#include "fun.h"
#ifndef EVAL
#include "grader.cpp"
#endif
#include <bits/stdc++.h>
#define pii pair<int, int>
#define F first
#define S second
using namespace std;
vector<int> createFunTour(int N, int Q)
{
priority_queue<pii> pq;
for (int i = 1; i < N; i++)
pq.push(pii(attractionsBehind(0, i), i)); // N - 1
int c = 0;
while (!pq.empty() && pq.top().F > N / 2)
{
auto [sz, u] = pq.top();
pq.pop();
if (hoursRequired(c, u) == 1) // <= (N - 1) / 2
c = u;
}
vector<int> d(N), order(N), sol, tree[3];
vector<int> tmp[2];
for (int i = 0; i < N; i++)
d[i] = hoursRequired(c, i), order[i] = i;
sort(order.begin(), order.end(), [&](int i, int j)
{ return d[i] < d[j]; });
auto diffSubtree = [&](int i, int j)
{
if (i == c || j == c)
return true;
return hoursRequired(i, j) == d[i] + d[j];
};
for (int i = 0; i < N; i++)
if (i != c)
{
if (tree[0].empty() || !diffSubtree(tree[0].front(), i))
tree[0].emplace_back(i);
else if (tree[1].empty() || !diffSubtree(tree[1].front(), i))
tree[1].emplace_back(i);
else
tree[2].emplace_back(i);
}
if (tree[2].size() > tree[1].size())
tree[1].emplace_back(c);
else
tree[2].emplace_back(c);
for (int i = 0; i < 3; i++)
sort(tree[i].begin(), tree[i].end(), [&](int i, int j)
{ return d[i] > d[j]; });
vector<int> color(N);
for (int i = 0; i < 3; i++)
for (int j : tree[i])
color[j] = i;
auto solve = [&](vector<int> A, vector<int> B, vector<int> C)
{
vector<int> res(N);
int L = (N + 1) / 2, R = N / 2;
reverse(B.begin(), B.end());
while (A.size() < L)
{
A.emplace_back(C.back());
C.pop_back();
}
while (B.size() < R)
{
B.emplace_back(C.back());
C.pop_back();
}
reverse(B.begin(), B.end());
stable_sort(A.begin(), A.end(), [&](int i, int j)
{ return d[i] > d[j]; });
stable_sort(B.begin(), B.end(), [&](int i, int j)
{ return d[i] > d[j]; });
for (int i = 0; i < L; i++)
res[i * 2] = A[i];
for (int i = 0; i < R; i++)
res[i * 2 + 1] = B[i];
for (int i = 0; i + 1 < N; i++)
if (color[res[i]] == color[res[i + 1]])
return vector<int>{};
return res;
};
sol = solve(tree[0], tree[1], tree[2]);
if (sol.size())
return sol;
sol = solve(tree[0], tree[2], tree[1]);
if (sol.size())
return sol;
sol = solve(tree[1], tree[0], tree[2]);
if (sol.size())
return sol;
sol = solve(tree[1], tree[2], tree[0]);
if (sol.size())
return sol;
sol = solve(tree[2], tree[1], tree[0]);
if (sol.size())
return sol;
sol = solve(tree[2], tree[0], tree[1]);
if (sol.size())
return sol;
return sol;
}
