import numpy as np
from collections import defaultdict
w=10; pattern=(0,1); n=2*w+1; N=1<<n; T=w+16; L=n+2*T+4; off=T+2
idx=np.arange(N,dtype=np.int64)
X=np.zeros((N,L),dtype=np.uint8)
for j in range(n): X[:,off+j]=(idx>>j)&1
alive=np.ones(N,bool); death=np.full(N,T)
for t in range(T):
    bad=alive&(X[:,off+w]!=pattern[t%2]); death[bad]=t; alive&=~bad
    X=np.roll(X,1,axis=1)^(X|np.roll(X,-1,axis=1))
bits=((idx[:,None]>>np.arange(n))&1).astype(bool)          # position j -> cell j-w
pos=np.arange(n)-w
R=np.where(bits.any(1),np.max(np.where(bits,np.abs(pos),-1),axis=1),-1)
gap=death-R
# delay from removing the outermost lamp(s)
outer_mask=np.zeros(N,dtype=np.int64)
for j in range(n): outer_mask|=((np.abs(pos[j])==R)&bits[:,j]).astype(np.int64)<<j
core=idx & ~outer_mask
delay=death-death[core]
print("R : max gap D(R)=T-R | record seed(s) (lit cells) | delay added by the outermost lamp(s) for record holders | max delay over all seeds with this R")
for r in range(1,w+1):
    sel=(R==r)
    if not sel.any(): continue
    D=int(gap[sel].max()); rec=idx[sel&(gap==D)]
    cells=[sorted((int(j)-w) for j in range(n) if (int(s)>>j)&1) for s in rec[:2]]
    dl=[int(delay[np.searchsorted(idx,s)]) for s in rec[:2]]
    print(f"R={r:2d}: D={D:2d} | {cells} | delays {dl} | max delay {int(delay[sel].max())}")