#include<bits/stdc++.h>
using namespace std;
const int64_t MOD = 1e9;
int64_t n, ans;
void dfs(int64_t nod, int64_t p, vector<vector<int64_t>>& T, vector<int64_t>& SZ, vector<int64_t>& s){
SZ[nod] = s[nod] - 1;
for (auto &son : T[nod]) {
if (son == p) continue;
dfs(son, nod, T, SZ, s);
SZ[nod] += SZ[son];
ans += (n - SZ[son]) * SZ[son];
}
}
int64_t solve(map<int64_t, vector<int64_t>>& mp) {
vector<vector<int64_t>>T;
map<pair<int64_t, int64_t>, int64_t>id;
vector<int64_t>s;
int64_t cnt = 0, idx = 0;
for (auto &it : mp) {
auto &v = it.first;
auto &ap = it.second;
sort(ap.begin(), ap.end());
++idx;
for (int64_t i = 0; i < 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();
if (idx != 1 && id.find({v - 1, ap[i]}) != id.end() && (T[cnt].empty() || id[{v - 1, ap[i]}]) != T[cnt].back()) {
T[cnt].push_back(id[{v - 1, ap[i]}]);
T[id[{v - 1, ap[i]}]].push_back(cnt);
}
}
}
vector<int64_t>SZ(cnt + 1, 0);
ans = 0;
dfs(0, -1, T, SZ, s);
return ans;
}
int DistanceSum(int N, int *X, int *Y) {
n = N;
map<int64_t, vector<int64_t>>lin, col;
for (int64_t i = 0; i < N; ++i) {
col[X[i]].push_back(Y[i]);
lin[Y[i]].push_back(X[i]);
}
return (int)(solve(lin) + solve(col)) % MOD;
}
