



'''simple docstring'''





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__a          =		{
    "configuration_timesformer": ["TIMESFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP", "TimesformerConfig"],
}

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       __a          =		[
           "TIMESFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
           "TimesformerModel",
           "TimesformerForVideoClassification",
           "TimesformerPreTrainedModel",
       ]

if TYPE_CHECKING:
       from .configuration_timesformer import TIMESFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, TimesformerConfig

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_timesformer import (
                  TIMESFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
                  TimesformerForVideoClassification,
                  TimesformerModel,
                  TimesformerPreTrainedModel,
              )

else:
       import sys

       __a          =		_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)

'''simple docstring'''




def 	UpperCamelCase_							(					_UpperCAmelCase  :      int			,	_UpperCAmelCase  :      int    )    ->    int:


       """simple docstring"""







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

def 	UpperCamelCase_							(					_UpperCAmelCase  :      int    )    ->    int:


       """simple docstring"""







       return binomial_coefficient(2 * node_count			,	_UpperCAmelCase    ) // (node_count + 1)

def 	UpperCamelCase_							(					_UpperCAmelCase  :      int    )    ->    int:


       """simple docstring"""







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

def 	UpperCamelCase_							(					_UpperCAmelCase  :      int    )    ->    int:


       """simple docstring"""







       return catalan_number(_UpperCAmelCase    ) * factorial(_UpperCAmelCase    )


if __name__ == "__main__":
  __SCREAMING_SNAKE_CASE       :     Dict     =  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.'
  )

