#include "insects.h"
#include <vector>
#include <algorithm>
#include <cassert>
#include <iostream>
using namespace std;
int N, T;
int cnt_inside;
vector<bool> inside;
void MOVE_IN(int n) {
// cerr << "+ " << n << endl;
assert(!inside[n]);
move_inside(n);
inside[n] = true;
++cnt_inside;
}
void MOVE_OUT(int n) {
// cerr << "- " << n << endl;
assert(inside[n]);
move_outside(n);
inside[n] = false;
--cnt_inside;
}
bool check(int x) {
// clear machine
for (int n = 0; n < N; ++n) {
if (inside[n])
MOVE_OUT(n);
}
MOVE_IN(0);
for (int n = 1; n < N; ++n) {
MOVE_IN(n);
int f = press_button();
if (f > x)
MOVE_OUT(n);
}
return cnt_inside == T * x;
}
int min_cardinality(int _N) {
N = _N;
cnt_inside = 0;
inside.assign(N, false);
check(1);
T = cnt_inside;
int res = 1;
int lo = 1, hi = N / T;
while (lo <= hi) {
int mid = lo + (hi - lo) / 2;
if (check(mid)) {
lo = mid+1;
res = mid;
}
else {
hi = mid-1;
}
}
return res;
}
