uGZ0zfQQVAs0wDW2famnX/uFvNvsFtKzLT69YDSR8VdhjVpD4W5fQpo3xy/cH4fjf6+Z/c+IpuT9/3D7/Ba80eZJhv7xGCLSAFS2RJoIfx8HuV1GcnddZ9qG78IZE4AxhqD27TnYzsGsaRlMbp3K1Y6/U7tiE4y0P+dF0a0Yf14OoYX1rC1L4OQIiG7W/OfbI+2PYBsfPz9im7cAWvz8tZiYGLLca/DtnU1QYhmeAAtnA6zL4fCjQ2kicVv3EFTWivC4QDAGk9SZmKQDL7N+3dcEZ0WzO/dszt01Cy7r3QBJROSP0m5EkSbCGMMpk7/gxg3ruXVaOFd9PON3x++adCefFz5Az6DpvN9pA3Ed1zdKzqxdfdnU4k8s6NeOTtPugNqG2a12rJr94DvELV+Pe+4KXsm6FB+fhrluojEG94QZ1K+qpyrb4ttZd//u+LuXbuHOZS1ZOOwsWnbaRe/Y5r87XkQaj8qWSBPhqndTU+skaGsxmTmT2VGax4x1sw441vJ4WPjeEmJnV1Lvb1Ecm4BfQmyj5AytCOXOJaEMWbKF2h+XMPudOxtlvd6wZPocFu2ZTVFIWzrW1pFiVVDeQJcfqnXXUmSV0qw4k6SKOWzJKWbt1INcS9Lj4dL3r+X+rDeprQ5id2kcjuZN6w0IIsczlS0RLyvIW8+4KZeTk7Pld8f5+Dq55Z0nqT+/hu2nbCO0YwUrp66nurx8v7E73/8J0/YKQoZ0YVnElTzX41yyqwwTXh/Fey92462Pzz2ijBVVNVwyZjFPzVl9yLFdHhhF6KAU6jNPZXLKIBYbJ9t3LDyi9TUF9fUVZOa9iqNzNJ3S2tLjP/P5z203EObz+zsRK7buYdmjX1O4defvjvN3+nP1fxYx9qa/8XbfGwhb24e5477GVVyy39gfX5jFyoIBpNafxF/Dl3DGHaMpKC3koi/H0++T77jk81lH9Nhqq8qY+uO9zF/63hEtJyIHprIl4iVl+RtY8szHTHv7C970Gc7n8w/9h83Hz4fYro8TtvUCzl2eQUI+uEtq9xtXWVJMdbM1uJL20Dv7P/zw1Atk5ZdQUBhIyY5z8fmuH2Of/OyQ6/O4PSx8cwKPvP8RtTn/oG7iRfzrh78ecrmYwWn8NLw5b7a6lJVtWlFYuOSQyzQ1VVVVfBPdneyaID6sd1CwNJ9g58GL1obiSt776zeMe/R15pDNMzMOvU0CfAL4R7rFkILXCN21lfqKGsqL9/9+uwryiQkJITosgVfL2zLh7icpyN6BM2w7gZUf0mLjzTzz/jWHXJ/H42bS5L/z1p/v4am17fhk6i4e+nr+IZcTkd+nA+RFvODSL5YSWXAHfarPJ8+/I6ftmkNe0fcsXp1On86XH3AZl8vF1Bm3kbewFP+C9libI6hLLCKkecx+YzvdfzaB24LZvOU9ijO3UOyXTty6/kyMbsWojauxArOIKUrAXV2PM/DAl8t5euZ9MHk7frmdiG4TRXPXNlqvGkZhTSjWcOug55K65stlhOT+lV7lQ7ioKI7MnYaeT9xx9BvrGBUeHkd6oS8m5DOC1p3LT59so3jBRrr+eRQOv1+Xrrnz7uCelUPoW+Ghg5+TH1rEs7vQkL4qmyu7JB/w/l319ax+bhL/7rad0lYWI4qn4IhsS2TL+P3Gnv6vi8lftI7cHzcxbOM6Sp1ZbCkJZ9T2YjZZG+g3qyM5zdpTe0k9/kEH/n7fOXYlFTvep9Oy6Xj8TsLf46Q/77GxaAmW9W2DnTtM5ESksiXiBTkFO7mhxM3bwasZvDMOx/ZoospuZYurjj6dD7yMw+FgW6GLsAgHO0InYJX58fhDCw66jpYth9Ky5VD2tMhk8tOL6ZcUyhU3nsrqtbP5MNuf4MLvqakeRXDggd8fuKqkgsGFa/B1pzGwvCsun4co6lJNm7rfPwB8V34Wd5e6+Dg0g/o953LhHdcft3+oH7jkXp57fgxxfZaxqM0AgorG0M15/n7jdmfm4UyFGRVbqHZNY8immWSH5jJh8xlc2eWFA9630+kkZ082FWnxZLmvZn3aNl7+830HzRLbtyOxfTvim53CXVFXcXdEGqee/QzF41czr89PNKsMgMoyCIo+4PJZu7PpX11LrCeMGnowalMNtUXXkRTr4Pj87ok0Hu1GFGkEZRvW8tn177B13N53EN7d9lM+6H0BQ2t6ctH9Qyn3ZDLhvBBe8Avhpm9mA2BZFj+sGcefXuxO2Z6VGDf0XzMKsgeSunY4j/59Hj7OQ79eSmyXwtWvnk3b20/H4efkHxmd6b5iHV8VOPnipVnUVtcD4CouZtVTY1n0/Fgsy8LjdxuliSez6RSL6BsT2dB9LpWpU1nY4hkefe0ULGvv9feqd23hqxvfYcVbEwG4r+1Yvu5/KidXD+Lyv55GfFrjHJjvDcbh4P675/Fx9D18mTmUDP9wautrWZqzkbte7cnaxe8A0GHzFfxpfgE3byjn5Yv/Q4851XQquYBzXVv4auo/gb3f70+XbuW0Zz5nVWEFbrfFjqpwhk1YzOOL/80L992L03noX9ntknsw6fJFjDj/Dnz9nGT4vsJ/BsN9qXnc8s2NVNZV7l1fZSE/3P8B3z/4LpZlcUvbhWQNCCVv0HmceUt/WgUHMHlkR97v0YWLXx/z8/d7bUkOD77Zj1k/PGrPRhU5DmlmS8RGhUXbeer762g9tYhKVz++nrkWT1IqaV/154LQTNLMYOrKygmL9yUsqpDI7M/p8m0ub+ZdyLiaoVy0cy1dd1/OF6s+oONV4awLmErS8pEUxTTH13ng3UEH4hMU8PPH7oA01oZlc3rJFaSWlzLhyf8wq2d3Tv50HAFnbmROfEt2/vAjty3rzDxHBwbGf0y952QC/T1UFvvhnz+KlFwHH+1+ik79N5P61XQiQx9m47ZdzPxkKdHzB3BW4FI6mjPwx9+OzXps8fHj+oKJZG1bzrq4SK56eRY96r5g0LwaVk35iOrH/Jge9xa9pvbFFd6Z+oJyguPSCPdtwZu5rRi+OYNXl35Mi5bf8bLLj76uJSx49GU83R9hSgcf+jCXqaGhnONz+K+Nff3/d9JY33AHO7ckMiArkj7LHHy6+FE6XubHirlf0638z+SH1fPZW7Mp2tyZPq7v6eEchKOTh+AgPwIiswnPXkDHXat45f++pnnCTcwN+In284eyfnYFxbvfpGV3f7p0uea4nb0UaQia2RKxyeZXpzNjzBMUO4rY0MKiLqiaoD57iJ/6Nwp8y8jPDmNNYAHJnTtxwyMvcxPF9C7dQ7OcC+iyOo1mZbmUlcVS69lORUAmb7n8mB/qT2bEh+w+O/Oo/7h9e2VfbjrrX7TCn60BhYyPNvRY/iyFoU52+zgZm3kGSzZmsIlK+ldGUbXgBtq3O5dLR75H8Rn/IqwqgZZRUYTE5PCib2u2xcZS5iyhPH0aETuepdJ3D+XZySzxbCQouSmfwvTwDWwWRnzWSM7OGkViWR2ry9oTXhZMZOpIXijMY7YjhuUtvqOg21Qi+/Wkzxef0KpZM4KxcAZPJmLVHigPpJtrPf1WeOi8zJ+NW3dS7lODb1Uf4sIeOurv9/BT3+HZ0waSbgzVnq1UBm7nbXcQK4LjqPAporLzdzxPAWtcUJvXjrlFs0ge0pUBj13FAwmJnGwyabflIppv7UP9ro3s8QknpLya1hFJjImr4cGl9Zzx8kTKauobeKuKHD/Mf6eGG1uvXr2sjIwMr6xbpDGsuP9DVvgWUNN+IYvzR/DAWQOZtfV1wrfnsNm9CR9nFH+78