Lab 1 - solutions.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Lab 1 - Problem 1 Solutions.ipynb",
      "version": "0.3.2",
      "views": {},
      "default_view": {},
      "provenance": [
        {
          "file_id": "0B6ArzxpJJ4WVLWxtVzBsYUJYNTA",
          "timestamp": 1509146167480
        }
      ],
      "collapsed_sections": []
    }
  },
  "cells": [
    {
      "metadata": {
        "id": "AcKwkqnlNAtn",
        "colab_type": "text"
      },
      "source": [
        "## Preface from mike\n",
        "\n",
        "I modified the notebook from lab1 of the Berkley reinforcement bootcamp 2017 to run on google's colab. This save you from having to set up your own environment.\n",
        "\n",
        "Make a copy of this notebook, (so you don't give everyone the answers). Click file=>make a copy\n",
        "\n",
        "Run the first few cells to download the required code so you run it on a google cloud backend (for free for now). We can also share comments "
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "ID64OlylIvZO",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        "import os\n",
        "os.sys.path.append('.')"
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "m7E23obBN_8v",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            },
            {
              "item_id": 2
            }
          ],
          "base_uri": "https://localhost:8080/",
          "height": 411
        },
        "outputId": "0ce3d585-c327-40f6-e4bc-9f833711f7fc",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1509183268349,
          "user_tz": -480,
          "elapsed": 1224,
          "user": {
            "displayName": "Mike C",
            "photoUrl": "//lh3.googleusercontent.com/-xWyBhueI0Vo/AAAAAAAAAAI/AAAAAAAAIg8/rU-qliu5l-M/s50-c-k-no/photo.jpg",
            "userId": "110113503404408134511"
          }
        }
      },
      "source": [
        "%%bash\n",
        "echo \"downloading lab\"\n",
        "wget --no-check-certificate 'https://docs.google.com/uc?export=download&id=0B1BwaUH2mk-EdXI5dzlLbWl5R0E' -O lab1.zip"
      ],
      "cell_type": "code",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "downloading lab\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "--2017-10-28 09:34:27--  https://docs.google.com/uc?export=download&id=0B1BwaUH2mk-EdXI5dzlLbWl5R0E\n",
            "Resolving docs.google.com (docs.google.com)... 74.125.141.100, 74.125.141.101, 74.125.141.113, ...\n",
            "Connecting to docs.google.com (docs.google.com)|74.125.141.100|:443... connected.\n",
            "HTTP request sent, awaiting response... 302 Moved Temporarily\n",
            "Location: https://doc-04-0s-docs.googleusercontent.com/docs/securesc/ha0ro937gcuc7l7deffksulhg5h7mbp1/r006jdgtpcjbvrkrlt32o289qf8pd96d/1509177600000/16080780047704686699/*/0B1BwaUH2mk-EdXI5dzlLbWl5R0E?e=download [following]\n",
            "Warning: wildcards not supported in HTTP.\n",
            "--2017-10-28 09:34:27--  https://doc-04-0s-docs.googleusercontent.com/docs/securesc/ha0ro937gcuc7l7deffksulhg5h7mbp1/r006jdgtpcjbvrkrlt32o289qf8pd96d/1509177600000/16080780047704686699/*/0B1BwaUH2mk-EdXI5dzlLbWl5R0E?e=download\n",
            "Resolving doc-04-0s-docs.googleusercontent.com (doc-04-0s-docs.googleusercontent.com)... 74.125.141.132, 2607:f8b0:400c:c06::84\n",
            "Connecting to doc-04-0s-docs.googleusercontent.com (doc-04-0s-docs.googleusercontent.com)|74.125.141.132|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 239828 (234K) [application/zip]\n",
            "Saving to: ‘lab1.zip’\n",
            "\n",
            "     0K .......... .......... .......... .......... .......... 21% 46.5M 0s\n",
            "    50K .......... .......... .......... .......... .......... 42% 50.8M 0s\n",
            "   100K .......... .......... .......... .......... .......... 64% 72.3M 0s\n",
            "   150K .......... .......... .......... .......... .......... 85% 76.1M 0s\n",
            "   200K .......... .......... .......... ....                 100% 74.5M=0.004s\n",
            "\n",
            "2017-10-28 09:34:28 (60.6 MB/s) - ‘lab1.zip’ saved [239828/239828]\n",
            "\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "metadata": {
        "id": "UcLJdMutIzCX",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            },
            {
              "item_id": 2
            }
          ],
          "base_uri": "https://localhost:8080/",
          "height": 1071
        },
        "outputId": "ec124f07-ec12-454a-9129-c9b014921a31",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1509183274501,
          "user_tz": -480,
          "elapsed": 5965,
          "user": {
            "displayName": "Mike C",
            "photoUrl": "//lh3.googleusercontent.com/-xWyBhueI0Vo/AAAAAAAAAAI/AAAAAAAAIg8/rU-qliu5l-M/s50-c-k-no/photo.jpg",
            "userId": "110113503404408134511"
          }
        }
      },
      "source": [
        "%%bash\n",
        "echo \"unzipping lab\"\n",
        "unzip -o lab1.zip\n",
        "mv -f lab1/* .\n",
        "rm lab1/ -rf\n",
        "\n",
        "# this notebook is python2, the code is python3, make it compatible with this\n",
        "echo \"\"\n",
        "echo \"python 3 to 2\"\n",
        "pasteurize -w *.py > pasteurize.log\n",
        "\n",
        "echo \"\"\n",
        "echo \"install dependencies\"\n",
        "pip install gym"
      ],
      "cell_type": "code",
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "unzipping lab\n",
            "Archive:  lab1.zip\n",
            "   creating: lab1/\n",
            "  inflating: lab1/misc.py            \n",
            "  inflating: lab1/crawler_env.py     \n",
            "  inflating: lab1/Lab 1 - Problem 3.ipynb  \n",
            "  inflating: lab1/frozen_lake.py     \n",
            "  inflating: lab1/LICENSE            \n",
            "  inflating: lab1/environment.yml    \n",
            "  inflating: lab1/discrete_env.py    \n",
