#include <bits/stdc++.h>
#include "cave.h"
using namespace std;
typedef long long ll;
ll INF = 1e18+7;
long long MOD = 998244353;
typedef pair<ll,ll> ii;
#define iii pair<ii,ll>
#define f(i,a,b) for(long long i = a;i < b;i++)
#define rf(i,a,b) for(long long i=a;i>=b;i--)
#define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define w(t) while(t--)
#define c(n); cin>>n;
#define p(n) cout<<n;
#define pl(n) cout<<n<<endl;
#define ps(n); cout<<n<<" ";
#define F first
#define S second
#define pb(a) push_back(a)
#define all(x) (x).begin(), (x).end()
#define ull unsigned long long
#define vll vector<ll>
#define vii vector<ii>
#define mkp make_pair
#define ld long double
#define arrin(a,n) f(i,0,n){cin>>a[i];}
#define arrout(a,n) f(i,0,n){cout<<a[i]<<" ";}
#define printclock cerr<<"Time : "<<1000*(ld)clock()/(ld)CLOCKS_PER_SEC<<"ms\n";
#define PI (2*acos(0))
const long long N = 1e6+5;
vll visit,dist,taken;
vector<vll> adj;
vector<vii> adj2;
priority_queue<ii,vector<ii>, greater<ii> > pq;
ll bit[N][2];
ll siz;
ll res = 0;
ll lcm(ll a,ll b){return (a * b) / __gcd(a,b);}
ll gcd(ll a,ll b){return __gcd(a,b);}
long long power(long long a,long long b){if(b == 0)return 1;if(b == 1)return a;long long ans = power(a,b/2) % MOD;ans *= ans;ans %= MOD;if(b % 2 == 1)ans *= a;return ans%MOD;}
ll inverse(ll x){x%=MOD;return power(x,MOD-2);}
void BITup(ll k, ll x,ll pos){while(k <= siz){bit[k][pos]+=x;k += k & -k;}}
ll BITq(ll k,ll pos){ll s=0;while(k>=1){s+=bit[k][pos];k -= k &-k;}return s;}
struct node{ll lazy,val;}seg[4000000];
struct point{ll x,y;};
void dfs(ll v){visit[v] = 1;for(auto x:adj[v]){if(!visit[x])dfs(x);}}
void bfs(ll s){visit[s] = 1;queue<ll>q;q.push(s);while(!q.empty()){ll u = q.front();ps(u);q.pop();for(auto x:adj[u]){if(!visit[x]){visit[x] = 1;q.push(x);}}}}
void dijkstra(ll s){pq.push(ii(0,s));dist[s] = 0;while(!pq.empty()){ii f = pq.top();pq.pop();ll w = f.F;ll u = f.S;if(w > dist[u]){continue;}for(auto v:adj2[u]){if(dist[u] + v.S < dist[v.F]){dist[v.F] = dist[u] + v.S;pq.push(ii(dist[v.F],v.F));}}}}
void prim(ll edge) {taken[edge] = 1;for(auto v:adj2[edge]) {if (taken[v.first]==0)pq.push(ii(v.second, v.first));}}
ll mst(ll s){taken.assign(N, 0);prim(s);ll cost = 0;while(!pq.empty()){ii front = pq.top();pq.pop();ll w = front.first;ll u = front.second;if(taken[u]==0)cost += w;prim(u);}return cost;}
void YESNO(ll a){if(!!a){pl("Yes");}else{pl("No");}}
void filesin(void){freopen("tracing.in","r",stdin);}
void filesout(void){freopen("tracing.out","w",stdout);}
///I hope I will get uprating and don't make mistakes
///I will never stop programming
///sqrt(-1) Love C++
///Please don't hack me
///@TheofanisOrfanou Theo830
///Training
set<ll>exo;
ll cur = 1;
ll u = 0;
int n;
/*
int tryCombination(int arr[]){
f(i,0,n){
ps(arr[i]);
}
cout<<endl;
int a;
c(a);
return a;
}
void answer(int arr[],int a[]){
f(i,0,n){
ps(arr[i]);
}
cout<<endl;
f(i,0,n){
ps(a[i]);
}
}
*/
void solve(set<ll>left,set<ll>right,int sosto,int ans[]){
for(auto x:left){
ans[x] = sosto;
}
for(auto x:right){
ans[x] = (sosto^1);
}
int a = tryCombination(ans);
set<ll>l,r;
if(a > cur || a == -1){
if(left.size() == 1){
ll val;
for(auto x:left){
val = x;
}
exo.erase(val);
u = val;
return;
}
ll i = 0;
for(auto x:left){
if(i < left.size()/2){
l.insert(x);
}
else{
r.insert(x);
}
i++;
}
}
else{
if(right.size() == 1){
ll val;
for(auto x:right){
val = x;
}
exo.erase(val);
u = val;
return;
}
ll i = 0;
for(auto x:right){
if(i < right.size()/2){
l.insert(x);
}
else{
r.insert(x);
}
i++;
}
}
if(l.size() == 1 && r.empty()){
ll val;
for(auto x:l){
val = x;
}
exo.erase(val);
u = val;
return;
}
if(r.size() == 1 && l.empty()){
ll val;
for(auto x:r){
val = x;
}
exo.erase(val);
u = val;
return;
}
solve(l,r,sosto,ans);
}
void exploreCave(int N){
int n = N;
f(i,0,n){
exo.insert(i);
}
int ans[n]={0};
int ans2[n] = {0};
while(cur <= n){
for(auto x:exo){
ans[x] = 0;
}
int a = tryCombination(ans);
int sosto;
if(a > cur || a == -1){
sosto = 0;
}
else{
sosto = 1;
}
ll i = 0;
set<ll>l,r;
for(auto x:exo){
if(i < exo.size()/2){
l.insert(x);
}
else{
r.insert(x);
}
i++;
}
solve(l,r,sosto,ans);
ans[u] = sosto;
ans2[u] = cur;
cur++;
}
answer(ans,ans2);
}
/*
int main(){
c(n);
exploreCave(n);
}
*/
