A permutation perm of $n + 1$ integers in the range $[0, n]$ can be represented as a string s of length $n$ such that for all $0 \leq i < n$:

• perm[i] < perm[i + 1] if s[i] == 'I'

• perm[i] > perm[i + 1] if s[i] == 'D'

Given a string s, reconstruct and return any valid permutation perm. If there are multiple valid permutations, return any of them.

Constraints:

• $1 \leq$ s.length $\leq 10^5$

• s[i] is either 'I' or 'D'.

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