/*
author: Maksim1744
created: 25.04.2021 21:32:49
*/
#include "bits/stdc++.h"
using namespace std;
using ll = long long;
using ld = long double;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define sum(a) ( accumulate ((a).begin(), (a).end(), 0ll))
#define mine(a) (*min_element((a).begin(), (a).end()))
#define maxe(a) (*max_element((a).begin(), (a).end()))
#define mini(a) ( min_element((a).begin(), (a).end()) - (a).begin())
#define maxi(a) ( max_element((a).begin(), (a).end()) - (a).begin())
#define lowb(a, x) ( lower_bound((a).begin(), (a).end(), (x)) - (a).begin())
#define uppb(a, x) ( upper_bound((a).begin(), (a).end(), (x)) - (a).begin())
template<typename T> vector<T>& operator-- (vector<T> &v){for (auto& i : v) --i; return v;}
template<typename T> vector<T>& operator++ (vector<T> &v){for (auto& i : v) ++i; return v;}
template<typename T> istream& operator>>(istream& is, vector<T> &v){for (auto& i : v) is >> i; return is;}
template<typename T> ostream& operator<<(ostream& os, vector<T> v){for (auto& i : v) os << i << ' '; return os;}
template<typename T, typename U> pair<T,U>& operator-- (pair<T, U> &p){--p.first; --p.second; return p;}
template<typename T, typename U> pair<T,U>& operator++ (pair<T, U> &p){++p.first; ++p.second; return p;}
template<typename T, typename U> istream& operator>>(istream& is, pair<T, U> &p){is >> p.first >> p.second; return is;}
template<typename T, typename U> ostream& operator<<(ostream& os, pair<T, U> p){os << p.first << ' ' << p.second; return os;}
template<typename T, typename U> pair<T,U> operator-(pair<T,U> a, pair<T,U> b){return mp(a.first-b.first, a.second-b.second);}
template<typename T, typename U> pair<T,U> operator+(pair<T,U> a, pair<T,U> b){return mp(a.first+b.first, a.second+b.second);}
template<typename T, typename U> void umin(T& a, U b){if (a > b) a = b;}
template<typename T, typename U> void umax(T& a, U b){if (a < b) a = b;}
#ifdef HOME
#define SHOW_COLORS
#include "C:/C++ libs/print.cpp"
#else
#define show(...) void(0)
#define mclock void(0)
#define shows void(0)
#define debug if (false)
#endif
int DistanceSum(int n, int *X, int *Y) {
vector<pair<int, int>> v;
for (int i = 0; i < n; ++i) {
v.eb(*X, *Y);
++X;
++Y;
}
show(v);
ll ans = 0;
for (int iii = 0; iii < 2; ++iii) {
sort(v.begin(), v.end());
set<pair<int, int>> sv(v.begin(), v.end());
vector<vector<int>> g(n);
int e = 0;
set<pair<int, int>> hor;
for (int i = 0; i < n; ++i) {
auto [x, y] = v[i];
if (sv.count({x, y + 1})) {
int u = lowb(v, mp(x, y + 1));
++e;
g[i].pb(u);
g[u].pb(i);
}
if (sv.count({x + 1, y}) && (!sv.count({x, y + 1}) || !sv.count({x + 1, y + 1}))) {
int u = lowb(v, mp(x + 1, y));
++e;
g[i].pb(u);
g[u].pb(i);
hor.emplace(min(u, i), max(u, i));
}
}
show(g);
assert(e == n - 1);
vector<bool> u(n, false);
vector<int> sz(n);
show(hor);
function<void(int)> dfs = [&](int v) {
u[v] = true;
sz[v] = 1;
for (int k : g[v]) {
if (!u[k]) {
dfs(k);
sz[v] += sz[k];
if (hor.count({min(v, k), max(v, k)})) {
show(sz[k]);
ans += (ll)sz[k] * (n - sz[k]);
}
}
}
};
dfs(0);
show(sz);
show(ans);
for (int i = 0; i < n; ++i) {
swap(v[i].first, v[i].second);
}
}
return ans % (int)1e9;
}
