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 factorial, gcd
import itertools

n = int(input())
if n <= 3:
	print(factorial(n))
	exit()
ans = 0
for a, b, c in itertools.product(range(max(n - 50, 1), n + 1), range(max(n - 50, 1), n + 1), range(max(n - 50, 1), n + 1)):
	x = a * b // gcd(a, b)
	x = x * c // gcd(x, c)
	ans = max(x, ans)
print(ans)
