Mind Your Ps And Qs

Logic Level 2

$\begin{array} { l l l l l } & &P & P & Q \\ & &P & Q & Q \\ + && Q & Q & Q \\ \hline & & 8 & 7 & 6 \\ \end{array}$

In the sum shown above, $P$ and $Q$ each represent a digit. What is the value of $P+Q$ ?