#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define pb push_back
#define endl '\n'
#define conts continue
#define ff first
#define ss second
#define all(a) a.begin(),a.end()
#define rall(a) a.rbegin(),a.rend()
#define sz(a) (int)a.size()
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &x, T y){
x = min(x,y);
}
template<typename T>
void amax(T &x, T y){
x = max(x,y);
}
template<typename A,typename B>
string to_string(pair<A,B> p);
string to_string(const string &s){
return "'"+s+"'";
}
string to_string(const char* s){
return to_string((string)s);
}
string to_string(bool b){
return b?"true":"false";
}
template<typename A>
string to_string(A v){
string res = "{";
trav(x,v){
res += to_string(x)+",";
}
if(res.back() == ',') res.pop_back();
res += "}";
return res;
}
template<typename A,typename B>
string to_string(pair<A,B> p){
return "("+to_string(p.ff)+","+to_string(p.ss)+")";
}
#define debug(x) cout << "[" << #x << "]: "; cout << to_string(x) << endl
const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = 1e9 + 5;
const ll inf2 = (ll)1e18 + 5;
#include "mushrooms.h"
int count_mushrooms(int n) {
int B = min(n,2);
vector<int> a(B);
rep1(i,B-1){
vector<int> v = {i-1,i};
a[i] = a[i-1]^use_machine(v);
}
vector<int> v0,v1;
rep(i,B){
if(!a[i]){
v0.pb(i);
}
else{
v1.pb(i);
}
}
int ptr = B-1;
int ans = count(all(a),0);
while(ptr < n-1){
int siz = max(sz(v0),sz(v1));
if(sz(v0) > sz(v1)){
vector<int> v;
for(int i = ptr+1; i < n; ++i){
if(sz(v) >= siz) break;
ptr = i;
v.pb(i);
}
vector<int> ask;
rep(i,sz(v)){
ask.pb(v0[i]);
ask.pb(v[i]);
}
int res = use_machine(ask);
int sum = (sz(v)-1)*2+1;
res = sum-res;
if(res&1){
ans++;
v0.pb(v.back());
}
else{
v1.pb(v.back());
}
ans += res/2;
}
else{
vector<int> v;
for(int i = ptr+1; i < n; ++i){
if(sz(v) >= siz) break;
ptr = i;
v.pb(i);
}
vector<int> ask;
rep(i,sz(v)){
ask.pb(v1[i]);
ask.pb(v[i]);
}
int res = use_machine(ask);
if(res&1){
ans++;
v0.pb(v.back());
}
else{
v1.pb(v.back());
}
ans += res/2;
}
}
return ans;
// for (int i = 0; i < n; i++)
// m.push_back(i);
// int c1 = use_machine(m);
// m = {0, 1};
// int c2 = use_machine(m);
// return c1+c2;
}
