code: 
  
  
  
  
  class 							lowerCamelCase		:
  
  
  
  
  
  
  
     def __init__(							self    ,      SCREAMING_SNAKE_CASE_ ):
         UpperCamelCase				:   Union[str, Any]          =							val
         # Number of nodes in left subtree
         UpperCamelCase				:   Dict          =							0
         UpperCamelCase				:   str          =							None
         UpperCamelCase				:   int          =							None
         UpperCamelCase				:   Dict          =							None
  
  
  
  
  
  
  
     def       a_							(							self    ,      SCREAMING_SNAKE_CASE_ ):
         assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"
  
         if self.val < other.val:
             UpperCamelCase				:   int          =							self.right
             UpperCamelCase				:   Any          =							None
             if self.right:
                 UpperCamelCase				:   Optional[Any]          =							other
             UpperCamelCase				:   Union[str, Any]          =							other
             UpperCamelCase				:   List[Any]          =							self.left_tree_size * 2 + 1
             return self
         else:
             UpperCamelCase				:   str          =							other.right
             UpperCamelCase				:   List[Any]          =							None
             if other.right:
                 UpperCamelCase				:   Union[str, Any]          =							self
             UpperCamelCase				:   Optional[int]          =							self
             UpperCamelCase				:   Optional[int]          =							other.left_tree_size * 2 + 1
             return other
  
  
  
  
  
  
  
  class 							lowerCamelCase		:
  
  
  
  
  
  
  
     def __init__(							self    ,      SCREAMING_SNAKE_CASE_=None    ,      SCREAMING_SNAKE_CASE_=None    ,      SCREAMING_SNAKE_CASE_=0 ):
         UpperCamelCase				:   Any          =							heap_size
         UpperCamelCase				:   int          =							bottom_root
         UpperCamelCase				:   Any          =							min_node
  
  
  
  
  
  
  
     def       a_							(							self    ,      SCREAMING_SNAKE_CASE_ ):
  
         # Empty heaps corner cases
         if other.size == 0:
             return None
         if self.size == 0:
             UpperCamelCase				:   List[str]          =							other.size
             UpperCamelCase				:   Tuple          =							other.bottom_root
             UpperCamelCase				:   Tuple          =							other.min_node
             return None
         # Update size
         UpperCamelCase				:   Optional[Any]          =							self.size + other.size
  
         # Update min.node
         if self.min_node.val > other.min_node.val:
             UpperCamelCase				:   Optional[Any]          =							other.min_node
         # Merge
  
         # Order roots by left_subtree_size
         UpperCamelCase				:   Dict          =							[]
         UpperCamelCase				:   Optional[Any]          =							self.bottom_root, other.bottom_root
         while i or j:
             if i and ((not j) or i.left_tree_size < j.left_tree_size):
                 combined_roots_list.append((i, True) )
                 UpperCamelCase				:   Tuple          =							i.parent
             else:
                 combined_roots_list.append((j, False) )
                 UpperCamelCase				:   Optional[Any]          =							j.parent
          # Insert links between them
         for i in range(len(SCREAMING_SNAKE_CASE_ ) - 1 ):
             if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
                 UpperCamelCase				:   Dict          =							combined_roots_list[i + 1][0]
                 UpperCamelCase				:   Optional[int]          =							combined_roots_list[i][0]
          # Consecutively merge roots with same left_tree_size
         UpperCamelCase				:   Any          =							combined_roots_list[0][0]
         while i.parent:
             if (
                 (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
             ) or (
                 i.left_tree_size == i.parent.left_tree_size
                 and i.left_tree_size != i.parent.parent.left_tree_size
             ):
                 # Neighbouring Nodes
                 UpperCamelCase				:   Dict          =							i.left
                 UpperCamelCase				:   int          =							i.parent.parent
  
                 # Merging trees
                 UpperCamelCase				:   str          =							i.merge_trees(i.parent )
  
                 # Updating links
                 UpperCamelCase				:   Union[str, Any]          =							previous_node
                 UpperCamelCase				:   List[Any]          =							next_node
                 if previous_node:
                     UpperCamelCase				:   List[str]          =							i
                 if next_node:
                     UpperCamelCase				:   Dict          =							i
             else:
                 UpperCamelCase				:   List[str]          =							i.parent
          # Updating self.bottom_root
         while i.left:
             UpperCamelCase				:   Union[str, Any]          =							i.left
         UpperCamelCase				:   Any          =							i
  
         # Update other
         UpperCamelCase				:   Optional[int]          =							self.size
         UpperCamelCase				:   Optional[Any]          =							self.bottom_root
         UpperCamelCase				:   str          =							self.min_node
  
         # Return the merged heap
         return self
  
  
  
  
  
