
def  lowerCAmelCase__			(  SCREAMING_SNAKE_CASE_     )				->		int:
			assert isinstance(SCREAMING_SNAKE_CASE_       ,							SCREAMING_SNAKE_CASE_     ), F'''The input value of [n={number}] is not an integer'''

			if number == 1:
						return 2
			elif number < 1:
						lowerCAmelCase__      :      Dict         =		F'''The input value of [n={number}] has to be > 0'''
						raise ValueError(SCREAMING_SNAKE_CASE_     )
			else:
						lowerCAmelCase__      :      List[str]         =		sylvester(number - 1     )
						lowerCAmelCase__      :      Union[str, Any]         =		num - 1
						lowerCAmelCase__      :      List[Any]         =		num
						return lower * upper + 1


if __name__ == "__main__":
					print(F"""The 8th number in Sylvester's sequence: {sylvester(8)}""")

class      A__							:






				def __init__(						self					:      Dict    ,     a					:      list[int]   ):






							'''simple docstring'''







							lowerCAmelCase__      :      Union[str, Any]         =		len(a   )
							lowerCAmelCase__      :      Optional[Any]         =		[0] * len_array

							if len_array > 0:
										lowerCAmelCase__      :      List[Any]         =		array[0]

							for i in range(1    ,     a   ):
										lowerCAmelCase__      :      Optional[int]         =		self.prefix_sum[i - 1] + array[i]






				def 							_lowerCamelCase		(						self					:      int    ,     a					:      int    ,     a					:      int   ):






							'''simple docstring'''







							if start == 0:
										return self.prefix_sum[end]

							return self.prefix_sum[end] - self.prefix_sum[start - 1]






				def 							_lowerCamelCase		(						self					:      Optional[Any]    ,     a					:      int   ):






							'''simple docstring'''







							lowerCAmelCase__      :      Any         =		{0}
							for sum_item in self.prefix_sum:
										if sum_item - target_sum in sums:
													return True

										sums.add(a   )

							return False


if __name__ == "__main__":
					import doctest

					doctest.testmod()