python3 - <<'PY'
N=7**6
M=lambda x:x-7*(x//7)
D=lambda x:[(x//7**i)-7*((x//7**i)//7) for i in range(5,-1,-1)]
ax=[0]*N
qx=[0]*N
for x in range(N):
 a,b,c,d,e,f=D(x)
 ax[x]=sum([M(-b)*16807,M(a-b)*2401,M(-d)*343,c*49,M(-f)*7,e])
 qx[x]=M(sum([(2*a-b)**2,(c-d)**2,(e-f)**2,b*sum([c,d,e,f])]))
ids=[]
for x in range(N):
 y=x
 Q=0
 T=0
 ok=True
 mn=x
 for j in range(12):
  q=qx[y]
  Q=sum([Q,q])
  T=sum([T,q if j&1==0 else -q])
  mn=min(mn,y)
  y=ax[y]
  if j<11 and y==x:
   ok=False
 if ok and M(Q)==0 and M(T)==0 and x==mn:
  ids.append(x)
def H(k,x,s):
 a,b,c,d,e,f=D(x)
 if k&1:
  a,b,c,d,e,f=M(-a),M(-b),M(-c),M(-d),M(-e),M(-f)
 if k&2:
  c,d,e,f=e,f,c,d
 if k&4:
  a,b=b,a
  d=M(-d)
  f=M(-f)
  s=M(-s)
 return sum([a*16807,b*2401,c*343,d*49,e*7,f]),s
def K(x,s):
 bx=x
 bs=s
 y=x
 t=s
 for j in range(12):
  if y<bx:
   bx=y
   bs=t
  t=M(sum([t,qx[y]]))
  y=ax[y]
 return sum([bx*7,bs])
tot=0
for x in ids:
 for s in range(7):
  kk=sum([x*7,s])
  for k in range(8):
   y,t=H(k,x,s)
   if K(y,t)==kk:
    tot=sum([tot,1])
print(len(ids),tot//8)
PY