#include <bits/stdc++.h>
using namespace std;
#define ALL(x) x.begin(), x.end()
#define DBGY(x) cerr << #x << ": " << x << ", ";
#define DBG(x) cerr << #x << ": " << x << endl;
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 old_k = K;
for (int i:s) {
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 = old_k;
return false;
}
int min_cardinality(int N) {
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, l = 0, r = N+1;
while (l+1 < r) {
assert(in.empty());
int m = (l+r)/2;
if (check(m, K)) {
l = m;
} else {
r = m;
}
}
return l;
}
