What is P, Q and R=?

PQP+RQQQ 2009\begin{array} { l l l l l } & & P & Q & P \\+ &R& Q& Q& Q \\\hline & \ 2 &0 &0 &9\\ \end{array}

What is P+Q+R=?P+ Q+ R= ?, knowing that each letter represents a positive distinct integer.

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