'''simple docstring'''




# using dfs for finding eulerian path traversal










def __lowerCAmelCase (							UpperCamelCase__				,  UpperCamelCase__				,  UpperCamelCase__				,  UpperCamelCase__=None				)	->    str:
    __lowerCamelCase		=  (path or []) + [u]
    for v in graph[u]:
        if visited_edge[u][v] is False:
            __lowerCamelCase	,  __lowerCamelCase		=  True, True
            __lowerCamelCase		=  dfs(_A				,  _A				,  _A				,  _A				)
    return path






def __lowerCAmelCase (							UpperCamelCase__				,  UpperCamelCase__				)	->    Tuple:
    __lowerCamelCase		=  0
    __lowerCamelCase		=  -1
    for i in range(_A				):
        if i not in graph.keys():
            continue
        if len(graph[i]				) % 2 == 1:
            odd_degree_nodes += 1
            __lowerCamelCase		=  i
    if odd_degree_nodes == 0:
        return 1, odd_node
    if odd_degree_nodes == 2:
        return 2, odd_node
    return 3, odd_node






def __lowerCAmelCase (							UpperCamelCase__				,  UpperCamelCase__				)	->    Optional[Any]:
    __lowerCamelCase		=  [[False for _ in range(max_node + 1				)] for _ in range(max_node + 1				)]
    __lowerCamelCase	,  __lowerCamelCase		=  check_circuit_or_path(_A				,  _A				)
    if check == 3:
        print('''graph is not Eulerian'''				)
        print('''no path'''				)
        return
    __lowerCamelCase		=  1
    if check == 2:
        __lowerCamelCase		=  odd_node
        print('''graph has a Euler path'''				)
    if check == 1:
        print('''graph has a Euler cycle'''				)
    __lowerCamelCase		=  dfs(_A				,  _A				,  _A				)
    print(_A				)






def __lowerCAmelCase (							)	->    int:
    __lowerCamelCase		=  {1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
    __lowerCamelCase		=  {1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
    __lowerCamelCase		=  {1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
    __lowerCamelCase		=  {1: [2, 3], 2: [1, 3], 3: [1, 2]}
    __lowerCamelCase		=  {
        1: [],
        2: []
        # all degree is zero
    }
    __lowerCamelCase		=  10
    check_euler(_A				,  _A				)
    check_euler(_A				,  _A				)
    check_euler(_A				,  _A				)
    check_euler(_A				,  _A				)
    check_euler(_A				,  _A				)


if __name__ == "__main__":
  main()



from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tokenizers_available, is_torch_available


lowerCamelCase           =					{
    '''configuration_mvp''': ['''MVP_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''MvpConfig''', '''MvpOnnxConfig'''],
    '''tokenization_mvp''': ['''MvpTokenizer'''],
}

try:
       if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       lowerCamelCase           =					['''MvpTokenizerFast''']

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       lowerCamelCase           =					[
           '''MVP_PRETRAINED_MODEL_ARCHIVE_LIST''',
           '''MvpForCausalLM''',
           '''MvpForConditionalGeneration''',
           '''MvpForQuestionAnswering''',
           '''MvpForSequenceClassification''',
           '''MvpModel''',
           '''MvpPreTrainedModel''',
       ]

if TYPE_CHECKING:
       from .configuration_mvp import MVP_PRETRAINED_CONFIG_ARCHIVE_MAP, MvpConfig, MvpOnnxConfig
       from .tokenization_mvp import MvpTokenizer

       try:
              if not is_tokenizers_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_mvp_fast import MvpTokenizerFast

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_mvp import (
                  MVP_PRETRAINED_MODEL_ARCHIVE_LIST,
                  MvpForCausalLM,
                  MvpForConditionalGeneration,
                  MvpForQuestionAnswering,
                  MvpForSequenceClassification,
                  MvpModel,
                  MvpPreTrainedModel,
              )

else:
       import sys

       lowerCamelCase           =					_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)
