



from collections import OrderedDict
from typing import TYPE_CHECKING, Any, Mapping, Optional

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


if TYPE_CHECKING:
							from ... import FeatureExtractionMixin, TensorType

lowercase_						=       logging.get_logger(__name__)

lowercase_						=       {
    """openai/imagegpt-small""": """""",
    """openai/imagegpt-medium""": """""",
    """openai/imagegpt-large""": """""",
}
class 			_snake_case     (   lowercase__):
				UpperCamelCase__			:   List[Any]       						="""imagegpt"""
				UpperCamelCase__			:   List[str]       						=["""past_key_values"""]
				UpperCamelCase__			:   str       						={
				    """hidden_size""": """n_embd""",
				    """max_position_embeddings""": """n_positions""",
				    """num_attention_heads""": """n_head""",
				    """num_hidden_layers""": """n_layer""",
				}




				def __init__(  self   :  Union[str, Any],   __lowercase   :  List[str]=512 + 1,   __lowercase   :  Optional[Any]=32 * 32,   __lowercase   :  str=512,   __lowercase   :  List[str]=24,   __lowercase   :  int=8,   __lowercase   :  List[Any]=None,   __lowercase   :  int="quick_gelu",   __lowercase   :  Dict=0.1,   __lowercase   :  Dict=0.1,   __lowercase   :  Optional[Any]=0.1,   __lowercase   :  Union[str, Any]=1e-5,   __lowercase   :  Any=0.02,   __lowercase   :  Union[str, Any]=True,   __lowercase   :  Dict=True,   __lowercase   :  int=False,   __lowercase   :  int=False,   __lowercase   :  Any=False,   **__lowercase   :  Tuple,   ):
							lowercase__   					=			vocab_size
							lowercase__   					=			n_positions
							lowercase__   					=			n_embd
							lowercase__   					=			n_layer
							lowercase__   					=			n_head
							lowercase__   					=			n_inner
							lowercase__   					=			activation_function
							lowercase__   					=			resid_pdrop
							lowercase__   					=			embd_pdrop
							lowercase__   					=			attn_pdrop
							lowercase__   					=			layer_norm_epsilon
							lowercase__   					=			initializer_range
							lowercase__   					=			scale_attn_weights
							lowercase__   					=			use_cache
							lowercase__   					=			scale_attn_by_inverse_layer_idx
							lowercase__   					=			reorder_and_upcast_attn
							lowercase__   					=			tie_word_embeddings

							super().__init__(tie_word_embeddings=__lowercase,   **__lowercase  )
class 			_snake_case     (   lowercase__):




				@property
				def 							A__ (  self   :  Union[str, Any]  ):
							return OrderedDict(
							    [
							        ("input_ids", {0: "batch", 1: "sequence"}),
							    ]  )




				def 							A__ (  self   :  Tuple,   __lowercase   :  "FeatureExtractionMixin",   __lowercase   :  int = 1,   __lowercase   :  int = -1,   __lowercase   :  bool = False,   __lowercase   :  Optional["TensorType"] = None,   __lowercase   :  int = 3,   __lowercase   :  int = 32,   __lowercase   :  int = 32,   ):
							lowercase__   					=			self._generate_dummy_images(__lowercase,   __lowercase,   __lowercase,   __lowercase  )
							lowercase__   					=			dict(preprocessor(images=__lowercase,   return_tensors=__lowercase  )  )

							return inputs









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



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			return binomial_coefficient(2 * node_count  ,					SCREAMING_SNAKE_CASE_					) // (node_count + 1)



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



def __lowerCAmelCase	(       SCREAMING_SNAKE_CASE_					):
			return catalan_number(SCREAMING_SNAKE_CASE_					) * factorial(SCREAMING_SNAKE_CASE_					)


if __name__ == "__main__":
							lowercase_						=       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.'
							)




