#!/usr/local/bin/python3
def hit(c,q):
 for i in range(3):
  if c[i]==q:return i
 return -1
def N(c,b,o,q,a,bb):
 c=c[:];b=b[:];h=hit(c,q)
 if h<0:
  e=o[2];m=(c[e]+b[e]+a)%7;c[e]=(q+bb)%7;b[e]=a%2
 else:
  e=h;m=(c[h]+b[h]+a)%7;c[h]=(c[h]+bb)%7;b[h]=1-b[h]
 o=[e]+[x for x in o if x!=e]
 return c,b,o,m
def mv(o,h):
 return [h]+[x for x in o if x!=h]
def run(I,J,K,F):
 if I==0:c=[(J+1)%7,(K+2)%7,(J+K+3)%7];o=[0,1,2]
 elif I==1:c=[(K+3)%7,(J+4)%7,(J+2*K+1)%7];o=[1,2,0]
 else:c=[(J+K+2)%7,(K+5)%7,(2*J+4)%7];o=[2,0,1]
 b=[(I+F)%2,(J+F)%2,(K+F)%2]
 C0=c[:];B0=b[:];O0=o[:]
 q1=(I+K+F)%7;q2=(J+2*K+F)%7;q3=(2*I+J+K)%7
 h0=hit(c,q1)
 c,b,o,s=N(c,b,o,q1,I+F,J+K)
 C1=c[:]
 rho=0
 if h0<0 and B0[O0[2]]==1:rho=1
 elif h0>=0 and (s+c[o[2]])%2!=(I+C0[O0[2]])%2:rho=1
 elif (o[0]+o[2]+s+F)%2!=(O0[0]+O0[2]+I)%2:rho=1
 if rho:
  k=o[2];c[k]=C0[k];b[k]=B0[k]
  m=o[1];u=(c[m]+b[m]+s)%7;c[m]=(q2+u)%7;b[m]=max(b[m],(J+K+F)%2);o=mv(o,m)
 else:
  c,b,o,u=N(c,b,o,q2,J+F,K+I)
 w=(2*c[0]+3*c[1]+c[2]+o[0]+2*o[1]+u)%7
 delta=0
 if w==c[o[0]]:delta=1
 elif rho and b[o[2]]==B0[o[2]]:delta=1
 elif rho==0 and o[0]<o[2]:delta=1
 if rho and delta:
  c=C0[:];c[o[0]]=(q3+w+F)%7
 elif delta==0 and w in (1,3,6):
  f=o[0];k=o[2];c[f],c[k]=c[k],c[f];b[f],b[k]=b[k],b[f];c[f]=(c[f]+w+I)%7
 else:
  c,b,o,_=N(c,b,o,q3,K+F,I+J)
 eps=0
 if b[o[0]]==b[o[1]] and c[o[0]]!=c[o[1]]:eps=1
 if rho and delta and c[o[2]]==C0[o[2]]:eps=1
 if I==2 and F==1:eps=1
 if I==0 and (o[0]+F)%2==0:eps=0
 if eps and F==0:
  c[o[0]]=C1[o[0]];c[o[2]]=C1[o[2]];c[o[1]]=(c[o[1]]+w+rho)%7
 elif eps==0 and F==0:
  b[o[0]]=0
  if (F+J+K)%2:o=[o[1],o[2],o[0]]
 elif F==1 and rho:
  c[o[2]]=C0[o[2]];c[o[0]]=(c[o[0]]+s+delta)%7
 elif F==1 and rho==0:
  c[o[1]]=(c[o[1]]+u+eps)%7
 omega=0
 if sum(b)>=2 and c[o[0]]==q3:omega=1
 elif rho and (C0[O0[0]]+c[o[2]])%7!=(c[o[0]]+C0[O0[2]])%7:omega=1
 elif delta and o[0]==O0[2]:omega=1
 elif eps and b[o[2]]:omega=1
 R=(2*c[0]+c[1]+3*c[2]+o[0]+2*o[1]+rho+delta+2*eps+omega)%11
 S=(c[o[0]]+2*c[o[1]]+3*c[o[2]]+I+J+K+F+omega)%10
 p=(c[o[2]]+o[0]+I+F+omega)%2
 psi=(F+J+K)%2
 M=1 if R in (2,4,8) and S in (3,4,5,6) and p!=psi else 0
 Hh=1 if M and rho and delta and eps and omega else 0
 return [I,J,K,F,rho,delta,eps,omega,R,S,p,psi,M,Hh,s,u,w,c,b,o,C0,B0,O0,C1]
cases=[(0,1,2,0),(0,1,2,1),(0,1,0,0),(0,1,0,1),(0,2,0,0),(0,2,0,1),(0,2,1,0),(0,2,1,1),(1,2,0,0),(1,2,0,1),(1,2,1,0),(1,2,1,1),(1,0,1,0),(1,0,1,1),(1,0,2,0),(1,0,2,1),(2,0,1,0),(2,0,1,1),(2,0,2,0),(2,0,2,1),(2,1,2,0),(2,1,2,1),(2,1,0,0),(2,1,0,1)]
num=0;den=0
for z in cases:
 r=run(*z);I,J,K,F=r[:4]
 if I==0:wt=5
 elif I==1:wt=6 if F else 4
 else:wt=6 if F==0 else 4
 den+=wt*r[12];num+=wt*r[12]*r[13]
 print(r[:17])
print('NUM',num,'DEN',den)