IBM_max_Army.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/OptimizationExpert/Pyomo/blob/main/IBM_max_Army.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "google",
      "metadata": {
        "id": "google"
      },
      "source": [
        "##### Copyright 2022 Google LLC."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "apache",
      "metadata": {
        "id": "apache"
      },
      "source": [
        "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "you may not use this file except in compliance with the License.\n",
        "You may obtain a copy of the License at\n",
        "\n",
        "    http://www.apache.org/licenses/LICENSE-2.0\n",
        "\n",
        "Unless required by applicable law or agreed to in writing, software\n",
        "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "See the License for the specific language governing permissions and\n",
        "limitations under the License.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "basename",
      "metadata": {
        "id": "basename"
      },
      "source": [
        "# solve_with_time_limit_sample_sat"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "link",
      "metadata": {
        "id": "link"
      },
      "source": [
        "<table align=\"left\">\n",
        "<td>\n",
        "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/sat/solve_with_time_limit_sample_sat.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
        "</td>\n",
        "<td>\n",
        "<a href=\"https://github.com/google/or-tools/blob/main/ortools/sat/samples/solve_with_time_limit_sample_sat.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
        "</td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "doc",
      "metadata": {
        "id": "doc"
      },
      "source": [
        "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "id": "install",
      "metadata": {
        "id": "install",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "491981dc-0c77-4e25-b0db-8d34cbbd5ef7"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Collecting ortools\n",
            "  Downloading ortools-9.8.3296-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (22.9 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m22.9/22.9 MB\u001b[0m \u001b[31m39.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hCollecting absl-py>=2.0.0 (from ortools)\n",
            "  Downloading absl_py-2.1.0-py3-none-any.whl (133 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m133.7/133.7 kB\u001b[0m \u001b[31m14.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: numpy>=1.13.3 in /usr/local/lib/python3.10/dist-packages (from ortools) (1.25.2)\n",
            "Collecting pandas>=2.0.0 (from ortools)\n",
            "  Downloading pandas-2.2.1-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (13.0 MB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m13.0/13.0 MB\u001b[0m \u001b[31m44.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hCollecting protobuf>=4.25.0 (from ortools)\n",
