

"""simple docstring"""


def    a__   (   __SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE=False			)     ->     Any:

		if isinstance(__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			) and isinstance(__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			):
				__lowerCAmelCase:	List[Any]   				=      len(set_a.intersection(__SCREAMING_SNAKE_CASE			)			)

				if alternative_union:
						__lowerCAmelCase:	Any   				=      len(__SCREAMING_SNAKE_CASE			) + len(__SCREAMING_SNAKE_CASE			)
				else:
						__lowerCAmelCase:	List[str]   				=      len(set_a.union(__SCREAMING_SNAKE_CASE			)			)

				return intersection / union

		if isinstance(__SCREAMING_SNAKE_CASE ,			(list, tuple)			) and isinstance(__SCREAMING_SNAKE_CASE ,			(list, tuple)			):
				__lowerCAmelCase:	Any   				=      [element for element in set_a if element in set_b]

				if alternative_union:
						__lowerCAmelCase:	Any   				=      len(__SCREAMING_SNAKE_CASE			) + len(__SCREAMING_SNAKE_CASE			)
						return len(__SCREAMING_SNAKE_CASE			) / union
				else:
						__lowerCAmelCase:	Optional[int]   				=      set_a + [element for element in set_b if element not in set_a]
						return len(__SCREAMING_SNAKE_CASE			) / len(__SCREAMING_SNAKE_CASE			)

				return len(__SCREAMING_SNAKE_CASE			) / len(__SCREAMING_SNAKE_CASE			)
		return None


if __name__ == "__main__":
			__A						       =      {"a", "b", "c", "d", "e"}
			__A						       =      {"c", "d", "e", "f", "h", "i"}
			print(jaccard_similarity(set_a, set_b))





"""simple docstring"""


import math
import sys






def    a__   (   __SCREAMING_SNAKE_CASE			)     ->     int:
		if number != int(__SCREAMING_SNAKE_CASE			):
				raise ValueError("the value of input must be a natural number"			)
		if number < 0:
				raise ValueError("the value of input must not be a negative number"			)
		if number == 0:
				return 1
		__lowerCAmelCase:	int   				=      [-1] * (number + 1)
		__lowerCAmelCase:	Optional[Any]   				=      0
		for i in range(1 ,			number + 1			):
				__lowerCAmelCase:	List[str]   				=      sys.maxsize
				__lowerCAmelCase:	int   				=      int(math.sqrt(__SCREAMING_SNAKE_CASE			)			)
				for j in range(1 ,			root + 1			):
						__lowerCAmelCase:	Optional[Any]   				=      1 + answers[i - (j**2)]
						__lowerCAmelCase:	List[Any]   				=      min(__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			)
				__lowerCAmelCase:	Optional[Any]   				=      answer
		return answers[number]


if __name__ == "__main__":
			import doctest

			doctest.testmod()


