





'''simple docstring'''

import colorsys
import io

import cva
import matplotlib as mpl
import matplotlib.colors as mplc
import matplotlib.figure as mplfigure
import numpy as np
import torch
from matplotlib.backends.backend_agg import FigureCanvasAgg

from utils import img_tensorize


lowerCAmelCase__      :   str      	=			10_00


class      SCREAMING_SNAKE_CASE__      :







					"""simple docstring"""






					def __init__(   self       :      List[str]		,	UpperCAmelCase_       :      Dict		,	UpperCAmelCase_       :      List[Any]=1.2		,	UpperCAmelCase_       :      Union[str, Any]="g"		,	UpperCAmelCase_       :      Optional[int]=0.5		,	UpperCAmelCase_       :      Optional[Any]="-"		,	UpperCAmelCase_       :      List[Any]="test_out.jpg"		,	UpperCAmelCase_       :      Union[str, Any]=True		,	UpperCAmelCase_       :      List[str]=False		,	UpperCAmelCase_       :      Optional[Any]=None		,	UpperCAmelCase_       :      Union[str, Any]=None		,	UpperCAmelCase_       :      Any=0.7		,	):







							"""simple docstring"""
							if isinstance(UpperCAmelCase_		,	torch.Tensor		):
									__UpperCAmelCase	:							List[Any]     =     img.numpy().astype("np.uint8"		)
							if isinstance(UpperCAmelCase_		,	UpperCAmelCase_		):
									__UpperCAmelCase	:							str     =     img_tensorize(UpperCAmelCase_		)
							assert isinstance(UpperCAmelCase_		,	np.ndarray		)

							__UpperCAmelCase  ,			__UpperCAmelCase	:							Optional[int]     =     img.shape[1], img.shape[0]
							__UpperCAmelCase	:							Any     =     mplfigure.Figure(frameon=UpperCAmelCase_		)
							__UpperCAmelCase	:							str     =     fig.get_dpi()
							__UpperCAmelCase	:							Dict     =     (width * scale + 1e-2) / dpi
							__UpperCAmelCase	:							str     =     (height * scale + 1e-2) / dpi
							fig.set_size_inches(UpperCAmelCase_		,	UpperCAmelCase_		)
							__UpperCAmelCase	:							List[str]     =     fig.add_axes([0.0, 0.0, 1.0, 1.0]		)
							ax.axis("off"		)
							ax.set_xlim(0.0		,	UpperCAmelCase_		)
							ax.set_ylim(UpperCAmelCase_		)

							__UpperCAmelCase	:							Union[str, Any]     =     saveas
							__UpperCAmelCase	:							Optional[int]     =     rgb
							__UpperCAmelCase	:							Optional[Any]     =     pynb
							__UpperCAmelCase	:							Optional[Any]     =     img
							__UpperCAmelCase	:							List[Any]     =     edgecolor
							__UpperCAmelCase	:							Optional[Any]     =     0.5
							__UpperCAmelCase	:							int     =     linestyle
							__UpperCAmelCase	:							int     =     int(np.sqrt(min(UpperCAmelCase_		,	UpperCAmelCase_		)		) * scale // 3		)
							__UpperCAmelCase	:							str     =     width
							__UpperCAmelCase	:							Dict     =     height
							__UpperCAmelCase	:							Optional[int]     =     scale
							__UpperCAmelCase	:							Optional[int]     =     fig
							__UpperCAmelCase	:							Dict     =     ax
							__UpperCAmelCase	:							List[Any]     =     pad
							__UpperCAmelCase	:							Tuple     =     idaobj
							__UpperCAmelCase	:							Union[str, Any]     =     idaattr
							__UpperCAmelCase	:							Dict     =     FigureCanvasAgg(UpperCAmelCase_		)
					def 		lowerCamelCase_   (   self       :      Optional[Any]		,	UpperCAmelCase_       :      str		,	UpperCAmelCase_       :      List[Any]=None		):







