code: 
  
  
  
  
  
  class 				A    :
  
  
  
        def __init__(					self     ,  lowercase_					)      ->   List[str]:
  
  
  
               '''simple docstring'''
  
               _snake_case      :							Dict     				=						val
               # Number of nodes in left subtree
               _snake_case      :							List[Any]     				=						0
               _snake_case      :							Dict     				=						None
               _snake_case      :							str     				=						None
               _snake_case      :							Any     				=						None
  
  
  
        def    __a (					self     ,  lowercase_					)      ->   Optional[int]:
  
  
  
               '''simple docstring'''
  
               assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"
  
               if self.val < other.val:
                      _snake_case      :							Any     				=						self.right
                      _snake_case      :							Tuple     				=						None
                      if self.right:
                             _snake_case      :							List[str]     				=						other
                      _snake_case      :							str     				=						other
                      _snake_case      :							List[Any]     				=						self.left_tree_size * 2 + 1
                      return self
               else:
                      _snake_case      :							Dict     				=						other.right
                      _snake_case      :							str     				=						None
                      if other.right:
                             _snake_case      :							Union[str, Any]     				=						self
                      _snake_case      :							Any     				=						self
                      _snake_case      :							Tuple     				=						other.left_tree_size * 2 + 1
                      return other
  
  
  class 				A    :
  
  
  
        def __init__(					self     ,  lowercase_=None     ,  lowercase_=None     ,  lowercase_=0					)      ->   Union[str, Any]:
  
  
  
               '''simple docstring'''
  
               _snake_case      :							List[str]     				=						heap_size
               _snake_case      :							Any     				=						bottom_root
               _snake_case      :							Dict     				=						min_node
  
  
  
        def    __a (					self     ,  lowercase_					)      ->   str:
  
  
  
               '''simple docstring'''
  
               if other.size == 0:
                      return None
               if self.size == 0:
                      _snake_case      :							Optional[int]     				=						other.size
                      _snake_case      :							Optional[int]     				=						other.bottom_root
                      _snake_case      :							Dict     				=						other.min_node
                      return None
               # Update size
               _snake_case      :							Any     				=						self.size + other.size
  
               # Update min.node
               if self.min_node.val > other.min_node.val:
                      _snake_case      :							Tuple     				=						other.min_node
               # Merge
  
               # Order roots by left_subtree_size
               _snake_case      :							Union[str, Any]     				=						[]
               _snake_case				,    _snake_case      :							str     				=						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)					)
                             _snake_case      :							List[Any]     				=						i.parent
                      else:
                             combined_roots_list.append((j, False)					)
                             _snake_case      :							Dict     				=						j.parent
          # Insert links between them
               for i in range(len(lowercase_					) - 1					):
                      if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
                             _snake_case      :							Optional[Any]     				=						combined_roots_list[i + 1][0]
                             _snake_case      :							int     				=						combined_roots_list[i][0]
          # Consecutively merge roots with same left_tree_size
               _snake_case      :							Union[str, 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
                             _snake_case      :							Optional[Any]     				=						i.left
                             _snake_case      :							List[str]     				=						i.parent.parent
  
                             # Merging trees
                             _snake_case      :							Tuple     				=						i.merge_trees(i.parent					)
  
                             # Updating links
                             _snake_case      :							Any     				=						previous_node
                             _snake_case      :							Dict     				=						next_node
                             if previous_node:
                                    _snake_case      :							Optional[Any]     				=						i
                             if next_node:
                                    _snake_case      :							Optional[int]     				=						i
                      else:
                             _snake_case      :							Optional[Any]     				=						i.parent
          # Updating self.bottom_root
               while i.left:
                      _snake_case      :							List[Any]     				=						i.left
               _snake_case      :							int     				=						i
  
               # Update other
               _snake_case      :							List[str]     				=						self.size
               _snake_case      :							List[str]     				=						self.bottom_root
               _snake_case      :							str     				=						self.min_node
  
               # Return the merged heap
               return self
  
  
  
        def    __a (					self     ,  lowercase_					)      ->   int:
  
  
  
