from __future__ import annotations

from collections import defaultdict
from dataclasses import dataclass



@dataclass
class 						snake_case_ :
   __A			:	int
   __A			:	TreeNode | None        =       None
   __A			:	TreeNode | None        =       None



def     lowercase_       (    ):
    return TreeNode(3	,			TreeNode(9)	,			TreeNode(20	,			TreeNode(15)	,			TreeNode(7)))

def     lowercase_       (    _lowerCamelCase							: TreeNode):

    def depth_first_search(
        _lowerCamelCase							: TreeNode | None	,			_lowerCamelCase							: int	,			_lowerCamelCase							: list[int]) -> None:
        if not root:
            return

        if depth == len(_lowerCamelCase):
            right_view.append(root.val)

        depth_first_search(root.right	,			depth + 1	,			_lowerCamelCase)
        depth_first_search(root.left	,			depth + 1	,			_lowerCamelCase)

    lowercase__				:     list					      =       []
    if not root:
        return right_view

    depth_first_search(_lowerCamelCase	,			0	,			_lowerCamelCase)
    return right_view

def     lowercase_       (    _lowerCamelCase							: TreeNode):

    def depth_first_search(
        _lowerCamelCase							: TreeNode | None	,			_lowerCamelCase							: int	,			_lowerCamelCase							: list[int]) -> None:
        if not root:
            return

        if depth == len(_lowerCamelCase):
            left_view.append(root.val)

        depth_first_search(root.left	,			depth + 1	,			_lowerCamelCase)
        depth_first_search(root.right	,			depth + 1	,			_lowerCamelCase)

    lowercase__				:     list					      =       []
    if not root:
        return left_view

    depth_first_search(_lowerCamelCase	,			0	,			_lowerCamelCase)
    return left_view

def     lowercase_       (    _lowerCamelCase							: TreeNode):

    def breadth_first_search(_lowerCamelCase							: TreeNode	,			_lowerCamelCase							: list[int]) -> None:
        lowercase__				:     Tuple					      =       [(root, 0)]
        lowercase__				:     Tuple					      =       defaultdict(_lowerCamelCase)

        while queue:
            lowercase__				:     int					      =       queue.pop(0)
            lowercase__      ,     lowercase__				:     Union[str, Any]					      =       first

            lookup[hd].append(node.val)

            if node.left:
                queue.append((node.left, hd - 1))
            if node.right:
                queue.append((node.right, hd + 1))

        for pair in sorted(lookup.items()	,			key=lambda _lowerCamelCase: each[0]):
            top_view.append(pair[1][0])

    lowercase__				:     list					      =       []
    if not root:
        return top_view

    breadth_first_search(_lowerCamelCase	,			_lowerCamelCase)
    return top_view

def     lowercase_       (    _lowerCamelCase							: TreeNode):
    from collections import defaultdict

    def breadth_first_search(_lowerCamelCase							: TreeNode	,			_lowerCamelCase							: list[int]) -> None:
        lowercase__				:     Optional[Any]					      =       [(root, 0)]
        lowercase__				:     int					      =       defaultdict(_lowerCamelCase)

        while queue:
            lowercase__				:     Optional[Any]					      =       queue.pop(0)
            lowercase__      ,     lowercase__				:     Tuple					      =       first
            lookup[hd].append(node.val)

            if node.left:
                queue.append((node.left, hd - 1))
            if node.right:
                queue.append((node.right, hd + 1))

        for pair in sorted(lookup.items()	,			key=lambda _lowerCamelCase: each[0]):
            bottom_view.append(pair[1][-1])

    lowercase__				:     list					      =       []
    if not root:
        return bottom_view

    breadth_first_search(_lowerCamelCase	,			_lowerCamelCase)
    return bottom_view


if __name__ == "__main__":
      import doctest

      doctest.testmod()




def     lowercase_       (    _lowerCamelCase							: str	,			_lowerCamelCase							: Optional[int]):
    if len(str(_lowerCamelCase)) == 1 or len(str(_lowerCamelCase)) == 1:
        return a * b

    lowercase__				:     Tuple					      =       max(len(str(_lowerCamelCase))	,			len(str(_lowerCamelCase)))
    lowercase__				:     Union[str, Any]					      =       ma // 2

    lowercase__      ,     lowercase__				:     Union[str, Any]					      =       divmod(_lowerCamelCase	,			10**ma)
    lowercase__      ,     lowercase__				:     Tuple					      =       divmod(_lowerCamelCase	,			10**ma)

    lowercase__				:     int					      =       karatsuba(_lowerCamelCase	,			_lowerCamelCase)
    lowercase__				:     Dict					      =       karatsuba((aa + aa)	,			(ba + ba))
    lowercase__				:     Optional[int]					      =       karatsuba(_lowerCamelCase	,			_lowerCamelCase)

    return (z * 10 ** (2 * ma)) + ((y - z - x) * 10 ** (ma)) + (x)

def     lowercase_       (    ):
    print(karatsuba(1_5463	,			2_3489))


if __name__ == "__main__":
      main()



