Counting Domino Spots

Time limit2sMemory limit512 MB

Summary

Compute the total number of spots over all distinct unordered pairs of mark values from 0 to N.

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

Problem

Dominoes are pieces used in many tile games. Each domino piece has two marks, and each mark carries $0$ or more spots. The size of the set decides how many spots a mark can carry: in a set of size $N$ , every mark carries between $0$ and $N$ spots, inclusive.

Two pieces are the same piece if their two marks carry the same numbers of spots, whatever the reading order. A piece with marks of $2$ and $8$ spots is the same as a piece with marks of $8$ and $2$ spots. A proper domino set never holds the same piece twice. The complete set of size $N$ holds one copy of every possible piece whose marks carry at most $N$ spots. For example, the complete set of size $2$ consists of $6$ pieces.

the complete domino set of size 2

Write a program that computes the total number of spots on all pieces of the complete set of size $N$ .

Input

The first and only line contains the size $N$ of the complete set. ( $1 \le N \le 1000$ )

Output

Print the total number of spots in the complete set of size $N$ .

Examples3

Example 1
Input
```
2
```
Expected output
```
12
```
Example 2
Input
```
3
```
Expected output
```
30
```
Example 3
Input
```
15
```
Expected output
```
2040
```