Some solutions for n=3 (movement: 0=n 1=e 2=s 3=w)
..2..1..3....2..3..3....1..2..3....2..3..2....1..3..2....1..1..2....1..2..3
..2..3..0....1..1..3....2..1..0....2..1..0....2..3..2....2..2..3....2..3..0
..1..0..3....1..3..3....1..1..3....0..1..3....0..1..3....0..0..3....0..0..0
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