


"""simple docstring"""




from typing import Mapping

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


__SCREAMING_SNAKE_CASE      		=    logging.get_logger(__name__)

__SCREAMING_SNAKE_CASE      		=    {
    "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 __snake_case		(       __snake_case   ):







   """simple docstring"""




   lowerCAmelCase_					: List[Any]  						=      't5'
   lowerCAmelCase_					: List[str]  						=      ['past_key_values']
   lowerCAmelCase_					: List[str]  						=      {'hidden_size': 'd_model', 'num_attention_heads': 'num_heads', 'num_hidden_layers': 'num_layers'}




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

          _a							 =					self.feed_forward_proj.split("-"							)
          _a							 =					act_info[-1]
          _a							 =					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":
                 _a							 =					"gelu_new"

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






class __snake_case		(       __snake_case   ):







   """simple docstring"""




   @property
   def SCREAMING_SNAKE_CASE_   (		self				:List[str]							):
          _a							 =					{
              "input_ids": {0: "batch", 1: "encoder_sequence"},
              "attention_mask": {0: "batch", 1: "encoder_sequence"},
          }
          if self.use_past:
                 _a							 =					"past_encoder_sequence + sequence"
                 _a							 =					{0: "batch"}
                 _a							 =					{0: "batch", 1: "past_decoder_sequence + sequence"}
          else:
                 _a							 =					{0: "batch", 1: "decoder_sequence"}
                 _a							 =					{0: "batch", 1: "decoder_sequence"}

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

          return common_inputs




   @property
   def SCREAMING_SNAKE_CASE_   (		self				:Dict							):
          return 13







from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE				)							-> bool:




    """simple docstring"""




    _A     =							int(number**0.5				)
    return number == sq * sq





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)							-> tuple[int, int]:




    """simple docstring"""




    _A     =							x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
    _A     =							x_den * y_den * z_den
    _A     =							gcd(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
    top //= hcf
    bottom //= hcf
    return top, bottom





def 				__lowerCAmelCase(       _SCREAMING_SNAKE_CASE = 35				)							-> int:




    """simple docstring"""




    _A     =							set()
    _A     =							42
    _A     =							Fraction(0				)
    _A     =							42

    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     =							x_num * y_den + x_den * y_num
                    _A     =							x_den * y_den
                    _A     =							gcd(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        _A     =							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     =							(
                        x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
                    )
                    _A     =							x_den * x_den * y_den * y_den
                    if is_sq(_SCREAMING_SNAKE_CASE				) and is_sq(_SCREAMING_SNAKE_CASE				):
                        _A     =							int(sqrt(_SCREAMING_SNAKE_CASE				)				)
                        _A     =							int(sqrt(_SCREAMING_SNAKE_CASE				)				)
                        _A     =							gcd(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            _A     =							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     =							x_num * y_num
                    _A     =							x_den * y_num + x_num * y_den
                    _A     =							gcd(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                    z_num //= hcf
                    z_den //= hcf
                    if 0 < z_num < z_den <= order:
                        _A     =							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     =							x_num * x_num * y_num * y_num
                    _A     =							(
                        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     =							int(sqrt(_SCREAMING_SNAKE_CASE				)				)
                        _A     =							int(sqrt(_SCREAMING_SNAKE_CASE				)				)
                        _A     =							gcd(_SCREAMING_SNAKE_CASE							,     _SCREAMING_SNAKE_CASE				)
                        z_num //= hcf
                        z_den //= hcf
                        if 0 < z_num < z_den <= order:
                            _A     =							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() = }")





