You are given an integer array nums of size n containing distinct integers from $0$ to $n - 1$. The number $0$ represents an empty space.

In a single operation, you can choose any element and move it to the empty space, swapping that element with $0$.

The array nums is considered sorted if the numbers from $1$ to $n - 1$ are in ascending order, with $0$ placed either at index $0$ or at index $n - 1$.

Return the minimum number of operations needed to sort nums.

Constraints:

• n == nums.length

• $2 \leq$ n $\leq 10^5$

• $0 \leq$ nums[i] $<$ n

• All the values of nums are unique.

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.