#include "scales.h"
#include <bits/stdc++.h>
#define BS bitset <720>
//#define NAM
using namespace std;
#ifdef NAM
vector <int> order={6,3,5,1,2,4};
int w[7],cnt;
int getLightest(int i, int j, int k){
cnt++;
if (w[i]<w[j]&&w[i]<w[k])
return i;
return (w[j]<w[k]?j:k);
}
int getHeaviest(int i, int j, int k){
cnt++;
if (w[i]>w[j]&&w[i]>w[k])
return i;
return (w[j]>w[k]?j:k);
}
int getMedian(int i, int j, int k){
cnt--;
return i+j+k-getLightest(i,j,k)-getHeaviest(i,j,k);
}
int getNextLightest(int i, int j, int k, int l){
if (w[l]>max(w[i],max(w[j],w[k])))
return getLightest(i,j,k);
cnt++;
int mn=100,res=-1;
if (w[i]>w[l]&&mn>w[i]){
mn=w[i];
res=i;
}
if (w[j]>w[l]&&mn>w[j]){
mn=w[j];
res=j;
}
if (w[k]>w[l]&&mn>w[k]){
mn=w[k];
res=k;
}
return res;
}
void answer(int W[]){
for (int i=0;i<6;i++){
cout << W[i] << ' ';
assert(W[i]==order[i]);
}
}
#endif
struct question{
int a[4];
int type;
};
unordered_map <BS, int> mp[7];
BS p[120][3];
vector <vector <int>> v;
vector <question> vq;
int pw[7];
int ask(int i){
int res=0;
if (!vq[i].type)
res=getLightest(vq[i].a[0],vq[i].a[1],vq[i].a[2]);
if (vq[i].type==1)
res=getMedian(vq[i].a[0],vq[i].a[1],vq[i].a[2]);
if (vq[i].type==2)
res=getHeaviest(vq[i].a[0],vq[i].a[1],vq[i].a[2]);
if (vq[i].type==3)
res=getNextLightest(vq[i].a[0],vq[i].a[1],vq[i].a[2],vq[i].a[3]);
return (res==vq[i].a[0]?0:(res==vq[i].a[1]?1:2));
}
int f(BS b, int id){
if (b.count()>pw[id])
return -1;
if (!id)
return -2;
if (b.count()<2)
return -2;
if (mp[id].count(b))
return mp[id][b];
for (int i=0;i<vq.size();i++){
bool ch=true;
for (int j=0;j<3;j++)
if (f(b&p[i][j],id-1)==-1){
ch=false;
break;
}
if (ch)
return mp[id][b]=i;
}
return mp[id][b]=-1;
}
bool isLightest(vector <int> a, int i, int j, int k){
return (a[i]<min(a[j],a[k]));
}
bool isMedian(vector <int> a, int i, int j, int k){
return (a[j]-a[i])*(a[j]-a[k])<0;
}
bool isHeaviest(vector <int> a, int i, int j, int k){
return (a[i]>max(a[j],a[k]));
}
bool isNextLightest(vector <int> a, int i, int j, int k, int l){
if (max(a[i],max(a[j],a[k]))<a[l])
return isLightest(a,i,j,k);
if (a[i]<a[l])
return false;
return (!((a[j]>a[l]&&a[j]<a[i])||(a[k]>a[l]&&a[k]<a[i])));
}
void init(int T){
v.clear();
vq.clear();
pw[0]=1;
for (int i=1;i<=6;i++)
pw[i]=pw[i-1]*3;
vector <int> ve;
for (int i=1;i<=6;i++)
ve.push_back(i);
do{
v.push_back(ve);
}while (next_permutation(ve.begin(),ve.end()));
int id=0;
for (int i=1;i<=6;i++)
for (int j=i+1;j<=6;j++)
for (int k=j+1;k<=6;k++){
for (int l=0;l<3;l++)
vq.push_back({i,j,k,0,l});
for (int l=1;l<=6;l++)
if (l!=i&&l!=j&&l!=k)
vq.push_back({i,j,k,l,3});
}
for (int i=0;i<vq.size();i++)
for (int j=0;j<v.size();j++){
for (int k=0;k<3;k++){
if (!vq[i].type&&isLightest(v[j],vq[i].a[k]-1,vq[i].a[(k+1)%3]-1,vq[i].a[(k+2)%3]-1))
p[i][k][j]=1;
if (vq[i].type==1&&isMedian(v[j],vq[i].a[(k+1)%3]-1,vq[i].a[k]-1,vq[i].a[(k+2)%3]-1))
p[i][k][j]=1;
if (vq[i].type==2&&isHeaviest(v[j],vq[i].a[k]-1,vq[i].a[(k+1)%3]-1,vq[i].a[(k+2)%3]-1))
p[i][k][j]=1;
if (vq[i].type==3&&isNextLightest(v[j],vq[i].a[k]-1,vq[i].a[(k+1)%3]-1,vq[i].a[(k+2)%3]-1,vq[i].a[3]-1))
p[i][k][j]=1;
}
}
}
void orderCoins(){
int W[] = {1, 2, 3, 4, 5, 6};
BS b;
for (int i=0;i<720;i++)
b[i]=1;
int tmp=f(b,6);
for (int i=6;i>=1;i--){
int x=mp[i][b];
int y=ask(x);
b&=p[x][y];
if (b.count()==1)
break;
}
int pos=0;
for (int i=0;i<720;i++)
if (b[i]){
pos=i;
break;
}
for (int i=0;i<6;i++)
W[v[pos][i]-1]=i+1;
answer(W);
}
#ifdef NAM
void run(){
init(1);
cnt=0;
for (int i=0;i<order.size();i++)
w[order[i]]=i+1;
orderCoins();
cout << '\n' << cnt << '\n';
}
int main(){
for (int i=0;i<18;i++){
run();
random_shuffle(order.begin(),order.end());
}
}
#endif // NAM
