Score : $200$ points

问题描述

给定一个整数 $B$。

如果存在一个正整数 $A$，使得 $A^A = B$，则输出 $A$ 的值；否则，输出 -1。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given an integer $B$.
If there exists a positive integer $A$ such that $A^A = B$, print its value; otherwise, output -1.

Constraints

• $1 \leq B \leq 10^{18}$
• $B$ is an integer.

Input

The input is given from Standard Input in the following format:

$B$

Output

If there exists a positive integer $A$ such that $A^A = B$, print its value; otherwise, print -1.
If there are multiple positive integers $A$ such that $A^A = B$, any of them will be accepted.

Sample Input 1

27

Sample Output 1

3

$3^3 = 27$, so print $3$.

Sample Input 2

100

Sample Output 2

-1

There is no $A$ such that $A^A = B$.

Sample Input 3

10000000000

Sample Output 3

10

update @ 2024/3/10 01:50:34