






from collections import defaultdict

def   a_   (			lowerCAmelCase_				:      int     ):
   __lowerCAmelCase							     =     1
   __lowerCAmelCase							     =     True
   for v in tree[start]:
      if v not in visited:
         ret += dfs(lowerCAmelCase_     )
   if ret % 2 == 0:
      cuts.append(lowerCAmelCase_     )
   return ret

def   a_   (			):
   dfs(1     )


if __name__ == "__main__":
     _snake_case  :   List[Any]						   =  10, 9
     _snake_case  :   List[str]						   =  defaultdict(list)
     _snake_case  :   dict[int, bool]						   =  {}
     _snake_case  :   list[int]						   =  []
     _snake_case  :   str						   =  0
     _snake_case  :   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)








import math
from typing import Optional

import numpy as np

from ...configuration_utils import PretrainedConfig
from ...utils import logging


_snake_case  :   List[str]						   =  logging.get_logger(__name__)

_snake_case  :   Dict						   =  {
    'facebook/encodec_24khz': 'https://huggingface.co/facebook/encodec_24khz/resolve/main/config.json',
    'facebook/encodec_48khz': 'https://huggingface.co/facebook/encodec_48khz/resolve/main/config.json',
}



class     _UpperCAmelCase   (   _UpperCamelCase   ):

  """simple docstring"""


  a_      =			"""encodec"""






  def __init__(    self			:		Optional[Any] ,  lowerCAmelCase_			:		List[Any]=[1.5, 3.0, 6.0, 12.0, 24.0] ,  lowerCAmelCase_			:		Optional[Any]=2_4_0_0_0 ,  lowerCAmelCase_			:		int=1 ,  lowerCAmelCase_			:		Union[str, Any]=False ,  lowerCAmelCase_			:		Optional[Any]=None ,  lowerCAmelCase_			:		Union[str, Any]=None ,  lowerCAmelCase_			:		Optional[Any]=1_2_8 ,  lowerCAmelCase_			:		List[Any]=3_2 ,  lowerCAmelCase_			:		Optional[Any]=1 ,  lowerCAmelCase_			:		Optional[int]=[8, 5, 4, 2] ,  lowerCAmelCase_			:		Optional[Any]="weight_norm" ,  lowerCAmelCase_			:		Tuple=7 ,  lowerCAmelCase_			:		Optional[int]=7 ,  lowerCAmelCase_			:		Dict=3 ,  lowerCAmelCase_			:		Optional[Any]=2 ,  lowerCAmelCase_			:		List[Any]=True ,  lowerCAmelCase_			:		Dict="reflect" ,  lowerCAmelCase_			:		List[Any]=2 ,  lowerCAmelCase_			:		int=2 ,  lowerCAmelCase_			:		Dict=1.0 ,  lowerCAmelCase_			:		str=1_0_2_4 ,  lowerCAmelCase_			:		Dict=None ,  lowerCAmelCase_			:		List[Any]=True ,  **lowerCAmelCase_			:		Optional[Any] ,  )							->						Union[str, Any]:
     __lowerCAmelCase							     =     target_bandwidths
     __lowerCAmelCase							     =     sampling_rate
     __lowerCAmelCase							     =     audio_channels
     __lowerCAmelCase							     =     normalize
     __lowerCAmelCase							     =     chunk_length_s
     __lowerCAmelCase							     =     overlap
     __lowerCAmelCase							     =     hidden_size
     __lowerCAmelCase							     =     num_filters
     __lowerCAmelCase							     =     num_residual_layers
     __lowerCAmelCase							     =     upsampling_ratios
     __lowerCAmelCase							     =     norm_type
     __lowerCAmelCase							     =     kernel_size
     __lowerCAmelCase							     =     last_kernel_size
     __lowerCAmelCase							     =     residual_kernel_size
     __lowerCAmelCase							     =     dilation_growth_rate
     __lowerCAmelCase							     =     use_causal_conv
     __lowerCAmelCase							     =     pad_mode
     __lowerCAmelCase							     =     compress
     __lowerCAmelCase							     =     num_lstm_layers
     __lowerCAmelCase							     =     trim_right_ratio
     __lowerCAmelCase							     =     codebook_size
     __lowerCAmelCase							     =     codebook_dim if codebook_dim is not None else hidden_size
     __lowerCAmelCase							     =     use_conv_shortcut

     if self.norm_type not in ["weight_norm", "time_group_norm"]:
        raise ValueError(
            f"""self.norm_type must be one of `\"weight_norm\"`, `\"time_group_norm\"`), got {self.norm_type}"""					)

     super().__init__(**lowerCAmelCase_					)






  @property
  def     lowercase		(    self			:		Union[str, Any]					)							->						Optional[int]:
     if self.chunk_length_s is None:
        return None
     else:
        return int(self.chunk_length_s * self.sampling_rate					)






  @property
  def     lowercase		(    self			:		Optional[Any]					)							->						Optional[int]:
     if self.chunk_length_s is None or self.overlap is None:
        return None
     else:
        return max(1 ,  int((1.0 - self.overlap) * self.chunk_length					)					)






  @property
  def     lowercase		(    self			:		Any					)							->						int:
     __lowerCAmelCase							     =     np.prod(self.upsampling_ratios					)
     return math.ceil(self.sampling_rate / hop_length					)






  @property
  def     lowercase		(    self			:		str					)							->						int:
     return int(1_0_0_0 * self.target_bandwidths[-1] // (self.frame_rate * 1_0)					)

