


"""simple docstring"""




def       a_ (	lowercase__ :int = 1000     ):
			__lowerCamelCase          =      -1
			__lowerCamelCase          =      0
			for a in range(1,			n // 3     ):
						# Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
						__lowerCamelCase          =      (n * n - 2 * a * n) // (2 * n - 2 * a)
						__lowerCamelCase          =      n - a - b
						if c * c == (a * a + b * b):
									__lowerCamelCase          =      a * b * c
									if candidate >= product:
												__lowerCamelCase          =      candidate
			return product


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








"""simple docstring"""




from collections import defaultdict





def       a_ (	lowercase__ :int     ):
			__lowerCamelCase          =      1
			__lowerCamelCase          =      True
			for v in tree[start]:
						if v not in visited:
									ret += dfs(lowercase__     )
			if ret % 2 == 0:
						cuts.append(lowercase__     )
			return ret





def       a_ (	):
			dfs(1     )


if __name__ == "__main__":
					__magic_name__  , __magic_name__						: Tuple    =				1_0, 9
					__magic_name__						: Tuple    =				defaultdict(list)
					__magic_name__						: dict[int, bool]    =				{}
					__magic_name__						: list[int]    =				[]
					__magic_name__						: List[str]    =				0
					__magic_name__						: Tuple    =				[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (1_0, 8)]
					for u, v in edges:
										tree[u].append(v)
										tree[v].append(u)
					even_tree()
					print(len(cuts) - 1)




