#A. ARC106A - 106

Type: Default

1000ms

256MiB

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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

$1 \leq N \leq 1 0^{18}$
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

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

Sample Output 2

-1

Sample Input 3

10460353208

Sample Output 3

21 1

ARC106

Not Attended

Status: Done
Rule: IOI
Problem: 6
Start at: 2023-7-5 8:15
End at: 2023-7-5 10:15
Duration: 2 hour(s)
Host: 梁泽贤 (liangzexian)
Partic.: 13

#A. ARC106A - 106

ARC106A - 106

Problem Statement

Constraints

Input

Output

Sample Input 1

Sample Output 1

Sample Input 2

Sample Output 2

Sample Input 3

Sample Output 3

ARC106

Status

Development

Support

#A. ARC106A - 106

ARC106A - 106

Problem Statement

Constraints

Input

Output

Sample Input 1

Sample Output 1

Sample Input 2

Sample Output 2

Sample Input 3

Sample Output 3

ARC106

Status

Development

Support

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