def 	UpperCAmelCase       (		lowerCAmelCase_       )	->	str:
     if len(lowerCAmelCase_       ) == 0 or not all(len(lowerCAmelCase_       ) == 2 for pair in coordinates       ):
          raise ValueError('''The program cannot work out a fitting polynomial.'''       )

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

     a  :    List[Any]				=						{x for x, _ in coordinates}
     if len(lowerCAmelCase_       ) == 1:
          return f"""x={coordinates[0][0]}"""

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

     a  :    Union[str, Any]				=						len(lowerCAmelCase_       )

     a  :    Union[str, Any]				=						0
     a  :    list[list[float]]				=						[]
     # put the x and x to the power values in a matrix
     while count_of_line < x:
          a  :    Union[str, Any]				=						0
          a  :    List[str]				=						coordinates[count_of_line][0]
          a  :    list[float]				=						[]
          while count_in_line < x:
               count_line.append(a ** (x - (count_in_line + 1))       )
               count_in_line += 1
          matrix.append(lowerCAmelCase_       )
          count_of_line += 1

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

     a  :    Optional[Any]				=						0

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

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

     a  :    List[Any]				=						0
     a  :    Union[str, Any]				=						'''f(x)='''

     while count < x:
          a  :    list[str]				=						solution[count].split('''E'''       )
          if len(lowerCAmelCase_       ) > 1:
               a  :    Tuple				=						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]]))
import unittest

from transformers import BlenderbotTokenizer, BlenderbotTokenizerFast
from transformers.utils import cached_property






class 							_SCREAMING_SNAKE_CASE(   unittest.TestCase	):
   @cached_property
   def _lowercase(    self    )	->List[str]:
        return BlenderbotTokenizer.from_pretrained('''facebook/blenderbot-3B'''    )
   @cached_property
   def _lowercase(    self    )	->str:
        return BlenderbotTokenizerFast.from_pretrained('''facebook/blenderbot-3B'''    )
   def _lowercase(    self    )	->str:
        a  :    Optional[int]				=						self.tokenizer_ab
        a  :    List[Any]				=						''' I am a small frog.'''
        a  :    Optional[Any]				=						tok([src_text]							,     padding=lowerCAmelCase_							,     truncation=lowerCAmelCase_    )['''input_ids''']
        a  :    int				=						tok.batch_decode(lowerCAmelCase_							,     skip_special_tokens=lowerCAmelCase_							,     clean_up_tokenization_spaces=lowerCAmelCase_    )[0]
        assert src_text == decoded
   def _lowercase(    self    )	->Dict:
        a  :    List[Any]				=						self.rust_tokenizer_ab
        a  :    str				=						''' I am a small frog.'''
        a  :    Tuple				=						tok([src_text]							,     padding=lowerCAmelCase_							,     truncation=lowerCAmelCase_    )['''input_ids''']
        a  :    Optional[Any]				=						tok.batch_decode(lowerCAmelCase_							,     skip_special_tokens=lowerCAmelCase_							,     clean_up_tokenization_spaces=lowerCAmelCase_    )[0]
        assert src_text == decoded
   def _lowercase(    self    )	->Tuple:
        assert self.tokenizer_ab.add_prefix_space
        assert self.tokenizer_ab([''' Sam''', '''Sam''']    ).input_ids == [[55_02, 2], [55_02, 2]]


   def _lowercase(    self    )	->Optional[Any]:
        assert self.rust_tokenizer_ab.add_prefix_space
        assert self.rust_tokenizer_ab([''' Sam''', '''Sam''']    ).input_ids == [[55_02, 2], [55_02, 2]]