#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define mp make_pair
#define pii pair<int, int>
#define fi first
#define se second
int min_cardinality(int n){
int uq=1;
move_inside(0);
vector<bool> got(n, 0);
for (int i=1; i<n; ++i){
move_inside(i);
got[i]=1;
if (press_button()==2)move_outside(i), got[i]=0;
else ++uq;
}
if (uq==1)return n;
int low=1, high=n/uq+1;
while (low+1<high){
int mid=(low+high)/2, c=0;
for (int i=0; i<n; ++i)if (got[i])++c;
for (int i=0; i<n; ++i)if (!got[i]){
move_inside(i);
got[i]=1;
if (press_button()>mid)move_outside(i), got[i]=0;
else ++c;
}
if (c==uq*mid)low=mid;
else{
high=mid;
for (int i=0; i<n; ++i)if (got[i])move_outside(i), got[i]=0;
}
}
return low;
}
