Let \(n>0\) be an odd integer. Prove that there exists a set \(=\{A_1, \ldots, A_{2n}\}\) of \(2n\) distinct points in the plane which are not collinear and such that if \(i+j\neq 2n+1\) then the line \(A_iA_j\) contains a third point from \(S\).