


'''simple docstring'''
def       a				(      __a       )  ->     list:






					if bit_count < 0:
										raise ValueError('''The given input must be positive'''       )

					# get the generated string sequence
					UpperCamelCase__       :int							 =			gray_code_sequence_string(__a       )
					#
					# convert them to integers
					for i in range(len(__a       )       ):
										UpperCamelCase__       :Union[str, Any]							 =			int(sequence[i]			, 2       )

					return sequence


def       a				(      __a       )  ->     list:






					if bit_count == 0:
										return ["0"]

					if bit_count == 1:
										return ["0", "1"]

					UpperCamelCase__       :Tuple							 =			1 << bit_count  # defines the length of the sequence
					# 1<< n is equivalent to 2^n

					# recursive answer will generate answer for n-1 bits
					UpperCamelCase__       :Optional[Any]							 =			gray_code_sequence_string(bit_count - 1       )

					UpperCamelCase__       :Tuple							 =			[]

					# append 0 to first half of the smaller sequence generated
					for i in range(seq_len // 2       ):
										UpperCamelCase__       :Any							 =			'''0''' + smaller_sequence[i]
										sequence.append(__a       )

					# append 1 to second half ... start from the end of the list
					for i in reversed(range(seq_len // 2       )       ):
										UpperCamelCase__       :List[Any]							 =			'''1''' + smaller_sequence[i]
										sequence.append(__a       )

					return sequence


if __name__ == "__main__":
		import doctest

		doctest.testmod()



'''simple docstring'''
from collections import Counter
from timeit import timeit


def       a				(      __a = ""			, )  ->     bool:



					'''simple docstring'''






					return sum(c % 2 for c in Counter(input_str.replace(''' '''			, ''''''       ).lower()       ).values()       ) < 2


def       a				(      __a = ""       )  ->     bool:



					'''simple docstring'''






					if len(__a       ) == 0:
										return True
					UpperCamelCase__       :List[Any]							 =			input_str.replace(''' '''			, ''''''       ).lower()
					# character_freq_dict: Stores the frequency of every character in the input string
					UpperCamelCase__       :dict[str, int]							 =			{}

					for character in lower_case_input_str:
										UpperCamelCase__       :Optional[int]							 =			character_freq_dict.get(__a			, 0       ) + 1
					UpperCamelCase__       :List[str]							 =			0

					for character_count in character_freq_dict.values():
										if character_count % 2:
															odd_char += 1
					if odd_char > 1:
										return False
					return True


def       a				(      __a = ""       )  ->     None:



					'''simple docstring'''






					print('''\nFor string = '''			, __a			, ''':'''       )
					print(
					    '''> can_string_be_rearranged_as_palindrome_counter()'''			, '''\tans ='''			, can_string_be_rearranged_as_palindrome_counter(__a       )			, '''\ttime ='''			, timeit(
					        '''z.can_string_be_rearranged_as_palindrome_counter(z.check_str)'''			, setup='''import __main__ as z'''			, )			, '''seconds'''			, )
					print(
					    '''> can_string_be_rearranged_as_palindrome()'''			, '''\tans ='''			, can_string_be_rearranged_as_palindrome(__a       )			, '''\ttime ='''			, timeit(
					        '''z.can_string_be_rearranged_as_palindrome(z.check_str)'''			, setup='''import __main__ as z'''			, )			, '''seconds'''			, )


if __name__ == "__main__":
		__snake_case											=					input(
		    '''Enter string to determine if it can be rearranged as a palindrome or not: '''
		).strip()
		benchmark(check_str)
		__snake_case											=					can_string_be_rearranged_as_palindrome_counter(check_str)
		print(F"""{check_str} can {'' if status else 'not '}be rearranged as a palindrome""")