
from __future__ import annotations




def   UpperCamelCase__     (    SCREAMING_SNAKE_CASE_  :  list[int | float]		,      SCREAMING_SNAKE_CASE_  :  int		,      SCREAMING_SNAKE_CASE_  :  int					)     ->    Optional[int]:







						if len(SCREAMING_SNAKE_CASE_					) == 0:
												raise ValueError("""find_min() arg is an empty sequence"""					)
						if (
						    left >= len(SCREAMING_SNAKE_CASE_					)
						    or left < -len(SCREAMING_SNAKE_CASE_					)
						    or right >= len(SCREAMING_SNAKE_CASE_					)
						    or right < -len(SCREAMING_SNAKE_CASE_					)
						):
												raise IndexError("""list index out of range"""					)
						if left == right:
												return nums[left]
						_lowercase									=				(left + right) >> 1  # the middle
						_lowercase									=				find_min(SCREAMING_SNAKE_CASE_		,      SCREAMING_SNAKE_CASE_		,      SCREAMING_SNAKE_CASE_					)  # find min in range[left, mid]
						_lowercase									=				find_min(SCREAMING_SNAKE_CASE_		,      mid + 1		,      SCREAMING_SNAKE_CASE_					)  # find min in range[mid + 1, right]

						return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
		import doctest

		doctest.testmod(verbose=True)

def   UpperCamelCase__     (    SCREAMING_SNAKE_CASE_  :  int					)     ->    int:
						return n * (2 * n - 1)




def   UpperCamelCase__     (    SCREAMING_SNAKE_CASE_  :  int					)     ->    bool:
						_lowercase									=				(1 + 24 * n) ** 0.5
						return ((1 + root) / 6) % 1 == 0




def   UpperCamelCase__     (    SCREAMING_SNAKE_CASE_  :  int = 1_44					)     ->    int:
						_lowercase									=				start
						_lowercase									=				hexagonal_num(SCREAMING_SNAKE_CASE_					)
						while not is_pentagonal(SCREAMING_SNAKE_CASE_					):
												n += 1
												_lowercase									=				hexagonal_num(SCREAMING_SNAKE_CASE_					)
						return num


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