You are given a binary string boxes of length n, where boxes[i] is '0' if the box at index i is empty, and '1' if it contains a ball.

In one operation, you can move $1$ ball from a box at index j to an adjacent box at index j + 1 or j - 1.

Return an array answer of length n, where answer[i] is the minimum number of operations required to move all the balls to the box at index i.

Constraints:

• n $==$ boxes.length

• $1 \leq$ n $\leq 2000$

• boxes[i] is either '0' or '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.