An n x n matrix that is filled with the whole 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.
Here is a magic square where n = 3:
8 1 6
3 5 7
4 9 2
Write a program that reads n2 numbers from standard input and tests whether they form a magic square when put into matrix form. The value of n is NOT an input to the program; n must be determined from the number of inputs.
For example, the input that creates the example matrix above is 8 1 6 3 5 7 4 9 2.
The output is a single word, "true" if the input produces a magic square, "false" otherwise. Your program may assume that each input token is a whole number.
The program must verify:
1. The proper number of input values was provided.
2. Each of the numbers between 1 and n2 occurs exactly once in the input.
3. When the numbers are arranged in a matrix,
·the sum of the rows,
·columns,
·and diagonals
must be the same value.