#pragma warning(disable:4996)
#include<stdio.h>
#include<algorithm>
#include<vector>
using namespace std;
#define N_ 200010
vector<int>E[N_];
int n, Len, Cyc[N_], m, Deq[N_ * 2];
int deg[N_], Q[N_];
bool v[N_];
long long res, S[N_];
struct Table{
int a, cnt;
}D[N_][2], D2[N_];
void Find_Cycle(int st)
{
int x = st, i, p = -1;
while (1){
Cyc[m++] = x;
for (i = 0; i < E[x].size(); i++){
if (deg[E[x][i]] != 1 && p != E[x][i])break;
}
p = x;
x = E[x][i];
if (x == st)break;
}
for (i = 0; i < m; i++)D2[i] = D[Cyc[i]][0];
}
void PrePro(){
int i, h = 0, t = 0, x, y, ck, tp;
for (i = 1; i <= n; i++){
D[i][0].cnt = 1;
if (deg[i] == 1)Q[++t] = i;
}
while (h < t){
x = Q[++h];
for (i = 0; i < E[x].size(); i++){
y = E[x][i];
if (deg[y] != 1){
deg[y]--;
if (deg[y] == 1)Q[++t] = y;
tp = D[x][0].a + 1;
if (D[y][0].a <= tp){
if (D[y][0].a < tp){
D[y][1] = D[y][0], D[y][0].cnt = 0;
v[y] = false, S[y] = (long long)D[y][1].cnt*D[x][0].cnt;
}
else if (v[y] == false)v[y] = true, S[y] = 0;
S[y] += (long long)D[y][0].cnt * D[x][0].cnt;
D[y][0].a = tp, D[y][0].cnt += D[x][0].cnt;
}
else if (D[y][1].a <= tp){
if (D[y][1].a < tp){
D[y][1].cnt = 0;
if (!v[y])S[y] = 0;
}
if (!v[y]) S[y] += (long long)D[y][0].cnt*D[x][0].cnt;
D[y][1].a = tp, D[y][1].cnt += D[x][0].cnt;
}
}
}
}
ck = 1;
for (i = 1; i <= n; i++){
if (v[i]){
if (Len < D[i][0].a * 2)Len = D[i][0].a * 2;
}
else if (Len < D[i][0].a + D[i][1].a)Len = D[i][0].a + D[i][1].a;
}
for (i = 1; i <= n; i++)if (deg[i] != 1)break;
Find_Cycle(i);
}
int dist(int a, int b){
return a>b ? m + b - a : b - a;
}
int Gap(int a, int b){
return dist(a, b) + D2[a].a + D2[b].a;
}
void Pro1(){
int i, cc, h = 1, t = 0;
Deq[++t] = 0;
for (i = 1, cc = 1; cc < 2 * m; cc++, i++){
if (i == m)i = 0;
while (h <= t && dist(Deq[h], i) * 2 > m)h++;
Len = max(Len, Gap(Deq[h], i));
while (h <= t && D2[Deq[t]].a + dist(Deq[t], i) <= D2[i].a) t--;
Deq[++t] = i;
}
}
void TreeMax(){
int i;
long long tp;
for (i = 1; i <= n; i++){
if (v[i]){
if (Len == D[i][0].a * 2)res += S[i];
}
else if (Len == D[i][0].a + D[i][1].a) res += S[i];
}
}
void Pro2()
{
int i, C = 0, cc, h = 1, t = 0, tp, k;
Deq[++t] = 0, C += D2[0].cnt;
for (i = 1, cc = 1; cc < 2 * m; cc++, i++){
if (i == m)i = 0;
while (h <= t && dist(Deq[h], i) * 2 > m) C -= D2[Deq[h]].cnt, h++;
if (C == 0){
C = D2[Deq[h]].cnt;
k = h + 1;
while (k <= t && Gap(Deq[h], i) == Gap(Deq[k], i))C += D2[Deq[k]].cnt, k++;
}
tp = Gap(Deq[h], i);
if (cc >= m && tp == Len){
res += (long long)C * D2[i].cnt;
}
while (h <= t && D2[Deq[t]].a + dist(Deq[t], i) < D2[i].a) t--;
if (h > t) C = 0;
Deq[++t] = i;
if (D2[Deq[h]].a + dist(Deq[h], i) == D2[i].a) C += D2[i].cnt;
}
}
int main(){
int i, a, b;
scanf("%d", &n);
for (i = 0; i < n; i++){
scanf("%d%d", &a, &b);
E[a].push_back(b);
E[b].push_back(a);
deg[a]++, deg[b]++;
}
PrePro();
Pro1();
TreeMax();
Pro2();
printf("%lld\n", res);
}
