#include <bits/stdc++.h>
#ifdef MINA
#include "grader.cpp"
#endif
#include "fun.h"
using namespace std;
#define ll long long
#define sz(x) (int) x.size()
int n;
vector<int> ans;
const int MAXN = 100'005;
vector<int> gud[3];
int dist[MAXN], comp[MAXN];
int c, lst = -1;
void solve() {
if (sz(gud[1]) < sz(gud[0])) {
swap(gud[0], gud[1]);
if (lst != -1) lst = !lst;
}
if (sz(gud[1]) > sz(gud[0])) lst = 0;
// for (auto i : gud[0]) {
// cout << dist[i] << ' ';
// }
// cout << '\n';
// for (auto i : gud[1]) {
// cout << dist[i] << ' ';
// }
// cout << '\n';
// for (auto i : ans) {
// cout << i << ' ';
// }
// cout << '\n';
while (sz(gud[0]) || sz(gud[1])) {
array<int, 3> mx = {-1, -1, -1};
for (int k = 0; k < 2; k++) {
if (lst == k || gud[k].empty()) continue;
mx = max(mx, {dist[gud[k].back()], k, gud[k].back()});
}
lst = mx[1];
ans.push_back(mx[2]);
gud[lst].pop_back();
}
ans.push_back(c);
// for (auto i : ans) {
// cout << i << ' ';
// }
// cout << '\n';
}
vector<int> createFunTour(int _n, int q) {
n = _n;
array<int, 2> mn = {(int)1e9, -1};
for (int i = 0; i < n; i++) {
int sz = attractionsBehind(0, i);
if (sz >= (n + 1) / 2) {
mn = min(mn, {sz, i});
}
}
c = mn[1];
vector<int> v;
for (int i = 0; i < n; i++) {
dist[i] = hoursRequired(c, i);
if (dist[i] == 1) v.push_back(i);
}
for (int i = 0; i < n; i++) {
if (i == c) continue;
if (hoursRequired(i, v[0]) + 1 == dist[i]) {
comp[i] = 0;
gud[0].push_back(i);
} else if (hoursRequired(i, v[1]) + 1 == dist[i]) {
comp[i] = 1;
gud[1].push_back(i);
} else {
comp[i] = 2;
gud[2].push_back(i);
}
}
if (gud[2].empty()) {
for (int k = 0; k < 3; k++) {
sort(gud[k].begin(), gud[k].end(), [&] (int x, int y) {return dist[x] < dist[y];});
}
solve();
return ans;
}
for (int k = 0; k < 3; k++) {
sort(gud[k].begin(), gud[k].end(), [&] (int x, int y) {return dist[x] < dist[y];});
}
int mxm;
while ((mxm = max({sz(gud[0]), sz(gud[1]), sz(gud[2])})) < sz(gud[0]) + sz(gud[1]) + sz(gud[2]) - mxm) {
array<int, 3> mx = {-1, -1, -1};
for (int k = 0; k < 3; k++) {
if (lst == k || gud[k].empty()) continue;
mx = max(mx, {dist[gud[k].back()], gud[k].back(), k});
}
lst = mx[2];
ans.push_back(mx[1]);
gud[lst].pop_back();
}
if (sz(gud[0]) + sz(gud[1]) + sz(gud[2]) == 0) return ans;
int LST = lst;
for (int k = 0; k < 3; k++) {
if (sz(gud[k]) == mxm) {
vector<int> v2;
for (int j = 0; j < 3; j++) if (j != k) v2.push_back(j);
if (lst == v2.back()) lst = v2[0];
for (auto j : gud[v2.back()]) gud[v2[0]].push_back(j);
gud[v2.back()].clear();
break;
}
}
for (int k = 0; k < 3; k++) {
sort(gud[k].begin(), gud[k].end(), [&] (int x, int y) {return dist[x] < dist[y];});
}
// cout << lst << '\n';
// for (auto i : gud[0]) {
// cout << dist[i] << ' ';
// }
// cout << '\n';
// for (auto i : gud[1]) {
// cout << dist[i] << ' ';
// }
// cout << '\n';
// for (auto i : gud[2]) {
// cout << dist[i] << ' ';
// }
// cout << '\n';
if (lst != -1) {
for (int i = sz(gud[lst]) - 1; i >= 0; i--) {
if (dist[gud[lst][i]] != dist[gud[lst].back()]) break;
if (comp[gud[lst][i]] != LST) {
swap(gud[lst][i], gud[lst][sz(gud[lst]) - 1]);
lst = -1;
break;
}
}
}
// cout << ">>> ";
// for (auto i : ans) cout << i << ' ';
// cout << '\n';
if (gud[0].empty()) {
swap(gud[0], gud[2]);
if (lst == 2) lst = 0;
}
if (gud[1].empty()) {
swap(gud[1], gud[2]);
if (lst == 2) lst = 1;
}
solve();
return ans;
}
