#include "fun.h"
#include <bits/stdc++.h>
#define F first
#define S second
#define pb push_back
#define all(x) x.begin(), x.end()
using namespace std;
typedef pair<int, int> pii;
const int N = 1e5 + 10;
int sub[N];
int dep[N], com[N];
vector<int> R[N], G;
int Sum(){
int res = 0;
for(auto x : G)
res += R[x].size();
return res;
}
int Max(){
int res = 0;
for(auto x : G)
res = max(res, (int)R[x].size());
return res;
}
bool Check(vector<int> An){
for(int i = 0; i + 2 < (int) An.size(); i++){
if(dep[An[i]] < dep[An[i + 2]]) return false;
}
for(int i = 0; i + 1 < (int) An.size(); i++){
if(com[An[i]] == com[An[i + 1]]) return false;
}
return true;
}
vector<int> createFunTour(int n, int Q) {
assert(Q == 400000);
int rt = 0;
for(int i = 0; i < n; i++)
sub[i] = attractionsBehind(rt, i);
int cen = 0;
for(int i = 0; i < n; i++){
if(sub[i] + sub[i] >= n && sub[i] < sub[cen]) cen = i;
}
//cerr << "centroid : " << cen << '\n';
for(int i = 0; i < n; i++)
dep[i] = hoursRequired(cen, i);
//vector<int> G;
for(int i = 0; i < n; i++){
if(dep[i] == 1) G.pb(i);
}
for(int i = 0; i < n; i++){
if(i == cen) continue;
int par = G.back();
for(auto x : G){
if(x == par) continue;
if(hoursRequired(x, i) == dep[i] - 1){
par = x;
break;
}
}
R[par].pb(i);
com[i] = par;
//cerr << i << " -> " << par << '\n';
}
sort(all(G), [&](int u, int v){
return R[u].size() > R[v].size();
});
vector<int> A, B, C, P;
for(auto x : G){
sort(all(R[x]), [&](int i, int j){
return dep[i] < dep[j];
});
//for(auto y : R[x]) C.pb(y);
}
while(Max()*2 < Sum()){
int la = (P.empty() ? -1 : com[P.back()]);
int cand = -1;;
for(auto x : G){
if(x == la) continue;
if(R[x].empty()) continue;
if(cand == -1) cand = x;
else {
if(dep[R[x].back()] > dep[R[cand].back()])
cand = x;
}
}
assert(cand != -1);
P.pb(R[cand].back());
R[cand].pop_back();
}
sort(all(G), [&](int u, int v){
return R[u].size() > R[v].size();
});
for(auto x : G){
sort(all(R[x]), [&](int i, int j){
return dep[i] > dep[j];
});
for(auto y : R[x]) C.pb(y);
}
int sz = C.size();
for(int i = 0; i < (sz + 1) / 2; i++) A.pb(C[i]);
for(int i = (sz + 1) / 2; i < sz; i++) B.pb(C[i]);
sort(all(B), [&](int i, int j){
return dep[i] > dep[j];
});
if(sz % 2 == 0){
for(int i = 0; i < sz/2; i++){
P.pb(A[i]);
P.pb(B[i]);
}
if(!Check(P)){
for(int i = 0; i < sz; i++) P.pop_back();
for(int i = 0; i < sz/2; i++){
P.pb(B[i]);
P.pb(A[i]);
}
}
} else {
for(int i = 0; i < sz/2; i++){
P.pb(A[i]);
P.pb(B[i]);
}
P.pb(A.back());
}
assert((Check(P) == true));
P.pb(cen);
/*
cerr << "ans : ";
for(auto x : P) cerr << x << ' ';
cerr << '\n';
cerr << '\n';
*/
assert(((int) P.size() == n));
return P;
}
/*
7 400000
0 1
0 5
0 6
1 2
1 4
2 3
*/
