






"""simple docstring"""



from __future__ import annotations

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

class 			a	:







    def __init__(     self				,						_lowerCamelCase			):
      lowercase				       =			-1
      lowercase				       =			-1
      lowercase				       =			[-1] * length
      lowercase				       =			None
      lowercase				       =			None







    def __repr__(     self			):
      return F'Node(min_value={self.minn} max_value={self.maxx})'


def 		_SCREAMING_SNAKE_CASE					(       __snake_case     :    list[int]       ):





  '''simple docstring'''





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

  lowercase				       =			[]
  lowercase				       =			[]

  for index, num in enumerate(__snake_case       ):
    if num <= pivot:
      left_arr.append(__snake_case       )
    else:
      right_arr.append(__snake_case       )
    lowercase				       =			len(__snake_case       )
  lowercase				       =			build_tree(__snake_case       )
  lowercase				       =			build_tree(__snake_case       )
  return root
def 		_SCREAMING_SNAKE_CASE					(       __snake_case     :    Node | None						,   __snake_case     :    int						,   __snake_case     :    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
  lowercase				       =			(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						,   __snake_case						,   node.map_left[index] - 1       )
  else:
    # go to the right subtree and map index to the right subtree
    return rank_till_index(node.right						,   __snake_case						,   index - node.map_left[index]       )
def 		_SCREAMING_SNAKE_CASE					(       __snake_case     :    Node | None						,   __snake_case     :    int						,   __snake_case     :    int						,   __snake_case     :    int       ):





  '''simple docstring'''





  if start > end:
    return 0
  lowercase				       =			rank_till_index(__snake_case						,   __snake_case						,   __snake_case       )
  lowercase				       =			rank_till_index(__snake_case						,   __snake_case						,   start - 1       )
  return rank_till_end - rank_before_start
def 		_SCREAMING_SNAKE_CASE					(       __snake_case     :    Node | None						,   __snake_case     :    int						,   __snake_case     :    int						,   __snake_case     :    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]
  lowercase				       =			node.map_left[end] - (
      node.map_left[start - 1] if start else 0
  )
  if num_elements_in_left_tree > index:
    return quantile(
        node.left						,   __snake_case						,   (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 		_SCREAMING_SNAKE_CASE					(       __snake_case     :    Node | None						,   __snake_case     :    int						,   __snake_case     :    int						,   __snake_case     :    int						,   __snake_case     :    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
  lowercase				       =			range_counting(
      node.left						,   (node.map_left[start - 1] if start else 0)						,   node.map_left[end] - 1						,   __snake_case						,   __snake_case						,   )
  lowercase				       =			range_counting(
      node.right						,   start - (node.map_left[start - 1] if start else 0)						,   end - node.map_left[end]						,   __snake_case						,   __snake_case						,   )
  return left + right


if __name__ == "__main__":
    import doctest

    doctest.testmod()








'''simple docstring'''






def      __lowerCAmelCase   (       snake_case__		):

			for insert_index, insert_value in enumerate(collection[1:]		):
						__UpperCamelCase :     Union[str, Any]										=  insert_index
						while insert_index >= 0 and insert_value < collection[insert_index]:
									__UpperCamelCase :     int										=  collection[insert_index]
									insert_index -= 1
						if insert_index != temp_index:
									__UpperCamelCase :     Tuple										=  insert_value
			return collection


if __name__ == "__main__":
				from doctest import testmod

				testmod()

				_lowerCAmelCase       =   input('''Enter numbers separated by a comma:\n''').strip()
				_lowerCAmelCase       =   [int(item) for item in user_input.split(''',''')]
				print(f'{insertion_sort(unsorted) = }')



