#include <bits/stdc++.h>
using namespace std;
const int N = 300005;
int n, m, r[N], u[N], v[N], c[N], fa1[N], fa2[N], siz[N], nxt[N];
set<int> good_keys[N];
map<int, vector<int>> bad_edges[N];
vector<int> good_edges[N];
int find1(int v){return v==fa1[v]?v:fa1[v]=find1(fa1[v]);}
int find2(int v){return v==fa2[v]?v:fa2[v]=find2(fa2[v]);}
void unite1(int u, int v){
u = find1(u), v = find1(v);
if(u==v) return;
fa1[u] = v;
}
void unite2(int u, int v){
u = find2(u), v = find2(v);
if(u==v) return;
fa2[u] = v; siz[v] += siz[u];
good_edges[v].insert(good_edges[v].end(), good_edges[u].begin(), good_edges[u].end());
for(auto x : good_keys[u]){
good_keys[v].insert(x);
if(bad_edges[v].count(x)){
good_edges[v].insert(good_edges[v].end(), bad_edges[v][x].begin(), bad_edges[v][x].end());
bad_edges[v].erase(x);
}
}
for(auto [x, y] : bad_edges[u])
if(good_keys[v].count(x))
good_edges[v].insert(good_edges[v].end(), y.begin(), y.end());
else
bad_edges[v][x].insert(bad_edges[v][x].begin(), y.begin(), y.end());
}
vector<int> find_reachable(vector<int> _r, vector<int> _u, vector<int> _v, vector<int> _c){
n = _r.size(), m = _u.size();
for(int i = 0; i<n; ++i)
r[i] = _r[i];
for(int i = 0; i<m; ++i)
u[i] = _u[i], v[i] = _v[i], c[i] = _c[i];
vector<int> res(n, 0);
priority_queue<pair<int, int>> todo;
for(int i = 0; i<n; ++i)
todo.push({good_edges[i].size(), i});
iota(fa1, fa1+n, 0);
iota(fa2, fa2+n, 0);
memset(nxt, -1, sizeof nxt);
fill(siz, siz+n, 1);
for(int i = 0; i<n; ++i)
good_keys[i].insert(r[i]);
for(int i = 0; i<m; ++i){
if(c[i]!=r[u[i]]) bad_edges[u[i]][c[i]].push_back(v[i]);
else good_edges[u[i]].push_back(v[i]);
if(c[i]!=r[v[i]]) bad_edges[v[i]][c[i]].push_back(u[i]);
else good_edges[v[i]].push_back(u[i]);
}
while(!todo.empty()){
int cur = todo.top().second; todo.pop();
cur = find2(cur);
if(good_edges[cur].empty() || nxt[cur]>=0) continue;
int to = good_edges[cur].back(); to = find2(to);
good_edges[cur].pop_back();
if(cur==to){
todo.push({good_edges[cur].size(), cur});
continue;
}
if(find1(cur)!=find1(to)){
nxt[cur] = to;
unite1(cur, to);
continue;
}
while(to!=cur){
unite2(to, cur);
to = find2(nxt[to]);
} nxt[cur] = -1;
todo.push({good_edges[cur].size(), cur});
}
int ans = 1e9;
for(int i = 0; i<n; ++i)
if(find2(i)==i && nxt[i]==-1)
ans = min(ans, siz[i]);
for(int i = 0; i<n; ++i){
int x = find2(i);
res[i] = (nxt[x]==-1 && siz[x]==ans)?1:0;
}
return res;
}
