I'm trying to implement mouse interaction in a 2d isometric game, but I'm not sure if it's possible given the coordinate system used for tile maps in the game.

I've read some helpful articles like this one: How to convert mouse coordinates to isometric indexes?

However, this game's coordinate system is "jagged" for lack of a better word, and looks like this:

Is it even possible to map mouse coordinates to this successfully, since the y-axis can't be drawn on this tile-map as a straight line?

I've thought about doing odd-y-value translations and even-y-value translations with two different matricies, but that only makes sense going from tile->screen.