#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>;
mt19937 rnd(1e9+7);
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){
shuffle(all(b),rnd);
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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