






"""simple docstring"""






def       _A    (__a							)				-> str:
    """simple docstring"""






    SCREAMING_SNAKE_CASE_   :						Any							=	0

    # if input_string is "aba" than new_input_string become "a|b|a"
    SCREAMING_SNAKE_CASE_   :						str							=	''''''
    SCREAMING_SNAKE_CASE_   :						str							=	''''''

    # append each character + "|" in new_string for range(0, length-1)
    for i in input_string[: len(__a							) - 1]:
        new_input_string += i + "|"
    # append last character
    new_input_string += input_string[-1]

    # we will store the starting and ending of previous furthest ending palindromic
    # substring
    SCREAMING_SNAKE_CASE_   :						Any							=	0, 0

    # length[i] shows the length of palindromic substring with center i
    SCREAMING_SNAKE_CASE_   :						Any							=	[1 for i in range(len(__a							)							)]

    # for each character in new_string find corresponding palindromic string
    SCREAMING_SNAKE_CASE_   :						List[Any]							=	0
    for j in range(len(__a							)							):
        SCREAMING_SNAKE_CASE_   :						List[str]							=	1 if j > r else min(length[l + r - j] // 2					,       r - j + 1							)
        while (
            j - k >= 0
            and j + k < len(__a							)
            and new_input_string[k + j] == new_input_string[j - k]
        ):
            k += 1

        SCREAMING_SNAKE_CASE_   :						int							=	2 * k - 1

        # does this string is ending after the previously explored end (that is r) ?
        # if yes the update the new r to the last index of this
        if j + k - 1 > r:
            SCREAMING_SNAKE_CASE_   :						str							=	j - k + 1  # noqa: E741
            SCREAMING_SNAKE_CASE_   :						str							=	j + k - 1

        # update max_length and start position
        if max_length < length[j]:
            SCREAMING_SNAKE_CASE_   :						Tuple							=	length[j]
            SCREAMING_SNAKE_CASE_   :						Optional[int]							=	j

    # create that string
    SCREAMING_SNAKE_CASE_   :						str							=	new_input_string[start - max_length // 2 : start + max_length // 2 + 1]
    for i in s:
        if i != "|":
            output_string += i

    return output_string


if __name__ == "__main__":
  import doctest

  doctest.testmod()










"""simple docstring"""






def       _A    (__a = 1_00							)				-> int:
    """simple docstring"""






    SCREAMING_SNAKE_CASE_   :						int							=	(n * (n + 1) // 2) ** 2
    SCREAMING_SNAKE_CASE_   :						Optional[Any]							=	n * (n + 1) * (2 * n + 1) // 6
    return sum_cubes - sum_squares


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


