SUMPRODUCT: Multiple criteria in same column and criteria NOT hard coded

My data would be arranged something like this:

A B C D

ab 1 2 3
cd 4 5 6
ef 7 8 9
gh 2 5 8

(Text in column A and numbers in columns B,C and D)


I would like to sum for "ab" an "cd" across all columns B,C and D. "ab" and "cd" would be linked to cells that I would like to keep variable i.e. I DO NOT want to hard code them in the formula. So if i enter "ab" in "cd" in the linked cells, I should get (1+2+3)+(4+5+6)=21 as the answer. As another example, if i change the linked cells to "gh" and "cd", I should get (2+5+8)+(4+5+6)= 30 as the answer. Please help.

Note: I have tried using sumifs with multiple criteria in the same column, but apparently it cannot handle multiple columns (i cannot add a "total" column in the end because the sumrange would be dynamic). Sumproduct can handle multiple columns but then I would have to hard code the criteria, which I cant (as the criteria would be dynamic as well and there would be more than 50 criteria in some cases).

I have attached a file for reference.

@dannylonglegs
I would like to specify F2 and G2 as an array as in:
=SUMPRODUCT((A2:A10=F2:G2)*B2:D10)

because there would be more than 50 criteria in some cases. But specifying the criteria cells as an array does not work as it searches for both cells as a single item (in the exact order) within column A, rather than searching for them as two separate items. In a nutshell, I would like to tell excel that I want you to look for F2:G2 in A2:A10, where the value can be EITHER F2 or G2 and return TRUE or FALSE. So if I enter "cd" and "gh" in F2 and G2, it should return FALSE, TRUE, FALSE, TRUE in A2:A5. Hope I was clear enough.

SOLVED.
Hey I did something rather unusual and got it working. I used the MATCH function and switched the lookup value with the lookup array. Assuming F2:F4 contain the lookup values of "ab", "cd" and "gh" respectively, I enter:

=IF(ISNUMBER(MATCH(A2:A5,F2:F4,0))=TRUE,1,0)

I get an array: {1,1,0,1} in A2:A5 which is exactly what I wanted! Now I can simply sumproduct this array with B2:D5 to get the desired results.

Regardless, thanks a lot for all your help.

Yeap, thats what I figured. Thankyou!