Dealing with "0" and "-" in Data Validation

I thought I had this worked out but alas my solution only works when addressing empty (blank) cells. I need a solution that will deal with cells that have zero (0 or 0.00) or absolute zero (-) in them. Here's my problem:

A cell (C1) references two adjacent cells, A1 and B1. A1 or B1 should never BOTH have non-zero values. C1 is calculated by multiplying whichever cell has a non-zero value by a referenced factor. If both A1 and B1 happen to be zero, that's fine, then so is C1. I entered this formula into C1:

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I then added this Data Validation formula into A1 and B1:

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The problem lies in the Data Validation formula. I need to have A1 and B1 be able to display "0" (with or without decimals, and absolute zero (-), and blank/empty cells, but still only allow one of them to have a non-zero value. I am certainly open to skipping the data validation approach if there is a clean formula that will work in C1. Any ideas?

Thanks for your help, as always. This forum is a huge help. David

That's close but not quite. It works when non-zero values are entered into both A1 and B1 but if zero ("0") is entered into both then I still get the error message. Zero in both A1 and B1 is a possible condition for this spreadsheet.

Also, as it turns out, cell B1 always as to be either a zero or a positive value. Is it difficult to code that condition?

Thanks for your help, I really appreciate it. David