Given a Binary Search Tree of size N, that may be unbalanced. Your task is to complete the function buildBalancedTree(), that convert the given BST into a balanced BST that has minimum possible height.

Examples :

Input:
       30
      /
     20
    /
   10
Output:
     20
   /   \
 10     30

Input:
         4
        /
       3
      /
     2
    /
   1
Output:
      3            3           2
    /  \         /  \        /  \
   1    4   OR  2    4  OR  1    3   OR ..
    \          /                   \
     2        1                     4 

Input:
The function takes a single argument as input, the reference pointer to the root of the Binary Search Tree.
There are T, test cases and for each test case the function will be called separately.

Output:
For each test case output will be the new height of the BST.

Constraints:
1<=T<=100
1<=N<=200

Example:
Input:
2
3
30 20 10
5
10 8 7 6 5
Output:
2
3

Note:The Input/Ouput format and Example given are used for system's internal purpose, and should be used by a user for Expected Output only. As it is a function problem, hence a user should not read any input from stdin/console. The task is to complete the function specified, and not to write the full code.

** For More Input/Output Examples Use 'Expected Output' option **