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EXAMPLE
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a(2) = 1: [2].
a(4) = 2: [2,2], [4].
a(6) = 2: [2,2,2], [6].
a(7) = 6: [1,2,4], [1,4,2], [2,1,4], [2,4,1], [4,1,2], [4,2,1].
a(8) = 15: [2,2,2,2], [1,1,2,4], [1,1,4,2], [1,2,1,4], [1,2,4,1], [1,4,1,2], [1,4,2,1], [2,1,1,4], [2,1,4,1], [2,4,1,1], [4,1,1,2], [4,1,2,1], [4,2,1,1], [4,4], [8].
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