#include <vector>
#include <bits/stdc++.h>
#include "messy.h"
#define pb push_back
#define mp make_pair
using namespace std;
const int maxn = 130;
bool taken[130];
string zeros;
int n;
void add(int l, int r) {
if(l == r) return;
else {
int mid = (l + r) / 2;
string tmp = zeros;
for(int i=0;i<n;i++) {
if(i < l || i > r) tmp[i] = '1';
}
for(int i=l;i<=mid;i++) {
tmp[i] = '1';
add_element(tmp);
tmp[i] = '0';
}
add(l, mid);
add(mid+1, r);
}
}
vector<int>result;
bool here[maxn];
void solve(int l, int r, vector<int>possible) {
if(l == r) {
result[possible[0]] = l;
return;
}
else {
// for each element that is not in possible put 1 on bit searching mask
int mid = (l + r) / 2;
memset(here,false,sizeof(here));
string tmp = zeros;
for(int i:possible) here[i] = true;
vector<int>ls;
vector<int>rs;
for(int i=0;i<n;i++) {
if(!here[i]) tmp[i] = '1';
}
for(int i=0;i<n;i++) {
if(here[i]) {
tmp[i] = '1';
if(check_element(tmp)) {
ls.pb(i);
}
else {
rs.pb(i);
}
tmp[i] = '0';
}
}
/*cout<<"["<<l<<", "<<mid<<"] -> ";
for(int i:ls) cout<<i<<" ";
cout<<"\n";
cout<<"["<<mid+1<<", "<<r<<"] -> ";
for(int i:rs) cout<<i<<" ";
cout<<"\n";*/
solve(l, mid, ls);
solve(mid+1,r, rs);
}
}
std::vector<int> restore_permutation(int N, int w, int r) {
n = N;
vector<int>possible;
for(int i=0;i<n;i++) {
zeros += "0";
result.pb(0);
possible.pb(i);
}
add(0, n-1);
compile_set();
solve(0, n-1, possible);
return result;
}
