#include<stdio.h>
#include<algorithm>
#include<string.h>
#include<vector>
#include<math.h>
#include<stdlib.h>
#include<set>
#include<ctype.h>
using namespace std;
#define X first
#define Y second
typedef long long ll;
typedef pair<int,int> Pi;
int st[200020], en[400040], nxt[400040];
int N;
int cycle[200020];
int ind[200020];
int down[200020];
int dp[200020][5];
int cycle_sz;
int L;
ll ans;
void addedge(int s,int e,int c){nxt[c]=st[s],st[s]=c,en[c]=e;}
int Que[200020];
void dfs_cycle(int x,int fa,int num)
{
if(num == cycle_sz)return;
cycle[num] = x;
for(int i=st[x];i;i=nxt[i])if(ind[en[i]] == 2 && en[i]!=fa)dfs_cycle(en[i],x,num+1);
}
struct Deque{
Pi p[200020];
int f,r;
void init(){f=r=0;}
void push(Pi x){
while(f!=r&&p[f-1].X<x.X)f--;
if(p[f-1].X == x.X)p[f-1].Y += x.Y;
else p[f++]=x;
}
inline void pop(Pi x){
if(p[r].X==x.X)p[r].Y -= x.Y;
if(!p[r].Y)r++;
}
inline Pi read(){return p[r];}
};
void bfs()
{
int *fr = Que, *re = Que, i;
for(i=1;i<=N;i++)dp[i][1] = 1;
for(i=1;i<=N;i++)if(ind[i] == 1){
*fr++ = i;
dp[i][4] = 1;
}
while(fr!=re){
int t = *re++;
for(i=st[t];i;i=nxt[i]){
if(ind[en[i]]){
int &a = dp[en[i]][0], &b = dp[en[i]][2];
if(!a || a < dp[t][0]+1){
b = a, dp[en[i]][3] = dp[en[i]][1];
a = dp[t][0]+1, dp[en[i]][1] = dp[t][1];
dp[en[i]][4] = 1;
}
else if(a==dp[t][0]+1)dp[en[i]][1] += dp[t][1], dp[en[i]][4]++;
else if(!b || dp[t][0]+1 > b)dp[en[i]][3] = dp[t][3], b = dp[t][0]+1;
else if(dp[t][0]+1 == b)dp[en[i]][3] += dp[t][3];
ind[t]--, ind[en[i]]--;
if(ind[en[i]] == 1)*fr++ = en[i];
}
}
}
for(i=1;i<=N;i++)if(ind[i] == 2)cycle_sz++;
for(i=1;i<=N;i++)if(ind[i] == 2){
dfs_cycle(i,-1,0);
break;
}
}
void solve(){
Deque Dq;
int i;
for(i=1;i<=N;i++){
if(dp[i][4] != 1)L = max(L, dp[i][0]*2);
else L = max(L, dp[i][0] + dp[i][2]);
}
Dq.init();
int half = cycle_sz>>1;
for(i=0;i<half;i++){
Dq.push(Pi(i + dp[cycle[i]][0], dp[cycle[i]][1]));
}
for(i=0;i<cycle_sz;i++){
int e = (i+half) % cycle_sz;
Dq.push(Pi(i + half + dp[cycle[e]][0], dp[cycle[e]][1]));
Dq.pop(Pi(i + dp[cycle[i]][0], dp[cycle[i]][1]));
Pi tmp = Dq.read();
int len = tmp.X - i + dp[cycle[i]][0];
if(L < len)ans = (ll)dp[cycle[i]][1] * tmp.Y, L = len;
else if(L == len)ans += (ll)dp[cycle[i]][1] * tmp.Y;
}
for(i=1;i<=N;i++){
if(dp[i][4]!=1 && L==dp[i][0]*2){
ll tmp = (ll)dp[i][1] * dp[i][1];
for(int j=st[i];j;j=nxt[j]){
if(ind[i]==2 && ind[en[j]]==2)continue;
if(dp[en[j]][0] + 1 == dp[i][0])tmp -= (ll)dp[en[j]][1] * dp[en[j]][1];
}
ans += tmp/2;
}
if(dp[i][4]==1 && L==dp[i][0] + dp[i][2])ans += (ll)dp[i][1] * dp[i][3];
}
printf("%lld",ans);
}
int main()
{
scanf("%d",&N);
int i;
for(i=1;i<=N;i++){
int x, y;
scanf("%d%d",&x,&y);
addedge(x,y,i<<1);
addedge(y,x,i<<1|1);
ind[x]++, ind[y]++;
}
bfs();
solve();
return 0;
}
