"""simple docstring"""






import math


def      UpperCAmelCase__			(							lowerCAmelCase__	:Union[str, Any]						)					->       bool:
      '''simple docstring'''


      assert isinstance(lowerCAmelCase__   ,						lowerCAmelCase__						) and (
          number >= 0
      ), "'number' must been an int and positive"

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

      lowercase								=      range(3   ,						int(math.sqrt(lowerCAmelCase__						) + 1						)   ,						2						)
      return not any(not number % i for i in odd_numbers						)






def      UpperCAmelCase__			(							lowerCAmelCase__	:Union[str, Any]   ,						lowerCAmelCase__	:Tuple=1   ,						**lowerCAmelCase__	:Union[str, Any]						)					->       str:
      '''simple docstring'''


      lowercase								=      factor * value
      lowercase								=      value

      while not is_prime(lowerCAmelCase__						):
            value += 1 if not ("desc" in kwargs and kwargs["desc"] is True) else -1

      if value == first_value_val:
            return next_prime(value + 1   ,						**lowerCAmelCase__						)
      return value





"""simple docstring"""






def      lowerCAmelCase__			(		__magic_name__ = 1_0      )						->str:
			if not isinstance(__magic_name__			,   __magic_name__      ) or n < 0:
						raise ValueError("Invalid input"      )
			__lowercase       =       1_0**n
			__lowercase       =       2_8_4_3_3 * (pow(2			,   7_8_3_0_4_5_7			,   __magic_name__      )) + 1
			return str(number % modulus      )


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

					testmod()
					print(F"{solution(10) = }")





