Let A₁, A₂, A₃, …, A_n be finite sets such that |A_i| is odd for all 1≤i≤n and |A_i∩A_j| is even for all 1≤i<j≤n. Prove that it is possible to pick one element a_i in each set A_i so that a₁, a₂, …,a_n are distinct.