//khodaya khodet komak kon
# include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair <int, int> pii;
typedef pair <pii, int> ppi;
typedef pair <int, pii> pip;
typedef pair <pii, pii> ppp;
typedef pair <ll, ll> pll;
# define A first
# define B second
# define endl '\n'
# define sep ' '
# define all(x) x.begin(), x.end()
# define kill(x) return cout << x << endl, 0
# define SZ(x) int(x.size())
# define lc id << 1
# define rc id << 1 | 1
# define InTheNameOfGod ios::sync_with_stdio(0);cin.tie(0); cout.tie(0);
ll power(ll a, ll b, ll md) {return (!b ? 1 : (b & 1 ? a * power(a * a % md, b / 2, md) % md : power(a * a % md, b / 2, md) % md));}
const int xn = 1e5 + 10;
const int xm = - 20 + 10;
const int sq = 320;
const int inf = 1e9 + 10;
const ll INF = 1e18 + 10;
const ld eps = 1e-15;
const int mod = 1e9;// + 7;//998244353;
const int base = 257;
int n, par[xn], P[xn], sz[xn], dsu[xn], H[xn];
pii a[xn];
ll ans;
map <pii, int> mp;
vector <int> adj[xn], vec[xn];
vector <pii> E, G[2][xn];
bool mark[xn];
int get_root(int v){
if (v == par[v])
return v;
return par[v] = get_root(par[v]);
}
void merge(int v, int u){
v = get_root(v);
u = get_root(u);
par[u] = v;
dsu[v] += dsu[u];
}
void preDFS(int v){
mark[v] = true;
for (int u : adj[v]){
if (mark[u]){
if (H[v] <= H[u] + 1)
continue;
int res = v;
while (get_root(res) != get_root(u)){
res = get_root(res);
merge(P[res], res);
}
continue;
}
P[u] = v;
H[u] = H[v] + 1;
preDFS(u);
}
}
void add_edge(int v, int u){
adj[v].push_back(u);
adj[u].push_back(v);
E.push_back({v, u});
}
bool cmp1(int v, int u){
return a[v].A < a[u].A;
}
bool cmp2(int v, int u){
return a[v].B < a[u].B;
}
void DFS(int v, int id, int p = - 1){
sz[v] = 1;
for (pii U : G[id][v]){
int u = U.A, w = U.B;
if (u == p)
continue;
DFS(u, id, v);
ans += 1ll * w * sz[u] % mod * (n - sz[u]) % mod;
ans %= mod;
sz[v] += sz[u];
}
}
ll DistanceSum(int N, int *X, int *Y){
n = N;
ans = 0;
mp.clear(), E.clear();
for (int i = 1; i <= n; ++ i){
adj[i].clear(), vec[i].clear();
G[0][i].clear(), G[1][i].clear();
H[i] = mark[i] = 0;
}
for (int i = 1; i <= n; ++ i)
a[i] = {X[i - 1], Y[i - 1]}, mp[a[i]] = i;
for (int i = 1; i <= n; ++ i){
int x = a[i].A, y = a[i].B;
if (mp[{x - 1, y}])
add_edge(i, mp[{x - 1, y}]);
if (mp[{x, y - 1}])
add_edge(i, mp[{x, y - 1}]);
par[i] = i, dsu[i] = 1;
}
preDFS(1);
for (int i = 1; i <= n; ++ i)
vec[get_root(i)].push_back(i);
for (pii e : E){
int v = e.A, u = e.B, pv, pu;
pv = get_root(v);
pu = get_root(u);
if (pv == pu)
continue;
G[0][v].push_back({u, 1});
G[0][u].push_back({v, 1});
G[1][v].push_back({u, 0});
G[1][u].push_back({v, 0});
}
for (int i = 1; i <= n; ++ i){
if (i != get_root(i))
continue;
sort(all(vec[i]), cmp1);
for (int j = 1; j < SZ(vec[i]); ++ j){
int v = vec[i][j], u = vec[i][j - 1];
G[0][v].push_back({u, (a[v].A - a[u].A)});
G[0][u].push_back({v, (a[v].A - a[u].A)});
}
sort(all(vec[i]), cmp2);
for (int j = 1; j < SZ(vec[i]); ++ j){
int v = vec[i][j], u = vec[i][j - 1];
G[1][v].push_back({u, (a[v].B - a[u].B)});
G[1][u].push_back({v, (a[v].B - a[u].B)});
}
}
for (int i = 0; i < 2; ++ i)
DFS(1, i);
return ans;
}
/*
int main(){
//InTheNameOfGod;
int X[11] = {2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5};
int Y[11] = {5, 6, 3, 6, 3, 4, 5, 6, 3, 4, 6};
cout << DistanceSum(11, X, Y) << endl;
return 0;
}
*/
