#include "insects.h"
#include <variant>
#include <vector>
#include <iostream>
#include <algorithm>
#include <set>
using namespace std;
#define ll int
#define F first
#define S second
#define pb push_back
#define sz(x) (ll)x.size()
#define endl "\n"
#define ins insert
typedef vector <ll> vi;
typedef pair <ll, ll> ii;
typedef vector <ii> vii;
typedef set <ll> si;
#define dbg(x) cout<<#x<<": "<<x<<endl;
#define dbg2(x,y) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<endl;
#define dbg3(x,y,z) cout<<#x<<": "<<x<<" "<<#y<<": "<<y<<" "<<#z<<": "<<z<<endl;
void printVct(vi &v){
for (ll i =0; i<sz(v); i++){
cout<<v[i]<<" ";
}
cout<<endl;
}
#define MID ((l+r)/2)
void solve(vi &u, si &machine_u, ll l, ll r, vi test_subjects, vi &id){
if (!sz(test_subjects)) return;
if (l == r){
for (ll i =0; i<sz(test_subjects); i++){
id[test_subjects[i]] = u[l];
}
}
else{
vi remaining_test_subjects, opposite_remaining_test_subjects;
//left:
for (ll i = 0; i<sz(u); i++){
if (l <= i && i <= MID){ //wanted
if (machine_u.find(u[i]) == machine_u.end()){
//add
move_inside(u[i]);
machine_u.ins(u[i]);
}
}
else{ //unwanted
if (machine_u.find(u[i]) != machine_u.end()){
//remove
move_outside(u[i]);
machine_u.erase(u[i]);
}
}
}
for (ll i = 0; i<sz(test_subjects); i++){
move_inside(test_subjects[i]);
ll x = press_button();
if (x == 2){
remaining_test_subjects.pb(test_subjects[i]);
}
else{
opposite_remaining_test_subjects.pb(test_subjects[i]);
}
move_outside(test_subjects[i]);
}
solve(u, machine_u, l, MID, remaining_test_subjects, id);
//right:
solve(u, machine_u, MID+1, r, opposite_remaining_test_subjects, id);
}
}
int min_cardinality(int N){
ll n = N;
vi v(n);
//step 1: make list of unique elements
vi u(1,0);
move_inside(0);
for (ll i =1; i<n;i++){
move_inside(i);
ll x = press_button();
if (x == 2){
move_outside(i);
}
else{
u.pb(i);
}
}
// printVct(u);
//step 2: binary search
set <ll> st;
for (ll i =0; i<sz(u); i++){
st.insert(u[i]);
}
vi test_subjects, id(n);
for (ll i =0; i<n; i++){
if (st.find(i) == st.end()){
test_subjects.pb(i);
id[i] = -1;
}
else{
id[i] = i;
}
}
si machine_u;
for (ll i = 0; i<sz(u); i++) machine_u.insert(u[i]);
solve(u, machine_u, 0, sz(u)-1, test_subjects, id);
// printVct(id);
sort(id.begin(), id.end());
vi f(n,0);
for (ll i =0; i<n; i++){
f[id[i]]++;
}
ll ans = 1000000000;
for (ll i =0; i<n; i++){
if (f[i]){
ans = min(ans, f[i]);
}
}
return ans;
}
/*
6
5 8 9 5 9 9
5
1 2 2 3 4
10
1 2 2 6 1 3 3 2 6 1
6
1 2 3 4 5 6
1
1
*/
