#include "islands.h"
#include <bits/stdc++.h>
#define pb push_back
#define f first
#define sc second
using namespace std;
typedef long long int ll;
typedef string str;
int n, m, k;
vector<vector<int>> initial_graph;
vector<bool> reachable;
vector<multiset<int>> in(n), out(n);
set<pair<int, int>> st;
void dfs_reachability(int nd){
if(reachable[nd]) return;
reachable[nd] = 1;
for(int x: initial_graph[nd]) dfs_reachability(x);
}
void remove_node(int nd){
st.erase({out[nd].size(), nd});
for(int x: in[nd]){
st.erase({out[x].size(), x});
out[x].erase(out[x].find(nd));
st.insert({out[x].size(), x});
}
for(int x: out[nd]) in[x].erase(in[x].find(nd));
out[nd].clear();
in[nd].clear();
}
void preprocess(const vector<int>& U, const vector<int>& V){
in.resize(n);
out.resize(n);
for(int i = 0; i < m; i++){
if(!reachable[U[i]] || !reachable[V[i]]) continue;
out[U[i]].insert(V[i]);
in[V[i]].insert(U[i]);
}
for(int i = 0; i < n; i++){
st.insert({out[i].size(), i});
}
while(!st.empty() && st.begin()->f == 0) remove_node(st.begin()->sc);
};
variant<bool, vector<int>> find_journey(int _n, int _m, vector<int> U, vector<int> V){
n = _n, m = _m;
initial_graph.assign(n, {});
reachable.assign(n, 0);
for(int i = 0; i < m; i++) initial_graph[U[i]].pb(V[i]);
dfs_reachability(0);
preprocess(U, V);
set<int> cur = {0};
bool ok = 0;
while(!cur.empty()){
for(int x: cur){
if(out[x].size() >= 2) ok = 1;
}
if(ok) break;
set<int> _cur;
for(int x: cur) for(int y: out[x]) _cur.insert(y);
for(int x: cur) remove_node(x);
swap(cur, _cur);
}
return ok;
}
