#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;
int DistanceSum(int n, int *X, int *Y) {
int 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;
}
