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EXAMPLE
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a(1) = 1 via [1]
a(2) = 1 via [1,2]
a(3) = 2 via [1,2,3]
a(4) = 4 via [1,3,2,4]
a(5) = 5 via [1,2,4,3,5]
a(6) = 9 via [1,4,2,5,3,6]
a(7) = 6 via [1,2,3,4,6,5,7]
a(8) = 16 via [1,5,2,6,3,7,4,8]
a(9) = 9 via [1,2,3,4,6,5,8,7,9]
a(10) = 25 via [1,6,2,7,3,8,4,9,5,10]
For n=4, the first player would take 4, the second player would take 2, the first player would take 3, and the second player would take 1. The resulting score difference would be 4 - 2 + 3 - 1 = 4.
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