2000006507

The bases of the prism shown in the figure are regular hexagons $ABCDEF$ and $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }{E}^{\prime }{F}^{\prime }$. The lateral edges are perpendicular to the bases. Let $\pi$ be a plane through the points $B$, $D$, $D^{\prime }$, $B^{\prime }$ (see the picture). How many diagonals of the prism are perpendicular to the plane $\pi$?