#include "cave.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define eb emplace_back
#define pb push_back
#define ft first
#define sd second
#define pi pair<int, int>
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define dbg(...) dbg_out(__VA_ARGS__)
using ll = long long;
using ld = long double;
using namespace std;
using namespace __gnu_pbds;
//Constants
const ll INF = 5 * 1e18;
const int IINF = 2 * 1e9;
const ll MOD = 1e9 + 7;
// const ll MOD = 998244353;
const ll dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const ld PI = 3.14159265359;
//Templates
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) {return os << '(' << p.first << ", " << p.second << ')';}
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> ostream& operator<<(ostream &os, const T_container &v) {os << '['; string sep; for (const T &x : v) os << sep << x, sep = ", "; return os << ']';}
void dbg_out() {cerr << endl;}
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cerr << H << ' '; dbg_out(T...); }
template<typename T> void mins(T& x, T y) {x = min(x, y);}
template<typename T> void maxs(T& x, T y) {x = max(x, y);}
template<typename T> using oset = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T> using omset = tree<T, null_type, less_equal<T>, rb_tree_tag, tree_order_statistics_node_update>;
//
void exploreCave(int n) {
int S[n], D[n];
vector<int> right_pos(n, -1);
for (int _i = 0; _i < n; _i++) {
// find the switch that opens the _i's door
for (int i = 0; i < n; i++) {
if (right_pos[i] == -1) {
S[i] = 1;
} else {
S[i] = right_pos[i];
}
}
int pos = tryCombination(S);
bool on = (pos == -1 || pos > _i);
int lo = 0, hi = n - 1, res;
while (lo <= hi) {
int mi = (lo + hi) / 2;
for (int i = 0; i < n; i++) {
if (right_pos[i] == -1) {
if (i <= mi)
S[i] = on;
else
S[i] = !on;
} else {
S[i] = right_pos[i];
}
}
pos = tryCombination(S);
if (pos == -1 || pos > _i) {
res = mi;
hi = mi - 1;
} else {
lo = mi + 1;
}
}
D[res] = _i;
right_pos[res] = on;
}
for (int i = 0; i < n; i++)
S[i] = right_pos[i];
answer(S, D);
}
