code: import os
  
  def      SCREAMING_SNAKE_CASE_  (		)  ->			Tuple:
  				lowerCAmelCase				=	os.path.dirname(os.path.realpath(snake_case__							)							)
  				lowerCAmelCase				=	os.path.join(snake_case__     ,						'''triangle.txt'''							)
  
  				with open(snake_case__							) as in_file:
  								lowerCAmelCase				=	[[int(snake_case__							) for i in line.split()] for line in in_file]
  
  				while len(snake_case__							) != 1:
  								lowerCAmelCase				=	triangle.pop()
  								lowerCAmelCase				=	triangle[-1]
  								for j in range(len(snake_case__							) - 1							):
  												curr_row[j] += max(last_row[j]     ,						last_row[j + 1]							)
  				return triangle[0][0]
  
  
  if __name__ == "__main__":
  	print(solution())
  
  
  
  
style_context: 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 SchedulerMixin
  
  
  lowercase__    :       List[Any]						=			logging.get_logger(__name__)  # pylint: disable=invalid-name
  
  
  
  
  @dataclass
  class      lowercase_						(						UpperCamelCase_		):
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  	UpperCAmelCase_						:      torch.FloatTensor
  
  
  
  
  class      lowercase_						(						UpperCamelCase_   ,  UpperCamelCase_		):
  
  
  
  	"""simple docstring"""
  
  
  
  
  
  	UpperCAmelCase_						:      Tuple     =       1
  
  
  	@register_to_config
  	def __init__(							self	,    __SCREAMING_SNAKE_CASE = 40	,    __SCREAMING_SNAKE_CASE = 0.0_0_2	,    __SCREAMING_SNAKE_CASE = 8_0.0	,    __SCREAMING_SNAKE_CASE = 0.5	,    __SCREAMING_SNAKE_CASE = 1.0	,    __SCREAMING_SNAKE_CASE = 7.0	,    __SCREAMING_SNAKE_CASE = True	,    )		->Tuple:
  								# standard deviation of the initial noise distribution
  								lowerCAmelCase				=	sigma_max
  
  								lowerCAmelCase				=	np.linspace(0	,    1	,    __SCREAMING_SNAKE_CASE       )
  								lowerCAmelCase				=	self._convert_to_karras(__SCREAMING_SNAKE_CASE       )
  								lowerCAmelCase				=	self.sigma_to_t(__SCREAMING_SNAKE_CASE       )
  
  								# setable values
  								lowerCAmelCase				=	None
  								lowerCAmelCase				=	torch.from_numpy(__SCREAMING_SNAKE_CASE       )
  								lowerCAmelCase				=	torch.from_numpy(__SCREAMING_SNAKE_CASE       )
  								lowerCAmelCase				=	False
  								lowerCAmelCase				=	False
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE	,    __SCREAMING_SNAKE_CASE=None       )		->Optional[Any]:
  								if schedule_timesteps is None:
  															lowerCAmelCase				=	self.timesteps
  
  								lowerCAmelCase				=	(schedule_timesteps == timestep).nonzero()
  								return indices.item()
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE	,    __SCREAMING_SNAKE_CASE       )		->torch.FloatTensor:
  								# Get sigma corresponding to timestep
  								if isinstance(__SCREAMING_SNAKE_CASE	,    torch.Tensor       ):
  															lowerCAmelCase				=	timestep.to(self.timesteps.device       )
  								lowerCAmelCase				=	self.index_for_timestep(__SCREAMING_SNAKE_CASE       )
  								lowerCAmelCase				=	self.sigmas[step_idx]
  
  								lowerCAmelCase				=	sample / ((sigma**2 + self.config.sigma_data**2) ** 0.5)
  
  								lowerCAmelCase				=	True
  								return sample
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE       )		->Union[str, Any]:
  								if not isinstance(__SCREAMING_SNAKE_CASE	,    np.ndarray       ):
  															lowerCAmelCase				=	np.array(__SCREAMING_SNAKE_CASE	,    dtype=np.floataa       )
  
  								lowerCAmelCase				=	1000 * 0.2_5 * np.log(sigmas + 1e-44       )
  
  								return timesteps
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE = None	,    __SCREAMING_SNAKE_CASE = None	,    __SCREAMING_SNAKE_CASE = None	,    )		->str:
  								if num_inference_steps is None and timesteps is None:
  															raise ValueError('''Exactly one of `num_inference_steps` or `timesteps` must be supplied.'''       )
  
  								if num_inference_steps is not None and timesteps is not None:
  															raise ValueError('''Can only pass one of `num_inference_steps` or `timesteps`.'''       )
  
