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 $N$ ($1 \le N \le 100000$), the number of days.

Each of the following $N$ lines contains two integers $L$ and $R$ ($1 \le L < R \le 100000$). 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.

-----Examples-----
Sample Input:
4
1 4
3 7
1 6
2 6
Sample Output:
0
1
1
2

Source: kattis | Difficulty: HARD


Solutions: