1, 2, 3, 4, 5, 6, 7, 8, 9

Victor's mathematics teacher gave him a $3 \times 3$ grid filled with the numbers $1, 2, 3, 4, 5, 6, 7, 8$ and $9$ in an unspecified order, with each number appearing only once.

Given any row

$\begin{array}{ | l | c | r | } \hline a & b & c \\ \hline \end{array}$

or column

$\begin{array}{ | l | c | r | } \hline d \\ \hline e \\ \hline f \\ \hline \end{array}$

in the grid, Victor is allowed to perform the following operations:

Row:

• $a+k$ , $b-k$ , $c-k$

• $a-k$ , $b-k$ , $c+k$

Column:

• $d+k$ , $e-k$ , $f-k$

• $d-k$ , $e-k$ , $f+k$

with $k$ being a non-negative real number and that the numbers in the grid must always be greater than $0$ .

Given that it is possible to perform row and/or column operations such that all the numbers in the grid are equal to a positive real number $N$ , find the maximum value that $N$ can take.