



from math import factorial

class        UpperCAmelCase_  :

						'''simple docstring'''




						def __init__(   self				,							_A				,							_A		):







													'''simple docstring'''

													__SCREAMING_SNAKE_CASE									= real
													if isinstance(_A				,							_A		):
																				__SCREAMING_SNAKE_CASE									= [1] * rank
													else:
																				__SCREAMING_SNAKE_CASE									= rank






						def __repr__(   self		):







													'''simple docstring'''

													return (
													    f"""{self.real}+"""
													    f"""{"+".join(str(_A		)+"E"+str(n+1		)for n,dual in enumerate(self.duals		)		)}"""
													)






						def 	_A     (   self		):







													'''simple docstring'''

													__SCREAMING_SNAKE_CASE									= self.duals.copy()
													while cur[-1] == 0:
																				cur.pop(-1		)
													return Dual(self.real				,							_A		)






						def __add__(   self				,							_A		):







													'''simple docstring'''

													if not isinstance(_A				,							_A		):
																				return Dual(self.real + other				,							self.duals		)
													__SCREAMING_SNAKE_CASE									= self.duals.copy()
													__SCREAMING_SNAKE_CASE									= other.duals.copy()
													if len(_A		) > len(_A		):
																				o_dual.extend([1] * (len(_A		) - len(_A		))		)
													elif len(_A		) < len(_A		):
																				s_dual.extend([1] * (len(_A		) - len(_A		))		)
													__SCREAMING_SNAKE_CASE									= []
													for i in range(len(_A		)		):
																				new_duals.append(s_dual[i] + o_dual[i]		)
													return Dual(self.real + other.real				,							_A		)

						UpperCamelCase__      :			List[Any]      =  __add__






						def __sub__(   self				,							_A		):







													'''simple docstring'''

													return self + other * -1






						def __mul__(   self				,							_A		):







													'''simple docstring'''

													if not isinstance(_A				,							_A		):
																				__SCREAMING_SNAKE_CASE									= []
																				for i in self.duals:
																											new_duals.append(i * other		)
																				return Dual(self.real * other				,							_A		)
													__SCREAMING_SNAKE_CASE									= [0] * (len(self.duals		) + len(other.duals		) + 1)
													for i, item in enumerate(self.duals		):
																				for j, jtem in enumerate(other.duals		):
																											new_duals[i + j + 1] += item * jtem
													for k in range(len(self.duals		)		):
																				new_duals[k] += self.duals[k] * other.real
													for index in range(len(other.duals		)		):
																				new_duals[index] += other.duals[index] * self.real
													return Dual(self.real * other.real				,							_A		)

						UpperCamelCase__      :			Any      =  __mul__






						def __truediv__(   self				,							_A		):







													'''simple docstring'''

													if not isinstance(_A				,							_A		):
																				__SCREAMING_SNAKE_CASE									= []
																				for i in self.duals:
																											new_duals.append(i / other		)
																				return Dual(self.real / other				,							_A		)
													raise ValueError






						def __floordiv__(   self				,							_A		):







													'''simple docstring'''

													if not isinstance(_A				,							_A		):
																				__SCREAMING_SNAKE_CASE									= []
																				for i in self.duals:
																											new_duals.append(i // other		)
																				return Dual(self.real // other				,							_A		)
													raise ValueError






						def __pow__(   self				,							_A		):







													'''simple docstring'''

													if n < 0 or isinstance(_A				,							_A		):
																				raise ValueError('power must be a positive integer'		)
													if n == 0:
																				return 1
													if n == 1:
																				return self
													__SCREAMING_SNAKE_CASE									= self
													for _ in range(n - 1		):
																				x *= self
													return x







def      __lowercase       (			a__							,       a__							,       a__       )    ->			Union[str, Any]:
							if not callable(a__       ):
														raise ValueError('differentiate() requires a function as input for func'       )
							if not isinstance(a__							,       (float, int)       ):
														raise ValueError('differentiate() requires a float as input for position'       )
							if not isinstance(a__							,       a__       ):
														raise ValueError('differentiate() requires an int as input for order'       )
							__SCREAMING_SNAKE_CASE									= Dual(a__							,       1       )
							__SCREAMING_SNAKE_CASE									= func(a__       )
							if order == 0:
														return result.real
							return result.duals[order - 1] * factorial(a__       )


if __name__ == "__main__":
			import doctest

			doctest.testmod()






			def      __lowercase       (			a__       )    ->			Tuple:
										return y**2 * y**4

			print(differentiate(f, 9, 2))











import os
import unittest

from transformers import LayoutLMTokenizer, LayoutLMTokenizerFast
from transformers.models.layoutlm.tokenization_layoutlm import VOCAB_FILES_NAMES
from transformers.testing_utils import require_tokenizers

from ...test_tokenization_common import TokenizerTesterMixin

@require_tokenizers
class        UpperCAmelCase_  (       UpperCamelCase_   ,   unittest.TestCase	):

						'''simple docstring'''




						UpperCamelCase__      :			Optional[int]      =  LayoutLMTokenizer
						UpperCamelCase__      :			Any      =  LayoutLMTokenizerFast
						UpperCamelCase__      :			Optional[int]      =  True
						UpperCamelCase__      :			int      =  True






						def 	_A     (   self		):







													'''simple docstring'''

													super().setUp()

													__SCREAMING_SNAKE_CASE									= [
													    '[UNK]',
													    '[CLS]',
													    '[SEP]',
													    'want',
													    '##want',
													    '##ed',
													    'wa',
													    'un',
													    'runn',
													    '##ing',
													    ',',
													    'low',
													    'lowest',
													]
													__SCREAMING_SNAKE_CASE									= os.path.join(self.tmpdirname				,							VOCAB_FILES_NAMES['vocab_file']		)
													with open(self.vocab_file				,							'w'				,							encoding='utf-8'		) as vocab_writer:
																				vocab_writer.write(''.join([x + '\n' for x in vocab_tokens]		)		)






						def 	_A     (   self				,							**_A		):







													'''simple docstring'''

													return LayoutLMTokenizer.from_pretrained(self.tmpdirname				,							**_A		)






						def 	_A     (   self				,							_A		):







													'''simple docstring'''

													__SCREAMING_SNAKE_CASE									= 'UNwant\u00E9d,running'
													__SCREAMING_SNAKE_CASE									= 'unwanted, running'
													return input_text, output_text






						def 	_A     (   self		):







													'''simple docstring'''

													__SCREAMING_SNAKE_CASE									= self.tokenizer_class(self.vocab_file		)

													__SCREAMING_SNAKE_CASE									= tokenizer.tokenize('UNwant\u00E9d,running'		)
													self.assertListEqual(_A				,							['un', '##want', '##ed', ',', 'runn', '##ing']		)
													self.assertListEqual(tokenizer.convert_tokens_to_ids(_A		)				,							[7, 4, 5, 10, 8, 9]		)






						def 	_A     (   self		):







													'''simple docstring'''

													pass






