#define DEBUG 0
#include <bits/stdc++.h>
using namespace std;
#if DEBUG
// basic debugging macros
int __i__,__j__;
#define printLine(l) for(__i__=0;__i__<l;__i__++){cout<<"-";}cout<<endl
#define printLine2(l,c) for(__i__=0;__i__<l;__i__++){cout<<c;}cout<<endl
#define printVar(n) cout<<#n<<": "<<n<<endl
#define printArr(a,l) cout<<#a<<": ";for(__i__=0;__i__<l;__i__++){cout<<a[__i__]<<" ";}cout<<endl
#define print2dArr(a,r,c) cout<<#a<<":\n";for(__i__=0;__i__<r;__i__++){for(__j__=0;__j__<c;__j__++){cout<<a[__i__][__j__]<<" ";}cout<<endl;}
#define print2dArr2(a,r,c,l) cout<<#a<<":\n";for(__i__=0;__i__<r;__i__++){for(__j__=0;__j__<c;__j__++){cout<<setw(l)<<setfill(' ')<<a[__i__][__j__]<<" ";}cout<<endl;}
// advanced debugging class
// debug 1,2,'A',"test";
class _Debug {
public:
template<typename T>
_Debug& operator,(T val) {
cout << val << endl;
return *this;
}
};
#define debug _Debug(),
#else
#define printLine(l)
#define printLine2(l,c)
#define printVar(n)
#define printArr(a,l)
#define print2dArr(a,r,c)
#define print2dArr2(a,r,c,l)
#define debug
#endif
// define
#define MAX_VAL 999999999
#define MAX_VAL_2 999999999999999999LL
#define EPS 1e-6
#define mp make_pair
#define pb push_back
// typedef
typedef unsigned int UI;
typedef long long int LLI;
typedef unsigned long long int ULLI;
typedef unsigned short int US;
typedef pair<int,int> pii;
typedef pair<LLI,LLI> plli;
typedef vector<int> vi;
typedef vector<LLI> vlli;
typedef vector<pii> vpii;
typedef vector<plli> vplli;
// ---------- END OF TEMPLATE ----------
#include "mushrooms.h"
int order[20000];
int query(vi v) {
int i;
for (i = 0; i < v.size(); i++) v[i] = order[v[i]];
return use_machine(v);
}
int count_mushrooms(int n) {
srand(4321);
int i,j,ans = 0;
if (n <= 220) {
for (i = 1; i < n; i++) ans += !use_machine({0,i});
return ans+1;
}
vi v,a,b,q;
a.pb(0);
for (i = 0; i < n; i++) order[i] = i;
random_shuffle(order+1,order+n);
for (i = 0; i < n; i++) q.pb(order[i]);
query(q);
for (i = 1; i <= 2; i++) {
if (query({0,i})) b.pb(i);
else a.pb(i);
}
for (i = 3; i <= 5; i += 2) {
if (a.size() >= 2) {
int r = query({i,a[0],i+1,a[1]});
if (r & 1) b.pb(i);
else a.pb(i);
if (r & 2) b.pb(i+1);
else a.pb(i+1);
}
else {
int r = query({i,b[0],i+1,b[1]});
if (r & 1) a.pb(i);
else b.pb(i);
if (r & 2) a.pb(i+1);
else b.pb(i+1);
}
}
int s = 0,x,y,z;
for (i = 7; i < n; i++) {
v.pb(i);
if ((max(a.size(),b.size()) < 100) || (s != 0)) {
if ((s == 0) && (v.size() == 3)) {
if (a.size() >= 3) {
int r = query({v[0],a[0],v[1],a[1],v[2],a[2]});
if (r & 1) b.pb(v[0]);
else a.pb(v[0]);
if (r/2 == 0) a.pb(v[1]),a.pb(v[2]);
else if (r/2 == 2) b.pb(v[1]),b.pb(v[2]);
else s = 1,x = v[1],y = v[2];
}
else {
int r = query({v[0],b[0],v[1],b[1],v[2],b[2]});
if (r & 1) a.pb(v[0]);
else b.pb(v[0]);
if (r/2 == 0) b.pb(v[1]),b.pb(v[2]);
else if (r/2 == 2) a.pb(v[1]),a.pb(v[2]);
else s = 1,x = v[1],y = v[2];
}
v.clear();
}
else if ((s == 1) && (v.size() == 2)) {
if (a.size() >= 3) {
int r = query({v[0],a[0],v[1],a[1],x,a[2]});
if (r & 1) b.pb(v[0]);
else a.pb(v[0]);
if (r/2 == 0) a.pb(v[1]),a.pb(x),b.pb(y),s = 0;
else if (r/2 == 2) b.pb(v[1]),b.pb(x),a.pb(y),s = 0;
else s = 2,z = v[1];
}
else {
int r = query({v[0],b[0],v[1],b[1],x,b[2]});
if (r & 1) a.pb(v[0]);
else b.pb(v[0]);
if (r/2 == 0) b.pb(v[1]),b.pb(x),a.pb(y),s = 0;
else if (r/2 == 2) a.pb(v[1]),a.pb(x),b.pb(y),s = 0;
else s = 2,z = v[1];
}
v.clear();
}
else if ((s == 2) && (v.size() == 2)) {
if (a.size() >= 4) {
int r = query({v[0],a[0],v[1],a[1],y,a[2],z,a[3]});
if (r & 1) b.pb(v[0]);
else a.pb(v[0]);
if (r & 2) b.pb(v[1]);
else a.pb(v[1]);
if (r & 4) b.pb(y),b.pb(z),a.pb(x),s = 0;
else a.pb(y),a.pb(z),b.pb(x),s = 0;
}
else {
int r = query({v[0],b[0],v[1],b[1],y,b[2],z,b[3]});
if (r & 1) a.pb(v[0]);
else b.pb(v[0]);
if (r & 2) a.pb(v[1]);
else b.pb(v[1]);
if (r & 4) a.pb(y),a.pb(z),b.pb(x),s = 0;
else b.pb(y),b.pb(z),a.pb(x),s = 0;
}
v.clear();
}
}
else if (v.size() == max(a.size(),b.size())) {
if (a.size() > b.size()) {
vi q;
for (j = 0; j < v.size(); j++) q.pb(v[j]),q.pb(a[j]);
int r = query(q);
ans += v.size()-r/2-1;
if (r & 1) b.pb(v[0]);
else a.pb(v[0]);
}
else {
vi q;
for (j = 0; j < v.size(); j++) q.pb(v[j]),q.pb(b[j]);
int r = query(q);
ans += r/2;
if (r & 1) a.pb(v[0]);
else b.pb(v[0]);
}
v.clear();
}
}
if (!v.empty()) {
if (a.size() > b.size()) {
vi q;
for (j = 0; j < v.size(); j++) q.pb(v[j]),q.pb(a[j]);
int r = query(q);
ans += v.size()-r/2-1;
if (r & 1) b.pb(v[0]);
else a.pb(v[0]);
}
else {
vi q;
for (j = 0; j < v.size(); j++) q.pb(v[j]),q.pb(b[j]);
int r = query(q);
ans += r/2;
if (r & 1) a.pb(v[0]);
else b.pb(v[0]);
}
v.clear();
}
return a.size()+ans;
}
