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Let $P_0$ be a point outside an equilateral triangle $A B C$ such that $A P_0 C$ is an isosceles triangle with a right angle at $P_0$. A grasshopper starts at $P_0$ and turns around the triangle as follows. From $P_0$, the grasshopper jumps to the point $P_1$ symmetric to $P_0$ with respect to $A$; then it jumps to the point $P_2$ symmetric to $P_1$ with respect to $B$, then to the point $P_3$ symmetric to $P_2$ with respect to $C$, etc. For each $n \in \mathbb{N}$, compare the distances $P_0 P_1$ and $P_0 P_n$.
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