Part I: An n X n matrix that is filled with the numbers 1, 2, 3 , n2 is a magic square if the sum of the elements in each row, in each column and in the two diagonals is the same value. Write a Java application that reads in 16 values from the keyboard and tests whether they form a magic square when put into a 4 X 4 array. You need to test two features: 1. Does each of the numbers 1, 2, , 16 occur in the user input? 2. When the numbers are put into a square, are the sums of the rows, columns, and diagonals equal to each other?

Part II: Implement the following algorithm to construct magic n X n squares; it works only if n is odd. set row = n - 1, column = n / 2 for k = 1 .. n * n place k at [row][column] increment row and column by 1 if the row or column is n, replace it with 0 if the element at [row][column] has already been filled set row and column to their previous values decrement row.

Here is the 5 X 5 square that you get if you follow this method:

11	18	25	2	9
10	12	19	21	3
4	6	13	20	22
23	5	7	14	16
17	24	1	8	15

Write a Java application whose input is the number n and whose output is the magic square of order n if n is odd.