#include"insects.h"
#include<iostream>
#include<vector>
#include<set>
using namespace std;
vector<bool>inside;
int num_inside;
int n,distinct;
int low_bound,high_bound;
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);
}
void check(int c){
for(int i=0;i<n;i++){
c_move_inside(i);
if(c_press_button()>c)
c_move_outside(i);
}
bool res=num_inside==c*distinct;
if(res){
low_bound=max(low_bound,c);
high_bound=min(high_bound,c+(n-c*distinct)/distinct+1);
}else{
low_bound=max(low_bound,c-(c*distinct-num_inside));
high_bound=min(high_bound,c);
}
vector<int>inside_vec={inside.begin(),inside.end()};
for(int i=0;i<n;i++)
if(inside[i])
c_move_outside(i);
}
int get_distinct(){
for(int i=0;i<n;i++){
c_move_inside(i);
if(c_press_button()>1)
c_move_outside(i);
}
int res=num_inside;
vector<int>inside_vec={inside.begin(),inside.end()};
for(int i=0;i<n;i++)
if(inside[i])
c_move_outside(i);
return res;
}
int min_cardinality(int N){
n=N;
inside.resize(n);
distinct=get_distinct();
if(distinct>n/2)
return 1;
if(distinct==1)
return n;
low_bound=1;
high_bound=n/distinct+1;
while(low_bound<high_bound-1){
int m=(low_bound+high_bound)/2;
check(m);
}
return low_bound;
}
