

"""simple docstring"""




import math
import warnings
from dataclasses import dataclass
from typing import List, Optional, Tuple, Union

import numpy as np
import torch
from scipy import integrate

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





@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->LMSDiscrete
class 			__UpperCamelCase (   _A						):
		SCREAMING_SNAKE_CASE								=    42
		SCREAMING_SNAKE_CASE								=    None

def    __SCREAMING_SNAKE_CASE						(						lowercase__			,							lowercase__=0.9_99			,							lowercase__="cosine"			,							):
					"""simple docstring"""
					if alpha_transform_type == "cosine":

										def alpha_bar_fn(lowercase__      ):
															return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2      ) ** 2

					elif alpha_transform_type == "exp":

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

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

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





class 			__UpperCamelCase (   _A     ,		_A						):
		SCREAMING_SNAKE_CASE								=    [e.name for e in KarrasDiffusionSchedulers]
		SCREAMING_SNAKE_CASE								=    1


		@register_to_config
		def __init__(self :		Tuple     ,     __SCREAMING_SNAKE_CASE :		int = 1_0_0_0     ,     __SCREAMING_SNAKE_CASE :		float = 0.0_0_0_1     ,     __SCREAMING_SNAKE_CASE :		float = 0.0_2     ,     __SCREAMING_SNAKE_CASE :		str = "linear"     ,     __SCREAMING_SNAKE_CASE :		Optional[Union[np.ndarray, List[float]]] = None     ,     __SCREAMING_SNAKE_CASE :		Optional[bool] = False     ,     __SCREAMING_SNAKE_CASE :		str = "epsilon"     ,     __SCREAMING_SNAKE_CASE :		str = "linspace"     ,     __SCREAMING_SNAKE_CASE :		int = 0     ,     ):
							if trained_betas is not None:
												A			=					torch.tensor(__SCREAMING_SNAKE_CASE     ,     dtype=torch.floataa)
							elif beta_schedule == "linear":
												A			=					torch.linspace(__SCREAMING_SNAKE_CASE     ,     __SCREAMING_SNAKE_CASE     ,     __SCREAMING_SNAKE_CASE     ,     dtype=torch.floataa)
							elif beta_schedule == "scaled_linear":
												# this schedule is very specific to the latent diffusion model.
												A			=					(
												    torch.linspace(beta_start**0.5     ,     beta_end**0.5     ,     __SCREAMING_SNAKE_CASE     ,     dtype=torch.floataa) ** 2
												)
							elif beta_schedule == "squaredcos_cap_v2":
												# Glide cosine schedule
												A			=					betas_for_alpha_bar(__SCREAMING_SNAKE_CASE)
							else:
												raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}""")

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

							A			=					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
							A			=					np.concatenate([sigmas[::-1], [0.0]]).astype(np.floataa)
							A			=					torch.from_numpy(__SCREAMING_SNAKE_CASE)

							# setable values
							A			=					None
							A			=					use_karras_sigmas
							self.set_timesteps(__SCREAMING_SNAKE_CASE     ,     __SCREAMING_SNAKE_CASE)
							A			=					[]
							A			=					False


		@property
		def 					SCREAMING_SNAKE_CASE__   (self :		Tuple):
							# standard deviation of the initial noise distribution
							if self.config.timestep_spacing in ["linspace", "trailing"]:
												return self.sigmas.max()

							return (self.sigmas.max() ** 2 + 1) ** 0.5


		def 					SCREAMING_SNAKE_CASE__   (self :		Tuple     ,     __SCREAMING_SNAKE_CASE :		torch.FloatTensor     ,     __SCREAMING_SNAKE_CASE :		Union[float, torch.FloatTensor]):
							if isinstance(__SCREAMING_SNAKE_CASE     ,     torch.Tensor):
												A			=					timestep.to(self.timesteps.device)
							A			=					(self.timesteps == timestep).nonzero().item()
							A			=					self.sigmas[step_index]
							A			=					sample / ((sigma**2 + 1) ** 0.5)
							A			=					True
							return sample


		def 					SCREAMING_SNAKE_CASE__   (self :		List[str]     ,     __SCREAMING_SNAKE_CASE :		str     ,     __SCREAMING_SNAKE_CASE :		Dict     ,     __SCREAMING_SNAKE_CASE :		int):

							def lms_derivative(__SCREAMING_SNAKE_CASE :		int):
												A			=					1.0
												for k in range(__SCREAMING_SNAKE_CASE):
																	if current_order == k:
																						continue
																	prod *= (tau - self.sigmas[t - k]) / (self.sigmas[t - current_order] - self.sigmas[t - k])
												return prod

