From atop a satellite, Nick has drawn $N$ lines on the surface of a plane, no three of which intersect at a common point. He counts many triangles, but how many of them contain no triangles with a strictly smaller area?

Constraints

$1\le N\le 500$

$|x_i|,|y_i|\le 2\cdot {10}^3$

All lines are pairwise distinct.

No three lines intersect at a common point.

Input Specification

The first line contains a single positive integer, $N$.

The next $N$ lines contain four space-separated integers, $x_1$, $y_1$, $x_2$, $y_2$, indicating a line going through distinct points $(x_1,y_1)$ and $(x_2,y_2)$.

Output Specification

Output the number of such triangles.

Sample Input

4
0 0 0 10
0 0 10 0
0 5 5 5
0 10 10 0

Sample Output

1