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Default Sum If Formula with 3 criteria

I need to create an array formula with 3 criteria. I have done it with 2
before, but I can't seem to get it to work with 3. I have to use the Sumif
array instead of the sumproduct because I need to have blank cells within my
table.

This is essentially the formula I have, but all it returns is n/a.

=SUM(IF((A6:A500=A1)*(B6:B500=A2)*(C6:C500=A3),D6: D500=A4))

where column A is region, B is product, C is month of sale, and D is price.

I've looked in the archive questions, but I can't find anything similar that
doesn't use sumproduct.

Can anyone help me?
 
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