code: def get_default_backdoor_set_id(
      graph: nx.DiGraph,
      action_nodes: List[str],
      outcome_nodes: List[str],
      backdoor_sets_dict: Dict,
  ):
      # Adding a None estimand if no backdoor set found
      if len(backdoor_sets_dict) == 0:
          return None
  
      # Default set contains minimum possible number of instrumental variables, to prevent lowering variance in the treatment variable.
      instrument_names = set(
          get_instruments(graph, action_nodes, outcome_nodes)
      )
      iv_count_dict = {
          key: len(set(bdoor_set).intersection(instrument_names))
          for key, bdoor_set in backdoor_sets_dict.items()
      }
      min_iv_count = min(iv_count_dict.values())
      min_iv_keys = {
          key
          for key, iv_count in iv_count_dict.items()
          if iv_count == min_iv_count
      }
      min_iv_backdoor_sets_dict = {
          key: backdoor_sets_dict[key] for key in min_iv_keys
      }
  
      # Default set is the one with the least number of adjustment variables (optimizing for efficiency)
      min_set_length = 1000000
      default_key = None
      for key, bdoor_set in min_iv_backdoor_sets_dict.items():
          if len(bdoor_set) < min_set_length:
              min_set_length = len(bdoor_set)
              default_key = key
      return default_key
  
imports: import itertools
  import logging
  from enum import Enum
  from typing import Dict, List, Optional, Union
  import networkx
  import sympy
  import sympy.stats
  from dowhy.causal_identifier.efficient_backdoor import EfficientBackdoor
  from dowhy.causal_identifier.identified_estimand import IdentifiedEstimand
  from dowhy.graph import check_dseparation, check_valid_backdoor_set, check_valid_frontdoor_set, check_valid_mediation_set, do_surgery, get_all_directed_paths, get_backdoor_paths, get_descendants, get_instruments, has_directed_path
  from dowhy.utils.api import parse_state
label_desc: Use image node_id 9 for calling a global function with example usage: get_default_backdoor_set_id(graph, action_nodes, outcome_nodes, backdoor_sets_dict) and returns: default_key, None