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

from functools import lru_cache
from math import ceil

SCREAMING_SNAKE_CASE__   =					100

SCREAMING_SNAKE_CASE__   =					set(range(3, NUM_PRIMES, 2))
primes.add(2)
SCREAMING_SNAKE_CASE__   =					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_0_0   )
def 				lowerCAmelCase__      (     _UpperCamelCase    :			int   )   ->			set[int]:





						"""simple docstring"""






						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 				lowerCAmelCase__      (     _UpperCamelCase    :			int = 5_0_0_0   )   ->			int | None:





						"""simple docstring"""






						for number_to_partition in range(1	,     _UpperCamelCase   ):
												if len(partition(_UpperCamelCase   )   ) > number_unique_partitions:
																		return number_to_partition
						return None


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



"""simple docstring"""
SCREAMING_SNAKE_CASE__   =					{str(digit): digit**5 for digit in range(10)}





def 				lowerCAmelCase__      (     _UpperCamelCase    :			int   )   ->			int:





						"""simple docstring"""






						return sum(DIGITS_FIFTH_POWER[digit] for digit in str(_UpperCamelCase   )   )





def 				lowerCAmelCase__      (     )   ->			int:





						"""simple docstring"""






						return sum(
						    number
						    for number in range(1_0_0_0	,     1_0_0_0_0_0_0   )
						    if number == digits_fifth_powers_sum(_UpperCamelCase   )   )


if __name__ == "__main__":
					print(solution())


