hdu1395

//一个数对某个数取摸，等于这个数的因数分别取摸在相乘 在取摸，
//m%n = （m1%n*m2%n*m3%n.......)%n;
#include<iostream>
using namespace std;
int main()
{
    int n;
    while(cin >> n)
    {
        if(n%2==0||n==1)
        {
            cout << 2<<"^"<<"?"<<" mod " << n <<" = "<< 1<<endl;
            continue;
        }
        int temp = 2;
        int k = 1;
        while(temp!=1)
        {
            temp = temp*2%n;
            k++;
        }
        cout << 2<<"^"<<k <<" mod " << n <<" = "<< 1<<endl;
    }
}