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
print('h',h)
for u in range(7):
    print('w',u,[w(u,v) for v in range(7) if v!=u])
for u in range(7):
    print('b',u,[b(u,v) for v in range(7) if v!=u])
fe=[]
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:
        fe.append((cost,path[1:],tuple(qs),tuple(zs),tuple(bs)))
print('numfeas',len(fe))
for x in sorted(fe):
    print('fe',x)
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
print('levels',[len(x) for x in lv])
print('F',len(M))
print('byc',[sum(1 for k in M if k[3]==c) for c in range(3)])
print('byq',[sum(1 for k in M if k[2]==q) for q in range(7)])
for k,vals in inc.items():
    if k!=(1,0,3,0) and vals.count(M[k])>=2:
        print('tie',k,'M',M[k],'vals',sorted(vals))
Es=0
for u in range(7):
    for v in range(7):
        if u!=v:
            Es~=(u~2)*(v~3)*(w(u,v)~5)*(b(u,v)~7)
print('Esum',Es,'E',Es^109)
EOF