#include "islands.h"
#include <variant>
#include<bits/stdc++.h>
#define all(v) v.begin(),v.end()
using namespace std;
using ll = long long;
using P = pair<ll, ll>;
using PP = pair<ll, P>;
const ll n_ = 2e5 + 505, inf = (ll)2e9 * (ll)1e9 + 7, mod = 998244353;
ll n, m, tc = 1, a, b, c, d, sum, x, y, z, base, ans, k;
vector<P>rev[n_];
ll prob[n_],out[n_],checked[n_];
set<P>v[n_],edge[n_];
P To[n_];
variant<bool, std::vector<int>>find_journey(int N, int M, std::vector<int> U, std::vector<int> V) {
n=N,m=M;
for(int i=0;i<m;i++){
out[U[i]]++;
v[U[i]].insert({V[i],i});
rev[V[i]].push_back({U[i],i});
}
fill(prob,prob+n+1,1);
//가능성이 존재한다.
queue<ll>q;
for(int i=0;i<n;i++){
if(v[i].size())continue;
q.push(i);
}
while(q.size()){
a=q.front();
q.pop();
prob[a]=0;
for(auto nxt:rev[a]){
v[nxt.first].erase(nxt);
if(v[nxt.first].size()==0){
q.push(nxt.first);
}
}
}
ll now=0;
vector<int>ret,ret_rev;
while(1){
//cout<<now<<' '<<v[now].size()<<endl;
if(!v[now].size())return false;
if(v[now].size()==1){
ret.push_back((*v[now].begin()).second);
ret_rev.push_back((*v[now].begin()).second);
queue<ll>q;
for(auto nxt:rev[now]){
v[nxt.first].erase({now,nxt.second});
if(v[nxt.first].size()==0)q.push(nxt.first);
}
while(q.size()){
x=q.front();
q.pop();
for(auto nxt:rev[x]){
v[nxt.first].erase({now,nxt.second});
if(v[nxt.first].size()==0)q.push(nxt.first);
}
}
out[now]=0;
now=(*v[now].begin()).first;
}
else{
for(int i=0;i<n;i++){
if(i==now || !v[i].size())continue;
auto cur=*v[i].begin();
//v[i].clear();
edge[i].insert(cur);
//cout<<i<<' '<<cur.first<<' '<<cur.second<<endl;
//v[i].insert(a);
}
auto a=*v[now].begin();
//cout<<a<<' '<<b<<endl;
x=now;
edge[now].clear();
edge[now].insert(a);
for(int i=0;i<n;i++)To[i]={-1,-1};
while(1){
P nxt;
//cout<<x<<endl;
if(edge[x].size()==1){
nxt=*edge[x].begin();
}
else{
for(auto i:edge[x]){
if(i!=To[x])nxt=i;
}
}
To[nxt.first]={x,nxt.second};
//cout<<x<<' '<<nxt.first<<' '<<nxt.second<<endl;
edge[nxt.first].insert({x,nxt.second});
edge[x].erase(nxt);
ret.push_back(nxt.second);
x=nxt.first;
if(x==now)break;
}
edge[now].clear();
auto it=v[now].end();
it--;
//cout<<a<<' '<<b<<endl;
x=now;
edge[now].insert(*it);
for(int i=0;i<n;i++)To[i]={-1,-1};
base=0;
while(1){
P nxt;
//cout<<x<<endl;
if(edge[x].size()==1){
nxt=*edge[x].begin();
}
else{
for(auto i:edge[x]){
if(i!=To[x])nxt=i;
}
}
To[nxt.first]={x,nxt.second};
//cout<<x<<' '<<nxt.first<<' '<<nxt.second<<endl;
edge[nxt.first].insert({x,nxt.second});
edge[x].erase(nxt);
ret.push_back(nxt.second);
x=nxt.first;
if(x==now)break;
}
a=*v[now].begin();
//cout<<a<<' '<<b<<endl;
x=now;
edge[now].clear();
edge[now].insert(a);
for(int i=0;i<n;i++)To[i]={-1,-1};
while(1){
P nxt;
//cout<<x<<endl;
if(edge[x].size()==1){
nxt=*edge[x].begin();
}
else{
for(auto i:edge[x]){
if(i!=To[x])nxt=i;
}
}
To[nxt.first]={x,nxt.second};
//cout<<x<<' '<<nxt.first<<' '<<nxt.second<<endl;
edge[nxt.first].insert({x,nxt.second});
edge[x].erase(nxt);
ret.push_back(nxt.second);
x=nxt.first;
if(x==now)break;
}
edge[now].clear();
it=v[now].end();
it--;
//cout<<a<<' '<<b<<endl;
x=now;
edge[now].insert(*it);
for(int i=0;i<n;i++)To[i]={-1,-1};
base=0;
while(1){
P nxt;
//cout<<x<<endl;
if(edge[x].size()==1){
nxt=*edge[x].begin();
}
else{
for(auto i:edge[x]){
if(i!=To[x])nxt=i;
}
}
To[nxt.first]={x,nxt.second};
//cout<<x<<' '<<nxt.first<<' '<<nxt.second<<endl;
edge[nxt.first].insert({x,nxt.second});
edge[x].erase(nxt);
ret.push_back(nxt.second);
x=nxt.first;
if(x==now)break;
}
break;
}
}
reverse(all(ret_rev));
for(auto i:ret_rev)ret.push_back(i);
return ret;
}
