from pmap import from_word
GENS = {"X":(2,2),"T":(2,1),"Ts":(1,2),"cup":(0,2),"cap":(2,0)}
def words(m, maxlen, maxw=4):
    out=[]
    def rec(cur, layers):
        out.append((m, list(layers)))
        if len(layers)==maxlen: return
        for g,(i,o) in GENS.items():
            for pos in range(0, cur-i+1):
                nc = cur-i+o
                if nc>maxw: continue
                rec(nc, layers+[(g,pos)])
    rec(m, [])
    return out
def seeds_from(maxk,maxlen,maxw=4):
    seeds=[]
    for m in range(0,maxw+1):
        for mm, layers in words(m, maxlen, maxw):
            M,n = from_word(mm, layers)
            if 1 <= M.k <= maxk: seeds.append(M)
    return seeds