#include "keys.h"
#include <bits/stdc++.h>
using namespace std;
vector<int> find_reachable(vector<int> r, vector<int> U, vector<int> V, vector<int> C) {
int n = r.size(), mn = INT_MAX;
vector<vector<array<int, 2>>> G(n);
for (int i = 0; i < U.size(); i++) {
G[U[i]].push_back({V[i], C[i]});
G[V[i]].push_back({U[i], C[i]});
}
vector<int> ans, perm(n), vis(n, -1), visc(n, -1);
vector<vector<int>> cand(n);
iota(perm.begin(), perm.end(), 0);
mt19937 rnd(time(0));
for (int i = 0; i < n; i++) {
shuffle(G[i].begin(), G[i].end(), rnd);
}
shuffle(perm.begin(), perm.end(), rnd);
queue<int> Q;
vector<bool> solved(n);
vector<int> ver, col;
for (int x : perm) {
ver = {x}, col.clear();
while (!Q.empty()) Q.pop();
Q.push(x), vis[x] = x, solved[x] = 1;
while (!Q.empty()) {
int u = Q.front(); Q.pop();
if (visc[r[u]] ^ x) {
for (int v : cand[r[u]]) if (vis[v] ^ x) {
ver.push_back(v), Q.push(v), vis[v] = x;
if (solved[v] || ver.size() > mn) goto nxt;
}
visc[r[u]] = x;
}
for (auto &e : G[u]) if (vis[e[0]] ^ x) {
if (visc[e[1]] == x) {
ver.push_back(e[0]), Q.push(e[0]), vis[e[0]] = x;
if (solved[e[0]] || ver.size() > mn) goto nxt;
} else {
col.push_back(e[1]);
if (solved[e[0]]) cand[e[1]].clear();
cand[e[1]].push_back(e[0]);
}
}
}
if (ver.size() < mn) mn = ver.size(), ans = ver;
else copy(ver.begin(), ver.end(), back_inserter(ans));
nxt:;
for (int c : col) cand[c].clear();
}
vector<int> res(n);
for (int x : ans) res[x] = 1;
return res;
}
