#include <bits/stdc++.h>
#include "insects.h"
using namespace std;
int min_cardinality(int n) {
vector <bool> vis (n);
int tp = 0;
for (int i = 0; i < n; i++){
move_inside(i);
if (press_button() == 2) {
move_outside(i);
}
else {
vis[i] = 1;
tp++;
}
}
for (int i = 0; i < n; i++) if (vis[i]) move_outside(i);
int l = 0, r = n, rs = -1;
while (l <= r){
int mid = (l + r) / 2;
auto check = [n, tp] (int x) -> bool {
vector <int> vis (n);
int ins = 0;
for (int i = 0; i < n; i++){
move_inside(i);
// cout << x << " " << i << " " << ins << " " << press_button() << "\n";
if (press_button() > x) {
move_outside(i);
}
else {
ins++;
vis[i] = 1;
}
}
for (int i = 0; i < n; i++) if (vis[i]) move_outside(i);
return ins == x * tp;
};
if (check(mid)) {
rs = mid;
l = mid + 1;
}
else {
r = mid - 1;
}
}
return rs;
}
