#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define all(a) (a).begin(), (a).end()
#define ll long long
const int mod = 1000002022;
vector<int> state, p;
int n, m;
vector<vector<int>> g;
template<typename T>
int len(T &a){return a.size();}
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
void shuffle(vector<int> &a, int n){
if(n == 1) return;
random_shuffle(a.begin(), a.begin() + n);
for(int i = 0; i < n; i ++){
int aa = rng() % n, bb = rng() % n;
while(bb == aa) bb = rng() % n;
swap(a[aa], a[bb]);
}
}
int min_cardinality(int n) {
vector<int> v;
vector<int> done(n);
for(int i = 0; i < n; i ++){
move_inside(i);
if(press_button() == 2){
move_outside(i);
}else v.push_back(i), done[i] = 1;
}
if(len(v) == 1){
return n;
}
int dis = len(v);
auto check = [&](int m)->int{
vector<int> rem;
for(int i = 0; i < n; i ++){
if(done[i]) continue;
move_inside(i);
if(press_button() <= m){
rem.push_back(i);
}else{
move_outside(i);
}
}
for(auto u : rem) move_outside(u);
return dis + len(rem);
};
int cur = n / dis;
while(cur > 1){
int cnt = check(cur);
//cout << cur << ' ' << cnt << endl;
if(cnt == cur * dis){
return cur;
}else cur = cnt / dis;
}
return cur;
}