  								# Follow DDPMScheduler custom timesteps logic
  								if timesteps is not None:
  															for i in range(1	,    len(__SCREAMING_SNAKE_CASE       )       ):
  																						if timesteps[i] >= timesteps[i - 1]:
  																													raise ValueError('''`timesteps` must be in descending order.'''       )
  
  															if timesteps[0] >= self.config.num_train_timesteps:
  																						raise ValueError(
  																						    F"`timesteps` must start before `self.config.train_timesteps`:"
  																						    F" {self.config.num_train_timesteps}."       )
  
  															lowerCAmelCase				=	np.array(__SCREAMING_SNAKE_CASE	,    dtype=np.intaa       )
  															lowerCAmelCase				=	True
  								else:
  															if num_inference_steps > self.config.num_train_timesteps:
  																						raise ValueError(
  																						    F"`num_inference_steps`: {num_inference_steps} cannot be larger than `self.config.train_timesteps`:"
  																						    F" {self.config.num_train_timesteps} as the unet model trained with this scheduler can only handle"
  																						    F" maximal {self.config.num_train_timesteps} timesteps."       )
  
  															lowerCAmelCase				=	num_inference_steps
  
  															lowerCAmelCase				=	self.config.num_train_timesteps // self.num_inference_steps
  															lowerCAmelCase				=	(np.arange(0	,    __SCREAMING_SNAKE_CASE       ) * step_ratio).round()[::-1].copy().astype(np.intaa       )
  															lowerCAmelCase				=	False
  
  								# Map timesteps to Karras sigmas directly for multistep sampling
  								# See https://github.com/openai/consistency_models/blob/main/cm/karras_diffusion.py#L675
  								lowerCAmelCase				=	self.config.num_train_timesteps
  								lowerCAmelCase				=	timesteps[::-1].copy()
  								lowerCAmelCase				=	ramp / (num_train_timesteps - 1)
  								lowerCAmelCase				=	self._convert_to_karras(__SCREAMING_SNAKE_CASE       )
  								lowerCAmelCase				=	self.sigma_to_t(__SCREAMING_SNAKE_CASE       )
  
  								lowerCAmelCase				=	np.concatenate([sigmas, [self.sigma_min]]       ).astype(np.floataa       )
  								lowerCAmelCase				=	torch.from_numpy(__SCREAMING_SNAKE_CASE       ).to(device=__SCREAMING_SNAKE_CASE       )
  
  								if str(__SCREAMING_SNAKE_CASE       ).startswith('''mps'''       ):
  															# mps does not support float64
  															lowerCAmelCase				=	torch.from_numpy(__SCREAMING_SNAKE_CASE       ).to(__SCREAMING_SNAKE_CASE	,    dtype=torch.floataa       )
  								else:
  															lowerCAmelCase				=	torch.from_numpy(__SCREAMING_SNAKE_CASE       ).to(device=__SCREAMING_SNAKE_CASE       )
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE       )		->Union[str, Any]:
  								lowerCAmelCase				=	self.config.sigma_min
  								lowerCAmelCase				=	self.config.sigma_max
  
  								lowerCAmelCase				=	self.config.rho
  								lowerCAmelCase				=	sigma_min ** (1 / rho)
  								lowerCAmelCase				=	sigma_max ** (1 / rho)
  								lowerCAmelCase				=	(max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
  								return sigmas
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE       )		->Union[str, Any]:
  								lowerCAmelCase				=	self.config.sigma_data
  
  								lowerCAmelCase				=	sigma_data**2 / (sigma**2 + sigma_data**2)
  								lowerCAmelCase				=	sigma * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
  								return c_skip, c_out
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE       )		->List[str]:
  								lowerCAmelCase				=	self.config.sigma_min
  								lowerCAmelCase				=	self.config.sigma_data
  
