#include "messy.h"
#include<bits/stdc++.h>
using namespace std;
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
#define ll long long
#define ordered_set tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update>
#define fall(i,a,b) for(int i=a;i<=b;i++)
#define rfall(i,a,b) for(int i=a;i>=b;i--)
#define pb push_back
#define sz(x) (int)x.size()
typedef pair<ll,ll> pii;
int n,cur=2,tin[1005],rest[1005],quan=7,q=0;
vector<int> p,rev;
void build(int ind,int l,int r){
if(n==8) return;
rest[ind]=r-l+1;
fall(i,l,r) if(i<=quan) rest[ind]--;
if(l==r) return;
int m=(l+r)/2;
if(m<=7) build(2*ind+1,m+1,r);
else{
tin[ind]=cur;
string s="";
fall(i,0,n-1) s+="1";
fall(j,0,cur-2) s[j]='0';
fall(i,l,m){
if(i<=7) continue;
s[i]='0';
add_element(s);
s[i]='1';
}
cur++;
build(2*ind,l,m);
build(2*ind+1,m+1,r);
}
}
void walk(int ind,int l,int r,vector<int> v){
if(l==r){
p[v[0]]=l;
rev[l]=v[0];
return;
}
int m=(l+r)/2;
if(m<=7) walk(2*ind+1,m+1,r,v);
else{
vector<int> g1,g2;
string s="";
fall(i,0,n-1) s+="1";
fall(j,0,tin[ind]-2) s[rev[j]]='0';
fall(i,0,sz(v)-1){
auto u=v[i];
if(rest[2*ind]==0){
g2.pb(u);
rest[2*ind+1]--;
continue;
}
else if(rest[2*ind+1]==0){
g1.pb(u);
rest[2*ind]--;
continue;
}
q++;
s[u]='0';
if(check_element(s)) g1.pb(u),rest[2*ind]--;
else g2.pb(u),rest[2*ind+1]--;
s[u]='1';
}
cur++;
walk(2*ind,l,m,g1); walk(2*ind+1,m+1,r,g2);
}
}
std::vector<int> restore_permutation(int N, int lx, int lx2){
n=N;
if(n==8){
string s="";
fall(i,0,n-1) s+="0";
fall(i,0,n-1){
s[i]='1';
add_element(s);
}
compile_set();
bool open=0;
fall(i,0,n-1) s[i]='0';
int a=0,b=0;
vector<int> p;
fall(i,0,n-1) p.pb(i);
fall(i,0,n-1){
s[i]='1';
bool z=check_element(s);
if(z==0 && !open){
a=i;
open=1;
}
else if(z==1 && open){
b=i;
open=0;
}
}
swap(p[a],p[b]);
return p;
}
string s="";
p.resize(n,-1); rev.resize(n);
fall(i,0,n-1) s+="1";
fall(i,0,quan){
s[i]='0';
add_element(s);
s[i]='1';
}
fall(i,0,n-1) s[i]='0';
rfall(i,quan,1){
s[i]='1';
add_element(s);
}
build(1,0,n-1);
compile_set();
fall(i,0,n-1) s[i]='1';
vector<int> candidates;
fall(i,0,n-1){
s[i]='0';
q++;
if(check_element(s)) candidates.pb(i);
s[i]='1';
}
fall(i,0,n-1) s[i]='0';
rfall(i,quan,0){
for(auto u:candidates){
s[u]='1';
q++;
if(sz(candidates)==1 || check_element(s)){
vector<int> cand;
for(auto x:candidates) if(x!=u) cand.pb(x);
p[u]=i;
rev[i]=u;
candidates=cand;
break;
}
s[u]='0';
}
}
if(n==8) return p;
cur=quan;
candidates.clear();
fall(i,0,n-1) if(p[i]==-1) candidates.pb(i);
walk(1,0,n-1,candidates);
return p;
}
