Given a list of words, each word consists of English lowercase letters.
Let's say word1 is a predecessor of word2 if and only if we can add exactly one letter anywhere in word1 to make it equal to word2.  For example, "abc" is a predecessor of "abac".
A word chain is a sequence of words [word_1, word_2, ..., word_k] with k >= 1, where word_1 is a predecessor of word_2, word_2 is a predecessor of word_3, and so on.
Return the longest possible length of a word chain with words chosen from the given list of words.
 
Example 1:
Input: ["a","b","ba","bca","bda","bdca"]
Output: 4
Explanation: one of the longest word chain is "a","ba","bda","bdca".

 
Note:

1 <= words.length <= 1000
1 <= words[i].length <= 16
words[i] only consists of English lowercase letters.

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = '# DFS | Time: O(n * k) | Space: O(n)\n# n: len(words)\n# k: length of each word\nclass Solution:\n    \n    # @param words: List[str]\n    # @return int\n    def longestStrChain(self, words):\n        if not words:\n            return 0\n\n        # build word table\n        wordTable = self.buildWordTable(words) # { length: list of words }\n\n        # dfs - search from shortest word to longest word\n        maxLen = 0\n        visited = set()\n        for wordLen in range(min(wordTable), max(wordTable) + 1):\n            for word in wordTable[wordLen]:\n                if word not in visited:\n                    maxLen = max(maxLen, self.dfs(wordTable, word, visited))\n\n        return maxLen\n\n    # Derive word table.\n    # Key: word length.\n    # Value: list of words that have length of key.\n    # @param words: List[str]\n    # @return dict({ int: List[str] })\n    def buildWordTable(self, words):\n\n        # initialize\n        wordTable = {} # { length: list of words }\n\n        for word in words:\n            if len(word) not in wordTable:\n                wordTable[len(word)] = []\n            wordTable[len(word)].append(word)\n\n        return wordTable\n\n    # DFS - search the successors and find the longest chain\n    #   - Apply Divide & Conquer coding framework\n    # @param wordTable: dict({ int: List[str] })\n    # @param word: str\n    # @param visited: set(str)\n    # @return int\n    def dfs(self, wordTable, word, visited):\n\n        # initialize\n        maxLen = 0\n        visited.add(word)\n\n        # divide\n        #   - Find successors and update the max length that subtasks responded\n        if len(word) + 1 in wordTable:\n            for neighbor in wordTable[len(word) + 1]:\n                if self.isAncestor(word, neighbor):\n                    maxLen = max(maxLen, self.dfs(wordTable, neighbor, visited))\n\n        # conquer\n        #   - Calculate the max length found\n        #   - +1 to count itself\n        return maxLen + 1\n\n    # @param ancestor: str\n    # @param successor: str\n    # @return bool\n    def isAncestor(self, ancestor, successor):\n        if len(ancestor) + 1 != len(successor):\n            return False\n\n        # initialize\n        i, j = 0, 0\n\n        while i < len(ancestor) and j < len(successor):\n            if ancestor[i] != successor[j]:\n                j += 1\n                continue\n            else:\n                i += 1\n                j += 1\n\n        return i == j or i == j - 1\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'longestStrChain'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 8436