You are given a $0$ indexed string pattern of length $n$ consisting of the characters 'I' meaning increasing and 'D' meaning decreasing.

Create a string num of length $n + 1$ that satisfies the following conditions:

• num consists of the digits $'1'$ through $'9'$, where each digit is used at most once.

• If pattern[i] is equal to 'I', then num[i] < num[i + 1].

• If pattern[i] is equal to 'D', then num[i] > num[i + 1].

Return the lexicographically smallest possible string num that meets these conditions.

Constraints:

• $1 \leq$ pattern.length $\leq 8$

• pattern consists of only the letters 'I' and '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.