Fill The Grid

You have a grid with $N$ rows and $M$ columns. You have two types of tiles — one of dimensions $2 \times 2$ and the other of dimensions $1 \times 1$. You want to cover the grid using these two types of tiles in such a way that: - Each cell of the grid is covered by exactly one tile; and - The number of $1 \times 1$ tiles used is minimized. Find the **minimum** number of $1 \times 1$ tiles you hav