
"""simple docstring"""




def   __magic_name__     (				__snake_case    :	list[list[int]]  )			->    str:





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

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

       lowercase   :    Union[str, Any]			=							{x for x, _ in coordinates}
       if len(SCREAMING_SNAKE_CASE_  ) == 1:
              return f"""x={coordinates[0][0]}"""

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

       lowercase   :    List[Any]			=							len(SCREAMING_SNAKE_CASE_  )

       lowercase   :    List[Any]			=							0
       lowercase   :    str			=							[]
       # put the x and x to the power values in a matrix
       while count_of_line < x:
              lowercase   :    Any			=							0
              lowercase   :    Dict			=							coordinates[count_of_line][0]
              lowercase   :    int			=							[]
              while count_in_line < x:
                     count_line.append(a ** (x - (count_in_line + 1))  )
                     count_in_line += 1
              matrix.append(SCREAMING_SNAKE_CASE_  )
              count_of_line += 1

       lowercase   :    Union[str, Any]			=							0
       # put the y values into a vector
       lowercase   :    List[str]			=							[]
       while count_of_line < x:
              vector.append(coordinates[count_of_line][1]  )
              count_of_line += 1

       lowercase   :    int			=							0

       while count < x:
              lowercase   :    str			=							0
              while zahlen < x:
                     if count == zahlen:
                            zahlen += 1
                     if zahlen == x:
                            break
                     lowercase   :    Union[str, Any]			=							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

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

       lowercase   :    Optional[Any]			=							0
       lowercase   :    str			=							"f(x)="

       while count < x:
              lowercase   :    List[str]			=							solution[count].split("E"  )
              if len(SCREAMING_SNAKE_CASE_  ) > 1:
                     lowercase   :    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]]))




"""simple docstring"""




from ...configuration_utils import PretrainedConfig
from ...utils import logging


_A      :	str       		=	logging.get_logger(__name__)

_A      :	Optional[int]       		=	{
    """ZinengTang/tvlt-base""": """https://huggingface.co/ZinengTang/tvlt-base/blob/main/config.json""",
}

class 		a__						(				a_						):
   __lowerCAmelCase						=    """tvlt"""
   def __init__(      self     ,   _a=224     ,   _a=2_048     ,   _a=128     ,   _a=[16, 16]     ,   _a=[16, 16]     ,   _a=3     ,   _a=1     ,   _a=8     ,   _a=768     ,   _a=12     ,   _a=12     ,   _a=3_072     ,   _a="gelu"     ,   _a=0.0     ,   _a=0.0     ,   _a=0.0_2     ,   _a=1E-6     ,   _a=True     ,   _a=False     ,   _a=16     ,   _a=512     ,   _a=8     ,   _a=2_048     ,   _a=0.7_5     ,   _a=0.1_5     ,   _a="frame-level"     ,   _a=True     ,   _a=True     ,   _a="classification"     ,   **_a     ,   ):
          super().__init__(**_a    )

          if audio_mask_type not in ("frame-level", "patch_level"):
                 raise ValueError(
                     "audio_mask_type must be one of two acceptable strategies - {'frame_level', 'patch-level') "
                     f"""got {audio_mask_type}"""    )

          lowercase   :    Union[str, Any]			=							image_size
          lowercase   :    Dict			=							spectrogram_length
          lowercase   :    Union[str, Any]			=							frequency_length
          lowercase   :    Union[str, Any]			=							image_patch_size
          lowercase   :    Any			=							audio_patch_size
          lowercase   :    int			=							num_image_channels
          lowercase   :    Union[str, Any]			=							num_audio_channels
          lowercase   :    Any			=							num_frames

          lowercase   :    List[str]			=							hidden_size
          lowercase   :    List[str]			=							num_hidden_layers
          lowercase   :    List[Any]			=							num_attention_heads
          lowercase   :    int			=							intermediate_size
          lowercase   :    Tuple			=							hidden_act
          lowercase   :    int			=							hidden_dropout_prob
          lowercase   :    Dict			=							attention_probs_dropout_prob
          lowercase   :    List[Any]			=							initializer_range
          lowercase   :    Union[str, Any]			=							layer_norm_eps
          lowercase   :    Dict			=							qkv_bias
          lowercase   :    List[Any]			=							use_mean_pooling

          lowercase   :    List[Any]			=							decoder_num_attention_heads
          lowercase   :    Union[str, Any]			=							decoder_hidden_size
          lowercase   :    Dict			=							decoder_num_hidden_layers
          lowercase   :    Union[str, Any]			=							decoder_intermediate_size
          lowercase   :    List[str]			=							pixel_mask_ratio
          lowercase   :    str			=							audio_mask_ratio
          lowercase   :    Any			=							audio_mask_type

          lowercase   :    Union[str, Any]			=							task_matching
          lowercase   :    Optional[Any]			=							task_mae
          lowercase   :    List[str]			=							loss_type


