#include <bits/stdc++.h>
#include "messy.h"
using namespace std;
vector<int> restore_permutation(int n, int w, int r)
{
vector<int> ans(n, -1);
auto init = [&](auto init, int l, int r) -> void
{
if (l == r) return;
string s(n, '1');
for (int i = l; i <= r; i++) s[i] = '0';
int mid = (l + r) / 2;
for (int i = l; i <= mid; i++) {
s[i] = '1';
add_element(s);
s[i] = '0';
}
init(init, l, mid);
init(init, mid + 1, r);
};
init(init, 0, n - 1);
compile_set();
auto process = [&](auto process, int l, int r, vector<int> can) -> void
{
if (l == r) {
ans[can[0]] = l;
return;
}
string s(n, '1');
for (int x : can) s[x] = '0';
vector<int> nxcan[2];
for (int x : can) {
s[x] = '1';
nxcan[!check_element(s)].push_back(x);
s[x] = '0';
}
int mid = (l + r) >> 1;
process(process, l, mid, nxcan[0]);
process(process, mid + 1, r, nxcan[1]);
};
vector<int> can(n);
iota(can.begin(), can.end(), 0);
process(process, 0, n - 1, can);
return ans;
}
