#include "insects.h"

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


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

        // strategy 1 : large distinct (> 20)

        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()<=20) {
                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(auto x:pos) {
                        move_outside(x);
                }
                pos.clear();
                
                while(true) {
                        vector<int> inc;
                        int lst=0;
                        for(int i=0;i<N;i++) {
                                if(vis[i]) continue;

                                move_inside(i);
                                int cur=press_button();
                                if(cur>lst) {
                                        lst=cur;
                                        inc.push_back(i);
                                }
                        }

                        for(int i=N-1;i>inc.back();i--) {
                                if(vis[i]) continue;
                                move_outside(i);
                        }
                        vector<int> pnd;
                        for(int i=inc.back();i>=0;i--) {
                                if(vis[i]) continue;
                                move_outside(i);
                                int cur=press_button();
                                if(cur<lst) {
                                        pnd.push_back(i);
                                }
                                move_inside(i);
                        }
                        for(int i=0;i<=inc.back();i++) {
                                if(vis[i]) continue;
                                move_outside(i);
                        }
                        for(auto x:pnd) {
                                vis[x]=true;
                        }

                        int n=0;
                        for(int i=0;i<N;i++) n+=!vis[i];
                        if(n==0) return lst;
                }
        }
}