A. 2025
time limit per test
2 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

In Japan, the multiplication table below is learned in elementary schools.

Such a table with $$$9\times9$$$ items, called kuku in Japanese, is not necessarily a world standard. In some cultures, $$$12\times12$$$ or $$$20\times20$$$ tables are learned.

Interestingly, the total of all the $$$9\times9$$$ items in the kuku table is 2025, which happens to be this year. Are there any other interesting cases like this?

Your task is to compute, for a given integer $$$n$$$, the sum of all the items in an $$$n\times n$$$ multiplication table. More specifically, find $$$$$$ \sum_{a = 1}^n \sum_{b = 1}^n ab. $$$$$$

Input

The input consists of at most $$$100$$$ test cases. Each test case is a line containing one integer $$$n$$$ $$$(1 \le n \le 100).$$$

The end of the input is indicated by a line consisting only of a zero.

Output

For each test case, output the value of $$$$$$ \sum_{a = 1}^n \sum_{b = 1}^n ab $$$$$$ in a line.

Example
Input
9
1
2
100
0
Output
2025
1
9
25502500