903. Valid Permutations for DI Sequence

You are given a string s of length n where s[i] is either: - 'D' means decreasing, or - 'I' means increasing. A permutation perm of n + 1 integers of all the integers in the range [0, n] is called a valid permutation if for all valid i: - If s[i] == 'D', then perm[i] > perm[i + 1], and - If s[i] == 'I', then perm[i] < perm[i + 1]. Return the number of valid permutations perm. Since the answe