#include "insects.h"
#include<iostream>
#include<vector>
using namespace std;
#define forn(i, n) for(int i=0; i<(int)n; ++i)
#define PB push_back
int solve(vector<int> v, int k){
int sz = (int)v.size();
if(sz < k) return 0;
int x = (sz+k)/(2*k);
vector<int> us, nus;
for(int el:v){
move_inside(el);
int ret = press_button();
if(ret > x) move_outside(el), nus.PB(el);
else us.PB(el);
}
for(int el:us) move_outside(el);
if((int)us.size() == k*x) return x + solve(nus, k);
else return solve(us, k);
}
int min_cardinality(int N) {
vector<int> v;
forn(i, N){
move_inside(i);
if(press_button() > 1) move_outside(i);
else v.PB(i);
}
int sz = (int)v.size();
for(int el:v) move_outside(el);
vector<int> al(N);
forn(i, N) al[i]=i;
return solve(al, sz);
}
