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.

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).

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.

Sample Input 1

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

Sample Output 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.

Sample Input 2

5
5 5
100 100
70 20
81 70
800 1

Sample Output 2

985
985
1065
1034
0

Sample Input 3

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

Sample Output 3

2
2
9
9
3
3
24
5
0
25

见题面 Input 部分

见题面 Output 部分