[math-fun] Root-factorial representation?

Can every integer be represented by a composition of integer square root ($) and factorial (!) applied to 3? Some example representations: 3 = 3 6 = 3! 1 = 3$ 2 = 3!$ 720 = 3!! 26 = 3!!$ 5 = 3!!$$ 120 = 3!!$$! 10 = 3!!$$! ... If not, what is the smallest counterexample?