


"""simple docstring"""



from __future__ import annotations

from collections.abc import Callable

__snake_case       =       list[list[float | int]]







def     __lowerCAmelCase		(		lowercase    :    Matrix		,				lowercase    :    Matrix					)      ->		Matrix:


    """simple docstring"""





    snake_case       : int    =       len(lowercase					)
    snake_case       : Matrix    =       [[0 for _ in range(size + 1					)] for _ in range(lowercase					)]
    snake_case       : int
    snake_case       : int
    snake_case       : int
    snake_case       : int
    snake_case       : int
    snake_case       : float

    for row in range(lowercase					):
        for col in range(lowercase					):
            snake_case       : Optional[int]    =       matrix[row][col]

        snake_case       : Optional[Any]    =       vector[row][0]

    snake_case       : str    =       0
    snake_case       : Optional[int]    =       0
    while row < size and col < size:
        # pivoting
        snake_case       : int    =       max((abs(augmented[rowa][col]					), rowa) for rowa in range(lowercase		,				lowercase					)					)[
            1
        ]
        if augmented[pivot_row][col] == 0:
            col += 1
            continue
        else:
            snake_case   ,snake_case       : Tuple    =       augmented[pivot_row], augmented[row]

        for rowa in range(row + 1		,				lowercase					):
            snake_case       : Optional[int]    =       augmented[rowa][col] / augmented[row][col]
            snake_case       : Union[str, Any]    =       0
            for cola in range(col + 1		,				size + 1					):
                augmented[rowa][cola] -= augmented[row][cola] * ratio

        row += 1
        col += 1

    # back substitution
    for col in range(1		,				lowercase					):
        for row in range(lowercase					):
            snake_case       : Tuple    =       augmented[row][col] / augmented[col][col]
            for cola in range(lowercase		,				size + 1					):
                augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
    return [
        [round(augmented[row][size] / augmented[row][row]		,				10					)] for row in range(lowercase					)
    ]







def     __lowerCAmelCase		(		lowercase    :    list[int]					)      ->		Callable[[int], int]:


    """simple docstring"""





    snake_case       : int    =       len(lowercase					)
    snake_case       : Matrix    =       [[0 for _ in range(lowercase					)] for _ in range(lowercase					)]
    snake_case       : Matrix    =       [[0] for _ in range(lowercase					)]
    snake_case       : Matrix
    snake_case       : int
    snake_case       : int
    snake_case       : int

    for x_val, y_val in enumerate(lowercase					):
        for col in range(lowercase					):
            snake_case       : Optional[int]    =       (x_val + 1) ** (size - col - 1)
        snake_case       : Any    =       y_val

    snake_case       : Any    =       solve(lowercase		,				lowercase					)

    def interpolated_func(lowercase    :    int					) -> int:
        return sum(
            round(coeffs[x_val][0]					) * (var ** (size - x_val - 1))
            for x_val in range(lowercase					)					)

    return interpolated_func







def     __lowerCAmelCase		(		lowercase    :    int					)      ->		int:


    """simple docstring"""





    return (
        1
        - variable
        + variable**2
        - variable**3
        + variable**4
        - variable**5
        + variable**6
        - variable**7
        + variable**8
        - variable**9
        + variable**10
    )







def     __lowerCAmelCase		(		lowercase    :    Callable[[int], int] = question_function		,				lowercase    :    int = 10					)      ->		int:


    """simple docstring"""





    snake_case       : list[int]    =       [func(lowercase					) for x_val in range(1		,				order + 1					)]

    snake_case       : list[Callable[[int], int]]    =       [
        interpolate(data_points[:max_coeff]					) for max_coeff in range(1		,				order + 1					)
    ]

    snake_case       : int    =       0
    snake_case       : Callable[[int], int]
    snake_case       : int

    for poly in polynomials:
        snake_case       : Union[str, Any]    =       1
        while func(lowercase					) == poly(lowercase					):
            x_val += 1

        ret += poly(lowercase					)

    return ret


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









"""simple docstring"""



from typing import Mapping

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


__snake_case       =       logging.get_logger(__name__)

__snake_case       =       {
    """google/umt5-small""": """https://huggingface.co/google/umt5-small/resolve/main/config.json""",
    # See all umt5 models at https://huggingface.co/models?filter=umt5
}







