#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define sz(a) (int)a.size()
#define all(a) begin(a), end(a)
using vi = vector<int>;
using ll = long long;
using ar2 = array<ll,2>;
using ar3 = array<ll,3>;
const int mxN = (int)2e3+10;
int n, cnt[mxN];
vi v, others;
set<int> S;
map<set<int>,int> M;

void move_in(int i){
	if(S.count(i)) return;
	S.insert(i); move_inside(i);
}

void move_out(int i){
	if(!S.count(i)) return;
	S.erase(i); move_outside(i);
}

int press(){
	if(M.count(S)) return M[S];
	return M[S] = press_button(); 
}

void dnc(int l, int r, vi query){
	if(l>r) return;
	if(l==r or !sz(query)){
		cnt[v[l]]+=sz(query);
		return;
	}
	int mid = (l+r)/2;
	vi qL, qR; qL.clear(), qR.clear();
	for(int i = l; i <= mid; i++) move_in(v[i]);
	for(auto i : query){
		move_in(i);
		if(press()==2) qL.pb(i);
		else qR.pb(i);
		move_out(i);
	}
	dnc(mid+1,r,qR);
	for(int i = mid+1; i <= r; i++) move_out(v[i]);
	dnc(l,mid,qL); 
}

int min_cardinality(int N) {
	n = N; int ans = n;
	for(int i = 0; i < n; i++){
		move_in(i); v.pb(i);
		if(press()==2) 
			move_out(i), v.pop_back(), others.pb(i);
	}
	for(auto u : v) move_out(u);
	for(auto u : v) cnt[u]++;
	dnc(0,sz(v)-1,others);
	for(auto u : v) ans = min(ans, cnt[u]);
	return ans;
}