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




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




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




def       __lowerCAmelCase      (						A_   : int					)    ->  int:
  return catalan_number(A_					) * factorial(A_					)


if __name__ == "__main__":
       a_							=      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."
       )




from ...configuration_utils import PretrainedConfig
from ...utils import logging


a_							=      logging.get_logger(__name__)

a_							=      {
    """facebook/vit-mae-base""": """https://huggingface.co/facebook/vit-mae-base/resolve/main/config.json""",
    # See all ViT MAE models at https://huggingface.co/models?filter=vit-mae
}


class 			UpperCAmelCase__    (		snake_case					):



  """simple docstring"""






  lowerCAmelCase__		:	Dict    		= 'vit_mae'






  def __init__(				self:			List[Any]				,				__lowerCAmelCase:			Any=768				,				__lowerCAmelCase:			List[str]=12				,				__lowerCAmelCase:			Optional[int]=12				,				__lowerCAmelCase:			Tuple=3_072				,				__lowerCAmelCase:			List[Any]="gelu"				,				__lowerCAmelCase:			Dict=0.0				,				__lowerCAmelCase:			Tuple=0.0				,				__lowerCAmelCase:			Any=0.02				,				__lowerCAmelCase:			List[Any]=1E-12				,				__lowerCAmelCase:			List[str]=224				,				__lowerCAmelCase:			Optional[Any]=16				,				__lowerCAmelCase:			Union[str, Any]=3				,				__lowerCAmelCase:			Tuple=True				,				__lowerCAmelCase:			Union[str, Any]=16				,				__lowerCAmelCase:			Optional[int]=512				,				__lowerCAmelCase:			int=8				,				__lowerCAmelCase:			int=2_048				,				__lowerCAmelCase:			str=0.75				,				__lowerCAmelCase:			Union[str, Any]=False				,				**__lowerCAmelCase:			List[Any]				,				) -> Optional[int]:




    '''simple docstring'''




    super().__init__(**__lowerCAmelCase   )

    __UpperCAmelCase						    =       hidden_size
    __UpperCAmelCase						    =       num_hidden_layers
    __UpperCAmelCase						    =       num_attention_heads
    __UpperCAmelCase						    =       intermediate_size
    __UpperCAmelCase						    =       hidden_act
    __UpperCAmelCase						    =       hidden_dropout_prob
    __UpperCAmelCase						    =       attention_probs_dropout_prob
    __UpperCAmelCase						    =       initializer_range
    __UpperCAmelCase						    =       layer_norm_eps
    __UpperCAmelCase						    =       image_size
    __UpperCAmelCase						    =       patch_size
    __UpperCAmelCase						    =       num_channels
    __UpperCAmelCase						    =       qkv_bias
    __UpperCAmelCase						    =       decoder_num_attention_heads
    __UpperCAmelCase						    =       decoder_hidden_size
    __UpperCAmelCase						    =       decoder_num_hidden_layers
    __UpperCAmelCase						    =       decoder_intermediate_size
    __UpperCAmelCase						    =       mask_ratio
    __UpperCAmelCase						    =       norm_pix_loss



