#include <iostream>
#include <vector>
#include <string>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <limits.h>
#include <math.h>
#include <chrono>
#include <queue>
#include <stack>
#include <algorithm>
using namespace std;
#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
#define ll long long
#define vi vector<ll>
#define vvi vector<vi>
#define p2 pair<ll, ll>
#define p3 tuple<ll,ll,ll>
#define p4 vi
#define ip3 tuple<int,int,int>
#define ip4 tuple<int,int,int,int>
#define vp2 vector<p2>
#define vp3 vector<p3>
#define inf 2e9
#define linf 1e17
#define read(a) cin >> a
#define write(a) cout << (a) << "\n"
#define dread(type, a) type a; cin >> a
#define dread2(type, a, b) dread(type, a); dread(type, b)
#define dread3(type, a, b, c) dread2(type, a, b); dread(type, c)
#define dread4(type, a, b, c, d) dread3(type, a, b, c); dread(type, d)
#define dread5(type, a, b, c, d, e) dread4(type, a, b, c, d); dread(type, e)
#ifdef _DEBUG
#define deb __debugbreak();
#else
#define deb ;
#endif
#define rep(i, high) for (ll i = 0; i < high; i++)
#define repp(i, low, high) for (ll i = low; i < high; i++)
#define repe(i, container) for (auto& i : container)
#define per(i, high) for (ll i = high; i >= 0; i--)
#define readpush(type,vect) type temp; read(temp); vect.push_back(temp);
#define readvector(type, name, size) vector<type> name(size); rep(i,size) {dread(type,temp); name[i]=temp;}
#define readinsert(type,a) {type temp; read(temp); a.insert(temp);}
#define all(a) begin(a),end(a)
#define setcontains(set, x) (set.find(x) != set.end())
#define stringcontains(str, x) (str.find(x) != string::npos)
#define within(a, b, c, d) (a >= 0 && a < b && c >= 0 && c < d)
#define ceildiv(x,y) ((x + y - 1) / y)
#define fract(a) (a-floor(a))
#define sign(a) ((a>0) ? 1 : -1)
auto Start = chrono::high_resolution_clock::now();
inline void fast()
{
ios::sync_with_stdio(false);
cin.tie(NULL); cout.tie(NULL);
}
int use_machine(vector<int> x);
int submit_query(vector<int> x) {
cerr << "x = {";
for(int v : x) cerr << v << ", ";
cerr << "}\n";
return use_machine(x);
}
vector<int> apos = { 0 }, bpos;
int num_checked = 1, a_count = 1;
int n;
int get_num_to_discover() {
return (apos.size() < 2 && bpos.size() < 2) || n - num_checked < 2 ? 1 : 2;
}
int get_num_to_count() {
return min(n - num_checked, (int)max(apos.size(), bpos.size()));
}
void discover() {
if(get_num_to_discover() == 1) {
cerr << "Discover 1" << endl;
int res = submit_query({ 0, num_checked });
(res == 0 ? apos : bpos).push_back(num_checked);
if(res == 0) a_count++;
num_checked++;
} else {
cerr << "Discover 2" << endl;
bool a_used = apos.size() > bpos.size();
vector<int>& arr = a_used ? apos : bpos;
int res = submit_query({ arr[0], num_checked, arr[1], num_checked + 1 });
pair<bool, bool> same;
if(res == 0) same = { true, true };
else if(res == 1) same = { true, false };
else if(res == 2) same = { false, true };
else same = { false, false };
if(a_used ^ same.first) {
bpos.push_back(num_checked);
} else {
apos.push_back(num_checked);
a_count++;
}
if(a_used ^ same.second) {
bpos.push_back(num_checked + 1);
} else {
apos.push_back(num_checked + 1);
a_count++;
}
num_checked += 2;
}
}
void count() {
cerr << "Counting" << endl;
bool a_used = apos.size() > bpos.size();
vector<int>& arr = a_used ? apos : bpos;
int num_query = get_num_to_count();
vector<int> q;
for(int i = 0; i < num_query; i++) {
q.push_back(arr[i]);
q.push_back(num_checked + i);
}
int res = submit_query(q);
int num_same = num_query - ceildiv(res, 2);
num_checked += num_query;
if(a_used) a_count += num_same;
else a_count += num_query - num_same;
if((res % 2 == 1) ^ a_used) apos.push_back(num_checked - 1);
else bpos.push_back(num_checked - 1);
}
int count_mushrooms(int N) {
n = N;
int k = 69;
while(num_checked < n) {
int end_now = ceildiv((n - num_checked), max(apos.size(), bpos.size()));
//int worst_a = apos.size(), worst_b = bpos.size();
int num_to_discover = get_num_to_discover();
//for(int i = 0; i < num_to_discover; i++) (worst_a < worst_b ? worst_a : worst_b)++;
int end_next = 1 + ceildiv((n - num_checked - num_to_discover), (max(apos.size(), bpos.size()) + 1));
k--;
if(k == 0) break;
if(end_now < end_next) break;
cerr << "Checked: " << num_checked << endl;
discover();
}
while(num_checked < n) {
count();
}
return a_count;
}
