#include "fun.h"
#include <bits/stdc++.h>
using namespace std;
vector<int> createFunTour(int N, int Q) {
int centroid = 0, tmp = N;
for (int i = 1; i < N; i++) {
int siz = attractionsBehind(0, i);
if (siz > N / 2 && siz < tmp)
centroid = i, tmp = siz;
}
vector<int> depth(N, 0), group(N, 0);
for (int i = 0; i < N; i++) if (i != centroid) {
depth[i] = hoursRequired(centroid, i);
}
vector<int> branch;
for (int i = 0; i < N; i++)
if (depth[i] == 1)
branch.push_back(i);
int M = branch.size();
for (int i = 0; i < N; i++) if (i != centroid) {
for (int j = 1; j < M; j++)
if (hoursRequired(branch[j], i) == depth[i] - 1) {
group[i] = j; break;
}
}
vector<vector<int>> list_val(M = 3);
for (int i = 0; i < N; i++) if (i != centroid) {
list_val[group[i]].push_back(i);
}
for (int i = 0; i < M; i++) {
sort(list_val[i].begin(), list_val[i].end(), [&](const int &i, const int &j){
return depth[i] < depth[j];
});
}
vector<int> res, p = {0, 1, 2};
int last = -1;
while (true) {
sort(p.begin(), p.end(), [&](const int &i, const int &j){
return list_val[i].size() > list_val[j].size();
});
if (list_val[p[0]].size() >= list_val[p[1]].size() + list_val[p[2]].size())
break ;
for (int i = 0; i < 3; i++)
assert(!list_val[i].empty());
sort(p.begin(), p.end(), [&](const int &i, const int &j){
return depth[list_val[i].back()] > depth[list_val[j].back()];
});
int cur = last == p[0] ? 1 : 0;
res.push_back(list_val[cur].back());
list_val[cur].pop_back(), last = cur;
}
list_val[p[1]].insert(list_val[p[1]].end(), list_val[p[2]].begin(), list_val[p[2]].end());
sort(list_val[p[1]].begin(), list_val[p[1]].end(), [&](const int &i, const int &j){
return depth[i] < depth[j];
});
last = ((int) res.size() >= 2
&& group[res[res.size() - 2]] != p[0]
&& depth[res[res.size() - 2]] > depth[res.back()]
&& depth[list_val[p[1]].back()] > depth[res.back()]
) ? 1 : 0;
for (; list_val[p[last]].size(); last ^= 1) {
res.push_back(list_val[p[last]].back());
list_val[p[last]].pop_back();
}
res.push_back(centroid);
return res;
}
