Description

For an $n$-vertex convex polygon in which no three diagonals intersect at a single point, find the number of intersection points among its diagonals.

For example, a $6$-gon:

Input Format

The input contains a single line with an integer $n$, the number of sides.

Output Format

Output a single integer on one line: the answer.

3

0

6

15

Hint

Constraints

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

Translated by ChatGPT 5