


def     __lowerCamelCase						(			UpperCAmelCase_						:		int						):




						"""simple docstring"""





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

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

						return sequence
def     __lowerCamelCase						(			UpperCAmelCase_						:		int						):




						"""simple docstring"""





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

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

						a						:Union[str, Any]										=	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
						a						:Optional[int]										=	gray_code_sequence_string(bit_count - 1						)

						a						:Optional[Any]										=	[]

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

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

						return sequence


if __name__ == "__main__":
					import doctest

					doctest.testmod()









def     __lowerCamelCase						(			UpperCAmelCase_						:		int = 100						):




      """simple docstring"""





      a						:List[Any]										=	0
      a						:List[Any]										=	0
      for i in range(1			,  n + 1						):
            sum_of_squares += i**2
            sum_of_ints += i
      return sum_of_ints**2 - sum_of_squares


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





