



'''simple docstring'''





def   a_   (		_UpperCAmelCase    :      int ,_UpperCAmelCase    :      int				)    ->  int:
      __snake_case :   Optional[int]													=    1  # To kept the Calculated Value
      # Since C(n, k) = C(n, n-k)
      if k > (n - k):
            __snake_case :   List[str]													=    n - k
      # Calculate C(n,k)
      for i in range(_UpperCAmelCase				):
            result *= n - i
            result //= i + 1
      return result





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





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





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


if __name__ == "__main__":
    A__    :   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'''





import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto.configuration_auto import CONFIG_MAPPING


A__    :   Union[str, Any]           =					logging.get_logger(__name__)



class  snake_case__						(    SCREAMING_SNAKE_CASE_				):
 A__				= '''upernet'''
 def __init__(   self						:							Optional[int]      ,     __a						:							Dict=None      ,     __a						:							List[str]=512      ,     __a						:							int=0.0_2      ,     __a						:							Optional[Any]=[1, 2, 3, 6]      ,     __a						:							Union[str, Any]=True      ,     __a						:							Any=0.4      ,     __a						:							int=384      ,     __a						:							int=256      ,     __a						:							str=1      ,     __a						:							List[Any]=False      ,     __a						:							Dict=255      ,     **__a						:							Dict      ,     )      ->   Optional[int]:







       '''simple docstring'''
       super().__init__(**__a  )

       if backbone_config is None:
             logger.info('`backbone_config` is `None`. Initializing the config with the default `ResNet` backbone.'  )
             __snake_case :   Optional[int]													=    CONFIG_MAPPING['resnet'](out_features=['stage1', 'stage2', 'stage3', 'stage4']  )
       elif isinstance(__a      ,     __a  ):
             __snake_case :   List[Any]													=    backbone_config.get('model_type'  )
             __snake_case :   List[str]													=    CONFIG_MAPPING[backbone_model_type]
             __snake_case :   int													=    config_class.from_dict(__a  )

       __snake_case :   Any													=    backbone_config
       __snake_case :   Tuple													=    hidden_size
       __snake_case :   str													=    initializer_range
       __snake_case :   Dict													=    pool_scales
       __snake_case :   Optional[Any]													=    use_auxiliary_head
       __snake_case :   Optional[Any]													=    auxiliary_loss_weight
       __snake_case :   Optional[int]													=    auxiliary_in_channels
       __snake_case :   Dict													=    auxiliary_channels
       __snake_case :   Any													=    auxiliary_num_convs
       __snake_case :   Optional[Any]													=    auxiliary_concat_input
       __snake_case :   List[str]													=    loss_ignore_index





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







       '''simple docstring'''
       __snake_case :   Union[str, Any]													=    copy.deepcopy(self.__dict__  )
       __snake_case :   str													=    self.backbone_config.to_dict()
       __snake_case :   Optional[int]													=    self.__class__.model_type
       return output



