



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     __snake_case						(					UpperCamelCase_						):
							_a      				=			42
							_a      				=			None





def       UpperCamelCase(  __UpperCamelCase							:		Dict					,__UpperCamelCase							:		int=0.9_9_9					,__UpperCamelCase							:		Optional[Any]="cosine"					,):
		if alpha_transform_type == "cosine":

				def alpha_bar_fn(__UpperCamelCase							:		Any			):
						return math.cos((t + 0.0_0_8) / 1.0_0_8 * math.pi / 2			) ** 2

		elif alpha_transform_type == "exp":

				def alpha_bar_fn(__UpperCamelCase							:		Optional[Any]			):
						return math.exp(t * -1_2.0			)

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

		lowerCAmelCase_      :					Tuple     =			[]
		for i in range(__UpperCamelCase			):
				lowerCAmelCase_      :					Union[str, Any]     =			i / num_diffusion_timesteps
				lowerCAmelCase_      :					Optional[int]     =			(i + 1) / num_diffusion_timesteps
				betas.append(min(1 - alpha_bar_fn(__UpperCamelCase			) / alpha_bar_fn(__UpperCamelCase			)					,__UpperCamelCase			)			)
		return torch.tensor(__UpperCamelCase					,dtype=torch.floataa			)





class     __snake_case						(					UpperCamelCase_						,UpperCamelCase_						):
							_a      				=			[e.name for e in KarrasDiffusionSchedulers]
							_a      				=			1




							@register_to_config
							def __init__(	self					:	Optional[int]    ,    A_					:	int = 1_0_0_0    ,    A_					:	float = 0.0001    ,    A_					:	float = 0.02    ,    A_					:	str = "linear"    ,    A_					:	Optional[Union[np.ndarray, List[float]]] = None    ,    A_					:	Optional[bool] = False    ,    A_					:	str = "epsilon"    ,    A_					:	str = "linspace"    ,    A_					:	int = 0    ,    ):
									if trained_betas is not None:
											lowerCAmelCase_      :					Dict     =			torch.tensor(A_    ,    dtype=torch.floataa)
									elif beta_schedule == "linear":
											lowerCAmelCase_      :					Dict     =			torch.linspace(A_    ,    A_    ,    A_    ,    dtype=torch.floataa)
									elif beta_schedule == "scaled_linear":
											# this schedule is very specific to the latent diffusion model.
											lowerCAmelCase_      :					int     =			(
											    torch.linspace(beta_start**0.5    ,    beta_end**0.5    ,    A_    ,    dtype=torch.floataa) ** 2
											)
									elif beta_schedule == "squaredcos_cap_v2":
											# Glide cosine schedule
											lowerCAmelCase_      :					List[str]     =			betas_for_alpha_bar(A_)
									else:
											raise NotImplementedError(F"""{beta_schedule} does is not implemented for {self.__class__}""")

									lowerCAmelCase_      :					Dict     =			1.0 - self.betas
									lowerCAmelCase_      :					Optional[Any]     =			torch.cumprod(self.alphas    ,    dim=0)

									lowerCAmelCase_      :					List[Any]     =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
									lowerCAmelCase_      :					str     =			np.concatenate([sigmas[::-1], [0.0]]).astype(np.floataa)
									lowerCAmelCase_      :					int     =			torch.from_numpy(A_)

									# setable values
									lowerCAmelCase_      :					int     =			None
									lowerCAmelCase_      :					Union[str, Any]     =			use_karras_sigmas
									self.set_timesteps(A_    ,    A_)
									lowerCAmelCase_      :					Optional[Any]     =			[]
									lowerCAmelCase_      :					Dict     =			False




							@property
							def        UpperCAmelCase__      (	self					:	Dict):
									# 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        UpperCAmelCase__      (	self					:	Optional[Any]    ,    A_					:	torch.FloatTensor    ,    A_					:	Union[float, torch.FloatTensor]):
									if isinstance(A_    ,    torch.Tensor):
											lowerCAmelCase_      :					Tuple     =			timestep.to(self.timesteps.device)
									lowerCAmelCase_      :					Union[str, Any]     =			(self.timesteps == timestep).nonzero().item()
									lowerCAmelCase_      :					List[Any]     =			self.sigmas[step_index]
									lowerCAmelCase_      :					Dict     =			sample / ((sigma**2 + 1) ** 0.5)
									lowerCAmelCase_      :					List[Any]     =			True
									return sample




							def        UpperCAmelCase__      (	self					:	Tuple    ,    A_					:	Optional[int]    ,    A_					:	Optional[Any]    ,    A_					:	Optional[int]):

