Forming a Magic Square

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

You will be given a matrix of integers in the inclusive range . We can convert any digit to any other digit in the range at cost of . Given , convert it into a magic square at minimal cost. Print this cost on a new line.

Note: The resulting magic square must contain distinct integers in the inclusive range .

Example

$s = [[5, 3, 4], [1, 5, 8], [6, 4, 2]]

The matrix looks like this:

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 .

Function Description

Complete the formingMagicSquare function in the editor below.

formingMagicSquare has the following parameter(s):

int s[3][3]: a array of integers

Returns

int: the minimal total cost of converting the input square to a magic square

Input Format

Each of the lines contains three space-separated integers of row .

Constraints

Sample Input 0

4 9 2
3 5 7
8 1 5

Sample Output 0

Explanation 0

If we change the bottom right value, , from to at a cost of , becomes a magic square at the minimum possible cost.

Sample Input 1

4 8 2
4 5 7
6 1 6

Sample Output 1

Explanation 1

Using 0-based indexing, if we make

-> at a cost of
-> at a cost of
-> at a cost of ,

then the total cost will be .