#include<bits/stdc++.h>
using namespace std;
#define mp make_pair
#define INF 10000000
#define MOD 1000000000
#define MID ((l+r)/2)
#define HASHMOD 2305843009213693951
#define ll long long
#define ull unsigned long long
#define F first
#define S second
typedef pair<int, int> ii;
typedef pair<ii, int> iii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef map<int, int> mii;
#define EPS 1e-6
#define FOR(i,n) for(int i=0;i<((int)(n));i++)
#define FORi(i,a,b) for(int i=((int)(a));i<((int)(b));i++)
#define FOA(v, a) for(auto v : a)
vi a, b;
ii diag[4] = {{0,-1}, {0,1}, {-1,0}, {1,0}};
ll paris(ii x){
return ((ll)x.F)*(INT_MAX+1ll) + x.S;
}
ii unparis(ll x){
return {x/(INT_MAX+1ll), x%(INT_MAX+1ll)};
}
int DistanceSum(int n, int *X, int *Y) {
if(n<=2000){
unordered_map<ll, vector<ll> > adj;
FOR(i,n){
FORi(j,i+1,n){
if(abs(X[i]-X[j])+abs(Y[i]-Y[j])==1){
adj[paris({X[i], Y[i]})].push_back(paris({X[j], Y[j]}));
adj[paris({X[j], Y[j]})].push_back(paris({X[i], Y[i]}));
}
}
}
int ans=0;
FOR(i,n){
// bfs from i
unordered_set<ll> used;
queue<ll> q;
q.push(paris({X[i], Y[i]}));
used.insert(paris({X[i], Y[i]}));
q.push(-1);
int d=0;
//cout<<X[i]<<" "<<Y[i]<<": "<<endl;
while(q.size()>1){
ll t = q.front();
q.pop();
if(t==-1){
d++;
q.push(-1);
continue;
}
//cout<<t.F<<" "<<t.S<<" "<<d<<endl;
ans+=d;
ans%=MOD;
FOA(x, adj[t]){
if(!used.count(x)){
q.push(x);
used.insert(x);
}
}
}
}
return ans/2;
}
ll ans=0;
int minx=INT_MAX, maxx=0;
int miny=INT_MAX, maxy=0;
FOR(i,n){
minx = min(minx, X[i]);
maxx = max(maxx, X[i]);
miny = min(miny, Y[i]);
maxy = max(maxy, Y[i]);
}
int c=maxx-minx+1;
int r=maxy-miny+1;
FOR(i,n){
X[i]-=minx;
Y[i]-=miny;
if(X[i]>0 && Y[i]>0){
int xx = X[i];
int yy = Y[i];
ans+=(xx+yy - 2)*xx*yy/2;
ans+=(xx*yy)*2;
ans%=MOD;
}
if(X[i]>0 && Y[i]<r-1){
int xx = X[i];
int yy = r - Y[i]-1;
ans+=(xx+yy - 2)*xx*yy/2;
ans+=(xx*yy)*2;
ans%=MOD;
}
if(X[i]<c-1 && Y[i]>0){
int xx = c - X[i]-1;
int yy = Y[i];
ans+=(xx+yy - 2)*xx*yy/2;
ans+=(xx*yy)*2;
ans%=MOD;
}
if(X[i]<c-1 && Y[i]<r-1){
int xx = c - X[i]-1;
int yy = r - Y[i]-1;
ans+=(xx+yy - 2)*xx*yy/2;
ans+=(xx*yy)*2;
ans%=MOD;
}
ans+=X[i]*(X[i]+1)/2;
ans%=MOD;
ans+=Y[i]*(Y[i]+1)/2;
ans%=MOD;
ans+=(c-X[i]-1)*(c-X[i])/2;
ans%=MOD;
ans+=(r-Y[i]-1)*(r-Y[i])/2;
ans%=MOD;
}
return ans/2;
}
