






'''simple docstring'''


from collections import OrderedDict
from typing import Any, Mapping, Optional

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


lowerCamelCase_				: Any    	=							logging.get_logger(__name__)

lowerCamelCase_				: int    	=							{
    '''Helsinki-NLP/opus-mt-en-de''': '''https://huggingface.co/Helsinki-NLP/opus-mt-en-de/resolve/main/config.json''',
    # See all Marian models at https://huggingface.co/models?filter=marian
}
class    _SCREAMING_SNAKE_CASE							(		SCREAMING_SNAKE_CASE	):


			'''simple docstring'''





			__a							:							int					     =					"marian"
			__a							:							Optional[Any]					     =					["past_key_values"]
			__a							:							List[Any]					     =					{"num_attention_heads": "encoder_attention_heads", "hidden_size": "d_model"}






			def __init__(   self							:						int ,      lowercase							:						Optional[Any]=5_8_1_0_1 ,      lowercase							:						int=None ,      lowercase							:						Optional[int]=1_0_2_4 ,      lowercase							:						Dict=1_2 ,      lowercase							:						List[str]=4_0_9_6 ,      lowercase							:						Dict=1_6 ,      lowercase							:						List[Any]=1_2 ,      lowercase							:						List[Any]=4_0_9_6 ,      lowercase							:						Any=1_6 ,      lowercase							:						List[str]=0.0 ,      lowercase							:						Optional[Any]=0.0 ,      lowercase							:						List[Any]=True ,      lowercase							:						Optional[Any]=True ,      lowercase							:						int="gelu" ,      lowercase							:						int=1_0_2_4 ,      lowercase							:						List[str]=0.1 ,      lowercase							:						Union[str, Any]=0.0 ,      lowercase							:						Optional[int]=0.0 ,      lowercase							:						int=0.0_2 ,      lowercase							:						Dict=5_8_1_0_0 ,      lowercase							:						Tuple=False ,      lowercase							:						List[str]=5_8_1_0_0 ,      lowercase							:						Optional[int]=0 ,      lowercase							:						List[str]=0 ,      lowercase							:						Any=True ,      **lowercase							:						Dict ,      )							->    Union[str, Any]:

									'''simple docstring'''







									UpperCamelCase__         = vocab_size
									UpperCamelCase__         = decoder_vocab_size or vocab_size
									UpperCamelCase__         = max_position_embeddings
									UpperCamelCase__         = d_model
									UpperCamelCase__         = encoder_ffn_dim
									UpperCamelCase__         = encoder_layers
									UpperCamelCase__         = encoder_attention_heads
									UpperCamelCase__         = decoder_ffn_dim
									UpperCamelCase__         = decoder_layers
									UpperCamelCase__         = decoder_attention_heads
									UpperCamelCase__         = dropout
									UpperCamelCase__         = attention_dropout
									UpperCamelCase__         = activation_dropout
									UpperCamelCase__         = activation_function
									UpperCamelCase__         = init_std
									UpperCamelCase__         = encoder_layerdrop
									UpperCamelCase__         = decoder_layerdrop
									UpperCamelCase__         = use_cache
									UpperCamelCase__         = encoder_layers
									UpperCamelCase__         = scale_embedding  # scale factor will be sqrt(d_model) if True
									UpperCamelCase__         = share_encoder_decoder_embeddings
									super().__init__(
									    pad_token_id=lowercase ,      eos_token_id=lowercase ,      is_encoder_decoder=lowercase ,      decoder_start_token_id=lowercase ,      forced_eos_token_id=lowercase ,      **lowercase ,      )
class    _SCREAMING_SNAKE_CASE							(		SCREAMING_SNAKE_CASE	):


			'''simple docstring'''





			@property
			# Copied from transformers.models.bart.configuration_bart.BartOnnxConfig.inputs
			def 				A      (   self							:						Any			)							->    Mapping[str, Mapping[int, str]]:

