Doh! Quite correct about Ainur covering both.
Btw, if maia included there would be difficult choices
since they include Osse, Uinen, Melian, Gothmog.
Sauron, etc. In that case should heavyweights like
Gandalf, Saruman, Sauron, be excluded if they've
already been participants- or seperate
games for Valar and Maiar?
But, of course, there are other interesting contests
suggested above and in the past.