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Default Addition formulas problem

For example:
addition formula: A+B+C=D
Condition 1: If A=B=C=N/A, shows N/A since all = N/A
Condition 2: If A=B=C=0, the shows 0 since 0+0+0+0+0=0
Condition 3: If A=0, B=0, C=0, but D= N/A, shows 0 since A+B+C=0
Condition 4: If A=N/A, B=N/A, C=N/A, but C=0, shows 0
Condition 5: If A=4, B=4, C=4, D=N/A, shows 12 since 4+4+4=12
Condition 6: If A= 4, B=4, C= 0, D=N/A, shows 8 since 4+4+0=8
Etc...

Problem:
If example formula is =SUM(E8:E12), then if all(E8 to E12) are N/A then it
shows 0( I want it to show N/A if all is N/A) --- only condition 2 is met

If example formula is =IF(SUM(D8:D12)=0,"N/A",SUM(D8:D12)) then when all is
0, it shows N/A( I want it to shows 0 if all is 0)----only condition 1 is met

I am looking for a formula where both conditions can be true.

Any help is greatly appreciated!!

 
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