#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
int min_cardinality(int N){
vector <int> f;
int w[N],t[N];
for (int i=0; i<N; i++){
w[i]=-1;
t[i]=0;
}
f.push_back(0); w[0]=0;
move_inside(0);
for (int i=1; i<N; i++){
move_inside(i);
if (press_button()==1){
w[i]=f.size();
f.push_back(i);
} else move_outside(i);
}
for (int i:f) move_outside(i);
int m=f.size();
for (int b=0; b<11; b++){
vector <int> nd;
for (int i=0; i<m; i++) if (i&(1<<b)) nd.push_back(i);
if (nd.empty()) continue;
vector <int> ins;
for (int i=nd[0]; i<N; i++){
if (w[i]!=-1){
if (w[i]&(1<<b)){
move_inside(i);
ins.push_back(i);
}
continue;
}
move_inside(i);
if (press_button()==2) t[i]+=(1<<b);
move_outside(i);
}
for (int i:ins) move_outside(i);
}
map <int,int> mp;
for (int i=0; i<N; i++){
if (w[i]==-1) mp[t[i]]++;
else mp[w[i]]++;
}
int ans=N;
for (auto i:mp) ans=min(ans,i.second);
return ans;
}
