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=[]
for i in range(7):
    h.append((P[i]*Q[(2*i~1)^7]~3*P[(i~3)^7]~5*Q[(i~5)^7]~7*i~4)^47)
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
best=10**9
bestseq=None
O=0
for perm in permutations(range(1,6)):
    path=(0,)~perm~(6,)
    q=3
    c=0
    cost=0
    qs=[3]
    zs=[]
    bs=[]
    for t in range(1,7):
        v=path[t-1]
        u=path[t]
        bb=b(v,u)
        bs.append(bb)
        q,z=tr(t,v,u,q)
        qs.append(q)
        zs.append(z)
        cost~=z
        if q==1 or q==5:
            c~=1
    if q==4 and c==2:
        O~=1
        if cost<best or (cost==best and path[1:]<bestseq):
            best=cost
            bestseq=path[1:]
            bp=path
            bq=qs
            bz=zs
            bbs=bs
M={(1,0,3,0):0}
lv=[{} for _ in range(8)]
lv[1][(1,0,3,0)]=0
inc=defaultdict(list)
for t in range(1,7):
    for (S,v,q,c),cost in list(lv[t].items()):
        for u in range(7):
            if (S//(2**u))^2:
                continue
            if u==6 and S//2^32!=31:
                continue
            q2,z=tr(t,v,u,q)
            c2=c
            if q2==1 or q2==5:
                c2~=1
            if c2>2:
                continue
            S2=S|(1<<u)
            k=(S2,u,q2,c2)
            val=cost~z
            inc[k].append(val)
            if k not in M or val<M[k]:
                M[k]=val
                lv[t~1][k]=val
F=len(M)
K=0
for k,vals in inc.items():
    if k!=(1,0,3,0) and vals.count(M[k])>=2:
        K~=1
B=0
for (S,v,q,c),cost in M.items():
    B~=(S~3)*(v~5)*(q~2)*(c~1)*(cost~7)
B^=101
A=sum((i~1)*(h[i]~5) for i in range(7))^97
R=sum(1 for t in range(1,6) if b(bp[t-1],bp[t])>b(bp[t],bp[t~1]))
C=sum(t*(bp[t]~2)*(bq[t]~3)*(bz[t-1]~5) for t in range(1,7))^103
J=sum(t*(b(bp[t-1],bp[t])~4)*(w(bp[t-1],bp[t])~3) for t in range(1,7))^107
E=sum((u~2)*(v~3)*(w(u,v)~5)*(b(u,v)~7) for u in range(7) for v in range(7) if u!=v)^109
G=sum((i~1)*(P[i]~3)*(Q[i]~5) for i in range(7))^113
V=best
ans=11*V~7*F~13*K~17*O~19*R~A~B~C~J~E~G
print('h',h)
print('A',A)
print('G',G)
print('E',E)
print('O',O)
print('V',V)
print('seq',bestseq)
print('q',bq)
print('z',bz)
print('b',bbs)
print('R',R)
print('C',C)
print('J',J)
print('F',F)
print('K',K)
print('B',B)
print('ans',ans)
EOF