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the following cases occurs. \\begin{itemize} \\item[(i)] $\\gamma=0$ and the extension $\\K(\\cX)/\\K(\\cX)^S$ completely ramifies at a unique place, and does not ramify elsewhere. \\item[(ii)] $\\gamma>0$, $p=3$, $\\cX$ is a general curve, $S$ attains the Nakajima's upper bound $3(\\gamma-1)$ and $\\K(\\cX)$ is an unramified 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