#include "fun.h"
#include <bits/stdc++.h>
#ifdef LOCAL
#define clog std::cerr
#else
#define clog if (0) std::cerr
#endif
std::vector<int> createFunTour(int N, int Q) {
std::vector<std::pair<int, int>> subtree_size(N);
subtree_size[0] = {N, 0};
for (int i = 1; i < N; i++) {
subtree_size[i] = {attractionsBehind(0, i), i};
}
std::sort(subtree_size.begin(), subtree_size.end());
int centroid = -1;
for (centroid = 0; centroid < N; centroid++) {
if (subtree_size[centroid].first >= (N + 1) / 2) {
centroid = subtree_size[centroid].second;
break;
}
}
assert(centroid != -1);
std::vector<int> adj;
std::vector<int> d(N);
for (int i = 0; i < N; i++) {
if (i == centroid) {
d[i] = 0;
} else {
d[i] = hoursRequired(centroid, i);
}
if (d[i] == 1) {
adj.push_back(i);
}
}
std::vector<int> g(N, -1);
std::vector<std::vector<int>> f(3);
for (int i = 0; i < N; i++) {
if (i == centroid) continue;
g[i] = 0;
while (g[i] + 1 < (int) adj.size() && hoursRequired(adj[g[i]], i) > d[i]) {
g[i]++;
}
f[g[i]].push_back(i);
}
std::vector<int> p = {0, 1, 2};
std::vector<int> tour;
auto shortest = [&](int i, int j) {
return d[i] < d[j];
};
for (int i = 0; i < 3; i++) {
std::sort(f[i].begin(), f[i].end(), shortest);
}
auto bigger_size = [&](int i, int j) {
return f[i].size() > f[j].size();
};
auto farthest = [&](int i, int j) {
return d[f[i].back()] > d[f[j].back()];
};
std::sort(p.begin(), p.end(), bigger_size);
int last = -1;
while (f[p[0]].size() < f[p[1]].size() + f[p[2]].size()) {
std::sort(p.begin(), p.end(), farthest);
int now = p[p[0] == last];
tour.push_back(f[now].back());
f[now].pop_back();
last = now;
std::sort(p.begin(), p.end(), bigger_size);
}
f[p[1]].insert(f[p[1]].end(), f[p[2]].begin(), f[p[2]].end());
std::sort(f[p[1]].begin(), f[p[1]].end(), shortest);
int from = 0;
if (tour.size() && d[tour.back()] < d[f[p[1]].back()]) {
from = 1;
}
while (f[p[from]].size()) {
tour.push_back(f[p[from]].back());
f[p[from]].pop_back();
from ^= 1;
}
tour.push_back(centroid);
return tour;
}