            "  inflating: lab1/Lab 1 - Problem 1.ipynb  \n",
            "  inflating: lab1/lab1.md            \n",
            "  inflating: lab1/Lab 1 - Problem 2.ipynb  \n",
            "   creating: lab1/.ipynb_checkpoints/\n",
            "  inflating: lab1/.ipynb_checkpoints/Lab 1 - Problem 3-checkpoint.ipynb  \n",
            "  inflating: lab1/.ipynb_checkpoints/Lab 1 - Problem 2-checkpoint.ipynb  \n",
            "  inflating: lab1/.ipynb_checkpoints/Lab 1 - Problem 1-checkpoint.ipynb  \n",
            "\n",
            "python 3 to 2\n",
            "\n",
            "install dependencies\n",
            "Collecting gym\n",
            "  Downloading gym-0.9.4.tar.gz (157kB)\n",
            "Requirement already satisfied: numpy>=1.10.4 in /usr/local/lib/python2.7/dist-packages (from gym)\n",
            "Requirement already satisfied: requests>=2.0 in /usr/local/lib/python2.7/dist-packages (from gym)\n",
            "Requirement already satisfied: six in /usr/local/lib/python2.7/dist-packages (from gym)\n",
            "Collecting pyglet>=1.2.0 (from gym)\n",
            "  Downloading pyglet-1.2.4-py2-none-any.whl (964kB)\n",
            "Requirement already satisfied: urllib3<1.23,>=1.21.1 in /usr/local/lib/python2.7/dist-packages (from requests>=2.0->gym)\n",
            "Requirement already satisfied: idna<2.7,>=2.5 in /usr/local/lib/python2.7/dist-packages (from requests>=2.0->gym)\n",
            "Requirement already satisfied: chardet<3.1.0,>=3.0.2 in /usr/local/lib/python2.7/dist-packages (from requests>=2.0->gym)\n",
            "Requirement already satisfied: certifi>=2017.4.17 in /usr/local/lib/python2.7/dist-packages (from requests>=2.0->gym)\n",
            "Building wheels for collected packages: gym\n",
            "  Running setup.py bdist_wheel for gym: started\n",
            "  Running setup.py bdist_wheel for gym: finished with status 'done'\n",
            "  Stored in directory: /content/.cache/pip/wheels/ad/46/5a/1833d0ef8149a50e78fdb24a41f47e22a7f4a9dcd649b8db53\n",
            "Successfully built gym\n",
            "Installing collected packages: pyglet, gym\n",
            "Successfully installed gym-0.9.4 pyglet-1.2.4\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "stream",
          "text": [
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "root: Generating grammar tables from /usr/lib/python2.7/lib2to3/PatternGrammar.txt\n",
            "RefactoringTool: Refactored crawler_env.py\n",
            "RefactoringTool: Refactored discrete_env.py\n",
            "RefactoringTool: Refactored frozen_lake.py\n",
            "RefactoringTool: Refactored misc.py\n",
            "RefactoringTool: Files that were modified:\n",
            "RefactoringTool: crawler_env.py\n",
            "RefactoringTool: discrete_env.py\n",
            "RefactoringTool: frozen_lake.py\n",
            "RefactoringTool: misc.py\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "metadata": {
        "id": "sqd9E3XIN-mF",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        ""
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "3lmax9fHIr7U",
        "colab_type": "text"
      },
      "source": [
        "# Lab 1: Markov Decision Processes - Problem 1\n",
        "\n",
        "\n",
        "## Lab Instructions\n",
        "All your answers should be written in this notebook.  You shouldn't need to write or modify any other files.\n",
        "\n",
        "**You should execute every block of code to not miss any dependency.**\n",
        "\n",
        "\n",
        "*This project was developed by Peter Chen, Rocky Duan, Pieter Abbeel for the Berkeley Deep RL Bootcamp, August 2017. Bootcamp website with slides and lecture videos: https://sites.google.com/view/deep-rl-bootcamp/. It is adapted from Berkeley Deep RL Class [HW2](https://github.com/berkeleydeeprlcourse/homework/blob/c1027d83cd542e67ebed982d44666e0d22a00141/hw2/HW2.ipynb) [(license)](https://github.com/berkeleydeeprlcourse/homework/blob/master/LICENSE)*\n",
        "\n",
        "--------------------------"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "6ApImLdOIr7V",
        "colab_type": "text"
      },
      "source": [
        "## Introduction\n",
        "\n",
        "This assignment will review the two classic methods for solving Markov Decision Processes (MDPs) with finite state and action spaces.\n",
        "We will implement value iteration (VI) and policy iteration (PI) for a finite MDP, both of which find the optimal policy in a finite number of iterations.\n",
        "\n",
        "The experiments here will use the Frozen Lake environment, a simple gridworld MDP that is taken from `gym` and slightly modified for this assignment. In this MDP, the agent must navigate from the start state to the goal state on a 4x4 grid, with stochastic transitions."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "xK-1GF-hIr7W",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "base_uri": "https://localhost:8080/",
          "height": 425
        },
        "outputId": "169ceb0b-2b50-4fc0-a972-f217885b90df",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1509183276304,
          "user_tz": -480,
          "elapsed": 710,
          "user": {
            "displayName": "Mike C",
            "photoUrl": "//lh3.googleusercontent.com/-xWyBhueI0Vo/AAAAAAAAAAI/AAAAAAAAIg8/rU-qliu5l-M/s50-c-k-no/photo.jpg",
            "userId": "110113503404408134511"
          }
        }
      },
      "source": [
        "from misc import FrozenLakeEnv, make_grader\n",
        "env = FrozenLakeEnv()\n",
        "print(env.__doc__)"
      ],
      "cell_type": "code",
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "    Winter is here. You and your friends were tossing around a frisbee at the park\n",
            "    when you made a wild throw that left the frisbee out in the middle of the lake.\n",
            "    The water is mostly frozen, but there are a few holes where the ice has melted.\n",
