#include <bits/stdc++.h>
using namespace std;
#define all(x) begin(x), end(x)
void move_inside(int i);
void move_outside(int i);
int press_button();
stack<int> in;
set<int> s;
int T;
bool check(int m, int &K) {
int oldK = K;
vector<int> v(all(s));
random_shuffle(all(v));
for (int i:v) {
move_inside(i);
if (press_button() <= m) {
in.push(i);
if (++K == m*T) {
while (!in.empty()) {
s.erase(in.top());
in.pop();
}
return true;
}
} else {
move_outside(i);
}
}
s.clear();
while (!in.empty()) {
s.insert(in.top());
move_outside(in.top());
in.pop();
}
K = oldK;
return false;
}
int min_cardinality(int N) {
srand(time(0));
move_inside(0);
in.push(0);
s.insert(0);
T = 1;
for (int i = 1; i < N; i++) {
s.insert(i);
move_inside(i);
if (press_button() == 1) {
in.push(i);
T++;
} else {
move_outside(i);
}
}
while (!in.empty()) {
move_outside(in.top());
in.pop();
}
int K = 0;
int l = 0, r = N / T + 1;
while (r - l > 1) {
int m = (l + r) / 2;
if (check(m, K)) {
l = m;
} else {
r = m;
}
}
return l;
}
