Given a 2D array rooks of length n, where rooks[i] = [xi, yi] indicates the position of a rook on an n x n chess board. Your task is to move the rooks 1 cell at a time vertically or horizontally (to an adjacent cell) such that the board becomes peaceful.

A board is peaceful if there is exactly one rook in each row and each column.

Return the minimum number of moves required to get a peaceful board.

Note that at no point can there be two rooks in the same cell.

 

Example 1:

Example 2:

 

Constraints:

• 1 <= n == rooks.length <= 500
• 0 <= xi, yi <= n - 1
• The input is generated such that there are no 2 rooks in the same cell.