#include "cave.h"
#include <bits/stdc++.h>
using namespace std;
int tryCombination(int S[]);
void answer(int S[], int D[]);
void exploreCave(int N);
const int MaxN = 5e3;
int S[MaxN], D[MaxN];
int knownD[MaxN], knownS[MaxN], mark[MaxN];
void exploreCave(int N) {
vector<int> pos;
for (int i = 0; i < N; ++i)
pos.push_back(i);
function<int(int, int)> setup = [&](int u, int mid) {
for (int i = 0; i < N; ++i) S[i] = !knownS[u];
for (int i = 0; i <= mid; ++i) S[i] = knownS[u];
for (int i = 0; i < u; ++i)
S[knownD[i]] = knownS[i];
return tryCombination(S);
};
function<void(int)> query = [&](int u) {
int l = 0, r = N - u - 1;
knownS[u] = 0;
int p = setup(u, -1);
knownS[u] = p == -1 || p > u;
while (l <= r) {
int mid = (l + r) >> 1;
//cout << " -> " << l << " " << r << " = " << mid << endl;
int res = setup(u, pos[mid]);
if (res == -1 || res > u)
r = mid - 1;
else
l = mid + 1;
} ++r;
//cout << u << " " << pos[r] << endl;
knownD[u] = pos[r];
pos.erase(pos.begin() + r);
};
for (int i = 0; i < N; ++i)
query(i);
for (int i = 0; i < N; ++i)
S[knownD[i]] = knownS[i];
for (int i = 0; i < N; ++i)
D[knownD[i]] = i;
answer(S, D);
}
