






'''simple docstring'''
from __future__ import annotations

from collections import deque
from enum import Enum
from math import atana, degrees
from sys import maxsize


class    _snake_case   (				snake_case					):

					"""simple docstring"""





					_UpperCamelCase		 =      1
					_UpperCamelCase		 =      2
					_UpperCamelCase		 =      3




					def __repr__(     self     )      ->	Any:
										return F'''{self.__class__.__name__}.{self.name}'''



def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase					,  _UpperCAmelCase )				->				float:






					"""simple docstring"""







					a_							,					a_									=   point
					return degrees(atana(y - miny					,  x - minx ) )

def 							a	(   _UpperCAmelCase					,  _UpperCAmelCase					,  _UpperCAmelCase )				->				Direction:






					"""simple docstring"""







					a_							,					a_									=   starting
					a_							,					a_									=   via
					a_							,					a_									=   target
					a_									=   degrees(atana(ya - ya					,  xa - xa ) )
					via_angle %= 3_6_0
					a_									=   degrees(atana(ya - ya					,  xa - xa ) )
					target_angle %= 3_6_0
					# t-
					#  \ \
					#   \ v
					#    \|
					#     s
					# via_angle is always lower than target_angle, if direction is left.
					# If they are same, it means they are on a same line of convex hull.
					if target_angle > via_angle:
										return Direction.left
					elif target_angle == via_angle:
										return Direction.straight
					else:
										return Direction.right





def 							a	(   _UpperCAmelCase )				->				list[tuple[int, int]]:






					"""simple docstring"""







					if len(_UpperCAmelCase ) <= 2:
										# There is no convex hull
										raise ValueError('graham_scan: argument must contain more than 3 points.' )
					if len(_UpperCAmelCase ) == 3:
										return points
					# find the lowest and the most left point
					a_									=   0
					a_							,					a_									=   maxsize, maxsize
					for i, point in enumerate(_UpperCAmelCase ):
										a_									=   point[0]
										a_									=   point[1]
										if y < miny:
															a_									=   y
															a_									=   x
															a_									=   i
										if y == miny and x < minx:
															a_									=   x
															a_									=   i

    # remove the lowest and the most left point from points for preparing for sort
					points.pop(_UpperCAmelCase )

					a_									=   sorted(_UpperCAmelCase					,  key=lambda _UpperCAmelCase : angle_comparer(_UpperCAmelCase					,  _UpperCAmelCase					,  _UpperCAmelCase ) )
					# This insert actually costs complexity,
					# and you should instead add (minx, miny) into stack later.
					# I'm using insert just for easy understanding.
					sorted_points.insert(0					,  (minx, miny) )

					a_									=   deque()
					stack.append(sorted_points[0] )
					stack.append(sorted_points[1] )
					stack.append(sorted_points[2] )
					# In any ways, the first 3 points line are towards left.
					# Because we sort them the angle from minx, miny.
					a_									=   Direction.left

					for i in range(3					,  len(_UpperCAmelCase ) ):
										while True:
															a_									=   stack[-2]
															a_									=   stack[-1]
															a_									=   sorted_points[i]
															a_									=   check_direction(_UpperCAmelCase					,  _UpperCAmelCase					,  _UpperCAmelCase )

															if next_direction == Direction.left:
																				a_									=   Direction.left
																				break
															if next_direction == Direction.straight:
																				if current_direction == Direction.left:
																									# We keep current_direction as left.
																									# Because if the straight line keeps as straight,
																									# we want to know if this straight line is towards left.
																									break
																				elif current_direction == Direction.right:
																									# If the straight line is towards right,
																									# every previous points on those straigh line is not convex hull.
																									stack.pop()
															if next_direction == Direction.right:
																				stack.pop()
										stack.append(sorted_points[i] )
					return list(_UpperCAmelCase )









'''simple docstring'''
from typing import List, Optional, Tuple, Union

import torch

from ...models import UNetaDModel
from ...schedulers import PNDMScheduler
from ...utils import randn_tensor
from ..pipeline_utils import DiffusionPipeline, ImagePipelineOutput


class    _snake_case   (				snake_case					):

					"""simple docstring"""





					_UpperCamelCase		 =      42
					_UpperCamelCase		 =      42




					def __init__(     self   , UpperCAmelCase__   , UpperCAmelCase__     )      ->	int:
										super().__init__()

										a_									=   PNDMScheduler.from_config(scheduler.config     )

										self.register_modules(unet=UpperCAmelCase__   , scheduler=UpperCAmelCase__     )




					@torch.no_grad()
					def __call__(     self   , UpperCAmelCase__ = 1   , UpperCAmelCase__ = 50   , UpperCAmelCase__ = None   , UpperCAmelCase__ = "pil"   , UpperCAmelCase__ = True   , **UpperCAmelCase__   , )      ->	Union[ImagePipelineOutput, Tuple]:
										a_									=   randn_tensor(
										    (batch_size, self.unet.config.in_channels, self.unet.config.sample_size, self.unet.config.sample_size)   , generator=UpperCAmelCase__   , device=self.device   , )

										self.scheduler.set_timesteps(UpperCAmelCase__     )
										for t in self.progress_bar(self.scheduler.timesteps     ):
															a_									=   self.unet(UpperCAmelCase__   , UpperCAmelCase__     ).sample

															a_									=   self.scheduler.step(UpperCAmelCase__   , UpperCAmelCase__   , UpperCAmelCase__     ).prev_sample

										a_									=   (image / 2 + 0.5).clamp(0   , 1     )
										a_									=   image.cpu().permute(0   , 2   , 3   , 1     ).numpy()
										if output_type == "pil":
															a_									=   self.numpy_to_pil(UpperCAmelCase__     )

										if not return_dict:
															return (image,)

										return ImagePipelineOutput(images=UpperCAmelCase__     )