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

									lowerCAmelCase_      :					Union[str, Any]     =			integrate.quad(A_    ,    self.sigmas[t]    ,    self.sigmas[t + 1]    ,    epsrel=1e-4)[0]

									return integrated_coeff




							def        UpperCAmelCase__      (	self					:	Optional[Any]    ,    A_					:	int    ,    A_					:	Union[str, torch.device] = None):
									lowerCAmelCase_      :					List[str]     =			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":
											lowerCAmelCase_      :					List[str]     =			np.linspace(0    ,    self.config.num_train_timesteps - 1    ,    A_    ,    dtype=A_)[
											    ::-1
											].copy()
									elif self.config.timestep_spacing == "leading":
											lowerCAmelCase_      :					Optional[Any]     =			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
											lowerCAmelCase_      :					Optional[Any]     =			(np.arange(0    ,    A_) * step_ratio).round()[::-1].copy().astype(A_)
											timesteps += self.config.steps_offset
									elif self.config.timestep_spacing == "trailing":
											lowerCAmelCase_      :					Dict     =			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
											lowerCAmelCase_      :					str     =			(np.arange(self.config.num_train_timesteps    ,    0    ,    -step_ratio)).round().copy().astype(A_)
											timesteps -= 1
									else:
											raise ValueError(
											    F"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'.""")

									lowerCAmelCase_      :					Any     =			np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
									lowerCAmelCase_      :					Optional[int]     =			np.log(A_)
									lowerCAmelCase_      :					Dict     =			np.interp(A_    ,    np.arange(0    ,    len(A_))    ,    A_)

									if self.use_karras_sigmas:
											lowerCAmelCase_      :					Any     =			self._convert_to_karras(in_sigmas=A_)
											lowerCAmelCase_      :					List[str]     =			np.array([self._sigma_to_t(A_    ,    A_) for sigma in sigmas])

									lowerCAmelCase_      :					Optional[int]     =			np.concatenate([sigmas, [0.0]]).astype(np.floataa)

									lowerCAmelCase_      :					Dict     =			torch.from_numpy(A_).to(device=A_)
									if str(A_).startswith('''mps'''):
											# mps does not support float64
											lowerCAmelCase_      :					Dict     =			torch.from_numpy(A_).to(A_    ,    dtype=torch.floataa)
									else:
											lowerCAmelCase_      :					List[str]     =			torch.from_numpy(A_).to(device=A_)

									lowerCAmelCase_      :					Tuple     =			[]




							def        UpperCAmelCase__      (	self					:	List[Any]    ,    A_					:	List[str]    ,    A_					:	Optional[int]):
									# get log sigma
									lowerCAmelCase_      :					Optional[int]     =			np.log(A_)

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

									# get sigmas range
									lowerCAmelCase_      :					List[Any]     =			np.cumsum((dists >= 0)    ,    axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
									lowerCAmelCase_      :					Union[str, Any]     =			low_idx + 1

									lowerCAmelCase_      :					str     =			log_sigmas[low_idx]
									lowerCAmelCase_      :					Dict     =			log_sigmas[high_idx]

									# interpolate sigmas
									lowerCAmelCase_      :					Union[str, Any]     =			(low - log_sigma) / (low - high)
									lowerCAmelCase_      :					str     =			np.clip(A_    ,    0    ,    1)

