Skew-Line Angle Between Two Perpendicular Squares

As shown in the figure, the quadrilaterals $ABCD$ and $ADPQ$ are both squares, and the planes containing them are perpendicular to each other. A point $M$ moves along the segment $PQ$, and $E$, $F$ are the midpoints of $AB$ and $BC$ respectively. Let $\alpha$ be the angle between the skew lines $EM$ and $AF$. Find the maximum value of $\cos \alpha$.