For a positive integer N, let An be the set of integers 1 through N. A permutation of the set Ay is the ordered sequence (a1,a2,...,an) such that each integer appears exactly once. For instance, (1,2,4,3) and (2,4,3,1) are two permutations of the set A4. A permutation (a1, a2, ...,an) can be represented as an array P of length N where P[i] = a;. Given an integer N and array P of integers of length N, design an algorithm which checks whether P represents any permutation of An.