LCM Challenge

题意翻译

找到3个不超过n的正整数（可以相同），使得它们的lcm（最小公倍数）最大。输出最大的lcm

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?

输入输出格式

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

输入样例 #1

9

输出样例 #1

504

输入样例 #2

7

输出样例 #2

210

说明

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.