You are trying to break a Vigenere cipher using frequency analysis of the ciphertext `

lcyfqpngcytnkvveakkynktfswdyrnaeerqqoccmhspfshaekrziuvleiwpyyazinwaevydfizcydfidzejvloairlooddcdsrxceokycalrechhztfpntiwatjkfpmvjqlgvrseodrrtcrcjjaeuqpnujgebrtizncpyqrzvlolprgcpcrlpijrqdudvbeoyrtptyvazrivaekvpazmgrpptyvkpsjrepfifkehvgjlnvngehkycnoiicntcpcycipneeudcdsrxctfkycjmrkastyvnwaevgdfizcydcpgqnfkgeskycpnvdwsonvtprkycpnvdwnaejcydrcycgvesxbvimqcyfqpndvqdaxvqeofeczfpfscpcrlpsrebwofbyetyvppslcrtnxtgahvirpxkjgqtyzqllcfudtyvkeouvbfcvkfpkvprsevecxytrlpqlznehvzpalrecdsfkfpytrlxajhsprruclswigpnucw

(a) Use the method from 2.3.1 of the textbook to find the number of matching characters in the first line of the ciphertext and its displacement by 2 characters. Do this using only paper and pencil and show your work.

(b) Find the number of matching characters in the entire given ciphertext and its displacement by j characters for j = 1, 2, . . . , 13. You may (and probably want to) use the function MatchCount() from Problem 5 to collect the data.

(c) Use the result of (b) to guess the length of the key used to encrypt the above ciphertext.

(d) Use the method from 2.3.2 of the textbook (the first method for finding the key) to guess the first letter of the key