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?
The first line contains an integer *n* (1 ≤ *n* ≤ 10<sup class="upper-index">6</sup>) — the *n* mentioned in the statement.
import math

n = int(input())
if (n <= 2): 
    print(n)
    exit

elif (n % 2 == 1): 
    print(n * (n - 1) * (n - 2))
    exit

mx1 = n * (n - 1) * (n - 2) // 2
mx2 = (n - 1) * (n - 2) * (n - 3)

mx3 = n * (n - 1)
for i in range(n - 2, 0, -1):
    if (math.gcd(i, n) == 1 and (math.gcd(i, (n - 1))) == 1):
        mx3 *= i
        break
    
print(max([mx1, mx2, mx3]));
    
