Sukaku (Daily Sudoku League #105)

Sukaku recently appeared in the 4th Round of the 2015 Sudoku Grand Prix. I found this puzzle very interesting and thought of creating one.

Sukaku is my 105th contribution to The League of Extraordinary Ladies and Gentlemen.

Rules of Sukaku

Classic Sudoku Rules apply. Additionally, the grid must be divided into some rectangles with each rectangle containing exactly one shaded cell and each cell in the grid belonging to exactly one rectangle. The digit in each shaded cell must indicate the area of the rectangle it is part of. Digits cannot repeat within a rectangle.