							"""simple docstring"""
							if color is None:
									__UpperCAmelCase	:							int     =     self.edgecolor
							((__UpperCAmelCase)  ,			(__UpperCAmelCase)  ,			(__UpperCAmelCase)  ,			(__UpperCAmelCase))	:							Optional[Any]     =     box
							__UpperCAmelCase	:							Optional[int]     =     xa - xa
							__UpperCAmelCase	:							List[str]     =     ya - ya
							self.ax.add_patch(
							    mpl.patches.Rectangle(
							        (xa, ya)		,	UpperCAmelCase_		,	UpperCAmelCase_		,	fill=UpperCAmelCase_		,	edgecolor=UpperCAmelCase_		,	linewidth=self.font_size // 3		,	alpha=self.alpha		,	linestyle=self.linestyle		,	)		)
					def 		lowerCamelCase_   (   self       :      Union[str, Any]		,	UpperCAmelCase_       :      Tuple		,	UpperCAmelCase_       :      Dict=None		,	UpperCAmelCase_       :      Optional[Any]=None		,	UpperCAmelCase_       :      Optional[Any]=None		,	UpperCAmelCase_       :      Tuple=None		):







							"""simple docstring"""
							if len(boxes.shape		) > 2:
									__UpperCAmelCase	:							int     =     boxes[0]
							if len(obj_ids.shape		) > 1:
									__UpperCAmelCase	:							Union[str, Any]     =     obj_ids[0]
							if len(obj_scores.shape		) > 1:
									__UpperCAmelCase	:							Tuple     =     obj_scores[0]
							if len(attr_ids.shape		) > 1:
									__UpperCAmelCase	:							Union[str, Any]     =     attr_ids[0]
							if len(attr_scores.shape		) > 1:
									__UpperCAmelCase	:							Optional[int]     =     attr_scores[0]
							if isinstance(UpperCAmelCase_		,	torch.Tensor		):
									__UpperCAmelCase	:							List[Any]     =     boxes.numpy()
							if isinstance(UpperCAmelCase_		,	UpperCAmelCase_		):
									__UpperCAmelCase	:							Optional[int]     =     np.array(UpperCAmelCase_		)
							assert isinstance(UpperCAmelCase_		,	np.ndarray		)
							__UpperCAmelCase	:							str     =     np.prod(boxes[:, 2:] - boxes[:, :2]		,	axis=1		)
							__UpperCAmelCase	:							int     =     np.argsort(-areas		).tolist()
							__UpperCAmelCase	:							Optional[int]     =     boxes[sorted_idxs] if boxes is not None else None
							__UpperCAmelCase	:							int     =     obj_ids[sorted_idxs] if obj_ids is not None else None
							__UpperCAmelCase	:							List[str]     =     obj_scores[sorted_idxs] if obj_scores is not None else None
							__UpperCAmelCase	:							int     =     attr_ids[sorted_idxs] if attr_ids is not None else None
							__UpperCAmelCase	:							List[str]     =     attr_scores[sorted_idxs] if attr_scores is not None else None

							__UpperCAmelCase	:							Tuple     =     [self._random_color(maximum=1		) for _ in range(len(UpperCAmelCase_		)		)]
							__UpperCAmelCase	:							str     =     [assigned_colors[idx] for idx in sorted_idxs]
							if obj_ids is not None:
									__UpperCAmelCase	:							Tuple     =     self._create_text_labels_attr(UpperCAmelCase_		,	UpperCAmelCase_		,	UpperCAmelCase_		,	UpperCAmelCase_		)
									for i in range(len(UpperCAmelCase_		)		):
											__UpperCAmelCase	:							Any     =     assigned_colors[i]
											self.add_box(boxes[i]		,	UpperCAmelCase_		)
											self.draw_labels(labels[i]		,	boxes[i]		,	UpperCAmelCase_		)
					def 		lowerCamelCase_   (   self       :      int		,	UpperCAmelCase_       :      Any		,	UpperCAmelCase_       :      Union[str, Any]		,	UpperCAmelCase_       :      List[Any]		):







							"""simple docstring"""
							__UpperCAmelCase  ,			__UpperCAmelCase  ,			__UpperCAmelCase  ,			__UpperCAmelCase	:							Optional[Any]     =     box
							__UpperCAmelCase	:							Dict     =     (xa, ya)
							__UpperCAmelCase	:							Optional[int]     =     (ya - ya) * (xa - xa)
							__UpperCAmelCase	:							Dict     =     _SMALL_OBJ * self.scale
							if instance_area < small or ya - ya < 40 * self.scale:
									if ya >= self.height - 5:
											__UpperCAmelCase	:							List[str]     =     (xa, ya)
									else:
											__UpperCAmelCase	:							Optional[Any]     =     (xa, ya)

