Uva 11728 - Alternate Task

 // Problem :: Uva 11728 - Alternate Task 
 //Link: Uva 11728 - Alternate Task 

// Verdict:: Accepted
// Time :: 0.00 

#include <iostream>
#include <cstdio>
#include <cstring>
#include <map>
#include <string>
#include <vector>
#include <cmath>
#include <cctype>
#include <sstream>
#include <set>
#include <list>
#include <stack>
#include <queue>
#include <algorithm>
#define sf scanf
#define pf printf
#define sfint(a,b) scanf("%d %d",&a,&b)
#define sfl(a,b) scanf("%ld %ld",&a,&b)
#define sfll(a,b) scanf("%lld %lld",&a,&b)
#define sfd(a,b) scanf("%lf %lf",&a,&b)
#define sff(a,b) scanf("%f %f",&a,&b)
#define lp1(i,n) for(i=0;i<n;i++)
#define lp2(i,n) for(i=1;i<=n;i++)
#define LL long long
#define L long
#define mem(c,v) memset(c,v,sizeof(c))
#define ui unsigned int
#define cp(a) cout<<" "<<a<<" "<<endl
#define ull unsigned long long int
#define nl puts("")
#define all(x) x.begin(),x.end()
#define sq(x) ((x)*(x))
#define mx7 20000100
#define mx6 1500000
#define mx5 1005
#define inf 1<<30                                           //infinity value
#define eps 1e-9
#define mx (65540)
#define mod 1000000007
#define pb push_back
#define pi acos(-1.0)
#define sz size()
#define gc getchar ()


using namespace std;
//..................................................................................................................

template<class T> T setbit(T n, T pos){n=n|(1<<pos); return n;}
template<class T> T checkbit(T n, T pos){n=n&(1<<pos); return n;}
template<class T> T gcd(T a, T b ) {return b==0?a:gcd(b,a%b);}
template<class T> T large(T a, T b ) {return a>b?a:b;}
template<class T> T small(T a, T b ) {return a<b?a:b;}


/*
template <class T>
 T some_function(T arg)
{
   .... ... ....
}

*/
//...................................................................................................................
int prime[(mx5/2)+1],plen;
vector<int>prm;
vector<int>sig;

void seieve(int n)
{
    int i,j,x=(int)sqrt(double(n));

    prime[0]=setbit(prime[0],0);
    prime[0]=setbit(prime[0],1);

    for(i=4;i<=n;i+=2)prime[i>>5]=setbit(prime[i>>5],i&31);

    for(i=3;i<=x;i+=2)
    {
        if(!checkbit(prime[i>>5],i&31))
        {
            for(j=i*i;j<=n;j+=i)
            {
                prime[j>>5]=setbit(prime[j>>5],j&31);
            }
        }
    }

    for(i=2;i<=n;i++)
    {
        if(!checkbit(prime[i>>5],i&31))
        {
            prm.push_back(i);
        }
    }

    plen=prm.size();
}

map<int,int>mpi;

int sigma(int n)
{
    int i,m=1;

    mpi.clear();

    for(i=0;i<plen and sq(prm[i])<=n;i++)
    {
        if(!(n%prm[i]))
        {
            int s=1;

            while(!(n%prm[i]))
            {
                s++;
                mpi[prm[i]]++;
                n/=prm[i];
                if(n==0 or n==1) break;
            }

            int tmp=powl(prm[i], mpi[prm[i]]+1) - 1;
            m*=tmp / (prm[i]-1);
        }
    }

    if(n>1)
    {
        int tmp=powl(n,2) - 1;
        m*=tmp / (n-1);
    }

    //sig.push_back(m);

    //lp1(i,sig.size())cout << sig[i] << " ";
    return m;
}

struct my
{
    int x;
    int y;
};

int main()
{
    seieve(mx5);

    int n,i,t=0;
    my ar[mx5];

    for(i=2;i<=mx5;i++) // store all divisors from 2 to mx5 in a structure array.
    {
        //sig.push_back(sigma(i));
        ar[i].x=i;
        ar[i].y=sigma(i);
    }

    //for(i=2;i<=200;i++) cout << " x = " << ar[i].x << " y= " << ar[i].y << " ;";

    while(sf("%d",&n)==1 and n)
    {
        int maxi=-1;

        if(n==1)
        {
            pf("Case %d: 1\n",++t);
            continue;
        }



        //sort(all(sig));

        //lp1(i,sig.size()) cout << sig[i] << " ";

//        if(binary_search(all(sig),n))
//        {
//            flag=1;
//        }
//
//        if(flag)
//        {
//            cout << sig[n-1];
//        }

        //for(i=2;i<=200;i++) cout << " x = " << ar[i].x << " y= " << ar[i].y << " ;";

        bool f=false;

        for(i=2;i<=1000;i++)
        {
            if(n == ar[i].y)
            {
                maxi=max(maxi,ar[i].x);

                f=true;
            }
        }

        if(f)
        {
            pf("Case %d: %d\n",++t,maxi);
        }

        else
        {
            pf("Case %d: -1\n",++t);
        }
    }

    return 0;
}