#include "insects.h"
#include <stdio.h>
#include <vector>
#include <queue>
#include <algorithm>
#include <iostream>
#include <string>
#include <bitset>
#include <map>
#include <set>
#include <tuple>
#include <string.h>
#include <math.h>
#include <random>
#include <functional>
#include <assert.h>
#include <math.h>
#define all(x) (x).begin(), (x).end()
#define xx first
#define yy second
using namespace std;
template<typename T, typename Pr = less<T>>
using pq = priority_queue<T, vector<T>, Pr>;
using i64 = long long int;
using ii = pair<int, int>;
using ii64 = pair<i64, i64>;
int min_cardinality(int n)
{
int group = 1;
move_inside(0);
vector<int> sel = { 0, };
for (int i = 1; i < n; i++)
{
move_inside(i);
if (press_button() > 1)
{
move_outside(i);
continue;
}
sel.push_back(i);
group++;
}
for (auto& si : sel)
move_outside(si);
sel.clear();
int lo = 1, hi = n / group;
int ans = n;
while (lo <= hi)
{
int mid = (lo + hi) / 2;
for (int i = 0; i < n; i++)
{
move_inside(i);
if (press_button() > mid)
{
move_outside(i);
continue;
}
sel.push_back(i);
}
int sz = sel.size();
for (auto& si : sel)
move_outside(si);
sel.clear();
if (sz == mid * group)
{
ans = mid;
lo = mid + 1;
}
else
{
hi = mid - 1;
}
}
return ans;
}
