#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
signed min_cardinality(signed N) {
using ll = long long;
#define int ll
bool placed[2005];
int num_unique = 0;
for (int i = 0; i < N; ++i) {
move_inside(i);
int call = press_button();
if (call > 1) {
move_outside(i);
}
else {
placed[i] = true;
num_unique++;
}
}
// pigeonhole principle
if (num_unique * 2 > N) return 1;
constexpr int LOG = 9;
int curr = 1;
for (int l = LOG; l >= 0; --l) {
int tgt = curr + (1 << l);
set<int> this_iter;
for (int j = 0; j < N; ++j) {
if (placed[j]) continue;
move_inside(j);
int call = press_button();
if (call > tgt) {
move_outside(j); continue;
}
this_iter.emplace(j);
}
if (this_iter.size() == (num_unique << l)) {
for (int i : this_iter) placed[i] = true;
curr = tgt;
}
else {
for (int i : this_iter) move_outside(i);
}
}
return curr;
}