            "  Downloading protobuf-4.25.3-cp37-abi3-manylinux2014_x86_64.whl (294 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m294.6/294.6 kB\u001b[0m \u001b[31m26.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: python-dateutil>=2.8.2 in /usr/local/lib/python3.10/dist-packages (from pandas>=2.0.0->ortools) (2.8.2)\n",
            "Requirement already satisfied: pytz>=2020.1 in /usr/local/lib/python3.10/dist-packages (from pandas>=2.0.0->ortools) (2023.4)\n",
            "Collecting tzdata>=2022.7 (from pandas>=2.0.0->ortools)\n",
            "  Downloading tzdata-2024.1-py2.py3-none-any.whl (345 kB)\n",
            "\u001b[2K     \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m345.4/345.4 kB\u001b[0m \u001b[31m31.3 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
            "\u001b[?25hRequirement already satisfied: six>=1.5 in /usr/local/lib/python3.10/dist-packages (from python-dateutil>=2.8.2->pandas>=2.0.0->ortools) (1.16.0)\n",
            "Installing collected packages: tzdata, protobuf, absl-py, pandas, ortools\n",
            "  Attempting uninstall: protobuf\n",
            "    Found existing installation: protobuf 3.20.3\n",
            "    Uninstalling protobuf-3.20.3:\n",
            "      Successfully uninstalled protobuf-3.20.3\n",
            "  Attempting uninstall: absl-py\n",
            "    Found existing installation: absl-py 1.4.0\n",
            "    Uninstalling absl-py-1.4.0:\n",
            "      Successfully uninstalled absl-py-1.4.0\n",
            "  Attempting uninstall: pandas\n",
            "    Found existing installation: pandas 1.5.3\n",
            "    Uninstalling pandas-1.5.3:\n",
            "      Successfully uninstalled pandas-1.5.3\n",
            "\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
            "bigframes 0.21.0 requires pandas<2.1.4,>=1.5.0, but you have pandas 2.2.1 which is incompatible.\n",
            "google-colab 1.0.0 requires pandas==1.5.3, but you have pandas 2.2.1 which is incompatible.\n",
            "tensorflow-metadata 1.14.0 requires absl-py<2.0.0,>=0.9, but you have absl-py 2.1.0 which is incompatible.\n",
            "tensorflow-metadata 1.14.0 requires protobuf<4.21,>=3.20.3, but you have protobuf 4.25.3 which is incompatible.\u001b[0m\u001b[31m\n",
            "\u001b[0mSuccessfully installed absl-py-2.1.0 ortools-9.8.3296 pandas-2.2.1 protobuf-4.25.3 tzdata-2024.1\n"
          ]
        }
      ],
      "source": [
        "!pip install ortools\n",
        "from ortools.sat.python import cp_model # CP-SAT solver\n",
        "import numpy as np\n",
        "from random import randint\n",
        "import random\n",
        "from math import ceil\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt # Data visualization\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "counter = 0\n",
        "data = {}\n",
