Normal sudoku rules apply. Digits are not allowed to repeat on any positive diagonal (i.e. any diagonal going from the lower-left part of the grid to the upper-right part of the grid). A digit x in a black circle indicates exactly how many of the up to 8 neighboring cells (i.e. orthogonally and diagonally adjacent cells) contain a digit that is in a 1:2 ratio with x. All black circles are given. The sum of the digits in Phistomefel's ring (marked by the cage) is prime.
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