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)