
"""simple docstring"""







from math import ceil




def       A_      (       lowercase = 1001   )  ->				int:


     """simple docstring"""







     UpperCAmelCase_    :     Any            =	1

     for i in range(1    ,			int(ceil(n / 2.0   )   )   ):
          UpperCAmelCase_    :     Dict            =	2 * i + 1
          UpperCAmelCase_    :     Optional[Any]            =	2 * i
          UpperCAmelCase_    :     Optional[Any]            =	total + 4 * odd**2 - 6 * even

     return total


if __name__ == "__main__":
       import sys

       if len(sys.argv) == 1:
              print(solution())
       else:
              try:
                     lowercase_         =       int(sys.argv[1])
                     print(solution(n))
              except ValueError:
                     print("Invalid entry - please enter a number")



"""simple docstring"""







def       A_      (       lowercase   )  ->				str:


     """simple docstring"""







     UpperCAmelCase_    :     Any            =	0

     # if input_string is "aba" than new_input_string become "a|b|a"
     UpperCAmelCase_    :     Union[str, Any]            =	""""""
     UpperCAmelCase_    :     List[Any]            =	""""""

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

     # length[i] shows the length of palindromic substring with center i
     UpperCAmelCase_    :     Dict            =	[1 for i in range(len(lowercase   )   )]

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

          UpperCAmelCase_    :     Union[str, Any]            =	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:
               UpperCAmelCase_    :     List[Any]            =	j - k + 1  # noqa: E741
               UpperCAmelCase_    :     Union[str, Any]            =	j + k - 1

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

    # create that string
     UpperCAmelCase_    :     List[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()

