Conditional SUM across multiple worksheets

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I need to summarize values in particular cell across multiple worksheets and to put a result into some other sheet, let's say TOTAL. It's simple to do using SUM and 3-D reference array. My issue is that some of worksheets I have to exclude from the calculation basing on criteria, which is in the worksheet. The functions like SUMIF don't work with 3-D. I've tried to create auxiliary array in TOTAL sheet, which keeps 0/1 reflecting exclude/include the corresponding sheet from/to calculation and then to use multiplication 3-D with aux array (something like SUM(Val_3_D * Aux_Array)), but it doesn't work too.
Please, help to find a solution
 

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