3. The following table shows dimensions of six matrices.

Please fully parenthesize the product A₁A₂A₃A₄A₅A₆ in a way such that the number of scalar multiplications is minimum and compute this minimum number. (15%)

(For example, the number of scalar multiplications of (A₁(A₂(A₃(A₄(A₅A₆))))is 47500).