
"""simple docstring"""






from collections.abc import Callable





class 				a__					:



     def __init__(							self :Tuple      ,  _lowerCamelCase :Callable | None = None   ):







      '''simple docstring'''



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



     def  lowerCamelCase_						(							self :Tuple      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



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



     def  lowerCamelCase_						(							self :Optional[Any]      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					List[str]   	=int(2 * i + 1   )
      return left if 0 < left < self.size else None



     def  lowerCamelCase_						(							self :Tuple      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					Optional[Any]   	=int(2 * i + 2   )
      return right if 0 < right < self.size else None



     def  lowerCamelCase_						(							self :Dict      ,  _lowerCamelCase :int      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_	,     UpperCamelCase_     :					Optional[int]   	=(
          self.pos_map[self.arr[j][0]],
          self.pos_map[self.arr[i][0]],
      )
      # Then swap the items in the list.
      UpperCamelCase_	,     UpperCamelCase_     :					Union[str, Any]   	=self.arr[j], self.arr[i]



     def  lowerCamelCase_						(							self :Optional[Any]      ,  _lowerCamelCase :int      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



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



     def  lowerCamelCase_						(							self :Any      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					int   	=self._left(_lowerCamelCase   )
      UpperCamelCase_     :					List[Any]   	=self._right(_lowerCamelCase   )
      UpperCamelCase_     :					Optional[Any]   	=i

      if left is not None and not self._cmp(_lowerCamelCase      ,  _lowerCamelCase   ):
       UpperCamelCase_     :					Optional[int]   	=left
      if right is not None and not self._cmp(_lowerCamelCase      ,  _lowerCamelCase   ):
       UpperCamelCase_     :					List[Any]   	=right

      return valid_parent



     def  lowerCamelCase_						(							self :Any      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					Dict   	=self._parent(_lowerCamelCase   )
      while parent is not None and not self._cmp(_lowerCamelCase      ,  _lowerCamelCase   ):
       self._swap(_lowerCamelCase      ,  _lowerCamelCase   )
       UpperCamelCase_	,     UpperCamelCase_     :					Dict   	=parent, self._parent(_lowerCamelCase   )



     def  lowerCamelCase_						(							self :List[str]      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					Optional[Any]   	=self._get_valid_parent(_lowerCamelCase   )
      while valid_parent != index:
       self._swap(_lowerCamelCase      ,  _lowerCamelCase   )
       UpperCamelCase_	,     UpperCamelCase_     :					int   	=valid_parent, self._get_valid_parent(_lowerCamelCase   )



     def  lowerCamelCase_						(							self :Optional[Any]      ,  _lowerCamelCase :int      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



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



     def  lowerCamelCase_						(							self :Tuple      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      if item not in self.pos_map:
       return
      UpperCamelCase_     :					Any   	=self.pos_map[item]
      del self.pos_map[item]
      UpperCamelCase_     :					Dict   	=self.arr[self.size - 1]
      UpperCamelCase_     :					Optional[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(_lowerCamelCase   )
       self._heapify_down(_lowerCamelCase   )



     def  lowerCamelCase_						(							self :Optional[int]      ,  _lowerCamelCase :int      ,  _lowerCamelCase :int   ):







      '''simple docstring'''



      UpperCamelCase_     :					Optional[int]   	=len(self.arr   )
      if arr_len == self.size:
       self.arr.append([item, self.key(_lowerCamelCase   )]   )
      else:
       UpperCamelCase_     :					str   	=[item, self.key(_lowerCamelCase   )]
      UpperCamelCase_     :					Optional[int]   	=self.size
      self.size += 1
      self._heapify_up(self.size - 1   )



     def  lowerCamelCase_						(							self :List[Any]   ):







      '''simple docstring'''



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




     def  lowerCamelCase_						(							self :Tuple   ):







      '''simple docstring'''



      UpperCamelCase_     :					int   	=self.get_top()
      if top_item_tuple:
       self.delete_item(top_item_tuple[0]   )
      return top_item_tuple




def       A_  (				):
 pass


if __name__ == "__main__":
 import doctest

 doctest.testmod()


"""simple docstring"""






# This code is adapted from OpenAI's release
# https://github.com/openai/human-eval/blob/master/human_eval/execution.py

import contextlib
import faulthandler
import io
import multiprocessing
import os
import platform
import signal
import tempfile




def       A_  (				__lowercase						,	__lowercase						,	__lowercase						,	__lowercase	):
 UpperCamelCase_     :					Tuple   	=multiprocessing.Manager()
 UpperCamelCase_     :					Dict   	=manager.list()

 UpperCamelCase_     :					Union[str, Any]   	=multiprocessing.Process(target=__lowercase						,	args=(check_program, result, timeout)	)
 p.start()
 p.join(timeout=timeout + 1	)
 if p.is_alive():
  p.kill()

 if not result:
  result.append('timed out'	)

 return {
     "task_id": task_id,
     "passed": result[0] == "passed",
     "result": result[0],
     "completion_id": completion_id,
 }




def       A_  (				__lowercase						,	__lowercase						,	__lowercase	):
 with create_tempdir():
  # These system calls are needed when cleaning up tempdir.
  import os
  import shutil

  UpperCamelCase_     :					Tuple   	=shutil.rmtree
  UpperCamelCase_     :					List[str]   	=os.rmdir
  UpperCamelCase_     :					Any   	=os.chdir

