You are given an integer array nums where each element is $1$, $2$, or $3$. You are also given a binary array locked of the same length, where locked[i] == 1 indicates that index i is locked and locked[i] == 0 indicates that index i is unlocked.

You can perform the following operation any number of times:

• Choose an unlocked index i such that $0 \leq i <$ nums.length $- 1$ and nums[i] $-$ nums[i + 1] $== 1$, and swap nums[i] with nums[i + 1].

You may unlock any number of locked indices by changing their corresponding value in locked from $1$ to $0$.

Return the minimum number of indices that must be unlocked so that nums can be sorted in nondecreasing order. If it is impossible to sort nums, return $-1$.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 3$

• locked.length $==$ nums.length

• $0 \leq$ locked[i] $\leq 1$

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.