#include "mushrooms.h"
#include <bits/stdc++.h>
#define vi vector<int>
#define ve vector
#define ll long long
#define vf vector<float>
#define vll vector<pair<ll,ll>>
#define ii pair<int,int>
#define vvi vector<vi>
#define vii vector<ii>
#define gii greater<ii>
#define pb push_back
#define fi first
#define se second
#define INF 1e7
#define eps 1e-18
#define eps1 1e-25
#define optimise ios_base::sync_with_stdio(false);cin.tie(NULL);
#define MAX_A 1e5+5
#define V 450
using namespace std;
const int MOD = 1e9+7;
const int nax = 2000005;
int count_mushrooms(int n) {
int X = 200;
vi typ[2];
typ[0].pb(0);
if(n < 300){
int cnt = 1;
for(int i = 1;i<n;i++){
vector<int> a;
a.push_back(0);
a.push_back(i);
int x = use_machine(a);
if(x == 0)cnt++;
}
return cnt;
}
for(int i = 1; i <= 2; i++){
typ[use_machine({0,i})].pb(i);
}
bool B = false;
if(typ[1].size() == 2)
B = true;
for (int i = 3; i <= min(n-2,4); i+=2)
{
int res = 0;
res = use_machine({typ[B][0],i,typ[B][1], i+1});
if(res == 0){
typ[B].pb(i);
typ[B].pb(i+1);
} else if(res == 1){
typ[B].pb(i);
typ[B^1].pb(i+1);
} else if(res == 2){
typ[B^1].pb(i);
typ[B].pb(i+1);
} else {
typ[B^1].pb(i);
typ[B^1].pb(i+1);
}
}
if(n%2 == 0 && n-2 < X && n >= 3){
typ[use_machine({0,n-1})].pb(n-1);
}
B = false;
if(typ[1].size() >= 3)
B = true;
for (int i = 5; i < X; i+=5)
{
int res = use_machine({typ[B][0], i, typ[B][1],i+1, typ[B][2], i+2});
if(B)
typ[(res%2) ^ 1].pb(i+2);
else typ[res%2].pb(i+2);
res -= res%2;
if(res%4==0){
if(res == 4){
typ[B^1].pb(i);
typ[B^1].pb(i+1);
} else if(res == 0){
typ[B].pb(i);
typ[B].pb(i+1);
}
res = use_machine({typ[B][0], i+2, typ[B][1],i+3});
if(res == 0){
typ[B].pb(i+2);
typ[B].pb(i+3);
} else if(res == 1){
typ[B].pb(i+2);
typ[B^1].pb(i+3);
} else if(res == 2){
typ[B^1].pb(i+2);
typ[B].pb(i+3);
} else {
typ[B^1].pb(i+2);
typ[B^1].pb(i+3);
}
} else {
if(min(typ[0].size(), typ[1].size())>=2){
res = use_machine({typ[B^1][0], i, typ[B^1][1], typ[B][0],i+1, typ[B][1], i+2 ,typ[B][2], i+3});
if(B)
typ[(res%2) ^ 1].pb(i+3);
else typ[res%2].pb(i+3);
res -= res%2;
if(res>=4){
typ[B].pb(i);
typ[1-B].pb(i+1);
if(res == 5) typ[B].pb(i+2);
else typ[1-B].pb(i+2);
} else {
typ[1-B].pb(i);
typ[B].pb(i+1);
if(res == 1) typ[B].pb(i+2);
else typ[1-B].pb(i+2);
}
} else {
res = use_machine({0,i});
typ[res].pb(i);
typ[1-res].pb(i+1);
res = use_machine({typ[B][0], i+2, typ[B][1],i+3});
if(res == 0){
typ[B].pb(i+2);
typ[B].pb(i+3);
} else if(res == 1){
typ[B].pb(i+2);
typ[B^1].pb(i+3);
} else if(res == 2){
typ[B^1].pb(i+2);
typ[B].pb(i+3);
} else {
typ[B^1].pb(i+2);
typ[B^1].pb(i+3);
}
}
}
}
int cnt = typ[0].size();
for (int i = X; i < n; i+=X)
{
vi a;
for(int j = i; j < i+typ[0].size() && j < n;j++){
a.pb(typ[0][j-i]);
a.pb(j);
}
int res = use_machine(a);
cnt += min((int) typ[0].size(),n-i)-((res+1)/2);
res = 0;
a.clear();
for(int j = i+typ[0].size(); j < i+X && j < n;j++){
a.pb(typ[1][j-i-typ[0].size()]);
a.pb(j);
}
if(a.size())
res = use_machine(a);
cnt += ((res+1)/2);
}
return cnt;
}
