#include<bits/stdc++.h>
#include "cave.h"
using namespace std;
#define ll long long
#define pb push_back
#define ff first
#define ss second
#define _ << " " <<
#define yes cout<<"YES\n"
#define no cout<<"NO\n"
#define ull unsigned long long
#define lll __int128
#define all(x) x.begin(),x.end()
#define rall(x) x.rbegin(),x.rend()
#define BlueCrowner ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define FORD(i, a, b) for (ll i = (a); i >= (b); i--)
void exploreCave(int n) {
int s[n], d[n], used[n];
FOR(i, 0, n) {
s[i] = d[i] = used[i] = 0;
}
FOR(i, 0, n) {
ll cur = tryCombination(s);
if(cur == i) {
FOR(i, 0, n) if(!used[i]) s[i] ^= 1;
}
ll l = 0, r = n - 1;
ll pos = 0;
while(l <= r) {
ll m = (l + r) / 2;
int a[n];
FOR(i, 0, n) a[i] = s[i];
FOR(i, l, m + 1) {
if(!used[i]) a[i] ^= 1;
}
ll cur = tryCombination(a);
if(cur == i) {
pos = m;
r = m - 1;
}
else {
l = m + 1;
}
}
used[pos] = 1;
d[i] = pos;
}
int d1[n];
FOR(i, 0, n) {
d1[d[i]] = i;
}
answer(s, d1);
}
