2. (10 pts) Design a minimal DFA for the following language and describe how your DFA works (i.e., the strings corresponding to each state). {x over {a, b ) I ( 2 x na(x) + nb(x)) mod 3 = 0 } Functions na(x) and nv(x) give the numbers of a's and b's in string a, respectively. For example, the following strings are members of L: , ab, aabb, bbb, baba