									'''simple docstring'''







									if self.task in ["default", "seq2seq-lm"]:
															UpperCamelCase__         = OrderedDict(
															    [
															        ("""input_ids""", {0: """batch""", 1: """encoder_sequence"""}),
															        ("""attention_mask""", {0: """batch""", 1: """encoder_sequence"""}),
															    ]			)

															if self.use_past:
																					UpperCamelCase__         = {0: """batch"""}
																					UpperCamelCase__         = {0: """batch""", 1: """past_decoder_sequence + sequence"""}
															else:
																					UpperCamelCase__         = {0: """batch""", 1: """decoder_sequence"""}
																					UpperCamelCase__         = {0: """batch""", 1: """decoder_sequence"""}

															if self.use_past:
																					self.fill_with_past_key_values_(lowercase ,      direction="""inputs"""			)
									elif self.task == "causal-lm":
															# TODO: figure this case out.
															UpperCamelCase__         = OrderedDict(
															    [
															        ("""input_ids""", {0: """batch""", 1: """encoder_sequence"""}),
															        ("""attention_mask""", {0: """batch""", 1: """encoder_sequence"""}),
															    ]			)
															if self.use_past:
																					UpperCamelCase__    ,   UpperCamelCase__         = self.num_layers
																					for i in range(lowercase			):
																											UpperCamelCase__         = {0: """batch""", 2: """past_sequence + sequence"""}
																											UpperCamelCase__         = {0: """batch""", 2: """past_sequence + sequence"""}
									else:
															UpperCamelCase__         = OrderedDict(
															    [
															        ("""input_ids""", {0: """batch""", 1: """encoder_sequence"""}),
															        ("""attention_mask""", {0: """batch""", 1: """encoder_sequence"""}),
															        ("""decoder_input_ids""", {0: """batch""", 1: """decoder_sequence"""}),
															        ("""decoder_attention_mask""", {0: """batch""", 1: """decoder_sequence"""}),
															    ]			)

									return common_inputs






			@property
			# Copied from transformers.models.bart.configuration_bart.BartOnnxConfig.outputs
			def 				A      (   self							:						Tuple			)							->    Mapping[str, Mapping[int, str]]:

									'''simple docstring'''







									if self.task in ["default", "seq2seq-lm"]:
															UpperCamelCase__         = super().outputs
									else:
															UpperCamelCase__         = super(lowercase ,      self			).outputs
															if self.use_past:
																					UpperCamelCase__    ,   UpperCamelCase__         = self.num_layers
																					for i in range(lowercase			):
																											UpperCamelCase__         = {0: """batch""", 2: """past_sequence + sequence"""}
																											UpperCamelCase__         = {0: """batch""", 2: """past_sequence + sequence"""}
									return common_outputs






			def 				A      (   self							:						Union[str, Any] ,      lowercase							:						PreTrainedTokenizer ,      lowercase							:						int = -1 ,      lowercase							:						int = -1 ,      lowercase							:						bool = False ,      lowercase							:						Optional[TensorType] = None ,      )							->    Mapping[str, Any]:

									'''simple docstring'''







									UpperCamelCase__         = self._generate_dummy_inputs_for_encoder_and_decoder(
									    lowercase ,      lowercase ,      lowercase ,      lowercase ,      lowercase			)

									# Generate decoder inputs
									UpperCamelCase__         = seq_length if not self.use_past else 1
									UpperCamelCase__         = self._generate_dummy_inputs_for_encoder_and_decoder(
									    lowercase ,      lowercase ,      lowercase ,      lowercase ,      lowercase			)
									UpperCamelCase__         = {f"decoder_{name}": tensor for name, tensor in decoder_inputs.items()}
									UpperCamelCase__         = dict(**lowercase ,      **lowercase			)

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

															UpperCamelCase__         = torch.cat(
															    [common_inputs["""decoder_attention_mask"""], torch.ones(lowercase ,      lowercase			)] ,      dim=1			)

															UpperCamelCase__         = []
															# If the number of encoder and decoder layers are present in the model configuration, both are considered
															UpperCamelCase__    ,   UpperCamelCase__         = self.num_layers
															UpperCamelCase__         = min(lowercase ,      lowercase			)
															UpperCamelCase__         = max(lowercase ,      lowercase			) - min_num_layers
															UpperCamelCase__         = """encoder""" if num_encoder_layers > num_decoder_layers else """decoder"""

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






			def 				A      (   self							:						Dict ,      lowercase							:						PreTrainedTokenizer ,      lowercase							:						int = -1 ,      lowercase							:						int = -1 ,      lowercase							:						bool = False ,      lowercase							:						Optional[TensorType] = None ,      )							->    Mapping[str, Any]:

									'''simple docstring'''







									UpperCamelCase__         = self._generate_dummy_inputs_for_encoder_and_decoder(
									    lowercase ,      lowercase ,      lowercase ,      lowercase ,      lowercase			)

									if self.use_past:
															if not is_torch_available():
																					raise ValueError("""Cannot generate dummy past_keys inputs without PyTorch installed."""			)
															else:
																					import torch
															UpperCamelCase__    ,   UpperCamelCase__         = common_inputs["""input_ids"""].shape
															# Not using the same length for past_key_values
															UpperCamelCase__         = seqlen + 2
															UpperCamelCase__    ,   UpperCamelCase__         = self.num_layers
															UpperCamelCase__    ,   UpperCamelCase__         = self.num_attention_heads
															UpperCamelCase__         = (
															    batch,
															    num_encoder_attention_heads,
															    past_key_values_length,
															    self._config.hidden_size // num_encoder_attention_heads,
															)

