Behold, the light of Gensokyo is right before your eyes! Touhou Eiyashou ~ Imperishable Night.

The secret technique capable of hiding the true moon requires a tremendous amount of energy. Please peer into the secrets of the eternal night from these astronomical numbers.

There are two unknown integers $n, m$ hidden by Eirin. You only know that they satisfy $1 \le m < n \le 10^6$. You are now given the value of $n!/m$. Please find the values of $n$ and $m$. It can be proven that if a solution exists, there will be only one pair of $n, m$.

Input

A single line containing a large integer representing the value of $n!/m$.

Output

Output two integers $n$ and $m$, separated by a space, representing the solution you found.

Examples

Input 1

725760

Output 1

10 5

Input 2

222205274866533696861188663943492144025514210153289574925221342607660952364833132402241580895610757824413566478160056567264726692659200000000000000000000000

Output 2

100 42

Note

To prevent display errors in the problem statement, some line breaks were added to the sample input. The actual input will not contain extra line breaks. $10^6!$ has 5,565,709 digits; please pay attention to the efficiency of your solution.