





UpperCAmelCase__            =							{0: [1, 2], 1: [0, 3], 2: [0], 3: [1], 4: [5, 6], 5: [4, 6], 6: [4, 5]}

UpperCAmelCase__            =							{0: [1, 2, 3], 1: [0, 3], 2: [0], 3: [0, 1], 4: [], 5: []}
def     UpperCAmelCase_ (							__snake_case					,						__snake_case					,						__snake_case						)					->      List[str]:







 """simple docstring"""


 _lowercase											=True
 _lowercase											=[]

 for neighbour in graph[vert]:
  if not visited[neighbour]:
   connected_verts += dfs(__snake_case					,						__snake_case					,						__snake_case						)

 return [vert, *connected_verts]
def     UpperCAmelCase_ (							__snake_case						)					->      Optional[int]:







 """simple docstring"""


 _lowercase											=len(__snake_case						)
 _lowercase											=graph_size * [False]
 _lowercase											=[]

 for i in range(__snake_case						):
  if not visited[i]:
   _lowercase											=dfs(__snake_case					,						__snake_case					,						__snake_case						)
   components_list.append(__snake_case						)

 return components_list


if __name__ == "__main__":
  import doctest

  doctest.testmod()





from __future__ import annotations

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







class 				lowerCamelCase__       :





     def __init__(self		,					UpperCAmelCase	)					->       None:
      _lowercase											=-1
      _lowercase											=-1
      _lowercase											=[-1] * length
      _lowercase											=None
      _lowercase											=None





     def __repr__(self	)					->       str:
      return f"Node(min_value={self.minn} max_value={self.maxx})"



def     UpperCAmelCase_ (							__snake_case						)					->      Node | None:







 """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     UpperCAmelCase_ (							__snake_case					,						__snake_case					,						__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     UpperCAmelCase_ (							__snake_case					,						__snake_case					,						__snake_case					,						__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     UpperCAmelCase_ (							__snake_case					,						__snake_case					,						__snake_case					,						__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     UpperCAmelCase_ (							__snake_case					,						__snake_case					,						__snake_case					,						__snake_case					,						__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()

