Monday Mutant 1: Polyominous (inequality)

Monday Mutants is a series in which I will attempt to experiment with "mutant" puzzles. These could be existing puzzle types with an unusual change in the rules, hybrids combining elements from multiple puzzle types, or puzzle types neither invented nor popularized by Nikoli.
In this Polyominous puzzle, there are no given numbers; instead, there are inequality signs in the grid. Each inequality sign must point from a larger polyomino to a smaller one. The rules are otherwise unchanged.