#include "insects.h"
#include <vector>
#include <bits/stdc++.h>
#define rep(a,b,c) for(ll a=b; a<c; a++)
#define repr(a,b,c) for(ll a=b-1; a>c-1; a--)
#define repa(a,b) for(auto a:b)
#define ll long long
#define pll pair<ll, ll>
#define fi first
#define se second
#define pb push_back
#define mid ((l+r)>>1)
#define ppb pop_back
#define all(a) a.begin(), a.end()
using namespace std;
using vi = vector<int>;
int min_cardinality(int n) {
	vi a, b, c, d;
	rep(i,0,n){
		move_inside(i);
		a.pb(i);
		if(press_button()==2){
			move_outside(i);
			a.ppb();
			b.pb(i);
		}
	}
	int l=1, r=n/a.size(), y=a.size();
	repa(e,a) move_outside(e);
	while(l<=r){
		repa(e,b){
			if(y==mid*a.size()){
				d.pb(e);
				continue;
			}
			move_inside(e);
			c.pb(e);
			y++;
			if(press_button()==mid){
				move_outside(e);
				c.ppb();
				d.pb(e);
				y--;
			}
		}
		if(y==mid*a.size()){
			y=mid*a.size();
			l=mid+1;
			b=d;
			c.clear();
			d.clear();
		}else{
			repa(e,c) move_outside(e), y--;
			r=mid-1;
			b=c;
			c.clear();
			d.clear();
		}
	}
	return r;
}
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