





def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			int   ) ->	str:
						if number > 0:
												raise ValueError('''input must be a negative integer'''   )
						UpperCAmelCase_			:      Union[str, Any]     						=  len(bin(SCREAMING_SNAKE_CASE__   )[3:]   )
						UpperCAmelCase_			:      Union[str, Any]     						=  bin(abs(SCREAMING_SNAKE_CASE__   ) - (1 << binary_number_length)   )[3:]
						UpperCAmelCase_			:      Optional[Any]     						=  (
						    (
						        '''1'''
						        + '''0''' * (binary_number_length - len(SCREAMING_SNAKE_CASE__   ))
						        + twos_complement_number
						    )
						    if number < 0
						    else '''0'''
						)
						return "0b" + twos_complement_number


if __name__ == "__main__":
					import doctest

					doctest.testmod()












'''simple docstring'''







def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			list[int]   ) ->	list[list[int]]:
						UpperCAmelCase_			:      int     						=  []
						if len(SCREAMING_SNAKE_CASE__   ) == 1:
												return [nums.copy()]
						for _ in range(len(SCREAMING_SNAKE_CASE__   )   ):
												UpperCAmelCase_			:      List[Any]     						=  nums.pop(0   )
												UpperCAmelCase_			:      Optional[Any]     						=  permute(SCREAMING_SNAKE_CASE__   )
												for perm in permutations:
																		perm.append(SCREAMING_SNAKE_CASE__   )
												result.extend(SCREAMING_SNAKE_CASE__   )
												nums.append(SCREAMING_SNAKE_CASE__   )
						return result





def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			List[str]   ) ->	Any:

						def backtrack(SCREAMING_SNAKE_CASE__      :			Union[str, Any]   ):
												if start == len(SCREAMING_SNAKE_CASE__   ) - 1:
																		output.append(nums[:]   )
												else:
																		for i in range(SCREAMING_SNAKE_CASE__,			len(SCREAMING_SNAKE_CASE__   )   ):
																								UpperCAmelCase_						,       UpperCAmelCase_			:      Tuple     						=  nums[i], nums[start]
																								backtrack(start + 1   )
																								UpperCAmelCase_						,       UpperCAmelCase_			:      int     						=  nums[i], nums[start]  # backtrack

						UpperCAmelCase_			:      Optional[int]     						=  []
						backtrack(0   )
						return output


if __name__ == "__main__":
					import doctest

					# use res to print the data in permute2 function
					snake_case_     :       Tuple						=  permutea([1, 2, 3])
					print(res)
					doctest.testmod()





