HZNUOJ

Perfect Pth Powers

Tags:
Time Limit:  1 s      Memory Limit:   128 MB
Submission:39     AC:15     Score:99.79

Description

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.

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.

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

Samples

input
17 1073741824 25 0
output
1 30 2