



"""simple docstring"""
def 			_SCREAMING_SNAKE_CASE						(__lowerCAmelCase							) ->						int:







  '''simple docstring'''


  lowercase_								= 0
  while num > 0:
    digit_sum += num % 10
    num //= 10
  return digit_sum


def 			_SCREAMING_SNAKE_CASE						(__lowerCAmelCase = 1_00							) ->						int:







  '''simple docstring'''


  lowercase_								= 1
  lowercase_								= 2

  for i in range(2 ,  max_n + 1							):
    lowercase_								= pre_numerator
    lowercase_								= 2 * i // 3 if i % 3 == 0 else 1
    lowercase_								= cur_numerator
    lowercase_								= e_cont * pre_numerator + temp

  return sum_digits(__lowerCAmelCase							)


if __name__ == "__main__":
       print(F"{solution() = }")






"""simple docstring"""
from typing import Optional

import numpy as np
import torch
from torch import nn
from transformers import GPTaConfig, GPTaLMHeadModel
from transformers.modeling_utils import ModuleUtilsMixin

from ...configuration_utils import ConfigMixin, register_to_config
from ...models import ModelMixin


class    SCREAMING_SNAKE_CASE__ (							__UpperCAmelCase      ,  __UpperCAmelCase      ,  __UpperCAmelCase   ):
    lowercase__      =   [r"h\.\d+\.attn\.bias", r"h\.\d+\.attn\.masked_bias"]

    @register_to_config
    def __init__(				self			:				int ,  lowerCAmelCase_			:				int ,  lowerCAmelCase_			:				int ,  lowerCAmelCase_			:				Optional[int] = None ,  lowerCAmelCase_			:				int = 5_0_2_5_7 ,  lowerCAmelCase_			:				int = 1_0_2_4 ,  lowerCAmelCase_			:				int = 7_6_8 ,  lowerCAmelCase_			:				int = 1_2 ,  lowerCAmelCase_			:				int = 1_2 ,  lowerCAmelCase_			:				Optional[int] = None ,  lowerCAmelCase_			:				str = "gelu_new" ,  lowerCAmelCase_			:				float = 0.1 ,  lowerCAmelCase_			:				float = 0.1 ,  lowerCAmelCase_			:				float = 0.1 ,  lowerCAmelCase_			:				float = 1E-5 ,  lowerCAmelCase_			:				float = 0.02 ,  lowerCAmelCase_			:				bool = True ,  lowerCAmelCase_			:				bool = True ,  lowerCAmelCase_			:				bool = False ,  lowerCAmelCase_			:				bool = False ,  ):







      """simple docstring"""







      super().__init__()

      lowercase_								= prefix_length

      if prefix_inner_dim != n_embd and prefix_hidden_dim is None:
        raise ValueError(
            F'''`prefix_hidden_dim` cannot be `None` when `prefix_inner_dim`: {prefix_hidden_dim} and'''
            F''' `n_embd`: {n_embd} are not equal.''')

      lowercase_								= prefix_inner_dim
      lowercase_								= prefix_hidden_dim

      lowercase_								= (
          nn.Linear(self.prefix_inner_dim ,  self.prefix_hidden_dim)
          if self.prefix_hidden_dim is not None
          else nn.Identity()
      )
      lowercase_								= (
          nn.Linear(self.prefix_hidden_dim ,  lowerCAmelCase_) if self.prefix_hidden_dim is not None else nn.Identity()
      )

      lowercase_								= GPTaConfig(
          vocab_size=lowerCAmelCase_ ,  n_positions=lowerCAmelCase_ ,  n_embd=lowerCAmelCase_ ,  n_layer=lowerCAmelCase_ ,  n_head=lowerCAmelCase_ ,  n_inner=lowerCAmelCase_ ,  activation_function=lowerCAmelCase_ ,  resid_pdrop=lowerCAmelCase_ ,  embd_pdrop=lowerCAmelCase_ ,  attn_pdrop=lowerCAmelCase_ ,  layer_norm_epsilon=lowerCAmelCase_ ,  initializer_range=lowerCAmelCase_ ,  scale_attn_weights=lowerCAmelCase_ ,  use_cache=lowerCAmelCase_ ,  scale_attn_by_inverse_layer_idx=lowerCAmelCase_ ,  reorder_and_upcast_attn=lowerCAmelCase_ ,  )
      lowercase_								= GPTaLMHeadModel(lowerCAmelCase_)

    def 					_UpperCAmelCase	(				self			:				int ,  lowerCAmelCase_			:				torch.Tensor ,  lowerCAmelCase_			:				torch.Tensor ,  lowerCAmelCase_			:				Optional[torch.Tensor] = None ,  lowerCAmelCase_			:				Optional[torch.Tensor] = None ,  ):







      """simple docstring"""







      lowercase_								= self.transformer.transformer.wte(lowerCAmelCase_)
      lowercase_								= self.encode_prefix(lowerCAmelCase_)
      lowercase_								= self.decode_prefix(lowerCAmelCase_)
      lowercase_								= torch.cat((prefix_embeds, embedding_text) ,  dim=1)

      if labels is not None:
        lowercase_								= self.get_dummy_token(input_ids.shape[0] ,  input_ids.device)
        lowercase_								= torch.cat((dummy_token, input_ids) ,  dim=1)
      lowercase_								= self.transformer(inputs_embeds=lowerCAmelCase_ ,  labels=lowerCAmelCase_ ,  attention_mask=lowerCAmelCase_)
      if self.prefix_hidden_dim is not None:
        return out, hidden
      else:
        return out

    def 					_UpperCAmelCase	(				self			:				Optional[int] ,  lowerCAmelCase_			:				int ,  lowerCAmelCase_			:				torch.device):







