Problem 270 -- Lining Up

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Tips

I wrote a function that inputs 3 points (six coordinates) and check whether the points are on a straight line.

The main program call this function repeatively to check combinations of points, meanwhile I record the counts of points-on-a-straight-line.

Note that if we have checked point 1-2-3, it is not necessary to check point 1-3-2 or 2-3-1, etc. Eliminate as much unnecessary checking as possible.

If there is no three points on a straight line, the minimum output should be 2, not 0, because any two points can form a straight line.

Be careful this problem's input is in 'multiple input format'.

Test Cases

Input

2

1 1
2 2
3 3 
4 4
10 10
8 8
9 10
10 11

10 3
30 18
6 0
0 0
2 -3

Output

6
4