#include<iostream>
#include<cstdio>
#include<cstring>
#include<string>
#include<algorithm>
#include<cctype>
#include<cmath>
#include<cstdlib>
#include<queue>
#include<ctime>
#include<vector>
#include<set>
#include<map>
#include<stack>
using namespace std;
int n,L,R,num,Max,cnt,col[1200000],d[1200000],sum[1200000],du[260000];
long long Ans;
vector<int>high[260000],low[260000];
inline void build(int le,int ri,int wh){sum[wh]=1;d[wh]=ri;if(le==ri)return;int mid=(le+ri)>>1;build(le,mid,wh<<1);build(mid+1,ri,wh<<1|1);
}
inline void pd(int wh){if(col[wh]){d[wh<<1]+=col[wh];col[wh<<1]+=col[wh];d[wh<<1|1]+=col[wh];col[wh<<1|1]+=col[wh];col[wh]=0;}
}
inline void up(int wh){d[wh]=max(d[wh<<1],d[wh<<1|1]);sum[wh]=(d[wh<<1]==d[wh]?sum[wh<<1]:0)+(d[wh<<1|1]==d[wh]?sum[wh<<1|1]:0);
}
inline void update(int le,int ri,int wh,int x,int y){if(le>=x&&ri<=y){col[wh]++;d[wh]++;return;}pd(wh);int mid=(le+ri)>>1;if(mid>=x)update(le,mid,wh<<1,x,y);if(mid<y)update(mid+1,ri,wh<<1|1,x,y);up(wh);
}
inline void que(int le,int ri,int wh,int x,int y){if(le>=x&&ri<=y){if(d[wh]>Max)Max=d[wh],cnt=sum[wh];else if(d[wh]==Max)cnt+=sum[wh];return;}pd(wh);int mid=(le+ri)>>1;if(mid>=x)que(le,mid,wh<<1,x,y);if(mid<y)que(mid+1,ri,wh<<1|1,x,y);up(wh);
}
inline void add(int x){for(int i=0;i<low[x].size();i++){update(1,n,1,1,low[x][i]);if(low[x][i]>=L)num+=((++du[x])==3)+((++du[low[x][i]])==3);}
}
inline void deal(int x){for(int i=0;i<high[x].size();i++){if(high[x][i]<=R)num-=((--du[x])==2)+((--du[high[x][i]])==2);}
}
int main(){int i,j,k;scanf("%d",&n);for(i=1;i<n;i++){int x,y;scanf("%d%d",&x,&y);if(x>y)swap(x,y);high[x].push_back(y);low[y].push_back(x);}L=1;build(1,n,1);for(i=1;i<=n;i++){R=i;add(i);while(num)deal(L),L++;Max=0;que(1,n,1,L,i);if(Max==i)Ans+=1ll*cnt;}cout<<Ans;return 0;
}