INMO 2012 Problem 2

Let $p_{1}<p_{2}<p_{3}<p_{4}$ and $q_{1}<q_{2}<q_{3}<q_{4}$ be two sets of prime numbers such that $p_{4}-p_{1}=8$ and $q_{4}-q_{1}=8$. Suppose $p_{1}>5$ and $q_{1}>5$. Prove that 30 divides $p_{1}-q_{1}$.