#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define ff first
#define ss second
ll ttt;
const ll INF=1e18;
const ll MOD=1e9+7;
const ll N=5007;
ll n,m;
ll t;
void calc_t(){
int cur=0;
vector<int>inside;
for(int i=0;i<n;i++){
move_inside(i);
cur++;
int res=press_button();
if(res>1){
cur--;
move_outside(i);
}
else{
inside.push_back(i);
}
}
t=cur;
for(int x:inside)move_outside(x);
}
bool is_smaller_equal(int k){
int cur=0;
vector<int>inside;
for(int i=0;i<n;i++){
move_inside(i);
cur++;
int res=press_button();
if(res>k+1){
cur--;
move_outside(i);
}
else{
inside.push_back(i);
}
}
for(int x:inside)move_outside(x);
if(cur==t*(k+1))return false;
return true;
}
int min_cardinality(int NN) {
n=NN;
calc_t();
// cout<<"t: "<<t<<endl;
int l=1,r=n-t+2;
while(l<r){
int mid=(l+r)/2;
if(is_smaller_equal(mid)){
r=mid;
}
else{
l=mid+1;
}
}
return l;
}
