Lab04/task2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Zadanie 2\n",
    "\n",
    "## Obraz binarny\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import imageio\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import cm\n",
    "\n",
    "from random import random, randrange"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## Matter representation\n",
    "\n",
    "Matter is represented as an array with boolean values (later called colors).\n",
    "\n",
    "## Energy function\n",
    "\n",
    "Energy is defined as a matrix with an odd-number of columns and rows. The central element is always zero and it represents the point for which we are calculating the energy. Every other element is mapped to the matter array and is multiplied by (-1) when is of different color and by 1 when the same. The resulting sum is an energy of a point. Total energy will be the sum of energies of each point.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Implemented energy functions\n",
    "\n",
    "philia = [[0, -1, 0], [-1, 0, -1], [0, -1, 0]]\n",
    "phobia = [[0, 1, 0], [1, 0, 1], [0, 1, 0]]\n",
    "horizontal = [[1, 1, 1], [-1, 0, -1], [1, 1, 1]]\n",
    "diagonal = [[-1, 0.5, 1], [-0.5, 0, -0.5], [1, 0.5, -1]]\n",
    "grid = [\n",
    "    [-1, 0, -1, 0, -1],\n",
    "    [0, 1, 0, 1, 0],\n",
    "    [-1, 0, 0, 0, -1],\n",
    "    [0, 1, 0, 1, 0],\n",
    "    [-1, 0, -1, 0, -1],\n",
    "]\n",
    "cubic = [\n",
    "    [1, 0.5, -0.5, 0.5, 1],\n",
    "    [0.5, -0.5, -1, -0.5, 0.5],\n",
    "    [-0.5, -1, 0, -1, -0.5],\n",
    "    [0.5, -0.5, -1, -0.5, 0.5],\n",
    "    [1, 0.5, -0.5, 0.5, 1],\n",
    "]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Functions that calculate single cell energy and energy of the whole system\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def calculate_cell_energy(point, matter, energy_system):\n",
    "    mat_x, mat_y = len(matter[0]), len(matter)\n",
    "    r_y = len(energy_system) // 2\n",
    "    r_x = len(energy_system[0]) // 2\n",
    "\n",
    "    x, y = point\n",
    "    element = matter[y][x]\n",
    "    energy = 0\n",
    "    for dy in range(-r_y, r_y + 1):\n",
    "        for dx in range(-r_x, r_x + 1):\n",
    "            if 0 <= y + dy < mat_y and 0 <= x + dx < mat_x and (dy != 0 or dx != 0):\n",
    "                energy += (\n",
    "                    1 if matter[y + dy][x + dx] == element else -1\n",
    "                ) * energy_system[r_y + dy][r_x + dx]\n",
    "    return energy\n",
    "\n",
    "\n",
    "def calculate_total_energy(matter, energy_system):\n",
    "    mat_x, mat_y = len(matter[0]), len(matter)\n",
    "\n",
    "    energy = 0\n",
    "    for y in range(mat_y):\n",
    "        for x in range(mat_x):\n",
    "            energy += calculate_cell_energy(\n",
    "                point=(x, y), matter=matter, energy_system=energy_system\n",
    "            )\n",
    "    return energy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "This function swaps two points (passed in points_changed) and returns the energy difference resulted from this swap\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Returns energy difference\n",
    "def update_matter(matter, energy_system, points_changed):\n",
    "    mat_x, mat_y = len(matter[0]), len(matter)\n",
    "    r_y = len(energy_system) // 2\n",
    "    r_x = len(energy_system[0]) // 2\n",
    "\n",
    "    delta_energy = 0\n",
    "    for x, y in points_changed:\n",
    "        for dy in range(-r_y, r_y + 1):\n",
    "            for dx in range(-r_x, r_x + 1):\n",
    "                if 0 <= y + dy < mat_y and 0 <= x + dx < mat_x:\n",
    "                    delta_energy -= calculate_cell_energy(\n",
    "                        (x + dx, y + dy), matter, energy_system\n",
    "                    )\n",
    "\n",
    "    for x, y in points_changed:\n",
    "        matter[y][x] = not matter[y][x]\n",
    "\n",
    "    for x, y in points_changed:\n",
    "        for dy in range(-r_y, r_y + 1):\n",
    "            for dx in range(-r_x, r_x + 1):\n",
    "                if 0 <= y + dy < mat_y and 0 <= x + dx < mat_x:\n",
    "                    delta_energy += calculate_cell_energy(\n",
    "                        (x + dx, y + dy), matter, energy_system\n",
    "                    )\n",
    "\n",
    "    return delta_energy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Function that returns random matter array with given size and share of black points\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def generate_random_matter(size=(10, 20), share=0.5):\n",
    "    return [[random() > share for _ in range(size[1])] for _ in range(size[0])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def get_two_random_contrary_points(matter):\n",
    "    max_x, max_y = len(matter[0]), len(matter)\n",
    "    while True:\n",
    "        x1, x2 = [randrange(max_x) for _ in range(2)]\n",
    "        y1, y2 = [randrange(max_y) for _ in range(2)]\n",
    "        if matter[y1][x1] != matter[y2][x2]:\n",
    "            return (x1, y1), (x2, y2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Simulation function\n",
