



from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType
class 			_snake_case     (   lowercase__):
				UpperCamelCase__			:   Tuple       						=["""image_processor""", """tokenizer"""]
				UpperCamelCase__			:   Any       						="""Pix2StructImageProcessor"""
				UpperCamelCase__			:   Tuple       						=("""T5Tokenizer""", """T5TokenizerFast""")




				def __init__(  self   :  Tuple,   __lowercase   :  Optional[int],   __lowercase   :  Dict  ):
							lowercase__   					=			False
							super().__init__(__lowercase,   __lowercase  )




				def __call__(  self   :  List[Any],   __lowercase   :  List[Any]=None,   __lowercase   :  Union[TextInput, PreTokenizedInput, List[TextInput], List[PreTokenizedInput]] = None,   __lowercase   :  bool = True,   __lowercase   :  Union[bool, str, PaddingStrategy] = False,   __lowercase   :  Union[bool, str, TruncationStrategy] = None,   __lowercase   :  Optional[int] = None,   __lowercase   :  Optional[int] = 2048,   __lowercase   :  int = 0,   __lowercase   :  Optional[int] = None,   __lowercase   :  Optional[bool] = None,   __lowercase   :  bool = False,   __lowercase   :  bool = False,   __lowercase   :  bool = False,   __lowercase   :  bool = False,   __lowercase   :  bool = False,   __lowercase   :  bool = True,   __lowercase   :  Optional[Union[str, TensorType]] = None,   **__lowercase   :  Tuple,   ):
							if images is None and text is None:
										raise ValueError("You have to specify either images or text."  )

							# Get only text
							if images is None and not self.image_processor.is_vqa:
										lowercase__   					=			self.tokenizer
										lowercase__   					=			self.tokenizer(
										    text=__lowercase,   add_special_tokens=__lowercase,   padding=__lowercase,   truncation=__lowercase,   max_length=__lowercase,   stride=__lowercase,   pad_to_multiple_of=__lowercase,   return_attention_mask=__lowercase,   return_overflowing_tokens=__lowercase,   return_special_tokens_mask=__lowercase,   return_offsets_mapping=__lowercase,   return_token_type_ids=__lowercase,   return_length=__lowercase,   verbose=__lowercase,   return_tensors=__lowercase,   **__lowercase,   )
										return text_encoding

							if not self.image_processor.is_vqa:
										# add pixel_values
										lowercase__   					=			self.image_processor(
										    __lowercase,   return_tensors=__lowercase,   max_patches=__lowercase,   **__lowercase  )
							else:
										# add pixel_values and bbox
										lowercase__   					=			self.image_processor(
										    __lowercase,   return_tensors=__lowercase,   max_patches=__lowercase,   header_text=__lowercase,   **__lowercase  )

							if text is not None and not self.image_processor.is_vqa:
										lowercase__   					=			self.tokenizer(
										    text=__lowercase,   add_special_tokens=__lowercase,   padding=__lowercase,   truncation=__lowercase,   max_length=__lowercase,   stride=__lowercase,   pad_to_multiple_of=__lowercase,   return_attention_mask=__lowercase,   return_overflowing_tokens=__lowercase,   return_special_tokens_mask=__lowercase,   return_offsets_mapping=__lowercase,   return_token_type_ids=__lowercase,   return_length=__lowercase,   verbose=__lowercase,   return_tensors=__lowercase,   **__lowercase,   )

										if "attention_mask" in text_encoding:
													lowercase__   					=			text_encoding.pop("attention_mask"  )
										if "input_ids" in text_encoding:
													lowercase__   					=			text_encoding.pop("input_ids"  )
							else:
										lowercase__   					=			None

							if text_encoding is not None:
										encoding_image_processor.update(__lowercase  )

							return encoding_image_processor




				def 							A__ (  self   :  List[str],   *__lowercase   :  Union[str, Any],   **__lowercase   :  Optional[Any]  ):
							return self.tokenizer.batch_decode(*__lowercase,   **__lowercase  )




				def 							A__ (  self   :  Tuple,   *__lowercase   :  List[Any],   **__lowercase   :  int  ):
							return self.tokenizer.decode(*__lowercase,   **__lowercase  )




				@property
				def 							A__ (  self   :  int  ):
							lowercase__   					=			self.tokenizer.model_input_names
							lowercase__   					=			self.image_processor.model_input_names
							return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names  )  )









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.'
							)




