"""simple docstring"""


import itertools





def       lowerCamelCase_			( __lowerCAmelCase = 100_0000    )							-> int:




						'''simple docstring'''



						lowerCamelCase__ =[1]

						for i in itertools.count(len(__lowerCAmelCase    )    ):
												lowerCamelCase__ =0
												for j in itertools.count(1    ):
																		lowerCamelCase__ =-1 if j % 2 == 0 else +1
																		lowerCamelCase__ =(j * j * 3 - j) // 2
																		if index > i:
																								break
																		item += partitions[i - index] * sign
																		item %= number
																		index += j
																		if index > i:
																								break
																		item += partitions[i - index] * sign
																		item %= number

												if item == 0:
																		return i
												partitions.append(__lowerCAmelCase    )

						return 0


if __name__ == "__main__":
	import doctest

	doctest.testmod()

	print(F'''{solution() = }''')



"""simple docstring"""


import random
import unittest

import torch

from diffusers import IFSuperResolutionPipeline
from diffusers.utils import floats_tensor
from diffusers.utils.import_utils import is_xformers_available
from diffusers.utils.testing_utils import skip_mps, torch_device

from ..pipeline_params import TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS, TEXT_GUIDED_IMAGE_VARIATION_PARAMS
from ..test_pipelines_common import PipelineTesterMixin
from . import IFPipelineTesterMixin






@skip_mps
class        __UpperCAmelCase						(     __lowerCAmelCase				,				__lowerCAmelCase				,				unittest.TestCase     ):
				A__				:       Any  							=	IFSuperResolutionPipeline
				A__				:       Tuple  							=	TEXT_GUIDED_IMAGE_VARIATION_PARAMS - {'''width''', '''height'''}
				A__				:       Optional[int]  							=	TEXT_GUIDED_IMAGE_VARIATION_BATCH_PARAMS
				A__				:       List[Any]  							=	PipelineTesterMixin.required_optional_params - {'''latents'''}

				def 		_a     (				self				):
										return self._get_superresolution_dummy_components()

				def 		_a     (				self     ,			_lowerCamelCase     ,			_lowerCamelCase=0				):
										if str(_lowerCamelCase				).startswith("mps"				):
																lowerCamelCase__ =torch.manual_seed(_lowerCamelCase				)
										else:
																lowerCamelCase__ =torch.Generator(device=_lowerCamelCase				).manual_seed(_lowerCamelCase				)

										lowerCamelCase__ =floats_tensor((1, 3, 32, 32)     ,			rng=random.Random(_lowerCamelCase				)				).to(_lowerCamelCase				)

										lowerCamelCase__ ={
										    "prompt": "A painting of a squirrel eating a burger",
										    "image": image,
										    "generator": generator,
										    "num_inference_steps": 2,
										    "output_type": "numpy",
										}

										return inputs

				@unittest.skipIf(
				    torch_device != "cuda" or not is_xformers_available()     ,			reason="XFormers attention is only available with CUDA and `xformers` installed"     ,			)
				def 		_a     (				self				):
										self._test_xformers_attention_forwardGenerator_pass(expected_max_diff=1E-3				)

				def 		_a     (				self				):
										self._test_save_load_optional_components()

				@unittest.skipIf(torch_device != "cuda"     ,			reason="float16 requires CUDA"				)
				def 		_a     (				self				):
										# Due to non-determinism in save load of the hf-internal-testing/tiny-random-t5 text encoder
										super().test_save_load_floataa(expected_max_diff=1E-1				)

				def 		_a     (				self				):
										self._test_attention_slicing_forward_pass(expected_max_diff=1E-2				)

				def 		_a     (				self				):
										self._test_save_load_local()






				def 		_a     (				self				):
										self._test_inference_batch_single_identical(
										    expected_max_diff=1E-2     ,			)


