Compute the number of (not necessarily convex) polygons in the coordinate plane with the following properties:

- If the coordinates of a vertex are $(x,y)$, then $x,y$ are integers and $1\leq |x|+|y|\leq 3$.
- Every side of the polygon is parallel to either the x or y axis.
- The point $(0,0)$ is contained in the interior of the polygon.

Let's think step by step and output the final answer within \boxed{}.
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