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.
from math import gcd
n = int(input())
p = n * (n - 1)
ans, g = n * (n - 1), gcd(n, n - 1)
for i in range(n, 0, -1):
    b = gcd(g, i)
    a = gcd(n, i) * gcd(n - 1, i) * g
    ans = max(ans, p * i * b // a)
print(ans)
