import math
from collections import defaultdict
from typing import List, Optional, Tuple, Union

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from ..utils import randn_tensor
from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput



def    lowerCamelCase_   (  _lowercase ,     _lowercase=0.9_99 ,     _lowercase="cosine" ,     )							->	Optional[Any]:
  if alpha_transform_type == "cosine":

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

  elif alpha_transform_type == "exp":

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

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

  __A							:   Dict	  =				[]
  for i in range(__UpperCamelCase    ):
    __A							:   int	  =				i / num_diffusion_timesteps
    __A							:   List[Any]	  =				(i + 1) / num_diffusion_timesteps
    betas.append(min(1 - alpha_bar_fn(__UpperCamelCase    ) / alpha_bar_fn(__UpperCamelCase    ) ,     __UpperCamelCase    )    )
  return torch.tensor(__UpperCamelCase ,     dtype=torch.floataa    )





class _a       (	__lowerCamelCase   ,							__lowerCamelCase ):

 '''simple docstring'''



 lowerCamelCase_   :      List[str]       =	[e.name for e in KarrasDiffusionSchedulers]
 lowerCamelCase_   :      Union[str, Any]       =	2

 @register_to_config
 def __init__(       self							,			__UpperCAmelCase = 1_000							,			__UpperCAmelCase = 0.0_00_85							,			__UpperCAmelCase = 0.0_12							,			__UpperCAmelCase = "linear"							,			__UpperCAmelCase = None							,			__UpperCAmelCase = "epsilon"							,			__UpperCAmelCase = "linspace"							,			__UpperCAmelCase = 0							,			):





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

   __A							:   Dict	  =				1.0 - self.betas
   __A							:   Tuple	  =				torch.cumprod(self.alphas							,			dim=0   )

   #  set all values
   self.set_timesteps(_UpperCamelCase							,			_UpperCamelCase							,			_UpperCamelCase   )

 def 					__UpperCAmelCase(       self							,			__UpperCAmelCase							,			__UpperCAmelCase=None   ):





   if schedule_timesteps is None:
     __A							:   Optional[int]	  =				self.timesteps

   __A							:   Union[str, Any]	  =				(schedule_timesteps == timestep).nonzero()

   # The sigma index that is taken for the **very** first `step`
   # is always the second index (or the last index if there is only 1)
   # This way we can ensure we don't accidentally skip a sigma in
   # case we start in the middle of the denoising schedule (e.g. for image-to-image)
   if len(self._index_counter   ) == 0:
     __A							:   str	  =				1 if len(_UpperCamelCase   ) > 1 else 0
   else:
     __A							:   List[str]	  =				timestep.cpu().item() if torch.is_tensor(_UpperCamelCase   ) else timestep
     __A							:   Dict	  =				self._index_counter[timestep_int]

   return indices[pos].item()

 @property
 def 					__UpperCAmelCase(       self   ):





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

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

 def 					__UpperCAmelCase(       self							,			__UpperCAmelCase							,			__UpperCAmelCase							,			):
   __A							:   str	  =				self.index_for_timestep(_UpperCamelCase   )

   if self.state_in_first_order:
     __A							:   Tuple	  =				self.sigmas[step_index]
   else:
     __A							:   Tuple	  =				self.sigmas_interpol[step_index - 1]

   __A							:   Optional[int]	  =				sample / ((sigma**2 + 1) ** 0.5)
   return sample

 def 					__UpperCAmelCase(       self							,			__UpperCAmelCase							,			__UpperCAmelCase = None							,			__UpperCAmelCase = None							,			):
   __A							:   str	  =				num_inference_steps

   __A							:   Optional[Any]	  =				num_train_timesteps or self.config.num_train_timesteps

   # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
   if self.config.timestep_spacing == "linspace":
     __A							:   Any	  =				np.linspace(0							,			num_train_timesteps - 1							,			_UpperCamelCase							,			dtype=_UpperCamelCase   )[::-1].copy()
   elif self.config.timestep_spacing == "leading":
     __A							:   Optional[int]	  =				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
     __A							:   Union[str, Any]	  =				(np.arange(0							,			_UpperCamelCase   ) * step_ratio).round()[::-1].copy().astype(_UpperCamelCase   )
     timesteps += self.config.steps_offset
   elif self.config.timestep_spacing == "trailing":
     __A							:   Optional[Any]	  =				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
     __A							:   str	  =				(np.arange(_UpperCamelCase							,			0							,			-step_ratio   )).round().copy().astype(_UpperCamelCase   )
     timesteps -= 1
   else:
     raise ValueError(
         F"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', 'leading' or 'trailing'."   )

   __A							:   int	  =				np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5   )
   __A							:   List[str]	  =				torch.from_numpy(np.log(_UpperCamelCase   )   ).to(_UpperCamelCase   )

