sum of a range of values based on count of occurrence of letter in range

My range of cells contains as below

10,10,10,10,F.

If my range of cells contain atleast one F ,then there should not be sum.
Otherwise sum of the cells in the range should be happend

I used

=SUMIF(A1:E1,COUNTIF(A1:E1,"F")=0,A1:E1)

But I didn't get the answer ....What is the error pls let me know.