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 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 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