





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	(							_SCREAMING_SNAKE_CASE	):







					'''simple docstring'''

					lowerCamelCase  :  Any           =							42
					lowerCamelCase  :  Optional[Any]           =							None




def  A_(      A					,   A=0.999					,   A="cosine"					,   ):



	if alpha_transform_type == "cosine":

		def alpha_bar_fn(A ):
			return math.cos((t + 0.008) / 1.008 * math.pi / 2 ) ** 2

	elif alpha_transform_type == "exp":

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

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

	UpperCAmelCase_		    =  []
	for i in range(lowerCAmelCase__ ):
		UpperCAmelCase_		    =  i / num_diffusion_timesteps
		UpperCAmelCase_		    =  (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	(							_SCREAMING_SNAKE_CASE    ,							_SCREAMING_SNAKE_CASE	):







					'''simple docstring'''

					lowerCamelCase  :  Any           =							[e.name for e in KarrasDiffusionSchedulers]
					lowerCamelCase  :  int           =							1





					@register_to_config
					def __init__(    self     :	Optional[Any]			,       __lowercase     :	str = 10_00			,       __lowercase     :	str = 0.0001			,       __lowercase     :	Tuple = 0.02			,       __lowercase     :	Optional[int] = "linear"			,       __lowercase     :	Any = None			,       __lowercase     :	Union[str, Any] = False			,       __lowercase     :	Any = "epsilon"			,       __lowercase     :	Union[str, Any] = "linspace"			,       __lowercase     :	str = 0			,       ):






						'''simple docstring'''







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

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

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

						# setable values
						UpperCAmelCase_		    =  None
						UpperCAmelCase_		    =  use_karras_sigmas
						self.set_timesteps(__lowercase			,       __lowercase		)
						UpperCAmelCase_		    =  []
						UpperCAmelCase_		    =  False





					@property
					def 							SCREAMING_SNAKE_CASE				(    self     :	Union[str, Any]		):






						'''simple docstring'''







						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     :	int			,       __lowercase     :	int			,       __lowercase     :	str		):






						'''simple docstring'''







						if isinstance(__lowercase			,       torch.Tensor		):
							UpperCAmelCase_		    =  timestep.to(self.timesteps.device		)
						UpperCAmelCase_		    =  (self.timesteps == timestep).nonzero().item()
						UpperCAmelCase_		    =  self.sigmas[step_index]
						UpperCAmelCase_		    =  sample / ((sigma**2 + 1) ** 0.5)
						UpperCAmelCase_		    =  True
						return sample





					def 							SCREAMING_SNAKE_CASE				(    self     :	List[str]			,       __lowercase     :	str			,       __lowercase     :	Tuple			,       __lowercase     :	str		):






						'''simple docstring'''







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

						UpperCAmelCase_		    =  integrate.quad(__lowercase			,       self.sigmas[t]			,       self.sigmas[t + 1]			,       epsrel=1e-4		)[0]

						return integrated_coeff





					def 							SCREAMING_SNAKE_CASE				(    self     :	Union[str, Any]			,       __lowercase     :	Any			,       __lowercase     :	Union[str, Any] = None		):






						'''simple docstring'''







						UpperCAmelCase_		    =  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":
							UpperCAmelCase_		    =  np.linspace(0			,       self.config.num_train_timesteps - 1			,       __lowercase			,       dtype=__lowercase		)[
							    ::-1
							].copy()
						elif self.config.timestep_spacing == "leading":
							UpperCAmelCase_		    =  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
							UpperCAmelCase_		    =  (np.arange(0			,       __lowercase		) * step_ratio).round()[::-1].copy().astype(__lowercase		)
							timesteps += self.config.steps_offset
						elif self.config.timestep_spacing == "trailing":
							UpperCAmelCase_		    =  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
							UpperCAmelCase_		    =  (np.arange(self.config.num_train_timesteps			,       0			,       -step_ratio		)).round().copy().astype(__lowercase		)
							timesteps -= 1
						else:
							raise ValueError(
							    F"""{self.config.timestep_spacing} is not supported. Please make sure to choose one of \'linspace\', \'leading\' or \'trailing\'."""		)

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

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

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

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

						UpperCAmelCase_		    =  []





					def 							SCREAMING_SNAKE_CASE				(    self     :	Optional[int]			,       __lowercase     :	str			,       __lowercase     :	Dict		):






						'''simple docstring'''







						UpperCAmelCase_		    =  np.log(__lowercase		)

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

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

						UpperCAmelCase_		    =  log_sigmas[low_idx]
						UpperCAmelCase_		    =  log_sigmas[high_idx]

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

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





					def 							SCREAMING_SNAKE_CASE				(    self     :	Optional[Any]			,       __lowercase     :	int		):






						'''simple docstring'''







						UpperCAmelCase_		    =  in_sigmas[-1].item()
						UpperCAmelCase_		    =  in_sigmas[0].item()

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





					def 							SCREAMING_SNAKE_CASE				(    self     :	str			,       __lowercase     :	Tuple			,       __lowercase     :	Optional[int]			,       __lowercase     :	Dict			,       __lowercase     :	Tuple = 4			,       __lowercase     :	Tuple = True			,       ):






						'''simple docstring'''







						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(__lowercase			,       torch.Tensor		):
							UpperCAmelCase_		    =  timestep.to(self.timesteps.device		)
						UpperCAmelCase_		    =  (self.timesteps == timestep).nonzero().item()
						UpperCAmelCase_		    =  self.sigmas[step_index]

						# 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
						if self.config.prediction_type == "epsilon":
							UpperCAmelCase_		    =  sample - sigma * model_output
						elif self.config.prediction_type == "v_prediction":
							# * c_out + input * c_skip
							UpperCAmelCase_		    =  model_output * (-sigma / (sigma**2 + 1) ** 0.5) + (sample / (sigma**2 + 1))
						elif self.config.prediction_type == "sample":
							UpperCAmelCase_		    =  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
						UpperCAmelCase_		    =  (sample - pred_original_sample) / sigma
						self.derivatives.append(__lowercase		)
						if len(self.derivatives		) > order:
							self.derivatives.pop(0		)

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

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

						if not return_dict:
							return (prev_sample,)

						return LMSDiscreteSchedulerOutput(prev_sample=__lowercase			,       pred_original_sample=__lowercase		)





					def 							SCREAMING_SNAKE_CASE				(    self     :	Optional[Any]			,       __lowercase     :	Union[str, Any]			,       __lowercase     :	str			,       __lowercase     :	List[str]			,       ):






						'''simple docstring'''







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

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

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

						UpperCAmelCase_		    =  original_samples + noise * sigma
						return noisy_samples





					def __len__(    self     :	Tuple		):






						'''simple docstring'''







						return self.config.num_train_timesteps






'''simple docstring'''






import os






def 						_A					() ->	int:




     '''simple docstring'''



     _a         =				os.path.dirname(os.path.realpath(lowerCAmelCase__		)		)
     _a         =				os.path.join(lowerCAmelCase__					,    'triangle.txt'		)

     with open(lowerCAmelCase__		) as in_file:
          _a         =				[[int(lowerCAmelCase__		) for i in line.split()] for line in in_file]

     while len(lowerCAmelCase__		) != 1:
          _a         =				triangle.pop()
          _a         =				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())

