
'''simple docstring'''
from typing import Dict, List, Optional, Tuple

from ...tokenization_utils import AddedToken, PreTrainedTokenizer
from ...utils import logging


lowerCAmelCase :  Dict      =      logging.get_logger(__name__)


class        SCREAMING_SNAKE_CASE__	(			snake_case_):
				lowerCAmelCase_			       =				["""input_ids""", """attention_mask"""]







				def __init__(    self		,							A_="[PAD]"		,							A_="[BOS]"		,							A_="[EOS]"		,							A_="[MASK]"		,							A_="[CLS]"		,							A_="[SEP]"		,							A_=2048		,							**A_		,							)->						None:







											'''simple docstring'''






											UpperCamelCase					       =			AddedToken(A_		,							lstrip=A_		,							rstrip=A_			) if isinstance(A_		,							A_			) else pad_token
											UpperCamelCase					       =			AddedToken(A_		,							lstrip=A_		,							rstrip=A_			) if isinstance(A_		,							A_			) else bos_token
											UpperCamelCase					       =			AddedToken(A_		,							lstrip=A_		,							rstrip=A_			) if isinstance(A_		,							A_			) else eos_token
											UpperCamelCase					       =			AddedToken(A_		,							lstrip=A_		,							rstrip=A_			) if isinstance(A_		,							A_			) else mask_token
											UpperCamelCase					       =			AddedToken(A_		,							lstrip=A_		,							rstrip=A_			) if isinstance(A_		,							A_			) else cls_token
											UpperCamelCase					       =			AddedToken(A_		,							lstrip=A_		,							rstrip=A_			) if isinstance(A_		,							A_			) else sep_token

											super().__init__(
											    pad_token=A_		,							bos_token=A_		,							eos_token=A_		,							mask_token=A_		,							cls_token=A_		,							sep_token=A_		,							model_max_length=A_		,							**A_		,							)

											UpperCamelCase					       =			2**8  # utf is 8 bits

											# define special tokens dict
											UpperCamelCase					       =			{
											    self.pad_token: 0,
											    self.bos_token: 1,
											    self.eos_token: 2,
											    self.mask_token: 3,
											    self.cls_token: 4,
											    self.sep_token: 5,
											}
											UpperCamelCase					       =			len(self.special_tokens_encoder			)
											UpperCamelCase					       =			{v: k for k, v in self.special_tokens_encoder.items()}







				def 		UpperCAmelCase_  (    self			)->						Dict[str, int]:







											'''simple docstring'''






											UpperCamelCase					       =			self.special_tokens_encoder.copy()
											vocab.update(self.added_tokens_encoder			)
											for i in range(self._utf_vocab_size			):
																		UpperCamelCase					       =			chr(A_			)
																		UpperCamelCase					       =			i + len(self.special_tokens_encoder			)
											return vocab







				@property
				def 		UpperCAmelCase_  (    self			)->						Optional[Any]:







											'''simple docstring'''






											return self._utf_vocab_size + self._num_special_tokens







				def 		UpperCAmelCase_  (    self		,							A_		,							A_ = None		,							A_ = False			)->						List[int]:







											'''simple docstring'''






											if already_has_special_tokens:
																		return super().get_special_tokens_mask(
																		    token_ids_a=A_		,							token_ids_a=A_		,							already_has_special_tokens=A_			)

											# normal case: some special tokens
											if token_ids_a is None:
																		return [1] + [0] * len(A_			) + [1]
											return [1] + ([0] * len(A_			)) + [1] + ([0] * len(A_			)) + [1]







				def 		UpperCAmelCase_  (    self		,							A_		,							A_ = None			)->						List[int]:







											'''simple docstring'''






											if token_ids_a is None:
																		return [self.cls_token_id] + token_ids_a + [self.sep_token_id]
											else:
																		return [self.cls_token_id] + token_ids_a + [self.sep_token_id] + token_ids_a + [self.sep_token_id]







				def 		UpperCAmelCase_  (    self		,							A_			)->						List[str]:







											'''simple docstring'''






											UpperCamelCase					       =			[chr(A_			) for i in text.encode('utf-8'			)]
											return tokens







				def 		UpperCAmelCase_  (    self		,							A_			)->						Any:







											'''simple docstring'''






											if token in self.special_tokens_encoder:
																		UpperCamelCase					       =			self.special_tokens_encoder[token]
											elif token in self.added_tokens_encoder:
																		UpperCamelCase					       =			self.added_tokens_encoder[token]
											elif len(A_			) != 1:
																		UpperCamelCase					       =			self.unk_token_id
											else:
																		UpperCamelCase					       =			ord(A_			) + self._num_special_tokens
											return token_id







				def 		UpperCAmelCase_  (    self		,							A_			)->						Union[str, Any]:







											'''simple docstring'''






											if index in self.special_tokens_decoder:
																		UpperCamelCase					       =			self.special_tokens_decoder[index]
											elif index in self.added_tokens_decoder:
																		UpperCamelCase					       =			self.added_tokens_decoder[index]
											else:
																		UpperCamelCase					       =			chr(index - self._num_special_tokens			)
											return token







				def 		UpperCAmelCase_  (    self		,							A_			)->						Any:







											'''simple docstring'''






											UpperCamelCase					       =			B''
											for token in tokens:
																		if token in self.special_tokens_decoder:
																									UpperCamelCase					       =			self.special_tokens_decoder[token].encode('utf-8'			)
																		elif token in self.added_tokens_decoder:
																									UpperCamelCase					       =			self.special_tokens_decoder[token].encode('utf-8'			)
																		elif token in self.special_tokens_encoder:
																									UpperCamelCase					       =			token.encode('utf-8'			)
																		elif token in self.added_tokens_encoder:
																									UpperCamelCase					       =			token.encode('utf-8'			)
																		else:
																									UpperCamelCase					       =			bytes([ord(A_			)]			)
																		bstring += tok_string
											UpperCamelCase					       =			bstring.decode('utf-8'		,							errors='replace'			)
											return string







				def 		UpperCAmelCase_  (    self		,							A_		,							A_ = None			)->						Tuple[str]:







											'''simple docstring'''






											return ()






'''simple docstring'''
def 						A_(			A		:						list[list[int]]):
							if len(A) == 0 or not all(len(A) == 2 for pair in coordinates):
														raise ValueError('The program cannot work out a fitting polynomial.')

							if len({tuple(A) for pair in coordinates}) != len(A):
														raise ValueError('The program cannot work out a fitting polynomial.')

							UpperCamelCase					       =			{x for x, _ in coordinates}
							if len(A) == 1:
														return f'''x={coordinates[0][0]}'''

							if len(A) != len(A):
														raise ValueError('The program cannot work out a fitting polynomial.')

							UpperCamelCase					       =			len(A)

							UpperCamelCase					       =			0
							UpperCamelCase					       =			[]
							# put the x and x to the power values in a matrix
							while count_of_line < x:
														UpperCamelCase					       =			0
														UpperCamelCase					       =			coordinates[count_of_line][0]
														UpperCamelCase					       =			[]
														while count_in_line < x:
																					count_line.append(a ** (x - (count_in_line + 1)))
																					count_in_line += 1
														matrix.append(A)
														count_of_line += 1

							UpperCamelCase					       =			0
							# put the y values into a vector
							UpperCamelCase					       =			[]
							while count_of_line < x:
														vector.append(coordinates[count_of_line][1])
														count_of_line += 1

							UpperCamelCase					       =			0

							while count < x:
														UpperCamelCase					       =			0
														while zahlen < x:
																					if count == zahlen:
																												zahlen += 1
																					if zahlen == x:
																												break
																					UpperCamelCase					       =			matrix[zahlen][count] / matrix[count][count]
																					for counting_columns, item in enumerate(matrix[count]):
																												# manipulating all the values in the matrix
																												matrix[zahlen][counting_columns] -= item * bruch
																					# manipulating the values in the vector
																					vector[zahlen] -= vector[count] * bruch
																					zahlen += 1
														count += 1

							UpperCamelCase					       =			0
							# make solutions
							UpperCamelCase					       =			[]
							while count < x:
														solution.append(str(vector[count] / matrix[count][count]))
														count += 1

							UpperCamelCase					       =			0
							UpperCamelCase					       =			'f(x)='

							while count < x:
														UpperCamelCase					       =			solution[count].split('E')
														if len(A) > 1:
																					UpperCamelCase					       =			f'''{remove_e[0]}*10^{remove_e[1]}'''
														solved += f'''x^{x - (count + 1)}*{solution[count]}'''
														if count + 1 != x:
																					solved += "+"
														count += 1

							return solved


if __name__ == "__main__":
						print(points_to_polynomial([]))
						print(points_to_polynomial([[]]))
						print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
						print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
						print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
						print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
						print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
						print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
						print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
						print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))