      """simple docstring"""







      return torch.zeros(lowerCAmelCase_ ,  self.prefix_length ,  dtype=torch.intaa ,  device=lowerCAmelCase_)

    def 					_UpperCAmelCase	(				self			:				List[str] ,  lowerCAmelCase_			:				List[Any]):







      """simple docstring"""







      return self.encode_prefix(lowerCAmelCase_)

    @torch.no_grad()
    def 					_UpperCAmelCase	(				self			:				Tuple ,  lowerCAmelCase_			:				str ,  lowerCAmelCase_			:				Dict ,  lowerCAmelCase_			:				Union[str, Any]):







      """simple docstring"""







      lowercase_								= torch.split(lowerCAmelCase_ ,  1 ,  dim=0)
      lowercase_								= []
      lowercase_								= []
      for feature in features:
        lowercase_								= self.decode_prefix(feature.to(lowerCAmelCase_))  # back to the clip feature
        # Only support beam search for now
        lowercase_					,    lowercase_								= self.generate_beam(
            input_embeds=lowerCAmelCase_ ,  device=lowerCAmelCase_ ,  eos_token_id=lowerCAmelCase_)
        generated_tokens.append(output_tokens[0])
        generated_seq_lengths.append(seq_lengths[0])
      lowercase_								= torch.stack(lowerCAmelCase_)
      lowercase_								= torch.stack(lowerCAmelCase_)
      return generated_tokens, generated_seq_lengths




    @torch.no_grad()
    def 					_UpperCAmelCase	(				self			:				int ,  lowerCAmelCase_			:				List[str]=None ,  lowerCAmelCase_			:				Tuple=None ,  lowerCAmelCase_			:				str=None ,  lowerCAmelCase_			:				int = 5 ,  lowerCAmelCase_			:				int = 6_7 ,  lowerCAmelCase_			:				float = 1.0 ,  lowerCAmelCase_			:				Optional[int] = None ,  ):







      """simple docstring"""







      lowercase_								= eos_token_id
      lowercase_								= None
      lowercase_								= None
      lowercase_								= torch.ones(lowerCAmelCase_ ,  device=lowerCAmelCase_ ,  dtype=torch.int)
      lowercase_								= torch.zeros(lowerCAmelCase_ ,  device=lowerCAmelCase_ ,  dtype=torch.bool)

      if input_embeds is not None:
        lowercase_								= input_embeds
      else:
        lowercase_								= self.transformer.transformer.wte(lowerCAmelCase_)

      for i in range(lowerCAmelCase_):
        lowercase_								= self.transformer(inputs_embeds=lowerCAmelCase_)
        lowercase_								= outputs.logits
        lowercase_								= logits[:, -1, :] / (temperature if temperature > 0 else 1.0)
        lowercase_								= logits.softmax(-1).log()

        if scores is None:
          lowercase_					,    lowercase_								= logits.topk(lowerCAmelCase_ ,  -1)
          lowercase_								= generated.expand(lowerCAmelCase_ ,  *generated.shape[1:])
          lowercase_					,    lowercase_								= next_tokens.permute(1 ,  0), scores.squeeze(0)
          if tokens is None:
            lowercase_								= next_tokens
          else:
            lowercase_								= tokens.expand(lowerCAmelCase_ ,  *tokens.shape[1:])
            lowercase_								= torch.cat((tokens, next_tokens) ,  dim=1)
        else:
          lowercase_								= -float(np.inf)
          lowercase_								= 0
          lowercase_								= scores[:, None] + logits
          seq_lengths[~is_stopped] += 1
          lowercase_								= scores_sum / seq_lengths[:, None]
          lowercase_					,    lowercase_								= scores_sum_average.view(-1).topk(lowerCAmelCase_ ,  -1)
          lowercase_								= next_tokens // scores_sum.shape[1]
          lowercase_								= seq_lengths[next_tokens_source]
          lowercase_								= next_tokens % scores_sum.shape[1]
          lowercase_								= next_tokens.unsqueeze(1)
          lowercase_								= tokens[next_tokens_source]
          lowercase_								= torch.cat((tokens, next_tokens) ,  dim=1)
          lowercase_								= generated[next_tokens_source]
          lowercase_								= scores_sum_average * seq_lengths
          lowercase_								= is_stopped[next_tokens_source]

        lowercase_								= self.transformer.transformer.wte(next_tokens.squeeze()).view(generated.shape[0] ,  1 ,  -1)
        lowercase_								= torch.cat((generated, next_token_embed) ,  dim=1)
        lowercase_								= is_stopped + next_tokens.eq(lowerCAmelCase_).squeeze()
        if is_stopped.all():
          break

      lowercase_								= scores / seq_lengths
      lowercase_								= scores.argsort(descending=lowerCAmelCase_)
      # tokens tensors are already padded to max_seq_length
      lowercase_								= [tokens[i] for i in order]
      lowercase_								= torch.stack(lowerCAmelCase_ ,  dim=0)
      lowercase_								= torch.tensor([seq_lengths[i] for i in order] ,  dtype=seq_lengths.dtype)
      return output_texts, seq_lengths

