






class 					a					:



      """simple docstring"""


      def __init__(   self      :    Optional[int]	,   __lowercase      :    List[str]      )							->   List[str]:
        __UpperCAmelCase							:			int     =						val
        # Number of nodes in left subtree
        __UpperCAmelCase							:			Any     =						0
        __UpperCAmelCase							:			List[str]     =						None
        __UpperCAmelCase							:			int     =						None
        __UpperCAmelCase							:			Dict     =						None




      def 			UpperCAmelCase   (   self      :    Tuple	,   __lowercase      :    Optional[Any]      )							->   Optional[int]:
        assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

        if self.val < other.val:
          __UpperCAmelCase							:			Dict     =						self.right
          __UpperCAmelCase							:			int     =						None
          if self.right:
            __UpperCAmelCase							:			Optional[Any]     =						other
          __UpperCAmelCase							:			List[Any]     =						other
          __UpperCAmelCase							:			Optional[int]     =						self.left_tree_size * 2 + 1
          return self
        else:
          __UpperCAmelCase							:			Dict     =						other.right
          __UpperCAmelCase							:			Optional[Any]     =						None
          if other.right:
            __UpperCAmelCase							:			int     =						self
          __UpperCAmelCase							:			int     =						self
          __UpperCAmelCase							:			int     =						other.left_tree_size * 2 + 1
          return other


class 					a					:



      """simple docstring"""


      def __init__(   self      :    Union[str, Any]	,   __lowercase      :    Union[str, Any]=None	,   __lowercase      :    str=None	,   __lowercase      :    List[Any]=0      )							->   Dict:
        __UpperCAmelCase							:			Any     =						heap_size
        __UpperCAmelCase							:			Optional[Any]     =						bottom_root
        __UpperCAmelCase							:			List[str]     =						min_node
      def 			UpperCAmelCase   (   self      :    Optional[int]	,   __lowercase      :    List[str]      )							->   Union[str, Any]:

        # Empty heaps corner cases
        if other.size == 0:
          return None
        if self.size == 0:
          __UpperCAmelCase							:			str     =						other.size
          __UpperCAmelCase							:			Any     =						other.bottom_root
          __UpperCAmelCase							:			Optional[Any]     =						other.min_node
          return None
        # Update size
        __UpperCAmelCase							:			int     =						self.size + other.size

        # Update min.node
        if self.min_node.val > other.min_node.val:
          __UpperCAmelCase							:			List[str]     =						other.min_node
        # Merge

        # Order roots by left_subtree_size
        __UpperCAmelCase							:			Optional[Any]     =						[]
        __UpperCAmelCase   ,				__UpperCAmelCase							:			List[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							:			List[Any]     =						i.parent
          else:
            combined_roots_list.append((j, False)      )
            __UpperCAmelCase							:			List[Any]     =						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]:
            __UpperCAmelCase							:			List[str]     =						combined_roots_list[i + 1][0]
            __UpperCAmelCase							:			List[Any]     =						combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
        __UpperCAmelCase							:			Optional[int]     =						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							:			Any     =						i.left
            __UpperCAmelCase							:			List[str]     =						i.parent.parent

            # Merging trees
            __UpperCAmelCase							:			Optional[int]     =						i.merge_trees(i.parent      )

            # Updating links
            __UpperCAmelCase							:			Dict     =						previous_node
            __UpperCAmelCase							:			str     =						next_node
            if previous_node:
              __UpperCAmelCase							:			Any     =						i
            if next_node:
              __UpperCAmelCase							:			str     =						i
          else:
            __UpperCAmelCase							:			str     =						i.parent
        # Updating self.bottom_root
        while i.left:
          __UpperCAmelCase							:			Union[str, Any]     =						i.left
        __UpperCAmelCase							:			Optional[Any]     =						i

        # Update other
        __UpperCAmelCase							:			List[Any]     =						self.size
        __UpperCAmelCase							:			List[str]     =						self.bottom_root
        __UpperCAmelCase							:			Dict     =						self.min_node

        # Return the merged heap
        return self
      def 			UpperCAmelCase   (   self      :    Dict	,   __lowercase      :    Any      )							->   Tuple:
        if self.size == 0:
          __UpperCAmelCase							:			int     =						Node(__lowercase      )
          __UpperCAmelCase							:			List[str]     =						1
          __UpperCAmelCase							:			List[Any]     =						self.bottom_root
        else:
          # Create new node
          __UpperCAmelCase							:			Dict     =						Node(__lowercase      )

