

'''simple docstring'''
import math
from dataclasses import dataclass
from typing import Optional, Tuple, Union

import numpy as np
import torch

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







@dataclass
# Copied from diffusers.schedulers.scheduling_ddpm.DDPMSchedulerOutput with DDPM->UnCLIP
class 							A__   (	a__  ):
  A__					=    42
  A__					=    None


def 	_lowerCAmelCase (						_UpperCamelCase						:					List[Any]							,			_UpperCamelCase						:					Optional[Any]=0.9_99							,			_UpperCamelCase						:					List[Any]="cosine"							,			)				->      Any:
     """simple docstring"""




     if alpha_transform_type == "cosine":

          def alpha_bar_fn(_UpperCamelCase						:					str    ):
               return math.cos((t + 0.0_08) / 1.0_08 * math.pi / 2    ) ** 2

     elif alpha_transform_type == "exp":

          def alpha_bar_fn(_UpperCamelCase						:					List[str]    ):
               return math.exp(t * -12.0    )

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

     _SCREAMING_SNAKE_CASE							   =[]
     for i in range(_lowerCamelCase    ):
          _SCREAMING_SNAKE_CASE							   =i / num_diffusion_timesteps
          _SCREAMING_SNAKE_CASE							   =(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 							A__   (	a__					,       a__  ):





  @register_to_config
  def __init__(		self				:     List[str]							, _a				:     int = 1000							, _a				:     str = "fixed_small_log"							, _a				:     bool = True							, _a				:     Optional[float] = 1.0							, _a				:     str = "epsilon"							, _a				:     str = "squaredcos_cap_v2"							, )     ->   Union[str, Any]:





       '''simple docstring'''






       if beta_schedule != "squaredcos_cap_v2":
            raise ValueError('UnCLIPScheduler only supports `beta_schedule`: \'squaredcos_cap_v2\''			)

       _SCREAMING_SNAKE_CASE							   =betas_for_alpha_bar(_a			)

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

       # standard deviation of the initial noise distribution
       _SCREAMING_SNAKE_CASE							   =1.0

       # setable values
       _SCREAMING_SNAKE_CASE							   =None
       _SCREAMING_SNAKE_CASE							   =torch.from_numpy(np.arange(0							, _a			)[::-1].copy()			)

       _SCREAMING_SNAKE_CASE							   =variance_type





  def 						A  (		self				:     Any							, _a				:     torch.FloatTensor							, _a				:     Optional[int] = None			)     ->   int:





       '''simple docstring'''






       return sample





  def 						A  (		self				:     Optional[Any]							, _a				:     int							, _a				:     Union[str, torch.device] = None			)     ->   str:





       '''simple docstring'''






       _SCREAMING_SNAKE_CASE							   =num_inference_steps
       _SCREAMING_SNAKE_CASE							   =(self.config.num_train_timesteps - 1) / (self.num_inference_steps - 1)
       _SCREAMING_SNAKE_CASE							   =(np.arange(0							, _a			) * step_ratio).round()[::-1].copy().astype(np.intaa			)
       _SCREAMING_SNAKE_CASE							   =torch.from_numpy(_a			).to(_a			)





  def 						A  (		self				:     str							, _a				:     Dict							, _a				:     str=None							, _a				:     Any=None							, _a				:     Dict=None			)     ->   Union[str, Any]:





       '''simple docstring'''






       if prev_timestep is None:
            _SCREAMING_SNAKE_CASE							   =t - 1

       _SCREAMING_SNAKE_CASE							   =self.alphas_cumprod[t]
       _SCREAMING_SNAKE_CASE							   =self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
       _SCREAMING_SNAKE_CASE							   =1 - alpha_prod_t
       _SCREAMING_SNAKE_CASE							   =1 - alpha_prod_t_prev

       if prev_timestep == t - 1:
            _SCREAMING_SNAKE_CASE							   =self.betas[t]
       else:
            _SCREAMING_SNAKE_CASE							   =1 - alpha_prod_t / alpha_prod_t_prev

       # For t > 0, compute predicted variance βt (see formula (6) and (7) from https://arxiv.org/pdf/2006.11239.pdf)
       # and sample from it to get previous sample
       # x_{t-1} ~ N(pred_prev_sample, variance) == add variance to pred_sample
       _SCREAMING_SNAKE_CASE							   =beta_prod_t_prev / beta_prod_t * beta

       if variance_type is None:
            _SCREAMING_SNAKE_CASE							   =self.config.variance_type

       # hacks - were probably added for training stability
       if variance_type == "fixed_small_log":
            _SCREAMING_SNAKE_CASE							   =torch.log(torch.clamp(_a							, min=1e-20			)			)
            _SCREAMING_SNAKE_CASE							   =torch.exp(0.5 * variance			)
       elif variance_type == "learned_range":
            # NOTE difference with DDPM scheduler
            _SCREAMING_SNAKE_CASE							   =variance.log()
            _SCREAMING_SNAKE_CASE							   =beta.log()

            _SCREAMING_SNAKE_CASE							   =(predicted_variance + 1) / 2
            _SCREAMING_SNAKE_CASE							   =frac * max_log + (1 - frac) * min_log

       return variance





  def 						A  (		self				:     str							, _a				:     torch.FloatTensor							, _a				:     int							, _a				:     torch.FloatTensor							, _a				:     Optional[int] = None							, _a				:     Union[str, Any]=None							, _a				:     bool = True							, )     ->   str:





       '''simple docstring'''






