Consider the problem of a chain <$A_{1} , A_{2} , A_{3},A_{4}$> of four matrices. Suppose that the dimensions of the matrices $A_{1} , A_{2} , A_{3}$ and $A_{4}$ are $30 \times 35, 35 \times 15, 15 \times 5$ and $5 \times 10$ respectively. The minimum number of scalar multiplications needed to compute the product $A_{1}A_{2}A_{3}A_{4}$ is ____.
- $14875$
- $21000$
- $9375$
- $11875$
