#include "cave.h"
#include <bits/stdc++.h>
#pragma optimize("Ofast")
#pragma target("avx2")
using namespace std;
#define ll long long
#define ld long double
#define pb push_back
#define pf push_front
#define pii pair<int,int>
#define all(v) v.begin(),v.end()
#define F first
#define S second
#define mem(a,i) memset(a,i,sizeof(a))
#define sz(s) (int)s.size()
#define y1 yy
#define ppb pop_back
#define lb lower_bound
#define ub upper_bound
#define gcd(a,b) __gcd(a,b)
#define in insert
// #define int ll
const int MAX=5000+15;
const int N=104;
const ll inf=1e18;
const int mod=1e9+7;
const int mod1=1e9+9;
const ld eps=1e-9;
int dx[8]={1,0,-1,0,1,-1,-1,1};
int dy[8]={0,1,0,-1,1,-1,1,-1};
int binpow(int a,int n){
if(!n)return 1;
if(n%2==1)return a*binpow(a,n-1)%mod;
int k=binpow(a,n/2);
return k*k%mod;
}
int s[MAX],d[MAX];
int pos[MAX];
void exploreCave(int N) {
mem(pos,-1);
for(int i=0;i<N;i++){
vector<int> vec;
for(int j=0;j<N;j++){
if(pos[j]==-1){
vec.pb(j);
}
}
int l=0,r=sz(vec)-1;
for(int j=0;j<N;j++){
if(pos[j]==-1){
s[j]=0;
}
}
int x=tryCombination(s);
bool ok;
if(x==-1||x>i)ok=0;
else ok=1;
while(l<r){
int m=(l+r)/2;
for(int j=0;j<=m;j++){
s[vec[j]]=ok;
}
for(int j=m+1;j<sz(vec);j++)s[vec[j]]=ok^1;
int x=tryCombination(s);
if(x==-1||x>i){
r=m;
}
else{
l=m+1;
}
}
pos[vec[l]]=1;
s[vec[l]]=ok;
d[vec[l]]=i;
}
answer(s,d);
}
