Problem Statement

You are given positions $(X_i, Y_i)$ of $N$ enemy rooks on an infinite chessboard. No two rooks attack each other (at most one rook per row or column).

You're going to replace one rook with a king and then move the king repeatedly to beat as many rooks as possible.

You can't enter a cell that is being attacked by a rook. Additionally, you can't move diagonally to an empty cell (but you can beat a rook diagonally).

(So this king moves like a superpawn that beats diagonally in 4 directions and moves horizontally/vertically in 4 directions.)

For each rook, consider replacing it with a king, and find the minimum possible number of moves needed to beat the maximum possible number of rooks.

Constraints

• $2 \leq N \leq 200\,000$
• $1 \leq X_i, Y_i \leq 10^6$
• $X_i \neq X_j$
• $Y_i \neq Y_j$
• All values in input are integers.

Input

Input is given from Standard Input in the following format.

N
X_1 Y_1
X_2 Y_2
\vdots
X_N Y_N

Output

Print $N$ lines. The $i$-th line is for scenario of replacing the rook at $(X_i, Y_i)$ with your king. This line should contain one integer: the minimum number of moves to beat $M_i$ rooks where $M_i$ denotes the maximum possible number of beaten rooks in this scenario (in infinite time).