Score : $2200$ points

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).

6
1 8
6 10
2 7
4 4
9 3
5 1

5
0
7
5
0
0

See the drawing below. If we replace rook 3 with a king, we can beat at most two other rooks. The red path is one of optimal sequences of moves: beat rook 1, then keep going down and right until you can beat rook 4. There are 7 steps and that's the third number in the output.

x-coordinate increases from left to right, while y increases bottom to top.

Starting from rook 2, 5 or 6, we can't beat any other rook. The optimal number of moves is 0.

5
5 5
100 100
70 20
81 70
800 1

985
985
1065
1034
0

10
2 5
4 4
13 12
12 13
14 17
17 19
22 22
16 18
19 27
25 26

2
2
9
9
3
3
24
5
0
25