#include <bits/stdc++.h>
using namespace std;
#include "insects.h"
int min_cardinality(int N) {
    int a[N],freq[N];
    for(int i=0;i<N;i++){
        a[i]=-1;
        freq[i]=0;
    }
    int cnt=0;
    for(int i=0;i<N;i++){
        if(a[i]==-1)a[i]=cnt++;
        move_inside(i);
        for(int j=i+1;j<N;j++){
            move_inside(j);
            if(press_button()>1)a[j]=a[i];
            move_outside(j);
        }
        move_outside(i);
        freq[a[i]]++;
    }
    int mn=N;
    for(int i=0;i<N;i++){
        if(freq[i]>0)mn=min(mn,freq[i]);
    }
    return mn;
}
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