#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
#define MASK(i) (1ULL << (i))
#define GETBIT(mask, i) (((mask) >> (i)) & 1)
#define ALL(v) (v).begin(), (v).end()
ll max(ll a, ll b){return (a > b) ? a : b;}
ll min(ll a, ll b){return (a < b) ? a : b;}
ll gcd(ll a, ll b){return __gcd(a, b);}
ll lcm(ll a, ll b){return a / gcd(a, b) * b;}
ll LASTBIT(ll mask){return (mask) & (-mask);}
int pop_cnt(ull mask){return __builtin_popcountll(mask);}
int ctz(ull mask){return __builtin_ctzll(mask);}
int logOf(ull mask){return 63 - __builtin_clzll(mask);}
mt19937_64 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
ll rngesus(ll l, ll r){return l + (ull) rng() % (r - l + 1);}
double rngesus_d(double l, double r){
double cur = rngesus(0, MASK(60) - 1);
cur /= MASK(60) - 1;
return l + cur * (r - l);
}
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
template <class T>
void remove_dup(vector<T> &a){
sort(ALL(a));
a.resize(unique(ALL(a)) - a.begin());
}
const int N = 3e5 + 69, INF = 1e9 + 69;
int n, m;
vector<pair<int, int>> graph[N];
bool add_set(vector<int> &S, vector<bool> &mark, int c){
if (mark[c] == false){
mark[c] = true;
S.push_back(c);
return true;
}
return false;
}
void clear_set(vector<int> &S, vector<bool> &mark){
for(int i: S) mark[i] = false;
S.clear();
}
vector<int> find_reachable(vector<int> r, vector<int> U, vector<int> V, vector<int> C) {
n = r.size(), m = U.size();
int mi = INF;
vector<int> optimal_vertice_set;
for(int i = 0; i < m; ++i){
int u= U[i], v = V[i], c = C[i];
graph[u].push_back({v, c});
graph[v].push_back({u, c});
}
for(int i = 0; i < n; ++i) shuffle(ALL(graph[i]), rng);
vector<int> perm(n);
for(int i = 0; i < n; ++i) perm[i] = i;
shuffle(ALL(perm), rng);
vector<int> p(n, 1);
vector<vector<int>> reached(n);
vector<bool> color_mark(n), vertice_mark(n);
vector<int> reached_color, reached_vertices;
vector<vector<int>> waiting_edge(n);
int operation_cnt = 0;
deque<int> st;
for(int i: perm){
add_set(reached_vertices, vertice_mark, i);
st.clear();
st.push_back(i);
vector<int> color_used;
while(st.size()){
int u = st.front(); st.pop_front();
add_set(reached_color, color_mark, r[u]);
bool stop_signal = false;
for(int v: waiting_edge[r[u]]){
if (add_set(reached_vertices, vertice_mark, v)) {
if (p[v] > mi) {
p[i] = p[v];
stop_signal = true;
break;
}
else if (binary_search(ALL(reached[v]), i)){
p[i] = p[v];
stop_signal = true;
break;
}
st.push_back(v);
}
}
if (stop_signal || p[i] > mi) break;
waiting_edge[r[u]].clear();
for(pair<int, int> v: graph[u]) {
operation_cnt++;
if (color_mark[v.second]) {
if (add_set(reached_vertices, vertice_mark, v.first)){
if (p[v.first] > mi) {
p[i] = p[v.first];
stop_signal = true;
break;
}
else if (binary_search(ALL(reached[v.first]), i)){
p[i] = p[v.first];
stop_signal = true;
break;
}
st.push_back(v.first);
}
}
else{
if (vertice_mark[v.first] == false){
color_used.push_back(v.second);
waiting_edge[v.second].push_back(v.first);
}
}
}
maximize(p[i], reached_vertices.size());
if (stop_signal || p[i] > mi) break;
}
reached[i] = reached_vertices;
sort(ALL(reached[i]));
minimize(mi, p[i]);
for(int i: color_used) waiting_edge[i].clear();
clear_set(reached_color, color_mark);
clear_set(reached_vertices, vertice_mark);
}
cerr << operation_cnt << " " << mi << "\n";
vector<int> ans(n);
for(int i = 0; i < n; ++i) {
if (mi == p[i]){
ans[i] = true;
}
}
return ans;
}
