'''simple docstring'''
def 			_UpperCamelCase			(  _a						:						Dict      ):




    """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.'      )

    __UpperCamelCase						:						List[Any]		     =	{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.'      )

    __UpperCamelCase						:						Dict		     =	len(UpperCAmelCase__      )

    __UpperCamelCase						:						Tuple		     =	0
    __UpperCamelCase						:						Dict		     =	[]
    # put the x and x to the power values in a matrix
    while count_of_line < x:
        __UpperCamelCase						:						Tuple		     =	0
        __UpperCamelCase						:						Dict		     =	coordinates[count_of_line][0]
        __UpperCamelCase						:						Dict		     =	[]
        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

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

    __UpperCamelCase						:						Any		     =	0

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

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

    __UpperCamelCase						:						Tuple		     =	0
    __UpperCamelCase						:						int		     =	'f(x)='

    while count < x:
        __UpperCamelCase						:						Optional[int]		     =	solution[count].split('E'      )
        if len(UpperCAmelCase__      ) > 1:
            __UpperCamelCase						:						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, 1_1]]))
  print(points_to_polynomial([[1, -3], [2, -6], [3, -1_1]]))
  print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))






import os

from apache_beam.io.filesystems import FileSystems
from apache_beam.pipeline import Pipeline

from .logging import get_logger


lowerCamelCase   					=  2 << 2_0  # 2mb
lowerCamelCase   					=  get_logger(__name__)





class      snake_case_      (					_a				):


							"""simple docstring"""





							def 							A__	(			self				):
												__lowerCAmelCase       =				self._options.get_all_options().get('runner'				)
												return runner in [None, "DirectRunner", "PortableRunner"]


def 							__lowercase     (	UpperCAmelCase__		,       UpperCAmelCase__		,       UpperCAmelCase__=False   ):

					"""simple docstring"""






					__lowerCAmelCase       =				FileSystems
					if fs.exists(UpperCAmelCase__   ):
										if force_upload:
															logger.info(F"""Remote path already exist: {remote_file_path}. Overwriting it as force_upload=True."""   )
										else:
															logger.info(F"""Remote path already exist: {remote_file_path}. Skipping it as force_upload=False."""   )
															return
					with fs.create(UpperCAmelCase__   ) as remote_file:
										with open(UpperCAmelCase__		,       'rb'   ) as local_file:
															__lowerCAmelCase       =				local_file.read(UpperCAmelCase__   )
															while chunk:
																				remote_file.write(UpperCAmelCase__   )
																				__lowerCAmelCase       =				local_file.read(UpperCAmelCase__   )


def 							__lowercase     (	UpperCAmelCase__		,       UpperCAmelCase__		,       UpperCAmelCase__=False   ):

					"""simple docstring"""






					__lowerCAmelCase       =				FileSystems
					if os.path.exists(UpperCAmelCase__   ):
										if force_download:
															logger.info(F"""Local path already exist: {remote_file_path}. Overwriting it as force_upload=True."""   )
										else:
															logger.info(F"""Local path already exist: {remote_file_path}. Skipping it as force_upload=False."""   )
															return
					with fs.open(UpperCAmelCase__   ) as remote_file:
										with open(UpperCAmelCase__		,       'wb'   ) as local_file:
															__lowerCAmelCase       =				remote_file.read(UpperCAmelCase__   )
															while chunk:
																				local_file.write(UpperCAmelCase__   )
																				__lowerCAmelCase       =				remote_file.read(UpperCAmelCase__   )






