Square $$ABCD$$ has center $$O, AB=900, E$$ and $$F$$ are on $$AB$$ with $$AE< BF$$ and $$E$$ between $$A$$ and $$F, m\angle EOF =45^\circ,$$ and $$EF=400.$$ Given that $$BF=p+q\sqrt{r},$$ where $$p,q,$$ and $$r$$ are positive integers and $$r$$ is not divisible by the square of any prime, find $$p+q+r.$$

(第二十三届AIME2 2005 第12题)