






'''simple docstring'''


import math
import time
from typing import Dict, List, Optional

from torch.utils.data import Dataset

from transformers import SeqaSeqTrainer, is_torch_tpu_available
from transformers.trainer_utils import PredictionOutput, speed_metrics


if is_torch_tpu_available(check_device=False):
					import torch_xla.core.xla_model as xm
					import torch_xla.debug.metrics as met
class    _SCREAMING_SNAKE_CASE							(		SCREAMING_SNAKE_CASE	):


			'''simple docstring'''





			def __init__(   self							:						Dict ,      *lowercase							:						Optional[int] ,      lowercase							:						Tuple=None ,      lowercase							:						Tuple=None ,      **lowercase							:						Optional[Any]			)							->    Optional[int]:

									'''simple docstring'''







									super().__init__(*lowercase ,      **lowercase			)
									UpperCamelCase__         = eval_examples
									UpperCamelCase__         = post_process_function






			def 				A      (   self							:						int ,      lowercase							:						Optional[Dataset] = None ,      lowercase							:						Union[str, Any]=None ,      lowercase							:						Optional[List[str]] = None ,      lowercase							:						str = "eval" ,      **lowercase							:						Optional[int] ,      )							->    Dict[str, float]:

									'''simple docstring'''







									UpperCamelCase__         = gen_kwargs.copy()
									UpperCamelCase__         = (
									    gen_kwargs["""max_length"""] if gen_kwargs.get("""max_length"""			) is not None else self.args.generation_max_length
									)
									UpperCamelCase__         = (
									    gen_kwargs["""num_beams"""] if gen_kwargs.get("""num_beams"""			) is not None else self.args.generation_num_beams
									)
									UpperCamelCase__         = gen_kwargs

									UpperCamelCase__         = self.eval_dataset if eval_dataset is None else eval_dataset
									UpperCamelCase__         = self.get_eval_dataloader(lowercase			)
									UpperCamelCase__         = self.eval_examples if eval_examples is None else eval_examples

									# Temporarily disable metric computation, we will do it in the loop here.
									UpperCamelCase__         = self.compute_metrics
									UpperCamelCase__         = None
									UpperCamelCase__         = time.time()
									UpperCamelCase__         = self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
									try:
															UpperCamelCase__         = eval_loop(
															    lowercase ,      description="""Evaluation""" ,      prediction_loss_only=True if compute_metrics is None else None ,      ignore_keys=lowercase ,      metric_key_prefix=lowercase ,      )
									finally:
															UpperCamelCase__         = compute_metrics
									UpperCamelCase__         = self.args.eval_batch_size * self.args.world_size
									if f"{metric_key_prefix}_jit_compilation_time" in output.metrics:
															start_time += output.metrics[f"{metric_key_prefix}_jit_compilation_time"]
									output.metrics.update(
									    speed_metrics(
									        lowercase ,      lowercase ,      num_samples=output.num_samples ,      num_steps=math.ceil(output.num_samples / total_batch_size			) ,      )			)

									if self.post_process_function is not None and self.compute_metrics is not None and self.args.should_save:
															# Only the main node write the results by default
															UpperCamelCase__         = self.post_process_function(lowercase ,      lowercase ,      lowercase			)
															UpperCamelCase__         = self.compute_metrics(lowercase			)

															# Prefix all keys with metric_key_prefix + '_'
															for key in list(metrics.keys()			):
																					if not key.startswith(f"{metric_key_prefix}_"			):
																											UpperCamelCase__         = metrics.pop(lowercase			)

															metrics.update(output.metrics			)
									else:
															UpperCamelCase__         = output.metrics

									if self.args.should_log:
															# Only the main node log the results by default
															self.log(lowercase			)

									if self.args.tpu_metrics_debug or self.args.debug:
															# tpu-comment: Logging debug metrics for PyTorch/XLA (compile, execute times, ops, etc.)
															xm.master_print(met.metrics_report()			)

									UpperCamelCase__         = self.callback_handler.on_evaluate(self.args ,      self.state ,      self.control ,      lowercase			)
									return metrics







			def 				A      (   self							:						Tuple ,      lowercase							:						Tuple ,      lowercase							:						Optional[Any] ,      lowercase							:						Optional[int]=None ,      lowercase							:						str = "test" ,      **lowercase							:						List[str]			)							->    Dict:

									'''simple docstring'''







									UpperCamelCase__         = gen_kwargs.copy()

									UpperCamelCase__         = self.get_test_dataloader(lowercase			)

									# Temporarily disable metric computation, we will do it in the loop here.
									UpperCamelCase__         = self.compute_metrics
									UpperCamelCase__         = None
									UpperCamelCase__         = time.time()
									UpperCamelCase__         = self.prediction_loop if self.args.use_legacy_prediction_loop else self.evaluation_loop
									try:
															UpperCamelCase__         = eval_loop(
															    lowercase ,      description="""Prediction""" ,      prediction_loss_only=True if compute_metrics is None else None ,      ignore_keys=lowercase ,      metric_key_prefix=lowercase ,      )
									finally:
															UpperCamelCase__         = compute_metrics

									UpperCamelCase__         = self.args.eval_batch_size * self.args.world_size
									if f"{metric_key_prefix}_jit_compilation_time" in output.metrics:
															start_time += output.metrics[f"{metric_key_prefix}_jit_compilation_time"]
									output.metrics.update(
									    speed_metrics(
									        lowercase ,      lowercase ,      num_samples=output.num_samples ,      num_steps=math.ceil(output.num_samples / total_batch_size			) ,      )			)
									if self.post_process_function is None or self.compute_metrics is None:
															return output

									UpperCamelCase__         = self.post_process_function(lowercase ,      lowercase ,      lowercase ,      """predict"""			)
									UpperCamelCase__         = self.compute_metrics(lowercase			)

									# Prefix all keys with metric_key_prefix + '_'
									for key in list(metrics.keys()			):
															if not key.startswith(f"{metric_key_prefix}_"			):
																					UpperCamelCase__         = metrics.pop(lowercase			)
									metrics.update(output.metrics			)
									return PredictionOutput(predictions=predictions.predictions ,      label_ids=predictions.label_ids ,      metrics=lowercase			)








'''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)
