Lowest Common Ancestor of a Binary Tree III

You are given two nodes of a binary tree p and q, return their lowest common ancestor (LCA).

Each node will have a reference to its parent node. The definition for Node is below:

class Node {
    public int val;
    public Node left;
    public Node right;
    public Node parent;
}

According to the definition of LCA on Wikipedia: "The lowest common ancestor of two nodes p and q in a tree T is the lowest node that has both p and q as descendants (where we allow a node to be a descendant of itself)."

Example 1:

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

Output: 3

Example 2:

Input: root = [5,3,4,2,1,null,9,null,11,10,12], p = 3, q = 12

Output: 3

Constraints:

• 2 <= The number of nodes in the tree <= 100,000.
• -1,000,000,000 <= Node.val <= 1,000,000,000
• All Node.val are unique.
• p != q
• p and q will both exist in the tree.

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