          # Update size
          self.size += 1

          # update min_node
          if val < self.min_node.val:
            __UpperCAmelCase							:			Any     =						new_node
          # Put new_node as a bottom_root in heap
          __UpperCAmelCase							:			Union[str, Any]     =						new_node
          __UpperCAmelCase							:			List[Any]     =						self.bottom_root
          __UpperCAmelCase							:			Optional[int]     =						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							:			Optional[int]     =						self.bottom_root.parent.parent

            # Merge
            __UpperCAmelCase							:			int     =						self.bottom_root.merge_trees(self.bottom_root.parent      )

            # Update Links
            __UpperCAmelCase							:			Union[str, Any]     =						next_node
            __UpperCAmelCase							:			Optional[Any]     =						None
            if next_node:
              __UpperCAmelCase							:			List[Any]     =						self.bottom_root
      def 			UpperCAmelCase   (   self      :    int      )							->   Tuple:
        return self.min_node.val
      def 			UpperCAmelCase   (   self      :    str      )							->   str:
        return self.size == 0
      def 			UpperCAmelCase   (   self      :    Dict      )							->   List[Any]:
        __UpperCAmelCase							:			Optional[Any]     =						self.min_node.val

        # Last element in heap corner case
        if self.size == 1:
          # Update size
          __UpperCAmelCase							:			Optional[Any]     =						0

          # Update bottom root
          __UpperCAmelCase							:			List[str]     =						None

          # Update min_node
          __UpperCAmelCase							:			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							:			List[Any]     =						self.bottom_root.parent
          __UpperCAmelCase							:			Any     =						None

          # Update min_node
          __UpperCAmelCase							:			List[Any]     =						self.bottom_root
          __UpperCAmelCase							:			Tuple     =						self.bottom_root.parent
          while i:
            if i.val < self.min_node.val:
              __UpperCAmelCase							:			Union[str, Any]     =						i
            __UpperCAmelCase							:			List[Any]     =						i.parent
          return min_value
        # General case
        # Find the BinomialHeap of the right subtree of min_node
        __UpperCAmelCase							:			Any     =						self.min_node.right
        __UpperCAmelCase							:			Tuple     =						None
        __UpperCAmelCase							:			Dict     =						bottom_of_new
        __UpperCAmelCase							:			Tuple     =						1

        # Size, min_node and bottom_root
        while bottom_of_new.left:
          __UpperCAmelCase							:			int     =						size_of_new * 2 + 1
          __UpperCAmelCase							:			Optional[Any]     =						bottom_of_new.left
          if bottom_of_new.val < min_of_new.val:
            __UpperCAmelCase							:			Any     =						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							:			Optional[Any]     =						size_of_new
          __UpperCAmelCase							:			List[str]     =						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=__lowercase	,   min_node=__lowercase	,   heap_size=__lowercase      )

        # Update size
        __UpperCAmelCase							:			str     =						self.size - 1 - size_of_new

        # Neighbour nodes
        __UpperCAmelCase							:			str     =						self.min_node.left
        __UpperCAmelCase							:			int     =						self.min_node.parent

        # Initialize new bottom_root and min_node
        __UpperCAmelCase							:			int     =						previous_node or next_node
        __UpperCAmelCase							:			Optional[Any]     =						next_node

        # Update links of previous_node and search below for new min_node and
        # bottom_root
        if previous_node:
          __UpperCAmelCase							:			List[str]     =						next_node

          # Update bottom_root and search for min_node below
          __UpperCAmelCase							:			Optional[int]     =						previous_node
          __UpperCAmelCase							:			int     =						previous_node
          while self.bottom_root.left:
            __UpperCAmelCase							:			Any     =						self.bottom_root.left
            if self.bottom_root.val < self.min_node.val:
              __UpperCAmelCase							:			Optional[int]     =						self.bottom_root
        if next_node:
          __UpperCAmelCase							:			int     =						previous_node

          # Search for new min_node above min_node
          __UpperCAmelCase							:			Union[str, Any]     =						next_node
          while i:
            if i.val < self.min_node.val:
              __UpperCAmelCase							:			Tuple     =						i
            __UpperCAmelCase							:			List[str]     =						i.parent
        # Merge heaps
        self.merge_heaps(__lowercase      )

        return min_value
      def 			UpperCAmelCase   (   self      :    Optional[Any]      )							->   Any:
        __UpperCAmelCase							:			Any     =						self.bottom_root
        while top_root.parent:
          __UpperCAmelCase							:			Optional[int]     =						top_root.parent
        # preorder
        __UpperCAmelCase							:			str     =						[]
        self.__traversal(__lowercase	,   __lowercase      )
        return heap_pre_order
      def 			UpperCAmelCase   (   self      :    Optional[int]	,   __lowercase      :    Dict	,   __lowercase      :    Union[str, Any]	,   __lowercase      :    Dict=0      )							->   List[str]:
        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      :    int      )							->   Optional[int]:
        if self.is_empty():
          return ""
        __UpperCAmelCase							:			Optional[int]     =						self.pre_order()

        return "\n".join(("""-""" * level + str(__lowercase      )) for value, level in preorder_heap      )


