


"""simple docstring"""


from doctest import testmod
from math import sqrt






def    a__       ( __lowercase      )		->		list:
				_A         =	[]
				if num < 1:
								return facs
				facs.append(1      )
				if num == 1:
								return facs
				facs.append(__lowercase      )
				for i in range(2   ,	int(sqrt(__lowercase      )      ) + 1      ):
								if num % i == 0:  # If i is a factor of num
												facs.append(__lowercase      )
												_A         =	num // i  # num//i is the other factor of num
												if d != i:  # If d and i are distinct
																facs.append(__lowercase      )  # we have found another factor
				facs.sort()
				return facs


if __name__ == "__main__":
		testmod(name="factors_of_a_number", verbose=True)



"""simple docstring"""


from __future__ import annotations

a_											=			[2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]
class snake_case					:







		def __init__(    self					:				Optional[int]			,      a__					:				int						)				->  None:





						'''simple docstring'''







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







		def __repr__(    self					:				Any						)				->  str:





						'''simple docstring'''







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






def    a__       ( __lowercase      )		->		Node | None:
				_A         =	Node(len(__lowercase      )      )
				_A     ,						_A         =	min(__lowercase      ), max(__lowercase      )
				# Leaf node case where the node contains only one unique value
				if root.minn == root.maxx:
								return root
				_A         =	(root.minn + root.maxx) // 2

				_A         =	[]
				_A         =	[]

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






def    a__       ( __lowercase   ,	__lowercase   ,	__lowercase      )		->		int:
				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
				_A         =	(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   ,	__lowercase   ,	node.map_left[index] - 1      )
				else:
								# go to the right subtree and map index to the right subtree
								return rank_till_index(node.right   ,	__lowercase   ,	index - node.map_left[index]      )






def    a__       ( __lowercase   ,	__lowercase   ,	__lowercase   ,	__lowercase      )		->		int:
				if start > end:
								return 0
				_A         =	rank_till_index(__lowercase   ,	__lowercase   ,	__lowercase      )
				_A         =	rank_till_index(__lowercase   ,	__lowercase   ,	start - 1      )
				return rank_till_end - rank_before_start






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


if __name__ == "__main__":
		import doctest

		doctest.testmod()