You are given an integer array nums of length $n$, which is a permutation of integers from $0$ to $n - 1$, and an integer array pre containing unique integers.

In one operation, you can choose any integer $k$ from pre and reverse the prefix of nums of length $k$ (i.e., reverse the subarray from index $0$ to index $k - 1$).

Return the minimum number of operations required to sort nums in ascending order. If it is impossible to sort nums, return $-1$.

Constraints:

• $1 \leq n ==$ nums.length $\leq 8$

• $0 \leq$ nums[i] $\leq n - 1$

• $1 \leq$ pre.length $\leq n$

• $1 \leq$ pre[i] $\leq n$

• nums is a permutation of integers from $0$ to $n - 1$.

• pre consists of unique integers.

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.