							__UpperCAmelCase	:							int     =     (ya - ya) / np.sqrt(self.height * self.width		)
							__UpperCAmelCase	:							Optional[Any]     =     self._change_color_brightness(UpperCAmelCase_		,	brightness_factor=0.7		)
							__UpperCAmelCase	:							Optional[Any]     =     np.clip((height_ratio - 0.02) / 0.08 + 1		,	1.2		,	2		)
							font_size *= 0.75 * self.font_size

							self.draw_text(
							    text=UpperCAmelCase_		,	position=UpperCAmelCase_		,	color=UpperCAmelCase_		,	)
					def 		lowerCamelCase_   (   self       :      Tuple		,	UpperCAmelCase_       :      List[str]		,	UpperCAmelCase_       :      List[Any]		,	UpperCAmelCase_       :      str="g"		,	UpperCAmelCase_       :      Union[str, Any]="left"		,	):







							"""simple docstring"""
							__UpperCAmelCase	:							Union[str, Any]     =     0
							__UpperCAmelCase	:							Tuple     =     self.font_size
							__UpperCAmelCase	:							List[str]     =     np.maximum(list(mplc.to_rgb(UpperCAmelCase_		)		)		,	0.2		)
							__UpperCAmelCase	:							Optional[Any]     =     max(0.8		,	np.max(UpperCAmelCase_		)		)
							__UpperCAmelCase	:							List[str]     =     {
							    "facecolor": "black",
							    "alpha": self.alpha,
							    "pad": self.pad,
							    "edgecolor": "none",
							}
							__UpperCAmelCase  ,			__UpperCAmelCase	:							Dict     =     position
							self.ax.text(
							    UpperCAmelCase_		,	UpperCAmelCase_		,	UpperCAmelCase_		,	size=font_size * self.scale		,	family="sans-serif"		,	bbox=UpperCAmelCase_		,	verticalalignment="top"		,	horizontalalignment=UpperCAmelCase_		,	color=UpperCAmelCase_		,	zorder=10		,	rotation=UpperCAmelCase_		,	)
					def 		lowerCamelCase_   (   self       :      Dict		,	UpperCAmelCase_       :      Union[str, Any]=None		):







							"""simple docstring"""
							if saveas is None:
									__UpperCAmelCase	:							Dict     =     self.saveas
							if saveas.lower().endswith(".jpg"		) or saveas.lower().endswith(".png"		):
									cva.imwrite(
									    UpperCAmelCase_		,	self._get_buffer()[:, :, ::-1]		,	)
							else:
									self.fig.savefig(UpperCAmelCase_		)
					def 		lowerCamelCase_   (   self       :      List[Any]		,	UpperCAmelCase_       :      List[Any]		,	UpperCAmelCase_       :      List[str]		,	UpperCAmelCase_       :      Union[str, Any]		,	UpperCAmelCase_       :      int		):







							"""simple docstring"""
							__UpperCAmelCase	:							Union[str, Any]     =     [self.idaobj[i] for i in classes]
							__UpperCAmelCase	:							Optional[int]     =     [self.idaattr[i] for i in attr_classes]
							__UpperCAmelCase	:							int     =     [
							    f"{label} {score:.2f} {attr} {attr_score:.2f}"
							    for label, score, attr, attr_score in zip(UpperCAmelCase_		,	UpperCAmelCase_		,	UpperCAmelCase_		,	UpperCAmelCase_		)
							]
							return labels
					def 		lowerCamelCase_   (   self       :      Any		,	UpperCAmelCase_       :      Optional[Any]		,	UpperCAmelCase_       :      Optional[int]		):







							"""simple docstring"""
							__UpperCAmelCase	:							Optional[Any]     =     [self.idaobj[i] for i in classes]
							if scores is not None:
									if labels is None:
											__UpperCAmelCase	:							Union[str, Any]     =     ["{:.0f}%".format(s * 100		) for s in scores]
									else:
											__UpperCAmelCase	:							int     =     ["{} {:.0f}%".format(UpperCAmelCase_		,	s * 100		) for li, s in zip(UpperCAmelCase_		,	UpperCAmelCase_		)]
							return labels
					def 		lowerCamelCase_   (   self       :      str		,	UpperCAmelCase_       :      Union[str, Any]=255		):







