#include<bits/stdc++.h>

typedef long long int ll;
typedef unsigned long long int ull;
#define pii pair<int,int>
#define YES cout<<"YES\n"
#define Yes cout<<"Yes\n"
#define yes cout<<"yes\n"
#define NO cout<<"NO\n"
#define No cout<<"No\n"
#define no cout<<"no\n"
#define pb push_back
#define lowbit(x) ((x) & (-x))

using namespace std;
const int INF = 0x3f3f3f3f;
const double EPS=1e-10;
const double Pi=3.1415926535897;
const int mod=1e9+7;
const int maxn=1e5+5;

int n;
vector<int>g[maxn];
int deg[maxn];
int x,y,z;
vector<int>anc;
vector<bool>vis;
vector<pii>r;
bool ok;

void dfs(int u, int fa){
	for(auto v:g[u]){
		if(v==fa) continue;
		if(vis[v]){
			r.pb({u,v});
			for(int i=anc.size()-2;i>=0;i--){
				r.pb({anc[i],anc[i+1]});
				if(anc[i]==v) break;
			}
			ok=true;
			return;
		}
		
		vis[v]=true;
		anc.pb(v);
		dfs(v,u);
		anc.pop_back();
		if(ok) return;
	}
}

int main(){
	ios::sync_with_stdio(false);
	cin.tie(0),cout.tie(0);
	
	cin>>n;
	for(int i=1;i<=n;i++) deg[i]=0;

	for(int i=1;i<=n;i++){
		int u,v;
		cin>>u>>v;
		deg[u]++;
		deg[v]++;
		g[u].pb(v);
		g[v].pb(u);
	}

	for(int i=1;i<=n;i++){
		if(deg[i]<4) x++;
		else if(deg[i]==4) y++;
		else z++;
	}
	vis.resize(n+1);
	fill(vis.begin(), vis.end(),false);
	ok=false;
	dfs(1,0);
	ll ans=0;
	for(auto p:r){
		int u=p.first, v=p.second;
		// cout<<u<<" "<<v<<"\n";
		int tx=x, ty=y, tz=z;
		if(deg[u]==5) tz--, ty++; 
		else if(deg[u]==4) ty--, tx--;

		if(deg[v]==5) tz--, ty++; 
		else if(deg[v]==4) ty--, tx--;
		if(tz>0) continue;
		else ans += n-ty;
	}
	cout<<ans<<"\n";


	return 0;
}

/*

*/