import numpy as np,functools,operator

grid = [
    [ 8, 2,22,97,38,15, 0,40, 0,75, 4, 5, 7,78,52,12,50,77,91, 8],
    [49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48, 4,56,62, 0],
    [81,49,31,73,55,79,14,29,93,71,40,67,53,88,30, 3,49,13,36,65],
    [52,70,95,23, 4,60,11,42,69,24,68,56, 1,32,56,71,37, 2,36,91],
    [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, 3,45, 2,44,75,33,53,78,36,84,20,35,17,12,50],
    [32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70],
    [67,26,20,68, 2,62,12,20,95,63,94,39,63, 8,40,91,66,49,94,21],
    [24,55,58, 5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72],
    [21,36,23, 9,75, 0,76,44,20,45,35,14, 0,61,33,97,34,31,33,95],
    [78,17,53,28,22,75,31,67,15,94, 3,80, 4,62,16,14, 9,53,56,92],
    [16,39, 5,42,96,35,31,47,55,58,88,24, 0,17,54,24,36,29,85,57],
    [86,56, 0,48,35,71,89, 7, 5,44,44,37,44,60,21,58,51,54,17,58],
    [19,80,81,68, 5,94,47,69,28,73,92,13,86,52,17,77, 4,89,55,40],
    [ 4,52, 8,83,97,35,99,16, 7,97,57,32,16,26,26,79,33,27,98,66],
    [88,36,68,87,57,62,20,72, 3,46,33,67,46,55,12,32,63,93,53,69],
    [ 4,42,16,73,38,25,39,11,24,94,72,18, 8,46,29,32,40,62,76,36],
    [20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74, 4,36,16],
    [20,73,35,29,78,31,90, 1,74,31,49,71,48,86,81,16,23,57, 5,54],
    [ 1,70,54,71,83,51,54,69,16,92,33,48,61,43,52, 1,89,19,67,48],
]

# There are 4 directions to check; up=down, left=right, 2 diagonals
highest = 0

for i in range(0,17):
    '''
    take 4 wide full height slices, turn them into a cumulative product,
    snag just the last column, and take the highest number from it
    '''
    prod = np.cumprod(np.take(grid, range(i,i+4), axis = 1), axis = 1)
    rowmax = max(np.take(prod, 3, axis = 1))
    if rowmax > highest:
        highest = rowmax

grid = np.swapaxes(grid, 0, 1)
for i in range(0,17):
    '''
    same as above, but transposed, so the columns were the rows
    '''
    prod = np.cumprod(np.take(grid, range(i,i+4), axis = 1), axis = 1)
    rowmax = max(np.take(prod, 3, axis = 1))
    if rowmax > highest:
        highest = rowmax

for i in range(-16,17):
    diag = np.diagonal(grid, i)
    # diagonals are indexed from the longest/middle and vary in length
    # so I have an inner loop checking each group of 4 individually
    for j in range(0,len(diag)-3):
        prod = functools.reduce(operator.mul, diag[j:j+4])
        if prod > highest:
            highest = prod

# same as above, with new diagonals
grid = np.fliplr(grid)
for i in range(-16,17):
    diag = np.diagonal(grid, i)
    for j in range(0,len(diag)-3):
        prod = functools.reduce(operator.mul, diag[j:j+4])
        if prod > highest:
            highest = prod

print(highest)
