#include<bits/stdc++.h>
#include "cave.h"
using namespace std;
#define FOR(i, a, b) for (int i = (a), _b = (b); i <= _b; i++)
#define FORD(i, a, b) for (int i = (a), _b = (b); i >= _b; i--)
#define fi first
#define se second
#define pb push_back
#define ALL(a) (a).begin(), (a).end()
#define task "kbsiudthw"
typedef vector<int> vi;
typedef pair<int, int> ii;
typedef pair<int, ii> pii;
const int N = 1e5 + 5;
const int INF = 0x3f3f3f3f;
const int MOD = 1e9 + 2277;
void exploreCave(int N){
int S[N] = {0}, P[N] = {0}, B[N] = {0};
bool marked[N] = {0};
FOR (i, 0, N - 1){
FOR (j, 0, N-1) if (marked[j]) S[j] = P[j]; else S[j] = 0;
int cur =0 ;
if (tryCombination(S) == i) cur ^= 1;
int pos = 0;
FOR (bit, 0, 12){
FOR (j, 0, N-1) {
if (marked[j]) S[j] = P[j];
else if ((j>>bit)&1) S[j] = cur;
else S[j] = cur ^ 1;
}
if (tryCombination(S) != i) pos += (1<<bit);
}
marked[pos] = 1;
P[pos] = cur;
B[pos] = i;
}
answer(P, B);
}
