Problem Description

Calculate the sum of $\sum{x} + \sum{y}$ for all non-negative integer pairs $(x, y)$ that satisfy $0 \le x \le y \le N$.

Input Format

A single line containing an integer $N$, as described in the problem statement.

Output Format

A single line containing an integer, representing the value of $\sum{x} + \sum{y}$.

Sample Input and Output

Sample Input #1

2

Sample Output #1

12

Sample Input #2

3

Sample Output #2

30

Sample Input #3

15

Sample Output #3

2040

Notes

Sample 2 Explanation

All pairs that meet the criteria are: $(0,0)$, $(0,1)$, $(0,2)$, $(0,3)$, $(1,1)$, $(1,2)$, $(1,3)$, $(2,2)$, $(2,3)$, $(3,3)$.

Data Range

For $100\%$ of the data, $1 \le n \le 10^3$.

Notes

This problem's score is set according to the original COCI contest, with a maximum score of $50$.

The problem is translated from COCI2009-2010 CONTEST #1 T2 DOMINO.

见题面 Input 部分

见题面 Output 部分