Polygon Diagonal Intersections

Interview

Time limit1sMemory limit128 MB

Summary

Given N, a convex N-gon with no three diagonals concurrent, compute the number of interior diagonal intersection points using the combinatorial formula C(N,4).

Level: Easy3 of 10
Topics: Combinatorics, Math
Solved: No attempts yet

Problem

You are given a convex N-gon. No three diagonals meet at the same point. Count the number of points inside the polygon where two diagonals intersect.

A polygon is convex if every interior angle is less than 180 degrees.

Input

The first line contains an integer N. (3 ≤ N ≤ 100)

Output

Print the number of diagonal intersection points.

Examples3

Example 1
Input
```
3
```
Expected output
```
0
```
Example 2
Input
```
4
```
Expected output
```
1
```
Example 3
Input
```
6
```
Expected output
```
15
```