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

You will be given a $3\times3$ matrix $\boldsymbol{\mathrm{~S~}}$ of integers in the inclusive range $[1,9]$. We can convert any digit $\boldsymbol{a}$ to any other digit $\boldsymbol{b}$ in the range $[1,9]$ at cost of $\left|a-b\right|$. Given $\boldsymbol{\mathrm{~S~}}$, 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 $[1,9]$.

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 $|5-8|+|8-9|+|4-7|=7$.

Function Description

Complete the formingMagicSquare function in the editor below.

formingMagicSquare has the following parameter(s):

int s[3][3]: a $3\times3$ array of integers

Returns

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

Input Format

Each of the $3$ lines contains three space-separated integers of row $s[i]$.

Constraints

$s[i][j]\in[1,9]$

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, $s[2][2]$, from $5$ to $\boldsymbol{6}$ at a cost of $|6-5|=1$, $\boldsymbol{\mathrm{~S~}}$ 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

$s[0][1]$->$\mbox{9}$ at a cost of $|9-8|=1$
$s[\mathbf{1}][\mathbf{0}]$->$3$ at a cost of $|3-4|=1$
$s[2][0]$->$8$ at a cost of $|8-6|=2$,

then the total cost will be $1+1+2=4$.

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