    "\n",
    "The simulation will have given number of iterations.\n",
    "The temperature is represented by the function:\n",
    "_y = a ^i^_\n",
    "where _a_ is _temp_exponent_ parameter.\n",
    "In each iteration the neibouring state is generated. If it's energy is lower, then the state always accepted. Otherwise, it is determined by the current temperature, _acceptance_factor_ parameter and a random factor. If state is not accepted, then the changes are reverted. One per _save_one_in_n_frames_ states is saved as a _.png_ for _.gif_ file to be generated later.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def simulation(\n",
    "    matter,\n",
    "    energy_system,\n",
    "    iterations,\n",
    "    temp_exponent=0.95,\n",
    "    acceptance_factor=50,\n",
    "    save_one_in_n_frames=None,\n",
    "):\n",
    "    results = []\n",
    "    current_energy = calculate_total_energy(matter, energy_system)\n",
    "    frame_index = 0\n",
    "\n",
    "    temperature = 1\n",
    "\n",
    "    for i in range(iterations):\n",
    "        (x1, y1), (x2, y2) = get_two_random_contrary_points(matter)\n",
    "\n",
    "        temperature *= temp_exponent\n",
    "        new_energy = current_energy + update_matter(\n",
    "            matter, energy_system, points_changed=[(x1, y1), (x2, y2)]\n",
    "        )\n",
    "\n",
    "        if (new_energy - current_energy) * random() < acceptance_factor * temperature:\n",
    "            current_energy = new_energy\n",
    "        # Revert changes\n",
    "        else:\n",
    "            matter[y1][x1], matter[y2][x2] = matter[y2][x2], matter[y1][x1]\n",
    "\n",
    "        if save_one_in_n_frames is not None and i % save_one_in_n_frames == 0:\n",
    "            plt.imshow(matter, interpolation=\"nearest\", cmap=cm.Greys_r)\n",
    "            plt.savefig(\n",
    "                f\"./tmp/task2/img_{frame_index}.png\",\n",
    "                transparent=False,\n",
    "                facecolor=\"white\",\n",
    "            )\n",
    "            plt.close()\n",
    "            frame_index += 1\n",
    "\n",
    "        results.append(current_energy)\n",
    "    return results, frame_index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def create_gif(frames_number, looping=False):\n",
    "    frames = []\n",
    "    for i in range(frames_number):\n",
    "        image = imageio.v2.imread(f\"./tmp/Task2/img_{i}.png\")\n",
    "        frames.append(image)\n",
    "\n",
    "    imageio.mimsave(\"./example.gif\", ims=frames, fps=5, loop=0 if looping else 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Examples\n",
    "\n",
    "#### \"Philia\" grid\n",
    "\n",
    "Energy is lower when the same colors are next to each other\n",
    "\n",
    "![title](examples/Task2/philia_chart.png)\n",
    "![title](examples/Task2/philia.gif)\n",
    "\n",
    "#### \"Phobia\" grid\n",
    "\n",
    "Energy is higher when the same colors are next to each other\n",
    "\n",
    "![title](examples/Task2/phobia_chart.png)\n",
    "![title](examples/Task2/phobia.gif)\n",
    "\n",
    "#### \"Diagonal\" grid\n",
    "\n",
    "Energy is lower when the same colors are on the one diagonal and higher when on the other\n",
    "\n",
    "![title](examples/Task2/diagonal_chart.png)\n",
    "![title](examples/Task2/diagonal.gif)\n",
    "\n",
    "#### \"Grid\" grid\n",
    "\n",
    "Energy is lower when the same colors are in the row or column next to the other color row/column\n",
    "\n",
    "![title](examples/Task2/grid_chart.png)\n",
    "![title](examples/Task2/grid.gif)\n",
    "\n",
    "#### \"Cubic\" grid\n",
    "\n",
    "Energy is lower when the same colors are next to each other, but one slot further is the other color\n",
    "\n",
    "![title](examples/Task2/cubic_chart.png)\n",
    "![title](examples/Task2/cubic.gif)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Code to generate simulations\n",
    "\n",
    "Result will be saved as _example.gif_\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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Y/r+oIiIiIu1iMaVjpIaFj5Thg46JiIjqBxZTOqboYce5BYKWMyEiIiKAxZTOMTYq/Mpy8jk1AhERUX3AYkrHJN3LBgCsO3Jdu4kQERERABZTOmf7uTvaToGIiIiKYTFFREREVA0spoiIiIiqgcWUjvlyeGfxvVrNO/qIiIi0jcWUjimaGgEAMh/nazETIiIiAnSomProo4/QvXt3mJqawsrKqtSYpKQkBAQEwNTUFHZ2dpg9ezby8zULjv3796Nz586QyWRo2bIl1q9fX2I/X3zxBVxcXCCXy+Hj44Njx47VwhFVTUdnhfg+NfOxFjMhIiIiQIeKqdzcXLz22muYOHFiqesLCgoQEBCA3NxcHD16FBs2bMD69esRGhoqxiQmJiIgIAD9+vXD6dOnERwcjLFjx2LXrl1izObNmzFjxgy89957OHnyJDp27Ah/f3+kpqbW+jFWhLWpVHx/J4PFFBERkbZJBEHQqYE369evR3BwMNLT0zXad+7ciRdeeAG3b9+GvX3h8+vCw8Mxd+5c3L17F1KpFHPnzsX27dsRFxcnbjd06FCkp6cjIiICAODj44OuXbvi888/BwCo1Wo4OztjypQpCAkJqVCOKpUKCoUCGRkZsLS0rIGj1uQSsh0A4KSQ4+i8/jW+fyIiooaoqr/fOtMz9TTR0dHw9PQUCykA8Pf3h0qlwvnz58UYPz8/je38/f0RHR0NoLD3KzY2ViPGwMAAfn5+YkxpcnJyoFKpNF514TZ7poiIiLROb4oppVKpUUgBEJeVSmW5MSqVCo8ePUJaWhoKCgpKjSnaR2mWLl0KhUIhvpydnWvikIiIiEgHaLWYCgkJgUQiKfcVHx+vzRQrZN68ecjIyBBfycnJ2k6JiIiI6oiRNj985syZGD16dLkxbm5uFdqXg4NDibvuUlJSxHVF/y1qKx5jaWkJExMTGBoawtDQsNSYon2URiaTQSaTVShPIiIi0i9a7