
from collections import defaultdict

def 				SCREAMING_SNAKE_CASE     (      __UpperCamelCase :						int       ) ->       int:

						"""simple docstring"""







						A__  :	List[Any]         =							1
						A__  :	int         =							True
						for v in tree[start]:
												if v not in visited:
																		ret += dfs(__snake_case       )
						if ret % 2 == 0:
												cuts.append(__snake_case       )
						return ret

def 				SCREAMING_SNAKE_CASE     (      ) ->       Optional[int]:

						"""simple docstring"""







						dfs(1       )


if __name__ == "__main__":
					_SCREAMING_SNAKE_CASE    :      Tuple          =			1_0, 9
					_SCREAMING_SNAKE_CASE    :      Tuple          =			defaultdict(list)
					_SCREAMING_SNAKE_CASE    :      dict[int, bool]          =			{}
					_SCREAMING_SNAKE_CASE    :      list[int]          =			[]
					_SCREAMING_SNAKE_CASE    :      int          =			0
					_SCREAMING_SNAKE_CASE    :      str          =			[(2, 1), (3, 1), (4, 3), (5, 2), (6, 1), (7, 2), (8, 6), (9, 8), (1_0, 8)]
					for u, v in edges:
										tree[u].append(v)
										tree[v].append(u)
					even_tree()
					print(len(cuts) - 1)

import numpy as np

_SCREAMING_SNAKE_CASE    :      Any          =			[
    ['a', 'b', 'c', 'd', 'e'],
    ['f', 'g', 'h', 'i', 'k'],
    ['l', 'm', 'n', 'o', 'p'],
    ['q', 'r', 's', 't', 'u'],
    ['v', 'w', 'x', 'y', 'z'],
]







class  UpperCamelCase__		:







	'''simple docstring'''





	def __init__(			self		):
					A__  :	List[Any]         =							np.array(UpperCamelCase__		)





	def   __snake_case				(			self				,       UpperCamelCase__		):
					A__       ,							A__  :	Any         =							np.where(letter == self.SQUARE		)
					A__  :	int         =							np.concatenate([indexa + 1, indexa + 1]		)
					return indexes





	def   __snake_case				(			self				,       UpperCamelCase__				,       UpperCamelCase__		):
					A__  :	Union[str, Any]         =							self.SQUARE[indexa - 1, indexa - 1]
					return letter





	def   __snake_case				(			self				,       UpperCamelCase__		):
					A__  :	List[str]         =							message.lower()
					A__  :	str         =							message.replace(''' '''				,       ''''''		)
					A__  :	Union[str, Any]         =							message.replace('''j'''				,       '''i'''		)

					A__  :	List[Any]         =							np.empty((2, len(UpperCamelCase__		))		)
					for letter_index in range(len(UpperCamelCase__		)		):
									A__  :	Any         =							self.letter_to_numbers(message[letter_index]		)

									A__  :	Optional[Any]         =							numbers[0]
									A__  :	List[str]         =							numbers[1]

					A__  :	List[str]         =							first_step.reshape(2 * len(UpperCamelCase__		)		)
					A__  :	List[Any]         =							''''''
					for numbers_index in range(len(UpperCamelCase__		)		):
									A__  :	Dict         =							int(second_step[numbers_index * 2]		)
									A__  :	List[str]         =							int(second_step[(numbers_index * 2) + 1]		)
									A__  :	Dict         =							self.numbers_to_letter(UpperCamelCase__				,       UpperCamelCase__		)
									A__  :	Tuple         =							encoded_message + letter

					return encoded_message





	def   __snake_case				(			self				,       UpperCamelCase__		):
					A__  :	str         =							message.lower()
					message.replace(''' '''				,       ''''''		)
					A__  :	List[Any]         =							np.empty(2 * len(UpperCamelCase__		)		)
					for letter_index in range(len(UpperCamelCase__		)		):
									A__  :	List[str]         =							self.letter_to_numbers(message[letter_index]		)
									A__  :	Dict         =							numbers[0]
									A__  :	int         =							numbers[1]

					A__  :	Optional[Any]         =							first_step.reshape((2, len(UpperCamelCase__		))		)
					A__  :	int         =							''''''
					for numbers_index in range(len(UpperCamelCase__		)		):
									A__  :	Tuple         =							int(second_step[0, numbers_index]		)
									A__  :	Dict         =							int(second_step[1, numbers_index]		)
									A__  :	List[str]         =							self.numbers_to_letter(UpperCamelCase__				,       UpperCamelCase__		)
									A__  :	Tuple         =							decoded_message + letter

					return decoded_message