### Problem Statement

In a binary tree, every node has an optional left, and optional right child node. A BST (binary search tree) is a binary tree that satsifies the following properties:

1) Every node has a unique value

2) The value at a given node must be greater than the value at every node in its left subtree

3) The value at a given node must be less than the value at every node in its right subtree

The depth of a node in a BST is defined as such:

1) The top node (root) has depth 0

2) Every node has depth 1 higher than its parent

Usually, when given a list of distinct values, it is best to build a balanced binary search tree - a tree where the size of the left subtree is approximately the same as the size of the right subtree at each node. A balanced tree isn't always the best solution though. Given a int[] values of distinct values and a int[] probs containing the percentage chance of each element being accessed, your method will return the best (lowest) access score achievable by a BST containing the given values. The access score of any BST is computed by adding together the access scores for all of its nodes. The access score for a particular node is calculated by the formula p*(d+1) where p is the probability of that node being accessed, and d is the depth of that node in the tree.

### Definition

 Class: SkewTree Method: bestScore Parameters: int[], int[] Returns: int Method signature: int bestScore(int[] values, int[] probs) (be sure your method is public)

### Constraints

-values and probs will both contain between 1 and 50 elements, inclusive.
-Each element of values and probs will be between 1 and 1000, inclusive.
-Each element of values will be unique.
-values and probs will contain the same number of elements.

### Examples

0)

 `{1,2}` `{1,2}`
`Returns: 4`
 The best tree looks like: ``` 2 \ 1 ```
1)

 `{1,2,4,3,5,6}` `{1,2,3,4,5,6}`
`Returns: 44`
 Here the best tree is: ``` 5 / \ / \ 3 6 / \ 2 4 / 1 ``` The score is 5*1 + 4*2 + 6*2 + 2*3 + 3*3 + 1*4 = 44
2)

 `{6,5,3,7,51,36}` `{65,13,49,62,34,16}`
`Returns: 492`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=1641

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4497&pm=1641

brett1479

#### Testers:

zoidal , lbackstrom , schveiguy

#### Problem categories:

Dynamic Programming