



"""simple docstring"""
from typing import Mapping

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxSeqaSeqConfigWithPast
from ...utils import logging


__a      =				logging.get_logger(__name__)

__a      =				{
    "t5-small": "https://huggingface.co/t5-small/resolve/main/config.json",
    "t5-base": "https://huggingface.co/t5-base/resolve/main/config.json",
    "t5-large": "https://huggingface.co/t5-large/resolve/main/config.json",
    "t5-3b": "https://huggingface.co/t5-3b/resolve/main/config.json",
    "t5-11b": "https://huggingface.co/t5-11b/resolve/main/config.json",
}
class 				lowerCamelCase  (			_lowerCAmelCase				):






					'''simple docstring'''





					_A		:			Any						=     """t5"""
					_A		:			int						=     ["""past_key_values"""]
					_A		:			List[str]						=     {"""hidden_size""": """d_model""", """num_attention_heads""": """num_heads""", """num_hidden_layers""": """num_layers"""}






					def __init__(       self:							List[Any]						,     snake_case:							Tuple=32_128						,     snake_case:							Tuple=512						,     snake_case:							int=64						,     snake_case:							List[Any]=2_048						,     snake_case:							str=6						,     snake_case:							List[Any]=None						,     snake_case:							List[Any]=8						,     snake_case:							int=32						,     snake_case:							List[str]=128						,     snake_case:							str=0.1						,     snake_case:							Union[str, Any]=1E-6						,     snake_case:							str=1.0						,     snake_case:							Union[str, Any]="relu"						,     snake_case:							List[str]=True						,     snake_case:							List[str]=True						,     snake_case:							Tuple=0						,     snake_case:							Tuple=1						,     **snake_case:							List[str]						,     )   ->	int:
											snake_case_ :Optional[int]						=			vocab_size
											snake_case_ :str						=			d_model
											snake_case_ :str						=			d_kv
											snake_case_ :Tuple						=			d_ff
											snake_case_ :str						=			num_layers
											snake_case_ :List[Any]						=			(
											    num_decoder_layers if num_decoder_layers is not None else self.num_layers
											)  # default = symmetry
											snake_case_ :List[str]						=			num_heads
											snake_case_ :List[Any]						=			relative_attention_num_buckets
											snake_case_ :Optional[int]						=			relative_attention_max_distance
											snake_case_ :List[str]						=			dropout_rate
											snake_case_ :Tuple						=			layer_norm_epsilon
											snake_case_ :List[str]						=			initializer_factor
											snake_case_ :Optional[int]						=			feed_forward_proj
											snake_case_ :str						=			use_cache

											snake_case_ :str						=			self.feed_forward_proj.split("""-"""						)
											snake_case_ :Optional[Any]						=			act_info[-1]
											snake_case_ :Union[str, Any]						=			act_info[0] == """gated"""

											if len(snake_case						) > 1 and act_info[0] != "gated" or len(snake_case						) > 2:
																	raise ValueError(
																	    f"""`feed_forward_proj`: {feed_forward_proj} is not a valid activation function of the dense layer."""
																	    """Please make sure `feed_forward_proj` is of the format `gated-{ACT_FN}` or `{ACT_FN}`, e.g. """
																	    """'gated-gelu' or 'relu'"""						)

											# for backwards compatibility
											if feed_forward_proj == "gated-gelu":
																	snake_case_ :Optional[Any]						=			"""gelu_new"""

											super().__init__(
											    pad_token_id=snake_case						,     eos_token_id=snake_case						,     is_encoder_decoder=snake_case						,     **snake_case						,     )

class 				lowerCamelCase  (			_lowerCAmelCase				):






					'''simple docstring'''





					@property
					def    lowerCAmelCase_				(       self:							Optional[Any]						)   ->	Mapping[str, Mapping[int, str]]:
											snake_case_ :str						=			{
											    """input_ids""": {0: """batch""", 1: """encoder_sequence"""},
											    """attention_mask""": {0: """batch""", 1: """encoder_sequence"""},
											}
											if self.use_past:
																	snake_case_ :Dict						=			"""past_encoder_sequence + sequence"""
																	snake_case_ :Dict						=			{0: """batch"""}
																	snake_case_ :Optional[int]						=			{0: """batch""", 1: """past_decoder_sequence + sequence"""}
											else:
																	snake_case_ :int						=			{0: """batch""", 1: """decoder_sequence"""}
																	snake_case_ :Optional[int]						=			{0: """batch""", 1: """decoder_sequence"""}

											if self.use_past:
																	self.fill_with_past_key_values_(snake_case						,     direction="""inputs"""						)

											return common_inputs






					@property
					def    lowerCAmelCase_				(       self:							str						)   ->	int:
											return 13

'''simple docstring'''

from math import pow
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     UpperCAmelCase		,     ):
 if current_sum == needed_sum:
  # If the sum of the powers is equal to needed_sum, then we have a solution.
  solutions_count += 1
  return current_sum, solutions_count

 lowercase__				:    Optional[Any]  =					int(pow(UpperCAmelCase		,     UpperCAmelCase     )     )
 if current_sum + i_to_n <= needed_sum:
  # If the sum of the powers is less than needed_sum, then continue adding powers.
  current_sum += i_to_n
  lowercase__ ,							lowercase__				:    Dict  =					backtrack(
      UpperCAmelCase		,     UpperCAmelCase		,     current_number + 1		,     UpperCAmelCase		,     UpperCAmelCase     )
  current_sum -= i_to_n
 if i_to_n < needed_sum:
  # If the power of i is less than needed_sum, then try with the next power.
  lowercase__ ,							lowercase__				:    str  =					backtrack(
      UpperCAmelCase		,     UpperCAmelCase		,     current_number + 1		,     UpperCAmelCase		,     UpperCAmelCase     )
 return current_sum, solutions_count
def 			__UpperCamelCase       (   UpperCAmelCase		,     UpperCAmelCase     ):
 if not (1 <= needed_sum <= 1000 and 2 <= power <= 10):
  raise ValueError(
      '''Invalid input\n'''
      '''needed_sum must be between 1 and 1000, power between 2 and 10.'''     )

 return backtrack(UpperCAmelCase		,     UpperCAmelCase		,     1		,     0		,     0     )[1]  # Return the solutions_count


if __name__ == "__main__":
  import doctest

  doctest.testmod()

