






"""simple docstring"""






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

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

   UpperCamelCase_     ={x for x, _ in coordinates}
   if len(A			) == 1:
      return f"""x={coordinates[0][0]}"""

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

   UpperCamelCase_     =len(A			)

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

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

   UpperCamelCase_     =0

   while count < x:
      UpperCamelCase_     =0
      while zahlen < x:
         if count == zahlen:
            zahlen += 1
         if zahlen == x:
            break
         UpperCamelCase_     =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_     =0
   # make solutions
   UpperCamelCase_     =[]
   while count < x:
      solution.append(str(vector[count] / matrix[count][count]			)			)
      count += 1

   UpperCamelCase_     =0
   UpperCamelCase_     ="f(x)="

   while count < x:
      UpperCamelCase_     =solution[count].split("E"			)
      if len(A			) > 1:
         UpperCamelCase_     =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 collections import defaultdict




def 						_UpperCamelCase			(  A = 5			):
   UpperCamelCase_     =defaultdict(A			)
   UpperCamelCase_     =0

   while True:
      UpperCamelCase_     =get_digits(A			)
      freqs[digits].append(A			)

      if len(freqs[digits]			) == max_base:
         UpperCamelCase_     =freqs[digits][0] ** 3
         return base

      num += 1




def 						_UpperCamelCase			(  A			):
   return "".join(sorted(str(num**3			)			)			)


if __name__ == "__main__":
    print(f'''{solution() = }''')
