A. Spilled Milk I
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Mr. Milky has been playing with dice a lot. Recently, he has played a game where he rolls a standard six sided die an arbitrary number of times, and each time he rolls the die, he writes the number down on a piece of paper. At the end, he takes the product of all his rolls and writes it down as well.

However, he spilled his glass of milk all over the paper and cannot remember his individual rolls, only the final product. Given that the final product of his rolls is $$$N$$$, find the maximum possible sum of the numbers he rolled.

Input

An integer $$$N$$$ ($$$1 ≤ N ≤ 10^5$$$), representing the product of all individual dice rolls.

Output

Print the maximum possible sum of the individual dice rolls. If there is no possible configuration of dice rolls that multiply to $$$N$$$, print $$$-1$$$. If the number exceeds $$$10^9$$$, print $$$10^9 + 7$$$.

Example
Input
7
Output
-1
Note

In the example test case, the output is $$$-1$$$ as you cannot contribute a factor of $$$7$$$ from a standard six sided die.