#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
int min_cardinality(int N) {
// move_inside(int i);
// void move_outside(int i);
// press_button();
int l = 1, r = N + 1, mid;
vector<int> used;
queue<int> q;
for (int i = 0; i < N; i++)
{
q.push(i);
}
while (l + 1 < r)
{
mid = (l + r) / 2;
if (used.size() > 0)
{
for (auto x : used)
{
move_outside(x);
}
used = {};
}
int k = q.size();
queue<int> to_remove;
while (k--)
{
int y = q.front();
q.pop();
move_inside(y);
if (press_button() > mid)
{
to_remove.push(y);
continue;
}
used.push_back(y);
q.push(y);
}
if (used.size() % mid == 0)
{
while (!to_remove.empty())
{
used.push_back(to_remove.front());
q.push(to_remove.front());
to_remove.pop();
}
l = mid;
}
else
{
while (!to_remove.empty())
{
move_outside(to_remove.front());
to_remove.pop();
}
r = mid;
}
}
return l;
}
