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EXAMPLE
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The longest paths for n = 13. The ones marked with (*) are also the longest paths for n = 12.
[5, 10, 2, 8, 4, 12, 6, 3, 9, 1, 7], (*)
[5, 10, 2, 8, 4, 12, 6, 3, 9, 1, 11], (*)
[5, 10, 2, 8, 4, 12, 6, 3, 9, 1, 13],
[7, 1, 5, 10, 2, 8, 4, 12, 6, 3, 9], (*)
[7, 1, 9, 3, 6, 12, 4, 8, 2, 10, 5], (*)
[9, 3, 6, 12, 4, 8, 2, 10, 5, 1, 7], (*)
[9, 3, 6, 12, 4, 8, 2, 10, 5, 1, 11], (*)
[9, 3, 6, 12, 4, 8, 2, 10, 5, 1, 13],
[11, 1, 5, 10, 2, 8, 4, 12, 6, 3, 9], (*)
[11, 1, 9, 3, 6, 12, 4, 8, 2, 10, 5], (*)
[13, 1, 5, 10, 2, 8, 4, 12, 6, 3, 9],
[13, 1, 9, 3, 6, 12, 4, 8, 2, 10, 5].
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