       _SCREAMING_SNAKE_CASE							   =timestep

       if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type == "learned_range":
            _SCREAMING_SNAKE_CASE							   =torch.split(_a							, sample.shape[1]							, dim=1			)
       else:
            _SCREAMING_SNAKE_CASE							   =None

       # 1. compute alphas, betas
       if prev_timestep is None:
            _SCREAMING_SNAKE_CASE							   =t - 1

       _SCREAMING_SNAKE_CASE							   =self.alphas_cumprod[t]
       _SCREAMING_SNAKE_CASE							   =self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
       _SCREAMING_SNAKE_CASE							   =1 - alpha_prod_t
       _SCREAMING_SNAKE_CASE							   =1 - alpha_prod_t_prev

       if prev_timestep == t - 1:
            _SCREAMING_SNAKE_CASE							   =self.betas[t]
            _SCREAMING_SNAKE_CASE							   =self.alphas[t]
       else:
            _SCREAMING_SNAKE_CASE							   =1 - alpha_prod_t / alpha_prod_t_prev
            _SCREAMING_SNAKE_CASE							   =1 - beta

       # 2. compute predicted original sample from predicted noise also called
       # "predicted x_0" of formula (15) from https://arxiv.org/pdf/2006.11239.pdf
       if self.config.prediction_type == "epsilon":
            _SCREAMING_SNAKE_CASE							   =(sample - beta_prod_t ** 0.5 * model_output) / alpha_prod_t ** 0.5
       elif self.config.prediction_type == "sample":
            _SCREAMING_SNAKE_CASE							   =model_output
       else:
            raise ValueError(
                f"prediction_type given as {self.config.prediction_type} must be one of `epsilon` or `sample`"
                ' for the UnCLIPScheduler.'			)

       # 3. Clip "predicted x_0"
       if self.config.clip_sample:
            _SCREAMING_SNAKE_CASE							   =torch.clamp(
                _a							, -self.config.clip_sample_range							, self.config.clip_sample_range			)

       # 4. Compute coefficients for pred_original_sample x_0 and current sample x_t
       # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
       _SCREAMING_SNAKE_CASE							   =(alpha_prod_t_prev ** 0.5 * beta) / beta_prod_t
       _SCREAMING_SNAKE_CASE							   =alpha ** 0.5 * beta_prod_t_prev / beta_prod_t

       # 5. Compute predicted previous sample µ_t
       # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
       _SCREAMING_SNAKE_CASE							   =pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample

       # 6. Add noise
       _SCREAMING_SNAKE_CASE							   =0
       if t > 0:
            _SCREAMING_SNAKE_CASE							   =randn_tensor(
                model_output.shape							, dtype=model_output.dtype							, generator=_a							, device=model_output.device			)

            _SCREAMING_SNAKE_CASE							   =self._get_variance(
                _a							, predicted_variance=_a							, prev_timestep=_a							, )

            if self.variance_type == "fixed_small_log":
                 _SCREAMING_SNAKE_CASE							   =variance
            elif self.variance_type == "learned_range":
                 _SCREAMING_SNAKE_CASE							   =(0.5 * variance).exp()
            else:
                 raise ValueError(
                     f"variance_type given as {self.variance_type} must be one of `fixed_small_log` or `learned_range`"
                     ' for the UnCLIPScheduler.'			)

            _SCREAMING_SNAKE_CASE							   =variance * variance_noise

       _SCREAMING_SNAKE_CASE							   =pred_prev_sample + variance

       if not return_dict:
            return (pred_prev_sample,)

       return UnCLIPSchedulerOutput(prev_sample=_a							, pred_original_sample=_a			)





  def 						A  (		self				:     Tuple							, _a				:     torch.FloatTensor							, _a				:     torch.FloatTensor							, _a				:     torch.IntTensor							, )     ->   List[Any]:





       '''simple docstring'''






       _SCREAMING_SNAKE_CASE							   =self.alphas_cumprod.to(device=original_samples.device							, dtype=original_samples.dtype			)
       _SCREAMING_SNAKE_CASE							   =timesteps.to(original_samples.device			)

       _SCREAMING_SNAKE_CASE							   =alphas_cumprod[timesteps] ** 0.5
       _SCREAMING_SNAKE_CASE							   =sqrt_alpha_prod.flatten()
       while len(sqrt_alpha_prod.shape			) < len(original_samples.shape			):
            _SCREAMING_SNAKE_CASE							   =sqrt_alpha_prod.unsqueeze(-1			)

       _SCREAMING_SNAKE_CASE							   =(1 - alphas_cumprod[timesteps]) ** 0.5
       _SCREAMING_SNAKE_CASE							   =sqrt_one_minus_alpha_prod.flatten()
       while len(sqrt_one_minus_alpha_prod.shape			) < len(original_samples.shape			):
            _SCREAMING_SNAKE_CASE							   =sqrt_one_minus_alpha_prod.unsqueeze(-1			)

       _SCREAMING_SNAKE_CASE							   =sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
       return noisy_samples



'''simple docstring'''
import os


def 	_lowerCAmelCase (						)				->      List[str]:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							   =os.path.dirname(os.path.realpath(_UpperCamelCase    )    )
     _SCREAMING_SNAKE_CASE							   =os.path.join(_UpperCamelCase							,			'triangle.txt'    )

     with open(_UpperCamelCase    ) as f:
          _SCREAMING_SNAKE_CASE							   =f.readlines()

     _SCREAMING_SNAKE_CASE							   =[]
     for line in triangle:
          _SCREAMING_SNAKE_CASE							   =[]
          for number in line.strip().split(' '    ):
               numbers_from_line.append(int(_UpperCamelCase    )    )
          a.append(_UpperCamelCase    )

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


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