Logic Masters Deutschland e.V.

With an air of near-inevitability given how I got into setting these puzzles in the first place, I'm following up a Cracking The Cryptic-inspired Friendly Sudoku with a Cracking The Cryptic-inspired Checkered Fillomino. I suppose my next puzzle really ought to be inspired by one of Mark's solves, 'cause right now it's 2-0 to Simon... sorry, Mark! Turns out, I have no control over which concepts wind up tickling my fancy, so I can't promise anything. Oh, and I must also give credit to Jonas Gleim, whose formulation of the rules was to good not to borrow and then immediately ruin by making wordier...

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Rules
Normal fillomino rules apply: divide the grid into regions and place a number in each cell. The numbers within a region must all be the same and equal to the size of the region. Regions of equal size must not touch orthogonally, but may touch diagonally. A region may contain zero, one or more of the given numbers.
In addition, a "checkered" constraint applies: it must be possible to shade some regions fully such that two shaded regions or two unshaded regions never touch orthogonally. This is equivalent to saying that there are no T-junctions between regions, if that's how you'd rather think about it.

You can poke the puzzle on Penpa+ here, and as always, I wish you good luck and a (hopefully) enjoyable solve!