#include <bits/stdc++.h>
#define NN 100005
#define ll long long int
#define fo(i,x,y) for(int i=x;i<=y;i++)
#define fs(ar,n) fo(i,1,n) cin>>ar[i]
#define sp " "
// #define fast cin.tie(0);cout.tie(0);ios_base::sync_with_stdio(false)
#define pb push_back
#define ppb pop_back
#define fi first
#define se second
#define ii pair<int,int>
#define lli pair<ll,ll>
#define fast2 freopen ("in.txt","r",stdin);freopen ("out.txt","w",stdout);
#define mod 1000000007
#include "cave.h"
using namespace std;
int n,m,ar[NN],sum,t,tutmac[NN],tut[NN],flag,ans[NN];
bool check(int l,int r,int x)
{
fo(i,0,n-1)
tutmac[i]=!flag;
// fo(i,0,n-1)
// cout<<tutmac[i]<<sp;
// cout<<endl;
fo(i,l,r)
tutmac[i]=flag;
fo(i,0,n-1)
if(tut[i]!=-1)
tutmac[i]=tut[i];
int y=tryCombination(tutmac);
// cout<<"[d]"<<sp<<x<<sp<<l<<sp<<r<<endl;
// y<<endl;
// cout<<y<<endl<<endl;
if(y>x || y==-1)
return 1;
return 0;
}
void bs(int x)
{
int l=0,r=n-1;
flag=1;
fo(i,0,n-1)
tutmac[i]=0;
fo(i,0,n-1)
if(tut[i]!=-1)
tutmac[i]=tut[i];
int y=tryCombination(tutmac);
if(y>x || y==-1)
flag=0;
// cout<<"[d2]"<<sp;
// cout<<x<<sp<<flag<<endl;
while(l<r)
{
if(l==r-1)
{
if(check(r,r,x))
l=r;
break;
}
int mid=(l+r)/2;
if(check(l,mid,x))
r=mid;
else
l=mid+1;
}
tut[l]=flag;
ans[l]=x;
}
void exploreCave(int N) {
n=N;
memset(tut,-1,sizeof(tut));
fo(i,0,n-1)
bs(i);
// fo(i,0,n-1)
// cout<<tut[i]<<sp;
// fo(i,0,n-1)
// cout<<ans[i]<<sp;
answer(tut,ans);
}
