#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
int min_cardinality(int N) {
vector<int> roots;
int nbCC = 0;
for (int i = 0; i < N; ++i) {
move_inside(i);
if (i and press_button() == 2)
move_outside(i);
else
roots.push_back(i), nbCC++;
}
vector<bool> isRoot(N);
for (int r : roots)
isRoot[r] = true;
vector<int> toProcess;
for (int i = 0; i < N; ++i)
if (!isRoot[i])
toProcess.push_back(i);
int lo = 1, up = N / nbCC;
// invariant : everything outside of toProcess has majority element >= lo
while (lo < up) {
int mid = (lo + up + 1) / 2;
vector<int> kept;
vector<int> popped;
for (int i : toProcess) {
move_inside(i);
if (press_button() > mid)
popped.push_back(i), move_outside(i);
else
kept.push_back(i);
}
int cntPopped = popped.size();
if (cntPopped == N - nbCC * mid) {
lo = mid;
toProcess = move(popped);
} else {
up = mid - 1;
for (int i : kept)
move_outside(i);
}
}
return lo;
}
