A permutation perm of n integers of all the integers in the range [1, n] can be represented as a string s of length n - 1 where:

• s[i] == 'I' if perm[i] < perm[i + 1], and
• s[i] == 'D' if perm[i] > perm[i + 1].

Given a string s, reconstruct the lexicographically smallest permutation perm and return it.

 

Example 1:

Input: s = "I"
Output: [1,2]
Explanation: [1,2] is the only legal permutation that can represented by s, where the number 1 and 2 construct an increasing relationship.

Example 2:

Input: s = "DI"
Output: [2,1,3]
Explanation: Both [2,1,3] and [3,1,2] can be represented as "DI", but since we want to find the smallest lexicographical permutation, you should return [2,1,3]

 

Constraints:

• 1 <= s.length <= 105
• s[i] is either 'I' or 'D'.