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The constant $s_A(G)$ is defined as the smallest integer $\\ell$ such that any sequence over $G$ of length at least $\\ell$ has an $A$-weighted zero-sum of length $n$ and $\\eta_A(G)$ defined as the smallest integer $\\ell$ such that any sequence over $G$ of length at least $\\ell$ has an $A$-weighted zero-sum of length at most $n$. 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