

'''simple docstring'''



def    a__       (  a__ = 1_00						):




     """simple docstring"""


     __SCREAMING_SNAKE_CASE     =      n * (n + 1) * (2 * n + 1) / 6
     __SCREAMING_SNAKE_CASE     =      (n * (n + 1) / 2) ** 2
     return int(square_of_sum - sum_of_squares						)


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













'''simple docstring'''




import math






def        _lowerCAmelCase			(  __snake_case  : int			)     ->     bool:

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






def        _lowerCAmelCase			(  __snake_case  : float = 0.1			)     ->     int:
     __A						: Tuple      =       3
     __A						: Optional[int]      =       3

     while primes / (2 * j - 1) >= ratio:
          for i in range(j * j + j + 1 ,							(j + 2) * (j + 2) ,							j + 1			):
               primes += is_prime(__snake_case			)
          j += 2
     return j


if __name__ == "__main__":
  import doctest

  doctest.testmod()