Given the root node of a binary tree, determine the length of the longest path consisting of consecutive integers (increasing by 1) from parent to child. The path must be downward (from parent to child), and can start at any node. Return the length of the longest such path.
Example 1
Input: TreeNode(7, TreeNode(8, TreeNode(9)), TreeNode(6))
Output: 3
Explanation: The path 7 -> 8 -> 9 is consecutive and has length 3.
Example 2
Input: TreeNode(10, TreeNode(11, None, TreeNode(12)), TreeNode(9))
Output: 3
Explanation: The path 10 -> 11 -> 12 is consecutive and has length 3.
Example 3
Input: TreeNode(5, TreeNode(4), TreeNode(6, TreeNode(7)))
Output: 2
Explanation: The path 6 -> 7 is consecutive and has length 2.
Constraints
Case 1
Input: TreeNode(1, TreeNode(2, TreeNode(3)), TreeNode(4))
Expected: 3
Case 2
Input: TreeNode(15, TreeNode(16, TreeNode(17)), TreeNode(14, TreeNode(15)))
Expected: 3
Case 3
Input: TreeNode(20, TreeNode(21), TreeNode(22, TreeNode(23)))
Expected: 2
Case 4
Input: TreeNode(100)
Expected: 1