P, Q and R are three metals that undergo chemical reactions as follows:

$P_2{O}_3+2Q\to Q_2{O}_3+2P$

$2P+3RO\to P_2{O}_3+3R$

$3RS{O}_4+2Q\to Q_2{\left(S{O}_4\right)}_3+3R$

Observe the reactions and arrange the metals in the increasing order of their reactivity.