Tile Covering

You have a horizontal strip length $N$ and width $1$ . You have infinite supply of $1 \times 1$ tile and $2 \times 1$ tile. You plan to cover the horizontal strip with these two types of tiles.

If $N$ is 1, you can cover the strip in only one way.(placing a $1 \times 1$ tile). For $N = 2$ , there are two ways, placing two $1 \times 1$ block or placing one $2 \times 1$ block.

What are last three digits of the number of ways to cover a horizontal strip of length 23 ( $N = 23$ )?