Sjecista

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.

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

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 |