"""simple docstring"""






def   a_						(					lowerCamelCase					,			lowerCamelCase       ):
				if number < 0 or shift_amount < 0:
								raise ValueError('both inputs must be positive integers'       )

				UpperCAmelCase__             =							str(bin(lowerCamelCase       )       )
				binary_number += "0" * shift_amount
				return binary_number



def   a_						(					lowerCamelCase					,			lowerCamelCase       ):
				if number < 0 or shift_amount < 0:
								raise ValueError('both inputs must be positive integers'       )

				UpperCAmelCase__             =							str(bin(lowerCamelCase       )       )[2:]
				if shift_amount >= len(lowerCamelCase       ):
								return "0b0"
				UpperCAmelCase__             =							binary_number[: len(lowerCamelCase       ) - shift_amount]
				return "0b" + shifted_binary_number



def   a_						(					lowerCamelCase					,			lowerCamelCase       ):
				if number >= 0:  # Get binary representation of positive number
								UpperCAmelCase__             =							'0' + str(bin(lowerCamelCase       )       ).strip('-'       )[2:]
				else:  # Get binary (2's complement) representation of negative number
								UpperCAmelCase__             =							len(bin(lowerCamelCase       )[3:]       )  # Find 2's complement of number
								UpperCAmelCase__             =							bin(abs(lowerCamelCase       ) - (1 << binary_number_length)       )[3:]
								UpperCAmelCase__             =							(
								    '1' + '0' * (binary_number_length - len(lowerCamelCase       )) + binary_number
								)

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


if __name__ == "__main__":
						import doctest

						doctest.testmod()




"""simple docstring"""






def   a_						(					lowerCamelCase       ):
				return str(lowerCamelCase       ) == str(lowerCamelCase       )[::-1]



def   a_						(					lowerCamelCase       ):
				return int(lowerCamelCase       ) + int(str(lowerCamelCase       )[::-1]       )



def   a_						(					lowerCamelCase = 1_0_0_0_0       ):
				UpperCAmelCase__             =							[]
				for num in range(1					,			lowerCamelCase       ):
								UpperCAmelCase__             =							0
								UpperCAmelCase__             =							num
								while iterations < 5_0:
												UpperCAmelCase__             =							sum_reverse(lowerCamelCase       )
												iterations += 1
												if is_palindrome(lowerCamelCase       ):
																break
								else:
												lychrel_nums.append(lowerCamelCase       )
				return len(lowerCamelCase       )


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