ZmytbWFu7t7uS+pVPr0HQHw9fXFuXPnNO66i4yMhKWlJTw8PMSYqKgoje0iIyPh6+sLAJBKpfD29taIUavViIqKEmPqg7D/dBDf69j9A0RERHpHZ8ZMJSUl4fTp00hKSkJBQQFOnz6N06dP4+HDhwCAAQMGwMPDAyNGjMCZM2ewa9cuLFiwAJMmTRJ7jSZMmIBr165hzpw5iI+Px5dffolffvkF06dPFz9nxowZ+Oabb7BhwwZcvHgREydORFZWFsaMGaOV4y7NAI8nY7oKOAs6ERGRVmn1Ml9lhIaGYsOGDeJyp06dAAD79u1D3759YWhoiG3btmHixInw9fWFmZkZRo0ahQ8++EDcxtXVFdu3b8f06dOxatUqNG3aFN9++y38/f3FmCFDhuDu3bsIDQ2FUqmEl5cXIiIiSgxK1yajYrOg56sFGBlqMRkiIqIGTufmmdIFtT3PVE5+AdosKJwX68egbujVyrbGP4OIiKihafDzTDUkxgZPvrYfom9oMRMiIiJiMaWDDAwk4nszKa/xERERaROLKR239fRtbadARETUoLGYIiIiIqoGFlNERERE1cBiioiIiKgaWEzpqPmD2orvObsFERGR9rCY0lHujhbi+7wCFlNERETawmJKR9laPHmw8sOcfC1mQkRE1LCxmNJRre2e9Ezl5BdoMRMiIqKGjcWUjio+cefSHfFazISIiKhhYzGlB/46w4k7iYiItIXFFBEREVE1sJgiIiIiqgYWUzqsWSNTAMAo3+ZazoSIiKjhYjGlwwZ42AMAkh880nImREREDReLKR2W9jAHAOCgkGs5EyIiooaLxZQOc3e0BADk5Km1nAkREVHDxWJKh8mMCr8+TtpJRESkPSymdJjMyBAAkJPPnikiIiJtYTGlwwz//+2dvPFAu4kQERE1YCymdNj2c0oAwL2sXC1nQkRE1HCxmNJhQ7s6i+93nLujxUyIiIgaLhZTOsyx2JQI72w8qcVMiIiIGi4WUzrMTGak7RSIiIgaPBZTOszIQKLtFIiIiBo8FlM6rLGZTGM5r4BTJBAREdU1FlM6TGFqjA8D24vLv5+8qcVsiIiIGiYWUzpueLdm4vu5v53DldSHWsyGiIio4WExpeMM/jVuihN4EhER1S2dKKauX7+OoKAguLq6wsTEBC1atMB7772H3FzNySrPnj2LXr16QS6Xw9nZGWFhYSX2tWXLFri7u0Mul8PT0xM7duzQWC8IAkJDQ+Ho6AgTExP4+fnh8uXLtXp8Nen87Qxtp0BERNSg6EQxFR8fD7Vaja+//hrnz5/HZ599hvDwcLz77rtijEqlwoABA9C8eXPExsZi+fLlWLRoEdauXSvGHD16FMOGDUNQUBBOnTqFwMBABAYGIi4uTowJCwvD6tWrER4ejpiYGJiZmcHf3x+PHz+u02Ouqg3RN7SdAhERUYMiEQRB0HYSVbF8+XJ89dVXuHbtGgDgq6++wvz586FUKiGVSgEAISEh2Lp1K+Lj4wEAQ4YMQVZWFrZt2ybu55lnnoGXlxfCw8MhCAKcnJwwc+ZMzJo1CwCQkZEBe3t7rF+/HkOHDq1QbiqVCgqFAhkZGbC0tKzJwy6VS8h2jeWrSwbBkNMmEBERVUpVf791omeqNBkZGWjUqJG4HB0djd69e4uFFAD4+/sjISEBDx48EGP8/Pw09uPv74/o6GgAQGJiIpRKpUaMQqGAj4+PGFMfFb+jDwD+E35US5kQERE1PDpZTF25cgVr1qzB22+/LbYplUrY29trxBUtK5XKcmOKry++XWkxpcnJyYFKpdJ41aVhxZ7RBwCnktKR+TivTnMgIiJqqLRaTIWEhEAikZT7KrpEV+TWrVt4/vnn8dprr2HcuHFaylzT0qVLoVAoxJezs/PTN6pBRoYG2D29t0bb3vjUOs2BiIioodLqw91mzpyJ0aNHlxvj5uYmvr99+zb69euH7t27awwsBwAHBwekpKRotBUtOzg4lBtTfH1Rm6Ojo0aMl5dXmTnOmzcPM2bMEJdVKlWdF1St7S00lgvUOjkUjoiISOdotZiytbWFra1thWJv3bqFfv36wdvbG+vWrYOBgWanmq+vL+bPn4+8vDwYGxsDACIjI9GmTRtYW1uLMVFRUQgODha3i4yMhK+vLwDA1dUVDg4OiIqKEosnlUqFmJgYTJw4sczcZDIZZDJZmeu1IepiKl7p3FTbaRAREek9nRgzdevWLfTt2xfNmjXDJ598grt370KpVGqMY3rjjTcglUoRFBSE8+fPY/PmzVi1apVGj9G0adMQERGBFStWID4+HosWLcKJEycwefJkAIBEIkFwcDAWL16Mv/76C+fOncPIkSPh5OSEwMDAuj7sajl46a62UyAiImoQtNozVVGRkZG4cuUKrly5gqZNNXtbimZ2UCgU2L17NyZNmgRvb2/Y2NggNDQU48ePF2O7d++OTZs2YcGCBXj33XfRqlUrbN26Fe3bP7kbbs6cOcjKysL48eORnp6Onj17IiIiAnK5vG4Othp6tbLBoctpAIBXOjfRcjZEREQNg87OM1Wf1fU8U0Ue5xXAfWEEAKCjsxX+nNSjzj6biIhI1zW4eaaoJLmxIRwVhT1oZ5LTtZsMERFRA8FiSs+0c3pSSW+M4aNliIiIahuLKT0zwtdFfD//j7iyA4mIiKhGsJjSM+dvZ2g7BSIiogaFxZSe8W/noO0UiIiIGhQWU3rGwbLsKRwe5xXgv//cwM0H2XWYERERkX7TiXmmqOLkxoYay10W78F3o7rATGaIkN/O4cSNBwCA68sCtJEeERGR3mExpWcMDSQay2kPczD4iyMl4sb/cAJrR3apq7SIiIj0Fi/zNVC7L6Q8PYiIiIieisVUA5adm6/tFIiIiHQeiyk91M21UYXiui7eU8uZEBER6T8WU3po8/hnKhSXlVtQy5kQERHpPxZTekgikTw96P/4nGsiIqLqYTHVwM397ay2UyAiItJpLKYamK+Gd9ZY/uXETbz94wm4hGzHsp3xWsqKiIhId7GY0lO/vO1bartXMyucWOCn0bbrfOE0CeEHruLcTT7bj4iIqDJYTOmpbq6NcH1ZAPbM6I3erW3FdjsLOWzMZWVu9+Lnh+siPSIiIr3BGdD1XEs7C2wY0xXfHU5Eh6ZW4gzp9pYypKhySt0mJ78AMiPDUtcRERGRJvZMNQASiQRje7lpzD/1fDuHMuPbLIjAhdsqXErJrIv0iIiIdBqLqQZqbC+3ctcPWn0IAz47iIc5nCWdiIioPCymGiiZkeZXP6FPi1Ljku5l10U6REREOovFVANla/FkEPqJBX54q6dLqXFJ97PqKCMiIiLdxAHoDZREIkHi0kHi+7J8GnkJPVvZwlzGPypERESlYc9UAyaRSJ766JlLKQ/R/r1dWLXnch1lRUREpFtYTJFo57Re6NhUUeq6z/ZcquNsiIiIdAOLKRK1dbTEn5N7ajsNIiIincJiikrYPb13qe3KjMd1nAkREVH9x2KKSmhtb4HBXk4l2p9ZGqWFbIiIiOo33qJFpfrgpfZoam2CTs7WGPvDCbH9YU4+7+wjIiIqhj1TVCqFqTFm+7vDz8Neo33shuNayoiIiKh+0pli6qWXXkKzZs0gl8vh6OiIESNG4Pbt2xoxZ8+eRa9evSCXy+Hs7IywsLAS+9myZQvc3d0hl8vh6emJHTt2aKwXBAGhoaFwdHSEiYkJ/Pz8cPlyw54WwNXGTHz/z7X7WsyEiIio/tGZYqpfv3745ZdfkJCQgN9++w1Xr17Ff/7zH3G9SqXCgAED0Lx5c8TGxmL58uVYtGgR1q5dK8YcPXoUw4YNQ1BQEE6dOoXAwEAEBgYiLi5OjAkLC8Pq1asRHh6OmJgYmJmZwd/fH48fN9zB1/tm9dVYFgRBO4kQERHVQxJBR38Z//rrLwQGBiInJwfGxsb46quvMH/+fCiVSkilUgBASEgItm7divj4eADAkCFDkJWVhW3bton7eeaZZ+Dl5YXw8HAIggAnJyfMnDkTs2bNAgBkZGTA3t4e69evx9ChQyuUm0qlgkKhQEZGBiwtLWv4yLXDJWS7+H7WgNaY/GwrLWZDRERU86r6+60zPVPF3b9/Hxs3bkT37t1hbGwMAIiOjkbv3r3FQgoA/P39kZCQgAcPHogxfn5+Gvvy9/dHdHQ0ACAxMRFKpVIjRqFQwMfHR4wh4JPdl3A/K1fbaRAREdULOlVMzZ07F2ZmZmjcuDGSkpLw559/iuuUSiXs7TUHSxctK5XKcmOKry++XWkxpcnJyYFKpdJ46ZvfJvpqLP9yIhkA8OfpW3AJ2Q6XkO1Qq3Wyk5OIiKhatFpMhYSEiM+HK+tVdIkOAGbPno1Tp05h9+7dMDQ0xMiRI+vF+J2lS5dCoVCIL2dnZ22nVOOcrU01lpftLPxepv18Wmz76sBV5BeoS2xbH74jIiKi2qLVCYNmzpyJ0aNHlxvj5uYmvrexsYGNjQ1at26Ntm3bwtnZGf/88w98fX3h4OCAlJQUjW2Llh0cHMT/lhZTfH1Rm6Ojo0aMl5dXmTnOmzcPM2bMEJdVKpXeFVR2lvKnxizflYDfT95E1My+Ytu9hznwXrwHjcykOLnwuVrMkIiISDu02jNla2sLd3f3cl/Fx0AVp1YX9oDk5OQAAHx9fXHw4EHk5eWJMZGRkWjTpg2sra3FmKgozVm8IyMj4etbeAnL1dUVDg4OGjEqlQoxMTFiTGlkMhksLS01Xvpo01gfjeXig9KLXL2bpbHsvXgPAHCMFRER6S2dGDMVExODzz//HKdPn8aNGzewd+9eDBs2DC1atBCLnDfeeANSqRRBQUE4f/48Nm/ejFWrVmn0GE2bNg0RERFYsWIF4uPjsWjRIpw4cQKTJ08GAEgkEgQHB2Px4sX466+/cO7cOYwcORJOTk4IDAzUxqHXK91b2sCvrd1T47Jz8+sgGyIiovpBJ4opU1NT/P777+jfvz/atGmDoKAgdOjQAQcOHIBMJgNQeNfd7t27kZiYCG9vb8ycOROhoaEYP368uJ/u3btj06ZNWLt2LTp27Ihff/0VW7duRfv27cWYOXPmYMqUKRg/fjy6du2Khw8fIiIiAnL50y9zNQTtnBRPjbmamlVqO8dOERGRPtLZeabqM32cZ6rInYxH8F26t9