  
  
     def       a_							(							self    ,      SCREAMING_SNAKE_CASE_ ):
         if self.size == 0:
             UpperCamelCase				:   Tuple          =							Node(SCREAMING_SNAKE_CASE_ )
             UpperCamelCase				:   Optional[int]          =							1
             UpperCamelCase				:   Optional[int]          =							self.bottom_root
         else:
             # Create new node
             UpperCamelCase				:   List[Any]          =							Node(SCREAMING_SNAKE_CASE_ )
  
             # Update size
             self.size += 1
  
             # update min_node
             if val < self.min_node.val:
                 UpperCamelCase				:   List[str]          =							new_node
             # Put new_node as a bottom_root in heap
             UpperCamelCase				:   int          =							new_node
             UpperCamelCase				:   Tuple          =							self.bottom_root
             UpperCamelCase				:   Any          =							new_node
  
             # Consecutively merge roots with same left_tree_size
             while (
                 self.bottom_root.parent
                 and self.bottom_root.left_tree_size
                 == self.bottom_root.parent.left_tree_size
             ):
                 # Next node
                 UpperCamelCase				:   Any          =							self.bottom_root.parent.parent
  
                 # Merge
                 UpperCamelCase				:   int          =							self.bottom_root.merge_trees(self.bottom_root.parent )
  
                 # Update Links
                 UpperCamelCase				:   Dict          =							next_node
                 UpperCamelCase				:   Optional[Any]          =							None
                 if next_node:
                     UpperCamelCase				:   Union[str, Any]          =							self.bottom_root
  
  
  
  
  
  
  
     def       a_							(							self ):
         return self.min_node.val
  
  
  
  
  
  
  
     def       a_							(							self ):
         return self.size == 0
  
  
  
  
  
  
  
     def       a_							(							self ):
         UpperCamelCase				:   Tuple          =							self.min_node.val
  
         # Last element in heap corner case
         if self.size == 1:
             # Update size
             UpperCamelCase				:   Optional[Any]          =							0
  
             # Update bottom root
             UpperCamelCase				:   Any          =							None
  
             # Update min_node
             UpperCamelCase				:   List[str]          =							None
  
             return min_value
         # No right subtree corner case
         # The structure of the tree implies that this should be the bottom root
         # and there is at least one other root
         if self.min_node.right is None:
             # Update size
             self.size -= 1
  
             # Update bottom root
             UpperCamelCase				:   Union[str, Any]          =							self.bottom_root.parent
             UpperCamelCase				:   Union[str, Any]          =							None
  
             # Update min_node
             UpperCamelCase				:   Union[str, Any]          =							self.bottom_root
             UpperCamelCase				:   Union[str, Any]          =							self.bottom_root.parent
             while i:
                 if i.val < self.min_node.val:
                     UpperCamelCase				:   Union[str, Any]          =							i
                 UpperCamelCase				:   Optional[int]          =							i.parent
             return min_value
         # General case
         # Find the BinomialHeap of the right subtree of min_node
         UpperCamelCase				:   Dict          =							self.min_node.right
         UpperCamelCase				:   Dict          =							None
         UpperCamelCase				:   Tuple          =							bottom_of_new
         UpperCamelCase				:   Dict          =							1
  
         # Size, min_node and bottom_root
         while bottom_of_new.left:
             UpperCamelCase				:   Any          =							size_of_new * 2 + 1
             UpperCamelCase				:   Tuple          =							bottom_of_new.left
             if bottom_of_new.val < min_of_new.val:
                 UpperCamelCase				:   int          =							bottom_of_new
          # Corner case of single root on top left path
         if (not self.min_node.left) and (not self.min_node.parent):
             UpperCamelCase				:   Union[str, Any]          =							size_of_new
             UpperCamelCase				:   Union[str, Any]          =							bottom_of_new
             UpperCamelCase				:   Tuple          =							min_of_new
             # print("Single root, multiple nodes case")
             return min_value
         # Remaining cases
         # Construct heap of right subtree
         UpperCamelCase				:   Optional[Any]          =							BinomialHeap(
             bottom_root=SCREAMING_SNAKE_CASE_    ,      min_node=SCREAMING_SNAKE_CASE_    ,      heap_size=SCREAMING_SNAKE_CASE_ )
  
         # Update size
         UpperCamelCase				:   Union[str, Any]          =							self.size - 1 - size_of_new
  
         # Neighbour nodes
         UpperCamelCase				:   Union[str, Any]          =							self.min_node.left
         UpperCamelCase				:   Optional[Any]          =							self.min_node.parent
  
         # Initialize new bottom_root and min_node
         UpperCamelCase				:   Optional[int]          =							previous_node or next_node
         UpperCamelCase				:   Tuple          =							next_node
  
         # Update links of previous_node and search below for new min_node and
         # bottom_root
         if previous_node:
             UpperCamelCase				:   Dict          =							next_node
  
