#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
refs:
https://youtu.be/mm5Nv81P5u8?t=19948
edi
*/
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "insects.h"
int min_cardinality(int n) {
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
vector<int> order(n);
rep(i,n) order[i] = i;
vector<int> uniq_guys;
rep(i,n){
move_inside(i);
int res = press_button();
if(res >= 2){
move_outside(i);
}
else{
uniq_guys.pb(i);
}
}
trav(i,uniq_guys){
move_outside(i);
}
if(sz(uniq_guys) == 1){
return n;
}
if(sz(uniq_guys) == n){
return 1;
}
vector<bool> ignore(n);
vector<int> in_machine;
auto ok = [&](int mid){
// check if ans <= mid
// check if ans < mid+1
vector<int> good, bad;
shuffle(all(order),rng);
rep(ind,n){
int i = order[ind];
if(ignore[i]) conts;
if(sz(in_machine)+sz(good) == sz(uniq_guys)*(mid+1)){
break;
}
move_inside(i);
int res = press_button();
if(res > mid+1){
bad.pb(i);
move_outside(i);
}
else{
good.pb(i);
}
}
if(sz(in_machine)+sz(good) == sz(uniq_guys)*(mid+1)){
// everybody occurs at least mid+1 times
// anybody in the machine would stay in the machine forever
trav(i,good){
in_machine.pb(i);
ignore[i] = 1;
}
return false;
}
else{
// at least one guy occurs < (mid+1) #of times
// i.e at least one guys occurs <= mid #of times
// right endpoint of range decreases
// so ignore all bad guys in future iterations
// remove all good guys in this iteration from the machine
trav(i,bad){
ignore[i] = 1;
}
trav(i,good){
move_outside(i);
}
return true;
}
};
int l = 1, r = n/sz(uniq_guys)-1;
int ans = n/sz(uniq_guys);
while(l <= r){
int mid = (l+r) >> 1;
// is min <= mid?
if(ok(mid)){
ans = mid;
r = mid-1;
}
else{
l = mid+1;
}
}
return ans;
}
