Problem 3. Consider finite strings over the alphabet Σ = {a, b, c, d}. The power operation represents string repetition, for example a 3 b 4 c denotes the string aaac. Define a contextfree grammar G generating the language L(G) = {w|(∃i, j, k)w = a i b (i+j+k) c jd k}, the set of words where the number of b’s is the same as the number of all other letters together and the letters are ordered alphabetically. For example, the words ab, aaad, abbbcd belong to the language, words abba, aac, abc do not belong to the language. Justify your answers