#include<bits/stdc++.h>

using namespace std;
using LL = long long;
using ll = long long;
const int N = 111111;
#define rep(i,a ,b )  for(int i = a ;i<=b;i++)
#define pre(i,a ,b )  for(int i = a ;i>=b;i--)
#define int long long
int n;
vector<int>v[100005];
vector<int> aa;
int d[100005], dd[100005];
bool st[100005];

void huan()
{
    queue<LL> q;
    for (int i = 1; i <= n; i++)
    {
        if (d[i] == 1)
        {
            q.push(i);
            st[i] = 1;
        }
    }

    while (q.size())
    {
        LL t = q.front();
        q.pop();

        for (auto x : v[t])
        {
            if (!st[x])
            {
                d[x]--;
                if (d[x] == 1)
                {
                    q.push(x);
                    st[x] = 1;
                }
            }
        }

    }
	rep(i, 1, n) {
		if (st[i] == 0) {
			aa.push_back(i);
	  }
	}
}


void solve()
{
	cin >> n;
	rep(i, 1, n) {
		int x, y; cin >> x >> y;
		v[x].push_back(y);
		v[y].push_back(x);
		d[x]++;
		d[y]++;
	}
	int num4 = 0, num5 = 0;
	rep(i, 1, n)
	{
		if (d[i] == 4) num4++;
		else if (d[i] == 5) num5++;
		dd[i] = d[i];
	}

	huan();

	int m = aa.size();
	rep(i, 0, m - 1) aa.push_back(aa[i]);
	if (num5 == 2) {
		cout << n - num4 - num5 << endl;
		return;
	}
	else if (num5 == 1)
	{
		int ans = 0;
		rep(i, 1, m)
		{
			if (dd[aa[i]] == 5)
			{
				int n4 = num4;
				if (dd[aa[i - 1]] == 4) n4--;
				ans += n - num5 - n4;
				n4 = num4;
				if (dd[aa[i + 1]] == 4) n4--;
				ans += n - num5 - n4;
			}
		}
		cout << ans << endl;
		return;
	}
	int ans = 0;
	rep(i, 1, m)
	{
		int n4 = num4;
		if (dd[aa[i - 1]] == 4) n4--;
		if (dd[aa[i + 1]] == 4) n4--;
		ans += (n - n4);
	}
	cout << ans << endl;
	return;
}


signed main() {

	ios::sync_with_stdio(false);
	cin.tie(nullptr);

	int t = 1;
	//cin >> t ;
	while (t--) {
		solve();
	}
	return 0;

}