






'''simple docstring'''
class     _UpperCAmelCase  :




    def __init__(     self					:    Tuple					,       a					:    Union[str, Any]     ):






       '''simple docstring'''






       lowercase_		:      Optional[int]          =       val
       # Number of nodes in left subtree
       lowercase_		:      int          =       0
       lowercase_		:      List[Any]          =       None
       lowercase_		:      Union[str, Any]          =       None
       lowercase_		:      Optional[Any]          =       None





    def 			lowerCAmelCase__			(     self					:    Optional[int]					,       a					:    Optional[Any]     ):






       '''simple docstring'''






       assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

       if self.val < other.val:
          lowercase_		:      Tuple          =       self.right
          lowercase_		:      Optional[Any]          =       None
          if self.right:
             lowercase_		:      str          =       other
          lowercase_		:      Any          =       other
          lowercase_		:      List[Any]          =       self.left_tree_size * 2 + 1
          return self
       else:
          lowercase_		:      List[Any]          =       other.right
          lowercase_		:      Optional[int]          =       None
          if other.right:
             lowercase_		:      List[Any]          =       self
          lowercase_		:      Optional[Any]          =       self
          lowercase_		:      Dict          =       other.left_tree_size * 2 + 1
          return other


class     _UpperCAmelCase  :




    def __init__(     self					:    Optional[Any]					,       a					:    int=None					,       a					:    Union[str, Any]=None					,       a					:    int=0     ):






       '''simple docstring'''






       lowercase_		:      Optional[int]          =       heap_size
       lowercase_		:      List[str]          =       bottom_root
       lowercase_		:      List[str]          =       min_node




    def 			lowerCAmelCase__			(     self					:    str					,       a					:    Dict     ):






       '''simple docstring'''






       if other.size == 0:
          return None
       if self.size == 0:
          lowercase_		:      Dict          =       other.size
          lowercase_		:      List[Any]          =       other.bottom_root
          lowercase_		:      Dict          =       other.min_node
          return None
       # Update size
       lowercase_		:      Dict          =       self.size + other.size

       # Update min.node
       if self.min_node.val > other.min_node.val:
          lowercase_		:      Optional[Any]          =       other.min_node
       # Merge

       # Order roots by left_subtree_size
       lowercase_		:      List[Any]          =       []
       lowercase_      ,						lowercase_		:      Any          =       self.bottom_root, other.bottom_root
       while i or j:
          if i and ((not j) or i.left_tree_size < j.left_tree_size):
             combined_roots_list.append((i, True)     )
             lowercase_		:      Optional[int]          =       i.parent
          else:
             combined_roots_list.append((j, False)     )
             lowercase_		:      int          =       j.parent
        # Insert links between them
       for i in range(len(__lowerCAmelCase     ) - 1     ):
          if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
             lowercase_		:      Dict          =       combined_roots_list[i + 1][0]
             lowercase_		:      str          =       combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
       lowercase_		:      Optional[Any]          =       combined_roots_list[0][0]
       while i.parent:
          if (
              (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
          ) or (
              i.left_tree_size == i.parent.left_tree_size
              and i.left_tree_size != i.parent.parent.left_tree_size
          ):
             # Neighbouring Nodes
             lowercase_		:      Dict          =       i.left
             lowercase_		:      Optional[Any]          =       i.parent.parent

             # Merging trees
             lowercase_		:      Union[str, Any]          =       i.merge_trees(i.parent     )

             # Updating links
             lowercase_		:      List[str]          =       previous_node
             lowercase_		:      Union[str, Any]          =       next_node
             if previous_node:
                lowercase_		:      Union[str, Any]          =       i
             if next_node:
                lowercase_		:      Optional[Any]          =       i
          else:
             lowercase_		:      Union[str, Any]          =       i.parent
        # Updating self.bottom_root
       while i.left:
          lowercase_		:      Tuple          =       i.left
       lowercase_		:      Optional[int]          =       i

       # Update other
       lowercase_		:      Any          =       self.size
       lowercase_		:      List[str]          =       self.bottom_root
       lowercase_		:      List[str]          =       self.min_node

       # Return the merged heap
       return self




    def 			lowerCAmelCase__			(     self					:    Tuple					,       a					:    List[Any]     ):






       '''simple docstring'''






       if self.size == 0:
          lowercase_		:      List[str]          =       Node(__lowerCAmelCase     )
          lowercase_		:      List[str]          =       1
          lowercase_		:      Any          =       self.bottom_root
       else:
          # Create new node
          lowercase_		:      Tuple          =       Node(__lowerCAmelCase     )

          # Update size
          self.size += 1

          # update min_node
          if val < self.min_node.val:
             lowercase_		:      Optional[int]          =       new_node
          # Put new_node as a bottom_root in heap
          lowercase_		:      Dict          =       new_node
          lowercase_		:      int          =       self.bottom_root
          lowercase_		:      Any          =       new_node

