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
def check(b):
    for i in range(2,int(math.sqrt(b))+1):
        if b%i==0:
            return 0
    return 1

def gcd(p,q):
    if q==0:
        return p
    return gcd(q,p%q)

n=int(input())

if n<=2:
    print (n)
else:
    a=n*(n-1)
    ans1=(a*(n-2))//gcd(a,n-2)

    b=n*(n-1)
    ans2=0

    for i in range(n-2,max(0,n-52),-1):
        if check(i):
            ans2=(b*(i))//gcd(b,i)
            break
    
    print (max(ans1,ans2))
