#!/usr/bin/env python3
E=[(0,1,8),(0,2,9),(0,3,7),(0,4,11),(1,2,11),(1,3,8),(1,4,12),(2,3,12),(2,4,9),(3,4,5)]
C=[8,9,7,11,11,8,12,12,9,5]
W=[0,184320,103680,58320,32805]
N=1024
R=range(N)
P=[]
for x in R:
 A=[0]*5
 for k in range(10):
  if x>>k&1:
   u,v,c=E[k]
   A[u]|=1<<v
   A[v]|=1<<u
 p=[]
 for s in range(5):
  d=[9]*5
  d[s]=0
  q=[s]
  for z in q:
   for v in range(5):
    if A[z]>>v&1 and d[v]>4:
     d[v]=d[z]+1
     q.append(v)
  p.append(sum(W[t] if t<5 else 0 for t in d)-sum(C[k]*16384 for k in range(10) if x>>k&1 and (E[k][0]==s or E[k][1]==s)))
 P.append(p)
SUB=[]
for m in range(N):
 a=[]
 s=m
 while 1:
  a.append(s)
  if s==0:
   break
  s=(s-1)&m
 SUB.append(a)
bad=0
for S in range(1,32):
 im=0
 cm=0
 for k in range(10):
  a=(S>>E[k][0])&1
  b=(S>>E[k][1])&1
  if a and b:
   im|=1<<k
  elif a or b:
   cm|=1<<k
 out=1023^im^cm
 bits=[i for i in range(5) if (S>>i)&1]
 for x in R:
  fixed=x&out
  cav=x&cm
  go=any(all(P[fixed|a|b][i]>=P[x][i] for i in bits) and any(P[fixed|a|b][i]>P[x][i] for i in bits) for a in SUB[im] for b in SUB[cav])
  if go:
   bad|=1<<x
print(N-bin(bad).count('1'))