          # Consecutively merge roots with same left_tree_size
          while (
              self.bottom_root.parent
              and self.bottom_root.left_tree_size
              == self.bottom_root.parent.left_tree_size
          ):
             # Next node
             lowercase_		:      List[Any]          =       self.bottom_root.parent.parent

             # Merge
             lowercase_		:      List[str]          =       self.bottom_root.merge_trees(self.bottom_root.parent     )

             # Update Links
             lowercase_		:      Optional[Any]          =       next_node
             lowercase_		:      List[str]          =       None
             if next_node:
                lowercase_		:      Optional[int]          =       self.bottom_root




    def 			lowerCAmelCase__			(     self					:    Dict     ):






       '''simple docstring'''






       return self.min_node.val




    def 			lowerCAmelCase__			(     self					:    Any     ):






       '''simple docstring'''






       return self.size == 0




    def 			lowerCAmelCase__			(     self					:    List[str]     ):






       '''simple docstring'''






       lowercase_		:      List[str]          =       self.min_node.val

       # Last element in heap corner case
       if self.size == 1:
          # Update size
          lowercase_		:      Union[str, Any]          =       0

          # Update bottom root
          lowercase_		:      str          =       None

          # Update min_node
          lowercase_		:      int          =       None

          return min_value
       # No right subtree corner case
       # The structure of the tree implies that this should be the bottom root
       # and there is at least one other root
       if self.min_node.right is None:
          # Update size
          self.size -= 1

          # Update bottom root
          lowercase_		:      Dict          =       self.bottom_root.parent
          lowercase_		:      Optional[int]          =       None

          # Update min_node
          lowercase_		:      Union[str, Any]          =       self.bottom_root
          lowercase_		:      Optional[int]          =       self.bottom_root.parent
          while i:
             if i.val < self.min_node.val:
                lowercase_		:      int          =       i
             lowercase_		:      Tuple          =       i.parent
          return min_value
       # General case
       # Find the BinomialHeap of the right subtree of min_node
       lowercase_		:      Union[str, Any]          =       self.min_node.right
       lowercase_		:      Dict          =       None
       lowercase_		:      Union[str, Any]          =       bottom_of_new
       lowercase_		:      str          =       1

       # Size, min_node and bottom_root
       while bottom_of_new.left:
          lowercase_		:      str          =       size_of_new * 2 + 1
          lowercase_		:      Optional[Any]          =       bottom_of_new.left
          if bottom_of_new.val < min_of_new.val:
             lowercase_		:      Tuple          =       bottom_of_new
        # Corner case of single root on top left path
       if (not self.min_node.left) and (not self.min_node.parent):
          lowercase_		:      Optional[Any]          =       size_of_new
          lowercase_		:      Any          =       bottom_of_new
          lowercase_		:      Optional[int]          =       min_of_new
          # print("Single root, multiple nodes case")
          return min_value
       # Remaining cases
       # Construct heap of right subtree
       lowercase_		:      Optional[Any]          =       BinomialHeap(
           bottom_root=__lowerCAmelCase					,       min_node=__lowerCAmelCase					,       heap_size=__lowerCAmelCase     )

       # Update size
       lowercase_		:      str          =       self.size - 1 - size_of_new

       # Neighbour nodes
       lowercase_		:      str          =       self.min_node.left
       lowercase_		:      List[Any]          =       self.min_node.parent

       # Initialize new bottom_root and min_node
       lowercase_		:      Dict          =       previous_node or next_node
       lowercase_		:      Tuple          =       next_node

       # Update links of previous_node and search below for new min_node and
       # bottom_root
       if previous_node:
          lowercase_		:      List[str]          =       next_node

          # Update bottom_root and search for min_node below
          lowercase_		:      List[Any]          =       previous_node
          lowercase_		:      Union[str, Any]          =       previous_node
          while self.bottom_root.left:
             lowercase_		:      Optional[Any]          =       self.bottom_root.left
             if self.bottom_root.val < self.min_node.val:
                lowercase_		:      List[Any]          =       self.bottom_root
       if next_node:
          lowercase_		:      Union[str, Any]          =       previous_node

          # Search for new min_node above min_node
          lowercase_		:      Optional[int]          =       next_node
          while i:
             if i.val < self.min_node.val:
                lowercase_		:      Optional[Any]          =       i
             lowercase_		:      Optional[int]          =       i.parent
        # Merge heaps
       self.merge_heaps(__lowerCAmelCase     )

       return min_value




    def 			lowerCAmelCase__			(     self					:    Tuple     ):






