#include <bits/stdc++.h>
using namespace std;
#define f first
#define s second
//#define int long long
#define pii pair <int, int>
#define pb push_back
const int N = 3e5 + 5, inf = 1e9, mod = 1e9;
int n, x[N], y[N], mnx, mny, nx, ny;
long long ans,sz[N];
vector <int> vx[N], vy[N],v[N];
map <int, int> vert[N], vert1[N];
void dfs(int a, int p) {
for (int to : v[a]) {
if (to == p) continue;
dfs(to, a);
sz[a] += sz[to];
}
ans += sz[a] * (n - sz[a]) % mod; ans %= mod;
}
int DistanceSum(int N, int *X, int *Y) {
n = N;
int mnx = inf, mny = inf;
for (int i = 1; i <= n; i++) {
x[i] = X[i - 1]; y[i] = Y[i - 1];
mnx = min(mnx, x[i]); mny = min(mny, y[i]);
}
for (int i = 1; i <= n; i++) {
x[i] -= mnx; y[i] -= mny;
nx = max(nx, x[i]); ny = max(ny, y[i]);
}
for (int i = 1; i <= n; i++) {
vx[x[i]].pb(y[i]);
}
int cnt = 0;
for (int i = 0; i <= nx; i++) {
sort(vx[i].begin(), vx[i].end());
for (int j = 0; j < vx[i].size(); j++) {
int cy = vx[i][j];
if (j == 0 || cy != vx[i][j - 1] + 1) cnt++;
sz[cnt]++;
vert[i][cy] = cnt;
}
}
for (int i = 1; i <= nx; i++) {
for (int j = 0; j < vx[i].size(); j++) {
int cy = vx[i][j];
if (vert[i - 1][cy]) {
int a = vert[i - 1][cy]; int b = vert[i][cy];
if (v[a].size() && v[a].back() == b) continue;
v[a].pb(b); v[b].pb(a);
}
}
}
dfs(1, 0);
for (int i = 1; i <= cnt; i++) {
v[i].clear(); sz[i] = 0;
}
for (int i = 1; i <= n; i++) {
vy[y[i]].pb(x[i]);
}
cnt = 0;
for (int i = 0; i <= ny; i++) {
sort(vy[i].begin(), vy[i].end());
for (int j = 0; j < vy[i].size(); j++) {
int cx = vy[i][j];
if (j == 0 || cx != vy[i][j - 1] + 1) cnt++;
sz[cnt]++;
vert1[cx][i] = cnt;
}
}
for (int i = 1; i <= ny; i++) {
for (int j = 0; j < vy[i].size(); j++) {
int cx = vy[i][j];
if (vert1[cx][i - 1]) {
int a = vert1[cx][i - 1]; int b = vert1[cx][i];
if (v[a].size() && v[a].back() == b) continue;
v[a].pb(b); v[b].pb(a);
}
}
}
dfs(1, 0);
return ans;
}
