'''simple docstring'''




def     snake_case__							(      _A: Optional[int]				,       _A: Union[str, Any]			)   ->     str:

		'''simple docstring'''


		if len(str(_A			)			) == 1 or len(str(_A			)			) == 1:
				return a * b

		lowerCAmelCase        =  max(len(str(_A			)			)				,       len(str(_A			)			)			)
		lowerCAmelCase        =  ma // 2

		lowerCAmelCase ,					lowerCAmelCase        =  divmod(_A				,       10**ma			)
		lowerCAmelCase ,					lowerCAmelCase        =  divmod(_A				,       10**ma			)

		lowerCAmelCase        =  karatsuba(_A				,       _A			)
		lowerCAmelCase        =  karatsuba((aa + aa)				,       (ba + ba)			)
		lowerCAmelCase        =  karatsuba(_A				,       _A			)

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






def     snake_case__							(      )   ->     Tuple:

		'''simple docstring'''


		print(karatsuba(15463				,       23489			)			)


if __name__ == "__main__":
						main()





'''simple docstring'''




from __future__ import annotations

__lowercase				   =  [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]






class     a__:


			'''simple docstring'''






			def __init__(       self	,   __lowerCAmelCase):




					"""simple docstring"""


					lowerCAmelCase        =  -1
					lowerCAmelCase        =  -1
					lowerCAmelCase        =  [-1] * length
					lowerCAmelCase        =  None
					lowerCAmelCase        =  None







			def __repr__(       self):




					"""simple docstring"""


					return f"Node(min_value={self.minn} max_value={self.maxx})"







def     snake_case__							(      _A: list[int]			)   ->     Node | None:

		'''simple docstring'''


		lowerCAmelCase        =  Node(len(_A			)			)
		lowerCAmelCase ,					lowerCAmelCase        =  min(_A			), max(_A			)
		# Leaf node case where the node contains only one unique value
		if root.minn == root.maxx:
				return root
		lowerCAmelCase        =  (root.minn + root.maxx) // 2

		lowerCAmelCase        =  []
		lowerCAmelCase        =  []

		for index, num in enumerate(_A			):
				if num <= pivot:
						left_arr.append(_A			)
				else:
						right_arr.append(_A			)
				lowerCAmelCase        =  len(_A			)
		lowerCAmelCase        =  build_tree(_A			)
		lowerCAmelCase        =  build_tree(_A			)
		return root






def     snake_case__							(      _A: Node | None				,       _A: int				,       _A: int			)   ->     int:

		'''simple docstring'''


		if index < 0 or node is None:
				return 0
		# Leaf node cases
		if node.minn == node.maxx:
				return index + 1 if node.minn == num else 0
		lowerCAmelCase        =  (node.minn + node.maxx) // 2
		if num <= pivot:
				# go the left subtree and map index to the left subtree
				return rank_till_index(node.left				,       _A				,       node.map_left[index] - 1			)
		else:
				# go to the right subtree and map index to the right subtree
				return rank_till_index(node.right				,       _A				,       index - node.map_left[index]			)






def     snake_case__							(      _A: Node | None				,       _A: int				,       _A: int				,       _A: int			)   ->     int:

		'''simple docstring'''


		if start > end:
				return 0
		lowerCAmelCase        =  rank_till_index(_A				,       _A				,       _A			)
		lowerCAmelCase        =  rank_till_index(_A				,       _A				,       start - 1			)
		return rank_till_end - rank_before_start






def     snake_case__							(      _A: Node | None				,       _A: int				,       _A: int				,       _A: int			)   ->     int:

		'''simple docstring'''


		if index > (end - start) or start > end or node is None:
				return -1
		# Leaf node case
		if node.minn == node.maxx:
				return node.minn
		# Number of elements in the left subtree in interval [start, end]
		lowerCAmelCase        =  node.map_left[end] - (
		    node.map_left[start - 1] if start else 0
		)
		if num_elements_in_left_tree > index:
				return quantile(
				    node.left				,       _A				,       (node.map_left[start - 1] if start else 0)				,       node.map_left[end] - 1				,       )
		else:
				return quantile(
				    node.right				,       index - num_elements_in_left_tree				,       start - (node.map_left[start - 1] if start else 0)				,       end - node.map_left[end]				,       )






def     snake_case__							(      _A: Node | None				,       _A: int				,       _A: int				,       _A: int				,       _A: int			)   ->     int:

		'''simple docstring'''


		if (
		    start > end
		    or node is None
		    or start_num > end_num
		    or node.minn > end_num
		    or node.maxx < start_num
		):
				return 0
		if start_num <= node.minn and node.maxx <= end_num:
				return end - start + 1
		lowerCAmelCase        =  range_counting(
		    node.left				,       (node.map_left[start - 1] if start else 0)				,       node.map_left[end] - 1				,       _A				,       _A				,       )
		lowerCAmelCase        =  range_counting(
		    node.right				,       start - (node.map_left[start - 1] if start else 0)				,       end - node.map_left[end]				,       _A				,       _A				,       )
		return left + right


if __name__ == "__main__":
						import doctest

						doctest.testmod()




