You are given a $2$D integer array rooks of length $n$, where rooks[i] = [x_i, y_i] represents the position of the $i^{ ext{th}}$ rook on an $n imes n$ chessboard.

A chessboard is considered peaceful if each row contains exactly $1$ rook and each column contains exactly $1$ rook.

In a single move, you can move any rook to an adjacent cell horizontally or vertically.

Return the minimum number of moves required to make the chessboard peaceful.

Constraints:

• $1 \leq n ==$ rooks.length $\leq 500$

• rooks[i].length $== 2$

• $0 \leq x_i, y_i \leq n - 1$

• The input is generated such that there are no $2$ rooks in the same cell.

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.