You are given a string s of length n, where s[i] is either 'I' representing an increase or 'D' representing a decrease.

A permutation perm of the integers in the range $[0, n]$ is considered valid if for all $0 \leq i < n$:

• If s[i] == 'I', then perm[i] < perm[i + 1]

• If s[i] == 'D', then perm[i] > perm[i + 1]

Return the total number of valid permutations perm. Since the answer may be large, return it modulo $10^9 + 7$.

Constraints:

• n == s.length

• $1 \leq n \leq 200$

• s[i] is either 'I' or 'D'

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.