       '''simple docstring'''






       lowercase_		:      Dict          =       self.bottom_root
       while top_root.parent:
          lowercase_		:      int          =       top_root.parent
       # preorder
       lowercase_		:      Dict          =       []
       self.__traversal(__lowerCAmelCase					,       __lowerCAmelCase     )
       return heap_pre_order




    def 			lowerCAmelCase__			(     self					:    Dict					,       a					:    int					,       a					:    Union[str, Any]					,       a					:    List[str]=0     ):






       '''simple docstring'''






       if curr_node:
          preorder.append((curr_node.val, level)     )
          self.__traversal(curr_node.left					,       __lowerCAmelCase					,       level + 1     )
          self.__traversal(curr_node.right					,       __lowerCAmelCase					,       level + 1     )
       else:
          preorder.append(("#", level)     )





    def __str__(     self					:    Any     ):






       '''simple docstring'''






       if self.is_empty():
          return ""
       lowercase_		:      Optional[int]          =       self.pre_order()

       return "\n".join(("-" * level + str(__lowerCAmelCase     )) for value, level in preorder_heap     )


# Unit Tests
if __name__ == "__main__":
 import doctest

 doctest.testmod()












'''simple docstring'''
from collections import OrderedDict
from typing import Any, Mapping, Optional

from ... import PreTrainedTokenizer
from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig, OnnxSeqaSeqConfigWithPast
from ...onnx.utils import compute_effective_axis_dimension
from ...utils import TensorType, is_torch_available, logging


UpperCamelCase__	=     logging.get_logger(__name__)

UpperCamelCase__	=     {
    'facebook/m2m100_418M': 'https://huggingface.co/facebook/m2m100_418M/resolve/main/config.json',
    # See all M2M100 models at https://huggingface.co/models?filter=m2m_100
}


class     _UpperCAmelCase  (						snake_case     ):
    __lowerCamelCase:				List[Any]						    =      'm2m_100'
    __lowerCamelCase:				Union[str, Any]						    =      ['past_key_values']
    __lowerCamelCase:				Union[str, Any]						    =      {'num_attention_heads': 'encoder_attention_heads', 'hidden_size': 'd_model'}




    def __init__(     self					:    str					,       a					:    Optional[Any]=1_2_8_1_1_2					,       a					:    Optional[int]=1_0_2_4					,       a					:    Any=1_2					,       a					:    Tuple=4_0_9_6					,       a					:    Any=1_6					,       a					:    Any=1_2					,       a					:    Dict=4_0_9_6					,       a					:    List[str]=1_6					,       a					:    List[Any]=0.05					,       a					:    Optional[int]=0.05					,       a					:    List[Any]=True					,       a					:    List[Any]=True					,       a					:    Union[str, Any]="relu"					,       a					:    Optional[Any]=1_0_2_4					,       a					:    List[str]=0.1					,       a					:    Union[str, Any]=0.1					,       a					:    int=0.0					,       a					:    List[str]=0.02					,       a					:    Optional[int]=2					,       a					:    Tuple=True					,       a					:    List[str]=1					,       a					:    int=0					,       a					:    int=2					,       **a					:    Tuple					,       ):






       '''simple docstring'''






       lowercase_		:      List[str]          =       vocab_size
       lowercase_		:      Tuple          =       max_position_embeddings
       lowercase_		:      int          =       d_model
       lowercase_		:      Optional[int]          =       encoder_ffn_dim
       lowercase_		:      Any          =       encoder_layers
       lowercase_		:      Optional[Any]          =       encoder_attention_heads
       lowercase_		:      List[Any]          =       decoder_ffn_dim
       lowercase_		:      Union[str, Any]          =       decoder_layers
       lowercase_		:      Optional[Any]          =       decoder_attention_heads
       lowercase_		:      Optional[int]          =       dropout
       lowercase_		:      Optional[Any]          =       attention_dropout
       lowercase_		:      Optional[int]          =       activation_dropout
       lowercase_		:      Any          =       activation_function
       lowercase_		:      Optional[Any]          =       init_std
       lowercase_		:      Tuple          =       encoder_layerdrop
       lowercase_		:      Optional[Any]          =       decoder_layerdrop
       lowercase_		:      List[Any]          =       use_cache
       lowercase_		:      Dict          =       encoder_layers
       lowercase_		:      Tuple          =       scale_embedding  # scale factor will be sqrt(d_model) if True

       super().__init__(
           pad_token_id=a					,       bos_token_id=a					,       eos_token_id=a					,       is_encoder_decoder=a					,       decoder_start_token_id=a					,       **a					,       )


class     _UpperCAmelCase  (						snake_case     ):




    @property
    def 			lowerCAmelCase__			(     self					:    Optional[Any]     ):