yYlUO88FLHwgclu737ZIb5Yd2aYekrnrWaHxERUVU1qHmmSHscFSZPjbG1kMHt3R0ahRQA/HQsCarHeWVsRUREpJsqXUz16dMHP/zwAx49elQb+ZCOmvFca/H9hqPXy4zrsGg3CyoiItIrlS6mOnXqhFmzZsHBwQHjxo3DP//8Uxt5kY6Z2v/J42V2X0gpJxIY8d2x2k6HiIiozlS6mFq5ciVu376NdevWITU1Fb1794aHhwc++eSTEnM4EZXmTHJ6uesf5uSjx7K9iFfq30zyRESkf6o0ZsrIyAivvPIK/vzzT9y8eRNvvPEGFi5cCGdnZwQGBmLv3vIHKJNu+29Q4XxTrjZmAIDZ/m1qbN/J97PR/r1duJX+CM+vPFRj+yUiIqot1ZoB/dixY1i3bh1+/vln2NnZYfTo0bh16xZeeOEFvPPOO/jkk09qKk+qR3q2ssGRkGfhYCmHoYFEbLeQGSEzp2JzTK2OuqxxabDIzC1nNJY/3Z2AGQNqrlgjIiKqaZXumUpNTcWKFSvQvn179OrVC3fv3sVPP/2E69ev4/3338e3336L3bt3Izw8vDbypXqiiZWJRiEFAIteaqexbCErrNV/eKsbri8L0Fj3aeSlUvd7LPG+xvLqvVeQmFb6vFVERET1QaV7ppo2bYoWLVrgrbfewujRo2Fra1sipkOHDujatWuNJEi6406G5h2e26b2hL2lHHJjQwBAl+bWOHHjgbh+xe4ETOrXEr+fvIV3/ziHdaNL/zPT75P9aGptgsNzn6295ImIiKqo0pN2Hjp0CL169aqtfPSCPk/aWZ5rdx/i2RUHxOUjIc+iiZXmvFSlPc+vol7s6IQ1wzpVeXsiIqLy1NmknSykqCxFA9KLGP/rMiAAzH3evcr7//vM7SpvS0REVFsqfZmvU6dOkEhK/khKJBLI5XK0bNkSo0ePRr9+/WokQdId//5zYWshKxEzsW8LfBwR/9R9nQkdgI4f7C7Rnnw/G86NTKueJBERUQ2rdM/U888/j2vXrsHMzAz9+vVDv379YG5ujqtXr6Jr1664c+cO/Pz88Oeff9ZGvlTPPePWSHxfWtENABc/eP6p+zGXl17nbz6eXLXEiIiIakmli6m0tDTMnDkThw4dwooVK7BixQocPHgQs2bNQlZWFnbv3o0FCxbgww8/rI18qZ77adwzmPpsS/w1uUeZMSZSw6fux9BAggBPRwDA612aiu2f77tS/SSJiIhqUKUHoCsUCsTGxqJly5Ya7VeuXIG3tzcyMjIQHx+Prl27IjMzs0aT1RUNdQB6ZTxtIPr1ZQEoUAu4lJKJNvYW8PpgN1SP8zHI0wFfDveuoyyJiKghqbMB6HK5HEePHi3RfvToUcjlcgCAWq0W3xOV5uDsfpjYt4XGcpExPVwAFPZOtXW0hIGBBIGdmgAAKlf6ExER1b5KD0CfMmUKJkyYgNjYWHEuqePHj+Pbb7/Fu+++CwDYtWsXvLy8ajRR0i/NGpti7vPuMJMawkJujGaNTRH+pjcSlJmY8mzLEvEpqscAAAcFi3QiIqpfKn2ZDwA2btyIzz//HAkJCQCANm3aYMqUKXjjjTcAAI8ePRLv7muIeJmv5o1edwz7E+4CAK4tGQSDUqZdICIiqo6q/n5XqmcqPz8fS5YswVtvvYXhw4eXGWdiYlLmOqKqKCqkAODI1TT0alVy5n0iIiJtqNSYKSMjI4SFhSE/v2IPsyWqKb1a2YjvR3x3TIuZEBERaar0APT+/fvjwIEDTw8kqkFdXRo9PYiIiEgLKj0AfeDAgQgJCcG5c+fg7e0NMzPNR4i89NJLNZYcUZFRvi74NPKSuJybr4bUqNL/FtCQk18AQYD4IGYiIqKqqPQAdAODsn/AJBIJCgoKqp2UruMA9Nrxwd8X8P2RRACAZxMF/p7SE1tP3ULw5tPY8FY39Gld8XFUarUAt3d3ACickb0iE4kSEZF+q7N5ptRqdZkvFlJUm0Jf9BDfn7uVgff/Po/gzacBAKO+r/g4qsd5BWIhBQCxNx7UWI5ERNTwVOs6yePHj2sqD6JKW3fkepW2+0+45qSzt9KzayAbIiJqqCpdTBUUFODDDz9EkyZNYG5ujmvXrgEAFi5ciO+++67GEyQqrr+7XbX3EXdLpbE897dz1d4nERE1XJUupj766COsX78eYWFhkEqlYnv79u3x7bff1mhyRP8WPqLs5/IduvxkLqriQwGVGY+hepxXq3kREVHDVem7+X744QesXbsW/fv3x4QJE8T2jh07Ij4+vkaTI/o3Y8Oy6/9R3x/Dsfl+8P/sIO5l5ZZYf+zd/rCzlMNRIcedDF6iJiKimlHpnqlbt26hZcuSz05Tq9XIy+O//kl71ALQZfGeUgspAOi2JAqpmY9LFFJNrEyQnZsPQRBwJ+MRqvCEJSIiasAqXUx5eHjg0KFDJdp//fVXdOrUqUaSIirPoTn9EDLQHYsD2+PtPm6V2rbbR1El2m6lP4JH6C58uf8qfJfuxeAvjgAAziSn4+djSSyuiIioXJW+zBcaGopRo0bh1q1bUKvV+P3335GQkIAffvgB27Ztq40ciTQ4NzLFhD4txOXNx5ORnl35XtFdwb3hv/KguLx8V+GDu8/ezAAAsaiSGRvg5U5Nq5MyERHpsUr3TA0ePBh///039uzZAzMzM4SGhuLixYv4+++/8dxzz9VGjhpycnLg5eUFiUSC06dPa6w7e/YsevXqBblcDmdnZ4SFhZXYfsuWLXB3d4dcLoenpyd27NihsV4QBISGhsLR0REmJibw8/PD5cuXa/OQqJrWjuhS6W3a2Fugtb15mes3xtwQ30dfvVelvIiIqGGo0jxTvXr1QmRkJFJTU5GdnY3Dhw9jwIABNZ1bqebMmQMnJ6cS7SqVCgMGDEDz5s0RGxuL5cuXY9GiRVi7dq0Yc/ToUQwbNgxBQUE4deoUAgMDERgYiLi4ODEmLCwMq1evRnh4OGJiYmBmZgZ/f3/OqVWPdXNtBCtT41LXeTZRYP6gtiXaE1IyIZFIytzn/D+e/Jn45cTN6idJRER6q8qTdubm5uLmzZtISkrSeNWmnTt3Yvfu3fjkk09KrNu4cSNyc3Px/fffo127dhg6dCimTp2KTz/9VIxZtWoVnn/+ecyePRtt27bFhx9+iM6dO+Pzzz8HUNgrtXLlSixYsACDBw9Ghw4d8MMPP+D27dvYunVrrR4bVU9jM2mJtmHdnPHnpB4Y19sN15cFINivlRYyIyIifVfpYury5cvo1asXTExM0Lx5c7i6usLV1RUuLi5wdXWtjRwBACkpKRg3bhx+/PFHmJqallgfHR2N3r17a8x95e/vj4SEBDx48ECM8fPz09jO398f0dHRAIDExEQolUqNGIVCAR8fHzGG6qderZ48l2/pK56IXeCHJS97wsDgSe/T9bSsEtvJjSv2VyA1kz2TRERUukoXU6NHj4aBgQG2bduG2NhYnDx5EidPnsSpU6dw8uTJ2sgRgiBg9OjRmDBhArp0KX18jFKphL29vUZb0bJSqSw3pvj64tuVFlOanJwcqFQqjRfVrZCB7uL7Vzs3RWNzWYnLeK90fjKIfNVQLwDAH+/0qND+S7sLkIiICKjC3XynT59GbGws3N3dnx78FCEhIfj444/Ljbl48SJ2796NzMxMzJs3r9qfWRuWLl2K999/X9tpNGhyY0PEf/g8AEBqVPq/ETo6W4nvc/LUAIC2jpa4tHggWi/YCQDYPrUnbj54hLd/jK3dhImISG9Uupjy8PBAWlpajXz4zJkzMXr06HJj3NzcsHfvXkRHR0Mmk2ms69KlC4YPH44NGzbAwcEBKSkpGuuLlh0cHMT/lhZTfH1Rm6Ojo0aMl5dXmTnOmzcPM2bMEJdVKhWcnZ3LPS6qeXJjw3LXK0yeDFJ/rcuTXiqpkQGuLwsQl9XqJ9s0sTLBrfRHNZckERHpnUoXUx9//DHmzJmDJUuWwNPTE8bGmndRWVpaVnhftra2sLW1fWrc6tWrsXjxYnH59u3b8Pf3x+bNm+Hj4wMA8PX1xfz585GXlyfmFBkZiTZt2sDa2lqMiYqKQnBwsLivyMhI+Pr6AgBcXV3h4OCAqKgosXhSqVSIiYnBxIkTy8xPJpOVKPSofipeNJXFs6kCCwLaoqm1CZpYmeLFzw/XQWZERKSrKl1MFQ3O7t+/v0a7IAiQSCQoKCiomcyKadasmcayuXnh/EAtWrRA06aFPQxvvPEG3n//fQQFBWHu3LmIi4vDqlWr8Nlnn4nbTZs2DX369MGKFSsQEBCAn3/+GSdOnBCnT5BIJAgODsbixYvRqlUruLq6YuHChXByckJgYGCNHxfVX2N7Fc6sfu7/E3gChYPQ7Szk2kqJiIjqqUoXU/v27auNPKpNoVBg9+7dmDRpEry9vWFjY4PQ0FCMHz9ejOnevTs2bdqEBQsW4N1330WrVq2wdetWtG/fXoyZM2cOsrKyMH78eKSnp6Nnz56IiIiAXM4f0YaoVbGJPUd+dwwRwb21mA0REdVHEoEPHqtxKpUKCoUCGRkZlbrsSfWTS8h2AMBzHvb4ZmTlZ1snIiLdUNXf7ypN2nno0CG8+eab6N69O27dugUA+PHHH3H4MMeWkP6Z2r9wss+8AvVTIomIqCGqdDH122+/wd/fHyYmJjh58iRycnIAABkZGViyZEmNJ0ikbdb/f1TN/oS7YEcuERH9W6WLqcWLFyM8PBzffPONxp18PXr0qLVJO4m06VHek5sqDl2umWlBiIhIf1S6mEpISEDv3iUH4SoUCqSnp9dETkT1yohnmovvR35/DJ9FXkJWTr4WMyIiovqk0sWUg4MDrly5UqL98OHDcHNzq5GkiOoTC7nmXGqroi5j2Df/aCkbIiKqbypdTI0bNw7Tpk1DTEwMJBIJbt++jY0bN2LWrFnlTmxJpE/OFpt/ioiIGrZKzzMVEhICtVqN/v37Izs7G71794ZMJsOsWbMwZcqU2siRqN4xlZb/6BoiImo4qjzPVG5uLq5cuYKHDx/Cw8NDnJWcOM+UPtpyIhmzfz2r0VaRR9MQEZHuqOrvd6V7popIpVJ4eHhUdXMinRLYqQmOXr0Hl8Zm+GzPJQBAbr4aUqMqTdVGRER6pMrFFFFDYmxogM+GeCG/QC0WU3G3M5Cbr4