               '''simple docstring'''
  
               if self.size == 0:
                      _snake_case      :							Optional[Any]     				=						Node(lowercase_					)
                      _snake_case      :							int     				=						1
                      _snake_case      :							Tuple     				=						self.bottom_root
               else:
                      # Create new node
                      _snake_case      :							Tuple     				=						Node(lowercase_					)
  
                      # Update size
                      self.size += 1
  
                      # update min_node
                      if val < self.min_node.val:
                             _snake_case      :							List[str]     				=						new_node
                      # Put new_node as a bottom_root in heap
                      _snake_case      :							Union[str, Any]     				=						new_node
                      _snake_case      :							int     				=						self.bottom_root
                      _snake_case      :							Tuple     				=						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
                             _snake_case      :							Any     				=						self.bottom_root.parent.parent
  
                             # Merge
                             _snake_case      :							str     				=						self.bottom_root.merge_trees(self.bottom_root.parent					)
  
                             # Update Links
                             _snake_case      :							List[str]     				=						next_node
                             _snake_case      :							Any     				=						None
                             if next_node:
                                    _snake_case      :							Tuple     				=						self.bottom_root
  
  
  
        def    __a (					self					)      ->   List[Any]:
  
  
  
               '''simple docstring'''
  
               return self.min_node.val
  
  
  
        def    __a (					self					)      ->   Any:
  
  
  
               '''simple docstring'''
  
               return self.size == 0
  
  
  
        def    __a (					self					)      ->   Optional[int]:
  
  
  
               '''simple docstring'''
  
               _snake_case      :							Any     				=						self.min_node.val
  
               # Last element in heap corner case
               if self.size == 1:
                      # Update size
                      _snake_case      :							Any     				=						0
  
                      # Update bottom root
                      _snake_case      :							Dict     				=						None
  
                      # Update min_node
                      _snake_case      :							Dict     				=						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
                      _snake_case      :							int     				=						self.bottom_root.parent
                      _snake_case      :							List[Any]     				=						None
  
                      # Update min_node
                      _snake_case      :							int     				=						self.bottom_root
                      _snake_case      :							Any     				=						self.bottom_root.parent
                      while i:
                             if i.val < self.min_node.val:
                                    _snake_case      :							str     				=						i
                             _snake_case      :							Union[str, Any]     				=						i.parent
                      return min_value
               # General case
               # Find the BinomialHeap of the right subtree of min_node
               _snake_case      :							Optional[Any]     				=						self.min_node.right
               _snake_case      :							Tuple     				=						None
               _snake_case      :							Union[str, Any]     				=						bottom_of_new
               _snake_case      :							Any     				=						1
  
               # Size, min_node and bottom_root
               while bottom_of_new.left:
                      _snake_case      :							Any     				=						size_of_new * 2 + 1
                      _snake_case      :							Tuple     				=						bottom_of_new.left
                      if bottom_of_new.val < min_of_new.val:
                             _snake_case      :							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):
                      _snake_case      :							Optional[int]     				=						size_of_new
                      _snake_case      :							List[str]     				=						bottom_of_new
                      _snake_case      :							str     				=						min_of_new
                      # print("Single root, multiple nodes case")
                      return min_value
               # Remaining cases
               # Construct heap of right subtree
               _snake_case      :							int     				=						BinomialHeap(
                   bottom_root=lowercase_     ,  min_node=lowercase_     ,  heap_size=lowercase_					)
  
               # Update size
               _snake_case      :							Tuple     				=						self.size - 1 - size_of_new
  
               # Neighbour nodes
               _snake_case      :							List[str]     				=						self.min_node.left
               _snake_case      :							Tuple     				=						self.min_node.parent
  
               # Initialize new bottom_root and min_node
               _snake_case      :							List[Any]     				=						previous_node or next_node
               _snake_case      :							Tuple     				=						next_node
  
               # Update links of previous_node and search below for new min_node and
               # bottom_root
               if previous_node:
                      _snake_case      :							Union[str, Any]     				=						next_node
  
                      # Update bottom_root and search for min_node below
                      _snake_case      :							Tuple     				=						previous_node
                      _snake_case      :							Union[str, Any]     				=						previous_node
                      while self.bottom_root.left:
                             _snake_case      :							int     				=						self.bottom_root.left
                             if self.bottom_root.val < self.min_node.val:
                                    _snake_case      :							Optional[Any]     				=						self.bottom_root
               if next_node:
                      _snake_case      :							Any     				=						previous_node
  
