import numpy as np, itertools
cp=(0,1,1,1,1,1); p=6
def rows_lean(nu,K):
    A=1<<nu; idx=np.arange(A,dtype=np.int64)
    U=((idx[:,None]>>np.arange(nu-1,-1,-1))&1).astype(np.uint8)
    T=nu*p
    e=np.zeros((A,T),dtype=np.uint8)
    for t in range(T):
        ph=t%p; e[:,t]=U[:,t//p] if ph==0 else (1 if ph==5 else 0)
    d=np.array([cp[t%p] for t in range(T)],dtype=np.uint8)
    prev=np.broadcast_to(d,(A,T)); cur=e; out=np.zeros((A,K),dtype=np.uint8); out[:,0]=cur[:,0]
    for k in range(1,K):
        nxt=cur[:,1:]^(cur[:,:-1]|prev[:,:cur.shape[1]-1]); prev,cur=cur,nxt; out[:,k]=cur[:,0]
    return out
nu=19; K=6*nu-6
B=rows_lean(nu,K)
res=[]
for M in range(6,K-6):
    alive=np.ones(B.shape[0],bool); stall=0; longest=0; emptied=False
    for k in range(M,K):
        lantern=k+1; before=int(alive.sum()); alive&=(B[:,k]==0); after=int(alive.sum())
        if after==0: emptied=True; break
        if (lantern-1)%6!=0:
            stall = stall+1 if after==before else 0; longest=max(longest,stall)
    res.append((M,longest,emptied))
for lo,hi in ((6,30),(31,55),(56,80),(81,K-7)):
    sel=[(l,e) for m,l,e in res if lo<=m<=hi]
    full=[l for l,e in sel if e]; part=[l for l,e in sel if not e]
    print(f"  M in [{lo:3d},{hi:3d}]: fully eliminated runs: max stall {max(full) if full else '-'} (mean {np.mean(full) if full else 0:.2f});  runs NOT eliminated by lantern {K}: {len(part)} (stall so far up to {max(part) if part else '-'})")