            "    If you step into one of those holes, you'll fall into the freezing water.\n",
            "    At this time, there's an international frisbee shortage, so it's absolutely imperative that\n",
            "    you navigate across the lake and retrieve the disc.\n",
            "    However, the ice is slippery, so you won't always move in the direction you intend.\n",
            "    The surface is described using a grid like the following\n",
            "\n",
            "        SFFF\n",
            "        FHFH\n",
            "        FFFH\n",
            "        HFFG\n",
            "\n",
            "    S : starting point, safe\n",
            "    F : frozen surface, safe\n",
            "    H : hole, fall to your doom\n",
            "    G : goal, where the frisbee is located\n",
            "\n",
            "    The episode ends when you reach the goal or fall in a hole.\n",
            "    You receive a reward of 1 if you reach the goal, and zero otherwise.\n",
            "\n",
            "    \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "fgBzqHUDIr7d",
        "colab_type": "text"
      },
      "source": [
        "Let's look at what a random episode looks like."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "nbkijLqSIr7d",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "outputId": "5ea6b03b-0ed5-4fcc-b664-136e3d9299bc",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1509183277217,
          "user_tz": -480,
          "elapsed": 761,
          "user": {
            "displayName": "Mike C",
            "photoUrl": "//lh3.googleusercontent.com/-xWyBhueI0Vo/AAAAAAAAAAI/AAAAAAAAIg8/rU-qliu5l-M/s50-c-k-no/photo.jpg",
            "userId": "110113503404408134511"
          }
        }
      },
      "source": [
        "# Some basic imports and setup\n",
        "import numpy as np, numpy.random as nr, gym\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "np.set_printoptions(precision=3)\n",
        "\n",
        "# Seed RNGs so you get the same printouts as me\n",
        "env.seed(0); from gym.spaces import prng; prng.seed(10)\n",
        "# Generate the episode\n",
        "env.reset()\n",
        "for t in range(100):\n",
        "    env.render()\n",
        "    a = env.action_space.sample()\n",
        "    ob, rew, done, _ = env.step(a)\n",
        "    if done:\n",
        "        break\n",
        "assert done\n",
        "env.render();"
      ],
      "cell_type": "code",
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "\n",
            "\u001b[41mS\u001b[0mFFF\n",
            "FHFH\n",
            "FFFH\n",
            "HFFG\n",
            "  (Down)\n",
            "S\u001b[41mF\u001b[0mFF\n",
            "FHFH\n",
            "FFFH\n",
            "HFFG\n",
            "  (Down)\n",
            "SFFF\n",
            "F\u001b[41mH\u001b[0mFH\n",
            "FFFH\n",
            "HFFG\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "Ornbk2HvIr7h",
        "colab_type": "text"
      },
      "source": [
        "In the episode above, the agent falls into a hole after two timesteps. Also note the stochasticity--on the first step, the DOWN action is selected, but the agent moves to the right.\n",
        "\n",
        "We extract the relevant information from the gym Env into the MDP class below.\n",
        "The `env` object won't be used any further, we'll just use the `mdp` object."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "D9E7P9PaIr7h",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "outputId": "bf0b74ef-9cf7-4d00-bd6f-e8ecbd5ef4df",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1509183278291,
          "user_tz": -480,
          "elapsed": 893,
          "user": {
            "displayName": "Mike C",
            "photoUrl": "//lh3.googleusercontent.com/-xWyBhueI0Vo/AAAAAAAAAAI/AAAAAAAAIg8/rU-qliu5l-M/s50-c-k-no/photo.jpg",
            "userId": "110113503404408134511"
          }
        }
      },
      "source": [
        "class MDP(object):\n",
        "    \"\"\"Markov decision process\"\"\"\n",
        "    def __init__(self, P, nS, nA, desc=None):\n",
        "        self.P = P # state transition and reward probabilities, explained below\n",
        "        self.nS = nS # number of states\n",
        "        self.nA = nA # number of actions\n",
        "        self.desc = desc # 2D array specifying what each grid cell means (used for plotting)\n",
        "\n",
        "mdp = MDP( {s : {a : [tup[:3] for tup in tups] for (a, tups) in a2d.items()} for (s, a2d) in env.P.items()}, env.nS, env.nA, env.desc)\n",
        "\n",
        "print(\"mdp.P is a two-level dict where the first key is the state and the second key is the action.\")\n",
        "print(\"The 2D grid cells are associated with indices [0, 1, 2, ..., 15] from left to right and top to down, as in\")\n",
        "print(np.arange(16).reshape(4,4))\n",
        "print(\"Action indices [0, 1, 2, 3] correspond to West, South, East and North.\")\n",
        "print(\"mdp.P[state][action] is a list of tuples (probability, nextstate, reward).\\n\")\n",
        "print(\"For example, state 0 is the initial state, and the transition information for s=0, a=0 is \\nP[0][0] =\", mdp.P[0][0], \"\\n\")\n",
        "print(\"As another example, state 5 corresponds to a hole in the ice, in which all actions lead to the same state with probability 1 and reward 0.\")\n",
        "for i in range(4):\n",
        "    print(\"P[5][%i] =\" % i, mdp.P[5][i])"
      ],
      "cell_type": "code",
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "mdp.P is a two-level dict where the first key is the state and the second key is the action.\n",
            "The 2D grid cells are associated with indices [0, 1, 2, ..., 15] from left to right and top to down, as in\n",
            "[[ 0  1  2  3]\n",
            " [ 4  5  6  7]\n",
            " [ 8  9 10 11]\n",
            " [12 13 14 15]]\n",
            "Action indices [0, 1, 2, 3] correspond to West, South, East and North.\n",