       '''simple docstring'''






       lowercase_		:      List[Any]          =       OrderedDict(
           [
               ("input_ids", {0: "batch", 1: "encoder_sequence"}),
               ("attention_mask", {0: "batch", 1: "encoder_sequence"}),
           ]     )

       if self.use_past:
          lowercase_		:      Optional[int]          =       {0: "batch"}
          lowercase_		:      str          =       {0: "batch", 1: "past_decoder_sequence + sequence"}
       else:
          lowercase_		:      Optional[Any]          =       {0: "batch", 1: "decoder_sequence"}
          lowercase_		:      Union[str, Any]          =       {0: "batch", 1: "decoder_sequence"}

       if self.use_past:
          self.fill_with_past_key_values_(a					,       direction="inputs"     )
       return common_inputs




    def 			lowerCAmelCase__			(     self					:    Dict					,       a					:    PreTrainedTokenizer					,       a					:    int = -1					,       a					:    int = -1					,       a					:    bool = False					,       a					:    Optional[TensorType] = None					,       ):






       '''simple docstring'''






       lowercase_		:      int          =       compute_effective_axis_dimension(
           a					,       fixed_dimension=OnnxConfig.default_fixed_batch					,       num_token_to_add=0     )

       # If dynamic axis (-1) we forward with a fixed dimension of 8 tokens to avoid optimizations made by ONNX
       lowercase_		:      Dict          =       tokenizer.num_special_tokens_to_add(a     )
       lowercase_		:      str          =       compute_effective_axis_dimension(
           a					,       fixed_dimension=OnnxConfig.default_fixed_sequence					,       num_token_to_add=a     )

       # Generate dummy inputs according to compute batch and sequence
       lowercase_		:      Union[str, Any]          =       [" ".join([tokenizer.unk_token]     ) * seq_length] * batch_size
       lowercase_		:      Tuple          =       dict(tokenizer(a					,       return_tensors=a     )     )
       return common_inputs




    def 			lowerCAmelCase__			(     self					:    Any					,       a					:    PreTrainedTokenizer					,       a					:    int = -1					,       a					:    int = -1					,       a					:    bool = False					,       a					:    Optional[TensorType] = None					,       ):






       '''simple docstring'''






       lowercase_		:      Optional[Any]          =       self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
           a					,       a					,       a					,       a					,       a     )

       # Generate decoder inputs
       lowercase_		:      List[str]          =       seq_length if not self.use_past else 1
       lowercase_		:      Dict          =       self._generate_dummy_inputs_for_sequence_classification_and_question_answering(
           a					,       a					,       a					,       a					,       a     )
       lowercase_		:      Union[str, Any]          =       {f"""decoder_{name}""": tensor for name, tensor in decoder_inputs.items()}
       lowercase_		:      Union[str, Any]          =       dict(**a					,       **a     )

       if self.use_past:
          if not is_torch_available():
             raise ValueError("Cannot generate dummy past_keys inputs without PyTorch installed."     )
          else:
             import torch
          lowercase_      ,						lowercase_		:      Union[str, Any]          =       common_inputs["input_ids"].shape
          lowercase_		:      List[Any]          =       common_inputs["decoder_input_ids"].shape[1]
          lowercase_      ,						lowercase_		:      Optional[Any]          =       self.num_attention_heads
          lowercase_		:      Any          =       (
              batch,
              num_encoder_attention_heads,
              encoder_seq_length,
              self._config.hidden_size // num_encoder_attention_heads,
          )
          lowercase_		:      Optional[Any]          =       decoder_seq_length + 3
          lowercase_		:      int          =       (
              batch,
              num_decoder_attention_heads,
              decoder_past_length,
              self._config.hidden_size // num_decoder_attention_heads,
          )

          lowercase_		:      Dict          =       torch.cat(
              [common_inputs["decoder_attention_mask"], torch.ones(a					,       a     )]					,       dim=1     )

          lowercase_		:      Tuple          =       []
          # If the number of encoder and decoder layers are present in the model configuration, both are considered
          lowercase_      ,						lowercase_		:      Tuple          =       self.num_layers
          lowercase_		:      Optional[Any]          =       min(a					,       a     )
          lowercase_		:      Tuple          =       max(a					,       a     ) - min_num_layers
          lowercase_		:      Optional[int]          =       "encoder" if num_encoder_layers > num_decoder_layers else "decoder"

          for _ in range(a     ):
             common_inputs["past_key_values"].append(
                 (
                     torch.zeros(a     ),
                     torch.zeros(a     ),
                     torch.zeros(a     ),
                     torch.zeros(a     ),
                 )     )
          # TODO: test this.
          lowercase_		:      Union[str, Any]          =       encoder_shape if remaining_side_name == "encoder" else decoder_shape
          for _ in range(a					,       a     ):
             common_inputs["past_key_values"].append((torch.zeros(a     ), torch.zeros(a     ))     )
       return common_inputs





    __lowerCamelCase:				str						    =      _generate_dummy_inputs_for_default_and_seqaseq_lm




