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Let w be a string and divide it into two strings x and y such that w = xy. We say that a string z = yx is a cyclic shift of w. The analogy here is that the we shift the front of the word around until y is at the front. For example, if w = 12345678 and x = 123 and y = 45678, then z = 45678123. If x is a string of length n such that each letter in x occurs exactly once, how many permutations of x are distinct with respect to cyclic shifts? In other words, count only those permutations that are not the cyclic shift of another permutation. Let w be a string and divide it into two strings x and y such that w = xy. We say that a string z = yx is a cyclic shift of w. The analogy here is that the we shift the front of the word around until y is at the front. For example, if w = 12345678 and x = 123 and y = 45678, then z = 45678123. If x is a string of length n such that each letter in x occurs exactly once, how many permutations of x are distinct with respect to cyclic shifts? In other words, count only those permutations that are not the cyclic shift of another permutation