SMO Primes!

Let pp, qq and rr be prime numbers such that

pqr=19(p+q+r).pqr=19(p+q+r).

What is the value of p2+q2+r2?p^2+q^2+r^2?


This problem appeared in the SMO - 2014.
This problem is a part of the set "Olympiads and Contests Around the World - 2." You can see the rest of the problems here.
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