


'''simple docstring'''



from __future__ import annotations

from functools import lru_cache
from math import ceil

_lowercase      :      Any            =					100

_lowercase      :      List[Any]            =					set(range(3, NUM_PRIMES, 2))
primes.add(2)
_lowercase      :      Optional[int]            =					42

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=1_00					)
def 				lowerCamelCase__				(	A       :      Union[str, Any]					):




						'''simple docstring'''






						if number_to_partition < 0:
												return set()
						elif number_to_partition == 0:
												return {1}

						UpperCAmelCase					    =     set()
						UpperCAmelCase					    =     42
						UpperCAmelCase					    =     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 				lowerCamelCase__				(	A       :      Dict = 50_00					):




						'''simple docstring'''






						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 				lowerCamelCase__				(	A       :      int				,       A       :      int					):




						'''simple docstring'''






						return int(input_a == input_a == 0					)


def 				lowerCamelCase__				(	):




						'''simple docstring'''






						print('''Truth Table of NOR Gate:'''					)
						print('''|   Input 1   |  Input 2  | Output |'''					)
						print(f"""|      0      |    0      |  {nor_gate(0				,       0					)}     |"""					)
						print(f"""|      0      |    1      |  {nor_gate(0				,       1					)}     |"""					)
						print(f"""|      1      |    0      |  {nor_gate(1				,       0					)}     |"""					)
						print(f"""|      1      |    1      |  {nor_gate(1				,       1					)}     |"""					)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()





