#include <bits/stdc++.h>
#define FOR(i, x, y) for (int i = x; i < y; i++)
typedef long long ll;
using namespace std;
const ll MOD = 1e9;
pair<int, int> sorted[2][100001];
vector<int> graphs[2][100001];
ll num_blocks[2][100001], dp[2][100001];
int x = 0, y = 0;
map<pair<int, int>, int> x_cmp, y_cmp;
int DistanceSum(int N, int *X, int *Y) {
FOR(i, 0, N) {
sorted[0][i] = {X[i], Y[i]};
sorted[1][i] = {Y[i], X[i]};
}
sort(sorted[0], sorted[0] + N);
sort(sorted[1], sorted[1] + N);
FOR(i, 0, N) {
if (i == 0 || sorted[0][i].second - sorted[0][i - 1].second != 1 || sorted[0][i].first != sorted[0][i - 1].first) {
y++;
if (y_cmp[{sorted[0][i].first - 1, sorted[0][i].second}])
graphs[0][y_cmp[{sorted[0][i].first - 1, sorted[0][i].second}]].push_back(y);
}
num_blocks[0][y]++;
y_cmp[sorted[0][i]] = y;
}
FOR(i, 0, N) {
if (i == 0 || sorted[1][i].second - sorted[1][i - 1].second != 1 || sorted[1][i].first != sorted[1][i - 1].first) {
x++;
if (x_cmp[{sorted[1][i].first - 1, sorted[1][i].second}])
graphs[1][x_cmp[{sorted[1][i].first - 1, sorted[1][i].second}]].push_back(x);
}
num_blocks[1][x]++;
x_cmp[sorted[1][i]] = x;
}
ll ans = 0;
FOR(i, 1, y + 1) {
ans = (ans + dp[0][i]) % MOD;
for (int j : graphs[0][i])
dp[0][j] = (dp[0][j] + dp[0][i] * num_blocks[0][i] + num_blocks[0][i] * num_blocks[0][j]) % MOD;
}
FOR(i, 1, x + 1) {
ans = (ans + dp[1][i]) % MOD;
for (int j : graphs[1][i])
dp[1][j] = (dp[1][j] + dp[1][i] * num_blocks[1][i] + num_blocks[1][i] * num_blocks[1][j]) % MOD;
}
return (int)ans;
}
