#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<ll, ll>
#define fi first
#define sec second
#define ld long double
const int MAXN = 2e5;
const ll INF = 1e18;
const int MOD = 998244353;
const ld eps = 1e-6;
ll vis[MAXN + 5], cycle[MAXN + 5];
vector<ll> adj[MAXN + 5];
ll p[MAXN + 5], st, en;
ll d[MAXN + 5];
map<ll, ll> freq;
void dfs2(ll idx, ll par){
vis[idx] = 1;
freq[d[idx]]++;
for(auto i : adj[idx]){
if(!vis[i] && !cycle[i]){
d[i] = d[idx] + 1;
dfs2(i, idx);
}
}
}
void dfs(ll idx, ll par){
vis[idx] = 1;
for(auto i : adj[idx]){
if(i == par) continue;
if(vis[i]) st = i, en = idx;
else{
p[i] = idx;
dfs(i, idx);
}
}
}
struct node{
ll MX, cnt;
};
struct ST{
ll N;
vector<node> sg;
ST(ll _n){
N = _n;
sg.resize(4 * N + 5);
for(int i = 0; i <= 4 * N; i++) sg[i] = {-INF, 0};
}
node comb(node a, node b){
node c;
if(a.MX == b.MX) c = {a.MX, a.cnt + b.cnt};
else if(a.MX > b.MX) c = a;
else c = b;
return c;
}
void upd(ll l, ll r, ll cur, ll idx, node val){
if(l == r){
sg[cur] = val;
}
else{
ll mid = (l + r) / 2;
if(idx <= mid) upd(l, mid, cur * 2, idx, val);
else upd(mid + 1, r, cur * 2 + 1, idx, val);
sg[cur] = comb(sg[cur * 2], sg[cur * 2 + 1]);
}
}
node query(ll l, ll r, ll cur, ll x, ll y){
if(l > y || r < x) return {-INF, 0};
if(l >= x && r <= y) return sg[cur];
ll mid = (l + r) / 2;
return comb(query(l, mid, cur * 2, x, y), query(mid + 1, r, cur * 2 + 1, x, y));
}
};
int main(){
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int tc = 1;
// cin >> tc;
for(;tc--;){
ll N; cin >> N;
for(int i = 1; i <= N; i++){
ll u, v; cin >> u >> v;
adj[u].push_back(v), adj[v].push_back(u);
}
dfs(1, -1);
ll sz = 1;
d[st] = 0;
while(st != en){
cycle[st] = 1;
d[p[st]] = d[st] + 1;
sz++;
st = p[st];
}
cycle[en] = 1;
ST pos(sz), neg(sz);
for(int i = 1; i <= N; i++) vis[i] = 0;
ll cur = 0, ans = 0;
for(int tt = 1; tt <= N; tt++){
if(cycle[tt]){
freq.clear();
dfs2(tt, -1);
vector<pii> v;
for(auto x : freq) v.push_back(x);
sort(v.begin(), v.end(), greater<pii>());
ll cur_mx = v[0].fi, cur_cnt = v[0].sec;
ll i = d[tt], j = cur_mx - d[tt];
ll batas = i - sz / 2;
if(v[0].sec == 1){
if(v.size() > 1){
if(cur < v[0].fi + v[1].fi - 2 * i){
ans = v[0].sec * v[1].sec;
cur = v[0].fi + v[1].fi - 2 * i;
}
else if(cur == v[0].fi + v[1].fi - 2 * i){
ans += v[0].sec * v[1].sec;
}
}
else{
if(cur < v[0].fi - i){
ans = v[0].sec;
cur = v[0].fi - i;
}
else if(cur == v[0].fi - i){
ans += v[0].sec;
}
}
}
else{
if(cur < v[0].fi * 2 - 2 * i){
ans = v[0].sec * (v[0].sec - 1) / 2;
cur = v[0].fi * 2 - 2 * i;
}
else if(cur == v[0].fi * 2 - 2 * i){
ans += v[0].sec * (v[0].sec - 1) / 2;
}
}
if(batas < 0){
node now = neg.query(0, sz - 1, 1, 0, i);
if(cur < now.MX + i + j){
ans = now.cnt * cur_cnt;
cur = now.MX + i + j;
}
else if(cur == now.MX + i + j){
ans += now.cnt * cur_cnt;
}
now = neg.query(0, sz - 1, 1, sz + batas, sz - 1);
if(cur < now.MX + sz + i + j){
ans = now.cnt * cur_cnt;
cur = now.MX + sz + i + j;
}
else if(cur == now.MX + sz + i + j){
ans += now.cnt * cur_cnt;
}
now = pos.query(0, sz - 1, 1, i, sz + batas - 1);
if(cur < now.MX - i + j){
ans = now.cnt * cur_cnt;
cur = now.MX - i + j;
}
else if(cur == now.MX - i + j){
ans += now.cnt * cur_cnt;
}
if(sz % 2 == 0){
now = pos.query(0, sz - 1, 1, i - sz / 2 + sz, i - sz / 2 + sz);
if(cur < now.MX - i + j){
ans = now.cnt * cur_cnt;
cur = now.MX - i + j;
}
else if(cur == now.MX - i + j){
ans += now.cnt * cur_cnt;
}
}
}
else{
node now = neg.query(0, sz - 1, 1, batas, i);
if(cur < now.MX + i + j){
ans = now.cnt * cur_cnt;
cur = now.MX + i + j;
}
else if(cur == now.MX + i + j){
ans += now.cnt * cur_cnt;
}
now = pos.query(0, sz - 1, 1, 0, batas - 1);
if(cur < now.MX + sz - i + j){
ans = now.cnt * cur_cnt;
cur = now.MX + sz - i + j;
}
else if(cur == now.MX + sz - i + j){
ans += now.cnt * cur_cnt;
}
now = pos.query(0, sz - 1, 1, i, sz);
if(cur < now.MX - i + j){
ans = now.cnt * cur_cnt;
cur = now.MX - i + j;
}
else if(cur == now.MX - i + j){
ans += now.cnt * cur_cnt;
}
if(sz % 2 == 0){
now = neg.query(0, sz - 1, 1, i - sz / 2, i - sz / 2);
if(cur < now.MX + i + j){
ans = now.cnt * cur_cnt;
cur = now.MX + i + j;
}
else if(cur == now.MX + i + j){
ans += now.cnt * cur_cnt;
}
}
}
pos.upd(0, sz - 1, 1, i, {cur_mx, cur_cnt});
neg.upd(0, sz - 1, 1, i, {cur_mx - 2 * i, cur_cnt});
}
}
cout << ans << "\n";
}
}
