#include <bits/stdc++.h>
using namespace std;
const int n_max = 300500;
const int k_max = 300500;
vector<pair<int,int>> adj[n_max];
bool visited[n_max];
int original_key[n_max];
int has_key[k_max];
int cc[n_max];
vector<int> blocked[k_max];
int ufds[n_max];
int findset(int x) {
while(ufds[x] != x) {
x = ufds[x] = ufds[ufds[x]];
}
return x;
}
void unionset(int x, int y) {
ufds[findset(x)] = findset(y);
}
void reset() {
for(int i=0; i<n_max; i++) {
visited[i] = false;
}
}
vector<int> ans2;
vector<int> keylist;
vector<int> v2;
vector<pair<int,int>> delayed_merge;
bool change = false;
void compress(int a, int b) {
change = true;
//unionset(a, b);
delayed_merge.emplace_back(a,b);
for(int k: keylist) {
has_key[k] = false;
blocked[k].clear();
}
keylist.clear();
}
int zz = 1e9;
void explore(int x) {
keylist.clear();
x = findset(x);
if(visited[x]) return;
visited[x] = true;
queue<int> q;
q.push(x);
v2.push_back(x);
int cc_count = 1;
while(!q.empty()) {
const int next = q.front();
ans2.push_back(next);
if(findset(next) != findset(x)) { // different component, merge, cleanup and bye
compress(x, next);
//assert(findset(x)!=x);
return;
}
q.pop();
for(pair<int,int> p: adj[next]) {
if(has_key[p.first]) { // i have the key
if(!visited[p.second]) { // put in the queue
visited[p.second] = true;
q.push(p.second);
v2.push_back(p.second);
cc_count++;
} else if(findset(p.second) != findset(x)) {
compress(x, p.second);
return;
}
} else { // it may be unblocked later
//assert(p.first < k_max);
blocked[p.first].push_back(p.second);
keylist.push_back(p.first);
}
}
int new_key = original_key[next];
has_key[new_key] = true;
keylist.push_back(new_key);
for(int i: blocked[new_key]) {
if(!visited[i]) {
visited[i] = true;
q.push(i);
v2.push_back(i);
cc_count++;
} else if(findset(i) != findset(x)) {
compress(x, i);
return;
}
}
blocked[new_key].clear();
}
cc[x] = cc_count;
zz = min(zz, cc_count);
for(int k: keylist) {
has_key[k] = false;
blocked[k].clear();
}
keylist.clear();
return;
}
vector<int> find_reachable(vector<int> r, vector<int> u, vector<int> v, vector<int> c) {
int m = c.size();
int n = r.size();
for(int i=0; i<n; i++) {
original_key[i] = r[i];
ufds[i] = i;
}
for(int i=0; i<m; i++) {
adj[u[i]].emplace_back(c[i], v[i]);
adj[v[i]].emplace_back(c[i], u[i]);
}
for(int i=0; i<20; i++) {
reset();
change = false;
for(int j=0; j<n; j++) {
if(j == findset(j)) {
explore(j);
for(int a: v2) {
visited[a] = false;
}
v2.clear();
}
}
for(pair<int,int> pp: delayed_merge) {
unionset(pp.first, pp.second);
}
if(!change) break;
}
int a = n+1;
for(int i=0; i<n; i++) {
if(i==findset(i)) {
a = min(a, cc[i]);
assert(a>0);
}
}
vector<int> ans(n);
ans2.clear();
reset();
for(int i=0; i<n; i++) {
if(i==findset(i) and cc[findset(i)] == a) {
explore(i);
}
}
for(int i: ans2) {
ans[i] = 1;
}
return ans;
}
