"""simple docstring"""




import math






def   UpperCAmelCase					(	UpperCamelCase__				):






							"""simple docstring"""





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

							return exponent == int(UpperCamelCase__				)






def   UpperCAmelCase					(	UpperCamelCase__ = 1 / 12_345				):






							"""simple docstring"""





							A__	     =							0
							A__	     =							0

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


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






"""simple docstring"""




import unittest

import torch
from torch import nn

from diffusers.models.activations import get_activation
class     UpperCamelCase__(			unittest.TestCase ):





						def 				snake_case__	(       self     )					->				str:
													A__	     =							get_activation('swish'     )

													self.assertIsInstance(__UpperCAmelCase		,nn.SiLU     )

													self.assertEqual(act(torch.tensor(-1_00		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertNotEqual(act(torch.tensor(-1		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertEqual(act(torch.tensor(0		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertEqual(act(torch.tensor(20		,dtype=torch.floataa     )     ).item()		,20     )





						def 				snake_case__	(       self     )					->				Optional[Any]:
													A__	     =							get_activation('silu'     )

													self.assertIsInstance(__UpperCAmelCase		,nn.SiLU     )

													self.assertEqual(act(torch.tensor(-1_00		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertNotEqual(act(torch.tensor(-1		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertEqual(act(torch.tensor(0		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertEqual(act(torch.tensor(20		,dtype=torch.floataa     )     ).item()		,20     )





						def 				snake_case__	(       self     )					->				List[str]:
													A__	     =							get_activation('mish'     )

													self.assertIsInstance(__UpperCAmelCase		,nn.Mish     )

													self.assertEqual(act(torch.tensor(-2_00		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertNotEqual(act(torch.tensor(-1		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertEqual(act(torch.tensor(0		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertEqual(act(torch.tensor(20		,dtype=torch.floataa     )     ).item()		,20     )





						def 				snake_case__	(       self     )					->				List[str]:
													A__	     =							get_activation('gelu'     )

													self.assertIsInstance(__UpperCAmelCase		,nn.GELU     )

													self.assertEqual(act(torch.tensor(-1_00		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertNotEqual(act(torch.tensor(-1		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertEqual(act(torch.tensor(0		,dtype=torch.floataa     )     ).item()		,0     )
													self.assertEqual(act(torch.tensor(20		,dtype=torch.floataa     )     ).item()		,20     )





