Some solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
..0..7..7....0..0..0....6..4..7....0..7..0....0..7..0....0..0..0....0..6..4
..3..3..0....6..4..0....0..3..0....3..6..4....3..7..0....6..4..0....6..4..7
..6..4..0....0..6..4....0..6..4....6..4..0....3..0..0....0..0..0....0..3..0
..0..0..0....6..4..7....6..4..0....0..7..0....0..7..0....0..0..0....0..0..7
..0..7..0....0..3..0....0..6..4....3..7..0....3..7..7....0..0..7....0..3..0
..3..0..0....0..6..4....0..6..4....3..6..4....3..3..0....0..3..0....6..4..0
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