#include "mushrooms.h"
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
//#define int ll
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
using pi=pair<int,int>;
using vi=vc<int>;
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
return os<<"{"<<p.a<<","<<p.b<<"}";
}
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
os<<"{";
for(auto e:v)os<<e<<",";
return os<<"}";
}
#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
os<<t<<" ";
dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif
using uint=unsigned;
using ull=unsigned long long;
template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
return os<<vc<t>(all(a));
}
template<int i,class T>
void print_tuple(ostream&,const T&){
}
template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
if(i)os<<",";
os<<get<i>(t);
print_tuple<i+1,T,Args...>(os,t);
}
template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
os<<"{";
print_tuple<0,tuple<Args...>,Args...>(os,t);
return os<<"}";
}
template<class t>
void print(t x,int suc=1){
cout<<x;
if(suc==1)
cout<<"\n";
if(suc==2)
cout<<" ";
}
ll read(){
ll i;
cin>>i;
return i;
}
vi readvi(int n,int off=0){
vi v(n);
rep(i,n)v[i]=read()+off;
return v;
}
pi readpi(int off=0){
int a,b;cin>>a>>b;
return pi(a+off,b+off);
}
template<class t,class u>
void print(const pair<t,u>&p,int suc=1){
print(p.a,2);
print(p.b,suc);
}
template<class T>
void print(const vector<T>&v,int suc=1){
rep(i,v.size())
print(v[i],i==int(v.size())-1?suc:2);
}
string readString(){
string s;
cin>>s;
return s;
}
template<class T>
T sq(const T& t){
return t*t;
}
//#define CAPITAL
void yes(bool ex=true){
#ifdef CAPITAL
cout<<"YES"<<"\n";
#else
cout<<"Yes"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void no(bool ex=true){
#ifdef CAPITAL
cout<<"NO"<<"\n";
#else
cout<<"No"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void possible(bool ex=true){
#ifdef CAPITAL
cout<<"POSSIBLE"<<"\n";
#else
cout<<"Possible"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void impossible(bool ex=true){
#ifdef CAPITAL
cout<<"IMPOSSIBLE"<<"\n";
#else
cout<<"Impossible"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
constexpr ll ten(int n){
return n==0?1:ten(n-1)*10;
}
const ll infLL=LLONG_MAX/3;
#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif
int topbit(signed t){
return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
return __builtin_popcount(t);
}
int popcount(ll t){
return __builtin_popcountll(t);
}
bool ispow2(int i){
return i&&(i&-i)==i;
}
ll mask(int i){
return (ll(1)<<i)-1;
}
bool inc(int a,int b,int c){
return a<=b&&b<=c;
}
template<class t> void mkuni(vc<t>&v){
sort(all(v));
v.erase(unique(all(v)),v.ed);
}
ll rand_int(ll l, ll r) { //[l, r]
#ifdef LOCAL
static mt19937_64 gen;
#else
static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
#endif
return uniform_int_distribution<ll>(l, r)(gen);
}
template<class t>
void myshuffle(vc<t>&a){
rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}
template<class t>
int lwb(const vc<t>&v,const t&a){
return lower_bound(all(v),a)-v.bg;
}
vvc<int> readGraph(int n,int m){
vvc<int> g(n);
rep(i,m){
int a,b;
cin>>a>>b;
//sc.read(a,b);
a--;b--;
g[a].pb(b);
g[b].pb(a);
}
return g;
}
vvc<int> readTree(int n){
return readGraph(n,n-1);
}
struct sub_solver{
const int nmax;
vi dp,pre;
vvc<vi> qs;
vi flip(int n,vi x){
assert(is_sorted(all(x)));
vi y;
rep(i,n)if(!binary_search(all(x),i)){
y.pb(i);
}
return y;
}
sub_solver(const int nmax_):nmax(nmax_),dp(nmax),pre(nmax,-1),qs(nmax){
dp[1]=1;
qs[1].pb(vi{0});
rng(n,2,nmax){
auto check=[&](int m){
return m+dp[m/2]-1>=n;
};
int lw=1,up=n;
while(up-lw>1){
int mid=(lw+up)/2;
if(check(mid))up=mid;
else lw=mid;
}
pre[n]=up;
int a=(up+1)/2,b=up/2;
dp[n]=dp[a]+dp[b];
int dif=dp[a]-dp[b];
rep(i,dif){
qs[n].pb(qs[a][i]);
}
rep(i,dp[b]-1){
{
vi tmp=flip(a,qs[a][dif+i]);
for(auto j:qs[b][i])
tmp.pb(a+j);
qs[n].pb(tmp);
}
{
vi tmp=qs[a][dif+i];
for(auto j:qs[b][i])
tmp.pb(a+j);
if(up+i<n)tmp.pb(up+i);
qs[n].pb(tmp);
}
}
qs[n].pb(qs[a].back());
vi tmp(n);iota(all(tmp),0);
qs[n].pb(tmp);
assert(si(qs[n])==dp[n]);
}
}
vi restore(int n,vi vs){
assert(dp[n]==si(vs));
if(n==1){
return vs;
}else{
int a=(pre[n]+1)/2,b=pre[n]/2;
int dif=dp[a]-dp[b];
vi res(n);
int w=vs[dp[n]-2];
vi x,y;
rep(i,dif){
x.pb(vs[i]);
}
int tot=0;
rep(i,dp[b]-1){
int p=vs[dif+i*2],q=vs[dif+i*2+1];
int z=(p+q)-w;
if(a+b+i<n){
res[a+b+i]=z%2;
tot+=z%2;
}
y.pb(z/2);
x.pb(w-p+z/2);
}
x.pb(w);
y.pb(vs.back()-w-tot);
auto xx=restore(a,x);
auto yy=restore(b,y);
rep(i,a)res[i]=xx[i];
rep(i,b)res[a+i]=yy[i];
return res;
}
}
template<class F>
vi test(int n,F f){
vi y;
for(auto x:qs[n])
y.pb(f(x));
return restore(n,y);
}
};
int count_mushrooms(int n){
vi idx[2];
idx[0].pb(0);
int head=1;
int off[2]{};
int vmax=150;
sub_solver sub(vmax);
vmax=lwb(sub.dp,48)-1;
while(head<n){
int k=si(idx[0])<si(idx[1]);
int len=si(idx[k]);
if(inc(2,len,vmax)){
int u=min(n-head,len-1);
vi vs;
for(auto ls:sub.qs[u]){
int z=-1;
if(head+u<n){
z=--n;
}
vi tmp;
if(z!=-1)tmp.pb(z);
tmp.pb(idx[k][0]);
rep(i,si(ls)){
tmp.pb(head+ls[i]);
tmp.pb(idx[k][i+1]);
}
int val=use_machine(tmp);
if(z!=-1){
idx[k^(val%2)].pb(z);
}
vs.pb(val/2);
}
vi res=sub.restore(u,vs);
rep(i,u)idx[k^res[i]].pb(head+i);
head+=u;
}else{
vi tmp;
rep(i,len){
tmp.pb(idx[k][i]);
if(head<n){
tmp.pb(head++);
}
}
int use=si(tmp)-len;
int val=use_machine(tmp);
int dif=(val+1)/2;
off[k^1]+=dif;
off[k]+=use-dif;
if(use==len){
k^=val%2;
off[k]--;
idx[k].pb(head-1);
}
}
}
return si(idx[0])+off[0];
}
