






"""simple docstring"""







def      UpperCamelCase       ( _A  ,				_A )     ->       int:
				lowercase    :      int       = 1  # To kept the Calculated Value
				# Since C(n, k) = C(n, n-k)
				if k > (n - k):
								lowercase    :      List[Any]       = n - k
				# Calculate C(n,k)
				for i in range(_A ):
								result *= n - i
								result //= i + 1
				return result


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


def      UpperCamelCase       ( _A )     ->       int:
				if n < 0:
								raise ValueError("""factorial() not defined for negative values""" )
				lowercase    :      Union[str, Any]       = 1
				for i in range(1  ,				n + 1 ):
								result *= i
				return result


def      UpperCamelCase       ( _A )     ->       int:
				return catalan_number(_A ) * factorial(_A )


if __name__ == "__main__":
				_lowerCAmelCase            =	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.'
				)








"""simple docstring"""







from dataclasses import dataclass, field
from typing import Tuple

from ..utils import cached_property, is_torch_available, is_torch_tpu_available, logging, requires_backends
from .benchmark_args_utils import BenchmarkArguments


if is_torch_available():
				import torch

if is_torch_tpu_available(check_device=False):
				import torch_xla.core.xla_model as xm


_lowerCAmelCase            =	logging.get_logger(__name__)


@dataclass
class      UpperCamelCase		(__snake_case     ):
						_SCREAMING_SNAKE_CASE  : str												=		[
						    """no_inference""",
						    """no_cuda""",
						    """no_tpu""",
						    """no_speed""",
						    """no_memory""",
						    """no_env_print""",
						    """no_multi_process""",
						]






						def __init__(		self  :Union[str, Any]			, **__magic_name__  :int				)      ->Any:
										for deprecated_arg in self.deprecated_args:
														if deprecated_arg in kwargs:
																		lowercase    :      int       = deprecated_arg[3:]
																		setattr(self			, __magic_name__			, not kwargs.pop(__magic_name__				)				)
																		logger.warning(
																		    f"""{deprecated_arg} is depreciated. Please use --no_{positive_arg} or"""
																		    f""" {positive_arg}={kwargs[positive_arg]}"""				)

										lowercase    :      List[str]       = kwargs.pop("""torchscript"""			, self.torchscript				)
										lowercase    :      Any       = kwargs.pop("""torch_xla_tpu_print_metrics"""			, self.torch_xla_tpu_print_metrics				)
										lowercase    :      Union[str, Any]       = kwargs.pop("""fp16_opt_level"""			, self.fpaa_opt_level				)
										super().__init__(**__magic_name__				)

						_SCREAMING_SNAKE_CASE  : bool												=		field(default=__snake_case						,						metadata={"""help""": """Trace the models using torchscript"""}     )
						_SCREAMING_SNAKE_CASE  : bool												=		field(default=__snake_case						,						metadata={"""help""": """Print Xla/PyTorch tpu metrics"""}     )
						_SCREAMING_SNAKE_CASE  : str												=		field(
						    default="""O1"""						,						metadata={
						        """help""": (
						            """For fp16: Apex AMP optimization level selected in ['O0', 'O1', 'O2', and 'O3']. """
						            """See details at https://nvidia.github.io/apex/amp.html"""
						        )
						    }						,						)






						@cached_property
						def      __snake_case      (		self  :Optional[int]				)      ->Tuple["torch.device", int]:
										requires_backends(self			, ["""torch"""]				)
										logger.info("""PyTorch: setting up devices"""				)
										if not self.cuda:
														lowercase    :      Optional[Any]       = torch.device("""cpu"""				)
														lowercase    :      int       = 0
										elif is_torch_tpu_available():
														lowercase    :      Any       = xm.xla_device()
														lowercase    :      List[str]       = 0
										else:
														lowercase    :      int       = torch.device("""cuda""" if torch.cuda.is_available() else """cpu"""				)
														lowercase    :      Any       = torch.cuda.device_count()
										return device, n_gpu






						@property
						def      __snake_case      (		self  :Optional[int]				)      ->Union[str, Any]:
										return is_torch_tpu_available() and self.tpu






						@property
						def      __snake_case      (		self  :Optional[int]				)      ->int:
										requires_backends(self			, ["""torch"""]				)
										# TODO(PVP): currently only single GPU is supported
										return torch.cuda.current_device()






						@property
						def      __snake_case      (		self  :Optional[int]				)      ->"torch.device":
										requires_backends(self			, ["""torch"""]				)
										return self._setup_devices[0]






						@property
						def      __snake_case      (		self  :Optional[Any]				)      ->str:
										requires_backends(self			, ["""torch"""]				)
										return self._setup_devices[1]






						@property
						def      __snake_case      (		self  :int				)      ->List[str]:
										return self.n_gpu > 0
