Diagonals

Problem Description

For a convex polygon with $n$ vertices, no three of its diagonals intersect at a single point. Find the number of intersection points of the diagonals in the figure.

For example, a hexagon ($6$ vertices):

Input Format

The input is a single line containing one integer $n$: the number of sides (vertices).

Output Format

Output one line containing one integer: the answer.

Sample Input 1

3

Sample Output 1

0

Sample Input 2

6

Sample Output 2

15

Hint

Data Scale and Constraints

• For $50\%$ of the data, $3 \leq n \leq 100$ is guaranteed.
• For $100\%$ of the data, $3 \leq n \leq 10^5$ is guaranteed.