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.

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分