

"""simple docstring"""






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





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





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





def 	lowercase      (   __UpperCamelCase						) ->      int:
 return catalan_number(__UpperCamelCase						) * factorial(__UpperCamelCase						)


if __name__ == "__main__":
 __lowerCamelCase										=		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 typing import List, Optional, Union

import numpy as np
import PIL.Image

from ...image_processing_utils import BaseImageProcessor, BatchFeature
from ...image_transforms import rescale, resize, to_channel_dimension_format
from ...image_utils import (
    ChannelDimension,
    PILImageResampling,
    get_image_size,
    make_list_of_images,
    to_numpy_array,
    valid_images,
)
from ...utils import TensorType, logging


__lowerCamelCase										=		logging.get_logger(__name__)
class        _lowercase					(     __UpperCAmelCase     ):
     _lowerCamelCase     =       ['''pixel_values''']







     def __init__(      self ,						UpperCamelCase_ = True ,						UpperCamelCase_ = 32 ,						UpperCamelCase_=PILImageResampling.BILINEAR ,						UpperCamelCase_ = True ,						**UpperCamelCase_ ,						):
      __magic_name__     =      do_resize
      __magic_name__     =      do_rescale
      __magic_name__     =      size_divisor
      __magic_name__     =      resample
      super().__init__(**UpperCamelCase_       )







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_ ,						UpperCamelCase_ ,						UpperCamelCase_ = None ,						**UpperCamelCase_       ):
      __magic_name__   ,						__magic_name__     =      get_image_size(UpperCamelCase_       )
      # Rounds the height and width down to the closest multiple of size_divisor
      __magic_name__     =      height // size_divisor * size_divisor
      __magic_name__     =      width // size_divisor * size_divisor
      __magic_name__     =      resize(UpperCamelCase_ ,						(new_h, new_w) ,						resample=UpperCamelCase_ ,						data_format=UpperCamelCase_ ,						**UpperCamelCase_       )
      return image







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_ ,						UpperCamelCase_ = None ,						**UpperCamelCase_       ):
      return rescale(image=UpperCamelCase_ ,						scale=UpperCamelCase_ ,						data_format=UpperCamelCase_ ,						**UpperCamelCase_       )







     def 	lowerCAmelCase__    (      self ,						UpperCamelCase_ ,						UpperCamelCase_ = None ,						UpperCamelCase_ = None ,						UpperCamelCase_=None ,						UpperCamelCase_ = None ,						UpperCamelCase_ = None ,						UpperCamelCase_ = ChannelDimension.FIRST ,						**UpperCamelCase_ ,						):
      __magic_name__     =      do_resize if do_resize is not None else self.do_resize
      __magic_name__     =      do_rescale if do_rescale is not None else self.do_rescale
      __magic_name__     =      size_divisor if size_divisor is not None else self.size_divisor
      __magic_name__     =      resample if resample is not None else self.resample

      if do_resize and size_divisor is None:
       raise ValueError('''size_divisor is required for resizing'''       )

      __magic_name__     =      make_list_of_images(UpperCamelCase_       )

      if not valid_images(UpperCamelCase_       ):
       raise ValueError('''Invalid image(s)'''       )

      # All transformations expect numpy arrays.
      __magic_name__     =      [to_numpy_array(UpperCamelCase_       ) for img in images]

      if do_resize:
       __magic_name__     =      [self.resize(UpperCamelCase_ ,						size_divisor=UpperCamelCase_ ,						resample=UpperCamelCase_       ) for image in images]

      if do_rescale:
       __magic_name__     =      [self.rescale(UpperCamelCase_ ,						scale=1 / 255       ) for image in images]

      __magic_name__     =      [to_channel_dimension_format(UpperCamelCase_ ,						UpperCamelCase_       ) for image in images]

      __magic_name__     =      {'''pixel_values''': images}
      return BatchFeature(data=UpperCamelCase_ ,						tensor_type=UpperCamelCase_       )

