Problem Description

As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:

Yuta has a non-direct graph with n vertices and n+1 edges. Rikka can choose some of the edges (at least one) and delete them from the graph.

Yuta wants to know the number of the ways to choose the edges in order to make the remaining graph connected.

It is too difficult for Rikka. Can you help her?

 

Input

The first line contains a number T(T≤30)——The number of the testcases.

For each testcase, the first line contains a number n(n≤100).

Then n+1 lines follow. Each line contains two numbers u,v , which means there is an edge between u and v.

 

Output

For each testcase, print a single number.

 

Sample Input

 

Sample Output

 

Source

 

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a+b-c+(a+b-c-1)*(a+b-c)/2-(a-c)*(a-c-1)/2-(b-c)*(b-c-1)/2-c*(c-1)/2，就是只删一条边有a+b-c种情况，删两条边用总可能数-不合法数得到。

 #include <iostream>

 #include <cstdio>

 #include <cstring>

 using namespace std;

 const int maxn=;

 int edge[maxn][];

 int fa[maxn],cnt=,fir[maxn],nxt[maxn<<],to[maxn<<];

 int dep[maxn],pre[maxn],ret[maxn],ID[maxn<<];

 int find(int x)

 {

     return fa[x]==x?x:fa[x]=find(fa[x]);

 }

 void addedge(int a,int b,int id)

 {

     nxt[++cnt]=fir[a];ID[cnt]=id;

     to[cnt]=b;fir[a]=cnt;

 }

 void DFS(int node)

 {

     for(int i=fir[node];i;i=nxt[i])

     {

         if(dep[to[i]])continue;

         dep[to[i]]=dep[node]+;

         pre[to[i]]=i;

         DFS(to[i]);

     }

 }

 int Search(int x,int y,int d)

 {

     while(x!=y){

         if(dep[x]<dep[y])

             swap(x,y);

         ret[ID[pre[x]]]+=d;

         x=to[pre[x]^];

     }

 }

 void Init()

 {

     memset(fir,,sizeof(fir));

     memset(ret,,sizeof(ret));

     cnt=;

 }

 int main()

 {

     freopen("data.in","r",stdin);

     freopen("wrong.out","w",stdout);

     int T,n;

     scanf("%d",&T);

     while(T--)

     {

         Init();

         scanf("%d",&n);

         for(int i=;i<=n+;i++){

             fa[i]=i;

         }

         for(int i=;i<=n+;i++)

             scanf("%d%d",&edge[i][],&edge[i][]);

         for(int i=;i<=n+;i++){

             int a=find(edge[i][]),b=find(edge[i][]);

             if(a==b)

                 edge[i][]=;

             else{

                 fa[a]=b;

                 addedge(edge[i][],edge[i][],i);

                 addedge(edge[i][],edge[i][],i);

             }

         }

         int flag=;

         for(int i=;i<=n;i++)

         if(find(i)!=find(i-)){

             printf("0\n");

             flag=;

             break;

         }

         if(flag==)continue;

         dep[]=;

         DFS();

         int ans=,a=,b=,c=;

         for(int i=;i<=n+;i++){

             if(edge[i][]){

                 if(!ans){

                     Search(edge[i][],edge[i][],);

                     ret[i]+=;

                 }

                 else {

                     Search(edge[i][],edge[i][],);

                     ret[i]+=;

                 }

                 ans+=;

             }

         }

         for(int i=;i<=n+;i++){

             if(ret[i]==)a++;

             else if(ret[i]==)b++;

             else if(ret[i]==)c++,b++,a++;

         }

         printf("%d\n",a+b-c+(a+b-c-)*(a+b-c)/-(a-c)*(a-c-)/-(b-c)*(b-c-)/-c*(c-)/);

     }

     return ;

 }