Puzzle

You are given N^2 decimal digits from $1$ to $9$.

Consider arranging these digits in an N \times N square grid, placing one digit in each cell. Reading each row from left to right forms a decimal representation of an $N$-digit number. Similarly, reading each column from top to bottom also forms a decimal representation of an $N$-digit number. Let $S$ be the sum of all $N$ numbers from the rows and all $N$ numbers from the columns.

Arrange the digits in the grid so that $S$ is maximized.