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	:     str						      =    {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	:     int						      =    len(lowerCAmelCase_							)

     a	:     List[str]						      =    0
     a	:     list[list[float]]						      =    []
     # put the x and x to the power values in a matrix
     while count_of_line < x:
          a	:     str						      =    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	:     Union[str, Any]						      =    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	:     int						      =    0

     while count < x:
          a	:     Any						      =    0
          while zahlen < x:
               if count == zahlen:
                    zahlen += 1
               if zahlen == x:
                    break
               a	:     Optional[int]						      =    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	:     Union[str, Any]						      =    0
     # make solutions
     a	:     list[str]						      =    []
     while count < x:
          solution.append(str(vector[count] / matrix[count][count]							)							)
          count += 1

     a	:     List[str]						      =    0
     a	:     Optional[int]						      =    '''f(x)='''

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

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
)


UpperCAmelCase				 =   {
    """configuration_gptsan_japanese""": ["""GPTSAN_JAPANESE_PRETRAINED_CONFIG_ARCHIVE_MAP""", """GPTSanJapaneseConfig"""],
    """tokenization_gptsan_japanese""": ["""GPTSanJapaneseTokenizer"""],
}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  UpperCAmelCase				 =   [
      """GPTSAN_JAPANESE_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """GPTSanJapaneseForConditionalGeneration""",
      """GPTSanJapaneseModel""",
      """GPTSanJapanesePreTrainedModel""",
  ]
  UpperCAmelCase				 =   [
      """GPTSanJapaneseTokenizer""",
  ]


if TYPE_CHECKING:
  from .configuration_gptsan_japanese import GPTSAN_JAPANESE_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTSanJapaneseConfig
  from .tokenization_gptsan_japanese import GPTSanJapaneseTokenizer

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_gptsan_japanese import (
        GPTSAN_JAPANESE_PRETRAINED_MODEL_ARCHIVE_LIST,
        GPTSanJapaneseForConditionalGeneration,
        GPTSanJapaneseModel,
        GPTSanJapanesePreTrainedModel,
    )
    from .tokenization_gptsan_japanese import GPTSanJapaneseTokenizer


else:
  import sys

  UpperCAmelCase				 =   _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)