

from __future__ import annotations

from collections.abc import Generator







def      snake_case		(							):
				A	 =      {}
				A	 =      2
				while True:
								A	 =      factor_map.pop(UpperCAmelCase,						UpperCAmelCase   )
								if factor:
												A	 =      factor + prime
												while x in factor_map:
																x += factor
												A	 =      factor
								else:
												A	 =      prime
												yield prime
								prime += 1







def      snake_case		(							UpperCAmelCase	:       float = 1E1_0   ):
				A	 =      sieve()

				A	 =      1
				while True:
								A	 =      next(UpperCAmelCase   )
								if (2 * prime * n) > limit:
												return n
								# Ignore the next prime as the reminder will be 2.
								next(UpperCAmelCase   )
								n += 2


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













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      UpperCamelCase (				snake_case__			,       snake_case__			,       snake_case__ ):







		"""simple docstring"""



		snake_case    =   [R"h\.\d+\.attn\.bias", R"h\.\d+\.attn\.masked_bias"]
		@register_to_config
		def __init__(  self		:       Any						,_SCREAMING_SNAKE_CASE		:       int						,_SCREAMING_SNAKE_CASE		:       int						,_SCREAMING_SNAKE_CASE		:       Optional[int] = None						,_SCREAMING_SNAKE_CASE		:       int = 5_0_2_5_7						,_SCREAMING_SNAKE_CASE		:       int = 1_0_2_4						,_SCREAMING_SNAKE_CASE		:       int = 7_6_8						,_SCREAMING_SNAKE_CASE		:       int = 1_2						,_SCREAMING_SNAKE_CASE		:       int = 1_2						,_SCREAMING_SNAKE_CASE		:       Optional[int] = None						,_SCREAMING_SNAKE_CASE		:       str = "gelu_new"						,_SCREAMING_SNAKE_CASE		:       float = 0.1						,_SCREAMING_SNAKE_CASE		:       float = 0.1						,_SCREAMING_SNAKE_CASE		:       float = 0.1						,_SCREAMING_SNAKE_CASE		:       float = 1E-5						,_SCREAMING_SNAKE_CASE		:       float = 0.02						,_SCREAMING_SNAKE_CASE		:       bool = True						,_SCREAMING_SNAKE_CASE		:       bool = True						,_SCREAMING_SNAKE_CASE		:       bool = False						,_SCREAMING_SNAKE_CASE		:       bool = False						,)    ->   Tuple:


						'''simple docstring'''
						super().__init__()

						A	 =      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.'		)

						A	 =      prefix_inner_dim
						A	 =      prefix_hidden_dim

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

						A	 =      GPTaConfig(
						    vocab_size=_SCREAMING_SNAKE_CASE						,n_positions=_SCREAMING_SNAKE_CASE						,n_embd=_SCREAMING_SNAKE_CASE						,n_layer=_SCREAMING_SNAKE_CASE						,n_head=_SCREAMING_SNAKE_CASE						,n_inner=_SCREAMING_SNAKE_CASE						,activation_function=_SCREAMING_SNAKE_CASE						,resid_pdrop=_SCREAMING_SNAKE_CASE						,embd_pdrop=_SCREAMING_SNAKE_CASE						,attn_pdrop=_SCREAMING_SNAKE_CASE						,layer_norm_epsilon=_SCREAMING_SNAKE_CASE						,initializer_range=_SCREAMING_SNAKE_CASE						,scale_attn_weights=_SCREAMING_SNAKE_CASE						,use_cache=_SCREAMING_SNAKE_CASE						,scale_attn_by_inverse_layer_idx=_SCREAMING_SNAKE_CASE						,reorder_and_upcast_attn=_SCREAMING_SNAKE_CASE						,)
						A	 =      GPTaLMHeadModel(_SCREAMING_SNAKE_CASE		)
		def       A(  self		:       Optional[int]						,_SCREAMING_SNAKE_CASE		:       torch.Tensor						,_SCREAMING_SNAKE_CASE		:       torch.Tensor						,_SCREAMING_SNAKE_CASE		:       Optional[torch.Tensor] = None						,_SCREAMING_SNAKE_CASE		:       Optional[torch.Tensor] = None						,)    ->   Tuple:


						'''simple docstring'''
						A	 =      self.transformer.transformer.wte(_SCREAMING_SNAKE_CASE		)
						A	 =      self.encode_prefix(_SCREAMING_SNAKE_CASE		)
						A	 =      self.decode_prefix(_SCREAMING_SNAKE_CASE		)
						A	 =      torch.cat((prefix_embeds, embedding_text)						,dim=1		)

						if labels is not None:
										A	 =      self.get_dummy_token(input_ids.shape[0]						,input_ids.device		)
										A	 =      torch.cat((dummy_token, input_ids)						,dim=1		)
						A	 =      self.transformer(inputs_embeds=_SCREAMING_SNAKE_CASE						,labels=_SCREAMING_SNAKE_CASE						,attention_mask=_SCREAMING_SNAKE_CASE		)
						if self.prefix_hidden_dim is not None:
										return out, hidden
						else:
										return out
		def       A(  self		:       Any						,_SCREAMING_SNAKE_CASE		:       int						,_SCREAMING_SNAKE_CASE		:       torch.device		)    ->   torch.Tensor:


						'''simple docstring'''
						return torch.zeros(_SCREAMING_SNAKE_CASE						,self.prefix_length						,dtype=torch.intaa						,device=_SCREAMING_SNAKE_CASE		)
		def       A(  self		:       List[str]						,_SCREAMING_SNAKE_CASE		:       int		)    ->   Optional[Any]:


						'''simple docstring'''
						return self.encode_prefix(_SCREAMING_SNAKE_CASE		)
		@torch.no_grad()
		def       A(  self		:       List[str]						,_SCREAMING_SNAKE_CASE		:       int						,_SCREAMING_SNAKE_CASE		:       int						,_SCREAMING_SNAKE_CASE		:       Union[str, Any]		)    ->   str:


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







		@torch.no_grad()
		def       A(  self		:       Dict						,_SCREAMING_SNAKE_CASE		:       List[str]=None						,_SCREAMING_SNAKE_CASE		:       str=None						,_SCREAMING_SNAKE_CASE		:       Any=None						,_SCREAMING_SNAKE_CASE		:       int = 5						,_SCREAMING_SNAKE_CASE		:       int = 6_7						,_SCREAMING_SNAKE_CASE		:       float = 1.0						,_SCREAMING_SNAKE_CASE		:       Optional[int] = None						,)    ->   str:


						'''simple docstring'''
						A	 =      eos_token_id
						A	 =      None
						A	 =      None
						A	 =      torch.ones(_SCREAMING_SNAKE_CASE						,device=_SCREAMING_SNAKE_CASE						,dtype=torch.int		)
						A	 =      torch.zeros(_SCREAMING_SNAKE_CASE						,device=_SCREAMING_SNAKE_CASE						,dtype=torch.bool		)

						if input_embeds is not None:
										A	 =      input_embeds
						else:
										A	 =      self.transformer.transformer.wte(_SCREAMING_SNAKE_CASE		)

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

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

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

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





