The grid above can be partitioned into 9 L-shaped “hooks”. The largest is 9-by-9 (contains 17 squares), the next largest is 8-by-8 (contains 15 squares), and so on. The smallest hook is just a single square. Find where the hooks are located, and place nine 9’s in one of the hooks, eight 8’s in another, seven 7’s in another, and so on.

The filled squares must form a connected region. (Squares are “connected” if they are orthogonally adjacent.) Furthermore, every 2-by-2 region must contain at least one unfilled square.

The numbers outside the grid denote the greatest common divisors (GCDs) of the numbers formed by concatenating digits in consecutive squares when reading left-to-right (within rows) or top-to-bottom (within columns).

The answer to this puzzle is the product of the areas of the connected groups of empty squares in the completed grid.