#include "insects.h"
#include<bits/stdc++.h>
using namespace std;
int min_cardinality(int n) {
int am = 1;
move_inside(0);
vector<int> st(n,0);
st[0] = 1;
int sz = 1;
for(int i = 1; i < n; ++i){
move_inside(i);
if(press_button() != 1)move_outside(i);
else am++, st[i] = 1, sz++;
}
int l = 2, r = n/am, cur = 1;
vector<int> per(n);
iota(per.begin(),per.end(),0);
srand(time(0));
while(l <= r){
int m = (l+r)>>1;
vector<int> rem;
random_shuffle(per.begin(),per.end());
for(int x = 0; x < n; ++x){
int i = per[x];
if(st[i])continue;
sz++;
move_inside(i);
if(press_button() > m){
rem.push_back(i);
sz--;
move_outside(i);
}
if(sz == am*m){
for(int j = x+1; j < n; ++j){
if(st[per[j]])continue;
rem.push_back(per[j]);
}
break;
}
}
if(sz == am*m){
for(int i = 0; i < n; ++i)st[i] = 1;
for(auto x : rem)st[x] = 0;
cur = m;
l = m + 1;
}
else{
r = m - 1;
if(l <= r){
for(auto x : rem)st[x] = 1;
for(int i = 0; i < n; ++i){
if(!st[i]){move_outside(i);sz--;}
}
}
}
}
return cur;
}
