


from collections.abc import Sequence
from queue import Queue






class 					lowercase__ :

   '''simple docstring'''


   def __init__(					self,	__magic_name__,	__magic_name__,	__magic_name__,	__magic_name__=None,	__magic_name__=None							)				->   List[str]:






       """simple docstring"""
       UpperCamelCase__							:       Any      =   start
       UpperCamelCase__							:       Optional[Any]      =   end
       UpperCamelCase__							:       List[Any]      =   val
       UpperCamelCase__							:       List[str]      =   (start + end) // 2
       UpperCamelCase__							:       List[Any]      =   left
       UpperCamelCase__							:       Dict      =   right




   def __repr__(					self							)				->   Optional[int]:






       """simple docstring"""
       return f"SegmentTreeNode(start={self.start}, end={self.end}, val={self.val})"






class 					lowercase__ :

   '''simple docstring'''


   def __init__(					self,	__magic_name__,	__magic_name__							)				->   List[Any]:






       """simple docstring"""
       UpperCamelCase__							:       Union[str, Any]      =   collection
       UpperCamelCase__							:       Optional[int]      =   function
       if self.collection:
           UpperCamelCase__							:       Dict      =   self._build_tree(0,	len(__magic_name__							) - 1							)




   def    UpperCamelCase__						(					self,	__magic_name__,	__magic_name__							)				->   Tuple:






       """simple docstring"""
       self._update_tree(self.root,	__magic_name__,	__magic_name__							)




   def    UpperCamelCase__						(					self,	__magic_name__,	__magic_name__							)				->   Union[str, Any]:






       """simple docstring"""
       return self._query_range(self.root,	__magic_name__,	__magic_name__							)




   def    UpperCamelCase__						(					self,	__magic_name__,	__magic_name__							)				->   Union[str, Any]:






       """simple docstring"""

       if start == end:
           return SegmentTreeNode(__magic_name__,	__magic_name__,	self.collection[start]							)
       UpperCamelCase__							:       Union[str, Any]      =   (start + end) // 2
       UpperCamelCase__							:       List[Any]      =   self._build_tree(__magic_name__,	__magic_name__							)
       UpperCamelCase__							:       List[str]      =   self._build_tree(mid + 1,	__magic_name__							)
       return SegmentTreeNode(__magic_name__,	__magic_name__,	self.fn(left.val,	right.val							),	__magic_name__,	__magic_name__							)




   def    UpperCamelCase__						(					self,	__magic_name__,	__magic_name__,	__magic_name__							)				->   List[Any]:






       """simple docstring"""

       if node.start == i and node.end == i:
           UpperCamelCase__							:       List[str]      =   val
           return
       if i <= node.mid:
           self._update_tree(node.left,	__magic_name__,	__magic_name__							)
       else:
           self._update_tree(node.right,	__magic_name__,	__magic_name__							)
       UpperCamelCase__							:       List[Any]      =   self.fn(node.left.val,	node.right.val							)




   def    UpperCamelCase__						(					self,	__magic_name__,	__magic_name__,	__magic_name__							)				->   Any:






       """simple docstring"""

       if node.start == i and node.end == j:
           return node.val

       if i <= node.mid:
           if j <= node.mid:
               # range in left child tree
               return self._query_range(node.left,	__magic_name__,	__magic_name__							)
           else:
               # range in left child tree and right child tree
               return self.fn(
                   self._query_range(node.left,	__magic_name__,	node.mid							),	self._query_range(node.right,	node.mid + 1,	__magic_name__							),	)
       else:
           # range in right child tree
           return self._query_range(node.right,	__magic_name__,	__magic_name__							)




   def    UpperCamelCase__						(					self							)				->   Optional[int]:






       """simple docstring"""

       if self.root is not None:
           UpperCamelCase__							:       Dict      =   Queue()
           queue.put(self.root							)
           while not queue.empty():
               UpperCamelCase__							:       Tuple      =   queue.get()
               yield node

               if node.left is not None:
                   queue.put(node.left							)

               if node.right is not None:
                   queue.put(node.right							)


if __name__ == "__main__":
  import operator

  for fn in [operator.add, max, min]:
    print('*' * 50)
    UpperCAmelCase_  							=				SegmentTree([2, 1, 5, 3, 4], fn)
    for node in arr.traverse():
      print(node)
    print()

    arr.update(1, 5)
    for node in arr.traverse():
      print(node)
    print()

    print(arr.query_range(3, 4))  # 7
    print(arr.query_range(2, 2))  # 5
    print(arr.query_range(1, 3))  # 13
    print()








def 	lowerCAmelCase_					(						__UpperCAmelCase:    dict   )   ->			set:
    UpperCamelCase__							:       int      =   set()
    # edges = list of graph's edges
    UpperCamelCase__							:       str      =   get_edges(__UpperCAmelCase   )

    # While there are still elements in edges list, take an arbitrary edge
    # (from_node, to_node) and add his extremity to chosen_vertices and then
    # remove all arcs adjacent to the from_node and to_node
    while edges:
        UpperCamelCase__     ,UpperCamelCase__							:       List[Any]      =   edges.pop()
        chosen_vertices.add(__UpperCAmelCase   )
        chosen_vertices.add(__UpperCAmelCase   )
        for edge in edges.copy():
            if from_node in edge or to_node in edge:
                edges.discard(__UpperCAmelCase   )
    return chosen_vertices




def 	lowerCAmelCase_					(						__UpperCAmelCase:    dict   )   ->			set:
    UpperCamelCase__							:       Optional[int]      =   set()
    for from_node, to_nodes in graph.items():
        for to_node in to_nodes:
            edges.add((from_node, to_node)   )
    return edges


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  # graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
  # print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")