        "for r in range(8):\n",
        "  for c in range(8):\n",
        "    counter+=1\n",
        "    data[counter,'X'] = c\n",
        "    data[counter,'Y'] = r\n",
        "allowed = [ (1,2),(1,-2) , (-1,2), (-1,-2) , (2,1), (2,-1) , (-2,-1),(-2,1) ]"
      ],
      "metadata": {
        "id": "3huYW2ytVkqt"
      },
      "id": "3huYW2ytVkqt",
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize=(8,8))\n",
        "NR= {}\n",
        "NQ = {}\n",
        "Nking= {}\n",
        "Nknight = {}\n",
        "NB= {}\n",
        "def dist(n,counter):\n",
        "  return np.sqrt( (data[counter,'X'] - data[n,'X'])**2 + (data[counter,'Y'] - data[n,'Y'])**2  )\n",
        "nodes = [n for n in range(1,1+64)]\n",
        "\n",
        "for counter in nodes:\n",
        "  x = data[counter,'X']\n",
        "  y = data[counter,'Y']\n",
        "  plt.scatter(x,y,s=900, marker = 's', c='grey')\n",
        "  plt.text(x,y,s=str(counter), c='w')\n",
        "  NR[counter] = [n for n in nodes if n!=counter and (data[counter,'X'] == data[n,'X'] or data[counter,'Y'] == data[n,'Y'] )]\n",
        "  Nking[counter] = [n for n in nodes if n!=counter and dist(n,counter)<= np.sqrt(2) ]\n",
        "  NQ[counter] = [n for n in nodes if n!=counter and (data[counter,'X'] == data[n,'X'] or data[counter,'Y'] == data[n,'Y'] or   abs(data[counter,'X'] - data[n,'X']) == abs( data[counter,'Y'] - data[n,'Y'] )  )]\n",
        "  Nknight[counter] = [n for n in nodes if n!=counter and (data[counter,'X']- data[n,'X'], data[counter,'Y'] - data[n,'Y']) in allowed]\n",
        "  NB[counter] = [n for n in nodes if n!=counter and (abs(data[counter,'X'] - data[n,'X']) == abs( data[counter,'Y'] - data[n,'Y'] )  )]\n",
        ""
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 676
        },
        "id": "5a-27NyRLMeR",
        "outputId": "e33df3ff-9bd0-4c7e-e42c-250c65e7761c"
      },
      "id": "5a-27NyRLMeR",
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 800x800 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "-YC91kDnjTVh"
      },
      "id": "-YC91kDnjTVh",
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "id": "description",
      "metadata": {
        "id": "description"
      },
      "source": [
        "\n",
        "Solves a problem with a time limit.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "id": "code",
      "metadata": {
        "id": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 742
        },
        "outputId": "eeeb0de4-a48c-46fa-d374-81872dfb6bc8"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "OF =  2 278.0\n",
            "success\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 700x700 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "from ortools.sat.python import cp_model\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "import matplotlib.pyplot as pyplot\n",
        "from matplotlib.font_manager import FontProperties\n",
        "\n",
