



def  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__						):

				"""simple docstring"""


				lowercase__					:   int													=					len(lowerCamelCase__						)
				lowercase__					:   Union[str, Any]													=					[[False] * (required_sum + 1) for _ in range(arr_len + 1						)]

				# for each arr value, a sum of zero(0) can be formed by not taking any element
				# hence True/1
				for i in range(arr_len + 1						):
								lowercase__					:   Any													=					True

				# sum is not zero and set is empty then false
				for i in range(1					,			required_sum + 1						):
								lowercase__					:   Union[str, Any]													=					False

				for i in range(1					,			arr_len + 1						):
								for j in range(1					,			required_sum + 1						):
												if arr[i - 1] > j:
																lowercase__					:   List[str]													=					subset[i - 1][j]
												if arr[i - 1] <= j:
																lowercase__					:   int													=					subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

				return subset[arr_len][required_sum]


if __name__ == "__main__":
				import doctest

				doctest.testmod()









def  __lowerCamelCase (       lowerCamelCase__ = 1_000						):

				"""simple docstring"""


				lowercase__							,							lowercase__					:   int													=					1, 1
				lowercase__					:   List[Any]													=					[]
				for i in range(1					,			n + 1						):
								lowercase__					:   Dict													=					prev_numerator + 2 * prev_denominator
								lowercase__					:   Tuple													=					prev_numerator + prev_denominator
								if len(str(lowerCamelCase__						)						) > len(str(lowerCamelCase__						)						):
												result.append(lowerCamelCase__						)
								lowercase__					:   int													=					numerator
								lowercase__					:   int													=					denominator

				return len(lowerCamelCase__						)


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




