



"""simple docstring"""

def __lowercase			(							_a		,			_a		,			_a		,			_a=None    ):
    snake_case_ :     Any				=	(path or []) + [u]
    for v in graph[u]:
        if visited_edge[u][v] is False:
            snake_case_ :     Tuple				=	True, True
            snake_case_ :     List[Any]				=	dfs(lowerCAmelCase_		,			lowerCAmelCase_		,			lowerCAmelCase_		,			lowerCAmelCase_    )
    return path




def __lowercase			(							_a		,			_a    ):
    snake_case_ :     Optional[Any]				=	0
    snake_case_ :     Optional[int]				=	-1
    for i in range(lowerCAmelCase_    ):
        if i not in graph.keys():
            continue
        if len(graph[i]    ) % 2 == 1:
            odd_degree_nodes += 1
            snake_case_ :     Optional[int]				=	i
    if odd_degree_nodes == 0:
        return 1, odd_node
    if odd_degree_nodes == 2:
        return 2, odd_node
    return 3, odd_node




def __lowercase			(							_a		,			_a    ):
    snake_case_ :     str				=	[[False for _ in range(max_node + 1    )] for _ in range(max_node + 1    )]
    snake_case_ :     int				=	check_circuit_or_path(lowerCAmelCase_		,			lowerCAmelCase_    )
    if check == 3:
        print('''graph is not Eulerian'''    )
        print('''no path'''    )
        return
    snake_case_ :     Dict				=	1
    if check == 2:
        snake_case_ :     Dict				=	odd_node
        print('''graph has a Euler path'''    )
    if check == 1:
        print('''graph has a Euler cycle'''    )
    snake_case_ :     Dict				=	dfs(lowerCAmelCase_		,			lowerCAmelCase_		,			lowerCAmelCase_    )
    print(lowerCAmelCase_    )




def __lowercase			(							):
    snake_case_ :     Any				=	{1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
    snake_case_ :     int				=	{1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
    snake_case_ :     Tuple				=	{1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
    snake_case_ :     List[Any]				=	{1: [2, 3], 2: [1, 3], 3: [1, 2]}
    snake_case_ :     List[str]				=	{
        1: [],
        2: []
        # all degree is zero
    }
    snake_case_ :     Union[str, Any]				=	10
    check_euler(lowerCAmelCase_		,			lowerCAmelCase_    )
    check_euler(lowerCAmelCase_		,			lowerCAmelCase_    )
    check_euler(lowerCAmelCase_		,			lowerCAmelCase_    )
    check_euler(lowerCAmelCase_		,			lowerCAmelCase_    )
    check_euler(lowerCAmelCase_		,			lowerCAmelCase_    )


if __name__ == "__main__":
     main()










'''simple docstring'''






from torch import nn



class 							lowercase       (  nn.Module				):


 """simple docstring"""


 def __init__(							self  ,a_  ,a_							)		->   List[Any]:
        super().__init__()
        _UpperCAmelCase  :						Dict			     = class_size
        _UpperCAmelCase  :						Union[str, Any]			     = embed_size
        # self.mlp1 = nn.Linear(embed_size, embed_size)
        # self.mlp2 = (nn.Linear(embed_size, class_size))
        _UpperCAmelCase  :						List[Any]			     = nn.Linear(a_  ,a_							)







 def _snake_case (							self  ,a_							)		->   Tuple:
        # hidden_state = nn.functional.relu(self.mlp1(hidden_state))
        # hidden_state = self.mlp2(hidden_state)
        _UpperCAmelCase  :						Optional[int]			     = self.mlp(a_							)
        return logits



