National University of Singapore


Avoidland is a puzzle played on an $n \times n$ board with $n$ pawns. The pawns are initially placed on the squares of the board, at most one pawn per square. The goal is to move the pawns so that they “avoid” each other—there cannot be a row or a column with more than one pawn. In one move a pawn can move to a neighboring unoccupied square, that is, a square that shares a side with the pawn’s current location and there is no pawn on it. Given the initial locations of the pawns, what is the minimum number of moves needed to solve the puzzle?


The first line contains an integer $n$, then $n$ lines follow. The $i$-th line contains the initial row and column coordinates of the $i$-th pawn, separated by space. Each coordinate is an integer between $1$ and $n$. You may assume that $n$ is at most $1\, 000\, 000$.


The line contains the minimum number of moves needed to solve the puzzle.

Sample Input 1 Sample Output 1
1 3
2 3
3 1
Sample Input 2 Sample Output 2
1 4
4 1
1 1
4 4