



"""simple docstring"""




from math import isqrt, loga

def 						__snake_case						(				SCREAMING_SNAKE_CASE__     :						int    )  ->       list[int]:





     '''simple docstring'''

     _UpperCAmelCase      :     Union[str, Any]        =   [True] * max_number
     for i in range(2						,  isqrt(max_number - 1    ) + 1    ):
          if is_prime[i]:
               for j in range(i**2						,  SCREAMING_SNAKE_CASE__						,  SCREAMING_SNAKE_CASE__    ):
                    _UpperCAmelCase      :     List[str]        =   False

     return [i for i in range(2						,  SCREAMING_SNAKE_CASE__    ) if is_prime[i]]

def 						__snake_case						(				SCREAMING_SNAKE_CASE__     :						int = 800_800						,  SCREAMING_SNAKE_CASE__     :						int = 800_800    )  ->       int:





     '''simple docstring'''

     _UpperCAmelCase      :     Tuple        =   degree * loga(SCREAMING_SNAKE_CASE__    )
     _UpperCAmelCase      :     List[str]        =   int(SCREAMING_SNAKE_CASE__    )
     _UpperCAmelCase      :     Any        =   calculate_prime_numbers(SCREAMING_SNAKE_CASE__    )

     _UpperCAmelCase      :     Optional[Any]        =   0
     _UpperCAmelCase      :     Union[str, Any]        =   0
     _UpperCAmelCase      :     Optional[Any]        =   len(SCREAMING_SNAKE_CASE__    ) - 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"""




def 						__snake_case						(				SCREAMING_SNAKE_CASE__     :						List[str]    )  ->       str:





     '''simple docstring'''

     _UpperCAmelCase    ,	_UpperCAmelCase      :     Dict        =   [], []
     while len(SCREAMING_SNAKE_CASE__    ) > 1:
          _UpperCAmelCase    ,	_UpperCAmelCase      :     int        =   min(SCREAMING_SNAKE_CASE__    ), max(SCREAMING_SNAKE_CASE__    )
          start.append(SCREAMING_SNAKE_CASE__    )
          end.append(SCREAMING_SNAKE_CASE__    )
          collection.remove(SCREAMING_SNAKE_CASE__    )
          collection.remove(SCREAMING_SNAKE_CASE__    )
     end.reverse()
     return start + collection + end


if __name__ == "__main__":
 _lowerCAmelCase    : int							=							input("Enter numbers separated by a comma:\n").strip()
 _lowerCAmelCase    : List[str]							=							[int(item) for item in user_input.split(",")]
 print(*merge_sort(unsorted), sep=",")
