






from __future__ import annotations

from bisect import bisect_left
from functools import total_ordering
from heapq import merge


@total_ordering
class      lowercase__     (			_UpperCAmelCase	):

	def __lt__(							self		,    __UpperCAmelCase       )->					List[Any]:







							'''simple docstring'''





							return self[-1] < other[-1]


	def __eq__(							self		,    __UpperCAmelCase       )->					Dict:







							'''simple docstring'''





							return self[-1] == other[-1]





def        _a  (     UpperCamelCase_					:				list   ) ->   list:
						"""simple docstring"""







						lowerCAmelCase__       =						[]
						# sort into stacks
						for element in collection:
												lowerCAmelCase__       =						Stack([element]   )
												lowerCAmelCase__       =						bisect_left(UpperCamelCase_    ,   UpperCamelCase_   )
												if i != len(UpperCamelCase_   ):
																		stacks[i].append(UpperCamelCase_   )
												else:
																		stacks.append(UpperCamelCase_   )

    # use a heap-based merge to merge stack efficiently
						lowerCAmelCase__       =						merge(*(reversed(UpperCamelCase_   ) for stack in stacks)   )
						return collection


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














import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput


def        _a  (     UpperCamelCase_					:				Union[str, Any]    ,   UpperCamelCase_					:				Tuple=0.999    ,   UpperCamelCase_					:				Union[str, Any]="cosine"    ,   ) ->   str:
						"""simple docstring"""







						if alpha_transform_type == "cosine":

												def alpha_bar_fn(UpperCamelCase_					:				List[Any]   ):
																		return math.cos((t + 0.008) / 1.008 * math.pi / 2   ) ** 2

						elif alpha_transform_type == "exp":

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

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

						lowerCAmelCase__       =						[]
						for i in range(UpperCamelCase_   ):
												lowerCAmelCase__       =						i / num_diffusion_timesteps
												lowerCAmelCase__       =						(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      lowercase__     (			_UpperCAmelCase,					_UpperCAmelCase	):
	a_         =[e.name for e in KarrasDiffusionSchedulers]
	a_         =2

	@register_to_config
	def __init__(							self		,    __UpperCAmelCase = 1000		,    __UpperCAmelCase = 0.00_085		,    __UpperCAmelCase = 0.012		,    __UpperCAmelCase = "linear"		,    __UpperCAmelCase = None		,    __UpperCAmelCase = "epsilon"		,    __UpperCAmelCase = "linspace"		,    __UpperCAmelCase = 0		,    )->					int:







							'''simple docstring'''





							if trained_betas is not None:
													lowerCAmelCase__       =						torch.tensor(__UpperCAmelCase		,    dtype=torch.floataa       )
							elif beta_schedule == "linear":
													lowerCAmelCase__       =						torch.linspace(__UpperCAmelCase		,    __UpperCAmelCase		,    __UpperCAmelCase		,    dtype=torch.floataa       )
							elif beta_schedule == "scaled_linear":
													# this schedule is very specific to the latent diffusion model.
													lowerCAmelCase__       =						(
													    torch.linspace(beta_start**0.5		,    beta_end**0.5		,    __UpperCAmelCase		,    dtype=torch.floataa       ) ** 2
													)
							elif beta_schedule == "squaredcos_cap_v2":
													# Glide cosine schedule
													lowerCAmelCase__       =						betas_for_alpha_bar(__UpperCAmelCase       )
							else:
													raise NotImplementedError(F"{beta_schedule} does is not implemented for {self.__class__}"       )

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

							#  set all values
							self.set_timesteps(__UpperCAmelCase		,    __UpperCAmelCase		,    __UpperCAmelCase       )

	def 		UpperCAmelCase  (							self		,    __UpperCAmelCase		,    __UpperCAmelCase=None       )->					str:







							'''simple docstring'''





							if schedule_timesteps is None:
													lowerCAmelCase__       =						self.timesteps

							lowerCAmelCase__       =						(schedule_timesteps == timestep).nonzero()

							# The sigma index that is taken for the **very** first `step`
							# is always the second index (or the last index if there is only 1)
							# This way we can ensure we don't accidentally skip a sigma in
							# case we start in the middle of the denoising schedule (e.g. for image-to-image)
							if len(self._index_counter       ) == 0:
													lowerCAmelCase__       =						1 if len(__UpperCAmelCase       ) > 1 else 0
							else:
													lowerCAmelCase__       =						timestep.cpu().item() if torch.is_tensor(__UpperCAmelCase       ) else timestep
													lowerCAmelCase__       =						self._index_counter[timestep_int]

							return indices[pos].item()

