from __future__ import annotations

from collections.abc import Callable
from typing import Any, Generic, TypeVar

lowerCamelCase_    :		Dict							=	TypeVar("""T""")


class 						a__							(       Generic[T]		):



			def __init__(						self				,						UpperCAmelCase				,						UpperCAmelCase   )			->   None:
								__a		 =       None

								__a		 =       len(UpperCAmelCase   )
								__a		 =       [any_type for _ in range(self.N   )] + arr
								__a		 =       fnc
								self.build()



			def __SCREAMING_SNAKE_CASE							(						self   )			->   None:
								for p in range(self.N - 1				,						0				,						-1   ):
													__a		 =       self.fn(self.st[p * 2]				,						self.st[p * 2 + 1]   )



			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase				,						UpperCAmelCase   )			->   None:
								p += self.N
								__a		 =       v
								while p > 1:
													__a		 =       p // 2
													__a		 =       self.fn(self.st[p * 2]				,						self.st[p * 2 + 1]   )







			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase				,						UpperCAmelCase   )			->   T | None:  # noqa: E741
								__a ,				__a		 =       l + self.N, r + self.N

								__a		 =       None
								while l <= r:
													if l % 2 == 1:
																		__a		 =       self.st[l] if res is None else self.fn(UpperCAmelCase				,						self.st[l]   )
													if r % 2 == 0:
																		__a		 =       self.st[r] if res is None else self.fn(UpperCAmelCase				,						self.st[r]   )
													__a ,				__a		 =       (l + 1) // 2, (r - 1) // 2
								return res


if __name__ == "__main__":
						from functools import reduce

						lowerCamelCase_    :		Optional[int]							=	[1, 10, -2, 9, -3, 8, 4, -7, 5, 6, 11, -12]

						lowerCamelCase_    :		Any							=	{
						    0: 7,
						    1: 2,
						    2: 6,
						    3: -14,
						    4: 5,
						    5: 4,
						    6: 7,
						    7: -10,
						    8: 9,
						    9: 10,
						    10: 12,
						    11: 1,
						}

						lowerCamelCase_    :		Dict							=	SegmentTree(test_array, min)
						lowerCamelCase_    :		Optional[int]							=	SegmentTree(test_array, max)
						lowerCamelCase_    :		List[Any]							=	SegmentTree(test_array, lambda a, b: a + b)
						def 							lowerCAmelCase(     ):
											for i in range(len(__lowerCamelCase						)						):
																for j in range(__lowerCamelCase				,    len(__lowerCamelCase						)						):
																					__a		 =       reduce(__lowerCamelCase				,    test_array[i : j + 1]						)
																					__a		 =       reduce(__lowerCamelCase				,    test_array[i : j + 1]						)
																					__a		 =       reduce(lambda __lowerCamelCase				,    __lowerCamelCase						: a + b				,    test_array[i : j + 1]						)
																					assert min_range == min_segment_tree.query(__lowerCamelCase				,    __lowerCamelCase						)
																					assert max_range == max_segment_tree.query(__lowerCamelCase				,    __lowerCamelCase						)
																					assert sum_range == sum_segment_tree.query(__lowerCamelCase				,    __lowerCamelCase						)

						test_all_segments()

						for index, value in test_updates.items():
												lowerCamelCase_    :		Optional[Any]							=	value
												min_segment_tree.update(index, value)
												max_segment_tree.update(index, value)
												sum_segment_tree.update(index, value)
												test_all_segments()





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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import BaseOutput, randn_tensor
from .scheduling_utils import SchedulerMixin


@dataclass
class 						a__							(       __snake_case		):
			A__    :       torch.FloatTensor
			A__    :       torch.FloatTensor
			A__    :       Optional[torch.FloatTensor]        =      None






class 						a__							(       __snake_case				,						__snake_case		):
			A__    :       Optional[Any]        =      2



			@register_to_config
			def __init__(						self				,						UpperCAmelCase = 0.02				,						UpperCAmelCase = 1_0_0				,						UpperCAmelCase = 1.007				,						UpperCAmelCase = 8_0				,						UpperCAmelCase = 0.05				,						UpperCAmelCase = 5_0				,						)			->   Optional[Any]:
								# standard deviation of the initial noise distribution
								__a		 =       sigma_max

								# setable values
								__a		 =       None
								__a		 =       None
								__a		 =       None  # sigma(t_i)



			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase				,						UpperCAmelCase = None   )			->   torch.FloatTensor:
								return sample



			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase				,						UpperCAmelCase = None   )			->   int:
								__a		 =       num_inference_steps
								__a		 =       np.arange(0				,						self.num_inference_steps   )[::-1].copy()
								__a		 =       torch.from_numpy(UpperCAmelCase   ).to(UpperCAmelCase   )
								__a		 =       [
								    (
								        self.config.sigma_max**2
								        * (self.config.sigma_min**2 / self.config.sigma_max**2) ** (i / (num_inference_steps - 1))
								    )
								    for i in self.timesteps
								]
								__a		 =       torch.tensor(UpperCAmelCase				,						dtype=torch.floataa				,						device=UpperCAmelCase   )



			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase				,						UpperCAmelCase				,						UpperCAmelCase = None   )			->   Tuple[torch.FloatTensor, float]:
								if self.config.s_min <= sigma <= self.config.s_max:
													__a		 =       min(self.config.s_churn / self.num_inference_steps				,						2**0.5 - 1   )
								else:
													__a		 =       0

								# sample eps ~ N(0, S_noise^2 * I)
								__a		 =       self.config.s_noise * randn_tensor(sample.shape				,						generator=UpperCAmelCase   ).to(sample.device   )
								__a		 =       sigma + gamma * sigma
								__a		 =       sample + ((sigma_hat**2 - sigma**2) ** 0.5 * eps)

								return sample_hat, sigma_hat



			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase				,						UpperCAmelCase				,						UpperCAmelCase				,						UpperCAmelCase				,						UpperCAmelCase = True				,						)			->   Union[KarrasVeOutput, Tuple]:
								__a		 =       sample_hat + sigma_hat * model_output
								__a		 =       (sample_hat - pred_original_sample) / sigma_hat
								__a		 =       sample_hat + (sigma_prev - sigma_hat) * derivative

								if not return_dict:
													return (sample_prev, derivative)

								return KarrasVeOutput(
								    prev_sample=UpperCAmelCase				,						derivative=UpperCAmelCase				,						pred_original_sample=UpperCAmelCase   )



			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase				,						UpperCAmelCase				,						UpperCAmelCase				,						UpperCAmelCase				,						UpperCAmelCase				,						UpperCAmelCase				,						UpperCAmelCase = True				,						)			->   Union[KarrasVeOutput, Tuple]:
								__a		 =       sample_prev + sigma_prev * model_output
								__a		 =       (sample_prev - pred_original_sample) / sigma_prev
								__a		 =       sample_hat + (sigma_prev - sigma_hat) * (0.5 * derivative + 0.5 * derivative_corr)

								if not return_dict:
													return (sample_prev, derivative)

								return KarrasVeOutput(
								    prev_sample=UpperCAmelCase				,						derivative=UpperCAmelCase				,						pred_original_sample=UpperCAmelCase   )







			def __SCREAMING_SNAKE_CASE							(						self				,						UpperCAmelCase				,						UpperCAmelCase				,						UpperCAmelCase   )			->   List[Any]:
								raise NotImplementedError()




