In a rectangle $$ABCD$$, point $$E$$ lies on $$BC$$ such that $$\frac{BE}{EC}=2$$ and point $$F$$ lies on $$CD$$ such that $$\frac{CF}{FD}=2$$. Lines $$AE$$ and $$AC$$ intersect $$BF$$ at $$X$$ and $$Y$$ respectively. If $$FY:YX:XB=a:b:c$$ are relatively prime positive integers, then the minimum value of $$a+b+c$$ is

A

4

B

8

C

12

D

16