


'''simple docstring'''







from typing import Mapping

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


A   :  List[Any]       		=				logging.get_logger(__name__)


class 				__lowerCamelCase				( _a ):
    """simple docstring"""
    a									=					'mt5'
    a									=					['past_key_values']


    def __init__(						self    :							Optional[int]   ,							SCREAMING_SNAKE_CASE    :							int=250112   ,							SCREAMING_SNAKE_CASE    :							List[str]=512   ,							SCREAMING_SNAKE_CASE    :							Any=64   ,							SCREAMING_SNAKE_CASE    :							int=1024   ,							SCREAMING_SNAKE_CASE    :							List[Any]=8   ,							SCREAMING_SNAKE_CASE    :							Union[str, Any]=None   ,							SCREAMING_SNAKE_CASE    :							Optional[int]=6   ,							SCREAMING_SNAKE_CASE    :							List[Any]=32   ,							SCREAMING_SNAKE_CASE    :							Optional[Any]=128   ,							SCREAMING_SNAKE_CASE    :							Optional[int]=0.1   ,							SCREAMING_SNAKE_CASE    :							Optional[Any]=1e-6   ,							SCREAMING_SNAKE_CASE    :							int=1.0   ,							SCREAMING_SNAKE_CASE    :							Any="gated-gelu"   ,							SCREAMING_SNAKE_CASE    :							Optional[int]=True   ,							SCREAMING_SNAKE_CASE    :							Union[str, Any]=True   ,							SCREAMING_SNAKE_CASE    :							Tuple="T5Tokenizer"   ,							SCREAMING_SNAKE_CASE    :							Dict=False   ,							SCREAMING_SNAKE_CASE    :							List[str]=0   ,							SCREAMING_SNAKE_CASE    :							Optional[int]=1   ,							SCREAMING_SNAKE_CASE    :							int=0   ,							**SCREAMING_SNAKE_CASE    :							int   ,							):
           super().__init__(
               is_encoder_decoder=SCREAMING_SNAKE_CASE   ,							tokenizer_class=SCREAMING_SNAKE_CASE   ,							tie_word_embeddings=SCREAMING_SNAKE_CASE   ,							pad_token_id=SCREAMING_SNAKE_CASE   ,							eos_token_id=SCREAMING_SNAKE_CASE   ,							decoder_start_token_id=SCREAMING_SNAKE_CASE   ,							**SCREAMING_SNAKE_CASE   ,							)
           _A  :			List[Any]											=      vocab_size
           _A  :			int											=      d_model
           _A  :			List[Any]											=      d_kv
           _A  :			Dict											=      d_ff
           _A  :			Tuple											=      num_layers
           _A  :			List[Any]											=      (
               num_decoder_layers if num_decoder_layers is not None else self.num_layers
           )  # default = symmetry
           _A  :			Tuple											=      num_heads
           _A  :			Optional[Any]											=      relative_attention_num_buckets
           _A  :			List[str]											=      relative_attention_max_distance
           _A  :			str											=      dropout_rate
           _A  :			Optional[Any]											=      layer_norm_epsilon
           _A  :			int											=      initializer_factor
           _A  :			str											=      feed_forward_proj
           _A  :			Optional[Any]											=      use_cache

           _A  :			List[str]											=      self.feed_forward_proj.split('-')
           _A  :			List[str]											=      act_info[-1]
           _A  :			Any											=      act_info[0] == 'gated'

           if len(SCREAMING_SNAKE_CASE) > 1 and act_info[0] != "gated" or len(SCREAMING_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  :			Any											=      'gelu_new'


    @property
    def      A					(						self    :							Tuple):
           return self.d_model


    @property
    def      A					(						self    :							Union[str, Any]):
           return self.num_heads


    @property
    def      A					(						self    :							Dict):
           return self.num_layers




class 				__lowerCamelCase				( _a ):
    """simple docstring"""


    @property
    # Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.inputs
    def      A					(						self    :							Optional[Any]):
           _A  :			int											=      {
               'input_ids': {0: 'batch', 1: 'encoder_sequence'},
               'attention_mask': {0: 'batch', 1: 'encoder_sequence'},
           }
           if self.use_past:
                  _A  :			Union[str, Any]											=      'past_encoder_sequence + sequence'
                  _A  :			List[str]											=      {0: 'batch'}
                  _A  :			Optional[Any]											=      {0: 'batch', 1: 'past_decoder_sequence + sequence'}
           else:
                  _A  :			int											=      {0: 'batch', 1: 'decoder_sequence'}
                  _A  :			Any											=      {0: 'batch', 1: 'decoder_sequence'}

           if self.use_past:
                  self.fill_with_past_key_values_(SCREAMING_SNAKE_CASE   ,							direction='inputs')

           return common_inputs


    @property
    # Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.default_onnx_opset
    def      A					(						self    :							List[Any]):
           return 13


    @property
    def      A					(						self    :							Tuple):
           return 5e-4










'''simple docstring'''







import itertools






def    lowerCAmelCase__ (       lowerCamelCase  :    int = 1000000     ):
       _A  :			str											=      [1]

       for i in itertools.count(len(lowerCamelCase     )     ):
              _A  :			Optional[Any]											=      0
              for j in itertools.count(1     ):
                     _A  :			int											=      -1 if j % 2 == 0 else +1
                     _A  :			Optional[Any]											=      (j * j * 3 - j) // 2
                     if index > i:
                            break
                     item += partitions[i - index] * sign
                     item %= number
                     index += j
                     if index > i:
                            break
                     item += partitions[i - index] * sign
                     item %= number

              if item == 0:
                     return i
              partitions.append(lowerCamelCase     )

       return 0


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   print(f"""{solution() = }""")






