#include "messy.h"
#include "bits/stdc++.h"
using namespace std;
#define FAST ios_base::sync_with_stdio(false); cin.tie(0);
#define pb push_back
#define eb emplace_back
#define ins insert
#define f first
#define s second
#define cbr cerr<<"hi\n"
#define mmst(x, v) memset((x), v, sizeof ((x)))
#define siz(x) ll(x.size())
#define all(x) (x).begin(), (x).end()
#define lbd(x,y) (lower_bound(all(x),y)-x.begin())
#define ubd(x,y) (upper_bound(all(x),y)-x.begin())
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
inline long long rand(long long x, long long y) { return rng() % (y+1-x) + x; } //inclusive
string inline to_string(char c) {string s(1,c);return s;} template<typename T> inline T gcd(T a,T b){ return a==0?llabs(b):gcd(b%a,a); }
using ll=long long;
using ld=long double;
#define FOR(i,s,e) for(ll i=s;i<=ll(e);++i)
#define DEC(i,s,e) for(ll i=s;i>=ll(e);--i)
using pi=pair<ll,ll>; using spi=pair<ll,pi>; using dpi=pair<pi,pi>;
long long LLINF = 1e18;
int INF = 1e9+1e6;
#define MAXN (200006)
int n;
vector<int> ans;
void dnc1(int s,int e) {
if(s==e) return;
string S(n, '1');
FOR(i,s,e) S[i]='0';
int m=(s+e)>>1;
FOR(i,s,m) S[i]='1', add_element(S), S[i]='0';
dnc1(s, m), dnc1(m+1, e);
}
void dnc2(int s,int e,vector<int> v) {
if(s==e) {
assert(siz(v)==1), ans[v[0]]=s;
return;
}
string S(n, '1');
for(auto i:v) S[i]='0';
vector<int> l, r;
for(auto i:v) {
S[i]='1';
if(check_element(S)) l.eb(i);
else r.eb(i);
S[i]='0';
}
int m=(s+e)>>1;
dnc2(s, m, l);
dnc2(m+1, e, r);
}
vector<int> restore_permutation(int _n, int w, int r) {
n = _n;
dnc1(0, n-1);
compile_set();
ans.resize(n);
vector<int> v;
FOR(i,0,n-1) v.eb(i);
dnc2(0, n-1, v);
return ans;
}
