An organic compound \(P\) with molecular formula \(C_9H_{18}O_2\) decolorizes bromine water and also shows positive iodoform test. \(P\) on ozonolysis followed by treatment with \(H_2O_2\) gives \(Q\) and \(R\). While compound \(Q\) shows positive iodoform test, compound \(R\) does not give positive iodoform test. \(Q\) and \(R\) on oxidation with pyridinium chlorochromate (\(PCC\)) followed by heating give \(S\) and \(T\), respectively. Both \(S\) and \(T\) show positive iodoform test.
Complete copolymerization of 500 moles of \(Q\) and 500 moles of \(R\) gives one mole of a single acyclic copolymer \(U\).
[Given, atomic mass: \(H = 1, C = 12, O = 16\)]
(1) Sum of number of oxygen atoms in \(S\) and \(T\) is _____.
(2) The molecular weight of \(U\) is _____.