A Magic Square is a square matrix of consecutive integers, such that the integers in each row, each column and each diagonal add up to the same sum. For instance, the first 3 x 3 matrix below is a magic square and the rows, columns and diagonal add up to 15. The second 5 x 5 matrix has 25 consecutive integers - starting at 1 - where each row, column and diagonal has the sum of 65.

8	1	6
3	5	7
5	9	2

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

Magic squares have special algorithms that will create a magic square for any size. For the purpose of this question you are only concerned with odd-sized magic squares, like the two above. There are different algorithms for even-sided magic squares. The steps below describe the algorithm for any odd-sized magic square size 3 or larger.

1. Start number 1 in the top row, middle column.
2. Place the next number one row higher and one column to the right.
3. If (the number mod size) = 1, place the next number one row lower. In the5 x 5 square above, size = 5. So, 6 is below 5, 11 is below 10, 16 is below 15,

Wrap around: If the above instructions ask you to place a number:

• above the first row, place it in the last row.
• below the last row, place it in the first row.
• to the right of the last column, place it in the first column.

Write a program to prompt for an odd number n less than 20, and solve that n-sized magic square.

Name the class and file name Magic.