





'''simple docstring'''




def        _lowerCAmelCase			(  __snake_case  : int = 50			)     ->     int:
     __A						: Optional[Any]      =       [[0] * 3 for _ in range(length + 1			)]

     for row_length in range(length + 1			):
          for tile_length in range(2 ,							5			):
               for tile_start in range(row_length - tile_length + 1			):
                    different_colour_ways_number[row_length][tile_length - 2] += (
                        different_colour_ways_number[row_length - tile_start - tile_length][
                            tile_length - 2
                        ]
                        + 1
                    )

     return sum(different_colour_ways_number[length]			)


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()