zcnJq0s4Lu/jSOndAM9esSzo+dOhoTcyJgxnzGtbwcyd0TQLT6Yty8+vUEyZm7eyHNLVtF9zzcs813P4JBWfOnzJy7OepYJweEMzhvFFX85m8DQ/81QWW43O9+czZI9G/mih4OSTUF065ZGN89n+O/II7tmGzmOYJ66a84JNdsx+YkJZG6eQ9/2rdkx4CcGx93Oyi/W8mp6ADtKg0h3VfLRrb9+80NBnYv/fHI2bSdUYbX+M22ahdP2zACWPPQ069t1I7jrcqywLlx6+qMNkrFo5QrGjPmU6X07kL0tjK5JIZwfPZ433L3JXFdBesCPvHT1R0T88jg+j5sZz/3AltVzCW4biKvbEmIrhhKxMZYn4r/n/PnLWNktglfunX9Cfb/lxGOMWWpZVq+jWlZlS8QeU+77hC3527FcY7n6+Q8JT+jKb3/eDvTH6b9jLGvvO/6MMViWhWVZOByOn7/eUH573//NZXk8ey8Pc5B1/Xe5X2Y81GM7nv13W3g8niPbJpaFhfe/37/M/XvL/TLjx7e9RGihoazDeK7+6wQICG+wnCLHmj9StnTMlohNhv3rfHj6FMbG1FNpggnn8ArIf8f8cuwv/wg2dIk52H0bx+8fZfDbP8wnWrn6rf8+/l9eGPqwtokxGLz//XYc4fe71l3LpPhwKluE8/fSu/AQrONSRA5CPxsiNpkx6yGykqOo3HU1U6/7M/lrlno7kkiD8Hg8PPP4ySREvsQF9V+xLH08Hr10FzkolS0Rm1hWAhF+vowwMbSqrmL+X67bb7eSSFP0yYMvEL9xIN3Xnk1UdA3RsVF4PA1zTUiR45Fei4jYZMTpD1BXUcOi3Ed57+Rsutam8tfZm3hqSDtvRxM5ajX5pfj6BVPTuxJPZTjn3Tbe25FEjnma2RKxkV9IACfd9xSuHrfzQtI9RBfoTSHStDnD/MmNgTHdB5LXYiIvjLmE2so6b8cSOaapbInYbMfURZy9zMP9rd4guWyNt+OI/CG+/gGcfG53ytcF0Gp6GkmTU3j7tkeprXZ5O5rIMUtlS8RGbreb1cGhROfU4/tRJDGZ/bwdSeQPqw9oS1pUAklxwyhuHURggIV/oI5KETkY/XSI2GjutNt4uaYf59eMJyEvj+LzyoFzvR1L5KhU1VTy4vL3eXtKAh1ahfPW6bVsLW1PUqtUrvNYOBwn9uk/RA5GZUvEJhUlNeTm5TIqfBpp3SPYPqCOYT4BLNyRT1CYHwmuWuLi4rwdU+SQ3O4advw0jfqJ0GzPFO6qrOatnn9j+JwaRu7MZEOrhVTW9SQ04PCv1ylyIjlk2TLGvA+cDeRZlpV+gNuHABOA7fu+NM6yrMcbMKNIkzTniXHUV99KL/9drGq3jtIWKSzdPIN53wynm9WF6kQfbjjtFQKjgg99ZyJeYlkWT05/DT+fpbQO7UrtrtYERcdyT+YU/NwplFavIc41h1AeA3QGeZEDOZxjtj4ARhxizFzLsrrt+6eiJQK0D99NbP54FuU9x1eJrVjgSQdHIgNWnYt/ZRURdXmMe/Z1b8cU+V0VeWsZvPo1NhX3JdcRRkjSSXQYcj7drF7Ul2+jPDKHsoFDwT/M21FFjlmHnNmyLGuOMSa1EbKIHFda/uN+Ui0PvQo20W7hHnLmbyCy8ALcrVviH5xO/eIcNpbmUJ6ZR2iKdifKsenJ6bez1r8V/Xa25vw7TiUpPGDfLZ3oy2VezSbSVDTUMVv9jTErgd3A/ZZlrT3QIGPMTcBNACkpKQ20apFjl8M4iI5tz2lnt2NbnS/Jw7oREB7CtLeux6xZh0lNYlvWGrqmnOLtqCL7uXXBJlaE3k/L6A2Ejp1FlPM0b0cSaZIa4tQPy4AWlmV1BV4BvjnYQMuy3rYsq5dlWb1iY2MbYNUiTYMxhlYXDCIgPASAouJacofXsblvFhM++YDZY7/3ckKRX6vNz2TklD8RtjKbunp/qk0eNZWF3o4l0iT94bJlWVaZZVkV+z6eDPgaY2L+cDKR49jwO9+nPv1STm/mIqymnlXffEp9bYW3Y4n87POn/k3QjHpODn2Hh5t15rK77iMiPsHbsUSapD9ctowxCcYYs+/jPvvuUy9/RH5HVLAf1428h1bLLiaxqiO11nJ+XPy8t2OJAFBXUU1ZbiClXc+mbdFV+DfrRUqnLt6OJdJkHbJsGWM+B34C2hljsowx1xtjbjHG3LJvyGhgzb5jtl4GLrEsy7IvssjxwRgnyfdcSWWftcR1COLL2vO9HUkEAL+QQBJaxlHa70eeiY7njDe/4/01n+P2uL0dTaRJOpx3I156iNtfBV5tsEQiJ5A1a95nZpfOrF57FQNKq70dR+Rn5//tT3w2YQUXrdpNSE0tJU9/Ss4bg0kOSfZ2NJEmR9dGFPGSP41dyX8y1tJ/UTGPZu3g/qWbvB1J5Gc+Ab6cc9rLdAlxkhhYRUzQIJJDknG5apkx6x/szPzJ2xFFmgxdrkfEC+rrq5idm8lLZZtZsaGMTN8UmieXeTuWyK9ERkaSENucsjRfXN02M3vaM6ybtoU1w6PwWTaLhyti8RBIXEfNdon8HpUtES/44u0xtEmrYUabHlx/zeVEBvQmLCbQ27FE9tP2T6fT5ZO59Fm2gG5LP6YifCAVa6Lp6HiVz8fsITIggE4d+9Dt7vMxPtpZInIg+skQ8QLP7jKGL8sidYmLKZvCVLTkmBUQFkyXsAAurMwn2JFEdE0PykpTcJeHE3vqKnaeU87G0iIsj94XJXIwmtkS8YLEtJ5s//FTjCca38p/8rfiNC5u40vXLv/0djSR/Xx5+cmU1Q+Eyl043Am0ePJT6re2IdK5m8eGnc2NPfbg8HN6O6bIMUszWyJecNoNA4nuv4vpPadQE2KRHxiM2+XydiyRA3IaQ6SfL5GRLQkK9SfU7Y9v+9MJTjydeF8Pd597nbcjihzTNLMl0sjqPB7G/HA3heGGR9zPsbRwFyfNr6THPx/xdjSRQ6qvKSfLmU9dxzkYk8h3V5yJw6HX7SK/R2VLpJFYlsWGsbO5NbeEizaGEpLbm+XRaykt9wPnRzw9dR0Pnv6mt2OK/K5KRyBjwwOIr+xJdYcWnOOj3Ycih6KXIyKNwF1dzbIrrmTV8o046wqJzPUjLSocn07r8DfvsSWtkvm1Id6OKQJAZvkeBr09k5u/XbrfbX4+VUQnvMWw0kmkRPfyQjqRpkdlS6QRjLvzFCo3raOkPptbkidQc0U5zVq1ojI3nennX8lGx10kRN7g7ZhygrMsi93lu/nrS2fRYvX7/JBTxJeTxvxqTJCrlj5zHeSsP40Ok75mxcr30RXaRH6fdiOK2GxKZgH5kZGs6LWT9r03MHr0BMCCsw1tgMs9bsxIJw6H8XZUOYF9//2L7LJm4794IAM3DCaiLpSok+ZSuzwO62wLY/Y+P31DE0iKHk6AK5p3e3h4bkUd/nNmMfXGQYQF+Hr5UYgcm1S2RGzmKSjn6ci7aNl/DadFb933R+t/xcrp1I+heIfH7cFYHoyPD59sbkZpxTBOCVhG67AulHtg5PwyQgjE7Xbj4/O/5+mZz/+LBU9+Adtf4prFNcS07ECo/xDvPRCRY5x2I4rY6PHJt7D7lbu5vOUcLnLMx5NX4u1IIgDU51cx5a7PGXfPh1iWhYlN49SazXwfvYCQawOprfmATQXlrCl38+bEP+HxeADIyZzJxoe/JSopjtErR9Os5kZahUT+PPMlIvvTS2oRm7jqq6jZOpfSIIuUyc3okjAak+KmvtaF03LhcFrgu/+Z42