挂钩 #5

The grid presented here 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 the largest hook, eight 8’s in the next-largest, etc., down to one 1 in the smallest hook.

The filled squares must form a connected region. (Squares are “connected” if they are orthogonally adjacent.)

A number outside the grid indicates the sum of the first consecutive block of filled squares when looking in that direction. (As shown in the example.) Furthermore, every 2-by-2 region must contain at least one unfilled square.

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