Using SUMIF with multiple criteria

Hi,

I am trying to use a SUMIF function to lookup a value in multiple columns, but not sure if this is possible! Example below:

A B C
X C 1
Y B 2
Z A 3

I want to be able to do a SUMIF to look up my value "Z" in columns A:B to SUM what is in column C. So for this example the sum would be 3.

The formula I have tried is =SUMIF(A:B,"Z",C:C) which works for any value I try to look up in column A. However if I try it on a value in column B it doesn't work. e.g. =SUMIF(A:B,"A",C:C).

**Note items in column A and B would be unique and would never appear in both columns.**

Any suggestions welcome!