code: def from_dict(input_dict):
      primitive_deserializer = PrimitivesDeserializer()
  
      primitives = {}
      for prim_key, prim_dict in input_dict["primitives"].items():
          primitive = primitive_deserializer.deserialize_primitive(
              prim_dict,
          )
          assert isinstance(primitive, PrimitiveBase)
          primitives[prim_key] = primitive
  
      hydrated_features: Dict[str, LiteFeature] = {}
  
      feature_ids: List[str] = cast(
          List[str], input_dict["feature_ids"]
      )
      all_features: Dict[str, Any] = cast(
          Dict[str, Any], input_dict["all_features"]
      )
  
      def hydrate_feature(feature_id: str) -> LiteFeature:
          if feature_id in hydrated_features:
              return hydrated_features[feature_id]
  
          feature_dict = all_features[feature_id]
          base_features = [
              hydrate_feature(x) for x in feature_dict["base_features"]
          ]
  
          logical_type = (
              logical_types_map[feature_dict["logical_type"]]
              if feature_dict["logical_type"]
              else None
          )
  
          hydrated_feature = LiteFeature(
              name=feature_dict["name"],
              logical_type=logical_type,
              tags=set(feature_dict["tags"]),
              primitive=primitives[feature_dict["primitive"]]
              if feature_dict["primitive"]
              else None,
              base_features=base_features,
              df_id=feature_dict["df_id"],
              related_features=set(),
              idx=feature_dict["idx"],
          )
  
          assert hydrated_feature.id == feature_dict["id"] == feature_id
          hydrated_features[feature_id] = hydrated_feature
  
          # need to link after features are stored on cache
          related_features = [
              hydrate_feature(x)
              for x in feature_dict["related_features"]
          ]
          hydrated_feature.related_features = set(related_features)
  
          return hydrated_feature
  
      return FeatureCollection(
          [hydrate_feature(x) for x in feature_ids]
      )
  
imports: from __future__ import annotations
  import hashlib
  from itertools import combinations
  from typing import Any, Dict, List, Optional, Set, Type, Union, cast
  from woodwork.logical_types import LogicalType
  from featuretools.feature_discovery.LiteFeature import LiteFeature
  from featuretools.feature_discovery.type_defs import ANY
  from featuretools.feature_discovery.utils import hash_primitive, logical_types_map
  from featuretools.primitives.base.primitive_base import PrimitiveBase
  from featuretools.primitives.utils import PrimitivesDeserializer
label_desc: Use image node_id 20 for calling the FeatureCollection obj's underlying member method code with example usage: obj.from_dict(input_dict) and returns: FeatureCollection, hydrated_feature, hydrated_features