#include "insects.h"
#include <algorithm>
#include <numeric>
#include <random>
#include <vector>
using namespace std;
int min_cardinality(int n) {
mt19937_64 gen{312321321321};
vector<int> inds(n);
iota(inds.begin(), inds.end(), 0);
shuffle(inds.begin(), inds.end(), gen);
vector<int> avail;
int inside = 0, types = 0;
for (int i : inds) {
move_inside(i), inside++;
if (press_button() == 1) {
types++;
} else {
avail.push_back(i);
move_outside(i), inside--;
}
}
if (types == 1 || types == n) {
return 1 ^ n ^ types;
}
int l = 1, r = n / types;
while (l < r) {
int m = (l + r) / 2, k = m + 1;
vector<int> vin, vout;
shuffle(avail.begin(), avail.end(), gen);
for (int i : avail) {
if (inside == k * types) {
vout.push_back(i);
continue;
}
move_inside(i), inside++;
if (press_button() > k) {
move_outside(i), inside--;
vout.push_back(i);
} else {
vin.push_back(i);
}
}
if (inside < k * types) {
for (int u : vin) {
move_outside(u), inside--;
}
avail = vin;
r = m;
} else {
avail = vout;
l = m + 1;
}
}
return l;
}
