
import sys
from collections import defaultdict


class 						__lowerCAmelCase	:



      """simple docstring"""







      def __init__(      self		:       List[Any]				):
          __lowercase		:			Tuple	    =       []




      def 		snake_case_			(      self		:       Optional[Any]				,       _snake_case		:       Dict				):
          return self.node_position[vertex]




      def 		snake_case_			(      self		:       List[Any]				,       _snake_case		:       Any				,       _snake_case		:       Any				):
          __lowercase		:			int	    =       pos




      def 		snake_case_			(      self		:       Union[str, Any]				,       _snake_case		:       Tuple				,       _snake_case		:       Optional[Any]				,       _snake_case		:       Dict				,       _snake_case		:       Optional[Any]				):
          if start > size // 2 - 1:
              return
          else:
              if 2 * start + 2 >= size:
                  __lowercase		:			str	    =       2 * start + 1
              else:
                  if heap[2 * start + 1] < heap[2 * start + 2]:
                      __lowercase		:			Optional[Any]	    =       2 * start + 1
                  else:
                      __lowercase		:			Any	    =       2 * start + 2
              if heap[smallest_child] < heap[start]:
                  __lowercase		:			List[str]	    =       heap[smallest_child], positions[smallest_child]
                  __lowercase		:			Dict	    =       (
                      heap[start],
                      positions[start],
                  )
                  __lowercase		:			Dict	    =       temp, tempa

                  __lowercase		:			int	    =       self.get_position(positions[smallest_child]				)
                  self.set_position(
                      positions[smallest_child]				,       self.get_position(positions[start]				)				)
                  self.set_position(positions[start]				,       _snake_case				)

                  self.top_to_bottom(_snake_case				,       _snake_case				,       _snake_case				,       _snake_case				)




      def 		snake_case_			(      self		:       List[Any]				,       _snake_case		:       Optional[int]				,       _snake_case		:       Optional[int]				,       _snake_case		:       Tuple				,       _snake_case		:       Union[str, Any]				):
          __lowercase		:			Tuple	    =       position[index]

          while index != 0:
              __lowercase		:			Dict	    =       int((index - 2) / 2				) if index % 2 == 0 else int((index - 1) / 2				)

              if val < heap[parent]:
                  __lowercase		:			Union[str, Any]	    =       heap[parent]
                  __lowercase		:			Optional[int]	    =       position[parent]
                  self.set_position(position[parent]				,       _snake_case				)
              else:
                  __lowercase		:			Union[str, Any]	    =       val
                  __lowercase		:			Union[str, Any]	    =       temp
                  self.set_position(_snake_case				,       _snake_case				)
                  break
              __lowercase		:			Tuple	    =       parent
          else:
              __lowercase		:			List[Any]	    =       val
              __lowercase		:			Any	    =       temp
              self.set_position(_snake_case				,       0				)




      def 		snake_case_			(      self		:       Dict				,       _snake_case		:       str				,       _snake_case		:       Optional[int]				):
          __lowercase		:			Optional[Any]	    =       len(_snake_case				) // 2 - 1
          for i in range(_snake_case				,       -1				,       -1				):
              self.top_to_bottom(_snake_case				,       _snake_case				,       len(_snake_case				)				,       _snake_case				)




      def 		snake_case_			(      self		:       Union[str, Any]				,       _snake_case		:       Dict				,       _snake_case		:       Optional[Any]				):
          __lowercase		:			List[Any]	    =       positions[0]
          __lowercase		:			Optional[int]	    =       sys.maxsize
          self.top_to_bottom(_snake_case				,       0				,       len(_snake_case				)				,       _snake_case				)
          return temp






def     UpperCAmelCase_  (						__lowerCAmelCase	) ->						int:
    __lowercase		:			Union[str, Any]	    =       Heap()

    __lowercase		:			Tuple	    =       [0] * len(__lowerCAmelCase	)
    __lowercase		:			Optional[int]	    =       [-1] * len(__lowerCAmelCase	)  # Neighboring Tree Vertex of selected vertex
    # Minimum Distance of explored vertex with neighboring vertex of partial tree
    # formed in graph
    __lowercase		:			List[str]	    =       []  # Heap of Distance of vertices from their neighboring vertex
    __lowercase		:			Optional[Any]	    =       []

    for vertex in range(len(__lowerCAmelCase	)	):
        distance_tv.append(sys.maxsize	)
        positions.append(__lowerCAmelCase	)
        heap.node_position.append(__lowerCAmelCase	)

    __lowercase		:			Any	    =       []
    __lowercase		:			str	    =       1
    __lowercase		:			List[Any]	    =       sys.maxsize
    for neighbor, distance in adjacency_list[0]:
        __lowercase		:			List[str]	    =       0
        __lowercase		:			Optional[int]	    =       distance
    heap.heapify(__lowerCAmelCase	,					__lowerCAmelCase	)

    for _ in range(1	,					len(__lowerCAmelCase	)	):
        __lowercase		:			Tuple	    =       heap.delete_minimum(__lowerCAmelCase	,					__lowerCAmelCase	)
        if visited[vertex] == 0:
            tree_edges.append((nbr_tv[vertex], vertex)	)
            __lowercase		:			List[Any]	    =       1
            for neighbor, distance in adjacency_list[vertex]:
                if (
                    visited[neighbor] == 0
                    and distance < distance_tv[heap.get_position(__lowerCAmelCase	)]
                ):
                    __lowercase		:			Dict	    =       distance
                    heap.bottom_to_top(
                        __lowerCAmelCase	,					heap.get_position(__lowerCAmelCase	)	,					__lowerCAmelCase	,					__lowerCAmelCase	)
                    __lowercase		:			Optional[Any]	    =       vertex
    return tree_edges


if __name__ == "__main__":  # pragma: no cover
 # < --------- Prims Algorithm --------- >
 __lowerCAmelCase					:			Any			      =		int(input("Enter number of edges: ").strip())
 __lowerCAmelCase					:			Any			      =		defaultdict(list)
 for _ in range(edges_number):
  __lowerCAmelCase					:			str			      =		[int(x) for x in input().strip().split()]
  adjacency_list[edge[0]].append([edge[1], edge[2]])
  adjacency_list[edge[1]].append([edge[0], edge[2]])
 print(prisms_algorithm(adjacency_list))


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


