



'''simple docstring'''




import logging
import os
import threading
import time


try:
						import warnings
except ImportError:
						lowerCamelCase							:Tuple       = None

try:
						import msvcrt
except ImportError:
						lowerCamelCase							:int       = None

try:
						import fcntl
except ImportError:
						lowerCamelCase							:Optional[Any]       = None


# Backward compatibility
# ------------------------------------------------
try:
						TimeoutError
except NameError:
						lowerCamelCase							:Any       = OSError


# Data
# ------------------------------------------------
lowerCamelCase							:Union[str, Any]       = [
    '''Timeout''',
    '''BaseFileLock''',
    '''WindowsFileLock''',
    '''UnixFileLock''',
    '''SoftFileLock''',
    '''FileLock''',
]

lowerCamelCase							:Any       = '''3.0.12'''


lowerCamelCase							:Optional[int]       = None



def      a      (			):
			'''simple docstring'''





			global _logger
			A_     :						str     =					_logger or logging.getLogger(__name__   )
			return _logger







class      _lowerCAmelCase							(      __UpperCAmelCase			):


	def __init__(self	,				lowercase							):
				A_     :						str     =					lock_file
				return None


	def __str__(self							):
				A_     :						str     =					F'The file lock \'{self.lock_file}\' could not be acquired.'
				return temp







class      _lowerCAmelCase							:


	def __init__(self	,				lowercase							):
				A_     :						Any     =					lock
				return None


	def __enter__(self							):
				return self.lock


	def __exit__(self	,				lowercase	,				lowercase	,				lowercase							):
				self.lock.release()
				return None







class      _lowerCAmelCase							:


	def __init__(self	,				lowercase	,				lowercase=-1	,				lowercase=None							):
				A_     :						List[str]     =					max_filename_length if max_filename_length is not None else 255
				# Hash the filename if it's too long
				A_     :						List[str]     =					self.hash_filename_if_too_long(lowercase	,				lowercase							)
				# The path to the lock file.
				A_     :						Optional[int]     =					lock_file

				# The file descriptor for the *_lock_file* as it is returned by the
				# os.open() function.
				# This file lock is only NOT None, if the object currently holds the
				# lock.
				A_     :						Any     =					None

				# The default timeout value.
				A_     :						Union[str, Any]     =					timeout

				# We use this lock primarily for the lock counter.
				A_     :						Dict     =					threading.Lock()

				# The lock counter is used for implementing the nested locking
				# mechanism. Whenever the lock is acquired, the counter is increased and
				# the lock is only released, when this value is 0 again.
				A_     :						Dict     =					0
				return None


	@property
	def    _a     (self							):
				return self._lock_file


	@property
	def    _a     (self							):
				return self._timeout


	@timeout.setter
	def    _a     (self	,				lowercase							):
				A_     :						Dict     =					float(lowercase							)
				return None


	def    _a     (self							):
				raise NotImplementedError()


	def    _a     (self							):
				raise NotImplementedError()


	@property
	def    _a     (self							):
				return self._lock_file_fd is not None


	def    _a     (self	,				lowercase=None	,				lowercase=0.05							):
				# Use the default timeout, if no timeout is provided.
				if timeout is None:
							A_     :						List[Any]     =					self.timeout

				# Increment the number right at the beginning.
				# We can still undo it, if something fails.
				with self._thread_lock:
							self._lock_counter += 1

				A_     :						Union[str, Any]     =					id(self							)
				A_     :						Optional[Any]     =					self._lock_file
				A_     :						Any     =					time.time()
				try:
							while True:
										with self._thread_lock:
													if not self.is_locked:
																logger().debug(F'Attempting to acquire lock {lock_id} on {lock_filename}'							)
																self._acquire()

										if self.is_locked:
													logger().debug(F'Lock {lock_id} acquired on {lock_filename}'							)
													break
										elif timeout >= 0 and time.time() - start_time > timeout:
													logger().debug(F'Timeout on acquiring lock {lock_id} on {lock_filename}'							)
													raise Timeout(self._lock_file							)
										else:
													logger().debug(
													    F'Lock {lock_id} not acquired on {lock_filename}, waiting {poll_intervall} seconds ...'							)
													time.sleep(lowercase							)
				except:  # noqa
							# Something did go wrong, so decrement the counter.
							with self._thread_lock:
										A_     :						List[str]     =					max(0	,				self._lock_counter - 1							)

							raise
				return _Acquire_ReturnProxy(lock=self							)


