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Default SUMPRODUCT with conditional OR

Hi chaps,
Am using the following formula to check two columns of numbers (G3-G1002 &
H3-H1002). If the value in either column is 4 or greater, I'm summing a
corresponding value in column AK (AK3-AK1002):

=IF(AK1014="","",SUMPRODUCT(--(($G$3:$G$1002=4)+($H$3:$H$1002=4)),--($G$3:$G$1002<""),--($H$3:$H$1002<""),AK3:AK1002))

This works fine except when both values are 4 or greater, as it then sums
the value in column AK twice.

Would appreciate any help to tweak the formula into submission.
Thanks for looking.
 
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