#include"insects.h"
#include<iostream>
#include<vector>
#include<set>
using namespace std;
vector<bool>inside;
vector<bool>dead;
int num_inside;
int n,distinct;
int c_press_button(){
return press_button();
}
void c_move_inside(int a){
inside[a]=true;
num_inside++;
move_inside(a);
}
void c_move_outside(int a){
inside[a]=false;
num_inside--;
move_outside(a);
}
int get_distinct(){
for(int i=0;i<n;i++){
c_move_inside(i);
if(c_press_button()>1)
c_move_outside(i);
}
return num_inside;
}
int min_cardinality(int N){
n=N;
inside.resize(n);
distinct=get_distinct();
dead=inside;
int f=1;
int r=N-distinct;
while(distinct<=r){
int c=(r+2*distinct+1)/(2*distinct);
for(int i=0;i<n;i++)
if(!dead[i]&&inside[i]&&num_inside>distinct*f+c)
c_move_outside(i);
for(int i=0;i<n;i++)
if(!dead[i]&&!inside[i]){
c_move_inside(i);
if(c_press_button()>f+c)
c_move_outside(i);
}
if(num_inside==(f+c)*distinct){
f+=c;
for(int i=0;i<n;i++)
if(!dead[i]&&inside[i]){
r--;
dead[i]=true;
}
}else{
for(int i=0;i<n;i++)
if(!dead[i]&&!inside[i]){
r--;
dead[i]=true;
}
}
}
return f;
}