            "mdp.P[state][action] is a list of tuples (probability, nextstate, reward).\n",
            "\n",
            "('For example, state 0 is the initial state, and the transition information for s=0, a=0 is \\nP[0][0] =', [(0.1, 0, 0.0), (0.8, 0, 0.0), (0.1, 4, 0.0)], '\\n')\n",
            "As another example, state 5 corresponds to a hole in the ice, in which all actions lead to the same state with probability 1 and reward 0.\n",
            "('P[5][0] =', [(1.0, 5, 0)])\n",
            "('P[5][1] =', [(1.0, 5, 0)])\n",
            "('P[5][2] =', [(1.0, 5, 0)])\n",
            "('P[5][3] =', [(1.0, 5, 0)])\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "bLzBMbn3VITA",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        ""
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "ATXtdEbcIr7k",
        "colab_type": "text"
      },
      "source": [
        "## Part 1: Value Iteration"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "mYiCzZzSIr7l",
        "colab_type": "text"
      },
      "source": [
        "### Problem 1: implement value iteration\n",
        "In this problem, you'll implement value iteration, which has the following pseudocode:\n",
        "\n",
        "---\n",
        "Initialize $V^{(0)}(s)=0$, for all $s$\n",
        "\n",
        "For $i=0, 1, 2, \\dots$\n",
        "- $V^{(i+1)}(s) = \\max_a \\sum_{s'} P(s,a,s') [ R(s,a,s') + \\gamma V^{(i)}(s')]$, for all $s$\n",
        "\n",
        "---\n",
        "\n",
        "We additionally define the sequence of greedy policies $\\pi^{(0)}, \\pi^{(1)}, \\dots, \\pi^{(n-1)}$, where\n",
        "$$\\pi^{(i)}(s) = \\arg \\max_a \\sum_{s'} P(s,a,s') [ R(s,a,s') + \\gamma V^{(i)}(s')]$$\n",
        "\n",
        "Your code will return two lists: $[V^{(0)}, V^{(1)}, \\dots, V^{(n)}]$ and $[\\pi^{(0)}, \\pi^{(1)}, \\dots, \\pi^{(n-1)}]$\n",
        "\n",
        "To ensure that you get the same policies as the reference solution, choose the lower-index action to break ties in $\\arg \\max_a$. This is done automatically by np.argmax. This will only affect the \"# chg actions\" printout below--it won't affect the values computed.\n",
        "\n",
        "<div class=\"alert alert-warning\">\n",
        "Warning: make a copy of your value function each iteration and use that copy for the update--don't update your value function in place. \n",
        "Updating in-place is also a valid algorithm, sometimes called Gauss-Seidel value iteration or asynchronous value iteration, but it will cause you to get different results than our reference solution (which in turn will mean that our testing code won’t be able to help in verifying your code).\n",
        "</div>"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "nkqLgeKJUNGj",
        "colab_type": "text"
      },
      "source": [
        "Note the slides for this are Lecuture 1, search \"value iteaction\" https://drive.google.com/file/d/0BxXI_RttTZAhVXBlMUVkQ1BVVDQ/view - mike"
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "oI4KFEVdIr7l",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            }
          ],
          "base_uri": "https://localhost:8080/",
          "height": 408
        },
        "outputId": "8a96b090-086a-473b-a60a-22451bc513b3",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1509186049059,
          "user_tz": -480,
          "elapsed": 816,
          "user": {
            "displayName": "Mike C",
            "photoUrl": "//lh3.googleusercontent.com/-xWyBhueI0Vo/AAAAAAAAAAI/AAAAAAAAIg8/rU-qliu5l-M/s50-c-k-no/photo.jpg",
            "userId": "110113503404408134511"
          }
        }
      },
      "source": [
        "def value_iteration(mdp, gamma, nIt, grade_print):\n",
        "    \"\"\"\n",
        "    Inputs:\n",
        "        mdp: MDP\n",
        "        gamma: discount factor\n",
        "        nIt: number of iterations, corresponding to n above\n",
        "    Outputs:\n",
        "        (value_functions, policies)\n",
        "        \n",
        "    len(value_functions) == nIt+1 and len(policies) == nIt\n",
        "    \"\"\"\n",
        "    grade_print(\"Iteration | max|V-Vprev| | # chg actions | V[0]\")\n",
        "    grade_print(\"----------+--------------+---------------+---------\")\n",
        "    Vs = [np.zeros(mdp.nS)] # list of value functions contains the initial value function V^{(0)}, which is zero\n",
        "    pis = []\n",
        "    for it in range(nIt):\n",
        "        oldpi = pis[-1] if len(pis) > 0 else None # \\pi^{(it)} = Greedy[V^{(it-1)}]. Just used for printout\n",
        "        Vprev = Vs[-1] # V^{(it)}\n",
        "        \n",
        "        # Your code should fill in meaningful values for the following two variables\n",
        "        # pi: greedy policy for Vprev (not V), \n",
        "        #     corresponding to the math above: \\pi^{(it)} = Greedy[V^{(it)}]\n",
        "        #     ** it needs to be numpy array of ints **\n",
        "        # V: bellman backup on Vprev\n",
        "        #     corresponding to the math above: V^{(it+1)} = T[V^{(it)}]\n",
        "        #     ** numpy array of floats **        \n",
        "        \n",
        "        # ----- solution ------------------------------------------------------#\n",
        "        # work out the next Value and policy as a function of state $V^{i+1}(s)$\n",
        "        V = np.zeros(mdp.nS)\n",
        "        pi = np.zeros(mdp.nS)\n",
        "        for state in range(mdp.nS):\n",
        "            # work out quality for each action so we can take the argmax\n",
        "            Qis = np.zeros(mdp.nA) # Quality of each action for step=i, and state=state\n",
        "            for action in range(mdp.nA):\n",
        "                # sum over all possible next states (s'), corresponds to the summation over s' in the above equations\n",
        "                for probability, nextstate, reward in mdp.P[state][action]:\n",
        "                    # the $P*(R+y*V)$ from the equations\n",
