



"""simple docstring"""




from __future__ import annotations

UpperCAmelCase				:							int								=[2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]


class  _lowercase				:
				'''simple docstring'''







				def __init__(	self       ,	snake_case__      ):

									'''simple docstring'''


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

				def __repr__(	self      ):

									'''simple docstring'''


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




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

					UpperCamelCase_											=				[]
					UpperCamelCase_											=				[]

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



def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase):
					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
					UpperCamelCase_											=				(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				,		_lowerCAmelCase				,		node.map_left[index] - 1)
					else:
										# go to the right subtree and map index to the right subtree
										return rank_till_index(node.right				,		_lowerCAmelCase				,		index - node.map_left[index])



def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase):
					if start > end:
										return 0
					UpperCamelCase_											=				rank_till_index(_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase)
					UpperCamelCase_											=				rank_till_index(_lowerCAmelCase				,		_lowerCAmelCase				,		start - 1)
					return rank_till_end - rank_before_start



def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase):
					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]
					UpperCamelCase_											=				node.map_left[end] - (
					    node.map_left[start - 1] if start else 0
					)
					if num_elements_in_left_tree > index:
										return quantile(
										    node.left				,		_lowerCAmelCase				,		(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 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase				,		_lowerCAmelCase):
					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
					UpperCamelCase_											=				range_counting(
					    node.left				,		(node.map_left[start - 1] if start else 0)				,		node.map_left[end] - 1				,		_lowerCAmelCase				,		_lowerCAmelCase				,		)
					UpperCamelCase_											=				range_counting(
					    node.right				,		start - (node.map_left[start - 1] if start else 0)				,		end - node.map_left[end]				,		_lowerCAmelCase				,		_lowerCAmelCase				,		)
					return left + right


if __name__ == "__main__":
	import doctest

	doctest.testmod()





def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase):
					UpperCamelCase_											=				0
					for ele in arr:
										total_sum += product_sum(_lowerCAmelCase				,		depth + 1) if isinstance(_lowerCAmelCase				,		_lowerCAmelCase) else ele
					return total_sum * depth



def 				_lowerCAmelCase      (_lowerCAmelCase):
					return product_sum(_lowerCAmelCase				,		1)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
