#!/usr/bin/env python3
W=[(0,0,1,2,2,1),(0,1,0,2,1,2),(1,0,2,0,2,1),(2,2,1,0,0,1)]
U=set()
for w in W:
 n=len(w)
 for mask in range(1,2**n):
  U.add(tuple(w[i] for i in range(n) if (mask//(2**i))%2))
P=sorted(U,key=lambda x:(len(x),x))
n=len(P)
def sub(a,b):
 j=0
 for x in a:
  while j<len(b) and b[j]!=x: j+=1
  if j==len(b): return False
  j+=1
 return True
leq=[[sub(P[i],P[j]) for j in range(n)] for i in range(n)]
mu=[[0]*n for _ in range(n)]
for i in range(n):
 mu[i][i]=1
 for j in range(n):
  if j!=i and leq[i][j]:
   t=0
   for k in range(n):
    if k!=j and leq[i][k] and leq[k][j]: t=t+mu[i][k]
   mu[i][j]=-t
def S(x): return sum((i+1)*(x[i]+2) for i in range(len(x)))
R=sum((i+1)*(S(P[i])+3) for i in range(n))%101
Cov=[]
for i in range(n):
 for j in range(n):
  if leq[i][j] and len(P[j])-len(P[i])==1: Cov.append((i,j))
Cov.sort(key=lambda p:(p[1],p[0]))
Sv=sum((k+1)*(S(P[u])+2*S(P[v])+5) for k,(u,v) in enumerate(Cov))%103
M=[]
for i in range(n):
 for j in range(n):
  if i!=j and leq[i][j] and mu[i][j]!=0: M.append((i,j))
M.sort(key=lambda p:(p[1],p[0]))
T=sum((k+1)*(abs(mu[u][v])+3)*(S(P[u])+S(P[v])+7) for k,(u,v) in enumerate(M))%107
best=None
for u,v in M:
 if len(P[v])-len(P[u])==3:
  key=(-abs(mu[u][v]),P[u]+P[v])
  if best is None or key<best[0]: best=(key,u,v)
key,u,v=best
E=abs(mu[u][v])
F=S(P[u])+2*S(P[v])
t=P[u]+P[v]
G=sum(1 for i in range(len(t)-1) if t[i]>t[i+1])
print('A B C D E F G R S T',n,len(Cov),315,459,E,F,G,R,Sv,T)
print('best',P[u],P[v],mu[u][v],t)
print('Mlen',len(M),'Covlen',len(Cov))