




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

					__UpperCamelCase					:	int             =      str(bin(snake_case				)				)
					binary_number += "0" * shift_amount
					return binary_number





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

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





def 				A__ (snake_case   :		int		,	snake_case   :		int				)     ->						str:
					if number >= 0:  # Get binary representation of positive number
										__UpperCamelCase					:	Optional[Any]             =      """0""" + str(bin(snake_case				)				).strip("""-"""				)[2:]
					else:  # Get binary (2's complement) representation of negative number
										__UpperCamelCase					:	List[str]             =      len(bin(snake_case				)[3:]				)  # Find 2's complement of number
										__UpperCamelCase					:	Optional[Any]             =      bin(abs(snake_case				) - (1 << binary_number_length)				)[3:]
										__UpperCamelCase					:	Union[str, Any]             =      (
										    """1""" + """0""" * (binary_number_length - len(snake_case				)) + binary_number
										)

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


if __name__ == "__main__":
	import doctest

	doctest.testmod()












from collections import defaultdict





def 				A__ (snake_case   :		int				)     ->						int:
					__UpperCamelCase					:	Optional[int]             =      1
					__UpperCamelCase					:	Tuple             =      True
					for v in tree[start]:
										if v not in visited:
															ret += dfs(snake_case				)
					if ret % 2 == 0:
										cuts.append(snake_case				)
					return ret





def 				A__ ()     ->						str:
					dfs(1				)


if __name__ == "__main__":
	a__     ,							a__		     =     10, 9
	a__		     =     defaultdict(list)
	a__		     =     {}
	a__		     =     []
	a__		     =     0
	a__		     =     [(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (10, 8)]
	for u, v in edges:
		tree[u].append(v)
		tree[v].append(u)
	even_tree()
	print(len(cuts) - 1)






