examples/queens_puzzle.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cfd38372",
   "metadata": {},
   "source": [
    "# 'N' queens puzzle\n",
    "---\n",
    "Description:\n",
    "\n",
    "- Optimization (combinatorial)\n",
    "- Single-objective\n",
    "- Constraints (yes)\n",
    "---\n",
    "\n",
    "The 'N' queens puzzle is the problem of placing eight chess queens on an N×N chessboard so that no two queens\n",
    "threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. \n",
    "\n",
    "An example for N=8 can be found here: https://en.wikipedia.org/wiki/Eight_queens_puzzle"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "376f3427",
   "metadata": {},
   "source": [
    "### First we import python libraries and set up the directory of our code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b9991c80",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import os, sys, copy\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import namedtuple\n",
    "\n",
    "PROJECT_DIR = os.path.abspath('..')\n",
    "sys.path.append(PROJECT_DIR)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7659349d",
   "metadata": {},
   "source": [
    "### Here we import all our custom GA code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bb85558f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import main classes.\n",
    "from pygenalgo.genome.gene import Gene\n",
    "from pygenalgo.genome.chromosome import Chromosome\n",
    "from pygenalgo.engines.island_model_ga import IslandModelGA\n",
    "\n",
    "# Import Selection Operator(s).\n",
    "from pygenalgo.operators.selection.linear_rank_selector import LinearRankSelector\n",
    "\n",
    "# Import Crossover Operator(s).\n",
    "from pygenalgo.operators.crossover.single_point_crossover import SinglePointCrossover\n",
    "\n",
    "# Import Mutation Operator(s).\n",
    "from pygenalgo.operators.mutation.swap_mutator import SwapMutator\n",
    "\n",
    "# Import Migration Operator(s).\n",
    "from pygenalgo.operators.migration.clockwise_migration import ClockwiseMigration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f0160089",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the fitness function.\n",
    "def fun_Queens(individual: Chromosome, n_queen: int = 8, f_min: bool = True):\n",
    "    \"\"\"\n",
    "    This function counts the number of violations in the positions of the queens\n",
    "    on the chessboard. We check horizontaly, vertically and diagonally.\n",
    "    \"\"\"\n",
    "\n",
    "    # Reshape the chromosome into a 2D array.\n",
    "    chess_board = np.reshape(individual.values(), (n_queen, n_queen))\n",
    "    \n",
    "    # Sum the entries row-wise.\n",
    "    sum_row = np.sum(chess_board, axis=0)\n",
    "\n",
    "    # Sum the entries column-wise.\n",
    "    sum_col = np.sum(chess_board, axis=1)\n",
    "\n",
    "    # Compute limits of the diagonal test.\n",
    "    low = -n_queen + 2\n",
    "    high = n_queen - 1\n",
    "\n",
    "    # Sum the entries diagonally.\n",
    "    sum_diag = []\n",
    "    for k in range(low, high):\n",
    "        sum_diag.append(sum(np.diag(chess_board, k)))\n",
    "    # _end_for_\n",
    "\n",
    "    # We flip to count the violations in the anti-diagonal way.\n",
    "    flip_arr = np.flip(chess_board, axis=1)\n",
    "    sum_flip = []\n",
    "    \n",
    "    # Sum the entries anti-diagonally.\n",
    "    for k in range(low, high):\n",
    "        sum_flip.append(sum(np.diag(flip_arr, k)))\n",
    "    # _end_for_\n",
    "\n",
    "    # Count the total violations.\n",
    "    f_val = 0.0\n",
    "\n",
    "    for i, j in zip(sum_row, sum_col):\n",
    "        f_val += max(i - 1, 0)\n",
    "        f_val += max(j - 1, 0)\n",
    "    # _end_for_\n",
    "    \n",
    "    for k, l in zip(sum_diag, sum_flip):\n",
    "        f_val += max(k - 1, 0)\n",
    "        f_val += max(l - 1, 0)\n",
    "    # _end_for_\n",
    "\n",
    "    # Condition for termination.\n",
    "    solution_found = f_val == 0\n",
    "\n",
    "    # Assign the fitness value (check for minimization).\n",
    "    fit_value = -f_val if f_min else f_val\n",
    "    \n",
    "    # Return the solution tuple.\n",
    "    return fit_value, solution_found\n",
    "# _end_def_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3838a453",
   "metadata": {},
   "source": [
    "## Important note\n",
    "\n",
    "Similar to the TSP problem, here we would require special crossover operator for permutations, in order to avoid creating \n",
    "invalid offsprings. Otherwise the number of queens on the board could be higher (or less) than 'N'.\n",
    "\n",
    "The way we can bypass this hard constraint here, with our current implementation, is to set the crossover operator (any of \n",
    "them) with zero probability (i.e. probability=0.0). At the same time, to ensure that the new offsprings will be modified we \n",
    "set the mutation probability to 0.8 (i.e 80%). The mutation operators that are suitable for these types of problems are the: \n",
    "SwapMutator and ShuffleMutator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b29ff8f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set a random generator.\n",
