Greatest Least Common Multiple

Time Limit: 1 Second    Memory Limit: 32768 KB

Calculate the greatest least common multiple of positive integers whose sum is given.

Input

Input has many test cases, each has a positive integer m on its own line. Proceed until EOF.

Output

The greatest least common multiple for the corresponding m. One number per line. You may assume that the result is always less than 10^25.

Sample Input

4
7

Sample Output

4
12

Submit

Source: ZOJ Monthly, January 2004