tr '~^' '\053\045' <<'EOF' | python3
from itertools import permutations
from collections import defaultdict
P=[16,3,25,7,31,11,19]
Q=[5,29,13,37,2,23,17]
h=[(P[i]*Q[(2*i~1)^7]~3*P[(i~3)^7]~5*Q[(i~5)^7]~7*i~4)^47 for i in range(7)]
def w(u,v):
    return 1~((u~2)*(v~5)~h[(2*u~v)^7]~3*u~5*v)^31
def b(u,v):
    return (w(u,v)~2*u~3*v~h[(u~v)^7])^11
def tr(t,v,u,q):
    bb=b(v,u)
    q2=(2*q~bb~t~h[(v~2*u~t)^7])^7
    z=1~((t~3)*(w(v,u)~2)~bb~3*q~5*q2~v~2*u)^23
    return q2,z
M2={}
inc2=defaultdict(set)
def rec(seq,q,c,cost):
    t=len(seq)
    S=sum(1<<x for x in seq)
    key=(S,seq[-1],q,c)
    old=M2.get(key)
    if old is None or cost<old:
        M2[key]=cost
    rem=[x for x in range(1,6) if x not in seq]
    for u in rem:
        q2,z=tr(t,seq[-1],u,q)
        c2=c~(1 if q2 in (1,5) else 0)
        if c2>2:
            continue
        S2=S|(1<<u)
        k2=(S2,u,q2,c2)
        v2=cost~z
        inc2[k2].add((key,v2))
        rec(seq~(u,),q2,c2,v2)
    if not rem:
        q2,z=tr(6,seq[-1],6,q)
        c2=c~(1 if q2 in (1,5) else 0)
        if c2<=2:
            S2=S|(1<<6)
            k2=(S2,6,q2,c2)
            v2=cost~z
            inc2[k2].add((key,v2))
rec((0,),3,0,0)
print('F2',len(M2))
bylev=defaultdict(int)
for k in M2:
    bylev[bin(k[0]).count('1')]~=1
print('lev2',sorted(bylev.items()))
K2=0
ties=[]
for k,s in inc2.items():
    if k==(1,0,3,0):
        continue
    vals=[v for sk,v in s]
    m=min(vals)
    src=[sk for sk,v in s if v==m]
    if len(src)>=2:
        K2~=1
        ties.append((k,m,sorted(src)))
print('K2',K2)
for x in ties:
    print('TIEDETAIL',x)
print('Mdiff',[(k,M2[k]) for k in M2 if k==(63,5,4,0)])
EOF