vq3fg66nG7wWDw9fPH7a7BUwNOPydYFg4/Py88Ijke5FVVcNWYNZyxs4CooELqNmcw79lxnBcbSGZWB0ZsbUvq4GQWnJ1MwPaFBNTswr+imjGPvcz6tuOpjm5BQvog4n/cRGXRHr7pfwF/L2yOp8aFI0B/UkQORD8ZIjb5ceZDpAW3YGb4EE7buZBul1axeEEAP979BrlZUyk+JY9B186gV8Qv3oVoWTz8ygtMM6mktihl2JwMzhwykMlhUzh5eU/mL9tIfHwfznv+eu89MGmytmau5LGPbmSzdSkFLZpzj2M6pYUuttUEMy25B139VhJlpZHW9iz+3vYsxq/PYdv3y+iwNpfNuzcRvrUCq3M9HwfFcHvFYiL8V3JBvYel6X709TlHu0pEDkJlS8QmlpVAhN82RpgYWlXXMP2VZ5k4OoozkiMpL2lFrVnNy/95ixuqWtHr8r4EpSby8rNXkr58BTkD4iF0OLUFWax77jVyevbl9dA2jA4PpmzzdrZ+cCOtrnnH2w9RmhDLsvjxb28y2HU2CanNqWm2mRZBrZgUfTFbcstoVVdIcqqHC+++7+dlzuuQAB3OZMMjr1DhTMDUhbCbdIYktKT8/CLcOb7E+1cTHBv/825GEdmfypaITUac/gB1FTVkRa7gywA3W0IcrHK2ZXSiRV3/4eyoiGZHWAR7arMY8/cMmnUdglmZiL9PLAMyd3PKaX1Y4fqekrASrMQSioODGRvzGS1DS6jcnU6ax6Mzd8th2z52PuEtulEWN482VfHcOOyvAAz65aCzD7xs+8fupD0Ad3Hhz18dZ1NSkeOPypaIjfxCAmh5Vj9uGvYtV326gP8b1J7hreIZAUz+fhd98iZTlJmOnyeY2qgQ3u84iBY+dTxU5UvbtkOJfi6Mt2b8jdtG/pPk8GReH7uTf0am0duzk8vLcyA8ydsPUZoAV52bguB1TG7xOrXNz+ZaR4G3I4mcUPSyWKQRRPv78t11JzO8VfzPXztzxO1sSn6Mk33GkdByBjlcS4XvT6yOiWBr1/EAxCT34u9X/kByeDKWy0PUynruDviSi/mAV144lYryMm89JGlCJt73LEu+ctJzjh/dlu/i67IzvR1J5ISisiXiRZemp3BOyvN8NPBMQupSuD63PeenLaF5csz+b6V3GFpHhZP8fTgFP3SjOryKt776l3eCS5Ox5fNF7Ikvo0VwBWnuINb4DyXaVzs1RBqTfuJEvKhLfBgP+lVgfvLBZ/dwerdL5tRTrjngWOMw9Lr7YlrtHMaDUxaTX9KK0JRScnLWkZDQsXGDS5PxaOQStqR3Iyw4iK8fHc850VHejiRywtHMloiXXXPx6fSPS+Os527m1AeGH3J8ZItonh7Zn6GuPM7Zvp2YyFaNkFKaqpiw1jy16lXO2zSPcQ/8SNHsdd6OJHLCUdkS8TK/4CDS7zybgIjQw15m7v9NJG7PALrnjsBU1NiYTpq6p3oPZ3JMDb4BWTgGfcqP0+az5OXPvR1L5ISi3YgiTUxB5g78Oywk7MtSIuvm4vRbAoR7O5Yco3KK19IsuR0lPpV8FHIdg9OziK2q8HYskROKypZIE1JWXMGK56ewvXUFzU/J4pX6UVxXF0qKt4PJMae2poyFj3xJzqb5+ARlsObc17hj+dtsTt5Aq5STvB1P5ISisiXShMy55yKCgkbQZsdw3Omr2ZF8BVfOW0s733zuXu9HTEoicRd28nZM8bIJS7fC7ktwtO5IbHkvQvJWk1nxI2FmCD2WDGFJqUXzc7ydUuTEoWO2RJqIWnct212Z5OSsoXD3CjICyug28QUuWPgyeyo2M7NmOpuWLMNdr8umnMjWT/4E1/g/MS+vKzsrA6l3+vDskD+zp0UQHp8ySqvXEu7UmypEGpNmtkSaCH+nP2e9OpHLxqygviaKc9b8iE/FTq7In0WPXovZ6BnAkl27CfrrbHr8+11vxxUvcNXUsenNedT7bCWgm5MzBvyL8JAQpsYFUVXYhjIfCDupmIhTTvF2VJETisqWSBPSMqIls69rgcfyMPG+eeTRD+fgGHqcdAfFs74jtPxbNuTk0MPbQcUrNn01l/nN2nBOQD/q1m6g1ej/7VL2T4olUld3EvEKlS2RJsbfxwk4Oe+pB8hbsIr4YbcBsGBAIacl7OB5cztxz0xj2GGcs0uOH4Xf3cPsip9oE5XCF23SGB20y9uRRGQfHbMl0kT5BfnRbFgvAOrqCtgd58/9CU9TFd6MwvnTWb5+kZcTSmOxPB5mfPYTpYvKKAuoY0tsOxxxEd6OJSL7aGZL5Djg5xfD630vZ+vCBWwr3YBfyUR2fL6ZLo+NxfnbayzKcSd70VoCgkbQff1kgm9+lEvSEkmKv9bbsURkH81siRwngkNSSDotnYCW37DznECKjS+5FbXejiWNoGjOFmI7JFP293h8fWaTFB+3/4XMRcRrNLMlcjyor+aZMVcSMLkl0ae0ZHL74fTxc5MUGuDtZNII2t9xBl0+nEH39fH0XPY2WVTQuU0gbR+519vRRATNbIkcH9z1hK9eTWhFJmmrzufWJcH87dRbvZ1KGolfcADdwkI4rzIXh39fdlgbKazx93YsEdlHZUukidozewXLnxxLdXk5BS5/1vtcgNXNw6dnB3P6A5fidDq9HVEa0WeXn0Sfm58iefgu/Fq2JyqhNR6Phwd/XM8NX83D5bG8HVHkhKXdiCJNzKTt+VQ+P5nQjl+R0wnmzllJS6eHrfEDWJzWnVauApzBvt6OKY3MYQzVhdl8HzwQf2opzN5Dq3FX81OhiwG7l/FCwQDOi7mOVqMH6XgukUamsiXSRLhcLqb8eBsFi0qpr28PDjcvZt9Ix+r51K2Ywu2RSezOLeO0Lmd6O6p4SYcOpzFi8gecVjGfj/Ivx1leR7/69fRecSGBCQksT1zJQr/niPE/mxEjbvB2XJEThnYjijQRTqeTHUUuHBEOdrabwMqcInqFxtOtvp4kTyiZlT6k1gTQ7KIu3o4qXjTqxpewXEGEV2fRctW5jCy5k7D0jmSWb2Bt0FZeXT+aLzaHeTumyAlFM1siTYXLov+aUax1ZZJamMzVb/4ffj5+1Hn6Y+qrcfoEaveQ4B8Wi/8LK7my3sL4+WIswFiErzO8tuARrtxTzuK027wdU+SEopktkSbC+Dpwxk8ianMZoZ44fBx7Xyv5ORz4+gfjcDowDpUtAXz8cAb6731O+DjA4cBdupshNam4Mjvwp9W6uoBIY9LMlkgTYVkWG8vKyYn8nLld/Yh5KIpT/3m9ZrPkkO6YOIuVGxJI6TqUS0sqiaxN8HYkkROKZrZEjgHu2vpDjql1eXgr/g4+GHQPfm0uxFNSyle33dcI6aQpe/rHf9BjzB30dLyEpz4GU5uMf4d2h1zOctXj8rgaIaHI8U8zWyLe5PGQ9e23fDcul+HntabluUMPOjTA18nMGwexcWMBK77eycbyWox7JlUFmwiKaduIoaUpSRwfSZDrNnqXfs1lQ87FnB17yNnQpcVFvPfFcPpZzbjqtgmNlFTk+KWZLREvWb9uIn/5uB8L3nuMMmseX8+fjGX9/oknPS4X1qIgXgkeQFq771g72EV1YETjBJYmyUEO1Sn1VPjczfAxW8iqLD/o2Jrdhfz47ERen/4JPX8aRtWcVL599YdGTCtyfNLMlogXrPjnWNbEfU1moJOabvXElhqcp+5myZLn6dPnwLsGPbW1TLjheUqS/YiJCuB153X08jVEB8c1cnppShK6taTAbzKfOGK5cN27PPLv7VzfrS8DR733q3Ez/v0ju1fOxa9lDPVBlQRWOYlp3or4nSVYlqVjA0X+AM1siTSSzLLqn2euagsqMVt7MbS6DY4Wj9O8uYfSuc14Z3VnPHXuXy1XXp4DgMPfn1JHJUXVBYwKWMMN3Vfx+PU3N/rjkKZl2A0307JdG/rFbcZ/ZyIDNlxE5eo+AFRVVVBXVwpAbdVmauqhtC6fM6pXkHdNDeOHVrKh+zhqKn99TGF1USmWy9Poj0WkqVLZErHZho2P8+Z3t3D3s2/x4neTAVhd7qIsq4LamRn8c3AAZ2b8SKtN5dy0oZwfn/sUgIJxG5jz1mO8uug+lm5ZSK27lhl9JmEFTMZZXsSo01715sOSJqRP339zW9kwIlN7YvXfzE4f2PnBT3w39XyenPp/eDwe6lt+xMK2X1HjWE5mylPM2N6Jmz94j/oJrfnwrpeora7F8njI+3Icq5+ezuxXxnj7YYk0GdqNKGIXy2LbxFmsz1vDT4k9+HfJ69T925fVa2t5v3Mc/1fxf8yMisNEt8HTfzQVS0JZ2mUiX8UPZ92Y0+m4fAQv+qXSqsBFzsJn2JE9kvTBvXgh9EpODsznCu3WkSMQmp7M0prl7IhtScy214lbcRVvplzEnZXj+XD+c4S3Tian76VM396Rr5pFkrGpE2v9/WgfGsOOKMOzL45nSXktN815gy23dOSbuOEs+3wIOBK4/awP8Q/x9/ZDFDlmaWZLxCZPjTmHVe+8Qs2KWxi+uJpAh4NVYaeTUbSNy5O+4qlujzDy9GcJiEwl7k8vcfYlZ+Af7KRwUwju3Vv5NGgblTX1xFql9NmQwZ7SdaSvHMwV+Zt5ZdjpOoZGjkhs+zT8WyXQKreaTvMsMouqKakLZ2noNqJXrcJaeSvDlrj5W5yH3kkRfHVFPy549gOCWyUR0GEWM9vWMsh/PDuTajFWFVUbnbQcv5ugcVH8594vqa069OlLRE5UmtkSscnCuhisdgsIcs3jwvRLSTj3b4Q9MZ7s+i2E74njT2030rPllT+Pb33WQFpZA5j1xSICss7EPz6Qx9L7MvDsq/B85UPcnEocrmLO9Y8mOlLXtpMj91DfC3jXL4Gec5ZTVF3BB5V7+LbbKWzKW0WM3xYuST+D+PP+dxqRyGZ9iHywD46VKxhZmEGLCIutw/y5KjKRDEcSUfHXsju+gtT8MvwC9edE5GDMod5qbpdevXpZGRkZXlm3SGO4aMIK6tbPI6xXKf/X/gyaNevh7UgiDeqKKS+ztTyOiN1hjLtxMIHBId6OJGIbY8xSy7J6Hc2y2o0oYpP3T27PqXVFnLVtM3nO5oc8h5ZIU1KfU8mpk3y5Z2Im/Yp/wOXUMVsiB6OyJWKTOU+MIyKnD6nrB7J0wv/x9baF3o4k0iCKikoZ+9qntPMNo7R6I/GuyYRS5e1YIscslS0Rm7QP301c/ngW5T3PmKRmfL5hM+6aOm/HEvnD7p07iRf7RrK12xeUR+VSNnAoBIR7O5bIMUtHNIrYpOU/7ifV8lA94VmudM8hcPkwNmZOp+OtZ3o7mshR21hUwUlLJtE6YiPOUF/uenkBzkBfb8cSOaZpZkvERg7jYOQ591I6LgJrZy7lmdu8HUnkD2kXFUKUp4r2c8+mZvtlvPP843w/5TVvxxI5pqlsidhs5qLnqbWWUlUVzKbcAm/HEfnDutz2LC6ni3fjUvkssh2f+5Xhch38AtciJzqVLREbzfl4NdVjWxDf1Yfa9DWM6dHb25FE/hDLsqicls0p155KN0cGj5b9hdblQfj4hHo7msgxS8dsidjEY3nYPn8a1SUbqUm5grU9S7nDNRM4y9vRRI7K4k35RH67geWbPThrMujjnMiuipPpkB1G3QgXfgH6kyJyIPrJELHJnT9tpnP2WCpDy2hjOnFlx7NYsuJb3nz2MaqK/OkS0Y1hD47wdkyRQ8r59i6+yVyEc3cKG9s2p0/0Nny/yKRmWGu+69Sd678DHz+nt2OKHLO0G1HEJps2FvNsz9uYcm5XVm9dzlf3fcOS2e0ITNxIkMtF4YIZLFoxy9sxRX6X5XYz9+NFFCwtozLAxYaYtvgGVsMgB/U1PlRWh1HqU0x9jc6zJXIwmtkSscn3V/dl6vw9WGWZ7KpPwbhctC/bzCt7ruQBswxnySSyxmyiZ5eT8XHootJybNo5bwX+YcPpu/57Am99gotTYomPuZHMomrC/XIZWugmckg0/kHB3o4qcsxS2RKxidNhOPOk8/B4ziUzZhyvffYPitp0o3fyaNLajGNOfBD+pf5kllXTMiLI23FFDihz/jL8O5RTekESgzqEERgcB0BqTDDQEl0TXeTQVLZEbOZwOEjtO5p7U1qRGN8VHA7eeaoL0zr1pKVjLRdMuAOueBuc+nGUY8tPf3mDgk2LyQpcyPRO93JeQLy3I4k0STpmS6SRJCZ2B8feH7mgOienr8ym1cpyPHN+YMYnf/VyOpFf27JyLXNzF5EX1IJ2dS6aV9aQVaeLqYscDb2UFvGCyx6+lc2fzWb2jE18H1fBJlc1HXM2k5DQxtvRRPB46li39jl8u/nRKiuBAQ/Nom9QPBG++pMhcjQ0syXiBcYY4k+LZ9EpqTzb5ka2tEimtHSVt2OJAOByeRgT1YmdNbH8x/iTNTNbRUvkD9BPj4gXXPL5UqIK72BQ0flcUBpO4Q5/2j1+gbdjiQDg5xdAa08SgQEv0zX7djKmFuKfl0Hzy7rgDPHzdjyRJkczWyJekFu4k/NL3EwJWs32en9G3nWTtyOJ/MqjZ16Ky78V8XmT+b5rCdNzlmF89SdD5GjoJ0ekEZRuWMOn173Dlq9nAHBP20/5uPf5DK3pxdWPjyIsOsTLCUX29/cbp/L9fa8yqyaaadEVlFSWsaYkhwfe6MvMqf/wdjyRJkO7EUVsVFi4jaemXkeb74up8PRn7Jy1uJJTaPVlf84L20WqYxD+Tn9vxxQ5MKcv5fUeBm39jLDITfzwVRuWhCyj3YJT2DCnkpI9r5PWzZ+uXa/DGJ2YV+RgNLMlYpNNr05nxldPUuQoYV0a1AVWEdQ7h8QfHqLAv4z83WGsDSzEJzTA21FFDur14W05J6cFp2eNwrFnJ7t9Iwkpr6Z1RDJj4ur461IXZ7w0gbKaem9HFTlmqWyJ2KRqRzZVO9PpXduW8rC7OP/+h/GLjCUwykNJ24kUnLSAy5+8xdsxRX5XYEAAsQOHUOAqoc6nmDOCfiT8khaEJMZTkpnB6Bkv0db9DKH+2lEicjD66RCxSY7lpCy7CmvnJp5//u+EJ7ShTduXvR1L5IgNv3soljUEy7IwxmCMwbIsLr0tn5D6PvQoG4+pLYOAcG9HFTkmaWZLxCan/us82raZxJqT6qk0e699+N8/VP/9J9JUGGNwOBw/P29r3DVMTIjgnZ7NaVN3Jx50IWqRg1HZErHJjFkPsTM5ivJd1zD1uj+TtzrD25FEGoTH7ebfjw0hIeJFRteNYWn6BDzaTyJyUCpbIjaxrCQi/Pw5w0TTqqaaBX+9HsvSteWk6fv0Ly8Qt2kAPdaeTXR0NXFxkXg8Hm/HEjlm6bWIiE1GnP5n6qvuZPZLt/H+4Cy61qXxl9mbeHpIO29HEzlq1fml+PiFYHpX4akMZ9Rt33g7ksgxTzNbInaxLHZN+4nymApqel3JC0n3ckZajLdTifwhPuEB5MbAl90HkZsykee/vITailpvxxI5pqlsidjkqS/PZtXbr1Cz4hZOXhTE/WHVDGkR7e1YIn+Ir58/Q0Z1p3KdP52