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 = "from collections import Counter, defaultdict\n\nclass Solution:\n    def is_one_away(self, c_1, c_2) -> bool:\n        # c_1 will be shorter than c_2\n        diff = 0\n        for k, v in list(c_2.items()):\n            diff += v - c_1.get(k, 0)\n            if diff > 1:\n                return False\n        \n        for k in c_1:\n            if k not in c_2:\n                return False\n        \n        return True\n    \n    def helper(self, word, words_for_len, counters_for_words):\n        w_counter = counters_for_words[word]\n        max_chain = 0\n        for w in words_for_len[len(word) + 1]:\n            if self.is_one_away(w_counter, counters_for_words[w]):\n                max_chain = max(max_chain, self.helper(w, words_for_len, counters_for_words))\n        return max_chain + 1\n    \n    def longestStrChain(self, words: List[str]) -> int:\n        # Logic:\n        # define the longest string chain starting at word w as L[w]\n        #   L[w] = 1 + max over all w' in W such that dist(w, w') == 1(L[w'])\n        # Compute map of length to word counters to easily find all words 1 letter increased from a given word\n        # Given some w,\n        #     max_chain := 0\n        #     For all w' one letter away\n        #          max_chain := max(max_chain, max_chain(w')) + 1\n        # return max_chain\n        # Time Complexity analysis: ??\n        # Space: recursive stack O(n) will be the depth of the tree, hashmap O(n)\n        words_for_len = defaultdict(list)\n        counters_for_words = {w: Counter(w) for w in words}\n        for w in words:\n            words_for_len[len(w)].append(w)\n        \n        max_chain = 0\n        for w in words:\n            max_chain = max(max_chain, self.helper(w, words_for_len, counters_for_words))\n        return max_chain\n        \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: 13470