    "rng = np.random.default_rng()\n",
    "\n",
    "# Random function: Return a random (0, 1).\n",
    "rand_fc = lambda: rng.integers(0, 1, endpoint=True)\n",
    "\n",
    "# The number of queens can be parameterized.\n",
    "n_queen = 8\n",
    "\n",
    "# Make sure they are at least '4'.\n",
    "n_queen = max(n_queen, 4)\n",
    "\n",
    "# Define the number of chromosomes.\n",
    "N = 200\n",
    "\n",
    "# Initial population.\n",
    "population = []\n",
    "\n",
    "for i in range(N):\n",
    "    \n",
    "    arr = np.zeros(n_queen*n_queen)\n",
    "    \n",
    "    arr[np.random.permutation(n_queen*n_queen)[:n_queen]] = 1.0\n",
    "    \n",
    "    population.append(Chromosome([Gene(c, rand_fc) for c in arr.tolist()],\n",
    "                                 np.nan, True))\n",
    "# _end_for_\n",
    "\n",
    "# Create the IslandModelGA object that will carry on the optimization.\n",
    "test_GA = IslandModelGA(initial_pop=population,\n",
    "                        fit_func=lambda x: fun_Queens(x, n_queen=n_queen),\n",
    "                        num_islands=4,\n",
    "                        select_op=LinearRankSelector(),\n",
    "                        mutate_op=SwapMutator(0.8),\n",
    "                        crossx_op=SinglePointCrossover(0.0),\n",
    "                        migrate_op=ClockwiseMigration())"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82698a61",
   "metadata": {},
   "source": [
    "## Plot a random initial configuration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e785c853",
   "metadata": {},
   "outputs": [
    {
     "data": {
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eyiOCRZcuXZSfn6+OHTsqPT1d8fHxSktLU2Jior744gsFBwfr0KFDWr58uQ4dOqRevXopJiam9rFu3TqrWwCAOhrzuSZJd9xxh2bPnq0XXnhBV111ld544w29//77GjhwoMUdwFs5FSwSEhJks9nqPTIyMpqqPqdqmzdvnoqLi+VwOJSZmanc3Fxt27at9rhhGA0+rr/+emuLB4AGXOpzrcaDDz6ogoICnT59Wlu3btWIESMsqhhw8lsh+fn5qq6urn3+9ddfKzU1VXfffbfphf1UWVlZSkhI0MaNG9WvXz/5+HjE4gwAL8bnGtyBU8GiTZs2dZ7PmDFDnTp1arZfaXrggQesLgEATMXnGpq7y97H4uzZs3r33Xc1adIk2Wy2C86z2+2y2+21zysqKiSd/4ZGVVXV5b6926np1Zt6luibvr0DfdO3N2hsvzajob2uG+G9997TyJEjdfDgQcXGxl5w3rRp05SVlVVvfMGCBQoKCrqctwYAAC5WWVmpkSNHqry8/KJ7QF12sBg6dKgCAgL04YcfXnReQysWcXFxKioq8qp9JKqqqpSXl6fU1FT5+/tbXY7L0Dd9ewP6pm9vUFFRocjIyEsGi8s6FXLgwAGtXLlSS5YsueTcwMBABQYG1hv39/f3ql9IDfr2LvTtXejbu3hb343t9bIuKZ47d66ioqJ0yy23XM7LAQCAh3I6WDgcDs2dO1djxoypvQEOAACAdBnBYuXKlTp48KAefPDBpqgHAAC4MaeXHIYMGaLLvN4TAAB4OLZtAwAApiFYAAAA0xAsAACAaQgWAADANAQLAABgGoIFAAAwDcECAACYhmABAABMQ7AAAACmIVgAAADTECwAAIBpCBYAAMA0BAsAAGAaggUAADANwQIAAJiGYAEAAExDsAAAAKYhWAAAANMQLAAAgGkIFgAAwDQECwAAYBqCBQAAMA3BAgAAmIZgAQAATEOwAAAApiFYAAAA0xAsAACAaQgWAADANAQLAABgGoIFAAAwDcECAACYhmABAABMQ7AAAACmIVgAAADTECwAAIBpnA4Whw8f1ujRoxUREaGgoCD16tVLmzdvboraAACAm/FzZvKxY8c0YMAA3XDDDfr4448VFRWlb7/9VuHh4U1UHgAAcCdOBYvnn39ecXFxmjt3bu1YQkKC2TUBAAA35VSwWL58uYYOHaq7775bq1ev1s9+9jONHz9ev/71ry/4GrvdLrvdXvu8oqJCklRVVaWqqqrLLNv91PTqTT1L9E3f3oG+6dsbNLZfm2EYRmN/aIsWLSRJkyZN0t13360vv/xSEydO1Guvvab777+/wddMmzZNWVlZ9cYXLFigoKCgxr41AACwUGVlpUaOHKny8nKFhoZecJ5TwSIgIEDJyclat25d7dhvf/tb5efna/369Q2+pqEVi7i4OBUVFSkiIqKxb+32qqqqlJeXp9TUVPn7+1tdjsvQN317A/qmb29QUVGhyMjISwYLp06FxMTEqFu3bnXGkpKS9P7771/wNYGBgQoMDKw37u/v71W/kBr07V3o27vQt3fxtr4b26tTXzcdMGCAdu/eXWdsz549io+Pd+bHAAAAD+VUsHjiiSe0YcMGPffcc9q7d68WLFigOXPmKCMjo6nqAwAAbsSpYNG3b18tXbpUCxcuVPfu3fU///M/evnllzVq1Kimqg8AALgRp66xkKRbb71Vt956a1PUAgAA3Bz3CgEAAKYhWAAAANMQLAAAgGkIFgAAwDQECwAAYBqCBQAAMA3BAgAAmIZgAQAATEOwAAAApiFYAAAA0xAsAACAaZy+VwgAAFZyOBw6cOCATp48qeDgYMXHx8vHh78nNxcECwCA29i5c6dycnJUUVFROxYaGqphw4apW7duFlaGGkQ8AIBb2Llzp9577706oUKSKioq9N5772nnzp0WVYb/RrAAADR7DodDOTk5F52Tk5Mjh8PhoopwIQQLAECzd+DAgXorFT9WUVGhAwcOuKgiXAjBAgDQ7J08edLUeWg6BAsAQLMXHBxs6jw0HYIFAKDZi4+PV2ho6EXnhIaGKj4+3kUV4UIIFgCAZs/Hx0fDhg276Jxhw4axn0UzwG8AAOAWunXrpvT09HorF6GhoUpPT2cfi2aCDbIAAG6jW7du6tq1KztvNmMECwCAW/Hx8VGHDh2sLgMXQMQDAACmIVgAAADTECwAAIBpCBYAgGalsLBQ48aNU2xsrAICAhQfH68JEybo6NGjtXNOnjypxx57TO3atVPLli2VlJSk7OxsC6tGDYIFAKDZ2Ldvn5KTk7Vnzx4tXLhQe/fu1ezZs/XJJ58oJSVFZWVlkqQnnnhCOTk5evfdd/XNN9/oiSee0OOPP64PPvjA4g5AsAAANBsZGRkKCAhQbm6uBg0apPbt2ystLU0rV67U4cOHNXXqVEnS+vXrNWbMGF1//fVKSEjQww8/rJ49e2rTpk0WdwCCBQCgWSgrK9OKFSs0fvx4tWzZss6x6OhojRo1SosXL5ZhGBo4cKCWL1+uw4cPyzAMffbZZ9qzZ4+GDh1qUfWowT4WAIBmoaCgQIZhKCkpqcHjSUlJOnbsmEpLS/Xqq6/q17/+tdq1ayc/Pz/5+PjojTfe0MCBA11cNX6MYAEAcAuGYUiSAgIC9Oqrr2rDhg1avny54uPjtWbNGo0fP14xMTEaPHiwxZV6N4IFAKBZ6Ny5s2w2m3bu3Knbb7+93vFdu3apTZs2CgwM1JQpU7R06VLdcsstkqQePXpo69at+t///V+ChcW4xgIA0CxEREQoNTVVs2bN0unTp+scKy4u1vz58zV27FhVVVWpqqqq3v1BfH195XA4XFkyGkCwAAA0GzNnzpTdbtfQoUO1Zs0aFRYWKicnR6mpqUpMTFRmZqZCQ0M1aNAgPfXUU1q1apX279+vefPm6Z133tEdd9xhdQtez6lgMW3aNNlstjqP6OjopqoNAOBlunTpovz8fHXs2FHp6emKj49XWlqaEhMT9cUXXyg4OFiStGjRIvXt21ejRo1St27dNGPGDP35z3/Wo48+anEHcPoaiyuvvFIrV66sfe7r62tqQQAA75aQkKB58+bVPn/mmWf00ksvadu2bUpJSZF0/uunc+fOtahCXIzTwcLPz49VCgCAy2RlZSkhIUEbN25Uv3796l1bgebF6WBRUFCg2NhYBQYGql+/fnruuefUsWPHC8632+2y2+21zysqKiSp9uIbb1HTqzf1LNE3fXsH+m76vkePHi1Jqq6uVnV1dZO/38V4++/7UmxGzReDG+Hjjz9WZWWlEhMTdeTIET377LPatWuXduzYoYiIiAZfM23aNGVlZdUbX7BggYKCghr71gAAwEKVlZUaOXKkysvLFRoaesF5TgWLHzt16pQ6deqk3//+95o0aVKDcxpasYiLi1NRUdEFw4gnqqqqUl5enlJTU+Xv7291OS5D3/TtDeibvr1BRUWFIiMjLxksftIGWa1atdJVV12lgoKCC84JDAxUYGBgvXF/f3+v+oXUoG/vQt/ehb69i7f13dhef9IVMHa7Xd98