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 connect. 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.

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 ≤ N ≤ 100 000), the number of days.

Each of the following N lines contains two integers L and R (1 ≤ L < R ≤ 100 000), the coordinates of the stems of a plant.

Output

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

Example

Input
4
1 4
3 7
1 6
2 6
Output
0
1
1
2
Input
5
1 3
3 5
3 9
2 4
3 8
Output
0
0
0
3
2