




'''simple docstring'''




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

import numpy as np
import torch

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


snake_case__ 							=    logging.get_logger(__name__)  # pylint: disable=invalid-name






@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->EulerDiscrete
class      UpperCamelCase_  (a__  ):







						"""simple docstring"""


						_lowerCAmelCase         =       42
						_lowerCAmelCase         =       None






def     snake_case__     (			lowerCamelCase__					: Tuple      ,		lowerCamelCase__					: Tuple=0.999      ,		lowerCamelCase__					: Optional[int]="cosine"      ,		) -> Any:
					if alpha_transform_type == "cosine":

										def alpha_bar_fn(lowerCamelCase__					: Optional[int]      ):
															return math.cos((t + 0.008) / 1.008 * math.pi / 2      ) ** 2

					elif alpha_transform_type == "exp":

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

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

					A_			:  str			=				[]
					for i in range(lowerCamelCase__      ):
										A_			:  List[str]			=				i / num_diffusion_timesteps
										A_			:  Union[str, Any]			=				(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      UpperCamelCase_  (a__,   a__  ):







						"""simple docstring"""


						_lowerCAmelCase         =       [e.name for e in KarrasDiffusionSchedulers]
						_lowerCAmelCase         =       1







						@register_to_config
						def __init__(  self   :							Any				,			_lowerCamelCase   :							int = 1000				,			_lowerCamelCase   :							float = 0.00_01				,			_lowerCamelCase   :							float = 0.02				,			_lowerCamelCase   :							str = "linear"				,			_lowerCamelCase   :							Optional[Union[np.ndarray, List[float]]] = None				,			_lowerCamelCase   :							str = "epsilon"				,			_lowerCamelCase   :							str = "linear"				,			_lowerCamelCase   :							Optional[bool] = False				,			_lowerCamelCase   :							str = "linspace"				,			_lowerCamelCase   :							int = 0				,			):





											"""simple docstring"""







											if trained_betas is not None:
																A_			:  List[Any]			=				torch.tensor(_lowerCamelCase				,			dtype=torch.floataa     )
											elif beta_schedule == "linear":
																A_			:  List[str]			=				torch.linspace(_lowerCamelCase				,			_lowerCamelCase				,			_lowerCamelCase				,			dtype=torch.floataa     )
											elif beta_schedule == "scaled_linear":
																# this schedule is very specific to the latent diffusion model.
																A_			:  int			=				(
																    torch.linspace(beta_start**0.5				,			beta_end**0.5				,			_lowerCamelCase				,			dtype=torch.floataa     ) ** 2
																)
											elif beta_schedule == "squaredcos_cap_v2":
																# Glide cosine schedule
																A_			:  Tuple			=				betas_for_alpha_bar(_lowerCamelCase     )
											else:
																raise NotImplementedError(f'{beta_schedule} does is not implemented for {self.__class__}'     )

											A_			:  Dict			=				1.0 - self.betas
											A_			:  Dict			=				torch.cumprod(self.alphas				,			dim=0     )

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

											# setable values
											A_			:  Union[str, Any]			=				None
											A_			:  Tuple			=				np.linspace(0				,			num_train_timesteps - 1				,			_lowerCamelCase				,			dtype=_lowerCamelCase     )[::-1].copy()
											A_			:  List[Any]			=				torch.from_numpy(_lowerCamelCase     )
											A_			:  List[Any]			=				False
											A_			:  Any			=				use_karras_sigmas







						@property
						def    _a     (  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    _a     (  self   :							Any				,			_lowerCamelCase   :							torch.FloatTensor				,			_lowerCamelCase   :							Union[float, torch.FloatTensor]     ):





											"""simple docstring"""







											if isinstance(_lowerCamelCase				,			torch.Tensor     ):
																A_			:  List[Any]			=				timestep.to(self.timesteps.device     )
											A_			:  Any			=				(self.timesteps == timestep).nonzero().item()
											A_			:  Tuple			=				self.sigmas[step_index]

											A_			:  Dict			=				sample / ((sigma**2 + 1) ** 0.5)

											A_			:  Tuple			=				True
											return sample







						def    _a     (  self   :							int				,			_lowerCamelCase   :							int				,			_lowerCamelCase   :							Union[str, torch.device] = None     ):





											"""simple docstring"""







