You are given ~n~ points on the plane, such that no three points lie on the same line.

We say that line segments ~\overline{AB}~ and ~\overline{CD}~ cross if they share a point ~X~ different from the points ~A~, ~B~, ~C~ and ~D~.

Let ~\mathcal S~ be the set of all line segments between pairs of the given points. Find the number of segments in ~\mathcal S~ that don't cross with any other segment in ~\mathcal S~.

Input Specification

The first line contains an integer ~n~ ~(3 \le n \le 1\,000)~, the number of points.

The following ~n~ lines contain integers ~x_i~ and ~y_i~ ~(-10^9 \le x_i, y_i \le 10^9)~, the coordinates of the points.

Output Specification

Output the requested number of segments.

Constraints

Subtask	Points	Constraints
1	20	~3 \le n \le 40~
2	30	~3 \le n \le 200~
3	60	No additional constraints.

Sample Input 1

4
1 1
-1 1
-1 -1
1 -1

Sample Output 1

4

Sample Input 2

4
-1 -1
1 -1
0 1
0 0

Sample Output 2

6

Explanation for Sample Output 1 and 2