#include <iostream>
#include <algorithm>
#include <map>
#include <vector>
#define x first
#define y second
using namespace std;
const int nmax=100005;
long long mod=1000*1000*1000;
map< pair<int,int>,int > m,much;
pair<int,int> v[nmax];
pair<int,int> el,pp;
vector<int> ad[nmax];
long long en;
int i,compo,j,n,a,b,cc;
int xcord[nmax],ystart[nmax],len[nmax],c[nmax];
long long w[nmax];
long long sum;
void dfs(int x)
{
w[x]=len[x];
for(int i=0;i<ad[x].size();i++)
if(!w[ad[x][i]])
{
dfs(ad[x][i]);
w[x]+=w[ad[x][i]];
}
sum+=1LL*(en-w[x])*w[x];
}
long long solve(int N,int *X,int *Y)
{
en=n=N;
for(int i=0;i<N;i++)
{
v[i+1].x=X[i];
v[i+1].y=Y[i];
}
sort(v+1,v+N+1);
for(i=1;i<=N;i++)
{
m[v[i]]=i;
compo++;
xcord[compo]=v[i].x;
ystart[compo]=v[i].y;
len[compo]=0;
j=i;
while(j<=N&&v[j].x==v[i].x&&v[j].y==ystart[compo]+len[compo])
c[j]=compo,j++,len[compo]++;
j--;
i=j;
}
for(i=1;i<=N;i++)
m[v[i]]=i;
for(i=1;i<=compo;i++)
{
a=xcord[i];b=ystart[i];
for(b=ystart[i];b<ystart[i]+len[i];b++)
{
el={a-1,b};
if(m[el])
{
cc=c[m[el]];
pp={i,cc};
if(!much[pp])
{
ad[i].push_back(cc);
ad[cc].push_back(i);
much[pp]=1;
}
}
}
}
sum=0;
dfs(1);
for(i=1;i<=compo;i++)
ad[i].clear(),w[i]=0;
m.clear();much.clear();compo=0;
return sum;
}
int DistanceSum(int N, int *X, int *Y) {
long long ret= 1LL*((solve(N,X,Y)+solve(N,Y,X)))%mod;
return ret;
}
