Sudoku Mochikoro - 200 Hard to Master Puzzles 9x9 (Volume 6)

Mochikoro ("Mochinuri") is a logic puzzle. It consists of a grid, with numbers in some cells. The aim is to blacken some cells of a grid according to the following rules:
- The black cells divide the grid in rectangular areas ("islands") of white cells.
- No two islands may share an edge, but all of the islands must be connected to each other through their corners.
- Each numbered cell must be a part of a white island. Some white areas may not include a cell with a number.
- Each island must have the same number of white cells as the number it contains (including the numbered cell).
- No 2 x 2 cell area within the grid can contain all black cells.