How to Calculate an Average to exclude zeros and the largest value

I am trying to write 1 formula that would calculate the average of 6 data points if they are greater than zero but I also want to exclude the largest value in the data set as well. I would prefer this to be a single formula with no helper column if possible. I have attached a small sample of data. You will see in column "G" I would need the average of A:F but I would exclude column F since it is the largest value.

Any help would be greatly appreciated