## Points on a Line

In this particular problem, you will be given a set of points that lie on the Cartesian plane. Given two points, p1 and p2, determine how many points in the set lie on the line created by p1 and p2.

The input will contain one set of data. The first line will contain N, the number of points in the set, 10 ≤ N ≤ 100. The next N lines will contain two integers each, x and y, which represent the x-coordinate and the y-coordinate of the point. -1000 ≤ x, y ≤ 1000. After these N lines, there will be five lines that will contain the coordinates of the points p1 and p2; p1 and p2 are not part of the original set. -1000 ≤ p1 and p2 ≤ 1000.

The output will contain five lines of data. Each line will contain the number of points in the set that lie on the line created by p1 and p2.

```12
0 0
-1 3
1 3
1 7
2 9
3 -1
6 0
3 1
5 3
3 5
3 8
6 6
2 2 0 4
3 0 3 9
2 2 3 3
0 4 1 5
3 -3 4 -2```

```2
4
2
1
1```

### Sample Input Analysis

There are 2 points [(1,3) and (3,1)] from the set that lie on the line created by the two points (2,2 and (0,4).
There are 4 points [(3,8), (3,5), (3,1) and (3,-1)] from the set that lie on the line created by the two points (3,0) and (3,9).
There are 2 points [(6,6) and (0,0)] from the set that lie on the line created by the two points (2,2) and (3,3).
There is 1 point [(-1,3)] from the set that lie on the line created by the two points (0,4) and (1,5).
There is 1 point [(6,0)] from the set that lie on the line created by the two points (3,-3) and (4,-2).

Point Value: 7
Time Limit: 1.00s
Memory Limit: 16M