Creating An Array From Several Seperate Cells

I am trying to do is, to sum up the values in an array, given that the cell value is not an error.
If the cells were in order, the following array formula would solve it easily:
{SUM(IF(ISERROR(A1:A3),0,A1:A3))}

But my problem is that, my cells are not in order. To be more specific, I want to look at A1, B12 and C13, and sum them up with an array formula given the condition that cell value is not an error. Of course, in my case, I have too many cells.