Problem D
Cvjitici

On a faraway planet, strange plants with two stems can be found. Every plant on the planet can be described by three numbers: the $x$-coordinates $L$ and $R$ of the two stems, and the height $H$ at which the stems are connected. The following image depicts a plant with $L=2$, $R=5$ and $H=4$.

Every day a new plant grows on the planet. The plant that grows on day $1$ is of height $1$, and every subsequent plant is one higher than the previous one.

When a stem of a new plant intersects the horizontal segment of another plant, a small flower grows (if one was not there already). If segments merely touch in a point, a flower will not grow there.

The following images are a visualization of the first sample input.

     

Write a program that, given the coordinates of all plants, calculates the number of new flower every day.

Input

The first line contains an integer $N$ ($1 \le N \le 100\, 000$), the number of days.

Each of the following $N$ lines contains two integers $L$ and $R$ ($1 \le L < R \le 100\, 000$). The $i$’th of these lines describes the coordinates of the plant that grows on day $i$.

Output

Output $N$ lines, the number of new flowers after each plant grows.

4
1 4
3 7
1 6
2 6

0
1
1
2

5
1 3
3 5
3 9
2 4
3 8

0
0
0
3
2