• Each nodes has at most 2 children.
• Each node except the root has exactly one parent.
• There is exactly one root node. The root node does not have any parents.
• If a node has a left child, all values in the left subtree are less than or equal to the value of the value of the node itself.
• If a node has a right child, all values in the right subtree are strictly greater than the value of the node itself.

• The difference between sum of all values in the left subtree and sum of all values in the right subtree is minimum.
• If there is more than one way to minimize the difference, sum of all values in the left subtree is maximum.
• The right and left subtrees are also kuPellaKeS BST's.

The following rules describe a representation way for a BST:

• A BST with no subtrees is denoted by "value_of_root" (Quotes included for clarity).
• A BST which have only one subtree (Either left or right subtree), is denoted by "value_of_root(representation_of_subtree)" (Quotes included for clarity).
• A BST which have both of its subtrees, is denoted by "value_of_root(representation_of_left_subtree,representation_of_right_subtree)".

Input
The first line of input gives the number of cases, T. Then, T test cases follow. Each one starts with a line containing number of values 1<=n<=1000. Next line contains n integer numbers separated by a single space.

Output
For the xth test case, your program must output the line containing "Case #x:", followed by representation of the kuPellaKeS BST having the given numbers as node values.

Case #1: 7(5(3(2(1),4),6),9(8,10))
Case #2: 1(1(1(0(0))))
Case #3: -3(-4,-2(-1))

1st Amirkabir UT Annual Programming Contest  Final Round