(Problem 3.3 in the book). Let n be a positive integer. A Latin square of order n is an nn array L containing only the integers 1,,n such that every integer occurs exactly once in each row and column of L. [This is like a Sudoko]. Here is an example of a Latin Square of order 3: 132213321. Given a Latin square L of order n we define the Latin square cryptosystem as follows: The Keyspace, Ciphertext space and Plaintext space are all the integers {1..n}. The encryption function for the key i is given by ei(j)=L(i,j), i.e., the value in the i th row and j th place of L. Prove that the Latin square cryptosystem has perfect secrecy provided that every key is equally likely