#include <bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define bl ' '
#define endl '\n'
#define all(v) (v).begin(), (v).end()
#define comp(v) (v).erase(unique(all(v)), (v).end())
#define lbd(v,x) lower_bound(all(v), (x))-(v).begin()
#define ubd(v,x) upper_bound(all(v), (x))-(v).begin()
typedef long long ll;
typedef pair<int, int> pi;
typedef pair<pi, int> pii;
typedef pair<int, pi> ipi;
typedef pair<pi, pi> pipi;
typedef pair<ll, ll> pll;
const int MAXN = 100100*3;
const ll MOD = 998244353;
const ll INF = 1e16;
vector<pi> adj[MAXN];
int nx[MAXN], idx[MAXN];
//vector<int> pv[MAXN];
set<int> col[MAXN];
set<pi> edge[MAXN];
int cnt[MAXN];
vector<int> cnct, pnt;
int root(int x, vector<int>& par) { return par[x]==x?x:par[x]=root(par[x], par); }
void merge(int x, int y, vector<int>& par) {
x = root(x, par), y = root(y, par);
if(x^y) par[y] = x;
}
void merge_stl(int a, int b, bool flag) {
merge(a, b, pnt);
if(flag) {
nx[a] = -1;
vector<pi> tmp;
for(int c : col[b]) {
while(nx[a]==-1) {
auto it = edge[a].lower_bound(pi(c,0));
if(it == edge[a].end() || it->ff != c) break;
int x = it->ss;
if(root(x, pnt)==a || root(x, pnt)==b) {
edge[a].erase(it); continue;
}
nx[a] = x;
}
} for(auto [c,x] : edge[b]) { if(nx[a]!=-1) break;
if(root(x,pnt)==a || root(x,pnt)==b) {
tmp.push_back(pi(c,x)); continue;
}
if(col[a].find(c)!=col[a].end()) {
nx[a] = x; break;
}
} for(auto x:tmp) edge[b].erase(x);
}
cnt[a] += cnt[b];
for(int x : col[b]) {
col[a].insert(x);
} for(auto x : edge[b]) {
edge[a].insert(x);
} col[b].clear(); edge[b].clear();
}
queue<vector<int> > cycle;
vector<pi> cand;
vector<int> ans;
int vst[MAXN]; // -1: already vst, 0: not vst, 1: current vst
vector<int> track;
void dfs(int here) {
vst[here] = 1;
track.push_back(here);
int there = nx[here];
if(there == -1) return;
if(vst[there] == -1) return;
if(vst[there] == 1) {
vector<int> v;
int i=0; while(track[i]^there) i++;
for(; i<track.size(); i++) v.push_back(track[i]);
cycle.push(v); return;
} dfs(there);
}
std::vector<int> find_reachable(std::vector<int> r, std::vector<int> u, std::vector<int> v, std::vector<int> c) {
int n = r.size(), m = u.size();
for(int i=0; i<m; i++) {
adj[u[i]].push_back(pi(v[i], c[i]));
adj[v[i]].push_back(pi(u[i], c[i]));
} for(int i=0; i<n; i++) {
col[i].insert(r[i]);
cnt[i] = 1;
for(auto [j,w] : adj[i]) {
edge[i].insert(pi(w, j));
}
}
cnct.resize(n); pnt.resize(n); ans.resize(n);
for(int i=0; i<n; i++) cnct[i] = pnt[i] = i;
// nx init
bool chk = 0;
memset(nx, -1, sizeof nx);
for(int i=0; i<n; i++) {
for(int &j = idx[i]; j<adj[i].size(); j++) {
int x = adj[i][j].ff, w = adj[i][j].ss;
if(w == r[i]) {
nx[i] = x; //pv[x].push_back(i);
merge(i, nx[i], cnct); break;
}
} if(nx[i] == -1) {
chk=1; ans[i]=1;
}
} if(chk) return ans;
// find cycle
for(int i=0; i<n; i++) {
if(!vst[i]) {
track.clear();
dfs(i);
for(int x:track) vst[x]=-1;
}
}
while(cycle.size()) {
// union cycle, update new nx
vector<int> v = cycle.front(); cycle.pop();
for(int i=1; i<v.size(); i++) {
if(col[v[0]].size()+edge[v[0]].size() < col[v[i]].size()+edge[v[i]].size()) swap(v[0], v[i]);
merge_stl(v[0], v[i], i+1==v.size());
}
if(nx[v[0]] == -1) {
cand.push_back(pi(cnt[v[0]], v[0]));
continue;
}
// update new cycle
vector<int> tmp;
vector<int> new_cycle;
int x = root(v[0], cnct), y = root(nx[v[0]], cnct);
if(x == y) {
new_cycle.push_back(v[0]);
for(int here = root(nx[v[0]], pnt); here != v[0]; here=root(nx[here], pnt))
new_cycle.push_back(here);
} else {
merge(x, y, cnct);
}
// push new cycle
if(new_cycle.size() > 1) cycle.push(new_cycle);
}
// return smallest root
sort(all(cand)); int mn = cand[0].ff;
for(auto x:cand) { assert(pnt[x.ss]==x.ss);
if(x.ff==mn) ans[x.ss]=1;
} for(int i=0; i<n; i++) {
ans[i] = ans[root(i, pnt)];
}
return ans;
}
