



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

def     __lowercase(	UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__ ):


      """simple docstring"""



      lowerCamelCase								=		multiprocessing.Manager()
      lowerCamelCase								=		manager.list()

      lowerCamelCase								=		multiprocessing.Process(target=lowerCamelCase__   ,   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     __lowercase(	UpperCAmelCase__   ,   UpperCAmelCase__   ,   UpperCAmelCase__ ):


      """simple docstring"""



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

            lowerCamelCase								=		shutil.rmtree
            lowerCamelCase								=		os.rmdir
            lowerCamelCase								=		os.chdir

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

            # Run program.
            try:
                  lowerCamelCase								=		{}
                  with swallow_io():
                        with time_limit(lowerCamelCase__ ):
                              exec(lowerCamelCase__   ,   lowerCamelCase__ )
                  result.append("passed" )
            except TimeoutException:
                  result.append("timed out" )
            except BaseException as e:
                  result.append(F"""failed: {e}""" )

            # Needed for cleaning up.
            lowerCamelCase								=		rmtree
            lowerCamelCase								=		rmdir
            lowerCamelCase								=		chdir

@contextlib.contextmanager
def     __lowercase(	UpperCAmelCase__ ):


      """simple docstring"""



      def signal_handler(UpperCAmelCase__   ,   UpperCAmelCase__ ):
            raise TimeoutException("Timed out!" )

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

@contextlib.contextmanager
def     __lowercase(	):


      """simple docstring"""



      lowerCamelCase								=		WriteOnlyStringIO()
      with contextlib.redirect_stdout(lowerCamelCase__ ):
            with contextlib.redirect_stderr(lowerCamelCase__ ):
                  with redirect_stdin(lowerCamelCase__ ):
                        yield

@contextlib.contextmanager
def     __lowercase(	):


      """simple docstring"""



      with tempfile.TemporaryDirectory() as dirname:
            with chdir(lowerCamelCase__ ):
                  yield dirname





class    lowerCamelCase__  (						UpperCAmelCase_):
     """simple docstring"""



     pass





class    lowerCamelCase__  (						io.StringIO):
     """simple docstring"""



     def 						_a      (self				,			*__a				,			**__a    ):






           '''simple docstring'''



           raise OSError







     def 						_a      (self				,			*__a				,			**__a    ):






           '''simple docstring'''



           raise OSError







     def 						_a      (self				,			*__a				,			**__a    ):






           '''simple docstring'''



           raise OSError







     def 						_a      (self				,			*__a				,			**__a    ):






           '''simple docstring'''



           return False





class    lowerCamelCase__  (						contextlib._RedirectStream):  # type: ignore
     """simple docstring"""



     _A       =			"stdin"



@contextlib.contextmanager
def     __lowercase(	UpperCAmelCase__ ):


      """simple docstring"""



      if root == ".":
            yield
            return
      lowerCamelCase								=		os.getcwd()
      os.chdir(lowerCamelCase__ )
      try:
            yield
      except BaseException as exc:
            raise exc
      finally:
            os.chdir(lowerCamelCase__ )






def     __lowercase(	UpperCAmelCase__=None ):


      """simple docstring"""



      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

      lowerCamelCase								=		None
      lowerCamelCase								=		None

      import os

      lowerCamelCase								=		"1"

      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None

      import shutil

      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None

      import subprocess

      lowerCamelCase								=		None  # type: ignore

      lowerCamelCase								=		None

      import sys

      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None
      lowerCamelCase								=		None




from math import pi

def     __lowercase(	UpperCAmelCase__   ,   UpperCAmelCase__ ):


      """simple docstring"""



      return 2 * pi * radius * (angle / 360)


if __name__ == "__main__":
     print(arc_length(9_0, 1_0))