#include "mushrooms.h"
#include "bits/stdc++.h"
using namespace std;
#define FAST ios_base::sync_with_stdio(false); cin.tie(0);
#define pb push_back
#define eb emplace_back
#define ins insert
#define f first
#define s second
#define cbr cerr<<"hi\n"
#define mmst(x, v) memset((x), v, sizeof ((x)))
#define siz(x) ll(x.size())
#define all(x) (x).begin(), (x).end()
#define lbd(x,y) (lower_bound(all(x),y)-x.begin())
#define ubd(x,y) (upper_bound(all(x),y)-x.begin())
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
inline long long rand(long long x, long long y) { return rng() % (y+1-x) + x; } //inclusive
string inline to_string(char c) {string s(1,c);return s;} template<typename T> inline T gcd(T a,T b){ return a==0?llabs(b):gcd(b%a,a); }
using ll=long long;
using ld=long double;
#define FOR(i,s,e) for(int i=s;i<=ll(e);++i)
#define DEC(i,s,e) for(ll i=s;i>=ll(e);--i)
using pi=pair<ll,ll>; using spi=pair<ll,pi>; using dpi=pair<pi,pi>;
long long LLINF = 1e18;
int INF = 1e9+1e6;
#define MAXN (200006)
int B = 1, T = 95;
vector<int> join(int x, deque<int> dq) {
vector<int> v;
if(~x) v.eb(x);
for(auto i:dq) v.eb(i);
return v;
}
int count_mushrooms(int n) {
int ans = 1;
deque<int> dq, co[2];
FOR(i,1,n-1) dq.eb(i);
co[0].eb(0);
// do T times
if(n > 200) {
while(max(co[0].size(), co[1].size()) < 2) {
int res = use_machine({0, dq.front()});
ans += res == 0, co[res].eb(dq.front()), dq.pop_front();
}
FOR(i,1,T) {
int x = dq.front(); dq.pop_front();
int y = dq.front(); dq.pop_front();
vector<int> v;
if(co[0].size()>1) v.eb(co[0][0]);
else v.eb(co[1][0]);
v.eb(x);
if(co[0].size()>1) v.eb(co[0][1]);
else v.eb(co[1][1]);
v.eb(y);
int res = use_machine(v);
auto declare=[&](int x,bool b){
ans += b == 0, co[b].eb(x);
};
if(co[0].size()>1) {
if(res & 1) declare(y, 1);
else declare(y, 0);
if(res > 1) declare(x, 1);
else declare(x, 0);
} else {
if(res & 1) declare(y, 0);
else declare(y, 1);
if(res > 1) declare(x, 0);
else declare(x, 1);
}
}
}
int b = 0;
if(co[b].size() < B) b = 1;
for(int i=0;i<siz(dq);i+=B) {
B = max(co[0].size(), co[1].size());
if(siz(co[b]) ^ B) b ^= 1;
vector<int> tmp;
FOR(j,i,min((int)siz(dq)-1, i+B-1)) {
tmp.eb(co[b][j-i]);
tmp.eb(dq[j]);
}
int res = use_machine(tmp), cnt = 0;
if(res & 1) ++ cnt, -- res, co[!b].eb(dq[min((int)siz(dq)-1, i+B-1)]);
else co[b].eb(dq[min((int)siz(dq)-1, i+B-1)]);
res /= 2;
cnt += res;
if(b==0) ans += min((int)siz(dq)-1, i+B-1) - i + 1 - cnt;
else ans += cnt;
}
return ans;
}
