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 $n$ $(3\le n\le 1000)$, 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