  # Disable functionalities that can make destructive changes to the test.
  reliability_guard()

  # Run program.
  try:
   UpperCamelCase_     :					List[str]   	={}
   with swallow_io():
    with time_limit(__lowercase	):
     exec(__lowercase						,	__lowercase	)
   result.append('passed'	)
  except TimeoutException:
   result.append('timed out'	)
  except BaseException as e:
   result.append(F'''failed: {e}'''	)

  # Needed for cleaning up.
  UpperCamelCase_     :					Optional[Any]   	=rmtree
  UpperCamelCase_     :					str   	=rmdir
  UpperCamelCase_     :					Dict   	=chdir




@contextlib.contextmanager
def       A_  (				__lowercase	):
 def signal_handler(__lowercase						,	__lowercase	):
  raise TimeoutException('Timed out!'	)

 signal.setitimer(signal.ITIMER_REAL						,	__lowercase	)
 signal.signal(signal.SIGALRM						,	__lowercase	)
 try:
  yield
 finally:
  signal.setitimer(signal.ITIMER_REAL						,	0	)




@contextlib.contextmanager
def       A_  (				):
 UpperCamelCase_     :					str   	=WriteOnlyStringIO()
 with contextlib.redirect_stdout(__lowercase	):
  with contextlib.redirect_stderr(__lowercase	):
   with redirect_stdin(__lowercase	):
    yield




@contextlib.contextmanager
def       A_  (				):
 with tempfile.TemporaryDirectory() as dirname:
  with chdir(__lowercase	):
   yield dirname





class 				a__					(						A__       ):
     pass





class 				a__					(						io.StringIO       ):



     def  lowerCamelCase_						(							self :Any      ,  *_lowerCamelCase :Any      ,  **_lowerCamelCase :Tuple   ):







      '''simple docstring'''



      raise OSError



     def  lowerCamelCase_						(							self :Union[str, Any]      ,  *_lowerCamelCase :Any      ,  **_lowerCamelCase :Tuple   ):







      '''simple docstring'''



      raise OSError



     def  lowerCamelCase_						(							self :Tuple      ,  *_lowerCamelCase :str      ,  **_lowerCamelCase :List[str]   ):







      '''simple docstring'''



      raise OSError




     def  lowerCamelCase_						(							self :List[str]      ,  *_lowerCamelCase :Optional[int]      ,  **_lowerCamelCase :str   ):







      '''simple docstring'''



      return False





class 				a__					(						contextlib._RedirectStream       ):  # type: ignore
     UpperCAmelCase__         =      '''stdin'''




@contextlib.contextmanager
def       A_  (				__lowercase	):
 if root == ".":
  yield
  return
 UpperCamelCase_     :					List[str]   	=os.getcwd()
 os.chdir(__lowercase	)
 try:
  yield
 except BaseException as exc:
  raise exc
 finally:
  os.chdir(__lowercase	)





def       A_  (				__lowercase=None	):

 if maximum_memory_bytes is not None:
  import resource

  resource.setrlimit(resource.RLIMIT_AS						,	(maximum_memory_bytes, maximum_memory_bytes)	)
  resource.setrlimit(resource.RLIMIT_DATA						,	(maximum_memory_bytes, maximum_memory_bytes)	)
  if not platform.uname().system == "Darwin":
   resource.setrlimit(resource.RLIMIT_STACK						,	(maximum_memory_bytes, maximum_memory_bytes)	)

 faulthandler.disable()

 import builtins

 UpperCamelCase_     :					Any   	=None
 UpperCamelCase_     :					Any   	=None

 import os

 UpperCamelCase_     :					Union[str, Any]   	='1'

 UpperCamelCase_     :					Union[str, Any]   	=None
 UpperCamelCase_     :					Optional[Any]   	=None
 UpperCamelCase_     :					Optional[Any]   	=None
 UpperCamelCase_     :					Optional[Any]   	=None
 UpperCamelCase_     :					Dict   	=None
 UpperCamelCase_     :					List[Any]   	=None
 UpperCamelCase_     :					Any   	=None
 UpperCamelCase_     :					str   	=None
 UpperCamelCase_     :					Optional[int]   	=None
 UpperCamelCase_     :					Union[str, Any]   	=None
 UpperCamelCase_     :					str   	=None
 UpperCamelCase_     :					str   	=None
 UpperCamelCase_     :					List[Any]   	=None
 UpperCamelCase_     :					Optional[Any]   	=None
 UpperCamelCase_     :					str   	=None
 UpperCamelCase_     :					List[str]   	=None
 UpperCamelCase_     :					Optional[Any]   	=None
 UpperCamelCase_     :					int   	=None
 UpperCamelCase_     :					Optional[Any]   	=None
 UpperCamelCase_     :					Tuple   	=None
 UpperCamelCase_     :					List[Any]   	=None
 UpperCamelCase_     :					Tuple   	=None
 UpperCamelCase_     :					Dict   	=None
 UpperCamelCase_     :					Optional[int]   	=None
 UpperCamelCase_     :					str   	=None
 UpperCamelCase_     :					Union[str, Any]   	=None
 UpperCamelCase_     :					int   	=None

 import shutil

 UpperCamelCase_     :					List[str]   	=None
 UpperCamelCase_     :					Optional[Any]   	=None
 UpperCamelCase_     :					Dict   	=None

 import subprocess

 UpperCamelCase_     :					Optional[int]   	=None  # type: ignore

 UpperCamelCase_     :					Union[str, Any]   	=None

 import sys

 UpperCamelCase_     :					Union[str, Any]   	=None
 UpperCamelCase_     :					Tuple   	=None
 UpperCamelCase_     :					Union[str, Any]   	=None
 UpperCamelCase_     :					Dict   	=None
 UpperCamelCase_     :					Any   	=None