        "                    Qis[action] += probability * (reward + gamma * Vprev[nextstate])\n",
        "\n",
        "            # Now take the max value/ and max action as in the above equations\n",
        "            V[state] = np.max(Qis)\n",
        "            pi[state] = np.argmax(Qis)\n",
        "\n",
        "        # Store new state and policy\n",
        "        Vs.append(V)\n",
        "        pis.append(pi)\n",
        "        \n",
        "#         V = Vprev # REPLACE THIS LINE WITH YOUR CODE\n",
        "#         pi = oldpi # REPLACE THIS LINE WITH YOUR CODE\n",
        "        # ----- end solution --------------------------------------------------#\n",
        "        \n",
        "        max_diff = np.abs(V - Vprev).max()\n",
        "        nChgActions=\"N/A\" if oldpi is None else (pi != oldpi).sum()\n",
        "        grade_print(\"%4i      | %6.5f      | %4s          | %5.3f\"%(it, max_diff, nChgActions, V[0]))\n",
        "        Vs.append(V)\n",
        "        pis.append(pi)\n",
        "    return Vs, pis\n",
        "\n",
        "GAMMA = 0.95 # we'll be using this same value in subsequent problems\n",
        "\n",
        "\n",
        "# The following is the output of a correct implementation; when\n",
        "#   this code block is run, your implementation's print output will be\n",
        "#   compared with expected output.\n",
        "#   (incorrect line in red background with correct line printed side by side to help you debug)\n",
        "expected_output = \"\"\"Iteration | max|V-Vprev| | # chg actions | V[0]\n",
        "----------+--------------+---------------+---------\n",
        "   0      | 0.80000      |  N/A          | 0.000\n",
        "   1      | 0.60800      |    2          | 0.000\n",
        "   2      | 0.51984      |    2          | 0.000\n",
        "   3      | 0.39508      |    2          | 0.000\n",
        "   4      | 0.30026      |    2          | 0.000\n",
        "   5      | 0.25355      |    1          | 0.254\n",
        "   6      | 0.10478      |    0          | 0.345\n",
        "   7      | 0.09657      |    0          | 0.442\n",
        "   8      | 0.03656      |    0          | 0.478\n",
        "   9      | 0.02772      |    0          | 0.506\n",
        "  10      | 0.01111      |    0          | 0.517\n",
        "  11      | 0.00735      |    0          | 0.524\n",
        "  12      | 0.00310      |    0          | 0.527\n",
        "  13      | 0.00190      |    0          | 0.529\n",
        "  14      | 0.00083      |    0          | 0.530\n",
        "  15      | 0.00049      |    0          | 0.531\n",
        "  16      | 0.00022      |    0          | 0.531\n",
        "  17      | 0.00013      |    0          | 0.531\n",
        "  18      | 0.00006      |    0          | 0.531\n",
        "  19      | 0.00003      |    0          | 0.531\"\"\"\n",
        "Vs_VI, pis_VI = value_iteration(mdp, gamma=GAMMA, nIt=20, grade_print=make_grader(expected_output))"
      ],
      "cell_type": "code",
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Iteration | max|V-Vprev| | # chg actions | V[0]\n",
            "----------+--------------+---------------+---------\n",
            "   0      | 0.80000      |  N/A          | 0.000\n",
            "   1      | 0.60800      |    2          | 0.000\n",
            "   2      | 0.51984      |    2          | 0.000\n",
            "   3      | 0.39508      |    2          | 0.000\n",
            "   4      | 0.30026      |    2          | 0.000\n",
            "   5      | 0.25355      |    1          | 0.254\n",
            "   6      | 0.10478      |    0          | 0.345\n",
            "   7      | 0.09657      |    0          | 0.442\n",
            "   8      | 0.03656      |    0          | 0.478\n",
            "   9      | 0.02772      |    0          | 0.506\n",
            "  10      | 0.01111      |    0          | 0.517\n",
            "  11      | 0.00735      |    0          | 0.524\n",
            "  12      | 0.00310      |    0          | 0.527\n",
            "  13      | 0.00190      |    0          | 0.529\n",
            "  14      | 0.00083      |    0          | 0.530\n",
            "  15      | 0.00049      |    0          | 0.531\n",
            "  16      | 0.00022      |    0          | 0.531\n",
            "  17      | 0.00013      |    0          | 0.531\n",
            "  18      | 0.00006      |    0          | 0.531\n",
            "  19      | 0.00003      |    0          | 0.531\n",
            "Test succeeded\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "metadata": {
        "id": "VPaC_21OfrEf",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        ""
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    },
    {
      "metadata": {
        "id": "8ZbcNuabIr7o",
        "colab_type": "text"
      },
      "source": [
        "Below, we've illustrated the progress of value iteration. Your optimal actions are shown by arrows.\n",
        "At the bottom, the value of the different states are plotted."
      ],
      "cell_type": "markdown"
    },
    {
      "metadata": {
        "id": "FVq2XltvIr7p",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          },
          "output_extras": [
            {
              "item_id": 1
            },
            {
              "item_id": 2
            },
            {
              "item_id": 3
            },
            {
              "item_id": 4
            },
            {
              "item_id": 5
            },
            {
              "item_id": 6
            },
            {
              "item_id": 7
            },
            {
              "item_id": 8
            },
            {
              "item_id": 9
            },
            {
              "item_id": 10
            },
            {
              "item_id": 11
            }
          ],
          "base_uri": "https://localhost:8080/",
          "height": 2050
        },
        "outputId": "e4c3393a-773b-424c-9f97-05e41c96c4c9",
