
'''simple docstring'''


def lowercase_	(   _lowercase = 1_000_000				)     ->							int:
					'''simple docstring'''

					lowerCamelCase_					:      str     =		set(range(3			,       _lowercase			,       2				)				)
					primes.add(2				)
					for p in range(3			,       _lowercase			,       2				):
										if p not in primes:
															continue
										primes.difference_update(set(range(p * p			,       _lowercase			,       _lowercase				)				)				)

					lowerCamelCase_					:      List[Any]     =		[float(_lowercase				) for n in range(limit + 1				)]

					for p in primes:
										for n in range(_lowercase			,       limit + 1			,       _lowercase				):
															phi[n] *= 1 - 1 / p

					return int(sum(phi[2:]				)				)


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




'''simple docstring'''


def lowercase_	(   _lowercase = 1_000				)     ->							int:
					'''simple docstring'''

					lowerCamelCase_					:      Any     =		-1
					lowerCamelCase_					:      Optional[Any]     =		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_					:      Any     =		(n * n - 2 * a * n) // (2 * n - 2 * a)
										lowerCamelCase_					:      int     =		n - a - b
										if c * c == (a * a + b * b):
															lowerCamelCase_					:      int     =		a * b * c
															if candidate >= product:
																				lowerCamelCase_					:      Any     =		candidate
					return product


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