							"""simple docstring"""
							__UpperCAmelCase	:							List[str]     =     np.random.randint(0		,	len(_COLORS		)		)
							__UpperCAmelCase	:							Dict     =     _COLORS[idx] * maximum
							if not self.rgb:
									__UpperCAmelCase	:							Optional[Any]     =     ret[::-1]
							return ret
					def 		lowerCamelCase_   (   self       :      Optional[int]		):







							"""simple docstring"""
							if not self.pynb:
									__UpperCAmelCase  ,			__UpperCAmelCase	:							Tuple     =     self.canvas.print_to_buffer()
									if (width, height) != (self.width, self.height):
											__UpperCAmelCase	:							List[str]     =     cva.resize(self.img		,	(width, height)		)
									else:
											__UpperCAmelCase	:							Optional[Any]     =     self.img
							else:
									__UpperCAmelCase	:							Union[str, Any]     =     io.BytesIO()  # works for cairo backend
									self.canvas.print_rgba(UpperCAmelCase_		)
									__UpperCAmelCase  ,			__UpperCAmelCase	:							Optional[Any]     =     self.width, self.height
									__UpperCAmelCase	:							List[Any]     =     buf.getvalue()
									__UpperCAmelCase	:							Optional[Any]     =     self.img

							__UpperCAmelCase	:							Any     =     np.frombuffer(UpperCAmelCase_		,	dtype="uint8"		)
							__UpperCAmelCase	:							str     =     buffer.reshape(UpperCAmelCase_		,	UpperCAmelCase_		,	4		)
							__UpperCAmelCase  ,			__UpperCAmelCase	:							Any     =     np.split(UpperCAmelCase_		,	[3]		,	axis=2		)

							try:
									import numexpr as ne  # fuse them with numexpr

									__UpperCAmelCase	:							str     =     ne.evaluate("img * (1 - alpha / 255.0) + rgb * (alpha / 255.0)"		)
							except ImportError:
									__UpperCAmelCase	:							List[Any]     =     alpha.astype("float32"		) / 255.0
									__UpperCAmelCase	:							Tuple     =     img * (1 - alpha) + rgb * alpha

							return visualized_image.astype("uint8"		)






					def 		lowerCamelCase_   (   self       :      Optional[int]		,	UpperCAmelCase_       :      str		,	UpperCAmelCase_       :      int		):







							"""simple docstring"""
							assert brightness_factor >= -1.0 and brightness_factor <= 1.0
							__UpperCAmelCase	:							Union[str, Any]     =     mplc.to_rgb(UpperCAmelCase_		)
							__UpperCAmelCase	:							Any     =     colorsys.rgb_to_hls(*mplc.to_rgb(UpperCAmelCase_		)		)
							__UpperCAmelCase	:							Tuple     =     polygon_color[1] + (brightness_factor * polygon_color[1])
							__UpperCAmelCase	:							List[Any]     =     0.0 if modified_lightness < 0.0 else modified_lightness
							__UpperCAmelCase	:							List[str]     =     1.0 if modified_lightness > 1.0 else modified_lightness
							__UpperCAmelCase	:							Dict     =     colorsys.hls_to_rgb(polygon_color[0]		,	UpperCAmelCase_		,	polygon_color[2]		)
							return modified_color