mlBM0Lor/3DuG2mqXt6OJHLO0G1HEJgvrY/F0WEBw/TwuTL+IxPPaeDuSSIPoltaXNlEuIuOvIzu+grT8UvwCnN6OJXLMOmTZMsa8D5wN5FmWlX6A2w3wEnAmUAVcY1nWsoYOKtLUWDU3sCi6F+G9S7mgfSXGV3+M5Pjx8eUDuSI6gy0VrYgMCWFoVSWBwbrGp8iBHM7M1gfAq8BHB7n9DKDNvn99gTf2/S9yQns8P59ZdbnE7ciE1Bv3nhAyZxXluz1UR6QSGeKHb/z+5yYqKCggx+FDcWkdUWH5dIruxLLSchIKFuIKSicqIIqQyIa7nqK1cwn5WX4EtWhJYLg/nsoiKsvK8NT440wpITyi637LVLk9ZJYWYYqWEOLsS2JKBI6CDVTn1VHim0x0WCB+SSfWH97Kykpyq6rZXGYRH7qHrrGdWVNRTcuiVez0CyPeSiH6ANukaHcW1S4PTv895Ne3p3OzcDJ37WKDFURyQCUxwf7EB8c3WM5lJWXEFfyEFdSVqOBIgimgvrCY3MJAYuNj8U8J22+Zuro6sgsLWV/lJCkkl/TYDmyuqifaL57b1r7AdKsPLufwBssocrw5ZNmyLGuOMSb1d4acC3xk7X1P+0JjTIQxJtGyrD0NFVKkKZrmCsexJZfZLh/ynvyItqe2IHPt3/Hd0If2Lc5gZ1glI+69mMjI/511u66shm+m38Nj3ExQ1ufcsHoOq2/5B5s3LaLllCmUBN1DgGMnV7/+MD5+fn844/rZXxL98n1843shXVNPYmtwPmZbCVX12+jTpzlvp5dxfusqhqb0/3kZy/Jw/oc/cHf2E2zeFIrH5yxiQ/PJifuK6IXptEg9g5wINyffci6JzeL+cMamwHJ7mPH9zfzN7zKqV6/hguwP2TXsOj7N9OX6eS+xPeB2ah35XPHMvUTGx/68XHlpBRnPTGRTy2Ws8w2m5558arpfyROFRZyVO4n3HWsZsTOIq16ag8P/jxfsb7YvYuvMj4mdNpeygDvx99nFjh4/MPyzIMq7/R3C5tPmnF6079fxf4/NYzHr+5t5wnkaZ6z8nMmFWzklOpU3wy7mz7P+SUhbPx7w/YIAHgd0BnmRA2mIA+STgV2/+Dxr39f2Y4y5yRiTYYzJyM/Pb4BVixy7qtvHkN8xkb5+aTSLC2R56WwKEtxUBsWytcsXvNgvmvvmTvrVMmOffoWAumIS9mRz6aZehNQMYmJuCd/HdqDQ4SEtqJzK1lUs/ezbP5zP5apm808fkZOaSpVPAPO6fEe171R8istJDu/FMwU9SVlQSv6Ym/G46n5eriK7iMxqN28Hd6bek02NM4OV6bXUhNVSGhbHni5jeHeAHzcvnPWHMzYVE597gfLKMtrnbOSsrNa0Kjib2cXwk087dvj40y4ITEs/Zn/1n18tN+PBO/CprSclKhdf/xmErFnOip/W0iG7AN8aD2cvH4G7ojvfvjjhD2d019Xz2dp1TIptR7GpIzWkjNknxeFbX8jSDj2oSX+fCQN3cMmOndS5/nfOrMId+RSXFJOev57kYifnLAxkWchANjiakeXjS8nqGqqdZ+pSPSK/o1EPkLcs623gbYBevXrp7I5yXHv4oi7gSWfHR/PZvmcJGzsksH3NE3Q6P4VLoz/hmvnfsLS6NZtPqqJNZBC1RWXk7SyiVfFQ7o3eTljrXpjtNUQvr6e2+w+Ejb6CoK3NWJTuJszzLr09o3A4jv710k8Ln+XLbgPZsaIlvVtHMTTqa4o2+7Kn92QyWyQRzMNUZJSwtcTFhNkPc96pTwOw/d05fOlXTE7LbFqc/CRLZyxkXasQFm14nNSRqdyQ+AUjF84muyyK6b1OZVjq8f8OzKyVmURt7MGNsU5q2sZSszaVvtt8Se/8HomXnUfUzk5sSl5KeegKhpTsIiKiOVUVeewsX0REXRiVM08h7oI1FMb54M6t4Ly41mS1OBtT46bWv4qEAoPH4/lD3+9NH83gwqxKqjpOxd3nHBKrUiB+OzPdDxM5oBl/aT2Briu30nPPJv4Wk8q/h3UAYN5zU/F4bubBZoVUjx5FXdl7dMmL5ZH279P88tNJP+VBIoNPjBlMkaPVEGUrG2j+i8+b7fuaiDgcpF5zEi2sQYQte4+ON51BYGAkrz2+gcB1BZyR6CCsYipEnse2jYupD9lJ0Jp5zL3Qw9N3/oX66pPY+e1iWo68BYfDwY3vnkX61xXsIY3F2z+n3x2XH1WsB8avpjh7D4M9tZxTHErPkjra3Po249vkkeCBM9rEUTRhM5vNObx86gV8szuBBat2cKnrDf4dksbZq9YQNyWPlhMH07bnuXRY+QVpV/QnPLwFs94NJHz5LNIja+ngmoJlXYYxx+9ZZnZ9sIj17fK5YNo2ViZt5e47lmM5B7F13Dyan3YZ/qFBXPHxtSSu+ok99SPxRPpBT6idvYya9Ha08kzlobAnmHnmPdQPqWHdp7PpfP1w+jkcnPnml1z2/Xj2VFSy6h95dHvy9qPKuHrNQ7ztF8ZJmUXUrG9Hm9ap9PznaB7ZPJeAjhbNmw9mzueJhCyYTllCASlbn2NK/Wl0KWiJX4sfiJ5URYhnKamdl8FbrxH63QISeo4mKCGygbemyPGpIcrWROAOY8wX7D0wvlTHa4n8mjGGnj1v+PnzqC25eALyadM6nDs3bWPEjLfImzef7cPakxZbyurqq7AsC99Af1pfeNLehepr6Jy1mZDCPrRMGcKqvGIiN++kXZsWR5TF7a5lbt5O/q90Pss3dKDaUUxJs73Hf53X6n8zFEXZWawNzqIuwpfBCxfTe3sty1sXsCDxTJJXf0t1n0ra+VTQnEi6db3k5+WqV6/G7bOVhNZt+FvmNoZUfM3V3S76A1vv2LVj007WLvuJ3MGD2Mw8VtVfQZnLQZiPofUFJ/08LrV0LUNmdqC2yxlMHv8N7gVFJH82jqDho3llwBBudn6BZV2Ib1AAXW88HYAatwfqKoj3XcvOuOvYtmMDwcvX0Kb7fm8K/11WvYdta7cyL+Iy2vn/mzIrn5RevYDbaNPmfxnrtm2jzr2BhLDmrGntYGfxLnyW5LOjlS9xZ5QyofIi/lQdQEoQtDxrQINsP5EThTnUtdqMMZ8DQ4AYIBd4BPAFsCzrzX2nfngVGMHeUz9ca1nWIa+426tXLysjQxfmlROTq7iYTe9N5x9VIYw071K2wUmtx4fW7ToSf9kZtEzsRFxowH7LWXkbmfjoT9T2msTTcVcTWeZh2qXnsvfH8PB8+eHnvJTkz+D6BYxMTieG02jTJXG/+/B43KxY8BlFxU/R7bsKJpadTmHrNKJC2xM4PJ228aX0Suy13/17KivZ8uFUnsgJoovfeBIDpzPqxjmEhB3wUM6my7L47PoL2FPlQ0xSP7rf2gVncG86JR3g2KWqIhY8M4HspKl80XwgZ4z9gtari8i7qDenjrqDkGZp+PvH7rfYpopq3vzmDE5bNZLNwcXEJ5Zx4Y0vHtH3e/wT/2JXrZNQ/0R8zjqZpKjtnNJi8H73Ybnd7Pl6KntWOXm9+ybOGfMh2xytCYnuxUn3dqDM9KVvS10BQU5cxpillmXt/0vvMBzOuxEvPcTtFnB0c9siJyifyEja33s+KeNWMy07ha5mKmmOS+hAMG3b9jzociauHee8mMbSFav4+4S3WW+as2jPEPolRRz2ums3FXBtbiaBYdn4tr6Ftm2TDjjO4XDSY9CV1FWegcv9KpVf19B6j5tmMbX06tr6oH/wHcHBtLn1PBLGrqRkVjUJO/wZ3/ZRrjznncPO2BQUFm4mt3YDzeqGUlpURWpYF8LiD3KQeFAU/R++ipWrNpK0qQiTkMzM7nVcmRJKdKs+B11H25BAnr9kKttcy/k+dCZbIyo5KWcNiYmdDzvn7o17CHMGEhNbQ5+INsSlnnzAccbpJOniMwk5q5p2OxPJ8n2DFtWBpESE0r7lmUdU8ETk1w45s2UXzWyJ/M/KNZ/TpePFmMM8ADp7xlI2PP4qXVtPI+a5RRB++LNG37/+I9kLxuJXHUh9+13k90ninLbhdOzw2O8uV7B4DX7NmxGWGHFY66mrqGH6/S+xo3gbrdPP5rSHzznsjE3Fm69dTfPibTztfys3FxcTH9qKU/9y+iGLyWfrdnNJ+4TDPuB924bxrPj2dqY1v4+Hz72TpIDDP+3Hy5//hQ5vLWHlSTmsG3wxt6yJpVXqKUSf9/sXRM/ZPhMiU0mISDvsdYkcz/7IzNbxe9SqSBPSNf3Swy5aALO+WceifpdS2OJV3O4je8v96beeQkDzdUztOpWqQA/LfZtTVlZ+yOVi+qQfdtECyJq9nLxme3Bcnkt+wqIjythUXHz9q0zsdzp3pnxMaV0+eUum4amoOORyl3VMOqJ3Fn66/CUmOgbQbnVrAqvcR5TxT5f8ixWjh7DEuoby6jA25NZQXlhwyOUS0oaqaIk0EJUtkSZm6tirqGnxCgl+7/EdOZjQwCNafsnSN+CUXtwS809K68/ipJ+gb5/nGjTjtsf/zZpPJ1OwYSZTNzfnu5rD3+3VVLhcNSxf+Az3p3ZiY34YcRvHU9lhG87Q0AZdz9VTVzKBe3B37onJ/Z7QkCM7me1rKzLJaTWKUVFtGTZ5CyXZq2hxvQ5wF2lMKlsiTcjuFYtxvbyS9cXVuEN8WBPjS0l56WEtm5WxllPemc63U14h9tGp1OzcRejOIqoLv+WZH+9qsIyWx8N32VlsdboIscK4smor7pjWDXb/3ma53cz78TXe/tudfF3v4tXV65lYfSHr+wzGt1sYNTU1DbaukvVLeGjKJXTYvp6KygjqnLVUFB/eCaF3z1nGVxOuZtKPP3Dnj+dRF/cFmwJmsDvVwa1fr2ywjCJyaI16UlMR+WM2fb6RD254hF0OH1ZaMTydPoHPl/6FxHX5bPfbzWmJXek86u1fLWO53Wx99AmWepJwxjjptGY0Pl1iqExZRfN161kflcfSqm4NlnFJxoPsONvB8i0RtGzekT8P/Se+kzKYccFAitztiG7Tl6HP3txg62tM94xbSVnWi3RYlEFl2CAq10TR0fEqV4UO4PP2o7is4gf8G+CyOv81/oUfKQo8n5P8s0lybKf7SXey5o05vNbNzY7iKLq1acEbg9r/eiGPm9KP/8xX0wMIG1ZLesDrLN18CbEVyQxIy2a6uzmlOZlAtwbLKSK/TzNbIk2Eq66O2royTGQWVWX1VK+dxNZVG1lY0ZKcQifWogo2vbmC+qrKXy33+dN3s3Pad5TW53JDqy/ISU/FLzCeXXkpTL58ODuCLiMs+MYGy1lSVszs8oHsKAul/fjljP3oA3aX5ZDjW0BRYAJLcuex5Me5Dba+xuJ21zMrdyfnlO4m2JFIdG0Pykub4y4PJ/TbSu6avocBa0Zh1R7ZMVUH46mtJbCkgoiAcKKid5NZmMXaxcvJ9mzBBOzkiu2fcNvHl+Gu+fX3e+an/4BZnxJauYf0VaOptdqQkxzAjtJlFPmcTYs+m7m67YYGySgih0fvRhRpQurr6pi/4HGqaj04/5XBnt5X4wrw8HlIBNf9NJ3whHhCktsx5OELAFhVVMHCf5yLO3cPgSM7c+XFH2E56sAKwO2qp7a+FLczmsjgP35R61/6fFUmL8/fyZULP6eycwdmd3MyIPNd+q27hlVJG0lILOaC0W/j6xvSoOu10+ZvFvC2tRrfsOXc2ekqIkN64x/sg6kuxl3noNbtT0CoHw4/Z4Ot011by4b3puEyNZQV/4UxRQNoW5lI22EryV6whZi1Z1PYJ4prH/8HAHl523ntuxfovG07E1rdy/sXn4TTAA4PVm0ttdVufCMtfH115neRI2XrebZE5Njh6+fHkCFPAjBjzZe41vlz/iXtuX5YO97/aiZ5/qvpVLQa2Fu2Vu4swhkVg0+bAk6u34HTzx/Yu5vLx9cX/8AgW3Je2iWFS7ukUDSkJVM/mcToLRuIb/EQ3xdH4Krew9iCnpxVU9ukylbRxjyuLAyipHA50Y89hF+I794bgqJwBoEdW9Lp70+n284G4L3v5rM250duankX6UOeYtK6twju6Et06f9OfltcspJtzROZZJ1Fv+AAfAN/8Svez4+ghj12X0QOk8qWSBM19N6LGFhaiX9ECJZlMSEvnbtmzCDHDObbVW+w6pytBI/LYeXJ/WkeEMnWmmIa+438UR2SueDBK/ENDcIYw3e7RtJnyTY6xz7Irv9sosOtfTC+DTcTZJcff7yZ+52ncs/aDwnzeDCJ8Y2e4fozn+fS6iKCgqKxLItdbZcRk5vPTvc2lr/7GRsjn8SVOZ5Tc9txiWsnbXxC4cL+jZ5TRPanY7ZEmihjDP4Re2eGCupdeJyBbPevISW+GzgNxWumEVq8lL4Tsxg+/xTC94zySk6/sOCfT/LZPMyDn+t0ojvPYX7Kv3hi6lNeyXQkprzwFlv2FOFsG8B7vfry1TkR5Fcf3jsCG5QxBAVFA1BZWYnl66CiOAD/raPwn96bWTmZdKt04d75DTsLXZQ6yxo/o4gckI7ZEjlO1HvcfDvtfsKnt2JzyhKCyGVxTk/uuOU+2iZFYJzHxmurrB+Xsmz307wZNoyytYE8fNHpnN467tALeoGntpZ3bvk7ofEt6eDbnHYPj8DXB3wdvt6Ohsvl5t4ZG+n/0Xf4+BWz+9RmlCcu4s4e9xMS2gnnMfL9Fjle/JFjtlS2RI4zdTXVzJ/3BOW1i0np9BndUo+9ImNZFm/f2ptVqZW4up/PW6f/09uRDqi+zsXnN79DfFEm64bMoF/fy+jb784jOvu73TyVlWx4fxpWrpuEu9KIju3h7UgixyUdIC8iP/MLCGTIqf/Esjw4HMfm8VCbJ2XgX3EXQzeMYWs3L+ySO0y+fj7knLyMokVzmeuXxtLKajY+ch8X3P13QqNjvB0P2Hvh7w53nIvlsXBoNkvkmKSfTJHjkDHmmC1aHsvDVncNb3UMx5F0CadsGurtSL/rgWveYVWf/2Ob5ybKimIoyq8kMGzv9ShrXW48Xto78EvGGBUtkWOYfjpFpFF9++6FfL7tDi6v+ZAp3TdSlDzO25EO6f1rz+eOnO2MGpdLWFg6Pr6+TN25kM7P/MDt3y3xdjwROcZpN6KINJpp/1nE7hmJnGxaE9JzGymhpcQltPJ2rMMSd2o+60K/IDPtdr59eiyLdz/P0KoWTG91Le89+xrp7jj63HcuxrdhTxArIk2fypaINJrsrYuw2kfh8eRxwbVv4RMV5e1Ih+3Mk59kRa6bokgH1et3065wGCkYUmum4cmPZdnO2cx+9nEeuHceBIR7O66IHEO0G1FEGo0zNoiFPaLI7r6LByePpCx7m7cjHTYfp5NekW0YVb6ICiqp9Q+l5cDhDF7VmpDSaoxnM9W+QSpaIrIfnfpBRBpNbV0VPd6dyS3rXyGpqitZdT4MTk2m+xO3eTvaEXMVFjL2ln9T2zqevJ7rmefXl0c6taN7q4HejiYiNvgjp37QzJaINJryOie9YhNJ9BlKdVoUwRHhRPuXezvWUXFERVLpB4XVhcTsMVzvt0VFS0QOSMdsiYjtLMtiyYQb2bR5FUOqWhJ3QU/eraxlzc5+bBnUhmP/oj37K64pZnafyfQtdOBX2ZZzRrzp7UgicozSzJaI2KqoYDVr/zGBDfNCCJtagWW5mb3Fj1M+TeLRzW+wJ+vYntnKzd1K9QGuhejv9qdZ4lD+2epl1vc4wwvJRKSpUNkSEdusKdjIk6s+wEpcSkhxKJVho9jdyoe2mwOpsbZRuHsrHaxXvR3zgOpra1g44Qsmrbidh+e8g8vzm+Nby2vot6IbN+9ez+ANacfEyU1F5NiksiUi9rAs1nx4Dc0WlPBESX/KQ5OJO+k0Tq46jShXNZ6gLFYOisSEJnk76a9YlsW3m2Zwyft9mf3tFMauP4+zMj7jlY9f/9W44PhoHNVlJK5dzPbFSxnw5jwKCgu9lFpEjmU6ZktEbDFj4XNkrSwjsSaZs0MWcNX7T+67ZQgAw72W7Pdd/uUyhm95iaEbgqjzS6em2I9NW9wsD3wTy3MrZt9FqI3DkH5pV2oeeovppy7hhtKlvDE9gj+f+xwBAQFefhQicizRzJaINLjqOjf5Nel0vNRQ2mINreOTvR3pdxUuXk3uml0A+OZv4h2f0UTUBtCjvpArdm+hPKAvp+WdwtLMkl8tVxGYRchNnbnSqqdVSCZdrVIVLRHZj2a2RKRheTx8/Mbf2ZrnYmuf6zgtqILoqJbeTnVAVWV7eGXybUROPp0az3qufPFhhpjtnNLyJ/yrLyK+ZSvKl63j2yEt2LUjjL+/fyVpVzxJdVQab2yaT/6k/2NoaThZlbdR7lpHzaA8RtZXg2+gtx+aiBxDVLZEpEHNen85fj/FcnpkLSsdBQwKGoIpt7h+zEx2BvmQFhbLO4Pb77fc0z/eQ9XKzcSFncm1/S8isGM0xd9+y9TsXNwBuUQnJHHGiGsbJKNlWayYPYaXarfQaf1GWgadRF7/bVw37kvarmlJWnEewaFZtPnbdYQ5o/jS/yfSg9+kauEgZj2XQV6zlVSn7OTkjcOJj09lbMv5XDitghUtt4LRDgMR+TX9VhCRBlW9ehWWzzYSWweyPDCYR2p2sDp/FaUB67hqxcsMnHs5j38wgrzMXT8vk5WzByvjewZ9G0fHNR3Z/fUcPnzmLOY/+y9cu0rJT1zJWKuY0rr6Bsk45f0vmfL1dKrrA1jpvhL/EB+cDn/WxHRgXOp6yvx/IOn0ZHz8/Um+ohfvnnIj7VLaUBnqS0HZUuJ8d+Ifm0NtbDOqfSCv00lsOi2UVVxBmUu/VkXk13S5HhFpUJ7KSrZ8+APs8Gd+0qfULyqljCBan5dLi+xqNs47jYDYZtRGG6wOywiPPot5dVu5fdnLfLfzbsJ94/ngPB8u/OwZEnN9SO72AH9vVsB91Y+xIu5y7rruj50CtaIih3dv+Qtuy4cu6QnEX3YNUWFJBHqq2VlTz+ZCFwmR2zm5+Un7LeuuqKBk+TJqTSR+rYuJiutHzpZtlLtc1Prn4hPYi45JujaiyPHoj1yuR7sRRaRBOYKDaXvbedRX15K5opSVGU+QVj+StLUD6PDwTazf/A6vpoXiqa8nOTaFS9zL2BXsz6gWz5ASH8Fn1w1hxg+zcaWm8tPA7VyTMIv4XQPJmxXBhsHfYXn+7+d3BB6NSfOexMVy4lwXkre5iuEtWu+7JYhooEcyQLMDLusMCSH6pMG/+lpS2//uEk0/6kwicnzTzJaI2Grduq9p03Ykvj5+ALhLSrht5my6br+XSHd3Ss59nMiPPqHY15f04mROevEmXB4PX23M4dIOe8/BNe8vX/Bq+yCyAp00C07ii7O7H1WWWe8soW7tWqoSn2exazhbwk5hzJ1nNdhjFZHjly5ELSLHrI4dR/9ctACcERGcFjKLqmVxbAoYwMrlkwnYNJb6zdXsdIViWRY+DsfPRctVV0dpTS6uqF345OTyyLwr2TVj7BHnqKqrYtes79maO48dIVdg9a/iurYrG+xxiogcjHYjikijG3Xqv3n9w1soDvRlfWw0517aj3N6/4nmcYkYY3411sfPjyGPXY3PT/czx38RexaEk7szg9GDzsXX7/B/hW344C78yxewPsXJrYPvIzLVSUho24Z+aCIi+9HMlog0OqfDyYgLb6LrjgBuypwOAWeS1qwZPn7OA44PDo/gtNPfIbTdWSxt14VcHycVm3cdcOzBbCgsw7dvCM07OqjYVqCiJSKNRjNbIuIVbc7tTWznZCJa3nhY440xnBHdgyX9viB3UQ0m5shOHJp0Zjf+nnk+F5X9wPdjf+CLlS8QNLQjD5705KEXFhH5AzSzJSJeE9HyyC5CnbVmLv7bfFmd3Jty39AjWnZI17/y6Lpa+q88i7D6CpptXQu15Ud0HyIiR0MzWyLSJCx6/gvY2JziymAebv4RSeE3H/ayltvNpk9/JNY/gnc6hBDkF0zv8C7cOOwlGxOLiOylsiUix7wfFj3KktZZ9IwoI2ySL8lVpTjLsiCyxSGXfWnJNpJf/prgwQtZlxbIIGPYleSidmEfdr63gBbXD2iERyAiJzKVLRE55r26rCX3/jCJ3VZXIlqczOvnNMN6dhTxu/rSPr4/JtXBwDuu/NUyLpeL5z4bT8zmrynyaU2FTz2vZt/KmXUv0CN3IAl1UXi2ZgIqWyJiLx2zJSLHtBq3h0pnDFn+lbh8w6h1hpOzbgbBRaFUEUtO+mS+SlvP6nWP/Wq5MU++xYaSAghzsrjHd1QU1NE9KIhTKxzUZU5jS5GHcp8CLz0qETmRaGZLRI5pAU4H024YwcwOyyivc5G7chb9A0JYG9mLLgFprAoqI2NzOlmlfnzdce8yhYtWU767hFH1ycRHnc81t32Cx7i5zfhgMQmPqxqHIwCnU683RcR+KlsicsxzOBycetJDACwLe4s9eYs486RbGdChJdv/PZqzsx9lSWhPLOsCjDGU1NThW5OGc/s4ZvcJoJ9zNM5fTOQ7fYO89VBE5ASksiUiTUqP3jfjdl+P0+mDVV9P8pJWFCa350Kfdbw77S6G77qMVSXjKQ6dyfr4UtbVj+BBb4cWkROaypaINDlO595fXZ7KSsLCk3AE+PJ+fiq9M1ezNWcZrpAWZIy4jqK1ATSL7uPltCJyolPZEpEmyxkRwci372Lrd/N5I7OCJMezfBxTTK/cU3i994VEnhPs7YgiIipbItL0tTprILMsiwlzryA5aw7X3jGS4FgVLRE5NqhsichxwWkM5w9+mPO9HURE5Df0vmcRERERG6lsiYiIiNhIZUtERETERipbIiIiIjZS2RIRERGxkcqWiIiIiI1UtkRERERspLIlIiIiYiOVLREREREbqWyJiIiI2EhlS0RERMRGKlsiIiIiNlLZEhEREbGRypaIiIiIjVS2RERERGyksiUiIiJiI5UtERERERupbImIiIjYSGVLRERExEYqWyIiIiI2UtkSERERsZHKloiIiIiNVLZEREREbKSyJSIiImIjlS0RERERG6lsiYiIiNhIZUtERETERipbIiIiIjZS2RIRERGxkcqWiIiIiI1UtkRERERspLIlIiIiYiOVLREREREbHVbZMsaMMMZsNMZsMcb85QC3X2OMyTfGrNj374aGjyoiIiLS9PgcaoAxxgm8BgwHsoAlxpiJlmWt+83QLy3LusOGjCIiIiJN1uHMbPUBtliWtc2yrDrgC+Bce2OJiIiIHB8Op2wlA7t+8XnWvq/91gXGmFXGmK+NMc0PdEfGmJuMMRnGmIz8/PyjiCsiIiLStDTUAfKTgFTLsroA04APDzTIsqy3LcvqZVlWr9jY2AZatYiIiMix63DKVjbwy5mqZvu+9jPLsgoty6rd9+m7QM+GiSciIiLStB1O2VoCtDHGpBlj/IBLgIm/HGCMSfzFpyOB9Q0XUURERKTpOuS7ES3Lchlj7gCmAk7gfcuy1hpjHgcyLMuaCPzJGDMScAFFwDU2ZhYRERFpMoxlWV5Zca9evayMjAyvrFtERETkSBhjllqW1etoltUZ5EVERERspLIlIiIiYiOVLREREREbqWyJiIiI2EhlS0RERMRGKlsiIiIiNlLZEhEREbGRypaIiIiIjVS2RERERGyksiUiIiJiI5UtERERERupbImIiIjYSGVLRERExEYqWyIiIiI2UtkSERERsZHKloiIiIiNVLZEREREbKSyJSIiImIjlS0RERERG6lsiYiIiNhIZUtERETERipbIiIiIjZS2RIRERGxkcqWiIiIiI1UtkRERERspLIlIiIiYiOVLREREREbqWyJiIiI2EhlS0RERMRGKlsiIiIiNlLZEhEREbGRypaIiIiIjVS2RERERGyksiUiIiJiI5UtERERERupbImIiIjYSGVLRERExEYqWyIiIiI2UtkSERERsZHKloiIiIiNVLZEREREbKSyJSIiImIjlS0RERERG6lsiYiIiNhIZUtERETERipbIiIiIjZS2RIRERGxkcqWiIiIiI1UtkRERERspLIlIiIiYiOVLREREREbqWyJiIiI2EhlS0RERMRGKlsiIiIiNlLZEhEREbGRypaIiIiIjVS2RERERGyksiUiIiJiI5UtERERERupbImIiIjYSGVLRERExEYqWyIiIiI2UtkSERERsZHKloiIiIiNVLZEREREbKSyJSIiImIjlS0RERERG6lsiYiIiNhIZUtERETERipbIiIiIjZS2RIRERGxkcqWiIiIiI1UtkRERERspLIlIiIiYiOVLREREREbqWyJiIiI2EhlS0RERMRGKlsiIiIiNlLZEhEREbGRypaIiIiIjVS2RERERGyksiUiIiJio8MqW8aYEcaYjcaYLcaYvxzgdn9jzJf7bl9kjElt8KQiIiIiTdAhy5Yxxgm8BpwBdAQuNcZ0/M2w64Fiy7JaAy8ATzd0UBEREZGm6HBmtvoAWyzL2mZZVh3wBXDub8acC3y47+OvgVONMabhYoqIiIg0TT6HMSYZ2PWLz7OAvgcbY1mWyxhTCkQDBb8cZIy5Cbhp36e1xpg1RxNajloMv/meiO20zRuftnnj0zZvfNrmja/d0S54OGWrwViW9TbwNoAxJsOyrF6Nuf4TnbZ549M2b3za5o1P27zxaZs3PmNMxtEuezi7EbOB5r/4vNm+rx1wjDHGBwgHCo82lIiIiMjx4nDK1hKgjTEmzRjjB1wCTPzNmInA1fs+Hg3MsCzLariYIiIiIk3TIXcj7jsG6w5gKuAE3rcsa60x5nEgw7KsicB7wMfGmC1AEXsL2aG8/Qdyy9HRNm982uaNT9u88WmbNz5t88Z31NvcaAJKRERExD46g7yIiIiIjVS2RERERGxke9nSpX4a32Fs82uMMfnGmBX7/t3gjZzHC2PM+8aYvIOdN87s9fK+78cqY0yPxs54vDmMbT7EGFP6i+f4Pxo74/HGGNPcGDPTGLPOGLPWGHPXAcboud6ADnOb67negIwxAcaYxcaYlfu2+WMHGHPEvcXWsqVL/TS+w9zmAF9altVt3793GzXk8ecDYMTv3H4G0Gbfv5uANxoh0/HuA35/mwPM/cVz/PFGyHS8cwH3WZbVEegH3H6A3y16rjesw9nmoOd6Q6oFTrEsqyvQDRhhjOn3mzFH3FvsntnSpX4a3+Fsc2lAlmXNYe+7cA/mXOAja6+FQIQxJrFx0h2fDmObSwOzLGuPZVnL9n1cDqxn79VDfknP9QZ0mNtcGtC+527Fvk999/377TsJj7i32F22DnSpn98+UX51qR/gv5f6kaNzONsc4IJ90/xfG2OaH+B2aTiH+z2RhtV/366AKcaYTt4OczzZt9ukO7DoNzfpuW6T39nmoOd6gzLGOI0xK4A8YJplWQd9nh9ub9EB8iemSUCqZVldgGn8r6GLHC+WAS327Qp4BfjGu3GOH8aYEGAscLdlWWXeznMiOMQ213O9gVmW5bYsqxt7r5jTxxiT/kfv0+6ypUv9NL5DbnPLsgoty6rd9+m7QM9GynaiOpyfA2lAlmWV/XdXgGVZkwFfY0yMl2M1ecYYX/b+0f/UsqxxBxii53oDO9Q213PdPpZllQAz2f/40CPuLXaXLV3qp/Edcpv/5hiKkew9DkDsMxG4at87tfoBpZZl7fF2qOOZMSbhv8dQGGP6sPd3nV7E/QH7tud7wHrLsp4/yDA91xvQ4WxzPdcbljEm1hgTse/jQGA4sOE3w464txzycj1/hI2X+pGDOMxt/idjzEj2vtOlCLjGa4GPA8aYz4EhQIwxJgt4hL0HVWJZ1pvAZOBMYAtQBVzrnaTHj8PY5qOBW40xLqAauEQv4v6wgcCVwOp9x7MA/A1IAT3XbXI421zP9YaVCHy47539DmCMZVnf/tHeosv1iIiIiNhIB8iLiIiI2EhlS0RERMRGKlsiIiIiNlLZEhEREbGRypaIiIiIjVS2RERERGyksiUiIiJio/8HGe1QChaIPRgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = pl.subplots(figsize=(10,10))\n",
    "for item in conjunto_lineas[5]:\n",
    "    ax.plot(item.x_s, item.y_s)\n",
    "    ax.set_ylim(0,3)\n",
    "    ax.set_xlim(0,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Propiedades\n",
    "\n",
    "### Area\n",
    "\n",
    "En la primera iteracion, pensando en solo un segmento, tendremos un triangulo equilatero de base $ \\frac{1}{3} $. Mediante el Teorema de Pitagoras, deducimos que el area de este triangulo es:\n",
    "\n",
    "### $$A_1 = \\frac{1}{4}*(\\sqrt{3}*a^2)$$\n",
    "\n",
    "El tamaño de a, que es la base, decrece $\\frac{1}{3}$ por cada iteracion, por lo que, dada la iteracion $ i $ el area del triangulo sera\n",
    "\n",
    "### $$A_i = \\frac{1}{4}*(\\sqrt{3}*(\\frac{a}{3^i})^2)$$\n",
    "\n",
    "En cada iteracion, se agregan dos nuevos triangulos que no forman parte del triangulo original, por lo que para obtener el area total, debemos multiplicar esta area por dos y sumar las areas anteriores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}