#include <bits/stdc++.h>
using namespace std;
struct pair_hash
{
int operator() (const pair<int, int> p) const {
return hash<int>()(p.first) ^ hash<int>()(p.second);
}
};
int N, C;
vector<int> graph[100005];
int sz[100005];
unordered_set<pair<int, int>, pair_hash> st;
unordered_map<pair<int, int>, pair<int, int>, pair_hash> par;
vector<pair<int, int>> coords;
unordered_map<pair<int, int>, int, pair_hash> who;
pair<int, int> getrt(pair<int, int> n){
return par[n] = (par[n] == n ? n : getrt(par[n]));
}
void dfs(int n, int p){
for(int e : graph[n]){
if(e != p){
dfs(e, n);
sz[n] += sz[e];
}
}
}
void build(){
for(auto p : coords){
par[p] = p;
if(st.count({p.first-1, p.second})){
par[getrt({p.first-1, p.second})] = p;
}
if(st.count({p.first+1, p.second})){
par[getrt({p.first+1, p.second})] = p;
}
st.insert({p.first, p.second});
}
C = 0;
for(int i = 0; i<N; i++){
if(par[coords[i]] == coords[i]){
who[coords[i]] = ++C;
sz[C] = 0;
}
}
for(auto p : coords){
sz[who[getrt(p)]]++;
}
for(auto p : coords){
auto n = who[getrt(p)];
if(st.count({p.first, p.second-1})){
auto a = who[getrt({p.first, p.second-1})];
graph[a].push_back(n);
}
if(st.count({p.first, p.second+1})){
auto a = who[getrt({p.first, p.second+1})];
graph[a].push_back(n);
}
}
for(int i = 1; i<=C; i++){
sort(graph[i].begin(), graph[i].end());
graph[i].erase(unique(graph[i].begin(), graph[i].end()), graph[i].end());
}
}
long long calc(int *X, int *Y){
for(int i = 0; i<N; i++){
coords.push_back({X[i], Y[i]});
}
build();
dfs(1, 0);
long long ans = 0;
for(int i = 1; i<=C; i++){
ans += 1LL*sz[i]*(N-sz[i]);
ans %= 1000000000;
graph[i].clear();
}
coords.clear();
par.clear();
st.clear();
who.clear();
return ans;
}
int DistanceSum(int NN, int *X, int *Y){
N = NN;
long long ret = calc(X, Y);
ret += calc(Y, X);
return ret%1000000000;
}
/*
int main(){
cin.sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int NNN;
cin >> NNN;
int X[NNN], Y[NNN];
for(int i = 0; i<NNN; i++){
cin >> X[i] >> Y[i];
}
cout << DistanceSum(NNN, X, Y) << endl;
}
*/