841iYmJ+yo8BAAAewqlg8eSTT2r16tXav3+/Nm7cqLvuuksVFRUaM2ZMU9UHAADciFOnQg4dOqRf/epX+uGHH9SmTRtde+212rBhg+Lj45uqPgAA4EacChaLFi1qqjoAAIAHYJcRAABgGoIFAAAwDcECAACYhmABAABMQ7AAAACmIVgAAADTECwAAIBpCBYAAMA0BAsAAGAaggUAADANwQIAAJjGqXuFwP0Y1dWq3LRZ50pL5demjYKS+8jm62t1WQAAD0Ww8GAVubk68tx0nSsurh3zi45W2yl/UOiQIRZWBgDwVJwK8VAVubk6PGFinVAhSeeOHNHhCRNVkZtrUWUAAE9GsPBARnW1jjw3XTKMBg6eHzvy3HQZ1dUurgwA4OkIFh6octPmeisVdRiGzhUXq3LTZtcVBQDwCgQLD3SutNTUeQAANBbBwgP5tWlj6jwAABqLYOGBgpL7yC86WrLZGp5gs8kvOlpByX1cWxgAwOMRLDyQzddXbaf84T9PfhQu/vO87ZQ/sJ8FAMB0BAsPFTpkiH72ysvya9u2zrhf27b62Ssvs48FAKBJsEGWBwsdMkQhN93EzpsAAJchWHg4m6+vWvW7xuoyAABeglMhAADANAQLAABgGoIFAAAwDcHCzRUWFmrcuHGKjY1VQECA4uPjNWHCBB09erTB+Y888ohsNptefvll1xYKAPAKBAs3tm/fPiUnJ2vPnj1auHCh9u7dq9mzZ+uTTz5RSkqKysrK6sxftmyZNm7cqNjYWIsqBgB4OoKFG8vIyFBAQIByc3M1aNAgtW/fXmlpaVq5cqUOHz6sqVOn1s49fPiwHnvsMc2fP1/+/v4WVg0A8GQECzdVVlamFStWaPz48WrZsmWdY9HR0Ro1apQWL14swzDkcDh033336amnntKVV15pUcUAAG/APhZuqqCgQIZhKCkpqcHjSUlJOnbsmEpLS/Xmm2/Kz89Pv/3tb11cJQDA2xAsPJRhGJLOX9z5yiuvaMuWLbJd6KZkAACYhFMhbqpz586y2WzauXNng8d37dqlNm3aaO3atSopKVH79u3l5+cnPz8/HThwQL/73e+UkJDg2qIBAB6PYOGmIiIilJqaqlmzZun06dN1jhUXF2v+/PkaO3as7rvvPv373//W1q1bax+xsbF66qmntGLFCouqBwB4Kk6FuLGZM2eqf//+Gjp0qJ599ll16NBBO3bs0FNPPaXExERlZmYqODhYERERdV7n7++v6Oho/fznP7eocgCAp2LFwo116dJF+fn56tixo9LT0xUfH6+0tDQlJibqiy++UHBwsNUlAgC8zE8KFtOnT5fNZtPEiRNNKgfOSkhI0Lx581RcXCyHw6HMzEzl5uZq27ZtF3zNd999x+8MANAkLvtUSH5+vubMmaMePXqYWQ9+oqysLCUkJGjjxo3q16+ffHxYlAIAuM5lBYuTJ09q1KhRev311/Xss89edK7dbpfdbq99XlFRIUmqqqpSVVXV5by9W6rp1RU9jx49WpJUXV2t6urqJn+/i3Fl380JfdO3N6Bv7+z7UmxGzYYHThgzZoxat26tv/71r7r++uvVq1evC97Uatq0acrKyqo3vmDBAgUFBTn71gAAwAKVlZUaOXKkysvLFRoaesF5Tq9YLFq0SFu2bFF+fn6j5v/hD3/QpEmTap9XVFQoLi5ON9xwQ71vK3iyqqoq5eXlKTU11avu1UHf9O0N6Ju+vUHNGYdLcSpYFBYWasKECcrNzVWLFi0a9ZrAwEAFBgbWG/f39/eqX0gN+vYu9O1d6Nu7eFvfje3VqWCxefNmlZSUqE+fPrVj1dXVWrNmjWbOnCm73S5fX1/nKgUAAB7DqWBx0003afv27XXGHnjgAXXt2lVPP/00oQIAAC/nVLAICQlR9+7d64y1atVKERER9cYBAID3YZMDAABgmp98r5BVq1aZUAYAAPAErFgAAADTECwAAIBpCBYAAMA0BAsAAGAaggUAADANwQIAAJiGYAEAAExDsAAAAKYhWAAAANMQLAAAgGkIFgAAwDQ/+V4h7qLaYejL/WUqOXFGUSEtdE2H1vL1sVldVpOrdlRrS8kWlVaWqk1QG10ddbV8fbi9PQCgaXhFsMj5ukhZH+5UUfmZ2rGYsBZ6Zng3DeseY2FlTWvlgZWa8eUMHak8UjvWNqitJl8zWYPjB1tYGQDAU3n8qZCcr4v0m3e31AkVklRcfka/eXeLcr4usqiyprXywEpNWjWpTqiQpJLKEk1aNUkrD6y0qDIAgCfz6GBR7TCU9eFOGQ0cqxnL+nCnqh0NzXBf1Y5qzfhyhowGOq8Ze/7L51XtqHZ1aQAAD+fRweLL/WX1Vir+myGpqPyMvtxf5rqiXGBLyZZ6KxX/zZCh4spibSnZ4sKqAADewKODRcmJC4eKy5nnLkorS02dBwBAY3l0sIgKaWHqPHfRJqiNqfMAAGgsjw4W13RorZiwFrrQl0ptOv/tkGs6tHZlWU3u6qir1TaorWwX6Nwmm6KDonV11NUurgwA4Ok8Olj4+tj0zPBuklTvj9ia588M7+Zx+1n4+vhq8jWTJaleuKh5/vQ1T7OfBQDAdB4dLCRpWPcYZY++WtFhdU93RIe1UPboqz12H4vB8YP10vUvKSooqs5426C2eun6l9jHAgDQJLxig6xh3WOU2i3a63beHBw/WDfE3cDOmwAAl/GKYCGdPy2S0inC6jJcztfHV32j+1pdBgDAS3j8qRAAAOA6BAsAAGAajwkWhYWFGjdunGJjYxUQEKD4+HhNmDBBR48erZ2zZMkSDR06VJGRkbLZbNq6dat1BZukMX1PmzZNXbt2VatWrXTFFVdo8ODB2rhxo4VVAwA8lUcEi3379ik5OVl79uzRwoULtXfvXs2ePVuffPKJUlJSVFZ2fsvuU6dOacCAAZoxY4bFFZujsX0nJiZq5syZ2r59uz7//HMlJCRoyJAhKi1l500AgLk84uLNjIwMBQQEKDc3Vy1btpQktW/fXr1791anTp00depUZWdn67777pMkfffddxZWa57G9j1y5Mg6r3vppZf05ptv6t///rduuukmK0oHAHgot1+xKCsr04oVKzR+/PjaP1xrREdHa9SoUVq8eLEMw7PuYHq5fZ89e1Zz5sxRWFiYevbs6cqSAQBewO2DRUFBgQzDUFJSUoPHk5KSdOzYMY9b9ne273/+858KDg5WixYt9Ne//lV5eXmKjIx0ZckAAC/g9sHiUmr+xh4QEGBxJa71475vuOEGbd26VevWrdOwYcOUnp6ukpISK0sEAHggtw8WnTt3ls1m086dOxs8vmvXLrVp00bh4eGuLayJOdt3q1at1LlzZ1177bV688035efnpzfffNOFFQMAvIHbB4uIiAilpqZq1qxZOn36dJ1jxcXFmj9/vsaOHWtNcU3op/ZtGIbsdnsTVwkA8DZuHywkaebMmbLb7Ro6dKjWrFmjwsJC5eTkKDU1VYmJicrMzJR0/oLHrVu31v4tf/fu3dq6dauKi4utLP+yNabvU6dOacqUKdqwYYMOHDigLVu26KGHHtKhQ4d09913W90CAMDDeESw6NKli/Lz89WxY0elp6crPj5eaWlpSkxM1BdffKHg4GBJ0vLly9W7d2/dcsstkqR7771XvXv31uzZs60s/7I1pm9fX1/t2rVLv/zlL5WYmKhbb71VpaWlWrt2ra688kqrWwAAeBingkV2drZ69Oih0NBQhYaGKiUlRR9//HFT1eaUhIQEzZs3T8XFxXI4HMrMzFRubq62bdtWO2fs2LEyDKPeY9q0adYV/hNdqu8WLVpoyZIlOnz4sOx2u77//nt98MEH6tuXG5MBAMzn1AZZ7dq104wZM9S5c2dJ0ttvv60RI0boq6++anZ/+83KylJCQoI2btyofv36ycfHIxZnLslb+wYANA9OBYvhw4fXef7nP/9Z2dnZ2rBhQ7MLFpL0wAMPWF2CJby1bwCA9S57S+/q6mr94x//0KlTp5SSknLBeXa7vc63DyoqKiRJVVVVqqqquty3dzs1vXpTzxJ907d3oG/69gaN7ddmOLnX9fbt25WSkqIzZ84oODhYCxYs0M0333zB+dOmTVNWVla98QULFigoKMiZtwYAABaprKzUyJEjVV5ertDQ0AvOczpYnD17VgcPHtTx48f1/vvv64033tDq1avVrVu3Buc3tGIRFxenoqIiRUREOPPWbq2qqkp5eXlKTU2Vv7+/1eW4DH3Ttzegb/r2BhUVFYqMjLxksHD6VEhAQEDtxZvJycnKz8/XK6+8otdee63B+YGBgQoMDKw37u/v71W/kBr07V3o27vQt3fxtr4b2+tP/soAOzgCAIAaTq1YTJkyRWlpaYqLi9OJEye0aNEirVq1Sjk5OU1VHwAAcCNOBYsjR47ovvvuU1FRkcLCwtSjR4/aLaQBAACcChbcDRMAAFwM2zICAADTECwAAIBpCBYAAMA0BAsAAGAaggUAADANwQIAAJiGYAEAAExDsAAAAKYhWAAAANMQLAAAgGkIFgAAwDRO3SsEQPPmcBgqKjiuUxV2tQoNVEyXcPn42KwuC4AXIVgAHuLbr0q0dnGBTh231461Cg/Udfd0UafeURZWBsCbcCoE8ADfflWinNe+rhMqJOnUcbtyXvta335VYlFlALwNwQJwcw6HobWLCy465/P3CuRwGC6qCIA3I1gAbq6o4Hi9lYofO3nMrqKC464pCIBXI1gAbu5UxcVDhbPzAOCnIFgAbq5VaKCp8wDgpyBYAG4upku4WoVfPDQEX3H+q6cA0NQIFoCb8/Gx6bp7ulx0zsD0LuxnAcAlCBaAB+jUO0rDHuleb+Ui+IpADXukO/tYAHAZNsgCPESn3lHq0LMNO28CsBTBAvAgPj42/eznV1hdBgAvxqkQAABgGoIFAAAwDcECcCOFhYUaN26cYmNjFRAQoPj4eE2YMEFHjx6tnTN27FjZbLY6j2uvvdbCqgF4E4IF4Cb27dun5ORk7dmzRwsXLtTevXs1e/ZsffLJJ0pJSVFZWVnt3GHDhqmoqKj28a9//cvCygF4Ey7eBNxERkaGAgIClJubq5YtW0qS2rdvr969e6tTp06aOnWqsrOzJUmBgYGKjo62slwAXooVC8ANlJWVacWKFRo/fnxtqKgRHR2tUaNGafHixTKM83cwXbVqlaKiopSYmKhf//rXKinhtukAXINgAbiBgoICGYahpKSkBo8nJSXp2LFjKi0tVVpamubPn69