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Default SumProduct problem

Hello,

One of the ranges I use in my sumproduct formula includes cells with formula
like

=IF(A1=0, "", A1)

The sumproduct returns a #VALUE! error whenever the cell A1 is 0, otherwise
it works fine.

How to deal with the problem by modifying the sumproduct ?
(The formula IF(A1=0, "", A1) is fixed and cannot be modified)

Any suggestions would be appreciated. I use Excel XP. Thanks.