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
.
For example, we start with the following matrix
:
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. It should return an integer that represents the minimal total cost of converting the input square to a magic square.
formingMagicSquare has the following parameter(s):
s: a
array of integers
Input Format
Each of the lines contains three space-separated integers of row
.
Constraints
Output Format
Print an integer denoting the minimum cost of turning matrix
into a magic square.
Sample Input 0
4 9 2 3 5 7 8 1 5
Sample Output 0
1
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
4
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 .