  Let $\mathcal A$ be a hyperplane arrangement in $\mathbb C^n$. We show that
the number of decomposition factors as a perverse sheaf of the direct image
$Rj_*\mathbb C_U $ of the constant sheaf on the complement $U$ to the
arrangement is given by the Poincar\'e polynomial of the arrangement.
Furthermore we describe the composition factors of $Rj_*\mathbb C_U $ as
certain local cohomology sheaves and give their multiplicity.