        "def SolveWithTimeLimitSampleSat():\n",
        "    \"\"\"Minimal CP-SAT example to showcase calling the solver.\"\"\"\n",
        "    # Creates the model.\n",
        "    model = cp_model.CpModel()\n",
        "    # Creates the variables.\n",
        "    pieces = ['K', 'R', 'Q', 'N', 'B' ]\n",
        "    val= {'K':14, 'R':28, 'Q':28, 'N':7, 'B':16 }\n",
        "    symb= {'K':\"\\u265A\", 'R':\"\\u265C\", 'Q':\"\\u265B\", 'N':\"\\u265E\", 'B':\"\\u265D\" }\n",
        "    U = {(n,p):model.NewBoolVar(f'assign_{n}_{p}') for n in nodes for p in pieces}\n",
        "    Occupied = {n:model.NewBoolVar(f'O_{n}') for n in nodes}\n",
        "\n",
        "    for p in pieces:\n",
        "      expressions = [U[n,p] for n in nodes]\n",
        "      model.AddAtLeastOne(expressions)\n",
        "\n",
        "    for n in nodes:\n",
        "      expressions = [U[n,p] for p in pieces]\n",
        "      model.Add(sum(expressions) == Occupied[n])\n",
        "      model.AddAtMostOne(expressions)\n",
        "      expressions_king_around   = [U[counter,'K'] for counter in nodes if counter in Nking[n] ]\n",
        "      expressions_rook_around   = [U[counter,'R'] for counter in nodes if counter in NR[n] ]\n",
        "      expressions_queen_around  = [U[counter,'Q'] for counter in nodes if counter in NQ[n] ]\n",
        "      expressions_knight_around = [U[counter,'N'] for counter in nodes if counter in Nknight[n] ]\n",
        "      expressions_bishop_around = [U[counter,'B'] for counter in nodes if counter in NB[n] ]\n",
        "\n",
        "      around = expressions_king_around + expressions_rook_around + expressions_queen_around + expressions_knight_around + expressions_bishop_around\n",
        "      model.Add( sum(around) == 0 ).OnlyEnforceIf(Occupied[n])\n",
        "\n",
        "\n",
        "    expressions_of = [val[p]*v for (n,p),v in U.items() ]\n",
        "    model.Maximize(sum(expressions_of))\n",
        "    solver = cp_model.CpSolver()\n",
        "    solver.parameters.max_time_in_seconds = 30.0\n",
        "    status = solver.Solve(model)\n",
        "\n",
        "    if status == cp_model.OPTIMAL or status == cp_model.FEASIBLE:\n",
        "      print('OF = ', status, solver.ObjectiveValue())\n",
        "      print('success')\n",
        "      KOLOR = ['r','g', 'gold','navy', 'k']\n",
        "      plt.figure(figsize=(7,7))\n",
        "      for (n,p),v in U.items():\n",
        "        x,y =data[n,'X'],data[n,'Y']\n",
        "\n",
        "        if solver.Value(Occupied[n])==0:\n",
        "          plt.scatter(x,y,s=1100, marker = 's', c='grey', alpha= 0.1)\n",
        "        if solver.Value(v)>0:\n",
        "          cc= KOLOR[pieces.index(p)]\n",
        "\n",
        "          plt.scatter(x,y,s=1100, marker = 's', c=cc)\n",
        "          prop = FontProperties()\n",
        "          plt.text(x-0.25,y-0.2,s=symb[p], c='w', fontsize= 30, fontproperties=prop)\n",
