#include "insects.h"
#include <bits/stdc++.h>
//#include "segments.h"
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2")
#define pb push_back
#define F first
#define pii pair<int,int>
#define all(a) a.begin(),a.end()
#define S second
#define sz(a) (int)a.size()
#define rep(i , a , b) for(int i = (a) ; i <= (b) ; i++)
#define per(i , a , b) for(int i = (a) ; i >= (b) ; i--)
#define ld double
#define ll long long
using namespace std ;
const int maxn = 5000 + 10 , inf = 1e9+ 10 , mod = 998244353;
int ted= 0 , n;
int ch(int x){
vector <int> vec;
rep(i , 0 , n-1){
move_inside(i) ;
if(press_button() == x+1){
move_outside(i) ;
}else{
vec.pb(i);
}
}
for(int x : vec)move_outside(x);
if(sz(vec)==1ll*x*ted)return 1;
return 0 ;
}
int min_cardinality(int N){
n = N ;
vector <int> vec;
rep(i ,0, n-1){
move_inside(i) ;
if(press_button() == 2){
move_outside(i);
}else{
vec.pb(i);
ted++;
}
}
for(int x : vec)move_outside(x) ;
int l =0 , r = n + 2;
while(r-l > 1){
int m = (l+r)/2 ;
if(ch(m) == 1){
l = m ;
}else{
r = m ;
}
}
return l ;
}
