#include "insects.h"

#include <bits/stdc++.h>
using namespace std;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

int cnt[2005];

int min_cardinality(int N) {
        vector<bool> vis(N);

        // strategy 1 : large distinct (>= 52)

        vector<int> pos;
        for(int i=0;i<N;i++) {
                if(vis[i]) continue;
                move_inside(i);

                if(press_button()==2) {
                        move_outside(i);
                } else {
                        vis[i]=true;
                        pos.push_back(i);
                }
        }

        if(pos.size()>=52) {
                int p=pos.size(),res=1;
                while(true) {
                        for(auto x:pos) {
                                move_outside(x);
                        }
                        pos.clear();

                        for(int i=0;i<N;i++) {
                                if(vis[i]) continue;
                                move_inside(i);

                                if(press_button()==2) {
                                        move_outside(i);
                                } else {
                                        vis[i]=true;
                                        pos.push_back(i);
                                }
                        }

                        if(pos.size()!=p) break;
                        res++;
                }

                return res;
        } else {
                for(int i=0;i<N;i++) {
                        if(vis[i]) continue;

                        move_inside(i);

                        vector<bool> done(pos.size());
                        while(true) {
                                int id=rng()%pos.size();
                                if(done[id]) continue;
                                done[id]=true;
                                move_outside(pos[id]);
                                if(press_button()==1) {
                                        cnt[pos[id]]+=1;
                                        break;
                                }
                                move_inside(pos[id]);
                        }

                        move_outside(i);
                }

                int res=N;
                for(auto j:pos) {
                        res=min(res,cnt[j]);
                }

                return res+1;
        }
}