Given a sorted array keys[0.. n-1] of search keys and an array freq[0.. n-1] of frequency counts, where freq[i] is the number of searches to keys[i]. Construct a binary search tree of all keys such that the total cost of all the searches is as small as possible.
Let us first define the cost of a BST. The cost of a BST node is level of that node multiplied by its frequency. Level of root is 1.

Example 1:

Input:
n = 2
keys = {10, 12}
freq = {34, 50}
Output: 118
Explaination:
There can be following two possible BSTs 
        10                       12
          \                     / 
           12                 10
                              
The cost of tree I is 34*1 + 50*2 = 134
The cost of tree II is 50*1 + 34*2 = 118

Example 2:


Input:
N = 3
keys = {10, 12, 20}
freq = {34, 8, 50}
Output: 142
Explaination: There can be many possible BSTs
     20
    /
   10  
    \
     12  
     
Among all possible BSTs, 
cost of this BST is minimum.  
Cost of this BST is 1*50 + 2*34 + 3*8 = 142

Your Task:
You don't need to read input or print anything. Your task is to complete the function optimalSearchTree() which takes the array keys[], freq[] and their size n as input parameters and returns the total cost of all the searches is as small as possible.

Expected Time Complexity: O(n³)
Expected Auxiliary Space: O(n²)

Constraints:
1 ≤ N ≤ 100