Yy4zGeb+8AuTEv/RERNUQspogqwcjwSU/UK18efbJiM/DnpB7o6GxV90kREZFW8RoFUQ2Z8N9YbadARERawGKKqJJGd3cptf1OxmO4hGyHS8h2PMotKDWGiIj0T4Xu5vvrr78qvMOXXnqpWgnpA97Np98e5xXAfWHEU+MuLR7IAepERDqkqr/fFSqmDAwq9oMgkUhQUMB/kbOY0n+nk9MR+MURAIBEApT2t6hXKxv8GORTx5kREVFV1erUCGq1usqJEekjL2crXPzgeWTn5iMxLQv/CY8uEcOHIhMRNQy8m4+oikykhjCRGqKxuQzmMiM8LOXhxwVqAYYGEi1kR0REdaVKxVRWVhYOHDiApKQk5ObmaqybOnVqjSRGpEv82zngt5M3AQAT+7bAV/uvAgBavLuDM6UTEem5ShdTp06dwqBBg5CdnY2srCw0atQIaWlpMDU1hZ2dHYspapBkxk/GFfq6NRaLKSIi0n+VvtVo+vTpePHFF/HgwQOYmJjgn3/+wY0bN+Dt7Y1PPvmkNnIkqveea2svvu/VygYDPJ4s/xp7UxspERFRHan0g46trKwQExODNm3awMrKCtHR0Wjbti1iYmIwatQoxMfH11auOoN38zVMO8/dQSt7C7S0M0degRqt5u8U1/FSHxFR/VfV3+9K90wZGxuLUyXY2dkhKSkJAKBQKJCcnFzZ3RHpjYGejmhpZw6g8Fl+RETUMFR6zFSnTp1w/PhxtGrVCn369EFoaCjS0tLw448/on379rWRIxEREVG9Vel/Pi9ZsgSOjo4AgI8++gjW1taYOHEi7t69i6+//rrGEyTSVSte6yi+r+TVdCIi0iGV7pnq0qWL+N7Ozg4REU9/rAZRQ9Ti/5f8AGD+1jgsedlTi9kQEVFtqXTP1LPPPov09PQS7SqVCs8++2xN5ESkF9rYW4jvN8UksXeKiEhPVbqY2r9/f4mJOgHg8ePHOHToUI0kRaQPTKSGMDZ8Mvu567wd+DgiHqeT07WXFBER1bgKX+Y7e/as+P7ChQtQKpXickFBASIiItCkSZOazY5Ix/VqZYu98ani8lf7r+Kr/Vc5VQIRkR6pcDHl5eUFiUQCiURS6uU8ExMTrFmzpkaTI9J1C1/w0Cimigxb+w9+DOoGoypOofDFvitwspLj5U5Nq5siERFVU4WLqcTERAiCADc3Nxw7dgy2trbiOqlUCjs7OxgaGtZKkkS6yqWxaant0dfu4cjVe+jT2rbU9eWJuXYPy3clAAD6tbGDlam0WjkSEVH1VLiYat68OQBArVbXWjJE+kYikZS5bu3Bq1UqpiIvpIjvD11Ow4sdnaqUGxER1YwqXWO4evUqpkyZAj8/P/j5+WHq1Km4erV2H+zq4uIiXmYsei1btkwj5uzZs+jVqxfkcjmcnZ0RFhZWYj9btmyBu7s75HI5PD09sWPHDo31giAgNDQUjo6OMDExgZ+fHy5fvlyrx0b6bcNb3TDimea4tmSQRvuRK/ew/eydSu1rf0Iqvj2cKC5P+elUjeRIRERVV+liateuXfDw8MCxY8fQoUMHdOjQATExMWjXrh0iIyNrI0fRBx98gDt37oivKVOmiOtUKhUGDBiA5s2bIzY2FsuXL8eiRYuwdu1aMebo0aMYNmwYgoKCcOrUKQQGBiIwMBBxcXFiTFhYGFavXo3w8HDExMTAzMwM/v7+ePz4ca0eG+mvPq1t8WFgexgYSPDPvP4a6yZtOlmhfQiCAJeQ7Ri97niJdS4h27GnWG8VERHVrUo/6LhTp07w9/cv0SsUEhKC3bt34+TJiv04VJaLiwuCg4MRHBxc6vqvvvoK8+fPh1KphFQqFXPaunWr+PDlIUOGICsrC9u2bRO3e+aZZ+Dl5YXw8HAIggAnJyfMnDkTs2bNAgBkZGTA3t4e69evx9ChQyuUKx90TOVRqwW4vfukR/RM6AAoTI3L3eb9v89j3ZHr5caEvdoBr3VpWu6lRSIiKludPej44sWLCAoKKtH+1ltv4cKFC5XdXaUsW7YMjRs3RqdOnbB8+XLk5+eL66Kjo9G7d2+xkAIAf39/JCQk4MGDB2KMn5+fxj79/f0RHR0NoHCQvVKp1IhRKBTw8fERY0qTk5MDlUql8SIqi4GBBMfmP+mh6vjB7qdu87RCCgDm/HYWrvN24PeTN6uTHhERVVKliylbW1ucPn26RPvp06dhZ2dXEzmVaurUqfj555+xb98+vP3221iyZAnmzJkjrlcqlbC3t9fYpmi5aE6ssmKKry++XWkxpVm6dCkUCoX4cnZ2ruJRUkNhZyGv9j5+m9i91PYZv5zBiev3q71/IiKqmAoXUx988AGys7Mxbtw4jB8/Hh9//DEOHTqEQ4cOYdmyZXj77bcxbty4Sn14SEhIiUHl/34VXaKbMWMG+vbtiw4dOmDChAlYsWIF1qxZg5ycnModcS2YN28eMjIyxFdycrK2UyIdMG+gOwCgUzOrcuNy85/cQbvsFU+sG9MVv030hXdza3w4uF2p2/wnvOyeVCIiqlkVnhrh/fffx4QJE7Bw4UJYWFhgxYoVmDdvHgDAyckJixYtwtSpUyv14TNnzsTo0aPLjXFzcyu13cfHB/n5+bh+/TratGkDBwcHpKRoDsItWnZwcBD/W1pM8fVFbY6OjhoxXl5eZeYok8kgk8nKPQ6if2vfRAEAuJtZ+A8CtVqAgUHJ8U7R1+6J7wd6OkJhYqyxvPDP87WcKRERlafCxVTROHWJRILp06dj+vTpyMzMBABYWFiUt2mZbG1tNSb/rIzTp0/DwMBAvLTo6+uL+fPnIy8vD8bGhT82kZGRaNOmDaytrcWYqKgojUHskZGR8PX1BQC4urrCwcEBUVFRYvGkUqkQExODiRMnVilPorJIjQo7hm8+eISJ/43Fzjgl3unbAlP7t4Lc+MkEuKO+Pya+L15IAYCNuQwx7/bHg+xctLG3wFcHriIsonBCz0spmWhtX7W/m0REVHGVGjP177uELCwsqlxIVUZ0dDRWrlyJM2fO4Nq1a9i4cSOmT5+ON998UyyU3njjDUilUgQFBeH8+fPYvHkzVq1ahRkzZoj7mTZtGiIiIrBixQrEx8dj0aJFOHHiBCZPniweX3BwMBYvXoy//voL586dw8iRI+Hk5ITAwMBaP05qWNxszMT3O+MKx+R9uf8q3BdGIDEtC8n3s9Fj2d6n7sfeUg53B0tIJBKM9HUR23+L5UB0IqK6UOGeKQBo3br1U2+7vn+/5ge+ymQy/Pzzz1i0aBFycnLg6uqK6dOnaxRKCoUCu3fvxqRJk+Dt7Q0bGxuEhoZi/PjxYkz37t2xadMmLFiwAO+++y5atWqFrVu3on379mLMnDlzkJWVhfHjxyM9PR09e/ZEREQE5PLqDxgmKq6xedmXhvt9sr9E20/jnnnqPs1lT/5Kf33wGuYNalul3IiIqOIqPM+UgYEBVq5cCYVCUW7cqFGjaiQxXcZ5pqiiXEK2Vzg2cemgCs0h9fzKg4hXFl6CPzC7L5o3NnvKFkREBFT997tSxZRSqazV6Q/0BYspqqjTyekI/OJIhWKvLwuoUFxGdp44d5WFzAjn3vevcn5ERA1JrU/ayVmViWqel7MVnm9XeBfpH+90x5WPBmLntF4l4pa87FnhfRafTT0zJ7+cSCIiqgmVvpuPiGrWl8M7Q/U4D1amhbP3t3W0rHAvVEWUNeUCERHVjAr3TKnVal7iI6oFBgYSsZCqKXtm9Bbfu727A2kPtT+5LRGRvqr042SIqP5raac5ZYnPkigtZUJEpP9YTBHpqdXDOonvC9QCjl5N02I2RET6i8UUkZ56qaOTxvI3B69pKRMiIv3GYopIj/3+Tnfx/b6Eu1rMhIhIf7GYItJjnZtZ4+fxT2ZOzy9QazEbIiL9xGKKSM91aW4tvt/x/2cAEhFRzWExRaTnjAyf/DWf+tMpJCgzUaDmvHFERDWlUg86JiLd57/yIICKP56GiIjKx54pogbg25FdSrQpMx5rIRMiIv3DYoqoAWjrVPKBnTO3nEZOfoEWsiEi0i8spogagCZWJiXajly5hzYLIvDff25AzTFURERVxmKKqIGInvdsqe0LtsbB79MDdZwNEZH+YDFF1EA4KkywK7g3vh7hXWLdtbQsHL7Mx80QEVWFRBAE9u/XMJVKBYVCgYyMDFhalhyrQqRtZ5LTMfiLIyXa/drawcvZCpOfbQUAuJ+VC2tTY0gkkrpOkYiozlX195s9U0QNUEdnK5wJHVCifc/FVHyy+xKOXk1DRNwddP4wEuN/jIVLyHa4hGwv9Q7AI1fS4Ls0Csev36+L1ImI6h32TNUC9kyRrnAJ2V7pbeY83wZBPV0hMzLEo9wCtA2NENdx7ioi0mXsmSKiStszow8m9m1RqW3CIhLQZkEErqRmahRSAJCRnVeT6RER6QT2TNUC9kyRLur8YSTuZ+VWax9GBhJcWTKohjIiIqpb7JkiomqJnvcsNo31gYOlvMr7yFcLyC9Q12BWRET1H4spIgIAyIwM0b2lDf55tz9m+7cR278b1QVnQgfgu1ElH0lT5Ph8P/F9y/k7azVPIqL6hg86JqISJvVribuZOVBmPEaf1rYwMjRA/7b2uL4sAPN+P4ufjiWLsSED3WFrIdNitkRE2sUxU7WAY6ZInwmCgPtZuQg/cBUt7cwxpGszAMD2s3cwadNJAMC1JYNgYMC5qYhIt1T195s9U0RUKRKJBI3NZZgf4KHR7udhJ77/b8wNhP55Xlze8FY39GltW2c5EhHVJY6ZIqIaITMyFN8XL6QAYNT3x/A4rwB5HJxORHqIxRQR1ZgRzzQvc537wgi0mr+TBRUR6R0WU0RUY9o6Pn2Mwf6Eu3WQCRFR3dGpYmr79u3w8fGBiYkJrK2tERgYqLE+KSkJAQEBMDU1hZ2dHWbPno38/HyNmP3796Nz586QyWRo2bIl1q9fX+JzvvjiC7i4uEAul8PHxwfHjh2rxaMi0h+vdWkqvh/f2w09W9rg3UHuGjF/n7ld12kREdUqnRmA/ttvv2HcuHFYsmQJnn32WeTn5yMuLk5cX1BQgICAADg4OODo0aO4c+cORo4cCWNjYyxZsgQAkJiYiICAAEyYMAEbN25EVFQUxo4dC0dHR/j7+wMANm/ejBkzZiA8PBw