POJ 3696

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#define LL __int64
using namespace std;

LL gcd(LL a,LL b){
	if(b==0) return a;
	return gcd(b,a%b);
}
LL fac[10000]; int cnt;
LL Euler(LL m){
	LL res=m;
	LL k=(LL)sqrt((double)m);
	for(LL i=2;i<=k;i++){
		if(m%i==0){
			res=res-res/i;
			while(m%i==0)
			m/=i;
		}
	}
	if(m>1)
	res=res-res/m;
	return res;
}

LL multi(LL a,LL b,LL m){
    LL ret=0;
    while(b>0){
        if(b&1) ret=(ret+a)%m;
        b>>=1;
        a=(a<<1)%m;
    }
    return ret;
}

LL quick(LL a,LL k,LL m){
	LL ans=1;
	while(k){
		if(k&1)
		ans=multi(ans,a,m);
		k=(k>>1);
		a=multi(a,a,m);
	}
	return ans;
}

int main(){
	LL l; int kase=0; 
	while(scanf("%I64d",&l),l){
		if(l%16==0||l%5==0) {
			printf("Case %d: 0\n",++kase);
			continue;
		}
		cnt=0;
		LL m=l*9/gcd(l,(LL)8);
		LL phi=Euler(m);
		LL ans;
		LL k=(LL)sqrt((double)phi);
		for(LL i=1;i<=k;i++){
			if(phi%i==0){
				fac[cnt++]=i;
				fac[cnt++]=phi/i;
			}
		}
		sort(fac,fac+cnt);
		for(int i=0;i<cnt;i++){
			ans=quick((LL)10,fac[i],m);
			if(ans==1){
				printf("Case %d: %I64d\n",++kase,fac[i]);
				break;
			}
		}
	}
	return 0;
}