code: def global_n_instances_by_state(self) -> Counter[str]:
      return sum(
          (
              inst_coll.all_versions_instances_by_state
              for inst_coll in self.name_inst_coll.values()
          ),
          collections.Counter(),
      )
  
imports: import asyncio
  import collections
  import logging
  import re
  import secrets
  from typing import Any, Counter, Dict, List, Optional, Tuple
  import sortedcontainers
  from gear import Database
  from gear.time_limited_max_size_cache import TimeLimitedMaxSizeCache
  from hailtop import aiotools
  from hailtop.utils import periodically_call, secret_alnum_string, time_msecs
  from ...globals import INSTANCE_VERSION, live_instance_states
  from ...instance_config import QuantifiedResource
  from ..instance import Instance
  from ..location import CloudLocationMonitor
  from ..resource_manager import CloudResourceManager, UnknownVMState, VMDoesNotExist, VMStateCreating, VMStateRunning, VMStateTerminated
label_desc: Use image node_id 11 for calling the InstanceCollectionManager obj's underlying member method code with example usage: obj.global_n_instances_by_state() and returns: sum