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.

Input Specification

The first and only line of input contains a single integer $N$ $(3\le N\le 100)$.

Output Specification

Output the number of intersections on a single line.

Sample Input 1

3

Sample Output 1

0

Sample Input 2

4

Sample Output 2

1

Sample Input 3

6

Sample Output 3

15