


"""simple docstring"""



from __future__ import annotations

from collections import defaultdict
from dataclasses import dataclass







@dataclass
class       __a	:
				lowerCamelCase    :					int
				lowerCamelCase    :					TreeNode | None 					=None
				lowerCamelCase    :					TreeNode | None 					=None




def     UpperCAmelCase    (					)	->   TreeNode:


	"""simple docstring"""




	return TreeNode(3 ,      TreeNode(9  ) ,      TreeNode(2_0 ,      TreeNode(1_5  ) ,      TreeNode(7  )  )  )
def     UpperCAmelCase    (					_lowercase   :      TreeNode  )	->   list[int]:


	"""simple docstring"""




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

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

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

	lowerCAmelCase_			       = []
	if not root:
		return right_view

	depth_first_search(_lowercase ,      0 ,      _lowercase  )
	return right_view
def     UpperCAmelCase    (					_lowercase   :      TreeNode  )	->   list[int]:


	"""simple docstring"""




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

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

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

	lowerCAmelCase_			       = []
	if not root:
		return left_view

	depth_first_search(_lowercase ,      0 ,      _lowercase  )
	return left_view
def     UpperCAmelCase    (					_lowercase   :      TreeNode  )	->   list[int]:


	"""simple docstring"""




	def breadth_first_search(_lowercase   :      TreeNode ,      _lowercase   :      list[int]  ) -> None:
		lowerCAmelCase_			       = [(root, 0)]
		lowerCAmelCase_			       = defaultdict(_lowercase  )

		while queue:
			lowerCAmelCase_			       = queue.pop(0  )
			lowerCAmelCase_       ,  lowerCAmelCase_			       = 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 _lowercase  : each[0]  ):
			top_view.append(pair[1][0]  )

	lowerCAmelCase_			       = []
	if not root:
		return top_view

	breadth_first_search(_lowercase ,      _lowercase  )
	return top_view
def     UpperCAmelCase    (					_lowercase   :      TreeNode  )	->   list[int]:


	"""simple docstring"""




	from collections import defaultdict

	def breadth_first_search(_lowercase   :      TreeNode ,      _lowercase   :      list[int]  ) -> None:
		lowerCAmelCase_			       = [(root, 0)]
		lowerCAmelCase_			       = defaultdict(_lowercase  )

		while queue:
			lowerCAmelCase_			       = queue.pop(0  )
			lowerCAmelCase_       ,  lowerCAmelCase_			       = 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 _lowercase  : each[0]  ):
			bottom_view.append(pair[1][-1]  )

	lowerCAmelCase_			       = []
	if not root:
		return bottom_view

	breadth_first_search(_lowercase ,      _lowercase  )
	return bottom_view


if __name__ == "__main__":
			import doctest

			doctest.testmod()



"""simple docstring"""



def     UpperCAmelCase    (					_lowercase   :      list[int]  )	->   int:


	"""simple docstring"""




	lowerCAmelCase_			       = len(_lowercase  )
	if n in (0, 1):
		return 0
	return sum(query * (n - i - 1) for i, query in enumerate(sorted(_lowercase  )  )  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()