Triangle Counting

You are given $n$ rods of length $1,2,...,n$. You have to pick any three of them and build a triangle. How many distinct triangles can you make? Note that, two triangles will be considered different if they have at least one pair of arms with different length.

Input

Each line has one positive integer $n(3\le n\le 10^6)$. The end of input will be indicated by a case with $n<3$. This case should not be processed.

Output

For each test case, print the number of distinct triangles you can make.

Examples