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.
def gcd(a, b):
    while a != 0 and b != 0:
        if (a > b): a %= b
        else: b %= a
    return a + b

n = int(input())

if n == 1:
    print(1)
elif n == 2:
    print(2)
elif n == 3:
    print(6)
else:
    mx = 0
    for a in range(n, max(n - 50, 1), -1):
        for b in range(a - 1,  max(n - 50, 1), -1):
            for c in range(b - 1, max(n - 50, 1), -1):
                h = a * b / gcd(a, b)
                res = h * c / gcd(h, c)
                mx = max(mx, res)
    print(int(mx))