#include <bits/stdc++.h>
const int MOD = 1e9;
using namespace std;
int n;
int solve(map<int, vector<int>>& mp) {
vector<vector<int>> T;
map<pair<int, int>, int> id;
vector<int> s;
int cnt = -1;
int idx = 0;
for (auto &[v, ap] : mp) {
sort(ap.begin(), ap.end());
++idx;
for (int i = 0; i < (int)ap.size(); ++i) {
if (i == 0 || ap[i] != ap[i - 1] + 1) {
++cnt;
T.push_back({});
s.push_back(0);
}
id[{v, ap[i]}] = cnt;
++s.back();
auto it_prev = id.find({v - 1, ap[i]});
if (idx != 1 && it_prev != id.end()) {
int neigh = it_prev->second;
if (cnt < (int)T.size() && neigh < (int)T.size()) {
if (T[cnt].empty() || neigh != T[cnt].back()) {
T[cnt].push_back(neigh);
T[neigh].push_back(cnt);
}
}
}
}
}
vector<int> SZ(cnt + 1, 0);
long long ans = 0;
function<void(int, int)> dfs = [&](int nod, int p) {
SZ[nod] = s[nod];
for (int son : T[nod]) {
if (son == p) continue;
dfs(son, nod);
SZ[nod] += SZ[son];
ans += 1LL * (n - SZ[son]) * SZ[son];
}
};
dfs(0, -1);
return (int)(ans % MOD);
}
int DistanceSum(int N, int *X, int *Y) {
n = N;
map<int, vector<int>> lin, col;
for (int i = 0; i < n; ++i) {
col[X[i]].push_back(Y[i]);
lin[Y[i]].push_back(X[i]);
}
return (solve(lin) + solve(col)) % MOD;
}
