#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)
{
if (N == 2)
return {0, 1};
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();
c = u;
}
vector<int> d(N), order(N), sol(2 * N, -1), large(2 * N, 0);
vector<int> tmp[2];
for (int i = 0; i < N; i++)
{
if (i != c)
d[i] = hoursRequired(c, i); // N - 1
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];
};
int t = 0;
for (int i = 0; i < N - 1; i++)
{
if (tmp[t ^ 1].empty() || diffSubtree(order[i], tmp[t ^ 1].back()))
{
tmp[t].emplace_back(order[i]);
if (tmp[t].size() + t > tmp[t ^ 1].size())
t ^= 1;
}
else
tmp[t ^ 1].emplace_back(order[i]);
}
for (int i = 0; i < tmp[0].size(); i++)
sol[i * 2] = tmp[0][i];
for (int i = 0; i < tmp[1].size(); i++)
sol[i * 2 + 1] = tmp[1][i];
tmp[0].clear(), tmp[1].clear();
int over = -1, in = 0, out = 0, last = 2 * N;
for (int i = 2 * N - 1; i > 0; i--)
if (sol[i] == -1 && sol[i - 1] >= 0)
{
over = sol[i - 1];
break;
}
for (int i = 0; i < 2 * N; i++)
if (sol[i] >= 0)
{
if (!diffSubtree(sol[i], over))
large[i] = 1;
(large[i] ? in : out)++;
}
for (int i = 0; i < 2 * N; i++)
{
if (in >= out)
{
last = i;
break;
}
(large[i] ? in : out)--;
}
for (int i = last; i < 2 * N; i++)
if (sol[i] >= 0)
tmp[large[i]].emplace_back(sol[i]);
sort(tmp[0].begin(), tmp[0].end(), [&](int i, int j)
{ return d[i] > d[j]; });
sort(tmp[1].begin(), tmp[1].end(), [&](int i, int j)
{ return d[i] > d[j]; });
// x, y, b, a valid
{
int a = tmp[1].front(), b = tmp[0].front();
if ((last < 1 || diffSubtree(sol[last - 1], b)) && // y, b different
(last < 2 || d[b] <= d[sol[last - 2]]) && // x >= b
(last < 1 || d[a] <= d[sol[last - 1]])) // x <= b;
swap(tmp[0], tmp[1]);
}
for (int i = last; i < 2 * N; i++)
sol[i] = -1;
for (int i = 0; i < tmp[1].size(); i++)
sol[last + i * 2] = tmp[1][i];
for (int i = 0; i < tmp[0].size(); i++)
sol[last + i * 2 + 1] = tmp[0][i];
int off = 0;
for (int i = 0; i < 2 * N; i++)
if (sol[i] == -1)
off++;
else
sol[i - off] = sol[i];
sol.resize(N);
sol[N - 1] = c;
return sol;
}
