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We provide an elementary constructive proof of shock formation from smooth initial datum of finite energy, with no vacuum regions, and with {nontrivial vorticity}. We prove that for initial data which has minimum slope $- {\\sfrac{1}{ \\eps}}$, for $ \\eps>0$ taken sufficiently small relative to the $\\OO(1)$ amplitude, there exist smooth solutions to the Euler equations which form a shock in time $\\OO(\\eps)$. 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