





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


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






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

			'''simple docstring'''







			lowerCAmelCase_												=						42
			lowerCAmelCase_												=						None





def lowerCAmelCase__(__snake_case	,__snake_case=0.9_9_9	,__snake_case="cosine"	,)    ->				str:







	'''simple docstring'''







	if alpha_transform_type == "cosine":

		def alpha_bar_fn(__snake_case							):
			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(__snake_case							):
			return math.exp(t * -1_2.0							)

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

	lowerCamelCase__        =		[]
	for i in range(__snake_case							):
		lowerCamelCase__        =		i / num_diffusion_timesteps
		lowerCamelCase__        =		(i + 1) / num_diffusion_timesteps
		betas.append(min(1 - alpha_bar_fn(__snake_case							) / alpha_bar_fn(__snake_case							)	,__snake_case							)							)
	return torch.tensor(__snake_case	,dtype=torch.floataa							)






class  __A   (   lowerCAmelCase      ,    lowerCAmelCase			):

			'''simple docstring'''







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





			@register_to_config
			def __init__(   self	,  __lowerCAmelCase = 1_0_0_0	,  __lowerCAmelCase = 0.0001	,  __lowerCAmelCase = 0.02	,  __lowerCAmelCase = "linear"	,  __lowerCAmelCase = None	,  __lowerCAmelCase = "epsilon"	,  __lowerCAmelCase = "linear"	,  __lowerCAmelCase = False	,  __lowerCAmelCase = "linspace"	,  __lowerCAmelCase = 0	,  ):



				'''simple docstring'''







				if trained_betas is not None:
					lowerCamelCase__        =		torch.tensor(__lowerCAmelCase	,  dtype=torch.floataa							)
				elif beta_schedule == "linear":
					lowerCamelCase__        =		torch.linspace(__lowerCAmelCase	,  __lowerCAmelCase	,  __lowerCAmelCase	,  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	,  __lowerCAmelCase	,  dtype=torch.floataa							) ** 2
					)
				elif beta_schedule == "squaredcos_cap_v2":
					# Glide cosine schedule
					lowerCamelCase__        =		betas_for_alpha_bar(__lowerCAmelCase							)
				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							)

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

				# setable values
				lowerCamelCase__        =		None
				lowerCamelCase__        =		np.linspace(0	,  num_train_timesteps - 1	,  __lowerCAmelCase	,  dtype=__lowerCAmelCase							)[::-1].copy()
				lowerCamelCase__        =		torch.from_numpy(__lowerCAmelCase							)
				lowerCamelCase__        =		False
				lowerCamelCase__        =		use_karras_sigmas





			@property
			def 		__lowerCamelCase    (   self							):



				'''simple docstring'''







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

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





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase							):



				'''simple docstring'''







				if isinstance(__lowerCAmelCase	,  torch.Tensor							):
					lowerCamelCase__        =		timestep.to(self.timesteps.device							)
				lowerCamelCase__        =		(self.timesteps == timestep).nonzero().item()
				lowerCamelCase__        =		self.sigmas[step_index]

				lowerCamelCase__        =		sample / ((sigma**2 + 1) ** 0.5)

				lowerCamelCase__        =		True
				return sample





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase = None							):



				'''simple docstring'''







				lowerCamelCase__        =		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":
					lowerCamelCase__        =		np.linspace(0	,  self.config.num_train_timesteps - 1	,  __lowerCAmelCase	,  dtype=__lowerCAmelCase							)[
					    ::-1
					].copy()
				elif self.config.timestep_spacing == "leading":
					lowerCamelCase__        =		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
					lowerCamelCase__        =		(np.arange(0	,  __lowerCAmelCase							) * step_ratio).round()[::-1].copy().astype(__lowerCAmelCase							)
					timesteps += self.config.steps_offset
				elif self.config.timestep_spacing == "trailing":
					lowerCamelCase__        =		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
					lowerCamelCase__        =		(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\'.'							)

				lowerCamelCase__        =		np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5							)
				lowerCamelCase__        =		np.log(__lowerCAmelCase							)