	@property
	def 		UpperCAmelCase  (							self       )->					List[str]:







							'''simple docstring'''





							if self.config.timestep_spacing in ["linspace", "trailing"]:
													return self.sigmas.max()

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

	def 		UpperCAmelCase  (							self		,    __UpperCAmelCase		,    __UpperCAmelCase		,    )->					torch.FloatTensor:







							'''simple docstring'''





							lowerCAmelCase__       =						self.index_for_timestep(__UpperCAmelCase       )

							if self.state_in_first_order:
													lowerCAmelCase__       =						self.sigmas[step_index]
							else:
													lowerCAmelCase__       =						self.sigmas_interpol[step_index]

							lowerCAmelCase__       =						sample / ((sigma**2 + 1) ** 0.5)
							return sample

	def 		UpperCAmelCase  (							self		,    __UpperCAmelCase		,    __UpperCAmelCase = None		,    __UpperCAmelCase = None		,    )->					Optional[int]:







							'''simple docstring'''





							lowerCAmelCase__       =						num_inference_steps

							lowerCAmelCase__       =						num_train_timesteps or self.config.num_train_timesteps

							# "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
							if self.config.timestep_spacing == "linspace":
													lowerCAmelCase__       =						np.linspace(0		,    num_train_timesteps - 1		,    __UpperCAmelCase		,    dtype=__UpperCAmelCase       )[::-1].copy()
							elif self.config.timestep_spacing == "leading":
													lowerCAmelCase__       =						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__       =						(np.arange(0		,    __UpperCAmelCase       ) * step_ratio).round()[::-1].copy().astype(__UpperCAmelCase       )
													timesteps += self.config.steps_offset
							elif self.config.timestep_spacing == "trailing":
													lowerCAmelCase__       =						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__       =						(np.arange(__UpperCAmelCase		,    0		,    -step_ratio       )).round().copy().astype(__UpperCAmelCase       )
													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__       =						np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5       )
							lowerCAmelCase__       =						torch.from_numpy(np.log(__UpperCAmelCase       )       ).to(__UpperCAmelCase       )

							lowerCAmelCase__       =						np.interp(__UpperCAmelCase		,    np.arange(0		,    len(__UpperCAmelCase       )       )		,    __UpperCAmelCase       )
							lowerCAmelCase__       =						np.concatenate([sigmas, [0.0]]       ).astype(np.floataa       )
							lowerCAmelCase__       =						torch.from_numpy(__UpperCAmelCase       ).to(device=__UpperCAmelCase       )

							# interpolate sigmas
							lowerCAmelCase__       =						sigmas.log().lerp(sigmas.roll(1       ).log()		,    0.5       ).exp()

							lowerCAmelCase__       =						torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2       ), sigmas[-1:]]       )
							lowerCAmelCase__       =						torch.cat(
							    [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2       ), sigmas_interpol[-1:]]       )

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

							# interpolate timesteps
							lowerCAmelCase__       =						self.sigma_to_t(__UpperCAmelCase       ).to(__UpperCAmelCase		,    dtype=timesteps.dtype       )
							lowerCAmelCase__       =						torch.stack((timesteps_interpol[1:-1, None], timesteps[1:, None])		,    dim=-1       ).flatten()

							lowerCAmelCase__       =						torch.cat([timesteps[:1], interleaved_timesteps]       )

							lowerCAmelCase__       =						None

							# for exp beta schedules, such as the one for `pipeline_shap_e.py`
							# we need an index counter
							lowerCAmelCase__       =						defaultdict(__UpperCAmelCase       )

	def 		UpperCAmelCase  (							self		,    __UpperCAmelCase       )->					Tuple:







							'''simple docstring'''





							lowerCAmelCase__       =						sigma.log()

							# get distribution
							lowerCAmelCase__       =						log_sigma - self.log_sigmas[:, None]

							# get sigmas range
							lowerCAmelCase__       =						dists.ge(0       ).cumsum(dim=0       ).argmax(dim=0       ).clamp(max=self.log_sigmas.shape[0] - 2       )
							lowerCAmelCase__       =						low_idx + 1

							lowerCAmelCase__       =						self.log_sigmas[low_idx]
							lowerCAmelCase__       =						self.log_sigmas[high_idx]

