Given a binary tree, write a program to compute the length of the diameter of the tree.

Problem Note

• The diameter of a binary tree is defined as the length of the longest path between any two nodes in a tree. This path may or may not contain the root in it.
• The length of the path between two nodes is represented by the number of edges between them.

Example

Input: Given a binary tree
          2
         / \
        4   5
       / \     
      6   7    
Output: 3
Explanation: Return 3, which is the length(number of edges) of the path [6,4,2,5] or [5,2,4,6]