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?

Input

The first line contains an integer $*n*$ ($1 ≤ *n* ≤ 10^{6}$) — the $*n*$ mentioned in the statement.

Output

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

Note

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.