




import math
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
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class       a__   ( snake_case__				):
						_a							:   Union[str, Any] =   4_2
						_a							:   Any =   None







def      _a				(						SCREAMING_SNAKE_CASE_							:    List[Any]				,				SCREAMING_SNAKE_CASE_							:    Dict=0.9_99				,				SCREAMING_SNAKE_CASE_							:    str="cosine"				,				):



					if alpha_transform_type == "cosine":

										def alpha_bar_fn(SCREAMING_SNAKE_CASE_							:    List[Any]					):
															return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2					) ** 2

					elif alpha_transform_type == "exp":

										def alpha_bar_fn(SCREAMING_SNAKE_CASE_							:    Any					):
															return math.exp(t * -12.0					)

					else:
										raise ValueError(F"""Unsupported alpha_tranform_type: {alpha_transform_type}"""					)

					__lowerCAmelCase           =	[]
					for i in range(_lowerCAmelCase					):
										__lowerCAmelCase           =	i / num_diffusion_timesteps
										__lowerCAmelCase           =	(i + 1) / num_diffusion_timesteps
										betas.append(min(1 - alpha_bar_fn(_lowerCAmelCase					) / alpha_bar_fn(_lowerCAmelCase					)				,				_lowerCAmelCase					)					)
					return torch.tensor(_lowerCAmelCase				,				dtype=torch.floataa					)


class       a__   ( snake_case__			,    snake_case__				):






						@register_to_config
						def __init__(       self		,      _A = 1_0_0_0		,      _A = "fixed_small_log"		,      _A = True		,      _A = 1.0		,      _A = "epsilon"		,      _A = "squaredcos_cap_v2"		,      ):




											"""simple docstring"""



											if beta_schedule != "squaredcos_cap_v2":
																raise ValueError("UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\'"      )

											__lowerCAmelCase           =	betas_for_alpha_bar(_lowerCAmelCase      )

											__lowerCAmelCase           =	1.0 - self.betas
											__lowerCAmelCase           =	torch.cumprod(self.alphas		,      dim=0      )
											__lowerCAmelCase           =	torch.tensor(1.0      )

											# standard deviation of the initial noise distribution
											__lowerCAmelCase           =	1.0

											# setable values
											__lowerCAmelCase           =	None
											__lowerCAmelCase           =	torch.from_numpy(np.arange(0		,      _lowerCAmelCase      )[::-1].copy()      )

											__lowerCAmelCase           =	variance_type






						def     __SCREAMING_SNAKE_CASE(       self		,      _A		,      _A = None      ):




											"""simple docstring"""



											return sample






						def     __SCREAMING_SNAKE_CASE(       self		,      _A		,      _A = None      ):




											"""simple docstring"""



											__lowerCAmelCase           =	num_inference_steps
											__lowerCAmelCase           =	(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
											__lowerCAmelCase           =	(np.arange(0		,      _lowerCAmelCase      ) * step_ratio).round()[::-1].copy().astype(np.intaa      )
											__lowerCAmelCase           =	torch.from_numpy(_lowerCAmelCase      ).to(_lowerCAmelCase      )






						def     __SCREAMING_SNAKE_CASE(       self		,      _A		,      _A=None		,      _A=None		,      _A=None      ):




											"""simple docstring"""



											if prev_timestep is None:
																__lowerCAmelCase           =	t - 1

											__lowerCAmelCase           =	self.alphas_cumprod[t]
											__lowerCAmelCase           =	self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
											__lowerCAmelCase           =	1 - alpha_prod_t
											__lowerCAmelCase           =	1 - alpha_prod_t_prev

											if prev_timestep == t - 1:
																__lowerCAmelCase           =	self.betas[t]
											else:
																__lowerCAmelCase           =	1 - alpha_prod_t / alpha_prod_t_prev

											# For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
											# and sample from it to get previous sample
											# x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
											__lowerCAmelCase           =	beta_prod_t_prev / beta_prod_t * beta

											if variance_type is None:
																__lowerCAmelCase           =	self.config.variance_type

											# hacks - were probably added for training stability
											if variance_type == "fixed_small_log":
																__lowerCAmelCase           =	torch.log(torch.clamp(_lowerCAmelCase		,      min=1E-2_0      )      )
																__lowerCAmelCase           =	torch.exp(0.5 * variance      )
											elif variance_type == "learned_range":
																# NOTE difference with DDPM scheduler
																__lowerCAmelCase           =	variance.log()
																__lowerCAmelCase           =	beta.log()

