Square center angle condition on side

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. $