Triangle inside a Triangle

In triangle ABC, D, E, and F are on AB, AC, and BC respectively. AD:BD = 2:1; AE:EC = 1:1; BF:FC = 3:1.  AF and BE intersects at G; BE and CD intersects at H; AF and CD intersects at I. If the area of triangle ABC is 504, what is the area of triangle GHI?