											A_			:  int			=				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_			:  str			=				np.linspace(0				,			self.config.num_train_timesteps - 1				,			_lowerCamelCase				,			dtype=_lowerCamelCase     )[
																    ::-1
																].copy()
											elif self.config.timestep_spacing == "leading":
																A_			:  Union[str, 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
																A_			:  Dict			=				(np.arange(0				,			_lowerCamelCase     ) * step_ratio).round()[::-1].copy().astype(_lowerCamelCase     )
																timesteps += self.config.steps_offset
											elif self.config.timestep_spacing == "trailing":
																A_			:  Tuple			=				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_			:  Any			=				(np.arange(self.config.num_train_timesteps				,			0				,			-step_ratio     )).round().copy().astype(_lowerCamelCase     )
																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_			:  Optional[int]			=				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5     )
											A_			:  str			=				np.log(_lowerCamelCase     )

											if self.config.interpolation_type == "linear":
																A_			:  Tuple			=				np.interp(_lowerCamelCase				,			np.arange(0				,			len(_lowerCamelCase     )     )				,			_lowerCamelCase     )
											elif self.config.interpolation_type == "log_linear":
																A_			:  Optional[Any]			=				torch.linspace(np.log(sigmas[-1]     )				,			np.log(sigmas[0]     )				,			num_inference_steps + 1     ).exp()
											else:
																raise ValueError(
																    f'{self.config.interpolation_type} is not implemented. Please specify interpolation_type to either'
																    ''' \'linear\' or \'log_linear\''''     )

											if self.use_karras_sigmas:
																A_			:  List[str]			=				self._convert_to_karras(in_sigmas=_lowerCamelCase				,			num_inference_steps=self.num_inference_steps     )
																A_			:  Optional[int]			=				np.array([self._sigma_to_t(_lowerCamelCase				,			_lowerCamelCase     ) for sigma in sigmas]     )

											A_			:  List[Any]			=				np.concatenate([sigmas, [0.0]]     ).astype(np.floataa     )
											A_			:  List[Any]			=				torch.from_numpy(_lowerCamelCase     ).to(device=_lowerCamelCase     )
											if str(_lowerCamelCase     ).startswith('''mps'''     ):
																# mps does not support float64
																A_			:  List[str]			=				torch.from_numpy(_lowerCamelCase     ).to(_lowerCamelCase				,			dtype=torch.floataa     )
											else:
																A_			:  Any			=				torch.from_numpy(_lowerCamelCase     ).to(device=_lowerCamelCase     )







						def    _a     (  self   :							int				,			_lowerCamelCase   :							Union[str, Any]				,			_lowerCamelCase   :							Optional[int]     ):





											"""simple docstring"""







											A_			:  str			=				np.log(_lowerCamelCase     )

											# get distribution
											A_			:  List[str]			=				log_sigma - log_sigmas[:, np.newaxis]

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

											A_			:  Union[str, Any]			=				log_sigmas[low_idx]
											A_			:  Dict			=				log_sigmas[high_idx]

											# interpolate sigmas
											A_			:  Tuple			=				(low - log_sigma) / (low - high)
											A_			:  List[Any]			=				np.clip(_lowerCamelCase				,			0				,			1     )

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







						def    _a     (  self   :							Dict				,			_lowerCamelCase   :							torch.FloatTensor				,			_lowerCamelCase   :							Optional[Any]     ):





											"""simple docstring"""







											A_			:  float			=				in_sigmas[-1].item()
											A_			:  float			=				in_sigmas[0].item()

											A_			:  str			=				7.0  # 7.0 is the value used in the paper
											A_			:  Optional[int]			=				np.linspace(0				,			1				,			_lowerCamelCase     )
											A_			:  str			=				sigma_min ** (1 / rho)
											A_			:  int			=				sigma_max ** (1 / rho)
											A_			:  Tuple			=				(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
											return sigmas







						def    _a     (  self   :							List[str]				,			_lowerCamelCase   :							torch.FloatTensor				,			_lowerCamelCase   :							Union[float, torch.FloatTensor]				,			_lowerCamelCase   :							torch.FloatTensor				,			_lowerCamelCase   :							float = 0.0				,			_lowerCamelCase   :							float = 0.0				,			_lowerCamelCase   :							float = float('''inf'''     )				,			_lowerCamelCase   :							float = 1.0				,			_lowerCamelCase   :							Optional[torch.Generator] = None				,			_lowerCamelCase   :							bool = True				,			):





