






class       __UpperCAmelCase		:







			def __init__(	self:  List[str]      ,	UpperCAmelCase_:  Optional[int]     ):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE	      =  len(UpperCAmelCase_     )
									_SCREAMING_SNAKE_CASE	      =  [0] * len_array

									if len_array > 0:
															_SCREAMING_SNAKE_CASE	      =  array[0]

									for i in range(1      ,	UpperCAmelCase_     ):
															_SCREAMING_SNAKE_CASE	      =  self.prefix_sum[i - 1] + array[i]







			def 							UpperCamelCase      (	self:  int      ,	UpperCAmelCase_:  str      ,	UpperCAmelCase_:  str     ):







									'''simple docstring'''




									if start == 0:
															return self.prefix_sum[end]

									return self.prefix_sum[end] - self.prefix_sum[start - 1]







			def 							UpperCamelCase      (	self:  List[str]      ,	UpperCAmelCase_:  Union[str, Any]     ):







									'''simple docstring'''




									_SCREAMING_SNAKE_CASE	      =  {0}
									for sum_item in self.prefix_sum:
															if sum_item - target_sum in sums:
																					return True

															sums.add(UpperCAmelCase_     )

									return False


if __name__ == "__main__":
		import doctest

		doctest.testmod()





'''simple docstring'''

from __future__ import annotations

from typing import Generic, TypeVar

a_  :				List[str]						= TypeVar("""T""")





class      snake_case    (    Generic[T]			):





  """simple docstring"""




  def __init__(    self			,  UpperCamelCase     ):







   """simple docstring"""
   lowerCamelCase_      =  data
   lowerCamelCase_      =  self
   lowerCamelCase_      =  0





class      snake_case    (    Generic[T]			):





  """simple docstring"""




  def __init__(    self     ):







   """simple docstring"""
   # map from node name to the node object
   lowerCamelCase_      =  {}






  def   snake_case		(    self			,  UpperCamelCase     ):







   """simple docstring"""
   # create a new set with x as its member
   lowerCamelCase_      =  DisjointSetTreeNode(UpperCamelCase     )






  def   snake_case		(    self			,  UpperCamelCase     ):







   """simple docstring"""
   # find the set x belongs to (with path-compression)
   lowerCamelCase_      =  self.map[data]
   if elem_ref != elem_ref.parent:
    lowerCamelCase_      =  self.find_set(elem_ref.parent.data     )
   return elem_ref.parent






  def   snake_case		(    self			,  UpperCamelCase			,  UpperCamelCase     ):







   """simple docstring"""
   # helper function for union operation
   if nodea.rank > nodea.rank:
    lowerCamelCase_      =  nodea
   else:
    lowerCamelCase_      =  nodea
    if nodea.rank == nodea.rank:
     nodea.rank += 1







  def   snake_case		(    self			,  UpperCamelCase			,  UpperCamelCase     ):







   """simple docstring"""
   # merge 2 disjoint sets
   self.link(self.find_set(UpperCamelCase     )			,  self.find_set(UpperCamelCase     )     )





class      snake_case    (    Generic[T]			):





  """simple docstring"""




  def __init__(    self     ):







   """simple docstring"""
   # connections: map from the node to the neighbouring nodes (with weights)
   lowerCamelCase_      =  {}






  def   snake_case		(    self			,  UpperCamelCase     ):







   """simple docstring"""
   # add a node ONLY if its not present in the graph
   if node not in self.connections:
    lowerCamelCase_      =  {}






  def   snake_case		(    self			,  UpperCamelCase			,  UpperCamelCase			,  UpperCamelCase     ):







   """simple docstring"""
   # add an edge with the given weight
   self.add_node(UpperCamelCase     )
   self.add_node(UpperCamelCase     )
   lowerCamelCase_      =  weight
   lowerCamelCase_      =  weight







  def   snake_case		(    self     ):







   """simple docstring"""
   lowerCamelCase_      =  []
   lowerCamelCase_      =  set()
   for start in self.connections:
    for end in self.connections[start]:
     if (start, end) not in seen:
      seen.add((end, start)     )
      edges.append((start, end, self.connections[start][end])     )
   edges.sort(key=lambda UpperCamelCase     : x[2]     )

   # creating the disjoint set
   lowerCamelCase_      =  DisjointSetTree[T]()
   for node in self.connections:
    disjoint_set.make_set(UpperCamelCase     )

   # MST generation
   lowerCamelCase_      =  0
   lowerCamelCase_      =  0
   lowerCamelCase_      =  GraphUndirectedWeighted[T]()
   while num_edges < len(self.connections     ) - 1:
    lowerCamelCase_ ,lowerCamelCase_ ,lowerCamelCase_      =  edges[index]
    index += 1
    lowerCamelCase_      =  disjoint_set.find_set(UpperCamelCase     )
    lowerCamelCase_      =  disjoint_set.find_set(UpperCamelCase     )
    if parent_u != parent_v:
     num_edges += 1
     graph.add_edge(UpperCamelCase			,  UpperCamelCase			,  UpperCamelCase     )
     disjoint_set.union(UpperCamelCase			,  UpperCamelCase     )
   return graph



