Contest Duration: - (local time) (100 minutes) Back to Home
A - 106 /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 制約

• 1 \leq N \leq 10^{18}
• 入力はすべて整数である。

### 入力

N


### 入力例 1

106


### 出力例 1

4 2


3^4 + 5^2 = 81 + 25 = 106 なので、(A, B) = (4, 2) は条件を満たします。

### 入力例 2

1024


### 出力例 2

-1


### 入力例 3

10460353208


### 出力例 3

21 1


Score : 300 points

### 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