Given the root of a binary tree, return the length of the diameter of the tree.

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 a path between two nodes is represented by the number of edges between them.

Examples

Example 1

Input:  root = [1,2,3,4,5]
Output: 3

3 is the length of the path [4,2,1,3] or [5,2,1,3].

Example 2

Input:  root = [1,2]
Output: 1

Constraints

• The number of nodes in the tree is in the range [1, 10⁴].
• -100 <= Node.val <= 100

How the tests work: trees are written as level-order arrays — [1,null,2] is a root 1 with a right child 2. Your function receives real TreeNode objects.