#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> ii;
#define f(i,a,b) for(int i = a; i < b; i++)
#define ff first
#define ss second
const int N = 2e5 + 5;
const ll inf = 1e17 + 100;
ll ans, a[N], c[N], diam;
ii val[N], ra[N];
int n, ct, H, pu, pv;
int h[N], p[N];
bool vis[N], revis[N], on[N];
vector <int> adj[N], cycle;
vector <ii> ADJ[N];
void dfs(int u, int f){
vis[u] = 1;
p[u] = f;
for(int v: adj[u]){
if(v == f) continue;
if(vis[v])
{if(pv == 0) pv = v, pu = u; }
else dfs(v, u);
}
}
void cal(int u){
revis[u] = 1;
H = max(H, h[u]);
ii p = {0, 0}, ct;
for(int v: adj[u]){
if(revis[v]) continue;
h[v] = h[u] + 1;
cal(v);
map <ll,ll> m;
for(auto p: ADJ[v]) m[-p.ff] += p.ss;
ll wi = 0, ta = 0;
for(auto p: m){
wi = -p.ff, ta = p.ss;
break;
}
ADJ[u].push_back({++wi, ta});
if(val[v].ff + 1 > p.ff) {
p.ss = p.ff, p.ff = val[v].ff + 1;
ct = val[v];
ct.ff++;
}
else {
if(val[v].ff + 1 == p.ff) ct.ss++;
if(val[v].ff + 1 > p.ss) p.ss = val[v].ff + 1;
}
}
val[u] = ct;
ra[u].ff = p.ff, ra[u].ss = p.ss;
if(ADJ[u].empty()) ADJ[u].push_back({0, 1});
//cout << u << "\n";
//for(auto p: ADJ[u]) cout << p.ff << " " << p.ss << "\n";
diam = max(diam, p.ff + p.ss);
}
void get(int u){
on[u] = 1;
if(h[u] == H) ct++;
for(int v: adj[u]){
if(!on[v]) get(v);
}
}
void DFS(int u){
on[u] = 1;
if(ra[u].ff + ra[u].ss == diam){
int l = ADJ[u].size();
if(l) {
sort(ADJ[u].begin(), ADJ[u].end());
reverse(ADJ[u].begin(), ADJ[u].end());
}
if(l == 1) ans += ADJ[u][0].ss;
else{
ll s = 0, s_2 = 0;
//for(auto p: ADJ[u]){
// cout << p.ff << " " << p.ss << "\n";
//}
f(i,0,2) s += ADJ[u][i].ss, s_2 += ADJ[u][i].ss * ADJ[u][i].ss;
f(i,2,l){
if(ADJ[u][i].ff != ADJ[u][1].ff) break;
s_2 += ADJ[u][i].ss * ADJ[u][i].ss;
s += ADJ[u][i].ss;
}
if(ADJ[u][0].ff == ADJ[u][1].ff){
ans += (s*s - s_2) / 2;
}
else{
ans += ADJ[u][0].ss * (s - ADJ[u][0].ss);
}
}
}
for(int v: adj[u]) if(!on[v]) DFS(v);
}
int main(){
cin >> n;
f(i,0,n){
int x, y; cin >> x >> y;
adj[x].push_back(y), adj[y].push_back(x);
}
dfs(1, 0);
while(pu != p[pv]) cycle.push_back(pu), pu = p[pu];
for(int x: cycle) revis[x] = on[x] = 1;
int id = 0;
for(int x: cycle){
H = 0, ct = 0;
id++;
cal(x), get(x);
a[id] = H, c[id] = ct;
}
ll x = id/2;
map <int,ll> ml, mr;
multiset <int> sl, sr;
f(i,1,id+1){
if(!sr.empty())
diam = max(diam, i + a[i] + *sr.rbegin());
if(!sl.empty())
diam = max(diam, id - i + a[i] + *sl.rbegin());
sr.insert(a[i] - i);
if(i >= x + 1){
sl.insert(a[i-x] + i-x);
auto it = sr.find(a[i-x] - (i-x));
sr.erase(it);
}
}
f(i,1,id+1){
ans += c[i] * (mr[diam - a[i] - i] + ml[diam - id - a[i] + i]);
mr[a[i] - i] += c[i];
if(i >= x + 1){
ml[a[i-x] + i - x] += c[i-x];
mr[a[i-x] - i + x] -= c[i-x];
}
if(2*x == id and i >= x+1 and a[i] + x + a[i-x] == diam)
ans += c[i] * c[i-x];
}
f(i,1,n+1) on[i] = 0;
for(int x: cycle) on[x] = 1;
for(int x: cycle)
DFS(x);
cout << ans << "\n";
return 0;
}
