Sashigane Fillomino

Rules: In addition to regular Fillomino rules, every region must be in the shape of a unit-width L (as in Sashigane). The unit-width L-shaped polyominoes are exactly the ones formed by removing an $a$ by $b$ block from an $(a + 1)$ by $(b + 1)$ rectangle for some positive integers $a$ and $b$.

Example:

[Solution]

This variant was invented by Brian Chen (betaveros). His first two Sashigane Fillomino puzzles can be found here and here.