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 = 'class Solution:\n    def longestStrChain(self, words: List[str]) -> int:\n        self._len_to_words = collections.defaultdict(list)\n        for w in words:\n            self._len_to_words[len(w)].append(w)\n        if len(self._len_to_words) == 1:\n            return 1\n        self._cache = {}\n            \n        self._visited = {}\n        max_so_far = 0\n        for w in words:\n            max_so_far = max(max_so_far, self._find_longest(w))\n        return max_so_far\n    \n    def _find_longest(self, w):\n        if w in self._visited:\n            return self._visited[w]\n        \n        len_w = len(w)\n        if len_w+1 not in self._len_to_words:\n            self._visited[w] = 1\n            return 1\n        \n        max_chain_len = 1\n        for cand in self._len_to_words[len_w+1]:\n            if self.is_predecessor(w, cand):\n                max_chain_len = max(max_chain_len, 1+self._find_longest(cand))\n        \n        self._visited[w] = max_chain_len\n        return max_chain_len\n        \n    def is_predecessor(self, w1, w2):\n        if (w1, w2) in self._cache:\n            return self._cache[(w1, w2)]\n        \n        is_p = True\n        if len(w1) + 1 != len(w2):\n            is_p = False\n        else:\n            count = {}\n            for c in w1:\n                if c in count:\n                    count[c] += 1\n                else:\n                    count[c] = 1\n            found_diff = False\n            for c in w2:\n                if c in count:\n                    count[c] -= 1\n                    if count[c] == 0:\n                        del count[c]\n                else:\n                    if found_diff:\n                        is_p = False\n                        break\n                    else:\n                        found_diff = True\n                        count[c] = 1\n        if is_p:\n            keys = list(count.keys())\n            is_p = len(keys) == 1 and count[keys[0]] == 1\n        \n        self._cache[(w1, w2)] = is_p\n        return is_p'
_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: 8780