                      # Search for new min_node above min_node
                      _snake_case      :							Optional[int]     				=						next_node
                      while i:
                             if i.val < self.min_node.val:
                                    _snake_case      :							Optional[int]     				=						i
                             _snake_case      :							str     				=						i.parent
          # Merge heaps
               self.merge_heaps(lowercase_					)
  
               return min_value
  
  
  
        def    __a (					self					)      ->   Optional[Any]:
  
  
  
               '''simple docstring'''
  
               _snake_case      :							Any     				=						self.bottom_root
               while top_root.parent:
                      _snake_case      :							List[str]     				=						top_root.parent
               # preorder
               _snake_case      :							int     				=						[]
               self.__traversal(lowercase_     ,  lowercase_					)
               return heap_pre_order
  
  
  
        def    __a (					self     ,  lowercase_     ,  lowercase_     ,  lowercase_=0					)      ->   Optional[int]:
  
  
  
               '''simple docstring'''
  
               if curr_node:
                      preorder.append((curr_node.val, level)					)
                      self.__traversal(curr_node.left     ,  lowercase_     ,  level + 1					)
                      self.__traversal(curr_node.right     ,  lowercase_     ,  level + 1					)
               else:
                      preorder.append(('''#''', level)					)
  
  
  
        def __str__(					self					)      ->   Dict:
  
  
  
               '''simple docstring'''
  
               if self.is_empty():
                      return ""
               _snake_case      :							Tuple     				=						self.pre_order()
  
               return "\n".join(('''-''' * level + str(lowercase_					)) for value, level in preorder_heap					)
  
  
  # Unit Tests
  if __name__ == "__main__":
     import doctest
  
     doctest.testmod()
  
  
  
  
  
  
  
style_context: 
  
  
  
  
  
  from functools import partial
  from typing import Any, Callable, Dict, List, Type, TypeVar, Union, overload
  
  import torch
  import torch.nn as nn
  import torch.types
  
  
  
  
  def 						A_			(  lowercase_      ,		lowercase_      ,		lowercase_  )			->						torch.Tensor:
         # The first operation in a checkpoint can't be in-place, but it's
         # nice to have in-place addition during inference. Thus...
         if not inplace:
                _snake_case      :							Any     				=						ma + ma
         else:
                ma += ma
  
         return ma
  
  
  
  
  def 						A_			(  lowercase_      ,		lowercase_  )			->						torch.Tensor:
         _snake_case      :							str     				=						-1 * len(lowercase_  )
         _snake_case      :							Any     				=						list(range(len(tensor.shape[:zero_index]  )  )  )
         return tensor.permute(first_inds + [zero_index + i for i in inds]  )
  
  
  
  
  def 						A_			(  lowercase_      ,		lowercase_  )			->						torch.Tensor:
         return t.reshape(t.shape[:-no_dims] + (-1,)  )
  
  
  
  
  def 						A_			(  lowercase_      ,		lowercase_      ,		lowercase_      ,		lowercase_ = 1E-4  )			->						torch.Tensor:
         _snake_case      :							Any     				=						mask.expand(*value.shape  )
         return torch.sum(mask * value      ,		dim=lowercase_  ) / (eps + torch.sum(lowercase_      ,		dim=lowercase_  ))
  
  
  
  
  def 						A_			(  lowercase_      ,		lowercase_ = 2.31_25      ,		lowercase_ = 21.68_75      ,		lowercase_ = 64  )			->						torch.Tensor:
         _snake_case      :							int     				=						torch.linspace(lowercase_      ,		lowercase_      ,		no_bins - 1      ,		device=pts.device  )
         _snake_case      :							Optional[Any]     				=						torch.sqrt(torch.sum((pts.unsqueeze(-2  ) - pts.unsqueeze(-3  )) ** 2      ,		dim=-1  )  )
         return torch.bucketize(lowercase_      ,		lowercase_  )
  
