#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
typedef int ll;
const ll INF = 1e9+7;
const ll MOD = 998244353;
typedef pair<ll,ll> ii;
#define iii pair<ii,ll>
#define f(i,a,b) for(int i = a;i < b;i++)
#define pb push_back
#define vll vector<ll>
#define F first
#define S second
#define all(x) (x).begin(), (x).end()
///I hope I will get uprating and don't make mistakes
///I will never stop programming
///sqrt(-1) Love C++
///Please don't hack me
///@TheofanisOrfanou Theo830
///Think different approaches (bs,dp,greedy,graphs,shortest paths,mst)
///Stay Calm
///Look for special cases
///Beware of overflow and array bounds
///Think the problem backwards
///Training
int min_cardinality(int N){
srand(time(0));
ll n = N;
set<ll>ex;
set<ll>olo;
bool v[n] = {0};
f(i,0,n){
move_inside(i);
olo.insert(i);
ex.insert(i);
v[i] = 1;
if(1 != press_button()){
ex.erase(i);
v[i] = 0;
move_outside(i);
}
}
ll d = ex.size();
ll l = 2,r = n / d;
ll ans = 1;
set<ll>cur = ex;
while(l <= r){
ll mid = (l+r)/2 + rand() % 2;
mid = min(mid,r);
for(auto x:olo){
if(!v[x]){
move_inside(x);
v[x] = 1;
cur.insert(x);
if(press_button() > mid){
move_outside(x);
cur.erase(x);
v[x] = 0;
}
}
}
if((ll)cur.size() == d * mid){
l = mid + 1;
ex = cur;
ans = max(ans,mid);
}
else{
olo = cur;
for(auto x:cur){
if(!ex.count(x)){
v[x] = 0;
move_outside(x);
}
}
cur = ex;
r = mid - 1;
}
}
return ans;
}
