In this exercise you will write code to determine whether a square is magic.

File Square.java contains the shell for a class that represents a square matrix. It contains headers for a constructor that gives

the size of the square and methods to read values into the square, print the square, find the sum of a given row, find the sum

of a given column, find the sum of the main $($or other$)$ diagonal, and determine whether the square is magic. The read method

is given for you; you will need to write the others. Note that the read method takes a Scanner object as a parameter.

File SquareTest.java contains the shell for a program that reads input for squares from a file named magicData and tells

whether each is a magic square. Following the comments, fill in the remaining code. Note that the main method reads the

size of a square, then after constructing the square of that size, it calls the readSquare method to read the square in$.$ The

readSquare method must be sent the Scanner object as a parameter.

$5.$ You should find that the first, second, and third squares in the input are magic, and that the rest $($fourth through

seventh$)$ are not. Note that the $-1$ at the bottom tells the test program to stop reading.

$//***************************************************************$

$//$ Square.java

$//$

$//$ Define a Square class with methods to create and read in

$//$ info for a square matrix and to compute the sum of a row,

$//$ a col, either diagonal, and whether it is magic.

$//$

$//***************************************************************$

import java.util.Scanner;

public class Square

$\{$

int$[][]$ square;

$//--------------------------------------$

$//$create new square of given size

$//--------------------------------------$

public Square$($int size$)$

$\{$

$\}$

$//--------------------------------------$

$//$return the sum of the values in the given

row $//--------------------------------------$

public int sumRow$($int row$)$

$\{$

$\}$

$//--------------------------------------$

$//$return the sum of the values in the given

column $//--------------------------------------$

public int sumCol$($int col$)$

$\{$

$\}$

$//-----------------------------------$

$//$return the sum of the values in the main

diagonal $//---------------------------------------$

public int sumMainDiag$()$

$\{$

$\}$

$//--------------------------------------$

$//$return the sum of the values in the other $("$reverse$")$

diagonal $//--------------------------------------$

public int sumOtherDiag$()$

$\{$

$\}$

$//--------------------------------------$

$//$return true if the square is magic $($all rows, cols, and diags have

$//$same sum$),$ false otherwise

$//--------------------------------------$

public boolean magic$()$

$\{$

$\}$

$//--------------------------------------$

$//$read info into the square from the input stream associated with the

$//$Scanner parameter

$//--------------------------------------$

public void readSquare$($Scanner scan$)$

$\{$

for $($int row $=0$; row $<$ square.length; row$++)$

for $($int col $=0$; col $<$ square.length; col $++)$

square$[$row$][$col$]=$ scan.nextInt$()$;

$\}$

$//----------------------------------------$

$//$print the contents of the square, neatly

formatted $//----------------------------------------$

public void printSquare$()$

$\{$

$\}$

$\}$

$//***************************************************************$

$//$ SquareTest.java

$//$

$//$ Uses the Square class to read in square data and tell if

$//$ each square is magic.

$//$

$//***************************************************************$

import java.util.Scanner;

public class SquareTest

$\{$

public static void main$($String$[]$ args$)$ throws

IOException $\{$

Scanner scan $=$ new Scanner$($new File$("$magicData$"))$;

int count $=1$; $//$count which square we're on

int size $=$ scan.nextInt$()$; $//$size of next square

$//$Expecting $-1$ at bottom of input file

while $($size $!=-1)$

$\{$

$//$create a new Square of the given size

$//$call its read method to read the values of the square

System.out.println$("$

$********$ Square $"+$ count $+"$

$********")$; $//$print the square

$//$print the sums of its rows

$//$print the sums of its columns

$//$print the sum of the main diagonal

$//$print the sum of the other diagonal

$//$determine and print whether it is a magic square

$//$get size of next square

size $=$ scan.nextInt$()$;

$\}$

$\}$

$\}$

Magic Data

$3$

$816$

$357$

$492$

$7$

$3039481101928$

$384779182729$

$466817263537$

$5141625343645$

$1315243342444$

$2123324143312$

$2231404921120$

$4$

$489639$

$27182136$

$15303324$

$1245423$

$3$

$627$

$153$

$294$

$4$

$316213$

$69712$

$105118$

$154141$

$5$

$17241581$

$23516147$