A. Is It A Math Problem?
time limit per test
1 second
memory limit per test
1024 megabytes
input
standard input
output
standard output

As the title said, this is a Mathementation problem!

You will be given a number $$$n$$$ and you have to print two integer numbers $$$a$$$ and $$$b$$$ satisfying the following conditions: $$$$$$a^b = \prod_{d|n} d$$$$$$ $$$$$$0 \le a,b \le 10^{18}$$$$$$

$$$(\prod_{d|n} d)$$$ is the product of all divisors of $$$n$$$.

Input

The first and the only line of the input will contain a single integer $$$n$$$ $$$(1 \le n \le 10^{12})$$$.

Output

Print two integers $$$a , b$$$ $$$(0 \le a , b \le 10^{18})$$$. if there are many solutions print any one of them.

Example
Input
10
Output
100 1
Note

For the first test case, the divisors of $$$10$$$ are:

$$$1 , 2 , 5 , 10$$$ .

So, $$$a$$$ could be equal to $$$100$$$ and $$$b$$$ could be equal to $$$1$$$.

and $$$100^1$$$ = $$$1*2*5*10$$$.