#include <bits/stdc++.h>
#define forn(i, a, b) for(int i = int (a); i <= int(b); ++ i)
#define fora(i, a, b) for(int i = int (a); i >= int(b); -- i)
#define pb push_back
#define fi first
#define se second
#define mp make_pair
using namespace std;
typedef pair<int, int> pii;
typedef long long ll;
int mx[4] = {0, 0, 1, -1};
int my[4] = {1, -1, 0, 0};
map<pii, pii> mapa;
queue<pii> q;
int mod = 1e9;
int res = 0;
void bfs(int ind){
pii act;
while(!q.empty()){
act = q.front();
q.pop();
forn(i, 0, 3){
if(mapa.count(mp(act.fi + mx[i], act.se + my[i]))){
if(mapa[mp(act.fi + mx[i], act.se + my[i])].fi == -1){
mapa[mp(act.fi + mx[i], act.se + my[i])].fi = mapa[mp(act.fi, act.se)].fi + 1;
if(mapa[mp(act.fi + mx[i], act.se + my[i])].se > ind){
res += mapa[mp(act.fi + mx[i], act.se + my[i])].fi;
res %= mod;
}
q.push(mp(act.fi + mx[i], act.se + my[i]));
}
}
}
}
}
int DistanceSum(int N, int *X, int *Y) {
forn(i, 0, N - 1){
mapa[mp(X[i], Y[i])] = mp(0, i);
forn(j, 0, N - 1){
if(j != i){
mapa[mp(X[j], Y[j])] = mp(-1, j);
}
}
q.push(mp(X[i], Y[i]));
bfs(i);
}
return res;
}
