 # Matrix Chain Multiplication

Given an array of integers A representing chain of 2-D matices such that the dimensions of ith matrix is
A[i-1] x A[i].

Find the most efficient way to multiply these matrices together. The problem is not actually to perform the multiplications,
but merely to decide in which order to perform the multiplications.

Return the minimum number of multiplications needed to multiply the chain.

Input Format

``````The only argument given is the integer array A.
``````

Output Format

``````Return the minimum number of multiplications needed to multiply the chain.
``````

Constraints

``````1 <= length of the array <= 1000
1 <= A[i] <= 100
``````

For Example

``````Input 1:
A = [40, 20, 30, 10, 30]
Output 1:
26000
Explanation 1:
Dimensions of A1 = 40 x 20
Dimensions of A2 = 20 x 30
Dimensions of A3 = 30 x 10
Dimensions of A4 = 10 x 30
First, multiply A2 and A3 ,cost = 20*30*10 = 6000
Second, multilpy A1 and (Matrix obtained after multilying A2 and A3) =  40 * 20 * 10 = 8000
Third, multiply (Matrix obtained after multiplying A1, A2 and A3) and A4 =  40 * 10 * 30 = 12000
Total Cost = 12000 + 8000 + 6000 =26000

Input 2:
A = [10, 20, 30]
Output 2:
6000
``````
NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details. 