Nemotron-IMO-Bench 2026 G29

A point $P$ inside the convex $n$-gon $A_1\ldots A_n$ has the property that all angles $A_i P A_{i+1}$ are equal to $2\pi/n$. Prove that for any point $Q$ in the plane of the polygon $$QA_1+\ldots+QA_n\geq PA_1+\ldots+PA_n.$$