"""simple docstring"""







def   __UpperCAmelCase    (   UpperCAmelCase_   :    str  )							->      List[Any]:

	'''simple docstring'''





	__snake_case      :							str						=			0

	# if input_string is "aba" than new_input_string become "a|b|a"
	__snake_case      :							List[Any]						=			""""""
	__snake_case      :							Optional[int]						=			""""""

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

	# length[i] shows the length of palindromic substring with center i
	__snake_case      :							Optional[int]						=			[1 for i in range(len(snake_case_  )  )]

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

		__snake_case      :							Dict						=			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:
			__snake_case      :							int						=			j - k + 1  # noqa: E741
			__snake_case      :							str						=			j + k - 1

		# update max_length and start position
		if max_length < length[j]:
			__snake_case      :							Tuple						=			length[j]
			__snake_case      :							List[Any]						=			j

    # create that string
	__snake_case      :							int						=			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   __UpperCAmelCase    (   UpperCAmelCase_   :    list      ,							UpperCAmelCase_   :    int      ,							UpperCAmelCase_   :    int = 0      ,							UpperCAmelCase_   :    int = 0  )							->      int:

	'''simple docstring'''





	__snake_case      :							str						=			right or len(UpperCAmelCase_  ) - 1
	if left > right:
		return -1
	elif list_data[left] == key:
		return left
	elif list_data[right] == key:
		return right
	else:
		return search(UpperCAmelCase_      ,							UpperCAmelCase_      ,							left + 1      ,							right - 1  )


if __name__ == "__main__":
	import doctest

	doctest.testmod()





