Description

We say that x is a perfect square if, for some integer b, x = b

. Similarly, x is a perfect cube if, for some integer b, x = b

. More generally, x is a perfect pth power if, for some integer b, x = b

. Given an integer x you are to determine the largest p such that x is a perfect p

power.

Input

Each test case is given by a line of input containing x. The value of x will have magnitude at least 2 and be within the range of a (32-bit) int in C, C++, and Java. A line containing 0 follows the last test case.

Output

For each test case, output a line giving the largest integer p such that x is a perfect p

power.

17
1073741824
25
0

1
30
2

Source