   __A							:   str	  =				np.interp(_UpperCamelCase							,			np.arange(0							,			len(_UpperCamelCase   )   )							,			_UpperCamelCase   )
   __A							:   Tuple	  =				np.concatenate([sigmas, [0.0]]   ).astype(np.floataa   )
   __A							:   Union[str, Any]	  =				torch.from_numpy(_UpperCamelCase   ).to(device=_UpperCamelCase   )

   # compute up and down sigmas
   __A							:   Union[str, Any]	  =				sigmas.roll(-1   )
   __A							:   Optional[Any]	  =				0.0
   __A							:   int	  =				(sigmas_next**2 * (sigmas**2 - sigmas_next**2) / sigmas**2) ** 0.5
   __A							:   Any	  =				(sigmas_next**2 - sigmas_up**2) ** 0.5
   __A							:   str	  =				0.0

   # compute interpolated sigmas
   __A							:   Dict	  =				sigmas.log().lerp(sigmas_down.log()							,			0.5   ).exp()
   __A							:   str	  =				0.0

   # set sigmas
   __A							:   Union[str, Any]	  =				torch.cat([sigmas[:1], sigmas[1:].repeat_interleave(2   ), sigmas[-1:]]   )
   __A							:   Optional[Any]	  =				torch.cat(
       [sigmas_interpol[:1], sigmas_interpol[1:].repeat_interleave(2   ), sigmas_interpol[-1:]]   )
   __A							:   Any	  =				torch.cat([sigmas_up[:1], sigmas_up[1:].repeat_interleave(2   ), sigmas_up[-1:]]   )
   __A							:   List[Any]	  =				torch.cat([sigmas_down[:1], sigmas_down[1:].repeat_interleave(2   ), sigmas_down[-1:]]   )

   if str(_UpperCamelCase   ).startswith("mps"   ):
     # mps does not support float64
     __A							:   str	  =				torch.from_numpy(_UpperCamelCase   ).to(_UpperCamelCase							,			dtype=torch.floataa   )
   else:
     __A							:   List[Any]	  =				torch.from_numpy(_UpperCamelCase   ).to(_UpperCamelCase   )

   __A							:   Any	  =				self.sigma_to_t(_UpperCamelCase   ).to(_UpperCamelCase							,			dtype=timesteps.dtype   )
   __A							:   int	  =				torch.stack((timesteps_interpol[:-2, None], timesteps[1:, None])							,			dim=-1   ).flatten()

   __A							:   Union[str, Any]	  =				torch.cat([timesteps[:1], interleaved_timesteps]   )

   __A							:   str	  =				None

   # for exp beta schedules, such as the one for `pipeline_shap_e.py`
   # we need an index counter
   __A							:   List[str]	  =				defaultdict(_UpperCamelCase   )

 def 					__UpperCAmelCase(       self							,			__UpperCAmelCase   ):
   __A							:   Tuple	  =				sigma.log()

   # get distribution
   __A							:   Any	  =				log_sigma - self.log_sigmas[:, None]

   # get sigmas range
   __A							:   int	  =				dists.ge(0   ).cumsum(dim=0   ).argmax(dim=0   ).clamp(max=self.log_sigmas.shape[0] - 2   )
   __A							:   List[str]	  =				low_idx + 1

   __A							:   Optional[Any]	  =				self.log_sigmas[low_idx]
   __A							:   int	  =				self.log_sigmas[high_idx]

   # interpolate sigmas
   __A							:   List[Any]	  =				(low - log_sigma) / (low - high)
   __A							:   Dict	  =				w.clamp(0							,			1   )

   # transform interpolation to time range
   __A							:   Dict	  =				(1 - w) * low_idx + w * high_idx
   __A							:   List[Any]	  =				t.view(sigma.shape   )
   return t

 @property
 def 					__UpperCAmelCase(       self   ):
   return self.sample is None

 def 					__UpperCAmelCase(       self							,			__UpperCAmelCase							,			__UpperCAmelCase							,			__UpperCAmelCase							,			__UpperCAmelCase = None							,			__UpperCAmelCase = True							,			):
   __A							:   Optional[Any]	  =				self.index_for_timestep(_UpperCamelCase   )

   # advance index counter by 1
   __A							:   int	  =				timestep.cpu().item() if torch.is_tensor(_UpperCamelCase   ) else timestep
   self._index_counter[timestep_int] += 1

   if self.state_in_first_order:
     __A							:   Union[str, Any]	  =				self.sigmas[step_index]
     __A							:   Union[str, Any]	  =				self.sigmas_interpol[step_index]
     __A							:   Optional[int]	  =				self.sigmas_up[step_index]
     __A							:   Any	  =				self.sigmas_down[step_index - 1]
   else:
     # 2nd order / KPDM2's method
     __A							:   List[str]	  =				self.sigmas[step_index - 1]
     __A							:   List[Any]	  =				self.sigmas_interpol[step_index - 1]
     __A							:   Optional[int]	  =				self.sigmas_up[step_index - 1]
     __A							:   List[str]	  =				self.sigmas_down[step_index - 1]

