


'''simple docstring'''





from __future__ import annotations

__UpperCamelCase    		=       1_0
def        UpperCamelCase_(				_A   :list[int]  )->		Dict:
			UpperCamelCase__					=       1
			UpperCamelCase__					=       max(_A  )
			while placement <= max_digit:
						# declare and initialize empty buckets
						UpperCamelCase__					=       [[] for _ in range(_A  )]
						# split list_of_ints between the buckets
						for i in list_of_ints:
									UpperCamelCase__					=       int((i / placement) % RADIX  )
									buckets[tmp].append(_A  )
						# put each buckets' contents into list_of_ints
						UpperCamelCase__					=       0
						for b in range(_A  ):
									for i in buckets[b]:
												UpperCamelCase__					=       i
												a += 1
												# move to next
						placement *= RADIX
			return list_of_ints


if __name__ == "__main__":
						import doctest

						doctest.testmod()






def        UpperCamelCase_(				_A   :int				,     _A   :int  )->		str:
			if number < 0 or shift_amount < 0:
						raise ValueError("both inputs must be positive integers"  )

			UpperCamelCase__					=       str(bin(_A  )  )
			binary_number += "0" * shift_amount
			return binary_number
def        UpperCamelCase_(				_A   :int				,     _A   :int  )->		str:
			if number < 0 or shift_amount < 0:
						raise ValueError("both inputs must be positive integers"  )

			UpperCamelCase__					=       str(bin(_A  )  )[2:]
			if shift_amount >= len(_A  ):
						return "0b0"
			UpperCamelCase__					=       binary_number[: len(_A  ) - shift_amount]
			return "0b" + shifted_binary_number
def        UpperCamelCase_(				_A   :int				,     _A   :int  )->		str:
			if number >= 0:  # Get binary representation of positive number
						UpperCamelCase__					=       "0" + str(bin(_A  )  ).strip("-"  )[2:]
			else:  # Get binary (2's complement) representation of negative number
						UpperCamelCase__					=       len(bin(_A  )[3:]  )  # Find 2's complement of number
						UpperCamelCase__					=       bin(abs(_A  ) - (1 << binary_number_length)  )[3:]
						UpperCamelCase__					=       (
						    "1" + "0" * (binary_number_length - len(_A  )) + binary_number
						)

			if shift_amount >= len(_A  ):
						return "0b" + binary_number[0] * len(_A  )
			return (
			    "0b"
			    + binary_number[0] * shift_amount
			    + binary_number[: len(_A  ) - shift_amount]
			)


if __name__ == "__main__":
						import doctest

						doctest.testmod()