							A			=					integrate.quad(__SCREAMING_SNAKE_CASE     ,     self.sigmas[t]     ,     self.sigmas[t + 1]     ,     epsrel=1E-4)[0]

							return integrated_coeff


		def 					SCREAMING_SNAKE_CASE__   (self :		List[str]     ,     __SCREAMING_SNAKE_CASE :		int     ,     __SCREAMING_SNAKE_CASE :		Union[str, torch.device] = None):
							A			=					num_inference_steps

							# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
							if self.config.timestep_spacing == "linspace":
												A			=					np.linspace(0     ,     self.config.num_train_timesteps - 1     ,     __SCREAMING_SNAKE_CASE     ,     dtype=__SCREAMING_SNAKE_CASE)[
												    ::-1
												].copy()
							elif self.config.timestep_spacing == "leading":
												A			=					self.config.num_train_timesteps // self.num_inference_steps
												# creates integer timesteps by multiplying by ratio
												# casting to int to avoid issues when num_inference_step is power of 3
												A			=					(np.arange(0     ,     __SCREAMING_SNAKE_CASE) * step_ratio).round()[::-1].copy().astype(__SCREAMING_SNAKE_CASE)
												timesteps += self.config.steps_offset
							elif self.config.timestep_spacing == "trailing":
												A			=					self.config.num_train_timesteps / self.num_inference_steps
												# creates integer timesteps by multiplying by ratio
												# casting to int to avoid issues when num_inference_step is power of 3
												A			=					(np.arange(self.config.num_train_timesteps     ,     0     ,     -step_ratio)).round().copy().astype(__SCREAMING_SNAKE_CASE)
												timesteps -= 1
							else:
												raise ValueError(
												    F"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'.""")

							A			=					np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
							A			=					np.log(__SCREAMING_SNAKE_CASE)
							A			=					np.interp(__SCREAMING_SNAKE_CASE     ,     np.arange(0     ,     len(__SCREAMING_SNAKE_CASE))     ,     __SCREAMING_SNAKE_CASE)

							if self.use_karras_sigmas:
												A			=					self._convert_to_karras(in_sigmas=__SCREAMING_SNAKE_CASE)
												A			=					np.array([self._sigma_to_t(__SCREAMING_SNAKE_CASE     ,     __SCREAMING_SNAKE_CASE) for sigma in sigmas])

							A			=					np.concatenate([sigmas, [0.0]]).astype(np.floataa)

							A			=					torch.from_numpy(__SCREAMING_SNAKE_CASE).to(device=__SCREAMING_SNAKE_CASE)
							if str(__SCREAMING_SNAKE_CASE).startswith("mps"):
												# mps does not support float64
												A			=					torch.from_numpy(__SCREAMING_SNAKE_CASE).to(__SCREAMING_SNAKE_CASE     ,     dtype=torch.floataa)
							else:
												A			=					torch.from_numpy(__SCREAMING_SNAKE_CASE).to(device=__SCREAMING_SNAKE_CASE)

							A			=					[]


		def 					SCREAMING_SNAKE_CASE__   (self :		Optional[Any]     ,     __SCREAMING_SNAKE_CASE :		Union[str, Any]     ,     __SCREAMING_SNAKE_CASE :		List[str]):
							# get log sigma
							A			=					np.log(__SCREAMING_SNAKE_CASE)

							# get distribution
							A			=					log_sigma - log_sigmas[:, np.newaxis]

							# get sigmas range
							A			=					np.cumsum((dists >= 0)     ,     axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
							A			=					low_idx + 1

							A			=					log_sigmas[low_idx]
							A			=					log_sigmas[high_idx]

							# interpolate sigmas
							A			=					(low - log_sigma) / (low - high)
							A			=					np.clip(__SCREAMING_SNAKE_CASE     ,     0     ,     1)

							# transform interpolation to time range
							A			=					(1 - w) * low_idx + w * high_idx
							A			=					t.reshape(sigma.shape)
							return t


		def 					SCREAMING_SNAKE_CASE__   (self :		Any     ,     __SCREAMING_SNAKE_CASE :		torch.FloatTensor):
							A			=					in_sigmas[-1].item()
							A			=					in_sigmas[0].item()

							A			=					7.0  # 7.0 is the value used in the paper
							A			=					np.linspace(0     ,     1     ,     self.num_inference_steps)
							A			=					sigma_min ** (1 / rho)
							A			=					sigma_max ** (1 / rho)
							A			=					(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
							return sigmas


		def 					SCREAMING_SNAKE_CASE__   (self :		Optional[Any]     ,     __SCREAMING_SNAKE_CASE :		torch.FloatTensor     ,     __SCREAMING_SNAKE_CASE :		Union[float, torch.FloatTensor]     ,     __SCREAMING_SNAKE_CASE :		torch.FloatTensor     ,     __SCREAMING_SNAKE_CASE :		int = 4     ,     __SCREAMING_SNAKE_CASE :		bool = True     ,     ):
							if not self.is_scale_input_called:
												warnings.warn(
												    "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
												    "See `StableDiffusionPipeline` for a usage example.")

