import numpy as np
from collections import Counter
def history(cp,left0,T,depth=80):
    p=len(cp); L=len(left0)+T+2; left=np.zeros(L,dtype=np.uint8); left[:len(left0)]=left0; H=[]
    for t in range(T):
        H.append(left[:depth].copy()); c=cp[t%p]
        right=np.concatenate([[c],left[:-1]]); leftnb=np.concatenate([left[1:],[0]])
        left=leftnb^(left|right)
    return np.array(H)
rng=np.random.default_rng(21)
for cp in ((0,1),(0,0,0,1),(0,0,1)):
    p=len(cp); T=200; w=14
    stats=Counter(); gaps=Counter(); bounces_per_pair=[]; pairs=0
    for _ in range(4000):
        s=rng.integers(0,2,size=w).astype(np.uint8); s[-1]=1
        H=history(cp,s,T+p)
        A=H[:T]; B=H[p:T+p]                        # evolutions of s and s(p) under the same drive
        D=A^B
        lit=[cp[t%p]==1 for t in range(T)]
        first=next((t for t in range(T) if lit[t] and D[t,0]),T)
        if first<25: continue
        pairs+=1; nb=0
        for t in range(first-1):
            nz=np.nonzero(D[t])[0]; nz1=np.nonzero(D[t+1])[0]
            if len(nz)==0 or len(nz1)==0: continue
            d=nz[0]+1; d1=nz1[0]+1
            if d==1 and not lit[t] and d1>=2:      # a bounce
                nb+=1
                d2=(nz[1]+1) if len(nz)>1 else None
                if d2 is None: stats["no second layer"]+=1
                elif d1==d2-1: stats["consumed: old 2nd layer marched in"]+=1
                elif d1<d2-1: stats["NEW closer difference created"]+=1
                else: stats["other"]+=1
        bounces_per_pair.append(nb)
        nz=np.nonzero(D[first//2])[0]+1
        for a,b in zip(nz[:-1],nz[1:]): gaps[(b-a)%p]+=1
    print(f"Mia {''.join(map(str,cp)):5s}: {pairs} long-agreeing pairs (>=25 min); bounces per pair: mean {np.mean(bounces_per_pair) if bounces_per_pair else 0:.1f}, max {max(bounces_per_pair) if bounces_per_pair else 0}")
    print(f"     at each bounce: {dict(stats)}")
    print(f"     spacing between difference layers, mod {p}: {dict(sorted(gaps.items()))}")