#include "keys.h"
#include <bits/stdc++.h>
#define pb push_back
#define f first
#define sc second
using namespace std;
typedef long long int ll;
typedef string str;
struct dsu{
int n;
vector<int> sz, p;
vector<bool> bl;
dsu(int _n): n(_n){
sz.resize(n, 1);
bl.assign(n, 0);
p.resize(n);
for(int i = 0; i < n; i++) p[i] = i;
}
int get(int x){
if(p[x] != x) p[x] = get(p[x]);
return p[x];
}
void unite(int a, int b){
a = get(a), b = get(b);
if(a == b) return;
if(sz[b] > sz[a]) swap(a, b);
sz[a]+=sz[b];
sz[b] = 0;
p[b] = a;
bl[a] = 1;
}
void reset_bl(){
bl.assign(n, 0);
}
};
dsu ds(0);
int n, m;
vector<int> r;
vector<vector<pair<int, int>>> graph;
vector<bool> candidate;
vector<vector<int>> waiting_list;
vector<bool> has_key;
vector<bool> bl;
void reduce_candidates(int s){
vector<int> has_key_v, waiting_list_v, reachable;
has_key[r[s]] = 1;
has_key_v.pb(r[s]);
queue<int> Q;
Q.push(s);
while(!Q.empty()){
int nd = Q.front(); Q.pop();
if(bl[nd]) continue;
bl[nd] = 1;
reachable.pb(nd);
if(candidate[nd] && nd != s){
candidate[s] = 0;
ds.unite(nd, s);
break;
}
if(!has_key[r[nd]]){
for(int x: waiting_list[r[nd]]) if(!bl[x]) Q.push(x);
waiting_list[r[nd]].clear();
has_key[r[nd]] = 1;
has_key_v.pb(r[nd]);
}
for(auto [x, c]: graph[nd]) if(!bl[x]){
if(has_key[c]) Q.push(x);
else{
waiting_list[c].pb(x);
waiting_list_v.pb(c);
}
}
}
for(int x: has_key_v) has_key[x] = 0;
for(int x: waiting_list_v) waiting_list[x].clear();
for(int x: reachable) bl[x] = 0;
}
int P;
vector<int> ans, p;
void bfs(int s){
vector<int> has_key_v, waiting_list_v, reachable;
has_key[r[s]] = 1;
has_key_v.pb(r[s]);
queue<int> Q;
Q.push(s);
while(!Q.empty()){
int nd = Q.front(); Q.pop();
if(bl[nd]) continue;
bl[nd] = 1;
reachable.pb(nd);
if(!has_key[r[nd]]){
for(int x: waiting_list[r[nd]]) if(!bl[x]) Q.push(x);
waiting_list[r[nd]].clear();
has_key[r[nd]] = 1;
has_key_v.pb(r[nd]);
}
for(auto [x, c]: graph[nd]) if(!bl[x]){
if(has_key[c]) Q.push(x);
else{
waiting_list[c].pb(x);
waiting_list_v.pb(c);
}
}
}
for(int x: has_key_v) has_key[x] = 0;
for(int x: waiting_list_v) waiting_list[x].clear();
for(int x: reachable) bl[x] = 0;
if(reachable.size() < P){
P = reachable.size();
for(int x: p) ans[x] = 0;
p = reachable;
for(int x: reachable) ans[x] = 1;
}
else if(reachable.size() == P){
p.insert(p.begin(), reachable.begin(), reachable.end());
for(int x: reachable) ans[x] = 1;
}
}
vector<int> find_reachable(vector<int> _r, vector<int> U, vector<int> V, vector<int> C){
swap(r, _r);
n = r.size(), m = U.size();
graph.resize(n);
candidate.assign(n, 1);
has_key.assign(n, 0);
bl.assign(n, 0);
waiting_list.resize(n);
ans.resize(n);
P = n;
ds = dsu(n);
for(int i = 0; i < m; i++){
graph[U[i]].pb({V[i], C[i]});
graph[V[i]].pb({U[i], C[i]});
}
vector<bool> called(n, 0);
for(int k = 0; k < 100; k++){
for(int s = 0; s < n; s++) if(candidate[s] && !ds.bl[ds.get(s)] && !called[s]){
called[s] = 1;
reduce_candidates(s);
}
ds.reset_bl();
}
for(int s = 0; s < n; s++) if(candidate[s]) bfs(s);
return ans;
}
