



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

import numpy as np
import torch

from ..configuration_utils import ConfigMixin, register_to_config
from .scheduling_utils import SchedulerMixin, SchedulerOutput







class     __lowerCAmelCase					(    A       ,		A		):
			UpperCamelCase           =  1



			@register_to_config
			def __init__(		self     :						Optional[int]				,	A     :						int = 10_00				,	A     :						Optional[Union[np.ndarray, List[float]]] = None)     ->					Optional[int]:



						"""simple docstring"""






						self.set_timesteps(A)

						# standard deviation of the initial noise distribution
						_UpperCAmelCase	 =     1.0

						# For now we only support F-PNDM, i.e. the runge-kutta method
						# For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
						# mainly at formula (9), (12), (13) and the Algorithm 2.
						_UpperCAmelCase	 =     4

						# running values
						_UpperCAmelCase	 =     []



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



						"""simple docstring"""






						_UpperCAmelCase	 =     num_inference_steps
						_UpperCAmelCase	 =     torch.linspace(1				,	0				,	num_inference_steps + 1)[:-1]
						_UpperCAmelCase	 =     torch.cat([steps, torch.tensor([0.0])])

						if self.config.trained_betas is not None:
									_UpperCAmelCase	 =     torch.tensor(self.config.trained_betas				,	dtype=torch.floataa)
						else:
									_UpperCAmelCase	 =     torch.sin(steps * math.pi / 2) ** 2

						_UpperCAmelCase	 =     (1.0 - self.betas**2) ** 0.5

						_UpperCAmelCase	 =     (torch.atana(self.betas				,	self.alphas) / math.pi * 2)[:-1]
						_UpperCAmelCase	 =     timesteps.to(A)

						_UpperCAmelCase	 =     []



			def 					_lowerCamelCase (		self     :						Dict				,	A     :						torch.FloatTensor				,	A     :						int				,	A     :						torch.FloatTensor				,	A     :						bool = True				,	)     ->					Union[SchedulerOutput, Tuple]:



						"""simple docstring"""






						if self.num_inference_steps is None:
									raise ValueError(
									    'Number of inference steps is \'None\', you need to run \'set_timesteps\' after creating the scheduler')

						_UpperCAmelCase	 =     (self.timesteps == timestep).nonzero().item()
						_UpperCAmelCase	 =     timestep_index + 1

						_UpperCAmelCase	 =     sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
						self.ets.append(A)

						if len(self.ets) == 1:
									_UpperCAmelCase	 =     self.ets[-1]
						elif len(self.ets) == 2:
									_UpperCAmelCase	 =     (3 * self.ets[-1] - self.ets[-2]) / 2
						elif len(self.ets) == 3:
									_UpperCAmelCase	 =     (23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
						else:
									_UpperCAmelCase	 =     (1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

						_UpperCAmelCase	 =     self._get_prev_sample(A				,	A				,	A				,	A)

						if not return_dict:
									return (prev_sample,)

						return SchedulerOutput(prev_sample=A)



			def 					_lowerCamelCase (		self     :						Union[str, Any]				,	A     :						torch.FloatTensor				,	*A     :						Union[str, Any]				,	**A     :						Any)     ->					torch.FloatTensor:



						"""simple docstring"""






						return sample



			def 					_lowerCamelCase (		self     :						List[str]				,	A     :						Dict				,	A     :						int				,	A     :						List[str]				,	A     :						Optional[int])     ->					int:



						"""simple docstring"""






						_UpperCAmelCase	 =     self.alphas[timestep_index]
						_UpperCAmelCase	 =     self.betas[timestep_index]

						_UpperCAmelCase	 =     self.alphas[prev_timestep_index]
						_UpperCAmelCase	 =     self.betas[prev_timestep_index]

						_UpperCAmelCase	 =     (sample - sigma * ets) / max(A				,	1E-8)
						_UpperCAmelCase	 =     next_alpha * pred + ets * next_sigma

						return prev_sample



			def __len__(		self     :						Tuple)     ->					List[Any]:



						"""simple docstring"""






						return self.config.num_train_timesteps





import os

# Precomputes a list of the 100 first triangular numbers
UpperCAmelCase__     = [int(0.5 * n * (n + 1)) for n in range(1, 101)]





def 							A			(  )       ->				List[str]:







			'''simple docstring'''
			_UpperCAmelCase	 =     os.path.dirname(os.path.realpath(_UpperCAmelCase					)					)
			_UpperCAmelCase	 =     os.path.join(_UpperCAmelCase							,     'words.txt'					)

			_UpperCAmelCase	 =     ''
			with open(_UpperCAmelCase					) as f:
						_UpperCAmelCase	 =     f.readline()

			_UpperCAmelCase	 =     [word.strip('"'					) for word in words.strip('\r\n'					).split(','					)]
			_UpperCAmelCase	 =     [
			    word
			    for word in [sum(ord(_UpperCAmelCase					) - 64 for x in word					) for word in words]
			    if word in TRIANGULAR_NUMBERS
			]
			return len(_UpperCAmelCase					)


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