lowerCAmelCase__      :   int      	=			(
    np.array(
        [
            0.000,
            0.447,
            0.741,
            0.850,
            0.325,
            0.098,
            0.929,
            0.694,
            0.125,
            0.494,
            0.184,
            0.556,
            0.466,
            0.674,
            0.188,
            0.301,
            0.745,
            0.933,
            0.635,
            0.078,
            0.184,
            0.300,
            0.300,
            0.300,
            0.600,
            0.600,
            0.600,
            1.000,
            0.000,
            0.000,
            1.000,
            0.500,
            0.000,
            0.749,
            0.749,
            0.000,
            0.000,
            1.000,
            0.000,
            0.000,
            0.000,
            1.000,
            0.667,
            0.000,
            1.000,
            0.333,
            0.333,
            0.000,
            0.333,
            0.667,
            0.000,
            0.333,
            1.000,
            0.000,
            0.667,
            0.333,
            0.000,
            0.667,
            0.667,
            0.000,
            0.667,
            1.000,
            0.000,
            1.000,
            0.333,
            0.000,
            1.000,
            0.667,
            0.000,
            1.000,
            1.000,
            0.000,
            0.000,
            0.333,
            0.500,
            0.000,
            0.667,
            0.500,
            0.000,
            1.000,
            0.500,
            0.333,
            0.000,
            0.500,
            0.333,
            0.333,
            0.500,
            0.333,
            0.667,
            0.500,
            0.333,
            1.000,
            0.500,
            0.667,
            0.000,
            0.500,
            0.667,
            0.333,
            0.500,
            0.667,
            0.667,
            0.500,
            0.667,
            1.000,
            0.500,
            1.000,
            0.000,
            0.500,
            1.000,
            0.333,
            0.500,
            1.000,
            0.667,
            0.500,
            1.000,
            1.000,
            0.500,
            0.000,
            0.333,
            1.000,
            0.000,
            0.667,
            1.000,
            0.000,
            1.000,
            1.000,
            0.333,
            0.000,
            1.000,
            0.333,
            0.333,
            1.000,
            0.333,
            0.667,
            1.000,
            0.333,
            1.000,
            1.000,
            0.667,
            0.000,
            1.000,
            0.667,
            0.333,
            1.000,
            0.667,
            0.667,
            1.000,
            0.667,
            1.000,
            1.000,
            1.000,
            0.000,
            1.000,
            1.000,
            0.333,
            1.000,
            1.000,
            0.667,
            1.000,
            0.333,
            0.000,
            0.000,
            0.500,
            0.000,
            0.000,
            0.667,
            0.000,
            0.000,
            0.833,
            0.000,
            0.000,
            1.000,
            0.000,
            0.000,
            0.000,
            0.167,
            0.000,
            0.000,
            0.333,
            0.000,
            0.000,
            0.500,
            0.000,
            0.000,
            0.667,
            0.000,
            0.000,
            0.833,
            0.000,
            0.000,
            1.000,
            0.000,
            0.000,
            0.000,
            0.167,
            0.000,
            0.000,
            0.333,
            0.000,
            0.000,
            0.500,
            0.000,
            0.000,
            0.667,
            0.000,
            0.000,
            0.833,
            0.000,
            0.000,
            1.000,
            0.000,
            0.000,
            0.000,
            0.143,
            0.143,
            0.143,
            0.857,
            0.857,
            0.857,
            1.000,
            1.000,
            1.000,
        ]
    )
    .astype(np.floataa)
    .reshape(-1, 3)
)











'''simple docstring'''

class      SCREAMING_SNAKE_CASE__      :







					"""simple docstring"""






					def __init__(   self       :      Tuple		,	UpperCAmelCase_       :      Dict		):







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






					def 		lowerCamelCase_   (   self       :      int		,	UpperCAmelCase_       :      Optional[Any]		):







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

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






class      SCREAMING_SNAKE_CASE__      :







					"""simple docstring"""






					def __init__(   self       :      Optional[int]		,	UpperCAmelCase_       :      Optional[int]=None		,	UpperCAmelCase_       :      Optional[int]=None		,	UpperCAmelCase_       :      Optional[int]=0		):







							"""simple docstring"""
							__UpperCAmelCase	:							Any     =     heap_size
							__UpperCAmelCase	:							Any     =     bottom_root
							__UpperCAmelCase	:							List[str]     =     min_node
					def 		lowerCamelCase_   (   self       :      List[str]		,	UpperCAmelCase_       :      Dict		):







							"""simple docstring"""

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

							# Update min.node
							if self.min_node.val > other.min_node.val:
									__UpperCAmelCase	:							Tuple     =     other.min_node
							# Merge

							# Order roots by left_subtree_size
							__UpperCAmelCase	:							int     =     []
							__UpperCAmelCase  ,			__UpperCAmelCase	:							List[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)		)
											__UpperCAmelCase	:							Optional[Any]     =     i.parent
									else:
											combined_roots_list.append((j, False)		)
											__UpperCAmelCase	:							Tuple     =     j.parent
        # Insert links between them
							for i in range(len(UpperCAmelCase_		) - 1		):
									if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
											__UpperCAmelCase	:							Optional[Any]     =     combined_roots_list[i + 1][0]
											__UpperCAmelCase	:							Any     =     combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
							__UpperCAmelCase	:							List[str]     =     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	:							List[str]     =     i.left
											__UpperCAmelCase	:							Dict     =     i.parent.parent

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

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

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

							# Return the merged heap
							return self
					def 		lowerCamelCase_   (   self       :      Tuple		,	UpperCAmelCase_       :      Optional[int]		):