	def    _a     (self	,				lowercase=False							):
				with self._thread_lock:
							if self.is_locked:
										self._lock_counter -= 1

										if self._lock_counter == 0 or force:
													A_     :						str     =					id(self							)
													A_     :						List[Any]     =					self._lock_file

													logger().debug(F'Attempting to release lock {lock_id} on {lock_filename}'							)
													self._release()
													A_     :						Optional[Any]     =					0
													logger().debug(F'Lock {lock_id} released on {lock_filename}'							)

				return None


	def __enter__(self							):
				self.acquire()
				return self


	def __exit__(self	,				lowercase	,				lowercase	,				lowercase							):
				self.release()
				return None


	def __del__(self							):
				self.release(force=lowercase							)
				return None


	def    _a     (self	,				lowercase	,				lowercase							):
				A_     :						Any     =					os.path.basename(lowercase							)
				if len(lowercase							) > max_length and max_length > 0:
							A_     :						List[Any]     =					os.path.dirname(lowercase							)
							A_     :						List[str]     =					str(hash(lowercase							)							)
							A_     :						int     =					filename[: max_length - len(lowercase							) - 8] + """...""" + hashed_filename + """.lock"""
							return os.path.join(lowercase	,				lowercase							)
				else:
							return path







class      _lowerCAmelCase							(      __UpperCAmelCase			):


	def __init__(self	,				lowercase	,				lowercase=-1	,				lowercase=None							):
				from .file_utils import relative_to_absolute_path

				super().__init__(lowercase	,				timeout=lowercase	,				max_filename_length=lowercase							)
				A_     :						Union[str, Any]     =					"""\\\\?\\""" + relative_to_absolute_path(self.lock_file							)


	def    _a     (self							):
				A_     :						str     =					os.O_RDWR | os.O_CREAT | os.O_TRUNC

				try:
							A_     :						Optional[int]     =					os.open(self._lock_file	,				lowercase							)
				except OSError:
							pass
				else:
							try:
										msvcrt.locking(lowercase	,				msvcrt.LK_NBLCK	,				1							)
							except OSError:
										os.close(lowercase							)
							else:
										A_     :						Dict     =					fd
				return None


	def    _a     (self							):
				A_     :						Optional[int]     =					self._lock_file_fd
				A_     :						Optional[int]     =					None
				msvcrt.locking(lowercase	,				msvcrt.LK_UNLCK	,				1							)
				os.close(lowercase							)

				try:
							os.remove(self._lock_file							)
				# Probably another instance of the application
				# that acquired the file lock.
				except OSError:
							pass
				return None







class      _lowerCAmelCase							(      __UpperCAmelCase			):


	def __init__(self	,				lowercase	,				lowercase=-1	,				lowercase=None							):
				A_     :						str     =					os.statvfs(os.path.dirname(lowercase							)							).f_namemax
				super().__init__(lowercase	,				timeout=lowercase	,				max_filename_length=lowercase							)


	def    _a     (self							):
				A_     :						int     =					os.O_RDWR | os.O_CREAT | os.O_TRUNC
				A_     :						List[Any]     =					os.open(self._lock_file	,				lowercase							)

				try:
							fcntl.flock(lowercase	,				fcntl.LOCK_EX | fcntl.LOCK_NB							)
				except OSError:
							os.close(lowercase							)
				else:
							A_     :						Tuple     =					fd
				return None


	def    _a     (self							):
				# Do not remove the lockfile:
				#
				#   https://github.com/benediktschmitt/py-filelock/issues/31
				#   https://stackoverflow.com/questions/17708885/flock-removing-locked-file-without-race-condition
				A_     :						Optional[Any]     =					self._lock_file_fd
				A_     :						int     =					None
				fcntl.flock(lowercase	,				fcntl.LOCK_UN							)
				os.close(lowercase							)
				return None







class      _lowerCAmelCase							(      __UpperCAmelCase			):


	def    _a     (self							):
				A_     :						Tuple     =					os.O_WRONLY | os.O_CREAT | os.O_EXCL | os.O_TRUNC
				try:
							A_     :						Tuple     =					os.open(self._lock_file	,				lowercase							)
				except OSError:
							pass
				else:
							A_     :						Optional[int]     =					fd
				return None


	def    _a     (self							):
				os.close(self._lock_file_fd							)
				A_     :						int     =					None

				try:
							os.remove(self._lock_file							)
				# The file is already deleted and that's what we want.
				except OSError:
							pass
				return None






lowerCamelCase							:Optional[Any]       = None

if msvcrt:
						lowerCamelCase							:Optional[Any]       = WindowsFileLock
elif fcntl:
						lowerCamelCase							:Tuple       = UnixFileLock
else:
						lowerCamelCase							:Optional[Any]       = SoftFileLock

						if warnings is not None:
												warnings.warn('''only soft file lock is available''')




