'''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 				lowercase    (    a__			):
   lowerCamelCase_            =4_2
   lowerCamelCase_            =None




def __a			(						__lowerCamelCase      :    Dict			,		__lowerCamelCase      :    str=0.9_9_9			,		__lowerCamelCase      :    Optional[int]="cosine"			,		)						->				Union[str, Any]:
      '''simple docstring'''


      if alpha_transform_type == "cosine":

            def alpha_bar_fn(__lowerCamelCase      :    Optional[int]					):
                  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(__lowerCamelCase      :    Dict					):
                  return math.exp(t * -12.0					)

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

      lowercase_     			=   []
      for i in range(__lowerCamelCase					):
            lowercase_     			=   i / num_diffusion_timesteps
            lowercase_     			=   (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 				lowercase    (    a__			,					a__			):
   lowerCamelCase_            =[e.name for e in KarrasDiffusionSchedulers]
   lowerCamelCase_            =1


   @register_to_config
   def __init__( self					:						Optional[Any] ,		__lowerCAmelCase					:						str = 1000 ,		__lowerCAmelCase					:						List[str] = 0.0001 ,		__lowerCAmelCase					:						int = 0.02 ,		__lowerCAmelCase					:						Optional[int] = "linear" ,		__lowerCAmelCase					:						Any = None ,		__lowerCAmelCase					:						Optional[Any] = False ,		__lowerCAmelCase					:						Optional[Any] = "epsilon" ,		__lowerCAmelCase					:						List[str] = "linspace" ,		__lowerCAmelCase					:						Optional[int] = 0 ,		)   ->       List[Any]:







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

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

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

         # setable values
         lowercase_     			=   None
         lowercase_     			=   use_karras_sigmas
         self.set_timesteps(__A ,		__A)
         lowercase_     			=   []
         lowercase_     			=   False


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







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

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


   def __UpperCAmelCase							( self					:						List[str] ,		__lowerCAmelCase					:						Dict ,		__lowerCAmelCase					:						Dict)   ->       torch.FloatTensor:







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


   def __UpperCAmelCase							( self					:						Optional[int] ,		__lowerCAmelCase					:						str ,		__lowerCAmelCase					:						List[Any] ,		__lowerCAmelCase					:						Optional[int])   ->       List[Any]:







         def lms_derivative(__lowerCAmelCase					:						List[str]):
               lowercase_     			=   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

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

         return integrated_coeff


   def __UpperCAmelCase							( self					:						Dict ,		__lowerCAmelCase					:						Optional[Any] ,		__lowerCAmelCase					:						Union[str, Any] = None)   ->       Optional[int]:
         lowercase_     			=   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":
               lowercase_     			=   np.linspace(0 ,		self.config.num_train_timesteps - 1 ,		__A ,		dtype=__A)[
                   ::-1
               ].copy()
         elif self.config.timestep_spacing == "leading":
               lowercase_     			=   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
               lowercase_     			=   (np.arange(0 ,		__A) * step_ratio).round()[::-1].copy().astype(__A)
               timesteps += self.config.steps_offset
         elif self.config.timestep_spacing == "trailing":
               lowercase_     			=   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
               lowercase_     			=   (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\'.')

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

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

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

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

         lowercase_     			=   []


   def __UpperCAmelCase							( self					:						Optional[Any] ,		__lowerCAmelCase					:						Union[str, Any] ,		__lowerCAmelCase					:						str)   ->       Optional[Any]:
         lowercase_     			=   np.log(__A)

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

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

         lowercase_     			=   log_sigmas[low_idx]
         lowercase_     			=   log_sigmas[high_idx]

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

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


   def __UpperCAmelCase							( self					:						List[str] ,		__lowerCAmelCase					:						List[Any])   ->       torch.FloatTensor:
         lowercase_     			=   in_sigmas[-1].item()
         lowercase_     			=   in_sigmas[0].item()

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


   def __UpperCAmelCase							( self					:						Dict ,		__lowerCAmelCase					:						str ,		__lowerCAmelCase					:						Any ,		__lowerCAmelCase					:						List[Any] ,		__lowerCAmelCase					:						Union[str, Any] = 4 ,		__lowerCAmelCase					:						Optional[Any] = True ,		)   ->       Union[LMSDiscreteSchedulerOutput, Tuple]:







         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):
               lowercase_     			=   timestep.to(self.timesteps.device)
         lowercase_     			=   (self.timesteps == timestep).nonzero().item()
         lowercase_     			=   self.sigmas[step_index]

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

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

         # 4. Compute previous sample based on the derivatives path
         lowercase_     			=   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 ,		__lowerCAmelCase					:						int ,		__lowerCAmelCase					:						Optional[int] ,		__lowerCAmelCase					:						Union[str, Any] ,		)   ->       torch.FloatTensor:
         lowercase_     			=   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
               lowercase_     			=   self.timesteps.to(original_samples.device ,		dtype=torch.floataa)
               lowercase_     			=   timesteps.to(original_samples.device ,		dtype=torch.floataa)
         else:
               lowercase_     			=   self.timesteps.to(original_samples.device)
               lowercase_     			=   timesteps.to(original_samples.device)

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

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

         lowercase_     			=   original_samples + noise * sigma
         return noisy_samples


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










'''simple docstring'''




import os





def 				a_							(    )      ->int:






				'''simple docstring'''

				__lowerCamelCase		:   Dict           =       os.path.dirname(os.path.realpath(lowercase     )     )
				__lowerCamelCase		:   Any           =       os.path.join(lowercase				,    "triangle.txt"     )

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

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


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





