// CF template, version 3.0
#include <bits/stdc++.h>
#include "longesttrip.h"
using namespace std;
#define improvePerformance ios_base::sync_with_stdio(false); cin.tie(0)
#define getTest int t; cin >> t
#define eachTest for (int _var=0;_var<t;_var++)
#define get(name) int (name); cin >> (name)
#define out(o) cout << (o)
#define getList(cnt, name) vector<int> (name); for (int _=0;_<(cnt);_++) { get(a); (name).push_back(a); }
#define sortl(name) sort((name).begin(), (name).end())
#define rev(name) reverse((name).begin(), (name).end())
#define forto(name, var) for (int (var) = 0; (var) < (name); (var)++)
#define decision(b) if (b){out("YES");}else{out("NO");}
//#define int long long int
template <typename T, typename I>
struct segtree {
int n;
vector<T> tree;
vector<I> initial;
T id;
segtree(int i_n, vector<I> i_initial, T i_id): n(i_n), initial(i_initial), id(i_id) {
tree.resize(4 * n);
}
T conquer(T left, T right) {
// write your conquer function
}
T value(I inp) {
// write your value function
}
void build(int v, int l, int r) {
if (l == r) tree[v] = value(initial[l]);
else {
int middle = (l + r) / 2;
build(2 * v, l, middle);
build(2 * v + 1, middle + 1, r);
tree[v] = conquer(tree[2 * v], tree[2 * v + 1]);
}
}
void upd(int v, int l, int r, int i, I x) {
if (l == r) tree[v] = value(x);
else {
int middle = (l + r) / 2;
if (middle >= i) upd(2 * v, l, middle, i, x);
else upd(2 * v + 1, middle + 1, r, i, x);
tree[v] = conquer(tree[2 * v], tree[2 * v + 1]);
}
}
T query(int v, int l, int r, int ql, int qr) {
if (ql <= l && r <= qr) return tree[v];
else if (r < ql || qr < l) return id;
int middle = (l + r) / 2;
T left = query(2 * v, l, middle, ql, qr);
T right = query(2 * v + 1, middle + 1, r, ql, qr);
return conquer(left, right);
}
};
// vector<int>
vector<int> parent;
int find(int v) {
if (v == parent[v]) return v;
return parent[v] = find(parent[v]);
}
void unite(int a, int b) {
a = find(a);
b = find(b);
parent[a] = b;
}
vector<int> longest_trip(int N, int _D) {
vector<vector<bool>> adjMatrix(N, vector<bool>(N, false));
vector<int> path;
vector<int> other(N, true);
forto(N, i) parent.push_back(i);
forto(N, i) {
vector<int> A;
A.push_back(i);
for (int j = i + 1; j < N; j++) {
vector<int> B;
B.push_back(j);
bool edge = are_connected(A, B);
if (edge) {
unite(i, j);
adjMatrix[i][j] = adjMatrix[j][i] = true;
if (path.empty()) path.push_back(i), path.push_back(j), other[i] = other[j] = false;
}
}
}
bool connected = true;
forto(N, i) if (find(i) != find(0)) connected = false;
if (!connected) {
vector<int> one;
vector<int> two;
forto(N, i) {
if (find(i) == find(0)) one.push_back(i);
else two.push_back(i);
}
if (one.size() > two.size()) swap(one, two);
return two;
}
vector<int> newpath;
while (path.size() < N) {
int s = path.size();
newpath.clear();
if (adjMatrix[path[0]][path[s - 1]]) {
forto(N, i) {
if (!other[i]) continue;
int j = 0;
bool found = false;
for (int p: path) {
if (adjMatrix[i][p]) {
other[i] = false;
found = true;
newpath.push_back(i);
for (int k = j; k < s; k++) newpath.push_back(path[k]);
forto(j, k) newpath.push_back(path[k]);
swap(path, newpath);
break;
}
j++;
}
if (found) break;
}
} else {
forto(N, i) {
if (!other[i]) continue;
if (adjMatrix[i][path[0]]) {
rev(path);
path.push_back(i);
other[i] = false;
break;
}
if (adjMatrix[i][path[s - 1]]) {
path.push_back(i);
other[i] = false;
break;
}
}
}
}
return path;
}
