






'''simple docstring'''

def 	_UpperCAmelCase    (  a		:	int							)			->			bool:





						"""simple docstring"""
						if number < 0:
												raise ValueError('number must not be negative'							)
						return number & (number - 1) == 0


if __name__ == "__main__":
						import doctest

						doctest.testmod()








'''simple docstring'''

def 	_UpperCAmelCase    (  a		:	str							)			->			str:





						"""simple docstring"""
						lowercase_      :   Dict        =			0

						# if input_string is "aba" than new_input_string become "a|b|a"
						lowercase_      :   Dict        =			''
						lowercase_      :   Any        =			''

						# 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
						lowercase_  ,      lowercase_      :   Dict        =			0, 0

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

						# for each character in new_string find corresponding palindromic string
						lowercase_      :   Dict        =			0
						for j in range(len(a							)							):
												lowercase_      :   Tuple        =			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

												lowercase_      :   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:
																		lowercase_      :   Tuple        =			j - k + 1  # noqa: E741
																		lowercase_      :   Tuple        =			j + k - 1

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

    # create that string
						lowercase_      :   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()
