
"""simple docstring"""





import math



def  lowerCamelCase__						(     __snake_case      )				->						bool:


					"""simple docstring"""





					_UpperCamelCase									=    math.loga(math.sqrt(4 * positive_integer + 1      ) / 2 + 1 / 2      )

					return exponent == int(__snake_case      )



def  lowerCamelCase__						(     __snake_case = 1 / 1_23_45      )				->						int:


					"""simple docstring"""





					_UpperCamelCase									=    0
					_UpperCamelCase									=    0

					_UpperCamelCase									=    3
					while True:
										_UpperCamelCase									=    (integer**2 - 1) / 4
										# if candidate is an integer, then there is a partition for k
										if partition_candidate == int(__snake_case      ):
															_UpperCamelCase									=    int(__snake_case      )
															total_partitions += 1
															if check_partition_perfect(__snake_case      ):
																				perfect_partitions += 1
										if perfect_partitions > 0:
															if perfect_partitions / total_partitions < max_proportion:
																				return int(__snake_case      )
										integer += 1


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














def     a     (		lowerCamelCase_						,  lowerCamelCase_							):






				'''simple docstring'''
				lowercase__  					=     len(lowerCamelCase_							)
				lowercase__  					=     [[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__  					=     True

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

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




