Uolevi is designing a weird gas tank for a new car. Though the shape of the tank is strange, it's volume can be calculated by using only 2 of it's dimensions: $A$ and $B$. The tank's volume is $A^2 \times B + B^2 \times A$. The tank should hold as much gas as possible but not more than $N$ volume units. $A$ and $B$ are still not locked in place so Uolevi is tasked to find the optimal dimensions for the tank.

Input

A single line contains a single integer $N$.

Output

Print the dimensions of the tank that has the greatest volume less than or equal to $N$. If there are multiple answers, print any.

$A\ B$

Constraints

• $1 \leq N \leq 10^{12}$
• $A, B, N$ are all integers

Example 1

Input:

16

Output:

2 2

Example 2

Input:

778

Output:

12 4

Example 3

Input:

1000000000000

Output:

499998 4