


'''simple docstring'''



import math







def       _UpperCamelCase (						UpperCamelCase__   ):
			UpperCAmelCase__					:   int       				=       math.loga(math.sqrt(4 * positive_integer + 1   ) / 2 + 1 / 2   )

			return exponent == int(A__   )







def       _UpperCamelCase (						UpperCamelCase__ = 1 / 1_2_3_4_5   ):
			UpperCAmelCase__					:   int       				=       0
			UpperCAmelCase__					:   List[str]       				=       0

			UpperCAmelCase__					:   str       				=       3
			while True:
						UpperCAmelCase__					:   Union[str, Any]       				=       (integer**2 - 1) / 4
						# if candidate is an integer, then there is a partition for k
						if partition_candidate == int(A__   ):
									UpperCAmelCase__					:   Dict       				=       int(A__   )
									total_partitions += 1
									if check_partition_perfect(A__   ):
												perfect_partitions += 1
						if perfect_partitions > 0:
									if perfect_partitions / total_partitions < max_proportion:
												return int(A__   )
						integer += 1


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








'''simple docstring'''



def       _UpperCamelCase (						UpperCamelCase__   ):
			UpperCAmelCase__					:   List[str]       				=       len(UpperCamelCase__   )
			UpperCAmelCase__					:   List[Any]       				=       sum(UpperCamelCase__   )

			UpperCAmelCase__					:   List[str]       				=       [[False for x in range(s + 1   )] for y in range(n + 1   )]

			for i in range(1	, n + 1   ):
						UpperCAmelCase__					:   int       				=       True

			for i in range(1	, s + 1   ):
						UpperCAmelCase__					:   Dict       				=       False

			for i in range(1	, n + 1   ):
						for j in range(1	, s + 1   ):
									UpperCAmelCase__					:   int       				=       dp[i][j - 1]

									if arr[i - 1] <= j:
												UpperCAmelCase__					:   str       				=       dp[i][j] or dp[i - 1][j - arr[i - 1]]

			for j in range(int(s / 2   )	, -1	, -1   ):
						if dp[n][j] is True:
									UpperCAmelCase__					:   int       				=       s - 2 * j
									break

			return diff