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 random import randrange
import time
import threading
from math import sqrt, ceil, inf, comb, log2, gcd
from itertools import *
import functools
from collections import *
from copy import *
import heapq
from math import *
import sys
# from pprint import pprint as pprint
# from sympy.ntheory.modular import crt
from fractions import Fraction


def solve():
    n = int(input())
    if n <= 2:
        print(n)
        return

    a = n - 2
    b = n - 1
    c = n
    print(Fraction((a * b * c) / gcd(a * b, c)))


if __name__ == "__main__":
    solve()
