A secret permutation of integers from $1$ to $n + 1$ is encoded as a string s of length $n$, where for each index i:

• s[i] == 'I' indicates that the permutation satisfies perm[i] < perm[i + 1] (increasing).

• s[i] == 'D' indicates that the permutation satisfies perm[i] > perm[i + 1] (decreasing).

Given the encoded string s, reconstruct and return the lexicographically smallest valid permutation.

Constraints:

• $1 \leq$ s.length $\leq 10^5$

• 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.