             # Update bottom_root and search for min_node below
             UpperCamelCase				:   int          =							previous_node
             UpperCamelCase				:   Tuple          =							previous_node
             while self.bottom_root.left:
                 UpperCamelCase				:   Union[str, Any]          =							self.bottom_root.left
                 if self.bottom_root.val < self.min_node.val:
                     UpperCamelCase				:   Any          =							self.bottom_root
         if next_node:
             UpperCamelCase				:   Any          =							previous_node
  
             # Search for new min_node above min_node
             UpperCamelCase				:   List[str]          =							next_node
             while i:
                 if i.val < self.min_node.val:
                     UpperCamelCase				:   List[Any]          =							i
                 UpperCamelCase				:   Dict          =							i.parent
          # Merge heaps
         self.merge_heaps(SCREAMING_SNAKE_CASE_ )
  
         return min_value
  
  
  
  
  
  
  
     def       a_							(							self ):
         UpperCamelCase				:   List[Any]          =							self.bottom_root
         while top_root.parent:
             UpperCamelCase				:   Tuple          =							top_root.parent
         # preorder
         UpperCamelCase				:   str          =							[]
         self.__traversal(SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_ )
         return heap_pre_order
  
  
  
  
  
  
  
     def       a_							(							self    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_    ,      SCREAMING_SNAKE_CASE_=0 ):
         if curr_node:
             preorder.append((curr_node.val, level) )
             self.__traversal(curr_node.left    ,      SCREAMING_SNAKE_CASE_    ,      level + 1 )
             self.__traversal(curr_node.right    ,      SCREAMING_SNAKE_CASE_    ,      level + 1 )
         else:
             preorder.append(("""#""", level) )
  
  
  
  
  
  
  
     def __str__(							self ):
         if self.is_empty():
             return ""
         UpperCamelCase				:   str          =							self.pre_order()
  
         return "\n".join(("""-""" * level + str(SCREAMING_SNAKE_CASE_ )) for value, level in preorder_heap )
  
  
  # Unit Tests
  if __name__ == "__main__":
    import doctest
  
    doctest.testmod()
  
  
  
  
  
style_context: 
  
  
  
  
  """simple docstring"""
  
  
  
  
  import numpy as np
  import PIL
  import torch
  import torchvision.transforms as T
  import torchvision.transforms.functional as TF
  from PIL import Image
  def 					A_			(		snake_case_     :       List[str]						,snake_case_     :       Union[str, Any]=2_5_6    ):
  
  
  
  
  
  
  
      '''simple docstring'''
      UpperCamelCase				:   Optional[int]          =							min(img.size    )
  
      if s < target_image_size:
          raise ValueError(f'min dim for image {s} < {target_image_size}'    )
  
      UpperCamelCase				:   Dict          =							target_image_size / s
      UpperCamelCase				:   Any          =							(round(r * img.size[1]    ), round(r * img.size[0]    ))
      UpperCamelCase				:   Union[str, Any]          =							TF.resize(snake_case_						,snake_case_						,interpolation=PIL.Image.LANCZOS    )
      UpperCamelCase				:   Optional[int]          =							TF.center_crop(snake_case_						,output_size=2 * [target_image_size]    )
      UpperCamelCase				:   Optional[Any]          =							torch.unsqueeze(T.ToTensor()(snake_case_    )						,0    )
      return img
  def 					A_			(		snake_case_     :       List[Any]    ):
  
  
  
  
  
  
  
      '''simple docstring'''
      UpperCamelCase				:   Any          =							2.0 * x - 1.0
      return x
  def 					A_			(		snake_case_     :       Tuple						,snake_case_     :       Optional[Any]=True						,snake_case_     :       Dict="RGB"    ):
  
  
  
  
  
  
  
      '''simple docstring'''
      UpperCamelCase				:   Dict          =							x.detach().cpu()
      if process:
          UpperCamelCase				:   str          =							post_process_tensor(snake_case_    )
      UpperCamelCase				:   List[Any]          =							x.numpy()
      if process:
          UpperCamelCase				:   Optional[int]          =							(2_5_5 * x).astype(np.uinta    )
      UpperCamelCase				:   List[Any]          =							Image.fromarray(snake_case_    )
      if not x.mode == mode:
          UpperCamelCase				:   Any          =							x.convert(snake_case_    )
      return x
  def 					A_			(		snake_case_     :       int    ):
  
  
  
  
  
  
  
      '''simple docstring'''
      UpperCamelCase				:   int          =							torch.clamp(snake_case_						,-1.0						,1.0    )
      UpperCamelCase				:   Optional[Any]          =							(x + 1.0) / 2.0
      UpperCamelCase				:   Dict          =							x.permute(1						,2						,0    )
      return x
  
  
  def 					A_			(		snake_case_     :       int    ):
  
  
  
  
  
  
  
      '''simple docstring'''
      UpperCamelCase				:   Optional[Any]          =							post_process_tensor(x.squeeze()    )
      return x.permute(2						,0						,1    ).unsqueeze(0    )
  
  
  
  
  