/*
#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
*/
#include<bits/stdc++.h>
#include "insects.h"
//#include <ext/pb_ds/assoc_container.hpp>
//#include <ext/pb_ds/tree_policy.hpp>
//using namespace __gnu_pbds;
using namespace std;
typedef long double ld;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int>vi;
typedef vector<vector<int>>vvi;
typedef vector<ll>vl;
typedef vector<vl> vvl;
typedef pair<int,int>pi;
typedef pair<ll,ll> pl;
typedef vector<pl> vpl;
typedef vector<ld> vld;
typedef pair<ld,ld> pld;
typedef vector<pi> vpi;
//typedef tree<ll, null_type, less_equal<ll>,rb_tree_tag,tree_order_statistics_node_update> ordered_set;
template<typename T> ostream& operator<<(ostream& os, vector<T>& a){os<<"[";for(int i=0; i<ll(a.size()); i++){os << a[i] << ((i!=ll(a.size()-1)?" ":""));}os << "]\n"; return os;}
#define all(x) x.begin(),x.end()
#define YES out("YES")
#define NO out("NO")
#define out(x){cout << x << "\n"; return;}
#define outfl(x){cout << x << endl;return;}
#define GLHF ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL)
#define print(x){for(auto ait:x) cout << ait << " "; cout << "\n";}
#define pb push_back
#define umap unordered_map
int min_cardinality(int n){
int diff=0;
vector<bool>in(n);
vi a(n);
iota(all(a),0);
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
shuffle(all(a),rng);
for(int i=0; i<n; i++){
move_inside(a[i]),in[a[i]]=1;
diff++;
if(press_button()!=1)
move_outside(a[i]),diff--,in[a[i]]=0;
}
int l=2,r=n/diff,ans=1;
while(l<=r){
int m=(l+r)/2;
int good=n;
for(int i=0; i<n;i ++){
if(in[a[i]])continue;
move_inside(a[i]);
in[a[i]]=1;
int p=press_button();
if(p>m)
good--, move_outside(a[i]), in[a[i]]=0;
}
if(diff*m<=good)
l=m+1,ans=m;
else {
r = m - 1;
if(l>r)break;
for(int i=0; i<n;i ++)
if(in[a[i]])
in[a[i]]=0, move_outside(a[i]);
}
}
return ans;
}
