Monday Mutant 81: Polyominous / Quad-Wrangle

In this Polyominous puzzle, every region must be shaped like a rectangle. (Thus, the puzzle is similar to a Quad-Wrangle puzzle, but without the restriction that every region must contain exactly one number, and with the restriction that regions with the same area may not share an edge.) The rules are otherwise unchanged.
I constructed three Shikaku Fillomino puzzles for Fillomino-Fillia, of which this puzzle was considered by me to be the median in difficulty level. I didn't think it was possible to make a Shikaku Fillomino much harder than this one; MellowMelon proved me to be dreadfully wrong, and my hardest puzzle was relegated to being a preview as a result.

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