        "executionInfo": {
          "status": "ok",
          "timestamp": 1509186064743,
          "user_tz": -480,
          "elapsed": 2865,
          "user": {
            "displayName": "Mike C",
            "photoUrl": "//lh3.googleusercontent.com/-xWyBhueI0Vo/AAAAAAAAAAI/AAAAAAAAIg8/rU-qliu5l-M/s50-c-k-no/photo.jpg",
            "userId": "110113503404408134511"
          }
        }
      },
      "source": [
        "for (V, pi) in zip(Vs_VI[:10], pis_VI[:10]):\n",
        "    plt.figure(figsize=(3,3))\n",
        "    plt.imshow(V.reshape(4,4), cmap='gray', interpolation='none', clim=(0,1))\n",
        "    ax = plt.gca()\n",
        "    ax.set_xticks(np.arange(4)-.5)\n",
        "    ax.set_yticks(np.arange(4)-.5)\n",
        "    ax.set_xticklabels([])\n",
        "    ax.set_yticklabels([])\n",
        "    Y, X = np.mgrid[0:4, 0:4]\n",
        "    a2uv = {0: (-1, 0), 1:(0, -1), 2:(1,0), 3:(-1, 0)}\n",
        "    Pi = pi.reshape(4,4)\n",
        "    for y in range(4):\n",
        "        for x in range(4):\n",
        "            a = Pi[y, x]\n",
        "            u, v = a2uv[a]\n",
        "            plt.arrow(x, y,u*.3, -v*.3, color='m', head_width=0.1, head_length=0.1) \n",
        "            plt.text(x, y, str(env.desc[y,x].item().decode()),\n",
        "                     color='g', size=12,  verticalalignment='center',\n",
        "                     horizontalalignment='center', fontweight='bold')\n",
        "    plt.grid(color='b', lw=2, ls='-')\n",
        "plt.figure()\n",
        "plt.plot(Vs_VI)\n",
        "plt.title(\"Values of different states\");"
      ],
      "cell_type": "code",
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALEAAACxCAYAAACLKVzFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nPJVYzFOJxTyVWMz7P5WtHsuk2lv4AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f893343f990>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALEAAACxCAYAAACLKVzFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAAC+tJREFUeJzt3WtsVHUexvFvpx25tFhRBAsVSxvA\ngIXKRQQBo7SQ4FqkUMSs4MYXQqQkho2Jrza8IBiDN9wF1ISYiFkXRJZgIho3rq67QVY27BBACwLa\nkOK6WFxKuZXO2RczLSNt55yZ9pyZH3k+zVA7p//Ow5mnp2fGKb8cx3EQsSyU6QAiPaUSi3kqsZin\nEot5KrGYpxKLeXnJNubkoOffJEvk4DhOTldbkpa4fXH2av8eU8aesZCxezqdEPNUYjFPJRbzVGIx\nTyUW81RiMU8lFvNUYjFPJRbzVGIxTyUW81RiMU8lFvM8vIqtFxQDs4AiYt82PwFfAIcDuXV3JcBv\nurj+R2BjoEm6V4IydsP/EvcFHgfOAO/Hr6sEFgK/j1+fLf4JHEj4uDVTQZJQxk56VOIQIaJEk3/S\nIGJF/hY4Gr+uCSgEzvfk1r3JIQfH62v7zwInfY3Tiad9mEgZO0nrnHgMY1jNapaxzP2TfyL2nTgN\nWABUxD8+DlxK59a9mcUsXuEVHuAB74tyiO2R9ouPrxHPI4/FLOZN3qQvfb0vDDBjIYXUUcc61qW2\nMMCMkOKReAxjWMQiJjGJfPLZyU4GMjD5ogvQ+qdWzs85T7Q8CuXx6w8BfwaupJW7W7OYxUM8RDnl\n5JHH53zumrGVVs5xLnbePithwxHgj72bL488FrKQSiopo4yf+ZmBDOQiF7MmYyGFLGEJ05nOEIZw\nkIPu93PAGROlVOKRjKSIIvLJB2AEI1jAAveFx4CNELkpwlelX8G9wFigAdibcuZu5ZDDKEZxG7eR\nF/+rzWAGgxiUdF0jjXzIh4zZO4ZzkXM00BDbkLxXaSmggFJKOzKFCDGf+VzmsueM30e+p4UW3zLe\nzu0MYxg3cRMA/ejn6X5uzzhq7yiORI5c3eBDxl9wHKfbC8T+SLzkkuvUUuu8wRtOHXWdtne6FOEw\nA4f+11y3Gocql7WuF8fpKmM++c5yljvv8q5TRZX71ymJ55ne0zzeMw5nuPMczznb2Ob0pW9WZryH\ne5y1rHU2sMHb1/E1I053Pc1J9g8Kxn7buesTmlxyuYVb+JEfu10PwEjg18SOxnuANmACsdOKd4g9\n4Etbe/auM+aTT4gQzTQn/zIlxJ4a+gvw957k6UryjEUU8QM/4Prgs4SMZRzKUBppdP8yJfiYkZ78\ntnPX2mhzLzDEnpF4H5gK1AK5xB7s7aCHBXbX8SM3i53iVKYjuPJU4AxK+0icHZIfQbKDMvaW7o7E\n+t/OYp5KLOapxGKeSizmqcRinkos5qnEYp5KLOapxGKeSizmqcRinkos5qnEYp5KLOZ5eD2xy4u1\ns4Iy9o5sztj9y0R1JBbzNMfOd8roNx2JxTyVWMxTicU8lVjMU4nFPJVYzFOJxTyVWMxTicU8lVjM\nU4nFPJVYzFOJxbxg5tiVkN0z2Ero+h+HfobYTJE/BB+pkxK0D7sRTInbWZjBlu20DzsJtsQZmMF2\n3dE+7CTtc+IwYYooSm1RwPPNCinkRm70vuDafAEoppicVHZEwPsQYDjDvX9yBvZhykfiMGEWsIBK\nKtnPfjawwfvigOabJc5h28xmPuGT9PIBnO7tdDGllLKYxVRQwVKWus6x6xDgjLhpTGMe8yiggBWs\n8LYowH3YLqUS11DDXOZSRhkA5zlPHXWu605ykp3spHhvMScjCT8Le3m+WQ45rGBFxxBBgGqqGc1o\nT/nK95bTHGnmO76LbXisd/MBDGQgddQxmckMYABnOcvTPO06x64947i94zgWOebrHLtyylnCEsYz\nnhu4geMcd72fE/fhiMgIdrErtsGHfXitlEp8iEOMYQxDGEIBBRzhCJvZ7LqujTYAGpsb8XMQj4PD\nAQ5QQgk3czNhwnzER3zKp57yfd38NU6jk7ih153lLN/wDcUUM4ABRInyFm+5HonbMx5uPkxbow/B\nEhznOCc4QTHFFFFECy2u93PiPjzaeDRxg+9SKnE99axhDaMZTS21tNHGBS54Xp/SkOs0/S3+NpOZ\nzGMeF+JvXlzp7Rm9XWijjfd4jx3soIYaqqjiAhc8n04EkbGFFjaxibd5m6UspZTSlPZhEBkTpfXs\nRHuZU3pAErD2Mmer9jJvZ7v7IMYMaS9zNt/PoDl2AVDG3qI5dnLdUonFPJVYzFOJxTyVWMxTicU8\nlVjMU4nFPJVYzFOJxTyVWMxTicU8lVjMU4nFPJVYzNMwxsAoY89oGKNcxzSM0XfK6DcdicU8lVjM\nU4nFPJVYzFOJxTyVWMxTicU8lVjMU4nFPJVYzFOJxTyVWMxTicU8DWOE7M8H2Z+xBA1jzArZng9s\nZAyYhjEmyvZ8YCNjwNI+Jy6jjHu5N7VFAQ8SnMY0SijxviDgfCFCzGc+ueR6XxRwxv7052Ee9r7A\nwjDGMspYzGKmMIXd7OZLvvS+OKBBgu1DBCuo4EVevDqXLkvyhQgxj3nMZjZFFLGb3R0jtLIlY3/6\n8ziPM5OZNNHEB3yQXj7IrmGMK1lJFVUMYAAAd3EXz/Ks67oGGtjKVobvHU5DpOHqBh+GMb7ACx1D\nBAEWspAKKjzlu3vv3ZyNnOUYx3zJBzCIQaxlLSMZCcTm2q1iFa0uJ7eJGb+NfEszzb5lnMpU6qhj\nKEMBuMQl1/s5MV9ZpIztbI9tyLZhjK/zOmc4w4M8yAhGcJCDbGKT5/UNzQ2+D2N8nuc7RuLeyq1s\nZ7vnsbj7m/f7mg/gNKd5iZeopZYpTCFKlJd52fMcuyAy7mEPYcJUU804xtFCC+tY5znf/sb9V6/I\ntmGMrbTyDu+wla08yqNc4pJfudJ2hjO8xmtsYQtP8ARNNGU6UieJQy0f4zHvpxIBShxqOZnJmY6T\nVFrPTrSXOZud4Qyv8mqmYyRVTz2rWZ3pGEll+1BL0DDGAChjb9EwRrluqcRinkos5qnEYp5KLOap\nxGKeSizmqcRinkos5qnEYp5KLOapxGKeSizmqcRinkos5mkYY2CUsWc0jFGuYxrG6LtYxn37/pXh\nHN2bNGli/L+yeT92T0diMU8lFvNUYjFPJRbzVGIxTyUW81RiMU8lFvNUYjFPJRbzVGIxTyUW81Ri\nMc//EWAlZGxIn2clZPegQ2Df6X0s/3J5p+tLB5Sy7f5tGUjUhRAwAxgHFAKXiY0r+ytwyr+bDXaO\nXbYzMOiw9o5a5hbP7fi4b27fDKa5xgJgLLH9WA8UAA8ATwKvAz/5c7MqcSIDgw6H9BtC+cDyTMfo\nbAixAh8APky4/hQwCNqHPfkhrXPiECFqqKGaau+LAh7S15/+LGOZ6/ivXwh40GE6ok6UK9ErHZeo\nE3Vdc/HFi7TuSe/HygQmsJKV7p84PP7+64TrQsRm2H2Drz/VUjoShwjxCI9QRRV3cifbSOFcLKAh\nfYlDBIcxjOMc9744oEGHPbGxfiMb66+eqE8fPJ1X70k+YKftSButO1ppndxKeHGY8NSw6+1MYAI1\n1DCRiRzlqHuwPvH35+PvQ8DvErb/G9jp/mXSkfIwxjnMoR/9AG/DGBOH9PWJ9Lk6gdSHIX055LCG\nNYxjXMeo2WwbxthTi+5YxOwvZuOcj/3aU8GhAi58dCH5ov8Bl6HtH21Ej0ThtxCu7L7IU5nKMzzD\nYAYDkE++6/18sPkgu9lNdX41xRSzKboJ5834r4895fmvl5aUSrye9XzGZyxgAROZmNIwxk5DBH0Y\n3ebgsIpVzGEOc5nLWMZm3TDGnhrcbzAVT6dwigS0PNUCgyB8f5jwk2FyhySfJb2HPdRTzxKWcB/3\neRvGGN9vu+7aBYcTrgvg1DHlB3aR+Nt4xlNIoR+Zeuzj+Nsc5nCCE5mOk3F5M/LIm53nWt5ETTSx\nnvVsYQuVVLov+C+xU4YK4FfEzo37AlPi2893s64XpP3sRIRIb+bwxcd8nOkIWaHPkj7un9SNJpq8\nP/bZBZwBxgN3E3ue+D/x6/cnWddDGsboO/3Kfm/RMEa5bqnEYp5KLOapxGKeSizmqcRinkos5qnE\nYp5KLOapxGKeSizmqcRinkos5qnEYp5KLOapxGJe0hfFi1igI7GYpxKLeSqxmKcSi3kqsZinEot5\n/wd/zDww58nKiAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f89333de8d0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALEAAACxCAYAAACLKVzFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8932edc350>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALEAAACxCAYAAACLKVzFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8933478290>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALEAAACxCAYAAACLKVzFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8RRiMZ5CLMZTiMV4CrEYTyEW4/0fbQ9IRvSojD8AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8932e56990>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALEAAACxCAYAAACLKVzFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAADfBJREFUeJzt3X1wFPd9x/H33ekJ9HAIZAnJQhFS\nACMZI4QNwgFaWzw4dhEOAkOnxu14nDozxo3/aFymmenYQ+xO48mkbuvgMMPUk3gSoHbDkIlJTJPa\nVWus5A9VDhgDRbFkRVBThLGQhCTfbf+4k3RGuru9k+52f5rPS3OMbvd+2i+7Hy17x+5+PZZlIWIy\nr9MFiEyVQizGU4jFeAqxGE8hFuMpxGK8jFgzPR70+Zu4hAfLsjyTzYkZ4tHB7jX6O6Yap8aEGqPT\n4YQYTyEW4ynEYjyFWIynEIvxFGIxnkIsxlOIxXgKsRhPIRbjKcRiPIVYjKcQi/FsnMU2DcqBRqCU\n0K/NFaAFeD8tS4+vEvizSaZ/DHwvrZVEV4lqjCL1Ic4BHgauAq+Hp20AtgP/GJ7uFr8G3ot4PuJU\nITGoxgmmFGIvXoIEY7+oiFCQ/wc4H57WC/iBgaks3R4PHiy75/Z/CnSntJwJbK3DSKpxgqSOiWuo\n4Rme4XEej//iK4R+E+8GmoG68PMOYCiZpdvTSCPf5bvcwz32B3kIrZHRRwrPEc8gg13s4gAHyCHH\n/sA01ujHzx728AIvJDYwjTVCgnviGmp4iIe4kzvJJZejHKWQwtiDBmHk0AgDmwcILgvCsvD008BP\ngM+SqjuqRhp5gAdYxjIyyOBt3o5b4wgjXOd66Li9MWLGOeBH01tfBhlsZzsb2EA11XzCJxRSyA1u\nuKZGP352s5u1rKWEEk5xKv52TnONkRIK8SIWUUopueQCsJCFNNMcf+AF4HvQPqed31T9BhqAWqAL\naE245qg8eFjMYuYzn4zwX20d6yiiKOa4Hnp4gzeoaa3hevt1uugKzYidq6TkkUcVVWM1efHyFb7C\nMMO2a+xs76Sf/pTVuIAF3MqtzGEOALOYZWs7j9a4uHUx59rPjc9IQY2fY1lW1AeE/oh8+PBZO9hh\nfZ/vW3vYM2H+hEcpFuuwmH3TtGew2BhnbNyHZU1WYy651tf4mvVjfmxtZGP8n1MZrmftVOuxX2MF\nFdZe9lpHOGLlkOPKGlexynqe562XeMnez0lpjVjRcuqJdUPB0NXOkx/Q+PAxj3l8zMdRxwOwCPgT\nQnvjk0AAqCd0WPEqoTd8SRutffIac8nFi5c++mL/mEpCHw39G/CfU6lnMrFrLKWUS1wi7pvPShyr\nsYwyeuiJ/2MqSWGNTOVq58kFCMQPMIQ+kXgdWAPsAHyE3uz9K1MMcHxj/+S62EUuOl1CXLYC7KCk\n98TuEHsP4g6qcbpE2xPrv53FeAqxGE8hFuMpxGI8hViMpxCL8RRiMZ5CLMZTiMV4CrEYTyEW4ynE\nYjyFWIynEIvxbJxPHOdkbVdQjdPDzTVGP01Ue2IxnvrYpVyoxqef/iuH64ju29/+u/B3bl6P0WlP\nLMZTiMV4CrEYTyEW4ynEYjyFWIynEIvxFGIxnkIsxlOIxXgKsRhPIRbjKcRivPT0savE3T3YKpn8\n5tBPEeop8k/pL+lmXd4uDuUcmjC9KFjEozcedaCim1Ti2DpMT4hHmdCDzeVWjKygNlA79jzDSu8m\ndKP0rgEHerDNNPlWPmXBMqfLcJWkj4kzyaSU0sQGpbm/mR8/BRTYH3BzfS5kYRGM+LLdaHIKKqiw\n/2IH1mHCe+JMMmmmmQ1soI02XuIl+4PT1N8ssg/bQQ5yghPJ1Qfwf9Nd3dS0ZLXQktUy9rwqUMX2\noe0pWdbd3M1WtpJHHk/whL1BDqzDhEK8jW3cz/1UUw3AAAPsYU/ccd10c5SjlLeW090ecTwxzf3N\nPHh4gifGmggCNNHEEpbYqm9Z6zL62vv4kA9DM/54euubDvUj9dRdr2NkVugNRY6VQDdSm5axjN3s\nZjnLySKLDjribufIdbiwfSHHOBaakYZ1mFCIT3OaGmoooYQ88jjHOQ5yMO64AAEAevp6SGUjHguL\n93iPSiqZy1wyyeTn/Jxf8Stb9Z3pO4PVY0XOcJ2CkQLWtazjzIYzKVtGBx38jt9RTjmllNJPf9zt\nHLkOz/ecj5yRcgmF+Cxn+RbfYglL2MEOAgQYZND2+ISaXCfpP8Jf61nPVrYyGP6y47Pp7tFrqH76\n2c9+fsAPeIRHqKIqoXWY7vWY1KcTo2H2uPjq2NEwS/JGw+zm7QzqY5cG03vJvm/Ix+KWxdN6OGHK\nJfvqYyczlkIsxlOIxXgKsRhPIRbjKcRiPIVYjKcQG8Q37MM34sMb8OIb9rn7nthppDOqTWFBw48a\nyPk0BywovlBM685WBuYNOF2Z47QnNoUHfl/ze7JuZJE1lEXvgl4FOEwhNkjnyk6uFV9jJHuEjlUd\nTpfjGjqcMIjls+ip6cF/0U9fSZ/T5biGQmyYzpWdZA5mOl2Gq+hwwjCWz2I4b9jpMlxFIRbj2Tif\nWMQNPDqfWGauGdGM8bnnnne4jui++c2/BuDIkX9xuJLoHnpoR/g7N2/r6LQnFuMpxGI8hViMpxCL\n8RRiMZ5CLMZTiMV4CrEYTyEW4ynEYjyFWIynEIvxFGIxnpoxAh3BDg4GJt7Ov5hivp75dQcqmuh0\n/2me7Xx2wvQF2Qv4TvV3HKjoJpWoGaMbrPaups5TN/Y8y5PlYDWT21S4ifX+9WPPs73ZDlbjDmrG\nGMGPnwpvAj3bHFCUWcTi2YudLsNVkj4mrqaaBhoSG5TmZoyJsrAIWIGxR9BKfaOcRAWtYFprnM1s\ntrDF/gATmjFWU80udrGa1RznOO/yrv3BaWrGmKwTwROcCI43blziWcIjGY84WNFEhy4f4tDl8Ubl\n9Xn17K3YO+3Lmc1sHuZh1rOeXnr5KT+1N9DtzRif5Ek2spF88gG4ndv5Bt+IO66LLg5zmIrWCrra\nu8ZnTHMzxqlq8Daw9tJa+kv7AZjlmeVwRRPdN+c+7u27l0BFqEFcri932pexhjXsYQ9lhHpIDzEU\ndzuPbuMVrSuobq/mNV4LzXBbM8aXeZmrXOVe7mUhCznFKfaz3/b4rr6ulDZjnKoCCrjz3Tu50HzB\n6VKimuuZS+07tfQv6U/ZMk5ykkwyaaKJO7iDfvp5gRdsjW3ra6Otp218gtuaMY4wwqu8ymEOs5Od\nDDGUqrrEYZFNLe/iLqfLiSmpTydGwywznwlNLdPzEduHwDNpWVJSqrxVPOd9zukyYqrNreVIzRE8\ngy77SGfUh0y+jf8+9YvWfzuL8RRiMZ5CLMZTiMV4CrEYTyEW4ynEYjz17Ajzn/eTeT2T3Eu5FLUV\n0V/Wz2DJoNNljbMg+7+yYRAyL2SS/XY2w3XDWH7dB10hDpv7/lxKf10KwBd/8kXO7jrrrhADOb/M\nIet06ER97xUvw3Xq3QE6nBjTfU83QwWhc0GuLbzG1ZqrDld0Ew8MbhrE8ob2vEOrhrQXDlOIw0YK\nRuhd2kvQF+TS6ktOlzOp4YZhhmuGCcwLMLBN3URH6XAiQvcfdpNzJcd9e+FRHrix8QaZZzK1F46g\nEEcYKRjhzJ+ecbqMmIYbhhlerWPhSArxzdx+gOXBddcmOs3tm0wkLjVjFEOoGaPMYDOiGeMvfvGm\nw3VEt3nzJgA++eSaw5VEN2eOP/ydm7d1dNoTi/EUYjGeQizGU4jFeAqxGE8hFuMpxGI8hViMpxCL\n8RRiMZ5CLMZTiMV4CrEYL/VXdlTiWJM+u9qvtfP0+09PmP6FWV/gQN0BByqaqOWjFra8PrGL0dJ5\nSzm5+6QDFU3CC6wD7gD8wDChlm//DlxM3WJ1eVKELSVbaLxlvPWPGxsdPnbHY+xcunPs+awMFzXH\naQZqCTXdPAvkAfcAjwIvA1dSs1iFOMIt2bewNH+p02XEdGv+rdxV6sIeGiWEAvwe8EbE9ItAEdCX\nukUndUzsxcs2ttFEk/1BDjTpS1QyjQ69r3nx/swLaerbGLSCfBb8bOxhp8buvd18+stPk1pePfU8\nyZPxXzjaiDXyYnEvoR52H5DSFsgJ7Ym9eHmQB9nIRm7jNo5wxP5gB5r0JeqVj17hlY9eGXu+as4q\n9i3dF3OMp8eD92devG96CW4KEvxyMKW/pPve2ce+d8Zr2rxwM4e3Ho45ZuC3A1z+58vk/0E+xY8X\nU9BYEHc59dSzjW2sZCXnOR+/sNEjr9F7uniBv4mY/9/A0fg/JhkJN2PczGZmEToOs9OMMbJJX3Z7\n9ngH0jQ06UtU0/wmNn2wCU9X6DKdvEAevuO+mGM8nR48ePB84Al9f9FD4LHUNW/76vKv0vhWI8Hr\noT1wfmc+nSc6Y44JXA3AEPS92cfgbwcp/9tyCh8sjPr6NazhKZ6imGIAcsmNu51P9Z3iOMdpym2i\nnHL2B/djHQhfZ/znCfwFk5BQiF/kRd7iLZppZiUrE2rG2NbX9vlGjGlo0peooqwiFn150eemBeIU\n6vsHH1anRfCuIIHmANyWygqhLK+M+569L6Ex5x44R8b8DPz3+5n/l/PJKsuK+fqTnOQsZ9nNbr7E\nl+w1Ywxv22O3H4P3I6al4dAx4Td27eGv5SzHjz/+gBkuWBsksCn14Z0K/2Y/hdsL44Y3Ui+9vMiL\n/JAfsoEN8QdcJnTIUAf8EaFj4xxgdXh+Cm8dl/SnE+20T2cdxrIa3X9rjpK/KEl6bC+99t/7HAOu\nAsuBFYQ+J/7f8PS2GOOmyMbNU9x8Gbcu2Z8Oplyyr5unyIylEIvxFGIxnkIsxlOIxXgKsRhPIRbj\nKcRiPIVYjKcQi/EUYjGeQizGU4jFeAqxGE8hFuMpxGK8mCfFi5hAe2IxnkIsxlOIxXgKsRhPIRbj\nKcRivP8Hb7uxQNbrt9EAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8932d69cd0>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALEAAACxCAYAAACLKVzFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMS4wLCBo\ndHRwOi8vbWF0cGxvdGxpYi5vcmcvpW3