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Problems

Triangle Counting

Triangle Counting

Time limit 1 second
Memory limit 128 MiB

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 data

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 data

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

Examples

Input example #1
5
8
0
Output example #1
3
22