There is a chess tournament, every participant wears a red or a white hat. and everyone plays 1 match with each other. winner gets 1 point, loser gets 0 point and in draw, they get 0,5 points. at the end of the tournament, referee multiplies with two the total points of red side and white side. and after this multiplication, ratio of total points of participants with red hat to participants white hat is 9/2.

so, what is the sum of the possible numbers of participants with red hat?