#include "islands.h"
#include <bits/stdc++.h>
#define pb push_back
#define ll long long
#define ff first
#define ss second
#include <variant>
#include <vector>
using namespace std;
vector<pair<int, int > >child[5005];
int devuelta[200005];
vector<pair<int, int > > adj[5005];
vector<int>tempRoute;
vector<int>rt;
bool dfs(int node, int parent){
//cout << " at node " << node << endl;
for(int i = 0 ; i < adj[node].size() ; i ++){
if(adj[node][i].ff == parent)continue;
child[node].pb(adj[node][i]);
}
if(child[node].size() >= 2){
int a = child[node][0].ss;
int b = devuelta[child[node][0].ss];
int c = child[node][1].ss;
int d = devuelta[c];
tempRoute = {a, b, c, d, b, a, d, c};
return true;
}
for(auto i : child[node]){
if(dfs(i.ff, node)){
rt.pb(i.ss);
return true;
}
}
return false;
}
int vis[5005];
#define ancestor 1
#define past 2
#define unvisited -1
int used[5005];
bool isCycle[5005];
vector<int>lastNodes;
vector<int>ciclo, ejesCiclo[2], cicloCompleto;
vector<int>finalRoute;
vector<int>finalReal;
bool dfs2(int node){
//cout << " at " << node << endl;
finalRoute.pb(node);
vis[node] = ancestor;
for(int i = 0 ; i < adj[node].size() ; i ++){
if(adj[node][i].ss % 2 == 1)continue;
if(vis[adj[node][i].ff] == ancestor){
used[node] = adj[node][i].ss;
//cout << "found cicle: " << endl;
while(finalRoute.back() != adj[node][i].ff){
ciclo.pb(finalRoute.back());
finalRoute.pop_back();
}
ciclo.pb(finalRoute.back());
finalRoute.pop_back();
for(auto j : ciclo)isCycle[j] = true;
reverse(ciclo.begin(), ciclo.end());
for(auto j : ciclo){
ejesCiclo[0].pb(used[j]);
//cout << "eje ciclo " << used[j] << endl;
ejesCiclo[1].pb(used[j]+1);
}
cicloCompleto = ejesCiclo[0];
for(auto j : ejesCiclo[1])cicloCompleto.pb(j);
vector<int>aux = ejesCiclo[0];
reverse(aux.begin(), aux.end());
for(auto j : aux)cicloCompleto.pb(j);
aux = ejesCiclo[1];
reverse(aux.begin(), aux.end());
for(auto j : aux)cicloCompleto.pb(j);
return true;
}
}
for(int i = 0 ; i < adj[node].size() ; i ++){
if(adj[node][i].ss % 2 == 1)continue;
if(vis[adj[node][i].ff] == past)continue;
// this is unvisited
used[node] = adj[node][i].ss;
if(dfs2(adj[node][i].ff)){
if(!isCycle[node]){
finalReal.pb(adj[node][i].ss);
}
return true;
}
}
vis[node] = past;
finalRoute.pop_back();
return false;
}
std::variant<bool, std::vector<int>> find_journey(
int N, int M, std::vector<int> U, std::vector<int> V) {
int cuenta[N][N];
vector<int>parejas[N][N];
for(int i = 0 ; i < N ; i ++){
for(int j = 0 ; j < N ; j ++){
cuenta[i][j] = 0;
}
}
for(int i = 0 ; i < M ; i ++ ){
cuenta[U[i]][V[i]] ++ ;
parejas[U[i]][V[i]].pb(i);
adj[U[i]].pb({V[i], i});
}
if (N == 2) {
if(cuenta[0][1] >= 2 and cuenta[1][0] >= 1){
int a = parejas[0][1][0];
int b = parejas[1][0][0];
int c = parejas[0][1][1];
vector<int>ans = {a, b, c, a, b, c};
return ans;
}
return false;
}else{
bool case3 = true;
bool case4 = true;
if( M % 2 == 1){
case3 = false;
case4 = false;
}
if(case3 or case4){
for(int i = 0 ; i < M ; i += 2){
if(U[i] != V[i+1] or V[i] != U[i+1] )case3 = false;
if(U[i] != U[i+1] or V[i] != V[i+1] )case4 = false;
devuelta[i] = i+1;
devuelta[i+1] = i;
}
}
if(!case3 and !case4){
//cout << "wrong case : " << endl;
int a = parejas[0][1][0];
int b = parejas[1][0][0];
int c = parejas[0][2][0];
int d = parejas[2][0][0];
vector<int>ans = {a, b, c, d, b, a, d, c};
return ans;
}else if(case3){
//cout << "case 3 " << endl;
if(!dfs(0, -1))return false;
vector<int>ans = rt;
reverse(ans.begin(), ans.end());
for(auto i : tempRoute)ans.pb(i);
for(auto i : rt)ans.pb(i);
return ans;
}else{
//cout << " ! " << endl;
for(int i = 0 ; i < 5005 ; i ++)vis[i] = unvisited;
if(!dfs2(0))return false;
vector<int>ans;
reverse(finalReal.begin(), finalReal.end());
ans = finalReal;
for(auto i : cicloCompleto)ans.pb(i);
reverse(finalReal.begin(), finalReal.end());
for(auto j : finalReal)ans.pb(j);
return ans;
}
}
}
