import numpy as np, itertools
from collections import defaultdict
from pin import fiber
cp=(0,1,1,1,1,1); p=len(cp); Z=7
rng=np.random.default_rng(89)
table=defaultdict(set)
for _ in range(1500):
    c=fiber(cp,60,Z+3)
    for k in range(1,Z+1):
        for t in range(5,55):
            a=lambda kk,tt: c[kk][tt]
            Dk=a(k,t)^a(k,t+p); Dk1=a(k-1,t)^a(k-1,t+p)
            corr=(a(k,t)|a(k-1,t))^(a(k,t+p)|a(k-1,t+p))
            table[(k,t%p,Dk1,Dk)].add(corr)
def corr_options(k,ph,Dk1,Dk):
    s=table.get((k,ph,Dk1,Dk))
    return s if s else {0,1}           # unseen situation: allow both (conservative)
def nexts(ph,D,x):                      # D = (D1..DZ), x = input D_{Z+1}
    full=(0,)+D+(x,)                    # D0=0 (same lighthouse), D_{Z+1}=x
    opts=[[full[k+1]^c for c in corr_options(k,ph,full[k-1],full[k])] for k in range(1,Z+1)]
    return [((ph+1)%p,tuple(o)) for o in itertools.product(*opts)]
states=[(ph,D) for ph in range(p) for D in itertools.product((0,1),repeat=Z)]
def ok(ph,D): return not (cp[ph]==1 and D[0]==1)      # watchman: no difference at lantern 1 on lit nights
safe={s for s in states if ok(*s)}
while True:
    new={s for s in safe if any(all(n in safe for n in nexts(*s,x)) for x in (0,1))}
    if new==safe: break
    safe=new
forced=both=0
for s in safe:
    good=[x for x in (0,1) if all(n in safe for n in nexts(*s,x))]
    if len(good)==1: forced+=1
    elif len(good)==2: both+=1
print(f"pinned-zone machine for 011111 (lanterns 1-{Z}): {len(states)} states, {len(safe)} safe")
print(f"   in safe states, the incoming difference is FORCED in {forced}, free in {both}")
nz=[s for s in safe if any(s[1])]
print(f"   safe states with any difference inside the zone: {len(nz)}")
print("   safe states (phase, differences at lanterns 1-7) -> allowed incoming difference -> next state:")
for s in sorted(safe):
    good=[x for x in (0,1) if all(n in safe for n in nexts(*s,x))]
    nx={x:sorted(set(nexts(*s,x))) for x in good}
    print(f"     phase {s[0]}  D={''.join(map(str,s[1]))}   input {good}   ->", {x:[(n[0],''.join(map(str,n[1]))) for n in v] for x,v in nx.items()})