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 of the stems $L$ and $R$, and the height $H$ at which the stems are connected. The 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 wasn't there already). If segments merely touch in a point, a flower will not grow there. The following images are a visualization of the first example on the next page.

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

Input Specification

The first line contains an integer $N$ $(1\le N\le 100000)$, the number of days. Each of the following $N$ lines contains two integers $L$ and $R$ $(1\le L<R\le 100000)$, the coordinates of the stems of a plant.

Output Specification

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

Sample Input 1

4
1 4
3 7
1 6
2 6

Sample Output 1

0
1
1
2

Sample Input 2

5
1 3
3 5
3 9
2 4
3 8

Sample Output 2

0
0
0
3
2