Consider a convex polygon with $N$ vertices, with the additional property that no three diagonals intersect in a single point. Find the number of intersections between pairs of diagonals in such a polygon.

The figure below shows one such polygon with 6 vertices.

Note that a polygon is convex if all of its interior angles are less than 180 degrees.

-----Input-----
The first and only line of input contains a single integer $N, 3\leq N\leq 100$ denoting the number of vertices.

-----Output-----
Output the number of intersections on a single line.

-----Examples-----
Sample Input 1:
3
Sample Output 1:
0

Sample Input 2:
4
Sample Output 2:
1

Source: kattis | Difficulty: EASY
Tags: Mathematics


Solutions: