






"""simple docstring"""
def 			__UpperCamelCase	(		snake_case__   ,   snake_case__					):
	_enforce_args(snake_case__   ,   snake_case__					)
	if n == 0:
		return 0
	A_		:						Dict	    =   float("""-inf"""					)
	for i in range(1   ,   n + 1					):
		A_		:						Dict	    =   max(
		    snake_case__   ,   prices[i - 1] + naive_cut_rod_recursive(n - i   ,   snake_case__					)					)

	return max_revue






def 			__UpperCamelCase	(		snake_case__   ,   snake_case__					):
	_enforce_args(snake_case__   ,   snake_case__					)
	A_		:						Any	    =   [float("""-inf"""					) for _ in range(n + 1					)]
	return _top_down_cut_rod_recursive(snake_case__   ,   snake_case__   ,   snake_case__					)






def 			__UpperCamelCase	(		snake_case__   ,   snake_case__   ,   snake_case__					):
	if max_rev[n] >= 0:
		return max_rev[n]
	elif n == 0:
		return 0
	else:
		A_		:						str	    =   float("""-inf"""					)
		for i in range(1   ,   n + 1					):
			A_		:						List[str]	    =   max(
			    snake_case__   ,   prices[i - 1] + _top_down_cut_rod_recursive(n - i   ,   snake_case__   ,   snake_case__					)   ,   )

		A_		:						List[Any]	    =   max_revenue

	return max_rev[n]






def 			__UpperCamelCase	(		snake_case__   ,   snake_case__					):
	_enforce_args(snake_case__   ,   snake_case__					)

	# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
	# length 0.
	A_		:						Dict	    =   [float("""-inf"""					) for _ in range(n + 1					)]
	A_		:						Optional[Any]	    =   0

	for i in range(1   ,   n + 1					):
		A_		:						Optional[int]	    =   max_rev[i]
		for j in range(1   ,   i + 1					):
			A_		:						List[str]	    =   max(snake_case__   ,   prices[j - 1] + max_rev[i - j]					)

		A_		:						int	    =   max_revenue_i

	return max_rev[n]






def 			__UpperCamelCase	(		snake_case__   ,   snake_case__					):
	if n < 0:
		A_		:						List[Any]	    =   F"""n must be greater than or equal to 0. Got n = {n}"""
		raise ValueError(snake_case__					)

	if n > len(snake_case__					):
		A_		:						Union[str, Any]	    =   (
		    """Each integral piece of rod must have a corresponding price. """
		    F"""Got n = {n} but length of prices = {len(snake_case__					)}"""
		)
		raise ValueError(snake_case__					)






def 			__UpperCamelCase	(		):
	A_		:						List[Any]	    =   [6, 10, 12, 15, 20, 23]
	A_		:						Any	    =   len(snake_case__					)

	# the best revenue comes from cutting the rod into 6 pieces, each
	# of length 1 resulting in a revenue of 6 * 6 = 36.
	A_		:						str	    =   36

	A_		:						int	    =   top_down_cut_rod(snake_case__   ,   snake_case__					)
	A_		:						Any	    =   bottom_up_cut_rod(snake_case__   ,   snake_case__					)
	A_		:						List[Any]	    =   naive_cut_rod_recursive(snake_case__   ,   snake_case__					)

	assert expected_max_revenue == max_rev_top_down
	assert max_rev_top_down == max_rev_bottom_up
	assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
							main()









"""simple docstring"""
from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors






def 			__UpperCamelCase	(		snake_case__					):
	A_		:						List[str]	    =   prime_factors(snake_case__					)
	if is_square_free(snake_case__					):
		return -1 if len(snake_case__					) % 2 else 1
	return 0


if __name__ == "__main__":
							import doctest

							doctest.testmod()

