March Mutant 16: Polyominous / Quad-Wrangle (non-consecutive)

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.) Additionally, no two horizontally or vertically adjacent cells may contain two consecutive numbers.