Description

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.

Format

Input

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

Output

Output the number of intersections on a single line.

Samples

3

0

4

1

6

15