103271: [Atcoder]ABC327 B - A^A

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

问题描述

给你一个整数$B$。

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

约束条件

• $1 \leq B \leq 10^{18}$
• $B$是一个整数。

输入

输入从标准输入按以下格式给出：

$B$

输出

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

如果存在多个正整数$A$，使得$A^A = B$，则任意一个都会被接受。

样例输入1

27

样例输出1

3

$3^3 = 27$，所以输出$3$。

样例输入2

100

样例输出2

-1

不存在$A$使得$A^A = B$。

样例输入3

10000000000

样例输出3

10