#include "insects.h"
#include<bits/stdc++.h>
using namespace std;
int min_cardinality(int N){
  vector<bool> in(N, false);
  int t = 0;
  for (int i=0; i<N; i++){
    move_inside(i);
    in[i] = true;
    t++;
    if (press_button() > 1){
      move_outside(i);
      in[i] = false;
      t--;
    }
  }
  if (t == 1) return N;
  int k = t;
  int l = 1, r = N/t+1;
  vector<int> w;
  for (int i=0; i<N; i++) w.push_back(i);
  while (l < r-1){
    vector<int> v;
    int m = (l+r)/2;
    for (int j=0; j<w.size(); j++){
      if (k+(int)w.size()-j < t*m) break;
      int i = w[j];
      if (in[i]) continue;
      move_inside(i);
      in[i] = true;
      k++;
      if (press_button() > m){
        move_outside(i);
        in[i] = false;
        k--;
      }
      else v.push_back(i);
    }
    if (k == t*m) l = m;
    else {
      r = m;
      for (int x : v){
        move_outside(x);
        in[x] = false;
        k--;
      }
      w = v;
    }
  }
  return l;
}
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