The Least Common Multiple

Find the Least Common Multiple for all integers from 1 to n.

The Least Common Multiple of positive integers a[1], a[2], ..., a[k] is an integer A, such that A is divisible by a[i] for all i from 1 to k, and A is the least positive integer with such property.

Input

One integer n (1 ≤ n ≤ 1000).

Output

Print one number - the Least Common Multiple of all numbers from 1 to n.

Examples