
"""simple docstring"""


from __future__ import annotations



def        _lowerCamelCase(__UpperCamelCase			)							->					set[int]:
	_lowerCAmelCase								={1}
	_lowerCAmelCase								=[1]
	for _ in range(2       ,					depth + 1			):
		_lowerCAmelCase								=[*previous_coefficients, 0]
		_lowerCAmelCase								=[0, *previous_coefficients]
		_lowerCAmelCase								=[]
		for x, y in zip(__UpperCamelCase       ,					__UpperCamelCase			):
			coefficients.add(x + y			)
			previous_coefficients.append(x + y			)
	return coefficients



def        _lowerCamelCase(__UpperCamelCase			)							->					set[int]:
	_lowerCAmelCase								=set()
	for number in unique_coefficients:
		_lowerCAmelCase								=2
		_lowerCAmelCase								=number
		while divisor**2 <= copy_number:
			_lowerCAmelCase								=0
			while copy_number % divisor == 0:
				copy_number //= divisor
				multiplicity += 1
			if multiplicity >= 2:
				non_squarefrees.add(__UpperCamelCase			)
				break
			divisor += 1

	return unique_coefficients.difference(__UpperCamelCase			)



def        _lowerCamelCase(__UpperCamelCase = 51			)							->					int:
	_lowerCAmelCase								=get_pascal_triangle_unique_coefficients(__UpperCamelCase			)
	_lowerCAmelCase								=get_squarefrees(__UpperCamelCase			)
	return sum(__UpperCamelCase			)


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





"""simple docstring"""


import math



def        _lowerCamelCase(__UpperCamelCase			)							->					bool:

	if 1 < number < 4:
		# 2 and 3 are primes
		return True
	elif number < 2 or number % 2 == 0 or number % 3 == 0:
		# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
		return False

	# All primes number are in format of 6k +/- 1
	for i in range(5       ,					int(math.sqrt(__UpperCamelCase			) + 1			)       ,					6			):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True



def        _lowerCamelCase(__UpperCamelCase = 600851475143			)							->					int:

	try:
		_lowerCAmelCase								=int(__UpperCamelCase			)
	except (TypeError, ValueError):
		raise TypeError("""Parameter n must be int or castable to int."""			)
	if n <= 0:
		raise ValueError("""Parameter n must be greater than or equal to one."""			)
	_lowerCAmelCase								=0
	if is_prime(__UpperCamelCase			):
		return n
	while n % 2 == 0:
		n //= 2
	if is_prime(__UpperCamelCase			):
		return n
	for i in range(3       ,					int(math.sqrt(__UpperCamelCase			)			) + 1       ,					2			):
		if n % i == 0:
			if is_prime(n // i			):
				_lowerCAmelCase								=n // i
				break
			elif is_prime(__UpperCamelCase			):
				_lowerCAmelCase								=i
	return max_number


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