  								lowerCAmelCase				=	sigma_data**2 / ((sigma - sigma_min) ** 2 + sigma_data**2)
  								lowerCAmelCase				=	(sigma - sigma_min) * sigma_data / (sigma**2 + sigma_data**2) ** 0.5
  								return c_skip, c_out
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE	,    __SCREAMING_SNAKE_CASE	,    __SCREAMING_SNAKE_CASE	,    __SCREAMING_SNAKE_CASE = None	,    __SCREAMING_SNAKE_CASE = True	,    )		->Union[CMStochasticIterativeSchedulerOutput, Tuple]:
  
  								if (
  								    isinstance(__SCREAMING_SNAKE_CASE	,    __SCREAMING_SNAKE_CASE       )
  								    or isinstance(__SCREAMING_SNAKE_CASE	,    torch.IntTensor       )
  								    or isinstance(__SCREAMING_SNAKE_CASE	,    torch.LongTensor       )
  								):
  															raise ValueError(
  															    (
  															        '''Passing integer indices (e.g. from `enumerate(timesteps)`) as timesteps to'''
  															        F" `{self.__class__}.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(__SCREAMING_SNAKE_CASE	,    torch.Tensor       ):
  															lowerCAmelCase				=	timestep.to(self.timesteps.device       )
  
  								lowerCAmelCase				=	self.config.sigma_min
  								lowerCAmelCase				=	self.config.sigma_max
  
  								lowerCAmelCase				=	self.index_for_timestep(__SCREAMING_SNAKE_CASE       )
  
  								# sigma_next corresponds to next_t in original implementation
  								lowerCAmelCase				=	self.sigmas[step_index]
  								if step_index + 1 < self.config.num_train_timesteps:
  															lowerCAmelCase				=	self.sigmas[step_index + 1]
  								else:
  															# Set sigma_next to sigma_min
  															lowerCAmelCase				=	self.sigmas[-1]
  
  								# Get scalings for boundary conditions
  								lowerCAmelCase	,   lowerCAmelCase				=	self.get_scalings_for_boundary_condition(__SCREAMING_SNAKE_CASE       )
  
  								# 1. Denoise model output using boundary conditions
  								lowerCAmelCase				=	c_out * model_output + c_skip * sample
  								if self.config.clip_denoised:
  															lowerCAmelCase				=	denoised.clamp(-1	,    1       )
  
  								# 2. Sample z ~ N(0, s_noise^2 * I)
  								# Noise is not used for onestep sampling.
  								if len(self.timesteps       ) > 1:
  															lowerCAmelCase				=	randn_tensor(
  															    model_output.shape	,    dtype=model_output.dtype	,    device=model_output.device	,    generator=__SCREAMING_SNAKE_CASE       )
  								else:
  															lowerCAmelCase				=	torch.zeros_like(__SCREAMING_SNAKE_CASE       )
  								lowerCAmelCase				=	noise * self.config.s_noise
  
  								lowerCAmelCase				=	sigma_next.clamp(min=__SCREAMING_SNAKE_CASE	,    max=__SCREAMING_SNAKE_CASE       )
  
  								# 3. Return noisy sample
  								# tau = sigma_hat, eps = sigma_min
  								lowerCAmelCase				=	denoised + z * (sigma_hat**2 - sigma_min**2) ** 0.5
  
  								if not return_dict:
  															return (prev_sample,)
  
  								return CMStochasticIterativeSchedulerOutput(prev_sample=__SCREAMING_SNAKE_CASE       )
  
  
  	def     SCREAMING_SNAKE_CASE_       (							self	,    __SCREAMING_SNAKE_CASE	,    __SCREAMING_SNAKE_CASE	,    __SCREAMING_SNAKE_CASE	,    )		->torch.FloatTensor:
  								# Make sure sigmas and timesteps have the same device and dtype as original_samples
  								lowerCAmelCase				=	self.sigmas.to(device=original_samples.device	,    dtype=original_samples.dtype       )
  								if original_samples.device.type == "mps" and torch.is_floating_point(__SCREAMING_SNAKE_CASE       ):
  															# 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				=	[(schedule_timesteps == t).nonzero().item() 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       )		->int:
  								return self.config.num_train_timesteps
  
  
  
  