Some solutions for n=1
..1....0....0....0....1....0....2....0....1....1....1....1....0....2....0....1
..1....1....2....3....1....3....2....1....2....2....0....0....2....0....4....0
..0....2....4....4....3....0....3....3....4....5....5....5....2....1....1....6
..6....6....6....5....6....2....6....4....4....6....0....2....1....6....6....1
..6....0....6....1....2....1....1....6....5....4....4....2....3....2....2....6
..0....4....3....1....0....5....2....2....5....0....1....5....1....4....0....3
..3....6....3....0....0....5....0....2....5....5....4....3....0....4....3....0
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