



from typing import Optional, Tuple, Union

import torch
from einops import rearrange, reduce

from diffusers import DDIMScheduler, DDPMScheduler, DiffusionPipeline, ImagePipelineOutput, UNetaDConditionModel
from diffusers.schedulers.scheduling_ddim import DDIMSchedulerOutput
from diffusers.schedulers.scheduling_ddpm import DDPMSchedulerOutput


lowercase_													=      8






def        __lowerCAmelCase		(	__lowerCamelCase						:     Tuple					, __lowerCamelCase						:     List[Any]=BITS						)	->    Optional[int]:
					__lowerCAmelCase						 =x.device

					__lowerCAmelCase						 =(x * 255).int().clamp(0					, 255						)

					__lowerCAmelCase						 =2 ** torch.arange(bits - 1					, -1					, -1					, device=__lowerCamelCase						)
					__lowerCAmelCase						 =rearrange(__lowerCamelCase					, """d -> d 1 1"""						)
					__lowerCAmelCase						 =rearrange(__lowerCamelCase					, """b c h w -> b c 1 h w"""						)

					__lowerCAmelCase						 =((x & mask) != 0).float()
					__lowerCAmelCase						 =rearrange(__lowerCamelCase					, """b c d h w -> b (c d) h w"""						)
					__lowerCAmelCase						 =bits * 2 - 1
					return bits






def        __lowerCAmelCase		(	__lowerCamelCase						:     Tuple					, __lowerCamelCase						:     Dict=BITS						)	->    Any:
					__lowerCAmelCase						 =x.device

					__lowerCAmelCase						 =(x > 0).int()
					__lowerCAmelCase						 =2 ** torch.arange(bits - 1					, -1					, -1					, device=__lowerCamelCase					, dtype=torch.intaa						)

					__lowerCAmelCase						 =rearrange(__lowerCamelCase					, """d -> d 1 1"""						)
					__lowerCAmelCase						 =rearrange(__lowerCamelCase					, """b (c d) h w -> b c d h w"""					, d=8						)
					__lowerCAmelCase						 =reduce(x * mask					, """b c d h w -> b c h w"""					, """sum"""						)
					return (dec / 255).clamp(0.0					, 1.0						)






def        __lowerCAmelCase		(	self						:     Any					, __lowerCamelCase						:     torch.FloatTensor					, __lowerCamelCase						:     int					, __lowerCamelCase						:     torch.FloatTensor					, __lowerCamelCase						:     float = 0.0					, __lowerCamelCase						:     bool = True					, __lowerCamelCase						:     Optional[int]=None					, __lowerCamelCase						:     bool = True					, )	->    Union[DDIMSchedulerOutput, Tuple]:
					if self.num_inference_steps is None:
										raise ValueError(
										    """Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"""						)

					# See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
					# Ideally, read DDIM paper in-detail understanding

					# Notation (<variable name> -> <name in paper>
					# - pred_noise_t -> e_theta(x_t, t)
					# - pred_original_sample -> f_theta(x_t, t) or x_0
					# - std_dev_t -> sigma_t
					# - eta -> η
					# - pred_sample_direction -> "direction pointing to x_t"
					# - pred_prev_sample -> "x_t-1"

					# 1. get previous step value (=t-1)
					__lowerCAmelCase						 =timestep - self.config.num_train_timesteps // self.num_inference_steps

					# 2. compute alphas, betas
					__lowerCAmelCase						 =self.alphas_cumprod[timestep]
					__lowerCAmelCase						 =self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod

					__lowerCAmelCase						 =1 - alpha_prod_t

					# 3. compute predicted original sample from predicted noise also called
					# "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
					__lowerCAmelCase						 =(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5

					# 4. Clip "predicted x_0"
					__lowerCAmelCase						 =self.bit_scale
					if self.config.clip_sample:
										__lowerCAmelCase						 =torch.clamp(__lowerCamelCase					, -scale					, __lowerCamelCase						)

					# 5. compute variance: "sigma_t(η)" -> see formula (16)
					# σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
					__lowerCAmelCase						 =self._get_variance(__lowerCamelCase					, __lowerCamelCase						)
					__lowerCAmelCase						 =eta * variance ** 0.5

					if use_clipped_model_output:
										# the model_output is always re-derived from the clipped x_0 in Glide
										__lowerCAmelCase						 =(sample - alpha_prod_t ** 0.5 * pred_original_sample) / beta_prod_t ** 0.5

					# 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
					__lowerCAmelCase						 =(1 - alpha_prod_t_prev - std_dev_t**2) ** 0.5 * model_output

