


'''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      a    (		_a     ,  _a     ,  _a	):


     """simple docstring"""






     SCREAMING_SNAKE_CASE	:			Optional[int]							       =       [r"h\.\d+\.attn\.bias", r"h\.\d+\.attn\.masked_bias"]

     @register_to_config
     def __init__(    self					:		Any							,			snake_case					:		int							,			snake_case					:		int							,			snake_case					:		Optional[int] = None							,			snake_case					:		int = 5_0257							,			snake_case					:		int = 1024							,			snake_case					:		int = 768							,			snake_case					:		int = 12							,			snake_case					:		int = 12							,			snake_case					:		Optional[int] = None							,			snake_case					:		str = "gelu_new"							,			snake_case					:		float = 0.1							,			snake_case					:		float = 0.1							,			snake_case					:		float = 0.1							,			snake_case					:		float = 1E-5							,			snake_case					:		float = 0.02							,			snake_case					:		bool = True							,			snake_case					:		bool = True							,			snake_case					:		bool = False							,			snake_case					:		bool = False							,			)						->							List[str]:
          super().__init__()

          __UpperCAmelCase     :			Any  							=      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.'      )

          __UpperCAmelCase     :			Any  							=      prefix_inner_dim
          __UpperCAmelCase     :			Optional[Any]  							=      prefix_hidden_dim

          __UpperCAmelCase     :			int  							=      (
              nn.Linear(self.prefix_inner_dim							,			self.prefix_hidden_dim      )
              if self.prefix_hidden_dim is not None
              else nn.Identity()
          )
          __UpperCAmelCase     :			Dict  							=      (
              nn.Linear(self.prefix_hidden_dim							,			snake_case      ) if self.prefix_hidden_dim is not None else nn.Identity()
          )

          __UpperCAmelCase     :			List[str]  							=      GPTaConfig(
              vocab_size=snake_case							,			n_positions=snake_case							,			n_embd=snake_case							,			n_layer=snake_case							,			n_head=snake_case							,			n_inner=snake_case							,			activation_function=snake_case							,			resid_pdrop=snake_case							,			embd_pdrop=snake_case							,			attn_pdrop=snake_case							,			layer_norm_epsilon=snake_case							,			initializer_range=snake_case							,			scale_attn_weights=snake_case							,			use_cache=snake_case							,			scale_attn_by_inverse_layer_idx=snake_case							,			reorder_and_upcast_attn=snake_case							,			)
          __UpperCAmelCase     :			Tuple  							=      GPTaLMHeadModel(snake_case      )

     def 			lowerCamelCase__			(    self					:		Optional[Any]							,			snake_case					:		torch.Tensor							,			snake_case					:		torch.Tensor							,			snake_case					:		Optional[torch.Tensor] = None							,			snake_case					:		Optional[torch.Tensor] = None							,			)						->							int:
          __UpperCAmelCase     :			Any  							=      self.transformer.transformer.wte(snake_case      )
          __UpperCAmelCase     :			Union[str, Any]  							=      self.encode_prefix(snake_case      )
          __UpperCAmelCase     :			Dict  							=      self.decode_prefix(snake_case      )
          __UpperCAmelCase     :			List[str]  							=      torch.cat((prefix_embeds, embedding_text)							,			dim=1      )

          if labels is not None:
               __UpperCAmelCase     :			List[str]  							=      self.get_dummy_token(input_ids.shape[0]							,			input_ids.device      )
               __UpperCAmelCase     :			Union[str, Any]  							=      torch.cat((dummy_token, input_ids)							,			dim=1      )
          __UpperCAmelCase     :			Optional[int]  							=      self.transformer(inputs_embeds=snake_case							,			labels=snake_case							,			attention_mask=snake_case      )
          if self.prefix_hidden_dim is not None:
               return out, hidden
          else:
               return out

     def 			lowerCamelCase__			(    self					:		Union[str, Any]							,			snake_case					:		int							,			snake_case					:		torch.device      )						->							torch.Tensor:
          return torch.zeros(snake_case							,			self.prefix_length							,			dtype=torch.intaa							,			device=snake_case      )

     def 			lowerCamelCase__			(    self					:		str							,			snake_case					:		Dict      )						->							List[Any]:
          return self.encode_prefix(snake_case      )

     @torch.no_grad()
     def 			lowerCamelCase__			(    self					:		Optional[Any]							,			snake_case					:		Union[str, Any]							,			snake_case					:		List[Any]							,			snake_case					:		Any      )						->							Any:
          __UpperCAmelCase     :			Dict  							=      torch.split(snake_case							,			1							,			dim=0      )
          __UpperCAmelCase     :			Optional[Any]  							=      []
          __UpperCAmelCase     :			Union[str, Any]  							=      []
          for feature in features:
               __UpperCAmelCase     :			List[str]  							=      self.decode_prefix(feature.to(snake_case      )      )  # back to the clip feature
               # Only support beam search for now
               __UpperCAmelCase							,       __UpperCAmelCase     :			List[str]  							=      self.generate_beam(
                   input_embeds=snake_case							,			device=snake_case							,			eos_token_id=snake_case      )
               generated_tokens.append(output_tokens[0]      )
               generated_seq_lengths.append(seq_lengths[0]      )
          __UpperCAmelCase     :			Dict  							=      torch.stack(snake_case      )
          __UpperCAmelCase     :			Dict  							=      torch.stack(snake_case      )
          return generated_tokens, generated_seq_lengths






