code: 
  
  
  
  def 			__lowercase     (				a__     )       ->				int:
  							return int(a__     ) if x - int(a__     ) <= 0 else int(a__     ) + 1
  
  
  if __name__ == "__main__":
  			import doctest
  
  			doctest.testmod()
  
  
  
  
  
  
  
style_context: 
  
  
  
  from __future__ import annotations
  
  from collections.abc import Iterable
  from dataclasses import dataclass
  from typing import Any
  
  class      UpperCAmelCase_						:
  
  						'''simple docstring'''
  
  
  
  
  						UpperCamelCase__    :				List[str]       						=						('''_front''', '''_back''', '''_len''')
  
  						@dataclass
  						class      UpperCAmelCase_						:
  
  												'''simple docstring'''
  
  
  
  
  												UpperCamelCase__    :				Any       						=						None
  												UpperCamelCase__    :				Deque._Node | None       						=						None
  												UpperCamelCase__    :				Deque._Node | None       						=						None
  
  
  
  
  
  
  
  						class      UpperCAmelCase_						:
  
  												'''simple docstring'''
  
  
  
  
  												UpperCamelCase__    :				Optional[int]       						=						('''_cur''',)
  
  
  
  
  
  
  												def __init__(					self   ,							_A	):
  
  
  
  
  
  
  
  																			'''simple docstring'''
  
  																			__SCREAMING_SNAKE_CASE								=      cur
  
  
  
  
  
  
  												def __iter__(					self	):
  
  
  
  
  
  
  
  																			'''simple docstring'''
  
  																			return self
  
  
  
  
  
  
  												def  _A			(					self	):
  
  
  
  
  
  
  
  																			'''simple docstring'''
  
  																			if self._cur is None:
  																										# finished iterating
  																										raise StopIteration
  																			__SCREAMING_SNAKE_CASE								=      self._cur.val
  																			__SCREAMING_SNAKE_CASE								=      self._cur.next_node
  
  																			return val
  
  
  
  
  
  
  
  						def __init__(					self   ,							_A = None	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      None
  													__SCREAMING_SNAKE_CASE								=      None
  													__SCREAMING_SNAKE_CASE								=      0
  
  													if iterable is not None:
  																				# append every value to the deque
  																				for val in iterable:
  																											self.append(_A	)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      self._Node(_A   ,							_A   ,							_A	)
  													if self.is_empty():
  																				# front = back
  																				__SCREAMING_SNAKE_CASE								=      __SCREAMING_SNAKE_CASE								=      node
  																				__SCREAMING_SNAKE_CASE								=      1
  													else:
  																				# connect nodes
  																				__SCREAMING_SNAKE_CASE								=      node
  																				__SCREAMING_SNAKE_CASE								=      self._back
  																				__SCREAMING_SNAKE_CASE								=      node  # assign new back to the new node
  
  																				self._len += 1
  
  																				# make sure there were no errors
  																				assert not self.is_empty(), "Error on appending value."
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      self._Node(_A   ,							_A   ,							_A	)
  													if self.is_empty():
  																				# front = back
  																				__SCREAMING_SNAKE_CASE								=      __SCREAMING_SNAKE_CASE								=      node
  																				__SCREAMING_SNAKE_CASE								=      1
  													else:
  																				# connect nodes
  																				__SCREAMING_SNAKE_CASE								=      self._front
  																				__SCREAMING_SNAKE_CASE								=      node
  																				__SCREAMING_SNAKE_CASE								=      node  # assign new front to the new node
  
  																				self._len += 1
  
  																				# make sure there were no errors
  																				assert not self.is_empty(), "Error on appending value."
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													for val in iterable:
  																				self.append(_A	)
  
  
  
  
  
  
  						def  _A			(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													for val in iterable:
  																				self.appendleft(_A	)
  
  
  
  
  
  
  						def  _A			(					self	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													assert not self.is_empty(), "Deque is empty."
  
  													__SCREAMING_SNAKE_CASE								=      self._back
  													__SCREAMING_SNAKE_CASE								=      self._back.prev_node  # set new back
  													# drop the last node - python will deallocate memory automatically
  													__SCREAMING_SNAKE_CASE								=      None
  
  													self._len -= 1
  
  													return topop.val
  
  
  
  
  
  
  						def  _A			(					self	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													assert not self.is_empty(), "Deque is empty."
  
  													__SCREAMING_SNAKE_CASE								=      self._front
  													__SCREAMING_SNAKE_CASE								=      self._front.next_node  # set new front and drop the first node
  													__SCREAMING_SNAKE_CASE								=      None
  
  													self._len -= 1
  
  													return topop.val
  
  
  
  
  
  
  						def  _A			(					self	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													return self._front is None
  
  
  
  
  
  
  						def __len__(					self	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													return self._len
  
  
  
  
  
  
  						def __eq__(					self   ,							_A	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													if not isinstance(_A   ,							_A	):
  																				return NotImplemented
  
  													__SCREAMING_SNAKE_CASE								=      self._front
  													__SCREAMING_SNAKE_CASE								=      other._front
  
  													# if the length of the dequeues are not the same, they are not equal
  													if len(self	) != len(_A	):
  																				return False
  
  													while me is not None and oth is not None:
  																				# compare every value
  																				if me.val != oth.val:
  																											return False
  																				__SCREAMING_SNAKE_CASE								=      me.next_node
  																				__SCREAMING_SNAKE_CASE								=      oth.next_node
  
  													return True
  
  
  
  
  
  
  						def __iter__(					self	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													return Deque._Iterator(self._front	)
  
  
  
  
  
  
  						def __repr__(					self	):
  
  
  
  
  
  
  
  													'''simple docstring'''
  
  													__SCREAMING_SNAKE_CASE								=      []
  													__SCREAMING_SNAKE_CASE								=      self._front
  													while aux is not None:
  																				# append the values in a list to display
  																				values_list.append(aux.val	)
  																				__SCREAMING_SNAKE_CASE								=      aux.next_node
  
  													return f"""[{", ".join(repr(_A	) for val in values_list	)}]"""
  
  
  if __name__ == "__main__":
  			import doctest
  
  			doctest.testmod()
  
  
  
  
  
  
  