DWITE Online Computer Programming Contest, February 2006, Problem 1

In this particular problem, you will be given a set of points that lie on the Cartesian plane. Given two points, ~p_1~ and ~p_2~, determine how many points in the set lie on the line created by ~p_1~ and ~p_2~.

The input will contain one set of data. The first line will contain ~N~, the number of points in the set, ~10 \le N \le 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. ~-1\,000 \le x, y \le 1\,000~. After these ~N~ lines, there will be five lines that will contain the coordinates of the points ~p_1~ and ~p_2~; ~p_1~ and ~p_2~ are not part of the original set. ~-1\,000 \le p_1~ and ~p_2 \le 1\,000~.

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 ~p_1~ and ~p_2~.

Sample Input

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

Sample Output

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