        "\n",
        "      plt.tight_layout()\n",
        "      plt.show()\n",
        "\n",
        "\n",
        "SolveWithTimeLimitSampleSat()"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "VT9zHAO9hggq"
      },
      "id": "VT9zHAO9hggq",
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "Cq4f8wW9tag3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 455
        },
        "outputId": "6d1c779b-7a7b-4424-cef5-1df93709df61"
      },
      "id": "Cq4f8wW9tag3",
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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AZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZAgXACAZwgUASIZwAQCSMaJwaWpqijlz5kRJSUlUVlbGrl27Trh2y5YtccUVV8TUqVNj6tSpUV1d/YHrAQBOJO9w2bZtW9TX10dDQ0Ps3r075s+fHzU1NfHWW28Nu37nzp1x3XXXxQ9+8INobW2NioqK+MxnPhM//elPP/TwAMDkUpBlWZbPCZWVlXHppZfGQw89FBERAwMDUVFREbfddlusWbPmt57f398fU6dOjYceeiiWL19+Uo/Z3d0dZWVl0dXVFaWlpfmMCwCMk9F4/c7riktfX1+0tbVFdXX1r++gsDCqq6ujtbX1pO7jnXfeiffeey8++tGPnnBNb29vdHd3D7kBAOQVLkeOHIn+/v4oLy8fcry8vDw6OjpO6j7uuOOOmDVr1pD4+U2NjY1RVlY2eKuoqMhnTABgghrTnyrauHFjbN26NZ555pkoKSk54bq1a9dGV1fX4O3QoUNjOCUAcLqaks/iadOmRVFRUXR2dg453tnZGTNmzPjAc++///7YuHFjfP/7349LLrnkA9fmcrnI5XL5jAYATAJ5XXEpLi6ORYsWRUtLy+CxgYGBaGlpiaqqqhOed99998W9994bzc3NsXjx4pFPCwBManldcYmIqK+vjxUrVsTixYtjyZIlsWnTpujp6YmVK1dGRMTy5ctj9uzZ0djYGBERf/u3fxvr16+PJ554IubMmTP4WZiPfOQj8ZGPfOQUPhUAYKLLO1zq6uri8OHDsX79+ujo6IgFCxZEc3Pz4Ad2Dx48GIWFv76Q841vfCP6+vric5/73JD7aWhoiC9/+csfbnoAYFLJ+3tcxoPvcQGA9Iz797gAAIwn4QIAJEO4AADJEC4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJEC4AQDKECwCQDOECACRDuAAAyRAuAEAyhAsAkAzhAgAkQ7gAAMkQLgBAMoQLAJAM4QIAJEO4AADJGFG4NDU1xZw5c6KkpCQqKytj165dH7j+O9/5Tlx44YVRUlISF198cezYsWNEwwIAk1ve4bJt27aor6+PhoaG2L17d8yfPz9qamrirbfeGnb9Sy+9FNddd13ceOONsWfPnli6dGksXbo0fvzjH3/o4QGAyaUgy7IsnxMqKyvj0ksvjYceeigiIgYGBqKioiJuu+22WLNmzXHr6+rqoqenJ773ve8NHvvDP/zDWLBgQWzevPmkHrO7uzvKysqiq6srSktL8xkXABgno/H6PSWfxX19fdHW1hZr164dPFZYWBjV1dXR2to67Dmtra1RX18/5FhNTU08++yzJ3yc3t7e6O3tHfxzV1dXRPzfvwAAIA3vv27neY3kA+UVLkeOHIn+/v4oLy8fcry8vDz27ds37DkdHR3Dru/o6Djh4zQ2NsY999xz3PGKiop8xgUATgP/+7//G2VlZafkvvIKl7Gydu3aIVdp3n777TjvvPPi4MGDp+yJMzLd3d1RUVERhw4d8rbdOLMXpw97cXqxH6ePrq6uOPfcc+OjH/3oKbvPvMJl2rRpUVRUFJ2dnUOOd3Z2xowZM4Y9Z8aMGXmtj4jI5XKRy+WOO15WVuY/wtNEaWmpvThN2IvTh704vdiP00dh4an79pW87qm4uDgWLVoULS0tg8cGBgaipaUlqqqqhj2nqqpqyPqIiOeff/6E6wEATiTvt4rq6+tjxYoVsXjx4liyZEls2rQpenp6YuXKlRERsXz58pg9e3Y0NjZGRMTtt98eV155ZTzwwANxzTXXxNatW+NHP/pRPPLII6f2mQAAE17e4VJXVxeHDx+O9evXR0dHRyxYsCCam5sHP4B78ODBIZeELrvssnjiiSfirrvuijvvvDP+4A/+IJ599tm46KKLTvoxc7lcNDQ0DPv2EWPLXpw+7MXpw16cXuzH6WM09iLv73EBABgvflcRAJAM4QIAJEO4AADJEC4AQDJOm3BpamqKOXPmRElJSVRWVsauXbs+cP13vvOduPDCC6OkpCQuvvji2LFjxxhNOvHlsxdbtmyJK664IqZOnRpTp06N6urq37p3nLx8/168b+vWrVFQUBBLly4d3QEnkXz34u23345Vq1bFzJkzI5fLxQUXXOD/U6dIvnuxadOm+NjHPhZnnnlmVFRUxOrVq+Pdd98do2knrh/+8IdRW1sbs2bNioKCgg/8HYTv27lzZ3zqU5+KXC4X559/fjz++OP5P3B2Gti6dWtWXFycPfbYY9l//dd/ZTfffHN2zjnnZJ2dncOuf/HFF7OioqLsvvvuy1555ZXsrrvuys4444zs5ZdfHuPJJ5589+L666/Pmpqasj179mR79+7N/uIv/iIrKyvL/vu//3uMJ5948t2L973xxhvZ7NmzsyuuuCL70z/907EZdoLLdy96e3uzxYsXZ1dffXX2wgsvZG+88Ua2c+fOrL29fYwnn3jy3Ytvf/vbWS6Xy7797W9nb7zxRvbcc89lM2fOzFavXj3Gk088O3bsyNatW5c9/fTTWURkzzzzzAeuP3DgQHbWWWdl9fX12SuvvJJ9/etfz4qKirLm5ua8Hve0CJclS5Zkq1atGvxzf39/NmvWrKyxsXHY9ddee212zTXXDDlWWVmZ/eVf/uWozjkZ5LsXv+nYsWPZ2WefnX3rW98arREnjZHsxbFjx7LLLrss++Y3v5mtWLFCuJwi+e7FN77xjWzu3LlZX1/fWI04aeS7F6tWrcr++I//eMix+vr67PLLLx/VOSebkwmXL33pS9knP/nJIcfq6uqympqavB5r3N8q6uvri7a2tqiurh48VlhYGNXV1dHa2jrsOa2trUPWR0TU1NSccD0nZyR78ZveeeedeO+9907pL9SajEa6F1/5yldi+vTpceONN47FmJPCSPbiu9/9blRVVcWqVauivLw8LrrootiwYUP09/eP1dgT0kj24rLLLou2trbBt5MOHDgQO3bsiKuvvnpMZubXTtVr97j/dugjR45Ef3//4Dfvvq+8vDz27ds37DkdHR3Dru/o6Bi1OSeDkezFb7rjjjti1qxZx/3HSX5GshcvvPBCPProo9He3j4GE04eI9mLAwcOxL/927/FDTfcEDt27Ij9+/fHF77whXjvvfeioaFhLMaekEayF9dff30cOXIkPv3pT0eWZXHs2LG49dZb48477xyLkfn/nOi1u7u7O371q1/FmWeeeVL3M+5XXJg4Nm7cGFu3bo1nnnkmSkpKxnucSeXo0aOxbNmy2LJlS0ybNm28x5n0BgYGYvr06fHII4/EokWLoq6uLtatWxebN28e79EmnZ07d8aGDRvi4Ycfjt27d8fTTz8d27dvj3vvvXe8R2OExv2Ky7Rp06KoqCg6OzuHHO/s7IwZM2YMe86MGTPyWs/JGclevO/++++PjRs3xve///245JJLRnPMSSHfvXj99dfjzTffjNra2sFjAwMDERExZcqUePXVV2PevHmjO/QENZK/FzNnzowzzjgjioqKBo99/OMfj46Ojujr64vi4uJRnXmiGsle3H333bFs2bK46aabIiLi4osvjp6enrjlllti3bp1Q363HqPrRK/dpaWlJ321JeI0uOJSXFwcixYtipaWlsFjAwMD0dLSElVVVcOeU1VVNWR9RMTzzz9/wvWcnJHsRUTEfffdF/fee280NzfH4sWLx2LUCS/fvbjwwgvj5Zdfjvb29sHbZz/72bjqqquivb09KioqxnL8CWUkfy8uv/zy2L9//2A8RkS89tprMXPmTNHyIYxkL955553j4uT9oMz8qr4xdcpeu/P73PDo2Lp1a5bL5bLHH388e+WVV7JbbrklO+ecc7KOjo4sy7Js2bJl2Zo1awbXv/jii9mUKVOy+++/P9u7d2/W0NDgx6FPkXz3YuPGjVlxcXH21FNPZT/72c8Gb0ePHh2vpzBh5LsXv8lPFZ06+e7FwYMHs7PPPjv7q7/6q+zVV1/Nvve972XTp0/PvvrVr47XU5gw8t2LhoaG7Oyzz87+6Z/+KTtw4ED2r//6r9m8efOya6+9dryewoRx9OjRbM+ePdmePXuyiMgefPDBbM+ePdlPfvKTLMuybM2aNdmyZcsG17//49B/8zd/k+3duzdrampK98ehsyzLvv71r2fnnntuVlxcnC1ZsiT7j//4j8F/duWVV2YrVqwYsv7JJ5/MLrjggqy4uDj75Cc/mW3fvn2MJ5648tmL8847L4uI424NDQ1jP/gElO/fi/+fcDm18t2Ll156KausrMxyuVw2d+7c7Gtf+1p27NixMZ56YspnL957773sy1/+cjZv3ryspKQkq6ioyL7whS9kv/jFL8Z+8AnmBz/4wbD//3//3/+KFSuyK6+88rhzFixYkBUXF2dz587N/uEf/iHvxy3IMtfKAIA0jPtnXAAATpZwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBRhXvb294z0CkBDhAoyr7du3x7Fjx8Z7DCARwgUYVy+99FLs3bt3vMcAEiFcgDG1f//++Od//ufBt4ja29tjz549ERHxP//zP/Hkk0/Gu+++O54jAqexKeM9ADC5nH/++dHW1hbnnXdeXHPNNdHW1hbHjh2Lxx9/PH7xi1/Ev/zLv0RJScl4jwmcpvx2aGBc/Pu//3vU1tZGV1dXRERcddVV8eyzz0Zpaek4TwaczrxVBIyLvXv3xi9/+cvBPx88eDA6OzvHcSIgBcIFGFNZlsWdd94Z//iP/xh///d/H7NmzYobbrgh/uzP/iyuvfbaePHFF8d7ROA05q0iYEy9/vrrMWXKlDjvvPMiIqK2tjZWrFgRn/vc5yLLsvjP//zPuOSSS3zOBRiWD+cCY2revHlD/rxw4cJYuHBhREQUFBTEkiVLxmMsIBHeKgLG1R/90R/F3Llzx3sMIBHeKgLGVZZlUVBQMN5jAIlwxQUYV6IFyIdwAQCSIVwAgGQIFwAgGcIFAEiGcAEAkiFcAIBkCBcAIBnCBQBIhnABAJIhXACAZPw/5DUmFPrMv9YAAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "language_info": {
      "name": "python"
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "gpuClass": "standard"
  },
  "nbformat": 4,
  "nbformat_minor": 5
}