

'''simple docstring'''
def        _lowerCAmelCase					(						_UpperCamelCase						:     List[str]				)      ->			int:  # noqa: E741
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							    =len(_UpperCamelCase				)
     _SCREAMING_SNAKE_CASE							    =0
     _SCREAMING_SNAKE_CASE							    =[0] * n
     _SCREAMING_SNAKE_CASE							    =[False] * n
     _SCREAMING_SNAKE_CASE							    =[False] * n

     def dfs(_UpperCamelCase						:     Union[str, Any]							, _UpperCamelCase						:     Optional[Any]							, _UpperCamelCase						:     Any							, _UpperCamelCase						:     List[str]				):
          if parent == root:
               out_edge_count += 1
          _SCREAMING_SNAKE_CASE							    =True
          _SCREAMING_SNAKE_CASE							    =at

          for to in l[at]:
               if to == parent:
                    pass
               elif not visited[to]:
                    _SCREAMING_SNAKE_CASE							    =dfs(_UpperCamelCase							, _UpperCamelCase							, _UpperCamelCase							, _UpperCamelCase				)
                    _SCREAMING_SNAKE_CASE							    =min(low[at]							, low[to]				)

                    # AP found via bridge
                    if at < low[to]:
                         _SCREAMING_SNAKE_CASE							    =True
                    # AP found via cycle
                    if at == low[to]:
                         _SCREAMING_SNAKE_CASE							    =True
               else:
                    _SCREAMING_SNAKE_CASE							    =min(low[at]							, _UpperCamelCase				)
          return out_edge_count

     for i in range(_UpperCamelCase				):
          if not visited[i]:
               _SCREAMING_SNAKE_CASE							    =0
               _SCREAMING_SNAKE_CASE							    =dfs(_UpperCamelCase							, _UpperCamelCase							, -1							, _UpperCamelCase				)
               _SCREAMING_SNAKE_CASE							    =out_edge_count > 1

     for x in range(len(_UpperCamelCase				)				):
          if is_art[x] is True:
               print(_UpperCamelCase				)


# Adjacency list of graph
lowerCamelCase :      int					 =     {
    0: [1, 2],
    1: [0, 2],
    2: [0, 1, 3, 5],
    3: [2, 4],
    4: [3],
    5: [2, 6, 8],
    6: [5, 7],
    7: [6, 8],
    8: [5, 7],
}







compute_ap(data)

"""simple docstring"""


from .constants import (
    MODEL_NAME,
    OPTIMIZER_NAME,
    RNG_STATE_NAME,
    SAFE_WEIGHTS_INDEX_NAME,
    SAFE_WEIGHTS_NAME,
    SCALER_NAME,
    SCHEDULER_NAME,
    TORCH_LAUNCH_PARAMS,
    WEIGHTS_INDEX_NAME,
    WEIGHTS_NAME,
)
from .dataclasses import (
    BnbQuantizationConfig,
    ComputeEnvironment,
    CustomDtype,
    DeepSpeedPlugin,
    DistributedDataParallelKwargs,
    DistributedType,
    DynamoBackend,
    FPaRecipeKwargs,
    FullyShardedDataParallelPlugin,
    GradientAccumulationPlugin,
    GradScalerKwargs,
    InitProcessGroupKwargs,
    KwargsHandler,
    LoggerType,
    MegatronLMPlugin,
    PrecisionType,
    ProjectConfiguration,
    RNGType,
    SageMakerDistributedType,
    TensorInformation,
    TorchDynamoPlugin,
)
from .environment import get_int_from_env, parse_choice_from_env, parse_flag_from_env
from .imports import (
    get_ccl_version,
    is_abit_bnb_available,
    is_abit_bnb_available,
    is_aim_available,
    is_bfaa_available,
    is_bnb_available,
    is_botoa_available,
    is_ccl_available,
    is_comet_ml_available,
    is_datasets_available,
    is_deepspeed_available,
    is_fpa_available,
    is_ipex_available,
    is_megatron_lm_available,
    is_mlflow_available,
    is_mps_available,
    is_npu_available,
    is_rich_available,
    is_safetensors_available,
    is_sagemaker_available,
    is_tensorboard_available,
    is_tpu_available,
    is_transformers_available,
    is_wandb_available,
    is_xpu_available,
)
from .modeling import (
    check_device_map,
    check_tied_parameters_in_config,
    check_tied_parameters_on_same_device,
    compute_module_sizes,
    convert_file_size_to_int,
    dtype_byte_size,
    find_tied_parameters,
    get_balanced_memory,
    get_max_layer_size,
    get_max_memory,
    get_mixed_precision_context_manager,
    id_tensor_storage,
    infer_auto_device_map,
    load_checkpoint_in_model,
    load_offloaded_weights,
    load_state_dict,
    named_module_tensors,
    retie_parameters,
    set_module_tensor_to_device,
    shard_checkpoint,
)
from .offload import (
    OffloadedWeightsLoader,
    PrefixedDataset,
    extract_submodules_state_dict,
    load_offloaded_weight,
    offload_state_dict,
    offload_weight,
    save_offload_index,
)
from .operations import (
    broadcast,
    broadcast_object_list,
    concatenate,
    convert_outputs_to_fpaa,
    convert_to_fpaa,
    find_batch_size,
    find_device,
    gather,
    gather_object,
    get_data_structure,
    honor_type,
    initialize_tensors,
    is_namedtuple,
    is_tensor_information,
    is_torch_tensor,
    listify,
    pad_across_processes,
    recursively_apply,
    reduce,
    send_to_device,
    slice_tensors,
)
from .versions import compare_versions, is_torch_version


if is_deepspeed_available():
    from .deepspeed import (
        DeepSpeedEngineWrapper,
        DeepSpeedOptimizerWrapper,
        DeepSpeedSchedulerWrapper,
        DummyOptim,
        DummyScheduler,
        HfDeepSpeedConfig,
    )

from .bnb import has_abit_bnb_layers, load_and_quantize_model
from .fsdp_utils import load_fsdp_model, load_fsdp_optimizer, save_fsdp_model, save_fsdp_optimizer
from .launch import (
    PrepareForLaunch,
    _filter_args,
    prepare_deepspeed_cmd_env,
    prepare_multi_gpu_env,
    prepare_sagemager_args_inputs,
    prepare_simple_launcher_cmd_env,
    prepare_tpu,
)
from .megatron_lm import (
    AbstractTrainStep,
    BertTrainStep,
    GPTTrainStep,
    MegatronEngine,
    MegatronLMDummyDataLoader,
    MegatronLMDummyScheduler,
    MegatronLMOptimizerWrapper,
    MegatronLMSchedulerWrapper,
    TaTrainStep,
    avg_losses_across_data_parallel_group,
    gather_across_data_parallel_groups,
)
from .megatron_lm import initialize as megatron_lm_initialize
from .megatron_lm import prepare_data_loader as megatron_lm_prepare_data_loader
from .megatron_lm import prepare_model as megatron_lm_prepare_model
from .megatron_lm import prepare_optimizer as megatron_lm_prepare_optimizer
from .megatron_lm import prepare_scheduler as megatron_lm_prepare_scheduler
from .memory import find_executable_batch_size, release_memory
from .other import (
    extract_model_from_parallel,
    get_pretty_name,
    is_port_in_use,
    merge_dicts,
    patch_environment,
    save,
    wait_for_everyone,
    write_basic_config,
)
from .random import set_seed, synchronize_rng_state, synchronize_rng_states
from .torch_xla import install_xla
from .tqdm import tqdm
from .transformer_engine import convert_model, has_transformer_engine_layers
