Divide the grid into orthogonally-connected regions of cells. Each cell should have a digit in it equal to the size (in number of cells) of its region. Two regions of the same size cannot share an edge (but may touch at a corner). Every region in the grid must then be shaded one of two colours. Any two regions touching at an edge must have different colouring. One or more arrows in a cell indicate that the number in the cell equals the number of cells of the same shading in all of the directions combined.
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