





'''simple docstring'''


def 	__a(SCREAMING_SNAKE_CASE_  :					str    ):



    '''simple docstring'''





    _lowerCAmelCase				=      0

    # if input_string is "aba" than new_input_string become "a|b|a"
    _lowerCAmelCase				=      ""
    _lowerCAmelCase				=      ""

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

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

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

        _lowerCAmelCase				=      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:
            _lowerCAmelCase				=      j - k + 1  # noqa: E741
            _lowerCAmelCase				=      j + k - 1

        # update max_length and start position
        if max_length < length[j]:
            _lowerCAmelCase				=      length[j]
            _lowerCAmelCase				=      j

    # create that string
    _lowerCAmelCase				=      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'''


import math


def 	__a(SCREAMING_SNAKE_CASE_  :					int = 100    ):



    '''simple docstring'''





    _lowerCAmelCase				=      sum(i * i for i in range(1		,       n + 1    )    )
    _lowerCAmelCase				=      int(math.pow(sum(range(1		,       n + 1    )    )		,       2    )    )
    return square_of_sum - sum_of_squares


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