# Unit Tests
if __name__ == "__main__":
       import doctest

       doctest.testmod()










import enum
import inspect
import warnings
from functools import wraps
from typing import Callable, Optional

from .logging import get_logger


a	: Any      =				set()
a	: List[Any]      =				get_logger(__name__)






def        lowerCamelCase__   (					__lowerCamelCase    :  Optional[str] = None	):

  def decorator(__lowerCamelCase    :  Callable	):
    global _emitted_deprecation_warnings

    if inspect.isclass(__lowerCamelCase	):
      __UpperCAmelCase							:			Optional[Any]     =						deprecated_class_or_function.__init__
      __UpperCAmelCase							:			int     =						deprecated_class_or_function.__name__
    else:
      __UpperCAmelCase							:			Any     =						deprecated_class_or_function
      __UpperCAmelCase							:			Any     =						deprecated_function.__name__
      # Support deprecating __init__ class method: class name instead
      __UpperCAmelCase							:			List[str]     =						name if name != """__init__""" else deprecated_function.__qualname__.split("""."""	)[-2]

    __UpperCAmelCase							:			Union[str, Any]     =						(
        f"""{name} is deprecated and will be removed in the next major version of datasets.""" + f""" {help_message}"""
        if help_message
        else """"""
    )

    @wraps(__lowerCamelCase	)
    def wrapper(*__lowerCamelCase    :  List[str]						,	**__lowerCamelCase    :  Tuple	):
      __UpperCAmelCase							:			Optional[Any]     =						hash(__lowerCamelCase	)
      if func_hash not in _emitted_deprecation_warnings:
        warnings.warn(__lowerCamelCase						,	category=__lowerCamelCase						,	stacklevel=2	)
        _emitted_deprecation_warnings.add(__lowerCamelCase	)
      return deprecated_function(*__lowerCamelCase						,	**__lowerCamelCase	)

    __UpperCAmelCase							:			List[str]     =						"""deprecated"""

    if inspect.isclass(__lowerCamelCase	):
      __UpperCAmelCase							:			int     =						wrapper
      return deprecated_class_or_function
    else:
      return wrapper

  return decorator
class 					a					(				enum.EnumMeta     ):



      """simple docstring"""


      def __getattribute__(   cls      :    Optional[int]	,   __lowercase      :    List[Any]      )							->   str:
        __UpperCAmelCase							:			List[Any]     =						super().__getattribute__(__lowercase      )
        if isinstance(__lowercase	,   enum.Enum      ) and obj._on_access:
          obj._on_access()
        return obj
      def __getitem__(   cls      :    Union[str, Any]	,   __lowercase      :    Optional[int]      )							->   Optional[int]:
        __UpperCAmelCase							:			Union[str, Any]     =						super().__getitem__(__lowercase      )
        if member._on_access:
          member._on_access()
        return member




      def __call__(   cls      :    List[str]	,   __lowercase      :    Dict	,   __lowercase      :    List[Any]=None	,   *, __lowercase      :    Dict=None	,   __lowercase      :    Any=None	,   __lowercase      :    Optional[Any]=None	,   __lowercase      :    Dict=1      )							->   List[Any]:
        __UpperCAmelCase							:			Union[str, Any]     =						super().__call__(__lowercase	,   __lowercase	,   module=__lowercase	,   qualname=__lowercase	,   type=__lowercase	,   start=__lowercase      )
        if isinstance(__lowercase	,   enum.Enum      ) and obj._on_access:
          obj._on_access()
        return obj


class 					a					(				enum.Enum							, metaclass=lowercase__     ):



      """simple docstring"""


      def __new__(   cls      :    Dict	,   __lowercase      :    Tuple      )							->   Optional[Any]:
        __UpperCAmelCase							:			List[Any]     =						object.__new__(cls      )
        __UpperCAmelCase							:			Any     =						value
        __UpperCAmelCase							:			int     =						member.deprecate
        return member
      @property
      def 			UpperCAmelCase   (   self      :    Optional[Any]      )							->   Dict:
        return ""




      def 			UpperCAmelCase   (   self      :    str      )							->   Dict:
        __UpperCAmelCase							:			Optional[int]     =						f""" {self.help_message}""" if self.help_message else """"""
        warnings.warn(
            f"""'{self.__objclass__.__name__}' is deprecated and will be removed in the next major version of datasets."""
            + help_message	,   __lowercase	,   stacklevel=3	,   )


