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).

Examples

Input

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

Output

5
0
7
5
0
0

Input

5
5 5
100 100
70 20
81 70
800 1

Output

985
985
1065
1034
0

Input

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

Output

2
2
9
9
3
3
24
5
0
25

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