문제

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

입력

The first and only line of input contains a single integer $N$, $3 \leq N \leq 100$.

출력

Output the number of intersections on a single line.

예제 입력 1

3

예제 출력 1

0

예제 입력 2

4

예제 출력 2

1

예제 입력 3

6

예제 출력 3

15