
"""simple docstring"""




from typing import List, Optional, Union

import numpy as np
import tensorflow as tf

from .utils import logging


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



def     __magic_name__		(					UpperCamelCase     :		Union[tf.Tensor, np.ndarray]     )     ->						List[int]:
    if isinstance(UpperCamelCase							,		np.ndarray     ):
        return list(tensor.shape     )

    a__		=			tf.shape(UpperCamelCase     )

    if tensor.shape == tf.TensorShape(UpperCamelCase     ):
        return dynamic

    a__		=			tensor.shape.as_list()

    return [dynamic[i] if s is None else s for i, s in enumerate(UpperCamelCase     )]



def     __magic_name__		(					UpperCamelCase     :		tf.Tensor							,		UpperCamelCase     :		Optional[int] = None							,		UpperCamelCase     :		Optional[str] = None     )     ->						tf.Tensor:
    return tf.nn.softmax(logits=logits + 1E-9							,		axis=UpperCamelCase							,		name=UpperCamelCase     )



def     __magic_name__		(					UpperCamelCase     :		Optional[Any]							,		UpperCamelCase     :		Union[str, Any]							,		UpperCamelCase     :		Union[str, Any]							,		UpperCamelCase     :		str=1E-5							,		UpperCamelCase     :		List[str]=-1     )     ->						List[str]:
    # This is a very simplified functional layernorm, designed to duplicate
    # the functionality of PyTorch nn.functional.layer_norm when this is needed to port
    # models in Transformers.

    if weight.shape.rank != 1 or bias.shape.rank != 1 or not isinstance(UpperCamelCase							,		UpperCamelCase     ):
        raise NotImplementedError('Only 1D weight and bias tensors are supported for now, with only a single axis.'     )

    # Get mean and variance on the axis to be normalized
    a__	,     a__		=			tf.nn.moments(UpperCamelCase							,		axes=[axis]							,		keepdims=UpperCamelCase     )

    if axis != -1:
        # Reshape scale and weight to have the same rank as inputs, but with 1 dimensions
        # on every dimension except axis
        a__		=			[1] * inputs.shape.rank
        a__		=			shape_list(UpperCamelCase     )[axis]
        a__		=			tf.reshape(UpperCamelCase							,		UpperCamelCase     )
        a__		=			tf.reshape(UpperCamelCase							,		UpperCamelCase     )

    # Compute layer normalization using the batch_normalization
    # function.
    a__		=			tf.nn.batch_normalization(
        UpperCamelCase							,		UpperCamelCase							,		UpperCamelCase							,		offset=UpperCamelCase							,		scale=UpperCamelCase							,		variance_epsilon=UpperCamelCase							,		)
    return outputs



def     __magic_name__		(					UpperCamelCase     :		Any							,		UpperCamelCase     :		Union[str, Any]=0							,		UpperCamelCase     :		Any=-1     )     ->						Dict:
    # Replicates the behavior of torch.flatten in TF

    # If end_dim or start_dim is negative, count them from the end
    if end_dim < 0:
        end_dim += input.shape.rank
    if start_dim < 0:
        start_dim += input.shape.rank

    if start_dim == end_dim:
        return input

    a__		=			tf.shape(UpperCamelCase     )
    a__		=			tf.math.reduce_prod(in_shape[start_dim : end_dim + 1]     )
    a__		=			tf.concat([in_shape[:start_dim], [flattened_dim], in_shape[end_dim + 1 :]]							,		axis=0     )
    return tf.reshape(UpperCamelCase							,		UpperCamelCase     )



def     __magic_name__		(					UpperCamelCase     :		tf.Tensor     )     ->						tf.Tensor:
    if not isinstance(UpperCamelCase							,		tf.Tensor     ):
        a__		=			tf.convert_to_tensor(UpperCamelCase     )  # Catches stray NumPy inputs
    if encoder_attention_mask.shape.rank == 3:
        a__		=			encoder_attention_mask[:, None, :, :]
    if encoder_attention_mask.shape.rank == 2:
        a__		=			encoder_attention_mask[:, None, None, :]
    # T5 has a mask that can compare sequence ids, we can simulate this here with this transposition
    # Cf. https://github.com/tensorflow/mesh/blob/8d2465e9bc93129b913b5ccc6a59aa97abd96ec6/mesh_tensorflow
    # /transformer/transformer_layers.py#L270
    # encoder_extended_attention_mask = (encoder_extended_attention_mask ==
    # encoder_extended_attention_mask.transpose(-1, -2))
    a__		=			(
        tf.cast(1							,		encoder_attention_mask.dtype     ) - encoder_extended_attention_mask
    ) * encoder_extended_attention_mask.dtype.min

