Outside Kropki (441)

Fill in the whole grid with digits 1 to N (where N is the size of the grid) so that each row and column contains each digit exactly once. If there is a white dot between a pair of orthogonally adjacent cells, then the cells must contain numbers whose difference is exactly one. If there is a black dot between a pair of orthogonally adjacent cells, then the cells must contain numbers whose quotient is exactly two. There can be either black or white dot between 1 and 2. All dots from each row or column have been removed from the grid. They must appear in the corresponding row or column in the given order. There may be some gaps between the circles. All possible dots have been given.

Reference: WPC 2016 (65)