# What is the greatest product of four adjacent numbers in any direction (up, down, left, right, or diagonally) in the 20X20 grid? 

import numpy
import timeit


start = timeit.default_timer()

n = '''08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
       49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
       81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
       52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
       22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
       24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
       32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
       67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
       24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
       21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
       78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
       16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
       86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
       19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
       04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
       88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
       04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
       20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
       20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
       01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48'''

def array_position(col, row, shift, grid):
    if shift + 4 < grid and col < grid:
        shift += 1
        col += 1
    elif shift + 4 >= grid and col < grid:
        col += 1
    elif shift + 4 >= grid and col >= grid:
        shift = 0
        col = 0
        if row + 4 <= grid:
            row += 1
    return col, row, shift 

def euler_11(x):
    grid = [map(int, row.split()) for row in x.splitlines()]
    grid = numpy.array(grid, numpy.int32)
    mul = lambda x, y: x * y
    high = list()
    row = col = shift = 0
    while row + 4 <= len(grid):
        chk = grid[row, shift:shift + 4:]
        high.append(reduce(mul, chk))
        if col < 20:
            chk = grid[0:4, col]
            high.append(reduce(mul, chk))
        if col < 17 and row + 4 <= len(grid):
            chk = [grid[i + row][i + col] for i in range(4)]
            high.append(reduce(mul, chk))
        if col > 3 and row + 4 <= len(grid):
            chk = [grid[i + row][col - i - 1] for i in range(4)]
            high.append(reduce(mul, chk))
        col, row, shift = array_position(col, row, shift, len(grid))
    return max(high)

print "Answer: %s" % euler_11(n)    
stop = timeit.default_timer()
print "Time: %f" % (stop - start)

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