    return encoder_extended_attention_mask



def     __magic_name__		(					UpperCamelCase     :		tf.Tensor							,		UpperCamelCase     :		int							,		UpperCamelCase     :		str = "input_ids"     )     ->						None:
    tf.debugging.assert_less(
        UpperCamelCase							,		tf.cast(UpperCamelCase							,		dtype=tensor.dtype     )							,		message=(
            f'The maximum value of {tensor_name} ({tf.math.reduce_max(UpperCamelCase     )}) must be smaller than the embedding '
            f'layer\'s input dimension ({embed_dim}). The likely cause is some problem at tokenization time.'
        )							,		)



def     __magic_name__		(					UpperCamelCase     :		Optional[int]							,		UpperCamelCase     :		Tuple							,		UpperCamelCase     :		Union[str, Any]     )     ->						List[str]:
    a__		=			64512
    # Check that no item in `data` is larger than `HDF5_OBJECT_HEADER_LIMIT`
    # because in that case even chunking the array would not make the saving
    # possible.
    a__		=			[x for x in data if len(UpperCamelCase     ) > HDF5_OBJECT_HEADER_LIMIT]

    # Expecting this to never be true.
    if bad_attributes:
        raise RuntimeError(
            'The following attributes cannot be saved to HDF5 file because '
            f'they are larger than {HDF5_OBJECT_HEADER_LIMIT} '
            f'bytes: {bad_attributes}'     )

    a__		=			np.asarray(UpperCamelCase     )

    a__		=			1
    a__		=			np.array_split(UpperCamelCase							,		UpperCamelCase     )

    # This will never loop forever thanks to the test above.
    while any(x.nbytes > HDF5_OBJECT_HEADER_LIMIT for x in chunked_data     ):
        num_chunks += 1
        a__		=			np.array_split(UpperCamelCase							,		UpperCamelCase     )

    if num_chunks > 1:
        for chunk_id, chunk_data in enumerate(UpperCamelCase     ):
            a__		=			chunk_data
    else:
        a__		=			data



def     __magic_name__		(					UpperCamelCase     :		Tuple							,		UpperCamelCase     :		Tuple     )     ->						List[Any]:
    if name in group.attrs:
        a__		=			[n.decode('utf8'     ) if hasattr(UpperCamelCase							,		'decode'     ) else n for n in group.attrs[name]]
    else:
        a__		=			[]
        a__		=			0
        while "%s%d" % (name, chunk_id) in group.attrs:
            data.extend(
                [n.decode('utf8'     ) if hasattr(UpperCamelCase							,		'decode'     ) else n for n in group.attrs['%s%d' % (name, chunk_id)]]     )
            chunk_id += 1
    return data



def     __magic_name__		(					UpperCamelCase     :		Optional[Any]     )     ->						Any:

    def _expand_single_ad_tensor(UpperCamelCase     :		int     ):
        if isinstance(UpperCamelCase							,		tf.Tensor     ) and t.shape.rank == 1:
            return tf.expand_dims(UpperCamelCase							,		axis=-1     )
        return t

    return tf.nest.map_structure(_expand_single_ad_tensor							,		UpperCamelCase     )




"""simple docstring"""




from itertools import product



def     __magic_name__		(					UpperCamelCase     :		int							,		UpperCamelCase     :		int     )     ->						list[int]:
    a__		=			sides_number
    a__		=			max_face_number * dice_number
    a__		=			[0] * (max_total + 1)

    a__		=			1
    a__		=			range(UpperCamelCase							,		max_face_number + 1     )
    for dice_numbers in product(UpperCamelCase							,		repeat=UpperCamelCase     ):
        a__		=			sum(UpperCamelCase     )
        totals_frequencies[total] += 1

    return totals_frequencies



def     __magic_name__		(					)     ->						float:
    a__		=			total_frequency_distribution(
        sides_number=4							,		dice_number=9     )
    a__		=			total_frequency_distribution(
        sides_number=6							,		dice_number=6     )

    a__		=			0
    a__		=			9
    a__		=			4 * 9
    a__		=			6
    for peter_total in range(UpperCamelCase							,		max_peter_total + 1     ):
        peter_wins_count += peter_totals_frequencies[peter_total] * sum(
            colin_totals_frequencies[min_colin_total:peter_total]     )

    a__		=			(4**9) * (6**6)
    a__		=			peter_wins_count / total_games_number

    a__		=			round(UpperCamelCase							,		ndigits=7     )

    return rounded_peter_win_probability


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


