




def     __SCREAMING_SNAKE_CASE      (     lowercase_					)				->		str:

    """simple docstring"""


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

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

    __UpperCamelCase     						=  {x for x, _ in coordinates}
    if len(lowercase_					) == 1:
        return F"x={coordinates[0][0]}"

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

    __UpperCamelCase     						=  len(lowercase_					)

    __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(lowercase_					)
        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(lowercase_					) > 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"""
import os






def        lowerCamelCase_  (						):
 lowerCamelCase__     :			List[Any]     				=						os.path.dirname(os.path.realpath(_lowerCamelCase				)				)
 lowerCamelCase__     :			Any     				=						os.path.join(_lowerCamelCase			,   'triangle.txt'				)

 with open(_lowerCamelCase				) as in_file:
  lowerCamelCase__     :			Dict     				=						[[int(_lowerCamelCase				) for i in line.split()] for line in in_file]

 while len(_lowerCamelCase				) != 1:
  lowerCamelCase__     :			Dict     				=						triangle.pop()
  lowerCamelCase__     :			Optional[Any]     				=						triangle[-1]
  for j in range(len(_lowerCamelCase				) - 1				):
   curr_row[j] += max(last_row[j]			,   last_row[j + 1]				)
 return triangle[0][0]


if __name__ == "__main__":
      print(solution())

