Given a Binary Tree, find diameter of it.  The diameter of a tree is the number of nodes on the longest path between two leaves in the tree. The diagram below shows two trees each with diameter nine, the leaves that form the ends of a longest path are shaded (note that there is more than one path in each tree of length nine, but no path longer than nine nodes).

Input:
The task is to complete the method which takes one argument, root of Binary Tree. The struct Node has a data part which stores the data, pointer to left child and pointer to right child.
There are multiple test cases. For each test case, this method will be called individually.

Output:
The function should return diameter of binary tree.

Constraints:
1 <=T<= 30
1 <=Number of nodes<= 100
1 <=Data of a node<= 1000

Example:
Input:
2
2
1 2 L 1 3 R
4
10 20 L 10 30 R 20 40 L 20 60 R

Output:
3
4

There are two test casess.  First case represents a tree with 3 nodes and 2 edges where root is 1, left child of 1 is 2 and right child of 1 is 3.   Second test case represents a tree with 4 edges and 5 nodes.

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, and should not print anything on stdout/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 **