Annu wanted to invent a board game to play with his girlfriend Chunnu on their next date. He came across the following problem while trying to look for optimal coloring for his board game.

Consider an $N\times N$ board where each cell can be coloured black or white. Let $x_i$ denote the number of white cells in the $i$th row and $y_j$ denote the number of white cells in the $j$th column. Define $f(N)$ as the maximum possible value of the sum: $$\sum_{i=1}^{N} x_i\cdot(N - y_i)$$

Calculate $f(13579)$.