flQAADh1JREFUeJzt3X9wFPUZx/H33uVyCRdy/AgJwUBD\nKEQSIyEgPyzQavillOAkou2M2I5jtTNi6x/VOm2no0O1o06nta2izjB1xFEEi4ijtlKtNi0Y6zSN\nggiUaDANVCQIySXk4t32j70kV8Ld7V1ub/ebPq/MMbnd+7IPu59svnfc3qPpuo4QKnPZXYAQIyUh\nFsqTEAvlSYiF8iTEQnkSYqG8rHgrNQ15/U04hIau69qF1sQN8cBg5xr4GZMaR0aFGmOT6YRQnoRY\nKE9CLJQnIRbKkxAL5UmIhfIkxEJ5EmKhPAmxUJ6EWChPQiyUJyEWypMQC+WZeBdbGpQAtUAxxo/N\nKaAR+CAjW0+sFPj2BZZ/Cjya0UpiK0VqjMH6EOcANwCngd9Hli0HrgV+E1nuFO8A70Xd77erkDik\nxmFGFGIXLsKE4z+oACPI/wKORJZ1An6gZyRbN0dDQzf73v6zQLul5YycDTWaOs7RMlxjSnPiCiq4\nh3u4lVsTP/gUxk/i5UADUB253wr0pbJ1c2qp5Zf8kiu4wvwgDWOPDNyc+B7xDNbox89GNvIQDyU3\nMMP7MakzcQUVXMd1zGc+PnzsYhfjGR9/UC/0b+unZ1UP4aowVEWWHwBeAL5Iqe6YaqllDWuoooos\nsniLtxLW2E8/3XQb8/baqBWHgWfSW9+IZaBGP342sIElLKGIIvazP/Fxxr79mFSIZzKTYorx4QNg\nOtNpoCHxwKPAo9AyroW/l/0dFgGVwDGgKemaY9LQmMUsJjOZrMg/bSlLKaAg7rgOOniFV6hoqqC7\npZtjHDNWnEtfbenibnKzpmUNu9ltLLCgxqlM5SIuYhzjAMgl19RxHtiPs5pmcbjl8NAKq/ejrusx\nb2D8EX1z49bXs15/nMf1jWwctn7YrRidpeiMOW/ZPeisSDA24U3XL1SjD5/+Xb6rP8uz+gpWJP57\nSiP1LBlpPeZrTPoWqTFrSZa5/Z6GGhewQL+f+/VHeCSpGq3Zj+ixcpr0E7sQIXawg53sZCITEw/I\nw/jVUgrsA0JATWTdR8lu3ZwAAR7jMbayFZe8FJ6ydyJfU5hidylxpfzqRIgQn/Jp4gcewXhpbTGw\nHnBjPNnbifGKhYUCBKzdwP+JDjrsLiG+ZKcTzrql6Ve1QjXmkpux6YTTbrFyKr9rhfIkxEJ5EmKh\nPAmxUJ6EWChPQiyUJyEWytPitQAzPp/YiW/lGjBQ++ivUUPjQR7EixcfPs5xjgd4YOh9HiOiwn4k\n5ucTy5lYETo6rbRSRRVllNFNd5oCrD4JsUKe4imOc5wgQV7kRbvLcYzMXGMn0iJAgEYamc509rLX\n7nIcQ+bElktvjT58lFHG+7yflr/PoMJ+jD0nlhBbTmpMF3liJ0YtE3Pi2Gdq55Aa08PJNcb+LSFn\nYqE86WNnOaPGu+76oc11xPbggw9EvnPyfoxNzsRCeRJioTwJsVCehFgoT0IslCchFsqTEAvlSYiF\n8iTEQnkSYqE8CbFQnoRYKE9CLJSXmWvsSnF2D7ZSjPr+BPw1avkdGD1Ffpv5ks53zHWMbTnbhi0v\nCBdw07mbbKjoPKXYtg8ze6GoCj3YHG5u/1wqQ5WD97N0udY3s3tAhT5xDjdWH8uUsLPbD2RaynNi\nDx6KKU5uUIb7m/nxk0+++QHn1+dAOjrhqC/TjSZHYBrTzD/Yhn2Y9JnYg4cGGljOcppp5hEeMT84\nQ/3NovuwbWELe9iTWn0An6W7upFpzG6kMbtx8H5ZqIxr+661ZFuXcznrWEceedzGbeYG2bAPkwpx\nPfVczdXMYAYAPfSwkY0Jx7XTzi52UdJUQntL1Hwizf3NNDRu47bBJoIAddRRTrmp+qqaquhq6eJj\nPjZWfDO99aVDTX8N1d3V9OcaTyhy9Jy0b6OKKjawgTnMIZtsWmlNeJyj9+H0lulDffYysA+TCvEB\nDlBBBUUUkUcehznMFrYkHBciBEBHVwdWNuLR0XmP9yillAlMwIOHP/AH3uANU/Ud7DqI3qFHr3Cc\n/P58ljYu5eDyg5Zto5VWPuIjSiihmGICBBIe5+h9eKTjSPQKyyUV4kMc4mf8jHLKWc96QoTopdf0\n+KSaXKfoL5GvZSxjHevojXyZ8UW6e/QqKkCAzWzmKZ7iRm6kjLKk9mGm92NKr04MhFlz8NWxA2EW\nqRsIs5OPM8jHWGVAei/Zd/e5mdU4K63TCVUu2ZePsRKjloRYKE9CLJQnIRbKkxAL5UmIhfIkxEJ5\nEmKFuINu3P1uXCEX7qDb2Z+JnUHyjmpV6LDomUXknM0BHQqPFtJ0fRM9E3vsrsx2ciZWhQb/rvg3\n2eeyye7LpnNqpwQ4QkKskLZ5bZwpPEO/t5/WBa12l+MYMp1QiO7W6ajowH/cT1dRl93lOIaEWDFt\n89rw9HrsLsNRZDqhGN2tE8wL2l2Go0iIhfJMvJ9YCCfQ5P3EYvQaFc0Y77vvfpvriO3HP/4RANu3\n77C5ktiuu2595DsnH+vY5EwslCchFsqTEAvlSYiF8iTEQnkSYqE8CbFQnoRYKE9CLJQnIRbKkxAL\n5UmIhfIkxEJ50owRaA23siU0/OP8Cynk+57v21DRcAcCB7i37d5hy6d6p/KLGb+woaLzlCLNGJ1g\noWsh1Vr14P1sLdvGai5s5fiVLPMvG7zvdXltrMYZpBljFD9+prmS6NlmgwJPAbPGzLK7DEfJ7Jw4\nyWaM5ZQzn/nW1xWhoxPSQ4O3sG59o5xkhfVwRmscwxjWstb8ABWaMY5Iks0YK6nkFm7hH/yDnezk\nXd61tLw94T3sCQ81bizXyrkx60ZLt5msbSe3se3kUKPymrwa7p52d9q3M4Yx3MANLGMZnXTyEi+Z\nG+j0ZowjNalpEqtbVg/e957zMp7xMR8/k5l48bKYxdRQw7u8y0/4iWX1LXItYsmJJQSKAwDkarmW\nbStVq8et5squKwlNMxrE+dy+tG9jMYvZyEamYPSQ7qOPO7kz7phjHOM5nmNu01xmtMzgeZ43Vjit\nGeNInew6ydaOraYfX089M5nJCU7QSCNP87SF1UE++cx/ez5HG45aup2RmKBNoHJvJYHygGXb2Mc+\nPHioo45LuZQAAR7iIVNjm7uaae5oHlrgtGaMmfYZn7GDHTzN05zlrN3l/F+Jbmp5GZfZXU5cjg6x\nNFS0nwrHIDMh/hi4JyNbSkmZq4z7XPfZXUZclb5KtldsR+t16GX1H3PhY/wr6zct/+0slCchFsqT\nEAvlSYiF8iTEQnkSYqE8CbFQnqP/syOT/Ef8eLo9+E74KGguIDAlQG9Rr91lDdHB+zcv9ILnqAfv\nW16C1UF0v3wOuoQ4YsIHEyh+pxiAL7/wZQ5945CzQgzkvJ5D9gHjjfquUy6C1dK7A2Q6Maj9inb6\n8vsAODP9DKcrTttc0Xk06F3Zi+4yzrx9C/rkLBwhIY7oz++nc3YnYXeYEwtP2F3OBQUXBQlWBAlN\nDNFTL91EB8h0Ikr719rJOZXjvLPwAA3OrTiH56BHzsJRJMRR+vP7Ofitg3aXEVdwUZDgQpkLR5MQ\nn8/pEywNVfvDWMbph0yIhKQZo1CENGMUo9ioaMb4xz++ZnMdsa1atRKAzz8/Y3MlsY0b54985+Rj\nHZuciYXyJMRCeRJioTwJsVCehFgoT0IslCchFsqTEAvlSYiF8iTEQnkSYqE8CbFQnoRYKM/6KztK\nsa1Jn1ktZ1q464O7hi3/Uu6XeKL6CRsqGq7xk0bW/n54F6PZE2ezb8M+Gyq6ABewFLgU8ANBjJZv\nfwaOW7dZuTwpytqitdROGmr948RGhzdfejPXz75+8H5uloOa4zQAlRhNNw8BecAVwE3AY8ApazYr\nIY4yyTuJ2WNn211GXBeNvYjLih3YQ6MII8DvAa9ELT8OFABd1m06pTmxCxf11FNHnflBNjTpS1Yq\njQ5dz7twveyCDPVtDOthvgh/MXgzU2P73e2cfT21xj011HA7tyd+4EAj1uiLxV0YPew+xNIWyEmd\niV24uIZrWMEKLuZitrPd/GAbmvQl68lPnuTJT54cvL9g3AI2zd4Ud4zWoeF62YXrNRfhlWHCV4Ut\n/SHdtHcTm/YO1bRq+iqeW/dc3DE97/dw8ncnGfvVsRTeWkh+bX7C7dRQQz31zGMeRziSuLCBmdfA\nZ7q4gJ9Grf8nsCvxX5OKpEJ8O7ezilXkYszDLuGSpJr0eVu8vM3bxooMNOlLVt3kOlZ+uBLtmHGZ\nTl4oD/er7rhjtDYNDQ3tQ834/rhG6Gbrmrd9Z853qH2zlnC3cQYe2zaWtj1tcceEToegD7pe66L3\n/V5Kfl7C+GtiN8FczGLu4A4KKQTAhy/hcd7ftZ9XeZU6Xx0llLA5vBn9ich1xrck8Q9MQVIhfpiH\neZM3aaCBecxjP/vZzGZTY5u7mqEjakEGmvQlqyC7gJlXzfyfZaEEhbp/7UZv0wlfFibUEIKLrawQ\npuRNYfW9qxM/MMrhNYfJmpyF/2o/k38wmewp2XEfv499HOIQG9jAV/iKuWaMkWO7+5Ld8EHUsgxM\nHZN+YtcS+ZrDHPz4Ew8Y5cKVYUIrrQ/vSPhX+Rl/7fiE4Y3WSScP8zBb2cpylicecBJjylANfB1j\nbpwDLIyst/Cj41J+daKFlnTWoSy91vkfzVH0vaKUx3bSaf65z27gNDAHmIvxOvF/Isub44wbIRMf\nnuLky7jlkv10UOWSffnwFDFqSYiF8iTEQnkSYqE8CbFQnoRYKE9CLJQnIRbKkxAL5UmIhfIkxEJ5\nEmKhPAmxUJ6EWChPQiyUJyEWyov7pnghVCBnYqE8CbFQnoRYKE9CLJQnIRbKkxAL5f0XHfKIF9iS\nfzEAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8932cfab50>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALEAAACxCAYAAACLKVzFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8932c80b50>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALEAAACxCAYAAACLKVzFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8932b97550>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALEAAACxCAYAAACLKVzFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f8932c80850>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAEHCAYAAACzy817AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nyBer7cCMjecAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f893343f910>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "metadata": {
        "id": "I9JLqRp1MJrI",
        "colab_type": "code",
        "colab": {
          "autoexec": {
            "startup": false,
            "wait_interval": 0
          }
        }
      },
      "source": [
        ""
      ],
      "cell_type": "code",
      "execution_count": 0,
      "outputs": []
    }
  ]
}