#include <iostream>
#include <vector>
#include <set>
#include <cassert>
#include <queue>
#include <map>
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(xs) xs.begin(), xs.end()
#define pb push_back
#define _1 first
#define _2 second
#define INF 1145141919
#define MOD 1000000000
using namespace std;
int DX[4] = {-1, 0, 1, 0};
int DY[4] = {0, -1, 0, 1};
typedef pair<int, int> P;
map<P, int> mp;
int D[2000][2000];
int DistanceSum(int N, int *X, int *Y) {
if (N > 2000) abort();
rep(i, N) {
mp[P(X[i], Y[i])] = i;
}
rep(i, N) rep(j, N) D[i][j] = INF;
rep(s, N) {
queue<int> q;
q.push(s);
D[s][s] = 0;
while (!q.empty()) {
int x = q.front();
q.pop();
rep(k, 4) {
P tp = P(X[x]+DX[k], Y[x]+DY[k]);
if (mp.find(tp) != mp.end()) {
int t = mp[tp];
if (D[s][t] == INF) {
D[s][t] = D[s][x]+1;
q.push(t);
}
}
}
}
}
int s = 0;
rep(i, N) rep(j, i) s = (s + D[i][j]) % MOD;
return s;
}
