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Competitions

III Командный Студенческий Чемпионат Урала, Екатеринбург, Март 19 - 20, 1999

Stars

Astronomers often examine star maps where stars are represented by points on a plane and each star has Cartesian coordinates. Let the level of a star be an amount of the stars that are not higher and not to the right of the given star. Astronomers want to know the distribution of the levels of the stars.

prb5619

For example, look at the map shown on the figure above. Level of the star number 5 is equal to 3 (it's formed by three stars with a numbers 1, 2 and 4). And the levels of the stars numbered by 2 and 4 are 1. At this map there are only one star of the level 0, two stars of the level 1, one star of the level 2, and one star of the level 3.

You are to write a program that will count the amounts of the stars of each level on a given map.

Input

The first line contains a number of stars n (1n15000). The following n lines describe coordinates of stars (two integers x and y per line separated by a space, 0x, y32000). There can be only one star at one point of the plane. Stars are listed in ascending order of y coordinate. Stars with equal y coordinates are listed in ascending order of x coordinate.

Output

Print n lines, one number per line. The first line contains amount of stars of the level 0, the second does amount of stars of the level 1 and so on, the last line contains amount of stars of the level n1.

Time limit 1 second
Memory limit 122.17 MiB
Input example #1
5
1 1
5 1
7 1
3 3
5 5
Output example #1
1
2
1
1
0
Author Pavel Zaletsky
Source 1999 III Ural Collegiate Programming Contest, Ekaterinburg, March 19 - 20, Problem А