#include "islands.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define eb emplace_back
using ii = pair<int, int>;
vector<int> cyc, path;
vector<bool> vis;
vector<vector<ii> > adj;
namespace ufds {
vector<int> lnk, sz, num_edges;
void init(int n) {
lnk.resize(n);
iota(lnk.begin(), lnk.end(), 0);
sz.resize(n);
fill(sz.begin(), sz.end(), 1);
num_edges.resize(n);
fill(num_edges.begin(), num_edges.end(), 0);
}
int find(int x) {
if (x == lnk[x]) {
return x;
}
return lnk[x] = find(lnk[x]);
}
void unite(int a, int b) {
a = find(a);
b = find(b);
if (a == b) {
return;
}
if (sz[b] > sz[a]) {
swap(a, b);
}
sz[a] += sz[b];
num_edges[a] += num_edges[b];
lnk[b] = a;
}
};
int dfs(int u) {
vis[u] = 1;
for (auto [v, idx] : adj[u]) {
if (vis[v]) {
cyc.pb(idx);
return v;
}
}
for (auto [v, idx] : adj[u]) {
int tmp = dfs(v);
if (tmp != -1) {
if (tmp == -2) {
path.pb(idx);
} else {
cyc.pb(idx);
if (tmp == u) {
tmp = -2;
}
}
return tmp;
}
}
return -1;
}
variant<bool, vector<int> > find_journey(int N, int M, vector<int> U, vector<int> V) {
ufds::init(N);
adj.resize(N);
for (int i = 0; i < M; i++) {
if (i % 2 == 0) {
adj[U[i]].eb(V[i], i);
ufds::unite(U[i], V[i]);
ufds::num_edges[ufds::find(U[i])]++;
}
}
if (ufds::num_edges[ufds::find(0)] != ufds::sz[ufds::find(0)] - 1) {
vis.resize(N);
dfs(0);
reverse(path.begin(), path.end());
reverse(cyc.begin(), cyc.end());
vector<int> out;
for (int i : path) {
out.pb(i);
}
for (int i : cyc) {
out.pb(i);
}
reverse(cyc.begin(), cyc.end());
for (int i : cyc) {
out.pb(i ^ 1);
}
for (int i : cyc) {
out.pb(i);
}
reverse(cyc.begin(), cyc.end());
for (int i : cyc) {
out.pb(i ^ 1);
}
reverse(cyc.begin(), cyc.end());
reverse(path.begin(), path.end());
for (int i : path) {
out.pb(i);
}
return out;
} else {
vector<int> deg(N, 0);
for (int i = 0; i < M; i++) {
if (ufds::find(U[i]) == ufds::find(0)) {
deg[U[i]]++;
}
}
if (deg[0] > 1 || *max_element(deg.begin(), deg.end()) > 2) {
if (deg[0] > 1) {
vector<int> outgoing;
for (int i = 0; i < M; i++) {
if (U[i] == 0) {
outgoing.pb(i);
}
}
auto ret = {outgoing[0], outgoing[0] ^ 1, outgoing[1], outgoing[1] ^ 1, outgoing[0] ^ 1, outgoing[0], outgoing[1] ^ 1, outgoing[1]};
return ret;
} else {
return true;
}
} else {
return false;
}
}
}
