#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using lld = long double;
using ii = pair<int,int>;
using pll = pair<ll, ll>;
using vi = vector<int>;
using vll = vector<ll>;
using vii = vector<ii>;
using vpll = vector<pll>;
using vlld = vector<lld>;
// #define endl '\n'
#define all(x) x.begin(),x.end()
#define lsb(x) x&(-x)
#define gcd(a,b) __gcd(a,b)
#define sz(x) (int)x.size()
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define fls cout.flush()
#define fore(i,l,r) for(auto i=l;i<r;i++)
#define fo(i,n) fore(i,0,n)
#define forex(i,r,l) for(auto i=r; i>=l;i--)
#define ffo(i,n) forex(i,n-1,0)
bool cmin(ll &a, ll b) { if(b<a){a=b;return 1;}return 0; }
bool cmax(ll &a, ll b) { if(b>a){a=b;return 1;}return 0; }
void valid(ll in) { cout<<((in)?"Yes\n":"No\n"); }
ll lcm(ll a, ll b) { return (a/gcd(a,b))*b; }
ll gauss(ll n) { return (n*(n+1))/2; }
int min_cardinality(int n) {
vll A, B, wh(n, 0);
A.pb(0);
move_inside(0);
fore (i, 1, n) {
move_inside(i);
if (press_button() == 2) {
move_outside(i);
B.pb(i);
continue;
}
A.pb(i);
}
for (ll v: A) move_outside(v);
ll m = sz(A);
ll p = 0;
while ((1ll<<p) < m) p++;
fo (b, p) {
fo (i, sz(A)) {
if (i&(1ll<<b)) move_inside(A[i]);
}
for (ll i: B) {
move_inside(i);
if (press_button() == 2) {
wh[i] += 1ll<<b;
}
move_outside(i);
}
fo (i, sz(A)) {
if (i&(1ll<<b)) move_outside(A[i]);
}
}
vll cnt(sz(A), 1);
for (ll i: B) cnt[wh[i]]++;
// for (ll c: cnt) cout << c << ' ';
// cout << '\n';
return *min_element(all(cnt));
}