PP/1UL774ovLz83XjjTfKbucmZACaHqdCAA9Qs1IREBCge+65p3a8e/fuSk5OVnx8vD766CPdeeedVpUIwEuwYgG4gc6dO8tms2nnzp0NHt+1a5fatGmj8PDwesdiYmIUHx+vgoKCJq4SAAgWgFuIiIhQamqqZs2apdOnT9c5VlxcrPnz52vs2LENvvbo0aMqLCxUTEyMCyoF4O0IFoCbmDlzpux2u4YOHao1a9aosLBQOTk5Sk1NVWJiojIzM3Xy5Ek9+eSTWr9+vb777jutWrVKw4cPV2RkpO644w6rWwDgBQgWgJvo0qWL8vPz1bFjR6Wnpys+Pl5paWlKTEzUF198oeDgYPn6+mr79u0aMWKEEhMTNWbMGCUmJmr9+vUKCQmxugUAXsCpYDF9+nT17dtXISEhioqK0u23367du3c3VW0AfiQhIUHz5s1TcXGxHA6HMjMzlZubq23btkmSWrZsqRUrVqikpERnz57VgQMHNG/ePMXFxVlcOQBv4VSwWL16tTIyMrRhwwbl5eXp3LlzGjJkiE6dOtVU9QG4iKysLL366qvauHGjHA6H1eUAgHNfN83JyanzfO7cuYqKitLmzZv1i1/8wtTCADTOAw88YHUJAFDrJ+1jUV5eLklq3br1BefY7fY6G/NUVFRIkqqqqlRVVfVT3t6t1PTqTT1L9E3f3oG+6dsbNLZfm1Gzs46TDMPQiBEjdOzYMa1du/aC86ZNm6asrKx64wsWLFBQUNDlvDUAAHCxyspKjRw5UuXl5QoNDb3gvMsOFhkZGfroo4/0+eefq127dhec19CKRVxcnIqKihQREXE5b+2WqqqqlJeXp9TUVPn7+1tdjsvQN317A/qmb29QUVGhyMjISwaLyzoV8vjjj2v58uVas2bNRUOFdP4ui4GBgfXG/f39veoXUoO+vQt9exf69i7e1ndje3UqWBiGoccff1xLly7VqlWr1KFDh8sqDgAAeCangkVGRoYWLFigDz74QCEhISouLpYkhYWF1buVMwAA8D5O7WORnZ2t8vJyXX/99YqJial9LF68uKnqAwAAbsTpUyEAAAAXwr1CAACAaQgWAADANAQLAABgGoIFAAAwDcECAACYhmABAABMQ7AAAACmIVgAAADTECwAAIBpCBYAAMA0BAsAAGAap+4VAgCA1QyHIfv+cjlOnJVPSIACO4TJ5mOzuiz8B8ECAOA2Tn/9g45/+K2qy8/WjvmGBSh8eCe17B5pYWWowakQAIBbOP31Dzr67jd1QoUkVZef1dF3v9Hpr3+wqDL8N4IFAKDZMxyGjn/47UXnHP9wnwyH4aKKcCEECwBAs2ffX15vpeLHqsvtsu8vd1FFuBCCBQCg2XOcuHiocHYemg7BAgDQ7PmEBJg6D02HYAEAaPYCO4TJN+ziocE3LFCBHcJcVBEuhGABAGj2bD42hQ/vdNE54cM7sp9FM0CwAAC4hZbdIxUxOqneyoVvWKAiRiexj0UzwQZZAAC30bJ7pFp0i2DnzWaMYAEAcCs2H5tadAq3ugxcAKdCAACAaQgWAADANAQLAABgGoIFAKBZKSws1Lhx4xQbG6uAgADFx8drwoQJOnr0aO0cm83W4OMvf/mLhZVDIlgAAJqRffv2KTk5WXv27NHChQu1d+9ezZ49W5988olSUlJUVlYmSSoqKqrzeOutt2Sz2fTLX/7S4g7At0IAAM1GRkaGAgIClJubq5YtW0qS2rdvr969e6tTp06aOnWqsrOzFR0dXed1H3zwgW644QZ17NjRirLxX1ixAAA0C2VlZVqxYoXGjx9fGypqREdHa9SoUVq8eLEMo+6t0Y8cOaKPPvpI48aNc2W5uACCBQCgWSgoKJBhGEpKSmrweFJSko4dO6bS0tI642+//bZCQkJ05513uqJMXALBAgDgFmpWKgIC6m7p/dZbb2nUqFFq0aKFFWXhRwgWAIBmoXPnzrLZbNq5c2eDx3ft2qU2bdooPDy8dmzt2rXavXu3HnroIRdViUshWAAAmoWIiAilpqZq1qxZOn36dJ1jxcXFmj9/vsaOHVtn/M0331SfPn3Us2dPF1aKiyFYAACajZkzZ8put2vo0KFas2aNCgsLlZOTo9TUVCUmJiozM7N2bkVFhf7xj3+wWtHMOB0s1qxZo+HDhys2NlY2m03Lli1rgrIAAN6oS5cuys/PV8eOHZWenq74+HilpaUpMTFRX3zxhYKDg2vnLlq0SIZh6Fe/+pWFFePHnA4Wp06dUs+ePTVz5symqAcA4OUSEhI0b948FRcXy+FwKDMzU7m5udq2bVudeQ8//LAqKysVFhZmUaVoiNMbZKWlpSktLa0pagEAoJ6srCwlJCRo48aN6tevn3x8OIvfnDX5zpt2u112u732eUVFhSSpqqpKVVVVTf32zUZNr97Us0Tf9O0d6Lvp+x49erQkqbq6WtXV1U3+fhfj7b/vS7EZP97CzAk2m01Lly7V7bfffsE506ZNU1ZWVr3xBQsWKCgo6HLfGgAAuFBlZaVGjhyp8vJyhYaGXnBekweLhlYs4uLiVFRUpIiIiMt9a7dTVVWlvLw8paamyt/f3+pyXIa+6dsb0Dd9e4OKigpFRkZeMlg0+amQwMBABQYG1hv39/f3ql9IDfr2LvTtXejbu3hb343tlStgAACAaZxesTh58qT27t1b+3z//v3aunWrWrdurfbt25taHAAAcC9OB4tNmzbphhtuqH0+adIkSdKYMWM0b9480woDAADux+lgcf311+snXO8JAAA8GNdYAAAA0xAsAACAaQgWAADANAQLAABgGoIFAAAwDcECAACYhmABAABMQ7AAAACmIVgAAADTECwAAIBpCBYAAMA0BAsAAGAaggUAADANwQIAAJiGYAEAAExDsAAAAKYhWAAAANMQLAAAgGkIFgAAwDQECwAAYBqCBQAAMA3BAgAAmIZgAQAATEOwAAAApiFYAAAA0xAsAACAaQgWAADANAQLAABgGoIFAAAwDcECAACYhmABAABMQ7AAAACmIVgAAADTECwAAIBpCBYAAMA0lxUsZs2apQ4dOqhFixbq06eP1q5da3ZdAADADTkdLBYvXqyJEydq6tSp+uqrr3TdddcpLS1NBw8ebIr6AACAG3E6WLz00ksaN26cHnroISUlJenll19WXFycsrOzm6I+AADgRvycmXz27Flt3rxZkydPrjM+ZMgQrVu3rsHX2O122e322ufl5eWSpLKyMmdrdWtVVVWqrKzU0aNH5e/vb3U5LkPf9O0N6Ju+vcGJEyckSYZhXHSeU8Hihx9+UHV1tdq2bVtnvG3btiouLm7wNdOnT1dWVla98cTERGfeGgAANAMnTpxQWFjYBY87FSxq2Gy2Os8Nw6g3VuMPf/iDJk2aVPv8+PHjio+P18GDBy9amKepqKhQXFycCgsLFRoaanU5LkPf9O0N6Ju+vYFhGDpx4oRiY2MvOs+pYBEZGSlfX996qxMlJSX1VjFqBAYGKjAwsN54WFiYV/1CaoSGhtK3F6Fv70Lf3sUb+27MgoBTF28GBASoT58+ysvLqzOel5en/v37O1cdAADwOE6fCpk0aZLuu+8+JScnKyUlRXPmzNHBgwf16KOPNkV9AADAjTgdLO655x4dPXpUf/rTn1RUVKTu3bvrX//6l+Lj4xv1+sDAQD3zzDMNnh7xZPRN396AvunbG3hr341lMy71vREAAIBG4l4hAADANAQLAABgGoIFAAAwDcECAACYhmABAABM49JgMWvWLHXo0EEtWrRQnz59tHbtWle+vSXWrFmj4cOHKzY2VjabTcuWLbO6pCY3ffp09e3bVyEhIYqKitLtt9+u3bt3W11Wk8vOzlaPHj1qd+NLSUnRxx9/bHVZLjd9+nTZbDZNnDjR6lKa1LRp02Sz2eo8oqOjrS7LJQ4fPqzRo0crIiJCQUFB6tWrlzZv3mx1WU0qISGh3u/bZrMpIyPD6tKaHZcFi8WLF2vixImaOnWqvvrqK1133XVKS0vTwYMHXVWCJU6dOqWePXtq5syZVpfiMqtXr1ZGRoY2bNigvLw8nTt3TkOGDNGpU6esLq1JtWvXTjNmzNCmTZu0adMm3XjjjRoxYoR27NhhdWkuk5+frzlz5qhHjx5Wl+ISV155pYqKimof27dvt7qkJnfs2DENGDBA/v7++vjjj7Vz5069+OKLCg8Pt7q0JpWfn1/nd12zA/Xdd99tcWXNkOEi11xzjfHoo4/WGevatasxefJkV5VgOUnG0qVLrS7D5UpKSgxJxurVq60uxeWuuOIK44033rC6DJc4ceKE0aVLFyMvL88YNGiQMWHCBKtLalLPPPOM0bNnT6vLcLmnn37aGDhwoNVlWG7ChAlGp06dDIfDYXUpzY5LVizOnj2rzZs3a8iQIXXGhwwZonXr1rmiBFiovLxcktS6dWuLK3Gd6upqLVq0SKdOnVJKSorV5bhERkaGbrnlFg0ePNjqUlymoKBAsbGx6tChg+69917t27fP6pKa3PLly5WcnKy7775bUVFR6t27t15//XWry3Kps2fP6t1339WDDz54wTt7ezOXBIsffvhB1dXV9e6A2rZt23p3SoVnMQxDkyZN0sCBA9W9e3ery2ly27dvV3BwsAIDA/Xoo49q6dKl6tatm9VlNblFixZpy5Ytmj59utWluEy/fv30zjvvaMWKFXr99ddVXFys/v376+jRo1aX1qT27dun7OxsdenSRStWrNCjjz6q3/72t3rnnXesLs1lli1bpuPHj2vs2LFWl9IsOX2vkJ/ix8nOMAzSnod77LHH9O9//1uff/651aW4xM9//nNt3bpVx48f1/vvv68xY8Zo9erVHh0uCgsLNWHCBOXm5qpFixZWl+MyaWlptf981VVXKSUlRZ06ddLbb7+tSZMmWVhZ03I4HEpOTtZzzz0nSerdu7d27Nih7Oxs3X///RZX5xpvvvmm0tLSFBsba3UpzZJLViwiIyPl6+tbb3WipKSk3ioGPMfjjz+u5cuX67PPPlO7du2sLsclAgIC1LlzZyUnJ2v69Onq2bOnXnnlFavLalKbN29WSUmJ+vTpIz8/P/n5+Wn16tV69dVX5efnp+rqaqtLdIlWrVrpqquuUkFBgdWlNKmYmJh6QTkpKcnjL8SvceDAAa1cuVIPPfSQ1aU0Wy4JFgEBAerTp0/tVbQ18vLy1L9/f1eUABcyDEOPPfaYlixZok8//VQdOnSwuiTLGIYhu91udRlN6qabbtL27du1devW2kdycrJGjRqlrVu3ytfX1+oSXcJut+ubb75RTEyM1aU0qQEDBtT7+viePXsafYdrdzd37lxFRUXplltusbqUZstlp0ImTZqk++67T8nJyUpJSdGcOXN08OBBPfroo64qwRInT57U3r17a5/v379fW7duVevWrdW+fXsLK2s6GRkZWrBggT744AOFhITUrlSFhYWpZcuWFlfXdKZMmaK0tDTFxcXpxIkTWrRokVatWqWcnByrS2tSISEh9a6fadWqlSIiIjz6uponn3xSw4cPV/v27VVSUqJnn31WFRUVGjNmjNWlNaknnnhC/fv313PPPaf09HR9+eWXmjNnjubMmWN1aU3O4XBo7ty5GjNmjPz8XHolgXtx5VdQ/v73vxvx8fFGQECAcfXVV3vF1w8/++wzQ1K9x5gxY6wurck01K8kY+7cuVaX1qQefPDB2v++27RpY9x0001Gbm6u1WVZwhu+bnrPPfcYMTExhr+/vxEbG2vceeedxo4dO6wuyyU+/PBDo3v37kZgYKDRtWtXY86cOVaX5BIrVqwwJBm7d++2upRmzWYYhmFNpAEAAJ6Ge4UAAADTECwAAIBpCBYAAMA0BAsAAGAaggUAADANwQIAAJiGYAEAAExDsAAAAKYhWAAAANMQLAAAgGkIFgAAwDT/H+LfHEQ8bvszAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "arr = [g.value for g in population[0].genome]\n",
