


from math import isqrt, loga
def   _UpperCamelCase				(						lowerCAmelCase_   )						->list[int]:
   UpperCAmelCase							=     [True] * max_number
   for i in range(2  ,						isqrt(max_number - 1   ) + 1   ):
      if is_prime[i]:
         for j in range(i**2  ,						lowerCAmelCase_  ,						lowerCAmelCase_   ):
            UpperCAmelCase							=     False

   return [i for i in range(2  ,						lowerCAmelCase_   ) if is_prime[i]]
def   _UpperCamelCase				(						lowerCAmelCase_ = 8_0_0_8_0_0  ,						lowerCAmelCase_ = 8_0_0_8_0_0   )						->int:
   UpperCAmelCase							=     degree * loga(lowerCAmelCase_   )
   UpperCAmelCase							=     int(lowerCAmelCase_   )
   UpperCAmelCase							=     calculate_prime_numbers(lowerCAmelCase_   )

   UpperCAmelCase							=     0
   UpperCAmelCase							=     0
   UpperCAmelCase							=     len(lowerCAmelCase_   ) - 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() = }""")







from __future__ import annotations
def   _UpperCamelCase				(						lowerCAmelCase_   )						->None:
   create_state_space_tree(lowerCAmelCase_  ,						[]  ,						0  ,						[0 for i in range(len(lowerCAmelCase_   )   )]   )
def   _UpperCamelCase				(						lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_  ,						lowerCAmelCase_  ,						)						->None:

   if index == len(lowerCAmelCase_   ):
      print(lowerCAmelCase_   )
      return

   for i in range(len(lowerCAmelCase_   )   ):
      if not index_used[i]:
         current_sequence.append(sequence[i]   )
         UpperCAmelCase							=     True
         create_state_space_tree(lowerCAmelCase_  ,						lowerCAmelCase_  ,						index + 1  ,						lowerCAmelCase_   )
         current_sequence.pop()
         UpperCAmelCase							=     False
__a     =			[3, 1, 2, 4]
generate_all_permutations(sequence)

__a     =			["A", "B", "C"]







generate_all_permutations(sequence_a)



