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ZOJ Problem Set - 2124
Perfect Pth Powers

Time Limit: 2 Seconds      Memory Limit: 65536 KB

We say that x is a perfect square if, for some integer b, x = b2. Similarly, x is a perfect cube if, for some integer b, x = b3. More generally, x is a perfect pth power if, for some integer b, x = bp. Given an integer x you are to determine the largest p such that x is a perfect pth 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 pth power.


Sample Input

17
1073741824
25
0


Sample Output

1
30
2


Source: University of Waterloo Local Contest 2004.01.31
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