Problem 55315. Chain multiplication - 04

Asif Newaz

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Following up on the problem in 55305, you found the optimal way to multiply a chain of matrices.
However, here in this problem, you will be given a chain of matrices as a string with parenthesis placed in certain places along with their dimensions. You have to find out the number of multiplications required if you multiply the matrices that way.
For example, 
d= [1, 2, 3, 2] and s = "A(BC)".
here, the sizes of the matrices are - A(1,2), B(2,3), and C(3,2).
First, B and C are to be multiplied (since they are inside parenthesis). The resultant matrix is to be multiplied with A. You need to find out the total number of multiplications required, which is 12+4=16.
n.b. only valid parenthesization are given in this problem for simplicity.