Define

We define a magic square to be an n x n matrix of distinct positive integers from 1 to n^2 to where the sum of any row, column, or diagonal of length is always equal to the same number: the magic constant.

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Assesment

You will be given a 3 x 3 matrix of integers in the inclusive range [1,9]. We can convert any digit a to any other digit b in the range [1,9] at cost of |a-b|(the absolute of the amount changed). Given s, convert it into a magic square at minimal cost. Return this cost.

Example 1:

Given s:

5 3 4

1 5 8

6 4 2

We can convert it to the following magic square:

8 3 4

1 5 9

6 7 2

This took three replacements at a cost of |5-8| + |8-9| + |4-7| = 7.

The formingMagicSquare function should return an integer that represents the minimal total cost of converting the input square to a magic square.

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Input

An array of each row with an array of each number. [ [], [], [] ]

Output

Return an integer denoting the minimum cost of turning the matrix into a magic square.

Example 2:

Given s:

4 9 2

3 5 7

8 1 5

Output is: 1

Since changing s[2][2] from 5 to 6 makes this a magic square and |5-6| = 1.

to get you started, ask yourself how many possible magic squares can exist?.