Sum column based on value of row sum

I got an equation to work, but it will get really large when I apply it to my data set of 104 people vice 3. Does anyone have any ideas how to streamline this equation, so I will be easier to work with. I have attached a updated file with the working equation.

=SUM(IF(16-SUM($C$3:D3)>=0,D3,IF(16-SUM($C$3:D3)<0,0,16-SUM($C$3:C3))),IF(16-SUM($C$4:D4)>=0,D4,IF(16-SUM($C$4:D4)<0,0,16-SUM($C$4:C4))),IF(16-SUM($C$5:D5)>=0,D5,IF(16-SUM($C$5:C5)<0,0,16-SUM($C$5:C5))))