#include "bits/stdc++.h"
#include "keys.h"
using namespace std;
using ll = long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
template<typename T>
int sz(const T &a){return int(a.size());}
const int MN=3e5+1;
struct dsu {
pii t[MN];
void reset(int n) {
for (int i = 0; i <= n; i++)t[i] = {i, 1};
}
int find(int a) {
if (t[a].first == a)return a;
return t[a].first = find(t[a].first);
}
bool uni(int a, int b) {
int ap = find(a), bp = find(b);
if (ap == bp)return false;
if (t[ap].second < t[bp].second)swap(ap, bp);
t[bp].first = ap;
t[ap].second += t[bp].second;
return true;
}
}cn,cc;
int parent[MN],n,m;
vector<int> totake[MN];
map<int,vector<int>> notkeyed[MN];
set<int> keys[MN];
priority_queue<pii> tocheck;
void merge(int a, int b){
cn.uni(a,b);
int par=cn.find(a);
int ch=(a==par?b:a);
parent[par]=-1;
totake[par].insert(totake[par].end(),totake[ch].begin(),totake[ch].end());
for(auto x:keys[ch]){
keys[par].insert(x);
if(notkeyed[par].count(x)){
totake[par].insert(totake[par].end(),notkeyed[par][x].begin(),notkeyed[par][x].end());
notkeyed[par].erase(x);
}
}
for(auto x:notkeyed[ch]){
if(keys[par].count(x.first))totake[par].insert(totake[par].end(),x.second.begin(),x.second.end());
else notkeyed[par][x.first].insert(notkeyed[par][x.first].end(),x.second.begin(),x.second.end());
}
}
vector<int> find_reachable(vector<int> r, vector<int> u, vector<int> v, vector<int> c){
n=sz(r),m=sz(u);
for(int i=0;i<m;i++)notkeyed[u[i]][c[i]].push_back(v[i]),notkeyed[v[i]][c[i]].push_back(u[i]);
vector<int> ans(n);
cn.reset(n),cc.reset(n);
for(int i=0;i<n;i++){
parent[i]=-1;
keys[i].insert(r[i]);
if(notkeyed[i].count(r[i])){
totake[i].insert(totake[i].end(),notkeyed[i][r[i]].begin(),notkeyed[i][r[i]].end());
notkeyed[i].erase(r[i]);
}
tocheck.push({sz(totake[i]),i});
}
while(sz(tocheck)){
auto cur=tocheck.top().second;
tocheck.pop();
cur=cn.find(cur);
if(parent[cur]!=-1)continue;
if(!sz(totake[cur]))continue;
int oth=cn.find(totake[cur].back());
totake[cur].pop_back();
if(oth==cur){
tocheck.push({sz(totake[cur]),cur});
continue;
}
if(cc.find(oth)!=cc.find(cur)){
parent[cur]=oth;
cc.uni(oth,cur);
}
else{
vector<int> route;
while(oth!=cur){
route.push_back(oth);
oth=cn.find(parent[oth]);
}
while(sz(route)){
merge(cur,route.back());
cur=cn.find(cur);
route.pop_back();
}
tocheck.push({sz(totake[cur]),cur});
}
}
int misize=INT_MAX;
for(int i=0;i<n;i++){
if(cn.find(i)==i){
if(parent[i]==-1){
misize=min(misize,cn.t[i].second);
}
}
}
for(int i=0;i<n;i++)ans[i]=(cn.t[cn.find(i)].second==misize&&parent[cn.find(i)]==-1);
return ans;
}
//int main(){
// cin.tie(NULL);
// ios_base::sync_with_stdio(false);
// int nn,mm;
// cin>>nn>>mm;
// vector<int> kkeys(nn),ledge(mm),redge(nn),cedge(nn);
// for(int i=0;i<nn;i++){
// cin>>kkeys[i];
// }
// for(int i=0;i<mm;i++){
// cin>>ledge[i]>>redge[i]>>cedge[i];
// }
// auto te=find_reachable(kkeys,ledge,redge,cedge);
// for(auto x:te)printf("%d ",x);
// return 0;
//}
