Problem 3 The ABRACADABRA language has just five lowercase letters a, b, c,d, r, and every combination of these letters (but no other letters) is a word in the ABRACADABRA language. For example, abba is a word in the language, but aBBa and abbe are not. The good people of ABRACADABRA often en crypt their words, so that they can send each other messages which their adversaries cannot understand. To this end, they use the following simple encryption process, called a substitution cipher First consider the natural (or lexicographic) order of the five letters, where a is the first letter, b is the second letter, and so on, with r being the last letter. Two parties who wish to communicate with each other agree in advance on a a secret order of the five letters in the language, also called the encryption key (for example r,b,c,d, a). To encrypt a message, they create a table consisting of two rows. The first row lists the letters a, b,c,d, r in their natural order, while the second row lists these same letters in the secret order of the encryption key. Here is an example of such a table: natural order a b c d r encryption key r b d a An arbitrary word in the ABRACADABRA language can be now encrypted by replacing every letter in the word by an encrypted version thereof that appears in the second row of the table. For example, if the encryption key is rbcda as above, every a is replaced by r and every r is replaced by a, while the letters b, c, d remain unchanged. Thus the word abba gets encrypted rbbr. Warm up exercises: . If the secret key is abedr and the source word is abbaca, what is the encrypted word? .If the secret key is arcdb and the source word is abbacar, what is the encrypted word