#include <bits/stdc++.h>
using namespace std;
#define ll long long
const ll MOD=1000000000;
bool vis[100005];
vector<ll>adj[100005];
map<pair<ll,ll>,bool>mp;
map<pair<ll,ll>,bool>exist;
map<pair<ll,ll>,ll>assigned;
ll nodesize[100005], subsize[100005], dist[100005];
vector<pair<ll,ll> > nds;
ll totdist=0,ans=0;
void dfs(ll s){
vis[s]=1;
subsize[s]=nodesize[s];
for(auto& u: adj[s]){
if(!vis[u]){
dist[u]=dist[s]+1;
dfs(u);
subsize[s]+=subsize[u];
}
}
}
void compute(ll s){
vis[s]=1;
ans+=nodesize[s]*totdist;
for(auto& u: adj[s]){
if(!vis[u]){
totdist+=(subsize[1]-subsize[u]);
totdist-=subsize[u];
compute(u);
totdist-=(subsize[1]-subsize[u]);
totdist+=subsize[u];
}
}
}
void clear(){
for(int i=1;i<=100000;i++){
vis[i]=0; adj[i].clear(); nodesize[i]=0; subsize[i]=0; dist[i]=0;
}
mp.clear(); exist.clear(); assigned.clear(); nds.clear();
totdist=0;
}
int DistanceSum(int N, int *X, int *Y){
for(int i=0;i<N;i++){
mp[{X[i],Y[i]}]=1;
nds.push_back({X[i],Y[i]});
}
ll assign=1;
sort(nds.begin(),nds.end());
for(int i=0;i<nds.size();i++){
if(i==0) assigned[nds[i]]=assign, nodesize[assign]++;
else{
if(nds[i].first==nds[i-1].first&&nds[i].second==nds[i-1].second+1){
assigned[nds[i]]=assign; nodesize[assign]++;
}
else{
assigned[nds[i]]=assign+1; nodesize[assign+1]++; assign++;
}
}
}
for(int i=0;i<nds.size();i++){
if(mp[{nds[i].first+1,nds[i].second}]){
if(!exist[{assigned[nds[i]],assigned[{nds[i].first+1,nds[i].second}]}]){
ll u=assigned[nds[i]]; ll v=assigned[{nds[i].first+1,nds[i].second}];
adj[u].push_back(v); adj[v].push_back(u);
exist[{u,v}]=exist[{v,u}]=1;
}
}
}
dist[1]=0;
dfs(1);
for(int i=1;i<=100000;i++) vis[i]=0;
for(int i=1;i<=assign;i++){
totdist+=nodesize[i]*dist[i];
}
compute(1);
clear();
for(int i=0;i<N;i++){
mp[{Y[i],X[i]}]=1;
nds.push_back({Y[i],X[i]});
}
assign=1;
sort(nds.begin(),nds.end());
for(int i=0;i<nds.size();i++){
if(i==0) assigned[nds[i]]=assign, nodesize[assign]++;
else{
if(nds[i].first==nds[i-1].first&&nds[i].second==nds[i-1].second+1){
assigned[nds[i]]=assign; nodesize[assign]++;
}
else{
assigned[nds[i]]=assign+1; nodesize[assign+1]++; assign++;
}
}
}
for(int i=0;i<nds.size();i++){
if(mp[{nds[i].first+1,nds[i].second}]){
if(!exist[{assigned[nds[i]],assigned[{nds[i].first+1,nds[i].second}]}]){
ll u=assigned[nds[i]]; ll v=assigned[{nds[i].first+1,nds[i].second}];
adj[u].push_back(v); adj[v].push_back(u);
exist[{u,v}]=exist[{v,u}]=1;
}
}
}
dfs(1);
for(int i=1;i<=100000;i++) vis[i]=0;
for(int i=1;i<=assign;i++){
totdist+=nodesize[i]*dist[i];
}
compute(1);
clear();
ans/=2;
return (ans%MOD);
}
