2. Closure (15 points) Let L be a language, and let the GT() operation be defined as below GT(L)={w1Bw2Uw3Zw4Zw5w1w2w3w4w5L,i,wi\{}}. Note that each wi can represent one or multiple characters, but they cannot be the empty string. In other words, GT(L) is formed by weaving BUZZ into the middle of words from L in all possible ways. If 10101,10111011,10101000001L, then 1B0U1Z0Z1,1B01U11Z01Z1,1B01U010Z0000Z1 are all examples of strings that will be in GT(L). Since each wi is non-empty, B and Z will never be the first or last characters in a word. Furthermore, no letters from BUZZ will ever be adjacent. This implies that words of length 4 or less contained in L will not appear in GT(L). Prove that if L is regular, then GT(L) is also regular