CF235A.LCM Challenge

普及/提高-

通过率：0%

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题目描述

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?

输入格式

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

输出格式

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

输入输出样例

输入#1
```
9
```
输出#1
```
504
```
输入#2
```
7
```
输出#2
```
210
```

说明/提示

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.

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