#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
int D;
int solve(int K, vector<int> rem, int off) {
if (K == 0) {
return 0;
}
int mid = (K + 1) / 2;
vector<int> in, out;
int cnt = 0;
for (auto x: rem) {
move_inside(x);
if (press_button() > off + mid) {
move_outside(x);
out.push_back(x);
}
else {
cnt++;
if (cnt == mid * D) {
break;
}
}
}
if (cnt == mid * D) {
return mid + solve(K - mid, out, off + mid);
}
else {
for (auto x: in) {
move_outside(x);
}
return solve(mid - 1, rem, off);
}
}
int min_cardinality(int N) {
vector<int> rem;
for (int i = 0; i < N; i++) {
move_inside(i);
if (press_button() == 2) {
move_outside(i);
rem.push_back(i);
}
else {
D++;
}
}
return 1 + solve(N / D - 1, rem, 1);
}
