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 max(a, b)

def lcm(a, b):
    return a * b // gcd(a, b)

def main():
    n = int(input())
    if n > 3:
        res_ = 0
        for i in range(n, 3, -1):
            curr = lcm(lcm(i, i-1), i-2)
            if curr > res_:
                res_ = curr
        res = n * (n-1)
        for i in range(n, 1, -1):
            if gcd(n, i) == 1 and gcd(n-1, i) == 1:
                res *= i
                break
        if res == n * (n-1):
            res *= 2
        print(max(res, res_))
    else:
        if n == 1:
            print(1)
        elif n == 2:
            print(2)
        else:
            print(6)

if __name__ == "__main__":
    main()