"""simple docstring"""





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  _snake_case     (					a__				, a__		):
						snake_case__			  =			1






						@register_to_config
						def __init__(       self      :			str							,					UpperCAmelCase      :			int = 1000							,					UpperCAmelCase      :			Optional[Union[np.ndarray, List[float]]] = None    ):
													# set `betas`, `alphas`, `timesteps`
													self.set_timesteps(UpperCAmelCase    )

													# standard deviation of the initial noise distribution
													__lowerCamelCase					:		Union[str, Any]		   =     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.
													__lowerCamelCase					:		Dict		   =     4

													# running values
													__lowerCamelCase					:		Optional[int]		   =     []






						def       lowerCamelCase__     (       self      :			Union[str, Any]							,					UpperCAmelCase      :			int							,					UpperCAmelCase      :			Union[str, torch.device] = None    ):
													__lowerCamelCase					:		Any		   =     num_inference_steps
													__lowerCamelCase					:		List[str]		   =     torch.linspace(1							,					0							,					num_inference_steps + 1    )[:-1]
													__lowerCamelCase					:		Tuple		   =     torch.cat([steps, torch.tensor([0.0]    )]    )

													if self.config.trained_betas is not None:
																				__lowerCamelCase					:		List[Any]		   =     torch.tensor(self.config.trained_betas							,					dtype=torch.floataa    )
													else:
																				__lowerCamelCase					:		str		   =     torch.sin(steps * math.pi / 2    ) ** 2

													__lowerCamelCase					:		Dict		   =     (1.0 - self.betas**2) ** 0.5

													__lowerCamelCase					:		Union[str, Any]		   =     (torch.atana(self.betas							,					self.alphas    ) / math.pi * 2)[:-1]
													__lowerCamelCase					:		Optional[Any]		   =     timesteps.to(UpperCAmelCase    )

													__lowerCamelCase					:		Union[str, Any]		   =     []






						def       lowerCamelCase__     (       self      :			Optional[Any]							,					UpperCAmelCase      :			torch.FloatTensor							,					UpperCAmelCase      :			int							,					UpperCAmelCase      :			torch.FloatTensor							,					UpperCAmelCase      :			bool = True							,					):
													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"    )

													__lowerCamelCase					:		Any		   =     (self.timesteps == timestep).nonzero().item()
													__lowerCamelCase					:		List[Any]		   =     timestep_index + 1

													__lowerCamelCase					:		Any		   =     sample * self.betas[timestep_index] + model_output * self.alphas[timestep_index]
													self.ets.append(UpperCAmelCase    )

													if len(self.ets    ) == 1:
																				__lowerCamelCase					:		List[Any]		   =     self.ets[-1]
													elif len(self.ets    ) == 2:
																				__lowerCamelCase					:		Optional[int]		   =     (3 * self.ets[-1] - self.ets[-2]) / 2
													elif len(self.ets    ) == 3:
																				__lowerCamelCase					:		Union[str, Any]		   =     (23 * self.ets[-1] - 16 * self.ets[-2] + 5 * self.ets[-3]) / 12
													else:
																				__lowerCamelCase					:		Tuple		   =     (1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])

													__lowerCamelCase					:		Any		   =     self._get_prev_sample(UpperCAmelCase							,					UpperCAmelCase							,					UpperCAmelCase							,					UpperCAmelCase    )

													if not return_dict:
																				return (prev_sample,)

													return SchedulerOutput(prev_sample=UpperCAmelCase    )






						def       lowerCamelCase__     (       self      :			Tuple							,					UpperCAmelCase      :			torch.FloatTensor							,					*UpperCAmelCase      :			str							,					**UpperCAmelCase      :			str    ):
													return sample






						def       lowerCamelCase__     (       self      :			Dict							,					UpperCAmelCase      :			int							,					UpperCAmelCase      :			Tuple							,					UpperCAmelCase      :			List[Any]							,					UpperCAmelCase      :			Dict    ):
													__lowerCamelCase					:		Optional[Any]		   =     self.alphas[timestep_index]
													__lowerCamelCase					:		int		   =     self.betas[timestep_index]

													__lowerCamelCase					:		str		   =     self.alphas[prev_timestep_index]
													__lowerCamelCase					:		Dict		   =     self.betas[prev_timestep_index]

													__lowerCamelCase					:		Dict		   =     (sample - sigma * ets) / max(UpperCAmelCase							,					1E-8    )
													__lowerCamelCase					:		List[str]		   =     next_alpha * pred + ets * next_sigma

													return prev_sample







						def __len__(       self      :			Optional[int]    ):
													return self.config.num_train_timesteps

"""simple docstring"""





import os


def    lowercase_   (   ) ->      List[str]:



							'''simple docstring'''

							__lowerCamelCase					:		Union[str, Any]		   =     os.path.dirname(os.path.realpath(_lowerCamelCase      )      )
							__lowerCamelCase					:		int		   =     os.path.join(_lowerCamelCase						,   "triangle.txt"      )

							with open(_lowerCamelCase      ) as f:
														__lowerCamelCase					:		List[str]		   =     f.readlines()

							__lowerCamelCase					:		List[str]		   =     []
							for line in triangle:
														__lowerCamelCase					:		Optional[int]		   =     []
														for number in line.strip().split(" "      ):
																					numbers_from_line.append(int(_lowerCamelCase      )      )
														a.append(_lowerCamelCase      )

							for i in range(1						,   len(_lowerCamelCase      )      ):
														for j in range(len(a[i]      )      ):
																					__lowerCamelCase					:		int		   =     a[i - 1][j] if j != len(a[i - 1]      ) else 0
																					__lowerCamelCase					:		Union[str, Any]		   =     a[i - 1][j - 1] if j > 0 else 0
																					a[i][j] += max(_lowerCamelCase						,   _lowerCamelCase      )
							return max(a[-1]      )


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