



"""simple docstring"""
from __future__ import annotations





def 				lowerCamelCase_		(UpperCamelCase__	:	int							):
    _UpperCAmelCase							:						Optional[Any]       							=					{1}
    _UpperCAmelCase							:						str       							=					[1]
    for _ in range(2  , depth + 1							):
        _UpperCAmelCase							:						List[str]       							=					[*previous_coefficients, 0]
        _UpperCAmelCase							:						int       							=					[0, *previous_coefficients]
        _UpperCAmelCase							:						Optional[Any]       							=					[]
        for x, y in zip(UpperCamelCase__  , UpperCamelCase__							):
            coefficients.add(x + y							)
            previous_coefficients.append(x + y							)
    return coefficients





def 				lowerCamelCase_		(UpperCamelCase__	:	set[int]							):
    _UpperCAmelCase							:						Union[str, Any]       							=					set()
    for number in unique_coefficients:
        _UpperCAmelCase							:						Optional[int]       							=					2
        _UpperCAmelCase							:						List[str]       							=					number
        while divisor**2 <= copy_number:
            _UpperCAmelCase							:						str       							=					0
            while copy_number % divisor == 0:
                copy_number //= divisor
                multiplicity += 1
            if multiplicity >= 2:
                non_squarefrees.add(UpperCamelCase__							)
                break
            divisor += 1

    return unique_coefficients.difference(UpperCamelCase__							)





def 				lowerCamelCase_		(UpperCamelCase__	:	int = 51							):
    _UpperCAmelCase							:						Any       							=					get_pascal_triangle_unique_coefficients(UpperCamelCase__							)
    _UpperCAmelCase							:						Dict       							=					get_squarefrees(UpperCamelCase__							)
    return sum(UpperCamelCase__							)


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









"""simple docstring"""
from collections import OrderedDict
from typing import Any, List, Mapping, Optional

from ... import PreTrainedTokenizer, TensorType, is_torch_available
from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfigWithPast, PatchingSpec
from ...utils import logging


_lowerCAmelCase					:Union[str, Any]  =      logging.get_logger(__name__)

_lowerCAmelCase					:List[str]  =      {
    'gpt2': 'https://huggingface.co/gpt2/resolve/main/config.json',
    'gpt2-medium': 'https://huggingface.co/gpt2-medium/resolve/main/config.json',
    'gpt2-large': 'https://huggingface.co/gpt2-large/resolve/main/config.json',
    'gpt2-xl': 'https://huggingface.co/gpt2-xl/resolve/main/config.json',
    'distilgpt2': 'https://huggingface.co/distilgpt2/resolve/main/config.json',
}
class 							_UpperCAmelCase							(				a   ):





     '''simple docstring'''



     a__             ='''gpt2'''
     a__             =['''past_key_values''']
     a__             ={
         '''hidden_size''': '''n_embd''',
         '''max_position_embeddings''': '''n_positions''',
         '''num_attention_heads''': '''n_head''',
         '''num_hidden_layers''': '''n_layer''',
     }





     def __init__(      self ,			A=5_0_2_5_7 ,			A=1_0_2_4 ,			A=7_6_8 ,			A=1_2 ,			A=1_2 ,			A=None ,			A="gelu_new" ,			A=0.1 ,			A=0.1 ,			A=0.1 ,			A=1E-5 ,			A=0.02 ,			A="cls_index" ,			A=True ,			A=None ,			A=True ,			A=0.1 ,			A=True ,			A=True ,			A=5_0_2_5_6 ,			A=5_0_2_5_6 ,			A=False ,			A=False ,			**A ,			)							->      Union[str, Any]:
         _UpperCAmelCase							:						Optional[int]       							=					vocab_size
         _UpperCAmelCase							:						Union[str, Any]       							=					n_positions
         _UpperCAmelCase							:						Optional[Any]       							=					n_embd
         _UpperCAmelCase							:						Tuple       							=					n_layer
         _UpperCAmelCase							:						Any       							=					n_head
         _UpperCAmelCase							:						Union[str, Any]       							=					n_inner
         _UpperCAmelCase							:						Optional[int]       							=					activation_function
         _UpperCAmelCase							:						Optional[int]       							=					resid_pdrop
         _UpperCAmelCase							:						Dict       							=					embd_pdrop
         _UpperCAmelCase							:						List[Any]       							=					attn_pdrop
         _UpperCAmelCase							:						Tuple       							=					layer_norm_epsilon
         _UpperCAmelCase							:						Optional[int]       							=					initializer_range
         _UpperCAmelCase							:						List[str]       							=					summary_type
         _UpperCAmelCase							:						Tuple       							=					summary_use_proj
         _UpperCAmelCase							:						List[Any]       							=					summary_activation
         _UpperCAmelCase							:						Optional[int]       							=					summary_first_dropout
         _UpperCAmelCase							:						int       							=					summary_proj_to_labels
         _UpperCAmelCase							:						Union[str, Any]       							=					scale_attn_weights
         _UpperCAmelCase							:						Any       							=					use_cache
         _UpperCAmelCase							:						Tuple       							=					scale_attn_by_inverse_layer_idx
         _UpperCAmelCase							:						Optional[Any]       							=					reorder_and_upcast_attn

