Alice and Bob are playing a game on a $n \times m$ grid. Initially, the grid is empty. On each move, a player can place either a $1\times1$ domino, or a $1\times2$ domino (either vertically or horizontally), such that the new domino does not partially or completely overlap with any previously placed domino. Alice moves first. The player who cannot make a move loses the game.

For an $i\times j$ board, define $f(i, j) =$

$1$, if Alice wins with optimal play.

$2$, if Bob wins with optimal play.

Calculate $\displaystyle \sum_{i=1}^{989898}\sum_{j=1}^{989898} f(i, j) \cdot (i+j)$