Dominoes

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Time limit1sMemory limit128 MB

Summary

Given N, compute the total dot count across all unique dominoes with halves ranging from 0 to N.

Level: Easy2 of 10
Topics: Math, Combinatorics
Solved: No attempts yet

Problem

A domino is a tile used in many tile games. Each domino has two halves, and each half may have zero or more dots.

In a domino set of size N, each half can contain from 0 to N dots. Two dominoes are considered the same if the two dot counts match, regardless of order. For example, a domino with 2 dots on one half and 8 dots on the other is the same as a domino with 8 dots and 2 dots.

A domino set of size N contains every possible domino exactly once. The following image shows a domino set of size 2.

Given N, compute the total number of dots printed on all dominoes in the set of size N.

Input

The first line contains the size N of the domino set.

1 <= N <= 1000

Output

Print the total number of dots printed on all dominoes in the domino 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
```