															UpperCamelCase__         = common_inputs["""attention_mask"""].dtype
															UpperCamelCase__         = torch.cat(
															    [common_inputs["""attention_mask"""], torch.ones(lowercase ,      lowercase ,      dtype=lowercase			)] ,      dim=1			)
															UpperCamelCase__         = [
															    (torch.zeros(lowercase			), torch.zeros(lowercase			)) for _ in range(lowercase			)
															]
									return common_inputs






			def 				A      (   self							:						Union[str, Any] ,      lowercase							:						PreTrainedTokenizer ,      lowercase							:						int = -1 ,      lowercase							:						int = -1 ,      lowercase							:						bool = False ,      lowercase							:						Optional[TensorType] = None ,      )							->    Mapping[str, Any]:

									'''simple docstring'''







									UpperCamelCase__         = compute_effective_axis_dimension(
									    lowercase ,      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
									UpperCamelCase__         = tokenizer.num_special_tokens_to_add(lowercase			)
									UpperCamelCase__         = compute_effective_axis_dimension(
									    lowercase ,      fixed_dimension=OnnxConfig.default_fixed_sequence ,      num_token_to_add=lowercase			)

									# Generate dummy inputs according to compute batch and sequence
									UpperCamelCase__         = [""" """.join([tokenizer.unk_token]			) * seq_length] * batch_size
									UpperCamelCase__         = dict(tokenizer(lowercase ,      return_tensors=lowercase			)			)
									return common_inputs






			def 				A      (   self							:						Optional[Any] ,      lowercase							:						PreTrainedTokenizer ,      lowercase							:						int = -1 ,      lowercase							:						int = -1 ,      lowercase							:						bool = False ,      lowercase							:						Optional[TensorType] = None ,      )							->    Mapping[str, Any]:

									'''simple docstring'''







									if self.task in ["default", "seq2seq-lm"]:
															UpperCamelCase__         = self._generate_dummy_inputs_for_default_and_seqaseq_lm(
															    lowercase ,      batch_size=lowercase ,      seq_length=lowercase ,      is_pair=lowercase ,      framework=lowercase			)

									else:
															UpperCamelCase__         = self._generate_dummy_inputs_for_causal_lm(
															    lowercase ,      batch_size=lowercase ,      seq_length=lowercase ,      is_pair=lowercase ,      framework=lowercase			)

									return common_inputs






			def 				A      (   self							:						int ,      lowercase							:						Union[str, Any] ,      lowercase							:						Union[str, Any] ,      lowercase							:						Optional[int] ,      lowercase							:						Tuple			)							->    Union[str, Any]:

									'''simple docstring'''







									if self.task in ["default", "seq2seq-lm"]:
															UpperCamelCase__         = super()._flatten_past_key_values_(lowercase ,      lowercase ,      lowercase ,      lowercase			)
									else:
															UpperCamelCase__         = super(lowercase ,      self			)._flatten_past_key_values_(
															    lowercase ,      lowercase ,      lowercase ,      lowercase			)







			@property
			def 				A      (   self							:						Optional[int]			)							->    float:

									'''simple docstring'''







									return 1e-4








'''simple docstring'''


from collections import defaultdict







def 	__magic_name__( _A					):
						'''simple docstring'''





						UpperCamelCase__         = 1
						UpperCamelCase__         = True
						for v in tree[start]:
												if v not in visited:
																		ret += dfs(_A					)
						if ret % 2 == 0:
												cuts.append(_A					)
						return ret







def 	__magic_name__( ):
						'''simple docstring'''





						dfs(1					)


if __name__ == "__main__":
					lowerCamelCase_	,     lowerCamelCase_				: int    	=							10, 9
					lowerCamelCase_				: int    	=							defaultdict(list)
					lowerCamelCase_				: dict[int, bool]    	=							{}
					lowerCamelCase_				: list[int]    	=							[]
					lowerCamelCase_				: Union[str, Any]    	=							0
					lowerCamelCase_				: Tuple    	=							[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (10, 8)]
					for u, v in edges:
										tree[u].append(v)
										tree[v].append(u)
					even_tree()
					print(len(cuts) - 1)
