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