#include "insects.h"
#include <algorithm>
#include <bitset>
#include <cstdint>
#include <cstring>
#include <iostream>
#include <limits.h>
#include <math.h>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
//#define int long long
#define loop(X, N) for(int X = 0; X < (N); X++)
#define all(V) V.begin(), V.end()
#define rall(V) V.rbegin(), V.rend()
using namespace std;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int, int> ii;
typedef vector<ii> vii;
typedef vector<vector<ii>> vvii;
typedef vector<bool> vb;
typedef vector<vector<bool>> vvb;
typedef uint64_t u64;
typedef int64_t i64;
struct Manager {
vb state;
map<int, int> toChange;
int n;
Manager(int _n) {
n = _n;
state = vb(n);
}
void inside(int i) {
//move_inside(i);
//todo[i] = 1;
toChange[i] = 1;
}
void outside(int i) {
//move_outside(i);
//todo[i] = 0;
toChange[i] = 0;
}
int press() {
for (auto [i, action] : toChange) {
if (action == 0) {
move_outside(i);
}
else {
move_inside(i);
}
}
toChange.clear();
return press_button();
}
};
int min_cardinality(int N) {
Manager manager(N);
vb isDone(N);
vi madeItBigger(N, 0);
vb isRemoved(N);
loop(i, N) {
manager.inside(i);
int res = manager.press();
if (res > 1) {
madeItBigger[i] = 1;
manager.outside(i);
isRemoved[i] = true;
}
}
int diffCount = 0;
loop(i, N) {
if (!isRemoved[i]) {
diffCount++;
isDone[i] = true;
}
}
int prevRes = 1;
loop(i, N) {
if (isDone[i]) continue;
manager.inside(i);
int res = manager.press();
if (res > prevRes) {
madeItBigger[i] = max(madeItBigger[i], prevRes);
prevRes = res;
}
}
int maxCount = prevRes;
loop(i, N) {
if (isDone[i]) continue;
manager.outside(i);
}
int total = N;
vi possible;
for (int x = 1; x <= N; x++) {
if (diffCount == 2 && x + maxCount != total) continue;
if (diffCount == 1 && (x != maxCount || x != total)) continue;
if ((diffCount - 1) * x + maxCount <= total && total <= (diffCount - 1) * maxCount + x) {
possible.push_back(x);
}
}
int extra = 1;
int l = 0, r = possible.size() - 1;
while (l < r) {
int m = (l + r + 1) / 2;
int lessThanM = diffCount * extra;
isRemoved = vb(N);
int prevPress = extra;
loop(i, N) {
if (isDone[i]) continue;
if (madeItBigger[i] >= possible[m]) {
isRemoved[i] = true;
}
else {
manager.inside(i);
int res = manager.press();
if (res > prevPress) {
madeItBigger[i] = max(madeItBigger[i], prevPress);
prevPress = res;
}
if (res > possible[m]) {
madeItBigger[i] = max(madeItBigger[i], possible[m]);
manager.outside(i);
isRemoved[i] = true;
}
else {
lessThanM++;
}
}
}
if (lessThanM == diffCount * possible[m]) {
l = m;
loop(i, N) {
if (!isRemoved[i] && !isDone[i]) {
isDone[i] = true;
}
}
extra = possible[m];
}
else {
r = m - 1;
loop(i, N) {
if (!isRemoved[i] && !isDone[i]) {
manager.outside(i);
}
}
}
}
return possible[l];
}
