#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
int N;
vector<int> machine;
vector<bool> in_set;
void my_move_inside(int x) {
in_set[x] = 1;
}
void my_move_outside(int x) {
in_set[x] = 0;
}
int my_press_button() {
vector<int> cur;
for (int i = 0; i < N; i++) {
if (in_set[i]) {
cur.pb(i);
}
}
vector<int> tmp;
set_symmetric_difference(cur.begin(), cur.end(), machine.begin(), machine.end(), back_inserter(tmp));
sort(cur.begin(), cur.end());
for (auto i : tmp) {
if (binary_search(cur.begin(), cur.end(), i)) {
move_inside(i);
} else {
move_outside(i);
}
}
machine = cur;
return press_button();
}
int min_cardinality(int N) {
::N = N;
in_set.resize(N);
vector<int> v, alr_in;
my_move_inside(0);
v.pb(0);
for (int i = 1; i < N; i++) {
my_move_inside(i);
if (my_press_button() != 1) {
my_move_outside(i);
} else {
v.pb(i);
}
}
vector<int> insects;
insects.resize(N);
iota(insects.begin(), insects.end(), 0);
int lo = 1, hi = N / (int)v.size(), ans = -1;
while (lo <= hi) {
int mid = (lo + hi) / 2;
vector<int> to_remove = alr_in;
for (int i : insects) {
if (!binary_search(v.begin(), v.end(), i) && !binary_search(alr_in.begin(), alr_in.end(), i)) {
my_move_inside(i);
if (my_press_button() > mid) {
my_move_outside(i);
} else {
to_remove.pb(i);
}
}
}
if ((int)to_remove.size() == (int)v.size() * (mid - 1)) {
ans = mid;
lo = mid + 1;
alr_in = to_remove;
sort(alr_in.begin(), alr_in.end());
} else {
insects = v;
hi = mid - 1;
for (auto i : to_remove) {
my_move_outside(i);
insects.pb(i);
}
alr_in.clear();
}
}
return ans;
}
