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#3341. [Ceoi2013]adriatic

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Description

琪琪在大海上搜索涛涛,琪琪把大海分为2500*2500的网格,现在琪琪拥有N条小帆船,她可以在船之间移动,由于风向的原因,她只能从一条船移动到位于这条船严格左上方或严格右下方的船。对于

每条帆船,琪琪想要知道从这条船跳到其他各条船的最小跳转次数和。

Input

The first line of input contains an integer   N (3 ≤ N ≤ 250 000), the number of islands. The following   N lines

contain the locations of the islands. Each location is a pair of integers between 1 and 2500 (inclusive), the row and column numbers, respectively.


第一行包含一个数N,表示帆船的个数。
接下来的N行,每行包含一对数(x,y),表示帆船的位置

Output

The output should contain   N lines. For each island, in the same order they were given in the input, output

the sum of sailing distances from all other islands on a single line.


输出需要包含N行,表示琪琪想要知道的答案。

Sample Input

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

Sample Output

16
11
12
11
12
16
8

Hint

Source