Monday Mutant 117: The Inner Limits (multiplicative)

In this The Inner Limits puzzle, a number indicates the product of two quantities: the number of cells in an uninterrupted horizontal line from that cell (up to the nearest edges of the loop, and including the cell itself), and the number of cells in an uninterrupted vertical line from that cell (up to the nearest edges of the loop, and including the cell itself). The rules are otherwise unchanged.
Thomas Snyder posted a beautiful puzzle in preparation for the recent United States Puzzle Competition. It is my hope that I have made a puzzle at least as excellent as his.
 

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