				if self.config.interpolation_type == "linear":
					lowerCamelCase__        =		np.interp(__lowerCAmelCase	,  np.arange(0	,  len(__lowerCAmelCase							)							)	,  __lowerCAmelCase							)
				elif self.config.interpolation_type == "log_linear":
					lowerCamelCase__        =		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:
					lowerCamelCase__        =		self._convert_to_karras(in_sigmas=__lowerCAmelCase	,  num_inference_steps=self.num_inference_steps							)
					lowerCamelCase__        =		np.array([self._sigma_to_t(__lowerCAmelCase	,  __lowerCAmelCase							) for sigma in sigmas]							)

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





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase							):



				'''simple docstring'''







				lowerCamelCase__        =		np.log(__lowerCAmelCase							)

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

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

				lowerCamelCase__        =		log_sigmas[low_idx]
				lowerCamelCase__        =		log_sigmas[high_idx]

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

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





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase							):



				'''simple docstring'''







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

				lowerCamelCase__        =		7.0  # 7.0 is the value used in the paper
				lowerCamelCase__        =		np.linspace(0	,  1	,  __lowerCAmelCase							)
				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 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase	,  __lowerCAmelCase	,  __lowerCAmelCase = 0.0	,  __lowerCAmelCase = 0.0	,  __lowerCAmelCase = float('''inf'''							)	,  __lowerCAmelCase = 1.0	,  __lowerCAmelCase = None	,  __lowerCAmelCase = 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							):
					lowerCamelCase__        =		timestep.to(self.timesteps.device							)

				lowerCamelCase__        =		(self.timesteps == timestep).nonzero().item()
				lowerCamelCase__        =		self.sigmas[step_index]

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

				lowerCamelCase__        =		randn_tensor(
				    model_output.shape	,  dtype=model_output.dtype	,  device=model_output.device	,  generator=__lowerCAmelCase							)

				lowerCamelCase__        =		noise * s_noise
				lowerCamelCase__        =		sigma * (gamma + 1)

				if gamma > 0:
					lowerCamelCase__        =		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":
					lowerCamelCase__        =		model_output
				elif self.config.prediction_type == "epsilon":
					lowerCamelCase__        =		sample - sigma_hat * model_output
				elif self.config.prediction_type == "v_prediction":
					# * c_out + input * c_skip
					lowerCamelCase__        =		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
				lowerCamelCase__        =		(sample - pred_original_sample) / sigma_hat

				lowerCamelCase__        =		self.sigmas[step_index + 1] - sigma_hat

				lowerCamelCase__        =		sample + derivative * dt

				if not return_dict:
					return (prev_sample,)

				return EulerDiscreteSchedulerOutput(prev_sample=__lowerCAmelCase	,  pred_original_sample=__lowerCAmelCase							)





			def 		__lowerCamelCase    (   self	,  __lowerCAmelCase	,  __lowerCAmelCase	,  __lowerCAmelCase	,  ):



				'''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(__lowerCAmelCase							):
					# 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							):



				'''simple docstring'''







				return self.config.num_train_timesteps










import os





def lowerCAmelCase__()    ->				Optional[Any]:







	'''simple docstring'''







	lowerCamelCase__        =		os.path.dirname(os.path.realpath(__snake_case							)							)
	lowerCamelCase__        =		os.path.join(__snake_case	,'''triangle.txt'''							)

	with open(__snake_case							) as f:
		lowerCamelCase__        =		f.readlines()

	lowerCamelCase__        =		[[int(__snake_case							) for y in x.rstrip('''\r\n'''							).split(''' '''							)] for x in triangle]

	for i in range(1	,len(__snake_case							)							):
		for j in range(len(a[i]							)							):
			lowerCamelCase__        =		a[i - 1][j] if j != len(a[i - 1]							) else 0
			lowerCamelCase__        =		a[i - 1][j - 1] if j > 0 else 0
			a[i][j] += max(__snake_case	,__snake_case							)
	return max(a[-1]							)


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



