Conformal mapping with 1 fixed point

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Let $H=\{z\in \mathbb C\mid\operatorname{Re}z>0 \text{ and } \operatorname{Im}z>0\}$ be the right-upper plane, and $f:H\longrightarrow H$ a nontrivial conformal map such that $f\circ f=id$. Proof f has exactly 1 fixed point.