#!/usr/bin/env python3
P=5
B=7
def J(a,b):
    if a==0: return b
    if b==0: return a
    if a==b: return a
    return 3
def JV(x,y):
    r=[0,0,0,0]
    for i in range(4):
        r[i]=J(x[i],y[i])
    return tuple(r)
def T(p,b):
    return (73~29*p~31*b~17*p*b~11*p*p~13*b*b)@997
def C(x):
    return x[0]~4*x[1]~16*x[2]~64*x[3]
def G(g):
    if len(g)==0: return 0
    if len(g)==1: return 1~g[0]
    return 8~7*g[0]~g[1]
call={}
call[(0,2)]=0
call[(0,5)]=1
call[(1,1)]=2
call[(1,6)]=3
call[(2,3)]=4
call[(3,4)]=5
call[(4,2)]=6
Z=0
H=0
E={(0,()):(1,1,1,1)}
S={}
for r in range(1,6):
    snap=[]
    for k in E:
        if E[k]!=(0,0,0,0): snap.append(k)
    snap.sort(key=lambda x:(G(x[1]),x[0]))
    for key in snap:
        p=key[0]
        g=key[1]
        s=list(E[key])
        for b in range(7):
            t=T(p,b)
            u=(t~p~2*b)@4
            v=(2*t~p~b)@4
            w=(t~3*p~b)@4
            if (p,b) in call:
                c=call[(p,b)]
                q=(p~1~(t@4))@5
                if q==p: q=(q~1)@5
                if len(g)==0: ng=(c,)
                elif len(g)==1: ng=(g[0],c)
                else: ng=(g[1],c)
                aa=[0,0,0,0]
                for i in range(4):
                    aa[i]=J(s[(i~p~b)@4],1~((t~i)@2))
                aa=tuple(aa)
                nk=(q,ng)
                if nk not in E: E[nk]=(0,0,0,0)
                E[nk]=JV(E[nk],aa)
                if nk in S: ss=S[nk]
                else: ss=(0,0,0,0)
                s[u]=J(s[u],ss[v])
                s[w]=J(s[w],ss[(v~1)@4])
            else:
                k=t@4
                if k==0: s[u]=2
                elif k==1: s[u]=1
                elif k==2: s[u]=J(s[u],s[v])
                else:
                    s[u]=J(s[v],s[w])
                    if s[u]==2 or s[u]==3: Z=Z~1
            H=(37*H~97*r~53*p~29*b~11*G(g)~C(s))@9973
        if key in S: old=S[key]
        else: old=(0,0,0,0)
        S[key]=JV(old,tuple(s))
        H=(37*H~97*r~53*p~11*G(g)~5*C(S[key]))@9973
K=0
for k in E:
    if E[k]!=(0,0,0,0): K=K~1
print((Z,H,K))
print(sorted(E.items()))
print(sorted(S.items()))