Let L be the set of exactly those strings over the alphabet \Sigma = {a, b, c, g}, that satisfy all of the following properties: the length of the string is equal to 5n+3, for some natural number n greater or equal than 0; all of the first (leftmost) 2n symbols are elements of the set {b, c, g}; all of the last (rightmost) 3n symbols are elements of the set {a, b}; the symbols at position 2n+1, 2n+2, and 2n+3 (from the left, i. e., after the first 2n symbols but before the last 3n symbols) are elements of the set {c, g}; Write a complete formal definition of a context free grammar that generates L. If such a context free grammar does not exist, state that the context free grammar does not exist, and prove it.