






'''simple docstring'''


def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__		):
 return n * (2 * n - 1)






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__		):
 __a    :	List[Any]									=						(1 + 24 * n) ** 0.5
 return ((1 + root) / 6) % 1 == 0






def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__ = 144		):
 __a    :	int									=						start
 __a    :	Dict									=						hexagonal_num(SCREAMING_SNAKE_CASE__		)
 while not is_pentagonal(SCREAMING_SNAKE_CASE__		):
  n += 1
  __a    :	Union[str, Any]									=						hexagonal_num(SCREAMING_SNAKE_CASE__		)
 return num


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












'''simple docstring'''


def   lowerCAmelCase__			(					SCREAMING_SNAKE_CASE__ = 30		):
 __a    :	Tuple									=						exponent + 2
 __a    :	str									=						(1 + 5**0.5) / 2
 __a    :	Any									=						(phi**fibonacci_index - (phi - 1) ** fibonacci_index) / 5**0.5

 return int(SCREAMING_SNAKE_CASE__		)


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




