#!/usr/bin/env python3
from collections import defaultdict
B={1:{2,5,8,9},2:{5,7,8},4:{1,2,5,7},5:{7,11},6:{1,2,4,5,8},7:{1,6,8},8:{4,5,9},9:{2,4,5,6,7},11:{1,2,4,6,7,8,9}}
def w(a,u):
 return a if a==u else (10 if u==10 else u) if a==10 else (a if u==10 else (a if u in B.get(a,()) else u))
items=tuple(range(1,10))
allc=items+(10,11)
init={c:(c if c in {11,1,2,4,5,6,7,8,9} else 10) for c in allc}
dp={0:{tuple(init[c] for c in allc)}}
mask={}
for m in range(512):
 if m not in dp: continue
 S=[i for i in range(9) if m>> i&1]
 out=[c for c in allc if c not in [items[i] for i in S]]
 for j,p in enumerate(items):
  if m>>j&1: continue
  nm=m|(1<<j)
  no=[c for c in out if c!=p]
  tgt=dp.setdefault(nm,set())
  idx={c:k for k,c in enumerate(out)}
  for v in dp[m]:
   vp=v[idx[p]]
   tgt.add(tuple(w(v[idx[c]],vp) for c in no))
fin=dp[511]
print(len(fin))
O=set()
for v in fin:
 O.add(w(v[0],v[1]))
print(sorted(O))