






def     lowerCamelCase__				(   __lowerCamelCase      :					list[list[int]]		):





  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."""		)

  __UpperCAmelCase							:     Optional[int]									=  {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."""		)

  __UpperCAmelCase							:     Tuple									=  len(SCREAMING_SNAKE_CASE_		)

  __UpperCAmelCase							:     Optional[int]									=  0
  __UpperCAmelCase							:     Tuple									=  []
  # put the x and x to the power values in a matrix
  while count_of_line < x:
    __UpperCAmelCase							:     Optional[int]									=  0
    __UpperCAmelCase							:     List[str]									=  coordinates[count_of_line][0]
    __UpperCAmelCase							:     List[str]									=  []
    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

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

  __UpperCAmelCase							:     List[str]									=  0

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

  __UpperCAmelCase							:     Dict									=  0
  __UpperCAmelCase							:     Optional[Any]									=  """f(x)="""

  while count < x:
    __UpperCAmelCase							:     int									=  solution[count].split("""E"""		)
    if len(SCREAMING_SNAKE_CASE_		) > 1:
      __UpperCAmelCase							:     Any									=  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]]))










def     lowerCamelCase__				(   ):

  for a in range(300		):
    for b in range(a + 1  ,		400		):
      for c in range(b + 1  ,		500		):
        if (a + b + c) == 1000 and (a**2) + (b**2) == (c**2):
          return a * b * c

  return -1






def     lowerCamelCase__				(   ):

  for a in range(300		):
    for b in range(400		):
      __UpperCAmelCase							:     Optional[Any]									=  1000 - a - b
      if a < b < c and (a**2) + (b**2) == (c**2):
        return a * b * c

  return -1






def     lowerCamelCase__				(   ):
  import timeit

  print(
      timeit.timeit("""solution()"""  ,		setup="""from __main__ import solution"""  ,		number=1000		)		)
  print(
      timeit.timeit(
          """solution_fast()"""  ,		setup="""from __main__ import solution_fast"""  ,		number=1000		)		)


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


