Page Hopping UVA - 821

//#pragma GCC optimize("Ofast")
//#pragma GCC target("avx,avx2,fma")
//#pragma GCC optimization ("unroll-loops")

#include<bits/stdc++.h>
#include<string.h>
using namespace std;
#define pb          push_back
#define all(v)      v.begin(),v.end()
#define yes         cout<<"YES"<<endl;
#define no          cout<<"NO"<<endl;
#define ff          first
#define sc          second
#define inf         999999999
#define pi          3.14159265359
#define printv(v)   for(auto x:v)cout<<x<<' ';cout<<endl;
#define takev(v)    for(auto &x:v)cin>>x;
inline  int         random(int a=1,int b=10)
{
    return a+rand()%(b-a+1);
}
typedef long long ll;
inline ll           lcm(ll a,ll b)
{
    return (a*b)/__gcd(a,b);
}
//#define see(x)  cout<<endl<<#x<<" : "<<(x)<<endl;
#define see(args...) \
{ \
    string _s = #args; replace(_s.begin(), _s.end(), ',', ' ');\
    stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args);\
}
void err(istream_iterator<string> it) {}
template<typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args)
{
    cout<< *it << " = " << a <<",\n"[++it==istream_iterator<string>()];
    err(it, args...);
}
#define scc(n) scanf("%d",&n);
#define sccc(n) scanf("%lld",&n);

typedef pair<ll,ll> pll;
typedef pair<int,int> pii;
const int N=1e5+9,mod=1e9+7;


int main()
{
//    ios::sync_with_stdio(0);
//    cin.tie(NULL);


    int _ = 0;
    while(true)
    {

        int x,y;
        scc(x)
        scc(y)
        if(!x)break;

        set<int>s;
        vector< pii > v;
        vector< int >change(102);
        v.pb({x,y});

        s.insert(x);
        s.insert(y);
        change[x] = x;
        change[y] = y;

        while(true)
        {
            scc(x)
            scc(y)
            if(!x)break;
            v.pb({x,y});
            s.insert(x);
            s.insert(y);
            change[x] = x;
            change[y] = y;
        }

        int nodes = s.size();

        int cur = 1;
        for(auto x:s)
        {
            if(cur == x)
            {
                cur++;
                continue;
            }
            change[x] = cur;
            cur++;
        }

        vector< vector<int> > G(101,vector<int>(101,inf));

        for(int i=1;i<=nodes;i++)G[i][i] = 0;

        for(auto [l,r] : v)
        {
            G[change[l]][change[r]] = 1;
        }

        for(int k=1;k<=nodes;k++)
        {
            for(int i=1;i<=nodes;i++)
            {
                for(int j=1;j<=nodes;j++)
                {
                    if(G[i][j] > G[i][k] + G[k][j]) G[i][j] = G[i][k] + G[k][j];
                }
            }
        }

        double total = 0;
        double total_pairs = nodes*(nodes-1);
        for(int i=1;i<=nodes;i++)
        {
            for(int j=1;j<=nodes;j++)
            {
                total += G[i][j];
            }
        }
        printf("Case %d: average length between pages = %.3lf clicks\n",++_,total/total_pairs);

    }

    return 0;
}