         _UpperCAmelCase							:						Union[str, Any]       							=					bos_token_id
         _UpperCAmelCase							:						Optional[int]       							=					eos_token_id

         super().__init__(bos_token_id=A ,			eos_token_id=A ,			**A	)



class 							_UpperCAmelCase							(				a   ):





     '''simple docstring'''



     def __init__(      self ,			A ,			A = "default" ,			A = None ,			A = False ,			)							->      str:
         super().__init__(A ,			task=A ,			patching_specs=A ,			use_past=A	)
         if not getattr(self._config ,			'''pad_token_id''' ,			A	):
             # TODO: how to do that better?
             _UpperCAmelCase							:						Optional[int]       							=					0





     @property
     def 				__lowerCAmelCase			(      self	)							->      Mapping[str, Mapping[int, str]]:
         _UpperCAmelCase							:						List[str]       							=					OrderedDict({'''input_ids''': {0: '''batch''', 1: '''sequence'''}}	)
         if self.use_past:
             self.fill_with_past_key_values_(A ,			direction='''inputs'''	)
             _UpperCAmelCase							:						Union[str, Any]       							=					{0: '''batch''', 1: '''past_sequence + sequence'''}
         else:
             _UpperCAmelCase							:						Tuple       							=					{0: '''batch''', 1: '''sequence'''}

         return common_inputs





     @property
     def 				__lowerCAmelCase			(      self	)							->      int:
         return self._config.n_layer





     @property
     def 				__lowerCAmelCase			(      self	)							->      int:
         return self._config.n_head





     def 				__lowerCAmelCase			(      self ,			A ,			A = -1 ,			A = -1 ,			A = False ,			A = None ,			)							->      Mapping[str, Any]:
         _UpperCAmelCase							:						int       							=					super(A ,			self	).generate_dummy_inputs(
             A ,			batch_size=A ,			seq_length=A ,			is_pair=A ,			framework=A	)

         # We need to order the input in the way they appears in the forward()
         _UpperCAmelCase							:						List[Any]       							=					OrderedDict({'''input_ids''': common_inputs['''input_ids''']}	)

         # Need to add the past_keys
         if self.use_past:
             if not is_torch_available():
                 raise ValueError('''Cannot generate dummy past_keys inputs without PyTorch installed.'''	)
             else:
                 import torch

                 _UpperCAmelCase							,       _UpperCAmelCase							:						Optional[Any]       							=					common_inputs['''input_ids'''].shape
                 # Not using the same length for past_key_values
                 _UpperCAmelCase							:						Optional[Any]       							=					seqlen + 2
                 _UpperCAmelCase							:						Union[str, Any]       							=					(
                     batch,
                     self.num_attention_heads,
                     past_key_values_length,
                     self._config.hidden_size // self.num_attention_heads,
                 )
                 _UpperCAmelCase							:						List[Any]       							=					[
                     (torch.zeros(A	), torch.zeros(A	)) for _ in range(self.num_layers	)
                 ]

         _UpperCAmelCase							:						int       							=					common_inputs['''attention_mask''']
         if self.use_past:
             _UpperCAmelCase							:						int       							=					ordered_inputs['''attention_mask'''].dtype
             _UpperCAmelCase							:						Dict       							=					torch.cat(
                 [ordered_inputs['''attention_mask'''], torch.ones(A ,			A ,			dtype=A	)] ,			dim=1	)

         return ordered_inputs





     @property
     def 				__lowerCAmelCase			(      self	)							->      int:
         return 1_3


