Perfect Pth PowersTime Limit: 1000MS Memory Limit: 10000K

Total Submissions: 15918 Accepted: 3605

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.

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

Waterloo local 2004.01.31

//184K    32MS    C++    694B    //我会告诉你我WA了很多次吗- -//直接暴力的思想，时间复杂度为O(sqrt(n)) #include
     
      #include
      
       __int64 _abs(__int64 a){    return a>0?a:-a;}int main(void){    __int64 n;    while(scanf("%I64d",&n),n)    {        __int64 i,flag;        __int64 ans;        if(n<0) flag=-1;        else flag=1;        __int64 m=(__int64)sqrt(_abs(n)*1.0);        for(i=2;i<=m;i++){            ans=1;            __int64 temp=i*flag;            while(_abs(temp)<_abs(n)){ //每一个数都试一次                 temp*=(i*flag);                ans++;            }            if(temp==n) break;//符合条件跳出循环             else ans=1;        }        printf("%d\n",ans);    }    return 0;}