#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef long double ld;
typedef pair<ll, ll> pll;
#define FOR(i, a, b) for(int i = a; i < b; i++)
#define ROF(i, a, b) for(int i = a; i >= b; i--)
#define ms memset
#define pb push_back
#define fi first
#define se second
#define mi(i) move_inside(i)
#define mo(i) move_outside(i)
#define pr press_button()
int L = 3;
int min_cardinality(int n) {
vi diff; vi used(n);
FOR(i,0,n){
mi(i);
int val = pr;
if (val >= 2){
mo(i);
}else{
diff.pb(i);
used[i] = 1;
}
}
int cnt = diff.size();
for (int u : diff) mo(u);
if (cnt <= L){
vi num(cnt);
FOR(i,0,n){
if (used[i]) continue;
mi(i);
FOR(j,0,cnt){
mi(diff[j]);
if (pr >= 2){
num[j]++;
}
mo(diff[j]);
}
mo(i);
}
int mn = num[0]+1;
FOR(i,0,cnt){
mn = min(mn, num[i]+1);
}
return mn;
}
vi rem(n); vi taken(n), t;
int l = 1; int r = n / cnt + 1;
int len=0; vi a;
while (r-l>1){
int mid = (l+r)/2;
FOR(i,0,n){
if (taken[i] || rem[i]) continue;
mi(i); len++;
if (pr > mid){
mo(i); len--;
}else{
a.pb(i);
}
}
if (len == mid * cnt){
l = mid;
for (int i : a){
taken[i]=1; t.pb(i);
}
}else{
r = len/cnt + 1;
FOR(i,0,n) rem[i]=1;
for (int u : a){
rem[u]=0;
if (!taken[u]){mo(u); len--;}
}
a=t;
}
}
return l;
}
