You are given an integer array nums of length n, representing a permutation of integers from $0$ to n $- 1$.

In one operation, you can perform either of the following actions:

• Shift the array cyclically to the left by $1$ position (the element at index $0$ moves to index n $- 1$).

• Reverse the entire array.

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

Constraints:

• $1 \leq$ n $==$ nums.length $\leq 10^5$

• $0 \leq$ nums[i] $\leq$ n $- 1$

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

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.