题目描述

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 = b^p. 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.

样例 1

输入

17
1073741824
25
0

输出

1
30
2

题目来源：http://plg1.cs.uwaterloo.ca/~acm00/040131/E.html；FPS 共享题包，题包内第 5 题。保留原作者与原赛事署名。