




class        __SCREAMING_SNAKE_CASE							:

					def __init__(       self				, __lowercase      ):







						'''simple docstring'''




						lowerCamelCase_							:	Optional[Any]							     =							val
						# Number of nodes in left subtree
						lowerCamelCase_							:	str							     =							0
						lowerCamelCase_							:	List[str]							     =							None
						lowerCamelCase_							:	Optional[int]							     =							None
						lowerCamelCase_							:	Dict							     =							None





					def 			lowercase_							(       self				, __lowercase      ):







						'''simple docstring'''




						assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

						if self.val < other.val:
							lowerCamelCase_							:	str							     =							self.right
							lowerCamelCase_							:	Any							     =							None
							if self.right:
								lowerCamelCase_							:	Any							     =							other
							lowerCamelCase_							:	List[Any]							     =							other
							lowerCamelCase_							:	List[str]							     =							self.left_tree_size * 2 + 1
							return self
						else:
							lowerCamelCase_							:	int							     =							other.right
							lowerCamelCase_							:	Tuple							     =							None
							if other.right:
								lowerCamelCase_							:	str							     =							self
							lowerCamelCase_							:	int							     =							self
							lowerCamelCase_							:	List[Any]							     =							other.left_tree_size * 2 + 1
							return other


class        __SCREAMING_SNAKE_CASE							:

					def __init__(       self				, __lowercase=None				, __lowercase=None				, __lowercase=0      ):







						'''simple docstring'''




						lowerCamelCase_							:	int							     =							heap_size
						lowerCamelCase_							:	Optional[Any]							     =							bottom_root
						lowerCamelCase_							:	Optional[int]							     =							min_node

					def 			lowercase_							(       self				, __lowercase      ):







						'''simple docstring'''




						if other.size == 0:
							return None
						if self.size == 0:
							lowerCamelCase_							:	Dict							     =							other.size
							lowerCamelCase_							:	Optional[Any]							     =							other.bottom_root
							lowerCamelCase_							:	Optional[Any]							     =							other.min_node
							return None
						# Update size
						lowerCamelCase_							:	List[str]							     =							self.size + other.size

						# Update min.node
						if self.min_node.val > other.min_node.val:
							lowerCamelCase_							:	Optional[int]							     =							other.min_node
						# Merge

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

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

								# Updating links
								lowerCamelCase_							:	List[Any]							     =							previous_node
								lowerCamelCase_							:	str							     =							next_node
								if previous_node:
									lowerCamelCase_							:	int							     =							i
								if next_node:
									lowerCamelCase_							:	List[Any]							     =							i
							else:
								lowerCamelCase_							:	Any							     =							i.parent
        # Updating self.bottom_root
						while i.left:
							lowerCamelCase_							:	Tuple							     =							i.left
						lowerCamelCase_							:	Tuple							     =							i

						# Update other
						lowerCamelCase_							:	int							     =							self.size
						lowerCamelCase_							:	Optional[Any]							     =							self.bottom_root
						lowerCamelCase_							:	List[str]							     =							self.min_node

						# Return the merged heap
						return self

					def 			lowercase_							(       self				, __lowercase      ):







						'''simple docstring'''




						if self.size == 0:
							lowerCamelCase_							:	List[str]							     =							Node(__lowercase      )
							lowerCamelCase_							:	Union[str, Any]							     =							1
							lowerCamelCase_							:	Optional[Any]							     =							self.bottom_root
						else:
							# Create new node
							lowerCamelCase_							:	List[Any]							     =							Node(__lowercase      )

							# Update size
							self.size += 1

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

								# Merge
								lowerCamelCase_							:	Any							     =							self.bottom_root.merge_trees(self.bottom_root.parent      )

								# Update Links
								lowerCamelCase_							:	int							     =							next_node
								lowerCamelCase_							:	Any							     =							None
								if next_node:
									lowerCamelCase_							:	Any							     =							self.bottom_root

					def 			lowercase_							(       self      ):







						'''simple docstring'''




						return self.min_node.val

					def 			lowercase_							(       self      ):







						'''simple docstring'''




						return self.size == 0

					def 			lowercase_							(       self      ):







						'''simple docstring'''




						lowerCamelCase_							:	Tuple							     =							self.min_node.val

						# Last element in heap corner case
						if self.size == 1:
							# Update size
							lowerCamelCase_							:	int							     =							0

							# Update bottom root
							lowerCamelCase_							:	List[Any]							     =							None

							# Update min_node
							lowerCamelCase_							:	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
							lowerCamelCase_							:	Tuple							     =							self.bottom_root.parent
							lowerCamelCase_							:	Optional[Any]							     =							None

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

						# Size, min_node and bottom_root
						while bottom_of_new.left:
							lowerCamelCase_							:	Optional[int]							     =							size_of_new * 2 + 1
							lowerCamelCase_							:	List[str]							     =							bottom_of_new.left
							if bottom_of_new.val < min_of_new.val:
								lowerCamelCase_							:	Dict							     =							bottom_of_new
        # Corner case of single root on top left path
						if (not self.min_node.left) and (not self.min_node.parent):
							lowerCamelCase_							:	Union[str, Any]							     =							size_of_new
							lowerCamelCase_							:	Union[str, Any]							     =							bottom_of_new
							lowerCamelCase_							:	List[str]							     =							min_of_new
							# print("Single root, multiple nodes case")
							return min_value
						# Remaining cases
						# Construct heap of right subtree
						lowerCamelCase_							:	Optional[Any]							     =							BinomialHeap(
						    bottom_root=__lowercase				, min_node=__lowercase				, heap_size=__lowercase      )

						# Update size
						lowerCamelCase_							:	Optional[Any]							     =							self.size - 1 - size_of_new

						# Neighbour nodes
						lowerCamelCase_							:	Any							     =							self.min_node.left
						lowerCamelCase_							:	Tuple							     =							self.min_node.parent

						# Initialize new bottom_root and min_node
						lowerCamelCase_							:	Union[str, Any]							     =							previous_node or next_node
						lowerCamelCase_							:	Tuple							     =							next_node

						# Update links of previous_node and search below for new min_node and
						# bottom_root
						if previous_node:
							lowerCamelCase_							:	Optional[int]							     =							next_node

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

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

						return min_value

					def 			lowercase_							(       self      ):







						'''simple docstring'''




						lowerCamelCase_							:	Dict							     =							self.bottom_root
						while top_root.parent:
							lowerCamelCase_							:	Optional[int]							     =							top_root.parent
						# preorder
						lowerCamelCase_							:	Union[str, Any]							     =							[]
						self.__traversal(__lowercase				, __lowercase      )
						return heap_pre_order

					def 			lowercase_							(       self				, __lowercase				, __lowercase				, __lowercase=0      ):







						'''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      ):







						'''simple docstring'''




						if self.is_empty():
							return ""
						lowerCamelCase_							:	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()






from dataclasses import dataclass
from typing import List, Optional, Union

import numpy as np
import PIL
from PIL import Image

from ...utils import is_torch_available, is_transformers_available


if is_transformers_available() and is_torch_available():
							from .image_encoder import PaintByExampleImageEncoder
							from .pipeline_paint_by_example import PaintByExamplePipeline
