Description

Original problem from: Ural 1028

There are some stars in the sky, each located at different positions with specific coordinates. A star is said to be of level $k$ if there are $k$ stars strictly to its lower left (including directly left and directly below).

For example, in the figure above, star $5$ is level $3$ (since stars $1, 2, 4$ are to its lower left), and stars $2, 4$ are level $1$. The example has $1$ level $0$ star, $2$ level $1$ stars, $1$ level $2$ star, and $1$ level $3$ star.

Given the positions of the stars, output the count of stars at each level.

In one sentence $\$ Given $n$ points, define the level of each point as the number of points strictly to its lower left (including directly left and below). Count how many points exist at each level.

Input Format

The first line contains an integer $N$, the number of stars;
The next $N$ lines provide the coordinates of each star, given as two integers $x, y$;
No two stars overlap. The stars are given in increasing order of $y$-coordinate. If two stars share the same $y$-coordinate, they are given in increasing order of $x$-coordinate.

Output Format

$N$ lines, each containing an integer, representing the count of stars at level $0$, level $1$, level $2$, ..., level $N-1$.

Sample 1

5
1 1
5 1
7 1
3 3
5 5

1
2
1
1
0

Data Range and Hints

For all data, $1\le N\le 1.5\times 10^4$, $0\le x,y\le 3.2\times 10^4$.