import enum


class NodeType(enum.IntEnum):
    LEAF = 0
    UNARY = 1
    BINARY = 2


class Node:
    def __init__(self, value, left=None, right=None, parent=None):
        self.parent = parent
        self.left = left
        self.right = right

        self.value = value
        self.rank = 0

    @property
    def type(self):
        if self.left and self.right:
            return NodeType.BINARY

        if self.left or self.right:
            return NodeType.UNARY

        return NodeType.LEAF

    def __repr__(self):
        return f"Node(value={self.value}, rank={self.rank}, left={self.left}, right={self.right}, parent={self.parent})"

    def __str__(self):
        return f"Node(value={self.value}, rank={self.rank})"

    @staticmethod
    def height(node):
        return 1 + max(Node.height(node.left), Node.height(node.right)) if node else -1

    @staticmethod
    def rank(node):
        return -1 if not node else node.rank

    @staticmethod
    def difference(node, parent=None):
        if not parent:
            parent = node.parent if node else None
        return Node.rank(parent) - Node.rank(node)

    @staticmethod
    def differences(node):
        node_rank = Node.rank(node)
        (left, right) = (node.left, node.right) if node else (None, None)

        return (node_rank - Node.rank(left), node_rank - Node.rank(right))

    def promote(self):
        self.rank += 1
        return self

    def demote(self):
        self.rank -= 1
        return self

    @staticmethod
    def rotate_right(x):
        parent = x.parent
        y = x.left
        z = x.right

        assert y is not None
        if parent:
            if parent.left is x:
                parent.left = y
            else:
                parent.right = y

        x.left = y.right
        if x.left:
            x.left.parent = x

        y.right = x
        x.parent = y
        y.parent = parent

        return y

    @staticmethod
    def rotate_left(x):
        parent = x.parent
        y = x.left
        z = x.right

        assert z is not None
        if parent:
            if parent.left is x:
                parent.left = z
            else:
                parent.right = z

        x.right = z.left
        if x.right:
            x.right.parent = x

        z.left = x
        x.parent = z
        z.parent = parent

        return z

    @staticmethod
    def find_parent_node(value, node, missing=True):
        new_node = node

        while new_node and (missing or new_node.value != value):
            node = new_node
            new_node = node.left if value < node.value else node.right

        return node

    @staticmethod
    def search(value, node):
        while node and node.value != value:
            node = node.left if value < node.value else node.right

        return node

    @staticmethod
    def minimum(node):
        while node.left:
            node = node.left

        return node

    @staticmethod
    def maximum(node):
        while node.right:
            node = node.right

        return node