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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Project Euler problem 11\n",
      "Find the largest product of four adjacent numbers in the grid."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Constants"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ROWS = COLUMNS = 20\n",
      "SECTION_LEN = 4"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 97
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Data structure\n",
      "Convert the text of the numbers into a 2d array of integers.\n",
      "\n",
      "(Alterntive data structures include a 1d list of integers, or a dict with keys of (r, c) pairs.)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "GRID_STRING = \"\"\"08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08\n",
      "49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00\n",
      "81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65\n",
      "52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91\n",
      "22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80\n",
      "24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50\n",
      "32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70\n",
      "67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21\n",
      "24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72\n",
      "21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95\n",
      "78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92\n",
      "16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57\n",
      "86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58\n",
      "19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40\n",
      "04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66\n",
      "88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69\n",
      "04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36\n",
      "20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16\n",
      "20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54\n",
      "01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48\"\"\"\n",
      "\n",
      "GRID_LIST = [int(n) for n in GRID_STRING.split()]\n",
      "GRID = [GRID_LIST[i:i+COLUMNS] for i in range(0, ROWS * COLUMNS, COLUMNS)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 98
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for row in GRID:\n",
      "    print(row)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8]\n",
        "[49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0]\n",
        "[81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65]\n",
        "[52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91]\n",
        "[22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80]\n",
        "[24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50]\n",
        "[32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70]\n",
        "[67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21]\n",
        "[24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72]\n",
        "[21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95]\n",
        "[78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92]\n",
        "[16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57]\n",
        "[86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58]\n",
        "[19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40]\n",
        "[4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66]\n",
        "[88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69]\n",
        "[4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36]\n",
        "[20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16]\n",
        "[20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54]\n",
        "[1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48]\n"
       ]
      }
     ],
     "prompt_number": 99
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Directions\n",
      "What lines do we examine? Each number paricipates in up to 8 \u00d7 4 = 32 lines (fewer near the edges), but we can use the fact that multipication is commutative to only examine four lines that start at a number.\n",
      "\n",
      "`directions` stores those directions, and how to move in the direction."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Directions, as the pair (difference-in-row, difference-in-column)\n",
      "DIRECTIONS = {'N': (-1, 0), 'NW': (-1, -1), 'W': (0, -1), 'SW': (1, -1)}"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Finding the right numbers\n",
      "Given a starting position and a direction, find the right numbers.\n",
      "\n",
      "### Question:\n",
      "Should we worry if the request goes out of the bounds of the grid?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def numbers(row, column, direction):\n",
      "    nums = []\n",
      "    dr, dc = DIRECTIONS[direction]\n",
      "    for _ in range(SECTION_LEN):\n",
      "        nums.append(GRID[row][column])\n",
      "        row += dr\n",
      "        column += dc\n",
      "    return nums"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 71
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Test it."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "numbers(0, 3, 'W')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 72,
       "text": [
        "[97, 22, 2, 8]"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "numbers(3, 0, 'N')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 73,
       "text": [
        "[52, 81, 49, 8]"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "numbers(3, 3, 'NW')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 74,
       "text": [
        "[23, 31, 49, 8]"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "numbers(3, 3, 'SW')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 75,
       "text": [
        "[23, 16, 47, 32]"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Product of a list"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def product(ns):\n",
      "    p = 1\n",
      "    for n in ns:\n",
      "        p *= n\n",
      "    return p"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "product(numbers(0, 3, 'W'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "34144"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "97 * 22 * 2 * 8"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "34144"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## What directions don't take us out outside of the boundaries?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def valid_direction_explicit(row, column, direction):\n",
      "    if direction == 'N' and row >= SECTION_LEN -1:\n",
      "        return True\n",
      "    elif direction == 'W' and column >= SECTION_LEN -1:\n",
      "        return True\n",
      "    elif direction == 'NW' and row >= SECTION_LEN -1 and column >= SECTION_LEN -1:\n",
      "        return True\n",
      "    elif direction == 'SW' and row + SECTION_LEN <= ROWS and column >= SECTION_LEN -1:\n",
      "        return True\n",
      "    else:\n",