					# 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
					__lowerCAmelCase						 =alpha_prod_t_prev ** 0.5 * pred_original_sample + pred_sample_direction

					if eta > 0:
										# randn_like does not support generator https://github.com/pytorch/pytorch/issues/27072
										__lowerCAmelCase						 =model_output.device if torch.is_tensor(__lowerCamelCase						) else """cpu"""
										__lowerCAmelCase						 =torch.randn(model_output.shape					, dtype=model_output.dtype					, generator=__lowerCamelCase						).to(__lowerCamelCase						)
										__lowerCAmelCase						 =self._get_variance(__lowerCamelCase					, __lowerCamelCase						) ** 0.5 * eta * noise

										__lowerCAmelCase						 =prev_sample + variance

					if not return_dict:
										return (prev_sample,)

					return DDIMSchedulerOutput(prev_sample=__lowerCamelCase					, pred_original_sample=__lowerCamelCase						)






def        __lowerCAmelCase		(	self						:     Any					, __lowerCamelCase						:     torch.FloatTensor					, __lowerCamelCase						:     int					, __lowerCamelCase						:     torch.FloatTensor					, __lowerCamelCase						:     Dict="epsilon"					, __lowerCamelCase						:     Dict=None					, __lowerCamelCase						:     bool = True					, )	->    Union[DDPMSchedulerOutput, Tuple]:
					__lowerCAmelCase						 =timestep

					if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
										__lowerCAmelCase ,						__lowerCAmelCase						 =torch.split(__lowerCamelCase					, sample.shape[1]					, dim=1						)
					else:
										__lowerCAmelCase						 =None

					# 1. compute alphas, betas
					__lowerCAmelCase						 =self.alphas_cumprod[t]
					__lowerCAmelCase						 =self.alphas_cumprod[t - 1] if t > 0 else self.one
					__lowerCAmelCase						 =1 - alpha_prod_t
					__lowerCAmelCase						 =1 - alpha_prod_t_prev

					# 2. compute predicted original sample from predicted noise also called
					# "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
					if prediction_type == "epsilon":
										__lowerCAmelCase						 =(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
					elif prediction_type == "sample":
										__lowerCAmelCase						 =model_output
					else:
										raise ValueError(f"""Unsupported prediction_type {prediction_type}."""						)

					# 3. Clip "predicted x_0"
					__lowerCAmelCase						 =self.bit_scale
					if self.config.clip_sample:
										__lowerCAmelCase						 =torch.clamp(__lowerCamelCase					, -scale					, __lowerCamelCase						)

					# 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
					# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
					__lowerCAmelCase						 =(alpha_prod_t_prev ** 0.5 * self.betas[t]) / beta_prod_t
					__lowerCAmelCase						 =self.alphas[t] ** 0.5 * beta_prod_t_prev / beta_prod_t

					# 5. Compute predicted previous sample µ_t
					# See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
					__lowerCAmelCase						 =pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

					# 6. Add noise
					__lowerCAmelCase						 =0
					if t > 0:
										__lowerCAmelCase						 =torch.randn(
										    model_output.size()					, dtype=model_output.dtype					, layout=model_output.layout					, generator=__lowerCamelCase						).to(model_output.device						)
										__lowerCAmelCase						 =(self._get_variance(__lowerCamelCase					, predicted_variance=__lowerCamelCase						) ** 0.5) * noise

					__lowerCAmelCase						 =pred_prev_sample + variance

					if not return_dict:
										return (pred_prev_sample,)

					return DDPMSchedulerOutput(prev_sample=__lowerCamelCase					, pred_original_sample=__lowerCamelCase						)






class     __a			(  SCREAMING_SNAKE_CASE					):



	def __init__(    self				:     Tuple					,						snake_case_				:     UNetaDConditionModel					,						snake_case_				:     Union[DDIMScheduler, DDPMScheduler]					,						snake_case_				:     Optional[float] = 1.0					,						)->				Optional[Any]:
						super().__init__()
						__lowerCAmelCase						 =bit_scale
						__lowerCAmelCase						 =(
						    ddim_bit_scheduler_step if isinstance(snake_case_					,						snake_case_) else ddpm_bit_scheduler_step
						)

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



	@torch.no_grad()
	def __call__(    self				:     Tuple					,						snake_case_				:     Optional[int] = 2_56					,						snake_case_				:     Optional[int] = 2_56					,						snake_case_				:     Optional[int] = 50					,						snake_case_				:     Optional[torch.Generator] = None					,						snake_case_				:     Optional[int] = 1					,						snake_case_				:     Optional[str] = "pil"					,						snake_case_				:     bool = True					,						**snake_case_				:     Optional[int]					,						)->				Union[Tuple, ImagePipelineOutput]:
						__lowerCAmelCase						 =torch.randn(
						    (batch_size, self.unet.config.in_channels, height, width)					,						generator=snake_case_					,						)
						__lowerCAmelCase						 =decimal_to_bits(snake_case_) * self.bit_scale
						__lowerCAmelCase						 =latents.to(self.device)

						self.scheduler.set_timesteps(snake_case_)

						for t in self.progress_bar(self.scheduler.timesteps):
											# predict the noise residual
											__lowerCAmelCase						 =self.unet(snake_case_					,						snake_case_).sample

