#include <bits/stdc++.h>
using namespace std;
struct Solver {
int n;
vector<vector<int>> active;
vector<multimap<int, int>> inactive;
vector<set<int>> cols;
vector<int> parent, df, link, bad;
Solver(int n) :
n(n), active(n), inactive(n), cols(n),
parent(n, -1), df(n, -1), link(n, -1), bad(n, 0) {}
void AddEdge(int u, int v, int c) {
if (cols[u].count(c))
active[u].push_back(v);
else
inactive[u].emplace(c, v);
}
void AddCol(int u, int c) {
while (true) {
auto it = inactive[u].find(c);
if (it == inactive[u].end()) break;
active[u].push_back(it->second);
inactive[u].erase(it);
}
cols[u].insert(c);
}
void merge(int node, int anc) {
while (true) {
node = find(node);
anc = find(anc);
if (node == anc) return;
int par = find(parent[node]);
assert(par != node);
link[node] = par;
if (active[node].size() + cols[node].size() + inactive[node].size() >
active[par].size() + cols[par].size() + inactive[par].size()) {
swap(active[node], active[par]);
swap(cols[node], cols[par]);
swap(inactive[node], inactive[par]);
swap(bad[node], bad[par]);
}
for (auto x : cols[node])
AddCol(par, x);
for (auto x : active[node])
active[par].push_back(x);
for (auto [c, x] : inactive[node])
AddEdge(par, x, c);
bad[par] |= bad[node];
inactive[node].clear();
active[node].clear();
cols[node].clear();
bad[node] = 0;
}
}
int find(int x) {
if (link[x] == -1) return x;
return link[x] = find(link[x]);
}
void dfs(int node, int par) {
df[node] = 0;
parent[node] = par;
while (true) {
node = find(node);
if (active[node].empty()) break;
int vec = active[node].back();
active[node].pop_back();
vec = find(vec);
if (vec == node) continue;
if (df[vec] == -1) {
dfs(vec, node);
if (find(vec) != find(node))
bad[find(node)] = 1;
} else if (df[vec] == 0) {
merge(node, vec);
} else {
bad[find(node)] = 1;
}
}
df[node] = 1;
}
vector<int> Solve() {
for (int i = 0; i < n; ++i)
if (find(i) == i && df[i] == -1)
dfs(i, -1);
vector<int> ret(n, 0), sz(n, 0);
int min_sz = 1e9;
for (int i = 0; i < n; ++i) {
if (bad[find(i)])
continue;
sz[find(i)] += 1;
}
for (int i = 0; i < n; ++i) {
if (bad[find(i)])
continue;
min_sz = min(min_sz, sz[find(i)]);
}
for (int i = 0; i < n; ++i) {
if (bad[find(i)])
continue;
ret[i] = (sz[find(i)] == min_sz);
}
return ret;
}
};
vector<int> find_reachable(
vector<int> r, vector<int> u,
vector<int> v, vector<int> c) {
int n = r.size(), m = u.size();
Solver S(n);
for (int i = 0; i < n; ++i)
S.AddCol(i, r[i]);
for (int i = 0; i < m; ++i) {
S.AddEdge(u[i], v[i], c[i]);
S.AddEdge(v[i], u[i], c[i]);
}
return S.Solve();
}
