Consider a convex polygon with 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.
The first and only line of input contains a single integer .
Output the number of intersections on a single line.
Sample Input 1
Sample Output 1
Sample Input 2
Sample Output 2
Sample Input 3
Sample Output 3