Rooks

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

inputFormat

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

outputFormat

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

样例

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

5
0
7
5
0
0

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