Largest product in a grid

Author: Moritz Lenz

In the 20×20 grid below, four numbers along a diagonal line have been marked in bold.

    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 Pod::FormattingCode<94304245322624> 38 40 67 59 54 70 66 18 38 64 70
    67 26 20 68 02 62 12 20 95 Pod::FormattingCode<94304245322560> 94 39 63 08 40 91 66 49 94 21
    24 55 58 05 66 73 99 26 97 17 Pod::FormattingCode<94304245322496> 78 96 83 14 88 34 89 63 72
    21 36 23 09 75 00 76 44 20 45 35 Pod::FormattingCode<94304245322432> 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

The product of these numbers is 26 × 63 × 78 × 14 = 1788696.

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

Source code: prob011-moritz.pl

use v6;

my @m =
    [<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>];

sub prod ($x is copy, $y is copy, $dx, $dy) {
    my $prod =  @m[$y][$x];
    for 1..3 {
        $x += $dx;
        $y += $dy;
        $prod *= @m[$y][$x];
    }
    return $prod;
}

my $max = 0;

# diagonals
for 0 .. 16 -> $x {
    for 0 .. 16 -> $y {
        $max = $max max prod($x, $y,     1, 1)
                    max prod($x, $y + 3, 1, -1);
    }
}

# horizontal
for 0..16 -> $x {
    for 0..19 -> $y {
        $max = $max max prod($x, $y, 1, 0);
    }
}

# vertical
for 0..19 -> $x {
    for 0..10 -> $y {
        $max = $max max prod($x, $y, 0, 1);
    }
}

say $max;