#include "worldmap.h"
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
template<typename T>
bool assign_min(T& a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template<typename T>
bool assign_max(T& a, T b) {
if (a < b) {
a = b;
return true;
}
return false;
}
int n, m;
vector<vector<int>> g, neigh, full;
vector<int> t, sz;
int root(int x) {
if (t[x] == x) {
return x;
}
return t[x] = root(t[x]);
}
void join(int a, int b) {
a = root(a);
b = root(b);
if (a == b) {
return;
}
if (sz[a] < sz[b]) {
swap(a, b);
}
t[b] = a;
sz[a] += sz[b];
}
vector<vector<int>> c;
void solve(int u, vector<int> kids) {
vector<int> l;
l.push_back(u);
for (auto v : kids) {
l.push_back(v);
l.push_back(u);
}
c.push_back(l);
}
void dfs(int u, int p = 0) {
c.push_back({u});
solve(u, full[u]);
c.push_back({u});
for (auto v : g[u]) {
if (v != p) {
dfs(v, u);
c.push_back({u});
}
}
}
vector<vector<int>> reshape(vector<vector<int>> c) {
int k = c.size();
for (int i = 0; i < c.size(); i++) {
k = max(k, (int) c[i].size());
}
for (int i = 0; i < c.size(); i++) {
while (c[i].size() < k) {
c[i].push_back(c[i].back());
}
}
while (c.size() < k) {
c.push_back(c.back());
}
return c;
}
vector<vector<int>> create_map(int N, int M, vector<int> a, vector<int> b) {
n = N;
m = M;
c.clear();
g.assign(n + 1, {});
t.resize(n + 1);
sz.resize(n + 1);
full.assign(n + 1, {});
for (int i = 1; i <= n; i++) {
t[i] = i;
sz[i] = 1;
}
neigh.assign(n + 1, vector<int>(n + 1, 0));
for (int i = 0; i < m; i++) {
full[a[i]].push_back(b[i]);
full[b[i]].push_back(a[i]);
neigh[a[i]][b[i]] = neigh[b[i]][a[i]] = 1;
if (root(a[i]) == root(b[i])) {
continue;
}
join(a[i], b[i]);
g[a[i]].push_back(b[i]);
g[b[i]].push_back(a[i]);
}
dfs(1);
assert(c.size() <= 4 * n);
return reshape(c);
}
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