Find $P + Q + R$ I was doing questions from previous year's exam paper and I'm stuck on this question.

Suppose $P, Q, R$ are positive integers such that $$PQR + PQ + QR + RP + P + Q + R = 1000$$ Find $P + Q + R$.

It seems easy but I am not getting the point from where I should start. Thank you.

If you allow some $p,q,r$ to be $0$, you also get $$p+q+r=1000$$ $$p+q+r=88$$ $$p+q+r=100$$ $$p+q+r=148$$
for $$p=1000,q=0,r=0$$ $$p=76,q=12,r=0$$ $$p=90,q=10,r=0$$ $$p=142,q=6,r=0$$
respectively, or any permutation thereof.