     @torch.no_grad()
     def 			lowerCamelCase__			(    self					:		Optional[Any]							,			snake_case					:		Tuple=None							,			snake_case					:		Union[str, Any]=None							,			snake_case					:		List[Any]=None							,			snake_case					:		int = 5							,			snake_case					:		int = 67							,			snake_case					:		float = 1.0							,			snake_case					:		Optional[int] = None							,			)						->							Optional[Any]:
          __UpperCAmelCase     :			Dict  							=      eos_token_id
          __UpperCAmelCase     :			Optional[Any]  							=      None
          __UpperCAmelCase     :			Optional[int]  							=      None
          __UpperCAmelCase     :			str  							=      torch.ones(snake_case							,			device=snake_case							,			dtype=torch.int      )
          __UpperCAmelCase     :			Dict  							=      torch.zeros(snake_case							,			device=snake_case							,			dtype=torch.bool      )

          if input_embeds is not None:
               __UpperCAmelCase     :			str  							=      input_embeds
          else:
               __UpperCAmelCase     :			Any  							=      self.transformer.transformer.wte(snake_case      )

          for i in range(snake_case      ):
               __UpperCAmelCase     :			Union[str, Any]  							=      self.transformer(inputs_embeds=snake_case      )
               __UpperCAmelCase     :			List[Any]  							=      outputs.logits
               __UpperCAmelCase     :			Dict  							=      logits[:, -1, :] / (temperature if temperature > 0 else 1.0)
               __UpperCAmelCase     :			Optional[int]  							=      logits.softmax(-1      ).log()

               if scores is None:
                    __UpperCAmelCase							,       __UpperCAmelCase     :			Optional[int]  							=      logits.topk(snake_case							,			-1      )
                    __UpperCAmelCase     :			Dict  							=      generated.expand(snake_case							,			*generated.shape[1:]      )
                    __UpperCAmelCase							,       __UpperCAmelCase     :			Any  							=      next_tokens.permute(1							,			0      ), scores.squeeze(0      )
                    if tokens is None:
                         __UpperCAmelCase     :			str  							=      next_tokens
                    else:
                         __UpperCAmelCase     :			Union[str, Any]  							=      tokens.expand(snake_case							,			*tokens.shape[1:]      )
                         __UpperCAmelCase     :			int  							=      torch.cat((tokens, next_tokens)							,			dim=1      )
               else:
                    __UpperCAmelCase     :			int  							=      -float(np.inf      )
                    __UpperCAmelCase     :			List[Any]  							=      0
                    __UpperCAmelCase     :			Optional[int]  							=      scores[:, None] + logits
                    seq_lengths[~is_stopped] += 1
                    __UpperCAmelCase     :			int  							=      scores_sum / seq_lengths[:, None]
                    __UpperCAmelCase							,       __UpperCAmelCase     :			str  							=      scores_sum_average.view(-1      ).topk(snake_case							,			-1      )
                    __UpperCAmelCase     :			Dict  							=      next_tokens // scores_sum.shape[1]
                    __UpperCAmelCase     :			str  							=      seq_lengths[next_tokens_source]
                    __UpperCAmelCase     :			Dict  							=      next_tokens % scores_sum.shape[1]
                    __UpperCAmelCase     :			Union[str, Any]  							=      next_tokens.unsqueeze(1      )
                    __UpperCAmelCase     :			str  							=      tokens[next_tokens_source]
                    __UpperCAmelCase     :			Optional[int]  							=      torch.cat((tokens, next_tokens)							,			dim=1      )
                    __UpperCAmelCase     :			Union[str, Any]  							=      generated[next_tokens_source]
                    __UpperCAmelCase     :			List[Any]  							=      scores_sum_average * seq_lengths
                    __UpperCAmelCase     :			Tuple  							=      is_stopped[next_tokens_source]

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

          __UpperCAmelCase     :			Any  							=      scores / seq_lengths
          __UpperCAmelCase     :			str  							=      scores.argsort(descending=snake_case      )
          # tokens tensors are already padded to max_seq_length
          __UpperCAmelCase     :			Dict  							=      [tokens[i] for i in order]
          __UpperCAmelCase     :			Optional[int]  							=      torch.stack(snake_case							,			dim=0      )
          __UpperCAmelCase     :			Optional[Any]  							=      torch.tensor([seq_lengths[i] for i in order]							,			dtype=seq_lengths.dtype      )
          return output_texts, seq_lengths



'''simple docstring'''



def      _a     (						_lowercase :     List[str]  ):





     '''simple docstring'''






     __UpperCAmelCase     :			str  							=      1
     __UpperCAmelCase     :			List[str]  							=      2
     while i * i <= n:
          __UpperCAmelCase     :			Optional[Any]  							=      0
          while n % i == 0:
               n //= i
               multiplicity += 1
          n_divisors *= multiplicity + 1
          i += 1
     if n > 1:
          n_divisors *= 2
     return n_divisors




def      _a     (						):





     '''simple docstring'''






     __UpperCAmelCase     :			Optional[Any]  							=      1
     __UpperCAmelCase     :			List[Any]  							=      1

     while True:
          i += 1
          t_num += i

          if count_divisors(_lowercase  ) > 500:
               break

     return t_num


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