#include "mushrooms.h"
#include <bits/stdc++.h>
#ifdef NON_SUBMIT
#define TEST(n) (n)
#define tout cerr
#else
#define TEST(n) ((void)0)
#define tout cin
#endif
using namespace std;
vector<pair<int,int>> V;
vector<int> A, B, Q;
int D[3];
void query2()
{
int a=V[0].first, b=V[1].first, r;
if(A.size()>1) {
r=use_machine({A[0],a,A[1],b});
if(r&1) {
B.push_back(b);
A.push_back(V[1].second);
}
else {
A.push_back(b);
B.push_back(V[1].second);
}
if(r>1) {
B.push_back(a);
A.push_back(V[0].second);
}
else {
A.push_back(a);
B.push_back(V[0].second);
}
}
else {
r=use_machine({B[0],a,B[1],b});
if(r&1) {
A.push_back(b);
B.push_back(V[1].second);
}
else {
B.push_back(b);
A.push_back(V[1].second);
}
if(r>1) {
A.push_back(a);
B.push_back(V[0].second);
}
else {
B.push_back(a);
A.push_back(V[0].second);
}
}
V.clear();
}
void query3()
{
int a, b, c, r;
if(Q.size()==1) {
a=Q.back(); Q.pop_back();
if(use_machine({0,a})) B.push_back(a);
else A.push_back(a);
}
else if(Q.size()==2) {
a=Q.back(); Q.pop_back();
b=Q.back(); Q.pop_back();
if(A.size()>1) {
r=use_machine({A[0],a,A[1],b});
if(r&1) B.push_back(b);
else A.push_back(b);
if(r>1) B.push_back(a);
else A.push_back(a);
}
else {
r=use_machine({B[0],a,B[1],b});
if(r&1) A.push_back(b);
else B.push_back(b);
if(r>1) A.push_back(a);
else B.push_back(a);
}
}
else {
a=Q.back(); Q.pop_back();
b=Q.back(); Q.pop_back();
c=Q.back(); Q.pop_back();
if(A.size()>1) {
r=use_machine({A[0],a,A[1],b,c});
if(r&1) B.push_back(c);
else A.push_back(c);
if(r==0) {
A.push_back(a);
A.push_back(b);
}
else if(r==1) {
A.push_back(a);
Q.push_back(b);
}
else if(r==2) {
V.emplace_back(a,b);
if(V.size()>1) query2();
}
else if(r==3) {
B.push_back(a);
Q.push_back(b);
}
else {
B.push_back(a);
B.push_back(b);
}
}
else {
r=use_machine({B[0],a,B[1],b,c});
if(r&1) A.push_back(c);
else B.push_back(c);
if(r==0) {
B.push_back(a);
B.push_back(b);
}
else if(r==1) {
B.push_back(a);
Q.push_back(b);
}
else if(r==2) {
V.emplace_back(a,b);
if(V.size()>1) query2();
}
else if(r==3) {
A.push_back(a);
Q.push_back(b);
}
else {
A.push_back(a);
A.push_back(b);
}
}
}
}
int query()
{
int m=min(Q.size(),max(A.size(),B.size())), r;
vector<int> I;
if(A.size()>=m) {
for(int i=0;i<m;i++) {
I.push_back(A[i]); I.push_back(Q.back());
Q.pop_back();
}
r=use_machine(I);
if(r&1) B.push_back(I.back());
else A.push_back(I.back());
return m-1-(r>>1);
}
else {
for(int i=0;i<m;i++) {
I.push_back(B[i]); I.push_back(Q.back());
Q.pop_back();
}
r=use_machine(I);
if(r&1) A.push_back(I.back());
else B.push_back(I.back());
return r>>1;
}
}
int count_mushrooms(int n)
{
int ret=0;
mt19937 mt(chrono::high_resolution_clock::now().time_since_epoch().count());
if(n-1<=226) {
ret=1;
for(int i=1;i<n;i++) ret+=!use_machine({0,i});
return ret;
}
for(int i=1;i<n;i++) Q.push_back(i);
shuffle(Q.begin(),Q.end(),mt);
A.push_back(0);
while(max(A.size(),B.size())<2) {
int c=Q.back();
Q.pop_back();
if(use_machine({0,c})) B.push_back(c);
else A.push_back(c);
}
for(int i=0;i<80;i++) {
if(Q.empty()) break;
query3();
}
if(V.size()) {
if(use_machine({0,V[0].first})) {
B.push_back(V[0].first);
A.push_back(V[0].second);
}
else {
A.push_back(V[0].first);
B.push_back(V[0].second);
}
}
while(Q.size()) ret+=query();
return ret+A.size();
}