																__lowerCAmelCase           =	(predicted_variance + 1) / 2
																__lowerCAmelCase           =	frac * max_log + (1 - frac) * min_log

											return variance






						def     __SCREAMING_SNAKE_CASE(       self		,      _A		,      _A		,      _A		,      _A = None		,      _A=None		,      _A = True		,      ):




											"""simple docstring"""



											__lowerCAmelCase           =	timestep

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

											# 1. compute alphas, betas
											if prev_timestep is None:
																__lowerCAmelCase           =	t - 1

											__lowerCAmelCase           =	self.alphas_cumprod[t]
											__lowerCAmelCase           =	self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
											__lowerCAmelCase           =	1 - alpha_prod_t
											__lowerCAmelCase           =	1 - alpha_prod_t_prev

											if prev_timestep == t - 1:
																__lowerCAmelCase           =	self.betas[t]
																__lowerCAmelCase           =	self.alphas[t]
											else:
																__lowerCAmelCase           =	1 - alpha_prod_t / alpha_prod_t_prev
																__lowerCAmelCase           =	1 - beta

											# 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 self.config.prediction_type == "epsilon":
																__lowerCAmelCase           =	(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
											elif self.config.prediction_type == "sample":
																__lowerCAmelCase           =	model_output
											else:
																raise ValueError(
																    f"""prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`"""
																    " for the UnCLIPScheduler."      )

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

											# 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 * beta) / beta_prod_t
											__lowerCAmelCase           =	alpha ** 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           =	randn_tensor(
																    model_output.shape		,      dtype=model_output.dtype		,      generator=_lowerCAmelCase		,      device=model_output.device      )

																__lowerCAmelCase           =	self._get_variance(
																    _lowerCAmelCase		,      predicted_variance=_lowerCAmelCase		,      prev_timestep=_lowerCAmelCase		,      )

																if self.variance_type == "fixed_small_log":
																					__lowerCAmelCase           =	variance
																elif self.variance_type == "learned_range":
																					__lowerCAmelCase           =	(0.5 * variance).exp()
																else:
																					raise ValueError(
																					    f"""variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`"""
																					    " for the UnCLIPScheduler."      )

																__lowerCAmelCase           =	variance * variance_noise

											__lowerCAmelCase           =	pred_prev_sample + variance

											if not return_dict:
																return (pred_prev_sample,)

											return UnCLIPSchedulerOutput(prev_sample=_lowerCAmelCase		,      pred_original_sample=_lowerCAmelCase      )






						def     __SCREAMING_SNAKE_CASE(       self		,      _A		,      _A		,      _A		,      ):




											"""simple docstring"""



											__lowerCAmelCase           =	self.alphas_cumprod.to(device=original_samples.device		,      dtype=original_samples.dtype      )
											__lowerCAmelCase           =	timesteps.to(original_samples.device      )

											__lowerCAmelCase           =	alphas_cumprod[timesteps] ** 0.5
											__lowerCAmelCase           =	sqrt_alpha_prod.flatten()
											while len(sqrt_alpha_prod.shape      ) < len(original_samples.shape      ):
																__lowerCAmelCase           =	sqrt_alpha_prod.unsqueeze(-1      )

											__lowerCAmelCase           =	(1 - alphas_cumprod[timesteps]) ** 0.5
											__lowerCAmelCase           =	sqrt_one_minus_alpha_prod.flatten()
											while len(sqrt_one_minus_alpha_prod.shape      ) < len(original_samples.shape      ):
																__lowerCAmelCase           =	sqrt_one_minus_alpha_prod.unsqueeze(-1      )

											__lowerCAmelCase           =	sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
											return noisy_samples










def      _a				(						SCREAMING_SNAKE_CASE_							:    List[Any]					):
					__lowerCAmelCase       ,							__lowerCAmelCase           =	[], []
					while len(SCREAMING_SNAKE_CASE_					) > 1:
										__lowerCAmelCase       ,							__lowerCAmelCase           =	min(SCREAMING_SNAKE_CASE_					), max(SCREAMING_SNAKE_CASE_					)
										start.append(SCREAMING_SNAKE_CASE_					)
										end.append(SCREAMING_SNAKE_CASE_					)
										collection.remove(SCREAMING_SNAKE_CASE_					)
										collection.remove(SCREAMING_SNAKE_CASE_					)
					end.reverse()
					return start + collection + end


if __name__ == "__main__":
					UpperCamelCase__         =      input("""Enter numbers separated by a comma:\n""").strip()
					UpperCamelCase__         =      [int(item) for item in user_input.split(""",""")]
					print(*merge_sort(unsorted), sep=""",""")




