#include <vector>
#include <bits/stdc++.h>
#ifndef BALBIT
#include "keys.h"
#endif
using namespace std;
#define ll long long
#define pii pair<int, int>
#define f first
#define s second
#define REP(i,n) for (int i = 0; i<n; ++i)
#define REP1(i,n) for (int i = 1; i<=n; ++i)
#define MX(a,b) a = max(a,b)
#define MN(a,b) a = min(a,b)
#define pb push_back
#define SZ(x) (int)(x).size()
#define ALL(x) (x).begin(), (x).end()
#ifdef BALBIT
#define bug(...) cerr<<"#"<<__LINE__<<": "<<#__VA_ARGS__<<"- ", _do(__VA_ARGS__)
template<typename T> void _do(T && x) {cerr<<x<<endl;}
template<typename T, typename ...S> void _do(T && x, S && ...y) {cerr<<x<<", "; _do(y...);}
#else
#define bug(...)
#endif // BALBIT
const int maxn = 3e5+5;
int /*head[maxn], */par[maxn];
int szedges[maxn]; // size of number of edges left
map<int, vector<int> > E[maxn]; // edges not done being worked
set<int> todo[maxn];
set<int> owned[maxn]; // todo is a subset of owned
vector<int> nhere[maxn]; // nodes in this set
int find(int x){return x == par[x]? x : par[x] = find(par[x]);}
inline int WHO(int x){return find(x);}
int dead[maxn]; // 1: this head is dead, 2: this head touches a dead, so it's super dead
int getone(int v) {
while (!todo[v].empty()) {
int c = *todo[v].begin();
if (!E[v].count(c)) {
todo[v].erase(c); continue;
}
// bug(v,c,SZ(E[v][c]));
while (SZ(E[v][c])) {
int go = WHO(E[v][c].back());
E[v][c].pop_back();
if (dead[go]) {
bug(v, go, "dead!");
return -2;
}
if (go != v) bug(v,go);
if (go!=v) return go;
}
E[v].erase(c); todo[v].erase(c);
}
return -1;
}
void mrg(int a, int b, int newhead) {
if (SZ(nhere[a]) < SZ(nhere[b])) swap(a,b);
// a is the greater one
for (int x : owned[b]) {
if (owned[a].insert(x).s) {
if (E[a].count(x)) {
todo[a].insert(x);
}
}
}
for (auto &p : E[b]) {
if (owned[a].count(p.f)) todo[a].insert(p.f); // consider merging todo later (?)
E[a][p.f].insert(E[a][p.f].end(), ALL(p.s));
}
nhere[a].insert(nhere[a].end(), ALL(nhere[b]));
map<int, vector<int> >().swap(E[b]);
set<int>().swap(owned[b]);
set<int>().swap(todo[b]);
vector<int>().swap(nhere[b]);
if (newhead != a) {
assert(newhead == b);
E[a].swap(E[b]);
owned[a].swap(owned[b]);
todo[a].swap(todo[b]);
nhere[a].swap(nhere[b]);
}
}
vector<int> stk;
bool instk[maxn];
void runstack(){
while (!stk.empty()) {
int v = stk.back();
int to = getone(v);
assert(to != v);
if (to == -1) {
dead[v] = 1;
instk[v] = 0;
stk.pop_back();
to = -2;
}
if (to == -2) {
for (int e : stk) {
dead[e] = 2;
instk[e] = 0;
}
stk.clear();
return;
}
if (!instk[to]) {
instk[to] = 1;
stk.pb(to);
continue;
}else{
while (stk.back() != to) {
int last = stk.back(); instk[last] = 0; stk.pop_back();
int pl = stk.back();
mrg(last, pl, pl);
}
}
}
}
std::vector<int> find_reachable(std::vector<int> r, std::vector<int> u, std::vector<int> v, std::vector<int> c) {
std::vector<int> ans(r.size(), 1);
int n = SZ(r);
int m = SZ(u);
REP(i,m) {
int U = u[i], V = v[i], C = c[i];
REP(barbar, 2) {
E[U][C].pb(V);
swap(U,V);
}
}
REP(i,n) {
par[i] = i;
nhere[i].pb(i);
owned[i].insert(r[i]);
if (E[i].count(r[i])) {
todo[i].insert(r[i]);
bug(i, "todo", r[i]);
}
}
REP(i,n) {
if (!dead[i]) {
instk[i] = 1;
stk.pb(i);
runstack();
}
}
vector<int> raw(n, n+1);
REP(i,n) {
int FI = find(i);
bug(i, dead[i], FI);
if (FI == i && dead[i] != 2) {
for (int e : nhere[i]) {
raw[e] = SZ(nhere[i]);
}
}
}
REP(i,n) {
bug(i, raw[i]);
}
int mne = *min_element(ALL(raw));
for (int &e : raw) {
e = (e==mne?1:0);
}
return raw;
}
#ifdef BALBIT
signed main(){
// vector<int> yay = find_reachable({0, 1, 1, 2, 2, 1, 2},
// {0, 0, 1, 1, 2, 3, 3, 4, 4, 5},
// {1, 2, 2, 3, 3, 4, 5, 5, 6, 6},
// {0, 0, 1, 0, 0, 1, 2, 0, 2, 1});
vector<int> yay = find_reachable({0, 0, 0}, {0}, {1}, {0});
for (int t : yay) bug(t);
}
#endif
