#include "messy.h"
#include <bits/stdc++.h>
#define pb push_back
#define pf push_front
using namespace std;
#define F first
#define S second
typedef long long ll;
#define pii pair <int, int>
#define pll pair <ll, ll>
typedef long double ld;
const ll N = 128 + 100, M = 1e7 + 10, len = 21, inf = 1e18;
const ll mod = 998244353;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
ll um(ll a, ll b){
return (1LL * a * b) % mod;
}
ll subr(ll a, ll b){
return ((1LL * a - b) % mod + mod) % mod;
}
int n, cnt, pos[N], per[N];
string orig = "";
void calc(int l, int r){
//cout << l << " "<< r << endl;
if(r - l == 1) return;
int mid = (l + r) / 2;
calc(l, mid);
calc(mid, r);
string s = orig;
for(ll i = 0; i < l; i++){
s[i] = '1';
}
for(ll i = r; i < n; i++){
s[i] = '1';
}
for(ll i = l; i < mid; i++){
s[i] = '1';
add_element(s);
s[i] = '0';
}
}
vector <int> over;
vector <int> nums[N][N];
bool need[N];
string nw;
void gt(int from, int to, int l = 0, int r = n){
if(from <= l && r <= to) return;
int mid = (r + l) / 2;
if(to <= mid){
for(auto u : nums[mid][r]){
nw[u] = '1';
}
gt(from, to, l, mid);
} else{
for(auto u : nums[l][mid]){
nw[u] = '1';
}
gt(from, to, mid, r);
}
}
vector<int> restore_permutation(int nx, int w, int r){
n = nx;
for(int i = 0; i < n; i++){
orig += '0';
}
calc(0, n);
for(int i = 0; i < n; i++){
nums[0][n].pb(i);
}
compile_set();
vector <int> vec;
for(int len = n; len >= 2; len /= 2){
for(int i = 0; i < n; i += len){
nw = orig;
gt(i, i + len);
//cout << nw << " nw\n";
int mid = i + len/2;
for(auto u : nums[i][i + len]){
need[u] = true;
//cout << u << " upd\n";
}
for(auto u : nums[i][i + len]){
nw[u] = '1';
bool rs = check_element(nw);
if(rs){
for(int k = 0; k < (int)nw.size(); k++){
if(nw[k] == '1' && need[k]){
nums[i][mid].pb(k);
need[k] = false;
}
}
}
nw[u] = '0';
}
for(auto u : nums[i][i + len]){
if(need[u]) nums[mid][i + len].pb(u);
need[u] = false;
}
}
}
for(int i = 0; i < n; i++){
pos[nums[i][i + 1][0]] = i;
}
for(int i = 0; i < n; i++){
vec.pb(pos[i]);
}
return vec;
}
