DIV3E 基环树

#include<bits/stdc++.h>
using namespace std;
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define rush! ios::sync_with_stdio(false);cin.tie(0);
const int inf = 0x3f3f3f3f;
const long long linf = 0x3f3f3f3f3f3f3f3f;
vector<int >g[200005];
typedef long long ll;
const int N=200005;
ll f[N];
 
//void init(ll n){
//    f[0]=1;
//    for(ll i=1;i<=n;++i){
//        f[i]=f[i-1]*i;
//    }
//}
ll C(ll n){
    if( 2>n) return 0;
    return n*(n-1)/2;
}
int ind;
int dfn[N],fa[N];
int loop[N],cnt;
int vis[N];
void loops(int u){
    dfn[u]=++ind;
    for(auto i:g[u]){
        if(i==fa[u])continue;
        if(dfn[i]){
            if(dfn[i]<dfn[u])continue;
            loop[++cnt]=i;
            vis[i]=1;
            for(;i!=u;i=fa[i]){
                loop[++cnt]=fa[i];
                vis[fa[i]]=1;
            }
            return ;
        }
        else{
            fa[i]=u;
            loops(i);
        }
    }
}
ll dfs(int u,int fa){
    ll res=1;
    for(auto i:g[u]){
        if(i!=fa&&!vis[i]){
            res+=dfs(i,u);
        }
    }
    return res;
}
void solve(){
    int n;
    cin>>n;
    for(int i=1;i<=n;i++){
        ind=0;
        dfn[i]=0,fa[i]=0;
        loop[i]=0;
        cnt=0;
        vis[i]=0;
        g[i].clear();
    }
    for(int i=1;i<=n;i++){
        int x,y;
         cin>>x>>y;
         g[x].push_back(y);
         g[y].push_back(x);
    }
    ll ans=C(n)*2;
//    cout<<ans<<endl;
    loops(1);
    for(int i=1;i<=cnt;i++){
        ans-=C(dfs(loop[i],-1));
    }
    cout<<ans<<endl;
}
int main(){

    int t;
    cin>>t;
//    cout<<C(5,2);
    while(t--){
        solve();
    }
}