#include "insects.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;
int solve(int P, vi r)
{
shuffle(all(r),mt);
if(P == 1) return siz(r);
if(P == 2)
{
forall(it,r) move_inside(it);
int p = siz(r) - press_button();
forall(it,r) move_outside(it);
return p;
}
if(siz(r) < P)
{
return 0;
}
if(siz(r) < P*2)
{
int p2 = 0;
forall(it,r)
{
move_inside(it);
if(press_button() == 1)
{
p2++;
}
else
{
move_outside(it);
}
}
if(p2 != P) return 0;
return 1;
}
vi Ps;
vi new_r;
vi new_r2;
forall(it,r)
{
move_inside(it);
if(press_button() == 2)
{
new_r.pb(it);
move_outside(it);
}
else
{
if(siz(Ps) == (P+1)/2)
{
new_r2.pb(it);
move_outside(it);
}
else
{
Ps.pb(it);
}
}
}
forall(it,Ps) move_outside(it);
return min(solve(siz(Ps),new_r)+1,solve(P-siz(Ps),new_r2));
}
int min_cardinality(int n)
{
random_start();
vi nums;
rep(i,n) nums.pb(i);
shuffle(all(nums),mt);
vi rest;
vi Ps;
forall(it,nums)
{
move_inside(it);
if(press_button() == 2)
{
rest.pb(it);
move_outside(it);
}
else
{
Ps.pb(it);
}
}
forall(it,Ps) move_outside(it);
return solve(siz(Ps),rest)+1;
}
