Nabiya Nabiya

Time limit2sMemory limit1024 MB

Summary

Given N points with no three collinear, count the 4-point cycles whose two opposite sides cross, with each segment set counted once.

Level: Medium6 of 10
Topics: Combinatorics, Geometry, Sorting
Solved: No attempts yet

Problem

Yonghan is afraid of insects. Seongwoo saw this and wants to help Yonghan stop being afraid of bugs. After some thought, Seongwoo decided to use the butterfly, a pretty insect, to help him.

First, Seongwoo marks $N$ points on a two-dimensional sheet of paper. Then he picks 4 distinct points from them in order. Call these points $A, B, C, D$ . Seongwoo draws $\overline{\rm AB}, \overline{\rm BC}, \overline{\rm CD}, \overline{\rm DA}$ . If two of these segments cross at a point that is not an endpoint of both, Seongwoo calls the figure a butterfly.

Seongwoo also defines when two butterflies $a$ and $b$ are the same:

The set of segments belonging to butterfly $a$ is identical to the set of segments belonging to butterfly $b$ .

Seongwoo wonders how many distinct butterflies he can draw. Find that number for him.

No three of the points lie on a single line.

Input

The first line contains the number of points $N$ . $(4 \leq N \leq 2\ 000)$

The next $N$ lines each contain the coordinates of one point. For each integer $i$ with $1 \leq i \leq N$ , the two integers $x_i, y_i$ on line $i+1$ are the coordinates of the $i$ -th point, separated by a space. $(-1\ 000\ 000 \leq x_i, y_i \leq 1\ 000\ 000)$

Output

Print the number of distinct butterflies Seongwoo can draw.

Examples2

Example 1
Input
```
4
0 0
0 1
1 0
1 1
```
Expected output
```
2
```
Example 2
Input
```
5
0 0
1 0
0 2
2 1
1 1
```
Expected output
```
6
```