






'''simple docstring'''







a__  : Optional[Any]				=	{
    "0000": "0",
    "0001": "1",
    "0010": "2",
    "0011": "3",
    "0100": "4",
    "0101": "5",
    "0110": "6",
    "0111": "7",
    "1000": "8",
    "1001": "9",
    "1010": "a",
    "1011": "b",
    "1100": "c",
    "1101": "d",
    "1110": "e",
    "1111": "f",
}







def _UpperCamelCase	(					__A   )							->		str:


      '''simple docstring'''



      UpperCamelCase__  =    str(__lowercase   ).strip()

      # Exceptions
      if not binary_str:
            raise ValueError("Empty string was passed to the function"   )
      UpperCamelCase__  =    binary_str[0] == "-"
      UpperCamelCase__  =    binary_str[1:] if is_negative else binary_str
      if not all(char in "01" for char in binary_str   ):
            raise ValueError("Non-binary value was passed to the function"   )

      UpperCamelCase__  =    (
          "0" * (4 * (divmod(len(__lowercase   )				,      4   )[0] + 1) - len(__lowercase   )) + binary_str
      )

      UpperCamelCase__  =    []
      for x in range(0				,      len(__lowercase   )				,      4   ):
            hexadecimal.append(BITS_TO_HEX[binary_str[x : x + 4]]   )
      UpperCamelCase__  =    "0x" + "".join(__lowercase   )

      return "-" + hexadecimal_str if is_negative else hexadecimal_str


if __name__ == "__main__":
  from doctest import testmod

  testmod()









'''simple docstring'''







import math







def _UpperCamelCase	(					__A   )							->		bool:


      '''simple docstring'''



      if 1 < number < 4:
            # 2 and 3 are primes
            return True
      elif number < 2 or number % 2 == 0 or number % 3 == 0:
            # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
            return False

      # All primes number are in format of 6k +/- 1
      for i in range(5				,      int(math.sqrt(__A   ) + 1   )				,      6   ):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True







def _UpperCamelCase	(					__A = 1000				,      __A = 1000   )							->		int:


      '''simple docstring'''



      UpperCamelCase__  =    [0, 0, 0]  # length, a, b
      for a in range((a_limit * -1) + 1				,      __A   ):
            for b in range(2				,      __A   ):
                  if is_prime(__A   ):
                        UpperCamelCase__  =    0
                        UpperCamelCase__  =    0
                        while is_prime((n**2) + (a * n) + b   ):
                              count += 1
                              n += 1
                        if count > longest[0]:
                              UpperCamelCase__  =    [count, a, b]
      UpperCamelCase__  =    longest[1] * longest[2]
      return ans


if __name__ == "__main__":
  print(solution(1_0_0_0, 1_0_0_0))