+Pj5YuXIl/P39kZCQADs7u1JzI6JCxoYGOLXwOTzMyYdzI1Ox/Vjifey5mAoAiDiv1FZ6RES1QiemRsjPz4eLiwvef/99BAUFlRqzc+dOvPDCC7h9+zbs7e0BAOHh4Zg7dy7u3r0LqVSKuXPnYvv27RpF2NChQ5Geno6IiMJnjPn4+KBr1674/PPPAQBqtRrOzs6YMmUKQkJCKpQvp0Yg0pT2MAcfbruAP08X9kqdCR0AhamxlrMiItKk14+TOXnyJG7dugUDAwN06tQJjo6OGDhwoEZRFB0dDU9PT7GQAgB/f3+oVCqcP39ejPHz89PYt7+/P6KjowEAubm5iI2N1YgxMDCAn5+fGFOanJwcqFQqjRcRPWFjLsPHr3YQl5dFXNRiNkRENUsniqlr164BABYtWoQFCxZg27ZtsLa2Rt++fXH//n0AgFKp1CikAIjLSqWy3BiVSoVHjx4hLS0NBQUFpcYU7aM0S5cuhUKhEF/Ozs7VO2AiPSQ3NkQ3l0YAgFNJ6dpNhoioBmm1mAoJCYFEIin3FR8fD7W68Fbq+fPn49VXX4W3tzfWrVsHiUSCLVu2aPMQAADz5s1DRkaG+EpOTn76RkQN0PBnCmdLj1dmIiM7D7+fvImuH+3Bsp3xGnFnb6Yj+uo9/PefG1i157I2UiUiqjCtDkCfOXMmRo8eXW6Mm5sb7ty5AwDw8Hgy47JMJoObmxuSkpIAAA4ODiXuuktJSRHXFf23qK14jKWlJUxMTGBoaAhDQ8NSY4r2URqZTAaZjM8mI3qaHi1txPcdP9gtvg8/cBVnb6Zj07hnEHvjPl79SvOyev+2dmjfRFFneRIRVYZWe6ZsbW3h7u5e7ksqlcLb2xsymQwJCQnitnl5ebh+/TqaNy+cJNDX1xfnzp1DamqqGBMZGQlLS0uxCPP19UVUVJRGDpGRkfD19QUA8bOKx6jVakRFRYkxRFR1NuZl/6Pj6NV7SFU9LlFIAcDc387WZlpERNWiE2OmLC0tMWHCBLz33nvYvXs3EhISMHHiRADAa6+9BgAYMGAAPDw8MGLECJw5cwa7du3CggULMGnSJLHXaMKECbh27RrmzJmD+Ph4fPnll/jll18wffp08bNmzJiBb775Bhs2bMDFixcxceJEZGVlYcyYMXV/4ER6yN3Bosx13ZZEldp+/jZv6iCi+ksniikAWL58OYYOHYoRI0aga9euuHHjBvbu3Qtra2sAgKGhIbZt2wZDQ0P4+vrizTffxMiRI/HBBx+I+3B1dcX27dsRGRmJjh07YsWKFfj222/FOaYAYMiQIfjkk08QGhoKLy8vnD59GhERESUGpRNR1YS/6S2+//T1jri+LACW8qePOBj3w4naTIuIqMp0Yp4pXcN5pojKt+u8Eo9yCxDYqQkA4IO/L+D7I4kaMWcXDYCFzAiBXxzBmZsZYvvVJYNgaCCp03yJqGHQ63mmiEi/+LdzEAspAAgZqPnImW1TesJSbgyJRIKtk3porPst9mad5EhEVFHsmaoF7Jkiqrz8AjXO3MxAW0cLmEo1L/t9sisBn++7Uup2/d3t8O2oLgAAiYQ9VkRUdVX9/WYxVQtYTBHVLEEQ4Dpvx1PjDs3pB+dGpsjNVyP9US6MDAzQyExaBxkSkT7gZT4i0lsSiQQ+ro2eGvftoWvIK1Cj9YKd6PZRFDp/GImzN9NrP0EiatBYTBGRTlg/pht8XBth5nOtMfd5dzg3MikRsyH6Bqb9fEqjLfTP83WVIhE1ULzMVwt4mY+o7giCgF9jb2L2r2VP7HltySAY8A5AInoKXuYjogZJIpEgoINjifb2TZ78j3DTsaS6TImIGhgWU0Sk80ylRnirhysAwMFSjmn9W+HVzk3F9Qu2xmkrNSJqALT6oGMiopoS+qIHQl988jD0/AI13v/7AgCgiVXJ8VVERDWFPVNEpJeMDA2wfkxXAMCt9Edo/94u3tlHRLWCxRQR6S3PJgrx/cOcfLz0+RHkFai1mBER6SMWU0Sktxqby6AwMdZoi73xQEvZEJG+YjFFRHrt5MLncP59f3E5+X42EtOyMGjVISzYek6LmRGRvuAAdCLSa4YGEpjJjPB8OwdEnFdqzEd14Y4KiwM9tZgdEekD9kwRUYPQ1rH0CfiOX79fx5kQkb5hMUVEDcLkZ1uW2v5aeDTSs3PrOBsi0icspoioQTA0kGDeQHcAhXf5vf9SO3Gd1weR6L9iP745eE1b6RGRDuOz+WoBn81HVP8JggDXeTtKtG+b0hPti02pQEQNB5/NR0RUCRKJBHHF7vIrEvJ72Q9MJiIqDYspImqwzGVG2DOjj0Zb3C0VHmRxDBURVRyLKSJq0FramWPVUC98Obyz2Nbpw0g8zMnXYlZEpEtYTBFRgzfYqwkGeTpqtLV/bxd+i72ppYyISJewmCIi+r9p/VtpLM/ccgaroy5rKRsi0hUspoiI/m/6c62xcogX3nymmdj2aeQlpKgeazErIqrvWEwRERUT2KlJiUfMLNsZXyJOrRZwnwPViQh8Nh8RUalG+TbHhugbAIA/Tt3CZ0O8sGTHRfx+8ibSHj4popo3NkXYqx3g49ZYW6kSkZZx0s5awEk7ifTDkStpGP5tTIViExY/D5mRYS1nRES1iZN2EhHVsB4tbeBmY1ah2CmbTtVyNkRUX7GYIiIqx95ZfTWWDQ0k2DalJ658NBDXlwWgnVPhv153X0jB0atpWsiQiLSNxRQR0VPsCu4tvv/jne5o30QBI8PC/32uHdlFXPfGNzHYG5+C/AJ1nedIRNqjE8XU/v37IZFISn0dP35cjDt79ix69eoFuVwOZ2dnhIWFldjXli1b4O7uDrlcDk9PT+zYofmgU0EQEBoaCkdHR5iYmMDPzw+XL3OeGaKGrI2DBa4vC8D1ZQHo0NRKY10TKxNseKubuPzW+hNoOX8ntpxIxpYTyTiTnK4Rr1YLyGOxRaRXdKKY6t69O+7cuaPxGjt2LFxdXdGlS+G/ClUqFQYMGIDmzZsjNjYWy5cvx6JFi7B27VpxP0ePHsWwYcMQFBSEU6dOITAwEIGBgYiLixNjwsLCsHr1aoSHhyMmJgZmZmbw9/fH48ecZ4aIStentS3mDXTXaJv961nM/vUsBn9xBO4Ld2LnuTuY/8c5uL27A94fRvL5f0R6RCfv5svLy0OTJk0wZcoULFy4EADw1VdfYf78+VAqlZBKpQCAkJAQbN26FfHxhXPEDBkyBFlZWdi2bZu4r2eeeQZeXl4IDw+HIAhwcnLCzJkzMWvWLABARkYG7O3tsX79egwdOrRC+fFuPqKG6XRyOgK/OFLh+B/e6oberW1rMSMiqowGdTffX3/9hXv37mHMmDFiW3R0NHr37i0WUgDg7++PhIQEPHjwQIzx8/PT2Je/vz+io6MBAImJiVAqlRoxCoUCPj4+YkxpcnJyoFKpNF5E1PB4OVvh+rIAXFo8EFOebYkWtuXfCTjy+2NYsPVcHWVHRLVFJ4up7777Dv7+/mjatKnYplQqYW9vrxFXtKxUKsuNKb6++HalxZRm6dKlUCgU4svZ2bmKR0ZE+kBqZICZA9ogamZfXFo8EP7t7GFtaoyd03rhr8k9YG1qLMb+958kJKZlaTFbIqourRZTISEhZQ4sL3oVXaIrcvPmTezatQtBQUFayrqkefPmISMjQ3wlJydrOyUiqiekRgb4ekQXnAodgLaOlujQ1AqnQgegv7udGNPvk/14nFdQYtuLd1RYe/Aqx1cR1XNafZzMzJkzMXr06HJj3NzcNJbXrVuHxo0b46WXXtJod3BwQEpKikZb0bKDg0O5McXXF7U5OjpqxHh5eZWZo0wmg0wmK/c4iIiK+250V0z96RT+OnMbAPDKl0exfWpPpGfnwdpMitTMxxi46hAAYMmOeCQuHQSJRKLNlImoDFotpmxtbWFrW/HBl4IgYN26dRg5ciSMjY011vn6+mL+/PnIy8sT10VGRqJNmzawtrYWY6KiohAcHCxuFxkZCV9fXwCAq6srHBwcEBUVJRZPKpUKMTExmDhxYjWOlIioJD8Pe7GYunBHhXE/nMCei6kAABNjzUfTPLM0CuFveqNTM+s6z5OIyqdTY6b27t2LxMREjB07tsS6N954A1KpFEFBQTh//jw2b96MVatWYcaMGWLMtGnTEBERgRUrViA+Ph6LFi3CiRMnMHnyZACARCJBcHAwFi9ejL/++gvnzp3DyJEj4eTkhMDAwLo6TCJqIF7q6ITPhnQUl4sKKQB49K/LfimqHLz85dFK3S1IRHVDp4qp7777Dt27d4e7u3uJdQqFArt370ZiYiK8vb0xc+ZMhIaGYvz48WJM9+7dsWnTJqxduxYdO3bEr7/+iq1bt6J9+/ZizJw5czBlyhSMHz8eXbt2xcOHDxEREQG5XF4nx0hEDcvLnZriP95Ny1y/5GVPjeXTyemY9/s5pKo49x1RfaGT80zVd5xniogqQxAEfBZ5Cav3XoHMyADGhgZ4mJMPALi+LADv/30e645c19imWSNTHJzTTwvZEumvqv5+s5iqBSymiKgqUlSPIQjA/axc7Iy7gzefaQ57y8Je8Ue5BZjw31gcuHRXjP9rco8Sj7choqpjMVWPsJgiotryOK8A7gsjxOVrSwbBwIB3+RHVhAY1AzoRUUMlNzbE/EFtxWW3d3fg+PX7WsyIiFhMERHpmLG9XFF8yqnXwqORX6DG47wCCIKAK6mZyCtQay9BogaGl/lqAS/zEVFte5RbgLahEeXGbBrng45NrWAm0+qUgkQ6g5f5iIgaEBOpIQ7PLf9uvje+iUG793ahQM1/MxPVJhZTREQ6qqm1Ka4uGfTUuDYLdkLNgoqo1vAyXy3gZT4iqkvZufmIuXYfLjZmcLUxw630R/jz9C2ERSRoxHEqBaLycWqEeoTFFBHVB4IgoM3CCOTmaw5Gn/N8Gwz3aQ6FiXEZWxI1TBwzRUREGiQSCc4tGoAxPVw02sMiEtDx/d34cNsF7SRGpGdYTBER6TGZkSHee7EdWtialVj33eFEfLHvCniBgqh6eJmvFvAyHxHVRzn5BZAZGeJBVi46fRipse7Vzk3xho8zvJytYcgZ1amB4pipeoTFFBHVd8n3s9ErbF+p6/q0tkU310YoUAsY39sNcmPDOs6OSDtYTNUjLKaISBcIgoD9l+5izLrj5cZ9NqQjAjydIDXiyBDSbyym6hEWU0SkS+JuZWDWljNwsjLB5dRMqNXArfRHJeIGeNhj8cvtYWch10KWRLWPxVQ9wmKKiPTB3vgUvLX+RIl2C5kR/Ns74LeTNyEIgHdza3w9whsG/39goNTIAOZ8hA3pIBZT9QiLKSLSJwnKTPivPFjp7d7u44bLKQ+x9BVP2FuyN4vqPxZT9QiLKSLSN4Ig4OrdLKw9eBW/nLhZ6e3f7uOGeQPbarSlqB5j4dY49Gxlg5G+LjWUKVHVsZiqR1hMEZE+U6sFTP7pJAI8nRDQwVFjnqqoi6mY+vMpZOcWlNiuqbUJRjzTHJ5NFOje0gZvfPMPjl69BwAY6dscrjZmGNLVGaZSXiIk7WAxVY+wmCKihu7q3Ye4nJIJWwsZXv0qulLbvtKpCdo4WOANn2awkD955E1iWhbuZDxCN5dGMDLknYVU81hM1SMspoiInniQlYvwA1dxO+Mx/j5zu8R6S7kRzGRGuJPxuMQ6M6khPh3iBRtzqViUTerXArP93Z/6uY/+3ztmIuU8WVQxLKbqERZTRESlEwQBBy+n4dfYmzh/OwPtnRT45LWOkBoZ4J9r97AxJgnxd1S4nPqw3P1c/OB5sUgSBAFbT99C0r1HiFeqsDNOiZG+zfFD9A0AgLuDBfLVAto6WqKVnTm8m1ujR0ubWj9W0j0spuoRFlNERNWTV6DGu7+fw8mkB1BmPEZWKWOwWtubo0At4GFOPlJUOZXa/9t93NCzpQ16tbKtqZRJD7CYqkdYTBER1SxBEPAgOw+f7E7AppikCm/XqZkVxvRwxaFLd2FkaICfjmlu+2NQNxZUJGIxVY+wmCIiqj2pqse4cvchsnMKsOdiCowNDWBoIIGRgQTfHk6Eh6MldkzrVeq2By7dxY6zd7D5RLLY5tfWDs952OOVzk1hzIHtDRqLqXqExRQRkXbkFahhZCCB5P+zsZclIu4OJvz3ZIn2AE9HBHZqgt6tbSAz4sD1hobFVD3CYoqIqP47cf0+oq/ew4rIS6WuX/aKJ1rZW6CVvTksi03RQPqLxVQ9wmKKiEi3nL+dgbCIBBy+koYCdcmfxR4tG2Nge0e83sUZUiNeCtRXLKbqERZTRES667//3MDKPZcgNzbEzQePSqxv38QSFjJjmMmMYGshhV9be/i2aKwxc3tOfgG2n72D+X/EwVxuhNHdXTCpX8u6PAyqAhZT9QiLKSIi/ZCYloVjifcw97dzT43t6mINK1MpHCzl2H7uDu5n5ZaIeaVzExhIJGhhaw6ZkQH+06UpLyHWI1X9/daZvspLly5h8ODBsLGxgaWlJXr27Il9+/ZpxCQlJSEgIACmpqaws7PD7NmzkZ+frxGzf/9+dO7cGTKZDC1btsT69etLfNYXX3wBFxcXyOVy+Pj44NixY7V5aEREVE8VPi+wGRKXDsKJBX744o3OWD2sEyb3a4kBHvZQmDwphI5ff4DICyn48Z8bpRZSAPD7yVv4NfYmPo6IxwfbLqDDot0Y+T1/Y3SdzjxN8oUXXkCrVq2wd+9emJiYYOXKlXjhhRdw9epVODg4oKCgAAEBAXBwcMDRo0dx584djBw5EsbGxliyZAkAIDExEQEBAZgwYQI2btyIqKgojB07Fo6OjvD39wcAbN68GTNmzEB4eDh8fHywcuVK+Pv7IyEhAXZ2dto8BUREpCUSiQQ25jIEdHAsbOj4ZN3FOypcSS18FuGp5HQoMx7D0ECCZo1MMT+gLZo1MsXe+FScu5WBU0mF65PuZ+NRXuFEpAcv3cWqPZcxza8VIuLuwEFhgnM303H2ZgYAwNXWDO/05SXC+kwnLvOlpaXB1tYWBw8eRK9ehXOHZGZmwtLSEpGRkfDz88POnTvxwgsv4Pbt27C3twcAhIeHY+7cubh79y6kUinmzp2L7du3Iy4uTtz30KFDkZ6ejoiICACAj48Punbtis8//xwAoFar4ezsjClTpiAkJKRC+fIyHxERPU3Gozx0fH93hWJdGptixesd4d28US1n1bBV9fdbJ3qmGjdujDZt2uCHH34QL9F9/fXXsLOzg7e3NwAgOjoanp6eYiEFAP7+/pg4cSLOnz+PTp06ITo6Gn5+fhr79vf3R3BwMAAgNzcXsbGxmDdvnrjewMAAfn5+iI4u+6nnOTk5yMl58igDlUpVE4dNRER6TGFijKiZfdB/xYGnxl6/l41Xv4rGYC8nsS0nTw1TqSF2X0iBWhBgayHD+N5uaGptiu4tGnMC0jqkE8WURCLBnj17EBgYCAsLCxgYGMDOzg4RERGwtrYGACiVSo1CCoC4rFQqy41RqVR49OgRHjx4gIKCglJj4uPjy8xv6dKleP/996t9nERE1LC0sDVH4tJBuJPxGCmqx9hzMQW7zqfAQm6EYd2aob+7HVZFXRYf2vzn6dtl7uvGvWzM/yNOo21oV2cE9XSFkaEBXBqb4mTSA/wQfQNZOQWY8VxreDjx6klN0GoxFRISgo8//rjcmIsXL6JNmzaYNGkS7OzscOjQIZiYmODbb7/Fiy++iOPHj8PR0bGOMi7dvHnzMGPGDHFZpVLB2dlZixkREZGukEgkcLIygZOVCTo1s8Zsf3eN9R8Mbo9+bexwLS1LbDtx/T4iL6Qg//9zYg3wsEdqZg6S7mdrDH7/+Xgyfj6ejNLsuZgCABju0wyLXmrHnqxq0GoxNXPmTIwePbrcGDc3N+zduxfbtm3DgwcPxGuYX375JSIjI7FhwwaEhITAwcGhxF13KSmFf1AcHBzE/xa1FY+xtLSEiYkJDA0NYWhoWGpM0T5KI5PJIJPJKnTMREREldXP3Q79ii0H9XQFAGRk58HYSKIxx1Xm4zycuPEAH/x9ARmP8sq8s7DIxpgkbIxJgpuNGQAgXy3ghQ6OCPZrzQlKK0irxZStrS1sbZ/+tO7s7GwAheOXijMwMIBarQYA+Pr64qOPPkJqaqp4111kZCQsLS3h4eEhxuzYsUNjH5GRkfD19QUASKVSeHt7IyoqCoGBgQAKB6BHRUVh8uTJVT9QIiKiWqAwLTlHlYXcGP3a2KFfmyd3oF9KycSAzw4CANxszRAxrTdu3MvC0LX/4N7/i63iPV9f7r+KL/dfRRt7C4zv7QYzmRH6trGF3JjPKyyNztzN5+7ujj59+iA0NBQmJib45ptvsGrVKhw/fhwdO3ZEQUEBvLy84OTkhLCwMCiVSowYMQJjx47VmBqhffv2mDRpEt566y3s3bsXU6dOxfbt2zWmRhg1ahS+/vprdOvWDStXrsQvv/yC+Pj4EmOpysK7+YiIqD7KzVeX6G26nf4It9ILZ3q/9zCn1AdAF/d6l6bi/Fr93O3QvYVN7SSrBXo/A/qJEycwf/58nDhxAnl5eWjXrh1CQ0MxcOBAMebGjRuYOHEi9u/fDzMzM4waNQrLli2DkdGTDrj9+/dj+vTpuHDhApo2bYqFCxeWuNT4+eefY/ny5VAqlfDy8sLq1avh4+NT4VxZTBERkS7LyM7D4u0XkJqZg5M3HiAzJ7/MWEu5EV7u1ASDOzWBlYkxXG3MIJFI6jDbmqP3xZQuYTFFRET6JCe/AIcupeH4jfsAgEe5BeIdhqVZENAWMmNDqNUCWtmbw6CM4qqtg2Wplyq1hcVUPcJiioiI9N3jvAJsPp6MI1fSsPtCytM3KIONuQxtHS3wfHsHvNq5qVbHZbGYqkdYTBERUUOyLz4VY9YfBwA8367w7ve7D3PwIDsXpfVJFagFXL+XXeq+TKWG4uSkcmNDPOteOJDeUCKBVzMrjTsXaxqLqXqExRQRETU0D3PyYWQgqXDPUlZOPk4lpWNLbDLO3sxAYrG7CctjKTfCm880x9u9W9T4JUK9fpwMERER1W/mssqVFGYyI/RsZYOerQrvBszIzsOuC0qkZDwGAOy6oERB4exHyMjOxe3/t6se5+PL/VeRV6DG/ACPmjuAamAxRURERFqnMDXG612ePD1kSv9WGutVj/Pwz9V7GP9jLGRGBjCpR3Ne8TJfLeBlPiIiIt1T1d9vzhNPREREVA0spoiIiIiqgcUUERERUTWwmCIiIiKqBhZTRERERNXAYoqIiIioGlhMEREREVUDiykiIiKiamAxRURERFQNLKaIiIiIqoHFFBEREVE1sJgiIiIiqgYWU0RERETVwGKKiIiIqBqMtJ2APhIEAQCgUqm0nAkRERFVVNHvdtHveEWxmKoFmZmZAABnZ2ctZ0JERESVlZmZCYVCUeF4iVDZ8oueSq1W4/bt27CwsIBEIqnRfatUKjg7OyM5ORmWlpY1um96gue5bvA81w2e57rB81w3avM8C4KAzMxMODk5wcCg4iOh2DNVCwwMDNC0adNa/QxLS0v+Za0DPM91g+e5bvA81w2e57pRW+e5Mj1SRTgAnYiIiKgaWEwRERERVQOLKR0jk8nw3nvvQSaTaTsVvcbzXDd4nusGz3Pd4HmuG/XxPHMAOhEREVE1sGeKiIiIqBpYTBERERFVA4spIiIiompgMUVERERUDSymdMgXX3wBFxcXyOVy+Pj44NixY9pOqd5YunQpunbtCgsLC9jZ2SEwMBAJCQkaMY8fP8akSZPQuHFjmJub49VXX0VKSopGTFJSEgICAmBqago7OzvMnj0b+fn5GjH79+9H586dIZPJ0LJlS6xfv75EPg3lu1q2bBkkEgmCg4PFNp7nmnHr1i28+eabaNy4MUxMTODp6YkTJ06I6wVBQGhoKBwdHWFiYgI/Pz9cvnxZYx/379/H8OHDYWlpCSsrKwQFBeHhw4caMWfPnkWvXr0gl8vh7OyMsLCwErls2bIF7u7ukMvl8PT0xI4dO2rnoOtYQUEBFi5cCFdXV5iYmKBFixb48MMPNZ7LxvNcNQcPHsSLL74IJycnSCQSbN26VWN9fTqvFcnlqQTSCT///LMglUqF77//Xjh//rwwbtw4wcrKSkhJSdF2avWCv7+/sG7dOiEuLk44ffq0MGjQIKFZs2bCw4cPxZgJEyYIzs7OQlRUlHDixAnhmWeeEbp37y6uz8/PF9q3by/4+fkJp06dEnbs2CHY2NgI8+bNE2OuXbsmmJqaCjNmzBAuXLggrFmzRjA0NBQiIiLEmIbyXR07dkxwcXEROnToIEybNk1s53muvvv37wvNmzcXRo8eLcTExAjXrl0Tdu3aJVy5ckWMWbZsmaBQKIStW7cKZ86cEV566SXB1dVVePTokRjz/PPPCx07dhT++ecf4dChQ0LLli2FYcOGieszMjIEe3t7Yfjw4UJcXJzw008/CSYmJsLXX38txhw5ckQwNDQUwsLChAsXLggLFiwQjI2NhXPnztXNyahFH330kdC4cWNh27ZtQmJiorBlyxbB3NxcWLVqlRjD81w1O3bsEObPny/8/vvvAgDhjz/+0Fhfn85rRXJ5GhZTOqJbt27CpEmTxOWCggLByclJWLp0qRazqr9SU1MFAMKBAwcEQRCE9PR0wdjYWNiyZYsYc/HiRQGAEB0dLQhC4V9+AwMDQalUijFfffWVYGlpKeTk5AiCIAhz5swR2rVrp/FZQ4YMEfz9/cXlhvBdZWZmCq1atRIiIyOFPn36iMUUz3PNmDt3rtCzZ88y16vVasHBwUFYvny52Jaeni7IZDLhp59+EgRBEC5cuCAAEI4fPy7G7Ny5U5BIJMKtW7cEQRCEL7/8UrC2thbPe9Fnt2nTRlx+/fXXhYCAAI3P9/HxEd5+++3qHWQ9EBAQILz11lsaba+88oowfPhwQRB4nmvKv4up+nReK5JLRfAynw7Izc1FbGws/Pz8xDYDAwP4+fkhOjpai5nVXxkZGQCARo0aAQBiY2ORl5encQ7d3d3RrFkz8RxGR0fD09MT9vb2Yoy/vz9UKhXOnz8vxhTfR1FM0T4aync1adIkBAQElDgXPM8146+//kKXLl3w2muvwc7ODp06dcI333wjrk9MTIRSqdQ4foVCAR8fH43zbGVlhS5duogxfn5+MDAwQExMjBjTu3dvSKVSMcbf3x8JCQl48OCBGFPed6HLunfvjqioKFy6dAkAcObMGRw+fBgDBw4EwPNcW+rTea1ILhXBYkoHpKWloaCgQOPHBwDs7e2hVCq1lFX9pVarERwcjB49eqB9+/YAAKVSCalUCisrK43Y4udQqVSWeo6L1pUXo1Kp8OjRowbxXf388884efIkli5dWmIdz3PNuHbtGr766iu0atUKu3btwsSJEzF16lRs2LABwJPzVN7xK5VK2NnZaaw3MjJCo0aNauS70IfzHBISgqFDh8Ld3R3Gxsbo1KkTgoODMXz4cAA8z7WlPp3XiuRSEUYVjiTSEZMmTUJcXBwOHz6s7VT0TnJyMqZNm4bIyEjI5XJtp6O31Go1unTpgiVLlgAAOnXqhLi4OISHh2PUqFFazk5//PLLL9i4cSM2bdqEdu3a4fTp0wgODoaTkxPPM1UKe6Z0gI2NDQwNDUvcEZWSkgIHBwctZVU/TZ48Gdu2bcO+ffvQtGlTsd3BwQG5ublIT0/XiC9+Dh0cHEo9x0XryouxtLSEiYmJ3n9XsbGxSE1NRefOnWFkZAQjIyMcOHAAq1evhpGREezt7Xmea4CjoyM8PDw02tq2bYukpCQAT85Tecfv4OCA1NRUjfX5+fm4f/9+jXwX+nCeZ8+eLfZOeXp6YsSIEZg+fbrY68rzXDvq03mtSC4VwWJKB0ilUnh7eyMqKkpsU6vViIqKgq+vrxYzqz8EQcDkyZPxxx9/YO/evXB1ddVY7+3tDWNjY41zmJCQgKSkJPEc+vr64ty5cxp/gSMjI2FpaSn+sPn6+mrsoyimaB/6/l31798f586dw+nTp8VXly5dMHz4cPE9z3P19ejRo8TUHpcuXULz5s0BAK6urnBwcNA4fpVKhZiYGI3znJ6ejtjYWDFm7969UKvV8PHxEWMOHjyIvLw8MSYyMhJt2rSBtbW1GFPed6HLsrOzYWCg+TNoaGgItVoNgOe5ttSn81qRXCqkwkPVSat+/vlnQSaTCevXrxcuXLggjB8/XrCystK4I6ohmzhxoqBQKIT9+/cLd+7cEV/Z2dlizIQJE4RmzZoJe/fuFU6cOCH4+voKvr6+4vqiW/YHDBggnD59WoiIiBBsbW1LvWV/9uzZwsWLF4Uvvvii1Fv2G9J3VfxuPkHgea4Jx44dE4yMjISPPvpIuHz5srBx40bB1NRU+O9//yvGLFu2TLCyshL+/PNP4ezZs8LgwYNLvbW8U6dOQkxMjHD48GGhVatWGreWp6enC/b29sKIESOEuLg44eeffxZMTU1L3FpuZGQkfPLJJ8LFixeF9957T6dv2S9u1KhRQpMmTcSpEX7//XfBxsZGmDNnjhjD81w1mZmZwqlTp4RTp04JAIRPP/1UOHXqlHDjxg1BEOrXea1ILk/DYkqHrFmzRmjWrJkglUqFbt26Cf/884+2U6o3AJT6WrdunRjz6NEj4Z133hGsra0FU1NT4eWXXxbu3LmjsZ/r168LAwcOFExMTAQbGxth5syZQl5enkbMvn37BC8vL0EqlQpubm4an1GkIX1X/y6meJ5rxt9//y20b99ekMlkgru7u7B27VqN9Wq1Wli4cKFgb28vyGQyoX///kJCQoJGzL1794Rhw4YJ5ubmgqWlpTBmzBghMzNTI+bMmTNCz549BZlMJjRp0kRYtmxZiVx++eUXoXXr1oJUKhXatWsnbN++veYPWAtUKpUwbdo0oVmzZoJcLhfc3NyE+fPna9xqz/NcNfv27Sv1/8mjRo0SBKF+ndeK5PI0EkEoNtUrEREREVUKx0wRERERVQOLKSIiIqJqYDFFREREVA0spoiIiIiqgcUUERERUTWwmCIiIiKqBhZTRERERNXAYoqIqBa4uLhg5cqV2k6DiOoAiyki0nmjR49GYGAgAKBv374IDg6us89ev349rKysSrQfP34c48ePr7M8iEh7jLSdABFRfZSbmwupVFrl7W1tbWswGyKqz9gzRUR6Y/To0Thw4ABWrVoFiUQCiUSC69evAwDi4uIwcOBAmJubw97eHiNGjEBaWpq4bd++fTF58mQEBwfDxsYG/v7+AIBPP/0Unp6eMDMzg7OzM9555x08fPgQALB//36MGTMGGRkZ4uctWrQIQMnLfElJSRg8eDDMzc1haWmJ119/HSkpKeL6RYsWwcvLCz/++CNcXFygUCgwdOhQZGZm1u5JI6JqYzFFRHpj1apV8PX1xbhx43Dnzh3cuXMHzs7OSE9Px7PPPotOnTrhxIkTiIiIQEpKCl5//XWN7Tds2ACpVIojR44gPDwcAGBgYIDVq1fj/Pnz2LBhA/bu3Ys5c+YAALp3746VK1fC0tJS/LxZs2aVyEutVmPw4MG4f/8+Dhw4gMjISFy7dg1DhgzRiLt69Sq2bt2Kbdu2Ydu2bThw4ACWLVtWS2eLiGoKL/MRkd5QKBSQSqUwNTWFg4OD2P7555+jU6dOWLJkidj2/fffw9nZGZcuXULr1q0BAK1atUJYWJjGPouPv3JxccHixYsxYcIEfPnll5BKpVAoFJBIJBqf929RUVE4d+4cEhMT4ezsDAD44Ycf0K5dOxw/fhxdu3YFUFh0rV+/HhYWFgCAESNGICoqCh999FH1TgwR1Sr2TBGR3jtz5gz27dsHc3Nz8eXu7g6gsDeoiLe3d4lt9+zZg/79+6NJkyawsLDAiBEjcO/ePWRnZ1f48y9evAhnZ2exkAIADw8PWFlZ4eLFi2Kbi4uLWEgBgKOjI1JTUyt1rERU99gzRUR67+HDh3jxxRfx8ccfl1jn6OgovjczM9NYd/36dbzwwguYOHEiPvroIzRq1AiHDx9GUFAQcnNzYWpqWqN5GhsbayxLJBKo1eoa/QwiqnkspohIr0ilUhQUFGi0de7cGb/99htcXFxgZFTx/+3FxsZCrVZjxYoVMDAo7Mj/5Zdfnvp5/9a2bVskJycjOTlZ7J26cOEC0tPT4eHhUeF8iKh+4mU+ItIrLi4uiImJwfXr15GWlga1Wo1Jkybh/v37GDZsGI4fP46rV69i165dGDNmTLmFUMuWLZGXl4c1a9bg2rVr+PHHH8WB6cU/7+HDh4iKikJaWlqpl//8/Pzg6emJ4cOH4+TJkzh27BhGjhyJPn36oEuXLjV+DoiobrGYIiK9MmvWLBgaGsLDwwO2trZISkqCk5MTjhw5goKCAgwYMACenp4IDg6GlZWV2ONUmo4dO+LTTz/Fxx9/jPbt22Pjxo1YunSpRkz37t0xYcIEDBkyBLa2tiUGsAOFl+v+/PNPWFtbo3fv3vDz84Obmxs2b95c48dPRHVPIgiCoO0kiIiIiHQVe6aIiIiIqoHFFBEREVE1sJgiIiIiqgYWU0RERETVwGKKiIiIqBpYTBERERFVA4spIiIiompgMUVERERUDSymiIiIiKqBxRQRERFRNbCYIiIiIqoGFlNERERE1fA/xvgPQhbkCBYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "matter = generate_random_matter(size=(50, 50), share=0.5)\n",
    "results, frames_number = simulation(\n",
    "    matter,\n",
    "    iterations=100_000,\n",
    "    temp_exponent=0.99993,\n",
    "    acceptance_factor=3,\n",
    "    save_one_in_n_frames=4000,\n",
    "    energy_system=philia,\n",
    "    # energy_system=phobia\n",
    "    # energy_system=diagonal\n",
    "    # energy_system=grid\n",
    "    # energy_system=cubic\n",
    ")\n",
    "\n",
    "plt.plot([i for i in range(len(results))], results)\n",
    "plt.title(\"Custom simulation\")\n",
    "plt.xlabel(\"Iteration\")\n",
    "plt.ylabel(\"Total energy\")\n",
    "\n",
    "create_gif(frames_number, looping=False)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}