    "\n",
    "x_coord, y_coord = np.nonzero(np.reshape(arr, (n_queen, n_queen)))\n",
    "\n",
    "for i, (x, y) in enumerate(zip(x_coord, y_coord), start=1):\n",
    "    ax.plot(x+0.5, y+0.5, 'o')\n",
    "    ax.annotate(f'Q{i}', xy=(x+0.3, y+0.1))\n",
    "# _end_for_\n",
    "\n",
    "ax.grid()\n",
    "\n",
    "ax.set_xlim([0, n_queen])\n",
    "ax.set_ylim([0, n_queen])\n",
    "\n",
    "ax.set(xticks=range(0, n_queen, 1),\n",
    "       yticks=range(0, n_queen, 1))\n",
    "\n",
    "plt.title(\"Queens[0]\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5863d543",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parallel evolution in progress with 4 islands ...\n",
      "Island population 0, finished in 437 iterations.\n",
      "Final Avg. Fitness = -1.7250.\n",
      "Elapsed time: 22.806 seconds.\n"
     ]
    }
   ],
   "source": [
    "test_GA(epochs=500, elitism=True, allow_migration=False, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac13eea2",
   "metadata": {},
   "source": [
    "### Display the final (optimal) solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "eca7113c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimal configuration found: 0.00000\n",
      "\n",
      "[[0. 0. 0. 0. 1. 0. 0. 0.]\n",
      " [1. 0. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 0. 1.]\n",
      " [0. 0. 0. 1. 0. 0. 0. 0.]\n",
      " [0. 1. 0. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 0. 1. 0.]\n",
      " [0. 0. 1. 0. 0. 0. 0. 0.]\n",
      " [0. 0. 0. 0. 0. 1. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "# Extract the optimal solution from the GA.\n",
    "optimal_solution = test_GA.best_chromosome()\n",
    "\n",
    "# Extract the fitness value from the optimal solution.\n",
    "optimal_fit, _ = fun_Queens(optimal_solution, n_queen=n_queen, f_min=False)\n",
    "\n",
    "# Display the (final) optimal value.\n",
    "print(f\"Optimal configuration found: {optimal_fit:.5f}\\n\")\n",
    "\n",
    "# Display the positions of the queens.\n",
    "sol_chess_board = np.reshape(optimal_solution.values(), (n_queen, n_queen))\n",
    "\n",
    "print(sol_chess_board)\n",
    "\n",
    "# NOTE: The absolute minimum is 0.0."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12afcb63",
   "metadata": {},
   "source": [
    "## Plot the optimal solution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "375efb87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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A9REs4DZC/UMdOg8AUH0EC7iNn4X9TI38G8kiS4X7LbIo3D9cPwv7mZMrAwDPQbCA2/D28tZztz8nSeXCRdn2s7c/y3oWAFCDCBZwK70je+u1O19TmH+Y3Xgj/0Z67c7XWMcCAGoYC2TB7fSO7K1eTXqx8iYAmIBgAbfk7eWtLuFdzC4DADwOl0IAAIDDECwAAIDDECzgknJycjRq1ChFRETIarUqMjJS48ePV15enm1OSkqKbrvtNtWrV0833XSTevfura1bt5pYNQC4P4IFXM7BgwcVGxur/fv3a/HixTpw4IDmzJmjtWvXKi4uTvn5+ZKk6OhozZw5U19//bU+++wzRUVFqU+fPjp1ipU3AaCmcPMmXE5ycrKsVqsyMjJUt25dSVLTpk3VqVMntWjRQpMnT9bs2bM1ePBgu++99tprmjdvnr766ivdfffdZpQOAG6PMxZwKfn5+Vq9erXGjBljCxVlwsPDNWTIEKWlpckw7N9wevnyZc2dO1f169dXhw4dnFkyAHgUggVcSnZ2tgzDUExMTIX7Y2JidPr0advljo8++kgBAQGqU6eO/vKXvygzM1MhISHOLBkAPArBAm6l7EyF1WqVJPXq1Us7d+7U559/rr59+yopKUknT540s0QAcGsEC7iUli1bymKxaM+ePRXu37dvn0JDQ9WgQQNJUr169dSyZUvdcccdmjdvnnx8fDRv3jwnVgwAnoVgAZcSHBys+Ph4zZo1SxcvXrTbl5ubq4ULF2rEiBGVft8wDBUVFdVwlQDguQgWcDkzZ85UUVGREhIStGHDBuXk5Cg9PV3x8fGKjo7WlClTdP78eb3wwgvasmWLjhw5oh07dujxxx/Xd999pwcffNDsFgDAbREs4HJatWqlrKwsNW/eXElJSYqMjFRiYqKio6O1adMmBQQEyNvbW/v27dMvf/lLRUdHq3///jp16pQ2btyoNm3amN0CALitagWLqKgoWSyWcp/k5OSaqg+oUFRUlBYsWKDc3FyVlpZqypQpysjI0K5duyRJderU0bJly3Ts2DEVFRXp+++/1wcffKAuXXgxGQDUpGotkJWVlaWSkhLb9jfffKP4+HhOLcN0qampioqK0tatW9W1a1d5eXEyDgDMUK1gERoaarc9ffp0tWjRQj179nRoUcCNeOyxx8wuAQA83g0v6X358mW99957mjRpkiwWS6XzioqK7O7CLywslCQVFxeruLj4Rg/vcsp69aSeJfqmb89A3/TtCarar8X48drHVfT+++9r8ODBOnr0qCIiIiqdl5KSotTU1HLjixYtkr+//40cGgAAONmFCxc0ePBgFRQUKCgoqNJ5NxwsEhISZLVa9eGHH15zXkVnLJo0aaLjx48rODj4Rg7tkoqLi5WZman4+Hj5+vqaXY7T0Dd9ewL6pm9PUFhYqJCQkOsGixu6FHLkyBGtWbNGy5Ytu+5cPz8/+fn5lRv39fX1qD9IGfr2LPTtWejbs3ha31Xt9YZunZ8/f77CwsLUr1+/G/k6AABwU9UOFqWlpZo/f76GDx8uH58bvvcTAAC4oWoHizVr1ujo0aMaOXJkTdQDAABcWLVPOfTp00c3eL8nAABwcyxPCAAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIbXkwKAiyotLdGxvbt17sxpBTS4STfHtJGXl7fZZcHDESwAwAVlb/1cnyyYq3P5P9jGAhqG6K4RT6pV124mVgZPx6UQAHAx2Vs/18rXXrYLFZJ0Lv8HrXztZWVv/dykygCCBQC4lNLSEn2yYO4153z6zlyVlpY4qSLAHsECAFzIsb27y52p+LGzeT/o2N7dTqoIsEewAAAXcu7MaYfOAxyNYAEALiSgwU0OnQc4GsECAFzIzTFtFNAw5JpzAoNDdHNMGydVBNgjWACAC/Hy8tZdI5685pxew59