Problem 4 [15 points] Given a language A over the alphabet = {a, b)", define SORT(A) = {a-b" l there exists some we A with exactly m as and exactly n bs) For example. SORT((, a, bab, bba, abba)) = {, a, abb, aabb). We can apply SoRT to infinite languages as well. For example, SORT( (ab)* ) = {a"b" l n 0} Prove that if A is a regular language, then SORT(A) is a context-free language. [Hint: Let M = (Q, Sigma, delta, q0, F) be a DFA that recognizes A and construct a CFG G = (V, Sigma, R, S) that generates SORT(A). Review the DFA/NFA to CFG construction presented in class and modify it to produce a CFG that generates SORT(A) rather than A.]