// Fifth submission after reading edi
#include "insects.h"
#include<bits/stdc++.h>
#define all(x) x.begin(), x.end()
using ll = long long;
using namespace std;
template<typename T>
using matrix = vector<vector<T>>;
struct Machine {
set<int> s;
void insert(int id){
s.insert(id);
move_inside(id);
}
void erase(int id){
s.erase(id);
move_outside(id);
}
int resp(){
return press_button();
}
void clear(){
auto it = s.begin();
while(it!=s.end()){
move_outside(*it);
it = s.erase(it);
}
}
};
int min_cardinality(int N) {
mt19937 rng(time(nullptr));
vector<int> dif;
vector<int> v;
Machine m;
for(int i = 0; i < N; i++){
m.insert(i);
if(m.resp() == 1){
dif.push_back(i);
} else m.erase(i);
v.push_back(i);
}
shuffle(all(v),rng);
m.clear();
int ini = 1, fim = N/dif.size();
vector<int> curinsert, lastinsert;
auto putless =[&](int mx){
for(int i : v){
if(m.s.count(i))
continue;
m.insert(i);
if(m.resp() > mx)
m.erase(i);
else curinsert.push_back(i);
if(m.s.size() == dif.size()*mx)
break;
}
};
int last = -1;
while(ini!=fim){
int mid = (ini+fim+1)>>1;
// cerr << "mid = " << mid << '\n';
if(mid < last){
vector<int> newv;
for(int i : m.s)
newv.push_back(i);
swap(v,newv);
for(int i : lastinsert)
m.erase(i);
}
putless(mid);
bool ok = m.s.size()%mid == 0 && m.s.size()/mid == dif.size();
if(ok)
ini = mid;
else fim = mid-1;
last = mid;
swap(curinsert,lastinsert);
curinsert.clear();
}
return ini;
}
