#!/usr/local/bin/python3
def rk(m,n):
 m=list(m);r=0
 for c in range(n):
  b=1<<c;p=-1
  for i in range(r,n):
   if m[i]&b:p=i;break
  if p<0:continue
  m[r],m[p]=m[p],m[r]
  x=m[r]
  for i in range(r+1,n):
   if m[i]&b:m[i]^=x
  r+=1
 return r
def iv(m,n):
 a=[m[i]|(1<<(n+i)) for i in range(n)]
 for c in range(n):
  b=1<<c;p=-1
  for i in range(c,n):
   if a[i]&b:p=i;break
  if p<0:return None
  a[c],a[p]=a[p],a[c]
  x=a[c]
  for i in range(n):
   if i!=c and a[i]&b:a[i]^=x
 return [a[i]>>n for i in range(n)]
t=6;n=8;full=(1<<t)-1
Ls=[]
for lm in range(1,full):
 top0=lm;top1=full^lm
 rl=[1 if (lm>>i)&1 else 2 for i in range(t)]
 dot=[0]*t
 for i in range(t):
  for j in range(t):
   if ((lm>>i)&1)==((lm>>j)&1):dot[i]|=1<<j
 Ls.append((lm,top0,top1,rl,dot))
cnt={}
for mask in range(1<<15):
 W=[0]*t;k=0
 for i in range(t):
  for j in range(i+1,t):
   if (mask>>k)&1:W[i]|=1<<j;W[j]|=1<<i
   k+=1
 if rk(W,t)<t:continue
 F=iv(W,t)
 for lm,t0,t1,rl,dot in Ls:
  A=[t0<<2,t1<<2]
  for i in range(t):A.append(rl[i]|((F[i]^dot[i])<<2)^(1<<(2+i)))
  if rk(A,n)==n:cnt[lm]=cnt.get(lm,0)+1
print(sum(cnt.values()),len(cnt))
print('typeI',sum(v for k,v in cnt.items() if bin(k).count('1')%2))
print('typeZ',sum(v for k,v in cnt.items() if not bin(k).count('1')%2))
print(sorted(set(cnt.values())))