




"""simple docstring"""


from collections.abc import Callable






class  lowercase:







 '''simple docstring'''





 def __init__(    self:		Dict,				a_:		Callable | None = None		):




   '''simple docstring'''



   _snake_case							:		list								=  []
   # Stores indexes of each item for supporting updates and deletion.
   _snake_case							:		dict								=  {}
   # Stores current size of heap.
   _snake_case							:		Optional[Any]								=  0
   # Stores function used to evaluate the score of an item on which basis ordering
   # will be done.
   _snake_case							:		Tuple								=  key or (lambda a_		: x)


 def 			UpperCamelCase_       (    self:		int,				a_:		int		):




   '''simple docstring'''



   return int((i - 1) / 2		) if i > 0 else None


 def 			UpperCamelCase_       (    self:		Dict,				a_:		int		):




   '''simple docstring'''



   _snake_case							:		int								=  int(2 * i + 1		)
   return left if 0 < left < self.size else None


 def 			UpperCamelCase_       (    self:		Optional[Any],				a_:		int		):




   '''simple docstring'''



   _snake_case							:		List[str]								=  int(2 * i + 2		)
   return right if 0 < right < self.size else None


 def 			UpperCamelCase_       (    self:		Any,				a_:		int,				a_:		int		):




   '''simple docstring'''



   _snake_case		, _snake_case							:		List[str]								=  (
       self.pos_map[self.arr[j][0]],
       self.pos_map[self.arr[i][0]],
   )
   # Then swap the items in the list.
   _snake_case		, _snake_case							:		Any								=  self.arr[j], self.arr[i]


 def 			UpperCamelCase_       (    self:		Optional[Any],				a_:		int,				a_:		int		):




   '''simple docstring'''



   return self.arr[i][1] < self.arr[j][1]


 def 			UpperCamelCase_       (    self:		int,				a_:		int		):




   '''simple docstring'''



   _snake_case							:		List[str]								=  self._left(a_		)
   _snake_case							:		int								=  self._right(a_		)
   _snake_case							:		int								=  i

   if left is not None and not self._cmp(a_,				a_		):
     _snake_case							:		List[str]								=  left
   if right is not None and not self._cmp(a_,				a_		):
     _snake_case							:		Optional[int]								=  right

   return valid_parent


 def 			UpperCamelCase_       (    self:		Dict,				a_:		int		):




   '''simple docstring'''



   _snake_case							:		str								=  self._parent(a_		)
   while parent is not None and not self._cmp(a_,				a_		):
     self._swap(a_,				a_		)
     _snake_case		, _snake_case							:		Optional[int]								=  parent, self._parent(a_		)


 def 			UpperCamelCase_       (    self:		Optional[int],				a_:		int		):




   '''simple docstring'''



   _snake_case							:		Optional[Any]								=  self._get_valid_parent(a_		)
   while valid_parent != index:
     self._swap(a_,				a_		)
     _snake_case		, _snake_case							:		Tuple								=  valid_parent, self._get_valid_parent(a_		)


 def 			UpperCamelCase_       (    self:		List[str],				a_:		int,				a_:		int		):




   '''simple docstring'''



   if item not in self.pos_map:
     return
   _snake_case							:		List[str]								=  self.pos_map[item]
   _snake_case							:		List[Any]								=  [item, self.key(a_		)]
   # Make sure heap is right in both up and down direction.
   # Ideally only one of them will make any change.
   self._heapify_up(a_		)
   self._heapify_down(a_		)


 def 			UpperCamelCase_       (    self:		Optional[Any],				a_:		int		):




   '''simple docstring'''



   if item not in self.pos_map:
     return
   _snake_case							:		Optional[Any]								=  self.pos_map[item]
   del self.pos_map[item]
   _snake_case							:		Union[str, Any]								=  self.arr[self.size - 1]
   _snake_case							:		int								=  index
   self.size -= 1
   # Make sure heap is right in both up and down direction. Ideally only one
   # of them will make any change- so no performance loss in calling both.
   if self.size > index:
     self._heapify_up(a_		)
     self._heapify_down(a_		)


 def 			UpperCamelCase_       (    self:		Any,				a_:		int,				a_:		int		):




   '''simple docstring'''



   _snake_case							:		Tuple								=  len(self.arr		)
   if arr_len == self.size:
     self.arr.append([item, self.key(a_		)]		)
   else:
     _snake_case							:		int								=  [item, self.key(a_		)]
   _snake_case							:		Dict								=  self.size
   self.size += 1
   self._heapify_up(self.size - 1		)


 def 			UpperCamelCase_       (    self:		Optional[Any]		):




   '''simple docstring'''



   return self.arr[0] if self.size else None


 def 			UpperCamelCase_       (    self:		Optional[Any]		):




   '''simple docstring'''



   _snake_case							:		Tuple								=  self.get_top()
   if top_item_tuple:
     self.delete_item(top_item_tuple[0]		)
   return top_item_tuple







def  UpperCAmelCase__	():
  """simple docstring"""



if __name__ == "__main__":
     import doctest

     doctest.testmod()








"""simple docstring"""


def  UpperCAmelCase__	(snake_case__							: Optional[Any]   ):
  """simple docstring"""

  _snake_case							:		Union[str, Any]								=  []
  _snake_case							:		Dict								=  set({"""(""", """[""", """{"""}   )
  _snake_case							:		Union[str, Any]								=  set({""")""", """]""", """}"""}   )
  _snake_case							:		Tuple								=  {"""{""": """}""", """[""": """]""", """(""": """)"""}

  for i in range(len(snake_case__   )   ):
    if s[i] in open_brackets:
      stack.append(s[i]   )

    elif s[i] in closed_brackets and (
        len(snake_case__   ) == 0 or (len(snake_case__   ) > 0 and open_to_closed[stack.pop()] != s[i])
    ):
      return False

  return len(snake_case__   ) == 0


def  UpperCAmelCase__	():
  """simple docstring"""

  _snake_case							:		Any								=  input("""Enter sequence of brackets: """   )
  if is_balanced(snake_case__   ):
    print(snake_case__		,       """is balanced"""   )
  else:
    print(snake_case__		,       """is not balanced"""   )


if __name__ == "__main__":
     main()


