Point $M$ of rectangle $ABCD$ is the midpoint of side $BC$ and point $N$ lies on $CD$ such that $DN:NC = 1:4$. Segment $BN$ intersects $AM$ and $AC$ at points $R$ and $S$. If $NS:SR:RB$ = $x:y:z$, what is the minimum possible value of $x + y + z$?