


"""simple docstring"""
from __future__ import annotations







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







def     _a					(   _SCREAMING_SNAKE_CASE					)     ->					set[int]:
							snake_case_     							=		set()
							for number in unique_coefficients:
														snake_case_     							=		2
														snake_case_     							=		number
														while divisor**2 <= copy_number:
																					snake_case_     							=		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     _a					(   _SCREAMING_SNAKE_CASE = 51					)     ->					int:
							snake_case_     							=		get_pascal_triangle_unique_coefficients(__UpperCamelCase					)
							snake_case_     							=		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() = }""")



