#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
// mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
int n;
int unq;
bool ok(int k) {
vector<int> in;
for (int i=0; i<n; i++) {
move_inside(i);
if (press_button() > k) move_outside(i);
else in.pb(i);
}
bool ret = unq * k == in.size();
while (!in.empty()) {
move_outside(in.back());
in.pop_back();
}
return ret;
}
int min_cardinality(int N) {
vector<int> in;
for (int i = 0; i < N; i++) {
move_inside(i);
if (press_button() == 2) move_outside(i);
else in.pb(i);
}
unq = in.size();
while (!in.empty()) {
move_outside(in.back());
in.pop_back();
}
if (unq == 1) return N;
n = N;
int l = 1, r = 1000 + 4;
while (l != r) {
int mid = (l+r+1) / 2;
ok(mid) ? l = mid : r = mid - 1;
}
return l;
}
