#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <string>
#include <time.h>
#include <stack>
#include <queue>
#include <random>
#include <fstream>
#define endl '\n'
#define flush fflush(stdout), cout.flush()
#define fast ios::sync_with_stdio(0), cin.tie(0), cout.tie(0)
#define debug cout << "ok" << endl
#define finish(x) return cout << x << endl, 0
typedef long long ll;
typedef long double ldb;
const int md = 1e9 + 7, inf = 1e9 + 7;
const ll hs = 199;
const ldb eps = 1e-9, pi = acos(-1);
using namespace std;
#include "cave.h"
int tryCombination(int S[]);
void answer(int S[], int D[]);
void exploreCave(int N);
struct tag {
int to, correct;
tag(int ii = 0) {
to = ii;
correct = 0;
}
};
int n, send[5000], solved;
vector<tag> a;
int check(int first) {
for (int i = 0; i < n; i++)
if (i <= first)
send[a[i].to] = a[i].correct;
else
send[a[i].to] = 1 ^ a[i].correct;
return tryCombination(send);
}
void findnext() {
static int lo, hi, mid, nval;
lo = solved;
hi = n - 1;
if (check(solved - 1) == solved) {
nval = 0;
// find first point where check(k) != solved
while (lo < hi) {
mid = (lo + hi) / 2;
if (check(mid) == solved) lo = mid + 1;
else hi = mid;
}
}
else {
nval = 1;
// find first point where check(k) == solved
while (lo < hi) {
mid = (lo + hi) / 2;
if (check(mid) != solved) lo = mid + 1;
else hi = mid;
}
}
swap(a[lo], a[solved]);
a[solved].correct = nval;
}
void exploreCave(int N) {
n = N;
a.resize(n);
for (int i = 0; i < n; i++) a[i] = tag(i);
for (solved = 0; solved < n; solved++)
findnext();
int S[5000], D[5000];
for (int i = 0; i < n; i++) S[a[i].to] = a[i].correct;
for (int i = 0; i < n; i++) D[a[i].to] = i;
answer(S, D);
}
