Problem Statement

You are given an integer $K$ greater than or equal to $2$.
Find the minimum positive integer $N$ such that $N!$ is a multiple of $K$.

Here, $N!$ denotes the factorial of $N$. Under the Constraints of this problem, we can prove that such an $N$ always exists.

Constraints

• $2\\leq K\\leq 10^{12}$
• $K$ is an integer.

Input

The input is given from Standard Input in the following format:

$K$

Output

Print the minimum positive integer $N$ such that $N!$ is a multiple of $K$.

Sample Input 1

30

Sample Output 1

5

• $1!=1$
• $2!=2\\times 1=2$
• $3!=3\\times 2\\times 1=6$
• $4!=4\\times 3\\times 2\\times 1=24$
• $5!=5\\times 4\\times 3\\times 2\\times 1=120$

Therefore, $5$ is the minimum positive integer $N$ such that $N!$ is a multiple of $30$. Thus, $5$ should be printed.

Sample Input 2

123456789011

Sample Output 2

123456789011

Sample Input 3

280

Sample Output 3

7