# Product puzzle

Write a single positive digit $$(\leq 6)$$ into each empty square in the figure below, such that every number $$(1, 2, 3, 4, 5, 6)$$ appears in each row and in each column. The number in a circle shows the product of the four numbers around it.

If you are finished, find the minimum value of the product of the numbers in the pink squares!


Note: Here is a sample, with digits $$1, 2, 3, 4$$:

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