




"""simple docstring"""


def 	lowercase_				(			__UpperCAmelCase    ,		__UpperCAmelCase    ,		__UpperCAmelCase    ,		__UpperCAmelCase=None				):
      lowerCAmelCase__      :			int   =	(path or []) + [u]
      for v in graph[u]:
            if visited_edge[u][v] is False:
                  lowerCAmelCase__      :			Optional[Any]   =	True, True
                  lowerCAmelCase__      :			List[str]   =	dfs(__UpperCAmelCase    ,		__UpperCAmelCase    ,		__UpperCAmelCase    ,		__UpperCAmelCase				)
      return path



def 	lowercase_				(			__UpperCAmelCase    ,		__UpperCAmelCase				):
      lowerCAmelCase__      :			Any   =	0
      lowerCAmelCase__      :			int   =	-1
      for i in range(__UpperCAmelCase				):
            if i not in graph.keys():
                  continue
            if len(graph[i]				) % 2 == 1:
                  odd_degree_nodes += 1
                  lowerCAmelCase__      :			Any   =	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_				(			__UpperCAmelCase    ,		__UpperCAmelCase				):
      lowerCAmelCase__      :			Union[str, Any]   =	[[False for _ in range(max_node + 1				)] for _ in range(max_node + 1				)]
      lowerCAmelCase__      :			str   =	check_circuit_or_path(__UpperCAmelCase    ,		__UpperCAmelCase				)
      if check == 3:
            print("""graph is not Eulerian"""				)
            print("""no path"""				)
            return
      lowerCAmelCase__      :			Optional[Any]   =	1
      if check == 2:
            lowerCAmelCase__      :			str   =	odd_node
            print("""graph has a Euler path"""				)
      if check == 1:
            print("""graph has a Euler cycle"""				)
      lowerCAmelCase__      :			List[Any]   =	dfs(__UpperCAmelCase    ,		__UpperCAmelCase    ,		__UpperCAmelCase				)
      print(__UpperCAmelCase				)



def 	lowercase_				(			):
      lowerCAmelCase__      :			List[Any]   =	{1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
      lowerCAmelCase__      :			List[Any]   =	{1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
      lowerCAmelCase__      :			Any   =	{1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
      lowerCAmelCase__      :			str   =	{1: [2, 3], 2: [1, 3], 3: [1, 2]}
      lowerCAmelCase__      :			List[str]   =	{
          1: [],
          2: []
          # all degree is zero
      }
      lowerCAmelCase__      :			Tuple   =	10
      check_euler(__UpperCAmelCase    ,		__UpperCAmelCase				)
      check_euler(__UpperCAmelCase    ,		__UpperCAmelCase				)
      check_euler(__UpperCAmelCase    ,		__UpperCAmelCase				)
      check_euler(__UpperCAmelCase    ,		__UpperCAmelCase				)
      check_euler(__UpperCAmelCase    ,		__UpperCAmelCase				)


if __name__ == "__main__":
  main()











"""simple docstring"""


from .configuration_bert_masked import MaskedBertConfig
from .modeling_bert_masked import (
    MaskedBertForMultipleChoice,
    MaskedBertForQuestionAnswering,
    MaskedBertForSequenceClassification,
    MaskedBertForTokenClassification,
    MaskedBertModel,
)
from .modules import *





