Four positive integers a,b,c, and d have a product of 8! and satisfy\begin{align*}ab \plus{} a \plus{} b &\equal{} 524\\
bc \plus{} b \plus{} c &\equal{} 146\\
cd \plus{} c \plus{} d &\equal{} 104.\end{align*} What is a \minus{} d?<spanclass=′latex−bold′>(A)</span>4<spanclass=′latex−bold′>(B)</span>6<spanclass=′latex−bold′>(C)</span>8<spanclass=′latex−bold′>(D)</span>10<spanclass=′latex−bold′>(E)</span>12