9995. (C. L. Dodgson, M.A.)—A certain school contains not less than 90 boys nor more than 130. Latin, Greek, and French are taught, but no other languages. For every boy learning Latin, at least two learn Greek, but not French; for every three learning Greek, at least one learns French, but not Latin; and, for every two learning French, at least three learn Latin, but not Greek. Exactly half the school learn no languages. Find how many boys are learning each language.