903 - Valid Permutations for DI Sequence.

Hard

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 answer may be large, return it modulo <code>10⁹ + 7</code>.

Example 1:

Input: s = "DID"

Output: 5

Explanation: The 5 valid permutations of (0, 1, 2, 3) are:

(1, 0, 3, 2)
(2, 0, 3, 1)
(2, 1, 3, 0)
(3, 0, 2, 1)
(3, 1, 2, 0)

Example 2:

Input: s = "D"

Output: 1

Constraints:

• n == s.length

• 1 <= n <= 200

• s[i] is either 'I' or 'D'.