





def A_	(		A__		,      A__				)  ->		Any:
       a__						:	List[str] =				1  # To kept the Calculated Value
       # Since C(n, k) = C(n, n-k)
       if k > (n - k):
              a__						:	Tuple =				n - k
       # Calculate C(n,k)
       for i in range(SCREAMING_SNAKE_CASE_				):
              result *= n - i
              result //= i + 1
       return result



def A_	(		A__				)  ->		Any:
       return binomial_coefficient(2 * node_count		,      SCREAMING_SNAKE_CASE_				) // (node_count + 1)



def A_	(		A__				)  ->		Union[str, Any]:

       if n < 0:
              raise ValueError('factorial() not defined for negative values'				)
       a__						:	int =				1
       for i in range(1		,      n + 1				):
              result *= i
       return result



def A_	(		A__				)  ->		Optional[Any]:
       return catalan_number(SCREAMING_SNAKE_CASE_				) * factorial(SCREAMING_SNAKE_CASE_				)


if __name__ == "__main__":
    lowercase      :       Optional[int]									=  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 argparse

import intel_extension_for_pytorch as ipex
import torch

from diffusers import DPMSolverMultistepScheduler, StableDiffusionPipeline


_snake_case             =     argparse.ArgumentParser('''Stable Diffusion script with intel optimization''', add_help=False)
parser.add_argument('''--dpm''', action='''store_true''', help='''Enable DPMSolver or not''')
parser.add_argument('''--steps''', default=None, type=int, help='''Num inference steps''')
_snake_case             =     parser.parse_args()


_snake_case             =     '''cpu'''
_snake_case             =     '''a lovely <dicoo> in red dress and hat, in the snowly and brightly night, with many brighly buildings'''

_snake_case             =     '''path-to-your-trained-model'''
_snake_case             =     StableDiffusionPipeline.from_pretrained(model_id)
if args.dpm:
   _snake_case             =     DPMSolverMultistepScheduler.from_config(pipe.scheduler.config)
_snake_case             =     pipe.to(device)

# to channels last
_snake_case             =     pipe.unet.to(memory_format=torch.channels_last)
_snake_case             =     pipe.vae.to(memory_format=torch.channels_last)
_snake_case             =     pipe.text_encoder.to(memory_format=torch.channels_last)
if pipe.requires_safety_checker:
   _snake_case             =     pipe.safety_checker.to(memory_format=torch.channels_last)

# optimize with ipex
_snake_case             =     torch.randn(2, 4, 64, 64)
_snake_case             =     torch.rand(1) * 9_99
_snake_case             =     torch.randn(2, 77, 7_68)
_snake_case             =     (sample, timestep, encoder_hidden_status)
try:
   _snake_case             =     ipex.optimize(pipe.unet.eval(), dtype=torch.bfloataa, inplace=True, sample_input=input_example)
except Exception:
   _snake_case             =     ipex.optimize(pipe.unet.eval(), dtype=torch.bfloataa, inplace=True)
_snake_case             =     ipex.optimize(pipe.vae.eval(), dtype=torch.bfloataa, inplace=True)
_snake_case             =     ipex.optimize(pipe.text_encoder.eval(), dtype=torch.bfloataa, inplace=True)
if pipe.requires_safety_checker:
   _snake_case             =     ipex.optimize(pipe.safety_checker.eval(), dtype=torch.bfloataa, inplace=True)

# compute
_snake_case             =     6_66
_snake_case             =     torch.Generator(device).manual_seed(seed)
_snake_case             =     {'''generator''': generator}
if args.steps is not None:
   _snake_case             =     args.steps

with torch.cpu.amp.autocast(enabled=True, dtype=torch.bfloataa):
   _snake_case             =     pipe(prompt, **generate_kwargs).images[0]

# save image
image.save('''generated.png''')



