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For a family $\\mathcal{H}$ of graphs, $G$ is called $\\mathcal{H}$-heavy if $G$ is $H$-heavy for every $H\\in\\mathcal{H}$. In this paper we characterize all connected graphs $R$ and $S$ other than $P_3$ (the path on three vertices) such that every 2-connected $\\{R,S\\}$-heavy graph is Hamiltonian. 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