									# transform interpolation to time range
									lowerCAmelCase_      :					Tuple     =			(1 - w) * low_idx + w * high_idx
									lowerCAmelCase_      :					List[str]     =			t.reshape(sigma.shape)
									return t




							def        UpperCAmelCase__      (	self					:	Tuple    ,    A_					:	torch.FloatTensor):
									lowerCAmelCase_      :					float     =			in_sigmas[-1].item()
									lowerCAmelCase_      :					float     =			in_sigmas[0].item()

									lowerCAmelCase_      :					Tuple     =			7.0  # 7.0 is the value used in the paper
									lowerCAmelCase_      :					Optional[int]     =			np.linspace(0    ,    1    ,    self.num_inference_steps)
									lowerCAmelCase_      :					List[Any]     =			sigma_min ** (1 / rho)
									lowerCAmelCase_      :					Dict     =			sigma_max ** (1 / rho)
									lowerCAmelCase_      :					Dict     =			(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
									return sigmas




							def        UpperCAmelCase__      (	self					:	Union[str, Any]    ,    A_					:	torch.FloatTensor    ,    A_					:	Union[float, torch.FloatTensor]    ,    A_					:	torch.FloatTensor    ,    A_					:	int = 4    ,    A_					:	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(A_    ,    torch.Tensor):
											lowerCAmelCase_      :					int     =			timestep.to(self.timesteps.device)
									lowerCAmelCase_      :					Dict     =			(self.timesteps == timestep).nonzero().item()
									lowerCAmelCase_      :					List[Any]     =			self.sigmas[step_index]

									# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
									if self.config.prediction_type == "epsilon":
											lowerCAmelCase_      :					Dict     =			sample - sigma * model_output
									elif self.config.prediction_type == "v_prediction":
											# * c_out + input * c_skip
											lowerCAmelCase_      :					List[Any]     =			model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
									elif self.config.prediction_type == "sample":
											lowerCAmelCase_      :					int     =			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
									lowerCAmelCase_      :					List[str]     =			(sample - pred_original_sample) / sigma
									self.derivatives.append(A_)
									if len(self.derivatives) > order:
											self.derivatives.pop(0)

									# 3. Compute linear multistep coefficients
									lowerCAmelCase_      :					List[str]     =			min(step_index + 1    ,    A_)
									lowerCAmelCase_      :					List[Any]     =			[self.get_lms_coefficient(A_    ,    A_    ,    A_) for curr_order in range(A_)]

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

									if not return_dict:
											return (prev_sample,)

									return LMSDiscreteSchedulerOutput(prev_sample=A_    ,    pred_original_sample=A_)




							def        UpperCAmelCase__      (	self					:	Any    ,    A_					:	torch.FloatTensor    ,    A_					:	torch.FloatTensor    ,    A_					:	torch.FloatTensor    ,    ):
									# Make sure sigmas and timesteps have the same device and dtype as original_samples
									lowerCAmelCase_      :					Dict     =			self.sigmas.to(device=original_samples.device    ,    dtype=original_samples.dtype)
									if original_samples.device.type == "mps" and torch.is_floating_point(A_):
											# mps does not support float64
											lowerCAmelCase_      :					Union[str, Any]     =			self.timesteps.to(original_samples.device    ,    dtype=torch.floataa)
											lowerCAmelCase_      :					Union[str, Any]     =			timesteps.to(original_samples.device    ,    dtype=torch.floataa)
									else:
											lowerCAmelCase_      :					Dict     =			self.timesteps.to(original_samples.device)
											lowerCAmelCase_      :					Any     =			timesteps.to(original_samples.device)

									lowerCAmelCase_      :					int     =			[(schedule_timesteps == t).nonzero().item() for t in timesteps]

									lowerCAmelCase_      :					int     =			sigmas[step_indices].flatten()
									while len(sigma.shape) < len(original_samples.shape):
											lowerCAmelCase_      :					Union[str, Any]     =			sigma.unsqueeze(-1)

									lowerCAmelCase_      :					List[Any]     =			original_samples + noise * sigma
									return noisy_samples







							def __len__(	self					:	Optional[int]):
									return self.config.num_train_timesteps










def       UpperCamelCase(  __UpperCamelCase							:		list			):
		for i, _ in enumerate(__UpperCamelCase			):
				if (i % 2 == 1) == (nums[i - 1] > nums[i]):
						lowerCAmelCase_ ,  lowerCAmelCase_      :					Union[str, Any]     =			nums[i], nums[i - 1]

		return nums


if __name__ == "__main__":
						print('''Enter the array elements:''')
						A__  :  str       = list(map(int, input().split()))
						print('''The unsorted array is:''')
						print(array)
						print('''Array after Wiggle sort:''')
						print(wiggle_sort(array))





