#define _CRT_SECURE_NO_WARNINGS
#include <bits/stdc++.h>
//#include "temp.cpp"
#include <cstdio>
using namespace std;
#ifndef ONLINE_JUDGE
#define dbg(x) cerr << #x <<" "; print(x); cerr << endl;
#else
#define dbg(x)
#endif
#define sz(x) (int)x.size()
#define len(x) (int)x.length()
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define clr(x) (x).clear()
#define uniq(x) x.resize(unique(all(x)) - x.begin());
#define blt __builtin_popcount
#define pb push_back
#define popf pop_front
#define popb pop_back
#define ld long double
#define ll long long
void print(long long t) {cerr << t;}
void print(int t) {cerr << t;}
void print(string t) {cerr << t;}
void print(char t) {cerr << t;}
void print(double t) {cerr << t;}
void print(long double t) {cerr << t;}
void print(unsigned long long t) {cerr << t;}
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define nl '\n'
// Indexed Set
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template <class T, class V> void print(pair <T, V> p);
template <class T> void print(vector <T> v);
template <class T> void print(set <T> v);
template <class T, class V> void print(map <T, V> v);
template <class T> void print(multiset <T> v);
template <class T, class V> void print(T v[],V n) {cerr << "["; for(int i = 0; i < n; i++) {print(v[i]); cerr << " "; } cerr << "]";}
template <class T, class V> void print(pair <T, V> p) {cerr << "{"; print(p.first); cerr << ","; print(p.second); cerr << "}";}
template <class T> void print(vector <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
// template <class T> void print(vector <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(set <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(multiset <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(Tree <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T, class V> void print(map <T, V> v) {cerr << "[ "; for (auto i : v) {print(i); cerr << " ";} cerr << "]";}
template <class T> void print(deque <T> v) {cerr << "[ "; for (T i : v) {print(i); cerr << " ";} cerr << "]";}
// for random generations
mt19937 myrand(chrono::steady_clock::now().time_since_epoch().count());
// mt19937 myrand(131);
// for grid problems
int dx[8] = {-1,0,1,0,1,-1,1,-1};
int dy[8] = {0,1,0,-1,1,1,-1,-1};
// lowest / (1 << 17) >= 1e5 / (1 << 18) >= 2e5 / (1 << 21) >= 1e6
void fastIO() {
ios_base::sync_with_stdio(false);
cin.tie(nullptr); cout.tie(nullptr);
}
// file in/out
void setIO(string str = "") {
fastIO();
// if(str == "input") {
// freopen("input.txt", "r", stdin);
// freopen("output.txt", "w", stdout);
// } else if(str != "") {
// freopen((str + ".in").c_str(), "r", stdin);
// freopen((str + ".out").c_str(), "w", stdout);
// }
}
void move_inside(int i);
void move_outside(int i);
int press_button();
int min_cardinality(int N) {
int diff = 0;
vector<int> het;
for(int i = 0; i < N; i++) {
move_inside(i);
int cr = press_button();
if(cr > 1) {
move_outside(i);
} else {
het.push_back(i);
diff++;
}
}
for(auto i: het) {
move_outside(i);
}
vector<int> hh;
for(int i = 0; i < N; i++) {
hh.push_back(i);
}
random_shuffle(all(hh));
if(diff == 2) {
for(int i = 0; i < N; i++) {
move_inside(i);
}
int cr = press_button();
return N - cr;
} else if(diff == 1) {
return N;
}
int ina = 1, inb = N / diff, answ = -1;
vector<bool> vi(N), rad(N);
while(ina <= inb) {
int mid = (ina + inb) / 2;
int ss = 0;
for(int i = 0; i < N; i++) {
if(vi[i]) {
ss++;
}
}
random_shuffle(all(hh));
int cnt = 0;
vector<int> this_turn, vabshe_eli;
for(int in = 0; in < N; in++) {
int i = hh[in];
if(rad[i]) continue;
if(vi[i]) continue;
move_inside(i);
int cur = press_button();
if(cur > mid) {
move_outside(i);
vabshe_eli.push_back(i);
} else {
vi[i] = true;
this_turn.push_back(i);
ss++;
}
if(ss == diff * mid) {
break;
}
}
if(ss == diff * mid) {
answ = mid;
ina = mid + 1;
} else {
for(auto i: this_turn) {
vi[i] = false;
move_outside(i);
}
for(auto i: vabshe_eli) {
rad[i] = true;
}
inb = mid - 1;
}
}
return answ;
}
