





def        _lowercase   (  _UpperCAmelCase     , _UpperCAmelCase			)  ->					int:
				lowerCamelCase			=1  # To kept the Calculated Value
				# Since C(n, k) = C(n, n-k)
				if k > (n - k):
								lowerCamelCase			=n - k
				# Calculate C(n,k)
				for i in range(_UpperCAmelCase			):
								result *= n - i
								result //= i + 1
				return result





def        _lowercase   (  _UpperCAmelCase			)  ->					int:
				return binomial_coefficient(2 * node_count     , _UpperCAmelCase			) // (node_count + 1)





def        _lowercase   (  _UpperCAmelCase			)  ->					int:
				if n < 0:
								raise ValueError("""factorial() not defined for negative values"""			)
				lowerCamelCase			=1
				for i in range(1     , n + 1			):
								result *= i
				return result





def        _lowercase   (  _UpperCAmelCase			)  ->					int:
				return catalan_number(_UpperCAmelCase			) * factorial(_UpperCAmelCase			)


if __name__ == "__main__":
							UpperCAmelCase__  :     Dict   			=int(input('''Enter the number of nodes: ''').strip() or 0)
							if node_count <= 0:
														raise ValueError('''We need some nodes to work with.''')
							print(
							    F"Given {node_count} nodes, there are {binary_tree_count(node_count)} "
							    F"binary trees and {catalan_number(node_count)} binary search trees."
							)












import random
import unittest

import torch

from diffusers import IFInpaintingSuperResolutionPipeline
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_INPAINTING_BATCH_PARAMS,
    TEXT_GUIDED_IMAGE_INPAINTING_PARAMS,
)
from ..test_pipelines_common import PipelineTesterMixin
from . import IFPipelineTesterMixin

@skip_mps
class  __A       (  a      ,   a      ,   unittest.TestCase      ):
				__A								=			IFInpaintingSuperResolutionPipeline
				__A								=			TEXT_GUIDED_IMAGE_INPAINTING_PARAMS - {"""width""", """height"""}
				__A								=			TEXT_GUIDED_IMAGE_INPAINTING_BATCH_PARAMS.union({"""original_image"""}      )
				__A								=			PipelineTesterMixin.required_optional_params - {"""latents"""}


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


				def _snake_case    (						self				,	UpperCAmelCase_				,	UpperCAmelCase_=0							):
								if str(UpperCAmelCase_							).startswith("""mps"""							):
												lowerCamelCase			=torch.manual_seed(UpperCAmelCase_							)
								else:
												lowerCamelCase			=torch.Generator(device=UpperCAmelCase_							).manual_seed(UpperCAmelCase_							)

								lowerCamelCase			=floats_tensor((1, 3, 16, 16)				,	rng=random.Random(UpperCAmelCase_							)							).to(UpperCAmelCase_							)
								lowerCamelCase			=floats_tensor((1, 3, 32, 32)				,	rng=random.Random(UpperCAmelCase_							)							).to(UpperCAmelCase_							)
								lowerCamelCase			=floats_tensor((1, 3, 32, 32)				,	rng=random.Random(UpperCAmelCase_							)							).to(UpperCAmelCase_							)

								lowerCamelCase			={
								    """prompt""": """A painting of a squirrel eating a burger""",
								    """image""": image,
								    """original_image""": original_image,
								    """mask_image""": mask_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 _snake_case    (						self							):
								self._test_xformers_attention_forwardGenerator_pass(expected_max_diff=1E-3							)


				def _snake_case    (						self							):
								self._test_save_load_optional_components()


				@unittest.skipIf(torch_device != """cuda"""				,	reason="""float16 requires CUDA"""							)
				def _snake_case    (						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 _snake_case    (						self							):
								self._test_attention_slicing_forward_pass(expected_max_diff=1E-2							)


				def _snake_case    (						self							):
								self._test_save_load_local()


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





