#include <bits/stdc++.h>
#include "insects.h"
#define dbg(x) cerr << #x << ": " << x << "\n";
using namespace std;
int min_cardinality(int N) {
  	int sz = 0, lim = 1;
	multiset<int> hey;
	set<int> lista;
	for(int i = 0; i < N; i++){
		lista.insert(i);
	}
  	while(sz != N){
		vector<int> toerase;
		for(const int &i : lista){
			move_inside(i);
			if(press_button() > lim){
				move_outside(i);
				continue;
			} 
			sz++;
			toerase.push_back(i);
			if(hey.empty()){
				hey.insert(lim);
				continue;
			}
			if(hey.count(lim - 1)){
				hey.erase(hey.find(lim - 1));
				hey.insert(lim);
				continue;
			}
			hey.insert(lim);
		}
		for(const int &i : toerase) lista.erase(i);
		lim++;
  	}
  	return *hey.begin();
}
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