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 the length of the longest path between any two nodes in a tree. This path may or may not pass through the root.
  • The length of the path between two nodes is represented by the number of edges between them.

Example

Input: Given a binary tree
          1
         / \
        2   3
       / \     
      4   5    
Output: 3
Explanation: Return 3, which is the length of the path [4,2,1,3] or [5,2,1,3]