#include "insects.h"
#include <bits/stdc++.h>
using namespace std;
const int maxN = 2e3 + 20;
int order[maxN];
int pref[maxN];
vector<int> diff;
mt19937 gen(chrono::steady_clock::now().time_since_epoch().count());
int res;
struct state {
int lt, rt;
vector<int> rem;
bool on;
state() {};
state(int _lt, int _rt, vector<int> _rem, bool _on): lt(_lt), rt(_rt), rem(_rem), on(_on) {};
};
bool operator<(state S1, state S2) {
return S1.rem.size() > S2.rem.size();
}
priority_queue<state> Q;
void solve(int lt, int rt, vector<int> rem, bool on) {
if (res == 1) {
return;
}
if (lt == rt) {
res = min(res, (int)rem.size() + 1);
return;
}
if (rem.empty()) {
res = 1;
return;
}
int mt = (lt + rt) / 2;
bool all_left = true;
for (auto x: rem) {
all_left &= (pref[x] <= mt);
}
if (all_left) {
res = 1;
return;
}
if (on) {
for (int i = mt + 1; i <= rt; i++) {
if (diff[i] == -1) {
continue;
}
move_outside(diff[i]);
}
vector<int> left_rem;
vector<int> right_rem;
for (auto x: rem) {
if (pref[x] <= mt) {
left_rem.push_back(x);
continue;
}
move_inside(x);
if (press_button() == 2) {
left_rem.push_back(x);
}
else {
right_rem.push_back(x);
}
move_outside(x);
}
Q.emplace(lt, mt, left_rem, true);
Q.emplace(mt + 1, rt, right_rem, false);
}
else {
for (int i = mt + 1; i <= rt; i++) {
if (diff[i] == -1) {
continue;
}
move_inside(diff[i]);
}
vector<int> left_rem;
vector<int> right_rem;
for (auto x: rem) {
if (pref[x] <= mt) {
left_rem.push_back(x);
continue;
}
move_inside(x);
if (press_button() == 2) {
right_rem.push_back(x);
}
else {
left_rem.push_back(x);
}
move_outside(x);
}
Q.emplace(lt, mt, left_rem, false);
Q.emplace(mt + 1, rt, right_rem, true);
}
}
int min_cardinality(int N) {
for (int i = 0; i < N; i++) {
order[i] = i;
}
shuffle(order, order + N, gen);
diff.push_back(order[0]);
move_inside(order[0]);
vector<int> rem;
for (int i = 1; i < N; i++) {
move_inside(order[i]);
if (press_button() == 1) {
diff.push_back(order[i]);
}
else {
pref[order[i]] = (int)diff.size() - 1;
rem.push_back(order[i]);
move_outside(order[i]);
}
}
res = N + 1;
Q.emplace(0, (int)diff.size() - 1, rem, true);
while (!Q.empty()) {
int lt = Q.top().lt;
int rt = Q.top().rt;
rem = Q.top().rem;
bool on = Q.top().on;
Q.pop();
solve(lt, rt, rem, on);
}
return res;
}