  
  
  
  def 						A_			(  lowercase_      ,		lowercase_  )			->						dict:
         _snake_case      :							Dict     				=						dicts[0]
         _snake_case      :							str     				=						{}
         for k, v in first.items():
                _snake_case      :							List[Any]     				=						[d[k] for d in dicts]
                if isinstance(lowercase_      ,		lowercase_  ):
                       _snake_case      :							Any     				=						dict_multimap(lowercase_      ,		lowercase_  )
                else:
                       _snake_case      :							Dict     				=						fn(lowercase_  )
  
         return new_dict
  
  
  
  
  def 						A_			(  lowercase_      ,		lowercase_  )			->						torch.Tensor:
         _snake_case      :							str     				=						v_bins.view(((1,) * len(x.shape  )) + (len(lowercase_  ),)  )
         _snake_case      :							Union[str, Any]     				=						x[..., None] - reshaped_bins
         _snake_case      :							Optional[Any]     				=						torch.argmin(torch.abs(lowercase_  )      ,		dim=-1  )
         return nn.functional.one_hot(lowercase_      ,		num_classes=len(lowercase_  )  ).float()
  
  
  
  
  def 						A_			(  lowercase_      ,		lowercase_      ,		lowercase_ = 0      ,		lowercase_ = 0  )			->						torch.Tensor:
         _snake_case      :							List[Union[slice, torch.Tensor]]     				=						[]
         for i, s in enumerate(data.shape[:no_batch_dims]  ):
                _snake_case      :							Optional[Any]     				=						torch.arange(lowercase_  )
                _snake_case      :							Union[str, Any]     				=						r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape  ) - i - 1)))  )
                ranges.append(lowercase_  )
  
         _snake_case      :							List[Union[slice, torch.Tensor]]     				=						[slice(lowercase_  ) for _ in range(len(data.shape  ) - no_batch_dims  )]
         _snake_case      :							Union[str, Any]     				=						inds
         ranges.extend(lowercase_  )
         # Matt note: Editing this to get around the behaviour of using a list as an array index changing
         # in recent Numpy versions
         return data[tuple(lowercase_  )]
  
  
  lowerCAmelCase_   =   TypeVar("T")
  
  
  
  
  def 						A_			(  lowercase_      ,		lowercase_      ,		lowercase_  )			->						Dict[Any, Union[dict, list, tuple, Any]]:
         _snake_case      :							Dict[Any, Union[dict, list, tuple, Any]]     				=						{}
         for k, v in dic.items():
                if isinstance(lowercase_      ,		lowercase_  ):
                       _snake_case      :							Dict     				=						dict_map(lowercase_      ,		lowercase_      ,		lowercase_  )
                else:
                       _snake_case      :							List[Any]     				=						tree_map(lowercase_      ,		lowercase_      ,		lowercase_  )
  
         return new_dict
  
  
  
  
  @overload
  def 						A_			(  lowercase_      ,		lowercase_      ,		lowercase_  )			->						Any:
         ...
  
  
  
  
  @overload
  def 						A_			(  lowercase_      ,		lowercase_      ,		lowercase_  )			->						dict:
         ...
  
  
  
  
  @overload
  def 						A_			(  lowercase_      ,		lowercase_      ,		lowercase_  )			->						list:
         ...
  
  
  
  
  @overload
  def 						A_			(  lowercase_      ,		lowercase_      ,		lowercase_  )			->						tuple:
         ...
  
  
  
  
  def 						A_			(  lowercase_      ,		lowercase_      ,		lowercase_  )			->						Any:
         if isinstance(lowercase_      ,		lowercase_  ):
                return dict_map(lowercase_      ,		lowercase_      ,		lowercase_  )
         elif isinstance(lowercase_      ,		lowercase_  ):
                return [tree_map(lowercase_      ,		lowercase_      ,		lowercase_  ) for x in tree]
         elif isinstance(lowercase_      ,		lowercase_  ):
                return tuple(tree_map(lowercase_      ,		lowercase_      ,		lowercase_  ) for x in tree  )
         elif isinstance(lowercase_      ,		lowercase_  ):
                return fn(lowercase_  )
         else:
                print(type(lowercase_  )  )
                raise ValueError('''Not supported'''  )
  lowerCAmelCase_   =   partial(tree_map, leaf_type=torch.Tensor)
  
  
  
  
  
  
  