#include <bits/stdc++.h>
#include "insects.h"
using namespace std;
int min_cardinality(int N) {
int d = 0;
bool marked[N]; memset(marked,false,sizeof(marked));
set<int> s;
vector<int> to_remove;
for(int i=0;i<N;i++) {
if(s.find(i)==s.end()){
move_inside(i);
s.insert(i);
}
int res = press_button();
if(res>1) {
if(s.find(i)!=s.end()){
move_outside(i);
s.erase(i);
}
}
else {
d++;
}
}
int ans = 0;
int lo=1,hi=N/d;
while(lo<=hi) {
int mid = (lo+hi)/2;
to_remove.clear();
vector<int> to_mark;
int cnt=0;
for(int i=0;i<N;i++) {
if(cnt==d*mid) break;
if(marked[i])continue;
if(s.find(i)==s.end()){
move_inside(i);
s.insert(i);
int res = press_button();
if(res > mid) {
if(s.find(i)!=s.end()) {
move_outside(i);
s.erase(i);
to_mark.push_back(i);
}
}
else {
cnt++;
to_remove.push_back(i);
}
}
else cnt++;
}
if(cnt==d*mid) {
lo=mid+1;
ans=max(ans,mid);
}
else {
hi=mid-1;
for(int x: to_remove) {
if(s.find(x)!=s.end()) {
move_outside(x);
s.erase(x);
}
}
for(int x: to_mark) marked[x]=true;
}
}
return ans;
}