											"""simple docstring"""







											if (
											    isinstance(_lowerCamelCase				,			_lowerCamelCase     )
											    or isinstance(_lowerCamelCase				,			torch.IntTensor     )
											    or isinstance(_lowerCamelCase				,			torch.LongTensor     )
											):
																raise ValueError(
																    (
																        '''Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'''
																        ''' `EulerDiscreteScheduler.step()` is not supported. Make sure to pass'''
																        ''' one of the `scheduler.timesteps` as a timestep.'''
																    )				,			)

											if not self.is_scale_input_called:
																logger.warning(
																    '''The `scale_model_input` function should be called before `step` to ensure correct denoising. '''
																    '''See `StableDiffusionPipeline` for a usage example.'''     )

											if isinstance(_lowerCamelCase				,			torch.Tensor     ):
																A_			:  Any			=				timestep.to(self.timesteps.device     )

											A_			:  Tuple			=				(self.timesteps == timestep).nonzero().item()
											A_			:  List[Any]			=				self.sigmas[step_index]

											A_			:  Tuple			=				min(s_churn / (len(self.sigmas     ) - 1)				,			2**0.5 - 1     ) if s_tmin <= sigma <= s_tmax else 0.0

											A_			:  Optional[int]			=				randn_tensor(
											    model_output.shape				,			dtype=model_output.dtype				,			device=model_output.device				,			generator=_lowerCamelCase     )

											A_			:  List[str]			=				noise * s_noise
											A_			:  Optional[int]			=				sigma * (gamma + 1)

											if gamma > 0:
																A_			:  int			=				sample + eps * (sigma_hat**2 - sigma**2) ** 0.5

											# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
											# NOTE: "original_sample" should not be an expected prediction_type but is left in for
											# backwards compatibility
											if self.config.prediction_type == "original_sample" or self.config.prediction_type == "sample":
																A_			:  Optional[int]			=				model_output
											elif self.config.prediction_type == "epsilon":
																A_			:  List[str]			=				sample - sigma_hat * model_output
											elif self.config.prediction_type == "v_prediction":
																# * c_out + input * c_skip
																A_			:  Any			=				model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
											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_			:  Dict			=				(sample - pred_original_sample) / sigma_hat

											A_			:  List[Any]			=				self.sigmas[step_index + 1] - sigma_hat

											A_			:  Union[str, Any]			=				sample + derivative * dt

											if not return_dict:
																return (prev_sample,)

											return EulerDiscreteSchedulerOutput(prev_sample=_lowerCamelCase				,			pred_original_sample=_lowerCamelCase     )







						def    _a     (  self   :							Dict				,			_lowerCamelCase   :							torch.FloatTensor				,			_lowerCamelCase   :							torch.FloatTensor				,			_lowerCamelCase   :							torch.FloatTensor				,			):





											"""simple docstring"""







											A_			:  Union[str, Any]			=				self.sigmas.to(device=original_samples.device				,			dtype=original_samples.dtype     )
											if original_samples.device.type == "mps" and torch.is_floating_point(_lowerCamelCase     ):
																# mps does not support float64
																A_			:  Optional[int]			=				self.timesteps.to(original_samples.device				,			dtype=torch.floataa     )
																A_			:  Optional[Any]			=				timesteps.to(original_samples.device				,			dtype=torch.floataa     )
											else:
																A_			:  int			=				self.timesteps.to(original_samples.device     )
																A_			:  str			=				timesteps.to(original_samples.device     )

											A_			:  Any			=				[(schedule_timesteps == t).nonzero().item() for t in timesteps]

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

											A_			:  int			=				original_samples + noise * sigma
											return noisy_samples







						def __len__(  self   :							List[Any]     ):





											"""simple docstring"""







											return self.config.num_train_timesteps









'''simple docstring'''




import os




def     snake_case__     (			) -> int:
					A_			:  List[str]			=				os.path.dirname(os.path.realpath(lowerCamelCase__      )      )
					A_			:  str			=				os.path.join(lowerCamelCase__      ,		'''triangle.txt'''      )

					with open(lowerCamelCase__      ) as in_file:
										A_			:  List[str]			=				[[int(lowerCamelCase__      ) for i in line.split()] for line in in_file]

					while len(lowerCamelCase__      ) != 1:
										A_			:  List[str]			=				triangle.pop()
										A_			:  Optional[Any]			=				triangle[-1]
										for j in range(len(lowerCamelCase__      ) - 1      ):
															curr_row[j] += max(last_row[j]      ,		last_row[j + 1]      )
					return triangle[0][0]


if __name__ == "__main__":
							print(solution())



