



"""simple docstring"""
from math import isqrt, loga
def    A_  (			_lowercase	):







						'''simple docstring'''


						snake_case_ :Tuple						=			[True] * max_number
						for i in range(2,					isqrt(max_number - 1	) + 1	):
												if is_prime[i]:
																		for j in range(i**2,					_lowercase,					_lowercase	):
																								snake_case_ :Dict						=			False

						return [i for i in range(2,					_lowercase	) if is_prime[i]]
def    A_  (			_lowercase = 800800,					_lowercase = 800800	):







						'''simple docstring'''


						snake_case_ :Union[str, Any]						=			degree * loga(_lowercase	)
						snake_case_ :Tuple						=			int(_lowercase	)
						snake_case_ :List[str]						=			calculate_prime_numbers(_lowercase	)

						snake_case_ :Union[str, Any]						=			0
						snake_case_ :List[str]						=			0
						snake_case_ :Optional[Any]						=			len(_lowercase	) - 1
						while left < right:
												while (
												    prime_numbers[right] * loga(prime_numbers[left]	)
												    + prime_numbers[left] * loga(prime_numbers[right]	)
												    > upper_bound
												):
																		right -= 1
												hybrid_integers_count += right - left
												left += 1

						return hybrid_integers_count


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








"""simple docstring"""






from __future__ import annotations




class 							lowerCAmelCase__				:






      '''simple docstring'''

      def __init__(						self     :  Any						,	lowercase_     :  int = 0):




          '''simple docstring'''


          SCREAMING_SNAKE_CASE_      :  List[Any]    						=		key
      def _SCREAMING_SNAKE_CASE (						self     :  Any						,	lowercase_     :  str						,	lowercase_     :  int):




          '''simple docstring'''


          assert isinstance(lowercase_						,	lowercase_) and isinstance(lowercase_						,	lowercase_)

          SCREAMING_SNAKE_CASE_      :  Dict    						=		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 _SCREAMING_SNAKE_CASE (						self     :  str						,	lowercase_     :  str						,	lowercase_     :  int):




          '''simple docstring'''


          assert isinstance(lowercase_						,	lowercase_) and isinstance(lowercase_						,	lowercase_)

          SCREAMING_SNAKE_CASE_      :  Union[str, Any]    						=		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 _SCREAMING_SNAKE_CASE (						self     :  Tuple						,	lowercase_     :  str						,	lowercase_     :  int = 0):




          '''simple docstring'''


          assert isinstance(lowercase_						,	lowercase_) and isinstance(lowercase_						,	lowercase_)

          SCREAMING_SNAKE_CASE_      :  int    						=		key or self.__key or 1

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

          # This will be returned
          SCREAMING_SNAKE_CASE_      :  List[str]    						=		''''''

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

          return ans
      def _SCREAMING_SNAKE_CASE (						self     :  int						,	lowercase_     :  str						,	lowercase_     :  int = 0):




          '''simple docstring'''


          assert isinstance(lowercase_						,	lowercase_) and isinstance(lowercase_						,	lowercase_)

          SCREAMING_SNAKE_CASE_      :  Union[str, Any]    						=		key or self.__key or 1

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

          # This will be returned
          SCREAMING_SNAKE_CASE_      :  List[Any]    						=		''''''

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

          return ans
      def _SCREAMING_SNAKE_CASE (						self     :  str						,	lowercase_     :  str						,	lowercase_     :  int = 0):




          '''simple docstring'''


          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 _SCREAMING_SNAKE_CASE (						self     :  Optional[int]						,	lowercase_     :  str						,	lowercase_     :  int):




          '''simple docstring'''


          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")


