



'''simple docstring'''




from __future__ import annotations







class      _lowerCAmelCase							:


	def __init__(self	,				lowercase = 0							):
				A_     :						Dict     =					key


	def    _a     (self	,				lowercase	,				lowercase							):
				assert isinstance(lowercase	,				lowercase							) and isinstance(lowercase	,				lowercase							)

				A_     :						Tuple     =					key or self.__key or 1

				# make sure key is an appropriate size
				key %= 255

				return [chr(ord(lowercase							) ^ key							) for ch in content]


	def    _a     (self	,				lowercase	,				lowercase							):
				assert isinstance(lowercase	,				lowercase							) and isinstance(lowercase	,				lowercase							)

				A_     :						int     =					key or self.__key or 1

				# make sure key is an appropriate size
				key %= 255

				return [chr(ord(lowercase							) ^ key							) for ch in content]


	def    _a     (self	,				lowercase	,				lowercase = 0							):
				assert isinstance(lowercase	,				lowercase							) and isinstance(lowercase	,				lowercase							)

				A_     :						str     =					key or self.__key or 1

				# make sure key can be any size
				while key > 255:
							key -= 255

				# This will be returned
				A_     :						Optional[int]     =					""""""

				for ch in content:
							ans += chr(ord(lowercase							) ^ key							)

				return ans


	def    _a     (self	,				lowercase	,				lowercase = 0							):
				assert isinstance(lowercase	,				lowercase							) and isinstance(lowercase	,				lowercase							)

				A_     :						int     =					key or self.__key or 1

				# make sure key can be any size
				while key > 255:
							key -= 255

				# This will be returned
				A_     :						Any     =					""""""

				for ch in content:
							ans += chr(ord(lowercase							) ^ key							)

				return ans


	def    _a     (self	,				lowercase	,				lowercase = 0							):
				assert isinstance(lowercase	,				lowercase							) and isinstance(lowercase	,				lowercase							)

				try:
							with open(lowercase							) as fin, open("""encrypt.out"""	,				"""w+"""							) as fout:
										# actual encrypt-process
										for line in fin:
													fout.write(self.encrypt_string(lowercase	,				lowercase							)							)

				except OSError:
							return False

				return True


	def    _a     (self	,				lowercase	,				lowercase							):
				assert isinstance(lowercase	,				lowercase							) and isinstance(lowercase	,				lowercase							)

				try:
							with open(lowercase							) as fin, open("""decrypt.out"""	,				"""w+"""							) as fout:
										# actual encrypt-process
										for line in fin:
													fout.write(self.decrypt_string(lowercase	,				lowercase							)							)

				except OSError:
							return False

				return True


# Tests
# crypt = XORCipher()
# key = 67

# # test encrypt
# print(crypt.encrypt("hallo welt",key))
# # test decrypt
# print(crypt.decrypt(crypt.encrypt("hallo welt",key), key))

# # test encrypt_string
# print(crypt.encrypt_string("hallo welt",key))

# # test decrypt_string
# print(crypt.decrypt_string(crypt.encrypt_string("hallo welt",key),key))

# if (crypt.encrypt_file("test.txt",key)):
#       print("encrypt successful")
# else:
#       print("encrypt unsuccessful")

# if (crypt.decrypt_file("encrypt.out",key)):
#       print("decrypt successful")
# else:
#       print("decrypt unsuccessful")




'''simple docstring'''




from __future__ import annotations

from functools import lru_cache
from math import ceil

lowerCamelCase							:List[str]       = 1_0_0

lowerCamelCase							:Dict       = set(range(3, NUM_PRIMES, 2))
primes.add(2)
lowerCamelCase							: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=1_00   )
def      a      (			lowerCamelCase__   ):
			'''simple docstring'''





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

			A_     :						set[int]     =					set()
			A_     :						int
			A_     :						int

			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      a      (			lowerCamelCase__ = 50_00   ):
			'''simple docstring'''





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


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