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.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分