
'''simple docstring'''







from __future__ import annotations

from functools import lru_cache
from math import ceil

lowercase    :							Tuple      =					100

lowercase    :							Dict      =					set(range(3, NUM_PRIMES, 2))
primes.add(2)
lowercase    :							int

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
					if prime not in primes:
										continue
					primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))







@lru_cache(maxsize=100	)
def 				SCREAMING_SNAKE_CASE__	(   __A	)       ->	set[int]:
	if number_to_partition < 0:
		return set()
	elif number_to_partition == 0:
		return {1}

	_snake_case   						=		set()
	_snake_case   						=		42
	_snake_case   						=		42

	for prime in primes:
		if prime > number_to_partition:
			continue
		for sub in partition(number_to_partition - prime	):
			ret.add(sub * prime	)

	return ret







def 				SCREAMING_SNAKE_CASE__	(   __A = 5_000	)       ->	int | None:
	for number_to_partition in range(1			,				__A	):
		if len(partition(__A	)	) > number_unique_partitions:
			return number_to_partition
	return None


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



'''simple docstring'''







def 				SCREAMING_SNAKE_CASE__	(   __A = 100	)       ->	int:
	_snake_case   						=		n * (n + 1) * (2 * n + 1) / 6
	_snake_case   						=		(n * (n + 1) / 2) ** 2
	return int(square_of_sum - sum_of_squares	)


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

