Perfect Pth Powers

Description

We say that x is a perfect square if, for some integer b, x = b ². Similarly, x is a perfect cube if, for some integer b, x = b ³. 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 p th 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 th power.

Sample Input

17
1073741824
25
0

Sample Output

1
30
2

#include <stdio.h>
#include <math.h>
typedef long long LL;
LL POW(int b,int p)
{
    int i;
    LL s=1;
    for(i=0; i< p; i++) s*=b;
    return s;
}

int main()
{
    LL x,n;
    int i,y;
    while(scanf("%lld",&n)&&n)
    {
        x=n>0?n:-n;
        for(i=32; i>=2; i--)
        {
            y=(int)(pow((double)x,1.0/i)+0.5);
            if(POW(y,i)==x)
            {
                if(n<0 && i%2==0) continue;
                else printf("%d\n",i);
                break;
            }
        }
        if(i==1) printf("1\n");
    }

    return 0;
}