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Katz, a version of which was asked earlier by M.Gromov.\n  We also prove that a Riemannian $2$-sphere $M$ of diameter $d$ and area $A$ can be swept out by loops based at any prescribed point $p\\in M$ of length $\\leq 200 d\\max\\{1,\\ln{\\sqrt{A}\\over d} \\}$. This estimate is optimal up to a constant factor. 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