#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
const int I_AM_A_BLACK_HOLE = 1;
#define pb push_back
#define MP make_pair
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
int n;
int unq;
vector<int> in;
vector<int> res;
vector<bool> is_in;
vector<int> save;
pair<bool, int> ok(int k) {
vector<int> killed;
while (!res.empty() && k < res.back()) {
move_outside(in.back());
killed.pb(in.back());
is_in[in.back()] = false;
in.pop_back();
res.pop_back();
}
if (killed.empty()) killed = save;
vector<int> all = killed;
shuffle(all.begin(), all.end(), rng);
for (int i : all) {
if (is_in[i]) continue;
move_inside(i);
int t = press_button();
if (t > k) move_outside(i);
else in.pb(i), is_in[i] = true, res.pb(t);
if (unq * k == in.size()) return MP(true, 0);
}
if (unq * k == in.size()) return MP(true, 0);
else {
save = in;
return MP(false, in.size() / unq);
}
}
int min_cardinality(int N) {
is_in.resize(N);
for (int i = 0; i < N; i++) {
save.pb(i);
move_inside(i);
int t = press_button();
if (t == 2) move_outside(i);
else in.pb(i), is_in[i] = true, res.pb(t);
}
unq = in.size();
if (unq == 1) return N;
if (unq == N) return 1;
if (unq <= I_AM_A_BLACK_HOLE) {
while (!in.empty()) {
move_outside(in.back());
is_in[in.back()] = false;
in.pop_back();
}
vector<int> all;
for (int i=0; i<N; i++) all.pb(i);
unq--;
int ans = N;
while (unq--) {
vector<int> rem;
int cur = 0;
shuffle(all.begin(), all.end(), rng);
while (!all.empty()) {
int i = all.back();
all.pop_back();
move_inside(i);
int res = press_button();
if (res == cur) {
move_outside(i);
rem.pb(i);
}
else {
in.pb(i);
}
cur = res;
}
ans = min(ans, cur);
if (ans == 1) return 1;
all = rem;
while (!in.empty()) {
move_outside(in.back());
in.pop_back();
}
}
return min((int) all.size(), ans);
}
n = N;
int l = 1, r = n / unq;
while (l != r) {
int mid = (l+r+1) / 2;
auto [can, lim] = ok(mid);
if (can) l = mid;
else r = min(mid - 1, lim);
}
return l;
}
