// correct/solution-pwypeanut.cpp
#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
int find_ans(set<int> S, int mx, int tt) {
if (mx <= 0) return 0;
if (S.size() == 0) return 0;
int test = (mx + 1) / 2;
set<int> lefty = S;
vector<int> inside;
for (auto it = (S.begin()); it != S.end(); it++) {
move_inside(*it);
if (press_button() > test) {
move_outside(*it);
} else {
inside.push_back(*it);
lefty.erase(*it);
}
}
for (int i = 0; i < (int)inside.size(); i++) move_outside(inside[i]);
if ((int)inside.size() == test * tt) {
return find_ans(lefty, mx - test, tt) + test;
} else {
set<int> res;
for (int i = 0; i < (int)inside.size(); i++) res.insert(inside[i]);
return find_ans(res, test - 1, tt);
}
}
int min_cardinality(int N) {
set<int> lefty;
for (int i = 1; i < N; i++) lefty.insert(i);
vector<int> types;
types.push_back(0);
move_inside(0);
for (int i = 1; i < N; i++) {
move_inside(i);
if (press_button() == 2) {
move_outside(i);
} else {
types.push_back(i);
lefty.erase(i);
}
}
for (int i = 0; i < (int)types.size(); i++) move_outside(types[i]);
if (types.size() == 1) return N;
return find_ans(lefty, ceil((double)N / types.size()) - 1, types.size()) + 1;
}
