3. The following table shows dimensions of six matrices.

| matrix | A₁ | A₂ | A₃ | A₄ | A₅ | A₆ |
| --- | --- | --- | --- | --- | --- | --- |
| dimension | 30×35 | 35×15 | 15×5 | 5×10 | 10×20 | 20×25 |

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).