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EXAMPLE
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The orbits are:
{1},
{8, 15},
{7, 8, 15},
{4, 7, 8, 15},
{3, 4, 7, 8, 15},
{2, 3, 4, 7, 8, 15},
{19, 11, 3, 4, 7, 8, 15},
{12, 19, 11, 3, 4, 7, 8, 15},
{6, 12, 19, 11, 3, 4, 7, 8, 15},
{5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{10, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{16, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{34, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{66, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{162, 66, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{924, 168, 102, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
{71820, 1104, 168, 102, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15}
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