							# interpolate sigmas
							lowerCAmelCase__       =						(low - log_sigma) / (low - high)
							lowerCAmelCase__       =						w.clamp(0		,    1       )

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

	@property
	def 		UpperCAmelCase  (							self       )->					List[str]:







							'''simple docstring'''





							return self.sample is None

	def 		UpperCAmelCase  (							self		,    __UpperCAmelCase		,    __UpperCAmelCase		,    __UpperCAmelCase		,    __UpperCAmelCase = True		,    )->					Union[SchedulerOutput, Tuple]:







							'''simple docstring'''





							lowerCAmelCase__       =						self.index_for_timestep(__UpperCAmelCase       )

							# advance index counter by 1
							lowerCAmelCase__       =						timestep.cpu().item() if torch.is_tensor(__UpperCAmelCase       ) else timestep
							self._index_counter[timestep_int] += 1

							if self.state_in_first_order:
													lowerCAmelCase__       =						self.sigmas[step_index]
													lowerCAmelCase__       =						self.sigmas_interpol[step_index + 1]
													lowerCAmelCase__       =						self.sigmas[step_index + 1]
							else:
													# 2nd order / KDPM2's method
													lowerCAmelCase__       =						self.sigmas[step_index - 1]
													lowerCAmelCase__       =						self.sigmas_interpol[step_index]
													lowerCAmelCase__       =						self.sigmas[step_index]

							# currently only gamma=0 is supported. This usually works best anyways.
							# We can support gamma in the future but then need to scale the timestep before
							# passing it to the model which requires a change in API
							lowerCAmelCase__       =						0
							lowerCAmelCase__       =						sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

							# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
							if self.config.prediction_type == "epsilon":
													lowerCAmelCase__       =						sigma_hat if self.state_in_first_order else sigma_interpol
													lowerCAmelCase__       =						sample - sigma_input * model_output
							elif self.config.prediction_type == "v_prediction":
													lowerCAmelCase__       =						sigma_hat if self.state_in_first_order else sigma_interpol
													lowerCAmelCase__       =						model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
													    sample / (sigma_input**2 + 1)
													)
							elif self.config.prediction_type == "sample":
													raise NotImplementedError("prediction_type not implemented yet: sample"       )
							else:
													raise ValueError(
													    F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"       )

							if self.state_in_first_order:
													# 2. Convert to an ODE derivative for 1st order
													lowerCAmelCase__       =						(sample - pred_original_sample) / sigma_hat
													# 3. delta timestep
													lowerCAmelCase__       =						sigma_interpol - sigma_hat

													# store for 2nd order step
													lowerCAmelCase__       =						sample
							else:
													# DPM-Solver-2
													# 2. Convert to an ODE derivative for 2nd order
													lowerCAmelCase__       =						(sample - pred_original_sample) / sigma_interpol

													# 3. delta timestep
													lowerCAmelCase__       =						sigma_next - sigma_hat

													lowerCAmelCase__       =						self.sample
													lowerCAmelCase__       =						None

							lowerCAmelCase__       =						sample + derivative * dt

							if not return_dict:
													return (prev_sample,)

							return SchedulerOutput(prev_sample=__UpperCAmelCase       )

	def 		UpperCAmelCase  (							self		,    __UpperCAmelCase		,    __UpperCAmelCase		,    __UpperCAmelCase		,    )->					torch.FloatTensor:







							'''simple docstring'''





							lowerCAmelCase__       =						self.sigmas.to(device=original_samples.device		,    dtype=original_samples.dtype       )
							if original_samples.device.type == "mps" and torch.is_floating_point(__UpperCAmelCase       ):
													# mps does not support float64
													lowerCAmelCase__       =						self.timesteps.to(original_samples.device		,    dtype=torch.floataa       )
													lowerCAmelCase__       =						timesteps.to(original_samples.device		,    dtype=torch.floataa       )
							else:
													lowerCAmelCase__       =						self.timesteps.to(original_samples.device       )
													lowerCAmelCase__       =						timesteps.to(original_samples.device       )

							lowerCAmelCase__       =						[self.index_for_timestep(__UpperCAmelCase		,    __UpperCAmelCase       ) for t in timesteps]

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

							lowerCAmelCase__       =						original_samples + noise * sigma
							return noisy_samples


	def __len__(							self       )->					List[Any]:







							'''simple docstring'''





							return self.config.num_train_timesteps






