#include <bits/stdc++.h>
using namespace std;
#define ALL(x) x.begin(), x.end()
void move_inside(int i);
void move_outside(int i);
int press_button();
int min_cardinality(int N) {
vector <bool> done(N, 0);
stack <int> in;
move_inside(0);
done[0] = true;
in.push(0);
int T = 1;
for (int i=1; i<N; i++) {
move_inside(i);
if (press_button() == 1) {
done[i] = true;
in.push(i);
T++;
} else {
move_outside(i);
}
}
int ans = 1;
vector <int> p(N);
for (int i=0; i<N; i++) {
p[i] = i;
}
while (true) {
random_shuffle(ALL(p));
int K = 0;
bool b = 0;
while (!in.empty()) {
move_outside(in.top());
in.pop();
}
for (int i:p) {
if (done[i]) {
continue;
}
b = 1;
move_inside(i);
if (press_button() == 1) {
done[i] = true;
in.push(i);
K++;
} else {
move_outside(i);
}
if (K == T) {
break;
}
}
if (K < T || !b) {
break;
}
ans++;
}
return ans;
}
