// Om Namah Shivaya
#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;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x, y) ((x + y - 1) / (y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i, n) for(int i = 0; i < n; ++i)
#define rep1(i, n) for(int i = 1; i <= n; ++i)
#define rev(i, s, e) for(int i = s; i >= e; --i)
#define trav(i, a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a, b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a, b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "cave.h"
void exploreCave(int n) {
int s[n], d[n];
memset(s, 0, sizeof s);
memset(d, -1, sizeof d);
rep(door, n) {
int curr = tryCombination(s);
assert(curr >= door);
int l = 0, r = n - 1;
int pos = -1, typ = -1;
while (l <= r) {
int mid = (l + r) >> 1;
rep(i, mid + 1) {
if (d[i] == -1) {
s[i] ^= 1;
}
}
int res = tryCombination(s);
if (res == -1) res = n;
rep(i, mid + 1) {
if (d[i] == -1) {
s[i] ^= 1;
}
}
bool ok = false;
if (curr == door and res > door) {
ok = true;
typ = 0;
}
if (curr > door and res == door) {
ok = true;
typ = 1;
}
if (ok) {
pos = mid;
r = mid - 1;
}
else {
l = mid + 1;
}
}
assert(pos != -1);
if (typ == 0) {
// door is open after inverting
s[pos] ^= 1;
}
d[pos] = door;
}
answer(s, d);
}
