Yellow Jackets - 2017 - Practice #3

#### Start

2017-09-13 23:10 CEST

## Yellow Jackets - 2017 - Practice #3

#### End

2017-09-14 00:10 CEST
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# Problem FSjecista

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.

Sample Input 1 Sample Output 1
3

0

Sample Input 2 Sample Output 2
4

1

Sample Input 3 Sample Output 3
6

15