


"""simple docstring"""



def       lowerCamelCase					(a_						:int				,				a_						:int)     ->							int:
       lowercase		:Dict       							=				1  # To kept the Calculated Value
       # Since C(n, k) = C(n, n-k)
       if k > (n - k):
              lowercase		:List[str]       							=				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''')
       lowercase		:Optional[int]       							=				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__":
 UpperCAmelCase      		=			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 collections import OrderedDict
from typing import Mapping

from packaging import version

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging


UpperCAmelCase      		=			logging.get_logger(__name__)

UpperCAmelCase      		=			{
    '''facebook/deit-base-distilled-patch16-224''': (
        '''https://huggingface.co/facebook/deit-base-patch16-224/resolve/main/config.json'''
    ),
    # See all DeiT models at https://huggingface.co/models?filter=deit
}
class 					__magic_name__		(			__UpperCAmelCase     ):
       __A			:      Tuple        =   "deit"






       def __init__(   self  :    List[str]  ,     snake_case__  :    int=7_6_8  ,     snake_case__  :    List[Any]=1_2  ,     snake_case__  :    Dict=1_2  ,     snake_case__  :    List[Any]=3_0_7_2  ,     snake_case__  :    Optional[int]="gelu"  ,     snake_case__  :    Dict=0.0  ,     snake_case__  :    str=0.0  ,     snake_case__  :    List[str]=0.02  ,     snake_case__  :    Optional[int]=1e-1_2  ,     snake_case__  :    Any=2_2_4  ,     snake_case__  :    Optional[int]=1_6  ,     snake_case__  :    int=3  ,     snake_case__  :    str=True  ,     snake_case__  :    Optional[int]=1_6  ,     **snake_case__  :    List[Any]  ,     ):

              '''simple docstring'''






              super().__init__(**snake_case__				)

              lowercase		:List[str]       							=				hidden_size
              lowercase		:Union[str, Any]       							=				num_hidden_layers
              lowercase		:Optional[Any]       							=				num_attention_heads
              lowercase		:Optional[Any]       							=				intermediate_size
              lowercase		:int       							=				hidden_act
              lowercase		:int       							=				hidden_dropout_prob
              lowercase		:Dict       							=				attention_probs_dropout_prob
              lowercase		:Optional[int]       							=				initializer_range
              lowercase		:Tuple       							=				layer_norm_eps
              lowercase		:Optional[int]       							=				image_size
              lowercase		:Union[str, Any]       							=				patch_size
              lowercase		:Optional[Any]       							=				num_channels
              lowercase		:Tuple       							=				qkv_bias
              lowercase		:Optional[Any]       							=				encoder_stride







class 					__magic_name__		(			__UpperCAmelCase     ):
       __A			:      Optional[int]        =   version.parse("1.11"     )






       @property
       def  __snake_case						(   self  :    int				):

              '''simple docstring'''






              return OrderedDict(
                  [
                      ('''pixel_values''', {0: '''batch''', 1: '''num_channels''', 2: '''height''', 3: '''width'''}),
                  ]				)







       @property
       def  __snake_case						(   self  :    Optional[int]				):

              '''simple docstring'''






              return 1e-4

