import numpy as np
from collections import Counter
rng=np.random.default_rng(151)
cp=(0,1,1,1,1,1); p=6
def row(u,K):
    T=len(u)*p; d=[cp[t%p] for t in range(T+K+2)]
    e=[(u[t//p] if t%p==0 else (1 if t%p==5 else 0)) for t in range(T)]
    prev,cur=d[:T],e; out=[cur[0]]
    for k in range(1,K):
        nxt=[cur[t+1]^(cur[t]|prev[t]) for t in range(len(cur)-1)]; prev,cur=cur,nxt; out.append(cur[0])
    return out
def forced_tail(prefix,nu,K):
    u=list(prefix)
    while len(u)<nu:
        n=len(u)
        for v in (0,1):
            if row(u+[v]+[0]*(nu-n-1),6*n+1)[6*n]==0: u.append(v); break
    return row(u,K)
res=Counter(); onset=[]
for _ in range(120):
    n0=int(rng.integers(3,10)); prefix=list(rng.integers(0,2,size=n0))
    nu=n0+14; K=6*nu-6; b=forced_tail(prefix,nu,K)
    tail=b[6*n0:]
    alt=lambda s: all(s[i]!=s[i+1] for i in range(len(s)-1))
    if alt(tail[-24:]):
        j=len(tail)-24
        while j>0 and alt(tail[j-1:]): j-=1
        res["ends in the alternating tail"]+=1; onset.append(j)
    else: res["does not end alternating"]+=1
print(dict(res))
if onset: print(f"alternation starts within {min(onset)}-{max(onset)} lanterns into the tail (median {int(np.median(onset))})")