							if isinstance(__SCREAMING_SNAKE_CASE     ,     torch.Tensor):
												A			=					timestep.to(self.timesteps.device)
							A			=					(self.timesteps == timestep).nonzero().item()
							A			=					self.sigmas[step_index]

							# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
							if self.config.prediction_type == "epsilon":
												A			=					sample - sigma * model_output
							elif self.config.prediction_type == "v_prediction":
												# * c_out + input * c_skip
												A			=					model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
							elif self.config.prediction_type == "sample":
												A			=					model_output
							else:
												raise ValueError(
												    F"""prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`""")

							# 2. Convert to an ODE derivative
							A			=					(sample - pred_original_sample) / sigma
							self.derivatives.append(__SCREAMING_SNAKE_CASE)
							if len(self.derivatives) > order:
												self.derivatives.pop(0)

							# 3. Compute linear multistep coefficients
							A			=					min(step_index + 1     ,     __SCREAMING_SNAKE_CASE)
							A			=					[self.get_lms_coefficient(__SCREAMING_SNAKE_CASE     ,     __SCREAMING_SNAKE_CASE     ,     __SCREAMING_SNAKE_CASE) for curr_order in range(__SCREAMING_SNAKE_CASE)]

							# 4. Compute previous sample based on the derivatives path
							A			=					sample + sum(
							    coeff * derivative for coeff, derivative in zip(__SCREAMING_SNAKE_CASE     ,     reversed(self.derivatives)))

							if not return_dict:
												return (prev_sample,)

							return LMSDiscreteSchedulerOutput(prev_sample=__SCREAMING_SNAKE_CASE     ,     pred_original_sample=__SCREAMING_SNAKE_CASE)


		def 					SCREAMING_SNAKE_CASE__   (self :		str     ,     __SCREAMING_SNAKE_CASE :		torch.FloatTensor     ,     __SCREAMING_SNAKE_CASE :		torch.FloatTensor     ,     __SCREAMING_SNAKE_CASE :		torch.FloatTensor     ,     ):
							# Make sure sigmas and timesteps have the same device and dtype as original_samples
							A			=					self.sigmas.to(device=original_samples.device     ,     dtype=original_samples.dtype)
							if original_samples.device.type == "mps" and torch.is_floating_point(__SCREAMING_SNAKE_CASE):
												# mps does not support float64
												A			=					self.timesteps.to(original_samples.device     ,     dtype=torch.floataa)
												A			=					timesteps.to(original_samples.device     ,     dtype=torch.floataa)
							else:
												A			=					self.timesteps.to(original_samples.device)
												A			=					timesteps.to(original_samples.device)

							A			=					[(schedule_timesteps == t).nonzero().item() for t in timesteps]

							A			=					sigmas[step_indices].flatten()
							while len(sigma.shape) < len(original_samples.shape):
												A			=					sigma.unsqueeze(-1)

							A			=					original_samples + noise * sigma
							return noisy_samples


		def __len__(self :		str):
							return self.config.num_train_timesteps








"""simple docstring"""




def    __SCREAMING_SNAKE_CASE						(						lowercase__			,							lowercase__			,							lowercase__      ):
					"""simple docstring"""
					A			=					index
					A			=					2 * index + 1
					A			=					2 * index + 2
					if left_index < heap_size and unsorted[left_index] > unsorted[largest]:
										A			=					left_index

					if right_index < heap_size and unsorted[right_index] > unsorted[largest]:
										A			=					right_index

					if largest != index:
										A			,    A			=					unsorted[index], unsorted[largest]
										heapify(lowercase__			,							lowercase__			,							lowercase__      )
def    __SCREAMING_SNAKE_CASE						(						lowercase__      ):
					"""simple docstring"""
					A			=					len(lowercase__      )
					for i in range(n // 2 - 1			,							-1			,							-1      ):
										heapify(lowercase__			,							lowercase__			,							lowercase__      )
					for i in range(n - 1			,							0			,							-1      ):
										A			,    A			=					unsorted[i], unsorted[0]
										heapify(lowercase__			,							0			,							lowercase__      )
					return unsorted


if __name__ == "__main__":
	__A     :    List[Any]    =		input('Enter numbers separated by a comma:\n').strip()
	__A     :    List[str]    =		[int(item) for item in user_input.split(',')]
	print(heap_sort(unsorted))





