#!/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)]
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
allw=[]
def gen(pref,L):
 if len(pref)==L:
  allw.append(tuple(pref))
  return
 for x in range(3): gen(pref+[x],L)
for L in range(1,7): gen([],L)
P=sorted([x for x in allw if any(sub(x,w) for w in W)],key=lambda x:(len(x),x))
n=len(P)
leq=[[sub(P[i],P[j]) for j in range(n)] for i in range(n)]
def norm(a,b):
 L=len(b)
 first=[i==0 or b[i]!=b[i-1] for i in range(L)]
 cnt=0
 for mask in range(1,2**L):
  inds=[i for i in range(L) if (mask//(2**i))%2]
  if len(inds)!=len(a): continue
  if tuple(b[i] for i in inds)!=a: continue
  ok=True
  for i in range(L):
   if i not in inds and not first[i]: ok=False
  if ok: cnt+=1
 return cnt
mu=[[0]*n for _ in range(n)]
for i in range(n):
 for j in range(n):
  if i==j: mu[i][j]=1
  elif leq[i][j]:
   N=norm(P[i],P[j])
   mu[i][j]=((-1)**(len(P[j])-len(P[i])))*N
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
Cover=sorted([(i,j) for i in range(n) for j in range(n) if i!=j and leq[i][j] and len(P[j])-len(P[i])==1],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(Cover))%103
M=sorted([(i,j) for i in range(n) for j in range(n) if i!=j and leq[i][j] and mu[i][j]!=0],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
B=len(Cover)
C=sum(1 for u,v in M if len(P[v])-len(P[u])==2)
D=sum(1 for u,v in M if mu[u][v]<0)
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,B,C,D,E,F,G,R,Sv,T)
print('best',P[u],P[v],mu[u][v])
print('final',29*n+23*B+19*C+17*D+13*E+11*F+7*G+R+Sv+T)