Stars in a Regular Polygon

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Time limit1sMemory limit1024 MB

Summary

Given the vertex count N of a regular polygon, count the distinct stars that can be drawn by connecting its vertices.

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

Problem

The clock is about to strike six, and the first star is already visible. How many stars can appear in a sky shaped like a regular $N$ -gon?

Given the number of vertices $N$ of a regular $N$ -gon, print how many distinct stars can be formed by connecting its vertices.

Label the five vertices of a star clockwise. The star connects those vertices in the order 1-3-5-2-4-1. A star that looks the same after flipping or rotating still counts as a different star if it is drawn through different vertices of the regular $N$ -gon.

Input

A single integer $N$ is given, the number of vertices of a regular $N$ -gon. $(5 \leq N \leq 100)$

Output

Print the number of distinct stars that can be formed by connecting the vertices of the regular $N$ -gon.

Hint

A regular $6$ -gon has $6$ distinct stars that can be formed by connecting its vertices.

Examples2

Example 1
Input
```
6
```
Expected output
```
6
```
Example 2
Input
```
100
```
Expected output
```
75287520
```