Rukkuea

Rukkuea (Look-Air, Line of Sight) is a Japanese logic puzzle. The task is to determine the colour of each cell according to the given rules.

Rules: Colour the cells of the grid black or white to form squares of black cells. The squares must not touch each other orthogonally, but diagonally.
Squares of the same size must not “see” each other, i.e., in the horizontal and vertical lines of sight, there must always be a square of a different size between them.
A numbered cell together with its orthogonal neighbours defines a “cross” that consists of the cell and up to four orthogonal neighbours. The number indicates how many of these neighbouring cells should be blackened.