




from __future__ import annotations





def 				A__ (snake_case   :		list[list[int]]				)     ->						bool:
					__UpperCamelCase					:	List[str]             =      len(snake_case				)
					# We need to create solution object to save path.
					__UpperCamelCase					:	List[str]             =      [[0 for _ in range(snake_case				)] for _ in range(snake_case				)]
					__UpperCamelCase					:	Any             =      run_maze(snake_case		,	0		,	0		,	snake_case				)
					if solved:
										print("""\n""".join(str(snake_case				) for row in solutions				)				)
					else:
										print("""No solution exists!"""				)
					return solved





def 				A__ (snake_case   :		list[list[int]]		,	snake_case   :		int		,	snake_case   :		int		,	snake_case   :		list[list[int]]				)     ->						bool:
					__UpperCamelCase					:	List[Any]             =      len(snake_case				)
					# Final check point.
					if i == j == (size - 1):
										__UpperCamelCase					:	str             =      1
										return True

					__UpperCamelCase					:	Optional[int]             =      (not i < 0) and (not j < 0)  # Check lower bounds
					__UpperCamelCase					:	str             =      (i < size) and (j < size)  # Check upper bounds

					if lower_flag and upper_flag:
										# check for already visited and block points.
										__UpperCamelCase					:	Optional[int]             =      (not solutions[i][j]) and (not maze[i][j])
										if block_flag:
															# check visited
															__UpperCamelCase					:	Dict             =      1

															# check for directions
															if (
															    run_maze(snake_case		,	i + 1		,	snake_case		,	snake_case				)
															    or run_maze(snake_case		,	snake_case		,	j + 1		,	snake_case				)
															    or run_maze(snake_case		,	i - 1		,	snake_case		,	snake_case				)
															    or run_maze(snake_case		,	snake_case		,	j - 1		,	snake_case				)
															):
																				return True

															__UpperCamelCase					:	Optional[int]             =      0
															return False
					return False


if __name__ == "__main__":
	import doctest

	doctest.testmod()












from collections import defaultdict





def 				A__ (snake_case   :		int				)     ->						int:
					__UpperCamelCase					:	Optional[int]             =      1
					__UpperCamelCase					:	Tuple             =      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 				A__ ()     ->						str:
					dfs(1				)


if __name__ == "__main__":
	a__     ,							a__		     =     10, 9
	a__		     =     defaultdict(list)
	a__		     =     {}
	a__		     =     []
	a__		     =     0
	a__		     =     [(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)






