#include <bits/stdc++.h>
#include "cave.h"
#pragma GCC optimize("O3")
#define FOR(i, x, y) for(int i = x; i < y; i++)
typedef long long ll;
using namespace std;
void exploreCave(int N) {
int known[5000], D[5000], S[5000], T[5000];
fill(known, known + N, -1);
FOR(i, 0, N) {
fill(S, S + N, 1);
FOR(j, 0, i) S[D[j]] = known[j];
// Find state of i-th gate
int res = tryCombination(S);
if (res <= i && res != -1) known[i] = 0;
else known[i] = 1;
// cout << known[i] << '\n';
// Binary search for D[i]
int l = 0, r = N - 1;
while (l != r) {
int mid = (l + r) / 2;
fill(T, T + N, 1 - known[i]);
fill(T + l, T + mid + 1, known[i]);
FOR(j, 0, i) T[D[j]] = known[j];
// FOR(i, 0, N) cout << T[i] << ' '; cout << '\n';
int res = tryCombination(T);
// cout << res << ' ' << mid << '\n';
if (res <= i && res != -1) l = mid + 1;
else r = mid;
}
D[i] = l;
// FOR(i, 0, N) cout << D[i] << ' ';
// cout << "\n\n";
}
// FOR(i, 0, N) cout << known[i] << ' '; cout << '\n';
// FOR(i, 0, N) cout << D[i] << ' '; cout << '\n';
int a[5001], b[5001];
FOR(i, 0, N) {
a[D[i]] = known[i];
b[D[i]] = i;
}
answer(a, b);
}
