### DWITE Online Computer Programming Contest

February 2006

### Problem 1

## 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, 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 ≤**. The next N lines will contain two integers each,

`N`≤ 100**and**

`x`**, which represent the x-coordinate and the y-coordinate of the point.**

`y`**-1000 ≤**. After these N lines, there will be five lines that will contain the coordinates of the points p

`x, y`≤ 1000_{1}and p

_{2}; p

_{1}and p

_{2}are not part of the original set. -1000 ≤ p

_{1}and p

_{2}≤ 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 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 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).

All Submissions

Best Solutions

**Point Value:** 7

**Time Limit:** 1.00s

**Memory Limit:** 16M

**Added:** Nov 13, 2008

**Languages Allowed:**

C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

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