Some days ago, I learned the concept of LCM (least common multiple). I've played with it for several times and I want to make a big number with it. But I also don't want to use many numbers, so I'll choose three positive integers (they don't have to be distinct) which are not greater than n . Can you help me to find the maximum possible least common multiple of these three integers?

输入描述:

The first line contains an integer n (1 ≤ n ≤ 106) — the n mentioned in the statement.

输出描述:

Print a single integer — the maximum possible LCM of three not necessarily distinct positive integers that are not greater than n.

备注:

The least common multiple of some positive integers is the least positive integer which is multiple for each of them.The result may become very large, 32-bit integer won't be enough. So using 64-bit integers is recommended.For the last example, we can chose numbers 7, 6, 5 and the LCM of them is 7·6·5 = 210. It is the maximum value we can get.