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Ohh dear!
(a*b)%p == ((a%p)*(b%p)) % p => 5! % 7 = (1 * 2 * 3 * 4 * 5) % 7 = ((((1 * 2)%7 * 3)%7 * 4)%7 * 5)%7 = (((2 * 3)%7 * 4)%7 * 5)%7 = (((6 * 4)%7 * 5)%7 = (24%7 * 5)%7 = (3 * 5)%7 = 15%7 = 1
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Sherlock and Permutations
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Ohh dear!