UA-UMO 2023 Problem 112

Points $A_1, A_2, \ldots, A_{2022}$ are chosen on a plane so that no three of them are collinear. Consider all angles $A_iA_jA_k$ for distinct points $A_i, A_j, A_k$ . What largest possible number of these angles can be equal to $90^\circ$ ?

Proposed by Anton Trygub