#include "cave.h"
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#pragma GCC optimize("unroll-loops,no-stack-protector")
//order_of_key #of elements less than x
// find_by_order kth element
typedef long long int ll;
#define ld long double
#define pii pair<ll,ll>
typedef tree<pii, null_type, less<pii>, rb_tree_tag, tree_order_statistics_node_update> indexed_set;
#define f first
#define s second
#define pb push_back
#define REP(i,n) for(ll i=0;i<n;i++)
#define REP1(i,n) for(int i=1;i<=n;i++)
#define FILL(n,x) memset(n,x,sizeof(n))
#define ALL(_a) _a.begin(),_a.end()
#define sz(x) (int)x.size()
const ll maxn=5e3+5;
const ll maxlg=__lg(maxn)+2;
const ll INF64=4e18;
const int INF=0x3f3f3f3f;
const ll MOD=998244353;
const ld PI=acos(-1);
const ld eps=1e-9;
#define lowb(x) x&(-x)
#define MNTO(x,y) x=min(x,(__typeof__(x))y)
#define MXTO(x,y) x=max(x,(__typeof__(x))y)
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define GET_POS(c,x) (lower_bound(c.begin(),c.end(),x)-c.begin())
ll mult(ll a,ll b){
return (a*b)%MOD;
}
ll mypow(ll a,ll b){
if(b<=0) return 1;
ll res=1LL;
while(b){
if(b&1) res=mult(res,a);
a=mult(a,a);
b>>=1;
}
return res;
}
int n;
bool done[maxn];
int door[maxn],col[maxn];
int query[maxn];
void rec(int target,int l,int r,int ans){
if(l==r){
done[l]=1;
col[l]=ans;
door[l]=target;
return;
}
int mid=(l+r)/2;
REP(i,n) query[i]=(1^ans);
for(int i=l;i<=mid;i++) query[i]=ans;
REP(i,n){
if(done[i]) query[i]=col[i];
}
int z=tryCombination(query);
if(z==-1 or z>target){
rec(target,l,mid,ans);
}
else{
rec(target,mid+1,r,ans);
}
}
int findcol(int i){
REP(i,n){
if(done[i]) query[i]=col[i];
else query[i]=0;
}
int ans=tryCombination(query);
if(ans==-1 or ans>i){
return 0;
}
return 1;
}
void exploreCave(int N) {
n=N;
REP(i,n){
rec(i,0,n-1,findcol(i));
}
answer(col,door);
}
