Split the grid into areas and place a number in each cell. The numbers within an area must all be equal, equal to the size of the area. Areas of equal size must not touch by edge, but may touch diagonally. Different given numbers may be part of the same area. There may be areas that don’t contain any given numbers. Their size may be larger than any given number.
In addition, it must be possible to shade some areas fully, such that two shaded areas or two unshaded areas never touch along an edge.