An nxn 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.

Square

Write a class Square with a constructor that takes in an integer matrix.  You will write the following instance methods:

• boolean method to check whether each number 1 – n² occurs exactly once
• int method that computes the row sum
• int method that computes the column sum
• int method that computes the diagonal sum
• isMagic method that returns whether or not the square is magic

MagicSquare

Write a class MagicSquare with a constructor that constructs a magic square based on this algorithm.  You may want to pick a random initial value to make things interesting.  Your class should also have a toString method that returns a representation of the square.

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