kPQuYhmABAC6mVdduunfSC+XOXAQGh+jeSS+wjgVMxQJZAOCCWnXtphZdurLyJmodggUAuCgvL281adPe7DIAO1wKAQAADkOwAAAADkOwAAAADkOwAIBaKicnR6NGjVJERISsVqsiIyM1fvx45eXl2c3bu3ev7r33XtWvX1+BgYG64447dPToUZOqhqcjWABALXTw4EHFxsZq//79Wrx4sQ4cOKA5c+Zo7dq1iouLU35+viTpP//5j3r06KHbbrtN69at065du/T73/9ederUMbkDeCqeCgGAWig5OVlWq1UZGRmqW7euJKlp06bq1KmTWrRoocmTJ2v27NmaPHmy7rnnHr3yyiu27zZv3tyssgHOWABAbZOfn6/Vq1drzJgxtlBRJjw8XEOGDFFaWppKSkr08ccfKzo6WgkJCQoLC1PXrl21YsUKcwoHRLAAgFonOztbhmEoJiamwv0xMTE6ffq0jh07pnPnzmn69Onq27evMjIyNHDgQA0aNEjr1693ctXAVVwKAQAXYxiGJMnH5+r/hd93332aOHGiJKljx476/PPPNWfOHPXs2dO0GuG5OGMBALVMy5YtZbFYtGfPngr379u3T6GhoQoJCZGPj49at25ttz8mJoanQmAaggUA1DLBwcGKj4/XrFmzdPHiRbt9ubm5WrhwoUaMGCGr1aouXbro22+/tZuzf/9+RUZGOrNkwIZgAQC10MyZM1VUVKSEhARt2LBBOTk5Sk9PV3x8vKKjozVlyhRJ0jPPPKO0tDS9+eabOnDggGbOnKkPP/xQY8aMMbkDeKpqB4tjx45p6NChCg4Olr+/vzp27Kjt27fXRG0A4LFatWqlrKwsNW/eXElJSYqMjFRiYqKio6O1adMmBQQESJIGDhyoOXPm6JVXXlG7du301ltvaenSperRo4fJHcBTVevmzdOnT6t79+7q1auXVq1apbCwMP3nP/9RgwYNaqg8APBcUVFRWrBggW176tSpeu2117Rr1y7FxcXZxkeOHKmRI0eaUCFQXrWCxZ/+9Cc1adJE8+fPt41FRUU5uiYAQAVSU1MVFRWlrVu3qmvXrvLy4mo2ap9qBYuVK1cqISFBDz74oNavX6+bb75ZY8aM0RNPPFHpd4qKilRUVGTbLiwslCQVFxeruLj4Bst2PWW9elLPEn3Tt2dwZt9Dhw6VJJWUlKikpKTGj3ct/L09s+/rsRhlD0RXQdna85MmTdKDDz6oL774QhMmTNDf//53PfrooxV+JyUlRampqeXGFy1aJH9//6oeGgAAmOjChQsaPHiwCgoKFBQUVOm8agULq9Wq2NhYff7557axcePGKSsrS5s3b67wOxWdsWjSpImOHz+u4ODgqh7a5RUXFyszM1Px8fHy9fU1uxynoW/69gT0Td+eoLCwUCEhIdcNFtW6FNK4ceMKF2JZunRppd/x8/OTn59fuXFfX1+P+oOUoW/PQt+ehb49i6f1XdVeq3XnT/fu3VmIBQAAVKpawWLixInasmWLXn75ZR04cECLFi3S3LlzlZycXFP1AQAAF1KtYNGlSxctX75cixcvVtu2bfXiiy9qxowZGjJkSE3VBwAAXEi1327av39/9e/fvyZqAQAALo7VVQAAgMMQLAAAgMMQLAAAgMMQLAAAgMMQLAAAgMMQLAAAgMMQLAAAgMMQLAAAgMMQLAAAgMMQLAAAgMMQLAAAgMNU+10hAADA+UpLS3XkyBGdO3dOAQEBioyMlJdX7Ts/QLAAAKCW27Nnj9LT01VYWGgbCwoKUt++fdW6dWsTKyuv9kUdAABgs2fPHr3//vt2oUKSCgsL9f7772vPnj0mVVYxggUAALVUaWmp0tPTrzknPT1dpaWlTqro+ggWAADUUkeOHCl3puLHCgsLdeTIESdVdH0ECwAAaqlz5845dJ4zECwAAKilAgICHDrPGQgWAADUUpGRkQoKCrrmnKCgIEVGRjqpousjWAAAUEt5eXmpb9++15zTt2/fWrWeRe2pBAAAlNO6dWslJSWVO3MRFBSkpKSkWreOBQtkAQBQy7Vu3Vq33XYbK28CAADH8PLyUrNmzcwu47pqX9QBAAAui2ABAAAchmABAAAchmABAEAtkJOTo1GjRikiIkJWq1WRkZEaP3688vLybHPOnTunsWPH6pZbblHdunUVExOj2bNnm1h1eQQLAABMdvDgQcXGxmr//v1avHixDhw4oDlz5mjt2rWKi4tTfn6+JGnixIlKT0/Xe++9p71792rixIl66qmn9MEHH5jcwf8hWAAAYLLk5GRZrVZlZGSoZ8+eatq0qRITE7VmzRodO3ZMkydPliRt3rxZw4cP15133qmoqCg9+eST6tChg7Zt22ZyB/+HYAEAgIny8/O1evVqjRkzRnXr1rXbFx4eriFDhigtLU2GYahHjx5auXKljh07JsMw9Omnn2r//v1KSEgwqfryWMcCAAATZWdnyzAMxcTEVLg/JiZGp0+f1qlTp/TGG2/oiSee0C233CIfHx95eXnprbfeUo8ePZxcdeUIFgAA1GKGYUiSrFar3njjDW3ZskUrV65UZGSkNmzYoDFjxqhx48bq3bu3yZVeRbAAAMBELVu2lMVi0Z49e3T//feX279v3z6FhobKz89PL7zwgpYvX65+/fpJktq3b6+dO3fqz3/+c60JFtxjAQCAiYKDgxUfH69Zs2bp4sWLdvtyc3O1cOFCjRgxQsXFxSouLi73fhBvb2+VlpY6s+RrIlgAAGCymTNnqqioSAkJCdqwYYNycnKUnp6u+Ph4RUdHa8qUKQoKClLPnj31zDPPaN26dTp06JAWLFigd999VwMHDjS7BZtqBYuUlBRZLBa7T3h4eE3VBgCAR2jVqpWysrLUvHlzJSUlKTIyUomJiYqOjtamTZsUEBAgSVqyZIm6dOmiIUOGqHXr1po+fbr++Mc/avTo0SZ38H+qfY9FmzZttGbNGtu2t7e3QwsCAMATRUVFacGCBbbtqVOn6rXXXtOuXbsUFxcn6erjp/PnzzepwqqpdrDw8fHhLAUAADUsNTVVUVFR2rp1q7p27Vru3oraqtrBIjs7WxEREfLz81PXrl318ssvq3nz5pXOLyoqUlFRkW27sLBQkmw3oXiKsl49qWeJvunbM9A3fdeUoUOHSpJKSkpUUlJS48e7lqr2azHKHpCtglWrVunChQuKjo7WiRMn9NJLL2nfvn3avXu3goODK/xOSkqKUlNTy40vWrRI/v7+VT00AAAw0YULFzR48GAVFBQoKCio0nnVChY/dv78ebVo0UK//e1vNWnSpArnVHTGokmTJjp+/HilYcQdFRcXKzMzU/Hx8fL19TW7HKehb/r2BPRN356gsLBQISEh1w0WP2mBrHr16qldu3bKzs6udI6fn5/8/PzKjfv6+nrUH6QMfXsW+vYs9O1ZPK3vqvb6k+4EKSoq0t69e9W4ceOf8mMAAICbqFawePrpp7V+/XodOnRIW7du1QMPPKDCwkINHz68puoDAAAupFqXQr777js98sgj+uGHHxQaGqo77rhDW7ZsUWRkZE3VBwAAXEi1gsWSJUtqqg4AAOAGXGO1DQAA4BIIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGGq9a4QV1ZSauiLQ/k6efaSwgLr6PZmDeXtZTG7LAAA3IpHBIv0b44r9cM9Ol5wyTbWuH4dTR3QWn3bNjaxMgAA3IvbXwpJ/+a4fv3eDrtQIUm5BZf06/d2KP2b4yZVBgCA+3HrYFFSaij1wz0yKthXNpb64R6VlFY0AwAAVJdbB4svDuWXO1PxvwxJxwsu6YtD+c4rCgAAN+bWweLk2cpDxY3MAwAA1+bWwSIssI5D5wEAgGtz62Bxe7OGaly/jip7qNSiq0+H3N6soTPLAgDAbbl1sPD2smjqgNaSVC5clG1PHdCa9SwAAHAQtw4WktS3bWPNHvozhde3v9wRXr+OZg/9GetYAADgQB6xQFbfto0V3zqclTcBAKhhHhEspKuXReJaBJtdBgAAbs3tL4UAAADnIVgAAACHIVgAAACHcZtgkZOTo1GjRikiIkJWq1WRkZEaP3688vLybHOWLVumhIQEhYSEyGKxaOfOneYVDACAG3KLYHHw4EHFxsZq//79Wrx4sQ4cOKA5c+Zo7dq1iouLU37+1XeBnD9/Xt27d9f06dNNrhgAAPfkFk+FJCcny2q1KiMjQ3Xr1pUkNW3aVJ06dVKLFi00efJkzZ49W8OGDZMkHT582MRqAQBwXy5/xiI/P1+rV6/WmDFjbKGiTHh4uIYMGaK0tDQZBq9GBwCgprl8sMjOzpZhGIqJialwf0xMjE6fPq1Tp045uTIAADyPyweL6yk7U2G1Wk2uBAAA9+fywaJly5ayWCzas2dPhfv37dun0NBQNWjQwLmFAQDggVw+WAQHBys+Pl6zZs3SxYsX7fbl5uZq4cKFGjFihDnFAQDgYVw+WEjSzJkzVVRUpISEBG3YsEE5OTlKT09XfHy8oqOjNWXKFElXb/TcuXOn7ezGt99+q507dyo3N9fM8gEAcBtuESxatWqlrKwsNW/eXElJSYqMjFRiYqKio6O1adMmBQQESJJWrlypTp06qV+/fpKkhx9+WJ06ddKcOXPMLB8AALfxk4LFtGnTZLFYNGHCBAeVc+OioqK0YMEC5ebmqrS0VFOmTFFGRoZ27dplmzNixAgZhlHuk5KSYl7hAAC4kRteICsrK0tz585V+/btHVmPw6SmpioqKkpbt25V165d5eXlFidnAACo1W4oWJw7d05DhgzRm2++qZdeeumac4uKilRUVGTbLiwslCQVFxeruLj4Rg5fZUOHDpUklZSUqKSkpEaPdT1lvdZ0z7UNfdO3J6Bv+vYEVe3XYtzAkpTDhw9Xw4YN9Ze//EV33nmnOnbsqBkzZlQ4NyUlRampqeXGFy1aJH9//+oeGgAAmODChQsaPHiwCgoKFBQUVOm8ap+xWLJkiXbs2KGsrKwqzX/++ec1adIk23ZhYaGaNGmiXr16KTg4uLqHd1nFxcXKzMxUfHy8fH19zS7Haeibvj0BfdO3Jyi74nA91QoWOTk5Gj9+vDIyMlSnTp0qfcfPz09+fn7lxn19fT3qD1KGvj0LfXsW+vYsntZ3VXutVrDYvn27Tp48qc6dO9vGSkpKtGHDBttaEt7e3tWrFAAAuI1qBYu7775bX3/9td3YY489pttuu03PPvssoQIAAA9XrWARGBiotm3b2o3Vq1dPwcHB5cYBAIDnYXEHAADgMDe8QFaZdevWOaAMAADgDjhjAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHIZgAQAAHOYnvysEQO1hlJTowrbtunLqlHxCQ+Uf21kWb2+zywLgQQgWgJsozMjQiZen6Upurm3MJzxcjV54XkF9+phYGQBPwqUQwA0UZmTo2PgJdqFCkq6cOKFj4yeoMCPDpMoAeBqCBeDijJISnXh5mmQYFey8Onbi5WkySkqcXBkAT0SwAFzchW3by52psGMYupKbqwvbtjuvKAAei2ABuLgrp045dB4A/BQEC8DF+YSGOnQeAPwUBAvAxfnHdpZPeLhksVQ8wWKRT3i4/GM7O7cwAB6JYAG4OIu3txq98Px/N34ULv673eiF51nPAoBTECwANxDUp49ufn2GfBo1shv3adRIN78+g3UsADgNC2QBbiKoTx8F3n03K28CMBXBAnAjFm9v1et6u9llAPBgXAoBAAAOQ7AAAAAOQ7AAXEhOTo5GjRqliIgIWa1WRUZGavz48crLy6tw/q9+9StZLBbNmDHDuYUC8FgEC8BFHDx4ULGxsdq/f78WL16sAwcOaM6cOVq7dq3i4uKUn59vN3/FihXaunWrIiIiTKoYgCciWAAuIjk5WVarVRkZGerZs6eaNm2qxMRErVmzRseOHdPkyZNtc48dO6axY8dq4cKF8vX1NbFqAJ6GYAG4gPz8fK1evVpjxoxR3bp17faFh4dryJAhSktLk2EYKi0t1bBhw/TMM8+oTZs2JlUMwFPxuCngArKzs2UYhmJiYircHxMTo9OnT+vUqVOaN2+efHx8NG7cOCdXCQAEC8AtGIYh6erNna+//rp27NghS2XvDgGAGsSlEMAFtGzZUhaLRXv27Klw/759+xQaGqqNGzfq5MmTatq0qXx8fOTj46MjR47oN7/5jaKiopxbNACPRLAAXEBwcLDi4+M1a9YsXbx40W5fbm6uFi5cqBEjRmjYsGH66quvtHPnTtsnIiJCzzzzjFavXm1S9QA8CZdCABcxc+ZMdevWTQkJCXrppZfUrFkz7d69W88884yio6M1ZcoUBQQEKDg42O57vr6+Cg8P16233mpS5QA8CWcsABfRqlUrZWVlqXnz5kpKSlJkZKQSExMVHR2tTZs2KSAgwOwSAaB6wWL27Nlq3769goKCFBQUpLi4OK1ataqmagPwI1FRUVqwYIFyc3NVWlqqKVOmKCMjQ7t27ar0O4cPH9aECROcVyQAj1atSyG33HKLpk+frpYtW0qS3nnnHd1333368ssveV4eMEFqaqqioqK0detWde3aVV5enIQEYK5qBYsBAwbYbf/xj3/U7NmztWXLFoIFYJLHHnvM7BIAwOaGb94sKSnRP//5T50/f15xcXGVzisqKlJRUZFtu7CwUJJUXFys4uLiGz28yynr1ZN6luibvj0DfdO3J6hqvxajbGWdKvr6668VFxenS5cuKSAgQIsWLdI999xT6fyUlBSlpqaWG1+0aJH8/f2rc2gAAGCSCxcuaPDgwSooKFBQUFCl86odLC5fvqyjR4/qzJkzWrp0qd566y2tX79erVu3rnB+RWcsmjRpouPHj5d7LM6dFRcXKzMzU/Hx8R71Uij6pm9PQN/07QkKCwsVEhJy3WBR7UshVqvVdvNmbGyssrKy9Prrr+vvf/97hfP9/Pzk5+dXbtzX19ej/iBl6Nuz0LdnoW/P4ml9V7XXn3wLuWEYdmckAACA56rWGYsXXnhBiYmJatKkic6ePaslS5Zo3bp1Sk9Pr6n6AACAC6lWsDhx4oSGDRum48ePq379+mrfvr3S09MVHx9fU/UBAAAXUq1gMW/evJqqAwAAuAGW6QMAAA5DsAAAAA5DsAAAAA5DsAAAAA5DsAAAAA5DsAAAAA5DsAAAAA5DsAAAAA5DsAAAAA5DsAAAAA5DsAAAAA5TrXeFAABgNqPUUNGhApWevSyvQKv8mtWXxctidln4L4IFAMBlXPzmB5358D8qKbhsG/Oub1WDAS1Ut22IiZWhDJdCAAAu4eI3Pyjvvb12oUKSSgouK++9vbr4zQ8mVYb/RbAAANR6RqmhMx/+55pzznx4UEap4aSKUBmCBQCg1is6VFDuTMWPlRQUqehQgZMqQmUIFgCAWq/07LVDRXXnoeYQLAAAtZ5XoNWh81BzCBYAgFrPr1l9ede/dmjwru8nv2b1nVQRKkOwAADUehYvixoMaHHNOQ0GNGc9i1qAYAEAcAl124YoeGhMuTMX3vX9FDw0hnUsagkWyAIAuIy6bUNUp3UwK2/WYgQLAIBLsXhZVKdFA7PLQCW4FAIAAByGYAEAAByGYAEAqFVycnI0atQoRUREyGq1KjIyUuPHj1deXp5tjsViqfDz//7f/zOxckgECwBALXLw4EHFxsZq//79Wrx4sQ4cOKA5c+Zo7dq1iouLU35+viTp+PHjdp+3335bFotFv/zlL03uANy8CQCoNZKTk2W1WpWRkaG6detKkpo2bapOnTqpRYsWmjx5smbPnq3w8HC7733wwQfq1auXmjdvbkbZ+B+csQAA1Ar5+flavXq1xowZYwsVZcLDwzVkyBClpaXJMOzfYHrixAl9/PHHGjVqlDPLRSUIFgCAWiE7O1uGYSgmJqbC/TExMTp9+rROnTplN/7OO+8oMDBQgwYNckaZuA6CBQDAJZSdqbBa7VfefPvttzVkyBDVqVPHjLLwIwQLAECt0LJlS1ksFu3Zs6fC/fv27VNoaKgaNGhgG9u4caO+/fZbPf74406qEtdDsAAA1ArBwcGKj4/XrFmzdPHiRbt9ubm5WrhwoUaMGGE3Pm/ePHXu3FkdOnRwYqW4FoIFAKDWmDlzpoqKipSQkKANGzYoJydH6enpio+PV3R0tKZMmWKbW1hYqH/+85+crahlCBYAgFqjVatWysrKUvPmzZWUlKTIyEglJiYqOjpamzZtUkBAgG3ukiVLZBiGHnnkERMrxo9VK1hMmzZNXbp0UWBgoMLCwnT//ffr22+/ranaAAAeKCoqSgsWLFBubq5KS0s1ZcoUZWRkaNeuXXbznnzySV24cEH169c3qVJUpFrBYv369UpOTtaWLVuUmZmpK1euqE+fPjp//nxN1QcA8HCpqal64403tHXrVpWWlppdDq6jWitvpqen223Pnz9fYWFh2r59u37xi184tDAAAMo89thjZpeAKvpJS3oXFBRIkho2bFjpnKKiIhUVFdm2CwsLJUnFxcUqLi7+KYd3KWW9elLPEn3Tt2egb/r2BFXt12L8eG3UKjIMQ/fdd59Onz6tjRs3VjovJSVFqamp5cYXLVokf3//Gzk0AABwsgsXLmjw4MEqKChQUFBQpfNuOFgkJyfr448/1meffaZbbrml0nkVnbFo0qSJjh8/ruDg4Bs5tEsqLi5WZmam4uPj5evra3Y5TkPf9O0J6Ju+PUFhYaFCQkKuGyxu6FLIU089pZUrV2rDhg3XDBWS5OfnJz8/v3Ljvr6+HvUHKUPfnoW+PQt9exZP67uqvVYrWBiGoaeeekrLly/XunXr1KxZsxsqDgAAuKdqBYvk5GQtWrRIH3zwgQIDA5WbmytJql+/frlX3AIAAM9TrXUsZs+erYKCAt15551q3Lix7ZOWllZT9QEAABdS7UshAAAAleFdIQAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGEIFgAAwGGq9a4QAKiNSksNHc8+o/OFRaoX5KfGrRrIy8tidlmARyJYAHBp//nypDamZev8mSLbWL0Gfvr5Q63UolOYiZUBnolLIQBc1n++PKn0v39jFyok6fyZIqX//Rv958uTJlUGeC6CBQCXVFpqaGNa9jXnfPZ+tkpLDSdVBEAiWABwUcezz5Q7U/Fj504X6Xj2GecUBEASwQKAizpfeO1QUd15AByDYAHAJdUL8nPoPACOQbAA4JIat2qgeg2uHRoCbrr66CkA5yFYAHBJXl4W/fyhVtec0yOpFetZAE5GsADgslp0ClPfX7Utd+Yi4CY/9f1VW9axAEzAAlkAXFqLTmFq1iGUlTeBWoJgAcDleXlZdPOtN5ldBgBxKQQAADgQwQIAADgMwQIAADgMwQJArZeTk6NRo0YpIiJCVqtVkZGRGj9+vPLy8mxzRowYIYvFYve54447TKwa8EwECwC12sGDBxUbG6v9+/dr8eLFOnDggObMmaO1a9cqLi5O+fn5trl9+/bV8ePHbZ9///vfJlYOeCaeCgFQqyUnJ8tqtSojI0N169aVJDVt2lSdOnVSixYtNHnyZM2ePVuS5Ofnp/DwcDPLBTweZywA1Fr5+flavXq1xowZYwsVZcLDwzVkyBClpaXJMK6+Gn3dunUKCwtTdHS0nnjiCZ08edKMsgGPRrAAUGtlZ2fLMAzFxMRUuD8mJkanT5/WqVOnlJiYqIULF+qTTz7Rq6++qqysLN11110qKuLtpoAzcSkEgMsqO1NhtVr10EMP2cbbtm2r2NhYRUZG6uOPP9agQYPMKhHwOJyxAFBrtWzZUhaLRXv27Klw/759+xQaGqoGDRqU29e4cWNFRkYqOzu7hqsE8L8IFgBqreDgYMXHx2vWrFm6ePGi3b7c3FwtXLhQI0aMqPC7eXl5ysnJUePGjZ1QKYAyBAsAtdrMmTNVVFSkhIQEbdiwQTk5OUpPT1d8fLyio6M1ZcoUnTt3Tk8//bQ2b96sw4cPa926dRowYIBCQkI0cOBAs1sAPEq1g8WGDRs0YMAARUREyGKxaMWKFTVQFgBc1apVK2VlZal58+ZKSkpSZGSkEhMTFR0drU2bNikgIEDe3t76+uuvdd999yk6OlrDhw9XdHS0Nm/erMDAQLNbADxKtW/ePH/+vDp06KDHHntMv/zlL2uiJgCwExUVpQULFti2p06dqtdee027du1SXFyc6tatq9WrV5tXIACbageLxMREJSYm1kQtAFAlqampioqK0tatW9W1a1d5eXFVF6gtavxx06KiIrvnyAsLCyVJxcXFKi4urunD1xplvXpSzxJ903fNGTp0qCSppKREJSUlNX68a+HvTd+eoKr9WoyyB8FvgMVi0fLly3X//fdXOiclJUWpqanlxhctWiR/f/8bPTQAAHCiCxcuaPDgwSooKFBQUFCl82o8WFR0xqJJkyY6fvy4goODb/TQLqe4uFiZmZmKj4+Xr6+v2eU4DX3Ttyegb/r2BIWFhQoJCblusKjxSyF+fn7y8/MrN+7r6+tRf5Ay9O1Z6Nuz0Ldn8bS+q9ordzwBAACHqfYZi3PnzunAgQO27UOHDmnnzp1q2LChmjZt6tDiAACAa6l2sNi2bZt69epl2540aZIkafjw4XbPmQMAAM9T7WBx55136ifc7wkAANwY91gAAACHIVgAAACHIVgAAACHIVgAAACHIVgAAACHIVgAAACHIVgAAACHIVgAAACHIVgAAACHIVgAAACHIVgAAACHqfa7QuBiSkukI59L505IAY2kyG6Sl7fZVQEA3BTBwp3tWSmlPysVfv9/Y0ERUt8/Sa3vNa8uAIDb4lKIu9qzUnr/UftQIUmFx6+O71lpTl0AALdGsHBHpSVXz1Sootfb/3cs/bmr8wAAcCCChTs68nn5MxV2DKnw2NV5AAA4EMHCHZ074dh5AABUEcHCHQU0cuw8AACqiGDhjiK7XX36Q5ZKJlikoJuvzgMAwIEIFu7Iy/vqI6WSyoeL/273nc56FgAAhyNYuKvW90pJ70pBje3HgyKujrOOBQCgBrBAljtrfa90Wz9W3gQAOA3Bwt15eUvNfm52FQAAD8GlEAAA4DAECwAA4DAECwAA4DAECxeXk5OjUaNGKSIiQlarVZGRkRo/frzy8vIkScXFxXr22WfVrl071atXTxEREXr00Uf1/ffXWvIbAIAbQ7BwYQcPHlRsbKz279+vxYsX68CBA5ozZ47Wrl2ruLg45efn68KFC9qxY4d+//vfa8eOHVq2bJn279+ve+/lcVMAgOPxVIgLS05OltVqVUZGhurWrStJatq0qTp16qQWLVpo8uTJmj17tjIzM+2+99e//lW33367jh49qqZNm5pROgDATXHGwkXl5+dr9erVGjNmjC1UlAkPD9eQIUOUlpYmwyj/6vSCggJZLBY1aNDASdUCADwFwcJFZWdnyzAMxcTEVLg/JiZGp0+f1qlTp+zGL126pOeee06DBw9WUFCQM0oFAHgQgoWbKjtTYbVabWPFxcV6+OGHVVpaqlmzZplVGgDAjREsXFTLli1lsVi0Z8+eCvfv27dPoaGhtssdxcXFSkpK0qFDh5SZmcnZCgBAjSBYuKjg4GDFx8dr1qxZunjxot2+3NxcLVy4UCNGjJD0f6EiOztba9asUXBwsAkVAwA8AcHChc2cOVNFRUVKSEjQhg0blJOTo/T0dMXHxys6OlpTpkzRlStX9MADD2jbtm1auHChSkpKlJubq9zcXF2+fNnsFgAAbuaGgsWsWbPUrFkz1alTR507d9bGjRsdXReqoFWrVsrKylLz5s2VlJSkyMhIJSYmKjo6Wps2bVJAQIC+++47rVy5Ut999506duyoxo0b2z6ff/652S0AANxMtYNFWlqaJkyYoMmTJ+vLL7/Uz3/+cyUmJuro0aM1UR+uIyoqSgsWLFBubq5KS0s1ZcoUZWRkaNeuXbb9hmFU+LnzzjvNLR4A4HaqHSxee+01jRo1So8//rhiYmI0Y8YMNWnSRLNnz66J+lBNqampeuONN7R161aVlpaaXQ4AwMNUa+XNy5cva/v27Xruuefsxvv06VPpafWioiIVFRXZtgsKCiRdXeDJkxQXF+vChQvKy8uTr69vjR6rbLnu06dP1+hxqsKZfdcm9E3fnoC+Pavvs2fPSlKFCy/+r2oFix9++EElJSVq1KiR3XijRo2Um5tb4XemTZum1NTUcuPR0dHVOTQAAKgFzp49q/r161e6/4beFWKxWOy2DcMoN1bm+eef16RJk2zbZ86cUWRkpI4ePXrNwtxNYWGhmjRpopycHI9aQ4K+6dsT0Dd9ewLDMHT27FlFRERcc161gkVISIi8vb3LnZ04efJkubMYZfz8/OTn51duvH79+h71BykTFBRE3x6Evj0LfXsWT+y7KicEqnXzptVqVefOncu9LTMzM1PdunWrXnUAAMDtVPtSyKRJkzRs2DDFxsYqLi5Oc+fO1dGjRzV69OiaqA8AALiQageLhx56SHl5efrDH/6g48ePq23btvr3v/+tyMjIKn3fz89PU6dOrfDyiDujb/r2BPRN357AU/uuKotxvedGAAAAqoh3hQAAAIchWAAAAIchWAAAAIchWAAAAIchWAAAAIdxarCYNWuWmjVrpjp16qhz587auHGjMw9vig0bNmjAgAGKiIiQxWLRihUrzC6pxk2bNk1dunRRYGCgwsLCdP/99+vbb781u6waN3v2bLVv3962Gl9cXJxWrVpldllON23aNFksFk2YMMHsUmpUSkqKLBaL3Sc8PNzsspzi2LFjGjp0qIKDg+Xv76+OHTtq+/btZpdVo6Kiosr9vS0Wi5KTk80urdZxWrBIS0vThAkTNHnyZH355Zf6+c9/rsTERB09etRZJZji/Pnz6tChg2bOnGl2KU6zfv16JScna8uWLcrMzNSVK1fUp08fnT9/3uzSatQtt9yi6dOna9u2bdq2bZvuuusu3Xfffdq9e7fZpTlNVlaW5s6dq/bt25tdilO0adNGx48ft32+/vprs0uqcadPn1b37t3l6+urVatWac+ePXr11VfVoEEDs0urUVlZWXZ/67IVqB988EGTK6uFDCe5/fbbjdGjR9uN3XbbbcZzzz3nrBJMJ8lYvny52WU43cmTJw1Jxvr1680uxeluuukm46233jK7DKc4e/as0apVKyMzM9Po2bOnMX78eLNLqlFTp041OnToYHYZTvfss88aPXr0MLsM040fP95o0aKFUVpaanYptY5TzlhcvnxZ27dvV58+fezG+/Tpo88//9wZJcBEBQUFkqSGDRuaXInzlJSUaMmSJTp//rzi4uLMLscpkpOT1a9fP/Xu3dvsUpwmOztbERERatasmR5++GEdPHjQ7JJq3MqVKxUbG6sHH3xQYWFh6tSpk958802zy3Kqy5cv67333tPIkSMrfbO3J3NKsPjhhx9UUlJS7g2ojRo1KvemVLgXwzA0adIk9ejRQ23btjW7nBr39ddfKyAgQH5+fho9erSWL1+u1q1bm11WjVuyZIl27NihadOmmV2K03Tt2lXvvvuuVq9erTfffFO5ubnq1q2b8vLyzC6tRh08eFCzZ89Wq1attHr1ao0ePVrjxo3Tu+++a3ZpTrNixQqdOXNGI0aMMLuUWqna7wr5KX6c7AzDIO25ubFjx+qrr77SZ599ZnYpTnHrrbdq586dOnPmjJYuXarhw4dr/fr1bh0ucnJyNH78eGVkZKhOnTpml+M0iYmJtv/drl07xcXFqUWLFnrnnXc0adIkEyurWaWlpYqNjdXLL78sSerUqZN2796t2bNn69FHHzW5OueYN2+eEhMTFRERYXYptZJTzliEhITI29u73NmJkydPljuLAffx1FNPaeXKlfr00091yy23mF2OU1itVrVs2VKxsbGaNm2aOnTooNdff93ssmrU9u3bdfLkSXXu3Fk+Pj7y8fHR+vXr9cYbb8jHx0clJSVml+gU9erVU7t27ZSdnW12KTWqcePG5YJyTEyM29+IX+bIkSNas2aNHn/8cbNLqbWcEiysVqs6d+5su4u2TGZmprp16+aMEuBEhmFo7NixWrZsmT755BM1a9bM7JJMYxiGioqKzC6jRt199936+uuvtXPnTtsnNjZWQ4YM0c6dO+Xt7W12iU5RVFSkvXv3qnHjxmaXUqO6d+9e7vHx/fv3V/kN165u/vz5CgsLU79+/cwupdZy2qWQSZMmadiwYYqNjVVcXJzmzp2ro0ePavTo0c4qwRTnzp3TgQMHbNuHDh3Szp071bBhQzVt2tTEympOcnKyFi1apA8++ECBgYG2M1X169dX3bp1Ta6u5rzwwgtKTExUkyZNdPbsWS1ZskTr1q1Tenq62aXVqMDAwHL3z9SrV0/BwcFufV/N008/rQEDBqhp06Y6efKkXnrpJRUWFmr48OFml1ajJk6cqG7duunll19WUlKSvvjiC82dO1dz5841u7QaV1paqvnz52v48OHy8XHqnQSuxZmPoPztb38zIiMjDavVavzsZz/ziMcPP/30U0NSuc/w4cPNLq3GVNSvJGP+/Plml1ajRo4cafvnOzQ01Lj77ruNjIwMs8syhSc8bvrQQw8ZjRs3Nnx9fY2IiAhj0KBBxu7du80uyyk+/PBDo23btoafn59x2223GXPnzjW7JKdYvXq1Icn49ttvzS6lVrMYhmGYE2kAAIC74V0hAADAYQgWAADAYQgWAADAYQgWAADAYQgWAADAYQgWAADAYQgWAADAYQgWAADAYQgWAADAYQgWAADAYQgWAADAYf4/HqIoaqeek4wAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "\n",
    "x_coord, y_coord = np.nonzero(sol_chess_board)\n",
    "\n",
    "for i, (x, y) in enumerate(zip(x_coord, y_coord), start=1):\n",
    "    ax.plot(x+0.5, y+0.5, 'o')\n",
    "    ax.annotate(f'Q{i}', xy=(x+0.3, y+0.1))\n",
    "# _end_for_\n",
    "\n",
    "ax.grid()\n",
    "\n",
    "ax.set_xlim([0, n_queen])\n",
    "ax.set_ylim([0, n_queen])\n",
    "\n",
    "ax.set(xticks=range(0, n_queen, 1),\n",
    "       yticks=range(0, n_queen, 1))\n",
    "\n",
    "plt.title(f\"Optimal Queens-{n_queen}\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bc942926",
   "metadata": {},
   "source": [
    "### End of file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8eeb9156",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv_tf",
   "language": "python",
   "name": "venv_tf"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}