#include "insects.h"
#include<bits/stdc++.h>
#define vi vector<int>
#define pb push_back
#define FOR(i, k, n) for(int i = k; i<n; i++)
#define f0r(i,n) for(int i = 0; i< n; i++)
#define mp make_pair
#define pii pair<int,int>
#define vb vector<bool>
#define vout(x) for(auto u : x)cout<<u<<' '; cout<<'\n';
#define push(x); move_inside(x); v[x] = 1;
#define pull(x); move_outside(x); v[x] = 0;
using namespace std;
vector<bool>v;
vi rep;
int n;
int solve(int l, int r, int y){
// cout<<y<<' '<<'y'<<'\n';
// cout<<l<<' '<<r<<'\n';
int mid = (l + r) / 2;
vb cur(n);
FOR(i, l, mid + 1){
cur[rep[i]] = 1;
}
cur[y] = 1;
f0r(i,n){
if(v[i] && (!cur[i])){pull(i);}
else if((!v[i]) && cur[i]){push(i);}
}
// vout(v);
int x = press_button();
if(x == 2){
if(l == mid){
return l;
}
else{
return solve(l, mid, y);
}
}
else{
if(mid + 1 == r)return r;
else{
return solve(mid + 1, r, y);
}
}
}
int min_cardinality(int n) {
::n = n;
v.resize(n);
vi col(n, -1);
int cur = 1;
col[0] = 0;
rep.resize(n);
f0r(i,n) rep[i] = 0;
rep[0] = 0;
FOR(ii, 1, n){
vb cura(n);
FOR(i, 0, cur){
cura[rep[i]] = 1;
}
cura[ii] = 1;
f0r(i,n){
if(v[i] && (!cura[i])){pull(i);}
else if((!v[i]) && cura[i]){push(i);}
}
int x = press_button();
if(x == 1){
col[ii] = cur;
rep[ii] = cur;
cur++;
}
else{
// cout<<ii<<' '<<"ii"<<'\n';
int nc = solve(0, cur - 1, ii);
col[ii] = nc;
}
}
// vout(col);
vi cnt(cur + 1);
f0r(i, n)cnt[col[i]]++;
int ans = 1e9;
f0r(i, cur){
ans = min(ans, cnt[i]);
}
return ans;
}
