#include <bits/stdc++.h>
#include "insects.h"
using namespace std;
int min_cardinality(int n) {
unsigned seed = std::chrono::system_clock::now().time_since_epoch().count();
std::default_random_engine rng(seed);
vector <bool> tr (n);
int tp = 0;
for (int i = 0; i < n; i++){
move_inside(i);
if (press_button() == 2) {
move_outside(i);
}
else {
tr[i] = 1;
tp++;
}
}
for (int i = 0; i < n; i++) if (tr[i]) move_outside(i);
int l = 0, r = n / tp, rs = -1;
int btn = 0;
vector <int> in (n);
while (l <= r){
int mid = (l + r) / 2;
auto check = [&] (int x) -> bool {
int ins = btn;
vector <int> vis (n);
vector <int> ord (n);
iota(ord.begin(), ord.end(), 0);
shuffle(ord.begin(), ord.end(), rng);
for (int i: ord) {
if (in[i]) continue;
move_inside(i);
if (press_button() > x) {
move_outside(i);
}
else {
ins++;
vis[i] = in[i] = 1;
}
}
if (ins != x * tp) {
for (int i = 0; i < n; i++)
if (vis[i]) {
in[i] = 0;
move_outside(i);
}
return 0;
}
else {
btn = ins;
return 1;
}
};
if (check(mid)) {
rs = mid;
l = mid + 1;
}
else {
r = mid - 1;
}
}
return rs;
}