											# compute the previous noisy sample x_t -> x_t-1
											__lowerCAmelCase						 =self.scheduler.step(snake_case_					,						snake_case_					,						snake_case_).prev_sample

						__lowerCAmelCase						 =bits_to_decimal(snake_case_)

						if output_type == "pil":
											__lowerCAmelCase						 =self.numpy_to_pil(snake_case_)

						if not return_dict:
											return (image,)

						return ImagePipelineOutput(images=snake_case_)









from collections.abc import Sequence
from queue import Queue






class     __a			:



	def __init__(    self				:     str					,						snake_case_				:     List[str]					,						snake_case_				:     Tuple					,						snake_case_				:     Tuple					,						snake_case_				:     Optional[Any]=None					,						snake_case_				:     Dict=None)->				Optional[int]:
						__lowerCAmelCase						 =start
						__lowerCAmelCase						 =end
						__lowerCAmelCase						 =val
						__lowerCAmelCase						 =(start + end) // 2
						__lowerCAmelCase						 =left
						__lowerCAmelCase						 =right



	def __repr__(    self				:     List[Any])->				Dict:
						return F"""SegmentTreeNode(start={self.start}, end={self.end}, val={self.val})"""






class     __a			:



	def __init__(    self				:     List[str]					,						snake_case_				:     Sequence					,						snake_case_				:     int)->				str:
						__lowerCAmelCase						 =collection
						__lowerCAmelCase						 =function
						if self.collection:
											__lowerCAmelCase						 =self._build_tree(0					,						len(snake_case_) - 1)



	def 		UpperCamelCase				(    self				:     Dict					,						snake_case_				:     Tuple					,						snake_case_				:     Optional[int])->				Optional[int]:
						self._update_tree(self.root					,						snake_case_					,						snake_case_)



	def 		UpperCamelCase				(    self				:     Optional[Any]					,						snake_case_				:     Any					,						snake_case_				:     Union[str, Any])->				Union[str, Any]:
						return self._query_range(self.root					,						snake_case_					,						snake_case_)



	def 		UpperCamelCase				(    self				:     List[str]					,						snake_case_				:     List[str]					,						snake_case_				:     List[str])->				List[Any]:
						if start == end:
											return SegmentTreeNode(snake_case_					,						snake_case_					,						self.collection[start])
						__lowerCAmelCase						 =(start + end) // 2
						__lowerCAmelCase						 =self._build_tree(snake_case_					,						snake_case_)
						__lowerCAmelCase						 =self._build_tree(mid + 1					,						snake_case_)
						return SegmentTreeNode(snake_case_					,						snake_case_					,						self.fn(left.val					,						right.val)					,						snake_case_					,						snake_case_)



	def 		UpperCamelCase				(    self				:     Dict					,						snake_case_				:     Tuple					,						snake_case_				:     int					,						snake_case_				:     int)->				List[Any]:
						if node.start == i and node.end == i:
											__lowerCAmelCase						 =val
											return
						if i <= node.mid:
											self._update_tree(node.left					,						snake_case_					,						snake_case_)
						else:
											self._update_tree(node.right					,						snake_case_					,						snake_case_)
						__lowerCAmelCase						 =self.fn(node.left.val					,						node.right.val)



	def 		UpperCamelCase				(    self				:     Tuple					,						snake_case_				:     str					,						snake_case_				:     str					,						snake_case_				:     List[Any])->				Optional[int]:
						if node.start == i and node.end == j:
											return node.val

						if i <= node.mid:
											if j <= node.mid:
																# range in left child tree
																return self._query_range(node.left					,						snake_case_					,						snake_case_)
											else:
																# range in left child tree and right child tree
																return self.fn(
																    self._query_range(node.left					,						snake_case_					,						node.mid)					,						self._query_range(node.right					,						node.mid + 1					,						snake_case_)					,						)
						else:
											# range in right child tree
											return self._query_range(node.right					,						snake_case_					,						snake_case_)



	def 		UpperCamelCase				(    self				:     List[str])->				Tuple:
						if self.root is not None:
											__lowerCAmelCase						 =Queue()
											queue.put(self.root)
											while not queue.empty():
																__lowerCAmelCase						 =queue.get()
																yield node

																if node.left is not None:
																					queue.put(node.left)

																if node.right is not None:
																					queue.put(node.right)


if __name__ == "__main__":
				import operator

				for fn in [operator.add, max, min]:
								print('''*''' * 50)
								lowercase_													=      SegmentTree([2, 1, 5, 3, 4], fn)
								for node in arr.traverse():
												print(node)
								print()

								arr.update(1, 5)
								for node in arr.traverse():
												print(node)
								print()

								print(arr.query_range(3, 4))  # 7
								print(arr.query_range(2, 2))  # 5
								print(arr.query_range(1, 3))  # 13
								print()




