This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
// In the name of Allah
#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef complex<ld> cld;
#define all(x) (x).begin(),(x).end()
#define len(x) ((ll) (x).size())
#define F first
#define S second
#define pb push_back
#define sep ' '
#define endl '\n'
#define Mp make_pair
#define kill(x) cout << x << '\n', exit(0)
#define set_dec(x) cout << fixed << setprecision(x);
#define file_io(x,y) freopen(x, "r", stdin); freopen(y, "w", stdout);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int maxn = 1e5 + 7;
const int mod = 1e9;
int n;
set<int> adj[maxn];
pii A[maxn]; map<pii, int> ind;
int p[maxn], sz[maxn];
ll res;
int get(int a) {
return (p[a] == a) ? a : p[a] = get(p[a]);
}
void merge(int a, int b) {
a = get(a); b = get(b);
if (a == b) return ;
if (sz[a] > sz[b]) swap(a, b);
p[a] = b; sz[b] += sz[a]; sz[a] = 0;
}
void dfs(int v, int p = -1) {
for (int u : adj[v]) {
if (u == p) continue;
dfs(u, v);
sz[v] += sz[u];
res += 1ll * sz[u] * (n - sz[u]) % mod;
res %= mod;
}
}
int DistanceSum(int N, int X[], int Y[]) {
n = N; ind.clear();
for (int i = 0; i < n; i++) {
A[i] = Mp(X[i], Y[i]);
ind[A[i]] = i;
}
res = 0;
iota(p, p + n, 0); fill(sz, sz + n, 1);
for (int i = 0; i < n; i++) adj[i].clear();
for (int i = 0; i < n; i++) {
int x = A[i].F, y = A[i].S;
for (int x1 : {x - 1, x + 1}) {
if (ind.find(Mp(x1, y)) == ind.end()) continue;
int j = ind[Mp(x1, y)];
merge(i, j);
}
}
for (int i = 0; i < n; i++) {
int x = A[i].F, y = A[i].S;
for (int y1 : {y - 1, y + 1}) {
if (ind.find(Mp(x, y1)) == ind.end()) continue;
int j = ind[Mp(x, y1)];
int u = get(i), v = get(j);
adj[u].insert(v); adj[v].insert(u);
}
}
dfs(get(0));
iota(p, p + n, 0); fill(sz, sz + n, 1);
for (int i = 0; i < n; i++) adj[i].clear();
for (int i = 0; i < n; i++) {
int x = A[i].F, y = A[i].S;
for (int y1 : {y - 1, y + 1}) {
if (ind.find(Mp(x, y1)) == ind.end()) continue;
int j = ind[Mp(x, y1)];
merge(i, j);
}
}
for (int i = 0; i < n; i++) {
int x = A[i].F, y = A[i].S;
for (int x1 : {x - 1, x + 1}) {
if (ind.find(Mp(x1, y)) == ind.end()) continue;
int j = ind[Mp(x1, y)];
int u = get(i), v = get(j);
adj[u].insert(v); adj[v].insert(u);
}
}
dfs(get(0));
return res;
}
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