





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'''




			__lowerCamelCase     :	Optional[int]          =   [R'''h\.\d+\.attn\.bias''', R'''h\.\d+\.attn\.masked_bias''']






			@register_to_config
			def __init__(      self       :   Optional[int]							,     __lowerCAmelCase       :   int							,     __lowerCAmelCase       :   int							,     __lowerCAmelCase       :   Optional[int] = None							,     __lowerCAmelCase       :   int = 5_02_57							,     __lowerCAmelCase       :   int = 10_24							,     __lowerCAmelCase       :   int = 7_68							,     __lowerCAmelCase       :   int = 12							,     __lowerCAmelCase       :   int = 12							,     __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 = 0.0_2							,     __lowerCAmelCase       :   bool = True							,     __lowerCAmelCase       :   bool = True							,     __lowerCAmelCase       :   bool = False							,     __lowerCAmelCase       :   bool = False							,     )     ->     Dict:







					"""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							,     snake_case_       ) if self.prefix_hidden_dim is not None else nn.Identity()
					)

					A__  				=       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_							,     )
					A__  				=       GPTaLMHeadModel(snake_case_       )






			def        a_	(      self       :   Optional[int]							,     __lowerCAmelCase       :   torch.Tensor							,     __lowerCAmelCase       :   torch.Tensor							,     __lowerCAmelCase       :   Optional[torch.Tensor] = None							,     __lowerCAmelCase       :   Optional[torch.Tensor] = None							,     )     ->     List[Any]:







					"""simple docstring"""






					A__  				=       self.transformer.transformer.wte(snake_case_       )
					A__  				=       self.encode_prefix(snake_case_       )
					A__  				=       self.decode_prefix(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=snake_case_							,     labels=snake_case_							,     attention_mask=snake_case_       )
					if self.prefix_hidden_dim is not None:
							return out, hidden
					else:
							return out






			def        a_	(      self       :   Optional[Any]							,     __lowerCAmelCase       :   int							,     __lowerCAmelCase       :   torch.device       )     ->     int:







					"""simple docstring"""






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






			def        a_	(      self       :   Tuple							,     __lowerCAmelCase       :   Tuple       )     ->     int:







					"""simple docstring"""






					return self.encode_prefix(snake_case_       )






			@torch.no_grad()
			def        a_	(      self       :   List[str]							,     __lowerCAmelCase       :   Optional[int]							,     __lowerCAmelCase       :   Optional[Any]							,     __lowerCAmelCase       :   List[str]       )     ->     Optional[int]:







					"""simple docstring"""






					A__  				=       torch.split(snake_case_							,     1							,     dim=0       )
					A__  				=       []
					A__  				=       []
					for feature in features:
							A__  				=       self.decode_prefix(feature.to(snake_case_       )       )  # back to the clip feature
							# Only support beam search for now
							A__  				=       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]       )
					A__  				=       torch.stack(snake_case_       )
					A__  				=       torch.stack(snake_case_       )
					return generated_tokens, generated_seq_lengths







			@torch.no_grad()
			def        a_	(      self       :   Optional[int]							,     __lowerCAmelCase       :   Optional[Any]=None							,     __lowerCAmelCase       :   Optional[int]=None							,     __lowerCAmelCase       :   Union[str, Any]=None							,     __lowerCAmelCase       :   int = 5							,     __lowerCAmelCase       :   int = 67							,     __lowerCAmelCase       :   float = 1.0							,     __lowerCAmelCase       :   Optional[int] = None							,     )     ->     Dict:







					"""simple docstring"""






					A__  				=       eos_token_id
					A__  				=       None
					A__  				=       None
					A__  				=       torch.ones(snake_case_							,     device=snake_case_							,     dtype=torch.int       )
					A__  				=       torch.zeros(snake_case_							,     device=snake_case_							,     dtype=torch.bool       )

					if input_embeds is not None:
							A__  				=       input_embeds
					else:
							A__  				=       self.transformer.transformer.wte(snake_case_       )

					for i in range(snake_case_       ):
							A__  				=       self.transformer(inputs_embeds=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__  				=       logits.topk(snake_case_							,     -1       )
									A__  				=       generated.expand(snake_case_							,     *generated.shape[1:]       )
									A__  				=       next_tokens.permute(1							,     0       ), scores.squeeze(0       )
									if tokens is None:
											A__  				=       next_tokens
									else:
											A__  				=       tokens.expand(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__  				=       scores_sum_average.view(-1       ).topk(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(snake_case_       ).squeeze()
							if is_stopped.all():
									break

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






import math







def        __lowerCamelCase (							__a       :int   )		->    bool:






		"""simple docstring"""

		A__  				=       math.loga(math.sqrt(4 * positive_integer + 1   ) / 2 + 1 / 2   )

		return exponent == int(__a   )







def        __lowerCamelCase (							__a       :float = 1 / 1_2_3_4_5   )		->    int:






		"""simple docstring"""

		A__  				=       0
		A__  				=       0

		A__  				=       3
		while True:
				A__  				=       (integer**2 - 1) / 4
				# if candidate is an integer, then there is a partition for k
				if partition_candidate == int(__a   ):
						A__  				=       int(__a   )
						total_partitions += 1
						if check_partition_perfect(__a   ):
								perfect_partitions += 1
				if perfect_partitions > 0:
						if perfect_partitions / total_partitions < max_proportion:
								return int(__a   )
				integer += 1


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



