import numpy as np, itertools
cp=(0,1,1,1,1,1); p=6
def rows_all(nu,K):
    """exact b_1..b_K for ALL assignments of u_0..u_{nu-1} (vectorised over assignments)"""
    U=np.array(list(itertools.product((0,1),repeat=nu)),dtype=np.uint8)   # (2^nu, nu)
    T=nu*p; A=U.shape[0]
    d=np.array([cp[t%p] for t in range(T+K+2)],dtype=np.uint8)
    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)
    cols={0:np.tile(d,(A,1)),1:e}
    for k in range(1,K):
        x,y=cols[k],cols[k-1]; cols[k+1]=x[:,1:]^(x[:,:-1]|y[:,:x.shape[1]-1])
    return np.stack([cols[k][:,0] for k in range(1,K+1)],1)          # (2^nu, K)
nu=16; K=6*nu-6
B=rows_all(nu,K)
print(f"exact rows for all 2^{nu} assignments, lanterns 1..{K}")
for M in (30,40,50,60,70):
    alive=np.ones(B.shape[0],bool); blocks=[]; cur=[]
    for k in range(M,K):                                 # constraint b_{k+1}=0
        before=alive.sum(); alive&=(B[:,k]==0); cur.append(int(alive.sum()<before))
        if len(cur)==6: blocks.append(sum(cur)); cur=[]
        if alive.sum()==0: break
    blocks.append(sum(cur)) if cur else None
    print(f"  support bound M={M}: genuinely new constraints per block of 6 tail lanterns: {blocks}   (emptied after {k+1-M} tail lanterns)")