class _lowerCAmelCase							( snake_case_      ):
   __UpperCAmelCase					:			Dict				    =    '''umt5'''
   __UpperCAmelCase					:			str				    =    ['''past_key_values''']







   def __init__(      self		,      UpperCamelCase__=25_0112		,      UpperCamelCase__=512		,      UpperCamelCase__=64		,      UpperCamelCase__=1024		,      UpperCamelCase__=8		,      UpperCamelCase__=None		,      UpperCamelCase__=6		,      UpperCamelCase__=32		,      UpperCamelCase__=128		,      UpperCamelCase__=0.1		,      UpperCamelCase__=1e-6		,      UpperCamelCase__=1.0		,      UpperCamelCase__="gated-gelu"		,      UpperCamelCase__=True		,      UpperCamelCase__=True		,      UpperCamelCase__="T5Tokenizer"		,      UpperCamelCase__=True		,      UpperCamelCase__=0		,      UpperCamelCase__=1		,      UpperCamelCase__=0		,      **UpperCamelCase__		,      )      ->						Dict:

       '''simple docstring'''




       super().__init__(
           is_encoder_decoder=UpperCamelCase__		,      tokenizer_class=UpperCamelCase__		,      tie_word_embeddings=UpperCamelCase__		,      pad_token_id=UpperCamelCase__		,      eos_token_id=UpperCamelCase__		,      decoder_start_token_id=UpperCamelCase__		,      **UpperCamelCase__		,      )
       snake_case       : Optional[int]    =       vocab_size
       snake_case       : Any    =       d_model
       snake_case       : Optional[Any]    =       d_kv
       snake_case       : Any    =       d_ff
       snake_case       : Optional[Any]    =       num_layers
       snake_case       : Optional[Any]    =       (
           num_decoder_layers if num_decoder_layers is not None else self.num_layers
       )  # default = symmetry
       snake_case       : Optional[Any]    =       num_heads
       snake_case       : Optional[Any]    =       relative_attention_num_buckets
       snake_case       : Dict    =       relative_attention_max_distance
       snake_case       : Tuple    =       dropout_rate
       snake_case       : List[Any]    =       layer_norm_epsilon
       snake_case       : Any    =       initializer_factor
       snake_case       : Optional[Any]    =       feed_forward_proj
       snake_case       : Tuple    =       use_cache

       snake_case       : Any    =       self.feed_forward_proj.split("-"		)
       snake_case       : Tuple    =       act_info[-1]
       snake_case       : Optional[int]    =       act_info[0] == "gated"

       if len(UpperCamelCase__		) > 1 and act_info[0] != "gated" or len(UpperCamelCase__		) > 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'"		)

       if feed_forward_proj == "gated-gelu":
           snake_case       : List[str]    =       "gelu_new"







   @property
   def 					lowerCamelCase						(      self		)      ->						Any:

       '''simple docstring'''




       return self.d_model







   @property
   def 					lowerCamelCase						(      self		)      ->						str:

       '''simple docstring'''




       return self.num_heads







   @property
   def 					lowerCamelCase						(      self		)      ->						Union[str, Any]:

       '''simple docstring'''




       return self.num_layers







class _lowerCAmelCase							( snake_case_      ):







   @property
   # Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.inputs
   def 					lowerCamelCase						(      self		)      ->						Mapping[str, Mapping[int, str]]:

       '''simple docstring'''




       snake_case       : Optional[int]    =       {
           "input_ids": {0: "batch", 1: "encoder_sequence"},
           "attention_mask": {0: "batch", 1: "encoder_sequence"},
       }
       if self.use_past:
           snake_case       : Tuple    =       "past_encoder_sequence + sequence"
           snake_case       : int    =       {0: "batch"}
           snake_case       : int    =       {0: "batch", 1: "past_decoder_sequence + sequence"}
       else:
           snake_case       : List[Any]    =       {0: "batch", 1: "decoder_sequence"}
           snake_case       : Any    =       {0: "batch", 1: "decoder_sequence"}

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

       return common_inputs







   @property
   # Copied from transformers.models.t5.configuration_t5.T5OnnxConfig.default_onnx_opset
   def 					lowerCamelCase						(      self		)      ->						int:

       '''simple docstring'''




       return 13







   @property
   def 					lowerCamelCase						(      self		)      ->						float:

       '''simple docstring'''




       return 5e-4





