Tom is a commander, his task is destroying his enemy’s transportation system.

Let’s represent his enemy’s transportation system as a simple directed graph G with n nodes and m edges. Each node is a city and each directed edge is a directed road. Each edge from node u to node v is associated with two values D and B, D is the cost to destroy/remove such edge, B is the cost to build an undirected edge between u and v.

His enemy can deliver supplies from city u to city v if and only if there is a directed path from u to v. At first they can deliver supplies from any city to any other cities. So the graph is a strongly-connected graph.

He will choose a non-empty proper subset of cities, let’s denote this set as S. Let’s denote the complement set of S as T. He will command his soldiers to destroy all the edges (u, v) that u belongs to set S and v belongs to set T.

To destroy an edge, he must pay the related cost D. The total cost he will pay is X. You can use this formula to calculate X:

After that, all the edges from S to T are destroyed. In order to deliver huge number of supplies from S to T, his enemy will change all the remained directed edges (u, v) that u belongs to set T and v belongs to set S into undirected edges. (Surely, those edges exist because the original graph is strongly-connected)

To change an edge, they must remove the original directed edge at first, whose cost is D, then they have to build a new undirected edge, whose cost is B. The total cost they will pay is Y. You can use this formula to calculate Y:

At last, if Y>=X, Tom will achieve his goal. But Tom is so lazy that he is unwilling to take a cup of time to choose a set S to make Y>=X, he hope to choose set S randomly! So he asks you if there is a set S, such that Y<X. If such set exists, he will feel unhappy, because he must choose set S carefully, otherwise he will become very happy.

There are multiply test cases.

The first line contains an integer T(T<=200), indicates the number of cases.

For each test case, the first line has two numbers n and m.

Next m lines describe each edge. Each line has four numbers u, v, D, B.
(2=<n<=200, 2=<m<=5000, 1=<u, v<=n, 0=<D, B<=100000)

The meaning of all characters are described above. It is guaranteed that the input graph is strongly-connected.

For each case, output "Case #X: " first, X is the case number starting from 1.If such set doesn’t exist, print “happy”, else print “unhappy”.

2
3 3
1 2 2 2
2 3 2 2
3 1 2 2
3 3
1 2 10 2
2 3 2 2
3 1 2 2

Case #1: happy
Case #2: unhappy

Hint
In first sample, for any set S, X=2, Y=4. 
In second sample. S= {1}, T= {2, 3}, X=10, Y=4.
 

UESTC

//#pragma warning (disable:4786)
#include <cstdio>
#include <cstring>
typedef long long LL;
#define N 1017
LL X[N], Y[N];
void init()
{
    memset(X, 0, sizeof(X));
    memset(Y, 0, sizeof(Y));
}
int main()
{
    int n, m;
    int u, v, D, B;
    int t;
    int cas = 0;
    int flag = 0;
    int i;
    scanf("%d", &t);
    while(t--)
    {
        init();
        flag = 0;
        scanf("%d%d", &n,&m);
        for(i=1; i<=m; i++)
        {
            scanf("%d%d%d%d", &u, &v, &D, &B);
            X[u]+=D;
            Y[v]+=(D+B);

        }
        for(i = 1; i <= n; i++)
        {
            if(Y[i] < X[i])
            {
                 flag = 1;
                 break;
            }
        }
        if(flag)
            printf("Case #%d: unhappy\n",++cas);
        else
            printf("Case #%d: happy\n",++cas);
    }
    return 0;
}