   # currently only gamma=0 is supported. This usually works best anyways.
   # We can support gamma in the future but then need to scale the timestep before
   # passing it to the model which requires a change in API
   __A							:   List[Any]	  =				0
   __A							:   Dict	  =				sigma * (gamma + 1)  # Note: sigma_hat == sigma for now

   __A							:   List[str]	  =				model_output.device
   __A							:   int	  =				randn_tensor(model_output.shape							,			dtype=model_output.dtype							,			device=_UpperCamelCase							,			generator=_UpperCamelCase   )

   # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
   if self.config.prediction_type == "epsilon":
     __A							:   Optional[Any]	  =				sigma_hat if self.state_in_first_order else sigma_interpol
     __A							:   Optional[int]	  =				sample - sigma_input * model_output
   elif self.config.prediction_type == "v_prediction":
     __A							:   str	  =				sigma_hat if self.state_in_first_order else sigma_interpol
     __A							:   Optional[int]	  =				model_output * (-sigma_input / (sigma_input**2 + 1) ** 0.5) + (
         sample / (sigma_input**2 + 1)
     )
   elif self.config.prediction_type == "sample":
     raise NotImplementedError("prediction_type not implemented yet: sample"   )
   else:
     raise ValueError(
         F"prediction_type given as {self.config.prediction_type} must be one of `epsilon`, or `v_prediction`"   )

   if self.state_in_first_order:
     # 2. Convert to an ODE derivative for 1st order
     __A							:   int	  =				(sample - pred_original_sample) / sigma_hat
     # 3. delta timestep
     __A							:   Dict	  =				sigma_interpol - sigma_hat

     # store for 2nd order step
     __A							:   int	  =				sample
     __A							:   Optional[int]	  =				dt
     __A							:   List[Any]	  =				sample + derivative * dt
   else:
     # DPM-Solver-2
     # 2. Convert to an ODE derivative for 2nd order
     __A							:   List[str]	  =				(sample - pred_original_sample) / sigma_interpol
     # 3. delta timestep
     __A							:   str	  =				sigma_down - sigma_hat

     __A							:   List[str]	  =				self.sample
     __A							:   Union[str, Any]	  =				None

     __A							:   List[Any]	  =				sample + derivative * dt
     __A							:   str	  =				prev_sample + noise * sigma_up

   if not return_dict:
     return (prev_sample,)

   return SchedulerOutput(prev_sample=_UpperCamelCase   )

 def 					__UpperCAmelCase(       self							,			__UpperCAmelCase							,			__UpperCAmelCase							,			__UpperCAmelCase							,			):
   __A							:   List[str]	  =				self.sigmas.to(device=original_samples.device							,			dtype=original_samples.dtype   )
   if original_samples.device.type == "mps" and torch.is_floating_point(_UpperCamelCase   ):
     # mps does not support float64
     __A							:   Optional[Any]	  =				self.timesteps.to(original_samples.device							,			dtype=torch.floataa   )
     __A							:   Optional[int]	  =				timesteps.to(original_samples.device							,			dtype=torch.floataa   )
   else:
     __A							:   str	  =				self.timesteps.to(original_samples.device   )
     __A							:   List[Any]	  =				timesteps.to(original_samples.device   )

   __A							:   List[str]	  =				[self.index_for_timestep(_UpperCamelCase							,			_UpperCamelCase   ) for t in timesteps]

   __A							:   Union[str, Any]	  =				sigmas[step_indices].flatten()
   while len(sigma.shape   ) < len(original_samples.shape   ):
     __A							:   int	  =				sigma.unsqueeze(-1   )

   __A							:   Tuple	  =				original_samples + noise * sigma
   return noisy_samples







 def __len__(       self   ):
   return self.config.num_train_timesteps






import os



def    lowerCamelCase_   (  )							->	List[str]:
		__A							:   Any	  =				0
		__A							:   Any	  =				0
		with open(os.path.dirname(_lowercase    ) + "/p022_names.txt"    ) as file:
				__A							:   int	  =				str(file.readlines()[0]    )
				__A							:   Optional[Any]	  =				name.replace("\"" ,     ""    ).split(","    )

		name.sort()
		for i in range(len(_lowercase    )    ):
				for j in name[i]:
						temp_sum += ord(_lowercase    ) - ord("A"    ) + 1
				total_sum += (i + 1) * temp_sum
				__A							:   List[Any]	  =				0
		return total_sum


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





