#include <bits/stdc++.h>
#include <bits/extc++.h>
#define StarBurstStream ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define iter(a) a.begin(), a.end()
#define riter(a) a.rbegin(), a.rend()
#define lsort(a) sort(iter(a))
#define gsort(a) sort(riter(a))
#define pb(a) push_back(a)
#define eb(a) emplace_back(a)
#define pf(a) push_front(a)
#define ef(a) emplace_front(a)
#define pob pop_back()
#define pof pop_front()
#define mp(a, b) make_pair(a, b)
#define F first
#define S second
#define mt make_tuple
#define gt(t, i) get<i>(t)
#define tomax(a, b) ((a) = max((a), (b)))
#define tomin(a, b) ((a) = min((a), (b)))
#define topos(a) ((a) = (((a) % MOD + MOD) % MOD))
#define uni(a) a.resize(unique(iter(a)) - a.begin())
#define printv(a, b) {bool pvaspace=false; \
for(auto pva : a){ \
if(pvaspace) b << " "; pvaspace=true;\
b << pva;\
}\
b << "\n";}
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>;
const ll MOD = 1000000007;
const ll MAX = 2147483647;
template<typename A, typename B>
ostream& operator<<(ostream& o, pair<A, B> p){
return o << '(' << p.F << ',' << p.S << ')';
}
ll ifloor(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a < 0) return (a - b + 1) / b;
else return a / b;
}
ll iceil(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a > 0) return (a + b - 1) / b;
else return a / b;
}
int n, m;
vector<set<pii>> g, todo; // color, to
vector<vector<pii>> tg; // to, color
vector<int> dsu, sz;
vector<int> dsu2;
vector<int> f;
vector<set<int>> key;
vector<int> r, U, V, C;
void init(){
g.resize(n);
tg.resize(n);
dsu.resize(n);
sz.resize(n, 1);
iota(iter(dsu), 0);
f.resize(n);
iota(iter(f), 0);
key.resize(n);
todo.resize(n);
dsu2.resize(n);
iota(iter(dsu2), 0);
}
int findDSU(int a){
if(dsu[a] != a) dsu[a] = findDSU(dsu[a]);
return dsu[a];
}
void unionDSU(int a, int b){
a = findDSU(a);
b = findDSU(b);
if(dsu[a] == dsu[b]) return;
/*if(sz[a] < sz[b]){
swap(sz[a], sz[b]);
g[a].swap(g[b]);
todo[a].swap(todo[b]);
key[a].swap(key[b]);
}*/
//if(key[a].size() < key[b].size()) key[a].swap(key[b]);
/*for(int i : key[b]){
set<pii>::iterator it;
while(it = g[a].lower_bound(mp(i, -1)),
it != g[a].end() && it->F == i){
todo[a].insert(*it);
g[a].erase(it);
}
key[a].insert(i);
}
for(pii i : todo[b]) todo[a].insert(i);
for(pii i : g[b]){
if(key[a].find(i.F) != key[a].end()){
todo[a].insert(i);
}
else{
g[a].insert(i);
}
}*/
for(int i : key[b]) key[a].insert(i);
for(pii i : todo[b]) todo[a].insert(i);
for(pii i : g[b]) g[a].insert(i);
for(pii i : g[a]){
if(key[a].find(i.F) != key[a].end()){
todo[a].insert(i);
}
}
for(pii i : todo[a]) g[a].erase(i);
//check
/*for(pii i : g[a]){
assert(key[a].find(i.F) == key[a].end());
}
for(pii i : todo[a]){
assert(key[a].find(i.F) != key[a].end());
}*/
sz[a] += sz[b];
dsu[b] = a;
}
int findDSU2(int a){
if(dsu2[a] != a) dsu2[a] = findDSU2(dsu2[a]);
return dsu2[a];
}
void unionDSU2(int a, int b){
a = findDSU2(a);
b = findDSU2(b);
dsu2[b] = a;
}
bool sameWCC(int a, int b){
return findDSU2(a) == findDSU2(b);
}
bool sameSCC(int a, int b){
return findDSU(a) == findDSU(b);
}
int outver(int a){
int p = findDSU(a);
int v = f[p];
return findDSU(v);
}
void setout(int a, int v){
int p = findDSU(a);
f[p] = v;
}
bool isroot(int a){
a = findDSU(a);
return outver(a) == a;
}
vector<bool> checkans(int s){
vector<vector<int>> can(n);
vector<bool> ok(n), vst(n);
queue<int> q;
q.push(s);
vst[s] = true;
int cnt = 0;
vector<int> ans;
while(!q.empty()){
int now = q.front();
cnt++;
ans.eb(now);
q.pop();
if(!ok[r[now]]){
ok[r[now]] = true;
for(int i : can[r[now]]){
if(vst[i]) continue;
vst[i] = true;
q.push(i);
}
}
for(pii i : tg[now]){
if(!ok[i.S]){
can[i.S].eb(i.F);
continue;
}
if(vst[i.F]) continue;
vst[i.F] = true;
q.push(i.F);
}
}
return vst;
}
vector<int> find_reachable(vector<int> _r, vector<int> _U, vector<int> _V, vector<int> _C){
r = _r; U = _U; V = _V; C = _C;
n = r.size();
m = U.size();
init();
for(int i = 0; i < m; i++){
int u = U[i], v = V[i], c = C[i];
sz[u]++; sz[v]++;
tg[u].eb(mp(v, c));
tg[v].eb(mp(u, c));
if(c == r[u]) todo[u].insert(mp(c, v));
else g[u].insert(mp(c, v));
if(c == r[v]) todo[v].insert(mp(c, u));
else g[v].insert(mp(c, u));
}
for(int i = 0; i < n; i++){
key[i].insert(r[i]);
if(!todo[i].empty()) f[i] = todo[i].begin()->S;
}
//printv(f, cerr);
for(int i = 0; i < n; i++){
unionDSU2(i, f[i]);
}
vector<bool> vst(n);
auto findcycle = [&](int s){
vector<int> path;
while(!vst[s]){
vst[s] = true;
path.eb(s);
s = f[s];
}
bool ok = false;
for(int i : path){
if(i == s) ok = true;
}
if(!ok) return;
while(path.back() != s){
unionDSU(s, path.back());
path.pob;
}
};
for(int i = 0; i < n; i++){
if(!vst[i]) findcycle(i);
}
/*cerr << "cycle\n";
for(int i = 0; i < n; i++) cerr << findDSU(i) << " ";
cerr << "\n";*/
auto solve = [&](int rt){
rt = findDSU(rt);
while(!todo[rt].empty()){
pii i = *todo[rt].begin();
todo[rt].erase(todo[rt].begin());
int to = findDSU(i.S);
if(!sameWCC(rt, to)){
setout(rt, to);
unionDSU2(rt, to);
break;
}
while(to != rt){
unionDSU(rt, to);
to = outver(to);
}
}
};
for(int i = 0; i < n; i++){
if(findDSU(i) != i) continue;
if(isroot(i)) solve(i);
}
for(int i = 0; i < n; i++){
if(!isroot(i)) continue;
/*vector<bool> v = checkans(i);
for(int j = 0; j < n; j++){
if(!v[j]) continue;
if(sameSCC(i, j)) continue;
vector<bool> t = checkans(j);
assert(sameWCC(i, j));
}*/
int p = findDSU(i);
for(int j = 0; j < n; j++){
if(findDSU(j) != p) continue;
for(pii e : tg[j]){
if(key[p].find(e.S) == key[p].end()) continue;
assert(sameSCC(j, e.F) || g[p].find(mp(e.S, e.F)) != g[p].end());
}
}
}
vector<int> cnt(n);
for(int i = 0; i < n; i++){
if(isroot(i)) cnt[findDSU(i)]++;
}
int mn = MAX;
for(int i = 0; i < n; i++){
if(findDSU(i) == i && isroot(i)) mn = min(mn, cnt[i]);
}
/*cerr << "end\n";
for(int i = 0; i < n; i++) cerr << findDSU(i) << " ";
cerr << "\n";
for(int i = 0; i < n; i++) cerr << findDSU(f[findDSU(i)]) << " ";
cerr << "\n";
printv(cnt, cerr);*/
vector<int> ans(n);
for(int i = 0; i < n; i++){
int p = findDSU(i);
if(!isroot(i)) continue;
//int tmp = checkans(i);
//assert(cnt[p] <= tmp);
if(cnt[p] == mn) ans[i] = 1;
}
return ans;
}
