16. Let L b e a ny la ngu a ge. Define even (w) b as the string o t ained b y extra cting from w the letters in even-numb ered positions; th a t is, if w = a1a2a3a4..., then even (w) = a2a4.... Corresponding to this, we c a n define a la ngu ge a even (L ) = {even (w) : w ? L }.Prove th a t if L is regular, so is even (L)