The initial idioms of the letter N

not give the time of day	not give a hoot
not going to win any beauty contests	not grow on trees
not hack it	not half
Not half!	not half bad
not have a bean	not have a bone in body
not have a care in the world	not have a chance in hell
not have a clue	not have a leg to stand on
not have a prayer	not have a snowball's chance in hell and not a
not have a stitch of clothes	without a stitch on
not have all marbles	not have all (one's) buttons
not have an earthly chance	not have anything on
have nothing to do with	have to do with
not have it	not have one's heart in it
not have (one's) heart in (something)	not have the faintest idea
not have the foggiest notion	not have the heart