'''simple docstring'''




from __future__ import annotations

from collections.abc import Callable

lowerCamelCase							:List[Any]       = list[list[float | int]]



def      a      (			lowerCamelCase__						,				lowerCamelCase__   ):
			'''simple docstring'''





			A_     :						int     =					len(lowerCamelCase__   )
			A_     :						Matrix     =					[[0 for _ in range(size + 1   )] for _ in range(lowerCamelCase__   )]
			A_     :						int
			A_     :						int
			A_     :						int
			A_     :						int
			A_     :						int
			A_     :						float

			for row in range(lowerCamelCase__   ):
						for col in range(lowerCamelCase__   ):
									A_     :						List[str]     =					matrix[row][col]

						A_     :						Optional[int]     =					vector[row][0]

			A_     :						Tuple     =					0
			A_     :						Tuple     =					0
			while row < size and col < size:
						# pivoting
						A_     :						Dict     =					max((abs(augmented[rowa][col]   ), rowa) for rowa in range(lowerCamelCase__						,				lowerCamelCase__   )   )[
						    1
						]
						if augmented[pivot_row][col] == 0:
									col += 1
									continue
						else:
									A_,   A_     :						Optional[Any]     =					augmented[pivot_row], augmented[row]

						for rowa in range(row + 1						,				lowerCamelCase__   ):
									A_     :						int     =					augmented[rowa][col] / augmented[row][col]
									A_     :						Union[str, Any]     =					0
									for cola in range(col + 1						,				size + 1   ):
												augmented[rowa][cola] -= augmented[row][cola] * ratio

						row += 1
						col += 1

			# back substitution
			for col in range(1						,				lowerCamelCase__   ):
						for row in range(lowerCamelCase__   ):
									A_     :						Tuple     =					augmented[row][col] / augmented[col][col]
									for cola in range(lowerCamelCase__						,				size + 1   ):
												augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
			return [
			    [round(augmented[row][size] / augmented[row][row]						,				10   )] for row in range(lowerCamelCase__   )
			]



def      a      (			lowerCamelCase__   ):
			'''simple docstring'''





			A_     :						int     =					len(lowerCamelCase__   )
			A_     :						Matrix     =					[[0 for _ in range(lowerCamelCase__   )] for _ in range(lowerCamelCase__   )]
			A_     :						Matrix     =					[[0] for _ in range(lowerCamelCase__   )]
			A_     :						Matrix
			A_     :						int
			A_     :						int
			A_     :						int

			for x_val, y_val in enumerate(lowerCamelCase__   ):
						for col in range(lowerCamelCase__   ):
									A_     :						Dict     =					(x_val + 1) ** (size - col - 1)
						A_     :						Any     =					y_val

			A_     :						Dict     =					solve(lowerCamelCase__						,				lowerCamelCase__   )

			def interpolated_func(lowerCamelCase__   ) -> int:
						return sum(
						    round(coeffs[x_val][0]   ) * (var ** (size - x_val - 1))
						    for x_val in range(lowerCamelCase__   )   )

			return interpolated_func



def      a      (			lowerCamelCase__   ):
			'''simple docstring'''





			return (
			    1
			    - variable
			    + variable**2
			    - variable**3
			    + variable**4
			    - variable**5
			    + variable**6
			    - variable**7
			    + variable**8
			    - variable**9
			    + variable**10
			)



def      a      (			lowerCamelCase__ = question_function						,				lowerCamelCase__ = 10   ):
			'''simple docstring'''





			A_     :						list[int]     =					[func(lowerCamelCase__   ) for x_val in range(1						,				order + 1   )]

			A_     :						list[Callable[[int], int]]     =					[
			    interpolate(data_points[:max_coeff]   ) for max_coeff in range(1						,				order + 1   )
			]

			A_     :						int     =					0
			A_     :						Callable[[int], int]
			A_     :						int

			for poly in polynomials:
						A_     :						int     =					1
						while func(lowerCamelCase__   ) == poly(lowerCamelCase__   ):
									x_val += 1

						ret += poly(lowerCamelCase__   )

			return ret


if __name__ == "__main__":
						print(F"{solution() = }")