import numpy as np
def survive(gtab,cp,w,T):
    p=len(cp); N=1<<(w-1); L=w+T+p+4
    S=np.zeros((N,L),dtype=np.uint8); idx=np.arange(N)
    for j in range(w-1): S[:,j]=(idx>>j)&1
    S[:,w-1]=1
    g=np.array(gtab,dtype=np.uint8)                    # g[2*c + r], c = self, r = near neighbour
    e=np.zeros((N,T+p+1),dtype=np.uint8)
    for t in range(T+p+1):
        e[:,t]=S[:,0]
        near=np.concatenate([np.full((N,1),cp[t%p],dtype=np.uint8),S[:,:-1]],1)
        far=np.concatenate([S[:,1:],np.zeros((N,1),dtype=np.uint8)],1)
        S=far^g[2*S+near]
    alive=np.ones(N,bool); death=np.full(N,T)
    for t in range(T):
        if cp[t%p]==1:
            bad=alive&(e[:,t]!=e[:,t+p]); death[bad]=t; alive&=~bad
    return int(alive.sum()), int(death.max())
names={(0,0,0,0):"0",(0,0,0,1):"self AND near",(0,0,1,0):"self AND NOT near",(0,0,1,1):"self",
       (0,1,0,0):"NOT self AND near",(0,1,0,1):"near   (Rule 90)",(0,1,1,0):"self XOR near",(0,1,1,1):"self OR near (Rule 30)",
       (1,0,0,0):"NOR",(1,0,0,1):"XNOR",(1,0,1,0):"NOT near",(1,0,1,1):"self OR NOT near",
       (1,1,0,0):"NOT self",(1,1,0,1):"NOT self OR near",(1,1,1,0):"NAND",(1,1,1,1):"1"}
T=80
for gtab,name in names.items():
    row=[]
    for cp in ((0,1),(0,0,1)):
        fooled=0; worst=0
        for w in range(1,13):
            a,dmax=survive(gtab,cp,w,T); fooled+=a; worst=max(worst,dmax if a==0 else T)
        row.append(f"{''.join(map(str,cp))}: {'FOOLED by '+str(fooled)+' starts' if fooled else 'never fooled (latest catch: night '+str(worst)+')'}")
    print(f"  g = {name:24s} | "+" | ".join(row))