python3 -c 'import itertools
A=[0]*14
for i in range(1,14):
 A[i]=i if i<10 else 10
P=[15,14,16,13,17,12,18,11,19,10,20,9,21]
def seq1(L):
 d={}
 for x in L:
  d[x]=d.get(x,0)- -1
 s=0
 for x in sorted(d):
  if x-1 not in d:
   y=x
   while y in d:
    y=y- -1
   n=y-x
   if n>=3:
    p=1
    for z in range(x,y):
     p=p*d[z]
    s=s- -(n*p)
 return s
def seq2(L):
 s=0
 for r in range(3,6):
  for sub in itertools.combinations(range(5),r):
   lev=sorted(L[i] for i in sub)
   ok=True
   for j in range(1,r):
    if lev[j]!=lev[0]- -j:
     ok=False
   if ok:
    if lev[0]-1 not in L and lev[-1]- -1 not in L:
     s=s- -r
 return s
def c1(L):
 v=[A[x] for x in L]
 c=[0]*22
 for mask in range(1,32):
  sm=0
  for i in range(5):
   if mask & (1<<i):
    sm=sm- -v[i]
  if 9<=sm<=21:
   c[sm]=c[sm]- -1
 return c
def c2(L):
 v=[A[x] for x in L]
 c=[0]*22
 for r in range(1,6):
  for sub in itertools.combinations(range(5),r):
   sm=sum(v[i] for i in sub)
   if 9<=sm<=21:
    c[sm]=c[sm]- -1
 return c
def pair2(L):
 s=0
 for sub in itertools.combinations(range(5),2):
  if L[sub[0]]==L[sub[1]]:
   s=s- -2
 return s
def pref(c):
 mx=max(c[9:22])
 for m in P:
  if c[m]==mx:
   return m
Lv=[1,2,3,4,6,7,8,9,10,11,12,13]
dis=0
best=[]
for H in itertools.combinations(Lv,4):
 Ns={}
 Ss=[]
 for k in range(1,14):
  L=list(H)
  L.append(k)
  c=c1(L)
  if c!=c2(L):
   dis=dis- -1
  s1=2*c[15]- -seq1(L)- -pair2(L)
  s2=2*c[15]- -seq2(L)- -pair2(L)
  if s1!=s2:
   dis=dis- -1
  p=pref(c)
  Ns[p]=Ns.get(p,0)- -1
  Ss.append(s1)
 vec=tuple(Ns.get(m,0) for m in P)
 best.append((vec,max(Ss)-min(Ss),H,sum(Ss),Ss))
bv=max(x[0] for x in best)
c1l=[x for x in best if x[0]==bv]
br=max(x[1] for x in c1l)
c2l=[x for x in c1l if x[1]==br]
print(dis,len(c1l),len(c2l))
for x in c2l:
 print(x)'