							"""simple docstring"""
							if self.size == 0:
									__UpperCAmelCase	:							Optional[Any]     =     Node(UpperCAmelCase_		)
									__UpperCAmelCase	:							Optional[Any]     =     1
									__UpperCAmelCase	:							Optional[Any]     =     self.bottom_root
							else:
									# Create new node
									__UpperCAmelCase	:							Optional[Any]     =     Node(UpperCAmelCase_		)

									# Update size
									self.size += 1

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

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

											# Update Links
											__UpperCAmelCase	:							int     =     next_node
											__UpperCAmelCase	:							Any     =     None
											if next_node:
													__UpperCAmelCase	:							Any     =     self.bottom_root
					def 		lowerCamelCase_   (   self       :      Any		):







							"""simple docstring"""
							return self.min_node.val
					def 		lowerCamelCase_   (   self       :      str		):







							"""simple docstring"""
							return self.size == 0
					def 		lowerCamelCase_   (   self       :      int		):







							"""simple docstring"""
							__UpperCAmelCase	:							str     =     self.min_node.val

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

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

									# Update min_node
									__UpperCAmelCase	:							int     =     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	:							str     =     None

									# Update min_node
									__UpperCAmelCase	:							int     =     self.bottom_root
									__UpperCAmelCase	:							int     =     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	:							Optional[int]     =     self.min_node.right
							__UpperCAmelCase	:							List[Any]     =     None
							__UpperCAmelCase	:							Optional[int]     =     bottom_of_new
							__UpperCAmelCase	:							Union[str, Any]     =     1

							# Size, min_node and bottom_root
							while bottom_of_new.left:
									__UpperCAmelCase	:							str     =     size_of_new * 2 + 1
									__UpperCAmelCase	:							List[str]     =     bottom_of_new.left
									if bottom_of_new.val < min_of_new.val:
											__UpperCAmelCase	:							Union[str, 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	:							List[Any]     =     min_of_new
									# print("Single root, multiple nodes case")
									return min_value
							# Remaining cases
							# Construct heap of right subtree
							__UpperCAmelCase	:							Union[str, Any]     =     BinomialHeap(
							    bottom_root=UpperCAmelCase_		,	min_node=UpperCAmelCase_		,	heap_size=UpperCAmelCase_		)

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

							# Neighbour nodes
							__UpperCAmelCase	:							Union[str, Any]     =     self.min_node.left
							__UpperCAmelCase	:							List[str]     =     self.min_node.parent

							# Initialize new bottom_root and min_node
							__UpperCAmelCase	:							Optional[Any]     =     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	:							List[str]     =     previous_node
									__UpperCAmelCase	:							int     =     previous_node
									while self.bottom_root.left:
											__UpperCAmelCase	:							Dict     =     self.bottom_root.left
											if self.bottom_root.val < self.min_node.val:
													__UpperCAmelCase	:							Union[str, Any]     =     self.bottom_root
							if next_node:
									__UpperCAmelCase	:							Tuple     =     previous_node

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

							return min_value
					def 		lowerCamelCase_   (   self       :      Union[str, Any]		):







							"""simple docstring"""
							__UpperCAmelCase	:							Tuple     =     self.bottom_root
							while top_root.parent:
									__UpperCAmelCase	:							Optional[int]     =     top_root.parent
							# preorder
							__UpperCAmelCase	:							Union[str, Any]     =     []
							self.__traversal(UpperCAmelCase_		,	UpperCAmelCase_		)
							return heap_pre_order
					def 		lowerCamelCase_   (   self       :      Optional[int]		,	UpperCAmelCase_       :      Optional[Any]		,	UpperCAmelCase_       :      int		,	UpperCAmelCase_       :      Dict=0		):







							"""simple docstring"""
							if curr_node:
									preorder.append((curr_node.val, level)		)
									self.__traversal(curr_node.left		,	UpperCAmelCase_		,	level + 1		)
									self.__traversal(curr_node.right		,	UpperCAmelCase_		,	level + 1		)
							else:
									preorder.append(("#", level)		)






					def __str__(   self       :      Optional[int]		):







							"""simple docstring"""
							if self.is_empty():
									return ""
							__UpperCAmelCase	:							Optional[Any]     =     self.pre_order()

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


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

			doctest.testmod()




