




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase ):
				__magic_name__						:						Optional[int]										=1  # To kept the Calculated Value
				# Since C(n, k) = C(n, n-k)
				if k > (n - k):
								__magic_name__						:						Union[str, Any]										=n - k
				# Calculate C(n,k)
				for i in range(lowerCamelCase ):
								result *= n - i
								result //= i + 1
				return result




def 		lowerCAmelCase_ (						lowerCamelCase ):
				return binomial_coefficient(2 * node_count						,  lowerCamelCase ) // (node_count + 1)




def 		lowerCAmelCase_ (						lowerCamelCase ):
				if n < 0:
								raise ValueError("""factorial() not defined for negative values""" )
				__magic_name__						:						List[str]										=1
				for i in range(1						,  n + 1 ):
								result *= i
				return result




def 		lowerCAmelCase_ (						lowerCamelCase ):
				return catalan_number(lowerCamelCase ) * factorial(lowerCamelCase )


if __name__ == "__main__":
							UpperCAmelCase_		:					Union[str, Any]          =  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 ...configuration_utils import PretrainedConfig
from ...utils import logging


_UpperCamelCase											=		logging.get_logger(__name__)

_UpperCamelCase											=		{
    'google/pegasus-large': 'https://huggingface.co/google/pegasus-large/resolve/main/config.json',
    # See all PEGASUS models at https://huggingface.co/models?filter=pegasus
}






class    lowerCamelCase_       (							SCREAMING_SNAKE_CASE_	):
  """simple docstring"""




  a_				   ="""pegasus"""
  a_				   =["""past_key_values"""]
  a_				   ={"""num_attention_heads""": """encoder_attention_heads""", """hidden_size""": """d_model"""}




  def __init__(					self :      Any     ,      _a :      int=5_0265     ,      _a :      Tuple=1024     ,      _a :      Optional[Any]=12     ,      _a :      int=4096     ,      _a :      str=16     ,      _a :      Union[str, Any]=12     ,      _a :      Optional[Any]=4096     ,      _a :      Optional[int]=16     ,      _a :      Union[str, Any]=0.0     ,      _a :      str=0.0     ,      _a :      List[Any]=True     ,      _a :      Optional[int]=True     ,      _a :      Tuple="gelu"     ,      _a :      Dict=1024     ,      _a :      int=0.1     ,      _a :      Any=0.0     ,      _a :      Union[str, Any]=0.0     ,      _a :      Any=0.02     ,      _a :      Optional[Any]=0     ,      _a :      str=False     ,      _a :      Tuple=0     ,      _a :      Optional[int]=1     ,      _a :      Union[str, Any]=1     ,      **_a :      Optional[int]     ,      )   ->   Any:
    __lowerCamelCase			:			Union[str, Any]       			=					vocab_size
    __lowerCamelCase			:			int       			=					max_position_embeddings
    __lowerCamelCase			:			Union[str, Any]       			=					d_model
    __lowerCamelCase			:			Union[str, Any]       			=					encoder_ffn_dim
    __lowerCamelCase			:			Union[str, Any]       			=					encoder_layers
    __lowerCamelCase			:			List[Any]       			=					encoder_attention_heads
    __lowerCamelCase			:			Optional[int]       			=					decoder_ffn_dim
    __lowerCamelCase			:			int       			=					decoder_layers
    __lowerCamelCase			:			Tuple       			=					decoder_attention_heads
    __lowerCamelCase			:			Optional[Any]       			=					dropout
    __lowerCamelCase			:			Tuple       			=					attention_dropout
    __lowerCamelCase			:			int       			=					activation_dropout
    __lowerCamelCase			:			Dict       			=					activation_function
    __lowerCamelCase			:			List[Any]       			=					init_std
    __lowerCamelCase			:			List[str]       			=					encoder_layerdrop
    __lowerCamelCase			:			Union[str, Any]       			=					decoder_layerdrop
    __lowerCamelCase			:			Union[str, Any]       			=					use_cache
    __lowerCamelCase			:			Tuple       			=					encoder_layers
    __lowerCamelCase			:			int       			=					scale_embedding  # scale factor will be sqrt(d_model) if True
    super().__init__(
        pad_token_id=_a     ,      eos_token_id=_a     ,      is_encoder_decoder=_a     ,      decoder_start_token_id=_a     ,      forced_eos_token_id=_a     ,      **_a     ,      )




  @property
  def 		_lowercase	(					self :      Optional[int]  )   ->   int:
    return self.encoder_attention_heads




  @property
  def 		_lowercase	(					self :      Any  )   ->   int:
    return self.d_model






