
'''simple docstring'''

def   A     (      UpperCamelCase_					:     List[Any]      )					->       str:







			'''simple docstring'''



			if len(_UpperCAmelCase      ) == 0 or not all(len(_UpperCAmelCase      ) == 2 for pair in coordinates      ):
						raise ValueError("The program cannot work out a fitting polynomial."      )

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

			lowerCAmelCase__								=							{x for x, _ in coordinates}
			if len(_UpperCAmelCase      ) == 1:
						return F"""x={coordinates[0][0]}"""

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

			lowerCAmelCase__								=							len(_UpperCAmelCase      )

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

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

			lowerCAmelCase__								=							0

			while count < x:
						lowerCAmelCase__								=							0
						while zahlen < x:
									if count == zahlen:
												zahlen += 1
									if zahlen == x:
												break
									lowerCAmelCase__								=							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

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

			lowerCAmelCase__								=							0
			lowerCAmelCase__								=							"f(x)="

			while count < x:
						lowerCAmelCase__								=							solution[count].split("E"      )
						if len(_UpperCAmelCase      ) > 1:
									lowerCAmelCase__								=							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]]))





'''simple docstring'''

import json
from typing import List, Optional, Tuple

from tokenizers import normalizers

from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import logging
from .tokenization_layoutlm import LayoutLMTokenizer


UpperCAmelCase__   : Optional[Any]					=		logging.get_logger(__name__)

UpperCAmelCase__   : str					=		{"vocab_file": "vocab.txt", "tokenizer_file": "tokenizer.json"}

UpperCAmelCase__   : Union[str, Any]					=		{
    "vocab_file": {
        "microsoft/layoutlm-base-uncased": (
            "https://huggingface.co/microsoft/layoutlm-base-uncased/resolve/main/vocab.txt"
        ),
        "microsoft/layoutlm-large-uncased": (
            "https://huggingface.co/microsoft/layoutlm-large-uncased/resolve/main/vocab.txt"
        ),
    },
    "tokenizer_file": {
        "microsoft/layoutlm-base-uncased": (
            "https://huggingface.co/microsoft/layoutlm-base-uncased/resolve/main/tokenizer.json"
        ),
        "microsoft/layoutlm-large-uncased": (
            "https://huggingface.co/microsoft/layoutlm-large-uncased/resolve/main/tokenizer.json"
        ),
    },
}

UpperCAmelCase__   : List[Any]					=		{
    "microsoft/layoutlm-base-uncased": 5_12,
    "microsoft/layoutlm-large-uncased": 5_12,
}

UpperCAmelCase__   : List[str]					=		{
    "microsoft/layoutlm-base-uncased": {"do_lower_case": True},
    "microsoft/layoutlm-large-uncased": {"do_lower_case": True},
}






class    A     (	SCREAMING_SNAKE_CASE__    ):
	snake_case__      :Union[str, Any]        =     VOCAB_FILES_NAMES
	snake_case__      :List[str]        =     PRETRAINED_VOCAB_FILES_MAP
	snake_case__      :Union[str, Any]        =     PRETRAINED_INIT_CONFIGURATION
	snake_case__      :int        =     PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
	snake_case__      :int        =     LayoutLMTokenizer





	def __init__(					self			:       Any      ,							__magic_name__			:       List[Any]=None      ,							__magic_name__			:       Optional[int]=None      ,							__magic_name__			:       Dict=True      ,							__magic_name__			:       Dict="[UNK]"      ,							__magic_name__			:       List[str]="[SEP]"      ,							__magic_name__			:       int="[PAD]"      ,							__magic_name__			:       Tuple="[CLS]"      ,							__magic_name__			:       int="[MASK]"      ,							__magic_name__			:       Dict=True      ,							__magic_name__			:       Tuple=None      ,							**__magic_name__			:       Optional[int]      ,							):


				"""simple docstring"""

				super().__init__(
				    __magic_name__      ,							tokenizer_file=__magic_name__      ,							do_lower_case=__magic_name__      ,							unk_token=__magic_name__      ,							sep_token=__magic_name__      ,							pad_token=__magic_name__      ,							cls_token=__magic_name__      ,							mask_token=__magic_name__      ,							tokenize_chinese_chars=__magic_name__      ,							strip_accents=__magic_name__      ,							**__magic_name__      ,							)

				lowerCAmelCase__								=							json.loads(self.backend_tokenizer.normalizer.__getstate__()							)
				if (
				    normalizer_state.get("lowercase"      ,							__magic_name__							) != do_lower_case
				    or normalizer_state.get("strip_accents"      ,							__magic_name__							) != strip_accents
				    or normalizer_state.get("handle_chinese_chars"      ,							__magic_name__							) != tokenize_chinese_chars
				):
							lowerCAmelCase__								=							getattr(__magic_name__      ,							normalizer_state.pop("type"							)							)
							lowerCAmelCase__								=							do_lower_case
							lowerCAmelCase__								=							strip_accents
							lowerCAmelCase__								=							tokenize_chinese_chars
							lowerCAmelCase__								=							normalizer_class(**__magic_name__							)

				lowerCAmelCase__								=							do_lower_case





	def 							__SCREAMING_SNAKE_CASE  (					self			:       List[str]      ,							__magic_name__			:       Optional[int]      ,							__magic_name__			:       List[str]=None							):


				"""simple docstring"""

				lowerCAmelCase__								=							[self.cls_token_id] + token_ids_a + [self.sep_token_id]

				if token_ids_a:
							output += token_ids_a + [self.sep_token_id]

				return output





	def 							__SCREAMING_SNAKE_CASE  (					self			:       Tuple      ,							__magic_name__			:       List[int]      ,							__magic_name__			:       Optional[List[int]] = None							):


				"""simple docstring"""

				lowerCAmelCase__								=							[self.sep_token_id]
				lowerCAmelCase__								=							[self.cls_token_id]
				if token_ids_a is None:
							return len(cls + token_ids_a + sep							) * [0]
				return len(cls + token_ids_a + sep							) * [0] + len(token_ids_a + sep							) * [1]







	def 							__SCREAMING_SNAKE_CASE  (					self			:       Optional[Any]      ,							__magic_name__			:       str      ,							__magic_name__			:       Optional[str] = None							):


				"""simple docstring"""

				lowerCAmelCase__								=							self._tokenizer.model.save(__magic_name__      ,							name=__magic_name__							)
				return tuple(__magic_name__							)





