#define here cerr<<"===========================================\n"
#define dbg(x) cerr<<#x<<": "<<x<<endl;
#include <bits/stdc++.h>
#define ld double
#define ll int
#define ull unsigned long long
#define llinf 100000000000000000LL // 10^17
#define iinf 2000000000 // 2*10^9
#define pb push_back
#define popb pop_back
#define fi first
#define sc second
#define endl '\n'
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pld pair<ld,ld>
#define all(a) a.begin(),a.end()
#define ceri(a,l,r) {cerr<<#a<<": ";for(ll i_ = l;i_<=r;i_++) cerr<<a[i_]<< " ";cerr<<endl;}
#define cer(a) {cerr<<#a<<": ";for(ll x_ : a) cerr<<x_<< " ";cerr<<endl;}
#define si(a) (ll)(a.size())
using namespace std;
#define maxn 300005
ll n,m;
vector<pll> g[maxn];
set<ll> key[maxn];
map<ll,vector<ll> > mp[maxn];
vector<ll> use[maxn];
ll a[maxn];
vector<ll> ans;
ll dsu[maxn],sz[maxn];
ll root(ll x){
while(x!=dsu[x]){
dsu[x] = dsu[dsu[x]];
x = dsu[x];
}
return x;
}
ll par[maxn];
void upd(ll x,ll y){
x = root(x); y = root(y);
ll fa = par[y];
if(sz[x]<sz[y]) swap(x,y);
dsu[y] = x;
sz[x]+=sz[y];
for(ll z : use[y]) use[x].pb(z);
for(auto it : mp[y]){
for(ll z : it.sc){
if(key[x].count(it.fi)==0){
mp[x][it.fi].pb(z);
}else{
use[x].pb(z);
}
}
}
for(ll z : key[y]){
while(mp[x][z].size()){
use[x].pb(mp[x][z].back());
mp[x][z].popb();
}
key[x].insert(z);
}
par[x] = fa;
vector<ll>().swap(use[y]);
map<ll,vector<ll> >().swap(mp[y]);
set<ll>().swap(key[y]);
}
bool check0(){
bool bad = 0;
for(ll i = 1;i<=n;i++){
ll cnt = 0;
for(pll p : g[i]){
if(p.sc==a[i]) cnt++;
}
if(cnt==0) ans[i] = 1,bad = 1;
}
return bad;
}
ll dsu2[maxn];
ll sz2[maxn];
ll root2(ll u){
while(u!=dsu2[u]){
dsu2[u] = dsu2[dsu2[u]];
u = dsu2[u];
}
return u;
}
void upd2(ll x,ll y){
x = root2(x); y = root2(y);
if(sz2[x]>sz2[y]) swap(x,y);
dsu2[x] = y;
sz2[y]+=sz2[x];
}
vector<int> find_reachable(vector<int> r,vector<int> u,vector<int> v,vector<int> c) {
n = si(r);
m = si(u);
for(ll i = 1;i<=n;i++) a[i] = r[i-1];
for(ll i = 1;i<=m;i++){
ll x,y,w;
x = u[i-1];
y = v[i-1];
w = c[i-1];
x++; y++;
g[x].pb({y,w});
g[y].pb({x,w});
}
ans.resize(n+1);
if(check0()){
reverse(all(ans));
ans.popb();
reverse(all(ans));
return ans;
}
iota(dsu+1,dsu+1+n,1);
iota(dsu2+1,dsu2+1+n,1);
fill(sz+1,sz+1+n,1);
fill(sz2+1,sz2+1+n,1);
for(ll i = 1;i<=n;i++){
for(pll p : g[i]){
ll j = p.fi,z = p.sc;
if(z==a[i]){
use[i].pb(j);
}else{
mp[i][z].pb(j);
}
}
key[i].insert(a[i]);
}
vector<ll> roots;
for(ll i = 1;i<=n;i++) roots.pb(i);
ll mn = llinf;
while(roots.size()){
ll i = roots.back();
i = root(i);
roots.popb();
while(use[i].size()){
ll j = use[i].back();
use[i].popb();
j = root(j);
if(root(i)==root(j)) continue;
if(root2(i)==root2(j)){
while(par[j]){
upd(j,par[j]);
j = root(j);
}
i = root(i);
}else{
par[i] = j;
upd2(i,j);
break;
}
}
if(!par[i]) mn = min(mn,sz[i]);
}
for(ll i = 1;i<=n;i++) ans[i] = (mn==sz[root(i)]);
reverse(all(ans));
ans.popb();
reverse(all(ans));
return ans;
}
/**
4 5
0 1 1 2
0 1 0
0 2 0
1 2 1
1 3 0
3 1 2
**/
