


'''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 							__UpperCamelCase				(		lowerCAmelCase_		,      lowerCAmelCase_		,      lowerCAmelCase_					):
	A_				=    [r"h\.\d+\.attn\.bias", r"h\.\d+\.attn\.masked_bias"]




	@register_to_config
	def __init__(   self						,				__a						,				__a						,				__a = None						,				__a = 5_0257						,				__a = 1024						,				__a = 768						,				__a = 12						,				__a = 12						,				__a = None						,				__a = "gelu_new"						,				__a = 0.1						,				__a = 0.1						,				__a = 0.1						,				__a = 1E-5						,				__a = 0.02						,				__a = True						,				__a = True						,				__a = False						,				__a = False						,				):

						'''simple docstring'''





						super().__init__()

						__a			:       List[str]					    =  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			:       Union[str, Any]					    =  prefix_inner_dim
						__a			:       Any					    =  prefix_hidden_dim

						__a			:       Any					    =  (
						    nn.Linear(self.prefix_inner_dim						,				self.prefix_hidden_dim							)
						    if self.prefix_hidden_dim is not None
						    else nn.Identity()
						)
						__a			:       Union[str, Any]					    =  (
						    nn.Linear(self.prefix_hidden_dim						,				__a							) if self.prefix_hidden_dim is not None else nn.Identity()
						)

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




	def       __UpperCAmelCase							(   self						,				__a						,				__a						,				__a = None						,				__a = None						,				):

						'''simple docstring'''





						__a			:       Union[str, Any]					    =  self.transformer.transformer.wte(__a							)
						__a			:       Dict					    =  self.encode_prefix(__a							)
						__a			:       str					    =  self.decode_prefix(__a							)
						__a			:       Optional[Any]					    =  torch.cat((prefix_embeds, embedding_text)						,				dim=1							)

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




	def       __UpperCAmelCase							(   self						,				__a						,				__a							):

						'''simple docstring'''





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




	def       __UpperCAmelCase							(   self						,				__a							):

						'''simple docstring'''





						return self.encode_prefix(__a							)




	@torch.no_grad()
	def       __UpperCAmelCase							(   self						,				__a						,				__a						,				__a							):

						'''simple docstring'''





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





	@torch.no_grad()
	def       __UpperCAmelCase							(   self						,				__a=None						,				__a=None						,				__a=None						,				__a = 5						,				__a = 67						,				__a = 1.0						,				__a = None						,				):

						'''simple docstring'''





						__a			:       Any					    =  eos_token_id
						__a			:       Any					    =  None
						__a			:       Union[str, Any]					    =  None
						__a			:       List[Any]					    =  torch.ones(__a						,				device=__a						,				dtype=torch.int							)
						__a			:       Optional[Any]					    =  torch.zeros(__a						,				device=__a						,				dtype=torch.bool							)

						if input_embeds is not None:
											__a			:       Optional[Any]					    =  input_embeds
						else:
											__a			:       Union[str, Any]					    =  self.transformer.transformer.wte(__a							)

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

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

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

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







'''simple docstring'''



from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int   ):
					__a			:       int					    =  int(number**0.5   )
					return number == sq * sq






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int						,      _SCREAMING_SNAKE_CASE      :   int   ):
					__a			:       int					    =  x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
					__a			:       int					    =  x_den * y_den * z_den
					__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
					top //= hcf
					bottom //= hcf
					return top, bottom






def   lowerCamelCase							(_SCREAMING_SNAKE_CASE      :   int = 35   ):
					__a			:       set					    =  set()
					__a			:       int
					__a			:       Fraction					    =  Fraction(0   )
					__a			:       tuple[int, int]

					for x_num in range(1						,      order + 1   ):
										for x_den in range(x_num + 1						,      order + 1   ):
															for y_num in range(1						,      order + 1   ):
																				for y_den in range(y_num + 1						,      order + 1   ):
																									# n=1
																									__a			:       Union[str, Any]					    =  x_num * y_den + x_den * y_num
																									__a			:       Optional[Any]					    =  x_den * y_den
																									__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a			:       Any					    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														unique_s.add(_SCREAMING_SNAKE_CASE   )

																									# n=2
																									__a			:       Optional[int]					    =  (
																									    x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
																									)
																									__a			:       Union[str, Any]					    =  x_den * x_den * y_den * y_den
																									if is_sq(_SCREAMING_SNAKE_CASE   ) and is_sq(_SCREAMING_SNAKE_CASE   ):
																														__a			:       List[Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Any					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Optional[int]					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			__a			:       List[Any]					    =  add_three(
																																			    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																																			unique_s.add(_SCREAMING_SNAKE_CASE   )

                    # n=-1
																									__a			:       int					    =  x_num * y_num
																									__a			:       Optional[Any]					    =  x_den * y_num + x_num * y_den
																									__a			:       Tuple					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																									z_num //= hcf
																									z_den //= hcf
																									if 0 < z_num < z_den <= order:
																														__a			:       Any					    =  add_three(
																														    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														unique_s.add(_SCREAMING_SNAKE_CASE   )

																									# n=2
																									__a			:       List[Any]					    =  x_num * x_num * y_num * y_num
																									__a			:       List[Any]					    =  (
																									    x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
																									)
																									if is_sq(_SCREAMING_SNAKE_CASE   ) and is_sq(_SCREAMING_SNAKE_CASE   ):
																														__a			:       Optional[Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       Union[str, Any]					    =  int(sqrt(_SCREAMING_SNAKE_CASE   )   )
																														__a			:       int					    =  gcd(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																														z_num //= hcf
																														z_den //= hcf
																														if 0 < z_num < z_den <= order:
																																			__a			:       List[str]					    =  add_three(
																																			    _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )
																																			unique_s.add(_SCREAMING_SNAKE_CASE   )

					for num, den in unique_s:
										total += Fraction(_SCREAMING_SNAKE_CASE						,      _SCREAMING_SNAKE_CASE   )

					return total.denominator + total.numerator


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



