





"""simple docstring"""





import math


def       UpperCAmelCase__							(  SCREAMING_SNAKE_CASE					:						int      ):







      '''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(SCREAMING_SNAKE_CASE      ) + 1      )							,						6      ):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True


def       UpperCAmelCase__							(  SCREAMING_SNAKE_CASE					:						int = 2_00_00_00      ):







      '''simple docstring'''




      return sum(num for num in range(3							,						SCREAMING_SNAKE_CASE							,						2      ) if is_prime(SCREAMING_SNAKE_CASE      )      ) + 2 if n > 2 else 0


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













"""simple docstring"""





def       UpperCAmelCase__							(  SCREAMING_SNAKE_CASE					:						int							,						SCREAMING_SNAKE_CASE					:						int      ):







      '''simple docstring'''




      lowerCAmelCase  						=	1.0
      for i in range(1							,						r + 1      ):
            ret *= (n + 1 - i) / i
      return round(SCREAMING_SNAKE_CASE      )


def       UpperCAmelCase__							(  SCREAMING_SNAKE_CASE					:						int      ):







      '''simple docstring'''




      return choose(8 + n							,						SCREAMING_SNAKE_CASE      ) + choose(9 + n							,						SCREAMING_SNAKE_CASE      ) - 10


def       UpperCAmelCase__							(  SCREAMING_SNAKE_CASE					:						int      ):







      '''simple docstring'''




      return sum(non_bouncy_exact(SCREAMING_SNAKE_CASE      ) for i in range(1							,						n + 1      )      )


def       UpperCAmelCase__							(  SCREAMING_SNAKE_CASE					:						int = 1_00      ):







      '''simple docstring'''




      return non_bouncy_upto(SCREAMING_SNAKE_CASE      )


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






