



import math






def  UpperCAmelCase__    (    lowercase__   ) ->      bool:
						__lowercase					=				math.loga(math.sqrt(4 * positive_integer + 1   ) / 2 + 1 / 2   )

						return exponent == int(lowercase__   )






def  UpperCAmelCase__    (    lowercase__ = 1 / 12_345   ) ->      int:
						__lowercase					=				0
						__lowercase					=				0

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


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










UpperCamelCase__ =						{
    "joule": 1.0,
    "kilojoule": 10_00,
    "megajoule": 1_00_00_00,
    "gigajoule": 10_00_00_00_00,
    "wattsecond": 1.0,
    "watthour": 36_00,
    "kilowatthour": 3_60_00_00,
    "newtonmeter": 1.0,
    "calorie_nutr": 41_86.8,
    "kilocalorie_nutr": 4_18_68_00.00,
    "electronvolt": 1.6_0217_6634e-19,
    "britishthermalunit_it": 10_55.0_55_85,
    "footpound": 1.355_818,
}






def  UpperCAmelCase__    (    lowercase__						,       lowercase__						,       lowercase__   ) ->      float:
						if to_type not in ENERGY_CONVERSION or from_type not in ENERGY_CONVERSION:
												__lowercase					=				(
												    F"Incorrect 'from_type' or 'to_type' value: {from_type!r}, {to_type!r}\n"
												    F"Valid values are: {', '.join(lowercase__   )}"
												)
												raise ValueError(lowercase__   )
						return value * ENERGY_CONVERSION[from_type] / ENERGY_CONVERSION[to_type]


if __name__ == "__main__":
			import doctest

			doctest.testmod()





