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 and , and the height at which the stems are connected. The image depicts a plant with , and .

Every day a new plant grows on the planet. The plant that grows on day 1 is of height , 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 , the number of days. Each of the following lines contains two integers and , the coordinates of the stems of a plant.

#### Output Specification

Output 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
```

## Comments