      "        return False"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction_explicit(0, 0, 'N')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction_explicit(5, 5, 'N')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction_explicit(5, 5, 'NW')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction_explicit(5, 5, 'W')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction_explicit(5, 5, 'SW')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction_explicit(17, 5, 'SW')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 61,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction_explicit(16, 5, 'SW')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 64,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 64
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction_explicit(2, 2, 'NW')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def valid_direction(row, column, direction):\n",
      "    dr, dc = DIRECTIONS[direction]\n",
      "    end_row = row + dr * (SECTION_LEN -1)\n",
      "    end_col = column + dc * (SECTION_LEN -1)\n",
      "    if end_row >= 0 and end_row < ROWS and end_col >= 0 and end_col < COLUMNS:\n",
      "        return True\n",
      "    else:\n",
      "        return False"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 79
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction(0, 0, 'N')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 80,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 80
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction(3, 3, 'N')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 81,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 81
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction(3, 3, 'NW')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 82,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 82
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction(3, 3, 'W')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 83,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction(3, 3, 'SW')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 84,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 84
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction(17, 17, 'N')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 85,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 85
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction(17, 17, 'NW')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 86,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 86
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction(17, 17, 'W')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 87,
       "text": [
        "True"
       ]
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "valid_direction(17, 17, 'SW')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 89,
       "text": [
        "False"
       ]
      }
     ],
     "prompt_number": 89
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Now to solve the problem"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "best_product = 0\n",
      "for row in range(ROWS):\n",
      "    for column in range(COLUMNS):\n",
      "        for direction in DIRECTIONS:\n",
      "            if valid_direction(row, column, direction):\n",
      "                this_product = product(numbers(row, column, direction))\n",
      "                if this_product > best_product:\n",
      "                    best_product = this_product\n",
      "best_product"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 94,
       "text": [
        "70600674"
       ]
      }
     ],
     "prompt_number": 94
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "max(product(numbers(r, c, d)) \n",
      "     for r in range(ROWS) \n",
      "     for c in range(COLUMNS) \n",
      "     for d in DIRECTIONS \n",
      "     if valid_direction(r, c, d))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 101,
       "text": [
        "70600674"
       ]
      }
     ],
     "prompt_number": 101
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# All the code in one place"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ROWS = COLUMNS = 20\n",
      "SECTION_LEN = 4\n",
      "\n",
      "GRID_STRING = \"\"\"08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08\n",
      "49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00\n",
      "81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65\n",
      "52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91\n",
      "22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80\n",
      "24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50\n",
      "32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70\n",
      "67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21\n",
      "24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72\n",
      "21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95\n",
      "78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92\n",
      "16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57\n",
      "86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58\n",
      "19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40\n",
      "04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66\n",
      "88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69\n",
      "04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36\n",
      "20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16\n",
      "20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54\n",
      "01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48\"\"\"\n",
      "\n",
      "GRID_LIST = [int(n) for n in GRID_STRING.split()]\n",
      "GRID = [GRID_LIST[i:i+COLUMNS] for i in range(0, ROWS * COLUMNS, COLUMNS)]\n",
      "\n",
      "# Directions, as the pair (difference-in-row, difference-in-column)\n",
      "DIRECTIONS = {'N': (-1, 0), 'NW': (-1, -1), 'W': (0, -1), 'SW': (1, -1)}\n",
      "\n",
      "def numbers(row, column, direction):\n",
      "    nums = []\n",
      "    dr, dc = DIRECTIONS[direction]\n",
      "    for _ in range(SECTION_LEN):\n",
      "        nums.append(GRID[row][column])\n",
      "        row += dr\n",
      "        column += dc\n",
      "    return nums\n",
      "\n",
      "def product(ns):\n",
      "    p = 1\n",
      "    for n in ns:\n",
      "        p *= n\n",
      "    return p\n",
      "\n",
      "def valid_direction(row, column, direction):\n",
      "    dr, dc = DIRECTIONS[direction]\n",
      "    end_row = row + dr * (SECTION_LEN -1)\n",
      "    end_col = column + dc * (SECTION_LEN -1)\n",
      "    if end_row >= 0 and end_row < ROWS and end_col >= 0 and end_col < COLUMNS:\n",
      "        return True\n",
      "    else:\n",
      "        return False\n",
      "\n",
      "max(product(numbers(r, c, d)) \n",
      "     for r in range(ROWS) \n",
      "     for c in range(COLUMNS) \n",
      "     for d in DIRECTIONS \n",
      "     if valid_direction(r, c, d))    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 102,
       "text": [
        "70600674"
       ]
      }
     ],
     "prompt_number": 102
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}