201060: [AtCoder]ARC106 A - 106

Problem Statement

Given is an integer $N$. Determine whether there is a pair of positive integers $(A, B)$ such that $3^A + 5^B = N$, and find one such pair if it exists.

Constraints

• $1 \leq N \leq 10^{18}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

Output

If there is no pair $(A, B)$ that satisfies the condition, print -1.

If there is such a pair, print $A$ and $B$ of one such pair with space in between. If there are multiple such pairs, any of them will be accepted.

Sample Input 1

106

Sample Output 1

4 2

We have $3^4 + 5^2 = 81 + 25 = 106$, so $(A, B) = (4, 2)$ satisfies the condition.

Sample Input 2

1024

Sample Output 2

-1

Sample Input 3

10460353208

Sample Output 3

21 1