my %dirs = (
    # IN   [ preferred output directions ]
#    '1' => [qw( 3 4 5 6 7 8 2 )],
#    '2' => [qw( 3 4 5 6 7 8 1 )],
#    '3' => [qw( 4 5 6 7 8 1 2 )],
#    '4' => [qw( 5 6 7 8 1 2 3 )],
#    '5' => [qw( 6 7 8 1 2 3 4 )],
#    '6' => [qw( 7 8 1 2 3 4 5 )],
#    '7' => [qw( 1 2 3 4 5 6 )],
#    '8' => [qw( 3 4 5 6 7 )],
    'nw' => [qw( ne e  se s  sw w     n                  )],
    'n'  => [qw( ne e  se s  sw w  nw                    )],
    'ne' => [qw(    e  se s  sw w  nw n                  )],
    'e'  => [qw(       se s  sw w  nw n  ne              )],
    'se' => [qw(          s  sw w  nw n  ne e            )],
    's'  => [qw(             sw w  nw n  ne e  se        )],
    'sw' => [qw(                   nw n  ne e  se s      )],
    'w'  => [qw(                         ne e  se s  sw  )],
);

my %dels = (
    # IN   [ dx, dy, new_in_dir ]
#nw   '1' => [ -1, -1, '5' ],
#n    '2' => [  0, -1, '6' ],
#ne   '3' => [  1, -1, '7' ],
#e    '4' => [  1,  0, '8' ],
#se   '5' => [  1,  1, '1' ],
#s    '6' => [  0,  1, '2' ],
#sw   '7' => [ -1,  1, '3' ],
#w    '8' => [ -1,  0, '4' ],

    'nw' => [ -1, -1, 'se' ],
    'n'  => [  0, -1, 's'  ],
    'ne' => [  1, -1, 'sw' ],
    'e'  => [  1,  0, 'w'  ],
    'se' => [  1,  1, 'nw' ],
    's'  => [  0,  1, 'n'  ],
    'sw' => [ -1,  1, 'ne' ],
    'w'  => [ -1,  0, 'e'  ],
);